diff --git a/Tools/fix_code_style_ubuntu.sh b/Tools/fix_code_style_ubuntu.sh new file mode 100755 index 0000000000..90ab57b895 --- /dev/null +++ b/Tools/fix_code_style_ubuntu.sh @@ -0,0 +1,19 @@ +#!/bin/sh +astyle \ + --style=linux \ + --indent=force-tab=8 \ + --indent-cases \ + --indent-preprocessor \ + --break-blocks=all \ + --pad-oper \ + --pad-header \ + --unpad-paren \ + --keep-one-line-blocks \ + --keep-one-line-statements \ + --align-pointer=name \ + --suffix=none \ + --lineend=linux \ + $* + #--ignore-exclude-errors-x \ + #--exclude=EASTL \ + #--align-reference=name \ diff --git a/apps/controllib/Makefile b/apps/controllib/Makefile new file mode 100644 index 0000000000..99cf910690 --- /dev/null +++ b/apps/controllib/Makefile @@ -0,0 +1,53 @@ +############################################################################ +# +# Copyright (C) 2012 PX4 Development Team. All rights reserved. +# +# Redistribution and use in source and binary forms, with or without +# modification, are permitted provided that the following conditions +# are met: +# +# 1. Redistributions of source code must retain the above copyright +# notice, this list of conditions and the following disclaimer. +# 2. Redistributions in binary form must reproduce the above copyright +# notice, this list of conditions and the following disclaimer in +# the documentation and/or other materials provided with the +# distribution. +# 3. Neither the name PX4 nor the names of its contributors may be +# used to endorse or promote products derived from this software +# without specific prior written permission. +# +# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS +# FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE +# COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, +# INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, +# BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS +# OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED +# AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN +# ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +# POSSIBILITY OF SUCH DAMAGE. +# +############################################################################ + +# +# Control library +# +CSRCS = test_params.c + +CXXSRCS = block/Block.cpp \ + block/BlockParam.cpp \ + block/UOrbPublication.cpp \ + block/UOrbSubscription.cpp \ + blocks.cpp \ + fixedwing.cpp + +CXXHDRS = block/Block.hpp \ + block/BlockParam.hpp \ + block/UOrbPublication.hpp \ + block/UOrbSubscription.hpp \ + blocks.hpp \ + fixedwing.hpp + +include $(APPDIR)/mk/app.mk diff --git a/apps/controllib/block/Block.cpp b/apps/controllib/block/Block.cpp new file mode 100644 index 0000000000..5994d23154 --- /dev/null +++ b/apps/controllib/block/Block.cpp @@ -0,0 +1,210 @@ +/**************************************************************************** + * + * Copyright (C) 2012 PX4 Development Team. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * 3. Neither the name PX4 nor the names of its contributors may be + * used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS + * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE + * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, + * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS + * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED + * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN + * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + * + ****************************************************************************/ + +/** + * @file Block.cpp + * + * Controller library code + */ + +#include +#include +#include + +#include "Block.hpp" +#include "BlockParam.hpp" +#include "UOrbSubscription.hpp" +#include "UOrbPublication.hpp" + +namespace control +{ + +Block::Block(SuperBlock *parent, const char *name) : + _name(name), + _parent(parent), + _dt(0), + _subscriptions(), + _params() +{ + if (getParent() != NULL) { + getParent()->getChildren().add(this); + } +} + +void Block::getName(char *buf, size_t n) +{ + if (getParent() == NULL) { + strncpy(buf, _name, n); + + } else { + char parentName[blockNameLengthMax]; + getParent()->getName(parentName, n); + + if (!strcmp(_name, "")) { + strncpy(buf, parentName, blockNameLengthMax); + + } else { + snprintf(buf, blockNameLengthMax, "%s_%s", parentName, _name); + } + } +} + +void Block::updateParams() +{ + BlockParamBase *param = getParams().getHead(); + int count = 0; + + while (param != NULL) { + if (count++ > maxParamsPerBlock) { + char name[blockNameLengthMax]; + getName(name, blockNameLengthMax); + printf("exceeded max params for block: %s\n", name); + break; + } + + //printf("updating param: %s\n", param->getName()); + param->update(); + param = param->getSibling(); + } +} + +void Block::updateSubscriptions() +{ + UOrbSubscriptionBase *sub = getSubscriptions().getHead(); + int count = 0; + + while (sub != NULL) { + if (count++ > maxSubscriptionsPerBlock) { + char name[blockNameLengthMax]; + getName(name, blockNameLengthMax); + printf("exceeded max subscriptions for block: %s\n", name); + break; + } + + sub->update(); + sub = sub->getSibling(); + } +} + +void Block::updatePublications() +{ + UOrbPublicationBase *pub = getPublications().getHead(); + int count = 0; + + while (pub != NULL) { + if (count++ > maxPublicationsPerBlock) { + char name[blockNameLengthMax]; + getName(name, blockNameLengthMax); + printf("exceeded max publications for block: %s\n", name); + break; + } + + pub->update(); + pub = pub->getSibling(); + } +} + +void SuperBlock::setDt(float dt) +{ + Block::setDt(dt); + Block *child = getChildren().getHead(); + int count = 0; + + while (child != NULL) { + if (count++ > maxChildrenPerBlock) { + char name[40]; + getName(name, 40); + printf("exceeded max children for block: %s\n", name); + break; + } + + child->setDt(dt); + child = child->getSibling(); + } +} + +void SuperBlock::updateChildParams() +{ + Block *child = getChildren().getHead(); + int count = 0; + + while (child != NULL) { + if (count++ > maxChildrenPerBlock) { + char name[40]; + getName(name, 40); + printf("exceeded max children for block: %s\n", name); + break; + } + + child->updateParams(); + child = child->getSibling(); + } +} + +void SuperBlock::updateChildSubscriptions() +{ + Block *child = getChildren().getHead(); + int count = 0; + + while (child != NULL) { + if (count++ > maxChildrenPerBlock) { + char name[40]; + getName(name, 40); + printf("exceeded max children for block: %s\n", name); + break; + } + + child->updateSubscriptions(); + child = child->getSibling(); + } +} + +void SuperBlock::updateChildPublications() +{ + Block *child = getChildren().getHead(); + int count = 0; + + while (child != NULL) { + if (count++ > maxChildrenPerBlock) { + char name[40]; + getName(name, 40); + printf("exceeded max children for block: %s\n", name); + break; + } + + child->updatePublications(); + child = child->getSibling(); + } +} + +} // namespace control diff --git a/apps/controllib/block/Block.hpp b/apps/controllib/block/Block.hpp new file mode 100644 index 0000000000..258701f279 --- /dev/null +++ b/apps/controllib/block/Block.hpp @@ -0,0 +1,131 @@ +/**************************************************************************** + * + * Copyright (C) 2012 PX4 Development Team. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * 3. Neither the name PX4 nor the names of its contributors may be + * used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS + * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE + * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, + * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS + * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED + * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN + * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + * + ****************************************************************************/ + +/** + * @file Block.h + * + * Controller library code + */ + +#pragma once + +#include +#include + +#include "List.hpp" + +namespace control +{ + +static const uint16_t maxChildrenPerBlock = 100; +static const uint16_t maxParamsPerBlock = 100; +static const uint16_t maxSubscriptionsPerBlock = 100; +static const uint16_t maxPublicationsPerBlock = 100; +static const uint8_t blockNameLengthMax = 80; + +// forward declaration +class BlockParamBase; +class UOrbSubscriptionBase; +class UOrbPublicationBase; +class SuperBlock; + +/** + */ +class __EXPORT Block : + public ListNode +{ +public: + friend class BlockParamBase; +// methods + Block(SuperBlock *parent, const char *name); + void getName(char *name, size_t n); + virtual ~Block() {}; + virtual void updateParams(); + virtual void updateSubscriptions(); + virtual void updatePublications(); + virtual void setDt(float dt) { _dt = dt; } +// accessors + float getDt() { return _dt; } +protected: +// accessors + SuperBlock *getParent() { return _parent; } + List & getSubscriptions() { return _subscriptions; } + List & getPublications() { return _publications; } + List & getParams() { return _params; } +// attributes + const char *_name; + SuperBlock *_parent; + float _dt; + List _subscriptions; + List _publications; + List _params; +}; + +class __EXPORT SuperBlock : + public Block +{ +public: + friend class Block; +// methods + SuperBlock(SuperBlock *parent, const char *name) : + Block(parent, name), + _children() { + } + virtual ~SuperBlock() {}; + virtual void setDt(float dt); + virtual void updateParams() { + Block::updateParams(); + + if (getChildren().getHead() != NULL) updateChildParams(); + } + virtual void updateSubscriptions() { + Block::updateSubscriptions(); + + if (getChildren().getHead() != NULL) updateChildSubscriptions(); + } + virtual void updatePublications() { + Block::updatePublications(); + + if (getChildren().getHead() != NULL) updateChildPublications(); + } +protected: +// methods + List & getChildren() { return _children; } + void updateChildParams(); + void updateChildSubscriptions(); + void updateChildPublications(); +// attributes + List _children; +}; + +} // namespace control diff --git a/apps/controllib/block/BlockParam.cpp b/apps/controllib/block/BlockParam.cpp new file mode 100644 index 0000000000..b3f49f7db4 --- /dev/null +++ b/apps/controllib/block/BlockParam.cpp @@ -0,0 +1,77 @@ +/**************************************************************************** + * + * Copyright (C) 2012 PX4 Development Team. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * 3. Neither the name PX4 nor the names of its contributors may be + * used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS + * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE + * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, + * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS + * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED + * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN + * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + * + ****************************************************************************/ + +/** + * @file Blockparam.cpp + * + * Controller library code + */ + +#include +#include +#include + +#include "BlockParam.hpp" + +namespace control +{ + +BlockParamBase::BlockParamBase(Block *parent, const char *name) : + _handle(PARAM_INVALID) +{ + char fullname[blockNameLengthMax]; + + if (parent == NULL) { + strncpy(fullname, name, blockNameLengthMax); + + } else { + char parentName[blockNameLengthMax]; + parent->getName(parentName, blockNameLengthMax); + + if (!strcmp(name, "")) { + strncpy(fullname, parentName, blockNameLengthMax); + + } else { + snprintf(fullname, blockNameLengthMax, "%s_%s", parentName, name); + } + + parent->getParams().add(this); + } + + _handle = param_find(fullname); + + if (_handle == PARAM_INVALID) + printf("error finding param: %s\n", fullname); +}; + +} // namespace control diff --git a/apps/controllib/block/BlockParam.hpp b/apps/controllib/block/BlockParam.hpp new file mode 100644 index 0000000000..7f86d17178 --- /dev/null +++ b/apps/controllib/block/BlockParam.hpp @@ -0,0 +1,85 @@ +/**************************************************************************** + * + * Copyright (C) 2012 PX4 Development Team. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * 3. Neither the name PX4 nor the names of its contributors may be + * used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS + * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE + * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, + * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS + * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED + * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN + * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + * + ****************************************************************************/ + +/** + * @file BlockParam.h + * + * Controller library code + */ + +#pragma once + +#include + +#include "Block.hpp" +#include "List.hpp" + +namespace control +{ + +/** + * A base class for block params that enables traversing linked list. + */ +class __EXPORT BlockParamBase : public ListNode +{ +public: + BlockParamBase(Block *parent, const char *name); + virtual ~BlockParamBase() {}; + virtual void update() = 0; + const char *getName() { return param_name(_handle); } +protected: + param_t _handle; +}; + +/** + * Parameters that are tied to blocks for updating and nameing. + */ +template +class __EXPORT BlockParam : public BlockParamBase +{ +public: + BlockParam(Block *block, const char *name) : + BlockParamBase(block, name), + _val() { + update(); + } + T get() { return _val; } + void set(T val) { _val = val; } + void update() { + if (_handle != PARAM_INVALID) param_get(_handle, &_val); + } +protected: + T _val; +}; + +} // namespace control diff --git a/apps/controllib/block/List.hpp b/apps/controllib/block/List.hpp new file mode 100644 index 0000000000..96b0b94d10 --- /dev/null +++ b/apps/controllib/block/List.hpp @@ -0,0 +1,71 @@ +/**************************************************************************** + * + * Copyright (C) 2012 PX4 Development Team. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * 3. Neither the name PX4 nor the names of its contributors may be + * used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS + * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE + * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, + * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS + * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED + * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN + * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + * + ****************************************************************************/ + +/** + * @file Node.h + * + * A node of a linked list. + */ + +#pragma once + +template +class __EXPORT ListNode +{ +public: + ListNode() : _sibling(NULL) { + } + void setSibling(T sibling) { _sibling = sibling; } + T getSibling() { return _sibling; } + T get() { + return _sibling; + } +protected: + T _sibling; +}; + +template +class __EXPORT List +{ +public: + List() : _head() { + } + void add(T newNode) { + newNode->setSibling(getHead()); + setHead(newNode); + } + T getHead() { return _head; } +private: + void setHead(T &head) { _head = head; } + T _head; +}; diff --git a/apps/controllib/block/UOrbPublication.cpp b/apps/controllib/block/UOrbPublication.cpp new file mode 100644 index 0000000000..f69b39d90d --- /dev/null +++ b/apps/controllib/block/UOrbPublication.cpp @@ -0,0 +1,39 @@ +/**************************************************************************** + * + * Copyright (C) 2012 PX4 Development Team. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * 3. Neither the name PX4 nor the names of its contributors may be + * used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS + * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE + * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, + * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS + * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED + * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN + * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + * + ****************************************************************************/ + +/** + * @file UOrbPublication.cpp + * + */ + +#include "UOrbPublication.hpp" diff --git a/apps/controllib/block/UOrbPublication.hpp b/apps/controllib/block/UOrbPublication.hpp new file mode 100644 index 0000000000..a36f4429f4 --- /dev/null +++ b/apps/controllib/block/UOrbPublication.hpp @@ -0,0 +1,118 @@ +/**************************************************************************** + * + * Copyright (C) 2012 PX4 Development Team. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * 3. Neither the name PX4 nor the names of its contributors may be + * used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS + * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE + * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, + * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS + * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED + * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN + * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + * + ****************************************************************************/ + +/** + * @file UOrbPublication.h + * + */ + +#pragma once + +#include +#include "Block.hpp" +#include "List.hpp" + + +namespace control +{ + +class Block; + +/** + * Base publication warapper class, used in list traversal + * of various publications. + */ +class __EXPORT UOrbPublicationBase : public ListNode +{ +public: + + UOrbPublicationBase( + List * list, + const struct orb_metadata *meta) : + _meta(meta), + _handle() { + if (list != NULL) list->add(this); + } + void update() { + orb_publish(getMeta(), getHandle(), getDataVoidPtr()); + } + virtual void *getDataVoidPtr() = 0; + virtual ~UOrbPublicationBase() { + orb_unsubscribe(getHandle()); + } + const struct orb_metadata *getMeta() { return _meta; } + int getHandle() { return _handle; } +protected: + void setHandle(orb_advert_t handle) { _handle = handle; } + const struct orb_metadata *_meta; + orb_advert_t _handle; +}; + +/** + * UOrb Publication wrapper class + */ +template +class UOrbPublication : + public T, // this must be first! + public UOrbPublicationBase +{ +public: + /** + * Constructor + * + * @param list A list interface for adding to list during construction + * @param meta The uORB metadata (usually from the ORB_ID() macro) + * for the topic. + */ + UOrbPublication( + List * list, + const struct orb_metadata *meta) : + T(), // initialize data structure to zero + UOrbPublicationBase(list, meta) { + // It is important that we call T() + // before we publish the data, so we + // call this here instead of the base class + setHandle(orb_advertise(getMeta(), getDataVoidPtr())); + } + virtual ~UOrbPublication() {} + /* + * XXX + * This function gets the T struct, assuming + * the struct is the first base class, this + * should use dynamic cast, but doesn't + * seem to be available + */ + void *getDataVoidPtr() { return (void *)(T *)(this); } +}; + +} // namespace control diff --git a/apps/controllib/block/UOrbSubscription.cpp b/apps/controllib/block/UOrbSubscription.cpp new file mode 100644 index 0000000000..022cadd245 --- /dev/null +++ b/apps/controllib/block/UOrbSubscription.cpp @@ -0,0 +1,51 @@ +/**************************************************************************** + * + * Copyright (C) 2012 PX4 Development Team. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * 3. Neither the name PX4 nor the names of its contributors may be + * used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS + * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE + * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, + * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS + * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED + * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN + * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + * + ****************************************************************************/ + +/** + * @file UOrbSubscription.cpp + * + */ + +#include "UOrbSubscription.hpp" + +namespace control +{ + +bool __EXPORT UOrbSubscriptionBase::updated() +{ + bool isUpdated = false; + orb_check(_handle, &isUpdated); + return isUpdated; +} + +} // namespace control diff --git a/apps/controllib/block/UOrbSubscription.hpp b/apps/controllib/block/UOrbSubscription.hpp new file mode 100644 index 0000000000..22cc2e1145 --- /dev/null +++ b/apps/controllib/block/UOrbSubscription.hpp @@ -0,0 +1,137 @@ +/**************************************************************************** + * + * Copyright (C) 2012 PX4 Development Team. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * 3. Neither the name PX4 nor the names of its contributors may be + * used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS + * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE + * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, + * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS + * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED + * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN + * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + * + ****************************************************************************/ + +/** + * @file UOrbSubscription.h + * + */ + +#pragma once + +#include +#include "Block.hpp" +#include "List.hpp" + + +namespace control +{ + +class Block; + +/** + * Base subscription warapper class, used in list traversal + * of various subscriptions. + */ +class __EXPORT UOrbSubscriptionBase : + public ListNode +{ +public: +// methods + + /** + * Constructor + * + * @param meta The uORB metadata (usually from the ORB_ID() macro) + * for the topic. + */ + UOrbSubscriptionBase( + List * list, + const struct orb_metadata *meta) : + _meta(meta), + _handle() { + if (list != NULL) list->add(this); + } + bool updated(); + void update() { + if (updated()) { + orb_copy(_meta, _handle, getDataVoidPtr()); + } + } + virtual void *getDataVoidPtr() = 0; + virtual ~UOrbSubscriptionBase() { + orb_unsubscribe(_handle); + } +// accessors + const struct orb_metadata *getMeta() { return _meta; } + int getHandle() { return _handle; } +protected: +// accessors + void setHandle(int handle) { _handle = handle; } +// attributes + const struct orb_metadata *_meta; + int _handle; +}; + +/** + * UOrb Subscription wrapper class + */ +template +class __EXPORT UOrbSubscription : + public T, // this must be first! + public UOrbSubscriptionBase +{ +public: + /** + * Constructor + * + * @param list A list interface for adding to list during construction + * @param meta The uORB metadata (usually from the ORB_ID() macro) + * for the topic. + * @param interval The minimum interval in milliseconds between updates + */ + UOrbSubscription( + List * list, + const struct orb_metadata *meta, unsigned interval) : + T(), // initialize data structure to zero + UOrbSubscriptionBase(list, meta) { + setHandle(orb_subscribe(getMeta())); + orb_set_interval(getHandle(), interval); + } + + /** + * Deconstructor + */ + virtual ~UOrbSubscription() {} + + /* + * XXX + * This function gets the T struct, assuming + * the struct is the first base class, this + * should use dynamic cast, but doesn't + * seem to be available + */ + void *getDataVoidPtr() { return (void *)(T *)(this); } + T getData() { return T(*this); } +}; + +} // namespace control diff --git a/apps/controllib/blocks.cpp b/apps/controllib/blocks.cpp new file mode 100644 index 0000000000..c6c374300e --- /dev/null +++ b/apps/controllib/blocks.cpp @@ -0,0 +1,486 @@ +/**************************************************************************** + * + * Copyright (C) 2012 PX4 Development Team. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * 3. Neither the name PX4 nor the names of its contributors may be + * used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS + * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE + * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, + * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS + * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED + * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN + * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + * + ****************************************************************************/ + +/** + * @file blocks.cpp + * + * Controller library code + */ + +#include +#include + +#include "blocks.hpp" + +namespace control +{ + +int basicBlocksTest() +{ + blockLimitTest(); + blockLimitSymTest(); + blockLowPassTest(); + blockHighPassTest(); + blockIntegralTest(); + blockIntegralTrapTest(); + blockDerivativeTest(); + blockPTest(); + blockPITest(); + blockPDTest(); + blockPIDTest(); + blockOutputTest(); + blockRandUniformTest(); + blockRandGaussTest(); + return 0; +} + +float BlockLimit::update(float input) +{ + if (input > getMax()) { + input = _max.get(); + + } else if (input < getMin()) { + input = getMin(); + } + + return input; +} + +int blockLimitTest() +{ + printf("Test BlockLimit\t\t\t: "); + BlockLimit limit(NULL, "TEST"); + // initial state + ASSERT(equal(1.0f, limit.getMax())); + ASSERT(equal(-1.0f, limit.getMin())); + ASSERT(equal(0.0f, limit.getDt())); + // update + ASSERT(equal(-1.0f, limit.update(-2.0f))); + ASSERT(equal(1.0f, limit.update(2.0f))); + ASSERT(equal(0.0f, limit.update(0.0f))); + printf("PASS\n"); + return 0; +} + +float BlockLimitSym::update(float input) +{ + if (input > getMax()) { + input = _max.get(); + + } else if (input < -getMax()) { + input = -getMax(); + } + + return input; +} + +int blockLimitSymTest() +{ + printf("Test BlockLimitSym\t\t: "); + BlockLimitSym limit(NULL, "TEST"); + // initial state + ASSERT(equal(1.0f, limit.getMax())); + ASSERT(equal(0.0f, limit.getDt())); + // update + ASSERT(equal(-1.0f, limit.update(-2.0f))); + ASSERT(equal(1.0f, limit.update(2.0f))); + ASSERT(equal(0.0f, limit.update(0.0f))); + printf("PASS\n"); + return 0; +} + +float BlockLowPass::update(float input) +{ + float b = 2 * float(M_PI) * getFCut() * getDt(); + float a = b / (1 + b); + setState(a * input + (1 - a)*getState()); + return getState(); +} + +int blockLowPassTest() +{ + printf("Test BlockLowPass\t\t: "); + BlockLowPass lowPass(NULL, "TEST_LP"); + // test initial state + ASSERT(equal(10.0f, lowPass.getFCut())); + ASSERT(equal(0.0f, lowPass.getState())); + ASSERT(equal(0.0f, lowPass.getDt())); + // set dt + lowPass.setDt(0.1f); + ASSERT(equal(0.1f, lowPass.getDt())); + // set state + lowPass.setState(1.0f); + ASSERT(equal(1.0f, lowPass.getState())); + // test update + ASSERT(equal(1.8626974f, lowPass.update(2.0f))); + + // test end condition + for (int i = 0; i < 100; i++) { + lowPass.update(2.0f); + } + + ASSERT(equal(2.0f, lowPass.getState())); + ASSERT(equal(2.0f, lowPass.update(2.0f))); + printf("PASS\n"); + return 0; +}; + +float BlockHighPass::update(float input) +{ + float b = 2 * float(M_PI) * getFCut() * getDt(); + float a = 1 / (1 + b); + setY(a * (getY() + input - getU())); + setU(input); + return getY(); +} + +int blockHighPassTest() +{ + printf("Test BlockHighPass\t\t: "); + BlockHighPass highPass(NULL, "TEST_HP"); + // test initial state + ASSERT(equal(10.0f, highPass.getFCut())); + ASSERT(equal(0.0f, highPass.getU())); + ASSERT(equal(0.0f, highPass.getY())); + ASSERT(equal(0.0f, highPass.getDt())); + // set dt + highPass.setDt(0.1f); + ASSERT(equal(0.1f, highPass.getDt())); + // set state + highPass.setU(1.0f); + ASSERT(equal(1.0f, highPass.getU())); + highPass.setY(1.0f); + ASSERT(equal(1.0f, highPass.getY())); + // test update + ASSERT(equal(0.2746051f, highPass.update(2.0f))); + + // test end condition + for (int i = 0; i < 100; i++) { + highPass.update(2.0f); + } + + ASSERT(equal(0.0f, highPass.getY())); + ASSERT(equal(0.0f, highPass.update(2.0f))); + printf("PASS\n"); + return 0; +} + +float BlockIntegral::update(float input) +{ + // trapezoidal integration + setY(_limit.update(getY() + input * getDt())); + return getY(); +} + +int blockIntegralTest() +{ + printf("Test BlockIntegral\t\t: "); + BlockIntegral integral(NULL, "TEST_I"); + // test initial state + ASSERT(equal(1.0f, integral.getMax())); + ASSERT(equal(0.0f, integral.getDt())); + // set dt + integral.setDt(0.1f); + ASSERT(equal(0.1f, integral.getDt())); + // set Y + integral.setY(0.9f); + ASSERT(equal(0.9f, integral.getY())); + + // test exceed max + for (int i = 0; i < 100; i++) { + integral.update(1.0f); + } + + ASSERT(equal(1.0f, integral.update(1.0f))); + // test exceed min + integral.setY(-0.9f); + ASSERT(equal(-0.9f, integral.getY())); + + for (int i = 0; i < 100; i++) { + integral.update(-1.0f); + } + + ASSERT(equal(-1.0f, integral.update(-1.0f))); + // test update + integral.setY(0.1f); + ASSERT(equal(0.2f, integral.update(1.0))); + ASSERT(equal(0.2f, integral.getY())); + printf("PASS\n"); + return 0; +} + +float BlockIntegralTrap::update(float input) +{ + // trapezoidal integration + setY(_limit.update(getY() + + (getU() + input) / 2.0f * getDt())); + setU(input); + return getY(); +} + +int blockIntegralTrapTest() +{ + printf("Test BlockIntegralTrap\t\t: "); + BlockIntegralTrap integral(NULL, "TEST_I"); + // test initial state + ASSERT(equal(1.0f, integral.getMax())); + ASSERT(equal(0.0f, integral.getDt())); + // set dt + integral.setDt(0.1f); + ASSERT(equal(0.1f, integral.getDt())); + // set U + integral.setU(1.0f); + ASSERT(equal(1.0f, integral.getU())); + // set Y + integral.setY(0.9f); + ASSERT(equal(0.9f, integral.getY())); + + // test exceed max + for (int i = 0; i < 100; i++) { + integral.update(1.0f); + } + + ASSERT(equal(1.0f, integral.update(1.0f))); + // test exceed min + integral.setU(-1.0f); + integral.setY(-0.9f); + ASSERT(equal(-0.9f, integral.getY())); + + for (int i = 0; i < 100; i++) { + integral.update(-1.0f); + } + + ASSERT(equal(-1.0f, integral.update(-1.0f))); + // test update + integral.setU(2.0f); + integral.setY(0.1f); + ASSERT(equal(0.25f, integral.update(1.0))); + ASSERT(equal(0.25f, integral.getY())); + ASSERT(equal(1.0f, integral.getU())); + printf("PASS\n"); + return 0; +} + +float BlockDerivative::update(float input) +{ + float output = _lowPass.update((input - getU()) / getDt()); + setU(input); + return output; +} + +int blockDerivativeTest() +{ + printf("Test BlockDerivative\t\t: "); + BlockDerivative derivative(NULL, "TEST_D"); + // test initial state + ASSERT(equal(0.0f, derivative.getU())); + ASSERT(equal(10.0f, derivative.getLP())); + // set dt + derivative.setDt(0.1f); + ASSERT(equal(0.1f, derivative.getDt())); + // set U + derivative.setU(1.0f); + ASSERT(equal(1.0f, derivative.getU())); + // test update + ASSERT(equal(8.6269744f, derivative.update(2.0f))); + ASSERT(equal(2.0f, derivative.getU())); + printf("PASS\n"); + return 0; +} + +int blockPTest() +{ + printf("Test BlockP\t\t\t: "); + BlockP blockP(NULL, "TEST_P"); + // test initial state + ASSERT(equal(0.2f, blockP.getKP())); + ASSERT(equal(0.0f, blockP.getDt())); + // set dt + blockP.setDt(0.1f); + ASSERT(equal(0.1f, blockP.getDt())); + // test update + ASSERT(equal(0.4f, blockP.update(2.0f))); + printf("PASS\n"); + return 0; +} + +int blockPITest() +{ + printf("Test BlockPI\t\t\t: "); + BlockPI blockPI(NULL, "TEST"); + // test initial state + ASSERT(equal(0.2f, blockPI.getKP())); + ASSERT(equal(0.1f, blockPI.getKI())); + ASSERT(equal(0.0f, blockPI.getDt())); + ASSERT(equal(1.0f, blockPI.getIntegral().getMax())); + // set dt + blockPI.setDt(0.1f); + ASSERT(equal(0.1f, blockPI.getDt())); + // set integral state + blockPI.getIntegral().setY(0.1f); + ASSERT(equal(0.1f, blockPI.getIntegral().getY())); + // test update + // 0.2*2 + 0.1*(2*0.1 + 0.1) = 0.43 + ASSERT(equal(0.43f, blockPI.update(2.0f))); + printf("PASS\n"); + return 0; +} + +int blockPDTest() +{ + printf("Test BlockPD\t\t\t: "); + BlockPD blockPD(NULL, "TEST"); + // test initial state + ASSERT(equal(0.2f, blockPD.getKP())); + ASSERT(equal(0.01f, blockPD.getKD())); + ASSERT(equal(0.0f, blockPD.getDt())); + ASSERT(equal(10.0f, blockPD.getDerivative().getLP())); + // set dt + blockPD.setDt(0.1f); + ASSERT(equal(0.1f, blockPD.getDt())); + // set derivative state + blockPD.getDerivative().setU(1.0f); + ASSERT(equal(1.0f, blockPD.getDerivative().getU())); + // test update + // 0.2*2 + 0.1*(0.1*8.626...) = 0.486269744 + ASSERT(equal(0.486269744f, blockPD.update(2.0f))); + printf("PASS\n"); + return 0; +} + +int blockPIDTest() +{ + printf("Test BlockPID\t\t\t: "); + BlockPID blockPID(NULL, "TEST"); + // test initial state + ASSERT(equal(0.2f, blockPID.getKP())); + ASSERT(equal(0.1f, blockPID.getKI())); + ASSERT(equal(0.01f, blockPID.getKD())); + ASSERT(equal(0.0f, blockPID.getDt())); + ASSERT(equal(10.0f, blockPID.getDerivative().getLP())); + ASSERT(equal(1.0f, blockPID.getIntegral().getMax())); + // set dt + blockPID.setDt(0.1f); + ASSERT(equal(0.1f, blockPID.getDt())); + // set derivative state + blockPID.getDerivative().setU(1.0f); + ASSERT(equal(1.0f, blockPID.getDerivative().getU())); + // set integral state + blockPID.getIntegral().setY(0.1f); + ASSERT(equal(0.1f, blockPID.getIntegral().getY())); + // test update + // 0.2*2 + 0.1*(2*0.1 + 0.1) + 0.1*(0.1*8.626...) = 0.5162697 + ASSERT(equal(0.5162697f, blockPID.update(2.0f))); + printf("PASS\n"); + return 0; +} + +int blockOutputTest() +{ + printf("Test BlockOutput\t\t: "); + BlockOutput blockOutput(NULL, "TEST"); + // test initial state + ASSERT(equal(0.0f, blockOutput.getDt())); + ASSERT(equal(0.5f, blockOutput.get())); + ASSERT(equal(-1.0f, blockOutput.getMin())); + ASSERT(equal(1.0f, blockOutput.getMax())); + // test update below min + blockOutput.update(-2.0f); + ASSERT(equal(-1.0f, blockOutput.get())); + // test update above max + blockOutput.update(2.0f); + ASSERT(equal(1.0f, blockOutput.get())); + // test trim + blockOutput.update(0.0f); + ASSERT(equal(0.5f, blockOutput.get())); + printf("PASS\n"); + return 0; +} + +int blockRandUniformTest() +{ + srand(1234); + printf("Test BlockRandUniform\t\t: "); + BlockRandUniform blockRandUniform(NULL, "TEST"); + // test initial state + ASSERT(equal(0.0f, blockRandUniform.getDt())); + ASSERT(equal(-1.0f, blockRandUniform.getMin())); + ASSERT(equal(1.0f, blockRandUniform.getMax())); + // test update + int n = 10000; + float mean = blockRandUniform.update(); + + // recursive mean algorithm from Knuth + for (int i = 2; i < n + 1; i++) { + float val = blockRandUniform.update(); + mean += (val - mean) / i; + ASSERT(val <= blockRandUniform.getMax()); + ASSERT(val >= blockRandUniform.getMin()); + } + + ASSERT(equal(mean, (blockRandUniform.getMin() + + blockRandUniform.getMax()) / 2, 1e-1)); + printf("PASS\n"); + return 0; +} + +int blockRandGaussTest() +{ + srand(1234); + printf("Test BlockRandGauss\t\t: "); + BlockRandGauss blockRandGauss(NULL, "TEST"); + // test initial state + ASSERT(equal(0.0f, blockRandGauss.getDt())); + ASSERT(equal(1.0f, blockRandGauss.getMean())); + ASSERT(equal(2.0f, blockRandGauss.getStdDev())); + // test update + int n = 10000; + float mean = blockRandGauss.update(); + float sum = 0; + + // recursive mean, stdev algorithm from Knuth + for (int i = 2; i < n + 1; i++) { + float val = blockRandGauss.update(); + float newMean = mean + (val - mean) / i; + sum += (val - mean) * (val - newMean); + mean = newMean; + } + + float stdDev = sqrt(sum / (n - 1)); + ASSERT(equal(mean, blockRandGauss.getMean(), 1e-1)); + ASSERT(equal(stdDev, blockRandGauss.getStdDev(), 1e-1)); + printf("PASS\n"); + return 0; +} + +} // namespace control diff --git a/apps/controllib/blocks.hpp b/apps/controllib/blocks.hpp new file mode 100644 index 0000000000..7a785d12e2 --- /dev/null +++ b/apps/controllib/blocks.hpp @@ -0,0 +1,494 @@ +/**************************************************************************** + * + * Copyright (C) 2012 PX4 Development Team. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * 3. Neither the name PX4 nor the names of its contributors may be + * used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS + * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE + * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, + * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS + * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED + * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN + * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + * + ****************************************************************************/ + +/** + * @file blocks.h + * + * Controller library code + */ + +#pragma once + +#include +#include +#include +#include + +#include "block/Block.hpp" +#include "block/BlockParam.hpp" + +namespace control +{ + +int __EXPORT basicBlocksTest(); + +/** + * A limiter/ saturation. + * The output of update is the input, bounded + * by min/max. + */ +class __EXPORT BlockLimit : public Block +{ +public: +// methods + BlockLimit(SuperBlock *parent, const char *name) : + Block(parent, name), + _min(this, "MIN"), + _max(this, "MAX") + {}; + virtual ~BlockLimit() {}; + float update(float input); +// accessors + float getMin() { return _min.get(); } + float getMax() { return _max.get(); } +protected: +// attributes + BlockParam _min; + BlockParam _max; +}; + +int __EXPORT blockLimitTest(); + +/** + * A symmetric limiter/ saturation. + * Same as limiter but with only a max, is used for + * upper limit of +max, and lower limit of -max + */ +class __EXPORT BlockLimitSym : public Block +{ +public: +// methods + BlockLimitSym(SuperBlock *parent, const char *name) : + Block(parent, name), + _max(this, "MAX") + {}; + virtual ~BlockLimitSym() {}; + float update(float input); +// accessors + float getMax() { return _max.get(); } +protected: +// attributes + BlockParam _max; +}; + +int __EXPORT blockLimitSymTest(); + +/** + * A low pass filter as described here: + * http://en.wikipedia.org/wiki/Low-pass_filter. + */ +class __EXPORT BlockLowPass : public Block +{ +public: +// methods + BlockLowPass(SuperBlock *parent, const char *name) : + Block(parent, name), + _state(0), + _fCut(this, "") // only one parameter, no need to name + {}; + virtual ~BlockLowPass() {}; + float update(float input); +// accessors + float getState() { return _state; } + float getFCut() { return _fCut.get(); } + void setState(float state) { _state = state; } +protected: +// attributes + float _state; + BlockParam _fCut; +}; + +int __EXPORT blockLowPassTest(); + +/** + * A high pass filter as described here: + * http://en.wikipedia.org/wiki/High-pass_filter. + */ +class __EXPORT BlockHighPass : public Block +{ +public: +// methods + BlockHighPass(SuperBlock *parent, const char *name) : + Block(parent, name), + _u(0), + _y(0), + _fCut(this, "") // only one parameter, no need to name + {}; + virtual ~BlockHighPass() {}; + float update(float input); +// accessors + float getU() {return _u;} + float getY() {return _y;} + float getFCut() {return _fCut.get();} + void setU(float u) {_u = u;} + void setY(float y) {_y = y;} +protected: +// attributes + float _u; /**< previous input */ + float _y; /**< previous output */ + BlockParam _fCut; /**< cut-off frequency, Hz */ +}; + +int __EXPORT blockHighPassTest(); + +/** + * A rectangular integrator. + * A limiter is built into the class to bound the + * integral's internal state. This is important + * for windup protection. + * @see Limit + */ +class __EXPORT BlockIntegral: public SuperBlock +{ +public: +// methods + BlockIntegral(SuperBlock *parent, const char *name) : + SuperBlock(parent, name), + _y(0), + _limit(this, "") {}; + virtual ~BlockIntegral() {}; + float update(float input); +// accessors + float getY() {return _y;} + float getMax() {return _limit.getMax();} + void setY(float y) {_y = y;} +protected: +// attributes + float _y; /**< previous output */ + BlockLimitSym _limit; /**< limiter */ +}; + +int __EXPORT blockIntegralTest(); + +/** + * A trapezoidal integrator. + * http://en.wikipedia.org/wiki/Trapezoidal_rule + * A limiter is built into the class to bound the + * integral's internal state. This is important + * for windup protection. + * @see Limit + */ +class __EXPORT BlockIntegralTrap : public SuperBlock +{ +public: +// methods + BlockIntegralTrap(SuperBlock *parent, const char *name) : + SuperBlock(parent, name), + _u(0), + _y(0), + _limit(this, "") {}; + virtual ~BlockIntegralTrap() {}; + float update(float input); +// accessors + float getU() {return _u;} + float getY() {return _y;} + float getMax() {return _limit.getMax();} + void setU(float u) {_u = u;} + void setY(float y) {_y = y;} +protected: +// attributes + float _u; /**< previous input */ + float _y; /**< previous output */ + BlockLimitSym _limit; /**< limiter */ +}; + +int __EXPORT blockIntegralTrapTest(); + +/** + * A simple derivative approximation. + * This uses the previous and current input. + * This has a built in low pass filter. + * @see LowPass + */ +class __EXPORT BlockDerivative : public SuperBlock +{ +public: +// methods + BlockDerivative(SuperBlock *parent, const char *name) : + SuperBlock(parent, name), + _u(0), + _lowPass(this, "LP") + {}; + virtual ~BlockDerivative() {}; + float update(float input); +// accessors + void setU(float u) {_u = u;} + float getU() {return _u;} + float getLP() {return _lowPass.getFCut();} +protected: +// attributes + float _u; /**< previous input */ + BlockLowPass _lowPass; /**< low pass filter */ +}; + +int __EXPORT blockDerivativeTest(); + +/** + * A proportional controller. + * @link http://en.wikipedia.org/wiki/PID_controller + */ +class __EXPORT BlockP: public Block +{ +public: +// methods + BlockP(SuperBlock *parent, const char *name) : + Block(parent, name), + _kP(this, "") // only one param, no need to name + {}; + virtual ~BlockP() {}; + float update(float input) { + return getKP() * input; + } +// accessors + float getKP() { return _kP.get(); } +protected: + BlockParam _kP; +}; + +int __EXPORT blockPTest(); + +/** + * A proportional-integral controller. + * @link http://en.wikipedia.org/wiki/PID_controller + */ +class __EXPORT BlockPI: public SuperBlock +{ +public: +// methods + BlockPI(SuperBlock *parent, const char *name) : + SuperBlock(parent, name), + _integral(this, "I"), + _kP(this, "P"), + _kI(this, "I") + {}; + virtual ~BlockPI() {}; + float update(float input) { + return getKP() * input + + getKI() * getIntegral().update(input); + } +// accessors + float getKP() { return _kP.get(); } + float getKI() { return _kI.get(); } + BlockIntegral &getIntegral() { return _integral; } +private: + BlockIntegral _integral; + BlockParam _kP; + BlockParam _kI; +}; + +int __EXPORT blockPITest(); + +/** + * A proportional-derivative controller. + * @link http://en.wikipedia.org/wiki/PID_controller + */ +class __EXPORT BlockPD: public SuperBlock +{ +public: +// methods + BlockPD(SuperBlock *parent, const char *name) : + SuperBlock(parent, name), + _derivative(this, "D"), + _kP(this, "P"), + _kD(this, "D") + {}; + virtual ~BlockPD() {}; + float update(float input) { + return getKP() * input + + getKD() * getDerivative().update(input); + } +// accessors + float getKP() { return _kP.get(); } + float getKD() { return _kD.get(); } + BlockDerivative &getDerivative() { return _derivative; } +private: + BlockDerivative _derivative; + BlockParam _kP; + BlockParam _kD; +}; + +int __EXPORT blockPDTest(); + +/** + * A proportional-integral-derivative controller. + * @link http://en.wikipedia.org/wiki/PID_controller + */ +class __EXPORT BlockPID: public SuperBlock +{ +public: +// methods + BlockPID(SuperBlock *parent, const char *name) : + SuperBlock(parent, name), + _integral(this, "I"), + _derivative(this, "D"), + _kP(this, "P"), + _kI(this, "I"), + _kD(this, "D") + {}; + virtual ~BlockPID() {}; + float update(float input) { + return getKP() * input + + getKI() * getIntegral().update(input) + + getKD() * getDerivative().update(input); + } +// accessors + float getKP() { return _kP.get(); } + float getKI() { return _kI.get(); } + float getKD() { return _kD.get(); } + BlockIntegral &getIntegral() { return _integral; } + BlockDerivative &getDerivative() { return _derivative; } +private: +// attributes + BlockIntegral _integral; + BlockDerivative _derivative; + BlockParam _kP; + BlockParam _kI; + BlockParam _kD; +}; + +int __EXPORT blockPIDTest(); + +/** + * An output trim/ saturation block + */ +class __EXPORT BlockOutput: public SuperBlock +{ +public: +// methods + BlockOutput(SuperBlock *parent, const char *name) : + SuperBlock(parent, name), + _trim(this, "TRIM"), + _limit(this, ""), + _val(0) { + update(0); + }; + virtual ~BlockOutput() {}; + void update(float input) { + _val = _limit.update(input + getTrim()); + } +// accessors + float getMin() { return _limit.getMin(); } + float getMax() { return _limit.getMax(); } + float getTrim() { return _trim.get(); } + float get() { return _val; } +private: +// attributes + BlockParam _trim; + BlockLimit _limit; + float _val; +}; + +int __EXPORT blockOutputTest(); + +/** + * A uniform random number generator + */ +class __EXPORT BlockRandUniform: public Block +{ +public: +// methods + BlockRandUniform(SuperBlock *parent, + const char *name) : + Block(parent, name), + _min(this, "MIN"), + _max(this, "MAX") { + // seed should be initialized somewhere + // in main program for all calls to rand + // XXX currently in nuttx if you seed to 0, rand breaks + }; + virtual ~BlockRandUniform() {}; + float update() { + static float rand_max = MAX_RAND; + float rand_val = rand(); + float bounds = getMax() - getMin(); + return getMin() + (rand_val * bounds) / rand_max; + } +// accessors + float getMin() { return _min.get(); } + float getMax() { return _max.get(); } +private: +// attributes + BlockParam _min; + BlockParam _max; +}; + +int __EXPORT blockRandUniformTest(); + +class __EXPORT BlockRandGauss: public Block +{ +public: +// methods + BlockRandGauss(SuperBlock *parent, + const char *name) : + Block(parent, name), + _mean(this, "MEAN"), + _stdDev(this, "DEV") { + // seed should be initialized somewhere + // in main program for all calls to rand + // XXX currently in nuttx if you seed to 0, rand breaks + }; + virtual ~BlockRandGauss() {}; + float update() { + static float V1, V2, S; + static int phase = 0; + float X; + + if (phase == 0) { + do { + float U1 = (float)rand() / MAX_RAND; + float U2 = (float)rand() / MAX_RAND; + V1 = 2 * U1 - 1; + V2 = 2 * U2 - 1; + S = V1 * V1 + V2 * V2; + } while (S >= 1 || fabsf(S) < 1e-8f); + + X = V1 * float(sqrt(-2 * float(log(S)) / S)); + + } else + X = V2 * float(sqrt(-2 * float(log(S)) / S)); + + phase = 1 - phase; + return X * getStdDev() + getMean(); + } +// accessors + float getMean() { return _mean.get(); } + float getStdDev() { return _stdDev.get(); } +private: +// attributes + BlockParam _mean; + BlockParam _stdDev; +}; + +int __EXPORT blockRandGaussTest(); + +} // namespace control diff --git a/apps/controllib/fixedwing.cpp b/apps/controllib/fixedwing.cpp new file mode 100644 index 0000000000..6956537145 --- /dev/null +++ b/apps/controllib/fixedwing.cpp @@ -0,0 +1,351 @@ +/**************************************************************************** + * + * Copyright (C) 2012 PX4 Development Team. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * 3. Neither the name PX4 nor the names of its contributors may be + * used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS + * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE + * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, + * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS + * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED + * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN + * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + * + ****************************************************************************/ + +/** + * @file fixedwing.cpp + * + * Controller library code + */ + +#include "fixedwing.hpp" + +namespace control +{ + +namespace fixedwing +{ + +BlockYawDamper::BlockYawDamper(SuperBlock *parent, const char *name) : + SuperBlock(parent, name), + _rLowPass(this, "R_LP"), + _rWashout(this, "R_HP"), + _r2Rdr(this, "R2RDR"), + _rudder(0) +{ +} + +BlockYawDamper::~BlockYawDamper() {}; + +void BlockYawDamper::update(float rCmd, float r) +{ + _rudder = _r2Rdr.update(rCmd - + _rWashout.update(_rLowPass.update(r))); +} + +BlockStabilization::BlockStabilization(SuperBlock *parent, const char *name) : + SuperBlock(parent, name), + _yawDamper(this, ""), + _pLowPass(this, "P_LP"), + _qLowPass(this, "Q_LP"), + _p2Ail(this, "P2AIL"), + _q2Elv(this, "Q2ELV"), + _aileron(0), + _elevator(0) +{ +} + +BlockStabilization::~BlockStabilization() {}; + +void BlockStabilization::update(float pCmd, float qCmd, float rCmd, + float p, float q, float r) +{ + _aileron = _p2Ail.update( + pCmd - _pLowPass.update(p)); + _elevator = _q2Elv.update( + qCmd - _qLowPass.update(q)); + _yawDamper.update(rCmd, r); +} + +BlockHeadingHold::BlockHeadingHold(SuperBlock *parent, const char *name) : + SuperBlock(parent, name), + _psi2Phi(this, "PSI2PHI"), + _phi2P(this, "PHI2P"), + _phiLimit(this, "PHI_LIM") +{ +} + +BlockHeadingHold::~BlockHeadingHold() {}; + +float BlockHeadingHold::update(float psiCmd, float phi, float psi, float p) +{ + float psiError = _wrap_pi(psiCmd - psi); + float phiCmd = _phiLimit.update(_psi2Phi.update(psiError)); + return _phi2P.update(phiCmd - phi); +} + +BlockVelocityHoldBackside::BlockVelocityHoldBackside(SuperBlock *parent, const char *name) : + SuperBlock(parent, name), + _v2Theta(this, "V2THE"), + _theta2Q(this, "THE2Q"), + _theLimit(this, "THE"), + _vLimit(this, "V") +{ +} + +BlockVelocityHoldBackside::~BlockVelocityHoldBackside() {}; + +float BlockVelocityHoldBackside::update(float vCmd, float v, float theta, float q) +{ + // negative sign because nose over to increase speed + float thetaCmd = _theLimit.update(-_v2Theta.update(_vLimit.update(vCmd) - v)); + return _theta2Q.update(thetaCmd - theta); +} + +BlockVelocityHoldFrontside::BlockVelocityHoldFrontside(SuperBlock *parent, const char *name) : + SuperBlock(parent, name), + _v2Thr(this, "V2THR") +{ +} + +BlockVelocityHoldFrontside::~BlockVelocityHoldFrontside() {}; + +float BlockVelocityHoldFrontside::update(float vCmd, float v) +{ + return _v2Thr.update(vCmd - v); +} + +BlockAltitudeHoldBackside::BlockAltitudeHoldBackside(SuperBlock *parent, const char *name) : + SuperBlock(parent, name), + _h2Thr(this, "H2THR"), + _throttle(0) +{ +} + +BlockAltitudeHoldBackside::~BlockAltitudeHoldBackside() {}; + +void BlockAltitudeHoldBackside::update(float hCmd, float h) +{ + _throttle = _h2Thr.update(hCmd - h); +} + +BlockAltitudeHoldFrontside::BlockAltitudeHoldFrontside(SuperBlock *parent, const char *name) : + SuperBlock(parent, name), + _h2Theta(this, "H2THE"), + _theta2Q(this, "THE2Q") +{ +} + +BlockAltitudeHoldFrontside::~BlockAltitudeHoldFrontside() {}; + +float BlockAltitudeHoldFrontside::update(float hCmd, float h, float theta, float q) +{ + float thetaCmd = _h2Theta.update(hCmd - h); + return _theta2Q.update(thetaCmd - theta); +} + +BlockBacksideAutopilot::BlockBacksideAutopilot(SuperBlock *parent, + const char *name, + BlockStabilization *stabilization) : + SuperBlock(parent, name), + _stabilization(stabilization), + _headingHold(this, ""), + _velocityHold(this, ""), + _altitudeHold(this, ""), + _trimAil(this, "TRIM_AIL"), + _trimElv(this, "TRIM_ELV"), + _trimRdr(this, "TRIM_RDR"), + _trimThr(this, "TRIM_THR") +{ +} + +BlockBacksideAutopilot::~BlockBacksideAutopilot() {}; + +void BlockBacksideAutopilot::update(float hCmd, float vCmd, float rCmd, float psiCmd, + float h, float v, + float phi, float theta, float psi, + float p, float q, float r) +{ + _altitudeHold.update(hCmd, h); + _stabilization->update( + _headingHold.update(psiCmd, phi, psi, p), + _velocityHold.update(vCmd, v, theta, q), + rCmd, + p, q, r); +} + +BlockWaypointGuidance::BlockWaypointGuidance(SuperBlock *parent, const char *name) : + SuperBlock(parent, name), + _xtYawLimit(this, "XT2YAW"), + _xt2Yaw(this, "XT2YAW"), + _psiCmd(0) +{ +} + +BlockWaypointGuidance::~BlockWaypointGuidance() {}; + +void BlockWaypointGuidance::update(vehicle_global_position_s &pos, + vehicle_attitude_s &att, + vehicle_global_position_setpoint_s &posCmd, + vehicle_global_position_setpoint_s &lastPosCmd) +{ + + // heading to waypoint + float psiTrack = get_bearing_to_next_waypoint( + (double)pos.lat / (double)1e7d, + (double)pos.lon / (double)1e7d, + (double)posCmd.lat / (double)1e7d, + (double)posCmd.lon / (double)1e7d); + + // cross track + struct crosstrack_error_s xtrackError; + get_distance_to_line(&xtrackError, + (double)pos.lat / (double)1e7d, + (double)pos.lon / (double)1e7d, + (double)lastPosCmd.lat / (double)1e7d, + (double)lastPosCmd.lon / (double)1e7d, + (double)posCmd.lat / (double)1e7d, + (double)posCmd.lon / (double)1e7d); + + _psiCmd = _wrap_2pi(psiTrack - + _xtYawLimit.update(_xt2Yaw.update(xtrackError.distance))); +} + +BlockUorbEnabledAutopilot::BlockUorbEnabledAutopilot(SuperBlock *parent, const char *name) : + SuperBlock(parent, name), + // subscriptions + _att(&getSubscriptions(), ORB_ID(vehicle_attitude), 20), + _attCmd(&getSubscriptions(), ORB_ID(vehicle_attitude_setpoint), 20), + _ratesCmd(&getSubscriptions(), ORB_ID(vehicle_rates_setpoint), 20), + _pos(&getSubscriptions() , ORB_ID(vehicle_global_position), 20), + _posCmd(&getSubscriptions(), ORB_ID(vehicle_global_position_setpoint), 20), + _manual(&getSubscriptions(), ORB_ID(manual_control_setpoint), 20), + _status(&getSubscriptions(), ORB_ID(vehicle_status), 20), + _param_update(&getSubscriptions(), ORB_ID(parameter_update), 1000), // limit to 1 Hz + // publications + _actuators(&getPublications(), ORB_ID(actuator_controls_0)) +{ +} + +BlockUorbEnabledAutopilot::~BlockUorbEnabledAutopilot() {}; + +BlockMultiModeBacksideAutopilot::BlockMultiModeBacksideAutopilot(SuperBlock *parent, const char *name) : + BlockUorbEnabledAutopilot(parent, name), + _stabilization(this, ""), // no name needed, already unique + _backsideAutopilot(this, "", &_stabilization), + _guide(this, ""), + _vCmd(this, "V_CMD"), + _attPoll(), + _lastPosCmd(), + _timeStamp(0) +{ + _attPoll.fd = _att.getHandle(); + _attPoll.events = POLLIN; +} + +void BlockMultiModeBacksideAutopilot::update() +{ + // wait for a sensor update, check for exit condition every 100 ms + if (poll(&_attPoll, 1, 100) < 0) return; // poll error + + uint64_t newTimeStamp = hrt_absolute_time(); + float dt = (newTimeStamp - _timeStamp) / 1.0e6f; + _timeStamp = newTimeStamp; + + // check for sane values of dt + // to prevent large control responses + if (dt > 1.0f || dt < 0) return; + + // set dt for all child blocks + setDt(dt); + + // store old position command before update if new command sent + if (_posCmd.updated()) { + _lastPosCmd = _posCmd.getData(); + } + + // check for new updates + if (_param_update.updated()) updateParams(); + + // get new information from subscriptions + updateSubscriptions(); + + // default all output to zero unless handled by mode + for (unsigned i = 4; i < NUM_ACTUATOR_CONTROLS; i++) + _actuators.control[i] = 0.0f; + + // handle autopilot modes + if (_status.state_machine == SYSTEM_STATE_STABILIZED) { + _stabilization.update( + _ratesCmd.roll, _ratesCmd.pitch, _ratesCmd.yaw, + _att.rollspeed, _att.pitchspeed, _att.yawspeed); + _actuators.control[CH_AIL] = _stabilization.getAileron(); + _actuators.control[CH_ELV] = _stabilization.getElevator(); + _actuators.control[CH_RDR] = _stabilization.getRudder(); + _actuators.control[CH_THR] = _manual.throttle; + + } else if (_status.state_machine == SYSTEM_STATE_AUTO) { + // update guidance + _guide.update(_pos, _att, _posCmd, _lastPosCmd); + + // calculate velocity, XXX should be airspeed, but using ground speed for now + float v = sqrtf(_pos.vx * _pos.vx + _pos.vy * _pos.vy + _pos.vz * _pos.vz); + + // commands + float rCmd = 0; + + _backsideAutopilot.update( + _posCmd.altitude, _vCmd.get(), rCmd, _guide.getPsiCmd(), + _pos.alt, v, + _att.roll, _att.pitch, _att.yaw, + _att.rollspeed, _att.pitchspeed, _att.yawspeed + ); + _actuators.control[CH_AIL] = _backsideAutopilot.getAileron(); + _actuators.control[CH_ELV] = _backsideAutopilot.getElevator(); + _actuators.control[CH_RDR] = _backsideAutopilot.getRudder(); + _actuators.control[CH_THR] = _backsideAutopilot.getThrottle(); + + } else if (_status.state_machine == SYSTEM_STATE_MANUAL) { + _actuators.control[CH_AIL] = _manual.roll; + _actuators.control[CH_ELV] = _manual.pitch; + _actuators.control[CH_RDR] = _manual.yaw; + _actuators.control[CH_THR] = _manual.throttle; + } + + // update all publications + updatePublications(); +} + +BlockMultiModeBacksideAutopilot::~BlockMultiModeBacksideAutopilot() +{ + // send one last publication when destroyed, setting + // all output to zero + for (unsigned i = 0; i < NUM_ACTUATOR_CONTROLS; i++) + _actuators.control[i] = 0.0f; + + updatePublications(); +} + +} // namespace fixedwing + +} // namespace control + diff --git a/apps/controllib/fixedwing.hpp b/apps/controllib/fixedwing.hpp new file mode 100644 index 0000000000..ea742641c6 --- /dev/null +++ b/apps/controllib/fixedwing.hpp @@ -0,0 +1,438 @@ +/**************************************************************************** + * + * Copyright (C) 2012 PX4 Development Team. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * 3. Neither the name PX4 nor the names of its contributors may be + * used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS + * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE + * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, + * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS + * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED + * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN + * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + * + ****************************************************************************/ + +/** + * @file fixedwing.h + * + * Controller library code + */ + +#pragma once + +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#include +#include +#include +#include + +#include +#include + +#include "blocks.hpp" +#include "block/UOrbSubscription.hpp" +#include "block/UOrbPublication.hpp" + +extern "C" { +#include +} + +namespace control +{ + +namespace fixedwing +{ + +/** + * BlockYawDamper + * + * This block has more explations to help new developers + * add their own blocks. It includes a limited explanation + * of some C++ basics. + * + * Block: The generic class describing a typical block as you + * would expect in Simulink or ScicosLab. A block can have + * parameters. It cannot have other blocks. + * + * SuperBlock: A superblock is a block that can have other + * blocks. It has methods that manage the blocks beneath it. + * + * BlockYawDamper inherits from SuperBlock publically, this + * means that any public function in SuperBlock are public within + * BlockYawDamper and may be called from outside the + * class methods. Any protected function within block + * are private to the class and may not be called from + * outside this class. Protected should be preferred + * where possible to public as it is important to + * limit access to the bare minimum to prevent + * accidental errors. + */ +class __EXPORT BlockYawDamper : public SuperBlock +{ +private: + /** + * Declaring other blocks used by this block + * + * In this section we declare all child blocks that + * this block is composed of. They are private + * members so only this block has direct access to + * them. + */ + BlockLowPass _rLowPass; + BlockHighPass _rWashout; + BlockP _r2Rdr; + + /** + * Declaring output values and accessors + * + * If we have any output values for the block we + * declare them here. Output can be directly returned + * through the update function, but outputs should be + * declared here if the information will likely be requested + * again, or if there are multiple outputs. + * + * You should only be able to set outputs from this block, + * so the outputs are declared in the private section. + * A get accessor is provided + * in the public section for other blocks to get the + * value of the output. + */ + float _rudder; +public: + /** + * BlockYawDamper Constructor + * + * The job of the constructor is to initialize all + * parameter in this block and initialize all child + * blocks. Note also, that the output values must be + * initialized here. The order of the members in the + * member initialization list should follow the + * order in which they are declared within the class. + * See the private member declarations above. + * + * Block Construction + * + * All blocks are constructed with their parent block + * and their name. This allows parameters within the + * block to construct a fully qualified name from + * concatenating the two. If the name provided to the + * block is "", then the block will use the parent + * name as it's name. This is useful in cases where + * you have a block that has parameters "MIN", "MAX", + * such as BlockLimit and you do not want an extra name + * to qualify them since the parent block has no "MIN", + * "MAX" parameters. + * + * Block Parameter Construction + * + * Block parameters are named constants, they are + * constructed using: + * BlockParam::BlockParam(Block * parent, const char * name) + * This funciton takes both a parent block and a name. + * The constructore then uses the parent name and the name of + * the paramter to ask the px4 param library if it has any + * parameters with this name. If it does, a handle to the + * parameter is retrieved. + * + * Block/ BlockParam Naming + * + * When desigining new blocks, the naming of the parameters and + * blocks determines the fully qualified name of the parameters + * within the ground station, so it is important to choose + * short, easily understandable names. Again, when a name of + * "" is passed, the parent block name is used as the value to + * prepend to paramters names. + */ + BlockYawDamper(SuperBlock *parent, const char *name); + /** + * Block deconstructor + * + * It is always a good idea to declare a virtual + * deconstructor so that upon calling delete from + * a class derived from this, all of the + * deconstructors all called, the derived class first, and + * then the base class + */ + virtual ~BlockYawDamper(); + + /** + * Block update function + * + * The job of the update function is to compute the output + * values for the block. In a simple block with one output, + * the output may be returned directly. If the output is + * required frequenly by other processses, it might be a + * good idea to declare a member to store the temporary + * variable. + */ + void update(float rCmd, float r); + + /** + * Rudder output value accessor + * + * This is a public accessor function, which means that the + * private value _rudder is returned to anyone calling + * BlockYawDamper::getRudder(). Note thate a setRudder() is + * not provided, this is because the updateParams() call + * for a block provides the mechanism for updating the + * paramter. + */ + float getRudder() { return _rudder; } +}; + +/** + * Stability augmentation system. + * Aircraft Control and Simulation, Stevens and Lewis, pg. 292, 299 + */ +class __EXPORT BlockStabilization : public SuperBlock +{ +private: + BlockYawDamper _yawDamper; + BlockLowPass _pLowPass; + BlockLowPass _qLowPass; + BlockP _p2Ail; + BlockP _q2Elv; + float _aileron; + float _elevator; +public: + BlockStabilization(SuperBlock *parent, const char *name); + virtual ~BlockStabilization(); + void update(float pCmd, float qCmd, float rCmd, + float p, float q, float r); + float getAileron() { return _aileron; } + float getElevator() { return _elevator; } + float getRudder() { return _yawDamper.getRudder(); } +}; + +/** + * Heading hold autopilot block. + * Aircraft Control and Simulation, Stevens and Lewis + * Heading hold, pg. 348 + */ +class __EXPORT BlockHeadingHold : public SuperBlock +{ +private: + BlockP _psi2Phi; + BlockP _phi2P; + BlockLimitSym _phiLimit; +public: + BlockHeadingHold(SuperBlock *parent, const char *name); + virtual ~BlockHeadingHold(); + /** + * returns pCmd + */ + float update(float psiCmd, float phi, float psi, float p); +}; + +/** + * Frontside/ Backside Control Systems + * + * Frontside : + * velocity error -> throttle + * altitude error -> elevator + * + * Backside : + * velocity error -> elevator + * altitude error -> throttle + * + * Backside control systems are more resilient at + * slow speeds on the back-side of the power + * required curve/ landing etc. Less performance + * than frontside at high speeds. + */ + +/** + * Backside velocity hold autopilot block. + * v -> theta -> q -> elevator + */ +class __EXPORT BlockVelocityHoldBackside : public SuperBlock +{ +private: + BlockPID _v2Theta; + BlockPID _theta2Q; + BlockLimit _theLimit; + BlockLimit _vLimit; +public: + BlockVelocityHoldBackside(SuperBlock *parent, const char *name); + virtual ~BlockVelocityHoldBackside(); + /** + * returns qCmd + */ + float update(float vCmd, float v, float theta, float q); +}; + +/** + * Frontside velocity hold autopilot block. + * v -> throttle + */ +class __EXPORT BlockVelocityHoldFrontside : public SuperBlock +{ +private: + BlockPID _v2Thr; +public: + BlockVelocityHoldFrontside(SuperBlock *parent, const char *name); + virtual ~BlockVelocityHoldFrontside(); + /** + * returns throttle + */ + float update(float vCmd, float v); +}; + +/** + * Backside altitude hold autopilot block. + * h -> throttle + */ +class __EXPORT BlockAltitudeHoldBackside : public SuperBlock +{ +private: + BlockPID _h2Thr; + float _throttle; +public: + BlockAltitudeHoldBackside(SuperBlock *parent, const char *name); + virtual ~BlockAltitudeHoldBackside(); + void update(float hCmd, float h); + float getThrottle() { return _throttle; } +}; + +/** + * Frontside altitude hold autopilot block. + * h -> theta > q -> elevator + */ +class __EXPORT BlockAltitudeHoldFrontside : public SuperBlock +{ +private: + BlockPID _h2Theta; + BlockPID _theta2Q; +public: + BlockAltitudeHoldFrontside(SuperBlock *parent, const char *name); + virtual ~BlockAltitudeHoldFrontside(); + /** + * return qCmd + */ + float update(float hCmd, float h, float theta, float q); +}; + +/** + * Backside autopilot + */ +class __EXPORT BlockBacksideAutopilot : public SuperBlock +{ +private: + BlockStabilization *_stabilization; + BlockHeadingHold _headingHold; + BlockVelocityHoldBackside _velocityHold; + BlockAltitudeHoldBackside _altitudeHold; + BlockParam _trimAil; + BlockParam _trimElv; + BlockParam _trimRdr; + BlockParam _trimThr; +public: + BlockBacksideAutopilot(SuperBlock *parent, + const char *name, + BlockStabilization *stabilization); + virtual ~BlockBacksideAutopilot(); + void update(float hCmd, float vCmd, float rCmd, float psiCmd, + float h, float v, + float phi, float theta, float psi, + float p, float q, float r); + float getRudder() { return _stabilization->getRudder() + _trimRdr.get(); } + float getAileron() { return _stabilization->getAileron() + _trimAil.get(); } + float getElevator() { return _stabilization->getElevator() + _trimElv.get(); } + float getThrottle() { return _altitudeHold.getThrottle() + _trimThr.get(); } +}; + +/** + * Waypoint Guidance block + */ +class __EXPORT BlockWaypointGuidance : public SuperBlock +{ +private: + BlockLimitSym _xtYawLimit; + BlockP _xt2Yaw; + float _psiCmd; +public: + BlockWaypointGuidance(SuperBlock *parent, const char *name); + virtual ~BlockWaypointGuidance(); + void update(vehicle_global_position_s &pos, + vehicle_attitude_s &att, + vehicle_global_position_setpoint_s &posCmd, + vehicle_global_position_setpoint_s &lastPosCmd); + float getPsiCmd() { return _psiCmd; } +}; + +/** + * UorbEnabledAutopilot + */ +class __EXPORT BlockUorbEnabledAutopilot : public SuperBlock +{ +protected: + // subscriptions + UOrbSubscription _att; + UOrbSubscription _attCmd; + UOrbSubscription _ratesCmd; + UOrbSubscription _pos; + UOrbSubscription _posCmd; + UOrbSubscription _manual; + UOrbSubscription _status; + UOrbSubscription _param_update; + // publications + UOrbPublication _actuators; +public: + BlockUorbEnabledAutopilot(SuperBlock *parent, const char *name); + virtual ~BlockUorbEnabledAutopilot(); +}; + +/** + * Multi-mode Autopilot + */ +class __EXPORT BlockMultiModeBacksideAutopilot : public BlockUorbEnabledAutopilot +{ +private: + BlockStabilization _stabilization; + BlockBacksideAutopilot _backsideAutopilot; + BlockWaypointGuidance _guide; + BlockParam _vCmd; + + struct pollfd _attPoll; + vehicle_global_position_setpoint_s _lastPosCmd; + enum {CH_AIL, CH_ELV, CH_RDR, CH_THR}; + uint64_t _timeStamp; +public: + BlockMultiModeBacksideAutopilot(SuperBlock *parent, const char *name); + void update(); + virtual ~BlockMultiModeBacksideAutopilot(); +}; + + +} // namespace fixedwing + +} // namespace control + diff --git a/apps/controllib/test_params.c b/apps/controllib/test_params.c new file mode 100644 index 0000000000..7c609cad39 --- /dev/null +++ b/apps/controllib/test_params.c @@ -0,0 +1,22 @@ +#include +// WARNING: +// do not changes these unless +// you want to recompute the +// answers for all of the unit tests + +PARAM_DEFINE_FLOAT(TEST_MIN, -1.0f); +PARAM_DEFINE_FLOAT(TEST_MAX, 1.0f); +PARAM_DEFINE_FLOAT(TEST_TRIM, 0.5f); +PARAM_DEFINE_FLOAT(TEST_HP, 10.0f); +PARAM_DEFINE_FLOAT(TEST_LP, 10.0f); + +PARAM_DEFINE_FLOAT(TEST_P, 0.2f); + +PARAM_DEFINE_FLOAT(TEST_I, 0.1f); +PARAM_DEFINE_FLOAT(TEST_I_MAX, 1.0f); + +PARAM_DEFINE_FLOAT(TEST_D, 0.01f); +PARAM_DEFINE_FLOAT(TEST_D_LP, 10.0f); + +PARAM_DEFINE_FLOAT(TEST_MEAN, 1.0f); +PARAM_DEFINE_FLOAT(TEST_DEV, 2.0f); diff --git a/apps/examples/control_demo/Makefile b/apps/examples/control_demo/Makefile new file mode 100644 index 0000000000..6e40e645f8 --- /dev/null +++ b/apps/examples/control_demo/Makefile @@ -0,0 +1,42 @@ +############################################################################ +# +# Copyright (C) 2012 PX4 Development Team. All rights reserved. +# +# Redistribution and use in source and binary forms, with or without +# modification, are permitted provided that the following conditions +# are met: +# +# 1. Redistributions of source code must retain the above copyright +# notice, this list of conditions and the following disclaimer. +# 2. Redistributions in binary form must reproduce the above copyright +# notice, this list of conditions and the following disclaimer in +# the documentation and/or other materials provided with the +# distribution. +# 3. Neither the name PX4 nor the names of its contributors may be +# used to endorse or promote products derived from this software +# without specific prior written permission. +# +# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS +# FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE +# COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, +# INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, +# BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS +# OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED +# AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN +# ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +# POSSIBILITY OF SUCH DAMAGE. +# +############################################################################ + +# +# Basic example application +# + +APPNAME = control_demo +PRIORITY = SCHED_PRIORITY_DEFAULT +STACKSIZE = 2048 + +include $(APPDIR)/mk/app.mk diff --git a/apps/examples/control_demo/control_demo.cpp b/apps/examples/control_demo/control_demo.cpp new file mode 100644 index 0000000000..d9c773c052 --- /dev/null +++ b/apps/examples/control_demo/control_demo.cpp @@ -0,0 +1,168 @@ +/**************************************************************************** + * + * Copyright (C) 2012 PX4 Development Team. All rights reserved. + * Author: @author Example User + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * 3. Neither the name PX4 nor the names of its contributors may be + * used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS + * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE + * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, + * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS + * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED + * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN + * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + * + ****************************************************************************/ + +/** + * @file control_demo.cpp + * Demonstration of control library + */ + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +static bool thread_should_exit = false; /**< Deamon exit flag */ +static bool thread_running = false; /**< Deamon status flag */ +static int deamon_task; /**< Handle of deamon task / thread */ + +/** + * Deamon management function. + */ +extern "C" __EXPORT int control_demo_main(int argc, char *argv[]); + +/** + * Mainloop of deamon. + */ +int control_demo_thread_main(int argc, char *argv[]); + +/** + * Test function + */ +void test(); + +/** + * Print the correct usage. + */ +static void usage(const char *reason); + +static void +usage(const char *reason) +{ + if (reason) + fprintf(stderr, "%s\n", reason); + + fprintf(stderr, "usage: control_demo {start|stop|status} [-p ]\n\n"); + exit(1); +} + +/** + * The deamon app only briefly exists to start + * the background job. The stack size assigned in the + * Makefile does only apply to this management task. + * + * The actual stack size should be set in the call + * to task_create(). + */ +int control_demo_main(int argc, char *argv[]) +{ + + if (argc < 1) + usage("missing command"); + + if (!strcmp(argv[1], "start")) { + + if (thread_running) { + printf("control_demo already running\n"); + /* this is not an error */ + exit(0); + } + + thread_should_exit = false; + deamon_task = task_spawn("control_demo", + SCHED_DEFAULT, + SCHED_PRIORITY_MAX - 10, + 4096, + control_demo_thread_main, + (argv) ? (const char **)&argv[2] : (const char **)NULL); + exit(0); + } + + if (!strcmp(argv[1], "test")) { + test(); + exit(0); + } + + if (!strcmp(argv[1], "stop")) { + thread_should_exit = true; + exit(0); + } + + if (!strcmp(argv[1], "status")) { + if (thread_running) { + printf("\tcontrol_demo app is running\n"); + + } else { + printf("\tcontrol_demo app not started\n"); + } + + exit(0); + } + + usage("unrecognized command"); + exit(1); +} + +int control_demo_thread_main(int argc, char *argv[]) +{ + + printf("[control_Demo] starting\n"); + + using namespace control; + + fixedwing::BlockMultiModeBacksideAutopilot autopilot(NULL, "FWB"); + + thread_running = true; + + while (!thread_should_exit) { + autopilot.update(); + } + + printf("[control_demo] exiting.\n"); + + thread_running = false; + + return 0; +} + +void test() +{ + printf("beginning control lib test\n"); + control::basicBlocksTest(); +} diff --git a/apps/examples/control_demo/params.c b/apps/examples/control_demo/params.c new file mode 100644 index 0000000000..4eec456fb1 --- /dev/null +++ b/apps/examples/control_demo/params.c @@ -0,0 +1,63 @@ +#include + +// currently tuned for easystar from arkhangar in HIL +//https://github.com/arktools/arkhangar + +// 16 is max name length + +// gyro low pass filter +PARAM_DEFINE_FLOAT(FWB_P_LP, 10.0f); // roll rate low pass cut freq +PARAM_DEFINE_FLOAT(FWB_Q_LP, 10.0f); // pitch rate low pass cut freq +PARAM_DEFINE_FLOAT(FWB_R_LP, 10.0f); // yaw rate low pass cut freq + +// yaw washout +PARAM_DEFINE_FLOAT(FWB_R_HP, 1.0f); // yaw rate high pass + +// stabilization mode +PARAM_DEFINE_FLOAT(FWB_P2AIL, 0.1f); // roll rate 2 aileron +PARAM_DEFINE_FLOAT(FWB_Q2ELV, 0.1f); // pitch rate 2 elevator +PARAM_DEFINE_FLOAT(FWB_R2RDR, 0.1f); // yaw rate 2 rudder + +// psi -> phi -> p +PARAM_DEFINE_FLOAT(FWB_PSI2PHI, 2.0f); // heading 2 roll +PARAM_DEFINE_FLOAT(FWB_PHI2P, 2.0f); // roll to roll rate +PARAM_DEFINE_FLOAT(FWB_PHI_LIM_MAX, 1.0f); // roll limit + +// velocity -> theta +PARAM_DEFINE_FLOAT(FWB_V2THE_P, 0.5f); +PARAM_DEFINE_FLOAT(FWB_V2THE_I, 0.0f); +PARAM_DEFINE_FLOAT(FWB_V2THE_D, 0.0f); +PARAM_DEFINE_FLOAT(FWB_V2THE_D_LP, 0.0f); +PARAM_DEFINE_FLOAT(FWB_V2THE_I_MAX, 0.0f); +PARAM_DEFINE_FLOAT(FWB_THE_MIN, -1.0f); +PARAM_DEFINE_FLOAT(FWB_THE_MAX, 1.0f); + + +// theta -> q +PARAM_DEFINE_FLOAT(FWB_THE2Q_P, 1.0f); +PARAM_DEFINE_FLOAT(FWB_THE2Q_I, 0.0f); +PARAM_DEFINE_FLOAT(FWB_THE2Q_D, 0.0f); +PARAM_DEFINE_FLOAT(FWB_THE2Q_D_LP, 0.0f); +PARAM_DEFINE_FLOAT(FWB_THE2Q_I_MAX, 0.0f); + +// h -> thr +PARAM_DEFINE_FLOAT(FWB_H2THR_P, 0.005f); +PARAM_DEFINE_FLOAT(FWB_H2THR_I, 0.001f); +PARAM_DEFINE_FLOAT(FWB_H2THR_D, 0.01f); +PARAM_DEFINE_FLOAT(FWB_H2THR_D_LP, 1.0f); +PARAM_DEFINE_FLOAT(FWB_H2THR_I_MAX, 250.0f); + +// crosstrack +PARAM_DEFINE_FLOAT(FWB_XT2YAW_MAX, 1.0f); +PARAM_DEFINE_FLOAT(FWB_XT2YAW, 0.01f); + +// speed command +PARAM_DEFINE_FLOAT(FWB_V_MIN, 20.0f); +PARAM_DEFINE_FLOAT(FWB_V_CMD, 22.0f); +PARAM_DEFINE_FLOAT(FWB_V_MAX, 24.0f); + +// trim +PARAM_DEFINE_FLOAT(FWB_TRIM_AIL, 0.0f); +PARAM_DEFINE_FLOAT(FWB_TRIM_ELV, 0.0f); +PARAM_DEFINE_FLOAT(FWB_TRIM_RDR, 0.0f); +PARAM_DEFINE_FLOAT(FWB_TRIM_THR, 0.7f); diff --git a/apps/examples/kalman_demo/KalmanNav.cpp b/apps/examples/kalman_demo/KalmanNav.cpp new file mode 100644 index 0000000000..c2faa89de8 --- /dev/null +++ b/apps/examples/kalman_demo/KalmanNav.cpp @@ -0,0 +1,627 @@ +/**************************************************************************** + * + * Copyright (C) 2012 PX4 Development Team. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * 3. Neither the name PX4 nor the names of its contributors may be + * used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS + * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE + * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, + * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS + * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED + * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN + * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + * + ****************************************************************************/ + +/** + * @file KalmanNav.cpp + * + * kalman filter navigation code + */ + +#include + +#include "KalmanNav.hpp" + +// constants +static const float omega = 7.2921150e-5f; // earth rotation rate, rad/s +static const float R = 6.371000e6f; // earth radius, m +static const float RSq = 4.0589641e13f; // radius squared +static const float g = 9.8f; // gravitational accel. m/s^2 + +KalmanNav::KalmanNav(SuperBlock *parent, const char *name) : + SuperBlock(parent, name), + // ekf matrices + F(9, 9), + G(9, 6), + P(9, 9), + V(6, 6), + // attitude measurement ekf matrices + HAtt(6, 9), + RAtt(6, 6), + // gps measurement ekf matrices + HGps(6, 9), + RGps(6, 6), + // attitude representations + C_nb(), + q(), + // subscriptions + _sensors(&getSubscriptions(), ORB_ID(sensor_combined), 5), // limit to 200 Hz + _gps(&getSubscriptions(), ORB_ID(vehicle_gps_position), 1000), // limit to 1 Hz + _param_update(&getSubscriptions(), ORB_ID(parameter_update), 1000), // limit to 1 Hz + // publications + _pos(&getPublications(), ORB_ID(vehicle_global_position)), + _att(&getPublications(), ORB_ID(vehicle_attitude)), + // timestamps + _pubTimeStamp(hrt_absolute_time()), + _fastTimeStamp(hrt_absolute_time()), + _slowTimeStamp(hrt_absolute_time()), + _attTimeStamp(hrt_absolute_time()), + _outTimeStamp(hrt_absolute_time()), + // frame count + _navFrames(0), + // state + fN(0), fE(0), fD(0), + phi(0), theta(0), psi(0), + vN(0), vE(0), vD(0), + lat(0), lon(0), alt(0), + // parameters for ground station + _vGyro(this, "V_GYRO"), + _vAccel(this, "V_ACCEL"), + _rMag(this, "R_MAG"), + _rGpsV(this, "R_GPS_V"), + _rGpsGeo(this, "R_GPS_GEO"), + _rGpsAlt(this, "R_GPS_ALT"), + _rAccel(this, "R_ACCEL") +{ + using namespace math; + + // initial state covariance matrix + P = Matrix::identity(9) * 1.0f; + + // wait for gps lock + while (1) { + updateSubscriptions(); + + if (_gps.fix_type > 2) break; + + printf("[kalman_demo] waiting for gps lock\n"); + usleep(1000000); + } + + // initial state + phi = 0.0f; + theta = 0.0f; + psi = 0.0f; + vN = _gps.vel_n; + vE = _gps.vel_e; + vD = _gps.vel_d; + setLatDegE7(_gps.lat); + setLonDegE7(_gps.lon); + setAltE3(_gps.alt); + + // initialize quaternions + q = Quaternion(EulerAngles(phi, theta, psi)); + + // initialize dcm + C_nb = Dcm(q); + + // initialize F to identity + F = Matrix::identity(9); + + // HGps is constant + HGps(0, 3) = 1.0f; + HGps(1, 4) = 1.0f; + HGps(2, 5) = 1.0f; + HGps(3, 6) = 1.0f; + HGps(4, 7) = 1.0f; + HGps(5, 8) = 1.0f; + + // initialize all parameters + updateParams(); +} + +void KalmanNav::update() +{ + using namespace math; + + struct pollfd fds[2]; + fds[0].fd = _sensors.getHandle(); + fds[0].events = POLLIN; + fds[1].fd = _param_update.getHandle(); + fds[1].events = POLLIN; + + // poll 20 milliseconds for new data + int ret = poll(fds, 2, 20); + + // check return value + if (ret < 0) { + // XXX this is seriously bad - should be an emergency + return; + + } else if (ret == 0) { // timeout + // run anyway + } else if (ret > 0) { + // update params when requested + if (fds[1].revents & POLLIN) { + printf("updating params\n"); + updateParams(); + } + + // if no new sensor data, return + if (!(fds[0].revents & POLLIN)) return; + } + + // get new timestamp + uint64_t newTimeStamp = hrt_absolute_time(); + + // check updated subscriptions + bool gpsUpdate = _gps.updated(); + + // get new information from subscriptions + // this clears update flag + updateSubscriptions(); + + // count fast frames + _navFrames += 1; + + // fast prediciton step + // note, using sensors timestamp so we can account + // for packet lag + float dtFast = (_sensors.timestamp - _fastTimeStamp) / 1.0e6f; + _fastTimeStamp = _sensors.timestamp; + predictFast(dtFast); + + // slow prediction step + float dtSlow = (_sensors.timestamp - _slowTimeStamp) / 1.0e6f; + + if (dtSlow > 1.0f / 200) { // 200 Hz + _slowTimeStamp = _sensors.timestamp; + predictSlow(dtSlow); + } + + // gps correction step + if (gpsUpdate) { + correctGps(); + } + + // attitude correction step + if (_sensors.timestamp - _attTimeStamp > 1e6 / 1) { // 1 Hz + _attTimeStamp = _sensors.timestamp; + correctAtt(); + } + + // publication + if (newTimeStamp - _pubTimeStamp > 1e6 / 50) { // 50 Hz + _pubTimeStamp = newTimeStamp; + updatePublications(); + } + + // output + if (newTimeStamp - _outTimeStamp > 1e6) { // 1 Hz + _outTimeStamp = newTimeStamp; + printf("nav: %4d Hz\n", _navFrames); + _navFrames = 0; + } +} + +void KalmanNav::updatePublications() +{ + using namespace math; + + // position publication + _pos.timestamp = _pubTimeStamp; + _pos.time_gps_usec = _gps.timestamp; + _pos.valid = true; + _pos.lat = getLatDegE7(); + _pos.lon = getLonDegE7(); + _pos.alt = float(alt); + _pos.relative_alt = float(alt); // TODO, make relative + _pos.vx = vN; + _pos.vy = vE; + _pos.vz = vD; + _pos.hdg = psi; + + // attitude publication + _att.timestamp = _pubTimeStamp; + _att.roll = phi; + _att.pitch = theta; + _att.yaw = psi; + _att.rollspeed = _sensors.gyro_rad_s[0]; + _att.pitchspeed = _sensors.gyro_rad_s[1]; + _att.yawspeed = _sensors.gyro_rad_s[2]; + // TODO, add gyro offsets to filter + _att.rate_offsets[0] = 0.0f; + _att.rate_offsets[1] = 0.0f; + _att.rate_offsets[2] = 0.0f; + + for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) + _att.R[i][j] = C_nb(i, j); + + for (int i = 0; i < 4; i++) _att.q[i] = q(i); + + _att.R_valid = true; + _att.q_valid = true; + _att.counter = _navFrames; + + // update publications + SuperBlock::updatePublications(); +} + +void KalmanNav::predictFast(float dt) +{ + using namespace math; + Vector3 w(_sensors.gyro_rad_s); + + // attitude + q = q + q.derivative(w) * dt; + + // renormalize quaternion if needed + if (fabsf(q.norm() - 1.0f) > 1e-4f) { + q = q.unit(); + } + + // C_nb update + C_nb = Dcm(q); + + // euler update + EulerAngles euler(C_nb); + phi = euler.getPhi(); + theta = euler.getTheta(); + psi = euler.getPsi(); + + // specific acceleration in nav frame + Vector3 accelB(_sensors.accelerometer_m_s2); + Vector3 accelN = C_nb * accelB; + fN = accelN(0); + fE = accelN(1); + fD = accelN(2); + + // trig + float sinL = sinf(lat); + float cosL = cosf(lat); + + // position update + // neglects angular deflections in local gravity + // see Titerton pg. 70 + float LDot = vN / (R + float(alt)); + float lDot = vE / (cosL * (R + float(alt))); + float vNDot = fN - vE * (2 * omega + + lDot) * sinL + + vD * LDot; + float vDDot = fD - vE * (2 * omega + lDot) * cosL - + vN * LDot + g; + float vEDot = fE + vN * (2 * omega + lDot) * sinL + + vDDot * (2 * omega * cosL); + + // rectangular integration + vN += vNDot * dt; + vE += vEDot * dt; + vD += vDDot * dt; + lat += double(LDot * dt); + lon += double(lDot * dt); + alt += double(-vD * dt); +} + +void KalmanNav::predictSlow(float dt) +{ + using namespace math; + + // trig + float sinL = sinf(lat); + float cosL = cosf(lat); + float cosLSq = cosL * cosL; + float tanL = tanf(lat); + + // F Matrix + // Titterton pg. 291 + // + // difference from Jacobian + // multiplity by dt for all elements + // add 1.0 to diagonal elements + + F(0, 1) = (-(omega * sinL + vE * tanL / R)) * dt; + F(0, 2) = (vN / R) * dt; + F(0, 4) = (1.0f / R) * dt; + F(0, 6) = (-omega * sinL) * dt; + F(0, 8) = (-vE / RSq) * dt; + + F(1, 0) = (omega * sinL + vE * tanL / R) * dt; + F(1, 2) = (omega * cosL + vE / R) * dt; + F(1, 3) = (-1.0f / R) * dt; + F(1, 8) = (vN / RSq) * dt; + + F(2, 0) = (-vN / R) * dt; + F(2, 1) = (-omega * cosL - vE / R) * dt; + F(2, 4) = (-tanL / R) * dt; + F(2, 6) = (-omega * cosL - vE / (R * cosLSq)) * dt; + F(2, 8) = (vE * tanL / RSq) * dt; + + F(3, 1) = (-fD) * dt; + F(3, 2) = (fE) * dt; + F(3, 3) = 1.0f + (vD / R) * dt; // on diagonal + F(3, 4) = (-2 * (omega * sinL + vE * tanL / R)) * dt; + F(3, 5) = (vN / R) * dt; + F(3, 6) = (-vE * (2 * omega * cosL + vE / (R * cosLSq))) * dt; + F(3, 8) = ((vE * vE * tanL - vN * vD) / RSq) * dt; + + F(4, 0) = (fD) * dt; + F(4, 2) = (-fN) * dt; + F(4, 3) = (2 * omega * sinL + vE * tanL / R) * dt; + F(4, 4) = 1.0f + ((vN * tanL + vD) / R) * dt; // on diagonal + F(4, 5) = (2 * omega * cosL + vE / R) * dt; + F(4, 6) = (2 * omega * (vN * cosL - vD * sinL) + + vN * vE / (R * cosLSq)) * dt; + F(4, 8) = (-vE * (vN * tanL + vD) / RSq) * dt; + + F(5, 0) = (-fE) * dt; + F(5, 1) = (fN) * dt; + F(5, 3) = (-2 * vN / R) * dt; + F(5, 4) = (-2 * (omega * cosL + vE / R)) * dt; + F(5, 6) = (2 * omega * vE * sinL) * dt; + F(5, 8) = ((vN * vN + vE * vE) / RSq) * dt; + + F(6, 3) = (1 / R) * dt; + F(6, 8) = (-vN / RSq) * dt; + + F(7, 4) = (1 / (R * cosL)) * dt; + F(7, 6) = (vE * tanL / (R * cosL)) * dt; + F(7, 8) = (-vE / (cosL * RSq)) * dt; + + F(8, 5) = (-1) * dt; + + // G Matrix + // Titterton pg. 291 + G(0, 0) = -C_nb(0, 0) * dt; + G(0, 1) = -C_nb(0, 1) * dt; + G(0, 2) = -C_nb(0, 2) * dt; + G(1, 0) = -C_nb(1, 0) * dt; + G(1, 1) = -C_nb(1, 1) * dt; + G(1, 2) = -C_nb(1, 2) * dt; + G(2, 0) = -C_nb(2, 0) * dt; + G(2, 1) = -C_nb(2, 1) * dt; + G(2, 2) = -C_nb(2, 2) * dt; + + G(3, 3) = C_nb(0, 0) * dt; + G(3, 4) = C_nb(0, 1) * dt; + G(3, 5) = C_nb(0, 2) * dt; + G(4, 3) = C_nb(1, 0) * dt; + G(4, 4) = C_nb(1, 1) * dt; + G(4, 5) = C_nb(1, 2) * dt; + G(5, 3) = C_nb(2, 0) * dt; + G(5, 4) = C_nb(2, 1) * dt; + G(5, 5) = C_nb(2, 2) * dt; + + // predict equations for kalman filter + P = F * P * F.transpose() + G * V * G.transpose(); +} + +void KalmanNav::correctAtt() +{ + using namespace math; + + // trig + float cosPhi = cosf(phi); + float cosTheta = cosf(theta); + float cosPsi = cosf(psi); + float sinPhi = sinf(phi); + float sinTheta = sinf(theta); + float sinPsi = sinf(psi); + + // mag measurement + Vector3 zMag(_sensors.magnetometer_ga); + zMag = zMag.unit(); + + // mag predicted measurement + // choosing some typical magnetic field properties, + // TODO dip/dec depend on lat/ lon/ time + static const float dip = 60.0f / M_RAD_TO_DEG_F; // dip, inclination with level + static const float dec = 0.0f / M_RAD_TO_DEG_F; // declination, clockwise rotation from north + float bN = cosf(dip) * cosf(dec); + float bE = cosf(dip) * sinf(dec); + float bD = sinf(dip); + Vector3 bNav(bN, bE, bD); + Vector3 zMagHat = (C_nb.transpose() * bNav).unit(); + + // accel measurement + Vector3 zAccel(_sensors.accelerometer_m_s2); + zAccel = zAccel.unit(); + + // accel predicted measurement + Vector3 zAccelHat = (C_nb.transpose() * Vector3(0, 0, -1)).unit(); + + // combined measurement + Vector zAtt(6); + Vector zAttHat(6); + + for (int i = 0; i < 3; i++) { + zAtt(i) = zMag(i); + zAtt(i + 3) = zAccel(i); + zAttHat(i) = zMagHat(i); + zAttHat(i + 3) = zAccelHat(i); + } + + // HMag , HAtt (0-2,:) + float tmp1 = + cosPsi * cosTheta * bN + + sinPsi * cosTheta * bE - + sinTheta * bD; + HAtt(0, 1) = -( + cosPsi * sinTheta * bN + + sinPsi * sinTheta * bE + + cosTheta * bD + ); + HAtt(0, 2) = -cosTheta * (sinPsi * bN - cosPsi * bE); + HAtt(1, 0) = + (cosPhi * cosPsi * sinTheta + sinPhi * sinPsi) * bN + + (cosPhi * sinPsi * sinTheta - sinPhi * cosPsi) * bE + + cosPhi * cosTheta * bD; + HAtt(1, 1) = sinPhi * tmp1; + HAtt(1, 2) = -( + (sinPhi * sinPsi * sinTheta + cosPhi * cosPsi) * bN - + (sinPhi * cosPsi * sinTheta - cosPhi * sinPsi) * bE + ); + HAtt(2, 0) = -( + (sinPhi * cosPsi * sinTheta - cosPhi * sinPsi) * bN + + (sinPhi * sinPsi * sinTheta + cosPhi * cosPsi) * bE + + (sinPhi * cosTheta) * bD + ); + HAtt(2, 1) = cosPhi * tmp1; + HAtt(2, 2) = -( + (cosPhi * sinPsi * sinTheta - sinPhi * cosTheta) * bN - + (cosPhi * cosPsi * sinTheta + sinPhi * sinPsi) * bE + ); + + // HAccel , HAtt (3-5,:) + HAtt(3, 1) = cosTheta; + HAtt(4, 0) = -cosPhi * cosTheta; + HAtt(4, 1) = sinPhi * sinTheta; + HAtt(5, 0) = sinPhi * cosTheta; + HAtt(5, 1) = cosPhi * sinTheta; + + // compute correction + Vector y = zAtt - zAttHat; // residual + Matrix S = HAtt * P * HAtt.transpose() + RAtt; // residual covariance + Matrix K = P * HAtt.transpose() * S.inverse(); + Vector xCorrect = K * y; + + // check correciton is sane + for (size_t i = 0; i < xCorrect.getRows(); i++) { + float val = xCorrect(i); + + if (isnan(val) || isinf(val)) { + // abort correction and return + printf("[kalman_demo] numerical failure in att correction\n"); + return; + } + } + + // correct state + phi += xCorrect(PHI); + theta += xCorrect(THETA); + psi += xCorrect(PSI); + + // update state covariance + P = P - K * HAtt * P; + + // fault detection + float beta = y.dot(S.inverse() * y); + printf("attitude: beta = %8.4f\n", (double)beta); + + if (beta > 10.0f) { + //printf("fault in attitude: beta = %8.4f\n", (double)beta); + //printf("y:\n"); y.print(); + } + + // update quaternions from euler + // angle correction + q = Quaternion(EulerAngles(phi, theta, psi)); +} + +void KalmanNav::correctGps() +{ + using namespace math; + Vector y(6); + y(0) = _gps.vel_n - vN; + y(1) = _gps.vel_e - vE; + y(2) = _gps.vel_d - vD; + y(3) = double(_gps.lat) / 1.0e7 / M_RAD_TO_DEG - lat; + y(4) = double(_gps.lon) / 1.0e7 / M_RAD_TO_DEG - lon; + y(5) = double(_gps.alt) / 1.0e3 - alt; + + // compute correction + Matrix S = HGps * P * HGps.transpose() + RGps; // residual covariance + Matrix K = P * HGps.transpose() * S.inverse(); + Vector xCorrect = K * y; + + // check correction is sane + for (size_t i = 0; i < xCorrect.getRows(); i++) { + float val = xCorrect(i); + + if (isnan(val) || isinf(val)) { + // abort correction and return + printf("[kalman_demo] numerical failure in gps correction\n"); + // fallback to GPS + vN = _gps.vel_n; + vE = _gps.vel_e; + vD = _gps.vel_d; + setLatDegE7(_gps.lat); + setLonDegE7(_gps.lon); + setAltE3(_gps.alt); + return; + } + } + + // correct state + vN += xCorrect(VN); + vE += xCorrect(VE); + vD += xCorrect(VD); + lat += double(xCorrect(LAT)); + lon += double(xCorrect(LON)); + alt += double(xCorrect(ALT)); + + // update state covariance + P = P - K * HGps * P; + + // fault detetcion + float beta = y.dot(S.inverse() * y); + printf("gps: beta = %8.4f\n", (double)beta); + + if (beta > 100.0f) { + //printf("fault in gps: beta = %8.4f\n", (double)beta); + //printf("y:\n"); y.print(); + } +} + +void KalmanNav::updateParams() +{ + using namespace math; + using namespace control; + SuperBlock::updateParams(); + + // gyro noise + V(0, 0) = _vGyro.get(); // gyro x, rad/s + V(1, 1) = _vGyro.get(); // gyro y + V(2, 2) = _vGyro.get(); // gyro z + + // accel noise + V(3, 3) = _vAccel.get(); // accel x, m/s^2 + V(4, 4) = _vAccel.get(); // accel y + V(5, 5) = _vAccel.get(); // accel z + + // magnetometer noise + RAtt(0, 0) = _rMag.get(); // normalized direction + RAtt(1, 1) = _rMag.get(); + RAtt(2, 2) = _rMag.get(); + + // accelerometer noise + RAtt(3, 3) = _rAccel.get(); // normalized direction + RAtt(4, 4) = _rAccel.get(); + RAtt(5, 5) = _rAccel.get(); + + // gps noise + RGps(0, 0) = _rGpsV.get(); // vn, m/s + RGps(1, 1) = _rGpsV.get(); // ve + RGps(2, 2) = _rGpsV.get(); // vd + RGps(3, 3) = _rGpsGeo.get(); // L, rad + RGps(4, 4) = _rGpsGeo.get(); // l, rad + RGps(5, 5) = _rGpsAlt.get(); // h, m +} diff --git a/apps/examples/kalman_demo/KalmanNav.hpp b/apps/examples/kalman_demo/KalmanNav.hpp new file mode 100644 index 0000000000..dc4a81f4a1 --- /dev/null +++ b/apps/examples/kalman_demo/KalmanNav.hpp @@ -0,0 +1,116 @@ +/**************************************************************************** + * + * Copyright (C) 2012 PX4 Development Team. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * 3. Neither the name PX4 nor the names of its contributors may be + * used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS + * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE + * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, + * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS + * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED + * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN + * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + * + ****************************************************************************/ + +/** + * @file KalmanNav.hpp + * + * kalman filter navigation code + */ + +#pragma once + +//#define MATRIX_ASSERT +//#define VECTOR_ASSERT + +#include + +#include +#include +#include +#include +#include + +#include +#include +#include +#include +#include + +#include +#include +#include + +class KalmanNav : public control::SuperBlock +{ +public: + KalmanNav(SuperBlock *parent, const char *name); + virtual ~KalmanNav() {}; + void update(); + virtual void updatePublications(); + void predictFast(float dt); + void predictSlow(float dt); + void correctAtt(); + void correctGps(); + virtual void updateParams(); +protected: + math::Matrix F; + math::Matrix G; + math::Matrix P; + math::Matrix V; + math::Matrix HAtt; + math::Matrix RAtt; + math::Matrix HGps; + math::Matrix RGps; + math::Dcm C_nb; + math::Quaternion q; + control::UOrbSubscription _sensors; + control::UOrbSubscription _gps; + control::UOrbSubscription _param_update; + control::UOrbPublication _pos; + control::UOrbPublication _att; + uint64_t _pubTimeStamp; + uint64_t _fastTimeStamp; + uint64_t _slowTimeStamp; + uint64_t _attTimeStamp; + uint64_t _outTimeStamp; + uint16_t _navFrames; + float fN, fE, fD; + // states + enum {PHI = 0, THETA, PSI, VN, VE, VD, LAT, LON, ALT}; + float phi, theta, psi; + float vN, vE, vD; + double lat, lon, alt; + control::BlockParam _vGyro; + control::BlockParam _vAccel; + control::BlockParam _rMag; + control::BlockParam _rGpsV; + control::BlockParam _rGpsGeo; + control::BlockParam _rGpsAlt; + control::BlockParam _rAccel; + int32_t getLatDegE7() { return int32_t(lat * 1.0e7 * M_RAD_TO_DEG); } + void setLatDegE7(int32_t val) { lat = val / 1.0e7 / M_RAD_TO_DEG; } + int32_t getLonDegE7() { return int32_t(lon * 1.0e7 * M_RAD_TO_DEG); } + void setLonDegE7(int32_t val) { lon = val / 1.0e7 / M_RAD_TO_DEG; } + int32_t getAltE3() { return int32_t(alt * 1.0e3); } + void setAltE3(int32_t val) { alt = double(val) / 1.0e3; } +}; diff --git a/apps/examples/kalman_demo/Makefile b/apps/examples/kalman_demo/Makefile new file mode 100644 index 0000000000..99c34d934e --- /dev/null +++ b/apps/examples/kalman_demo/Makefile @@ -0,0 +1,42 @@ +############################################################################ +# +# Copyright (C) 2012 PX4 Development Team. All rights reserved. +# +# Redistribution and use in source and binary forms, with or without +# modification, are permitted provided that the following conditions +# are met: +# +# 1. Redistributions of source code must retain the above copyright +# notice, this list of conditions and the following disclaimer. +# 2. Redistributions in binary form must reproduce the above copyright +# notice, this list of conditions and the following disclaimer in +# the documentation and/or other materials provided with the +# distribution. +# 3. Neither the name PX4 nor the names of its contributors may be +# used to endorse or promote products derived from this software +# without specific prior written permission. +# +# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS +# FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE +# COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, +# INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, +# BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS +# OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED +# AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN +# ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +# POSSIBILITY OF SUCH DAMAGE. +# +############################################################################ + +# +# Basic example application +# + +APPNAME = kalman_demo +PRIORITY = SCHED_PRIORITY_MAX - 30 +STACKSIZE = 2048 + +include $(APPDIR)/mk/app.mk diff --git a/apps/examples/kalman_demo/kalman_demo.cpp b/apps/examples/kalman_demo/kalman_demo.cpp new file mode 100644 index 0000000000..581b68b016 --- /dev/null +++ b/apps/examples/kalman_demo/kalman_demo.cpp @@ -0,0 +1,152 @@ +/**************************************************************************** + * + * Copyright (C) 2012 PX4 Development Team. All rights reserved. + * Author: @author Example User + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * 3. Neither the name PX4 nor the names of its contributors may be + * used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS + * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE + * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, + * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS + * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED + * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN + * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + * + ****************************************************************************/ + +/** + * @file kalman_demo.cpp + * Demonstration of control library + */ + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include "KalmanNav.hpp" + +static bool thread_should_exit = false; /**< Deamon exit flag */ +static bool thread_running = false; /**< Deamon status flag */ +static int deamon_task; /**< Handle of deamon task / thread */ + +/** + * Deamon management function. + */ +extern "C" __EXPORT int kalman_demo_main(int argc, char *argv[]); + +/** + * Mainloop of deamon. + */ +int kalman_demo_thread_main(int argc, char *argv[]); + +/** + * Print the correct usage. + */ +static void usage(const char *reason); + +static void +usage(const char *reason) +{ + if (reason) + fprintf(stderr, "%s\n", reason); + + fprintf(stderr, "usage: kalman_demo {start|stop|status} [-p ]\n\n"); + exit(1); +} + +/** + * The deamon app only briefly exists to start + * the background job. The stack size assigned in the + * Makefile does only apply to this management task. + * + * The actual stack size should be set in the call + * to task_create(). + */ +int kalman_demo_main(int argc, char *argv[]) +{ + + if (argc < 1) + usage("missing command"); + + if (!strcmp(argv[1], "start")) { + + if (thread_running) { + printf("kalman_demo already running\n"); + /* this is not an error */ + exit(0); + } + + thread_should_exit = false; + deamon_task = task_spawn("kalman_demo", + SCHED_DEFAULT, + SCHED_PRIORITY_MAX - 5, + 4096, + kalman_demo_thread_main, + (argv) ? (const char **)&argv[2] : (const char **)NULL); + exit(0); + } + + if (!strcmp(argv[1], "stop")) { + thread_should_exit = true; + exit(0); + } + + if (!strcmp(argv[1], "status")) { + if (thread_running) { + printf("\tkalman_demo app is running\n"); + + } else { + printf("\tkalman_demo app not started\n"); + } + + exit(0); + } + + usage("unrecognized command"); + exit(1); +} + +int kalman_demo_thread_main(int argc, char *argv[]) +{ + + printf("[kalman_demo] starting\n"); + + using namespace math; + + thread_running = true; + + KalmanNav nav(NULL, "KF"); + + while (!thread_should_exit) { + nav.update(); + } + + printf("[kalman_demo] exiting.\n"); + + thread_running = false; + + return 0; +} diff --git a/apps/examples/kalman_demo/params.c b/apps/examples/kalman_demo/params.c new file mode 100644 index 0000000000..327e2cda66 --- /dev/null +++ b/apps/examples/kalman_demo/params.c @@ -0,0 +1,10 @@ +#include + +/*PARAM_DEFINE_FLOAT(NAME,0.0f);*/ +PARAM_DEFINE_FLOAT(KF_V_GYRO, 0.01f); +PARAM_DEFINE_FLOAT(KF_V_ACCEL, 0.01f); +PARAM_DEFINE_FLOAT(KF_R_MAG, 0.01f); +PARAM_DEFINE_FLOAT(KF_R_GPS_V, 0.1f); +PARAM_DEFINE_FLOAT(KF_R_GPS_GEO, 1.0e-7f); +PARAM_DEFINE_FLOAT(KF_R_GPS_ALT, 10.0f); +PARAM_DEFINE_FLOAT(KF_R_ACCEL, 0.01f); diff --git a/apps/examples/math_demo/Makefile b/apps/examples/math_demo/Makefile new file mode 100644 index 0000000000..a1105899a7 --- /dev/null +++ b/apps/examples/math_demo/Makefile @@ -0,0 +1,42 @@ +############################################################################ +# +# Copyright (C) 2012 PX4 Development Team. All rights reserved. +# +# Redistribution and use in source and binary forms, with or without +# modification, are permitted provided that the following conditions +# are met: +# +# 1. Redistributions of source code must retain the above copyright +# notice, this list of conditions and the following disclaimer. +# 2. Redistributions in binary form must reproduce the above copyright +# notice, this list of conditions and the following disclaimer in +# the documentation and/or other materials provided with the +# distribution. +# 3. Neither the name PX4 nor the names of its contributors may be +# used to endorse or promote products derived from this software +# without specific prior written permission. +# +# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS +# FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE +# COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, +# INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, +# BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS +# OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED +# AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN +# ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +# POSSIBILITY OF SUCH DAMAGE. +# +############################################################################ + +# +# Basic example application +# + +APPNAME = math_demo +PRIORITY = SCHED_PRIORITY_DEFAULT +STACKSIZE = 8192 + +include $(APPDIR)/mk/app.mk diff --git a/apps/examples/math_demo/math_demo.cpp b/apps/examples/math_demo/math_demo.cpp new file mode 100644 index 0000000000..a9c5567480 --- /dev/null +++ b/apps/examples/math_demo/math_demo.cpp @@ -0,0 +1,105 @@ +/**************************************************************************** + * + * Copyright (C) 2012 PX4 Development Team. All rights reserved. + * Author: @author Example User + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * 3. Neither the name PX4 nor the names of its contributors may be + * used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS + * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE + * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, + * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS + * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED + * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN + * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + * + ****************************************************************************/ + +/** + * @file math_demo.cpp + * Demonstration of math library + */ + +#include +#include +#include +#include +#include +#include +#include + +/** + * Management function. + */ +extern "C" __EXPORT int math_demo_main(int argc, char *argv[]); + +/** + * Test function + */ +void test(); + +/** + * Print the correct usage. + */ +static void usage(const char *reason); + +static void +usage(const char *reason) +{ + if (reason) + fprintf(stderr, "%s\n", reason); + fprintf(stderr, "usage: math_demo {test}\n\n"); + exit(1); +} + +/** + * The deamon app only briefly exists to start + * the background job. The stack size assigned in the + * Makefile does only apply to this management task. + * + * The actual stack size should be set in the call + * to task_create(). + */ +int math_demo_main(int argc, char *argv[]) +{ + + if (argc < 1) + usage("missing command"); + + if (!strcmp(argv[1], "test")) { + test(); + exit(0); + } + + usage("unrecognized command"); + exit(1); +} + +void test() +{ + printf("beginning math lib test\n"); + using namespace math; + vectorTest(); + matrixTest(); + vector3Test(); + eulerAnglesTest(); + quaternionTest(); + dcmTest(); +} diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_abs_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_abs_f32.c new file mode 100644 index 0000000000..7070274da2 --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_abs_f32.c @@ -0,0 +1,159 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_abs_f32.c +* +* Description: Vector absolute value. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* ---------------------------------------------------------------------------- */ + +#include "arm_math.h" +#include + +/** + * @ingroup groupMath + */ + +/** + * @defgroup BasicAbs Vector Absolute Value + * + * Computes the absolute value of a vector on an element-by-element basis. + * + * 
        
+ *     pDst[n] = abs(pSrcA[n]),   0 <= n < blockSize.        
+ *
+ * + * The operation can be done in-place by setting the input and output pointers to the same buffer. + * There are separate functions for floating-point, Q7, Q15, and Q31 data types. + */ + +/** + * @addtogroup BasicAbs + * @{ + */ + +/** + * @brief Floating-point vector absolute value. + * @param[in] *pSrc points to the input buffer + * @param[out] *pDst points to the output buffer + * @param[in] blockSize number of samples in each vector + * @return none. + */ + +void arm_abs_f32( + float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counter */ + +#ifndef ARM_MATH_CM0 + + /* Run the below code for Cortex-M4 and Cortex-M3 */ + float32_t in1, in2, in3, in4; /* temporary variables */ + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = |A| */ + /* Calculate absolute and then store the results in the destination buffer. */ + /* read sample from source */ + in1 = *pSrc; + in2 = *(pSrc + 1); + in3 = *(pSrc + 2); + + /* find absolute value */ + in1 = fabsf(in1); + + /* read sample from source */ + in4 = *(pSrc + 3); + + /* find absolute value */ + in2 = fabsf(in2); + + /* read sample from source */ + *pDst = in1; + + /* find absolute value */ + in3 = fabsf(in3); + + /* find absolute value */ + in4 = fabsf(in4); + + /* store result to destination */ + *(pDst + 1) = in2; + + /* store result to destination */ + *(pDst + 2) = in3; + + /* store result to destination */ + *(pDst + 3) = in4; + + + /* Update source pointer to process next sampels */ + pSrc += 4u; + + /* Update destination pointer to process next sampels */ + pDst += 4u; + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + +#endif /* #ifndef ARM_MATH_CM0 */ + + while(blkCnt > 0u) + { + /* C = |A| */ + /* Calculate absolute and then store the results in the destination buffer. */ + *pDst++ = fabsf(*pSrc++); + + /* Decrement the loop counter */ + blkCnt--; + } +} + +/** + * @} end of BasicAbs group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_abs_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_abs_q15.c new file mode 100644 index 0000000000..6d6a4b6d80 --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_abs_q15.c @@ -0,0 +1,173 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_abs_q15.c +* +* Description: Q15 vector absolute value. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @addtogroup BasicAbs + * @{ + */ + +/** + * @brief Q15 vector absolute value. + * @param[in] *pSrc points to the input buffer + * @param[out] *pDst points to the output buffer + * @param[in] blockSize number of samples in each vector + * @return none. + * + * Scaling and Overflow Behavior: + * \par + * The function uses saturating arithmetic. + * The Q15 value -1 (0x8000) will be saturated to the maximum allowable positive value 0x7FFF. + */ + +void arm_abs_q15( + q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counter */ + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + + q15_t in1; /* Input value1 */ + q15_t in2; /* Input value2 */ + + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = |A| */ + /* Read two inputs */ + in1 = *pSrc++; + in2 = *pSrc++; + + + /* Store the Absolute result in the destination buffer by packing the two values, in a single cycle */ + +#ifndef ARM_MATH_BIG_ENDIAN + + *__SIMD32(pDst)++ = + __PKHBT(((in1 > 0) ? in1 : __QSUB16(0, in1)), + ((in2 > 0) ? in2 : __QSUB16(0, in2)), 16); + +#else + + + *__SIMD32(pDst)++ = + __PKHBT(((in2 > 0) ? in2 : __QSUB16(0, in2)), + ((in1 > 0) ? in1 : __QSUB16(0, in1)), 16); + +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + in1 = *pSrc++; + in2 = *pSrc++; + + +#ifndef ARM_MATH_BIG_ENDIAN + + *__SIMD32(pDst)++ = + __PKHBT(((in1 > 0) ? in1 : __QSUB16(0, in1)), + ((in2 > 0) ? in2 : __QSUB16(0, in2)), 16); + +#else + + + *__SIMD32(pDst)++ = + __PKHBT(((in2 > 0) ? in2 : __QSUB16(0, in2)), + ((in1 > 0) ? in1 : __QSUB16(0, in1)), 16); + +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + + while(blkCnt > 0u) + { + /* C = |A| */ + /* Read the input */ + in1 = *pSrc++; + + /* Calculate absolute value of input and then store the result in the destination buffer. */ + *pDst++ = (in1 > 0) ? in1 : __QSUB16(0, in1); + + /* Decrement the loop counter */ + blkCnt--; + } + +#else + + /* Run the below code for Cortex-M0 */ + + q15_t in; /* Temporary input variable */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + + while(blkCnt > 0u) + { + /* C = |A| */ + /* Read the input */ + in = *pSrc++; + + /* Calculate absolute value of input and then store the result in the destination buffer. */ + *pDst++ = (in > 0) ? in : ((in == (q15_t) 0x8000) ? 0x7fff : -in); + + /* Decrement the loop counter */ + blkCnt--; + } + +#endif /* #ifndef ARM_MATH_CM0 */ + +} + +/** + * @} end of BasicAbs group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_abs_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_abs_q31.c new file mode 100644 index 0000000000..d9e3e7aa3c --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_abs_q31.c @@ -0,0 +1,125 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_abs_q31.c +* +* Description: Q31 vector absolute value. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @addtogroup BasicAbs + * @{ + */ + + +/** + * @brief Q31 vector absolute value. + * @param[in] *pSrc points to the input buffer + * @param[out] *pDst points to the output buffer + * @param[in] blockSize number of samples in each vector + * @return none. + * + * Scaling and Overflow Behavior: + * \par + * The function uses saturating arithmetic. + * The Q31 value -1 (0x80000000) will be saturated to the maximum allowable positive value 0x7FFFFFFF. + */ + +void arm_abs_q31( + q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counter */ + q31_t in; /* Input value */ + +#ifndef ARM_MATH_CM0 + + /* Run the below code for Cortex-M4 and Cortex-M3 */ + q31_t in1, in2, in3, in4; + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = |A| */ + /* Calculate absolute of input (if -1 then saturated to 0x7fffffff) and then store the results in the destination buffer. */ + in1 = *pSrc++; + in2 = *pSrc++; + in3 = *pSrc++; + in4 = *pSrc++; + + *pDst++ = (in1 > 0) ? in1 : __QSUB(0, in1); + *pDst++ = (in2 > 0) ? in2 : __QSUB(0, in2); + *pDst++ = (in3 > 0) ? in3 : __QSUB(0, in3); + *pDst++ = (in4 > 0) ? in4 : __QSUB(0, in4); + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + +#endif /* #ifndef ARM_MATH_CM0 */ + + while(blkCnt > 0u) + { + /* C = |A| */ + /* Calculate absolute value of the input (if -1 then saturated to 0x7fffffff) and then store the results in the destination buffer. */ + in = *pSrc++; + *pDst++ = (in > 0) ? in : ((in == 0x80000000) ? 0x7fffffff : -in); + + /* Decrement the loop counter */ + blkCnt--; + } + +} + +/** + * @} end of BasicAbs group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_abs_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_abs_q7.c new file mode 100644 index 0000000000..258ecef2c8 --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_abs_q7.c @@ -0,0 +1,152 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_abs_q7.c +* +* Description: Q7 vector absolute value. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @addtogroup BasicAbs + * @{ + */ + +/** + * @brief Q7 vector absolute value. + * @param[in] *pSrc points to the input buffer + * @param[out] *pDst points to the output buffer + * @param[in] blockSize number of samples in each vector + * @return none. + * + * \par Conditions for optimum performance + * Input and output buffers should be aligned by 32-bit + * + * + * Scaling and Overflow Behavior: + * \par + * The function uses saturating arithmetic. + * The Q7 value -1 (0x80) will be saturated to the maximum allowable positive value 0x7F. + */ + +void arm_abs_q7( + q7_t * pSrc, + q7_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counter */ + q7_t in; /* Input value1 */ + +#ifndef ARM_MATH_CM0 + + /* Run the below code for Cortex-M4 and Cortex-M3 */ + q31_t in1, in2, in3, in4; /* temporary input variables */ + q31_t out1, out2, out3, out4; /* temporary output variables */ + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = |A| */ + /* Read inputs */ + in1 = (q31_t) * pSrc; + in2 = (q31_t) * (pSrc + 1); + in3 = (q31_t) * (pSrc + 2); + + /* find absolute value */ + out1 = (in1 > 0) ? in1 : __QSUB8(0, in1); + + /* read input */ + in4 = (q31_t) * (pSrc + 3); + + /* find absolute value */ + out2 = (in2 > 0) ? in2 : __QSUB8(0, in2); + + /* store result to destination */ + *pDst = (q7_t) out1; + + /* find absolute value */ + out3 = (in3 > 0) ? in3 : __QSUB8(0, in3); + + /* find absolute value */ + out4 = (in4 > 0) ? in4 : __QSUB8(0, in4); + + /* store result to destination */ + *(pDst + 1) = (q7_t) out2; + + /* store result to destination */ + *(pDst + 2) = (q7_t) out3; + + /* store result to destination */ + *(pDst + 3) = (q7_t) out4; + + /* update pointers to process next samples */ + pSrc += 4u; + pDst += 4u; + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; +#else + + /* Run the below code for Cortex-M0 */ + blkCnt = blockSize; + +#endif // #define ARM_MATH_CM0 + + while(blkCnt > 0u) + { + /* C = |A| */ + /* Read the input */ + in = *pSrc++; + + /* Store the Absolute result in the destination buffer */ + *pDst++ = (in > 0) ? in : ((in == (q7_t) 0x80) ? 0x7f : -in); + + /* Decrement the loop counter */ + blkCnt--; + } +} + +/** + * @} end of BasicAbs group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_add_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_add_f32.c new file mode 100644 index 0000000000..0961dd1db3 --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_add_f32.c @@ -0,0 +1,145 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_add_f32.c +* +* Description: Floating-point vector addition. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* ---------------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @defgroup BasicAdd Vector Addition + * + * Element-by-element addition of two vectors. + * + * 
        
+ *     pDst[n] = pSrcA[n] + pSrcB[n],   0 <= n < blockSize.        
+ *
+ * + * There are separate functions for floating-point, Q7, Q15, and Q31 data types. + */ + +/** + * @addtogroup BasicAdd + * @{ + */ + +/** + * @brief Floating-point vector addition. + * @param[in] *pSrcA points to the first input vector + * @param[in] *pSrcB points to the second input vector + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in each vector + * @return none. + */ + +void arm_add_f32( + float32_t * pSrcA, + float32_t * pSrcB, + float32_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counter */ + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + float32_t inA1, inA2, inA3, inA4; /* temporary input variabels */ + float32_t inB1, inB2, inB3, inB4; /* temporary input variables */ + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = A + B */ + /* Add and then store the results in the destination buffer. */ + + /* read four inputs from sourceA and four inputs from sourceB */ + inA1 = *pSrcA; + inB1 = *pSrcB; + inA2 = *(pSrcA + 1); + inB2 = *(pSrcB + 1); + inA3 = *(pSrcA + 2); + inB3 = *(pSrcB + 2); + inA4 = *(pSrcA + 3); + inB4 = *(pSrcB + 3); + + /* C = A + B */ + /* add and store result to destination */ + *pDst = inA1 + inB1; + *(pDst + 1) = inA2 + inB2; + *(pDst + 2) = inA3 + inB3; + *(pDst + 3) = inA4 + inB4; + + /* update pointers to process next samples */ + pSrcA += 4u; + pSrcB += 4u; + pDst += 4u; + + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + +#endif /* #ifndef ARM_MATH_CM0 */ + + while(blkCnt > 0u) + { + /* C = A + B */ + /* Add and then store the results in the destination buffer. */ + *pDst++ = (*pSrcA++) + (*pSrcB++); + + /* Decrement the loop counter */ + blkCnt--; + } +} + +/** + * @} end of BasicAdd group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_add_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_add_q15.c new file mode 100644 index 0000000000..788b2ebb2c --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_add_q15.c @@ -0,0 +1,135 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_add_q15.c +* +* Description: Q15 vector addition +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @addtogroup BasicAdd + * @{ + */ + +/** + * @brief Q15 vector addition. + * @param[in] *pSrcA points to the first input vector + * @param[in] *pSrcB points to the second input vector + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in each vector + * @return none. + * + * Scaling and Overflow Behavior: + * \par + * The function uses saturating arithmetic. + * Results outside of the allowable Q15 range [0x8000 0x7FFF] will be saturated. + */ + +void arm_add_q15( + q15_t * pSrcA, + q15_t * pSrcB, + q15_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counter */ + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + q31_t inA1, inA2, inB1, inB2; + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = A + B */ + /* Add and then store the results in the destination buffer. */ + inA1 = *__SIMD32(pSrcA)++; + inA2 = *__SIMD32(pSrcA)++; + inB1 = *__SIMD32(pSrcB)++; + inB2 = *__SIMD32(pSrcB)++; + + *__SIMD32(pDst)++ = __QADD16(inA1, inB1); + *__SIMD32(pDst)++ = __QADD16(inA2, inB2); + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + + while(blkCnt > 0u) + { + /* C = A + B */ + /* Add and then store the results in the destination buffer. */ + *pDst++ = (q15_t) __QADD16(*pSrcA++, *pSrcB++); + + /* Decrement the loop counter */ + blkCnt--; + } + +#else + + /* Run the below code for Cortex-M0 */ + + + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + + while(blkCnt > 0u) + { + /* C = A + B */ + /* Add and then store the results in the destination buffer. */ + *pDst++ = (q15_t) __SSAT(((q31_t) * pSrcA++ + *pSrcB++), 16); + + /* Decrement the loop counter */ + blkCnt--; + } + +#endif /* #ifndef ARM_MATH_CM0 */ + + +} + +/** + * @} end of BasicAdd group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_add_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_add_q31.c new file mode 100644 index 0000000000..c5b18711d4 --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_add_q31.c @@ -0,0 +1,143 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_add_q31.c +* +* Description: Q31 vector addition. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @addtogroup BasicAdd + * @{ + */ + + +/** + * @brief Q31 vector addition. + * @param[in] *pSrcA points to the first input vector + * @param[in] *pSrcB points to the second input vector + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in each vector + * @return none. + * + * Scaling and Overflow Behavior: + * \par + * The function uses saturating arithmetic. + * Results outside of the allowable Q31 range[0x80000000 0x7FFFFFFF] will be saturated. + */ + +void arm_add_q31( + q31_t * pSrcA, + q31_t * pSrcB, + q31_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counter */ + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + q31_t inA1, inA2, inA3, inA4; + q31_t inB1, inB2, inB3, inB4; + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = A + B */ + /* Add and then store the results in the destination buffer. */ + inA1 = *pSrcA++; + inA2 = *pSrcA++; + inB1 = *pSrcB++; + inB2 = *pSrcB++; + + inA3 = *pSrcA++; + inA4 = *pSrcA++; + inB3 = *pSrcB++; + inB4 = *pSrcB++; + + *pDst++ = __QADD(inA1, inB1); + *pDst++ = __QADD(inA2, inB2); + *pDst++ = __QADD(inA3, inB3); + *pDst++ = __QADD(inA4, inB4); + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + + while(blkCnt > 0u) + { + /* C = A + B */ + /* Add and then store the results in the destination buffer. */ + *pDst++ = __QADD(*pSrcA++, *pSrcB++); + + /* Decrement the loop counter */ + blkCnt--; + } + +#else + + /* Run the below code for Cortex-M0 */ + + + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + + while(blkCnt > 0u) + { + /* C = A + B */ + /* Add and then store the results in the destination buffer. */ + *pDst++ = (q31_t) clip_q63_to_q31((q63_t) * pSrcA++ + *pSrcB++); + + /* Decrement the loop counter */ + blkCnt--; + } + +#endif /* #ifndef ARM_MATH_CM0 */ + +} + +/** + * @} end of BasicAdd group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_add_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_add_q7.c new file mode 100644 index 0000000000..5407c006fb --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_add_q7.c @@ -0,0 +1,129 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_add_q7.c +* +* Description: Q7 vector addition. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @addtogroup BasicAdd + * @{ + */ + +/** + * @brief Q7 vector addition. + * @param[in] *pSrcA points to the first input vector + * @param[in] *pSrcB points to the second input vector + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in each vector + * @return none. + * + * Scaling and Overflow Behavior: + * \par + * The function uses saturating arithmetic. + * Results outside of the allowable Q7 range [0x80 0x7F] will be saturated. + */ + +void arm_add_q7( + q7_t * pSrcA, + q7_t * pSrcB, + q7_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counter */ + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = A + B */ + /* Add and then store the results in the destination buffer. */ + *__SIMD32(pDst)++ = __QADD8(*__SIMD32(pSrcA)++, *__SIMD32(pSrcB)++); + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + + while(blkCnt > 0u) + { + /* C = A + B */ + /* Add and then store the results in the destination buffer. */ + *pDst++ = (q7_t) __SSAT(*pSrcA++ + *pSrcB++, 8); + + /* Decrement the loop counter */ + blkCnt--; + } + +#else + + /* Run the below code for Cortex-M0 */ + + + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + + while(blkCnt > 0u) + { + /* C = A + B */ + /* Add and then store the results in the destination buffer. */ + *pDst++ = (q7_t) __SSAT((q15_t) * pSrcA++ + *pSrcB++, 8); + + /* Decrement the loop counter */ + blkCnt--; + } + +#endif /* #ifndef ARM_MATH_CM0 */ + + +} + +/** + * @} end of BasicAdd group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_dot_prod_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_dot_prod_f32.c new file mode 100644 index 0000000000..6f7fbcebf2 --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_dot_prod_f32.c @@ -0,0 +1,125 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_dot_prod_f32.c +* +* Description: Floating-point dot product. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* ---------------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @defgroup dot_prod Vector Dot Product + * + * Computes the dot product of two vectors. + * The vectors are multiplied element-by-element and then summed. + * There are separate functions for floating-point, Q7, Q15, and Q31 data types. + */ + +/** + * @addtogroup dot_prod + * @{ + */ + +/** + * @brief Dot product of floating-point vectors. + * @param[in] *pSrcA points to the first input vector + * @param[in] *pSrcB points to the second input vector + * @param[in] blockSize number of samples in each vector + * @param[out] *result output result returned here + * @return none. + */ + + +void arm_dot_prod_f32( + float32_t * pSrcA, + float32_t * pSrcB, + uint32_t blockSize, + float32_t * result) +{ + float32_t sum = 0.0f; /* Temporary result storage */ + uint32_t blkCnt; /* loop counter */ + + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = A[0]* B[0] + A[1]* B[1] + A[2]* B[2] + .....+ A[blockSize-1]* B[blockSize-1] */ + /* Calculate dot product and then store the result in a temporary buffer */ + sum += (*pSrcA++) * (*pSrcB++); + sum += (*pSrcA++) * (*pSrcB++); + sum += (*pSrcA++) * (*pSrcB++); + sum += (*pSrcA++) * (*pSrcB++); + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + +#endif /* #ifndef ARM_MATH_CM0 */ + + + while(blkCnt > 0u) + { + /* C = A[0]* B[0] + A[1]* B[1] + A[2]* B[2] + .....+ A[blockSize-1]* B[blockSize-1] */ + /* Calculate dot product and then store the result in a temporary buffer. */ + sum += (*pSrcA++) * (*pSrcB++); + + /* Decrement the loop counter */ + blkCnt--; + } + /* Store the result back in the destination buffer */ + *result = sum; +} + +/** + * @} end of dot_prod group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_dot_prod_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_dot_prod_q15.c new file mode 100644 index 0000000000..24611a05f5 --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_dot_prod_q15.c @@ -0,0 +1,135 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_dot_prod_q15.c +* +* Description: Q15 dot product. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @addtogroup dot_prod + * @{ + */ + +/** + * @brief Dot product of Q15 vectors. + * @param[in] *pSrcA points to the first input vector + * @param[in] *pSrcB points to the second input vector + * @param[in] blockSize number of samples in each vector + * @param[out] *result output result returned here + * @return none. + * + * Scaling and Overflow Behavior: + * \par + * The intermediate multiplications are in 1.15 x 1.15 = 2.30 format and these + * results are added to a 64-bit accumulator in 34.30 format. + * Nonsaturating additions are used and given that there are 33 guard bits in the accumulator + * there is no risk of overflow. + * The return result is in 34.30 format. + */ + +void arm_dot_prod_q15( + q15_t * pSrcA, + q15_t * pSrcB, + uint32_t blockSize, + q63_t * result) +{ + q63_t sum = 0; /* Temporary result storage */ + uint32_t blkCnt; /* loop counter */ + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = A[0]* B[0] + A[1]* B[1] + A[2]* B[2] + .....+ A[blockSize-1]* B[blockSize-1] */ + /* Calculate dot product and then store the result in a temporary buffer. */ + sum = __SMLALD(*__SIMD32(pSrcA)++, *__SIMD32(pSrcB)++, sum); + sum = __SMLALD(*__SIMD32(pSrcA)++, *__SIMD32(pSrcB)++, sum); + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + + while(blkCnt > 0u) + { + /* C = A[0]* B[0] + A[1]* B[1] + A[2]* B[2] + .....+ A[blockSize-1]* B[blockSize-1] */ + /* Calculate dot product and then store the results in a temporary buffer. */ + sum = __SMLALD(*pSrcA++, *pSrcB++, sum); + + /* Decrement the loop counter */ + blkCnt--; + } + + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + + while(blkCnt > 0u) + { + /* C = A[0]* B[0] + A[1]* B[1] + A[2]* B[2] + .....+ A[blockSize-1]* B[blockSize-1] */ + /* Calculate dot product and then store the results in a temporary buffer. */ + sum += (q63_t) ((q31_t) * pSrcA++ * *pSrcB++); + + /* Decrement the loop counter */ + blkCnt--; + } + +#endif /* #ifndef ARM_MATH_CM0 */ + + /* Store the result in the destination buffer in 34.30 format */ + *result = sum; + +} + +/** + * @} end of dot_prod group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_dot_prod_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_dot_prod_q31.c new file mode 100644 index 0000000000..5e4031338c --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_dot_prod_q31.c @@ -0,0 +1,138 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_dot_prod_q31.c +* +* Description: Q31 dot product. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @addtogroup dot_prod + * @{ + */ + +/** + * @brief Dot product of Q31 vectors. + * @param[in] *pSrcA points to the first input vector + * @param[in] *pSrcB points to the second input vector + * @param[in] blockSize number of samples in each vector + * @param[out] *result output result returned here + * @return none. + * + * Scaling and Overflow Behavior: + * \par + * The intermediate multiplications are in 1.31 x 1.31 = 2.62 format and these + * are truncated to 2.48 format by discarding the lower 14 bits. + * The 2.48 result is then added without saturation to a 64-bit accumulator in 16.48 format. + * There are 15 guard bits in the accumulator and there is no risk of overflow as long as + * the length of the vectors is less than 2^16 elements. + * The return result is in 16.48 format. + */ + +void arm_dot_prod_q31( + q31_t * pSrcA, + q31_t * pSrcB, + uint32_t blockSize, + q63_t * result) +{ + q63_t sum = 0; /* Temporary result storage */ + uint32_t blkCnt; /* loop counter */ + + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + q31_t inA1, inA2, inA3, inA4; + q31_t inB1, inB2, inB3, inB4; + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = A[0]* B[0] + A[1]* B[1] + A[2]* B[2] + .....+ A[blockSize-1]* B[blockSize-1] */ + /* Calculate dot product and then store the result in a temporary buffer. */ + inA1 = *pSrcA++; + inA2 = *pSrcA++; + inA3 = *pSrcA++; + inA4 = *pSrcA++; + inB1 = *pSrcB++; + inB2 = *pSrcB++; + inB3 = *pSrcB++; + inB4 = *pSrcB++; + + sum += ((q63_t) inA1 * inB1) >> 14u; + sum += ((q63_t) inA2 * inB2) >> 14u; + sum += ((q63_t) inA3 * inB3) >> 14u; + sum += ((q63_t) inA4 * inB4) >> 14u; + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + +#endif /* #ifndef ARM_MATH_CM0 */ + + + while(blkCnt > 0u) + { + /* C = A[0]* B[0] + A[1]* B[1] + A[2]* B[2] + .....+ A[blockSize-1]* B[blockSize-1] */ + /* Calculate dot product and then store the result in a temporary buffer. */ + sum += ((q63_t) * pSrcA++ * *pSrcB++) >> 14u; + + /* Decrement the loop counter */ + blkCnt--; + } + + /* Store the result in the destination buffer in 16.48 format */ + *result = sum; +} + +/** + * @} end of dot_prod group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_dot_prod_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_dot_prod_q7.c new file mode 100644 index 0000000000..ddf2d0c243 --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_dot_prod_q7.c @@ -0,0 +1,154 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_dot_prod_q7.c +* +* Description: Q7 dot product. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @addtogroup dot_prod + * @{ + */ + +/** + * @brief Dot product of Q7 vectors. + * @param[in] *pSrcA points to the first input vector + * @param[in] *pSrcB points to the second input vector + * @param[in] blockSize number of samples in each vector + * @param[out] *result output result returned here + * @return none. + * + * Scaling and Overflow Behavior: + * \par + * The intermediate multiplications are in 1.7 x 1.7 = 2.14 format and these + * results are added to an accumulator in 18.14 format. + * Nonsaturating additions are used and there is no danger of wrap around as long as + * the vectors are less than 2^18 elements long. + * The return result is in 18.14 format. + */ + +void arm_dot_prod_q7( + q7_t * pSrcA, + q7_t * pSrcB, + uint32_t blockSize, + q31_t * result) +{ + uint32_t blkCnt; /* loop counter */ + + q31_t sum = 0; /* Temporary variables to store output */ + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + + q31_t input1, input2; /* Temporary variables to store input */ + q31_t inA1, inA2, inB1, inB2; /* Temporary variables to store input */ + + + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* read 4 samples at a time from sourceA */ + input1 = *__SIMD32(pSrcA)++; + /* read 4 samples at a time from sourceB */ + input2 = *__SIMD32(pSrcB)++; + + /* extract two q7_t samples to q15_t samples */ + inA1 = __SXTB16(__ROR(input1, 8)); + /* extract reminaing two samples */ + inA2 = __SXTB16(input1); + /* extract two q7_t samples to q15_t samples */ + inB1 = __SXTB16(__ROR(input2, 8)); + /* extract reminaing two samples */ + inB2 = __SXTB16(input2); + + /* multiply and accumulate two samples at a time */ + sum = __SMLAD(inA1, inB1, sum); + sum = __SMLAD(inA2, inB2, sum); + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + + while(blkCnt > 0u) + { + /* C = A[0]* B[0] + A[1]* B[1] + A[2]* B[2] + .....+ A[blockSize-1]* B[blockSize-1] */ + /* Dot product and then store the results in a temporary buffer. */ + sum = __SMLAD(*pSrcA++, *pSrcB++, sum); + + /* Decrement the loop counter */ + blkCnt--; + } + +#else + + /* Run the below code for Cortex-M0 */ + + + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + + while(blkCnt > 0u) + { + /* C = A[0]* B[0] + A[1]* B[1] + A[2]* B[2] + .....+ A[blockSize-1]* B[blockSize-1] */ + /* Dot product and then store the results in a temporary buffer. */ + sum += (q31_t) ((q15_t) * pSrcA++ * *pSrcB++); + + /* Decrement the loop counter */ + blkCnt--; + } + +#endif /* #ifndef ARM_MATH_CM0 */ + + + /* Store the result in the destination buffer in 18.14 format */ + *result = sum; +} + +/** + * @} end of dot_prod group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_mult_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_mult_f32.c new file mode 100644 index 0000000000..88a458b40a --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_mult_f32.c @@ -0,0 +1,172 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_mult_f32.c +* +* Description: Floating-point vector multiplication. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.5 2010/04/26 +* incorporated review comments and updated with latest CMSIS layer +* +* Version 0.0.3 2010/03/10 +* Initial version +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @defgroup BasicMult Vector Multiplication + * + * Element-by-element multiplication of two vectors. + * + * 
        
+ *     pDst[n] = pSrcA[n] * pSrcB[n],   0 <= n < blockSize.        
+ *
+ * + * There are separate functions for floating-point, Q7, Q15, and Q31 data types. + */ + +/** + * @addtogroup BasicMult + * @{ + */ + +/** + * @brief Floating-point vector multiplication. + * @param[in] *pSrcA points to the first input vector + * @param[in] *pSrcB points to the second input vector + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in each vector + * @return none. + */ + +void arm_mult_f32( + float32_t * pSrcA, + float32_t * pSrcB, + float32_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counters */ +#ifndef ARM_MATH_CM0 + + /* Run the below code for Cortex-M4 and Cortex-M3 */ + float32_t inA1, inA2, inA3, inA4; /* temporary input variables */ + float32_t inB1, inB2, inB3, inB4; /* temporary input variables */ + float32_t out1, out2, out3, out4; /* temporary output variables */ + + /* loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = A * B */ + /* Multiply the inputs and store the results in output buffer */ + /* read sample from sourceA */ + inA1 = *pSrcA; + /* read sample from sourceB */ + inB1 = *pSrcB; + /* read sample from sourceA */ + inA2 = *(pSrcA + 1); + /* read sample from sourceB */ + inB2 = *(pSrcB + 1); + + /* out = sourceA * sourceB */ + out1 = inA1 * inB1; + + /* read sample from sourceA */ + inA3 = *(pSrcA + 2); + /* read sample from sourceB */ + inB3 = *(pSrcB + 2); + + /* out = sourceA * sourceB */ + out2 = inA2 * inB2; + + /* read sample from sourceA */ + inA4 = *(pSrcA + 3); + + /* store result to destination buffer */ + *pDst = out1; + + /* read sample from sourceB */ + inB4 = *(pSrcB + 3); + + /* out = sourceA * sourceB */ + out3 = inA3 * inB3; + + /* store result to destination buffer */ + *(pDst + 1) = out2; + + /* out = sourceA * sourceB */ + out4 = inA4 * inB4; + /* store result to destination buffer */ + *(pDst + 2) = out3; + /* store result to destination buffer */ + *(pDst + 3) = out4; + + + /* update pointers to process next samples */ + pSrcA += 4u; + pSrcB += 4u; + pDst += 4u; + + /* Decrement the blockSize loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + +#endif /* #ifndef ARM_MATH_CM0 */ + + while(blkCnt > 0u) + { + /* C = A * B */ + /* Multiply the inputs and store the results in output buffer */ + *pDst++ = (*pSrcA++) * (*pSrcB++); + + /* Decrement the blockSize loop counter */ + blkCnt--; + } +} + +/** + * @} end of BasicMult group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_mult_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_mult_q15.c new file mode 100644 index 0000000000..99d44a4ba3 --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_mult_q15.c @@ -0,0 +1,152 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_mult_q15.c +* +* Description: Q15 vector multiplication. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.5 2010/04/26 +* incorporated review comments and updated with latest CMSIS layer +* +* Version 0.0.3 2010/03/10 +* Initial version +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @addtogroup BasicMult + * @{ + */ + + +/** + * @brief Q15 vector multiplication + * @param[in] *pSrcA points to the first input vector + * @param[in] *pSrcB points to the second input vector + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in each vector + * @return none. + * + * Scaling and Overflow Behavior: + * \par + * The function uses saturating arithmetic. + * Results outside of the allowable Q15 range [0x8000 0x7FFF] will be saturated. + */ + +void arm_mult_q15( + q15_t * pSrcA, + q15_t * pSrcB, + q15_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counters */ + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + q31_t inA1, inA2, inB1, inB2; /* temporary input variables */ + q15_t out1, out2, out3, out4; /* temporary output variables */ + q31_t mul1, mul2, mul3, mul4; /* temporary variables */ + + /* loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* read two samples at a time from sourceA */ + inA1 = *__SIMD32(pSrcA)++; + /* read two samples at a time from sourceB */ + inB1 = *__SIMD32(pSrcB)++; + /* read two samples at a time from sourceA */ + inA2 = *__SIMD32(pSrcA)++; + /* read two samples at a time from sourceB */ + inB2 = *__SIMD32(pSrcB)++; + + /* multiply mul = sourceA * sourceB */ + mul1 = (q31_t) ((q15_t) (inA1 >> 16) * (q15_t) (inB1 >> 16)); + mul2 = (q31_t) ((q15_t) inA1 * (q15_t) inB1); + mul3 = (q31_t) ((q15_t) (inA2 >> 16) * (q15_t) (inB2 >> 16)); + mul4 = (q31_t) ((q15_t) inA2 * (q15_t) inB2); + + /* saturate result to 16 bit */ + out1 = (q15_t) __SSAT(mul1 >> 15, 16); + out2 = (q15_t) __SSAT(mul2 >> 15, 16); + out3 = (q15_t) __SSAT(mul3 >> 15, 16); + out4 = (q15_t) __SSAT(mul4 >> 15, 16); + + /* store the result */ +#ifndef ARM_MATH_BIG_ENDIAN + + *__SIMD32(pDst)++ = __PKHBT(out2, out1, 16); + *__SIMD32(pDst)++ = __PKHBT(out4, out3, 16); + +#else + + *__SIMD32(pDst)++ = __PKHBT(out2, out1, 16); + *__SIMD32(pDst)++ = __PKHBT(out4, out3, 16); + +#endif // #ifndef ARM_MATH_BIG_ENDIAN + + /* Decrement the blockSize loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + +#endif /* #ifndef ARM_MATH_CM0 */ + + + while(blkCnt > 0u) + { + /* C = A * B */ + /* Multiply the inputs and store the result in the destination buffer */ + *pDst++ = (q15_t) __SSAT((((q31_t) (*pSrcA++) * (*pSrcB++)) >> 15), 16); + + /* Decrement the blockSize loop counter */ + blkCnt--; + } +} + +/** + * @} end of BasicMult group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_mult_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_mult_q31.c new file mode 100644 index 0000000000..37ec8e25e1 --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_mult_q31.c @@ -0,0 +1,143 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_mult_q31.c +* +* Description: Q31 vector multiplication. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.5 2010/04/26 +* incorporated review comments and updated with latest CMSIS layer +* +* Version 0.0.3 2010/03/10 +* Initial version +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @addtogroup BasicMult + * @{ + */ + +/** + * @brief Q31 vector multiplication. + * @param[in] *pSrcA points to the first input vector + * @param[in] *pSrcB points to the second input vector + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in each vector + * @return none. + * + * Scaling and Overflow Behavior: + * \par + * The function uses saturating arithmetic. + * Results outside of the allowable Q31 range[0x80000000 0x7FFFFFFF] will be saturated. + */ + +void arm_mult_q31( + q31_t * pSrcA, + q31_t * pSrcB, + q31_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counters */ + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + q31_t inA1, inA2, inA3, inA4; /* temporary input variables */ + q31_t inB1, inB2, inB3, inB4; /* temporary input variables */ + q31_t out1, out2, out3, out4; /* temporary output variables */ + + /* loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = A * B */ + /* Multiply the inputs and then store the results in the destination buffer. */ + inA1 = *pSrcA++; + inA2 = *pSrcA++; + inA3 = *pSrcA++; + inA4 = *pSrcA++; + inB1 = *pSrcB++; + inB2 = *pSrcB++; + inB3 = *pSrcB++; + inB4 = *pSrcB++; + + out1 = ((q63_t) inA1 * inB1) >> 32; + out2 = ((q63_t) inA2 * inB2) >> 32; + out3 = ((q63_t) inA3 * inB3) >> 32; + out4 = ((q63_t) inA4 * inB4) >> 32; + + out1 = __SSAT(out1, 31); + out2 = __SSAT(out2, 31); + out3 = __SSAT(out3, 31); + out4 = __SSAT(out4, 31); + + *pDst++ = out1 << 1u; + *pDst++ = out2 << 1u; + *pDst++ = out3 << 1u; + *pDst++ = out4 << 1u; + + /* Decrement the blockSize loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + +#endif /* #ifndef ARM_MATH_CM0 */ + + while(blkCnt > 0u) + { + /* C = A * B */ + /* Multiply the inputs and then store the results in the destination buffer. */ + *pDst++ = + (q31_t) clip_q63_to_q31(((q63_t) (*pSrcA++) * (*pSrcB++)) >> 31); + + /* Decrement the blockSize loop counter */ + blkCnt--; + } +} + +/** + * @} end of BasicMult group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_mult_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_mult_q7.c new file mode 100644 index 0000000000..14ee23ea6a --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_mult_q7.c @@ -0,0 +1,128 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_mult_q7.c +* +* Description: Q7 vector multiplication. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* +* Version 0.0.5 2010/04/26 +* incorporated review comments and updated with latest CMSIS layer +* +* Version 0.0.3 2010/03/10 DP +* Initial version +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @addtogroup BasicMult + * @{ + */ + +/** + * @brief Q7 vector multiplication + * @param[in] *pSrcA points to the first input vector + * @param[in] *pSrcB points to the second input vector + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in each vector + * @return none. + * + * Scaling and Overflow Behavior: + * \par + * The function uses saturating arithmetic. + * Results outside of the allowable Q7 range [0x80 0x7F] will be saturated. + */ + +void arm_mult_q7( + q7_t * pSrcA, + q7_t * pSrcB, + q7_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counters */ + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + q7_t out1, out2, out3, out4; /* Temporary variables to store the product */ + + /* loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = A * B */ + /* Multiply the inputs and store the results in temporary variables */ + out1 = (q7_t) __SSAT((((q15_t) (*pSrcA++) * (*pSrcB++)) >> 7), 8); + out2 = (q7_t) __SSAT((((q15_t) (*pSrcA++) * (*pSrcB++)) >> 7), 8); + out3 = (q7_t) __SSAT((((q15_t) (*pSrcA++) * (*pSrcB++)) >> 7), 8); + out4 = (q7_t) __SSAT((((q15_t) (*pSrcA++) * (*pSrcB++)) >> 7), 8); + + /* Store the results of 4 inputs in the destination buffer in single cycle by packing */ + *__SIMD32(pDst)++ = __PACKq7(out1, out2, out3, out4); + + /* Decrement the blockSize loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + +#endif /* #ifndef ARM_MATH_CM0 */ + + + while(blkCnt > 0u) + { + /* C = A * B */ + /* Multiply the inputs and store the result in the destination buffer */ + *pDst++ = (q7_t) __SSAT((((q15_t) (*pSrcA++) * (*pSrcB++)) >> 7), 8); + + /* Decrement the blockSize loop counter */ + blkCnt--; + } +} + +/** + * @} end of BasicMult group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_negate_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_negate_f32.c new file mode 100644 index 0000000000..4f4d423ac9 --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_negate_f32.c @@ -0,0 +1,137 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_negate_f32.c +* +* Description: Negates floating-point vectors. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* ---------------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @defgroup negate Vector Negate + * + * Negates the elements of a vector. + * + * 
        
+ *     pDst[n] = -pSrc[n],   0 <= n < blockSize.        
+ *
+ */ + +/** + * @addtogroup negate + * @{ + */ + +/** + * @brief Negates the elements of a floating-point vector. + * @param[in] *pSrc points to the input vector + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in the vector + * @return none. + */ + +void arm_negate_f32( + float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counter */ + + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + float32_t in1, in2, in3, in4; /* temporary variables */ + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* read inputs from source */ + in1 = *pSrc; + in2 = *(pSrc + 1); + in3 = *(pSrc + 2); + in4 = *(pSrc + 3); + + /* negate the input */ + in1 = -in1; + in2 = -in2; + in3 = -in3; + in4 = -in4; + + /* store the result to destination */ + *pDst = in1; + *(pDst + 1) = in2; + *(pDst + 2) = in3; + *(pDst + 3) = in4; + + /* update pointers to process next samples */ + pSrc += 4u; + pDst += 4u; + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + +#endif /* #ifndef ARM_MATH_CM0 */ + + while(blkCnt > 0u) + { + /* C = -A */ + /* Negate and then store the results in the destination buffer. */ + *pDst++ = -*pSrc++; + + /* Decrement the loop counter */ + blkCnt--; + } +} + +/** + * @} end of negate group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_negate_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_negate_q15.c new file mode 100644 index 0000000000..21d58d1a4a --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_negate_q15.c @@ -0,0 +1,137 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_negate_q15.c +* +* Description: Negates Q15 vectors. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* -------------------------------------------------------------------- */ +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @addtogroup negate + * @{ + */ + +/** + * @brief Negates the elements of a Q15 vector. + * @param[in] *pSrc points to the input vector + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in the vector + * @return none. + * + * \par Conditions for optimum performance + * Input and output buffers should be aligned by 32-bit + * + * + * Scaling and Overflow Behavior: + * \par + * The function uses saturating arithmetic. + * The Q15 value -1 (0x8000) will be saturated to the maximum allowable positive value 0x7FFF. + */ + +void arm_negate_q15( + q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counter */ + q15_t in; + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + + q31_t in1, in2; /* Temporary variables */ + + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = -A */ + /* Read two inputs at a time */ + in1 = _SIMD32_OFFSET(pSrc); + in2 = _SIMD32_OFFSET(pSrc + 2); + + /* negate two samples at a time */ + in1 = __QSUB16(0, in1); + + /* negate two samples at a time */ + in2 = __QSUB16(0, in2); + + /* store the result to destination 2 samples at a time */ + _SIMD32_OFFSET(pDst) = in1; + /* store the result to destination 2 samples at a time */ + _SIMD32_OFFSET(pDst + 2) = in2; + + + /* update pointers to process next samples */ + pSrc += 4u; + pDst += 4u; + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + +#endif /* #ifndef ARM_MATH_CM0 */ + + while(blkCnt > 0u) + { + /* C = -A */ + /* Negate and then store the result in the destination buffer. */ + in = *pSrc++; + *pDst++ = (in == (q15_t) 0x8000) ? 0x7fff : -in; + + /* Decrement the loop counter */ + blkCnt--; + } +} + +/** + * @} end of negate group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_negate_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_negate_q31.c new file mode 100644 index 0000000000..fc28c36218 --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_negate_q31.c @@ -0,0 +1,124 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_negate_q31.c +* +* Description: Negates Q31 vectors. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @addtogroup negate + * @{ + */ + +/** + * @brief Negates the elements of a Q31 vector. + * @param[in] *pSrc points to the input vector + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in the vector + * @return none. + * + * Scaling and Overflow Behavior: + * \par + * The function uses saturating arithmetic. + * The Q31 value -1 (0x80000000) will be saturated to the maximum allowable positive value 0x7FFFFFFF. + */ + +void arm_negate_q31( + q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize) +{ + q31_t in; /* Temporary variable */ + uint32_t blkCnt; /* loop counter */ + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + q31_t in1, in2, in3, in4; + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = -A */ + /* Negate and then store the results in the destination buffer. */ + in1 = *pSrc++; + in2 = *pSrc++; + in3 = *pSrc++; + in4 = *pSrc++; + + *pDst++ = __QSUB(0, in1); + *pDst++ = __QSUB(0, in2); + *pDst++ = __QSUB(0, in3); + *pDst++ = __QSUB(0, in4); + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + +#endif /* #ifndef ARM_MATH_CM0 */ + + + while(blkCnt > 0u) + { + /* C = -A */ + /* Negate and then store the result in the destination buffer. */ + in = *pSrc++; + *pDst++ = (in == 0x80000000) ? 0x7fffffff : -in; + + /* Decrement the loop counter */ + blkCnt--; + } +} + +/** + * @} end of negate group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_negate_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_negate_q7.c new file mode 100644 index 0000000000..601fb73934 --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_negate_q7.c @@ -0,0 +1,120 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_negate_q7.c +* +* Description: Negates Q7 vectors. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @addtogroup negate + * @{ + */ + +/** + * @brief Negates the elements of a Q7 vector. + * @param[in] *pSrc points to the input vector + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in the vector + * @return none. + * + * Scaling and Overflow Behavior: + * \par + * The function uses saturating arithmetic. + * The Q7 value -1 (0x80) will be saturated to the maximum allowable positive value 0x7F. + */ + +void arm_negate_q7( + q7_t * pSrc, + q7_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counter */ + q7_t in; + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + q31_t input; /* Input values1-4 */ + q31_t zero = 0x00000000; + + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = -A */ + /* Read four inputs */ + input = *__SIMD32(pSrc)++; + + /* Store the Negated results in the destination buffer in a single cycle by packing the results */ + *__SIMD32(pDst)++ = __QSUB8(zero, input); + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + +#endif /* #ifndef ARM_MATH_CM0 */ + + while(blkCnt > 0u) + { + /* C = -A */ + /* Negate and then store the results in the destination buffer. */ \ + in = *pSrc++; + *pDst++ = (in == (q7_t) 0x80) ? 0x7f : -in; + + /* Decrement the loop counter */ + blkCnt--; + } +} + +/** + * @} end of negate group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_offset_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_offset_f32.c new file mode 100644 index 0000000000..4bdf06ee8d --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_offset_f32.c @@ -0,0 +1,158 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_offset_f32.c +* +* Description: Floating-point vector offset. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* ---------------------------------------------------------------------------- */ +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @defgroup offset Vector Offset + * + * Adds a constant offset to each element of a vector. + * + * 
        
+ *     pDst[n] = pSrc[n] + offset,   0 <= n < blockSize.        
+ *
+ * + * There are separate functions for floating-point, Q7, Q15, and Q31 data types. + */ + +/** + * @addtogroup offset + * @{ + */ + +/** + * @brief Adds a constant offset to a floating-point vector. + * @param[in] *pSrc points to the input vector + * @param[in] offset is the offset to be added + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in the vector + * @return none. + */ + + +void arm_offset_f32( + float32_t * pSrc, + float32_t offset, + float32_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counter */ + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + float32_t in1, in2, in3, in4; + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = A + offset */ + /* Add offset and then store the results in the destination buffer. */ + /* read samples from source */ + in1 = *pSrc; + in2 = *(pSrc + 1); + + /* add offset to input */ + in1 = in1 + offset; + + /* read samples from source */ + in3 = *(pSrc + 2); + + /* add offset to input */ + in2 = in2 + offset; + + /* read samples from source */ + in4 = *(pSrc + 3); + + /* add offset to input */ + in3 = in3 + offset; + + /* store result to destination */ + *pDst = in1; + + /* add offset to input */ + in4 = in4 + offset; + + /* store result to destination */ + *(pDst + 1) = in2; + + /* store result to destination */ + *(pDst + 2) = in3; + + /* store result to destination */ + *(pDst + 3) = in4; + + /* update pointers to process next samples */ + pSrc += 4u; + pDst += 4u; + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + +#endif /* #ifndef ARM_MATH_CM0 */ + + while(blkCnt > 0u) + { + /* C = A + offset */ + /* Add offset and then store the result in the destination buffer. */ + *pDst++ = (*pSrc++) + offset; + + /* Decrement the loop counter */ + blkCnt--; + } +} + +/** + * @} end of offset group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_offset_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_offset_q15.c new file mode 100644 index 0000000000..f8158f066f --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_offset_q15.c @@ -0,0 +1,131 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_offset_q15.c +* +* Description: Q15 vector offset. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @addtogroup offset + * @{ + */ + +/** + * @brief Adds a constant offset to a Q15 vector. + * @param[in] *pSrc points to the input vector + * @param[in] offset is the offset to be added + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in the vector + * @return none. + * + * Scaling and Overflow Behavior: + * \par + * The function uses saturating arithmetic. + * Results outside of the allowable Q15 range [0x8000 0x7FFF] are saturated. + */ + +void arm_offset_q15( + q15_t * pSrc, + q15_t offset, + q15_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counter */ + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + q31_t offset_packed; /* Offset packed to 32 bit */ + + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* Offset is packed to 32 bit in order to use SIMD32 for addition */ + offset_packed = __PKHBT(offset, offset, 16); + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = A + offset */ + /* Add offset and then store the results in the destination buffer, 2 samples at a time. */ + *__SIMD32(pDst)++ = __QADD16(*__SIMD32(pSrc)++, offset_packed); + *__SIMD32(pDst)++ = __QADD16(*__SIMD32(pSrc)++, offset_packed); + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + + while(blkCnt > 0u) + { + /* C = A + offset */ + /* Add offset and then store the results in the destination buffer. */ + *pDst++ = (q15_t) __QADD16(*pSrc++, offset); + + /* Decrement the loop counter */ + blkCnt--; + } + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + + while(blkCnt > 0u) + { + /* C = A + offset */ + /* Add offset and then store the results in the destination buffer. */ + *pDst++ = (q15_t) __SSAT(((q31_t) * pSrc++ + offset), 16); + + /* Decrement the loop counter */ + blkCnt--; + } + +#endif /* #ifndef ARM_MATH_CM0 */ + +} + +/** + * @} end of offset group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_offset_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_offset_q31.c new file mode 100644 index 0000000000..8b03ee3727 --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_offset_q31.c @@ -0,0 +1,135 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_offset_q31.c +* +* Description: Q31 vector offset. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @addtogroup offset + * @{ + */ + +/** + * @brief Adds a constant offset to a Q31 vector. + * @param[in] *pSrc points to the input vector + * @param[in] offset is the offset to be added + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in the vector + * @return none. + * + * Scaling and Overflow Behavior: + * \par + * The function uses saturating arithmetic. + * Results outside of the allowable Q31 range [0x80000000 0x7FFFFFFF] are saturated. + */ + +void arm_offset_q31( + q31_t * pSrc, + q31_t offset, + q31_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counter */ + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + q31_t in1, in2, in3, in4; + + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = A + offset */ + /* Add offset and then store the results in the destination buffer. */ + in1 = *pSrc++; + in2 = *pSrc++; + in3 = *pSrc++; + in4 = *pSrc++; + + *pDst++ = __QADD(in1, offset); + *pDst++ = __QADD(in2, offset); + *pDst++ = __QADD(in3, offset); + *pDst++ = __QADD(in4, offset); + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + + while(blkCnt > 0u) + { + /* C = A + offset */ + /* Add offset and then store the result in the destination buffer. */ + *pDst++ = __QADD(*pSrc++, offset); + + /* Decrement the loop counter */ + blkCnt--; + } + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + + while(blkCnt > 0u) + { + /* C = A + offset */ + /* Add offset and then store the result in the destination buffer. */ + *pDst++ = (q31_t) clip_q63_to_q31((q63_t) * pSrc++ + offset); + + /* Decrement the loop counter */ + blkCnt--; + } + +#endif /* #ifndef ARM_MATH_CM0 */ + +} + +/** + * @} end of offset group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_offset_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_offset_q7.c new file mode 100644 index 0000000000..56643816f3 --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_offset_q7.c @@ -0,0 +1,130 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_offset_q7.c +* +* Description: Q7 vector offset. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @addtogroup offset + * @{ + */ + +/** + * @brief Adds a constant offset to a Q7 vector. + * @param[in] *pSrc points to the input vector + * @param[in] offset is the offset to be added + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in the vector + * @return none. + * + * Scaling and Overflow Behavior: + * \par + * The function uses saturating arithmetic. + * Results outside of the allowable Q7 range [0x80 0x7F] are saturated. + */ + +void arm_offset_q7( + q7_t * pSrc, + q7_t offset, + q7_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counter */ + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + q31_t offset_packed; /* Offset packed to 32 bit */ + + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* Offset is packed to 32 bit in order to use SIMD32 for addition */ + offset_packed = __PACKq7(offset, offset, offset, offset); + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = A + offset */ + /* Add offset and then store the results in the destination bufferfor 4 samples at a time. */ + *__SIMD32(pDst)++ = __QADD8(*__SIMD32(pSrc)++, offset_packed); + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + + while(blkCnt > 0u) + { + /* C = A + offset */ + /* Add offset and then store the result in the destination buffer. */ + *pDst++ = (q7_t) __SSAT(*pSrc++ + offset, 8); + + /* Decrement the loop counter */ + blkCnt--; + } + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + + while(blkCnt > 0u) + { + /* C = A + offset */ + /* Add offset and then store the result in the destination buffer. */ + *pDst++ = (q7_t) __SSAT((q15_t) * pSrc++ + offset, 8); + + /* Decrement the loop counter */ + blkCnt--; + } + +#endif /* #ifndef ARM_MATH_CM0 */ + +} + +/** + * @} end of offset group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_scale_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_scale_f32.c new file mode 100644 index 0000000000..b77144a3ef --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_scale_f32.c @@ -0,0 +1,161 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_scale_f32.c +* +* Description: Multiplies a floating-point vector by a scalar. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* ---------------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @defgroup scale Vector Scale + * + * Multiply a vector by a scalar value. For floating-point data, the algorithm used is: + * + * 
        
+ *     pDst[n] = pSrc[n] * scale,   0 <= n < blockSize.        
+ *
+ * + * In the fixed-point Q7, Q15, and Q31 functions, scale is represented by + * a fractional multiplication scaleFract and an arithmetic shift shift. + * The shift allows the gain of the scaling operation to exceed 1.0. + * The algorithm used with fixed-point data is: + * + * 
        
+ *     pDst[n] = (pSrc[n] * scaleFract) << shift,   0 <= n < blockSize.        
+ *
+ * + * The overall scale factor applied to the fixed-point data is + * 
        
+ *     scale = scaleFract * 2^shift.        
+ *
+ */ + +/** + * @addtogroup scale + * @{ + */ + +/** + * @brief Multiplies a floating-point vector by a scalar. + * @param[in] *pSrc points to the input vector + * @param[in] scale scale factor to be applied + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in the vector + * @return none. + */ + + +void arm_scale_f32( + float32_t * pSrc, + float32_t scale, + float32_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counter */ +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + float32_t in1, in2, in3, in4; /* temporary variabels */ + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = A * scale */ + /* Scale the input and then store the results in the destination buffer. */ + /* read input samples from source */ + in1 = *pSrc; + in2 = *(pSrc + 1); + + /* multiply with scaling factor */ + in1 = in1 * scale; + + /* read input sample from source */ + in3 = *(pSrc + 2); + + /* multiply with scaling factor */ + in2 = in2 * scale; + + /* read input sample from source */ + in4 = *(pSrc + 3); + + /* multiply with scaling factor */ + in3 = in3 * scale; + in4 = in4 * scale; + /* store the result to destination */ + *pDst = in1; + *(pDst + 1) = in2; + *(pDst + 2) = in3; + *(pDst + 3) = in4; + + /* update pointers to process next samples */ + pSrc += 4u; + pDst += 4u; + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + +#endif /* #ifndef ARM_MATH_CM0 */ + + while(blkCnt > 0u) + { + /* C = A * scale */ + /* Scale the input and then store the result in the destination buffer. */ + *pDst++ = (*pSrc++) * scale; + + /* Decrement the loop counter */ + blkCnt--; + } +} + +/** + * @} end of scale group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_scale_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_scale_q15.c new file mode 100644 index 0000000000..9e79202fe3 --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_scale_q15.c @@ -0,0 +1,157 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_scale_q15.c +* +* Description: Multiplies a Q15 vector by a scalar. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @addtogroup scale + * @{ + */ + +/** + * @brief Multiplies a Q15 vector by a scalar. + * @param[in] *pSrc points to the input vector + * @param[in] scaleFract fractional portion of the scale value + * @param[in] shift number of bits to shift the result by + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in the vector + * @return none. + * + * Scaling and Overflow Behavior: + * \par + * The input data *pSrc and scaleFract are in 1.15 format. + * These are multiplied to yield a 2.30 intermediate result and this is shifted with saturation to 1.15 format. + */ + + +void arm_scale_q15( + q15_t * pSrc, + q15_t scaleFract, + int8_t shift, + q15_t * pDst, + uint32_t blockSize) +{ + int8_t kShift = 15 - shift; /* shift to apply after scaling */ + uint32_t blkCnt; /* loop counter */ + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + q15_t in1, in2, in3, in4; + q31_t inA1, inA2; /* Temporary variables */ + q31_t out1, out2, out3, out4; + + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* Reading 2 inputs from memory */ + inA1 = *__SIMD32(pSrc)++; + inA2 = *__SIMD32(pSrc)++; + + /* C = A * scale */ + /* Scale the inputs and then store the 2 results in the destination buffer + * in single cycle by packing the outputs */ + out1 = (q31_t) ((q15_t) (inA1 >> 16) * scaleFract); + out2 = (q31_t) ((q15_t) inA1 * scaleFract); + out3 = (q31_t) ((q15_t) (inA2 >> 16) * scaleFract); + out4 = (q31_t) ((q15_t) inA2 * scaleFract); + + /* apply shifting */ + out1 = out1 >> kShift; + out2 = out2 >> kShift; + out3 = out3 >> kShift; + out4 = out4 >> kShift; + + /* saturate the output */ + in1 = (q15_t) (__SSAT(out1, 16)); + in2 = (q15_t) (__SSAT(out2, 16)); + in3 = (q15_t) (__SSAT(out3, 16)); + in4 = (q15_t) (__SSAT(out4, 16)); + + /* store the result to destination */ + *__SIMD32(pDst)++ = __PKHBT(in2, in1, 16); + *__SIMD32(pDst)++ = __PKHBT(in4, in3, 16); + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + + while(blkCnt > 0u) + { + /* C = A * scale */ + /* Scale the input and then store the result in the destination buffer. */ + *pDst++ = (q15_t) (__SSAT(((*pSrc++) * scaleFract) >> kShift, 16)); + + /* Decrement the loop counter */ + blkCnt--; + } + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + + while(blkCnt > 0u) + { + /* C = A * scale */ + /* Scale the input and then store the result in the destination buffer. */ + *pDst++ = (q15_t) (__SSAT(((q31_t) * pSrc++ * scaleFract) >> kShift, 16)); + + /* Decrement the loop counter */ + blkCnt--; + } + +#endif /* #ifndef ARM_MATH_CM0 */ + +} + +/** + * @} end of scale group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_scale_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_scale_q31.c new file mode 100644 index 0000000000..8e9b50e72f --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_scale_q31.c @@ -0,0 +1,221 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_scale_q31.c +* +* Description: Multiplies a Q31 vector by a scalar. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @addtogroup scale + * @{ + */ + +/** + * @brief Multiplies a Q31 vector by a scalar. + * @param[in] *pSrc points to the input vector + * @param[in] scaleFract fractional portion of the scale value + * @param[in] shift number of bits to shift the result by + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in the vector + * @return none. + * + * Scaling and Overflow Behavior: + * \par + * The input data *pSrc and scaleFract are in 1.31 format. + * These are multiplied to yield a 2.62 intermediate result and this is shifted with saturation to 1.31 format. + */ + +void arm_scale_q31( + q31_t * pSrc, + q31_t scaleFract, + int8_t shift, + q31_t * pDst, + uint32_t blockSize) +{ + int8_t kShift = shift + 1; /* Shift to apply after scaling */ + int8_t sign = (kShift & 0x80); + uint32_t blkCnt; /* loop counter */ + q31_t in, out; + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + + q31_t in1, in2, in3, in4; /* temporary input variables */ + q31_t out1, out2, out3, out4; /* temporary output variabels */ + + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + if(sign == 0u) + { + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* read four inputs from source */ + in1 = *pSrc; + in2 = *(pSrc + 1); + in3 = *(pSrc + 2); + in4 = *(pSrc + 3); + + /* multiply input with scaler value */ + in1 = ((q63_t) in1 * scaleFract) >> 32; + in2 = ((q63_t) in2 * scaleFract) >> 32; + in3 = ((q63_t) in3 * scaleFract) >> 32; + in4 = ((q63_t) in4 * scaleFract) >> 32; + + /* apply shifting */ + out1 = in1 << kShift; + out2 = in2 << kShift; + + /* saturate the results. */ + if(in1 != (out1 >> kShift)) + out1 = 0x7FFFFFFF ^ (in1 >> 31); + + if(in2 != (out2 >> kShift)) + out2 = 0x7FFFFFFF ^ (in2 >> 31); + + out3 = in3 << kShift; + out4 = in4 << kShift; + + *pDst = out1; + *(pDst + 1) = out2; + + if(in3 != (out3 >> kShift)) + out3 = 0x7FFFFFFF ^ (in3 >> 31); + + if(in4 != (out4 >> kShift)) + out4 = 0x7FFFFFFF ^ (in4 >> 31); + + /* Store result destination */ + *(pDst + 2) = out3; + *(pDst + 3) = out4; + + /* Update pointers to process next sampels */ + pSrc += 4u; + pDst += 4u; + + /* Decrement the loop counter */ + blkCnt--; + } + + } + else + { + kShift = -kShift; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* read four inputs from source */ + in1 = *pSrc; + in2 = *(pSrc + 1); + in3 = *(pSrc + 2); + in4 = *(pSrc + 3); + + /* multiply input with scaler value */ + in1 = ((q63_t) in1 * scaleFract) >> 32; + in2 = ((q63_t) in2 * scaleFract) >> 32; + in3 = ((q63_t) in3 * scaleFract) >> 32; + in4 = ((q63_t) in4 * scaleFract) >> 32; + + /* apply shifting */ + out1 = in1 >> kShift; + out2 = in2 >> kShift; + + out3 = in3 >> kShift; + out4 = in4 >> kShift; + + /* Store result destination */ + *pDst = out1; + *(pDst + 1) = out2; + + *(pDst + 2) = out3; + *(pDst + 3) = out4; + + /* Update pointers to process next sampels */ + pSrc += 4u; + pDst += 4u; + + /* Decrement the loop counter */ + blkCnt--; + } + } + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + +#endif /* #ifndef ARM_MATH_CM0 */ + + while(blkCnt > 0u) + { + /* C = A * scale */ + /* Scale the input and then store the result in the destination buffer. */ + in = *pSrc++; + in = ((q63_t) in * scaleFract) >> 32; + + if(sign == 0) + { + out = in << kShift; + if(in != (out >> kShift)) + out = 0x7FFFFFFF ^ (in >> 31); + } + else + { + out = in >> kShift; + } + + *pDst++ = out; + + /* Decrement the loop counter */ + blkCnt--; + } +} + +/** + * @} end of scale group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_scale_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_scale_q7.c new file mode 100644 index 0000000000..76c35e6561 --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_scale_q7.c @@ -0,0 +1,144 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_scale_q7.c +* +* Description: Multiplies a Q7 vector by a scalar. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @addtogroup scale + * @{ + */ + +/** + * @brief Multiplies a Q7 vector by a scalar. + * @param[in] *pSrc points to the input vector + * @param[in] scaleFract fractional portion of the scale value + * @param[in] shift number of bits to shift the result by + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in the vector + * @return none. + * + * Scaling and Overflow Behavior: + * \par + * The input data *pSrc and scaleFract are in 1.7 format. + * These are multiplied to yield a 2.14 intermediate result and this is shifted with saturation to 1.7 format. + */ + +void arm_scale_q7( + q7_t * pSrc, + q7_t scaleFract, + int8_t shift, + q7_t * pDst, + uint32_t blockSize) +{ + int8_t kShift = 7 - shift; /* shift to apply after scaling */ + uint32_t blkCnt; /* loop counter */ + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + q7_t in1, in2, in3, in4, out1, out2, out3, out4; /* Temporary variables to store input & output */ + + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* Reading 4 inputs from memory */ + in1 = *pSrc++; + in2 = *pSrc++; + in3 = *pSrc++; + in4 = *pSrc++; + + /* C = A * scale */ + /* Scale the inputs and then store the results in the temporary variables. */ + out1 = (q7_t) (__SSAT(((in1) * scaleFract) >> kShift, 8)); + out2 = (q7_t) (__SSAT(((in2) * scaleFract) >> kShift, 8)); + out3 = (q7_t) (__SSAT(((in3) * scaleFract) >> kShift, 8)); + out4 = (q7_t) (__SSAT(((in4) * scaleFract) >> kShift, 8)); + + /* Packing the individual outputs into 32bit and storing in + * destination buffer in single write */ + *__SIMD32(pDst)++ = __PACKq7(out1, out2, out3, out4); + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + + while(blkCnt > 0u) + { + /* C = A * scale */ + /* Scale the input and then store the result in the destination buffer. */ + *pDst++ = (q7_t) (__SSAT(((*pSrc++) * scaleFract) >> kShift, 8)); + + /* Decrement the loop counter */ + blkCnt--; + } + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + + while(blkCnt > 0u) + { + /* C = A * scale */ + /* Scale the input and then store the result in the destination buffer. */ + *pDst++ = (q7_t) (__SSAT((((q15_t) * pSrc++ * scaleFract) >> kShift), 8)); + + /* Decrement the loop counter */ + blkCnt--; + } + +#endif /* #ifndef ARM_MATH_CM0 */ + +} + +/** + * @} end of scale group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_shift_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_shift_q15.c new file mode 100644 index 0000000000..b8301e63d8 --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_shift_q15.c @@ -0,0 +1,243 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_shift_q15.c +* +* Description: Shifts the elements of a Q15 vector by a specified number of bits. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @addtogroup shift + * @{ + */ + +/** + * @brief Shifts the elements of a Q15 vector a specified number of bits. + * @param[in] *pSrc points to the input vector + * @param[in] shiftBits number of bits to shift. A positive value shifts left; a negative value shifts right. + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in the vector + * @return none. + * + * Scaling and Overflow Behavior: + * \par + * The function uses saturating arithmetic. + * Results outside of the allowable Q15 range [0x8000 0x7FFF] will be saturated. + */ + +void arm_shift_q15( + q15_t * pSrc, + int8_t shiftBits, + q15_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counter */ + uint8_t sign; /* Sign of shiftBits */ + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + + q15_t in1, in2; /* Temporary variables */ + + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* Getting the sign of shiftBits */ + sign = (shiftBits & 0x80); + + /* If the shift value is positive then do right shift else left shift */ + if(sign == 0u) + { + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* Read 2 inputs */ + in1 = *pSrc++; + in2 = *pSrc++; + /* C = A << shiftBits */ + /* Shift the inputs and then store the results in the destination buffer. */ +#ifndef ARM_MATH_BIG_ENDIAN + + *__SIMD32(pDst)++ = __PKHBT(__SSAT((in1 << shiftBits), 16), + __SSAT((in2 << shiftBits), 16), 16); + +#else + + *__SIMD32(pDst)++ = __PKHBT(__SSAT((in2 << shiftBits), 16), + __SSAT((in1 << shiftBits), 16), 16); + +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + in1 = *pSrc++; + in2 = *pSrc++; + +#ifndef ARM_MATH_BIG_ENDIAN + + *__SIMD32(pDst)++ = __PKHBT(__SSAT((in1 << shiftBits), 16), + __SSAT((in2 << shiftBits), 16), 16); + +#else + + *__SIMD32(pDst)++ = __PKHBT(__SSAT((in2 << shiftBits), 16), + __SSAT((in1 << shiftBits), 16), 16); + +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + + while(blkCnt > 0u) + { + /* C = A << shiftBits */ + /* Shift and then store the results in the destination buffer. */ + *pDst++ = __SSAT((*pSrc++ << shiftBits), 16); + + /* Decrement the loop counter */ + blkCnt--; + } + } + else + { + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* Read 2 inputs */ + in1 = *pSrc++; + in2 = *pSrc++; + + /* C = A >> shiftBits */ + /* Shift the inputs and then store the results in the destination buffer. */ +#ifndef ARM_MATH_BIG_ENDIAN + + *__SIMD32(pDst)++ = __PKHBT((in1 >> -shiftBits), + (in2 >> -shiftBits), 16); + +#else + + *__SIMD32(pDst)++ = __PKHBT((in2 >> -shiftBits), + (in1 >> -shiftBits), 16); + +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + in1 = *pSrc++; + in2 = *pSrc++; + +#ifndef ARM_MATH_BIG_ENDIAN + + *__SIMD32(pDst)++ = __PKHBT((in1 >> -shiftBits), + (in2 >> -shiftBits), 16); + +#else + + *__SIMD32(pDst)++ = __PKHBT((in2 >> -shiftBits), + (in1 >> -shiftBits), 16); + +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + + while(blkCnt > 0u) + { + /* C = A >> shiftBits */ + /* Shift the inputs and then store the results in the destination buffer. */ + *pDst++ = (*pSrc++ >> -shiftBits); + + /* Decrement the loop counter */ + blkCnt--; + } + } + +#else + + /* Run the below code for Cortex-M0 */ + + /* Getting the sign of shiftBits */ + sign = (shiftBits & 0x80); + + /* If the shift value is positive then do right shift else left shift */ + if(sign == 0u) + { + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + + while(blkCnt > 0u) + { + /* C = A << shiftBits */ + /* Shift and then store the results in the destination buffer. */ + *pDst++ = __SSAT(((q31_t) * pSrc++ << shiftBits), 16); + + /* Decrement the loop counter */ + blkCnt--; + } + } + else + { + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + + while(blkCnt > 0u) + { + /* C = A >> shiftBits */ + /* Shift the inputs and then store the results in the destination buffer. */ + *pDst++ = (*pSrc++ >> -shiftBits); + + /* Decrement the loop counter */ + blkCnt--; + } + } + +#endif /* #ifndef ARM_MATH_CM0 */ + +} + +/** + * @} end of shift group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_shift_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_shift_q31.c new file mode 100644 index 0000000000..561225a899 --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_shift_q31.c @@ -0,0 +1,195 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_shift_q31.c +* +* Description: Shifts the elements of a Q31 vector by a specified number of bits. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ +/** + * @defgroup shift Vector Shift + * + * Shifts the elements of a fixed-point vector by a specified number of bits. + * There are separate functions for Q7, Q15, and Q31 data types. + * The underlying algorithm used is: + * + * 
        
+ *     pDst[n] = pSrc[n] << shift,   0 <= n < blockSize.        
+ *
+ * + * If shift is positive then the elements of the vector are shifted to the left. + * If shift is negative then the elements of the vector are shifted to the right. + */ + +/** + * @addtogroup shift + * @{ + */ + +/** + * @brief Shifts the elements of a Q31 vector a specified number of bits. + * @param[in] *pSrc points to the input vector + * @param[in] shiftBits number of bits to shift. A positive value shifts left; a negative value shifts right. + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in the vector + * @return none. + * + * + * Scaling and Overflow Behavior: + * \par + * The function uses saturating arithmetic. + * Results outside of the allowable Q31 range [0x80000000 0x7FFFFFFF] will be saturated. + */ + +void arm_shift_q31( + q31_t * pSrc, + int8_t shiftBits, + q31_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counter */ + uint8_t sign = (shiftBits & 0x80); /* Sign of shiftBits */ + +#ifndef ARM_MATH_CM0 + + q31_t in1, in2, in3, in4; /* Temporary input variables */ + q31_t out1, out2, out3, out4; /* Temporary output variables */ + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + + if(sign == 0u) + { + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = A << shiftBits */ + /* Shift the input and then store the results in the destination buffer. */ + in1 = *pSrc; + in2 = *(pSrc + 1); + out1 = in1 << shiftBits; + in3 = *(pSrc + 2); + out2 = in2 << shiftBits; + in4 = *(pSrc + 3); + if(in1 != (out1 >> shiftBits)) + out1 = 0x7FFFFFFF ^ (in1 >> 31); + + if(in2 != (out2 >> shiftBits)) + out2 = 0x7FFFFFFF ^ (in2 >> 31); + + *pDst = out1; + out3 = in3 << shiftBits; + *(pDst + 1) = out2; + out4 = in4 << shiftBits; + + if(in3 != (out3 >> shiftBits)) + out3 = 0x7FFFFFFF ^ (in3 >> 31); + + if(in4 != (out4 >> shiftBits)) + out4 = 0x7FFFFFFF ^ (in4 >> 31); + + *(pDst + 2) = out3; + *(pDst + 3) = out4; + + /* Update destination pointer to process next sampels */ + pSrc += 4u; + pDst += 4u; + + /* Decrement the loop counter */ + blkCnt--; + } + } + else + { + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = A >> shiftBits */ + /* Shift the input and then store the results in the destination buffer. */ + in1 = *pSrc; + in2 = *(pSrc + 1); + in3 = *(pSrc + 2); + in4 = *(pSrc + 3); + + *pDst = (in1 >> -shiftBits); + *(pDst + 1) = (in2 >> -shiftBits); + *(pDst + 2) = (in3 >> -shiftBits); + *(pDst + 3) = (in4 >> -shiftBits); + + + pSrc += 4u; + pDst += 4u; + + blkCnt--; + } + + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + +#else + + /* Run the below code for Cortex-M0 */ + + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + +#endif /* #ifndef ARM_MATH_CM0 */ + + + while(blkCnt > 0u) + { + /* C = A (>> or <<) shiftBits */ + /* Shift the input and then store the result in the destination buffer. */ + *pDst++ = (sign == 0u) ? clip_q63_to_q31((q63_t) * pSrc++ << shiftBits) : + (*pSrc++ >> -shiftBits); + + /* Decrement the loop counter */ + blkCnt--; + } + + +} + +/** + * @} end of shift group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_shift_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_shift_q7.c new file mode 100644 index 0000000000..6dfd25f650 --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_shift_q7.c @@ -0,0 +1,215 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_shift_q7.c +* +* Description: Processing function for the Q7 Shifting +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @addtogroup shift + * @{ + */ + + +/** + * @brief Shifts the elements of a Q7 vector a specified number of bits. + * @param[in] *pSrc points to the input vector + * @param[in] shiftBits number of bits to shift. A positive value shifts left; a negative value shifts right. + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in the vector + * @return none. + * + * \par Conditions for optimum performance + * Input and output buffers should be aligned by 32-bit + * + * + * Scaling and Overflow Behavior: + * \par + * The function uses saturating arithmetic. + * Results outside of the allowable Q7 range [0x8 0x7F] will be saturated. + */ + +void arm_shift_q7( + q7_t * pSrc, + int8_t shiftBits, + q7_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counter */ + uint8_t sign; /* Sign of shiftBits */ + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + q7_t in1; /* Input value1 */ + q7_t in2; /* Input value2 */ + q7_t in3; /* Input value3 */ + q7_t in4; /* Input value4 */ + + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* Getting the sign of shiftBits */ + sign = (shiftBits & 0x80); + + /* If the shift value is positive then do right shift else left shift */ + if(sign == 0u) + { + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = A << shiftBits */ + /* Read 4 inputs */ + in1 = *pSrc; + in2 = *(pSrc + 1); + in3 = *(pSrc + 2); + in4 = *(pSrc + 3); + + /* Store the Shifted result in the destination buffer in single cycle by packing the outputs */ + *__SIMD32(pDst)++ = __PACKq7(__SSAT((in1 << shiftBits), 8), + __SSAT((in2 << shiftBits), 8), + __SSAT((in3 << shiftBits), 8), + __SSAT((in4 << shiftBits), 8)); + /* Update source pointer to process next sampels */ + pSrc += 4u; + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + + while(blkCnt > 0u) + { + /* C = A << shiftBits */ + /* Shift the input and then store the result in the destination buffer. */ + *pDst++ = (q7_t) __SSAT((*pSrc++ << shiftBits), 8); + + /* Decrement the loop counter */ + blkCnt--; + } + } + else + { + shiftBits = -shiftBits; + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = A >> shiftBits */ + /* Read 4 inputs */ + in1 = *pSrc; + in2 = *(pSrc + 1); + in3 = *(pSrc + 2); + in4 = *(pSrc + 3); + + /* Store the Shifted result in the destination buffer in single cycle by packing the outputs */ + *__SIMD32(pDst)++ = __PACKq7((in1 >> shiftBits), (in2 >> shiftBits), + (in3 >> shiftBits), (in4 >> shiftBits)); + + + pSrc += 4u; + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + + while(blkCnt > 0u) + { + /* C = A >> shiftBits */ + /* Shift the input and then store the result in the destination buffer. */ + in1 = *pSrc++; + *pDst++ = (in1 >> shiftBits); + + /* Decrement the loop counter */ + blkCnt--; + } + } + +#else + + /* Run the below code for Cortex-M0 */ + + /* Getting the sign of shiftBits */ + sign = (shiftBits & 0x80); + + /* If the shift value is positive then do right shift else left shift */ + if(sign == 0u) + { + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + + while(blkCnt > 0u) + { + /* C = A << shiftBits */ + /* Shift the input and then store the result in the destination buffer. */ + *pDst++ = (q7_t) __SSAT(((q15_t) * pSrc++ << shiftBits), 8); + + /* Decrement the loop counter */ + blkCnt--; + } + } + else + { + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + + while(blkCnt > 0u) + { + /* C = A >> shiftBits */ + /* Shift the input and then store the result in the destination buffer. */ + *pDst++ = (*pSrc++ >> -shiftBits); + + /* Decrement the loop counter */ + blkCnt--; + } + } + +#endif /* #ifndef ARM_MATH_CM0 */ +} + +/** + * @} end of shift group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_sub_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_sub_f32.c new file mode 100644 index 0000000000..4a660db49b --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_sub_f32.c @@ -0,0 +1,145 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_sub_f32.c +* +* Description: Floating-point vector subtraction. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* ---------------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @defgroup BasicSub Vector Subtraction + * + * Element-by-element subtraction of two vectors. + * + * 
        
+ *     pDst[n] = pSrcA[n] - pSrcB[n],   0 <= n < blockSize.        
+ *
+ * + * There are separate functions for floating-point, Q7, Q15, and Q31 data types. + */ + +/** + * @addtogroup BasicSub + * @{ + */ + + +/** + * @brief Floating-point vector subtraction. + * @param[in] *pSrcA points to the first input vector + * @param[in] *pSrcB points to the second input vector + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in each vector + * @return none. + */ + +void arm_sub_f32( + float32_t * pSrcA, + float32_t * pSrcB, + float32_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counter */ + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + float32_t inA1, inA2, inA3, inA4; /* temporary variables */ + float32_t inB1, inB2, inB3, inB4; /* temporary variables */ + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = A - B */ + /* Subtract and then store the results in the destination buffer. */ + /* Read 4 input samples from sourceA and sourceB */ + inA1 = *pSrcA; + inB1 = *pSrcB; + inA2 = *(pSrcA + 1); + inB2 = *(pSrcB + 1); + inA3 = *(pSrcA + 2); + inB3 = *(pSrcB + 2); + inA4 = *(pSrcA + 3); + inB4 = *(pSrcB + 3); + + /* dst = srcA - srcB */ + /* subtract and store the result */ + *pDst = inA1 - inB1; + *(pDst + 1) = inA2 - inB2; + *(pDst + 2) = inA3 - inB3; + *(pDst + 3) = inA4 - inB4; + + + /* Update pointers to process next sampels */ + pSrcA += 4u; + pSrcB += 4u; + pDst += 4u; + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + +#endif /* #ifndef ARM_MATH_CM0 */ + + while(blkCnt > 0u) + { + /* C = A - B */ + /* Subtract and then store the results in the destination buffer. */ + *pDst++ = (*pSrcA++) - (*pSrcB++); + + /* Decrement the loop counter */ + blkCnt--; + } +} + +/** + * @} end of BasicSub group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_sub_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_sub_q15.c new file mode 100644 index 0000000000..d8cc12220a --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_sub_q15.c @@ -0,0 +1,135 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_sub_q15.c +* +* Description: Q15 vector subtraction. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @addtogroup BasicSub + * @{ + */ + +/** + * @brief Q15 vector subtraction. + * @param[in] *pSrcA points to the first input vector + * @param[in] *pSrcB points to the second input vector + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in each vector + * @return none. + * + * Scaling and Overflow Behavior: + * \par + * The function uses saturating arithmetic. + * Results outside of the allowable Q15 range [0x8000 0x7FFF] will be saturated. + */ + +void arm_sub_q15( + q15_t * pSrcA, + q15_t * pSrcB, + q15_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counter */ + + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + q31_t inA1, inA2; + q31_t inB1, inB2; + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = A - B */ + /* Subtract and then store the results in the destination buffer two samples at a time. */ + inA1 = *__SIMD32(pSrcA)++; + inA2 = *__SIMD32(pSrcA)++; + inB1 = *__SIMD32(pSrcB)++; + inB2 = *__SIMD32(pSrcB)++; + + *__SIMD32(pDst)++ = __QSUB16(inA1, inB1); + *__SIMD32(pDst)++ = __QSUB16(inA2, inB2); + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + + while(blkCnt > 0u) + { + /* C = A - B */ + /* Subtract and then store the result in the destination buffer. */ + *pDst++ = (q15_t) __QSUB16(*pSrcA++, *pSrcB++); + + /* Decrement the loop counter */ + blkCnt--; + } + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + + while(blkCnt > 0u) + { + /* C = A - B */ + /* Subtract and then store the result in the destination buffer. */ + *pDst++ = (q15_t) __SSAT(((q31_t) * pSrcA++ - *pSrcB++), 16); + + /* Decrement the loop counter */ + blkCnt--; + } + +#endif /* #ifndef ARM_MATH_CM0 */ + + +} + +/** + * @} end of BasicSub group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_sub_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_sub_q31.c new file mode 100644 index 0000000000..34642f32e7 --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_sub_q31.c @@ -0,0 +1,141 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_sub_q31.c +* +* Description: Q31 vector subtraction. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @addtogroup BasicSub + * @{ + */ + +/** + * @brief Q31 vector subtraction. + * @param[in] *pSrcA points to the first input vector + * @param[in] *pSrcB points to the second input vector + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in each vector + * @return none. + * + * Scaling and Overflow Behavior: + * \par + * The function uses saturating arithmetic. + * Results outside of the allowable Q31 range [0x80000000 0x7FFFFFFF] will be saturated. + */ + +void arm_sub_q31( + q31_t * pSrcA, + q31_t * pSrcB, + q31_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counter */ + + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + q31_t inA1, inA2, inA3, inA4; + q31_t inB1, inB2, inB3, inB4; + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = A - B */ + /* Subtract and then store the results in the destination buffer. */ + inA1 = *pSrcA++; + inA2 = *pSrcA++; + inB1 = *pSrcB++; + inB2 = *pSrcB++; + + inA3 = *pSrcA++; + inA4 = *pSrcA++; + inB3 = *pSrcB++; + inB4 = *pSrcB++; + + *pDst++ = __QSUB(inA1, inB1); + *pDst++ = __QSUB(inA2, inB2); + *pDst++ = __QSUB(inA3, inB3); + *pDst++ = __QSUB(inA4, inB4); + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + + while(blkCnt > 0u) + { + /* C = A - B */ + /* Subtract and then store the result in the destination buffer. */ + *pDst++ = __QSUB(*pSrcA++, *pSrcB++); + + /* Decrement the loop counter */ + blkCnt--; + } + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + + while(blkCnt > 0u) + { + /* C = A - B */ + /* Subtract and then store the result in the destination buffer. */ + *pDst++ = (q31_t) clip_q63_to_q31((q63_t) * pSrcA++ - *pSrcB++); + + /* Decrement the loop counter */ + blkCnt--; + } + +#endif /* #ifndef ARM_MATH_CM0 */ + +} + +/** + * @} end of BasicSub group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_sub_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_sub_q7.c new file mode 100644 index 0000000000..adbc7d0c08 --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_sub_q7.c @@ -0,0 +1,126 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_sub_q7.c +* +* Description: Q7 vector subtraction. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.7 2010/06/10 +* Misra-C changes done +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupMath + */ + +/** + * @addtogroup BasicSub + * @{ + */ + +/** + * @brief Q7 vector subtraction. + * @param[in] *pSrcA points to the first input vector + * @param[in] *pSrcB points to the second input vector + * @param[out] *pDst points to the output vector + * @param[in] blockSize number of samples in each vector + * @return none. + * + * Scaling and Overflow Behavior: + * \par + * The function uses saturating arithmetic. + * Results outside of the allowable Q7 range [0x80 0x7F] will be saturated. + */ + +void arm_sub_q7( + q7_t * pSrcA, + q7_t * pSrcB, + q7_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counter */ + +#ifndef ARM_MATH_CM0 + +/* Run the below code for Cortex-M4 and Cortex-M3 */ + + /*loop Unrolling */ + blkCnt = blockSize >> 2u; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + while(blkCnt > 0u) + { + /* C = A - B */ + /* Subtract and then store the results in the destination buffer 4 samples at a time. */ + *__SIMD32(pDst)++ = __QSUB8(*__SIMD32(pSrcA)++, *__SIMD32(pSrcB)++); + + /* Decrement the loop counter */ + blkCnt--; + } + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + blkCnt = blockSize % 0x4u; + + while(blkCnt > 0u) + { + /* C = A - B */ + /* Subtract and then store the result in the destination buffer. */ + *pDst++ = __SSAT(*pSrcA++ - *pSrcB++, 8); + + /* Decrement the loop counter */ + blkCnt--; + } + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initialize blkCnt with number of samples */ + blkCnt = blockSize; + + while(blkCnt > 0u) + { + /* C = A - B */ + /* Subtract and then store the result in the destination buffer. */ + *pDst++ = (q7_t) __SSAT((q15_t) * pSrcA++ - *pSrcB++, 8); + + /* Decrement the loop counter */ + blkCnt--; + } + +#endif /* #ifndef ARM_MATH_CM0 */ + + +} + +/** + * @} end of BasicSub group + */ diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/CommonTables/arm_common_tables.c b/apps/mathlib/CMSIS/DSP_Lib/Source/CommonTables/arm_common_tables.c new file mode 100644 index 0000000000..bf7ab3bed7 --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/CommonTables/arm_common_tables.c @@ -0,0 +1,4689 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_common_tables.c +* +* Description: This file has common tables like fft twiddle factors, Bitreverse, reciprocal etc which are used across different functions +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* -------------------------------------------------------------------- */ + + +#include "arm_math.h" +#include "arm_common_tables.h" + +/** + * @ingroup groupTransforms + */ + +/** + * @addtogroup CFFT_CIFFT Complex FFT Tables + * @{ + */ + +/** +* \par +* Pseudo code for Generation of Bit reversal Table is +* \par +* 
for(l=1;l <= N/4;l++)    
+* {    
+*   for(i=0;i> 1;    
+*  }
+* \par +* where N = 4096 logN2 = 12 +* \par +* N is the maximum FFT Size supported +*/ + +/* +* @brief Table for bit reversal process +*/ +const uint16_t armBitRevTable[1024] = { + 0x400, 0x200, 0x600, 0x100, 0x500, 0x300, 0x700, + 0x80, 0x480, 0x280, 0x680, 0x180, 0x580, 0x380, + 0x780, 0x40, 0x440, 0x240, 0x640, 0x140, 0x540, + 0x340, 0x740, 0xc0, 0x4c0, 0x2c0, 0x6c0, 0x1c0, + 0x5c0, 0x3c0, 0x7c0, 0x20, 0x420, 0x220, 0x620, + 0x120, 0x520, 0x320, 0x720, 0xa0, 0x4a0, 0x2a0, + 0x6a0, 0x1a0, 0x5a0, 0x3a0, 0x7a0, 0x60, 0x460, + 0x260, 0x660, 0x160, 0x560, 0x360, 0x760, 0xe0, + 0x4e0, 0x2e0, 0x6e0, 0x1e0, 0x5e0, 0x3e0, 0x7e0, + 0x10, 0x410, 0x210, 0x610, 0x110, 0x510, 0x310, + 0x710, 0x90, 0x490, 0x290, 0x690, 0x190, 0x590, + 0x390, 0x790, 0x50, 0x450, 0x250, 0x650, 0x150, + 0x550, 0x350, 0x750, 0xd0, 0x4d0, 0x2d0, 0x6d0, + 0x1d0, 0x5d0, 0x3d0, 0x7d0, 0x30, 0x430, 0x230, + 0x630, 0x130, 0x530, 0x330, 0x730, 0xb0, 0x4b0, + 0x2b0, 0x6b0, 0x1b0, 0x5b0, 0x3b0, 0x7b0, 0x70, + 0x470, 0x270, 0x670, 0x170, 0x570, 0x370, 0x770, + 0xf0, 0x4f0, 0x2f0, 0x6f0, 0x1f0, 0x5f0, 0x3f0, + 0x7f0, 0x8, 0x408, 0x208, 0x608, 0x108, 0x508, + 0x308, 0x708, 0x88, 0x488, 0x288, 0x688, 0x188, + 0x588, 0x388, 0x788, 0x48, 0x448, 0x248, 0x648, + 0x148, 0x548, 0x348, 0x748, 0xc8, 0x4c8, 0x2c8, + 0x6c8, 0x1c8, 0x5c8, 0x3c8, 0x7c8, 0x28, 0x428, + 0x228, 0x628, 0x128, 0x528, 0x328, 0x728, 0xa8, + 0x4a8, 0x2a8, 0x6a8, 0x1a8, 0x5a8, 0x3a8, 0x7a8, + 0x68, 0x468, 0x268, 0x668, 0x168, 0x568, 0x368, + 0x768, 0xe8, 0x4e8, 0x2e8, 0x6e8, 0x1e8, 0x5e8, + 0x3e8, 0x7e8, 0x18, 0x418, 0x218, 0x618, 0x118, + 0x518, 0x318, 0x718, 0x98, 0x498, 0x298, 0x698, + 0x198, 0x598, 0x398, 0x798, 0x58, 0x458, 0x258, + 0x658, 0x158, 0x558, 0x358, 0x758, 0xd8, 0x4d8, + 0x2d8, 0x6d8, 0x1d8, 0x5d8, 0x3d8, 0x7d8, 0x38, + 0x438, 0x238, 0x638, 0x138, 0x538, 0x338, 0x738, + 0xb8, 0x4b8, 0x2b8, 0x6b8, 0x1b8, 0x5b8, 0x3b8, + 0x7b8, 0x78, 0x478, 0x278, 0x678, 0x178, 0x578, + 0x378, 0x778, 0xf8, 0x4f8, 0x2f8, 0x6f8, 0x1f8, + 0x5f8, 0x3f8, 0x7f8, 0x4, 0x404, 0x204, 0x604, + 0x104, 0x504, 0x304, 0x704, 0x84, 0x484, 0x284, + 0x684, 0x184, 0x584, 0x384, 0x784, 0x44, 0x444, + 0x244, 0x644, 0x144, 0x544, 0x344, 0x744, 0xc4, + 0x4c4, 0x2c4, 0x6c4, 0x1c4, 0x5c4, 0x3c4, 0x7c4, + 0x24, 0x424, 0x224, 0x624, 0x124, 0x524, 0x324, + 0x724, 0xa4, 0x4a4, 0x2a4, 0x6a4, 0x1a4, 0x5a4, + 0x3a4, 0x7a4, 0x64, 0x464, 0x264, 0x664, 0x164, + 0x564, 0x364, 0x764, 0xe4, 0x4e4, 0x2e4, 0x6e4, + 0x1e4, 0x5e4, 0x3e4, 0x7e4, 0x14, 0x414, 0x214, + 0x614, 0x114, 0x514, 0x314, 0x714, 0x94, 0x494, + 0x294, 0x694, 0x194, 0x594, 0x394, 0x794, 0x54, + 0x454, 0x254, 0x654, 0x154, 0x554, 0x354, 0x754, + 0xd4, 0x4d4, 0x2d4, 0x6d4, 0x1d4, 0x5d4, 0x3d4, + 0x7d4, 0x34, 0x434, 0x234, 0x634, 0x134, 0x534, + 0x334, 0x734, 0xb4, 0x4b4, 0x2b4, 0x6b4, 0x1b4, + 0x5b4, 0x3b4, 0x7b4, 0x74, 0x474, 0x274, 0x674, + 0x174, 0x574, 0x374, 0x774, 0xf4, 0x4f4, 0x2f4, + 0x6f4, 0x1f4, 0x5f4, 0x3f4, 0x7f4, 0xc, 0x40c, + 0x20c, 0x60c, 0x10c, 0x50c, 0x30c, 0x70c, 0x8c, + 0x48c, 0x28c, 0x68c, 0x18c, 0x58c, 0x38c, 0x78c, + 0x4c, 0x44c, 0x24c, 0x64c, 0x14c, 0x54c, 0x34c, + 0x74c, 0xcc, 0x4cc, 0x2cc, 0x6cc, 0x1cc, 0x5cc, + 0x3cc, 0x7cc, 0x2c, 0x42c, 0x22c, 0x62c, 0x12c, + 0x52c, 0x32c, 0x72c, 0xac, 0x4ac, 0x2ac, 0x6ac, + 0x1ac, 0x5ac, 0x3ac, 0x7ac, 0x6c, 0x46c, 0x26c, + 0x66c, 0x16c, 0x56c, 0x36c, 0x76c, 0xec, 0x4ec, + 0x2ec, 0x6ec, 0x1ec, 0x5ec, 0x3ec, 0x7ec, 0x1c, + 0x41c, 0x21c, 0x61c, 0x11c, 0x51c, 0x31c, 0x71c, + 0x9c, 0x49c, 0x29c, 0x69c, 0x19c, 0x59c, 0x39c, + 0x79c, 0x5c, 0x45c, 0x25c, 0x65c, 0x15c, 0x55c, + 0x35c, 0x75c, 0xdc, 0x4dc, 0x2dc, 0x6dc, 0x1dc, + 0x5dc, 0x3dc, 0x7dc, 0x3c, 0x43c, 0x23c, 0x63c, + 0x13c, 0x53c, 0x33c, 0x73c, 0xbc, 0x4bc, 0x2bc, + 0x6bc, 0x1bc, 0x5bc, 0x3bc, 0x7bc, 0x7c, 0x47c, + 0x27c, 0x67c, 0x17c, 0x57c, 0x37c, 0x77c, 0xfc, + 0x4fc, 0x2fc, 0x6fc, 0x1fc, 0x5fc, 0x3fc, 0x7fc, + 0x2, 0x402, 0x202, 0x602, 0x102, 0x502, 0x302, + 0x702, 0x82, 0x482, 0x282, 0x682, 0x182, 0x582, + 0x382, 0x782, 0x42, 0x442, 0x242, 0x642, 0x142, + 0x542, 0x342, 0x742, 0xc2, 0x4c2, 0x2c2, 0x6c2, + 0x1c2, 0x5c2, 0x3c2, 0x7c2, 0x22, 0x422, 0x222, + 0x622, 0x122, 0x522, 0x322, 0x722, 0xa2, 0x4a2, + 0x2a2, 0x6a2, 0x1a2, 0x5a2, 0x3a2, 0x7a2, 0x62, + 0x462, 0x262, 0x662, 0x162, 0x562, 0x362, 0x762, + 0xe2, 0x4e2, 0x2e2, 0x6e2, 0x1e2, 0x5e2, 0x3e2, + 0x7e2, 0x12, 0x412, 0x212, 0x612, 0x112, 0x512, + 0x312, 0x712, 0x92, 0x492, 0x292, 0x692, 0x192, + 0x592, 0x392, 0x792, 0x52, 0x452, 0x252, 0x652, + 0x152, 0x552, 0x352, 0x752, 0xd2, 0x4d2, 0x2d2, + 0x6d2, 0x1d2, 0x5d2, 0x3d2, 0x7d2, 0x32, 0x432, + 0x232, 0x632, 0x132, 0x532, 0x332, 0x732, 0xb2, + 0x4b2, 0x2b2, 0x6b2, 0x1b2, 0x5b2, 0x3b2, 0x7b2, + 0x72, 0x472, 0x272, 0x672, 0x172, 0x572, 0x372, + 0x772, 0xf2, 0x4f2, 0x2f2, 0x6f2, 0x1f2, 0x5f2, + 0x3f2, 0x7f2, 0xa, 0x40a, 0x20a, 0x60a, 0x10a, + 0x50a, 0x30a, 0x70a, 0x8a, 0x48a, 0x28a, 0x68a, + 0x18a, 0x58a, 0x38a, 0x78a, 0x4a, 0x44a, 0x24a, + 0x64a, 0x14a, 0x54a, 0x34a, 0x74a, 0xca, 0x4ca, + 0x2ca, 0x6ca, 0x1ca, 0x5ca, 0x3ca, 0x7ca, 0x2a, + 0x42a, 0x22a, 0x62a, 0x12a, 0x52a, 0x32a, 0x72a, + 0xaa, 0x4aa, 0x2aa, 0x6aa, 0x1aa, 0x5aa, 0x3aa, + 0x7aa, 0x6a, 0x46a, 0x26a, 0x66a, 0x16a, 0x56a, + 0x36a, 0x76a, 0xea, 0x4ea, 0x2ea, 0x6ea, 0x1ea, + 0x5ea, 0x3ea, 0x7ea, 0x1a, 0x41a, 0x21a, 0x61a, + 0x11a, 0x51a, 0x31a, 0x71a, 0x9a, 0x49a, 0x29a, + 0x69a, 0x19a, 0x59a, 0x39a, 0x79a, 0x5a, 0x45a, + 0x25a, 0x65a, 0x15a, 0x55a, 0x35a, 0x75a, 0xda, + 0x4da, 0x2da, 0x6da, 0x1da, 0x5da, 0x3da, 0x7da, + 0x3a, 0x43a, 0x23a, 0x63a, 0x13a, 0x53a, 0x33a, + 0x73a, 0xba, 0x4ba, 0x2ba, 0x6ba, 0x1ba, 0x5ba, + 0x3ba, 0x7ba, 0x7a, 0x47a, 0x27a, 0x67a, 0x17a, + 0x57a, 0x37a, 0x77a, 0xfa, 0x4fa, 0x2fa, 0x6fa, + 0x1fa, 0x5fa, 0x3fa, 0x7fa, 0x6, 0x406, 0x206, + 0x606, 0x106, 0x506, 0x306, 0x706, 0x86, 0x486, + 0x286, 0x686, 0x186, 0x586, 0x386, 0x786, 0x46, + 0x446, 0x246, 0x646, 0x146, 0x546, 0x346, 0x746, + 0xc6, 0x4c6, 0x2c6, 0x6c6, 0x1c6, 0x5c6, 0x3c6, + 0x7c6, 0x26, 0x426, 0x226, 0x626, 0x126, 0x526, + 0x326, 0x726, 0xa6, 0x4a6, 0x2a6, 0x6a6, 0x1a6, + 0x5a6, 0x3a6, 0x7a6, 0x66, 0x466, 0x266, 0x666, + 0x166, 0x566, 0x366, 0x766, 0xe6, 0x4e6, 0x2e6, + 0x6e6, 0x1e6, 0x5e6, 0x3e6, 0x7e6, 0x16, 0x416, + 0x216, 0x616, 0x116, 0x516, 0x316, 0x716, 0x96, + 0x496, 0x296, 0x696, 0x196, 0x596, 0x396, 0x796, + 0x56, 0x456, 0x256, 0x656, 0x156, 0x556, 0x356, + 0x756, 0xd6, 0x4d6, 0x2d6, 0x6d6, 0x1d6, 0x5d6, + 0x3d6, 0x7d6, 0x36, 0x436, 0x236, 0x636, 0x136, + 0x536, 0x336, 0x736, 0xb6, 0x4b6, 0x2b6, 0x6b6, + 0x1b6, 0x5b6, 0x3b6, 0x7b6, 0x76, 0x476, 0x276, + 0x676, 0x176, 0x576, 0x376, 0x776, 0xf6, 0x4f6, + 0x2f6, 0x6f6, 0x1f6, 0x5f6, 0x3f6, 0x7f6, 0xe, + 0x40e, 0x20e, 0x60e, 0x10e, 0x50e, 0x30e, 0x70e, + 0x8e, 0x48e, 0x28e, 0x68e, 0x18e, 0x58e, 0x38e, + 0x78e, 0x4e, 0x44e, 0x24e, 0x64e, 0x14e, 0x54e, + 0x34e, 0x74e, 0xce, 0x4ce, 0x2ce, 0x6ce, 0x1ce, + 0x5ce, 0x3ce, 0x7ce, 0x2e, 0x42e, 0x22e, 0x62e, + 0x12e, 0x52e, 0x32e, 0x72e, 0xae, 0x4ae, 0x2ae, + 0x6ae, 0x1ae, 0x5ae, 0x3ae, 0x7ae, 0x6e, 0x46e, + 0x26e, 0x66e, 0x16e, 0x56e, 0x36e, 0x76e, 0xee, + 0x4ee, 0x2ee, 0x6ee, 0x1ee, 0x5ee, 0x3ee, 0x7ee, + 0x1e, 0x41e, 0x21e, 0x61e, 0x11e, 0x51e, 0x31e, + 0x71e, 0x9e, 0x49e, 0x29e, 0x69e, 0x19e, 0x59e, + 0x39e, 0x79e, 0x5e, 0x45e, 0x25e, 0x65e, 0x15e, + 0x55e, 0x35e, 0x75e, 0xde, 0x4de, 0x2de, 0x6de, + 0x1de, 0x5de, 0x3de, 0x7de, 0x3e, 0x43e, 0x23e, + 0x63e, 0x13e, 0x53e, 0x33e, 0x73e, 0xbe, 0x4be, + 0x2be, 0x6be, 0x1be, 0x5be, 0x3be, 0x7be, 0x7e, + 0x47e, 0x27e, 0x67e, 0x17e, 0x57e, 0x37e, 0x77e, + 0xfe, 0x4fe, 0x2fe, 0x6fe, 0x1fe, 0x5fe, 0x3fe, + 0x7fe, 0x1 +}; + + +/* +* @brief Floating-point Twiddle factors Table Generation +*/ + + +/** +* \par +* Example code for Floating-point Twiddle factors Generation: +* \par +* 
for(i = 0; i< 3N/4; i++)    
+* {    
+*	twiddleCoef[2*i]= cos(i * 2*PI/(float)N);    
+*	twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);    
+* }
+* \par +* where N = 4096 and PI = 3.14159265358979 +* \par +* Cos and Sin values are in interleaved fashion +* +*/ +const float32_t twiddleCoef[6144] = { + 1.000000000000000000f, 0.000000000000000000f, 0.999998823451701880f, + 0.001533980186284766f, 0.999995293809576190f, 0.003067956762965976f, + 0.999989411081928400f, 0.004601926120448571f, 0.999981175282601110f, + 0.006135884649154475f, 0.999970586430974140f, 0.007669828739531097f, + 0.999957644551963900f, 0.009203754782059819f, 0.999942349676023910f, + 0.010737659167264491f, 0.999924701839144500f, 0.012271538285719925f, + 0.999904701082852900f, 0.013805388528060391f, 0.999882347454212560f, + 0.015339206284988100f, 0.999857641005823860f, 0.016872987947281710f, + 0.999830581795823400f, 0.018406729905804820f, 0.999801169887884260f, + 0.019940428551514441f, 0.999769405351215280f, 0.021474080275469508f, + 0.999735288260561680f, 0.023007681468839369f, 0.999698818696204250f, + 0.024541228522912288f, 0.999659996743959220f, 0.026074717829103901f, + 0.999618822495178640f, 0.027608145778965740f, 0.999575296046749220f, + 0.029141508764193722f, 0.999529417501093140f, 0.030674803176636626f, + 0.999481186966166950f, 0.032208025408304586f, 0.999430604555461730f, + 0.033741171851377580f, 0.999377670388002850f, 0.035274238898213947f, + 0.999322384588349540f, 0.036807222941358832f, 0.999264747286594420f, + 0.038340120373552694f, 0.999204758618363890f, 0.039872927587739811f, + 0.999142418724816910f, 0.041405640977076739f, 0.999077727752645360f, + 0.042938256934940820f, 0.999010685854073380f, 0.044470771854938668f, + 0.998941293186856870f, 0.046003182130914623f, 0.998869549914283560f, + 0.047535484156959303f, 0.998795456205172410f, 0.049067674327418015f, + 0.998719012233872940f, 0.050599749036899282f, 0.998640218180265270f, + 0.052131704680283324f, 0.998559074229759310f, 0.053663537652730520f, + 0.998475580573294770f, 0.055195244349689934f, 0.998389737407340160f, + 0.056726821166907748f, 0.998301544933892890f, 0.058258264500435752f, + 0.998211003360478190f, 0.059789570746639868f, 0.998118112900149180f, + 0.061320736302208578f, 0.998022873771486240f, 0.062851757564161406f, + 0.997925286198596000f, 0.064382630929857465f, 0.997825350411111640f, + 0.065913352797003805f, 0.997723066644191640f, 0.067443919563664051f, + 0.997618435138519550f, 0.068974327628266746f, 0.997511456140303450f, + 0.070504573389613856f, 0.997402129901275300f, 0.072034653246889332f, + 0.997290456678690210f, 0.073564563599667426f, 0.997176436735326190f, + 0.075094300847921305f, 0.997060070339482960f, 0.076623861392031492f, + 0.996941357764982160f, 0.078153241632794232f, 0.996820299291165670f, + 0.079682437971430126f, 0.996696895202896060f, 0.081211446809592441f, + 0.996571145790554840f, 0.082740264549375692f, 0.996443051350042630f, + 0.084268887593324071f, 0.996312612182778000f, 0.085797312344439894f, + 0.996179828595696980f, 0.087325535206192059f, 0.996044700901251970f, + 0.088853552582524600f, 0.995907229417411720f, 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-0.999995293809576190f, -0.001533980186285111f, -0.999998823451701880f, +}; + +/* +* @brief Q31 Twiddle factors Table +*/ + +/** +* \par +* Example code for Q31 Twiddle factors Generation:: +* \par +* 
for(i = 0; i< 3N/4; i++)    
+* {    
+*    twiddleCoefQ31[2*i]= cos(i * 2*PI/(float)N);    
+*    twiddleCoefQ31[2*i+1]= sin(i * 2*PI/(float)N);    
+* }
+* \par +* where N = 4096 and PI = 3.14159265358979 +* \par +* Cos and Sin values are interleaved fashion +* \par +* Convert Floating point to Q31(Fixed point 1.31): +* round(twiddleCoefQ31(i) * pow(2, 31)) +* +*/ + +const q31_t twiddleCoefQ31[6144] = { + 0x7fffffff, 0x0, 0x7ffff621, 0x3243f5, 0x7fffd886, 0x6487e3, 0x7fffa72c, + 0x96cbc1, + 0x7fff6216, 0xc90f88, 0x7fff0943, 0xfb5330, 0x7ffe9cb2, 0x12d96b1, + 0x7ffe1c65, 0x15fda03, + 0x7ffd885a, 0x1921d20, 0x7ffce093, 0x1c45ffe, 0x7ffc250f, 0x1f6a297, + 0x7ffb55ce, 0x228e4e2, + 0x7ffa72d1, 0x25b26d7, 0x7ff97c18, 0x28d6870, 0x7ff871a2, 0x2bfa9a4, + 0x7ff75370, 0x2f1ea6c, + 0x7ff62182, 0x3242abf, 0x7ff4dbd9, 0x3566a96, 0x7ff38274, 0x388a9ea, + 0x7ff21553, 0x3bae8b2, + 0x7ff09478, 0x3ed26e6, 0x7feeffe1, 0x41f6480, 0x7fed5791, 0x451a177, + 0x7feb9b85, 0x483ddc3, + 0x7fe9cbc0, 0x4b6195d, 0x7fe7e841, 0x4e8543e, 0x7fe5f108, 0x51a8e5c, + 0x7fe3e616, 0x54cc7b1, + 0x7fe1c76b, 0x57f0035, 0x7fdf9508, 0x5b137df, 0x7fdd4eec, 0x5e36ea9, + 0x7fdaf519, 0x615a48b, + 0x7fd8878e, 0x647d97c, 0x7fd6064c, 0x67a0d76, 0x7fd37153, 0x6ac406f, + 0x7fd0c8a3, 0x6de7262, + 0x7fce0c3e, 0x710a345, 0x7fcb3c23, 0x742d311, 0x7fc85854, 0x77501be, + 0x7fc560cf, 0x7a72f45, + 0x7fc25596, 0x7d95b9e, 0x7fbf36aa, 0x80b86c2, 0x7fbc040a, 0x83db0a7, + 0x7fb8bdb8, 0x86fd947, + 0x7fb563b3, 0x8a2009a, 0x7fb1f5fc, 0x8d42699, 0x7fae7495, 0x9064b3a, + 0x7faadf7c, 0x9386e78, + 0x7fa736b4, 0x96a9049, 0x7fa37a3c, 0x99cb0a7, 0x7f9faa15, 0x9cecf89, + 0x7f9bc640, 0xa00ece8, + 0x7f97cebd, 0xa3308bd, 0x7f93c38c, 0xa6522fe, 0x7f8fa4b0, 0xa973ba5, + 0x7f8b7227, 0xac952aa, + 0x7f872bf3, 0xafb6805, 0x7f82d214, 0xb2d7baf, 0x7f7e648c, 0xb5f8d9f, + 0x7f79e35a, 0xb919dcf, + 0x7f754e80, 0xbc3ac35, 0x7f70a5fe, 0xbf5b8cb, 0x7f6be9d4, 0xc27c389, + 0x7f671a05, 0xc59cc68, + 0x7f62368f, 0xc8bd35e, 0x7f5d3f75, 0xcbdd865, 0x7f5834b7, 0xcefdb76, + 0x7f531655, 0xd21dc87, + 0x7f4de451, 0xd53db92, 0x7f489eaa, 0xd85d88f, 0x7f434563, 0xdb7d376, + 0x7f3dd87c, 0xde9cc40, + 0x7f3857f6, 0xe1bc2e4, 0x7f32c3d1, 0xe4db75b, 0x7f2d1c0e, 0xe7fa99e, + 0x7f2760af, 0xeb199a4, + 0x7f2191b4, 0xee38766, 0x7f1baf1e, 0xf1572dc, 0x7f15b8ee, 0xf475bff, + 0x7f0faf25, 0xf7942c7, + 0x7f0991c4, 0xfab272b, 0x7f0360cb, 0xfdd0926, 0x7efd1c3c, 0x100ee8ad, + 0x7ef6c418, 0x1040c5bb, + 0x7ef05860, 0x1072a048, 0x7ee9d914, 0x10a4784b, 0x7ee34636, 0x10d64dbd, + 0x7edc9fc6, 0x11082096, + 0x7ed5e5c6, 0x1139f0cf, 0x7ecf1837, 0x116bbe60, 0x7ec8371a, 0x119d8941, + 0x7ec14270, 0x11cf516a, + 0x7eba3a39, 0x120116d5, 0x7eb31e78, 0x1232d979, 0x7eabef2c, 0x1264994e, + 0x7ea4ac58, 0x1296564d, + 0x7e9d55fc, 0x12c8106f, 0x7e95ec1a, 0x12f9c7aa, 0x7e8e6eb2, 0x132b7bf9, + 0x7e86ddc6, 0x135d2d53, + 0x7e7f3957, 0x138edbb1, 0x7e778166, 0x13c0870a, 0x7e6fb5f4, 0x13f22f58, + 0x7e67d703, 0x1423d492, + 0x7e5fe493, 0x145576b1, 0x7e57dea7, 0x148715ae, 0x7e4fc53e, 0x14b8b17f, + 0x7e47985b, 0x14ea4a1f, + 0x7e3f57ff, 0x151bdf86, 0x7e37042a, 0x154d71aa, 0x7e2e9cdf, 0x157f0086, + 0x7e26221f, 0x15b08c12, + 0x7e1d93ea, 0x15e21445, 0x7e14f242, 0x16139918, 0x7e0c3d29, 0x16451a83, + 0x7e0374a0, 0x1676987f, + 0x7dfa98a8, 0x16a81305, 0x7df1a942, 0x16d98a0c, 0x7de8a670, 0x170afd8d, + 0x7ddf9034, 0x173c6d80, + 0x7dd6668f, 0x176dd9de, 0x7dcd2981, 0x179f429f, 0x7dc3d90d, 0x17d0a7bc, + 0x7dba7534, 0x1802092c, + 0x7db0fdf8, 0x183366e9, 0x7da77359, 0x1864c0ea, 0x7d9dd55a, 0x18961728, + 0x7d9423fc, 0x18c7699b, + 0x7d8a5f40, 0x18f8b83c, 0x7d808728, 0x192a0304, 0x7d769bb5, 0x195b49ea, + 0x7d6c9ce9, 0x198c8ce7, + 0x7d628ac6, 0x19bdcbf3, 0x7d58654d, 0x19ef0707, 0x7d4e2c7f, 0x1a203e1b, + 0x7d43e05e, 0x1a517128, + 0x7d3980ec, 0x1a82a026, 0x7d2f0e2b, 0x1ab3cb0d, 0x7d24881b, 0x1ae4f1d6, + 0x7d19eebf, 0x1b161479, + 0x7d0f4218, 0x1b4732ef, 0x7d048228, 0x1b784d30, 0x7cf9aef0, 0x1ba96335, + 0x7ceec873, 0x1bda74f6, + 0x7ce3ceb2, 0x1c0b826a, 0x7cd8c1ae, 0x1c3c8b8c, 0x7ccda169, 0x1c6d9053, + 0x7cc26de5, 0x1c9e90b8, + 0x7cb72724, 0x1ccf8cb3, 0x7cabcd28, 0x1d00843d, 0x7ca05ff1, 0x1d31774d, + 0x7c94df83, 0x1d6265dd, + 0x7c894bde, 0x1d934fe5, 0x7c7da505, 0x1dc4355e, 0x7c71eaf9, 0x1df5163f, + 0x7c661dbc, 0x1e25f282, + 0x7c5a3d50, 0x1e56ca1e, 0x7c4e49b7, 0x1e879d0d, 0x7c4242f2, 0x1eb86b46, + 0x7c362904, 0x1ee934c3, + 0x7c29fbee, 0x1f19f97b, 0x7c1dbbb3, 0x1f4ab968, 0x7c116853, 0x1f7b7481, + 0x7c0501d2, 0x1fac2abf, + 0x7bf88830, 0x1fdcdc1b, 0x7bebfb70, 0x200d888d, 0x7bdf5b94, 0x203e300d, + 0x7bd2a89e, 0x206ed295, + 0x7bc5e290, 0x209f701c, 0x7bb9096b, 0x20d0089c, 0x7bac1d31, 0x21009c0c, + 0x7b9f1de6, 0x21312a65, + 0x7b920b89, 0x2161b3a0, 0x7b84e61f, 0x219237b5, 0x7b77ada8, 0x21c2b69c, + 0x7b6a6227, 0x21f3304f, + 0x7b5d039e, 0x2223a4c5, 0x7b4f920e, 0x225413f8, 0x7b420d7a, 0x22847de0, + 0x7b3475e5, 0x22b4e274, + 0x7b26cb4f, 0x22e541af, 0x7b190dbc, 0x23159b88, 0x7b0b3d2c, 0x2345eff8, + 0x7afd59a4, 0x23763ef7, + 0x7aef6323, 0x23a6887f, 0x7ae159ae, 0x23d6cc87, 0x7ad33d45, 0x24070b08, + 0x7ac50dec, 0x243743fa, + 0x7ab6cba4, 0x24677758, 0x7aa8766f, 0x2497a517, 0x7a9a0e50, 0x24c7cd33, + 0x7a8b9348, 0x24f7efa2, + 0x7a7d055b, 0x25280c5e, 0x7a6e648a, 0x2558235f, 0x7a5fb0d8, 0x2588349d, + 0x7a50ea47, 0x25b84012, + 0x7a4210d8, 0x25e845b6, 0x7a332490, 0x26184581, 0x7a24256f, 0x26483f6c, + 0x7a151378, 0x26783370, + 0x7a05eead, 0x26a82186, 0x79f6b711, 0x26d809a5, 0x79e76ca7, 0x2707ebc7, + 0x79d80f6f, 0x2737c7e3, + 0x79c89f6e, 0x27679df4, 0x79b91ca4, 0x27976df1, 0x79a98715, 0x27c737d3, + 0x7999dec4, 0x27f6fb92, + 0x798a23b1, 0x2826b928, 0x797a55e0, 0x2856708d, 0x796a7554, 0x288621b9, + 0x795a820e, 0x28b5cca5, + 0x794a7c12, 0x28e5714b, 0x793a6361, 0x29150fa1, 0x792a37fe, 0x2944a7a2, + 0x7919f9ec, 0x29743946, + 0x7909a92d, 0x29a3c485, 0x78f945c3, 0x29d34958, 0x78e8cfb2, 0x2a02c7b8, + 0x78d846fb, 0x2a323f9e, + 0x78c7aba2, 0x2a61b101, 0x78b6fda8, 0x2a911bdc, 0x78a63d11, 0x2ac08026, + 0x789569df, 0x2aefddd8, + 0x78848414, 0x2b1f34eb, 0x78738bb3, 0x2b4e8558, 0x786280bf, 0x2b7dcf17, + 0x7851633b, 0x2bad1221, + 0x78403329, 0x2bdc4e6f, 0x782ef08b, 0x2c0b83fa, 0x781d9b65, 0x2c3ab2b9, + 0x780c33b8, 0x2c69daa6, + 0x77fab989, 0x2c98fbba, 0x77e92cd9, 0x2cc815ee, 0x77d78daa, 0x2cf72939, + 0x77c5dc01, 0x2d263596, + 0x77b417df, 0x2d553afc, 0x77a24148, 0x2d843964, 0x7790583e, 0x2db330c7, + 0x777e5cc3, 0x2de2211e, + 0x776c4edb, 0x2e110a62, 0x775a2e89, 0x2e3fec8b, 0x7747fbce, 0x2e6ec792, + 0x7735b6af, 0x2e9d9b70, + 0x77235f2d, 0x2ecc681e, 0x7710f54c, 0x2efb2d95, 0x76fe790e, 0x2f29ebcc, + 0x76ebea77, 0x2f58a2be, + 0x76d94989, 0x2f875262, 0x76c69647, 0x2fb5fab2, 0x76b3d0b4, 0x2fe49ba7, + 0x76a0f8d2, 0x30133539, + 0x768e0ea6, 0x3041c761, 0x767b1231, 0x30705217, 0x76680376, 0x309ed556, + 0x7654e279, 0x30cd5115, + 0x7641af3d, 0x30fbc54d, 0x762e69c4, 0x312a31f8, 0x761b1211, 0x3158970e, + 0x7607a828, 0x3186f487, + 0x75f42c0b, 0x31b54a5e, 0x75e09dbd, 0x31e39889, 0x75ccfd42, 0x3211df04, + 0x75b94a9c, 0x32401dc6, + 0x75a585cf, 0x326e54c7, 0x7591aedd, 0x329c8402, 0x757dc5ca, 0x32caab6f, + 0x7569ca99, 0x32f8cb07, + 0x7555bd4c, 0x3326e2c3, 0x75419de7, 0x3354f29b, 0x752d6c6c, 0x3382fa88, + 0x751928e0, 0x33b0fa84, + 0x7504d345, 0x33def287, 0x74f06b9e, 0x340ce28b, 0x74dbf1ef, 0x343aca87, + 0x74c7663a, 0x3468aa76, + 0x74b2c884, 0x34968250, 0x749e18cd, 0x34c4520d, 0x7489571c, 0x34f219a8, + 0x74748371, 0x351fd918, + 0x745f9dd1, 0x354d9057, 0x744aa63f, 0x357b3f5d, 0x74359cbd, 0x35a8e625, + 0x74208150, 0x35d684a6, + 0x740b53fb, 0x36041ad9, 0x73f614c0, 0x3631a8b8, 0x73e0c3a3, 0x365f2e3b, + 0x73cb60a8, 0x368cab5c, + 0x73b5ebd1, 0x36ba2014, 0x73a06522, 0x36e78c5b, 0x738acc9e, 0x3714f02a, + 0x73752249, 0x37424b7b, + 0x735f6626, 0x376f9e46, 0x73499838, 0x379ce885, 0x7333b883, 0x37ca2a30, + 0x731dc70a, 0x37f76341, + 0x7307c3d0, 0x382493b0, 0x72f1aed9, 0x3851bb77, 0x72db8828, 0x387eda8e, + 0x72c54fc1, 0x38abf0ef, + 0x72af05a7, 0x38d8fe93, 0x7298a9dd, 0x39060373, 0x72823c67, 0x3932ff87, + 0x726bbd48, 0x395ff2c9, + 0x72552c85, 0x398cdd32, 0x723e8a20, 0x39b9bebc, 0x7227d61c, 0x39e6975e, + 0x7211107e, 0x3a136712, + 0x71fa3949, 0x3a402dd2, 0x71e35080, 0x3a6ceb96, 0x71cc5626, 0x3a99a057, + 0x71b54a41, 0x3ac64c0f, + 0x719e2cd2, 0x3af2eeb7, 0x7186fdde, 0x3b1f8848, 0x716fbd68, 0x3b4c18ba, + 0x71586b74, 0x3b78a007, + 0x71410805, 0x3ba51e29, 0x7129931f, 0x3bd19318, 0x71120cc5, 0x3bfdfecd, + 0x70fa74fc, 0x3c2a6142, + 0x70e2cbc6, 0x3c56ba70, 0x70cb1128, 0x3c830a50, 0x70b34525, 0x3caf50da, + 0x709b67c0, 0x3cdb8e09, + 0x708378ff, 0x3d07c1d6, 0x706b78e3, 0x3d33ec39, 0x70536771, 0x3d600d2c, + 0x703b44ad, 0x3d8c24a8, + 0x7023109a, 0x3db832a6, 0x700acb3c, 0x3de4371f, 0x6ff27497, 0x3e10320d, + 0x6fda0cae, 0x3e3c2369, + 0x6fc19385, 0x3e680b2c, 0x6fa90921, 0x3e93e950, 0x6f906d84, 0x3ebfbdcd, + 0x6f77c0b3, 0x3eeb889c, + 0x6f5f02b2, 0x3f1749b8, 0x6f463383, 0x3f430119, 0x6f2d532c, 0x3f6eaeb8, + 0x6f1461b0, 0x3f9a5290, + 0x6efb5f12, 0x3fc5ec98, 0x6ee24b57, 0x3ff17cca, 0x6ec92683, 0x401d0321, + 0x6eaff099, 0x40487f94, + 0x6e96a99d, 0x4073f21d, 0x6e7d5193, 0x409f5ab6, 0x6e63e87f, 0x40cab958, + 0x6e4a6e66, 0x40f60dfb, + 0x6e30e34a, 0x4121589b, 0x6e174730, 0x414c992f, 0x6dfd9a1c, 0x4177cfb1, + 0x6de3dc11, 0x41a2fc1a, + 0x6dca0d14, 0x41ce1e65, 0x6db02d29, 0x41f93689, 0x6d963c54, 0x42244481, + 0x6d7c3a98, 0x424f4845, + 0x6d6227fa, 0x427a41d0, 0x6d48047e, 0x42a5311b, 0x6d2dd027, 0x42d0161e, + 0x6d138afb, 0x42faf0d4, + 0x6cf934fc, 0x4325c135, 0x6cdece2f, 0x4350873c, 0x6cc45698, 0x437b42e1, + 0x6ca9ce3b, 0x43a5f41e, + 0x6c8f351c, 0x43d09aed, 0x6c748b3f, 0x43fb3746, 0x6c59d0a9, 0x4425c923, + 0x6c3f055d, 0x4450507e, + 0x6c242960, 0x447acd50, 0x6c093cb6, 0x44a53f93, 0x6bee3f62, 0x44cfa740, + 0x6bd3316a, 0x44fa0450, + 0x6bb812d1, 0x452456bd, 0x6b9ce39b, 0x454e9e80, 0x6b81a3cd, 0x4578db93, + 0x6b66536b, 0x45a30df0, + 0x6b4af279, 0x45cd358f, 0x6b2f80fb, 0x45f7526b, 0x6b13fef5, 0x4621647d, + 0x6af86c6c, 0x464b6bbe, + 0x6adcc964, 0x46756828, 0x6ac115e2, 0x469f59b4, 0x6aa551e9, 0x46c9405c, + 0x6a897d7d, 0x46f31c1a, + 0x6a6d98a4, 0x471cece7, 0x6a51a361, 0x4746b2bc, 0x6a359db9, 0x47706d93, + 0x6a1987b0, 0x479a1d67, + 0x69fd614a, 0x47c3c22f, 0x69e12a8c, 0x47ed5be6, 0x69c4e37a, 0x4816ea86, + 0x69a88c19, 0x48406e08, + 0x698c246c, 0x4869e665, 0x696fac78, 0x48935397, 0x69532442, 0x48bcb599, + 0x69368bce, 0x48e60c62, + 0x6919e320, 0x490f57ee, 0x68fd2a3d, 0x49389836, 0x68e06129, 0x4961cd33, + 0x68c387e9, 0x498af6df, + 0x68a69e81, 0x49b41533, 0x6889a4f6, 0x49dd282a, 0x686c9b4b, 0x4a062fbd, + 0x684f8186, 0x4a2f2be6, + 0x683257ab, 0x4a581c9e, 0x68151dbe, 0x4a8101de, 0x67f7d3c5, 0x4aa9dba2, + 0x67da79c3, 0x4ad2a9e2, + 0x67bd0fbd, 0x4afb6c98, 0x679f95b7, 0x4b2423be, 0x67820bb7, 0x4b4ccf4d, + 0x676471c0, 0x4b756f40, + 0x6746c7d8, 0x4b9e0390, 0x67290e02, 0x4bc68c36, 0x670b4444, 0x4bef092d, + 0x66ed6aa1, 0x4c177a6e, + 0x66cf8120, 0x4c3fdff4, 0x66b187c3, 0x4c6839b7, 0x66937e91, 0x4c9087b1, + 0x6675658c, 0x4cb8c9dd, + 0x66573cbb, 0x4ce10034, 0x66390422, 0x4d092ab0, 0x661abbc5, 0x4d31494b, + 0x65fc63a9, 0x4d595bfe, + 0x65ddfbd3, 0x4d8162c4, 0x65bf8447, 0x4da95d96, 0x65a0fd0b, 0x4dd14c6e, + 0x65826622, 0x4df92f46, + 0x6563bf92, 0x4e210617, 0x6545095f, 0x4e48d0dd, 0x6526438f, 0x4e708f8f, + 0x65076e25, 0x4e984229, + 0x64e88926, 0x4ebfe8a5, 0x64c99498, 0x4ee782fb, 0x64aa907f, 0x4f0f1126, + 0x648b7ce0, 0x4f369320, + 0x646c59bf, 0x4f5e08e3, 0x644d2722, 0x4f857269, 0x642de50d, 0x4faccfab, + 0x640e9386, 0x4fd420a4, + 0x63ef3290, 0x4ffb654d, 0x63cfc231, 0x50229da1, 0x63b0426d, 0x5049c999, + 0x6390b34a, 0x5070e92f, + 0x637114cc, 0x5097fc5e, 0x635166f9, 0x50bf031f, 0x6331a9d4, 0x50e5fd6d, + 0x6311dd64, 0x510ceb40, + 0x62f201ac, 0x5133cc94, 0x62d216b3, 0x515aa162, 0x62b21c7b, 0x518169a5, + 0x6292130c, 0x51a82555, + 0x6271fa69, 0x51ced46e, 0x6251d298, 0x51f576ea, 0x62319b9d, 0x521c0cc2, + 0x6211557e, 0x524295f0, + 0x61f1003f, 0x5269126e, 0x61d09be5, 0x528f8238, 0x61b02876, 0x52b5e546, + 0x618fa5f7, 0x52dc3b92, + 0x616f146c, 0x53028518, 0x614e73da, 0x5328c1d0, 0x612dc447, 0x534ef1b5, + 0x610d05b7, 0x537514c2, + 0x60ec3830, 0x539b2af0, 0x60cb5bb7, 0x53c13439, 0x60aa7050, 0x53e73097, + 0x60897601, 0x540d2005, + 0x60686ccf, 0x5433027d, 0x604754bf, 0x5458d7f9, 0x60262dd6, 0x547ea073, + 0x6004f819, 0x54a45be6, + 0x5fe3b38d, 0x54ca0a4b, 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0x8b0f9462, + 0xcc210d79, 0x8afb2cbb, 0xcc4f057c, 0x8ae6d720, 0xcc7d0578, 0x8ad29394, + 0xccab0d65, 0x8abe6219, + 0xccd91d3d, 0x8aaa42b4, 0xcd0734f9, 0x8a963567, 0xcd355491, 0x8a823a36, + 0xcd637bfe, 0x8a6e5123, + 0xcd91ab39, 0x8a5a7a31, 0xcdbfe23a, 0x8a46b564, 0xcdee20fc, 0x8a3302be, + 0xce1c6777, 0x8a1f6243, + 0xce4ab5a2, 0x8a0bd3f5, 0xce790b79, 0x89f857d8, 0xcea768f2, 0x89e4edef, + 0xced5ce08, 0x89d1963c, + 0xcf043ab3, 0x89be50c3, 0xcf32aeeb, 0x89ab1d87, 0xcf612aaa, 0x8997fc8a, + 0xcf8fade9, 0x8984edcf, + 0xcfbe389f, 0x8971f15a, 0xcfeccac7, 0x895f072e, 0xd01b6459, 0x894c2f4c, + 0xd04a054e, 0x893969b9, + 0xd078ad9e, 0x8926b677, 0xd0a75d42, 0x89141589, 0xd0d61434, 0x890186f2, + 0xd104d26b, 0x88ef0ab4, + 0xd13397e2, 0x88dca0d3, 0xd1626490, 0x88ca4951, 0xd191386e, 0x88b80432, + 0xd1c01375, 0x88a5d177, + 0xd1eef59e, 0x8893b125, 0xd21ddee2, 0x8881a33d, 0xd24ccf39, 0x886fa7c2, + 0xd27bc69c, 0x885dbeb8, + 0xd2aac504, 0x884be821, 0xd2d9ca6a, 0x883a23ff, 0xd308d6c7, 0x88287256, + 0xd337ea12, 0x8816d327, + 0xd3670446, 0x88054677, 0xd396255a, 0x87f3cc48, 0xd3c54d47, 0x87e2649b, + 0xd3f47c06, 0x87d10f75, + 0xd423b191, 0x87bfccd7, 0xd452eddf, 0x87ae9cc5, 0xd48230e9, 0x879d7f41, + 0xd4b17aa8, 0x878c744d, + 0xd4e0cb15, 0x877b7bec, 0xd5102228, 0x876a9621, 0xd53f7fda, 0x8759c2ef, + 0xd56ee424, 0x87490258, + 0xd59e4eff, 0x8738545e, 0xd5cdc062, 0x8727b905, 0xd5fd3848, 0x8717304e, + 0xd62cb6a8, 0x8706ba3d, + 0xd65c3b7b, 0x86f656d3, 0xd68bc6ba, 0x86e60614, 0xd6bb585e, 0x86d5c802, + 0xd6eaf05f, 0x86c59c9f, + 0xd71a8eb5, 0x86b583ee, 0xd74a335b, 0x86a57df2, 0xd779de47, 0x86958aac, + 0xd7a98f73, 0x8685aa20, + 0xd7d946d8, 0x8675dc4f, 0xd809046e, 0x8666213c, 0xd838c82d, 0x865678eb, + 0xd868920f, 0x8646e35c, + 0xd898620c, 0x86376092, 0xd8c8381d, 0x8627f091, 0xd8f81439, 0x86189359, + 0xd927f65b, 0x860948ef, + 0xd957de7a, 0x85fa1153, 0xd987cc90, 0x85eaec88, 0xd9b7c094, 0x85dbda91, + 0xd9e7ba7f, 0x85ccdb70, + 0xda17ba4a, 0x85bdef28, 0xda47bfee, 0x85af15b9, 0xda77cb63, 0x85a04f28, + 0xdaa7dca1, 0x85919b76, + 0xdad7f3a2, 0x8582faa5, 0xdb08105e, 0x85746cb8, 0xdb3832cd, 0x8565f1b0, + 0xdb685ae9, 0x85578991, + 0xdb9888a8, 0x8549345c, 0xdbc8bc06, 0x853af214, 0xdbf8f4f8, 0x852cc2bb, + 0xdc293379, 0x851ea652, + 0xdc597781, 0x85109cdd, 0xdc89c109, 0x8502a65c, 0xdcba1008, 0x84f4c2d4, + 0xdcea6478, 0x84e6f244, + 0xdd1abe51, 0x84d934b1, 0xdd4b1d8c, 0x84cb8a1b, 0xdd7b8220, 0x84bdf286, + 0xddabec08, 0x84b06df2, + 0xdddc5b3b, 0x84a2fc62, 0xde0ccfb1, 0x84959dd9, 0xde3d4964, 0x84885258, + 0xde6dc84b, 0x847b19e1, + 0xde9e4c60, 0x846df477, 0xdeced59b, 0x8460e21a, 0xdeff63f4, 0x8453e2cf, + 0xdf2ff764, 0x8446f695, + 0xdf608fe4, 0x843a1d70, 0xdf912d6b, 0x842d5762, 0xdfc1cff3, 0x8420a46c, + 0xdff27773, 0x84140490, + 0xe02323e5, 0x840777d0, 0xe053d541, 0x83fafe2e, 0xe0848b7f, 0x83ee97ad, + 0xe0b54698, 0x83e2444d, + 0xe0e60685, 0x83d60412, 0xe116cb3d, 0x83c9d6fc, 0xe14794ba, 0x83bdbd0e, + 0xe17862f3, 0x83b1b649, + 0xe1a935e2, 0x83a5c2b0, 0xe1da0d7e, 0x8399e244, 0xe20ae9c1, 0x838e1507, + 0xe23bcaa2, 0x83825afb, + 0xe26cb01b, 0x8376b422, 0xe29d9a23, 0x836b207d, 0xe2ce88b3, 0x835fa00f, + 0xe2ff7bc3, 0x835432d8, + 0xe330734d, 0x8348d8dc, 0xe3616f48, 0x833d921b, 0xe3926fad, 0x83325e97, + 0xe3c37474, 0x83273e52, + 0xe3f47d96, 0x831c314e, 0xe4258b0a, 0x8311378d, 0xe4569ccb, 0x83065110, + 0xe487b2d0, 0x82fb7dd8, + 0xe4b8cd11, 0x82f0bde8, 0xe4e9eb87, 0x82e61141, 0xe51b0e2a, 0x82db77e5, + 0xe54c34f3, 0x82d0f1d5, + 0xe57d5fda, 0x82c67f14, 0xe5ae8ed8, 0x82bc1fa2, 0xe5dfc1e5, 0x82b1d381, + 0xe610f8f9, 0x82a79ab3, + 0xe642340d, 0x829d753a, 0xe6737319, 0x82936317, 0xe6a4b616, 0x8289644b, + 0xe6d5fcfc, 0x827f78d8, + 0xe70747c4, 0x8275a0c0, 0xe7389665, 0x826bdc04, 0xe769e8d8, 0x82622aa6, + 0xe79b3f16, 0x82588ca7, + 0xe7cc9917, 0x824f0208, 0xe7fdf6d4, 0x82458acc, 0xe82f5844, 0x823c26f3, + 0xe860bd61, 0x8232d67f, + 0xe8922622, 0x82299971, 0xe8c39280, 0x82206fcc, 0xe8f50273, 0x82175990, + 0xe92675f4, 0x820e56be, + 0xe957ecfb, 0x82056758, 0xe9896781, 0x81fc8b60, 0xe9bae57d, 0x81f3c2d7, + 0xe9ec66e8, 0x81eb0dbe, + 0xea1debbb, 0x81e26c16, 0xea4f73ee, 0x81d9dde1, 0xea80ff7a, 0x81d16321, + 0xeab28e56, 0x81c8fbd6, + 0xeae4207a, 0x81c0a801, 0xeb15b5e1, 0x81b867a5, 0xeb474e81, 0x81b03ac2, + 0xeb78ea52, 0x81a82159, + 0xebaa894f, 0x81a01b6d, 0xebdc2b6e, 0x819828fd, 0xec0dd0a8, 0x81904a0c, + 0xec3f78f6, 0x81887e9a, + 0xec71244f, 0x8180c6a9, 0xeca2d2ad, 0x8179223a, 0xecd48407, 0x8171914e, + 0xed063856, 0x816a13e6, + 0xed37ef91, 0x8162aa04, 0xed69a9b3, 0x815b53a8, 0xed9b66b2, 0x815410d4, + 0xedcd2687, 0x814ce188, + 0xedfee92b, 0x8145c5c7, 0xee30ae96, 0x813ebd90, 0xee6276bf, 0x8137c8e6, + 0xee9441a0, 0x8130e7c9, + 0xeec60f31, 0x812a1a3a, 0xeef7df6a, 0x8123603a, 0xef29b243, 0x811cb9ca, + 0xef5b87b5, 0x811626ec, + 0xef8d5fb8, 0x810fa7a0, 0xefbf3a45, 0x81093be8, 0xeff11753, 0x8102e3c4, + 0xf022f6da, 0x80fc9f35, + 0xf054d8d5, 0x80f66e3c, 0xf086bd39, 0x80f050db, 0xf0b8a401, 0x80ea4712, + 0xf0ea8d24, 0x80e450e2, + 0xf11c789a, 0x80de6e4c, 0xf14e665c, 0x80d89f51, 0xf1805662, 0x80d2e3f2, + 0xf1b248a5, 0x80cd3c2f, + 0xf1e43d1c, 0x80c7a80a, 0xf21633c0, 0x80c22784, 0xf2482c8a, 0x80bcba9d, + 0xf27a2771, 0x80b76156, + 0xf2ac246e, 0x80b21baf, 0xf2de2379, 0x80ace9ab, 0xf310248a, 0x80a7cb49, + 0xf342279b, 0x80a2c08b, + 0xf3742ca2, 0x809dc971, 0xf3a63398, 0x8098e5fb, 0xf3d83c77, 0x8094162c, + 0xf40a4735, 0x808f5a02, + 0xf43c53cb, 0x808ab180, 0xf46e6231, 0x80861ca6, 0xf4a07261, 0x80819b74, + 0xf4d28451, 0x807d2dec, + 0xf50497fb, 0x8078d40d, 0xf536ad56, 0x80748dd9, 0xf568c45b, 0x80705b50, + 0xf59add02, 0x806c3c74, + 0xf5ccf743, 0x80683143, 0xf5ff1318, 0x806439c0, 0xf6313077, 0x806055eb, + 0xf6634f59, 0x805c85c4, + 0xf6956fb7, 0x8058c94c, 0xf6c79188, 0x80552084, 0xf6f9b4c6, 0x80518b6b, + 0xf72bd967, 0x804e0a04, + 0xf75dff66, 0x804a9c4d, 0xf79026b9, 0x80474248, 0xf7c24f59, 0x8043fbf6, + 0xf7f4793e, 0x8040c956, + 0xf826a462, 0x803daa6a, 0xf858d0bb, 0x803a9f31, 0xf88afe42, 0x8037a7ac, + 0xf8bd2cef, 0x8034c3dd, + 0xf8ef5cbb, 0x8031f3c2, 0xf9218d9e, 0x802f375d, 0xf953bf91, 0x802c8ead, + 0xf985f28a, 0x8029f9b4, + 0xf9b82684, 0x80277872, 0xf9ea5b75, 0x80250ae7, 0xfa1c9157, 0x8022b114, + 0xfa4ec821, 0x80206af8, + 0xfa80ffcb, 0x801e3895, 0xfab3384f, 0x801c19ea, 0xfae571a4, 0x801a0ef8, + 0xfb17abc2, 0x801817bf, + 0xfb49e6a3, 0x80163440, 0xfb7c223d, 0x8014647b, 0xfbae5e89, 0x8012a86f, + 0xfbe09b80, 0x8011001f, + 0xfc12d91a, 0x800f6b88, 0xfc45174e, 0x800deaad, 0xfc775616, 0x800c7d8c, + 0xfca9956a, 0x800b2427, + 0xfcdbd541, 0x8009de7e, 0xfd0e1594, 0x8008ac90, 0xfd40565c, 0x80078e5e, + 0xfd729790, 0x800683e8, + 0xfda4d929, 0x80058d2f, 0xfdd71b1e, 0x8004aa32, 0xfe095d69, 0x8003daf1, + 0xfe3ba002, 0x80031f6d, + 0xfe6de2e0, 0x800277a6, 0xfea025fd, 0x8001e39b, 0xfed2694f, 0x8001634e, + 0xff04acd0, 0x8000f6bd, + 0xff36f078, 0x80009dea, 0xff69343f, 0x800058d4, 0xff9b781d, 0x8000277a, + 0xffcdbc0b, 0x800009df, + +}; + + +/* +* @brief Q15 Twiddle factors Table +*/ + +/** +* \par +* Example code for Q15 Twiddle factors Generation:: +* \par +* 
for(i = 0; i< 3N/4; i++)    
+* {    
+*	twiddleCoefQ15[2*i]= cos(i * 2*PI/(float)N);    
+*	twiddleCoefQ15[2*i+1]= sin(i * 2*PI/(float)N);    
+* }
+* \par +* where N = 4096 and PI = 3.14159265358979 +* \par +* Cos and Sin values are interleaved fashion +* \par +* Convert Floating point to Q15(Fixed point 1.15): +* round(twiddleCoefQ15(i) * pow(2, 15)) +* +*/ + +const q15_t ALIGN4 twiddleCoefQ15[6144] = { + + 0x7fff, 0x0, 0x7fff, 0x32, 0x7fff, 0x65, 0x7fff, 0x97, + 0x7fff, 0xc9, 0x7fff, 0xfb, 0x7fff, 0x12e, 0x7ffe, 0x160, + 0x7ffe, 0x192, 0x7ffd, 0x1c4, 0x7ffc, 0x1f7, 0x7ffb, 0x229, + 0x7ffa, 0x25b, 0x7ff9, 0x28d, 0x7ff8, 0x2c0, 0x7ff7, 0x2f2, + 0x7ff6, 0x324, 0x7ff5, 0x356, 0x7ff4, 0x389, 0x7ff2, 0x3bb, + 0x7ff1, 0x3ed, 0x7fef, 0x41f, 0x7fed, 0x452, 0x7fec, 0x484, + 0x7fea, 0x4b6, 0x7fe8, 0x4e8, 0x7fe6, 0x51b, 0x7fe4, 0x54d, + 0x7fe2, 0x57f, 0x7fe0, 0x5b1, 0x7fdd, 0x5e3, 0x7fdb, 0x616, + 0x7fd9, 0x648, 0x7fd6, 0x67a, 0x7fd3, 0x6ac, 0x7fd1, 0x6de, + 0x7fce, 0x711, 0x7fcb, 0x743, 0x7fc8, 0x775, 0x7fc5, 0x7a7, + 0x7fc2, 0x7d9, 0x7fbf, 0x80c, 0x7fbc, 0x83e, 0x7fb9, 0x870, + 0x7fb5, 0x8a2, 0x7fb2, 0x8d4, 0x7fae, 0x906, 0x7fab, 0x938, + 0x7fa7, 0x96b, 0x7fa3, 0x99d, 0x7fa0, 0x9cf, 0x7f9c, 0xa01, + 0x7f98, 0xa33, 0x7f94, 0xa65, 0x7f90, 0xa97, 0x7f8b, 0xac9, + 0x7f87, 0xafb, 0x7f83, 0xb2d, 0x7f7e, 0xb60, 0x7f7a, 0xb92, + 0x7f75, 0xbc4, 0x7f71, 0xbf6, 0x7f6c, 0xc28, 0x7f67, 0xc5a, + 0x7f62, 0xc8c, 0x7f5d, 0xcbe, 0x7f58, 0xcf0, 0x7f53, 0xd22, + 0x7f4e, 0xd54, 0x7f49, 0xd86, 0x7f43, 0xdb8, 0x7f3e, 0xdea, + 0x7f38, 0xe1c, 0x7f33, 0xe4e, 0x7f2d, 0xe80, 0x7f27, 0xeb2, + 0x7f22, 0xee4, 0x7f1c, 0xf15, 0x7f16, 0xf47, 0x7f10, 0xf79, + 0x7f0a, 0xfab, 0x7f03, 0xfdd, 0x7efd, 0x100f, 0x7ef7, 0x1041, + 0x7ef0, 0x1073, 0x7eea, 0x10a4, 0x7ee3, 0x10d6, 0x7edd, 0x1108, + 0x7ed6, 0x113a, 0x7ecf, 0x116c, 0x7ec8, 0x119e, 0x7ec1, 0x11cf, + 0x7eba, 0x1201, 0x7eb3, 0x1233, 0x7eac, 0x1265, 0x7ea5, 0x1296, + 0x7e9d, 0x12c8, 0x7e96, 0x12fa, 0x7e8e, 0x132b, 0x7e87, 0x135d, + 0x7e7f, 0x138f, 0x7e78, 0x13c1, 0x7e70, 0x13f2, 0x7e68, 0x1424, + 0x7e60, 0x1455, 0x7e58, 0x1487, 0x7e50, 0x14b9, 0x7e48, 0x14ea, + 0x7e3f, 0x151c, 0x7e37, 0x154d, 0x7e2f, 0x157f, 0x7e26, 0x15b1, + 0x7e1e, 0x15e2, 0x7e15, 0x1614, 0x7e0c, 0x1645, 0x7e03, 0x1677, + 0x7dfb, 0x16a8, 0x7df2, 0x16da, 0x7de9, 0x170b, 0x7de0, 0x173c, + 0x7dd6, 0x176e, 0x7dcd, 0x179f, 0x7dc4, 0x17d1, 0x7dba, 0x1802, + 0x7db1, 0x1833, 0x7da7, 0x1865, 0x7d9e, 0x1896, 0x7d94, 0x18c7, + 0x7d8a, 0x18f9, 0x7d81, 0x192a, 0x7d77, 0x195b, 0x7d6d, 0x198d, + 0x7d63, 0x19be, 0x7d58, 0x19ef, 0x7d4e, 0x1a20, 0x7d44, 0x1a51, + 0x7d3a, 0x1a83, 0x7d2f, 0x1ab4, 0x7d25, 0x1ae5, 0x7d1a, 0x1b16, + 0x7d0f, 0x1b47, 0x7d05, 0x1b78, 0x7cfa, 0x1ba9, 0x7cef, 0x1bda, + 0x7ce4, 0x1c0c, 0x7cd9, 0x1c3d, 0x7cce, 0x1c6e, 0x7cc2, 0x1c9f, + 0x7cb7, 0x1cd0, 0x7cac, 0x1d01, 0x7ca0, 0x1d31, 0x7c95, 0x1d62, + 0x7c89, 0x1d93, 0x7c7e, 0x1dc4, 0x7c72, 0x1df5, 0x7c66, 0x1e26, + 0x7c5a, 0x1e57, 0x7c4e, 0x1e88, 0x7c42, 0x1eb8, 0x7c36, 0x1ee9, + 0x7c2a, 0x1f1a, 0x7c1e, 0x1f4b, 0x7c11, 0x1f7b, 0x7c05, 0x1fac, + 0x7bf9, 0x1fdd, 0x7bec, 0x200e, 0x7bdf, 0x203e, 0x7bd3, 0x206f, + 0x7bc6, 0x209f, 0x7bb9, 0x20d0, 0x7bac, 0x2101, 0x7b9f, 0x2131, + 0x7b92, 0x2162, 0x7b85, 0x2192, 0x7b78, 0x21c3, 0x7b6a, 0x21f3, + 0x7b5d, 0x2224, 0x7b50, 0x2254, 0x7b42, 0x2284, 0x7b34, 0x22b5, + 0x7b27, 0x22e5, 0x7b19, 0x2316, 0x7b0b, 0x2346, 0x7afd, 0x2376, + 0x7aef, 0x23a7, 0x7ae1, 0x23d7, 0x7ad3, 0x2407, 0x7ac5, 0x2437, + 0x7ab7, 0x2467, 0x7aa8, 0x2498, 0x7a9a, 0x24c8, 0x7a8c, 0x24f8, + 0x7a7d, 0x2528, 0x7a6e, 0x2558, 0x7a60, 0x2588, 0x7a51, 0x25b8, + 0x7a42, 0x25e8, 0x7a33, 0x2618, 0x7a24, 0x2648, 0x7a15, 0x2678, + 0x7a06, 0x26a8, 0x79f7, 0x26d8, 0x79e7, 0x2708, 0x79d8, 0x2738, + 0x79c9, 0x2768, 0x79b9, 0x2797, 0x79aa, 0x27c7, 0x799a, 0x27f7, + 0x798a, 0x2827, 0x797a, 0x2856, 0x796a, 0x2886, 0x795b, 0x28b6, + 0x794a, 0x28e5, 0x793a, 0x2915, 0x792a, 0x2945, 0x791a, 0x2974, + 0x790a, 0x29a4, 0x78f9, 0x29d3, 0x78e9, 0x2a03, 0x78d8, 0x2a32, + 0x78c8, 0x2a62, 0x78b7, 0x2a91, 0x78a6, 0x2ac1, 0x7895, 0x2af0, + 0x7885, 0x2b1f, 0x7874, 0x2b4f, 0x7863, 0x2b7e, 0x7851, 0x2bad, + 0x7840, 0x2bdc, 0x782f, 0x2c0c, 0x781e, 0x2c3b, 0x780c, 0x2c6a, + 0x77fb, 0x2c99, 0x77e9, 0x2cc8, 0x77d8, 0x2cf7, 0x77c6, 0x2d26, + 0x77b4, 0x2d55, 0x77a2, 0x2d84, 0x7790, 0x2db3, 0x777e, 0x2de2, + 0x776c, 0x2e11, 0x775a, 0x2e40, 0x7748, 0x2e6f, 0x7736, 0x2e9e, + 0x7723, 0x2ecc, 0x7711, 0x2efb, 0x76fe, 0x2f2a, 0x76ec, 0x2f59, + 0x76d9, 0x2f87, 0x76c7, 0x2fb6, 0x76b4, 0x2fe5, 0x76a1, 0x3013, + 0x768e, 0x3042, 0x767b, 0x3070, 0x7668, 0x309f, 0x7655, 0x30cd, + 0x7642, 0x30fc, 0x762e, 0x312a, 0x761b, 0x3159, 0x7608, 0x3187, + 0x75f4, 0x31b5, 0x75e1, 0x31e4, 0x75cd, 0x3212, 0x75b9, 0x3240, + 0x75a6, 0x326e, 0x7592, 0x329d, 0x757e, 0x32cb, 0x756a, 0x32f9, + 0x7556, 0x3327, 0x7542, 0x3355, 0x752d, 0x3383, 0x7519, 0x33b1, + 0x7505, 0x33df, 0x74f0, 0x340d, 0x74dc, 0x343b, 0x74c7, 0x3469, + 0x74b3, 0x3497, 0x749e, 0x34c4, 0x7489, 0x34f2, 0x7475, 0x3520, + 0x7460, 0x354e, 0x744b, 0x357b, 0x7436, 0x35a9, 0x7421, 0x35d7, + 0x740b, 0x3604, 0x73f6, 0x3632, 0x73e1, 0x365f, 0x73cb, 0x368d, + 0x73b6, 0x36ba, 0x73a0, 0x36e8, 0x738b, 0x3715, 0x7375, 0x3742, + 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0xab81, 0x9fda, 0xaba7, 0x9fb9, + 0xabcd, 0x9f98, 0xabf3, 0x9f77, 0xac19, 0x9f56, 0xac3f, 0x9f35, + 0xac65, 0x9f14, 0xac8b, 0x9ef3, 0xacb1, 0x9ed2, 0xacd7, 0x9eb2, + 0xacfd, 0x9e91, 0xad24, 0x9e70, 0xad4a, 0x9e50, 0xad70, 0x9e2f, + 0xad97, 0x9e0f, 0xadbd, 0x9def, 0xade4, 0x9dce, 0xae0b, 0x9dae, + 0xae31, 0x9d8e, 0xae58, 0x9d6e, 0xae7f, 0x9d4e, 0xaea5, 0x9d2e, + 0xaecc, 0x9d0e, 0xaef3, 0x9cee, 0xaf1a, 0x9cce, 0xaf41, 0x9caf, + 0xaf68, 0x9c8f, 0xaf8f, 0x9c6f, 0xafb6, 0x9c50, 0xafdd, 0x9c30, + 0xb005, 0x9c11, 0xb02c, 0x9bf1, 0xb053, 0x9bd2, 0xb07b, 0x9bb3, + 0xb0a2, 0x9b94, 0xb0c9, 0x9b75, 0xb0f1, 0x9b55, 0xb118, 0x9b36, + 0xb140, 0x9b17, 0xb168, 0x9af9, 0xb18f, 0x9ada, 0xb1b7, 0x9abb, + 0xb1df, 0x9a9c, 0xb207, 0x9a7e, 0xb22f, 0x9a5f, 0xb257, 0x9a40, + 0xb27f, 0x9a22, 0xb2a7, 0x9a04, 0xb2cf, 0x99e5, 0xb2f7, 0x99c7, + 0xb31f, 0x99a9, 0xb347, 0x998b, 0xb36f, 0x996d, 0xb398, 0x994e, + 0xb3c0, 0x9930, 0xb3e9, 0x9913, 0xb411, 0x98f5, 0xb439, 0x98d7, + 0xb462, 0x98b9, 0xb48b, 0x989c, 0xb4b3, 0x987e, 0xb4dc, 0x9860, + 0xb505, 0x9843, 0xb52d, 0x9826, 0xb556, 0x9808, 0xb57f, 0x97eb, + 0xb5a8, 0x97ce, 0xb5d1, 0x97b0, 0xb5fa, 0x9793, 0xb623, 0x9776, + 0xb64c, 0x9759, 0xb675, 0x973c, 0xb69e, 0x9720, 0xb6c7, 0x9703, + 0xb6f1, 0x96e6, 0xb71a, 0x96c9, 0xb743, 0x96ad, 0xb76d, 0x9690, + 0xb796, 0x9674, 0xb7c0, 0x9657, 0xb7e9, 0x963b, 0xb813, 0x961f, + 0xb83c, 0x9603, 0xb866, 0x95e6, 0xb890, 0x95ca, 0xb8b9, 0x95ae, + 0xb8e3, 0x9592, 0xb90d, 0x9577, 0xb937, 0x955b, 0xb961, 0x953f, + 0xb98b, 0x9523, 0xb9b5, 0x9508, 0xb9df, 0x94ec, 0xba09, 0x94d0, + 0xba33, 0x94b5, 0xba5d, 0x949a, 0xba87, 0x947e, 0xbab1, 0x9463, + 0xbadc, 0x9448, 0xbb06, 0x942d, 0xbb30, 0x9412, 0xbb5b, 0x93f7, + 0xbb85, 0x93dc, 0xbbb0, 0x93c1, 0xbbda, 0x93a6, 0xbc05, 0x938b, + 0xbc2f, 0x9371, 0xbc5a, 0x9356, 0xbc85, 0x933c, 0xbcaf, 0x9321, + 0xbcda, 0x9307, 0xbd05, 0x92ec, 0xbd30, 0x92d2, 0xbd5b, 0x92b8, + 0xbd86, 0x929e, 0xbdb1, 0x9284, 0xbddc, 0x926a, 0xbe07, 0x9250, + 0xbe32, 0x9236, 0xbe5d, 0x921c, 0xbe88, 0x9202, 0xbeb3, 0x91e9, + 0xbedf, 0x91cf, 0xbf0a, 0x91b6, 0xbf35, 0x919c, 0xbf61, 0x9183, + 0xbf8c, 0x9169, 0xbfb8, 0x9150, 0xbfe3, 0x9137, 0xc00f, 0x911e, + 0xc03a, 0x9105, 0xc066, 0x90ec, 0xc091, 0x90d3, 0xc0bd, 0x90ba, + 0xc0e9, 0x90a1, 0xc114, 0x9088, 0xc140, 0x9070, 0xc16c, 0x9057, + 0xc198, 0x903e, 0xc1c4, 0x9026, 0xc1f0, 0x900e, 0xc21c, 0x8ff5, + 0xc248, 0x8fdd, 0xc274, 0x8fc5, 0xc2a0, 0x8fad, 0xc2cc, 0x8f95, + 0xc2f8, 0x8f7d, 0xc324, 0x8f65, 0xc351, 0x8f4d, 0xc37d, 0x8f35, + 0xc3a9, 0x8f1d, 0xc3d6, 0x8f06, 0xc402, 0x8eee, 0xc42e, 0x8ed6, + 0xc45b, 0x8ebf, 0xc487, 0x8ea8, 0xc4b4, 0x8e90, 0xc4e0, 0x8e79, + 0xc50d, 0x8e62, 0xc53a, 0x8e4b, 0xc566, 0x8e34, 0xc593, 0x8e1d, + 0xc5c0, 0x8e06, 0xc5ed, 0x8def, 0xc619, 0x8dd8, 0xc646, 0x8dc1, + 0xc673, 0x8dab, 0xc6a0, 0x8d94, 0xc6cd, 0x8d7e, 0xc6fa, 0x8d67, + 0xc727, 0x8d51, 0xc754, 0x8d3b, 0xc781, 0x8d24, 0xc7ae, 0x8d0e, + 0xc7db, 0x8cf8, 0xc809, 0x8ce2, 0xc836, 0x8ccc, 0xc863, 0x8cb6, + 0xc890, 0x8ca1, 0xc8be, 0x8c8b, 0xc8eb, 0x8c75, 0xc918, 0x8c60, + 0xc946, 0x8c4a, 0xc973, 0x8c35, 0xc9a1, 0x8c1f, 0xc9ce, 0x8c0a, + 0xc9fc, 0x8bf5, 0xca29, 0x8bdf, 0xca57, 0x8bca, 0xca85, 0x8bb5, + 0xcab2, 0x8ba0, 0xcae0, 0x8b8b, 0xcb0e, 0x8b77, 0xcb3c, 0x8b62, + 0xcb69, 0x8b4d, 0xcb97, 0x8b39, 0xcbc5, 0x8b24, 0xcbf3, 0x8b10, + 0xcc21, 0x8afb, 0xcc4f, 0x8ae7, 0xcc7d, 0x8ad3, 0xccab, 0x8abe, + 0xccd9, 0x8aaa, 0xcd07, 0x8a96, 0xcd35, 0x8a82, 0xcd63, 0x8a6e, + 0xcd92, 0x8a5a, 0xcdc0, 0x8a47, 0xcdee, 0x8a33, 0xce1c, 0x8a1f, + 0xce4b, 0x8a0c, 0xce79, 0x89f8, 0xcea7, 0x89e5, 0xced6, 0x89d2, + 0xcf04, 0x89be, 0xcf33, 0x89ab, 0xcf61, 0x8998, 0xcf90, 0x8985, + 0xcfbe, 0x8972, 0xcfed, 0x895f, 0xd01b, 0x894c, 0xd04a, 0x8939, + 0xd079, 0x8927, 0xd0a7, 0x8914, 0xd0d6, 0x8902, 0xd105, 0x88ef, + 0xd134, 0x88dd, 0xd162, 0x88ca, 0xd191, 0x88b8, 0xd1c0, 0x88a6, + 0xd1ef, 0x8894, 0xd21e, 0x8882, 0xd24d, 0x8870, 0xd27c, 0x885e, + 0xd2ab, 0x884c, 0xd2da, 0x883a, 0xd309, 0x8828, 0xd338, 0x8817, + 0xd367, 0x8805, 0xd396, 0x87f4, 0xd3c5, 0x87e2, 0xd3f4, 0x87d1, + 0xd424, 0x87c0, 0xd453, 0x87af, 0xd482, 0x879d, 0xd4b1, 0x878c, + 0xd4e1, 0x877b, 0xd510, 0x876b, 0xd53f, 0x875a, 0xd56f, 0x8749, + 0xd59e, 0x8738, 0xd5ce, 0x8728, 0xd5fd, 0x8717, 0xd62d, 0x8707, + 0xd65c, 0x86f6, 0xd68c, 0x86e6, 0xd6bb, 0x86d6, 0xd6eb, 0x86c6, + 0xd71b, 0x86b6, 0xd74a, 0x86a5, 0xd77a, 0x8696, 0xd7aa, 0x8686, + 0xd7d9, 0x8676, 0xd809, 0x8666, 0xd839, 0x8656, 0xd869, 0x8647, + 0xd898, 0x8637, 0xd8c8, 0x8628, 0xd8f8, 0x8619, 0xd928, 0x8609, + 0xd958, 0x85fa, 0xd988, 0x85eb, 0xd9b8, 0x85dc, 0xd9e8, 0x85cd, + 0xda18, 0x85be, 0xda48, 0x85af, 0xda78, 0x85a0, 0xdaa8, 0x8592, + 0xdad8, 0x8583, 0xdb08, 0x8574, 0xdb38, 0x8566, 0xdb68, 0x8558, + 0xdb99, 0x8549, 0xdbc9, 0x853b, 0xdbf9, 0x852d, 0xdc29, 0x851f, + 0xdc59, 0x8511, 0xdc8a, 0x8503, 0xdcba, 0x84f5, 0xdcea, 0x84e7, + 0xdd1b, 0x84d9, 0xdd4b, 0x84cc, 0xdd7c, 0x84be, 0xddac, 0x84b0, + 0xdddc, 0x84a3, 0xde0d, 0x8496, 0xde3d, 0x8488, 0xde6e, 0x847b, + 0xde9e, 0x846e, 0xdecf, 0x8461, 0xdeff, 0x8454, 0xdf30, 0x8447, + 0xdf61, 0x843a, 0xdf91, 0x842d, 0xdfc2, 0x8421, 0xdff2, 0x8414, + 0xe023, 0x8407, 0xe054, 0x83fb, 0xe085, 0x83ef, 0xe0b5, 0x83e2, + 0xe0e6, 0x83d6, 0xe117, 0x83ca, 0xe148, 0x83be, 0xe178, 0x83b2, + 0xe1a9, 0x83a6, 0xe1da, 0x839a, 0xe20b, 0x838e, 0xe23c, 0x8382, + 0xe26d, 0x8377, 0xe29e, 0x836b, 0xe2cf, 0x8360, 0xe2ff, 0x8354, + 0xe330, 0x8349, 0xe361, 0x833e, 0xe392, 0x8332, 0xe3c3, 0x8327, + 0xe3f4, 0x831c, 0xe426, 0x8311, 0xe457, 0x8306, 0xe488, 0x82fb, + 0xe4b9, 0x82f1, 0xe4ea, 0x82e6, 0xe51b, 0x82db, 0xe54c, 0x82d1, + 0xe57d, 0x82c6, 0xe5af, 0x82bc, 0xe5e0, 0x82b2, 0xe611, 0x82a8, + 0xe642, 0x829d, 0xe673, 0x8293, 0xe6a5, 0x8289, 0xe6d6, 0x827f, + 0xe707, 0x8276, 0xe739, 0x826c, 0xe76a, 0x8262, 0xe79b, 0x8259, + 0xe7cd, 0x824f, 0xe7fe, 0x8246, 0xe82f, 0x823c, 0xe861, 0x8233, + 0xe892, 0x822a, 0xe8c4, 0x8220, 0xe8f5, 0x8217, 0xe926, 0x820e, + 0xe958, 0x8205, 0xe989, 0x81fd, 0xe9bb, 0x81f4, 0xe9ec, 0x81eb, + 0xea1e, 0x81e2, 0xea4f, 0x81da, 0xea81, 0x81d1, 0xeab3, 0x81c9, + 0xeae4, 0x81c1, 0xeb16, 0x81b8, 0xeb47, 0x81b0, 0xeb79, 0x81a8, + 0xebab, 0x81a0, 0xebdc, 0x8198, 0xec0e, 0x8190, 0xec3f, 0x8188, + 0xec71, 0x8181, 0xeca3, 0x8179, 0xecd5, 0x8172, 0xed06, 0x816a, + 0xed38, 0x8163, 0xed6a, 0x815b, 0xed9b, 0x8154, 0xedcd, 0x814d, + 0xedff, 0x8146, 0xee31, 0x813f, 0xee62, 0x8138, 0xee94, 0x8131, + 0xeec6, 0x812a, 0xeef8, 0x8123, 0xef2a, 0x811d, 0xef5c, 0x8116, + 0xef8d, 0x8110, 0xefbf, 0x8109, 0xeff1, 0x8103, 0xf023, 0x80fd, + 0xf055, 0x80f6, 0xf087, 0x80f0, 0xf0b9, 0x80ea, 0xf0eb, 0x80e4, + 0xf11c, 0x80de, 0xf14e, 0x80d9, 0xf180, 0x80d3, 0xf1b2, 0x80cd, + 0xf1e4, 0x80c8, 0xf216, 0x80c2, 0xf248, 0x80bd, 0xf27a, 0x80b7, + 0xf2ac, 0x80b2, 0xf2de, 0x80ad, 0xf310, 0x80a8, 0xf342, 0x80a3, + 0xf374, 0x809e, 0xf3a6, 0x8099, 0xf3d8, 0x8094, 0xf40a, 0x808f, + 0xf43c, 0x808b, 0xf46e, 0x8086, 0xf4a0, 0x8082, 0xf4d3, 0x807d, + 0xf505, 0x8079, 0xf537, 0x8075, 0xf569, 0x8070, 0xf59b, 0x806c, + 0xf5cd, 0x8068, 0xf5ff, 0x8064, 0xf631, 0x8060, 0xf663, 0x805d, + 0xf695, 0x8059, 0xf6c8, 0x8055, 0xf6fa, 0x8052, 0xf72c, 0x804e, + 0xf75e, 0x804b, 0xf790, 0x8047, 0xf7c2, 0x8044, 0xf7f4, 0x8041, + 0xf827, 0x803e, 0xf859, 0x803b, 0xf88b, 0x8038, 0xf8bd, 0x8035, + 0xf8ef, 0x8032, 0xf922, 0x802f, 0xf954, 0x802d, 0xf986, 0x802a, + 0xf9b8, 0x8027, 0xf9ea, 0x8025, 0xfa1d, 0x8023, 0xfa4f, 0x8020, + 0xfa81, 0x801e, 0xfab3, 0x801c, 0xfae5, 0x801a, 0xfb18, 0x8018, + 0xfb4a, 0x8016, 0xfb7c, 0x8014, 0xfbae, 0x8013, 0xfbe1, 0x8011, + 0xfc13, 0x800f, 0xfc45, 0x800e, 0xfc77, 0x800c, 0xfcaa, 0x800b, + 0xfcdc, 0x800a, 0xfd0e, 0x8009, 0xfd40, 0x8008, 0xfd73, 0x8007, + 0xfda5, 0x8006, 0xfdd7, 0x8005, 0xfe09, 0x8004, 0xfe3c, 0x8003, + 0xfe6e, 0x8002, 0xfea0, 0x8002, 0xfed2, 0x8001, 0xff05, 0x8001, + 0xff37, 0x8001, 0xff69, 0x8000, 0xff9b, 0x8000, 0xffce, 0x8000, +}; + +/** + * @} end of CFFT_CIFFT group + */ + +/* +* @brief Q15 table for reciprocal +*/ +const q15_t ALIGN4 armRecipTableQ15[64] = { + 0x7F03, 0x7D13, 0x7B31, 0x795E, 0x7798, 0x75E0, + 0x7434, 0x7294, 0x70FF, 0x6F76, 0x6DF6, 0x6C82, + 0x6B16, 0x69B5, 0x685C, 0x670C, 0x65C4, 0x6484, + 0x634C, 0x621C, 0x60F3, 0x5FD0, 0x5EB5, 0x5DA0, + 0x5C91, 0x5B88, 0x5A85, 0x5988, 0x5890, 0x579E, + 0x56B0, 0x55C8, 0x54E4, 0x5405, 0x532B, 0x5255, + 0x5183, 0x50B6, 0x4FEC, 0x4F26, 0x4E64, 0x4DA6, + 0x4CEC, 0x4C34, 0x4B81, 0x4AD0, 0x4A23, 0x4978, + 0x48D1, 0x482D, 0x478C, 0x46ED, 0x4651, 0x45B8, + 0x4521, 0x448D, 0x43FC, 0x436C, 0x42DF, 0x4255, + 0x41CC, 0x4146, 0x40C2, 0x4040 +}; + +/* +* @brief Q31 table for reciprocal +*/ +const q31_t armRecipTableQ31[64] = { + 0x7F03F03F, 0x7D137420, 0x7B31E739, 0x795E9F94, 0x7798FD29, 0x75E06928, + 0x7434554D, 0x72943B4B, 0x70FF9C40, 0x6F760031, 0x6DF6F593, 0x6C8210E3, + 0x6B16EC3A, 0x69B526F6, 0x685C655F, 0x670C505D, 0x65C4952D, 0x6484E519, + 0x634CF53E, 0x621C7E4F, 0x60F33C61, 0x5FD0EEB3, 0x5EB55785, 0x5DA03BEB, + 0x5C9163A1, 0x5B8898E6, 0x5A85A85A, 0x598860DF, 0x58909373, 0x579E1318, + 0x56B0B4B8, 0x55C84F0B, 0x54E4BA80, 0x5405D124, 0x532B6E8F, 0x52556FD0, + 0x5183B35A, 0x50B618F3, 0x4FEC81A2, 0x4F26CFA2, 0x4E64E64E, 0x4DA6AA1D, + 0x4CEC008B, 0x4C34D010, 0x4B810016, 0x4AD078EF, 0x4A2323C4, 0x4978EA96, + 0x48D1B827, 0x482D77FE, 0x478C1657, 0x46ED801D, 0x4651A2E5, 0x45B86CE2, + 0x4521CCE1, 0x448DB244, 0x43FC0CFA, 0x436CCD78, 0x42DFE4B4, 0x42554426, + 0x41CCDDB6, 0x4146A3C6, 0x40C28923, 0x40408102 +}; diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_conj_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_conj_f32.c new file mode 100644 index 0000000000..31bbaa7a80 --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_conj_f32.c @@ -0,0 +1,174 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_cmplx_conj_f32.c +* +* Description: Floating-point complex conjugate. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* ---------------------------------------------------------------------------- */ +#include "arm_math.h" + +/** + * @ingroup groupCmplxMath + */ + +/** + * @defgroup cmplx_conj Complex Conjugate + * + * Conjugates the elements of a complex data vector. + * + * The pSrc points to the source data and + * pDst points to the where the result should be written. + * numSamples specifies the number of complex samples + * and the data in each array is stored in an interleaved fashion + * (real, imag, real, imag, ...). + * Each array has a total of 2*numSamples values. + * The underlying algorithm is used: + * + * 
        
+ * for(n=0; n        
+ *        
+ * There are separate functions for floating-point, Q15, and Q31 data types.        
+ */
+
+/**        
+ * @addtogroup cmplx_conj        
+ * @{        
+ */
+
+/**        
+ * @brief  Floating-point complex conjugate.        
+ * @param  *pSrc points to the input vector        
+ * @param  *pDst points to the output vector        
+ * @param  numSamples number of complex samples in each vector        
+ * @return none.        
+ */
+
+void arm_cmplx_conj_f32(
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t numSamples)
+{
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  float32_t inR1, inR2, inR3, inR4;
+  float32_t inI1, inI2, inI3, inI4;
+
+  /*loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.        
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C[0]+jC[1] = A[0]+ j (-1) A[1] */
+    /* Calculate Complex Conjugate and then store the results in the destination buffer. */
+    /* read real input samples */
+    inR1 = pSrc[0];
+    /* store real samples to destination */
+    pDst[0] = inR1;
+    inR2 = pSrc[2];
+    pDst[2] = inR2;
+    inR3 = pSrc[4];
+    pDst[4] = inR3;
+    inR4 = pSrc[6];
+    pDst[6] = inR4;
+
+    /* read imaginary input samples */
+    inI1 = pSrc[1];
+    inI2 = pSrc[3];
+
+    /* conjugate input */
+    inI1 = -inI1;
+
+    /* read imaginary input samples */
+    inI3 = pSrc[5];
+
+    /* conjugate input */
+    inI2 = -inI2;
+
+    /* read imaginary input samples */
+    inI4 = pSrc[7];
+
+    /* conjugate input */
+    inI3 = -inI3;
+
+    /* store imaginary samples to destination */
+    pDst[1] = inI1;
+    pDst[3] = inI2;
+
+    /* conjugate input */
+    inI4 = -inI4;
+
+    /* store imaginary samples to destination */
+    pDst[5] = inI3;
+
+    /* increment source pointer by 8 to process next sampels */
+    pSrc += 8u;
+
+    /* store imaginary sample to destination */
+    pDst[7] = inI4;
+
+    /* increment destination pointer by 8 to store next samples */
+    pDst += 8u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.        
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  blkCnt = numSamples;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* realOut + j (imagOut) = realIn + j (-1) imagIn */
+    /* Calculate Complex Conjugate and then store the results in the destination buffer. */
+    *pDst++ = *pSrc++;
+    *pDst++ = -*pSrc++;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**        
+ * @} end of cmplx_conj group        
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_conj_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_conj_q15.c
new file mode 100644
index 0000000000..c5a3703157
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_conj_q15.c
@@ -0,0 +1,153 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_cmplx_conj_q15.c    
+*    
+* Description:	Q15 complex conjugate.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupCmplxMath    
+ */
+
+/**    
+ * @addtogroup cmplx_conj    
+ * @{    
+ */
+
+/**    
+ * @brief  Q15 complex conjugate.    
+ * @param  *pSrc points to the input vector    
+ * @param  *pDst points to the output vector    
+ * @param  numSamples number of complex samples in each vector    
+ * @return none.    
+ *    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * The Q15 value -1 (0x8000) will be saturated to the maximum allowable positive value 0x7FFF.    
+ */
+
+void arm_cmplx_conj_q15(
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t numSamples)
+{
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  uint32_t blkCnt;                               /* loop counter */
+  q31_t in1, in2, in3, in4;
+  q31_t zero = 0;
+
+  /*loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C[0]+jC[1] = A[0]+ j (-1) A[1] */
+    /* Calculate Complex Conjugate and then store the results in the destination buffer. */
+    in1 = *__SIMD32(pSrc)++;
+    in2 = *__SIMD32(pSrc)++;
+    in3 = *__SIMD32(pSrc)++;
+    in4 = *__SIMD32(pSrc)++;
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    in1 = __QASX(zero, in1);
+    in2 = __QASX(zero, in2);
+    in3 = __QASX(zero, in3);
+    in4 = __QASX(zero, in4);
+
+#else
+
+    in1 = __QSAX(zero, in1);
+    in2 = __QSAX(zero, in2);
+    in3 = __QSAX(zero, in3);
+    in4 = __QSAX(zero, in4);
+
+#endif //       #ifndef ARM_MATH_BIG_ENDIAN
+
+    in1 = ((uint32_t) in1 >> 16) | ((uint32_t) in1 << 16);
+    in2 = ((uint32_t) in2 >> 16) | ((uint32_t) in2 << 16);
+    in3 = ((uint32_t) in3 >> 16) | ((uint32_t) in3 << 16);
+    in4 = ((uint32_t) in4 >> 16) | ((uint32_t) in4 << 16);
+
+    *__SIMD32(pDst)++ = in1;
+    *__SIMD32(pDst)++ = in2;
+    *__SIMD32(pDst)++ = in3;
+    *__SIMD32(pDst)++ = in4;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C[0]+jC[1] = A[0]+ j (-1) A[1] */
+    /* Calculate Complex Conjugate and then store the results in the destination buffer. */
+    *pDst++ = *pSrc++;
+    *pDst++ = __SSAT(-*pSrc++, 16);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  q15_t in;
+
+  /* Run the below code for Cortex-M0 */
+
+  while(numSamples > 0u)
+  {
+    /* realOut + j (imagOut) = realIn+ j (-1) imagIn */
+    /* Calculate Complex Conjugate and then store the results in the destination buffer. */
+    *pDst++ = *pSrc++;
+    in = *pSrc++;
+    *pDst++ = (in == (q15_t) 0x8000) ? 0x7fff : -in;
+
+    /* Decrement the loop counter */
+    numSamples--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of cmplx_conj group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_conj_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_conj_q31.c
new file mode 100644
index 0000000000..7475962d53
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_conj_q31.c
@@ -0,0 +1,172 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_cmplx_conj_q31.c    
+*    
+* Description:	Q31 complex conjugate.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupCmplxMath        
+ */
+
+/**        
+ * @addtogroup cmplx_conj        
+ * @{        
+ */
+
+/**        
+ * @brief  Q31 complex conjugate.        
+ * @param  *pSrc points to the input vector        
+ * @param  *pDst points to the output vector        
+ * @param  numSamples number of complex samples in each vector        
+ * @return none.        
+ *        
+ * Scaling and Overflow Behavior:        
+ * \par        
+ * The function uses saturating arithmetic.        
+ * The Q31 value -1 (0x80000000) will be saturated to the maximum allowable positive value 0x7FFFFFFF.        
+ */
+
+void arm_cmplx_conj_q31(
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t numSamples)
+{
+  uint32_t blkCnt;                               /* loop counter */
+  q31_t in;                                      /* Input value */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t inR1, inR2, inR3, inR4;                  /* Temporary real variables */
+  q31_t inI1, inI2, inI3, inI4;                  /* Temporary imaginary variables */
+
+  /*loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.        
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C[0]+jC[1] = A[0]+ j (-1) A[1] */
+    /* Calculate Complex Conjugate and then store the results in the destination buffer. */
+    /* Saturated to 0x7fffffff if the input is -1(0x80000000) */
+    /* read real input sample */
+    inR1 = pSrc[0];
+    /* store real input sample */
+    pDst[0] = inR1;
+
+    /* read imaginary input sample */
+    inI1 = pSrc[1];
+
+    /* read real input sample */
+    inR2 = pSrc[2];
+    /* store real input sample */
+    pDst[2] = inR2;
+
+    /* read imaginary input sample */
+    inI2 = pSrc[3];
+
+    /* negate imaginary input sample */
+    inI1 = __QSUB(0, inI1);
+
+    /* read real input sample */
+    inR3 = pSrc[4];
+    /* store real input sample */
+    pDst[4] = inR3;
+
+    /* read imaginary input sample */
+    inI3 = pSrc[5];
+
+    /* negate imaginary input sample */
+    inI2 = __QSUB(0, inI2);
+
+    /* read real input sample */
+    inR4 = pSrc[6];
+    /* store real input sample */
+    pDst[6] = inR4;
+
+    /* negate imaginary input sample */
+    inI3 = __QSUB(0, inI3);
+
+    /* store imaginary input sample */
+    inI4 = pSrc[7];
+
+    /* store imaginary input samples */
+    pDst[1] = inI1;
+
+    /* negate imaginary input sample */
+    inI4 = __QSUB(0, inI4);
+
+    /* store imaginary input samples */
+    pDst[3] = inI2;
+
+    /* increment source pointer by 8 to proecess next samples */
+    pSrc += 8u;
+
+    /* store imaginary input samples */
+    pDst[5] = inI3;
+    pDst[7] = inI4;
+
+    /* increment destination pointer by 8 to process next samples */
+    pDst += 8u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.        
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  blkCnt = numSamples;
+
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C[0]+jC[1] = A[0]+ j (-1) A[1] */
+    /* Calculate Complex Conjugate and then store the results in the destination buffer. */
+    /* Saturated to 0x7fffffff if the input is -1(0x80000000) */
+    *pDst++ = *pSrc++;
+    in = *pSrc++;
+    *pDst++ = (in == 0x80000000) ? 0x7fffffff : -in;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**        
+ * @} end of cmplx_conj group        
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_dot_prod_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_dot_prod_f32.c
new file mode 100644
index 0000000000..4f265d6902
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_dot_prod_f32.c
@@ -0,0 +1,160 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_cmplx_dot_prod_f32.c    
+*    
+* Description:	Floating-point complex dot product    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupCmplxMath    
+ */
+
+/**    
+ * @defgroup cmplx_dot_prod Complex Dot Product    
+ *    
+ * Computes the dot product of two complex vectors.    
+ * The vectors are multiplied element-by-element and then summed.    
+ *   
+ * The pSrcA points to the first complex input vector and    
+ * pSrcB points to the second complex input vector.    
+ * numSamples specifies the number of complex samples    
+ * and the data in each array is stored in an interleaved fashion    
+ * (real, imag, real, imag, ...).    
+ * Each array has a total of 2*numSamples values.    
+ *    
+ * The underlying algorithm is used:    
+ * 
    
+ * realResult=0;    
+ * imagResult=0;    
+ * for(n=0; n    
+ *    
+ * There are separate functions for floating-point, Q15, and Q31 data types.    
+ */
+
+/**    
+ * @addtogroup cmplx_dot_prod    
+ * @{    
+ */
+
+/**    
+ * @brief  Floating-point complex dot product    
+ * @param  *pSrcA points to the first input vector    
+ * @param  *pSrcB points to the second input vector    
+ * @param  numSamples number of complex samples in each vector    
+ * @param  *realResult real part of the result returned here    
+ * @param  *imagResult imaginary part of the result returned here    
+ * @return none.    
+ */
+
+void arm_cmplx_dot_prod_f32(
+  float32_t * pSrcA,
+  float32_t * pSrcB,
+  uint32_t numSamples,
+  float32_t * realResult,
+  float32_t * imagResult)
+{
+  float32_t real_sum = 0.0f, imag_sum = 0.0f;    /* Temporary result storage */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  uint32_t blkCnt;                               /* loop counter */
+
+  /*loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* CReal = A[0]* B[0] + A[2]* B[2] + A[4]* B[4] + .....+ A[numSamples-2]* B[numSamples-2] */
+    real_sum += (*pSrcA++) * (*pSrcB++);
+    /* CImag = A[1]* B[1] + A[3]* B[3] + A[5]* B[5] + .....+ A[numSamples-1]* B[numSamples-1] */
+    imag_sum += (*pSrcA++) * (*pSrcB++);
+
+    real_sum += (*pSrcA++) * (*pSrcB++);
+    imag_sum += (*pSrcA++) * (*pSrcB++);
+
+    real_sum += (*pSrcA++) * (*pSrcB++);
+    imag_sum += (*pSrcA++) * (*pSrcB++);
+
+    real_sum += (*pSrcA++) * (*pSrcB++);
+    imag_sum += (*pSrcA++) * (*pSrcB++);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* CReal = A[0]* B[0] + A[2]* B[2] + A[4]* B[4] + .....+ A[numSamples-2]* B[numSamples-2] */
+    real_sum += (*pSrcA++) * (*pSrcB++);
+    /* CImag = A[1]* B[1] + A[3]* B[3] + A[5]* B[5] + .....+ A[numSamples-1]* B[numSamples-1] */
+    imag_sum += (*pSrcA++) * (*pSrcB++);
+
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  while(numSamples > 0u)
+  {
+    /* CReal = A[0]* B[0] + A[2]* B[2] + A[4]* B[4] + .....+ A[numSamples-2]* B[numSamples-2] */
+    real_sum += (*pSrcA++) * (*pSrcB++);
+    /* CImag = A[1]* B[1] + A[3]* B[3] + A[5]* B[5] + .....+ A[numSamples-1]* B[numSamples-1] */
+    imag_sum += (*pSrcA++) * (*pSrcB++);
+
+
+    /* Decrement the loop counter */
+    numSamples--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  /* Store the real and imaginary results in the destination buffers */
+  *realResult = real_sum;
+  *imagResult = imag_sum;
+}
+
+/**    
+ * @} end of cmplx_dot_prod group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_dot_prod_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_dot_prod_q15.c
new file mode 100644
index 0000000000..33df820a5c
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_dot_prod_q15.c
@@ -0,0 +1,144 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_cmplx_dot_prod_q15.c    
+*    
+* Description:	Processing function for the Q15 Complex Dot product    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupCmplxMath    
+ */
+
+/**    
+ * @addtogroup cmplx_dot_prod    
+ * @{    
+ */
+
+/**    
+ * @brief  Q15 complex dot product    
+ * @param  *pSrcA points to the first input vector    
+ * @param  *pSrcB points to the second input vector    
+ * @param  numSamples number of complex samples in each vector    
+ * @param  *realResult real part of the result returned here    
+ * @param  *imagResult imaginary part of the result returned here    
+ * @return none.    
+ *    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function is implemented using an internal 64-bit accumulator.    
+ * The intermediate 1.15 by 1.15 multiplications are performed with full precision and yield a 2.30 result.    
+ * These are accumulated in a 64-bit accumulator with 34.30 precision.    
+ * As a final step, the accumulators are converted to 8.24 format.    
+ * The return results realResult and imagResult are in 8.24 format.    
+ */
+
+void arm_cmplx_dot_prod_q15(
+  q15_t * pSrcA,
+  q15_t * pSrcB,
+  uint32_t numSamples,
+  q31_t * realResult,
+  q31_t * imagResult)
+{
+  q63_t real_sum = 0, imag_sum = 0;              /* Temporary result storage */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  uint32_t blkCnt;                               /* loop counter */
+
+
+  /*loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* CReal = A[0]* B[0] + A[2]* B[2] + A[4]* B[4] + .....+ A[numSamples-2]* B[numSamples-2] */
+    real_sum += ((q31_t) * pSrcA++ * *pSrcB++);
+
+    /* CImag = A[1]* B[1] + A[3]* B[3] + A[5]* B[5] + .....+ A[numSamples-1]* B[numSamples-1] */
+    imag_sum += ((q31_t) * pSrcA++ * *pSrcB++);
+
+    real_sum += ((q31_t) * pSrcA++ * *pSrcB++);
+    imag_sum += ((q31_t) * pSrcA++ * *pSrcB++);
+
+    real_sum += ((q31_t) * pSrcA++ * *pSrcB++);
+    imag_sum += ((q31_t) * pSrcA++ * *pSrcB++);
+
+    real_sum += ((q31_t) * pSrcA++ * *pSrcB++);
+    imag_sum += ((q31_t) * pSrcA++ * *pSrcB++);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* CReal = A[0]* B[0] + A[2]* B[2] + A[4]* B[4] + .....+ A[numSamples-2]* B[numSamples-2] */
+    real_sum += ((q31_t) * pSrcA++ * *pSrcB++);
+    /* CImag = A[1]* B[1] + A[3]* B[3] + A[5]* B[5] + .....+ A[numSamples-1]* B[numSamples-1] */
+    imag_sum += ((q31_t) * pSrcA++ * *pSrcB++);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  while(numSamples > 0u)
+  {
+    /* CReal = A[0]* B[0] + A[2]* B[2] + A[4]* B[4] + .....+ A[numSamples-2]* B[numSamples-2] */
+    real_sum += ((q31_t) * pSrcA++ * *pSrcB++);
+    /* CImag = A[1]* B[1] + A[3]* B[3] + A[5]* B[5] + .....+ A[numSamples-1]* B[numSamples-1] */
+    imag_sum += ((q31_t) * pSrcA++ * *pSrcB++);
+
+    /* Decrement the loop counter */
+    numSamples--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  /* Store the real and imaginary results in 8.24 format  */
+  /* Convert real data in 34.30 to 8.24 by 6 right shifts */
+  *realResult = (q31_t) (real_sum) >> 6;
+  /* Convert imaginary data in 34.30 to 8.24 by 6 right shifts */
+  *imagResult = (q31_t) (imag_sum) >> 6;
+}
+
+/**    
+ * @} end of cmplx_dot_prod group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_dot_prod_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_dot_prod_q31.c
new file mode 100644
index 0000000000..d371dff8b2
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_dot_prod_q31.c
@@ -0,0 +1,145 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_cmplx_dot_prod_q31.c    
+*    
+* Description:	Q31 complex dot product    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupCmplxMath    
+ */
+
+/**    
+ * @addtogroup cmplx_dot_prod    
+ * @{    
+ */
+
+/**    
+ * @brief  Q31 complex dot product    
+ * @param  *pSrcA points to the first input vector    
+ * @param  *pSrcB points to the second input vector    
+ * @param  numSamples number of complex samples in each vector    
+ * @param  *realResult real part of the result returned here    
+ * @param  *imagResult imaginary part of the result returned here    
+ * @return none.    
+ *    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function is implemented using an internal 64-bit accumulator.    
+ * The intermediate 1.31 by 1.31 multiplications are performed with 64-bit precision and then shifted to 16.48 format.    
+ * The internal real and imaginary accumulators are in 16.48 format and provide 15 guard bits.    
+ * Additions are nonsaturating and no overflow will occur as long as numSamples is less than 32768.    
+ * The return results realResult and imagResult are in 16.48 format.    
+ * Input down scaling is not required.    
+ */
+
+void arm_cmplx_dot_prod_q31(
+  q31_t * pSrcA,
+  q31_t * pSrcB,
+  uint32_t numSamples,
+  q63_t * realResult,
+  q63_t * imagResult)
+{
+  q63_t real_sum = 0, imag_sum = 0;              /* Temporary result storage */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  uint32_t blkCnt;                               /* loop counter */
+
+
+  /*loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* CReal = A[0]* B[0] + A[2]* B[2] + A[4]* B[4] + .....+ A[numSamples-2]* B[numSamples-2] */
+    /* Convert real data in 2.62 to 16.48 by 14 right shifts */
+    real_sum += (q63_t) * pSrcA++ * (*pSrcB++) >> 14;
+    /* CImag = A[1]* B[1] + A[3]* B[3] + A[5]* B[5] + .....+ A[numSamples-1]* B[numSamples-1] */
+    /* Convert imag data in 2.62 to 16.48 by 14 right shifts */
+    imag_sum += (q63_t) * pSrcA++ * (*pSrcB++) >> 14;
+
+    real_sum += (q63_t) * pSrcA++ * (*pSrcB++) >> 14;
+    imag_sum += (q63_t) * pSrcA++ * (*pSrcB++) >> 14;
+
+    real_sum += (q63_t) * pSrcA++ * (*pSrcB++) >> 14;
+    imag_sum += (q63_t) * pSrcA++ * (*pSrcB++) >> 14;
+
+    real_sum += (q63_t) * pSrcA++ * (*pSrcB++) >> 14;
+    imag_sum += (q63_t) * pSrcA++ * (*pSrcB++) >> 14;
+
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples  is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* CReal = A[0]* B[0] + A[2]* B[2] + A[4]* B[4] + .....+ A[numSamples-2]* B[numSamples-2] */
+    real_sum += (q63_t) * pSrcA++ * (*pSrcB++) >> 14;
+    /* CImag = A[1]* B[1] + A[3]* B[3] + A[5]* B[5] + .....+ A[numSamples-1]* B[numSamples-1] */
+    imag_sum += (q63_t) * pSrcA++ * (*pSrcB++) >> 14;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  while(numSamples > 0u)
+  {
+    /* outReal = realA[0]* realB[0] + realA[2]* realB[2] + realA[4]* realB[4] + .....+ realA[numSamples-2]* realB[numSamples-2] */
+    real_sum += (q63_t) * pSrcA++ * (*pSrcB++) >> 14;
+    /* outImag = imagA[1]* imagB[1] + imagA[3]* imagB[3] + imagA[5]* imagB[5] + .....+ imagA[numSamples-1]* imagB[numSamples-1] */
+    imag_sum += (q63_t) * pSrcA++ * (*pSrcB++) >> 14;
+
+    /* Decrement the loop counter */
+    numSamples--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  /* Store the real and imaginary results in 16.48 format  */
+  *realResult = real_sum;
+  *imagResult = imag_sum;
+}
+
+/**    
+ * @} end of cmplx_dot_prod group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_f32.c
new file mode 100644
index 0000000000..59bbc27422
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_f32.c
@@ -0,0 +1,157 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_cmplx_mag_f32.c    
+*    
+* Description:	Floating-point complex magnitude.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupCmplxMath    
+ */
+
+/**    
+ * @defgroup cmplx_mag Complex Magnitude    
+ *    
+ * Computes the magnitude of the elements of a complex data vector.    
+ *   
+ * The pSrc points to the source data and    
+ * pDst points to the where the result should be written.    
+ * numSamples specifies the number of complex samples    
+ * in the input array and the data is stored in an interleaved fashion    
+ * (real, imag, real, imag, ...).    
+ * The input array has a total of 2*numSamples values;    
+ * the output array has a total of numSamples values.    
+ * The underlying algorithm is used:    
+ *    
+ * 
    
+ * for(n=0; n    
+ *    
+ * There are separate functions for floating-point, Q15, and Q31 data types.    
+ */
+
+/**    
+ * @addtogroup cmplx_mag    
+ * @{    
+ */
+/**    
+ * @brief Floating-point complex magnitude.    
+ * @param[in]       *pSrc points to complex input buffer    
+ * @param[out]      *pDst points to real output buffer    
+ * @param[in]       numSamples number of complex samples in the input vector    
+ * @return none.    
+ *    
+ */
+
+
+void arm_cmplx_mag_f32(
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t numSamples)
+{
+  float32_t realIn, imagIn;                      /* Temporary variables to hold input values */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  uint32_t blkCnt;                               /* loop counter */
+
+  /*loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+
+    /* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */
+    realIn = *pSrc++;
+    imagIn = *pSrc++;
+    /* store the result in the destination buffer. */
+    arm_sqrt_f32((realIn * realIn) + (imagIn * imagIn), pDst++);
+
+    realIn = *pSrc++;
+    imagIn = *pSrc++;
+    arm_sqrt_f32((realIn * realIn) + (imagIn * imagIn), pDst++);
+
+    realIn = *pSrc++;
+    imagIn = *pSrc++;
+    arm_sqrt_f32((realIn * realIn) + (imagIn * imagIn), pDst++);
+
+    realIn = *pSrc++;
+    imagIn = *pSrc++;
+    arm_sqrt_f32((realIn * realIn) + (imagIn * imagIn), pDst++);
+
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */
+    realIn = *pSrc++;
+    imagIn = *pSrc++;
+    /* store the result in the destination buffer. */
+    arm_sqrt_f32((realIn * realIn) + (imagIn * imagIn), pDst++);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  while(numSamples > 0u)
+  {
+    /* out = sqrt((real * real) + (imag * imag)) */
+    realIn = *pSrc++;
+    imagIn = *pSrc++;
+    /* store the result in the destination buffer. */
+    arm_sqrt_f32((realIn * realIn) + (imagIn * imagIn), pDst++);
+
+    /* Decrement the loop counter */
+    numSamples--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of cmplx_mag group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_q15.c
new file mode 100644
index 0000000000..122ca8bc1f
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_q15.c
@@ -0,0 +1,145 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_cmplx_mag_q15.c    
+*    
+* Description:	Q15 complex magnitude.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupCmplxMath    
+ */
+
+/**    
+ * @addtogroup cmplx_mag    
+ * @{    
+ */
+
+
+/**    
+ * @brief  Q15 complex magnitude    
+ * @param  *pSrc points to the complex input vector    
+ * @param  *pDst points to the real output vector    
+ * @param  numSamples number of complex samples in the input vector    
+ * @return none.    
+ *    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function implements 1.15 by 1.15 multiplications and finally output is converted into 2.14 format.    
+ */
+
+void arm_cmplx_mag_q15(
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t numSamples)
+{
+  q31_t acc0, acc1;                              /* Accumulators */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  uint32_t blkCnt;                               /* loop counter */
+  q31_t in1, in2, in3, in4;
+  q31_t acc2, acc3;
+
+
+  /*loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+
+    /* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */
+    in1 = *__SIMD32(pSrc)++;
+    in2 = *__SIMD32(pSrc)++;
+    in3 = *__SIMD32(pSrc)++;
+    in4 = *__SIMD32(pSrc)++;
+
+    acc0 = __SMUAD(in1, in1);
+    acc1 = __SMUAD(in2, in2);
+    acc2 = __SMUAD(in3, in3);
+    acc3 = __SMUAD(in4, in4);
+
+    /* store the result in 2.14 format in the destination buffer. */
+    arm_sqrt_q15((q15_t) ((acc0) >> 17), pDst++);
+    arm_sqrt_q15((q15_t) ((acc1) >> 17), pDst++);
+    arm_sqrt_q15((q15_t) ((acc2) >> 17), pDst++);
+    arm_sqrt_q15((q15_t) ((acc3) >> 17), pDst++);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */
+    in1 = *__SIMD32(pSrc)++;
+    acc0 = __SMUAD(in1, in1);
+
+    /* store the result in 2.14 format in the destination buffer. */
+    arm_sqrt_q15((q15_t) (acc0 >> 17), pDst++);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  q15_t real, imag;                              /* Temporary variables to hold input values */
+
+  while(numSamples > 0u)
+  {
+    /* out = sqrt(real * real + imag * imag) */
+    real = *pSrc++;
+    imag = *pSrc++;
+
+    acc0 = (real * real);
+    acc1 = (imag * imag);
+
+    /* store the result in 2.14 format in the destination buffer. */
+    arm_sqrt_q15((q15_t) (((q63_t) acc0 + acc1) >> 17), pDst++);
+
+    /* Decrement the loop counter */
+    numSamples--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of cmplx_mag group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_q31.c
new file mode 100644
index 0000000000..59384f5dc3
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_q31.c
@@ -0,0 +1,177 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_cmplx_mag_q31.c    
+*    
+* Description:	Q31 complex magnitude    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupCmplxMath        
+ */
+
+/**        
+ * @addtogroup cmplx_mag        
+ * @{        
+ */
+
+/**        
+ * @brief  Q31 complex magnitude        
+ * @param  *pSrc points to the complex input vector        
+ * @param  *pDst points to the real output vector        
+ * @param  numSamples number of complex samples in the input vector        
+ * @return none.        
+ *        
+ * Scaling and Overflow Behavior:        
+ * \par        
+ * The function implements 1.31 by 1.31 multiplications and finally output is converted into 2.30 format.        
+ * Input down scaling is not required.        
+ */
+
+void arm_cmplx_mag_q31(
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t numSamples)
+{
+  q31_t real, imag;                              /* Temporary variables to hold input values */
+  q31_t acc0, acc1;                              /* Accumulators */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t real1, real2, imag1, imag2;              /* Temporary variables to hold input values */
+  q31_t out1, out2, out3, out4;                  /* Accumulators */
+  q63_t mul1, mul2, mul3, mul4;                  /* Temporary variables */
+
+
+  /*loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.        
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* read complex input from source buffer */
+    real1 = pSrc[0];
+    imag1 = pSrc[1];
+    real2 = pSrc[2];
+    imag2 = pSrc[3];
+
+    /* calculate power of input values */
+    mul1 = (q63_t) real1 *real1;
+    mul2 = (q63_t) imag1 *imag1;
+    mul3 = (q63_t) real2 *real2;
+    mul4 = (q63_t) imag2 *imag2;
+
+    /* get the result to 3.29 format */
+    out1 = (q31_t) (mul1 >> 33);
+    out2 = (q31_t) (mul2 >> 33);
+    out3 = (q31_t) (mul3 >> 33);
+    out4 = (q31_t) (mul4 >> 33);
+
+    /* add real and imaginary accumulators */
+    out1 = out1 + out2;
+    out3 = out3 + out4;
+
+    /* read complex input from source buffer */
+    real1 = pSrc[4];
+    imag1 = pSrc[5];
+    real2 = pSrc[6];
+    imag2 = pSrc[7];
+
+    /* calculate square root */
+    arm_sqrt_q31(out1, &pDst[0]);
+
+    /* calculate power of input values */
+    mul1 = (q63_t) real1 *real1;
+
+    /* calculate square root */
+    arm_sqrt_q31(out3, &pDst[1]);
+
+    /* calculate power of input values */
+    mul2 = (q63_t) imag1 *imag1;
+    mul3 = (q63_t) real2 *real2;
+    mul4 = (q63_t) imag2 *imag2;
+
+    /* get the result to 3.29 format */
+    out1 = (q31_t) (mul1 >> 33);
+    out2 = (q31_t) (mul2 >> 33);
+    out3 = (q31_t) (mul3 >> 33);
+    out4 = (q31_t) (mul4 >> 33);
+
+    /* add real and imaginary accumulators */
+    out1 = out1 + out2;
+    out3 = out3 + out4;
+
+    /* calculate square root */
+    arm_sqrt_q31(out1, &pDst[2]);
+
+    /* increment destination by 8 to process next samples */
+    pSrc += 8u;
+
+    /* calculate square root */
+    arm_sqrt_q31(out3, &pDst[3]);
+
+    /* increment destination by 4 to process next samples */
+    pDst += 4u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.        
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  blkCnt = numSamples;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */
+    real = *pSrc++;
+    imag = *pSrc++;
+    acc0 = (q31_t) (((q63_t) real * real) >> 33);
+    acc1 = (q31_t) (((q63_t) imag * imag) >> 33);
+    /* store the result in 2.30 format in the destination buffer. */
+    arm_sqrt_q31(acc0 + acc1, pDst++);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**        
+ * @} end of cmplx_mag group        
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_squared_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_squared_f32.c
new file mode 100644
index 0000000000..7350fd1c9a
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_squared_f32.c
@@ -0,0 +1,207 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_cmplx_mag_squared_f32.c    
+*    
+* Description:	Floating-point complex magnitude squared.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupCmplxMath        
+ */
+
+/**        
+ * @defgroup cmplx_mag_squared Complex Magnitude Squared        
+ *        
+ * Computes the magnitude squared of the elements of a complex data vector.        
+ *       
+ * The pSrc points to the source data and        
+ * pDst points to the where the result should be written.        
+ * numSamples specifies the number of complex samples        
+ * in the input array and the data is stored in an interleaved fashion        
+ * (real, imag, real, imag, ...).        
+ * The input array has a total of 2*numSamples values;        
+ * the output array has a total of numSamples values.        
+ *        
+ * The underlying algorithm is used:        
+ *        
+ * 
        
+ * for(n=0; n        
+ *        
+ * There are separate functions for floating-point, Q15, and Q31 data types.        
+ */
+
+/**        
+ * @addtogroup cmplx_mag_squared        
+ * @{        
+ */
+
+
+/**        
+ * @brief  Floating-point complex magnitude squared        
+ * @param[in]  *pSrc points to the complex input vector        
+ * @param[out]  *pDst points to the real output vector        
+ * @param[in]  numSamples number of complex samples in the input vector        
+ * @return none.        
+ */
+
+void arm_cmplx_mag_squared_f32(
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t numSamples)
+{
+  float32_t real, imag;                          /* Temporary variables to store real and imaginary values */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0
+  float32_t real1, real2, real3, real4;          /* Temporary variables to hold real values */
+  float32_t imag1, imag2, imag3, imag4;          /* Temporary variables to hold imaginary values */
+  float32_t mul1, mul2, mul3, mul4;              /* Temporary variables */
+  float32_t mul5, mul6, mul7, mul8;              /* Temporary variables */
+  float32_t out1, out2, out3, out4;              /* Temporary variables to hold output values */
+
+  /*loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.        
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C[0] = (A[0] * A[0] + A[1] * A[1]) */
+    /* read real input sample from source buffer */
+    real1 = pSrc[0];
+    /* read imaginary input sample from source buffer */
+    imag1 = pSrc[1];
+
+    /* calculate power of real value */
+    mul1 = real1 * real1;
+
+    /* read real input sample from source buffer */
+    real2 = pSrc[2];
+
+    /* calculate power of imaginary value */
+    mul2 = imag1 * imag1;
+
+    /* read imaginary input sample from source buffer */
+    imag2 = pSrc[3];
+
+    /* calculate power of real value */
+    mul3 = real2 * real2;
+
+    /* read real input sample from source buffer */
+    real3 = pSrc[4];
+
+    /* calculate power of imaginary value */
+    mul4 = imag2 * imag2;
+
+    /* read imaginary input sample from source buffer */
+    imag3 = pSrc[5];
+
+    /* calculate power of real value */
+    mul5 = real3 * real3;
+    /* calculate power of imaginary value */
+    mul6 = imag3 * imag3;
+
+    /* read real input sample from source buffer */
+    real4 = pSrc[6];
+
+    /* accumulate real and imaginary powers */
+    out1 = mul1 + mul2;
+
+    /* read imaginary input sample from source buffer */
+    imag4 = pSrc[7];
+
+    /* accumulate real and imaginary powers */
+    out2 = mul3 + mul4;
+
+    /* calculate power of real value */
+    mul7 = real4 * real4;
+    /* calculate power of imaginary value */
+    mul8 = imag4 * imag4;
+
+    /* store output to destination */
+    pDst[0] = out1;
+
+    /* accumulate real and imaginary powers */
+    out3 = mul5 + mul6;
+
+    /* store output to destination */
+    pDst[1] = out2;
+
+    /* accumulate real and imaginary powers */
+    out4 = mul7 + mul8;
+
+    /* store output to destination */
+    pDst[2] = out3;
+
+    /* increment destination pointer by 8 to process next samples */
+    pSrc += 8u;
+
+    /* store output to destination */
+    pDst[3] = out4;
+
+    /* increment destination pointer by 4 to process next samples */
+    pDst += 4u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.        
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  blkCnt = numSamples;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C[0] = (A[0] * A[0] + A[1] * A[1]) */
+    real = *pSrc++;
+    imag = *pSrc++;
+
+    /* out = (real * real) + (imag * imag) */
+    /* store the result in the destination buffer. */
+    *pDst++ = (real * real) + (imag * imag);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**        
+ * @} end of cmplx_mag_squared group        
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_squared_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_squared_q15.c
new file mode 100644
index 0000000000..623229b8f7
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_squared_q15.c
@@ -0,0 +1,140 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_cmplx_mag_squared_q15.c    
+*    
+* Description:	Q15 complex magnitude squared.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupCmplxMath    
+ */
+
+/**    
+ * @addtogroup cmplx_mag_squared    
+ * @{    
+ */
+
+/**    
+ * @brief  Q15 complex magnitude squared    
+ * @param  *pSrc points to the complex input vector    
+ * @param  *pDst points to the real output vector    
+ * @param  numSamples number of complex samples in the input vector    
+ * @return none.    
+ *    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function implements 1.15 by 1.15 multiplications and finally output is converted into 3.13 format.    
+ */
+
+void arm_cmplx_mag_squared_q15(
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t numSamples)
+{
+  q31_t acc0, acc1;                              /* Accumulators */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  uint32_t blkCnt;                               /* loop counter */
+  q31_t in1, in2, in3, in4;
+  q31_t acc2, acc3;
+
+  /*loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C[0] = (A[0] * A[0] + A[1] * A[1]) */
+    in1 = *__SIMD32(pSrc)++;
+    in2 = *__SIMD32(pSrc)++;
+    in3 = *__SIMD32(pSrc)++;
+    in4 = *__SIMD32(pSrc)++;
+
+    acc0 = __SMUAD(in1, in1);
+    acc1 = __SMUAD(in2, in2);
+    acc2 = __SMUAD(in3, in3);
+    acc3 = __SMUAD(in4, in4);
+
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ = (q15_t) (acc0 >> 17);
+    *pDst++ = (q15_t) (acc1 >> 17);
+    *pDst++ = (q15_t) (acc2 >> 17);
+    *pDst++ = (q15_t) (acc3 >> 17);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C[0] = (A[0] * A[0] + A[1] * A[1]) */
+    in1 = *__SIMD32(pSrc)++;
+    acc0 = __SMUAD(in1, in1);
+
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ = (q15_t) (acc0 >> 17);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  q15_t real, imag;                              /* Temporary variables to store real and imaginary values */
+
+  while(numSamples > 0u)
+  {
+    /* out = ((real * real) + (imag * imag)) */
+    real = *pSrc++;
+    imag = *pSrc++;
+    acc0 = (real * real);
+    acc1 = (imag * imag);
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ = (q15_t) (((q63_t) acc0 + acc1) >> 17);
+
+    /* Decrement the loop counter */
+    numSamples--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of cmplx_mag_squared group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_squared_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_squared_q31.c
new file mode 100644
index 0000000000..d45ccfab2f
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_squared_q31.c
@@ -0,0 +1,153 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_cmplx_mag_squared_q31.c    
+*    
+* Description:	Q31 complex magnitude squared.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupCmplxMath    
+ */
+
+/**    
+ * @addtogroup cmplx_mag_squared    
+ * @{    
+ */
+
+
+/**    
+ * @brief  Q31 complex magnitude squared    
+ * @param  *pSrc points to the complex input vector    
+ * @param  *pDst points to the real output vector    
+ * @param  numSamples number of complex samples in the input vector    
+ * @return none.    
+ *    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function implements 1.31 by 1.31 multiplications and finally output is converted into 3.29 format.    
+ * Input down scaling is not required.    
+ */
+
+void arm_cmplx_mag_squared_q31(
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t numSamples)
+{
+  q31_t real, imag;                              /* Temporary variables to store real and imaginary values */
+  q31_t acc0, acc1;                              /* Accumulators */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  uint32_t blkCnt;                               /* loop counter */
+
+  /* loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C[0] = (A[0] * A[0] + A[1] * A[1]) */
+    real = *pSrc++;
+    imag = *pSrc++;
+    acc0 = (q31_t) (((q63_t) real * real) >> 33);
+    acc1 = (q31_t) (((q63_t) imag * imag) >> 33);
+    /* store the result in 3.29 format in the destination buffer. */
+    *pDst++ = acc0 + acc1;
+
+    real = *pSrc++;
+    imag = *pSrc++;
+    acc0 = (q31_t) (((q63_t) real * real) >> 33);
+    acc1 = (q31_t) (((q63_t) imag * imag) >> 33);
+    /* store the result in 3.29 format in the destination buffer. */
+    *pDst++ = acc0 + acc1;
+
+    real = *pSrc++;
+    imag = *pSrc++;
+    acc0 = (q31_t) (((q63_t) real * real) >> 33);
+    acc1 = (q31_t) (((q63_t) imag * imag) >> 33);
+    /* store the result in 3.29 format in the destination buffer. */
+    *pDst++ = acc0 + acc1;
+
+    real = *pSrc++;
+    imag = *pSrc++;
+    acc0 = (q31_t) (((q63_t) real * real) >> 33);
+    acc1 = (q31_t) (((q63_t) imag * imag) >> 33);
+    /* store the result in 3.29 format in the destination buffer. */
+    *pDst++ = acc0 + acc1;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C[0] = (A[0] * A[0] + A[1] * A[1]) */
+    real = *pSrc++;
+    imag = *pSrc++;
+    acc0 = (q31_t) (((q63_t) real * real) >> 33);
+    acc1 = (q31_t) (((q63_t) imag * imag) >> 33);
+    /* store the result in 3.29 format in the destination buffer. */
+    *pDst++ = acc0 + acc1;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  while(numSamples > 0u)
+  {
+    /* out = ((real * real) + (imag * imag)) */
+    real = *pSrc++;
+    imag = *pSrc++;
+    acc0 = (q31_t) (((q63_t) real * real) >> 33);
+    acc1 = (q31_t) (((q63_t) imag * imag) >> 33);
+    /* store the result in 3.29 format in the destination buffer. */
+    *pDst++ = acc0 + acc1;
+
+    /* Decrement the loop counter */
+    numSamples--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of cmplx_mag_squared group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_f32.c
new file mode 100644
index 0000000000..2ec9ee862b
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_f32.c
@@ -0,0 +1,199 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_cmplx_mult_cmplx_f32.c    
+*    
+* Description:	Floating-point complex-by-complex multiplication    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupCmplxMath        
+ */
+
+/**        
+ * @defgroup CmplxByCmplxMult Complex-by-Complex Multiplication        
+ *        
+ * Multiplies a complex vector by another complex vector and generates a complex result.        
+ * The data in the complex arrays is stored in an interleaved fashion        
+ * (real, imag, real, imag, ...).        
+ * The parameter numSamples represents the number of complex        
+ * samples processed.  The complex arrays have a total of 2*numSamples        
+ * real values.        
+ *        
+ * The underlying algorithm is used:        
+ *        
+ * 
        
+ * for(n=0; n        
+ *        
+ * There are separate functions for floating-point, Q15, and Q31 data types.        
+ */
+
+/**        
+ * @addtogroup CmplxByCmplxMult        
+ * @{        
+ */
+
+
+/**        
+ * @brief  Floating-point complex-by-complex multiplication        
+ * @param[in]  *pSrcA points to the first input vector        
+ * @param[in]  *pSrcB points to the second input vector        
+ * @param[out]  *pDst  points to the output vector        
+ * @param[in]  numSamples number of complex samples in each vector        
+ * @return none.        
+ */
+
+void arm_cmplx_mult_cmplx_f32(
+  float32_t * pSrcA,
+  float32_t * pSrcB,
+  float32_t * pDst,
+  uint32_t numSamples)
+{
+  float32_t a1, b1, c1, d1;                      /* Temporary variables to store real and imaginary values */
+  uint32_t blkCnt;                               /* loop counters */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  float32_t a2, b2, c2, d2;                      /* Temporary variables to store real and imaginary values */
+  float32_t acc1, acc2, acc3, acc4;
+
+
+  /* loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.        
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1].  */
+    /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i].  */
+    a1 = *pSrcA;                /* A[2 * i] */
+    c1 = *pSrcB;                /* B[2 * i] */
+
+    b1 = *(pSrcA + 1);          /* A[2 * i + 1] */
+    acc1 = a1 * c1;             /* acc1 = A[2 * i] * B[2 * i] */
+
+    a2 = *(pSrcA + 2);          /* A[2 * i + 2] */
+    acc2 = (b1 * c1);           /* acc2 = A[2 * i + 1] * B[2 * i] */
+
+    d1 = *(pSrcB + 1);          /* B[2 * i + 1] */
+    c2 = *(pSrcB + 2);          /* B[2 * i + 2] */
+    acc1 -= b1 * d1;            /* acc1 =      A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1] */
+
+    d2 = *(pSrcB + 3);          /* B[2 * i + 3] */
+    acc3 = a2 * c2;             /* acc3 =       A[2 * i + 2] * B[2 * i + 2] */
+
+    b2 = *(pSrcA + 3);          /* A[2 * i + 3] */
+    acc2 += (a1 * d1);          /* acc2 =      A[2 * i + 1] * B[2 * i] + A[2 * i] * B[2 * i + 1] */
+
+    a1 = *(pSrcA + 4);          /* A[2 * i + 4] */
+    acc4 = (a2 * d2);           /* acc4 =   A[2 * i + 2] * B[2 * i + 3] */
+
+    c1 = *(pSrcB + 4);          /* B[2 * i + 4] */
+    acc3 -= (b2 * d2);          /* acc3 =       A[2 * i + 2] * B[2 * i + 2] - A[2 * i + 3] * B[2 * i + 3] */
+    *pDst = acc1;               /* C[2 * i] = A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1] */
+
+    b1 = *(pSrcA + 5);          /* A[2 * i + 5] */
+    acc4 += b2 * c2;            /* acc4 =   A[2 * i + 2] * B[2 * i + 3] + A[2 * i + 3] * B[2 * i + 2] */
+
+    *(pDst + 1) = acc2;         /* C[2 * i + 1] = A[2 * i + 1] * B[2 * i] + A[2 * i] * B[2 * i + 1]  */
+    acc1 = (a1 * c1);
+
+    d1 = *(pSrcB + 5);
+    acc2 = (b1 * c1);
+
+    *(pDst + 2) = acc3;
+    *(pDst + 3) = acc4;
+
+    a2 = *(pSrcA + 6);
+    acc1 -= (b1 * d1);
+
+    c2 = *(pSrcB + 6);
+    acc2 += (a1 * d1);
+
+    b2 = *(pSrcA + 7);
+    acc3 = (a2 * c2);
+
+    d2 = *(pSrcB + 7);
+    acc4 = (b2 * c2);
+
+    *(pDst + 4) = acc1;
+    pSrcA += 8u;
+
+    acc3 -= (b2 * d2);
+    acc4 += (a2 * d2);
+
+    *(pDst + 5) = acc2;
+    pSrcB += 8u;
+
+    *(pDst + 6) = acc3;
+    *(pDst + 7) = acc4;
+
+    pDst += 8u;
+
+    /* Decrement the numSamples loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.        
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  blkCnt = numSamples;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1].  */
+    /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i].  */
+    a1 = *pSrcA++;
+    b1 = *pSrcA++;
+    c1 = *pSrcB++;
+    d1 = *pSrcB++;
+
+    /* store the result in the destination buffer. */
+    *pDst++ = (a1 * c1) - (b1 * d1);
+    *pDst++ = (a1 * d1) + (b1 * c1);
+
+    /* Decrement the numSamples loop counter */
+    blkCnt--;
+  }
+}
+
+/**        
+ * @} end of CmplxByCmplxMult group        
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_q15.c
new file mode 100644
index 0000000000..0219aea48a
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_q15.c
@@ -0,0 +1,185 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_cmplx_mult_cmplx_q15.c    
+*    
+* Description:	Q15 complex-by-complex multiplication    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupCmplxMath    
+ */
+
+/**    
+ * @addtogroup CmplxByCmplxMult    
+ * @{    
+ */
+
+/**    
+ * @brief  Q15 complex-by-complex multiplication    
+ * @param[in]  *pSrcA points to the first input vector    
+ * @param[in]  *pSrcB points to the second input vector    
+ * @param[out]  *pDst  points to the output vector    
+ * @param[in]  numSamples number of complex samples in each vector    
+ * @return none.    
+ *    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function implements 1.15 by 1.15 multiplications and finally output is converted into 3.13 format.    
+ */
+
+void arm_cmplx_mult_cmplx_q15(
+  q15_t * pSrcA,
+  q15_t * pSrcB,
+  q15_t * pDst,
+  uint32_t numSamples)
+{
+  q15_t a, b, c, d;                              /* Temporary variables to store real and imaginary values */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  uint32_t blkCnt;                               /* loop counters */
+
+  /* loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1].  */
+    /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i].  */
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ =
+      (q15_t) (q31_t) (((q31_t) a * c) >> 17) - (((q31_t) b * d) >> 17);
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ =
+      (q15_t) (q31_t) (((q31_t) a * d) >> 17) + (((q31_t) b * c) >> 17);
+
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ =
+      (q15_t) (q31_t) (((q31_t) a * c) >> 17) - (((q31_t) b * d) >> 17);
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ =
+      (q15_t) (q31_t) (((q31_t) a * d) >> 17) + (((q31_t) b * c) >> 17);
+
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ =
+      (q15_t) (q31_t) (((q31_t) a * c) >> 17) - (((q31_t) b * d) >> 17);
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ =
+      (q15_t) (q31_t) (((q31_t) a * d) >> 17) + (((q31_t) b * c) >> 17);
+
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ =
+      (q15_t) (q31_t) (((q31_t) a * c) >> 17) - (((q31_t) b * d) >> 17);
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ =
+      (q15_t) (q31_t) (((q31_t) a * d) >> 17) + (((q31_t) b * c) >> 17);
+
+    /* Decrement the blockSize loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1].  */
+    /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i].  */
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ =
+      (q15_t) (q31_t) (((q31_t) a * c) >> 17) - (((q31_t) b * d) >> 17);
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ =
+      (q15_t) (q31_t) (((q31_t) a * d) >> 17) + (((q31_t) b * c) >> 17);
+
+    /* Decrement the blockSize loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  while(numSamples > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1].  */
+    /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i].  */
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ =
+      (q15_t) (q31_t) (((q31_t) a * c) >> 17) - (((q31_t) b * d) >> 17);
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ =
+      (q15_t) (q31_t) (((q31_t) a * d) >> 17) + (((q31_t) b * c) >> 17);
+
+    /* Decrement the blockSize loop counter */
+    numSamples--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of CmplxByCmplxMult group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_q31.c
new file mode 100644
index 0000000000..13fc060a2e
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_q31.c
@@ -0,0 +1,318 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_cmplx_mult_cmplx_q31.c    
+*    
+* Description:	Q31 complex-by-complex multiplication    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupCmplxMath    
+ */
+
+/**    
+ * @addtogroup CmplxByCmplxMult    
+ * @{    
+ */
+
+
+/**    
+ * @brief  Q31 complex-by-complex multiplication    
+ * @param[in]  *pSrcA points to the first input vector    
+ * @param[in]  *pSrcB points to the second input vector    
+ * @param[out]  *pDst  points to the output vector    
+ * @param[in]  numSamples number of complex samples in each vector    
+ * @return none.    
+ *    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function implements 1.31 by 1.31 multiplications and finally output is converted into 3.29 format.    
+ * Input down scaling is not required.    
+ */
+
+void arm_cmplx_mult_cmplx_q31(
+  q31_t * pSrcA,
+  q31_t * pSrcB,
+  q31_t * pDst,
+  uint32_t numSamples)
+{
+  q31_t a, b, c, d;                              /* Temporary variables to store real and imaginary values */
+  uint32_t blkCnt;                               /* loop counters */
+  q31_t mul1, mul2, mul3, mul4;
+  q31_t out1, out2;
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /* loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1].  */
+    /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i].  */
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    mul1 = (q31_t) (((q63_t) a * c) >> 32);
+    mul2 = (q31_t) (((q63_t) b * d) >> 32);
+    mul3 = (q31_t) (((q63_t) a * d) >> 32);
+    mul4 = (q31_t) (((q63_t) b * c) >> 32);
+
+    mul1 = (mul1 >> 1);
+    mul2 = (mul2 >> 1);
+    mul3 = (mul3 >> 1);
+    mul4 = (mul4 >> 1);
+
+    out1 = mul1 - mul2;
+    out2 = mul3 + mul4;
+
+    /* store the real result in 3.29 format in the destination buffer. */
+    *pDst++ = out1;
+    /* store the imag result in 3.29 format in the destination buffer. */
+    *pDst++ = out2;
+
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    mul1 = (q31_t) (((q63_t) a * c) >> 32);
+    mul2 = (q31_t) (((q63_t) b * d) >> 32);
+    mul3 = (q31_t) (((q63_t) a * d) >> 32);
+    mul4 = (q31_t) (((q63_t) b * c) >> 32);
+
+    mul1 = (mul1 >> 1);
+    mul2 = (mul2 >> 1);
+    mul3 = (mul3 >> 1);
+    mul4 = (mul4 >> 1);
+
+    out1 = mul1 - mul2;
+    out2 = mul3 + mul4;
+
+    /* store the real result in 3.29 format in the destination buffer. */
+    *pDst++ = out1;
+    /* store the imag result in 3.29 format in the destination buffer. */
+    *pDst++ = out2;
+
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    mul1 = (q31_t) (((q63_t) a * c) >> 32);
+    mul2 = (q31_t) (((q63_t) b * d) >> 32);
+    mul3 = (q31_t) (((q63_t) a * d) >> 32);
+    mul4 = (q31_t) (((q63_t) b * c) >> 32);
+
+    mul1 = (mul1 >> 1);
+    mul2 = (mul2 >> 1);
+    mul3 = (mul3 >> 1);
+    mul4 = (mul4 >> 1);
+
+    out1 = mul1 - mul2;
+    out2 = mul3 + mul4;
+
+    /* store the real result in 3.29 format in the destination buffer. */
+    *pDst++ = out1;
+    /* store the imag result in 3.29 format in the destination buffer. */
+    *pDst++ = out2;
+
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    mul1 = (q31_t) (((q63_t) a * c) >> 32);
+    mul2 = (q31_t) (((q63_t) b * d) >> 32);
+    mul3 = (q31_t) (((q63_t) a * d) >> 32);
+    mul4 = (q31_t) (((q63_t) b * c) >> 32);
+
+    mul1 = (mul1 >> 1);
+    mul2 = (mul2 >> 1);
+    mul3 = (mul3 >> 1);
+    mul4 = (mul4 >> 1);
+
+    out1 = mul1 - mul2;
+    out2 = mul3 + mul4;
+
+    /* store the real result in 3.29 format in the destination buffer. */
+    *pDst++ = out1;
+    /* store the imag result in 3.29 format in the destination buffer. */
+    *pDst++ = out2;
+
+    /* Decrement the blockSize loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1].  */
+    /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i].  */
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    mul1 = (q31_t) (((q63_t) a * c) >> 32);
+    mul2 = (q31_t) (((q63_t) b * d) >> 32);
+    mul3 = (q31_t) (((q63_t) a * d) >> 32);
+    mul4 = (q31_t) (((q63_t) b * c) >> 32);
+
+    mul1 = (mul1 >> 1);
+    mul2 = (mul2 >> 1);
+    mul3 = (mul3 >> 1);
+    mul4 = (mul4 >> 1);
+
+    out1 = mul1 - mul2;
+    out2 = mul3 + mul4;
+
+    /* store the real result in 3.29 format in the destination buffer. */
+    *pDst++ = out1;
+    /* store the imag result in 3.29 format in the destination buffer. */
+    *pDst++ = out2;
+
+    /* Decrement the blockSize loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* loop Unrolling */
+  blkCnt = numSamples >> 1u;
+
+  /* First part of the processing with loop unrolling.  Compute 2 outputs at a time.     
+   ** a second loop below computes the remaining 1 sample. */
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1].  */
+    /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i].  */
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    mul1 = (q31_t) (((q63_t) a * c) >> 32);
+    mul2 = (q31_t) (((q63_t) b * d) >> 32);
+    mul3 = (q31_t) (((q63_t) a * d) >> 32);
+    mul4 = (q31_t) (((q63_t) b * c) >> 32);
+
+    mul1 = (mul1 >> 1);
+    mul2 = (mul2 >> 1);
+    mul3 = (mul3 >> 1);
+    mul4 = (mul4 >> 1);
+
+    out1 = mul1 - mul2;
+    out2 = mul3 + mul4;
+
+    /* store the real result in 3.29 format in the destination buffer. */
+    *pDst++ = out1;
+    /* store the imag result in 3.29 format in the destination buffer. */
+    *pDst++ = out2;
+
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    mul1 = (q31_t) (((q63_t) a * c) >> 32);
+    mul2 = (q31_t) (((q63_t) b * d) >> 32);
+    mul3 = (q31_t) (((q63_t) a * d) >> 32);
+    mul4 = (q31_t) (((q63_t) b * c) >> 32);
+
+    mul1 = (mul1 >> 1);
+    mul2 = (mul2 >> 1);
+    mul3 = (mul3 >> 1);
+    mul4 = (mul4 >> 1);
+
+    out1 = mul1 - mul2;
+    out2 = mul3 + mul4;
+
+    /* store the real result in 3.29 format in the destination buffer. */
+    *pDst++ = out1;
+    /* store the imag result in 3.29 format in the destination buffer. */
+    *pDst++ = out2;
+
+    /* Decrement the blockSize loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 2, compute any remaining output samples here.     
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x2u;
+
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1].  */
+    /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i].  */
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    mul1 = (q31_t) (((q63_t) a * c) >> 32);
+    mul2 = (q31_t) (((q63_t) b * d) >> 32);
+    mul3 = (q31_t) (((q63_t) a * d) >> 32);
+    mul4 = (q31_t) (((q63_t) b * c) >> 32);
+
+    mul1 = (mul1 >> 1);
+    mul2 = (mul2 >> 1);
+    mul3 = (mul3 >> 1);
+    mul4 = (mul4 >> 1);
+
+    out1 = mul1 - mul2;
+    out2 = mul3 + mul4;
+
+    /* store the real result in 3.29 format in the destination buffer. */
+    *pDst++ = out1;
+    /* store the imag result in 3.29 format in the destination buffer. */
+    *pDst++ = out2;
+
+    /* Decrement the blockSize loop counter */
+    blkCnt--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of CmplxByCmplxMult group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_real_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_real_f32.c
new file mode 100644
index 0000000000..7a5bdf9cda
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_real_f32.c
@@ -0,0 +1,217 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_cmplx_mult_real_f32.c    
+*    
+* Description:	Floating-point complex by real multiplication    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupCmplxMath        
+ */
+
+/**        
+ * @defgroup CmplxByRealMult Complex-by-Real Multiplication        
+ *        
+ * Multiplies a complex vector by a real vector and generates a complex result.        
+ * The data in the complex arrays is stored in an interleaved fashion        
+ * (real, imag, real, imag, ...).        
+ * The parameter numSamples represents the number of complex        
+ * samples processed.  The complex arrays have a total of 2*numSamples        
+ * real values while the real array has a total of numSamples        
+ * real values.        
+ *        
+ * The underlying algorithm is used:        
+ *        
+ * 
        
+ * for(n=0; n        
+ *        
+ * There are separate functions for floating-point, Q15, and Q31 data types.        
+ */
+
+/**        
+ * @addtogroup CmplxByRealMult        
+ * @{        
+ */
+
+
+/**        
+ * @brief  Floating-point complex-by-real multiplication        
+ * @param[in]  *pSrcCmplx points to the complex input vector        
+ * @param[in]  *pSrcReal points to the real input vector        
+ * @param[out]  *pCmplxDst points to the complex output vector        
+ * @param[in]  numSamples number of samples in each vector        
+ * @return none.        
+ */
+
+void arm_cmplx_mult_real_f32(
+  float32_t * pSrcCmplx,
+  float32_t * pSrcReal,
+  float32_t * pCmplxDst,
+  uint32_t numSamples)
+{
+  float32_t in;                                  /* Temporary variable to store input value */
+  uint32_t blkCnt;                               /* loop counters */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  float32_t inA1, inA2, inA3, inA4;              /* Temporary variables to hold input data */
+  float32_t inA5, inA6, inA7, inA8;              /* Temporary variables to hold input data */
+  float32_t inB1, inB2, inB3, inB4;              /* Temporary variables to hold input data */
+  float32_t out1, out2, out3, out4;              /* Temporary variables to hold output data */
+  float32_t out5, out6, out7, out8;              /* Temporary variables to hold output data */
+
+  /* loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.        
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[i].            */
+    /* C[2 * i + 1] = A[2 * i + 1] * B[i].        */
+    /* read input from complex input buffer */
+    inA1 = pSrcCmplx[0];
+    inA2 = pSrcCmplx[1];
+    /* read input from real input buffer */
+    inB1 = pSrcReal[0];
+
+    /* read input from complex input buffer */
+    inA3 = pSrcCmplx[2];
+
+    /* multiply complex buffer real input with real buffer input */
+    out1 = inA1 * inB1;
+
+    /* read input from complex input buffer */
+    inA4 = pSrcCmplx[3];
+
+    /* multiply complex buffer imaginary input with real buffer input */
+    out2 = inA2 * inB1;
+
+    /* read input from real input buffer */
+    inB2 = pSrcReal[1];
+    /* read input from complex input buffer */
+    inA5 = pSrcCmplx[4];
+
+    /* multiply complex buffer real input with real buffer input */
+    out3 = inA3 * inB2;
+
+    /* read input from complex input buffer */
+    inA6 = pSrcCmplx[5];
+    /* read input from real input buffer */
+    inB3 = pSrcReal[2];
+
+    /* multiply complex buffer imaginary input with real buffer input */
+    out4 = inA4 * inB2;
+
+    /* read input from complex input buffer */
+    inA7 = pSrcCmplx[6];
+
+    /* multiply complex buffer real input with real buffer input */
+    out5 = inA5 * inB3;
+
+    /* read input from complex input buffer */
+    inA8 = pSrcCmplx[7];
+
+    /* multiply complex buffer imaginary input with real buffer input */
+    out6 = inA6 * inB3;
+
+    /* read input from real input buffer */
+    inB4 = pSrcReal[3];
+
+    /* store result to destination bufer */
+    pCmplxDst[0] = out1;
+
+    /* multiply complex buffer real input with real buffer input */
+    out7 = inA7 * inB4;
+
+    /* store result to destination bufer */
+    pCmplxDst[1] = out2;
+
+    /* multiply complex buffer imaginary input with real buffer input */
+    out8 = inA8 * inB4;
+
+    /* store result to destination bufer */
+    pCmplxDst[2] = out3;
+    pCmplxDst[3] = out4;
+    pCmplxDst[4] = out5;
+
+    /* incremnet complex input buffer by 8 to process next samples */
+    pSrcCmplx += 8u;
+
+    /* store result to destination bufer */
+    pCmplxDst[5] = out6;
+
+    /* increment real input buffer by 4 to process next samples */
+    pSrcReal += 4u;
+
+    /* store result to destination bufer */
+    pCmplxDst[6] = out7;
+    pCmplxDst[7] = out8;
+
+    /* increment destination buffer by 8 to process next sampels */
+    pCmplxDst += 8u;
+
+    /* Decrement the numSamples loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.        
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  blkCnt = numSamples;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[i].            */
+    /* C[2 * i + 1] = A[2 * i + 1] * B[i].        */
+    in = *pSrcReal++;
+    /* store the result in the destination buffer. */
+    *pCmplxDst++ = (*pSrcCmplx++) * (in);
+    *pCmplxDst++ = (*pSrcCmplx++) * (in);
+
+    /* Decrement the numSamples loop counter */
+    blkCnt--;
+  }
+}
+
+/**        
+ * @} end of CmplxByRealMult group        
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_real_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_real_q15.c
new file mode 100644
index 0000000000..a44158c4ff
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_real_q15.c
@@ -0,0 +1,195 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_cmplx_mult_real_q15.c    
+*    
+* Description:	Q15 complex by real multiplication    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupCmplxMath    
+ */
+
+/**    
+ * @addtogroup CmplxByRealMult    
+ * @{    
+ */
+
+
+/**    
+ * @brief  Q15 complex-by-real multiplication    
+ * @param[in]  *pSrcCmplx points to the complex input vector    
+ * @param[in]  *pSrcReal points to the real input vector    
+ * @param[out]  *pCmplxDst points to the complex output vector    
+ * @param[in]  numSamples number of samples in each vector    
+ * @return none.    
+ *    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * Results outside of the allowable Q15 range [0x8000 0x7FFF] will be saturated.    
+ */
+
+void arm_cmplx_mult_real_q15(
+  q15_t * pSrcCmplx,
+  q15_t * pSrcReal,
+  q15_t * pCmplxDst,
+  uint32_t numSamples)
+{
+  q15_t in;                                      /* Temporary variable to store input value */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  uint32_t blkCnt;                               /* loop counters */
+  q31_t inA1, inA2;                              /* Temporary variables to hold input data */
+  q31_t inB1;                                    /* Temporary variables to hold input data */
+  q15_t out1, out2, out3, out4;                  /* Temporary variables to hold output data */
+  q31_t mul1, mul2, mul3, mul4;                  /* Temporary variables to hold intermediate data */
+
+  /* loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[i].            */
+    /* C[2 * i + 1] = A[2 * i + 1] * B[i].        */
+    /* read complex number both real and imaginary from complex input buffer */
+    inA1 = *__SIMD32(pSrcCmplx)++;
+    /* read two real values at a time from real input buffer */
+    inB1 = *__SIMD32(pSrcReal)++;
+    /* read complex number both real and imaginary from complex input buffer */
+    inA2 = *__SIMD32(pSrcCmplx)++;
+
+    /* multiply complex number with real numbers */
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    mul1 = (q31_t) ((q15_t) (inA1) * (q15_t) (inB1));
+    mul2 = (q31_t) ((q15_t) (inA1 >> 16) * (q15_t) (inB1));
+    mul3 = (q31_t) ((q15_t) (inA2) * (q15_t) (inB1 >> 16));
+    mul4 = (q31_t) ((q15_t) (inA2 >> 16) * (q15_t) (inB1 >> 16));
+
+#else
+
+    mul2 = (q31_t) ((q15_t) (inA1 >> 16) * (q15_t) (inB1 >> 16));
+    mul1 = (q31_t) ((q15_t) inA1 * (q15_t) (inB1 >> 16));
+    mul4 = (q31_t) ((q15_t) (inA2 >> 16) * (q15_t) inB1);
+    mul3 = (q31_t) ((q15_t) inA2 * (q15_t) inB1);
+
+#endif //      #ifndef ARM_MATH_BIG_ENDIAN
+
+    /* saturate the result */
+    out1 = (q15_t) __SSAT(mul1 >> 15u, 16);
+    out2 = (q15_t) __SSAT(mul2 >> 15u, 16);
+    out3 = (q15_t) __SSAT(mul3 >> 15u, 16);
+    out4 = (q15_t) __SSAT(mul4 >> 15u, 16);
+
+    /* pack real and imaginary outputs and store them to destination */
+    *__SIMD32(pCmplxDst)++ = __PKHBT(out1, out2, 16);
+    *__SIMD32(pCmplxDst)++ = __PKHBT(out3, out4, 16);
+
+    inA1 = *__SIMD32(pSrcCmplx)++;
+    inB1 = *__SIMD32(pSrcReal)++;
+    inA2 = *__SIMD32(pSrcCmplx)++;
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    mul1 = (q31_t) ((q15_t) (inA1) * (q15_t) (inB1));
+    mul2 = (q31_t) ((q15_t) (inA1 >> 16) * (q15_t) (inB1));
+    mul3 = (q31_t) ((q15_t) (inA2) * (q15_t) (inB1 >> 16));
+    mul4 = (q31_t) ((q15_t) (inA2 >> 16) * (q15_t) (inB1 >> 16));
+
+#else
+
+    mul2 = (q31_t) ((q15_t) (inA1 >> 16) * (q15_t) (inB1 >> 16));
+    mul1 = (q31_t) ((q15_t) inA1 * (q15_t) (inB1 >> 16));
+    mul4 = (q31_t) ((q15_t) (inA2 >> 16) * (q15_t) inB1);
+    mul3 = (q31_t) ((q15_t) inA2 * (q15_t) inB1);
+
+#endif //      #ifndef ARM_MATH_BIG_ENDIAN
+
+    out1 = (q15_t) __SSAT(mul1 >> 15u, 16);
+    out2 = (q15_t) __SSAT(mul2 >> 15u, 16);
+    out3 = (q15_t) __SSAT(mul3 >> 15u, 16);
+    out4 = (q15_t) __SSAT(mul4 >> 15u, 16);
+
+    *__SIMD32(pCmplxDst)++ = __PKHBT(out1, out2, 16);
+    *__SIMD32(pCmplxDst)++ = __PKHBT(out3, out4, 16);
+
+    /* Decrement the numSamples loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[i].            */
+    /* C[2 * i + 1] = A[2 * i + 1] * B[i].        */
+    in = *pSrcReal++;
+    /* store the result in the destination buffer. */
+    *pCmplxDst++ =
+      (q15_t) __SSAT((((q31_t) (*pSrcCmplx++) * (in)) >> 15), 16);
+    *pCmplxDst++ =
+      (q15_t) __SSAT((((q31_t) (*pSrcCmplx++) * (in)) >> 15), 16);
+
+    /* Decrement the numSamples loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  while(numSamples > 0u)
+  {
+    /* realOut = realA * realB.            */
+    /* imagOut = imagA * realB.                */
+    in = *pSrcReal++;
+    /* store the result in the destination buffer. */
+    *pCmplxDst++ =
+      (q15_t) __SSAT((((q31_t) (*pSrcCmplx++) * (in)) >> 15), 16);
+    *pCmplxDst++ =
+      (q15_t) __SSAT((((q31_t) (*pSrcCmplx++) * (in)) >> 15), 16);
+
+    /* Decrement the numSamples loop counter */
+    numSamples--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of CmplxByRealMult group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_real_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_real_q31.c
new file mode 100644
index 0000000000..b286acdb6d
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_real_q31.c
@@ -0,0 +1,215 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_cmplx_mult_real_q31.c    
+*    
+* Description:	Q31 complex by real multiplication    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupCmplxMath    
+ */
+
+/**    
+ * @addtogroup CmplxByRealMult    
+ * @{    
+ */
+
+
+/**    
+ * @brief  Q31 complex-by-real multiplication    
+ * @param[in]  *pSrcCmplx points to the complex input vector    
+ * @param[in]  *pSrcReal points to the real input vector    
+ * @param[out]  *pCmplxDst points to the complex output vector    
+ * @param[in]  numSamples number of samples in each vector    
+ * @return none.    
+ *    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * Results outside of the allowable Q31 range[0x80000000 0x7FFFFFFF] will be saturated.    
+ */
+
+void arm_cmplx_mult_real_q31(
+  q31_t * pSrcCmplx,
+  q31_t * pSrcReal,
+  q31_t * pCmplxDst,
+  uint32_t numSamples)
+{
+  q31_t inA1;                                    /* Temporary variable to store input value */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  uint32_t blkCnt;                               /* loop counters */
+  q31_t inA2, inA3, inA4;                        /* Temporary variables to hold input data */
+  q31_t inB1, inB2;                              /* Temporary variabels to hold input data */
+  q31_t out1, out2, out3, out4;                  /* Temporary variables to hold output data */
+
+  /* loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[i].            */
+    /* C[2 * i + 1] = A[2 * i + 1] * B[i].        */
+    /* read real input from complex input buffer */
+    inA1 = *pSrcCmplx++;
+    inA2 = *pSrcCmplx++;
+    /* read input from real input bufer */
+    inB1 = *pSrcReal++;
+    inB2 = *pSrcReal++;
+    /* read imaginary input from complex input buffer */
+    inA3 = *pSrcCmplx++;
+    inA4 = *pSrcCmplx++;
+
+    /* multiply complex input with real input */
+    out1 = ((q63_t) inA1 * inB1) >> 32;
+    out2 = ((q63_t) inA2 * inB1) >> 32;
+    out3 = ((q63_t) inA3 * inB2) >> 32;
+    out4 = ((q63_t) inA4 * inB2) >> 32;
+
+    /* sature the result */
+    out1 = __SSAT(out1, 31);
+    out2 = __SSAT(out2, 31);
+    out3 = __SSAT(out3, 31);
+    out4 = __SSAT(out4, 31);
+
+    /* get result in 1.31 format */
+    out1 = out1 << 1;
+    out2 = out2 << 1;
+    out3 = out3 << 1;
+    out4 = out4 << 1;
+
+    /* store the result to destination buffer */
+    *pCmplxDst++ = out1;
+    *pCmplxDst++ = out2;
+    *pCmplxDst++ = out3;
+    *pCmplxDst++ = out4;
+
+    /* read real input from complex input buffer */
+    inA1 = *pSrcCmplx++;
+    inA2 = *pSrcCmplx++;
+    /* read input from real input bufer */
+    inB1 = *pSrcReal++;
+    inB2 = *pSrcReal++;
+    /* read imaginary input from complex input buffer */
+    inA3 = *pSrcCmplx++;
+    inA4 = *pSrcCmplx++;
+
+    /* multiply complex input with real input */
+    out1 = ((q63_t) inA1 * inB1) >> 32;
+    out2 = ((q63_t) inA2 * inB1) >> 32;
+    out3 = ((q63_t) inA3 * inB2) >> 32;
+    out4 = ((q63_t) inA4 * inB2) >> 32;
+
+    /* sature the result */
+    out1 = __SSAT(out1, 31);
+    out2 = __SSAT(out2, 31);
+    out3 = __SSAT(out3, 31);
+    out4 = __SSAT(out4, 31);
+
+    /* get result in 1.31 format */
+    out1 = out1 << 1;
+    out2 = out2 << 1;
+    out3 = out3 << 1;
+    out4 = out4 << 1;
+
+    /* store the result to destination buffer */
+    *pCmplxDst++ = out1;
+    *pCmplxDst++ = out2;
+    *pCmplxDst++ = out3;
+    *pCmplxDst++ = out4;
+
+    /* Decrement the numSamples loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[i].            */
+    /* C[2 * i + 1] = A[2 * i + 1] * B[i].        */
+    /* read real input from complex input buffer */
+    inA1 = *pSrcCmplx++;
+    inA2 = *pSrcCmplx++;
+    /* read input from real input bufer */
+    inB1 = *pSrcReal++;
+
+    /* multiply complex input with real input */
+    out1 = ((q63_t) inA1 * inB1) >> 32;
+    out2 = ((q63_t) inA2 * inB1) >> 32;
+
+    /* sature the result */
+    out1 = __SSAT(out1, 31);
+    out2 = __SSAT(out2, 31);
+
+    /* get result in 1.31 format */
+    out1 = out1 << 1;
+    out2 = out2 << 1;
+
+    /* store the result to destination buffer */
+    *pCmplxDst++ = out1;
+    *pCmplxDst++ = out2;
+
+    /* Decrement the numSamples loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  while(numSamples > 0u)
+  {
+    /* realOut = realA * realB.            */
+    /* imagReal = imagA * realB.               */
+    inA1 = *pSrcReal++;
+    /* store the result in the destination buffer. */
+    *pCmplxDst++ =
+      (q31_t) clip_q63_to_q31(((q63_t) * pSrcCmplx++ * inA1) >> 31);
+    *pCmplxDst++ =
+      (q31_t) clip_q63_to_q31(((q63_t) * pSrcCmplx++ * inA1) >> 31);
+
+    /* Decrement the numSamples loop counter */
+    numSamples--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of CmplxByRealMult group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_pid_init_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_pid_init_f32.c
new file mode 100644
index 0000000000..37e48f609b
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_pid_init_f32.c
@@ -0,0 +1,79 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_pid_init_f32.c    
+*    
+* Description:	Floating-point PID Control initialization function    
+*				   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+ /**    
+ * @addtogroup PID    
+ * @{    
+ */
+
+/**    
+ * @brief  Initialization function for the floating-point PID Control.   
+ * @param[in,out] *S points to an instance of the PID structure.   
+ * @param[in]     resetStateFlag  flag to reset the state. 0 = no change in state & 1 = reset the state.   
+ * @return none.   
+ * \par Description:   
+ * \par    
+ * The resetStateFlag specifies whether to set state to zero or not. \n   
+ * The function computes the structure fields: A0, A1 A2    
+ * using the proportional gain( \c Kp), integral gain( \c Ki) and derivative gain( \c Kd)    
+ * also sets the state variables to all zeros.    
+ */
+
+void arm_pid_init_f32(
+  arm_pid_instance_f32 * S,
+  int32_t resetStateFlag)
+{
+
+  /* Derived coefficient A0 */
+  S->A0 = S->Kp + S->Ki + S->Kd;
+
+  /* Derived coefficient A1 */
+  S->A1 = (-S->Kp) - ((float32_t) 2.0 * S->Kd);
+
+  /* Derived coefficient A2 */
+  S->A2 = S->Kd;
+
+  /* Check whether state needs reset or not */
+  if(resetStateFlag)
+  {
+    /* Clear the state buffer.  The size will be always 3 samples */
+    memset(S->state, 0, 3u * sizeof(float32_t));
+  }
+
+}
+
+/**    
+ * @} end of PID group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_pid_init_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_pid_init_q15.c
new file mode 100644
index 0000000000..1816bc9aa1
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_pid_init_q15.c
@@ -0,0 +1,114 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_pid_init_q15.c    
+*    
+* Description:	Q15 PID Control initialization function    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+ /**    
+ * @addtogroup PID    
+ * @{    
+ */
+
+/**    
+ * @details    
+ * @param[in,out] *S points to an instance of the Q15 PID structure.    
+ * @param[in]     resetStateFlag  flag to reset the state. 0 = no change in state 1 = reset the state.    
+ * @return none.    
+ * \par Description:   
+ * \par    
+ * The resetStateFlag specifies whether to set state to zero or not. \n   
+ * The function computes the structure fields: A0, A1 A2    
+ * using the proportional gain( \c Kp), integral gain( \c Ki) and derivative gain( \c Kd)    
+ * also sets the state variables to all zeros.    
+ */
+
+void arm_pid_init_q15(
+  arm_pid_instance_q15 * S,
+  int32_t resetStateFlag)
+{
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /* Derived coefficient A0 */
+  S->A0 = __QADD16(__QADD16(S->Kp, S->Ki), S->Kd);
+
+  /* Derived coefficients and pack into A1 */
+
+#ifndef  ARM_MATH_BIG_ENDIAN
+
+  S->A1 = __PKHBT(-__QADD16(__QADD16(S->Kd, S->Kd), S->Kp), S->Kd, 16);
+
+#else
+
+  S->A1 = __PKHBT(S->Kd, -__QADD16(__QADD16(S->Kd, S->Kd), S->Kp), 16);
+
+#endif /*      #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+  /* Check whether state needs reset or not */
+  if(resetStateFlag)
+  {
+    /* Clear the state buffer.  The size will be always 3 samples */
+    memset(S->state, 0, 3u * sizeof(q15_t));
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  q31_t temp;                                    /*to store the sum */
+
+  /* Derived coefficient A0 */
+  temp = S->Kp + S->Ki + S->Kd;
+  S->A0 = (q15_t) __SSAT(temp, 16);
+
+  /* Derived coefficients and pack into A1 */
+  temp = -(S->Kd + S->Kd + S->Kp);
+  S->A1 = (q15_t) __SSAT(temp, 16);
+  S->A2 = S->Kd;
+
+
+
+  /* Check whether state needs reset or not */
+  if(resetStateFlag)
+  {
+    /* Clear the state buffer.  The size will be always 3 samples */
+    memset(S->state, 0, 3u * sizeof(q15_t));
+  }
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of PID group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_pid_init_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_pid_init_q31.c
new file mode 100644
index 0000000000..da40ce973d
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_pid_init_q31.c
@@ -0,0 +1,99 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_pid_init_q31.c    
+*    
+* Description:	Q31 PID Control initialization function     
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+ /**    
+ * @addtogroup PID    
+ * @{    
+ */
+
+/**    
+ * @brief  Initialization function for the Q31 PID Control.   
+ * @param[in,out] *S points to an instance of the Q31 PID structure.   
+ * @param[in]     resetStateFlag  flag to reset the state. 0 = no change in state 1 = reset the state.   
+ * @return none.    
+ * \par Description:   
+ * \par    
+ * The resetStateFlag specifies whether to set state to zero or not. \n   
+ * The function computes the structure fields: A0, A1 A2    
+ * using the proportional gain( \c Kp), integral gain( \c Ki) and derivative gain( \c Kd)    
+ * also sets the state variables to all zeros.    
+ */
+
+void arm_pid_init_q31(
+  arm_pid_instance_q31 * S,
+  int32_t resetStateFlag)
+{
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /* Derived coefficient A0 */
+  S->A0 = __QADD(__QADD(S->Kp, S->Ki), S->Kd);
+
+  /* Derived coefficient A1 */
+  S->A1 = -__QADD(__QADD(S->Kd, S->Kd), S->Kp);
+
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  q31_t temp;
+
+  /* Derived coefficient A0 */
+  temp = clip_q63_to_q31((q63_t) S->Kp + S->Ki);
+  S->A0 = clip_q63_to_q31((q63_t) temp + S->Kd);
+
+  /* Derived coefficient A1 */
+  temp = clip_q63_to_q31((q63_t) S->Kd + S->Kd);
+  S->A1 = -clip_q63_to_q31((q63_t) temp + S->Kp);
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  /* Derived coefficient A2 */
+  S->A2 = S->Kd;
+
+  /* Check whether state needs reset or not */
+  if(resetStateFlag)
+  {
+    /* Clear the state buffer.  The size will be always 3 samples */
+    memset(S->state, 0, 3u * sizeof(q31_t));
+  }
+
+}
+
+/**    
+ * @} end of PID group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_pid_reset_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_pid_reset_f32.c
new file mode 100644
index 0000000000..491ad5268b
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_pid_reset_f32.c
@@ -0,0 +1,57 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_pid_reset_f32.c    
+*    
+* Description:	Floating-point PID Control reset function   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+ /**    
+ * @addtogroup PID    
+ * @{    
+ */
+
+/**    
+* @brief  Reset function for the floating-point PID Control.   
+* @param[in] *S	Instance pointer of PID control data structure.   
+* @return none.    
+* \par Description:   
+* The function resets the state buffer to zeros.    
+*/
+void arm_pid_reset_f32(
+  arm_pid_instance_f32 * S)
+{
+
+  /* Clear the state buffer.  The size will be always 3 samples */
+  memset(S->state, 0, 3u * sizeof(float32_t));
+}
+
+/**    
+ * @} end of PID group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_pid_reset_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_pid_reset_q15.c
new file mode 100644
index 0000000000..dc00787460
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_pid_reset_q15.c
@@ -0,0 +1,56 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_pid_reset_q15.c    
+*    
+* Description:	Q15 PID Control reset function   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+ /**    
+ * @addtogroup PID    
+ * @{    
+ */
+
+/**    
+* @brief  Reset function for the Q15 PID Control.   
+* @param[in] *S		Instance pointer of PID control data structure.   
+* @return none.    
+* \par Description:   
+* The function resets the state buffer to zeros.    
+*/
+void arm_pid_reset_q15(
+  arm_pid_instance_q15 * S)
+{
+  /* Reset state to zero, The size will be always 3 samples */
+  memset(S->state, 0, 3u * sizeof(q15_t));
+}
+
+/**    
+ * @} end of PID group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_pid_reset_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_pid_reset_q31.c
new file mode 100644
index 0000000000..b1ff753af3
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_pid_reset_q31.c
@@ -0,0 +1,57 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_pid_reset_q31.c    
+*    
+* Description:	Q31 PID Control reset function   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+ /**    
+ * @addtogroup PID    
+ * @{    
+ */
+
+/**    
+* @brief  Reset function for the Q31 PID Control.   
+* @param[in] *S	Instance pointer of PID control data structure.   
+* @return none.    
+* \par Description:   
+* The function resets the state buffer to zeros.    
+*/
+void arm_pid_reset_q31(
+  arm_pid_instance_q31 * S)
+{
+
+  /* Clear the state buffer.  The size will be always 3 samples */
+  memset(S->state, 0, 3u * sizeof(q31_t));
+}
+
+/**    
+ * @} end of PID group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_sin_cos_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_sin_cos_f32.c
new file mode 100644
index 0000000000..1679a780c7
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_sin_cos_f32.c
@@ -0,0 +1,428 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_sin_cos_f32.c    
+*    
+* Description:	Sine and Cosine calculation for floating-point values.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupController    
+ */
+
+/**    
+ * @defgroup SinCos Sine Cosine   
+ *    
+ * Computes the trigonometric sine and cosine values using a combination of table lookup   
+ * and linear interpolation.     
+ * There are separate functions for Q31 and floating-point data types.   
+ * The input to the floating-point version is in degrees while the   
+ * fixed-point Q31 have a scaled input with the range   
+ * [-1 0.9999] mapping to [-180 179] degrees.   
+ *   
+ * The implementation is based on table lookup using 360 values together with linear interpolation.   
+ * The steps used are:   
+ *  -# Calculation of the nearest integer table index.   
+ *  -# Compute the fractional portion (fract) of the input.   
+ *  -# Fetch the value corresponding to \c index from sine table to \c y0 and also value from \c index+1 to \c y1.      
+ *  -# Sine value is computed as  *psinVal = y0 + (fract * (y1 - y0)).    
+ *  -# Fetch the value corresponding to \c index from cosine table to \c y0 and also value from \c index+1 to \c y1.      
+ *  -# Cosine value is computed as  *pcosVal = y0 + (fract * (y1 - y0)).    
+ */
+
+ /**    
+ * @addtogroup SinCos    
+ * @{    
+ */
+
+
+/**    
+* \par    
+* Cosine Table is generated from following loop    
+* 
for(i = 0; i < 360; i++)    
+* {    
+*    cosTable[i]= cos((i-180) * PI/180.0);    
+* } 
   
+*/
+
+static const float32_t cosTable[360] = {
+  -0.999847695156391270f, -0.999390827019095760f, -0.998629534754573830f,
+  -0.997564050259824200f, -0.996194698091745550f, -0.994521895368273290f,
+  -0.992546151641321980f, -0.990268068741570250f,
+  -0.987688340595137660f, -0.984807753012208020f, -0.981627183447663980f,
+  -0.978147600733805690f, -0.974370064785235250f, -0.970295726275996470f,
+  -0.965925826289068200f, -0.961261695938318670f,
+  -0.956304755963035440f, -0.951056516295153530f, -0.945518575599316740f,
+  -0.939692620785908320f, -0.933580426497201740f, -0.927183854566787310f,
+  -0.920504853452440150f, -0.913545457642600760f,
+  -0.906307787036649940f, -0.898794046299167040f, -0.891006524188367790f,
+  -0.882947592858926770f, -0.874619707139395740f, -0.866025403784438710f,
+  -0.857167300702112220f, -0.848048096156425960f,
+  -0.838670567945424160f, -0.829037572555041620f, -0.819152044288991580f,
+  -0.809016994374947340f, -0.798635510047292940f, -0.788010753606721900f,
+  -0.777145961456970680f, -0.766044443118977900f,
+  -0.754709580222772010f, -0.743144825477394130f, -0.731353701619170460f,
+  -0.719339800338651300f, -0.707106781186547460f, -0.694658370458997030f,
+  -0.681998360062498370f, -0.669130606358858240f,
+  -0.656059028990507500f, -0.642787609686539360f, -0.629320391049837280f,
+  -0.615661475325658290f, -0.601815023152048380f, -0.587785252292473030f,
+  -0.573576436351045830f, -0.559192903470746680f,
+  -0.544639035015027080f, -0.529919264233204790f, -0.515038074910054270f,
+  -0.499999999999999780f, -0.484809620246337000f, -0.469471562785890530f,
+  -0.453990499739546750f, -0.438371146789077510f,
+  -0.422618261740699330f, -0.406736643075800100f, -0.390731128489273600f,
+  -0.374606593415912070f, -0.358367949545300270f, -0.342020143325668710f,
+  -0.325568154457156420f, -0.309016994374947340f,
+  -0.292371704722736660f, -0.275637355816999050f, -0.258819045102520850f,
+  -0.241921895599667790f, -0.224951054343864810f, -0.207911690817759120f,
+  -0.190808995376544800f, -0.173648177666930300f,
+  -0.156434465040231040f, -0.139173100960065350f, -0.121869343405147370f,
+  -0.104528463267653330f, -0.087155742747658235f, -0.069756473744125330f,
+  -0.052335956242943620f, -0.034899496702500733f,
+  -0.017452406437283477f, 0.000000000000000061f, 0.017452406437283376f,
+  0.034899496702501080f, 0.052335956242943966f, 0.069756473744125455f,
+  0.087155742747658138f, 0.104528463267653460f,
+  0.121869343405147490f, 0.139173100960065690f, 0.156434465040230920f,
+  0.173648177666930410f, 0.190808995376544920f, 0.207911690817759450f,
+  0.224951054343864920f, 0.241921895599667900f,
+  0.258819045102520740f, 0.275637355816999160f, 0.292371704722736770f,
+  0.309016994374947450f, 0.325568154457156760f, 0.342020143325668820f,
+  0.358367949545300380f, 0.374606593415911960f,
+  0.390731128489273940f, 0.406736643075800210f, 0.422618261740699440f,
+  0.438371146789077460f, 0.453990499739546860f, 0.469471562785890860f,
+  0.484809620246337110f, 0.500000000000000110f,
+  0.515038074910054380f, 0.529919264233204900f, 0.544639035015027200f,
+  0.559192903470746790f, 0.573576436351046050f, 0.587785252292473140f,
+  0.601815023152048270f, 0.615661475325658290f,
+  0.629320391049837500f, 0.642787609686539360f, 0.656059028990507280f,
+  0.669130606358858240f, 0.681998360062498480f, 0.694658370458997370f,
+  0.707106781186547570f, 0.719339800338651190f,
+  0.731353701619170570f, 0.743144825477394240f, 0.754709580222772010f,
+  0.766044443118978010f, 0.777145961456970900f, 0.788010753606722010f,
+  0.798635510047292830f, 0.809016994374947450f,
+  0.819152044288991800f, 0.829037572555041620f, 0.838670567945424050f,
+  0.848048096156425960f, 0.857167300702112330f, 0.866025403784438710f,
+  0.874619707139395740f, 0.882947592858926990f,
+  0.891006524188367900f, 0.898794046299167040f, 0.906307787036649940f,
+  0.913545457642600870f, 0.920504853452440370f, 0.927183854566787420f,
+  0.933580426497201740f, 0.939692620785908430f,
+  0.945518575599316850f, 0.951056516295153530f, 0.956304755963035440f,
+  0.961261695938318890f, 0.965925826289068310f, 0.970295726275996470f,
+  0.974370064785235250f, 0.978147600733805690f,
+  0.981627183447663980f, 0.984807753012208020f, 0.987688340595137770f,
+  0.990268068741570360f, 0.992546151641321980f, 0.994521895368273290f,
+  0.996194698091745550f, 0.997564050259824200f,
+  0.998629534754573830f, 0.999390827019095760f, 0.999847695156391270f,
+  1.000000000000000000f, 0.999847695156391270f, 0.999390827019095760f,
+  0.998629534754573830f, 0.997564050259824200f,
+  0.996194698091745550f, 0.994521895368273290f, 0.992546151641321980f,
+  0.990268068741570360f, 0.987688340595137770f, 0.984807753012208020f,
+  0.981627183447663980f, 0.978147600733805690f,
+  0.974370064785235250f, 0.970295726275996470f, 0.965925826289068310f,
+  0.961261695938318890f, 0.956304755963035440f, 0.951056516295153530f,
+  0.945518575599316850f, 0.939692620785908430f,
+  0.933580426497201740f, 0.927183854566787420f, 0.920504853452440370f,
+  0.913545457642600870f, 0.906307787036649940f, 0.898794046299167040f,
+  0.891006524188367900f, 0.882947592858926990f,
+  0.874619707139395740f, 0.866025403784438710f, 0.857167300702112330f,
+  0.848048096156425960f, 0.838670567945424050f, 0.829037572555041620f,
+  0.819152044288991800f, 0.809016994374947450f,
+  0.798635510047292830f, 0.788010753606722010f, 0.777145961456970900f,
+  0.766044443118978010f, 0.754709580222772010f, 0.743144825477394240f,
+  0.731353701619170570f, 0.719339800338651190f,
+  0.707106781186547570f, 0.694658370458997370f, 0.681998360062498480f,
+  0.669130606358858240f, 0.656059028990507280f, 0.642787609686539360f,
+  0.629320391049837500f, 0.615661475325658290f,
+  0.601815023152048270f, 0.587785252292473140f, 0.573576436351046050f,
+  0.559192903470746790f, 0.544639035015027200f, 0.529919264233204900f,
+  0.515038074910054380f, 0.500000000000000110f,
+  0.484809620246337110f, 0.469471562785890860f, 0.453990499739546860f,
+  0.438371146789077460f, 0.422618261740699440f, 0.406736643075800210f,
+  0.390731128489273940f, 0.374606593415911960f,
+  0.358367949545300380f, 0.342020143325668820f, 0.325568154457156760f,
+  0.309016994374947450f, 0.292371704722736770f, 0.275637355816999160f,
+  0.258819045102520740f, 0.241921895599667900f,
+  0.224951054343864920f, 0.207911690817759450f, 0.190808995376544920f,
+  0.173648177666930410f, 0.156434465040230920f, 0.139173100960065690f,
+  0.121869343405147490f, 0.104528463267653460f,
+  0.087155742747658138f, 0.069756473744125455f, 0.052335956242943966f,
+  0.034899496702501080f, 0.017452406437283376f, 0.000000000000000061f,
+  -0.017452406437283477f, -0.034899496702500733f,
+  -0.052335956242943620f, -0.069756473744125330f, -0.087155742747658235f,
+  -0.104528463267653330f, -0.121869343405147370f, -0.139173100960065350f,
+  -0.156434465040231040f, -0.173648177666930300f,
+  -0.190808995376544800f, -0.207911690817759120f, -0.224951054343864810f,
+  -0.241921895599667790f, -0.258819045102520850f, -0.275637355816999050f,
+  -0.292371704722736660f, -0.309016994374947340f,
+  -0.325568154457156420f, -0.342020143325668710f, -0.358367949545300270f,
+  -0.374606593415912070f, -0.390731128489273600f, -0.406736643075800100f,
+  -0.422618261740699330f, -0.438371146789077510f,
+  -0.453990499739546750f, -0.469471562785890530f, -0.484809620246337000f,
+  -0.499999999999999780f, -0.515038074910054270f, -0.529919264233204790f,
+  -0.544639035015027080f, -0.559192903470746680f,
+  -0.573576436351045830f, -0.587785252292473030f, -0.601815023152048380f,
+  -0.615661475325658290f, -0.629320391049837280f, -0.642787609686539360f,
+  -0.656059028990507500f, -0.669130606358858240f,
+  -0.681998360062498370f, -0.694658370458997030f, -0.707106781186547460f,
+  -0.719339800338651300f, -0.731353701619170460f, -0.743144825477394130f,
+  -0.754709580222772010f, -0.766044443118977900f,
+  -0.777145961456970680f, -0.788010753606721900f, -0.798635510047292940f,
+  -0.809016994374947340f, -0.819152044288991580f, -0.829037572555041620f,
+  -0.838670567945424160f, -0.848048096156425960f,
+  -0.857167300702112220f, -0.866025403784438710f, -0.874619707139395740f,
+  -0.882947592858926770f, -0.891006524188367790f, -0.898794046299167040f,
+  -0.906307787036649940f, -0.913545457642600760f,
+  -0.920504853452440150f, -0.927183854566787310f, -0.933580426497201740f,
+  -0.939692620785908320f, -0.945518575599316740f, -0.951056516295153530f,
+  -0.956304755963035440f, -0.961261695938318670f,
+  -0.965925826289068200f, -0.970295726275996470f, -0.974370064785235250f,
+  -0.978147600733805690f, -0.981627183447663980f, -0.984807753012208020f,
+  -0.987688340595137660f, -0.990268068741570250f,
+  -0.992546151641321980f, -0.994521895368273290f, -0.996194698091745550f,
+  -0.997564050259824200f, -0.998629534754573830f, -0.999390827019095760f,
+  -0.999847695156391270f, -1.000000000000000000f
+};
+
+/**    
+* \par    
+* Sine Table is generated from following loop    
+* 
for(i = 0; i < 360; i++)    
+* {    
+*    sinTable[i]= sin((i-180) * PI/180.0);    
+* } 
    
+*/
+
+
+static const float32_t sinTable[360] = {
+  -0.017452406437283439f, -0.034899496702500699f, -0.052335956242943807f,
+  -0.069756473744125524f, -0.087155742747658638f, -0.104528463267653730f,
+  -0.121869343405147550f, -0.139173100960065740f,
+  -0.156434465040230980f, -0.173648177666930280f, -0.190808995376544970f,
+  -0.207911690817759310f, -0.224951054343864780f, -0.241921895599667730f,
+  -0.258819045102521020f, -0.275637355816999660f,
+  -0.292371704722737050f, -0.309016994374947510f, -0.325568154457156980f,
+  -0.342020143325668880f, -0.358367949545300210f, -0.374606593415912240f,
+  -0.390731128489274160f, -0.406736643075800430f,
+  -0.422618261740699500f, -0.438371146789077290f, -0.453990499739546860f,
+  -0.469471562785891080f, -0.484809620246337170f, -0.499999999999999940f,
+  -0.515038074910054380f, -0.529919264233204900f,
+  -0.544639035015026860f, -0.559192903470746900f, -0.573576436351046380f,
+  -0.587785252292473250f, -0.601815023152048160f, -0.615661475325658400f,
+  -0.629320391049837720f, -0.642787609686539470f,
+  -0.656059028990507280f, -0.669130606358858350f, -0.681998360062498590f,
+  -0.694658370458997140f, -0.707106781186547570f, -0.719339800338651410f,
+  -0.731353701619170570f, -0.743144825477394240f,
+  -0.754709580222771790f, -0.766044443118978010f, -0.777145961456971010f,
+  -0.788010753606722010f, -0.798635510047292720f, -0.809016994374947450f,
+  -0.819152044288992020f, -0.829037572555041740f,
+  -0.838670567945424050f, -0.848048096156426070f, -0.857167300702112330f,
+  -0.866025403784438710f, -0.874619707139395850f, -0.882947592858927100f,
+  -0.891006524188367900f, -0.898794046299166930f,
+  -0.906307787036650050f, -0.913545457642600980f, -0.920504853452440370f,
+  -0.927183854566787420f, -0.933580426497201740f, -0.939692620785908430f,
+  -0.945518575599316850f, -0.951056516295153640f,
+  -0.956304755963035550f, -0.961261695938318890f, -0.965925826289068310f,
+  -0.970295726275996470f, -0.974370064785235250f, -0.978147600733805690f,
+  -0.981627183447663980f, -0.984807753012208020f,
+  -0.987688340595137660f, -0.990268068741570360f, -0.992546151641322090f,
+  -0.994521895368273400f, -0.996194698091745550f, -0.997564050259824200f,
+  -0.998629534754573830f, -0.999390827019095760f,
+  -0.999847695156391270f, -1.000000000000000000f, -0.999847695156391270f,
+  -0.999390827019095760f, -0.998629534754573830f, -0.997564050259824200f,
+  -0.996194698091745550f, -0.994521895368273290f,
+  -0.992546151641321980f, -0.990268068741570250f, -0.987688340595137770f,
+  -0.984807753012208020f, -0.981627183447663980f, -0.978147600733805580f,
+  -0.974370064785235250f, -0.970295726275996470f,
+  -0.965925826289068310f, -0.961261695938318890f, -0.956304755963035440f,
+  -0.951056516295153530f, -0.945518575599316740f, -0.939692620785908320f,
+  -0.933580426497201740f, -0.927183854566787420f,
+  -0.920504853452440260f, -0.913545457642600870f, -0.906307787036649940f,
+  -0.898794046299167040f, -0.891006524188367790f, -0.882947592858926880f,
+  -0.874619707139395740f, -0.866025403784438600f,
+  -0.857167300702112220f, -0.848048096156426070f, -0.838670567945423940f,
+  -0.829037572555041740f, -0.819152044288991800f, -0.809016994374947450f,
+  -0.798635510047292830f, -0.788010753606722010f,
+  -0.777145961456970790f, -0.766044443118978010f, -0.754709580222772010f,
+  -0.743144825477394240f, -0.731353701619170460f, -0.719339800338651080f,
+  -0.707106781186547460f, -0.694658370458997250f,
+  -0.681998360062498480f, -0.669130606358858240f, -0.656059028990507160f,
+  -0.642787609686539250f, -0.629320391049837390f, -0.615661475325658180f,
+  -0.601815023152048270f, -0.587785252292473140f,
+  -0.573576436351046050f, -0.559192903470746900f, -0.544639035015027080f,
+  -0.529919264233204900f, -0.515038074910054160f, -0.499999999999999940f,
+  -0.484809620246337060f, -0.469471562785890810f,
+  -0.453990499739546750f, -0.438371146789077400f, -0.422618261740699440f,
+  -0.406736643075800150f, -0.390731128489273720f, -0.374606593415912010f,
+  -0.358367949545300270f, -0.342020143325668710f,
+  -0.325568154457156640f, -0.309016994374947400f, -0.292371704722736770f,
+  -0.275637355816999160f, -0.258819045102520740f, -0.241921895599667730f,
+  -0.224951054343865000f, -0.207911690817759310f,
+  -0.190808995376544800f, -0.173648177666930330f, -0.156434465040230870f,
+  -0.139173100960065440f, -0.121869343405147480f, -0.104528463267653460f,
+  -0.087155742747658166f, -0.069756473744125302f,
+  -0.052335956242943828f, -0.034899496702500969f, -0.017452406437283512f,
+  0.000000000000000000f, 0.017452406437283512f, 0.034899496702500969f,
+  0.052335956242943828f, 0.069756473744125302f,
+  0.087155742747658166f, 0.104528463267653460f, 0.121869343405147480f,
+  0.139173100960065440f, 0.156434465040230870f, 0.173648177666930330f,
+  0.190808995376544800f, 0.207911690817759310f,
+  0.224951054343865000f, 0.241921895599667730f, 0.258819045102520740f,
+  0.275637355816999160f, 0.292371704722736770f, 0.309016994374947400f,
+  0.325568154457156640f, 0.342020143325668710f,
+  0.358367949545300270f, 0.374606593415912010f, 0.390731128489273720f,
+  0.406736643075800150f, 0.422618261740699440f, 0.438371146789077400f,
+  0.453990499739546750f, 0.469471562785890810f,
+  0.484809620246337060f, 0.499999999999999940f, 0.515038074910054160f,
+  0.529919264233204900f, 0.544639035015027080f, 0.559192903470746900f,
+  0.573576436351046050f, 0.587785252292473140f,
+  0.601815023152048270f, 0.615661475325658180f, 0.629320391049837390f,
+  0.642787609686539250f, 0.656059028990507160f, 0.669130606358858240f,
+  0.681998360062498480f, 0.694658370458997250f,
+  0.707106781186547460f, 0.719339800338651080f, 0.731353701619170460f,
+  0.743144825477394240f, 0.754709580222772010f, 0.766044443118978010f,
+  0.777145961456970790f, 0.788010753606722010f,
+  0.798635510047292830f, 0.809016994374947450f, 0.819152044288991800f,
+  0.829037572555041740f, 0.838670567945423940f, 0.848048096156426070f,
+  0.857167300702112220f, 0.866025403784438600f,
+  0.874619707139395740f, 0.882947592858926880f, 0.891006524188367790f,
+  0.898794046299167040f, 0.906307787036649940f, 0.913545457642600870f,
+  0.920504853452440260f, 0.927183854566787420f,
+  0.933580426497201740f, 0.939692620785908320f, 0.945518575599316740f,
+  0.951056516295153530f, 0.956304755963035440f, 0.961261695938318890f,
+  0.965925826289068310f, 0.970295726275996470f,
+  0.974370064785235250f, 0.978147600733805580f, 0.981627183447663980f,
+  0.984807753012208020f, 0.987688340595137770f, 0.990268068741570250f,
+  0.992546151641321980f, 0.994521895368273290f,
+  0.996194698091745550f, 0.997564050259824200f, 0.998629534754573830f,
+  0.999390827019095760f, 0.999847695156391270f, 1.000000000000000000f,
+  0.999847695156391270f, 0.999390827019095760f,
+  0.998629534754573830f, 0.997564050259824200f, 0.996194698091745550f,
+  0.994521895368273400f, 0.992546151641322090f, 0.990268068741570360f,
+  0.987688340595137660f, 0.984807753012208020f,
+  0.981627183447663980f, 0.978147600733805690f, 0.974370064785235250f,
+  0.970295726275996470f, 0.965925826289068310f, 0.961261695938318890f,
+  0.956304755963035550f, 0.951056516295153640f,
+  0.945518575599316850f, 0.939692620785908430f, 0.933580426497201740f,
+  0.927183854566787420f, 0.920504853452440370f, 0.913545457642600980f,
+  0.906307787036650050f, 0.898794046299166930f,
+  0.891006524188367900f, 0.882947592858927100f, 0.874619707139395850f,
+  0.866025403784438710f, 0.857167300702112330f, 0.848048096156426070f,
+  0.838670567945424050f, 0.829037572555041740f,
+  0.819152044288992020f, 0.809016994374947450f, 0.798635510047292720f,
+  0.788010753606722010f, 0.777145961456971010f, 0.766044443118978010f,
+  0.754709580222771790f, 0.743144825477394240f,
+  0.731353701619170570f, 0.719339800338651410f, 0.707106781186547570f,
+  0.694658370458997140f, 0.681998360062498590f, 0.669130606358858350f,
+  0.656059028990507280f, 0.642787609686539470f,
+  0.629320391049837720f, 0.615661475325658400f, 0.601815023152048160f,
+  0.587785252292473250f, 0.573576436351046380f, 0.559192903470746900f,
+  0.544639035015026860f, 0.529919264233204900f,
+  0.515038074910054380f, 0.499999999999999940f, 0.484809620246337170f,
+  0.469471562785891080f, 0.453990499739546860f, 0.438371146789077290f,
+  0.422618261740699500f, 0.406736643075800430f,
+  0.390731128489274160f, 0.374606593415912240f, 0.358367949545300210f,
+  0.342020143325668880f, 0.325568154457156980f, 0.309016994374947510f,
+  0.292371704722737050f, 0.275637355816999660f,
+  0.258819045102521020f, 0.241921895599667730f, 0.224951054343864780f,
+  0.207911690817759310f, 0.190808995376544970f, 0.173648177666930280f,
+  0.156434465040230980f, 0.139173100960065740f,
+  0.121869343405147550f, 0.104528463267653730f, 0.087155742747658638f,
+  0.069756473744125524f, 0.052335956242943807f, 0.034899496702500699f,
+  0.017452406437283439f, 0.000000000000000122f
+};
+
+
+/**    
+ * @brief  Floating-point sin_cos function.   
+ * @param[in]  theta    input value in degrees    
+ * @param[out] *pSinVal points to the processed sine output.    
+ * @param[out] *pCosVal points to the processed cos output.    
+ * @return none.   
+ */
+
+
+void arm_sin_cos_f32(
+  float32_t theta,
+  float32_t * pSinVal,
+  float32_t * pCosVal)
+{
+  int32_t i;                                     /* Index for reading nearwst output values */
+  float32_t x1 = -179.0f;                        /* Initial input value */
+  float32_t y0, y1;                              /* nearest output values */
+  float32_t y2, y3;
+  float32_t fract;                               /* fractional part of input */
+
+  /* Calculation of fractional part */
+  if(theta > 0.0f)
+  {
+    fract = theta - (float32_t) ((int32_t) theta);
+  }
+  else
+  {
+    fract = (theta - (float32_t) ((int32_t) theta)) + 1.0f;
+  }
+
+  /* index calculation for reading nearest output values */
+  i = (uint32_t) (theta - x1);
+
+  /* Checking min and max index of table */
+  if(i < 0)
+  {
+    i = 0;
+  }
+  else if(i >= 359)
+  {
+    i = 358;
+  }
+
+  /* reading nearest sine output values */
+  y0 = sinTable[i];
+  y1 = sinTable[i + 1u];
+
+  /* reading nearest cosine output values */
+  y2 = cosTable[i];
+  y3 = cosTable[i + 1u];
+
+  y1 = y1 - y0;
+  y3 = y3 - y2;
+
+  y1 = fract * y1;
+  y3 = fract * y3;
+
+  /* Calculation of sine value */
+  *pSinVal = y0 + y1;
+
+  /* Calculation of cosine value */
+  *pCosVal = y2 + y3;
+
+}
+
+/**    
+ * @} end of SinCos group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_sin_cos_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_sin_cos_q31.c
new file mode 100644
index 0000000000..e22d25e539
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_sin_cos_q31.c
@@ -0,0 +1,324 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_sin_cos_q31.c    
+*    
+* Description:	Cosine & Sine calculation for Q31 values.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupController    
+ */
+
+ /**    
+ * @addtogroup SinCos    
+ * @{    
+ */
+
+/**    
+* \par    
+* Sine Table is generated from following loop    
+* 
for(i = 0; i < 360; i++)    
+* {    
+*    sinTable[i]= sin((i-180) * PI/180.0);    
+* } 
   
+* Convert above coefficients to fixed point 1.31 format.    
+*/
+
+static const int32_t sinTableQ31[360] = {
+
+  0x0, 0xfdc41e9b, 0xfb8869ce, 0xf94d0e2e, 0xf7123849, 0xf4d814a4, 0xf29ecfb2,
+  0xf06695da,
+  0xee2f9369, 0xebf9f498, 0xe9c5e582, 0xe7939223, 0xe5632654, 0xe334cdc9,
+  0xe108b40d, 0xdedf047d,
+  0xdcb7ea46, 0xda939061, 0xd8722192, 0xd653c860, 0xd438af17, 0xd220ffc0,
+  0xd00ce422, 0xcdfc85bb,
+  0xcbf00dbe, 0xc9e7a512, 0xc7e3744b, 0xc5e3a3a9, 0xc3e85b18, 0xc1f1c224,
+  0xc0000000, 0xbe133b7c,
+  0xbc2b9b05, 0xba4944a2, 0xb86c5df0, 0xb6950c1e, 0xb4c373ee, 0xb2f7b9af,
+  0xb1320139, 0xaf726def,
+  0xadb922b7, 0xac0641fb, 0xaa59eda4, 0xa8b4471a, 0xa7156f3c, 0xa57d8666,
+  0xa3ecac65, 0xa263007d,
+  0xa0e0a15f, 0x9f65ad2d, 0x9df24175, 0x9c867b2c, 0x9b2276b0, 0x99c64fc5,
+  0x98722192, 0x9726069c,
+  0x95e218c9, 0x94a6715d, 0x937328f5, 0x92485786, 0x9126145f, 0x900c7621,
+  0x8efb92c2, 0x8df37f8b,
+  0x8cf45113, 0x8bfe1b3f, 0x8b10f144, 0x8a2ce59f, 0x89520a1a, 0x88806fc4,
+  0x87b826f7, 0x86f93f50,
+  0x8643c7b3, 0x8597ce46, 0x84f56073, 0x845c8ae3, 0x83cd5982, 0x8347d77b,
+  0x82cc0f36, 0x825a0a5b,
+  0x81f1d1ce, 0x81936daf, 0x813ee55b, 0x80f43f69, 0x80b381ac, 0x807cb130,
+  0x804fd23a, 0x802ce84c,
+  0x8013f61d, 0x8004fda0, 0x80000000, 0x8004fda0, 0x8013f61d, 0x802ce84c,
+  0x804fd23a, 0x807cb130,
+  0x80b381ac, 0x80f43f69, 0x813ee55b, 0x81936daf, 0x81f1d1ce, 0x825a0a5b,
+  0x82cc0f36, 0x8347d77b,
+  0x83cd5982, 0x845c8ae3, 0x84f56073, 0x8597ce46, 0x8643c7b3, 0x86f93f50,
+  0x87b826f7, 0x88806fc4,
+  0x89520a1a, 0x8a2ce59f, 0x8b10f144, 0x8bfe1b3f, 0x8cf45113, 0x8df37f8b,
+  0x8efb92c2, 0x900c7621,
+  0x9126145f, 0x92485786, 0x937328f5, 0x94a6715d, 0x95e218c9, 0x9726069c,
+  0x98722192, 0x99c64fc5,
+  0x9b2276b0, 0x9c867b2c, 0x9df24175, 0x9f65ad2d, 0xa0e0a15f, 0xa263007d,
+  0xa3ecac65, 0xa57d8666,
+  0xa7156f3c, 0xa8b4471a, 0xaa59eda4, 0xac0641fb, 0xadb922b7, 0xaf726def,
+  0xb1320139, 0xb2f7b9af,
+  0xb4c373ee, 0xb6950c1e, 0xb86c5df0, 0xba4944a2, 0xbc2b9b05, 0xbe133b7c,
+  0xc0000000, 0xc1f1c224,
+  0xc3e85b18, 0xc5e3a3a9, 0xc7e3744b, 0xc9e7a512, 0xcbf00dbe, 0xcdfc85bb,
+  0xd00ce422, 0xd220ffc0,
+  0xd438af17, 0xd653c860, 0xd8722192, 0xda939061, 0xdcb7ea46, 0xdedf047d,
+  0xe108b40d, 0xe334cdc9,
+  0xe5632654, 0xe7939223, 0xe9c5e582, 0xebf9f498, 0xee2f9369, 0xf06695da,
+  0xf29ecfb2, 0xf4d814a4,
+  0xf7123849, 0xf94d0e2e, 0xfb8869ce, 0xfdc41e9b, 0x0, 0x23be165, 0x4779632,
+  0x6b2f1d2,
+  0x8edc7b7, 0xb27eb5c, 0xd61304e, 0xf996a26, 0x11d06c97, 0x14060b68,
+  0x163a1a7e, 0x186c6ddd,
+  0x1a9cd9ac, 0x1ccb3237, 0x1ef74bf3, 0x2120fb83, 0x234815ba, 0x256c6f9f,
+  0x278dde6e, 0x29ac37a0,
+  0x2bc750e9, 0x2ddf0040, 0x2ff31bde, 0x32037a45, 0x340ff242, 0x36185aee,
+  0x381c8bb5, 0x3a1c5c57,
+  0x3c17a4e8, 0x3e0e3ddc, 0x40000000, 0x41ecc484, 0x43d464fb, 0x45b6bb5e,
+  0x4793a210, 0x496af3e2,
+  0x4b3c8c12, 0x4d084651, 0x4ecdfec7, 0x508d9211, 0x5246dd49, 0x53f9be05,
+  0x55a6125c, 0x574bb8e6,
+  0x58ea90c4, 0x5a82799a, 0x5c13539b, 0x5d9cff83, 0x5f1f5ea1, 0x609a52d3,
+  0x620dbe8b, 0x637984d4,
+  0x64dd8950, 0x6639b03b, 0x678dde6e, 0x68d9f964, 0x6a1de737, 0x6b598ea3,
+  0x6c8cd70b, 0x6db7a87a,
+  0x6ed9eba1, 0x6ff389df, 0x71046d3e, 0x720c8075, 0x730baeed, 0x7401e4c1,
+  0x74ef0ebc, 0x75d31a61,
+  0x76adf5e6, 0x777f903c, 0x7847d909, 0x7906c0b0, 0x79bc384d, 0x7a6831ba,
+  0x7b0a9f8d, 0x7ba3751d,
+  0x7c32a67e, 0x7cb82885, 0x7d33f0ca, 0x7da5f5a5, 0x7e0e2e32, 0x7e6c9251,
+  0x7ec11aa5, 0x7f0bc097,
+  0x7f4c7e54, 0x7f834ed0, 0x7fb02dc6, 0x7fd317b4, 0x7fec09e3, 0x7ffb0260,
+  0x7fffffff, 0x7ffb0260,
+  0x7fec09e3, 0x7fd317b4, 0x7fb02dc6, 0x7f834ed0, 0x7f4c7e54, 0x7f0bc097,
+  0x7ec11aa5, 0x7e6c9251,
+  0x7e0e2e32, 0x7da5f5a5, 0x7d33f0ca, 0x7cb82885, 0x7c32a67e, 0x7ba3751d,
+  0x7b0a9f8d, 0x7a6831ba,
+  0x79bc384d, 0x7906c0b0, 0x7847d909, 0x777f903c, 0x76adf5e6, 0x75d31a61,
+  0x74ef0ebc, 0x7401e4c1,
+  0x730baeed, 0x720c8075, 0x71046d3e, 0x6ff389df, 0x6ed9eba1, 0x6db7a87a,
+  0x6c8cd70b, 0x6b598ea3,
+  0x6a1de737, 0x68d9f964, 0x678dde6e, 0x6639b03b, 0x64dd8950, 0x637984d4,
+  0x620dbe8b, 0x609a52d3,
+  0x5f1f5ea1, 0x5d9cff83, 0x5c13539b, 0x5a82799a, 0x58ea90c4, 0x574bb8e6,
+  0x55a6125c, 0x53f9be05,
+  0x5246dd49, 0x508d9211, 0x4ecdfec7, 0x4d084651, 0x4b3c8c12, 0x496af3e2,
+  0x4793a210, 0x45b6bb5e,
+  0x43d464fb, 0x41ecc484, 0x40000000, 0x3e0e3ddc, 0x3c17a4e8, 0x3a1c5c57,
+  0x381c8bb5, 0x36185aee,
+  0x340ff242, 0x32037a45, 0x2ff31bde, 0x2ddf0040, 0x2bc750e9, 0x29ac37a0,
+  0x278dde6e, 0x256c6f9f,
+  0x234815ba, 0x2120fb83, 0x1ef74bf3, 0x1ccb3237, 0x1a9cd9ac, 0x186c6ddd,
+  0x163a1a7e, 0x14060b68,
+  0x11d06c97, 0xf996a26, 0xd61304e, 0xb27eb5c, 0x8edc7b7, 0x6b2f1d2,
+  0x4779632, 0x23be165,
+
+
+};
+
+/**    
+* \par    
+* Cosine Table is generated from following loop    
+* 
for(i = 0; i < 360; i++)    
+* {    
+*    cosTable[i]= cos((i-180) * PI/180.0);    
+* } 
   
+* \par    
+* Convert above coefficients to fixed point 1.31 format.    
+*/
+static const int32_t cosTableQ31[360] = {
+  0x80000000, 0x8004fda0, 0x8013f61d, 0x802ce84c, 0x804fd23a, 0x807cb130,
+  0x80b381ac, 0x80f43f69,
+  0x813ee55b, 0x81936daf, 0x81f1d1ce, 0x825a0a5b, 0x82cc0f36, 0x8347d77b,
+  0x83cd5982, 0x845c8ae3,
+  0x84f56073, 0x8597ce46, 0x8643c7b3, 0x86f93f50, 0x87b826f7, 0x88806fc4,
+  0x89520a1a, 0x8a2ce59f,
+  0x8b10f144, 0x8bfe1b3f, 0x8cf45113, 0x8df37f8b, 0x8efb92c2, 0x900c7621,
+  0x9126145f, 0x92485786,
+  0x937328f5, 0x94a6715d, 0x95e218c9, 0x9726069c, 0x98722192, 0x99c64fc5,
+  0x9b2276b0, 0x9c867b2c,
+  0x9df24175, 0x9f65ad2d, 0xa0e0a15f, 0xa263007d, 0xa3ecac65, 0xa57d8666,
+  0xa7156f3c, 0xa8b4471a,
+  0xaa59eda4, 0xac0641fb, 0xadb922b7, 0xaf726def, 0xb1320139, 0xb2f7b9af,
+  0xb4c373ee, 0xb6950c1e,
+  0xb86c5df0, 0xba4944a2, 0xbc2b9b05, 0xbe133b7c, 0xc0000000, 0xc1f1c224,
+  0xc3e85b18, 0xc5e3a3a9,
+  0xc7e3744b, 0xc9e7a512, 0xcbf00dbe, 0xcdfc85bb, 0xd00ce422, 0xd220ffc0,
+  0xd438af17, 0xd653c860,
+  0xd8722192, 0xda939061, 0xdcb7ea46, 0xdedf047d, 0xe108b40d, 0xe334cdc9,
+  0xe5632654, 0xe7939223,
+  0xe9c5e582, 0xebf9f498, 0xee2f9369, 0xf06695da, 0xf29ecfb2, 0xf4d814a4,
+  0xf7123849, 0xf94d0e2e,
+  0xfb8869ce, 0xfdc41e9b, 0x0, 0x23be165, 0x4779632, 0x6b2f1d2, 0x8edc7b7,
+  0xb27eb5c,
+  0xd61304e, 0xf996a26, 0x11d06c97, 0x14060b68, 0x163a1a7e, 0x186c6ddd,
+  0x1a9cd9ac, 0x1ccb3237,
+  0x1ef74bf3, 0x2120fb83, 0x234815ba, 0x256c6f9f, 0x278dde6e, 0x29ac37a0,
+  0x2bc750e9, 0x2ddf0040,
+  0x2ff31bde, 0x32037a45, 0x340ff242, 0x36185aee, 0x381c8bb5, 0x3a1c5c57,
+  0x3c17a4e8, 0x3e0e3ddc,
+  0x40000000, 0x41ecc484, 0x43d464fb, 0x45b6bb5e, 0x4793a210, 0x496af3e2,
+  0x4b3c8c12, 0x4d084651,
+  0x4ecdfec7, 0x508d9211, 0x5246dd49, 0x53f9be05, 0x55a6125c, 0x574bb8e6,
+  0x58ea90c4, 0x5a82799a,
+  0x5c13539b, 0x5d9cff83, 0x5f1f5ea1, 0x609a52d3, 0x620dbe8b, 0x637984d4,
+  0x64dd8950, 0x6639b03b,
+  0x678dde6e, 0x68d9f964, 0x6a1de737, 0x6b598ea3, 0x6c8cd70b, 0x6db7a87a,
+  0x6ed9eba1, 0x6ff389df,
+  0x71046d3e, 0x720c8075, 0x730baeed, 0x7401e4c1, 0x74ef0ebc, 0x75d31a61,
+  0x76adf5e6, 0x777f903c,
+  0x7847d909, 0x7906c0b0, 0x79bc384d, 0x7a6831ba, 0x7b0a9f8d, 0x7ba3751d,
+  0x7c32a67e, 0x7cb82885,
+  0x7d33f0ca, 0x7da5f5a5, 0x7e0e2e32, 0x7e6c9251, 0x7ec11aa5, 0x7f0bc097,
+  0x7f4c7e54, 0x7f834ed0,
+  0x7fb02dc6, 0x7fd317b4, 0x7fec09e3, 0x7ffb0260, 0x7fffffff, 0x7ffb0260,
+  0x7fec09e3, 0x7fd317b4,
+  0x7fb02dc6, 0x7f834ed0, 0x7f4c7e54, 0x7f0bc097, 0x7ec11aa5, 0x7e6c9251,
+  0x7e0e2e32, 0x7da5f5a5,
+  0x7d33f0ca, 0x7cb82885, 0x7c32a67e, 0x7ba3751d, 0x7b0a9f8d, 0x7a6831ba,
+  0x79bc384d, 0x7906c0b0,
+  0x7847d909, 0x777f903c, 0x76adf5e6, 0x75d31a61, 0x74ef0ebc, 0x7401e4c1,
+  0x730baeed, 0x720c8075,
+  0x71046d3e, 0x6ff389df, 0x6ed9eba1, 0x6db7a87a, 0x6c8cd70b, 0x6b598ea3,
+  0x6a1de737, 0x68d9f964,
+  0x678dde6e, 0x6639b03b, 0x64dd8950, 0x637984d4, 0x620dbe8b, 0x609a52d3,
+  0x5f1f5ea1, 0x5d9cff83,
+  0x5c13539b, 0x5a82799a, 0x58ea90c4, 0x574bb8e6, 0x55a6125c, 0x53f9be05,
+  0x5246dd49, 0x508d9211,
+  0x4ecdfec7, 0x4d084651, 0x4b3c8c12, 0x496af3e2, 0x4793a210, 0x45b6bb5e,
+  0x43d464fb, 0x41ecc484,
+  0x40000000, 0x3e0e3ddc, 0x3c17a4e8, 0x3a1c5c57, 0x381c8bb5, 0x36185aee,
+  0x340ff242, 0x32037a45,
+  0x2ff31bde, 0x2ddf0040, 0x2bc750e9, 0x29ac37a0, 0x278dde6e, 0x256c6f9f,
+  0x234815ba, 0x2120fb83,
+  0x1ef74bf3, 0x1ccb3237, 0x1a9cd9ac, 0x186c6ddd, 0x163a1a7e, 0x14060b68,
+  0x11d06c97, 0xf996a26,
+  0xd61304e, 0xb27eb5c, 0x8edc7b7, 0x6b2f1d2, 0x4779632, 0x23be165, 0x0,
+  0xfdc41e9b,
+  0xfb8869ce, 0xf94d0e2e, 0xf7123849, 0xf4d814a4, 0xf29ecfb2, 0xf06695da,
+  0xee2f9369, 0xebf9f498,
+  0xe9c5e582, 0xe7939223, 0xe5632654, 0xe334cdc9, 0xe108b40d, 0xdedf047d,
+  0xdcb7ea46, 0xda939061,
+  0xd8722192, 0xd653c860, 0xd438af17, 0xd220ffc0, 0xd00ce422, 0xcdfc85bb,
+  0xcbf00dbe, 0xc9e7a512,
+  0xc7e3744b, 0xc5e3a3a9, 0xc3e85b18, 0xc1f1c224, 0xc0000000, 0xbe133b7c,
+  0xbc2b9b05, 0xba4944a2,
+  0xb86c5df0, 0xb6950c1e, 0xb4c373ee, 0xb2f7b9af, 0xb1320139, 0xaf726def,
+  0xadb922b7, 0xac0641fb,
+  0xaa59eda4, 0xa8b4471a, 0xa7156f3c, 0xa57d8666, 0xa3ecac65, 0xa263007d,
+  0xa0e0a15f, 0x9f65ad2d,
+  0x9df24175, 0x9c867b2c, 0x9b2276b0, 0x99c64fc5, 0x98722192, 0x9726069c,
+  0x95e218c9, 0x94a6715d,
+  0x937328f5, 0x92485786, 0x9126145f, 0x900c7621, 0x8efb92c2, 0x8df37f8b,
+  0x8cf45113, 0x8bfe1b3f,
+  0x8b10f144, 0x8a2ce59f, 0x89520a1a, 0x88806fc4, 0x87b826f7, 0x86f93f50,
+  0x8643c7b3, 0x8597ce46,
+  0x84f56073, 0x845c8ae3, 0x83cd5982, 0x8347d77b, 0x82cc0f36, 0x825a0a5b,
+  0x81f1d1ce, 0x81936daf,
+  0x813ee55b, 0x80f43f69, 0x80b381ac, 0x807cb130, 0x804fd23a, 0x802ce84c,
+  0x8013f61d, 0x8004fda0,
+
+};
+
+
+/**    
+ * @brief  Q31 sin_cos function.   
+ * @param[in]  theta    scaled input value in degrees    
+ * @param[out] *pSinVal points to the processed sine output.    
+ * @param[out] *pCosVal points to the processed cosine output.    
+ * @return none.   
+ *    
+ * The Q31 input value is in the range [-1 0.999999] and is mapped to a degree value in the range [-180 179].   
+ *    
+ */
+
+
+void arm_sin_cos_q31(
+  q31_t theta,
+  q31_t * pSinVal,
+  q31_t * pCosVal)
+{
+  q31_t x0;                                      /* Nearest input value */
+  q31_t y0, y1;                                  /* Nearest output values */
+  q31_t xSpacing = INPUT_SPACING;                /* Spaing between inputs */
+  int32_t i;                                     /* Index */
+  q31_t oneByXSpacing;                           /* 1/ xSpacing value */
+  q31_t out;                                     /* temporary variable */
+  uint32_t sign_bits;                            /* No.of sign bits */
+  uint32_t firstX = 0x80000000;                  /* First X value */
+
+  /* Calculation of index */
+  i = ((uint32_t) theta - firstX) / (uint32_t) xSpacing;
+
+  /* Checking min and max index of table */
+  if(i < 0)
+  {
+    i = 0;
+  }
+  else if(i >= 359)
+  {
+    i = 358;
+  }
+
+  /* Calculation of first nearest input value */
+  x0 = (q31_t) firstX + ((q31_t) i * xSpacing);
+
+  /* Reading nearest sine output values from table */
+  y0 = sinTableQ31[i];
+  y1 = sinTableQ31[i + 1u];
+
+  /* Calculation of 1/(x1-x0) */
+  /* (x1-x0) is xSpacing which is fixed value */
+  sign_bits = 8u;
+  oneByXSpacing = 0x5A000000;
+
+  /* Calculation of (theta - x0)/(x1-x0) */
+  out =
+    (((q31_t) (((q63_t) (theta - x0) * oneByXSpacing) >> 32)) << sign_bits);
+
+  /* Calculation of y0 + (y1 - y0) * ((theta - x0)/(x1-x0)) */
+  *pSinVal = __QADD(y0, ((q31_t) (((q63_t) (y1 - y0) * out) >> 30)));
+
+  /* Reading nearest cosine output values from table */
+  y0 = cosTableQ31[i];
+  y1 = cosTableQ31[i + 1u];
+
+  /* Calculation of y0 + (y1 - y0) * ((theta - x0)/(x1-x0)) */
+  *pCosVal = __QADD(y0, ((q31_t) (((q63_t) (y1 - y0) * out) >> 30)));
+
+}
+
+/**    
+ * @} end of SinCos group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_cos_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_cos_f32.c
new file mode 100644
index 0000000000..bee758bff7
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_cos_f32.c
@@ -0,0 +1,280 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_cos_f32.c    
+*    
+* Description:	Fast cosine calculation for floating-point values.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+/**    
+ * @ingroup groupFastMath    
+ */
+
+/**    
+ * @defgroup cos Cosine    
+ *    
+ * Computes the trigonometric cosine function using a combination of table lookup   
+ * and cubic interpolation.  There are separate functions for   
+ * Q15, Q31, and floating-point data types.   
+ * The input to the floating-point version is in radians while the   
+ * fixed-point Q15 and Q31 have a scaled input with the range   
+ * [0 +0.9999] mapping to [0 2*pi), Where range excludes 2*pi.   
+ *   
+ * The implementation is based on table lookup using 256 values together with cubic interpolation.   
+ * The steps used are:   
+ *  -# Calculation of the nearest integer table index   
+ *  -# Fetch the four table values a, b, c, and d     
+ *  -# Compute the fractional portion (fract) of the table index.   
+ *  -# Calculation of wa, wb, wc, wd    
+ *  -# The final result equals a*wa + b*wb + c*wc + d*wd   
+ *   
+ * where   
+ * 
    
+ *    a=Table[index-1];    
+ *    b=Table[index+0];    
+ *    c=Table[index+1];    
+ *    d=Table[index+2];    
+ * 
   
+ * and   
+ * 
    
+ *    wa=-(1/6)*fract.^3 + (1/2)*fract.^2 - (1/3)*fract;    
+ *    wb=(1/2)*fract.^3 - fract.^2 - (1/2)*fract + 1;    
+ *    wc=-(1/2)*fract.^3+(1/2)*fract.^2+fract;    
+ *    wd=(1/6)*fract.^3 - (1/6)*fract;    
+ * 
    
+ */
+
+ /**    
+ * @addtogroup cos    
+ * @{    
+ */
+
+
+/**    
+* \par    
+* Example code for Generation of Cos Table:   
+* tableSize = 256;    
+* 
for(n = -1; n < (tableSize + 2); n++)    
+* {    
+*	cosTable[n+1]= cos(2*pi*n/tableSize);    
+* } 
    
+* where pi value is  3.14159265358979    
+*/
+
+static const float32_t cosTable[260] = {
+  0.999698817729949950f, 1.000000000000000000f, 0.999698817729949950f,
+  0.998795449733734130f, 0.997290432453155520f, 0.995184719562530520f,
+  0.992479562759399410f, 0.989176511764526370f,
+  0.985277652740478520f, 0.980785250663757320f, 0.975702106952667240f,
+  0.970031261444091800f, 0.963776051998138430f, 0.956940352916717530f,
+  0.949528157711029050f, 0.941544055938720700f,
+  0.932992815971374510f, 0.923879504203796390f, 0.914209783077239990f,
+  0.903989315032958980f, 0.893224298954010010f, 0.881921291351318360f,
+  0.870086967945098880f, 0.857728600502014160f,
+  0.844853579998016360f, 0.831469595432281490f, 0.817584812641143800f,
+  0.803207516670227050f, 0.788346409797668460f, 0.773010432720184330f,
+  0.757208824157714840f, 0.740951120853424070f,
+  0.724247097969055180f, 0.707106769084930420f, 0.689540565013885500f,
+  0.671558976173400880f, 0.653172850608825680f, 0.634393274784088130f,
+  0.615231573581695560f, 0.595699310302734380f,
+  0.575808167457580570f, 0.555570244789123540f, 0.534997642040252690f,
+  0.514102756977081300f, 0.492898195981979370f, 0.471396744251251220f,
+  0.449611335992813110f, 0.427555084228515630f,
+  0.405241310596466060f, 0.382683426141738890f, 0.359895050525665280f,
+  0.336889863014221190f, 0.313681751489639280f, 0.290284663438797000f,
+  0.266712754964828490f, 0.242980182170867920f,
+  0.219101235270500180f, 0.195090323686599730f, 0.170961886644363400f,
+  0.146730467677116390f, 0.122410677373409270f, 0.098017141222953796f,
+  0.073564566671848297f, 0.049067676067352295f,
+  0.024541229009628296f, 0.000000000000000061f, -0.024541229009628296f,
+  -0.049067676067352295f, -0.073564566671848297f, -0.098017141222953796f,
+  -0.122410677373409270f, -0.146730467677116390f,
+  -0.170961886644363400f, -0.195090323686599730f, -0.219101235270500180f,
+  -0.242980182170867920f, -0.266712754964828490f, -0.290284663438797000f,
+  -0.313681751489639280f, -0.336889863014221190f,
+  -0.359895050525665280f, -0.382683426141738890f, -0.405241310596466060f,
+  -0.427555084228515630f, -0.449611335992813110f, -0.471396744251251220f,
+  -0.492898195981979370f, -0.514102756977081300f,
+  -0.534997642040252690f, -0.555570244789123540f, -0.575808167457580570f,
+  -0.595699310302734380f, -0.615231573581695560f, -0.634393274784088130f,
+  -0.653172850608825680f, -0.671558976173400880f,
+  -0.689540565013885500f, -0.707106769084930420f, -0.724247097969055180f,
+  -0.740951120853424070f, -0.757208824157714840f, -0.773010432720184330f,
+  -0.788346409797668460f, -0.803207516670227050f,
+  -0.817584812641143800f, -0.831469595432281490f, -0.844853579998016360f,
+  -0.857728600502014160f, -0.870086967945098880f, -0.881921291351318360f,
+  -0.893224298954010010f, -0.903989315032958980f,
+  -0.914209783077239990f, -0.923879504203796390f, -0.932992815971374510f,
+  -0.941544055938720700f, -0.949528157711029050f, -0.956940352916717530f,
+  -0.963776051998138430f, -0.970031261444091800f,
+  -0.975702106952667240f, -0.980785250663757320f, -0.985277652740478520f,
+  -0.989176511764526370f, -0.992479562759399410f, -0.995184719562530520f,
+  -0.997290432453155520f, -0.998795449733734130f,
+  -0.999698817729949950f, -1.000000000000000000f, -0.999698817729949950f,
+  -0.998795449733734130f, -0.997290432453155520f, -0.995184719562530520f,
+  -0.992479562759399410f, -0.989176511764526370f,
+  -0.985277652740478520f, -0.980785250663757320f, -0.975702106952667240f,
+  -0.970031261444091800f, -0.963776051998138430f, -0.956940352916717530f,
+  -0.949528157711029050f, -0.941544055938720700f,
+  -0.932992815971374510f, -0.923879504203796390f, -0.914209783077239990f,
+  -0.903989315032958980f, -0.893224298954010010f, -0.881921291351318360f,
+  -0.870086967945098880f, -0.857728600502014160f,
+  -0.844853579998016360f, -0.831469595432281490f, -0.817584812641143800f,
+  -0.803207516670227050f, -0.788346409797668460f, -0.773010432720184330f,
+  -0.757208824157714840f, -0.740951120853424070f,
+  -0.724247097969055180f, -0.707106769084930420f, -0.689540565013885500f,
+  -0.671558976173400880f, -0.653172850608825680f, -0.634393274784088130f,
+  -0.615231573581695560f, -0.595699310302734380f,
+  -0.575808167457580570f, -0.555570244789123540f, -0.534997642040252690f,
+  -0.514102756977081300f, -0.492898195981979370f, -0.471396744251251220f,
+  -0.449611335992813110f, -0.427555084228515630f,
+  -0.405241310596466060f, -0.382683426141738890f, -0.359895050525665280f,
+  -0.336889863014221190f, -0.313681751489639280f, -0.290284663438797000f,
+  -0.266712754964828490f, -0.242980182170867920f,
+  -0.219101235270500180f, -0.195090323686599730f, -0.170961886644363400f,
+  -0.146730467677116390f, -0.122410677373409270f, -0.098017141222953796f,
+  -0.073564566671848297f, -0.049067676067352295f,
+  -0.024541229009628296f, -0.000000000000000184f, 0.024541229009628296f,
+  0.049067676067352295f, 0.073564566671848297f, 0.098017141222953796f,
+  0.122410677373409270f, 0.146730467677116390f,
+  0.170961886644363400f, 0.195090323686599730f, 0.219101235270500180f,
+  0.242980182170867920f, 0.266712754964828490f, 0.290284663438797000f,
+  0.313681751489639280f, 0.336889863014221190f,
+  0.359895050525665280f, 0.382683426141738890f, 0.405241310596466060f,
+  0.427555084228515630f, 0.449611335992813110f, 0.471396744251251220f,
+  0.492898195981979370f, 0.514102756977081300f,
+  0.534997642040252690f, 0.555570244789123540f, 0.575808167457580570f,
+  0.595699310302734380f, 0.615231573581695560f, 0.634393274784088130f,
+  0.653172850608825680f, 0.671558976173400880f,
+  0.689540565013885500f, 0.707106769084930420f, 0.724247097969055180f,
+  0.740951120853424070f, 0.757208824157714840f, 0.773010432720184330f,
+  0.788346409797668460f, 0.803207516670227050f,
+  0.817584812641143800f, 0.831469595432281490f, 0.844853579998016360f,
+  0.857728600502014160f, 0.870086967945098880f, 0.881921291351318360f,
+  0.893224298954010010f, 0.903989315032958980f,
+  0.914209783077239990f, 0.923879504203796390f, 0.932992815971374510f,
+  0.941544055938720700f, 0.949528157711029050f, 0.956940352916717530f,
+  0.963776051998138430f, 0.970031261444091800f,
+  0.975702106952667240f, 0.980785250663757320f, 0.985277652740478520f,
+  0.989176511764526370f, 0.992479562759399410f, 0.995184719562530520f,
+  0.997290432453155520f, 0.998795449733734130f,
+  0.999698817729949950f, 1.000000000000000000f, 0.999698817729949950f,
+  0.998795449733734130f
+};
+
+/**   
+ * @brief  Fast approximation to the trigonometric cosine function for floating-point data.   
+ * @param[in] x input value in radians.   
+ * @return cos(x).   
+ */
+
+
+float32_t arm_cos_f32(
+  float32_t x)
+{
+  float32_t cosVal, fract, in;
+  int32_t index;
+  uint32_t tableSize = (uint32_t) TABLE_SIZE;
+  float32_t wa, wb, wc, wd;
+  float32_t a, b, c, d;
+  float32_t *tablePtr;
+  int32_t n;
+  float32_t fractsq, fractby2, fractby6, fractby3, fractsqby2;
+  float32_t oneminusfractby2;
+  float32_t frby2xfrsq, frby6xfrsq;
+
+  /* input x is in radians */
+  /* Scale the input to [0 1] range from [0 2*PI] , divide input by 2*pi */
+  in = x * 0.159154943092f;
+
+  /* Calculation of floor value of input */
+  n = (int32_t) in;
+
+  /* Make negative values towards -infinity */
+  if(x < 0.0f)
+  {
+    n = n - 1;
+  }
+
+  /* Map input value to [0 1] */
+  in = in - (float32_t) n;
+
+  /* Calculation of index of the table */
+  index = (uint32_t) (tableSize * in);
+
+  /* fractional value calculation */
+  fract = ((float32_t) tableSize * in) - (float32_t) index;
+
+  /* Checking min and max index of table */
+  if(index < 0)
+  {
+    index = 0;
+  }
+  else if(index > 256)
+  {
+    index = 256;
+  }
+
+  /* Initialise table pointer */
+  tablePtr = (float32_t *) & cosTable[index];
+
+  /* Read four nearest values of input value from the cos table */
+  a = tablePtr[0];
+  b = tablePtr[1];
+  c = tablePtr[2];
+  d = tablePtr[3];
+
+  /* Cubic interpolation process */
+  fractsq = fract * fract;
+  fractby2 = fract * 0.5f;
+  fractby6 = fract * 0.166666667f;
+  fractby3 = fract * 0.3333333333333f;
+  fractsqby2 = fractsq * 0.5f;
+  frby2xfrsq = (fractby2) * fractsq;
+  frby6xfrsq = (fractby6) * fractsq;
+  oneminusfractby2 = 1.0f - fractby2;
+  wb = fractsqby2 - fractby3;
+  wc = (fractsqby2 + fract);
+  wa = wb - frby6xfrsq;
+  wb = frby2xfrsq - fractsq;
+  cosVal = wa * a;
+  wc = wc - frby2xfrsq;
+  wd = (frby6xfrsq) - fractby6;
+  wb = wb + oneminusfractby2;
+
+  /* Calculate cos value */
+  cosVal = (cosVal + (b * wb)) + ((c * wc) + (d * wd));
+
+  /* Return the output value */
+  return (cosVal);
+
+}
+
+/**    
+ * @} end of cos group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_cos_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_cos_q15.c
new file mode 100644
index 0000000000..0edf68b893
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_cos_q15.c
@@ -0,0 +1,205 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_cos_q15.c    
+*    
+* Description:	Fast cosine calculation for Q15 values.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFastMath    
+ */
+
+ /**    
+ * @addtogroup cos    
+ * @{    
+ */
+
+/**   
+* \par    
+* Table Values are in Q15(1.15 Fixed point format) and generation is done in three steps    
+* \par    
+* First Generate cos values in floating point:    
+* tableSize = 256;     
+* 
for(n = -1; n < (tableSize + 1); n++)    
+* {    
+*	cosTable[n+1]= cos(2*pi*n/tableSize);    
+* }
   
+* where pi value is  3.14159265358979    
+* \par    
+* Secondly Convert Floating point to Q15(Fixed point):    
+*	(cosTable[i] * pow(2, 15))    
+* \par    
+* Finally Rounding to nearest integer is done    
+* 	cosTable[i] += (cosTable[i] > 0 ? 0.5 :-0.5);    
+*/
+
+static const q15_t cosTableQ15[259] = {
+  0x7ff6, 0x7fff, 0x7ff6, 0x7fd9, 0x7fa7, 0x7f62, 0x7f0a, 0x7e9d,
+  0x7e1e, 0x7d8a, 0x7ce4, 0x7c2a, 0x7b5d, 0x7a7d, 0x798a, 0x7885,
+  0x776c, 0x7642, 0x7505, 0x73b6, 0x7255, 0x70e3, 0x6f5f, 0x6dca,
+  0x6c24, 0x6a6e, 0x68a7, 0x66d0, 0x64e9, 0x62f2, 0x60ec, 0x5ed7,
+  0x5cb4, 0x5a82, 0x5843, 0x55f6, 0x539b, 0x5134, 0x4ec0, 0x4c40,
+  0x49b4, 0x471d, 0x447b, 0x41ce, 0x3f17, 0x3c57, 0x398d, 0x36ba,
+  0x33df, 0x30fc, 0x2e11, 0x2b1f, 0x2827, 0x2528, 0x2224, 0x1f1a,
+  0x1c0c, 0x18f9, 0x15e2, 0x12c8, 0xfab, 0xc8c, 0x96b, 0x648,
+  0x324, 0x0, 0xfcdc, 0xf9b8, 0xf695, 0xf374, 0xf055, 0xed38,
+  0xea1e, 0xe707, 0xe3f4, 0xe0e6, 0xdddc, 0xdad8, 0xd7d9, 0xd4e1,
+  0xd1ef, 0xcf04, 0xcc21, 0xc946, 0xc673, 0xc3a9, 0xc0e9, 0xbe32,
+  0xbb85, 0xb8e3, 0xb64c, 0xb3c0, 0xb140, 0xaecc, 0xac65, 0xaa0a,
+  0xa7bd, 0xa57e, 0xa34c, 0xa129, 0x9f14, 0x9d0e, 0x9b17, 0x9930,
+  0x9759, 0x9592, 0x93dc, 0x9236, 0x90a1, 0x8f1d, 0x8dab, 0x8c4a,
+  0x8afb, 0x89be, 0x8894, 0x877b, 0x8676, 0x8583, 0x84a3, 0x83d6,
+  0x831c, 0x8276, 0x81e2, 0x8163, 0x80f6, 0x809e, 0x8059, 0x8027,
+  0x800a, 0x8000, 0x800a, 0x8027, 0x8059, 0x809e, 0x80f6, 0x8163,
+  0x81e2, 0x8276, 0x831c, 0x83d6, 0x84a3, 0x8583, 0x8676, 0x877b,
+  0x8894, 0x89be, 0x8afb, 0x8c4a, 0x8dab, 0x8f1d, 0x90a1, 0x9236,
+  0x93dc, 0x9592, 0x9759, 0x9930, 0x9b17, 0x9d0e, 0x9f14, 0xa129,
+  0xa34c, 0xa57e, 0xa7bd, 0xaa0a, 0xac65, 0xaecc, 0xb140, 0xb3c0,
+  0xb64c, 0xb8e3, 0xbb85, 0xbe32, 0xc0e9, 0xc3a9, 0xc673, 0xc946,
+  0xcc21, 0xcf04, 0xd1ef, 0xd4e1, 0xd7d9, 0xdad8, 0xdddc, 0xe0e6,
+  0xe3f4, 0xe707, 0xea1e, 0xed38, 0xf055, 0xf374, 0xf695, 0xf9b8,
+  0xfcdc, 0x0, 0x324, 0x648, 0x96b, 0xc8c, 0xfab, 0x12c8,
+  0x15e2, 0x18f9, 0x1c0c, 0x1f1a, 0x2224, 0x2528, 0x2827, 0x2b1f,
+  0x2e11, 0x30fc, 0x33df, 0x36ba, 0x398d, 0x3c57, 0x3f17, 0x41ce,
+  0x447b, 0x471d, 0x49b4, 0x4c40, 0x4ec0, 0x5134, 0x539b, 0x55f6,
+  0x5843, 0x5a82, 0x5cb4, 0x5ed7, 0x60ec, 0x62f2, 0x64e9, 0x66d0,
+  0x68a7, 0x6a6e, 0x6c24, 0x6dca, 0x6f5f, 0x70e3, 0x7255, 0x73b6,
+  0x7505, 0x7642, 0x776c, 0x7885, 0x798a, 0x7a7d, 0x7b5d, 0x7c2a,
+  0x7ce4, 0x7d8a, 0x7e1e, 0x7e9d, 0x7f0a, 0x7f62, 0x7fa7, 0x7fd9,
+  0x7ff6, 0x7fff, 0x7ff6
+};
+
+
+/**   
+ * @brief Fast approximation to the trigonometric cosine function for Q15 data.   
+ * @param[in] x Scaled input value in radians.   
+ * @return  cos(x).   
+ *   
+ * The Q15 input value is in the range [0 +0.9999] and is mapped to a radian value in the range [0 2*pi), Here range excludes 2*pi.   
+ */
+
+q15_t arm_cos_q15(
+  q15_t x)
+{
+  q31_t cosVal;                                  /* Temporary variable for output */
+  q15_t *tablePtr;                               /* Pointer to table */
+  q15_t in, in2;                                 /* Temporary variables for input */
+  q31_t wa, wb, wc, wd;                          /* Cubic interpolation coefficients */
+  q15_t a, b, c, d;                              /* Four nearest output values */
+  q15_t fract, fractCube, fractSquare;           /* Variables for fractional value */
+  q15_t oneBy6 = 0x1555;                         /* Fixed point value of 1/6 */
+  q15_t tableSpacing = TABLE_SPACING_Q15;        /* Table spacing */
+  int32_t index;                                 /* Index variable */
+
+  in = x;
+
+  /* Calculate the nearest index */
+  index = (int32_t) in / tableSpacing;
+
+  /* Calculate the nearest value of input */
+  in2 = (q15_t) index *tableSpacing;
+
+  /* Calculation of fractional value */
+  fract = (in - in2) << 8;
+
+  /* fractSquare = fract * fract */
+  fractSquare = (q15_t) ((fract * fract) >> 15);
+
+  /* fractCube = fract * fract * fract */
+  fractCube = (q15_t) ((fractSquare * fract) >> 15);
+
+  /* Checking min and max index of table */
+  if(index < 0)
+  {
+    index = 0;
+  }
+  else if(index > 256)
+  {
+    index = 256;
+  }
+
+  /* Initialise table pointer */
+  tablePtr = (q15_t *) & cosTableQ15[index];
+
+  /* Cubic interpolation process */
+  /* Calculation of wa */
+  /* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAA)*fract; */
+  wa = (q31_t) oneBy6 *fractCube;
+  wa += (q31_t) 0x2AAA *fract;
+  wa = -(wa >> 15);
+  wa += (fractSquare >> 1u);
+
+  /* Read first nearest value of output from the cos table */
+  a = *tablePtr++;
+
+  /* cosVal = a * wa */
+  cosVal = a * wa;
+
+  /* Calculation of wb */
+  wb = (((fractCube >> 1u) - fractSquare) - (fract >> 1u)) + 0x7FFF;
+
+  /* Read second nearest value of output from the cos table */
+  b = *tablePtr++;
+
+  /*      cosVal += b*wb */
+  cosVal += b * wb;
+
+  /* Calculation of wc */
+  wc = -(q31_t) fractCube + fractSquare;
+  wc = (wc >> 1u) + fract;
+
+  /* Read third nearest value of output from the cos table */
+  c = *tablePtr++;
+
+  /* cosVal += c*wc */
+  cosVal += c * wc;
+
+  /* Calculation of wd */
+  /* wd = (oneBy6)*fractCube - (oneBy6)*fract; */
+  fractCube = fractCube - fract;
+  wd = ((q15_t) (((q31_t) oneBy6 * fractCube) >> 15));
+
+  /* Read fourth nearest value of output from the cos table */
+  d = *tablePtr++;
+
+  /* cosVal += d*wd; */
+  cosVal += d * wd;
+
+  /* Convert output value in 1.15(q15) format and saturate */
+  cosVal = __SSAT((cosVal >> 15), 16);
+
+  /* Return the output value in 1.15(q15) format */
+  return ((q15_t) cosVal);
+
+}
+
+/**    
+ * @} end of cos group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_cos_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_cos_q31.c
new file mode 100644
index 0000000000..1326215fe4
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_cos_q31.c
@@ -0,0 +1,239 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_cos_q31.c    
+*    
+* Description:	Fast cosine calculation for Q31 values.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFastMath    
+ */
+
+ /**    
+ * @addtogroup cos    
+ * @{    
+ */
+
+/**    
+ * \par    
+ * Table Values are in Q31(1.31 Fixed point format) and generation is done in three steps    
+ * First Generate cos values in floating point:    
+ * tableSize = 256;      
+ * 
for(n = -1; n < (tableSize + 1); n++)    
+ * {    
+ *	cosTable[n+1]= cos(2*pi*n/tableSize);    
+ * } 
     
+ * where pi value is  3.14159265358979    
+ * \par    
+ * Secondly Convert Floating point to Q31(Fixed point):    
+ *	(cosTable[i] * pow(2, 31))    
+ * \par    
+ * Finally Rounding to nearest integer is done    
+ * 	cosTable[i] += (cosTable[i] > 0 ? 0.5 :-0.5);    
+ */
+
+
+static const q31_t cosTableQ31[259] = {
+  0x7ff62182, 0x7fffffff, 0x7ff62182, 0x7fd8878e, 0x7fa736b4, 0x7f62368f,
+  0x7f0991c4, 0x7e9d55fc,
+  0x7e1d93ea, 0x7d8a5f40, 0x7ce3ceb2, 0x7c29fbee, 0x7b5d039e, 0x7a7d055b,
+  0x798a23b1, 0x78848414,
+  0x776c4edb, 0x7641af3d, 0x7504d345, 0x73b5ebd1, 0x72552c85, 0x70e2cbc6,
+  0x6f5f02b2, 0x6dca0d14,
+  0x6c242960, 0x6a6d98a4, 0x68a69e81, 0x66cf8120, 0x64e88926, 0x62f201ac,
+  0x60ec3830, 0x5ed77c8a,
+  0x5cb420e0, 0x5a82799a, 0x5842dd54, 0x55f5a4d2, 0x539b2af0, 0x5133cc94,
+  0x4ebfe8a5, 0x4c3fdff4,
+  0x49b41533, 0x471cece7, 0x447acd50, 0x41ce1e65, 0x3f1749b8, 0x3c56ba70,
+  0x398cdd32, 0x36ba2014,
+  0x33def287, 0x30fbc54d, 0x2e110a62, 0x2b1f34eb, 0x2826b928, 0x25280c5e,
+  0x2223a4c5, 0x1f19f97b,
+  0x1c0b826a, 0x18f8b83c, 0x15e21445, 0x12c8106f, 0xfab272b, 0xc8bd35e,
+  0x96a9049, 0x647d97c,
+  0x3242abf, 0x0, 0xfcdbd541, 0xf9b82684, 0xf6956fb7, 0xf3742ca2, 0xf054d8d5,
+  0xed37ef91,
+  0xea1debbb, 0xe70747c4, 0xe3f47d96, 0xe0e60685, 0xdddc5b3b, 0xdad7f3a2,
+  0xd7d946d8, 0xd4e0cb15,
+  0xd1eef59e, 0xcf043ab3, 0xcc210d79, 0xc945dfec, 0xc67322ce, 0xc3a94590,
+  0xc0e8b648, 0xbe31e19b,
+  0xbb8532b0, 0xb8e31319, 0xb64beacd, 0xb3c0200c, 0xb140175b, 0xaecc336c,
+  0xac64d510, 0xaa0a5b2e,
+  0xa7bd22ac, 0xa57d8666, 0xa34bdf20, 0xa1288376, 0x9f13c7d0, 0x9d0dfe54,
+  0x9b1776da, 0x99307ee0,
+  0x9759617f, 0x9592675c, 0x93dbd6a0, 0x9235f2ec, 0x90a0fd4e, 0x8f1d343a,
+  0x8daad37b, 0x8c4a142f,
+  0x8afb2cbb, 0x89be50c3, 0x8893b125, 0x877b7bec, 0x8675dc4f, 0x8582faa5,
+  0x84a2fc62, 0x83d60412,
+  0x831c314e, 0x8275a0c0, 0x81e26c16, 0x8162aa04, 0x80f66e3c, 0x809dc971,
+  0x8058c94c, 0x80277872,
+  0x8009de7e, 0x80000000, 0x8009de7e, 0x80277872, 0x8058c94c, 0x809dc971,
+  0x80f66e3c, 0x8162aa04,
+  0x81e26c16, 0x8275a0c0, 0x831c314e, 0x83d60412, 0x84a2fc62, 0x8582faa5,
+  0x8675dc4f, 0x877b7bec,
+  0x8893b125, 0x89be50c3, 0x8afb2cbb, 0x8c4a142f, 0x8daad37b, 0x8f1d343a,
+  0x90a0fd4e, 0x9235f2ec,
+  0x93dbd6a0, 0x9592675c, 0x9759617f, 0x99307ee0, 0x9b1776da, 0x9d0dfe54,
+  0x9f13c7d0, 0xa1288376,
+  0xa34bdf20, 0xa57d8666, 0xa7bd22ac, 0xaa0a5b2e, 0xac64d510, 0xaecc336c,
+  0xb140175b, 0xb3c0200c,
+  0xb64beacd, 0xb8e31319, 0xbb8532b0, 0xbe31e19b, 0xc0e8b648, 0xc3a94590,
+  0xc67322ce, 0xc945dfec,
+  0xcc210d79, 0xcf043ab3, 0xd1eef59e, 0xd4e0cb15, 0xd7d946d8, 0xdad7f3a2,
+  0xdddc5b3b, 0xe0e60685,
+  0xe3f47d96, 0xe70747c4, 0xea1debbb, 0xed37ef91, 0xf054d8d5, 0xf3742ca2,
+  0xf6956fb7, 0xf9b82684,
+  0xfcdbd541, 0x0, 0x3242abf, 0x647d97c, 0x96a9049, 0xc8bd35e, 0xfab272b,
+  0x12c8106f,
+  0x15e21445, 0x18f8b83c, 0x1c0b826a, 0x1f19f97b, 0x2223a4c5, 0x25280c5e,
+  0x2826b928, 0x2b1f34eb,
+  0x2e110a62, 0x30fbc54d, 0x33def287, 0x36ba2014, 0x398cdd32, 0x3c56ba70,
+  0x3f1749b8, 0x41ce1e65,
+  0x447acd50, 0x471cece7, 0x49b41533, 0x4c3fdff4, 0x4ebfe8a5, 0x5133cc94,
+  0x539b2af0, 0x55f5a4d2,
+  0x5842dd54, 0x5a82799a, 0x5cb420e0, 0x5ed77c8a, 0x60ec3830, 0x62f201ac,
+  0x64e88926, 0x66cf8120,
+  0x68a69e81, 0x6a6d98a4, 0x6c242960, 0x6dca0d14, 0x6f5f02b2, 0x70e2cbc6,
+  0x72552c85, 0x73b5ebd1,
+  0x7504d345, 0x7641af3d, 0x776c4edb, 0x78848414, 0x798a23b1, 0x7a7d055b,
+  0x7b5d039e, 0x7c29fbee,
+  0x7ce3ceb2, 0x7d8a5f40, 0x7e1d93ea, 0x7e9d55fc, 0x7f0991c4, 0x7f62368f,
+  0x7fa736b4, 0x7fd8878e,
+  0x7ff62182, 0x7fffffff, 0x7ff62182
+};
+
+/**   
+ * @brief Fast approximation to the trigonometric cosine function for Q31 data.   
+ * @param[in] x Scaled input value in radians.   
+ * @return  cos(x).   
+ *   
+ * The Q31 input value is in the range [0 +0.9999] and is mapped to a radian value in the range [0 2*pi), Here range excludes 2*pi.   
+ */
+
+q31_t arm_cos_q31(
+  q31_t x)
+{
+  q31_t cosVal, in, in2;                         /* Temporary variables for input, output */
+  q31_t wa, wb, wc, wd;                          /* Cubic interpolation coefficients */
+  q31_t a, b, c, d;                              /* Four nearest output values */
+  q31_t *tablePtr;                               /* Pointer to table */
+  q31_t fract, fractCube, fractSquare;           /* Temporary values for fractional values */
+  q31_t oneBy6 = 0x15555555;                     /* Fixed point value of 1/6 */
+  q31_t tableSpacing = TABLE_SPACING_Q31;        /* Table spacing */
+  q31_t temp;                                    /* Temporary variable for intermediate process */
+  int32_t index;                                 /* Index variable */
+
+  in = x;
+
+  /* Calculate the nearest index */
+  index = in / tableSpacing;
+
+  /* Calculate the nearest value of input */
+  in2 = ((q31_t) index) * tableSpacing;
+
+  /* Calculation of fractional value */
+  fract = (in - in2) << 8;
+
+  /* fractSquare = fract * fract */
+  fractSquare = ((q31_t) (((q63_t) fract * fract) >> 32));
+  fractSquare = fractSquare << 1;
+
+  /* fractCube = fract * fract * fract */
+  fractCube = ((q31_t) (((q63_t) fractSquare * fract) >> 32));
+  fractCube = fractCube << 1;
+
+  /* Checking min and max index of table */
+  if(index < 0)
+  {
+    index = 0;
+  }
+  else if(index > 256)
+  {
+    index = 256;
+  }
+
+  /* Initialise table pointer */
+  tablePtr = (q31_t *) & cosTableQ31[index];
+
+  /* Cubic interpolation process */
+  /* Calculation of wa */
+  /* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAAAAAA)*fract; */
+  wa = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32));
+  temp = 0x2AAAAAAA;
+  wa = (q31_t) ((((q63_t) wa << 32) + ((q63_t) temp * fract)) >> 32);
+  wa = -(wa << 1u);
+  wa += (fractSquare >> 1u);
+
+  /* Read first nearest value of output from the cos table */
+  a = *tablePtr++;
+
+  /* cosVal = a*wa */
+  cosVal = ((q31_t) (((q63_t) a * wa) >> 32));
+
+  /* q31(1.31) Fixed point value of 1 */
+  temp = 0x7FFFFFFF;
+
+  /* Calculation of wb */
+  wb = ((fractCube >> 1u) - (fractSquare + (fract >> 1u))) + temp;
+  /* Read second nearest value of output from the cos table */
+  b = *tablePtr++;
+
+  /*      cosVal += b*wb */
+  cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) b * (wb))) >> 32);
+
+  /* Calculation of wc */
+  wc = -fractCube + fractSquare;
+  wc = (wc >> 1u) + fract;
+  /* Read third nearest values of output value from the cos table */
+  c = *tablePtr++;
+
+  /*      cosVal += c*wc */
+  cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) c * (wc))) >> 32);
+
+  /* Calculation of wd */
+  /* wd = (oneBy6)*fractCube - (oneBy6)*fract; */
+  fractCube = fractCube - fract;
+  wd = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32));
+  wd = (wd << 1u);
+
+  /* Read fourth nearest value of output from the cos table */
+  d = *tablePtr++;
+
+  /* cosVal += d*wd; */
+  cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) d * (wd))) >> 32);
+
+
+  /* convert cosVal in 2.30 format to 1.31 format */
+  return (__QADD(cosVal, cosVal));
+
+}
+
+/**    
+ * @} end of cos group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_sin_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_sin_f32.c
new file mode 100644
index 0000000000..bfe58d5c81
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_sin_f32.c
@@ -0,0 +1,281 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_sin_f32.c    
+*    
+* Description:	Fast sine calculation for floating-point values.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFastMath    
+ */
+
+/**    
+ * @defgroup sin Sine    
+ *    
+ * Computes the trigonometric sine function using a combination of table lookup   
+ * and cubic interpolation.  There are separate functions for   
+ * Q15, Q31, and floating-point data types.   
+ * The input to the floating-point version is in radians while the   
+ * fixed-point Q15 and Q31 have a scaled input with the range   
+ * [0 +0.9999] mapping to [0 2*pi), Where range excludes 2*pi.   
+ *   
+ * The implementation is based on table lookup using 256 values together with cubic interpolation.   
+ * The steps used are:   
+ *  -# Calculation of the nearest integer table index   
+ *  -# Fetch the four table values a, b, c, and d     
+ *  -# Compute the fractional portion (fract) of the table index.   
+ *  -# Calculation of wa, wb, wc, wd    
+ *  -# The final result equals a*wa + b*wb + c*wc + d*wd   
+ *   
+ * where   
+ * 
    
+ *    a=Table[index-1];    
+ *    b=Table[index+0];    
+ *    c=Table[index+1];    
+ *    d=Table[index+2];    
+ * 
   
+ * and   
+ * 
    
+ *    wa=-(1/6)*fract.^3 + (1/2)*fract.^2 - (1/3)*fract;    
+ *    wb=(1/2)*fract.^3 - fract.^2 - (1/2)*fract + 1;    
+ *    wc=-(1/2)*fract.^3+(1/2)*fract.^2+fract;    
+ *    wd=(1/6)*fract.^3 - (1/6)*fract;    
+ * 
    
+ */
+
+/**    
+ * @addtogroup sin    
+ * @{    
+ */
+
+
+/**   
+ * \par    
+ * Example code for Generation of Floating-point Sin Table:   
+ * tableSize = 256;    
+ * 
for(n = -1; n < (tableSize + 1); n++)    
+ * {    
+ *	sinTable[n+1]=sin(2*pi*n/tableSize);    
+ * }
    
+ * \par    
+ * where pi value is  3.14159265358979    
+ */
+
+static const float32_t sinTable[259] = {
+  -0.024541229009628296f, 0.000000000000000000f, 0.024541229009628296f,
+  0.049067676067352295f, 0.073564566671848297f, 0.098017141222953796f,
+  0.122410677373409270f, 0.146730467677116390f,
+  0.170961886644363400f, 0.195090323686599730f, 0.219101235270500180f,
+  0.242980182170867920f, 0.266712754964828490f, 0.290284663438797000f,
+  0.313681751489639280f, 0.336889863014221190f,
+  0.359895050525665280f, 0.382683426141738890f, 0.405241310596466060f,
+  0.427555084228515630f, 0.449611335992813110f, 0.471396744251251220f,
+  0.492898195981979370f, 0.514102756977081300f,
+  0.534997642040252690f, 0.555570244789123540f, 0.575808167457580570f,
+  0.595699310302734380f, 0.615231573581695560f, 0.634393274784088130f,
+  0.653172850608825680f, 0.671558976173400880f,
+  0.689540565013885500f, 0.707106769084930420f, 0.724247097969055180f,
+  0.740951120853424070f, 0.757208824157714840f, 0.773010432720184330f,
+  0.788346409797668460f, 0.803207516670227050f,
+  0.817584812641143800f, 0.831469595432281490f, 0.844853579998016360f,
+  0.857728600502014160f, 0.870086967945098880f, 0.881921291351318360f,
+  0.893224298954010010f, 0.903989315032958980f,
+  0.914209783077239990f, 0.923879504203796390f, 0.932992815971374510f,
+  0.941544055938720700f, 0.949528157711029050f, 0.956940352916717530f,
+  0.963776051998138430f, 0.970031261444091800f,
+  0.975702106952667240f, 0.980785250663757320f, 0.985277652740478520f,
+  0.989176511764526370f, 0.992479562759399410f, 0.995184719562530520f,
+  0.997290432453155520f, 0.998795449733734130f,
+  0.999698817729949950f, 1.000000000000000000f, 0.999698817729949950f,
+  0.998795449733734130f, 0.997290432453155520f, 0.995184719562530520f,
+  0.992479562759399410f, 0.989176511764526370f,
+  0.985277652740478520f, 0.980785250663757320f, 0.975702106952667240f,
+  0.970031261444091800f, 0.963776051998138430f, 0.956940352916717530f,
+  0.949528157711029050f, 0.941544055938720700f,
+  0.932992815971374510f, 0.923879504203796390f, 0.914209783077239990f,
+  0.903989315032958980f, 0.893224298954010010f, 0.881921291351318360f,
+  0.870086967945098880f, 0.857728600502014160f,
+  0.844853579998016360f, 0.831469595432281490f, 0.817584812641143800f,
+  0.803207516670227050f, 0.788346409797668460f, 0.773010432720184330f,
+  0.757208824157714840f, 0.740951120853424070f,
+  0.724247097969055180f, 0.707106769084930420f, 0.689540565013885500f,
+  0.671558976173400880f, 0.653172850608825680f, 0.634393274784088130f,
+  0.615231573581695560f, 0.595699310302734380f,
+  0.575808167457580570f, 0.555570244789123540f, 0.534997642040252690f,
+  0.514102756977081300f, 0.492898195981979370f, 0.471396744251251220f,
+  0.449611335992813110f, 0.427555084228515630f,
+  0.405241310596466060f, 0.382683426141738890f, 0.359895050525665280f,
+  0.336889863014221190f, 0.313681751489639280f, 0.290284663438797000f,
+  0.266712754964828490f, 0.242980182170867920f,
+  0.219101235270500180f, 0.195090323686599730f, 0.170961886644363400f,
+  0.146730467677116390f, 0.122410677373409270f, 0.098017141222953796f,
+  0.073564566671848297f, 0.049067676067352295f,
+  0.024541229009628296f, 0.000000000000000122f, -0.024541229009628296f,
+  -0.049067676067352295f, -0.073564566671848297f, -0.098017141222953796f,
+  -0.122410677373409270f, -0.146730467677116390f,
+  -0.170961886644363400f, -0.195090323686599730f, -0.219101235270500180f,
+  -0.242980182170867920f, -0.266712754964828490f, -0.290284663438797000f,
+  -0.313681751489639280f, -0.336889863014221190f,
+  -0.359895050525665280f, -0.382683426141738890f, -0.405241310596466060f,
+  -0.427555084228515630f, -0.449611335992813110f, -0.471396744251251220f,
+  -0.492898195981979370f, -0.514102756977081300f,
+  -0.534997642040252690f, -0.555570244789123540f, -0.575808167457580570f,
+  -0.595699310302734380f, -0.615231573581695560f, -0.634393274784088130f,
+  -0.653172850608825680f, -0.671558976173400880f,
+  -0.689540565013885500f, -0.707106769084930420f, -0.724247097969055180f,
+  -0.740951120853424070f, -0.757208824157714840f, -0.773010432720184330f,
+  -0.788346409797668460f, -0.803207516670227050f,
+  -0.817584812641143800f, -0.831469595432281490f, -0.844853579998016360f,
+  -0.857728600502014160f, -0.870086967945098880f, -0.881921291351318360f,
+  -0.893224298954010010f, -0.903989315032958980f,
+  -0.914209783077239990f, -0.923879504203796390f, -0.932992815971374510f,
+  -0.941544055938720700f, -0.949528157711029050f, -0.956940352916717530f,
+  -0.963776051998138430f, -0.970031261444091800f,
+  -0.975702106952667240f, -0.980785250663757320f, -0.985277652740478520f,
+  -0.989176511764526370f, -0.992479562759399410f, -0.995184719562530520f,
+  -0.997290432453155520f, -0.998795449733734130f,
+  -0.999698817729949950f, -1.000000000000000000f, -0.999698817729949950f,
+  -0.998795449733734130f, -0.997290432453155520f, -0.995184719562530520f,
+  -0.992479562759399410f, -0.989176511764526370f,
+  -0.985277652740478520f, -0.980785250663757320f, -0.975702106952667240f,
+  -0.970031261444091800f, -0.963776051998138430f, -0.956940352916717530f,
+  -0.949528157711029050f, -0.941544055938720700f,
+  -0.932992815971374510f, -0.923879504203796390f, -0.914209783077239990f,
+  -0.903989315032958980f, -0.893224298954010010f, -0.881921291351318360f,
+  -0.870086967945098880f, -0.857728600502014160f,
+  -0.844853579998016360f, -0.831469595432281490f, -0.817584812641143800f,
+  -0.803207516670227050f, -0.788346409797668460f, -0.773010432720184330f,
+  -0.757208824157714840f, -0.740951120853424070f,
+  -0.724247097969055180f, -0.707106769084930420f, -0.689540565013885500f,
+  -0.671558976173400880f, -0.653172850608825680f, -0.634393274784088130f,
+  -0.615231573581695560f, -0.595699310302734380f,
+  -0.575808167457580570f, -0.555570244789123540f, -0.534997642040252690f,
+  -0.514102756977081300f, -0.492898195981979370f, -0.471396744251251220f,
+  -0.449611335992813110f, -0.427555084228515630f,
+  -0.405241310596466060f, -0.382683426141738890f, -0.359895050525665280f,
+  -0.336889863014221190f, -0.313681751489639280f, -0.290284663438797000f,
+  -0.266712754964828490f, -0.242980182170867920f,
+  -0.219101235270500180f, -0.195090323686599730f, -0.170961886644363400f,
+  -0.146730467677116390f, -0.122410677373409270f, -0.098017141222953796f,
+  -0.073564566671848297f, -0.049067676067352295f,
+  -0.024541229009628296f, -0.000000000000000245f, 0.024541229009628296f
+};
+
+
+/**   
+ * @brief  Fast approximation to the trigonometric sine function for floating-point data.   
+ * @param[in] x input value in radians.   
+ * @return  sin(x).   
+ */
+
+float32_t arm_sin_f32(
+  float32_t x)
+{
+  float32_t sinVal, fract, in;                   /* Temporary variables for input, output */
+  int32_t index;                                 /* Index variable */
+  uint32_t tableSize = (uint32_t) TABLE_SIZE;    /* Initialise tablesize */
+  float32_t wa, wb, wc, wd;                      /* Cubic interpolation coefficients */
+  float32_t a, b, c, d;                          /* Four nearest output values */
+  float32_t *tablePtr;                           /* Pointer to table */
+  int32_t n;
+  float32_t fractsq, fractby2, fractby6, fractby3, fractsqby2;
+  float32_t oneminusfractby2;
+  float32_t frby2xfrsq, frby6xfrsq;
+
+  /* input x is in radians */
+  /* Scale the input to [0 1] range from [0 2*PI] , divide input by 2*pi */
+  in = x * 0.159154943092f;
+
+  /* Calculation of floor value of input */
+  n = (int32_t) in;
+
+  /* Make negative values towards -infinity */
+  if(x < 0.0f)
+  {
+    n = n - 1;
+  }
+
+  /* Map input value to [0 1] */
+  in = in - (float32_t) n;
+
+  /* Calculation of index of the table */
+  index = (uint32_t) (tableSize * in);
+
+  /* fractional value calculation */
+  fract = ((float32_t) tableSize * in) - (float32_t) index;
+
+  /* Checking min and max index of table */
+  if(index < 0)
+  {
+    index = 0;
+  }
+  else if(index > 256)
+  {
+    index = 256;
+  }
+
+  /* Initialise table pointer */
+  tablePtr = (float32_t *) & sinTable[index];
+
+  /* Read four nearest values of input value from the sin table */
+  a = tablePtr[0];
+  b = tablePtr[1];
+  c = tablePtr[2];
+  d = tablePtr[3];
+
+  /* Cubic interpolation process */
+  fractsq = fract * fract;
+  fractby2 = fract * 0.5f;
+  fractby6 = fract * 0.166666667f;
+  fractby3 = fract * 0.3333333333333f;
+  fractsqby2 = fractsq * 0.5f;
+  frby2xfrsq = (fractby2) * fractsq;
+  frby6xfrsq = (fractby6) * fractsq;
+  oneminusfractby2 = 1.0f - fractby2;
+  wb = fractsqby2 - fractby3;
+  wc = (fractsqby2 + fract);
+  wa = wb - frby6xfrsq;
+  wb = frby2xfrsq - fractsq;
+  sinVal = wa * a;
+  wc = wc - frby2xfrsq;
+  wd = (frby6xfrsq) - fractby6;
+  wb = wb + oneminusfractby2;
+
+  /* Calculate sin value */
+  sinVal = (sinVal + (b * wb)) + ((c * wc) + (d * wd));
+
+  /* Return the output value */
+  return (sinVal);
+
+}
+
+/**    
+ * @} end of sin group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_sin_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_sin_q15.c
new file mode 100644
index 0000000000..b53ca3ecc4
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_sin_q15.c
@@ -0,0 +1,208 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_sin_q15.c    
+*    
+* Description:	Fast sine calculation for Q15 values.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFastMath    
+ */
+
+ /**    
+ * @addtogroup sin    
+ * @{    
+ */
+
+
+/**    
+ * \par    
+ * Example code for Generation of Q15 Sin Table:   
+ * \par    
+ * 
tableSize = 256;    
+ * for(n = -1; n < (tableSize + 1); n++)    
+ * {    
+ *	sinTable[n+1]=sin(2*pi*n/tableSize);    
+ * } 
    
+ * where pi value is  3.14159265358979    
+ * \par    
+ * Convert Floating point to Q15(Fixed point):    
+ *	(sinTable[i] * pow(2, 15))    
+ * \par    
+ * rounding to nearest integer is done    
+ * 	sinTable[i] += (sinTable[i] > 0 ? 0.5 :-0.5);    
+ */
+
+
+static const q15_t sinTableQ15[259] = {
+  0xfcdc, 0x0, 0x324, 0x648, 0x96b, 0xc8c, 0xfab, 0x12c8,
+  0x15e2, 0x18f9, 0x1c0c, 0x1f1a, 0x2224, 0x2528, 0x2827, 0x2b1f,
+  0x2e11, 0x30fc, 0x33df, 0x36ba, 0x398d, 0x3c57, 0x3f17, 0x41ce,
+  0x447b, 0x471d, 0x49b4, 0x4c40, 0x4ec0, 0x5134, 0x539b, 0x55f6,
+  0x5843, 0x5a82, 0x5cb4, 0x5ed7, 0x60ec, 0x62f2, 0x64e9, 0x66d0,
+  0x68a7, 0x6a6e, 0x6c24, 0x6dca, 0x6f5f, 0x70e3, 0x7255, 0x73b6,
+  0x7505, 0x7642, 0x776c, 0x7885, 0x798a, 0x7a7d, 0x7b5d, 0x7c2a,
+  0x7ce4, 0x7d8a, 0x7e1e, 0x7e9d, 0x7f0a, 0x7f62, 0x7fa7, 0x7fd9,
+  0x7ff6, 0x7fff, 0x7ff6, 0x7fd9, 0x7fa7, 0x7f62, 0x7f0a, 0x7e9d,
+  0x7e1e, 0x7d8a, 0x7ce4, 0x7c2a, 0x7b5d, 0x7a7d, 0x798a, 0x7885,
+  0x776c, 0x7642, 0x7505, 0x73b6, 0x7255, 0x70e3, 0x6f5f, 0x6dca,
+  0x6c24, 0x6a6e, 0x68a7, 0x66d0, 0x64e9, 0x62f2, 0x60ec, 0x5ed7,
+  0x5cb4, 0x5a82, 0x5843, 0x55f6, 0x539b, 0x5134, 0x4ec0, 0x4c40,
+  0x49b4, 0x471d, 0x447b, 0x41ce, 0x3f17, 0x3c57, 0x398d, 0x36ba,
+  0x33df, 0x30fc, 0x2e11, 0x2b1f, 0x2827, 0x2528, 0x2224, 0x1f1a,
+  0x1c0c, 0x18f9, 0x15e2, 0x12c8, 0xfab, 0xc8c, 0x96b, 0x648,
+  0x324, 0x0, 0xfcdc, 0xf9b8, 0xf695, 0xf374, 0xf055, 0xed38,
+  0xea1e, 0xe707, 0xe3f4, 0xe0e6, 0xdddc, 0xdad8, 0xd7d9, 0xd4e1,
+  0xd1ef, 0xcf04, 0xcc21, 0xc946, 0xc673, 0xc3a9, 0xc0e9, 0xbe32,
+  0xbb85, 0xb8e3, 0xb64c, 0xb3c0, 0xb140, 0xaecc, 0xac65, 0xaa0a,
+  0xa7bd, 0xa57e, 0xa34c, 0xa129, 0x9f14, 0x9d0e, 0x9b17, 0x9930,
+  0x9759, 0x9592, 0x93dc, 0x9236, 0x90a1, 0x8f1d, 0x8dab, 0x8c4a,
+  0x8afb, 0x89be, 0x8894, 0x877b, 0x8676, 0x8583, 0x84a3, 0x83d6,
+  0x831c, 0x8276, 0x81e2, 0x8163, 0x80f6, 0x809e, 0x8059, 0x8027,
+  0x800a, 0x8000, 0x800a, 0x8027, 0x8059, 0x809e, 0x80f6, 0x8163,
+  0x81e2, 0x8276, 0x831c, 0x83d6, 0x84a3, 0x8583, 0x8676, 0x877b,
+  0x8894, 0x89be, 0x8afb, 0x8c4a, 0x8dab, 0x8f1d, 0x90a1, 0x9236,
+  0x93dc, 0x9592, 0x9759, 0x9930, 0x9b17, 0x9d0e, 0x9f14, 0xa129,
+  0xa34c, 0xa57e, 0xa7bd, 0xaa0a, 0xac65, 0xaecc, 0xb140, 0xb3c0,
+  0xb64c, 0xb8e3, 0xbb85, 0xbe32, 0xc0e9, 0xc3a9, 0xc673, 0xc946,
+  0xcc21, 0xcf04, 0xd1ef, 0xd4e1, 0xd7d9, 0xdad8, 0xdddc, 0xe0e6,
+  0xe3f4, 0xe707, 0xea1e, 0xed38, 0xf055, 0xf374, 0xf695, 0xf9b8,
+  0xfcdc, 0x0, 0x324
+};
+
+
+/**   
+ * @brief Fast approximation to the trigonometric sine function for Q15 data.   
+ * @param[in] x Scaled input value in radians.   
+ * @return  sin(x).   
+ *   
+ * The Q15 input value is in the range [0 +0.9999] and is mapped to a radian value in the range [0 2*pi), Here range excludes 2*pi.   
+ */
+
+q15_t arm_sin_q15(
+  q15_t x)
+{
+  q31_t sinVal;                                  /* Temporary variables output */
+  q15_t *tablePtr;                               /* Pointer to table */
+  q15_t fract, in, in2;                          /* Temporary variables for input, output */
+  q31_t wa, wb, wc, wd;                          /* Cubic interpolation coefficients */
+  q15_t a, b, c, d;                              /* Four nearest output values */
+  q15_t fractCube, fractSquare;                  /* Temporary values for fractional value */
+  q15_t oneBy6 = 0x1555;                         /* Fixed point value of 1/6 */
+  q15_t tableSpacing = TABLE_SPACING_Q15;        /* Table spacing */
+  int32_t index;                                 /* Index variable */
+
+  in = x;
+
+  /* Calculate the nearest index */
+  index = (int32_t) in / tableSpacing;
+
+  /* Calculate the nearest value of input */
+  in2 = (q15_t) ((index) * tableSpacing);
+
+  /* Calculation of fractional value */
+  fract = (in - in2) << 8;
+
+  /* fractSquare = fract * fract */
+  fractSquare = (q15_t) ((fract * fract) >> 15);
+
+  /* fractCube = fract * fract * fract */
+  fractCube = (q15_t) ((fractSquare * fract) >> 15);
+
+  /* Checking min and max index of table */
+  if(index < 0)
+  {
+    index = 0;
+  }
+  else if(index > 256)
+  {
+    index = 256;
+  }
+
+  /* Initialise table pointer */
+  tablePtr = (q15_t *) & sinTableQ15[index];
+
+  /* Cubic interpolation process */
+  /* Calculation of wa */
+  /* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAA)*fract; */
+  wa = (q31_t) oneBy6 *fractCube;
+  wa += (q31_t) 0x2AAA *fract;
+  wa = -(wa >> 15);
+  wa += ((q31_t) fractSquare >> 1u);
+
+  /* Read first nearest value of output from the sin table */
+  a = *tablePtr++;
+
+  /* sinVal = a * wa */
+  sinVal = a * wa;
+
+  /* Calculation of wb */
+  wb = (((q31_t) fractCube >> 1u) - (q31_t) fractSquare) -
+    (((q31_t) fract >> 1u) - 0x7FFF);
+
+  /* Read second nearest value of output from the sin table */
+  b = *tablePtr++;
+
+  /*      sinVal += b*wb */
+  sinVal += b * wb;
+
+
+  /* Calculation of wc */
+  wc = -(q31_t) fractCube + fractSquare;
+  wc = (wc >> 1u) + fract;
+
+  /* Read third nearest value of output from the sin table */
+  c = *tablePtr++;
+
+  /* sinVal += c*wc */
+  sinVal += c * wc;
+
+  /* Calculation of wd */
+  /* wd = (oneBy6)*fractCube - (oneBy6)*fract; */
+  fractCube = fractCube - fract;
+  wd = ((q15_t) (((q31_t) oneBy6 * fractCube) >> 15));
+
+  /* Read fourth nearest value of output from the sin table */
+  d = *tablePtr++;
+
+  /* sinVal += d*wd; */
+  sinVal += d * wd;
+
+  /* Convert output value in 1.15(q15) format and saturate */
+  sinVal = __SSAT((sinVal >> 15), 16);
+
+  /* Return the output value in 1.15(q15) format */
+  return ((q15_t) sinVal);
+
+}
+
+/**    
+ * @} end of sin group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_sin_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_sin_q31.c
new file mode 100644
index 0000000000..336796b5c1
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_sin_q31.c
@@ -0,0 +1,240 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_sin_q31.c    
+*    
+* Description:	Fast sine calculation for Q31 values.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFastMath    
+ */
+
+ /**    
+ * @addtogroup sin    
+ * @{    
+ */
+
+/**   
+ * \par    
+ * Tables generated are in Q31(1.31 Fixed point format)    
+ * Generation of sin values in floating point:    
+ * 
tableSize = 256;      
+ * for(n = -1; n < (tableSize + 1); n++)    
+ * {    
+ *	sinTable[n+1]= sin(2*pi*n/tableSize);    
+ * } 
    
+ * where pi value is  3.14159265358979    
+ * \par    
+ * Convert Floating point to Q31(Fixed point):    
+ *	(sinTable[i] * pow(2, 31))    
+ * \par    
+ * rounding to nearest integer is done    
+ * 	sinTable[i] += (sinTable[i] > 0 ? 0.5 :-0.5);    
+ */
+
+static const q31_t sinTableQ31[259] = {
+  0xfcdbd541, 0x0, 0x3242abf, 0x647d97c, 0x96a9049, 0xc8bd35e, 0xfab272b,
+  0x12c8106f,
+  0x15e21445, 0x18f8b83c, 0x1c0b826a, 0x1f19f97b, 0x2223a4c5, 0x25280c5e,
+  0x2826b928, 0x2b1f34eb,
+  0x2e110a62, 0x30fbc54d, 0x33def287, 0x36ba2014, 0x398cdd32, 0x3c56ba70,
+  0x3f1749b8, 0x41ce1e65,
+  0x447acd50, 0x471cece7, 0x49b41533, 0x4c3fdff4, 0x4ebfe8a5, 0x5133cc94,
+  0x539b2af0, 0x55f5a4d2,
+  0x5842dd54, 0x5a82799a, 0x5cb420e0, 0x5ed77c8a, 0x60ec3830, 0x62f201ac,
+  0x64e88926, 0x66cf8120,
+  0x68a69e81, 0x6a6d98a4, 0x6c242960, 0x6dca0d14, 0x6f5f02b2, 0x70e2cbc6,
+  0x72552c85, 0x73b5ebd1,
+  0x7504d345, 0x7641af3d, 0x776c4edb, 0x78848414, 0x798a23b1, 0x7a7d055b,
+  0x7b5d039e, 0x7c29fbee,
+  0x7ce3ceb2, 0x7d8a5f40, 0x7e1d93ea, 0x7e9d55fc, 0x7f0991c4, 0x7f62368f,
+  0x7fa736b4, 0x7fd8878e,
+  0x7ff62182, 0x7fffffff, 0x7ff62182, 0x7fd8878e, 0x7fa736b4, 0x7f62368f,
+  0x7f0991c4, 0x7e9d55fc,
+  0x7e1d93ea, 0x7d8a5f40, 0x7ce3ceb2, 0x7c29fbee, 0x7b5d039e, 0x7a7d055b,
+  0x798a23b1, 0x78848414,
+  0x776c4edb, 0x7641af3d, 0x7504d345, 0x73b5ebd1, 0x72552c85, 0x70e2cbc6,
+  0x6f5f02b2, 0x6dca0d14,
+  0x6c242960, 0x6a6d98a4, 0x68a69e81, 0x66cf8120, 0x64e88926, 0x62f201ac,
+  0x60ec3830, 0x5ed77c8a,
+  0x5cb420e0, 0x5a82799a, 0x5842dd54, 0x55f5a4d2, 0x539b2af0, 0x5133cc94,
+  0x4ebfe8a5, 0x4c3fdff4,
+  0x49b41533, 0x471cece7, 0x447acd50, 0x41ce1e65, 0x3f1749b8, 0x3c56ba70,
+  0x398cdd32, 0x36ba2014,
+  0x33def287, 0x30fbc54d, 0x2e110a62, 0x2b1f34eb, 0x2826b928, 0x25280c5e,
+  0x2223a4c5, 0x1f19f97b,
+  0x1c0b826a, 0x18f8b83c, 0x15e21445, 0x12c8106f, 0xfab272b, 0xc8bd35e,
+  0x96a9049, 0x647d97c,
+  0x3242abf, 0x0, 0xfcdbd541, 0xf9b82684, 0xf6956fb7, 0xf3742ca2, 0xf054d8d5,
+  0xed37ef91,
+  0xea1debbb, 0xe70747c4, 0xe3f47d96, 0xe0e60685, 0xdddc5b3b, 0xdad7f3a2,
+  0xd7d946d8, 0xd4e0cb15,
+  0xd1eef59e, 0xcf043ab3, 0xcc210d79, 0xc945dfec, 0xc67322ce, 0xc3a94590,
+  0xc0e8b648, 0xbe31e19b,
+  0xbb8532b0, 0xb8e31319, 0xb64beacd, 0xb3c0200c, 0xb140175b, 0xaecc336c,
+  0xac64d510, 0xaa0a5b2e,
+  0xa7bd22ac, 0xa57d8666, 0xa34bdf20, 0xa1288376, 0x9f13c7d0, 0x9d0dfe54,
+  0x9b1776da, 0x99307ee0,
+  0x9759617f, 0x9592675c, 0x93dbd6a0, 0x9235f2ec, 0x90a0fd4e, 0x8f1d343a,
+  0x8daad37b, 0x8c4a142f,
+  0x8afb2cbb, 0x89be50c3, 0x8893b125, 0x877b7bec, 0x8675dc4f, 0x8582faa5,
+  0x84a2fc62, 0x83d60412,
+  0x831c314e, 0x8275a0c0, 0x81e26c16, 0x8162aa04, 0x80f66e3c, 0x809dc971,
+  0x8058c94c, 0x80277872,
+  0x8009de7e, 0x80000000, 0x8009de7e, 0x80277872, 0x8058c94c, 0x809dc971,
+  0x80f66e3c, 0x8162aa04,
+  0x81e26c16, 0x8275a0c0, 0x831c314e, 0x83d60412, 0x84a2fc62, 0x8582faa5,
+  0x8675dc4f, 0x877b7bec,
+  0x8893b125, 0x89be50c3, 0x8afb2cbb, 0x8c4a142f, 0x8daad37b, 0x8f1d343a,
+  0x90a0fd4e, 0x9235f2ec,
+  0x93dbd6a0, 0x9592675c, 0x9759617f, 0x99307ee0, 0x9b1776da, 0x9d0dfe54,
+  0x9f13c7d0, 0xa1288376,
+  0xa34bdf20, 0xa57d8666, 0xa7bd22ac, 0xaa0a5b2e, 0xac64d510, 0xaecc336c,
+  0xb140175b, 0xb3c0200c,
+  0xb64beacd, 0xb8e31319, 0xbb8532b0, 0xbe31e19b, 0xc0e8b648, 0xc3a94590,
+  0xc67322ce, 0xc945dfec,
+  0xcc210d79, 0xcf043ab3, 0xd1eef59e, 0xd4e0cb15, 0xd7d946d8, 0xdad7f3a2,
+  0xdddc5b3b, 0xe0e60685,
+  0xe3f47d96, 0xe70747c4, 0xea1debbb, 0xed37ef91, 0xf054d8d5, 0xf3742ca2,
+  0xf6956fb7, 0xf9b82684,
+  0xfcdbd541, 0x0, 0x3242abf
+};
+
+
+/**   
+ * @brief Fast approximation to the trigonometric sine function for Q31 data.   
+ * @param[in] x Scaled input value in radians.   
+ * @return  sin(x).   
+ *   
+ * The Q31 input value is in the range [0 +0.9999] and is mapped to a radian value in the range [0 2*pi), Here range excludes 2*pi.   
+ */
+
+q31_t arm_sin_q31(
+  q31_t x)
+{
+  q31_t sinVal, in, in2;                         /* Temporary variables for input, output */
+  int32_t index;                                 /* Index variables */
+  q31_t wa, wb, wc, wd;                          /* Cubic interpolation coefficients */
+  q31_t a, b, c, d;                              /* Four nearest output values */
+  q31_t *tablePtr;                               /* Pointer to table */
+  q31_t fract, fractCube, fractSquare;           /* Temporary values for fractional values */
+  q31_t oneBy6 = 0x15555555;                     /* Fixed point value of 1/6 */
+  q31_t tableSpacing = TABLE_SPACING_Q31;        /* Table spacing */
+  q31_t temp;                                    /* Temporary variable for intermediate process */
+
+  in = x;
+
+  /* Calculate the nearest index */
+  index = (uint32_t) in / (uint32_t) tableSpacing;
+
+  /* Calculate the nearest value of input */
+  in2 = (q31_t) index *tableSpacing;
+
+  /* Calculation of fractional value */
+  fract = (in - in2) << 8;
+
+  /* fractSquare = fract * fract */
+  fractSquare = ((q31_t) (((q63_t) fract * fract) >> 32));
+  fractSquare = fractSquare << 1;
+
+  /* fractCube = fract * fract * fract */
+  fractCube = ((q31_t) (((q63_t) fractSquare * fract) >> 32));
+  fractCube = fractCube << 1;
+
+  /* Checking min and max index of table */
+  if(index < 0)
+  {
+    index = 0;
+  }
+  else if(index > 256)
+  {
+    index = 256;
+  }
+
+  /* Initialise table pointer */
+  tablePtr = (q31_t *) & sinTableQ31[index];
+
+  /* Cubic interpolation process */
+  /* Calculation of wa */
+  /* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAAAAAA)*fract; */
+  wa = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32));
+  temp = 0x2AAAAAAA;
+  wa = (q31_t) ((((q63_t) wa << 32) + ((q63_t) temp * fract)) >> 32);
+  wa = -(wa << 1u);
+  wa += (fractSquare >> 1u);
+
+  /* Read first nearest value of output from the sin table */
+  a = *tablePtr++;
+
+  /* sinVal = a*wa */
+  sinVal = ((q31_t) (((q63_t) a * wa) >> 32));
+
+  /* q31(1.31) Fixed point value of 1 */
+  temp = 0x7FFFFFFF;
+
+  /* Calculation of wb */
+  wb = ((fractCube >> 1u) - (fractSquare + (fract >> 1u))) + temp;
+
+  /* Read second nearest value of output from the sin table */
+  b = *tablePtr++;
+
+  /*  sinVal += b*wb */
+  sinVal = (q31_t) ((((q63_t) sinVal << 32) + (q63_t) b * (wb)) >> 32);
+
+  /* Calculation of wc */
+  wc = -fractCube + fractSquare;
+  wc = (wc >> 1u) + fract;
+
+  /* Read third nearest value of output from the sin table */
+  c = *tablePtr++;
+
+  /*      sinVal += c*wc */
+  sinVal = (q31_t) ((((q63_t) sinVal << 32) + ((q63_t) c * wc)) >> 32);
+
+  /* Calculation of wd */
+  /* wd = (oneBy6) * fractCube - (oneBy6) * fract; */
+  fractCube = fractCube - fract;
+  wd = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32));
+  wd = (wd << 1u);
+
+  /* Read fourth nearest value of output from the sin table */
+  d = *tablePtr++;
+
+  /* sinVal += d*wd; */
+  sinVal = (q31_t) ((((q63_t) sinVal << 32) + ((q63_t) d * wd)) >> 32);
+
+  /* convert sinVal in 2.30 format to 1.31 format */
+  return (__QADD(sinVal, sinVal));
+
+}
+
+/**    
+ * @} end of sin group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_sqrt_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_sqrt_q15.c
new file mode 100644
index 0000000000..0a6d6a53a2
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_sqrt_q15.c
@@ -0,0 +1,131 @@
+/* ----------------------------------------------------------------------     
+* Copyright (C) 2011 ARM Limited. All rights reserved.  
+*     
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*     
+* Project:      CMSIS DSP Library  
+* Title:		arm_sqrt_q15.c     
+*     
+* Description:	Q15 square root function.    
+*     
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+* 
+* Version 1.0.0 2011/03/08 
+*     Alpha release. 
+* 
+* Version 1.0.1 2011/09/30 
+*     Beta release.  
+*     
+* -------------------------------------------------------------------- */
+#include "arm_math.h"
+#include "arm_common_tables.h"
+
+
+/**     
+ * @ingroup groupFastMath     
+ */
+
+/**     
+ * @addtogroup SQRT     
+ * @{     
+ */
+
+  /**    
+   * @brief  Q15 square root function.    
+   * @param[in]   in     input value.  The range of the input value is [0 +1) or 0x0000 to 0x7FFF.    
+   * @param[out]  *pOut  square root of input value.    
+   * @return The function returns ARM_MATH_SUCCESS if input value is positive value or ARM_MATH_ARGUMENT_ERROR if    
+   * in is negative value and returns zero output for negative values.    
+   */
+
+arm_status arm_sqrt_q15(
+  q15_t in,
+  q15_t * pOut)
+{
+  q15_t number, temp1, var1, signBits1, half;
+  q31_t bits_val1;
+  float32_t temp_float1;
+
+  number = in;
+
+  /* If the input is a positive number then compute the signBits. */
+  if(number > 0)
+  {
+    signBits1 = __CLZ(number) - 17;
+
+    /* Shift by the number of signBits1 */
+    if((signBits1 % 2) == 0)
+    {
+      number = number << signBits1;
+    }
+    else
+    {
+      number = number << (signBits1 - 1);
+    }
+
+    /* Calculate half value of the number */
+    half = number >> 1;
+    /* Store the number for later use */
+    temp1 = number;
+
+    /*Convert to float */
+    temp_float1 = number * 3.051757812500000e-005f;
+    /*Store as integer */
+    bits_val1 = *(int *) &temp_float1;
+    /* Subtract the shifted value from the magic number to give intial guess */
+    bits_val1 = 0x5f3759df - (bits_val1 >> 1);  // gives initial guess  
+    /* Store as float */
+    temp_float1 = *(float *) &bits_val1;
+    /* Convert to integer format */
+    var1 = (q31_t) (temp_float1 * 16384);
+
+    /* 1st iteration */
+    var1 = ((q15_t) ((q31_t) var1 * (0x3000 -
+                                     ((q15_t)
+                                      ((((q15_t)
+                                         (((q31_t) var1 * var1) >> 15)) *
+                                        (q31_t) half) >> 15))) >> 15)) << 2;
+    /* 2nd iteration */
+    var1 = ((q15_t) ((q31_t) var1 * (0x3000 -
+                                     ((q15_t)
+                                      ((((q15_t)
+                                         (((q31_t) var1 * var1) >> 15)) *
+                                        (q31_t) half) >> 15))) >> 15)) << 2;
+    /* 3rd iteration */
+    var1 = ((q15_t) ((q31_t) var1 * (0x3000 -
+                                     ((q15_t)
+                                      ((((q15_t)
+                                         (((q31_t) var1 * var1) >> 15)) *
+                                        (q31_t) half) >> 15))) >> 15)) << 2;
+
+    /* Multiply the inverse square root with the original value */
+    var1 = ((q15_t) (((q31_t) temp1 * var1) >> 15)) << 1;
+
+    /* Shift the output down accordingly */
+    if((signBits1 % 2) == 0)
+    {
+      var1 = var1 >> (signBits1 / 2);
+    }
+    else
+    {
+      var1 = var1 >> ((signBits1 - 1) / 2);
+    }
+    *pOut = var1;
+
+    return (ARM_MATH_SUCCESS);
+  }
+  /* If the number is a negative number then store zero as its square root value */
+  else
+  {
+    *pOut = 0;
+    return (ARM_MATH_ARGUMENT_ERROR);
+  }
+}
+
+/**     
+ * @} end of SQRT group     
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_sqrt_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_sqrt_q31.c
new file mode 100644
index 0000000000..2a3b7ac18d
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_sqrt_q31.c
@@ -0,0 +1,129 @@
+/* ----------------------------------------------------------------------     
+* Copyright (C) 2011 ARM Limited. All rights reserved.  
+*     
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*     
+* Project:      CMSIS DSP Library  
+* Title:		arm_sqrt_q31.c     
+*     
+* Description:	Q31 square root function.    
+*     
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+* 
+* Version 1.0.0 2011/03/08 
+*     Alpha release. 
+* 
+* Version 1.0.1 2011/09/30 
+*     Beta release.  
+*     
+* -------------------------------------------------------------------- */
+#include "arm_math.h"
+#include "arm_common_tables.h"
+
+/**     
+ * @ingroup groupFastMath     
+ */
+
+/**     
+ * @addtogroup SQRT     
+ * @{     
+ */
+
+/**    
+ * @brief Q31 square root function.    
+ * @param[in]   in    input value.  The range of the input value is [0 +1) or 0x00000000 to 0x7FFFFFFF.    
+ * @param[out]  *pOut square root of input value.    
+ * @return The function returns ARM_MATH_SUCCESS if input value is positive value or ARM_MATH_ARGUMENT_ERROR if    
+ * in is negative value and returns zero output for negative values.    
+ */
+
+arm_status arm_sqrt_q31(
+  q31_t in,
+  q31_t * pOut)
+{
+  q31_t number, temp1, bits_val1, var1, signBits1, half;
+  float32_t temp_float1;
+
+  number = in;
+
+  /* If the input is a positive number then compute the signBits. */
+  if(number > 0)
+  {
+    signBits1 = __CLZ(number) - 1;
+
+    /* Shift by the number of signBits1 */
+    if((signBits1 % 2) == 0)
+    {
+      number = number << signBits1;
+    }
+    else
+    {
+      number = number << (signBits1 - 1);
+    }
+
+    /* Calculate half value of the number */
+    half = number >> 1;
+    /* Store the number for later use */
+    temp1 = number;
+
+    /*Convert to float */
+    temp_float1 = number * 4.6566128731e-010f;
+    /*Store as integer */
+    bits_val1 = *(int *) &temp_float1;
+    /* Subtract the shifted value from the magic number to give intial guess */
+    bits_val1 = 0x5f3759df - (bits_val1 >> 1);  // gives initial guess  
+    /* Store as float */
+    temp_float1 = *(float *) &bits_val1;
+    /* Convert to integer format */
+    var1 = (q31_t) (temp_float1 * 1073741824);
+
+    /* 1st iteration */
+    var1 = ((q31_t) ((q63_t) var1 * (0x30000000 -
+                                     ((q31_t)
+                                      ((((q31_t)
+                                         (((q63_t) var1 * var1) >> 31)) *
+                                        (q63_t) half) >> 31))) >> 31)) << 2;
+    /* 2nd iteration */
+    var1 = ((q31_t) ((q63_t) var1 * (0x30000000 -
+                                     ((q31_t)
+                                      ((((q31_t)
+                                         (((q63_t) var1 * var1) >> 31)) *
+                                        (q63_t) half) >> 31))) >> 31)) << 2;
+    /* 3rd iteration */
+    var1 = ((q31_t) ((q63_t) var1 * (0x30000000 -
+                                     ((q31_t)
+                                      ((((q31_t)
+                                         (((q63_t) var1 * var1) >> 31)) *
+                                        (q63_t) half) >> 31))) >> 31)) << 2;
+
+    /* Multiply the inverse square root with the original value */
+    var1 = ((q31_t) (((q63_t) temp1 * var1) >> 31)) << 1;
+
+    /* Shift the output down accordingly */
+    if((signBits1 % 2) == 0)
+    {
+      var1 = var1 >> (signBits1 / 2);
+    }
+    else
+    {
+      var1 = var1 >> ((signBits1 - 1) / 2);
+    }
+    *pOut = var1;
+
+    return (ARM_MATH_SUCCESS);
+  }
+  /* If the number is a negative number then store zero as its square root value */
+  else
+  {
+    *pOut = 0;
+    return (ARM_MATH_ARGUMENT_ERROR);
+  }
+}
+
+/**     
+ * @} end of SQRT group     
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_32x64_init_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_32x64_init_q31.c
new file mode 100644
index 0000000000..a6745c0cd4
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_32x64_init_q31.c
@@ -0,0 +1,105 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_biquad_cascade_df1_32x64_init_q31.c    
+*    
+* Description:	High precision Q31 Biquad cascade filter initialization function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup BiquadCascadeDF1_32x64    
+ * @{    
+ */
+
+/**    
+ * @details    
+ *    
+ * @param[in,out] *S           	points to an instance of the high precision Q31 Biquad cascade filter structure.    
+ * @param[in]     numStages     number of 2nd order stages in the filter.    
+ * @param[in]     *pCoeffs      points to the filter coefficients.    
+ * @param[in]     *pState       points to the state buffer.    
+ * @param[in]     postShift     Shift to be applied after the accumulator.  Varies according to the coefficients format.    
+ * @return        none    
+ *    
+ * Coefficient and State Ordering:    
+ *    
+ * \par    
+ * The coefficients are stored in the array pCoeffs in the following order:    
+ * 
    
+ *     {b10, b11, b12, a11, a12, b20, b21, b22, a21, a22, ...}    
+ * 
    
+ * where b1x and a1x are the coefficients for the first stage,    
+ * b2x and a2x are the coefficients for the second stage,    
+ * and so on.  The pCoeffs array contains a total of 5*numStages values.    
+ *    
+ * \par    
+ * The pState points to state variables array and size of each state variable is 1.63 format.    
+ * Each Biquad stage has 4 state variables x[n-1], x[n-2], y[n-1], and y[n-2].    
+ * The state variables are arranged in the state array as:    
+ * 
    
+ *     {x[n-1], x[n-2], y[n-1], y[n-2]}    
+ * 
    
+ * The 4 state variables for stage 1 are first, then the 4 state variables for stage 2, and so on.    
+ * The state array has a total length of 4*numStages values.    
+ * The state variables are updated after each block of data is processed; the coefficients are untouched.    
+ */
+
+void arm_biquad_cas_df1_32x64_init_q31(
+  arm_biquad_cas_df1_32x64_ins_q31 * S,
+  uint8_t numStages,
+  q31_t * pCoeffs,
+  q63_t * pState,
+  uint8_t postShift)
+{
+  /* Assign filter stages */
+  S->numStages = numStages;
+
+  /* Assign postShift to be applied to the output */
+  S->postShift = postShift;
+
+  /* Assign coefficient pointer */
+  S->pCoeffs = pCoeffs;
+
+  /* Clear state buffer and size is always 4 * numStages */
+  memset(pState, 0, (4u * (uint32_t) numStages) * sizeof(q63_t));
+
+  /* Assign state pointer */
+  S->pState = pState;
+}
+
+/**    
+ * @} end of BiquadCascadeDF1_32x64 group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_32x64_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_32x64_q31.c
new file mode 100644
index 0000000000..82d6164ee1
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_32x64_q31.c
@@ -0,0 +1,553 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_biquad_cascade_df1_32x64_q31.c    
+*    
+* Description:	High precision Q31 Biquad cascade filter processing function    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @defgroup BiquadCascadeDF1_32x64 High Precision Q31 Biquad Cascade Filter    
+ *    
+ * This function implements a high precision Biquad cascade filter which operates on    
+ * Q31 data values.  The filter coefficients are in 1.31 format and the state variables    
+ * are in 1.63 format.  The double precision state variables reduce quantization noise    
+ * in the filter and provide a cleaner output.    
+ * These filters are particularly useful when implementing filters in which the    
+ * singularities are close to the unit circle.  This is common for low pass or high    
+ * pass filters with very low cutoff frequencies.    
+ *    
+ * The function operates on blocks of input and output data    
+ * and each call to the function processes blockSize samples through    
+ * the filter. pSrc and pDst points to input and output arrays    
+ * containing blockSize Q31 values.    
+ *    
+ * \par Algorithm    
+ * Each Biquad stage implements a second order filter using the difference equation:    
+ * 
    
+ *     y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]    
+ * 
    
+ * A Direct Form I algorithm is used with 5 coefficients and 4 state variables per stage.    
+ * \image html Biquad.gif "Single Biquad filter stage"    
+ * Coefficients b0, b1, and b2  multiply the input signal x[n] and are referred to as the feedforward coefficients.    
+ * Coefficients a1 and a2 multiply the output signal y[n] and are referred to as the feedback coefficients.    
+ * Pay careful attention to the sign of the feedback coefficients.    
+ * Some design tools use the difference equation    
+ * 
    
+ *     y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] - a1 * y[n-1] - a2 * y[n-2]    
+ * 
    
+ * In this case the feedback coefficients a1 and a2 must be negated when used with the CMSIS DSP Library.    
+ *    
+ * \par    
+ * Higher order filters are realized as a cascade of second order sections.    
+ * numStages refers to the number of second order stages used.    
+ * For example, an 8th order filter would be realized with numStages=4 second order stages.    
+ * \image html BiquadCascade.gif "8th order filter using a cascade of Biquad stages"    
+ * A 9th order filter would be realized with numStages=5 second order stages with the coefficients for one of the stages configured as a first order filter (b2=0 and a2=0).    
+ *    
+ * \par    
+ * The pState points to state variables array .    
+ * Each Biquad stage has 4 state variables x[n-1], x[n-2], y[n-1], and y[n-2] and each state variable in 1.63 format to improve precision.    
+ * The state variables are arranged in the array as:    
+ * 
    
+ *     {x[n-1], x[n-2], y[n-1], y[n-2]}    
+ * 
    
+ *    
+ * \par    
+ * The 4 state variables for stage 1 are first, then the 4 state variables for stage 2, and so on.    
+ * The state array has a total length of 4*numStages values of data in 1.63 format.    
+ * The state variables are updated after each block of data is processed; the coefficients are untouched.    
+ *    
+ * \par Instance Structure    
+ * The coefficients and state variables for a filter are stored together in an instance data structure.    
+ * A separate instance structure must be defined for each filter.    
+ * Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.    
+ *    
+ * \par Init Function    
+ * There is also an associated initialization function which performs the following operations:    
+ * - Sets the values of the internal structure fields.    
+ * - Zeros out the values in the state buffer.    
+ * \par    
+ * Use of the initialization function is optional.    
+ * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.    
+ * To place an instance structure into a const data section, the instance structure must be manually initialized.    
+ * Set the values in the state buffer to zeros before static initialization.    
+ * For example, to statically initialize the filter instance structure use    
+ * 
    
+ *     arm_biquad_cas_df1_32x64_ins_q31 S1 = {numStages, pState, pCoeffs, postShift};    
+ * 
    
+ * where numStages is the number of Biquad stages in the filter; pState is the address of the state buffer;    
+ * pCoeffs is the address of the coefficient buffer; postShift shift to be applied which is described in detail below.    
+ * \par Fixed-Point Behavior    
+ * Care must be taken while using Biquad Cascade 32x64 filter function.    
+ * Following issues must be considered:    
+ * - Scaling of coefficients    
+ * - Filter gain    
+ * - Overflow and saturation    
+ *    
+ * \par    
+ * Filter coefficients are represented as fractional values and    
+ * restricted to lie in the range [-1 +1).    
+ * The processing function has an additional scaling parameter postShift    
+ * which allows the filter coefficients to exceed the range [+1 -1).    
+ * At the output of the filter's accumulator is a shift register which shifts the result by postShift bits.    
+ * \image html BiquadPostshift.gif "Fixed-point Biquad with shift by postShift bits after accumulator"    
+ * This essentially scales the filter coefficients by 2^postShift.    
+ * For example, to realize the coefficients    
+ * 
    
+ *    {1.5, -0.8, 1.2, 1.6, -0.9}    
+ * 
    
+ * set the Coefficient array to:    
+ * 
    
+ *    {0.75, -0.4, 0.6, 0.8, -0.45}    
+ * 
    
+ * and set postShift=1    
+ *    
+ * \par    
+ * The second thing to keep in mind is the gain through the filter.    
+ * The frequency response of a Biquad filter is a function of its coefficients.    
+ * It is possible for the gain through the filter to exceed 1.0 meaning that the filter increases the amplitude of certain frequencies.    
+ * This means that an input signal with amplitude < 1.0 may result in an output > 1.0 and these are saturated or overflowed based on the implementation of the filter.    
+ * To avoid this behavior the filter needs to be scaled down such that its peak gain < 1.0 or the input signal must be scaled down so that the combination of input and filter are never overflowed.    
+ *    
+ * \par    
+ * The third item to consider is the overflow and saturation behavior of the fixed-point Q31 version.    
+ * This is described in the function specific documentation below.    
+ */
+
+/**    
+ * @addtogroup BiquadCascadeDF1_32x64    
+ * @{    
+ */
+
+/**    
+ * @details    
+    
+ * @param[in]  *S points to an instance of the high precision Q31 Biquad cascade filter.    
+ * @param[in]  *pSrc points to the block of input data.    
+ * @param[out] *pDst points to the block of output data.    
+ * @param[in]  blockSize number of samples to process.    
+ * @return none.    
+ *    
+ * \par    
+ * The function is implemented using an internal 64-bit accumulator.    
+ * The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit.    
+ * Thus, if the accumulator result overflows it wraps around rather than clip.    
+ * In order to avoid overflows completely the input signal must be scaled down by 2 bits and lie in the range [-0.25 +0.25).    
+ * After all 5 multiply-accumulates are performed, the 2.62 accumulator is shifted by postShift bits and the result truncated to    
+ * 1.31 format by discarding the low 32 bits.    
+ *    
+ * \par    
+ * Two related functions are provided in the CMSIS DSP library.    
+ * arm_biquad_cascade_df1_q31() implements a Biquad cascade with 32-bit coefficients and state variables with a Q63 accumulator.    
+ * arm_biquad_cascade_df1_fast_q31() implements a Biquad cascade with 32-bit coefficients and state variables with a Q31 accumulator.    
+ */
+
+void arm_biquad_cas_df1_32x64_q31(
+  const arm_biquad_cas_df1_32x64_ins_q31 * S,
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize)
+{
+  q31_t *pIn = pSrc;                             /*  input pointer initialization  */
+  q31_t *pOut = pDst;                            /*  output pointer initialization */
+  q63_t *pState = S->pState;                     /*  state pointer initialization  */
+  q31_t *pCoeffs = S->pCoeffs;                   /*  coeff pointer initialization  */
+  q63_t acc;                                     /*  accumulator                   */
+  q31_t Xn1, Xn2;                                /*  Input Filter state variables        */
+  q63_t Yn1, Yn2;                                /*  Output Filter state variables        */
+  q31_t b0, b1, b2, a1, a2;                      /*  Filter coefficients           */
+  q31_t Xn;                                      /*  temporary input               */
+  int32_t shift = (int32_t) S->postShift + 1;    /*  Shift to be applied to the output */
+  uint32_t sample, stage = S->numStages;         /*  loop counters                     */
+  q31_t acc_l, acc_h;                            /*  temporary output               */
+  uint32_t uShift = ((uint32_t) S->postShift + 1u);
+  uint32_t lShift = 32u - uShift;                /*  Shift to be applied to the output */
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  do
+  {
+    /* Reading the coefficients */
+    b0 = *pCoeffs++;
+    b1 = *pCoeffs++;
+    b2 = *pCoeffs++;
+    a1 = *pCoeffs++;
+    a2 = *pCoeffs++;
+
+    /* Reading the state values */
+    Xn1 = (q31_t) (pState[0]);
+    Xn2 = (q31_t) (pState[1]);
+    Yn1 = pState[2];
+    Yn2 = pState[3];
+
+    /* Apply loop unrolling and compute 4 output values simultaneously. */
+    /* The variable acc hold output value that is being computed and    
+     * stored in the destination buffer    
+     * acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]    
+     */
+
+    sample = blockSize >> 2u;
+
+    /* First part of the processing with loop unrolling. Compute 4 outputs at a time.    
+     ** a second loop below computes the remaining 1 to 3 samples. */
+    while(sample > 0u)
+    {
+      /* Read the input */
+      Xn = *pIn++;
+
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+
+      /* acc =  b0 * x[n] */
+      acc = (q63_t) Xn *b0;
+
+      /* acc +=  b1 * x[n-1] */
+      acc += (q63_t) Xn1 *b1;
+
+      /* acc +=  b[2] * x[n-2] */
+      acc += (q63_t) Xn2 *b2;
+
+      /* acc +=  a1 * y[n-1] */
+      acc += mult32x64(Yn1, a1);
+
+      /* acc +=  a2 * y[n-2] */
+      acc += mult32x64(Yn2, a2);
+
+      /* The result is converted to 1.63 , Yn2 variable is reused */
+      Yn2 = acc << shift;
+
+      /* Calc lower part of acc */
+      acc_l = acc & 0xffffffff;
+
+      /* Calc upper part of acc */
+      acc_h = (acc >> 32) & 0xffffffff;
+
+      /* Apply shift for lower part of acc and upper part of acc */
+      acc_h = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+      /* Store the output in the destination buffer in 1.31 format. */
+      *pOut = acc_h;
+
+      /* Read the second input into Xn2, to reuse the value */
+      Xn2 = *pIn++;
+
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+
+      /* acc +=  b1 * x[n-1] */
+      acc = (q63_t) Xn *b1;
+
+      /* acc =  b0 * x[n] */
+      acc += (q63_t) Xn2 *b0;
+
+      /* acc +=  b[2] * x[n-2] */
+      acc += (q63_t) Xn1 *b2;
+
+      /* acc +=  a1 * y[n-1] */
+      acc += mult32x64(Yn2, a1);
+
+      /* acc +=  a2 * y[n-2] */
+      acc += mult32x64(Yn1, a2);
+
+      /* The result is converted to 1.63, Yn1 variable is reused */
+      Yn1 = acc << shift;
+
+      /* Calc lower part of acc */
+      acc_l = acc & 0xffffffff;
+
+      /* Calc upper part of acc */
+      acc_h = (acc >> 32) & 0xffffffff;
+
+      /* Apply shift for lower part of acc and upper part of acc */
+      acc_h = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+      /* Read the third input into Xn1, to reuse the value */
+      Xn1 = *pIn++;
+
+      /* The result is converted to 1.31 */
+      /* Store the output in the destination buffer. */
+      *(pOut + 1u) = acc_h;
+
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+
+      /* acc =  b0 * x[n] */
+      acc = (q63_t) Xn1 *b0;
+
+      /* acc +=  b1 * x[n-1] */
+      acc += (q63_t) Xn2 *b1;
+
+      /* acc +=  b[2] * x[n-2] */
+      acc += (q63_t) Xn *b2;
+
+      /* acc +=  a1 * y[n-1] */
+      acc += mult32x64(Yn1, a1);
+
+      /* acc +=  a2 * y[n-2] */
+      acc += mult32x64(Yn2, a2);
+
+      /* The result is converted to 1.63, Yn2 variable is reused  */
+      Yn2 = acc << shift;
+
+      /* Calc lower part of acc */
+      acc_l = acc & 0xffffffff;
+
+      /* Calc upper part of acc */
+      acc_h = (acc >> 32) & 0xffffffff;
+
+      /* Apply shift for lower part of acc and upper part of acc */
+      acc_h = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+      /* Store the output in the destination buffer in 1.31 format. */
+      *(pOut + 2u) = acc_h;
+
+      /* Read the fourth input into Xn, to reuse the value */
+      Xn = *pIn++;
+
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+      /* acc =  b0 * x[n] */
+      acc = (q63_t) Xn *b0;
+
+      /* acc +=  b1 * x[n-1] */
+      acc += (q63_t) Xn1 *b1;
+
+      /* acc +=  b[2] * x[n-2] */
+      acc += (q63_t) Xn2 *b2;
+
+      /* acc +=  a1 * y[n-1] */
+      acc += mult32x64(Yn2, a1);
+
+      /* acc +=  a2 * y[n-2] */
+      acc += mult32x64(Yn1, a2);
+
+      /* The result is converted to 1.63, Yn1 variable is reused  */
+      Yn1 = acc << shift;
+
+      /* Calc lower part of acc */
+      acc_l = acc & 0xffffffff;
+
+      /* Calc upper part of acc */
+      acc_h = (acc >> 32) & 0xffffffff;
+
+      /* Apply shift for lower part of acc and upper part of acc */
+      acc_h = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+      /* Store the output in the destination buffer in 1.31 format. */
+      *(pOut + 3u) = acc_h;
+
+      /* Every time after the output is computed state should be updated. */
+      /* The states should be updated as:  */
+      /* Xn2 = Xn1    */
+      /* Xn1 = Xn     */
+      /* Yn2 = Yn1    */
+      /* Yn1 = acc    */
+      Xn2 = Xn1;
+      Xn1 = Xn;
+
+      /* update output pointer */
+      pOut += 4u;
+
+      /* decrement the loop counter */
+      sample--;
+    }
+
+    /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+     ** No loop unrolling is used. */
+    sample = (blockSize & 0x3u);
+
+    while(sample > 0u)
+    {
+      /* Read the input */
+      Xn = *pIn++;
+
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+
+      /* acc =  b0 * x[n] */
+      acc = (q63_t) Xn *b0;
+      /* acc +=  b1 * x[n-1] */
+      acc += (q63_t) Xn1 *b1;
+      /* acc +=  b[2] * x[n-2] */
+      acc += (q63_t) Xn2 *b2;
+      /* acc +=  a1 * y[n-1] */
+      acc += mult32x64(Yn1, a1);
+      /* acc +=  a2 * y[n-2] */
+      acc += mult32x64(Yn2, a2);
+
+      /* Every time after the output is computed state should be updated. */
+      /* The states should be updated as:  */
+      /* Xn2 = Xn1    */
+      /* Xn1 = Xn     */
+      /* Yn2 = Yn1    */
+      /* Yn1 = acc    */
+      Xn2 = Xn1;
+      Xn1 = Xn;
+      Yn2 = Yn1;
+      /* The result is converted to 1.63, Yn1 variable is reused  */
+      Yn1 = acc << shift;
+
+      /* Calc lower part of acc */
+      acc_l = acc & 0xffffffff;
+
+      /* Calc upper part of acc */
+      acc_h = (acc >> 32) & 0xffffffff;
+
+      /* Apply shift for lower part of acc and upper part of acc */
+      acc_h = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+      /* Store the output in the destination buffer in 1.31 format. */
+      *pOut++ = acc_h;
+      //Yn1 = acc << shift; 
+
+      /* Store the output in the destination buffer in 1.31 format. */
+//      *pOut++ = (q31_t) (acc >> (32 - shift)); 
+
+      /* decrement the loop counter */
+      sample--;
+    }
+
+    /*  The first stage output is given as input to the second stage. */
+    pIn = pDst;
+
+    /* Reset to destination buffer working pointer */
+    pOut = pDst;
+
+    /*  Store the updated state variables back into the pState array */
+    /*  Store the updated state variables back into the pState array */
+    *pState++ = (q63_t) Xn1;
+    *pState++ = (q63_t) Xn2;
+    *pState++ = Yn1;
+    *pState++ = Yn2;
+
+  } while(--stage);
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  do
+  {
+    /* Reading the coefficients */
+    b0 = *pCoeffs++;
+    b1 = *pCoeffs++;
+    b2 = *pCoeffs++;
+    a1 = *pCoeffs++;
+    a2 = *pCoeffs++;
+
+    /* Reading the state values */
+    Xn1 = pState[0];
+    Xn2 = pState[1];
+    Yn1 = pState[2];
+    Yn2 = pState[3];
+
+    /* The variable acc hold output value that is being computed and        
+     * stored in the destination buffer            
+     * acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]            
+     */
+
+    sample = blockSize;
+
+    while(sample > 0u)
+    {
+      /* Read the input */
+      Xn = *pIn++;
+
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+      /* acc =  b0 * x[n] */
+      acc = (q63_t) Xn *b0;
+      /* acc +=  b1 * x[n-1] */
+      acc += (q63_t) Xn1 *b1;
+      /* acc +=  b[2] * x[n-2] */
+      acc += (q63_t) Xn2 *b2;
+      /* acc +=  a1 * y[n-1] */
+      acc += mult32x64(Yn1, a1);
+      /* acc +=  a2 * y[n-2] */
+      acc += mult32x64(Yn2, a2);
+
+      /* Every time after the output is computed state should be updated. */
+      /* The states should be updated as:  */
+      /* Xn2 = Xn1    */
+      /* Xn1 = Xn     */
+      /* Yn2 = Yn1    */
+      /* Yn1 = acc    */
+      Xn2 = Xn1;
+      Xn1 = Xn;
+      Yn2 = Yn1;
+
+      /* The result is converted to 1.63, Yn1 variable is reused  */
+      Yn1 = acc << shift;
+
+      /* Calc lower part of acc */
+      acc_l = acc & 0xffffffff;
+
+      /* Calc upper part of acc */
+      acc_h = (acc >> 32) & 0xffffffff;
+
+      /* Apply shift for lower part of acc and upper part of acc */
+      acc_h = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+      /* Store the output in the destination buffer in 1.31 format. */
+      *pOut++ = acc_h;
+
+      //Yn1 = acc << shift; 
+
+      /* Store the output in the destination buffer in 1.31 format. */
+      //*pOut++ = (q31_t) (acc >> (32 - shift)); 
+
+      /* decrement the loop counter */
+      sample--;
+    }
+
+    /*  The first stage output is given as input to the second stage. */
+    pIn = pDst;
+
+    /* Reset to destination buffer working pointer */
+    pOut = pDst;
+
+    /*  Store the updated state variables back into the pState array */
+    *pState++ = (q63_t) Xn1;
+    *pState++ = (q63_t) Xn2;
+    *pState++ = Yn1;
+    *pState++ = Yn2;
+
+  } while(--stage);
+
+#endif /*    #ifndef ARM_MATH_CM0     */
+}
+
+  /**    
+   * @} end of BiquadCascadeDF1_32x64 group    
+   */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_f32.c
new file mode 100644
index 0000000000..ee20dfeec2
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_f32.c
@@ -0,0 +1,421 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_biquad_cascade_df1_f32.c    
+*    
+* Description:	Processing function for the    
+*               floating-point Biquad cascade DirectFormI(DF1) filter.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+* 	 incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @defgroup BiquadCascadeDF1 Biquad Cascade IIR Filters Using Direct Form I Structure    
+ *    
+ * This set of functions implements arbitrary order recursive (IIR) filters.    
+ * The filters are implemented as a cascade of second order Biquad sections.    
+ * The functions support Q15, Q31 and floating-point data types.  
+ * Fast version of Q15 and Q31 also supported on CortexM4 and Cortex-M3.    
+ *    
+ * The functions operate on blocks of input and output data and each call to the function    
+ * processes blockSize samples through the filter.    
+ * pSrc points to the array of input data and    
+ * pDst points to the array of output data.    
+ * Both arrays contain blockSize values.    
+ *    
+ * \par Algorithm    
+ * Each Biquad stage implements a second order filter using the difference equation:    
+ * 
    
+ *     y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]    
+ * 
    
+ * A Direct Form I algorithm is used with 5 coefficients and 4 state variables per stage.    
+ * \image html Biquad.gif "Single Biquad filter stage"    
+ * Coefficients b0, b1 and b2  multiply the input signal x[n] and are referred to as the feedforward coefficients.    
+ * Coefficients a1 and a2 multiply the output signal y[n] and are referred to as the feedback coefficients.    
+ * Pay careful attention to the sign of the feedback coefficients.    
+ * Some design tools use the difference equation    
+ * 
    
+ *     y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] - a1 * y[n-1] - a2 * y[n-2]    
+ * 
    
+ * In this case the feedback coefficients a1 and a2 must be negated when used with the CMSIS DSP Library.    
+ *    
+ * \par    
+ * Higher order filters are realized as a cascade of second order sections.    
+ * numStages refers to the number of second order stages used.    
+ * For example, an 8th order filter would be realized with numStages=4 second order stages.    
+ * \image html BiquadCascade.gif "8th order filter using a cascade of Biquad stages"    
+ * A 9th order filter would be realized with numStages=5 second order stages with the coefficients for one of the stages configured as a first order filter (b2=0 and a2=0).    
+ *    
+ * \par    
+ * The pState points to state variables array.    
+ * Each Biquad stage has 4 state variables x[n-1], x[n-2], y[n-1], and y[n-2].    
+ * The state variables are arranged in the pState array as:    
+ * 
    
+ *     {x[n-1], x[n-2], y[n-1], y[n-2]}    
+ * 
    
+ *    
+ * \par    
+ * The 4 state variables for stage 1 are first, then the 4 state variables for stage 2, and so on.    
+ * The state array has a total length of 4*numStages values.    
+ * The state variables are updated after each block of data is processed, the coefficients are untouched.    
+ *    
+ * \par Instance Structure    
+ * The coefficients and state variables for a filter are stored together in an instance data structure.    
+ * A separate instance structure must be defined for each filter.    
+ * Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.    
+ * There are separate instance structure declarations for each of the 3 supported data types.    
+ *    
+ * \par Init Functions    
+ * There is also an associated initialization function for each data type.    
+ * The initialization function performs following operations:    
+ * - Sets the values of the internal structure fields.    
+ * - Zeros out the values in the state buffer.    
+ *    
+ * \par    
+ * Use of the initialization function is optional.    
+ * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.    
+ * To place an instance structure into a const data section, the instance structure must be manually initialized.    
+ * Set the values in the state buffer to zeros before static initialization.    
+ * The code below statically initializes each of the 3 different data type filter instance structures    
+ * 
    
+ *     arm_biquad_casd_df1_inst_f32 S1 = {numStages, pState, pCoeffs};    
+ *     arm_biquad_casd_df1_inst_q15 S2 = {numStages, pState, pCoeffs, postShift};    
+ *     arm_biquad_casd_df1_inst_q31 S3 = {numStages, pState, pCoeffs, postShift};    
+ * 
    
+ * where numStages is the number of Biquad stages in the filter; pState is the address of the state buffer;    
+ * pCoeffs is the address of the coefficient buffer; postShift shift to be applied.    
+ *    
+ * \par Fixed-Point Behavior    
+ * Care must be taken when using the Q15 and Q31 versions of the Biquad Cascade filter functions.    
+ * Following issues must be considered:    
+ * - Scaling of coefficients    
+ * - Filter gain    
+ * - Overflow and saturation    
+ *    
+ * \par    
+ * Scaling of coefficients:     
+ * Filter coefficients are represented as fractional values and    
+ * coefficients are restricted to lie in the range [-1 +1).    
+ * The fixed-point functions have an additional scaling parameter postShift    
+ * which allow the filter coefficients to exceed the range [+1 -1).    
+ * At the output of the filter's accumulator is a shift register which shifts the result by postShift bits.    
+ * \image html BiquadPostshift.gif "Fixed-point Biquad with shift by postShift bits after accumulator"    
+ * This essentially scales the filter coefficients by 2^postShift.    
+ * For example, to realize the coefficients    
+ * 
    
+ *    {1.5, -0.8, 1.2, 1.6, -0.9}    
+ * 
    
+ * set the pCoeffs array to:    
+ * 
    
+ *    {0.75, -0.4, 0.6, 0.8, -0.45}    
+ * 
    
+ * and set postShift=1    
+ *    
+ * \par    
+ * Filter gain:     
+ * The frequency response of a Biquad filter is a function of its coefficients.    
+ * It is possible for the gain through the filter to exceed 1.0 meaning that the filter increases the amplitude of certain frequencies.    
+ * This means that an input signal with amplitude < 1.0 may result in an output > 1.0 and these are saturated or overflowed based on the implementation of the filter.    
+ * To avoid this behavior the filter needs to be scaled down such that its peak gain < 1.0 or the input signal must be scaled down so that the combination of input and filter are never overflowed.    
+ *    
+ * \par    
+ * Overflow and saturation:     
+ * For Q15 and Q31 versions, it is described separately as part of the function specific documentation below.    
+ */
+
+/**    
+ * @addtogroup BiquadCascadeDF1    
+ * @{    
+ */
+
+/**    
+ * @param[in]  *S         points to an instance of the floating-point Biquad cascade structure.    
+ * @param[in]  *pSrc      points to the block of input data.    
+ * @param[out] *pDst      points to the block of output data.    
+ * @param[in]  blockSize  number of samples to process per call.    
+ * @return     none.    
+ *    
+ */
+
+void arm_biquad_cascade_df1_f32(
+  const arm_biquad_casd_df1_inst_f32 * S,
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize)
+{
+  float32_t *pIn = pSrc;                         /*  source pointer            */
+  float32_t *pOut = pDst;                        /*  destination pointer       */
+  float32_t *pState = S->pState;                 /*  pState pointer            */
+  float32_t *pCoeffs = S->pCoeffs;               /*  coefficient pointer       */
+  float32_t acc;                                 /*  Simulates the accumulator */
+  float32_t b0, b1, b2, a1, a2;                  /*  Filter coefficients       */
+  float32_t Xn1, Xn2, Yn1, Yn2;                  /*  Filter pState variables   */
+  float32_t Xn;                                  /*  temporary input           */
+  uint32_t sample, stage = S->numStages;         /*  loop counters             */
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  do
+  {
+    /* Reading the coefficients */
+    b0 = *pCoeffs++;
+    b1 = *pCoeffs++;
+    b2 = *pCoeffs++;
+    a1 = *pCoeffs++;
+    a2 = *pCoeffs++;
+
+    /* Reading the pState values */
+    Xn1 = pState[0];
+    Xn2 = pState[1];
+    Yn1 = pState[2];
+    Yn2 = pState[3];
+
+    /* Apply loop unrolling and compute 4 output values simultaneously. */
+    /*      The variable acc hold output values that are being computed:    
+     *    
+     *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]    
+     *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]    
+     *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]    
+     *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]    
+     */
+
+    sample = blockSize >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+     ** a second loop below computes the remaining 1 to 3 samples. */
+    while(sample > 0u)
+    {
+      /* Read the first input */
+      Xn = *pIn++;
+
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+      Yn2 = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2);
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = Yn2;
+
+      /* Every time after the output is computed state should be updated. */
+      /* The states should be updated as:  */
+      /* Xn2 = Xn1    */
+      /* Xn1 = Xn     */
+      /* Yn2 = Yn1    */
+      /* Yn1 = acc   */
+
+      /* Read the second input */
+      Xn2 = *pIn++;
+
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+      Yn1 = (b0 * Xn2) + (b1 * Xn) + (b2 * Xn1) + (a1 * Yn2) + (a2 * Yn1);
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = Yn1;
+
+      /* Every time after the output is computed state should be updated. */
+      /* The states should be updated as:  */
+      /* Xn2 = Xn1    */
+      /* Xn1 = Xn     */
+      /* Yn2 = Yn1    */
+      /* Yn1 = acc   */
+
+      /* Read the third input */
+      Xn1 = *pIn++;
+
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+      Yn2 = (b0 * Xn1) + (b1 * Xn2) + (b2 * Xn) + (a1 * Yn1) + (a2 * Yn2);
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = Yn2;
+
+      /* Every time after the output is computed state should be updated. */
+      /* The states should be updated as: */
+      /* Xn2 = Xn1    */
+      /* Xn1 = Xn     */
+      /* Yn2 = Yn1    */
+      /* Yn1 = acc   */
+
+      /* Read the forth input */
+      Xn = *pIn++;
+
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+      Yn1 = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn2) + (a2 * Yn1);
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = Yn1;
+
+      /* Every time after the output is computed state should be updated. */
+      /* The states should be updated as:  */
+      /* Xn2 = Xn1    */
+      /* Xn1 = Xn     */
+      /* Yn2 = Yn1    */
+      /* Yn1 = acc   */
+      Xn2 = Xn1;
+      Xn1 = Xn;
+
+      /* decrement the loop counter */
+      sample--;
+
+    }
+
+    /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+     ** No loop unrolling is used. */
+    sample = blockSize & 0x3u;
+
+    while(sample > 0u)
+    {
+      /* Read the input */
+      Xn = *pIn++;
+
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+      acc = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2);
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = acc;
+
+      /* Every time after the output is computed state should be updated. */
+      /* The states should be updated as:    */
+      /* Xn2 = Xn1    */
+      /* Xn1 = Xn     */
+      /* Yn2 = Yn1    */
+      /* Yn1 = acc   */
+      Xn2 = Xn1;
+      Xn1 = Xn;
+      Yn2 = Yn1;
+      Yn1 = acc;
+
+      /* decrement the loop counter */
+      sample--;
+
+    }
+
+    /*  Store the updated state variables back into the pState array */
+    *pState++ = Xn1;
+    *pState++ = Xn2;
+    *pState++ = Yn1;
+    *pState++ = Yn2;
+
+    /*  The first stage goes from the input buffer to the output buffer. */
+    /*  Subsequent numStages  occur in-place in the output buffer */
+    pIn = pDst;
+
+    /* Reset the output pointer */
+    pOut = pDst;
+
+    /* decrement the loop counter */
+    stage--;
+
+  } while(stage > 0u);
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  do
+  {
+    /* Reading the coefficients */
+    b0 = *pCoeffs++;
+    b1 = *pCoeffs++;
+    b2 = *pCoeffs++;
+    a1 = *pCoeffs++;
+    a2 = *pCoeffs++;
+
+    /* Reading the pState values */
+    Xn1 = pState[0];
+    Xn2 = pState[1];
+    Yn1 = pState[2];
+    Yn2 = pState[3];
+
+    /*      The variables acc holds the output value that is computed:        
+     *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]        
+     */
+
+    sample = blockSize;
+
+    while(sample > 0u)
+    {
+      /* Read the input */
+      Xn = *pIn++;
+
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+      acc = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2);
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = acc;
+
+      /* Every time after the output is computed state should be updated. */
+      /* The states should be updated as:    */
+      /* Xn2 = Xn1    */
+      /* Xn1 = Xn     */
+      /* Yn2 = Yn1    */
+      /* Yn1 = acc   */
+      Xn2 = Xn1;
+      Xn1 = Xn;
+      Yn2 = Yn1;
+      Yn1 = acc;
+
+      /* decrement the loop counter */
+      sample--;
+    }
+
+    /*  Store the updated state variables back into the pState array */
+    *pState++ = Xn1;
+    *pState++ = Xn2;
+    *pState++ = Yn1;
+    *pState++ = Yn2;
+
+    /*  The first stage goes from the input buffer to the output buffer. */
+    /*  Subsequent numStages  occur in-place in the output buffer */
+    pIn = pDst;
+
+    /* Reset the output pointer */
+    pOut = pDst;
+
+    /* decrement the loop counter */
+    stage--;
+
+  } while(stage > 0u);
+
+#endif /*   #ifndef ARM_MATH_CM0         */
+
+}
+
+
+  /**    
+   * @} end of BiquadCascadeDF1 group    
+   */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_fast_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_fast_q15.c
new file mode 100644
index 0000000000..29afffa03c
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_fast_q15.c
@@ -0,0 +1,283 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_biquad_cascade_df1_fast_q15.c    
+*    
+* Description:	Fast processing function for the    
+*				Q15 Biquad cascade filter.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.9  2010/08/16     
+*    Initial version    
+*    
+*    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup BiquadCascadeDF1    
+ * @{    
+ */
+
+/**    
+ * @details    
+ * @param[in]  *S points to an instance of the Q15 Biquad cascade structure.    
+ * @param[in]  *pSrc points to the block of input data.    
+ * @param[out] *pDst points to the block of output data.    
+ * @param[in]  blockSize number of samples to process per call.    
+ * @return none.    
+ *    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * This fast version uses a 32-bit accumulator with 2.30 format.    
+ * The accumulator maintains full precision of the intermediate multiplication results but provides only a single guard bit.    
+ * Thus, if the accumulator result overflows it wraps around and distorts the result.    
+ * In order to avoid overflows completely the input signal must be scaled down by two bits and lie in the range [-0.25 +0.25).    
+ * The 2.30 accumulator is then shifted by postShift bits and the result truncated to 1.15 format by discarding the low 16 bits.    
+ *    
+ * \par    
+ * Refer to the function arm_biquad_cascade_df1_q15() for a slower implementation of this function which uses 64-bit accumulation to avoid wrap around distortion.  Both the slow and the fast versions use the same instance structure.    
+ * Use the function arm_biquad_cascade_df1_init_q15() to initialize the filter structure.    
+ *    
+ */
+
+void arm_biquad_cascade_df1_fast_q15(
+  const arm_biquad_casd_df1_inst_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+  q15_t *pIn = pSrc;                             /*  Source pointer                               */
+  q15_t *pOut = pDst;                            /*  Destination pointer                          */
+  q31_t in;                                      /*  Temporary variable to hold input value       */
+  q31_t out;                                     /*  Temporary variable to hold output value      */
+  q31_t b0;                                      /*  Temporary variable to hold bo value          */
+  q31_t b1, a1;                                  /*  Filter coefficients                          */
+  q31_t state_in, state_out;                     /*  Filter state variables                       */
+  q31_t acc;                                     /*  Accumulator                                  */
+  int32_t shift = (int32_t) (15 - S->postShift); /*  Post shift                                   */
+  q15_t *pState = S->pState;                     /*  State pointer                                */
+  q15_t *pCoeffs = S->pCoeffs;                   /*  Coefficient pointer                          */
+  uint32_t sample, stage = S->numStages;         /*  Stage loop counter                           */
+
+
+
+  do
+  {
+
+    /* Read the b0 and 0 coefficients using SIMD  */
+    b0 = *__SIMD32(pCoeffs)++;
+
+    /* Read the b1 and b2 coefficients using SIMD */
+    b1 = *__SIMD32(pCoeffs)++;
+
+    /* Read the a1 and a2 coefficients using SIMD */
+    a1 = *__SIMD32(pCoeffs)++;
+
+    /* Read the input state values from the state buffer:  x[n-1], x[n-2] */
+    state_in = *__SIMD32(pState)++;
+
+    /* Read the output state values from the state buffer:  y[n-1], y[n-2] */
+    state_out = *__SIMD32(pState)--;
+
+    /* Apply loop unrolling and compute 2 output values simultaneously. */
+    /*      The variable acc hold output values that are being computed:       
+     *    
+     *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]       
+     *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]       
+     */
+    sample = blockSize >> 1u;
+
+    /* First part of the processing with loop unrolling.  Compute 2 outputs at a time.    
+     ** a second loop below computes the remaining 1 sample. */
+    while(sample > 0u)
+    {
+
+      /* Read the input */
+      in = *__SIMD32(pIn)++;
+
+      /* out =  b0 * x[n] + 0 * 0 */
+      out = __SMUAD(b0, in);
+      /* acc =  b1 * x[n-1] + acc +=  b2 * x[n-2] + out */
+      acc = __SMLAD(b1, state_in, out);
+      /* acc +=  a1 * y[n-1] + acc +=  a2 * y[n-2] */
+      acc = __SMLAD(a1, state_out, acc);
+
+      /* The result is converted from 3.29 to 1.31 and then saturation is applied */
+      out = __SSAT((acc >> shift), 16);
+
+      /* Every time after the output is computed state should be updated. */
+      /* The states should be updated as:  */
+      /* Xn2 = Xn1    */
+      /* Xn1 = Xn     */
+      /* Yn2 = Yn1    */
+      /* Yn1 = acc   */
+      /* x[n-N], x[n-N-1] are packed together to make state_in of type q31 */
+      /* y[n-N], y[n-N-1] are packed together to make state_out of type q31 */
+
+#ifndef  ARM_MATH_BIG_ENDIAN
+
+      state_in = __PKHBT(in, state_in, 16);
+      state_out = __PKHBT(out, state_out, 16);
+
+#else
+
+      state_in = __PKHBT(state_in >> 16, (in >> 16), 16);
+      state_out = __PKHBT(state_out >> 16, (out), 16);
+
+#endif /*      #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+      /* out =  b0 * x[n] + 0 * 0 */
+      out = __SMUADX(b0, in);
+      /* acc0 =  b1 * x[n-1] , acc0 +=  b2 * x[n-2] + out */
+      acc = __SMLAD(b1, state_in, out);
+      /* acc +=  a1 * y[n-1] + acc +=  a2 * y[n-2] */
+      acc = __SMLAD(a1, state_out, acc);
+
+      /* The result is converted from 3.29 to 1.31 and then saturation is applied */
+      out = __SSAT((acc >> shift), 16);
+
+
+      /* Store the output in the destination buffer. */
+
+#ifndef  ARM_MATH_BIG_ENDIAN
+
+      *__SIMD32(pOut)++ = __PKHBT(state_out, out, 16);
+
+#else
+
+      *__SIMD32(pOut)++ = __PKHBT(out, state_out >> 16, 16);
+
+#endif /*      #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+      /* Every time after the output is computed state should be updated. */
+      /* The states should be updated as:  */
+      /* Xn2 = Xn1    */
+      /* Xn1 = Xn     */
+      /* Yn2 = Yn1    */
+      /* Yn1 = acc   */
+      /* x[n-N], x[n-N-1] are packed together to make state_in of type q31 */
+      /* y[n-N], y[n-N-1] are packed together to make state_out of type q31 */
+
+#ifndef  ARM_MATH_BIG_ENDIAN
+
+      state_in = __PKHBT(in >> 16, state_in, 16);
+      state_out = __PKHBT(out, state_out, 16);
+
+#else
+
+      state_in = __PKHBT(state_in >> 16, in, 16);
+      state_out = __PKHBT(state_out >> 16, out, 16);
+
+#endif /*      #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+
+      /* Decrement the loop counter */
+      sample--;
+
+    }
+
+    /* If the blockSize is not a multiple of 2, compute any remaining output samples here.    
+     ** No loop unrolling is used. */
+
+    if((blockSize & 0x1u) != 0u)
+    {
+      /* Read the input */
+      in = *pIn++;
+
+      /* out =  b0 * x[n] + 0 * 0 */
+
+#ifndef  ARM_MATH_BIG_ENDIAN
+
+      out = __SMUAD(b0, in);
+
+#else
+
+      out = __SMUADX(b0, in);
+
+#endif /*      #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+      /* acc =  b1 * x[n-1], acc +=  b2 * x[n-2] + out */
+      acc = __SMLAD(b1, state_in, out);
+      /* acc +=  a1 * y[n-1] + acc +=  a2 * y[n-2] */
+      acc = __SMLAD(a1, state_out, acc);
+
+      /* The result is converted from 3.29 to 1.31 and then saturation is applied */
+      out = __SSAT((acc >> shift), 16);
+
+      /* Store the output in the destination buffer. */
+      *pOut++ = (q15_t) out;
+
+      /* Every time after the output is computed state should be updated. */
+      /* The states should be updated as:  */
+      /* Xn2 = Xn1    */
+      /* Xn1 = Xn     */
+      /* Yn2 = Yn1    */
+      /* Yn1 = acc   */
+      /* x[n-N], x[n-N-1] are packed together to make state_in of type q31 */
+      /* y[n-N], y[n-N-1] are packed together to make state_out of type q31 */
+
+#ifndef  ARM_MATH_BIG_ENDIAN
+
+      state_in = __PKHBT(in, state_in, 16);
+      state_out = __PKHBT(out, state_out, 16);
+
+#else
+
+      state_in = __PKHBT(state_in >> 16, in, 16);
+      state_out = __PKHBT(state_out >> 16, out, 16);
+
+#endif /*   #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+    }
+
+    /*  The first stage goes from the input buffer to the output buffer.  */
+    /*  Subsequent (numStages - 1) occur in-place in the output buffer  */
+    pIn = pDst;
+
+    /* Reset the output pointer */
+    pOut = pDst;
+
+    /*  Store the updated state variables back into the state array */
+    *__SIMD32(pState)++ = state_in;
+    *__SIMD32(pState)++ = state_out;
+
+
+    /* Decrement the loop counter */
+    stage--;
+
+  } while(stage > 0u);
+}
+
+
+/**    
+ * @} end of BiquadCascadeDF1 group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_fast_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_fast_q31.c
new file mode 100644
index 0000000000..0a479fe6b8
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_fast_q31.c
@@ -0,0 +1,275 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_biquad_cascade_df1_fast_q31.c    
+*    
+* Description:	Processing function for the    
+*				Q31 Fast Biquad cascade DirectFormI(DF1) filter.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.9  2010/08/27     
+*    Initial version    
+*    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup BiquadCascadeDF1    
+ * @{    
+ */
+
+/**    
+ * @details    
+ *    
+ * @param[in]  *S        points to an instance of the Q31 Biquad cascade structure.    
+ * @param[in]  *pSrc     points to the block of input data.    
+ * @param[out] *pDst     points to the block of output data.    
+ * @param[in]  blockSize number of samples to process per call.    
+ * @return 	   none.    
+ *    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * This function is optimized for speed at the expense of fixed-point precision and overflow protection.    
+ * The result of each 1.31 x 1.31 multiplication is truncated to 2.30 format.    
+ * These intermediate results are added to a 2.30 accumulator.    
+ * Finally, the accumulator is saturated and converted to a 1.31 result.    
+ * The fast version has the same overflow behavior as the standard version and provides less precision since it discards the low 32 bits of each multiplication result.    
+ * In order to avoid overflows completely the input signal must be scaled down by two bits and lie in the range [-0.25 +0.25). Use the intialization function    
+ * arm_biquad_cascade_df1_init_q31() to initialize filter structure.    
+ *    
+ * \par    
+ * Refer to the function arm_biquad_cascade_df1_q31() for a slower implementation of this function which uses 64-bit accumulation to provide higher precision.  Both the slow and the fast versions use the same instance structure.    
+ * Use the function arm_biquad_cascade_df1_init_q31() to initialize the filter structure.    
+ */
+
+void arm_biquad_cascade_df1_fast_q31(
+  const arm_biquad_casd_df1_inst_q31 * S,
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize)
+{
+  q31_t acc;                                     /*  accumulator                   */
+  q31_t Xn1, Xn2, Yn1, Yn2;                      /*  Filter state variables        */
+  q31_t b0, b1, b2, a1, a2;                      /*  Filter coefficients           */
+  q31_t *pIn = pSrc;                             /*  input pointer initialization  */
+  q31_t *pOut = pDst;                            /*  output pointer initialization */
+  q31_t *pState = S->pState;                     /*  pState pointer initialization */
+  q31_t *pCoeffs = S->pCoeffs;                   /*  coeff pointer initialization  */
+  q31_t Xn;                                      /*  temporary input               */
+  int32_t shift = (int32_t) S->postShift + 1;    /*  Shift to be applied to the output */
+  uint32_t sample, stage = S->numStages;         /*  loop counters                     */
+
+
+  do
+  {
+    /* Reading the coefficients */
+    b0 = *pCoeffs++;
+    b1 = *pCoeffs++;
+    b2 = *pCoeffs++;
+    a1 = *pCoeffs++;
+    a2 = *pCoeffs++;
+
+    /* Reading the state values */
+    Xn1 = pState[0];
+    Xn2 = pState[1];
+    Yn1 = pState[2];
+    Yn2 = pState[3];
+
+    /* Apply loop unrolling and compute 4 output values simultaneously. */
+    /*      The variables acc ... acc3 hold output values that are being computed:       
+     *       
+     *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]       
+     */
+
+    sample = blockSize >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.       
+     ** a second loop below computes the remaining 1 to 3 samples. */
+    while(sample > 0u)
+    {
+      /* Read the input */
+      Xn = *pIn;
+
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+      /* acc =  b0 * x[n] */
+      acc = (q31_t) (((q63_t) b1 * Xn1) >> 32);
+      /* acc +=  b1 * x[n-1] */
+      acc = (q31_t) ((((q63_t) acc << 32) + ((q63_t) b0 * (Xn))) >> 32);
+      /* acc +=  b[2] * x[n-2] */
+      acc = (q31_t) ((((q63_t) acc << 32) + ((q63_t) b2 * (Xn2))) >> 32);
+      /* acc +=  a1 * y[n-1] */
+      acc = (q31_t) ((((q63_t) acc << 32) + ((q63_t) a1 * (Yn1))) >> 32);
+      /* acc +=  a2 * y[n-2] */
+      acc = (q31_t) ((((q63_t) acc << 32) + ((q63_t) a2 * (Yn2))) >> 32);
+
+      /* The result is converted to 1.31 , Yn2 variable is reused */
+      Yn2 = acc << shift;
+
+      /* Read the second input */
+      Xn2 = *(pIn + 1u);
+
+      /* Store the output in the destination buffer. */
+      *pOut = Yn2;
+
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+      /* acc =  b0 * x[n] */
+      acc = (q31_t) (((q63_t) b0 * (Xn2)) >> 32);
+      /* acc +=  b1 * x[n-1] */
+      acc = (q31_t) ((((q63_t) acc << 32) + ((q63_t) b1 * (Xn))) >> 32);
+      /* acc +=  b[2] * x[n-2] */
+      acc = (q31_t) ((((q63_t) acc << 32) + ((q63_t) b2 * (Xn1))) >> 32);
+      /* acc +=  a1 * y[n-1] */
+      acc = (q31_t) ((((q63_t) acc << 32) + ((q63_t) a1 * (Yn2))) >> 32);
+      /* acc +=  a2 * y[n-2] */
+      acc = (q31_t) ((((q63_t) acc << 32) + ((q63_t) a2 * (Yn1))) >> 32);
+
+      /* The result is converted to 1.31, Yn1 variable is reused  */
+      Yn1 = acc << shift;
+
+      /* Read the third input  */
+      Xn1 = *(pIn + 2u);
+
+      /* Store the output in the destination buffer. */
+      *(pOut + 1u) = Yn1;
+
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+      /* acc =  b0 * x[n] */
+      acc = (q31_t) (((q63_t) b0 * (Xn1)) >> 32);
+      /* acc +=  b1 * x[n-1] */
+      acc = (q31_t) ((((q63_t) acc << 32) + ((q63_t) b1 * (Xn2))) >> 32);
+      /* acc +=  b[2] * x[n-2] */
+      acc = (q31_t) ((((q63_t) acc << 32) + ((q63_t) b2 * (Xn))) >> 32);
+      /* acc +=  a1 * y[n-1] */
+      acc = (q31_t) ((((q63_t) acc << 32) + ((q63_t) a1 * (Yn1))) >> 32);
+      /* acc +=  a2 * y[n-2] */
+      acc = (q31_t) ((((q63_t) acc << 32) + ((q63_t) a2 * (Yn2))) >> 32);
+
+      /* The result is converted to 1.31, Yn2 variable is reused  */
+      Yn2 = acc << shift;
+
+      /* Read the forth input */
+      Xn = *(pIn + 3u);
+
+      /* Store the output in the destination buffer. */
+      *(pOut + 2u) = Yn2;
+      pIn += 4u;
+
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+      /* acc =  b0 * x[n] */
+      acc = (q31_t) (((q63_t) b0 * (Xn)) >> 32);
+      /* acc +=  b1 * x[n-1] */
+      acc = (q31_t) ((((q63_t) acc << 32) + ((q63_t) b1 * (Xn1))) >> 32);
+      /* acc +=  b[2] * x[n-2] */
+      acc = (q31_t) ((((q63_t) acc << 32) + ((q63_t) b2 * (Xn2))) >> 32);
+      /* acc +=  a1 * y[n-1] */
+      acc = (q31_t) ((((q63_t) acc << 32) + ((q63_t) a1 * (Yn2))) >> 32);
+      /* acc +=  a2 * y[n-2] */
+      acc = (q31_t) ((((q63_t) acc << 32) + ((q63_t) a2 * (Yn1))) >> 32);
+
+      /* Every time after the output is computed state should be updated. */
+      /* The states should be updated as:  */
+      /* Xn2 = Xn1    */
+      Xn2 = Xn1;
+
+      /* The result is converted to 1.31, Yn1 variable is reused  */
+      Yn1 = acc << shift;
+
+      /* Xn1 = Xn     */
+      Xn1 = Xn;
+
+      /* Store the output in the destination buffer. */
+      *(pOut + 3u) = Yn1;
+      pOut += 4u;
+
+      /* decrement the loop counter */
+      sample--;
+    }
+
+    /* If the blockSize is not a multiple of 4, compute any remaining output samples here.       
+     ** No loop unrolling is used. */
+    sample = (blockSize & 0x3u);
+
+    while(sample > 0u)
+    {
+      /* Read the input */
+      Xn = *pIn++;
+
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+      /* acc =  b0 * x[n] */
+      acc = (q31_t) (((q63_t) b0 * (Xn)) >> 32);
+      /* acc +=  b1 * x[n-1] */
+      acc = (q31_t) ((((q63_t) acc << 32) + ((q63_t) b1 * (Xn1))) >> 32);
+      /* acc +=  b[2] * x[n-2] */
+      acc = (q31_t) ((((q63_t) acc << 32) + ((q63_t) b2 * (Xn2))) >> 32);
+      /* acc +=  a1 * y[n-1] */
+      acc = (q31_t) ((((q63_t) acc << 32) + ((q63_t) a1 * (Yn1))) >> 32);
+      /* acc +=  a2 * y[n-2] */
+      acc = (q31_t) ((((q63_t) acc << 32) + ((q63_t) a2 * (Yn2))) >> 32);
+      /* The result is converted to 1.31  */
+      acc = acc << shift;
+
+      /* Every time after the output is computed state should be updated. */
+      /* The states should be updated as:  */
+      /* Xn2 = Xn1    */
+      /* Xn1 = Xn     */
+      /* Yn2 = Yn1    */
+      /* Yn1 = acc    */
+      Xn2 = Xn1;
+      Xn1 = Xn;
+      Yn2 = Yn1;
+      Yn1 = acc;
+
+      /* Store the output in the destination buffer. */
+      *pOut++ = acc;
+
+      /* decrement the loop counter */
+      sample--;
+    }
+
+    /*  The first stage goes from the input buffer to the output buffer. */
+    /*  Subsequent stages occur in-place in the output buffer */
+    pIn = pDst;
+
+    /* Reset to destination pointer */
+    pOut = pDst;
+
+    /*  Store the updated state variables back into the pState array */
+    *pState++ = Xn1;
+    *pState++ = Xn2;
+    *pState++ = Yn1;
+    *pState++ = Yn2;
+
+  } while(--stage);
+}
+
+/**    
+  * @} end of BiquadCascadeDF1 group    
+  */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_init_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_init_f32.c
new file mode 100644
index 0000000000..d50b69f3c1
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_init_f32.c
@@ -0,0 +1,107 @@
+/*-----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_biquad_cascade_df1_init_f32.c    
+*    
+* Description:  floating-point Biquad cascade DirectFormI(DF1) filter initialization function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+* 	 incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* ---------------------------------------------------------------------------*/
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup BiquadCascadeDF1    
+ * @{    
+ */
+
+/**    
+ * @details    
+ * @brief  Initialization function for the floating-point Biquad cascade filter.    
+ * @param[in,out] *S           points to an instance of the floating-point Biquad cascade structure.    
+ * @param[in]     numStages    number of 2nd order stages in the filter.    
+ * @param[in]     *pCoeffs     points to the filter coefficients array.    
+ * @param[in]     *pState      points to the state array.    
+ * @return        none    
+ *    
+ *    
+ * Coefficient and State Ordering:    
+ *    
+ * \par    
+ * The coefficients are stored in the array pCoeffs in the following order:    
+ * 
    
+ *     {b10, b11, b12, a11, a12, b20, b21, b22, a21, a22, ...}    
+ * 
    
+ *    
+ * \par    
+ * where b1x and a1x are the coefficients for the first stage,    
+ * b2x and a2x are the coefficients for the second stage,    
+ * and so on.  The pCoeffs array contains a total of 5*numStages values.    
+ *    
+ * \par    
+ * The pState is a pointer to state array.    
+ * Each Biquad stage has 4 state variables x[n-1], x[n-2], y[n-1], and y[n-2].    
+ * The state variables are arranged in the pState array as:    
+ * 
    
+ *     {x[n-1], x[n-2], y[n-1], y[n-2]}    
+ * 
    
+ * The 4 state variables for stage 1 are first, then the 4 state variables for stage 2, and so on.    
+ * The state array has a total length of 4*numStages values.    
+ * The state variables are updated after each block of data is processed; the coefficients are untouched.    
+ *    
+ */
+
+void arm_biquad_cascade_df1_init_f32(
+  arm_biquad_casd_df1_inst_f32 * S,
+  uint8_t numStages,
+  float32_t * pCoeffs,
+  float32_t * pState)
+{
+  /* Assign filter stages */
+  S->numStages = numStages;
+
+  /* Assign coefficient pointer */
+  S->pCoeffs = pCoeffs;
+
+  /* Clear state buffer and size is always 4 * numStages */
+  memset(pState, 0, (4u * (uint32_t) numStages) * sizeof(float32_t));
+
+  /* Assign state pointer */
+  S->pState = pState;
+}
+
+/**    
+ * @} end of BiquadCascadeDF1 group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_init_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_init_q15.c
new file mode 100644
index 0000000000..d5fda28ac5
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_init_q15.c
@@ -0,0 +1,109 @@
+/*-----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_biquad_cascade_df1_init_q15.c    
+*    
+* Description:  Q15 Biquad cascade DirectFormI(DF1) filter initialization function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+* 	 incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* ---------------------------------------------------------------------------*/
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup BiquadCascadeDF1    
+ * @{    
+ */
+
+/**    
+ * @details    
+ *    
+ * @param[in,out] *S           points to an instance of the Q15 Biquad cascade structure.    
+ * @param[in]     numStages    number of 2nd order stages in the filter.    
+ * @param[in]     *pCoeffs     points to the filter coefficients.    
+ * @param[in]     *pState      points to the state buffer.    
+ * @param[in]     postShift    Shift to be applied to the accumulator result. Varies according to the coefficients format    
+ * @return        none    
+ *    
+ * Coefficient and State Ordering:    
+ *    
+ * \par    
+ * The coefficients are stored in the array pCoeffs in the following order:    
+ * 
    
+ *     {b10, 0, b11, b12, a11, a12, b20, 0, b21, b22, a21, a22, ...}    
+ * 
    
+ * where b1x and a1x are the coefficients for the first stage,    
+ * b2x and a2x are the coefficients for the second stage,    
+ * and so on.  The pCoeffs array contains a total of 6*numStages values.    
+ * The zero coefficient between b1 and b2 facilities  use of 16-bit SIMD instructions on the Cortex-M4.    
+ *    
+ * \par    
+ * The state variables are stored in the array pState.    
+ * Each Biquad stage has 4 state variables x[n-1], x[n-2], y[n-1], and y[n-2].    
+ * The state variables are arranged in the pState array as:    
+ * 
    
+ *     {x[n-1], x[n-2], y[n-1], y[n-2]}    
+ * 
    
+ * The 4 state variables for stage 1 are first, then the 4 state variables for stage 2, and so on.    
+ * The state array has a total length of 4*numStages values.    
+ * The state variables are updated after each block of data is processed; the coefficients are untouched.    
+ */
+
+void arm_biquad_cascade_df1_init_q15(
+  arm_biquad_casd_df1_inst_q15 * S,
+  uint8_t numStages,
+  q15_t * pCoeffs,
+  q15_t * pState,
+  int8_t postShift)
+{
+  /* Assign filter stages */
+  S->numStages = numStages;
+
+  /* Assign postShift to be applied to the output */
+  S->postShift = postShift;
+
+  /* Assign coefficient pointer */
+  S->pCoeffs = pCoeffs;
+
+  /* Clear state buffer and size is always 4 * numStages */
+  memset(pState, 0, (4u * (uint32_t) numStages) * sizeof(q15_t));
+
+  /* Assign state pointer */
+  S->pState = pState;
+}
+
+/**    
+ * @} end of BiquadCascadeDF1 group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_init_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_init_q31.c
new file mode 100644
index 0000000000..dbbb8aa2b5
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_init_q31.c
@@ -0,0 +1,109 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_biquad_cascade_df1_init_q31.c    
+*    
+* Description:	Q31 Biquad cascade DirectFormI(DF1) filter initialization function.    
+*    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+* 	 incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup BiquadCascadeDF1    
+ * @{    
+ */
+
+/**    
+ * @details    
+ *    
+ * @param[in,out] *S           points to an instance of the Q31 Biquad cascade structure.    
+ * @param[in]     numStages    number of 2nd order stages in the filter.    
+ * @param[in]     *pCoeffs     points to the filter coefficients buffer.    
+ * @param[in]     *pState      points to the state buffer.    
+ * @param[in]     postShift    Shift to be applied after the accumulator.  Varies according to the coefficients format    
+ * @return        none    
+ *    
+ * Coefficient and State Ordering:    
+ *    
+ * \par    
+ * The coefficients are stored in the array pCoeffs in the following order:    
+ * 
    
+ *     {b10, b11, b12, a11, a12, b20, b21, b22, a21, a22, ...}    
+ * 
    
+ * where b1x and a1x are the coefficients for the first stage,    
+ * b2x and a2x are the coefficients for the second stage,    
+ * and so on.  The pCoeffs array contains a total of 5*numStages values.    
+ *    
+ * \par    
+ * The pState points to state variables array.    
+ * Each Biquad stage has 4 state variables x[n-1], x[n-2], y[n-1], and y[n-2].    
+ * The state variables are arranged in the pState array as:    
+ * 
    
+ *     {x[n-1], x[n-2], y[n-1], y[n-2]}    
+ * 
    
+ * The 4 state variables for stage 1 are first, then the 4 state variables for stage 2, and so on.    
+ * The state array has a total length of 4*numStages values.    
+ * The state variables are updated after each block of data is processed; the coefficients are untouched.    
+ */
+
+void arm_biquad_cascade_df1_init_q31(
+  arm_biquad_casd_df1_inst_q31 * S,
+  uint8_t numStages,
+  q31_t * pCoeffs,
+  q31_t * pState,
+  int8_t postShift)
+{
+  /* Assign filter stages */
+  S->numStages = numStages;
+
+  /* Assign postShift to be applied to the output */
+  S->postShift = postShift;
+
+  /* Assign coefficient pointer */
+  S->pCoeffs = pCoeffs;
+
+  /* Clear state buffer and size is always 4 * numStages */
+  memset(pState, 0, (4u * (uint32_t) numStages) * sizeof(q31_t));
+
+  /* Assign state pointer */
+  S->pState = pState;
+}
+
+/**    
+ * @} end of BiquadCascadeDF1 group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_q15.c
new file mode 100644
index 0000000000..484cd85e89
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_q15.c
@@ -0,0 +1,408 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_biquad_cascade_df1_q15.c    
+*    
+* Description:	Processing function for the    
+*				Q15 Biquad cascade DirectFormI(DF1) filter.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+* 	 incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup BiquadCascadeDF1    
+ * @{    
+ */
+
+/**    
+ * @brief Processing function for the Q15 Biquad cascade filter.    
+ * @param[in]  *S points to an instance of the Q15 Biquad cascade structure.    
+ * @param[in]  *pSrc points to the block of input data.    
+ * @param[out] *pDst points to the location where the output result is written.    
+ * @param[in]  blockSize number of samples to process per call.    
+ * @return none.    
+ *    
+ *    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function is implemented using a 64-bit internal accumulator.    
+ * Both coefficients and state variables are represented in 1.15 format and multiplications yield a 2.30 result.    
+ * The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format.    
+ * There is no risk of internal overflow with this approach and the full precision of intermediate multiplications is preserved.    
+ * The accumulator is then shifted by postShift bits to truncate the result to 1.15 format by discarding the low 16 bits.    
+ * Finally, the result is saturated to 1.15 format.    
+ *    
+ * \par    
+ * Refer to the function arm_biquad_cascade_df1_fast_q15() for a faster but less precise implementation of this filter for Cortex-M3 and Cortex-M4.    
+ */
+
+void arm_biquad_cascade_df1_q15(
+  const arm_biquad_casd_df1_inst_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q15_t *pIn = pSrc;                             /*  Source pointer                               */
+  q15_t *pOut = pDst;                            /*  Destination pointer                          */
+  q31_t in;                                      /*  Temporary variable to hold input value       */
+  q31_t out;                                     /*  Temporary variable to hold output value      */
+  q31_t b0;                                      /*  Temporary variable to hold bo value          */
+  q31_t b1, a1;                                  /*  Filter coefficients                          */
+  q31_t state_in, state_out;                     /*  Filter state variables                       */
+  q31_t acc_l, acc_h;
+  q63_t acc;                                     /*  Accumulator                                  */
+  int32_t lShift = (15 - (int32_t) S->postShift);       /*  Post shift                                   */
+  q15_t *pState = S->pState;                     /*  State pointer                                */
+  q15_t *pCoeffs = S->pCoeffs;                   /*  Coefficient pointer                          */
+  uint32_t sample, stage = (uint32_t) S->numStages;     /*  Stage loop counter                           */
+  int32_t uShift = (32 - lShift);
+
+  do
+  {
+    /* Read the b0 and 0 coefficients using SIMD  */
+    b0 = *__SIMD32(pCoeffs)++;
+
+    /* Read the b1 and b2 coefficients using SIMD */
+    b1 = *__SIMD32(pCoeffs)++;
+
+    /* Read the a1 and a2 coefficients using SIMD */
+    a1 = *__SIMD32(pCoeffs)++;
+
+    /* Read the input state values from the state buffer:  x[n-1], x[n-2] */
+    state_in = *__SIMD32(pState)++;
+
+    /* Read the output state values from the state buffer:  y[n-1], y[n-2] */
+    state_out = *__SIMD32(pState)--;
+
+    /* Apply loop unrolling and compute 2 output values simultaneously. */
+    /*      The variable acc hold output values that are being computed:    
+     *    
+     *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]    
+     *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]    
+     */
+    sample = blockSize >> 1u;
+
+    /* First part of the processing with loop unrolling.  Compute 2 outputs at a time.    
+     ** a second loop below computes the remaining 1 sample. */
+    while(sample > 0u)
+    {
+
+      /* Read the input */
+      in = *__SIMD32(pIn)++;
+
+      /* out =  b0 * x[n] + 0 * 0 */
+      out = __SMUAD(b0, in);
+
+      /* acc +=  b1 * x[n-1] +  b2 * x[n-2] + out */
+      acc = __SMLALD(b1, state_in, out);
+      /* acc +=  a1 * y[n-1] +  a2 * y[n-2] */
+      acc = __SMLALD(a1, state_out, acc);
+
+      /* The result is converted from 3.29 to 1.31 if postShift = 1, and then saturation is applied */
+      /* Calc lower part of acc */
+      acc_l = acc & 0xffffffff;
+
+      /* Calc upper part of acc */
+      acc_h = (acc >> 32) & 0xffffffff;
+
+      /* Apply shift for lower part of acc and upper part of acc */
+      out = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+      out = __SSAT(out, 16);
+
+      /* Every time after the output is computed state should be updated. */
+      /* The states should be updated as:  */
+      /* Xn2 = Xn1    */
+      /* Xn1 = Xn     */
+      /* Yn2 = Yn1    */
+      /* Yn1 = acc   */
+      /* x[n-N], x[n-N-1] are packed together to make state_in of type q31 */
+      /* y[n-N], y[n-N-1] are packed together to make state_out of type q31 */
+
+#ifndef  ARM_MATH_BIG_ENDIAN
+
+      state_in = __PKHBT(in, state_in, 16);
+      state_out = __PKHBT(out, state_out, 16);
+
+#else
+
+      state_in = __PKHBT(state_in >> 16, (in >> 16), 16);
+      state_out = __PKHBT(state_out >> 16, (out), 16);
+
+#endif /*      #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+      /* out =  b0 * x[n] + 0 * 0 */
+      out = __SMUADX(b0, in);
+      /* acc +=  b1 * x[n-1] +  b2 * x[n-2] + out */
+      acc = __SMLALD(b1, state_in, out);
+      /* acc +=  a1 * y[n-1] + a2 * y[n-2] */
+      acc = __SMLALD(a1, state_out, acc);
+
+      /* The result is converted from 3.29 to 1.31 if postShift = 1, and then saturation is applied */
+      /* Calc lower part of acc */
+      acc_l = acc & 0xffffffff;
+
+      /* Calc upper part of acc */
+      acc_h = (acc >> 32) & 0xffffffff;
+
+      /* Apply shift for lower part of acc and upper part of acc */
+      out = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+      out = __SSAT(out, 16);
+
+      /* Store the output in the destination buffer. */
+
+#ifndef  ARM_MATH_BIG_ENDIAN
+
+      *__SIMD32(pOut)++ = __PKHBT(state_out, out, 16);
+
+#else
+
+      *__SIMD32(pOut)++ = __PKHBT(out, state_out >> 16, 16);
+
+#endif /*      #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+      /* Every time after the output is computed state should be updated. */
+      /* The states should be updated as:  */
+      /* Xn2 = Xn1    */
+      /* Xn1 = Xn     */
+      /* Yn2 = Yn1    */
+      /* Yn1 = acc   */
+      /* x[n-N], x[n-N-1] are packed together to make state_in of type q31 */
+      /* y[n-N], y[n-N-1] are packed together to make state_out of type q31 */
+#ifndef  ARM_MATH_BIG_ENDIAN
+
+      state_in = __PKHBT(in >> 16, state_in, 16);
+      state_out = __PKHBT(out, state_out, 16);
+
+#else
+
+      state_in = __PKHBT(state_in >> 16, in, 16);
+      state_out = __PKHBT(state_out >> 16, out, 16);
+
+#endif /*      #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+
+      /* Decrement the loop counter */
+      sample--;
+
+    }
+
+    /* If the blockSize is not a multiple of 2, compute any remaining output samples here.    
+     ** No loop unrolling is used. */
+
+    if((blockSize & 0x1u) != 0u)
+    {
+      /* Read the input */
+      in = *pIn++;
+
+      /* out =  b0 * x[n] + 0 * 0 */
+
+#ifndef  ARM_MATH_BIG_ENDIAN
+
+      out = __SMUAD(b0, in);
+
+#else
+
+      out = __SMUADX(b0, in);
+
+#endif /*      #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+      /* acc =  b1 * x[n-1] + b2 * x[n-2] + out */
+      acc = __SMLALD(b1, state_in, out);
+      /* acc +=  a1 * y[n-1] + a2 * y[n-2] */
+      acc = __SMLALD(a1, state_out, acc);
+
+      /* The result is converted from 3.29 to 1.31 if postShift = 1, and then saturation is applied */
+      /* Calc lower part of acc */
+      acc_l = acc & 0xffffffff;
+
+      /* Calc upper part of acc */
+      acc_h = (acc >> 32) & 0xffffffff;
+
+      /* Apply shift for lower part of acc and upper part of acc */
+      out = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+      out = __SSAT(out, 16);
+
+      /* Store the output in the destination buffer. */
+      *pOut++ = (q15_t) out;
+
+      /* Every time after the output is computed state should be updated. */
+      /* The states should be updated as:  */
+      /* Xn2 = Xn1    */
+      /* Xn1 = Xn     */
+      /* Yn2 = Yn1    */
+      /* Yn1 = acc   */
+      /* x[n-N], x[n-N-1] are packed together to make state_in of type q31 */
+      /* y[n-N], y[n-N-1] are packed together to make state_out of type q31 */
+
+#ifndef  ARM_MATH_BIG_ENDIAN
+
+      state_in = __PKHBT(in, state_in, 16);
+      state_out = __PKHBT(out, state_out, 16);
+
+#else
+
+      state_in = __PKHBT(state_in >> 16, in, 16);
+      state_out = __PKHBT(state_out >> 16, out, 16);
+
+#endif /*   #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+    }
+
+    /*  The first stage goes from the input wire to the output wire.  */
+    /*  Subsequent numStages occur in-place in the output wire  */
+    pIn = pDst;
+
+    /* Reset the output pointer */
+    pOut = pDst;
+
+    /*  Store the updated state variables back into the state array */
+    *__SIMD32(pState)++ = state_in;
+    *__SIMD32(pState)++ = state_out;
+
+
+    /* Decrement the loop counter */
+    stage--;
+
+  } while(stage > 0u);
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  q15_t *pIn = pSrc;                             /*  Source pointer                               */
+  q15_t *pOut = pDst;                            /*  Destination pointer                          */
+  q15_t b0, b1, b2, a1, a2;                      /*  Filter coefficients           */
+  q15_t Xn1, Xn2, Yn1, Yn2;                      /*  Filter state variables        */
+  q15_t Xn;                                      /*  temporary input               */
+  q63_t acc;                                     /*  Accumulator                                  */
+  int32_t shift = (15 - (int32_t) S->postShift); /*  Post shift                                   */
+  q15_t *pState = S->pState;                     /*  State pointer                                */
+  q15_t *pCoeffs = S->pCoeffs;                   /*  Coefficient pointer                          */
+  uint32_t sample, stage = (uint32_t) S->numStages;     /*  Stage loop counter                           */
+
+  do
+  {
+    /* Reading the coefficients */
+    b0 = *pCoeffs++;
+    b1 = *pCoeffs++;
+    b2 = *pCoeffs++;
+    a1 = *pCoeffs++;
+    a2 = *pCoeffs++;
+
+    /* Reading the state values */
+    Xn1 = pState[0];
+    Xn2 = pState[1];
+    Yn1 = pState[2];
+    Yn2 = pState[3];
+
+    /*      The variables acc holds the output value that is computed:         
+     *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]         
+     */
+
+    sample = blockSize;
+
+    while(sample > 0u)
+    {
+      /* Read the input */
+      Xn = *pIn++;
+
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+      /* acc =  b0 * x[n] */
+      acc = (q31_t) b0 *Xn;
+
+      /* acc +=  b1 * x[n-1] */
+      acc += (q31_t) b1 *Xn1;
+      /* acc +=  b[2] * x[n-2] */
+      acc += (q31_t) b2 *Xn2;
+      /* acc +=  a1 * y[n-1] */
+      acc += (q31_t) a1 *Yn1;
+      /* acc +=  a2 * y[n-2] */
+      acc += (q31_t) a2 *Yn2;
+
+      /* The result is converted to 1.31  */
+      acc = __SSAT((acc >> shift), 16);
+
+      /* Every time after the output is computed state should be updated. */
+      /* The states should be updated as:  */
+      /* Xn2 = Xn1    */
+      /* Xn1 = Xn     */
+      /* Yn2 = Yn1    */
+      /* Yn1 = acc    */
+      Xn2 = Xn1;
+      Xn1 = Xn;
+      Yn2 = Yn1;
+      Yn1 = (q15_t) acc;
+
+      /* Store the output in the destination buffer. */
+      *pOut++ = (q15_t) acc;
+
+      /* decrement the loop counter */
+      sample--;
+    }
+
+    /*  The first stage goes from the input buffer to the output buffer. */
+    /*  Subsequent stages occur in-place in the output buffer */
+    pIn = pDst;
+
+    /* Reset to destination pointer */
+    pOut = pDst;
+
+    /*  Store the updated state variables back into the pState array */
+    *pState++ = Xn1;
+    *pState++ = Xn2;
+    *pState++ = Yn1;
+    *pState++ = Yn2;
+
+  } while(--stage);
+
+#endif /*     #ifndef ARM_MATH_CM0 */
+
+}
+
+
+/**    
+ * @} end of BiquadCascadeDF1 group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_q31.c
new file mode 100644
index 0000000000..5626bdd1ca
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_q31.c
@@ -0,0 +1,400 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_biquad_cascade_df1_q31.c    
+*    
+* Description:	Processing function for the    
+*				Q31 Biquad cascade filter    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+* 	 incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup BiquadCascadeDF1    
+ * @{    
+ */
+
+/**    
+ * @brief Processing function for the Q31 Biquad cascade filter.    
+ * @param[in]  *S         points to an instance of the Q31 Biquad cascade structure.    
+ * @param[in]  *pSrc      points to the block of input data.    
+ * @param[out] *pDst      points to the block of output data.    
+ * @param[in]  blockSize  number of samples to process per call.    
+ * @return none.    
+ *    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function is implemented using an internal 64-bit accumulator.    
+ * The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit.    
+ * Thus, if the accumulator result overflows it wraps around rather than clip.    
+ * In order to avoid overflows completely the input signal must be scaled down by 2 bits and lie in the range [-0.25 +0.25).    
+ * After all 5 multiply-accumulates are performed, the 2.62 accumulator is shifted by postShift bits and the result truncated to    
+ * 1.31 format by discarding the low 32 bits.    
+ *    
+ * \par    
+ * Refer to the function arm_biquad_cascade_df1_fast_q31() for a faster but less precise implementation of this filter for Cortex-M3 and Cortex-M4.    
+ */
+
+void arm_biquad_cascade_df1_q31(
+  const arm_biquad_casd_df1_inst_q31 * S,
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize)
+{
+  q63_t acc;                                     /*  accumulator                   */
+  uint32_t uShift = ((uint32_t) S->postShift + 1u);
+  uint32_t lShift = 32u - uShift;                /*  Shift to be applied to the output */
+  q31_t *pIn = pSrc;                             /*  input pointer initialization  */
+  q31_t *pOut = pDst;                            /*  output pointer initialization */
+  q31_t *pState = S->pState;                     /*  pState pointer initialization */
+  q31_t *pCoeffs = S->pCoeffs;                   /*  coeff pointer initialization  */
+  q31_t Xn1, Xn2, Yn1, Yn2;                      /*  Filter state variables        */
+  q31_t b0, b1, b2, a1, a2;                      /*  Filter coefficients           */
+  q31_t Xn;                                      /*  temporary input               */
+  uint32_t sample, stage = S->numStages;         /*  loop counters                     */
+
+
+#ifndef ARM_MATH_CM0
+
+  q31_t acc_l, acc_h;                            /*  temporary output variables    */
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  do
+  {
+    /* Reading the coefficients */
+    b0 = *pCoeffs++;
+    b1 = *pCoeffs++;
+    b2 = *pCoeffs++;
+    a1 = *pCoeffs++;
+    a2 = *pCoeffs++;
+
+    /* Reading the state values */
+    Xn1 = pState[0];
+    Xn2 = pState[1];
+    Yn1 = pState[2];
+    Yn2 = pState[3];
+
+    /* Apply loop unrolling and compute 4 output values simultaneously. */
+    /*      The variable acc hold output values that are being computed:    
+     *    
+     *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]    
+     */
+
+    sample = blockSize >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+     ** a second loop below computes the remaining 1 to 3 samples. */
+    while(sample > 0u)
+    {
+      /* Read the input */
+      Xn = *pIn++;
+
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+
+      /* acc =  b0 * x[n] */
+      acc = (q63_t) b0 *Xn;
+      /* acc +=  b1 * x[n-1] */
+      acc += (q63_t) b1 *Xn1;
+      /* acc +=  b[2] * x[n-2] */
+      acc += (q63_t) b2 *Xn2;
+      /* acc +=  a1 * y[n-1] */
+      acc += (q63_t) a1 *Yn1;
+      /* acc +=  a2 * y[n-2] */
+      acc += (q63_t) a2 *Yn2;
+
+      /* The result is converted to 1.31 , Yn2 variable is reused */
+
+      /* Calc lower part of acc */
+      acc_l = acc & 0xffffffff;
+
+      /* Calc upper part of acc */
+      acc_h = (acc >> 32) & 0xffffffff;
+
+      /* Apply shift for lower part of acc and upper part of acc */
+      Yn2 = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+      /* Store the output in the destination buffer. */
+      *pOut++ = Yn2;
+
+      /* Read the second input */
+      Xn2 = *pIn++;
+
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+
+      /* acc =  b0 * x[n] */
+      acc = (q63_t) b0 *Xn2;
+      /* acc +=  b1 * x[n-1] */
+      acc += (q63_t) b1 *Xn;
+      /* acc +=  b[2] * x[n-2] */
+      acc += (q63_t) b2 *Xn1;
+      /* acc +=  a1 * y[n-1] */
+      acc += (q63_t) a1 *Yn2;
+      /* acc +=  a2 * y[n-2] */
+      acc += (q63_t) a2 *Yn1;
+
+
+      /* The result is converted to 1.31, Yn1 variable is reused  */
+
+      /* Calc lower part of acc */
+      acc_l = acc & 0xffffffff;
+
+      /* Calc upper part of acc */
+      acc_h = (acc >> 32) & 0xffffffff;
+
+
+      /* Apply shift for lower part of acc and upper part of acc */
+      Yn1 = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+      /* Store the output in the destination buffer. */
+      *pOut++ = Yn1;
+
+      /* Read the third input  */
+      Xn1 = *pIn++;
+
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+
+      /* acc =  b0 * x[n] */
+      acc = (q63_t) b0 *Xn1;
+      /* acc +=  b1 * x[n-1] */
+      acc += (q63_t) b1 *Xn2;
+      /* acc +=  b[2] * x[n-2] */
+      acc += (q63_t) b2 *Xn;
+      /* acc +=  a1 * y[n-1] */
+      acc += (q63_t) a1 *Yn1;
+      /* acc +=  a2 * y[n-2] */
+      acc += (q63_t) a2 *Yn2;
+
+      /* The result is converted to 1.31, Yn2 variable is reused  */
+      /* Calc lower part of acc */
+      acc_l = acc & 0xffffffff;
+
+      /* Calc upper part of acc */
+      acc_h = (acc >> 32) & 0xffffffff;
+
+
+      /* Apply shift for lower part of acc and upper part of acc */
+      Yn2 = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+      /* Store the output in the destination buffer. */
+      *pOut++ = Yn2;
+
+      /* Read the forth input */
+      Xn = *pIn++;
+
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+
+      /* acc =  b0 * x[n] */
+      acc = (q63_t) b0 *Xn;
+      /* acc +=  b1 * x[n-1] */
+      acc += (q63_t) b1 *Xn1;
+      /* acc +=  b[2] * x[n-2] */
+      acc += (q63_t) b2 *Xn2;
+      /* acc +=  a1 * y[n-1] */
+      acc += (q63_t) a1 *Yn2;
+      /* acc +=  a2 * y[n-2] */
+      acc += (q63_t) a2 *Yn1;
+
+      /* The result is converted to 1.31, Yn1 variable is reused  */
+      /* Calc lower part of acc */
+      acc_l = acc & 0xffffffff;
+
+      /* Calc upper part of acc */
+      acc_h = (acc >> 32) & 0xffffffff;
+
+      /* Apply shift for lower part of acc and upper part of acc */
+      Yn1 = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+      /* Every time after the output is computed state should be updated. */
+      /* The states should be updated as:  */
+      /* Xn2 = Xn1    */
+      /* Xn1 = Xn     */
+      /* Yn2 = Yn1    */
+      /* Yn1 = acc    */
+      Xn2 = Xn1;
+      Xn1 = Xn;
+
+      /* Store the output in the destination buffer. */
+      *pOut++ = Yn1;
+
+      /* decrement the loop counter */
+      sample--;
+    }
+
+    /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+     ** No loop unrolling is used. */
+    sample = (blockSize & 0x3u);
+
+    while(sample > 0u)
+    {
+      /* Read the input */
+      Xn = *pIn++;
+
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+
+      /* acc =  b0 * x[n] */
+      acc = (q63_t) b0 *Xn;
+      /* acc +=  b1 * x[n-1] */
+      acc += (q63_t) b1 *Xn1;
+      /* acc +=  b[2] * x[n-2] */
+      acc += (q63_t) b2 *Xn2;
+      /* acc +=  a1 * y[n-1] */
+      acc += (q63_t) a1 *Yn1;
+      /* acc +=  a2 * y[n-2] */
+      acc += (q63_t) a2 *Yn2;
+
+      /* The result is converted to 1.31  */
+      acc = acc >> lShift;
+
+      /* Every time after the output is computed state should be updated. */
+      /* The states should be updated as:  */
+      /* Xn2 = Xn1    */
+      /* Xn1 = Xn     */
+      /* Yn2 = Yn1    */
+      /* Yn1 = acc    */
+      Xn2 = Xn1;
+      Xn1 = Xn;
+      Yn2 = Yn1;
+      Yn1 = (q31_t) acc;
+
+      /* Store the output in the destination buffer. */
+      *pOut++ = (q31_t) acc;
+
+      /* decrement the loop counter */
+      sample--;
+    }
+
+    /*  The first stage goes from the input buffer to the output buffer. */
+    /*  Subsequent stages occur in-place in the output buffer */
+    pIn = pDst;
+
+    /* Reset to destination pointer */
+    pOut = pDst;
+
+    /*  Store the updated state variables back into the pState array */
+    *pState++ = Xn1;
+    *pState++ = Xn2;
+    *pState++ = Yn1;
+    *pState++ = Yn2;
+
+  } while(--stage);
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  do
+  {
+    /* Reading the coefficients */
+    b0 = *pCoeffs++;
+    b1 = *pCoeffs++;
+    b2 = *pCoeffs++;
+    a1 = *pCoeffs++;
+    a2 = *pCoeffs++;
+
+    /* Reading the state values */
+    Xn1 = pState[0];
+    Xn2 = pState[1];
+    Yn1 = pState[2];
+    Yn2 = pState[3];
+
+    /*      The variables acc holds the output value that is computed:         
+     *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]         
+     */
+
+    sample = blockSize;
+
+    while(sample > 0u)
+    {
+      /* Read the input */
+      Xn = *pIn++;
+
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+      /* acc =  b0 * x[n] */
+      acc = (q63_t) b0 *Xn;
+
+      /* acc +=  b1 * x[n-1] */
+      acc += (q63_t) b1 *Xn1;
+      /* acc +=  b[2] * x[n-2] */
+      acc += (q63_t) b2 *Xn2;
+      /* acc +=  a1 * y[n-1] */
+      acc += (q63_t) a1 *Yn1;
+      /* acc +=  a2 * y[n-2] */
+      acc += (q63_t) a2 *Yn2;
+
+      /* The result is converted to 1.31  */
+      acc = acc >> lShift;
+
+      /* Every time after the output is computed state should be updated. */
+      /* The states should be updated as:  */
+      /* Xn2 = Xn1    */
+      /* Xn1 = Xn     */
+      /* Yn2 = Yn1    */
+      /* Yn1 = acc    */
+      Xn2 = Xn1;
+      Xn1 = Xn;
+      Yn2 = Yn1;
+      Yn1 = (q31_t) acc;
+
+      /* Store the output in the destination buffer. */
+      *pOut++ = (q31_t) acc;
+
+      /* decrement the loop counter */
+      sample--;
+    }
+
+    /*  The first stage goes from the input buffer to the output buffer. */
+    /*  Subsequent stages occur in-place in the output buffer */
+    pIn = pDst;
+
+    /* Reset to destination pointer */
+    pOut = pDst;
+
+    /*  Store the updated state variables back into the pState array */
+    *pState++ = Xn1;
+    *pState++ = Xn2;
+    *pState++ = Yn1;
+    *pState++ = Yn2;
+
+  } while(--stage);
+
+#endif /*  #ifndef ARM_MATH_CM0 */
+}
+
+/**    
+  * @} end of BiquadCascadeDF1 group    
+  */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df2T_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df2T_f32.c
new file mode 100644
index 0000000000..a8cb0c98c1
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df2T_f32.c
@@ -0,0 +1,377 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_biquad_cascade_df2T_f32.c    
+*    
+* Description:  Processing function for the floating-point transposed    
+*               direct form II Biquad cascade filter.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**       
+ * @ingroup groupFilters       
+ */
+
+/**       
+ * @defgroup BiquadCascadeDF2T Biquad Cascade IIR Filters Using a Direct Form II Transposed Structure       
+ *       
+ * This set of functions implements arbitrary order recursive (IIR) filters using a transposed direct form II structure.       
+ * The filters are implemented as a cascade of second order Biquad sections.       
+ * These functions provide a slight memory savings as compared to the direct form I Biquad filter functions.      
+ * Only floating-point data is supported.       
+ *       
+ * This function operate on blocks of input and output data and each call to the function       
+ * processes blockSize samples through the filter.       
+ * pSrc points to the array of input data and       
+ * pDst points to the array of output data.       
+ * Both arrays contain blockSize values.       
+ *       
+ * \par Algorithm       
+ * Each Biquad stage implements a second order filter using the difference equation:       
+ * 
       
+ *    y[n] = b0 * x[n] + d1       
+ *    d1 = b1 * x[n] + a1 * y[n] + d2       
+ *    d2 = b2 * x[n] + a2 * y[n]       
+ * 
       
+ * where d1 and d2 represent the two state values.       
+ *       
+ * \par       
+ * A Biquad filter using a transposed Direct Form II structure is shown below.       
+ * \image html BiquadDF2Transposed.gif "Single transposed Direct Form II Biquad"       
+ * Coefficients b0, b1, and b2  multiply the input signal x[n] and are referred to as the feedforward coefficients.       
+ * Coefficients a1 and a2 multiply the output signal y[n] and are referred to as the feedback coefficients.       
+ * Pay careful attention to the sign of the feedback coefficients.       
+ * Some design tools flip the sign of the feedback coefficients:       
+ * 
       
+ *    y[n] = b0 * x[n] + d1;       
+ *    d1 = b1 * x[n] - a1 * y[n] + d2;       
+ *    d2 = b2 * x[n] - a2 * y[n];       
+ * 
       
+ * In this case the feedback coefficients a1 and a2 must be negated when used with the CMSIS DSP Library.       
+ *       
+ * \par       
+ * Higher order filters are realized as a cascade of second order sections.       
+ * numStages refers to the number of second order stages used.       
+ * For example, an 8th order filter would be realized with numStages=4 second order stages.       
+ * A 9th order filter would be realized with numStages=5 second order stages with the       
+ * coefficients for one of the stages configured as a first order filter (b2=0 and a2=0).       
+ *       
+ * \par       
+ * pState points to the state variable array.       
+ * Each Biquad stage has 2 state variables d1 and d2.       
+ * The state variables are arranged in the pState array as:       
+ * 
       
+ *     {d11, d12, d21, d22, ...}       
+ * 
       
+ * where d1x refers to the state variables for the first Biquad and       
+ * d2x refers to the state variables for the second Biquad.       
+ * The state array has a total length of 2*numStages values.       
+ * The state variables are updated after each block of data is processed; the coefficients are untouched.       
+ *       
+ * \par       
+ * The CMSIS library contains Biquad filters in both Direct Form I and transposed Direct Form II.    
+ * The advantage of the Direct Form I structure is that it is numerically more robust for fixed-point data types.    
+ * That is why the Direct Form I structure supports Q15 and Q31 data types.    
+ * The transposed Direct Form II structure, on the other hand, requires a wide dynamic range for the state variables d1 and d2.    
+ * Because of this, the CMSIS library only has a floating-point version of the Direct Form II Biquad.    
+ * The advantage of the Direct Form II Biquad is that it requires half the number of state variables, 2 rather than 4, per Biquad stage.    
+ *       
+ * \par Instance Structure       
+ * The coefficients and state variables for a filter are stored together in an instance data structure.       
+ * A separate instance structure must be defined for each filter.       
+ * Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.       
+ *       
+ * \par Init Functions       
+ * There is also an associated initialization function.      
+ * The initialization function performs following operations:       
+ * - Sets the values of the internal structure fields.       
+ * - Zeros out the values in the state buffer.       
+ *       
+ * \par       
+ * Use of the initialization function is optional.       
+ * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.       
+ * To place an instance structure into a const data section, the instance structure must be manually initialized.       
+ * Set the values in the state buffer to zeros before static initialization.       
+ * For example, to statically initialize the instance structure use       
+ * 
       
+ *     arm_biquad_cascade_df2T_instance_f32 S1 = {numStages, pState, pCoeffs};       
+ * 
       
+ * where numStages is the number of Biquad stages in the filter; pState is the address of the state buffer.       
+ * pCoeffs is the address of the coefficient buffer;        
+ *       
+ */
+
+/**       
+ * @addtogroup BiquadCascadeDF2T       
+ * @{       
+ */
+
+/**      
+ * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter.      
+ * @param[in]  *S        points to an instance of the filter data structure.      
+ * @param[in]  *pSrc     points to the block of input data.      
+ * @param[out] *pDst     points to the block of output data      
+ * @param[in]  blockSize number of samples to process.      
+ * @return none.      
+ */
+
+void arm_biquad_cascade_df2T_f32(
+  const arm_biquad_cascade_df2T_instance_f32 * S,
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize)
+{
+
+  float32_t *pIn = pSrc;                         /*  source pointer            */
+  float32_t *pOut = pDst;                        /*  destination pointer       */
+  float32_t *pState = S->pState;                 /*  State pointer             */
+  float32_t *pCoeffs = S->pCoeffs;               /*  coefficient pointer       */
+  float32_t acc0;                                /*  accumulator               */
+  float32_t b0, b1, b2, a1, a2;                  /*  Filter coefficients       */
+  float32_t Xn;                                  /*  temporary input           */
+  float32_t d1, d2;                              /*  state variables           */
+  uint32_t sample, stage = S->numStages;         /*  loop counters             */
+
+#ifndef ARM_MATH_CM0
+
+  float32_t Xn1, Xn2;                            /*  Input State variables     */
+  float32_t acc1;                                /*  accumulator               */
+
+
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  do
+  {
+    /* Reading the coefficients */
+    b0 = *pCoeffs++;
+    b1 = *pCoeffs++;
+    b2 = *pCoeffs++;
+    a1 = *pCoeffs++;
+    a2 = *pCoeffs++;
+
+    /*Reading the state values */
+    d1 = pState[0];
+    d2 = pState[1];
+
+    /* Apply loop unrolling and compute 4 output values simultaneously. */
+    sample = blockSize >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.       
+     ** a second loop below computes the remaining 1 to 3 samples. */
+    while(sample > 0u)
+    {
+
+      /* y[n] = b0 * x[n] + d1 */
+      /* d1 = b1 * x[n] + a1 * y[n] + d2 */
+      /* d2 = b2 * x[n] + a2 * y[n] */
+
+      /* Read the first input */
+      Xn1 = *pIn++;
+
+      /* y[n] = b0 * x[n] + d1 */
+      acc0 = (b0 * Xn1) + d1;
+
+      /* d1 = b1 * x[n] + d2 */
+      d1 = (b1 * Xn1) + d2;
+
+      /* d2 = b2 * x[n] */
+      d2 = (b2 * Xn1);
+
+      /* Read the second input */
+      Xn2 = *pIn++;
+
+      /* d1 = b1 * x[n] + a1 * y[n] */
+      d1 = (a1 * acc0) + d1;
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = acc0;
+
+      d2 = (a2 * acc0) + d2;
+
+      /* y[n] = b0 * x[n] + d1 */
+      acc1 = (b0 * Xn2) + d1;
+
+      /* Read the third input */
+      Xn1 = *pIn++;
+
+      d1 = (b1 * Xn2) + d2;
+
+      d2 = (b2 * Xn2);
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = acc1;
+
+      d1 = (a1 * acc1) + d1;
+
+      d2 = (a2 * acc1) + d2;
+
+      /* y[n] = b0 * x[n] + d1 */
+      acc0 = (b0 * Xn1) + d1;
+
+      d1 = (b1 * Xn1) + d2;
+
+      d2 = (b2 * Xn1);
+
+      /* Read the fourth input */
+      Xn2 = *pIn++;
+
+      d1 = (a1 * acc0) + d1;
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = acc0;
+
+      d2 = (a2 * acc0) + d2;
+
+      /* y[n] = b0 * x[n] + d1 */
+      acc1 = (b0 * Xn2) + d1;
+
+      d1 = (b1 * Xn2) + d2;
+
+      d2 = (b2 * Xn2);
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = acc1;
+
+      d1 = (a1 * acc1) + d1;
+
+      d2 = (a2 * acc1) + d2;
+
+      /* decrement the loop counter */
+      sample--;
+
+    }
+
+    /* If the blockSize is not a multiple of 4, compute any remaining output samples here.       
+     ** No loop unrolling is used. */
+    sample = blockSize & 0x3u;
+
+    while(sample > 0u)
+    {
+      /* Read the input */
+      Xn = *pIn++;
+
+      /* y[n] = b0 * x[n] + d1 */
+      acc0 = (b0 * Xn) + d1;
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = acc0;
+
+      /* Every time after the output is computed state should be updated. */
+      /* d1 = b1 * x[n] + a1 * y[n] + d2 */
+      d1 = ((b1 * Xn) + (a1 * acc0)) + d2;
+
+      /* d2 = b2 * x[n] + a2 * y[n] */
+      d2 = (b2 * Xn) + (a2 * acc0);
+
+      /* decrement the loop counter */
+      sample--;
+    }
+
+    /* Store the updated state variables back into the state array */
+    *pState++ = d1;
+    *pState++ = d2;
+
+    /* The current stage input is given as the output to the next stage */
+    pIn = pDst;
+
+    /*Reset the output working pointer */
+    pOut = pDst;
+
+    /* decrement the loop counter */
+    stage--;
+
+  } while(stage > 0u);
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  do
+  {
+    /* Reading the coefficients */
+    b0 = *pCoeffs++;
+    b1 = *pCoeffs++;
+    b2 = *pCoeffs++;
+    a1 = *pCoeffs++;
+    a2 = *pCoeffs++;
+
+    /*Reading the state values */
+    d1 = pState[0];
+    d2 = pState[1];
+
+
+    sample = blockSize;
+
+    while(sample > 0u)
+    {
+      /* Read the input */
+      Xn = *pIn++;
+
+      /* y[n] = b0 * x[n] + d1 */
+      acc0 = (b0 * Xn) + d1;
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = acc0;
+
+      /* Every time after the output is computed state should be updated. */
+      /* d1 = b1 * x[n] + a1 * y[n] + d2 */
+      d1 = ((b1 * Xn) + (a1 * acc0)) + d2;
+
+      /* d2 = b2 * x[n] + a2 * y[n] */
+      d2 = (b2 * Xn) + (a2 * acc0);
+
+      /* decrement the loop counter */
+      sample--;
+    }
+
+    /* Store the updated state variables back into the state array */
+    *pState++ = d1;
+    *pState++ = d2;
+
+    /* The current stage input is given as the output to the next stage */
+    pIn = pDst;
+
+    /*Reset the output working pointer */
+    pOut = pDst;
+
+    /* decrement the loop counter */
+    stage--;
+
+  } while(stage > 0u);
+
+#endif /*  #ifndef ARM_MATH_CM0         */
+
+}
+
+
+  /**       
+   * @} end of BiquadCascadeDF2T group       
+   */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df2T_init_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df2T_init_f32.c
new file mode 100644
index 0000000000..e4225d008f
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df2T_init_f32.c
@@ -0,0 +1,97 @@
+/*-----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_biquad_cascade_df2T_init_f32.c    
+*    
+* Description:  Initialization function for the floating-point transposed   
+*               direct form II Biquad cascade filter.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ---------------------------------------------------------------------------*/
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup BiquadCascadeDF2T    
+ * @{    
+ */
+
+/**   
+ * @brief  Initialization function for the floating-point transposed direct form II Biquad cascade filter.   
+ * @param[in,out] *S           points to an instance of the filter data structure.   
+ * @param[in]     numStages    number of 2nd order stages in the filter.   
+ * @param[in]     *pCoeffs     points to the filter coefficients.   
+ * @param[in]     *pState      points to the state buffer.   
+ * @return        none   
+ *    
+ * Coefficient and State Ordering:    
+ * \par    
+ * The coefficients are stored in the array pCoeffs in the following order:    
+ * 
    
+ *     {b10, b11, b12, a11, a12, b20, b21, b22, a21, a22, ...}    
+ * 
    
+ *    
+ * \par    
+ * where b1x and a1x are the coefficients for the first stage,    
+ * b2x and a2x are the coefficients for the second stage,    
+ * and so on.  The pCoeffs array contains a total of 5*numStages values.    
+ *    
+ * \par    
+ * The pState is a pointer to state array.    
+ * Each Biquad stage has 2 state variables d1, and d2.    
+ * The 2 state variables for stage 1 are first, then the 2 state variables for stage 2, and so on.    
+ * The state array has a total length of 2*numStages values.    
+ * The state variables are updated after each block of data is processed; the coefficients are untouched.    
+ */
+
+void arm_biquad_cascade_df2T_init_f32(
+  arm_biquad_cascade_df2T_instance_f32 * S,
+  uint8_t numStages,
+  float32_t * pCoeffs,
+  float32_t * pState)
+{
+  /* Assign filter stages */
+  S->numStages = numStages;
+
+  /* Assign coefficient pointer */
+  S->pCoeffs = pCoeffs;
+
+  /* Clear state buffer and size is always 2 * numStages */
+  memset(pState, 0, (2u * (uint32_t) numStages) * sizeof(float32_t));
+
+  /* Assign state pointer */
+  S->pState = pState;
+}
+
+/**    
+ * @} end of BiquadCascadeDF2T group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_f32.c
new file mode 100644
index 0000000000..48dd45f2bd
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_f32.c
@@ -0,0 +1,646 @@
+/* ----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_conv_f32.c    
+*    
+* Description:	Convolution of floating-point sequences.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*  
+* Version 1.0.11 2011/10/18  
+*    Bug Fix in conv, correlation, partial convolution.  
+* 
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+*    
+* -------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @defgroup Conv Convolution    
+ *    
+ * Convolution is a mathematical operation that operates on two finite length vectors to generate a finite length output vector.    
+ * Convolution is similar to correlation and is frequently used in filtering and data analysis.    
+ * The CMSIS DSP library contains functions for convolving Q7, Q15, Q31, and floating-point data types.    
+ * The library also provides fast versions of the Q15 and Q31 functions on Cortex-M4 and Cortex-M3.    
+ *    
+ * \par Algorithm    
+ * Let a[n] and b[n] be sequences of length srcALen and srcBLen samples respectively.    
+ * Then the convolution    
+ *    
+ * 
    
+ *                   c[n] = a[n] * b[n]    
+ * 
    
+ *    
+ * \par    
+ * is defined as    
+ * \image html ConvolutionEquation.gif    
+ * \par    
+ * Note that c[n] is of length srcALen + srcBLen - 1 and is defined over the interval n=0, 1, 2, ..., srcALen + srcBLen - 2.    
+ * pSrcA points to the first input vector of length srcALen and    
+ * pSrcB points to the second input vector of length srcBLen.    
+ * The output result is written to pDst and the calling function must allocate srcALen+srcBLen-1 words for the result.    
+ *    
+ * \par    
+ * Conceptually, when two signals a[n] and b[n] are convolved,    
+ * the signal b[n] slides over a[n].    
+ * For each offset \c n, the overlapping portions of a[n] and b[n] are multiplied and summed together.    
+ *    
+ * \par    
+ * Note that convolution is a commutative operation:    
+ *    
+ * 
    
+ *                   a[n] * b[n] = b[n] * a[n].    
+ * 
    
+ *    
+ * \par    
+ * This means that switching the A and B arguments to the convolution functions has no effect.    
+ *    
+ * Fixed-Point Behavior    
+ *    
+ * \par    
+ * Convolution requires summing up a large number of intermediate products.    
+ * As such, the Q7, Q15, and Q31 functions run a risk of overflow and saturation.    
+ * Refer to the function specific documentation below for further details of the particular algorithm used.    
+ *
+ *
+ * Fast Versions
+ *
+ * \par 
+ * Fast versions are supported for Q31 and Q15.  Cycles for Fast versions are less compared to Q31 and Q15 of conv and the design requires
+ * the input signals should be scaled down to avoid intermediate overflows.   
+ *
+ *
+ * Opt Versions
+ *
+ * \par 
+ * Opt versions are supported for Q15 and Q7.  Design uses internal scratch buffer for getting good optimisation.
+ * These versions are optimised in cycles and consumes more memory(Scratch memory) compared to Q15 and Q7 versions 
+ */
+
+/**    
+ * @addtogroup Conv    
+ * @{    
+ */
+
+/**    
+ * @brief Convolution of floating-point sequences.    
+ * @param[in] *pSrcA points to the first input sequence.    
+ * @param[in] srcALen length of the first input sequence.    
+ * @param[in] *pSrcB points to the second input sequence.    
+ * @param[in] srcBLen length of the second input sequence.    
+ * @param[out] *pDst points to the location where the output result is written.  Length srcALen+srcBLen-1.    
+ * @return none.    
+ */
+
+void arm_conv_f32(
+  float32_t * pSrcA,
+  uint32_t srcALen,
+  float32_t * pSrcB,
+  uint32_t srcBLen,
+  float32_t * pDst)
+{
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  float32_t *pIn1;                               /* inputA pointer */
+  float32_t *pIn2;                               /* inputB pointer */
+  float32_t *pOut = pDst;                        /* output pointer */
+  float32_t *px;                                 /* Intermediate inputA pointer */
+  float32_t *py;                                 /* Intermediate inputB pointer */
+  float32_t *pSrc1, *pSrc2;                      /* Intermediate pointers */
+  float32_t sum, acc0, acc1, acc2, acc3;         /* Accumulator */
+  float32_t x0, x1, x2, x3, c0;                  /* Temporary variables to hold state and coefficient values */
+  uint32_t j, k, count, blkCnt, blockSize1, blockSize2, blockSize3;     /* loop counters */
+
+  /* The algorithm implementation is based on the lengths of the inputs. */
+  /* srcB is always made to slide across srcA. */
+  /* So srcBLen is always considered as shorter or equal to srcALen */
+  if(srcALen >= srcBLen)
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = pSrcA;
+
+    /* Initialization of inputB pointer */
+    pIn2 = pSrcB;
+  }
+  else
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = pSrcB;
+
+    /* Initialization of inputB pointer */
+    pIn2 = pSrcA;
+
+    /* srcBLen is always considered as shorter or equal to srcALen */
+    j = srcBLen;
+    srcBLen = srcALen;
+    srcALen = j;
+  }
+
+  /* conv(x,y) at n = x[n] * y[0] + x[n-1] * y[1] + x[n-2] * y[2] + ...+ x[n-N+1] * y[N -1] */
+  /* The function is internally    
+   * divided into three stages according to the number of multiplications that has to be    
+   * taken place between inputA samples and inputB samples. In the first stage of the    
+   * algorithm, the multiplications increase by one for every iteration.    
+   * In the second stage of the algorithm, srcBLen number of multiplications are done.    
+   * In the third stage of the algorithm, the multiplications decrease by one    
+   * for every iteration. */
+
+  /* The algorithm is implemented in three stages.    
+     The loop counters of each stage is initiated here. */
+  blockSize1 = srcBLen - 1u;
+  blockSize2 = srcALen - (srcBLen - 1u);
+  blockSize3 = blockSize1;
+
+  /* --------------------------    
+   * initializations of stage1    
+   * -------------------------*/
+
+  /* sum = x[0] * y[0]    
+   * sum = x[0] * y[1] + x[1] * y[0]    
+   * ....    
+   * sum = x[0] * y[srcBlen - 1] + x[1] * y[srcBlen - 2] +...+ x[srcBLen - 1] * y[0]    
+   */
+
+  /* In this stage the MAC operations are increased by 1 for every iteration.    
+     The count variable holds the number of MAC operations performed */
+  count = 1u;
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  py = pIn2;
+
+
+  /* ------------------------    
+   * Stage1 process    
+   * ----------------------*/
+
+  /* The first stage starts here */
+  while(blockSize1 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0.0f;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = count >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* x[0] * y[srcBLen - 1] */
+      sum += *px++ * *py--;
+
+      /* x[1] * y[srcBLen - 2] */
+      sum += *px++ * *py--;
+
+      /* x[2] * y[srcBLen - 3] */
+      sum += *px++ * *py--;
+
+      /* x[3] * y[srcBLen - 4] */
+      sum += *px++ * *py--;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, compute any remaining MACs here.    
+     ** No loop unrolling is used. */
+    k = count % 0x4u;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      sum += *px++ * *py--;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut++ = sum;
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    py = pIn2 + count;
+    px = pIn1;
+
+    /* Increment the MAC count */
+    count++;
+
+    /* Decrement the loop counter */
+    blockSize1--;
+  }
+
+  /* --------------------------    
+   * Initializations of stage2    
+   * ------------------------*/
+
+  /* sum = x[0] * y[srcBLen-1] + x[1] * y[srcBLen-2] +...+ x[srcBLen-1] * y[0]    
+   * sum = x[1] * y[srcBLen-1] + x[2] * y[srcBLen-2] +...+ x[srcBLen] * y[0]    
+   * ....    
+   * sum = x[srcALen-srcBLen-2] * y[srcBLen-1] + x[srcALen] * y[srcBLen-2] +...+ x[srcALen-1] * y[0]    
+   */
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  pSrc2 = pIn2 + (srcBLen - 1u);
+  py = pSrc2;
+
+  /* count is index by which the pointer pIn1 to be incremented */
+  count = 0u;
+
+  /* -------------------    
+   * Stage2 process    
+   * ------------------*/
+
+  /* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.    
+   * So, to loop unroll over blockSize2,    
+   * srcBLen should be greater than or equal to 4 */
+  if(srcBLen >= 4u)
+  {
+    /* Loop unroll over blockSize2, by 4 */
+    blkCnt = blockSize2 >> 2u;
+
+    while(blkCnt > 0u)
+    {
+      /* Set all accumulators to zero */
+      acc0 = 0.0f;
+      acc1 = 0.0f;
+      acc2 = 0.0f;
+      acc3 = 0.0f;
+
+      /* read x[0], x[1], x[2] samples */
+      x0 = *(px++);
+      x1 = *(px++);
+      x2 = *(px++);
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      do
+      {
+        /* Read y[srcBLen - 1] sample */
+        c0 = *(py--);
+
+        /* Read x[3] sample */
+        x3 = *(px);
+
+        /* Perform the multiply-accumulate */
+        /* acc0 +=  x[0] * y[srcBLen - 1] */
+        acc0 += x0 * c0;
+
+        /* acc1 +=  x[1] * y[srcBLen - 1] */
+        acc1 += x1 * c0;
+
+        /* acc2 +=  x[2] * y[srcBLen - 1] */
+        acc2 += x2 * c0;
+
+        /* acc3 +=  x[3] * y[srcBLen - 1] */
+        acc3 += x3 * c0;
+
+        /* Read y[srcBLen - 2] sample */
+        c0 = *(py--);
+
+        /* Read x[4] sample */
+        x0 = *(px + 1u);
+
+        /* Perform the multiply-accumulate */
+        /* acc0 +=  x[1] * y[srcBLen - 2] */
+        acc0 += x1 * c0;
+        /* acc1 +=  x[2] * y[srcBLen - 2] */
+        acc1 += x2 * c0;
+        /* acc2 +=  x[3] * y[srcBLen - 2] */
+        acc2 += x3 * c0;
+        /* acc3 +=  x[4] * y[srcBLen - 2] */
+        acc3 += x0 * c0;
+
+        /* Read y[srcBLen - 3] sample */
+        c0 = *(py--);
+
+        /* Read x[5] sample */
+        x1 = *(px + 2u);
+
+        /* Perform the multiply-accumulates */
+        /* acc0 +=  x[2] * y[srcBLen - 3] */
+        acc0 += x2 * c0;
+        /* acc1 +=  x[3] * y[srcBLen - 2] */
+        acc1 += x3 * c0;
+        /* acc2 +=  x[4] * y[srcBLen - 2] */
+        acc2 += x0 * c0;
+        /* acc3 +=  x[5] * y[srcBLen - 2] */
+        acc3 += x1 * c0;
+
+        /* Read y[srcBLen - 4] sample */
+        c0 = *(py--);
+
+        /* Read x[6] sample */
+        x2 = *(px + 3u);
+        px += 4u;
+
+        /* Perform the multiply-accumulates */
+        /* acc0 +=  x[3] * y[srcBLen - 4] */
+        acc0 += x3 * c0;
+        /* acc1 +=  x[4] * y[srcBLen - 4] */
+        acc1 += x0 * c0;
+        /* acc2 +=  x[5] * y[srcBLen - 4] */
+        acc2 += x1 * c0;
+        /* acc3 +=  x[6] * y[srcBLen - 4] */
+        acc3 += x2 * c0;
+
+
+      } while(--k);
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.    
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Read y[srcBLen - 5] sample */
+        c0 = *(py--);
+
+        /* Read x[7] sample */
+        x3 = *(px++);
+
+        /* Perform the multiply-accumulates */
+        /* acc0 +=  x[4] * y[srcBLen - 5] */
+        acc0 += x0 * c0;
+        /* acc1 +=  x[5] * y[srcBLen - 5] */
+        acc1 += x1 * c0;
+        /* acc2 +=  x[6] * y[srcBLen - 5] */
+        acc2 += x2 * c0;
+        /* acc3 +=  x[7] * y[srcBLen - 5] */
+        acc3 += x3 * c0;
+
+        /* Reuse the present samples for the next MAC */
+        x0 = x1;
+        x1 = x2;
+        x2 = x3;
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = acc0;
+      *pOut++ = acc1;
+      *pOut++ = acc2;
+      *pOut++ = acc3;
+
+      /* Increment the pointer pIn1 index, count by 4 */
+      count += 4u;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pSrc2;
+
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+
+    /* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.    
+     ** No loop unrolling is used. */
+    blkCnt = blockSize2 % 0x4u;
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0.0f;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum += *px++ * *py--;
+        sum += *px++ * *py--;
+        sum += *px++ * *py--;
+        sum += *px++ * *py--;
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.    
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulate */
+        sum += *px++ * *py--;
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = sum;
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pSrc2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+  else
+  {
+    /* If the srcBLen is not a multiple of 4,    
+     * the blockSize2 loop cannot be unrolled by 4 */
+    blkCnt = blockSize2;
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0.0f;
+
+      /* srcBLen number of MACS should be performed */
+      k = srcBLen;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulate */
+        sum += *px++ * *py--;
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = sum;
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pSrc2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+
+
+  /* --------------------------    
+   * Initializations of stage3    
+   * -------------------------*/
+
+  /* sum += x[srcALen-srcBLen+1] * y[srcBLen-1] + x[srcALen-srcBLen+2] * y[srcBLen-2] +...+ x[srcALen-1] * y[1]    
+   * sum += x[srcALen-srcBLen+2] * y[srcBLen-1] + x[srcALen-srcBLen+3] * y[srcBLen-2] +...+ x[srcALen-1] * y[2]    
+   * ....    
+   * sum +=  x[srcALen-2] * y[srcBLen-1] + x[srcALen-1] * y[srcBLen-2]    
+   * sum +=  x[srcALen-1] * y[srcBLen-1]    
+   */
+
+  /* In this stage the MAC operations are decreased by 1 for every iteration.    
+     The blockSize3 variable holds the number of MAC operations performed */
+
+  /* Working pointer of inputA */
+  pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
+  px = pSrc1;
+
+  /* Working pointer of inputB */
+  pSrc2 = pIn2 + (srcBLen - 1u);
+  py = pSrc2;
+
+  /* -------------------    
+   * Stage3 process    
+   * ------------------*/
+
+  while(blockSize3 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0.0f;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = blockSize3 >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* sum += x[srcALen - srcBLen + 1] * y[srcBLen - 1] */
+      sum += *px++ * *py--;
+
+      /* sum += x[srcALen - srcBLen + 2] * y[srcBLen - 2] */
+      sum += *px++ * *py--;
+
+      /* sum += x[srcALen - srcBLen + 3] * y[srcBLen - 3] */
+      sum += *px++ * *py--;
+
+      /* sum += x[srcALen - srcBLen + 4] * y[srcBLen - 4] */
+      sum += *px++ * *py--;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the blockSize3 is not a multiple of 4, compute any remaining MACs here.    
+     ** No loop unrolling is used. */
+    k = blockSize3 % 0x4u;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      /* sum +=  x[srcALen-1] * y[srcBLen-1] */
+      sum += *px++ * *py--;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut++ = sum;
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    px = ++pSrc1;
+    py = pSrc2;
+
+    /* Decrement the loop counter */
+    blockSize3--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  float32_t *pIn1 = pSrcA;                       /* inputA pointer */
+  float32_t *pIn2 = pSrcB;                       /* inputB pointer */
+  float32_t sum;                                 /* Accumulator */
+  uint32_t i, j;                                 /* loop counters */
+
+  /* Loop to calculate convolution for output length number of times */
+  for (i = 0u; i < ((srcALen + srcBLen) - 1u); i++)
+  {
+    /* Initialize sum with zero to carry out MAC operations */
+    sum = 0.0f;
+
+    /* Loop to perform MAC operations according to convolution equation */
+    for (j = 0u; j <= i; j++)
+    {
+      /* Check the array limitations */
+      if((((i - j) < srcBLen) && (j < srcALen)))
+      {
+        /* z[i] += x[i-j] * y[j] */
+        sum += pIn1[j] * pIn2[i - j];
+      }
+    }
+    /* Store the output in the destination buffer */
+    pDst[i] = sum;
+  }
+
+#endif /*   #ifndef ARM_MATH_CM0        */
+
+}
+
+/**    
+ * @} end of Conv group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_fast_opt_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_fast_opt_q15.c
new file mode 100644
index 0000000000..3e85a25ba7
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_fast_opt_q15.c
@@ -0,0 +1,538 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_conv_fast_opt_q15.c    
+*    
+* Description:	Fast Q15 Convolution.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*  
+* Version 1.0.11 2011/10/18  
+*    Bug Fix in conv, correlation, partial convolution.  
+* 
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup Conv    
+ * @{    
+ */
+
+/**    
+ * @brief Convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4.    
+ * @param[in] *pSrcA points to the first input sequence.    
+ * @param[in] srcALen length of the first input sequence.    
+ * @param[in] *pSrcB points to the second input sequence.    
+ * @param[in] srcBLen length of the second input sequence.    
+ * @param[out] *pDst points to the location where the output result is written.  Length srcALen+srcBLen-1.    
+ * @param[in]  *pScratch1 points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.   
+ * @param[in]  *pScratch2 points to scratch buffer of size min(srcALen, srcBLen).   
+ * @return none.    
+ *    
+ * \par Restrictions    
+ *  If the silicon does not support unaligned memory access enable the macro UNALIGNED_SUPPORT_DISABLE    
+ *	In this case input, output, scratch1 and scratch2 buffers should be aligned by 32-bit    
+ *     
+ * Scaling and Overflow Behavior:    
+ *    
+ * \par    
+ * This fast version uses a 32-bit accumulator with 2.30 format.    
+ * The accumulator maintains full precision of the intermediate multiplication results    
+ * but provides only a single guard bit. There is no saturation on intermediate additions.    
+ * Thus, if the accumulator overflows it wraps around and distorts the result.    
+ * The input signals should be scaled down to avoid intermediate overflows.    
+ * Scale down the inputs by log2(min(srcALen, srcBLen)) (log2 is read as log to the base 2) times to avoid overflows,    
+ * as maximum of min(srcALen, srcBLen) number of additions are carried internally.    
+ * The 2.30 accumulator is right shifted by 15 bits and then saturated to 1.15 format to yield the final result.    
+ *    
+ * \par    
+ * See arm_conv_q15() for a slower implementation of this function which uses 64-bit accumulation to avoid wrap around distortion.    
+ */
+
+void arm_conv_fast_opt_q15(
+  q15_t * pSrcA,
+  uint32_t srcALen,
+  q15_t * pSrcB,
+  uint32_t srcBLen,
+  q15_t * pDst,
+  q15_t * pScratch1,
+  q15_t * pScratch2)
+{
+  q31_t acc0, acc1, acc2, acc3;                  /* Accumulators */
+  q31_t x1, x2, x3;                              /* Temporary variables to hold state and coefficient values */
+  q31_t y1, y2;                                  /* State variables */
+  q15_t *pOut = pDst;                            /* output pointer */
+  q15_t *pScr1 = pScratch1;                      /* Temporary pointer for scratch1 */
+  q15_t *pScr2 = pScratch2;                      /* Temporary pointer for scratch1 */
+  q15_t *pIn1;                                   /* inputA pointer */
+  q15_t *pIn2;                                   /* inputB pointer */
+  q15_t *px;                                     /* Intermediate inputA pointer  */
+  q15_t *py;                                     /* Intermediate inputB pointer  */
+  uint32_t j, k, blkCnt;                         /* loop counter */
+  uint32_t tapCnt;                               /* loop count */
+#ifdef UNALIGNED_SUPPORT_DISABLE
+
+  q15_t a, b;
+
+#endif	/*	#ifdef UNALIGNED_SUPPORT_DISABLE	*/
+
+  /* The algorithm implementation is based on the lengths of the inputs. */
+  /* srcB is always made to slide across srcA. */
+  /* So srcBLen is always considered as shorter or equal to srcALen */
+  if(srcALen >= srcBLen)
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = pSrcA;
+
+    /* Initialization of inputB pointer */
+    pIn2 = pSrcB;
+  }
+  else
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = pSrcB;
+
+    /* Initialization of inputB pointer */
+    pIn2 = pSrcA;
+
+    /* srcBLen is always considered as shorter or equal to srcALen */
+    j = srcBLen;
+    srcBLen = srcALen;
+    srcALen = j;
+  }
+
+  /* Pointer to take end of scratch2 buffer */
+  pScr2 = pScratch2 + srcBLen - 1;
+
+  /* points to smaller length sequence */
+  px = pIn2;
+
+  /* Apply loop unrolling and do 4 Copies simultaneously. */
+  k = srcBLen >> 2u;
+
+  /* First part of the processing with loop unrolling copies 4 data points at a time.       
+   ** a second loop below copies for the remaining 1 to 3 samples. */
+
+  /* Copy smaller length input sequence in reverse order into second scratch buffer */
+  while(k > 0u)
+  {
+    /* copy second buffer in reversal manner */
+    *pScr2-- = *px++;
+    *pScr2-- = *px++;
+    *pScr2-- = *px++;
+    *pScr2-- = *px++;
+
+    /* Decrement the loop counter */
+    k--;
+  }
+
+  /* If the count is not a multiple of 4, copy remaining samples here.       
+   ** No loop unrolling is used. */
+  k = srcBLen % 0x4u;
+
+  while(k > 0u)
+  {
+    /* copy second buffer in reversal manner for remaining samples */
+    *pScr2-- = *px++;
+
+    /* Decrement the loop counter */
+    k--;
+  }
+
+  /* Initialze temporary scratch pointer */
+  pScr1 = pScratch1;
+
+  /* Assuming scratch1 buffer is aligned by 32-bit */
+  /* Fill (srcBLen - 1u) zeros in scratch1 buffer */
+  arm_fill_q15(0, pScr1, (srcBLen - 1u));
+
+  /* Update temporary scratch pointer */
+  pScr1 += (srcBLen - 1u);
+
+  /* Copy bigger length sequence(srcALen) samples in scratch1 buffer */
+
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+  /* Copy (srcALen) samples in scratch buffer */
+  arm_copy_q15(pIn1, pScr1, srcALen);
+
+  /* Update pointers */
+  pScr1 += srcALen;
+
+#else
+
+  /* Apply loop unrolling and do 4 Copies simultaneously. */
+  k = srcALen >> 2u;
+
+  /* First part of the processing with loop unrolling copies 4 data points at a time.       
+   ** a second loop below copies for the remaining 1 to 3 samples. */
+  while(k > 0u)
+  {
+    /* copy second buffer in reversal manner */
+    *pScr1++ = *pIn1++;
+    *pScr1++ = *pIn1++;
+    *pScr1++ = *pIn1++;
+    *pScr1++ = *pIn1++;
+
+    /* Decrement the loop counter */
+    k--;
+  }
+
+  /* If the count is not a multiple of 4, copy remaining samples here.       
+   ** No loop unrolling is used. */
+  k = srcALen % 0x4u;
+
+  while(k > 0u)
+  {
+    /* copy second buffer in reversal manner for remaining samples */
+    *pScr1++ = *pIn1++;
+
+    /* Decrement the loop counter */
+    k--;
+  }
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+  /* Fill (srcBLen - 1u) zeros at end of scratch buffer */
+  arm_fill_q15(0, pScr1, (srcBLen - 1u));
+
+  /* Update pointer */
+  pScr1 += (srcBLen - 1u);
+
+#else
+
+  /* Apply loop unrolling and do 4 Copies simultaneously. */
+  k = (srcBLen - 1u) >> 2u;
+
+  /* First part of the processing with loop unrolling copies 4 data points at a time.       
+   ** a second loop below copies for the remaining 1 to 3 samples. */
+  while(k > 0u)
+  {
+    /* copy second buffer in reversal manner */
+    *pScr1++ = 0;
+    *pScr1++ = 0;
+    *pScr1++ = 0;
+    *pScr1++ = 0;
+
+    /* Decrement the loop counter */
+    k--;
+  }
+
+  /* If the count is not a multiple of 4, copy remaining samples here.       
+   ** No loop unrolling is used. */
+  k = (srcBLen - 1u) % 0x4u;
+
+  while(k > 0u)
+  {
+    /* copy second buffer in reversal manner for remaining samples */
+    *pScr1++ = 0;
+
+    /* Decrement the loop counter */
+    k--;
+  }
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+  /* Temporary pointer for scratch2 */
+  py = pScratch2;
+
+
+  /* Initialization of pIn2 pointer */
+  pIn2 = py;
+
+  /* First part of the processing with loop unrolling process 4 data points at a time.       
+   ** a second loop below process for the remaining 1 to 3 samples. */
+
+  /* Actual convolution process starts here */
+  blkCnt = (srcALen + srcBLen - 1u) >> 2;
+
+  while(blkCnt > 0)
+  {
+    /* Initialze temporary scratch pointer as scratch1 */
+    pScr1 = pScratch1;
+
+    /* Clear Accumlators */
+    acc0 = 0;
+    acc1 = 0;
+    acc2 = 0;
+    acc3 = 0;
+
+    /* Read two samples from scratch1 buffer */
+    x1 = *__SIMD32(pScr1)++;
+
+    /* Read next two samples from scratch1 buffer */
+    x2 = *__SIMD32(pScr1)++;
+
+    tapCnt = (srcBLen) >> 2u;
+
+    while(tapCnt > 0u)
+    {
+
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+      /* Read four samples from smaller buffer */
+      y1 = _SIMD32_OFFSET(pIn2);
+      y2 = _SIMD32_OFFSET(pIn2 + 2u);
+
+      /* multiply and accumlate */
+      acc0 = __SMLAD(x1, y1, acc0);
+      acc2 = __SMLAD(x2, y1, acc2);
+
+      /* pack input data */
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x2, x1, 0);
+#else
+      x3 = __PKHBT(x1, x2, 0);
+#endif
+
+      /* multiply and accumlate */
+      acc1 = __SMLADX(x3, y1, acc1);
+
+      /* Read next two samples from scratch1 buffer */
+      x1 = _SIMD32_OFFSET(pScr1);
+
+      /* multiply and accumlate */
+      acc0 = __SMLAD(x2, y2, acc0);
+      acc2 = __SMLAD(x1, y2, acc2);
+
+      /* pack input data */
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x1, x2, 0);
+#else
+      x3 = __PKHBT(x2, x1, 0);
+#endif
+
+      acc3 = __SMLADX(x3, y1, acc3);
+      acc1 = __SMLADX(x3, y2, acc1);
+
+      x2 = _SIMD32_OFFSET(pScr1 + 2u);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x2, x1, 0);
+#else
+      x3 = __PKHBT(x1, x2, 0);
+#endif
+
+      acc3 = __SMLADX(x3, y2, acc3);
+
+#else	 
+
+      /* Read four samples from smaller buffer */
+	  a = *pIn2;
+	  b = *(pIn2 + 1);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      y1 = __PKHBT(a, b, 16);
+#else
+      y1 = __PKHBT(b, a, 16);
+#endif
+	  
+	  a = *(pIn2 + 2);
+	  b = *(pIn2 + 3);
+#ifndef ARM_MATH_BIG_ENDIAN
+      y2 = __PKHBT(a, b, 16);
+#else
+      y2 = __PKHBT(b, a, 16);
+#endif				
+
+      acc0 = __SMLAD(x1, y1, acc0);
+
+      acc2 = __SMLAD(x2, y1, acc2);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x2, x1, 0);
+#else
+      x3 = __PKHBT(x1, x2, 0);
+#endif
+
+      acc1 = __SMLADX(x3, y1, acc1);
+
+	  a = *pScr1;
+	  b = *(pScr1 + 1);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x1 = __PKHBT(a, b, 16);
+#else
+      x1 = __PKHBT(b, a, 16);
+#endif
+
+      acc0 = __SMLAD(x2, y2, acc0);
+
+      acc2 = __SMLAD(x1, y2, acc2);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x1, x2, 0);
+#else
+      x3 = __PKHBT(x2, x1, 0);
+#endif
+
+      acc3 = __SMLADX(x3, y1, acc3);
+
+      acc1 = __SMLADX(x3, y2, acc1);
+
+	  a = *(pScr1 + 2);
+	  b = *(pScr1 + 3);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x2 = __PKHBT(a, b, 16);
+#else
+      x2 = __PKHBT(b, a, 16);
+#endif
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x2, x1, 0);
+#else
+      x3 = __PKHBT(x1, x2, 0);
+#endif
+
+      acc3 = __SMLADX(x3, y2, acc3);
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+      /* update scratch pointers */
+      pIn2 += 4u;
+      pScr1 += 4u;
+
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Update scratch pointer for remaining samples of smaller length sequence */
+    pScr1 -= 4u;
+
+    /* apply same above for remaining samples of smaller length sequence */
+    tapCnt = (srcBLen) & 3u;
+
+    while(tapCnt > 0u)
+    {
+
+      /* accumlate the results */
+      acc0 += (*pScr1++ * *pIn2);
+      acc1 += (*pScr1++ * *pIn2);
+      acc2 += (*pScr1++ * *pIn2);
+      acc3 += (*pScr1++ * *pIn2++);
+
+      pScr1 -= 3u;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    blkCnt--;
+
+
+    /* Store the results in the accumulators in the destination buffer. */
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    *__SIMD32(pOut)++ =
+      __PKHBT(__SSAT((acc0 >> 15), 16), __SSAT((acc1 >> 15), 16), 16);
+
+    *__SIMD32(pOut)++ =
+      __PKHBT(__SSAT((acc2 >> 15), 16), __SSAT((acc3 >> 15), 16), 16);
+
+
+#else
+
+    *__SIMD32(pOut)++ =
+      __PKHBT(__SSAT((acc1 >> 15), 16), __SSAT((acc0 >> 15), 16), 16);
+
+    *__SIMD32(pOut)++ =
+      __PKHBT(__SSAT((acc3 >> 15), 16), __SSAT((acc2 >> 15), 16), 16);
+
+
+
+#endif /*      #ifndef ARM_MATH_BIG_ENDIAN       */
+
+    /* Initialization of inputB pointer */
+    pIn2 = py;
+
+    pScratch1 += 4u;
+
+  }
+
+
+  blkCnt = (srcALen + srcBLen - 1u) & 0x3;
+
+  /* Calculate convolution for remaining samples of Bigger length sequence */
+  while(blkCnt > 0)
+  {
+    /* Initialze temporary scratch pointer as scratch1 */
+    pScr1 = pScratch1;
+
+    /* Clear Accumlators */
+    acc0 = 0;
+
+    tapCnt = (srcBLen) >> 1u;
+
+    while(tapCnt > 0u)
+    {
+
+      acc0 += (*pScr1++ * *pIn2++);
+      acc0 += (*pScr1++ * *pIn2++);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    tapCnt = (srcBLen) & 1u;
+
+    /* apply same above for remaining samples of smaller length sequence */
+    while(tapCnt > 0u)
+    {
+
+      /* accumlate the results */
+      acc0 += (*pScr1++ * *pIn2++);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    blkCnt--;
+
+    /* The result is in 2.30 format.  Convert to 1.15 with saturation.       
+     ** Then store the output in the destination buffer. */
+    *pOut++ = (q15_t) (__SSAT((acc0 >> 15), 16));
+
+    /* Initialization of inputB pointer */
+    pIn2 = py;
+
+    pScratch1 += 1u;
+
+  }
+
+}
+
+/**    
+ * @} end of Conv group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_fast_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_fast_q15.c
new file mode 100644
index 0000000000..e21be35235
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_fast_q15.c
@@ -0,0 +1,1405 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010 ARM Limited. All rights reserved.   
+*   
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*   
+* Project: 	    CMSIS DSP Library   
+* Title:		arm_conv_fast_q15.c   
+*   
+* Description:	Fast Q15 Convolution.   
+*   
+* Target Processor: Cortex-M4/Cortex-M3
+* 
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+* 
+* Version 1.0.11 2011/10/18 
+*    Bug Fix in conv, correlation, partial convolution. 
+*
+* Version 1.0.10 2011/7/15 
+*    Big Endian support added and Merged M0 and M3/M4 Source code.  
+*   
+* Version 1.0.3 2010/11/29  
+*    Re-organized the CMSIS folders and updated documentation.   
+*    
+* Version 1.0.2 2010/11/11   
+*    Documentation updated.    
+*   
+* Version 1.0.1 2010/10/05    
+*    Production release and review comments incorporated.   
+*   
+* Version 1.0.0 2010/09/20    
+*    Production release and review comments incorporated.   
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**   
+ * @ingroup groupFilters   
+ */
+
+/**   
+ * @addtogroup Conv   
+ * @{   
+ */
+
+/**   
+ * @brief Convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4.   
+ * @param[in] *pSrcA points to the first input sequence.   
+ * @param[in] srcALen length of the first input sequence.   
+ * @param[in] *pSrcB points to the second input sequence.   
+ * @param[in] srcBLen length of the second input sequence.   
+ * @param[out] *pDst points to the location where the output result is written.  Length srcALen+srcBLen-1.   
+ * @return none.   
+ *   
+ * Scaling and Overflow Behavior:   
+ *   
+ * \par   
+ * This fast version uses a 32-bit accumulator with 2.30 format.   
+ * The accumulator maintains full precision of the intermediate multiplication results   
+ * but provides only a single guard bit. There is no saturation on intermediate additions.   
+ * Thus, if the accumulator overflows it wraps around and distorts the result.   
+ * The input signals should be scaled down to avoid intermediate overflows.   
+ * Scale down the inputs by log2(min(srcALen, srcBLen)) (log2 is read as log to the base 2) times to avoid overflows,   
+ * as maximum of min(srcALen, srcBLen) number of additions are carried internally.   
+ * The 2.30 accumulator is right shifted by 15 bits and then saturated to 1.15 format to yield the final result.   
+ *   
+ * \par   
+ * See arm_conv_q15() for a slower implementation of this function which uses 64-bit accumulation to avoid wrap around distortion.   
+ */
+
+void arm_conv_fast_q15(
+  q15_t * pSrcA,
+  uint32_t srcALen,
+  q15_t * pSrcB,
+  uint32_t srcBLen,
+  q15_t * pDst)
+{
+#ifndef UNALIGNED_SUPPORT_DISABLE
+  q15_t *pIn1;                                   /* inputA pointer */
+  q15_t *pIn2;                                   /* inputB pointer */
+  q15_t *pOut = pDst;                            /* output pointer */
+  q31_t sum, acc0, acc1, acc2, acc3;             /* Accumulator */
+  q15_t *px;                                     /* Intermediate inputA pointer  */
+  q15_t *py;                                     /* Intermediate inputB pointer  */
+  q15_t *pSrc1, *pSrc2;                          /* Intermediate pointers */
+  q31_t x0, x1, x2, x3, c0;                      /* Temporary variables to hold state and coefficient values */
+  uint32_t blockSize1, blockSize2, blockSize3, j, k, count, blkCnt;     /* loop counter */
+
+  /* The algorithm implementation is based on the lengths of the inputs. */
+  /* srcB is always made to slide across srcA. */
+  /* So srcBLen is always considered as shorter or equal to srcALen */
+  if(srcALen >= srcBLen)
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = pSrcA;
+
+    /* Initialization of inputB pointer */
+    pIn2 = pSrcB;
+  }
+  else
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = pSrcB;
+
+    /* Initialization of inputB pointer */
+    pIn2 = pSrcA;
+
+    /* srcBLen is always considered as shorter or equal to srcALen */
+    j = srcBLen;
+    srcBLen = srcALen;
+    srcALen = j;
+  }
+
+  /* conv(x,y) at n = x[n] * y[0] + x[n-1] * y[1] + x[n-2] * y[2] + ...+ x[n-N+1] * y[N -1] */
+  /* The function is internally   
+   * divided into three stages according to the number of multiplications that has to be   
+   * taken place between inputA samples and inputB samples. In the first stage of the   
+   * algorithm, the multiplications increase by one for every iteration.   
+   * In the second stage of the algorithm, srcBLen number of multiplications are done.   
+   * In the third stage of the algorithm, the multiplications decrease by one   
+   * for every iteration. */
+
+  /* The algorithm is implemented in three stages.   
+     The loop counters of each stage is initiated here. */
+  blockSize1 = srcBLen - 1u;
+  blockSize2 = srcALen - (srcBLen - 1u);
+  blockSize3 = blockSize1;
+
+  /* --------------------------   
+   * Initializations of stage1   
+   * -------------------------*/
+
+  /* sum = x[0] * y[0]   
+   * sum = x[0] * y[1] + x[1] * y[0]   
+   * ....   
+   * sum = x[0] * y[srcBlen - 1] + x[1] * y[srcBlen - 2] +...+ x[srcBLen - 1] * y[0]   
+   */
+
+  /* In this stage the MAC operations are increased by 1 for every iteration.   
+     The count variable holds the number of MAC operations performed */
+  count = 1u;
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  py = pIn2;
+
+
+  /* ------------------------   
+   * Stage1 process   
+   * ----------------------*/
+
+  /* For loop unrolling by 4, this stage is divided into two. */
+  /* First part of this stage computes the MAC operations less than 4 */
+  /* Second part of this stage computes the MAC operations greater than or equal to 4 */
+
+  /* The first part of the stage starts here */
+  while((count < 4u) && (blockSize1 > 0u))
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Loop over number of MAC operations between   
+     * inputA samples and inputB samples */
+    k = count;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      sum = __SMLAD(*px++, *py--, sum);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut++ = (q15_t) (sum >> 15);
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    py = pIn2 + count;
+    px = pIn1;
+
+    /* Increment the MAC count */
+    count++;
+
+    /* Decrement the loop counter */
+    blockSize1--;
+  }
+
+  /* The second part of the stage starts here */
+  /* The internal loop, over count, is unrolled by 4 */
+  /* To, read the last two inputB samples using SIMD:   
+   * y[srcBLen] and y[srcBLen-1] coefficients, py is decremented by 1 */
+  py = py - 1;
+
+  while(blockSize1 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = count >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      /* x[0], x[1] are multiplied with y[srcBLen - 1], y[srcBLen - 2] respectively */
+      sum = __SMLADX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
+      /* x[2], x[3] are multiplied with y[srcBLen - 3], y[srcBLen - 4] respectively */
+      sum = __SMLADX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* For the next MAC operations, the pointer py is used without SIMD   
+     * So, py is incremented by 1 */
+    py = py + 1u;
+
+    /* If the count is not a multiple of 4, compute any remaining MACs here.   
+     ** No loop unrolling is used. */
+    k = count % 0x4u;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      sum = __SMLAD(*px++, *py--, sum);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut++ = (q15_t) (sum >> 15);
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    py = pIn2 + (count - 1u);
+    px = pIn1;
+
+    /* Increment the MAC count */
+    count++;
+
+    /* Decrement the loop counter */
+    blockSize1--;
+  }
+
+  /* --------------------------   
+   * Initializations of stage2   
+   * ------------------------*/
+
+  /* sum = x[0] * y[srcBLen-1] + x[1] * y[srcBLen-2] +...+ x[srcBLen-1] * y[0]   
+   * sum = x[1] * y[srcBLen-1] + x[2] * y[srcBLen-2] +...+ x[srcBLen] * y[0]   
+   * ....   
+   * sum = x[srcALen-srcBLen-2] * y[srcBLen-1] + x[srcALen] * y[srcBLen-2] +...+ x[srcALen-1] * y[0]   
+   */
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  pSrc2 = pIn2 + (srcBLen - 1u);
+  py = pSrc2;
+
+  /* count is the index by which the pointer pIn1 to be incremented */
+  count = 0u;
+
+
+  /* --------------------   
+   * Stage2 process   
+   * -------------------*/
+
+  /* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.   
+   * So, to loop unroll over blockSize2,   
+   * srcBLen should be greater than or equal to 4 */
+  if(srcBLen >= 4u)
+  {
+    /* Loop unroll over blockSize2, by 4 */
+    blkCnt = blockSize2 >> 2u;
+
+    while(blkCnt > 0u)
+    {
+      py = py - 1u;
+
+      /* Set all accumulators to zero */
+      acc0 = 0;
+      acc1 = 0;
+      acc2 = 0;
+      acc3 = 0;
+
+
+      /* read x[0], x[1] samples */
+      x0 = *__SIMD32(px);
+      /* read x[1], x[2] samples */
+      x1 = _SIMD32_OFFSET(px+1);
+	  px+= 2u;
+
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      do
+      {
+        /* Read the last two inputB samples using SIMD:   
+         * y[srcBLen - 1] and y[srcBLen - 2] */
+        c0 = *__SIMD32(py)--;
+
+        /* acc0 +=  x[0] * y[srcBLen - 1] + x[1] * y[srcBLen - 2] */
+        acc0 = __SMLADX(x0, c0, acc0);
+
+        /* acc1 +=  x[1] * y[srcBLen - 1] + x[2] * y[srcBLen - 2] */
+        acc1 = __SMLADX(x1, c0, acc1);
+
+        /* Read x[2], x[3] */
+        x2 = *__SIMD32(px);
+
+        /* Read x[3], x[4] */
+        x3 = _SIMD32_OFFSET(px+1);
+
+        /* acc2 +=  x[2] * y[srcBLen - 1] + x[3] * y[srcBLen - 2] */
+        acc2 = __SMLADX(x2, c0, acc2);
+
+        /* acc3 +=  x[3] * y[srcBLen - 1] + x[4] * y[srcBLen - 2] */
+        acc3 = __SMLADX(x3, c0, acc3);
+
+        /* Read y[srcBLen - 3] and y[srcBLen - 4] */
+        c0 = *__SIMD32(py)--;
+
+        /* acc0 +=  x[2] * y[srcBLen - 3] + x[3] * y[srcBLen - 4] */
+        acc0 = __SMLADX(x2, c0, acc0);
+
+        /* acc1 +=  x[3] * y[srcBLen - 3] + x[4] * y[srcBLen - 4] */
+        acc1 = __SMLADX(x3, c0, acc1);
+
+        /* Read x[4], x[5] */
+        x0 = _SIMD32_OFFSET(px+2);
+
+        /* Read x[5], x[6] */
+        x1 = _SIMD32_OFFSET(px+3);
+		px += 4u;
+
+        /* acc2 +=  x[4] * y[srcBLen - 3] + x[5] * y[srcBLen - 4] */
+        acc2 = __SMLADX(x0, c0, acc2);
+
+        /* acc3 +=  x[5] * y[srcBLen - 3] + x[6] * y[srcBLen - 4] */
+        acc3 = __SMLADX(x1, c0, acc3);
+
+      } while(--k);
+
+      /* For the next MAC operations, SIMD is not used   
+       * So, the 16 bit pointer if inputB, py is updated */
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.   
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      if(k == 1u)
+      {
+        /* Read y[srcBLen - 5] */
+        c0 = *(py+1);
+
+#ifdef  ARM_MATH_BIG_ENDIAN
+
+        c0 = c0 << 16u;
+
+#else
+
+        c0 = c0 & 0x0000FFFF;
+
+#endif /*      #ifdef  ARM_MATH_BIG_ENDIAN     */
+
+        /* Read x[7] */
+        x3 = *__SIMD32(px);
+		px++;
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLAD(x0, c0, acc0);
+        acc1 = __SMLAD(x1, c0, acc1);
+        acc2 = __SMLADX(x1, c0, acc2);
+        acc3 = __SMLADX(x3, c0, acc3);
+      }
+
+      if(k == 2u)
+      {
+        /* Read y[srcBLen - 5], y[srcBLen - 6] */
+        c0 = _SIMD32_OFFSET(py);
+
+        /* Read x[7], x[8] */
+        x3 = *__SIMD32(px);
+
+        /* Read x[9] */
+        x2 = _SIMD32_OFFSET(px+1);
+		px += 2u;
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLADX(x0, c0, acc0);
+        acc1 = __SMLADX(x1, c0, acc1);
+        acc2 = __SMLADX(x3, c0, acc2);
+        acc3 = __SMLADX(x2, c0, acc3);
+      }
+
+      if(k == 3u)
+      {
+        /* Read y[srcBLen - 5], y[srcBLen - 6] */
+        c0 = _SIMD32_OFFSET(py);
+
+        /* Read x[7], x[8] */
+        x3 = *__SIMD32(px);
+
+        /* Read x[9] */
+        x2 = _SIMD32_OFFSET(px+1);
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLADX(x0, c0, acc0);
+        acc1 = __SMLADX(x1, c0, acc1);
+        acc2 = __SMLADX(x3, c0, acc2);
+        acc3 = __SMLADX(x2, c0, acc3);
+
+        /* Read y[srcBLen - 7] */
+		c0 = *(py-1);
+#ifdef  ARM_MATH_BIG_ENDIAN
+
+        c0 = c0 << 16u;
+#else
+
+        c0 = c0 & 0x0000FFFF;
+#endif /*      #ifdef  ARM_MATH_BIG_ENDIAN     */
+
+        /* Read x[10] */
+        x3 =  _SIMD32_OFFSET(px+2);
+		px += 3u;
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLADX(x1, c0, acc0);
+        acc1 = __SMLAD(x2, c0, acc1);
+        acc2 = __SMLADX(x2, c0, acc2);
+        acc3 = __SMLADX(x3, c0, acc3);
+      }
+
+      /* Store the results in the accumulators in the destination buffer. */
+#ifndef ARM_MATH_BIG_ENDIAN
+
+      *__SIMD32(pOut)++ = __PKHBT((acc0 >> 15), (acc1 >> 15), 16);
+      *__SIMD32(pOut)++ = __PKHBT((acc2 >> 15), (acc3 >> 15), 16);
+
+#else
+
+      *__SIMD32(pOut)++ = __PKHBT((acc1 >> 15), (acc0 >> 15), 16);
+      *__SIMD32(pOut)++ = __PKHBT((acc3 >> 15), (acc2 >> 15), 16);
+
+#endif /*      #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+      /* Increment the pointer pIn1 index, count by 4 */
+      count += 4u;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pSrc2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.   
+     ** No loop unrolling is used. */
+    blkCnt = blockSize2 % 0x4u;
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum += ((q31_t) * px++ * *py--);
+        sum += ((q31_t) * px++ * *py--);
+        sum += ((q31_t) * px++ * *py--);
+        sum += ((q31_t) * px++ * *py--);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.   
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum += ((q31_t) * px++ * *py--);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q15_t) (sum >> 15);
+
+      /* Increment the pointer pIn1 index, count by 1 */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pSrc2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+  else
+  {
+    /* If the srcBLen is not a multiple of 4,   
+     * the blockSize2 loop cannot be unrolled by 4 */
+    blkCnt = blockSize2;
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* srcBLen number of MACS should be performed */
+      k = srcBLen;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulate */
+        sum += ((q31_t) * px++ * *py--);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q15_t) (sum >> 15);
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pSrc2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+
+
+  /* --------------------------   
+   * Initializations of stage3   
+   * -------------------------*/
+
+  /* sum += x[srcALen-srcBLen+1] * y[srcBLen-1] + x[srcALen-srcBLen+2] * y[srcBLen-2] +...+ x[srcALen-1] * y[1]   
+   * sum += x[srcALen-srcBLen+2] * y[srcBLen-1] + x[srcALen-srcBLen+3] * y[srcBLen-2] +...+ x[srcALen-1] * y[2]   
+   * ....   
+   * sum +=  x[srcALen-2] * y[srcBLen-1] + x[srcALen-1] * y[srcBLen-2]   
+   * sum +=  x[srcALen-1] * y[srcBLen-1]   
+   */
+
+  /* In this stage the MAC operations are decreased by 1 for every iteration.   
+     The blockSize3 variable holds the number of MAC operations performed */
+
+  /* Working pointer of inputA */
+  pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
+  px = pSrc1;
+
+  /* Working pointer of inputB */
+  pSrc2 = pIn2 + (srcBLen - 1u);
+  pIn2 = pSrc2 - 1u;
+  py = pIn2;
+
+  /* -------------------   
+   * Stage3 process   
+   * ------------------*/
+
+  /* For loop unrolling by 4, this stage is divided into two. */
+  /* First part of this stage computes the MAC operations greater than 4 */
+  /* Second part of this stage computes the MAC operations less than or equal to 4 */
+
+  /* The first part of the stage starts here */
+  j = blockSize3 >> 2u;
+
+  while((j > 0u) && (blockSize3 > 0u))
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = blockSize3 >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* x[srcALen - srcBLen + 1], x[srcALen - srcBLen + 2] are multiplied   
+       * with y[srcBLen - 1], y[srcBLen - 2] respectively */
+      sum = __SMLADX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
+      /* x[srcALen - srcBLen + 3], x[srcALen - srcBLen + 4] are multiplied   
+       * with y[srcBLen - 3], y[srcBLen - 4] respectively */
+      sum = __SMLADX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* For the next MAC operations, the pointer py is used without SIMD   
+     * So, py is incremented by 1 */
+    py = py + 1u;
+
+    /* If the blockSize3 is not a multiple of 4, compute any remaining MACs here.   
+     ** No loop unrolling is used. */
+    k = blockSize3 % 0x4u;
+
+    while(k > 0u)
+    {
+      /* sum += x[srcALen - srcBLen + 5] * y[srcBLen - 5] */
+      sum = __SMLAD(*px++, *py--, sum);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut++ = (q15_t) (sum >> 15);
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    px = ++pSrc1;
+    py = pIn2;
+
+    /* Decrement the loop counter */
+    blockSize3--;
+
+    j--;
+  }
+
+  /* The second part of the stage starts here */
+  /* SIMD is not used for the next MAC operations,   
+   * so pointer py is updated to read only one sample at a time */
+  py = py + 1u;
+
+  while(blockSize3 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = blockSize3;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      /* sum +=  x[srcALen-1] * y[srcBLen-1] */
+      sum = __SMLAD(*px++, *py--, sum);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut++ = (q15_t) (sum >> 15);
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    px = ++pSrc1;
+    py = pSrc2;
+
+    /* Decrement the loop counter */
+    blockSize3--;
+  }
+
+#else
+  q15_t *pIn1;                                   /* inputA pointer */
+  q15_t *pIn2;                                   /* inputB pointer */
+  q15_t *pOut = pDst;                            /* output pointer */
+  q31_t sum, acc0, acc1, acc2, acc3;             /* Accumulator */
+  q15_t *px;                                     /* Intermediate inputA pointer  */
+  q15_t *py;                                     /* Intermediate inputB pointer  */
+  q15_t *pSrc1, *pSrc2;                          /* Intermediate pointers */
+  q31_t x0, x1, x2, x3, c0;                      /* Temporary variables to hold state and coefficient values */
+  uint32_t blockSize1, blockSize2, blockSize3, j, k, count, blkCnt;     /* loop counter */
+  q15_t a, b;
+
+  /* The algorithm implementation is based on the lengths of the inputs. */
+  /* srcB is always made to slide across srcA. */
+  /* So srcBLen is always considered as shorter or equal to srcALen */
+  if(srcALen >= srcBLen)
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = pSrcA;
+
+    /* Initialization of inputB pointer */
+    pIn2 = pSrcB;
+  }
+  else
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = pSrcB;
+
+    /* Initialization of inputB pointer */
+    pIn2 = pSrcA;
+
+    /* srcBLen is always considered as shorter or equal to srcALen */
+    j = srcBLen;
+    srcBLen = srcALen;
+    srcALen = j;
+  }
+
+  /* conv(x,y) at n = x[n] * y[0] + x[n-1] * y[1] + x[n-2] * y[2] + ...+ x[n-N+1] * y[N -1] */
+  /* The function is internally   
+   * divided into three stages according to the number of multiplications that has to be   
+   * taken place between inputA samples and inputB samples. In the first stage of the   
+   * algorithm, the multiplications increase by one for every iteration.   
+   * In the second stage of the algorithm, srcBLen number of multiplications are done.   
+   * In the third stage of the algorithm, the multiplications decrease by one   
+   * for every iteration. */
+
+  /* The algorithm is implemented in three stages.   
+     The loop counters of each stage is initiated here. */
+  blockSize1 = srcBLen - 1u;
+  blockSize2 = srcALen - (srcBLen - 1u);
+  blockSize3 = blockSize1;
+
+  /* --------------------------   
+   * Initializations of stage1   
+   * -------------------------*/
+
+  /* sum = x[0] * y[0]   
+   * sum = x[0] * y[1] + x[1] * y[0]   
+   * ....   
+   * sum = x[0] * y[srcBlen - 1] + x[1] * y[srcBlen - 2] +...+ x[srcBLen - 1] * y[0]   
+   */
+
+  /* In this stage the MAC operations are increased by 1 for every iteration.   
+     The count variable holds the number of MAC operations performed */
+  count = 1u;
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  py = pIn2;
+
+
+  /* ------------------------   
+   * Stage1 process   
+   * ----------------------*/
+
+  /* For loop unrolling by 4, this stage is divided into two. */
+  /* First part of this stage computes the MAC operations less than 4 */
+  /* Second part of this stage computes the MAC operations greater than or equal to 4 */
+
+  /* The first part of the stage starts here */
+  while((count < 4u) && (blockSize1 > 0u))
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Loop over number of MAC operations between   
+     * inputA samples and inputB samples */
+    k = count;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      sum += ((q31_t) * px++ * *py--);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut++ = (q15_t) (sum >> 15);
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    py = pIn2 + count;
+    px = pIn1;
+
+    /* Increment the MAC count */
+    count++;
+
+    /* Decrement the loop counter */
+    blockSize1--;
+  }
+
+  /* The second part of the stage starts here */
+  /* The internal loop, over count, is unrolled by 4 */
+  /* To, read the last two inputB samples using SIMD:   
+   * y[srcBLen] and y[srcBLen-1] coefficients, py is decremented by 1 */
+  py = py - 1;
+
+  while(blockSize1 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = count >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+	py++;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+        sum += ((q31_t) * px++ * *py--);
+        sum += ((q31_t) * px++ * *py--);
+        sum += ((q31_t) * px++ * *py--);
+        sum += ((q31_t) * px++ * *py--);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, compute any remaining MACs here.   
+     ** No loop unrolling is used. */
+    k = count % 0x4u;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      sum += ((q31_t) * px++ * *py--);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut++ = (q15_t) (sum >> 15);
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    py = pIn2 + (count - 1u);
+    px = pIn1;
+
+    /* Increment the MAC count */
+    count++;
+
+    /* Decrement the loop counter */
+    blockSize1--;
+  }
+
+  /* --------------------------   
+   * Initializations of stage2   
+   * ------------------------*/
+
+  /* sum = x[0] * y[srcBLen-1] + x[1] * y[srcBLen-2] +...+ x[srcBLen-1] * y[0]   
+   * sum = x[1] * y[srcBLen-1] + x[2] * y[srcBLen-2] +...+ x[srcBLen] * y[0]   
+   * ....   
+   * sum = x[srcALen-srcBLen-2] * y[srcBLen-1] + x[srcALen] * y[srcBLen-2] +...+ x[srcALen-1] * y[0]   
+   */
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  pSrc2 = pIn2 + (srcBLen - 1u);
+  py = pSrc2;
+
+  /* count is the index by which the pointer pIn1 to be incremented */
+  count = 0u;
+
+
+  /* --------------------   
+   * Stage2 process   
+   * -------------------*/
+
+  /* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.   
+   * So, to loop unroll over blockSize2,   
+   * srcBLen should be greater than or equal to 4 */
+  if(srcBLen >= 4u)
+  {
+    /* Loop unroll over blockSize2, by 4 */
+    blkCnt = blockSize2 >> 2u;
+
+    while(blkCnt > 0u)
+    {
+      py = py - 1u;
+
+      /* Set all accumulators to zero */
+      acc0 = 0;
+      acc1 = 0;
+      acc2 = 0;
+      acc3 = 0;	  
+
+      /* read x[0], x[1] samples */
+	  a = *px++;
+	  b = *px++;
+
+#ifndef ARM_MATH_BIG_ENDIAN
+	
+	  x0 = __PKHBT(a, b, 16);
+	  a = *px;
+	  x1 = __PKHBT(b, a, 16);
+
+#else
+
+	  x0 = __PKHBT(b, a, 16);
+	  a = *px;
+	  x1 = __PKHBT(a, b, 16);
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	   */
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      do
+      {
+        /* Read the last two inputB samples using SIMD:   
+         * y[srcBLen - 1] and y[srcBLen - 2] */
+		a = *py;
+		b = *(py+1);
+		py -= 2;
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+		c0 = __PKHBT(a, b, 16);
+
+#else
+
+ 		c0 = __PKHBT(b, a, 16);;
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	*/
+
+        /* acc0 +=  x[0] * y[srcBLen - 1] + x[1] * y[srcBLen - 2] */
+        acc0 = __SMLADX(x0, c0, acc0);
+
+        /* acc1 +=  x[1] * y[srcBLen - 1] + x[2] * y[srcBLen - 2] */
+        acc1 = __SMLADX(x1, c0, acc1);
+
+	  a = *px;
+	  b = *(px + 1);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+	
+	  x2 = __PKHBT(a, b, 16);
+	  a = *(px + 2);
+	  x3 = __PKHBT(b, a, 16);
+
+#else
+
+	  x2 = __PKHBT(b, a, 16);
+	  a = *(px + 2);
+	  x3 = __PKHBT(a, b, 16);
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	   */
+
+        /* acc2 +=  x[2] * y[srcBLen - 1] + x[3] * y[srcBLen - 2] */
+        acc2 = __SMLADX(x2, c0, acc2);
+
+        /* acc3 +=  x[3] * y[srcBLen - 1] + x[4] * y[srcBLen - 2] */
+        acc3 = __SMLADX(x3, c0, acc3);
+
+        /* Read y[srcBLen - 3] and y[srcBLen - 4] */
+		a = *py;
+		b = *(py+1);
+		py -= 2;
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+		c0 = __PKHBT(a, b, 16);
+
+#else
+
+ 		c0 = __PKHBT(b, a, 16);;
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	*/
+
+        /* acc0 +=  x[2] * y[srcBLen - 3] + x[3] * y[srcBLen - 4] */
+        acc0 = __SMLADX(x2, c0, acc0);
+
+        /* acc1 +=  x[3] * y[srcBLen - 3] + x[4] * y[srcBLen - 4] */
+        acc1 = __SMLADX(x3, c0, acc1);
+
+        /* Read x[4], x[5], x[6] */
+	  a = *(px + 2);
+	  b = *(px + 3);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+	
+	  x0 = __PKHBT(a, b, 16);
+	  a = *(px + 4);
+	  x1 = __PKHBT(b, a, 16);
+
+#else
+
+	  x0 = __PKHBT(b, a, 16);
+	  a = *(px + 4);
+	  x1 = __PKHBT(a, b, 16);
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	   */
+
+		px += 4u;
+
+        /* acc2 +=  x[4] * y[srcBLen - 3] + x[5] * y[srcBLen - 4] */
+        acc2 = __SMLADX(x0, c0, acc2);
+
+        /* acc3 +=  x[5] * y[srcBLen - 3] + x[6] * y[srcBLen - 4] */
+        acc3 = __SMLADX(x1, c0, acc3);
+
+      } while(--k);
+
+      /* For the next MAC operations, SIMD is not used   
+       * So, the 16 bit pointer if inputB, py is updated */
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.   
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      if(k == 1u)
+      {
+        /* Read y[srcBLen - 5] */
+        c0 = *(py+1);
+
+#ifdef  ARM_MATH_BIG_ENDIAN
+
+        c0 = c0 << 16u;
+
+#else
+
+        c0 = c0 & 0x0000FFFF;
+
+#endif /*      #ifdef  ARM_MATH_BIG_ENDIAN     */
+
+        /* Read x[7] */
+		a = *px;
+		b = *(px+1);
+		px++;
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+		x3 = __PKHBT(a, b, 16);
+
+#else
+
+ 		x3 = __PKHBT(b, a, 16);;
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	*/
+
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLAD(x0, c0, acc0);
+        acc1 = __SMLAD(x1, c0, acc1);
+        acc2 = __SMLADX(x1, c0, acc2);
+        acc3 = __SMLADX(x3, c0, acc3);
+      }
+
+      if(k == 2u)
+      {
+        /* Read y[srcBLen - 5], y[srcBLen - 6] */
+		a = *py;
+		b = *(py+1);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+		c0 = __PKHBT(a, b, 16);
+
+#else
+
+ 		c0 = __PKHBT(b, a, 16);;
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	*/
+
+        /* Read x[7], x[8], x[9] */
+	  a = *px;
+	  b = *(px + 1);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+	
+	  x3 = __PKHBT(a, b, 16);
+	  a = *(px + 2);
+	  x2 = __PKHBT(b, a, 16);
+
+#else
+
+	  x3 = __PKHBT(b, a, 16);
+	  a = *(px + 2);
+	  x2 = __PKHBT(a, b, 16);
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	   */
+		px += 2u;
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLADX(x0, c0, acc0);
+        acc1 = __SMLADX(x1, c0, acc1);
+        acc2 = __SMLADX(x3, c0, acc2);
+        acc3 = __SMLADX(x2, c0, acc3);
+      }
+
+      if(k == 3u)
+      {
+        /* Read y[srcBLen - 5], y[srcBLen - 6] */
+		a = *py;
+		b = *(py+1);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+		c0 = __PKHBT(a, b, 16);
+
+#else
+
+ 		c0 = __PKHBT(b, a, 16);;
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	*/
+
+        /* Read x[7], x[8], x[9] */
+	  a = *px;
+	  b = *(px + 1);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+	
+	  x3 = __PKHBT(a, b, 16);
+	  a = *(px + 2);
+	  x2 = __PKHBT(b, a, 16);
+
+#else
+
+	  x3 = __PKHBT(b, a, 16);
+	  a = *(px + 2);
+	  x2 = __PKHBT(a, b, 16);
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	   */
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLADX(x0, c0, acc0);
+        acc1 = __SMLADX(x1, c0, acc1);
+        acc2 = __SMLADX(x3, c0, acc2);
+        acc3 = __SMLADX(x2, c0, acc3);
+
+        /* Read y[srcBLen - 7] */
+		c0 = *(py-1);
+#ifdef  ARM_MATH_BIG_ENDIAN
+
+        c0 = c0 << 16u;
+#else
+
+        c0 = c0 & 0x0000FFFF;
+#endif /*      #ifdef  ARM_MATH_BIG_ENDIAN     */
+
+        /* Read x[10] */
+		a = *(px+2);
+		b = *(px+3);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+		x3 = __PKHBT(a, b, 16);
+
+#else
+
+ 		x3 = __PKHBT(b, a, 16);;
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	*/
+
+		px += 3u;
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLADX(x1, c0, acc0);
+        acc1 = __SMLAD(x2, c0, acc1);
+        acc2 = __SMLADX(x2, c0, acc2);
+        acc3 = __SMLADX(x3, c0, acc3);
+      }
+
+      /* Store the results in the accumulators in the destination buffer. */
+	  *pOut++ = (q15_t)(acc0 >> 15);
+	  *pOut++ = (q15_t)(acc1 >> 15);
+	  *pOut++ = (q15_t)(acc2 >> 15);
+	  *pOut++ = (q15_t)(acc3 >> 15);
+
+      /* Increment the pointer pIn1 index, count by 4 */
+      count += 4u;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pSrc2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.   
+     ** No loop unrolling is used. */
+    blkCnt = blockSize2 % 0x4u;
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum += ((q31_t) * px++ * *py--);
+        sum += ((q31_t) * px++ * *py--);
+        sum += ((q31_t) * px++ * *py--);
+        sum += ((q31_t) * px++ * *py--);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.   
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum += ((q31_t) * px++ * *py--);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q15_t) (sum >> 15);
+
+      /* Increment the pointer pIn1 index, count by 1 */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pSrc2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+  else
+  {
+    /* If the srcBLen is not a multiple of 4,   
+     * the blockSize2 loop cannot be unrolled by 4 */
+    blkCnt = blockSize2;
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* srcBLen number of MACS should be performed */
+      k = srcBLen;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulate */
+        sum += ((q31_t) * px++ * *py--);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q15_t) (sum >> 15);
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pSrc2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+
+
+  /* --------------------------   
+   * Initializations of stage3   
+   * -------------------------*/
+
+  /* sum += x[srcALen-srcBLen+1] * y[srcBLen-1] + x[srcALen-srcBLen+2] * y[srcBLen-2] +...+ x[srcALen-1] * y[1]   
+   * sum += x[srcALen-srcBLen+2] * y[srcBLen-1] + x[srcALen-srcBLen+3] * y[srcBLen-2] +...+ x[srcALen-1] * y[2]   
+   * ....   
+   * sum +=  x[srcALen-2] * y[srcBLen-1] + x[srcALen-1] * y[srcBLen-2]   
+   * sum +=  x[srcALen-1] * y[srcBLen-1]   
+   */
+
+  /* In this stage the MAC operations are decreased by 1 for every iteration.   
+     The blockSize3 variable holds the number of MAC operations performed */
+
+  /* Working pointer of inputA */
+  pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
+  px = pSrc1;
+
+  /* Working pointer of inputB */
+  pSrc2 = pIn2 + (srcBLen - 1u);
+  pIn2 = pSrc2 - 1u;
+  py = pIn2;
+
+  /* -------------------   
+   * Stage3 process   
+   * ------------------*/
+
+  /* For loop unrolling by 4, this stage is divided into two. */
+  /* First part of this stage computes the MAC operations greater than 4 */
+  /* Second part of this stage computes the MAC operations less than or equal to 4 */
+
+  /* The first part of the stage starts here */
+  j = blockSize3 >> 2u;
+
+  while((j > 0u) && (blockSize3 > 0u))
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = blockSize3 >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+	py++;
+
+    while(k > 0u)
+    {	
+        sum += ((q31_t) * px++ * *py--);
+        sum += ((q31_t) * px++ * *py--);
+        sum += ((q31_t) * px++ * *py--);
+        sum += ((q31_t) * px++ * *py--);
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the blockSize3 is not a multiple of 4, compute any remaining MACs here.   
+     ** No loop unrolling is used. */
+    k = blockSize3 % 0x4u;
+
+    while(k > 0u)
+    {
+      /* sum += x[srcALen - srcBLen + 5] * y[srcBLen - 5] */
+        sum += ((q31_t) * px++ * *py--);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut++ = (q15_t) (sum >> 15);
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    px = ++pSrc1;
+    py = pIn2;
+
+    /* Decrement the loop counter */
+    blockSize3--;
+
+    j--;
+  }
+
+  /* The second part of the stage starts here */
+  /* SIMD is not used for the next MAC operations,   
+   * so pointer py is updated to read only one sample at a time */
+  py = py + 1u;
+
+  while(blockSize3 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = blockSize3;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      /* sum +=  x[srcALen-1] * y[srcBLen-1] */
+        sum += ((q31_t) * px++ * *py--);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut++ = (q15_t) (sum >> 15);
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    px = ++pSrc1;
+    py = pSrc2;
+
+    /* Decrement the loop counter */
+    blockSize3--;
+  }
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+}
+
+/**   
+ * @} end of Conv group   
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_fast_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_fast_q31.c
new file mode 100644
index 0000000000..e675c11ced
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_fast_q31.c
@@ -0,0 +1,572 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_conv_fast_q31.c    
+*    
+* Description:	Q31 Convolution (fast version).    
+*    
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*  
+* Version 1.0.11 2011/10/18  
+*    Bug Fix in conv, correlation, partial convolution.  
+* 
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup Conv    
+ * @{    
+ */
+
+/**    
+ * @param[in] *pSrcA points to the first input sequence.    
+ * @param[in] srcALen length of the first input sequence.    
+ * @param[in] *pSrcB points to the second input sequence.    
+ * @param[in] srcBLen length of the second input sequence.    
+ * @param[out] *pDst points to the location where the output result is written.  Length srcALen+srcBLen-1.    
+ * @return none.    
+ *    
+ * @details    
+ * Scaling and Overflow Behavior:    
+ *    
+ * \par    
+ * This function is optimized for speed at the expense of fixed-point precision and overflow protection.    
+ * The result of each 1.31 x 1.31 multiplication is truncated to 2.30 format.    
+ * These intermediate results are accumulated in a 32-bit register in 2.30 format.    
+ * Finally, the accumulator is saturated and converted to a 1.31 result.    
+ *    
+ * \par    
+ * The fast version has the same overflow behavior as the standard version but provides less precision since it discards the low 32 bits of each multiplication result.    
+ * In order to avoid overflows completely the input signals must be scaled down.    
+ * Scale down the inputs by log2(min(srcALen, srcBLen)) (log2 is read as log to the base 2) times to avoid overflows,    
+ * as maximum of min(srcALen, srcBLen) number of additions are carried internally.    
+ *    
+ * \par    
+ * See arm_conv_q31() for a slower implementation of this function which uses 64-bit accumulation to provide higher precision.    
+ */
+
+void arm_conv_fast_q31(
+  q31_t * pSrcA,
+  uint32_t srcALen,
+  q31_t * pSrcB,
+  uint32_t srcBLen,
+  q31_t * pDst)
+{
+  q31_t *pIn1;                                   /* inputA pointer */
+  q31_t *pIn2;                                   /* inputB pointer */
+  q31_t *pOut = pDst;                            /* output pointer */
+  q31_t *px;                                     /* Intermediate inputA pointer  */
+  q31_t *py;                                     /* Intermediate inputB pointer  */
+  q31_t *pSrc1, *pSrc2;                          /* Intermediate pointers */
+  q31_t sum, acc0, acc1, acc2, acc3;             /* Accumulator */
+  q31_t x0, x1, x2, x3, c0;                      /* Temporary variables to hold state and coefficient values */
+  uint32_t j, k, count, blkCnt, blockSize1, blockSize2, blockSize3;     /* loop counter */
+
+  /* The algorithm implementation is based on the lengths of the inputs. */
+  /* srcB is always made to slide across srcA. */
+  /* So srcBLen is always considered as shorter or equal to srcALen */
+  if(srcALen >= srcBLen)
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = pSrcA;
+
+    /* Initialization of inputB pointer */
+    pIn2 = pSrcB;
+  }
+  else
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = pSrcB;
+
+    /* Initialization of inputB pointer */
+    pIn2 = pSrcA;
+
+    /* srcBLen is always considered as shorter or equal to srcALen */
+    j = srcBLen;
+    srcBLen = srcALen;
+    srcALen = j;
+  }
+
+  /* conv(x,y) at n = x[n] * y[0] + x[n-1] * y[1] + x[n-2] * y[2] + ...+ x[n-N+1] * y[N -1] */
+  /* The function is internally    
+   * divided into three stages according to the number of multiplications that has to be    
+   * taken place between inputA samples and inputB samples. In the first stage of the    
+   * algorithm, the multiplications increase by one for every iteration.    
+   * In the second stage of the algorithm, srcBLen number of multiplications are done.    
+   * In the third stage of the algorithm, the multiplications decrease by one    
+   * for every iteration. */
+
+  /* The algorithm is implemented in three stages.    
+     The loop counters of each stage is initiated here. */
+  blockSize1 = srcBLen - 1u;
+  blockSize2 = srcALen - (srcBLen - 1u);
+  blockSize3 = blockSize1;
+
+  /* --------------------------    
+   * Initializations of stage1    
+   * -------------------------*/
+
+  /* sum = x[0] * y[0]    
+   * sum = x[0] * y[1] + x[1] * y[0]    
+   * ....    
+   * sum = x[0] * y[srcBlen - 1] + x[1] * y[srcBlen - 2] +...+ x[srcBLen - 1] * y[0]    
+   */
+
+  /* In this stage the MAC operations are increased by 1 for every iteration.    
+     The count variable holds the number of MAC operations performed */
+  count = 1u;
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  py = pIn2;
+
+
+  /* ------------------------    
+   * Stage1 process    
+   * ----------------------*/
+
+  /* The first stage starts here */
+  while(blockSize1 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = count >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* x[0] * y[srcBLen - 1] */
+      sum = (q31_t) ((((q63_t) sum << 32) +
+                      ((q63_t) * px++ * (*py--))) >> 32);
+
+      /* x[1] * y[srcBLen - 2] */
+      sum = (q31_t) ((((q63_t) sum << 32) +
+                      ((q63_t) * px++ * (*py--))) >> 32);
+
+      /* x[2] * y[srcBLen - 3] */
+      sum = (q31_t) ((((q63_t) sum << 32) +
+                      ((q63_t) * px++ * (*py--))) >> 32);
+
+      /* x[3] * y[srcBLen - 4] */
+      sum = (q31_t) ((((q63_t) sum << 32) +
+                      ((q63_t) * px++ * (*py--))) >> 32);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, compute any remaining MACs here.    
+     ** No loop unrolling is used. */
+    k = count % 0x4u;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      sum = (q31_t) ((((q63_t) sum << 32) +
+                      ((q63_t) * px++ * (*py--))) >> 32);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut++ = sum << 1;
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    py = pIn2 + count;
+    px = pIn1;
+
+    /* Increment the MAC count */
+    count++;
+
+    /* Decrement the loop counter */
+    blockSize1--;
+  }
+
+  /* --------------------------    
+   * Initializations of stage2    
+   * ------------------------*/
+
+  /* sum = x[0] * y[srcBLen-1] + x[1] * y[srcBLen-2] +...+ x[srcBLen-1] * y[0]    
+   * sum = x[1] * y[srcBLen-1] + x[2] * y[srcBLen-2] +...+ x[srcBLen] * y[0]    
+   * ....    
+   * sum = x[srcALen-srcBLen-2] * y[srcBLen-1] + x[srcALen] * y[srcBLen-2] +...+ x[srcALen-1] * y[0]    
+   */
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  pSrc2 = pIn2 + (srcBLen - 1u);
+  py = pSrc2;
+
+  /* count is index by which the pointer pIn1 to be incremented */
+  count = 0u;
+
+  /* -------------------    
+   * Stage2 process    
+   * ------------------*/
+
+  /* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.    
+   * So, to loop unroll over blockSize2,    
+   * srcBLen should be greater than or equal to 4 */
+  if(srcBLen >= 4u)
+  {
+    /* Loop unroll over blockSize2, by 4 */
+    blkCnt = blockSize2 >> 2u;
+
+    while(blkCnt > 0u)
+    {
+      /* Set all accumulators to zero */
+      acc0 = 0;
+      acc1 = 0;
+      acc2 = 0;
+      acc3 = 0;
+
+      /* read x[0], x[1], x[2] samples */
+      x0 = *(px++);
+      x1 = *(px++);
+      x2 = *(px++);
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      do
+      {
+        /* Read y[srcBLen - 1] sample */
+        c0 = *(py--);
+
+        /* Read x[3] sample */
+        x3 = *(px++);
+
+        /* Perform the multiply-accumulates */
+        /* acc0 +=  x[0] * y[srcBLen - 1] */
+        acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x0 * c0)) >> 32);
+
+        /* acc1 +=  x[1] * y[srcBLen - 1] */
+        acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x1 * c0)) >> 32);
+
+        /* acc2 +=  x[2] * y[srcBLen - 1] */
+        acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x2 * c0)) >> 32);
+
+        /* acc3 +=  x[3] * y[srcBLen - 1] */
+        acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x3 * c0)) >> 32);
+
+        /* Read y[srcBLen - 2] sample */
+        c0 = *(py--);
+
+        /* Read x[4] sample */
+        x0 = *(px++);
+
+        /* Perform the multiply-accumulate */
+        /* acc0 +=  x[1] * y[srcBLen - 2] */
+        acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x1 * c0)) >> 32);
+        /* acc1 +=  x[2] * y[srcBLen - 2] */
+        acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x2 * c0)) >> 32);
+        /* acc2 +=  x[3] * y[srcBLen - 2] */
+        acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x3 * c0)) >> 32);
+        /* acc3 +=  x[4] * y[srcBLen - 2] */
+        acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x0 * c0)) >> 32);
+
+        /* Read y[srcBLen - 3] sample */
+        c0 = *(py--);
+
+        /* Read x[5] sample */
+        x1 = *(px++);
+
+        /* Perform the multiply-accumulates */
+        /* acc0 +=  x[2] * y[srcBLen - 3] */
+        acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x2 * c0)) >> 32);
+        /* acc1 +=  x[3] * y[srcBLen - 3] */
+        acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x3 * c0)) >> 32);
+        /* acc2 +=  x[4] * y[srcBLen - 3] */
+        acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x0 * c0)) >> 32);
+        /* acc3 +=  x[5] * y[srcBLen - 3] */
+        acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x1 * c0)) >> 32);
+
+        /* Read y[srcBLen - 4] sample */
+        c0 = *(py--);
+
+        /* Read x[6] sample */
+        x2 = *(px++);
+
+        /* Perform the multiply-accumulates */
+        /* acc0 +=  x[3] * y[srcBLen - 4] */
+        acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x3 * c0)) >> 32);
+        /* acc1 +=  x[4] * y[srcBLen - 4] */
+        acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x0 * c0)) >> 32);
+        /* acc2 +=  x[5] * y[srcBLen - 4] */
+        acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x1 * c0)) >> 32);
+        /* acc3 +=  x[6] * y[srcBLen - 4] */
+        acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x2 * c0)) >> 32);
+
+
+      } while(--k);
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.    
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Read y[srcBLen - 5] sample */
+        c0 = *(py--);
+
+        /* Read x[7] sample */
+        x3 = *(px++);
+
+        /* Perform the multiply-accumulates */
+        /* acc0 +=  x[4] * y[srcBLen - 5] */
+        acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x0 * c0)) >> 32);
+        /* acc1 +=  x[5] * y[srcBLen - 5] */
+        acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x1 * c0)) >> 32);
+        /* acc2 +=  x[6] * y[srcBLen - 5] */
+        acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x2 * c0)) >> 32);
+        /* acc3 +=  x[7] * y[srcBLen - 5] */
+        acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x3 * c0)) >> 32);
+
+        /* Reuse the present samples for the next MAC */
+        x0 = x1;
+        x1 = x2;
+        x2 = x3;
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the results in the accumulators in the destination buffer. */
+      *pOut++ = (q31_t) (acc0 << 1);
+      *pOut++ = (q31_t) (acc1 << 1);
+      *pOut++ = (q31_t) (acc2 << 1);
+      *pOut++ = (q31_t) (acc3 << 1);
+
+      /* Increment the pointer pIn1 index, count by 4 */
+      count += 4u;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pSrc2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.    
+     ** No loop unrolling is used. */
+    blkCnt = blockSize2 % 0x4u;
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum = (q31_t) ((((q63_t) sum << 32) +
+                        ((q63_t) * px++ * (*py--))) >> 32);
+        sum = (q31_t) ((((q63_t) sum << 32) +
+                        ((q63_t) * px++ * (*py--))) >> 32);
+        sum = (q31_t) ((((q63_t) sum << 32) +
+                        ((q63_t) * px++ * (*py--))) >> 32);
+        sum = (q31_t) ((((q63_t) sum << 32) +
+                        ((q63_t) * px++ * (*py--))) >> 32);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.    
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulate */
+        sum = (q31_t) ((((q63_t) sum << 32) +
+                        ((q63_t) * px++ * (*py--))) >> 32);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = sum << 1;
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pSrc2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+  else
+  {
+    /* If the srcBLen is not a multiple of 4,    
+     * the blockSize2 loop cannot be unrolled by 4 */
+    blkCnt = blockSize2;
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* srcBLen number of MACS should be performed */
+      k = srcBLen;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulate */
+        sum = (q31_t) ((((q63_t) sum << 32) +
+                        ((q63_t) * px++ * (*py--))) >> 32);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = sum << 1;
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pSrc2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+
+
+  /* --------------------------    
+   * Initializations of stage3    
+   * -------------------------*/
+
+  /* sum += x[srcALen-srcBLen+1] * y[srcBLen-1] + x[srcALen-srcBLen+2] * y[srcBLen-2] +...+ x[srcALen-1] * y[1]    
+   * sum += x[srcALen-srcBLen+2] * y[srcBLen-1] + x[srcALen-srcBLen+3] * y[srcBLen-2] +...+ x[srcALen-1] * y[2]    
+   * ....    
+   * sum +=  x[srcALen-2] * y[srcBLen-1] + x[srcALen-1] * y[srcBLen-2]    
+   * sum +=  x[srcALen-1] * y[srcBLen-1]    
+   */
+
+  /* In this stage the MAC operations are decreased by 1 for every iteration.    
+     The blockSize3 variable holds the number of MAC operations performed */
+
+  /* Working pointer of inputA */
+  pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
+  px = pSrc1;
+
+  /* Working pointer of inputB */
+  pSrc2 = pIn2 + (srcBLen - 1u);
+  py = pSrc2;
+
+  /* -------------------    
+   * Stage3 process    
+   * ------------------*/
+
+  while(blockSize3 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = blockSize3 >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* sum += x[srcALen - srcBLen + 1] * y[srcBLen - 1] */
+      sum = (q31_t) ((((q63_t) sum << 32) +
+                      ((q63_t) * px++ * (*py--))) >> 32);
+
+      /* sum += x[srcALen - srcBLen + 2] * y[srcBLen - 2] */
+      sum = (q31_t) ((((q63_t) sum << 32) +
+                      ((q63_t) * px++ * (*py--))) >> 32);
+
+      /* sum += x[srcALen - srcBLen + 3] * y[srcBLen - 3] */
+      sum = (q31_t) ((((q63_t) sum << 32) +
+                      ((q63_t) * px++ * (*py--))) >> 32);
+
+      /* sum += x[srcALen - srcBLen + 4] * y[srcBLen - 4] */
+      sum = (q31_t) ((((q63_t) sum << 32) +
+                      ((q63_t) * px++ * (*py--))) >> 32);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the blockSize3 is not a multiple of 4, compute any remaining MACs here.    
+     ** No loop unrolling is used. */
+    k = blockSize3 % 0x4u;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      sum = (q31_t) ((((q63_t) sum << 32) +
+                      ((q63_t) * px++ * (*py--))) >> 32);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut++ = sum << 1;
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    px = ++pSrc1;
+    py = pSrc2;
+
+    /* Decrement the loop counter */
+    blockSize3--;
+  }
+
+}
+
+/**    
+ * @} end of Conv group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_opt_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_opt_q15.c
new file mode 100644
index 0000000000..70b4125d9d
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_opt_q15.c
@@ -0,0 +1,544 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_conv_opt_q15.c    
+*    
+* Description:	Convolution of Q15 sequences.      
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.11 2011/10/18  
+*    Bug Fix in conv, correlation, partial convolution.  
+* 
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+*    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup Conv    
+ * @{    
+ */
+
+/**    
+ * @brief Convolution of Q15 sequences.    
+ * @param[in] *pSrcA points to the first input sequence.    
+ * @param[in] srcALen length of the first input sequence.    
+ * @param[in] *pSrcB points to the second input sequence.    
+ * @param[in] srcBLen length of the second input sequence.    
+ * @param[out] *pDst points to the location where the output result is written.  Length srcALen+srcBLen-1.    
+ * @param[in]  *pScratch1 points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.    
+ * @param[in]  *pScratch2 points to scratch buffer of size min(srcALen, srcBLen).    
+ * @return none.    
+ *    
+ * \par Restrictions    
+ *  If the silicon does not support unaligned memory access enable the macro UNALIGNED_SUPPORT_DISABLE    
+ *	In this case input, output, scratch1 and scratch2 buffers should be aligned by 32-bit    
+ *    
+ *       
+ * @details    
+ * Scaling and Overflow Behavior:    
+ *    
+ * \par    
+ * The function is implemented using a 64-bit internal accumulator.    
+ * Both inputs are in 1.15 format and multiplications yield a 2.30 result.    
+ * The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format.    
+ * This approach provides 33 guard bits and there is no risk of overflow.    
+ * The 34.30 result is then truncated to 34.15 format by discarding the low 15 bits and then saturated to 1.15 format.    
+ *  
+ *   
+ * \par    
+ * Refer to arm_conv_fast_q15() for a faster but less precise version of this function for Cortex-M3 and Cortex-M4.     
+ * 
+ *  
+ */
+
+void arm_conv_opt_q15(
+  q15_t * pSrcA,
+  uint32_t srcALen,
+  q15_t * pSrcB,
+  uint32_t srcBLen,
+  q15_t * pDst,
+  q15_t * pScratch1,
+  q15_t * pScratch2)
+{
+  q63_t acc0, acc1, acc2, acc3;                  /* Accumulator */
+  q31_t x1, x2, x3;                              /* Temporary variables to hold state and coefficient values */
+  q31_t y1, y2;                                  /* State variables */
+  q15_t *pOut = pDst;                            /* output pointer */
+  q15_t *pScr1 = pScratch1;                      /* Temporary pointer for scratch1 */
+  q15_t *pScr2 = pScratch2;                      /* Temporary pointer for scratch1 */
+  q15_t *pIn1;                                   /* inputA pointer */
+  q15_t *pIn2;                                   /* inputB pointer */
+  q15_t *px;                                     /* Intermediate inputA pointer  */
+  q15_t *py;                                     /* Intermediate inputB pointer  */
+  uint32_t j, k, blkCnt;                         /* loop counter */
+  uint32_t tapCnt;                               /* loop count */
+#ifdef UNALIGNED_SUPPORT_DISABLE
+
+  q15_t a, b;
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+  /* The algorithm implementation is based on the lengths of the inputs. */
+  /* srcB is always made to slide across srcA. */
+  /* So srcBLen is always considered as shorter or equal to srcALen */
+  if(srcALen >= srcBLen)
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = pSrcA;
+
+    /* Initialization of inputB pointer */
+    pIn2 = pSrcB;
+
+  }
+  else
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = pSrcB;
+
+    /* Initialization of inputB pointer */
+    pIn2 = pSrcA;
+
+    /* srcBLen is always considered as shorter or equal to srcALen */
+    j = srcBLen;
+    srcBLen = srcALen;
+    srcALen = j;
+  }
+
+  /* pointer to take end of scratch2 buffer */
+  pScr2 = pScratch2 + srcBLen - 1;
+
+  /* points to smaller length sequence */
+  px = pIn2;
+
+  /* Apply loop unrolling and do 4 Copies simultaneously. */
+  k = srcBLen >> 2u;
+
+  /* First part of the processing with loop unrolling copies 4 data points at a time.       
+   ** a second loop below copies for the remaining 1 to 3 samples. */
+  /* Copy smaller length input sequence in reverse order into second scratch buffer */
+  while(k > 0u)
+  {
+    /* copy second buffer in reversal manner */
+    *pScr2-- = *px++;
+    *pScr2-- = *px++;
+    *pScr2-- = *px++;
+    *pScr2-- = *px++;
+
+    /* Decrement the loop counter */
+    k--;
+  }
+
+  /* If the count is not a multiple of 4, copy remaining samples here.       
+   ** No loop unrolling is used. */
+  k = srcBLen % 0x4u;
+
+  while(k > 0u)
+  {
+    /* copy second buffer in reversal manner for remaining samples */
+    *pScr2-- = *px++;
+
+    /* Decrement the loop counter */
+    k--;
+  }
+
+  /* Initialze temporary scratch pointer */
+  pScr1 = pScratch1;
+
+  /* Assuming scratch1 buffer is aligned by 32-bit */
+  /* Fill (srcBLen - 1u) zeros in scratch buffer */
+  arm_fill_q15(0, pScr1, (srcBLen - 1u));
+
+  /* Update temporary scratch pointer */
+  pScr1 += (srcBLen - 1u);
+
+  /* Copy bigger length sequence(srcALen) samples in scratch1 buffer */
+
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+  /* Copy (srcALen) samples in scratch buffer */
+  arm_copy_q15(pIn1, pScr1, srcALen);
+
+  /* Update pointers */
+  pScr1 += srcALen;
+
+#else
+
+  /* Apply loop unrolling and do 4 Copies simultaneously. */
+  k = srcALen >> 2u;
+
+  /* First part of the processing with loop unrolling copies 4 data points at a time.       
+   ** a second loop below copies for the remaining 1 to 3 samples. */
+  while(k > 0u)
+  {
+    /* copy second buffer in reversal manner */
+    *pScr1++ = *pIn1++;
+    *pScr1++ = *pIn1++;
+    *pScr1++ = *pIn1++;
+    *pScr1++ = *pIn1++;
+
+    /* Decrement the loop counter */
+    k--;
+  }
+
+  /* If the count is not a multiple of 4, copy remaining samples here.       
+   ** No loop unrolling is used. */
+  k = srcALen % 0x4u;
+
+  while(k > 0u)
+  {
+    /* copy second buffer in reversal manner for remaining samples */
+    *pScr1++ = *pIn1++;
+
+    /* Decrement the loop counter */
+    k--;
+  }
+
+#endif
+
+
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+  /* Fill (srcBLen - 1u) zeros at end of scratch buffer */
+  arm_fill_q15(0, pScr1, (srcBLen - 1u));
+
+  /* Update pointer */
+  pScr1 += (srcBLen - 1u);
+
+#else
+
+  /* Apply loop unrolling and do 4 Copies simultaneously. */
+  k = (srcBLen - 1u) >> 2u;
+
+  /* First part of the processing with loop unrolling copies 4 data points at a time.       
+   ** a second loop below copies for the remaining 1 to 3 samples. */
+  while(k > 0u)
+  {
+    /* copy second buffer in reversal manner */
+    *pScr1++ = 0;
+    *pScr1++ = 0;
+    *pScr1++ = 0;
+    *pScr1++ = 0;
+
+    /* Decrement the loop counter */
+    k--;
+  }
+
+  /* If the count is not a multiple of 4, copy remaining samples here.       
+   ** No loop unrolling is used. */
+  k = (srcBLen - 1u) % 0x4u;
+
+  while(k > 0u)
+  {
+    /* copy second buffer in reversal manner for remaining samples */
+    *pScr1++ = 0;
+
+    /* Decrement the loop counter */
+    k--;
+  }
+
+#endif
+
+  /* Temporary pointer for scratch2 */
+  py = pScratch2;
+
+
+  /* Initialization of pIn2 pointer */
+  pIn2 = py;
+
+  /* First part of the processing with loop unrolling process 4 data points at a time.       
+   ** a second loop below process for the remaining 1 to 3 samples. */
+
+  /* Actual convolution process starts here */
+  blkCnt = (srcALen + srcBLen - 1u) >> 2;
+
+  while(blkCnt > 0)
+  {
+    /* Initialze temporary scratch pointer as scratch1 */
+    pScr1 = pScratch1;
+
+    /* Clear Accumlators */
+    acc0 = 0;
+    acc1 = 0;
+    acc2 = 0;
+    acc3 = 0;
+
+    /* Read two samples from scratch1 buffer */
+    x1 = *__SIMD32(pScr1)++;
+
+    /* Read next two samples from scratch1 buffer */
+    x2 = *__SIMD32(pScr1)++;
+
+    tapCnt = (srcBLen) >> 2u;
+
+    while(tapCnt > 0u)
+    {
+
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+      /* Read four samples from smaller buffer */
+      y1 = _SIMD32_OFFSET(pIn2);
+      y2 = _SIMD32_OFFSET(pIn2 + 2u);
+
+      /* multiply and accumlate */
+      acc0 = __SMLALD(x1, y1, acc0);
+      acc2 = __SMLALD(x2, y1, acc2);
+
+      /* pack input data */
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x2, x1, 0);
+#else
+      x3 = __PKHBT(x1, x2, 0);
+#endif
+
+      /* multiply and accumlate */
+      acc1 = __SMLALDX(x3, y1, acc1);
+
+      /* Read next two samples from scratch1 buffer */
+      x1 = _SIMD32_OFFSET(pScr1);
+
+      /* multiply and accumlate */
+      acc0 = __SMLALD(x2, y2, acc0);
+      acc2 = __SMLALD(x1, y2, acc2);
+
+      /* pack input data */
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x1, x2, 0);
+#else
+      x3 = __PKHBT(x2, x1, 0);
+#endif
+
+      acc3 = __SMLALDX(x3, y1, acc3);
+      acc1 = __SMLALDX(x3, y2, acc1);
+
+      x2 = _SIMD32_OFFSET(pScr1 + 2u);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x2, x1, 0);
+#else
+      x3 = __PKHBT(x1, x2, 0);
+#endif
+
+      acc3 = __SMLALDX(x3, y2, acc3);
+
+#else	 
+
+      /* Read four samples from smaller buffer */
+	  a = *pIn2;
+	  b = *(pIn2 + 1);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      y1 = __PKHBT(a, b, 16);
+#else
+      y1 = __PKHBT(b, a, 16);
+#endif
+	  
+	  a = *(pIn2 + 2);
+	  b = *(pIn2 + 3);
+#ifndef ARM_MATH_BIG_ENDIAN
+      y2 = __PKHBT(a, b, 16);
+#else
+      y2 = __PKHBT(b, a, 16);
+#endif				
+
+      acc0 = __SMLALD(x1, y1, acc0);
+
+      acc2 = __SMLALD(x2, y1, acc2);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x2, x1, 0);
+#else
+      x3 = __PKHBT(x1, x2, 0);
+#endif
+
+      acc1 = __SMLALDX(x3, y1, acc1);
+
+	  a = *pScr1;
+	  b = *(pScr1 + 1);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x1 = __PKHBT(a, b, 16);
+#else
+      x1 = __PKHBT(b, a, 16);
+#endif
+
+      acc0 = __SMLALD(x2, y2, acc0);
+
+      acc2 = __SMLALD(x1, y2, acc2);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x1, x2, 0);
+#else
+      x3 = __PKHBT(x2, x1, 0);
+#endif
+
+      acc3 = __SMLALDX(x3, y1, acc3);
+
+      acc1 = __SMLALDX(x3, y2, acc1);
+
+	  a = *(pScr1 + 2);
+	  b = *(pScr1 + 3);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x2 = __PKHBT(a, b, 16);
+#else
+      x2 = __PKHBT(b, a, 16);
+#endif
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x2, x1, 0);
+#else
+      x3 = __PKHBT(x1, x2, 0);
+#endif
+
+      acc3 = __SMLALDX(x3, y2, acc3);
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+      pIn2 += 4u;
+      pScr1 += 4u;
+
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Update scratch pointer for remaining samples of smaller length sequence */
+    pScr1 -= 4u;
+
+    /* apply same above for remaining samples of smaller length sequence */
+    tapCnt = (srcBLen) & 3u;
+
+    while(tapCnt > 0u)
+    {
+
+      /* accumlate the results */
+      acc0 += (*pScr1++ * *pIn2);
+      acc1 += (*pScr1++ * *pIn2);
+      acc2 += (*pScr1++ * *pIn2);
+      acc3 += (*pScr1++ * *pIn2++);
+
+      pScr1 -= 3u;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    blkCnt--;
+
+
+    /* Store the results in the accumulators in the destination buffer. */
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    *__SIMD32(pOut)++ =
+      __PKHBT(__SSAT((acc0 >> 15), 16), __SSAT((acc1 >> 15), 16), 16);
+
+    *__SIMD32(pOut)++ =
+      __PKHBT(__SSAT((acc2 >> 15), 16), __SSAT((acc3 >> 15), 16), 16);
+
+#else
+
+    *__SIMD32(pOut)++ =
+      __PKHBT(__SSAT((acc1 >> 15), 16), __SSAT((acc0 >> 15), 16), 16);
+
+    *__SIMD32(pOut)++ =
+      __PKHBT(__SSAT((acc3 >> 15), 16), __SSAT((acc2 >> 15), 16), 16);
+
+
+#endif /*      #ifndef ARM_MATH_BIG_ENDIAN       */
+
+    /* Initialization of inputB pointer */
+    pIn2 = py;
+
+    pScratch1 += 4u;
+
+  }
+
+
+  blkCnt = (srcALen + srcBLen - 1u) & 0x3;
+
+  /* Calculate convolution for remaining samples of Bigger length sequence */
+  while(blkCnt > 0)
+  {
+    /* Initialze temporary scratch pointer as scratch1 */
+    pScr1 = pScratch1;
+
+    /* Clear Accumlators */
+    acc0 = 0;
+
+    tapCnt = (srcBLen) >> 1u;
+
+    while(tapCnt > 0u)
+    {
+
+      /* Read next two samples from scratch1 buffer */
+      acc0 += (*pScr1++ * *pIn2++);
+      acc0 += (*pScr1++ * *pIn2++);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    tapCnt = (srcBLen) & 1u;
+
+    /* apply same above for remaining samples of smaller length sequence */
+    while(tapCnt > 0u)
+    {
+
+      /* accumlate the results */
+      acc0 += (*pScr1++ * *pIn2++);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    blkCnt--;
+
+    /* The result is in 2.30 format.  Convert to 1.15 with saturation.       
+     ** Then store the output in the destination buffer. */
+    *pOut++ = (q15_t) (__SSAT((acc0 >> 15), 16));
+
+
+    /* Initialization of inputB pointer */
+    pIn2 = py;
+
+    pScratch1 += 1u;
+
+  }
+
+}
+
+
+/**    
+ * @} end of Conv group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_opt_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_opt_q7.c
new file mode 100644
index 0000000000..7fe9f55cf7
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_opt_q7.c
@@ -0,0 +1,434 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_conv_opt_q7.c    
+*    
+* Description:	Convolution of Q7 sequences.  
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*  
+* Version 1.0.11 2011/10/18  
+*    Bug Fix in conv, correlation, partial convolution.  
+* 
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+*    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup Conv    
+ * @{    
+ */
+
+/**    
+ * @brief Convolution of Q7 sequences.    
+ * @param[in] *pSrcA points to the first input sequence.    
+ * @param[in] srcALen length of the first input sequence.    
+ * @param[in] *pSrcB points to the second input sequence.    
+ * @param[in] srcBLen length of the second input sequence.    
+ * @param[out] *pDst points to the location where the output result is written.  Length srcALen+srcBLen-1.    
+ * @param[in]  *pScratch1 points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.   
+ * @param[in]  *pScratch2 points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen).   
+ * @return none.    
+ *    
+ * \par Restrictions    
+ *  If the silicon does not support unaligned memory access enable the macro UNALIGNED_SUPPORT_DISABLE    
+ *	In this case input, output, scratch1 and scratch2 buffers should be aligned by 32-bit     
+ *       
+ * @details    
+ * Scaling and Overflow Behavior:    
+ *    
+ * \par    
+ * The function is implemented using a 32-bit internal accumulator.    
+ * Both the inputs are represented in 1.7 format and multiplications yield a 2.14 result.    
+ * The 2.14 intermediate results are accumulated in a 32-bit accumulator in 18.14 format.    
+ * This approach provides 17 guard bits and there is no risk of overflow as long as max(srcALen, srcBLen)<131072.    
+ * The 18.14 result is then truncated to 18.7 format by discarding the low 7 bits and then saturated to 1.7 format.    
+ *
+ */
+
+void arm_conv_opt_q7(
+  q7_t * pSrcA,
+  uint32_t srcALen,
+  q7_t * pSrcB,
+  uint32_t srcBLen,
+  q7_t * pDst,
+  q15_t * pScratch1,
+  q15_t * pScratch2)
+{
+
+  q15_t *pScr2, *pScr1;                          /* Intermediate pointers for scratch pointers */
+  q15_t x4;                                      /* Temporary input variable */
+  q7_t *pIn1, *pIn2;                             /* inputA and inputB pointer */
+  uint32_t j, k, blkCnt, tapCnt;                 /* loop counter */
+  q7_t *px;                                      /* Temporary input1 pointer */
+  q15_t *py;                                     /* Temporary input2 pointer */
+  q31_t acc0, acc1, acc2, acc3;                  /* Accumulator */
+  q31_t x1, x2, x3, y1;                          /* Temporary input variables */
+  q7_t *pOut = pDst;                             /* output pointer */
+  q7_t out0, out1, out2, out3;                   /* temporary variables */
+
+  /* The algorithm implementation is based on the lengths of the inputs. */
+  /* srcB is always made to slide across srcA. */
+  /* So srcBLen is always considered as shorter or equal to srcALen */
+  if(srcALen >= srcBLen)
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = pSrcA;
+
+    /* Initialization of inputB pointer */
+    pIn2 = pSrcB;
+  }
+  else
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = pSrcB;
+
+    /* Initialization of inputB pointer */
+    pIn2 = pSrcA;
+
+    /* srcBLen is always considered as shorter or equal to srcALen */
+    j = srcBLen;
+    srcBLen = srcALen;
+    srcALen = j;
+  }
+
+  /* pointer to take end of scratch2 buffer */
+  pScr2 = pScratch2;
+
+  /* points to smaller length sequence */
+  px = pIn2 + srcBLen - 1;
+
+  /* Apply loop unrolling and do 4 Copies simultaneously. */
+  k = srcBLen >> 2u;
+
+  /* First part of the processing with loop unrolling copies 4 data points at a time.       
+   ** a second loop below copies for the remaining 1 to 3 samples. */
+  while(k > 0u)
+  {
+    /* copy second buffer in reversal manner */
+    x4 = (q15_t) * px--;
+    *pScr2++ = x4;
+    x4 = (q15_t) * px--;
+    *pScr2++ = x4;
+    x4 = (q15_t) * px--;
+    *pScr2++ = x4;
+    x4 = (q15_t) * px--;
+    *pScr2++ = x4;
+
+    /* Decrement the loop counter */
+    k--;
+  }
+
+  /* If the count is not a multiple of 4, copy remaining samples here.       
+   ** No loop unrolling is used. */
+  k = srcBLen % 0x4u;
+
+  while(k > 0u)
+  {
+    /* copy second buffer in reversal manner for remaining samples */
+    x4 = (q15_t) * px--;
+    *pScr2++ = x4;
+
+    /* Decrement the loop counter */
+    k--;
+  }
+
+  /* Initialze temporary scratch pointer */
+  pScr1 = pScratch1;
+
+  /* Fill (srcBLen - 1u) zeros in scratch buffer */
+  arm_fill_q15(0, pScr1, (srcBLen - 1u));
+
+  /* Update temporary scratch pointer */
+  pScr1 += (srcBLen - 1u);
+
+  /* Copy (srcALen) samples in scratch buffer */
+  /* Apply loop unrolling and do 4 Copies simultaneously. */
+  k = srcALen >> 2u;
+
+  /* First part of the processing with loop unrolling copies 4 data points at a time.       
+   ** a second loop below copies for the remaining 1 to 3 samples. */
+  while(k > 0u)
+  {
+    /* copy second buffer in reversal manner */
+    x4 = (q15_t) * pIn1++;
+    *pScr1++ = x4;
+    x4 = (q15_t) * pIn1++;
+    *pScr1++ = x4;
+    x4 = (q15_t) * pIn1++;
+    *pScr1++ = x4;
+    x4 = (q15_t) * pIn1++;
+    *pScr1++ = x4;
+
+    /* Decrement the loop counter */
+    k--;
+  }
+
+  /* If the count is not a multiple of 4, copy remaining samples here.       
+   ** No loop unrolling is used. */
+  k = srcALen % 0x4u;
+
+  while(k > 0u)
+  {
+    /* copy second buffer in reversal manner for remaining samples */
+    x4 = (q15_t) * pIn1++;
+    *pScr1++ = x4;
+
+    /* Decrement the loop counter */
+    k--;
+  }
+
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+  /* Fill (srcBLen - 1u) zeros at end of scratch buffer */
+  arm_fill_q15(0, pScr1, (srcBLen - 1u));
+
+  /* Update pointer */
+  pScr1 += (srcBLen - 1u);
+
+#else
+
+  /* Apply loop unrolling and do 4 Copies simultaneously. */
+  k = (srcBLen - 1u) >> 2u;
+
+  /* First part of the processing with loop unrolling copies 4 data points at a time.       
+   ** a second loop below copies for the remaining 1 to 3 samples. */
+  while(k > 0u)
+  {
+    /* copy second buffer in reversal manner */
+    *pScr1++ = 0;
+    *pScr1++ = 0;
+    *pScr1++ = 0;
+    *pScr1++ = 0;
+
+    /* Decrement the loop counter */
+    k--;
+  }
+
+  /* If the count is not a multiple of 4, copy remaining samples here.       
+   ** No loop unrolling is used. */
+  k = (srcBLen - 1u) % 0x4u;
+
+  while(k > 0u)
+  {
+    /* copy second buffer in reversal manner for remaining samples */
+    *pScr1++ = 0;
+
+    /* Decrement the loop counter */
+    k--;
+  }
+
+#endif
+
+  /* Temporary pointer for scratch2 */
+  py = pScratch2;
+
+  /* Initialization of pIn2 pointer */
+  pIn2 = (q7_t *) py;
+
+  pScr2 = py;
+
+  /* Actual convolution process starts here */
+  blkCnt = (srcALen + srcBLen - 1u) >> 2;
+
+  while(blkCnt > 0)
+  {
+    /* Initialze temporary scratch pointer as scratch1 */
+    pScr1 = pScratch1;
+
+    /* Clear Accumlators */
+    acc0 = 0;
+    acc1 = 0;
+    acc2 = 0;
+    acc3 = 0;
+
+    /* Read two samples from scratch1 buffer */
+    x1 = *__SIMD32(pScr1)++;
+
+    /* Read next two samples from scratch1 buffer */
+    x2 = *__SIMD32(pScr1)++;
+
+    tapCnt = (srcBLen) >> 2u;
+
+    while(tapCnt > 0u)
+    {
+
+      /* Read four samples from smaller buffer */
+      y1 = _SIMD32_OFFSET(pScr2);
+
+      /* multiply and accumlate */
+      acc0 = __SMLAD(x1, y1, acc0);
+      acc2 = __SMLAD(x2, y1, acc2);
+
+      /* pack input data */
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x2, x1, 0);
+#else
+      x3 = __PKHBT(x1, x2, 0);
+#endif
+
+      /* multiply and accumlate */
+      acc1 = __SMLADX(x3, y1, acc1);
+
+      /* Read next two samples from scratch1 buffer */
+      x1 = *__SIMD32(pScr1)++;
+
+      /* pack input data */
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x1, x2, 0);
+#else
+      x3 = __PKHBT(x2, x1, 0);
+#endif
+
+      acc3 = __SMLADX(x3, y1, acc3);
+
+      /* Read four samples from smaller buffer */
+      y1 = _SIMD32_OFFSET(pScr2 + 2u);
+
+      acc0 = __SMLAD(x2, y1, acc0);
+
+      acc2 = __SMLAD(x1, y1, acc2);
+
+      acc1 = __SMLADX(x3, y1, acc1);
+
+      x2 = *__SIMD32(pScr1)++;
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x2, x1, 0);
+#else
+      x3 = __PKHBT(x1, x2, 0);
+#endif
+
+      acc3 = __SMLADX(x3, y1, acc3);
+
+      pScr2 += 4u;
+
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+
+
+    /* Update scratch pointer for remaining samples of smaller length sequence */
+    pScr1 -= 4u;
+
+
+    /* apply same above for remaining samples of smaller length sequence */
+    tapCnt = (srcBLen) & 3u;
+
+    while(tapCnt > 0u)
+    {
+
+      /* accumlate the results */
+      acc0 += (*pScr1++ * *pScr2);
+      acc1 += (*pScr1++ * *pScr2);
+      acc2 += (*pScr1++ * *pScr2);
+      acc3 += (*pScr1++ * *pScr2++);
+
+      pScr1 -= 3u;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    blkCnt--;
+
+    /* Store the result in the accumulator in the destination buffer. */
+    out0 = (q7_t) (__SSAT(acc0 >> 7u, 8));
+    out1 = (q7_t) (__SSAT(acc1 >> 7u, 8));
+    out2 = (q7_t) (__SSAT(acc2 >> 7u, 8));
+    out3 = (q7_t) (__SSAT(acc3 >> 7u, 8));
+
+    *__SIMD32(pOut)++ = __PACKq7(out0, out1, out2, out3);
+
+    /* Initialization of inputB pointer */
+    pScr2 = py;
+
+    pScratch1 += 4u;
+
+  }
+
+
+  blkCnt = (srcALen + srcBLen - 1u) & 0x3;
+
+  /* Calculate convolution for remaining samples of Bigger length sequence */
+  while(blkCnt > 0)
+  {
+    /* Initialze temporary scratch pointer as scratch1 */
+    pScr1 = pScratch1;
+
+    /* Clear Accumlators */
+    acc0 = 0;
+
+    tapCnt = (srcBLen) >> 1u;
+
+    while(tapCnt > 0u)
+    {
+      acc0 += (*pScr1++ * *pScr2++);
+      acc0 += (*pScr1++ * *pScr2++);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    tapCnt = (srcBLen) & 1u;
+
+    /* apply same above for remaining samples of smaller length sequence */
+    while(tapCnt > 0u)
+    {
+
+      /* accumlate the results */
+      acc0 += (*pScr1++ * *pScr2++);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    blkCnt--;
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut++ = (q7_t) (__SSAT(acc0 >> 7u, 8));
+
+    /* Initialization of inputB pointer */
+    pScr2 = py;
+
+    pScratch1 += 1u;
+
+  }
+
+}
+
+
+/**    
+ * @} end of Conv group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_f32.c
new file mode 100644
index 0000000000..58f5727353
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_f32.c
@@ -0,0 +1,661 @@
+/* ----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_conv_partial_f32.c    
+*    
+* Description:	Partial convolution of floating-point sequences.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+* 
+* Version 1.0.11 2011/10/18  
+*    Bug Fix in conv, correlation, partial convolution.  
+* 
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+*    
+* -------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @defgroup PartialConv Partial Convolution    
+ *    
+ * Partial Convolution is equivalent to Convolution except that a subset of the output samples is generated.    
+ * Each function has two additional arguments.    
+ * firstIndex specifies the starting index of the subset of output samples.    
+ * numPoints is the number of output samples to compute.    
+ * The function computes the output in the range    
+ * [firstIndex, ..., firstIndex+numPoints-1].    
+ * The output array pDst contains numPoints values.    
+ *    
+ * The allowable range of output indices is [0 srcALen+srcBLen-2].    
+ * If the requested subset does not fall in this range then the functions return ARM_MATH_ARGUMENT_ERROR.    
+ * Otherwise the functions return ARM_MATH_SUCCESS.    
+ * \note Refer arm_conv_f32() for details on fixed point behavior.   
+ *
+ * 
+ * Fast Versions
+ *
+ * \par 
+ * Fast versions are supported for Q31 and Q15 of partial convolution.  Cycles for Fast versions are less compared to Q31 and Q15 of partial conv and the design requires
+ * the input signals should be scaled down to avoid intermediate overflows.   
+ *
+ *
+ * Opt Versions
+ *
+ * \par 
+ * Opt versions are supported for Q15 and Q7.  Design uses internal scratch buffer for getting good optimisation.
+ * These versions are optimised in cycles and consumes more memory(Scratch memory) compared to Q15 and Q7 versions of partial convolution
+ */
+
+/**    
+ * @addtogroup PartialConv    
+ * @{    
+ */
+
+/**    
+ * @brief Partial convolution of floating-point sequences.    
+ * @param[in]       *pSrcA points to the first input sequence.    
+ * @param[in]       srcALen length of the first input sequence.    
+ * @param[in]       *pSrcB points to the second input sequence.    
+ * @param[in]       srcBLen length of the second input sequence.    
+ * @param[out]      *pDst points to the location where the output result is written.    
+ * @param[in]       firstIndex is the first output sample to start with.    
+ * @param[in]       numPoints is the number of output points to be computed.    
+ * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].    
+ */
+
+arm_status arm_conv_partial_f32(
+  float32_t * pSrcA,
+  uint32_t srcALen,
+  float32_t * pSrcB,
+  uint32_t srcBLen,
+  float32_t * pDst,
+  uint32_t firstIndex,
+  uint32_t numPoints)
+{
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  float32_t *pIn1 = pSrcA;                       /* inputA pointer */
+  float32_t *pIn2 = pSrcB;                       /* inputB pointer */
+  float32_t *pOut = pDst;                        /* output pointer */
+  float32_t *px;                                 /* Intermediate inputA pointer */
+  float32_t *py;                                 /* Intermediate inputB pointer */
+  float32_t *pSrc1, *pSrc2;                      /* Intermediate pointers */
+  float32_t sum, acc0, acc1, acc2, acc3;         /* Accumulator */
+  float32_t x0, x1, x2, x3, c0;                  /* Temporary variables to hold state and coefficient values */
+  uint32_t j, k, count = 0u, blkCnt, check;
+  int32_t blockSize1, blockSize2, blockSize3;    /* loop counters */
+  arm_status status;                             /* status of Partial convolution */
+
+
+  /* Check for range of output samples to be calculated */
+  if((firstIndex + numPoints) > ((srcALen + (srcBLen - 1u))))
+  {
+    /* Set status as ARM_MATH_ARGUMENT_ERROR */
+    status = ARM_MATH_ARGUMENT_ERROR;
+  }
+  else
+  {
+
+    /* The algorithm implementation is based on the lengths of the inputs. */
+    /* srcB is always made to slide across srcA. */
+    /* So srcBLen is always considered as shorter or equal to srcALen */
+    if(srcALen >= srcBLen)
+    {
+      /* Initialization of inputA pointer */
+      pIn1 = pSrcA;
+
+      /* Initialization of inputB pointer */
+      pIn2 = pSrcB;
+    }
+    else
+    {
+      /* Initialization of inputA pointer */
+      pIn1 = pSrcB;
+
+      /* Initialization of inputB pointer */
+      pIn2 = pSrcA;
+
+      /* srcBLen is always considered as shorter or equal to srcALen */
+      j = srcBLen;
+      srcBLen = srcALen;
+      srcALen = j;
+    }
+
+    /* Conditions to check which loopCounter holds    
+     * the first and last indices of the output samples to be calculated. */
+    check = firstIndex + numPoints;
+    blockSize3 = (int32_t) check - (int32_t) srcALen;
+    blockSize3 = (blockSize3 > 0) ? blockSize3 : 0;
+    blockSize1 = ((int32_t) srcBLen - 1) - (int32_t) firstIndex;
+    blockSize1 = (blockSize1 > 0) ? ((check > (srcBLen - 1u)) ? blockSize1 :
+                                     (int32_t) numPoints) : 0;
+    blockSize2 = ((int32_t) check - blockSize3) -
+      (blockSize1 + (int32_t) firstIndex);
+    blockSize2 = (blockSize2 > 0) ? blockSize2 : 0;
+
+    /* conv(x,y) at n = x[n] * y[0] + x[n-1] * y[1] + x[n-2] * y[2] + ...+ x[n-N+1] * y[N -1] */
+    /* The function is internally    
+     * divided into three stages according to the number of multiplications that has to be    
+     * taken place between inputA samples and inputB samples. In the first stage of the    
+     * algorithm, the multiplications increase by one for every iteration.    
+     * In the second stage of the algorithm, srcBLen number of multiplications are done.    
+     * In the third stage of the algorithm, the multiplications decrease by one    
+     * for every iteration. */
+
+    /* Set the output pointer to point to the firstIndex    
+     * of the output sample to be calculated. */
+    pOut = pDst + firstIndex;
+
+    /* --------------------------    
+     * Initializations of stage1    
+     * -------------------------*/
+
+    /* sum = x[0] * y[0]    
+     * sum = x[0] * y[1] + x[1] * y[0]    
+     * ....    
+     * sum = x[0] * y[srcBlen - 1] + x[1] * y[srcBlen - 2] +...+ x[srcBLen - 1] * y[0]    
+     */
+
+    /* In this stage the MAC operations are increased by 1 for every iteration.    
+       The count variable holds the number of MAC operations performed.    
+       Since the partial convolution starts from from firstIndex    
+       Number of Macs to be performed is firstIndex + 1 */
+    count = 1u + firstIndex;
+
+    /* Working pointer of inputA */
+    px = pIn1;
+
+    /* Working pointer of inputB */
+    pSrc1 = pIn2 + firstIndex;
+    py = pSrc1;
+
+    /* ------------------------    
+     * Stage1 process    
+     * ----------------------*/
+
+    /* The first stage starts here */
+    while(blockSize1 > 0)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0.0f;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = count >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      while(k > 0u)
+      {
+        /* x[0] * y[srcBLen - 1] */
+        sum += *px++ * *py--;
+
+        /* x[1] * y[srcBLen - 2] */
+        sum += *px++ * *py--;
+
+        /* x[2] * y[srcBLen - 3] */
+        sum += *px++ * *py--;
+
+        /* x[3] * y[srcBLen - 4] */
+        sum += *px++ * *py--;
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* If the count is not a multiple of 4, compute any remaining MACs here.    
+       ** No loop unrolling is used. */
+      k = count % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum += *px++ * *py--;
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = sum;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      py = ++pSrc1;
+      px = pIn1;
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Decrement the loop counter */
+      blockSize1--;
+    }
+
+    /* --------------------------    
+     * Initializations of stage2    
+     * ------------------------*/
+
+    /* sum = x[0] * y[srcBLen-1] + x[1] * y[srcBLen-2] +...+ x[srcBLen-1] * y[0]    
+     * sum = x[1] * y[srcBLen-1] + x[2] * y[srcBLen-2] +...+ x[srcBLen] * y[0]    
+     * ....    
+     * sum = x[srcALen-srcBLen-2] * y[srcBLen-1] + x[srcALen] * y[srcBLen-2] +...+ x[srcALen-1] * y[0]    
+     */
+
+    /* Working pointer of inputA */
+    px = pIn1;
+
+    /* Working pointer of inputB */
+    pSrc2 = pIn2 + (srcBLen - 1u);
+    py = pSrc2;
+
+    /* count is index by which the pointer pIn1 to be incremented */
+    count = 0u;
+
+    /* -------------------    
+     * Stage2 process    
+     * ------------------*/
+
+    /* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.    
+     * So, to loop unroll over blockSize2,    
+     * srcBLen should be greater than or equal to 4 */
+    if(srcBLen >= 4u)
+    {
+      /* Loop unroll over blockSize2, by 4 */
+      blkCnt = ((uint32_t) blockSize2 >> 2u);
+
+      while(blkCnt > 0u)
+      {
+        /* Set all accumulators to zero */
+        acc0 = 0.0f;
+        acc1 = 0.0f;
+        acc2 = 0.0f;
+        acc3 = 0.0f;
+
+        /* read x[0], x[1], x[2] samples */
+        x0 = *(px++);
+        x1 = *(px++);
+        x2 = *(px++);
+
+        /* Apply loop unrolling and compute 4 MACs simultaneously. */
+        k = srcBLen >> 2u;
+
+        /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+         ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+        do
+        {
+          /* Read y[srcBLen - 1] sample */
+          c0 = *(py--);
+
+          /* Read x[3] sample */
+          x3 = *(px++);
+
+          /* Perform the multiply-accumulate */
+          /* acc0 +=  x[0] * y[srcBLen - 1] */
+          acc0 += x0 * c0;
+
+          /* acc1 +=  x[1] * y[srcBLen - 1] */
+          acc1 += x1 * c0;
+
+          /* acc2 +=  x[2] * y[srcBLen - 1] */
+          acc2 += x2 * c0;
+
+          /* acc3 +=  x[3] * y[srcBLen - 1] */
+          acc3 += x3 * c0;
+
+          /* Read y[srcBLen - 2] sample */
+          c0 = *(py--);
+
+          /* Read x[4] sample */
+          x0 = *(px++);
+
+          /* Perform the multiply-accumulate */
+          /* acc0 +=  x[1] * y[srcBLen - 2] */
+          acc0 += x1 * c0;
+          /* acc1 +=  x[2] * y[srcBLen - 2] */
+          acc1 += x2 * c0;
+          /* acc2 +=  x[3] * y[srcBLen - 2] */
+          acc2 += x3 * c0;
+          /* acc3 +=  x[4] * y[srcBLen - 2] */
+          acc3 += x0 * c0;
+
+          /* Read y[srcBLen - 3] sample */
+          c0 = *(py--);
+
+          /* Read x[5] sample */
+          x1 = *(px++);
+
+          /* Perform the multiply-accumulates */
+          /* acc0 +=  x[2] * y[srcBLen - 3] */
+          acc0 += x2 * c0;
+          /* acc1 +=  x[3] * y[srcBLen - 2] */
+          acc1 += x3 * c0;
+          /* acc2 +=  x[4] * y[srcBLen - 2] */
+          acc2 += x0 * c0;
+          /* acc3 +=  x[5] * y[srcBLen - 2] */
+          acc3 += x1 * c0;
+
+          /* Read y[srcBLen - 4] sample */
+          c0 = *(py--);
+
+          /* Read x[6] sample */
+          x2 = *(px++);
+
+          /* Perform the multiply-accumulates */
+          /* acc0 +=  x[3] * y[srcBLen - 4] */
+          acc0 += x3 * c0;
+          /* acc1 +=  x[4] * y[srcBLen - 4] */
+          acc1 += x0 * c0;
+          /* acc2 +=  x[5] * y[srcBLen - 4] */
+          acc2 += x1 * c0;
+          /* acc3 +=  x[6] * y[srcBLen - 4] */
+          acc3 += x2 * c0;
+
+
+        } while(--k);
+
+        /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.    
+         ** No loop unrolling is used. */
+        k = srcBLen % 0x4u;
+
+        while(k > 0u)
+        {
+          /* Read y[srcBLen - 5] sample */
+          c0 = *(py--);
+
+          /* Read x[7] sample */
+          x3 = *(px++);
+
+          /* Perform the multiply-accumulates */
+          /* acc0 +=  x[4] * y[srcBLen - 5] */
+          acc0 += x0 * c0;
+          /* acc1 +=  x[5] * y[srcBLen - 5] */
+          acc1 += x1 * c0;
+          /* acc2 +=  x[6] * y[srcBLen - 5] */
+          acc2 += x2 * c0;
+          /* acc3 +=  x[7] * y[srcBLen - 5] */
+          acc3 += x3 * c0;
+
+          /* Reuse the present samples for the next MAC */
+          x0 = x1;
+          x1 = x2;
+          x2 = x3;
+
+          /* Decrement the loop counter */
+          k--;
+        }
+
+        /* Store the result in the accumulator in the destination buffer. */
+        *pOut++ = acc0;
+        *pOut++ = acc1;
+        *pOut++ = acc2;
+        *pOut++ = acc3;
+
+        /* Increment the pointer pIn1 index, count by 1 */
+        count += 4u;
+
+        /* Update the inputA and inputB pointers for next MAC calculation */
+        px = pIn1 + count;
+        py = pSrc2;
+
+        /* Decrement the loop counter */
+        blkCnt--;
+      }
+
+      /* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.    
+       ** No loop unrolling is used. */
+      blkCnt = (uint32_t) blockSize2 % 0x4u;
+
+      while(blkCnt > 0u)
+      {
+        /* Accumulator is made zero for every iteration */
+        sum = 0.0f;
+
+        /* Apply loop unrolling and compute 4 MACs simultaneously. */
+        k = srcBLen >> 2u;
+
+        /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+         ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+        while(k > 0u)
+        {
+          /* Perform the multiply-accumulates */
+          sum += *px++ * *py--;
+          sum += *px++ * *py--;
+          sum += *px++ * *py--;
+          sum += *px++ * *py--;
+
+          /* Decrement the loop counter */
+          k--;
+        }
+
+        /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.    
+         ** No loop unrolling is used. */
+        k = srcBLen % 0x4u;
+
+        while(k > 0u)
+        {
+          /* Perform the multiply-accumulate */
+          sum += *px++ * *py--;
+
+          /* Decrement the loop counter */
+          k--;
+        }
+
+        /* Store the result in the accumulator in the destination buffer. */
+        *pOut++ = sum;
+
+        /* Increment the MAC count */
+        count++;
+
+        /* Update the inputA and inputB pointers for next MAC calculation */
+        px = pIn1 + count;
+        py = pSrc2;
+
+        /* Decrement the loop counter */
+        blkCnt--;
+      }
+    }
+    else
+    {
+      /* If the srcBLen is not a multiple of 4,    
+       * the blockSize2 loop cannot be unrolled by 4 */
+      blkCnt = (uint32_t) blockSize2;
+
+      while(blkCnt > 0u)
+      {
+        /* Accumulator is made zero for every iteration */
+        sum = 0.0f;
+
+        /* srcBLen number of MACS should be performed */
+        k = srcBLen;
+
+        while(k > 0u)
+        {
+          /* Perform the multiply-accumulate */
+          sum += *px++ * *py--;
+
+          /* Decrement the loop counter */
+          k--;
+        }
+
+        /* Store the result in the accumulator in the destination buffer. */
+        *pOut++ = sum;
+
+        /* Increment the MAC count */
+        count++;
+
+        /* Update the inputA and inputB pointers for next MAC calculation */
+        px = pIn1 + count;
+        py = pSrc2;
+
+        /* Decrement the loop counter */
+        blkCnt--;
+      }
+    }
+
+
+    /* --------------------------    
+     * Initializations of stage3    
+     * -------------------------*/
+
+    /* sum += x[srcALen-srcBLen+1] * y[srcBLen-1] + x[srcALen-srcBLen+2] * y[srcBLen-2] +...+ x[srcALen-1] * y[1]    
+     * sum += x[srcALen-srcBLen+2] * y[srcBLen-1] + x[srcALen-srcBLen+3] * y[srcBLen-2] +...+ x[srcALen-1] * y[2]    
+     * ....    
+     * sum +=  x[srcALen-2] * y[srcBLen-1] + x[srcALen-1] * y[srcBLen-2]    
+     * sum +=  x[srcALen-1] * y[srcBLen-1]    
+     */
+
+    /* In this stage the MAC operations are decreased by 1 for every iteration.    
+       The count variable holds the number of MAC operations performed */
+    count = srcBLen - 1u;
+
+    /* Working pointer of inputA */
+    pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
+    px = pSrc1;
+
+    /* Working pointer of inputB */
+    pSrc2 = pIn2 + (srcBLen - 1u);
+    py = pSrc2;
+
+    while(blockSize3 > 0)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0.0f;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = count >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      while(k > 0u)
+      {
+        /* sum += x[srcALen - srcBLen + 1] * y[srcBLen - 1] */
+        sum += *px++ * *py--;
+
+        /* sum += x[srcALen - srcBLen + 2] * y[srcBLen - 2] */
+        sum += *px++ * *py--;
+
+        /* sum += x[srcALen - srcBLen + 3] * y[srcBLen - 3] */
+        sum += *px++ * *py--;
+
+        /* sum += x[srcALen - srcBLen + 4] * y[srcBLen - 4] */
+        sum += *px++ * *py--;
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* If the count is not a multiple of 4, compute any remaining MACs here.    
+       ** No loop unrolling is used. */
+      k = count % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        /* sum +=  x[srcALen-1] * y[srcBLen-1] */
+        sum += *px++ * *py--;
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = sum;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = ++pSrc1;
+      py = pSrc2;
+
+      /* Decrement the MAC count */
+      count--;
+
+      /* Decrement the loop counter */
+      blockSize3--;
+
+    }
+
+    /* set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+  }
+
+  /* Return to application */
+  return (status);
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  float32_t *pIn1 = pSrcA;                       /* inputA pointer */
+  float32_t *pIn2 = pSrcB;                       /* inputB pointer */
+  float32_t sum;                                 /* Accumulator */
+  uint32_t i, j;                                 /* loop counters */
+  arm_status status;                             /* status of Partial convolution */
+
+  /* Check for range of output samples to be calculated */
+  if((firstIndex + numPoints) > ((srcALen + (srcBLen - 1u))))
+  {
+    /* Set status as ARM_ARGUMENT_ERROR */
+    status = ARM_MATH_ARGUMENT_ERROR;
+  }
+  else
+  {
+    /* Loop to calculate convolution for output length number of values */
+    for (i = firstIndex; i <= (firstIndex + numPoints - 1); i++)
+    {
+      /* Initialize sum with zero to carry on MAC operations */
+      sum = 0.0f;
+
+      /* Loop to perform MAC operations according to convolution equation */
+      for (j = 0u; j <= i; j++)
+      {
+        /* Check the array limitations for inputs */
+        if((((i - j) < srcBLen) && (j < srcALen)))
+        {
+          /* z[i] += x[i-j] * y[j] */
+          sum += pIn1[j] * pIn2[i - j];
+        }
+      }
+      /* Store the output in the destination buffer */
+      pDst[i] = sum;
+    }
+    /* set status as ARM_SUCCESS as there are no argument errors */
+    status = ARM_MATH_SUCCESS;
+  }
+  return (status);
+
+#endif /*   #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of PartialConv group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_fast_opt_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_fast_opt_q15.c
new file mode 100644
index 0000000000..25b3ba8c30
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_fast_opt_q15.c
@@ -0,0 +1,763 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_conv_partial_fast_opt_q15.c    
+*    
+* Description:	Fast Q15 Partial convolution.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+* 
+* Version 1.0.11 2011/10/18  
+*    Bug Fix in conv, correlation, partial convolution.  
+* 
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup PartialConv    
+ * @{    
+ */
+
+/**    
+ * @brief Partial convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4.    
+ * @param[in]       *pSrcA points to the first input sequence.    
+ * @param[in]       srcALen length of the first input sequence.    
+ * @param[in]       *pSrcB points to the second input sequence.    
+ * @param[in]       srcBLen length of the second input sequence.    
+ * @param[out]      *pDst points to the location where the output result is written.    
+ * @param[in]       firstIndex is the first output sample to start with.    
+ * @param[in]       numPoints is the number of output points to be computed.    
+ * @param[in]       *pScratch1 points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.   
+ * @param[in]       *pScratch2 points to scratch buffer of size min(srcALen, srcBLen).   
+ * @return Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].    
+ *    
+ * See arm_conv_partial_q15() for a slower implementation of this function which uses a 64-bit accumulator to avoid wrap around distortion.    
+ *    
+ * \par Restrictions    
+ *  If the silicon does not support unaligned memory access enable the macro UNALIGNED_SUPPORT_DISABLE    
+ *	In this case input, output, scratch1 and scratch2 buffers should be aligned by 32-bit    
+ *     
+ */
+
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+arm_status arm_conv_partial_fast_opt_q15(
+  q15_t * pSrcA,
+  uint32_t srcALen,
+  q15_t * pSrcB,
+  uint32_t srcBLen,
+  q15_t * pDst,
+  uint32_t firstIndex,
+  uint32_t numPoints,
+  q15_t * pScratch1,
+  q15_t * pScratch2)
+{
+
+  q15_t *pOut = pDst;                            /* output pointer */
+  q15_t *pScr1 = pScratch1;                      /* Temporary pointer for scratch1 */
+  q15_t *pScr2 = pScratch2;                      /* Temporary pointer for scratch1 */
+  q31_t acc0, acc1, acc2, acc3;                  /* Accumulator */
+  q31_t x1, x2, x3;                              /* Temporary variables to hold state and coefficient values */
+  q31_t y1, y2;                                  /* State variables */
+  q15_t *pIn1;                                   /* inputA pointer */
+  q15_t *pIn2;                                   /* inputB pointer */
+  q15_t *px;                                     /* Intermediate inputA pointer  */
+  q15_t *py;                                     /* Intermediate inputB pointer  */
+  uint32_t j, k, blkCnt;                         /* loop counter */
+  arm_status status;
+
+  uint32_t tapCnt;                               /* loop count */
+
+  /* Check for range of output samples to be calculated */
+  if((firstIndex + numPoints) > ((srcALen + (srcBLen - 1u))))
+  {
+    /* Set status as ARM_MATH_ARGUMENT_ERROR */
+    status = ARM_MATH_ARGUMENT_ERROR;
+  }
+  else
+  {
+
+    /* The algorithm implementation is based on the lengths of the inputs. */
+    /* srcB is always made to slide across srcA. */
+    /* So srcBLen is always considered as shorter or equal to srcALen */
+    if(srcALen >= srcBLen)
+    {
+      /* Initialization of inputA pointer */
+      pIn1 = pSrcA;
+
+      /* Initialization of inputB pointer */
+      pIn2 = pSrcB;
+    }
+    else
+    {
+      /* Initialization of inputA pointer */
+      pIn1 = pSrcB;
+
+      /* Initialization of inputB pointer */
+      pIn2 = pSrcA;
+
+      /* srcBLen is always considered as shorter or equal to srcALen */
+      j = srcBLen;
+      srcBLen = srcALen;
+      srcALen = j;
+    }
+
+    /* Temporary pointer for scratch2 */
+    py = pScratch2;
+
+    /* pointer to take end of scratch2 buffer */
+    pScr2 = pScratch2 + srcBLen - 1;
+
+    /* points to smaller length sequence */
+    px = pIn2;
+
+    /* Apply loop unrolling and do 4 Copies simultaneously. */
+    k = srcBLen >> 2u;
+
+    /* First part of the processing with loop unrolling copies 4 data points at a time.       
+     ** a second loop below copies for the remaining 1 to 3 samples. */
+
+    /* Copy smaller length input sequence in reverse order into second scratch buffer */
+    while(k > 0u)
+    {
+      /* copy second buffer in reversal manner */
+      *pScr2-- = *px++;
+      *pScr2-- = *px++;
+      *pScr2-- = *px++;
+      *pScr2-- = *px++;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, copy remaining samples here.       
+     ** No loop unrolling is used. */
+    k = srcBLen % 0x4u;
+
+    while(k > 0u)
+    {
+      /* copy second buffer in reversal manner for remaining samples */
+      *pScr2-- = *px++;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Initialze temporary scratch pointer */
+    pScr1 = pScratch1;
+
+    /* Assuming scratch1 buffer is aligned by 32-bit */
+    /* Fill (srcBLen - 1u) zeros in scratch buffer */
+    arm_fill_q15(0, pScr1, (srcBLen - 1u));
+
+    /* Update temporary scratch pointer */
+    pScr1 += (srcBLen - 1u);
+
+    /* Copy bigger length sequence(srcALen) samples in scratch1 buffer */
+
+    /* Copy (srcALen) samples in scratch buffer */
+    arm_copy_q15(pIn1, pScr1, srcALen);
+
+    /* Update pointers */
+    pScr1 += srcALen;
+
+    /* Fill (srcBLen - 1u) zeros at end of scratch buffer */
+    arm_fill_q15(0, pScr1, (srcBLen - 1u));
+
+    /* Update pointer */
+    pScr1 += (srcBLen - 1u);
+
+    /* Initialization of pIn2 pointer */
+    pIn2 = py;
+
+    pScratch1 += firstIndex;
+
+    pOut = pDst + firstIndex;
+
+    /* First part of the processing with loop unrolling process 4 data points at a time.       
+     ** a second loop below process for the remaining 1 to 3 samples. */
+
+    /* Actual convolution process starts here */
+    blkCnt = (numPoints) >> 2;
+
+    while(blkCnt > 0)
+    {
+      /* Initialze temporary scratch pointer as scratch1 */
+      pScr1 = pScratch1;
+
+      /* Clear Accumlators */
+      acc0 = 0;
+      acc1 = 0;
+      acc2 = 0;
+      acc3 = 0;
+
+      /* Read two samples from scratch1 buffer */
+      x1 = *__SIMD32(pScr1)++;
+
+      /* Read next two samples from scratch1 buffer */
+      x2 = *__SIMD32(pScr1)++;
+
+      tapCnt = (srcBLen) >> 2u;
+
+      while(tapCnt > 0u)
+      {
+
+        /* Read four samples from smaller buffer */
+        y1 = _SIMD32_OFFSET(pIn2);
+        y2 = _SIMD32_OFFSET(pIn2 + 2u);
+
+        /* multiply and accumlate */
+        acc0 = __SMLAD(x1, y1, acc0);
+        acc2 = __SMLAD(x2, y1, acc2);
+
+        /* pack input data */
+#ifndef ARM_MATH_BIG_ENDIAN
+        x3 = __PKHBT(x2, x1, 0);
+#else
+        x3 = __PKHBT(x1, x2, 0);
+#endif
+
+        /* multiply and accumlate */
+        acc1 = __SMLADX(x3, y1, acc1);
+
+        /* Read next two samples from scratch1 buffer */
+        x1 = _SIMD32_OFFSET(pScr1);
+
+        /* multiply and accumlate */
+        acc0 = __SMLAD(x2, y2, acc0);
+
+        acc2 = __SMLAD(x1, y2, acc2);
+
+        /* pack input data */
+#ifndef ARM_MATH_BIG_ENDIAN
+        x3 = __PKHBT(x1, x2, 0);
+#else
+        x3 = __PKHBT(x2, x1, 0);
+#endif
+
+        acc3 = __SMLADX(x3, y1, acc3);
+        acc1 = __SMLADX(x3, y2, acc1);
+
+        x2 = _SIMD32_OFFSET(pScr1 + 2u);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+        x3 = __PKHBT(x2, x1, 0);
+#else
+        x3 = __PKHBT(x1, x2, 0);
+#endif
+
+        acc3 = __SMLADX(x3, y2, acc3);
+
+        /* update scratch pointers */
+        pIn2 += 4u;
+        pScr1 += 4u;
+
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      /* Update scratch pointer for remaining samples of smaller length sequence */
+      pScr1 -= 4u;
+
+      /* apply same above for remaining samples of smaller length sequence */
+      tapCnt = (srcBLen) & 3u;
+
+      while(tapCnt > 0u)
+      {
+
+        /* accumlate the results */
+        acc0 += (*pScr1++ * *pIn2);
+        acc1 += (*pScr1++ * *pIn2);
+        acc2 += (*pScr1++ * *pIn2);
+        acc3 += (*pScr1++ * *pIn2++);
+
+        pScr1 -= 3u;
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      blkCnt--;
+
+
+      /* Store the results in the accumulators in the destination buffer. */
+
+#ifndef  ARM_MATH_BIG_ENDIAN
+
+      *__SIMD32(pOut)++ =
+        __PKHBT(__SSAT((acc0 >> 15), 16), __SSAT((acc1 >> 15), 16), 16);
+      *__SIMD32(pOut)++ =
+        __PKHBT(__SSAT((acc2 >> 15), 16), __SSAT((acc3 >> 15), 16), 16);
+
+#else
+
+      *__SIMD32(pOut)++ =
+        __PKHBT(__SSAT((acc1 >> 15), 16), __SSAT((acc0 >> 15), 16), 16);
+      *__SIMD32(pOut)++ =
+        __PKHBT(__SSAT((acc3 >> 15), 16), __SSAT((acc2 >> 15), 16), 16);
+
+#endif /*      #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+      /* Initialization of inputB pointer */
+      pIn2 = py;
+
+      pScratch1 += 4u;
+
+    }
+
+
+    blkCnt = numPoints & 0x3;
+
+    /* Calculate convolution for remaining samples of Bigger length sequence */
+    while(blkCnt > 0)
+    {
+      /* Initialze temporary scratch pointer as scratch1 */
+      pScr1 = pScratch1;
+
+      /* Clear Accumlators */
+      acc0 = 0;
+
+      tapCnt = (srcBLen) >> 1u;
+
+      while(tapCnt > 0u)
+      {
+
+        /* Read next two samples from scratch1 buffer */
+        x1 = *__SIMD32(pScr1)++;
+
+        /* Read two samples from smaller buffer */
+        y1 = *__SIMD32(pIn2)++;
+
+        acc0 = __SMLAD(x1, y1, acc0);
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      tapCnt = (srcBLen) & 1u;
+
+      /* apply same above for remaining samples of smaller length sequence */
+      while(tapCnt > 0u)
+      {
+
+        /* accumlate the results */
+        acc0 += (*pScr1++ * *pIn2++);
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      blkCnt--;
+
+      /* The result is in 2.30 format.  Convert to 1.15 with saturation.       
+       ** Then store the output in the destination buffer. */
+      *pOut++ = (q15_t) (__SSAT((acc0 >> 15), 16));
+
+      /* Initialization of inputB pointer */
+      pIn2 = py;
+
+      pScratch1 += 1u;
+
+    }
+    /* set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+  }
+  /* Return to application */
+  return (status);
+}
+
+#else
+
+arm_status arm_conv_partial_fast_opt_q15(
+  q15_t * pSrcA,
+  uint32_t srcALen,
+  q15_t * pSrcB,
+  uint32_t srcBLen,
+  q15_t * pDst,
+  uint32_t firstIndex,
+  uint32_t numPoints,
+  q15_t * pScratch1,
+  q15_t * pScratch2)
+{
+
+  q15_t *pOut = pDst;                            /* output pointer */
+  q15_t *pScr1 = pScratch1;                      /* Temporary pointer for scratch1 */
+  q15_t *pScr2 = pScratch2;                      /* Temporary pointer for scratch1 */
+  q31_t acc0, acc1, acc2, acc3;                  /* Accumulator */
+  q15_t *pIn1;                                   /* inputA pointer */
+  q15_t *pIn2;                                   /* inputB pointer */
+  q15_t *px;                                     /* Intermediate inputA pointer  */
+  q15_t *py;                                     /* Intermediate inputB pointer  */
+  uint32_t j, k, blkCnt;                         /* loop counter */
+  arm_status status;                             /* Status variable */
+  uint32_t tapCnt;                               /* loop count */
+  q15_t x10, x11, x20, x21;                      /* Temporary variables to hold srcA buffer */
+  q15_t y10, y11;                                /* Temporary variables to hold srcB buffer */
+
+
+  /* Check for range of output samples to be calculated */
+  if((firstIndex + numPoints) > ((srcALen + (srcBLen - 1u))))
+  {
+    /* Set status as ARM_MATH_ARGUMENT_ERROR */
+    status = ARM_MATH_ARGUMENT_ERROR;
+  }
+  else
+  {
+
+    /* The algorithm implementation is based on the lengths of the inputs. */
+    /* srcB is always made to slide across srcA. */
+    /* So srcBLen is always considered as shorter or equal to srcALen */
+    if(srcALen >= srcBLen)
+    {
+      /* Initialization of inputA pointer */
+      pIn1 = pSrcA;
+
+      /* Initialization of inputB pointer */
+      pIn2 = pSrcB;
+    }
+    else
+    {
+      /* Initialization of inputA pointer */
+      pIn1 = pSrcB;
+
+      /* Initialization of inputB pointer */
+      pIn2 = pSrcA;
+
+      /* srcBLen is always considered as shorter or equal to srcALen */
+      j = srcBLen;
+      srcBLen = srcALen;
+      srcALen = j;
+    }
+
+    /* Temporary pointer for scratch2 */
+    py = pScratch2;
+
+    /* pointer to take end of scratch2 buffer */
+    pScr2 = pScratch2 + srcBLen - 1;
+
+    /* points to smaller length sequence */
+    px = pIn2;
+
+    /* Apply loop unrolling and do 4 Copies simultaneously. */
+    k = srcBLen >> 2u;
+
+    /* First part of the processing with loop unrolling copies 4 data points at a time.       
+     ** a second loop below copies for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* copy second buffer in reversal manner */
+      *pScr2-- = *px++;
+      *pScr2-- = *px++;
+      *pScr2-- = *px++;
+      *pScr2-- = *px++;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, copy remaining samples here.       
+     ** No loop unrolling is used. */
+    k = srcBLen % 0x4u;
+
+    while(k > 0u)
+    {
+      /* copy second buffer in reversal manner for remaining samples */
+      *pScr2-- = *px++;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Initialze temporary scratch pointer */
+    pScr1 = pScratch1;
+
+    /* Fill (srcBLen - 1u) zeros in scratch buffer */
+    arm_fill_q15(0, pScr1, (srcBLen - 1u));
+
+    /* Update temporary scratch pointer */
+    pScr1 += (srcBLen - 1u);
+
+    /* Copy bigger length sequence(srcALen) samples in scratch1 buffer */
+
+
+    /* Apply loop unrolling and do 4 Copies simultaneously. */
+    k = srcALen >> 2u;
+
+    /* First part of the processing with loop unrolling copies 4 data points at a time.       
+     ** a second loop below copies for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* copy second buffer in reversal manner */
+      *pScr1++ = *pIn1++;
+      *pScr1++ = *pIn1++;
+      *pScr1++ = *pIn1++;
+      *pScr1++ = *pIn1++;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, copy remaining samples here.       
+     ** No loop unrolling is used. */
+    k = srcALen % 0x4u;
+
+    while(k > 0u)
+    {
+      /* copy second buffer in reversal manner for remaining samples */
+      *pScr1++ = *pIn1++;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+
+    /* Apply loop unrolling and do 4 Copies simultaneously. */
+    k = (srcBLen - 1u) >> 2u;
+
+    /* First part of the processing with loop unrolling copies 4 data points at a time.       
+     ** a second loop below copies for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* copy second buffer in reversal manner */
+      *pScr1++ = 0;
+      *pScr1++ = 0;
+      *pScr1++ = 0;
+      *pScr1++ = 0;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, copy remaining samples here.       
+     ** No loop unrolling is used. */
+    k = (srcBLen - 1u) % 0x4u;
+
+    while(k > 0u)
+    {
+      /* copy second buffer in reversal manner for remaining samples */
+      *pScr1++ = 0;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+
+    /* Initialization of pIn2 pointer */
+    pIn2 = py;
+
+    pScratch1 += firstIndex;
+
+    pOut = pDst + firstIndex;
+
+    /* Actual convolution process starts here */
+    blkCnt = (numPoints) >> 2;
+
+    while(blkCnt > 0)
+    {
+      /* Initialze temporary scratch pointer as scratch1 */
+      pScr1 = pScratch1;
+
+      /* Clear Accumlators */
+      acc0 = 0;
+      acc1 = 0;
+      acc2 = 0;
+      acc3 = 0;
+
+      /* Read two samples from scratch1 buffer */
+      x10 = *pScr1++;
+      x11 = *pScr1++;
+
+      /* Read next two samples from scratch1 buffer */
+      x20 = *pScr1++;
+      x21 = *pScr1++;
+
+      tapCnt = (srcBLen) >> 2u;
+
+      while(tapCnt > 0u)
+      {
+
+        /* Read two samples from smaller buffer */
+        y10 = *pIn2;
+        y11 = *(pIn2 + 1u);
+
+        /* multiply and accumlate */
+        acc0 += (q31_t) x10 *y10;
+        acc0 += (q31_t) x11 *y11;
+        acc2 += (q31_t) x20 *y10;
+        acc2 += (q31_t) x21 *y11;
+
+        /* multiply and accumlate */
+        acc1 += (q31_t) x11 *y10;
+        acc1 += (q31_t) x20 *y11;
+
+        /* Read next two samples from scratch1 buffer */
+        x10 = *pScr1;
+        x11 = *(pScr1 + 1u);
+
+        /* multiply and accumlate */
+        acc3 += (q31_t) x21 *y10;
+        acc3 += (q31_t) x10 *y11;
+
+        /* Read next two samples from scratch2 buffer */
+        y10 = *(pIn2 + 2u);
+        y11 = *(pIn2 + 3u);
+
+        /* multiply and accumlate */
+        acc0 += (q31_t) x20 *y10;
+        acc0 += (q31_t) x21 *y11;
+        acc2 += (q31_t) x10 *y10;
+        acc2 += (q31_t) x11 *y11;
+        acc1 += (q31_t) x21 *y10;
+        acc1 += (q31_t) x10 *y11;
+
+        /* Read next two samples from scratch1 buffer */
+        x20 = *(pScr1 + 2);
+        x21 = *(pScr1 + 3);
+
+        /* multiply and accumlate */
+        acc3 += (q31_t) x11 *y10;
+        acc3 += (q31_t) x20 *y11;
+
+        /* update scratch pointers */
+        pIn2 += 4u;
+        pScr1 += 4u;
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      /* Update scratch pointer for remaining samples of smaller length sequence */
+      pScr1 -= 4u;
+
+      /* apply same above for remaining samples of smaller length sequence */
+      tapCnt = (srcBLen) & 3u;
+
+      while(tapCnt > 0u)
+      {
+        /* accumlate the results */
+        acc0 += (*pScr1++ * *pIn2);
+        acc1 += (*pScr1++ * *pIn2);
+        acc2 += (*pScr1++ * *pIn2);
+        acc3 += (*pScr1++ * *pIn2++);
+
+        pScr1 -= 3u;
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      blkCnt--;
+
+
+      /* Store the results in the accumulators in the destination buffer. */
+      *pOut++ = __SSAT((acc0 >> 15), 16);
+      *pOut++ = __SSAT((acc1 >> 15), 16);
+      *pOut++ = __SSAT((acc2 >> 15), 16);
+      *pOut++ = __SSAT((acc3 >> 15), 16);
+
+      /* Initialization of inputB pointer */
+      pIn2 = py;
+
+      pScratch1 += 4u;
+
+    }
+
+
+    blkCnt = numPoints & 0x3;
+
+    /* Calculate convolution for remaining samples of Bigger length sequence */
+    while(blkCnt > 0)
+    {
+      /* Initialze temporary scratch pointer as scratch1 */
+      pScr1 = pScratch1;
+
+      /* Clear Accumlators */
+      acc0 = 0;
+
+      tapCnt = (srcBLen) >> 1u;
+
+      while(tapCnt > 0u)
+      {
+
+        /* Read next two samples from scratch1 buffer */
+        x10 = *pScr1++;
+        x11 = *pScr1++;
+
+        /* Read two samples from smaller buffer */
+        y10 = *pIn2++;
+        y11 = *pIn2++;
+
+        /* multiply and accumlate */
+        acc0 += (q31_t) x10 *y10;
+        acc0 += (q31_t) x11 *y11;
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      tapCnt = (srcBLen) & 1u;
+
+      /* apply same above for remaining samples of smaller length sequence */
+      while(tapCnt > 0u)
+      {
+
+        /* accumlate the results */
+        acc0 += (*pScr1++ * *pIn2++);
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      blkCnt--;
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q15_t) (__SSAT((acc0 >> 15), 16));
+
+      /* Initialization of inputB pointer */
+      pIn2 = py;
+
+      pScratch1 += 1u;
+
+    }
+
+    /* set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+
+  }
+
+  /* Return to application */
+  return (status);
+}
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+/**    
+ * @} end of PartialConv group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_fast_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_fast_q15.c
new file mode 100644
index 0000000000..98216bb6ab
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_fast_q15.c
@@ -0,0 +1,1473 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010 ARM Limited. All rights reserved.   
+*   
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*   
+* Project: 	    CMSIS DSP Library   
+* Title:		arm_conv_partial_fast_q15.c   
+*   
+* Description:	Fast Q15 Partial convolution.   
+*   
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+* 
+* Version 1.0.11 2011/10/18 
+*    Bug Fix in conv, correlation, partial convolution. 
+*
+* Version 1.0.10 2011/7/15 
+*    Big Endian support added and Merged M0 and M3/M4 Source code.  
+*   
+* Version 1.0.3 2010/11/29  
+*    Re-organized the CMSIS folders and updated documentation.   
+*    
+* Version 1.0.2 2010/11/11   
+*    Documentation updated.    
+*   
+* Version 1.0.1 2010/10/05    
+*    Production release and review comments incorporated.   
+*   
+* Version 1.0.0 2010/09/20    
+*    Production release and review comments incorporated.   
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**   
+ * @ingroup groupFilters   
+ */
+
+/**   
+ * @addtogroup PartialConv   
+ * @{   
+ */
+
+/**   
+ * @brief Partial convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4.   
+ * @param[in]       *pSrcA points to the first input sequence.   
+ * @param[in]       srcALen length of the first input sequence.   
+ * @param[in]       *pSrcB points to the second input sequence.   
+ * @param[in]       srcBLen length of the second input sequence.   
+ * @param[out]      *pDst points to the location where the output result is written.   
+ * @param[in]       firstIndex is the first output sample to start with.   
+ * @param[in]       numPoints is the number of output points to be computed.   
+ * @return Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].   
+ *   
+ * See arm_conv_partial_q15() for a slower implementation of this function which uses a 64-bit accumulator to avoid wrap around distortion.   
+ */
+
+
+arm_status arm_conv_partial_fast_q15(
+  q15_t * pSrcA,
+  uint32_t srcALen,
+  q15_t * pSrcB,
+  uint32_t srcBLen,
+  q15_t * pDst,
+  uint32_t firstIndex,
+  uint32_t numPoints)
+{
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+  q15_t *pIn1;                                   /* inputA pointer               */
+  q15_t *pIn2;                                   /* inputB pointer               */
+  q15_t *pOut = pDst;                            /* output pointer               */
+  q31_t sum, acc0, acc1, acc2, acc3;             /* Accumulator                  */
+  q15_t *px;                                     /* Intermediate inputA pointer  */
+  q15_t *py;                                     /* Intermediate inputB pointer  */
+  q15_t *pSrc1, *pSrc2;                          /* Intermediate pointers        */
+  q31_t x0, x1, x2, x3, c0;
+  uint32_t j, k, count, check, blkCnt;
+  int32_t blockSize1, blockSize2, blockSize3;    /* loop counters                 */
+  arm_status status;                             /* status of Partial convolution */
+
+  /* Check for range of output samples to be calculated */
+  if((firstIndex + numPoints) > ((srcALen + (srcBLen - 1u))))
+  {
+    /* Set status as ARM_MATH_ARGUMENT_ERROR */
+    status = ARM_MATH_ARGUMENT_ERROR;
+  }
+  else
+  {
+
+    /* The algorithm implementation is based on the lengths of the inputs. */
+    /* srcB is always made to slide across srcA. */
+    /* So srcBLen is always considered as shorter or equal to srcALen */
+    if(srcALen >=srcBLen)
+    {
+      /* Initialization of inputA pointer */
+      pIn1 = pSrcA;
+
+      /* Initialization of inputB pointer */
+      pIn2 = pSrcB;
+    }
+    else
+    {
+      /* Initialization of inputA pointer */
+      pIn1 = pSrcB;
+
+      /* Initialization of inputB pointer */
+      pIn2 = pSrcA;
+
+      /* srcBLen is always considered as shorter or equal to srcALen */
+      j = srcBLen;
+      srcBLen = srcALen;
+      srcALen = j;
+    }
+
+    /* Conditions to check which loopCounter holds   
+     * the first and last indices of the output samples to be calculated. */
+    check = firstIndex + numPoints;
+    blockSize3 = ((int32_t) check - (int32_t) srcALen);
+    blockSize3 = (blockSize3 > 0) ? blockSize3 : 0;
+    blockSize1 = (((int32_t) srcBLen - 1) - (int32_t) firstIndex);
+    blockSize1 = (blockSize1 > 0) ? ((check > (srcBLen - 1u)) ? blockSize1 :
+                                     (int32_t) numPoints) : 0;
+    blockSize2 = (int32_t) check - ((blockSize3 + blockSize1) +
+                                    (int32_t) firstIndex);
+    blockSize2 = (blockSize2 > 0) ? blockSize2 : 0;
+
+    /* conv(x,y) at n = x[n] * y[0] + x[n-1] * y[1] + x[n-2] * y[2] + ...+ x[n-N+1] * y[N -1] */
+    /* The function is internally   
+     * divided into three stages according to the number of multiplications that has to be   
+     * taken place between inputA samples and inputB samples. In the first stage of the   
+     * algorithm, the multiplications increase by one for every iteration.   
+     * In the second stage of the algorithm, srcBLen number of multiplications are done.   
+     * In the third stage of the algorithm, the multiplications decrease by one   
+     * for every iteration. */
+
+    /* Set the output pointer to point to the firstIndex   
+     * of the output sample to be calculated. */
+    pOut = pDst + firstIndex;
+
+    /* --------------------------   
+     * Initializations of stage1   
+     * -------------------------*/
+
+    /* sum = x[0] * y[0]   
+     * sum = x[0] * y[1] + x[1] * y[0]   
+     * ....   
+     * sum = x[0] * y[srcBlen - 1] + x[1] * y[srcBlen - 2] +...+ x[srcBLen - 1] * y[0]   
+     */
+
+    /* In this stage the MAC operations are increased by 1 for every iteration.   
+       The count variable holds the number of MAC operations performed.   
+       Since the partial convolution starts from firstIndex   
+       Number of Macs to be performed is firstIndex + 1 */
+    count = 1u + firstIndex;
+
+    /* Working pointer of inputA */
+    px = pIn1;
+
+    /* Working pointer of inputB */
+    pSrc2 = pIn2 + firstIndex;
+    py = pSrc2;
+
+    /* ------------------------   
+     * Stage1 process   
+     * ----------------------*/
+
+    /* For loop unrolling by 4, this stage is divided into two. */
+    /* First part of this stage computes the MAC operations less than 4 */
+    /* Second part of this stage computes the MAC operations greater than or equal to 4 */
+
+    /* The first part of the stage starts here */
+    while((count < 4u) && (blockSize1 > 0))
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Loop over number of MAC operations between   
+       * inputA samples and inputB samples */
+      k = count;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum = __SMLAD(*px++, *py--, sum);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q15_t) (sum >> 15);
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      py = ++pSrc2;
+      px = pIn1;
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Decrement the loop counter */
+      blockSize1--;
+    }
+
+    /* The second part of the stage starts here */
+    /* The internal loop, over count, is unrolled by 4 */
+    /* To, read the last two inputB samples using SIMD:   
+     * y[srcBLen] and y[srcBLen-1] coefficients, py is decremented by 1 */
+    py = py - 1;
+
+    while(blockSize1 > 0)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = count >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        /* x[0], x[1] are multiplied with y[srcBLen - 1], y[srcBLen - 2] respectively */
+        sum = __SMLADX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
+        /* x[2], x[3] are multiplied with y[srcBLen - 3], y[srcBLen - 4] respectively */
+        sum = __SMLADX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* For the next MAC operations, the pointer py is used without SIMD   
+       * So, py is incremented by 1 */
+      py = py + 1u;
+
+      /* If the count is not a multiple of 4, compute any remaining MACs here.   
+       ** No loop unrolling is used. */
+      k = count % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum = __SMLAD(*px++, *py--, sum);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q15_t) (sum >> 15);
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      py = ++pSrc2 - 1u;
+      px = pIn1;
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Decrement the loop counter */
+      blockSize1--;
+    }
+
+    /* --------------------------   
+     * Initializations of stage2   
+     * ------------------------*/
+
+    /* sum = x[0] * y[srcBLen-1] + x[1] * y[srcBLen-2] +...+ x[srcBLen-1] * y[0]   
+     * sum = x[1] * y[srcBLen-1] + x[2] * y[srcBLen-2] +...+ x[srcBLen] * y[0]   
+     * ....   
+     * sum = x[srcALen-srcBLen-2] * y[srcBLen-1] + x[srcALen] * y[srcBLen-2] +...+ x[srcALen-1] * y[0]   
+     */
+
+    /* Working pointer of inputA */
+    px = pIn1;
+
+    /* Working pointer of inputB */
+    pSrc2 = pIn2 + (srcBLen - 1u);
+    py = pSrc2;
+
+    /* count is the index by which the pointer pIn1 to be incremented */
+    count = 0u;
+
+
+    /* --------------------   
+     * Stage2 process   
+     * -------------------*/
+
+    /* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.   
+     * So, to loop unroll over blockSize2,   
+     * srcBLen should be greater than or equal to 4 */
+    if(srcBLen >= 4u)
+    {
+      /* Loop unroll over blockSize2, by 4 */
+      blkCnt = ((uint32_t) blockSize2 >> 2u);
+
+      while(blkCnt > 0u)
+      {
+      py = py - 1u;
+
+        /* Set all accumulators to zero */
+        acc0 = 0;
+        acc1 = 0;
+        acc2 = 0;
+        acc3 = 0;
+
+
+        /* read x[0], x[1] samples */
+      x0 = *__SIMD32(px);
+        /* read x[1], x[2] samples */
+      x1 = _SIMD32_OFFSET(px+1);
+	  px+= 2u;
+
+
+        /* Apply loop unrolling and compute 4 MACs simultaneously. */
+        k = srcBLen >> 2u;
+
+        /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+         ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+        do
+        {
+          /* Read the last two inputB samples using SIMD:   
+           * y[srcBLen - 1] and y[srcBLen - 2] */
+        c0 = *__SIMD32(py)--;
+
+          /* acc0 +=  x[0] * y[srcBLen - 1] + x[1] * y[srcBLen - 2] */
+          acc0 = __SMLADX(x0, c0, acc0);
+
+          /* acc1 +=  x[1] * y[srcBLen - 1] + x[2] * y[srcBLen - 2] */
+          acc1 = __SMLADX(x1, c0, acc1);
+
+          /* Read x[2], x[3] */
+        x2 = *__SIMD32(px);
+
+          /* Read x[3], x[4] */
+        x3 = _SIMD32_OFFSET(px+1);
+
+          /* acc2 +=  x[2] * y[srcBLen - 1] + x[3] * y[srcBLen - 2] */
+          acc2 = __SMLADX(x2, c0, acc2);
+
+          /* acc3 +=  x[3] * y[srcBLen - 1] + x[4] * y[srcBLen - 2] */
+          acc3 = __SMLADX(x3, c0, acc3);
+
+          /* Read y[srcBLen - 3] and y[srcBLen - 4] */
+        c0 = *__SIMD32(py)--;
+
+          /* acc0 +=  x[2] * y[srcBLen - 3] + x[3] * y[srcBLen - 4] */
+          acc0 = __SMLADX(x2, c0, acc0);
+
+          /* acc1 +=  x[3] * y[srcBLen - 3] + x[4] * y[srcBLen - 4] */
+          acc1 = __SMLADX(x3, c0, acc1);
+
+          /* Read x[4], x[5] */
+        x0 = _SIMD32_OFFSET(px+2);
+
+          /* Read x[5], x[6] */
+        x1 = _SIMD32_OFFSET(px+3);
+		px += 4u;
+
+          /* acc2 +=  x[4] * y[srcBLen - 3] + x[5] * y[srcBLen - 4] */
+          acc2 = __SMLADX(x0, c0, acc2);
+
+          /* acc3 +=  x[5] * y[srcBLen - 3] + x[6] * y[srcBLen - 4] */
+          acc3 = __SMLADX(x1, c0, acc3);
+
+        } while(--k);
+
+        /* For the next MAC operations, SIMD is not used   
+         * So, the 16 bit pointer if inputB, py is updated */
+
+        /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.   
+         ** No loop unrolling is used. */
+        k = srcBLen % 0x4u;
+
+        if(k == 1u)
+        {
+          /* Read y[srcBLen - 5] */
+        c0 = *(py+1);
+#ifdef  ARM_MATH_BIG_ENDIAN
+
+        c0 = c0 << 16u;
+
+#else
+
+        c0 = c0 & 0x0000FFFF;
+
+#endif /*      #ifdef  ARM_MATH_BIG_ENDIAN     */
+
+          /* Read x[7] */
+        x3 = *__SIMD32(px);
+		px++;
+
+          /* Perform the multiply-accumulates */
+          acc0 = __SMLAD(x0, c0, acc0);
+          acc1 = __SMLAD(x1, c0, acc1);
+          acc2 = __SMLADX(x1, c0, acc2);
+          acc3 = __SMLADX(x3, c0, acc3);
+        }
+
+        if(k == 2u)
+        {
+          /* Read y[srcBLen - 5], y[srcBLen - 6] */
+        c0 = _SIMD32_OFFSET(py);
+
+          /* Read x[7], x[8] */
+        x3 = *__SIMD32(px);
+
+        /* Read x[9] */
+        x2 = _SIMD32_OFFSET(px+1);
+		px += 2u;
+
+          /* Perform the multiply-accumulates */
+          acc0 = __SMLADX(x0, c0, acc0);
+          acc1 = __SMLADX(x1, c0, acc1);
+          acc2 = __SMLADX(x3, c0, acc2);
+          acc3 = __SMLADX(x2, c0, acc3);
+        }
+
+        if(k == 3u)
+        {
+          /* Read y[srcBLen - 5], y[srcBLen - 6] */
+        c0 = _SIMD32_OFFSET(py);
+
+          /* Read x[7], x[8] */
+        x3 = *__SIMD32(px);
+
+          /* Read x[9] */
+        x2 = _SIMD32_OFFSET(px+1);
+
+          /* Perform the multiply-accumulates */
+          acc0 = __SMLADX(x0, c0, acc0);
+          acc1 = __SMLADX(x1, c0, acc1);
+          acc2 = __SMLADX(x3, c0, acc2);
+          acc3 = __SMLADX(x2, c0, acc3);
+
+		c0 = *(py-1);
+#ifdef  ARM_MATH_BIG_ENDIAN
+
+        c0 = c0 << 16u;
+#else
+
+        c0 = c0 & 0x0000FFFF;
+#endif /*      #ifdef  ARM_MATH_BIG_ENDIAN     */
+
+          /* Read x[10] */
+        x3 =  _SIMD32_OFFSET(px+2);
+		px += 3u;
+
+          /* Perform the multiply-accumulates */
+          acc0 = __SMLADX(x1, c0, acc0);
+          acc1 = __SMLAD(x2, c0, acc1);
+          acc2 = __SMLADX(x2, c0, acc2);
+          acc3 = __SMLADX(x3, c0, acc3);
+        }
+
+        /* Store the results in the accumulators in the destination buffer. */
+#ifndef ARM_MATH_BIG_ENDIAN
+
+        *__SIMD32(pOut)++ = __PKHBT(acc0 >> 15, acc1 >> 15, 16);
+        *__SIMD32(pOut)++ = __PKHBT(acc2 >> 15, acc3 >> 15, 16);
+
+#else
+
+        *__SIMD32(pOut)++ = __PKHBT(acc1 >> 15, acc0 >> 15, 16);
+        *__SIMD32(pOut)++ = __PKHBT(acc3 >> 15, acc2 >> 15, 16);
+
+#endif /*      #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+        /* Increment the pointer pIn1 index, count by 4 */
+        count += 4u;
+
+        /* Update the inputA and inputB pointers for next MAC calculation */
+        px = pIn1 + count;
+        py = pSrc2;
+
+        /* Decrement the loop counter */
+        blkCnt--;
+      }
+
+      /* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.   
+       ** No loop unrolling is used. */
+      blkCnt = (uint32_t) blockSize2 % 0x4u;
+
+      while(blkCnt > 0u)
+      {
+        /* Accumulator is made zero for every iteration */
+        sum = 0;
+
+        /* Apply loop unrolling and compute 4 MACs simultaneously. */
+        k = srcBLen >> 2u;
+
+        /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+         ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+        while(k > 0u)
+        {
+          /* Perform the multiply-accumulates */
+          sum += ((q31_t) * px++ * *py--);
+          sum += ((q31_t) * px++ * *py--);
+          sum += ((q31_t) * px++ * *py--);
+          sum += ((q31_t) * px++ * *py--);
+
+          /* Decrement the loop counter */
+          k--;
+        }
+
+        /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.   
+         ** No loop unrolling is used. */
+        k = srcBLen % 0x4u;
+
+        while(k > 0u)
+        {
+          /* Perform the multiply-accumulates */
+          sum += ((q31_t) * px++ * *py--);
+
+          /* Decrement the loop counter */
+          k--;
+        }
+
+        /* Store the result in the accumulator in the destination buffer. */
+        *pOut++ = (q15_t) (sum >> 15);
+
+        /* Increment the pointer pIn1 index, count by 1 */
+        count++;
+
+        /* Update the inputA and inputB pointers for next MAC calculation */
+        px = pIn1 + count;
+        py = pSrc2;
+
+        /* Decrement the loop counter */
+        blkCnt--;
+      }
+    }
+    else
+    {
+      /* If the srcBLen is not a multiple of 4,   
+       * the blockSize2 loop cannot be unrolled by 4 */
+      blkCnt = (uint32_t) blockSize2;
+
+      while(blkCnt > 0u)
+      {
+        /* Accumulator is made zero for every iteration */
+        sum = 0;
+
+        /* srcBLen number of MACS should be performed */
+        k = srcBLen;
+
+        while(k > 0u)
+        {
+          /* Perform the multiply-accumulate */
+          sum += ((q31_t) * px++ * *py--);
+
+          /* Decrement the loop counter */
+          k--;
+        }
+
+        /* Store the result in the accumulator in the destination buffer. */
+        *pOut++ = (q15_t) (sum >> 15);
+
+        /* Increment the MAC count */
+        count++;
+
+        /* Update the inputA and inputB pointers for next MAC calculation */
+        px = pIn1 + count;
+        py = pSrc2;
+
+        /* Decrement the loop counter */
+        blkCnt--;
+      }
+    }
+
+
+    /* --------------------------   
+     * Initializations of stage3   
+     * -------------------------*/
+
+    /* sum += x[srcALen-srcBLen+1] * y[srcBLen-1] + x[srcALen-srcBLen+2] * y[srcBLen-2] +...+ x[srcALen-1] * y[1]   
+     * sum += x[srcALen-srcBLen+2] * y[srcBLen-1] + x[srcALen-srcBLen+3] * y[srcBLen-2] +...+ x[srcALen-1] * y[2]   
+     * ....   
+     * sum +=  x[srcALen-2] * y[srcBLen-1] + x[srcALen-1] * y[srcBLen-2]   
+     * sum +=  x[srcALen-1] * y[srcBLen-1]   
+     */
+
+    /* In this stage the MAC operations are decreased by 1 for every iteration.   
+       The count variable holds the number of MAC operations performed */
+    count = srcBLen - 1u;
+
+    /* Working pointer of inputA */
+    pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
+    px = pSrc1;
+
+    /* Working pointer of inputB */
+    pSrc2 = pIn2 + (srcBLen - 1u);
+    pIn2 = pSrc2 - 1u;
+    py = pIn2;
+
+    /* -------------------   
+     * Stage3 process   
+     * ------------------*/
+
+    /* For loop unrolling by 4, this stage is divided into two. */
+    /* First part of this stage computes the MAC operations greater than 4 */
+    /* Second part of this stage computes the MAC operations less than or equal to 4 */
+
+    /* The first part of the stage starts here */
+    j = count >> 2u;
+
+    while((j > 0u) && (blockSize3 > 0))
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = count >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      while(k > 0u)
+      {
+        /* x[srcALen - srcBLen + 1], x[srcALen - srcBLen + 2] are multiplied   
+         * with y[srcBLen - 1], y[srcBLen - 2] respectively */
+        sum = __SMLADX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
+        /* x[srcALen - srcBLen + 3], x[srcALen - srcBLen + 4] are multiplied   
+         * with y[srcBLen - 3], y[srcBLen - 4] respectively */
+        sum = __SMLADX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* For the next MAC operations, the pointer py is used without SIMD   
+       * So, py is incremented by 1 */
+      py = py + 1u;
+
+      /* If the count is not a multiple of 4, compute any remaining MACs here.   
+       ** No loop unrolling is used. */
+      k = count % 0x4u;
+
+      while(k > 0u)
+      {
+        /* sum += x[srcALen - srcBLen + 5] * y[srcBLen - 5] */
+        sum = __SMLAD(*px++, *py--, sum);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q15_t) (sum >> 15);
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = ++pSrc1;
+      py = pIn2;
+
+      /* Decrement the MAC count */
+      count--;
+
+      /* Decrement the loop counter */
+      blockSize3--;
+
+      j--;
+    }
+
+    /* The second part of the stage starts here */
+    /* SIMD is not used for the next MAC operations,   
+     * so pointer py is updated to read only one sample at a time */
+    py = py + 1u;
+
+    while(blockSize3 > 0)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = count;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        /* sum +=  x[srcALen-1] * y[srcBLen-1] */
+        sum = __SMLAD(*px++, *py--, sum);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q15_t) (sum >> 15);
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = ++pSrc1;
+      py = pSrc2;
+
+      /* Decrement the MAC count */
+      count--;
+
+      /* Decrement the loop counter */
+      blockSize3--;
+    }
+
+    /* set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+  }
+
+  /* Return to application */
+  return (status);
+
+#else
+
+  q15_t *pIn1;                                   /* inputA pointer               */
+  q15_t *pIn2;                                   /* inputB pointer               */
+  q15_t *pOut = pDst;                            /* output pointer               */
+  q31_t sum, acc0, acc1, acc2, acc3;             /* Accumulator                  */
+  q15_t *px;                                     /* Intermediate inputA pointer  */
+  q15_t *py;                                     /* Intermediate inputB pointer  */
+  q15_t *pSrc1, *pSrc2;                          /* Intermediate pointers        */
+  q31_t x0, x1, x2, x3, c0;
+  uint32_t j, k, count, check, blkCnt;
+  int32_t blockSize1, blockSize2, blockSize3;    /* loop counters                 */
+  arm_status status;                             /* status of Partial convolution */
+  q15_t a, b;
+
+  /* Check for range of output samples to be calculated */
+  if((firstIndex + numPoints) > ((srcALen + (srcBLen - 1u))))
+  {
+    /* Set status as ARM_MATH_ARGUMENT_ERROR */
+    status = ARM_MATH_ARGUMENT_ERROR;
+  }
+  else
+  {
+
+    /* The algorithm implementation is based on the lengths of the inputs. */
+    /* srcB is always made to slide across srcA. */
+    /* So srcBLen is always considered as shorter or equal to srcALen */
+    if(srcALen >=srcBLen)
+    {
+      /* Initialization of inputA pointer */
+      pIn1 = pSrcA;
+
+      /* Initialization of inputB pointer */
+      pIn2 = pSrcB;
+    }
+    else
+    {
+      /* Initialization of inputA pointer */
+      pIn1 = pSrcB;
+
+      /* Initialization of inputB pointer */
+      pIn2 = pSrcA;
+
+      /* srcBLen is always considered as shorter or equal to srcALen */
+      j = srcBLen;
+      srcBLen = srcALen;
+      srcALen = j;
+    }
+
+    /* Conditions to check which loopCounter holds   
+     * the first and last indices of the output samples to be calculated. */
+    check = firstIndex + numPoints;
+    blockSize3 = ((int32_t) check - (int32_t) srcALen);
+    blockSize3 = (blockSize3 > 0) ? blockSize3 : 0;
+    blockSize1 = (((int32_t) srcBLen - 1) - (int32_t) firstIndex);
+    blockSize1 = (blockSize1 > 0) ? ((check > (srcBLen - 1u)) ? blockSize1 :
+                                     (int32_t) numPoints) : 0;
+    blockSize2 = (int32_t) check - ((blockSize3 + blockSize1) +
+                                    (int32_t) firstIndex);
+    blockSize2 = (blockSize2 > 0) ? blockSize2 : 0;
+
+    /* conv(x,y) at n = x[n] * y[0] + x[n-1] * y[1] + x[n-2] * y[2] + ...+ x[n-N+1] * y[N -1] */
+    /* The function is internally   
+     * divided into three stages according to the number of multiplications that has to be   
+     * taken place between inputA samples and inputB samples. In the first stage of the   
+     * algorithm, the multiplications increase by one for every iteration.   
+     * In the second stage of the algorithm, srcBLen number of multiplications are done.   
+     * In the third stage of the algorithm, the multiplications decrease by one   
+     * for every iteration. */
+
+    /* Set the output pointer to point to the firstIndex   
+     * of the output sample to be calculated. */
+    pOut = pDst + firstIndex;
+
+    /* --------------------------   
+     * Initializations of stage1   
+     * -------------------------*/
+
+    /* sum = x[0] * y[0]   
+     * sum = x[0] * y[1] + x[1] * y[0]   
+     * ....   
+     * sum = x[0] * y[srcBlen - 1] + x[1] * y[srcBlen - 2] +...+ x[srcBLen - 1] * y[0]   
+     */
+
+    /* In this stage the MAC operations are increased by 1 for every iteration.   
+       The count variable holds the number of MAC operations performed.   
+       Since the partial convolution starts from firstIndex   
+       Number of Macs to be performed is firstIndex + 1 */
+    count = 1u + firstIndex;
+
+    /* Working pointer of inputA */
+    px = pIn1;
+
+    /* Working pointer of inputB */
+    pSrc2 = pIn2 + firstIndex;
+    py = pSrc2;
+
+    /* ------------------------   
+     * Stage1 process   
+     * ----------------------*/
+
+    /* For loop unrolling by 4, this stage is divided into two. */
+    /* First part of this stage computes the MAC operations less than 4 */
+    /* Second part of this stage computes the MAC operations greater than or equal to 4 */
+
+    /* The first part of the stage starts here */
+  while((count < 4u) && (blockSize1 > 0u))
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Loop over number of MAC operations between   
+       * inputA samples and inputB samples */
+      k = count;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+      sum += ((q31_t) * px++ * *py--);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q15_t) (sum >> 15);
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      py = ++pSrc2;
+      px = pIn1;
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Decrement the loop counter */
+      blockSize1--;
+    }
+
+    /* The second part of the stage starts here */
+    /* The internal loop, over count, is unrolled by 4 */
+    /* To, read the last two inputB samples using SIMD:   
+     * y[srcBLen] and y[srcBLen-1] coefficients, py is decremented by 1 */
+    py = py - 1;
+
+  while(blockSize1 > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = count >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+	py++;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+        sum += ((q31_t) * px++ * *py--);
+        sum += ((q31_t) * px++ * *py--);
+        sum += ((q31_t) * px++ * *py--);
+        sum += ((q31_t) * px++ * *py--);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+      /* If the count is not a multiple of 4, compute any remaining MACs here.   
+       ** No loop unrolling is used. */
+      k = count % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+      sum += ((q31_t) * px++ * *py--);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q15_t) (sum >> 15);
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      py = ++pSrc2 - 1u;
+      px = pIn1;
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Decrement the loop counter */
+      blockSize1--;
+    }
+
+    /* --------------------------   
+     * Initializations of stage2   
+     * ------------------------*/
+
+    /* sum = x[0] * y[srcBLen-1] + x[1] * y[srcBLen-2] +...+ x[srcBLen-1] * y[0]   
+     * sum = x[1] * y[srcBLen-1] + x[2] * y[srcBLen-2] +...+ x[srcBLen] * y[0]   
+     * ....   
+     * sum = x[srcALen-srcBLen-2] * y[srcBLen-1] + x[srcALen] * y[srcBLen-2] +...+ x[srcALen-1] * y[0]   
+     */
+
+    /* Working pointer of inputA */
+    px = pIn1;
+
+    /* Working pointer of inputB */
+    pSrc2 = pIn2 + (srcBLen - 1u);
+    py = pSrc2;
+
+    /* count is the index by which the pointer pIn1 to be incremented */
+    count = 0u;
+
+
+    /* --------------------   
+     * Stage2 process   
+     * -------------------*/
+
+    /* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.   
+     * So, to loop unroll over blockSize2,   
+     * srcBLen should be greater than or equal to 4 */
+    if(srcBLen >= 4u)
+    {
+      /* Loop unroll over blockSize2, by 4 */
+      blkCnt = ((uint32_t) blockSize2 >> 2u);
+
+      while(blkCnt > 0u)
+      {
+      py = py - 1u;
+
+        /* Set all accumulators to zero */
+        acc0 = 0;
+        acc1 = 0;
+        acc2 = 0;
+        acc3 = 0;
+
+      /* read x[0], x[1] samples */
+	  a = *px++;
+	  b = *px++;
+
+#ifndef ARM_MATH_BIG_ENDIAN
+	
+	  x0 = __PKHBT(a, b, 16);
+	  a = *px;
+	  x1 = __PKHBT(b, a, 16);
+
+#else
+
+	  x0 = __PKHBT(b, a, 16);
+	  a = *px;
+	  x1 = __PKHBT(a, b, 16);
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	   */
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      do
+      {
+        /* Read the last two inputB samples using SIMD:   
+         * y[srcBLen - 1] and y[srcBLen - 2] */
+		a = *py;
+		b = *(py+1);
+		py -= 2;
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+		c0 = __PKHBT(a, b, 16);
+
+#else
+
+ 		c0 = __PKHBT(b, a, 16);;
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	*/
+
+        /* acc0 +=  x[0] * y[srcBLen - 1] + x[1] * y[srcBLen - 2] */
+        acc0 = __SMLADX(x0, c0, acc0);
+
+        /* acc1 +=  x[1] * y[srcBLen - 1] + x[2] * y[srcBLen - 2] */
+        acc1 = __SMLADX(x1, c0, acc1);
+
+	  a = *px;
+	  b = *(px + 1);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+	
+	  x2 = __PKHBT(a, b, 16);
+	  a = *(px + 2);
+	  x3 = __PKHBT(b, a, 16);
+
+#else
+
+	  x2 = __PKHBT(b, a, 16);
+	  a = *(px + 2);
+	  x3 = __PKHBT(a, b, 16);
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	   */
+
+        /* acc2 +=  x[2] * y[srcBLen - 1] + x[3] * y[srcBLen - 2] */
+        acc2 = __SMLADX(x2, c0, acc2);
+
+        /* acc3 +=  x[3] * y[srcBLen - 1] + x[4] * y[srcBLen - 2] */
+        acc3 = __SMLADX(x3, c0, acc3);
+
+        /* Read y[srcBLen - 3] and y[srcBLen - 4] */
+		a = *py;
+		b = *(py+1);
+		py -= 2;
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+		c0 = __PKHBT(a, b, 16);
+
+#else
+
+ 		c0 = __PKHBT(b, a, 16);;
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	*/
+
+        /* acc0 +=  x[2] * y[srcBLen - 3] + x[3] * y[srcBLen - 4] */
+        acc0 = __SMLADX(x2, c0, acc0);
+
+        /* acc1 +=  x[3] * y[srcBLen - 3] + x[4] * y[srcBLen - 4] */
+        acc1 = __SMLADX(x3, c0, acc1);
+
+        /* Read x[4], x[5], x[6] */
+	  a = *(px + 2);
+	  b = *(px + 3);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+	
+	  x0 = __PKHBT(a, b, 16);
+	  a = *(px + 4);
+	  x1 = __PKHBT(b, a, 16);
+
+#else
+
+	  x0 = __PKHBT(b, a, 16);
+	  a = *(px + 4);
+	  x1 = __PKHBT(a, b, 16);
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	   */
+
+		px += 4u;
+
+        /* acc2 +=  x[4] * y[srcBLen - 3] + x[5] * y[srcBLen - 4] */
+        acc2 = __SMLADX(x0, c0, acc2);
+
+        /* acc3 +=  x[5] * y[srcBLen - 3] + x[6] * y[srcBLen - 4] */
+        acc3 = __SMLADX(x1, c0, acc3);
+
+      } while(--k);
+
+      /* For the next MAC operations, SIMD is not used   
+       * So, the 16 bit pointer if inputB, py is updated */
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.   
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      if(k == 1u)
+      {
+        /* Read y[srcBLen - 5] */
+        c0 = *(py+1);
+
+#ifdef  ARM_MATH_BIG_ENDIAN
+
+        c0 = c0 << 16u;
+
+#else
+
+        c0 = c0 & 0x0000FFFF;
+
+#endif /*      #ifdef  ARM_MATH_BIG_ENDIAN     */
+
+        /* Read x[7] */
+		a = *px;
+		b = *(px+1);
+		px++;
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+		x3 = __PKHBT(a, b, 16);
+
+#else
+
+ 		x3 = __PKHBT(b, a, 16);;
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	*/
+
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLAD(x0, c0, acc0);
+        acc1 = __SMLAD(x1, c0, acc1);
+        acc2 = __SMLADX(x1, c0, acc2);
+        acc3 = __SMLADX(x3, c0, acc3);
+      }
+
+      if(k == 2u)
+      {
+        /* Read y[srcBLen - 5], y[srcBLen - 6] */
+		a = *py;
+		b = *(py+1);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+		c0 = __PKHBT(a, b, 16);
+
+#else
+
+ 		c0 = __PKHBT(b, a, 16);;
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	*/
+
+        /* Read x[7], x[8], x[9] */
+	  a = *px;
+	  b = *(px + 1);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+	
+	  x3 = __PKHBT(a, b, 16);
+	  a = *(px + 2);
+	  x2 = __PKHBT(b, a, 16);
+
+#else
+
+	  x3 = __PKHBT(b, a, 16);
+	  a = *(px + 2);
+	  x2 = __PKHBT(a, b, 16);
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	   */
+		px += 2u;
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLADX(x0, c0, acc0);
+        acc1 = __SMLADX(x1, c0, acc1);
+        acc2 = __SMLADX(x3, c0, acc2);
+        acc3 = __SMLADX(x2, c0, acc3);
+      }
+
+      if(k == 3u)
+      {
+        /* Read y[srcBLen - 5], y[srcBLen - 6] */
+		a = *py;
+		b = *(py+1);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+		c0 = __PKHBT(a, b, 16);
+
+#else
+
+ 		c0 = __PKHBT(b, a, 16);;
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	*/
+
+        /* Read x[7], x[8], x[9] */
+	  a = *px;
+	  b = *(px + 1);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+	
+	  x3 = __PKHBT(a, b, 16);
+	  a = *(px + 2);
+	  x2 = __PKHBT(b, a, 16);
+
+#else
+
+	  x3 = __PKHBT(b, a, 16);
+	  a = *(px + 2);
+	  x2 = __PKHBT(a, b, 16);
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	   */
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLADX(x0, c0, acc0);
+        acc1 = __SMLADX(x1, c0, acc1);
+        acc2 = __SMLADX(x3, c0, acc2);
+        acc3 = __SMLADX(x2, c0, acc3);
+
+        /* Read y[srcBLen - 7] */
+		c0 = *(py-1);
+#ifdef  ARM_MATH_BIG_ENDIAN
+
+        c0 = c0 << 16u;
+#else
+
+        c0 = c0 & 0x0000FFFF;
+#endif /*      #ifdef  ARM_MATH_BIG_ENDIAN     */
+
+        /* Read x[10] */
+		a = *(px+2);
+		b = *(px+3);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+		x3 = __PKHBT(a, b, 16);
+
+#else
+
+ 		x3 = __PKHBT(b, a, 16);;
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	*/
+
+		px += 3u;
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLADX(x1, c0, acc0);
+        acc1 = __SMLAD(x2, c0, acc1);
+        acc2 = __SMLADX(x2, c0, acc2);
+        acc3 = __SMLADX(x3, c0, acc3);
+      }
+
+      /* Store the results in the accumulators in the destination buffer. */
+	  *pOut++ = (q15_t)(acc0 >> 15);
+	  *pOut++ = (q15_t)(acc1 >> 15);
+	  *pOut++ = (q15_t)(acc2 >> 15);
+	  *pOut++ = (q15_t)(acc3 >> 15);
+
+        /* Increment the pointer pIn1 index, count by 4 */
+        count += 4u;
+
+        /* Update the inputA and inputB pointers for next MAC calculation */
+        px = pIn1 + count;
+        py = pSrc2;
+
+        /* Decrement the loop counter */
+        blkCnt--;
+      }
+
+      /* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.   
+       ** No loop unrolling is used. */
+      blkCnt = (uint32_t) blockSize2 % 0x4u;
+
+      while(blkCnt > 0u)
+      {
+        /* Accumulator is made zero for every iteration */
+        sum = 0;
+
+        /* Apply loop unrolling and compute 4 MACs simultaneously. */
+        k = srcBLen >> 2u;
+
+        /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+         ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+        while(k > 0u)
+        {
+          /* Perform the multiply-accumulates */
+          sum += ((q31_t) * px++ * *py--);
+          sum += ((q31_t) * px++ * *py--);
+          sum += ((q31_t) * px++ * *py--);
+          sum += ((q31_t) * px++ * *py--);
+
+          /* Decrement the loop counter */
+          k--;
+        }
+
+        /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.   
+         ** No loop unrolling is used. */
+        k = srcBLen % 0x4u;
+
+        while(k > 0u)
+        {
+          /* Perform the multiply-accumulates */
+          sum += ((q31_t) * px++ * *py--);
+
+          /* Decrement the loop counter */
+          k--;
+        }
+
+        /* Store the result in the accumulator in the destination buffer. */
+        *pOut++ = (q15_t) (sum >> 15);
+
+        /* Increment the pointer pIn1 index, count by 1 */
+        count++;
+
+        /* Update the inputA and inputB pointers for next MAC calculation */
+        px = pIn1 + count;
+        py = pSrc2;
+
+        /* Decrement the loop counter */
+        blkCnt--;
+      }
+    }
+    else
+    {
+      /* If the srcBLen is not a multiple of 4,   
+       * the blockSize2 loop cannot be unrolled by 4 */
+      blkCnt = (uint32_t) blockSize2;
+
+      while(blkCnt > 0u)
+      {
+        /* Accumulator is made zero for every iteration */
+        sum = 0;
+
+        /* srcBLen number of MACS should be performed */
+        k = srcBLen;
+
+        while(k > 0u)
+        {
+          /* Perform the multiply-accumulate */
+          sum += ((q31_t) * px++ * *py--);
+
+          /* Decrement the loop counter */
+          k--;
+        }
+
+        /* Store the result in the accumulator in the destination buffer. */
+        *pOut++ = (q15_t) (sum >> 15);
+
+        /* Increment the MAC count */
+        count++;
+
+        /* Update the inputA and inputB pointers for next MAC calculation */
+        px = pIn1 + count;
+        py = pSrc2;
+
+        /* Decrement the loop counter */
+        blkCnt--;
+      }
+    }
+
+
+    /* --------------------------   
+     * Initializations of stage3   
+     * -------------------------*/
+
+    /* sum += x[srcALen-srcBLen+1] * y[srcBLen-1] + x[srcALen-srcBLen+2] * y[srcBLen-2] +...+ x[srcALen-1] * y[1]   
+     * sum += x[srcALen-srcBLen+2] * y[srcBLen-1] + x[srcALen-srcBLen+3] * y[srcBLen-2] +...+ x[srcALen-1] * y[2]   
+     * ....   
+     * sum +=  x[srcALen-2] * y[srcBLen-1] + x[srcALen-1] * y[srcBLen-2]   
+     * sum +=  x[srcALen-1] * y[srcBLen-1]   
+     */
+
+    /* In this stage the MAC operations are decreased by 1 for every iteration.   
+       The count variable holds the number of MAC operations performed */
+    count = srcBLen - 1u;
+
+    /* Working pointer of inputA */
+    pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
+    px = pSrc1;
+
+    /* Working pointer of inputB */
+    pSrc2 = pIn2 + (srcBLen - 1u);
+    pIn2 = pSrc2 - 1u;
+    py = pIn2;
+
+    /* -------------------   
+     * Stage3 process   
+     * ------------------*/
+
+    /* For loop unrolling by 4, this stage is divided into two. */
+    /* First part of this stage computes the MAC operations greater than 4 */
+    /* Second part of this stage computes the MAC operations less than or equal to 4 */
+
+    /* The first part of the stage starts here */
+    j = count >> 2u;
+
+    while((j > 0u) && (blockSize3 > 0))
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = count >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+	py++;
+
+    while(k > 0u)
+    {	
+      /* Perform the multiply-accumulates */
+        sum += ((q31_t) * px++ * *py--);
+        sum += ((q31_t) * px++ * *py--);
+        sum += ((q31_t) * px++ * *py--);
+        sum += ((q31_t) * px++ * *py--);
+      /* Decrement the loop counter */
+      k--;
+    }
+
+
+      /* If the count is not a multiple of 4, compute any remaining MACs here.   
+       ** No loop unrolling is used. */
+      k = count % 0x4u;
+
+      while(k > 0u)
+      {
+      /* Perform the multiply-accumulates */
+        sum += ((q31_t) * px++ * *py--);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q15_t) (sum >> 15);
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = ++pSrc1;
+      py = pIn2;
+
+      /* Decrement the MAC count */
+      count--;
+
+      /* Decrement the loop counter */
+      blockSize3--;
+
+      j--;
+    }
+
+    /* The second part of the stage starts here */
+    /* SIMD is not used for the next MAC operations,   
+     * so pointer py is updated to read only one sample at a time */
+    py = py + 1u;
+
+  while(blockSize3 > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = count;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        /* sum +=  x[srcALen-1] * y[srcBLen-1] */
+        sum += ((q31_t) * px++ * *py--);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q15_t) (sum >> 15);
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = ++pSrc1;
+      py = pSrc2;
+
+      /* Decrement the MAC count */
+      count--;
+
+      /* Decrement the loop counter */
+      blockSize3--;
+    }
+
+    /* set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+  }
+
+  /* Return to application */
+  return (status);
+
+#endif /*     #ifndef UNALIGNED_SUPPORT_DISABLE      */
+}
+
+/**   
+ * @} end of PartialConv group   
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_fast_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_fast_q31.c
new file mode 100644
index 0000000000..17902f593f
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_fast_q31.c
@@ -0,0 +1,599 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_conv_partial_fast_q31.c    
+*    
+* Description:	Fast Q31 Partial convolution.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.11 2011/10/18  
+*    Bug Fix in conv, correlation, partial convolution.  
+* 
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup PartialConv    
+ * @{    
+ */
+
+/**    
+ * @brief Partial convolution of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4.    
+ * @param[in]       *pSrcA points to the first input sequence.    
+ * @param[in]       srcALen length of the first input sequence.    
+ * @param[in]       *pSrcB points to the second input sequence.    
+ * @param[in]       srcBLen length of the second input sequence.    
+ * @param[out]      *pDst points to the location where the output result is written.    
+ * @param[in]       firstIndex is the first output sample to start with.    
+ * @param[in]       numPoints is the number of output points to be computed.    
+ * @return Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].    
+ *    
+ * \par    
+ * See arm_conv_partial_q31() for a slower implementation of this function which uses a 64-bit accumulator to provide higher precision.    
+ */
+
+arm_status arm_conv_partial_fast_q31(
+  q31_t * pSrcA,
+  uint32_t srcALen,
+  q31_t * pSrcB,
+  uint32_t srcBLen,
+  q31_t * pDst,
+  uint32_t firstIndex,
+  uint32_t numPoints)
+{
+  q31_t *pIn1;                                   /* inputA pointer               */
+  q31_t *pIn2;                                   /* inputB pointer               */
+  q31_t *pOut = pDst;                            /* output pointer               */
+  q31_t *px;                                     /* Intermediate inputA pointer  */
+  q31_t *py;                                     /* Intermediate inputB pointer  */
+  q31_t *pSrc1, *pSrc2;                          /* Intermediate pointers        */
+  q31_t sum, acc0, acc1, acc2, acc3;             /* Accumulators                  */
+  q31_t x0, x1, x2, x3, c0;
+  uint32_t j, k, count, check, blkCnt;
+  int32_t blockSize1, blockSize2, blockSize3;    /* loop counters                 */
+  arm_status status;                             /* status of Partial convolution */
+
+
+  /* Check for range of output samples to be calculated */
+  if((firstIndex + numPoints) > ((srcALen + (srcBLen - 1u))))
+  {
+    /* Set status as ARM_MATH_ARGUMENT_ERROR */
+    status = ARM_MATH_ARGUMENT_ERROR;
+  }
+  else
+  {
+
+    /* The algorithm implementation is based on the lengths of the inputs. */
+    /* srcB is always made to slide across srcA. */
+    /* So srcBLen is always considered as shorter or equal to srcALen */
+    if(srcALen >= srcBLen)
+    {
+      /* Initialization of inputA pointer */
+      pIn1 = pSrcA;
+
+      /* Initialization of inputB pointer */
+      pIn2 = pSrcB;
+    }
+    else
+    {
+      /* Initialization of inputA pointer */
+      pIn1 = pSrcB;
+
+      /* Initialization of inputB pointer */
+      pIn2 = pSrcA;
+
+      /* srcBLen is always considered as shorter or equal to srcALen */
+      j = srcBLen;
+      srcBLen = srcALen;
+      srcALen = j;
+    }
+
+    /* Conditions to check which loopCounter holds    
+     * the first and last indices of the output samples to be calculated. */
+    check = firstIndex + numPoints;
+    blockSize3 = ((int32_t) check - (int32_t) srcALen);
+    blockSize3 = (blockSize3 > 0) ? blockSize3 : 0;
+    blockSize1 = (((int32_t) srcBLen - 1) - (int32_t) firstIndex);
+    blockSize1 = (blockSize1 > 0) ? ((check > (srcBLen - 1u)) ? blockSize1 :
+                                     (int32_t) numPoints) : 0;
+    blockSize2 = (int32_t) check - ((blockSize3 + blockSize1) +
+                                    (int32_t) firstIndex);
+    blockSize2 = (blockSize2 > 0) ? blockSize2 : 0;
+
+    /* conv(x,y) at n = x[n] * y[0] + x[n-1] * y[1] + x[n-2] * y[2] + ...+ x[n-N+1] * y[N -1] */
+    /* The function is internally    
+     * divided into three stages according to the number of multiplications that has to be    
+     * taken place between inputA samples and inputB samples. In the first stage of the    
+     * algorithm, the multiplications increase by one for every iteration.    
+     * In the second stage of the algorithm, srcBLen number of multiplications are done.    
+     * In the third stage of the algorithm, the multiplications decrease by one    
+     * for every iteration. */
+
+    /* Set the output pointer to point to the firstIndex    
+     * of the output sample to be calculated. */
+    pOut = pDst + firstIndex;
+
+    /* --------------------------    
+     * Initializations of stage1    
+     * -------------------------*/
+
+    /* sum = x[0] * y[0]    
+     * sum = x[0] * y[1] + x[1] * y[0]    
+     * ....    
+     * sum = x[0] * y[srcBlen - 1] + x[1] * y[srcBlen - 2] +...+ x[srcBLen - 1] * y[0]    
+     */
+
+    /* In this stage the MAC operations are increased by 1 for every iteration.    
+       The count variable holds the number of MAC operations performed.    
+       Since the partial convolution starts from firstIndex    
+       Number of Macs to be performed is firstIndex + 1 */
+    count = 1u + firstIndex;
+
+    /* Working pointer of inputA */
+    px = pIn1;
+
+    /* Working pointer of inputB */
+    pSrc2 = pIn2 + firstIndex;
+    py = pSrc2;
+
+    /* ------------------------    
+     * Stage1 process    
+     * ----------------------*/
+
+    /* The first loop starts here */
+    while(blockSize1 > 0)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = count >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      while(k > 0u)
+      {
+        /* x[0] * y[srcBLen - 1] */
+        sum = (q31_t) ((((q63_t) sum << 32) +
+                        ((q63_t) * px++ * (*py--))) >> 32);
+
+        /* x[1] * y[srcBLen - 2] */
+        sum = (q31_t) ((((q63_t) sum << 32) +
+                        ((q63_t) * px++ * (*py--))) >> 32);
+
+        /* x[2] * y[srcBLen - 3] */
+        sum = (q31_t) ((((q63_t) sum << 32) +
+                        ((q63_t) * px++ * (*py--))) >> 32);
+
+        /* x[3] * y[srcBLen - 4] */
+        sum = (q31_t) ((((q63_t) sum << 32) +
+                        ((q63_t) * px++ * (*py--))) >> 32);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* If the count is not a multiple of 4, compute any remaining MACs here.    
+       ** No loop unrolling is used. */
+      k = count % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum = (q31_t) ((((q63_t) sum << 32) +
+                        ((q63_t) * px++ * (*py--))) >> 32);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = sum << 1;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      py = ++pSrc2;
+      px = pIn1;
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Decrement the loop counter */
+      blockSize1--;
+    }
+
+    /* --------------------------    
+     * Initializations of stage2    
+     * ------------------------*/
+
+    /* sum = x[0] * y[srcBLen-1] + x[1] * y[srcBLen-2] +...+ x[srcBLen-1] * y[0]    
+     * sum = x[1] * y[srcBLen-1] + x[2] * y[srcBLen-2] +...+ x[srcBLen] * y[0]    
+     * ....    
+     * sum = x[srcALen-srcBLen-2] * y[srcBLen-1] + x[srcALen] * y[srcBLen-2] +...+ x[srcALen-1] * y[0]    
+     */
+
+    /* Working pointer of inputA */
+    px = pIn1;
+
+    /* Working pointer of inputB */
+    pSrc2 = pIn2 + (srcBLen - 1u);
+    py = pSrc2;
+
+    /* count is index by which the pointer pIn1 to be incremented */
+    count = 0u;
+
+    /* -------------------    
+     * Stage2 process    
+     * ------------------*/
+
+    /* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.    
+     * So, to loop unroll over blockSize2,    
+     * srcBLen should be greater than or equal to 4 */
+    if(srcBLen >= 4u)
+    {
+      /* Loop unroll over blockSize2 */
+      blkCnt = ((uint32_t) blockSize2 >> 2u);
+
+      while(blkCnt > 0u)
+      {
+        /* Set all accumulators to zero */
+        acc0 = 0;
+        acc1 = 0;
+        acc2 = 0;
+        acc3 = 0;
+
+        /* read x[0], x[1], x[2] samples */
+        x0 = *(px++);
+        x1 = *(px++);
+        x2 = *(px++);
+
+        /* Apply loop unrolling and compute 4 MACs simultaneously. */
+        k = srcBLen >> 2u;
+
+        /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+         ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+        do
+        {
+          /* Read y[srcBLen - 1] sample */
+          c0 = *(py--);
+
+          /* Read x[3] sample */
+          x3 = *(px++);
+
+          /* Perform the multiply-accumulate */
+          /* acc0 +=  x[0] * y[srcBLen - 1] */
+          acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x0 * c0)) >> 32);
+
+          /* acc1 +=  x[1] * y[srcBLen - 1] */
+          acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x1 * c0)) >> 32);
+
+          /* acc2 +=  x[2] * y[srcBLen - 1] */
+          acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x2 * c0)) >> 32);
+
+          /* acc3 +=  x[3] * y[srcBLen - 1] */
+          acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x3 * c0)) >> 32);
+
+          /* Read y[srcBLen - 2] sample */
+          c0 = *(py--);
+
+          /* Read x[4] sample */
+          x0 = *(px++);
+
+          /* Perform the multiply-accumulate */
+          /* acc0 +=  x[1] * y[srcBLen - 2] */
+          acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x1 * c0)) >> 32);
+          /* acc1 +=  x[2] * y[srcBLen - 2] */
+          acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x2 * c0)) >> 32);
+          /* acc2 +=  x[3] * y[srcBLen - 2] */
+          acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x3 * c0)) >> 32);
+          /* acc3 +=  x[4] * y[srcBLen - 2] */
+          acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x0 * c0)) >> 32);
+
+          /* Read y[srcBLen - 3] sample */
+          c0 = *(py--);
+
+          /* Read x[5] sample */
+          x1 = *(px++);
+
+          /* Perform the multiply-accumulates */
+          /* acc0 +=  x[2] * y[srcBLen - 3] */
+          acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x2 * c0)) >> 32);
+          /* acc1 +=  x[3] * y[srcBLen - 2] */
+          acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x3 * c0)) >> 32);
+          /* acc2 +=  x[4] * y[srcBLen - 2] */
+          acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x0 * c0)) >> 32);
+          /* acc3 +=  x[5] * y[srcBLen - 2] */
+          acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x1 * c0)) >> 32);
+
+          /* Read y[srcBLen - 4] sample */
+          c0 = *(py--);
+
+          /* Read x[6] sample */
+          x2 = *(px++);
+
+          /* Perform the multiply-accumulates */
+          /* acc0 +=  x[3] * y[srcBLen - 4] */
+          acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x3 * c0)) >> 32);
+          /* acc1 +=  x[4] * y[srcBLen - 4] */
+          acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x0 * c0)) >> 32);
+          /* acc2 +=  x[5] * y[srcBLen - 4] */
+          acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x1 * c0)) >> 32);
+          /* acc3 +=  x[6] * y[srcBLen - 4] */
+          acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x2 * c0)) >> 32);
+
+
+        } while(--k);
+
+        /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.    
+         ** No loop unrolling is used. */
+        k = srcBLen % 0x4u;
+
+        while(k > 0u)
+        {
+          /* Read y[srcBLen - 5] sample */
+          c0 = *(py--);
+
+          /* Read x[7] sample */
+          x3 = *(px++);
+
+          /* Perform the multiply-accumulates */
+          /* acc0 +=  x[4] * y[srcBLen - 5] */
+          acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x0 * c0)) >> 32);
+          /* acc1 +=  x[5] * y[srcBLen - 5] */
+          acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x1 * c0)) >> 32);
+          /* acc2 +=  x[6] * y[srcBLen - 5] */
+          acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x2 * c0)) >> 32);
+          /* acc3 +=  x[7] * y[srcBLen - 5] */
+          acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x3 * c0)) >> 32);
+
+          /* Reuse the present samples for the next MAC */
+          x0 = x1;
+          x1 = x2;
+          x2 = x3;
+
+          /* Decrement the loop counter */
+          k--;
+        }
+
+        /* Store the result in the accumulator in the destination buffer. */
+        *pOut++ = (q31_t) (acc0 << 1);
+        *pOut++ = (q31_t) (acc1 << 1);
+        *pOut++ = (q31_t) (acc2 << 1);
+        *pOut++ = (q31_t) (acc3 << 1);
+
+        /* Increment the pointer pIn1 index, count by 4 */
+        count += 4u;
+
+        /* Update the inputA and inputB pointers for next MAC calculation */
+        px = pIn1 + count;
+        py = pSrc2;
+
+        /* Decrement the loop counter */
+        blkCnt--;
+      }
+
+      /* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.    
+       ** No loop unrolling is used. */
+      blkCnt = (uint32_t) blockSize2 % 0x4u;
+
+      while(blkCnt > 0u)
+      {
+        /* Accumulator is made zero for every iteration */
+        sum = 0;
+
+        /* Apply loop unrolling and compute 4 MACs simultaneously. */
+        k = srcBLen >> 2u;
+
+        /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+         ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+        while(k > 0u)
+        {
+          /* Perform the multiply-accumulates */
+          sum = (q31_t) ((((q63_t) sum << 32) +
+                          ((q63_t) * px++ * (*py--))) >> 32);
+          sum = (q31_t) ((((q63_t) sum << 32) +
+                          ((q63_t) * px++ * (*py--))) >> 32);
+          sum = (q31_t) ((((q63_t) sum << 32) +
+                          ((q63_t) * px++ * (*py--))) >> 32);
+          sum = (q31_t) ((((q63_t) sum << 32) +
+                          ((q63_t) * px++ * (*py--))) >> 32);
+
+          /* Decrement the loop counter */
+          k--;
+        }
+
+        /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.    
+         ** No loop unrolling is used. */
+        k = srcBLen % 0x4u;
+
+        while(k > 0u)
+        {
+          /* Perform the multiply-accumulate */
+          sum = (q31_t) ((((q63_t) sum << 32) +
+                          ((q63_t) * px++ * (*py--))) >> 32);
+
+          /* Decrement the loop counter */
+          k--;
+        }
+
+        /* Store the result in the accumulator in the destination buffer. */
+        *pOut++ = sum << 1;
+
+        /* Increment the MAC count */
+        count++;
+
+        /* Update the inputA and inputB pointers for next MAC calculation */
+        px = pIn1 + count;
+        py = pSrc2;
+
+        /* Decrement the loop counter */
+        blkCnt--;
+      }
+    }
+    else
+    {
+      /* If the srcBLen is not a multiple of 4,    
+       * the blockSize2 loop cannot be unrolled by 4 */
+      blkCnt = (uint32_t) blockSize2;
+
+      while(blkCnt > 0u)
+      {
+        /* Accumulator is made zero for every iteration */
+        sum = 0;
+
+        /* srcBLen number of MACS should be performed */
+        k = srcBLen;
+
+        while(k > 0u)
+        {
+          /* Perform the multiply-accumulate */
+          sum = (q31_t) ((((q63_t) sum << 32) +
+                          ((q63_t) * px++ * (*py--))) >> 32);
+
+          /* Decrement the loop counter */
+          k--;
+        }
+
+        /* Store the result in the accumulator in the destination buffer. */
+        *pOut++ = sum << 1;
+
+        /* Increment the MAC count */
+        count++;
+
+        /* Update the inputA and inputB pointers for next MAC calculation */
+        px = pIn1 + count;
+        py = pSrc2;
+
+        /* Decrement the loop counter */
+        blkCnt--;
+      }
+    }
+
+
+    /* --------------------------    
+     * Initializations of stage3    
+     * -------------------------*/
+
+    /* sum += x[srcALen-srcBLen+1] * y[srcBLen-1] + x[srcALen-srcBLen+2] * y[srcBLen-2] +...+ x[srcALen-1] * y[1]    
+     * sum += x[srcALen-srcBLen+2] * y[srcBLen-1] + x[srcALen-srcBLen+3] * y[srcBLen-2] +...+ x[srcALen-1] * y[2]    
+     * ....    
+     * sum +=  x[srcALen-2] * y[srcBLen-1] + x[srcALen-1] * y[srcBLen-2]    
+     * sum +=  x[srcALen-1] * y[srcBLen-1]    
+     */
+
+    /* In this stage the MAC operations are decreased by 1 for every iteration.    
+       The count variable holds the number of MAC operations performed */
+    count = srcBLen - 1u;
+
+    /* Working pointer of inputA */
+    pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
+    px = pSrc1;
+
+    /* Working pointer of inputB */
+    pSrc2 = pIn2 + (srcBLen - 1u);
+    py = pSrc2;
+
+    /* -------------------    
+     * Stage3 process    
+     * ------------------*/
+
+    while(blockSize3 > 0)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = count >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      while(k > 0u)
+      {
+        /* sum += x[srcALen - srcBLen + 1] * y[srcBLen - 1] */
+        sum = (q31_t) ((((q63_t) sum << 32) +
+                        ((q63_t) * px++ * (*py--))) >> 32);
+
+        /* sum += x[srcALen - srcBLen + 2] * y[srcBLen - 2] */
+        sum = (q31_t) ((((q63_t) sum << 32) +
+                        ((q63_t) * px++ * (*py--))) >> 32);
+
+        /* sum += x[srcALen - srcBLen + 3] * y[srcBLen - 3] */
+        sum = (q31_t) ((((q63_t) sum << 32) +
+                        ((q63_t) * px++ * (*py--))) >> 32);
+
+        /* sum += x[srcALen - srcBLen + 4] * y[srcBLen - 4] */
+        sum = (q31_t) ((((q63_t) sum << 32) +
+                        ((q63_t) * px++ * (*py--))) >> 32);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* If the count is not a multiple of 4, compute any remaining MACs here.    
+       ** No loop unrolling is used. */
+      k = count % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        /* sum +=  x[srcALen-1] * y[srcBLen-1] */
+        sum = (q31_t) ((((q63_t) sum << 32) +
+                        ((q63_t) * px++ * (*py--))) >> 32);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = sum << 1;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = ++pSrc1;
+      py = pSrc2;
+
+      /* Decrement the MAC count */
+      count--;
+
+      /* Decrement the loop counter */
+      blockSize3--;
+
+    }
+
+    /* set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+  }
+
+  /* Return to application */
+  return (status);
+
+}
+
+/**    
+ * @} end of PartialConv group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_opt_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_opt_q15.c
new file mode 100644
index 0000000000..fe14f9fd3b
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_opt_q15.c
@@ -0,0 +1,764 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_conv_partial_opt_q15.c    
+*    
+* Description:	Partial convolution of Q15 sequences.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*  
+* Version 1.0.11 2011/10/18  
+*    Bug Fix in conv, correlation, partial convolution.  
+* 
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+*    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup PartialConv    
+ * @{    
+ */
+
+/**    
+ * @brief Partial convolution of Q15 sequences.    
+ * @param[in]       *pSrcA points to the first input sequence.    
+ * @param[in]       srcALen length of the first input sequence.    
+ * @param[in]       *pSrcB points to the second input sequence.    
+ * @param[in]       srcBLen length of the second input sequence.    
+ * @param[out]      *pDst points to the location where the output result is written.    
+ * @param[in]       firstIndex is the first output sample to start with.    
+ * @param[in]       numPoints is the number of output points to be computed.    
+ * @param[in]       *pScratch1 points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.   
+ * @param[in]       *pScratch2 points to scratch buffer of size min(srcALen, srcBLen).   
+ * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].    
+ *    
+ * \par Restrictions    
+ *  If the silicon does not support unaligned memory access enable the macro UNALIGNED_SUPPORT_DISABLE    
+ *	In this case input, output, state buffers should be aligned by 32-bit    
+ *    
+ * Refer to arm_conv_partial_fast_q15() for a faster but less precise version of this function for Cortex-M3 and Cortex-M4.   
+ *  
+ * 
+ */
+
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+arm_status arm_conv_partial_opt_q15(
+  q15_t * pSrcA,
+  uint32_t srcALen,
+  q15_t * pSrcB,
+  uint32_t srcBLen,
+  q15_t * pDst,
+  uint32_t firstIndex,
+  uint32_t numPoints,
+  q15_t * pScratch1,
+  q15_t * pScratch2)
+{
+
+  q15_t *pOut = pDst;                            /* output pointer */
+  q15_t *pScr1 = pScratch1;                      /* Temporary pointer for scratch1 */
+  q15_t *pScr2 = pScratch2;                      /* Temporary pointer for scratch1 */
+  q63_t acc0, acc1, acc2, acc3;                  /* Accumulator */
+  q31_t x1, x2, x3;                              /* Temporary variables to hold state and coefficient values */
+  q31_t y1, y2;                                  /* State variables */
+  q15_t *pIn1;                                   /* inputA pointer */
+  q15_t *pIn2;                                   /* inputB pointer */
+  q15_t *px;                                     /* Intermediate inputA pointer  */
+  q15_t *py;                                     /* Intermediate inputB pointer  */
+  uint32_t j, k, blkCnt;                         /* loop counter */
+  arm_status status;                             /* Status variable */
+  uint32_t tapCnt;                               /* loop count */
+
+  /* Check for range of output samples to be calculated */
+  if((firstIndex + numPoints) > ((srcALen + (srcBLen - 1u))))
+  {
+    /* Set status as ARM_MATH_ARGUMENT_ERROR */
+    status = ARM_MATH_ARGUMENT_ERROR;
+  }
+  else
+  {
+
+    /* The algorithm implementation is based on the lengths of the inputs. */
+    /* srcB is always made to slide across srcA. */
+    /* So srcBLen is always considered as shorter or equal to srcALen */
+    if(srcALen >= srcBLen)
+    {
+      /* Initialization of inputA pointer */
+      pIn1 = pSrcA;
+
+      /* Initialization of inputB pointer */
+      pIn2 = pSrcB;
+    }
+    else
+    {
+      /* Initialization of inputA pointer */
+      pIn1 = pSrcB;
+
+      /* Initialization of inputB pointer */
+      pIn2 = pSrcA;
+
+      /* srcBLen is always considered as shorter or equal to srcALen */
+      j = srcBLen;
+      srcBLen = srcALen;
+      srcALen = j;
+    }
+
+    /* Temporary pointer for scratch2 */
+    py = pScratch2;
+
+    /* pointer to take end of scratch2 buffer */
+    pScr2 = pScratch2 + srcBLen - 1;
+
+    /* points to smaller length sequence */
+    px = pIn2;
+
+    /* Apply loop unrolling and do 4 Copies simultaneously. */
+    k = srcBLen >> 2u;
+
+    /* First part of the processing with loop unrolling copies 4 data points at a time.       
+     ** a second loop below copies for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* copy second buffer in reversal manner */
+      *pScr2-- = *px++;
+      *pScr2-- = *px++;
+      *pScr2-- = *px++;
+      *pScr2-- = *px++;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, copy remaining samples here.       
+     ** No loop unrolling is used. */
+    k = srcBLen % 0x4u;
+
+    while(k > 0u)
+    {
+      /* copy second buffer in reversal manner for remaining samples */
+      *pScr2-- = *px++;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Initialze temporary scratch pointer */
+    pScr1 = pScratch1;
+
+    /* Fill (srcBLen - 1u) zeros in scratch buffer */
+    arm_fill_q15(0, pScr1, (srcBLen - 1u));
+
+    /* Update temporary scratch pointer */
+    pScr1 += (srcBLen - 1u);
+
+    /* Copy bigger length sequence(srcALen) samples in scratch1 buffer */
+
+    /* Copy (srcALen) samples in scratch buffer */
+    arm_copy_q15(pIn1, pScr1, srcALen);
+
+    /* Update pointers */
+    pScr1 += srcALen;
+
+    /* Fill (srcBLen - 1u) zeros at end of scratch buffer */
+    arm_fill_q15(0, pScr1, (srcBLen - 1u));
+
+    /* Update pointer */
+    pScr1 += (srcBLen - 1u);
+
+    /* Initialization of pIn2 pointer */
+    pIn2 = py;
+
+    pScratch1 += firstIndex;
+
+    pOut = pDst + firstIndex;
+
+    /* Actual convolution process starts here */
+    blkCnt = (numPoints) >> 2;
+
+    while(blkCnt > 0)
+    {
+      /* Initialze temporary scratch pointer as scratch1 */
+      pScr1 = pScratch1;
+
+      /* Clear Accumlators */
+      acc0 = 0;
+      acc1 = 0;
+      acc2 = 0;
+      acc3 = 0;
+
+      /* Read two samples from scratch1 buffer */
+      x1 = *__SIMD32(pScr1)++;
+
+      /* Read next two samples from scratch1 buffer */
+      x2 = *__SIMD32(pScr1)++;
+
+      tapCnt = (srcBLen) >> 2u;
+
+      while(tapCnt > 0u)
+      {
+
+        /* Read four samples from smaller buffer */
+        y1 = _SIMD32_OFFSET(pIn2);
+        y2 = _SIMD32_OFFSET(pIn2 + 2u);
+
+        /* multiply and accumlate */
+        acc0 = __SMLALD(x1, y1, acc0);
+        acc2 = __SMLALD(x2, y1, acc2);
+
+        /* pack input data */
+#ifndef ARM_MATH_BIG_ENDIAN
+        x3 = __PKHBT(x2, x1, 0);
+#else
+        x3 = __PKHBT(x1, x2, 0);
+#endif
+
+        /* multiply and accumlate */
+        acc1 = __SMLALDX(x3, y1, acc1);
+
+        /* Read next two samples from scratch1 buffer */
+        x1 = _SIMD32_OFFSET(pScr1);
+
+        /* multiply and accumlate */
+        acc0 = __SMLALD(x2, y2, acc0);
+        acc2 = __SMLALD(x1, y2, acc2);
+
+        /* pack input data */
+#ifndef ARM_MATH_BIG_ENDIAN
+        x3 = __PKHBT(x1, x2, 0);
+#else
+        x3 = __PKHBT(x2, x1, 0);
+#endif
+
+        acc3 = __SMLALDX(x3, y1, acc3);
+        acc1 = __SMLALDX(x3, y2, acc1);
+
+        x2 = _SIMD32_OFFSET(pScr1 + 2u);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+        x3 = __PKHBT(x2, x1, 0);
+#else
+        x3 = __PKHBT(x1, x2, 0);
+#endif
+
+        acc3 = __SMLALDX(x3, y2, acc3);
+
+        /* update scratch pointers */
+        pIn2 += 4u;
+        pScr1 += 4u;
+
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      /* Update scratch pointer for remaining samples of smaller length sequence */
+      pScr1 -= 4u;
+
+      /* apply same above for remaining samples of smaller length sequence */
+      tapCnt = (srcBLen) & 3u;
+
+      while(tapCnt > 0u)
+      {
+        /* accumlate the results */
+        acc0 += (*pScr1++ * *pIn2);
+        acc1 += (*pScr1++ * *pIn2);
+        acc2 += (*pScr1++ * *pIn2);
+        acc3 += (*pScr1++ * *pIn2++);
+
+        pScr1 -= 3u;
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      blkCnt--;
+
+
+      /* Store the results in the accumulators in the destination buffer. */
+
+#ifndef  ARM_MATH_BIG_ENDIAN
+
+      *__SIMD32(pOut)++ =
+        __PKHBT(__SSAT((acc0 >> 15), 16), __SSAT((acc1 >> 15), 16), 16);
+      *__SIMD32(pOut)++ =
+        __PKHBT(__SSAT((acc2 >> 15), 16), __SSAT((acc3 >> 15), 16), 16);
+
+#else
+
+      *__SIMD32(pOut)++ =
+        __PKHBT(__SSAT((acc1 >> 15), 16), __SSAT((acc0 >> 15), 16), 16);
+      *__SIMD32(pOut)++ =
+        __PKHBT(__SSAT((acc3 >> 15), 16), __SSAT((acc2 >> 15), 16), 16);
+
+#endif /*      #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+      /* Initialization of inputB pointer */
+      pIn2 = py;
+
+      pScratch1 += 4u;
+
+    }
+
+
+    blkCnt = numPoints & 0x3;
+
+    /* Calculate convolution for remaining samples of Bigger length sequence */
+    while(blkCnt > 0)
+    {
+      /* Initialze temporary scratch pointer as scratch1 */
+      pScr1 = pScratch1;
+
+      /* Clear Accumlators */
+      acc0 = 0;
+
+      tapCnt = (srcBLen) >> 1u;
+
+      while(tapCnt > 0u)
+      {
+
+        /* Read next two samples from scratch1 buffer */
+        x1 = *__SIMD32(pScr1)++;
+
+        /* Read two samples from smaller buffer */
+        y1 = *__SIMD32(pIn2)++;
+
+        acc0 = __SMLALD(x1, y1, acc0);
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      tapCnt = (srcBLen) & 1u;
+
+      /* apply same above for remaining samples of smaller length sequence */
+      while(tapCnt > 0u)
+      {
+
+        /* accumlate the results */
+        acc0 += (*pScr1++ * *pIn2++);
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      blkCnt--;
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q15_t) (__SSAT((acc0 >> 15), 16));
+
+      /* Initialization of inputB pointer */
+      pIn2 = py;
+
+      pScratch1 += 1u;
+
+    }
+
+    /* set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+
+  }
+
+  /* Return to application */
+  return (status);
+}
+
+#else
+
+arm_status arm_conv_partial_opt_q15(
+  q15_t * pSrcA,
+  uint32_t srcALen,
+  q15_t * pSrcB,
+  uint32_t srcBLen,
+  q15_t * pDst,
+  uint32_t firstIndex,
+  uint32_t numPoints,
+  q15_t * pScratch1,
+  q15_t * pScratch2)
+{
+
+  q15_t *pOut = pDst;                            /* output pointer */
+  q15_t *pScr1 = pScratch1;                      /* Temporary pointer for scratch1 */
+  q15_t *pScr2 = pScratch2;                      /* Temporary pointer for scratch1 */
+  q63_t acc0, acc1, acc2, acc3;                  /* Accumulator */
+  q15_t *pIn1;                                   /* inputA pointer */
+  q15_t *pIn2;                                   /* inputB pointer */
+  q15_t *px;                                     /* Intermediate inputA pointer  */
+  q15_t *py;                                     /* Intermediate inputB pointer  */
+  uint32_t j, k, blkCnt;                         /* loop counter */
+  arm_status status;                             /* Status variable */
+  uint32_t tapCnt;                               /* loop count */
+  q15_t x10, x11, x20, x21;                      /* Temporary variables to hold srcA buffer */
+  q15_t y10, y11;                                /* Temporary variables to hold srcB buffer */
+
+
+  /* Check for range of output samples to be calculated */
+  if((firstIndex + numPoints) > ((srcALen + (srcBLen - 1u))))
+  {
+    /* Set status as ARM_MATH_ARGUMENT_ERROR */
+    status = ARM_MATH_ARGUMENT_ERROR;
+  }
+  else
+  {
+
+    /* The algorithm implementation is based on the lengths of the inputs. */
+    /* srcB is always made to slide across srcA. */
+    /* So srcBLen is always considered as shorter or equal to srcALen */
+    if(srcALen >= srcBLen)
+    {
+      /* Initialization of inputA pointer */
+      pIn1 = pSrcA;
+
+      /* Initialization of inputB pointer */
+      pIn2 = pSrcB;
+    }
+    else
+    {
+      /* Initialization of inputA pointer */
+      pIn1 = pSrcB;
+
+      /* Initialization of inputB pointer */
+      pIn2 = pSrcA;
+
+      /* srcBLen is always considered as shorter or equal to srcALen */
+      j = srcBLen;
+      srcBLen = srcALen;
+      srcALen = j;
+    }
+
+    /* Temporary pointer for scratch2 */
+    py = pScratch2;
+
+    /* pointer to take end of scratch2 buffer */
+    pScr2 = pScratch2 + srcBLen - 1;
+
+    /* points to smaller length sequence */
+    px = pIn2;
+
+    /* Apply loop unrolling and do 4 Copies simultaneously. */
+    k = srcBLen >> 2u;
+
+    /* First part of the processing with loop unrolling copies 4 data points at a time.       
+     ** a second loop below copies for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* copy second buffer in reversal manner */
+      *pScr2-- = *px++;
+      *pScr2-- = *px++;
+      *pScr2-- = *px++;
+      *pScr2-- = *px++;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, copy remaining samples here.       
+     ** No loop unrolling is used. */
+    k = srcBLen % 0x4u;
+
+    while(k > 0u)
+    {
+      /* copy second buffer in reversal manner for remaining samples */
+      *pScr2-- = *px++;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Initialze temporary scratch pointer */
+    pScr1 = pScratch1;
+
+    /* Fill (srcBLen - 1u) zeros in scratch buffer */
+    arm_fill_q15(0, pScr1, (srcBLen - 1u));
+
+    /* Update temporary scratch pointer */
+    pScr1 += (srcBLen - 1u);
+
+    /* Copy bigger length sequence(srcALen) samples in scratch1 buffer */
+
+
+    /* Apply loop unrolling and do 4 Copies simultaneously. */
+    k = srcALen >> 2u;
+
+    /* First part of the processing with loop unrolling copies 4 data points at a time.       
+     ** a second loop below copies for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* copy second buffer in reversal manner */
+      *pScr1++ = *pIn1++;
+      *pScr1++ = *pIn1++;
+      *pScr1++ = *pIn1++;
+      *pScr1++ = *pIn1++;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, copy remaining samples here.       
+     ** No loop unrolling is used. */
+    k = srcALen % 0x4u;
+
+    while(k > 0u)
+    {
+      /* copy second buffer in reversal manner for remaining samples */
+      *pScr1++ = *pIn1++;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+
+    /* Apply loop unrolling and do 4 Copies simultaneously. */
+    k = (srcBLen - 1u) >> 2u;
+
+    /* First part of the processing with loop unrolling copies 4 data points at a time.       
+     ** a second loop below copies for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* copy second buffer in reversal manner */
+      *pScr1++ = 0;
+      *pScr1++ = 0;
+      *pScr1++ = 0;
+      *pScr1++ = 0;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, copy remaining samples here.       
+     ** No loop unrolling is used. */
+    k = (srcBLen - 1u) % 0x4u;
+
+    while(k > 0u)
+    {
+      /* copy second buffer in reversal manner for remaining samples */
+      *pScr1++ = 0;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+
+    /* Initialization of pIn2 pointer */
+    pIn2 = py;
+
+    pScratch1 += firstIndex;
+
+    pOut = pDst + firstIndex;
+
+    /* Actual convolution process starts here */
+    blkCnt = (numPoints) >> 2;
+
+    while(blkCnt > 0)
+    {
+      /* Initialze temporary scratch pointer as scratch1 */
+      pScr1 = pScratch1;
+
+      /* Clear Accumlators */
+      acc0 = 0;
+      acc1 = 0;
+      acc2 = 0;
+      acc3 = 0;
+
+      /* Read two samples from scratch1 buffer */
+      x10 = *pScr1++;
+      x11 = *pScr1++;
+
+      /* Read next two samples from scratch1 buffer */
+      x20 = *pScr1++;
+      x21 = *pScr1++;
+
+      tapCnt = (srcBLen) >> 2u;
+
+      while(tapCnt > 0u)
+      {
+
+        /* Read two samples from smaller buffer */
+        y10 = *pIn2;
+        y11 = *(pIn2 + 1u);
+
+        /* multiply and accumlate */
+        acc0 += (q63_t) x10 *y10;
+        acc0 += (q63_t) x11 *y11;
+        acc2 += (q63_t) x20 *y10;
+        acc2 += (q63_t) x21 *y11;
+
+        /* multiply and accumlate */
+        acc1 += (q63_t) x11 *y10;
+        acc1 += (q63_t) x20 *y11;
+
+        /* Read next two samples from scratch1 buffer */
+        x10 = *pScr1;
+        x11 = *(pScr1 + 1u);
+
+        /* multiply and accumlate */
+        acc3 += (q63_t) x21 *y10;
+        acc3 += (q63_t) x10 *y11;
+
+        /* Read next two samples from scratch2 buffer */
+        y10 = *(pIn2 + 2u);
+        y11 = *(pIn2 + 3u);
+
+        /* multiply and accumlate */
+        acc0 += (q63_t) x20 *y10;
+        acc0 += (q63_t) x21 *y11;
+        acc2 += (q63_t) x10 *y10;
+        acc2 += (q63_t) x11 *y11;
+        acc1 += (q63_t) x21 *y10;
+        acc1 += (q63_t) x10 *y11;
+
+        /* Read next two samples from scratch1 buffer */
+        x20 = *(pScr1 + 2);
+        x21 = *(pScr1 + 3);
+
+        /* multiply and accumlate */
+        acc3 += (q63_t) x11 *y10;
+        acc3 += (q63_t) x20 *y11;
+
+        /* update scratch pointers */
+        pIn2 += 4u;
+        pScr1 += 4u;
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      /* Update scratch pointer for remaining samples of smaller length sequence */
+      pScr1 -= 4u;
+
+      /* apply same above for remaining samples of smaller length sequence */
+      tapCnt = (srcBLen) & 3u;
+
+      while(tapCnt > 0u)
+      {
+        /* accumlate the results */
+        acc0 += (*pScr1++ * *pIn2);
+        acc1 += (*pScr1++ * *pIn2);
+        acc2 += (*pScr1++ * *pIn2);
+        acc3 += (*pScr1++ * *pIn2++);
+
+        pScr1 -= 3u;
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      blkCnt--;
+
+
+      /* Store the results in the accumulators in the destination buffer. */
+      *pOut++ = __SSAT((acc0 >> 15), 16);
+      *pOut++ = __SSAT((acc1 >> 15), 16);
+      *pOut++ = __SSAT((acc2 >> 15), 16);
+      *pOut++ = __SSAT((acc3 >> 15), 16);
+
+
+      /* Initialization of inputB pointer */
+      pIn2 = py;
+
+      pScratch1 += 4u;
+
+    }
+
+
+    blkCnt = numPoints & 0x3;
+
+    /* Calculate convolution for remaining samples of Bigger length sequence */
+    while(blkCnt > 0)
+    {
+      /* Initialze temporary scratch pointer as scratch1 */
+      pScr1 = pScratch1;
+
+      /* Clear Accumlators */
+      acc0 = 0;
+
+      tapCnt = (srcBLen) >> 1u;
+
+      while(tapCnt > 0u)
+      {
+
+        /* Read next two samples from scratch1 buffer */
+        x10 = *pScr1++;
+        x11 = *pScr1++;
+
+        /* Read two samples from smaller buffer */
+        y10 = *pIn2++;
+        y11 = *pIn2++;
+
+        /* multiply and accumlate */
+        acc0 += (q63_t) x10 *y10;
+        acc0 += (q63_t) x11 *y11;
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      tapCnt = (srcBLen) & 1u;
+
+      /* apply same above for remaining samples of smaller length sequence */
+      while(tapCnt > 0u)
+      {
+
+        /* accumlate the results */
+        acc0 += (*pScr1++ * *pIn2++);
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      blkCnt--;
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q15_t) (__SSAT((acc0 >> 15), 16));
+
+
+      /* Initialization of inputB pointer */
+      pIn2 = py;
+
+      pScratch1 += 1u;
+
+    }
+
+    /* set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+
+  }
+
+  /* Return to application */
+  return (status);
+}
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+
+/**    
+ * @} end of PartialConv group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_opt_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_opt_q7.c
new file mode 100644
index 0000000000..513d89d877
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_opt_q7.c
@@ -0,0 +1,806 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_conv_partial_opt_q7.c    
+*    
+* Description:	Partial convolution of Q7 sequences.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*  
+* Version 1.0.11 2011/10/18  
+*    Bug Fix in conv, correlation, partial convolution.  
+* 
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+*    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup PartialConv    
+ * @{    
+ */
+
+/**    
+ * @brief Partial convolution of Q7 sequences.    
+ * @param[in]       *pSrcA points to the first input sequence.    
+ * @param[in]       srcALen length of the first input sequence.    
+ * @param[in]       *pSrcB points to the second input sequence.    
+ * @param[in]       srcBLen length of the second input sequence.    
+ * @param[out]      *pDst points to the location where the output result is written.    
+ * @param[in]       firstIndex is the first output sample to start with.    
+ * @param[in]       numPoints is the number of output points to be computed.    
+ * @param[in]      *pScratch1 points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.    
+ * @param[in]      *pScratch2 points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen).    
+ * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].    
+ *    
+ * \par Restrictions    
+ *  If the silicon does not support unaligned memory access enable the macro UNALIGNED_SUPPORT_DISABLE    
+ *	In this case input, output, scratch1 and scratch2 buffers should be aligned by 32-bit   
+ * 
+ *
+ * 
+ */
+
+
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+arm_status arm_conv_partial_opt_q7(
+  q7_t * pSrcA,
+  uint32_t srcALen,
+  q7_t * pSrcB,
+  uint32_t srcBLen,
+  q7_t * pDst,
+  uint32_t firstIndex,
+  uint32_t numPoints,
+  q15_t * pScratch1,
+  q15_t * pScratch2)
+{
+
+  q15_t *pScr2, *pScr1;                          /* Intermediate pointers for scratch pointers */
+  q15_t x4;                                      /* Temporary input variable */
+  q7_t *pIn1, *pIn2;                             /* inputA and inputB pointer */
+  uint32_t j, k, blkCnt, tapCnt;                 /* loop counter */
+  q7_t *px;                                      /* Temporary input1 pointer */
+  q15_t *py;                                     /* Temporary input2 pointer */
+  q31_t acc0, acc1, acc2, acc3;                  /* Accumulator */
+  q31_t x1, x2, x3, y1;                          /* Temporary input variables */
+  arm_status status;
+  q7_t *pOut = pDst;                             /* output pointer */
+  q7_t out0, out1, out2, out3;                   /* temporary variables */
+
+  /* Check for range of output samples to be calculated */
+  if((firstIndex + numPoints) > ((srcALen + (srcBLen - 1u))))
+  {
+    /* Set status as ARM_MATH_ARGUMENT_ERROR */
+    status = ARM_MATH_ARGUMENT_ERROR;
+  }
+  else
+  {
+
+    /* The algorithm implementation is based on the lengths of the inputs. */
+    /* srcB is always made to slide across srcA. */
+    /* So srcBLen is always considered as shorter or equal to srcALen */
+    if(srcALen >= srcBLen)
+    {
+      /* Initialization of inputA pointer */
+      pIn1 = pSrcA;
+
+      /* Initialization of inputB pointer */
+      pIn2 = pSrcB;
+    }
+    else
+    {
+      /* Initialization of inputA pointer */
+      pIn1 = pSrcB;
+
+      /* Initialization of inputB pointer */
+      pIn2 = pSrcA;
+
+      /* srcBLen is always considered as shorter or equal to srcALen */
+      j = srcBLen;
+      srcBLen = srcALen;
+      srcALen = j;
+    }
+
+    /* pointer to take end of scratch2 buffer */
+    pScr2 = pScratch2;
+
+    /* points to smaller length sequence */
+    px = pIn2 + srcBLen - 1;
+
+    /* Apply loop unrolling and do 4 Copies simultaneously. */
+    k = srcBLen >> 2u;
+
+    /* First part of the processing with loop unrolling copies 4 data points at a time.       
+     ** a second loop below copies for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* copy second buffer in reversal manner */
+      x4 = (q15_t) * px--;
+      *pScr2++ = x4;
+      x4 = (q15_t) * px--;
+      *pScr2++ = x4;
+      x4 = (q15_t) * px--;
+      *pScr2++ = x4;
+      x4 = (q15_t) * px--;
+      *pScr2++ = x4;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, copy remaining samples here.       
+     ** No loop unrolling is used. */
+    k = srcBLen % 0x4u;
+
+    while(k > 0u)
+    {
+      /* copy second buffer in reversal manner for remaining samples */
+      x4 = (q15_t) * px--;
+      *pScr2++ = x4;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Initialze temporary scratch pointer */
+    pScr1 = pScratch1;
+
+    /* Fill (srcBLen - 1u) zeros in scratch buffer */
+    arm_fill_q15(0, pScr1, (srcBLen - 1u));
+
+    /* Update temporary scratch pointer */
+    pScr1 += (srcBLen - 1u);
+
+    /* Copy (srcALen) samples in scratch buffer */
+    /* Apply loop unrolling and do 4 Copies simultaneously. */
+    k = srcALen >> 2u;
+
+    /* First part of the processing with loop unrolling copies 4 data points at a time.       
+     ** a second loop below copies for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* copy second buffer in reversal manner */
+      x4 = (q15_t) * pIn1++;
+      *pScr1++ = x4;
+      x4 = (q15_t) * pIn1++;
+      *pScr1++ = x4;
+      x4 = (q15_t) * pIn1++;
+      *pScr1++ = x4;
+      x4 = (q15_t) * pIn1++;
+      *pScr1++ = x4;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, copy remaining samples here.       
+     ** No loop unrolling is used. */
+    k = srcALen % 0x4u;
+
+    while(k > 0u)
+    {
+      /* copy second buffer in reversal manner for remaining samples */
+      x4 = (q15_t) * pIn1++;
+      *pScr1++ = x4;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Fill (srcBLen - 1u) zeros at end of scratch buffer */
+    arm_fill_q15(0, pScr1, (srcBLen - 1u));
+
+    /* Update pointer */
+    pScr1 += (srcBLen - 1u);
+
+
+    /* Temporary pointer for scratch2 */
+    py = pScratch2;
+
+    /* Initialization of pIn2 pointer */
+    pIn2 = (q7_t *) py;
+
+    pScr2 = py;
+
+    pOut = pDst + firstIndex;
+
+    pScratch1 += firstIndex;
+
+    /* Actual convolution process starts here */
+    blkCnt = (numPoints) >> 2;
+
+
+    while(blkCnt > 0)
+    {
+      /* Initialze temporary scratch pointer as scratch1 */
+      pScr1 = pScratch1;
+
+      /* Clear Accumlators */
+      acc0 = 0;
+      acc1 = 0;
+      acc2 = 0;
+      acc3 = 0;
+
+      /* Read two samples from scratch1 buffer */
+      x1 = *__SIMD32(pScr1)++;
+
+      /* Read next two samples from scratch1 buffer */
+      x2 = *__SIMD32(pScr1)++;
+
+      tapCnt = (srcBLen) >> 2u;
+
+      while(tapCnt > 0u)
+      {
+
+        /* Read four samples from smaller buffer */
+        y1 = _SIMD32_OFFSET(pScr2);
+
+        /* multiply and accumlate */
+        acc0 = __SMLAD(x1, y1, acc0);
+        acc2 = __SMLAD(x2, y1, acc2);
+
+        /* pack input data */
+#ifndef ARM_MATH_BIG_ENDIAN
+        x3 = __PKHBT(x2, x1, 0);
+#else
+        x3 = __PKHBT(x1, x2, 0);
+#endif
+
+        /* multiply and accumlate */
+        acc1 = __SMLADX(x3, y1, acc1);
+
+        /* Read next two samples from scratch1 buffer */
+        x1 = *__SIMD32(pScr1)++;
+
+        /* pack input data */
+#ifndef ARM_MATH_BIG_ENDIAN
+        x3 = __PKHBT(x1, x2, 0);
+#else
+        x3 = __PKHBT(x2, x1, 0);
+#endif
+
+        acc3 = __SMLADX(x3, y1, acc3);
+
+        /* Read four samples from smaller buffer */
+        y1 = _SIMD32_OFFSET(pScr2 + 2u);
+
+        acc0 = __SMLAD(x2, y1, acc0);
+
+        acc2 = __SMLAD(x1, y1, acc2);
+
+        acc1 = __SMLADX(x3, y1, acc1);
+
+        x2 = *__SIMD32(pScr1)++;
+
+#ifndef ARM_MATH_BIG_ENDIAN
+        x3 = __PKHBT(x2, x1, 0);
+#else
+        x3 = __PKHBT(x1, x2, 0);
+#endif
+
+        acc3 = __SMLADX(x3, y1, acc3);
+
+        pScr2 += 4u;
+
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+
+
+      /* Update scratch pointer for remaining samples of smaller length sequence */
+      pScr1 -= 4u;
+
+
+      /* apply same above for remaining samples of smaller length sequence */
+      tapCnt = (srcBLen) & 3u;
+
+      while(tapCnt > 0u)
+      {
+
+        /* accumlate the results */
+        acc0 += (*pScr1++ * *pScr2);
+        acc1 += (*pScr1++ * *pScr2);
+        acc2 += (*pScr1++ * *pScr2);
+        acc3 += (*pScr1++ * *pScr2++);
+
+        pScr1 -= 3u;
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      blkCnt--;
+
+      /* Store the result in the accumulator in the destination buffer. */
+      out0 = (q7_t) (__SSAT(acc0 >> 7u, 8));
+      out1 = (q7_t) (__SSAT(acc1 >> 7u, 8));
+      out2 = (q7_t) (__SSAT(acc2 >> 7u, 8));
+      out3 = (q7_t) (__SSAT(acc3 >> 7u, 8));
+
+      *__SIMD32(pOut)++ = __PACKq7(out0, out1, out2, out3);
+
+      /* Initialization of inputB pointer */
+      pScr2 = py;
+
+      pScratch1 += 4u;
+
+    }
+
+    blkCnt = (numPoints) & 0x3;
+
+    /* Calculate convolution for remaining samples of Bigger length sequence */
+    while(blkCnt > 0)
+    {
+      /* Initialze temporary scratch pointer as scratch1 */
+      pScr1 = pScratch1;
+
+      /* Clear Accumlators */
+      acc0 = 0;
+
+      tapCnt = (srcBLen) >> 1u;
+
+      while(tapCnt > 0u)
+      {
+
+        /* Read next two samples from scratch1 buffer */
+        x1 = *__SIMD32(pScr1)++;
+
+        /* Read two samples from smaller buffer */
+        y1 = *__SIMD32(pScr2)++;
+
+        acc0 = __SMLAD(x1, y1, acc0);
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      tapCnt = (srcBLen) & 1u;
+
+      /* apply same above for remaining samples of smaller length sequence */
+      while(tapCnt > 0u)
+      {
+
+        /* accumlate the results */
+        acc0 += (*pScr1++ * *pScr2++);
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      blkCnt--;
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q7_t) (__SSAT(acc0 >> 7u, 8));
+
+      /* Initialization of inputB pointer */
+      pScr2 = py;
+
+      pScratch1 += 1u;
+
+    }
+
+    /* set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+
+
+  }
+
+  return (status);
+
+}
+
+#else
+
+arm_status arm_conv_partial_opt_q7(
+  q7_t * pSrcA,
+  uint32_t srcALen,
+  q7_t * pSrcB,
+  uint32_t srcBLen,
+  q7_t * pDst,
+  uint32_t firstIndex,
+  uint32_t numPoints,
+  q15_t * pScratch1,
+  q15_t * pScratch2)
+{
+
+  q15_t *pScr2, *pScr1;                          /* Intermediate pointers for scratch pointers */
+  q15_t x4;                                      /* Temporary input variable */
+  q7_t *pIn1, *pIn2;                             /* inputA and inputB pointer */
+  uint32_t j, k, blkCnt, tapCnt;                 /* loop counter */
+  q7_t *px;                                      /* Temporary input1 pointer */
+  q15_t *py;                                     /* Temporary input2 pointer */
+  q31_t acc0, acc1, acc2, acc3;                  /* Accumulator */
+  arm_status status;
+  q7_t *pOut = pDst;                             /* output pointer */
+  q15_t x10, x11, x20, x21;                      /* Temporary input variables */
+  q15_t y10, y11;                                /* Temporary input variables */
+  q7_t out0, out1, out2, out3;                   /* temporary variables */
+
+  /* Check for range of output samples to be calculated */
+  if((firstIndex + numPoints) > ((srcALen + (srcBLen - 1u))))
+  {
+    /* Set status as ARM_MATH_ARGUMENT_ERROR */
+    status = ARM_MATH_ARGUMENT_ERROR;
+  }
+  else
+  {
+
+    /* The algorithm implementation is based on the lengths of the inputs. */
+    /* srcB is always made to slide across srcA. */
+    /* So srcBLen is always considered as shorter or equal to srcALen */
+    if(srcALen >= srcBLen)
+    {
+      /* Initialization of inputA pointer */
+      pIn1 = pSrcA;
+
+      /* Initialization of inputB pointer */
+      pIn2 = pSrcB;
+    }
+    else
+    {
+      /* Initialization of inputA pointer */
+      pIn1 = pSrcB;
+
+      /* Initialization of inputB pointer */
+      pIn2 = pSrcA;
+
+      /* srcBLen is always considered as shorter or equal to srcALen */
+      j = srcBLen;
+      srcBLen = srcALen;
+      srcALen = j;
+    }
+
+    /* pointer to take end of scratch2 buffer */
+    pScr2 = pScratch2;
+
+    /* points to smaller length sequence */
+    px = pIn2 + srcBLen - 1;
+
+    /* Apply loop unrolling and do 4 Copies simultaneously. */
+    k = srcBLen >> 2u;
+
+    /* First part of the processing with loop unrolling copies 4 data points at a time.       
+     ** a second loop below copies for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* copy second buffer in reversal manner */
+      x4 = (q15_t) * px--;
+      *pScr2++ = x4;
+      x4 = (q15_t) * px--;
+      *pScr2++ = x4;
+      x4 = (q15_t) * px--;
+      *pScr2++ = x4;
+      x4 = (q15_t) * px--;
+      *pScr2++ = x4;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, copy remaining samples here.       
+     ** No loop unrolling is used. */
+    k = srcBLen % 0x4u;
+
+    while(k > 0u)
+    {
+      /* copy second buffer in reversal manner for remaining samples */
+      x4 = (q15_t) * px--;
+      *pScr2++ = x4;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Initialze temporary scratch pointer */
+    pScr1 = pScratch1;
+
+    /* Fill (srcBLen - 1u) zeros in scratch buffer */
+    arm_fill_q15(0, pScr1, (srcBLen - 1u));
+
+    /* Update temporary scratch pointer */
+    pScr1 += (srcBLen - 1u);
+
+    /* Copy (srcALen) samples in scratch buffer */
+    /* Apply loop unrolling and do 4 Copies simultaneously. */
+    k = srcALen >> 2u;
+
+    /* First part of the processing with loop unrolling copies 4 data points at a time.       
+     ** a second loop below copies for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* copy second buffer in reversal manner */
+      x4 = (q15_t) * pIn1++;
+      *pScr1++ = x4;
+      x4 = (q15_t) * pIn1++;
+      *pScr1++ = x4;
+      x4 = (q15_t) * pIn1++;
+      *pScr1++ = x4;
+      x4 = (q15_t) * pIn1++;
+      *pScr1++ = x4;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, copy remaining samples here.       
+     ** No loop unrolling is used. */
+    k = srcALen % 0x4u;
+
+    while(k > 0u)
+    {
+      /* copy second buffer in reversal manner for remaining samples */
+      x4 = (q15_t) * pIn1++;
+      *pScr1++ = x4;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Apply loop unrolling and do 4 Copies simultaneously. */
+    k = (srcBLen - 1u) >> 2u;
+
+    /* First part of the processing with loop unrolling copies 4 data points at a time.       
+     ** a second loop below copies for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* copy second buffer in reversal manner */
+      *pScr1++ = 0;
+      *pScr1++ = 0;
+      *pScr1++ = 0;
+      *pScr1++ = 0;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, copy remaining samples here.       
+     ** No loop unrolling is used. */
+    k = (srcBLen - 1u) % 0x4u;
+
+    while(k > 0u)
+    {
+      /* copy second buffer in reversal manner for remaining samples */
+      *pScr1++ = 0;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+
+    /* Temporary pointer for scratch2 */
+    py = pScratch2;
+
+    /* Initialization of pIn2 pointer */
+    pIn2 = (q7_t *) py;
+
+    pScr2 = py;
+
+    pOut = pDst + firstIndex;
+
+    pScratch1 += firstIndex;
+
+    /* Actual convolution process starts here */
+    blkCnt = (numPoints) >> 2;
+
+
+    while(blkCnt > 0)
+    {
+      /* Initialze temporary scratch pointer as scratch1 */
+      pScr1 = pScratch1;
+
+      /* Clear Accumlators */
+      acc0 = 0;
+      acc1 = 0;
+      acc2 = 0;
+      acc3 = 0;
+
+      /* Read two samples from scratch1 buffer */
+      x10 = *pScr1++;
+      x11 = *pScr1++;
+
+      /* Read next two samples from scratch1 buffer */
+      x20 = *pScr1++;
+      x21 = *pScr1++;
+
+      tapCnt = (srcBLen) >> 2u;
+
+      while(tapCnt > 0u)
+      {
+
+        /* Read four samples from smaller buffer */
+        y10 = *pScr2;
+        y11 = *(pScr2 + 1u);
+
+        /* multiply and accumlate */
+        acc0 += (q31_t) x10 *y10;
+        acc0 += (q31_t) x11 *y11;
+        acc2 += (q31_t) x20 *y10;
+        acc2 += (q31_t) x21 *y11;
+
+
+        acc1 += (q31_t) x11 *y10;
+        acc1 += (q31_t) x20 *y11;
+
+        /* Read next two samples from scratch1 buffer */
+        x10 = *pScr1;
+        x11 = *(pScr1 + 1u);
+
+        /* multiply and accumlate */
+        acc3 += (q31_t) x21 *y10;
+        acc3 += (q31_t) x10 *y11;
+
+        /* Read next two samples from scratch2 buffer */
+        y10 = *(pScr2 + 2u);
+        y11 = *(pScr2 + 3u);
+
+        /* multiply and accumlate */
+        acc0 += (q31_t) x20 *y10;
+        acc0 += (q31_t) x21 *y11;
+        acc2 += (q31_t) x10 *y10;
+        acc2 += (q31_t) x11 *y11;
+        acc1 += (q31_t) x21 *y10;
+        acc1 += (q31_t) x10 *y11;
+
+        /* Read next two samples from scratch1 buffer */
+        x20 = *(pScr1 + 2);
+        x21 = *(pScr1 + 3);
+
+        /* multiply and accumlate */
+        acc3 += (q31_t) x11 *y10;
+        acc3 += (q31_t) x20 *y11;
+
+        /* update scratch pointers */
+
+        pScr1 += 4u;
+        pScr2 += 4u;
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+
+
+      /* Update scratch pointer for remaining samples of smaller length sequence */
+      pScr1 -= 4u;
+
+
+      /* apply same above for remaining samples of smaller length sequence */
+      tapCnt = (srcBLen) & 3u;
+
+      while(tapCnt > 0u)
+      {
+
+        /* accumlate the results */
+        acc0 += (*pScr1++ * *pScr2);
+        acc1 += (*pScr1++ * *pScr2);
+        acc2 += (*pScr1++ * *pScr2);
+        acc3 += (*pScr1++ * *pScr2++);
+
+        pScr1 -= 3u;
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      blkCnt--;
+
+      /* Store the result in the accumulator in the destination buffer. */
+      out0 = (q7_t) (__SSAT(acc0 >> 7u, 8));
+      out1 = (q7_t) (__SSAT(acc1 >> 7u, 8));
+      out2 = (q7_t) (__SSAT(acc2 >> 7u, 8));
+      out3 = (q7_t) (__SSAT(acc3 >> 7u, 8));
+
+
+      *__SIMD32(pOut)++ = __PACKq7(out0, out1, out2, out3);
+
+      /* Initialization of inputB pointer */
+      pScr2 = py;
+
+      pScratch1 += 4u;
+
+    }
+
+    blkCnt = (numPoints) & 0x3;
+
+    /* Calculate convolution for remaining samples of Bigger length sequence */
+    while(blkCnt > 0)
+    {
+      /* Initialze temporary scratch pointer as scratch1 */
+      pScr1 = pScratch1;
+
+      /* Clear Accumlators */
+      acc0 = 0;
+
+      tapCnt = (srcBLen) >> 1u;
+
+      while(tapCnt > 0u)
+      {
+
+        /* Read next two samples from scratch1 buffer */
+        x10 = *pScr1++;
+        x11 = *pScr1++;
+
+        /* Read two samples from smaller buffer */
+        y10 = *pScr2++;
+        y11 = *pScr2++;
+
+        /* multiply and accumlate */
+        acc0 += (q31_t) x10 *y10;
+        acc0 += (q31_t) x11 *y11;
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      tapCnt = (srcBLen) & 1u;
+
+      /* apply same above for remaining samples of smaller length sequence */
+      while(tapCnt > 0u)
+      {
+
+        /* accumlate the results */
+        acc0 += (*pScr1++ * *pScr2++);
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      blkCnt--;
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q7_t) (__SSAT(acc0 >> 7u, 8));
+
+      /* Initialization of inputB pointer */
+      pScr2 = py;
+
+      pScratch1 += 1u;
+
+    }
+
+    /* set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+
+  }
+
+  return (status);
+
+}
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+
+
+/**    
+ * @} end of PartialConv group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_q15.c
new file mode 100644
index 0000000000..8c7ed5f861
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_q15.c
@@ -0,0 +1,778 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010 ARM Limited. All rights reserved.   
+*   
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*   
+* Project: 	    CMSIS DSP Library   
+* Title:		arm_conv_partial_q15.c   
+*   
+* Description:	Partial convolution of Q15 sequences.  
+*   
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+* 
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*  
+* Version 1.0.11 2011/10/18 
+*    Bug Fix in conv, correlation, partial convolution. 
+*
+* Version 1.0.10 2011/7/15 
+*    Big Endian support added and Merged M0 and M3/M4 Source code.  
+*   
+* Version 1.0.3 2010/11/29  
+*    Re-organized the CMSIS folders and updated documentation.   
+*    
+* Version 1.0.2 2010/11/11   
+*    Documentation updated.    
+*   
+* Version 1.0.1 2010/10/05    
+*    Production release and review comments incorporated.   
+*   
+* Version 1.0.0 2010/09/20    
+*    Production release and review comments incorporated   
+*   
+* Version 0.0.7  2010/06/10    
+*    Misra-C changes done   
+*   
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**   
+ * @ingroup groupFilters   
+ */
+
+/**   
+ * @addtogroup PartialConv   
+ * @{   
+ */
+
+/**   
+ * @brief Partial convolution of Q15 sequences.   
+ * @param[in]       *pSrcA points to the first input sequence.   
+ * @param[in]       srcALen length of the first input sequence.   
+ * @param[in]       *pSrcB points to the second input sequence.   
+ * @param[in]       srcBLen length of the second input sequence.   
+ * @param[out]      *pDst points to the location where the output result is written.   
+ * @param[in]       firstIndex is the first output sample to start with.   
+ * @param[in]       numPoints is the number of output points to be computed.   
+ * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].   
+ *   
+ * Refer to arm_conv_partial_fast_q15() for a faster but less precise version of this function for Cortex-M3 and Cortex-M4.  
+ * 
+ * \par    
+ * Refer the function arm_conv_partial_opt_q15() for a faster implementation of this function using scratch buffers.
+ * 
+ */
+
+
+arm_status arm_conv_partial_q15(
+  q15_t * pSrcA,
+  uint32_t srcALen,
+  q15_t * pSrcB,
+  uint32_t srcBLen,
+  q15_t * pDst,
+  uint32_t firstIndex,
+  uint32_t numPoints)
+{
+
+#if (defined(ARM_MATH_CM4) || defined(ARM_MATH_CM3)) && !defined(UNALIGNED_SUPPORT_DISABLE)
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q15_t *pIn1;                                   /* inputA pointer               */
+  q15_t *pIn2;                                   /* inputB pointer               */
+  q15_t *pOut = pDst;                            /* output pointer               */
+  q63_t sum, acc0, acc1, acc2, acc3;             /* Accumulator                  */
+  q15_t *px;                                     /* Intermediate inputA pointer  */
+  q15_t *py;                                     /* Intermediate inputB pointer  */
+  q15_t *pSrc1, *pSrc2;                          /* Intermediate pointers        */
+  q31_t x0, x1, x2, x3, c0;                      /* Temporary input variables */
+  uint32_t j, k, count, check, blkCnt;
+  int32_t blockSize1, blockSize2, blockSize3;    /* loop counter                 */
+  arm_status status;                             /* status of Partial convolution */
+
+  /* Check for range of output samples to be calculated */
+  if((firstIndex + numPoints) > ((srcALen + (srcBLen - 1u))))
+  {
+    /* Set status as ARM_MATH_ARGUMENT_ERROR */
+    status = ARM_MATH_ARGUMENT_ERROR;
+  }
+  else
+  {
+
+    /* The algorithm implementation is based on the lengths of the inputs. */
+    /* srcB is always made to slide across srcA. */
+    /* So srcBLen is always considered as shorter or equal to srcALen */
+    if(srcALen >= srcBLen)
+    {
+      /* Initialization of inputA pointer */
+      pIn1 = pSrcA;
+
+      /* Initialization of inputB pointer */
+      pIn2 = pSrcB;
+    }
+    else
+    {
+      /* Initialization of inputA pointer */
+      pIn1 = pSrcB;
+
+      /* Initialization of inputB pointer */
+      pIn2 = pSrcA;
+
+      /* srcBLen is always considered as shorter or equal to srcALen */
+      j = srcBLen;
+      srcBLen = srcALen;
+      srcALen = j;
+    }
+
+    /* Conditions to check which loopCounter holds   
+     * the first and last indices of the output samples to be calculated. */
+    check = firstIndex + numPoints;
+    blockSize3 = ((int32_t) check - (int32_t) srcALen);
+    blockSize3 = (blockSize3 > 0) ? blockSize3 : 0;
+    blockSize1 = (((int32_t) srcBLen - 1) - (int32_t) firstIndex);
+    blockSize1 = (blockSize1 > 0) ? ((check > (srcBLen - 1u)) ? blockSize1 :
+                                     (int32_t) numPoints) : 0;
+    blockSize2 = (int32_t) check - ((blockSize3 + blockSize1) +
+                                    (int32_t) firstIndex);
+    blockSize2 = (blockSize2 > 0) ? blockSize2 : 0;
+
+    /* conv(x,y) at n = x[n] * y[0] + x[n-1] * y[1] + x[n-2] * y[2] + ...+ x[n-N+1] * y[N -1] */
+    /* The function is internally   
+     * divided into three stages according to the number of multiplications that has to be   
+     * taken place between inputA samples and inputB samples. In the first stage of the   
+     * algorithm, the multiplications increase by one for every iteration.   
+     * In the second stage of the algorithm, srcBLen number of multiplications are done.   
+     * In the third stage of the algorithm, the multiplications decrease by one   
+     * for every iteration. */
+
+    /* Set the output pointer to point to the firstIndex   
+     * of the output sample to be calculated. */
+    pOut = pDst + firstIndex;
+
+    /* --------------------------   
+     * Initializations of stage1   
+     * -------------------------*/
+
+    /* sum = x[0] * y[0]   
+     * sum = x[0] * y[1] + x[1] * y[0]   
+     * ....   
+     * sum = x[0] * y[srcBlen - 1] + x[1] * y[srcBlen - 2] +...+ x[srcBLen - 1] * y[0]   
+     */
+
+    /* In this stage the MAC operations are increased by 1 for every iteration.   
+       The count variable holds the number of MAC operations performed.   
+       Since the partial convolution starts from firstIndex   
+       Number of Macs to be performed is firstIndex + 1 */
+    count = 1u + firstIndex;
+
+    /* Working pointer of inputA */
+    px = pIn1;
+
+    /* Working pointer of inputB */
+    pSrc2 = pIn2 + firstIndex;
+    py = pSrc2;
+
+    /* ------------------------   
+     * Stage1 process   
+     * ----------------------*/
+
+    /* For loop unrolling by 4, this stage is divided into two. */
+    /* First part of this stage computes the MAC operations less than 4 */
+    /* Second part of this stage computes the MAC operations greater than or equal to 4 */
+
+    /* The first part of the stage starts here */
+    while((count < 4u) && (blockSize1 > 0))
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Loop over number of MAC operations between   
+       * inputA samples and inputB samples */
+      k = count;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum = __SMLALD(*px++, *py--, sum);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q15_t) (__SSAT((sum >> 15), 16));
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      py = ++pSrc2;
+      px = pIn1;
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Decrement the loop counter */
+      blockSize1--;
+    }
+
+    /* The second part of the stage starts here */
+    /* The internal loop, over count, is unrolled by 4 */
+    /* To, read the last two inputB samples using SIMD:   
+     * y[srcBLen] and y[srcBLen-1] coefficients, py is decremented by 1 */
+    py = py - 1;
+
+    while(blockSize1 > 0)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = count >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        /* x[0], x[1] are multiplied with y[srcBLen - 1], y[srcBLen - 2] respectively */
+        sum = __SMLALDX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
+        /* x[2], x[3] are multiplied with y[srcBLen - 3], y[srcBLen - 4] respectively */
+        sum = __SMLALDX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* For the next MAC operations, the pointer py is used without SIMD   
+       * So, py is incremented by 1 */
+      py = py + 1u;
+
+      /* If the count is not a multiple of 4, compute any remaining MACs here.   
+       ** No loop unrolling is used. */
+      k = count % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum = __SMLALD(*px++, *py--, sum);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q15_t) (__SSAT((sum >> 15), 16));
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      py = ++pSrc2 - 1u;
+      px = pIn1;
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Decrement the loop counter */
+      blockSize1--;
+    }
+
+    /* --------------------------   
+     * Initializations of stage2   
+     * ------------------------*/
+
+    /* sum = x[0] * y[srcBLen-1] + x[1] * y[srcBLen-2] +...+ x[srcBLen-1] * y[0]   
+     * sum = x[1] * y[srcBLen-1] + x[2] * y[srcBLen-2] +...+ x[srcBLen] * y[0]   
+     * ....   
+     * sum = x[srcALen-srcBLen-2] * y[srcBLen-1] + x[srcALen] * y[srcBLen-2] +...+ x[srcALen-1] * y[0]   
+     */
+
+    /* Working pointer of inputA */
+    px = pIn1;
+
+    /* Working pointer of inputB */
+    pSrc2 = pIn2 + (srcBLen - 1u);
+    py = pSrc2;
+
+  /* count is the index by which the pointer pIn1 to be incremented */
+  count = 0u;
+
+
+  /* --------------------   
+   * Stage2 process   
+   * -------------------*/
+
+  /* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.   
+   * So, to loop unroll over blockSize2,   
+   * srcBLen should be greater than or equal to 4 */
+  if(srcBLen >= 4u)
+  {
+    /* Loop unroll over blockSize2, by 4 */
+    blkCnt = blockSize2 >> 2u;
+
+    while(blkCnt > 0u)
+    {
+      py = py - 1u;
+
+      /* Set all accumulators to zero */
+      acc0 = 0;
+      acc1 = 0;
+      acc2 = 0;
+      acc3 = 0;
+
+
+      /* read x[0], x[1] samples */
+      x0 = *__SIMD32(px);
+      /* read x[1], x[2] samples */
+      x1 = _SIMD32_OFFSET(px+1);
+	  px+= 2u;
+
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      do
+      {
+        /* Read the last two inputB samples using SIMD:   
+         * y[srcBLen - 1] and y[srcBLen - 2] */
+        c0 = *__SIMD32(py)--;
+
+        /* acc0 +=  x[0] * y[srcBLen - 1] + x[1] * y[srcBLen - 2] */
+        acc0 = __SMLALDX(x0, c0, acc0);
+
+        /* acc1 +=  x[1] * y[srcBLen - 1] + x[2] * y[srcBLen - 2] */
+        acc1 = __SMLALDX(x1, c0, acc1);
+
+        /* Read x[2], x[3] */
+        x2 = *__SIMD32(px);
+
+        /* Read x[3], x[4] */
+        x3 = _SIMD32_OFFSET(px+1);
+
+        /* acc2 +=  x[2] * y[srcBLen - 1] + x[3] * y[srcBLen - 2] */
+        acc2 = __SMLALDX(x2, c0, acc2);
+
+        /* acc3 +=  x[3] * y[srcBLen - 1] + x[4] * y[srcBLen - 2] */
+        acc3 = __SMLALDX(x3, c0, acc3);
+
+        /* Read y[srcBLen - 3] and y[srcBLen - 4] */
+        c0 = *__SIMD32(py)--;
+
+        /* acc0 +=  x[2] * y[srcBLen - 3] + x[3] * y[srcBLen - 4] */
+        acc0 = __SMLALDX(x2, c0, acc0);
+
+        /* acc1 +=  x[3] * y[srcBLen - 3] + x[4] * y[srcBLen - 4] */
+        acc1 = __SMLALDX(x3, c0, acc1);
+
+        /* Read x[4], x[5] */
+        x0 = _SIMD32_OFFSET(px+2);
+
+        /* Read x[5], x[6] */
+        x1 = _SIMD32_OFFSET(px+3);
+		px += 4u;
+
+        /* acc2 +=  x[4] * y[srcBLen - 3] + x[5] * y[srcBLen - 4] */
+        acc2 = __SMLALDX(x0, c0, acc2);
+
+        /* acc3 +=  x[5] * y[srcBLen - 3] + x[6] * y[srcBLen - 4] */
+        acc3 = __SMLALDX(x1, c0, acc3);
+
+      } while(--k);
+
+      /* For the next MAC operations, SIMD is not used   
+       * So, the 16 bit pointer if inputB, py is updated */
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.   
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      if(k == 1u)
+      {
+        /* Read y[srcBLen - 5] */
+        c0 = *(py+1);
+
+#ifdef  ARM_MATH_BIG_ENDIAN
+
+        c0 = c0 << 16u;
+
+#else
+
+        c0 = c0 & 0x0000FFFF;
+
+#endif /*      #ifdef  ARM_MATH_BIG_ENDIAN     */
+
+        /* Read x[7] */
+        x3 = *__SIMD32(px);
+		px++;
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLALD(x0, c0, acc0);
+        acc1 = __SMLALD(x1, c0, acc1);
+        acc2 = __SMLALDX(x1, c0, acc2);
+        acc3 = __SMLALDX(x3, c0, acc3);
+      }
+
+      if(k == 2u)
+      {
+        /* Read y[srcBLen - 5], y[srcBLen - 6] */
+        c0 = _SIMD32_OFFSET(py);
+
+        /* Read x[7], x[8] */
+        x3 = *__SIMD32(px);
+
+        /* Read x[9] */
+        x2 = _SIMD32_OFFSET(px+1);
+		px += 2u;
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLALDX(x0, c0, acc0);
+        acc1 = __SMLALDX(x1, c0, acc1);
+        acc2 = __SMLALDX(x3, c0, acc2);
+        acc3 = __SMLALDX(x2, c0, acc3);
+      }
+
+      if(k == 3u)
+      {
+        /* Read y[srcBLen - 5], y[srcBLen - 6] */
+        c0 = _SIMD32_OFFSET(py);
+
+        /* Read x[7], x[8] */
+        x3 = *__SIMD32(px);
+
+        /* Read x[9] */
+        x2 = _SIMD32_OFFSET(px+1);
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLALDX(x0, c0, acc0);
+        acc1 = __SMLALDX(x1, c0, acc1);
+        acc2 = __SMLALDX(x3, c0, acc2);
+        acc3 = __SMLALDX(x2, c0, acc3);
+
+		c0 = *(py-1);
+
+#ifdef  ARM_MATH_BIG_ENDIAN
+
+        c0 = c0 << 16u;
+#else
+
+        c0 = c0 & 0x0000FFFF;
+#endif /*      #ifdef  ARM_MATH_BIG_ENDIAN     */
+
+        /* Read x[10] */
+        x3 =  _SIMD32_OFFSET(px+2);
+		px += 3u;
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLALDX(x1, c0, acc0);
+        acc1 = __SMLALD(x2, c0, acc1);
+        acc2 = __SMLALDX(x2, c0, acc2);
+        acc3 = __SMLALDX(x3, c0, acc3);
+      }
+
+
+      /* Store the results in the accumulators in the destination buffer. */
+
+#ifndef  ARM_MATH_BIG_ENDIAN
+
+      *__SIMD32(pOut)++ =
+        __PKHBT(__SSAT((acc0 >> 15), 16), __SSAT((acc1 >> 15), 16), 16);
+      *__SIMD32(pOut)++ =
+        __PKHBT(__SSAT((acc2 >> 15), 16), __SSAT((acc3 >> 15), 16), 16);
+
+#else
+
+      *__SIMD32(pOut)++ =
+        __PKHBT(__SSAT((acc1 >> 15), 16), __SSAT((acc0 >> 15), 16), 16);
+      *__SIMD32(pOut)++ =
+        __PKHBT(__SSAT((acc3 >> 15), 16), __SSAT((acc2 >> 15), 16), 16);
+
+#endif /*      #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+      /* Increment the pointer pIn1 index, count by 4 */
+      count += 4u;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pSrc2;
+
+        /* Decrement the loop counter */
+        blkCnt--;
+      }
+
+      /* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.   
+       ** No loop unrolling is used. */
+      blkCnt = (uint32_t) blockSize2 % 0x4u;
+  	  
+      while(blkCnt > 0u)
+      {
+        /* Accumulator is made zero for every iteration */
+        sum = 0;
+
+        /* Apply loop unrolling and compute 4 MACs simultaneously. */
+        k = srcBLen >> 2u;
+
+        /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+         ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+        while(k > 0u)
+        {
+          /* Perform the multiply-accumulates */
+          sum += (q63_t) ((q31_t) * px++ * *py--);
+          sum += (q63_t) ((q31_t) * px++ * *py--);
+          sum += (q63_t) ((q31_t) * px++ * *py--);
+          sum += (q63_t) ((q31_t) * px++ * *py--);
+
+          /* Decrement the loop counter */
+          k--;
+        }
+
+        /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.   
+         ** No loop unrolling is used. */
+        k = srcBLen % 0x4u;
+
+        while(k > 0u)
+        {
+          /* Perform the multiply-accumulates */
+          sum += (q63_t) ((q31_t) * px++ * *py--);
+
+          /* Decrement the loop counter */
+          k--;
+        }
+
+        /* Store the result in the accumulator in the destination buffer. */
+        *pOut++ = (q15_t) (__SSAT(sum >> 15, 16));
+
+        /* Increment the pointer pIn1 index, count by 1 */
+        count++;
+
+        /* Update the inputA and inputB pointers for next MAC calculation */
+        px = pIn1 + count;
+        py = pSrc2;
+
+        /* Decrement the loop counter */
+        blkCnt--;
+      }
+    }
+    else
+    {
+      /* If the srcBLen is not a multiple of 4,   
+       * the blockSize2 loop cannot be unrolled by 4 */
+      blkCnt = (uint32_t) blockSize2;
+
+      while(blkCnt > 0u)
+      {
+        /* Accumulator is made zero for every iteration */
+        sum = 0;
+
+        /* srcBLen number of MACS should be performed */
+        k = srcBLen;
+
+        while(k > 0u)
+        {
+          /* Perform the multiply-accumulate */
+          sum += (q63_t) ((q31_t) * px++ * *py--);
+
+          /* Decrement the loop counter */
+          k--;
+        }
+
+        /* Store the result in the accumulator in the destination buffer. */
+        *pOut++ = (q15_t) (__SSAT(sum >> 15, 16));
+
+        /* Increment the MAC count */
+        count++;
+
+        /* Update the inputA and inputB pointers for next MAC calculation */
+        px = pIn1 + count;
+        py = pSrc2;
+  
+        /* Decrement the loop counter */
+        blkCnt--;
+      }
+    }
+
+
+    /* --------------------------   
+     * Initializations of stage3   
+     * -------------------------*/
+
+    /* sum += x[srcALen-srcBLen+1] * y[srcBLen-1] + x[srcALen-srcBLen+2] * y[srcBLen-2] +...+ x[srcALen-1] * y[1]   
+     * sum += x[srcALen-srcBLen+2] * y[srcBLen-1] + x[srcALen-srcBLen+3] * y[srcBLen-2] +...+ x[srcALen-1] * y[2]   
+     * ....   
+     * sum +=  x[srcALen-2] * y[srcBLen-1] + x[srcALen-1] * y[srcBLen-2]   
+     * sum +=  x[srcALen-1] * y[srcBLen-1]   
+     */
+
+    /* In this stage the MAC operations are decreased by 1 for every iteration.   
+       The count variable holds the number of MAC operations performed */
+    count = srcBLen - 1u;
+
+    /* Working pointer of inputA */
+    pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
+    px = pSrc1;
+
+    /* Working pointer of inputB */
+    pSrc2 = pIn2 + (srcBLen - 1u);
+    pIn2 = pSrc2 - 1u;
+    py = pIn2;
+
+    /* -------------------   
+     * Stage3 process   
+     * ------------------*/
+
+    /* For loop unrolling by 4, this stage is divided into two. */
+    /* First part of this stage computes the MAC operations greater than 4 */
+    /* Second part of this stage computes the MAC operations less than or equal to 4 */
+
+    /* The first part of the stage starts here */
+    j = count >> 2u;
+
+    while((j > 0u) && (blockSize3 > 0))
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = count >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      while(k > 0u)
+      {
+        /* x[srcALen - srcBLen + 1], x[srcALen - srcBLen + 2] are multiplied   
+         * with y[srcBLen - 1], y[srcBLen - 2] respectively */
+        sum = __SMLALDX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
+        /* x[srcALen - srcBLen + 3], x[srcALen - srcBLen + 4] are multiplied   
+         * with y[srcBLen - 3], y[srcBLen - 4] respectively */
+        sum = __SMLALDX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* For the next MAC operations, the pointer py is used without SIMD   
+       * So, py is incremented by 1 */
+      py = py + 1u;
+
+      /* If the count is not a multiple of 4, compute any remaining MACs here.   
+       ** No loop unrolling is used. */
+      k = count % 0x4u;
+
+      while(k > 0u)
+      {
+        /* sum += x[srcALen - srcBLen + 5] * y[srcBLen - 5] */
+        sum = __SMLALD(*px++, *py--, sum);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q15_t) (__SSAT((sum >> 15), 16));
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = ++pSrc1;
+      py = pIn2;
+
+      /* Decrement the MAC count */
+      count--;
+
+      /* Decrement the loop counter */
+      blockSize3--;
+
+      j--;
+    }
+
+    /* The second part of the stage starts here */
+    /* SIMD is not used for the next MAC operations,   
+     * so pointer py is updated to read only one sample at a time */
+    py = py + 1u;
+
+    while(blockSize3 > 0)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = count;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        /* sum +=  x[srcALen-1] * y[srcBLen-1] */
+        sum = __SMLALD(*px++, *py--, sum);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q15_t) (__SSAT((sum >> 15), 16));
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = ++pSrc1;
+      py = pSrc2;
+
+      /* Decrement the MAC count */
+      count--;
+
+      /* Decrement the loop counter */
+      blockSize3--;
+    }
+
+    /* set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+  }
+
+  /* Return to application */
+  return (status);
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  q15_t *pIn1 = pSrcA;                           /* inputA pointer */
+  q15_t *pIn2 = pSrcB;                           /* inputB pointer */
+  q63_t sum;                                     /* Accumulator */
+  uint32_t i, j;                                 /* loop counters */
+  arm_status status;                             /* status of Partial convolution */
+
+  /* Check for range of output samples to be calculated */
+  if((firstIndex + numPoints) > ((srcALen + (srcBLen - 1u))))
+  {
+    /* Set status as ARM_ARGUMENT_ERROR */
+    status = ARM_MATH_ARGUMENT_ERROR;
+  }
+  else
+  {
+    /* Loop to calculate convolution for output length number of values */
+    for (i = firstIndex; i <= (firstIndex + numPoints - 1); i++)
+    {
+      /* Initialize sum with zero to carry on MAC operations */
+      sum = 0;
+
+      /* Loop to perform MAC operations according to convolution equation */
+      for (j = 0; j <= i; j++)
+      {
+        /* Check the array limitations */
+        if(((i - j) < srcBLen) && (j < srcALen))
+        {
+          /* z[i] += x[i-j] * y[j] */
+          sum += ((q31_t) pIn1[j] * (pIn2[i - j]));
+        }
+      }
+
+      /* Store the output in the destination buffer */
+      pDst[i] = (q15_t) __SSAT((sum >> 15u), 16u);
+    }
+    /* set status as ARM_SUCCESS as there are no argument errors */
+    status = ARM_MATH_SUCCESS;
+  }
+  return (status);
+
+#endif /* #if (defined(ARM_MATH_CM4) || defined(ARM_MATH_CM3)) && !defined(UNALIGNED_SUPPORT_DISABLE)  */
+
+}
+
+/**   
+ * @} end of PartialConv group   
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_q31.c
new file mode 100644
index 0000000000..16a0606488
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_q31.c
@@ -0,0 +1,599 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_conv_partial_q31.c    
+*    
+* Description:	Partial convolution of Q31 sequences.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*  
+* Version 1.0.11 2011/10/18  
+*    Bug Fix in conv, correlation, partial convolution.  
+* 
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+*    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup PartialConv    
+ * @{    
+ */
+
+/**    
+ * @brief Partial convolution of Q31 sequences.    
+ * @param[in]       *pSrcA points to the first input sequence.    
+ * @param[in]       srcALen length of the first input sequence.    
+ * @param[in]       *pSrcB points to the second input sequence.    
+ * @param[in]       srcBLen length of the second input sequence.    
+ * @param[out]      *pDst points to the location where the output result is written.    
+ * @param[in]       firstIndex is the first output sample to start with.    
+ * @param[in]       numPoints is the number of output points to be computed.    
+ * @return Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].    
+ *    
+ * See arm_conv_partial_fast_q31() for a faster but less precise implementation of this function for Cortex-M3 and Cortex-M4.    
+ */
+
+arm_status arm_conv_partial_q31(
+  q31_t * pSrcA,
+  uint32_t srcALen,
+  q31_t * pSrcB,
+  uint32_t srcBLen,
+  q31_t * pDst,
+  uint32_t firstIndex,
+  uint32_t numPoints)
+{
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q31_t *pIn1;                                   /* inputA pointer               */
+  q31_t *pIn2;                                   /* inputB pointer               */
+  q31_t *pOut = pDst;                            /* output pointer               */
+  q31_t *px;                                     /* Intermediate inputA pointer  */
+  q31_t *py;                                     /* Intermediate inputB pointer  */
+  q31_t *pSrc1, *pSrc2;                          /* Intermediate pointers        */
+  q63_t sum, acc0, acc1, acc2;                   /* Accumulator                  */
+  q31_t x0, x1, x2, c0;
+  uint32_t j, k, count, check, blkCnt;
+  int32_t blockSize1, blockSize2, blockSize3;    /* loop counter                 */
+  arm_status status;                             /* status of Partial convolution */
+
+
+  /* Check for range of output samples to be calculated */
+  if((firstIndex + numPoints) > ((srcALen + (srcBLen - 1u))))
+  {
+    /* Set status as ARM_MATH_ARGUMENT_ERROR */
+    status = ARM_MATH_ARGUMENT_ERROR;
+  }
+  else
+  {
+
+    /* The algorithm implementation is based on the lengths of the inputs. */
+    /* srcB is always made to slide across srcA. */
+    /* So srcBLen is always considered as shorter or equal to srcALen */
+    if(srcALen >= srcBLen)
+    {
+      /* Initialization of inputA pointer */
+      pIn1 = pSrcA;
+
+      /* Initialization of inputB pointer */
+      pIn2 = pSrcB;
+    }
+    else
+    {
+      /* Initialization of inputA pointer */
+      pIn1 = pSrcB;
+
+      /* Initialization of inputB pointer */
+      pIn2 = pSrcA;
+
+      /* srcBLen is always considered as shorter or equal to srcALen */
+      j = srcBLen;
+      srcBLen = srcALen;
+      srcALen = j;
+    }
+
+    /* Conditions to check which loopCounter holds    
+     * the first and last indices of the output samples to be calculated. */
+    check = firstIndex + numPoints;
+    blockSize3 = ((int32_t) check - (int32_t) srcALen);
+    blockSize3 = (blockSize3 > 0) ? blockSize3 : 0;
+    blockSize1 = (((int32_t) srcBLen - 1) - (int32_t) firstIndex);
+    blockSize1 = (blockSize1 > 0) ? ((check > (srcBLen - 1u)) ? blockSize1 :
+                                     (int32_t) numPoints) : 0;
+    blockSize2 = (int32_t) check - ((blockSize3 + blockSize1) +
+                                    (int32_t) firstIndex);
+    blockSize2 = (blockSize2 > 0) ? blockSize2 : 0;
+
+    /* conv(x,y) at n = x[n] * y[0] + x[n-1] * y[1] + x[n-2] * y[2] + ...+ x[n-N+1] * y[N -1] */
+    /* The function is internally    
+     * divided into three stages according to the number of multiplications that has to be    
+     * taken place between inputA samples and inputB samples. In the first stage of the    
+     * algorithm, the multiplications increase by one for every iteration.    
+     * In the second stage of the algorithm, srcBLen number of multiplications are done.    
+     * In the third stage of the algorithm, the multiplications decrease by one    
+     * for every iteration. */
+
+    /* Set the output pointer to point to the firstIndex    
+     * of the output sample to be calculated. */
+    pOut = pDst + firstIndex;
+
+    /* --------------------------    
+     * Initializations of stage1    
+     * -------------------------*/
+
+    /* sum = x[0] * y[0]    
+     * sum = x[0] * y[1] + x[1] * y[0]    
+     * ....    
+     * sum = x[0] * y[srcBlen - 1] + x[1] * y[srcBlen - 2] +...+ x[srcBLen - 1] * y[0]    
+     */
+
+    /* In this stage the MAC operations are increased by 1 for every iteration.    
+       The count variable holds the number of MAC operations performed.    
+       Since the partial convolution starts from firstIndex    
+       Number of Macs to be performed is firstIndex + 1 */
+    count = 1u + firstIndex;
+
+    /* Working pointer of inputA */
+    px = pIn1;
+
+    /* Working pointer of inputB */
+    pSrc2 = pIn2 + firstIndex;
+    py = pSrc2;
+
+    /* ------------------------    
+     * Stage1 process    
+     * ----------------------*/
+
+    /* The first loop starts here */
+    while(blockSize1 > 0)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = count >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      while(k > 0u)
+      {
+        /* x[0] * y[srcBLen - 1] */
+        sum += (q63_t) * px++ * (*py--);
+        /* x[1] * y[srcBLen - 2] */
+        sum += (q63_t) * px++ * (*py--);
+        /* x[2] * y[srcBLen - 3] */
+        sum += (q63_t) * px++ * (*py--);
+        /* x[3] * y[srcBLen - 4] */
+        sum += (q63_t) * px++ * (*py--);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* If the count is not a multiple of 4, compute any remaining MACs here.    
+       ** No loop unrolling is used. */
+      k = count % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulate */
+        sum += (q63_t) * px++ * (*py--);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q31_t) (sum >> 31);
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      py = ++pSrc2;
+      px = pIn1;
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Decrement the loop counter */
+      blockSize1--;
+    }
+
+    /* --------------------------    
+     * Initializations of stage2    
+     * ------------------------*/
+
+    /* sum = x[0] * y[srcBLen-1] + x[1] * y[srcBLen-2] +...+ x[srcBLen-1] * y[0]    
+     * sum = x[1] * y[srcBLen-1] + x[2] * y[srcBLen-2] +...+ x[srcBLen] * y[0]    
+     * ....    
+     * sum = x[srcALen-srcBLen-2] * y[srcBLen-1] + x[srcALen] * y[srcBLen-2] +...+ x[srcALen-1] * y[0]    
+     */
+
+    /* Working pointer of inputA */
+    px = pIn1;
+
+    /* Working pointer of inputB */
+    pSrc2 = pIn2 + (srcBLen - 1u);
+    py = pSrc2;
+
+    /* count is index by which the pointer pIn1 to be incremented */
+    count = 0u;
+
+    /* -------------------    
+     * Stage2 process    
+     * ------------------*/
+
+    /* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.    
+     * So, to loop unroll over blockSize2,    
+     * srcBLen should be greater than or equal to 4 */
+    if(srcBLen >= 4u)
+    {
+      /* Loop unroll over blkCnt */
+
+      blkCnt = blockSize2 / 3;
+      while(blkCnt > 0u)
+      {
+        /* Set all accumulators to zero */
+        acc0 = 0;
+        acc1 = 0;
+        acc2 = 0;
+
+        /* read x[0], x[1] samples */
+        x0 = *(px++);
+        x1 = *(px++);
+
+        /* Apply loop unrolling and compute 3 MACs simultaneously. */
+        k = srcBLen / 3;
+
+        /* First part of the processing with loop unrolling.  Compute 3 MACs at a time.        
+         ** a second loop below computes MACs for the remaining 1 to 2 samples. */
+        do
+        {
+          /* Read y[srcBLen - 1] sample */
+          c0 = *(py);
+
+          /* Read x[2] sample */
+          x2 = *(px);
+
+          /* Perform the multiply-accumulates */
+          /* acc0 +=  x[0] * y[srcBLen - 1] */
+          acc0 += (q63_t) x0 *c0;
+          /* acc1 +=  x[1] * y[srcBLen - 1] */
+          acc1 += (q63_t) x1 *c0;
+          /* acc2 +=  x[2] * y[srcBLen - 1] */
+          acc2 += (q63_t) x2 *c0;
+
+          /* Read y[srcBLen - 2] sample */
+          c0 = *(py - 1u);
+
+          /* Read x[3] sample */
+          x0 = *(px + 1u);
+
+          /* Perform the multiply-accumulate */
+          /* acc0 +=  x[1] * y[srcBLen - 2] */
+          acc0 += (q63_t) x1 *c0;
+          /* acc1 +=  x[2] * y[srcBLen - 2] */
+          acc1 += (q63_t) x2 *c0;
+          /* acc2 +=  x[3] * y[srcBLen - 2] */
+          acc2 += (q63_t) x0 *c0;
+
+          /* Read y[srcBLen - 3] sample */
+          c0 = *(py - 2u);
+
+          /* Read x[4] sample */
+          x1 = *(px + 2u);
+
+          /* Perform the multiply-accumulates */
+          /* acc0 +=  x[2] * y[srcBLen - 3] */
+          acc0 += (q63_t) x2 *c0;
+          /* acc1 +=  x[3] * y[srcBLen - 2] */
+          acc1 += (q63_t) x0 *c0;
+          /* acc2 +=  x[4] * y[srcBLen - 2] */
+          acc2 += (q63_t) x1 *c0;
+
+
+          px += 3u;
+
+          py -= 3u;
+
+        } while(--k);
+
+        /* If the srcBLen is not a multiple of 3, compute any remaining MACs here.        
+         ** No loop unrolling is used. */
+        k = srcBLen - (3 * (srcBLen / 3));
+
+        while(k > 0u)
+        {
+          /* Read y[srcBLen - 5] sample */
+          c0 = *(py--);
+
+          /* Read x[7] sample */
+          x2 = *(px++);
+
+          /* Perform the multiply-accumulates */
+          /* acc0 +=  x[4] * y[srcBLen - 5] */
+          acc0 += (q63_t) x0 *c0;
+          /* acc1 +=  x[5] * y[srcBLen - 5] */
+          acc1 += (q63_t) x1 *c0;
+          /* acc2 +=  x[6] * y[srcBLen - 5] */
+          acc2 += (q63_t) x2 *c0;
+
+          /* Reuse the present samples for the next MAC */
+          x0 = x1;
+          x1 = x2;
+
+          /* Decrement the loop counter */
+          k--;
+        }
+
+        /* Store the result in the accumulator in the destination buffer. */
+        *pOut++ = (q31_t) (acc0 >> 31);
+        *pOut++ = (q31_t) (acc1 >> 31);
+        *pOut++ = (q31_t) (acc2 >> 31);
+
+        /* Increment the pointer pIn1 index, count by 3 */
+        count += 3u;
+
+        /* Update the inputA and inputB pointers for next MAC calculation */
+        px = pIn1 + count;
+        py = pSrc2;
+
+        /* Decrement the loop counter */
+        blkCnt--;
+      }
+
+      /* If the blockSize2 is not a multiple of 3, compute any remaining output samples here.        
+       ** No loop unrolling is used. */
+      blkCnt = blockSize2 - 3 * (blockSize2 / 3);
+
+      while(blkCnt > 0u)
+      {
+        /* Accumulator is made zero for every iteration */
+        sum = 0;
+
+        /* Apply loop unrolling and compute 4 MACs simultaneously. */
+        k = srcBLen >> 2u;
+
+        /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+         ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+        while(k > 0u)
+        {
+          /* Perform the multiply-accumulates */
+          sum += (q63_t) * px++ * (*py--);
+          sum += (q63_t) * px++ * (*py--);
+          sum += (q63_t) * px++ * (*py--);
+          sum += (q63_t) * px++ * (*py--);
+
+          /* Decrement the loop counter */
+          k--;
+        }
+
+        /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.    
+         ** No loop unrolling is used. */
+        k = srcBLen % 0x4u;
+
+        while(k > 0u)
+        {
+          /* Perform the multiply-accumulate */
+          sum += (q63_t) * px++ * (*py--);
+
+          /* Decrement the loop counter */
+          k--;
+        }
+
+        /* Store the result in the accumulator in the destination buffer. */
+        *pOut++ = (q31_t) (sum >> 31);
+
+        /* Increment the MAC count */
+        count++;
+
+        /* Update the inputA and inputB pointers for next MAC calculation */
+        px = pIn1 + count;
+        py = pSrc2;
+
+        /* Decrement the loop counter */
+        blkCnt--;
+      }
+    }
+    else
+    {
+      /* If the srcBLen is not a multiple of 4,    
+       * the blockSize2 loop cannot be unrolled by 4 */
+      blkCnt = (uint32_t) blockSize2;
+
+      while(blkCnt > 0u)
+      {
+        /* Accumulator is made zero for every iteration */
+        sum = 0;
+
+        /* srcBLen number of MACS should be performed */
+        k = srcBLen;
+
+        while(k > 0u)
+        {
+          /* Perform the multiply-accumulate */
+          sum += (q63_t) * px++ * (*py--);
+
+          /* Decrement the loop counter */
+          k--;
+        }
+
+        /* Store the result in the accumulator in the destination buffer. */
+        *pOut++ = (q31_t) (sum >> 31);
+
+        /* Increment the MAC count */
+        count++;
+
+        /* Update the inputA and inputB pointers for next MAC calculation */
+        px = pIn1 + count;
+        py = pSrc2;
+
+        /* Decrement the loop counter */
+        blkCnt--;
+      }
+    }
+
+
+    /* --------------------------    
+     * Initializations of stage3    
+     * -------------------------*/
+
+    /* sum += x[srcALen-srcBLen+1] * y[srcBLen-1] + x[srcALen-srcBLen+2] * y[srcBLen-2] +...+ x[srcALen-1] * y[1]    
+     * sum += x[srcALen-srcBLen+2] * y[srcBLen-1] + x[srcALen-srcBLen+3] * y[srcBLen-2] +...+ x[srcALen-1] * y[2]    
+     * ....    
+     * sum +=  x[srcALen-2] * y[srcBLen-1] + x[srcALen-1] * y[srcBLen-2]    
+     * sum +=  x[srcALen-1] * y[srcBLen-1]    
+     */
+
+    /* In this stage the MAC operations are decreased by 1 for every iteration.    
+       The blockSize3 variable holds the number of MAC operations performed */
+    count = srcBLen - 1u;
+
+    /* Working pointer of inputA */
+    pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
+    px = pSrc1;
+
+    /* Working pointer of inputB */
+    pSrc2 = pIn2 + (srcBLen - 1u);
+    py = pSrc2;
+
+    /* -------------------    
+     * Stage3 process    
+     * ------------------*/
+
+    while(blockSize3 > 0)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = count >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      while(k > 0u)
+      {
+        sum += (q63_t) * px++ * (*py--);
+        sum += (q63_t) * px++ * (*py--);
+        sum += (q63_t) * px++ * (*py--);
+        sum += (q63_t) * px++ * (*py--);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* If the blockSize3 is not a multiple of 4, compute any remaining MACs here.    
+       ** No loop unrolling is used. */
+      k = count % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulate */
+        sum += (q63_t) * px++ * (*py--);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q31_t) (sum >> 31);
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = ++pSrc1;
+      py = pSrc2;
+
+      /* Decrement the MAC count */
+      count--;
+
+      /* Decrement the loop counter */
+      blockSize3--;
+
+    }
+
+    /* set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+  }
+
+  /* Return to application */
+  return (status);
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  q31_t *pIn1 = pSrcA;                           /* inputA pointer */
+  q31_t *pIn2 = pSrcB;                           /* inputB pointer */
+  q63_t sum;                                     /* Accumulator */
+  uint32_t i, j;                                 /* loop counters */
+  arm_status status;                             /* status of Partial convolution */
+
+  /* Check for range of output samples to be calculated */
+  if((firstIndex + numPoints) > ((srcALen + (srcBLen - 1u))))
+  {
+    /* Set status as ARM_ARGUMENT_ERROR */
+    status = ARM_MATH_ARGUMENT_ERROR;
+  }
+  else
+  {
+    /* Loop to calculate convolution for output length number of values */
+    for (i = firstIndex; i <= (firstIndex + numPoints - 1); i++)
+    {
+      /* Initialize sum with zero to carry on MAC operations */
+      sum = 0;
+
+      /* Loop to perform MAC operations according to convolution equation */
+      for (j = 0; j <= i; j++)
+      {
+        /* Check the array limitations */
+        if(((i - j) < srcBLen) && (j < srcALen))
+        {
+          /* z[i] += x[i-j] * y[j] */
+          sum += ((q63_t) pIn1[j] * (pIn2[i - j]));
+        }
+      }
+
+      /* Store the output in the destination buffer */
+      pDst[i] = (q31_t) (sum >> 31u);
+    }
+    /* set status as ARM_SUCCESS as there are no argument errors */
+    status = ARM_MATH_SUCCESS;
+  }
+  return (status);
+
+#endif /*    #ifndef ARM_MATH_CM0      */
+
+}
+
+/**    
+ * @} end of PartialConv group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_q7.c
new file mode 100644
index 0000000000..ed205838ed
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_q7.c
@@ -0,0 +1,733 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010 ARM Limited. All rights reserved.   
+*   
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*   
+* Project: 	    CMSIS DSP Library   
+* Title:		arm_conv_partial_q7.c   
+*   
+* Description:	Partial convolution of Q7 sequences.   
+*   
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*  
+* Version 1.0.11 2011/10/18 
+*    Bug Fix in conv, correlation, partial convolution. 
+*
+* Version 1.0.10 2011/7/15 
+*    Big Endian support added and Merged M0 and M3/M4 Source code.  
+*   
+* Version 1.0.3 2010/11/29  
+*    Re-organized the CMSIS folders and updated documentation.   
+*    
+* Version 1.0.2 2010/11/11   
+*    Documentation updated.    
+*   
+* Version 1.0.1 2010/10/05    
+*    Production release and review comments incorporated.   
+*   
+* Version 1.0.0 2010/09/20    
+*    Production release and review comments incorporated   
+*   
+* Version 0.0.7  2010/06/10    
+*    Misra-C changes done   
+*   
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**   
+ * @ingroup groupFilters   
+ */
+
+/**   
+ * @addtogroup PartialConv   
+ * @{   
+ */
+
+/**   
+ * @brief Partial convolution of Q7 sequences.   
+ * @param[in]       *pSrcA points to the first input sequence.   
+ * @param[in]       srcALen length of the first input sequence.   
+ * @param[in]       *pSrcB points to the second input sequence.   
+ * @param[in]       srcBLen length of the second input sequence.   
+ * @param[out]      *pDst points to the location where the output result is written.   
+ * @param[in]       firstIndex is the first output sample to start with.   
+ * @param[in]       numPoints is the number of output points to be computed.   
+ * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].   
+ *  
+ * \par    
+ * Refer the function arm_conv_partial_opt_q7() for a faster implementation of this function.
+ *  
+ */
+
+arm_status arm_conv_partial_q7(
+  q7_t * pSrcA,
+  uint32_t srcALen,
+  q7_t * pSrcB,
+  uint32_t srcBLen,
+  q7_t * pDst,
+  uint32_t firstIndex,
+  uint32_t numPoints)
+{
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q7_t *pIn1;                                    /* inputA pointer */
+  q7_t *pIn2;                                    /* inputB pointer */
+  q7_t *pOut = pDst;                             /* output pointer */
+  q7_t *px;                                      /* Intermediate inputA pointer */
+  q7_t *py;                                      /* Intermediate inputB pointer */
+  q7_t *pSrc1, *pSrc2;                           /* Intermediate pointers */
+  q31_t sum, acc0, acc1, acc2, acc3;             /* Accumulator */
+  q31_t input1, input2;
+  q15_t in1, in2;
+  q7_t x0, x1, x2, x3, c0, c1;
+  uint32_t j, k, count, check, blkCnt;
+  int32_t blockSize1, blockSize2, blockSize3;    /* loop counter */
+  arm_status status;
+
+
+  /* Check for range of output samples to be calculated */
+  if((firstIndex + numPoints) > ((srcALen + (srcBLen - 1u))))
+  {
+    /* Set status as ARM_MATH_ARGUMENT_ERROR */
+    status = ARM_MATH_ARGUMENT_ERROR;
+  }
+  else
+  {
+
+    /* The algorithm implementation is based on the lengths of the inputs. */
+    /* srcB is always made to slide across srcA. */
+    /* So srcBLen is always considered as shorter or equal to srcALen */
+    if(srcALen >= srcBLen)
+    {
+      /* Initialization of inputA pointer */
+      pIn1 = pSrcA;
+
+      /* Initialization of inputB pointer */
+      pIn2 = pSrcB;
+    }
+    else
+    {
+      /* Initialization of inputA pointer */
+      pIn1 = pSrcB;
+
+      /* Initialization of inputB pointer */
+      pIn2 = pSrcA;
+
+      /* srcBLen is always considered as shorter or equal to srcALen */
+      j = srcBLen;
+      srcBLen = srcALen;
+      srcALen = j;
+    }
+
+    /* Conditions to check which loopCounter holds   
+     * the first and last indices of the output samples to be calculated. */
+    check = firstIndex + numPoints;
+    blockSize3 = ((int32_t) check - (int32_t) srcALen);
+    blockSize3 = (blockSize3 > 0) ? blockSize3 : 0;
+    blockSize1 = (((int32_t) srcBLen - 1) - (int32_t) firstIndex);
+    blockSize1 = (blockSize1 > 0) ? ((check > (srcBLen - 1u)) ? blockSize1 :
+                                     (int32_t) numPoints) : 0;
+    blockSize2 = (int32_t) check - ((blockSize3 + blockSize1) +
+                                    (int32_t) firstIndex);
+    blockSize2 = (blockSize2 > 0) ? blockSize2 : 0;
+
+    /* conv(x,y) at n = x[n] * y[0] + x[n-1] * y[1] + x[n-2] * y[2] + ...+ x[n-N+1] * y[N -1] */
+    /* The function is internally   
+     * divided into three stages according to the number of multiplications that has to be   
+     * taken place between inputA samples and inputB samples. In the first stage of the   
+     * algorithm, the multiplications increase by one for every iteration.   
+     * In the second stage of the algorithm, srcBLen number of multiplications are done.   
+     * In the third stage of the algorithm, the multiplications decrease by one   
+     * for every iteration. */
+
+    /* Set the output pointer to point to the firstIndex   
+     * of the output sample to be calculated. */
+    pOut = pDst + firstIndex;
+
+    /* --------------------------   
+     * Initializations of stage1   
+     * -------------------------*/
+
+    /* sum = x[0] * y[0]   
+     * sum = x[0] * y[1] + x[1] * y[0]   
+     * ....   
+     * sum = x[0] * y[srcBlen - 1] + x[1] * y[srcBlen - 2] +...+ x[srcBLen - 1] * y[0]   
+     */
+
+    /* In this stage the MAC operations are increased by 1 for every iteration.   
+       The count variable holds the number of MAC operations performed.   
+       Since the partial convolution starts from from firstIndex   
+       Number of Macs to be performed is firstIndex + 1 */
+    count = 1u + firstIndex;
+
+    /* Working pointer of inputA */
+    px = pIn1;
+
+    /* Working pointer of inputB */
+    pSrc2 = pIn2 + firstIndex;
+    py = pSrc2;
+
+    /* ------------------------   
+     * Stage1 process   
+     * ----------------------*/
+
+    /* The first stage starts here */
+    while(blockSize1 > 0)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = count >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      while(k > 0u)
+      {
+        /* x[0] , x[1] */
+        in1 = (q15_t) * px++;
+        in2 = (q15_t) * px++;
+        input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+        /* y[srcBLen - 1] , y[srcBLen - 2] */
+        in1 = (q15_t) * py--;
+        in2 = (q15_t) * py--;
+        input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+        /* x[0] * y[srcBLen - 1] */
+        /* x[1] * y[srcBLen - 2] */
+        sum = __SMLAD(input1, input2, sum);
+
+        /* x[2] , x[3] */
+        in1 = (q15_t) * px++;
+        in2 = (q15_t) * px++;
+        input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+        /* y[srcBLen - 3] , y[srcBLen - 4] */
+        in1 = (q15_t) * py--;
+        in2 = (q15_t) * py--;
+        input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+        /* x[2] * y[srcBLen - 3] */
+        /* x[3] * y[srcBLen - 4] */
+        sum = __SMLAD(input1, input2, sum);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* If the count is not a multiple of 4, compute any remaining MACs here.   
+       ** No loop unrolling is used. */
+      k = count % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum += ((q31_t) * px++ * *py--);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q7_t) (__SSAT(sum >> 7, 8));
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      py = ++pSrc2;
+      px = pIn1;
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Decrement the loop counter */
+      blockSize1--;
+    }
+
+    /* --------------------------   
+     * Initializations of stage2   
+     * ------------------------*/
+
+    /* sum = x[0] * y[srcBLen-1] + x[1] * y[srcBLen-2] +...+ x[srcBLen-1] * y[0]   
+     * sum = x[1] * y[srcBLen-1] + x[2] * y[srcBLen-2] +...+ x[srcBLen] * y[0]   
+     * ....   
+     * sum = x[srcALen-srcBLen-2] * y[srcBLen-1] + x[srcALen] * y[srcBLen-2] +...+ x[srcALen-1] * y[0]   
+     */
+
+    /* Working pointer of inputA */
+    px = pIn1;
+
+    /* Working pointer of inputB */
+    pSrc2 = pIn2 + (srcBLen - 1u);
+    py = pSrc2;
+
+    /* count is index by which the pointer pIn1 to be incremented */
+    count = 0u;
+
+    /* -------------------   
+     * Stage2 process   
+     * ------------------*/
+
+    /* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.   
+     * So, to loop unroll over blockSize2,   
+     * srcBLen should be greater than or equal to 4 */
+    if(srcBLen >= 4u)
+    {
+      /* Loop unroll over blockSize2, by 4 */
+      blkCnt = ((uint32_t) blockSize2 >> 2u);
+
+      while(blkCnt > 0u)
+      {
+        /* Set all accumulators to zero */
+        acc0 = 0;
+        acc1 = 0;
+        acc2 = 0;
+        acc3 = 0;
+
+        /* read x[0], x[1], x[2] samples */
+        x0 = *(px++);
+        x1 = *(px++);
+        x2 = *(px++);
+
+        /* Apply loop unrolling and compute 4 MACs simultaneously. */
+        k = srcBLen >> 2u;
+
+        /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+         ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+        do
+        {
+          /* Read y[srcBLen - 1] sample */
+          c0 = *(py--);
+          /* Read y[srcBLen - 2] sample */
+          c1 = *(py--);
+
+          /* Read x[3] sample */
+          x3 = *(px++);
+
+          /* x[0] and x[1] are packed */
+          in1 = (q15_t) x0;
+          in2 = (q15_t) x1;
+
+          input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+          /* y[srcBLen - 1]   and y[srcBLen - 2] are packed */
+          in1 = (q15_t) c0;
+          in2 = (q15_t) c1;
+
+          input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+          /* acc0 += x[0] * y[srcBLen - 1] + x[1] * y[srcBLen - 2]  */
+          acc0 = __SMLAD(input1, input2, acc0);
+
+          /* x[1] and x[2] are packed */
+          in1 = (q15_t) x1;
+          in2 = (q15_t) x2;
+
+          input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+          /* acc1 += x[1] * y[srcBLen - 1] + x[2] * y[srcBLen - 2]  */
+          acc1 = __SMLAD(input1, input2, acc1);
+
+          /* x[2] and x[3] are packed */
+          in1 = (q15_t) x2;
+          in2 = (q15_t) x3;
+
+          input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+          /* acc2 += x[2] * y[srcBLen - 1] + x[3] * y[srcBLen - 2]  */
+          acc2 = __SMLAD(input1, input2, acc2);
+
+          /* Read x[4] sample */
+          x0 = *(px++);
+
+          /* x[3] and x[4] are packed */
+          in1 = (q15_t) x3;
+          in2 = (q15_t) x0;
+
+          input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+          /* acc3 += x[3] * y[srcBLen - 1] + x[4] * y[srcBLen - 2]  */
+          acc3 = __SMLAD(input1, input2, acc3);
+
+          /* Read y[srcBLen - 3] sample */
+          c0 = *(py--);
+          /* Read y[srcBLen - 4] sample */
+          c1 = *(py--);
+
+          /* Read x[5] sample */
+          x1 = *(px++);
+
+          /* x[2] and x[3] are packed */
+          in1 = (q15_t) x2;
+          in2 = (q15_t) x3;
+
+          input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+          /* y[srcBLen - 3] and y[srcBLen - 4] are packed */
+          in1 = (q15_t) c0;
+          in2 = (q15_t) c1;
+
+          input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+          /* acc0 += x[2] * y[srcBLen - 3] + x[3] * y[srcBLen - 4]  */
+          acc0 = __SMLAD(input1, input2, acc0);
+
+          /* x[3] and x[4] are packed */
+          in1 = (q15_t) x3;
+          in2 = (q15_t) x0;
+
+          input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+          /* acc1 += x[3] * y[srcBLen - 3] + x[4] * y[srcBLen - 4]  */
+          acc1 = __SMLAD(input1, input2, acc1);
+
+          /* x[4] and x[5] are packed */
+          in1 = (q15_t) x0;
+          in2 = (q15_t) x1;
+
+          input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+          /* acc2 += x[4] * y[srcBLen - 3] + x[5] * y[srcBLen - 4]  */
+          acc2 = __SMLAD(input1, input2, acc2);
+
+          /* Read x[6] sample */
+          x2 = *(px++);
+
+          /* x[5] and x[6] are packed */
+          in1 = (q15_t) x1;
+          in2 = (q15_t) x2;
+
+          input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+          /* acc3 += x[5] * y[srcBLen - 3] + x[6] * y[srcBLen - 4]  */
+          acc3 = __SMLAD(input1, input2, acc3);
+
+        } while(--k);
+
+        /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.   
+         ** No loop unrolling is used. */
+        k = srcBLen % 0x4u;
+
+        while(k > 0u)
+        {
+          /* Read y[srcBLen - 5] sample */
+          c0 = *(py--);
+
+          /* Read x[7] sample */
+          x3 = *(px++);
+
+          /* Perform the multiply-accumulates */
+          /* acc0 +=  x[4] * y[srcBLen - 5] */
+          acc0 += ((q31_t) x0 * c0);
+          /* acc1 +=  x[5] * y[srcBLen - 5] */
+          acc1 += ((q31_t) x1 * c0);
+          /* acc2 +=  x[6] * y[srcBLen - 5] */
+          acc2 += ((q31_t) x2 * c0);
+          /* acc3 +=  x[7] * y[srcBLen - 5] */
+          acc3 += ((q31_t) x3 * c0);
+
+          /* Reuse the present samples for the next MAC */
+          x0 = x1;
+          x1 = x2;
+          x2 = x3;
+
+          /* Decrement the loop counter */
+          k--;
+        }
+
+        /* Store the result in the accumulator in the destination buffer. */
+        *pOut++ = (q7_t) (__SSAT(acc0 >> 7, 8));
+        *pOut++ = (q7_t) (__SSAT(acc1 >> 7, 8));
+        *pOut++ = (q7_t) (__SSAT(acc2 >> 7, 8));
+        *pOut++ = (q7_t) (__SSAT(acc3 >> 7, 8));
+
+        /* Increment the pointer pIn1 index, count by 4 */
+        count += 4u;
+
+        /* Update the inputA and inputB pointers for next MAC calculation */
+        px = pIn1 + count;
+        py = pSrc2;
+
+
+        /* Decrement the loop counter */
+        blkCnt--;
+      }
+
+      /* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.   
+       ** No loop unrolling is used. */
+      blkCnt = (uint32_t) blockSize2 % 0x4u;
+
+      while(blkCnt > 0u)
+      {
+        /* Accumulator is made zero for every iteration */
+        sum = 0;
+
+        /* Apply loop unrolling and compute 4 MACs simultaneously. */
+        k = srcBLen >> 2u;
+
+        /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+         ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+        while(k > 0u)
+        {
+
+          /* Reading two inputs of SrcA buffer and packing */
+          in1 = (q15_t) * px++;
+          in2 = (q15_t) * px++;
+          input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+          /* Reading two inputs of SrcB buffer and packing */
+          in1 = (q15_t) * py--;
+          in2 = (q15_t) * py--;
+          input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+          /* Perform the multiply-accumulates */
+          sum = __SMLAD(input1, input2, sum);
+
+          /* Reading two inputs of SrcA buffer and packing */
+          in1 = (q15_t) * px++;
+          in2 = (q15_t) * px++;
+          input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+          /* Reading two inputs of SrcB buffer and packing */
+          in1 = (q15_t) * py--;
+          in2 = (q15_t) * py--;
+          input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+          /* Perform the multiply-accumulates */
+          sum = __SMLAD(input1, input2, sum);
+
+          /* Decrement the loop counter */
+          k--;
+        }
+
+        /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.   
+         ** No loop unrolling is used. */
+        k = srcBLen % 0x4u;
+
+        while(k > 0u)
+        {
+          /* Perform the multiply-accumulates */
+          sum += ((q31_t) * px++ * *py--);
+
+          /* Decrement the loop counter */
+          k--;
+        }
+
+        /* Store the result in the accumulator in the destination buffer. */
+        *pOut++ = (q7_t) (__SSAT(sum >> 7, 8));
+
+        /* Increment the pointer pIn1 index, count by 1 */
+ 	    count++;
+
+        /* Update the inputA and inputB pointers for next MAC calculation */
+      	px = pIn1 + count;
+        py = pSrc2;	
+
+        /* Decrement the loop counter */
+        blkCnt--;
+      }
+    }
+    else
+    {
+      /* If the srcBLen is not a multiple of 4,   
+       * the blockSize2 loop cannot be unrolled by 4 */
+      blkCnt = (uint32_t) blockSize2;
+
+      while(blkCnt > 0u)
+      {
+        /* Accumulator is made zero for every iteration */
+        sum = 0;
+
+        /* srcBLen number of MACS should be performed */
+        k = srcBLen;
+
+        while(k > 0u)
+        {
+          /* Perform the multiply-accumulate */
+          sum += ((q31_t) * px++ * *py--);
+
+          /* Decrement the loop counter */
+          k--;
+        }
+
+        /* Store the result in the accumulator in the destination buffer. */
+        *pOut++ = (q7_t) (__SSAT(sum >> 7, 8));
+
+        /* Increment the MAC count */
+        count++;
+
+        /* Update the inputA and inputB pointers for next MAC calculation */
+        px = pIn1 + count;
+        py = pSrc2;
+
+        /* Decrement the loop counter */
+        blkCnt--;
+      }
+    }
+
+
+    /* --------------------------   
+     * Initializations of stage3   
+     * -------------------------*/
+
+    /* sum += x[srcALen-srcBLen+1] * y[srcBLen-1] + x[srcALen-srcBLen+2] * y[srcBLen-2] +...+ x[srcALen-1] * y[1]   
+     * sum += x[srcALen-srcBLen+2] * y[srcBLen-1] + x[srcALen-srcBLen+3] * y[srcBLen-2] +...+ x[srcALen-1] * y[2]   
+     * ....   
+     * sum +=  x[srcALen-2] * y[srcBLen-1] + x[srcALen-1] * y[srcBLen-2]   
+     * sum +=  x[srcALen-1] * y[srcBLen-1]   
+     */
+
+    /* In this stage the MAC operations are decreased by 1 for every iteration.   
+       The count variable holds the number of MAC operations performed */
+    count = srcBLen - 1u;
+
+    /* Working pointer of inputA */
+    pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
+    px = pSrc1;
+
+    /* Working pointer of inputB */
+    pSrc2 = pIn2 + (srcBLen - 1u);
+    py = pSrc2;
+
+    /* -------------------   
+     * Stage3 process   
+     * ------------------*/
+
+    while(blockSize3 > 0)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = count >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      while(k > 0u)
+      {
+        /* Reading two inputs, x[srcALen - srcBLen + 1] and x[srcALen - srcBLen + 2] of SrcA buffer and packing */
+        in1 = (q15_t) * px++;
+        in2 = (q15_t) * px++;
+        input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+        /* Reading two inputs, y[srcBLen - 1] and y[srcBLen - 2] of SrcB buffer and packing */
+        in1 = (q15_t) * py--;
+        in2 = (q15_t) * py--;
+        input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+        /* sum += x[srcALen - srcBLen + 1] * y[srcBLen - 1] */
+        /* sum += x[srcALen - srcBLen + 2] * y[srcBLen - 2] */
+        sum = __SMLAD(input1, input2, sum);
+
+        /* Reading two inputs, x[srcALen - srcBLen + 3] and x[srcALen - srcBLen + 4] of SrcA buffer and packing */
+        in1 = (q15_t) * px++;
+        in2 = (q15_t) * px++;
+        input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+        /* Reading two inputs, y[srcBLen - 3] and y[srcBLen - 4] of SrcB buffer and packing */
+        in1 = (q15_t) * py--;
+        in2 = (q15_t) * py--;
+        input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+        /* sum += x[srcALen - srcBLen + 3] * y[srcBLen - 3] */
+        /* sum += x[srcALen - srcBLen + 4] * y[srcBLen - 4] */
+        sum = __SMLAD(input1, input2, sum);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* If the count is not a multiple of 4, compute any remaining MACs here.   
+       ** No loop unrolling is used. */
+      k = count % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        /* sum +=  x[srcALen-1] * y[srcBLen-1] */
+        sum += ((q31_t) * px++ * *py--);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q7_t) (__SSAT(sum >> 7, 8));
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = ++pSrc1;
+      py = pSrc2;
+
+      /* Decrement the MAC count */
+      count--;
+
+      /* Decrement the loop counter */
+      blockSize3--;
+
+    }
+
+    /* set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+  }
+
+  /* Return to application */
+  return (status);
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  q7_t *pIn1 = pSrcA;                            /* inputA pointer */
+  q7_t *pIn2 = pSrcB;                            /* inputB pointer */
+  q31_t sum;                                     /* Accumulator */
+  uint32_t i, j;                                 /* loop counters */
+  arm_status status;                             /* status of Partial convolution */
+
+  /* Check for range of output samples to be calculated */
+  if((firstIndex + numPoints) > ((srcALen + (srcBLen - 1u))))
+  {
+    /* Set status as ARM_ARGUMENT_ERROR */
+    status = ARM_MATH_ARGUMENT_ERROR;
+  }
+  else
+  {
+    /* Loop to calculate convolution for output length number of values */
+    for (i = firstIndex; i <= (firstIndex + numPoints - 1); i++)
+    {
+      /* Initialize sum with zero to carry on MAC operations */
+      sum = 0;
+
+      /* Loop to perform MAC operations according to convolution equation */
+      for (j = 0; j <= i; j++)
+      {
+        /* Check the array limitations */
+        if(((i - j) < srcBLen) && (j < srcALen))
+        {
+          /* z[i] += x[i-j] * y[j] */
+          sum += ((q15_t) pIn1[j] * (pIn2[i - j]));
+        }
+      }
+
+      /* Store the output in the destination buffer */
+      pDst[i] = (q7_t) __SSAT((sum >> 7u), 8u);
+    }
+    /* set status as ARM_SUCCESS as there are no argument errors */
+    status = ARM_MATH_SUCCESS;
+  }
+  return (status);
+
+#endif /*  #ifndef ARM_MATH_CM0 */
+
+}
+
+/**   
+ * @} end of PartialConv group   
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_q15.c
new file mode 100644
index 0000000000..1907719e74
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_q15.c
@@ -0,0 +1,733 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010 ARM Limited. All rights reserved.   
+*   
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*   
+* Project: 	    CMSIS DSP Library   
+* Title:		arm_conv_q15.c   
+*   
+* Description:	Convolution of Q15 sequences.     
+*   
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.11 2011/10/18 
+*    Bug Fix in conv, correlation, partial convolution. 
+*
+* Version 1.0.10 2011/7/15 
+*    Big Endian support added and Merged M0 and M3/M4 Source code.  
+*   
+* Version 1.0.3 2010/11/29  
+*    Re-organized the CMSIS folders and updated documentation.   
+*    
+* Version 1.0.2 2010/11/11   
+*    Documentation updated.    
+*   
+* Version 1.0.1 2010/10/05    
+*    Production release and review comments incorporated.   
+*   
+* Version 1.0.0 2010/09/20    
+*    Production release and review comments incorporated   
+*   
+* Version 0.0.7  2010/06/10    
+*    Misra-C changes done   
+*   
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**   
+ * @ingroup groupFilters   
+ */
+
+/**   
+ * @addtogroup Conv   
+ * @{   
+ */
+
+/**   
+ * @brief Convolution of Q15 sequences.   
+ * @param[in] *pSrcA points to the first input sequence.   
+ * @param[in] srcALen length of the first input sequence.   
+ * @param[in] *pSrcB points to the second input sequence.   
+ * @param[in] srcBLen length of the second input sequence.   
+ * @param[out] *pDst points to the location where the output result is written.  Length srcALen+srcBLen-1.   
+ * @return none.   
+ *   
+ * @details   
+ * Scaling and Overflow Behavior:   
+ *   
+ * \par   
+ * The function is implemented using a 64-bit internal accumulator.   
+ * Both inputs are in 1.15 format and multiplications yield a 2.30 result.   
+ * The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format.   
+ * This approach provides 33 guard bits and there is no risk of overflow.   
+ * The 34.30 result is then truncated to 34.15 format by discarding the low 15 bits and then saturated to 1.15 format.   
+ *   
+ * \par   
+ * Refer to arm_conv_fast_q15() for a faster but less precise version of this function for Cortex-M3 and Cortex-M4. 
+ *
+ * \par    
+ * Refer the function arm_conv_opt_q15() for a faster implementation of this function using scratch buffers.
+ *  
+ */
+
+void arm_conv_q15(
+  q15_t * pSrcA,
+  uint32_t srcALen,
+  q15_t * pSrcB,
+  uint32_t srcBLen,
+  q15_t * pDst)
+{
+
+#if (defined(ARM_MATH_CM4) || defined(ARM_MATH_CM3)) && !defined(UNALIGNED_SUPPORT_DISABLE)
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q15_t *pIn1;                                   /* inputA pointer */
+  q15_t *pIn2;                                   /* inputB pointer */
+  q15_t *pOut = pDst;                            /* output pointer */
+  q63_t sum, acc0, acc1, acc2, acc3;             /* Accumulator */
+  q15_t *px;                                     /* Intermediate inputA pointer  */
+  q15_t *py;                                     /* Intermediate inputB pointer  */
+  q15_t *pSrc1, *pSrc2;                          /* Intermediate pointers */
+  q31_t x0, x1, x2, x3, c0;                      /* Temporary variables to hold state and coefficient values */
+  uint32_t blockSize1, blockSize2, blockSize3, j, k, count, blkCnt;     /* loop counter */
+
+  /* The algorithm implementation is based on the lengths of the inputs. */
+  /* srcB is always made to slide across srcA. */
+  /* So srcBLen is always considered as shorter or equal to srcALen */
+  if(srcALen >= srcBLen)
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = pSrcA;
+
+    /* Initialization of inputB pointer */
+    pIn2 = pSrcB;
+  }
+  else
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = pSrcB;
+
+    /* Initialization of inputB pointer */
+    pIn2 = pSrcA;
+
+    /* srcBLen is always considered as shorter or equal to srcALen */
+    j = srcBLen;
+    srcBLen = srcALen;
+    srcALen = j;
+  }
+
+  /* conv(x,y) at n = x[n] * y[0] + x[n-1] * y[1] + x[n-2] * y[2] + ...+ x[n-N+1] * y[N -1] */
+  /* The function is internally   
+   * divided into three stages according to the number of multiplications that has to be   
+   * taken place between inputA samples and inputB samples. In the first stage of the   
+   * algorithm, the multiplications increase by one for every iteration.   
+   * In the second stage of the algorithm, srcBLen number of multiplications are done.   
+   * In the third stage of the algorithm, the multiplications decrease by one   
+   * for every iteration. */
+
+  /* The algorithm is implemented in three stages.   
+     The loop counters of each stage is initiated here. */
+  blockSize1 = srcBLen - 1u;
+  blockSize2 = srcALen - (srcBLen - 1u);
+
+  /* --------------------------   
+   * Initializations of stage1   
+   * -------------------------*/
+
+  /* sum = x[0] * y[0]   
+   * sum = x[0] * y[1] + x[1] * y[0]   
+   * ....   
+   * sum = x[0] * y[srcBlen - 1] + x[1] * y[srcBlen - 2] +...+ x[srcBLen - 1] * y[0]   
+   */
+
+  /* In this stage the MAC operations are increased by 1 for every iteration.   
+     The count variable holds the number of MAC operations performed */
+  count = 1u;
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  py = pIn2;
+
+
+  /* ------------------------   
+   * Stage1 process   
+   * ----------------------*/
+
+  /* For loop unrolling by 4, this stage is divided into two. */
+  /* First part of this stage computes the MAC operations less than 4 */
+  /* Second part of this stage computes the MAC operations greater than or equal to 4 */
+
+  /* The first part of the stage starts here */
+  while((count < 4u) && (blockSize1 > 0u))
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Loop over number of MAC operations between   
+     * inputA samples and inputB samples */
+    k = count;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      sum = __SMLALD(*px++, *py--, sum);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut++ = (q15_t) (__SSAT((sum >> 15), 16));
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    py = pIn2 + count;
+    px = pIn1;
+
+    /* Increment the MAC count */
+    count++;
+
+    /* Decrement the loop counter */
+    blockSize1--;
+  }
+
+  /* The second part of the stage starts here */
+  /* The internal loop, over count, is unrolled by 4 */
+  /* To, read the last two inputB samples using SIMD:   
+   * y[srcBLen] and y[srcBLen-1] coefficients, py is decremented by 1 */
+  py = py - 1;
+
+  while(blockSize1 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = count >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      /* x[0], x[1] are multiplied with y[srcBLen - 1], y[srcBLen - 2] respectively */
+      sum = __SMLALDX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
+      /* x[2], x[3] are multiplied with y[srcBLen - 3], y[srcBLen - 4] respectively */
+      sum = __SMLALDX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* For the next MAC operations, the pointer py is used without SIMD   
+     * So, py is incremented by 1 */
+    py = py + 1u;
+
+    /* If the count is not a multiple of 4, compute any remaining MACs here.   
+     ** No loop unrolling is used. */
+    k = count % 0x4u;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      sum = __SMLALD(*px++, *py--, sum);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut++ = (q15_t) (__SSAT((sum >> 15), 16));
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    py = pIn2 + (count - 1u);
+    px = pIn1;
+
+    /* Increment the MAC count */
+    count++;
+
+    /* Decrement the loop counter */
+    blockSize1--;
+  }
+
+  /* --------------------------   
+   * Initializations of stage2   
+   * ------------------------*/
+
+  /* sum = x[0] * y[srcBLen-1] + x[1] * y[srcBLen-2] +...+ x[srcBLen-1] * y[0]   
+   * sum = x[1] * y[srcBLen-1] + x[2] * y[srcBLen-2] +...+ x[srcBLen] * y[0]   
+   * ....   
+   * sum = x[srcALen-srcBLen-2] * y[srcBLen-1] + x[srcALen] * y[srcBLen-2] +...+ x[srcALen-1] * y[0]   
+   */
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  pSrc2 = pIn2 + (srcBLen - 1u);
+  py = pSrc2;
+
+  /* count is the index by which the pointer pIn1 to be incremented */
+  count = 0u;
+
+
+  /* --------------------   
+   * Stage2 process   
+   * -------------------*/
+
+  /* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.   
+   * So, to loop unroll over blockSize2,   
+   * srcBLen should be greater than or equal to 4 */
+  if(srcBLen >= 4u)
+  {
+    /* Loop unroll over blockSize2, by 4 */
+    blkCnt = blockSize2 >> 2u;
+
+    while(blkCnt > 0u)
+    {
+      py = py - 1u;
+
+      /* Set all accumulators to zero */
+      acc0 = 0;
+      acc1 = 0;
+      acc2 = 0;
+      acc3 = 0;
+
+
+      /* read x[0], x[1] samples */
+      x0 = *__SIMD32(px);
+      /* read x[1], x[2] samples */
+      x1 = _SIMD32_OFFSET(px+1);
+	  px+= 2u;
+
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      do
+      {
+        /* Read the last two inputB samples using SIMD:   
+         * y[srcBLen - 1] and y[srcBLen - 2] */
+        c0 = *__SIMD32(py)--;
+
+        /* acc0 +=  x[0] * y[srcBLen - 1] + x[1] * y[srcBLen - 2] */
+        acc0 = __SMLALDX(x0, c0, acc0);
+
+        /* acc1 +=  x[1] * y[srcBLen - 1] + x[2] * y[srcBLen - 2] */
+        acc1 = __SMLALDX(x1, c0, acc1);
+
+        /* Read x[2], x[3] */
+        x2 = *__SIMD32(px);
+
+        /* Read x[3], x[4] */
+        x3 = _SIMD32_OFFSET(px+1);
+
+        /* acc2 +=  x[2] * y[srcBLen - 1] + x[3] * y[srcBLen - 2] */
+        acc2 = __SMLALDX(x2, c0, acc2);
+
+        /* acc3 +=  x[3] * y[srcBLen - 1] + x[4] * y[srcBLen - 2] */
+        acc3 = __SMLALDX(x3, c0, acc3);
+
+        /* Read y[srcBLen - 3] and y[srcBLen - 4] */
+        c0 = *__SIMD32(py)--;
+
+        /* acc0 +=  x[2] * y[srcBLen - 3] + x[3] * y[srcBLen - 4] */
+        acc0 = __SMLALDX(x2, c0, acc0);
+
+        /* acc1 +=  x[3] * y[srcBLen - 3] + x[4] * y[srcBLen - 4] */
+        acc1 = __SMLALDX(x3, c0, acc1);
+
+        /* Read x[4], x[5] */
+        x0 = _SIMD32_OFFSET(px+2);
+
+        /* Read x[5], x[6] */
+        x1 = _SIMD32_OFFSET(px+3);
+		px += 4u;
+
+        /* acc2 +=  x[4] * y[srcBLen - 3] + x[5] * y[srcBLen - 4] */
+        acc2 = __SMLALDX(x0, c0, acc2);
+
+        /* acc3 +=  x[5] * y[srcBLen - 3] + x[6] * y[srcBLen - 4] */
+        acc3 = __SMLALDX(x1, c0, acc3);
+
+      } while(--k);
+
+      /* For the next MAC operations, SIMD is not used   
+       * So, the 16 bit pointer if inputB, py is updated */
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.   
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      if(k == 1u)
+      {
+        /* Read y[srcBLen - 5] */
+        c0 = *(py+1);
+
+#ifdef  ARM_MATH_BIG_ENDIAN
+
+        c0 = c0 << 16u;
+
+#else
+
+        c0 = c0 & 0x0000FFFF;
+
+#endif /*      #ifdef  ARM_MATH_BIG_ENDIAN     */
+        /* Read x[7] */
+        x3 = *__SIMD32(px);
+		px++;
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLALD(x0, c0, acc0);
+        acc1 = __SMLALD(x1, c0, acc1);
+        acc2 = __SMLALDX(x1, c0, acc2);
+        acc3 = __SMLALDX(x3, c0, acc3);
+      }
+
+      if(k == 2u)
+      {
+        /* Read y[srcBLen - 5], y[srcBLen - 6] */
+        c0 = _SIMD32_OFFSET(py);
+
+        /* Read x[7], x[8] */
+        x3 = *__SIMD32(px);
+
+        /* Read x[9] */
+        x2 = _SIMD32_OFFSET(px+1);
+		px += 2u;
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLALDX(x0, c0, acc0);
+        acc1 = __SMLALDX(x1, c0, acc1);
+        acc2 = __SMLALDX(x3, c0, acc2);
+        acc3 = __SMLALDX(x2, c0, acc3);
+      }
+
+      if(k == 3u)
+      {
+        /* Read y[srcBLen - 5], y[srcBLen - 6] */
+        c0 = _SIMD32_OFFSET(py);
+
+        /* Read x[7], x[8] */
+        x3 = *__SIMD32(px);
+
+        /* Read x[9] */
+        x2 = _SIMD32_OFFSET(px+1);
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLALDX(x0, c0, acc0);
+        acc1 = __SMLALDX(x1, c0, acc1);
+        acc2 = __SMLALDX(x3, c0, acc2);
+        acc3 = __SMLALDX(x2, c0, acc3);
+
+		c0 = *(py-1);
+
+#ifdef  ARM_MATH_BIG_ENDIAN
+
+        c0 = c0 << 16u;
+#else
+
+        c0 = c0 & 0x0000FFFF;
+#endif /*      #ifdef  ARM_MATH_BIG_ENDIAN     */
+        /* Read x[10] */
+        x3 =  _SIMD32_OFFSET(px+2);
+		px += 3u;
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLALDX(x1, c0, acc0);
+        acc1 = __SMLALD(x2, c0, acc1);
+        acc2 = __SMLALDX(x2, c0, acc2);
+        acc3 = __SMLALDX(x3, c0, acc3);
+      }
+
+
+      /* Store the results in the accumulators in the destination buffer. */
+
+#ifndef  ARM_MATH_BIG_ENDIAN
+
+      *__SIMD32(pOut)++ =
+        __PKHBT(__SSAT((acc0 >> 15), 16), __SSAT((acc1 >> 15), 16), 16);
+      *__SIMD32(pOut)++ =
+        __PKHBT(__SSAT((acc2 >> 15), 16), __SSAT((acc3 >> 15), 16), 16);
+
+#else
+
+      *__SIMD32(pOut)++ =
+        __PKHBT(__SSAT((acc1 >> 15), 16), __SSAT((acc0 >> 15), 16), 16);
+      *__SIMD32(pOut)++ =
+        __PKHBT(__SSAT((acc3 >> 15), 16), __SSAT((acc2 >> 15), 16), 16);
+
+#endif /*      #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+      /* Increment the pointer pIn1 index, count by 4 */
+      count += 4u;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pSrc2;
+
+       /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.   
+     ** No loop unrolling is used. */
+    blkCnt = blockSize2 % 0x4u;
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum += (q63_t) ((q31_t) * px++ * *py--);
+        sum += (q63_t) ((q31_t) * px++ * *py--);
+        sum += (q63_t) ((q31_t) * px++ * *py--);
+        sum += (q63_t) ((q31_t) * px++ * *py--);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.   
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum += (q63_t) ((q31_t) * px++ * *py--);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q15_t) (__SSAT(sum >> 15, 16));
+
+      /* Increment the pointer pIn1 index, count by 1 */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pSrc2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+  else
+  {
+    /* If the srcBLen is not a multiple of 4,   
+     * the blockSize2 loop cannot be unrolled by 4 */
+    blkCnt = blockSize2;
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* srcBLen number of MACS should be performed */
+      k = srcBLen;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulate */
+        sum += (q63_t) ((q31_t) * px++ * *py--);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q15_t) (__SSAT(sum >> 15, 16));
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pSrc2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+
+
+  /* --------------------------   
+   * Initializations of stage3   
+   * -------------------------*/
+
+  /* sum += x[srcALen-srcBLen+1] * y[srcBLen-1] + x[srcALen-srcBLen+2] * y[srcBLen-2] +...+ x[srcALen-1] * y[1]   
+   * sum += x[srcALen-srcBLen+2] * y[srcBLen-1] + x[srcALen-srcBLen+3] * y[srcBLen-2] +...+ x[srcALen-1] * y[2]   
+   * ....   
+   * sum +=  x[srcALen-2] * y[srcBLen-1] + x[srcALen-1] * y[srcBLen-2]   
+   * sum +=  x[srcALen-1] * y[srcBLen-1]   
+   */
+
+  /* In this stage the MAC operations are decreased by 1 for every iteration.   
+     The blockSize3 variable holds the number of MAC operations performed */
+
+  blockSize3 = srcBLen - 1u;
+
+  /* Working pointer of inputA */
+  pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
+  px = pSrc1;
+
+  /* Working pointer of inputB */
+  pSrc2 = pIn2 + (srcBLen - 1u);
+  pIn2 = pSrc2 - 1u;
+  py = pIn2;
+
+  /* -------------------   
+   * Stage3 process   
+   * ------------------*/
+
+  /* For loop unrolling by 4, this stage is divided into two. */
+  /* First part of this stage computes the MAC operations greater than 4 */
+  /* Second part of this stage computes the MAC operations less than or equal to 4 */
+
+  /* The first part of the stage starts here */
+  j = blockSize3 >> 2u;
+
+  while((j > 0u) && (blockSize3 > 0u))
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = blockSize3 >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* x[srcALen - srcBLen + 1], x[srcALen - srcBLen + 2] are multiplied   
+       * with y[srcBLen - 1], y[srcBLen - 2] respectively */
+      sum = __SMLALDX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
+      /* x[srcALen - srcBLen + 3], x[srcALen - srcBLen + 4] are multiplied   
+       * with y[srcBLen - 3], y[srcBLen - 4] respectively */
+      sum = __SMLALDX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* For the next MAC operations, the pointer py is used without SIMD   
+     * So, py is incremented by 1 */
+    py = py + 1u;
+
+    /* If the blockSize3 is not a multiple of 4, compute any remaining MACs here.   
+     ** No loop unrolling is used. */
+    k = blockSize3 % 0x4u;
+
+    while(k > 0u)
+    {
+      /* sum += x[srcALen - srcBLen + 5] * y[srcBLen - 5] */
+      sum = __SMLALD(*px++, *py--, sum);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut++ = (q15_t) (__SSAT((sum >> 15), 16));
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    px = ++pSrc1;
+    py = pIn2;
+
+    /* Decrement the loop counter */
+    blockSize3--;
+
+    j--;
+  }
+
+  /* The second part of the stage starts here */
+  /* SIMD is not used for the next MAC operations,   
+   * so pointer py is updated to read only one sample at a time */
+  py = py + 1u;
+
+  while(blockSize3 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = blockSize3;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      /* sum +=  x[srcALen-1] * y[srcBLen-1] */
+      sum = __SMLALD(*px++, *py--, sum);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut++ = (q15_t) (__SSAT((sum >> 15), 16));
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    px = ++pSrc1;
+    py = pSrc2;
+
+    /* Decrement the loop counter */
+    blockSize3--;
+  }
+
+#else
+
+/* Run the below code for Cortex-M0 */
+
+  q15_t *pIn1 = pSrcA;                           /* input pointer */
+  q15_t *pIn2 = pSrcB;                           /* coefficient pointer */
+  q63_t sum;                                     /* Accumulator */
+  uint32_t i, j;                                 /* loop counter */
+
+  /* Loop to calculate output of convolution for output length number of times */
+  for (i = 0; i < (srcALen + srcBLen - 1); i++)
+  {
+    /* Initialize sum with zero to carry on MAC operations */
+    sum = 0;
+
+    /* Loop to perform MAC operations according to convolution equation */
+    for (j = 0; j <= i; j++)
+    {
+      /* Check the array limitations */
+      if(((i - j) < srcBLen) && (j < srcALen))
+      {
+        /* z[i] += x[i-j] * y[j] */
+        sum += (q31_t) pIn1[j] * (pIn2[i - j]);
+      }
+    }
+
+    /* Store the output in the destination buffer */
+    pDst[i] = (q15_t) __SSAT((sum >> 15u), 16u);
+  }
+
+#endif /*  #if (defined(ARM_MATH_CM4) || defined(ARM_MATH_CM3)) && !defined(UNALIGNED_SUPPORT_DISABLE)*/
+
+}
+
+/**   
+ * @} end of Conv group   
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_q31.c
new file mode 100644
index 0000000000..769b95abb0
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_q31.c
@@ -0,0 +1,564 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_conv_q31.c    
+*    
+* Description:	Convolution of Q31 sequences.  
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+* 
+* Version 1.0.11 2011/10/18  
+*    Bug Fix in conv, correlation, partial convolution.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+*    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup Conv    
+ * @{    
+ */
+
+/**    
+ * @brief Convolution of Q31 sequences.    
+ * @param[in] *pSrcA points to the first input sequence.    
+ * @param[in] srcALen length of the first input sequence.    
+ * @param[in] *pSrcB points to the second input sequence.    
+ * @param[in] srcBLen length of the second input sequence.    
+ * @param[out] *pDst points to the location where the output result is written.  Length srcALen+srcBLen-1.    
+ * @return none.    
+ *    
+ * @details    
+ * Scaling and Overflow Behavior:    
+ *    
+ * \par    
+ * The function is implemented using an internal 64-bit accumulator.    
+ * The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit.    
+ * There is no saturation on intermediate additions.    
+ * Thus, if the accumulator overflows it wraps around and distorts the result.    
+ * The input signals should be scaled down to avoid intermediate overflows.    
+ * Scale down the inputs by log2(min(srcALen, srcBLen)) (log2 is read as log to the base 2) times to avoid overflows,    
+ * as maximum of min(srcALen, srcBLen) number of additions are carried internally.    
+ * The 2.62 accumulator is right shifted by 31 bits and saturated to 1.31 format to yield the final result.    
+ *    
+ * \par    
+ * See arm_conv_fast_q31() for a faster but less precise implementation of this function for Cortex-M3 and Cortex-M4.    
+ */
+
+void arm_conv_q31(
+  q31_t * pSrcA,
+  uint32_t srcALen,
+  q31_t * pSrcB,
+  uint32_t srcBLen,
+  q31_t * pDst)
+{
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q31_t *pIn1;                                   /* inputA pointer */
+  q31_t *pIn2;                                   /* inputB pointer */
+  q31_t *pOut = pDst;                            /* output pointer */
+  q31_t *px;                                     /* Intermediate inputA pointer  */
+  q31_t *py;                                     /* Intermediate inputB pointer  */
+  q31_t *pSrc1, *pSrc2;                          /* Intermediate pointers */
+  q63_t sum;                                     /* Accumulator */
+  q63_t acc0, acc1, acc2;                        /* Accumulator */
+  q31_t x0, x1, x2, c0;                          /* Temporary variables to hold state and coefficient values */
+  uint32_t j, k, count, blkCnt, blockSize1, blockSize2, blockSize3;     /* loop counter */
+
+  /* The algorithm implementation is based on the lengths of the inputs. */
+  /* srcB is always made to slide across srcA. */
+  /* So srcBLen is always considered as shorter or equal to srcALen */
+  if(srcALen >= srcBLen)
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = pSrcA;
+
+    /* Initialization of inputB pointer */
+    pIn2 = pSrcB;
+  }
+  else
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = (q31_t *) pSrcB;
+
+    /* Initialization of inputB pointer */
+    pIn2 = (q31_t *) pSrcA;
+
+    /* srcBLen is always considered as shorter or equal to srcALen */
+    j = srcBLen;
+    srcBLen = srcALen;
+    srcALen = j;
+  }
+
+  /* conv(x,y) at n = x[n] * y[0] + x[n-1] * y[1] + x[n-2] * y[2] + ...+ x[n-N+1] * y[N -1] */
+  /* The function is internally    
+   * divided into three stages according to the number of multiplications that has to be    
+   * taken place between inputA samples and inputB samples. In the first stage of the    
+   * algorithm, the multiplications increase by one for every iteration.    
+   * In the second stage of the algorithm, srcBLen number of multiplications are done.    
+   * In the third stage of the algorithm, the multiplications decrease by one    
+   * for every iteration. */
+
+  /* The algorithm is implemented in three stages.    
+     The loop counters of each stage is initiated here. */
+  blockSize1 = srcBLen - 1u;
+  blockSize2 = srcALen - (srcBLen - 1u);
+  blockSize3 = blockSize1;
+
+  /* --------------------------    
+   * Initializations of stage1    
+   * -------------------------*/
+
+  /* sum = x[0] * y[0]    
+   * sum = x[0] * y[1] + x[1] * y[0]    
+   * ....    
+   * sum = x[0] * y[srcBlen - 1] + x[1] * y[srcBlen - 2] +...+ x[srcBLen - 1] * y[0]    
+   */
+
+  /* In this stage the MAC operations are increased by 1 for every iteration.    
+     The count variable holds the number of MAC operations performed */
+  count = 1u;
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  py = pIn2;
+
+
+  /* ------------------------    
+   * Stage1 process    
+   * ----------------------*/
+
+  /* The first stage starts here */
+  while(blockSize1 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = count >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* x[0] * y[srcBLen - 1] */
+      sum += (q63_t) * px++ * (*py--);
+      /* x[1] * y[srcBLen - 2] */
+      sum += (q63_t) * px++ * (*py--);
+      /* x[2] * y[srcBLen - 3] */
+      sum += (q63_t) * px++ * (*py--);
+      /* x[3] * y[srcBLen - 4] */
+      sum += (q63_t) * px++ * (*py--);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, compute any remaining MACs here.    
+     ** No loop unrolling is used. */
+    k = count % 0x4u;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      sum += (q63_t) * px++ * (*py--);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut++ = (q31_t) (sum >> 31);
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    py = pIn2 + count;
+    px = pIn1;
+
+    /* Increment the MAC count */
+    count++;
+
+    /* Decrement the loop counter */
+    blockSize1--;
+  }
+
+  /* --------------------------    
+   * Initializations of stage2    
+   * ------------------------*/
+
+  /* sum = x[0] * y[srcBLen-1] + x[1] * y[srcBLen-2] +...+ x[srcBLen-1] * y[0]    
+   * sum = x[1] * y[srcBLen-1] + x[2] * y[srcBLen-2] +...+ x[srcBLen] * y[0]    
+   * ....    
+   * sum = x[srcALen-srcBLen-2] * y[srcBLen-1] + x[srcALen] * y[srcBLen-2] +...+ x[srcALen-1] * y[0]    
+   */
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  pSrc2 = pIn2 + (srcBLen - 1u);
+  py = pSrc2;
+
+  /* count is index by which the pointer pIn1 to be incremented */
+  count = 0u;
+
+  /* -------------------    
+   * Stage2 process    
+   * ------------------*/
+
+  /* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.    
+   * So, to loop unroll over blockSize2,    
+   * srcBLen should be greater than or equal to 4 */
+  if(srcBLen >= 4u)
+  {
+    /* Loop unroll by 3 */
+    blkCnt = blockSize2 / 3;
+
+    while(blkCnt > 0u)
+    {
+      /* Set all accumulators to zero */
+      acc0 = 0;
+      acc1 = 0;
+      acc2 = 0;
+
+      /* read x[0], x[1], x[2] samples */
+      x0 = *(px++);
+      x1 = *(px++);
+
+      /* Apply loop unrolling and compute 3 MACs simultaneously. */
+      k = srcBLen / 3;
+
+      /* First part of the processing with loop unrolling.  Compute 3 MACs at a time.        
+       ** a second loop below computes MACs for the remaining 1 to 2 samples. */
+      do
+      {
+        /* Read y[srcBLen - 1] sample */
+        c0 = *(py);
+
+        /* Read x[3] sample */
+        x2 = *(px);
+
+        /* Perform the multiply-accumulates */
+        /* acc0 +=  x[0] * y[srcBLen - 1] */
+        acc0 += ((q63_t) x0 * c0);
+        /* acc1 +=  x[1] * y[srcBLen - 1] */
+        acc1 += ((q63_t) x1 * c0);
+        /* acc2 +=  x[2] * y[srcBLen - 1] */
+        acc2 += ((q63_t) x2 * c0);
+
+        /* Read y[srcBLen - 2] sample */
+        c0 = *(py - 1u);
+
+        /* Read x[4] sample */
+        x0 = *(px + 1u);
+
+        /* Perform the multiply-accumulate */
+        /* acc0 +=  x[1] * y[srcBLen - 2] */
+        acc0 += ((q63_t) x1 * c0);
+        /* acc1 +=  x[2] * y[srcBLen - 2] */
+        acc1 += ((q63_t) x2 * c0);
+        /* acc2 +=  x[3] * y[srcBLen - 2] */
+        acc2 += ((q63_t) x0 * c0);
+
+        /* Read y[srcBLen - 3] sample */
+        c0 = *(py - 2u);
+
+        /* Read x[5] sample */
+        x1 = *(px + 2u);
+
+        /* Perform the multiply-accumulates */
+        /* acc0 +=  x[2] * y[srcBLen - 3] */
+        acc0 += ((q63_t) x2 * c0);
+        /* acc1 +=  x[3] * y[srcBLen - 2] */
+        acc1 += ((q63_t) x0 * c0);
+        /* acc2 +=  x[4] * y[srcBLen - 2] */
+        acc2 += ((q63_t) x1 * c0);
+
+        /* update scratch pointers */
+        px += 3u;
+        py -= 3u;
+
+      } while(--k);
+
+      /* If the srcBLen is not a multiple of 3, compute any remaining MACs here.        
+       ** No loop unrolling is used. */
+      k = srcBLen - (3 * (srcBLen / 3));
+
+      while(k > 0u)
+      {
+        /* Read y[srcBLen - 5] sample */
+        c0 = *(py--);
+
+        /* Read x[7] sample */
+        x2 = *(px++);
+
+        /* Perform the multiply-accumulates */
+        /* acc0 +=  x[4] * y[srcBLen - 5] */
+        acc0 += ((q63_t) x0 * c0);
+        /* acc1 +=  x[5] * y[srcBLen - 5] */
+        acc1 += ((q63_t) x1 * c0);
+        /* acc2 +=  x[6] * y[srcBLen - 5] */
+        acc2 += ((q63_t) x2 * c0);
+
+        /* Reuse the present samples for the next MAC */
+        x0 = x1;
+        x1 = x2;
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the results in the accumulators in the destination buffer. */
+      *pOut++ = (q31_t) (acc0 >> 31);
+      *pOut++ = (q31_t) (acc1 >> 31);
+      *pOut++ = (q31_t) (acc2 >> 31);
+
+      /* Increment the pointer pIn1 index, count by 3 */
+      count += 3u;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pSrc2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the blockSize2 is not a multiple of 3, compute any remaining output samples here.        
+     ** No loop unrolling is used. */
+    blkCnt = blockSize2 - 3 * (blockSize2 / 3);
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum += (q63_t) * px++ * (*py--);
+        sum += (q63_t) * px++ * (*py--);
+        sum += (q63_t) * px++ * (*py--);
+        sum += (q63_t) * px++ * (*py--);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.    
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulate */
+        sum += (q63_t) * px++ * (*py--);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q31_t) (sum >> 31);
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pSrc2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+  else
+  {
+    /* If the srcBLen is not a multiple of 4,    
+     * the blockSize2 loop cannot be unrolled by 4 */
+    blkCnt = blockSize2;
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* srcBLen number of MACS should be performed */
+      k = srcBLen;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulate */
+        sum += (q63_t) * px++ * (*py--);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q31_t) (sum >> 31);
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pSrc2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+
+
+  /* --------------------------    
+   * Initializations of stage3    
+   * -------------------------*/
+
+  /* sum += x[srcALen-srcBLen+1] * y[srcBLen-1] + x[srcALen-srcBLen+2] * y[srcBLen-2] +...+ x[srcALen-1] * y[1]    
+   * sum += x[srcALen-srcBLen+2] * y[srcBLen-1] + x[srcALen-srcBLen+3] * y[srcBLen-2] +...+ x[srcALen-1] * y[2]    
+   * ....    
+   * sum +=  x[srcALen-2] * y[srcBLen-1] + x[srcALen-1] * y[srcBLen-2]    
+   * sum +=  x[srcALen-1] * y[srcBLen-1]    
+   */
+
+  /* In this stage the MAC operations are decreased by 1 for every iteration.    
+     The blockSize3 variable holds the number of MAC operations performed */
+
+  /* Working pointer of inputA */
+  pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
+  px = pSrc1;
+
+  /* Working pointer of inputB */
+  pSrc2 = pIn2 + (srcBLen - 1u);
+  py = pSrc2;
+
+  /* -------------------    
+   * Stage3 process    
+   * ------------------*/
+
+  while(blockSize3 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = blockSize3 >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* sum += x[srcALen - srcBLen + 1] * y[srcBLen - 1] */
+      sum += (q63_t) * px++ * (*py--);
+      /* sum += x[srcALen - srcBLen + 2] * y[srcBLen - 2] */
+      sum += (q63_t) * px++ * (*py--);
+      /* sum += x[srcALen - srcBLen + 3] * y[srcBLen - 3] */
+      sum += (q63_t) * px++ * (*py--);
+      /* sum += x[srcALen - srcBLen + 4] * y[srcBLen - 4] */
+      sum += (q63_t) * px++ * (*py--);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the blockSize3 is not a multiple of 4, compute any remaining MACs here.    
+     ** No loop unrolling is used. */
+    k = blockSize3 % 0x4u;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      sum += (q63_t) * px++ * (*py--);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut++ = (q31_t) (sum >> 31);
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    px = ++pSrc1;
+    py = pSrc2;
+
+    /* Decrement the loop counter */
+    blockSize3--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  q31_t *pIn1 = pSrcA;                           /* input pointer */
+  q31_t *pIn2 = pSrcB;                           /* coefficient pointer */
+  q63_t sum;                                     /* Accumulator */
+  uint32_t i, j;                                 /* loop counter */
+
+  /* Loop to calculate output of convolution for output length number of times */
+  for (i = 0; i < (srcALen + srcBLen - 1); i++)
+  {
+    /* Initialize sum with zero to carry on MAC operations */
+    sum = 0;
+
+    /* Loop to perform MAC operations according to convolution equation */
+    for (j = 0; j <= i; j++)
+    {
+      /* Check the array limitations */
+      if(((i - j) < srcBLen) && (j < srcALen))
+      {
+        /* z[i] += x[i-j] * y[j] */
+        sum += ((q63_t) pIn1[j] * (pIn2[i - j]));
+      }
+    }
+
+    /* Store the output in the destination buffer */
+    pDst[i] = (q31_t) (sum >> 31u);
+  }
+
+#endif /*     #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of Conv group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_q7.c
new file mode 100644
index 0000000000..eb78fd5333
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_q7.c
@@ -0,0 +1,689 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010 ARM Limited. All rights reserved.   
+*   
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*   
+* Project: 	    CMSIS DSP Library   
+* Title:		arm_conv_q7.c   
+*   
+* Description:	Convolution of Q7 sequences. 
+*   
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*  
+* Version 1.0.11 2011/10/18 
+*    Bug Fix in conv, correlation, partial convolution. 
+*
+* Version 1.0.10 2011/7/15 
+*    Big Endian support added and Merged M0 and M3/M4 Source code.  
+*   
+* Version 1.0.3 2010/11/29  
+*    Re-organized the CMSIS folders and updated documentation.   
+*    
+* Version 1.0.2 2010/11/11   
+*    Documentation updated.    
+*   
+* Version 1.0.1 2010/10/05    
+*    Production release and review comments incorporated.   
+*   
+* Version 1.0.0 2010/09/20    
+*    Production release and review comments incorporated   
+*   
+* Version 0.0.7  2010/06/10    
+*    Misra-C changes done   
+*   
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**   
+ * @ingroup groupFilters   
+ */
+
+/**   
+ * @addtogroup Conv   
+ * @{   
+ */
+
+/**   
+ * @brief Convolution of Q7 sequences.   
+ * @param[in] *pSrcA points to the first input sequence.   
+ * @param[in] srcALen length of the first input sequence.   
+ * @param[in] *pSrcB points to the second input sequence.   
+ * @param[in] srcBLen length of the second input sequence.   
+ * @param[out] *pDst points to the location where the output result is written.  Length srcALen+srcBLen-1.   
+ * @return none.   
+ *   
+ * @details   
+ * Scaling and Overflow Behavior:   
+ *   
+ * \par   
+ * The function is implemented using a 32-bit internal accumulator.   
+ * Both the inputs are represented in 1.7 format and multiplications yield a 2.14 result.   
+ * The 2.14 intermediate results are accumulated in a 32-bit accumulator in 18.14 format.   
+ * This approach provides 17 guard bits and there is no risk of overflow as long as max(srcALen, srcBLen)<131072.   
+ * The 18.14 result is then truncated to 18.7 format by discarding the low 7 bits and then saturated to 1.7 format.   
+ *
+ * \par    
+ * Refer the function arm_conv_opt_q7() for a faster implementation of this function.
+ * 
+ */
+
+void arm_conv_q7(
+  q7_t * pSrcA,
+  uint32_t srcALen,
+  q7_t * pSrcB,
+  uint32_t srcBLen,
+  q7_t * pDst)
+{
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q7_t *pIn1;                                    /* inputA pointer */
+  q7_t *pIn2;                                    /* inputB pointer */
+  q7_t *pOut = pDst;                             /* output pointer */
+  q7_t *px;                                      /* Intermediate inputA pointer */
+  q7_t *py;                                      /* Intermediate inputB pointer */
+  q7_t *pSrc1, *pSrc2;                           /* Intermediate pointers */
+  q7_t x0, x1, x2, x3, c0, c1;                   /* Temporary variables to hold state and coefficient values */
+  q31_t sum, acc0, acc1, acc2, acc3;             /* Accumulator */
+  q31_t input1, input2;                          /* Temporary input variables */
+  q15_t in1, in2;                                /* Temporary input variables */
+  uint32_t j, k, count, blkCnt, blockSize1, blockSize2, blockSize3;     /* loop counter */
+
+  /* The algorithm implementation is based on the lengths of the inputs. */
+  /* srcB is always made to slide across srcA. */
+  /* So srcBLen is always considered as shorter or equal to srcALen */
+  if(srcALen >= srcBLen)
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = pSrcA;
+
+    /* Initialization of inputB pointer */
+    pIn2 = pSrcB;
+  }
+  else
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = pSrcB;
+
+    /* Initialization of inputB pointer */
+    pIn2 = pSrcA;
+
+    /* srcBLen is always considered as shorter or equal to srcALen */
+    j = srcBLen;
+    srcBLen = srcALen;
+    srcALen = j;
+  }
+
+  /* conv(x,y) at n = x[n] * y[0] + x[n-1] * y[1] + x[n-2] * y[2] + ...+ x[n-N+1] * y[N -1] */
+  /* The function is internally   
+   * divided into three stages according to the number of multiplications that has to be   
+   * taken place between inputA samples and inputB samples. In the first stage of the   
+   * algorithm, the multiplications increase by one for every iteration.   
+   * In the second stage of the algorithm, srcBLen number of multiplications are done.   
+   * In the third stage of the algorithm, the multiplications decrease by one   
+   * for every iteration. */
+
+  /* The algorithm is implemented in three stages.   
+     The loop counters of each stage is initiated here. */
+  blockSize1 = srcBLen - 1u;
+  blockSize2 = (srcALen - srcBLen) + 1u;
+  blockSize3 = blockSize1;
+
+  /* --------------------------   
+   * Initializations of stage1   
+   * -------------------------*/
+
+  /* sum = x[0] * y[0]   
+   * sum = x[0] * y[1] + x[1] * y[0]   
+   * ....   
+   * sum = x[0] * y[srcBlen - 1] + x[1] * y[srcBlen - 2] +...+ x[srcBLen - 1] * y[0]   
+   */
+
+  /* In this stage the MAC operations are increased by 1 for every iteration.   
+     The count variable holds the number of MAC operations performed */
+  count = 1u;
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  py = pIn2;
+
+
+  /* ------------------------   
+   * Stage1 process   
+   * ----------------------*/
+
+  /* The first stage starts here */
+  while(blockSize1 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = count >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* x[0] , x[1] */
+      in1 = (q15_t) * px++;
+      in2 = (q15_t) * px++;
+      input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16u);
+
+      /* y[srcBLen - 1] , y[srcBLen - 2] */
+      in1 = (q15_t) * py--;
+      in2 = (q15_t) * py--;
+      input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16u);
+
+      /* x[0] * y[srcBLen - 1] */
+      /* x[1] * y[srcBLen - 2] */
+      sum = __SMLAD(input1, input2, sum);
+
+      /* x[2] , x[3] */
+      in1 = (q15_t) * px++;
+      in2 = (q15_t) * px++;
+      input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16u);
+
+      /* y[srcBLen - 3] , y[srcBLen - 4] */
+      in1 = (q15_t) * py--;
+      in2 = (q15_t) * py--;
+      input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16u);
+
+      /* x[2] * y[srcBLen - 3] */
+      /* x[3] * y[srcBLen - 4] */
+      sum = __SMLAD(input1, input2, sum);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, compute any remaining MACs here.   
+     ** No loop unrolling is used. */
+    k = count % 0x4u;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      sum += ((q15_t) * px++ * *py--);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut++ = (q7_t) (__SSAT(sum >> 7u, 8));
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    py = pIn2 + count;
+    px = pIn1;
+
+    /* Increment the MAC count */
+    count++;
+
+    /* Decrement the loop counter */
+    blockSize1--;
+  }
+
+  /* --------------------------   
+   * Initializations of stage2   
+   * ------------------------*/
+
+  /* sum = x[0] * y[srcBLen-1] + x[1] * y[srcBLen-2] +...+ x[srcBLen-1] * y[0]   
+   * sum = x[1] * y[srcBLen-1] + x[2] * y[srcBLen-2] +...+ x[srcBLen] * y[0]   
+   * ....   
+   * sum = x[srcALen-srcBLen-2] * y[srcBLen-1] + x[srcALen] * y[srcBLen-2] +...+ x[srcALen-1] * y[0]   
+   */
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  pSrc2 = pIn2 + (srcBLen - 1u);
+  py = pSrc2;
+
+  /* count is index by which the pointer pIn1 to be incremented */
+  count = 0u;
+
+  /* -------------------   
+   * Stage2 process   
+   * ------------------*/
+
+  /* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.   
+   * So, to loop unroll over blockSize2,   
+   * srcBLen should be greater than or equal to 4 */
+  if(srcBLen >= 4u)
+  {
+    /* Loop unroll over blockSize2, by 4 */
+    blkCnt = blockSize2 >> 2u;
+
+    while(blkCnt > 0u)
+    {
+      /* Set all accumulators to zero */
+      acc0 = 0;
+      acc1 = 0;
+      acc2 = 0;
+      acc3 = 0;
+
+      /* read x[0], x[1], x[2] samples */
+      x0 = *(px++);
+      x1 = *(px++);
+      x2 = *(px++);
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      do
+      {
+        /* Read y[srcBLen - 1] sample */
+        c0 = *(py--);
+        /* Read y[srcBLen - 2] sample */
+        c1 = *(py--);
+
+        /* Read x[3] sample */
+        x3 = *(px++);
+
+        /* x[0] and x[1] are packed */
+        in1 = (q15_t) x0;
+        in2 = (q15_t) x1;
+
+        input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16u);
+
+        /* y[srcBLen - 1]   and y[srcBLen - 2] are packed */
+        in1 = (q15_t) c0;
+        in2 = (q15_t) c1;
+
+        input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16u);
+
+        /* acc0 += x[0] * y[srcBLen - 1] + x[1] * y[srcBLen - 2]  */
+        acc0 = __SMLAD(input1, input2, acc0);
+
+        /* x[1] and x[2] are packed */
+        in1 = (q15_t) x1;
+        in2 = (q15_t) x2;
+
+        input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16u);
+
+        /* acc1 += x[1] * y[srcBLen - 1] + x[2] * y[srcBLen - 2]  */
+        acc1 = __SMLAD(input1, input2, acc1);
+
+        /* x[2] and x[3] are packed */
+        in1 = (q15_t) x2;
+        in2 = (q15_t) x3;
+
+        input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16u);
+
+        /* acc2 += x[2] * y[srcBLen - 1] + x[3] * y[srcBLen - 2]  */
+        acc2 = __SMLAD(input1, input2, acc2);
+
+        /* Read x[4] sample */
+        x0 = *(px++);
+
+        /* x[3] and x[4] are packed */
+        in1 = (q15_t) x3;
+        in2 = (q15_t) x0;
+
+        input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16u);
+
+        /* acc3 += x[3] * y[srcBLen - 1] + x[4] * y[srcBLen - 2]  */
+        acc3 = __SMLAD(input1, input2, acc3);
+
+        /* Read y[srcBLen - 3] sample */
+        c0 = *(py--);
+        /* Read y[srcBLen - 4] sample */
+        c1 = *(py--);
+
+        /* Read x[5] sample */
+        x1 = *(px++);
+
+        /* x[2] and x[3] are packed */
+        in1 = (q15_t) x2;
+        in2 = (q15_t) x3;
+
+        input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16u);
+
+        /* y[srcBLen - 3] and y[srcBLen - 4] are packed */
+        in1 = (q15_t) c0;
+        in2 = (q15_t) c1;
+
+        input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16u);
+
+        /* acc0 += x[2] * y[srcBLen - 3] + x[3] * y[srcBLen - 4]  */
+        acc0 = __SMLAD(input1, input2, acc0);
+
+        /* x[3] and x[4] are packed */
+        in1 = (q15_t) x3;
+        in2 = (q15_t) x0;
+
+        input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16u);
+
+        /* acc1 += x[3] * y[srcBLen - 3] + x[4] * y[srcBLen - 4]  */
+        acc1 = __SMLAD(input1, input2, acc1);
+
+        /* x[4] and x[5] are packed */
+        in1 = (q15_t) x0;
+        in2 = (q15_t) x1;
+
+        input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16u);
+
+        /* acc2 += x[4] * y[srcBLen - 3] + x[5] * y[srcBLen - 4]  */
+        acc2 = __SMLAD(input1, input2, acc2);
+
+        /* Read x[6] sample */
+        x2 = *(px++);
+
+        /* x[5] and x[6] are packed */
+        in1 = (q15_t) x1;
+        in2 = (q15_t) x2;
+
+        input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16u);
+
+        /* acc3 += x[5] * y[srcBLen - 3] + x[6] * y[srcBLen - 4]  */
+        acc3 = __SMLAD(input1, input2, acc3);
+
+      } while(--k);
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.   
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Read y[srcBLen - 5] sample */
+        c0 = *(py--);
+
+        /* Read x[7] sample */
+        x3 = *(px++);
+
+        /* Perform the multiply-accumulates */
+        /* acc0 +=  x[4] * y[srcBLen - 5] */
+        acc0 += ((q15_t) x0 * c0);
+        /* acc1 +=  x[5] * y[srcBLen - 5] */
+        acc1 += ((q15_t) x1 * c0);
+        /* acc2 +=  x[6] * y[srcBLen - 5] */
+        acc2 += ((q15_t) x2 * c0);
+        /* acc3 +=  x[7] * y[srcBLen - 5] */
+        acc3 += ((q15_t) x3 * c0);
+
+        /* Reuse the present samples for the next MAC */
+        x0 = x1;
+        x1 = x2;
+        x2 = x3;
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q7_t) (__SSAT(acc0 >> 7u, 8));
+      *pOut++ = (q7_t) (__SSAT(acc1 >> 7u, 8));
+      *pOut++ = (q7_t) (__SSAT(acc2 >> 7u, 8));
+      *pOut++ = (q7_t) (__SSAT(acc3 >> 7u, 8));
+
+      /* Increment the pointer pIn1 index, count by 4 */
+      count += 4u;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pSrc2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.   
+     ** No loop unrolling is used. */
+    blkCnt = blockSize2 % 0x4u;
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      while(k > 0u)
+      {
+
+        /* Reading two inputs of SrcA buffer and packing */
+        in1 = (q15_t) * px++;
+        in2 = (q15_t) * px++;
+        input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16u);
+
+        /* Reading two inputs of SrcB buffer and packing */
+        in1 = (q15_t) * py--;
+        in2 = (q15_t) * py--;
+        input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16u);
+
+        /* Perform the multiply-accumulates */
+        sum = __SMLAD(input1, input2, sum);
+
+        /* Reading two inputs of SrcA buffer and packing */
+        in1 = (q15_t) * px++;
+        in2 = (q15_t) * px++;
+        input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16u);
+
+        /* Reading two inputs of SrcB buffer and packing */
+        in1 = (q15_t) * py--;
+        in2 = (q15_t) * py--;
+        input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16u);
+
+        /* Perform the multiply-accumulates */
+        sum = __SMLAD(input1, input2, sum);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.   
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum += ((q15_t) * px++ * *py--);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q7_t) (__SSAT(sum >> 7u, 8));
+
+      /* Increment the pointer pIn1 index, count by 1 */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pSrc2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+  else
+  {
+    /* If the srcBLen is not a multiple of 4,   
+     * the blockSize2 loop cannot be unrolled by 4 */
+    blkCnt = blockSize2;
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* srcBLen number of MACS should be performed */
+      k = srcBLen;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulate */
+        sum += ((q15_t) * px++ * *py--);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = (q7_t) (__SSAT(sum >> 7u, 8));
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pSrc2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+
+
+  /* --------------------------   
+   * Initializations of stage3   
+   * -------------------------*/
+
+  /* sum += x[srcALen-srcBLen+1] * y[srcBLen-1] + x[srcALen-srcBLen+2] * y[srcBLen-2] +...+ x[srcALen-1] * y[1]   
+   * sum += x[srcALen-srcBLen+2] * y[srcBLen-1] + x[srcALen-srcBLen+3] * y[srcBLen-2] +...+ x[srcALen-1] * y[2]   
+   * ....   
+   * sum +=  x[srcALen-2] * y[srcBLen-1] + x[srcALen-1] * y[srcBLen-2]   
+   * sum +=  x[srcALen-1] * y[srcBLen-1]   
+   */
+
+  /* In this stage the MAC operations are decreased by 1 for every iteration.   
+     The blockSize3 variable holds the number of MAC operations performed */
+
+  /* Working pointer of inputA */
+  pSrc1 = pIn1 + (srcALen - (srcBLen - 1u));
+  px = pSrc1;
+
+  /* Working pointer of inputB */
+  pSrc2 = pIn2 + (srcBLen - 1u);
+  py = pSrc2;
+
+  /* -------------------   
+   * Stage3 process   
+   * ------------------*/
+
+  while(blockSize3 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = blockSize3 >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* Reading two inputs, x[srcALen - srcBLen + 1] and x[srcALen - srcBLen + 2] of SrcA buffer and packing */
+      in1 = (q15_t) * px++;
+      in2 = (q15_t) * px++;
+      input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16u);
+
+      /* Reading two inputs, y[srcBLen - 1] and y[srcBLen - 2] of SrcB buffer and packing */
+      in1 = (q15_t) * py--;
+      in2 = (q15_t) * py--;
+      input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16u);
+
+      /* sum += x[srcALen - srcBLen + 1] * y[srcBLen - 1] */
+      /* sum += x[srcALen - srcBLen + 2] * y[srcBLen - 2] */
+      sum = __SMLAD(input1, input2, sum);
+
+      /* Reading two inputs, x[srcALen - srcBLen + 3] and x[srcALen - srcBLen + 4] of SrcA buffer and packing */
+      in1 = (q15_t) * px++;
+      in2 = (q15_t) * px++;
+      input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16u);
+
+      /* Reading two inputs, y[srcBLen - 3] and y[srcBLen - 4] of SrcB buffer and packing */
+      in1 = (q15_t) * py--;
+      in2 = (q15_t) * py--;
+      input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16u);
+
+      /* sum += x[srcALen - srcBLen + 3] * y[srcBLen - 3] */
+      /* sum += x[srcALen - srcBLen + 4] * y[srcBLen - 4] */
+      sum = __SMLAD(input1, input2, sum);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the blockSize3 is not a multiple of 4, compute any remaining MACs here.   
+     ** No loop unrolling is used. */
+    k = blockSize3 % 0x4u;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      sum += ((q15_t) * px++ * *py--);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut++ = (q7_t) (__SSAT(sum >> 7u, 8));
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    px = ++pSrc1;
+    py = pSrc2;
+
+    /* Decrement the loop counter */
+    blockSize3--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  q7_t *pIn1 = pSrcA;                            /* input pointer */
+  q7_t *pIn2 = pSrcB;                            /* coefficient pointer */
+  q31_t sum;                                     /* Accumulator */
+  uint32_t i, j;                                 /* loop counter */
+
+  /* Loop to calculate output of convolution for output length number of times */
+  for (i = 0; i < (srcALen + srcBLen - 1); i++)
+  {
+    /* Initialize sum with zero to carry on MAC operations */
+    sum = 0;
+
+    /* Loop to perform MAC operations according to convolution equation */
+    for (j = 0; j <= i; j++)
+    {
+      /* Check the array limitations */
+      if(((i - j) < srcBLen) && (j < srcALen))
+      {
+        /* z[i] += x[i-j] * y[j] */
+        sum += (q15_t) pIn1[j] * (pIn2[i - j]);
+      }
+    }
+
+    /* Store the output in the destination buffer */
+    pDst[i] = (q7_t) __SSAT((sum >> 7u), 8u);
+  }
+
+#endif /*   #ifndef ARM_MATH_CM0        */
+
+}
+
+/**   
+ * @} end of Conv group   
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_f32.c
new file mode 100644
index 0000000000..6a99eafc15
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_f32.c
@@ -0,0 +1,738 @@
+/* ----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_correlate_f32.c    
+*    
+* Description:	 Correlation of floating-point sequences.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+* 
+* Version 1.0.11 2011/10/18  
+*    Bug Fix in conv, correlation, partial convolution.  
+* 
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+*    
+* -------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @defgroup Corr Correlation    
+ *    
+ * Correlation is a mathematical operation that is similar to convolution.    
+ * As with convolution, correlation uses two signals to produce a third signal.    
+ * The underlying algorithms in correlation and convolution are identical except that one of the inputs is flipped in convolution.    
+ * Correlation is commonly used to measure the similarity between two signals.    
+ * It has applications in pattern recognition, cryptanalysis, and searching.    
+ * The CMSIS library provides correlation functions for Q7, Q15, Q31 and floating-point data types.    
+ * Fast versions of the Q15 and Q31 functions are also provided.    
+ *    
+ * \par Algorithm    
+ * Let a[n] and b[n] be sequences of length srcALen and srcBLen samples respectively.    
+ * The convolution of the two signals is denoted by    
+ * 
    
+ *                   c[n] = a[n] * b[n]    
+ * 
    
+ * In correlation, one of the signals is flipped in time    
+ * 
    
+ *                   c[n] = a[n] * b[-n]    
+ * 
    
+ *    
+ * \par    
+ * and this is mathematically defined as    
+ * \image html CorrelateEquation.gif    
+ * \par    
+ * The pSrcA points to the first input vector of length srcALen and pSrcB points to the second input vector of length srcBLen.    
+ * The result c[n] is of length 2 * max(srcALen, srcBLen) - 1 and is defined over the interval n=0, 1, 2, ..., (2 * max(srcALen, srcBLen) - 2).    
+ * The output result is written to pDst and the calling function must allocate 2 * max(srcALen, srcBLen) - 1 words for the result.    
+ *    
+ * Note   
+ * \par  
+ * The pDst should be initialized to all zeros before being used.  
+ *  
+ * Fixed-Point Behavior    
+ * \par    
+ * Correlation requires summing up a large number of intermediate products.    
+ * As such, the Q7, Q15, and Q31 functions run a risk of overflow and saturation.    
+ * Refer to the function specific documentation below for further details of the particular algorithm used.    
+ *
+ *
+ * Fast Versions
+ *
+ * \par 
+ * Fast versions are supported for Q31 and Q15.  Cycles for Fast versions are less compared to Q31 and Q15 of correlate and the design requires
+ * the input signals should be scaled down to avoid intermediate overflows.   
+ *
+ *
+ * Opt Versions
+ *
+ * \par 
+ * Opt versions are supported for Q15 and Q7.  Design uses internal scratch buffer for getting good optimisation.
+ * These versions are optimised in cycles and consumes more memory(Scratch memory) compared to Q15 and Q7 versions of correlate 
+ */
+
+/**    
+ * @addtogroup Corr    
+ * @{    
+ */
+/**    
+ * @brief Correlation of floating-point sequences.    
+ * @param[in]  *pSrcA points to the first input sequence.    
+ * @param[in]  srcALen length of the first input sequence.    
+ * @param[in]  *pSrcB points to the second input sequence.    
+ * @param[in]  srcBLen length of the second input sequence.    
+ * @param[out] *pDst points to the location where the output result is written.  Length 2 * max(srcALen, srcBLen) - 1.    
+ * @return none.    
+ */
+
+void arm_correlate_f32(
+  float32_t * pSrcA,
+  uint32_t srcALen,
+  float32_t * pSrcB,
+  uint32_t srcBLen,
+  float32_t * pDst)
+{
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  float32_t *pIn1;                               /* inputA pointer */
+  float32_t *pIn2;                               /* inputB pointer */
+  float32_t *pOut = pDst;                        /* output pointer */
+  float32_t *px;                                 /* Intermediate inputA pointer */
+  float32_t *py;                                 /* Intermediate inputB pointer */
+  float32_t *pSrc1;                              /* Intermediate pointers */
+  float32_t sum, acc0, acc1, acc2, acc3;         /* Accumulators */
+  float32_t x0, x1, x2, x3, c0;                  /* temporary variables for holding input and coefficient values */
+  uint32_t j, k = 0u, count, blkCnt, outBlockSize, blockSize1, blockSize2, blockSize3;  /* loop counters */
+  int32_t inc = 1;                               /* Destination address modifier */
+
+
+  /* The algorithm implementation is based on the lengths of the inputs. */
+  /* srcB is always made to slide across srcA. */
+  /* So srcBLen is always considered as shorter or equal to srcALen */
+  /* But CORR(x, y) is reverse of CORR(y, x) */
+  /* So, when srcBLen > srcALen, output pointer is made to point to the end of the output buffer */
+  /* and the destination pointer modifier, inc is set to -1 */
+  /* If srcALen > srcBLen, zero pad has to be done to srcB to make the two inputs of same length */
+  /* But to improve the performance,    
+   * we include zeroes in the output instead of zero padding either of the the inputs*/
+  /* If srcALen > srcBLen,    
+   * (srcALen - srcBLen) zeroes has to included in the starting of the output buffer */
+  /* If srcALen < srcBLen,    
+   * (srcALen - srcBLen) zeroes has to included in the ending of the output buffer */
+  if(srcALen >= srcBLen)
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = pSrcA;
+
+    /* Initialization of inputB pointer */
+    pIn2 = pSrcB;
+
+    /* Number of output samples is calculated */
+    outBlockSize = (2u * srcALen) - 1u;
+
+    /* When srcALen > srcBLen, zero padding has to be done to srcB    
+     * to make their lengths equal.    
+     * Instead, (outBlockSize - (srcALen + srcBLen - 1))    
+     * number of output samples are made zero */
+    j = outBlockSize - (srcALen + (srcBLen - 1u));
+
+    /* Updating the pointer position to non zero value */
+    pOut += j;
+
+    //while(j > 0u)   
+    //{   
+    //  /* Zero is stored in the destination buffer */   
+    //  *pOut++ = 0.0f;   
+
+    //  /* Decrement the loop counter */   
+    //  j--;   
+    //}   
+
+  }
+  else
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = pSrcB;
+
+    /* Initialization of inputB pointer */
+    pIn2 = pSrcA;
+
+    /* srcBLen is always considered as shorter or equal to srcALen */
+    j = srcBLen;
+    srcBLen = srcALen;
+    srcALen = j;
+
+    /* CORR(x, y) = Reverse order(CORR(y, x)) */
+    /* Hence set the destination pointer to point to the last output sample */
+    pOut = pDst + ((srcALen + srcBLen) - 2u);
+
+    /* Destination address modifier is set to -1 */
+    inc = -1;
+
+  }
+
+  /* The function is internally    
+   * divided into three parts according to the number of multiplications that has to be    
+   * taken place between inputA samples and inputB samples. In the first part of the    
+   * algorithm, the multiplications increase by one for every iteration.    
+   * In the second part of the algorithm, srcBLen number of multiplications are done.    
+   * In the third part of the algorithm, the multiplications decrease by one    
+   * for every iteration.*/
+  /* The algorithm is implemented in three stages.    
+   * The loop counters of each stage is initiated here. */
+  blockSize1 = srcBLen - 1u;
+  blockSize2 = srcALen - (srcBLen - 1u);
+  blockSize3 = blockSize1;
+
+  /* --------------------------    
+   * Initializations of stage1    
+   * -------------------------*/
+
+  /* sum = x[0] * y[srcBlen - 1]    
+   * sum = x[0] * y[srcBlen-2] + x[1] * y[srcBlen - 1]    
+   * ....    
+   * sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen - 1] * y[srcBLen - 1]    
+   */
+
+  /* In this stage the MAC operations are increased by 1 for every iteration.    
+     The count variable holds the number of MAC operations performed */
+  count = 1u;
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  pSrc1 = pIn2 + (srcBLen - 1u);
+  py = pSrc1;
+
+  /* ------------------------    
+   * Stage1 process    
+   * ----------------------*/
+
+  /* The first stage starts here */
+  while(blockSize1 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0.0f;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = count >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* x[0] * y[srcBLen - 4] */
+      sum += *px++ * *py++;
+      /* x[1] * y[srcBLen - 3] */
+      sum += *px++ * *py++;
+      /* x[2] * y[srcBLen - 2] */
+      sum += *px++ * *py++;
+      /* x[3] * y[srcBLen - 1] */
+      sum += *px++ * *py++;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, compute any remaining MACs here.    
+     ** No loop unrolling is used. */
+    k = count % 0x4u;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      /* x[0] * y[srcBLen - 1] */
+      sum += *px++ * *py++;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut = sum;
+    /* Destination pointer is updated according to the address modifier, inc */
+    pOut += inc;
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    py = pSrc1 - count;
+    px = pIn1;
+
+    /* Increment the MAC count */
+    count++;
+
+    /* Decrement the loop counter */
+    blockSize1--;
+  }
+
+  /* --------------------------    
+   * Initializations of stage2    
+   * ------------------------*/
+
+  /* sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen-1] * y[srcBLen-1]    
+   * sum = x[1] * y[0] + x[2] * y[1] +...+ x[srcBLen] * y[srcBLen-1]    
+   * ....    
+   * sum = x[srcALen-srcBLen-2] * y[0] + x[srcALen-srcBLen-1] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]    
+   */
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  py = pIn2;
+
+  /* count is index by which the pointer pIn1 to be incremented */
+  count = 0u;
+
+  /* -------------------    
+   * Stage2 process    
+   * ------------------*/
+
+  /* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.    
+   * So, to loop unroll over blockSize2,    
+   * srcBLen should be greater than or equal to 4, to loop unroll the srcBLen loop */
+  if(srcBLen >= 4u)
+  {
+    /* Loop unroll over blockSize2, by 4 */
+    blkCnt = blockSize2 >> 2u;
+
+    while(blkCnt > 0u)
+    {
+      /* Set all accumulators to zero */
+      acc0 = 0.0f;
+      acc1 = 0.0f;
+      acc2 = 0.0f;
+      acc3 = 0.0f;
+
+      /* read x[0], x[1], x[2] samples */
+      x0 = *(px++);
+      x1 = *(px++);
+      x2 = *(px++);
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      do
+      {
+        /* Read y[0] sample */
+        c0 = *(py++);
+
+        /* Read x[3] sample */
+        x3 = *(px++);
+
+        /* Perform the multiply-accumulate */
+        /* acc0 +=  x[0] * y[0] */
+        acc0 += x0 * c0;
+        /* acc1 +=  x[1] * y[0] */
+        acc1 += x1 * c0;
+        /* acc2 +=  x[2] * y[0] */
+        acc2 += x2 * c0;
+        /* acc3 +=  x[3] * y[0] */
+        acc3 += x3 * c0;
+
+        /* Read y[1] sample */
+        c0 = *(py++);
+
+        /* Read x[4] sample */
+        x0 = *(px++);
+
+        /* Perform the multiply-accumulate */
+        /* acc0 +=  x[1] * y[1] */
+        acc0 += x1 * c0;
+        /* acc1 +=  x[2] * y[1] */
+        acc1 += x2 * c0;
+        /* acc2 +=  x[3] * y[1] */
+        acc2 += x3 * c0;
+        /* acc3 +=  x[4] * y[1] */
+        acc3 += x0 * c0;
+
+        /* Read y[2] sample */
+        c0 = *(py++);
+
+        /* Read x[5] sample */
+        x1 = *(px++);
+
+        /* Perform the multiply-accumulates */
+        /* acc0 +=  x[2] * y[2] */
+        acc0 += x2 * c0;
+        /* acc1 +=  x[3] * y[2] */
+        acc1 += x3 * c0;
+        /* acc2 +=  x[4] * y[2] */
+        acc2 += x0 * c0;
+        /* acc3 +=  x[5] * y[2] */
+        acc3 += x1 * c0;
+
+        /* Read y[3] sample */
+        c0 = *(py++);
+
+        /* Read x[6] sample */
+        x2 = *(px++);
+
+        /* Perform the multiply-accumulates */
+        /* acc0 +=  x[3] * y[3] */
+        acc0 += x3 * c0;
+        /* acc1 +=  x[4] * y[3] */
+        acc1 += x0 * c0;
+        /* acc2 +=  x[5] * y[3] */
+        acc2 += x1 * c0;
+        /* acc3 +=  x[6] * y[3] */
+        acc3 += x2 * c0;
+
+
+      } while(--k);
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.    
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Read y[4] sample */
+        c0 = *(py++);
+
+        /* Read x[7] sample */
+        x3 = *(px++);
+
+        /* Perform the multiply-accumulates */
+        /* acc0 +=  x[4] * y[4] */
+        acc0 += x0 * c0;
+        /* acc1 +=  x[5] * y[4] */
+        acc1 += x1 * c0;
+        /* acc2 +=  x[6] * y[4] */
+        acc2 += x2 * c0;
+        /* acc3 +=  x[7] * y[4] */
+        acc3 += x3 * c0;
+
+        /* Reuse the present samples for the next MAC */
+        x0 = x1;
+        x1 = x2;
+        x2 = x3;
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut = acc0;
+      /* Destination pointer is updated according to the address modifier, inc */
+      pOut += inc;
+
+      *pOut = acc1;
+      pOut += inc;
+
+      *pOut = acc2;
+      pOut += inc;
+
+      *pOut = acc3;
+      pOut += inc;
+
+      /* Increment the pointer pIn1 index, count by 4 */
+      count += 4u;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pIn2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.    
+     ** No loop unrolling is used. */
+    blkCnt = blockSize2 % 0x4u;
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0.0f;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum += *px++ * *py++;
+        sum += *px++ * *py++;
+        sum += *px++ * *py++;
+        sum += *px++ * *py++;
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.    
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulate */
+        sum += *px++ * *py++;
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut = sum;
+      /* Destination pointer is updated according to the address modifier, inc */
+      pOut += inc;
+
+      /* Increment the pointer pIn1 index, count by 1 */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pIn2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+  else
+  {
+    /* If the srcBLen is not a multiple of 4,    
+     * the blockSize2 loop cannot be unrolled by 4 */
+    blkCnt = blockSize2;
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0.0f;
+
+      /* Loop over srcBLen */
+      k = srcBLen;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulate */
+        sum += *px++ * *py++;
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut = sum;
+      /* Destination pointer is updated according to the address modifier, inc */
+      pOut += inc;
+
+      /* Increment the pointer pIn1 index, count by 1 */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pIn2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+
+  /* --------------------------    
+   * Initializations of stage3    
+   * -------------------------*/
+
+  /* sum += x[srcALen-srcBLen+1] * y[0] + x[srcALen-srcBLen+2] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]    
+   * sum += x[srcALen-srcBLen+2] * y[0] + x[srcALen-srcBLen+3] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]    
+   * ....    
+   * sum +=  x[srcALen-2] * y[0] + x[srcALen-1] * y[1]    
+   * sum +=  x[srcALen-1] * y[0]    
+   */
+
+  /* In this stage the MAC operations are decreased by 1 for every iteration.    
+     The count variable holds the number of MAC operations performed */
+  count = srcBLen - 1u;
+
+  /* Working pointer of inputA */
+  pSrc1 = pIn1 + (srcALen - (srcBLen - 1u));
+  px = pSrc1;
+
+  /* Working pointer of inputB */
+  py = pIn2;
+
+  /* -------------------    
+   * Stage3 process    
+   * ------------------*/
+
+  while(blockSize3 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0.0f;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = count >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      /* sum += x[srcALen - srcBLen + 4] * y[3] */
+      sum += *px++ * *py++;
+      /* sum += x[srcALen - srcBLen + 3] * y[2] */
+      sum += *px++ * *py++;
+      /* sum += x[srcALen - srcBLen + 2] * y[1] */
+      sum += *px++ * *py++;
+      /* sum += x[srcALen - srcBLen + 1] * y[0] */
+      sum += *px++ * *py++;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, compute any remaining MACs here.    
+     ** No loop unrolling is used. */
+    k = count % 0x4u;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      sum += *px++ * *py++;
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut = sum;
+    /* Destination pointer is updated according to the address modifier, inc */
+    pOut += inc;
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    px = ++pSrc1;
+    py = pIn2;
+
+    /* Decrement the MAC count */
+    count--;
+
+    /* Decrement the loop counter */
+    blockSize3--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  float32_t *pIn1 = pSrcA;                       /* inputA pointer */
+  float32_t *pIn2 = pSrcB + (srcBLen - 1u);      /* inputB pointer */
+  float32_t sum;                                 /* Accumulator */
+  uint32_t i = 0u, j;                            /* loop counters */
+  uint32_t inv = 0u;                             /* Reverse order flag */
+  uint32_t tot = 0u;                             /* Length */
+
+  /* The algorithm implementation is based on the lengths of the inputs. */
+  /* srcB is always made to slide across srcA. */
+  /* So srcBLen is always considered as shorter or equal to srcALen */
+  /* But CORR(x, y) is reverse of CORR(y, x) */
+  /* So, when srcBLen > srcALen, output pointer is made to point to the end of the output buffer */
+  /* and a varaible, inv is set to 1 */
+  /* If lengths are not equal then zero pad has to be done to  make the two    
+   * inputs of same length. But to improve the performance, we include zeroes    
+   * in the output instead of zero padding either of the the inputs*/
+  /* If srcALen > srcBLen, (srcALen - srcBLen) zeroes has to included in the    
+   * starting of the output buffer */
+  /* If srcALen < srcBLen, (srcALen - srcBLen) zeroes has to included in the   
+   * ending of the output buffer */
+  /* Once the zero padding is done the remaining of the output is calcualted   
+   * using convolution but with the shorter signal time shifted. */
+
+  /* Calculate the length of the remaining sequence */
+  tot = ((srcALen + srcBLen) - 2u);
+
+  if(srcALen > srcBLen)
+  {
+    /* Calculating the number of zeros to be padded to the output */
+    j = srcALen - srcBLen;
+
+    /* Initialise the pointer after zero padding */
+    pDst += j;
+  }
+
+  else if(srcALen < srcBLen)
+  {
+    /* Initialization to inputB pointer */
+    pIn1 = pSrcB;
+
+    /* Initialization to the end of inputA pointer */
+    pIn2 = pSrcA + (srcALen - 1u);
+
+    /* Initialisation of the pointer after zero padding */
+    pDst = pDst + tot;
+
+    /* Swapping the lengths */
+    j = srcALen;
+    srcALen = srcBLen;
+    srcBLen = j;
+
+    /* Setting the reverse flag */
+    inv = 1;
+
+  }
+
+  /* Loop to calculate convolution for output length number of times */
+  for (i = 0u; i <= tot; i++)
+  {
+    /* Initialize sum with zero to carry on MAC operations */
+    sum = 0.0f;
+
+    /* Loop to perform MAC operations according to convolution equation */
+    for (j = 0u; j <= i; j++)
+    {
+      /* Check the array limitations */
+      if((((i - j) < srcBLen) && (j < srcALen)))
+      {
+        /* z[i] += x[i-j] * y[j] */
+        sum += pIn1[j] * pIn2[-((int32_t) i - j)];
+      }
+    }
+    /* Store the output in the destination buffer */
+    if(inv == 1)
+      *pDst-- = sum;
+    else
+      *pDst++ = sum;
+  }
+
+#endif /*   #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of Corr group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_fast_opt_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_fast_opt_q15.c
new file mode 100644
index 0000000000..a99225a2f5
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_fast_opt_q15.c
@@ -0,0 +1,507 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_correlate_fast_opt_q15.c    
+*    
+* Description:	Fast Q15 Correlation.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+* 
+* Version 1.0.11 2011/10/18  
+*    Bug Fix in conv, correlation, partial convolution.  
+* 
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup Corr    
+ * @{    
+ */
+
+/**    
+ * @brief Correlation of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4.    
+ * @param[in] *pSrcA points to the first input sequence.    
+ * @param[in] srcALen length of the first input sequence.    
+ * @param[in] *pSrcB points to the second input sequence.    
+ * @param[in] srcBLen length of the second input sequence.    
+ * @param[out] *pDst points to the location where the output result is written.  Length 2 * max(srcALen, srcBLen) - 1.    
+ * @param[in]  *pScratch points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.   
+ * @return none.    
+ *    
+ *    
+ * \par Restrictions    
+ *  If the silicon does not support unaligned memory access enable the macro UNALIGNED_SUPPORT_DISABLE    
+ *	In this case input, output, scratch buffers should be aligned by 32-bit    
+ *    
+ *     
+ * Scaling and Overflow Behavior:    
+ *    
+ * \par    
+ * This fast version uses a 32-bit accumulator with 2.30 format.    
+ * The accumulator maintains full precision of the intermediate multiplication results but provides only a single guard bit.    
+ * There is no saturation on intermediate additions.    
+ * Thus, if the accumulator overflows it wraps around and distorts the result.    
+ * The input signals should be scaled down to avoid intermediate overflows.    
+ * Scale down one of the inputs by 1/min(srcALen, srcBLen) to avoid overflow since a    
+ * maximum of min(srcALen, srcBLen) number of additions is carried internally.    
+ * The 2.30 accumulator is right shifted by 15 bits and then saturated to 1.15 format to yield the final result.    
+ *    
+ * \par    
+ * See arm_correlate_q15() for a slower implementation of this function which uses a 64-bit accumulator to avoid wrap around distortion.    
+ */
+
+void arm_correlate_fast_opt_q15(
+  q15_t * pSrcA,
+  uint32_t srcALen,
+  q15_t * pSrcB,
+  uint32_t srcBLen,
+  q15_t * pDst,
+  q15_t * pScratch)
+{
+  q15_t *pIn1;                                   /* inputA pointer               */
+  q15_t *pIn2;                                   /* inputB pointer               */
+  q31_t acc0, acc1, acc2, acc3;                  /* Accumulators                  */
+  q15_t *py;                                     /* Intermediate inputB pointer  */
+  q31_t x1, x2, x3;                              /* temporary variables for holding input and coefficient values */
+  uint32_t j, blkCnt, outBlockSize;              /* loop counter                 */
+  int32_t inc = 1;                               /* Destination address modifier */
+  uint32_t tapCnt;
+  q31_t y1, y2;
+  q15_t *pScr;                                   /* Intermediate pointers        */
+  q15_t *pOut = pDst;                            /* output pointer               */
+#ifdef UNALIGNED_SUPPORT_DISABLE
+
+  q15_t a, b;
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+  /* The algorithm implementation is based on the lengths of the inputs. */
+  /* srcB is always made to slide across srcA. */
+  /* So srcBLen is always considered as shorter or equal to srcALen */
+  /* But CORR(x, y) is reverse of CORR(y, x) */
+  /* So, when srcBLen > srcALen, output pointer is made to point to the end of the output buffer */
+  /* and the destination pointer modifier, inc is set to -1 */
+  /* If srcALen > srcBLen, zero pad has to be done to srcB to make the two inputs of same length */
+  /* But to improve the performance,        
+   * we include zeroes in the output instead of zero padding either of the the inputs*/
+  /* If srcALen > srcBLen,        
+   * (srcALen - srcBLen) zeroes has to included in the starting of the output buffer */
+  /* If srcALen < srcBLen,        
+   * (srcALen - srcBLen) zeroes has to included in the ending of the output buffer */
+  if(srcALen >= srcBLen)
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = (pSrcA);
+
+    /* Initialization of inputB pointer */
+    pIn2 = (pSrcB);
+
+    /* Number of output samples is calculated */
+    outBlockSize = (2u * srcALen) - 1u;
+
+    /* When srcALen > srcBLen, zero padding is done to srcB        
+     * to make their lengths equal.        
+     * Instead, (outBlockSize - (srcALen + srcBLen - 1))        
+     * number of output samples are made zero */
+    j = outBlockSize - (srcALen + (srcBLen - 1u));
+
+    /* Updating the pointer position to non zero value */
+    pOut += j;
+
+  }
+  else
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = (pSrcB);
+
+    /* Initialization of inputB pointer */
+    pIn2 = (pSrcA);
+
+    /* srcBLen is always considered as shorter or equal to srcALen */
+    j = srcBLen;
+    srcBLen = srcALen;
+    srcALen = j;
+
+    /* CORR(x, y) = Reverse order(CORR(y, x)) */
+    /* Hence set the destination pointer to point to the last output sample */
+    pOut = pDst + ((srcALen + srcBLen) - 2u);
+
+    /* Destination address modifier is set to -1 */
+    inc = -1;
+
+  }
+
+  pScr = pScratch;
+
+  /* Fill (srcBLen - 1u) zeros in scratch buffer */
+  arm_fill_q15(0, pScr, (srcBLen - 1u));
+
+  /* Update temporary scratch pointer */
+  pScr += (srcBLen - 1u);
+
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+  /* Copy (srcALen) samples in scratch buffer */
+  arm_copy_q15(pIn1, pScr, srcALen);
+
+  /* Update pointers */
+  pScr += srcALen;
+
+#else
+
+  /* Apply loop unrolling and do 4 Copies simultaneously. */
+  j = srcALen >> 2u;
+
+  /* First part of the processing with loop unrolling copies 4 data points at a time.       
+   ** a second loop below copies for the remaining 1 to 3 samples. */
+  while(j > 0u)
+  {
+    /* copy second buffer in reversal manner */
+    *pScr++ = *pIn1++;
+    *pScr++ = *pIn1++;
+    *pScr++ = *pIn1++;
+    *pScr++ = *pIn1++;
+
+    /* Decrement the loop counter */
+    j--;
+  }
+
+  /* If the count is not a multiple of 4, copy remaining samples here.       
+   ** No loop unrolling is used. */
+  j = srcALen % 0x4u;
+
+  while(j > 0u)
+  {
+    /* copy second buffer in reversal manner for remaining samples */
+    *pScr++ = *pIn1++;
+
+    /* Decrement the loop counter */
+    j--;
+  }
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+  /* Fill (srcBLen - 1u) zeros at end of scratch buffer */
+  arm_fill_q15(0, pScr, (srcBLen - 1u));
+
+  /* Update pointer */
+  pScr += (srcBLen - 1u);
+
+#else
+
+/* Apply loop unrolling and do 4 Copies simultaneously. */
+  j = (srcBLen - 1u) >> 2u;
+
+  /* First part of the processing with loop unrolling copies 4 data points at a time.       
+   ** a second loop below copies for the remaining 1 to 3 samples. */
+  while(j > 0u)
+  {
+    /* copy second buffer in reversal manner */
+    *pScr++ = 0;
+    *pScr++ = 0;
+    *pScr++ = 0;
+    *pScr++ = 0;
+
+    /* Decrement the loop counter */
+    j--;
+  }
+
+  /* If the count is not a multiple of 4, copy remaining samples here.       
+   ** No loop unrolling is used. */
+  j = (srcBLen - 1u) % 0x4u;
+
+  while(j > 0u)
+  {
+    /* copy second buffer in reversal manner for remaining samples */
+    *pScr++ = 0;
+
+    /* Decrement the loop counter */
+    j--;
+  }
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+  /* Temporary pointer for scratch2 */
+  py = pIn2;
+
+
+  /* Actual correlation process starts here */
+  blkCnt = (srcALen + srcBLen - 1u) >> 2;
+
+  while(blkCnt > 0)
+  {
+    /* Initialze temporary scratch pointer as scratch1 */
+    pScr = pScratch;
+
+    /* Clear Accumlators */
+    acc0 = 0;
+    acc1 = 0;
+    acc2 = 0;
+    acc3 = 0;
+
+    /* Read four samples from scratch1 buffer */
+    x1 = *__SIMD32(pScr)++;
+
+    /* Read next four samples from scratch1 buffer */
+    x2 = *__SIMD32(pScr)++;
+
+    tapCnt = (srcBLen) >> 2u;
+
+    while(tapCnt > 0u)
+    {
+
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+      /* Read four samples from smaller buffer */
+      y1 = _SIMD32_OFFSET(pIn2);
+      y2 = _SIMD32_OFFSET(pIn2 + 2u);
+
+      acc0 = __SMLAD(x1, y1, acc0);
+
+      acc2 = __SMLAD(x2, y1, acc2);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x2, x1, 0);
+#else
+      x3 = __PKHBT(x1, x2, 0);
+#endif
+
+      acc1 = __SMLADX(x3, y1, acc1);
+
+      x1 = _SIMD32_OFFSET(pScr);
+
+      acc0 = __SMLAD(x2, y2, acc0);
+
+      acc2 = __SMLAD(x1, y2, acc2);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x1, x2, 0);
+#else
+      x3 = __PKHBT(x2, x1, 0);
+#endif
+
+      acc3 = __SMLADX(x3, y1, acc3);
+
+      acc1 = __SMLADX(x3, y2, acc1);
+
+      x2 = _SIMD32_OFFSET(pScr + 2u);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x2, x1, 0);
+#else
+      x3 = __PKHBT(x1, x2, 0);
+#endif
+
+      acc3 = __SMLADX(x3, y2, acc3);
+#else	 
+
+      /* Read four samples from smaller buffer */
+	  a = *pIn2;
+	  b = *(pIn2 + 1);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      y1 = __PKHBT(a, b, 16);
+#else
+      y1 = __PKHBT(b, a, 16);
+#endif
+	  
+	  a = *(pIn2 + 2);
+	  b = *(pIn2 + 3);
+#ifndef ARM_MATH_BIG_ENDIAN
+      y2 = __PKHBT(a, b, 16);
+#else
+      y2 = __PKHBT(b, a, 16);
+#endif				
+
+      acc0 = __SMLAD(x1, y1, acc0);
+
+      acc2 = __SMLAD(x2, y1, acc2);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x2, x1, 0);
+#else
+      x3 = __PKHBT(x1, x2, 0);
+#endif
+
+      acc1 = __SMLADX(x3, y1, acc1);
+
+	  a = *pScr;
+	  b = *(pScr + 1);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x1 = __PKHBT(a, b, 16);
+#else
+      x1 = __PKHBT(b, a, 16);
+#endif
+
+      acc0 = __SMLAD(x2, y2, acc0);
+
+      acc2 = __SMLAD(x1, y2, acc2);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x1, x2, 0);
+#else
+      x3 = __PKHBT(x2, x1, 0);
+#endif
+
+      acc3 = __SMLADX(x3, y1, acc3);
+
+      acc1 = __SMLADX(x3, y2, acc1);
+
+	  a = *(pScr + 2);
+	  b = *(pScr + 3);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x2 = __PKHBT(a, b, 16);
+#else
+      x2 = __PKHBT(b, a, 16);
+#endif
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x2, x1, 0);
+#else
+      x3 = __PKHBT(x1, x2, 0);
+#endif
+
+      acc3 = __SMLADX(x3, y2, acc3);
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+      pIn2 += 4u;
+
+      pScr += 4u;
+
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+
+
+    /* Update scratch pointer for remaining samples of smaller length sequence */
+    pScr -= 4u;
+
+
+    /* apply same above for remaining samples of smaller length sequence */
+    tapCnt = (srcBLen) & 3u;
+
+    while(tapCnt > 0u)
+    {
+
+      /* accumlate the results */
+      acc0 += (*pScr++ * *pIn2);
+      acc1 += (*pScr++ * *pIn2);
+      acc2 += (*pScr++ * *pIn2);
+      acc3 += (*pScr++ * *pIn2++);
+
+      pScr -= 3u;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    blkCnt--;
+
+
+    /* Store the results in the accumulators in the destination buffer. */
+    *pOut = (__SSAT(acc0 >> 15u, 16));
+    pOut += inc;
+    *pOut = (__SSAT(acc1 >> 15u, 16));
+    pOut += inc;
+    *pOut = (__SSAT(acc2 >> 15u, 16));
+    pOut += inc;
+    *pOut = (__SSAT(acc3 >> 15u, 16));
+    pOut += inc;
+
+
+    /* Initialization of inputB pointer */
+    pIn2 = py;
+
+    pScratch += 4u;
+
+  }
+
+
+  blkCnt = (srcALen + srcBLen - 1u) & 0x3;
+
+  /* Calculate correlation for remaining samples of Bigger length sequence */
+  while(blkCnt > 0)
+  {
+    /* Initialze temporary scratch pointer as scratch1 */
+    pScr = pScratch;
+
+    /* Clear Accumlators */
+    acc0 = 0;
+
+    tapCnt = (srcBLen) >> 1u;
+
+    while(tapCnt > 0u)
+    {
+
+      acc0 += (*pScr++ * *pIn2++);
+      acc0 += (*pScr++ * *pIn2++);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    tapCnt = (srcBLen) & 1u;
+
+    /* apply same above for remaining samples of smaller length sequence */
+    while(tapCnt > 0u)
+    {
+
+      /* accumlate the results */
+      acc0 += (*pScr++ * *pIn2++);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    blkCnt--;
+
+    /* Store the result in the accumulator in the destination buffer. */
+
+    *pOut = (q15_t) (__SSAT((acc0 >> 15), 16));
+
+    pOut += inc;
+
+    /* Initialization of inputB pointer */
+    pIn2 = py;
+
+    pScratch += 1u;
+
+  }
+}
+
+/**    
+ * @} end of Corr group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_fast_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_fast_q15.c
new file mode 100644
index 0000000000..0c79bc8968
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_fast_q15.c
@@ -0,0 +1,1314 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010 ARM Limited. All rights reserved.   
+*   
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*   
+* Project: 	    CMSIS DSP Library   
+* Title:		arm_correlate_fast_q15.c   
+*   
+* Description:	Fast Q15 Correlation.   
+*   
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+* 
+* Version 1.0.11 2011/10/18 
+*    Bug Fix in conv, correlation, partial convolution. 
+*
+* Version 1.0.10 2011/7/15 
+*    Big Endian support added and Merged M0 and M3/M4 Source code.  
+*   
+* Version 1.0.3 2010/11/29  
+*    Re-organized the CMSIS folders and updated documentation.   
+*    
+* Version 1.0.2 2010/11/11   
+*    Documentation updated.    
+*   
+* Version 1.0.1 2010/10/05    
+*    Production release and review comments incorporated.   
+*   
+* Version 1.0.0 2010/09/20    
+*    Production release and review comments incorporated.   
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**   
+ * @ingroup groupFilters   
+ */
+
+/**   
+ * @addtogroup Corr   
+ * @{   
+ */
+
+/**   
+ * @brief Correlation of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4.   
+ * @param[in] *pSrcA points to the first input sequence.   
+ * @param[in] srcALen length of the first input sequence.   
+ * @param[in] *pSrcB points to the second input sequence.   
+ * @param[in] srcBLen length of the second input sequence.   
+ * @param[out] *pDst points to the location where the output result is written.  Length 2 * max(srcALen, srcBLen) - 1.   
+ * @return none.   
+ *   
+ * Scaling and Overflow Behavior:   
+ *   
+ * \par   
+ * This fast version uses a 32-bit accumulator with 2.30 format.   
+ * The accumulator maintains full precision of the intermediate multiplication results but provides only a single guard bit.   
+ * There is no saturation on intermediate additions.   
+ * Thus, if the accumulator overflows it wraps around and distorts the result.   
+ * The input signals should be scaled down to avoid intermediate overflows.   
+ * Scale down one of the inputs by 1/min(srcALen, srcBLen) to avoid overflow since a   
+ * maximum of min(srcALen, srcBLen) number of additions is carried internally.   
+ * The 2.30 accumulator is right shifted by 15 bits and then saturated to 1.15 format to yield the final result.   
+ *   
+ * \par   
+ * See arm_correlate_q15() for a slower implementation of this function which uses a 64-bit accumulator to avoid wrap around distortion.   
+ */
+
+void arm_correlate_fast_q15(
+  q15_t * pSrcA,
+  uint32_t srcALen,
+  q15_t * pSrcB,
+  uint32_t srcBLen,
+  q15_t * pDst)
+{
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+  q15_t *pIn1;                                   /* inputA pointer               */
+  q15_t *pIn2;                                   /* inputB pointer               */
+  q15_t *pOut = pDst;                            /* output pointer               */
+  q31_t sum, acc0, acc1, acc2, acc3;             /* Accumulators                  */
+  q15_t *px;                                     /* Intermediate inputA pointer  */
+  q15_t *py;                                     /* Intermediate inputB pointer  */
+  q15_t *pSrc1;                                  /* Intermediate pointers        */
+  q31_t x0, x1, x2, x3, c0;                      /* temporary variables for holding input and coefficient values */
+  uint32_t j, k = 0u, count, blkCnt, outBlockSize, blockSize1, blockSize2, blockSize3;  /* loop counter                 */
+  int32_t inc = 1;                               /* Destination address modifier */
+
+
+  /* The algorithm implementation is based on the lengths of the inputs. */
+  /* srcB is always made to slide across srcA. */
+  /* So srcBLen is always considered as shorter or equal to srcALen */
+  /* But CORR(x, y) is reverse of CORR(y, x) */
+  /* So, when srcBLen > srcALen, output pointer is made to point to the end of the output buffer */
+  /* and the destination pointer modifier, inc is set to -1 */
+  /* If srcALen > srcBLen, zero pad has to be done to srcB to make the two inputs of same length */
+  /* But to improve the performance,   
+   * we include zeroes in the output instead of zero padding either of the the inputs*/
+  /* If srcALen > srcBLen,   
+   * (srcALen - srcBLen) zeroes has to included in the starting of the output buffer */
+  /* If srcALen < srcBLen,   
+   * (srcALen - srcBLen) zeroes has to included in the ending of the output buffer */
+  if(srcALen >= srcBLen)
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = (pSrcA);
+
+    /* Initialization of inputB pointer */
+    pIn2 = (pSrcB);
+
+    /* Number of output samples is calculated */
+    outBlockSize = (2u * srcALen) - 1u;
+
+    /* When srcALen > srcBLen, zero padding is done to srcB   
+     * to make their lengths equal.   
+     * Instead, (outBlockSize - (srcALen + srcBLen - 1))   
+     * number of output samples are made zero */
+    j = outBlockSize - (srcALen + (srcBLen - 1u));
+
+    /* Updating the pointer position to non zero value */
+    pOut += j;
+
+  }
+  else
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = (pSrcB);
+
+    /* Initialization of inputB pointer */
+    pIn2 = (pSrcA);
+
+    /* srcBLen is always considered as shorter or equal to srcALen */
+    j = srcBLen;
+    srcBLen = srcALen;
+    srcALen = j;
+
+    /* CORR(x, y) = Reverse order(CORR(y, x)) */
+    /* Hence set the destination pointer to point to the last output sample */
+    pOut = pDst + ((srcALen + srcBLen) - 2u);
+
+    /* Destination address modifier is set to -1 */
+    inc = -1;
+
+  }
+
+  /* The function is internally   
+   * divided into three parts according to the number of multiplications that has to be   
+   * taken place between inputA samples and inputB samples. In the first part of the   
+   * algorithm, the multiplications increase by one for every iteration.   
+   * In the second part of the algorithm, srcBLen number of multiplications are done.   
+   * In the third part of the algorithm, the multiplications decrease by one   
+   * for every iteration.*/
+  /* The algorithm is implemented in three stages.   
+   * The loop counters of each stage is initiated here. */
+  blockSize1 = srcBLen - 1u;
+  blockSize2 = srcALen - (srcBLen - 1u);
+  blockSize3 = blockSize1;
+
+  /* --------------------------   
+   * Initializations of stage1   
+   * -------------------------*/
+
+  /* sum = x[0] * y[srcBlen - 1]   
+   * sum = x[0] * y[srcBlen - 2] + x[1] * y[srcBlen - 1]   
+   * ....   
+   * sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen - 1] * y[srcBLen - 1]   
+   */
+
+  /* In this stage the MAC operations are increased by 1 for every iteration.   
+     The count variable holds the number of MAC operations performed */
+  count = 1u;
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  pSrc1 = pIn2 + (srcBLen - 1u);
+  py = pSrc1;
+
+  /* ------------------------   
+   * Stage1 process   
+   * ----------------------*/
+
+  /* The first loop starts here */
+  while(blockSize1 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = count >> 2;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* x[0] * y[srcBLen - 4] , x[1] * y[srcBLen - 3] */
+      sum = __SMLAD(*__SIMD32(px)++, *__SIMD32(py)++, sum);
+      /* x[3] * y[srcBLen - 1] , x[2] * y[srcBLen - 2] */
+      sum = __SMLAD(*__SIMD32(px)++, *__SIMD32(py)++, sum);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, compute any remaining MACs here.   
+     ** No loop unrolling is used. */
+    k = count % 0x4u;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      /* x[0] * y[srcBLen - 1] */
+      sum = __SMLAD(*px++, *py++, sum);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut = (q15_t) (sum >> 15);
+    /* Destination pointer is updated according to the address modifier, inc */
+    pOut += inc;
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    py = pSrc1 - count;
+    px = pIn1;
+
+    /* Increment the MAC count */
+    count++;
+
+    /* Decrement the loop counter */
+    blockSize1--;
+  }
+
+  /* --------------------------   
+   * Initializations of stage2   
+   * ------------------------*/
+
+  /* sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen-1] * y[srcBLen-1]   
+   * sum = x[1] * y[0] + x[2] * y[1] +...+ x[srcBLen] * y[srcBLen-1]   
+   * ....   
+   * sum = x[srcALen-srcBLen-2] * y[0] + x[srcALen-srcBLen-1] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]   
+   */
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  py = pIn2;
+
+  /* count is index by which the pointer pIn1 to be incremented */
+  count = 0u;
+
+  /* -------------------   
+   * Stage2 process   
+   * ------------------*/
+
+  /* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.   
+   * So, to loop unroll over blockSize2,   
+   * srcBLen should be greater than or equal to 4, to loop unroll the srcBLen loop */
+  if(srcBLen >= 4u)
+  {
+    /* Loop unroll over blockSize2, by 4 */
+    blkCnt = blockSize2 >> 2u;
+
+    while(blkCnt > 0u)
+    {
+      /* Set all accumulators to zero */
+      acc0 = 0;
+      acc1 = 0;
+      acc2 = 0;
+      acc3 = 0;
+
+      /* read x[0], x[1] samples */
+      x0 = *__SIMD32(px);
+      /* read x[1], x[2] samples */
+      x1 = _SIMD32_OFFSET(px + 1);
+	  px += 2u;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      do
+      {
+        /* Read the first two inputB samples using SIMD:   
+         * y[0] and y[1] */
+        c0 = *__SIMD32(py)++;
+
+        /* acc0 +=  x[0] * y[0] + x[1] * y[1] */
+        acc0 = __SMLAD(x0, c0, acc0);
+
+        /* acc1 +=  x[1] * y[0] + x[2] * y[1] */
+        acc1 = __SMLAD(x1, c0, acc1);
+
+        /* Read x[2], x[3] */
+        x2 = *__SIMD32(px);
+
+        /* Read x[3], x[4] */
+        x3 = _SIMD32_OFFSET(px + 1);
+
+        /* acc2 +=  x[2] * y[0] + x[3] * y[1] */
+        acc2 = __SMLAD(x2, c0, acc2);
+
+        /* acc3 +=  x[3] * y[0] + x[4] * y[1] */
+        acc3 = __SMLAD(x3, c0, acc3);
+
+        /* Read y[2] and y[3] */
+        c0 = *__SIMD32(py)++;
+
+        /* acc0 +=  x[2] * y[2] + x[3] * y[3] */
+        acc0 = __SMLAD(x2, c0, acc0);
+
+        /* acc1 +=  x[3] * y[2] + x[4] * y[3] */
+        acc1 = __SMLAD(x3, c0, acc1);
+
+        /* Read x[4], x[5] */
+        x0 = _SIMD32_OFFSET(px + 2);
+
+        /* Read x[5], x[6] */
+        x1 = _SIMD32_OFFSET(px + 3);
+		px += 4u;
+
+        /* acc2 +=  x[4] * y[2] + x[5] * y[3] */
+        acc2 = __SMLAD(x0, c0, acc2);
+
+        /* acc3 +=  x[5] * y[2] + x[6] * y[3] */
+        acc3 = __SMLAD(x1, c0, acc3);
+
+      } while(--k);
+
+      /* For the next MAC operations, SIMD is not used   
+       * So, the 16 bit pointer if inputB, py is updated */
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.   
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      if(k == 1u)
+      {
+        /* Read y[4] */
+        c0 = *py;
+#ifdef  ARM_MATH_BIG_ENDIAN
+
+        c0 = c0 << 16u;
+
+#else
+
+        c0 = c0 & 0x0000FFFF;
+
+#endif /*      #ifdef  ARM_MATH_BIG_ENDIAN     */
+
+        /* Read x[7] */
+        x3 = *__SIMD32(px);
+		px++;
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLAD(x0, c0, acc0);
+        acc1 = __SMLAD(x1, c0, acc1);
+        acc2 = __SMLADX(x1, c0, acc2);
+        acc3 = __SMLADX(x3, c0, acc3);
+      }
+
+      if(k == 2u)
+      {
+        /* Read y[4], y[5] */
+        c0 = *__SIMD32(py);
+
+        /* Read x[7], x[8] */
+        x3 = *__SIMD32(px);
+
+        /* Read x[9] */
+        x2 = _SIMD32_OFFSET(px + 1);
+		px += 2u;
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLAD(x0, c0, acc0);
+        acc1 = __SMLAD(x1, c0, acc1);
+        acc2 = __SMLAD(x3, c0, acc2);
+        acc3 = __SMLAD(x2, c0, acc3);
+      }
+
+      if(k == 3u)
+      {
+        /* Read y[4], y[5] */
+        c0 = *__SIMD32(py)++;
+
+        /* Read x[7], x[8] */
+        x3 = *__SIMD32(px);
+
+        /* Read x[9] */
+        x2 = _SIMD32_OFFSET(px + 1);
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLAD(x0, c0, acc0);
+        acc1 = __SMLAD(x1, c0, acc1);
+        acc2 = __SMLAD(x3, c0, acc2);
+        acc3 = __SMLAD(x2, c0, acc3);
+
+        c0 = (*py);
+        /* Read y[6] */
+#ifdef  ARM_MATH_BIG_ENDIAN
+
+        c0 = c0 << 16u;
+#else
+
+        c0 = c0 & 0x0000FFFF;
+#endif /*      #ifdef  ARM_MATH_BIG_ENDIAN     */
+
+        /* Read x[10] */
+        x3 = _SIMD32_OFFSET(px + 2);
+		px += 3u;
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLADX(x1, c0, acc0);
+        acc1 = __SMLAD(x2, c0, acc1);
+        acc2 = __SMLADX(x2, c0, acc2);
+        acc3 = __SMLADX(x3, c0, acc3);
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut = (q15_t) (acc0 >> 15);
+      /* Destination pointer is updated according to the address modifier, inc */
+      pOut += inc;
+
+      *pOut = (q15_t) (acc1 >> 15);
+      pOut += inc;
+
+      *pOut = (q15_t) (acc2 >> 15);
+      pOut += inc;
+
+      *pOut = (q15_t) (acc3 >> 15);
+      pOut += inc;
+
+      /* Increment the pointer pIn1 index, count by 1 */
+      count += 4u;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pIn2;
+
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.   
+     ** No loop unrolling is used. */
+    blkCnt = blockSize2 % 0x4u;
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum += ((q31_t) * px++ * *py++);
+        sum += ((q31_t) * px++ * *py++);
+        sum += ((q31_t) * px++ * *py++);
+        sum += ((q31_t) * px++ * *py++);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.   
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum += ((q31_t) * px++ * *py++);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut = (q15_t) (sum >> 15);
+      /* Destination pointer is updated according to the address modifier, inc */
+      pOut += inc;
+
+      /* Increment the pointer pIn1 index, count by 1 */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pIn2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+  else
+  {
+    /* If the srcBLen is not a multiple of 4,   
+     * the blockSize2 loop cannot be unrolled by 4 */
+    blkCnt = blockSize2;
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Loop over srcBLen */
+      k = srcBLen;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulate */
+        sum += ((q31_t) * px++ * *py++);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut = (q15_t) (sum >> 15);
+      /* Destination pointer is updated according to the address modifier, inc */
+      pOut += inc;
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pIn2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+
+  /* --------------------------   
+   * Initializations of stage3   
+   * -------------------------*/
+
+  /* sum += x[srcALen-srcBLen+1] * y[0] + x[srcALen-srcBLen+2] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]   
+   * sum += x[srcALen-srcBLen+2] * y[0] + x[srcALen-srcBLen+3] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]   
+   * ....   
+   * sum +=  x[srcALen-2] * y[0] + x[srcALen-1] * y[1]   
+   * sum +=  x[srcALen-1] * y[0]   
+   */
+
+  /* In this stage the MAC operations are decreased by 1 for every iteration.   
+     The count variable holds the number of MAC operations performed */
+  count = srcBLen - 1u;
+
+  /* Working pointer of inputA */
+  pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
+  px = pSrc1;
+
+  /* Working pointer of inputB */
+  py = pIn2;
+
+  /* -------------------   
+   * Stage3 process   
+   * ------------------*/
+
+  while(blockSize3 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = count >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      /* sum += x[srcALen - srcBLen + 4] * y[3] , sum += x[srcALen - srcBLen + 3] * y[2] */
+      sum = __SMLAD(*__SIMD32(px)++, *__SIMD32(py)++, sum);
+      /* sum += x[srcALen - srcBLen + 2] * y[1] , sum += x[srcALen - srcBLen + 1] * y[0] */
+      sum = __SMLAD(*__SIMD32(px)++, *__SIMD32(py)++, sum);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, compute any remaining MACs here.   
+     ** No loop unrolling is used. */
+    k = count % 0x4u;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      sum = __SMLAD(*px++, *py++, sum);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut = (q15_t) (sum >> 15);
+    /* Destination pointer is updated according to the address modifier, inc */
+    pOut += inc;
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    px = ++pSrc1;
+    py = pIn2;
+
+    /* Decrement the MAC count */
+    count--;
+
+    /* Decrement the loop counter */
+    blockSize3--;
+  }
+
+#else
+
+  q15_t *pIn1;                                   /* inputA pointer               */
+  q15_t *pIn2;                                   /* inputB pointer               */
+  q15_t *pOut = pDst;                            /* output pointer               */
+  q31_t sum, acc0, acc1, acc2, acc3;             /* Accumulators                  */
+  q15_t *px;                                     /* Intermediate inputA pointer  */
+  q15_t *py;                                     /* Intermediate inputB pointer  */
+  q15_t *pSrc1;                                  /* Intermediate pointers        */
+  q31_t x0, x1, x2, x3, c0;                      /* temporary variables for holding input and coefficient values */
+  uint32_t j, k = 0u, count, blkCnt, outBlockSize, blockSize1, blockSize2, blockSize3;  /* loop counter                 */
+  int32_t inc = 1;                               /* Destination address modifier */
+  q15_t a, b;
+
+
+  /* The algorithm implementation is based on the lengths of the inputs. */
+  /* srcB is always made to slide across srcA. */
+  /* So srcBLen is always considered as shorter or equal to srcALen */
+  /* But CORR(x, y) is reverse of CORR(y, x) */
+  /* So, when srcBLen > srcALen, output pointer is made to point to the end of the output buffer */
+  /* and the destination pointer modifier, inc is set to -1 */
+  /* If srcALen > srcBLen, zero pad has to be done to srcB to make the two inputs of same length */
+  /* But to improve the performance,   
+   * we include zeroes in the output instead of zero padding either of the the inputs*/
+  /* If srcALen > srcBLen,   
+   * (srcALen - srcBLen) zeroes has to included in the starting of the output buffer */
+  /* If srcALen < srcBLen,   
+   * (srcALen - srcBLen) zeroes has to included in the ending of the output buffer */
+  if(srcALen >= srcBLen)
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = (pSrcA);
+
+    /* Initialization of inputB pointer */
+    pIn2 = (pSrcB);
+
+    /* Number of output samples is calculated */
+    outBlockSize = (2u * srcALen) - 1u;
+
+    /* When srcALen > srcBLen, zero padding is done to srcB   
+     * to make their lengths equal.   
+     * Instead, (outBlockSize - (srcALen + srcBLen - 1))   
+     * number of output samples are made zero */
+    j = outBlockSize - (srcALen + (srcBLen - 1u));
+
+    /* Updating the pointer position to non zero value */
+    pOut += j;
+
+  }
+  else
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = (pSrcB);
+
+    /* Initialization of inputB pointer */
+    pIn2 = (pSrcA);
+
+    /* srcBLen is always considered as shorter or equal to srcALen */
+    j = srcBLen;
+    srcBLen = srcALen;
+    srcALen = j;
+
+    /* CORR(x, y) = Reverse order(CORR(y, x)) */
+    /* Hence set the destination pointer to point to the last output sample */
+    pOut = pDst + ((srcALen + srcBLen) - 2u);
+
+    /* Destination address modifier is set to -1 */
+    inc = -1;
+
+  }
+
+  /* The function is internally   
+   * divided into three parts according to the number of multiplications that has to be   
+   * taken place between inputA samples and inputB samples. In the first part of the   
+   * algorithm, the multiplications increase by one for every iteration.   
+   * In the second part of the algorithm, srcBLen number of multiplications are done.   
+   * In the third part of the algorithm, the multiplications decrease by one   
+   * for every iteration.*/
+  /* The algorithm is implemented in three stages.   
+   * The loop counters of each stage is initiated here. */
+  blockSize1 = srcBLen - 1u;
+  blockSize2 = srcALen - (srcBLen - 1u);
+  blockSize3 = blockSize1;
+
+  /* --------------------------   
+   * Initializations of stage1   
+   * -------------------------*/
+
+  /* sum = x[0] * y[srcBlen - 1]   
+   * sum = x[0] * y[srcBlen - 2] + x[1] * y[srcBlen - 1]   
+   * ....   
+   * sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen - 1] * y[srcBLen - 1]   
+   */
+
+  /* In this stage the MAC operations are increased by 1 for every iteration.   
+     The count variable holds the number of MAC operations performed */
+  count = 1u;
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  pSrc1 = pIn2 + (srcBLen - 1u);
+  py = pSrc1;
+
+  /* ------------------------   
+   * Stage1 process   
+   * ----------------------*/
+
+  /* The first loop starts here */
+  while(blockSize1 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = count >> 2;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* x[0] * y[srcBLen - 4] , x[1] * y[srcBLen - 3] */
+        sum += ((q31_t) * px++ * *py++);
+        sum += ((q31_t) * px++ * *py++);
+        sum += ((q31_t) * px++ * *py++);
+        sum += ((q31_t) * px++ * *py++);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, compute any remaining MACs here.   
+     ** No loop unrolling is used. */
+    k = count % 0x4u;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      /* x[0] * y[srcBLen - 1] */
+        sum += ((q31_t) * px++ * *py++);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut = (q15_t) (sum >> 15);
+    /* Destination pointer is updated according to the address modifier, inc */
+    pOut += inc;
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    py = pSrc1 - count;
+    px = pIn1;
+
+    /* Increment the MAC count */
+    count++;
+
+    /* Decrement the loop counter */
+    blockSize1--;
+  }
+
+  /* --------------------------   
+   * Initializations of stage2   
+   * ------------------------*/
+
+  /* sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen-1] * y[srcBLen-1]   
+   * sum = x[1] * y[0] + x[2] * y[1] +...+ x[srcBLen] * y[srcBLen-1]   
+   * ....   
+   * sum = x[srcALen-srcBLen-2] * y[0] + x[srcALen-srcBLen-1] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]   
+   */
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  py = pIn2;
+
+  /* count is index by which the pointer pIn1 to be incremented */
+  count = 0u;
+
+  /* -------------------   
+   * Stage2 process   
+   * ------------------*/
+
+  /* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.   
+   * So, to loop unroll over blockSize2,   
+   * srcBLen should be greater than or equal to 4, to loop unroll the srcBLen loop */
+  if(srcBLen >= 4u)
+  {
+    /* Loop unroll over blockSize2, by 4 */
+    blkCnt = blockSize2 >> 2u;
+
+    while(blkCnt > 0u)
+    {
+      /* Set all accumulators to zero */
+      acc0 = 0;
+      acc1 = 0;
+      acc2 = 0;
+      acc3 = 0;
+
+      /* read x[0], x[1], x[2] samples */
+	  a = *px;
+	  b = *(px + 1);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+	  x0 = __PKHBT(a, b, 16);
+	  a = *(px + 2);
+	  x1 = __PKHBT(b, a, 16);
+
+#else
+
+	  x0 = __PKHBT(b, a, 16);
+	  a = *(px + 2);
+	  x1 = __PKHBT(a, b, 16);
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	*/
+
+	  px += 2u;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      do
+      {
+        /* Read the first two inputB samples using SIMD:   
+         * y[0] and y[1] */
+		  a = *py;
+		  b = *(py + 1);
+	
+#ifndef ARM_MATH_BIG_ENDIAN
+	
+		  c0 = __PKHBT(a, b, 16);
+	
+#else
+	
+		  c0 = __PKHBT(b, a, 16);
+	
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	*/
+
+        /* acc0 +=  x[0] * y[0] + x[1] * y[1] */
+        acc0 = __SMLAD(x0, c0, acc0);
+
+        /* acc1 +=  x[1] * y[0] + x[2] * y[1] */
+        acc1 = __SMLAD(x1, c0, acc1);
+
+        /* Read x[2], x[3], x[4] */
+	  	a = *px;
+	  	b = *(px + 1);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+	  	x2 = __PKHBT(a, b, 16);
+	  	a = *(px + 2);
+	  	x3 = __PKHBT(b, a, 16);
+
+#else
+
+	  	x2 = __PKHBT(b, a, 16);
+	  	a = *(px + 2);
+	  	x3 = __PKHBT(a, b, 16);
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	*/
+
+        /* acc2 +=  x[2] * y[0] + x[3] * y[1] */
+        acc2 = __SMLAD(x2, c0, acc2);
+
+        /* acc3 +=  x[3] * y[0] + x[4] * y[1] */
+        acc3 = __SMLAD(x3, c0, acc3);
+
+        /* Read y[2] and y[3] */
+		  a = *(py + 2);
+		  b = *(py + 3);
+
+		  py += 4u;
+	
+#ifndef ARM_MATH_BIG_ENDIAN
+	
+		  c0 = __PKHBT(a, b, 16);
+	
+#else
+	
+		  c0 = __PKHBT(b, a, 16);
+	
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	*/
+
+        /* acc0 +=  x[2] * y[2] + x[3] * y[3] */
+        acc0 = __SMLAD(x2, c0, acc0);
+
+        /* acc1 +=  x[3] * y[2] + x[4] * y[3] */
+        acc1 = __SMLAD(x3, c0, acc1);
+
+        /* Read x[4], x[5], x[6] */
+	  	a = *(px + 2);
+	  	b = *(px + 3);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+	  	x0 = __PKHBT(a, b, 16);
+	  	a = *(px + 4);
+	  	x1 = __PKHBT(b, a, 16);
+
+#else
+
+	  	x0 = __PKHBT(b, a, 16);
+	  	a = *(px + 4);
+	  	x1 = __PKHBT(a, b, 16);
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	*/
+
+		px += 4u;
+
+        /* acc2 +=  x[4] * y[2] + x[5] * y[3] */
+        acc2 = __SMLAD(x0, c0, acc2);
+
+        /* acc3 +=  x[5] * y[2] + x[6] * y[3] */
+        acc3 = __SMLAD(x1, c0, acc3);
+
+      } while(--k);
+
+      /* For the next MAC operations, SIMD is not used   
+       * So, the 16 bit pointer if inputB, py is updated */
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.   
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      if(k == 1u)
+      {
+        /* Read y[4] */
+        c0 = *py;
+#ifdef  ARM_MATH_BIG_ENDIAN
+
+        c0 = c0 << 16u;
+
+#else
+
+        c0 = c0 & 0x0000FFFF;
+
+#endif /*      #ifdef  ARM_MATH_BIG_ENDIAN     */
+
+        /* Read x[7] */
+		a = *px;
+		b = *(px + 1);
+
+		px++;;
+	
+#ifndef ARM_MATH_BIG_ENDIAN
+	
+		x3 = __PKHBT(a, b, 16);
+	
+#else
+	
+		x3 = __PKHBT(b, a, 16);
+	
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	*/
+
+		px++;
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLAD(x0, c0, acc0);
+        acc1 = __SMLAD(x1, c0, acc1);
+        acc2 = __SMLADX(x1, c0, acc2);
+        acc3 = __SMLADX(x3, c0, acc3);
+      }
+
+      if(k == 2u)
+      {
+        /* Read y[4], y[5] */
+		  a = *py;
+		  b = *(py + 1);
+	
+#ifndef ARM_MATH_BIG_ENDIAN
+	
+		  c0 = __PKHBT(a, b, 16);
+	
+#else
+	
+		  c0 = __PKHBT(b, a, 16);
+	
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	*/
+
+        /* Read x[7], x[8], x[9] */
+	  	a = *px;
+	  	b = *(px + 1);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+	  	x3 = __PKHBT(a, b, 16);
+	  	a = *(px + 2);
+	  	x2 = __PKHBT(b, a, 16);
+
+#else
+
+	  	x3 = __PKHBT(b, a, 16);
+	  	a = *(px + 2);
+	  	x2 = __PKHBT(a, b, 16);
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	*/
+
+		px += 2u;
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLAD(x0, c0, acc0);
+        acc1 = __SMLAD(x1, c0, acc1);
+        acc2 = __SMLAD(x3, c0, acc2);
+        acc3 = __SMLAD(x2, c0, acc3);
+      }
+
+      if(k == 3u)
+      {
+        /* Read y[4], y[5] */
+		  a = *py;
+		  b = *(py + 1);
+	
+#ifndef ARM_MATH_BIG_ENDIAN
+	
+		  c0 = __PKHBT(a, b, 16);
+	
+#else
+	
+		  c0 = __PKHBT(b, a, 16);
+	
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	*/
+
+		py += 2u;
+
+        /* Read x[7], x[8], x[9] */
+	  	a = *px;
+	  	b = *(px + 1);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+	  	x3 = __PKHBT(a, b, 16);
+	  	a = *(px + 2);
+	  	x2 = __PKHBT(b, a, 16);
+
+#else
+
+	  	x3 = __PKHBT(b, a, 16);
+	  	a = *(px + 2);
+	  	x2 = __PKHBT(a, b, 16);
+
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	*/
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLAD(x0, c0, acc0);
+        acc1 = __SMLAD(x1, c0, acc1);
+        acc2 = __SMLAD(x3, c0, acc2);
+        acc3 = __SMLAD(x2, c0, acc3);
+
+        c0 = (*py);
+        /* Read y[6] */
+#ifdef  ARM_MATH_BIG_ENDIAN
+
+        c0 = c0 << 16u;
+#else
+
+        c0 = c0 & 0x0000FFFF;
+#endif /*      #ifdef  ARM_MATH_BIG_ENDIAN     */
+
+        /* Read x[10] */
+		b = *(px + 3);
+	
+#ifndef ARM_MATH_BIG_ENDIAN
+	
+		x3 = __PKHBT(a, b, 16);
+	
+#else
+	
+		x3 = __PKHBT(b, a, 16);
+	
+#endif	/*	#ifndef ARM_MATH_BIG_ENDIAN	*/
+
+		px += 3u;
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLADX(x1, c0, acc0);
+        acc1 = __SMLAD(x2, c0, acc1);
+        acc2 = __SMLADX(x2, c0, acc2);
+        acc3 = __SMLADX(x3, c0, acc3);
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut = (q15_t) (acc0 >> 15);
+      /* Destination pointer is updated according to the address modifier, inc */
+      pOut += inc;
+
+      *pOut = (q15_t) (acc1 >> 15);
+      pOut += inc;
+
+      *pOut = (q15_t) (acc2 >> 15);
+      pOut += inc;
+
+      *pOut = (q15_t) (acc3 >> 15);
+      pOut += inc;
+
+      /* Increment the pointer pIn1 index, count by 1 */
+      count += 4u;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pIn2;
+
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.   
+     ** No loop unrolling is used. */
+    blkCnt = blockSize2 % 0x4u;
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum += ((q31_t) * px++ * *py++);
+        sum += ((q31_t) * px++ * *py++);
+        sum += ((q31_t) * px++ * *py++);
+        sum += ((q31_t) * px++ * *py++);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.   
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum += ((q31_t) * px++ * *py++);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut = (q15_t) (sum >> 15);
+      /* Destination pointer is updated according to the address modifier, inc */
+      pOut += inc;
+
+      /* Increment the pointer pIn1 index, count by 1 */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pIn2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+  else
+  {
+    /* If the srcBLen is not a multiple of 4,   
+     * the blockSize2 loop cannot be unrolled by 4 */
+    blkCnt = blockSize2;
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Loop over srcBLen */
+      k = srcBLen;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulate */
+        sum += ((q31_t) * px++ * *py++);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut = (q15_t) (sum >> 15);
+      /* Destination pointer is updated according to the address modifier, inc */
+      pOut += inc;
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pIn2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+
+  /* --------------------------   
+   * Initializations of stage3   
+   * -------------------------*/
+
+  /* sum += x[srcALen-srcBLen+1] * y[0] + x[srcALen-srcBLen+2] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]   
+   * sum += x[srcALen-srcBLen+2] * y[0] + x[srcALen-srcBLen+3] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]   
+   * ....   
+   * sum +=  x[srcALen-2] * y[0] + x[srcALen-1] * y[1]   
+   * sum +=  x[srcALen-1] * y[0]   
+   */
+
+  /* In this stage the MAC operations are decreased by 1 for every iteration.   
+     The count variable holds the number of MAC operations performed */
+  count = srcBLen - 1u;
+
+  /* Working pointer of inputA */
+  pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
+  px = pSrc1;
+
+  /* Working pointer of inputB */
+  py = pIn2;
+
+  /* -------------------   
+   * Stage3 process   
+   * ------------------*/
+
+  while(blockSize3 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = count >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+        sum += ((q31_t) * px++ * *py++);
+        sum += ((q31_t) * px++ * *py++);
+        sum += ((q31_t) * px++ * *py++);
+        sum += ((q31_t) * px++ * *py++);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, compute any remaining MACs here.   
+     ** No loop unrolling is used. */
+    k = count % 0x4u;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+        sum += ((q31_t) * px++ * *py++);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut = (q15_t) (sum >> 15);
+    /* Destination pointer is updated according to the address modifier, inc */
+    pOut += inc;
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    px = ++pSrc1;
+    py = pIn2;
+
+    /* Decrement the MAC count */
+    count--;
+
+    /* Decrement the loop counter */
+    blockSize3--;
+  }
+
+#endif /*   #ifndef UNALIGNED_SUPPORT_DISABLE */
+
+}
+
+/**   
+ * @} end of Corr group   
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_fast_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_fast_q31.c
new file mode 100644
index 0000000000..628fd3ea55
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_fast_q31.c
@@ -0,0 +1,607 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_correlate_fast_q31.c    
+*    
+* Description:	Fast Q31 Correlation.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+* 
+* Version 1.0.11 2011/10/18  
+*    Bug Fix in conv, correlation, partial convolution.  
+* 
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup Corr    
+ * @{    
+ */
+
+/**    
+ * @brief Correlation of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4.    
+ * @param[in] *pSrcA points to the first input sequence.    
+ * @param[in] srcALen length of the first input sequence.    
+ * @param[in] *pSrcB points to the second input sequence.    
+ * @param[in] srcBLen length of the second input sequence.    
+ * @param[out] *pDst points to the location where the output result is written.  Length 2 * max(srcALen, srcBLen) - 1.    
+ * @return none.    
+ *    
+ * @details    
+ * Scaling and Overflow Behavior:    
+ *    
+ * \par    
+ * This function is optimized for speed at the expense of fixed-point precision and overflow protection.    
+ * The result of each 1.31 x 1.31 multiplication is truncated to 2.30 format.    
+ * These intermediate results are accumulated in a 32-bit register in 2.30 format.    
+ * Finally, the accumulator is saturated and converted to a 1.31 result.    
+ *    
+ * \par    
+ * The fast version has the same overflow behavior as the standard version but provides less precision since it discards the low 32 bits of each multiplication result.    
+ * In order to avoid overflows completely the input signals must be scaled down.    
+ * The input signals should be scaled down to avoid intermediate overflows.    
+ * Scale down one of the inputs by 1/min(srcALen, srcBLen)to avoid overflows since a    
+ * maximum of min(srcALen, srcBLen) number of additions is carried internally.    
+ *    
+ * \par    
+ * See arm_correlate_q31() for a slower implementation of this function which uses 64-bit accumulation to provide higher precision.    
+ */
+
+void arm_correlate_fast_q31(
+  q31_t * pSrcA,
+  uint32_t srcALen,
+  q31_t * pSrcB,
+  uint32_t srcBLen,
+  q31_t * pDst)
+{
+  q31_t *pIn1;                                   /* inputA pointer               */
+  q31_t *pIn2;                                   /* inputB pointer               */
+  q31_t *pOut = pDst;                            /* output pointer               */
+  q31_t *px;                                     /* Intermediate inputA pointer  */
+  q31_t *py;                                     /* Intermediate inputB pointer  */
+  q31_t *pSrc1;                                  /* Intermediate pointers        */
+  q31_t sum, acc0, acc1, acc2, acc3;             /* Accumulators                  */
+  q31_t x0, x1, x2, x3, c0;                      /* temporary variables for holding input and coefficient values */
+  uint32_t j, k = 0u, count, blkCnt, outBlockSize, blockSize1, blockSize2, blockSize3;  /* loop counter                 */
+  int32_t inc = 1;                               /* Destination address modifier */
+
+
+  /* The algorithm implementation is based on the lengths of the inputs. */
+  /* srcB is always made to slide across srcA. */
+  /* So srcBLen is always considered as shorter or equal to srcALen */
+  if(srcALen >= srcBLen)
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = (pSrcA);
+
+    /* Initialization of inputB pointer */
+    pIn2 = (pSrcB);
+
+    /* Number of output samples is calculated */
+    outBlockSize = (2u * srcALen) - 1u;
+
+    /* When srcALen > srcBLen, zero padding is done to srcB    
+     * to make their lengths equal.    
+     * Instead, (outBlockSize - (srcALen + srcBLen - 1))    
+     * number of output samples are made zero */
+    j = outBlockSize - (srcALen + (srcBLen - 1u));
+
+    /* Updating the pointer position to non zero value */
+    pOut += j;
+
+  }
+  else
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = (pSrcB);
+
+    /* Initialization of inputB pointer */
+    pIn2 = (pSrcA);
+
+    /* srcBLen is always considered as shorter or equal to srcALen */
+    j = srcBLen;
+    srcBLen = srcALen;
+    srcALen = j;
+
+    /* CORR(x, y) = Reverse order(CORR(y, x)) */
+    /* Hence set the destination pointer to point to the last output sample */
+    pOut = pDst + ((srcALen + srcBLen) - 2u);
+
+    /* Destination address modifier is set to -1 */
+    inc = -1;
+
+  }
+
+  /* The function is internally    
+   * divided into three parts according to the number of multiplications that has to be    
+   * taken place between inputA samples and inputB samples. In the first part of the    
+   * algorithm, the multiplications increase by one for every iteration.    
+   * In the second part of the algorithm, srcBLen number of multiplications are done.    
+   * In the third part of the algorithm, the multiplications decrease by one    
+   * for every iteration.*/
+  /* The algorithm is implemented in three stages.    
+   * The loop counters of each stage is initiated here. */
+  blockSize1 = srcBLen - 1u;
+  blockSize2 = srcALen - (srcBLen - 1u);
+  blockSize3 = blockSize1;
+
+  /* --------------------------    
+   * Initializations of stage1    
+   * -------------------------*/
+
+  /* sum = x[0] * y[srcBlen - 1]    
+   * sum = x[0] * y[srcBlen - 2] + x[1] * y[srcBlen - 1]    
+   * ....    
+   * sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen - 1] * y[srcBLen - 1]    
+   */
+
+  /* In this stage the MAC operations are increased by 1 for every iteration.    
+     The count variable holds the number of MAC operations performed */
+  count = 1u;
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  pSrc1 = pIn2 + (srcBLen - 1u);
+  py = pSrc1;
+
+  /* ------------------------    
+   * Stage1 process    
+   * ----------------------*/
+
+  /* The first stage starts here */
+  while(blockSize1 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = count >> 2;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* x[0] * y[srcBLen - 4] */
+      sum = (q31_t) ((((q63_t) sum << 32) +
+                      ((q63_t) * px++ * (*py++))) >> 32);
+      /* x[1] * y[srcBLen - 3] */
+      sum = (q31_t) ((((q63_t) sum << 32) +
+                      ((q63_t) * px++ * (*py++))) >> 32);
+      /* x[2] * y[srcBLen - 2] */
+      sum = (q31_t) ((((q63_t) sum << 32) +
+                      ((q63_t) * px++ * (*py++))) >> 32);
+      /* x[3] * y[srcBLen - 1] */
+      sum = (q31_t) ((((q63_t) sum << 32) +
+                      ((q63_t) * px++ * (*py++))) >> 32);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, compute any remaining MACs here.    
+     ** No loop unrolling is used. */
+    k = count % 0x4u;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      /* x[0] * y[srcBLen - 1] */
+      sum = (q31_t) ((((q63_t) sum << 32) +
+                      ((q63_t) * px++ * (*py++))) >> 32);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut = sum << 1;
+    /* Destination pointer is updated according to the address modifier, inc */
+    pOut += inc;
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    py = pSrc1 - count;
+    px = pIn1;
+
+    /* Increment the MAC count */
+    count++;
+
+    /* Decrement the loop counter */
+    blockSize1--;
+  }
+
+  /* --------------------------    
+   * Initializations of stage2    
+   * ------------------------*/
+
+  /* sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen-1] * y[srcBLen-1]    
+   * sum = x[1] * y[0] + x[2] * y[1] +...+ x[srcBLen] * y[srcBLen-1]    
+   * ....    
+   * sum = x[srcALen-srcBLen-2] * y[0] + x[srcALen-srcBLen-1] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]    
+   */
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  py = pIn2;
+
+  /* count is index by which the pointer pIn1 to be incremented */
+  count = 0u;
+
+  /* -------------------    
+   * Stage2 process    
+   * ------------------*/
+
+  /* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.    
+   * So, to loop unroll over blockSize2,    
+   * srcBLen should be greater than or equal to 4 */
+  if(srcBLen >= 4u)
+  {
+    /* Loop unroll over blockSize2, by 4 */
+    blkCnt = blockSize2 >> 2u;
+
+    while(blkCnt > 0u)
+    {
+      /* Set all accumulators to zero */
+      acc0 = 0;
+      acc1 = 0;
+      acc2 = 0;
+      acc3 = 0;
+
+      /* read x[0], x[1], x[2] samples */
+      x0 = *(px++);
+      x1 = *(px++);
+      x2 = *(px++);
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      do
+      {
+        /* Read y[0] sample */
+        c0 = *(py++);
+
+        /* Read x[3] sample */
+        x3 = *(px++);
+
+        /* Perform the multiply-accumulate */
+        /* acc0 +=  x[0] * y[0] */
+        acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x0 * c0)) >> 32);
+        /* acc1 +=  x[1] * y[0] */
+        acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x1 * c0)) >> 32);
+        /* acc2 +=  x[2] * y[0] */
+        acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x2 * c0)) >> 32);
+        /* acc3 +=  x[3] * y[0] */
+        acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x3 * c0)) >> 32);
+
+        /* Read y[1] sample */
+        c0 = *(py++);
+
+        /* Read x[4] sample */
+        x0 = *(px++);
+
+        /* Perform the multiply-accumulates */
+        /* acc0 +=  x[1] * y[1] */
+        acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x1 * c0)) >> 32);
+        /* acc1 +=  x[2] * y[1] */
+        acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x2 * c0)) >> 32);
+        /* acc2 +=  x[3] * y[1] */
+        acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x3 * c0)) >> 32);
+        /* acc3 +=  x[4] * y[1] */
+        acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x0 * c0)) >> 32);
+
+        /* Read y[2] sample */
+        c0 = *(py++);
+
+        /* Read x[5] sample */
+        x1 = *(px++);
+
+        /* Perform the multiply-accumulates */
+        /* acc0 +=  x[2] * y[2] */
+        acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x2 * c0)) >> 32);
+        /* acc1 +=  x[3] * y[2] */
+        acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x3 * c0)) >> 32);
+        /* acc2 +=  x[4] * y[2] */
+        acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x0 * c0)) >> 32);
+        /* acc3 +=  x[5] * y[2] */
+        acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x1 * c0)) >> 32);
+
+        /* Read y[3] sample */
+        c0 = *(py++);
+
+        /* Read x[6] sample */
+        x2 = *(px++);
+
+        /* Perform the multiply-accumulates */
+        /* acc0 +=  x[3] * y[3] */
+        acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x3 * c0)) >> 32);
+        /* acc1 +=  x[4] * y[3] */
+        acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x0 * c0)) >> 32);
+        /* acc2 +=  x[5] * y[3] */
+        acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x1 * c0)) >> 32);
+        /* acc3 +=  x[6] * y[3] */
+        acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x2 * c0)) >> 32);
+
+
+      } while(--k);
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.    
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Read y[4] sample */
+        c0 = *(py++);
+
+        /* Read x[7] sample */
+        x3 = *(px++);
+
+        /* Perform the multiply-accumulates */
+        /* acc0 +=  x[4] * y[4] */
+        acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x0 * c0)) >> 32);
+        /* acc1 +=  x[5] * y[4] */
+        acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x1 * c0)) >> 32);
+        /* acc2 +=  x[6] * y[4] */
+        acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x2 * c0)) >> 32);
+        /* acc3 +=  x[7] * y[4] */
+        acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x3 * c0)) >> 32);
+
+        /* Reuse the present samples for the next MAC */
+        x0 = x1;
+        x1 = x2;
+        x2 = x3;
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut = (q31_t) (acc0 << 1);
+      /* Destination pointer is updated according to the address modifier, inc */
+      pOut += inc;
+
+      *pOut = (q31_t) (acc1 << 1);
+      pOut += inc;
+
+      *pOut = (q31_t) (acc2 << 1);
+      pOut += inc;
+
+      *pOut = (q31_t) (acc3 << 1);
+      pOut += inc;
+
+      /* Increment the pointer pIn1 index, count by 4 */
+      count += 4u;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pIn2;
+
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.    
+     ** No loop unrolling is used. */
+    blkCnt = blockSize2 % 0x4u;
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum = (q31_t) ((((q63_t) sum << 32) +
+                        ((q63_t) * px++ * (*py++))) >> 32);
+        sum = (q31_t) ((((q63_t) sum << 32) +
+                        ((q63_t) * px++ * (*py++))) >> 32);
+        sum = (q31_t) ((((q63_t) sum << 32) +
+                        ((q63_t) * px++ * (*py++))) >> 32);
+        sum = (q31_t) ((((q63_t) sum << 32) +
+                        ((q63_t) * px++ * (*py++))) >> 32);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.    
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulate */
+        sum = (q31_t) ((((q63_t) sum << 32) +
+                        ((q63_t) * px++ * (*py++))) >> 32);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut = sum << 1;
+      /* Destination pointer is updated according to the address modifier, inc */
+      pOut += inc;
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pIn2;
+
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+  else
+  {
+    /* If the srcBLen is not a multiple of 4,    
+     * the blockSize2 loop cannot be unrolled by 4 */
+    blkCnt = blockSize2;
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Loop over srcBLen */
+      k = srcBLen;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulate */
+        sum = (q31_t) ((((q63_t) sum << 32) +
+                        ((q63_t) * px++ * (*py++))) >> 32);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut = sum << 1;
+      /* Destination pointer is updated according to the address modifier, inc */
+      pOut += inc;
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pIn2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+
+  /* --------------------------    
+   * Initializations of stage3    
+   * -------------------------*/
+
+  /* sum += x[srcALen-srcBLen+1] * y[0] + x[srcALen-srcBLen+2] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]    
+   * sum += x[srcALen-srcBLen+2] * y[0] + x[srcALen-srcBLen+3] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]    
+   * ....    
+   * sum +=  x[srcALen-2] * y[0] + x[srcALen-1] * y[1]    
+   * sum +=  x[srcALen-1] * y[0]    
+   */
+
+  /* In this stage the MAC operations are decreased by 1 for every iteration.    
+     The count variable holds the number of MAC operations performed */
+  count = srcBLen - 1u;
+
+  /* Working pointer of inputA */
+  pSrc1 = ((pIn1 + srcALen) - srcBLen) + 1u;
+  px = pSrc1;
+
+  /* Working pointer of inputB */
+  py = pIn2;
+
+  /* -------------------    
+   * Stage3 process    
+   * ------------------*/
+
+  while(blockSize3 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = count >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      /* sum += x[srcALen - srcBLen + 4] * y[3] */
+      sum = (q31_t) ((((q63_t) sum << 32) +
+                      ((q63_t) * px++ * (*py++))) >> 32);
+      /* sum += x[srcALen - srcBLen + 3] * y[2] */
+      sum = (q31_t) ((((q63_t) sum << 32) +
+                      ((q63_t) * px++ * (*py++))) >> 32);
+      /* sum += x[srcALen - srcBLen + 2] * y[1] */
+      sum = (q31_t) ((((q63_t) sum << 32) +
+                      ((q63_t) * px++ * (*py++))) >> 32);
+      /* sum += x[srcALen - srcBLen + 1] * y[0] */
+      sum = (q31_t) ((((q63_t) sum << 32) +
+                      ((q63_t) * px++ * (*py++))) >> 32);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, compute any remaining MACs here.    
+     ** No loop unrolling is used. */
+    k = count % 0x4u;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      sum = (q31_t) ((((q63_t) sum << 32) +
+                      ((q63_t) * px++ * (*py++))) >> 32);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut = sum << 1;
+    /* Destination pointer is updated according to the address modifier, inc */
+    pOut += inc;
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    px = ++pSrc1;
+    py = pIn2;
+
+    /* Decrement the MAC count */
+    count--;
+
+    /* Decrement the loop counter */
+    blockSize3--;
+  }
+
+}
+
+/**    
+ * @} end of Corr group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_opt_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_opt_q15.c
new file mode 100644
index 0000000000..cc33b54f5a
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_opt_q15.c
@@ -0,0 +1,512 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_correlate_opt_q15.c    
+*    
+* Description:	Correlation of Q15 sequences.  
+*    
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+* 
+* Version 1.0.11 2011/10/18  
+*    Bug Fix in conv, correlation, partial convolution.  
+* 
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+*    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup Corr    
+ * @{    
+ */
+
+/**    
+ * @brief Correlation of Q15 sequences.  
+ * @param[in] *pSrcA points to the first input sequence.    
+ * @param[in] srcALen length of the first input sequence.    
+ * @param[in] *pSrcB points to the second input sequence.    
+ * @param[in] srcBLen length of the second input sequence.    
+ * @param[out] *pDst points to the location where the output result is written.  Length 2 * max(srcALen, srcBLen) - 1.    
+ * @param[in]  *pScratch points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.    
+ * @return none.    
+ *    
+ * \par Restrictions    
+ *  If the silicon does not support unaligned memory access enable the macro UNALIGNED_SUPPORT_DISABLE    
+ *	In this case input, output, scratch buffers should be aligned by 32-bit    
+ *     
+ * @details    
+ * Scaling and Overflow Behavior:    
+ *    
+ * \par    
+ * The function is implemented using a 64-bit internal accumulator.    
+ * Both inputs are in 1.15 format and multiplications yield a 2.30 result.    
+ * The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format.    
+ * This approach provides 33 guard bits and there is no risk of overflow.    
+ * The 34.30 result is then truncated to 34.15 format by discarding the low 15 bits and then saturated to 1.15 format.    
+ *    
+ * \par    
+ * Refer to arm_correlate_fast_q15() for a faster but less precise version of this function for Cortex-M3 and Cortex-M4.   
+ *  
+ * 
+ */
+
+
+void arm_correlate_opt_q15(
+  q15_t * pSrcA,
+  uint32_t srcALen,
+  q15_t * pSrcB,
+  uint32_t srcBLen,
+  q15_t * pDst,
+  q15_t * pScratch)
+{
+  q15_t *pIn1;                                   /* inputA pointer               */
+  q15_t *pIn2;                                   /* inputB pointer               */
+  q63_t acc0, acc1, acc2, acc3;                  /* Accumulators                  */
+  q15_t *py;                                     /* Intermediate inputB pointer  */
+  q31_t x1, x2, x3;                              /* temporary variables for holding input1 and input2 values */
+  uint32_t j, blkCnt, outBlockSize;              /* loop counter                 */
+  int32_t inc = 1;                               /* output pointer increment     */
+  uint32_t tapCnt;
+  q31_t y1, y2;
+  q15_t *pScr;                                   /* Intermediate pointers        */
+  q15_t *pOut = pDst;                            /* output pointer               */
+#ifdef UNALIGNED_SUPPORT_DISABLE
+
+  q15_t a, b;
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+  /* The algorithm implementation is based on the lengths of the inputs. */
+  /* srcB is always made to slide across srcA. */
+  /* So srcBLen is always considered as shorter or equal to srcALen */
+  /* But CORR(x, y) is reverse of CORR(y, x) */
+  /* So, when srcBLen > srcALen, output pointer is made to point to the end of the output buffer */
+  /* and the destination pointer modifier, inc is set to -1 */
+  /* If srcALen > srcBLen, zero pad has to be done to srcB to make the two inputs of same length */
+  /* But to improve the performance,        
+   * we include zeroes in the output instead of zero padding either of the the inputs*/
+  /* If srcALen > srcBLen,        
+   * (srcALen - srcBLen) zeroes has to included in the starting of the output buffer */
+  /* If srcALen < srcBLen,        
+   * (srcALen - srcBLen) zeroes has to included in the ending of the output buffer */
+  if(srcALen >= srcBLen)
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = (pSrcA);
+
+    /* Initialization of inputB pointer */
+    pIn2 = (pSrcB);
+
+    /* Number of output samples is calculated */
+    outBlockSize = (2u * srcALen) - 1u;
+
+    /* When srcALen > srcBLen, zero padding is done to srcB        
+     * to make their lengths equal.        
+     * Instead, (outBlockSize - (srcALen + srcBLen - 1))        
+     * number of output samples are made zero */
+    j = outBlockSize - (srcALen + (srcBLen - 1u));
+
+    /* Updating the pointer position to non zero value */
+    pOut += j;
+
+  }
+  else
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = (pSrcB);
+
+    /* Initialization of inputB pointer */
+    pIn2 = (pSrcA);
+
+    /* srcBLen is always considered as shorter or equal to srcALen */
+    j = srcBLen;
+    srcBLen = srcALen;
+    srcALen = j;
+
+    /* CORR(x, y) = Reverse order(CORR(y, x)) */
+    /* Hence set the destination pointer to point to the last output sample */
+    pOut = pDst + ((srcALen + srcBLen) - 2u);
+
+    /* Destination address modifier is set to -1 */
+    inc = -1;
+
+  }
+
+  pScr = pScratch;
+
+  /* Fill (srcBLen - 1u) zeros in scratch buffer */
+  arm_fill_q15(0, pScr, (srcBLen - 1u));
+
+  /* Update temporary scratch pointer */
+  pScr += (srcBLen - 1u);
+
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+  /* Copy (srcALen) samples in scratch buffer */
+  arm_copy_q15(pIn1, pScr, srcALen);
+
+  /* Update pointers */
+  //pIn1 += srcALen;    
+  pScr += srcALen;
+
+#else
+
+  /* Apply loop unrolling and do 4 Copies simultaneously. */
+  j = srcALen >> 2u;
+
+  /* First part of the processing with loop unrolling copies 4 data points at a time.       
+   ** a second loop below copies for the remaining 1 to 3 samples. */
+  while(j > 0u)
+  {
+    /* copy second buffer in reversal manner */
+    *pScr++ = *pIn1++;
+    *pScr++ = *pIn1++;
+    *pScr++ = *pIn1++;
+    *pScr++ = *pIn1++;
+
+    /* Decrement the loop counter */
+    j--;
+  }
+
+  /* If the count is not a multiple of 4, copy remaining samples here.       
+   ** No loop unrolling is used. */
+  j = srcALen % 0x4u;
+
+  while(j > 0u)
+  {
+    /* copy second buffer in reversal manner for remaining samples */
+    *pScr++ = *pIn1++;
+
+    /* Decrement the loop counter */
+    j--;
+  }
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+  /* Fill (srcBLen - 1u) zeros at end of scratch buffer */
+  arm_fill_q15(0, pScr, (srcBLen - 1u));
+
+  /* Update pointer */
+  pScr += (srcBLen - 1u);
+
+#else
+
+/* Apply loop unrolling and do 4 Copies simultaneously. */
+  j = (srcBLen - 1u) >> 2u;
+
+  /* First part of the processing with loop unrolling copies 4 data points at a time.       
+   ** a second loop below copies for the remaining 1 to 3 samples. */
+  while(j > 0u)
+  {
+    /* copy second buffer in reversal manner */
+    *pScr++ = 0;
+    *pScr++ = 0;
+    *pScr++ = 0;
+    *pScr++ = 0;
+
+    /* Decrement the loop counter */
+    j--;
+  }
+
+  /* If the count is not a multiple of 4, copy remaining samples here.       
+   ** No loop unrolling is used. */
+  j = (srcBLen - 1u) % 0x4u;
+
+  while(j > 0u)
+  {
+    /* copy second buffer in reversal manner for remaining samples */
+    *pScr++ = 0;
+
+    /* Decrement the loop counter */
+    j--;
+  }
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+  /* Temporary pointer for scratch2 */
+  py = pIn2;
+
+
+  /* Actual correlation process starts here */
+  blkCnt = (srcALen + srcBLen - 1u) >> 2;
+
+  while(blkCnt > 0)
+  {
+    /* Initialze temporary scratch pointer as scratch1 */
+    pScr = pScratch;
+
+    /* Clear Accumlators */
+    acc0 = 0;
+    acc1 = 0;
+    acc2 = 0;
+    acc3 = 0;
+
+    /* Read four samples from scratch1 buffer */
+    x1 = *__SIMD32(pScr)++;
+
+    /* Read next four samples from scratch1 buffer */
+    x2 = *__SIMD32(pScr)++;
+
+    tapCnt = (srcBLen) >> 2u;
+
+    while(tapCnt > 0u)
+    {
+
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+      /* Read four samples from smaller buffer */
+      y1 = _SIMD32_OFFSET(pIn2);
+      y2 = _SIMD32_OFFSET(pIn2 + 2u);
+
+      acc0 = __SMLALD(x1, y1, acc0);
+
+      acc2 = __SMLALD(x2, y1, acc2);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x2, x1, 0);
+#else
+      x3 = __PKHBT(x1, x2, 0);
+#endif
+
+      acc1 = __SMLALDX(x3, y1, acc1);
+
+      x1 = _SIMD32_OFFSET(pScr);
+
+      acc0 = __SMLALD(x2, y2, acc0);
+
+      acc2 = __SMLALD(x1, y2, acc2);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x1, x2, 0);
+#else
+      x3 = __PKHBT(x2, x1, 0);
+#endif
+
+      acc3 = __SMLALDX(x3, y1, acc3);
+
+      acc1 = __SMLALDX(x3, y2, acc1);
+
+      x2 = _SIMD32_OFFSET(pScr + 2u);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x2, x1, 0);
+#else
+      x3 = __PKHBT(x1, x2, 0);
+#endif
+
+      acc3 = __SMLALDX(x3, y2, acc3);
+
+#else	 
+
+      /* Read four samples from smaller buffer */
+	  a = *pIn2;
+	  b = *(pIn2 + 1);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      y1 = __PKHBT(a, b, 16);
+#else
+      y1 = __PKHBT(b, a, 16);
+#endif
+	  
+	  a = *(pIn2 + 2);
+	  b = *(pIn2 + 3);
+#ifndef ARM_MATH_BIG_ENDIAN
+      y2 = __PKHBT(a, b, 16);
+#else
+      y2 = __PKHBT(b, a, 16);
+#endif				
+
+      acc0 = __SMLALD(x1, y1, acc0);
+
+      acc2 = __SMLALD(x2, y1, acc2);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x2, x1, 0);
+#else
+      x3 = __PKHBT(x1, x2, 0);
+#endif
+
+      acc1 = __SMLALDX(x3, y1, acc1);
+
+	  a = *pScr;
+	  b = *(pScr + 1);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x1 = __PKHBT(a, b, 16);
+#else
+      x1 = __PKHBT(b, a, 16);
+#endif
+
+      acc0 = __SMLALD(x2, y2, acc0);
+
+      acc2 = __SMLALD(x1, y2, acc2);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x1, x2, 0);
+#else
+      x3 = __PKHBT(x2, x1, 0);
+#endif
+
+      acc3 = __SMLALDX(x3, y1, acc3);
+
+      acc1 = __SMLALDX(x3, y2, acc1);
+
+	  a = *(pScr + 2);
+	  b = *(pScr + 3);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x2 = __PKHBT(a, b, 16);
+#else
+      x2 = __PKHBT(b, a, 16);
+#endif
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x2, x1, 0);
+#else
+      x3 = __PKHBT(x1, x2, 0);
+#endif
+
+      acc3 = __SMLALDX(x3, y2, acc3);
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+      pIn2 += 4u;
+
+      pScr += 4u;
+
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+
+
+    /* Update scratch pointer for remaining samples of smaller length sequence */
+    pScr -= 4u;
+
+
+    /* apply same above for remaining samples of smaller length sequence */
+    tapCnt = (srcBLen) & 3u;
+
+    while(tapCnt > 0u)
+    {
+
+      /* accumlate the results */
+      acc0 += (*pScr++ * *pIn2);
+      acc1 += (*pScr++ * *pIn2);
+      acc2 += (*pScr++ * *pIn2);
+      acc3 += (*pScr++ * *pIn2++);
+
+      pScr -= 3u;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    blkCnt--;
+
+
+    /* Store the results in the accumulators in the destination buffer. */
+    *pOut = (__SSAT(acc0 >> 15u, 16));
+    pOut += inc;
+    *pOut = (__SSAT(acc1 >> 15u, 16));
+    pOut += inc;
+    *pOut = (__SSAT(acc2 >> 15u, 16));
+    pOut += inc;
+    *pOut = (__SSAT(acc3 >> 15u, 16));
+    pOut += inc;
+
+    /* Initialization of inputB pointer */
+    pIn2 = py;
+
+    pScratch += 4u;
+
+  }
+
+
+  blkCnt = (srcALen + srcBLen - 1u) & 0x3;
+
+  /* Calculate correlation for remaining samples of Bigger length sequence */
+  while(blkCnt > 0)
+  {
+    /* Initialze temporary scratch pointer as scratch1 */
+    pScr = pScratch;
+
+    /* Clear Accumlators */
+    acc0 = 0;
+
+    tapCnt = (srcBLen) >> 1u;
+
+    while(tapCnt > 0u)
+    {
+
+      acc0 += (*pScr++ * *pIn2++);
+      acc0 += (*pScr++ * *pIn2++);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    tapCnt = (srcBLen) & 1u;
+
+    /* apply same above for remaining samples of smaller length sequence */
+    while(tapCnt > 0u)
+    {
+
+      /* accumlate the results */
+      acc0 += (*pScr++ * *pIn2++);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    blkCnt--;
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut = (q15_t) (__SSAT((acc0 >> 15), 16));
+
+    pOut += inc;
+
+    /* Initialization of inputB pointer */
+    pIn2 = py;
+
+    pScratch += 1u;
+
+  }
+
+
+}
+
+/**    
+ * @} end of Corr group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_opt_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_opt_q7.c
new file mode 100644
index 0000000000..6749b01b38
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_opt_q7.c
@@ -0,0 +1,463 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_correlate_opt_q7.c    
+*    
+* Description:	Correlation of Q7 sequences.  
+*    
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+* 
+* Version 1.0.11 2011/10/18  
+*    Bug Fix in conv, correlation, partial convolution.  
+* 
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+*    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup Corr    
+ * @{    
+ */
+
+/**    
+ * @brief Correlation of Q7 sequences.    
+ * @param[in] *pSrcA points to the first input sequence.    
+ * @param[in] srcALen length of the first input sequence.    
+ * @param[in] *pSrcB points to the second input sequence.    
+ * @param[in] srcBLen length of the second input sequence.    
+ * @param[out] *pDst points to the location where the output result is written.  Length 2 * max(srcALen, srcBLen) - 1.    
+ * @param[in]  *pScratch1 points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.    
+ * @param[in]  *pScratch2 points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen).    
+ * @return none.    
+ *    
+ *    
+ * \par Restrictions    
+ *  If the silicon does not support unaligned memory access enable the macro UNALIGNED_SUPPORT_DISABLE    
+ *	In this case input, output, scratch1 and scratch2 buffers should be aligned by 32-bit     
+ *        
+ * @details    
+ * Scaling and Overflow Behavior:    
+ *    
+ * \par    
+ * The function is implemented using a 32-bit internal accumulator.    
+ * Both the inputs are represented in 1.7 format and multiplications yield a 2.14 result.    
+ * The 2.14 intermediate results are accumulated in a 32-bit accumulator in 18.14 format.    
+ * This approach provides 17 guard bits and there is no risk of overflow as long as max(srcALen, srcBLen)<131072.    
+ * The 18.14 result is then truncated to 18.7 format by discarding the low 7 bits and saturated to 1.7 format.  
+ *  
+ * 
+ */
+
+
+
+void arm_correlate_opt_q7(
+  q7_t * pSrcA,
+  uint32_t srcALen,
+  q7_t * pSrcB,
+  uint32_t srcBLen,
+  q7_t * pDst,
+  q15_t * pScratch1,
+  q15_t * pScratch2)
+{
+  q7_t *pOut = pDst;                             /* output pointer                */
+  q15_t *pScr1 = pScratch1;                      /* Temporary pointer for scratch */
+  q15_t *pScr2 = pScratch2;                      /* Temporary pointer for scratch */
+  q7_t *pIn1;                                    /* inputA pointer                */
+  q7_t *pIn2;                                    /* inputB pointer                */
+  q15_t *py;                                     /* Intermediate inputB pointer   */
+  q31_t acc0, acc1, acc2, acc3;                  /* Accumulators                  */
+  uint32_t j, k = 0u, blkCnt;                    /* loop counter                  */
+  int32_t inc = 1;                               /* output pointer increment          */
+  uint32_t outBlockSize;                         /* loop counter                  */
+  q15_t x4;                                      /* Temporary input variable      */
+  uint32_t tapCnt;                               /* loop counter                  */
+  q31_t x1, x2, x3, y1;                          /* Temporary input variables     */
+
+  /* The algorithm implementation is based on the lengths of the inputs. */
+  /* srcB is always made to slide across srcA. */
+  /* So srcBLen is always considered as shorter or equal to srcALen */
+  /* But CORR(x, y) is reverse of CORR(y, x) */
+  /* So, when srcBLen > srcALen, output pointer is made to point to the end of the output buffer */
+  /* and the destination pointer modifier, inc is set to -1 */
+  /* If srcALen > srcBLen, zero pad has to be done to srcB to make the two inputs of same length */
+  /* But to improve the performance,        
+   * we include zeroes in the output instead of zero padding either of the the inputs*/
+  /* If srcALen > srcBLen,        
+   * (srcALen - srcBLen) zeroes has to included in the starting of the output buffer */
+  /* If srcALen < srcBLen,        
+   * (srcALen - srcBLen) zeroes has to included in the ending of the output buffer */
+  if(srcALen >= srcBLen)
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = (pSrcA);
+
+    /* Initialization of inputB pointer */
+    pIn2 = (pSrcB);
+
+    /* Number of output samples is calculated */
+    outBlockSize = (2u * srcALen) - 1u;
+
+    /* When srcALen > srcBLen, zero padding is done to srcB        
+     * to make their lengths equal.        
+     * Instead, (outBlockSize - (srcALen + srcBLen - 1))        
+     * number of output samples are made zero */
+    j = outBlockSize - (srcALen + (srcBLen - 1u));
+
+    /* Updating the pointer position to non zero value */
+    pOut += j;
+
+  }
+  else
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = (pSrcB);
+
+    /* Initialization of inputB pointer */
+    pIn2 = (pSrcA);
+
+    /* srcBLen is always considered as shorter or equal to srcALen */
+    j = srcBLen;
+    srcBLen = srcALen;
+    srcALen = j;
+
+    /* CORR(x, y) = Reverse order(CORR(y, x)) */
+    /* Hence set the destination pointer to point to the last output sample */
+    pOut = pDst + ((srcALen + srcBLen) - 2u);
+
+    /* Destination address modifier is set to -1 */
+    inc = -1;
+
+  }
+
+
+  /* Copy (srcBLen) samples in scratch buffer */
+  k = srcBLen >> 2u;
+
+  /* First part of the processing with loop unrolling copies 4 data points at a time.       
+   ** a second loop below copies for the remaining 1 to 3 samples. */
+  while(k > 0u)
+  {
+    /* copy second buffer in reversal manner */
+    x4 = (q15_t) * pIn2++;
+    *pScr2++ = x4;
+    x4 = (q15_t) * pIn2++;
+    *pScr2++ = x4;
+    x4 = (q15_t) * pIn2++;
+    *pScr2++ = x4;
+    x4 = (q15_t) * pIn2++;
+    *pScr2++ = x4;
+
+    /* Decrement the loop counter */
+    k--;
+  }
+
+  /* If the count is not a multiple of 4, copy remaining samples here.       
+   ** No loop unrolling is used. */
+  k = srcBLen % 0x4u;
+
+  while(k > 0u)
+  {
+    /* copy second buffer in reversal manner for remaining samples */
+    x4 = (q15_t) * pIn2++;
+    *pScr2++ = x4;
+
+    /* Decrement the loop counter */
+    k--;
+  }
+
+  /* Fill (srcBLen - 1u) zeros in scratch buffer */
+  arm_fill_q15(0, pScr1, (srcBLen - 1u));
+
+  /* Update temporary scratch pointer */
+  pScr1 += (srcBLen - 1u);
+
+  /* Copy (srcALen) samples in scratch buffer */
+  k = srcALen >> 2u;
+
+  /* First part of the processing with loop unrolling copies 4 data points at a time.       
+   ** a second loop below copies for the remaining 1 to 3 samples. */
+  while(k > 0u)
+  {
+    /* copy second buffer in reversal manner */
+    x4 = (q15_t) * pIn1++;
+    *pScr1++ = x4;
+    x4 = (q15_t) * pIn1++;
+    *pScr1++ = x4;
+    x4 = (q15_t) * pIn1++;
+    *pScr1++ = x4;
+    x4 = (q15_t) * pIn1++;
+    *pScr1++ = x4;
+
+    /* Decrement the loop counter */
+    k--;
+  }
+
+  /* If the count is not a multiple of 4, copy remaining samples here.       
+   ** No loop unrolling is used. */
+  k = srcALen % 0x4u;
+
+  while(k > 0u)
+  {
+    /* copy second buffer in reversal manner for remaining samples */
+    x4 = (q15_t) * pIn1++;
+    *pScr1++ = x4;
+
+    /* Decrement the loop counter */
+    k--;
+  }
+
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+  /* Fill (srcBLen - 1u) zeros at end of scratch buffer */
+  arm_fill_q15(0, pScr1, (srcBLen - 1u));
+
+  /* Update pointer */
+  pScr1 += (srcBLen - 1u);
+
+#else
+
+/* Apply loop unrolling and do 4 Copies simultaneously. */
+  k = (srcBLen - 1u) >> 2u;
+
+  /* First part of the processing with loop unrolling copies 4 data points at a time.       
+   ** a second loop below copies for the remaining 1 to 3 samples. */
+  while(k > 0u)
+  {
+    /* copy second buffer in reversal manner */
+    *pScr1++ = 0;
+    *pScr1++ = 0;
+    *pScr1++ = 0;
+    *pScr1++ = 0;
+
+    /* Decrement the loop counter */
+    k--;
+  }
+
+  /* If the count is not a multiple of 4, copy remaining samples here.       
+   ** No loop unrolling is used. */
+  k = (srcBLen - 1u) % 0x4u;
+
+  while(k > 0u)
+  {
+    /* copy second buffer in reversal manner for remaining samples */
+    *pScr1++ = 0;
+
+    /* Decrement the loop counter */
+    k--;
+  }
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+  /* Temporary pointer for second sequence */
+  py = pScratch2;
+
+  /* Initialization of pScr2 pointer */
+  pScr2 = pScratch2;
+
+  /* Actual correlation process starts here */
+  blkCnt = (srcALen + srcBLen - 1u) >> 2;
+
+  while(blkCnt > 0)
+  {
+    /* Initialze temporary scratch pointer as scratch1 */
+    pScr1 = pScratch1;
+
+    /* Clear Accumlators */
+    acc0 = 0;
+    acc1 = 0;
+    acc2 = 0;
+    acc3 = 0;
+
+    /* Read two samples from scratch1 buffer */
+    x1 = *__SIMD32(pScr1)++;
+
+    /* Read next two samples from scratch1 buffer */
+    x2 = *__SIMD32(pScr1)++;
+
+    tapCnt = (srcBLen) >> 2u;
+
+    while(tapCnt > 0u)
+    {
+
+      /* Read four samples from smaller buffer */
+      y1 = _SIMD32_OFFSET(pScr2);
+
+      /* multiply and accumlate */
+      acc0 = __SMLAD(x1, y1, acc0);
+      acc2 = __SMLAD(x2, y1, acc2);
+
+      /* pack input data */
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x2, x1, 0);
+#else
+      x3 = __PKHBT(x1, x2, 0);
+#endif
+
+      /* multiply and accumlate */
+      acc1 = __SMLADX(x3, y1, acc1);
+
+      /* Read next two samples from scratch1 buffer */
+      x1 = *__SIMD32(pScr1)++;
+
+      /* pack input data */
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x1, x2, 0);
+#else
+      x3 = __PKHBT(x2, x1, 0);
+#endif
+
+      acc3 = __SMLADX(x3, y1, acc3);
+
+      /* Read four samples from smaller buffer */
+      y1 = _SIMD32_OFFSET(pScr2 + 2u);
+
+      acc0 = __SMLAD(x2, y1, acc0);
+
+      acc2 = __SMLAD(x1, y1, acc2);
+
+      acc1 = __SMLADX(x3, y1, acc1);
+
+      x2 = *__SIMD32(pScr1)++;
+
+#ifndef ARM_MATH_BIG_ENDIAN
+      x3 = __PKHBT(x2, x1, 0);
+#else
+      x3 = __PKHBT(x1, x2, 0);
+#endif
+
+      acc3 = __SMLADX(x3, y1, acc3);
+
+      pScr2 += 4u;
+
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+
+
+    /* Update scratch pointer for remaining samples of smaller length sequence */
+    pScr1 -= 4u;
+
+
+    /* apply same above for remaining samples of smaller length sequence */
+    tapCnt = (srcBLen) & 3u;
+
+    while(tapCnt > 0u)
+    {
+
+      /* accumlate the results */
+      acc0 += (*pScr1++ * *pScr2);
+      acc1 += (*pScr1++ * *pScr2);
+      acc2 += (*pScr1++ * *pScr2);
+      acc3 += (*pScr1++ * *pScr2++);
+
+      pScr1 -= 3u;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    blkCnt--;
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut = (q7_t) (__SSAT(acc0 >> 7u, 8));
+    pOut += inc;
+    *pOut = (q7_t) (__SSAT(acc1 >> 7u, 8));
+    pOut += inc;
+    *pOut = (q7_t) (__SSAT(acc2 >> 7u, 8));
+    pOut += inc;
+    *pOut = (q7_t) (__SSAT(acc3 >> 7u, 8));
+    pOut += inc;
+
+    /* Initialization of inputB pointer */
+    pScr2 = py;
+
+    pScratch1 += 4u;
+
+  }
+
+
+  blkCnt = (srcALen + srcBLen - 1u) & 0x3;
+
+  /* Calculate correlation for remaining samples of Bigger length sequence */
+  while(blkCnt > 0)
+  {
+    /* Initialze temporary scratch pointer as scratch1 */
+    pScr1 = pScratch1;
+
+    /* Clear Accumlators */
+    acc0 = 0;
+
+    tapCnt = (srcBLen) >> 1u;
+
+    while(tapCnt > 0u)
+    {
+      acc0 += (*pScr1++ * *pScr2++);
+      acc0 += (*pScr1++ * *pScr2++);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    tapCnt = (srcBLen) & 1u;
+
+    /* apply same above for remaining samples of smaller length sequence */
+    while(tapCnt > 0u)
+    {
+
+      /* accumlate the results */
+      acc0 += (*pScr1++ * *pScr2++);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    blkCnt--;
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut = (q7_t) (__SSAT(acc0 >> 7u, 8));
+
+    pOut += inc;
+
+    /* Initialization of inputB pointer */
+    pScr2 = py;
+
+    pScratch1 += 1u;
+
+  }
+
+}
+
+/**    
+ * @} end of Corr group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_q15.c
new file mode 100644
index 0000000000..fc4134b7b8
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_q15.c
@@ -0,0 +1,718 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010 ARM Limited. All rights reserved.   
+*   
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*   
+* Project: 	    CMSIS DSP Library   
+* Title:		arm_correlate_q15.c   
+*   
+* Description:	Correlation of Q15 sequences. 
+*   
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*
+* Version 1.0.11 2011/10/18 
+*    Bug Fix in conv, correlation, partial convolution. 
+*
+* Version 1.0.10 2011/7/15 
+*    Big Endian support added and Merged M0 and M3/M4 Source code.  
+*   
+* Version 1.0.3 2010/11/29  
+*    Re-organized the CMSIS folders and updated documentation.   
+*    
+* Version 1.0.2 2010/11/11   
+*    Documentation updated.    
+*   
+* Version 1.0.1 2010/10/05    
+*    Production release and review comments incorporated.   
+*   
+* Version 1.0.0 2010/09/20    
+*    Production release and review comments incorporated   
+*   
+* Version 0.0.7  2010/06/10    
+*    Misra-C changes done   
+*   
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**   
+ * @ingroup groupFilters   
+ */
+
+/**   
+ * @addtogroup Corr   
+ * @{   
+ */
+
+/**   
+ * @brief Correlation of Q15 sequences. 
+ * @param[in] *pSrcA points to the first input sequence.   
+ * @param[in] srcALen length of the first input sequence.   
+ * @param[in] *pSrcB points to the second input sequence.   
+ * @param[in] srcBLen length of the second input sequence.   
+ * @param[out] *pDst points to the location where the output result is written.  Length 2 * max(srcALen, srcBLen) - 1.   
+ * @return none.   
+ *   
+ * @details   
+ * Scaling and Overflow Behavior:   
+ *   
+ * \par   
+ * The function is implemented using a 64-bit internal accumulator.   
+ * Both inputs are in 1.15 format and multiplications yield a 2.30 result.   
+ * The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format.   
+ * This approach provides 33 guard bits and there is no risk of overflow.   
+ * The 34.30 result is then truncated to 34.15 format by discarding the low 15 bits and then saturated to 1.15 format.   
+ *   
+ * \par   
+ * Refer to arm_correlate_fast_q15() for a faster but less precise version of this function for Cortex-M3 and Cortex-M4. 
+ *
+ * \par    
+ * Refer the function arm_correlate_opt_q15() for a faster implementation of this function using scratch buffers.
+ * 
+ */
+
+void arm_correlate_q15(
+  q15_t * pSrcA,
+  uint32_t srcALen,
+  q15_t * pSrcB,
+  uint32_t srcBLen,
+  q15_t * pDst)
+{
+
+#if (defined(ARM_MATH_CM4) || defined(ARM_MATH_CM3)) && !defined(UNALIGNED_SUPPORT_DISABLE)
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q15_t *pIn1;                                   /* inputA pointer               */
+  q15_t *pIn2;                                   /* inputB pointer               */
+  q15_t *pOut = pDst;                            /* output pointer               */
+  q63_t sum, acc0, acc1, acc2, acc3;             /* Accumulators                  */
+  q15_t *px;                                     /* Intermediate inputA pointer  */
+  q15_t *py;                                     /* Intermediate inputB pointer  */
+  q15_t *pSrc1;                                  /* Intermediate pointers        */
+  q31_t x0, x1, x2, x3, c0;                      /* temporary variables for holding input and coefficient values */
+  uint32_t j, k = 0u, count, blkCnt, outBlockSize, blockSize1, blockSize2, blockSize3;  /* loop counter                 */
+  int32_t inc = 1;                               /* Destination address modifier */
+
+
+  /* The algorithm implementation is based on the lengths of the inputs. */
+  /* srcB is always made to slide across srcA. */
+  /* So srcBLen is always considered as shorter or equal to srcALen */
+  /* But CORR(x, y) is reverse of CORR(y, x) */
+  /* So, when srcBLen > srcALen, output pointer is made to point to the end of the output buffer */
+  /* and the destination pointer modifier, inc is set to -1 */
+  /* If srcALen > srcBLen, zero pad has to be done to srcB to make the two inputs of same length */
+  /* But to improve the performance,   
+   * we include zeroes in the output instead of zero padding either of the the inputs*/
+  /* If srcALen > srcBLen,   
+   * (srcALen - srcBLen) zeroes has to included in the starting of the output buffer */
+  /* If srcALen < srcBLen,   
+   * (srcALen - srcBLen) zeroes has to included in the ending of the output buffer */
+  if(srcALen >= srcBLen)
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = (pSrcA);
+
+    /* Initialization of inputB pointer */
+    pIn2 = (pSrcB);
+
+    /* Number of output samples is calculated */
+    outBlockSize = (2u * srcALen) - 1u;
+
+    /* When srcALen > srcBLen, zero padding is done to srcB   
+     * to make their lengths equal.   
+     * Instead, (outBlockSize - (srcALen + srcBLen - 1))   
+     * number of output samples are made zero */
+    j = outBlockSize - (srcALen + (srcBLen - 1u));
+
+    /* Updating the pointer position to non zero value */
+    pOut += j;
+
+  }
+  else
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = (pSrcB);
+
+    /* Initialization of inputB pointer */
+    pIn2 = (pSrcA);
+
+    /* srcBLen is always considered as shorter or equal to srcALen */
+    j = srcBLen;
+    srcBLen = srcALen;
+    srcALen = j;
+
+    /* CORR(x, y) = Reverse order(CORR(y, x)) */
+    /* Hence set the destination pointer to point to the last output sample */
+    pOut = pDst + ((srcALen + srcBLen) - 2u);
+
+    /* Destination address modifier is set to -1 */
+    inc = -1;
+
+  }
+
+  /* The function is internally   
+   * divided into three parts according to the number of multiplications that has to be   
+   * taken place between inputA samples and inputB samples. In the first part of the   
+   * algorithm, the multiplications increase by one for every iteration.   
+   * In the second part of the algorithm, srcBLen number of multiplications are done.   
+   * In the third part of the algorithm, the multiplications decrease by one   
+   * for every iteration.*/
+  /* The algorithm is implemented in three stages.   
+   * The loop counters of each stage is initiated here. */
+  blockSize1 = srcBLen - 1u;
+  blockSize2 = srcALen - (srcBLen - 1u);
+  blockSize3 = blockSize1;
+
+  /* --------------------------   
+   * Initializations of stage1   
+   * -------------------------*/
+
+  /* sum = x[0] * y[srcBlen - 1]   
+   * sum = x[0] * y[srcBlen - 2] + x[1] * y[srcBlen - 1]   
+   * ....   
+   * sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen - 1] * y[srcBLen - 1]   
+   */
+
+  /* In this stage the MAC operations are increased by 1 for every iteration.   
+     The count variable holds the number of MAC operations performed */
+  count = 1u;
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  pSrc1 = pIn2 + (srcBLen - 1u);
+  py = pSrc1;
+
+  /* ------------------------   
+   * Stage1 process   
+   * ----------------------*/
+
+  /* The first loop starts here */
+  while(blockSize1 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = count >> 2;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* x[0] * y[srcBLen - 4] , x[1] * y[srcBLen - 3] */
+      sum = __SMLALD(*__SIMD32(px)++, *__SIMD32(py)++, sum);
+      /* x[3] * y[srcBLen - 1] , x[2] * y[srcBLen - 2] */
+      sum = __SMLALD(*__SIMD32(px)++, *__SIMD32(py)++, sum);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, compute any remaining MACs here.   
+     ** No loop unrolling is used. */
+    k = count % 0x4u;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      /* x[0] * y[srcBLen - 1] */
+      sum = __SMLALD(*px++, *py++, sum);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut = (q15_t) (__SSAT((sum >> 15), 16));
+    /* Destination pointer is updated according to the address modifier, inc */
+    pOut += inc;
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    py = pSrc1 - count;
+    px = pIn1;
+
+    /* Increment the MAC count */
+    count++;
+
+    /* Decrement the loop counter */
+    blockSize1--;
+  }
+
+  /* --------------------------   
+   * Initializations of stage2   
+   * ------------------------*/
+
+  /* sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen-1] * y[srcBLen-1]   
+   * sum = x[1] * y[0] + x[2] * y[1] +...+ x[srcBLen] * y[srcBLen-1]   
+   * ....   
+   * sum = x[srcALen-srcBLen-2] * y[0] + x[srcALen-srcBLen-1] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]   
+   */
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  py = pIn2;
+
+  /* count is index by which the pointer pIn1 to be incremented */
+  count = 0u;
+
+  /* -------------------   
+   * Stage2 process   
+   * ------------------*/
+
+  /* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.   
+   * So, to loop unroll over blockSize2,   
+   * srcBLen should be greater than or equal to 4, to loop unroll the srcBLen loop */
+  if(srcBLen >= 4u)
+  {
+    /* Loop unroll over blockSize2, by 4 */
+    blkCnt = blockSize2 >> 2u;
+
+    while(blkCnt > 0u)
+    {
+      /* Set all accumulators to zero */
+      acc0 = 0;
+      acc1 = 0;
+      acc2 = 0;
+      acc3 = 0;
+
+      /* read x[0], x[1] samples */
+      x0 = *__SIMD32(px);
+      /* read x[1], x[2] samples */
+      x1 = _SIMD32_OFFSET(px + 1);
+	  px += 2u;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      do
+      {
+        /* Read the first two inputB samples using SIMD:   
+         * y[0] and y[1] */
+        c0 = *__SIMD32(py)++;
+
+        /* acc0 +=  x[0] * y[0] + x[1] * y[1] */
+        acc0 = __SMLALD(x0, c0, acc0);
+
+        /* acc1 +=  x[1] * y[0] + x[2] * y[1] */
+        acc1 = __SMLALD(x1, c0, acc1);
+
+        /* Read x[2], x[3] */
+        x2 = *__SIMD32(px);
+
+        /* Read x[3], x[4] */
+        x3 = _SIMD32_OFFSET(px + 1);
+
+        /* acc2 +=  x[2] * y[0] + x[3] * y[1] */
+        acc2 = __SMLALD(x2, c0, acc2);
+
+        /* acc3 +=  x[3] * y[0] + x[4] * y[1] */
+        acc3 = __SMLALD(x3, c0, acc3);
+
+        /* Read y[2] and y[3] */
+        c0 = *__SIMD32(py)++;
+
+        /* acc0 +=  x[2] * y[2] + x[3] * y[3] */
+        acc0 = __SMLALD(x2, c0, acc0);
+
+        /* acc1 +=  x[3] * y[2] + x[4] * y[3] */
+        acc1 = __SMLALD(x3, c0, acc1);
+
+        /* Read x[4], x[5] */
+        x0 = _SIMD32_OFFSET(px + 2);
+
+        /* Read x[5], x[6] */
+        x1 = _SIMD32_OFFSET(px + 3);
+
+		px += 4u;
+
+        /* acc2 +=  x[4] * y[2] + x[5] * y[3] */
+        acc2 = __SMLALD(x0, c0, acc2);
+
+        /* acc3 +=  x[5] * y[2] + x[6] * y[3] */
+        acc3 = __SMLALD(x1, c0, acc3);
+
+      } while(--k);
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.   
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      if(k == 1u)
+      {
+        /* Read y[4] */
+        c0 = *py;
+#ifdef  ARM_MATH_BIG_ENDIAN
+
+        c0 = c0 << 16u;
+
+#else
+
+        c0 = c0 & 0x0000FFFF;
+
+#endif /*      #ifdef  ARM_MATH_BIG_ENDIAN     */
+        /* Read x[7] */
+        x3 = *__SIMD32(px);
+		px++;
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLALD(x0, c0, acc0);
+        acc1 = __SMLALD(x1, c0, acc1);
+        acc2 = __SMLALDX(x1, c0, acc2);
+        acc3 = __SMLALDX(x3, c0, acc3);
+      }
+
+      if(k == 2u)
+      {
+        /* Read y[4], y[5] */
+        c0 = *__SIMD32(py);
+
+        /* Read x[7], x[8] */
+        x3 = *__SIMD32(px);
+
+        /* Read x[9] */
+        x2 = _SIMD32_OFFSET(px + 1);
+		px += 2u;
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLALD(x0, c0, acc0);
+        acc1 = __SMLALD(x1, c0, acc1);
+        acc2 = __SMLALD(x3, c0, acc2);
+        acc3 = __SMLALD(x2, c0, acc3);
+      }
+
+      if(k == 3u)
+      {
+        /* Read y[4], y[5] */
+        c0 = *__SIMD32(py)++;
+
+        /* Read x[7], x[8] */
+        x3 = *__SIMD32(px);
+
+        /* Read x[9] */
+        x2 = _SIMD32_OFFSET(px + 1);
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLALD(x0, c0, acc0);
+        acc1 = __SMLALD(x1, c0, acc1);
+        acc2 = __SMLALD(x3, c0, acc2);
+        acc3 = __SMLALD(x2, c0, acc3);
+
+        c0 = (*py);
+
+        /* Read y[6] */
+#ifdef  ARM_MATH_BIG_ENDIAN
+
+        c0 = c0 << 16u;
+#else
+
+        c0 = c0 & 0x0000FFFF;
+#endif /*      #ifdef  ARM_MATH_BIG_ENDIAN     */
+        /* Read x[10] */
+        x3 = _SIMD32_OFFSET(px + 2);
+		px += 3u;
+
+        /* Perform the multiply-accumulates */
+        acc0 = __SMLALDX(x1, c0, acc0);
+        acc1 = __SMLALD(x2, c0, acc1);
+        acc2 = __SMLALDX(x2, c0, acc2);
+        acc3 = __SMLALDX(x3, c0, acc3);
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut = (q15_t) (__SSAT(acc0 >> 15, 16));
+      /* Destination pointer is updated according to the address modifier, inc */
+      pOut += inc;
+
+      *pOut = (q15_t) (__SSAT(acc1 >> 15, 16));
+      pOut += inc;
+
+      *pOut = (q15_t) (__SSAT(acc2 >> 15, 16));
+      pOut += inc;
+
+      *pOut = (q15_t) (__SSAT(acc3 >> 15, 16));
+      pOut += inc;
+
+      /* Increment the count by 4 as 4 output values are computed */
+      count += 4u;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pIn2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.   
+     ** No loop unrolling is used. */
+    blkCnt = blockSize2 % 0x4u;
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum += ((q63_t) * px++ * *py++);
+        sum += ((q63_t) * px++ * *py++);
+        sum += ((q63_t) * px++ * *py++);
+        sum += ((q63_t) * px++ * *py++);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.   
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum += ((q63_t) * px++ * *py++);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut = (q15_t) (__SSAT(sum >> 15, 16));
+      /* Destination pointer is updated according to the address modifier, inc */
+      pOut += inc;
+
+      /* Increment count by 1, as one output value is computed */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pIn2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+  else
+  {
+    /* If the srcBLen is not a multiple of 4,   
+     * the blockSize2 loop cannot be unrolled by 4 */
+    blkCnt = blockSize2;
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Loop over srcBLen */
+      k = srcBLen;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulate */
+        sum += ((q63_t) * px++ * *py++);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut = (q15_t) (__SSAT(sum >> 15, 16));
+      /* Destination pointer is updated according to the address modifier, inc */
+      pOut += inc;
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pIn2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+
+  /* --------------------------   
+   * Initializations of stage3   
+   * -------------------------*/
+
+  /* sum += x[srcALen-srcBLen+1] * y[0] + x[srcALen-srcBLen+2] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]   
+   * sum += x[srcALen-srcBLen+2] * y[0] + x[srcALen-srcBLen+3] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]   
+   * ....   
+   * sum +=  x[srcALen-2] * y[0] + x[srcALen-1] * y[1]   
+   * sum +=  x[srcALen-1] * y[0]   
+   */
+
+  /* In this stage the MAC operations are decreased by 1 for every iteration.   
+     The count variable holds the number of MAC operations performed */
+  count = srcBLen - 1u;
+
+  /* Working pointer of inputA */
+  pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
+  px = pSrc1;
+
+  /* Working pointer of inputB */
+  py = pIn2;
+
+  /* -------------------   
+   * Stage3 process   
+   * ------------------*/
+
+  while(blockSize3 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = count >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      /* sum += x[srcALen - srcBLen + 4] * y[3] , sum += x[srcALen - srcBLen + 3] * y[2] */
+      sum = __SMLALD(*__SIMD32(px)++, *__SIMD32(py)++, sum);
+      /* sum += x[srcALen - srcBLen + 2] * y[1] , sum += x[srcALen - srcBLen + 1] * y[0] */
+      sum = __SMLALD(*__SIMD32(px)++, *__SIMD32(py)++, sum);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, compute any remaining MACs here.   
+     ** No loop unrolling is used. */
+    k = count % 0x4u;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      sum = __SMLALD(*px++, *py++, sum);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut = (q15_t) (__SSAT((sum >> 15), 16));
+    /* Destination pointer is updated according to the address modifier, inc */
+    pOut += inc;
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    px = ++pSrc1;
+    py = pIn2;
+
+    /* Decrement the MAC count */
+    count--;
+
+    /* Decrement the loop counter */
+    blockSize3--;
+  }
+
+#else
+
+/* Run the below code for Cortex-M0 */
+
+  q15_t *pIn1 = pSrcA;                           /* inputA pointer               */
+  q15_t *pIn2 = pSrcB + (srcBLen - 1u);          /* inputB pointer               */
+  q63_t sum;                                     /* Accumulators                  */
+  uint32_t i = 0u, j;                            /* loop counters */
+  uint32_t inv = 0u;                             /* Reverse order flag */
+  uint32_t tot = 0u;                             /* Length */
+
+  /* The algorithm implementation is based on the lengths of the inputs. */
+  /* srcB is always made to slide across srcA. */
+  /* So srcBLen is always considered as shorter or equal to srcALen */
+  /* But CORR(x, y) is reverse of CORR(y, x) */
+  /* So, when srcBLen > srcALen, output pointer is made to point to the end of the output buffer */
+  /* and a varaible, inv is set to 1 */
+  /* If lengths are not equal then zero pad has to be done to  make the two   
+   * inputs of same length. But to improve the performance, we include zeroes   
+   * in the output instead of zero padding either of the the inputs*/
+  /* If srcALen > srcBLen, (srcALen - srcBLen) zeroes has to included in the   
+   * starting of the output buffer */
+  /* If srcALen < srcBLen, (srcALen - srcBLen) zeroes has to included in the  
+   * ending of the output buffer */
+  /* Once the zero padding is done the remaining of the output is calcualted  
+   * using convolution but with the shorter signal time shifted. */
+
+  /* Calculate the length of the remaining sequence */
+  tot = ((srcALen + srcBLen) - 2u);
+
+  if(srcALen > srcBLen)
+  {
+    /* Calculating the number of zeros to be padded to the output */
+    j = srcALen - srcBLen;
+
+    /* Initialise the pointer after zero padding */
+    pDst += j;
+  }
+
+  else if(srcALen < srcBLen)
+  {
+    /* Initialization to inputB pointer */
+    pIn1 = pSrcB;
+
+    /* Initialization to the end of inputA pointer */
+    pIn2 = pSrcA + (srcALen - 1u);
+
+    /* Initialisation of the pointer after zero padding */
+    pDst = pDst + tot;
+
+    /* Swapping the lengths */
+    j = srcALen;
+    srcALen = srcBLen;
+    srcBLen = j;
+
+    /* Setting the reverse flag */
+    inv = 1;
+
+  }
+
+  /* Loop to calculate convolution for output length number of times */
+  for (i = 0u; i <= tot; i++)
+  {
+    /* Initialize sum with zero to carry on MAC operations */
+    sum = 0;
+
+    /* Loop to perform MAC operations according to convolution equation */
+    for (j = 0u; j <= i; j++)
+    {
+      /* Check the array limitations */
+      if((((i - j) < srcBLen) && (j < srcALen)))
+      {
+        /* z[i] += x[i-j] * y[j] */
+        sum += ((q31_t) pIn1[j] * pIn2[-((int32_t) i - j)]);
+      }
+    }
+    /* Store the output in the destination buffer */
+    if(inv == 1)
+      *pDst-- = (q15_t) __SSAT((sum >> 15u), 16u);
+    else
+      *pDst++ = (q15_t) __SSAT((sum >> 15u), 16u);
+  }
+
+#endif /*#if (defined(ARM_MATH_CM4) || defined(ARM_MATH_CM3)) && !defined(UNALIGNED_SUPPORT_DISABLE) */
+
+}
+
+/**   
+ * @} end of Corr group   
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_q31.c
new file mode 100644
index 0000000000..c81f8600dc
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_q31.c
@@ -0,0 +1,664 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_correlate_q31.c    
+*    
+* Description:	Correlation of Q31 sequences.  
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.11 2011/10/18  
+*    Bug Fix in conv, correlation, partial convolution.  
+* 
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+*    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup Corr    
+ * @{    
+ */
+
+/**    
+ * @brief Correlation of Q31 sequences.    
+ * @param[in] *pSrcA points to the first input sequence.    
+ * @param[in] srcALen length of the first input sequence.    
+ * @param[in] *pSrcB points to the second input sequence.    
+ * @param[in] srcBLen length of the second input sequence.    
+ * @param[out] *pDst points to the location where the output result is written.  Length 2 * max(srcALen, srcBLen) - 1.    
+ * @return none.    
+ *    
+ * @details    
+ * Scaling and Overflow Behavior:    
+ *    
+ * \par    
+ * The function is implemented using an internal 64-bit accumulator.    
+ * The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit.    
+ * There is no saturation on intermediate additions.    
+ * Thus, if the accumulator overflows it wraps around and distorts the result.    
+ * The input signals should be scaled down to avoid intermediate overflows.    
+ * Scale down one of the inputs by 1/min(srcALen, srcBLen)to avoid overflows since a    
+ * maximum of min(srcALen, srcBLen) number of additions is carried internally.    
+ * The 2.62 accumulator is right shifted by 31 bits and saturated to 1.31 format to yield the final result.    
+ *    
+ * \par    
+ * See arm_correlate_fast_q31() for a faster but less precise implementation of this function for Cortex-M3 and Cortex-M4.    
+ */
+
+void arm_correlate_q31(
+  q31_t * pSrcA,
+  uint32_t srcALen,
+  q31_t * pSrcB,
+  uint32_t srcBLen,
+  q31_t * pDst)
+{
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q31_t *pIn1;                                   /* inputA pointer               */
+  q31_t *pIn2;                                   /* inputB pointer               */
+  q31_t *pOut = pDst;                            /* output pointer               */
+  q31_t *px;                                     /* Intermediate inputA pointer  */
+  q31_t *py;                                     /* Intermediate inputB pointer  */
+  q31_t *pSrc1;                                  /* Intermediate pointers        */
+  q63_t sum, acc0, acc1, acc2;                   /* Accumulators                  */
+  q31_t x0, x1, x2, c0;                          /* temporary variables for holding input and coefficient values */
+  uint32_t j, k = 0u, count, blkCnt, outBlockSize, blockSize1, blockSize2, blockSize3;  /* loop counter                 */
+  int32_t inc = 1;                               /* Destination address modifier */
+
+
+  /* The algorithm implementation is based on the lengths of the inputs. */
+  /* srcB is always made to slide across srcA. */
+  /* So srcBLen is always considered as shorter or equal to srcALen */
+  /* But CORR(x, y) is reverse of CORR(y, x) */
+  /* So, when srcBLen > srcALen, output pointer is made to point to the end of the output buffer */
+  /* and the destination pointer modifier, inc is set to -1 */
+  /* If srcALen > srcBLen, zero pad has to be done to srcB to make the two inputs of same length */
+  /* But to improve the performance,    
+   * we include zeroes in the output instead of zero padding either of the the inputs*/
+  /* If srcALen > srcBLen,    
+   * (srcALen - srcBLen) zeroes has to included in the starting of the output buffer */
+  /* If srcALen < srcBLen,    
+   * (srcALen - srcBLen) zeroes has to included in the ending of the output buffer */
+  if(srcALen >= srcBLen)
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = (pSrcA);
+
+    /* Initialization of inputB pointer */
+    pIn2 = (pSrcB);
+
+    /* Number of output samples is calculated */
+    outBlockSize = (2u * srcALen) - 1u;
+
+    /* When srcALen > srcBLen, zero padding is done to srcB    
+     * to make their lengths equal.    
+     * Instead, (outBlockSize - (srcALen + srcBLen - 1))    
+     * number of output samples are made zero */
+    j = outBlockSize - (srcALen + (srcBLen - 1u));
+
+    /* Updating the pointer position to non zero value */
+    pOut += j;
+
+  }
+  else
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = (pSrcB);
+
+    /* Initialization of inputB pointer */
+    pIn2 = (pSrcA);
+
+    /* srcBLen is always considered as shorter or equal to srcALen */
+    j = srcBLen;
+    srcBLen = srcALen;
+    srcALen = j;
+
+    /* CORR(x, y) = Reverse order(CORR(y, x)) */
+    /* Hence set the destination pointer to point to the last output sample */
+    pOut = pDst + ((srcALen + srcBLen) - 2u);
+
+    /* Destination address modifier is set to -1 */
+    inc = -1;
+
+  }
+
+  /* The function is internally    
+   * divided into three parts according to the number of multiplications that has to be    
+   * taken place between inputA samples and inputB samples. In the first part of the    
+   * algorithm, the multiplications increase by one for every iteration.    
+   * In the second part of the algorithm, srcBLen number of multiplications are done.    
+   * In the third part of the algorithm, the multiplications decrease by one    
+   * for every iteration.*/
+  /* The algorithm is implemented in three stages.    
+   * The loop counters of each stage is initiated here. */
+  blockSize1 = srcBLen - 1u;
+  blockSize2 = srcALen - (srcBLen - 1u);
+  blockSize3 = blockSize1;
+
+  /* --------------------------    
+   * Initializations of stage1    
+   * -------------------------*/
+
+  /* sum = x[0] * y[srcBlen - 1]    
+   * sum = x[0] * y[srcBlen - 2] + x[1] * y[srcBlen - 1]    
+   * ....    
+   * sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen - 1] * y[srcBLen - 1]    
+   */
+
+  /* In this stage the MAC operations are increased by 1 for every iteration.    
+     The count variable holds the number of MAC operations performed */
+  count = 1u;
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  pSrc1 = pIn2 + (srcBLen - 1u);
+  py = pSrc1;
+
+  /* ------------------------    
+   * Stage1 process    
+   * ----------------------*/
+
+  /* The first stage starts here */
+  while(blockSize1 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = count >> 2;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* x[0] * y[srcBLen - 4] */
+      sum += (q63_t) * px++ * (*py++);
+      /* x[1] * y[srcBLen - 3] */
+      sum += (q63_t) * px++ * (*py++);
+      /* x[2] * y[srcBLen - 2] */
+      sum += (q63_t) * px++ * (*py++);
+      /* x[3] * y[srcBLen - 1] */
+      sum += (q63_t) * px++ * (*py++);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, compute any remaining MACs here.    
+     ** No loop unrolling is used. */
+    k = count % 0x4u;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      /* x[0] * y[srcBLen - 1] */
+      sum += (q63_t) * px++ * (*py++);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut = (q31_t) (sum >> 31);
+    /* Destination pointer is updated according to the address modifier, inc */
+    pOut += inc;
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    py = pSrc1 - count;
+    px = pIn1;
+
+    /* Increment the MAC count */
+    count++;
+
+    /* Decrement the loop counter */
+    blockSize1--;
+  }
+
+  /* --------------------------    
+   * Initializations of stage2    
+   * ------------------------*/
+
+  /* sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen-1] * y[srcBLen-1]    
+   * sum = x[1] * y[0] + x[2] * y[1] +...+ x[srcBLen] * y[srcBLen-1]    
+   * ....    
+   * sum = x[srcALen-srcBLen-2] * y[0] + x[srcALen-srcBLen-1] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]    
+   */
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  py = pIn2;
+
+  /* count is index by which the pointer pIn1 to be incremented */
+  count = 0u;
+
+  /* -------------------    
+   * Stage2 process    
+   * ------------------*/
+
+  /* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.    
+   * So, to loop unroll over blockSize2,    
+   * srcBLen should be greater than or equal to 4 */
+  if(srcBLen >= 4u)
+  {
+    /* Loop unroll by 3 */
+    blkCnt = blockSize2 / 3;
+
+    while(blkCnt > 0u)
+    {
+      /* Set all accumulators to zero */
+      acc0 = 0;
+      acc1 = 0;
+      acc2 = 0;
+
+      /* read x[0], x[1] samples */
+      x0 = *(px++);
+      x1 = *(px++);
+
+      /* Apply loop unrolling and compute 3 MACs simultaneously. */
+      k = srcBLen / 3;
+
+      /* First part of the processing with loop unrolling.  Compute 3 MACs at a time.        
+       ** a second loop below computes MACs for the remaining 1 to 2 samples. */
+      do
+      {
+        /* Read y[0] sample */
+        c0 = *(py);
+
+        /* Read x[2] sample */
+        x2 = *(px);
+
+        /* Perform the multiply-accumulate */
+        /* acc0 +=  x[0] * y[0] */
+        acc0 += ((q63_t) x0 * c0);
+        /* acc1 +=  x[1] * y[0] */
+        acc1 += ((q63_t) x1 * c0);
+        /* acc2 +=  x[2] * y[0] */
+        acc2 += ((q63_t) x2 * c0);
+
+        /* Read y[1] sample */
+        c0 = *(py + 1u);
+
+        /* Read x[3] sample */
+        x0 = *(px + 1u);
+
+        /* Perform the multiply-accumulates */
+        /* acc0 +=  x[1] * y[1] */
+        acc0 += ((q63_t) x1 * c0);
+        /* acc1 +=  x[2] * y[1] */
+        acc1 += ((q63_t) x2 * c0);
+        /* acc2 +=  x[3] * y[1] */
+        acc2 += ((q63_t) x0 * c0);
+
+        /* Read y[2] sample */
+        c0 = *(py + 2u);
+
+        /* Read x[4] sample */
+        x1 = *(px + 2u);
+
+        /* Perform the multiply-accumulates */
+        /* acc0 +=  x[2] * y[2] */
+        acc0 += ((q63_t) x2 * c0);
+        /* acc1 +=  x[3] * y[2] */
+        acc1 += ((q63_t) x0 * c0);
+        /* acc2 +=  x[4] * y[2] */
+        acc2 += ((q63_t) x1 * c0);
+
+        /* update scratch pointers */
+        px += 3u;
+        py += 3u;
+
+      } while(--k);
+
+      /* If the srcBLen is not a multiple of 3, compute any remaining MACs here.        
+       ** No loop unrolling is used. */
+      k = srcBLen - (3 * (srcBLen / 3));
+
+      while(k > 0u)
+      {
+        /* Read y[4] sample */
+        c0 = *(py++);
+
+        /* Read x[7] sample */
+        x2 = *(px++);
+
+        /* Perform the multiply-accumulates */
+        /* acc0 +=  x[4] * y[4] */
+        acc0 += ((q63_t) x0 * c0);
+        /* acc1 +=  x[5] * y[4] */
+        acc1 += ((q63_t) x1 * c0);
+        /* acc2 +=  x[6] * y[4] */
+        acc2 += ((q63_t) x2 * c0);
+
+        /* Reuse the present samples for the next MAC */
+        x0 = x1;
+        x1 = x2;
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut = (q31_t) (acc0 >> 31);
+      /* Destination pointer is updated according to the address modifier, inc */
+      pOut += inc;
+
+      *pOut = (q31_t) (acc1 >> 31);
+      pOut += inc;
+
+      *pOut = (q31_t) (acc2 >> 31);
+      pOut += inc;
+
+      /* Increment the pointer pIn1 index, count by 3 */
+      count += 3u;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pIn2;
+
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the blockSize2 is not a multiple of 3, compute any remaining output samples here.        
+     ** No loop unrolling is used. */
+    blkCnt = blockSize2 - 3 * (blockSize2 / 3);
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum += (q63_t) * px++ * (*py++);
+        sum += (q63_t) * px++ * (*py++);
+        sum += (q63_t) * px++ * (*py++);
+        sum += (q63_t) * px++ * (*py++);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.    
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulate */
+        sum += (q63_t) * px++ * (*py++);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut = (q31_t) (sum >> 31);
+      /* Destination pointer is updated according to the address modifier, inc */
+      pOut += inc;
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pIn2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+  else
+  {
+    /* If the srcBLen is not a multiple of 4,    
+     * the blockSize2 loop cannot be unrolled by 4 */
+    blkCnt = blockSize2;
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Loop over srcBLen */
+      k = srcBLen;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulate */
+        sum += (q63_t) * px++ * (*py++);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut = (q31_t) (sum >> 31);
+      /* Destination pointer is updated according to the address modifier, inc */
+      pOut += inc;
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pIn2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+
+  /* --------------------------    
+   * Initializations of stage3    
+   * -------------------------*/
+
+  /* sum += x[srcALen-srcBLen+1] * y[0] + x[srcALen-srcBLen+2] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]    
+   * sum += x[srcALen-srcBLen+2] * y[0] + x[srcALen-srcBLen+3] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]    
+   * ....    
+   * sum +=  x[srcALen-2] * y[0] + x[srcALen-1] * y[1]    
+   * sum +=  x[srcALen-1] * y[0]    
+   */
+
+  /* In this stage the MAC operations are decreased by 1 for every iteration.    
+     The count variable holds the number of MAC operations performed */
+  count = srcBLen - 1u;
+
+  /* Working pointer of inputA */
+  pSrc1 = pIn1 + (srcALen - (srcBLen - 1u));
+  px = pSrc1;
+
+  /* Working pointer of inputB */
+  py = pIn2;
+
+  /* -------------------    
+   * Stage3 process    
+   * ------------------*/
+
+  while(blockSize3 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = count >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      /* sum += x[srcALen - srcBLen + 4] * y[3] */
+      sum += (q63_t) * px++ * (*py++);
+      /* sum += x[srcALen - srcBLen + 3] * y[2] */
+      sum += (q63_t) * px++ * (*py++);
+      /* sum += x[srcALen - srcBLen + 2] * y[1] */
+      sum += (q63_t) * px++ * (*py++);
+      /* sum += x[srcALen - srcBLen + 1] * y[0] */
+      sum += (q63_t) * px++ * (*py++);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, compute any remaining MACs here.    
+     ** No loop unrolling is used. */
+    k = count % 0x4u;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      sum += (q63_t) * px++ * (*py++);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut = (q31_t) (sum >> 31);
+    /* Destination pointer is updated according to the address modifier, inc */
+    pOut += inc;
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    px = ++pSrc1;
+    py = pIn2;
+
+    /* Decrement the MAC count */
+    count--;
+
+    /* Decrement the loop counter */
+    blockSize3--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  q31_t *pIn1 = pSrcA;                           /* inputA pointer               */
+  q31_t *pIn2 = pSrcB + (srcBLen - 1u);          /* inputB pointer               */
+  q63_t sum;                                     /* Accumulators                  */
+  uint32_t i = 0u, j;                            /* loop counters */
+  uint32_t inv = 0u;                             /* Reverse order flag */
+  uint32_t tot = 0u;                             /* Length */
+
+  /* The algorithm implementation is based on the lengths of the inputs. */
+  /* srcB is always made to slide across srcA. */
+  /* So srcBLen is always considered as shorter or equal to srcALen */
+  /* But CORR(x, y) is reverse of CORR(y, x) */
+  /* So, when srcBLen > srcALen, output pointer is made to point to the end of the output buffer */
+  /* and a varaible, inv is set to 1 */
+  /* If lengths are not equal then zero pad has to be done to  make the two    
+   * inputs of same length. But to improve the performance, we include zeroes    
+   * in the output instead of zero padding either of the the inputs*/
+  /* If srcALen > srcBLen, (srcALen - srcBLen) zeroes has to included in the    
+   * starting of the output buffer */
+  /* If srcALen < srcBLen, (srcALen - srcBLen) zeroes has to included in the   
+   * ending of the output buffer */
+  /* Once the zero padding is done the remaining of the output is calcualted   
+   * using correlation but with the shorter signal time shifted. */
+
+  /* Calculate the length of the remaining sequence */
+  tot = ((srcALen + srcBLen) - 2u);
+
+  if(srcALen > srcBLen)
+  {
+    /* Calculating the number of zeros to be padded to the output */
+    j = srcALen - srcBLen;
+
+    /* Initialise the pointer after zero padding */
+    pDst += j;
+  }
+
+  else if(srcALen < srcBLen)
+  {
+    /* Initialization to inputB pointer */
+    pIn1 = pSrcB;
+
+    /* Initialization to the end of inputA pointer */
+    pIn2 = pSrcA + (srcALen - 1u);
+
+    /* Initialisation of the pointer after zero padding */
+    pDst = pDst + tot;
+
+    /* Swapping the lengths */
+    j = srcALen;
+    srcALen = srcBLen;
+    srcBLen = j;
+
+    /* Setting the reverse flag */
+    inv = 1;
+
+  }
+
+  /* Loop to calculate correlation for output length number of times */
+  for (i = 0u; i <= tot; i++)
+  {
+    /* Initialize sum with zero to carry on MAC operations */
+    sum = 0;
+
+    /* Loop to perform MAC operations according to correlation equation */
+    for (j = 0u; j <= i; j++)
+    {
+      /* Check the array limitations */
+      if((((i - j) < srcBLen) && (j < srcALen)))
+      {
+        /* z[i] += x[i-j] * y[j] */
+        sum += ((q63_t) pIn1[j] * pIn2[-((int32_t) i - j)]);
+      }
+    }
+    /* Store the output in the destination buffer */
+    if(inv == 1)
+      *pDst-- = (q31_t) (sum >> 31u);
+    else
+      *pDst++ = (q31_t) (sum >> 31u);
+  }
+
+#endif /*   #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of Corr group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_q7.c
new file mode 100644
index 0000000000..e03e4997b6
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_q7.c
@@ -0,0 +1,789 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010 ARM Limited. All rights reserved.   
+*   
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*   
+* Project: 	    CMSIS DSP Library   
+* Title:		arm_correlate_q7.c   
+*   
+* Description:	Correlation of Q7 sequences. 
+*   
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*
+* Version 1.0.11 2011/10/18 
+*    Bug Fix in conv, correlation, partial convolution. 
+*
+* Version 1.0.10 2011/7/15 
+*    Big Endian support added and Merged M0 and M3/M4 Source code.  
+*   
+* Version 1.0.3 2010/11/29  
+*    Re-organized the CMSIS folders and updated documentation.   
+*    
+* Version 1.0.2 2010/11/11   
+*    Documentation updated.    
+*   
+* Version 1.0.1 2010/10/05    
+*    Production release and review comments incorporated.   
+*   
+* Version 1.0.0 2010/09/20    
+*    Production release and review comments incorporated   
+*   
+* Version 0.0.7  2010/06/10    
+*    Misra-C changes done   
+*   
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**   
+ * @ingroup groupFilters   
+ */
+
+/**   
+ * @addtogroup Corr   
+ * @{   
+ */
+
+/**   
+ * @brief Correlation of Q7 sequences.   
+ * @param[in] *pSrcA points to the first input sequence.   
+ * @param[in] srcALen length of the first input sequence.   
+ * @param[in] *pSrcB points to the second input sequence.   
+ * @param[in] srcBLen length of the second input sequence.   
+ * @param[out] *pDst points to the location where the output result is written.  Length 2 * max(srcALen, srcBLen) - 1.   
+ * @return none.   
+ *   
+ * @details   
+ * Scaling and Overflow Behavior:   
+ *   
+ * \par   
+ * The function is implemented using a 32-bit internal accumulator.   
+ * Both the inputs are represented in 1.7 format and multiplications yield a 2.14 result.   
+ * The 2.14 intermediate results are accumulated in a 32-bit accumulator in 18.14 format.   
+ * This approach provides 17 guard bits and there is no risk of overflow as long as max(srcALen, srcBLen)<131072.   
+ * The 18.14 result is then truncated to 18.7 format by discarding the low 7 bits and saturated to 1.7 format.   
+ *
+ * \par    
+ * Refer the function arm_correlate_opt_q7() for a faster implementation of this function.
+ * 
+ */
+
+void arm_correlate_q7(
+  q7_t * pSrcA,
+  uint32_t srcALen,
+  q7_t * pSrcB,
+  uint32_t srcBLen,
+  q7_t * pDst)
+{
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q7_t *pIn1;                                    /* inputA pointer               */
+  q7_t *pIn2;                                    /* inputB pointer               */
+  q7_t *pOut = pDst;                             /* output pointer               */
+  q7_t *px;                                      /* Intermediate inputA pointer  */
+  q7_t *py;                                      /* Intermediate inputB pointer  */
+  q7_t *pSrc1;                                   /* Intermediate pointers        */
+  q31_t sum, acc0, acc1, acc2, acc3;             /* Accumulators                  */
+  q31_t input1, input2;                          /* temporary variables */
+  q15_t in1, in2;                                /* temporary variables */
+  q7_t x0, x1, x2, x3, c0, c1;                   /* temporary variables for holding input and coefficient values */
+  uint32_t j, k = 0u, count, blkCnt, outBlockSize, blockSize1, blockSize2, blockSize3;  /* loop counter                 */
+  int32_t inc = 1;
+
+
+  /* The algorithm implementation is based on the lengths of the inputs. */
+  /* srcB is always made to slide across srcA. */
+  /* So srcBLen is always considered as shorter or equal to srcALen */
+  /* But CORR(x, y) is reverse of CORR(y, x) */
+  /* So, when srcBLen > srcALen, output pointer is made to point to the end of the output buffer */
+  /* and the destination pointer modifier, inc is set to -1 */
+  /* If srcALen > srcBLen, zero pad has to be done to srcB to make the two inputs of same length */
+  /* But to improve the performance,   
+   * we include zeroes in the output instead of zero padding either of the the inputs*/
+  /* If srcALen > srcBLen,   
+   * (srcALen - srcBLen) zeroes has to included in the starting of the output buffer */
+  /* If srcALen < srcBLen,   
+   * (srcALen - srcBLen) zeroes has to included in the ending of the output buffer */
+  if(srcALen >= srcBLen)
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = (pSrcA);
+
+    /* Initialization of inputB pointer */
+    pIn2 = (pSrcB);
+
+    /* Number of output samples is calculated */
+    outBlockSize = (2u * srcALen) - 1u;
+
+    /* When srcALen > srcBLen, zero padding is done to srcB   
+     * to make their lengths equal.   
+     * Instead, (outBlockSize - (srcALen + srcBLen - 1))   
+     * number of output samples are made zero */
+    j = outBlockSize - (srcALen + (srcBLen - 1u));
+
+    /* Updating the pointer position to non zero value */
+    pOut += j;
+
+  }
+  else
+  {
+    /* Initialization of inputA pointer */
+    pIn1 = (pSrcB);
+
+    /* Initialization of inputB pointer */
+    pIn2 = (pSrcA);
+
+    /* srcBLen is always considered as shorter or equal to srcALen */
+    j = srcBLen;
+    srcBLen = srcALen;
+    srcALen = j;
+
+    /* CORR(x, y) = Reverse order(CORR(y, x)) */
+    /* Hence set the destination pointer to point to the last output sample */
+    pOut = pDst + ((srcALen + srcBLen) - 2u);
+
+    /* Destination address modifier is set to -1 */
+    inc = -1;
+
+  }
+
+  /* The function is internally   
+   * divided into three parts according to the number of multiplications that has to be   
+   * taken place between inputA samples and inputB samples. In the first part of the   
+   * algorithm, the multiplications increase by one for every iteration.   
+   * In the second part of the algorithm, srcBLen number of multiplications are done.   
+   * In the third part of the algorithm, the multiplications decrease by one   
+   * for every iteration.*/
+  /* The algorithm is implemented in three stages.   
+   * The loop counters of each stage is initiated here. */
+  blockSize1 = srcBLen - 1u;
+  blockSize2 = srcALen - (srcBLen - 1u);
+  blockSize3 = blockSize1;
+
+  /* --------------------------   
+   * Initializations of stage1   
+   * -------------------------*/
+
+  /* sum = x[0] * y[srcBlen - 1]   
+   * sum = x[0] * y[srcBlen - 2] + x[1] * y[srcBlen - 1]   
+   * ....   
+   * sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen - 1] * y[srcBLen - 1]   
+   */
+
+  /* In this stage the MAC operations are increased by 1 for every iteration.   
+     The count variable holds the number of MAC operations performed */
+  count = 1u;
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  pSrc1 = pIn2 + (srcBLen - 1u);
+  py = pSrc1;
+
+  /* ------------------------   
+   * Stage1 process   
+   * ----------------------*/
+
+  /* The first stage starts here */
+  while(blockSize1 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = count >> 2;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* x[0] , x[1] */
+      in1 = (q15_t) * px++;
+      in2 = (q15_t) * px++;
+      input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+      /* y[srcBLen - 4] , y[srcBLen - 3] */
+      in1 = (q15_t) * py++;
+      in2 = (q15_t) * py++;
+      input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+      /* x[0] * y[srcBLen - 4] */
+      /* x[1] * y[srcBLen - 3] */
+      sum = __SMLAD(input1, input2, sum);
+
+      /* x[2] , x[3] */
+      in1 = (q15_t) * px++;
+      in2 = (q15_t) * px++;
+      input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+      /* y[srcBLen - 2] , y[srcBLen - 1] */
+      in1 = (q15_t) * py++;
+      in2 = (q15_t) * py++;
+      input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+      /* x[2] * y[srcBLen - 2] */
+      /* x[3] * y[srcBLen - 1] */
+      sum = __SMLAD(input1, input2, sum);
+
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, compute any remaining MACs here.   
+     ** No loop unrolling is used. */
+    k = count % 0x4u;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      /* x[0] * y[srcBLen - 1] */
+      sum += (q31_t) ((q15_t) * px++ * *py++);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut = (q7_t) (__SSAT(sum >> 7, 8));
+    /* Destination pointer is updated according to the address modifier, inc */
+    pOut += inc;
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    py = pSrc1 - count;
+    px = pIn1;
+
+    /* Increment the MAC count */
+    count++;
+
+    /* Decrement the loop counter */
+    blockSize1--;
+  }
+
+  /* --------------------------   
+   * Initializations of stage2   
+   * ------------------------*/
+
+  /* sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen-1] * y[srcBLen-1]   
+   * sum = x[1] * y[0] + x[2] * y[1] +...+ x[srcBLen] * y[srcBLen-1]   
+   * ....   
+   * sum = x[srcALen-srcBLen-2] * y[0] + x[srcALen-srcBLen-1] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]   
+   */
+
+  /* Working pointer of inputA */
+  px = pIn1;
+
+  /* Working pointer of inputB */
+  py = pIn2;
+
+  /* count is index by which the pointer pIn1 to be incremented */
+  count = 0u;
+
+  /* -------------------   
+   * Stage2 process   
+   * ------------------*/
+
+  /* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.   
+   * So, to loop unroll over blockSize2,   
+   * srcBLen should be greater than or equal to 4 */
+  if(srcBLen >= 4u)
+  {
+    /* Loop unroll over blockSize2, by 4 */
+    blkCnt = blockSize2 >> 2u;
+
+    while(blkCnt > 0u)
+    {
+      /* Set all accumulators to zero */
+      acc0 = 0;
+      acc1 = 0;
+      acc2 = 0;
+      acc3 = 0;
+
+      /* read x[0], x[1], x[2] samples */
+      x0 = *px++;
+      x1 = *px++;
+      x2 = *px++;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      do
+      {
+        /* Read y[0] sample */
+        c0 = *py++;
+        /* Read y[1] sample */
+        c1 = *py++;
+
+        /* Read x[3] sample */
+        x3 = *px++;
+
+        /* x[0] and x[1] are packed */
+        in1 = (q15_t) x0;
+        in2 = (q15_t) x1;
+
+        input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+        /* y[0] and y[1] are packed */
+        in1 = (q15_t) c0;
+        in2 = (q15_t) c1;
+
+        input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+        /* acc0 += x[0] * y[0] + x[1] * y[1]  */
+        acc0 = __SMLAD(input1, input2, acc0);
+
+        /* x[1] and x[2] are packed */
+        in1 = (q15_t) x1;
+        in2 = (q15_t) x2;
+
+        input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+        /* acc1 += x[1] * y[0] + x[2] * y[1] */
+        acc1 = __SMLAD(input1, input2, acc1);
+
+        /* x[2] and x[3] are packed */
+        in1 = (q15_t) x2;
+        in2 = (q15_t) x3;
+
+        input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+        /* acc2 += x[2] * y[0] + x[3] * y[1]  */
+        acc2 = __SMLAD(input1, input2, acc2);
+
+        /* Read x[4] sample */
+        x0 = *(px++);
+
+        /* x[3] and x[4] are packed */
+        in1 = (q15_t) x3;
+        in2 = (q15_t) x0;
+
+        input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+        /* acc3 += x[3] * y[0] + x[4] * y[1]  */
+        acc3 = __SMLAD(input1, input2, acc3);
+
+        /* Read y[2] sample */
+        c0 = *py++;
+        /* Read y[3] sample */
+        c1 = *py++;
+
+        /* Read x[5] sample */
+        x1 = *px++;
+
+        /* x[2] and x[3] are packed */
+        in1 = (q15_t) x2;
+        in2 = (q15_t) x3;
+
+        input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+        /* y[2] and y[3] are packed */
+        in1 = (q15_t) c0;
+        in2 = (q15_t) c1;
+
+        input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+        /* acc0 += x[2] * y[2] + x[3] * y[3]  */
+        acc0 = __SMLAD(input1, input2, acc0);
+
+        /* x[3] and x[4] are packed */
+        in1 = (q15_t) x3;
+        in2 = (q15_t) x0;
+
+        input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+        /* acc1 += x[3] * y[2] + x[4] * y[3]  */
+        acc1 = __SMLAD(input1, input2, acc1);
+
+        /* x[4] and x[5] are packed */
+        in1 = (q15_t) x0;
+        in2 = (q15_t) x1;
+
+        input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+        /* acc2 += x[4] * y[2] + x[5] * y[3]  */
+        acc2 = __SMLAD(input1, input2, acc2);
+
+        /* Read x[6] sample */
+        x2 = *px++;
+
+        /* x[5] and x[6] are packed */
+        in1 = (q15_t) x1;
+        in2 = (q15_t) x2;
+
+        input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+        /* acc3 += x[5] * y[2] + x[6] * y[3]  */
+        acc3 = __SMLAD(input1, input2, acc3);
+
+      } while(--k);
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.   
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Read y[4] sample */
+        c0 = *py++;
+
+        /* Read x[7] sample */
+        x3 = *px++;
+
+        /* Perform the multiply-accumulates */
+        /* acc0 +=  x[4] * y[4] */
+        acc0 += ((q15_t) x0 * c0);
+        /* acc1 +=  x[5] * y[4] */
+        acc1 += ((q15_t) x1 * c0);
+        /* acc2 +=  x[6] * y[4] */
+        acc2 += ((q15_t) x2 * c0);
+        /* acc3 +=  x[7] * y[4] */
+        acc3 += ((q15_t) x3 * c0);
+
+        /* Reuse the present samples for the next MAC */
+        x0 = x1;
+        x1 = x2;
+        x2 = x3;
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut = (q7_t) (__SSAT(acc0 >> 7, 8));
+      /* Destination pointer is updated according to the address modifier, inc */
+      pOut += inc;
+
+      *pOut = (q7_t) (__SSAT(acc1 >> 7, 8));
+      pOut += inc;
+
+      *pOut = (q7_t) (__SSAT(acc2 >> 7, 8));
+      pOut += inc;
+
+      *pOut = (q7_t) (__SSAT(acc3 >> 7, 8));
+      pOut += inc;
+
+	  count += 4u;
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pIn2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.   
+     ** No loop unrolling is used. */
+    blkCnt = blockSize2 % 0x4u;
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Apply loop unrolling and compute 4 MACs simultaneously. */
+      k = srcBLen >> 2u;
+
+      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+      while(k > 0u)
+      {
+        /* Reading two inputs of SrcA buffer and packing */
+        in1 = (q15_t) * px++;
+        in2 = (q15_t) * px++;
+        input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+        /* Reading two inputs of SrcB buffer and packing */
+        in1 = (q15_t) * py++;
+        in2 = (q15_t) * py++;
+        input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+        /* Perform the multiply-accumulates */
+        sum = __SMLAD(input1, input2, sum);
+
+        /* Reading two inputs of SrcA buffer and packing */
+        in1 = (q15_t) * px++;
+        in2 = (q15_t) * px++;
+        input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+        /* Reading two inputs of SrcB buffer and packing */
+        in1 = (q15_t) * py++;
+        in2 = (q15_t) * py++;
+        input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+        /* Perform the multiply-accumulates */
+        sum = __SMLAD(input1, input2, sum);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.   
+       ** No loop unrolling is used. */
+      k = srcBLen % 0x4u;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulates */
+        sum += ((q15_t) * px++ * *py++);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut = (q7_t) (__SSAT(sum >> 7, 8));
+      /* Destination pointer is updated according to the address modifier, inc */
+      pOut += inc;
+
+      /* Increment the pointer pIn1 index, count by 1 */
+	  count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pIn2;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+  else
+  {
+    /* If the srcBLen is not a multiple of 4,   
+     * the blockSize2 loop cannot be unrolled by 4 */
+    blkCnt = blockSize2;
+
+    while(blkCnt > 0u)
+    {
+      /* Accumulator is made zero for every iteration */
+      sum = 0;
+
+      /* Loop over srcBLen */
+      k = srcBLen;
+
+      while(k > 0u)
+      {
+        /* Perform the multiply-accumulate */
+        sum += ((q15_t) * px++ * *py++);
+
+        /* Decrement the loop counter */
+        k--;
+      }
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut = (q7_t) (__SSAT(sum >> 7, 8));
+      /* Destination pointer is updated according to the address modifier, inc */
+      pOut += inc;
+
+      /* Increment the MAC count */
+      count++;
+
+      /* Update the inputA and inputB pointers for next MAC calculation */
+      px = pIn1 + count;
+      py = pIn2;
+
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+
+  /* --------------------------   
+   * Initializations of stage3   
+   * -------------------------*/
+
+  /* sum += x[srcALen-srcBLen+1] * y[0] + x[srcALen-srcBLen+2] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]   
+   * sum += x[srcALen-srcBLen+2] * y[0] + x[srcALen-srcBLen+3] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]   
+   * ....   
+   * sum +=  x[srcALen-2] * y[0] + x[srcALen-1] * y[1]   
+   * sum +=  x[srcALen-1] * y[0]   
+   */
+
+  /* In this stage the MAC operations are decreased by 1 for every iteration.   
+     The count variable holds the number of MAC operations performed */
+  count = srcBLen - 1u;
+
+  /* Working pointer of inputA */
+  pSrc1 = pIn1 + (srcALen - (srcBLen - 1u));
+  px = pSrc1;
+
+  /* Working pointer of inputB */
+  py = pIn2;
+
+  /* -------------------   
+   * Stage3 process   
+   * ------------------*/
+
+  while(blockSize3 > 0u)
+  {
+    /* Accumulator is made zero for every iteration */
+    sum = 0;
+
+    /* Apply loop unrolling and compute 4 MACs simultaneously. */
+    k = count >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.   
+     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
+    while(k > 0u)
+    {
+      /* x[srcALen - srcBLen + 1] , x[srcALen - srcBLen + 2]  */
+      in1 = (q15_t) * px++;
+      in2 = (q15_t) * px++;
+      input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+      /* y[0] , y[1] */
+      in1 = (q15_t) * py++;
+      in2 = (q15_t) * py++;
+      input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+      /* sum += x[srcALen - srcBLen + 1] * y[0] */
+      /* sum += x[srcALen - srcBLen + 2] * y[1] */
+      sum = __SMLAD(input1, input2, sum);
+
+      /* x[srcALen - srcBLen + 3] , x[srcALen - srcBLen + 4] */
+      in1 = (q15_t) * px++;
+      in2 = (q15_t) * px++;
+      input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+      /* y[2] , y[3] */
+      in1 = (q15_t) * py++;
+      in2 = (q15_t) * py++;
+      input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
+
+      /* sum += x[srcALen - srcBLen + 3] * y[2] */
+      /* sum += x[srcALen - srcBLen + 4] * y[3] */
+      sum = __SMLAD(input1, input2, sum);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* If the count is not a multiple of 4, compute any remaining MACs here.   
+     ** No loop unrolling is used. */
+    k = count % 0x4u;
+
+    while(k > 0u)
+    {
+      /* Perform the multiply-accumulates */
+      sum += ((q15_t) * px++ * *py++);
+
+      /* Decrement the loop counter */
+      k--;
+    }
+
+    /* Store the result in the accumulator in the destination buffer. */
+    *pOut = (q7_t) (__SSAT(sum >> 7, 8));
+    /* Destination pointer is updated according to the address modifier, inc */
+    pOut += inc;
+
+    /* Update the inputA and inputB pointers for next MAC calculation */
+    px = ++pSrc1;
+    py = pIn2;
+
+    /* Decrement the MAC count */
+    count--;
+
+    /* Decrement the loop counter */
+    blockSize3--;
+  }
+
+#else
+
+/* Run the below code for Cortex-M0 */
+
+  q7_t *pIn1 = pSrcA;                            /* inputA pointer */
+  q7_t *pIn2 = pSrcB + (srcBLen - 1u);           /* inputB pointer */
+  q31_t sum;                                     /* Accumulator */
+  uint32_t i = 0u, j;                            /* loop counters */
+  uint32_t inv = 0u;                             /* Reverse order flag */
+  uint32_t tot = 0u;                             /* Length */
+
+  /* The algorithm implementation is based on the lengths of the inputs. */
+  /* srcB is always made to slide across srcA. */
+  /* So srcBLen is always considered as shorter or equal to srcALen */
+  /* But CORR(x, y) is reverse of CORR(y, x) */
+  /* So, when srcBLen > srcALen, output pointer is made to point to the end of the output buffer */
+  /* and a varaible, inv is set to 1 */
+  /* If lengths are not equal then zero pad has to be done to  make the two   
+   * inputs of same length. But to improve the performance, we include zeroes   
+   * in the output instead of zero padding either of the the inputs*/
+  /* If srcALen > srcBLen, (srcALen - srcBLen) zeroes has to included in the   
+   * starting of the output buffer */
+  /* If srcALen < srcBLen, (srcALen - srcBLen) zeroes has to included in the  
+   * ending of the output buffer */
+  /* Once the zero padding is done the remaining of the output is calcualted  
+   * using convolution but with the shorter signal time shifted. */
+
+  /* Calculate the length of the remaining sequence */
+  tot = ((srcALen + srcBLen) - 2u);
+
+  if(srcALen > srcBLen)
+  {
+    /* Calculating the number of zeros to be padded to the output */
+    j = srcALen - srcBLen;
+
+    /* Initialise the pointer after zero padding */
+    pDst += j;
+  }
+
+  else if(srcALen < srcBLen)
+  {
+    /* Initialization to inputB pointer */
+    pIn1 = pSrcB;
+
+    /* Initialization to the end of inputA pointer */
+    pIn2 = pSrcA + (srcALen - 1u);
+
+    /* Initialisation of the pointer after zero padding */
+    pDst = pDst + tot;
+
+    /* Swapping the lengths */
+    j = srcALen;
+    srcALen = srcBLen;
+    srcBLen = j;
+
+    /* Setting the reverse flag */
+    inv = 1;
+
+  }
+
+  /* Loop to calculate convolution for output length number of times */
+  for (i = 0u; i <= tot; i++)
+  {
+    /* Initialize sum with zero to carry on MAC operations */
+    sum = 0;
+
+    /* Loop to perform MAC operations according to convolution equation */
+    for (j = 0u; j <= i; j++)
+    {
+      /* Check the array limitations */
+      if((((i - j) < srcBLen) && (j < srcALen)))
+      {
+        /* z[i] += x[i-j] * y[j] */
+        sum += ((q15_t) pIn1[j] * pIn2[-((int32_t) i - j)]);
+      }
+    }
+    /* Store the output in the destination buffer */
+    if(inv == 1)
+      *pDst-- = (q7_t) __SSAT((sum >> 7u), 8u);
+    else
+      *pDst++ = (q7_t) __SSAT((sum >> 7u), 8u);
+  }
+
+#endif /*   #ifndef ARM_MATH_CM0 */
+
+}
+
+/**   
+ * @} end of Corr group   
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_f32.c
new file mode 100644
index 0000000000..1546f407dd
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_f32.c
@@ -0,0 +1,518 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_fir_decimate_f32.c    
+*    
+* Description:	FIR decimation for floating-point sequences.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+*    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @defgroup FIR_decimate Finite Impulse Response (FIR) Decimator    
+ *    
+ * These functions combine an FIR filter together with a decimator.    
+ * They are used in multirate systems for reducing the sample rate of a signal without introducing aliasing distortion.    
+ * Conceptually, the functions are equivalent to the block diagram below:    
+ * \image html FIRDecimator.gif "Components included in the FIR Decimator functions"    
+ * When decimating by a factor of M, the signal should be prefiltered by a lowpass filter with a normalized    
+ * cutoff frequency of 1/M in order to prevent aliasing distortion.    
+ * The user of the function is responsible for providing the filter coefficients.    
+ *    
+ * The FIR decimator functions provided in the CMSIS DSP Library combine the FIR filter and the decimator in an efficient manner.    
+ * Instead of calculating all of the FIR filter outputs and discarding M-1 out of every M, only the    
+ * samples output by the decimator are computed.    
+ * The functions operate on blocks of input and output data.    
+ * pSrc points to an array of blockSize input values and    
+ * pDst points to an array of blockSize/M output values.    
+ * In order to have an integer number of output samples blockSize    
+ * must always be a multiple of the decimation factor M.    
+ *    
+ * The library provides separate functions for Q15, Q31 and floating-point data types.    
+ *    
+ * \par Algorithm:    
+ * The FIR portion of the algorithm uses the standard form filter:    
+ * 
    
+ *    y[n] = b[0] * x[n] + b[1] * x[n-1] + b[2] * x[n-2] + ...+ b[numTaps-1] * x[n-numTaps+1]    
+ * 
    
+ * where, b[n] are the filter coefficients.    
+ * \par   
+ * The pCoeffs points to a coefficient array of size numTaps.    
+ * Coefficients are stored in time reversed order.    
+ * \par    
+ * 
    
+ *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}    
+ * 
    
+ * \par    
+ * pState points to a state array of size numTaps + blockSize - 1.    
+ * Samples in the state buffer are stored in the order:    
+ * \par    
+ * 
    
+ *    {x[n-numTaps+1], x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2]....x[0], x[1], ..., x[blockSize-1]}    
+ * 
    
+ * The state variables are updated after each block of data is processed, the coefficients are untouched.    
+ *    
+ * \par Instance Structure    
+ * The coefficients and state variables for a filter are stored together in an instance data structure.    
+ * A separate instance structure must be defined for each filter.    
+ * Coefficient arrays may be shared among several instances while state variable array should be allocated separately.    
+ * There are separate instance structure declarations for each of the 3 supported data types.    
+ *    
+ * \par Initialization Functions    
+ * There is also an associated initialization function for each data type.    
+ * The initialization function performs the following operations:    
+ * - Sets the values of the internal structure fields.    
+ * - Zeros out the values in the state buffer.    
+ * - Checks to make sure that the size of the input is a multiple of the decimation factor.    
+ *    
+ * \par    
+ * Use of the initialization function is optional.    
+ * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.    
+ * To place an instance structure into a const data section, the instance structure must be manually initialized.    
+ * The code below statically initializes each of the 3 different data type filter instance structures    
+ * 
    
+ *arm_fir_decimate_instance_f32 S = {M, numTaps, pCoeffs, pState};    
+ *arm_fir_decimate_instance_q31 S = {M, numTaps, pCoeffs, pState};    
+ *arm_fir_decimate_instance_q15 S = {M, numTaps, pCoeffs, pState};    
+ * 
    
+ * where M is the decimation factor; numTaps is the number of filter coefficients in the filter;    
+ * pCoeffs is the address of the coefficient buffer;    
+ * pState is the address of the state buffer.    
+ * Be sure to set the values in the state buffer to zeros when doing static initialization.    
+ *    
+ * \par Fixed-Point Behavior    
+ * Care must be taken when using the fixed-point versions of the FIR decimate filter functions.    
+ * In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.    
+ * Refer to the function specific documentation below for usage guidelines.    
+ */
+
+/**    
+ * @addtogroup FIR_decimate    
+ * @{    
+ */
+
+  /**    
+   * @brief Processing function for the floating-point FIR decimator.    
+   * @param[in] *S        points to an instance of the floating-point FIR decimator structure.    
+   * @param[in] *pSrc     points to the block of input data.    
+   * @param[out] *pDst    points to the block of output data.    
+   * @param[in] blockSize number of input samples to process per call.    
+   * @return none.    
+   */
+
+void arm_fir_decimate_f32(
+  const arm_fir_decimate_instance_f32 * S,
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize)
+{
+  float32_t *pState = S->pState;                 /* State pointer */
+  float32_t *pCoeffs = S->pCoeffs;               /* Coefficient pointer */
+  float32_t *pStateCurnt;                        /* Points to the current sample of the state */
+  float32_t *px, *pb;                            /* Temporary pointers for state and coefficient buffers */
+  float32_t sum0;                                /* Accumulator */
+  float32_t x0, c0;                              /* Temporary variables to hold state and coefficient values */
+  uint32_t numTaps = S->numTaps;                 /* Number of filter coefficients in the filter */
+  uint32_t i, tapCnt, blkCnt, outBlockSize = blockSize / S->M;  /* Loop counters */
+
+#ifndef ARM_MATH_CM0
+
+  uint32_t blkCntN4;
+  float32_t *px0, *px1, *px2, *px3;
+  float32_t acc0, acc1, acc2, acc3;
+  float32_t x1, x2, x3;
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /* S->pState buffer contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = S->pState + (numTaps - 1u);
+
+  /* Total number of output samples to be computed */
+  blkCnt = outBlockSize / 4;
+  blkCntN4 = outBlockSize - (4 * blkCnt);
+
+  while(blkCnt > 0u)
+  {
+    /* Copy 4 * decimation factor number of new input samples into the state buffer */
+    i = 4 * S->M;
+
+    do
+    {
+      *pStateCurnt++ = *pSrc++;
+
+    } while(--i);
+
+    /* Set accumulators to zero */
+    acc0 = 0.0f;
+    acc1 = 0.0f;
+    acc2 = 0.0f;
+    acc3 = 0.0f;
+
+    /* Initialize state pointer for all the samples */
+    px0 = pState;
+    px1 = pState + S->M;
+    px2 = pState + 2 * S->M;
+    px3 = pState + 3 * S->M;
+
+    /* Initialize coeff pointer */
+    pb = pCoeffs;
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2;
+
+    /* Loop over the number of taps.  Unroll by a factor of 4.       
+     ** Repeat until we've computed numTaps-4 coefficients. */
+
+    while(tapCnt > 0u)
+    {
+      /* Read the b[numTaps-1] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-1] sample for acc0 */
+      x0 = *(px0++);
+      /* Read x[n-numTaps-1] sample for acc1 */
+      x1 = *(px1++);
+      /* Read x[n-numTaps-1] sample for acc2 */
+      x2 = *(px2++);
+      /* Read x[n-numTaps-1] sample for acc3 */
+      x3 = *(px3++);
+
+      /* Perform the multiply-accumulate */
+      acc0 += x0 * c0;
+      acc1 += x1 * c0;
+      acc2 += x2 * c0;
+      acc3 += x3 * c0;
+
+      /* Read the b[numTaps-2] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-2] sample for acc0, acc1, acc2, acc3 */
+      x0 = *(px0++);
+      x1 = *(px1++);
+      x2 = *(px2++);
+      x3 = *(px3++);
+
+      /* Perform the multiply-accumulate */
+      acc0 += x0 * c0;
+      acc1 += x1 * c0;
+      acc2 += x2 * c0;
+      acc3 += x3 * c0;
+
+      /* Read the b[numTaps-3] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-3] sample acc0, acc1, acc2, acc3 */
+      x0 = *(px0++);
+      x1 = *(px1++);
+      x2 = *(px2++);
+      x3 = *(px3++);
+
+      /* Perform the multiply-accumulate */
+      acc0 += x0 * c0;
+      acc1 += x1 * c0;
+      acc2 += x2 * c0;
+      acc3 += x3 * c0;
+
+      /* Read the b[numTaps-4] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-4] sample acc0, acc1, acc2, acc3 */
+      x0 = *(px0++);
+      x1 = *(px1++);
+      x2 = *(px2++);
+      x3 = *(px3++);
+
+      /* Perform the multiply-accumulate */
+      acc0 += x0 * c0;
+      acc1 += x1 * c0;
+      acc2 += x2 * c0;
+      acc3 += x3 * c0;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = numTaps % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      /* Read coefficients */
+      c0 = *(pb++);
+
+      /* Fetch  state variables for acc0, acc1, acc2, acc3 */
+      x0 = *(px0++);
+      x1 = *(px1++);
+      x2 = *(px2++);
+      x3 = *(px3++);
+
+      /* Perform the multiply-accumulate */
+      acc0 += x0 * c0;
+      acc1 += x1 * c0;
+      acc2 += x2 * c0;
+      acc3 += x3 * c0;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Advance the state pointer by the decimation factor       
+     * to process the next group of decimation factor number samples */
+    pState = pState + 4 * S->M;
+
+    /* The result is in the accumulator, store in the destination buffer. */
+    *pDst++ = acc0;
+    *pDst++ = acc1;
+    *pDst++ = acc2;
+    *pDst++ = acc3;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  while(blkCntN4 > 0u)
+  {
+    /* Copy decimation factor number of new input samples into the state buffer */
+    i = S->M;
+
+    do
+    {
+      *pStateCurnt++ = *pSrc++;
+
+    } while(--i);
+
+    /* Set accumulator to zero */
+    sum0 = 0.0f;
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* Initialize coeff pointer */
+    pb = pCoeffs;
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2;
+
+    /* Loop over the number of taps.  Unroll by a factor of 4.       
+     ** Repeat until we've computed numTaps-4 coefficients. */
+    while(tapCnt > 0u)
+    {
+      /* Read the b[numTaps-1] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-1] sample */
+      x0 = *(px++);
+
+      /* Perform the multiply-accumulate */
+      sum0 += x0 * c0;
+
+      /* Read the b[numTaps-2] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-2] sample */
+      x0 = *(px++);
+
+      /* Perform the multiply-accumulate */
+      sum0 += x0 * c0;
+
+      /* Read the b[numTaps-3] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-3] sample */
+      x0 = *(px++);
+
+      /* Perform the multiply-accumulate */
+      sum0 += x0 * c0;
+
+      /* Read the b[numTaps-4] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-4] sample */
+      x0 = *(px++);
+
+      /* Perform the multiply-accumulate */
+      sum0 += x0 * c0;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = numTaps % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      /* Read coefficients */
+      c0 = *(pb++);
+
+      /* Fetch 1 state variable */
+      x0 = *(px++);
+
+      /* Perform the multiply-accumulate */
+      sum0 += x0 * c0;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Advance the state pointer by the decimation factor       
+     * to process the next group of decimation factor number samples */
+    pState = pState + S->M;
+
+    /* The result is in the accumulator, store in the destination buffer. */
+    *pDst++ = sum0;
+
+    /* Decrement the loop counter */
+    blkCntN4--;
+  }
+
+  /* Processing is complete.    
+   ** Now copy the last numTaps - 1 samples to the satrt of the state buffer.    
+   ** This prepares the state buffer for the next function call. */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+  i = (numTaps - 1u) >> 2;
+
+  /* copy data */
+  while(i > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    i--;
+  }
+
+  i = (numTaps - 1u) % 0x04u;
+
+  /* copy data */
+  while(i > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    i--;
+  }
+
+#else
+
+/* Run the below code for Cortex-M0 */
+
+  /* S->pState buffer contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = S->pState + (numTaps - 1u);
+
+  /* Total number of output samples to be computed */
+  blkCnt = outBlockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* Copy decimation factor number of new input samples into the state buffer */
+    i = S->M;
+
+    do
+    {
+      *pStateCurnt++ = *pSrc++;
+
+    } while(--i);
+
+    /* Set accumulator to zero */
+    sum0 = 0.0f;
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* Initialize coeff pointer */
+    pb = pCoeffs;
+
+    tapCnt = numTaps;
+
+    while(tapCnt > 0u)
+    {
+      /* Read coefficients */
+      c0 = *pb++;
+
+      /* Fetch 1 state variable */
+      x0 = *px++;
+
+      /* Perform the multiply-accumulate */
+      sum0 += x0 * c0;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Advance the state pointer by the decimation factor           
+     * to process the next group of decimation factor number samples */
+    pState = pState + S->M;
+
+    /* The result is in the accumulator, store in the destination buffer. */
+    *pDst++ = sum0;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Processing is complete.         
+   ** Now copy the last numTaps - 1 samples to the start of the state buffer.       
+   ** This prepares the state buffer for the next function call. */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+  /* Copy numTaps number of values */
+  i = (numTaps - 1u);
+
+  /* copy data */
+  while(i > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    i--;
+  }
+
+#endif /*   #ifndef ARM_MATH_CM0        */
+
+}
+
+/**    
+ * @} end of FIR_decimate group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_fast_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_fast_q15.c
new file mode 100644
index 0000000000..96f50e6f2b
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_fast_q15.c
@@ -0,0 +1,590 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_fir_decimate_fast_q15.c    
+*    
+* Description:	Fast Q15 FIR Decimator.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR_decimate    
+ * @{    
+ */
+
+/**    
+ * @brief Processing function for the Q15 FIR decimator (fast variant) for Cortex-M3 and Cortex-M4.    
+ * @param[in] *S points to an instance of the Q15 FIR decimator structure.    
+ * @param[in] *pSrc points to the block of input data.    
+ * @param[out] *pDst points to the block of output data    
+ * @param[in] blockSize number of input samples to process per call.    
+ * @return none    
+ *    
+ * \par Restrictions   
+ *  If the silicon does not support unaligned memory access enable the macro UNALIGNED_SUPPORT_DISABLE   
+ *	In this case input, output, state buffers should be aligned by 32-bit   
+ *    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * This fast version uses a 32-bit accumulator with 2.30 format.    
+ * The accumulator maintains full precision of the intermediate multiplication results but provides only a single guard bit.    
+ * Thus, if the accumulator result overflows it wraps around and distorts the result.    
+ * In order to avoid overflows completely the input signal must be scaled down by log2(numTaps) bits (log2 is read as log to the base 2).    
+ * The 2.30 accumulator is then truncated to 2.15 format and saturated to yield the 1.15 result.    
+ *    
+ * \par    
+ * Refer to the function arm_fir_decimate_q15() for a slower implementation of this function which uses 64-bit accumulation to avoid wrap around distortion.    
+ * Both the slow and the fast versions use the same instance structure.    
+ * Use the function arm_fir_decimate_init_q15() to initialize the filter structure.    
+ */
+
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+void arm_fir_decimate_fast_q15(
+  const arm_fir_decimate_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+  q15_t *pState = S->pState;                     /* State pointer */
+  q15_t *pCoeffs = S->pCoeffs;                   /* Coefficient pointer */
+  q15_t *pStateCurnt;                            /* Points to the current sample of the state */
+  q15_t *px;                                     /* Temporary pointer for state buffer */
+  q15_t *pb;                                     /* Temporary pointer coefficient buffer */
+  q31_t x0, x1, c0, c1;                          /* Temporary variables to hold state and coefficient values */
+  q31_t sum0;                                    /* Accumulators */
+  q31_t acc0, acc1;
+  q15_t *px0, *px1;
+  uint32_t blkCntN3;
+  uint32_t numTaps = S->numTaps;                 /* Number of taps */
+  uint32_t i, blkCnt, tapCnt, outBlockSize = blockSize / S->M;  /* Loop counters */
+
+
+  /* S->pState buffer contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = S->pState + (numTaps - 1u);
+
+
+  /* Total number of output samples to be computed */
+  blkCnt = outBlockSize / 2;
+  blkCntN3 = outBlockSize - (2 * blkCnt);
+
+
+  while(blkCnt > 0u)
+  {
+    /* Copy decimation factor number of new input samples into the state buffer */
+    i = 2 * S->M;
+
+    do
+    {
+      *pStateCurnt++ = *pSrc++;
+
+    } while(--i);
+
+    /* Set accumulator to zero */
+    acc0 = 0;
+    acc1 = 0;
+
+    /* Initialize state pointer */
+    px0 = pState;
+
+    px1 = pState + S->M;
+
+
+    /* Initialize coeff pointer */
+    pb = pCoeffs;
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2;
+
+    /* Loop over the number of taps.  Unroll by a factor of 4.       
+     ** Repeat until we've computed numTaps-4 coefficients. */
+    while(tapCnt > 0u)
+    {
+      /* Read the Read b[numTaps-1] and b[numTaps-2]  coefficients */
+      c0 = *__SIMD32(pb)++;
+
+      /* Read x[n-numTaps-1] and x[n-numTaps-2]sample */
+      x0 = *__SIMD32(px0)++;
+
+      x1 = *__SIMD32(px1)++;
+
+      /* Perform the multiply-accumulate */
+      acc0 = __SMLAD(x0, c0, acc0);
+
+      acc1 = __SMLAD(x1, c0, acc1);
+
+      /* Read the b[numTaps-3] and b[numTaps-4] coefficient */
+      c0 = *__SIMD32(pb)++;
+
+      /* Read x[n-numTaps-2] and x[n-numTaps-3] sample */
+      x0 = *__SIMD32(px0)++;
+
+      x1 = *__SIMD32(px1)++;
+
+      /* Perform the multiply-accumulate */
+      acc0 = __SMLAD(x0, c0, acc0);
+
+      acc1 = __SMLAD(x1, c0, acc1);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = numTaps % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      /* Read coefficients */
+      c0 = *pb++;
+
+      /* Fetch 1 state variable */
+      x0 = *px0++;
+
+      x1 = *px1++;
+
+      /* Perform the multiply-accumulate */
+      acc0 = __SMLAD(x0, c0, acc0);
+      acc1 = __SMLAD(x1, c0, acc1);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Advance the state pointer by the decimation factor       
+     * to process the next group of decimation factor number samples */
+    pState = pState + S->M * 2;
+
+    /* Store filter output, smlad returns the values in 2.14 format */
+    /* so downsacle by 15 to get output in 1.15 */
+    *pDst++ = (q15_t) (__SSAT((acc0 >> 15), 16));
+    *pDst++ = (q15_t) (__SSAT((acc1 >> 15), 16));
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+
+
+  while(blkCntN3 > 0u)
+  {
+    /* Copy decimation factor number of new input samples into the state buffer */
+    i = S->M;
+
+    do
+    {
+      *pStateCurnt++ = *pSrc++;
+
+    } while(--i);
+
+    /*Set sum to zero */
+    sum0 = 0;
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* Initialize coeff pointer */
+    pb = pCoeffs;
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2;
+
+    /* Loop over the number of taps.  Unroll by a factor of 4.       
+     ** Repeat until we've computed numTaps-4 coefficients. */
+    while(tapCnt > 0u)
+    {
+      /* Read the Read b[numTaps-1] and b[numTaps-2]  coefficients */
+      c0 = *__SIMD32(pb)++;
+
+      /* Read x[n-numTaps-1] and x[n-numTaps-2]sample */
+      x0 = *__SIMD32(px)++;
+
+      /* Read the b[numTaps-3] and b[numTaps-4] coefficient */
+      c1 = *__SIMD32(pb)++;
+
+      /* Perform the multiply-accumulate */
+      sum0 = __SMLAD(x0, c0, sum0);
+
+      /* Read x[n-numTaps-2] and x[n-numTaps-3] sample */
+      x0 = *__SIMD32(px)++;
+
+      /* Perform the multiply-accumulate */
+      sum0 = __SMLAD(x0, c1, sum0);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = numTaps % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      /* Read coefficients */
+      c0 = *pb++;
+
+      /* Fetch 1 state variable */
+      x0 = *px++;
+
+      /* Perform the multiply-accumulate */
+      sum0 = __SMLAD(x0, c0, sum0);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Advance the state pointer by the decimation factor       
+     * to process the next group of decimation factor number samples */
+    pState = pState + S->M;
+
+    /* Store filter output, smlad returns the values in 2.14 format */
+    /* so downsacle by 15 to get output in 1.15 */
+    *pDst++ = (q15_t) (__SSAT((sum0 >> 15), 16));
+
+    /* Decrement the loop counter */
+    blkCntN3--;
+  }
+
+  /* Processing is complete.       
+   ** Now copy the last numTaps - 1 samples to the satrt of the state buffer.       
+   ** This prepares the state buffer for the next function call. */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+  i = (numTaps - 1u) >> 2u;
+
+  /* copy data */
+  while(i > 0u)
+  {
+    *__SIMD32(pStateCurnt)++ = *__SIMD32(pState)++;
+    *__SIMD32(pStateCurnt)++ = *__SIMD32(pState)++;
+
+    /* Decrement the loop counter */
+    i--;
+  }
+
+  i = (numTaps - 1u) % 0x04u;
+
+  /* copy data */
+  while(i > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    i--;
+  }
+}
+
+#else
+
+
+void arm_fir_decimate_fast_q15(
+  const arm_fir_decimate_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+  q15_t *pState = S->pState;                     /* State pointer */
+  q15_t *pCoeffs = S->pCoeffs;                   /* Coefficient pointer */
+  q15_t *pStateCurnt;                            /* Points to the current sample of the state */
+  q15_t *px;                                     /* Temporary pointer for state buffer */
+  q15_t *pb;                                     /* Temporary pointer coefficient buffer */
+  q15_t x0, x1, c0;                              /* Temporary variables to hold state and coefficient values */
+  q31_t sum0;                                    /* Accumulators */
+  q31_t acc0, acc1;
+  q15_t *px0, *px1;
+  uint32_t blkCntN3;
+  uint32_t numTaps = S->numTaps;                 /* Number of taps */
+  uint32_t i, blkCnt, tapCnt, outBlockSize = blockSize / S->M;  /* Loop counters */
+
+
+  /* S->pState buffer contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = S->pState + (numTaps - 1u);
+
+
+  /* Total number of output samples to be computed */
+  blkCnt = outBlockSize / 2;
+  blkCntN3 = outBlockSize - (2 * blkCnt);
+
+  while(blkCnt > 0u)
+  {
+    /* Copy decimation factor number of new input samples into the state buffer */
+    i = 2 * S->M;
+
+    do
+    {
+      *pStateCurnt++ = *pSrc++;
+
+    } while(--i);
+
+    /* Set accumulator to zero */
+    acc0 = 0;
+    acc1 = 0;
+
+    /* Initialize state pointer */
+    px0 = pState;
+
+    px1 = pState + S->M;
+
+
+    /* Initialize coeff pointer */
+    pb = pCoeffs;
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2;
+
+    /* Loop over the number of taps.  Unroll by a factor of 4.       
+     ** Repeat until we've computed numTaps-4 coefficients. */
+    while(tapCnt > 0u)
+    {
+      /* Read the Read b[numTaps-1] coefficients */
+      c0 = *pb++;
+
+      /* Read x[n-numTaps-1] for sample 0 and for sample 1 */
+      x0 = *px0++;
+      x1 = *px1++;
+
+      /* Perform the multiply-accumulate */
+      acc0 += x0 * c0;
+      acc1 += x1 * c0;
+
+      /* Read the b[numTaps-2] coefficient */
+      c0 = *pb++;
+
+      /* Read x[n-numTaps-2] for sample 0 and sample 1 */
+      x0 = *px0++;
+      x1 = *px1++;
+
+      /* Perform the multiply-accumulate */
+      acc0 += x0 * c0;
+      acc1 += x1 * c0;
+
+      /* Read the b[numTaps-3]  coefficients */
+      c0 = *pb++;
+
+      /* Read x[n-numTaps-3] for sample 0 and sample 1 */
+      x0 = *px0++;
+      x1 = *px1++;
+
+      /* Perform the multiply-accumulate */
+      acc0 += x0 * c0;
+      acc1 += x1 * c0;
+
+      /* Read the b[numTaps-4] coefficient */
+      c0 = *pb++;
+
+      /* Read x[n-numTaps-4] for sample 0 and sample 1 */
+      x0 = *px0++;
+      x1 = *px1++;
+
+      /* Perform the multiply-accumulate */
+      acc0 += x0 * c0;
+      acc1 += x1 * c0;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = numTaps % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      /* Read coefficients */
+      c0 = *pb++;
+
+      /* Fetch 1 state variable */
+      x0 = *px0++;
+      x1 = *px1++;
+
+      /* Perform the multiply-accumulate */
+      acc0 += x0 * c0;
+      acc1 += x1 * c0;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Advance the state pointer by the decimation factor       
+     * to process the next group of decimation factor number samples */
+    pState = pState + S->M * 2;
+
+    /* Store filter output, smlad returns the values in 2.14 format */
+    /* so downsacle by 15 to get output in 1.15 */
+
+    *pDst++ = (q15_t) (__SSAT((acc0 >> 15), 16));
+    *pDst++ = (q15_t) (__SSAT((acc1 >> 15), 16));
+
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  while(blkCntN3 > 0u)
+  {
+    /* Copy decimation factor number of new input samples into the state buffer */
+    i = S->M;
+
+    do
+    {
+      *pStateCurnt++ = *pSrc++;
+
+    } while(--i);
+
+    /*Set sum to zero */
+    sum0 = 0;
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* Initialize coeff pointer */
+    pb = pCoeffs;
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2;
+
+    /* Loop over the number of taps.  Unroll by a factor of 4.       
+     ** Repeat until we've computed numTaps-4 coefficients. */
+    while(tapCnt > 0u)
+    {
+      /* Read the Read b[numTaps-1] coefficients */
+      c0 = *pb++;
+
+      /* Read x[n-numTaps-1] and sample */
+      x0 = *px++;
+
+      /* Perform the multiply-accumulate */
+      sum0 += x0 * c0;
+
+      /* Read the b[numTaps-2] coefficient */
+      c0 = *pb++;
+
+      /* Read x[n-numTaps-2] and  sample */
+      x0 = *px++;
+
+      /* Perform the multiply-accumulate */
+      sum0 += x0 * c0;
+
+      /* Read the b[numTaps-3]  coefficients */
+      c0 = *pb++;
+
+      /* Read x[n-numTaps-3] sample */
+      x0 = *px++;
+
+      /* Perform the multiply-accumulate */
+      sum0 += x0 * c0;
+
+      /* Read the b[numTaps-4] coefficient */
+      c0 = *pb++;
+
+      /* Read x[n-numTaps-4] sample */
+      x0 = *px++;
+
+      /* Perform the multiply-accumulate */
+      sum0 += x0 * c0;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = numTaps % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      /* Read coefficients */
+      c0 = *pb++;
+
+      /* Fetch 1 state variable */
+      x0 = *px++;
+
+      /* Perform the multiply-accumulate */
+      sum0 += x0 * c0;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Advance the state pointer by the decimation factor       
+     * to process the next group of decimation factor number samples */
+    pState = pState + S->M;
+
+    /* Store filter output, smlad returns the values in 2.14 format */
+    /* so downsacle by 15 to get output in 1.15 */
+    *pDst++ = (q15_t) (__SSAT((sum0 >> 15), 16));
+
+    /* Decrement the loop counter */
+    blkCntN3--;
+  }
+
+  /* Processing is complete.       
+   ** Now copy the last numTaps - 1 samples to the satrt of the state buffer.       
+   ** This prepares the state buffer for the next function call. */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+  i = (numTaps - 1u) >> 2u;
+
+  /* copy data */
+  while(i > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    i--;
+  }
+
+  i = (numTaps - 1u) % 0x04u;
+
+  /* copy data */
+  while(i > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    i--;
+  }
+}
+
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+/**    
+ * @} end of FIR_decimate group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_fast_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_fast_q31.c
new file mode 100644
index 0000000000..a43fd0b4c9
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_fast_q31.c
@@ -0,0 +1,343 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_fir_decimate_fast_q31.c    
+*    
+* Description:	Fast Q31 FIR Decimator.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR_decimate    
+ * @{    
+ */
+
+/**    
+ * @brief Processing function for the Q31 FIR decimator (fast variant) for Cortex-M3 and Cortex-M4.    
+ * @param[in] *S points to an instance of the Q31 FIR decimator structure.    
+ * @param[in] *pSrc points to the block of input data.    
+ * @param[out] *pDst points to the block of output data    
+ * @param[in] blockSize number of input samples to process per call.    
+ * @return none    
+ *    
+ * Scaling and Overflow Behavior:    
+ *    
+ * \par    
+ * This function is optimized for speed at the expense of fixed-point precision and overflow protection.    
+ * The result of each 1.31 x 1.31 multiplication is truncated to 2.30 format.    
+ * These intermediate results are added to a 2.30 accumulator.    
+ * Finally, the accumulator is saturated and converted to a 1.31 result.    
+ * The fast version has the same overflow behavior as the standard version and provides less precision since it discards the low 32 bits of each multiplication result.    
+ * In order to avoid overflows completely the input signal must be scaled down by log2(numTaps) bits (where log2 is read as log to the base 2).    
+ *    
+ * \par    
+ * Refer to the function arm_fir_decimate_q31() for a slower implementation of this function which uses a 64-bit accumulator to provide higher precision.    
+ * Both the slow and the fast versions use the same instance structure.    
+ * Use the function arm_fir_decimate_init_q31() to initialize the filter structure.    
+ */
+
+void arm_fir_decimate_fast_q31(
+  arm_fir_decimate_instance_q31 * S,
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize)
+{
+  q31_t *pState = S->pState;                     /* State pointer */
+  q31_t *pCoeffs = S->pCoeffs;                   /* Coefficient pointer */
+  q31_t *pStateCurnt;                            /* Points to the current sample of the state */
+  q31_t x0, c0;                                  /* Temporary variables to hold state and coefficient values */
+  q31_t *px;                                     /* Temporary pointers for state buffer */
+  q31_t *pb;                                     /* Temporary pointers for coefficient buffer */
+  q31_t sum0;                                    /* Accumulator */
+  uint32_t numTaps = S->numTaps;                 /* Number of taps */
+  uint32_t i, tapCnt, blkCnt, outBlockSize = blockSize / S->M;  /* Loop counters */
+  uint32_t blkCntN2;
+  q31_t x1;
+  q31_t acc0, acc1;
+  q31_t *px0, *px1;
+
+  /* S->pState buffer contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = S->pState + (numTaps - 1u);
+
+  /* Total number of output samples to be computed */
+
+  blkCnt = outBlockSize / 2;
+  blkCntN2 = outBlockSize - (2 * blkCnt);
+
+  while(blkCnt > 0u)
+  {
+    /* Copy decimation factor number of new input samples into the state buffer */
+    i = 2 * S->M;
+
+    do
+    {
+      *pStateCurnt++ = *pSrc++;
+
+    } while(--i);
+
+    /* Set accumulator to zero */
+    acc0 = 0;
+    acc1 = 0;
+
+    /* Initialize state pointer */
+    px0 = pState;
+    px1 = pState + S->M;
+
+    /* Initialize coeff pointer */
+    pb = pCoeffs;
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2;
+
+    /* Loop over the number of taps.  Unroll by a factor of 4.       
+     ** Repeat until we've computed numTaps-4 coefficients. */
+    while(tapCnt > 0u)
+    {
+      /* Read the b[numTaps-1] coefficient */
+      c0 = *(pb);
+
+      /* Read x[n-numTaps-1] for sample 0 sample 1 */
+      x0 = *(px0);
+      x1 = *(px1);
+
+      /* Perform the multiply-accumulate */
+      acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x0 * c0)) >> 32);
+      acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x1 * c0)) >> 32);
+
+      /* Read the b[numTaps-2] coefficient */
+      c0 = *(pb + 1u);
+
+      /* Read x[n-numTaps-2]  for sample 0 sample 1  */
+      x0 = *(px0 + 1u);
+      x1 = *(px1 + 1u);
+
+      /* Perform the multiply-accumulate */
+      acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x0 * c0)) >> 32);
+      acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x1 * c0)) >> 32);
+
+      /* Read the b[numTaps-3] coefficient */
+      c0 = *(pb + 2u);
+
+      /* Read x[n-numTaps-3]  for sample 0 sample 1 */
+      x0 = *(px0 + 2u);
+      x1 = *(px1 + 2u);
+      pb += 4u;
+
+      /* Perform the multiply-accumulate */
+      acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x0 * c0)) >> 32);
+      acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x1 * c0)) >> 32);
+
+      /* Read the b[numTaps-4] coefficient */
+      c0 = *(pb - 1u);
+
+      /* Read x[n-numTaps-4] for sample 0 sample 1 */
+      x0 = *(px0 + 3u);
+      x1 = *(px1 + 3u);
+
+
+      /* Perform the multiply-accumulate */
+      acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x0 * c0)) >> 32);
+      acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x1 * c0)) >> 32);
+
+      /* update state pointers */
+      px0 += 4u;
+      px1 += 4u;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = numTaps % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      /* Read coefficients */
+      c0 = *(pb++);
+
+      /* Fetch 1 state variable */
+      x0 = *(px0++);
+      x1 = *(px1++);
+
+      /* Perform the multiply-accumulate */
+      acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x0 * c0)) >> 32);
+      acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x1 * c0)) >> 32);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Advance the state pointer by the decimation factor       
+     * to process the next group of decimation factor number samples */
+    pState = pState + S->M * 2;
+
+    /* The result is in the accumulator, store in the destination buffer. */
+    *pDst++ = (q31_t) (acc0 << 1);
+    *pDst++ = (q31_t) (acc1 << 1);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  while(blkCntN2 > 0u)
+  {
+    /* Copy decimation factor number of new input samples into the state buffer */
+    i = S->M;
+
+    do
+    {
+      *pStateCurnt++ = *pSrc++;
+
+    } while(--i);
+
+    /* Set accumulator to zero */
+    sum0 = 0;
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* Initialize coeff pointer */
+    pb = pCoeffs;
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2;
+
+    /* Loop over the number of taps.  Unroll by a factor of 4.       
+     ** Repeat until we've computed numTaps-4 coefficients. */
+    while(tapCnt > 0u)
+    {
+      /* Read the b[numTaps-1] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-1] sample */
+      x0 = *(px++);
+
+      /* Perform the multiply-accumulate */
+      sum0 = (q31_t) ((((q63_t) sum0 << 32) + ((q63_t) x0 * c0)) >> 32);
+
+      /* Read the b[numTaps-2] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-2] sample */
+      x0 = *(px++);
+
+      /* Perform the multiply-accumulate */
+      sum0 = (q31_t) ((((q63_t) sum0 << 32) + ((q63_t) x0 * c0)) >> 32);
+
+      /* Read the b[numTaps-3] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-3] sample */
+      x0 = *(px++);
+
+      /* Perform the multiply-accumulate */
+      sum0 = (q31_t) ((((q63_t) sum0 << 32) + ((q63_t) x0 * c0)) >> 32);
+
+      /* Read the b[numTaps-4] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-4] sample */
+      x0 = *(px++);
+
+      /* Perform the multiply-accumulate */
+      sum0 = (q31_t) ((((q63_t) sum0 << 32) + ((q63_t) x0 * c0)) >> 32);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = numTaps % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      /* Read coefficients */
+      c0 = *(pb++);
+
+      /* Fetch 1 state variable */
+      x0 = *(px++);
+
+      /* Perform the multiply-accumulate */
+      sum0 = (q31_t) ((((q63_t) sum0 << 32) + ((q63_t) x0 * c0)) >> 32);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Advance the state pointer by the decimation factor       
+     * to process the next group of decimation factor number samples */
+    pState = pState + S->M;
+
+    /* The result is in the accumulator, store in the destination buffer. */
+    *pDst++ = (q31_t) (sum0 << 1);
+
+    /* Decrement the loop counter */
+    blkCntN2--;
+  }
+
+  /* Processing is complete.       
+   ** Now copy the last numTaps - 1 samples to the satrt of the state buffer.       
+   ** This prepares the state buffer for the next function call. */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+  i = (numTaps - 1u) >> 2u;
+
+  /* copy data */
+  while(i > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    i--;
+  }
+
+  i = (numTaps - 1u) % 0x04u;
+
+  /* copy data */
+  while(i > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    i--;
+  }
+}
+
+/**    
+ * @} end of FIR_decimate group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_init_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_init_f32.c
new file mode 100644
index 0000000000..b655a6be6d
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_init_f32.c
@@ -0,0 +1,112 @@
+/*-----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_fir_decimate_init_f32.c    
+*    
+* Description:  Floating-point FIR Decimator initialization function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ---------------------------------------------------------------------------*/
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR_decimate    
+ * @{    
+ */
+
+/**    
+ * @brief  Initialization function for the floating-point FIR decimator.    
+ * @param[in,out] *S points to an instance of the floating-point FIR decimator structure.    
+ * @param[in] numTaps  number of coefficients in the filter.    
+ * @param[in] M  decimation factor.    
+ * @param[in] *pCoeffs points to the filter coefficients.    
+ * @param[in] *pState points to the state buffer.    
+ * @param[in] blockSize number of input samples to process per call.    
+ * @return    The function returns ARM_MATH_SUCCESS if initialization was successful or ARM_MATH_LENGTH_ERROR if    
+ * blockSize is not a multiple of M.    
+ *    
+ * Description:    
+ * \par    
+ * pCoeffs points to the array of filter coefficients stored in time reversed order:    
+ * 
    
+ *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}    
+ * 
    
+ * \par    
+ * pState points to the array of state variables.    
+ * pState is of length numTaps+blockSize-1 words where blockSize is the number of input samples passed to arm_fir_decimate_f32().    
+ * M is the decimation factor.    
+ */
+
+arm_status arm_fir_decimate_init_f32(
+  arm_fir_decimate_instance_f32 * S,
+  uint16_t numTaps,
+  uint8_t M,
+  float32_t * pCoeffs,
+  float32_t * pState,
+  uint32_t blockSize)
+{
+  arm_status status;
+
+  /* The size of the input block must be a multiple of the decimation factor */
+  if((blockSize % M) != 0u)
+  {
+    /* Set status as ARM_MATH_LENGTH_ERROR */
+    status = ARM_MATH_LENGTH_ERROR;
+  }
+  else
+  {
+    /* Assign filter taps */
+    S->numTaps = numTaps;
+
+    /* Assign coefficient pointer */
+    S->pCoeffs = pCoeffs;
+
+    /* Clear state buffer and size is always (blockSize + numTaps - 1) */
+    memset(pState, 0, (numTaps + (blockSize - 1u)) * sizeof(float32_t));
+
+    /* Assign state pointer */
+    S->pState = pState;
+
+    /* Assign Decimation Factor */
+    S->M = M;
+
+    status = ARM_MATH_SUCCESS;
+  }
+
+  return (status);
+
+}
+
+/**    
+ * @} end of FIR_decimate group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_init_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_init_q15.c
new file mode 100644
index 0000000000..1a1fee8a2e
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_init_q15.c
@@ -0,0 +1,114 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_fir_decimate_init_q15.c    
+*    
+* Description:  Initialization function for the Q15 FIR Decimator.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR_decimate    
+ * @{    
+ */
+
+/**    
+ * @brief  Initialization function for the Q15 FIR decimator.    
+ * @param[in,out] *S points to an instance of the Q15 FIR decimator structure.    
+ * @param[in] numTaps  number of coefficients in the filter.    
+ * @param[in] M  decimation factor.    
+ * @param[in] *pCoeffs points to the filter coefficients.    
+ * @param[in] *pState points to the state buffer.    
+ * @param[in] blockSize number of input samples to process per call.    
+ * @return    The function returns ARM_MATH_SUCCESS if initialization was successful or ARM_MATH_LENGTH_ERROR if    
+ * blockSize is not a multiple of M.    
+ *    
+ * Description:    
+ * \par    
+ * pCoeffs points to the array of filter coefficients stored in time reversed order:    
+ * 
    
+ *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}    
+ * 
    
+ * \par    
+ * pState points to the array of state variables.    
+ * pState is of length numTaps+blockSize-1 words where blockSize is the number of input samples    
+ * to the call arm_fir_decimate_q15().    
+ * M is the decimation factor.    
+ */
+
+arm_status arm_fir_decimate_init_q15(
+  arm_fir_decimate_instance_q15 * S,
+  uint16_t numTaps,
+  uint8_t M,
+  q15_t * pCoeffs,
+  q15_t * pState,
+  uint32_t blockSize)
+{
+
+  arm_status status;
+
+  /* The size of the input block must be a multiple of the decimation factor */
+  if((blockSize % M) != 0u)
+  {
+    /* Set status as ARM_MATH_LENGTH_ERROR */
+    status = ARM_MATH_LENGTH_ERROR;
+  }
+  else
+  {
+    /* Assign filter taps */
+    S->numTaps = numTaps;
+
+    /* Assign coefficient pointer */
+    S->pCoeffs = pCoeffs;
+
+    /* Clear the state buffer.  The size of buffer is always (blockSize + numTaps - 1) */
+    memset(pState, 0, (numTaps + (blockSize - 1u)) * sizeof(q15_t));
+
+    /* Assign state pointer */
+    S->pState = pState;
+
+    /* Assign Decimation factor */
+    S->M = M;
+
+    status = ARM_MATH_SUCCESS;
+  }
+
+  return (status);
+
+}
+
+/**    
+ * @} end of FIR_decimate group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_init_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_init_q31.c
new file mode 100644
index 0000000000..e2ac8165e6
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_init_q31.c
@@ -0,0 +1,112 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_fir_decimate_init_q31.c    
+*    
+* Description:  Initialization function for Q31 FIR Decimation filter.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR_decimate    
+ * @{    
+ */
+
+/**    
+ * @brief  Initialization function for the Q31 FIR decimator.    
+ * @param[in,out] *S points to an instance of the Q31 FIR decimator structure.    
+ * @param[in] numTaps  number of coefficients in the filter.    
+ * @param[in] M  decimation factor.    
+ * @param[in] *pCoeffs points to the filter coefficients.    
+ * @param[in] *pState points to the state buffer.    
+ * @param[in] blockSize number of input samples to process per call.    
+ * @return    The function returns ARM_MATH_SUCCESS if initialization was successful or ARM_MATH_LENGTH_ERROR if    
+ * blockSize is not a multiple of M.    
+ *    
+ * Description:    
+ * \par    
+ * pCoeffs points to the array of filter coefficients stored in time reversed order:    
+ * 
    
+ *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}    
+ * 
    
+ * \par    
+ * pState points to the array of state variables.    
+ * pState is of length numTaps+blockSize-1 words where blockSize is the number of input samples passed to arm_fir_decimate_q31().    
+ * M is the decimation factor.    
+ */
+
+arm_status arm_fir_decimate_init_q31(
+  arm_fir_decimate_instance_q31 * S,
+  uint16_t numTaps,
+  uint8_t M,
+  q31_t * pCoeffs,
+  q31_t * pState,
+  uint32_t blockSize)
+{
+  arm_status status;
+
+  /* The size of the input block must be a multiple of the decimation factor */
+  if((blockSize % M) != 0u)
+  {
+    /* Set status as ARM_MATH_LENGTH_ERROR */
+    status = ARM_MATH_LENGTH_ERROR;
+  }
+  else
+  {
+    /* Assign filter taps */
+    S->numTaps = numTaps;
+
+    /* Assign coefficient pointer */
+    S->pCoeffs = pCoeffs;
+
+    /* Clear the state buffer.  The size is always (blockSize + numTaps - 1) */
+    memset(pState, 0, (numTaps + (blockSize - 1)) * sizeof(q31_t));
+
+    /* Assign state pointer */
+    S->pState = pState;
+
+    /* Assign Decimation factor */
+    S->M = M;
+
+    status = ARM_MATH_SUCCESS;
+  }
+
+  return (status);
+
+}
+
+/**    
+ * @} end of FIR_decimate group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_q15.c
new file mode 100644
index 0000000000..28b5f13dd6
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_q15.c
@@ -0,0 +1,691 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_fir_decimate_q15.c    
+*    
+* Description:	Q15 FIR Decimator.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR_decimate    
+ * @{    
+ */
+
+/**    
+ * @brief Processing function for the Q15 FIR decimator.    
+ * @param[in] *S points to an instance of the Q15 FIR decimator structure.    
+ * @param[in] *pSrc points to the block of input data.    
+ * @param[out] *pDst points to the location where the output result is written.    
+ * @param[in] blockSize number of input samples to process per call.    
+ * @return none.    
+ *    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function is implemented using a 64-bit internal accumulator.    
+ * Both coefficients and state variables are represented in 1.15 format and multiplications yield a 2.30 result.    
+ * The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format.    
+ * There is no risk of internal overflow with this approach and the full precision of intermediate multiplications is preserved.    
+ * After all additions have been performed, the accumulator is truncated to 34.15 format by discarding low 15 bits.    
+ * Lastly, the accumulator is saturated to yield a result in 1.15 format.    
+ *    
+ * \par    
+ * Refer to the function arm_fir_decimate_fast_q15() for a faster but less precise implementation of this function for Cortex-M3 and Cortex-M4.    
+ */
+
+#ifndef ARM_MATH_CM0
+
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+void arm_fir_decimate_q15(
+  const arm_fir_decimate_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+  q15_t *pState = S->pState;                     /* State pointer */
+  q15_t *pCoeffs = S->pCoeffs;                   /* Coefficient pointer */
+  q15_t *pStateCurnt;                            /* Points to the current sample of the state */
+  q15_t *px;                                     /* Temporary pointer for state buffer */
+  q15_t *pb;                                     /* Temporary pointer coefficient buffer */
+  q31_t x0, x1, c0, c1;                          /* Temporary variables to hold state and coefficient values */
+  q63_t sum0;                                    /* Accumulators */
+  q63_t acc0, acc1;
+  q15_t *px0, *px1;
+  uint32_t blkCntN3;
+  uint32_t numTaps = S->numTaps;                 /* Number of taps */
+  uint32_t i, blkCnt, tapCnt, outBlockSize = blockSize / S->M;  /* Loop counters */
+
+
+  /* S->pState buffer contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = S->pState + (numTaps - 1u);
+
+
+  /* Total number of output samples to be computed */
+  blkCnt = outBlockSize / 2;
+  blkCntN3 = outBlockSize - (2 * blkCnt);
+
+
+  while(blkCnt > 0u)
+  {
+    /* Copy decimation factor number of new input samples into the state buffer */
+    i = 2 * S->M;
+
+    do
+    {
+      *pStateCurnt++ = *pSrc++;
+
+    } while(--i);
+
+    /* Set accumulator to zero */
+    acc0 = 0;
+    acc1 = 0;
+
+    /* Initialize state pointer */
+    px0 = pState;
+
+    px1 = pState + S->M;
+
+
+    /* Initialize coeff pointer */
+    pb = pCoeffs;
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2;
+
+    /* Loop over the number of taps.  Unroll by a factor of 4.       
+     ** Repeat until we've computed numTaps-4 coefficients. */
+    while(tapCnt > 0u)
+    {
+      /* Read the Read b[numTaps-1] and b[numTaps-2]  coefficients */
+      c0 = *__SIMD32(pb)++;
+
+      /* Read x[n-numTaps-1] and x[n-numTaps-2]sample */
+      x0 = *__SIMD32(px0)++;
+
+      x1 = *__SIMD32(px1)++;
+
+      /* Perform the multiply-accumulate */
+      acc0 = __SMLALD(x0, c0, acc0);
+
+      acc1 = __SMLALD(x1, c0, acc1);
+
+      /* Read the b[numTaps-3] and b[numTaps-4] coefficient */
+      c0 = *__SIMD32(pb)++;
+
+      /* Read x[n-numTaps-2] and x[n-numTaps-3] sample */
+      x0 = *__SIMD32(px0)++;
+
+      x1 = *__SIMD32(px1)++;
+
+      /* Perform the multiply-accumulate */
+      acc0 = __SMLALD(x0, c0, acc0);
+
+      acc1 = __SMLALD(x1, c0, acc1);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = numTaps % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      /* Read coefficients */
+      c0 = *pb++;
+
+      /* Fetch 1 state variable */
+      x0 = *px0++;
+
+      x1 = *px1++;
+
+      /* Perform the multiply-accumulate */
+      acc0 = __SMLALD(x0, c0, acc0);
+      acc1 = __SMLALD(x1, c0, acc1);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Advance the state pointer by the decimation factor       
+     * to process the next group of decimation factor number samples */
+    pState = pState + S->M * 2;
+
+    /* Store filter output, smlad returns the values in 2.14 format */
+    /* so downsacle by 15 to get output in 1.15 */
+    *pDst++ = (q15_t) (__SSAT((acc0 >> 15), 16));
+    *pDst++ = (q15_t) (__SSAT((acc1 >> 15), 16));
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+
+
+  while(blkCntN3 > 0u)
+  {
+    /* Copy decimation factor number of new input samples into the state buffer */
+    i = S->M;
+
+    do
+    {
+      *pStateCurnt++ = *pSrc++;
+
+    } while(--i);
+
+    /*Set sum to zero */
+    sum0 = 0;
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* Initialize coeff pointer */
+    pb = pCoeffs;
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2;
+
+    /* Loop over the number of taps.  Unroll by a factor of 4.       
+     ** Repeat until we've computed numTaps-4 coefficients. */
+    while(tapCnt > 0u)
+    {
+      /* Read the Read b[numTaps-1] and b[numTaps-2]  coefficients */
+      c0 = *__SIMD32(pb)++;
+
+      /* Read x[n-numTaps-1] and x[n-numTaps-2]sample */
+      x0 = *__SIMD32(px)++;
+
+      /* Read the b[numTaps-3] and b[numTaps-4] coefficient */
+      c1 = *__SIMD32(pb)++;
+
+      /* Perform the multiply-accumulate */
+      sum0 = __SMLALD(x0, c0, sum0);
+
+      /* Read x[n-numTaps-2] and x[n-numTaps-3] sample */
+      x0 = *__SIMD32(px)++;
+
+      /* Perform the multiply-accumulate */
+      sum0 = __SMLALD(x0, c1, sum0);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = numTaps % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      /* Read coefficients */
+      c0 = *pb++;
+
+      /* Fetch 1 state variable */
+      x0 = *px++;
+
+      /* Perform the multiply-accumulate */
+      sum0 = __SMLALD(x0, c0, sum0);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Advance the state pointer by the decimation factor       
+     * to process the next group of decimation factor number samples */
+    pState = pState + S->M;
+
+    /* Store filter output, smlad returns the values in 2.14 format */
+    /* so downsacle by 15 to get output in 1.15 */
+    *pDst++ = (q15_t) (__SSAT((sum0 >> 15), 16));
+
+    /* Decrement the loop counter */
+    blkCntN3--;
+  }
+
+  /* Processing is complete.       
+   ** Now copy the last numTaps - 1 samples to the satrt of the state buffer.       
+   ** This prepares the state buffer for the next function call. */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+  i = (numTaps - 1u) >> 2u;
+
+  /* copy data */
+  while(i > 0u)
+  {
+    *__SIMD32(pStateCurnt)++ = *__SIMD32(pState)++;
+    *__SIMD32(pStateCurnt)++ = *__SIMD32(pState)++;
+
+    /* Decrement the loop counter */
+    i--;
+  }
+
+  i = (numTaps - 1u) % 0x04u;
+
+  /* copy data */
+  while(i > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    i--;
+  }
+}
+
+#else
+
+
+void arm_fir_decimate_q15(
+  const arm_fir_decimate_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+  q15_t *pState = S->pState;                     /* State pointer */
+  q15_t *pCoeffs = S->pCoeffs;                   /* Coefficient pointer */
+  q15_t *pStateCurnt;                            /* Points to the current sample of the state */
+  q15_t *px;                                     /* Temporary pointer for state buffer */
+  q15_t *pb;                                     /* Temporary pointer coefficient buffer */
+  q15_t x0, x1, c0;                              /* Temporary variables to hold state and coefficient values */
+  q63_t sum0;                                    /* Accumulators */
+  q63_t acc0, acc1;
+  q15_t *px0, *px1;
+  uint32_t blkCntN3;
+  uint32_t numTaps = S->numTaps;                 /* Number of taps */
+  uint32_t i, blkCnt, tapCnt, outBlockSize = blockSize / S->M;  /* Loop counters */
+
+
+  /* S->pState buffer contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = S->pState + (numTaps - 1u);
+
+
+  /* Total number of output samples to be computed */
+  blkCnt = outBlockSize / 2;
+  blkCntN3 = outBlockSize - (2 * blkCnt);
+
+  while(blkCnt > 0u)
+  {
+    /* Copy decimation factor number of new input samples into the state buffer */
+    i = 2 * S->M;
+
+    do
+    {
+      *pStateCurnt++ = *pSrc++;
+
+    } while(--i);
+
+    /* Set accumulator to zero */
+    acc0 = 0;
+    acc1 = 0;
+
+    /* Initialize state pointer */
+    px0 = pState;
+
+    px1 = pState + S->M;
+
+
+    /* Initialize coeff pointer */
+    pb = pCoeffs;
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2;
+
+    /* Loop over the number of taps.  Unroll by a factor of 4.       
+     ** Repeat until we've computed numTaps-4 coefficients. */
+    while(tapCnt > 0u)
+    {
+      /* Read the Read b[numTaps-1] coefficients */
+      c0 = *pb++;
+
+      /* Read x[n-numTaps-1] for sample 0 and for sample 1 */
+      x0 = *px0++;
+      x1 = *px1++;
+
+      /* Perform the multiply-accumulate */
+      acc0 += x0 * c0;
+      acc1 += x1 * c0;
+
+      /* Read the b[numTaps-2] coefficient */
+      c0 = *pb++;
+
+      /* Read x[n-numTaps-2] for sample 0 and sample 1 */
+      x0 = *px0++;
+      x1 = *px1++;
+
+      /* Perform the multiply-accumulate */
+      acc0 += x0 * c0;
+      acc1 += x1 * c0;
+
+      /* Read the b[numTaps-3] coefficients */
+      c0 = *pb++;
+
+      /* Read x[n-numTaps-3] for sample 0 and sample 1 */
+      x0 = *px0++;
+      x1 = *px1++;
+
+      /* Perform the multiply-accumulate */
+      acc0 += x0 * c0;
+      acc1 += x1 * c0;
+
+      /* Read the b[numTaps-4] coefficient */
+      c0 = *pb++;
+
+      /* Read x[n-numTaps-4] for sample 0 and sample 1 */
+      x0 = *px0++;
+      x1 = *px1++;
+
+      /* Perform the multiply-accumulate */
+      acc0 += x0 * c0;
+      acc1 += x1 * c0;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = numTaps % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      /* Read coefficients */
+      c0 = *pb++;
+
+      /* Fetch 1 state variable */
+      x0 = *px0++;
+      x1 = *px1++;
+
+      /* Perform the multiply-accumulate */
+      acc0 += x0 * c0;
+      acc1 += x1 * c0;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Advance the state pointer by the decimation factor       
+     * to process the next group of decimation factor number samples */
+    pState = pState + S->M * 2;
+
+    /* Store filter output, smlad returns the values in 2.14 format */
+    /* so downsacle by 15 to get output in 1.15 */
+
+    *pDst++ = (q15_t) (__SSAT((acc0 >> 15), 16));
+    *pDst++ = (q15_t) (__SSAT((acc1 >> 15), 16));
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  while(blkCntN3 > 0u)
+  {
+    /* Copy decimation factor number of new input samples into the state buffer */
+    i = S->M;
+
+    do
+    {
+      *pStateCurnt++ = *pSrc++;
+
+    } while(--i);
+
+    /*Set sum to zero */
+    sum0 = 0;
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* Initialize coeff pointer */
+    pb = pCoeffs;
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2;
+
+    /* Loop over the number of taps.  Unroll by a factor of 4.       
+     ** Repeat until we've computed numTaps-4 coefficients. */
+    while(tapCnt > 0u)
+    {
+      /* Read the Read b[numTaps-1] coefficients */
+      c0 = *pb++;
+
+      /* Read x[n-numTaps-1] and sample */
+      x0 = *px++;
+
+      /* Perform the multiply-accumulate */
+      sum0 += x0 * c0;
+
+      /* Read the b[numTaps-2] coefficient */
+      c0 = *pb++;
+
+      /* Read x[n-numTaps-2] and  sample */
+      x0 = *px++;
+
+      /* Perform the multiply-accumulate */
+      sum0 += x0 * c0;
+
+      /* Read the b[numTaps-3]  coefficients */
+      c0 = *pb++;
+
+      /* Read x[n-numTaps-3] sample */
+      x0 = *px++;
+
+      /* Perform the multiply-accumulate */
+      sum0 += x0 * c0;
+
+      /* Read the b[numTaps-4] coefficient */
+      c0 = *pb++;
+
+      /* Read x[n-numTaps-4] sample */
+      x0 = *px++;
+
+      /* Perform the multiply-accumulate */
+      sum0 += x0 * c0;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = numTaps % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      /* Read coefficients */
+      c0 = *pb++;
+
+      /* Fetch 1 state variable */
+      x0 = *px++;
+
+      /* Perform the multiply-accumulate */
+      sum0 += x0 * c0;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Advance the state pointer by the decimation factor       
+     * to process the next group of decimation factor number samples */
+    pState = pState + S->M;
+
+    /* Store filter output, smlad returns the values in 2.14 format */
+    /* so downsacle by 15 to get output in 1.15 */
+    *pDst++ = (q15_t) (__SSAT((sum0 >> 15), 16));
+
+    /* Decrement the loop counter */
+    blkCntN3--;
+  }
+
+  /* Processing is complete.       
+   ** Now copy the last numTaps - 1 samples to the satrt of the state buffer.       
+   ** This prepares the state buffer for the next function call. */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+  i = (numTaps - 1u) >> 2u;
+
+  /* copy data */
+  while(i > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    i--;
+  }
+
+  i = (numTaps - 1u) % 0x04u;
+
+  /* copy data */
+  while(i > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    i--;
+  }
+}
+
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+#else
+
+
+void arm_fir_decimate_q15(
+  const arm_fir_decimate_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+  q15_t *pState = S->pState;                     /* State pointer */
+  q15_t *pCoeffs = S->pCoeffs;                   /* Coefficient pointer */
+  q15_t *pStateCurnt;                            /* Points to the current sample of the state */
+  q15_t *px;                                     /* Temporary pointer for state buffer */
+  q15_t *pb;                                     /* Temporary pointer coefficient buffer */
+  q31_t x0, c0;                                  /* Temporary variables to hold state and coefficient values */
+  q63_t sum0;                                    /* Accumulators */
+  uint32_t numTaps = S->numTaps;                 /* Number of taps */
+  uint32_t i, blkCnt, tapCnt, outBlockSize = blockSize / S->M;  /* Loop counters */
+
+
+
+/* Run the below code for Cortex-M0 */
+
+  /* S->pState buffer contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = S->pState + (numTaps - 1u);
+
+  /* Total number of output samples to be computed */
+  blkCnt = outBlockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* Copy decimation factor number of new input samples into the state buffer */
+    i = S->M;
+
+    do
+    {
+      *pStateCurnt++ = *pSrc++;
+
+    } while(--i);
+
+    /*Set sum to zero */
+    sum0 = 0;
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* Initialize coeff pointer */
+    pb = pCoeffs;
+
+    tapCnt = numTaps;
+
+    while(tapCnt > 0u)
+    {
+      /* Read coefficients */
+      c0 = *pb++;
+
+      /* Fetch 1 state variable */
+      x0 = *px++;
+
+      /* Perform the multiply-accumulate */
+      sum0 += (q31_t) x0 *c0;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Advance the state pointer by the decimation factor           
+     * to process the next group of decimation factor number samples */
+    pState = pState + S->M;
+
+    /*Store filter output , smlad will return the values in 2.14 format */
+    /* so downsacle by 15 to get output in 1.15 */
+    *pDst++ = (q15_t) (__SSAT((sum0 >> 15), 16));
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Processing is complete.         
+   ** Now copy the last numTaps - 1 samples to the start of the state buffer.       
+   ** This prepares the state buffer for the next function call. */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+  i = numTaps - 1u;
+
+  /* copy data */
+  while(i > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    i--;
+  }
+
+
+}
+#endif /*   #ifndef ARM_MATH_CM0 */
+
+
+/**    
+ * @} end of FIR_decimate group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_q31.c
new file mode 100644
index 0000000000..59c0fed7f8
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_q31.c
@@ -0,0 +1,306 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_fir_decimate_q31.c    
+*    
+* Description:	Q31 FIR Decimator.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR_decimate    
+ * @{    
+ */
+
+/**    
+ * @brief Processing function for the Q31 FIR decimator.    
+ * @param[in] *S points to an instance of the Q31 FIR decimator structure.    
+ * @param[in] *pSrc points to the block of input data.    
+ * @param[out] *pDst points to the block of output data    
+ * @param[in] blockSize number of input samples to process per call.    
+ * @return none    
+ *    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function is implemented using an internal 64-bit accumulator.    
+ * The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit.    
+ * Thus, if the accumulator result overflows it wraps around rather than clip.    
+ * In order to avoid overflows completely the input signal must be scaled down by log2(numTaps) bits (where log2 is read as log to the base 2).    
+ * After all multiply-accumulates are performed, the 2.62 accumulator is truncated to 1.32 format and then saturated to 1.31 format.    
+ *    
+ * \par    
+ * Refer to the function arm_fir_decimate_fast_q31() for a faster but less precise implementation of this function for Cortex-M3 and Cortex-M4.    
+ */
+
+void arm_fir_decimate_q31(
+  const arm_fir_decimate_instance_q31 * S,
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize)
+{
+  q31_t *pState = S->pState;                     /* State pointer */
+  q31_t *pCoeffs = S->pCoeffs;                   /* Coefficient pointer */
+  q31_t *pStateCurnt;                            /* Points to the current sample of the state */
+  q31_t x0, c0;                                  /* Temporary variables to hold state and coefficient values */
+  q31_t *px;                                     /* Temporary pointers for state buffer */
+  q31_t *pb;                                     /* Temporary pointers for coefficient buffer */
+  q63_t sum0;                                    /* Accumulator */
+  uint32_t numTaps = S->numTaps;                 /* Number of taps */
+  uint32_t i, tapCnt, blkCnt, outBlockSize = blockSize / S->M;  /* Loop counters */
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /* S->pState buffer contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = S->pState + (numTaps - 1u);
+
+  /* Total number of output samples to be computed */
+  blkCnt = outBlockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* Copy decimation factor number of new input samples into the state buffer */
+    i = S->M;
+
+    do
+    {
+      *pStateCurnt++ = *pSrc++;
+
+    } while(--i);
+
+    /* Set accumulator to zero */
+    sum0 = 0;
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* Initialize coeff pointer */
+    pb = pCoeffs;
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2;
+
+    /* Loop over the number of taps.  Unroll by a factor of 4.    
+     ** Repeat until we've computed numTaps-4 coefficients. */
+    while(tapCnt > 0u)
+    {
+      /* Read the b[numTaps-1] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-1] sample */
+      x0 = *(px++);
+
+      /* Perform the multiply-accumulate */
+      sum0 += (q63_t) x0 *c0;
+
+      /* Read the b[numTaps-2] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-2] sample */
+      x0 = *(px++);
+
+      /* Perform the multiply-accumulate */
+      sum0 += (q63_t) x0 *c0;
+
+      /* Read the b[numTaps-3] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-3] sample */
+      x0 = *(px++);
+
+      /* Perform the multiply-accumulate */
+      sum0 += (q63_t) x0 *c0;
+
+      /* Read the b[numTaps-4] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-4] sample */
+      x0 = *(px++);
+
+      /* Perform the multiply-accumulate */
+      sum0 += (q63_t) x0 *c0;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = numTaps % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      /* Read coefficients */
+      c0 = *(pb++);
+
+      /* Fetch 1 state variable */
+      x0 = *(px++);
+
+      /* Perform the multiply-accumulate */
+      sum0 += (q63_t) x0 *c0;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Advance the state pointer by the decimation factor    
+     * to process the next group of decimation factor number samples */
+    pState = pState + S->M;
+
+    /* The result is in the accumulator, store in the destination buffer. */
+    *pDst++ = (q31_t) (sum0 >> 31);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Processing is complete.    
+   ** Now copy the last numTaps - 1 samples to the satrt of the state buffer.    
+   ** This prepares the state buffer for the next function call. */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+  i = (numTaps - 1u) >> 2u;
+
+  /* copy data */
+  while(i > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    i--;
+  }
+
+  i = (numTaps - 1u) % 0x04u;
+
+  /* copy data */
+  while(i > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    i--;
+  }
+
+#else
+
+/* Run the below code for Cortex-M0 */
+
+  /* S->pState buffer contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = S->pState + (numTaps - 1u);
+
+  /* Total number of output samples to be computed */
+  blkCnt = outBlockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* Copy decimation factor number of new input samples into the state buffer */
+    i = S->M;
+
+    do
+    {
+      *pStateCurnt++ = *pSrc++;
+
+    } while(--i);
+
+    /* Set accumulator to zero */
+    sum0 = 0;
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* Initialize coeff pointer */
+    pb = pCoeffs;
+
+    tapCnt = numTaps;
+
+    while(tapCnt > 0u)
+    {
+      /* Read coefficients */
+      c0 = *pb++;
+
+      /* Fetch 1 state variable */
+      x0 = *px++;
+
+      /* Perform the multiply-accumulate */
+      sum0 += (q63_t) x0 *c0;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Advance the state pointer by the decimation factor           
+     * to process the next group of decimation factor number samples */
+    pState = pState + S->M;
+
+    /* The result is in the accumulator, store in the destination buffer. */
+    *pDst++ = (q31_t) (sum0 >> 31);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Processing is complete.         
+   ** Now copy the last numTaps - 1 samples to the start of the state buffer.       
+   ** This prepares the state buffer for the next function call. */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+  i = numTaps - 1u;
+
+  /* copy data */
+  while(i > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    i--;
+  }
+
+#endif /*   #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of FIR_decimate group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_f32.c
new file mode 100644
index 0000000000..7f951f86bc
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_f32.c
@@ -0,0 +1,554 @@
+/* ----------------------------------------------------------------------  
+* Copyright (C) 2010 ARM Limited. All rights reserved.  
+*  
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*  
+* Project: 	    CMSIS DSP Library  
+* Title:	    arm_fir_f32.c  
+*  
+* Description:	Floating-point FIR filter processing function.  
+*  
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.2 2010/11/11  
+*    Documentation updated.   
+*  
+* Version 1.0.1 2010/10/05   
+*    Production release and review comments incorporated.  
+*  
+* Version 1.0.0 2010/09/20   
+*    Production release and review comments incorporated.  
+*  
+* Version 0.0.5  2010/04/26   
+* 	 incorporated review comments and updated with latest CMSIS layer  
+*  
+* Version 0.0.3  2010/03/10   
+*    Initial version  
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**  
+ * @ingroup groupFilters  
+ */
+
+/**  
+ * @defgroup FIR Finite Impulse Response (FIR) Filters  
+ *  
+ * This set of functions implements Finite Impulse Response (FIR) filters  
+ * for Q7, Q15, Q31, and floating-point data types.  Fast versions of Q15 and Q31 are also provided.  
+ * The functions operate on blocks of input and output data and each call to the function processes  
+ * blockSize samples through the filter.  pSrc and  
+ * pDst points to input and output arrays containing blockSize values.  
+ *  
+ * \par Algorithm:  
+ * The FIR filter algorithm is based upon a sequence of multiply-accumulate (MAC) operations.  
+ * Each filter coefficient b[n] is multiplied by a state variable which equals a previous input sample x[n].  
+ * 
  
+ *    y[n] = b[0] * x[n] + b[1] * x[n-1] + b[2] * x[n-2] + ...+ b[numTaps-1] * x[n-numTaps+1]  
+ * 
  
+ * \par  
+ * \image html FIR.gif "Finite Impulse Response filter"  
+ * \par  
+ * pCoeffs points to a coefficient array of size numTaps.  
+ * Coefficients are stored in time reversed order.  
+ * \par  
+ * 
  
+ *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}  
+ * 
  
+ * \par  
+ * pState points to a state array of size numTaps + blockSize - 1.  
+ * Samples in the state buffer are stored in the following order.  
+ * \par  
+ * 
  
+ *    {x[n-numTaps+1], x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2]....x[0], x[1], ..., x[blockSize-1]}  
+ * 
  
+ * \par  
+ * Note that the length of the state buffer exceeds the length of the coefficient array by blockSize-1.  
+ * The increased state buffer length allows circular addressing, which is traditionally used in the FIR filters,  
+ * to be avoided and yields a significant speed improvement.  
+ * The state variables are updated after each block of data is processed; the coefficients are untouched.  
+ * \par Instance Structure  
+ * The coefficients and state variables for a filter are stored together in an instance data structure.  
+ * A separate instance structure must be defined for each filter.  
+ * Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.  
+ * There are separate instance structure declarations for each of the 4 supported data types.  
+ *  
+ * \par Initialization Functions  
+ * There is also an associated initialization function for each data type.  
+ * The initialization function performs the following operations:  
+ * - Sets the values of the internal structure fields.  
+ * - Zeros out the values in the state buffer.  
+ *  
+ * \par  
+ * Use of the initialization function is optional.  
+ * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.  
+ * To place an instance structure into a const data section, the instance structure must be manually initialized.  
+ * Set the values in the state buffer to zeros before static initialization.  
+ * The code below statically initializes each of the 4 different data type filter instance structures  
+ * 
  
+ *arm_fir_instance_f32 S = {numTaps, pState, pCoeffs};  
+ *arm_fir_instance_q31 S = {numTaps, pState, pCoeffs};  
+ *arm_fir_instance_q15 S = {numTaps, pState, pCoeffs};  
+ *arm_fir_instance_q7 S =  {numTaps, pState, pCoeffs};  
+ * 
  
+ *  
+ * where numTaps is the number of filter coefficients in the filter; pState is the address of the state buffer;  
+ * pCoeffs is the address of the coefficient buffer.  
+ *  
+ * \par Fixed-Point Behavior  
+ * Care must be taken when using the fixed-point versions of the FIR filter functions.  
+ * In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.  
+ * Refer to the function specific documentation below for usage guidelines.  
+ */
+
+/**  
+ * @addtogroup FIR  
+ * @{  
+ */
+
+/**  
+ *  
+ * @param[in]  *S points to an instance of the floating-point FIR filter structure.  
+ * @param[in]  *pSrc points to the block of input data.  
+ * @param[out] *pDst points to the block of output data.  
+ * @param[in]  blockSize number of samples to process per call.  
+ * @return     none.  
+ *  
+ */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+void arm_fir_f32(
+  const arm_fir_instance_f32 * S,
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize)
+{
+  float32_t *pState = S->pState;                 /* State pointer */
+  float32_t *pCoeffs = S->pCoeffs;               /* Coefficient pointer */
+  float32_t *pStateCurnt;                        /* Points to the current sample of the state */
+  float32_t *px, *pb;                            /* Temporary pointers for state and coefficient buffers */
+  float32_t acc0, acc1, acc2, acc3, acc4, acc5, acc6, acc7;     /* Accumulators */
+  float32_t x0, x1, x2, x3, x4, x5, x6, x7, c0;  /* Temporary variables to hold state and coefficient values */
+  uint32_t numTaps = S->numTaps;                 /* Number of filter coefficients in the filter */
+  uint32_t i, tapCnt, blkCnt;                    /* Loop counters */
+
+  /* S->pState points to state array which contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = &(S->pState[(numTaps - 1u)]);
+
+  /* Apply loop unrolling and compute 4 output values simultaneously.  
+   * The variables acc0 ... acc3 hold output values that are being computed:  
+   *  
+   *    acc0 =  b[numTaps-1] * x[n-numTaps-1] + b[numTaps-2] * x[n-numTaps-2] + b[numTaps-3] * x[n-numTaps-3] +...+ b[0] * x[0]  
+   *    acc1 =  b[numTaps-1] * x[n-numTaps] +   b[numTaps-2] * x[n-numTaps-1] + b[numTaps-3] * x[n-numTaps-2] +...+ b[0] * x[1]  
+   *    acc2 =  b[numTaps-1] * x[n-numTaps+1] + b[numTaps-2] * x[n-numTaps] +   b[numTaps-3] * x[n-numTaps-1] +...+ b[0] * x[2]  
+   *    acc3 =  b[numTaps-1] * x[n-numTaps+2] + b[numTaps-2] * x[n-numTaps+1] + b[numTaps-3] * x[n-numTaps]   +...+ b[0] * x[3]  
+   */
+  blkCnt = blockSize >> 3;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.  
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* Copy four new input samples into the state buffer */
+    *pStateCurnt++ = *pSrc++;
+    *pStateCurnt++ = *pSrc++;
+    *pStateCurnt++ = *pSrc++;
+    *pStateCurnt++ = *pSrc++;
+    *pStateCurnt++ = *pSrc++;
+    *pStateCurnt++ = *pSrc++;
+    *pStateCurnt++ = *pSrc++;
+    *pStateCurnt++ = *pSrc++;
+
+    /* Set all accumulators to zero */
+    acc0 = 0.0f;
+    acc1 = 0.0f;
+    acc2 = 0.0f;
+    acc3 = 0.0f;
+    acc4 = 0.0f;
+    acc5 = 0.0f;
+    acc6 = 0.0f;
+    acc7 = 0.0f;
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* Initialize coeff pointer */
+    pb = (pCoeffs);
+
+    /* Read the first three samples from the state buffer:  x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2] */
+    x0 = *px++;
+    x1 = *px++;
+    x2 = *px++;
+    x3 = *px++;
+    x4 = *px++;
+    x5 = *px++;
+    x6 = *px++;
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 3u;
+
+    /* Loop over the number of taps.  Unroll by a factor of 4.  
+     ** Repeat until we've computed numTaps-4 coefficients. */
+    while(tapCnt > 0u)
+    {
+      /* Read the b[numTaps-1] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-3] sample */
+      x7 = *(px++);
+
+      /* acc0 +=  b[numTaps-1] * x[n-numTaps] */
+      acc0 += x0 * c0;
+
+      /* acc1 +=  b[numTaps-1] * x[n-numTaps-1] */
+      acc1 += x1 * c0;
+
+      /* acc2 +=  b[numTaps-1] * x[n-numTaps-2] */
+      acc2 += x2 * c0;
+
+      /* acc3 +=  b[numTaps-1] * x[n-numTaps-3] */
+      acc3 += x3 * c0;
+
+      /* acc4 +=  b[numTaps-1] * x[n-numTaps-4] */
+      acc4 += x4 * c0;
+
+      /* acc1 +=  b[numTaps-1] * x[n-numTaps-5] */
+      acc5 += x5 * c0;
+
+      /* acc2 +=  b[numTaps-1] * x[n-numTaps-6] */
+      acc6 += x6 * c0;
+
+      /* acc3 +=  b[numTaps-1] * x[n-numTaps-7] */
+      acc7 += x7 * c0;
+
+      /* Read the b[numTaps-2] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-4] sample */
+      x0 = *(px++);
+
+      /* Perform the multiply-accumulate */
+      acc0 += x1 * c0;
+      acc1 += x2 * c0;
+      acc2 += x3 * c0;
+      acc3 += x4 * c0;
+      acc4 += x5 * c0;
+      acc5 += x6 * c0;
+      acc6 += x7 * c0;
+      acc7 += x0 * c0;
+
+      /* Read the b[numTaps-3] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-5] sample */
+      x1 = *(px++);
+
+      /* Perform the multiply-accumulates */
+      acc0 += x2 * c0;
+      acc1 += x3 * c0;
+      acc2 += x4 * c0;
+      acc3 += x5 * c0;
+      acc4 += x6 * c0;
+      acc5 += x7 * c0;
+      acc6 += x0 * c0;
+      acc7 += x1 * c0;
+
+      /* Read the b[numTaps-4] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-6] sample */
+      x2 = *(px++);
+
+      /* Perform the multiply-accumulates */
+      acc0 += x3 * c0;
+      acc1 += x4 * c0;
+      acc2 += x5 * c0;
+      acc3 += x6 * c0;
+      acc4 += x7 * c0;
+      acc5 += x0 * c0;
+      acc6 += x1 * c0;
+      acc7 += x2 * c0;
+
+      /* Read the b[numTaps-4] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-6] sample */
+      x3 = *(px++);
+
+      /* Perform the multiply-accumulates */
+      acc0 += x4 * c0;
+      acc1 += x5 * c0;
+      acc2 += x6 * c0;
+      acc3 += x7 * c0;
+      acc4 += x0 * c0;
+      acc5 += x1 * c0;
+      acc6 += x2 * c0;
+      acc7 += x3 * c0;
+
+      /* Read the b[numTaps-4] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-6] sample */
+      x4 = *(px++);
+
+      /* Perform the multiply-accumulates */
+      acc0 += x5 * c0;
+      acc1 += x6 * c0;
+      acc2 += x7 * c0;
+      acc3 += x0 * c0;
+      acc4 += x1 * c0;
+      acc5 += x2 * c0;
+      acc6 += x3 * c0;
+      acc7 += x4 * c0;
+
+      /* Read the b[numTaps-4] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-6] sample */
+      x5 = *(px++);
+
+      /* Perform the multiply-accumulates */
+      acc0 += x6 * c0;
+      acc1 += x7 * c0;
+      acc2 += x0 * c0;
+      acc3 += x1 * c0;
+      acc4 += x2 * c0;
+      acc5 += x3 * c0;
+      acc6 += x4 * c0;
+      acc7 += x5 * c0;
+
+      /* Read the b[numTaps-4] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-6] sample */
+      x6 = *(px++);
+
+      /* Perform the multiply-accumulates */
+      acc0 += x7 * c0;
+      acc1 += x0 * c0;
+      acc2 += x1 * c0;
+      acc3 += x2 * c0;
+      acc4 += x3 * c0;
+      acc5 += x4 * c0;
+      acc6 += x5 * c0;
+      acc7 += x6 * c0;
+
+      tapCnt--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = numTaps % 0x8u;
+
+    while(tapCnt > 0u)
+    {
+      /* Read coefficients */
+      c0 = *(pb++);
+
+      /* Fetch 1 state variable */
+      x7 = *(px++);
+
+      /* Perform the multiply-accumulates */
+      acc0 += x0 * c0;
+      acc1 += x1 * c0;
+      acc2 += x2 * c0;
+      acc3 += x3 * c0;
+      acc4 += x4 * c0;
+      acc5 += x5 * c0;
+      acc6 += x6 * c0;
+      acc7 += x7 * c0;
+
+      /* Reuse the present sample states for next sample */
+      x0 = x1;
+      x1 = x2;
+      x2 = x3;
+      x3 = x4;
+      x4 = x5;
+      x5 = x6;
+      x6 = x7;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Advance the state pointer by 4 to process the next group of 4 samples */
+    pState = pState + 8;
+
+    /* The results in the 4 accumulators, store in the destination buffer. */
+    *pDst++ = acc0;
+    *pDst++ = acc1;
+    *pDst++ = acc2;
+    *pDst++ = acc3;
+    *pDst++ = acc4;
+    *pDst++ = acc5;
+    *pDst++ = acc6;
+    *pDst++ = acc7;
+
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.  
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x8u;
+
+  while(blkCnt > 0u)
+  {
+    /* Copy one sample at a time into state buffer */
+    *pStateCurnt++ = *pSrc++;
+
+    /* Set the accumulator to zero */
+    acc0 = 0.0f;
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* Initialize Coefficient pointer */
+    pb = (pCoeffs);
+
+    i = numTaps;
+
+    /* Perform the multiply-accumulates */
+    do
+    {
+      acc0 += *px++ * *pb++;
+      i--;
+
+    } while(i > 0u);
+
+    /* The result is store in the destination buffer. */
+    *pDst++ = acc0;
+
+    /* Advance state pointer by 1 for the next sample */
+    pState = pState + 1;
+
+    blkCnt--;
+  }
+
+  /* Processing is complete.  
+   ** Now copy the last numTaps - 1 samples to the satrt of the state buffer.  
+   ** This prepares the state buffer for the next function call. */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+  tapCnt = (numTaps - 1u) >> 2u;
+
+  /* copy data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+  /* Calculate remaining number of copies */
+  tapCnt = (numTaps - 1u) % 0x4u;
+
+  /* Copy the remaining q31_t data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+}
+
+#else
+
+void arm_fir_f32(
+  const arm_fir_instance_f32 * S,
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize)
+{
+  float32_t *pState = S->pState;                 /* State pointer */
+  float32_t *pCoeffs = S->pCoeffs;               /* Coefficient pointer */
+  float32_t *pStateCurnt;                        /* Points to the current sample of the state */
+  float32_t *px, *pb;                            /* Temporary pointers for state and coefficient buffers */
+  uint32_t numTaps = S->numTaps;                 /* Number of filter coefficients in the filter */
+  uint32_t i, tapCnt, blkCnt;                    /* Loop counters */
+
+  /* Run the below code for Cortex-M0 */
+
+  float32_t acc;
+
+  /* S->pState points to state array which contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = &(S->pState[(numTaps - 1u)]);
+
+  /* Initialize blkCnt with blockSize */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* Copy one sample at a time into state buffer */
+    *pStateCurnt++ = *pSrc++;
+
+    /* Set the accumulator to zero */
+    acc = 0.0f;
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* Initialize Coefficient pointer */
+    pb = pCoeffs;
+
+    i = numTaps;
+
+    /* Perform the multiply-accumulates */
+    do
+    {
+      /* acc =  b[numTaps-1] * x[n-numTaps-1] + b[numTaps-2] * x[n-numTaps-2] + b[numTaps-3] * x[n-numTaps-3] +...+ b[0] * x[0] */
+      acc += *px++ * *pb++;
+      i--;
+
+    } while(i > 0u);
+
+    /* The result is store in the destination buffer. */
+    *pDst++ = acc;
+
+    /* Advance state pointer by 1 for the next sample */
+    pState = pState + 1;
+
+    blkCnt--;
+  }
+
+  /* Processing is complete.         
+   ** Now copy the last numTaps - 1 samples to the starting of the state buffer.       
+   ** This prepares the state buffer for the next function call. */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+  /* Copy numTaps number of values */
+  tapCnt = numTaps - 1u;
+
+  /* Copy data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+}
+
+#endif /*   #ifndef ARM_MATH_CM0 */
+
+/**  
+ * @} end of FIR group  
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_fast_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_fast_q15.c
new file mode 100644
index 0000000000..59abff2f55
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_fast_q15.c
@@ -0,0 +1,341 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_fir_fast_q15.c    
+*    
+* Description:  Q15 Fast FIR filter processing function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.9  2010/08/16     
+*    Initial version    
+*    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR    
+ * @{    
+ */
+
+/**    
+ * @param[in] *S points to an instance of the Q15 FIR filter structure.    
+ * @param[in] *pSrc points to the block of input data.    
+ * @param[out] *pDst points to the block of output data.    
+ * @param[in] blockSize number of samples to process per call.    
+ * @return none.    
+ *    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * This fast version uses a 32-bit accumulator with 2.30 format.    
+ * The accumulator maintains full precision of the intermediate multiplication results but provides only a single guard bit.    
+ * Thus, if the accumulator result overflows it wraps around and distorts the result.    
+ * In order to avoid overflows completely the input signal must be scaled down by log2(numTaps) bits.    
+ * The 2.30 accumulator is then truncated to 2.15 format and saturated to yield the 1.15 result.    
+ *    
+ * \par    
+ * Refer to the function arm_fir_q15() for a slower implementation of this function which uses 64-bit accumulation to avoid wrap around distortion.  Both the slow and the fast versions use the same instance structure.    
+ * Use the function arm_fir_init_q15() to initialize the filter structure.    
+ */
+
+void arm_fir_fast_q15(
+  const arm_fir_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+  q15_t *pState = S->pState;                     /* State pointer */
+  q15_t *pCoeffs = S->pCoeffs;                   /* Coefficient pointer */
+  q15_t *pStateCurnt;                            /* Points to the current sample of the state */
+  q31_t acc0, acc1, acc2, acc3;                  /* Accumulators */
+  q15_t *pb;                                     /* Temporary pointer for coefficient buffer */
+  q15_t *px;                                     /* Temporary q31 pointer for SIMD state buffer accesses */
+  q31_t x0, x1, x2, c0;                          /* Temporary variables to hold SIMD state and coefficient values */
+  uint32_t numTaps = S->numTaps;                 /* Number of taps in the filter */
+  uint32_t tapCnt, blkCnt;                       /* Loop counters */
+
+
+  /* S->pState points to state array which contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = &(S->pState[(numTaps - 1u)]);
+
+  /* Apply loop unrolling and compute 4 output values simultaneously.      
+   * The variables acc0 ... acc3 hold output values that are being computed:      
+   *      
+   *    acc0 =  b[numTaps-1] * x[n-numTaps-1] + b[numTaps-2] * x[n-numTaps-2] + b[numTaps-3] * x[n-numTaps-3] +...+ b[0] * x[0]      
+   *    acc1 =  b[numTaps-1] * x[n-numTaps] +   b[numTaps-2] * x[n-numTaps-1] + b[numTaps-3] * x[n-numTaps-2] +...+ b[0] * x[1]      
+   *    acc2 =  b[numTaps-1] * x[n-numTaps+1] + b[numTaps-2] * x[n-numTaps] +   b[numTaps-3] * x[n-numTaps-1] +...+ b[0] * x[2]      
+   *    acc3 =  b[numTaps-1] * x[n-numTaps+2] + b[numTaps-2] * x[n-numTaps+1] + b[numTaps-3] * x[n-numTaps]   +...+ b[0] * x[3]      
+   */
+
+  blkCnt = blockSize >> 2;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.      
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* Copy four new input samples into the state buffer.      
+     ** Use 32-bit SIMD to move the 16-bit data.  Only requires two copies. */
+    *pStateCurnt++ = *pSrc++;
+    *pStateCurnt++ = *pSrc++;
+    *pStateCurnt++ = *pSrc++;
+    *pStateCurnt++ = *pSrc++;
+
+
+    /* Set all accumulators to zero */
+    acc0 = 0;
+    acc1 = 0;
+    acc2 = 0;
+    acc3 = 0;
+
+    /* Typecast q15_t pointer to q31_t pointer for state reading in q31_t */
+    px = pState;
+
+    /* Typecast q15_t pointer to q31_t pointer for coefficient reading in q31_t */
+    pb = pCoeffs;
+
+    /* Read the first two samples from the state buffer:  x[n-N], x[n-N-1] */
+    x0 = *__SIMD32(px)++;
+
+    /* Read the third and forth samples from the state buffer: x[n-N-2], x[n-N-3] */
+    x2 = *__SIMD32(px)++;
+
+    /* Loop over the number of taps.  Unroll by a factor of 4.      
+     ** Repeat until we've computed numTaps-(numTaps%4) coefficients. */
+    tapCnt = numTaps >> 2;
+
+    while(tapCnt > 0)
+    {
+      /* Read the first two coefficients using SIMD:  b[N] and b[N-1] coefficients */
+      c0 = *__SIMD32(pb)++;
+
+      /* acc0 +=  b[N] * x[n-N] + b[N-1] * x[n-N-1] */
+      acc0 = __SMLAD(x0, c0, acc0);
+
+      /* acc2 +=  b[N] * x[n-N-2] + b[N-1] * x[n-N-3] */
+      acc2 = __SMLAD(x2, c0, acc2);
+
+      /* pack  x[n-N-1] and x[n-N-2] */
+#ifndef ARM_MATH_BIG_ENDIAN
+      x1 = __PKHBT(x2, x0, 0);
+#else
+      x1 = __PKHBT(x0, x2, 0);
+#endif
+
+      /* Read state x[n-N-4], x[n-N-5] */
+      x0 = _SIMD32_OFFSET(px);
+
+      /* acc1 +=  b[N] * x[n-N-1] + b[N-1] * x[n-N-2] */
+      acc1 = __SMLADX(x1, c0, acc1);
+
+      /* pack  x[n-N-3] and x[n-N-4] */
+#ifndef ARM_MATH_BIG_ENDIAN
+      x1 = __PKHBT(x0, x2, 0);
+#else
+      x1 = __PKHBT(x2, x0, 0);
+#endif
+
+      /* acc3 +=  b[N] * x[n-N-3] + b[N-1] * x[n-N-4] */
+      acc3 = __SMLADX(x1, c0, acc3);
+
+      /* Read coefficients b[N-2], b[N-3] */
+      c0 = *__SIMD32(pb)++;
+
+      /* acc0 +=  b[N-2] * x[n-N-2] + b[N-3] * x[n-N-3] */
+      acc0 = __SMLAD(x2, c0, acc0);
+
+      /* Read state x[n-N-6], x[n-N-7] with offset */
+      x2 = _SIMD32_OFFSET(px + 2u);
+
+      /* acc2 +=  b[N-2] * x[n-N-4] + b[N-3] * x[n-N-5] */
+      acc2 = __SMLAD(x0, c0, acc2);
+
+      /* acc1 +=  b[N-2] * x[n-N-3] + b[N-3] * x[n-N-4] */
+      acc1 = __SMLADX(x1, c0, acc1);
+
+      /* pack  x[n-N-5] and x[n-N-6] */
+#ifndef ARM_MATH_BIG_ENDIAN
+      x1 = __PKHBT(x2, x0, 0);
+#else
+      x1 = __PKHBT(x0, x2, 0);
+#endif
+
+      /* acc3 +=  b[N-2] * x[n-N-5] + b[N-3] * x[n-N-6] */
+      acc3 = __SMLADX(x1, c0, acc3);
+
+      /* Update state pointer for next state reading */
+      px += 4u;
+
+      /* Decrement tap count */
+      tapCnt--;
+
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps.       
+     ** This is always be 2 taps since the filter length is even. */
+    if((numTaps & 0x3u) != 0u)
+    {
+
+      /* Read last two coefficients */
+      c0 = *__SIMD32(pb)++;
+
+      /* Perform the multiply-accumulates */
+      acc0 = __SMLAD(x0, c0, acc0);
+      acc2 = __SMLAD(x2, c0, acc2);
+
+      /* pack state variables */
+#ifndef ARM_MATH_BIG_ENDIAN
+      x1 = __PKHBT(x2, x0, 0);
+#else
+      x1 = __PKHBT(x0, x2, 0);
+#endif
+
+      /* Read last state variables */
+      x0 = *__SIMD32(px);
+
+      /* Perform the multiply-accumulates */
+      acc1 = __SMLADX(x1, c0, acc1);
+
+      /* pack state variables */
+#ifndef ARM_MATH_BIG_ENDIAN
+      x1 = __PKHBT(x0, x2, 0);
+#else
+      x1 = __PKHBT(x2, x0, 0);
+#endif
+
+      /* Perform the multiply-accumulates */
+      acc3 = __SMLADX(x1, c0, acc3);
+    }
+
+    /* The results in the 4 accumulators are in 2.30 format.  Convert to 1.15 with saturation.       
+     ** Then store the 4 outputs in the destination buffer. */
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    *__SIMD32(pDst)++ =
+      __PKHBT(__SSAT((acc0 >> 15), 16), __SSAT((acc1 >> 15), 16), 16);
+
+    *__SIMD32(pDst)++ =
+      __PKHBT(__SSAT((acc2 >> 15), 16), __SSAT((acc3 >> 15), 16), 16);
+
+#else
+
+    *__SIMD32(pDst)++ =
+      __PKHBT(__SSAT((acc1 >> 15), 16), __SSAT((acc0 >> 15), 16), 16);
+
+    *__SIMD32(pDst)++ =
+      __PKHBT(__SSAT((acc3 >> 15), 16), __SSAT((acc2 >> 15), 16), 16);
+
+
+#endif /*      #ifndef ARM_MATH_BIG_ENDIAN       */
+
+    /* Advance the state pointer by 4 to process the next group of 4 samples */
+    pState = pState + 4u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.      
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+  while(blkCnt > 0u)
+  {
+    /* Copy two samples into state buffer */
+    *pStateCurnt++ = *pSrc++;
+
+    /* Set the accumulator to zero */
+    acc0 = 0;
+
+    /* Use SIMD to hold states and coefficients */
+    px = pState;
+    pb = pCoeffs;
+
+    tapCnt = numTaps >> 1u;
+
+    do
+    {
+
+      acc0 += (q31_t) * px++ * *pb++;
+	  acc0 += (q31_t) * px++ * *pb++;
+
+      tapCnt--;
+    }
+    while(tapCnt > 0u);
+
+    /* The result is in 2.30 format.  Convert to 1.15 with saturation.      
+     ** Then store the output in the destination buffer. */
+    *pDst++ = (q15_t) (__SSAT((acc0 >> 15), 16));
+
+    /* Advance state pointer by 1 for the next sample */
+    pState = pState + 1u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Processing is complete.      
+   ** Now copy the last numTaps - 1 samples to the satrt of the state buffer.      
+   ** This prepares the state buffer for the next function call. */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+  /* Calculation of count for copying integer writes */
+  tapCnt = (numTaps - 1u) >> 2;
+
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+
+    tapCnt--;
+
+  }
+
+  /* Calculation of count for remaining q15_t data */
+  tapCnt = (numTaps - 1u) % 0x4u;
+
+  /* copy remaining data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+}
+
+/**    
+ * @} end of FIR group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_fast_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_fast_q31.c
new file mode 100644
index 0000000000..e384ff9732
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_fast_q31.c
@@ -0,0 +1,309 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_fir_fast_q31.c    
+*    
+* Description:	Processing function for the Q31 Fast FIR filter.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.9  2010/08/27     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR    
+ * @{    
+ */
+
+/**    
+ * @param[in] *S points to an instance of the Q31 structure.    
+ * @param[in] *pSrc points to the block of input data.    
+ * @param[out] *pDst points to the block output data.    
+ * @param[in] blockSize number of samples to process per call.    
+ * @return none.    
+ *    
+ * Scaling and Overflow Behavior:    
+ *    
+ * \par    
+ * This function is optimized for speed at the expense of fixed-point precision and overflow protection.    
+ * The result of each 1.31 x 1.31 multiplication is truncated to 2.30 format.    
+ * These intermediate results are added to a 2.30 accumulator.    
+ * Finally, the accumulator is saturated and converted to a 1.31 result.    
+ * The fast version has the same overflow behavior as the standard version and provides less precision since it discards the low 32 bits of each multiplication result.    
+ * In order to avoid overflows completely the input signal must be scaled down by log2(numTaps) bits.    
+ *    
+ * \par    
+ * Refer to the function arm_fir_q31() for a slower implementation of this function which uses a 64-bit accumulator to provide higher precision.  Both the slow and the fast versions use the same instance structure.    
+ * Use the function arm_fir_init_q31() to initialize the filter structure.    
+ */
+
+void arm_fir_fast_q31(
+  const arm_fir_instance_q31 * S,
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize)
+{
+  q31_t *pState = S->pState;                     /* State pointer */
+  q31_t *pCoeffs = S->pCoeffs;                   /* Coefficient pointer */
+  q31_t *pStateCurnt;                            /* Points to the current sample of the state */
+  q31_t x0, x1, x2, x3;                          /* Temporary variables to hold state */
+  q31_t c0;                                      /* Temporary variable to hold coefficient value */
+  q31_t *px;                                     /* Temporary pointer for state */
+  q31_t *pb;                                     /* Temporary pointer for coefficient buffer */
+  q31_t acc0, acc1, acc2, acc3;                  /* Accumulators */
+  uint32_t numTaps = S->numTaps;                 /* Number of filter coefficients in the filter */
+  uint32_t i, tapCnt, blkCnt;                    /* Loop counters */
+
+  /* S->pState points to buffer which contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = &(S->pState[(numTaps - 1u)]);
+
+  /* Apply loop unrolling and compute 4 output values simultaneously.    
+   * The variables acc0 ... acc3 hold output values that are being computed:    
+   *    
+   *    acc0 =  b[numTaps-1] * x[n-numTaps-1] + b[numTaps-2] * x[n-numTaps-2] + b[numTaps-3] * x[n-numTaps-3] +...+ b[0] * x[0]    
+   *    acc1 =  b[numTaps-1] * x[n-numTaps] +   b[numTaps-2] * x[n-numTaps-1] + b[numTaps-3] * x[n-numTaps-2] +...+ b[0] * x[1]    
+   *    acc2 =  b[numTaps-1] * x[n-numTaps+1] + b[numTaps-2] * x[n-numTaps] +   b[numTaps-3] * x[n-numTaps-1] +...+ b[0] * x[2]    
+   *    acc3 =  b[numTaps-1] * x[n-numTaps+2] + b[numTaps-2] * x[n-numTaps+1] + b[numTaps-3] * x[n-numTaps]   +...+ b[0] * x[3]    
+   */
+  blkCnt = blockSize >> 2;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* Copy four new input samples into the state buffer */
+    *pStateCurnt++ = *pSrc++;
+    *pStateCurnt++ = *pSrc++;
+    *pStateCurnt++ = *pSrc++;
+    *pStateCurnt++ = *pSrc++;
+
+    /* Set all accumulators to zero */
+    acc0 = 0;
+    acc1 = 0;
+    acc2 = 0;
+    acc3 = 0;
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* Initialize coefficient pointer */
+    pb = pCoeffs;
+
+    /* Read the first three samples from the state buffer:    
+     *  x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2] */
+    x0 = *(px++);
+    x1 = *(px++);
+    x2 = *(px++);
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2;
+    i = tapCnt;
+
+    while(i > 0u)
+    {
+      /* Read the b[numTaps] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-3] sample */
+      x3 = *(px++);
+
+      /* acc0 +=  b[numTaps] * x[n-numTaps] */
+      acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x0 * c0)) >> 32);
+
+      /* acc1 +=  b[numTaps] * x[n-numTaps-1] */
+      acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x1 * c0)) >> 32);
+
+      /* acc2 +=  b[numTaps] * x[n-numTaps-2] */
+      acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x2 * c0)) >> 32);
+
+      /* acc3 +=  b[numTaps] * x[n-numTaps-3] */
+      acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x3 * c0)) >> 32);
+
+      /* Read the b[numTaps-1] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-4] sample */
+      x0 = *(px++);
+
+      /* Perform the multiply-accumulates */
+      acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x1 * c0)) >> 32);
+      acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x2 * c0)) >> 32);
+      acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x3 * c0)) >> 32);
+      acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x0 * c0)) >> 32);
+
+      /* Read the b[numTaps-2] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-5] sample */
+      x1 = *(px++);
+
+      /* Perform the multiply-accumulates */
+      acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x2 * c0)) >> 32);
+      acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x3 * c0)) >> 32);
+      acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x0 * c0)) >> 32);
+      acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x1 * c0)) >> 32);
+
+      /* Read the b[numTaps-3] coefficients */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-6] sample */
+      x2 = *(px++);
+
+      /* Perform the multiply-accumulates */
+      acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x3 * c0)) >> 32);
+      acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x0 * c0)) >> 32);
+      acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x1 * c0)) >> 32);
+      acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x2 * c0)) >> 32);
+      i--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+
+    i = numTaps - (tapCnt * 4u);
+    while(i > 0u)
+    {
+      /* Read coefficients */
+      c0 = *(pb++);
+
+      /* Fetch 1 state variable */
+      x3 = *(px++);
+
+      /* Perform the multiply-accumulates */
+      acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x0 * c0)) >> 32);
+      acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x1 * c0)) >> 32);
+      acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x2 * c0)) >> 32);
+      acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x3 * c0)) >> 32);
+
+      /* Reuse the present sample states for next sample */
+      x0 = x1;
+      x1 = x2;
+      x2 = x3;
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Advance the state pointer by 4 to process the next group of 4 samples */
+    pState = pState + 4;
+
+    /* The results in the 4 accumulators are in 2.30 format.  Convert to 1.31    
+     ** Then store the 4 outputs in the destination buffer. */
+    *pDst++ = (q31_t) (acc0 << 1);
+    *pDst++ = (q31_t) (acc1 << 1);
+    *pDst++ = (q31_t) (acc2 << 1);
+    *pDst++ = (q31_t) (acc3 << 1);
+
+    /* Decrement the samples loop counter */
+    blkCnt--;
+  }
+
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 4u;
+
+  while(blkCnt > 0u)
+  {
+    /* Copy one sample at a time into state buffer */
+    *pStateCurnt++ = *pSrc++;
+
+    /* Set the accumulator to zero */
+    acc0 = 0;
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* Initialize Coefficient pointer */
+    pb = (pCoeffs);
+
+    i = numTaps;
+
+    /* Perform the multiply-accumulates */
+    do
+    {
+      acc0 =
+        (q31_t) ((((q63_t) acc0 << 32) +
+                  ((q63_t) (*px++) * (*(pb++)))) >> 32);
+      i--;
+    } while(i > 0u);
+
+    /* The result is in 2.30 format.  Convert to 1.31    
+     ** Then store the output in the destination buffer. */
+    *pDst++ = (q31_t) (acc0 << 1);
+
+    /* Advance state pointer by 1 for the next sample */
+    pState = pState + 1;
+
+    /* Decrement the samples loop counter */
+    blkCnt--;
+  }
+
+  /* Processing is complete.    
+   ** Now copy the last numTaps - 1 samples to the satrt of the state buffer.    
+   ** This prepares the state buffer for the next function call. */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+  tapCnt = (numTaps - 1u) >> 2u;
+
+  /* copy data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+  /* Calculate remaining number of copies */
+  tapCnt = (numTaps - 1u) % 0x4u;
+
+  /* Copy the remaining q31_t data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+
+}
+
+/**    
+ * @} end of FIR group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_init_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_init_f32.c
new file mode 100644
index 0000000000..aaeddf5f6b
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_init_f32.c
@@ -0,0 +1,94 @@
+/*-----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_fir_init_f32.c    
+*    
+* Description:  Floating-point FIR filter initialization function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+* 	 incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* ---------------------------------------------------------------------------*/
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR    
+ * @{    
+ */
+
+/**    
+ * @details    
+ *    
+ * @param[in,out] *S points to an instance of the floating-point FIR filter structure.    
+ * @param[in] 	  numTaps  Number of filter coefficients in the filter.    
+ * @param[in]     *pCoeffs points to the filter coefficients buffer.    
+ * @param[in]     *pState points to the state buffer.    
+ * @param[in] 	  blockSize number of samples that are processed per call.    
+ * @return 		  none.    
+ *    
+ * Description:    
+ * \par    
+ * pCoeffs points to the array of filter coefficients stored in time reversed order:    
+ * 
    
+ *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}    
+ * 
    
+ * \par    
+ * pState points to the array of state variables.    
+ * pState is of length numTaps+blockSize-1 samples, where blockSize is the number of input samples processed by each call to arm_fir_f32().    
+ */
+
+void arm_fir_init_f32(
+  arm_fir_instance_f32 * S,
+  uint16_t numTaps,
+  float32_t * pCoeffs,
+  float32_t * pState,
+  uint32_t blockSize)
+{
+  /* Assign filter taps */
+  S->numTaps = numTaps;
+
+  /* Assign coefficient pointer */
+  S->pCoeffs = pCoeffs;
+
+  /* Clear state buffer and the size of state buffer is (blockSize + numTaps - 1) */
+  memset(pState, 0, (numTaps + (blockSize - 1u)) * sizeof(float32_t));
+
+  /* Assign state pointer */
+  S->pState = pState;
+
+}
+
+/**    
+ * @} end of FIR group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_init_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_init_q15.c
new file mode 100644
index 0000000000..02bb336235
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_init_q15.c
@@ -0,0 +1,152 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_fir_init_q15.c    
+*    
+* Description:  Q15 FIR filter initialization function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+* 	 incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* ------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR    
+ * @{    
+ */
+
+/**    
+ * @param[in,out]  *S points to an instance of the Q15 FIR filter structure.    
+ * @param[in] 	   numTaps  Number of filter coefficients in the filter. Must be even and greater than or equal to 4.    
+ * @param[in]      *pCoeffs points to the filter coefficients buffer.    
+ * @param[in]      *pState points to the state buffer.    
+ * @param[in]      blockSize is number of samples processed per call.    
+ * @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if    
+ * numTaps is not greater than or equal to 4 and even.    
+ *    
+ * Description:    
+ * \par    
+ * pCoeffs points to the array of filter coefficients stored in time reversed order:    
+ * 
    
+ *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}    
+ * 
    
+ * Note that numTaps must be even and greater than or equal to 4.    
+ * To implement an odd length filter simply increase numTaps by 1 and set the last coefficient to zero.    
+ * For example, to implement a filter with numTaps=3 and coefficients    
+ * 
    
+ *     {0.3, -0.8, 0.3}    
+ * 
    
+ * set numTaps=4 and use the coefficients:    
+ * 
    
+ *     {0.3, -0.8, 0.3, 0}.    
+ * 
    
+ * Similarly, to implement a two point filter    
+ * 
    
+ *     {0.3, -0.3}    
+ * 
    
+ * set numTaps=4 and use the coefficients:    
+ * 
    
+ *     {0.3, -0.3, 0, 0}.    
+ * 
    
+ * \par    
+ * pState points to the array of state variables.    
+ * pState is of length numTaps+blockSize, when running on Cortex-M4 and Cortex-M3  and is of length numTaps+blockSize-1, when running on Cortex-M0 where blockSize is the number of input samples processed by each call to arm_fir_q15().    
+ */
+
+arm_status arm_fir_init_q15(
+  arm_fir_instance_q15 * S,
+  uint16_t numTaps,
+  q15_t * pCoeffs,
+  q15_t * pState,
+  uint32_t blockSize)
+{
+  arm_status status;
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /* The Number of filter coefficients in the filter must be even and at least 4 */
+  if(numTaps & 0x1u)
+  {
+    status = ARM_MATH_ARGUMENT_ERROR;
+  }
+  else
+  {
+    /* Assign filter taps */
+    S->numTaps = numTaps;
+
+    /* Assign coefficient pointer */
+    S->pCoeffs = pCoeffs;
+
+    /* Clear the state buffer.  The size is always (blockSize + numTaps ) */
+    memset(pState, 0, (numTaps + (blockSize)) * sizeof(q15_t));
+
+    /* Assign state pointer */
+    S->pState = pState;
+
+    status = ARM_MATH_SUCCESS;
+  }
+
+  return (status);
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Assign filter taps */
+  S->numTaps = numTaps;
+
+  /* Assign coefficient pointer */
+  S->pCoeffs = pCoeffs;
+
+  /* Clear the state buffer.  The size is always (blockSize + numTaps - 1) */
+  memset(pState, 0, (numTaps + (blockSize - 1u)) * sizeof(q15_t));
+
+  /* Assign state pointer */
+  S->pState = pState;
+
+  status = ARM_MATH_SUCCESS;
+
+  return (status);
+
+#endif /*  #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of FIR group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_init_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_init_q31.c
new file mode 100644
index 0000000000..997a78427f
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_init_q31.c
@@ -0,0 +1,94 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_fir_init_q31.c    
+*    
+* Description:	Q31 FIR filter initialization function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+* 	 incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR    
+ * @{    
+ */
+
+/**    
+ * @details    
+ *    
+ * @param[in,out] *S points to an instance of the Q31 FIR filter structure.    
+ * @param[in] 	  numTaps  Number of filter coefficients in the filter.    
+ * @param[in] 	  *pCoeffs points to the filter coefficients buffer.    
+ * @param[in] 	  *pState points to the state buffer.    
+ * @param[in] 	  blockSize number of samples that are processed per call.    
+ * @return        none.    
+ *    
+ * Description:    
+ * \par    
+ * pCoeffs points to the array of filter coefficients stored in time reversed order:    
+ * 
    
+ *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}    
+ * 
    
+ * \par    
+ * pState points to the array of state variables.    
+ * pState is of length numTaps+blockSize-1 samples, where blockSize is the number of input samples processed by each call to arm_fir_q31().    
+ */
+
+void arm_fir_init_q31(
+  arm_fir_instance_q31 * S,
+  uint16_t numTaps,
+  q31_t * pCoeffs,
+  q31_t * pState,
+  uint32_t blockSize)
+{
+  /* Assign filter taps */
+  S->numTaps = numTaps;
+
+  /* Assign coefficient pointer */
+  S->pCoeffs = pCoeffs;
+
+  /* Clear state buffer and state array size is (blockSize + numTaps - 1) */
+  memset(pState, 0, (blockSize + ((uint32_t) numTaps - 1u)) * sizeof(q31_t));
+
+  /* Assign state pointer */
+  S->pState = pState;
+
+}
+
+/**    
+ * @} end of FIR group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_init_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_init_q7.c
new file mode 100644
index 0000000000..65a49a823e
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_init_q7.c
@@ -0,0 +1,92 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_fir_init_q7.c    
+*    
+* Description:  Q7 FIR filter initialization function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+* 	 incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* ------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR    
+ * @{    
+ */
+/**    
+ * @param[in,out] *S points to an instance of the Q7 FIR filter structure.    
+ * @param[in] 	  numTaps  Number of filter coefficients in the filter.    
+ * @param[in] 	  *pCoeffs points to the filter coefficients buffer.    
+ * @param[in]     *pState points to the state buffer.    
+ * @param[in]     blockSize number of samples that are processed per call.    
+ * @return     	  none    
+ *    
+ * Description:    
+ * \par    
+ * pCoeffs points to the array of filter coefficients stored in time reversed order:    
+ * 
    
+ *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}    
+ * 
    
+ * \par    
+ * pState points to the array of state variables.    
+ * pState is of length numTaps+blockSize-1 samples, where blockSize is the number of input samples processed by each call to arm_fir_q7().    
+ */
+
+void arm_fir_init_q7(
+  arm_fir_instance_q7 * S,
+  uint16_t numTaps,
+  q7_t * pCoeffs,
+  q7_t * pState,
+  uint32_t blockSize)
+{
+
+  /* Assign filter taps */
+  S->numTaps = numTaps;
+
+  /* Assign coefficient pointer */
+  S->pCoeffs = pCoeffs;
+
+  /* Clear the state buffer.  The size is always (blockSize + numTaps - 1) */
+  memset(pState, 0, (numTaps + (blockSize - 1u)) * sizeof(q7_t));
+
+  /* Assign state pointer */
+  S->pState = pState;
+
+}
+
+/**    
+ * @} end of FIR group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_interpolate_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_interpolate_f32.c
new file mode 100644
index 0000000000..c966a0ced7
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_interpolate_f32.c
@@ -0,0 +1,574 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_fir_interpolate_f32.c    
+*    
+* Description:	FIR interpolation for floating-point sequences.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @defgroup FIR_Interpolate Finite Impulse Response (FIR) Interpolator    
+ *    
+ * These functions combine an upsampler (zero stuffer) and an FIR filter.    
+ * They are used in multirate systems for increasing the sample rate of a signal without introducing high frequency images.    
+ * Conceptually, the functions are equivalent to the block diagram below:    
+ * \image html FIRInterpolator.gif "Components included in the FIR Interpolator functions"    
+ * After upsampling by a factor of L, the signal should be filtered by a lowpass filter with a normalized    
+ * cutoff frequency of 1/L in order to eliminate high frequency copies of the spectrum.    
+ * The user of the function is responsible for providing the filter coefficients.    
+ *    
+ * The FIR interpolator functions provided in the CMSIS DSP Library combine the upsampler and FIR filter in an efficient manner.    
+ * The upsampler inserts L-1 zeros between each sample.    
+ * Instead of multiplying by these zero values, the FIR filter is designed to skip them.    
+ * This leads to an efficient implementation without any wasted effort.    
+ * The functions operate on blocks of input and output data.    
+ * pSrc points to an array of blockSize input values and    
+ * pDst points to an array of blockSize*L output values.    
+ *    
+ * The library provides separate functions for Q15, Q31, and floating-point data types.    
+ *    
+ * \par Algorithm:    
+ * The functions use a polyphase filter structure:    
+ * 
    
+ *    y[n] = b[0] * x[n] + b[L]   * x[n-1] + ... + b[L*(phaseLength-1)] * x[n-phaseLength+1]    
+ *    y[n+1] = b[1] * x[n] + b[L+1] * x[n-1] + ... + b[L*(phaseLength-1)+1] * x[n-phaseLength+1]    
+ *    ...    
+ *    y[n+(L-1)] = b[L-1] * x[n] + b[2*L-1] * x[n-1] + ....+ b[L*(phaseLength-1)+(L-1)] * x[n-phaseLength+1]    
+ * 
    
+ * This approach is more efficient than straightforward upsample-then-filter algorithms.    
+ * With this method the computation is reduced by a factor of 1/L when compared to using a standard FIR filter.    
+ * \par    
+ * pCoeffs points to a coefficient array of size numTaps.    
+ * numTaps must be a multiple of the interpolation factor L and this is checked by the    
+ * initialization functions.    
+ * Internally, the function divides the FIR filter's impulse response into shorter filters of length    
+ * phaseLength=numTaps/L.    
+ * Coefficients are stored in time reversed order.    
+ * \par    
+ * 
    
+ *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}    
+ * 
    
+ * \par    
+ * pState points to a state array of size blockSize + phaseLength - 1.    
+ * Samples in the state buffer are stored in the order:    
+ * \par    
+ * 
    
+ *    {x[n-phaseLength+1], x[n-phaseLength], x[n-phaseLength-1], x[n-phaseLength-2]....x[0], x[1], ..., x[blockSize-1]}    
+ * 
    
+ * The state variables are updated after each block of data is processed, the coefficients are untouched.    
+ *    
+ * \par Instance Structure    
+ * The coefficients and state variables for a filter are stored together in an instance data structure.    
+ * A separate instance structure must be defined for each filter.    
+ * Coefficient arrays may be shared among several instances while state variable array should be allocated separately.    
+ * There are separate instance structure declarations for each of the 3 supported data types.    
+ *    
+ * \par Initialization Functions    
+ * There is also an associated initialization function for each data type.    
+ * The initialization function performs the following operations:    
+ * - Sets the values of the internal structure fields.    
+ * - Zeros out the values in the state buffer.    
+ * - Checks to make sure that the length of the filter is a multiple of the interpolation factor.    
+ *    
+ * \par    
+ * Use of the initialization function is optional.    
+ * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.    
+ * To place an instance structure into a const data section, the instance structure must be manually initialized.    
+ * The code below statically initializes each of the 3 different data type filter instance structures    
+ * 
    
+ * arm_fir_interpolate_instance_f32 S = {L, phaseLength, pCoeffs, pState};    
+ * arm_fir_interpolate_instance_q31 S = {L, phaseLength, pCoeffs, pState};    
+ * arm_fir_interpolate_instance_q15 S = {L, phaseLength, pCoeffs, pState};    
+ * 
    
+ * where L is the interpolation factor; phaseLength=numTaps/L is the    
+ * length of each of the shorter FIR filters used internally,    
+ * pCoeffs is the address of the coefficient buffer;    
+ * pState is the address of the state buffer.    
+ * Be sure to set the values in the state buffer to zeros when doing static initialization.    
+ *    
+ * \par Fixed-Point Behavior    
+ * Care must be taken when using the fixed-point versions of the FIR interpolate filter functions.    
+ * In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.    
+ * Refer to the function specific documentation below for usage guidelines.    
+ */
+
+/**    
+ * @addtogroup FIR_Interpolate    
+ * @{    
+ */
+
+/**    
+ * @brief Processing function for the floating-point FIR interpolator.    
+ * @param[in] *S        points to an instance of the floating-point FIR interpolator structure.    
+ * @param[in] *pSrc     points to the block of input data.    
+ * @param[out] *pDst    points to the block of output data.    
+ * @param[in] blockSize number of input samples to process per call.    
+ * @return none.    
+ */
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+void arm_fir_interpolate_f32(
+  const arm_fir_interpolate_instance_f32 * S,
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize)
+{
+  float32_t *pState = S->pState;                 /* State pointer */
+  float32_t *pCoeffs = S->pCoeffs;               /* Coefficient pointer */
+  float32_t *pStateCurnt;                        /* Points to the current sample of the state */
+  float32_t *ptr1, *ptr2;                        /* Temporary pointers for state and coefficient buffers */
+  float32_t sum0;                                /* Accumulators */
+  float32_t x0, c0;                              /* Temporary variables to hold state and coefficient values */
+  uint32_t i, blkCnt, j;                         /* Loop counters */
+  uint16_t phaseLen = S->phaseLength, tapCnt;    /* Length of each polyphase filter component */
+  float32_t acc0, acc1, acc2, acc3;
+  float32_t x1, x2, x3;
+  uint32_t blkCntN4;
+  float32_t c1, c2, c3;
+
+  /* S->pState buffer contains previous frame (phaseLen - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = S->pState + (phaseLen - 1u);
+
+  /* Initialise  blkCnt */
+  blkCnt = blockSize / 4;
+  blkCntN4 = blockSize - (4 * blkCnt);
+
+  /* Samples loop unrolled by 4 */
+  while(blkCnt > 0u)
+  {
+    /* Copy new input sample into the state buffer */
+    *pStateCurnt++ = *pSrc++;
+    *pStateCurnt++ = *pSrc++;
+    *pStateCurnt++ = *pSrc++;
+    *pStateCurnt++ = *pSrc++;
+
+    /* Address modifier index of coefficient buffer */
+    j = 1u;
+
+    /* Loop over the Interpolation factor. */
+    i = (S->L);
+
+    while(i > 0u)
+    {
+      /* Set accumulator to zero */
+      acc0 = 0.0f;
+      acc1 = 0.0f;
+      acc2 = 0.0f;
+      acc3 = 0.0f;
+
+      /* Initialize state pointer */
+      ptr1 = pState;
+
+      /* Initialize coefficient pointer */
+      ptr2 = pCoeffs + (S->L - j);
+
+      /* Loop over the polyPhase length. Unroll by a factor of 4.        
+       ** Repeat until we've computed numTaps-(4*S->L) coefficients. */
+      tapCnt = phaseLen >> 2u;
+
+      x0 = *(ptr1++);
+      x1 = *(ptr1++);
+      x2 = *(ptr1++);
+
+      while(tapCnt > 0u)
+      {
+
+        /* Read the input sample */
+        x3 = *(ptr1++);
+
+        /* Read the coefficient */
+        c0 = *(ptr2);
+
+        /* Perform the multiply-accumulate */
+        acc0 += x0 * c0;
+        acc1 += x1 * c0;
+        acc2 += x2 * c0;
+        acc3 += x3 * c0;
+
+        /* Read the coefficient */
+        c1 = *(ptr2 + S->L);
+
+        /* Read the input sample */
+        x0 = *(ptr1++);
+
+        /* Perform the multiply-accumulate */
+        acc0 += x1 * c1;
+        acc1 += x2 * c1;
+        acc2 += x3 * c1;
+        acc3 += x0 * c1;
+
+        /* Read the coefficient */
+        c2 = *(ptr2 + S->L * 2);
+
+        /* Read the input sample */
+        x1 = *(ptr1++);
+
+        /* Perform the multiply-accumulate */
+        acc0 += x2 * c2;
+        acc1 += x3 * c2;
+        acc2 += x0 * c2;
+        acc3 += x1 * c2;
+
+        /* Read the coefficient */
+        c3 = *(ptr2 + S->L * 3);
+
+        /* Read the input sample */
+        x2 = *(ptr1++);
+
+        /* Perform the multiply-accumulate */
+        acc0 += x3 * c3;
+        acc1 += x0 * c3;
+        acc2 += x1 * c3;
+        acc3 += x2 * c3;
+
+
+        /* Upsampling is done by stuffing L-1 zeros between each sample.        
+         * So instead of multiplying zeros with coefficients,        
+         * Increment the coefficient pointer by interpolation factor times. */
+        ptr2 += 4 * S->L;
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      /* If the polyPhase length is not a multiple of 4, compute the remaining filter taps */
+      tapCnt = phaseLen % 0x4u;
+
+      while(tapCnt > 0u)
+      {
+
+        /* Read the input sample */
+        x3 = *(ptr1++);
+
+        /* Read the coefficient */
+        c0 = *(ptr2);
+
+        /* Perform the multiply-accumulate */
+        acc0 += x0 * c0;
+        acc1 += x1 * c0;
+        acc2 += x2 * c0;
+        acc3 += x3 * c0;
+
+        /* Increment the coefficient pointer by interpolation factor times. */
+        ptr2 += S->L;
+
+        /* update states for next sample processing */
+        x0 = x1;
+        x1 = x2;
+        x2 = x3;
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      /* The result is in the accumulator, store in the destination buffer. */
+      *pDst = acc0;
+      *(pDst + S->L) = acc1;
+      *(pDst + 2 * S->L) = acc2;
+      *(pDst + 3 * S->L) = acc3;
+
+      pDst++;
+
+      /* Increment the address modifier index of coefficient buffer */
+      j++;
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Advance the state pointer by 1        
+     * to process the next group of interpolation factor number samples */
+    pState = pState + 4;
+
+    pDst += S->L * 3;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.        
+   ** No loop unrolling is used. */
+
+  while(blkCntN4 > 0u)
+  {
+    /* Copy new input sample into the state buffer */
+    *pStateCurnt++ = *pSrc++;
+
+    /* Address modifier index of coefficient buffer */
+    j = 1u;
+
+    /* Loop over the Interpolation factor. */
+    i = S->L;
+    while(i > 0u)
+    {
+      /* Set accumulator to zero */
+      sum0 = 0.0f;
+
+      /* Initialize state pointer */
+      ptr1 = pState;
+
+      /* Initialize coefficient pointer */
+      ptr2 = pCoeffs + (S->L - j);
+
+      /* Loop over the polyPhase length. Unroll by a factor of 4.        
+       ** Repeat until we've computed numTaps-(4*S->L) coefficients. */
+      tapCnt = phaseLen >> 2u;
+      while(tapCnt > 0u)
+      {
+
+        /* Read the coefficient */
+        c0 = *(ptr2);
+
+        /* Upsampling is done by stuffing L-1 zeros between each sample.        
+         * So instead of multiplying zeros with coefficients,        
+         * Increment the coefficient pointer by interpolation factor times. */
+        ptr2 += S->L;
+
+        /* Read the input sample */
+        x0 = *(ptr1++);
+
+        /* Perform the multiply-accumulate */
+        sum0 += x0 * c0;
+
+        /* Read the coefficient */
+        c0 = *(ptr2);
+
+        /* Increment the coefficient pointer by interpolation factor times. */
+        ptr2 += S->L;
+
+        /* Read the input sample */
+        x0 = *(ptr1++);
+
+        /* Perform the multiply-accumulate */
+        sum0 += x0 * c0;
+
+        /* Read the coefficient */
+        c0 = *(ptr2);
+
+        /* Increment the coefficient pointer by interpolation factor times. */
+        ptr2 += S->L;
+
+        /* Read the input sample */
+        x0 = *(ptr1++);
+
+        /* Perform the multiply-accumulate */
+        sum0 += x0 * c0;
+
+        /* Read the coefficient */
+        c0 = *(ptr2);
+
+        /* Increment the coefficient pointer by interpolation factor times. */
+        ptr2 += S->L;
+
+        /* Read the input sample */
+        x0 = *(ptr1++);
+
+        /* Perform the multiply-accumulate */
+        sum0 += x0 * c0;
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      /* If the polyPhase length is not a multiple of 4, compute the remaining filter taps */
+      tapCnt = phaseLen % 0x4u;
+
+      while(tapCnt > 0u)
+      {
+        /* Perform the multiply-accumulate */
+        sum0 += *(ptr1++) * (*ptr2);
+
+        /* Increment the coefficient pointer by interpolation factor times. */
+        ptr2 += S->L;
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      /* The result is in the accumulator, store in the destination buffer. */
+      *pDst++ = sum0;
+
+      /* Increment the address modifier index of coefficient buffer */
+      j++;
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Advance the state pointer by 1        
+     * to process the next group of interpolation factor number samples */
+    pState = pState + 1;
+
+    /* Decrement the loop counter */
+    blkCntN4--;
+  }
+
+  /* Processing is complete.        
+   ** Now copy the last phaseLen - 1 samples to the satrt of the state buffer.        
+   ** This prepares the state buffer for the next function call. */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+  tapCnt = (phaseLen - 1u) >> 2u;
+
+  /* copy data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+  tapCnt = (phaseLen - 1u) % 0x04u;
+
+  /* copy data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+}
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+void arm_fir_interpolate_f32(
+  const arm_fir_interpolate_instance_f32 * S,
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize)
+{
+  float32_t *pState = S->pState;                 /* State pointer */
+  float32_t *pCoeffs = S->pCoeffs;               /* Coefficient pointer */
+  float32_t *pStateCurnt;                        /* Points to the current sample of the state */
+  float32_t *ptr1, *ptr2;                        /* Temporary pointers for state and coefficient buffers */
+
+
+  float32_t sum;                                 /* Accumulator */
+  uint32_t i, blkCnt;                            /* Loop counters */
+  uint16_t phaseLen = S->phaseLength, tapCnt;    /* Length of each polyphase filter component */
+
+
+  /* S->pState buffer contains previous frame (phaseLen - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = S->pState + (phaseLen - 1u);
+
+  /* Total number of intput samples */
+  blkCnt = blockSize;
+
+  /* Loop over the blockSize. */
+  while(blkCnt > 0u)
+  {
+    /* Copy new input sample into the state buffer */
+    *pStateCurnt++ = *pSrc++;
+
+    /* Loop over the Interpolation factor. */
+    i = S->L;
+
+    while(i > 0u)
+    {
+      /* Set accumulator to zero */
+      sum = 0.0f;
+
+      /* Initialize state pointer */
+      ptr1 = pState;
+
+      /* Initialize coefficient pointer */
+      ptr2 = pCoeffs + (i - 1u);
+
+      /* Loop over the polyPhase length */
+      tapCnt = phaseLen;
+
+      while(tapCnt > 0u)
+      {
+        /* Perform the multiply-accumulate */
+        sum += *ptr1++ * *ptr2;
+
+        /* Increment the coefficient pointer by interpolation factor times. */
+        ptr2 += S->L;
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      /* The result is in the accumulator, store in the destination buffer. */
+      *pDst++ = sum;
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Advance the state pointer by 1           
+     * to process the next group of interpolation factor number samples */
+    pState = pState + 1;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Processing is complete.         
+   ** Now copy the last phaseLen - 1 samples to the start of the state buffer.       
+   ** This prepares the state buffer for the next function call. */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+  tapCnt = phaseLen - 1u;
+
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+}
+
+#endif /*   #ifndef ARM_MATH_CM0 */
+
+
+
+ /**    
+  * @} end of FIR_Interpolate group    
+  */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_interpolate_init_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_interpolate_init_f32.c
new file mode 100644
index 0000000000..b193472647
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_interpolate_init_f32.c
@@ -0,0 +1,116 @@
+/*-----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_fir_interpolate_init_f32.c    
+*    
+* Description:  Floating-point FIR interpolator initialization function    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ---------------------------------------------------------------------------*/
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR_Interpolate    
+ * @{    
+ */
+
+/**    
+ * @brief  Initialization function for the floating-point FIR interpolator.    
+ * @param[in,out] *S        points to an instance of the floating-point FIR interpolator structure.    
+ * @param[in]     L         upsample factor.    
+ * @param[in]     numTaps   number of filter coefficients in the filter.    
+ * @param[in]     *pCoeffs  points to the filter coefficient buffer.    
+ * @param[in]     *pState   points to the state buffer.    
+ * @param[in]     blockSize number of input samples to process per call.    
+ * @return        The function returns ARM_MATH_SUCCESS if initialization was successful or ARM_MATH_LENGTH_ERROR if    
+ * the filter length numTaps is not a multiple of the interpolation factor L.    
+ *    
+ * Description:    
+ * \par    
+ * pCoeffs points to the array of filter coefficients stored in time reversed order:    
+ * 
    
+ *    {b[numTaps-1], b[numTaps-2], b[numTaps-2], ..., b[1], b[0]}    
+ * 
    
+ * The length of the filter numTaps must be a multiple of the interpolation factor L.    
+ * \par    
+ * pState points to the array of state variables.    
+ * pState is of length (numTaps/L)+blockSize-1 words    
+ * where blockSize is the number of input samples processed by each call to arm_fir_interpolate_f32().    
+ */
+
+arm_status arm_fir_interpolate_init_f32(
+  arm_fir_interpolate_instance_f32 * S,
+  uint8_t L,
+  uint16_t numTaps,
+  float32_t * pCoeffs,
+  float32_t * pState,
+  uint32_t blockSize)
+{
+  arm_status status;
+
+  /* The filter length must be a multiple of the interpolation factor */
+  if((numTaps % L) != 0u)
+  {
+    /* Set status as ARM_MATH_LENGTH_ERROR */
+    status = ARM_MATH_LENGTH_ERROR;
+  }
+  else
+  {
+
+    /* Assign coefficient pointer */
+    S->pCoeffs = pCoeffs;
+
+    /* Assign Interpolation factor */
+    S->L = L;
+
+    /* Assign polyPhaseLength */
+    S->phaseLength = numTaps / L;
+
+    /* Clear state buffer and size of state array is always phaseLength + blockSize - 1 */
+    memset(pState, 0,
+           (blockSize +
+            ((uint32_t) S->phaseLength - 1u)) * sizeof(float32_t));
+
+    /* Assign state pointer */
+    S->pState = pState;
+
+    status = ARM_MATH_SUCCESS;
+  }
+
+  return (status);
+
+}
+
+ /**    
+  * @} end of FIR_Interpolate group    
+  */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_interpolate_init_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_interpolate_init_q15.c
new file mode 100644
index 0000000000..b344fc785a
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_interpolate_init_q15.c
@@ -0,0 +1,115 @@
+/*-----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_fir_interpolate_init_q15.c    
+*    
+* Description:  Q15 FIR interpolator initialization function    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ---------------------------------------------------------------------------*/
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR_Interpolate    
+ * @{    
+ */
+
+/**    
+ * @brief  Initialization function for the Q15 FIR interpolator.    
+ * @param[in,out] *S        points to an instance of the Q15 FIR interpolator structure.    
+ * @param[in]     L         upsample factor.    
+ * @param[in]     numTaps   number of filter coefficients in the filter.    
+ * @param[in]     *pCoeffs  points to the filter coefficient buffer.    
+ * @param[in]     *pState   points to the state buffer.    
+ * @param[in]     blockSize number of input samples to process per call.    
+ * @return        The function returns ARM_MATH_SUCCESS if initialization was successful or ARM_MATH_LENGTH_ERROR if    
+ * the filter length numTaps is not a multiple of the interpolation factor L.    
+ *    
+ * Description:    
+ * \par    
+ * pCoeffs points to the array of filter coefficients stored in time reversed order:    
+ * 
    
+ *    {b[numTaps-1], b[numTaps-2], b[numTaps-2], ..., b[1], b[0]}    
+ * 
    
+ * The length of the filter numTaps must be a multiple of the interpolation factor L.    
+ * \par    
+ * pState points to the array of state variables.    
+ * pState is of length (numTaps/L)+blockSize-1 words    
+ * where blockSize is the number of input samples processed by each call to arm_fir_interpolate_q15().    
+ */
+
+arm_status arm_fir_interpolate_init_q15(
+  arm_fir_interpolate_instance_q15 * S,
+  uint8_t L,
+  uint16_t numTaps,
+  q15_t * pCoeffs,
+  q15_t * pState,
+  uint32_t blockSize)
+{
+  arm_status status;
+
+  /* The filter length must be a multiple of the interpolation factor */
+  if((numTaps % L) != 0u)
+  {
+    /* Set status as ARM_MATH_LENGTH_ERROR */
+    status = ARM_MATH_LENGTH_ERROR;
+  }
+  else
+  {
+
+    /* Assign coefficient pointer */
+    S->pCoeffs = pCoeffs;
+
+    /* Assign Interpolation factor */
+    S->L = L;
+
+    /* Assign polyPhaseLength */
+    S->phaseLength = numTaps / L;
+
+    /* Clear state buffer and size of buffer is always phaseLength + blockSize - 1 */
+    memset(pState, 0,
+           (blockSize + ((uint32_t) S->phaseLength - 1u)) * sizeof(q15_t));
+
+    /* Assign state pointer */
+    S->pState = pState;
+
+    status = ARM_MATH_SUCCESS;
+  }
+
+  return (status);
+
+}
+
+ /**    
+  * @} end of FIR_Interpolate group    
+  */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_interpolate_init_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_interpolate_init_q31.c
new file mode 100644
index 0000000000..f0383b8e9b
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_interpolate_init_q31.c
@@ -0,0 +1,116 @@
+/*-----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_fir_interpolate_init_q31.c    
+*    
+* Description:  Q31 FIR interpolator initialization function    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ---------------------------------------------------------------------------*/
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR_Interpolate    
+ * @{    
+ */
+
+
+/**    
+ * @brief  Initialization function for the Q31 FIR interpolator.    
+ * @param[in,out] *S        points to an instance of the Q31 FIR interpolator structure.    
+ * @param[in]     L         upsample factor.    
+ * @param[in]     numTaps   number of filter coefficients in the filter.    
+ * @param[in]     *pCoeffs  points to the filter coefficient buffer.    
+ * @param[in]     *pState   points to the state buffer.    
+ * @param[in]     blockSize number of input samples to process per call.    
+ * @return        The function returns ARM_MATH_SUCCESS if initialization was successful or ARM_MATH_LENGTH_ERROR if    
+ * the filter length numTaps is not a multiple of the interpolation factor L.    
+ *    
+ * Description:    
+ * \par    
+ * pCoeffs points to the array of filter coefficients stored in time reversed order:    
+ * 
    
+ *    {b[numTaps-1], b[numTaps-2], b[numTaps-2], ..., b[1], b[0]}    
+ * 
    
+ * The length of the filter numTaps must be a multiple of the interpolation factor L.    
+ * \par    
+ * pState points to the array of state variables.    
+ * pState is of length (numTaps/L)+blockSize-1 words    
+ * where blockSize is the number of input samples processed by each call to arm_fir_interpolate_q31().    
+ */
+
+arm_status arm_fir_interpolate_init_q31(
+  arm_fir_interpolate_instance_q31 * S,
+  uint8_t L,
+  uint16_t numTaps,
+  q31_t * pCoeffs,
+  q31_t * pState,
+  uint32_t blockSize)
+{
+  arm_status status;
+
+  /* The filter length must be a multiple of the interpolation factor */
+  if((numTaps % L) != 0u)
+  {
+    /* Set status as ARM_MATH_LENGTH_ERROR */
+    status = ARM_MATH_LENGTH_ERROR;
+  }
+  else
+  {
+
+    /* Assign coefficient pointer */
+    S->pCoeffs = pCoeffs;
+
+    /* Assign Interpolation factor */
+    S->L = L;
+
+    /* Assign polyPhaseLength */
+    S->phaseLength = numTaps / L;
+
+    /* Clear state buffer and size of buffer is always phaseLength + blockSize - 1 */
+    memset(pState, 0,
+           (blockSize + ((uint32_t) S->phaseLength - 1u)) * sizeof(q31_t));
+
+    /* Assign state pointer */
+    S->pState = pState;
+
+    status = ARM_MATH_SUCCESS;
+  }
+
+  return (status);
+
+}
+
+ /**    
+  * @} end of FIR_Interpolate group    
+  */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_interpolate_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_interpolate_q15.c
new file mode 100644
index 0000000000..d17d8d8037
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_interpolate_q15.c
@@ -0,0 +1,503 @@
+/*-----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_fir_interpolate_q15.c    
+*    
+* Description:	Q15 FIR interpolation.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ---------------------------------------------------------------------------*/
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR_Interpolate    
+ * @{    
+ */
+
+/**    
+ * @brief Processing function for the Q15 FIR interpolator.    
+ * @param[in] *S        points to an instance of the Q15 FIR interpolator structure.    
+ * @param[in] *pSrc     points to the block of input data.    
+ * @param[out] *pDst    points to the block of output data.    
+ * @param[in] blockSize number of input samples to process per call.    
+ * @return none.    
+ *    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function is implemented using a 64-bit internal accumulator.    
+ * Both coefficients and state variables are represented in 1.15 format and multiplications yield a 2.30 result.    
+ * The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format.    
+ * There is no risk of internal overflow with this approach and the full precision of intermediate multiplications is preserved.    
+ * After all additions have been performed, the accumulator is truncated to 34.15 format by discarding low 15 bits.    
+ * Lastly, the accumulator is saturated to yield a result in 1.15 format.    
+ */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+void arm_fir_interpolate_q15(
+  const arm_fir_interpolate_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+  q15_t *pState = S->pState;                     /* State pointer                                            */
+  q15_t *pCoeffs = S->pCoeffs;                   /* Coefficient pointer                                      */
+  q15_t *pStateCurnt;                            /* Points to the current sample of the state                */
+  q15_t *ptr1, *ptr2;                            /* Temporary pointers for state and coefficient buffers     */
+  q63_t sum0;                                    /* Accumulators                                             */
+  q15_t x0, c0;                                  /* Temporary variables to hold state and coefficient values */
+  uint32_t i, blkCnt, j, tapCnt;                 /* Loop counters                                            */
+  uint16_t phaseLen = S->phaseLength;            /* Length of each polyphase filter component */
+  uint32_t blkCntN2;
+  q63_t acc0, acc1;
+  q15_t x1;
+
+  /* S->pState buffer contains previous frame (phaseLen - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = S->pState + ((q31_t) phaseLen - 1);
+
+  /* Initialise  blkCnt */
+  blkCnt = blockSize / 2;
+  blkCntN2 = blockSize - (2 * blkCnt);
+
+  /* Samples loop unrolled by 2 */
+  while(blkCnt > 0u)
+  {
+    /* Copy new input sample into the state buffer */
+    *pStateCurnt++ = *pSrc++;
+    *pStateCurnt++ = *pSrc++;
+
+    /* Address modifier index of coefficient buffer */
+    j = 1u;
+
+    /* Loop over the Interpolation factor. */
+    i = (S->L);
+
+    while(i > 0u)
+    {
+      /* Set accumulator to zero */
+      acc0 = 0;
+      acc1 = 0;
+
+      /* Initialize state pointer */
+      ptr1 = pState;
+
+      /* Initialize coefficient pointer */
+      ptr2 = pCoeffs + (S->L - j);
+
+      /* Loop over the polyPhase length. Unroll by a factor of 4.        
+       ** Repeat until we've computed numTaps-(4*S->L) coefficients. */
+      tapCnt = phaseLen >> 2u;
+
+      x0 = *(ptr1++);
+
+      while(tapCnt > 0u)
+      {
+
+        /* Read the input sample */
+        x1 = *(ptr1++);
+
+        /* Read the coefficient */
+        c0 = *(ptr2);
+
+        /* Perform the multiply-accumulate */
+        acc0 += (q63_t) x0 *c0;
+        acc1 += (q63_t) x1 *c0;
+
+
+        /* Read the coefficient */
+        c0 = *(ptr2 + S->L);
+
+        /* Read the input sample */
+        x0 = *(ptr1++);
+
+        /* Perform the multiply-accumulate */
+        acc0 += (q63_t) x1 *c0;
+        acc1 += (q63_t) x0 *c0;
+
+
+        /* Read the coefficient */
+        c0 = *(ptr2 + S->L * 2);
+
+        /* Read the input sample */
+        x1 = *(ptr1++);
+
+        /* Perform the multiply-accumulate */
+        acc0 += (q63_t) x0 *c0;
+        acc1 += (q63_t) x1 *c0;
+
+        /* Read the coefficient */
+        c0 = *(ptr2 + S->L * 3);
+
+        /* Read the input sample */
+        x0 = *(ptr1++);
+
+        /* Perform the multiply-accumulate */
+        acc0 += (q63_t) x1 *c0;
+        acc1 += (q63_t) x0 *c0;
+
+
+        /* Upsampling is done by stuffing L-1 zeros between each sample.        
+         * So instead of multiplying zeros with coefficients,        
+         * Increment the coefficient pointer by interpolation factor times. */
+        ptr2 += 4 * S->L;
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      /* If the polyPhase length is not a multiple of 4, compute the remaining filter taps */
+      tapCnt = phaseLen % 0x4u;
+
+      while(tapCnt > 0u)
+      {
+
+        /* Read the input sample */
+        x1 = *(ptr1++);
+
+        /* Read the coefficient */
+        c0 = *(ptr2);
+
+        /* Perform the multiply-accumulate */
+        acc0 += (q63_t) x0 *c0;
+        acc1 += (q63_t) x1 *c0;
+
+        /* Increment the coefficient pointer by interpolation factor times. */
+        ptr2 += S->L;
+
+        /* update states for next sample processing */
+        x0 = x1;
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      /* The result is in the accumulator, store in the destination buffer. */
+      *pDst = (q15_t) (__SSAT((acc0 >> 15), 16));
+      *(pDst + S->L) = (q15_t) (__SSAT((acc1 >> 15), 16));
+
+      pDst++;
+
+      /* Increment the address modifier index of coefficient buffer */
+      j++;
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Advance the state pointer by 1        
+     * to process the next group of interpolation factor number samples */
+    pState = pState + 2;
+
+    pDst += S->L;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 2, compute any remaining output samples here.        
+   ** No loop unrolling is used. */
+  blkCnt = blkCntN2;
+
+  /* Loop over the blockSize. */
+  while(blkCnt > 0u)
+  {
+    /* Copy new input sample into the state buffer */
+    *pStateCurnt++ = *pSrc++;
+
+    /* Address modifier index of coefficient buffer */
+    j = 1u;
+
+    /* Loop over the Interpolation factor. */
+    i = S->L;
+    while(i > 0u)
+    {
+      /* Set accumulator to zero */
+      sum0 = 0;
+
+      /* Initialize state pointer */
+      ptr1 = pState;
+
+      /* Initialize coefficient pointer */
+      ptr2 = pCoeffs + (S->L - j);
+
+      /* Loop over the polyPhase length. Unroll by a factor of 4.        
+       ** Repeat until we've computed numTaps-(4*S->L) coefficients. */
+      tapCnt = phaseLen >> 2;
+      while(tapCnt > 0u)
+      {
+
+        /* Read the coefficient */
+        c0 = *(ptr2);
+
+        /* Upsampling is done by stuffing L-1 zeros between each sample.        
+         * So instead of multiplying zeros with coefficients,        
+         * Increment the coefficient pointer by interpolation factor times. */
+        ptr2 += S->L;
+
+        /* Read the input sample */
+        x0 = *(ptr1++);
+
+        /* Perform the multiply-accumulate */
+        sum0 += (q63_t) x0 *c0;
+
+        /* Read the coefficient */
+        c0 = *(ptr2);
+
+        /* Increment the coefficient pointer by interpolation factor times. */
+        ptr2 += S->L;
+
+        /* Read the input sample */
+        x0 = *(ptr1++);
+
+        /* Perform the multiply-accumulate */
+        sum0 += (q63_t) x0 *c0;
+
+        /* Read the coefficient */
+        c0 = *(ptr2);
+
+        /* Increment the coefficient pointer by interpolation factor times. */
+        ptr2 += S->L;
+
+        /* Read the input sample */
+        x0 = *(ptr1++);
+
+        /* Perform the multiply-accumulate */
+        sum0 += (q63_t) x0 *c0;
+
+        /* Read the coefficient */
+        c0 = *(ptr2);
+
+        /* Increment the coefficient pointer by interpolation factor times. */
+        ptr2 += S->L;
+
+        /* Read the input sample */
+        x0 = *(ptr1++);
+
+        /* Perform the multiply-accumulate */
+        sum0 += (q63_t) x0 *c0;
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      /* If the polyPhase length is not a multiple of 4, compute the remaining filter taps */
+      tapCnt = phaseLen & 0x3u;
+
+      while(tapCnt > 0u)
+      {
+        /* Read the coefficient */
+        c0 = *(ptr2);
+
+        /* Increment the coefficient pointer by interpolation factor times. */
+        ptr2 += S->L;
+
+        /* Read the input sample */
+        x0 = *(ptr1++);
+
+        /* Perform the multiply-accumulate */
+        sum0 += (q63_t) x0 *c0;
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      /* The result is in the accumulator, store in the destination buffer. */
+      *pDst++ = (q15_t) (__SSAT((sum0 >> 15), 16));
+
+      j++;
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Advance the state pointer by 1        
+     * to process the next group of interpolation factor number samples */
+    pState = pState + 1;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+
+  /* Processing is complete.    
+   ** Now copy the last phaseLen - 1 samples to the satrt of the state buffer.    
+   ** This prepares the state buffer for the next function call. */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+  i = ((uint32_t) phaseLen - 1u) >> 2u;
+
+  /* copy data */
+  while(i > 0u)
+  {
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+    *__SIMD32(pStateCurnt)++ = *__SIMD32(pState)++;
+    *__SIMD32(pStateCurnt)++ = *__SIMD32(pState)++;
+
+#else
+
+    *pStateCurnt++ = *pState++;
+	*pStateCurnt++ = *pState++;
+	*pStateCurnt++ = *pState++;
+	*pStateCurnt++ = *pState++;
+	
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+	
+	/* Decrement the loop counter */
+    i--;
+  }
+
+  i = ((uint32_t) phaseLen - 1u) % 0x04u;
+
+  while(i > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    i--;
+  }
+}
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+void arm_fir_interpolate_q15(
+  const arm_fir_interpolate_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+  q15_t *pState = S->pState;                     /* State pointer                                            */
+  q15_t *pCoeffs = S->pCoeffs;                   /* Coefficient pointer                                      */
+  q15_t *pStateCurnt;                            /* Points to the current sample of the state                */
+  q15_t *ptr1, *ptr2;                            /* Temporary pointers for state and coefficient buffers     */
+  q63_t sum;                                     /* Accumulator */
+  q15_t x0, c0;                                  /* Temporary variables to hold state and coefficient values */
+  uint32_t i, blkCnt, tapCnt;                    /* Loop counters                                            */
+  uint16_t phaseLen = S->phaseLength;            /* Length of each polyphase filter component */
+
+
+  /* S->pState buffer contains previous frame (phaseLen - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = S->pState + (phaseLen - 1u);
+
+  /* Total number of intput samples */
+  blkCnt = blockSize;
+
+  /* Loop over the blockSize. */
+  while(blkCnt > 0u)
+  {
+    /* Copy new input sample into the state buffer */
+    *pStateCurnt++ = *pSrc++;
+
+    /* Loop over the Interpolation factor. */
+    i = S->L;
+
+    while(i > 0u)
+    {
+      /* Set accumulator to zero */
+      sum = 0;
+
+      /* Initialize state pointer */
+      ptr1 = pState;
+
+      /* Initialize coefficient pointer */
+      ptr2 = pCoeffs + (i - 1u);
+
+      /* Loop over the polyPhase length */
+      tapCnt = (uint32_t) phaseLen;
+
+      while(tapCnt > 0u)
+      {
+        /* Read the coefficient */
+        c0 = *ptr2;
+
+        /* Increment the coefficient pointer by interpolation factor times. */
+        ptr2 += S->L;
+
+        /* Read the input sample */
+        x0 = *ptr1++;
+
+        /* Perform the multiply-accumulate */
+        sum += ((q31_t) x0 * c0);
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      /* Store the result after converting to 1.15 format in the destination buffer */
+      *pDst++ = (q15_t) (__SSAT((sum >> 15), 16));
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Advance the state pointer by 1           
+     * to process the next group of interpolation factor number samples */
+    pState = pState + 1;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Processing is complete.         
+   ** Now copy the last phaseLen - 1 samples to the start of the state buffer.       
+   ** This prepares the state buffer for the next function call. */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+  i = (uint32_t) phaseLen - 1u;
+
+  while(i > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    i--;
+  }
+
+}
+
+#endif /*   #ifndef ARM_MATH_CM0 */
+
+
+ /**    
+  * @} end of FIR_Interpolate group    
+  */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_interpolate_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_interpolate_q31.c
new file mode 100644
index 0000000000..689b4d3372
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_interpolate_q31.c
@@ -0,0 +1,499 @@
+/*-----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_fir_interpolate_q31.c    
+*    
+* Description:	Q31 FIR interpolation.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ---------------------------------------------------------------------------*/
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR_Interpolate    
+ * @{    
+ */
+
+/**    
+ * @brief Processing function for the Q31 FIR interpolator.    
+ * @param[in] *S        points to an instance of the Q31 FIR interpolator structure.    
+ * @param[in] *pSrc     points to the block of input data.    
+ * @param[out] *pDst    points to the block of output data.    
+ * @param[in] blockSize number of input samples to process per call.    
+ * @return none.    
+ *    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function is implemented using an internal 64-bit accumulator.    
+ * The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit.    
+ * Thus, if the accumulator result overflows it wraps around rather than clip.    
+ * In order to avoid overflows completely the input signal must be scaled down by 1/(numTaps/L).    
+ * since numTaps/L additions occur per output sample.    
+ * After all multiply-accumulates are performed, the 2.62 accumulator is truncated to 1.32 format and then saturated to 1.31 format.    
+ */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+void arm_fir_interpolate_q31(
+  const arm_fir_interpolate_instance_q31 * S,
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize)
+{
+  q31_t *pState = S->pState;                     /* State pointer */
+  q31_t *pCoeffs = S->pCoeffs;                   /* Coefficient pointer */
+  q31_t *pStateCurnt;                            /* Points to the current sample of the state */
+  q31_t *ptr1, *ptr2;                            /* Temporary pointers for state and coefficient buffers */
+  q63_t sum0;                                    /* Accumulators */
+  q31_t x0, c0;                                  /* Temporary variables to hold state and coefficient values */
+  uint32_t i, blkCnt, j;                         /* Loop counters */
+  uint16_t phaseLen = S->phaseLength, tapCnt;    /* Length of each polyphase filter component */
+
+  uint32_t blkCntN2;
+  q63_t acc0, acc1;
+  q31_t x1;
+
+  /* S->pState buffer contains previous frame (phaseLen - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = S->pState + ((q31_t) phaseLen - 1);
+
+  /* Initialise  blkCnt */
+  blkCnt = blockSize / 2;
+  blkCntN2 = blockSize - (2 * blkCnt);
+
+  /* Samples loop unrolled by 2 */
+  while(blkCnt > 0u)
+  {
+    /* Copy new input sample into the state buffer */
+    *pStateCurnt++ = *pSrc++;
+    *pStateCurnt++ = *pSrc++;
+
+    /* Address modifier index of coefficient buffer */
+    j = 1u;
+
+    /* Loop over the Interpolation factor. */
+    i = (S->L);
+
+    while(i > 0u)
+    {
+      /* Set accumulator to zero */
+      acc0 = 0;
+      acc1 = 0;
+
+      /* Initialize state pointer */
+      ptr1 = pState;
+
+      /* Initialize coefficient pointer */
+      ptr2 = pCoeffs + (S->L - j);
+
+      /* Loop over the polyPhase length. Unroll by a factor of 4.        
+       ** Repeat until we've computed numTaps-(4*S->L) coefficients. */
+      tapCnt = phaseLen >> 2u;
+
+      x0 = *(ptr1++);
+
+      while(tapCnt > 0u)
+      {
+
+        /* Read the input sample */
+        x1 = *(ptr1++);
+
+        /* Read the coefficient */
+        c0 = *(ptr2);
+
+        /* Perform the multiply-accumulate */
+        acc0 += (q63_t) x0 *c0;
+        acc1 += (q63_t) x1 *c0;
+
+
+        /* Read the coefficient */
+        c0 = *(ptr2 + S->L);
+
+        /* Read the input sample */
+        x0 = *(ptr1++);
+
+        /* Perform the multiply-accumulate */
+        acc0 += (q63_t) x1 *c0;
+        acc1 += (q63_t) x0 *c0;
+
+
+        /* Read the coefficient */
+        c0 = *(ptr2 + S->L * 2);
+
+        /* Read the input sample */
+        x1 = *(ptr1++);
+
+        /* Perform the multiply-accumulate */
+        acc0 += (q63_t) x0 *c0;
+        acc1 += (q63_t) x1 *c0;
+
+        /* Read the coefficient */
+        c0 = *(ptr2 + S->L * 3);
+
+        /* Read the input sample */
+        x0 = *(ptr1++);
+
+        /* Perform the multiply-accumulate */
+        acc0 += (q63_t) x1 *c0;
+        acc1 += (q63_t) x0 *c0;
+
+
+        /* Upsampling is done by stuffing L-1 zeros between each sample.        
+         * So instead of multiplying zeros with coefficients,        
+         * Increment the coefficient pointer by interpolation factor times. */
+        ptr2 += 4 * S->L;
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      /* If the polyPhase length is not a multiple of 4, compute the remaining filter taps */
+      tapCnt = phaseLen % 0x4u;
+
+      while(tapCnt > 0u)
+      {
+
+        /* Read the input sample */
+        x1 = *(ptr1++);
+
+        /* Read the coefficient */
+        c0 = *(ptr2);
+
+        /* Perform the multiply-accumulate */
+        acc0 += (q63_t) x0 *c0;
+        acc1 += (q63_t) x1 *c0;
+
+        /* Increment the coefficient pointer by interpolation factor times. */
+        ptr2 += S->L;
+
+        /* update states for next sample processing */
+        x0 = x1;
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      /* The result is in the accumulator, store in the destination buffer. */
+      *pDst = (q31_t) (acc0 >> 31);
+      *(pDst + S->L) = (q31_t) (acc1 >> 31);
+
+
+      pDst++;
+
+      /* Increment the address modifier index of coefficient buffer */
+      j++;
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Advance the state pointer by 1        
+     * to process the next group of interpolation factor number samples */
+    pState = pState + 2;
+
+    pDst += S->L;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 2, compute any remaining output samples here.        
+   ** No loop unrolling is used. */
+  blkCnt = blkCntN2;
+
+  /* Loop over the blockSize. */
+  while(blkCnt > 0u)
+  {
+    /* Copy new input sample into the state buffer */
+    *pStateCurnt++ = *pSrc++;
+
+    /* Address modifier index of coefficient buffer */
+    j = 1u;
+
+    /* Loop over the Interpolation factor. */
+    i = S->L;
+    while(i > 0u)
+    {
+      /* Set accumulator to zero */
+      sum0 = 0;
+
+      /* Initialize state pointer */
+      ptr1 = pState;
+
+      /* Initialize coefficient pointer */
+      ptr2 = pCoeffs + (S->L - j);
+
+      /* Loop over the polyPhase length. Unroll by a factor of 4.        
+       ** Repeat until we've computed numTaps-(4*S->L) coefficients. */
+      tapCnt = phaseLen >> 2;
+      while(tapCnt > 0u)
+      {
+
+        /* Read the coefficient */
+        c0 = *(ptr2);
+
+        /* Upsampling is done by stuffing L-1 zeros between each sample.        
+         * So instead of multiplying zeros with coefficients,        
+         * Increment the coefficient pointer by interpolation factor times. */
+        ptr2 += S->L;
+
+        /* Read the input sample */
+        x0 = *(ptr1++);
+
+        /* Perform the multiply-accumulate */
+        sum0 += (q63_t) x0 *c0;
+
+        /* Read the coefficient */
+        c0 = *(ptr2);
+
+        /* Increment the coefficient pointer by interpolation factor times. */
+        ptr2 += S->L;
+
+        /* Read the input sample */
+        x0 = *(ptr1++);
+
+        /* Perform the multiply-accumulate */
+        sum0 += (q63_t) x0 *c0;
+
+        /* Read the coefficient */
+        c0 = *(ptr2);
+
+        /* Increment the coefficient pointer by interpolation factor times. */
+        ptr2 += S->L;
+
+        /* Read the input sample */
+        x0 = *(ptr1++);
+
+        /* Perform the multiply-accumulate */
+        sum0 += (q63_t) x0 *c0;
+
+        /* Read the coefficient */
+        c0 = *(ptr2);
+
+        /* Increment the coefficient pointer by interpolation factor times. */
+        ptr2 += S->L;
+
+        /* Read the input sample */
+        x0 = *(ptr1++);
+
+        /* Perform the multiply-accumulate */
+        sum0 += (q63_t) x0 *c0;
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      /* If the polyPhase length is not a multiple of 4, compute the remaining filter taps */
+      tapCnt = phaseLen & 0x3u;
+
+      while(tapCnt > 0u)
+      {
+        /* Read the coefficient */
+        c0 = *(ptr2);
+
+        /* Increment the coefficient pointer by interpolation factor times. */
+        ptr2 += S->L;
+
+        /* Read the input sample */
+        x0 = *(ptr1++);
+
+        /* Perform the multiply-accumulate */
+        sum0 += (q63_t) x0 *c0;
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      /* The result is in the accumulator, store in the destination buffer. */
+      *pDst++ = (q31_t) (sum0 >> 31);
+
+      /* Increment the address modifier index of coefficient buffer */
+      j++;
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Advance the state pointer by 1        
+     * to process the next group of interpolation factor number samples */
+    pState = pState + 1;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Processing is complete.        
+   ** Now copy the last phaseLen - 1 samples to the satrt of the state buffer.        
+   ** This prepares the state buffer for the next function call. */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+  tapCnt = (phaseLen - 1u) >> 2u;
+
+  /* copy data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+  tapCnt = (phaseLen - 1u) % 0x04u;
+
+  /* copy data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+}
+
+
+#else
+
+void arm_fir_interpolate_q31(
+  const arm_fir_interpolate_instance_q31 * S,
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize)
+{
+  q31_t *pState = S->pState;                     /* State pointer */
+  q31_t *pCoeffs = S->pCoeffs;                   /* Coefficient pointer */
+  q31_t *pStateCurnt;                            /* Points to the current sample of the state */
+  q31_t *ptr1, *ptr2;                            /* Temporary pointers for state and coefficient buffers */
+
+  /* Run the below code for Cortex-M0 */
+
+  q63_t sum;                                     /* Accumulator */
+  q31_t x0, c0;                                  /* Temporary variables to hold state and coefficient values */
+  uint32_t i, blkCnt;                            /* Loop counters */
+  uint16_t phaseLen = S->phaseLength, tapCnt;    /* Length of each polyphase filter component */
+
+
+  /* S->pState buffer contains previous frame (phaseLen - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = S->pState + ((q31_t) phaseLen - 1);
+
+  /* Total number of intput samples */
+  blkCnt = blockSize;
+
+  /* Loop over the blockSize. */
+  while(blkCnt > 0u)
+  {
+    /* Copy new input sample into the state buffer */
+    *pStateCurnt++ = *pSrc++;
+
+    /* Loop over the Interpolation factor. */
+    i = S->L;
+
+    while(i > 0u)
+    {
+      /* Set accumulator to zero */
+      sum = 0;
+
+      /* Initialize state pointer */
+      ptr1 = pState;
+
+      /* Initialize coefficient pointer */
+      ptr2 = pCoeffs + (i - 1u);
+
+      tapCnt = phaseLen;
+
+      while(tapCnt > 0u)
+      {
+        /* Read the coefficient */
+        c0 = *(ptr2);
+
+        /* Increment the coefficient pointer by interpolation factor times. */
+        ptr2 += S->L;
+
+        /* Read the input sample */
+        x0 = *ptr1++;
+
+        /* Perform the multiply-accumulate */
+        sum += (q63_t) x0 *c0;
+
+        /* Decrement the loop counter */
+        tapCnt--;
+      }
+
+      /* The result is in the accumulator, store in the destination buffer. */
+      *pDst++ = (q31_t) (sum >> 31);
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Advance the state pointer by 1           
+     * to process the next group of interpolation factor number samples */
+    pState = pState + 1;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Processing is complete.         
+   ** Now copy the last phaseLen - 1 samples to the satrt of the state buffer.       
+   ** This prepares the state buffer for the next function call. */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+  tapCnt = phaseLen - 1u;
+
+  /* copy data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+}
+
+#endif /*   #ifndef ARM_MATH_CM0 */
+
+ /**    
+  * @} end of FIR_Interpolate group    
+  */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_lattice_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_lattice_f32.c
new file mode 100644
index 0000000000..3745ffb6a2
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_lattice_f32.c
@@ -0,0 +1,499 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_fir_lattice_f32.c    
+*    
+* Description:	Processing function for the floating-point FIR Lattice filter.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @defgroup FIR_Lattice Finite Impulse Response (FIR) Lattice Filters    
+ *    
+ * This set of functions implements Finite Impulse Response (FIR) lattice filters    
+ * for Q15, Q31 and floating-point data types.  Lattice filters are used in a     
+ * variety of adaptive filter applications.  The filter structure is feedforward and    
+ * the net impulse response is finite length.    
+ * The functions operate on blocks    
+ * of input and output data and each call to the function processes    
+ * blockSize samples through the filter.  pSrc and    
+ * pDst point to input and output arrays containing blockSize values.    
+ *    
+ * \par Algorithm:    
+ * \image html FIRLattice.gif "Finite Impulse Response Lattice filter"    
+ * The following difference equation is implemented:    
+ * 
    
+ *    f0[n] = g0[n] = x[n]    
+ *    fm[n] = fm-1[n] + km * gm-1[n-1] for m = 1, 2, ...M    
+ *    gm[n] = km * fm-1[n] + gm-1[n-1] for m = 1, 2, ...M    
+ *    y[n] = fM[n]    
+ * 
    
+ * \par    
+ * pCoeffs points to tha array of reflection coefficients of size numStages.    
+ * Reflection Coefficients are stored in the following order.    
+ * \par    
+ * 
    
+ *    {k1, k2, ..., kM}    
+ * 
    
+ * where M is number of stages    
+ * \par    
+ * pState points to a state array of size numStages.    
+ * The state variables (g values) hold previous inputs and are stored in the following order.    
+ * 
    
+ *    {g0[n], g1[n], g2[n] ...gM-1[n]}    
+ * 
    
+ * The state variables are updated after each block of data is processed; the coefficients are untouched.    
+ * \par Instance Structure    
+ * The coefficients and state variables for a filter are stored together in an instance data structure.    
+ * A separate instance structure must be defined for each filter.    
+ * Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.    
+ * There are separate instance structure declarations for each of the 3 supported data types.    
+ *    
+ * \par Initialization Functions    
+ * There is also an associated initialization function for each data type.    
+ * The initialization function performs the following operations:    
+ * - Sets the values of the internal structure fields.    
+ * - Zeros out the values in the state buffer.    
+ *    
+ * \par    
+ * Use of the initialization function is optional.    
+ * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.    
+ * To place an instance structure into a const data section, the instance structure must be manually initialized.    
+ * Set the values in the state buffer to zeros and then manually initialize the instance structure as follows:    
+ * 
    
+ *arm_fir_lattice_instance_f32 S = {numStages, pState, pCoeffs};    
+ *arm_fir_lattice_instance_q31 S = {numStages, pState, pCoeffs};    
+ *arm_fir_lattice_instance_q15 S = {numStages, pState, pCoeffs};    
+ * 
    
+ * \par    
+ * where numStages is the number of stages in the filter; pState is the address of the state buffer;    
+ * pCoeffs is the address of the coefficient buffer.    
+ * \par Fixed-Point Behavior    
+ * Care must be taken when using the fixed-point versions of the FIR Lattice filter functions.    
+ * In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.    
+ * Refer to the function specific documentation below for usage guidelines.    
+ */
+
+/**    
+ * @addtogroup FIR_Lattice    
+ * @{    
+ */
+
+
+  /**    
+   * @brief Processing function for the floating-point FIR lattice filter.    
+   * @param[in]  *S        points to an instance of the floating-point FIR lattice structure.    
+   * @param[in]  *pSrc     points to the block of input data.    
+   * @param[out] *pDst     points to the block of output data    
+   * @param[in]  blockSize number of samples to process.    
+   * @return none.    
+   */
+
+void arm_fir_lattice_f32(
+  const arm_fir_lattice_instance_f32 * S,
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize)
+{
+  float32_t *pState;                             /* State pointer */
+  float32_t *pCoeffs = S->pCoeffs;               /* Coefficient pointer */
+  float32_t *px;                                 /* temporary state pointer */
+  float32_t *pk;                                 /* temporary coefficient pointer */
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  float32_t fcurr1, fnext1, gcurr1, gnext1;      /* temporary variables for first sample in loop unrolling */
+  float32_t fcurr2, fnext2, gnext2;              /* temporary variables for second sample in loop unrolling */
+  float32_t fcurr3, fnext3, gnext3;              /* temporary variables for third sample in loop unrolling */
+  float32_t fcurr4, fnext4, gnext4;              /* temporary variables for fourth sample in loop unrolling */
+  uint32_t numStages = S->numStages;             /* Number of stages in the filter */
+  uint32_t blkCnt, stageCnt;                     /* temporary variables for counts */
+
+  gcurr1 = 0.0f;
+  pState = &S->pState[0];
+
+  blkCnt = blockSize >> 2;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+     a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+
+    /* Read two samples from input buffer */
+    /* f0(n) = x(n) */
+    fcurr1 = *pSrc++;
+    fcurr2 = *pSrc++;
+
+    /* Initialize coeff pointer */
+    pk = (pCoeffs);
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* Read g0(n-1) from state */
+    gcurr1 = *px;
+
+    /* Process first sample for first tap */
+    /* f1(n) = f0(n) +  K1 * g0(n-1) */
+    fnext1 = fcurr1 + ((*pk) * gcurr1);
+    /* g1(n) = f0(n) * K1  +  g0(n-1) */
+    gnext1 = (fcurr1 * (*pk)) + gcurr1;
+
+    /* Process second sample for first tap */
+    /* for sample 2 processing */
+    fnext2 = fcurr2 + ((*pk) * fcurr1);
+    gnext2 = (fcurr2 * (*pk)) + fcurr1;
+
+    /* Read next two samples from input buffer */
+    /* f0(n+2) = x(n+2) */
+    fcurr3 = *pSrc++;
+    fcurr4 = *pSrc++;
+
+    /* Copy only last input samples into the state buffer    
+       which will be used for next four samples processing */
+    *px++ = fcurr4;
+
+    /* Process third sample for first tap */
+    fnext3 = fcurr3 + ((*pk) * fcurr2);
+    gnext3 = (fcurr3 * (*pk)) + fcurr2;
+
+    /* Process fourth sample for first tap */
+    fnext4 = fcurr4 + ((*pk) * fcurr3);
+    gnext4 = (fcurr4 * (*pk++)) + fcurr3;
+
+    /* Update of f values for next coefficient set processing */
+    fcurr1 = fnext1;
+    fcurr2 = fnext2;
+    fcurr3 = fnext3;
+    fcurr4 = fnext4;
+
+    /* Loop unrolling.  Process 4 taps at a time . */
+    stageCnt = (numStages - 1u) >> 2u;
+
+    /* Loop over the number of taps.  Unroll by a factor of 4.    
+     ** Repeat until we've computed numStages-3 coefficients. */
+
+    /* Process 2nd, 3rd, 4th and 5th taps ... here */
+    while(stageCnt > 0u)
+    {
+      /* Read g1(n-1), g3(n-1) .... from state */
+      gcurr1 = *px;
+
+      /* save g1(n) in state buffer */
+      *px++ = gnext4;
+
+      /* Process first sample for 2nd, 6th .. tap */
+      /* Sample processing for K2, K6.... */
+      /* f2(n) = f1(n) +  K2 * g1(n-1) */
+      fnext1 = fcurr1 + ((*pk) * gcurr1);
+      /* Process second sample for 2nd, 6th .. tap */
+      /* for sample 2 processing */
+      fnext2 = fcurr2 + ((*pk) * gnext1);
+      /* Process third sample for 2nd, 6th .. tap */
+      fnext3 = fcurr3 + ((*pk) * gnext2);
+      /* Process fourth sample for 2nd, 6th .. tap */
+      fnext4 = fcurr4 + ((*pk) * gnext3);
+
+      /* g2(n) = f1(n) * K2  +  g1(n-1) */
+      /* Calculation of state values for next stage */
+      gnext4 = (fcurr4 * (*pk)) + gnext3;
+      gnext3 = (fcurr3 * (*pk)) + gnext2;
+      gnext2 = (fcurr2 * (*pk)) + gnext1;
+      gnext1 = (fcurr1 * (*pk++)) + gcurr1;
+
+
+      /* Read g2(n-1), g4(n-1) .... from state */
+      gcurr1 = *px;
+
+      /* save g2(n) in state buffer */
+      *px++ = gnext4;
+
+      /* Sample processing for K3, K7.... */
+      /* Process first sample for 3rd, 7th .. tap */
+      /* f3(n) = f2(n) +  K3 * g2(n-1) */
+      fcurr1 = fnext1 + ((*pk) * gcurr1);
+      /* Process second sample for 3rd, 7th .. tap */
+      fcurr2 = fnext2 + ((*pk) * gnext1);
+      /* Process third sample for 3rd, 7th .. tap */
+      fcurr3 = fnext3 + ((*pk) * gnext2);
+      /* Process fourth sample for 3rd, 7th .. tap */
+      fcurr4 = fnext4 + ((*pk) * gnext3);
+
+      /* Calculation of state values for next stage */
+      /* g3(n) = f2(n) * K3  +  g2(n-1) */
+      gnext4 = (fnext4 * (*pk)) + gnext3;
+      gnext3 = (fnext3 * (*pk)) + gnext2;
+      gnext2 = (fnext2 * (*pk)) + gnext1;
+      gnext1 = (fnext1 * (*pk++)) + gcurr1;
+
+
+      /* Read g1(n-1), g3(n-1) .... from state */
+      gcurr1 = *px;
+
+      /* save g3(n) in state buffer */
+      *px++ = gnext4;
+
+      /* Sample processing for K4, K8.... */
+      /* Process first sample for 4th, 8th .. tap */
+      /* f4(n) = f3(n) +  K4 * g3(n-1) */
+      fnext1 = fcurr1 + ((*pk) * gcurr1);
+      /* Process second sample for 4th, 8th .. tap */
+      /* for sample 2 processing */
+      fnext2 = fcurr2 + ((*pk) * gnext1);
+      /* Process third sample for 4th, 8th .. tap */
+      fnext3 = fcurr3 + ((*pk) * gnext2);
+      /* Process fourth sample for 4th, 8th .. tap */
+      fnext4 = fcurr4 + ((*pk) * gnext3);
+
+      /* g4(n) = f3(n) * K4  +  g3(n-1) */
+      /* Calculation of state values for next stage */
+      gnext4 = (fcurr4 * (*pk)) + gnext3;
+      gnext3 = (fcurr3 * (*pk)) + gnext2;
+      gnext2 = (fcurr2 * (*pk)) + gnext1;
+      gnext1 = (fcurr1 * (*pk++)) + gcurr1;
+
+      /* Read g2(n-1), g4(n-1) .... from state */
+      gcurr1 = *px;
+
+      /* save g4(n) in state buffer */
+      *px++ = gnext4;
+
+      /* Sample processing for K5, K9.... */
+      /* Process first sample for 5th, 9th .. tap */
+      /* f5(n) = f4(n) +  K5 * g4(n-1) */
+      fcurr1 = fnext1 + ((*pk) * gcurr1);
+      /* Process second sample for 5th, 9th .. tap */
+      fcurr2 = fnext2 + ((*pk) * gnext1);
+      /* Process third sample for 5th, 9th .. tap */
+      fcurr3 = fnext3 + ((*pk) * gnext2);
+      /* Process fourth sample for 5th, 9th .. tap */
+      fcurr4 = fnext4 + ((*pk) * gnext3);
+
+      /* Calculation of state values for next stage */
+      /* g5(n) = f4(n) * K5  +  g4(n-1) */
+      gnext4 = (fnext4 * (*pk)) + gnext3;
+      gnext3 = (fnext3 * (*pk)) + gnext2;
+      gnext2 = (fnext2 * (*pk)) + gnext1;
+      gnext1 = (fnext1 * (*pk++)) + gcurr1;
+
+      stageCnt--;
+    }
+
+    /* If the (filter length -1) is not a multiple of 4, compute the remaining filter taps */
+    stageCnt = (numStages - 1u) % 0x4u;
+
+    while(stageCnt > 0u)
+    {
+      gcurr1 = *px;
+
+      /* save g value in state buffer */
+      *px++ = gnext4;
+
+      /* Process four samples for last three taps here */
+      fnext1 = fcurr1 + ((*pk) * gcurr1);
+      fnext2 = fcurr2 + ((*pk) * gnext1);
+      fnext3 = fcurr3 + ((*pk) * gnext2);
+      fnext4 = fcurr4 + ((*pk) * gnext3);
+
+      /* g1(n) = f0(n) * K1  +  g0(n-1) */
+      gnext4 = (fcurr4 * (*pk)) + gnext3;
+      gnext3 = (fcurr3 * (*pk)) + gnext2;
+      gnext2 = (fcurr2 * (*pk)) + gnext1;
+      gnext1 = (fcurr1 * (*pk++)) + gcurr1;
+
+      /* Update of f values for next coefficient set processing */
+      fcurr1 = fnext1;
+      fcurr2 = fnext2;
+      fcurr3 = fnext3;
+      fcurr4 = fnext4;
+
+      stageCnt--;
+
+    }
+
+    /* The results in the 4 accumulators, store in the destination buffer. */
+    /* y(n) = fN(n) */
+    *pDst++ = fcurr1;
+    *pDst++ = fcurr2;
+    *pDst++ = fcurr3;
+    *pDst++ = fcurr4;
+
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* f0(n) = x(n) */
+    fcurr1 = *pSrc++;
+
+    /* Initialize coeff pointer */
+    pk = (pCoeffs);
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* read g2(n) from state buffer */
+    gcurr1 = *px;
+
+    /* for sample 1 processing */
+    /* f1(n) = f0(n) +  K1 * g0(n-1) */
+    fnext1 = fcurr1 + ((*pk) * gcurr1);
+    /* g1(n) = f0(n) * K1  +  g0(n-1) */
+    gnext1 = (fcurr1 * (*pk++)) + gcurr1;
+
+    /* save g1(n) in state buffer */
+    *px++ = fcurr1;
+
+    /* f1(n) is saved in fcurr1    
+       for next stage processing */
+    fcurr1 = fnext1;
+
+    stageCnt = (numStages - 1u);
+
+    /* stage loop */
+    while(stageCnt > 0u)
+    {
+      /* read g2(n) from state buffer */
+      gcurr1 = *px;
+
+      /* save g1(n) in state buffer */
+      *px++ = gnext1;
+
+      /* Sample processing for K2, K3.... */
+      /* f2(n) = f1(n) +  K2 * g1(n-1) */
+      fnext1 = fcurr1 + ((*pk) * gcurr1);
+      /* g2(n) = f1(n) * K2  +  g1(n-1) */
+      gnext1 = (fcurr1 * (*pk++)) + gcurr1;
+
+      /* f1(n) is saved in fcurr1    
+         for next stage processing */
+      fcurr1 = fnext1;
+
+      stageCnt--;
+
+    }
+
+    /* y(n) = fN(n) */
+    *pDst++ = fcurr1;
+
+    blkCnt--;
+
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  float32_t fcurr, fnext, gcurr, gnext;          /* temporary variables */
+  uint32_t numStages = S->numStages;             /* Length of the filter */
+  uint32_t blkCnt, stageCnt;                     /* temporary variables for counts */
+
+  pState = &S->pState[0];
+
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* f0(n) = x(n) */
+    fcurr = *pSrc++;
+
+    /* Initialize coeff pointer */
+    pk = pCoeffs;
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* read g0(n-1) from state buffer */
+    gcurr = *px;
+
+    /* for sample 1 processing */
+    /* f1(n) = f0(n) +  K1 * g0(n-1) */
+    fnext = fcurr + ((*pk) * gcurr);
+    /* g1(n) = f0(n) * K1  +  g0(n-1) */
+    gnext = (fcurr * (*pk++)) + gcurr;
+
+    /* save f0(n) in state buffer */
+    *px++ = fcurr;
+
+    /* f1(n) is saved in fcurr            
+       for next stage processing */
+    fcurr = fnext;
+
+    stageCnt = (numStages - 1u);
+
+    /* stage loop */
+    while(stageCnt > 0u)
+    {
+      /* read g2(n) from state buffer */
+      gcurr = *px;
+
+      /* save g1(n) in state buffer */
+      *px++ = gnext;
+
+      /* Sample processing for K2, K3.... */
+      /* f2(n) = f1(n) +  K2 * g1(n-1) */
+      fnext = fcurr + ((*pk) * gcurr);
+      /* g2(n) = f1(n) * K2  +  g1(n-1) */
+      gnext = (fcurr * (*pk++)) + gcurr;
+
+      /* f1(n) is saved in fcurr1            
+         for next stage processing */
+      fcurr = fnext;
+
+      stageCnt--;
+
+    }
+
+    /* y(n) = fN(n) */
+    *pDst++ = fcurr;
+
+    blkCnt--;
+
+  }
+
+#endif /*   #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of FIR_Lattice group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_lattice_init_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_lattice_init_f32.c
new file mode 100644
index 0000000000..a53ae92e2f
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_lattice_init_f32.c
@@ -0,0 +1,78 @@
+/*-----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_fir_lattice_init_f32.c    
+*    
+* Description:  Floating-point FIR Lattice filter initialization function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ---------------------------------------------------------------------------*/
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR_Lattice    
+ * @{    
+ */
+
+/**    
+ * @brief Initialization function for the floating-point FIR lattice filter.    
+ * @param[in] *S points to an instance of the floating-point FIR lattice structure.    
+ * @param[in] numStages  number of filter stages.    
+ * @param[in] *pCoeffs points to the coefficient buffer.  The array is of length numStages.    
+ * @param[in] *pState points to the state buffer.  The array is of length numStages.    
+ * @return none.    
+ */
+
+void arm_fir_lattice_init_f32(
+  arm_fir_lattice_instance_f32 * S,
+  uint16_t numStages,
+  float32_t * pCoeffs,
+  float32_t * pState)
+{
+  /* Assign filter taps */
+  S->numStages = numStages;
+
+  /* Assign coefficient pointer */
+  S->pCoeffs = pCoeffs;
+
+  /* Clear state buffer and size is always numStages */
+  memset(pState, 0, (numStages) * sizeof(float32_t));
+
+  /* Assign state pointer */
+  S->pState = pState;
+
+}
+
+/**    
+ * @} end of FIR_Lattice group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_lattice_init_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_lattice_init_q15.c
new file mode 100644
index 0000000000..8db4985090
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_lattice_init_q15.c
@@ -0,0 +1,78 @@
+/*-----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_fir_lattice_init_q15.c    
+*    
+* Description:  Q15 FIR Lattice filter initialization function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ---------------------------------------------------------------------------*/
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR_Lattice    
+ * @{    
+ */
+
+  /**    
+   * @brief Initialization function for the Q15 FIR lattice filter.    
+   * @param[in] *S points to an instance of the Q15 FIR lattice structure.    
+   * @param[in] numStages  number of filter stages.    
+   * @param[in] *pCoeffs points to the coefficient buffer.  The array is of length numStages.     
+   * @param[in] *pState points to the state buffer.  The array is of length numStages.     
+   * @return none.    
+   */
+
+void arm_fir_lattice_init_q15(
+  arm_fir_lattice_instance_q15 * S,
+  uint16_t numStages,
+  q15_t * pCoeffs,
+  q15_t * pState)
+{
+  /* Assign filter taps */
+  S->numStages = numStages;
+
+  /* Assign coefficient pointer */
+  S->pCoeffs = pCoeffs;
+
+  /* Clear state buffer and size is always numStages */
+  memset(pState, 0, (numStages) * sizeof(q15_t));
+
+  /* Assign state pointer */
+  S->pState = pState;
+
+}
+
+/**    
+ * @} end of FIR_Lattice group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_lattice_init_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_lattice_init_q31.c
new file mode 100644
index 0000000000..035c5e056a
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_lattice_init_q31.c
@@ -0,0 +1,78 @@
+/*-----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_fir_lattice_init_q31.c    
+*    
+* Description:  Q31 FIR lattice filter initialization function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ---------------------------------------------------------------------------*/
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR_Lattice    
+ * @{    
+ */
+
+  /**    
+   * @brief Initialization function for the Q31 FIR lattice filter.    
+   * @param[in] *S points to an instance of the Q31 FIR lattice structure.    
+   * @param[in] numStages  number of filter stages.    
+   * @param[in] *pCoeffs points to the coefficient buffer.  The array is of length numStages.    
+   * @param[in] *pState points to the state buffer.   The array is of length numStages.    
+   * @return none.    
+   */
+
+void arm_fir_lattice_init_q31(
+  arm_fir_lattice_instance_q31 * S,
+  uint16_t numStages,
+  q31_t * pCoeffs,
+  q31_t * pState)
+{
+  /* Assign filter taps */
+  S->numStages = numStages;
+
+  /* Assign coefficient pointer */
+  S->pCoeffs = pCoeffs;
+
+  /* Clear state buffer and size is always numStages */
+  memset(pState, 0, (numStages) * sizeof(q31_t));
+
+  /* Assign state pointer */
+  S->pState = pState;
+
+}
+
+/**    
+ * @} end of FIR_Lattice group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_lattice_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_lattice_q15.c
new file mode 100644
index 0000000000..abfb33cf24
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_lattice_q15.c
@@ -0,0 +1,531 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_fir_lattice_q15.c    
+*    
+* Description:	Q15 FIR lattice filter processing function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR_Lattice    
+ * @{    
+ */
+
+
+/**    
+ * @brief Processing function for the Q15 FIR lattice filter.    
+ * @param[in]  *S        points to an instance of the Q15 FIR lattice structure.    
+ * @param[in]  *pSrc     points to the block of input data.    
+ * @param[out] *pDst     points to the block of output data    
+ * @param[in]  blockSize number of samples to process.    
+ * @return none.    
+ */
+
+void arm_fir_lattice_q15(
+  const arm_fir_lattice_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+  q15_t *pState;                                 /* State pointer */
+  q15_t *pCoeffs = S->pCoeffs;                   /* Coefficient pointer */
+  q15_t *px;                                     /* temporary state pointer */
+  q15_t *pk;                                     /* temporary coefficient pointer */
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q31_t fcurnt1, fnext1, gcurnt1 = 0, gnext1;    /* temporary variables for first sample in loop unrolling */
+  q31_t fcurnt2, fnext2, gnext2;                 /* temporary variables for second sample in loop unrolling */
+  q31_t fcurnt3, fnext3, gnext3;                 /* temporary variables for third sample in loop unrolling */
+  q31_t fcurnt4, fnext4, gnext4;                 /* temporary variables for fourth sample in loop unrolling */
+  uint32_t numStages = S->numStages;             /* Number of stages in the filter */
+  uint32_t blkCnt, stageCnt;                     /* temporary variables for counts */
+
+  pState = &S->pState[0];
+
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+
+    /* Read two samples from input buffer */
+    /* f0(n) = x(n) */
+    fcurnt1 = *pSrc++;
+    fcurnt2 = *pSrc++;
+
+    /* Initialize coeff pointer */
+    pk = (pCoeffs);
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* Read g0(n-1) from state */
+    gcurnt1 = *px;
+
+    /* Process first sample for first tap */
+    /* f1(n) = f0(n) +  K1 * g0(n-1) */
+    fnext1 = (q31_t) ((gcurnt1 * (*pk)) >> 15u) + fcurnt1;
+    fnext1 = __SSAT(fnext1, 16);
+
+    /* g1(n) = f0(n) * K1  +  g0(n-1) */
+    gnext1 = (q31_t) ((fcurnt1 * (*pk)) >> 15u) + gcurnt1;
+    gnext1 = __SSAT(gnext1, 16);
+
+    /* Process second sample for first tap */
+    /* for sample 2 processing */
+    fnext2 = (q31_t) ((fcurnt1 * (*pk)) >> 15u) + fcurnt2;
+    fnext2 = __SSAT(fnext2, 16);
+
+    gnext2 = (q31_t) ((fcurnt2 * (*pk)) >> 15u) + fcurnt1;
+    gnext2 = __SSAT(gnext2, 16);
+
+
+    /* Read next two samples from input buffer */
+    /* f0(n+2) = x(n+2) */
+    fcurnt3 = *pSrc++;
+    fcurnt4 = *pSrc++;
+
+    /* Copy only last input samples into the state buffer    
+       which is used for next four samples processing */
+    *px++ = (q15_t) fcurnt4;
+
+    /* Process third sample for first tap */
+    fnext3 = (q31_t) ((fcurnt2 * (*pk)) >> 15u) + fcurnt3;
+    fnext3 = __SSAT(fnext3, 16);
+    gnext3 = (q31_t) ((fcurnt3 * (*pk)) >> 15u) + fcurnt2;
+    gnext3 = __SSAT(gnext3, 16);
+
+    /* Process fourth sample for first tap */
+    fnext4 = (q31_t) ((fcurnt3 * (*pk)) >> 15u) + fcurnt4;
+    fnext4 = __SSAT(fnext4, 16);
+    gnext4 = (q31_t) ((fcurnt4 * (*pk++)) >> 15u) + fcurnt3;
+    gnext4 = __SSAT(gnext4, 16);
+
+    /* Update of f values for next coefficient set processing */
+    fcurnt1 = fnext1;
+    fcurnt2 = fnext2;
+    fcurnt3 = fnext3;
+    fcurnt4 = fnext4;
+
+
+    /* Loop unrolling.  Process 4 taps at a time . */
+    stageCnt = (numStages - 1u) >> 2;
+
+
+    /* Loop over the number of taps.  Unroll by a factor of 4.    
+     ** Repeat until we've computed numStages-3 coefficients. */
+
+    /* Process 2nd, 3rd, 4th and 5th taps ... here */
+    while(stageCnt > 0u)
+    {
+      /* Read g1(n-1), g3(n-1) .... from state */
+      gcurnt1 = *px;
+
+      /* save g1(n) in state buffer */
+      *px++ = (q15_t) gnext4;
+
+      /* Process first sample for 2nd, 6th .. tap */
+      /* Sample processing for K2, K6.... */
+      /* f1(n) = f0(n) +  K1 * g0(n-1) */
+      fnext1 = (q31_t) ((gcurnt1 * (*pk)) >> 15u) + fcurnt1;
+      fnext1 = __SSAT(fnext1, 16);
+
+
+      /* Process second sample for 2nd, 6th .. tap */
+      /* for sample 2 processing */
+      fnext2 = (q31_t) ((gnext1 * (*pk)) >> 15u) + fcurnt2;
+      fnext2 = __SSAT(fnext2, 16);
+      /* Process third sample for 2nd, 6th .. tap */
+      fnext3 = (q31_t) ((gnext2 * (*pk)) >> 15u) + fcurnt3;
+      fnext3 = __SSAT(fnext3, 16);
+      /* Process fourth sample for 2nd, 6th .. tap */
+      /* fnext4 = fcurnt4 + (*pk) * gnext3; */
+      fnext4 = (q31_t) ((gnext3 * (*pk)) >> 15u) + fcurnt4;
+      fnext4 = __SSAT(fnext4, 16);
+
+      /* g1(n) = f0(n) * K1  +  g0(n-1) */
+      /* Calculation of state values for next stage */
+      gnext4 = (q31_t) ((fcurnt4 * (*pk)) >> 15u) + gnext3;
+      gnext4 = __SSAT(gnext4, 16);
+      gnext3 = (q31_t) ((fcurnt3 * (*pk)) >> 15u) + gnext2;
+      gnext3 = __SSAT(gnext3, 16);
+
+      gnext2 = (q31_t) ((fcurnt2 * (*pk)) >> 15u) + gnext1;
+      gnext2 = __SSAT(gnext2, 16);
+
+      gnext1 = (q31_t) ((fcurnt1 * (*pk++)) >> 15u) + gcurnt1;
+      gnext1 = __SSAT(gnext1, 16);
+
+
+      /* Read g2(n-1), g4(n-1) .... from state */
+      gcurnt1 = *px;
+
+      /* save g1(n) in state buffer */
+      *px++ = (q15_t) gnext4;
+
+      /* Sample processing for K3, K7.... */
+      /* Process first sample for 3rd, 7th .. tap */
+      /* f3(n) = f2(n) +  K3 * g2(n-1) */
+      fcurnt1 = (q31_t) ((gcurnt1 * (*pk)) >> 15u) + fnext1;
+      fcurnt1 = __SSAT(fcurnt1, 16);
+
+      /* Process second sample for 3rd, 7th .. tap */
+      fcurnt2 = (q31_t) ((gnext1 * (*pk)) >> 15u) + fnext2;
+      fcurnt2 = __SSAT(fcurnt2, 16);
+
+      /* Process third sample for 3rd, 7th .. tap */
+      fcurnt3 = (q31_t) ((gnext2 * (*pk)) >> 15u) + fnext3;
+      fcurnt3 = __SSAT(fcurnt3, 16);
+
+      /* Process fourth sample for 3rd, 7th .. tap */
+      fcurnt4 = (q31_t) ((gnext3 * (*pk)) >> 15u) + fnext4;
+      fcurnt4 = __SSAT(fcurnt4, 16);
+
+      /* Calculation of state values for next stage */
+      /* g3(n) = f2(n) * K3  +  g2(n-1) */
+      gnext4 = (q31_t) ((fnext4 * (*pk)) >> 15u) + gnext3;
+      gnext4 = __SSAT(gnext4, 16);
+
+      gnext3 = (q31_t) ((fnext3 * (*pk)) >> 15u) + gnext2;
+      gnext3 = __SSAT(gnext3, 16);
+
+      gnext2 = (q31_t) ((fnext2 * (*pk)) >> 15u) + gnext1;
+      gnext2 = __SSAT(gnext2, 16);
+
+      gnext1 = (q31_t) ((fnext1 * (*pk++)) >> 15u) + gcurnt1;
+      gnext1 = __SSAT(gnext1, 16);
+
+      /* Read g1(n-1), g3(n-1) .... from state */
+      gcurnt1 = *px;
+
+      /* save g1(n) in state buffer */
+      *px++ = (q15_t) gnext4;
+
+      /* Sample processing for K4, K8.... */
+      /* Process first sample for 4th, 8th .. tap */
+      /* f4(n) = f3(n) +  K4 * g3(n-1) */
+      fnext1 = (q31_t) ((gcurnt1 * (*pk)) >> 15u) + fcurnt1;
+      fnext1 = __SSAT(fnext1, 16);
+
+      /* Process second sample for 4th, 8th .. tap */
+      /* for sample 2 processing */
+      fnext2 = (q31_t) ((gnext1 * (*pk)) >> 15u) + fcurnt2;
+      fnext2 = __SSAT(fnext2, 16);
+
+      /* Process third sample for 4th, 8th .. tap */
+      fnext3 = (q31_t) ((gnext2 * (*pk)) >> 15u) + fcurnt3;
+      fnext3 = __SSAT(fnext3, 16);
+
+      /* Process fourth sample for 4th, 8th .. tap */
+      fnext4 = (q31_t) ((gnext3 * (*pk)) >> 15u) + fcurnt4;
+      fnext4 = __SSAT(fnext4, 16);
+
+      /* g4(n) = f3(n) * K4  +  g3(n-1) */
+      /* Calculation of state values for next stage */
+      gnext4 = (q31_t) ((fcurnt4 * (*pk)) >> 15u) + gnext3;
+      gnext4 = __SSAT(gnext4, 16);
+
+      gnext3 = (q31_t) ((fcurnt3 * (*pk)) >> 15u) + gnext2;
+      gnext3 = __SSAT(gnext3, 16);
+
+      gnext2 = (q31_t) ((fcurnt2 * (*pk)) >> 15u) + gnext1;
+      gnext2 = __SSAT(gnext2, 16);
+      gnext1 = (q31_t) ((fcurnt1 * (*pk++)) >> 15u) + gcurnt1;
+      gnext1 = __SSAT(gnext1, 16);
+
+
+      /* Read g2(n-1), g4(n-1) .... from state */
+      gcurnt1 = *px;
+
+      /* save g4(n) in state buffer */
+      *px++ = (q15_t) gnext4;
+
+      /* Sample processing for K5, K9.... */
+      /* Process first sample for 5th, 9th .. tap */
+      /* f5(n) = f4(n) +  K5 * g4(n-1) */
+      fcurnt1 = (q31_t) ((gcurnt1 * (*pk)) >> 15u) + fnext1;
+      fcurnt1 = __SSAT(fcurnt1, 16);
+
+      /* Process second sample for 5th, 9th .. tap */
+      fcurnt2 = (q31_t) ((gnext1 * (*pk)) >> 15u) + fnext2;
+      fcurnt2 = __SSAT(fcurnt2, 16);
+
+      /* Process third sample for 5th, 9th .. tap */
+      fcurnt3 = (q31_t) ((gnext2 * (*pk)) >> 15u) + fnext3;
+      fcurnt3 = __SSAT(fcurnt3, 16);
+
+      /* Process fourth sample for 5th, 9th .. tap */
+      fcurnt4 = (q31_t) ((gnext3 * (*pk)) >> 15u) + fnext4;
+      fcurnt4 = __SSAT(fcurnt4, 16);
+
+      /* Calculation of state values for next stage */
+      /* g5(n) = f4(n) * K5  +  g4(n-1) */
+      gnext4 = (q31_t) ((fnext4 * (*pk)) >> 15u) + gnext3;
+      gnext4 = __SSAT(gnext4, 16);
+      gnext3 = (q31_t) ((fnext3 * (*pk)) >> 15u) + gnext2;
+      gnext3 = __SSAT(gnext3, 16);
+      gnext2 = (q31_t) ((fnext2 * (*pk)) >> 15u) + gnext1;
+      gnext2 = __SSAT(gnext2, 16);
+      gnext1 = (q31_t) ((fnext1 * (*pk++)) >> 15u) + gcurnt1;
+      gnext1 = __SSAT(gnext1, 16);
+
+      stageCnt--;
+    }
+
+    /* If the (filter length -1) is not a multiple of 4, compute the remaining filter taps */
+    stageCnt = (numStages - 1u) % 0x4u;
+
+    while(stageCnt > 0u)
+    {
+      gcurnt1 = *px;
+
+      /* save g value in state buffer */
+      *px++ = (q15_t) gnext4;
+
+      /* Process four samples for last three taps here */
+      fnext1 = (q31_t) ((gcurnt1 * (*pk)) >> 15u) + fcurnt1;
+      fnext1 = __SSAT(fnext1, 16);
+      fnext2 = (q31_t) ((gnext1 * (*pk)) >> 15u) + fcurnt2;
+      fnext2 = __SSAT(fnext2, 16);
+
+      fnext3 = (q31_t) ((gnext2 * (*pk)) >> 15u) + fcurnt3;
+      fnext3 = __SSAT(fnext3, 16);
+
+      fnext4 = (q31_t) ((gnext3 * (*pk)) >> 15u) + fcurnt4;
+      fnext4 = __SSAT(fnext4, 16);
+
+      /* g1(n) = f0(n) * K1  +  g0(n-1) */
+      gnext4 = (q31_t) ((fcurnt4 * (*pk)) >> 15u) + gnext3;
+      gnext4 = __SSAT(gnext4, 16);
+      gnext3 = (q31_t) ((fcurnt3 * (*pk)) >> 15u) + gnext2;
+      gnext3 = __SSAT(gnext3, 16);
+      gnext2 = (q31_t) ((fcurnt2 * (*pk)) >> 15u) + gnext1;
+      gnext2 = __SSAT(gnext2, 16);
+      gnext1 = (q31_t) ((fcurnt1 * (*pk++)) >> 15u) + gcurnt1;
+      gnext1 = __SSAT(gnext1, 16);
+
+      /* Update of f values for next coefficient set processing */
+      fcurnt1 = fnext1;
+      fcurnt2 = fnext2;
+      fcurnt3 = fnext3;
+      fcurnt4 = fnext4;
+
+      stageCnt--;
+
+    }
+
+    /* The results in the 4 accumulators, store in the destination buffer. */
+    /* y(n) = fN(n) */
+
+#ifndef  ARM_MATH_BIG_ENDIAN
+
+    *__SIMD32(pDst)++ = __PKHBT(fcurnt1, fcurnt2, 16);
+    *__SIMD32(pDst)++ = __PKHBT(fcurnt3, fcurnt4, 16);
+
+#else
+
+    *__SIMD32(pDst)++ = __PKHBT(fcurnt2, fcurnt1, 16);
+    *__SIMD32(pDst)++ = __PKHBT(fcurnt4, fcurnt3, 16);
+
+#endif /*      #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* f0(n) = x(n) */
+    fcurnt1 = *pSrc++;
+
+    /* Initialize coeff pointer */
+    pk = (pCoeffs);
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* read g2(n) from state buffer */
+    gcurnt1 = *px;
+
+    /* for sample 1 processing */
+    /* f1(n) = f0(n) +  K1 * g0(n-1) */
+    fnext1 = (((q31_t) gcurnt1 * (*pk)) >> 15u) + fcurnt1;
+    fnext1 = __SSAT(fnext1, 16);
+
+
+    /* g1(n) = f0(n) * K1  +  g0(n-1) */
+    gnext1 = (((q31_t) fcurnt1 * (*pk++)) >> 15u) + gcurnt1;
+    gnext1 = __SSAT(gnext1, 16);
+
+    /* save g1(n) in state buffer */
+    *px++ = (q15_t) fcurnt1;
+
+    /* f1(n) is saved in fcurnt1    
+       for next stage processing */
+    fcurnt1 = fnext1;
+
+    stageCnt = (numStages - 1u);
+
+    /* stage loop */
+    while(stageCnt > 0u)
+    {
+      /* read g2(n) from state buffer */
+      gcurnt1 = *px;
+
+      /* save g1(n) in state buffer */
+      *px++ = (q15_t) gnext1;
+
+      /* Sample processing for K2, K3.... */
+      /* f2(n) = f1(n) +  K2 * g1(n-1) */
+      fnext1 = (((q31_t) gcurnt1 * (*pk)) >> 15u) + fcurnt1;
+      fnext1 = __SSAT(fnext1, 16);
+
+      /* g2(n) = f1(n) * K2  +  g1(n-1) */
+      gnext1 = (((q31_t) fcurnt1 * (*pk++)) >> 15u) + gcurnt1;
+      gnext1 = __SSAT(gnext1, 16);
+
+
+      /* f1(n) is saved in fcurnt1    
+         for next stage processing */
+      fcurnt1 = fnext1;
+
+      stageCnt--;
+
+    }
+
+    /* y(n) = fN(n) */
+    *pDst++ = __SSAT(fcurnt1, 16);
+
+
+    blkCnt--;
+
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  q31_t fcurnt, fnext, gcurnt, gnext;            /* temporary variables */
+  uint32_t numStages = S->numStages;             /* Length of the filter */
+  uint32_t blkCnt, stageCnt;                     /* temporary variables for counts */
+
+  pState = &S->pState[0];
+
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* f0(n) = x(n) */
+    fcurnt = *pSrc++;
+
+    /* Initialize coeff pointer */
+    pk = (pCoeffs);
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* read g0(n-1) from state buffer */
+    gcurnt = *px;
+
+    /* for sample 1 processing */
+    /* f1(n) = f0(n) +  K1 * g0(n-1) */
+    fnext = ((gcurnt * (*pk)) >> 15u) + fcurnt;
+    fnext = __SSAT(fnext, 16);
+
+
+    /* g1(n) = f0(n) * K1  +  g0(n-1) */
+    gnext = ((fcurnt * (*pk++)) >> 15u) + gcurnt;
+    gnext = __SSAT(gnext, 16);
+
+    /* save f0(n) in state buffer */
+    *px++ = (q15_t) fcurnt;
+
+    /* f1(n) is saved in fcurnt            
+       for next stage processing */
+    fcurnt = fnext;
+
+    stageCnt = (numStages - 1u);
+
+    /* stage loop */
+    while(stageCnt > 0u)
+    {
+      /* read g1(n-1) from state buffer */
+      gcurnt = *px;
+
+      /* save g0(n-1) in state buffer */
+      *px++ = (q15_t) gnext;
+
+      /* Sample processing for K2, K3.... */
+      /* f2(n) = f1(n) +  K2 * g1(n-1) */
+      fnext = ((gcurnt * (*pk)) >> 15u) + fcurnt;
+      fnext = __SSAT(fnext, 16);
+
+      /* g2(n) = f1(n) * K2  +  g1(n-1) */
+      gnext = ((fcurnt * (*pk++)) >> 15u) + gcurnt;
+      gnext = __SSAT(gnext, 16);
+
+
+      /* f1(n) is saved in fcurnt            
+         for next stage processing */
+      fcurnt = fnext;
+
+      stageCnt--;
+
+    }
+
+    /* y(n) = fN(n) */
+    *pDst++ = __SSAT(fcurnt, 16);
+
+
+    blkCnt--;
+
+  }
+
+#endif /*   #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of FIR_Lattice group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_lattice_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_lattice_q31.c
new file mode 100644
index 0000000000..9fb46459dc
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_lattice_q31.c
@@ -0,0 +1,348 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_fir_lattice_q31.c    
+*    
+* Description:	Q31 FIR lattice filter processing function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR_Lattice    
+ * @{    
+ */
+
+
+/**    
+ * @brief Processing function for the Q31 FIR lattice filter.    
+ * @param[in]  *S        points to an instance of the Q31 FIR lattice structure.    
+ * @param[in]  *pSrc     points to the block of input data.    
+ * @param[out] *pDst     points to the block of output data    
+ * @param[in]  blockSize number of samples to process.    
+ * @return none.    
+ *    
+ * @details    
+ * Scaling and Overflow Behavior:    
+ * In order to avoid overflows the input signal must be scaled down by 2*log2(numStages) bits.    
+ */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+void arm_fir_lattice_q31(
+  const arm_fir_lattice_instance_q31 * S,
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize)
+{
+  q31_t *pState;                                 /* State pointer */
+  q31_t *pCoeffs = S->pCoeffs;                   /* Coefficient pointer */
+  q31_t *px;                                     /* temporary state pointer */
+  q31_t *pk;                                     /* temporary coefficient pointer */
+  q31_t fcurr1, fnext1, gcurr1 = 0, gnext1;      /* temporary variables for first sample in loop unrolling */
+  q31_t fcurr2, fnext2, gnext2;                  /* temporary variables for second sample in loop unrolling */
+  uint32_t numStages = S->numStages;             /* Length of the filter */
+  uint32_t blkCnt, stageCnt;                     /* temporary variables for counts */
+  q31_t k;
+
+  pState = &S->pState[0];
+
+  blkCnt = blockSize >> 1u;
+
+  /* First part of the processing with loop unrolling.  Compute 2 outputs at a time.        
+     a second loop below computes the remaining 1 sample. */
+  while(blkCnt > 0u)
+  {
+    /* f0(n) = x(n) */
+    fcurr1 = *pSrc++;
+
+    /* f0(n) = x(n) */
+    fcurr2 = *pSrc++;
+
+    /* Initialize coeff pointer */
+    pk = (pCoeffs);
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* read g0(n - 1) from state buffer */
+    gcurr1 = *px;
+
+    /* Read the reflection coefficient */
+    k = *pk++;
+
+    /* for sample 1 processing */
+    /* f1(n) = f0(n) +  K1 * g0(n-1) */
+    fnext1 = (q31_t) (((q63_t) gcurr1 * k) >> 32);
+
+    /* g1(n) = f0(n) * K1  +  g0(n-1) */
+    gnext1 = (q31_t) (((q63_t) fcurr1 * (k)) >> 32);
+    fnext1 = fcurr1 + (fnext1 << 1u);
+    gnext1 = gcurr1 + (gnext1 << 1u);
+
+    /* for sample 1 processing */
+    /* f1(n) = f0(n) +  K1 * g0(n-1) */
+    fnext2 = (q31_t) (((q63_t) fcurr1 * k) >> 32);
+
+    /* g1(n) = f0(n) * K1  +  g0(n-1) */
+    gnext2 = (q31_t) (((q63_t) fcurr2 * (k)) >> 32);
+    fnext2 = fcurr2 + (fnext2 << 1u);
+    gnext2 = fcurr1 + (gnext2 << 1u);
+
+    /* save g1(n) in state buffer */
+    *px++ = fcurr2;
+
+    /* f1(n) is saved in fcurr1        
+       for next stage processing */
+    fcurr1 = fnext1;
+    fcurr2 = fnext2;
+
+    stageCnt = (numStages - 1u);
+
+    /* stage loop */
+    while(stageCnt > 0u)
+    {
+
+      /* Read the reflection coefficient */
+      k = *pk++;
+
+      /* read g2(n) from state buffer */
+      gcurr1 = *px;
+
+      /* save g1(n) in state buffer */
+      *px++ = gnext2;
+
+      /* Sample processing for K2, K3.... */
+      /* f2(n) = f1(n) +  K2 * g1(n-1) */
+      fnext1 = (q31_t) (((q63_t) gcurr1 * k) >> 32);
+      fnext2 = (q31_t) (((q63_t) gnext1 * k) >> 32);
+
+      fnext1 = fcurr1 + (fnext1 << 1u);
+      fnext2 = fcurr2 + (fnext2 << 1u);
+
+      /* g2(n) = f1(n) * K2  +  g1(n-1) */
+      gnext2 = (q31_t) (((q63_t) fcurr2 * (k)) >> 32);
+      gnext2 = gnext1 + (gnext2 << 1u);
+
+      /* g2(n) = f1(n) * K2  +  g1(n-1) */
+      gnext1 = (q31_t) (((q63_t) fcurr1 * (k)) >> 32);
+      gnext1 = gcurr1 + (gnext1 << 1u);
+
+      /* f1(n) is saved in fcurr1        
+         for next stage processing */
+      fcurr1 = fnext1;
+      fcurr2 = fnext2;
+
+      stageCnt--;
+
+    }
+
+    /* y(n) = fN(n) */
+    *pDst++ = fcurr1;
+    *pDst++ = fcurr2;
+
+    blkCnt--;
+
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.        
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x2u;
+
+  while(blkCnt > 0u)
+  {
+    /* f0(n) = x(n) */
+    fcurr1 = *pSrc++;
+
+    /* Initialize coeff pointer */
+    pk = (pCoeffs);
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* read g0(n - 1) from state buffer */
+    gcurr1 = *px;
+
+    /* Read the reflection coefficient */
+    k = *pk++;
+
+    /* for sample 1 processing */
+    /* f1(n) = f0(n) +  K1 * g0(n-1) */
+    fnext1 = (q31_t) (((q63_t) gcurr1 * k) >> 32);
+    fnext1 = fcurr1 + (fnext1 << 1u);
+
+    /* g1(n) = f0(n) * K1  +  g0(n-1) */
+    gnext1 = (q31_t) (((q63_t) fcurr1 * (k)) >> 32);
+    gnext1 = gcurr1 + (gnext1 << 1u);
+
+    /* save g1(n) in state buffer */
+    *px++ = fcurr1;
+
+    /* f1(n) is saved in fcurr1        
+       for next stage processing */
+    fcurr1 = fnext1;
+
+    stageCnt = (numStages - 1u);
+
+    /* stage loop */
+    while(stageCnt > 0u)
+    {
+      /* Read the reflection coefficient */
+      k = *pk++;
+
+      /* read g2(n) from state buffer */
+      gcurr1 = *px;
+
+      /* save g1(n) in state buffer */
+      *px++ = gnext1;
+
+      /* Sample processing for K2, K3.... */
+      /* f2(n) = f1(n) +  K2 * g1(n-1) */
+      fnext1 = (q31_t) (((q63_t) gcurr1 * k) >> 32);
+      fnext1 = fcurr1 + (fnext1 << 1u);
+
+      /* g2(n) = f1(n) * K2  +  g1(n-1) */
+      gnext1 = (q31_t) (((q63_t) fcurr1 * (k)) >> 32);
+      gnext1 = gcurr1 + (gnext1 << 1u);
+
+      /* f1(n) is saved in fcurr1        
+         for next stage processing */
+      fcurr1 = fnext1;
+
+      stageCnt--;
+
+    }
+
+
+    /* y(n) = fN(n) */
+    *pDst++ = fcurr1;
+
+    blkCnt--;
+
+  }
+
+
+}
+
+
+#else
+
+/* Run the below code for Cortex-M0 */
+
+void arm_fir_lattice_q31(
+  const arm_fir_lattice_instance_q31 * S,
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize)
+{
+  q31_t *pState;                                 /* State pointer */
+  q31_t *pCoeffs = S->pCoeffs;                   /* Coefficient pointer */
+  q31_t *px;                                     /* temporary state pointer */
+  q31_t *pk;                                     /* temporary coefficient pointer */
+  q31_t fcurr, fnext, gcurr, gnext;              /* temporary variables */
+  uint32_t numStages = S->numStages;             /* Length of the filter */
+  uint32_t blkCnt, stageCnt;                     /* temporary variables for counts */
+
+  pState = &S->pState[0];
+
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* f0(n) = x(n) */
+    fcurr = *pSrc++;
+
+    /* Initialize coeff pointer */
+    pk = (pCoeffs);
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* read g0(n-1) from state buffer */
+    gcurr = *px;
+
+    /* for sample 1 processing */
+    /* f1(n) = f0(n) +  K1 * g0(n-1) */
+    fnext = (q31_t) (((q63_t) gcurr * (*pk)) >> 31) + fcurr;
+    /* g1(n) = f0(n) * K1  +  g0(n-1) */
+    gnext = (q31_t) (((q63_t) fcurr * (*pk++)) >> 31) + gcurr;
+    /* save g1(n) in state buffer */
+    *px++ = fcurr;
+
+    /* f1(n) is saved in fcurr1            
+       for next stage processing */
+    fcurr = fnext;
+
+    stageCnt = (numStages - 1u);
+
+    /* stage loop */
+    while(stageCnt > 0u)
+    {
+      /* read g2(n) from state buffer */
+      gcurr = *px;
+
+      /* save g1(n) in state buffer */
+      *px++ = gnext;
+
+      /* Sample processing for K2, K3.... */
+      /* f2(n) = f1(n) +  K2 * g1(n-1) */
+      fnext = (q31_t) (((q63_t) gcurr * (*pk)) >> 31) + fcurr;
+      /* g2(n) = f1(n) * K2  +  g1(n-1) */
+      gnext = (q31_t) (((q63_t) fcurr * (*pk++)) >> 31) + gcurr;
+
+      /* f1(n) is saved in fcurr1            
+         for next stage processing */
+      fcurr = fnext;
+
+      stageCnt--;
+
+    }
+
+    /* y(n) = fN(n) */
+    *pDst++ = fcurr;
+
+    blkCnt--;
+
+  }
+
+}
+
+#endif /*   #ifndef ARM_MATH_CM0 */
+
+
+/**    
+ * @} end of FIR_Lattice group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_q15.c
new file mode 100644
index 0000000000..368014f435
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_q15.c
@@ -0,0 +1,689 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_fir_q15.c    
+*    
+* Description:  Q15 FIR filter processing function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+* 	 incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**       
+ * @ingroup groupFilters       
+ */
+
+/**       
+ * @addtogroup FIR       
+ * @{       
+ */
+
+/**       
+ * @brief Processing function for the Q15 FIR filter.       
+ * @param[in] *S points to an instance of the Q15 FIR structure.       
+ * @param[in] *pSrc points to the block of input data.       
+ * @param[out] *pDst points to the block of output data.       
+ * @param[in]  blockSize number of samples to process per call.       
+ * @return none.       
+ *   
+ *   
+ * \par Restrictions   
+ *  If the silicon does not support unaligned memory access enable the macro UNALIGNED_SUPPORT_DISABLE   
+ *	In this case input, output, state buffers should be aligned by 32-bit   
+ *   
+ * Scaling and Overflow Behavior:       
+ * \par       
+ * The function is implemented using a 64-bit internal accumulator.       
+ * Both coefficients and state variables are represented in 1.15 format and multiplications yield a 2.30 result.       
+ * The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format.       
+ * There is no risk of internal overflow with this approach and the full precision of intermediate multiplications is preserved.       
+ * After all additions have been performed, the accumulator is truncated to 34.15 format by discarding low 15 bits.       
+ * Lastly, the accumulator is saturated to yield a result in 1.15 format.       
+ *       
+ * \par       
+ * Refer to the function arm_fir_fast_q15() for a faster but less precise implementation of this function.       
+ */
+
+#ifndef ARM_MATH_CM0
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+
+void arm_fir_q15(
+  const arm_fir_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+  q15_t *pState = S->pState;                     /* State pointer */
+  q15_t *pCoeffs = S->pCoeffs;                   /* Coefficient pointer */
+  q15_t *pStateCurnt;                            /* Points to the current sample of the state */
+  q15_t *px1;                                    /* Temporary q15 pointer for state buffer */
+  q15_t *pb;                                     /* Temporary pointer for coefficient buffer */
+  q31_t x0, x1, x2, x3, c0;                      /* Temporary variables to hold SIMD state and coefficient values */
+  q63_t acc0, acc1, acc2, acc3;                  /* Accumulators */
+  uint32_t numTaps = S->numTaps;                 /* Number of taps in the filter */
+  uint32_t tapCnt, blkCnt;                       /* Loop counters */
+
+
+  /* S->pState points to state array which contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = &(S->pState[(numTaps - 1u)]);
+
+  /* Apply loop unrolling and compute 4 output values simultaneously.       
+   * The variables acc0 ... acc3 hold output values that are being computed:       
+   *       
+   *    acc0 =  b[numTaps-1] * x[n-numTaps-1] + b[numTaps-2] * x[n-numTaps-2] + b[numTaps-3] * x[n-numTaps-3] +...+ b[0] * x[0]       
+   *    acc1 =  b[numTaps-1] * x[n-numTaps] +   b[numTaps-2] * x[n-numTaps-1] + b[numTaps-3] * x[n-numTaps-2] +...+ b[0] * x[1]       
+   *    acc2 =  b[numTaps-1] * x[n-numTaps+1] + b[numTaps-2] * x[n-numTaps] +   b[numTaps-3] * x[n-numTaps-1] +...+ b[0] * x[2]       
+   *    acc3 =  b[numTaps-1] * x[n-numTaps+2] + b[numTaps-2] * x[n-numTaps+1] + b[numTaps-3] * x[n-numTaps]   +...+ b[0] * x[3]       
+   */
+
+  blkCnt = blockSize >> 2;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.       
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* Copy four new input samples into the state buffer.       
+     ** Use 32-bit SIMD to move the 16-bit data.  Only requires two copies. */
+    *__SIMD32(pStateCurnt)++ = *__SIMD32(pSrc)++;
+    *__SIMD32(pStateCurnt)++ = *__SIMD32(pSrc)++;
+
+    /* Set all accumulators to zero */
+    acc0 = 0;
+    acc1 = 0;
+    acc2 = 0;
+    acc3 = 0;
+
+    /* Initialize state pointer of type q15 */
+    px1 = pState;
+
+    /* Initialize coeff pointer of type q31 */
+    pb = pCoeffs;
+
+    /* Read the first two samples from the state buffer:  x[n-N], x[n-N-1] */
+    x0 = _SIMD32_OFFSET(px1);
+
+    /* Read the third and forth samples from the state buffer: x[n-N-1], x[n-N-2] */
+    x1 = _SIMD32_OFFSET(px1 + 1u);
+
+    px1 += 2u;
+
+    /* Loop over the number of taps.  Unroll by a factor of 4.       
+     ** Repeat until we've computed numTaps-4 coefficients. */
+    tapCnt = numTaps >> 2;
+
+    while(tapCnt > 0u)
+    {
+      /* Read the first two coefficients using SIMD:  b[N] and b[N-1] coefficients */
+      c0 = *__SIMD32(pb)++;
+
+      /* acc0 +=  b[N] * x[n-N] + b[N-1] * x[n-N-1] */
+      acc0 = __SMLALD(x0, c0, acc0);
+
+      /* acc1 +=  b[N] * x[n-N-1] + b[N-1] * x[n-N-2] */
+      acc1 = __SMLALD(x1, c0, acc1);
+
+      /* Read state x[n-N-2], x[n-N-3] */
+      x2 = _SIMD32_OFFSET(px1);
+
+      /* Read state x[n-N-3], x[n-N-4] */
+      x3 = _SIMD32_OFFSET(px1 + 1u);
+
+      /* acc2 +=  b[N] * x[n-N-2] + b[N-1] * x[n-N-3] */
+      acc2 = __SMLALD(x2, c0, acc2);
+
+      /* acc3 +=  b[N] * x[n-N-3] + b[N-1] * x[n-N-4] */
+      acc3 = __SMLALD(x3, c0, acc3);
+
+      /* Read coefficients b[N-2], b[N-3] */
+      c0 = *__SIMD32(pb)++;
+
+      /* acc0 +=  b[N-2] * x[n-N-2] + b[N-3] * x[n-N-3] */
+      acc0 = __SMLALD(x2, c0, acc0);
+
+      /* acc1 +=  b[N-2] * x[n-N-3] + b[N-3] * x[n-N-4] */
+      acc1 = __SMLALD(x3, c0, acc1);
+
+      /* Read state x[n-N-4], x[n-N-5] */
+      x0 = _SIMD32_OFFSET(px1 + 2u);
+
+      /* Read state x[n-N-5], x[n-N-6] */
+      x1 = _SIMD32_OFFSET(px1 + 3u);
+
+      /* acc2 +=  b[N-2] * x[n-N-4] + b[N-3] * x[n-N-5] */
+      acc2 = __SMLALD(x0, c0, acc2);
+
+      /* acc3 +=  b[N-2] * x[n-N-5] + b[N-3] * x[n-N-6] */
+      acc3 = __SMLALD(x1, c0, acc3);
+
+      px1 += 4u;
+
+      tapCnt--;
+
+    }
+
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps.       
+     ** This is always be 2 taps since the filter length is even. */
+    if((numTaps & 0x3u) != 0u)
+    {
+      /* Read 2 coefficients */
+      c0 = *__SIMD32(pb)++;
+
+      /* Fetch 4 state variables */
+      x2 = _SIMD32_OFFSET(px1);
+
+      x3 = _SIMD32_OFFSET(px1 + 1u);
+
+      /* Perform the multiply-accumulates */
+      acc0 = __SMLALD(x0, c0, acc0);
+
+      px1 += 2u;
+
+      acc1 = __SMLALD(x1, c0, acc1);
+      acc2 = __SMLALD(x2, c0, acc2);
+      acc3 = __SMLALD(x3, c0, acc3);
+    }
+
+    /* The results in the 4 accumulators are in 2.30 format.  Convert to 1.15 with saturation.       
+     ** Then store the 4 outputs in the destination buffer. */
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    *__SIMD32(pDst)++ =
+      __PKHBT(__SSAT((acc0 >> 15), 16), __SSAT((acc1 >> 15), 16), 16);
+    *__SIMD32(pDst)++ =
+      __PKHBT(__SSAT((acc2 >> 15), 16), __SSAT((acc3 >> 15), 16), 16);
+
+#else
+
+    *__SIMD32(pDst)++ =
+      __PKHBT(__SSAT((acc1 >> 15), 16), __SSAT((acc0 >> 15), 16), 16);
+    *__SIMD32(pDst)++ =
+      __PKHBT(__SSAT((acc3 >> 15), 16), __SSAT((acc2 >> 15), 16), 16);
+
+#endif /*      #ifndef ARM_MATH_BIG_ENDIAN       */
+
+
+
+    /* Advance the state pointer by 4 to process the next group of 4 samples */
+    pState = pState + 4;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.       
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+  while(blkCnt > 0u)
+  {
+    /* Copy two samples into state buffer */
+    *pStateCurnt++ = *pSrc++;
+
+    /* Set the accumulator to zero */
+    acc0 = 0;
+
+    /* Initialize state pointer of type q15 */
+    px1 = pState;
+
+    /* Initialize coeff pointer of type q31 */
+    pb = pCoeffs;
+
+    tapCnt = numTaps >> 1;
+
+    do
+    {
+
+      c0 = *__SIMD32(pb)++;
+      x0 = *__SIMD32(px1)++;
+
+      acc0 = __SMLALD(x0, c0, acc0);
+      tapCnt--;
+    }
+    while(tapCnt > 0u);
+
+    /* The result is in 2.30 format.  Convert to 1.15 with saturation.       
+     ** Then store the output in the destination buffer. */
+    *pDst++ = (q15_t) (__SSAT((acc0 >> 15), 16));
+
+    /* Advance state pointer by 1 for the next sample */
+    pState = pState + 1;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Processing is complete.       
+   ** Now copy the last numTaps - 1 samples to the satrt of the state buffer.       
+   ** This prepares the state buffer for the next function call. */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+  /* Calculation of count for copying integer writes */
+  tapCnt = (numTaps - 1u) >> 2;
+
+  while(tapCnt > 0u)
+  {
+
+    /* Copy state values to start of state buffer */
+    *__SIMD32(pStateCurnt)++ = *__SIMD32(pState)++;
+    *__SIMD32(pStateCurnt)++ = *__SIMD32(pState)++;
+
+    tapCnt--;
+
+  }
+
+  /* Calculation of count for remaining q15_t data */
+  tapCnt = (numTaps - 1u) % 0x4u;
+
+  /* copy remaining data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+}
+
+#else /* UNALIGNED_SUPPORT_DISABLE */
+
+void arm_fir_q15(
+  const arm_fir_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+  q15_t *pState = S->pState;                     /* State pointer */
+  q15_t *pCoeffs = S->pCoeffs;                   /* Coefficient pointer */
+  q15_t *pStateCurnt;                            /* Points to the current sample of the state */
+  q63_t acc0, acc1, acc2, acc3;                  /* Accumulators */
+  q15_t *pb;                                     /* Temporary pointer for coefficient buffer */
+  q15_t *px;                                     /* Temporary q31 pointer for SIMD state buffer accesses */
+  q31_t x0, x1, x2, c0;                          /* Temporary variables to hold SIMD state and coefficient values */
+  uint32_t numTaps = S->numTaps;                 /* Number of taps in the filter */
+  uint32_t tapCnt, blkCnt;                       /* Loop counters */
+
+
+  /* S->pState points to state array which contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = &(S->pState[(numTaps - 1u)]);
+
+  /* Apply loop unrolling and compute 4 output values simultaneously.      
+   * The variables acc0 ... acc3 hold output values that are being computed:      
+   *      
+   *    acc0 =  b[numTaps-1] * x[n-numTaps-1] + b[numTaps-2] * x[n-numTaps-2] + b[numTaps-3] * x[n-numTaps-3] +...+ b[0] * x[0]      
+   *    acc1 =  b[numTaps-1] * x[n-numTaps] +   b[numTaps-2] * x[n-numTaps-1] + b[numTaps-3] * x[n-numTaps-2] +...+ b[0] * x[1]      
+   *    acc2 =  b[numTaps-1] * x[n-numTaps+1] + b[numTaps-2] * x[n-numTaps] +   b[numTaps-3] * x[n-numTaps-1] +...+ b[0] * x[2]      
+   *    acc3 =  b[numTaps-1] * x[n-numTaps+2] + b[numTaps-2] * x[n-numTaps+1] + b[numTaps-3] * x[n-numTaps]   +...+ b[0] * x[3]      
+   */
+
+  blkCnt = blockSize >> 2;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.      
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* Copy four new input samples into the state buffer.      
+     ** Use 32-bit SIMD to move the 16-bit data.  Only requires two copies. */
+    *pStateCurnt++ = *pSrc++;
+    *pStateCurnt++ = *pSrc++;
+    *pStateCurnt++ = *pSrc++;
+    *pStateCurnt++ = *pSrc++;
+
+
+    /* Set all accumulators to zero */
+    acc0 = 0;
+    acc1 = 0;
+    acc2 = 0;
+    acc3 = 0;
+
+    /* Typecast q15_t pointer to q31_t pointer for state reading in q31_t */
+    px = pState;
+
+    /* Typecast q15_t pointer to q31_t pointer for coefficient reading in q31_t */
+    pb = pCoeffs;
+
+    /* Read the first two samples from the state buffer:  x[n-N], x[n-N-1] */
+    x0 = *__SIMD32(px)++;
+
+    /* Read the third and forth samples from the state buffer: x[n-N-2], x[n-N-3] */
+    x2 = *__SIMD32(px)++;
+
+    /* Loop over the number of taps.  Unroll by a factor of 4.      
+     ** Repeat until we've computed numTaps-(numTaps%4) coefficients. */
+    tapCnt = numTaps >> 2;
+
+    while(tapCnt > 0)
+    {
+      /* Read the first two coefficients using SIMD:  b[N] and b[N-1] coefficients */
+      c0 = *__SIMD32(pb)++;
+
+      /* acc0 +=  b[N] * x[n-N] + b[N-1] * x[n-N-1] */
+      acc0 = __SMLALD(x0, c0, acc0);
+
+      /* acc2 +=  b[N] * x[n-N-2] + b[N-1] * x[n-N-3] */
+      acc2 = __SMLALD(x2, c0, acc2);
+
+      /* pack  x[n-N-1] and x[n-N-2] */
+#ifndef ARM_MATH_BIG_ENDIAN
+      x1 = __PKHBT(x2, x0, 0);
+#else
+      x1 = __PKHBT(x0, x2, 0);
+#endif
+
+      /* Read state x[n-N-4], x[n-N-5] */
+      x0 = _SIMD32_OFFSET(px);
+
+      /* acc1 +=  b[N] * x[n-N-1] + b[N-1] * x[n-N-2] */
+      acc1 = __SMLALDX(x1, c0, acc1);
+
+      /* pack  x[n-N-3] and x[n-N-4] */
+#ifndef ARM_MATH_BIG_ENDIAN
+      x1 = __PKHBT(x0, x2, 0);
+#else
+      x1 = __PKHBT(x2, x0, 0);
+#endif
+
+      /* acc3 +=  b[N] * x[n-N-3] + b[N-1] * x[n-N-4] */
+      acc3 = __SMLALDX(x1, c0, acc3);
+
+      /* Read coefficients b[N-2], b[N-3] */
+      c0 = *__SIMD32(pb)++;
+
+      /* acc0 +=  b[N-2] * x[n-N-2] + b[N-3] * x[n-N-3] */
+      acc0 = __SMLALD(x2, c0, acc0);
+
+      /* Read state x[n-N-6], x[n-N-7] with offset */
+      x2 = _SIMD32_OFFSET(px + 2u);
+
+      /* acc2 +=  b[N-2] * x[n-N-4] + b[N-3] * x[n-N-5] */
+      acc2 = __SMLALD(x0, c0, acc2);
+
+      /* acc1 +=  b[N-2] * x[n-N-3] + b[N-3] * x[n-N-4] */
+      acc1 = __SMLALDX(x1, c0, acc1);
+
+      /* pack  x[n-N-5] and x[n-N-6] */
+#ifndef ARM_MATH_BIG_ENDIAN
+      x1 = __PKHBT(x2, x0, 0);
+#else
+      x1 = __PKHBT(x0, x2, 0);
+#endif
+
+      /* acc3 +=  b[N-2] * x[n-N-5] + b[N-3] * x[n-N-6] */
+      acc3 = __SMLALDX(x1, c0, acc3);
+
+      /* Update state pointer for next state reading */
+      px += 4u;
+
+      /* Decrement tap count */
+      tapCnt--;
+
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps.       
+     ** This is always be 2 taps since the filter length is even. */
+    if((numTaps & 0x3u) != 0u)
+    {
+
+      /* Read last two coefficients */
+      c0 = *__SIMD32(pb)++;
+
+      /* Perform the multiply-accumulates */
+      acc0 = __SMLALD(x0, c0, acc0);
+      acc2 = __SMLALD(x2, c0, acc2);
+
+      /* pack state variables */
+#ifndef ARM_MATH_BIG_ENDIAN
+      x1 = __PKHBT(x2, x0, 0);
+#else
+      x1 = __PKHBT(x0, x2, 0);
+#endif
+
+      /* Read last state variables */
+      x0 = *__SIMD32(px);
+
+      /* Perform the multiply-accumulates */
+      acc1 = __SMLALDX(x1, c0, acc1);
+
+      /* pack state variables */
+#ifndef ARM_MATH_BIG_ENDIAN
+      x1 = __PKHBT(x0, x2, 0);
+#else
+      x1 = __PKHBT(x2, x0, 0);
+#endif
+
+      /* Perform the multiply-accumulates */
+      acc3 = __SMLALDX(x1, c0, acc3);
+    }
+
+    /* The results in the 4 accumulators are in 2.30 format.  Convert to 1.15 with saturation.       
+     ** Then store the 4 outputs in the destination buffer. */
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    *__SIMD32(pDst)++ =
+      __PKHBT(__SSAT((acc0 >> 15), 16), __SSAT((acc1 >> 15), 16), 16);
+
+    *__SIMD32(pDst)++ =
+      __PKHBT(__SSAT((acc2 >> 15), 16), __SSAT((acc3 >> 15), 16), 16);
+
+#else
+
+    *__SIMD32(pDst)++ =
+      __PKHBT(__SSAT((acc1 >> 15), 16), __SSAT((acc0 >> 15), 16), 16);
+
+    *__SIMD32(pDst)++ =
+      __PKHBT(__SSAT((acc3 >> 15), 16), __SSAT((acc2 >> 15), 16), 16);
+
+#endif /*      #ifndef ARM_MATH_BIG_ENDIAN       */
+
+    /* Advance the state pointer by 4 to process the next group of 4 samples */
+    pState = pState + 4;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.      
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+  while(blkCnt > 0u)
+  {
+    /* Copy two samples into state buffer */
+    *pStateCurnt++ = *pSrc++;
+
+    /* Set the accumulator to zero */
+    acc0 = 0;
+
+    /* Use SIMD to hold states and coefficients */
+    px = pState;
+    pb = pCoeffs;
+
+    tapCnt = numTaps >> 1u;
+
+    do
+    {
+      acc0 += (q31_t) * px++ * *pb++;
+	  acc0 += (q31_t) * px++ * *pb++;
+      tapCnt--;
+    }
+    while(tapCnt > 0u);
+
+    /* The result is in 2.30 format.  Convert to 1.15 with saturation.      
+     ** Then store the output in the destination buffer. */
+    *pDst++ = (q15_t) (__SSAT((acc0 >> 15), 16));
+
+    /* Advance state pointer by 1 for the next sample */
+    pState = pState + 1u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Processing is complete.      
+   ** Now copy the last numTaps - 1 samples to the satrt of the state buffer.      
+   ** This prepares the state buffer for the next function call. */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+  /* Calculation of count for copying integer writes */
+  tapCnt = (numTaps - 1u) >> 2;
+
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+
+    tapCnt--;
+
+  }
+
+  /* Calculation of count for remaining q15_t data */
+  tapCnt = (numTaps - 1u) % 0x4u;
+
+  /* copy remaining data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+}
+
+
+#endif /* #ifndef UNALIGNED_SUPPORT_DISABLE */
+
+#else /* ARM_MATH_CM0 */
+
+
+/* Run the below code for Cortex-M0 */
+
+void arm_fir_q15(
+  const arm_fir_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+  q15_t *pState = S->pState;                     /* State pointer */
+  q15_t *pCoeffs = S->pCoeffs;                   /* Coefficient pointer */
+  q15_t *pStateCurnt;                            /* Points to the current sample of the state */
+
+
+
+  q15_t *px;                                     /* Temporary pointer for state buffer */
+  q15_t *pb;                                     /* Temporary pointer for coefficient buffer */
+  q63_t acc;                                     /* Accumulator */
+  uint32_t numTaps = S->numTaps;                 /* Number of nTaps in the filter */
+  uint32_t tapCnt, blkCnt;                       /* Loop counters */
+
+  /* S->pState buffer contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = &(S->pState[(numTaps - 1u)]);
+
+  /* Initialize blkCnt with blockSize */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* Copy one sample at a time into state buffer */
+    *pStateCurnt++ = *pSrc++;
+
+    /* Set the accumulator to zero */
+    acc = 0;
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* Initialize Coefficient pointer */
+    pb = pCoeffs;
+
+    tapCnt = numTaps;
+
+    /* Perform the multiply-accumulates */
+    do
+    {
+      /* acc =  b[numTaps-1] * x[n-numTaps-1] + b[numTaps-2] * x[n-numTaps-2] + b[numTaps-3] * x[n-numTaps-3] +...+ b[0] * x[0] */
+      acc += (q31_t) * px++ * *pb++;
+      tapCnt--;
+    } while(tapCnt > 0u);
+
+    /* The result is in 2.30 format.  Convert to 1.15         
+     ** Then store the output in the destination buffer. */
+    *pDst++ = (q15_t) __SSAT((acc >> 15u), 16);
+
+    /* Advance state pointer by 1 for the next sample */
+    pState = pState + 1;
+
+    /* Decrement the samples loop counter */
+    blkCnt--;
+  }
+
+  /* Processing is complete.         
+   ** Now copy the last numTaps - 1 samples to the satrt of the state buffer.       
+   ** This prepares the state buffer for the next function call. */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+  /* Copy numTaps number of values */
+  tapCnt = (numTaps - 1u);
+
+  /* copy data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+}
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+
+
+
+/**       
+ * @} end of FIR group       
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_q31.c
new file mode 100644
index 0000000000..b3b84ec51f
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_q31.c
@@ -0,0 +1,363 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_fir_q31.c    
+*    
+* Description:	Q31 FIR filter processing function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+* 	 incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR    
+ * @{    
+ */
+
+/**    
+ * @param[in] *S points to an instance of the Q31 FIR filter structure.    
+ * @param[in] *pSrc points to the block of input data.    
+ * @param[out] *pDst points to the block of output data.    
+ * @param[in] blockSize number of samples to process per call.    
+ * @return none.    
+ *    
+ * @details    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function is implemented using an internal 64-bit accumulator.    
+ * The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit.    
+ * Thus, if the accumulator result overflows it wraps around rather than clip.    
+ * In order to avoid overflows completely the input signal must be scaled down by log2(numTaps) bits.    
+ * After all multiply-accumulates are performed, the 2.62 accumulator is right shifted by 31 bits and saturated to 1.31 format to yield the final result.  
+ *    
+ * \par    
+ * Refer to the function arm_fir_fast_q31() for a faster but less precise implementation of this filter for Cortex-M3 and Cortex-M4.    
+ */
+
+void arm_fir_q31(
+  const arm_fir_instance_q31 * S,
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize)
+{
+  q31_t *pState = S->pState;                     /* State pointer */
+  q31_t *pCoeffs = S->pCoeffs;                   /* Coefficient pointer */
+  q31_t *pStateCurnt;                            /* Points to the current sample of the state */
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q31_t x0, x1, x2;                              /* Temporary variables to hold state */
+  q31_t c0;                                      /* Temporary variable to hold coefficient value */
+  q31_t *px;                                     /* Temporary pointer for state */
+  q31_t *pb;                                     /* Temporary pointer for coefficient buffer */
+  q63_t acc0, acc1, acc2;                        /* Accumulators */
+  uint32_t numTaps = S->numTaps;                 /* Number of filter coefficients in the filter */
+  uint32_t i, tapCnt, blkCnt, tapCntN3;          /* Loop counters */
+
+  /* S->pState points to state array which contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = &(S->pState[(numTaps - 1u)]);
+
+  /* Apply loop unrolling and compute 4 output values simultaneously.    
+   * The variables acc0 ... acc3 hold output values that are being computed:    
+   *    
+   *    acc0 =  b[numTaps-1] * x[n-numTaps-1] + b[numTaps-2] * x[n-numTaps-2] + b[numTaps-3] * x[n-numTaps-3] +...+ b[0] * x[0]    
+   *    acc1 =  b[numTaps-1] * x[n-numTaps] +   b[numTaps-2] * x[n-numTaps-1] + b[numTaps-3] * x[n-numTaps-2] +...+ b[0] * x[1]    
+   *    acc2 =  b[numTaps-1] * x[n-numTaps+1] + b[numTaps-2] * x[n-numTaps] +   b[numTaps-3] * x[n-numTaps-1] +...+ b[0] * x[2]    
+   *    acc3 =  b[numTaps-1] * x[n-numTaps+2] + b[numTaps-2] * x[n-numTaps+1] + b[numTaps-3] * x[n-numTaps]   +...+ b[0] * x[3]    
+   */
+  blkCnt = blockSize / 3;
+  blockSize = blockSize - (3 * blkCnt);
+
+  tapCnt = numTaps / 3;
+  tapCntN3 = numTaps - (3 * tapCnt);
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* Copy three new input samples into the state buffer */
+    *pStateCurnt++ = *pSrc++;
+    *pStateCurnt++ = *pSrc++;
+    *pStateCurnt++ = *pSrc++;
+
+    /* Set all accumulators to zero */
+    acc0 = 0;
+    acc1 = 0;
+    acc2 = 0;
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* Initialize coefficient pointer */
+    pb = pCoeffs;
+
+    /* Read the first two samples from the state buffer:    
+     *  x[n-numTaps], x[n-numTaps-1] */
+    x0 = *(px++);
+    x1 = *(px++);
+
+    /* Loop unrolling.  Process 3 taps at a time. */
+    i = tapCnt;
+
+    while(i > 0u)
+    {
+      /* Read the b[numTaps] coefficient */
+      c0 = *pb;
+
+      /* Read x[n-numTaps-2] sample */
+      x2 = *(px++);
+
+      /* Perform the multiply-accumulates */
+      acc0 += ((q63_t) x0 * c0);
+      acc1 += ((q63_t) x1 * c0);
+      acc2 += ((q63_t) x2 * c0);
+
+      /* Read the coefficient and state */
+      c0 = *(pb + 1u);
+      x0 = *(px++);
+
+      /* Perform the multiply-accumulates */
+      acc0 += ((q63_t) x1 * c0);
+      acc1 += ((q63_t) x2 * c0);
+      acc2 += ((q63_t) x0 * c0);
+
+      /* Read the coefficient and state */
+      c0 = *(pb + 2u);
+      x1 = *(px++);
+
+      /* update coefficient pointer */
+      pb += 3u;
+
+      /* Perform the multiply-accumulates */
+      acc0 += ((q63_t) x2 * c0);
+      acc1 += ((q63_t) x0 * c0);
+      acc2 += ((q63_t) x1 * c0);
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* If the filter length is not a multiple of 3, compute the remaining filter taps */
+
+    i = tapCntN3;
+
+    while(i > 0u)
+    {
+      /* Read coefficients */
+      c0 = *(pb++);
+
+      /* Fetch 1 state variable */
+      x2 = *(px++);
+
+      /* Perform the multiply-accumulates */
+      acc0 += ((q63_t) x0 * c0);
+      acc1 += ((q63_t) x1 * c0);
+      acc2 += ((q63_t) x2 * c0);
+
+      /* Reuse the present sample states for next sample */
+      x0 = x1;
+      x1 = x2;
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Advance the state pointer by 3 to process the next group of 3 samples */
+    pState = pState + 3;
+
+    /* The results in the 3 accumulators are in 2.30 format.  Convert to 1.31    
+     ** Then store the 3 outputs in the destination buffer. */
+    *pDst++ = (q31_t) (acc0 >> 31u);
+    *pDst++ = (q31_t) (acc1 >> 31u);
+    *pDst++ = (q31_t) (acc2 >> 31u);
+
+    /* Decrement the samples loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 3, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+
+  while(blockSize > 0u)
+  {
+    /* Copy one sample at a time into state buffer */
+    *pStateCurnt++ = *pSrc++;
+
+    /* Set the accumulator to zero */
+    acc0 = 0;
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* Initialize Coefficient pointer */
+    pb = (pCoeffs);
+
+    i = numTaps;
+
+    /* Perform the multiply-accumulates */
+    do
+    {
+      acc0 += (q63_t) * (px++) * (*(pb++));
+      i--;
+    } while(i > 0u);
+
+    /* The result is in 2.62 format.  Convert to 1.31    
+     ** Then store the output in the destination buffer. */
+    *pDst++ = (q31_t) (acc0 >> 31u);
+
+    /* Advance state pointer by 1 for the next sample */
+    pState = pState + 1;
+
+    /* Decrement the samples loop counter */
+    blockSize--;
+  }
+
+  /* Processing is complete.    
+   ** Now copy the last numTaps - 1 samples to the satrt of the state buffer.    
+   ** This prepares the state buffer for the next function call. */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+  tapCnt = (numTaps - 1u) >> 2u;
+
+  /* copy data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+  /* Calculate remaining number of copies */
+  tapCnt = (numTaps - 1u) % 0x4u;
+
+  /* Copy the remaining q31_t data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+#else
+
+/* Run the below code for Cortex-M0 */
+
+  q31_t *px;                                     /* Temporary pointer for state */
+  q31_t *pb;                                     /* Temporary pointer for coefficient buffer */
+  q63_t acc;                                     /* Accumulator */
+  uint32_t numTaps = S->numTaps;                 /* Length of the filter */
+  uint32_t i, tapCnt, blkCnt;                    /* Loop counters */
+
+  /* S->pState buffer contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = &(S->pState[(numTaps - 1u)]);
+
+  /* Initialize blkCnt with blockSize */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* Copy one sample at a time into state buffer */
+    *pStateCurnt++ = *pSrc++;
+
+    /* Set the accumulator to zero */
+    acc = 0;
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* Initialize Coefficient pointer */
+    pb = pCoeffs;
+
+    i = numTaps;
+
+    /* Perform the multiply-accumulates */
+    do
+    {
+      /* acc =  b[numTaps-1] * x[n-numTaps-1] + b[numTaps-2] * x[n-numTaps-2] + b[numTaps-3] * x[n-numTaps-3] +...+ b[0] * x[0] */
+      acc += (q63_t) * px++ * *pb++;
+      i--;
+    } while(i > 0u);
+
+    /* The result is in 2.62 format.  Convert to 1.31         
+     ** Then store the output in the destination buffer. */
+    *pDst++ = (q31_t) (acc >> 31u);
+
+    /* Advance state pointer by 1 for the next sample */
+    pState = pState + 1;
+
+    /* Decrement the samples loop counter */
+    blkCnt--;
+  }
+
+  /* Processing is complete.         
+   ** Now copy the last numTaps - 1 samples to the starting of the state buffer.       
+   ** This prepares the state buffer for the next function call. */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+  /* Copy numTaps number of values */
+  tapCnt = numTaps - 1u;
+
+  /* Copy the data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+
+#endif /*  #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of FIR group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_q7.c
new file mode 100644
index 0000000000..624afa130a
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_q7.c
@@ -0,0 +1,388 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_fir_q7.c    
+*    
+* Description:  Q7 FIR filter processing function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+* 	 incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR    
+ * @{    
+ */
+
+/**    
+ * @param[in]   *S points to an instance of the Q7 FIR filter structure.    
+ * @param[in]   *pSrc points to the block of input data.    
+ * @param[out]  *pDst points to the block of output data.    
+ * @param[in]   blockSize number of samples to process per call.    
+ * @return 	none.    
+ *    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function is implemented using a 32-bit internal accumulator.    
+ * Both coefficients and state variables are represented in 1.7 format and multiplications yield a 2.14 result.    
+ * The 2.14 intermediate results are accumulated in a 32-bit accumulator in 18.14 format.    
+ * There is no risk of internal overflow with this approach and the full precision of intermediate multiplications is preserved.    
+ * The accumulator is converted to 18.7 format by discarding the low 7 bits.    
+ * Finally, the result is truncated to 1.7 format.    
+ */
+
+void arm_fir_q7(
+  const arm_fir_instance_q7 * S,
+  q7_t * pSrc,
+  q7_t * pDst,
+  uint32_t blockSize)
+{
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q7_t *pState = S->pState;                      /* State pointer */
+  q7_t *pCoeffs = S->pCoeffs;                    /* Coefficient pointer */
+  q7_t *pStateCurnt;                             /* Points to the current sample of the state */
+  q7_t x0, x1, x2, x3;                           /* Temporary variables to hold state */
+  q7_t c0;                                       /* Temporary variable to hold coefficient value */
+  q7_t *px;                                      /* Temporary pointer for state */
+  q7_t *pb;                                      /* Temporary pointer for coefficient buffer */
+  q31_t acc0, acc1, acc2, acc3;                  /* Accumulators */
+  uint32_t numTaps = S->numTaps;                 /* Number of filter coefficients in the filter */
+  uint32_t i, tapCnt, blkCnt;                    /* Loop counters */
+
+  /* S->pState points to state array which contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = &(S->pState[(numTaps - 1u)]);
+
+  /* Apply loop unrolling and compute 4 output values simultaneously.    
+   * The variables acc0 ... acc3 hold output values that are being computed:    
+   *    
+   *    acc0 =  b[numTaps-1] * x[n-numTaps-1] + b[numTaps-2] * x[n-numTaps-2] + b[numTaps-3] * x[n-numTaps-3] +...+ b[0] * x[0]    
+   *    acc1 =  b[numTaps-1] * x[n-numTaps] +   b[numTaps-2] * x[n-numTaps-1] + b[numTaps-3] * x[n-numTaps-2] +...+ b[0] * x[1]    
+   *    acc2 =  b[numTaps-1] * x[n-numTaps+1] + b[numTaps-2] * x[n-numTaps] +   b[numTaps-3] * x[n-numTaps-1] +...+ b[0] * x[2]    
+   *    acc3 =  b[numTaps-1] * x[n-numTaps+2] + b[numTaps-2] * x[n-numTaps+1] + b[numTaps-3] * x[n-numTaps]   +...+ b[0] * x[3]    
+   */
+  blkCnt = blockSize >> 2;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* Copy four new input samples into the state buffer */
+    *pStateCurnt++ = *pSrc++;
+    *pStateCurnt++ = *pSrc++;
+    *pStateCurnt++ = *pSrc++;
+    *pStateCurnt++ = *pSrc++;
+
+    /* Set all accumulators to zero */
+    acc0 = 0;
+    acc1 = 0;
+    acc2 = 0;
+    acc3 = 0;
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* Initialize coefficient pointer */
+    pb = pCoeffs;
+
+    /* Read the first three samples from the state buffer:    
+     *  x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2] */
+    x0 = *(px++);
+    x1 = *(px++);
+    x2 = *(px++);
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2;
+    i = tapCnt;
+
+    while(i > 0u)
+    {
+      /* Read the b[numTaps] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-3] sample */
+      x3 = *(px++);
+
+      /* acc0 +=  b[numTaps] * x[n-numTaps] */
+      acc0 += ((q15_t) x0 * c0);
+
+      /* acc1 +=  b[numTaps] * x[n-numTaps-1] */
+      acc1 += ((q15_t) x1 * c0);
+
+      /* acc2 +=  b[numTaps] * x[n-numTaps-2] */
+      acc2 += ((q15_t) x2 * c0);
+
+      /* acc3 +=  b[numTaps] * x[n-numTaps-3] */
+      acc3 += ((q15_t) x3 * c0);
+
+      /* Read the b[numTaps-1] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-4] sample */
+      x0 = *(px++);
+
+      /* Perform the multiply-accumulates */
+      acc0 += ((q15_t) x1 * c0);
+      acc1 += ((q15_t) x2 * c0);
+      acc2 += ((q15_t) x3 * c0);
+      acc3 += ((q15_t) x0 * c0);
+
+      /* Read the b[numTaps-2] coefficient */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-5] sample */
+      x1 = *(px++);
+
+      /* Perform the multiply-accumulates */
+      acc0 += ((q15_t) x2 * c0);
+      acc1 += ((q15_t) x3 * c0);
+      acc2 += ((q15_t) x0 * c0);
+      acc3 += ((q15_t) x1 * c0);
+      /* Read the b[numTaps-3] coefficients */
+      c0 = *(pb++);
+
+      /* Read x[n-numTaps-6] sample */
+      x2 = *(px++);
+
+      /* Perform the multiply-accumulates */
+      acc0 += ((q15_t) x3 * c0);
+      acc1 += ((q15_t) x0 * c0);
+      acc2 += ((q15_t) x1 * c0);
+      acc3 += ((q15_t) x2 * c0);
+      i--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+
+    i = numTaps - (tapCnt * 4u);
+    while(i > 0u)
+    {
+      /* Read coefficients */
+      c0 = *(pb++);
+
+      /* Fetch 1 state variable */
+      x3 = *(px++);
+
+      /* Perform the multiply-accumulates */
+      acc0 += ((q15_t) x0 * c0);
+      acc1 += ((q15_t) x1 * c0);
+      acc2 += ((q15_t) x2 * c0);
+      acc3 += ((q15_t) x3 * c0);
+
+      /* Reuse the present sample states for next sample */
+      x0 = x1;
+      x1 = x2;
+      x2 = x3;
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Advance the state pointer by 4 to process the next group of 4 samples */
+    pState = pState + 4;
+
+    /* The results in the 4 accumulators are in 2.62 format.  Convert to 1.31    
+     ** Then store the 4 outputs in the destination buffer. */
+    acc0 = __SSAT((acc0 >> 7u), 8);
+    *pDst++ = acc0;
+    acc1 = __SSAT((acc1 >> 7u), 8);
+    *pDst++ = acc1;
+    acc2 = __SSAT((acc2 >> 7u), 8);
+    *pDst++ = acc2;
+    acc3 = __SSAT((acc3 >> 7u), 8);
+    *pDst++ = acc3;
+
+    /* Decrement the samples loop counter */
+    blkCnt--;
+  }
+
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 4u;
+
+  while(blkCnt > 0u)
+  {
+    /* Copy one sample at a time into state buffer */
+    *pStateCurnt++ = *pSrc++;
+
+    /* Set the accumulator to zero */
+    acc0 = 0;
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* Initialize Coefficient pointer */
+    pb = (pCoeffs);
+
+    i = numTaps;
+
+    /* Perform the multiply-accumulates */
+    do
+    {
+      acc0 += (q15_t) * (px++) * (*(pb++));
+      i--;
+    } while(i > 0u);
+
+    /* The result is in 2.14 format.  Convert to 1.7    
+     ** Then store the output in the destination buffer. */
+    *pDst++ = __SSAT((acc0 >> 7u), 8);
+
+    /* Advance state pointer by 1 for the next sample */
+    pState = pState + 1;
+
+    /* Decrement the samples loop counter */
+    blkCnt--;
+  }
+
+  /* Processing is complete.    
+   ** Now copy the last numTaps - 1 samples to the satrt of the state buffer.    
+   ** This prepares the state buffer for the next function call. */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+  tapCnt = (numTaps - 1u) >> 2u;
+
+  /* copy data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+  /* Calculate remaining number of copies */
+  tapCnt = (numTaps - 1u) % 0x4u;
+
+  /* Copy the remaining q31_t data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+#else
+
+/* Run the below code for Cortex-M0 */
+
+  uint32_t numTaps = S->numTaps;                 /* Number of taps in the filter */
+  uint32_t i, blkCnt;                            /* Loop counters */
+  q7_t *pState = S->pState;                      /* State pointer */
+  q7_t *pCoeffs = S->pCoeffs;                    /* Coefficient pointer */
+  q7_t *px, *pb;                                 /* Temporary pointers to state and coeff */
+  q31_t acc = 0;                                 /* Accumlator */
+  q7_t *pStateCurnt;                             /* Points to the current sample of the state */
+
+
+  /* S->pState points to state array which contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = S->pState + (numTaps - 1u);
+
+  /* Initialize blkCnt with blockSize */
+  blkCnt = blockSize;
+
+  /* Perform filtering upto BlockSize - BlockSize%4  */
+  while(blkCnt > 0u)
+  {
+    /* Copy one sample at a time into state buffer */
+    *pStateCurnt++ = *pSrc++;
+
+    /* Set accumulator to zero */
+    acc = 0;
+
+    /* Initialize state pointer of type q7 */
+    px = pState;
+
+    /* Initialize coeff pointer of type q7 */
+    pb = pCoeffs;
+
+
+    i = numTaps;
+
+    while(i > 0u)
+    {
+      /* acc =  b[numTaps-1] * x[n-numTaps-1] + b[numTaps-2] * x[n-numTaps-2] + b[numTaps-3] * x[n-numTaps-3] +...+ b[0] * x[0] */
+      acc += (q15_t) * px++ * *pb++;
+      i--;
+    }
+
+    /* Store the 1.7 format filter output in destination buffer */
+    *pDst++ = (q7_t) __SSAT((acc >> 7), 8);
+
+    /* Advance the state pointer by 1 to process the next sample */
+    pState = pState + 1;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Processing is complete.         
+   ** Now copy the last numTaps - 1 samples to the satrt of the state buffer.       
+   ** This prepares the state buffer for the next function call. */
+
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = S->pState;
+
+
+  /* Copy numTaps number of values */
+  i = (numTaps - 1u);
+
+  /* Copy q7_t data */
+  while(i > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+    i--;
+  }
+
+#endif /*   #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of FIR group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_f32.c
new file mode 100644
index 0000000000..e969d5c842
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_f32.c
@@ -0,0 +1,365 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_fir_sparse_f32.c    
+*    
+* Description:	Floating-point sparse FIR filter processing function.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ------------------------------------------------------------------- */
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @defgroup FIR_Sparse Finite Impulse Response (FIR) Sparse Filters    
+ *    
+ * This group of functions implements sparse FIR filters.     
+ * Sparse FIR filters are equivalent to standard FIR filters except that most of the coefficients are equal to zero.   
+ * Sparse filters are used for simulating reflections in communications and audio applications.   
+ *   
+ * There are separate functions for Q7, Q15, Q31, and floating-point data types.    
+ * The functions operate on blocks  of input and output data and each call to the function processes    
+ * blockSize samples through the filter.  pSrc and    
+ * pDst points to input and output arrays respectively containing blockSize values.    
+ *    
+ * \par Algorithm:    
+ * The sparse filter instant structure contains an array of tap indices pTapDelay which specifies the locations of the non-zero coefficients.   
+ * This is in addition to the coefficient array b.   
+ * The implementation essentially skips the multiplications by zero and leads to an efficient realization.   
+ * 
   
+ *     y[n] = b[0] * x[n-pTapDelay[0]] + b[1] * x[n-pTapDelay[1]] + b[2] * x[n-pTapDelay[2]] + ...+ b[numTaps-1] * x[n-pTapDelay[numTaps-1]]    
+ * 
    
+ * \par    
+ * \image html FIRSparse.gif "Sparse FIR filter.  b[n] represents the filter coefficients"   
+ * \par    
+ * pCoeffs points to a coefficient array of size numTaps;    
+ * pTapDelay points to an array of nonzero indices and is also of size numTaps;   
+ * pState points to a state array of size maxDelay + blockSize, where   
+ * maxDelay is the largest offset value that is ever used in the pTapDelay array.   
+ * Some of the processing functions also require temporary working buffers.   
+ *   
+ * \par Instance Structure    
+ * The coefficients and state variables for a filter are stored together in an instance data structure.    
+ * A separate instance structure must be defined for each filter.    
+ * Coefficient and offset arrays may be shared among several instances while state variable arrays cannot be shared.    
+ * There are separate instance structure declarations for each of the 4 supported data types.    
+ *    
+ * \par Initialization Functions    
+ * There is also an associated initialization function for each data type.    
+ * The initialization function performs the following operations:    
+ * - Sets the values of the internal structure fields.    
+ * - Zeros out the values in the state buffer.    
+ *    
+ * \par    
+ * Use of the initialization function is optional.    
+ * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.    
+ * To place an instance structure into a const data section, the instance structure must be manually initialized.    
+ * Set the values in the state buffer to zeros before static initialization.    
+ * The code below statically initializes each of the 4 different data type filter instance structures    
+ * 
    
+ *arm_fir_sparse_instance_f32 S = {numTaps, 0, pState, pCoeffs, maxDelay, pTapDelay};    
+ *arm_fir_sparse_instance_q31 S = {numTaps, 0, pState, pCoeffs, maxDelay, pTapDelay};    
+ *arm_fir_sparse_instance_q15 S = {numTaps, 0, pState, pCoeffs, maxDelay, pTapDelay};    
+ *arm_fir_sparse_instance_q7 S =  {numTaps, 0, pState, pCoeffs, maxDelay, pTapDelay};    
+ * 
    
+ * \par    
+ *    
+ * \par Fixed-Point Behavior    
+ * Care must be taken when using the fixed-point versions of the sparse FIR filter functions.    
+ * In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.    
+ * Refer to the function specific documentation below for usage guidelines.    
+ */
+
+/**    
+ * @addtogroup FIR_Sparse    
+ * @{    
+ */
+
+/**   
+ * @brief Processing function for the floating-point sparse FIR filter.   
+ * @param[in]  *S          points to an instance of the floating-point sparse FIR structure.   
+ * @param[in]  *pSrc       points to the block of input data.   
+ * @param[out] *pDst       points to the block of output data   
+ * @param[in]  *pScratchIn points to a temporary buffer of size blockSize.   
+ * @param[in]  blockSize   number of input samples to process per call.   
+ * @return none.   
+ */
+
+void arm_fir_sparse_f32(
+  arm_fir_sparse_instance_f32 * S,
+  float32_t * pSrc,
+  float32_t * pDst,
+  float32_t * pScratchIn,
+  uint32_t blockSize)
+{
+
+  float32_t *pState = S->pState;                 /* State pointer */
+  float32_t *pCoeffs = S->pCoeffs;               /* Coefficient pointer */
+  float32_t *px;                                 /* Scratch buffer pointer */
+  float32_t *py = pState;                        /* Temporary pointers for state buffer */
+  float32_t *pb = pScratchIn;                    /* Temporary pointers for scratch buffer */
+  float32_t *pOut;                               /* Destination pointer */
+  int32_t *pTapDelay = S->pTapDelay;             /* Pointer to the array containing offset of the non-zero tap values. */
+  uint32_t delaySize = S->maxDelay + blockSize;  /* state length */
+  uint16_t numTaps = S->numTaps;                 /* Number of filter coefficients in the filter  */
+  int32_t readIndex;                             /* Read index of the state buffer */
+  uint32_t tapCnt, blkCnt;                       /* loop counters */
+  float32_t coeff = *pCoeffs++;                  /* Read the first coefficient value */
+
+
+
+  /* BlockSize of Input samples are copied into the state buffer */
+  /* StateIndex points to the starting position to write in the state buffer */
+  arm_circularWrite_f32((int32_t *) py, delaySize, &S->stateIndex, 1,
+                        (int32_t *) pSrc, 1, blockSize);
+
+
+  /* Read Index, from where the state buffer should be read, is calculated. */
+  readIndex = ((int32_t) S->stateIndex - (int32_t) blockSize) - *pTapDelay++;
+
+  /* Wraparound of readIndex */
+  if(readIndex < 0)
+  {
+    readIndex += (int32_t) delaySize;
+  }
+
+  /* Working pointer for state buffer is updated */
+  py = pState;
+
+  /* blockSize samples are read from the state buffer */
+  arm_circularRead_f32((int32_t *) py, delaySize, &readIndex, 1,
+                       (int32_t *) pb, (int32_t *) pb, blockSize, 1,
+                       blockSize);
+
+  /* Working pointer for the scratch buffer */
+  px = pb;
+
+  /* Working pointer for destination buffer */
+  pOut = pDst;
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /* Loop over the blockSize. Unroll by a factor of 4.    
+   * Compute 4 Multiplications at a time. */
+  blkCnt = blockSize >> 2u;
+
+  while(blkCnt > 0u)
+  {
+    /* Perform Multiplications and store in destination buffer */
+    *pOut++ = *px++ * coeff;
+    *pOut++ = *px++ * coeff;
+    *pOut++ = *px++ * coeff;
+    *pOut++ = *px++ * coeff;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4,    
+   * compute the remaining samples */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* Perform Multiplications and store in destination buffer */
+    *pOut++ = *px++ * coeff;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Load the coefficient value and    
+   * increment the coefficient buffer for the next set of state values */
+  coeff = *pCoeffs++;
+
+  /* Read Index, from where the state buffer should be read, is calculated. */
+  readIndex = ((int32_t) S->stateIndex - (int32_t) blockSize) - *pTapDelay++;
+
+  /* Wraparound of readIndex */
+  if(readIndex < 0)
+  {
+    readIndex += (int32_t) delaySize;
+  }
+
+  /* Loop over the number of taps. */
+  tapCnt = (uint32_t) numTaps - 1u;
+
+  while(tapCnt > 0u)
+  {
+
+    /* Working pointer for state buffer is updated */
+    py = pState;
+
+    /* blockSize samples are read from the state buffer */
+    arm_circularRead_f32((int32_t *) py, delaySize, &readIndex, 1,
+                         (int32_t *) pb, (int32_t *) pb, blockSize, 1,
+                         blockSize);
+
+    /* Working pointer for the scratch buffer */
+    px = pb;
+
+    /* Working pointer for destination buffer */
+    pOut = pDst;
+
+    /* Loop over the blockSize. Unroll by a factor of 4.    
+     * Compute 4 MACS at a time. */
+    blkCnt = blockSize >> 2u;
+
+    while(blkCnt > 0u)
+    {
+      /* Perform Multiply-Accumulate */
+      *pOut++ += *px++ * coeff;
+      *pOut++ += *px++ * coeff;
+      *pOut++ += *px++ * coeff;
+      *pOut++ += *px++ * coeff;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the blockSize is not a multiple of 4,    
+     * compute the remaining samples */
+    blkCnt = blockSize % 0x4u;
+
+    while(blkCnt > 0u)
+    {
+      /* Perform Multiply-Accumulate */
+      *pOut++ += *px++ * coeff;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* Load the coefficient value and    
+     * increment the coefficient buffer for the next set of state values */
+    coeff = *pCoeffs++;
+
+    /* Read Index, from where the state buffer should be read, is calculated. */
+    readIndex = ((int32_t) S->stateIndex -
+                 (int32_t) blockSize) - *pTapDelay++;
+
+    /* Wraparound of readIndex */
+    if(readIndex < 0)
+    {
+      readIndex += (int32_t) delaySize;
+    }
+
+    /* Decrement the tap loop counter */
+    tapCnt--;
+  }
+
+#else
+
+/* Run the below code for Cortex-M0 */
+
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* Perform Multiplications and store in destination buffer */
+    *pOut++ = *px++ * coeff;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Load the coefficient value and           
+   * increment the coefficient buffer for the next set of state values */
+  coeff = *pCoeffs++;
+
+  /* Read Index, from where the state buffer should be read, is calculated. */
+  readIndex = ((int32_t) S->stateIndex - (int32_t) blockSize) - *pTapDelay++;
+
+  /* Wraparound of readIndex */
+  if(readIndex < 0)
+  {
+    readIndex += (int32_t) delaySize;
+  }
+
+  /* Loop over the number of taps. */
+  tapCnt = (uint32_t) numTaps - 1u;
+
+  while(tapCnt > 0u)
+  {
+
+    /* Working pointer for state buffer is updated */
+    py = pState;
+
+    /* blockSize samples are read from the state buffer */
+    arm_circularRead_f32((int32_t *) py, delaySize, &readIndex, 1,
+                         (int32_t *) pb, (int32_t *) pb, blockSize, 1,
+                         blockSize);
+
+    /* Working pointer for the scratch buffer */
+    px = pb;
+
+    /* Working pointer for destination buffer */
+    pOut = pDst;
+
+    blkCnt = blockSize;
+
+    while(blkCnt > 0u)
+    {
+      /* Perform Multiply-Accumulate */
+      *pOut++ += *px++ * coeff;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* Load the coefficient value and           
+     * increment the coefficient buffer for the next set of state values */
+    coeff = *pCoeffs++;
+
+    /* Read Index, from where the state buffer should be read, is calculated. */
+    readIndex =
+      ((int32_t) S->stateIndex - (int32_t) blockSize) - *pTapDelay++;
+
+    /* Wraparound of readIndex */
+    if(readIndex < 0)
+    {
+      readIndex += (int32_t) delaySize;
+    }
+
+    /* Decrement the tap loop counter */
+    tapCnt--;
+  }
+
+#endif /*   #ifndef ARM_MATH_CM0        */
+
+}
+
+/**    
+ * @} end of FIR_Sparse group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_init_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_init_f32.c
new file mode 100644
index 0000000000..2934352d05
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_init_f32.c
@@ -0,0 +1,102 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_fir_sparse_init_f32.c    
+*    
+* Description:	Floating-point sparse FIR filter initialization function.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ---------------------------------------------------------------------------*/
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR_Sparse    
+ * @{    
+ */
+
+/**   
+ * @brief  Initialization function for the floating-point sparse FIR filter.   
+ * @param[in,out] *S         points to an instance of the floating-point sparse FIR structure.   
+ * @param[in]     numTaps    number of nonzero coefficients in the filter.   
+ * @param[in]     *pCoeffs   points to the array of filter coefficients.   
+ * @param[in]     *pState    points to the state buffer.   
+ * @param[in]     *pTapDelay points to the array of offset times.   
+ * @param[in]     maxDelay   maximum offset time supported.   
+ * @param[in]     blockSize  number of samples that will be processed per block.   
+ * @return none   
+ *    
+ * Description:    
+ * \par    
+ * pCoeffs holds the filter coefficients and has length numTaps.    
+ * pState holds the filter's state variables and must be of length    
+ * maxDelay + blockSize, where maxDelay    
+ * is the maximum number of delay line values.    
+ * blockSize is the    
+ * number of samples processed by the arm_fir_sparse_f32() function.    
+ */
+
+void arm_fir_sparse_init_f32(
+  arm_fir_sparse_instance_f32 * S,
+  uint16_t numTaps,
+  float32_t * pCoeffs,
+  float32_t * pState,
+  int32_t * pTapDelay,
+  uint16_t maxDelay,
+  uint32_t blockSize)
+{
+  /* Assign filter taps */
+  S->numTaps = numTaps;
+
+  /* Assign coefficient pointer */
+  S->pCoeffs = pCoeffs;
+
+  /* Assign TapDelay pointer */
+  S->pTapDelay = pTapDelay;
+
+  /* Assign MaxDelay */
+  S->maxDelay = maxDelay;
+
+  /* reset the stateIndex to 0 */
+  S->stateIndex = 0u;
+
+  /* Clear state buffer and size is always maxDelay + blockSize */
+  memset(pState, 0, (maxDelay + blockSize) * sizeof(float32_t));
+
+  /* Assign state pointer */
+  S->pState = pState;
+
+}
+
+/**    
+ * @} end of FIR_Sparse group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_init_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_init_q15.c
new file mode 100644
index 0000000000..47a116e952
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_init_q15.c
@@ -0,0 +1,102 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_fir_sparse_init_q15.c    
+*    
+* Description:	Q15 sparse FIR filter initialization function.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ---------------------------------------------------------------------------*/
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR_Sparse    
+ * @{    
+ */
+
+/**   
+ * @brief  Initialization function for the Q15 sparse FIR filter.   
+ * @param[in,out] *S         points to an instance of the Q15 sparse FIR structure.   
+ * @param[in]     numTaps    number of nonzero coefficients in the filter.   
+ * @param[in]     *pCoeffs   points to the array of filter coefficients.   
+ * @param[in]     *pState    points to the state buffer.   
+ * @param[in]     *pTapDelay points to the array of offset times.   
+ * @param[in]     maxDelay   maximum offset time supported.   
+ * @param[in]     blockSize  number of samples that will be processed per block.   
+ * @return none   
+ *    
+ * Description:    
+ * \par    
+ * pCoeffs holds the filter coefficients and has length numTaps.    
+ * pState holds the filter's state variables and must be of length    
+ * maxDelay + blockSize, where maxDelay    
+ * is the maximum number of delay line values.    
+ * blockSize is the    
+ * number of words processed by arm_fir_sparse_q15() function.    
+ */
+
+void arm_fir_sparse_init_q15(
+  arm_fir_sparse_instance_q15 * S,
+  uint16_t numTaps,
+  q15_t * pCoeffs,
+  q15_t * pState,
+  int32_t * pTapDelay,
+  uint16_t maxDelay,
+  uint32_t blockSize)
+{
+  /* Assign filter taps */
+  S->numTaps = numTaps;
+
+  /* Assign coefficient pointer */
+  S->pCoeffs = pCoeffs;
+
+  /* Assign TapDelay pointer */
+  S->pTapDelay = pTapDelay;
+
+  /* Assign MaxDelay */
+  S->maxDelay = maxDelay;
+
+  /* reset the stateIndex to 0 */
+  S->stateIndex = 0u;
+
+  /* Clear state buffer and size is always maxDelay + blockSize */
+  memset(pState, 0, (maxDelay + blockSize) * sizeof(q15_t));
+
+  /* Assign state pointer */
+  S->pState = pState;
+
+}
+
+/**    
+ * @} end of FIR_Sparse group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_init_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_init_q31.c
new file mode 100644
index 0000000000..360a219b20
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_init_q31.c
@@ -0,0 +1,101 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_fir_sparse_init_q31.c    
+*    
+* Description:	Q31 sparse FIR filter initialization function.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ---------------------------------------------------------------------------*/
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR_Sparse    
+ * @{    
+ */
+
+/**   
+ * @brief  Initialization function for the Q31 sparse FIR filter.   
+ * @param[in,out] *S         points to an instance of the Q31 sparse FIR structure.   
+ * @param[in]     numTaps    number of nonzero coefficients in the filter.   
+ * @param[in]     *pCoeffs   points to the array of filter coefficients.   
+ * @param[in]     *pState    points to the state buffer.   
+ * @param[in]     *pTapDelay points to the array of offset times.   
+ * @param[in]     maxDelay   maximum offset time supported.   
+ * @param[in]     blockSize  number of samples that will be processed per block.   
+ * @return none   
+ *    
+ * Description:    
+ * \par    
+ * pCoeffs holds the filter coefficients and has length numTaps.    
+ * pState holds the filter's state variables and must be of length    
+ * maxDelay + blockSize, where maxDelay    
+ * is the maximum number of delay line values.    
+ * blockSize is the number of words processed by arm_fir_sparse_q31() function.    
+ */
+
+void arm_fir_sparse_init_q31(
+  arm_fir_sparse_instance_q31 * S,
+  uint16_t numTaps,
+  q31_t * pCoeffs,
+  q31_t * pState,
+  int32_t * pTapDelay,
+  uint16_t maxDelay,
+  uint32_t blockSize)
+{
+  /* Assign filter taps */
+  S->numTaps = numTaps;
+
+  /* Assign coefficient pointer */
+  S->pCoeffs = pCoeffs;
+
+  /* Assign TapDelay pointer */
+  S->pTapDelay = pTapDelay;
+
+  /* Assign MaxDelay */
+  S->maxDelay = maxDelay;
+
+  /* reset the stateIndex to 0 */
+  S->stateIndex = 0u;
+
+  /* Clear state buffer and size is always maxDelay + blockSize */
+  memset(pState, 0, (maxDelay + blockSize) * sizeof(q31_t));
+
+  /* Assign state pointer */
+  S->pState = pState;
+
+}
+
+/**    
+ * @} end of FIR_Sparse group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_init_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_init_q7.c
new file mode 100644
index 0000000000..b400297ca6
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_init_q7.c
@@ -0,0 +1,102 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_fir_sparse_init_q7.c    
+*    
+* Description:	Q7 sparse FIR filter initialization function.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ---------------------------------------------------------------------------*/
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR_Sparse    
+ * @{    
+ */
+
+/**   
+ * @brief  Initialization function for the Q7 sparse FIR filter.   
+ * @param[in,out] *S         points to an instance of the Q7 sparse FIR structure.   
+ * @param[in]     numTaps    number of nonzero coefficients in the filter.   
+ * @param[in]     *pCoeffs   points to the array of filter coefficients.   
+ * @param[in]     *pState    points to the state buffer.   
+ * @param[in]     *pTapDelay points to the array of offset times.   
+ * @param[in]     maxDelay   maximum offset time supported.   
+ * @param[in]     blockSize  number of samples that will be processed per block.   
+ * @return none   
+ *    
+ * Description:    
+ * \par    
+ * pCoeffs holds the filter coefficients and has length numTaps.    
+ * pState holds the filter's state variables and must be of length    
+ * maxDelay + blockSize, where maxDelay    
+ * is the maximum number of delay line values.    
+ * blockSize is the    
+ * number of samples processed by the arm_fir_sparse_q7() function.    
+ */
+
+void arm_fir_sparse_init_q7(
+  arm_fir_sparse_instance_q7 * S,
+  uint16_t numTaps,
+  q7_t * pCoeffs,
+  q7_t * pState,
+  int32_t * pTapDelay,
+  uint16_t maxDelay,
+  uint32_t blockSize)
+{
+  /* Assign filter taps */
+  S->numTaps = numTaps;
+
+  /* Assign coefficient pointer */
+  S->pCoeffs = pCoeffs;
+
+  /* Assign TapDelay pointer */
+  S->pTapDelay = pTapDelay;
+
+  /* Assign MaxDelay */
+  S->maxDelay = maxDelay;
+
+  /* reset the stateIndex to 0 */
+  S->stateIndex = 0u;
+
+  /* Clear state buffer and size is always maxDelay + blockSize */
+  memset(pState, 0, (maxDelay + blockSize) * sizeof(q7_t));
+
+  /* Assign state pointer */
+  S->pState = pState;
+
+}
+
+/**    
+ * @} end of FIR_Sparse group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_q15.c
new file mode 100644
index 0000000000..016f833456
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_q15.c
@@ -0,0 +1,406 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_fir_sparse_q15.c    
+*    
+* Description:	Q15 sparse FIR filter processing function.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ------------------------------------------------------------------- */
+#include "arm_math.h"
+
+/**    
+ * @addtogroup FIR_Sparse    
+ * @{    
+ */
+
+/**   
+ * @brief Processing function for the Q15 sparse FIR filter.   
+ * @param[in]  *S           points to an instance of the Q15 sparse FIR structure.   
+ * @param[in]  *pSrc        points to the block of input data.   
+ * @param[out] *pDst        points to the block of output data   
+ * @param[in]  *pScratchIn  points to a temporary buffer of size blockSize.   
+ * @param[in]  *pScratchOut points to a temporary buffer of size blockSize.   
+ * @param[in]  blockSize    number of input samples to process per call.   
+ * @return none.   
+ *    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function is implemented using an internal 32-bit accumulator.   
+ * The 1.15 x 1.15 multiplications yield a 2.30 result and these are added to a 2.30 accumulator.   
+ * Thus the full precision of the multiplications is maintained but there is only a single guard bit in the accumulator.   
+ * If the accumulator result overflows it will wrap around rather than saturate.   
+ * After all multiply-accumulates are performed, the 2.30 accumulator is truncated to 2.15 format and then saturated to 1.15 format.    
+ * In order to avoid overflows the input signal or coefficients must be scaled down by log2(numTaps) bits.   
+ */
+
+
+void arm_fir_sparse_q15(
+  arm_fir_sparse_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst,
+  q15_t * pScratchIn,
+  q31_t * pScratchOut,
+  uint32_t blockSize)
+{
+
+  q15_t *pState = S->pState;                     /* State pointer */
+  q15_t *pIn = pSrc;                             /* Working pointer for input */
+  q15_t *pOut = pDst;                            /* Working pointer for output */
+  q15_t *pCoeffs = S->pCoeffs;                   /* Coefficient pointer */
+  q15_t *px;                                     /* Temporary pointers for scratch buffer */
+  q15_t *pb = pScratchIn;                        /* Temporary pointers for scratch buffer */
+  q15_t *py = pState;                            /* Temporary pointers for state buffer */
+  int32_t *pTapDelay = S->pTapDelay;             /* Pointer to the array containing offset of the non-zero tap values. */
+  uint32_t delaySize = S->maxDelay + blockSize;  /* state length */
+  uint16_t numTaps = S->numTaps;                 /* Filter order */
+  int32_t readIndex;                             /* Read index of the state buffer */
+  uint32_t tapCnt, blkCnt;                       /* loop counters */
+  q15_t coeff = *pCoeffs++;                      /* Read the first coefficient value */
+  q31_t *pScr2 = pScratchOut;                    /* Working pointer for pScratchOut */
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q31_t in1, in2;                                /* Temporary variables */
+
+
+  /* BlockSize of Input samples are copied into the state buffer */
+  /* StateIndex points to the starting position to write in the state buffer */
+  arm_circularWrite_q15(py, delaySize, &S->stateIndex, 1, pIn, 1, blockSize);
+
+  /* Loop over the number of taps. */
+  tapCnt = numTaps;
+
+  /* Read Index, from where the state buffer should be read, is calculated. */
+  readIndex = (S->stateIndex - blockSize) - *pTapDelay++;
+
+  /* Wraparound of readIndex */
+  if(readIndex < 0)
+  {
+    readIndex += (int32_t) delaySize;
+  }
+
+  /* Working pointer for state buffer is updated */
+  py = pState;
+
+  /* blockSize samples are read from the state buffer */
+  arm_circularRead_q15(py, delaySize, &readIndex, 1,
+                       pb, pb, blockSize, 1, blockSize);
+
+  /* Working pointer for the scratch buffer of state values */
+  px = pb;
+
+  /* Working pointer for scratch buffer of output values */
+  pScratchOut = pScr2;
+
+  /* Loop over the blockSize. Unroll by a factor of 4.    
+   * Compute 4 multiplications at a time. */
+  blkCnt = blockSize >> 2;
+
+  while(blkCnt > 0u)
+  {
+    /* Perform multiplication and store in the scratch buffer */
+    *pScratchOut++ = ((q31_t) * px++ * coeff);
+    *pScratchOut++ = ((q31_t) * px++ * coeff);
+    *pScratchOut++ = ((q31_t) * px++ * coeff);
+    *pScratchOut++ = ((q31_t) * px++ * coeff);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4,    
+   * compute the remaining samples */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* Perform multiplication and store in the scratch buffer */
+    *pScratchOut++ = ((q31_t) * px++ * coeff);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Load the coefficient value and    
+   * increment the coefficient buffer for the next set of state values */
+  coeff = *pCoeffs++;
+
+  /* Read Index, from where the state buffer should be read, is calculated. */
+  readIndex = (S->stateIndex - blockSize) - *pTapDelay++;
+
+  /* Wraparound of readIndex */
+  if(readIndex < 0)
+  {
+    readIndex += (int32_t) delaySize;
+  }
+
+  /* Loop over the number of taps. */
+  tapCnt = (uint32_t) numTaps - 1u;
+
+  while(tapCnt > 0u)
+  {
+    /* Working pointer for state buffer is updated */
+    py = pState;
+
+    /* blockSize samples are read from the state buffer */
+    arm_circularRead_q15(py, delaySize, &readIndex, 1,
+                         pb, pb, blockSize, 1, blockSize);
+
+    /* Working pointer for the scratch buffer of state values */
+    px = pb;
+
+    /* Working pointer for scratch buffer of output values */
+    pScratchOut = pScr2;
+
+    /* Loop over the blockSize. Unroll by a factor of 4.    
+     * Compute 4 MACS at a time. */
+    blkCnt = blockSize >> 2;
+
+    while(blkCnt > 0u)
+    {
+      /* Perform Multiply-Accumulate */
+      *pScratchOut++ += (q31_t) * px++ * coeff;
+      *pScratchOut++ += (q31_t) * px++ * coeff;
+      *pScratchOut++ += (q31_t) * px++ * coeff;
+      *pScratchOut++ += (q31_t) * px++ * coeff;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the blockSize is not a multiple of 4,    
+     * compute the remaining samples */
+    blkCnt = blockSize % 0x4u;
+
+    while(blkCnt > 0u)
+    {
+      /* Perform Multiply-Accumulate */
+      *pScratchOut++ += (q31_t) * px++ * coeff;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* Load the coefficient value and    
+     * increment the coefficient buffer for the next set of state values */
+    coeff = *pCoeffs++;
+
+    /* Read Index, from where the state buffer should be read, is calculated. */
+    readIndex = (S->stateIndex - blockSize) - *pTapDelay++;
+
+    /* Wraparound of readIndex */
+    if(readIndex < 0)
+    {
+      readIndex += (int32_t) delaySize;
+    }
+
+    /* Decrement the tap loop counter */
+    tapCnt--;
+  }
+
+  /* All the output values are in pScratchOut buffer.    
+     Convert them into 1.15 format, saturate and store in the destination buffer. */
+  /* Loop over the blockSize. */
+  blkCnt = blockSize >> 2;
+
+  while(blkCnt > 0u)
+  {
+    in1 = *pScr2++;
+    in2 = *pScr2++;
+
+#ifndef  ARM_MATH_BIG_ENDIAN
+
+    *__SIMD32(pOut)++ =
+      __PKHBT((q15_t) __SSAT(in1 >> 15, 16), (q15_t) __SSAT(in2 >> 15, 16),
+              16);
+
+#else
+    *__SIMD32(pOut)++ =
+      __PKHBT((q15_t) __SSAT(in2 >> 15, 16), (q15_t) __SSAT(in1 >> 15, 16),
+              16);
+
+#endif /*      #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+    in1 = *pScr2++;
+
+    in2 = *pScr2++;
+
+#ifndef  ARM_MATH_BIG_ENDIAN
+
+    *__SIMD32(pOut)++ =
+      __PKHBT((q15_t) __SSAT(in1 >> 15, 16), (q15_t) __SSAT(in2 >> 15, 16),
+              16);
+
+#else
+
+    *__SIMD32(pOut)++ =
+      __PKHBT((q15_t) __SSAT(in2 >> 15, 16), (q15_t) __SSAT(in1 >> 15, 16),
+              16);
+
+#endif /*      #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+
+    blkCnt--;
+
+  }
+
+  /* If the blockSize is not a multiple of 4,    
+     remaining samples are processed in the below loop */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    *pOut++ = (q15_t) __SSAT(*pScr2++ >> 15, 16);
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* BlockSize of Input samples are copied into the state buffer */
+  /* StateIndex points to the starting position to write in the state buffer */
+  arm_circularWrite_q15(py, delaySize, &S->stateIndex, 1, pIn, 1, blockSize);
+
+  /* Loop over the number of taps. */
+  tapCnt = numTaps;
+
+  /* Read Index, from where the state buffer should be read, is calculated. */
+  readIndex = (S->stateIndex - blockSize) - *pTapDelay++;
+
+  /* Wraparound of readIndex */
+  if(readIndex < 0)
+  {
+    readIndex += (int32_t) delaySize;
+  }
+
+  /* Working pointer for state buffer is updated */
+  py = pState;
+
+  /* blockSize samples are read from the state buffer */
+  arm_circularRead_q15(py, delaySize, &readIndex, 1,
+                       pb, pb, blockSize, 1, blockSize);
+
+  /* Working pointer for the scratch buffer of state values */
+  px = pb;
+
+  /* Working pointer for scratch buffer of output values */
+  pScratchOut = pScr2;
+
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* Perform multiplication and store in the scratch buffer */
+    *pScratchOut++ = ((q31_t) * px++ * coeff);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Load the coefficient value and           
+   * increment the coefficient buffer for the next set of state values */
+  coeff = *pCoeffs++;
+
+  /* Read Index, from where the state buffer should be read, is calculated. */
+  readIndex = (S->stateIndex - blockSize) - *pTapDelay++;
+
+  /* Wraparound of readIndex */
+  if(readIndex < 0)
+  {
+    readIndex += (int32_t) delaySize;
+  }
+
+  /* Loop over the number of taps. */
+  tapCnt = (uint32_t) numTaps - 1u;
+
+  while(tapCnt > 0u)
+  {
+    /* Working pointer for state buffer is updated */
+    py = pState;
+
+    /* blockSize samples are read from the state buffer */
+    arm_circularRead_q15(py, delaySize, &readIndex, 1,
+                         pb, pb, blockSize, 1, blockSize);
+
+    /* Working pointer for the scratch buffer of state values */
+    px = pb;
+
+    /* Working pointer for scratch buffer of output values */
+    pScratchOut = pScr2;
+
+    blkCnt = blockSize;
+
+    while(blkCnt > 0u)
+    {
+      /* Perform Multiply-Accumulate */
+      *pScratchOut++ += (q31_t) * px++ * coeff;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* Load the coefficient value and           
+     * increment the coefficient buffer for the next set of state values */
+    coeff = *pCoeffs++;
+
+    /* Read Index, from where the state buffer should be read, is calculated. */
+    readIndex = (S->stateIndex - blockSize) - *pTapDelay++;
+
+    /* Wraparound of readIndex */
+    if(readIndex < 0)
+    {
+      readIndex += (int32_t) delaySize;
+    }
+
+    /* Decrement the tap loop counter */
+    tapCnt--;
+  }
+
+  /* All the output values are in pScratchOut buffer.       
+     Convert them into 1.15 format, saturate and store in the destination buffer. */
+  /* Loop over the blockSize. */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    *pOut++ = (q15_t) __SSAT(*pScr2++ >> 15, 16);
+    blkCnt--;
+  }
+
+#endif /*   #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of FIR_Sparse group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_q31.c
new file mode 100644
index 0000000000..3d2f6d4028
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_q31.c
@@ -0,0 +1,370 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_fir_sparse_q31.c    
+*    
+* Description:	Q31 sparse FIR filter processing function.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ------------------------------------------------------------------- */
+#include "arm_math.h"
+
+
+/**    
+ * @addtogroup FIR_Sparse    
+ * @{    
+ */
+
+/**   
+ * @brief Processing function for the Q31 sparse FIR filter.   
+ * @param[in]  *S          points to an instance of the Q31 sparse FIR structure.   
+ * @param[in]  *pSrc       points to the block of input data.   
+ * @param[out] *pDst       points to the block of output data   
+ * @param[in]  *pScratchIn points to a temporary buffer of size blockSize.   
+ * @param[in]  blockSize   number of input samples to process per call.   
+ * @return none.   
+ *    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function is implemented using an internal 32-bit accumulator.   
+ * The 1.31 x 1.31 multiplications are truncated to 2.30 format.   
+ * This leads to loss of precision on the intermediate multiplications and provides only a single guard bit.    
+ * If the accumulator result overflows, it wraps around rather than saturate.   
+ * In order to avoid overflows the input signal or coefficients must be scaled down by log2(numTaps) bits.   
+ */
+
+void arm_fir_sparse_q31(
+  arm_fir_sparse_instance_q31 * S,
+  q31_t * pSrc,
+  q31_t * pDst,
+  q31_t * pScratchIn,
+  uint32_t blockSize)
+{
+
+  q31_t *pState = S->pState;                     /* State pointer */
+  q31_t *pCoeffs = S->pCoeffs;                   /* Coefficient pointer */
+  q31_t *px;                                     /* Scratch buffer pointer */
+  q31_t *py = pState;                            /* Temporary pointers for state buffer */
+  q31_t *pb = pScratchIn;                        /* Temporary pointers for scratch buffer */
+  q31_t *pOut;                                   /* Destination pointer */
+  q63_t out;                                     /* Temporary output variable */
+  int32_t *pTapDelay = S->pTapDelay;             /* Pointer to the array containing offset of the non-zero tap values. */
+  uint32_t delaySize = S->maxDelay + blockSize;  /* state length */
+  uint16_t numTaps = S->numTaps;                 /* Filter order */
+  int32_t readIndex;                             /* Read index of the state buffer */
+  uint32_t tapCnt, blkCnt;                       /* loop counters */
+  q31_t coeff = *pCoeffs++;                      /* Read the first coefficient value */
+  q31_t in;
+
+
+  /* BlockSize of Input samples are copied into the state buffer */
+  /* StateIndex points to the starting position to write in the state buffer */
+  arm_circularWrite_f32((int32_t *) py, delaySize, &S->stateIndex, 1,
+                        (int32_t *) pSrc, 1, blockSize);
+
+  /* Read Index, from where the state buffer should be read, is calculated. */
+  readIndex = (int32_t) (S->stateIndex - blockSize) - *pTapDelay++;
+
+  /* Wraparound of readIndex */
+  if(readIndex < 0)
+  {
+    readIndex += (int32_t) delaySize;
+  }
+
+  /* Working pointer for state buffer is updated */
+  py = pState;
+
+  /* blockSize samples are read from the state buffer */
+  arm_circularRead_f32((int32_t *) py, delaySize, &readIndex, 1,
+                       (int32_t *) pb, (int32_t *) pb, blockSize, 1,
+                       blockSize);
+
+  /* Working pointer for the scratch buffer of state values */
+  px = pb;
+
+  /* Working pointer for scratch buffer of output values */
+  pOut = pDst;
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /* Loop over the blockSize. Unroll by a factor of 4.    
+   * Compute 4 Multiplications at a time. */
+  blkCnt = blockSize >> 2;
+
+  while(blkCnt > 0u)
+  {
+    /* Perform Multiplications and store in the destination buffer */
+    *pOut++ = (q31_t) (((q63_t) * px++ * coeff) >> 32);
+    *pOut++ = (q31_t) (((q63_t) * px++ * coeff) >> 32);
+    *pOut++ = (q31_t) (((q63_t) * px++ * coeff) >> 32);
+    *pOut++ = (q31_t) (((q63_t) * px++ * coeff) >> 32);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4,    
+   * compute the remaining samples */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* Perform Multiplications and store in the destination buffer */
+    *pOut++ = (q31_t) (((q63_t) * px++ * coeff) >> 32);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Load the coefficient value and    
+   * increment the coefficient buffer for the next set of state values */
+  coeff = *pCoeffs++;
+
+  /* Read Index, from where the state buffer should be read, is calculated. */
+  readIndex = (int32_t) (S->stateIndex - blockSize) - *pTapDelay++;
+
+  /* Wraparound of readIndex */
+  if(readIndex < 0)
+  {
+    readIndex += (int32_t) delaySize;
+  }
+
+  /* Loop over the number of taps. */
+  tapCnt = (uint32_t) numTaps - 1u;
+
+  while(tapCnt > 0u)
+  {
+    /* Working pointer for state buffer is updated */
+    py = pState;
+
+    /* blockSize samples are read from the state buffer */
+    arm_circularRead_f32((int32_t *) py, delaySize, &readIndex, 1,
+                         (int32_t *) pb, (int32_t *) pb, blockSize, 1,
+                         blockSize);
+
+    /* Working pointer for the scratch buffer of state values */
+    px = pb;
+
+    /* Working pointer for scratch buffer of output values */
+    pOut = pDst;
+
+    /* Loop over the blockSize. Unroll by a factor of 4.    
+     * Compute 4 MACS at a time. */
+    blkCnt = blockSize >> 2;
+
+    while(blkCnt > 0u)
+    {
+      out = *pOut;
+      out += ((q63_t) * px++ * coeff) >> 32;
+      *pOut++ = (q31_t) (out);
+
+      out = *pOut;
+      out += ((q63_t) * px++ * coeff) >> 32;
+      *pOut++ = (q31_t) (out);
+
+      out = *pOut;
+      out += ((q63_t) * px++ * coeff) >> 32;
+      *pOut++ = (q31_t) (out);
+
+      out = *pOut;
+      out += ((q63_t) * px++ * coeff) >> 32;
+      *pOut++ = (q31_t) (out);
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the blockSize is not a multiple of 4,    
+     * compute the remaining samples */
+    blkCnt = blockSize % 0x4u;
+
+    while(blkCnt > 0u)
+    {
+      /* Perform Multiply-Accumulate */
+      out = *pOut;
+      out += ((q63_t) * px++ * coeff) >> 32;
+      *pOut++ = (q31_t) (out);
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* Load the coefficient value and    
+     * increment the coefficient buffer for the next set of state values */
+    coeff = *pCoeffs++;
+
+    /* Read Index, from where the state buffer should be read, is calculated. */
+    readIndex = (int32_t) (S->stateIndex - blockSize) - *pTapDelay++;
+
+    /* Wraparound of readIndex */
+    if(readIndex < 0)
+    {
+      readIndex += (int32_t) delaySize;
+    }
+
+    /* Decrement the tap loop counter */
+    tapCnt--;
+  }
+
+  /* Working output pointer is updated */
+  pOut = pDst;
+
+  /* Output is converted into 1.31 format. */
+  /* Loop over the blockSize. Unroll by a factor of 4.    
+   * process 4 output samples at a time. */
+  blkCnt = blockSize >> 2;
+
+  while(blkCnt > 0u)
+  {
+    in = *pOut << 1;
+    *pOut++ = in;
+    in = *pOut << 1;
+    *pOut++ = in;
+    in = *pOut << 1;
+    *pOut++ = in;
+    in = *pOut << 1;
+    *pOut++ = in;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4,    
+   * process the remaining output samples */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    in = *pOut << 1;
+    *pOut++ = in;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* Perform Multiplications and store in the destination buffer */
+    *pOut++ = (q31_t) (((q63_t) * px++ * coeff) >> 32);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Load the coefficient value and           
+   * increment the coefficient buffer for the next set of state values */
+  coeff = *pCoeffs++;
+
+  /* Read Index, from where the state buffer should be read, is calculated. */
+  readIndex = (int32_t) (S->stateIndex - blockSize) - *pTapDelay++;
+
+  /* Wraparound of readIndex */
+  if(readIndex < 0)
+  {
+    readIndex += (int32_t) delaySize;
+  }
+
+  /* Loop over the number of taps. */
+  tapCnt = (uint32_t) numTaps - 1u;
+
+  while(tapCnt > 0u)
+  {
+    /* Working pointer for state buffer is updated */
+    py = pState;
+
+    /* blockSize samples are read from the state buffer */
+    arm_circularRead_f32((int32_t *) py, delaySize, &readIndex, 1,
+                         (int32_t *) pb, (int32_t *) pb, blockSize, 1,
+                         blockSize);
+
+    /* Working pointer for the scratch buffer of state values */
+    px = pb;
+
+    /* Working pointer for scratch buffer of output values */
+    pOut = pDst;
+
+    blkCnt = blockSize;
+
+    while(blkCnt > 0u)
+    {
+      /* Perform Multiply-Accumulate */
+      out = *pOut;
+      out += ((q63_t) * px++ * coeff) >> 32;
+      *pOut++ = (q31_t) (out);
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* Load the coefficient value and           
+     * increment the coefficient buffer for the next set of state values */
+    coeff = *pCoeffs++;
+
+    /* Read Index, from where the state buffer should be read, is calculated. */
+    readIndex = (int32_t) (S->stateIndex - blockSize) - *pTapDelay++;
+
+    /* Wraparound of readIndex */
+    if(readIndex < 0)
+    {
+      readIndex += (int32_t) delaySize;
+    }
+
+    /* Decrement the tap loop counter */
+    tapCnt--;
+  }
+
+  /* Working output pointer is updated */
+  pOut = pDst;
+
+  /* Output is converted into 1.31 format. */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    in = *pOut << 1;
+    *pOut++ = in;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#endif /*   #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of FIR_Sparse group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_q7.c
new file mode 100644
index 0000000000..ace5d07037
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_q7.c
@@ -0,0 +1,398 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_fir_sparse_q7.c    
+*    
+* Description:	Q7 sparse FIR filter processing function.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ------------------------------------------------------------------- */
+#include "arm_math.h"
+
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup FIR_Sparse    
+ * @{    
+ */
+
+
+/**   
+ * @brief Processing function for the Q7 sparse FIR filter.   
+ * @param[in]  *S           points to an instance of the Q7 sparse FIR structure.   
+ * @param[in]  *pSrc        points to the block of input data.   
+ * @param[out] *pDst        points to the block of output data   
+ * @param[in]  *pScratchIn  points to a temporary buffer of size blockSize.   
+ * @param[in]  *pScratchOut points to a temporary buffer of size blockSize.   
+ * @param[in]  blockSize    number of input samples to process per call.   
+ * @return none.   
+ *    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function is implemented using a 32-bit internal accumulator.    
+ * Both coefficients and state variables are represented in 1.7 format and multiplications yield a 2.14 result.    
+ * The 2.14 intermediate results are accumulated in a 32-bit accumulator in 18.14 format.    
+ * There is no risk of internal overflow with this approach and the full precision of intermediate multiplications is preserved.    
+ * The accumulator is then converted to 18.7 format by discarding the low 7 bits.   
+ * Finally, the result is truncated to 1.7 format.   
+ */
+
+void arm_fir_sparse_q7(
+  arm_fir_sparse_instance_q7 * S,
+  q7_t * pSrc,
+  q7_t * pDst,
+  q7_t * pScratchIn,
+  q31_t * pScratchOut,
+  uint32_t blockSize)
+{
+
+  q7_t *pState = S->pState;                      /* State pointer */
+  q7_t *pCoeffs = S->pCoeffs;                    /* Coefficient pointer */
+  q7_t *px;                                      /* Scratch buffer pointer */
+  q7_t *py = pState;                             /* Temporary pointers for state buffer */
+  q7_t *pb = pScratchIn;                         /* Temporary pointers for scratch buffer */
+  q7_t *pOut = pDst;                             /* Destination pointer */
+  int32_t *pTapDelay = S->pTapDelay;             /* Pointer to the array containing offset of the non-zero tap values. */
+  uint32_t delaySize = S->maxDelay + blockSize;  /* state length */
+  uint16_t numTaps = S->numTaps;                 /* Filter order */
+  int32_t readIndex;                             /* Read index of the state buffer */
+  uint32_t tapCnt, blkCnt;                       /* loop counters */
+  q7_t coeff = *pCoeffs++;                       /* Read the coefficient value */
+  q31_t *pScr2 = pScratchOut;                    /* Working pointer for scratch buffer of output values */
+  q31_t in;
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q7_t in1, in2, in3, in4;
+
+  /* BlockSize of Input samples are copied into the state buffer */
+  /* StateIndex points to the starting position to write in the state buffer */
+  arm_circularWrite_q7(py, (int32_t) delaySize, &S->stateIndex, 1, pSrc, 1,
+                       blockSize);
+
+  /* Loop over the number of taps. */
+  tapCnt = numTaps;
+
+  /* Read Index, from where the state buffer should be read, is calculated. */
+  readIndex = ((int32_t) S->stateIndex - (int32_t) blockSize) - *pTapDelay++;
+
+  /* Wraparound of readIndex */
+  if(readIndex < 0)
+  {
+    readIndex += (int32_t) delaySize;
+  }
+
+  /* Working pointer for state buffer is updated */
+  py = pState;
+
+  /* blockSize samples are read from the state buffer */
+  arm_circularRead_q7(py, (int32_t) delaySize, &readIndex, 1, pb, pb,
+                      (int32_t) blockSize, 1, blockSize);
+
+  /* Working pointer for the scratch buffer of state values */
+  px = pb;
+
+  /* Working pointer for scratch buffer of output values */
+  pScratchOut = pScr2;
+
+  /* Loop over the blockSize. Unroll by a factor of 4.    
+   * Compute 4 multiplications at a time. */
+  blkCnt = blockSize >> 2;
+
+  while(blkCnt > 0u)
+  {
+    /* Perform multiplication and store in the scratch buffer */
+    *pScratchOut++ = ((q31_t) * px++ * coeff);
+    *pScratchOut++ = ((q31_t) * px++ * coeff);
+    *pScratchOut++ = ((q31_t) * px++ * coeff);
+    *pScratchOut++ = ((q31_t) * px++ * coeff);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4,    
+   * compute the remaining samples */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* Perform multiplication and store in the scratch buffer */
+    *pScratchOut++ = ((q31_t) * px++ * coeff);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Load the coefficient value and    
+   * increment the coefficient buffer for the next set of state values */
+  coeff = *pCoeffs++;
+
+  /* Read Index, from where the state buffer should be read, is calculated. */
+  readIndex = ((int32_t) S->stateIndex - (int32_t) blockSize) - *pTapDelay++;
+
+  /* Wraparound of readIndex */
+  if(readIndex < 0)
+  {
+    readIndex += (int32_t) delaySize;
+  }
+
+  /* Loop over the number of taps. */
+  tapCnt = (uint32_t) numTaps - 1u;
+
+  while(tapCnt > 0u)
+  {
+    /* Working pointer for state buffer is updated */
+    py = pState;
+
+    /* blockSize samples are read from the state buffer */
+    arm_circularRead_q7(py, (int32_t) delaySize, &readIndex, 1, pb, pb,
+                        (int32_t) blockSize, 1, blockSize);
+
+    /* Working pointer for the scratch buffer of state values */
+    px = pb;
+
+    /* Working pointer for scratch buffer of output values */
+    pScratchOut = pScr2;
+
+    /* Loop over the blockSize. Unroll by a factor of 4.    
+     * Compute 4 MACS at a time. */
+    blkCnt = blockSize >> 2;
+
+    while(blkCnt > 0u)
+    {
+      /* Perform Multiply-Accumulate */
+      in = *pScratchOut + ((q31_t) * px++ * coeff);
+      *pScratchOut++ = in;
+      in = *pScratchOut + ((q31_t) * px++ * coeff);
+      *pScratchOut++ = in;
+      in = *pScratchOut + ((q31_t) * px++ * coeff);
+      *pScratchOut++ = in;
+      in = *pScratchOut + ((q31_t) * px++ * coeff);
+      *pScratchOut++ = in;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the blockSize is not a multiple of 4,    
+     * compute the remaining samples */
+    blkCnt = blockSize % 0x4u;
+
+    while(blkCnt > 0u)
+    {
+      /* Perform Multiply-Accumulate */
+      in = *pScratchOut + ((q31_t) * px++ * coeff);
+      *pScratchOut++ = in;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* Load the coefficient value and    
+     * increment the coefficient buffer for the next set of state values */
+    coeff = *pCoeffs++;
+
+    /* Read Index, from where the state buffer should be read, is calculated. */
+    readIndex = ((int32_t) S->stateIndex -
+                 (int32_t) blockSize) - *pTapDelay++;
+
+    /* Wraparound of readIndex */
+    if(readIndex < 0)
+    {
+      readIndex += (int32_t) delaySize;
+    }
+
+    /* Decrement the tap loop counter */
+    tapCnt--;
+  }
+
+  /* All the output values are in pScratchOut buffer.    
+     Convert them into 1.15 format, saturate and store in the destination buffer. */
+  /* Loop over the blockSize. */
+  blkCnt = blockSize >> 2;
+
+  while(blkCnt > 0u)
+  {
+    in1 = (q7_t) __SSAT(*pScr2++ >> 7, 8);
+    in2 = (q7_t) __SSAT(*pScr2++ >> 7, 8);
+    in3 = (q7_t) __SSAT(*pScr2++ >> 7, 8);
+    in4 = (q7_t) __SSAT(*pScr2++ >> 7, 8);
+
+    *__SIMD32(pOut)++ = __PACKq7(in1, in2, in3, in4);
+
+    /* Decrement the blockSize loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4,    
+     remaining samples are processed in the below loop */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    *pOut++ = (q7_t) __SSAT(*pScr2++ >> 7, 8);
+
+    /* Decrement the blockSize loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* BlockSize of Input samples are copied into the state buffer */
+  /* StateIndex points to the starting position to write in the state buffer */
+  arm_circularWrite_q7(py, (int32_t) delaySize, &S->stateIndex, 1, pSrc, 1,
+                       blockSize);
+
+  /* Loop over the number of taps. */
+  tapCnt = numTaps;
+
+  /* Read Index, from where the state buffer should be read, is calculated. */
+  readIndex = ((int32_t) S->stateIndex - (int32_t) blockSize) - *pTapDelay++;
+
+  /* Wraparound of readIndex */
+  if(readIndex < 0)
+  {
+    readIndex += (int32_t) delaySize;
+  }
+
+  /* Working pointer for state buffer is updated */
+  py = pState;
+
+  /* blockSize samples are read from the state buffer */
+  arm_circularRead_q7(py, (int32_t) delaySize, &readIndex, 1, pb, pb,
+                      (int32_t) blockSize, 1, blockSize);
+
+  /* Working pointer for the scratch buffer of state values */
+  px = pb;
+
+  /* Working pointer for scratch buffer of output values */
+  pScratchOut = pScr2;
+
+  /* Loop over the blockSize */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* Perform multiplication and store in the scratch buffer */
+    *pScratchOut++ = ((q31_t) * px++ * coeff);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Load the coefficient value and           
+   * increment the coefficient buffer for the next set of state values */
+  coeff = *pCoeffs++;
+
+  /* Read Index, from where the state buffer should be read, is calculated. */
+  readIndex = ((int32_t) S->stateIndex - (int32_t) blockSize) - *pTapDelay++;
+
+  /* Wraparound of readIndex */
+  if(readIndex < 0)
+  {
+    readIndex += (int32_t) delaySize;
+  }
+
+  /* Loop over the number of taps. */
+  tapCnt = (uint32_t) numTaps - 1u;
+
+  while(tapCnt > 0u)
+  {
+    /* Working pointer for state buffer is updated */
+    py = pState;
+
+    /* blockSize samples are read from the state buffer */
+    arm_circularRead_q7(py, (int32_t) delaySize, &readIndex, 1, pb, pb,
+                        (int32_t) blockSize, 1, blockSize);
+
+    /* Working pointer for the scratch buffer of state values */
+    px = pb;
+
+    /* Working pointer for scratch buffer of output values */
+    pScratchOut = pScr2;
+
+    /* Loop over the blockSize */
+    blkCnt = blockSize;
+
+    while(blkCnt > 0u)
+    {
+      /* Perform Multiply-Accumulate */
+      in = *pScratchOut + ((q31_t) * px++ * coeff);
+      *pScratchOut++ = in;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* Load the coefficient value and           
+     * increment the coefficient buffer for the next set of state values */
+    coeff = *pCoeffs++;
+
+    /* Read Index, from where the state buffer should be read, is calculated. */
+    readIndex =
+      ((int32_t) S->stateIndex - (int32_t) blockSize) - *pTapDelay++;
+
+    /* Wraparound of readIndex */
+    if(readIndex < 0)
+    {
+      readIndex += (int32_t) delaySize;
+    }
+
+    /* Decrement the tap loop counter */
+    tapCnt--;
+  }
+
+  /* All the output values are in pScratchOut buffer.       
+     Convert them into 1.15 format, saturate and store in the destination buffer. */
+  /* Loop over the blockSize. */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    *pOut++ = (q7_t) __SSAT(*pScr2++ >> 7, 8);
+
+    /* Decrement the blockSize loop counter */
+    blkCnt--;
+  }
+
+#endif /*   #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of FIR_Sparse group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_iir_lattice_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_iir_lattice_f32.c
new file mode 100644
index 0000000000..074605553d
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_iir_lattice_f32.c
@@ -0,0 +1,440 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_iir_lattice_f32.c    
+*    
+* Description:	Floating-point IIR Lattice filter processing function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @defgroup IIR_Lattice Infinite Impulse Response (IIR) Lattice Filters    
+ *    
+ * This set of functions implements lattice filters    
+ * for Q15, Q31 and floating-point data types.  Lattice filters are used in a     
+ * variety of adaptive filter applications.  The filter structure has feedforward and    
+ * feedback components and the net impulse response is infinite length.    
+ * The functions operate on blocks    
+ * of input and output data and each call to the function processes    
+ * blockSize samples through the filter.  pSrc and    
+ * pDst point to input and output arrays containing blockSize values.    
+    
+ * \par Algorithm:    
+ * \image html IIRLattice.gif "Infinite Impulse Response Lattice filter"    
+ * 
    
+ *    fN(n)   =  x(n)    
+ *    fm-1(n) = fm(n) - km * gm-1(n-1)   for m = N, N-1, ...1    
+ *    gm(n)   = km * fm-1(n) + gm-1(n-1) for m = N, N-1, ...1    
+ *    y(n)    = vN * gN(n) + vN-1 * gN-1(n) + ...+ v0 * g0(n)    
+ * 
    
+ * \par    
+ * pkCoeffs points to array of reflection coefficients of size numStages.     
+ * Reflection coefficients are stored in time-reversed order.    
+ * \par    
+ * 
    
+ *    {kN, kN-1, ....k1}    
+ * 
    
+ * pvCoeffs points to the array of ladder coefficients of size (numStages+1).     
+ * Ladder coefficients are stored in time-reversed order.    
+ * \par    
+ * 
    
+ *    {vN, vN-1, ...v0}    
+ * 
    
+ * pState points to a state array of size numStages + blockSize.    
+ * The state variables shown in the figure above (the g values) are stored in the pState array.    
+ * The state variables are updated after each block of data is processed; the coefficients are untouched.    
+ * \par Instance Structure    
+ * The coefficients and state variables for a filter are stored together in an instance data structure.    
+ * A separate instance structure must be defined for each filter.    
+ * Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.    
+ * There are separate instance structure declarations for each of the 3 supported data types.    
+  *    
+ * \par Initialization Functions    
+ * There is also an associated initialization function for each data type.    
+ * The initialization function performs the following operations:    
+ * - Sets the values of the internal structure fields.    
+ * - Zeros out the values in the state buffer.    
+ *    
+ * \par    
+ * Use of the initialization function is optional.    
+ * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.    
+ * To place an instance structure into a const data section, the instance structure must be manually initialized.    
+ * Set the values in the state buffer to zeros and then manually initialize the instance structure as follows:    
+ * 
    
+ *arm_iir_lattice_instance_f32 S = {numStages, pState, pkCoeffs, pvCoeffs};    
+ *arm_iir_lattice_instance_q31 S = {numStages, pState, pkCoeffs, pvCoeffs};    
+ *arm_iir_lattice_instance_q15 S = {numStages, pState, pkCoeffs, pvCoeffs};    
+ * 
    
+ * \par    
+ * where numStages is the number of stages in the filter; pState points to the state buffer array;    
+ * pkCoeffs points to array of the reflection coefficients; pvCoeffs points to the array of ladder coefficients.    
+ * \par Fixed-Point Behavior    
+ * Care must be taken when using the fixed-point versions of the IIR lattice filter functions.    
+ * In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.    
+ * Refer to the function specific documentation below for usage guidelines.    
+ */
+
+/**    
+ * @addtogroup IIR_Lattice    
+ * @{    
+ */
+
+/**    
+ * @brief Processing function for the floating-point IIR lattice filter.    
+ * @param[in] *S points to an instance of the floating-point IIR lattice structure.    
+ * @param[in] *pSrc points to the block of input data.    
+ * @param[out] *pDst points to the block of output data.    
+ * @param[in] blockSize number of samples to process.    
+ * @return none.    
+ */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+void arm_iir_lattice_f32(
+  const arm_iir_lattice_instance_f32 * S,
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize)
+{
+  float32_t fnext1, gcurr1, gnext;               /* Temporary variables for lattice stages */
+  float32_t acc;                                 /* Accumlator */
+  uint32_t blkCnt, tapCnt;                       /* temporary variables for counts */
+  float32_t *px1, *px2, *pk, *pv;                /* temporary pointers for state and coef */
+  uint32_t numStages = S->numStages;             /* number of stages */
+  float32_t *pState;                             /* State pointer */
+  float32_t *pStateCurnt;                        /* State current pointer */
+  float32_t k1, k2;
+  float32_t v1, v2, v3, v4;
+  float32_t gcurr2;
+  float32_t fnext2;
+
+  /* initialise loop count */
+  blkCnt = blockSize;
+
+  /* initialise state pointer */
+  pState = &S->pState[0];
+
+  /* Sample processing */
+  while(blkCnt > 0u)
+  {
+    /* Read Sample from input buffer */
+    /* fN(n) = x(n) */
+    fnext2 = *pSrc++;
+
+    /* Initialize Ladder coeff pointer */
+    pv = &S->pvCoeffs[0];
+    /* Initialize Reflection coeff pointer */
+    pk = &S->pkCoeffs[0];
+
+    /* Initialize state read pointer */
+    px1 = pState;
+    /* Initialize state write pointer */
+    px2 = pState;
+
+    /* Set accumulator to zero */
+    acc = 0.0;
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = (numStages) >> 2;
+
+    while(tapCnt > 0u)
+    {
+      /* Read gN-1(n-1) from state buffer */
+      gcurr1 = *px1;
+
+      /* read reflection coefficient kN */
+      k1 = *pk;
+
+      /* fN-1(n) = fN(n) - kN * gN-1(n-1) */
+      fnext1 = fnext2 - (k1 * gcurr1);
+
+      /* read ladder coefficient vN */
+      v1 = *pv;
+
+      /* read next reflection coefficient kN-1 */
+      k2 = *(pk + 1u);
+
+      /* Read gN-2(n-1) from state buffer */
+      gcurr2 = *(px1 + 1u);
+
+      /* read next ladder coefficient vN-1 */
+      v2 = *(pv + 1u);
+
+      /* fN-2(n) = fN-1(n) - kN-1 * gN-2(n-1) */
+      fnext2 = fnext1 - (k2 * gcurr2);
+
+      /* gN(n)   = kN * fN-1(n) + gN-1(n-1) */
+      gnext = gcurr1 + (k1 * fnext1);
+
+      /* read reflection coefficient kN-2 */
+      k1 = *(pk + 2u);
+
+      /* write gN(n) into state for next sample processing */
+      *px2++ = gnext;
+
+      /* Read gN-3(n-1) from state buffer */
+      gcurr1 = *(px1 + 2u);
+
+      /* y(n) += gN(n) * vN  */
+      acc += (gnext * v1);
+
+      /* fN-3(n) = fN-2(n) - kN-2 * gN-3(n-1) */
+      fnext1 = fnext2 - (k1 * gcurr1);
+
+      /* gN-1(n)   = kN-1 * fN-2(n) + gN-2(n-1) */
+      gnext = gcurr2 + (k2 * fnext2);
+
+      /* Read gN-4(n-1) from state buffer */
+      gcurr2 = *(px1 + 3u);
+
+      /* y(n) += gN-1(n) * vN-1  */
+      acc += (gnext * v2);
+
+      /* read reflection coefficient kN-3 */
+      k2 = *(pk + 3u);
+
+      /* write gN-1(n) into state for next sample processing */
+      *px2++ = gnext;
+
+      /* fN-4(n) = fN-3(n) - kN-3 * gN-4(n-1) */
+      fnext2 = fnext1 - (k2 * gcurr2);
+
+      /* gN-2(n) = kN-2 * fN-3(n) + gN-3(n-1) */
+      gnext = gcurr1 + (k1 * fnext1);
+
+      /* read ladder coefficient vN-2 */
+      v3 = *(pv + 2u);
+
+      /* y(n) += gN-2(n) * vN-2  */
+      acc += (gnext * v3);
+
+      /* write gN-2(n) into state for next sample processing */
+      *px2++ = gnext;
+
+      /* update pointer */
+      pk += 4u;
+
+      /* gN-3(n) = kN-3 * fN-4(n) + gN-4(n-1) */
+      gnext = (fnext2 * k2) + gcurr2;
+
+      /* read next ladder coefficient vN-3 */
+      v4 = *(pv + 3u);
+
+      /* y(n) += gN-4(n) * vN-4  */
+      acc += (gnext * v4);
+
+      /* write gN-3(n) into state for next sample processing */
+      *px2++ = gnext;
+
+      /* update pointers */
+      px1 += 4u;
+      pv += 4u;
+
+      tapCnt--;
+
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = (numStages) % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      gcurr1 = *px1++;
+      /* Process sample for last taps */
+      fnext1 = fnext2 - ((*pk) * gcurr1);
+      gnext = (fnext1 * (*pk++)) + gcurr1;
+      /* Output samples for last taps */
+      acc += (gnext * (*pv++));
+      *px2++ = gnext;
+      fnext2 = fnext1;
+
+      tapCnt--;
+
+    }
+
+    /* y(n) += g0(n) * v0 */
+    acc += (fnext2 * (*pv));
+
+    *px2++ = fnext2;
+
+    /* write out into pDst */
+    *pDst++ = acc;
+
+    /* Advance the state pointer by 4 to process the next group of 4 samples */
+    pState = pState + 1u;
+
+    blkCnt--;
+
+  }
+
+  /* Processing is complete. Now copy last S->numStages samples to start of the buffer        
+     for the preperation of next frame process */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = &S->pState[0];
+  pState = &S->pState[blockSize];
+
+  tapCnt = numStages >> 2u;
+
+  /* copy data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+
+  }
+
+  /* Calculate remaining number of copies */
+  tapCnt = (numStages) % 0x4u;
+
+  /* Copy the remaining q31_t data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+}
+
+#else
+
+void arm_iir_lattice_f32(
+  const arm_iir_lattice_instance_f32 * S,
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize)
+{
+  float32_t fcurr, fnext = 0, gcurr, gnext;      /* Temporary variables for lattice stages */
+  float32_t acc;                                 /* Accumlator */
+  uint32_t blkCnt, tapCnt;                       /* temporary variables for counts */
+  float32_t *px1, *px2, *pk, *pv;                /* temporary pointers for state and coef */
+  uint32_t numStages = S->numStages;             /* number of stages */
+  float32_t *pState;                             /* State pointer */
+  float32_t *pStateCurnt;                        /* State current pointer */
+
+
+  /* Run the below code for Cortex-M0 */
+
+  blkCnt = blockSize;
+
+  pState = &S->pState[0];
+
+  /* Sample processing */
+  while(blkCnt > 0u)
+  {
+    /* Read Sample from input buffer */
+    /* fN(n) = x(n) */
+    fcurr = *pSrc++;
+
+    /* Initialize state read pointer */
+    px1 = pState;
+    /* Initialize state write pointer */
+    px2 = pState;
+    /* Set accumulator to zero */
+    acc = 0.0f;
+    /* Initialize Ladder coeff pointer */
+    pv = &S->pvCoeffs[0];
+    /* Initialize Reflection coeff pointer */
+    pk = &S->pkCoeffs[0];
+
+
+    /* Process sample for numStages */
+    tapCnt = numStages;
+
+    while(tapCnt > 0u)
+    {
+      gcurr = *px1++;
+      /* Process sample for last taps */
+      fnext = fcurr - ((*pk) * gcurr);
+      gnext = (fnext * (*pk++)) + gcurr;
+
+      /* Output samples for last taps */
+      acc += (gnext * (*pv++));
+      *px2++ = gnext;
+      fcurr = fnext;
+
+      /* Decrementing loop counter */
+      tapCnt--;
+
+    }
+
+    /* y(n) += g0(n) * v0 */
+    acc += (fnext * (*pv));
+
+    *px2++ = fnext;
+
+    /* write out into pDst */
+    *pDst++ = acc;
+
+    /* Advance the state pointer by 1 to process the next group of samples */
+    pState = pState + 1u;
+    blkCnt--;
+
+  }
+
+  /* Processing is complete. Now copy last S->numStages samples to start of the buffer           
+     for the preperation of next frame process */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = &S->pState[0];
+  pState = &S->pState[blockSize];
+
+  tapCnt = numStages;
+
+  /* Copy the data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+}
+
+#endif /*   #ifndef ARM_MATH_CM0 */
+
+
+/**    
+ * @} end of IIR_Lattice group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_iir_lattice_init_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_iir_lattice_init_f32.c
new file mode 100644
index 0000000000..89c00c24df
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_iir_lattice_init_f32.c
@@ -0,0 +1,86 @@
+/*-----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_iir_lattice_init_f32.c    
+*    
+* Description:  Floating-point IIR lattice filter initialization function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ---------------------------------------------------------------------------*/
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup IIR_Lattice    
+ * @{    
+ */
+
+/**    
+ * @brief Initialization function for the floating-point IIR lattice filter.    
+ * @param[in] *S points to an instance of the floating-point IIR lattice structure.    
+ * @param[in] numStages number of stages in the filter.    
+ * @param[in] *pkCoeffs points to the reflection coefficient buffer.  The array is of length numStages.    
+ * @param[in] *pvCoeffs points to the ladder coefficient buffer.  The array is of length numStages+1.    
+ * @param[in] *pState points to the state buffer.  The array is of length numStages+blockSize.    
+ * @param[in] blockSize number of samples to process.    
+ * @return none.    
+ */
+
+void arm_iir_lattice_init_f32(
+  arm_iir_lattice_instance_f32 * S,
+  uint16_t numStages,
+  float32_t * pkCoeffs,
+  float32_t * pvCoeffs,
+  float32_t * pState,
+  uint32_t blockSize)
+{
+  /* Assign filter taps */
+  S->numStages = numStages;
+
+  /* Assign reflection coefficient pointer */
+  S->pkCoeffs = pkCoeffs;
+
+  /* Assign ladder coefficient pointer */
+  S->pvCoeffs = pvCoeffs;
+
+  /* Clear state buffer and size is always blockSize + numStages */
+  memset(pState, 0, (numStages + blockSize) * sizeof(float32_t));
+
+  /* Assign state pointer */
+  S->pState = pState;
+
+
+}
+
+  /**    
+   * @} end of IIR_Lattice group    
+   */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_iir_lattice_init_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_iir_lattice_init_q15.c
new file mode 100644
index 0000000000..7dac99fcab
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_iir_lattice_init_q15.c
@@ -0,0 +1,86 @@
+/*-----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_iir_lattice_init_q15.c    
+*    
+* Description:  Q15 IIR lattice filter initialization function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ---------------------------------------------------------------------------*/
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup IIR_Lattice    
+ * @{    
+ */
+
+  /**    
+   * @brief Initialization function for the Q15 IIR lattice filter.    
+   * @param[in] *S points to an instance of the Q15 IIR lattice structure.    
+   * @param[in] numStages  number of stages in the filter.    
+   * @param[in] *pkCoeffs points to reflection coefficient buffer.  The array is of length numStages.    
+   * @param[in] *pvCoeffs points to ladder coefficient buffer.  The array is of length numStages+1.    
+   * @param[in] *pState points to state buffer.  The array is of length numStages+blockSize.    
+   * @param[in] blockSize number of samples to process per call.    
+   * @return none.    
+   */
+
+void arm_iir_lattice_init_q15(
+  arm_iir_lattice_instance_q15 * S,
+  uint16_t numStages,
+  q15_t * pkCoeffs,
+  q15_t * pvCoeffs,
+  q15_t * pState,
+  uint32_t blockSize)
+{
+  /* Assign filter taps */
+  S->numStages = numStages;
+
+  /* Assign reflection coefficient pointer */
+  S->pkCoeffs = pkCoeffs;
+
+  /* Assign ladder coefficient pointer */
+  S->pvCoeffs = pvCoeffs;
+
+  /* Clear state buffer and size is always blockSize + numStages */
+  memset(pState, 0, (numStages + blockSize) * sizeof(q15_t));
+
+  /* Assign state pointer */
+  S->pState = pState;
+
+
+}
+
+/**    
+ * @} end of IIR_Lattice group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_iir_lattice_init_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_iir_lattice_init_q31.c
new file mode 100644
index 0000000000..73b18a5977
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_iir_lattice_init_q31.c
@@ -0,0 +1,86 @@
+/*-----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_iir_lattice_init_q31.c    
+*    
+* Description:  Initialization function for the Q31 IIR lattice filter.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ---------------------------------------------------------------------------*/
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup IIR_Lattice    
+ * @{    
+ */
+
+  /**    
+   * @brief Initialization function for the Q31 IIR lattice filter.    
+   * @param[in] *S points to an instance of the Q31 IIR lattice structure.    
+   * @param[in] numStages number of stages in the filter.    
+   * @param[in] *pkCoeffs points to the reflection coefficient buffer.  The array is of length numStages.    
+   * @param[in] *pvCoeffs points to the ladder coefficient buffer.  The array is of length numStages+1.    
+   * @param[in] *pState points to the state buffer.  The array is of length numStages+blockSize.    
+   * @param[in] blockSize number of samples to process.    
+   * @return none.    
+   */
+
+void arm_iir_lattice_init_q31(
+  arm_iir_lattice_instance_q31 * S,
+  uint16_t numStages,
+  q31_t * pkCoeffs,
+  q31_t * pvCoeffs,
+  q31_t * pState,
+  uint32_t blockSize)
+{
+  /* Assign filter taps */
+  S->numStages = numStages;
+
+  /* Assign reflection coefficient pointer */
+  S->pkCoeffs = pkCoeffs;
+
+  /* Assign ladder coefficient pointer */
+  S->pvCoeffs = pvCoeffs;
+
+  /* Clear state buffer and size is always blockSize + numStages */
+  memset(pState, 0, (numStages + blockSize) * sizeof(q31_t));
+
+  /* Assign state pointer */
+  S->pState = pState;
+
+
+}
+
+/**    
+ * @} end of IIR_Lattice group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_iir_lattice_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_iir_lattice_q15.c
new file mode 100644
index 0000000000..5f0f891d18
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_iir_lattice_q15.c
@@ -0,0 +1,457 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_iir_lattice_q15.c    
+*    
+* Description:	Q15 IIR lattice filter processing function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup IIR_Lattice    
+ * @{    
+ */
+
+/**    
+ * @brief Processing function for the Q15 IIR lattice filter.    
+ * @param[in] *S points to an instance of the Q15 IIR lattice structure.    
+ * @param[in] *pSrc points to the block of input data.    
+ * @param[out] *pDst points to the block of output data.    
+ * @param[in] blockSize number of samples to process.    
+ * @return none.    
+ *    
+ * @details    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function is implemented using a 64-bit internal accumulator.    
+ * Both coefficients and state variables are represented in 1.15 format and multiplications yield a 2.30 result.    
+ * The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format.    
+ * There is no risk of internal overflow with this approach and the full precision of intermediate multiplications is preserved.    
+ * After all additions have been performed, the accumulator is truncated to 34.15 format by discarding low 15 bits.    
+ * Lastly, the accumulator is saturated to yield a result in 1.15 format.    
+ */
+
+void arm_iir_lattice_q15(
+  const arm_iir_lattice_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q31_t fcurr, fnext, gcurr = 0, gnext;          /* Temporary variables for lattice stages */
+  q15_t gnext1, gnext2;                          /* Temporary variables for lattice stages */
+  uint32_t stgCnt;                               /* Temporary variables for counts */
+  q63_t acc;                                     /* Accumlator */
+  uint32_t blkCnt, tapCnt;                       /* Temporary variables for counts */
+  q15_t *px1, *px2, *pk, *pv;                    /* temporary pointers for state and coef */
+  uint32_t numStages = S->numStages;             /* number of stages */
+  q15_t *pState;                                 /* State pointer */
+  q15_t *pStateCurnt;                            /* State current pointer */
+  q15_t out;                                     /* Temporary variable for output */
+  q15_t v1, v2;
+  q31_t v;                                       /* Temporary variable for ladder coefficient */
+
+
+  blkCnt = blockSize;
+
+  pState = &S->pState[0];
+
+  /* Sample processing */
+  while(blkCnt > 0u)
+  {
+    /* Read Sample from input buffer */
+    /* fN(n) = x(n) */
+    fcurr = *pSrc++;
+
+    /* Initialize state read pointer */
+    px1 = pState;
+    /* Initialize state write pointer */
+    px2 = pState;
+    /* Set accumulator to zero */
+    acc = 0;
+    /* Initialize Ladder coeff pointer */
+    pv = &S->pvCoeffs[0];
+    /* Initialize Reflection coeff pointer */
+    pk = &S->pkCoeffs[0];
+
+
+    /* Process sample for first tap */
+    gcurr = *px1++;
+    /* fN-1(n) = fN(n) - kN * gN-1(n-1) */
+    fnext = fcurr - (((q31_t) gcurr * (*pk)) >> 15);
+    fnext = __SSAT(fnext, 16);
+    /* gN(n) = kN * fN-1(n) + gN-1(n-1) */
+    gnext = (((q31_t) fnext * (*pk++)) >> 15) + gcurr;
+    gnext = __SSAT(gnext, 16);
+    /* write gN(n) into state for next sample processing */
+    *px2++ = (q15_t) gnext;
+    /* y(n) += gN(n) * vN  */
+    acc += (q31_t) ((gnext * (*pv++)));
+
+
+    /* Update f values for next coefficient processing */
+    fcurr = fnext;
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = (numStages - 1u) >> 2;
+
+    while(tapCnt > 0u)
+    {
+
+      /* Process sample for 2nd, 6th ...taps */
+      /* Read gN-2(n-1) from state buffer */
+      gcurr = *px1++;
+      /* Process sample for 2nd, 6th .. taps */
+      /* fN-2(n) = fN-1(n) - kN-1 * gN-2(n-1) */
+      fnext = fcurr - (((q31_t) gcurr * (*pk)) >> 15);
+      fnext = __SSAT(fnext, 16);
+      /* gN-1(n) = kN-1 * fN-2(n) + gN-2(n-1) */
+      gnext = (((q31_t) fnext * (*pk++)) >> 15) + gcurr;
+      gnext1 = (q15_t) __SSAT(gnext, 16);
+      /* write gN-1(n) into state */
+      *px2++ = (q15_t) gnext1;
+
+
+      /* Process sample for 3nd, 7th ...taps */
+      /* Read gN-3(n-1) from state */
+      gcurr = *px1++;
+      /* Process sample for 3rd, 7th .. taps */
+      /* fN-3(n) = fN-2(n) - kN-2 * gN-3(n-1) */
+      fcurr = fnext - (((q31_t) gcurr * (*pk)) >> 15);
+      fcurr = __SSAT(fcurr, 16);
+      /* gN-2(n) = kN-2 * fN-3(n) + gN-3(n-1) */
+      gnext = (((q31_t) fcurr * (*pk++)) >> 15) + gcurr;
+      gnext2 = (q15_t) __SSAT(gnext, 16);
+      /* write gN-2(n) into state */
+      *px2++ = (q15_t) gnext2;
+
+      /* Read vN-1 and vN-2 at a time */
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+      v = *__SIMD32(pv)++;
+
+#else
+
+	  v1 = *pv++;
+	  v2 = *pv++;
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+	  v = __PKHBT(v1, v2, 16);
+
+#else
+
+	  v = __PKHBT(v2, v1, 16);
+
+#endif	/* 	#ifndef ARM_MATH_BIG_ENDIAN		*/
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE */
+
+
+      /* Pack gN-1(n) and gN-2(n) */
+
+#ifndef  ARM_MATH_BIG_ENDIAN
+
+      gnext = __PKHBT(gnext1, gnext2, 16);
+
+#else
+
+      gnext = __PKHBT(gnext2, gnext1, 16);
+
+#endif /*   #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+      /* y(n) += gN-1(n) * vN-1  */
+      /* process for gN-5(n) * vN-5, gN-9(n) * vN-9 ... */
+      /* y(n) += gN-2(n) * vN-2  */
+      /* process for gN-6(n) * vN-6, gN-10(n) * vN-10 ... */
+      acc = __SMLALD(gnext, v, acc);
+
+
+      /* Process sample for 4th, 8th ...taps */
+      /* Read gN-4(n-1) from state */
+      gcurr = *px1++;
+      /* Process sample for 4th, 8th .. taps */
+      /* fN-4(n) = fN-3(n) - kN-3 * gN-4(n-1) */
+      fnext = fcurr - (((q31_t) gcurr * (*pk)) >> 15);
+      fnext = __SSAT(fnext, 16);
+      /* gN-3(n) = kN-3 * fN-1(n) + gN-1(n-1) */
+      gnext = (((q31_t) fnext * (*pk++)) >> 15) + gcurr;
+      gnext1 = (q15_t) __SSAT(gnext, 16);
+      /* write  gN-3(n) for the next sample process */
+      *px2++ = (q15_t) gnext1;
+
+
+      /* Process sample for 5th, 9th ...taps */
+      /* Read gN-5(n-1) from state */
+      gcurr = *px1++;
+      /* Process sample for 5th, 9th .. taps */
+      /* fN-5(n) = fN-4(n) - kN-4 * gN-5(n-1) */
+      fcurr = fnext - (((q31_t) gcurr * (*pk)) >> 15);
+      fcurr = __SSAT(fcurr, 16);
+      /* gN-4(n) = kN-4 * fN-5(n) + gN-5(n-1) */
+      gnext = (((q31_t) fcurr * (*pk++)) >> 15) + gcurr;
+      gnext2 = (q15_t) __SSAT(gnext, 16);
+      /* write      gN-4(n) for the next sample process */
+      *px2++ = (q15_t) gnext2;
+
+      /* Read vN-3 and vN-4 at a time */
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+      v = *__SIMD32(pv)++;
+
+#else
+
+	  v1 = *pv++;
+	  v2 = *pv++;
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+	  v = __PKHBT(v1, v2, 16);
+
+#else
+
+	  v = __PKHBT(v2, v1, 16);
+
+#endif	/* #ifndef ARM_MATH_BIG_ENDIAN	 */
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE */
+
+
+      /* Pack gN-3(n) and gN-4(n) */
+#ifndef  ARM_MATH_BIG_ENDIAN
+
+      gnext = __PKHBT(gnext1, gnext2, 16);
+
+#else
+
+      gnext = __PKHBT(gnext2, gnext1, 16);
+
+#endif /*      #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+      /* y(n) += gN-4(n) * vN-4  */
+      /* process for gN-8(n) * vN-8, gN-12(n) * vN-12 ... */
+      /* y(n) += gN-3(n) * vN-3  */
+      /* process for gN-7(n) * vN-7, gN-11(n) * vN-11 ... */
+      acc = __SMLALD(gnext, v, acc);
+
+      tapCnt--;
+
+    }
+
+    fnext = fcurr;
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = (numStages - 1u) % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      gcurr = *px1++;
+      /* Process sample for last taps */
+      fnext = fcurr - (((q31_t) gcurr * (*pk)) >> 15);
+      fnext = __SSAT(fnext, 16);
+      gnext = (((q31_t) fnext * (*pk++)) >> 15) + gcurr;
+      gnext = __SSAT(gnext, 16);
+      /* Output samples for last taps */
+      acc += (q31_t) (((q31_t) gnext * (*pv++)));
+      *px2++ = (q15_t) gnext;
+      fcurr = fnext;
+
+      tapCnt--;
+    }
+
+    /* y(n) += g0(n) * v0 */
+    acc += (q31_t) (((q31_t) fnext * (*pv++)));
+
+    out = (q15_t) __SSAT(acc >> 15, 16);
+    *px2++ = (q15_t) fnext;
+
+    /* write out into pDst */
+    *pDst++ = out;
+
+    /* Advance the state pointer by 4 to process the next group of 4 samples */
+    pState = pState + 1u;
+    blkCnt--;
+
+  }
+
+  /* Processing is complete. Now copy last S->numStages samples to start of the buffer    
+     for the preperation of next frame process */
+  /* Points to the start of the state buffer */
+  pStateCurnt = &S->pState[0];
+  pState = &S->pState[blockSize];
+
+  stgCnt = (numStages >> 2u);
+
+  /* copy data */
+  while(stgCnt > 0u)
+  {
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+    *__SIMD32(pStateCurnt)++ = *__SIMD32(pState)++;
+    *__SIMD32(pStateCurnt)++ = *__SIMD32(pState)++;
+
+#else
+
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+
+#endif /*	#ifndef UNALIGNED_SUPPORT_DISABLE */
+
+    /* Decrement the loop counter */
+    stgCnt--;
+
+  }
+
+  /* Calculation of count for remaining q15_t data */
+  stgCnt = (numStages) % 0x4u;
+
+  /* copy data */
+  while(stgCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    stgCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  q31_t fcurr, fnext = 0, gcurr = 0, gnext;      /* Temporary variables for lattice stages */
+  uint32_t stgCnt;                               /* Temporary variables for counts */
+  q63_t acc;                                     /* Accumlator */
+  uint32_t blkCnt, tapCnt;                       /* Temporary variables for counts */
+  q15_t *px1, *px2, *pk, *pv;                    /* temporary pointers for state and coef */
+  uint32_t numStages = S->numStages;             /* number of stages */
+  q15_t *pState;                                 /* State pointer */
+  q15_t *pStateCurnt;                            /* State current pointer */
+  q15_t out;                                     /* Temporary variable for output */
+
+
+  blkCnt = blockSize;
+
+  pState = &S->pState[0];
+
+  /* Sample processing */
+  while(blkCnt > 0u)
+  {
+    /* Read Sample from input buffer */
+    /* fN(n) = x(n) */
+    fcurr = *pSrc++;
+
+    /* Initialize state read pointer */
+    px1 = pState;
+    /* Initialize state write pointer */
+    px2 = pState;
+    /* Set accumulator to zero */
+    acc = 0;
+    /* Initialize Ladder coeff pointer */
+    pv = &S->pvCoeffs[0];
+    /* Initialize Reflection coeff pointer */
+    pk = &S->pkCoeffs[0];
+
+    tapCnt = numStages;
+
+    while(tapCnt > 0u)
+    {
+      gcurr = *px1++;
+      /* Process sample */
+      /* fN-1(n) = fN(n) - kN * gN-1(n-1) */
+      fnext = fcurr - ((gcurr * (*pk)) >> 15);
+      fnext = __SSAT(fnext, 16);
+      /* gN(n) = kN * fN-1(n) + gN-1(n-1) */
+      gnext = ((fnext * (*pk++)) >> 15) + gcurr;
+      gnext = __SSAT(gnext, 16);
+      /* Output samples */
+      /* y(n) += gN(n) * vN */
+      acc += (q31_t) ((gnext * (*pv++)));
+      /* write gN(n) into state for next sample processing */
+      *px2++ = (q15_t) gnext;
+      /* Update f values for next coefficient processing */
+      fcurr = fnext;
+
+      tapCnt--;
+    }
+
+    /* y(n) += g0(n) * v0 */
+    acc += (q31_t) ((fnext * (*pv++)));
+
+    out = (q15_t) __SSAT(acc >> 15, 16);
+    *px2++ = (q15_t) fnext;
+
+    /* write out into pDst */
+    *pDst++ = out;
+
+    /* Advance the state pointer by 1 to process the next group of samples */
+    pState = pState + 1u;
+    blkCnt--;
+
+  }
+
+  /* Processing is complete. Now copy last S->numStages samples to start of the buffer           
+     for the preperation of next frame process */
+  /* Points to the start of the state buffer */
+  pStateCurnt = &S->pState[0];
+  pState = &S->pState[blockSize];
+
+  stgCnt = numStages;
+
+  /* copy data */
+  while(stgCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    stgCnt--;
+  }
+
+#endif /*   #ifndef ARM_MATH_CM0 */
+
+}
+
+
+
+
+/**    
+ * @} end of IIR_Lattice group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_iir_lattice_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_iir_lattice_q31.c
new file mode 100644
index 0000000000..adfd4dfb5d
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_iir_lattice_q31.c
@@ -0,0 +1,345 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_iir_lattice_q31.c    
+*    
+* Description:	Q31 IIR lattice filter processing function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup IIR_Lattice    
+ * @{    
+ */
+
+/**    
+ * @brief Processing function for the Q31 IIR lattice filter.    
+ * @param[in] *S points to an instance of the Q31 IIR lattice structure.    
+ * @param[in] *pSrc points to the block of input data.    
+ * @param[out] *pDst points to the block of output data.    
+ * @param[in] blockSize number of samples to process.    
+ * @return none.    
+ *    
+ * @details    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function is implemented using an internal 64-bit accumulator.    
+ * The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit.    
+ * Thus, if the accumulator result overflows it wraps around rather than clip.    
+ * In order to avoid overflows completely the input signal must be scaled down by 2*log2(numStages) bits.    
+ * After all multiply-accumulates are performed, the 2.62 accumulator is saturated to 1.32 format and then truncated to 1.31 format.    
+ */
+
+void arm_iir_lattice_q31(
+  const arm_iir_lattice_instance_q31 * S,
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize)
+{
+  q31_t fcurr, fnext = 0, gcurr = 0, gnext;      /* Temporary variables for lattice stages */
+  q63_t acc;                                     /* Accumlator */
+  uint32_t blkCnt, tapCnt;                       /* Temporary variables for counts */
+  q31_t *px1, *px2, *pk, *pv;                    /* Temporary pointers for state and coef */
+  uint32_t numStages = S->numStages;             /* number of stages */
+  q31_t *pState;                                 /* State pointer */
+  q31_t *pStateCurnt;                            /* State current pointer */
+
+  blkCnt = blockSize;
+
+  pState = &S->pState[0];
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /* Sample processing */
+  while(blkCnt > 0u)
+  {
+    /* Read Sample from input buffer */
+    /* fN(n) = x(n) */
+    fcurr = *pSrc++;
+
+    /* Initialize state read pointer */
+    px1 = pState;
+    /* Initialize state write pointer */
+    px2 = pState;
+    /* Set accumulator to zero */
+    acc = 0;
+    /* Initialize Ladder coeff pointer */
+    pv = &S->pvCoeffs[0];
+    /* Initialize Reflection coeff pointer */
+    pk = &S->pkCoeffs[0];
+
+
+    /* Process sample for first tap */
+    gcurr = *px1++;
+    /* fN-1(n) = fN(n) - kN * gN-1(n-1) */
+    fnext = __QSUB(fcurr, (q31_t) (((q63_t) gcurr * (*pk)) >> 31));
+    /* gN(n) = kN * fN-1(n) + gN-1(n-1) */
+    gnext = __QADD(gcurr, (q31_t) (((q63_t) fnext * (*pk++)) >> 31));
+    /* write gN-1(n-1) into state for next sample processing */
+    *px2++ = gnext;
+    /* y(n) += gN(n) * vN  */
+    acc += ((q63_t) gnext * *pv++);
+
+    /* Update f values for next coefficient processing */
+    fcurr = fnext;
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = (numStages - 1u) >> 2;
+
+    while(tapCnt > 0u)
+    {
+
+      /* Process sample for 2nd, 6th .. taps */
+      /* Read gN-2(n-1) from state buffer */
+      gcurr = *px1++;
+      /* fN-2(n) = fN-1(n) - kN-1 * gN-2(n-1) */
+      fnext = __QSUB(fcurr, (q31_t) (((q63_t) gcurr * (*pk)) >> 31));
+      /* gN-1(n) = kN-1 * fN-2(n) + gN-2(n-1) */
+      gnext = __QADD(gcurr, (q31_t) (((q63_t) fnext * (*pk++)) >> 31));
+      /* y(n) += gN-1(n) * vN-1  */
+      /* process for gN-5(n) * vN-5, gN-9(n) * vN-9 ... */
+      acc += ((q63_t) gnext * *pv++);
+      /* write gN-1(n) into state for next sample processing */
+      *px2++ = gnext;
+
+      /* Process sample for 3nd, 7th ...taps */
+      /* Read gN-3(n-1) from state buffer */
+      gcurr = *px1++;
+      /* Process sample for 3rd, 7th .. taps */
+      /* fN-3(n) = fN-2(n) - kN-2 * gN-3(n-1) */
+      fcurr = __QSUB(fnext, (q31_t) (((q63_t) gcurr * (*pk)) >> 31));
+      /* gN-2(n) = kN-2 * fN-3(n) + gN-3(n-1) */
+      gnext = __QADD(gcurr, (q31_t) (((q63_t) fcurr * (*pk++)) >> 31));
+      /* y(n) += gN-2(n) * vN-2  */
+      /* process for gN-6(n) * vN-6, gN-10(n) * vN-10 ... */
+      acc += ((q63_t) gnext * *pv++);
+      /* write gN-2(n) into state for next sample processing */
+      *px2++ = gnext;
+
+
+      /* Process sample for 4th, 8th ...taps */
+      /* Read gN-4(n-1) from state buffer */
+      gcurr = *px1++;
+      /* Process sample for 4th, 8th .. taps */
+      /* fN-4(n) = fN-3(n) - kN-3 * gN-4(n-1) */
+      fnext = __QSUB(fcurr, (q31_t) (((q63_t) gcurr * (*pk)) >> 31));
+      /* gN-3(n) = kN-3 * fN-4(n) + gN-4(n-1) */
+      gnext = __QADD(gcurr, (q31_t) (((q63_t) fnext * (*pk++)) >> 31));
+      /* y(n) += gN-3(n) * vN-3  */
+      /* process for gN-7(n) * vN-7, gN-11(n) * vN-11 ... */
+      acc += ((q63_t) gnext * *pv++);
+      /* write gN-3(n) into state for next sample processing */
+      *px2++ = gnext;
+
+
+      /* Process sample for 5th, 9th ...taps */
+      /* Read gN-5(n-1) from state buffer */
+      gcurr = *px1++;
+      /* Process sample for 5th, 9th .. taps */
+      /* fN-5(n) = fN-4(n) - kN-4 * gN-1(n-1) */
+      fcurr = __QSUB(fnext, (q31_t) (((q63_t) gcurr * (*pk)) >> 31));
+      /* gN-4(n) = kN-4 * fN-5(n) + gN-5(n-1) */
+      gnext = __QADD(gcurr, (q31_t) (((q63_t) fcurr * (*pk++)) >> 31));
+      /* y(n) += gN-4(n) * vN-4  */
+      /* process for gN-8(n) * vN-8, gN-12(n) * vN-12 ... */
+      acc += ((q63_t) gnext * *pv++);
+      /* write gN-4(n) into state for next sample processing */
+      *px2++ = gnext;
+
+      tapCnt--;
+
+    }
+
+    fnext = fcurr;
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = (numStages - 1u) % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      gcurr = *px1++;
+      /* Process sample for last taps */
+      fnext = __QSUB(fcurr, (q31_t) (((q63_t) gcurr * (*pk)) >> 31));
+      gnext = __QADD(gcurr, (q31_t) (((q63_t) fnext * (*pk++)) >> 31));
+      /* Output samples for last taps */
+      acc += ((q63_t) gnext * *pv++);
+      *px2++ = gnext;
+      fcurr = fnext;
+
+      tapCnt--;
+
+    }
+
+    /* y(n) += g0(n) * v0 */
+    acc += (q63_t) fnext *(
+  *pv++);
+
+    *px2++ = fnext;
+
+    /* write out into pDst */
+    *pDst++ = (q31_t) (acc >> 31u);
+
+    /* Advance the state pointer by 4 to process the next group of 4 samples */
+    pState = pState + 1u;
+    blkCnt--;
+
+  }
+
+  /* Processing is complete. Now copy last S->numStages samples to start of the buffer    
+     for the preperation of next frame process */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = &S->pState[0];
+  pState = &S->pState[blockSize];
+
+  tapCnt = numStages >> 2u;
+
+  /* copy data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+
+  }
+
+  /* Calculate remaining number of copies */
+  tapCnt = (numStages) % 0x4u;
+
+  /* Copy the remaining q31_t data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  };
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  /* Sample processing */
+  while(blkCnt > 0u)
+  {
+    /* Read Sample from input buffer */
+    /* fN(n) = x(n) */
+    fcurr = *pSrc++;
+
+    /* Initialize state read pointer */
+    px1 = pState;
+    /* Initialize state write pointer */
+    px2 = pState;
+    /* Set accumulator to zero */
+    acc = 0;
+    /* Initialize Ladder coeff pointer */
+    pv = &S->pvCoeffs[0];
+    /* Initialize Reflection coeff pointer */
+    pk = &S->pkCoeffs[0];
+
+    tapCnt = numStages;
+
+    while(tapCnt > 0u)
+    {
+      gcurr = *px1++;
+      /* Process sample */
+      /* fN-1(n) = fN(n) - kN * gN-1(n-1) */
+      fnext =
+        clip_q63_to_q31(((q63_t) fcurr -
+                         ((q31_t) (((q63_t) gcurr * (*pk)) >> 31))));
+      /* gN(n) = kN * fN-1(n) + gN-1(n-1) */
+      gnext =
+        clip_q63_to_q31(((q63_t) gcurr +
+                         ((q31_t) (((q63_t) fnext * (*pk++)) >> 31))));
+      /* Output samples */
+      /* y(n) += gN(n) * vN  */
+      acc += ((q63_t) gnext * *pv++);
+      /* write gN-1(n-1) into state for next sample processing */
+      *px2++ = gnext;
+      /* Update f values for next coefficient processing */
+      fcurr = fnext;
+
+      tapCnt--;
+    }
+
+    /* y(n) += g0(n) * v0 */
+    acc += (q63_t) fnext *(
+  *pv++);
+
+    *px2++ = fnext;
+
+    /* write out into pDst */
+    *pDst++ = (q31_t) (acc >> 31u);
+
+    /* Advance the state pointer by 1 to process the next group of samples */
+    pState = pState + 1u;
+    blkCnt--;
+
+  }
+
+  /* Processing is complete. Now copy last S->numStages samples to start of the buffer           
+     for the preperation of next frame process */
+
+  /* Points to the start of the state buffer */
+  pStateCurnt = &S->pState[0];
+  pState = &S->pState[blockSize];
+
+  tapCnt = numStages;
+
+  /* Copy the remaining q31_t data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+#endif /*   #ifndef ARM_MATH_CM0 */
+
+}
+
+
+
+
+/**    
+ * @} end of IIR_Lattice group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_f32.c
new file mode 100644
index 0000000000..90fa8ae1e9
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_f32.c
@@ -0,0 +1,434 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_lms_f32.c    
+*    
+* Description:	Processing function for the floating-point LMS filter.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @defgroup LMS Least Mean Square (LMS) Filters    
+ *    
+ * LMS filters are a class of adaptive filters that are able to "learn" an unknown transfer functions.    
+ * LMS filters use a gradient descent method in which the filter coefficients are updated based on the instantaneous error signal.    
+ * Adaptive filters are often used in communication systems, equalizers, and noise removal.    
+ * The CMSIS DSP Library contains LMS filter functions that operate on Q15, Q31, and floating-point data types.    
+ * The library also contains normalized LMS filters in which the filter coefficient adaptation is indepedent of the level of the input signal.    
+ *    
+ * An LMS filter consists of two components as shown below.    
+ * The first component is a standard transversal or FIR filter.    
+ * The second component is a coefficient update mechanism.    
+ * The LMS filter has two input signals.    
+ * The "input" feeds the FIR filter while the "reference input" corresponds to the desired output of the FIR filter.    
+ * That is, the FIR filter coefficients are updated so that the output of the FIR filter matches the reference input.    
+ * The filter coefficient update mechanism is based on the difference between the FIR filter output and the reference input.    
+ * This "error signal" tends towards zero as the filter adapts.    
+ * The LMS processing functions accept the input and reference input signals and generate the filter output and error signal.    
+ * \image html LMS.gif "Internal structure of the Least Mean Square filter"    
+ *    
+ * The functions operate on blocks of data and each call to the function processes    
+ * blockSize samples through the filter.    
+ * pSrc points to input signal, pRef points to reference signal,    
+ * pOut points to output signal and pErr points to error signal.    
+ * All arrays contain blockSize values.    
+ *    
+ * The functions operate on a block-by-block basis.    
+ * Internally, the filter coefficients b[n] are updated on a sample-by-sample basis.    
+ * The convergence of the LMS filter is slower compared to the normalized LMS algorithm.    
+ *    
+ * \par Algorithm:    
+ * The output signal y[n] is computed by a standard FIR filter:    
+ * 
    
+ *     y[n] = b[0] * x[n] + b[1] * x[n-1] + b[2] * x[n-2] + ...+ b[numTaps-1] * x[n-numTaps+1]    
+ * 
    
+ *    
+ * \par    
+ * The error signal equals the difference between the reference signal d[n] and the filter output:    
+ * 
    
+ *     e[n] = d[n] - y[n].    
+ * 
    
+ *    
+ * \par    
+ * After each sample of the error signal is computed, the filter coefficients b[k] are updated on a sample-by-sample basis:    
+ * 
    
+ *     b[k] = b[k] + e[n] * mu * x[n-k],  for k=0, 1, ..., numTaps-1    
+ * 
    
+ * where mu is the step size and controls the rate of coefficient convergence.    
+ *\par    
+ * In the APIs, pCoeffs points to a coefficient array of size numTaps.    
+ * Coefficients are stored in time reversed order.    
+ * \par    
+ * 
    
+ *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}    
+ * 
    
+ * \par    
+ * pState points to a state array of size numTaps + blockSize - 1.    
+ * Samples in the state buffer are stored in the order:    
+ * \par    
+ * 
    
+ *    {x[n-numTaps+1], x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2]....x[0], x[1], ..., x[blockSize-1]}    
+ * 
    
+ * \par    
+ * Note that the length of the state buffer exceeds the length of the coefficient array by blockSize-1 samples.    
+ * The increased state buffer length allows circular addressing, which is traditionally used in FIR filters,    
+ * to be avoided and yields a significant speed improvement.    
+ * The state variables are updated after each block of data is processed.    
+ * \par Instance Structure    
+ * The coefficients and state variables for a filter are stored together in an instance data structure.    
+ * A separate instance structure must be defined for each filter and    
+ * coefficient and state arrays cannot be shared among instances.    
+ * There are separate instance structure declarations for each of the 3 supported data types.    
+ *    
+ * \par Initialization Functions    
+ * There is also an associated initialization function for each data type.    
+ * The initialization function performs the following operations:    
+ * - Sets the values of the internal structure fields.    
+ * - Zeros out the values in the state buffer.    
+ * \par    
+ * Use of the initialization function is optional.    
+ * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.    
+ * To place an instance structure into a const data section, the instance structure must be manually initialized.    
+ * Set the values in the state buffer to zeros before static initialization.    
+ * The code below statically initializes each of the 3 different data type filter instance structures    
+ * 
    
+ *    arm_lms_instance_f32 S = {numTaps, pState, pCoeffs, mu};    
+ *    arm_lms_instance_q31 S = {numTaps, pState, pCoeffs, mu, postShift};    
+ *    arm_lms_instance_q15 S = {numTaps, pState, pCoeffs, mu, postShift};    
+ * 
    
+ * where numTaps is the number of filter coefficients in the filter; pState is the address of the state buffer;    
+ * pCoeffs is the address of the coefficient buffer; mu is the step size parameter; and postShift is the shift applied to coefficients.    
+ *    
+ * \par Fixed-Point Behavior:    
+ * Care must be taken when using the Q15 and Q31 versions of the LMS filter.    
+ * The following issues must be considered:    
+ * - Scaling of coefficients    
+ * - Overflow and saturation    
+ *    
+ * \par Scaling of Coefficients:    
+ * Filter coefficients are represented as fractional values and    
+ * coefficients are restricted to lie in the range [-1 +1).    
+ * The fixed-point functions have an additional scaling parameter postShift.    
+ * At the output of the filter's accumulator is a shift register which shifts the result by postShift bits.    
+ * This essentially scales the filter coefficients by 2^postShift and    
+ * allows the filter coefficients to exceed the range [+1 -1).    
+ * The value of postShift is set by the user based on the expected gain through the system being modeled.    
+ *    
+ * \par Overflow and Saturation:    
+ * Overflow and saturation behavior of the fixed-point Q15 and Q31 versions are    
+ * described separately as part of the function specific documentation below.    
+ */
+
+/**    
+ * @addtogroup LMS    
+ * @{    
+ */
+
+/**           
+ * @details           
+ * This function operates on floating-point data types.       
+ *    
+ * @brief Processing function for floating-point LMS filter.    
+ * @param[in]  *S points to an instance of the floating-point LMS filter structure.    
+ * @param[in]  *pSrc points to the block of input data.    
+ * @param[in]  *pRef points to the block of reference data.    
+ * @param[out] *pOut points to the block of output data.    
+ * @param[out] *pErr points to the block of error data.    
+ * @param[in]  blockSize number of samples to process.    
+ * @return     none.    
+ */
+
+void arm_lms_f32(
+  const arm_lms_instance_f32 * S,
+  float32_t * pSrc,
+  float32_t * pRef,
+  float32_t * pOut,
+  float32_t * pErr,
+  uint32_t blockSize)
+{
+  float32_t *pState = S->pState;                 /* State pointer */
+  float32_t *pCoeffs = S->pCoeffs;               /* Coefficient pointer */
+  float32_t *pStateCurnt;                        /* Points to the current sample of the state */
+  float32_t *px, *pb;                            /* Temporary pointers for state and coefficient buffers */
+  float32_t mu = S->mu;                          /* Adaptive factor */
+  uint32_t numTaps = S->numTaps;                 /* Number of filter coefficients in the filter */
+  uint32_t tapCnt, blkCnt;                       /* Loop counters */
+  float32_t sum, e, d;                           /* accumulator, error, reference data sample */
+  float32_t w = 0.0f;                            /* weight factor */
+
+  e = 0.0f;
+  d = 0.0f;
+
+  /* S->pState points to state array which contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = &(S->pState[(numTaps - 1u)]);
+
+  blkCnt = blockSize;
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  while(blkCnt > 0u)
+  {
+    /* Copy the new input sample into the state buffer */
+    *pStateCurnt++ = *pSrc++;
+
+    /* Initialize pState pointer */
+    px = pState;
+
+    /* Initialize coeff pointer */
+    pb = (pCoeffs);
+
+    /* Set the accumulator to zero */
+    sum = 0.0f;
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      sum += (*px++) * (*pb++);
+      sum += (*px++) * (*pb++);
+      sum += (*px++) * (*pb++);
+      sum += (*px++) * (*pb++);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = numTaps % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      sum += (*px++) * (*pb++);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* The result in the accumulator, store in the destination buffer. */
+    *pOut++ = sum;
+
+    /* Compute and store error */
+    d = (float32_t) (*pRef++);
+    e = d - sum;
+    *pErr++ = e;
+
+    /* Calculation of Weighting factor for the updating filter coefficients */
+    w = e * mu;
+
+    /* Initialize pState pointer */
+    px = pState;
+
+    /* Initialize coeff pointer */
+    pb = (pCoeffs);
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2;
+
+    /* Update filter coefficients */
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      *pb = *pb + (w * (*px++));
+      pb++;
+
+      *pb = *pb + (w * (*px++));
+      pb++;
+
+      *pb = *pb + (w * (*px++));
+      pb++;
+
+      *pb = *pb + (w * (*px++));
+      pb++;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = numTaps % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      *pb = *pb + (w * (*px++));
+      pb++;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Advance state pointer by 1 for the next sample */
+    pState = pState + 1;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+
+  /* Processing is complete. Now copy the last numTaps - 1 samples to the    
+     satrt of the state buffer. This prepares the state buffer for the    
+     next function call. */
+
+  /* Points to the start of the pState buffer */
+  pStateCurnt = S->pState;
+
+  /* Loop unrolling for (numTaps - 1u) samples copy */
+  tapCnt = (numTaps - 1u) >> 2u;
+
+  /* copy data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+  /* Calculate remaining number of copies */
+  tapCnt = (numTaps - 1u) % 0x4u;
+
+  /* Copy the remaining q31_t data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  while(blkCnt > 0u)
+  {
+    /* Copy the new input sample into the state buffer */
+    *pStateCurnt++ = *pSrc++;
+
+    /* Initialize pState pointer */
+    px = pState;
+
+    /* Initialize pCoeffs pointer */
+    pb = pCoeffs;
+
+    /* Set the accumulator to zero */
+    sum = 0.0f;
+
+    /* Loop over numTaps number of values */
+    tapCnt = numTaps;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      sum += (*px++) * (*pb++);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* The result is stored in the destination buffer. */
+    *pOut++ = sum;
+
+    /* Compute and store error */
+    d = (float32_t) (*pRef++);
+    e = d - sum;
+    *pErr++ = e;
+
+    /* Weighting factor for the LMS version */
+    w = e * mu;
+
+    /* Initialize pState pointer */
+    px = pState;
+
+    /* Initialize pCoeffs pointer */
+    pb = pCoeffs;
+
+    /* Loop over numTaps number of values */
+    tapCnt = numTaps;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      *pb = *pb + (w * (*px++));
+      pb++;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Advance state pointer by 1 for the next sample */
+    pState = pState + 1;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+
+  /* Processing is complete. Now copy the last numTaps - 1 samples to the        
+   * start of the state buffer. This prepares the state buffer for the        
+   * next function call. */
+
+  /* Points to the start of the pState buffer */
+  pStateCurnt = S->pState;
+
+  /*  Copy (numTaps - 1u) samples  */
+  tapCnt = (numTaps - 1u);
+
+  /* Copy the data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+#endif /*   #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+   * @} end of LMS group    
+   */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_init_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_init_f32.c
new file mode 100644
index 0000000000..a2f51240a5
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_init_f32.c
@@ -0,0 +1,90 @@
+/*-----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_lms_init_f32.c    
+*    
+* Description:  Floating-point LMS filter initialization function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ---------------------------------------------------------------------------*/
+
+#include "arm_math.h"
+
+/**    
+ * @addtogroup LMS    
+ * @{    
+ */
+
+  /**    
+   * @brief Initialization function for floating-point LMS filter.    
+   * @param[in] *S points to an instance of the floating-point LMS filter structure.    
+   * @param[in] numTaps  number of filter coefficients.    
+   * @param[in] *pCoeffs points to the coefficient buffer.    
+   * @param[in] *pState points to state buffer.    
+   * @param[in] mu step size that controls filter coefficient updates.    
+   * @param[in] blockSize number of samples to process.    
+   * @return none.    
+   */
+
+/**    
+ * \par Description:    
+ * pCoeffs points to the array of filter coefficients stored in time reversed order:    
+ * 
    
+ *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}    
+ * 
    
+ * The initial filter coefficients serve as a starting point for the adaptive filter.    
+ * pState points to an array of length numTaps+blockSize-1 samples, where blockSize is the number of input samples processed by each call to arm_lms_f32().    
+ */
+
+void arm_lms_init_f32(
+  arm_lms_instance_f32 * S,
+  uint16_t numTaps,
+  float32_t * pCoeffs,
+  float32_t * pState,
+  float32_t mu,
+  uint32_t blockSize)
+{
+  /* Assign filter taps */
+  S->numTaps = numTaps;
+
+  /* Assign coefficient pointer */
+  S->pCoeffs = pCoeffs;
+
+  /* Clear state buffer and size is always blockSize + numTaps */
+  memset(pState, 0, (numTaps + (blockSize - 1)) * sizeof(float32_t));
+
+  /* Assign state pointer */
+  S->pState = pState;
+
+  /* Assign Step size value */
+  S->mu = mu;
+}
+
+/**    
+ * @} end of LMS group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_init_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_init_q15.c
new file mode 100644
index 0000000000..8f42949a61
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_init_q15.c
@@ -0,0 +1,100 @@
+/*-----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_lms_init_q15.c    
+*    
+* Description:  Q15 LMS filter initialization function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ---------------------------------------------------------------------------*/
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup LMS    
+ * @{    
+ */
+
+/**    
+* @brief Initialization function for the Q15 LMS filter.    
+* @param[in] *S points to an instance of the Q15 LMS filter structure.    
+* @param[in] numTaps  number of filter coefficients.    
+* @param[in] *pCoeffs points to the coefficient buffer.    
+* @param[in] *pState points to the state buffer.    
+* @param[in] mu step size that controls filter coefficient updates.    
+* @param[in] blockSize number of samples to process.    
+* @param[in] postShift bit shift applied to coefficients.    
+* @return    none.    
+*    
+* \par Description:    
+* pCoeffs points to the array of filter coefficients stored in time reversed order:    
+* 
    
+*    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}    
+* 
    
+* The initial filter coefficients serve as a starting point for the adaptive filter.    
+* pState points to the array of state variables and size of array is    
+* numTaps+blockSize-1 samples, where blockSize is the number of    
+* input samples processed by each call to arm_lms_q15().    
+*/
+
+void arm_lms_init_q15(
+  arm_lms_instance_q15 * S,
+  uint16_t numTaps,
+  q15_t * pCoeffs,
+  q15_t * pState,
+  q15_t mu,
+  uint32_t blockSize,
+  uint32_t postShift)
+{
+  /* Assign filter taps */
+  S->numTaps = numTaps;
+
+  /* Assign coefficient pointer */
+  S->pCoeffs = pCoeffs;
+
+  /* Clear state buffer and size is always blockSize + numTaps - 1 */
+  memset(pState, 0, (numTaps + (blockSize - 1u)) * sizeof(q15_t));
+
+  /* Assign state pointer */
+  S->pState = pState;
+
+  /* Assign Step size value */
+  S->mu = mu;
+
+  /* Assign postShift value to be applied */
+  S->postShift = postShift;
+
+}
+
+/**    
+ * @} end of LMS group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_init_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_init_q31.c
new file mode 100644
index 0000000000..58edb659ba
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_init_q31.c
@@ -0,0 +1,100 @@
+/*-----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_lms_init_q31.c    
+*    
+* Description:  Q31 LMS filter initialization function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ---------------------------------------------------------------------------*/
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup LMS    
+ * @{    
+ */
+
+  /**    
+   * @brief Initialization function for Q31 LMS filter.    
+   * @param[in] *S points to an instance of the Q31 LMS filter structure.    
+   * @param[in] numTaps  number of filter coefficients.    
+   * @param[in] *pCoeffs points to coefficient buffer.    
+   * @param[in] *pState points to state buffer.    
+   * @param[in] mu step size that controls filter coefficient updates.    
+   * @param[in] blockSize number of samples to process.    
+   * @param[in] postShift bit shift applied to coefficients.    
+   * @return none.    
+ *    
+ * \par Description:    
+ * pCoeffs points to the array of filter coefficients stored in time reversed order:    
+ * 
    
+ *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}    
+ * 
    
+ * The initial filter coefficients serve as a starting point for the adaptive filter.    
+ * pState points to an array of length numTaps+blockSize-1 samples,    
+ * where blockSize is the number of input samples processed by each call to    
+ * arm_lms_q31().    
+ */
+
+void arm_lms_init_q31(
+  arm_lms_instance_q31 * S,
+  uint16_t numTaps,
+  q31_t * pCoeffs,
+  q31_t * pState,
+  q31_t mu,
+  uint32_t blockSize,
+  uint32_t postShift)
+{
+  /* Assign filter taps */
+  S->numTaps = numTaps;
+
+  /* Assign coefficient pointer */
+  S->pCoeffs = pCoeffs;
+
+  /* Clear state buffer and size is always blockSize + numTaps - 1 */
+  memset(pState, 0, ((uint32_t) numTaps + (blockSize - 1u)) * sizeof(q31_t));
+
+  /* Assign state pointer */
+  S->pState = pState;
+
+  /* Assign Step size value */
+  S->mu = mu;
+
+  /* Assign postShift value to be applied */
+  S->postShift = postShift;
+
+}
+
+/**    
+ * @} end of LMS group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_norm_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_norm_f32.c
new file mode 100644
index 0000000000..b2ac452069
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_norm_f32.c
@@ -0,0 +1,456 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_lms_norm_f32.c    
+*    
+* Description:	Processing function for the floating-point Normalised LMS.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @defgroup LMS_NORM Normalized LMS Filters    
+ *    
+ * This set of functions implements a commonly used adaptive filter.    
+ * It is related to the Least Mean Square (LMS) adaptive filter and includes an additional normalization    
+ * factor which increases the adaptation rate of the filter.    
+ * The CMSIS DSP Library contains normalized LMS filter functions that operate on Q15, Q31, and floating-point data types.    
+ *    
+ * A normalized least mean square (NLMS) filter consists of two components as shown below.    
+ * The first component is a standard transversal or FIR filter.    
+ * The second component is a coefficient update mechanism.    
+ * The NLMS filter has two input signals.    
+ * The "input" feeds the FIR filter while the "reference input" corresponds to the desired output of the FIR filter.    
+ * That is, the FIR filter coefficients are updated so that the output of the FIR filter matches the reference input.    
+ * The filter coefficient update mechanism is based on the difference between the FIR filter output and the reference input.    
+ * This "error signal" tends towards zero as the filter adapts.    
+ * The NLMS processing functions accept the input and reference input signals and generate the filter output and error signal.    
+ * \image html LMS.gif "Internal structure of the NLMS adaptive filter"    
+ *    
+ * The functions operate on blocks of data and each call to the function processes    
+ * blockSize samples through the filter.    
+ * pSrc points to input signal, pRef points to reference signal,    
+ * pOut points to output signal and pErr points to error signal.    
+ * All arrays contain blockSize values.    
+ *    
+ * The functions operate on a block-by-block basis.    
+ * Internally, the filter coefficients b[n] are updated on a sample-by-sample basis.    
+ * The convergence of the LMS filter is slower compared to the normalized LMS algorithm.    
+ *    
+ * \par Algorithm:    
+ * The output signal y[n] is computed by a standard FIR filter:    
+ * 
    
+ *     y[n] = b[0] * x[n] + b[1] * x[n-1] + b[2] * x[n-2] + ...+ b[numTaps-1] * x[n-numTaps+1]    
+ * 
    
+ *    
+ * \par    
+ * The error signal equals the difference between the reference signal d[n] and the filter output:    
+ * 
    
+ *     e[n] = d[n] - y[n].    
+ * 
    
+ *    
+ * \par    
+ * After each sample of the error signal is computed the instanteous energy of the filter state variables is calculated:    
+ * 
    
+ *    E = x[n]^2 + x[n-1]^2 + ... + x[n-numTaps+1]^2.    
+ * 
    
+ * The filter coefficients b[k] are then updated on a sample-by-sample basis:    
+ * 
    
+ *     b[k] = b[k] + e[n] * (mu/E) * x[n-k],  for k=0, 1, ..., numTaps-1    
+ * 
    
+ * where mu is the step size and controls the rate of coefficient convergence.    
+ *\par    
+ * In the APIs, pCoeffs points to a coefficient array of size numTaps.    
+ * Coefficients are stored in time reversed order.    
+ * \par    
+ * 
    
+ *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}    
+ * 
    
+ * \par    
+ * pState points to a state array of size numTaps + blockSize - 1.    
+ * Samples in the state buffer are stored in the order:    
+ * \par    
+ * 
    
+ *    {x[n-numTaps+1], x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2]....x[0], x[1], ..., x[blockSize-1]}    
+ * 
    
+ * \par    
+ * Note that the length of the state buffer exceeds the length of the coefficient array by blockSize-1 samples.    
+ * The increased state buffer length allows circular addressing, which is traditionally used in FIR filters,    
+ * to be avoided and yields a significant speed improvement.    
+ * The state variables are updated after each block of data is processed.    
+ * \par Instance Structure    
+ * The coefficients and state variables for a filter are stored together in an instance data structure.    
+ * A separate instance structure must be defined for each filter and    
+ * coefficient and state arrays cannot be shared among instances.    
+ * There are separate instance structure declarations for each of the 3 supported data types.    
+ *    
+ * \par Initialization Functions    
+ * There is also an associated initialization function for each data type.    
+ * The initialization function performs the following operations:    
+ * - Sets the values of the internal structure fields.    
+ * - Zeros out the values in the state buffer.    
+ * \par    
+ * Instance structure cannot be placed into a const data section and it is recommended to use the initialization function.    
+ * \par Fixed-Point Behavior:    
+ * Care must be taken when using the Q15 and Q31 versions of the normalised LMS filter.    
+ * The following issues must be considered:    
+ * - Scaling of coefficients    
+ * - Overflow and saturation    
+ *    
+ * \par Scaling of Coefficients:    
+ * Filter coefficients are represented as fractional values and    
+ * coefficients are restricted to lie in the range [-1 +1).    
+ * The fixed-point functions have an additional scaling parameter postShift.    
+ * At the output of the filter's accumulator is a shift register which shifts the result by postShift bits.    
+ * This essentially scales the filter coefficients by 2^postShift and    
+ * allows the filter coefficients to exceed the range [+1 -1).    
+ * The value of postShift is set by the user based on the expected gain through the system being modeled.    
+ *    
+ * \par Overflow and Saturation:    
+ * Overflow and saturation behavior of the fixed-point Q15 and Q31 versions are    
+ * described separately as part of the function specific documentation below.    
+ */
+
+
+/**    
+ * @addtogroup LMS_NORM    
+ * @{    
+ */
+
+
+  /**    
+   * @brief Processing function for floating-point normalized LMS filter.    
+   * @param[in] *S points to an instance of the floating-point normalized LMS filter structure.    
+   * @param[in] *pSrc points to the block of input data.    
+   * @param[in] *pRef points to the block of reference data.    
+   * @param[out] *pOut points to the block of output data.    
+   * @param[out] *pErr points to the block of error data.    
+   * @param[in] blockSize number of samples to process.    
+   * @return none.    
+   */
+
+void arm_lms_norm_f32(
+  arm_lms_norm_instance_f32 * S,
+  float32_t * pSrc,
+  float32_t * pRef,
+  float32_t * pOut,
+  float32_t * pErr,
+  uint32_t blockSize)
+{
+  float32_t *pState = S->pState;                 /* State pointer */
+  float32_t *pCoeffs = S->pCoeffs;               /* Coefficient pointer */
+  float32_t *pStateCurnt;                        /* Points to the current sample of the state */
+  float32_t *px, *pb;                            /* Temporary pointers for state and coefficient buffers */
+  float32_t mu = S->mu;                          /* Adaptive factor */
+  uint32_t numTaps = S->numTaps;                 /* Number of filter coefficients in the filter */
+  uint32_t tapCnt, blkCnt;                       /* Loop counters */
+  float32_t energy;                              /* Energy of the input */
+  float32_t sum, e, d;                           /* accumulator, error, reference data sample */
+  float32_t w, x0, in;                           /* weight factor, temporary variable to hold input sample and state */
+
+  /* Initializations of error,  difference, Coefficient update */
+  e = 0.0f;
+  d = 0.0f;
+  w = 0.0f;
+
+  energy = S->energy;
+  x0 = S->x0;
+
+  /* S->pState points to buffer which contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = &(S->pState[(numTaps - 1u)]);
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  while(blkCnt > 0u)
+  {
+    /* Copy the new input sample into the state buffer */
+    *pStateCurnt++ = *pSrc;
+
+    /* Initialize pState pointer */
+    px = pState;
+
+    /* Initialize coeff pointer */
+    pb = (pCoeffs);
+
+    /* Read the sample from input buffer */
+    in = *pSrc++;
+
+    /* Update the energy calculation */
+    energy -= x0 * x0;
+    energy += in * in;
+
+    /* Set the accumulator to zero */
+    sum = 0.0f;
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      sum += (*px++) * (*pb++);
+      sum += (*px++) * (*pb++);
+      sum += (*px++) * (*pb++);
+      sum += (*px++) * (*pb++);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = numTaps % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      sum += (*px++) * (*pb++);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* The result in the accumulator, store in the destination buffer. */
+    *pOut++ = sum;
+
+    /* Compute and store error */
+    d = (float32_t) (*pRef++);
+    e = d - sum;
+    *pErr++ = e;
+
+    /* Calculation of Weighting factor for updating filter coefficients */
+    /* epsilon value 0.000000119209289f */
+    w = (e * mu) / (energy + 0.000000119209289f);
+
+    /* Initialize pState pointer */
+    px = pState;
+
+    /* Initialize coeff pointer */
+    pb = (pCoeffs);
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2;
+
+    /* Update filter coefficients */
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      *pb += w * (*px++);
+      pb++;
+
+      *pb += w * (*px++);
+      pb++;
+
+      *pb += w * (*px++);
+      pb++;
+
+      *pb += w * (*px++);
+      pb++;
+
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = numTaps % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      *pb += w * (*px++);
+      pb++;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    x0 = *pState;
+
+    /* Advance state pointer by 1 for the next sample */
+    pState = pState + 1;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  S->energy = energy;
+  S->x0 = x0;
+
+  /* Processing is complete. Now copy the last numTaps - 1 samples to the    
+     satrt of the state buffer. This prepares the state buffer for the    
+     next function call. */
+
+  /* Points to the start of the pState buffer */
+  pStateCurnt = S->pState;
+
+  /* Loop unrolling for (numTaps - 1u)/4 samples copy */
+  tapCnt = (numTaps - 1u) >> 2u;
+
+  /* copy data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+  /* Calculate remaining number of copies */
+  tapCnt = (numTaps - 1u) % 0x4u;
+
+  /* Copy the remaining q31_t data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  while(blkCnt > 0u)
+  {
+    /* Copy the new input sample into the state buffer */
+    *pStateCurnt++ = *pSrc;
+
+    /* Initialize pState pointer */
+    px = pState;
+
+    /* Initialize pCoeffs pointer */
+    pb = pCoeffs;
+
+    /* Read the sample from input buffer */
+    in = *pSrc++;
+
+    /* Update the energy calculation */
+    energy -= x0 * x0;
+    energy += in * in;
+
+    /* Set the accumulator to zero */
+    sum = 0.0f;
+
+    /* Loop over numTaps number of values */
+    tapCnt = numTaps;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      sum += (*px++) * (*pb++);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* The result in the accumulator is stored in the destination buffer. */
+    *pOut++ = sum;
+
+    /* Compute and store error */
+    d = (float32_t) (*pRef++);
+    e = d - sum;
+    *pErr++ = e;
+
+    /* Calculation of Weighting factor for updating filter coefficients */
+    /* epsilon value 0.000000119209289f */
+    w = (e * mu) / (energy + 0.000000119209289f);
+
+    /* Initialize pState pointer */
+    px = pState;
+
+    /* Initialize pCcoeffs pointer */
+    pb = pCoeffs;
+
+    /* Loop over numTaps number of values */
+    tapCnt = numTaps;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      *pb += w * (*px++);
+      pb++;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    x0 = *pState;
+
+    /* Advance state pointer by 1 for the next sample */
+    pState = pState + 1;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  S->energy = energy;
+  S->x0 = x0;
+
+  /* Processing is complete. Now copy the last numTaps - 1 samples to the        
+     satrt of the state buffer. This prepares the state buffer for the        
+     next function call. */
+
+  /* Points to the start of the pState buffer */
+  pStateCurnt = S->pState;
+
+  /* Copy (numTaps - 1u) samples  */
+  tapCnt = (numTaps - 1u);
+
+  /* Copy the remaining q31_t data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+#endif /*   #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+   * @} end of LMS_NORM group    
+   */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_norm_init_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_norm_init_f32.c
new file mode 100644
index 0000000000..3d31cfb257
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_norm_init_f32.c
@@ -0,0 +1,100 @@
+/*-----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_lms_norm_init_f32.c    
+*    
+* Description:  Floating-point NLMS filter initialization function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ---------------------------------------------------------------------------*/
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup LMS_NORM    
+ * @{    
+ */
+
+  /**    
+   * @brief Initialization function for floating-point normalized LMS filter.    
+   * @param[in] *S points to an instance of the floating-point LMS filter structure.    
+   * @param[in] numTaps  number of filter coefficients.    
+   * @param[in] *pCoeffs points to coefficient buffer.    
+   * @param[in] *pState points to state buffer.    
+   * @param[in] mu step size that controls filter coefficient updates.    
+   * @param[in] blockSize number of samples to process.    
+   * @return none.    
+   *    
+ * \par Description:    
+ * pCoeffs points to the array of filter coefficients stored in time reversed order:    
+ * 
    
+ *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}    
+ * 
    
+ * The initial filter coefficients serve as a starting point for the adaptive filter.    
+ * pState points to an array of length numTaps+blockSize-1 samples,    
+ * where blockSize is the number of input samples processed by each call to arm_lms_norm_f32().    
+ */
+
+void arm_lms_norm_init_f32(
+  arm_lms_norm_instance_f32 * S,
+  uint16_t numTaps,
+  float32_t * pCoeffs,
+  float32_t * pState,
+  float32_t mu,
+  uint32_t blockSize)
+{
+  /* Assign filter taps */
+  S->numTaps = numTaps;
+
+  /* Assign coefficient pointer */
+  S->pCoeffs = pCoeffs;
+
+  /* Clear state buffer and size is always blockSize + numTaps - 1 */
+  memset(pState, 0, (numTaps + (blockSize - 1u)) * sizeof(float32_t));
+
+  /* Assign state pointer */
+  S->pState = pState;
+
+  /* Assign Step size value */
+  S->mu = mu;
+
+  /* Initialise Energy to zero */
+  S->energy = 0.0f;
+
+  /* Initialise x0 to zero */
+  S->x0 = 0.0f;
+
+}
+
+/**    
+ * @} end of LMS_NORM group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_norm_init_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_norm_init_q15.c
new file mode 100644
index 0000000000..a1cf1b001d
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_norm_init_q15.c
@@ -0,0 +1,107 @@
+/*-----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_lms_norm_init_q15.c    
+*    
+* Description:  Q15 NLMS initialization function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ---------------------------------------------------------------------------*/
+
+#include "arm_math.h"
+#include "arm_common_tables.h"
+
+/**    
+ * @addtogroup LMS_NORM    
+ * @{    
+ */
+
+  /**    
+   * @brief Initialization function for Q15 normalized LMS filter.    
+   * @param[in] *S points to an instance of the Q15 normalized LMS filter structure.    
+   * @param[in] numTaps  number of filter coefficients.    
+   * @param[in] *pCoeffs points to coefficient buffer.    
+   * @param[in] *pState points to state buffer.    
+   * @param[in] mu step size that controls filter coefficient updates.    
+   * @param[in] blockSize number of samples to process.    
+   * @param[in] postShift bit shift applied to coefficients.    
+   * @return none.    
+ *    
+ * Description:    
+ * \par    
+ * pCoeffs points to the array of filter coefficients stored in time reversed order:    
+ * 
    
+ *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}    
+ * 
    
+ * The initial filter coefficients serve as a starting point for the adaptive filter.    
+ * pState points to the array of state variables and size of array is    
+ * numTaps+blockSize-1 samples, where blockSize is the number of input samples processed    
+ * by each call to arm_lms_norm_q15().    
+ */
+
+void arm_lms_norm_init_q15(
+  arm_lms_norm_instance_q15 * S,
+  uint16_t numTaps,
+  q15_t * pCoeffs,
+  q15_t * pState,
+  q15_t mu,
+  uint32_t blockSize,
+  uint8_t postShift)
+{
+  /* Assign filter taps */
+  S->numTaps = numTaps;
+
+  /* Assign coefficient pointer */
+  S->pCoeffs = pCoeffs;
+
+  /* Clear state buffer and size is always blockSize + numTaps - 1 */
+  memset(pState, 0, (numTaps + (blockSize - 1u)) * sizeof(q15_t));
+
+  /* Assign post Shift value applied to coefficients */
+  S->postShift = postShift;
+
+  /* Assign state pointer */
+  S->pState = pState;
+
+  /* Assign Step size value */
+  S->mu = mu;
+
+  /* Initialize reciprocal pointer table */
+  S->recipTable = (q15_t *) armRecipTableQ15;
+
+  /* Initialise Energy to zero */
+  S->energy = 0;
+
+  /* Initialise x0 to zero */
+  S->x0 = 0;
+
+}
+
+/**    
+ * @} end of LMS_NORM group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_norm_init_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_norm_init_q31.c
new file mode 100644
index 0000000000..a2fae7b381
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_norm_init_q31.c
@@ -0,0 +1,106 @@
+/*-----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_lms_norm_init_q31.c    
+*    
+* Description:  Q31 NLMS initialization function.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ---------------------------------------------------------------------------*/
+
+#include "arm_math.h"
+#include "arm_common_tables.h"
+
+/**    
+ * @addtogroup LMS_NORM    
+ * @{    
+ */
+
+  /**    
+   * @brief Initialization function for Q31 normalized LMS filter.    
+   * @param[in] *S points to an instance of the Q31 normalized LMS filter structure.    
+   * @param[in] numTaps  number of filter coefficients.    
+   * @param[in] *pCoeffs points to coefficient buffer.    
+   * @param[in] *pState points to state buffer.    
+   * @param[in] mu step size that controls filter coefficient updates.    
+   * @param[in] blockSize number of samples to process.    
+   * @param[in] postShift bit shift applied to coefficients.    
+   * @return none.    
+ *    
+ * Description:    
+ * \par    
+ * pCoeffs points to the array of filter coefficients stored in time reversed order:    
+ * 
    
+ *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}    
+ * 
    
+ * The initial filter coefficients serve as a starting point for the adaptive filter.    
+ * pState points to an array of length numTaps+blockSize-1 samples,    
+ * where blockSize is the number of input samples processed by each call to arm_lms_norm_q31().    
+ */
+
+void arm_lms_norm_init_q31(
+  arm_lms_norm_instance_q31 * S,
+  uint16_t numTaps,
+  q31_t * pCoeffs,
+  q31_t * pState,
+  q31_t mu,
+  uint32_t blockSize,
+  uint8_t postShift)
+{
+  /* Assign filter taps */
+  S->numTaps = numTaps;
+
+  /* Assign coefficient pointer */
+  S->pCoeffs = pCoeffs;
+
+  /* Clear state buffer and size is always blockSize + numTaps - 1  */
+  memset(pState, 0, (numTaps + (blockSize - 1u)) * sizeof(q31_t));
+
+  /* Assign post Shift value applied to coefficients */
+  S->postShift = postShift;
+
+  /* Assign state pointer */
+  S->pState = pState;
+
+  /* Assign Step size value */
+  S->mu = mu;
+
+  /* Initialize reciprocal pointer table */
+  S->recipTable = (q31_t *) armRecipTableQ31;
+
+  /* Initialise Energy to zero */
+  S->energy = 0;
+
+  /* Initialise x0 to zero */
+  S->x0 = 0;
+
+}
+
+/**    
+ * @} end of LMS_NORM group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_norm_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_norm_q15.c
new file mode 100644
index 0000000000..a1229a2036
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_norm_q15.c
@@ -0,0 +1,435 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_lms_norm_q15.c    
+*    
+* Description:	Q15 NLMS filter.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup LMS_NORM    
+ * @{    
+ */
+
+/**    
+* @brief Processing function for Q15 normalized LMS filter.    
+* @param[in] *S points to an instance of the Q15 normalized LMS filter structure.    
+* @param[in] *pSrc points to the block of input data.    
+* @param[in] *pRef points to the block of reference data.    
+* @param[out] *pOut points to the block of output data.    
+* @param[out] *pErr points to the block of error data.    
+* @param[in] blockSize number of samples to process.    
+* @return none.    
+*    
+* Scaling and Overflow Behavior:     
+* \par     
+* The function is implemented using a 64-bit internal accumulator.     
+* Both coefficients and state variables are represented in 1.15 format and    
+* multiplications yield a 2.30 result. The 2.30 intermediate results are    
+* accumulated in a 64-bit accumulator in 34.30 format.     
+* There is no risk of internal overflow with this approach and the full    
+* precision of intermediate multiplications is preserved. After all additions    
+* have been performed, the accumulator is truncated to 34.15 format by    
+* discarding low 15 bits. Lastly, the accumulator is saturated to yield a    
+* result in 1.15 format.    
+*    
+* \par   
+* 	In this filter, filter coefficients are updated for each sample and the updation of filter cofficients are saturted.    
+*    
+ */
+
+void arm_lms_norm_q15(
+  arm_lms_norm_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pRef,
+  q15_t * pOut,
+  q15_t * pErr,
+  uint32_t blockSize)
+{
+  q15_t *pState = S->pState;                     /* State pointer */
+  q15_t *pCoeffs = S->pCoeffs;                   /* Coefficient pointer */
+  q15_t *pStateCurnt;                            /* Points to the current sample of the state */
+  q15_t *px, *pb;                                /* Temporary pointers for state and coefficient buffers */
+  q15_t mu = S->mu;                              /* Adaptive factor */
+  uint32_t numTaps = S->numTaps;                 /* Number of filter coefficients in the filter */
+  uint32_t tapCnt, blkCnt;                       /* Loop counters */
+  q31_t energy;                                  /* Energy of the input */
+  q63_t acc;                                     /* Accumulator */
+  q15_t e = 0, d = 0;                            /* error, reference data sample */
+  q15_t w = 0, in;                               /* weight factor and state */
+  q15_t x0;                                      /* temporary variable to hold input sample */
+  //uint32_t shift = (uint32_t) S->postShift + 1u; /* Shift to be applied to the output */ 
+  q15_t errorXmu, oneByEnergy;                   /* Temporary variables to store error and mu product and reciprocal of energy */
+  q15_t postShift;                               /* Post shift to be applied to weight after reciprocal calculation */
+  q31_t coef;                                    /* Teporary variable for coefficient */
+  q31_t acc_l, acc_h;
+  int32_t lShift = (15 - (int32_t) S->postShift);       /*  Post shift  */
+  int32_t uShift = (32 - lShift);
+
+  energy = S->energy;
+  x0 = S->x0;
+
+  /* S->pState points to buffer which contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = &(S->pState[(numTaps - 1u)]);
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  while(blkCnt > 0u)
+  {
+    /* Copy the new input sample into the state buffer */
+    *pStateCurnt++ = *pSrc;
+
+    /* Initialize pState pointer */
+    px = pState;
+
+    /* Initialize coeff pointer */
+    pb = (pCoeffs);
+
+    /* Read the sample from input buffer */
+    in = *pSrc++;
+
+    /* Update the energy calculation */
+    energy -= (((q31_t) x0 * (x0)) >> 15);
+    energy += (((q31_t) in * (in)) >> 15);
+
+    /* Set the accumulator to zero */
+    acc = 0;
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2;
+
+    while(tapCnt > 0u)
+    {
+
+      /* Perform the multiply-accumulate */
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+      acc = __SMLALD(*__SIMD32(px)++, (*__SIMD32(pb)++), acc);
+      acc = __SMLALD(*__SIMD32(px)++, (*__SIMD32(pb)++), acc);
+
+#else
+
+      acc += (((q31_t) * px++ * (*pb++)));
+      acc += (((q31_t) * px++ * (*pb++)));
+      acc += (((q31_t) * px++ * (*pb++)));
+      acc += (((q31_t) * px++ * (*pb++)));
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = numTaps % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      acc += (((q31_t) * px++ * (*pb++)));
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Calc lower part of acc */
+    acc_l = acc & 0xffffffff;
+
+    /* Calc upper part of acc */
+    acc_h = (acc >> 32) & 0xffffffff;
+
+    /* Apply shift for lower part of acc and upper part of acc */
+    acc = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+    /* Converting the result to 1.15 format and saturate the output */
+    acc = __SSAT(acc, 16u);
+
+    /* Store the result from accumulator into the destination buffer. */
+    *pOut++ = (q15_t) acc;
+
+    /* Compute and store error */
+    d = *pRef++;
+    e = d - (q15_t) acc;
+    *pErr++ = e;
+
+    /* Calculation of 1/energy */
+    postShift = arm_recip_q15((q15_t) energy + DELTA_Q15,
+                              &oneByEnergy, S->recipTable);
+
+    /* Calculation of e * mu value */
+    errorXmu = (q15_t) (((q31_t) e * mu) >> 15);
+
+    /* Calculation of (e * mu) * (1/energy) value */
+    acc = (((q31_t) errorXmu * oneByEnergy) >> (15 - postShift));
+
+    /* Weighting factor for the normalized version */
+    w = (q15_t) __SSAT((q31_t) acc, 16);
+
+    /* Initialize pState pointer */
+    px = pState;
+
+    /* Initialize coeff pointer */
+    pb = (pCoeffs);
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2;
+
+    /* Update filter coefficients */
+    while(tapCnt > 0u)
+    {
+      coef = *pb + (((q31_t) w * (*px++)) >> 15);
+      *pb++ = (q15_t) __SSAT((coef), 16);
+      coef = *pb + (((q31_t) w * (*px++)) >> 15);
+      *pb++ = (q15_t) __SSAT((coef), 16);
+      coef = *pb + (((q31_t) w * (*px++)) >> 15);
+      *pb++ = (q15_t) __SSAT((coef), 16);
+      coef = *pb + (((q31_t) w * (*px++)) >> 15);
+      *pb++ = (q15_t) __SSAT((coef), 16);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = numTaps % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      coef = *pb + (((q31_t) w * (*px++)) >> 15);
+      *pb++ = (q15_t) __SSAT((coef), 16);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Read the sample from state buffer */
+    x0 = *pState;
+
+    /* Advance state pointer by 1 for the next sample */
+    pState = pState + 1u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Save energy and x0 values for the next frame */
+  S->energy = (q15_t) energy;
+  S->x0 = x0;
+
+  /* Processing is complete. Now copy the last numTaps - 1 samples to the    
+     satrt of the state buffer. This prepares the state buffer for the    
+     next function call. */
+
+  /* Points to the start of the pState buffer */
+  pStateCurnt = S->pState;
+
+  /* Calculation of count for copying integer writes */
+  tapCnt = (numTaps - 1u) >> 2;
+
+  while(tapCnt > 0u)
+  {
+
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+    *__SIMD32(pStateCurnt)++ = *__SIMD32(pState)++;
+    *__SIMD32(pStateCurnt)++ = *__SIMD32(pState)++;
+
+#else
+
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+
+#endif
+
+    tapCnt--;
+
+  }
+
+  /* Calculation of count for remaining q15_t data */
+  tapCnt = (numTaps - 1u) % 0x4u;
+
+  /* copy data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  while(blkCnt > 0u)
+  {
+    /* Copy the new input sample into the state buffer */
+    *pStateCurnt++ = *pSrc;
+
+    /* Initialize pState pointer */
+    px = pState;
+
+    /* Initialize pCoeffs pointer */
+    pb = pCoeffs;
+
+    /* Read the sample from input buffer */
+    in = *pSrc++;
+
+    /* Update the energy calculation */
+    energy -= (((q31_t) x0 * (x0)) >> 15);
+    energy += (((q31_t) in * (in)) >> 15);
+
+    /* Set the accumulator to zero */
+    acc = 0;
+
+    /* Loop over numTaps number of values */
+    tapCnt = numTaps;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      acc += (((q31_t) * px++ * (*pb++)));
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Calc lower part of acc */
+    acc_l = acc & 0xffffffff;
+
+    /* Calc upper part of acc */
+    acc_h = (acc >> 32) & 0xffffffff;
+
+    /* Apply shift for lower part of acc and upper part of acc */
+    acc = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+    /* Converting the result to 1.15 format and saturate the output */
+    acc = __SSAT(acc, 16u);
+
+    /* Converting the result to 1.15 format */
+    //acc = __SSAT((acc >> (16u - shift)), 16u); 
+
+    /* Store the result from accumulator into the destination buffer. */
+    *pOut++ = (q15_t) acc;
+
+    /* Compute and store error */
+    d = *pRef++;
+    e = d - (q15_t) acc;
+    *pErr++ = e;
+
+    /* Calculation of 1/energy */
+    postShift = arm_recip_q15((q15_t) energy + DELTA_Q15,
+                              &oneByEnergy, S->recipTable);
+
+    /* Calculation of e * mu value */
+    errorXmu = (q15_t) (((q31_t) e * mu) >> 15);
+
+    /* Calculation of (e * mu) * (1/energy) value */
+    acc = (((q31_t) errorXmu * oneByEnergy) >> (15 - postShift));
+
+    /* Weighting factor for the normalized version */
+    w = (q15_t) __SSAT((q31_t) acc, 16);
+
+    /* Initialize pState pointer */
+    px = pState;
+
+    /* Initialize coeff pointer */
+    pb = (pCoeffs);
+
+    /* Loop over numTaps number of values */
+    tapCnt = numTaps;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      coef = *pb + (((q31_t) w * (*px++)) >> 15);
+      *pb++ = (q15_t) __SSAT((coef), 16);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Read the sample from state buffer */
+    x0 = *pState;
+
+    /* Advance state pointer by 1 for the next sample */
+    pState = pState + 1u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Save energy and x0 values for the next frame */
+  S->energy = (q15_t) energy;
+  S->x0 = x0;
+
+  /* Processing is complete. Now copy the last numTaps - 1 samples to the        
+     satrt of the state buffer. This prepares the state buffer for the        
+     next function call. */
+
+  /* Points to the start of the pState buffer */
+  pStateCurnt = S->pState;
+
+  /* copy (numTaps - 1u) data */
+  tapCnt = (numTaps - 1u);
+
+  /* copy data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+#endif /*   #ifndef ARM_MATH_CM0 */
+
+}
+
+
+/**    
+   * @} end of LMS_NORM group    
+   */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_norm_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_norm_q31.c
new file mode 100644
index 0000000000..791a8637cc
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_norm_q31.c
@@ -0,0 +1,426 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_lms_norm_q31.c    
+*    
+* Description:	Processing function for the Q31 NLMS filter.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup LMS_NORM    
+ * @{    
+ */
+
+/**    
+* @brief Processing function for Q31 normalized LMS filter.    
+* @param[in] *S points to an instance of the Q31 normalized LMS filter structure.    
+* @param[in] *pSrc points to the block of input data.    
+* @param[in] *pRef points to the block of reference data.    
+* @param[out] *pOut points to the block of output data.    
+* @param[out] *pErr points to the block of error data.    
+* @param[in] blockSize number of samples to process.    
+* @return none.    
+*    
+* Scaling and Overflow Behavior:     
+* \par     
+* The function is implemented using an internal 64-bit accumulator.     
+* The accumulator has a 2.62 format and maintains full precision of the intermediate   
+* multiplication results but provides only a single guard bit.     
+* Thus, if the accumulator result overflows it wraps around rather than clip.     
+* In order to avoid overflows completely the input signal must be scaled down by    
+* log2(numTaps) bits. The reference signal should not be scaled down.     
+* After all multiply-accumulates are performed, the 2.62 accumulator is shifted    
+* and saturated to 1.31 format to yield the final result.     
+* The output signal and error signal are in 1.31 format.     
+*    
+* \par    
+* 	In this filter, filter coefficients are updated for each sample and the    
+* updation of filter cofficients are saturted.    
+*     
+*/
+
+void arm_lms_norm_q31(
+  arm_lms_norm_instance_q31 * S,
+  q31_t * pSrc,
+  q31_t * pRef,
+  q31_t * pOut,
+  q31_t * pErr,
+  uint32_t blockSize)
+{
+  q31_t *pState = S->pState;                     /* State pointer */
+  q31_t *pCoeffs = S->pCoeffs;                   /* Coefficient pointer */
+  q31_t *pStateCurnt;                            /* Points to the current sample of the state */
+  q31_t *px, *pb;                                /* Temporary pointers for state and coefficient buffers */
+  q31_t mu = S->mu;                              /* Adaptive factor */
+  uint32_t numTaps = S->numTaps;                 /* Number of filter coefficients in the filter */
+  uint32_t tapCnt, blkCnt;                       /* Loop counters */
+  q63_t energy;                                  /* Energy of the input */
+  q63_t acc;                                     /* Accumulator */
+  q31_t e = 0, d = 0;                            /* error, reference data sample */
+  q31_t w = 0, in;                               /* weight factor and state */
+  q31_t x0;                                      /* temporary variable to hold input sample */
+//  uint32_t shift = 32u - ((uint32_t) S->postShift + 1u);        /* Shift to be applied to the output */      
+  q31_t errorXmu, oneByEnergy;                   /* Temporary variables to store error and mu product and reciprocal of energy */
+  q31_t postShift;                               /* Post shift to be applied to weight after reciprocal calculation */
+  q31_t coef;                                    /* Temporary variable for coef */
+  q31_t acc_l, acc_h;                            /*  temporary input */
+  uint32_t uShift = ((uint32_t) S->postShift + 1u);
+  uint32_t lShift = 32u - uShift;                /*  Shift to be applied to the output */
+
+  energy = S->energy;
+  x0 = S->x0;
+
+  /* S->pState points to buffer which contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = &(S->pState[(numTaps - 1u)]);
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  while(blkCnt > 0u)
+  {
+
+    /* Copy the new input sample into the state buffer */
+    *pStateCurnt++ = *pSrc;
+
+    /* Initialize pState pointer */
+    px = pState;
+
+    /* Initialize coeff pointer */
+    pb = (pCoeffs);
+
+    /* Read the sample from input buffer */
+    in = *pSrc++;
+
+    /* Update the energy calculation */
+    energy = (q31_t) ((((q63_t) energy << 32) -
+                       (((q63_t) x0 * x0) << 1)) >> 32);
+    energy = (q31_t) (((((q63_t) in * in) << 1) + (energy << 32)) >> 32);
+
+    /* Set the accumulator to zero */
+    acc = 0;
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      acc += ((q63_t) (*px++)) * (*pb++);
+      acc += ((q63_t) (*px++)) * (*pb++);
+      acc += ((q63_t) (*px++)) * (*pb++);
+      acc += ((q63_t) (*px++)) * (*pb++);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = numTaps % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      acc += ((q63_t) (*px++)) * (*pb++);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Converting the result to 1.31 format */
+    /* Calc lower part of acc */
+    acc_l = acc & 0xffffffff;
+
+    /* Calc upper part of acc */
+    acc_h = (acc >> 32) & 0xffffffff;
+
+    acc = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+    /* Store the result from accumulator into the destination buffer. */
+    *pOut++ = (q31_t) acc;
+
+    /* Compute and store error */
+    d = *pRef++;
+    e = d - (q31_t) acc;
+    *pErr++ = e;
+
+    /* Calculates the reciprocal of energy */
+    postShift = arm_recip_q31(energy + DELTA_Q31,
+                              &oneByEnergy, &S->recipTable[0]);
+
+    /* Calculation of product of (e * mu) */
+    errorXmu = (q31_t) (((q63_t) e * mu) >> 31);
+
+    /* Weighting factor for the normalized version */
+    w = clip_q63_to_q31(((q63_t) errorXmu * oneByEnergy) >> (31 - postShift));
+
+    /* Initialize pState pointer */
+    px = pState;
+
+    /* Initialize coeff pointer */
+    pb = (pCoeffs);
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2;
+
+    /* Update filter coefficients */
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+
+      /* coef is in 2.30 format */
+      coef = (q31_t) (((q63_t) w * (*px++)) >> (32));
+      /* get coef in 1.31 format by left shifting */
+      *pb = clip_q63_to_q31((q63_t) * pb + (coef << 1u));
+      /* update coefficient buffer to next coefficient */
+      pb++;
+
+      coef = (q31_t) (((q63_t) w * (*px++)) >> (32));
+      *pb = clip_q63_to_q31((q63_t) * pb + (coef << 1u));
+      pb++;
+
+      coef = (q31_t) (((q63_t) w * (*px++)) >> (32));
+      *pb = clip_q63_to_q31((q63_t) * pb + (coef << 1u));
+      pb++;
+
+      coef = (q31_t) (((q63_t) w * (*px++)) >> (32));
+      *pb = clip_q63_to_q31((q63_t) * pb + (coef << 1u));
+      pb++;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = numTaps % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      coef = (q31_t) (((q63_t) w * (*px++)) >> (32));
+      *pb = clip_q63_to_q31((q63_t) * pb + (coef << 1u));
+      pb++;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Read the sample from state buffer */
+    x0 = *pState;
+
+    /* Advance state pointer by 1 for the next sample */
+    pState = pState + 1;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Save energy and x0 values for the next frame */
+  S->energy = (q31_t) energy;
+  S->x0 = x0;
+
+  /* Processing is complete. Now copy the last numTaps - 1 samples to the    
+     satrt of the state buffer. This prepares the state buffer for the    
+     next function call. */
+
+  /* Points to the start of the pState buffer */
+  pStateCurnt = S->pState;
+
+  /* Loop unrolling for (numTaps - 1u) samples copy */
+  tapCnt = (numTaps - 1u) >> 2u;
+
+  /* copy data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+  /* Calculate remaining number of copies */
+  tapCnt = (numTaps - 1u) % 0x4u;
+
+  /* Copy the remaining q31_t data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  while(blkCnt > 0u)
+  {
+
+    /* Copy the new input sample into the state buffer */
+    *pStateCurnt++ = *pSrc;
+
+    /* Initialize pState pointer */
+    px = pState;
+
+    /* Initialize pCoeffs pointer */
+    pb = pCoeffs;
+
+    /* Read the sample from input buffer */
+    in = *pSrc++;
+
+    /* Update the energy calculation */
+    energy =
+      (q31_t) ((((q63_t) energy << 32) - (((q63_t) x0 * x0) << 1)) >> 32);
+    energy = (q31_t) (((((q63_t) in * in) << 1) + (energy << 32)) >> 32);
+
+    /* Set the accumulator to zero */
+    acc = 0;
+
+    /* Loop over numTaps number of values */
+    tapCnt = numTaps;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      acc += ((q63_t) (*px++)) * (*pb++);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Converting the result to 1.31 format */
+    /* Converting the result to 1.31 format */
+    /* Calc lower part of acc */
+    acc_l = acc & 0xffffffff;
+
+    /* Calc upper part of acc */
+    acc_h = (acc >> 32) & 0xffffffff;
+
+    acc = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+
+    //acc = (q31_t) (acc >> shift); 
+
+    /* Store the result from accumulator into the destination buffer. */
+    *pOut++ = (q31_t) acc;
+
+    /* Compute and store error */
+    d = *pRef++;
+    e = d - (q31_t) acc;
+    *pErr++ = e;
+
+    /* Calculates the reciprocal of energy */
+    postShift =
+      arm_recip_q31(energy + DELTA_Q31, &oneByEnergy, &S->recipTable[0]);
+
+    /* Calculation of product of (e * mu) */
+    errorXmu = (q31_t) (((q63_t) e * mu) >> 31);
+
+    /* Weighting factor for the normalized version */
+    w = clip_q63_to_q31(((q63_t) errorXmu * oneByEnergy) >> (31 - postShift));
+
+    /* Initialize pState pointer */
+    px = pState;
+
+    /* Initialize coeff pointer */
+    pb = (pCoeffs);
+
+    /* Loop over numTaps number of values */
+    tapCnt = numTaps;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      /* coef is in 2.30 format */
+      coef = (q31_t) (((q63_t) w * (*px++)) >> (32));
+      /* get coef in 1.31 format by left shifting */
+      *pb = clip_q63_to_q31((q63_t) * pb + (coef << 1u));
+      /* update coefficient buffer to next coefficient */
+      pb++;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Read the sample from state buffer */
+    x0 = *pState;
+
+    /* Advance state pointer by 1 for the next sample */
+    pState = pState + 1;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Save energy and x0 values for the next frame */
+  S->energy = (q31_t) energy;
+  S->x0 = x0;
+
+  /* Processing is complete. Now copy the last numTaps - 1 samples to the     
+     start of the state buffer. This prepares the state buffer for the        
+     next function call. */
+
+  /* Points to the start of the pState buffer */
+  pStateCurnt = S->pState;
+
+  /* Loop for (numTaps - 1u) samples copy */
+  tapCnt = (numTaps - 1u);
+
+  /* Copy the remaining q31_t data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+#endif /*   #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of LMS_NORM group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_q15.c
new file mode 100644
index 0000000000..91237c12d8
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_q15.c
@@ -0,0 +1,374 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_lms_q15.c    
+*    
+* Description:	Processing function for the Q15 LMS filter.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup LMS    
+ * @{    
+ */
+
+ /**    
+ * @brief Processing function for Q15 LMS filter.    
+ * @param[in] *S points to an instance of the Q15 LMS filter structure.    
+ * @param[in] *pSrc points to the block of input data.    
+ * @param[in] *pRef points to the block of reference data.    
+ * @param[out] *pOut points to the block of output data.    
+ * @param[out] *pErr points to the block of error data.    
+ * @param[in] blockSize number of samples to process.    
+ * @return none.    
+ *    
+ * \par Scaling and Overflow Behavior:    
+ * The function is implemented using a 64-bit internal accumulator.    
+ * Both coefficients and state variables are represented in 1.15 format and multiplications yield a 2.30 result.    
+ * The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format.    
+ * There is no risk of internal overflow with this approach and the full precision of intermediate multiplications is preserved.    
+ * After all additions have been performed, the accumulator is truncated to 34.15 format by discarding low 15 bits.    
+ * Lastly, the accumulator is saturated to yield a result in 1.15 format.    
+ *   
+ * \par   
+ * 	In this filter, filter coefficients are updated for each sample and the updation of filter cofficients are saturted.   
+ *    
+ */
+
+void arm_lms_q15(
+  const arm_lms_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pRef,
+  q15_t * pOut,
+  q15_t * pErr,
+  uint32_t blockSize)
+{
+  q15_t *pState = S->pState;                     /* State pointer */
+  uint32_t numTaps = S->numTaps;                 /* Number of filter coefficients in the filter */
+  q15_t *pCoeffs = S->pCoeffs;                   /* Coefficient pointer */
+  q15_t *pStateCurnt;                            /* Points to the current sample of the state */
+  q15_t mu = S->mu;                              /* Adaptive factor */
+  q15_t *px;                                     /* Temporary pointer for state */
+  q15_t *pb;                                     /* Temporary pointer for coefficient buffer */
+  uint32_t tapCnt, blkCnt;                       /* Loop counters */
+  q63_t acc;                                     /* Accumulator */
+  q15_t e = 0;                                   /* error of data sample */
+  q15_t alpha;                                   /* Intermediate constant for taps update */
+  q31_t acc_l, acc_h;
+  int32_t lShift = (15 - (int32_t) S->postShift);       /*  Post shift  */
+  int32_t uShift = (32 - lShift);
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q31_t coef;                                    /* Teporary variable for coefficient */
+
+  /* S->pState points to buffer which contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = &(S->pState[(numTaps - 1u)]);
+
+  /* Initializing blkCnt with blockSize */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* Copy the new input sample into the state buffer */
+    *pStateCurnt++ = *pSrc++;
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* Initialize coefficient pointer */
+    pb = pCoeffs;
+
+    /* Set the accumulator to zero */
+    acc = 0;
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2u;
+
+    while(tapCnt > 0u)
+    {
+      /* acc +=  b[N] * x[n-N] + b[N-1] * x[n-N-1] */
+      /* Perform the multiply-accumulate */
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+      acc = __SMLALD(*__SIMD32(px)++, (*__SIMD32(pb)++), acc);
+      acc = __SMLALD(*__SIMD32(px)++, (*__SIMD32(pb)++), acc);
+
+#else
+
+      acc += (q63_t) (((q31_t) (*px++) * (*pb++)));
+      acc += (q63_t) (((q31_t) (*px++) * (*pb++)));
+      acc += (q63_t) (((q31_t) (*px++) * (*pb++)));
+      acc += (q63_t) (((q31_t) (*px++) * (*pb++)));
+
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = numTaps % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      acc += (q63_t) (((q31_t) (*px++) * (*pb++)));
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Calc lower part of acc */
+    acc_l = acc & 0xffffffff;
+
+    /* Calc upper part of acc */
+    acc_h = (acc >> 32) & 0xffffffff;
+
+    /* Apply shift for lower part of acc and upper part of acc */
+    acc = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+    /* Converting the result to 1.15 format and saturate the output */
+    acc = __SSAT(acc, 16);
+
+    /* Store the result from accumulator into the destination buffer. */
+    *pOut++ = (q15_t) acc;
+
+    /* Compute and store error */
+    e = *pRef++ - (q15_t) acc;
+
+    *pErr++ = (q15_t) e;
+
+    /* Compute alpha i.e. intermediate constant for taps update */
+    alpha = (q15_t) (((q31_t) e * (mu)) >> 15);
+
+    /* Initialize state pointer */
+    /* Advance state pointer by 1 for the next sample */
+    px = pState++;
+
+    /* Initialize coefficient pointer */
+    pb = pCoeffs;
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2u;
+
+    /* Update filter coefficients */
+    while(tapCnt > 0u)
+    {
+      coef = (q31_t) * pb + (((q31_t) alpha * (*px++)) >> 15);
+      *pb++ = (q15_t) __SSAT((coef), 16);
+      coef = (q31_t) * pb + (((q31_t) alpha * (*px++)) >> 15);
+      *pb++ = (q15_t) __SSAT((coef), 16);
+      coef = (q31_t) * pb + (((q31_t) alpha * (*px++)) >> 15);
+      *pb++ = (q15_t) __SSAT((coef), 16);
+      coef = (q31_t) * pb + (((q31_t) alpha * (*px++)) >> 15);
+      *pb++ = (q15_t) __SSAT((coef), 16);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = numTaps % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      coef = (q31_t) * pb + (((q31_t) alpha * (*px++)) >> 15);
+      *pb++ = (q15_t) __SSAT((coef), 16);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Decrement the loop counter */
+    blkCnt--;
+
+  }
+
+  /* Processing is complete. Now copy the last numTaps - 1 samples to the    
+     satrt of the state buffer. This prepares the state buffer for the    
+     next function call. */
+
+  /* Points to the start of the pState buffer */
+  pStateCurnt = S->pState;
+
+  /* Calculation of count for copying integer writes */
+  tapCnt = (numTaps - 1u) >> 2;
+
+  while(tapCnt > 0u)
+  {
+
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+    *__SIMD32(pStateCurnt)++ = *__SIMD32(pState)++;
+    *__SIMD32(pStateCurnt)++ = *__SIMD32(pState)++;
+#else
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+#endif
+
+    tapCnt--;
+
+  }
+
+  /* Calculation of count for remaining q15_t data */
+  tapCnt = (numTaps - 1u) % 0x4u;
+
+  /* copy data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* S->pState points to buffer which contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = &(S->pState[(numTaps - 1u)]);
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* Copy the new input sample into the state buffer */
+    *pStateCurnt++ = *pSrc++;
+
+    /* Initialize pState pointer */
+    px = pState;
+
+    /* Initialize pCoeffs pointer */
+    pb = pCoeffs;
+
+    /* Set the accumulator to zero */
+    acc = 0;
+
+    /* Loop over numTaps number of values */
+    tapCnt = numTaps;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      acc += (q63_t) ((q31_t) (*px++) * (*pb++));
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Calc lower part of acc */
+    acc_l = acc & 0xffffffff;
+
+    /* Calc upper part of acc */
+    acc_h = (acc >> 32) & 0xffffffff;
+
+    /* Apply shift for lower part of acc and upper part of acc */
+    acc = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+    /* Converting the result to 1.15 format and saturate the output */
+    acc = __SSAT(acc, 16);
+
+    /* Store the result from accumulator into the destination buffer. */
+    *pOut++ = (q15_t) acc;
+
+    /* Compute and store error */
+    e = *pRef++ - (q15_t) acc;
+
+    *pErr++ = (q15_t) e;
+
+    /* Compute alpha i.e. intermediate constant for taps update */
+    alpha = (q15_t) (((q31_t) e * (mu)) >> 15);
+
+    /* Initialize pState pointer */
+    /* Advance state pointer by 1 for the next sample */
+    px = pState++;
+
+    /* Initialize pCoeffs pointer */
+    pb = pCoeffs;
+
+    /* Loop over numTaps number of values */
+    tapCnt = numTaps;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      *pb++ += (q15_t) (((q31_t) alpha * (*px++)) >> 15);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Decrement the loop counter */
+    blkCnt--;
+
+  }
+
+  /* Processing is complete. Now copy the last numTaps - 1 samples to the        
+     start of the state buffer. This prepares the state buffer for the   
+     next function call. */
+
+  /* Points to the start of the pState buffer */
+  pStateCurnt = S->pState;
+
+  /*  Copy (numTaps - 1u) samples  */
+  tapCnt = (numTaps - 1u);
+
+  /* Copy the data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+#endif /*   #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+   * @} end of LMS group    
+   */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_q31.c
new file mode 100644
index 0000000000..c43d55d1df
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_q31.c
@@ -0,0 +1,364 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_lms_q31.c    
+*    
+* Description:	Processing function for the Q31 LMS filter.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+/**    
+ * @ingroup groupFilters    
+ */
+
+/**    
+ * @addtogroup LMS    
+ * @{    
+ */
+
+ /**    
+ * @brief Processing function for Q31 LMS filter.    
+ * @param[in]  *S points to an instance of the Q15 LMS filter structure.    
+ * @param[in]  *pSrc points to the block of input data.    
+ * @param[in]  *pRef points to the block of reference data.    
+ * @param[out] *pOut points to the block of output data.    
+ * @param[out] *pErr points to the block of error data.    
+ * @param[in]  blockSize number of samples to process.    
+ * @return     none.    
+ *    
+ * \par Scaling and Overflow Behavior:     
+ * The function is implemented using an internal 64-bit accumulator.     
+ * The accumulator has a 2.62 format and maintains full precision of the intermediate    
+ * multiplication results but provides only a single guard bit.     
+ * Thus, if the accumulator result overflows it wraps around rather than clips.     
+ * In order to avoid overflows completely the input signal must be scaled down by    
+ * log2(numTaps) bits.     
+ * The reference signal should not be scaled down.     
+ * After all multiply-accumulates are performed, the 2.62 accumulator is shifted    
+ * and saturated to 1.31 format to yield the final result.     
+ * The output signal and error signal are in 1.31 format.     
+ *    
+ * \par    
+ * 	In this filter, filter coefficients are updated for each sample and the updation of filter cofficients are saturted.    
+ */
+
+void arm_lms_q31(
+  const arm_lms_instance_q31 * S,
+  q31_t * pSrc,
+  q31_t * pRef,
+  q31_t * pOut,
+  q31_t * pErr,
+  uint32_t blockSize)
+{
+  q31_t *pState = S->pState;                     /* State pointer */
+  uint32_t numTaps = S->numTaps;                 /* Number of filter coefficients in the filter */
+  q31_t *pCoeffs = S->pCoeffs;                   /* Coefficient pointer */
+  q31_t *pStateCurnt;                            /* Points to the current sample of the state */
+  q31_t mu = S->mu;                              /* Adaptive factor */
+  q31_t *px;                                     /* Temporary pointer for state */
+  q31_t *pb;                                     /* Temporary pointer for coefficient buffer */
+  uint32_t tapCnt, blkCnt;                       /* Loop counters */
+  q63_t acc;                                     /* Accumulator */
+  q31_t e = 0;                                   /* error of data sample */
+  q31_t alpha;                                   /* Intermediate constant for taps update */
+  q31_t coef;                                    /* Temporary variable for coef */
+  q31_t acc_l, acc_h;                            /*  temporary input */
+  uint32_t uShift = ((uint32_t) S->postShift + 1u);
+  uint32_t lShift = 32u - uShift;                /*  Shift to be applied to the output */
+
+  /* S->pState points to buffer which contains previous frame (numTaps - 1) samples */
+  /* pStateCurnt points to the location where the new input data should be written */
+  pStateCurnt = &(S->pState[(numTaps - 1u)]);
+
+  /* Initializing blkCnt with blockSize */
+  blkCnt = blockSize;
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  while(blkCnt > 0u)
+  {
+    /* Copy the new input sample into the state buffer */
+    *pStateCurnt++ = *pSrc++;
+
+    /* Initialize state pointer */
+    px = pState;
+
+    /* Initialize coefficient pointer */
+    pb = pCoeffs;
+
+    /* Set the accumulator to zero */
+    acc = 0;
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      /* acc +=  b[N] * x[n-N] */
+      acc += ((q63_t) (*px++)) * (*pb++);
+
+      /* acc +=  b[N-1] * x[n-N-1] */
+      acc += ((q63_t) (*px++)) * (*pb++);
+
+      /* acc +=  b[N-2] * x[n-N-2] */
+      acc += ((q63_t) (*px++)) * (*pb++);
+
+      /* acc +=  b[N-3] * x[n-N-3] */
+      acc += ((q63_t) (*px++)) * (*pb++);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = numTaps % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      acc += ((q63_t) (*px++)) * (*pb++);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Converting the result to 1.31 format */
+    /* Calc lower part of acc */
+    acc_l = acc & 0xffffffff;
+
+    /* Calc upper part of acc */
+    acc_h = (acc >> 32) & 0xffffffff;
+
+    acc = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+    /* Store the result from accumulator into the destination buffer. */
+    *pOut++ = (q31_t) acc;
+
+    /* Compute and store error */
+    e = *pRef++ - (q31_t) acc;
+
+    *pErr++ = (q31_t) e;
+
+    /* Compute alpha i.e. intermediate constant for taps update */
+    alpha = (q31_t) (((q63_t) e * mu) >> 31);
+
+    /* Initialize state pointer */
+    /* Advance state pointer by 1 for the next sample */
+    px = pState++;
+
+    /* Initialize coefficient pointer */
+    pb = pCoeffs;
+
+    /* Loop unrolling.  Process 4 taps at a time. */
+    tapCnt = numTaps >> 2;
+
+    /* Update filter coefficients */
+    while(tapCnt > 0u)
+    {
+      /* coef is in 2.30 format */
+      coef = (q31_t) (((q63_t) alpha * (*px++)) >> (32));
+      /* get coef in 1.31 format by left shifting */
+      *pb = clip_q63_to_q31((q63_t) * pb + (coef << 1u));
+      /* update coefficient buffer to next coefficient */
+      pb++;
+
+      coef = (q31_t) (((q63_t) alpha * (*px++)) >> (32));
+      *pb = clip_q63_to_q31((q63_t) * pb + (coef << 1u));
+      pb++;
+
+      coef = (q31_t) (((q63_t) alpha * (*px++)) >> (32));
+      *pb = clip_q63_to_q31((q63_t) * pb + (coef << 1u));
+      pb++;
+
+      coef = (q31_t) (((q63_t) alpha * (*px++)) >> (32));
+      *pb = clip_q63_to_q31((q63_t) * pb + (coef << 1u));
+      pb++;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* If the filter length is not a multiple of 4, compute the remaining filter taps */
+    tapCnt = numTaps % 0x4u;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      coef = (q31_t) (((q63_t) alpha * (*px++)) >> (32));
+      *pb = clip_q63_to_q31((q63_t) * pb + (coef << 1u));
+      pb++;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Processing is complete. Now copy the last numTaps - 1 samples to the    
+     satrt of the state buffer. This prepares the state buffer for the    
+     next function call. */
+
+  /* Points to the start of the pState buffer */
+  pStateCurnt = S->pState;
+
+  /* Loop unrolling for (numTaps - 1u) samples copy */
+  tapCnt = (numTaps - 1u) >> 2u;
+
+  /* copy data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+  /* Calculate remaining number of copies */
+  tapCnt = (numTaps - 1u) % 0x4u;
+
+  /* Copy the remaining q31_t data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  while(blkCnt > 0u)
+  {
+    /* Copy the new input sample into the state buffer */
+    *pStateCurnt++ = *pSrc++;
+
+    /* Initialize pState pointer */
+    px = pState;
+
+    /* Initialize pCoeffs pointer */
+    pb = pCoeffs;
+
+    /* Set the accumulator to zero */
+    acc = 0;
+
+    /* Loop over numTaps number of values */
+    tapCnt = numTaps;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      acc += ((q63_t) (*px++)) * (*pb++);
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Converting the result to 1.31 format */
+    /* Store the result from accumulator into the destination buffer. */
+    /* Calc lower part of acc */
+    acc_l = acc & 0xffffffff;
+
+    /* Calc upper part of acc */
+    acc_h = (acc >> 32) & 0xffffffff;
+
+    acc = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+    *pOut++ = (q31_t) acc;
+
+    /* Compute and store error */
+    e = *pRef++ - (q31_t) acc;
+
+    *pErr++ = (q31_t) e;
+
+    /* Weighting factor for the LMS version */
+    alpha = (q31_t) (((q63_t) e * mu) >> 31);
+
+    /* Initialize pState pointer */
+    /* Advance state pointer by 1 for the next sample */
+    px = pState++;
+
+    /* Initialize pCoeffs pointer */
+    pb = pCoeffs;
+
+    /* Loop over numTaps number of values */
+    tapCnt = numTaps;
+
+    while(tapCnt > 0u)
+    {
+      /* Perform the multiply-accumulate */
+      coef = (q31_t) (((q63_t) alpha * (*px++)) >> (32));
+      *pb += (coef << 1u);
+      pb++;
+
+      /* Decrement the loop counter */
+      tapCnt--;
+    }
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Processing is complete. Now copy the last numTaps - 1 samples to the     
+     start of the state buffer. This prepares the state buffer for the   
+     next function call. */
+
+  /* Points to the start of the pState buffer */
+  pStateCurnt = S->pState;
+
+  /*  Copy (numTaps - 1u) samples  */
+  tapCnt = (numTaps - 1u);
+
+  /* Copy the data */
+  while(tapCnt > 0u)
+  {
+    *pStateCurnt++ = *pState++;
+
+    /* Decrement the loop counter */
+    tapCnt--;
+  }
+
+#endif /*   #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+   * @} end of LMS group    
+   */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_add_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_add_f32.c
new file mode 100644
index 0000000000..09099ccb81
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_add_f32.c
@@ -0,0 +1,206 @@
+/* ----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_mat_add_f32.c    
+*    
+* Description:	Floating-point matrix addition    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+*    incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupMatrix        
+ */
+
+/**        
+ * @defgroup MatrixAdd Matrix Addition        
+ *        
+ * Adds two matrices.        
+ * \image html MatrixAddition.gif "Addition of two 3 x 3 matrices"        
+ *        
+ * The functions check to make sure that        
+ * pSrcA, pSrcB, and pDst have the same        
+ * number of rows and columns.        
+ */
+
+/**        
+ * @addtogroup MatrixAdd        
+ * @{        
+ */
+
+
+/**        
+ * @brief Floating-point matrix addition.        
+ * @param[in]       *pSrcA points to the first input matrix structure        
+ * @param[in]       *pSrcB points to the second input matrix structure        
+ * @param[out]      *pDst points to output matrix structure        
+ * @return     		The function returns either        
+ * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.        
+ */
+
+arm_status arm_mat_add_f32(
+  const arm_matrix_instance_f32 * pSrcA,
+  const arm_matrix_instance_f32 * pSrcB,
+  arm_matrix_instance_f32 * pDst)
+{
+  float32_t *pIn1 = pSrcA->pData;                /* input data matrix pointer A  */
+  float32_t *pIn2 = pSrcB->pData;                /* input data matrix pointer B  */
+  float32_t *pOut = pDst->pData;                 /* output data matrix pointer   */
+
+#ifndef ARM_MATH_CM0
+
+  float32_t inA1, inA2, inB1, inB2, out1, out2;  /* temporary variables */
+
+#endif //      #ifndef ARM_MATH_CM0
+
+  uint32_t numSamples;                           /* total number of elements in the matrix  */
+  uint32_t blkCnt;                               /* loop counters */
+  arm_status status;                             /* status of matrix addition */
+
+#ifdef ARM_MATH_MATRIX_CHECK
+  /* Check for matrix mismatch condition */
+  if((pSrcA->numRows != pSrcB->numRows) ||
+     (pSrcA->numCols != pSrcB->numCols) ||
+     (pSrcA->numRows != pDst->numRows) || (pSrcA->numCols != pDst->numCols))
+  {
+    /* Set status as ARM_MATH_SIZE_MISMATCH */
+    status = ARM_MATH_SIZE_MISMATCH;
+  }
+  else
+#endif
+  {
+
+    /* Total number of samples in the input matrix */
+    numSamples = (uint32_t) pSrcA->numRows * pSrcA->numCols;
+
+#ifndef ARM_MATH_CM0
+
+    /* Loop unrolling */
+    blkCnt = numSamples >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+     ** a second loop below computes the remaining 1 to 3 samples. */
+    while(blkCnt > 0u)
+    {
+      /* C(m,n) = A(m,n) + B(m,n) */
+      /* Add and then store the results in the destination buffer. */
+      /* Read values from source A */
+      inA1 = pIn1[0];
+
+      /* Read values from source B */
+      inB1 = pIn2[0];
+
+      /* Read values from source A */
+      inA2 = pIn1[1];
+
+      /* out = sourceA + sourceB */
+      out1 = inA1 + inB1;
+
+      /* Read values from source B */
+      inB2 = pIn2[1];
+
+      /* Read values from source A */
+      inA1 = pIn1[2];
+
+      /* out = sourceA + sourceB */
+      out2 = inA2 + inB2;
+
+      /* Read values from source B */
+      inB1 = pIn2[2];
+
+      /* Store result in destination */
+      pOut[0] = out1;
+      pOut[1] = out2;
+
+      /* Read values from source A */
+      inA2 = pIn1[3];
+
+      /* Read values from source B */
+      inB2 = pIn2[3];
+
+      /* out = sourceA + sourceB */
+      out1 = inA1 + inB1;
+
+      /* out = sourceA + sourceB */
+      out2 = inA2 + inB2;
+
+      /* Store result in destination */
+      pOut[2] = out1;
+
+      /* Store result in destination */
+      pOut[3] = out2;
+
+
+      /* update pointers to process next sampels */
+      pIn1 += 4u;
+      pIn2 += 4u;
+      pOut += 4u;
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the numSamples is not a multiple of 4, compute any remaining output samples here.    
+     ** No loop unrolling is used. */
+    blkCnt = numSamples % 0x4u;
+
+#else
+
+    /* Run the below code for Cortex-M0 */
+
+    /* Initialize blkCnt with number of samples */
+    blkCnt = numSamples;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+    while(blkCnt > 0u)
+    {
+      /* C(m,n) = A(m,n) + B(m,n) */
+      /* Add and then store the results in the destination buffer. */
+      *pOut++ = (*pIn1++) + (*pIn2++);
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+
+  }
+
+  /* Return to application */
+  return (status);
+}
+
+/**        
+ * @} end of MatrixAdd group        
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_add_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_add_q15.c
new file mode 100644
index 0000000000..4bfc878622
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_add_q15.c
@@ -0,0 +1,161 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_mat_add_q15.c    
+*    
+* Description:	Q15 matrix addition    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+*    incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMatrix    
+ */
+
+/**    
+ * @addtogroup MatrixAdd    
+ * @{    
+ */
+
+/**    
+ * @brief Q15 matrix addition.    
+ * @param[in]       *pSrcA points to the first input matrix structure    
+ * @param[in]       *pSrcB points to the second input matrix structure    
+ * @param[out]      *pDst points to output matrix structure    
+ * @return     		The function returns either    
+ * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.    
+ *    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * Results outside of the allowable Q15 range [0x8000 0x7FFF] will be saturated.    
+ */
+
+arm_status arm_mat_add_q15(
+  const arm_matrix_instance_q15 * pSrcA,
+  const arm_matrix_instance_q15 * pSrcB,
+  arm_matrix_instance_q15 * pDst)
+{
+  q15_t *pInA = pSrcA->pData;                    /* input data matrix pointer A  */
+  q15_t *pInB = pSrcB->pData;                    /* input data matrix pointer B */
+  q15_t *pOut = pDst->pData;                     /* output data matrix pointer */
+  uint16_t numSamples;                           /* total number of elements in the matrix  */
+  uint32_t blkCnt;                               /* loop counters  */
+  arm_status status;                             /* status of matrix addition  */
+
+#ifdef ARM_MATH_MATRIX_CHECK
+
+
+  /* Check for matrix mismatch condition */
+  if((pSrcA->numRows != pSrcB->numRows) ||
+     (pSrcA->numCols != pSrcB->numCols) ||
+     (pSrcA->numRows != pDst->numRows) || (pSrcA->numCols != pDst->numCols))
+  {
+    /* Set status as ARM_MATH_SIZE_MISMATCH */
+    status = ARM_MATH_SIZE_MISMATCH;
+  }
+  else
+#endif /*    #ifdef ARM_MATH_MATRIX_CHECK    */
+
+  {
+    /* Total number of samples in the input matrix */
+    numSamples = (uint16_t) (pSrcA->numRows * pSrcA->numCols);
+
+#ifndef ARM_MATH_CM0
+
+    /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+    /* Loop unrolling */
+    blkCnt = (uint32_t) numSamples >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+     ** a second loop below computes the remaining 1 to 3 samples. */
+    while(blkCnt > 0u)
+    {
+      /* C(m,n) = A(m,n) + B(m,n) */
+      /* Add, Saturate and then store the results in the destination buffer. */
+      *__SIMD32(pOut)++ = __QADD16(*__SIMD32(pInA)++, *__SIMD32(pInB)++);
+      *__SIMD32(pOut)++ = __QADD16(*__SIMD32(pInA)++, *__SIMD32(pInB)++);
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+     ** No loop unrolling is used. */
+    blkCnt = (uint32_t) numSamples % 0x4u;
+
+    /* q15 pointers of input and output are initialized */
+
+    while(blkCnt > 0u)
+    {
+      /* C(m,n) = A(m,n) + B(m,n) */
+      /* Add, Saturate and then store the results in the destination buffer. */
+      *pOut++ = (q15_t) __QADD16(*pInA++, *pInB++);
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+#else
+
+    /* Run the below code for Cortex-M0 */
+
+    /* Initialize blkCnt with number of samples */
+    blkCnt = (uint32_t) numSamples;
+
+
+    /* q15 pointers of input and output are initialized */
+    while(blkCnt > 0u)
+    {
+      /* C(m,n) = A(m,n) + B(m,n) */
+      /* Add, Saturate and then store the results in the destination buffer. */
+      *pOut++ = (q15_t) __SSAT(((q31_t) * pInA++ + *pInB++), 16);
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+    /* set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+  }
+
+  /* Return to application */
+  return (status);
+}
+
+/**    
+ * @} end of MatrixAdd group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_add_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_add_q31.c
new file mode 100644
index 0000000000..1f7be21c55
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_add_q31.c
@@ -0,0 +1,205 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_mat_add_q31.c    
+*    
+* Description:	Q31 matrix addition    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+*    incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**      
+ * @ingroup groupMatrix      
+ */
+
+/**      
+ * @addtogroup MatrixAdd      
+ * @{      
+ */
+
+/**      
+ * @brief Q31 matrix addition.      
+ * @param[in]       *pSrcA points to the first input matrix structure      
+ * @param[in]       *pSrcB points to the second input matrix structure      
+ * @param[out]      *pDst points to output matrix structure      
+ * @return     		The function returns either      
+ * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.      
+ *      
+ * Scaling and Overflow Behavior:      
+ * \par      
+ * The function uses saturating arithmetic.      
+ * Results outside of the allowable Q31 range [0x80000000 0x7FFFFFFF] will be saturated.      
+ */
+
+arm_status arm_mat_add_q31(
+  const arm_matrix_instance_q31 * pSrcA,
+  const arm_matrix_instance_q31 * pSrcB,
+  arm_matrix_instance_q31 * pDst)
+{
+  q31_t *pIn1 = pSrcA->pData;                    /* input data matrix pointer A */
+  q31_t *pIn2 = pSrcB->pData;                    /* input data matrix pointer B */
+  q31_t *pOut = pDst->pData;                     /* output data matrix pointer */
+  q31_t inA1, inB1;                              /* temporary variables */
+
+#ifndef ARM_MATH_CM0
+
+  q31_t inA2, inB2;                              /* temporary variables */
+  q31_t out1, out2;                              /* temporary variables */
+
+#endif //      #ifndef ARM_MATH_CM0
+
+  uint32_t numSamples;                           /* total number of elements in the matrix  */
+  uint32_t blkCnt;                               /* loop counters */
+  arm_status status;                             /* status of matrix addition */
+
+#ifdef ARM_MATH_MATRIX_CHECK
+  /* Check for matrix mismatch condition */
+  if((pSrcA->numRows != pSrcB->numRows) ||
+     (pSrcA->numCols != pSrcB->numCols) ||
+     (pSrcA->numRows != pDst->numRows) || (pSrcA->numCols != pDst->numCols))
+  {
+    /* Set status as ARM_MATH_SIZE_MISMATCH */
+    status = ARM_MATH_SIZE_MISMATCH;
+  }
+  else
+#endif
+  {
+    /* Total number of samples in the input matrix */
+    numSamples = (uint32_t) pSrcA->numRows * pSrcA->numCols;
+
+#ifndef ARM_MATH_CM0
+
+    /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+    /* Loop Unrolling */
+    blkCnt = numSamples >> 2u;
+
+
+    /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+     ** a second loop below computes the remaining 1 to 3 samples. */
+    while(blkCnt > 0u)
+    {
+      /* C(m,n) = A(m,n) + B(m,n) */
+      /* Add, saturate and then store the results in the destination buffer. */
+      /* Read values from source A */
+      inA1 = pIn1[0];
+
+      /* Read values from source B */
+      inB1 = pIn2[0];
+
+      /* Read values from source A */
+      inA2 = pIn1[1];
+
+      /* Add and saturate */
+      out1 = __QADD(inA1, inB1);
+
+      /* Read values from source B */
+      inB2 = pIn2[1];
+
+      /* Read values from source A */
+      inA1 = pIn1[2];
+
+      /* Add and saturate */
+      out2 = __QADD(inA2, inB2);
+
+      /* Read values from source B */
+      inB1 = pIn2[2];
+
+      /* Store result in destination */
+      pOut[0] = out1;
+      pOut[1] = out2;
+
+      /* Read values from source A */
+      inA2 = pIn1[3];
+
+      /* Read values from source B */
+      inB2 = pIn2[3];
+
+      /* Add and saturate */
+      out1 = __QADD(inA1, inB1);
+      out2 = __QADD(inA2, inB2);
+
+      /* Store result in destination */
+      pOut[2] = out1;
+      pOut[3] = out2;
+
+      /* update pointers to process next sampels */
+      pIn1 += 4u;
+      pIn2 += 4u;
+      pOut += 4u;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the numSamples is not a multiple of 4, compute any remaining output samples here.      
+     ** No loop unrolling is used. */
+    blkCnt = numSamples % 0x4u;
+
+#else
+
+    /* Run the below code for Cortex-M0 */
+
+    /* Initialize blkCnt with number of samples */
+    blkCnt = numSamples;
+
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+    while(blkCnt > 0u)
+    {
+      /* C(m,n) = A(m,n) + B(m,n) */
+      /* Add, saturate and then store the results in the destination buffer. */
+      inA1 = *pIn1++;
+      inB1 = *pIn2++;
+
+      inA1 = __QADD(inA1, inB1);
+
+      /* Decrement the loop counter */
+      blkCnt--;
+
+      *pOut++ = inA1;
+
+    }
+
+    /* set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+  }
+
+  /* Return to application */
+  return (status);
+}
+
+/**      
+ * @} end of MatrixAdd group      
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_init_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_init_f32.c
new file mode 100644
index 0000000000..9ffc96ee3e
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_init_f32.c
@@ -0,0 +1,86 @@
+/* ----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_mat_init_f32.c    
+*    
+* Description:	Floating-point matrix initialization.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+*    incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMatrix    
+ */
+
+/**    
+ * @defgroup MatrixInit Matrix Initialization    
+ *    
+ * Initializes the underlying matrix data structure.    
+ * The functions set the numRows,    
+ * numCols, and pData fields    
+ * of the matrix data structure.    
+ */
+
+/**    
+ * @addtogroup MatrixInit    
+ * @{    
+ */
+
+/**    
+   * @brief  Floating-point matrix initialization.    
+   * @param[in,out] *S             points to an instance of the floating-point matrix structure.    
+   * @param[in]     nRows          number of rows in the matrix.    
+   * @param[in]     nColumns       number of columns in the matrix.    
+   * @param[in]     *pData	   points to the matrix data array.    
+   * @return        none    
+   */
+
+void arm_mat_init_f32(
+  arm_matrix_instance_f32 * S,
+  uint16_t nRows,
+  uint16_t nColumns,
+  float32_t * pData)
+{
+  /* Assign Number of Rows */
+  S->numRows = nRows;
+
+  /* Assign Number of Columns */
+  S->numCols = nColumns;
+
+  /* Assign Data pointer */
+  S->pData = pData;
+}
+
+/**    
+ * @} end of MatrixInit group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_init_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_init_q15.c
new file mode 100644
index 0000000000..2bada7feda
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_init_q15.c
@@ -0,0 +1,78 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_mat_init_q15.c    
+*    
+* Description:	Q15 matrix initialization.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+*    incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------------- */
+
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMatrix    
+ */
+
+/**    
+ * @addtogroup MatrixInit    
+ * @{    
+ */
+
+  /**    
+   * @brief  Q15 matrix initialization.    
+   * @param[in,out] *S             points to an instance of the floating-point matrix structure.    
+   * @param[in]     nRows          number of rows in the matrix.    
+   * @param[in]     nColumns       number of columns in the matrix.    
+   * @param[in]     *pData	   points to the matrix data array.    
+   * @return        none    
+   */
+
+void arm_mat_init_q15(
+  arm_matrix_instance_q15 * S,
+  uint16_t nRows,
+  uint16_t nColumns,
+  q15_t * pData)
+{
+  /* Assign Number of Rows */
+  S->numRows = nRows;
+
+  /* Assign Number of Columns */
+  S->numCols = nColumns;
+
+  /* Assign Data pointer */
+  S->pData = pData;
+}
+
+/**    
+ * @} end of MatrixInit group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_init_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_init_q31.c
new file mode 100644
index 0000000000..8828c2d2ea
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_init_q31.c
@@ -0,0 +1,82 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_mat_init_q31.c    
+*    
+* Description:	Q31 matrix initialization.    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+*    incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------------- */
+
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMatrix    
+ */
+
+/**    
+ * @defgroup MatrixInit Matrix Initialization    
+ *    
+ */
+
+/**    
+ * @addtogroup MatrixInit    
+ * @{    
+ */
+
+  /**    
+   * @brief  Q31 matrix initialization.    
+   * @param[in,out] *S             points to an instance of the floating-point matrix structure.    
+   * @param[in]     nRows          number of rows in the matrix.    
+   * @param[in]     nColumns       number of columns in the matrix.    
+   * @param[in]     *pData	   points to the matrix data array.    
+   * @return        none    
+   */
+
+void arm_mat_init_q31(
+  arm_matrix_instance_q31 * S,
+  uint16_t nRows,
+  uint16_t nColumns,
+  q31_t * pData)
+{
+  /* Assign Number of Rows */
+  S->numRows = nRows;
+
+  /* Assign Number of Columns */
+  S->numCols = nColumns;
+
+  /* Assign Data pointer */
+  S->pData = pData;
+}
+
+/**    
+ * @} end of MatrixInit group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_inverse_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_inverse_f32.c
new file mode 100644
index 0000000000..f346916e0c
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_inverse_f32.c
@@ -0,0 +1,668 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_mat_inverse_f32.c    
+*    
+* Description:	Floating-point matrix inverse.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMatrix    
+ */
+
+/**    
+ * @defgroup MatrixInv Matrix Inverse    
+ *    
+ * Computes the inverse of a matrix.    
+ *    
+ * The inverse is defined only if the input matrix is square and non-singular (the determinant    
+ * is non-zero). The function checks that the input and output matrices are square and of the    
+ * same size.    
+ *    
+ * Matrix inversion is numerically sensitive and the CMSIS DSP library only supports matrix    
+ * inversion of floating-point matrices.    
+ *    
+ * \par Algorithm    
+ * The Gauss-Jordan method is used to find the inverse.    
+ * The algorithm performs a sequence of elementary row-operations till it    
+ * reduces the input matrix to an identity matrix. Applying the same sequence    
+ * of elementary row-operations to an identity matrix yields the inverse matrix.    
+ * If the input matrix is singular, then the algorithm terminates and returns error status    
+ * ARM_MATH_SINGULAR.    
+ * \image html MatrixInverse.gif "Matrix Inverse of a 3 x 3 matrix using Gauss-Jordan Method"    
+ */
+
+/**    
+ * @addtogroup MatrixInv    
+ * @{    
+ */
+
+/**    
+ * @brief Floating-point matrix inverse.    
+ * @param[in]       *pSrc points to input matrix structure    
+ * @param[out]      *pDst points to output matrix structure    
+ * @return     		The function returns    
+ * ARM_MATH_SIZE_MISMATCH if the input matrix is not square or if the size    
+ * of the output matrix does not match the size of the input matrix.    
+ * If the input matrix is found to be singular (non-invertible), then the function returns    
+ * ARM_MATH_SINGULAR.  Otherwise, the function returns ARM_MATH_SUCCESS.    
+ */
+
+arm_status arm_mat_inverse_f32(
+  const arm_matrix_instance_f32 * pSrc,
+  arm_matrix_instance_f32 * pDst)
+{
+  float32_t *pIn = pSrc->pData;                  /* input data matrix pointer */
+  float32_t *pOut = pDst->pData;                 /* output data matrix pointer */
+  float32_t *pInT1, *pInT2;                      /* Temporary input data matrix pointer */
+  float32_t *pInT3, *pInT4;                      /* Temporary output data matrix pointer */
+  float32_t *pPivotRowIn, *pPRT_in, *pPivotRowDst, *pPRT_pDst;  /* Temporary input and output data matrix pointer */
+  uint32_t numRows = pSrc->numRows;              /* Number of rows in the matrix  */
+  uint32_t numCols = pSrc->numCols;              /* Number of Cols in the matrix  */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  float32_t Xchg, in = 0.0f, in1;                /* Temporary input values  */
+  uint32_t i, rowCnt, flag = 0u, j, loopCnt, k, l;      /* loop counters */
+  arm_status status;                             /* status of matrix inverse */
+
+#ifdef ARM_MATH_MATRIX_CHECK
+
+
+  /* Check for matrix mismatch condition */
+  if((pSrc->numRows != pSrc->numCols) || (pDst->numRows != pDst->numCols)
+     || (pSrc->numRows != pDst->numRows))
+  {
+    /* Set status as ARM_MATH_SIZE_MISMATCH */
+    status = ARM_MATH_SIZE_MISMATCH;
+  }
+  else
+#endif /*    #ifdef ARM_MATH_MATRIX_CHECK    */
+
+  {
+
+    /*--------------------------------------------------------------------------------------------------------------    
+	 * Matrix Inverse can be solved using elementary row operations.    
+	 *    
+	 *	Gauss-Jordan Method:    
+	 *    
+	 *	   1. First combine the identity matrix and the input matrix separated by a bar to form an    
+	 *        augmented matrix as follows:    
+	 *				        _ 	      	       _         _	       _    
+	 *					   |  a11  a12 | 1   0  |       |  X11 X12  |    
+	 *					   |           |        |   =   |           |    
+	 *					   |_ a21  a22 | 0   1 _|       |_ X21 X21 _|    
+	 *    
+	 *		2. In our implementation, pDst Matrix is used as identity matrix.    
+	 *    
+	 *		3. Begin with the first row. Let i = 1.    
+	 *    
+	 *	    4. Check to see if the pivot for row i is zero.    
+	 *		   The pivot is the element of the main diagonal that is on the current row.    
+	 *		   For instance, if working with row i, then the pivot element is aii.    
+	 *		   If the pivot is zero, exchange that row with a row below it that does not    
+	 *		   contain a zero in column i. If this is not possible, then an inverse    
+	 *		   to that matrix does not exist.    
+	 *    
+	 *	    5. Divide every element of row i by the pivot.    
+	 *    
+	 *	    6. For every row below and  row i, replace that row with the sum of that row and    
+	 *		   a multiple of row i so that each new element in column i below row i is zero.    
+	 *    
+	 *	    7. Move to the next row and column and repeat steps 2 through 5 until you have zeros    
+	 *		   for every element below and above the main diagonal.    
+	 *    
+	 *		8. Now an identical matrix is formed to the left of the bar(input matrix, pSrc).    
+	 *		   Therefore, the matrix to the right of the bar is our solution(pDst matrix, pDst).    
+	 *----------------------------------------------------------------------------------------------------------------*/
+
+    /* Working pointer for destination matrix */
+    pInT2 = pOut;
+
+    /* Loop over the number of rows */
+    rowCnt = numRows;
+
+    /* Making the destination matrix as identity matrix */
+    while(rowCnt > 0u)
+    {
+      /* Writing all zeroes in lower triangle of the destination matrix */
+      j = numRows - rowCnt;
+      while(j > 0u)
+      {
+        *pInT2++ = 0.0f;
+        j--;
+      }
+
+      /* Writing all ones in the diagonal of the destination matrix */
+      *pInT2++ = 1.0f;
+
+      /* Writing all zeroes in upper triangle of the destination matrix */
+      j = rowCnt - 1u;
+      while(j > 0u)
+      {
+        *pInT2++ = 0.0f;
+        j--;
+      }
+
+      /* Decrement the loop counter */
+      rowCnt--;
+    }
+
+    /* Loop over the number of columns of the input matrix.    
+       All the elements in each column are processed by the row operations */
+    loopCnt = numCols;
+
+    /* Index modifier to navigate through the columns */
+    l = 0u;
+
+    while(loopCnt > 0u)
+    {
+      /* Check if the pivot element is zero..    
+       * If it is zero then interchange the row with non zero row below.    
+       * If there is no non zero element to replace in the rows below,    
+       * then the matrix is Singular. */
+
+      /* Working pointer for the input matrix that points    
+       * to the pivot element of the particular row  */
+      pInT1 = pIn + (l * numCols);
+
+      /* Working pointer for the destination matrix that points    
+       * to the pivot element of the particular row  */
+      pInT3 = pOut + (l * numCols);
+
+      /* Temporary variable to hold the pivot value */
+      in = *pInT1;
+
+      /* Destination pointer modifier */
+      k = 1u;
+
+      /* Check if the pivot element is zero */
+      if(*pInT1 == 0.0f)
+      {
+        /* Loop over the number rows present below */
+        i = numRows - (l + 1u);
+
+        while(i > 0u)
+        {
+          /* Update the input and destination pointers */
+          pInT2 = pInT1 + (numCols * l);
+          pInT4 = pInT3 + (numCols * k);
+
+          /* Check if there is a non zero pivot element to    
+           * replace in the rows below */
+          if(*pInT2 != 0.0f)
+          {
+            /* Loop over number of columns    
+             * to the right of the pilot element */
+            j = numCols - l;
+
+            while(j > 0u)
+            {
+              /* Exchange the row elements of the input matrix */
+              Xchg = *pInT2;
+              *pInT2++ = *pInT1;
+              *pInT1++ = Xchg;
+
+              /* Decrement the loop counter */
+              j--;
+            }
+
+            /* Loop over number of columns of the destination matrix */
+            j = numCols;
+
+            while(j > 0u)
+            {
+              /* Exchange the row elements of the destination matrix */
+              Xchg = *pInT4;
+              *pInT4++ = *pInT3;
+              *pInT3++ = Xchg;
+
+              /* Decrement the loop counter */
+              j--;
+            }
+
+            /* Flag to indicate whether exchange is done or not */
+            flag = 1u;
+
+            /* Break after exchange is done */
+            break;
+          }
+
+          /* Update the destination pointer modifier */
+          k++;
+
+          /* Decrement the loop counter */
+          i--;
+        }
+      }
+
+      /* Update the status if the matrix is singular */
+      if((flag != 1u) && (in == 0.0f))
+      {
+        status = ARM_MATH_SINGULAR;
+
+        break;
+      }
+
+      /* Points to the pivot row of input and destination matrices */
+      pPivotRowIn = pIn + (l * numCols);
+      pPivotRowDst = pOut + (l * numCols);
+
+      /* Temporary pointers to the pivot row pointers */
+      pInT1 = pPivotRowIn;
+      pInT2 = pPivotRowDst;
+
+      /* Pivot element of the row */
+      in = *(pIn + (l * numCols));
+
+      /* Loop over number of columns    
+       * to the right of the pilot element */
+      j = (numCols - l);
+
+      while(j > 0u)
+      {
+        /* Divide each element of the row of the input matrix    
+         * by the pivot element */
+        in1 = *pInT1;
+        *pInT1++ = in1 / in;
+
+        /* Decrement the loop counter */
+        j--;
+      }
+
+      /* Loop over number of columns of the destination matrix */
+      j = numCols;
+
+      while(j > 0u)
+      {
+        /* Divide each element of the row of the destination matrix    
+         * by the pivot element */
+        in1 = *pInT2;
+        *pInT2++ = in1 / in;
+
+        /* Decrement the loop counter */
+        j--;
+      }
+
+      /* Replace the rows with the sum of that row and a multiple of row i    
+       * so that each new element in column i above row i is zero.*/
+
+      /* Temporary pointers for input and destination matrices */
+      pInT1 = pIn;
+      pInT2 = pOut;
+
+      /* index used to check for pivot element */
+      i = 0u;
+
+      /* Loop over number of rows */
+      /*  to be replaced by the sum of that row and a multiple of row i */
+      k = numRows;
+
+      while(k > 0u)
+      {
+        /* Check for the pivot element */
+        if(i == l)
+        {
+          /* If the processing element is the pivot element,    
+             only the columns to the right are to be processed */
+          pInT1 += numCols - l;
+
+          pInT2 += numCols;
+        }
+        else
+        {
+          /* Element of the reference row */
+          in = *pInT1;
+
+          /* Working pointers for input and destination pivot rows */
+          pPRT_in = pPivotRowIn;
+          pPRT_pDst = pPivotRowDst;
+
+          /* Loop over the number of columns to the right of the pivot element,    
+             to replace the elements in the input matrix */
+          j = (numCols - l);
+
+          while(j > 0u)
+          {
+            /* Replace the element by the sum of that row    
+               and a multiple of the reference row  */
+            in1 = *pInT1;
+            *pInT1++ = in1 - (in * *pPRT_in++);
+
+            /* Decrement the loop counter */
+            j--;
+          }
+
+          /* Loop over the number of columns to    
+             replace the elements in the destination matrix */
+          j = numCols;
+
+          while(j > 0u)
+          {
+            /* Replace the element by the sum of that row    
+               and a multiple of the reference row  */
+            in1 = *pInT2;
+            *pInT2++ = in1 - (in * *pPRT_pDst++);
+
+            /* Decrement the loop counter */
+            j--;
+          }
+
+        }
+
+        /* Increment the temporary input pointer */
+        pInT1 = pInT1 + l;
+
+        /* Decrement the loop counter */
+        k--;
+
+        /* Increment the pivot index */
+        i++;
+      }
+
+      /* Increment the input pointer */
+      pIn++;
+
+      /* Decrement the loop counter */
+      loopCnt--;
+
+      /* Increment the index modifier */
+      l++;
+    }
+
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  float32_t Xchg, in = 0.0f;                     /* Temporary input values  */
+  uint32_t i, rowCnt, flag = 0u, j, loopCnt, k, l;      /* loop counters */
+  arm_status status;                             /* status of matrix inverse */
+
+#ifdef ARM_MATH_MATRIX_CHECK
+
+  /* Check for matrix mismatch condition */
+  if((pSrc->numRows != pSrc->numCols) || (pDst->numRows != pDst->numCols)
+     || (pSrc->numRows != pDst->numRows))
+  {
+    /* Set status as ARM_MATH_SIZE_MISMATCH */
+    status = ARM_MATH_SIZE_MISMATCH;
+  }
+  else
+#endif /*      #ifdef ARM_MATH_MATRIX_CHECK    */
+  {
+
+    /*--------------------------------------------------------------------------------------------------------------       
+	 * Matrix Inverse can be solved using elementary row operations.        
+	 *        
+	 *	Gauss-Jordan Method:       
+	 *	 	       
+	 *	   1. First combine the identity matrix and the input matrix separated by a bar to form an        
+	 *        augmented matrix as follows:        
+	 *				        _  _	      _	    _	   _   _         _	       _       
+	 *					   |  |  a11  a12  | | | 1   0  |   |       |  X11 X12  |         
+	 *					   |  |            | | |        |   |   =   |           |        
+	 *					   |_ |_ a21  a22 _| | |_0   1 _|  _|       |_ X21 X21 _|       
+	 *					          
+	 *		2. In our implementation, pDst Matrix is used as identity matrix.    
+	 *       
+	 *		3. Begin with the first row. Let i = 1.       
+	 *       
+	 *	    4. Check to see if the pivot for row i is zero.       
+	 *		   The pivot is the element of the main diagonal that is on the current row.       
+	 *		   For instance, if working with row i, then the pivot element is aii.       
+	 *		   If the pivot is zero, exchange that row with a row below it that does not        
+	 *		   contain a zero in column i. If this is not possible, then an inverse        
+	 *		   to that matrix does not exist.       
+	 *	       
+	 *	    5. Divide every element of row i by the pivot.       
+	 *	       
+	 *	    6. For every row below and  row i, replace that row with the sum of that row and        
+	 *		   a multiple of row i so that each new element in column i below row i is zero.       
+	 *	       
+	 *	    7. Move to the next row and column and repeat steps 2 through 5 until you have zeros       
+	 *		   for every element below and above the main diagonal.        
+	 *		   		          
+	 *		8. Now an identical matrix is formed to the left of the bar(input matrix, src).       
+	 *		   Therefore, the matrix to the right of the bar is our solution(dst matrix, dst).         
+	 *----------------------------------------------------------------------------------------------------------------*/
+
+    /* Working pointer for destination matrix */
+    pInT2 = pOut;
+
+    /* Loop over the number of rows */
+    rowCnt = numRows;
+
+    /* Making the destination matrix as identity matrix */
+    while(rowCnt > 0u)
+    {
+      /* Writing all zeroes in lower triangle of the destination matrix */
+      j = numRows - rowCnt;
+      while(j > 0u)
+      {
+        *pInT2++ = 0.0f;
+        j--;
+      }
+
+      /* Writing all ones in the diagonal of the destination matrix */
+      *pInT2++ = 1.0f;
+
+      /* Writing all zeroes in upper triangle of the destination matrix */
+      j = rowCnt - 1u;
+      while(j > 0u)
+      {
+        *pInT2++ = 0.0f;
+        j--;
+      }
+
+      /* Decrement the loop counter */
+      rowCnt--;
+    }
+
+    /* Loop over the number of columns of the input matrix.     
+       All the elements in each column are processed by the row operations */
+    loopCnt = numCols;
+
+    /* Index modifier to navigate through the columns */
+    l = 0u;
+    //for(loopCnt = 0u; loopCnt < numCols; loopCnt++)   
+    while(loopCnt > 0u)
+    {
+      /* Check if the pivot element is zero..    
+       * If it is zero then interchange the row with non zero row below.   
+       * If there is no non zero element to replace in the rows below,   
+       * then the matrix is Singular. */
+
+      /* Working pointer for the input matrix that points     
+       * to the pivot element of the particular row  */
+      pInT1 = pIn + (l * numCols);
+
+      /* Working pointer for the destination matrix that points     
+       * to the pivot element of the particular row  */
+      pInT3 = pOut + (l * numCols);
+
+      /* Temporary variable to hold the pivot value */
+      in = *pInT1;
+
+      /* Destination pointer modifier */
+      k = 1u;
+
+      /* Check if the pivot element is zero */
+      if(*pInT1 == 0.0f)
+      {
+        /* Loop over the number rows present below */
+        for (i = (l + 1u); i < numRows; i++)
+        {
+          /* Update the input and destination pointers */
+          pInT2 = pInT1 + (numCols * l);
+          pInT4 = pInT3 + (numCols * k);
+
+          /* Check if there is a non zero pivot element to     
+           * replace in the rows below */
+          if(*pInT2 != 0.0f)
+          {
+            /* Loop over number of columns     
+             * to the right of the pilot element */
+            for (j = 0u; j < (numCols - l); j++)
+            {
+              /* Exchange the row elements of the input matrix */
+              Xchg = *pInT2;
+              *pInT2++ = *pInT1;
+              *pInT1++ = Xchg;
+            }
+
+            for (j = 0u; j < numCols; j++)
+            {
+              Xchg = *pInT4;
+              *pInT4++ = *pInT3;
+              *pInT3++ = Xchg;
+            }
+
+            /* Flag to indicate whether exchange is done or not */
+            flag = 1u;
+
+            /* Break after exchange is done */
+            break;
+          }
+
+          /* Update the destination pointer modifier */
+          k++;
+        }
+      }
+
+      /* Update the status if the matrix is singular */
+      if((flag != 1u) && (in == 0.0f))
+      {
+        status = ARM_MATH_SINGULAR;
+
+        break;
+      }
+
+      /* Points to the pivot row of input and destination matrices */
+      pPivotRowIn = pIn + (l * numCols);
+      pPivotRowDst = pOut + (l * numCols);
+
+      /* Temporary pointers to the pivot row pointers */
+      pInT1 = pPivotRowIn;
+      pInT2 = pPivotRowDst;
+
+      /* Pivot element of the row */
+      in = *(pIn + (l * numCols));
+
+      /* Loop over number of columns     
+       * to the right of the pilot element */
+      for (j = 0u; j < (numCols - l); j++)
+      {
+        /* Divide each element of the row of the input matrix     
+         * by the pivot element */
+        *pInT1++ = *pInT1 / in;
+      }
+      for (j = 0u; j < numCols; j++)
+      {
+        /* Divide each element of the row of the destination matrix     
+         * by the pivot element */
+        *pInT2++ = *pInT2 / in;
+      }
+
+      /* Replace the rows with the sum of that row and a multiple of row i     
+       * so that each new element in column i above row i is zero.*/
+
+      /* Temporary pointers for input and destination matrices */
+      pInT1 = pIn;
+      pInT2 = pOut;
+
+      for (i = 0u; i < numRows; i++)
+      {
+        /* Check for the pivot element */
+        if(i == l)
+        {
+          /* If the processing element is the pivot element,     
+             only the columns to the right are to be processed */
+          pInT1 += numCols - l;
+          pInT2 += numCols;
+        }
+        else
+        {
+          /* Element of the reference row */
+          in = *pInT1;
+
+          /* Working pointers for input and destination pivot rows */
+          pPRT_in = pPivotRowIn;
+          pPRT_pDst = pPivotRowDst;
+
+          /* Loop over the number of columns to the right of the pivot element,     
+             to replace the elements in the input matrix */
+          for (j = 0u; j < (numCols - l); j++)
+          {
+            /* Replace the element by the sum of that row     
+               and a multiple of the reference row  */
+            *pInT1++ = *pInT1 - (in * *pPRT_in++);
+          }
+          /* Loop over the number of columns to     
+             replace the elements in the destination matrix */
+          for (j = 0u; j < numCols; j++)
+          {
+            /* Replace the element by the sum of that row     
+               and a multiple of the reference row  */
+            *pInT2++ = *pInT2 - (in * *pPRT_pDst++);
+          }
+
+        }
+        /* Increment the temporary input pointer */
+        pInT1 = pInT1 + l;
+      }
+      /* Increment the input pointer */
+      pIn++;
+
+      /* Decrement the loop counter */
+      loopCnt--;
+      /* Increment the index modifier */
+      l++;
+    }
+
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+    /* Set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+
+    if((flag != 1u) && (in == 0.0f))
+    {
+      status = ARM_MATH_SINGULAR;
+    }
+  }
+  /* Return to application */
+  return (status);
+}
+
+/**    
+ * @} end of MatrixInv group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_mult_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_mult_f32.c
new file mode 100644
index 0000000000..a2f513628e
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_mult_f32.c
@@ -0,0 +1,284 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_mat_mult_f32.c    
+*    
+* Description:  Floating-point matrix multiplication.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+*    incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMatrix    
+ */
+
+/**    
+ * @defgroup MatrixMult Matrix Multiplication    
+ *    
+ * Multiplies two matrices.    
+ *    
+ * \image html MatrixMultiplication.gif "Multiplication of two 3 x 3 matrices"    
+    
+ * Matrix multiplication is only defined if the number of columns of the    
+ * first matrix equals the number of rows of the second matrix.    
+ * Multiplying an M x N matrix with an N x P matrix results    
+ * in an M x P matrix.    
+ * When matrix size checking is enabled, the functions check: (1) that the inner dimensions of    
+ * pSrcA and pSrcB are equal; and (2) that the size of the output    
+ * matrix equals the outer dimensions of pSrcA and pSrcB.    
+ */
+
+
+/**    
+ * @addtogroup MatrixMult    
+ * @{    
+ */
+
+/**    
+ * @brief Floating-point matrix multiplication.    
+ * @param[in]       *pSrcA points to the first input matrix structure    
+ * @param[in]       *pSrcB points to the second input matrix structure    
+ * @param[out]      *pDst points to output matrix structure    
+ * @return     		The function returns either    
+ * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.    
+ */
+
+arm_status arm_mat_mult_f32(
+  const arm_matrix_instance_f32 * pSrcA,
+  const arm_matrix_instance_f32 * pSrcB,
+  arm_matrix_instance_f32 * pDst)
+{
+  float32_t *pIn1 = pSrcA->pData;                /* input data matrix pointer A */
+  float32_t *pIn2 = pSrcB->pData;                /* input data matrix pointer B */
+  float32_t *pInA = pSrcA->pData;                /* input data matrix pointer A  */
+  float32_t *pOut = pDst->pData;                 /* output data matrix pointer */
+  float32_t *px;                                 /* Temporary output data matrix pointer */
+  float32_t sum;                                 /* Accumulator */
+  uint16_t numRowsA = pSrcA->numRows;            /* number of rows of input matrix A */
+  uint16_t numColsB = pSrcB->numCols;            /* number of columns of input matrix B */
+  uint16_t numColsA = pSrcA->numCols;            /* number of columns of input matrix A */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  float32_t in1, in2, in3, in4;
+  uint16_t col, i = 0u, j, row = numRowsA, colCnt;      /* loop counters */
+  arm_status status;                             /* status of matrix multiplication */
+
+#ifdef ARM_MATH_MATRIX_CHECK
+
+
+  /* Check for matrix mismatch condition */
+  if((pSrcA->numCols != pSrcB->numRows) ||
+     (pSrcA->numRows != pDst->numRows) || (pSrcB->numCols != pDst->numCols))
+  {
+
+    /* Set status as ARM_MATH_SIZE_MISMATCH */
+    status = ARM_MATH_SIZE_MISMATCH;
+  }
+  else
+#endif /*      #ifdef ARM_MATH_MATRIX_CHECK    */
+
+  {
+    /* The following loop performs the dot-product of each row in pSrcA with each column in pSrcB */
+    /* row loop */
+    do
+    {
+      /* Output pointer is set to starting address of the row being processed */
+      px = pOut + i;
+
+      /* For every row wise process, the column loop counter is to be initiated */
+      col = numColsB;
+
+      /* For every row wise process, the pIn2 pointer is set    
+       ** to the starting address of the pSrcB data */
+      pIn2 = pSrcB->pData;
+
+      j = 0u;
+
+      /* column loop */
+      do
+      {
+        /* Set the variable sum, that acts as accumulator, to zero */
+        sum = 0.0f;
+
+        /* Initiate the pointer pIn1 to point to the starting address of the column being processed */
+        pIn1 = pInA;
+
+        /* Apply loop unrolling and compute 4 MACs simultaneously. */
+        colCnt = numColsA >> 2u;
+
+        /* matrix multiplication        */
+        while(colCnt > 0u)
+        {
+          /* c(m,n) = a(1,1)*b(1,1) + a(1,2) * b(2,1) + .... + a(m,p)*b(p,n) */
+          in3 = *pIn2;
+          pIn2 += numColsB;
+          in1 = pIn1[0];
+          in2 = pIn1[1];
+          sum += in1 * in3;
+          in4 = *pIn2;
+          pIn2 += numColsB;
+          sum += in2 * in4;
+
+          in3 = *pIn2;
+          pIn2 += numColsB;
+          in1 = pIn1[2];
+          in2 = pIn1[3];
+          sum += in1 * in3;
+          in4 = *pIn2;
+          pIn2 += numColsB;
+          sum += in2 * in4;
+          pIn1 += 4u;
+
+          /* Decrement the loop count */
+          colCnt--;
+        }
+
+        /* If the columns of pSrcA is not a multiple of 4, compute any remaining MACs here.    
+         ** No loop unrolling is used. */
+        colCnt = numColsA % 0x4u;
+
+        while(colCnt > 0u)
+        {
+          /* c(m,n) = a(1,1)*b(1,1) + a(1,2) * b(2,1) + .... + a(m,p)*b(p,n) */
+          sum += *pIn1++ * (*pIn2);
+          pIn2 += numColsB;
+
+          /* Decrement the loop counter */
+          colCnt--;
+        }
+
+        /* Store the result in the destination buffer */
+        *px++ = sum;
+
+        /* Update the pointer pIn2 to point to the  starting address of the next column */
+        j++;
+        pIn2 = pSrcB->pData + j;
+
+        /* Decrement the column loop counter */
+        col--;
+
+      } while(col > 0u);
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  float32_t *pInB = pSrcB->pData;                /* input data matrix pointer B */
+  uint16_t col, i = 0u, row = numRowsA, colCnt;  /* loop counters */
+  arm_status status;                             /* status of matrix multiplication */
+
+#ifdef ARM_MATH_MATRIX_CHECK
+
+  /* Check for matrix mismatch condition */
+  if((pSrcA->numCols != pSrcB->numRows) ||
+     (pSrcA->numRows != pDst->numRows) || (pSrcB->numCols != pDst->numCols))
+  {
+
+    /* Set status as ARM_MATH_SIZE_MISMATCH */
+    status = ARM_MATH_SIZE_MISMATCH;
+  }
+  else
+#endif /*      #ifdef ARM_MATH_MATRIX_CHECK    */
+
+  {
+    /* The following loop performs the dot-product of each row in pInA with each column in pInB */
+    /* row loop */
+    do
+    {
+      /* Output pointer is set to starting address of the row being processed */
+      px = pOut + i;
+
+      /* For every row wise process, the column loop counter is to be initiated */
+      col = numColsB;
+
+      /* For every row wise process, the pIn2 pointer is set     
+       ** to the starting address of the pSrcB data */
+      pIn2 = pSrcB->pData;
+
+      /* column loop */
+      do
+      {
+        /* Set the variable sum, that acts as accumulator, to zero */
+        sum = 0.0f;
+
+        /* Initialize the pointer pIn1 to point to the starting address of the row being processed */
+        pIn1 = pInA;
+
+        /* Matrix A columns number of MAC operations are to be performed */
+        colCnt = numColsA;
+
+        while(colCnt > 0u)
+        {
+          /* c(m,n) = a(1,1)*b(1,1) + a(1,2) * b(2,1) + .... + a(m,p)*b(p,n) */
+          sum += *pIn1++ * (*pIn2);
+          pIn2 += numColsB;
+
+          /* Decrement the loop counter */
+          colCnt--;
+        }
+
+        /* Store the result in the destination buffer */
+        *px++ = sum;
+
+        /* Decrement the column loop counter */
+        col--;
+
+        /* Update the pointer pIn2 to point to the  starting address of the next column */
+        pIn2 = pInB + (numColsB - col);
+
+      } while(col > 0u);
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+      /* Update the pointer pInA to point to the  starting address of the next row */
+      i = i + numColsB;
+      pInA = pInA + numColsA;
+
+      /* Decrement the row loop counter */
+      row--;
+
+    } while(row > 0u);
+    /* Set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+  }
+
+  /* Return to application */
+  return (status);
+}
+
+/**    
+ * @} end of MatrixMult group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_mult_fast_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_mult_fast_q15.c
new file mode 100644
index 0000000000..a88e3cdd1a
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_mult_fast_q15.c
@@ -0,0 +1,361 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_mat_mult_fast_q15.c    
+*    
+* Description:	 Q15 matrix multiplication (fast variant)    
+*    
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMatrix    
+ */
+
+/**    
+ * @addtogroup MatrixMult    
+ * @{    
+ */
+
+
+/**    
+ * @brief Q15 matrix multiplication (fast variant) for Cortex-M3 and Cortex-M4    
+ * @param[in]       *pSrcA points to the first input matrix structure    
+ * @param[in]       *pSrcB points to the second input matrix structure    
+ * @param[out]      *pDst points to output matrix structure    
+ * @param[in]		*pState points to the array for storing intermediate results    
+ * @return     		The function returns either    
+ * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.    
+ *    
+ * @details    
+ * Scaling and Overflow Behavior:    
+ *    
+ * \par    
+ * The difference between the function arm_mat_mult_q15() and this fast variant is that    
+ * the fast variant use a 32-bit rather than a 64-bit accumulator.    
+ * The result of each 1.15 x 1.15 multiplication is truncated to        
+ * 2.30 format. These intermediate results are accumulated in a 32-bit register in 2.30        
+ * format. Finally, the accumulator is saturated and converted to a 1.15 result.        
+ *        
+ * \par        
+ * The fast version has the same overflow behavior as the standard version but provides        
+ * less precision since it discards the low 16 bits of each multiplication result.        
+ * In order to avoid overflows completely the input signals must be scaled down.        
+ * Scale down one of the input matrices by log2(numColsA) bits to        
+ * avoid overflows, as a total of numColsA additions are computed internally for each        
+ * output element.        
+ *        
+ * \par    
+ * See arm_mat_mult_q15() for a slower implementation of this function    
+ * which uses 64-bit accumulation to provide higher precision.    
+ */
+
+arm_status arm_mat_mult_fast_q15(
+  const arm_matrix_instance_q15 * pSrcA,
+  const arm_matrix_instance_q15 * pSrcB,
+  arm_matrix_instance_q15 * pDst,
+  q15_t * pState)
+{
+  q31_t sum;                                     /* accumulator */
+  q15_t *pSrcBT = pState;                        /* input data matrix pointer for transpose */
+  q15_t *pInA = pSrcA->pData;                    /* input data matrix pointer A of Q15 type */
+  q15_t *pInB = pSrcB->pData;                    /* input data matrix pointer B of Q15 type */
+  q15_t *px;                                     /* Temporary output data matrix pointer */
+  uint16_t numRowsA = pSrcA->numRows;            /* number of rows of input matrix A    */
+  uint16_t numColsB = pSrcB->numCols;            /* number of columns of input matrix B */
+  uint16_t numColsA = pSrcA->numCols;            /* number of columns of input matrix A */
+  uint16_t numRowsB = pSrcB->numRows;            /* number of rows of input matrix A    */
+  uint16_t col, i = 0u, row = numRowsB, colCnt;  /* loop counters */
+  arm_status status;                             /* status of matrix multiplication */
+
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+  q31_t in;                                      /* Temporary variable to hold the input value */
+  q31_t inA1, inA2, inB1, inB2;
+
+#else
+
+  q15_t in;                                      /* Temporary variable to hold the input value */
+  q15_t inA1, inA2, inB1, inB2;
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+#ifdef ARM_MATH_MATRIX_CHECK
+  /* Check for matrix mismatch condition */
+  if((pSrcA->numCols != pSrcB->numRows) ||
+     (pSrcA->numRows != pDst->numRows) || (pSrcB->numCols != pDst->numCols))
+  {
+    /* Set status as ARM_MATH_SIZE_MISMATCH */
+    status = ARM_MATH_SIZE_MISMATCH;
+  }
+  else
+#endif
+  {
+    /* Matrix transpose */
+    do
+    {
+      /* Apply loop unrolling and exchange the columns with row elements */
+      col = numColsB >> 2;
+
+      /* The pointer px is set to starting address of the column being processed */
+      px = pSrcBT + i;
+
+      /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.        
+       ** a second loop below computes the remaining 1 to 3 samples. */
+      while(col > 0u)
+      {
+#ifndef UNALIGNED_SUPPORT_DISABLE
+        /* Read two elements from the row */
+        in = *__SIMD32(pInB)++;
+
+        /* Unpack and store one element in the destination */
+#ifndef ARM_MATH_BIG_ENDIAN
+
+        *px = (q15_t) in;
+
+#else
+
+        *px = (q15_t) ((in & (q31_t) 0xffff0000) >> 16);
+
+#endif /*    #ifndef ARM_MATH_BIG_ENDIAN    */
+
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += numRowsB;
+
+        /* Unpack and store the second element in the destination */
+#ifndef ARM_MATH_BIG_ENDIAN
+
+        *px = (q15_t) ((in & (q31_t) 0xffff0000) >> 16);
+
+#else
+
+        *px = (q15_t) in;
+
+#endif /*    #ifndef ARM_MATH_BIG_ENDIAN    */
+
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += numRowsB;
+
+        /* Read two elements from the row */
+        in = *__SIMD32(pInB)++;
+
+        /* Unpack and store one element in the destination */
+#ifndef ARM_MATH_BIG_ENDIAN
+
+        *px = (q15_t) in;
+
+#else
+
+        *px = (q15_t) ((in & (q31_t) 0xffff0000) >> 16);
+
+#endif /*    #ifndef ARM_MATH_BIG_ENDIAN    */
+
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += numRowsB;
+
+        /* Unpack and store the second element in the destination */
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+        *px = (q15_t) ((in & (q31_t) 0xffff0000) >> 16);
+
+#else
+
+        *px = (q15_t) in;
+
+#endif /*    #ifndef ARM_MATH_BIG_ENDIAN    */
+
+#else
+
+        /* Read one element from the row */
+        in = *pInB++;
+
+        /* Store one element in the destination */
+        *px = in;
+ 
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += numRowsB;
+
+        /* Read one element from the row */
+        in = *pInB++;
+
+        /* Store one element in the destination */
+        *px = in;
+ 
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += numRowsB;
+
+        /* Read one element from the row */
+        in = *pInB++;
+
+        /* Store one element in the destination */
+        *px = in;
+ 
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += numRowsB;
+
+        /* Read one element from the row */
+        in = *pInB++;
+
+        /* Store one element in the destination */
+        *px = in;
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+        
+		/* Update the pointer px to point to the next row of the transposed matrix */
+        px += numRowsB;
+
+        /* Decrement the column loop counter */
+        col--;
+      }
+
+      /* If the columns of pSrcB is not a multiple of 4, compute any remaining output samples here.        
+       ** No loop unrolling is used. */
+      col = numColsB % 0x4u;
+
+      while(col > 0u)
+      {
+        /* Read and store the input element in the destination */
+        *px = *pInB++;
+
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += numRowsB;
+
+        /* Decrement the column loop counter */
+        col--;
+      }
+
+      i++;
+
+      /* Decrement the row loop counter */
+      row--;
+
+    } while(row > 0u);
+
+    /* Reset the variables for the usage in the following multiplication process */
+    row = numRowsA;
+    i = 0u;
+    px = pDst->pData;
+
+    /* The following loop performs the dot-product of each row in pSrcA with each column in pSrcB */
+    /* row loop */
+    do
+    {
+      /* For every row wise process, the column loop counter is to be initiated */
+      col = numColsB;
+
+      /* For every row wise process, the pIn2 pointer is set        
+       ** to the starting address of the transposed pSrcB data */
+      pInB = pSrcBT;
+
+      /* column loop */
+      do
+      {
+        /* Set the variable sum, that acts as accumulator, to zero */
+        sum = 0;
+
+        /* Apply loop unrolling and compute 2 MACs simultaneously. */
+        colCnt = numColsA >> 2;
+
+        /* Initiate the pointer pIn1 to point to the starting address of the column being processed */
+        pInA = pSrcA->pData + i;
+
+        /* matrix multiplication */
+        while(colCnt > 0u)
+        {
+          /* c(m,n) = a(1,1)*b(1,1) + a(1,2) * b(2,1) + .... + a(m,p)*b(p,n) */
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+          inA1 = *__SIMD32(pInA)++;
+          inB1 = *__SIMD32(pInB)++;
+          inA2 = *__SIMD32(pInA)++;
+          inB2 = *__SIMD32(pInB)++;
+
+          sum = __SMLAD(inA1, inB1, sum);
+          sum = __SMLAD(inA2, inB2, sum);
+
+#else
+
+          inA1 = *pInA++;
+          inB1 = *pInB++;
+          inA2 = *pInA++;
+          sum += inA1 * inB1;
+          inB2 = *pInB++;
+
+          inA1 = *pInA++;
+          inB1 = *pInB++;
+          sum += inA2 * inB2;
+          inA2 = *pInA++;
+          inB2 = *pInB++;
+
+          sum += inA1 * inB1;
+          sum += inA2 * inB2;
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+          /* Decrement the loop counter */
+          colCnt--;
+        }
+
+        /* process odd column samples */
+        colCnt = numColsA % 0x4u;
+
+        while(colCnt > 0u)
+        {
+          /* c(m,n) = a(1,1)*b(1,1) + a(1,2) * b(2,1) + .... + a(m,p)*b(p,n) */
+          sum += (q31_t) (*pInA++) * (*pInB++);
+
+          colCnt--;
+        }
+
+        /* Saturate and store the result in the destination buffer */
+        *px = (q15_t) (sum >> 15);
+        px++;
+
+        /* Decrement the column loop counter */
+        col--;
+
+      } while(col > 0u);
+
+      i = i + numColsA;
+
+      /* Decrement the row loop counter */
+      row--;
+
+    } while(row > 0u);
+
+    /* set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+  }
+
+  /* Return to application */
+  return (status);
+}
+
+/**        
+ * @} end of MatrixMult group        
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_mult_fast_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_mult_fast_q31.c
new file mode 100644
index 0000000000..7fdbb1cb89
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_mult_fast_q31.c
@@ -0,0 +1,218 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_mat_mult_fast_q31.c    
+*    
+* Description:	 Q31 matrix multiplication (fast variant).    
+*    
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMatrix    
+ */
+
+/**    
+ * @addtogroup MatrixMult    
+ * @{    
+ */
+
+/**    
+ * @brief Q31 matrix multiplication (fast variant) for Cortex-M3 and Cortex-M4    
+ * @param[in]       *pSrcA points to the first input matrix structure    
+ * @param[in]       *pSrcB points to the second input matrix structure    
+ * @param[out]      *pDst points to output matrix structure    
+ * @return     		The function returns either    
+ * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.    
+ *    
+ * @details    
+ * Scaling and Overflow Behavior:    
+ *    
+ * \par    
+ * The difference between the function arm_mat_mult_q31() and this fast variant is that    
+ * the fast variant use a 32-bit rather than a 64-bit accumulator.    
+ * The result of each 1.31 x 1.31 multiplication is truncated to    
+ * 2.30 format. These intermediate results are accumulated in a 32-bit register in 2.30    
+ * format. Finally, the accumulator is saturated and converted to a 1.31 result.    
+ *    
+ * \par    
+ * The fast version has the same overflow behavior as the standard version but provides    
+ * less precision since it discards the low 32 bits of each multiplication result.    
+ * In order to avoid overflows completely the input signals must be scaled down.    
+ * Scale down one of the input matrices by log2(numColsA) bits to    
+ * avoid overflows, as a total of numColsA additions are computed internally for each    
+ * output element.    
+ *    
+ * \par    
+ * See arm_mat_mult_q31() for a slower implementation of this function    
+ * which uses 64-bit accumulation to provide higher precision.    
+ */
+
+arm_status arm_mat_mult_fast_q31(
+  const arm_matrix_instance_q31 * pSrcA,
+  const arm_matrix_instance_q31 * pSrcB,
+  arm_matrix_instance_q31 * pDst)
+{
+  q31_t *pIn1 = pSrcA->pData;                    /* input data matrix pointer A */
+  q31_t *pIn2 = pSrcB->pData;                    /* input data matrix pointer B */
+  q31_t *pInA = pSrcA->pData;                    /* input data matrix pointer A */
+//  q31_t *pSrcB = pSrcB->pData;                    /* input data matrix pointer B */    
+  q31_t *pOut = pDst->pData;                     /* output data matrix pointer */
+  q31_t *px;                                     /* Temporary output data matrix pointer */
+  q31_t sum;                                     /* Accumulator */
+  uint16_t numRowsA = pSrcA->numRows;            /* number of rows of input matrix A    */
+  uint16_t numColsB = pSrcB->numCols;            /* number of columns of input matrix B */
+  uint16_t numColsA = pSrcA->numCols;            /* number of columns of input matrix A */
+  uint16_t col, i = 0u, j, row = numRowsA, colCnt;      /* loop counters */
+  arm_status status;                             /* status of matrix multiplication */
+  q31_t inA1, inA2, inA3, inA4, inB1, inB2, inB3, inB4;
+
+#ifdef ARM_MATH_MATRIX_CHECK
+
+
+  /* Check for matrix mismatch condition */
+  if((pSrcA->numCols != pSrcB->numRows) ||
+     (pSrcA->numRows != pDst->numRows) || (pSrcB->numCols != pDst->numCols))
+  {
+    /* Set status as ARM_MATH_SIZE_MISMATCH */
+    status = ARM_MATH_SIZE_MISMATCH;
+  }
+  else
+#endif /*      #ifdef ARM_MATH_MATRIX_CHECK    */
+
+  {
+    /* The following loop performs the dot-product of each row in pSrcA with each column in pSrcB */
+    /* row loop */
+    do
+    {
+      /* Output pointer is set to starting address of the row being processed */
+      px = pOut + i;
+
+      /* For every row wise process, the column loop counter is to be initiated */
+      col = numColsB;
+
+      /* For every row wise process, the pIn2 pointer is set    
+       ** to the starting address of the pSrcB data */
+      pIn2 = pSrcB->pData;
+
+      j = 0u;
+
+      /* column loop */
+      do
+      {
+        /* Set the variable sum, that acts as accumulator, to zero */
+        sum = 0;
+
+        /* Initiate the pointer pIn1 to point to the starting address of pInA */
+        pIn1 = pInA;
+
+        /* Apply loop unrolling and compute 4 MACs simultaneously. */
+        colCnt = numColsA >> 2;
+
+
+        /* matrix multiplication */
+        while(colCnt > 0u)
+        {
+          /* c(m,n) = a(1,1)*b(1,1) + a(1,2) * b(2,1) + .... + a(m,p)*b(p,n) */
+          /* Perform the multiply-accumulates */
+          inB1 = *pIn2;
+          pIn2 += numColsB;
+
+          inA1 = pIn1[0];
+          inA2 = pIn1[1];
+
+          inB2 = *pIn2;
+          pIn2 += numColsB;
+
+          inB3 = *pIn2;
+          pIn2 += numColsB;
+
+          sum = (q31_t) ((((q63_t) sum << 32) + ((q63_t) inA1 * inB1)) >> 32);
+          sum = (q31_t) ((((q63_t) sum << 32) + ((q63_t) inA2 * inB2)) >> 32);
+
+          inA3 = pIn1[2];
+          inA4 = pIn1[3];
+
+          inB4 = *pIn2;
+          pIn2 += numColsB;
+
+          sum = (q31_t) ((((q63_t) sum << 32) + ((q63_t) inA3 * inB3)) >> 32);
+          sum = (q31_t) ((((q63_t) sum << 32) + ((q63_t) inA4 * inB4)) >> 32);
+
+          pIn1 += 4u;
+
+          /* Decrement the loop counter */
+          colCnt--;
+        }
+
+        /* If the columns of pSrcA is not a multiple of 4, compute any remaining output samples here.    
+         ** No loop unrolling is used. */
+        colCnt = numColsA % 0x4u;
+
+        while(colCnt > 0u)
+        {
+          /* c(m,n) = a(1,1)*b(1,1) + a(1,2) * b(2,1) + .... + a(m,p)*b(p,n) */
+          /* Perform the multiply-accumulates */
+          sum = (q31_t) ((((q63_t) sum << 32) +
+                          ((q63_t) * pIn1++ * (*pIn2))) >> 32);
+          pIn2 += numColsB;
+
+          /* Decrement the loop counter */
+          colCnt--;
+        }
+
+        /* Convert the result from 2.30 to 1.31 format and store in destination buffer */
+        *px++ = sum << 1;
+
+        /* Update the pointer pIn2 to point to the  starting address of the next column */
+        j++;
+        pIn2 = pSrcB->pData + j;
+
+        /* Decrement the column loop counter */
+        col--;
+
+      } while(col > 0u);
+
+      /* Update the pointer pInA to point to the  starting address of the next row */
+      i = i + numColsB;
+      pInA = pInA + numColsA;
+
+      /* Decrement the row loop counter */
+      row--;
+
+    } while(row > 0u);
+
+    /* set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+  }
+  /* Return to application */
+  return (status);
+}
+
+/**    
+ * @} end of MatrixMult group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_mult_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_mult_q15.c
new file mode 100644
index 0000000000..b48d204ed5
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_mult_q15.c
@@ -0,0 +1,467 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_mat_mult_q15.c    
+*    
+* Description:	 Q15 matrix multiplication.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+*    incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMatrix    
+ */
+
+/**    
+ * @addtogroup MatrixMult    
+ * @{    
+ */
+
+
+/**    
+ * @brief Q15 matrix multiplication    
+ * @param[in]       *pSrcA points to the first input matrix structure    
+ * @param[in]       *pSrcB points to the second input matrix structure    
+ * @param[out]      *pDst points to output matrix structure    
+ * @param[in]		*pState points to the array for storing intermediate results   
+ * @return     		The function returns either    
+ * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.    
+ *    
+ * @details    
+ * Scaling and Overflow Behavior:    
+ *    
+ * \par    
+ * The function is implemented using a 64-bit internal accumulator. The inputs to the    
+ * multiplications are in 1.15 format and multiplications yield a 2.30 result.    
+ * The 2.30 intermediate    
+ * results are accumulated in a 64-bit accumulator in 34.30 format. This approach    
+ * provides 33 guard bits and there is no risk of overflow. The 34.30 result is then    
+ * truncated to 34.15 format by discarding the low 15 bits and then saturated to    
+ * 1.15 format.    
+ *    
+ * \par    
+ * Refer to arm_mat_mult_fast_q15() for a faster but less precise version of this function for Cortex-M3 and Cortex-M4.    
+ *    
+ */
+
+arm_status arm_mat_mult_q15(
+  const arm_matrix_instance_q15 * pSrcA,
+  const arm_matrix_instance_q15 * pSrcB,
+  arm_matrix_instance_q15 * pDst,
+  q15_t * pState)
+{
+  q63_t sum;                                     /* accumulator */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q15_t *pSrcBT = pState;                        /* input data matrix pointer for transpose */
+  q15_t *pInA = pSrcA->pData;                    /* input data matrix pointer A of Q15 type */
+  q15_t *pInB = pSrcB->pData;                    /* input data matrix pointer B of Q15 type */
+  q15_t *px;                                     /* Temporary output data matrix pointer */
+  uint16_t numRowsA = pSrcA->numRows;            /* number of rows of input matrix A    */
+  uint16_t numColsB = pSrcB->numCols;            /* number of columns of input matrix B */
+  uint16_t numColsA = pSrcA->numCols;            /* number of columns of input matrix A */
+  uint16_t numRowsB = pSrcB->numRows;            /* number of rows of input matrix A    */
+  uint16_t col, i = 0u, row = numRowsB, colCnt;  /* loop counters */
+  arm_status status;                             /* status of matrix multiplication */
+
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+  q31_t in;                                      /* Temporary variable to hold the input value */
+  q31_t pSourceA1, pSourceB1, pSourceA2, pSourceB2;
+
+#else
+
+  q15_t in;                                      /* Temporary variable to hold the input value */
+  q15_t inA1, inB1, inA2, inB2;
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+#ifdef ARM_MATH_MATRIX_CHECK
+  /* Check for matrix mismatch condition */
+  if((pSrcA->numCols != pSrcB->numRows) ||
+     (pSrcA->numRows != pDst->numRows) || (pSrcB->numCols != pDst->numCols))
+  {
+    /* Set status as ARM_MATH_SIZE_MISMATCH */
+    status = ARM_MATH_SIZE_MISMATCH;
+  }
+  else
+#endif /*    #ifdef ARM_MATH_MATRIX_CHECK    */
+  {
+    /* Matrix transpose */
+    do
+    {
+      /* Apply loop unrolling and exchange the columns with row elements */
+      col = numColsB >> 2;
+
+      /* The pointer px is set to starting address of the column being processed */
+      px = pSrcBT + i;
+
+      /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.        
+       ** a second loop below computes the remaining 1 to 3 samples. */
+      while(col > 0u)
+      {
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+        /* Read two elements from the row */
+        in = *__SIMD32(pInB)++;
+
+        /* Unpack and store one element in the destination */
+#ifndef ARM_MATH_BIG_ENDIAN
+
+        *px = (q15_t) in;
+
+#else
+
+        *px = (q15_t) ((in & (q31_t) 0xffff0000) >> 16);
+
+#endif /*    #ifndef ARM_MATH_BIG_ENDIAN    */
+
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += numRowsB;
+
+        /* Unpack and store the second element in the destination */
+#ifndef ARM_MATH_BIG_ENDIAN
+
+        *px = (q15_t) ((in & (q31_t) 0xffff0000) >> 16);
+
+#else
+
+        *px = (q15_t) in;
+
+#endif /*    #ifndef ARM_MATH_BIG_ENDIAN    */
+
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += numRowsB;
+
+        /* Read two elements from the row */
+        in = *__SIMD32(pInB)++;
+
+        /* Unpack and store one element in the destination */
+#ifndef ARM_MATH_BIG_ENDIAN
+
+        *px = (q15_t) in;
+
+#else
+
+        *px = (q15_t) ((in & (q31_t) 0xffff0000) >> 16);
+
+#endif /*    #ifndef ARM_MATH_BIG_ENDIAN    */
+
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += numRowsB;
+
+        /* Unpack and store the second element in the destination */
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+        *px = (q15_t) ((in & (q31_t) 0xffff0000) >> 16);
+
+#else
+
+        *px = (q15_t) in;
+
+#endif /*    #ifndef ARM_MATH_BIG_ENDIAN    */
+
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += numRowsB;
+
+#else
+
+        /* Read one element from the row */
+        in = *pInB++;
+
+        /* Store one element in the destination */
+        *px = in;
+ 
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += numRowsB;
+
+        /* Read one element from the row */
+        in = *pInB++;
+
+        /* Store one element in the destination */
+        *px = in;
+ 
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += numRowsB;
+
+        /* Read one element from the row */
+        in = *pInB++;
+
+        /* Store one element in the destination */
+        *px = in;
+ 
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += numRowsB;
+
+        /* Read one element from the row */
+        in = *pInB++;
+
+        /* Store one element in the destination */
+        *px = in;
+ 
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += numRowsB;
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+       /* Decrement the column loop counter */
+        col--;
+      }
+
+      /* If the columns of pSrcB is not a multiple of 4, compute any remaining output samples here.        
+       ** No loop unrolling is used. */
+      col = numColsB % 0x4u;
+
+      while(col > 0u)
+      {
+        /* Read and store the input element in the destination */
+        *px = *pInB++;
+
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += numRowsB;
+
+        /* Decrement the column loop counter */
+        col--;
+      }
+
+      i++;
+
+      /* Decrement the row loop counter */
+      row--;
+
+    } while(row > 0u);
+
+    /* Reset the variables for the usage in the following multiplication process */
+    row = numRowsA;
+    i = 0u;
+    px = pDst->pData;
+
+    /* The following loop performs the dot-product of each row in pSrcA with each column in pSrcB */
+    /* row loop */
+    do
+    {
+      /* For every row wise process, the column loop counter is to be initiated */
+      col = numColsB;
+
+      /* For every row wise process, the pIn2 pointer is set        
+       ** to the starting address of the transposed pSrcB data */
+      pInB = pSrcBT;
+
+      /* column loop */
+      do
+      {
+        /* Set the variable sum, that acts as accumulator, to zero */
+        sum = 0;
+
+        /* Apply loop unrolling and compute 2 MACs simultaneously. */
+        colCnt = numColsA >> 2;
+
+        /* Initiate the pointer pIn1 to point to the starting address of the column being processed */
+        pInA = pSrcA->pData + i;
+
+
+        /* matrix multiplication */
+        while(colCnt > 0u)
+        {
+          /* c(m,n) = a(1,1)*b(1,1) + a(1,2) * b(2,1) + .... + a(m,p)*b(p,n) */
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+          /* read real and imag values from pSrcA and pSrcB buffer */
+          pSourceA1 = *__SIMD32(pInA)++;
+          pSourceB1 = *__SIMD32(pInB)++;
+
+          pSourceA2 = *__SIMD32(pInA)++;
+          pSourceB2 = *__SIMD32(pInB)++;
+
+          /* Multiply and Accumlates */
+          sum = __SMLALD(pSourceA1, pSourceB1, sum);
+          sum = __SMLALD(pSourceA2, pSourceB2, sum);
+
+#else
+          /* read real and imag values from pSrcA and pSrcB buffer */
+          inA1 = *pInA++;
+          inB1 = *pInB++;
+          inA2 = *pInA++;
+          /* Multiply and Accumlates */
+          sum += inA1 * inB1;
+          inB2 = *pInB++;
+
+          inA1 = *pInA++;
+          inB1 = *pInB++;
+          /* Multiply and Accumlates */
+          sum += inA2 * inB2;
+          inA2 = *pInA++;
+          inB2 = *pInB++;
+
+          /* Multiply and Accumlates */
+          sum += inA1 * inB1;
+          sum += inA2 * inB2;
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+          /* Decrement the loop counter */
+          colCnt--;
+        }
+
+        /* process remaining column samples */
+        colCnt = numColsA & 3u;
+
+        while(colCnt > 0u)
+        {
+          /* c(m,n) = a(1,1)*b(1,1) + a(1,2) * b(2,1) + .... + a(m,p)*b(p,n) */
+          sum += *pInA++ * *pInB++;
+
+          /* Decrement the loop counter */
+          colCnt--;
+        }
+
+        /* Saturate and store the result in the destination buffer */
+        *px = (q15_t) (__SSAT((sum >> 15), 16));
+        px++;
+
+        /* Decrement the column loop counter */
+        col--;
+
+      } while(col > 0u);
+
+      i = i + numColsA;
+
+      /* Decrement the row loop counter */
+      row--;
+
+    } while(row > 0u);
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  q15_t *pIn1 = pSrcA->pData;                    /* input data matrix pointer A */
+  q15_t *pIn2 = pSrcB->pData;                    /* input data matrix pointer B */
+  q15_t *pInA = pSrcA->pData;                    /* input data matrix pointer A of Q15 type */
+  q15_t *pInB = pSrcB->pData;                    /* input data matrix pointer B of Q15 type */
+  q15_t *pOut = pDst->pData;                     /* output data matrix pointer */
+  q15_t *px;                                     /* Temporary output data matrix pointer */
+  uint16_t numColsB = pSrcB->numCols;            /* number of columns of input matrix B */
+  uint16_t numColsA = pSrcA->numCols;            /* number of columns of input matrix A */
+  uint16_t numRowsA = pSrcA->numRows;            /* number of rows of input matrix A    */
+  uint16_t col, i = 0u, row = numRowsA, colCnt;  /* loop counters */
+  arm_status status;                             /* status of matrix multiplication */
+
+#ifdef ARM_MATH_MATRIX_CHECK
+
+  /* Check for matrix mismatch condition */
+  if((pSrcA->numCols != pSrcB->numRows) ||
+     (pSrcA->numRows != pDst->numRows) || (pSrcB->numCols != pDst->numCols))
+  {
+    /* Set status as ARM_MATH_SIZE_MISMATCH */
+    status = ARM_MATH_SIZE_MISMATCH;
+  }
+  else
+#endif /*    #ifdef ARM_MATH_MATRIX_CHECK    */
+
+  {
+    /* The following loop performs the dot-product of each row in pSrcA with each column in pSrcB */
+    /* row loop */
+    do
+    {
+      /* Output pointer is set to starting address of the row being processed */
+      px = pOut + i;
+
+      /* For every row wise process, the column loop counter is to be initiated */
+      col = numColsB;
+
+      /* For every row wise process, the pIn2 pointer is set          
+       ** to the starting address of the pSrcB data */
+      pIn2 = pSrcB->pData;
+
+      /* column loop */
+      do
+      {
+        /* Set the variable sum, that acts as accumulator, to zero */
+        sum = 0;
+
+        /* Initiate the pointer pIn1 to point to the starting address of pSrcA */
+        pIn1 = pInA;
+
+        /* Matrix A columns number of MAC operations are to be performed */
+        colCnt = numColsA;
+
+        /* matrix multiplication */
+        while(colCnt > 0u)
+        {
+          /* c(m,n) = a(1,1)*b(1,1) + a(1,2) * b(2,1) + .... + a(m,p)*b(p,n) */
+          /* Perform the multiply-accumulates */
+          sum += (q31_t) * pIn1++ * *pIn2;
+          pIn2 += numColsB;
+
+          /* Decrement the loop counter */
+          colCnt--;
+        }
+
+        /* Convert the result from 34.30 to 1.15 format and store the saturated value in destination buffer */
+        /* Saturate and store the result in the destination buffer */
+        *px++ = (q15_t) __SSAT((sum >> 15), 16);
+
+        /* Decrement the column loop counter */
+        col--;
+
+        /* Update the pointer pIn2 to point to the  starting address of the next column */
+        pIn2 = pInB + (numColsB - col);
+
+      } while(col > 0u);
+
+      /* Update the pointer pSrcA to point to the  starting address of the next row */
+      i = i + numColsB;
+      pInA = pInA + numColsA;
+
+      /* Decrement the row loop counter */
+      row--;
+
+    } while(row > 0u);
+
+#endif /* #ifndef ARM_MATH_CM0 */
+    /* set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+  }
+
+  /* Return to application */
+  return (status);
+}
+
+/**        
+ * @} end of MatrixMult group        
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_mult_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_mult_q31.c
new file mode 100644
index 0000000000..eb76522042
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_mult_q31.c
@@ -0,0 +1,292 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_mat_mult_q31.c    
+*    
+* Description:	 Q31 matrix multiplication.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+*    incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMatrix    
+ */
+
+/**    
+ * @addtogroup MatrixMult    
+ * @{    
+ */
+
+/**    
+ * @brief Q31 matrix multiplication    
+ * @param[in]       *pSrcA points to the first input matrix structure    
+ * @param[in]       *pSrcB points to the second input matrix structure    
+ * @param[out]      *pDst points to output matrix structure    
+ * @return     		The function returns either    
+ * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.    
+ *    
+ * @details    
+ * Scaling and Overflow Behavior:    
+ *    
+ * \par    
+ * The function is implemented using an internal 64-bit accumulator.    
+ * The accumulator has a 2.62 format and maintains full precision of the intermediate    
+ * multiplication results but provides only a single guard bit. There is no saturation    
+ * on intermediate additions. Thus, if the accumulator overflows it wraps around and    
+ * distorts the result. The input signals should be scaled down to avoid intermediate    
+ * overflows. The input is thus scaled down by log2(numColsA) bits    
+ * to avoid overflows, as a total of numColsA additions are performed internally.    
+ * The 2.62 accumulator is right shifted by 31 bits and saturated to 1.31 format to yield the final result.    
+ *    
+ * \par    
+ * See arm_mat_mult_fast_q31() for a faster but less precise implementation of this function for Cortex-M3 and Cortex-M4.    
+ *    
+ */
+
+arm_status arm_mat_mult_q31(
+  const arm_matrix_instance_q31 * pSrcA,
+  const arm_matrix_instance_q31 * pSrcB,
+  arm_matrix_instance_q31 * pDst)
+{
+  q31_t *pIn1 = pSrcA->pData;                    /* input data matrix pointer A */
+  q31_t *pIn2 = pSrcB->pData;                    /* input data matrix pointer B */
+  q31_t *pInA = pSrcA->pData;                    /* input data matrix pointer A */
+  q31_t *pOut = pDst->pData;                     /* output data matrix pointer */
+  q31_t *px;                                     /* Temporary output data matrix pointer */
+  q63_t sum;                                     /* Accumulator */
+  uint16_t numRowsA = pSrcA->numRows;            /* number of rows of input matrix A    */
+  uint16_t numColsB = pSrcB->numCols;            /* number of columns of input matrix B */
+  uint16_t numColsA = pSrcA->numCols;            /* number of columns of input matrix A */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  uint16_t col, i = 0u, j, row = numRowsA, colCnt;      /* loop counters */
+  arm_status status;                             /* status of matrix multiplication */
+  q31_t a0, a1, a2, a3, b0, b1, b2, b3;
+
+#ifdef ARM_MATH_MATRIX_CHECK
+
+
+  /* Check for matrix mismatch condition */
+  if((pSrcA->numCols != pSrcB->numRows) ||
+     (pSrcA->numRows != pDst->numRows) || (pSrcB->numCols != pDst->numCols))
+  {
+    /* Set status as ARM_MATH_SIZE_MISMATCH */
+    status = ARM_MATH_SIZE_MISMATCH;
+  }
+  else
+#endif /*    #ifdef ARM_MATH_MATRIX_CHECK    */
+
+  {
+    /* The following loop performs the dot-product of each row in pSrcA with each column in pSrcB */
+    /* row loop */
+    do
+    {
+      /* Output pointer is set to starting address of the row being processed */
+      px = pOut + i;
+
+      /* For every row wise process, the column loop counter is to be initiated */
+      col = numColsB;
+
+      /* For every row wise process, the pIn2 pointer is set    
+       ** to the starting address of the pSrcB data */
+      pIn2 = pSrcB->pData;
+
+      j = 0u;
+
+      /* column loop */
+      do
+      {
+        /* Set the variable sum, that acts as accumulator, to zero */
+        sum = 0;
+
+        /* Initiate the pointer pIn1 to point to the starting address of pInA */
+        pIn1 = pInA;
+
+        /* Apply loop unrolling and compute 4 MACs simultaneously. */
+        colCnt = numColsA >> 2;
+
+
+        /* matrix multiplication */
+        while(colCnt > 0u)
+        {
+          /* c(m,n) = a(1,1)*b(1,1) + a(1,2) * b(2,1) + .... + a(m,p)*b(p,n) */
+          /* Perform the multiply-accumulates */
+          b0 = *pIn2;
+          pIn2 += numColsB;
+
+          a0 = *pIn1++;
+          a1 = *pIn1++;
+
+          b1 = *pIn2;
+          pIn2 += numColsB;
+          b2 = *pIn2;
+          pIn2 += numColsB;
+
+          sum += (q63_t) a0 *b0;
+          sum += (q63_t) a1 *b1;
+
+          a2 = *pIn1++;
+          a3 = *pIn1++;
+
+          b3 = *pIn2;
+          pIn2 += numColsB;
+
+          sum += (q63_t) a2 *b2;
+          sum += (q63_t) a3 *b3;
+
+          /* Decrement the loop counter */
+          colCnt--;
+        }
+
+        /* If the columns of pSrcA is not a multiple of 4, compute any remaining output samples here.    
+         ** No loop unrolling is used. */
+        colCnt = numColsA % 0x4u;
+
+        while(colCnt > 0u)
+        {
+          /* c(m,n) = a(1,1)*b(1,1) + a(1,2) * b(2,1) + .... + a(m,p)*b(p,n) */
+          /* Perform the multiply-accumulates */
+          sum += (q63_t) * pIn1++ * *pIn2;
+          pIn2 += numColsB;
+
+          /* Decrement the loop counter */
+          colCnt--;
+        }
+
+        /* Convert the result from 2.62 to 1.31 format and store in destination buffer */
+        *px++ = (q31_t) (sum >> 31);
+
+        /* Update the pointer pIn2 to point to the  starting address of the next column */
+        j++;
+        pIn2 = (pSrcB->pData) + j;
+
+        /* Decrement the column loop counter */
+        col--;
+
+      } while(col > 0u);
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  q31_t *pInB = pSrcB->pData;                    /* input data matrix pointer B */
+  uint16_t col, i = 0u, row = numRowsA, colCnt;  /* loop counters */
+  arm_status status;                             /* status of matrix multiplication */
+
+
+#ifdef ARM_MATH_MATRIX_CHECK
+
+  /* Check for matrix mismatch condition */
+  if((pSrcA->numCols != pSrcB->numRows) ||
+     (pSrcA->numRows != pDst->numRows) || (pSrcB->numCols != pDst->numCols))
+  {
+    /* Set status as ARM_MATH_SIZE_MISMATCH */
+    status = ARM_MATH_SIZE_MISMATCH;
+  }
+  else
+#endif /*    #ifdef ARM_MATH_MATRIX_CHECK    */
+
+  {
+    /* The following loop performs the dot-product of each row in pSrcA with each column in pSrcB */
+    /* row loop */
+    do
+    {
+      /* Output pointer is set to starting address of the row being processed */
+      px = pOut + i;
+
+      /* For every row wise process, the column loop counter is to be initiated */
+      col = numColsB;
+
+      /* For every row wise process, the pIn2 pointer is set          
+       ** to the starting address of the pSrcB data */
+      pIn2 = pSrcB->pData;
+
+      /* column loop */
+      do
+      {
+        /* Set the variable sum, that acts as accumulator, to zero */
+        sum = 0;
+
+        /* Initiate the pointer pIn1 to point to the starting address of pInA */
+        pIn1 = pInA;
+
+        /* Matrix A columns number of MAC operations are to be performed */
+        colCnt = numColsA;
+
+        /* matrix multiplication */
+        while(colCnt > 0u)
+        {
+          /* c(m,n) = a(1,1)*b(1,1) + a(1,2) * b(2,1) + .... + a(m,p)*b(p,n) */
+          /* Perform the multiply-accumulates */
+          sum += (q63_t) * pIn1++ * *pIn2;
+          pIn2 += numColsB;
+
+          /* Decrement the loop counter */
+          colCnt--;
+        }
+
+        /* Convert the result from 2.62 to 1.31 format and store in destination buffer */
+        *px++ = (q31_t) (sum >> 31);
+
+        /* Decrement the column loop counter */
+        col--;
+
+        /* Update the pointer pIn2 to point to the  starting address of the next column */
+        pIn2 = pInB + (numColsB - col);
+
+      } while(col > 0u);
+
+#endif
+
+      /* Update the pointer pInA to point to the  starting address of the next row */
+      i = i + numColsB;
+      pInA = pInA + numColsA;
+
+      /* Decrement the row loop counter */
+      row--;
+
+    } while(row > 0u);
+
+    /* set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+  }
+  /* Return to application */
+  return (status);
+}
+
+/**    
+ * @} end of MatrixMult group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_scale_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_scale_f32.c
new file mode 100644
index 0000000000..e64cfd1d12
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_scale_f32.c
@@ -0,0 +1,179 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:        arm_mat_scale_f32.c    
+*    
+* Description:	Multiplies a floating-point matrix by a scalar.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+*    incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupMatrix        
+ */
+
+/**        
+ * @defgroup MatrixScale Matrix Scale        
+ *        
+ * Multiplies a matrix by a scalar.  This is accomplished by multiplying each element in the        
+ * matrix by the scalar.  For example:        
+ * \image html MatrixScale.gif "Matrix Scaling of a 3 x 3 matrix"        
+ *        
+ * The function checks to make sure that the input and output matrices are of the same size.        
+ *        
+ * In the fixed-point Q15 and Q31 functions, scale is represented by        
+ * a fractional multiplication scaleFract and an arithmetic shift shift.        
+ * The shift allows the gain of the scaling operation to exceed 1.0.        
+ * The overall scale factor applied to the fixed-point data is        
+ * 
        
+ *     scale = scaleFract * 2^shift.        
+ * 
        
+ */
+
+/**        
+ * @addtogroup MatrixScale        
+ * @{        
+ */
+
+/**        
+ * @brief Floating-point matrix scaling.        
+ * @param[in]       *pSrc points to input matrix structure        
+ * @param[in]       scale scale factor to be applied         
+ * @param[out]      *pDst points to output matrix structure        
+ * @return     		The function returns either ARM_MATH_SIZE_MISMATCH         
+ * or ARM_MATH_SUCCESS based on the outcome of size checking.        
+ *        
+ */
+
+arm_status arm_mat_scale_f32(
+  const arm_matrix_instance_f32 * pSrc,
+  float32_t scale,
+  arm_matrix_instance_f32 * pDst)
+{
+  float32_t *pIn = pSrc->pData;                  /* input data matrix pointer */
+  float32_t *pOut = pDst->pData;                 /* output data matrix pointer */
+  uint32_t numSamples;                           /* total number of elements in the matrix */
+  uint32_t blkCnt;                               /* loop counters */
+  arm_status status;                             /* status of matrix scaling     */
+
+#ifndef ARM_MATH_CM0
+
+  float32_t in1, in2, in3, in4;                  /* temporary variables */
+  float32_t out1, out2, out3, out4;              /* temporary variables */
+
+#endif //      #ifndef ARM_MATH_CM0
+
+#ifdef ARM_MATH_MATRIX_CHECK
+  /* Check for matrix mismatch condition */
+  if((pSrc->numRows != pDst->numRows) || (pSrc->numCols != pDst->numCols))
+  {
+    /* Set status as ARM_MATH_SIZE_MISMATCH */
+    status = ARM_MATH_SIZE_MISMATCH;
+  }
+  else
+#endif /*    #ifdef ARM_MATH_MATRIX_CHECK    */
+  {
+    /* Total number of samples in the input matrix */
+    numSamples = (uint32_t) pSrc->numRows * pSrc->numCols;
+
+#ifndef ARM_MATH_CM0
+
+    /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+    /* Loop Unrolling */
+    blkCnt = numSamples >> 2;
+
+    /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+     ** a second loop below computes the remaining 1 to 3 samples. */
+    while(blkCnt > 0u)
+    {
+      /* C(m,n) = A(m,n) * scale */
+      /* Scaling and results are stored in the destination buffer. */
+      in1 = pIn[0];
+      in2 = pIn[1];
+      in3 = pIn[2];
+      in4 = pIn[3];
+
+      out1 = in1 * scale;
+      out2 = in2 * scale;
+      out3 = in3 * scale;
+      out4 = in4 * scale;
+
+
+      pOut[0] = out1;
+      pOut[1] = out2;
+      pOut[2] = out3;
+      pOut[3] = out4;
+
+      /* update pointers to process next sampels */
+      pIn += 4u;
+      pOut += 4u;
+
+      /* Decrement the numSamples loop counter */
+      blkCnt--;
+    }
+
+    /* If the numSamples is not a multiple of 4, compute any remaining output samples here.    
+     ** No loop unrolling is used. */
+    blkCnt = numSamples % 0x4u;
+
+#else
+
+    /* Run the below code for Cortex-M0 */
+
+    /* Initialize blkCnt with number of samples */
+    blkCnt = numSamples;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+    while(blkCnt > 0u)
+    {
+      /* C(m,n) = A(m,n) * scale */
+      /* The results are stored in the destination buffer. */
+      *pOut++ = (*pIn++) * scale;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* Set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+  }
+
+  /* Return to application */
+  return (status);
+}
+
+/**        
+ * @} end of MatrixScale group        
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_scale_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_scale_q15.c
new file mode 100644
index 0000000000..58011254c8
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_scale_q15.c
@@ -0,0 +1,181 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_mat_scale_q15.c    
+*    
+* Description:	Multiplies a Q15 matrix by a scalar.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+*    incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMatrix    
+ */
+
+/**    
+ * @addtogroup MatrixScale    
+ * @{    
+ */
+
+/**    
+ * @brief Q15 matrix scaling.    
+ * @param[in]       *pSrc points to input matrix    
+ * @param[in]       scaleFract fractional portion of the scale factor    
+ * @param[in]       shift number of bits to shift the result by    
+ * @param[out]      *pDst points to output matrix structure    
+ * @return     		The function returns either    
+ * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.    
+ *    
+ * @details    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The input data *pSrc and scaleFract are in 1.15 format.    
+ * These are multiplied to yield a 2.30 intermediate result and this is shifted with saturation to 1.15 format.    
+ */
+
+arm_status arm_mat_scale_q15(
+  const arm_matrix_instance_q15 * pSrc,
+  q15_t scaleFract,
+  int32_t shift,
+  arm_matrix_instance_q15 * pDst)
+{
+  q15_t *pIn = pSrc->pData;                      /* input data matrix pointer */
+  q15_t *pOut = pDst->pData;                     /* output data matrix pointer */
+  uint32_t numSamples;                           /* total number of elements in the matrix */
+  int32_t totShift = 15 - shift;                 /* total shift to apply after scaling */
+  uint32_t blkCnt;                               /* loop counters */
+  arm_status status;                             /* status of matrix scaling     */
+
+#ifndef ARM_MATH_CM0
+
+  q15_t in1, in2, in3, in4;
+  q31_t out1, out2, out3, out4;
+  q31_t inA1, inA2;
+
+#endif //     #ifndef ARM_MATH_CM0
+
+#ifdef ARM_MATH_MATRIX_CHECK
+  /* Check for matrix mismatch */
+  if((pSrc->numRows != pDst->numRows) || (pSrc->numCols != pDst->numCols))
+  {
+    /* Set status as ARM_MATH_SIZE_MISMATCH */
+    status = ARM_MATH_SIZE_MISMATCH;
+  }
+  else
+#endif //    #ifdef ARM_MATH_MATRIX_CHECK
+  {
+    /* Total number of samples in the input matrix */
+    numSamples = (uint32_t) pSrc->numRows * pSrc->numCols;
+
+#ifndef ARM_MATH_CM0
+
+    /* Run the below code for Cortex-M4 and Cortex-M3 */
+    /* Loop Unrolling */
+    blkCnt = numSamples >> 2;
+
+    /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+     ** a second loop below computes the remaining 1 to 3 samples. */
+    while(blkCnt > 0u)
+    {
+      /* C(m,n) = A(m,n) * k */
+      /* Scale, saturate and then store the results in the destination buffer. */
+      /* Reading 2 inputs from memory */
+      inA1 = _SIMD32_OFFSET(pIn);
+      inA2 = _SIMD32_OFFSET(pIn + 2);
+
+      /* C = A * scale */
+      /* Scale the inputs and then store the 2 results in the destination buffer        
+       * in single cycle by packing the outputs */
+      out1 = (q31_t) ((q15_t) (inA1 >> 16) * scaleFract);
+      out2 = (q31_t) ((q15_t) inA1 * scaleFract);
+      out3 = (q31_t) ((q15_t) (inA2 >> 16) * scaleFract);
+      out4 = (q31_t) ((q15_t) inA2 * scaleFract);
+
+      out1 = out1 >> totShift;
+      inA1 = _SIMD32_OFFSET(pIn + 4);
+      out2 = out2 >> totShift;
+      inA2 = _SIMD32_OFFSET(pIn + 6);
+      out3 = out3 >> totShift;
+      out4 = out4 >> totShift;
+
+      in1 = (q15_t) (__SSAT(out1, 16));
+      in2 = (q15_t) (__SSAT(out2, 16));
+      in3 = (q15_t) (__SSAT(out3, 16));
+      in4 = (q15_t) (__SSAT(out4, 16));
+
+      _SIMD32_OFFSET(pOut) = __PKHBT(in2, in1, 16);
+      _SIMD32_OFFSET(pOut + 2) = __PKHBT(in4, in3, 16);
+
+      /* update pointers to process next sampels */
+      pIn += 4u;
+      pOut += 4u;
+
+
+      /* Decrement the numSamples loop counter */
+      blkCnt--;
+    }
+
+    /* If the numSamples is not a multiple of 4, compute any remaining output samples here.        
+     ** No loop unrolling is used. */
+    blkCnt = numSamples % 0x4u;
+
+#else
+
+    /* Run the below code for Cortex-M0 */
+
+    /* Initialize blkCnt with number of samples */
+    blkCnt = numSamples;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+    while(blkCnt > 0u)
+    {
+      /* C(m,n) = A(m,n) * k */
+      /* Scale, saturate and then store the results in the destination buffer. */
+      *pOut++ =
+        (q15_t) (__SSAT(((q31_t) (*pIn++) * scaleFract) >> totShift, 16));
+
+      /* Decrement the numSamples loop counter */
+      blkCnt--;
+    }
+    /* Set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+  }
+
+  /* Return to application */
+  return (status);
+}
+
+/**        
+ * @} end of MatrixScale group        
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_scale_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_scale_q31.c
new file mode 100644
index 0000000000..e5e1241254
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_scale_q31.c
@@ -0,0 +1,201 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_mat_scale_q31.c    
+*    
+* Description:	Multiplies a Q31 matrix by a scalar.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+*    incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupMatrix        
+ */
+
+/**        
+ * @addtogroup MatrixScale        
+ * @{        
+ */
+
+/**        
+ * @brief Q31 matrix scaling.        
+ * @param[in]       *pSrc points to input matrix        
+ * @param[in]       scaleFract fractional portion of the scale factor        
+ * @param[in]       shift number of bits to shift the result by        
+ * @param[out]      *pDst points to output matrix structure        
+ * @return     		The function returns either        
+ * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.        
+ *        
+ * @details        
+ * Scaling and Overflow Behavior:        
+ * \par        
+ * The input data *pSrc and scaleFract are in 1.31 format.        
+ * These are multiplied to yield a 2.62 intermediate result and this is shifted with saturation to 1.31 format.        
+ */
+
+arm_status arm_mat_scale_q31(
+  const arm_matrix_instance_q31 * pSrc,
+  q31_t scaleFract,
+  int32_t shift,
+  arm_matrix_instance_q31 * pDst)
+{
+  q31_t *pIn = pSrc->pData;                      /* input data matrix pointer */
+  q31_t *pOut = pDst->pData;                     /* output data matrix pointer */
+  uint32_t numSamples;                           /* total number of elements in the matrix */
+  int32_t totShift = shift + 1;                  /* shift to apply after scaling */
+  uint32_t blkCnt;                               /* loop counters  */
+  arm_status status;                             /* status of matrix scaling      */
+  q31_t in1, in2, out1;                          /* temporary variabels */
+
+#ifndef ARM_MATH_CM0
+
+  q31_t in3, in4, out2, out3, out4;              /* temporary variables */
+
+#endif //      #ifndef ARM_MAT_CM0
+
+#ifdef ARM_MATH_MATRIX_CHECK
+  /* Check for matrix mismatch  */
+  if((pSrc->numRows != pDst->numRows) || (pSrc->numCols != pDst->numCols))
+  {
+    /* Set status as ARM_MATH_SIZE_MISMATCH */
+    status = ARM_MATH_SIZE_MISMATCH;
+  }
+  else
+#endif //    #ifdef ARM_MATH_MATRIX_CHECK
+  {
+    /* Total number of samples in the input matrix */
+    numSamples = (uint32_t) pSrc->numRows * pSrc->numCols;
+
+#ifndef ARM_MATH_CM0
+
+    /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+    /* Loop Unrolling */
+    blkCnt = numSamples >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+     ** a second loop below computes the remaining 1 to 3 samples. */
+    while(blkCnt > 0u)
+    {
+      /* C(m,n) = A(m,n) * k */
+      /* Read values from input */
+      in1 = *pIn;
+      in2 = *(pIn + 1);
+      in3 = *(pIn + 2);
+      in4 = *(pIn + 3);
+
+      /* multiply input with scaler value */
+      in1 = ((q63_t) in1 * scaleFract) >> 32;
+      in2 = ((q63_t) in2 * scaleFract) >> 32;
+      in3 = ((q63_t) in3 * scaleFract) >> 32;
+      in4 = ((q63_t) in4 * scaleFract) >> 32;
+
+      /* apply shifting */
+      out1 = in1 << totShift;
+      out2 = in2 << totShift;
+
+      /* saturate the results. */
+      if(in1 != (out1 >> totShift))
+        out1 = 0x7FFFFFFF ^ (in1 >> 31);
+
+      if(in2 != (out2 >> totShift))
+        out2 = 0x7FFFFFFF ^ (in2 >> 31);
+
+      out3 = in3 << totShift;
+      out4 = in4 << totShift;
+
+      *pOut = out1;
+      *(pOut + 1) = out2;
+
+      if(in3 != (out3 >> totShift))
+        out3 = 0x7FFFFFFF ^ (in3 >> 31);
+
+      if(in4 != (out4 >> totShift))
+        out4 = 0x7FFFFFFF ^ (in4 >> 31);
+
+
+      *(pOut + 2) = out3;
+      *(pOut + 3) = out4;
+
+      /* update pointers to process next sampels */
+      pIn += 4u;
+      pOut += 4u;
+
+
+      /* Decrement the numSamples loop counter */
+      blkCnt--;
+    }
+
+    /* If the numSamples is not a multiple of 4, compute any remaining output samples here.    
+     ** No loop unrolling is used. */
+    blkCnt = numSamples % 0x4u;
+
+#else
+
+    /* Run the below code for Cortex-M0 */
+
+    /* Initialize blkCnt with number of samples */
+    blkCnt = numSamples;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+    while(blkCnt > 0u)
+    {
+      /* C(m,n) = A(m,n) * k */
+      /* Scale, saturate and then store the results in the destination buffer. */
+      in1 = *pIn++;
+
+      in2 = ((q63_t) in1 * scaleFract) >> 32;
+
+      out1 = in2 << totShift;
+
+      if(in2 != (out1 >> totShift))
+        out1 = 0x7FFFFFFF ^ (in2 >> 31);
+
+      *pOut++ = out1;
+
+      /* Decrement the numSamples loop counter */
+      blkCnt--;
+    }
+
+    /* Set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+  }
+
+  /* Return to application */
+  return (status);
+}
+
+/**        
+ * @} end of MatrixScale group        
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_sub_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_sub_f32.c
new file mode 100644
index 0000000000..3544d8e825
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_sub_f32.c
@@ -0,0 +1,207 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_mat_sub_f32.c    
+*    
+* Description:	Floating-point matrix subtraction.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+*    incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupMatrix        
+ */
+
+/**        
+ * @defgroup MatrixSub Matrix Subtraction        
+ *        
+ * Subtract two matrices.        
+ * \image html MatrixSubtraction.gif "Subraction of two 3 x 3 matrices"        
+ *        
+ * The functions check to make sure that        
+ * pSrcA, pSrcB, and pDst have the same        
+ * number of rows and columns.        
+ */
+
+/**        
+ * @addtogroup MatrixSub        
+ * @{        
+ */
+
+/**        
+ * @brief Floating-point matrix subtraction        
+ * @param[in]       *pSrcA points to the first input matrix structure        
+ * @param[in]       *pSrcB points to the second input matrix structure        
+ * @param[out]      *pDst points to output matrix structure        
+ * @return     		The function returns either        
+ * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.        
+ */
+
+arm_status arm_mat_sub_f32(
+  const arm_matrix_instance_f32 * pSrcA,
+  const arm_matrix_instance_f32 * pSrcB,
+  arm_matrix_instance_f32 * pDst)
+{
+  float32_t *pIn1 = pSrcA->pData;                /* input data matrix pointer A */
+  float32_t *pIn2 = pSrcB->pData;                /* input data matrix pointer B */
+  float32_t *pOut = pDst->pData;                 /* output data matrix pointer  */
+
+#ifndef ARM_MATH_CM0
+
+  float32_t inA1, inA2, inB1, inB2, out1, out2;  /* temporary variables */
+
+#endif //      #ifndef ARM_MATH_CM0
+
+  uint32_t numSamples;                           /* total number of elements in the matrix  */
+  uint32_t blkCnt;                               /* loop counters */
+  arm_status status;                             /* status of matrix subtraction */
+
+#ifdef ARM_MATH_MATRIX_CHECK
+  /* Check for matrix mismatch condition */
+  if((pSrcA->numRows != pSrcB->numRows) ||
+     (pSrcA->numCols != pSrcB->numCols) ||
+     (pSrcA->numRows != pDst->numRows) || (pSrcA->numCols != pDst->numCols))
+  {
+    /* Set status as ARM_MATH_SIZE_MISMATCH */
+    status = ARM_MATH_SIZE_MISMATCH;
+  }
+  else
+#endif /*    #ifdef ARM_MATH_MATRIX_CHECK    */
+  {
+    /* Total number of samples in the input matrix */
+    numSamples = (uint32_t) pSrcA->numRows * pSrcA->numCols;
+
+#ifndef ARM_MATH_CM0
+
+    /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+    /* Loop Unrolling */
+    blkCnt = numSamples >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+     ** a second loop below computes the remaining 1 to 3 samples. */
+    while(blkCnt > 0u)
+    {
+      /* C(m,n) = A(m,n) - B(m,n) */
+      /* Subtract and then store the results in the destination buffer. */
+      /* Read values from source A */
+      inA1 = pIn1[0];
+
+      /* Read values from source B */
+      inB1 = pIn2[0];
+
+      /* Read values from source A */
+      inA2 = pIn1[1];
+
+      /* out = sourceA - sourceB */
+      out1 = inA1 - inB1;
+
+      /* Read values from source B */
+      inB2 = pIn2[1];
+
+      /* Read values from source A */
+      inA1 = pIn1[2];
+
+      /* out = sourceA - sourceB */
+      out2 = inA2 - inB2;
+
+      /* Read values from source B */
+      inB1 = pIn2[2];
+
+      /* Store result in destination */
+      pOut[0] = out1;
+      pOut[1] = out2;
+
+      /* Read values from source A */
+      inA2 = pIn1[3];
+
+      /* Read values from source B */
+      inB2 = pIn2[3];
+
+      /* out = sourceA - sourceB */
+      out1 = inA1 - inB1;
+
+
+      /* out = sourceA - sourceB */
+      out2 = inA2 - inB2;
+
+      /* Store result in destination */
+      pOut[2] = out1;
+
+      /* Store result in destination */
+      pOut[3] = out2;
+
+
+      /* update pointers to process next sampels */
+      pIn1 += 4u;
+      pIn2 += 4u;
+      pOut += 4u;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the numSamples is not a multiple of 4, compute any remaining output samples here.    
+     ** No loop unrolling is used. */
+    blkCnt = numSamples % 0x4u;
+
+#else
+
+    /* Run the below code for Cortex-M0 */
+
+    /* Initialize blkCnt with number of samples */
+    blkCnt = numSamples;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+    while(blkCnt > 0u)
+    {
+      /* C(m,n) = A(m,n) - B(m,n) */
+      /* Subtract and then store the results in the destination buffer. */
+      *pOut++ = (*pIn1++) - (*pIn2++);
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* Set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+  }
+
+  /* Return to application */
+  return (status);
+}
+
+/**        
+ * @} end of MatrixSub group        
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_sub_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_sub_q15.c
new file mode 100644
index 0000000000..1857fd837c
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_sub_q15.c
@@ -0,0 +1,158 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_mat_sub_q15.c    
+*    
+* Description:	Q15 Matrix subtraction    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+*    incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMatrix    
+ */
+
+/**    
+ * @addtogroup MatrixSub    
+ * @{    
+ */
+
+/**    
+ * @brief Q15 matrix subtraction.    
+ * @param[in]       *pSrcA points to the first input matrix structure    
+ * @param[in]       *pSrcB points to the second input matrix structure    
+ * @param[out]      *pDst points to output matrix structure    
+ * @return     		The function returns either    
+ * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.    
+ *    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * Results outside of the allowable Q15 range [0x8000 0x7FFF] will be saturated.    
+ */
+
+arm_status arm_mat_sub_q15(
+  const arm_matrix_instance_q15 * pSrcA,
+  const arm_matrix_instance_q15 * pSrcB,
+  arm_matrix_instance_q15 * pDst)
+{
+  q15_t *pInA = pSrcA->pData;                    /* input data matrix pointer A */
+  q15_t *pInB = pSrcB->pData;                    /* input data matrix pointer B */
+  q15_t *pOut = pDst->pData;                     /* output data matrix pointer */
+  uint32_t numSamples;                           /* total number of elements in the matrix */
+  uint32_t blkCnt;                               /* loop counters  */
+  arm_status status;                             /* status of matrix subtraction  */
+
+
+#ifdef ARM_MATH_MATRIX_CHECK
+
+
+  /* Check for matrix mismatch condition */
+  if((pSrcA->numRows != pSrcB->numRows) ||
+     (pSrcA->numCols != pSrcB->numCols) ||
+     (pSrcA->numRows != pDst->numRows) || (pSrcA->numCols != pDst->numCols))
+  {
+    /* Set status as ARM_MATH_SIZE_MISMATCH */
+    status = ARM_MATH_SIZE_MISMATCH;
+  }
+  else
+#endif /*    #ifdef ARM_MATH_MATRIX_CHECK    */
+
+  {
+    /* Total number of samples in the input matrix */
+    numSamples = (uint32_t) pSrcA->numRows * pSrcA->numCols;
+
+#ifndef ARM_MATH_CM0
+
+    /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+    /* Apply loop unrolling */
+    blkCnt = numSamples >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+     ** a second loop below computes the remaining 1 to 3 samples. */
+    while(blkCnt > 0u)
+    {
+      /* C(m,n) = A(m,n) - B(m,n) */
+      /* Subtract, Saturate and then store the results in the destination buffer. */
+      *__SIMD32(pOut)++ = __QSUB16(*__SIMD32(pInA)++, *__SIMD32(pInB)++);
+      *__SIMD32(pOut)++ = __QSUB16(*__SIMD32(pInA)++, *__SIMD32(pInB)++);
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+     ** No loop unrolling is used. */
+    blkCnt = numSamples % 0x4u;
+
+    while(blkCnt > 0u)
+    {
+      /* C(m,n) = A(m,n) - B(m,n) */
+      /* Subtract and then store the results in the destination buffer. */
+      *pOut++ = (q15_t) __QSUB16(*pInA++, *pInB++);
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+#else
+
+    /* Run the below code for Cortex-M0 */
+
+    /* Initialize blkCnt with number of samples */
+    blkCnt = numSamples;
+
+    while(blkCnt > 0u)
+    {
+      /* C(m,n) = A(m,n) - B(m,n) */
+      /* Subtract and then store the results in the destination buffer. */
+      *pOut++ = (q15_t) __SSAT(((q31_t) * pInA++ - *pInB++), 16);
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+    /* Set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+  }
+
+  /* Return to application */
+  return (status);
+}
+
+/**    
+ * @} end of MatrixSub group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_sub_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_sub_q31.c
new file mode 100644
index 0000000000..279fd7f7c1
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_sub_q31.c
@@ -0,0 +1,206 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_mat_sub_q31.c    
+*    
+* Description:	Q31 matrix subtraction    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+*    incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupMatrix        
+ */
+
+/**        
+ * @addtogroup MatrixSub        
+ * @{        
+ */
+
+/**        
+ * @brief Q31 matrix subtraction.        
+ * @param[in]       *pSrcA points to the first input matrix structure        
+ * @param[in]       *pSrcB points to the second input matrix structure        
+ * @param[out]      *pDst points to output matrix structure        
+ * @return     		The function returns either        
+ * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.        
+ *        
+ * Scaling and Overflow Behavior:        
+ * \par        
+ * The function uses saturating arithmetic.        
+ * Results outside of the allowable Q31 range [0x80000000 0x7FFFFFFF] will be saturated.        
+ */
+
+
+arm_status arm_mat_sub_q31(
+  const arm_matrix_instance_q31 * pSrcA,
+  const arm_matrix_instance_q31 * pSrcB,
+  arm_matrix_instance_q31 * pDst)
+{
+  q31_t *pIn1 = pSrcA->pData;                    /* input data matrix pointer A */
+  q31_t *pIn2 = pSrcB->pData;                    /* input data matrix pointer B */
+  q31_t *pOut = pDst->pData;                     /* output data matrix pointer */
+  q31_t inA1, inB1;                              /* temporary variables */
+
+#ifndef ARM_MATH_CM0
+
+  q31_t inA2, inB2;                              /* temporary variables */
+  q31_t out1, out2;                              /* temporary variables */
+
+#endif //      #ifndef ARM_MATH_CM0
+
+  uint32_t numSamples;                           /* total number of elements in the matrix  */
+  uint32_t blkCnt;                               /* loop counters */
+  arm_status status;                             /* status of matrix subtraction */
+
+
+#ifdef ARM_MATH_MATRIX_CHECK
+  /* Check for matrix mismatch condition  */
+  if((pSrcA->numRows != pSrcB->numRows) ||
+     (pSrcA->numCols != pSrcB->numCols) ||
+     (pSrcA->numRows != pDst->numRows) || (pSrcA->numCols != pDst->numCols))
+  {
+    /* Set status as ARM_MATH_SIZE_MISMATCH */
+    status = ARM_MATH_SIZE_MISMATCH;
+  }
+  else
+#endif
+  {
+    /* Total number of samples in the input matrix */
+    numSamples = (uint32_t) pSrcA->numRows * pSrcA->numCols;
+
+#ifndef ARM_MATH_CM0
+
+    /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+    /* Loop Unrolling */
+    blkCnt = numSamples >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+     ** a second loop below computes the remaining 1 to 3 samples. */
+    while(blkCnt > 0u)
+    {
+      /* C(m,n) = A(m,n) - B(m,n) */
+      /* Subtract, saturate and then store the results in the destination buffer. */
+      /* Read values from source A */
+      inA1 = pIn1[0];
+
+      /* Read values from source B */
+      inB1 = pIn2[0];
+
+      /* Read values from source A */
+      inA2 = pIn1[1];
+
+      /* Subtract and saturate */
+      out1 = __QSUB(inA1, inB1);
+
+      /* Read values from source B */
+      inB2 = pIn2[1];
+
+      /* Read values from source A */
+      inA1 = pIn1[2];
+
+      /* Subtract and saturate */
+      out2 = __QSUB(inA2, inB2);
+
+      /* Read values from source B */
+      inB1 = pIn2[2];
+
+      /* Store result in destination */
+      pOut[0] = out1;
+      pOut[1] = out2;
+
+      /* Read values from source A */
+      inA2 = pIn1[3];
+
+      /* Read values from source B */
+      inB2 = pIn2[3];
+
+      /* Subtract and saturate */
+      out1 = __QSUB(inA1, inB1);
+
+      /* Subtract and saturate */
+      out2 = __QSUB(inA2, inB2);
+
+      /* Store result in destination */
+      pOut[2] = out1;
+      pOut[3] = out2;
+
+      /* update pointers to process next samples */
+      pIn1 += 4u;
+      pIn2 += 4u;
+      pOut += 4u;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the numSamples is not a multiple of 4, compute any remaining output samples here.        
+     ** No loop unrolling is used. */
+    blkCnt = numSamples % 0x4u;
+
+#else
+
+    /* Run the below code for Cortex-M0 */
+
+    /* Initialize blkCnt with number of samples */
+    blkCnt = numSamples;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+    while(blkCnt > 0u)
+    {
+      /* C(m,n) = A(m,n) - B(m,n) */
+      /* Subtract, saturate and then store the results in the destination buffer. */
+      inA1 = *pIn1++;
+      inB1 = *pIn2++;
+
+      inA1 = __QSUB(inA1, inB1);
+
+      *pOut++ = inA1;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* Set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+  }
+
+  /* Return to application */
+  return (status);
+}
+
+/**        
+ * @} end of MatrixSub group        
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_trans_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_trans_f32.c
new file mode 100644
index 0000000000..235028f5ab
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_trans_f32.c
@@ -0,0 +1,216 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_mat_trans_f32.c    
+*    
+* Description:	Floating-point matrix transpose.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+*    incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+/**    
+ * @defgroup MatrixTrans Matrix Transpose    
+ *    
+ * Tranposes a matrix.    
+ * Transposing an M x N matrix flips it around the center diagonal and results in an N x M matrix.    
+ * \image html MatrixTranspose.gif "Transpose of a 3 x 3 matrix"    
+ */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMatrix    
+ */
+
+/**    
+ * @addtogroup MatrixTrans    
+ * @{    
+ */
+
+/**    
+  * @brief Floating-point matrix transpose.    
+  * @param[in]  *pSrc points to the input matrix    
+  * @param[out] *pDst points to the output matrix    
+  * @return 	The function returns either  ARM_MATH_SIZE_MISMATCH    
+  * or ARM_MATH_SUCCESS based on the outcome of size checking.    
+  */
+
+
+arm_status arm_mat_trans_f32(
+  const arm_matrix_instance_f32 * pSrc,
+  arm_matrix_instance_f32 * pDst)
+{
+  float32_t *pIn = pSrc->pData;                  /* input data matrix pointer */
+  float32_t *pOut = pDst->pData;                 /* output data matrix pointer */
+  float32_t *px;                                 /* Temporary output data matrix pointer */
+  uint16_t nRows = pSrc->numRows;                /* number of rows */
+  uint16_t nColumns = pSrc->numCols;             /* number of columns */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  uint16_t blkCnt, i = 0u, row = nRows;          /* loop counters */
+  arm_status status;                             /* status of matrix transpose  */
+
+
+#ifdef ARM_MATH_MATRIX_CHECK
+
+
+  /* Check for matrix mismatch condition */
+  if((pSrc->numRows != pDst->numCols) || (pSrc->numCols != pDst->numRows))
+  {
+    /* Set status as ARM_MATH_SIZE_MISMATCH */
+    status = ARM_MATH_SIZE_MISMATCH;
+  }
+  else
+#endif /*    #ifdef ARM_MATH_MATRIX_CHECK    */
+
+  {
+    /* Matrix transpose by exchanging the rows with columns */
+    /* row loop     */
+    do
+    {
+      /* Loop Unrolling */
+      blkCnt = nColumns >> 2;
+
+      /* The pointer px is set to starting address of the column being processed */
+      px = pOut + i;
+
+      /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+       ** a second loop below computes the remaining 1 to 3 samples. */
+      while(blkCnt > 0u)        /* column loop */
+      {
+        /* Read and store the input element in the destination */
+        *px = *pIn++;
+
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += nRows;
+
+        /* Read and store the input element in the destination */
+        *px = *pIn++;
+
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += nRows;
+
+        /* Read and store the input element in the destination */
+        *px = *pIn++;
+
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += nRows;
+
+        /* Read and store the input element in the destination */
+        *px = *pIn++;
+
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += nRows;
+
+        /* Decrement the column loop counter */
+        blkCnt--;
+      }
+
+      /* Perform matrix transpose for last 3 samples here. */
+      blkCnt = nColumns % 0x4u;
+
+      while(blkCnt > 0u)
+      {
+        /* Read and store the input element in the destination */
+        *px = *pIn++;
+
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += nRows;
+
+        /* Decrement the column loop counter */
+        blkCnt--;
+      }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  uint16_t col, i = 0u, row = nRows;             /* loop counters */
+  arm_status status;                             /* status of matrix transpose  */
+
+
+#ifdef ARM_MATH_MATRIX_CHECK
+
+  /* Check for matrix mismatch condition */
+  if((pSrc->numRows != pDst->numCols) || (pSrc->numCols != pDst->numRows))
+  {
+    /* Set status as ARM_MATH_SIZE_MISMATCH */
+    status = ARM_MATH_SIZE_MISMATCH;
+  }
+  else
+#endif /*      #ifdef ARM_MATH_MATRIX_CHECK    */
+
+  {
+    /* Matrix transpose by exchanging the rows with columns */
+    /* row loop     */
+    do
+    {
+      /* The pointer px is set to starting address of the column being processed */
+      px = pOut + i;
+
+      /* Initialize column loop counter */
+      col = nColumns;
+
+      while(col > 0u)
+      {
+        /* Read and store the input element in the destination */
+        *px = *pIn++;
+
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += nRows;
+
+        /* Decrement the column loop counter */
+        col--;
+      }
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+      i++;
+
+      /* Decrement the row loop counter */
+      row--;
+
+    } while(row > 0u);          /* row loop end  */
+
+    /* Set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+  }
+
+  /* Return to application */
+  return (status);
+}
+
+/**    
+ * @} end of MatrixTrans group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_trans_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_trans_q15.c
new file mode 100644
index 0000000000..be9c78e003
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_trans_q15.c
@@ -0,0 +1,282 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_mat_trans_q15.c    
+*    
+* Description:	Q15 matrix transpose.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+*    incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMatrix    
+ */
+
+/**    
+ * @addtogroup MatrixTrans    
+ * @{    
+ */
+
+/*    
+ * @brief Q15 matrix transpose.    
+ * @param[in]  *pSrc points to the input matrix    
+ * @param[out] *pDst points to the output matrix    
+ * @return 	The function returns either  ARM_MATH_SIZE_MISMATCH    
+ * or ARM_MATH_SUCCESS based on the outcome of size checking.    
+ */
+
+arm_status arm_mat_trans_q15(
+  const arm_matrix_instance_q15 * pSrc,
+  arm_matrix_instance_q15 * pDst)
+{
+  q15_t *pSrcA = pSrc->pData;                    /* input data matrix pointer */
+  q15_t *pOut = pDst->pData;                     /* output data matrix pointer */
+  uint16_t nRows = pSrc->numRows;                /* number of nRows */
+  uint16_t nColumns = pSrc->numCols;             /* number of nColumns */
+  uint16_t col, row = nRows, i = 0u;             /* row and column loop counters */
+  arm_status status;                             /* status of matrix transpose */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+  q31_t in;                                      /* variable to hold temporary output  */
+
+#else
+
+  q15_t in;
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+#ifdef ARM_MATH_MATRIX_CHECK
+
+
+  /* Check for matrix mismatch condition */
+  if((pSrc->numRows != pDst->numCols) || (pSrc->numCols != pDst->numRows))
+  {
+    /* Set status as ARM_MATH_SIZE_MISMATCH */
+    status = ARM_MATH_SIZE_MISMATCH;
+  }
+  else
+#endif /*      #ifdef ARM_MATH_MATRIX_CHECK    */
+
+  {
+    /* Matrix transpose by exchanging the rows with columns */
+    /* row loop     */
+    do
+    {
+
+      /* Apply loop unrolling and exchange the columns with row elements */
+      col = nColumns >> 2u;
+
+      /* The pointer pOut is set to starting address of the column being processed */
+      pOut = pDst->pData + i;
+
+      /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+       ** a second loop below computes the remaining 1 to 3 samples. */
+      while(col > 0u)
+      {
+#ifndef UNALIGNED_SUPPORT_DISABLE
+
+        /* Read two elements from the row */
+        in = *__SIMD32(pSrcA)++;
+
+        /* Unpack and store one element in the destination */
+#ifndef ARM_MATH_BIG_ENDIAN
+
+        *pOut = (q15_t) in;
+
+#else
+
+        *pOut = (q15_t) ((in & (q31_t) 0xffff0000) >> 16);
+
+#endif /*    #ifndef ARM_MATH_BIG_ENDIAN    */
+
+        /* Update the pointer pOut to point to the next row of the transposed matrix */
+        pOut += nRows;
+
+        /* Unpack and store the second element in the destination */
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+        *pOut = (q15_t) ((in & (q31_t) 0xffff0000) >> 16);
+
+#else
+
+        *pOut = (q15_t) in;
+
+#endif /*    #ifndef ARM_MATH_BIG_ENDIAN    */
+
+        /* Update the pointer pOut to point to the next row of the transposed matrix */
+        pOut += nRows;
+
+        /* Read two elements from the row */
+#ifndef ARM_MATH_BIG_ENDIAN
+
+        in = *__SIMD32(pSrcA)++;
+
+#else
+
+        in = *__SIMD32(pSrcA)++;
+
+#endif /*    #ifndef ARM_MATH_BIG_ENDIAN    */
+
+        /* Unpack and store one element in the destination */
+#ifndef ARM_MATH_BIG_ENDIAN
+
+        *pOut = (q15_t) in;
+
+#else
+
+        *pOut = (q15_t) ((in & (q31_t) 0xffff0000) >> 16);
+
+#endif /*    #ifndef ARM_MATH_BIG_ENDIAN    */
+
+        /* Update the pointer pOut to point to the next row of the transposed matrix */
+        pOut += nRows;
+
+        /* Unpack and store the second element in the destination */
+#ifndef ARM_MATH_BIG_ENDIAN
+
+        *pOut = (q15_t) ((in & (q31_t) 0xffff0000) >> 16);
+
+#else
+
+        *pOut = (q15_t) in;
+
+#endif /*    #ifndef ARM_MATH_BIG_ENDIAN    */
+
+#else	 
+        /* Read one element from the row */
+        in = *pSrcA++;
+
+        /* Store one element in the destination */
+        *pOut = in;
+ 
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        pOut += nRows;
+
+        /* Read one element from the row */
+        in = *pSrcA++;
+
+        /* Store one element in the destination */
+        *pOut = in;
+ 
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        pOut += nRows;
+
+        /* Read one element from the row */
+        in = *pSrcA++;
+
+        /* Store one element in the destination */
+        *pOut = in;
+ 
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        pOut += nRows;
+
+        /* Read one element from the row */
+        in = *pSrcA++;
+
+        /* Store one element in the destination */
+        *pOut = in;
+
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+        /* Update the pointer pOut to point to the next row of the transposed matrix */
+        pOut += nRows;
+
+        /* Decrement the column loop counter */
+        col--;
+      }
+
+      /* Perform matrix transpose for last 3 samples here. */
+      col = nColumns % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+#ifdef ARM_MATH_MATRIX_CHECK
+
+  /* Check for matrix mismatch condition */
+  if((pSrc->numRows != pDst->numCols) || (pSrc->numCols != pDst->numRows))
+  {
+    /* Set status as ARM_MATH_SIZE_MISMATCH */
+    status = ARM_MATH_SIZE_MISMATCH;
+  }
+  else
+#endif /*    #ifdef ARM_MATH_MATRIX_CHECK    */
+
+  {
+    /* Matrix transpose by exchanging the rows with columns */
+    /* row loop     */
+    do
+    {
+      /* The pointer pOut is set to starting address of the column being processed */
+      pOut = pDst->pData + i;
+
+      /* Initialize column loop counter */
+      col = nColumns;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+      while(col > 0u)
+      {
+        /* Read and store the input element in the destination */
+        *pOut = *pSrcA++;
+
+        /* Update the pointer pOut to point to the next row of the transposed matrix */
+        pOut += nRows;
+
+        /* Decrement the column loop counter */
+        col--;
+      }
+
+      i++;
+
+      /* Decrement the row loop counter */
+      row--;
+
+    } while(row > 0u);
+
+    /* set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+  }
+  /* Return to application */
+  return (status);
+}
+
+/**    
+ * @} end of MatrixTrans group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_trans_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_trans_q31.c
new file mode 100644
index 0000000000..253a923d1c
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/MatrixFunctions/arm_mat_trans_q31.c
@@ -0,0 +1,208 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_mat_trans_q31.c    
+*    
+* Description:	Q31 matrix transpose.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+*    incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMatrix    
+ */
+
+/**    
+ * @addtogroup MatrixTrans    
+ * @{    
+ */
+
+/*    
+  * @brief Q31 matrix transpose.    
+  * @param[in]  *pSrc points to the input matrix    
+  * @param[out] *pDst points to the output matrix    
+  * @return 	The function returns either  ARM_MATH_SIZE_MISMATCH    
+  * or ARM_MATH_SUCCESS based on the outcome of size checking.    
+ */
+
+arm_status arm_mat_trans_q31(
+  const arm_matrix_instance_q31 * pSrc,
+  arm_matrix_instance_q31 * pDst)
+{
+  q31_t *pIn = pSrc->pData;                      /* input data matrix pointer  */
+  q31_t *pOut = pDst->pData;                     /* output data matrix pointer  */
+  q31_t *px;                                     /* Temporary output data matrix pointer */
+  uint16_t nRows = pSrc->numRows;                /* number of nRows */
+  uint16_t nColumns = pSrc->numCols;             /* number of nColumns  */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  uint16_t blkCnt, i = 0u, row = nRows;          /* loop counters */
+  arm_status status;                             /* status of matrix transpose */
+
+
+#ifdef ARM_MATH_MATRIX_CHECK
+
+
+  /* Check for matrix mismatch condition */
+  if((pSrc->numRows != pDst->numCols) || (pSrc->numCols != pDst->numRows))
+  {
+    /* Set status as ARM_MATH_SIZE_MISMATCH */
+    status = ARM_MATH_SIZE_MISMATCH;
+  }
+  else
+#endif /*    #ifdef ARM_MATH_MATRIX_CHECK    */
+
+  {
+    /* Matrix transpose by exchanging the rows with columns */
+    /* row loop     */
+    do
+    {
+      /* Apply loop unrolling and exchange the columns with row elements */
+      blkCnt = nColumns >> 2u;
+
+      /* The pointer px is set to starting address of the column being processed */
+      px = pOut + i;
+
+      /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+       ** a second loop below computes the remaining 1 to 3 samples. */
+      while(blkCnt > 0u)
+      {
+        /* Read and store the input element in the destination */
+        *px = *pIn++;
+
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += nRows;
+
+        /* Read and store the input element in the destination */
+        *px = *pIn++;
+
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += nRows;
+
+        /* Read and store the input element in the destination */
+        *px = *pIn++;
+
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += nRows;
+
+        /* Read and store the input element in the destination */
+        *px = *pIn++;
+
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += nRows;
+
+        /* Decrement the column loop counter */
+        blkCnt--;
+      }
+
+      /* Perform matrix transpose for last 3 samples here. */
+      blkCnt = nColumns % 0x4u;
+
+      while(blkCnt > 0u)
+      {
+        /* Read and store the input element in the destination */
+        *px = *pIn++;
+
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += nRows;
+
+        /* Decrement the column loop counter */
+        blkCnt--;
+      }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  uint16_t col, i = 0u, row = nRows;             /* loop counters */
+  arm_status status;                             /* status of matrix transpose */
+
+
+#ifdef ARM_MATH_MATRIX_CHECK
+
+  /* Check for matrix mismatch condition */
+  if((pSrc->numRows != pDst->numCols) || (pSrc->numCols != pDst->numRows))
+  {
+    /* Set status as ARM_MATH_SIZE_MISMATCH */
+    status = ARM_MATH_SIZE_MISMATCH;
+  }
+  else
+#endif /*    #ifdef ARM_MATH_MATRIX_CHECK    */
+
+  {
+    /* Matrix transpose by exchanging the rows with columns */
+    /* row loop     */
+    do
+    {
+      /* The pointer px is set to starting address of the column being processed */
+      px = pOut + i;
+
+      /* Initialize column loop counter */
+      col = nColumns;
+
+      while(col > 0u)
+      {
+        /* Read and store the input element in the destination */
+        *px = *pIn++;
+
+        /* Update the pointer px to point to the next row of the transposed matrix */
+        px += nRows;
+
+        /* Decrement the column loop counter */
+        col--;
+      }
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+      i++;
+
+      /* Decrement the row loop counter */
+      row--;
+
+    }
+    while(row > 0u);            /* row loop end */
+
+    /* set status as ARM_MATH_SUCCESS */
+    status = ARM_MATH_SUCCESS;
+  }
+
+  /* Return to application */
+  return (status);
+}
+
+/**    
+ * @} end of MatrixTrans group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_max_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_max_f32.c
new file mode 100644
index 0000000000..afd9648852
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_max_f32.c
@@ -0,0 +1,178 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_max_f32.c    
+*    
+* Description:	Maximum value of a floating-point vector.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupStats    
+ */
+
+/**    
+ * @defgroup Max Maximum    
+ *    
+ * Computes the maximum value of an array of data.     
+ * The function returns both the maximum value and its position within the array.     
+ * There are separate functions for floating-point, Q31, Q15, and Q7 data types.    
+ */
+
+/**    
+ * @addtogroup Max    
+ * @{    
+ */
+
+
+/**    
+ * @brief Maximum value of a floating-point vector.    
+ * @param[in]       *pSrc points to the input vector    
+ * @param[in]       blockSize length of the input vector    
+ * @param[out]      *pResult maximum value returned here    
+ * @param[out]      *pIndex index of maximum value returned here    
+ * @return none.    
+ */
+
+void arm_max_f32(
+  float32_t * pSrc,
+  uint32_t blockSize,
+  float32_t * pResult,
+  uint32_t * pIndex)
+{
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  float32_t maxVal1, maxVal2, out;               /* Temporary variables to store the output value. */
+  uint32_t blkCnt, outIndex, count;              /* loop counter */
+
+  /* Initialise the count value. */
+  count = 0u;
+  /* Initialise the index value to zero. */
+  outIndex = 0u;
+  /* Load first input value that act as reference value for comparision */
+  out = *pSrc++;
+
+  /* Loop unrolling */
+  blkCnt = (blockSize - 1u) >> 2u;
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  while(blkCnt > 0u)
+  {
+    /* Initialize maxVal to the next consecutive values one by one */
+    maxVal1 = *pSrc++;
+
+    maxVal2 = *pSrc++;
+
+    /* compare for the maximum value */
+    if(out < maxVal1)
+    {
+      /* Update the maximum value and its index */
+      out = maxVal1;
+      outIndex = count + 1u;
+    }
+
+    maxVal1 = *pSrc++;
+
+    /* compare for the maximum value */
+    if(out < maxVal2)
+    {
+      /* Update the maximum value and its index */
+      out = maxVal2;
+      outIndex = count + 2u;
+    }
+
+    maxVal2 = *pSrc++;
+
+    /* compare for the maximum value */
+    if(out < maxVal1)
+    {
+      /* Update the maximum value and its index */
+      out = maxVal1;
+      outIndex = count + 3u;
+    }
+
+    /* compare for the maximum value */
+    if(out < maxVal2)
+    {
+      /* Update the maximum value and its index */
+      out = maxVal2;
+      outIndex = count + 4u;
+    }
+
+    count += 4u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* if (blockSize - 1u) is not multiple of 4 */
+  blkCnt = (blockSize - 1u) % 4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  float32_t maxVal1, out;                        /* Temporary variables to store the output value. */
+  uint32_t blkCnt, outIndex;                     /* loop counter */
+
+  /* Initialise the index value to zero. */
+  outIndex = 0u;
+  /* Load first input value that act as reference value for comparision */
+  out = *pSrc++;
+
+  blkCnt = (blockSize - 1u);
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* Initialize maxVal to the next consecutive values one by one */
+    maxVal1 = *pSrc++;
+
+    /* compare for the maximum value */
+    if(out < maxVal1)
+    {
+      /* Update the maximum value and it's index */
+      out = maxVal1;
+      outIndex = blockSize - blkCnt;
+    }
+
+
+    /* Decrement the loop counter */
+    blkCnt--;
+
+  }
+
+  /* Store the maximum value and it's index into destination pointers */
+  *pResult = out;
+  *pIndex = outIndex;
+}
+
+/**    
+ * @} end of Max group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_max_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_max_q15.c
new file mode 100644
index 0000000000..939b5236f6
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_max_q15.c
@@ -0,0 +1,168 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_max_q15.c    
+*    
+* Description:	Maximum value of a Q15 vector.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupStats    
+ */
+
+/**    
+ * @addtogroup Max    
+ * @{    
+ */
+
+
+/**    
+ * @brief Maximum value of a Q15 vector.    
+ * @param[in]       *pSrc points to the input vector    
+ * @param[in]       blockSize length of the input vector    
+ * @param[out]      *pResult maximum value returned here    
+ * @param[out]      *pIndex index of maximum value returned here    
+ * @return none.    
+ */
+
+void arm_max_q15(
+  q15_t * pSrc,
+  uint32_t blockSize,
+  q15_t * pResult,
+  uint32_t * pIndex)
+{
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  q15_t maxVal1, maxVal2, out;                   /* Temporary variables to store the output value. */
+  uint32_t blkCnt, outIndex, count;              /* loop counter */
+
+  /* Initialise the count value. */
+  count = 0u;
+  /* Initialise the index value to zero. */
+  outIndex = 0u;
+  /* Load first input value that act as reference value for comparision */
+  out = *pSrc++;
+
+  /* Loop unrolling */
+  blkCnt = (blockSize - 1u) >> 2u;
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  while(blkCnt > 0u)
+  {
+    /* Initialize maxVal to the next consecutive values one by one */
+    maxVal1 = *pSrc++;
+
+    maxVal2 = *pSrc++;
+
+    /* compare for the maximum value */
+    if(out < maxVal1)
+    {
+      /* Update the maximum value and its index */
+      out = maxVal1;
+      outIndex = count + 1u;
+    }
+
+    maxVal1 = *pSrc++;
+
+    /* compare for the maximum value */
+    if(out < maxVal2)
+    {
+      /* Update the maximum value and its index */
+      out = maxVal2;
+      outIndex = count + 2u;
+    }
+
+    maxVal2 = *pSrc++;
+
+    /* compare for the maximum value */
+    if(out < maxVal1)
+    {
+      /* Update the maximum value and its index */
+      out = maxVal1;
+      outIndex = count + 3u;
+    }
+
+    /* compare for the maximum value */
+    if(out < maxVal2)
+    {
+      /* Update the maximum value and its index */
+      out = maxVal2;
+      outIndex = count + 4u;
+    }
+
+    count += 4u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* if (blockSize - 1u) is not multiple of 4 */
+  blkCnt = (blockSize - 1u) % 4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  q15_t maxVal1, out;                            /* Temporary variables to store the output value. */
+  uint32_t blkCnt, outIndex;                     /* loop counter */
+
+  blkCnt = (blockSize - 1u);
+
+  /* Initialise the index value to zero. */
+  outIndex = 0u;
+  /* Load first input value that act as reference value for comparision */
+  out = *pSrc++;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* Initialize maxVal to the next consecutive values one by one */
+    maxVal1 = *pSrc++;
+
+    /* compare for the maximum value */
+    if(out < maxVal1)
+    {
+      /* Update the maximum value and it's index */
+      out = maxVal1;
+      outIndex = blockSize - blkCnt;
+    }
+    /* Decrement the loop counter */
+    blkCnt--;
+
+  }
+
+  /* Store the maximum value and its index into destination pointers */
+  *pResult = out;
+  *pIndex = outIndex;
+}
+
+/**    
+ * @} end of Max group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_max_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_max_q31.c
new file mode 100644
index 0000000000..18e7572975
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_max_q31.c
@@ -0,0 +1,169 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_max_q31.c    
+*    
+* Description:	Maximum value of a Q31 vector.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupStats    
+ */
+
+/**    
+ * @addtogroup Max    
+ * @{    
+ */
+
+
+/**    
+ * @brief Maximum value of a Q31 vector.    
+ * @param[in]       *pSrc points to the input vector    
+ * @param[in]       blockSize length of the input vector    
+ * @param[out]      *pResult maximum value returned here    
+ * @param[out]      *pIndex index of maximum value returned here    
+ * @return none.    
+ */
+
+void arm_max_q31(
+  q31_t * pSrc,
+  uint32_t blockSize,
+  q31_t * pResult,
+  uint32_t * pIndex)
+{
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t maxVal1, maxVal2, out;                   /* Temporary variables to store the output value. */
+  uint32_t blkCnt, outIndex, count;              /* loop counter */
+
+  /* Initialise the count value. */
+  count = 0u;
+  /* Initialise the index value to zero. */
+  outIndex = 0u;
+  /* Load first input value that act as reference value for comparision */
+  out = *pSrc++;
+
+  /* Loop unrolling */
+  blkCnt = (blockSize - 1u) >> 2u;
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  while(blkCnt > 0u)
+  {
+    /* Initialize maxVal to the next consecutive values one by one */
+    maxVal1 = *pSrc++;
+
+    maxVal2 = *pSrc++;
+
+    /* compare for the maximum value */
+    if(out < maxVal1)
+    {
+      /* Update the maximum value and its index */
+      out = maxVal1;
+      outIndex = count + 1u;
+    }
+
+    maxVal1 = *pSrc++;
+
+    /* compare for the maximum value */
+    if(out < maxVal2)
+    {
+      /* Update the maximum value and its index */
+      out = maxVal2;
+      outIndex = count + 2u;
+    }
+
+    maxVal2 = *pSrc++;
+
+    /* compare for the maximum value */
+    if(out < maxVal1)
+    {
+      /* Update the maximum value and its index */
+      out = maxVal1;
+      outIndex = count + 3u;
+    }
+
+    /* compare for the maximum value */
+    if(out < maxVal2)
+    {
+      /* Update the maximum value and its index */
+      out = maxVal2;
+      outIndex = count + 4u;
+    }
+
+    count += 4u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* if (blockSize - 1u) is not multiple of 4 */
+  blkCnt = (blockSize - 1u) % 4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  q31_t maxVal1, out;                            /* Temporary variables to store the output value. */
+  uint32_t blkCnt, outIndex;                     /* loop counter */
+
+  /* Initialise the index value to zero. */
+  outIndex = 0u;
+  /* Load first input value that act as reference value for comparision */
+  out = *pSrc++;
+
+  blkCnt = (blockSize - 1u);
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* Initialize maxVal to the next consecutive values one by one */
+    maxVal1 = *pSrc++;
+
+    /* compare for the maximum value */
+    if(out < maxVal1)
+    {
+      /* Update the maximum value and it's index */
+      out = maxVal1;
+      outIndex = blockSize - blkCnt;
+    }
+
+    /* Decrement the loop counter */
+    blkCnt--;
+
+  }
+
+  /* Store the maximum value and its index into destination pointers */
+  *pResult = out;
+  *pIndex = outIndex;
+}
+
+/**    
+ * @} end of Max group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_max_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_max_q7.c
new file mode 100644
index 0000000000..110a8fe5f7
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_max_q7.c
@@ -0,0 +1,169 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_max_q7.c    
+*    
+* Description:	Maximum value of a Q7 vector.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupStats    
+ */
+
+/**    
+ * @addtogroup Max    
+ * @{    
+ */
+
+
+/**    
+ * @brief Maximum value of a Q7 vector.    
+ * @param[in]       *pSrc points to the input vector    
+ * @param[in]       blockSize length of the input vector    
+ * @param[out]      *pResult maximum value returned here    
+ * @param[out]      *pIndex index of maximum value returned here    
+  * @return none.    
+ */
+
+void arm_max_q7(
+  q7_t * pSrc,
+  uint32_t blockSize,
+  q7_t * pResult,
+  uint32_t * pIndex)
+{
+#ifndef ARM_MATH_CM0
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q7_t maxVal1, maxVal2, out;                    /* Temporary variables to store the output value. */
+  uint32_t blkCnt, outIndex, count;              /* loop counter */
+
+  /* Initialise the count value. */
+  count = 0u;
+  /* Initialise the index value to zero. */
+  outIndex = 0u;
+  /* Load first input value that act as reference value for comparision */
+  out = *pSrc++;
+
+  /* Loop unrolling */
+  blkCnt = (blockSize - 1u) >> 2u;
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  while(blkCnt > 0u)
+  {
+    /* Initialize maxVal to the next consecutive values one by one */
+    maxVal1 = *pSrc++;
+
+    maxVal2 = *pSrc++;
+
+    /* compare for the maximum value */
+    if(out < maxVal1)
+    {
+      /* Update the maximum value and its index */
+      out = maxVal1;
+      outIndex = count + 1u;
+    }
+
+    maxVal1 = *pSrc++;
+
+    /* compare for the maximum value */
+    if(out < maxVal2)
+    {
+      /* Update the maximum value and its index */
+      out = maxVal2;
+      outIndex = count + 2u;
+    }
+
+    maxVal2 = *pSrc++;
+
+    /* compare for the maximum value */
+    if(out < maxVal1)
+    {
+      /* Update the maximum value and its index */
+      out = maxVal1;
+      outIndex = count + 3u;
+    }
+
+    /* compare for the maximum value */
+    if(out < maxVal2)
+    {
+      /* Update the maximum value and its index */
+      out = maxVal2;
+      outIndex = count + 4u;
+    }
+
+    count += 4u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* if (blockSize - 1u) is not multiple of 4 */
+  blkCnt = (blockSize - 1u) % 4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  q7_t maxVal1, out;                             /* Temporary variables to store the output value. */
+  uint32_t blkCnt, outIndex;                     /* loop counter */
+
+  /* Initialise the index value to zero. */
+  outIndex = 0u;
+  /* Load first input value that act as reference value for comparision */
+  out = *pSrc++;
+
+  blkCnt = (blockSize - 1u);
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* Initialize maxVal to the next consecutive values one by one */
+    maxVal1 = *pSrc++;
+
+    /* compare for the maximum value */
+    if(out < maxVal1)
+    {
+      /* Update the maximum value and it's index */
+      out = maxVal1;
+      outIndex = blockSize - blkCnt;
+    }
+    /* Decrement the loop counter */
+    blkCnt--;
+
+  }
+
+  /* Store the maximum value and its index into destination pointers */
+  *pResult = out;
+  *pIndex = outIndex;
+
+}
+
+/**    
+ * @} end of Max group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_mean_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_mean_f32.c
new file mode 100644
index 0000000000..7823d746ca
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_mean_f32.c
@@ -0,0 +1,131 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_mean_f32.c    
+*    
+* Description:	Mean value of a floating-point vector.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupStats    
+ */
+
+/**    
+ * @defgroup mean Mean    
+ *    
+ * Calculates the mean of the input vector. Mean is defined as the average of the elements in the vector.    
+ * The underlying algorithm is used:    
+ *    
+ * 
    
+ * 	Result = (pSrc[0] + pSrc[1] + pSrc[2] + ... + pSrc[blockSize-1]) / blockSize;    
+ * 
    
+ *    
+ * There are separate functions for floating-point, Q31, Q15, and Q7 data types.    
+ */
+
+/**    
+ * @addtogroup mean    
+ * @{    
+ */
+
+
+/**    
+ * @brief Mean value of a floating-point vector.    
+ * @param[in]       *pSrc points to the input vector    
+ * @param[in]       blockSize length of the input vector    
+ * @param[out]      *pResult mean value returned here    
+ * @return none.    
+ */
+
+
+void arm_mean_f32(
+  float32_t * pSrc,
+  uint32_t blockSize,
+  float32_t * pResult)
+{
+  float32_t sum = 0.0f;                          /* Temporary result storage */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  float32_t in1, in2, in3, in4;
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
+    in1 = *pSrc++;
+    in2 = *pSrc++;
+    in3 = *pSrc++;
+    in4 = *pSrc++;
+
+    sum += in1;
+    sum += in2;
+    sum += in3;
+    sum += in4;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
+    sum += *pSrc++;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) / blockSize  */
+  /* Store the result to the destination */
+  *pResult = sum / (float32_t) blockSize;
+}
+
+/**    
+ * @} end of mean group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_mean_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_mean_q15.c
new file mode 100644
index 0000000000..49ec1e62e7
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_mean_q15.c
@@ -0,0 +1,125 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_mean_q15.c    
+*    
+* Description:	Mean value of a Q15 vector.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupStats    
+ */
+
+/**    
+ * @addtogroup mean    
+ * @{    
+ */
+
+/**    
+ * @brief Mean value of a Q15 vector.    
+ * @param[in]       *pSrc points to the input vector    
+ * @param[in]       blockSize length of the input vector    
+ * @param[out]      *pResult mean value returned here    
+ * @return none.    
+ *    
+ * @details    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function is implemented using a 32-bit internal accumulator.    
+ * The input is represented in 1.15 format and is accumulated in a 32-bit     
+ * accumulator in 17.15 format.     
+ * There is no risk of internal overflow with this approach, and the     
+ * full precision of intermediate result is preserved.     
+ * Finally, the accumulator is saturated and truncated to yield a result of 1.15 format.    
+ *    
+ */
+
+
+void arm_mean_q15(
+  q15_t * pSrc,
+  uint32_t blockSize,
+  q15_t * pResult)
+{
+  q31_t sum = 0;                                 /* Temporary result storage */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t in;
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
+    in = *__SIMD32(pSrc)++;
+    sum += ((in << 16) >> 16);
+    sum += (in >> 16);
+    in = *__SIMD32(pSrc)++;
+    sum += ((in << 16) >> 16);
+    sum += (in >> 16);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
+    sum += *pSrc++;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) / blockSize  */
+  /* Store the result to the destination */
+  *pResult = (q15_t) (sum / blockSize);
+}
+
+/**    
+ * @} end of mean group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_mean_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_mean_q31.c
new file mode 100644
index 0000000000..88a5de2995
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_mean_q31.c
@@ -0,0 +1,128 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_mean_q31.c    
+*    
+* Description:	Mean value of a Q31 vector.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupStats    
+ */
+
+/**    
+ * @addtogroup mean    
+ * @{    
+ */
+
+/**    
+ * @brief Mean value of a Q31 vector.    
+ * @param[in]       *pSrc points to the input vector    
+ * @param[in]       blockSize length of the input vector    
+ * @param[out]      *pResult mean value returned here    
+ * @return none.    
+ *    
+ * @details    
+ * Scaling and Overflow Behavior:    
+ *\par    
+ * The function is implemented using a 64-bit internal accumulator.    
+ * The input is represented in 1.31 format and is accumulated in a 64-bit    
+ * accumulator in 33.31 format.    
+ * There is no risk of internal overflow with this approach, and the     
+ * full precision of intermediate result is preserved.     
+ * Finally, the accumulator is truncated to yield a result of 1.31 format.    
+ *    
+ */
+
+
+void arm_mean_q31(
+  q31_t * pSrc,
+  uint32_t blockSize,
+  q31_t * pResult)
+{
+  q63_t sum = 0;                                 /* Temporary result storage */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t in1, in2, in3, in4;
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
+    in1 = *pSrc++;
+    in2 = *pSrc++;
+    in3 = *pSrc++;
+    in4 = *pSrc++;
+
+    sum += in1;
+    sum += in2;
+    sum += in3;
+    sum += in4;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
+    sum += *pSrc++;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) / blockSize  */
+  /* Store the result to the destination */
+  *pResult = (q31_t) (sum / (int32_t) blockSize);
+}
+
+/**    
+ * @} end of mean group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_mean_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_mean_q7.c
new file mode 100644
index 0000000000..a34c011bc1
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_mean_q7.c
@@ -0,0 +1,125 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_mean_q7.c    
+*    
+* Description:	Mean value of a Q7 vector.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupStats    
+ */
+
+/**    
+ * @addtogroup mean    
+ * @{    
+ */
+
+/**    
+ * @brief Mean value of a Q7 vector.    
+ * @param[in]       *pSrc points to the input vector    
+ * @param[in]       blockSize length of the input vector    
+ * @param[out]      *pResult mean value returned here    
+ * @return none.    
+ *    
+ * @details    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function is implemented using a 32-bit internal accumulator.     
+ * The input is represented in 1.7 format and is accumulated in a 32-bit    
+ * accumulator in 25.7 format.    
+ * There is no risk of internal overflow with this approach, and the     
+ * full precision of intermediate result is preserved.     
+ * Finally, the accumulator is truncated to yield a result of 1.7 format.    
+ *    
+ */
+
+
+void arm_mean_q7(
+  q7_t * pSrc,
+  uint32_t blockSize,
+  q7_t * pResult)
+{
+  q31_t sum = 0;                                 /* Temporary result storage */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t in;
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
+    in = *__SIMD32(pSrc)++;
+
+    sum += ((in << 24) >> 24);
+    sum += ((in << 16) >> 24);
+    sum += ((in << 8) >> 24);
+    sum += (in >> 24);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
+    sum += *pSrc++;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) / blockSize  */
+  /* Store the result to the destination */
+  *pResult = (q7_t) (sum / (int32_t) blockSize);
+}
+
+/**    
+ * @} end of mean group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_min_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_min_f32.c
new file mode 100644
index 0000000000..dc2fdf624f
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_min_f32.c
@@ -0,0 +1,175 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_min_f32.c    
+*    
+* Description:	Minimum value of a floating-point vector.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupStats    
+ */
+
+/**    
+ * @defgroup Min Minimum    
+ *    
+ * Computes the minimum value of an array of data.     
+ * The function returns both the minimum value and its position within the array.     
+ * There are separate functions for floating-point, Q31, Q15, and Q7 data types.    
+ */
+
+/**    
+ * @addtogroup Min    
+ * @{    
+ */
+
+
+/**    
+ * @brief Minimum value of a floating-point vector.    
+ * @param[in]       *pSrc points to the input vector    
+ * @param[in]       blockSize length of the input vector    
+ * @param[out]      *pResult minimum value returned here    
+ * @param[out]      *pIndex index of minimum value returned here    
+  * @return none.    
+ *    
+ */
+
+void arm_min_f32(
+  float32_t * pSrc,
+  uint32_t blockSize,
+  float32_t * pResult,
+  uint32_t * pIndex)
+{
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  float32_t minVal1, minVal2, out;               /* Temporary variables to store the output value. */
+  uint32_t blkCnt, outIndex, count;              /* loop counter */
+
+  /* Initialise the count value. */
+  count = 0u;
+  /* Initialise the index value to zero. */
+  outIndex = 0u;
+  /* Load first input value that act as reference value for comparision */
+  out = *pSrc++;
+
+  /* Loop unrolling */
+  blkCnt = (blockSize - 1u) >> 2u;
+
+  while(blkCnt > 0)
+  {
+    /* Initialize minVal to the next consecutive values one by one */
+    minVal1 = *pSrc++;
+    minVal2 = *pSrc++;
+
+    /* compare for the minimum value */
+    if(out > minVal1)
+    {
+      /* Update the minimum value and its index */
+      out = minVal1;
+      outIndex = count + 1u;
+    }
+
+    minVal1 = *pSrc++;
+
+    /* compare for the minimum value */
+    if(out > minVal2)
+    {
+      /* Update the minimum value and its index */
+      out = minVal2;
+      outIndex = count + 2u;
+    }
+
+    minVal2 = *pSrc++;
+
+    /* compare for the minimum value */
+    if(out > minVal1)
+    {
+      /* Update the minimum value and its index */
+      out = minVal1;
+      outIndex = count + 3u;
+    }
+
+    /* compare for the minimum value */
+    if(out > minVal2)
+    {
+      /* Update the minimum value and its index */
+      out = minVal2;
+      outIndex = count + 4u;
+    }
+
+    count += 4u;
+
+    blkCnt--;
+  }
+
+  /* if (blockSize - 1u ) is not multiple of 4 */
+  blkCnt = (blockSize - 1u) % 4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  float32_t minVal1, out;                        /* Temporary variables to store the output value. */
+  uint32_t blkCnt, outIndex;                     /* loop counter */
+
+  /* Initialise the index value to zero. */
+  outIndex = 0u;
+  /* Load first input value that act as reference value for comparision */
+  out = *pSrc++;
+
+  blkCnt = (blockSize - 1u);
+
+#endif //      #ifndef ARM_MATH_CM0
+
+  while(blkCnt > 0)
+  {
+    /* Initialize minVal to the next consecutive values one by one */
+    minVal1 = *pSrc++;
+
+    /* compare for the minimum value */
+    if(out > minVal1)
+    {
+      /* Update the minimum value and it's index */
+      out = minVal1;
+      outIndex = blockSize - blkCnt;
+    }
+
+    blkCnt--;
+
+  }
+
+  /* Store the minimum value and it's index into destination pointers */
+  *pResult = out;
+  *pIndex = outIndex;
+}
+
+/**    
+ * @} end of Min group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_min_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_min_q15.c
new file mode 100644
index 0000000000..35b67bb1e9
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_min_q15.c
@@ -0,0 +1,169 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_min_q15.c    
+*    
+* Description:	Minimum value of a Q15 vector.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupStats    
+ */
+
+
+/**    
+ * @addtogroup Min    
+ * @{    
+ */
+
+
+/**    
+ * @brief Minimum value of a Q15 vector.    
+ * @param[in]       *pSrc points to the input vector    
+ * @param[in]       blockSize length of the input vector    
+ * @param[out]      *pResult minimum value returned here    
+ * @param[out]      *pIndex index of minimum value returned here    
+ * @return none.    
+ *    
+ */
+
+void arm_min_q15(
+  q15_t * pSrc,
+  uint32_t blockSize,
+  q15_t * pResult,
+  uint32_t * pIndex)
+{
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  q15_t minVal1, minVal2, out;                   /* Temporary variables to store the output value. */
+  uint32_t blkCnt, outIndex, count;              /* loop counter */
+
+  /* Initialise the count value. */
+  count = 0u;
+  /* Initialise the index value to zero. */
+  outIndex = 0u;
+  /* Load first input value that act as reference value for comparision */
+  out = *pSrc++;
+
+  /* Loop unrolling */
+  blkCnt = (blockSize - 1u) >> 2u;
+
+  while(blkCnt > 0)
+  {
+    /* Initialize minVal to the next consecutive values one by one */
+    minVal1 = *pSrc++;
+    minVal2 = *pSrc++;
+
+    /* compare for the minimum value */
+    if(out > minVal1)
+    {
+      /* Update the minimum value and its index */
+      out = minVal1;
+      outIndex = count + 1u;
+    }
+
+    minVal1 = *pSrc++;
+
+    /* compare for the minimum value */
+    if(out > minVal2)
+    {
+      /* Update the minimum value and its index */
+      out = minVal2;
+      outIndex = count + 2u;
+    }
+
+    minVal2 = *pSrc++;
+
+    /* compare for the minimum value */
+    if(out > minVal1)
+    {
+      /* Update the minimum value and its index */
+      out = minVal1;
+      outIndex = count + 3u;
+    }
+
+    /* compare for the minimum value */
+    if(out > minVal2)
+    {
+      /* Update the minimum value and its index */
+      out = minVal2;
+      outIndex = count + 4u;
+    }
+
+    count += 4u;
+
+    blkCnt--;
+  }
+
+  /* if (blockSize - 1u ) is not multiple of 4 */
+  blkCnt = (blockSize - 1u) % 4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  q15_t minVal1, out;                            /* Temporary variables to store the output value. */
+  uint32_t blkCnt, outIndex;                     /* loop counter */
+
+  blkCnt = (blockSize - 1u);
+
+  /* Initialise the index value to zero. */
+  outIndex = 0u;
+  /* Load first input value that act as reference value for comparision */
+  out = *pSrc++;
+
+#endif //      #ifndef ARM_MATH_CM0
+
+  while(blkCnt > 0)
+  {
+    /* Initialize minVal to the next consecutive values one by one */
+    minVal1 = *pSrc++;
+
+    /* compare for the minimum value */
+    if(out > minVal1)
+    {
+      /* Update the minimum value and it's index */
+      out = minVal1;
+      outIndex = blockSize - blkCnt;
+    }
+
+    blkCnt--;
+
+  }
+
+
+
+  /* Store the minimum value and its index into destination pointers */
+  *pResult = out;
+  *pIndex = outIndex;
+}
+
+/**    
+ * @} end of Min group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_min_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_min_q31.c
new file mode 100644
index 0000000000..4a9befc75c
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_min_q31.c
@@ -0,0 +1,168 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_min_q31.c    
+*    
+* Description:	Minimum value of a Q31 vector.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupStats    
+ */
+
+
+/**    
+ * @addtogroup Min    
+ * @{    
+ */
+
+
+/**    
+ * @brief Minimum value of a Q31 vector.    
+ * @param[in]       *pSrc points to the input vector    
+ * @param[in]       blockSize length of the input vector    
+ * @param[out]      *pResult minimum value returned here    
+ * @param[out]      *pIndex index of minimum value returned here    
+ * @return none.    
+ *    
+ */
+
+void arm_min_q31(
+  q31_t * pSrc,
+  uint32_t blockSize,
+  q31_t * pResult,
+  uint32_t * pIndex)
+{
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t minVal1, minVal2, out;                   /* Temporary variables to store the output value. */
+  uint32_t blkCnt, outIndex, count;              /* loop counter */
+
+  /* Initialise the count value. */
+  count = 0u;
+  /* Initialise the index value to zero. */
+  outIndex = 0u;
+  /* Load first input value that act as reference value for comparision */
+  out = *pSrc++;
+
+
+  /* Loop unrolling */
+  blkCnt = (blockSize - 1u) >> 2u;
+
+  while(blkCnt > 0)
+  {
+    /* Initialize minVal to the next consecutive values one by one */
+    minVal1 = *pSrc++;
+    minVal2 = *pSrc++;
+
+    /* compare for the minimum value */
+    if(out > minVal1)
+    {
+      /* Update the minimum value and its index */
+      out = minVal1;
+      outIndex = count + 1u;
+    }
+
+    minVal1 = *pSrc++;
+
+    /* compare for the minimum value */
+    if(out > minVal2)
+    {
+      /* Update the minimum value and its index */
+      out = minVal2;
+      outIndex = count + 2u;
+    }
+
+    minVal2 = *pSrc++;
+
+    /* compare for the minimum value */
+    if(out > minVal1)
+    {
+      /* Update the minimum value and its index */
+      out = minVal1;
+      outIndex = count + 3u;
+    }
+
+    /* compare for the minimum value */
+    if(out > minVal2)
+    {
+      /* Update the minimum value and its index */
+      out = minVal2;
+      outIndex = count + 4u;
+    }
+
+    count += 4u;
+
+    blkCnt--;
+  }
+
+  /* if (blockSize - 1u ) is not multiple of 4 */
+  blkCnt = (blockSize - 1u) % 4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  q31_t minVal1, out;                            /* Temporary variables to store the output value. */
+  uint32_t blkCnt, outIndex;                     /* loop counter */
+
+  blkCnt = (blockSize - 1u);
+
+  /* Initialise the index value to zero. */
+  outIndex = 0u;
+  /* Load first input value that act as reference value for comparision */
+  out = *pSrc++;
+
+#endif //      #ifndef ARM_MATH_CM0
+
+  while(blkCnt > 0)
+  {
+    /* Initialize minVal to the next consecutive values one by one */
+    minVal1 = *pSrc++;
+
+    /* compare for the minimum value */
+    if(out > minVal1)
+    {
+      /* Update the minimum value and it's index */
+      out = minVal1;
+      outIndex = blockSize - blkCnt;
+    }
+
+    blkCnt--;
+
+  }
+
+  /* Store the minimum value and its index into destination pointers */
+  *pResult = out;
+  *pIndex = outIndex;
+}
+
+/**    
+ * @} end of Min group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_min_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_min_q7.c
new file mode 100644
index 0000000000..aaf8ad9ff8
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_min_q7.c
@@ -0,0 +1,170 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_min_q7.c    
+*    
+* Description:	Minimum value of a Q7 vector.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupStats    
+ */
+
+/**    
+ * @addtogroup Min    
+ * @{    
+ */
+
+
+/**    
+ * @brief Minimum value of a Q7 vector.    
+ * @param[in]       *pSrc points to the input vector    
+ * @param[in]       blockSize length of the input vector    
+ * @param[out]      *pResult minimum value returned here    
+ * @param[out]      *pIndex index of minimum value returned here    
+ * @return none.    
+ *    
+ */
+
+void arm_min_q7(
+  q7_t * pSrc,
+  uint32_t blockSize,
+  q7_t * pResult,
+  uint32_t * pIndex)
+{
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q7_t minVal1, minVal2, out;                    /* Temporary variables to store the output value. */
+  uint32_t blkCnt, outIndex, count;              /* loop counter */
+
+  /* Initialise the count value. */
+  count = 0u;
+  /* Initialise the index value to zero. */
+  outIndex = 0u;
+  /* Load first input value that act as reference value for comparision */
+  out = *pSrc++;
+
+  /* Loop unrolling */
+  blkCnt = (blockSize - 1u) >> 2u;
+
+  while(blkCnt > 0)
+  {
+    /* Initialize minVal to the next consecutive values one by one */
+    minVal1 = *pSrc++;
+    minVal2 = *pSrc++;
+
+    /* compare for the minimum value */
+    if(out > minVal1)
+    {
+      /* Update the minimum value and its index */
+      out = minVal1;
+      outIndex = count + 1u;
+    }
+
+    minVal1 = *pSrc++;
+
+    /* compare for the minimum value */
+    if(out > minVal2)
+    {
+      /* Update the minimum value and its index */
+      out = minVal2;
+      outIndex = count + 2u;
+    }
+
+    minVal2 = *pSrc++;
+
+    /* compare for the minimum value */
+    if(out > minVal1)
+    {
+      /* Update the minimum value and its index */
+      out = minVal1;
+      outIndex = count + 3u;
+    }
+
+    /* compare for the minimum value */
+    if(out > minVal2)
+    {
+      /* Update the minimum value and its index */
+      out = minVal2;
+      outIndex = count + 4u;
+    }
+
+    count += 4u;
+
+    blkCnt--;
+  }
+
+  /* if (blockSize - 1u ) is not multiple of 4 */
+  blkCnt = (blockSize - 1u) % 4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  q7_t minVal1, out;                             /* Temporary variables to store the output value. */
+  uint32_t blkCnt, outIndex;                     /* loop counter */
+
+  /* Initialise the index value to zero. */
+  outIndex = 0u;
+  /* Load first input value that act as reference value for comparision */
+  out = *pSrc++;
+
+  blkCnt = (blockSize - 1u);
+
+#endif //      #ifndef ARM_MATH_CM0
+
+  while(blkCnt > 0)
+  {
+    /* Initialize minVal to the next consecutive values one by one */
+    minVal1 = *pSrc++;
+
+    /* compare for the minimum value */
+    if(out > minVal1)
+    {
+      /* Update the minimum value and it's index */
+      out = minVal1;
+      outIndex = blockSize - blkCnt;
+    }
+
+    blkCnt--;
+
+  }
+
+  /* Store the minimum value and its index into destination pointers */
+  *pResult = out;
+  *pIndex = outIndex;
+
+
+}
+
+/**    
+ * @} end of Min group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_power_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_power_f32.c
new file mode 100644
index 0000000000..5ee0060d8f
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_power_f32.c
@@ -0,0 +1,138 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_power_f32.c    
+*    
+* Description:	Sum of the squares of the elements of a floating-point vector.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupStats    
+ */
+
+/**    
+ * @defgroup power Power    
+ *    
+ * Calculates the sum of the squares of the elements in the input vector.    
+ * The underlying algorithm is used:    
+ *    
+ * 
    
+ * 	Result = pSrc[0] * pSrc[0] + pSrc[1] * pSrc[1] + pSrc[2] * pSrc[2] + ... + pSrc[blockSize-1] * pSrc[blockSize-1];    
+ * 
    
+ *   
+ * There are separate functions for floating point, Q31, Q15, and Q7 data types.     
+ */
+
+/**    
+ * @addtogroup power    
+ * @{    
+ */
+
+
+/**    
+ * @brief Sum of the squares of the elements of a floating-point vector.    
+ * @param[in]       *pSrc points to the input vector    
+ * @param[in]       blockSize length of the input vector    
+ * @param[out]      *pResult sum of the squares value returned here    
+ * @return none.    
+ *    
+ */
+
+
+void arm_power_f32(
+  float32_t * pSrc,
+  uint32_t blockSize,
+  float32_t * pResult)
+{
+  float32_t sum = 0.0f;                          /* accumulator */
+  float32_t in;                                  /* Temporary variable to store input value */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
+    /* Compute Power and then store the result in a temporary variable, sum. */
+    in = *pSrc++;
+    sum += in * in;
+    in = *pSrc++;
+    sum += in * in;
+    in = *pSrc++;
+    sum += in * in;
+    in = *pSrc++;
+    sum += in * in;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+
+  while(blkCnt > 0u)
+  {
+    /* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
+    /* compute power and then store the result in a temporary variable, sum. */
+    in = *pSrc++;
+    sum += in * in;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Store the result to the destination */
+  *pResult = sum;
+}
+
+/**    
+ * @} end of power group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_power_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_power_q15.c
new file mode 100644
index 0000000000..aed06a17ac
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_power_q15.c
@@ -0,0 +1,144 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_power_q15.c    
+*    
+* Description:	Sum of the squares of the elements of a Q15 vector.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupStats    
+ */
+
+/**    
+ * @addtogroup power    
+ * @{    
+ */
+
+/**    
+ * @brief Sum of the squares of the elements of a Q15 vector.    
+ * @param[in]       *pSrc points to the input vector    
+ * @param[in]       blockSize length of the input vector    
+ * @param[out]      *pResult sum of the squares value returned here    
+ * @return none.    
+ *    
+ * @details    
+ * Scaling and Overflow Behavior:    
+ *    
+ * \par    
+ * The function is implemented using a 64-bit internal accumulator.     
+ * The input is represented in 1.15 format.   
+ * Intermediate multiplication yields a 2.30 format, and this    
+ * result is added without saturation to a 64-bit accumulator in 34.30 format.    
+ * With 33 guard bits in the accumulator, there is no risk of overflow, and the    
+ * full precision of the intermediate multiplication is preserved.    
+ * Finally, the return result is in 34.30 format.     
+ *    
+ */
+
+void arm_power_q15(
+  q15_t * pSrc,
+  uint32_t blockSize,
+  q63_t * pResult)
+{
+  q63_t sum = 0;                                 /* Temporary result storage */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q31_t in32;                                    /* Temporary variable to store input value */
+  q15_t in16;                                    /* Temporary variable to store input value */
+  uint32_t blkCnt;                               /* loop counter */
+
+
+  /* loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
+    /* Compute Power and then store the result in a temporary variable, sum. */
+    in32 = *__SIMD32(pSrc)++;
+    sum = __SMLALD(in32, in32, sum);
+    in32 = *__SIMD32(pSrc)++;
+    sum = __SMLALD(in32, in32, sum);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
+    /* Compute Power and then store the result in a temporary variable, sum. */
+    in16 = *pSrc++;
+    sum = __SMLALD(in16, in16, sum);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  q15_t in;                                      /* Temporary variable to store input value */
+  uint32_t blkCnt;                               /* loop counter */
+
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
+    /* Compute Power and then store the result in a temporary variable, sum. */
+    in = *pSrc++;
+    sum += ((q31_t) in * in);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  /* Store the results in 34.30 format  */
+  *pResult = sum;
+}
+
+/**    
+ * @} end of power group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_power_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_power_q31.c
new file mode 100644
index 0000000000..43f03f757f
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_power_q31.c
@@ -0,0 +1,135 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_power_q31.c    
+*    
+* Description:	Sum of the squares of the elements of a Q31 vector.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupStats    
+ */
+
+/**    
+ * @addtogroup power    
+ * @{    
+ */
+
+/**    
+ * @brief Sum of the squares of the elements of a Q31 vector.    
+ * @param[in]       *pSrc points to the input vector    
+ * @param[in]       blockSize length of the input vector    
+ * @param[out]      *pResult sum of the squares value returned here    
+ * @return none.    
+ *    
+ * @details    
+ * Scaling and Overflow Behavior:    
+ *    
+ * \par    
+ * The function is implemented using a 64-bit internal accumulator.    
+ * The input is represented in 1.31 format.    
+ * Intermediate multiplication yields a 2.62 format, and this    
+ * result is truncated to 2.48 format by discarding the lower 14 bits.    
+ * The 2.48 result is then added without saturation to a 64-bit accumulator in 16.48 format.    
+ * With 15 guard bits in the accumulator, there is no risk of overflow, and the    
+ * full precision of the intermediate multiplication is preserved.    
+ * Finally, the return result is in 16.48 format.     
+ *    
+ */
+
+void arm_power_q31(
+  q31_t * pSrc,
+  uint32_t blockSize,
+  q63_t * pResult)
+{
+  q63_t sum = 0;                                 /* Temporary result storage */
+  q31_t in;
+  uint32_t blkCnt;                               /* loop counter */
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
+    /* Compute Power then shift intermediate results by 14 bits to maintain 16.48 format and then store the result in a temporary variable sum, providing 15 guard bits. */
+    in = *pSrc++;
+    sum += ((q63_t) in * in) >> 14u;
+
+    in = *pSrc++;
+    sum += ((q63_t) in * in) >> 14u;
+
+    in = *pSrc++;
+    sum += ((q63_t) in * in) >> 14u;
+
+    in = *pSrc++;
+    sum += ((q63_t) in * in) >> 14u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
+    /* Compute Power and then store the result in a temporary variable, sum. */
+    in = *pSrc++;
+    sum += ((q63_t) in * in) >> 14u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Store the results in 16.48 format  */
+  *pResult = sum;
+}
+
+/**    
+ * @} end of power group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_power_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_power_q7.c
new file mode 100644
index 0000000000..5cb99b4c2f
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_power_q7.c
@@ -0,0 +1,133 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_power_q7.c    
+*    
+* Description:	Sum of the squares of the elements of a Q7 vector.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupStats    
+ */
+
+/**    
+ * @addtogroup power    
+ * @{    
+ */
+
+/**    
+ * @brief Sum of the squares of the elements of a Q7 vector.    
+ * @param[in]       *pSrc points to the input vector    
+ * @param[in]       blockSize length of the input vector    
+ * @param[out]      *pResult sum of the squares value returned here    
+ * @return none.    
+ *    
+ * @details    
+ * Scaling and Overflow Behavior:    
+ *    
+ * \par    
+ * The function is implemented using a 32-bit internal accumulator.     
+ * The input is represented in 1.7 format.   
+ * Intermediate multiplication yields a 2.14 format, and this    
+ * result is added without saturation to an accumulator in 18.14 format.    
+ * With 17 guard bits in the accumulator, there is no risk of overflow, and the    
+ * full precision of the intermediate multiplication is preserved.    
+ * Finally, the return result is in 18.14 format.     
+ *    
+ */
+
+void arm_power_q7(
+  q7_t * pSrc,
+  uint32_t blockSize,
+  q31_t * pResult)
+{
+  q31_t sum = 0;                                 /* Temporary result storage */
+  q7_t in;                                       /* Temporary variable to store input */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q31_t input1;                                  /* Temporary variable to store packed input */
+  q31_t in1, in2;                                /* Temporary variables to store input */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* Reading two inputs of pSrc vector and packing */
+    input1 = *__SIMD32(pSrc)++;
+
+    in1 = __SXTB16(__ROR(input1, 8));
+    in2 = __SXTB16(input1);
+
+    /* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
+    /* calculate power and accumulate to accumulator */
+    sum = __SMLAD(in1, in1, sum);
+    sum = __SMLAD(in2, in2, sum);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
+    /* Compute Power and then store the result in a temporary variable, sum. */
+    in = *pSrc++;
+    sum += ((q15_t) in * in);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Store the result in 18.14 format  */
+  *pResult = sum;
+}
+
+/**    
+ * @} end of power group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_rms_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_rms_f32.c
new file mode 100644
index 0000000000..573896ed4d
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_rms_f32.c
@@ -0,0 +1,133 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_rms_f32.c    
+*    
+* Description:	Root mean square value of an array of F32 type    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupStats    
+ */
+
+/**    
+ * @defgroup RMS Root mean square (RMS)    
+ *    
+ *     
+ * Calculates the Root Mean Sqaure of the elements in the input vector.    
+ * The underlying algorithm is used:    
+ *    
+ * 
    
+ * 	Result = sqrt(((pSrc[0] * pSrc[0] + pSrc[1] * pSrc[1] + ... + pSrc[blockSize-1] * pSrc[blockSize-1]) / blockSize));    
+ * 
    
+ *   
+ * There are separate functions for floating point, Q31, and Q15 data types.     
+ */
+
+/**    
+ * @addtogroup RMS    
+ * @{    
+ */
+
+
+/**    
+ * @brief Root Mean Square of the elements of a floating-point vector.    
+ * @param[in]       *pSrc points to the input vector    
+ * @param[in]       blockSize length of the input vector    
+ * @param[out]      *pResult rms value returned here    
+ * @return none.    
+ *    
+ */
+
+void arm_rms_f32(
+  float32_t * pSrc,
+  uint32_t blockSize,
+  float32_t * pResult)
+{
+  float32_t sum = 0.0f;                          /* Accumulator */
+  float32_t in;                                  /* Tempoprary variable to store input value */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /* loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
+    /* Compute sum of the squares and then store the result in a temporary variable, sum  */
+    in = *pSrc++;
+    sum += in * in;
+    in = *pSrc++;
+    sum += in * in;
+    in = *pSrc++;
+    sum += in * in;
+    in = *pSrc++;
+    sum += in * in;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
+    /* Compute sum of the squares and then store the results in a temporary variable, sum  */
+    in = *pSrc++;
+    sum += in * in;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Compute Rms and store the result in the destination */
+  arm_sqrt_f32(sum / (float32_t) blockSize, pResult);
+}
+
+/**    
+ * @} end of RMS group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_rms_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_rms_q15.c
new file mode 100644
index 0000000000..491c652e7a
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_rms_q15.c
@@ -0,0 +1,153 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_rms_q15.c    
+*    
+* Description:	Root Mean Square of the elements of a Q15 vector.  
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @addtogroup RMS    
+ * @{    
+ */
+
+/**    
+ * @brief Root Mean Square of the elements of a Q15 vector.    
+ * @param[in]       *pSrc points to the input vector    
+ * @param[in]       blockSize length of the input vector    
+ * @param[out]      *pResult rms value returned here    
+ * @return none.    
+ *    
+ * @details    
+ * Scaling and Overflow Behavior:    
+ *    
+ * \par    
+ * The function is implemented using a 64-bit internal accumulator.    
+ * The input is represented in 1.15 format.    
+ * Intermediate multiplication yields a 2.30 format, and this    
+ * result is added without saturation to a 64-bit accumulator in 34.30 format.    
+ * With 33 guard bits in the accumulator, there is no risk of overflow, and the    
+ * full precision of the intermediate multiplication is preserved.    
+ * Finally, the 34.30 result is truncated to 34.15 format by discarding the lower     
+ * 15 bits, and then saturated to yield a result in 1.15 format.    
+ *    
+ */
+
+void arm_rms_q15(
+  q15_t * pSrc,
+  uint32_t blockSize,
+  q15_t * pResult)
+{
+  q63_t sum = 0;                                 /* accumulator */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q31_t in;                                      /* temporary variable to store the input value */
+  q15_t in1;                                     /* temporary variable to store the input value */
+  uint32_t blkCnt;                               /* loop counter */
+
+  /* loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
+    /* Compute sum of the squares and then store the results in a temporary variable, sum */
+    in = *__SIMD32(pSrc)++;
+    sum = __SMLALD(in, in, sum);
+    in = *__SIMD32(pSrc)++;
+    sum = __SMLALD(in, in, sum);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
+    /* Compute sum of the squares and then store the results in a temporary variable, sum */
+    in1 = *pSrc++;
+    sum = __SMLALD(in1, in1, sum);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Truncating and saturating the accumulator to 1.15 format */
+  sum = __SSAT((q31_t) (sum >> 15), 16);
+
+  in1 = (q15_t) (sum / blockSize);
+
+  /* Store the result in the destination */
+  arm_sqrt_q15(in1, pResult);
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  q15_t in;                                      /* temporary variable to store the input value */
+  uint32_t blkCnt;                               /* loop counter */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
+    /* Compute sum of the squares and then store the results in a temporary variable, sum */
+    in = *pSrc++;
+    sum += ((q31_t) in * in);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Truncating and saturating the accumulator to 1.15 format */
+  sum = __SSAT((q31_t) (sum >> 15), 16);
+
+  in = (q15_t) (sum / blockSize);
+
+  /* Store the result in the destination */
+  arm_sqrt_q15(in, pResult);
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of RMS group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_rms_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_rms_q31.c
new file mode 100644
index 0000000000..54038eb12e
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_rms_q31.c
@@ -0,0 +1,146 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_rms_q31.c    
+*    
+* Description:	Root Mean Square of the elements of a Q31 vector.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**        
+ * @addtogroup RMS        
+ * @{        
+ */
+
+
+/**        
+ * @brief Root Mean Square of the elements of a Q31 vector.        
+ * @param[in]       *pSrc points to the input vector        
+ * @param[in]       blockSize length of the input vector        
+ * @param[out]      *pResult rms value returned here        
+ * @return none.        
+ *        
+ * @details        
+ * Scaling and Overflow Behavior:        
+ *        
+ *\par        
+ * The function is implemented using an internal 64-bit accumulator.        
+ * The input is represented in 1.31 format, and intermediate multiplication        
+ * yields a 2.62 format.        
+ * The accumulator maintains full precision of the intermediate multiplication results,         
+ * but provides only a single guard bit.        
+ * There is no saturation on intermediate additions.        
+ * If the accumulator overflows, it wraps around and distorts the result.         
+ * In order to avoid overflows completely, the input signal must be scaled down by         
+ * log2(blockSize) bits, as a total of blockSize additions are performed internally.         
+ * Finally, the 2.62 accumulator is right shifted by 31 bits to yield a 1.31 format value.        
+ *        
+ */
+
+void arm_rms_q31(
+  q31_t * pSrc,
+  uint32_t blockSize,
+  q31_t * pResult)
+{
+  q63_t sum = 0;                                 /* accumulator */
+  q31_t in;                                      /* Temporary variable to store the input */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q31_t in1, in2, in3, in4;                      /* Temporary input variables */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 8 outputs at a time.        
+   ** a second loop below computes the remaining 1 to 7 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
+    /* Compute sum of the squares and then store the result in a temporary variable, sum */
+    /* read two samples from source buffer */
+    in1 = pSrc[0];
+    in2 = pSrc[1];
+
+    /* calculate power and accumulate to accumulator */
+    sum += (q63_t) in1 *in1;
+    sum += (q63_t) in2 *in2;
+
+    /* read two samples from source buffer */
+    in3 = pSrc[2];
+    in4 = pSrc[3];
+
+    /* calculate power and accumulate to accumulator */
+    sum += (q63_t) in3 *in3;
+    sum += (q63_t) in4 *in4;
+
+
+    /* update source buffer to process next samples */
+    pSrc += 4u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 8, compute any remaining output samples here.        
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
+    /* Compute sum of the squares and then store the results in a temporary variable, sum */
+    in = *pSrc++;
+    sum += (q63_t) in *in;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Convert data in 2.62 to 1.31 by 31 right shifts and saturate */
+
+  sum = __SSAT(sum >> 31, 31);
+
+
+  /* Compute Rms and store the result in the destination vector */
+  arm_sqrt_q31((q31_t) ((q31_t) sum / (int32_t) blockSize), pResult);
+}
+
+/**        
+ * @} end of RMS group        
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_std_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_std_f32.c
new file mode 100644
index 0000000000..6442d5c295
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_std_f32.c
@@ -0,0 +1,188 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_std_f32.c    
+*    
+* Description:	Standard deviation of the elements of a floating-point vector.  
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupStats    
+ */
+
+/**    
+ * @defgroup STD Standard deviation    
+ *    
+ * Calculates the standard deviation of the elements in the input vector.     
+ * The underlying algorithm is used:    
+ *   
+ * 
    
+ * 	Result = sqrt((sumOfSquares - sum2 / blockSize) / (blockSize - 1))   
+ *   
+ *	   where, sumOfSquares = pSrc[0] * pSrc[0] + pSrc[1] * pSrc[1] + ... + pSrc[blockSize-1] * pSrc[blockSize-1]   
+ *   
+ *	                   sum = pSrc[0] + pSrc[1] + pSrc[2] + ... + pSrc[blockSize-1]   
+ * 
   
+ *    
+ * There are separate functions for floating point, Q31, and Q15 data types.    
+ */
+
+/**    
+ * @addtogroup STD    
+ * @{    
+ */
+
+
+/**    
+ * @brief Standard deviation of the elements of a floating-point vector.    
+ * @param[in]       *pSrc points to the input vector    
+ * @param[in]       blockSize length of the input vector    
+ * @param[out]      *pResult standard deviation value returned here    
+ * @return none.    
+ *    
+ */
+
+
+void arm_std_f32(
+  float32_t * pSrc,
+  uint32_t blockSize,
+  float32_t * pResult)
+{
+  float32_t sum = 0.0f;                          /* Temporary result storage */
+  float32_t sumOfSquares = 0.0f;                 /* Sum of squares */
+  float32_t in;                                  /* input value */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  float32_t meanOfSquares, mean, squareOfMean;
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1])  */
+    /* Compute Sum of squares of the input samples    
+     * and then store the result in a temporary variable, sum. */
+    in = *pSrc++;
+    sum += in;
+    sumOfSquares += in * in;
+    in = *pSrc++;
+    sum += in;
+    sumOfSquares += in * in;
+    in = *pSrc++;
+    sum += in;
+    sumOfSquares += in * in;
+    in = *pSrc++;
+    sum += in;
+    sumOfSquares += in * in;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
+    /* Compute Sum of squares of the input samples    
+     * and then store the result in a temporary variable, sum. */
+    in = *pSrc++;
+    sum += in;
+    sumOfSquares += in * in;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Compute Mean of squares of the input samples    
+   * and then store the result in a temporary variable, meanOfSquares. */
+  meanOfSquares = sumOfSquares / ((float32_t) blockSize - 1.0f);
+
+  /* Compute mean of all input values */
+  mean = sum / (float32_t) blockSize;
+
+  /* Compute square of mean */
+  squareOfMean = (mean * mean) * (((float32_t) blockSize) /
+                                  ((float32_t) blockSize - 1.0f));
+
+  /* Compute standard deviation and then store the result to the destination */
+  arm_sqrt_f32((meanOfSquares - squareOfMean), pResult);
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  float32_t squareOfSum;                         /* Square of Sum */
+  float32_t var;                                 /* Temporary varaince storage */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
+    /* Compute Sum of squares of the input samples     
+     * and then store the result in a temporary variable, sumOfSquares. */
+    in = *pSrc++;
+    sumOfSquares += in * in;
+
+    /* C = (A[0] + A[1] + ... + A[blockSize-1]) */
+    /* Compute Sum of the input samples     
+     * and then store the result in a temporary variable, sum. */
+    sum += in;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Compute the square of sum */
+  squareOfSum = ((sum * sum) / (float32_t) blockSize);
+
+  /* Compute the variance */
+  var = ((sumOfSquares - squareOfSum) / (float32_t) (blockSize - 1.0f));
+
+  /* Compute standard deviation and then store the result to the destination */
+  arm_sqrt_f32(var, pResult);
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of STD group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_std_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_std_q15.c
new file mode 100644
index 0000000000..2d1a49a505
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_std_q15.c
@@ -0,0 +1,197 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_std_q15.c    
+*    
+* Description:	Standard deviation of an array of Q15 type.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupStats    
+ */
+
+/**    
+ * @addtogroup STD    
+ * @{    
+ */
+
+/**    
+ * @brief Standard deviation of the elements of a Q15 vector.    
+ * @param[in]       *pSrc points to the input vector    
+ * @param[in]       blockSize length of the input vector    
+ * @param[out]      *pResult standard deviation value returned here    
+ * @return none.    
+ *    
+ * @details    
+ * Scaling and Overflow Behavior:    
+ *    
+ * \par    
+ * The function is implemented using a 64-bit internal accumulator.    
+ * The input is represented in 1.15 format.   
+ * Intermediate multiplication yields a 2.30 format, and this    
+ * result is added without saturation to a 64-bit accumulator in 34.30 format.    
+ * With 33 guard bits in the accumulator, there is no risk of overflow, and the    
+ * full precision of the intermediate multiplication is preserved.    
+ * Finally, the 34.30 result is truncated to 34.15 format by discarding the lower     
+ * 15 bits, and then saturated to yield a result in 1.15 format.    
+ */
+
+void arm_std_q15(
+  q15_t * pSrc,
+  uint32_t blockSize,
+  q15_t * pResult)
+{
+  q31_t sum = 0;                                 /* Accumulator */
+  q31_t meanOfSquares, squareOfMean;             /* square of mean and mean of square */
+  q15_t mean;                                    /* mean */
+  uint32_t blkCnt;                               /* loop counter */
+  q15_t t;                                       /* Temporary variable */
+  q63_t sumOfSquares = 0;                        /* Accumulator */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q31_t in;                                      /* input value */
+  q15_t in1;                                     /* input value */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1])  */
+    /* Compute Sum of squares of the input samples    
+     * and then store the result in a temporary variable, sum. */
+    in = *__SIMD32(pSrc)++;
+    sum += ((in << 16) >> 16);
+    sum += (in >> 16);
+    sumOfSquares = __SMLALD(in, in, sumOfSquares);
+    in = *__SIMD32(pSrc)++;
+    sum += ((in << 16) >> 16);
+    sum += (in >> 16);
+    sumOfSquares = __SMLALD(in, in, sumOfSquares);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
+    /* Compute Sum of squares of the input samples    
+     * and then store the result in a temporary variable, sum. */
+    in1 = *pSrc++;
+    sumOfSquares = __SMLALD(in1, in1, sumOfSquares);
+    sum += in1;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Compute Mean of squares of the input samples    
+   * and then store the result in a temporary variable, meanOfSquares. */
+  t = (q15_t) ((1.0 / (blockSize - 1)) * 16384LL);
+  sumOfSquares = __SSAT((sumOfSquares >> 15u), 16u);
+
+  meanOfSquares = (q31_t) ((sumOfSquares * t) >> 14u);
+
+  /* Compute mean of all input values */
+  t = (q15_t) ((1.0 / (blockSize * (blockSize - 1))) * 32768LL);
+  mean = (q15_t) __SSAT(sum, 16u);
+
+  /* Compute square of mean */
+  squareOfMean = ((q31_t) mean * mean) >> 15;
+  squareOfMean = (q31_t) (((q63_t) squareOfMean * t) >> 15);
+
+  /* mean of the squares minus the square of the mean. */
+  in1 = (q15_t) (meanOfSquares - squareOfMean);
+
+  /* Compute standard deviation and store the result to the destination */
+  arm_sqrt_q15(in1, pResult);
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  q15_t in;                                      /* input value */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
+    /* Compute Sum of squares of the input samples     
+     * and then store the result in a temporary variable, sumOfSquares. */
+    in = *pSrc++;
+    sumOfSquares += (in * in);
+
+    /* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
+    /* Compute sum of all input values and then store the result in a temporary variable, sum. */
+    sum += in;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Compute Mean of squares of the input samples     
+   * and then store the result in a temporary variable, meanOfSquares. */
+  t = (q15_t) ((1.0 / (blockSize - 1)) * 16384LL);
+  sumOfSquares = __SSAT((sumOfSquares >> 15u), 16u);
+  meanOfSquares = (q31_t) ((sumOfSquares * t) >> 14u);
+
+  /* Compute mean of all input values */
+  mean = (q15_t) __SSAT(sum, 16u);
+
+  /* Compute square of mean of the input samples   
+   * and then store the result in a temporary variable, squareOfMean.*/
+  t = (q15_t) ((1.0 / (blockSize * (blockSize - 1))) * 32768LL);
+  squareOfMean = ((q31_t) mean * mean) >> 15;
+  squareOfMean = (q31_t) (((q63_t) squareOfMean * t) >> 15);
+
+  /* mean of the squares minus the square of the mean. */
+  in = (q15_t) (meanOfSquares - squareOfMean);
+
+  /* Compute standard deviation and store the result to the destination */
+  arm_sqrt_q15(in, pResult);
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+
+}
+
+/**    
+ * @} end of STD group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_std_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_std_q31.c
new file mode 100644
index 0000000000..45bec01a1f
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_std_q31.c
@@ -0,0 +1,184 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_std_q31.c    
+*    
+* Description:	Standard deviation of an array of Q31 type.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupStats    
+ */
+
+/**    
+ * @addtogroup STD    
+ * @{    
+ */
+
+
+/**    
+ * @brief Standard deviation of the elements of a Q31 vector.    
+ * @param[in]       *pSrc points to the input vector    
+ * @param[in]       blockSize length of the input vector    
+ * @param[out]      *pResult standard deviation value returned here    
+ * @return none.    
+ * @details    
+ * Scaling and Overflow Behavior:    
+ *    
+ *\par    
+ * The function is implemented using an internal 64-bit accumulator.    
+ * The input is represented in 1.31 format, and intermediate multiplication    
+ * yields a 2.62 format.    
+ * The accumulator maintains full precision of the intermediate multiplication results,     
+ * but provides only a single guard bit.    
+ * There is no saturation on intermediate additions.    
+ * If the accumulator overflows it wraps around and distorts the result.    
+ * In order to avoid overflows completely the input signal must be scaled down by     
+ * log2(blockSize) bits, as a total of blockSize additions are performed internally.     
+ * Finally, the 2.62 accumulator is right shifted by 31 bits to yield a 1.31 format value.    
+ *    
+ */
+
+
+void arm_std_q31(
+  q31_t * pSrc,
+  uint32_t blockSize,
+  q31_t * pResult)
+{
+  q63_t sum = 0;                                 /* Accumulator */
+  q31_t meanOfSquares, squareOfMean;             /* square of mean and mean of square */
+  q31_t mean;                                    /* mean */
+  q31_t in;                                      /* input value */
+  q31_t t;                                       /* Temporary variable */
+  uint32_t blkCnt;                               /* loop counter */
+  q63_t sumOfSquares = 0;                        /* Accumulator */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1])  */
+    /* Compute Sum of squares of the input samples    
+     * and then store the result in a temporary variable, sum. */
+    in = *pSrc++;
+    sum += in;
+    sumOfSquares += ((q63_t) (in) * (in));
+    in = *pSrc++;
+    sum += in;
+    sumOfSquares += ((q63_t) (in) * (in));
+    in = *pSrc++;
+    sum += in;
+    sumOfSquares += ((q63_t) (in) * (in));
+    in = *pSrc++;
+    sum += in;
+    sumOfSquares += ((q63_t) (in) * (in));
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
+    /* Compute Sum of squares of the input samples    
+     * and then store the result in a temporary variable, sum. */
+    in = *pSrc++;
+    sum += in;
+    sumOfSquares += ((q63_t) (in) * (in));
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  t = (q31_t) ((1.0f / (float32_t) (blockSize - 1u)) * 1073741824.0f);
+
+  /* Compute Mean of squares of the input samples    
+   * and then store the result in a temporary variable, meanOfSquares. */
+  sumOfSquares = (sumOfSquares >> 31);
+  meanOfSquares = (q31_t) ((sumOfSquares * t) >> 30);
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
+    /* Compute Sum of squares of the input samples     
+     * and then store the result in a temporary variable, sumOfSquares. */
+    in = *pSrc++;
+    sumOfSquares += ((q63_t) (in) * (in));
+
+    /* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
+    /* Compute sum of all input values and then store the result in a temporary variable, sum. */
+    sum += in;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Compute Mean of squares of the input samples     
+   * and then store the result in a temporary variable, meanOfSquares. */
+  t = (q31_t) ((1.0f / (float32_t) (blockSize - 1u)) * 1073741824.0f);
+  sumOfSquares = (sumOfSquares >> 31);
+  meanOfSquares = (q31_t) ((sumOfSquares * t) >> 30);
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  /* Compute mean of all input values */
+  t = (q31_t) ((1.0f / (blockSize * (blockSize - 1u))) * 2147483648.0f);
+  mean = (q31_t) (sum);
+
+  /* Compute square of mean */
+  squareOfMean = (q31_t) (((q63_t) mean * mean) >> 31);
+  squareOfMean = (q31_t) (((q63_t) squareOfMean * t) >> 31);
+
+
+  /* Compute standard deviation and then store the result to the destination */
+  arm_sqrt_q31(meanOfSquares - squareOfMean, pResult);
+
+}
+
+/**    
+ * @} end of STD group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_var_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_var_f32.c
new file mode 100644
index 0000000000..2adcfb443b
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_var_f32.c
@@ -0,0 +1,184 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_var_f32.c    
+*    
+* Description:	Variance of the elements of a floating-point vector.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupStats    
+ */
+
+/**    
+ * @defgroup variance  Variance    
+ *    
+ * Calculates the variance of the elements in the input vector.    
+ * The underlying algorithm is used:    
+ *    
+ * 
    
+ * 	Result = (sumOfSquares - sum2 / blockSize) / (blockSize - 1)   
+ *   
+ *	   where, sumOfSquares = pSrc[0] * pSrc[0] + pSrc[1] * pSrc[1] + ... + pSrc[blockSize-1] * pSrc[blockSize-1]   
+ *   
+ *	                   sum = pSrc[0] + pSrc[1] + pSrc[2] + ... + pSrc[blockSize-1]   
+ * 
   
+ *    
+ * There are separate functions for floating point, Q31, and Q15 data types.    
+ */
+
+/**    
+ * @addtogroup variance    
+ * @{    
+ */
+
+
+/**    
+ * @brief Variance of the elements of a floating-point vector.    
+ * @param[in]       *pSrc points to the input vector    
+ * @param[in]       blockSize length of the input vector    
+ * @param[out]      *pResult variance value returned here    
+ * @return none.    
+ *    
+ */
+
+
+void arm_var_f32(
+  float32_t * pSrc,
+  uint32_t blockSize,
+  float32_t * pResult)
+{
+
+  float32_t sum = 0.0f;                          /* Temporary result storage */
+  float32_t sumOfSquares = 0.0f;                 /* Sum of squares */
+  float32_t in;                                  /* input value */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  float32_t meanOfSquares, mean, squareOfMean;   /* Temporary variables */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1])  */
+    /* Compute Sum of squares of the input samples    
+     * and then store the result in a temporary variable, sum. */
+    in = *pSrc++;
+    sum += in;
+    sumOfSquares += in * in;
+    in = *pSrc++;
+    sum += in;
+    sumOfSquares += in * in;
+    in = *pSrc++;
+    sum += in;
+    sumOfSquares += in * in;
+    in = *pSrc++;
+    sum += in;
+    sumOfSquares += in * in;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
+    /* Compute Sum of squares of the input samples    
+     * and then store the result in a temporary variable, sum. */
+    in = *pSrc++;
+    sum += in;
+    sumOfSquares += in * in;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Compute Mean of squares of the input samples    
+   * and then store the result in a temporary variable, meanOfSquares. */
+  meanOfSquares = sumOfSquares / ((float32_t) blockSize - 1.0f);
+
+  /* Compute mean of all input values */
+  mean = sum / (float32_t) blockSize;
+
+  /* Compute square of mean */
+  squareOfMean = (mean * mean) * (((float32_t) blockSize) /
+                                  ((float32_t) blockSize - 1.0f));
+
+  /* Compute variance and then store the result to the destination */
+  *pResult = meanOfSquares - squareOfMean;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  float32_t squareOfSum;                         /* Square of Sum */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
+    /* Compute Sum of squares of the input samples     
+     * and then store the result in a temporary variable, sumOfSquares. */
+    in = *pSrc++;
+    sumOfSquares += in * in;
+
+    /* C = (A[0] + A[1] + ... + A[blockSize-1]) */
+    /* Compute Sum of the input samples     
+     * and then store the result in a temporary variable, sum. */
+    sum += in;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Compute the square of sum */
+  squareOfSum = ((sum * sum) / (float32_t) blockSize);
+
+  /* Compute the variance */
+  *pResult = ((sumOfSquares - squareOfSum) / (float32_t) (blockSize - 1.0f));
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of variance group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_var_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_var_q15.c
new file mode 100644
index 0000000000..08dbc6587c
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_var_q15.c
@@ -0,0 +1,180 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_var_q15.c    
+*    
+* Description:	Variance of an array of Q15 type.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupStats    
+ */
+
+/**    
+ * @addtogroup variance    
+ * @{    
+ */
+
+/**    
+ * @brief Variance of the elements of a Q15 vector.    
+ * @param[in]       *pSrc points to the input vector    
+ * @param[in]       blockSize length of the input vector    
+ * @param[out]      *pResult variance value returned here    
+ * @return none.    
+ *    
+ * @details    
+ * Scaling and Overflow Behavior:    
+ *    
+ * \par    
+ * The function is implemented using a 64-bit internal accumulator.    
+ * The input is represented in 1.15 format.   
+ * Intermediate multiplication yields a 2.30 format, and this    
+ * result is added without saturation to a 64-bit accumulator in 34.30 format.    
+ * With 33 guard bits in the accumulator, there is no risk of overflow, and the    
+ * full precision of the intermediate multiplication is preserved.    
+ * Finally, the 34.30 result is truncated to 34.15 format by discarding the lower     
+ * 15 bits, and then saturated to yield a result in 1.15 format.    
+ *    
+ */
+
+
+void arm_var_q15(
+  q15_t * pSrc,
+  uint32_t blockSize,
+  q31_t * pResult)
+{
+  q31_t sum = 0;                                 /* Accumulator */
+  q31_t meanOfSquares, squareOfMean;             /* Mean of square and square of mean */
+  q15_t mean;                                    /* mean */
+  uint32_t blkCnt;                               /* loop counter */
+  q15_t t;                                       /* Temporary variable */
+  q63_t sumOfSquares = 0;                        /* Accumulator */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q31_t in;                                      /* Input variable */
+  q15_t in1;                                     /* Temporary variable */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1])  */
+    /* Compute Sum of squares of the input samples    
+     * and then store the result in a temporary variable, sum. */
+    in = *__SIMD32(pSrc)++;
+    sum += ((in << 16) >> 16);
+    sum += (in >> 16);
+    sumOfSquares = __SMLALD(in, in, sumOfSquares);
+    in = *__SIMD32(pSrc)++;
+    sum += ((in << 16) >> 16);
+    sum += (in >> 16);
+    sumOfSquares = __SMLALD(in, in, sumOfSquares);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
+    /* Compute Sum of squares of the input samples    
+     * and then store the result in a temporary variable, sum. */
+    in1 = *pSrc++;
+    sum += in1;
+    sumOfSquares = __SMLALD(in1, in1, sumOfSquares);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Compute Mean of squares of the input samples    
+   * and then store the result in a temporary variable, meanOfSquares. */
+  t = (q15_t) ((1.0f / (float32_t) (blockSize - 1u)) * 16384);
+  sumOfSquares = __SSAT((sumOfSquares >> 15u), 16u);
+
+  meanOfSquares = (q31_t) ((sumOfSquares * t) >> 14u);
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  q15_t in;                                      /* Temporary variable */
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
+    /* Compute Sum of squares of the input samples     
+     * and then store the result in a temporary variable, sumOfSquares. */
+    in = *pSrc++;
+    sumOfSquares += (in * in);
+
+    /* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
+    /* Compute sum of all input values and then store the result in a temporary variable, sum. */
+    sum += in;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Compute Mean of squares of the input samples     
+   * and then store the result in a temporary variable, meanOfSquares. */
+  t = (q15_t) ((1.0f / (float32_t) (blockSize - 1u)) * 16384);
+  sumOfSquares = __SSAT((sumOfSquares >> 15u), 16u);
+  meanOfSquares = (q31_t) ((sumOfSquares * t) >> 14u);
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  /* Compute mean of all input values */
+  t = (q15_t) ((1.0f / (float32_t) (blockSize * (blockSize - 1u))) * 32768);
+  mean = __SSAT(sum, 16u);
+
+  /* Compute square of mean */
+  squareOfMean = ((q31_t) mean * mean) >> 15;
+  squareOfMean = (q31_t) (((q63_t) squareOfMean * t) >> 15);
+
+  /* Compute variance and then store the result to the destination */
+  *pResult = (meanOfSquares - squareOfMean);
+
+}
+
+/**    
+ * @} end of variance group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_var_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_var_q31.c
new file mode 100644
index 0000000000..13d6c15cb5
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_var_q31.c
@@ -0,0 +1,170 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_var_q31.c    
+*    
+* Description:	Variance of an array of Q31 type.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupStats        
+ */
+
+/**        
+ * @addtogroup variance        
+ * @{        
+ */
+
+/**        
+ * @brief Variance of the elements of a Q31 vector.        
+ * @param[in]       *pSrc points to the input vector        
+ * @param[in]       blockSize length of the input vector        
+ * @param[out]      *pResult variance value returned here        
+ * @return none.        
+ *        
+ * @details        
+ * Scaling and Overflow Behavior:        
+ *        
+ *\par        
+ * The function is implemented using an internal 64-bit accumulator.        
+ * The input is represented in 1.31 format, and intermediate multiplication        
+ * yields a 2.62 format.        
+ * The accumulator maintains full precision of the intermediate multiplication results,         
+ * but provides only a single guard bit.        
+ * There is no saturation on intermediate additions.        
+ * If the accumulator overflows it wraps around and distorts the result.        
+ * In order to avoid overflows completely the input signal must be scaled down by         
+ * log2(blockSize) bits, as a total of blockSize additions are performed internally.         
+ * Finally, the 2.62 accumulator is right shifted by 31 bits to yield a 1.31 format value.        
+ *        
+ */
+
+
+void arm_var_q31(
+  q31_t * pSrc,
+  uint32_t blockSize,
+  q63_t * pResult)
+{
+  q63_t sum = 0, sumSquare = 0;                  /* Accumulator */
+  q31_t meanOfSquares, squareOfMean;             /* square of mean and mean of square */
+  q31_t mean;                                    /* mean */
+  q31_t in;                                      /* input value */
+  q31_t t;                                       /* Temporary variable */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  q63_t sumSquare1 = 0;                          /* Accumulator */
+  q31_t in1, in2, in3, in4;                      /* Temporary input variables */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1])  */
+    /* Compute Sum of squares of the input samples        
+     * and then store the result in a temporary variable, sum. */
+    /* read input samples from source buffer */
+    in1 = pSrc[0];
+    in2 = pSrc[1];
+
+    /* calculate sum of inputs */
+    sum += in1;
+    /* calculate sum of squares */
+    sumSquare += ((q63_t) (in1) * (in1));
+    in3 = pSrc[2];
+    sum += in2;
+    sumSquare1 += ((q63_t) (in2) * (in2));
+    in4 = pSrc[3];
+    sum += in3;
+    sumSquare += ((q63_t) (in3) * (in3));
+    sum += in4;
+    sumSquare1 += ((q63_t) (in4) * (in4));
+
+    /* update input pointer to process next samples */
+    pSrc += 4u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* add two accumulators */
+  sumSquare = sumSquare + sumSquare1;
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
+    /* Compute Sum of squares of the input samples        
+     * and then store the result in a temporary variable, sum. */
+    in = *pSrc++;
+    sumSquare += ((q63_t) (in) * (in));
+    sum += in;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  t = (q31_t) ((1.0f / (float32_t) (blockSize - 1u)) * 1073741824.0f);
+
+  /* Compute Mean of squares of the input samples        
+   * and then store the result in a temporary variable, meanOfSquares. */
+  sumSquare = (sumSquare >> 31);
+  meanOfSquares = (q31_t) ((sumSquare * t) >> 30);
+
+  /* Compute mean of all input values */
+  t = (q31_t) ((1.0f / (blockSize * (blockSize - 1u))) * 2147483648.0f);
+  mean = (q31_t) (sum);
+
+  /* Compute square of mean */
+  squareOfMean = (q31_t) (((q63_t) mean * mean) >> 31);
+  squareOfMean = (q31_t) (((q63_t) squareOfMean * t) >> 31);
+
+  /* Compute variance and then store the result to the destination */
+  *pResult = (q63_t) meanOfSquares - squareOfMean;
+
+}
+
+/**        
+ * @} end of variance group        
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_copy_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_copy_f32.c
new file mode 100644
index 0000000000..619c1577a6
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_copy_f32.c
@@ -0,0 +1,130 @@
+/* ----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_copy_f32.c    
+*    
+* Description:	Copies the elements of a floating-point vector.  
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupSupport    
+ */
+
+/**    
+ * @defgroup copy Vector Copy    
+ *    
+ * Copies sample by sample from source vector to destination vector.    
+ *    
+ * 
    
+ * 	pDst[n] = pSrc[n];   0 <= n < blockSize.    
+ * 
    
+ *   
+ * There are separate functions for floating point, Q31, Q15, and Q7 data types.     
+ */
+
+/**    
+ * @addtogroup copy    
+ * @{    
+ */
+
+/**    
+ * @brief Copies the elements of a floating-point vector.     
+ * @param[in]       *pSrc points to input vector    
+ * @param[out]      *pDst points to output vector    
+ * @param[in]       blockSize length of the input vector   
+ * @return none.    
+ *    
+ */
+
+
+void arm_copy_f32(
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  float32_t in1, in2, in3, in4;
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A */
+    /* Copy and then store the results in the destination buffer */
+    in1 = *pSrc++;
+    in2 = *pSrc++;
+    in3 = *pSrc++;
+    in4 = *pSrc++;
+
+    *pDst++ = in1;
+    *pDst++ = in2;
+    *pDst++ = in3;
+    *pDst++ = in4;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C = A */
+    /* Copy and then store the results in the destination buffer */
+    *pDst++ = *pSrc++;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**    
+ * @} end of BasicCopy group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_copy_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_copy_q15.c
new file mode 100644
index 0000000000..00be9dc0b2
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_copy_q15.c
@@ -0,0 +1,109 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_copy_q15.c    
+*    
+* Description:	Copies the elements of a Q15 vector.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupSupport    
+ */
+
+/**    
+ * @addtogroup copy    
+ * @{    
+ */
+/**    
+ * @brief Copies the elements of a Q15 vector.     
+ * @param[in]       *pSrc points to input vector    
+ * @param[out]      *pDst points to output vector    
+ * @param[in]       blockSize length of the input vector   
+ * @return none.    
+ *    
+ */
+
+void arm_copy_q15(
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A */
+    /* Read two inputs */
+    *__SIMD32(pDst)++ = *__SIMD32(pSrc)++;
+    *__SIMD32(pDst)++ = *__SIMD32(pSrc)++;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C = A */
+    /* Copy and then store the value in the destination buffer */
+    *pDst++ = *pSrc++;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**    
+ * @} end of BasicCopy group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_copy_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_copy_q31.c
new file mode 100644
index 0000000000..7ab0849f6e
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_copy_q31.c
@@ -0,0 +1,118 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_copy_q31.c    
+*    
+* Description:	Copies the elements of a Q31 vector.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupSupport    
+ */
+
+/**    
+ * @addtogroup copy    
+ * @{    
+ */
+
+/**    
+ * @brief Copies the elements of a Q31 vector.     
+ * @param[in]       *pSrc points to input vector    
+ * @param[out]      *pDst points to output vector    
+ * @param[in]       blockSize length of the input vector   
+ * @return none.    
+ *    
+ */
+
+void arm_copy_q31(
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t in1, in2, in3, in4;
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A */
+    /* Copy and then store the values in the destination buffer */
+    in1 = *pSrc++;
+    in2 = *pSrc++;
+    in3 = *pSrc++;
+    in4 = *pSrc++;
+
+    *pDst++ = in1;
+    *pDst++ = in2;
+    *pDst++ = in3;
+    *pDst++ = in4;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C = A */
+    /* Copy and then store the value in the destination buffer */
+    *pDst++ = *pSrc++;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**    
+ * @} end of BasicCopy group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_copy_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_copy_q7.c
new file mode 100644
index 0000000000..425885753e
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_copy_q7.c
@@ -0,0 +1,110 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_copy_q7.c    
+*    
+* Description:	Copies the elements of a Q7 vector.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupSupport    
+ */
+
+/**    
+ * @addtogroup copy    
+ * @{    
+ */
+
+/**    
+ * @brief Copies the elements of a Q7 vector.    
+ * @param[in]       *pSrc points to input vector    
+ * @param[out]      *pDst points to output vector    
+ * @param[in]       blockSize length of the input vector   
+ * @return none.    
+ *    
+ */
+
+void arm_copy_q7(
+  q7_t * pSrc,
+  q7_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A */
+    /* Copy and then store the results in the destination buffer */
+    /* 4 samples are copied and stored at a time using SIMD */
+    *__SIMD32(pDst)++ = *__SIMD32(pSrc)++;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+
+  while(blkCnt > 0u)
+  {
+    /* C = A */
+    /* Copy and then store the results in the destination buffer */
+    *pDst++ = *pSrc++;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**    
+ * @} end of BasicCopy group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_fill_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_fill_f32.c
new file mode 100644
index 0000000000..439e60db0c
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_fill_f32.c
@@ -0,0 +1,129 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_fill_f32.c    
+*    
+* Description:	Fills a constant value into a floating-point vector.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupSupport    
+ */
+
+/**    
+ * @defgroup Fill Vector Fill    
+ *    
+ * Fills the destination vector with a constant value.    
+ *    
+ * 
    
+ * 	pDst[n] = value;   0 <= n < blockSize.    
+ * 
    
+ *   
+ * There are separate functions for floating point, Q31, Q15, and Q7 data types.     
+ */
+
+/**    
+ * @addtogroup Fill    
+ * @{    
+ */
+
+/**    
+ * @brief Fills a constant value into a floating-point vector.     
+ * @param[in]       value input value to be filled   
+ * @param[out]      *pDst points to output vector    
+ * @param[in]       blockSize length of the output vector   
+ * @return none.    
+ *    
+ */
+
+
+void arm_fill_f32(
+  float32_t value,
+  float32_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  float32_t in1 = value;
+  float32_t in2 = value;
+  float32_t in3 = value;
+  float32_t in4 = value;
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = value */
+    /* Fill the value in the destination buffer */
+    *pDst++ = in1;
+    *pDst++ = in2;
+    *pDst++ = in3;
+    *pDst++ = in4;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+
+  while(blkCnt > 0u)
+  {
+    /* C = value */
+    /* Fill the value in the destination buffer */
+    *pDst++ = value;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**    
+ * @} end of Fill group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_fill_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_fill_q15.c
new file mode 100644
index 0000000000..8f60d3b4ef
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_fill_q15.c
@@ -0,0 +1,115 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_fill_q15.c    
+*    
+* Description:	Fills a constant value into a Q15 vector.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupSupport    
+ */
+
+/**    
+ * @addtogroup Fill    
+ * @{    
+ */
+
+/**    
+ * @brief Fills a constant value into a Q15 vector.    
+ * @param[in]       value input value to be filled   
+ * @param[out]      *pDst points to output vector    
+ * @param[in]       blockSize length of the output vector   
+ * @return none.    
+ *    
+ */
+
+void arm_fill_q15(
+  q15_t value,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q31_t packedValue;                             /* value packed to 32 bits */
+
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* Packing two 16 bit values to 32 bit value in order to use SIMD */
+  packedValue = __PKHBT(value, value, 16u);
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = value */
+    /* Fill the value in the destination buffer */
+    *__SIMD32(pDst)++ = packedValue;
+    *__SIMD32(pDst)++ = packedValue;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C = value */
+    /* Fill the value in the destination buffer */
+    *pDst++ = value;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**    
+ * @} end of Fill group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_fill_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_fill_q31.c
new file mode 100644
index 0000000000..35565c3cf7
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_fill_q31.c
@@ -0,0 +1,116 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_fill_q31.c    
+*    
+* Description:	Fills a constant value into a Q31 vector.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupSupport    
+ */
+
+/**    
+ * @addtogroup Fill    
+ * @{    
+ */
+
+/**    
+ * @brief Fills a constant value into a Q31 vector.    
+ * @param[in]       value input value to be filled   
+ * @param[out]      *pDst points to output vector    
+ * @param[in]       blockSize length of the output vector   
+ * @return none.    
+ *    
+ */
+
+void arm_fill_q31(
+  q31_t value,
+  q31_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t in1 = value;
+  q31_t in2 = value;
+  q31_t in3 = value;
+  q31_t in4 = value;
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = value */
+    /* Fill the value in the destination buffer */
+    *pDst++ = in1;
+    *pDst++ = in2;
+    *pDst++ = in3;
+    *pDst++ = in4;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C = value */
+    /* Fill the value in the destination buffer */
+    *pDst++ = value;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**    
+ * @} end of Fill group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_fill_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_fill_q7.c
new file mode 100644
index 0000000000..481d4c8f7b
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_fill_q7.c
@@ -0,0 +1,113 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_fill_q7.c    
+*    
+* Description:	Fills a constant value into a Q7 vector.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupSupport    
+ */
+
+/**    
+ * @addtogroup Fill    
+ * @{    
+ */
+
+/**    
+ * @brief Fills a constant value into a Q7 vector.    
+ * @param[in]       value input value to be filled   
+ * @param[out]      *pDst points to output vector    
+ * @param[in]       blockSize length of the output vector   
+ * @return none.    
+ *    
+ */
+
+void arm_fill_q7(
+  q7_t value,
+  q7_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q31_t packedValue;                             /* value packed to 32 bits */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* Packing four 8 bit values to 32 bit value in order to use SIMD */
+  packedValue = __PACKq7(value, value, value, value);
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = value */
+    /* Fill the value in the destination buffer */
+    *__SIMD32(pDst)++ = packedValue;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C = value */
+    /* Fill the value in the destination buffer */
+    *pDst++ = value;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**    
+ * @} end of Fill group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_float_to_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_float_to_q15.c
new file mode 100644
index 0000000000..1537b93ab9
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_float_to_q15.c
@@ -0,0 +1,196 @@
+/* ----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_float_to_q15.c    
+*    
+* Description:	Converts the elements of the floating-point vector to Q15 vector.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupSupport    
+ */
+
+/**    
+ * @addtogroup float_to_x    
+ * @{    
+ */
+
+/**    
+ * @brief Converts the elements of the floating-point vector to Q15 vector.    
+ * @param[in]       *pSrc points to the floating-point input vector    
+ * @param[out]      *pDst points to the Q15 output vector   
+ * @param[in]       blockSize length of the input vector    
+ * @return none.    
+ *    
+ * \par Description:    
+ * \par   
+ * The equation used for the conversion process is:    
+ * 
    
+ * 	pDst[n] = (q15_t)(pSrc[n] * 32768);   0 <= n < blockSize.    
+ * 
    
+ * \par Scaling and Overflow Behavior:    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * Results outside of the allowable Q15 range [0x8000 0x7FFF] will be saturated.    
+ * \note   
+ * In order to apply rounding, the library should be rebuilt with the ROUNDING macro     
+ * defined in the preprocessor section of project options.     
+ *    
+ */
+
+
+void arm_float_to_q15(
+  float32_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+  float32_t *pIn = pSrc;                         /* Src pointer */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifdef ARM_MATH_ROUNDING
+
+  float32_t in;
+
+#endif /*      #ifdef ARM_MATH_ROUNDING        */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+
+#ifdef ARM_MATH_ROUNDING
+    /* C = A * 32768 */
+    /* convert from float to q15 and then store the results in the destination buffer */
+    in = *pIn++;
+    in = (in * 32768.0f);
+    in += in > 0 ? 0.5 : -0.5;
+    *pDst++ = (q15_t) (__SSAT((q31_t) (in), 16));
+
+    in = *pIn++;
+    in = (in * 32768.0f);
+    in += in > 0 ? 0.5 : -0.5;
+    *pDst++ = (q15_t) (__SSAT((q31_t) (in), 16));
+
+    in = *pIn++;
+    in = (in * 32768.0f);
+    in += in > 0 ? 0.5 : -0.5;
+    *pDst++ = (q15_t) (__SSAT((q31_t) (in), 16));
+
+    in = *pIn++;
+    in = (in * 32768.0f);
+    in += in > 0 ? 0.5 : -0.5;
+    *pDst++ = (q15_t) (__SSAT((q31_t) (in), 16));
+
+#else
+
+    /* C = A * 32768 */
+    /* convert from float to q15 and then store the results in the destination buffer */
+    *pDst++ = (q15_t) __SSAT((q31_t) (*pIn++ * 32768.0f), 16);
+    *pDst++ = (q15_t) __SSAT((q31_t) (*pIn++ * 32768.0f), 16);
+    *pDst++ = (q15_t) __SSAT((q31_t) (*pIn++ * 32768.0f), 16);
+    *pDst++ = (q15_t) __SSAT((q31_t) (*pIn++ * 32768.0f), 16);
+
+#endif /*      #ifdef ARM_MATH_ROUNDING        */
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+
+#ifdef ARM_MATH_ROUNDING
+    /* C = A * 32768 */
+    /* convert from float to q15 and then store the results in the destination buffer */
+    in = *pIn++;
+    in = (in * 32768.0f);
+    in += in > 0 ? 0.5 : -0.5;
+    *pDst++ = (q15_t) (__SSAT((q31_t) (in), 16));
+
+#else
+
+    /* C = A * 32768 */
+    /* convert from float to q15 and then store the results in the destination buffer */
+    *pDst++ = (q15_t) __SSAT((q31_t) (*pIn++ * 32768.0f), 16);
+
+#endif /*      #ifdef ARM_MATH_ROUNDING        */
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+
+#ifdef ARM_MATH_ROUNDING
+    /* C = A * 32768 */
+    /* convert from float to q15 and then store the results in the destination buffer */
+    in = *pIn++;
+    in = (in * 32768.0f);
+    in += in > 0 ? 0.5f : -0.5f;
+    *pDst++ = (q15_t) (__SSAT((q31_t) (in), 16));
+
+#else
+
+    /* C = A * 32768 */
+    /* convert from float to q15 and then store the results in the destination buffer */
+    *pDst++ = (q15_t) __SSAT((q31_t) (*pIn++ * 32768.0f), 16);
+
+#endif /*      #ifdef ARM_MATH_ROUNDING        */
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of float_to_x group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_float_to_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_float_to_q31.c
new file mode 100644
index 0000000000..3ab52b9ff0
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_float_to_q31.c
@@ -0,0 +1,203 @@
+/* ----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_float_to_q31.c    
+*    
+* Description:	Converts the elements of the floating-point vector to Q31 vector.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupSupport    
+ */
+
+/**    
+ * @defgroup float_to_x  Convert 32-bit floating point value    
+ */
+
+/**    
+ * @addtogroup float_to_x    
+ * @{    
+ */
+
+/**    
+ * @brief Converts the elements of the floating-point vector to Q31 vector.    
+ * @param[in]       *pSrc points to the floating-point input vector    
+ * @param[out]      *pDst points to the Q31 output vector   
+ * @param[in]       blockSize length of the input vector    
+ * @return none.    
+ *    
+ *\par Description:    
+ * \par   
+ * The equation used for the conversion process is:    
+ *   
+ * 
    
+ * 	pDst[n] = (q31_t)(pSrc[n] * 2147483648);   0 <= n < blockSize.    
+ * 
    
+ * Scaling and Overflow Behavior:    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * Results outside of the allowable Q31 range[0x80000000 0x7FFFFFFF] will be saturated.    
+ *   
+ * \note In order to apply rounding, the library should be rebuilt with the ROUNDING macro     
+ * defined in the preprocessor section of project options.     
+ */
+
+
+void arm_float_to_q31(
+  float32_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize)
+{
+  float32_t *pIn = pSrc;                         /* Src pointer */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifdef ARM_MATH_ROUNDING
+
+  float32_t in;
+
+#endif /*      #ifdef ARM_MATH_ROUNDING        */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+
+#ifdef ARM_MATH_ROUNDING
+
+    /* C = A * 32768 */
+    /* convert from float to Q31 and then store the results in the destination buffer */
+    in = *pIn++;
+    in = (in * 2147483648.0f);
+    in += in > 0 ? 0.5 : -0.5;
+    *pDst++ = clip_q63_to_q31((q63_t) (in));
+
+    in = *pIn++;
+    in = (in * 2147483648.0f);
+    in += in > 0 ? 0.5 : -0.5;
+    *pDst++ = clip_q63_to_q31((q63_t) (in));
+
+    in = *pIn++;
+    in = (in * 2147483648.0f);
+    in += in > 0 ? 0.5 : -0.5;
+    *pDst++ = clip_q63_to_q31((q63_t) (in));
+
+    in = *pIn++;
+    in = (in * 2147483648.0f);
+    in += in > 0 ? 0.5 : -0.5;
+    *pDst++ = clip_q63_to_q31((q63_t) (in));
+
+#else
+
+    /* C = A * 2147483648 */
+    /* convert from float to Q31 and then store the results in the destination buffer */
+    *pDst++ = clip_q63_to_q31((q63_t) (*pIn++ * 2147483648.0f));
+    *pDst++ = clip_q63_to_q31((q63_t) (*pIn++ * 2147483648.0f));
+    *pDst++ = clip_q63_to_q31((q63_t) (*pIn++ * 2147483648.0f));
+    *pDst++ = clip_q63_to_q31((q63_t) (*pIn++ * 2147483648.0f));
+
+#endif /*      #ifdef ARM_MATH_ROUNDING        */
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+
+#ifdef ARM_MATH_ROUNDING
+
+    /* C = A * 2147483648 */
+    /* convert from float to Q31 and then store the results in the destination buffer */
+    in = *pIn++;
+    in = (in * 2147483648.0f);
+    in += in > 0 ? 0.5 : -0.5;
+    *pDst++ = clip_q63_to_q31((q63_t) (in));
+
+#else
+
+    /* C = A * 2147483648 */
+    /* convert from float to Q31 and then store the results in the destination buffer */
+    *pDst++ = clip_q63_to_q31((q63_t) (*pIn++ * 2147483648.0f));
+
+#endif /*      #ifdef ARM_MATH_ROUNDING        */
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+
+#ifdef ARM_MATH_ROUNDING
+
+    /* C = A * 2147483648 */
+    /* convert from float to Q31 and then store the results in the destination buffer */
+    in = *pIn++;
+    in = (in * 2147483648.0f);
+    in += in > 0 ? 0.5f : -0.5f;
+    *pDst++ = clip_q63_to_q31((q63_t) (in));
+
+#else
+
+    /* C = A * 2147483648 */
+    /* convert from float to Q31 and then store the results in the destination buffer */
+    *pDst++ = clip_q63_to_q31((q63_t) (*pIn++ * 2147483648.0f));
+
+#endif /*      #ifdef ARM_MATH_ROUNDING        */
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of float_to_x group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_float_to_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_float_to_q7.c
new file mode 100644
index 0000000000..dea14c6a14
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_float_to_q7.c
@@ -0,0 +1,195 @@
+/* ----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_float_to_q7.c    
+*    
+* Description:	Converts the elements of the floating-point vector to Q7 vector.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupSupport    
+ */
+
+/**    
+ * @addtogroup float_to_x    
+ * @{    
+ */
+
+/**    
+ * @brief Converts the elements of the floating-point vector to Q7 vector.    
+ * @param[in]       *pSrc points to the floating-point input vector    
+ * @param[out]      *pDst points to the Q7 output vector   
+ * @param[in]       blockSize length of the input vector    
+ * @return none.    
+ *    
+ *\par Description:    
+ * \par   
+ * The equation used for the conversion process is:    
+ * 
    
+ * 	pDst[n] = (q7_t)(pSrc[n] * 128);   0 <= n < blockSize.    
+ * 
    
+ * \par Scaling and Overflow Behavior:    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * Results outside of the allowable Q7 range [0x80 0x7F] will be saturated.    
+ * \note   
+ * In order to apply rounding, the library should be rebuilt with the ROUNDING macro     
+ * defined in the preprocessor section of project options.     
+ */
+
+
+void arm_float_to_q7(
+  float32_t * pSrc,
+  q7_t * pDst,
+  uint32_t blockSize)
+{
+  float32_t *pIn = pSrc;                         /* Src pointer */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifdef ARM_MATH_ROUNDING
+
+  float32_t in;
+
+#endif /*      #ifdef ARM_MATH_ROUNDING        */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+
+#ifdef ARM_MATH_ROUNDING
+    /* C = A * 128 */
+    /* convert from float to q7 and then store the results in the destination buffer */
+    in = *pIn++;
+    in = (in * 128);
+    in += in > 0 ? 0.5 : -0.5;
+    *pDst++ = (q7_t) (__SSAT((q15_t) (in), 8));
+
+    in = *pIn++;
+    in = (in * 128);
+    in += in > 0 ? 0.5 : -0.5;
+    *pDst++ = (q7_t) (__SSAT((q15_t) (in), 8));
+
+    in = *pIn++;
+    in = (in * 128);
+    in += in > 0 ? 0.5 : -0.5;
+    *pDst++ = (q7_t) (__SSAT((q15_t) (in), 8));
+
+    in = *pIn++;
+    in = (in * 128);
+    in += in > 0 ? 0.5 : -0.5;
+    *pDst++ = (q7_t) (__SSAT((q15_t) (in), 8));
+
+#else
+
+    /* C = A * 128 */
+    /* convert from float to q7 and then store the results in the destination buffer */
+    *pDst++ = __SSAT((q31_t) (*pIn++ * 128.0f), 8);
+    *pDst++ = __SSAT((q31_t) (*pIn++ * 128.0f), 8);
+    *pDst++ = __SSAT((q31_t) (*pIn++ * 128.0f), 8);
+    *pDst++ = __SSAT((q31_t) (*pIn++ * 128.0f), 8);
+
+#endif /*      #ifdef ARM_MATH_ROUNDING        */
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+
+#ifdef ARM_MATH_ROUNDING
+    /* C = A * 128 */
+    /* convert from float to q7 and then store the results in the destination buffer */
+    in = *pIn++;
+    in = (in * 128);
+    in += in > 0 ? 0.5 : -0.5;
+    *pDst++ = (q7_t) (__SSAT((q15_t) (in), 8));
+
+#else
+
+    /* C = A * 128 */
+    /* convert from float to q7 and then store the results in the destination buffer */
+    *pDst++ = __SSAT((q31_t) (*pIn++ * 128.0f), 8);
+
+#endif /*      #ifdef ARM_MATH_ROUNDING        */
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+#ifdef ARM_MATH_ROUNDING
+    /* C = A * 128 */
+    /* convert from float to q7 and then store the results in the destination buffer */
+    in = *pIn++;
+    in = (in * 128.0f);
+    in += in > 0 ? 0.5f : -0.5f;
+    *pDst++ = (q7_t) (__SSAT((q31_t) (in), 8));
+
+#else
+
+    /* C = A * 128 */
+    /* convert from float to q7 and then store the results in the destination buffer */
+    *pDst++ = (q7_t) __SSAT((q31_t) (*pIn++ * 128.0f), 8);
+
+#endif /*      #ifdef ARM_MATH_ROUNDING        */
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+ * @} end of float_to_x group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q15_to_float.c b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q15_to_float.c
new file mode 100644
index 0000000000..ce51e9a395
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q15_to_float.c
@@ -0,0 +1,126 @@
+/* ----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_q15_to_float.c    
+*    
+* Description:	Converts the elements of the Q15 vector to floating-point vector.     
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupSupport    
+ */
+
+/**    
+ * @defgroup q15_to_x  Convert 16-bit Integer value    
+ */
+
+/**    
+ * @addtogroup q15_to_x    
+ * @{    
+ */
+
+
+
+
+/**    
+ * @brief  Converts the elements of the Q15 vector to floating-point vector.     
+ * @param[in]       *pSrc points to the Q15 input vector    
+ * @param[out]      *pDst points to the floating-point output vector   
+ * @param[in]       blockSize length of the input vector    
+ * @return none.    
+ *    
+ * \par Description:    
+ *    
+ * The equation used for the conversion process is:    
+ *   
+ * 
    
+ * 	pDst[n] = (float32_t) pSrc[n] / 32768;   0 <= n < blockSize.    
+ * 
    
+ *   
+ */
+
+
+void arm_q15_to_float(
+  q15_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize)
+{
+  q15_t *pIn = pSrc;                             /* Src pointer */
+  uint32_t blkCnt;                               /* loop counter */
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = (float32_t) A / 32768 */
+    /* convert from q15 to float and then store the results in the destination buffer */
+    *pDst++ = ((float32_t) * pIn++ / 32768.0f);
+    *pDst++ = ((float32_t) * pIn++ / 32768.0f);
+    *pDst++ = ((float32_t) * pIn++ / 32768.0f);
+    *pDst++ = ((float32_t) * pIn++ / 32768.0f);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C = (float32_t) A / 32768 */
+    /* convert from q15 to float and then store the results in the destination buffer */
+    *pDst++ = ((float32_t) * pIn++ / 32768.0f);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**    
+ * @} end of q15_to_x group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q15_to_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q15_to_q31.c
new file mode 100644
index 0000000000..a0f66c29e8
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q15_to_q31.c
@@ -0,0 +1,148 @@
+/* ----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_q15_to_q31.c    
+*    
+* Description:	Converts the elements of the Q15 vector to Q31 vector.  
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupSupport    
+ */
+
+/**    
+ * @addtogroup q15_to_x    
+ * @{    
+ */
+
+/**    
+ * @brief Converts the elements of the Q15 vector to Q31 vector.     
+ * @param[in]       *pSrc points to the Q15 input vector    
+ * @param[out]      *pDst points to the Q31 output vector   
+ * @param[in]       blockSize length of the input vector    
+ * @return none.    
+ *    
+ * \par Description:    
+ *    
+ * The equation used for the conversion process is:   
+ *   
+ * 
    
+ * 	pDst[n] = (q31_t) pSrc[n] << 16;   0 <= n < blockSize.    
+ * 
    
+ *   
+ */
+
+
+void arm_q15_to_q31(
+  q15_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize)
+{
+  q15_t *pIn = pSrc;                             /* Src pointer */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t in1, in2;
+  q31_t out1, out2, out3, out4;
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = (q31_t)A << 16 */
+    /* convert from q15 to q31 and then store the results in the destination buffer */
+    in1 = *__SIMD32(pIn)++;
+    in2 = *__SIMD32(pIn)++;
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    /* extract lower 16 bits to 32 bit result */
+    out1 = in1 << 16u;
+    /* extract upper 16 bits to 32 bit result */
+    out2 = in1 & 0xFFFF0000;
+    /* extract lower 16 bits to 32 bit result */
+    out3 = in2 << 16u;
+    /* extract upper 16 bits to 32 bit result */
+    out4 = in2 & 0xFFFF0000;
+
+#else
+
+    /* extract upper 16 bits to 32 bit result */
+    out1 = in1 & 0xFFFF0000;
+    /* extract lower 16 bits to 32 bit result */
+    out2 = in1 << 16u;
+    /* extract upper 16 bits to 32 bit result */
+    out3 = in2 & 0xFFFF0000;
+    /* extract lower 16 bits to 32 bit result */
+    out4 = in2 << 16u;
+
+#endif //      #ifndef ARM_MATH_BIG_ENDIAN
+
+    *pDst++ = out1;
+    *pDst++ = out2;
+    *pDst++ = out3;
+    *pDst++ = out4;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C = (q31_t)A << 16 */
+    /* convert from q15 to q31 and then store the results in the destination buffer */
+    *pDst++ = (q31_t) * pIn++ << 16;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+}
+
+/**    
+ * @} end of q15_to_x group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q15_to_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q15_to_q7.c
new file mode 100644
index 0000000000..87fe63d9eb
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q15_to_q7.c
@@ -0,0 +1,146 @@
+/* ----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_q15_to_q7.c    
+*    
+* Description:	Converts the elements of the Q15 vector to Q7 vector.  
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupSupport    
+ */
+
+/**    
+ * @addtogroup q15_to_x    
+ * @{    
+ */
+
+
+/**    
+ * @brief Converts the elements of the Q15 vector to Q7 vector.     
+ * @param[in]       *pSrc points to the Q15 input vector    
+ * @param[out]      *pDst points to the Q7 output vector   
+ * @param[in]       blockSize length of the input vector    
+ * @return none.    
+ *    
+ * \par Description:    
+ *    
+ * The equation used for the conversion process is:    
+ *   
+ * 
    
+ * 	pDst[n] = (q7_t) pSrc[n] >> 8;   0 <= n < blockSize.    
+ * 
   
+ *   
+ */
+
+
+void arm_q15_to_q7(
+  q15_t * pSrc,
+  q7_t * pDst,
+  uint32_t blockSize)
+{
+  q15_t *pIn = pSrc;                             /* Src pointer */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t in1, in2;
+  q31_t out1, out2;
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = (q7_t) A >> 8 */
+    /* convert from q15 to q7 and then store the results in the destination buffer */
+    in1 = *__SIMD32(pIn)++;
+    in2 = *__SIMD32(pIn)++;
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    out1 = __PKHTB(in2, in1, 16);
+    out2 = __PKHBT(in2, in1, 16);
+
+#else
+
+    out1 = __PKHTB(in1, in2, 16);
+    out2 = __PKHBT(in1, in2, 16);
+
+#endif //      #ifndef ARM_MATH_BIG_ENDIAN
+
+    /* rotate packed value by 24 */
+    out2 = ((uint32_t) out2 << 8) | ((uint32_t) out2 >> 24);
+
+    /* anding with 0xff00ff00 to get two 8 bit values */
+    out1 = out1 & 0xFF00FF00;
+    /* anding with 0x00ff00ff to get two 8 bit values */
+    out2 = out2 & 0x00FF00FF;
+
+    /* oring two values(contains two 8 bit values) to get four packed 8 bit values */
+    out1 = out1 | out2;
+
+    /* store 4 samples at a time to destiantion buffer */
+    *__SIMD32(pDst)++ = out1;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C = (q7_t) A >> 8 */
+    /* convert from q15 to q7 and then store the results in the destination buffer */
+    *pDst++ = (q7_t) (*pIn++ >> 8);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+}
+
+/**    
+ * @} end of q15_to_x group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q31_to_float.c b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q31_to_float.c
new file mode 100644
index 0000000000..94deec9a1b
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q31_to_float.c
@@ -0,0 +1,123 @@
+/* ----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_q31_to_float.c    
+*    
+* Description:	Converts the elements of the Q31 vector to floating-point vector.      
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupSupport    
+ */
+
+/**    
+ * @defgroup q31_to_x  Convert 32-bit Integer value    
+ */
+
+/**    
+ * @addtogroup q31_to_x    
+ * @{    
+ */
+
+/**    
+ * @brief Converts the elements of the Q31 vector to floating-point vector.    
+ * @param[in]       *pSrc points to the Q31 input vector    
+ * @param[out]      *pDst points to the floating-point output vector   
+ * @param[in]       blockSize length of the input vector    
+ * @return none.    
+ *    
+ * \par Description:    
+ *    
+ * The equation used for the conversion process is:    
+ *   
+ * 
    
+ * 	pDst[n] = (float32_t) pSrc[n] / 2147483648;   0 <= n < blockSize.    
+ * 
    
+ *   
+ */
+
+
+void arm_q31_to_float(
+  q31_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize)
+{
+  q31_t *pIn = pSrc;                             /* Src pointer */
+  uint32_t blkCnt;                               /* loop counter */
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = (float32_t) A / 2147483648 */
+    /* convert from q31 to float and then store the results in the destination buffer */
+    *pDst++ = ((float32_t) * pIn++ / 2147483648.0f);
+    *pDst++ = ((float32_t) * pIn++ / 2147483648.0f);
+    *pDst++ = ((float32_t) * pIn++ / 2147483648.0f);
+    *pDst++ = ((float32_t) * pIn++ / 2147483648.0f);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C = (float32_t) A / 2147483648 */
+    /* convert from q31 to float and then store the results in the destination buffer */
+    *pDst++ = ((float32_t) * pIn++ / 2147483648.0f);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**    
+ * @} end of q31_to_x group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q31_to_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q31_to_q15.c
new file mode 100644
index 0000000000..ba79f85a13
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q31_to_q15.c
@@ -0,0 +1,137 @@
+/* ----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_q31_to_q15.c    
+*    
+* Description:	Converts the elements of the Q31 vector to Q15 vector.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupSupport    
+ */
+
+/**    
+ * @addtogroup q31_to_x    
+ * @{    
+ */
+
+/**    
+ * @brief Converts the elements of the Q31 vector to Q15 vector.    
+ * @param[in]       *pSrc points to the Q31 input vector    
+ * @param[out]      *pDst points to the Q15 output vector   
+ * @param[in]       blockSize length of the input vector    
+ * @return none.    
+ *     
+ * \par Description:    
+ *    
+ * The equation used for the conversion process is:    
+ *   
+ * 
    
+ * 	pDst[n] = (q15_t) pSrc[n] >> 16;   0 <= n < blockSize.    
+ * 
    
+ *   
+ */
+
+
+void arm_q31_to_q15(
+  q31_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+  q31_t *pIn = pSrc;                             /* Src pointer */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t in1, in2, in3, in4;
+  q31_t out1, out2;
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = (q15_t) A >> 16 */
+    /* convert from q31 to q15 and then store the results in the destination buffer */
+    in1 = *pIn++;
+    in2 = *pIn++;
+    in3 = *pIn++;
+    in4 = *pIn++;
+
+    /* pack two higher 16-bit values from two 32-bit values */
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    out1 = __PKHTB(in2, in1, 16);
+    out2 = __PKHTB(in4, in3, 16);
+
+#else
+
+    out1 = __PKHTB(in1, in2, 16);
+    out2 = __PKHTB(in3, in4, 16);
+
+#endif //      #ifdef ARM_MATH_BIG_ENDIAN
+
+    *__SIMD32(pDst)++ = out1;
+    *__SIMD32(pDst)++ = out2;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C = (q15_t) A >> 16 */
+    /* convert from q31 to q15 and then store the results in the destination buffer */
+    *pDst++ = (q15_t) (*pIn++ >> 16);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+}
+
+/**    
+ * @} end of q31_to_x group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q31_to_q7.c b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q31_to_q7.c
new file mode 100644
index 0000000000..afc8fdbed4
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q31_to_q7.c
@@ -0,0 +1,128 @@
+/* ----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_q31_to_q7.c    
+*    
+* Description:	Converts the elements of the Q31 vector to Q7 vector.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupSupport    
+ */
+
+/**    
+ * @addtogroup q31_to_x    
+ * @{    
+ */
+
+/**    
+ * @brief Converts the elements of the Q31 vector to Q7 vector.    
+ * @param[in]       *pSrc points to the Q31 input vector    
+ * @param[out]      *pDst points to the Q7 output vector   
+ * @param[in]       blockSize length of the input vector    
+ * @return none.    
+ *    
+ * \par Description:    
+ *    
+ * The equation used for the conversion process is:    
+ *   
+ * 
    
+ * 	pDst[n] = (q7_t) pSrc[n] >> 24;   0 <= n < blockSize.     
+ * 
    
+ *   
+ */
+
+
+void arm_q31_to_q7(
+  q31_t * pSrc,
+  q7_t * pDst,
+  uint32_t blockSize)
+{
+  q31_t *pIn = pSrc;                             /* Src pointer */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t in1, in2, in3, in4;
+  q7_t out1, out2, out3, out4;
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = (q7_t) A >> 24 */
+    /* convert from q31 to q7 and then store the results in the destination buffer */
+    in1 = *pIn++;
+    in2 = *pIn++;
+    in3 = *pIn++;
+    in4 = *pIn++;
+
+    out1 = (q7_t) (in1 >> 24);
+    out2 = (q7_t) (in2 >> 24);
+    out3 = (q7_t) (in3 >> 24);
+    out4 = (q7_t) (in4 >> 24);
+
+    *__SIMD32(pDst)++ = __PACKq7(out1, out2, out3, out4);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C = (q7_t) A >> 24 */
+    /* convert from q31 to q7 and then store the results in the destination buffer */
+    *pDst++ = (q7_t) (*pIn++ >> 24);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+}
+
+/**    
+ * @} end of q31_to_x group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q7_to_float.c b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q7_to_float.c
new file mode 100644
index 0000000000..be4ac5fe30
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q7_to_float.c
@@ -0,0 +1,123 @@
+/* ----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_q7_to_float.c    
+*    
+* Description:	Converts the elements of the Q7 vector to floating-point vector.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupSupport    
+ */
+
+/**    
+ * @defgroup q7_to_x  Convert 8-bit Integer value    
+ */
+
+/**    
+ * @addtogroup q7_to_x    
+ * @{    
+ */
+
+/**    
+ * @brief Converts the elements of the Q7 vector to floating-point vector.    
+ * @param[in]       *pSrc points to the Q7 input vector    
+ * @param[out]      *pDst points to the floating-point output vector   
+ * @param[in]       blockSize length of the input vector    
+ * @return none.    
+ *		     
+ * \par Description:    
+ *    
+ * The equation used for the conversion process is:    
+ *   
+ * 
    
+ * 	pDst[n] = (float32_t) pSrc[n] / 128;   0 <= n < blockSize.    
+ * 
    
+ *   
+ */
+
+
+void arm_q7_to_float(
+  q7_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize)
+{
+  q7_t *pIn = pSrc;                              /* Src pointer */
+  uint32_t blkCnt;                               /* loop counter */
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = (float32_t) A / 128 */
+    /* convert from q7 to float and then store the results in the destination buffer */
+    *pDst++ = ((float32_t) * pIn++ / 128.0f);
+    *pDst++ = ((float32_t) * pIn++ / 128.0f);
+    *pDst++ = ((float32_t) * pIn++ / 128.0f);
+    *pDst++ = ((float32_t) * pIn++ / 128.0f);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C = (float32_t) A / 128 */
+    /* convert from q7 to float and then store the results in the destination buffer */
+    *pDst++ = ((float32_t) * pIn++ / 128.0f);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**    
+ * @} end of q7_to_x group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q7_to_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q7_to_q15.c
new file mode 100644
index 0000000000..019ca48159
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q7_to_q15.c
@@ -0,0 +1,149 @@
+/* ----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_q7_to_q15.c    
+*    
+* Description:	Converts the elements of the Q7 vector to Q15 vector.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupSupport    
+ */
+
+/**    
+ * @addtogroup q7_to_x    
+ * @{    
+ */
+
+
+
+
+/**    
+ * @brief Converts the elements of the Q7 vector to Q15 vector.    
+ * @param[in]       *pSrc points to the Q7 input vector    
+ * @param[out]      *pDst points to the Q15 output vector   
+ * @param[in]       blockSize length of the input vector    
+ * @return none.    
+ *    
+ * \par Description:    
+ *    
+ * The equation used for the conversion process is:    
+ *   
+ * 
    
+ * 	pDst[n] = (q15_t) pSrc[n] << 8;   0 <= n < blockSize.    
+ * 
    
+ *   
+ */
+
+
+void arm_q7_to_q15(
+  q7_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+  q7_t *pIn = pSrc;                              /* Src pointer */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0
+  q31_t in;
+  q31_t in1, in2;
+  q31_t out1, out2;
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = (q15_t) A << 8 */
+    /* convert from q7 to q15 and then store the results in the destination buffer */
+    in = *__SIMD32(pIn)++;
+
+    /* rotatate in by 8 and extend two q7_t values to q15_t values */
+    in1 = __SXTB16(__ROR(in, 8));
+
+    /* extend remainig two q7_t values to q15_t values */
+    in2 = __SXTB16(in);
+
+    in1 = in1 << 8u;
+    in2 = in2 << 8u;
+
+    in1 = in1 & 0xFF00FF00;
+    in2 = in2 & 0xFF00FF00;
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    out2 = __PKHTB(in1, in2, 16);
+    out1 = __PKHBT(in2, in1, 16);
+
+#else
+
+    out1 = __PKHTB(in1, in2, 16);
+    out2 = __PKHBT(in2, in1, 16);
+
+#endif
+
+    *__SIMD32(pDst)++ = out1;
+    *__SIMD32(pDst)++ = out2;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C = (q15_t) A << 8 */
+    /* convert from q7 to q15 and then store the results in the destination buffer */
+    *pDst++ = (q15_t) * pIn++ << 8;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+}
+
+/**    
+ * @} end of q7_to_x group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q7_to_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q7_to_q31.c
new file mode 100644
index 0000000000..bbbcc6f4a3
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/SupportFunctions/arm_q7_to_q31.c
@@ -0,0 +1,134 @@
+/* ----------------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_q7_to_q31.c    
+*    
+* Description:	Converts the elements of the Q7 vector to Q31 vector.  
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupSupport    
+ */
+
+/**    
+ * @addtogroup q7_to_x    
+ * @{    
+ */
+
+/**    
+ * @brief Converts the elements of the Q7 vector to Q31 vector.    
+ * @param[in]       *pSrc points to the Q7 input vector    
+ * @param[out]      *pDst points to the Q31 output vector   
+ * @param[in]       blockSize length of the input vector    
+ * @return none.    
+ *    
+ * \par Description:    
+ *    
+ * The equation used for the conversion process is:    
+ *   
+ * 
    
+ * 	pDst[n] = (q31_t) pSrc[n] << 24;   0 <= n < blockSize.   
+ * 
     
+ *   
+ */
+
+
+void arm_q7_to_q31(
+  q7_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize)
+{
+  q7_t *pIn = pSrc;                              /* Src pointer */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0
+
+  q31_t in;
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = (q31_t) A << 24 */
+    /* convert from q7 to q31 and then store the results in the destination buffer */
+    in = *__SIMD32(pIn)++;
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    *pDst++ = (__ROR(in, 8)) & 0xFF000000;
+    *pDst++ = (__ROR(in, 16)) & 0xFF000000;
+    *pDst++ = (__ROR(in, 24)) & 0xFF000000;
+    *pDst++ = (in & 0xFF000000);
+
+#else
+
+    *pDst++ = (in & 0xFF000000);
+    *pDst++ = (__ROR(in, 24)) & 0xFF000000;
+    *pDst++ = (__ROR(in, 16)) & 0xFF000000;
+    *pDst++ = (__ROR(in, 8)) & 0xFF000000;
+
+#endif //              #ifndef ARM_MATH_BIG_ENDIAN
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Loop over blockSize number of values */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+  while(blkCnt > 0u)
+  {
+    /* C = (q31_t) A << 24 */
+    /* convert from q7 to q31 and then store the results in the destination buffer */
+    *pDst++ = (q31_t) * pIn++ << 24;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+}
+
+/**    
+ * @} end of q7_to_x group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_bitreversal.c b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_bitreversal.c
new file mode 100644
index 0000000000..3da790ebb1
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_bitreversal.c
@@ -0,0 +1,222 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_bitreversal.c    
+*    
+* Description:	This file has common tables like Bitreverse, reciprocal etc which are used across different functions    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Initial Version  
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+#include "arm_common_tables.h"
+
+/*    
+ * @brief  In-place bit reversal function.   
+ * @param[in, out] *pSrc        points to the in-place buffer of floating-point data type.   
+ * @param[in]      fftSize      length of the FFT.   
+ * @param[in]      bitRevFactor bit reversal modifier that supports different size FFTs with the same bit reversal table.   
+ * @param[in]      *pBitRevTab  points to the bit reversal table.   
+ * @return none.   
+ */
+
+void arm_bitreversal_f32(
+  float32_t * pSrc,
+  uint16_t fftSize,
+  uint16_t bitRevFactor,
+  uint16_t * pBitRevTab)
+{
+  uint16_t fftLenBy2, fftLenBy2p1;
+  uint16_t i, j;
+  float32_t in;
+
+  /*  Initializations */
+  j = 0u;
+  fftLenBy2 = fftSize >> 1u;
+  fftLenBy2p1 = (fftSize >> 1u) + 1u;
+
+  /* Bit Reversal Implementation */
+  for (i = 0u; i <= (fftLenBy2 - 2u); i += 2u)
+  {
+    if(i < j)
+    {
+      /*  pSrc[i] <-> pSrc[j]; */
+      in = pSrc[2u * i];
+      pSrc[2u * i] = pSrc[2u * j];
+      pSrc[2u * j] = in;
+
+      /*  pSrc[i+1u] <-> pSrc[j+1u] */
+      in = pSrc[(2u * i) + 1u];
+      pSrc[(2u * i) + 1u] = pSrc[(2u * j) + 1u];
+      pSrc[(2u * j) + 1u] = in;
+
+      /*  pSrc[i+fftLenBy2p1] <-> pSrc[j+fftLenBy2p1] */
+      in = pSrc[2u * (i + fftLenBy2p1)];
+      pSrc[2u * (i + fftLenBy2p1)] = pSrc[2u * (j + fftLenBy2p1)];
+      pSrc[2u * (j + fftLenBy2p1)] = in;
+
+      /*  pSrc[i+fftLenBy2p1+1u] <-> pSrc[j+fftLenBy2p1+1u] */
+      in = pSrc[(2u * (i + fftLenBy2p1)) + 1u];
+      pSrc[(2u * (i + fftLenBy2p1)) + 1u] =
+        pSrc[(2u * (j + fftLenBy2p1)) + 1u];
+      pSrc[(2u * (j + fftLenBy2p1)) + 1u] = in;
+
+    }
+
+    /*  pSrc[i+1u] <-> pSrc[j+1u] */
+    in = pSrc[2u * (i + 1u)];
+    pSrc[2u * (i + 1u)] = pSrc[2u * (j + fftLenBy2)];
+    pSrc[2u * (j + fftLenBy2)] = in;
+
+    /*  pSrc[i+2u] <-> pSrc[j+2u] */
+    in = pSrc[(2u * (i + 1u)) + 1u];
+    pSrc[(2u * (i + 1u)) + 1u] = pSrc[(2u * (j + fftLenBy2)) + 1u];
+    pSrc[(2u * (j + fftLenBy2)) + 1u] = in;
+
+    /*  Reading the index for the bit reversal */
+    j = *pBitRevTab;
+
+    /*  Updating the bit reversal index depending on the fft length  */
+    pBitRevTab += bitRevFactor;
+  }
+}
+
+
+
+/*    
+ * @brief  In-place bit reversal function.   
+ * @param[in, out] *pSrc        points to the in-place buffer of Q31 data type.   
+ * @param[in]      fftLen       length of the FFT.   
+ * @param[in]      bitRevFactor bit reversal modifier that supports different size FFTs with the same bit reversal table   
+ * @param[in]      *pBitRevTab  points to bit reversal table.   
+ * @return none.   
+ */
+
+void arm_bitreversal_q31(
+  q31_t * pSrc,
+  uint32_t fftLen,
+  uint16_t bitRevFactor,
+  uint16_t * pBitRevTable)
+{
+  uint32_t fftLenBy2, fftLenBy2p1, i, j;
+  q31_t in;
+
+  /*  Initializations      */
+  j = 0u;
+  fftLenBy2 = fftLen / 2u;
+  fftLenBy2p1 = (fftLen / 2u) + 1u;
+
+  /* Bit Reversal Implementation */
+  for (i = 0u; i <= (fftLenBy2 - 2u); i += 2u)
+  {
+    if(i < j)
+    {
+      /*  pSrc[i] <-> pSrc[j]; */
+      in = pSrc[2u * i];
+      pSrc[2u * i] = pSrc[2u * j];
+      pSrc[2u * j] = in;
+
+      /*  pSrc[i+1u] <-> pSrc[j+1u] */
+      in = pSrc[(2u * i) + 1u];
+      pSrc[(2u * i) + 1u] = pSrc[(2u * j) + 1u];
+      pSrc[(2u * j) + 1u] = in;
+
+      /*  pSrc[i+fftLenBy2p1] <-> pSrc[j+fftLenBy2p1] */
+      in = pSrc[2u * (i + fftLenBy2p1)];
+      pSrc[2u * (i + fftLenBy2p1)] = pSrc[2u * (j + fftLenBy2p1)];
+      pSrc[2u * (j + fftLenBy2p1)] = in;
+
+      /*  pSrc[i+fftLenBy2p1+1u] <-> pSrc[j+fftLenBy2p1+1u] */
+      in = pSrc[(2u * (i + fftLenBy2p1)) + 1u];
+      pSrc[(2u * (i + fftLenBy2p1)) + 1u] =
+        pSrc[(2u * (j + fftLenBy2p1)) + 1u];
+      pSrc[(2u * (j + fftLenBy2p1)) + 1u] = in;
+
+    }
+
+    /*  pSrc[i+1u] <-> pSrc[j+1u] */
+    in = pSrc[2u * (i + 1u)];
+    pSrc[2u * (i + 1u)] = pSrc[2u * (j + fftLenBy2)];
+    pSrc[2u * (j + fftLenBy2)] = in;
+
+    /*  pSrc[i+2u] <-> pSrc[j+2u] */
+    in = pSrc[(2u * (i + 1u)) + 1u];
+    pSrc[(2u * (i + 1u)) + 1u] = pSrc[(2u * (j + fftLenBy2)) + 1u];
+    pSrc[(2u * (j + fftLenBy2)) + 1u] = in;
+
+    /*  Reading the index for the bit reversal */
+    j = *pBitRevTable;
+
+    /*  Updating the bit reversal index depending on the fft length */
+    pBitRevTable += bitRevFactor;
+  }
+}
+
+
+
+/*    
+   * @brief  In-place bit reversal function.   
+   * @param[in, out] *pSrc        points to the in-place buffer of Q15 data type.   
+   * @param[in]      fftLen       length of the FFT.   
+   * @param[in]      bitRevFactor bit reversal modifier that supports different size FFTs with the same bit reversal table   
+   * @param[in]      *pBitRevTab  points to bit reversal table.   
+   * @return none.   
+ */
+
+void arm_bitreversal_q15(
+  q15_t * pSrc16,
+  uint32_t fftLen,
+  uint16_t bitRevFactor,
+  uint16_t * pBitRevTab)
+{
+  q31_t *pSrc = (q31_t *) pSrc16;
+  q31_t in;
+  uint32_t fftLenBy2, fftLenBy2p1;
+  uint32_t i, j;
+
+  /*  Initializations */
+  j = 0u;
+  fftLenBy2 = fftLen / 2u;
+  fftLenBy2p1 = (fftLen / 2u) + 1u;
+
+  /* Bit Reversal Implementation */
+  for (i = 0u; i <= (fftLenBy2 - 2u); i += 2u)
+  {
+    if(i < j)
+    {
+      /*  pSrc[i] <-> pSrc[j]; */
+      /*  pSrc[i+1u] <-> pSrc[j+1u] */
+      in = pSrc[i];
+      pSrc[i] = pSrc[j];
+      pSrc[j] = in;
+
+      /*  pSrc[i + fftLenBy2p1] <-> pSrc[j + fftLenBy2p1];  */
+      /*  pSrc[i + fftLenBy2p1+1u] <-> pSrc[j + fftLenBy2p1+1u] */
+      in = pSrc[i + fftLenBy2p1];
+      pSrc[i + fftLenBy2p1] = pSrc[j + fftLenBy2p1];
+      pSrc[j + fftLenBy2p1] = in;
+    }
+
+    /*  pSrc[i+1u] <-> pSrc[j+fftLenBy2];         */
+    /*  pSrc[i+2] <-> pSrc[j+fftLenBy2+1u]  */
+    in = pSrc[i + 1u];
+    pSrc[i + 1u] = pSrc[j + fftLenBy2];
+    pSrc[j + fftLenBy2] = in;
+
+    /*  Reading the index for the bit reversal */
+    j = *pBitRevTab;
+
+    /*  Updating the bit reversal index depending on the fft length  */
+    pBitRevTab += bitRevFactor;
+  }
+}
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix2_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix2_f32.c
new file mode 100644
index 0000000000..274b699281
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix2_f32.c
@@ -0,0 +1,511 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010 ARM Limited. All rights reserved.   
+*   
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*   
+* Project: 	    CMSIS DSP Library   
+* Title:	    arm_cfft_radix2_f32.c   
+*   
+* Description:	Radix-2 Decimation in Frequency CFFT & CIFFT Floating point processing function   
+*   
+*   
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.3 2010/11/29  
+*    Initial version   
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**   
+ * @ingroup groupTransforms   
+ */
+
+/**   
+ * @defgroup Radix2_CFFT_CIFFT Radix-2 Complex FFT Functions   
+ *   
+ * \par   
+ * Complex Fast Fourier Transform(CFFT) and Complex Inverse Fast Fourier Transform(CIFFT) is an efficient algorithm to compute Discrete Fourier Transform(DFT) and Inverse Discrete Fourier Transform(IDFT).   
+ * Computational complexity of CFFT reduces drastically when compared to DFT.   
+ * \par   
+ * This set of functions implements CFFT/CIFFT   
+ * for Q15, Q31, and floating-point data types.  The functions operates on in-place buffer which uses same buffer for input and output.   
+ * Complex input is stored in input buffer in an interleaved fashion.   
+ *   
+ * \par   
+ * The functions operate on blocks of input and output data and each call to the function processes   
+ * 2*fftLen samples through the transform.  pSrc  points to In-place arrays containing 2*fftLen values.   
+ * \par  
+ * The pSrc points to the array of in-place buffer of size 2*fftLen and inputs and outputs are stored in an interleaved fashion as shown below.   
+ * 
 {real[0], imag[0], real[1], imag[1],..} 
   
+ *   
+ * \par Lengths supported by the transform:  
+ * \par   
+ * Internally, the function utilize a radix-2 decimation in frequency(DIF) algorithm   
+ * and the size of the FFT supported are of the lengths [16, 32, 64, 128, 256, 512, 1024, 2048, 4096].  
+ *    
+ *   
+ * \par Algorithm:   
+ *   
+ * Complex Fast Fourier Transform:   
+ * \par    
+ * Input real and imaginary data:   
+ * 
   
+ * x(n) = xa + j * ya   
+ * x(n+N/2 ) = xb + j * yb   
+ * 
   
+ * where N is length of FFT   
+ * \par   
+ * Output real and imaginary data:   
+ * 
   
+ * X(2r) = xa'+ j * ya'   
+ * X(2r+1) = xb'+ j * yb'   
+ * 
   
+ * \par   
+ * Twiddle factors for radix-2 FFT:   
+ * 
   
+ * Wn = cosVal + j * (- sinVal)   
+ * 
   
+ *   
+ * \par   
+ * \image html CFFT_Radix2.gif "Radix-2 Decimation-in Frequency Complex Fast Fourier Transform"   
+ *   
+ * \par   
+ * Output from Radix-2 CFFT Results in Digit reversal order. Interchange middle two branches of every butterfly results in Bit reversed output.   
+ * \par   
+ *  Butterfly CFFT equations:   
+ * 
   
+ * xa' = xa + xb  
+ * ya' = ya + yb  
+ * xb' = (xa-xb)* cosVal + (ya-yb) * sinVal   
+ * yb' = (ya-yb)* cosVal - (xa-xb) * sinVal   
+ * 
   
+ *   
+ *   
+ * Complex Inverse Fast Fourier Transform:   
+ * \par   
+ * CIFFT uses same twiddle factor table as CFFT with modifications in the design equation as shown below.   
+ *   
+ * \par   
+ *  Modified Butterfly CIFFT equations:   
+ * 
   
+ * xa' = xa + xb  
+ * ya' = ya + yb  
+ * xb' = (xa-xb)* cosVal - (ya-yb) * sinVal   
+ * yb' = (ya-yb)* cosVal + (xa-xb) * sinVal   
+ * 
   
+ *   
+ * \par Instance Structure   
+ * A separate instance structure must be defined for each Instance but the twiddle factors and bit reversal tables can be reused.   
+ * There are separate instance structure declarations for each of the 3 supported data types.   
+ *   
+ * \par Initialization Functions   
+ * There is also an associated initialization function for each data type.   
+ * The initialization function performs the following operations:   
+ * - Sets the values of the internal structure fields.   
+ * - Initializes twiddle factor table and bit reversal table pointers   
+ * \par   
+ * Use of the initialization function is optional.   
+ * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.   
+ * To place an instance structure into a const data section, the instance structure must be manually initialized.   
+ * Manually initialize the instance structure as follows:   
+ * 
   
+ *arm_cfft_radix2_instance_f32 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor, onebyfftLen};   
+ *arm_cfft_radix2_instance_q31 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor};   
+ *arm_cfft_radix2_instance_q15 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor};   
+ * 
   
+ * \par   
+ * where fftLen length of CFFT/CIFFT; ifftFlag Flag for selection of CFFT or CIFFT(Set ifftFlag to calculate CIFFT otherwise calculates CFFT);   
+ * bitReverseFlag Flag for selection of output order(Set bitReverseFlag to output in normal order otherwise output in bit reversed order);    
+ * pTwiddlepoints to array of twiddle coefficients; pBitRevTable points to the array of bit reversal table.   
+ * twidCoefModifier modifier for twiddle factor table which supports all FFT lengths with same table;    
+ * pBitRevTable modifier for bit reversal table which supports all FFT lengths with same table.   
+ * onebyfftLen value of 1/fftLen to calculate CIFFT;   
+ *  
+ * \par Fixed-Point Behavior   
+ * Care must be taken when using the fixed-point versions of the CFFT/CIFFT function.   
+ * Refer to the function specific documentation below for usage guidelines.   
+ */
+
+
+/**   
+ * @addtogroup Radix2_CFFT_CIFFT   
+ * @{   
+ */
+
+/**   
+ * @details   
+ * @brief Processing function for the floating-point Radix-2 CFFT/CIFFT.  
+ * @param[in]      *S    points to an instance of the floating-point Radix-2 CFFT/CIFFT structure.  
+ * @param[in, out] *pSrc points to the complex data buffer of size 2*fftLen. Processing occurs in-place.  
+ * @return none.  
+ */
+
+void arm_cfft_radix2_f32(
+  const arm_cfft_radix2_instance_f32 * S,
+  float32_t * pSrc)
+{
+
+  if(S->ifftFlag == 1u)
+  {
+    /*  Complex IFFT radix-2  */
+    arm_radix2_butterfly_inverse_f32(pSrc, S->fftLen, S->pTwiddle,
+                                     S->twidCoefModifier, S->onebyfftLen);
+  }
+  else
+  {
+    /*  Complex FFT radix-2  */
+    arm_radix2_butterfly_f32(pSrc, S->fftLen, S->pTwiddle,
+                             S->twidCoefModifier);
+  }
+
+  if(S->bitReverseFlag == 1u)
+  {
+    /*  Bit Reversal */
+    arm_bitreversal_f32(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable);
+  }
+
+}
+
+
+/**    
+ * @} end of Radix2_CFFT_CIFFT group    
+ */
+
+
+
+/* ----------------------------------------------------------------------    
+** Internal helper function used by the FFTs    
+** ------------------------------------------------------------------- */
+
+/*    
+ * @brief  Core function for the floating-point CFFT butterfly process.   
+ * @param[in, out] *pSrc            points to the in-place buffer of floating-point data type.   
+ * @param[in]      fftLen           length of the FFT.   
+ * @param[in]      *pCoef           points to the twiddle coefficient buffer.   
+ * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.   
+ * @return none.   
+ */
+
+void arm_radix2_butterfly_f32(
+  float32_t * pSrc,
+  uint32_t fftLen,
+  float32_t * pCoef,
+  uint16_t twidCoefModifier)
+{
+
+  int i, j, k, l;
+  int n1, n2, ia;
+  float32_t xt, yt, cosVal, sinVal;
+
+#ifndef ARM_MATH_CM0
+
+  /*  Initializations for the first stage */
+  n2 = fftLen;
+
+  n1 = n2;
+  n2 = n2 >> 1;
+  ia = 0;
+
+  // loop for groups 
+  for (i = 0; i < n2; i++)
+  {
+    cosVal = pCoef[ia * 2];
+    sinVal = pCoef[(ia * 2) + 1];
+
+    /*  Twiddle coefficients index modifier */
+    ia = ia + twidCoefModifier;
+
+    /*  index calculation for the input as, */
+    /*  pSrc[i + 0], pSrc[i + fftLen/1] */
+    l = i + n2;
+
+    /*  Butterfly implementation */
+    xt = pSrc[2 * i] - pSrc[2 * l];
+    pSrc[2 * i] = pSrc[2 * i] + pSrc[2 * l];
+
+    yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+    pSrc[2 * i + 1] = pSrc[2 * l + 1] + pSrc[2 * i + 1];
+
+    pSrc[2u * l] = xt * cosVal + yt * sinVal;
+
+    pSrc[2u * l + 1u] = yt * cosVal - xt * sinVal;
+
+  }                             // groups loop end 
+
+  twidCoefModifier = twidCoefModifier << 1u;
+
+  // loop for stage 
+  for (k = fftLen / 2; k > 2; k = k >> 1)
+  {
+    n1 = n2;
+    n2 = n2 >> 1;
+    ia = 0;
+
+    // loop for groups 
+    for (j = 0; j < n2; j++)
+    {
+      cosVal = pCoef[ia * 2];
+      sinVal = pCoef[(ia * 2) + 1];
+      ia = ia + twidCoefModifier;
+
+      // loop for butterfly 
+      for (i = j; i < fftLen; i += n1)
+      {
+        l = i + n2;
+        xt = pSrc[2 * i] - pSrc[2 * l];
+        pSrc[2 * i] = pSrc[2 * i] + pSrc[2 * l];
+
+        yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+        pSrc[2 * i + 1] = pSrc[2 * l + 1] + pSrc[2 * i + 1];
+
+        pSrc[2u * l] = xt * cosVal + yt * sinVal;
+
+        pSrc[2u * l + 1u] = yt * cosVal - xt * sinVal;
+
+      }                         // butterfly loop end 
+
+    }                           // groups loop end 
+
+    twidCoefModifier = twidCoefModifier << 1u;
+  }                             // stages loop end 
+
+  n1 = n2;
+  n2 = n2 >> 1;
+  ia = 0;
+
+  cosVal = pCoef[ia * 2];
+  sinVal = pCoef[(ia * 2) + 1];
+  ia = ia + twidCoefModifier;
+
+  // loop for butterfly 
+  for (i = 0; i < fftLen; i += n1)
+  {
+    l = i + n2;
+    xt = pSrc[2 * i] - pSrc[2 * l];
+    pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]);
+
+    yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+    pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]);
+
+    pSrc[2u * l] = xt;
+
+    pSrc[2u * l + 1u] = yt;
+
+  }                             // groups loop end 
+
+#else
+
+  //N = fftLen; 
+  n2 = fftLen;
+
+  // loop for stage 
+  for (k = fftLen; k > 1; k = k >> 1)
+  {
+    n1 = n2;
+    n2 = n2 >> 1;
+    ia = 0;
+
+    // loop for groups 
+    for (j = 0; j < n2; j++)
+    {
+      cosVal = pCoef[ia * 2];
+      sinVal = pCoef[(ia * 2) + 1];
+      ia = ia + twidCoefModifier;
+
+      // loop for butterfly 
+      for (i = j; i < fftLen; i += n1)
+      {
+        l = i + n2;
+        xt = pSrc[2 * i] - pSrc[2 * l];
+        pSrc[2 * i] = pSrc[2 * i] + pSrc[2 * l];
+
+        yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+        pSrc[2 * i + 1] = pSrc[2 * l + 1] + pSrc[2 * i + 1];
+
+        pSrc[2 * l] = (cosVal * xt + sinVal * yt);      // >> 15; 
+        pSrc[2 * l + 1] = (cosVal * yt - sinVal * xt);  // >> 15; 
+
+      }
+    }
+    twidCoefModifier = twidCoefModifier << 1u;
+  }
+
+#endif //    #ifndef ARM_MATH_CM0
+
+}
+
+
+void arm_radix2_butterfly_inverse_f32(
+  float32_t * pSrc,
+  uint32_t fftLen,
+  float32_t * pCoef,
+  uint16_t twidCoefModifier,
+  float32_t onebyfftLen)
+{
+
+  int i, j, k, l;
+  int n1, n2, ia;
+  float32_t xt, yt, cosVal, sinVal;
+
+#ifndef ARM_MATH_CM0
+
+  //N = fftLen; 
+  n2 = fftLen;
+
+  n1 = n2;
+  n2 = n2 >> 1;
+  ia = 0;
+
+  // loop for groups 
+  for (i = 0; i < n2; i++)
+  {
+    cosVal = pCoef[ia * 2];
+    sinVal = pCoef[(ia * 2) + 1];
+    ia = ia + twidCoefModifier;
+
+    l = i + n2;
+    xt = pSrc[2 * i] - pSrc[2 * l];
+    pSrc[2 * i] = pSrc[2 * i] + pSrc[2 * l];
+
+    yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+    pSrc[2 * i + 1] = pSrc[2 * l + 1] + pSrc[2 * i + 1];
+
+    pSrc[2u * l] = xt * cosVal - yt * sinVal;
+
+    pSrc[2u * l + 1u] = yt * cosVal + xt * sinVal;
+
+  }                             // groups loop end 
+
+  twidCoefModifier = twidCoefModifier << 1u;
+
+  // loop for stage 
+  for (k = fftLen / 2; k > 2; k = k >> 1)
+  {
+    n1 = n2;
+    n2 = n2 >> 1;
+    ia = 0;
+
+    // loop for groups 
+    for (j = 0; j < n2; j++)
+    {
+      cosVal = pCoef[ia * 2];
+      sinVal = pCoef[(ia * 2) + 1];
+      ia = ia + twidCoefModifier;
+
+      // loop for butterfly 
+      for (i = j; i < fftLen; i += n1)
+      {
+        l = i + n2;
+        xt = pSrc[2 * i] - pSrc[2 * l];
+        pSrc[2 * i] = pSrc[2 * i] + pSrc[2 * l];
+
+        yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+        pSrc[2 * i + 1] = pSrc[2 * l + 1] + pSrc[2 * i + 1];
+
+        pSrc[2u * l] = xt * cosVal - yt * sinVal;
+
+        pSrc[2u * l + 1u] = yt * cosVal + xt * sinVal;
+
+      }                         // butterfly loop end 
+
+    }                           // groups loop end 
+
+    twidCoefModifier = twidCoefModifier << 1u;
+  }                             // stages loop end 
+
+  n1 = n2;
+  n2 = n2 >> 1;
+  ia = 0;
+
+  cosVal = pCoef[ia * 2];
+  sinVal = pCoef[(ia * 2) + 1];
+  ia = ia + twidCoefModifier;
+
+  // loop for butterfly 
+  for (i = 0; i < fftLen; i += n1)
+  {
+    l = i + n2;
+    xt = pSrc[2 * i] - pSrc[2 * l];
+    pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]) * onebyfftLen;
+
+    yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+    pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]) * onebyfftLen;
+
+    pSrc[2u * l] = xt * onebyfftLen;
+
+    pSrc[2u * l + 1u] = yt * onebyfftLen;
+
+  }                             // butterfly loop end 
+
+#else
+
+  //N = fftLen; 
+  n2 = fftLen;
+
+  // loop for stage 
+  for (k = fftLen; k > 2; k = k >> 1)
+  {
+    n1 = n2;
+    n2 = n2 >> 1;
+    ia = 0;
+
+    // loop for groups 
+    for (j = 0; j < n2; j++)
+    {
+      cosVal = pCoef[ia * 2];
+      sinVal = pCoef[(ia * 2) + 1];
+      ia = ia + twidCoefModifier;
+
+      // loop for butterfly 
+      for (i = j; i < fftLen; i += n1)
+      {
+        l = i + n2;
+        xt = pSrc[2 * i] - pSrc[2 * l];
+        pSrc[2 * i] = pSrc[2 * i] + pSrc[2 * l];
+
+        yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+        pSrc[2 * i + 1] = pSrc[2 * l + 1] + pSrc[2 * i + 1];
+
+        pSrc[2u * l] = xt * cosVal - yt * sinVal;
+
+        pSrc[2u * l + 1u] = yt * cosVal + xt * sinVal;
+
+      }                         // butterfly loop end 
+
+    }                           // groups loop end 
+
+    twidCoefModifier = twidCoefModifier << 1u;
+  }                             // stages loop end 
+
+  n1 = n2;
+  n2 = n2 >> 1;
+  ia = 0;
+
+  cosVal = pCoef[ia * 2];
+  sinVal = pCoef[(ia * 2) + 1];
+  ia = ia + twidCoefModifier;
+
+  // loop for butterfly 
+  for (i = 0; i < fftLen; i += n1)
+  {
+    l = i + n2;
+    xt = pSrc[2 * i] - pSrc[2 * l];
+    pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]) * onebyfftLen;
+
+    yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+    pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]) * onebyfftLen;
+
+    pSrc[2u * l] = xt * onebyfftLen;
+
+    pSrc[2u * l + 1u] = yt * onebyfftLen;
+
+  }                             // butterfly loop end 
+
+#endif //      #ifndef ARM_MATH_CM0
+
+}
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix2_init_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix2_init_f32.c
new file mode 100644
index 0000000000..a41ed25d2c
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix2_init_f32.c
@@ -0,0 +1,198 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010 ARM Limited. All rights reserved.   
+*   
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*   
+* Project: 	    CMSIS DSP Library   
+* Title:	    arm_cfft_radix4_init_f32.c   
+*   
+* Description:	Radix-4 Decimation in Frequency Floating-point CFFT & CIFFT Initialization function   
+*   
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.3 2010/11/29  
+*    Re-organized the CMSIS folders and updated documentation.   
+*    
+* Version 1.0.2 2010/11/11   
+*    Documentation updated.    
+*   
+* Version 1.0.1 2010/10/05    
+*    Production release and review comments incorporated.   
+*   
+* Version 1.0.0 2010/09/20    
+*    Production release and review comments incorporated.   
+*   
+* Version 0.0.5  2010/04/26    
+* 	 incorporated review comments and updated with latest CMSIS layer   
+*   
+* Version 0.0.3  2010/03/10    
+*    Initial version   
+* -------------------------------------------------------------------- */
+
+
+#include "arm_math.h"
+#include "arm_common_tables.h"
+
+/**   
+ * @ingroup groupTransforms   
+ */
+
+/**   
+ * @addtogroup Radix2_CFFT_CIFFT   
+ * @{   
+ */
+
+/**   
+* @brief  Initialization function for the floating-point CFFT/CIFFT.  
+* @param[in,out] *S             points to an instance of the floating-point CFFT/CIFFT structure.  
+* @param[in]     fftLen         length of the FFT.  
+* @param[in]     ifftFlag       flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform.  
+* @param[in]     bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.  
+* @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if fftLen is not a supported value.  
+*   
+* \par Description:  
+* \par   
+* The parameter ifftFlag controls whether a forward or inverse transform is computed.   
+* Set(=1) ifftFlag for calculation of CIFFT otherwise  CFFT is calculated  
+* \par   
+* The parameter bitReverseFlag controls whether output is in normal order or bit reversed order.   
+* Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order.   
+* \par   
+* The parameter fftLen	Specifies length of CFFT/CIFFT process. Supported FFT Lengths are 16, 64, 256, 1024.   
+* \par   
+* This Function also initializes Twiddle factor table pointer and Bit reversal table pointer.   
+*/
+arm_status arm_cfft_radix2_init_f32(
+  arm_cfft_radix2_instance_f32 * S,
+  uint16_t fftLen,
+  uint8_t ifftFlag,
+  uint8_t bitReverseFlag)
+{
+  /*  Initialise the default arm status */
+  arm_status status = ARM_MATH_SUCCESS;
+
+  /*  Initialise the FFT length */
+  S->fftLen = fftLen;
+
+  /*  Initialise the Twiddle coefficient pointer */
+  S->pTwiddle = (float32_t *) twiddleCoef;
+
+  /*  Initialise the Flag for selection of CFFT or CIFFT */
+  S->ifftFlag = ifftFlag;
+
+  /*  Initialise the Flag for calculation Bit reversal or not */
+  S->bitReverseFlag = bitReverseFlag;
+
+  /*  Initializations of structure parameters depending on the FFT length */
+  switch (S->fftLen)
+  {
+
+  case 4096u:
+    /*  Initializations of structure parameters for 4096 point FFT */
+
+    /*  Initialise the twiddle coef modifier value */
+    S->twidCoefModifier = 1u;
+    /*  Initialise the bit reversal table modifier */
+    S->bitRevFactor = 1u;
+    /*  Initialise the bit reversal table pointer */
+    S->pBitRevTable = (uint16_t *) armBitRevTable;
+    /*  Initialise the 1/fftLen Value */
+    S->onebyfftLen = 0.000244140625;
+    break;
+
+  case 2048u:
+    /*  Initializations of structure parameters for 2048 point FFT */
+
+    /*  Initialise the twiddle coef modifier value */
+    S->twidCoefModifier = 2u;
+    /*  Initialise the bit reversal table modifier */
+    S->bitRevFactor = 2u;
+    /*  Initialise the bit reversal table pointer */
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[1];
+    /*  Initialise the 1/fftLen Value */
+    S->onebyfftLen = 0.00048828125;
+    break;
+
+  case 1024u:
+    /*  Initializations of structure parameters for 1024 point FFT */
+
+    /*  Initialise the twiddle coef modifier value */
+    S->twidCoefModifier = 4u;
+    /*  Initialise the bit reversal table modifier */
+    S->bitRevFactor = 4u;
+    /*  Initialise the bit reversal table pointer */
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[3];
+    /*  Initialise the 1/fftLen Value */
+    S->onebyfftLen = 0.0009765625f;
+    break;
+
+  case 512u:
+    /*  Initializations of structure parameters for 512 point FFT */
+
+    /*  Initialise the twiddle coef modifier value */
+    S->twidCoefModifier = 8u;
+    /*  Initialise the bit reversal table modifier */
+    S->bitRevFactor = 8u;
+    /*  Initialise the bit reversal table pointer */
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[7];
+    /*  Initialise the 1/fftLen Value */
+    S->onebyfftLen = 0.001953125;
+    break;
+
+  case 256u:
+    /*  Initializations of structure parameters for 256 point FFT */
+    S->twidCoefModifier = 16u;
+    S->bitRevFactor = 16u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[15];
+    S->onebyfftLen = 0.00390625f;
+    break;
+
+  case 128u:
+    /*  Initializations of structure parameters for 128 point FFT */
+    S->twidCoefModifier = 32u;
+    S->bitRevFactor = 32u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[31];
+    S->onebyfftLen = 0.0078125;
+    break;
+
+  case 64u:
+    /*  Initializations of structure parameters for 64 point FFT */
+    S->twidCoefModifier = 64u;
+    S->bitRevFactor = 64u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[63];
+    S->onebyfftLen = 0.015625f;
+    break;
+
+  case 32u:
+    /*  Initializations of structure parameters for 64 point FFT */
+    S->twidCoefModifier = 128u;
+    S->bitRevFactor = 128u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[127];
+    S->onebyfftLen = 0.03125;
+    break;
+
+  case 16u:
+    /*  Initializations of structure parameters for 16 point FFT */
+    S->twidCoefModifier = 256u;
+    S->bitRevFactor = 256u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[255];
+    S->onebyfftLen = 0.0625f;
+    break;
+
+
+  default:
+    /*  Reporting argument error if fftSize is not valid value */
+    status = ARM_MATH_ARGUMENT_ERROR;
+    break;
+  }
+
+  return (status);
+}
+
+/**   
+ * @} end of Radix2_CFFT_CIFFT group   
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix2_init_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix2_init_q15.c
new file mode 100644
index 0000000000..86aa149b2d
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix2_init_q15.c
@@ -0,0 +1,186 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_cfft_radix2_init_q15.c    
+*    
+* Description:	Radix-2 Decimation in Frequency Q15 FFT & IFFT initialization function    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+* 	 incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+#include "arm_common_tables.h"
+
+/**    
+ * @ingroup groupTransforms    
+ */
+
+
+/**    
+ * @addtogroup Radix2_CFFT_CIFFT    
+ * @{    
+ */
+
+/**   
+* @brief Initialization function for the Q15 CFFT/CIFFT.   
+* @param[in,out] *S             points to an instance of the Q15 CFFT/CIFFT structure.   
+* @param[in]     fftLen         length of the FFT.   
+* @param[in]     ifftFlag       flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform.  
+* @param[in]     bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.  
+* @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if fftLen is not a supported value.  
+*   
+* \par Description:  
+* \par   
+* The parameter ifftFlag controls whether a forward or inverse transform is computed.   
+* Set(=1) ifftFlag for calculation of CIFFT otherwise  CFFT is calculated  
+* \par   
+* The parameter bitReverseFlag controls whether output is in normal order or bit reversed order.   
+* Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order.   
+* \par   
+* The parameter fftLen	Specifies length of CFFT/CIFFT process. Supported FFT Lengths are 16, 64, 256, 1024.   
+* \par   
+* This Function also initializes Twiddle factor table pointer and Bit reversal table pointer.   
+*/
+
+arm_status arm_cfft_radix2_init_q15(
+  arm_cfft_radix2_instance_q15 * S,
+  uint16_t fftLen,
+  uint8_t ifftFlag,
+  uint8_t bitReverseFlag)
+{
+  /*  Initialise the default arm status */
+  arm_status status = ARM_MATH_SUCCESS;
+
+  /*  Initialise the FFT length */
+  S->fftLen = fftLen;
+
+  /*  Initialise the Twiddle coefficient pointer */
+  S->pTwiddle = (q15_t *) twiddleCoefQ15;
+  /*  Initialise the Flag for selection of CFFT or CIFFT */
+  S->ifftFlag = ifftFlag;
+  /*  Initialise the Flag for calculation Bit reversal or not */
+  S->bitReverseFlag = bitReverseFlag;
+
+  /*  Initializations of structure parameters depending on the FFT length */
+  switch (S->fftLen)
+  {
+  case 4096u:
+    /*  Initializations of structure parameters for 4096 point FFT */
+
+    /*  Initialise the twiddle coef modifier value */
+    S->twidCoefModifier = 1u;
+    /*  Initialise the bit reversal table modifier */
+    S->bitRevFactor = 1u;
+    /*  Initialise the bit reversal table pointer */
+    S->pBitRevTable = (uint16_t *) armBitRevTable;
+
+    break;
+
+  case 2048u:
+    /*  Initializations of structure parameters for 2048 point FFT */
+
+    /*  Initialise the twiddle coef modifier value */
+    S->twidCoefModifier = 2u;
+    /*  Initialise the bit reversal table modifier */
+    S->bitRevFactor = 2u;
+    /*  Initialise the bit reversal table pointer */
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[1];
+
+    break;
+
+  case 1024u:
+    /*  Initializations of structure parameters for 1024 point FFT */
+    S->twidCoefModifier = 4u;
+    S->bitRevFactor = 4u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[3];
+
+    break;
+
+  case 512u:
+    /*  Initializations of structure parameters for 512 point FFT */
+    S->twidCoefModifier = 8u;
+    S->bitRevFactor = 8u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[7];
+
+    break;
+
+  case 256u:
+    /*  Initializations of structure parameters for 256 point FFT */
+    S->twidCoefModifier = 16u;
+    S->bitRevFactor = 16u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[15];
+
+    break;
+
+  case 128u:
+    /*  Initializations of structure parameters for 128 point FFT */
+    S->twidCoefModifier = 32u;
+    S->bitRevFactor = 32u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[31];
+
+    break;
+
+  case 64u:
+    /*  Initializations of structure parameters for 64 point FFT */
+    S->twidCoefModifier = 64u;
+    S->bitRevFactor = 64u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[63];
+
+    break;
+
+  case 32u:
+    /*  Initializations of structure parameters for 32 point FFT */
+    S->twidCoefModifier = 128u;
+    S->bitRevFactor = 128u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[127];
+
+    break;
+
+  case 16u:
+    /*  Initializations of structure parameters for 16 point FFT */
+    S->twidCoefModifier = 256u;
+    S->bitRevFactor = 256u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[255];
+
+    break;
+
+  default:
+    /*  Reporting argument error if fftSize is not valid value */
+    status = ARM_MATH_ARGUMENT_ERROR;
+    break;
+  }
+
+  return (status);
+}
+
+/**    
+ * @} end of Radix2_CFFT_CIFFT group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix2_init_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix2_init_q31.c
new file mode 100644
index 0000000000..29aa9a74bd
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix2_init_q31.c
@@ -0,0 +1,164 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010 ARM Limited. All rights reserved.   
+*   
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*   
+* Project: 	    CMSIS DSP Library   
+* Title:	    arm_cfft_radix2_init_q31.c   
+*   
+* Description:	Radix-2 Decimation in Frequency Fixed-point CFFT & CIFFT Initialization function   
+*   
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* -------------------------------------------------------------------- */
+
+
+#include "arm_math.h"
+#include "arm_common_tables.h"
+
+/**   
+ * @ingroup groupTransforms   
+ */
+
+/**   
+ * @addtogroup Radix2_CFFT_CIFFT   
+ * @{   
+ */
+
+
+/**    
+*    
+* @brief  Initialization function for the Q31 CFFT/CIFFT.   
+* @param[in,out] *S             points to an instance of the Q31 CFFT/CIFFT structure.   
+* @param[in]     fftLen         length of the FFT.  
+* @param[in]     ifftFlag       flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform.  
+* @param[in]     bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.  
+* @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if fftLen is not a supported value.  
+*   
+* \par Description:  
+* \par   
+* The parameter ifftFlag controls whether a forward or inverse transform is computed.   
+* Set(=1) ifftFlag for calculation of CIFFT otherwise  CFFT is calculated  
+* \par   
+* The parameter bitReverseFlag controls whether output is in normal order or bit reversed order.   
+* Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order.   
+* \par   
+* The parameter fftLen	Specifies length of CFFT/CIFFT process. Supported FFT Lengths are 16, 64, 256, 1024.   
+* \par   
+* This Function also initializes Twiddle factor table pointer and Bit reversal table pointer.   
+*/
+
+arm_status arm_cfft_radix2_init_q31(
+  arm_cfft_radix2_instance_q31 * S,
+  uint16_t fftLen,
+  uint8_t ifftFlag,
+  uint8_t bitReverseFlag)
+{
+  /*  Initialise the default arm status */
+  arm_status status = ARM_MATH_SUCCESS;
+
+  /*  Initialise the FFT length */
+  S->fftLen = fftLen;
+
+  /*  Initialise the Twiddle coefficient pointer */
+  S->pTwiddle = (q31_t *) twiddleCoefQ31;
+  /*  Initialise the Flag for selection of CFFT or CIFFT */
+  S->ifftFlag = ifftFlag;
+  /*  Initialise the Flag for calculation Bit reversal or not */
+  S->bitReverseFlag = bitReverseFlag;
+
+  /*  Initializations of Instance structure depending on the FFT length */
+  switch (S->fftLen)
+  {
+    /*  Initializations of structure parameters for 4096 point FFT */
+  case 4096u:
+    /*  Initialise the twiddle coef modifier value */
+    S->twidCoefModifier = 1u;
+    /*  Initialise the bit reversal table modifier */
+    S->bitRevFactor = 1u;
+    /*  Initialise the bit reversal table pointer */
+    S->pBitRevTable = (uint16_t *) armBitRevTable;
+    break;
+
+    /*  Initializations of structure parameters for 2048 point FFT */
+  case 2048u:
+    /*  Initialise the twiddle coef modifier value */
+    S->twidCoefModifier = 2u;
+    /*  Initialise the bit reversal table modifier */
+    S->bitRevFactor = 2u;
+    /*  Initialise the bit reversal table pointer */
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[1];
+    break;
+
+    /*  Initializations of structure parameters for 1024 point FFT */
+  case 1024u:
+    /*  Initialise the twiddle coef modifier value */
+    S->twidCoefModifier = 4u;
+    /*  Initialise the bit reversal table modifier */
+    S->bitRevFactor = 4u;
+    /*  Initialise the bit reversal table pointer */
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[3];
+    break;
+
+    /*  Initializations of structure parameters for 512 point FFT */
+  case 512u:
+    /*  Initialise the twiddle coef modifier value */
+    S->twidCoefModifier = 8u;
+    /*  Initialise the bit reversal table modifier */
+    S->bitRevFactor = 8u;
+    /*  Initialise the bit reversal table pointer */
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[7];
+    break;
+
+  case 256u:
+    /*  Initializations of structure parameters for 256 point FFT */
+    S->twidCoefModifier = 16u;
+    S->bitRevFactor = 16u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[15];
+    break;
+
+  case 128u:
+    /*  Initializations of structure parameters for 128 point FFT */
+    S->twidCoefModifier = 32u;
+    S->bitRevFactor = 32u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[31];
+    break;
+
+  case 64u:
+    /*  Initializations of structure parameters for 64 point FFT */
+    S->twidCoefModifier = 64u;
+    S->bitRevFactor = 64u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[63];
+    break;
+
+  case 32u:
+    /*  Initializations of structure parameters for 32 point FFT */
+    S->twidCoefModifier = 128u;
+    S->bitRevFactor = 128u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[127];
+    break;
+
+  case 16u:
+    /*  Initializations of structure parameters for 16 point FFT */
+    S->twidCoefModifier = 256u;
+    S->bitRevFactor = 256u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[255];
+    break;
+
+
+  default:
+    /*  Reporting argument error if fftSize is not valid value */
+    status = ARM_MATH_ARGUMENT_ERROR;
+    break;
+  }
+
+  return (status);
+}
+
+/**   
+ * @} end of Radix2_CFFT_CIFFT group   
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix2_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix2_q15.c
new file mode 100644
index 0000000000..00c7420cf4
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix2_q15.c
@@ -0,0 +1,712 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010 ARM Limited. All rights reserved.   
+*   
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*   
+* Project: 	    CMSIS DSP Library   
+* Title:	    arm_cfft_radix2_q15.c   
+*   
+* Description:	Radix-2 Decimation in Frequency CFFT & CIFFT Fixed point processing function   
+*   
+*   
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 0.0.3  2010/03/10    
+*    Initial version   
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**   
+ * @ingroup groupTransforms   
+ */
+
+/**   
+ * @defgroup Radix2_CFFT_CIFFT Radix-2 Complex FFT Functions   
+ *   
+ * \par   
+ * Complex Fast Fourier Transform(CFFT) and Complex Inverse Fast Fourier Transform(CIFFT) is an efficient algorithm to compute Discrete Fourier Transform(DFT) and Inverse Discrete Fourier Transform(IDFT).   
+ * Computational complexity of CFFT reduces drastically when compared to DFT.    
+ */
+
+
+/**   
+ * @addtogroup Radix2_CFFT_CIFFT   
+ * @{   
+ */
+
+/**   
+ * @details   
+ * @brief Processing function for the fixed-point CFFT/CIFFT.  
+ * @param[in]      *S    points to an instance of the fixed-point CFFT/CIFFT structure.  
+ * @param[in, out] *pSrc points to the complex data buffer of size 2*fftLen. Processing occurs in-place.  
+ * @return none.  
+ */
+
+void arm_cfft_radix2_q15(
+  const arm_cfft_radix2_instance_q15 * S,
+  q15_t * pSrc)
+{
+
+  if(S->ifftFlag == 1u)
+  {
+    arm_radix2_butterfly_inverse_q15(pSrc, S->fftLen,
+                                     S->pTwiddle, S->twidCoefModifier);
+  }
+  else
+  {
+    arm_radix2_butterfly_q15(pSrc, S->fftLen,
+                             S->pTwiddle, S->twidCoefModifier);
+  }
+
+  arm_bitreversal_q15(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable);
+}
+
+/**   
+ * @} end of Radix2_CFFT_CIFFT group   
+ */
+
+void arm_radix2_butterfly_q15(
+  q15_t * pSrc,
+  uint32_t fftLen,
+  q15_t * pCoef,
+  uint16_t twidCoefModifier)
+{
+#ifndef ARM_MATH_CM0
+
+  int i, j, k, l;
+  int n1, n2, ia;
+  q15_t in;
+  q31_t T, S, R;
+  q31_t coeff, out1, out2;
+
+  //N = fftLen; 
+  n2 = fftLen;
+
+  n1 = n2;
+  n2 = n2 >> 1;
+  ia = 0;
+
+  // loop for groups 
+  for (i = 0; i < n2; i++)
+  {
+    coeff = _SIMD32_OFFSET(pCoef + (ia * 2u));
+
+    ia = ia + twidCoefModifier;
+
+    l = i + n2;
+
+    T = _SIMD32_OFFSET(pSrc + (2 * i));
+    in = ((int16_t) (T & 0xFFFF)) >> 2;
+    T = ((T >> 2) & 0xFFFF0000) | (in & 0xFFFF);
+
+    S = _SIMD32_OFFSET(pSrc + (2 * l));
+    in = ((int16_t) (S & 0xFFFF)) >> 2;
+    S = ((S >> 2) & 0xFFFF0000) | (in & 0xFFFF);
+
+    R = __QSUB16(T, S);
+
+    _SIMD32_OFFSET(pSrc + (2 * i)) = __SHADD16(T, S);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    out1 = __SMUAD(coeff, R) >> 16;
+    out2 = __SMUSDX(coeff, R);
+
+#else
+
+    out1 = __SMUSDX(R, coeff) >> 16u;
+    out2 = __SMUAD(coeff, R);
+
+#endif //     #ifndef ARM_MATH_BIG_ENDIAN
+
+    _SIMD32_OFFSET(pSrc + (2u * l)) =
+      (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
+
+    coeff = _SIMD32_OFFSET(pCoef + (ia * 2u));
+
+    ia = ia + twidCoefModifier;
+
+    // loop for butterfly 
+    i++;
+    l++;
+
+    T = _SIMD32_OFFSET(pSrc + (2 * i));
+    in = ((int16_t) (T & 0xFFFF)) >> 2;
+    T = ((T >> 2) & 0xFFFF0000) | (in & 0xFFFF);
+
+    S = _SIMD32_OFFSET(pSrc + (2 * l));
+    in = ((int16_t) (S & 0xFFFF)) >> 2;
+    S = ((S >> 2) & 0xFFFF0000) | (in & 0xFFFF);
+
+    R = __QSUB16(T, S);
+
+    _SIMD32_OFFSET(pSrc + (2 * i)) = __SHADD16(T, S);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    out1 = __SMUAD(coeff, R) >> 16;
+    out2 = __SMUSDX(coeff, R);
+
+#else
+
+    out1 = __SMUSDX(R, coeff) >> 16u;
+    out2 = __SMUAD(coeff, R);
+
+#endif //     #ifndef ARM_MATH_BIG_ENDIAN
+
+    _SIMD32_OFFSET(pSrc + (2u * l)) =
+      (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
+
+  }                             // groups loop end 
+
+  twidCoefModifier = twidCoefModifier << 1u;
+
+  // loop for stage 
+  for (k = fftLen / 2; k > 2; k = k >> 1)
+  {
+    n1 = n2;
+    n2 = n2 >> 1;
+    ia = 0;
+
+    // loop for groups 
+    for (j = 0; j < n2; j++)
+    {
+      coeff = _SIMD32_OFFSET(pCoef + (ia * 2u));
+
+      ia = ia + twidCoefModifier;
+
+      // loop for butterfly 
+      for (i = j; i < fftLen; i += n1)
+      {
+        l = i + n2;
+
+        T = _SIMD32_OFFSET(pSrc + (2 * i));
+
+        S = _SIMD32_OFFSET(pSrc + (2 * l));
+
+        R = __QSUB16(T, S);
+
+        _SIMD32_OFFSET(pSrc + (2 * i)) = __SHADD16(T, S);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+        out1 = __SMUAD(coeff, R) >> 16;
+        out2 = __SMUSDX(coeff, R);
+
+#else
+
+        out1 = __SMUSDX(R, coeff) >> 16u;
+        out2 = __SMUAD(coeff, R);
+
+#endif //     #ifndef ARM_MATH_BIG_ENDIAN
+
+        _SIMD32_OFFSET(pSrc + (2u * l)) =
+          (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
+
+        i += n1;
+
+        l = i + n2;
+
+        T = _SIMD32_OFFSET(pSrc + (2 * i));
+
+        S = _SIMD32_OFFSET(pSrc + (2 * l));
+
+        R = __QSUB16(T, S);
+
+        _SIMD32_OFFSET(pSrc + (2 * i)) = __SHADD16(T, S);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+        out1 = __SMUAD(coeff, R) >> 16;
+        out2 = __SMUSDX(coeff, R);
+
+#else
+
+        out1 = __SMUSDX(R, coeff) >> 16u;
+        out2 = __SMUAD(coeff, R);
+
+#endif //     #ifndef ARM_MATH_BIG_ENDIAN
+
+        _SIMD32_OFFSET(pSrc + (2u * l)) =
+          (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
+
+      }                         // butterfly loop end 
+
+    }                           // groups loop end 
+
+    twidCoefModifier = twidCoefModifier << 1u;
+  }                             // stages loop end 
+
+  n1 = n2;
+  n2 = n2 >> 1;
+  ia = 0;
+
+  coeff = _SIMD32_OFFSET(pCoef + (ia * 2u));
+
+  ia = ia + twidCoefModifier;
+
+  // loop for butterfly 
+  for (i = 0; i < fftLen; i += n1)
+  {
+    l = i + n2;
+
+    T = _SIMD32_OFFSET(pSrc + (2 * i));
+
+    S = _SIMD32_OFFSET(pSrc + (2 * l));
+
+    R = __QSUB16(T, S);
+
+    _SIMD32_OFFSET(pSrc + (2 * i)) = __QADD16(T, S);
+
+    _SIMD32_OFFSET(pSrc + (2u * l)) = R;
+
+    i += n1;
+    l = i + n2;
+
+    T = _SIMD32_OFFSET(pSrc + (2 * i));
+
+    S = _SIMD32_OFFSET(pSrc + (2 * l));
+
+    R = __QSUB16(T, S);
+
+    _SIMD32_OFFSET(pSrc + (2 * i)) = __QADD16(T, S);
+
+    _SIMD32_OFFSET(pSrc + (2u * l)) = R;
+
+  }                             // groups loop end 
+
+
+#else
+
+  int i, j, k, l;
+  int n1, n2, ia;
+  q15_t xt, yt, cosVal, sinVal;
+
+
+  //N = fftLen; 
+  n2 = fftLen;
+
+  n1 = n2;
+  n2 = n2 >> 1;
+  ia = 0;
+
+  // loop for groups 
+  for (j = 0; j < n2; j++)
+  {
+    cosVal = pCoef[ia * 2];
+    sinVal = pCoef[(ia * 2) + 1];
+    ia = ia + twidCoefModifier;
+
+    // loop for butterfly 
+    for (i = j; i < fftLen; i += n1)
+    {
+      l = i + n2;
+      xt = (pSrc[2 * i] >> 2u) - (pSrc[2 * l] >> 2u);
+      pSrc[2 * i] = ((pSrc[2 * i] >> 2u) + (pSrc[2 * l] >> 2u)) >> 1u;
+
+      yt = (pSrc[2 * i + 1] >> 2u) - (pSrc[2 * l + 1] >> 2u);
+      pSrc[2 * i + 1] =
+        ((pSrc[2 * l + 1] >> 2u) + (pSrc[2 * i + 1] >> 2u)) >> 1u;
+
+      pSrc[2u * l] = (((int16_t) (((q31_t) xt * cosVal) >> 16)) +
+                      ((int16_t) (((q31_t) yt * sinVal) >> 16)));
+
+      pSrc[2u * l + 1u] = (((int16_t) (((q31_t) yt * cosVal) >> 16)) -
+                           ((int16_t) (((q31_t) xt * sinVal) >> 16)));
+
+    }                           // butterfly loop end 
+
+  }                             // groups loop end 
+
+  twidCoefModifier = twidCoefModifier << 1u;
+
+  // loop for stage 
+  for (k = fftLen / 2; k > 2; k = k >> 1)
+  {
+    n1 = n2;
+    n2 = n2 >> 1;
+    ia = 0;
+
+    // loop for groups 
+    for (j = 0; j < n2; j++)
+    {
+      cosVal = pCoef[ia * 2];
+      sinVal = pCoef[(ia * 2) + 1];
+      ia = ia + twidCoefModifier;
+
+      // loop for butterfly 
+      for (i = j; i < fftLen; i += n1)
+      {
+        l = i + n2;
+        xt = pSrc[2 * i] - pSrc[2 * l];
+        pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]) >> 1u;
+
+        yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+        pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]) >> 1u;
+
+        pSrc[2u * l] = (((int16_t) (((q31_t) xt * cosVal) >> 16)) +
+                        ((int16_t) (((q31_t) yt * sinVal) >> 16)));
+
+        pSrc[2u * l + 1u] = (((int16_t) (((q31_t) yt * cosVal) >> 16)) -
+                             ((int16_t) (((q31_t) xt * sinVal) >> 16)));
+
+      }                         // butterfly loop end 
+
+    }                           // groups loop end 
+
+    twidCoefModifier = twidCoefModifier << 1u;
+  }                             // stages loop end 
+
+  n1 = n2;
+  n2 = n2 >> 1;
+  ia = 0;
+
+  // loop for groups 
+  for (j = 0; j < n2; j++)
+  {
+    cosVal = pCoef[ia * 2];
+    sinVal = pCoef[(ia * 2) + 1];
+
+    ia = ia + twidCoefModifier;
+
+    // loop for butterfly 
+    for (i = j; i < fftLen; i += n1)
+    {
+      l = i + n2;
+      xt = pSrc[2 * i] - pSrc[2 * l];
+      pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]);
+
+      yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+      pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]);
+
+      pSrc[2u * l] = xt;
+
+      pSrc[2u * l + 1u] = yt;
+
+    }                           // butterfly loop end 
+
+  }                             // groups loop end 
+
+  twidCoefModifier = twidCoefModifier << 1u;
+
+#endif //             #ifndef ARM_MATH_CM0
+
+}
+
+
+void arm_radix2_butterfly_inverse_q15(
+  q15_t * pSrc,
+  uint32_t fftLen,
+  q15_t * pCoef,
+  uint16_t twidCoefModifier)
+{
+#ifndef ARM_MATH_CM0
+
+  int i, j, k, l;
+  int n1, n2, ia;
+  q15_t in;
+  q31_t T, S, R;
+  q31_t coeff, out1, out2;
+
+  //N = fftLen; 
+  n2 = fftLen;
+
+  n1 = n2;
+  n2 = n2 >> 1;
+  ia = 0;
+
+  // loop for groups 
+  for (i = 0; i < n2; i++)
+  {
+    coeff = _SIMD32_OFFSET(pCoef + (ia * 2u));
+
+    ia = ia + twidCoefModifier;
+
+    l = i + n2;
+
+    T = _SIMD32_OFFSET(pSrc + (2 * i));
+    in = ((int16_t) (T & 0xFFFF)) >> 2;
+    T = ((T >> 2) & 0xFFFF0000) | (in & 0xFFFF);
+
+    S = _SIMD32_OFFSET(pSrc + (2 * l));
+    in = ((int16_t) (S & 0xFFFF)) >> 2;
+    S = ((S >> 2) & 0xFFFF0000) | (in & 0xFFFF);
+
+    R = __QSUB16(T, S);
+
+    _SIMD32_OFFSET(pSrc + (2 * i)) = __SHADD16(T, S);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    out1 = __SMUSD(coeff, R) >> 16;
+    out2 = __SMUADX(coeff, R);
+#else
+
+    out1 = __SMUADX(R, coeff) >> 16u;
+    out2 = __SMUSD(__QSUB(0, coeff), R);
+
+#endif //     #ifndef ARM_MATH_BIG_ENDIAN
+
+    _SIMD32_OFFSET(pSrc + (2u * l)) =
+      (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
+
+    coeff = _SIMD32_OFFSET(pCoef + (ia * 2u));
+
+    ia = ia + twidCoefModifier;
+
+    // loop for butterfly 
+    i++;
+    l++;
+
+    T = _SIMD32_OFFSET(pSrc + (2 * i));
+    in = ((int16_t) (T & 0xFFFF)) >> 2;
+    T = ((T >> 2) & 0xFFFF0000) | (in & 0xFFFF);
+
+    S = _SIMD32_OFFSET(pSrc + (2 * l));
+    in = ((int16_t) (S & 0xFFFF)) >> 2;
+    S = ((S >> 2) & 0xFFFF0000) | (in & 0xFFFF);
+
+    R = __QSUB16(T, S);
+
+    _SIMD32_OFFSET(pSrc + (2 * i)) = __SHADD16(T, S);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    out1 = __SMUSD(coeff, R) >> 16;
+    out2 = __SMUADX(coeff, R);
+#else
+
+    out1 = __SMUADX(R, coeff) >> 16u;
+    out2 = __SMUSD(__QSUB(0, coeff), R);
+
+#endif //     #ifndef ARM_MATH_BIG_ENDIAN
+
+    _SIMD32_OFFSET(pSrc + (2u * l)) =
+      (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
+
+  }                             // groups loop end 
+
+  twidCoefModifier = twidCoefModifier << 1u;
+
+  // loop for stage 
+  for (k = fftLen / 2; k > 2; k = k >> 1)
+  {
+    n1 = n2;
+    n2 = n2 >> 1;
+    ia = 0;
+
+    // loop for groups 
+    for (j = 0; j < n2; j++)
+    {
+      coeff = _SIMD32_OFFSET(pCoef + (ia * 2u));
+
+      ia = ia + twidCoefModifier;
+
+      // loop for butterfly 
+      for (i = j; i < fftLen; i += n1)
+      {
+        l = i + n2;
+
+        T = _SIMD32_OFFSET(pSrc + (2 * i));
+
+        S = _SIMD32_OFFSET(pSrc + (2 * l));
+
+        R = __QSUB16(T, S);
+
+        _SIMD32_OFFSET(pSrc + (2 * i)) = __SHADD16(T, S);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+        out1 = __SMUSD(coeff, R) >> 16;
+        out2 = __SMUADX(coeff, R);
+
+#else
+
+        out1 = __SMUADX(R, coeff) >> 16u;
+        out2 = __SMUSD(__QSUB(0, coeff), R);
+
+#endif //     #ifndef ARM_MATH_BIG_ENDIAN
+
+        _SIMD32_OFFSET(pSrc + (2u * l)) =
+          (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
+
+        i += n1;
+
+        l = i + n2;
+
+        T = _SIMD32_OFFSET(pSrc + (2 * i));
+
+        S = _SIMD32_OFFSET(pSrc + (2 * l));
+
+        R = __QSUB16(T, S);
+
+        _SIMD32_OFFSET(pSrc + (2 * i)) = __SHADD16(T, S);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+        out1 = __SMUSD(coeff, R) >> 16;
+        out2 = __SMUADX(coeff, R);
+#else
+
+        out1 = __SMUADX(R, coeff) >> 16u;
+        out2 = __SMUSD(__QSUB(0, coeff), R);
+
+#endif //     #ifndef ARM_MATH_BIG_ENDIAN
+
+        _SIMD32_OFFSET(pSrc + (2u * l)) =
+          (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
+
+      }                         // butterfly loop end 
+
+    }                           // groups loop end 
+
+    twidCoefModifier = twidCoefModifier << 1u;
+  }                             // stages loop end 
+
+  n1 = n2;
+  n2 = n2 >> 1;
+  ia = 0;
+
+  // loop for groups 
+  for (j = 0; j < n2; j++)
+  {
+    coeff = _SIMD32_OFFSET(pCoef + (ia * 2u));
+
+    ia = ia + twidCoefModifier;
+
+    // loop for butterfly 
+    for (i = j; i < fftLen; i += n1)
+    {
+      l = i + n2;
+
+      T = _SIMD32_OFFSET(pSrc + (2 * i));
+
+      S = _SIMD32_OFFSET(pSrc + (2 * l));
+
+      R = __QSUB16(T, S);
+
+      _SIMD32_OFFSET(pSrc + (2 * i)) = __QADD16(T, S);
+
+      _SIMD32_OFFSET(pSrc + (2u * l)) = R;
+
+    }                           // butterfly loop end 
+
+  }                             // groups loop end 
+
+  twidCoefModifier = twidCoefModifier << 1u;
+
+#else
+
+
+  int i, j, k, l;
+  int n1, n2, ia;
+  q15_t xt, yt, cosVal, sinVal;
+
+  //N = fftLen; 
+  n2 = fftLen;
+
+  n1 = n2;
+  n2 = n2 >> 1;
+  ia = 0;
+
+  // loop for groups 
+  for (j = 0; j < n2; j++)
+  {
+    cosVal = pCoef[ia * 2];
+    sinVal = pCoef[(ia * 2) + 1];
+    ia = ia + twidCoefModifier;
+
+    // loop for butterfly 
+    for (i = j; i < fftLen; i += n1)
+    {
+      l = i + n2;
+      xt = (pSrc[2 * i] >> 2u) - (pSrc[2 * l] >> 2u);
+      pSrc[2 * i] = ((pSrc[2 * i] >> 2u) + (pSrc[2 * l] >> 2u)) >> 1u;
+
+      yt = (pSrc[2 * i + 1] >> 2u) - (pSrc[2 * l + 1] >> 2u);
+      pSrc[2 * i + 1] =
+        ((pSrc[2 * l + 1] >> 2u) + (pSrc[2 * i + 1] >> 2u)) >> 1u;
+
+      pSrc[2u * l] = (((int16_t) (((q31_t) xt * cosVal) >> 16)) -
+                      ((int16_t) (((q31_t) yt * sinVal) >> 16)));
+
+      pSrc[2u * l + 1u] = (((int16_t) (((q31_t) yt * cosVal) >> 16)) +
+                           ((int16_t) (((q31_t) xt * sinVal) >> 16)));
+
+    }                           // butterfly loop end 
+
+  }                             // groups loop end 
+
+  twidCoefModifier = twidCoefModifier << 1u;
+
+  // loop for stage 
+  for (k = fftLen / 2; k > 2; k = k >> 1)
+  {
+    n1 = n2;
+    n2 = n2 >> 1;
+    ia = 0;
+
+    // loop for groups 
+    for (j = 0; j < n2; j++)
+    {
+      cosVal = pCoef[ia * 2];
+      sinVal = pCoef[(ia * 2) + 1];
+      ia = ia + twidCoefModifier;
+
+      // loop for butterfly 
+      for (i = j; i < fftLen; i += n1)
+      {
+        l = i + n2;
+        xt = pSrc[2 * i] - pSrc[2 * l];
+        pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]) >> 1u;
+
+        yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+        pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]) >> 1u;
+
+        pSrc[2u * l] = (((int16_t) (((q31_t) xt * cosVal) >> 16)) -
+                        ((int16_t) (((q31_t) yt * sinVal) >> 16)));
+
+        pSrc[2u * l + 1u] = (((int16_t) (((q31_t) yt * cosVal) >> 16)) +
+                             ((int16_t) (((q31_t) xt * sinVal) >> 16)));
+
+      }                         // butterfly loop end 
+
+    }                           // groups loop end 
+
+    twidCoefModifier = twidCoefModifier << 1u;
+  }                             // stages loop end 
+
+  n1 = n2;
+  n2 = n2 >> 1;
+  ia = 0;
+
+  cosVal = pCoef[ia * 2];
+  sinVal = pCoef[(ia * 2) + 1];
+
+  ia = ia + twidCoefModifier;
+
+  // loop for butterfly 
+  for (i = 0; i < fftLen; i += n1)
+  {
+    l = i + n2;
+    xt = pSrc[2 * i] - pSrc[2 * l];
+    pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]);
+
+    yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+    pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]);
+
+    pSrc[2u * l] = xt;
+
+    pSrc[2u * l + 1u] = yt;
+
+  }                             // groups loop end 
+
+
+#endif //             #ifndef ARM_MATH_CM0
+
+}
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix2_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix2_q31.c
new file mode 100644
index 0000000000..dd4b9e6b24
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix2_q31.c
@@ -0,0 +1,310 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010 ARM Limited. All rights reserved.   
+*   
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*   
+* Project: 	    CMSIS DSP Library   
+* Title:	    arm_cfft_radix2_q31.c   
+*   
+* Description:	Radix-2 Decimation in Frequency CFFT & CIFFT Fixed point processing function   
+*   
+*   
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 0.0.3  2010/03/10    
+*    Initial version   
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**   
+ * @ingroup groupTransforms   
+ */
+
+/**   
+ * @defgroup Radix2_CFFT_CIFFT Radix-2 Complex FFT Functions   
+ *   
+ * \par   
+ * Complex Fast Fourier Transform(CFFT) and Complex Inverse Fast Fourier Transform(CIFFT) is an efficient algorithm to compute Discrete Fourier Transform(DFT) and Inverse Discrete Fourier Transform(IDFT).   
+ * Computational complexity of CFFT reduces drastically when compared to DFT.    
+ */
+
+
+/**   
+ * @addtogroup Radix2_CFFT_CIFFT   
+ * @{   
+ */
+
+/**   
+ * @details   
+ * @brief Processing function for the fixed-point CFFT/CIFFT.  
+ * @param[in]      *S    points to an instance of the fixed-point CFFT/CIFFT structure.  
+ * @param[in, out] *pSrc points to the complex data buffer of size 2*fftLen. Processing occurs in-place.  
+ * @return none.  
+ */
+
+void arm_cfft_radix2_q31(
+  const arm_cfft_radix2_instance_q31 * S,
+  q31_t * pSrc)
+{
+
+  if(S->ifftFlag == 1u)
+  {
+    arm_radix2_butterfly_inverse_q31(pSrc, S->fftLen,
+                                     S->pTwiddle, S->twidCoefModifier);
+  }
+  else
+  {
+    arm_radix2_butterfly_q31(pSrc, S->fftLen,
+                             S->pTwiddle, S->twidCoefModifier);
+  }
+
+  arm_bitreversal_q31(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable);
+}
+
+/**   
+ * @} end of Radix2_CFFT_CIFFT group   
+ */
+
+void arm_radix2_butterfly_q31(
+  q31_t * pSrc,
+  uint32_t fftLen,
+  q31_t * pCoef,
+  uint16_t twidCoefModifier)
+{
+
+  int i, j, k, l;
+  int n1, n2, ia;
+  q31_t xt, yt, cosVal, sinVal;
+
+  //N = fftLen; 
+  n2 = fftLen;
+
+  n1 = n2;
+  n2 = n2 >> 1;
+  ia = 0;
+
+  // loop for groups 
+  for (i = 0; i < n2; i++)
+  {
+    cosVal = pCoef[ia * 2];
+    sinVal = pCoef[(ia * 2) + 1];
+    ia = ia + twidCoefModifier;
+
+    l = i + n2;
+    xt = (pSrc[2 * i] >> 2u) - (pSrc[2 * l] >> 2u);
+    pSrc[2 * i] = ((pSrc[2 * i] >> 2u) + (pSrc[2 * l] >> 2u)) >> 1u;
+
+    yt = (pSrc[2 * i + 1] >> 2u) - (pSrc[2 * l + 1] >> 2u);
+    pSrc[2 * i + 1] =
+      ((pSrc[2 * l + 1] >> 2u) + (pSrc[2 * i + 1] >> 2u)) >> 1u;
+
+    pSrc[2u * l] = (((int32_t) (((q63_t) xt * cosVal) >> 32)) +
+                    ((int32_t) (((q63_t) yt * sinVal) >> 32)));
+
+    pSrc[2u * l + 1u] = (((int32_t) (((q63_t) yt * cosVal) >> 32)) -
+                         ((int32_t) (((q63_t) xt * sinVal) >> 32)));
+
+  }                             // groups loop end 
+
+  twidCoefModifier = twidCoefModifier << 1u;
+
+  // loop for stage 
+  for (k = fftLen / 2; k > 2; k = k >> 1)
+  {
+    n1 = n2;
+    n2 = n2 >> 1;
+    ia = 0;
+
+    // loop for groups 
+    for (j = 0; j < n2; j++)
+    {
+      cosVal = pCoef[ia * 2];
+      sinVal = pCoef[(ia * 2) + 1];
+      ia = ia + twidCoefModifier;
+
+      // loop for butterfly 
+      for (i = j; i < fftLen; i += n1)
+      {
+        l = i + n2;
+        xt = pSrc[2 * i] - pSrc[2 * l];
+        pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]) >> 1u;
+
+        yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+        pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]) >> 1u;
+
+        pSrc[2u * l] = (((int32_t) (((q63_t) xt * cosVal) >> 32)) +
+                        ((int32_t) (((q63_t) yt * sinVal) >> 32)));
+
+        pSrc[2u * l + 1u] = (((int32_t) (((q63_t) yt * cosVal) >> 32)) -
+                             ((int32_t) (((q63_t) xt * sinVal) >> 32)));
+
+      }                         // butterfly loop end 
+
+    }                           // groups loop end 
+
+    twidCoefModifier = twidCoefModifier << 1u;
+  }                             // stages loop end 
+
+  n1 = n2;
+  n2 = n2 >> 1;
+  ia = 0;
+
+  cosVal = pCoef[ia * 2];
+  sinVal = pCoef[(ia * 2) + 1];
+  ia = ia + twidCoefModifier;
+
+  // loop for butterfly 
+  for (i = 0; i < fftLen; i += n1)
+  {
+    l = i + n2;
+    xt = pSrc[2 * i] - pSrc[2 * l];
+    pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]);
+
+    yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+    pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]);
+
+    pSrc[2u * l] = xt;
+
+    pSrc[2u * l + 1u] = yt;
+
+    i += n1;
+    l = i + n2;
+
+    xt = pSrc[2 * i] - pSrc[2 * l];
+    pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]);
+
+    yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+    pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]);
+
+    pSrc[2u * l] = xt;
+
+    pSrc[2u * l + 1u] = yt;
+
+  }                             // butterfly loop end 
+
+}
+
+
+void arm_radix2_butterfly_inverse_q31(
+  q31_t * pSrc,
+  uint32_t fftLen,
+  q31_t * pCoef,
+  uint16_t twidCoefModifier)
+{
+
+  int i, j, k, l;
+  int n1, n2, ia;
+  q31_t xt, yt, cosVal, sinVal;
+
+  //N = fftLen; 
+  n2 = fftLen;
+
+  n1 = n2;
+  n2 = n2 >> 1;
+  ia = 0;
+
+  // loop for groups 
+  for (i = 0; i < n2; i++)
+  {
+    cosVal = pCoef[ia * 2];
+    sinVal = pCoef[(ia * 2) + 1];
+    ia = ia + twidCoefModifier;
+
+    l = i + n2;
+    xt = (pSrc[2 * i] >> 2u) - (pSrc[2 * l] >> 2u);
+    pSrc[2 * i] = ((pSrc[2 * i] >> 2u) + (pSrc[2 * l] >> 2u)) >> 1u;
+
+    yt = (pSrc[2 * i + 1] >> 2u) - (pSrc[2 * l + 1] >> 2u);
+    pSrc[2 * i + 1] =
+      ((pSrc[2 * l + 1] >> 2u) + (pSrc[2 * i + 1] >> 2u)) >> 1u;
+
+    pSrc[2u * l] = (((int32_t) (((q63_t) xt * cosVal) >> 32)) -
+                    ((int32_t) (((q63_t) yt * sinVal) >> 32)));
+
+    pSrc[2u * l + 1u] = (((int32_t) (((q63_t) yt * cosVal) >> 32)) +
+                         ((int32_t) (((q63_t) xt * sinVal) >> 32)));
+
+  }                             // groups loop end 
+
+  twidCoefModifier = twidCoefModifier << 1u;
+
+  // loop for stage 
+  for (k = fftLen / 2; k > 2; k = k >> 1)
+  {
+    n1 = n2;
+    n2 = n2 >> 1;
+    ia = 0;
+
+    // loop for groups 
+    for (j = 0; j < n2; j++)
+    {
+      cosVal = pCoef[ia * 2];
+      sinVal = pCoef[(ia * 2) + 1];
+      ia = ia + twidCoefModifier;
+
+      // loop for butterfly 
+      for (i = j; i < fftLen; i += n1)
+      {
+        l = i + n2;
+        xt = pSrc[2 * i] - pSrc[2 * l];
+        pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]) >> 1u;
+
+        yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+        pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]) >> 1u;
+
+        pSrc[2u * l] = (((int32_t) (((q63_t) xt * cosVal) >> 32)) -
+                        ((int32_t) (((q63_t) yt * sinVal) >> 32)));
+
+        pSrc[2u * l + 1u] = (((int32_t) (((q63_t) yt * cosVal) >> 32)) +
+                             ((int32_t) (((q63_t) xt * sinVal) >> 32)));
+
+      }                         // butterfly loop end 
+
+    }                           // groups loop end 
+
+    twidCoefModifier = twidCoefModifier << 1u;
+  }                             // stages loop end 
+
+  n1 = n2;
+  n2 = n2 >> 1;
+  ia = 0;
+
+  cosVal = pCoef[ia * 2];
+  sinVal = pCoef[(ia * 2) + 1];
+  ia = ia + twidCoefModifier;
+
+  // loop for butterfly 
+  for (i = 0; i < fftLen; i += n1)
+  {
+    l = i + n2;
+    xt = pSrc[2 * i] - pSrc[2 * l];
+    pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]);
+
+    yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+    pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]);
+
+    pSrc[2u * l] = xt;
+
+    pSrc[2u * l + 1u] = yt;
+
+    i += n1;
+    l = i + n2;
+
+    xt = pSrc[2 * i] - pSrc[2 * l];
+    pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]);
+
+    yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+    pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]);
+
+    pSrc[2u * l] = xt;
+
+    pSrc[2u * l + 1u] = yt;
+
+  }                             // butterfly loop end 
+
+}
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_f32.c
new file mode 100644
index 0000000000..d51e9830bc
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_f32.c
@@ -0,0 +1,1236 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_cfft_radix4_f32.c    
+*    
+* Description:	Radix-4 Decimation in Frequency CFFT & CIFFT Floating point processing function    
+*    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+* 	 incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupTransforms    
+ */
+
+/**    
+ * @defgroup Radix4_CFFT_CIFFT Radix-4 Complex FFT Functions    
+ *    
+ * \par    
+ * Complex Fast Fourier Transform(CFFT) and Complex Inverse Fast Fourier Transform(CIFFT) is an efficient algorithm to compute Discrete Fourier Transform(DFT) and Inverse Discrete Fourier Transform(IDFT).    
+ * Computational complexity of CFFT reduces drastically when compared to DFT.    
+ * \par    
+ * This set of functions implements CFFT/CIFFT    
+ * for Q15, Q31, and floating-point data types.  The functions operates on in-place buffer which uses same buffer for input and output.    
+ * Complex input is stored in input buffer in an interleaved fashion.    
+ *    
+ * \par    
+ * The functions operate on blocks of input and output data and each call to the function processes    
+ * 2*fftLen samples through the transform.  pSrc  points to In-place arrays containing 2*fftLen values.    
+ * \par   
+ * The pSrc points to the array of in-place buffer of size 2*fftLen and inputs and outputs are stored in an interleaved fashion as shown below.    
+ * 
 {real[0], imag[0], real[1], imag[1],..} 
    
+ *    
+ * \par Lengths supported by the transform:   
+ * \par    
+ * Internally, the function utilize a radix-4 decimation in frequency(DIF) algorithm    
+ * and the size of the FFT supported are of the lengths [16, 64, 256, 1024].   
+ *     
+ *    
+ * \par Algorithm:    
+ *    
+ * Complex Fast Fourier Transform:    
+ * \par     
+ * Input real and imaginary data:    
+ * 
    
+ * x(n) = xa + j * ya    
+ * x(n+N/4 ) = xb + j * yb    
+ * x(n+N/2 ) = xc + j * yc    
+ * x(n+3N 4) = xd + j * yd    
+ * 
    
+ * where N is length of FFT    
+ * \par    
+ * Output real and imaginary data:    
+ * 
    
+ * X(4r) = xa'+ j * ya'    
+ * X(4r+1) = xb'+ j * yb'    
+ * X(4r+2) = xc'+ j * yc'    
+ * X(4r+3) = xd'+ j * yd'    
+ * 
    
+ * \par    
+ * Twiddle factors for radix-4 FFT:    
+ * 
    
+ * Wn = co1 + j * (- si1)    
+ * W2n = co2 + j * (- si2)    
+ * W3n = co3 + j * (- si3)    
+ * 
    
+ *    
+ * \par    
+ * \image html CFFT.gif "Radix-4 Decimation-in Frequency Complex Fast Fourier Transform"    
+ *    
+ * \par    
+ * Output from Radix-4 CFFT Results in Digit reversal order. Interchange middle two branches of every butterfly results in Bit reversed output.    
+ * \par    
+ *  Butterfly CFFT equations:    
+ * 
    
+ * xa' = xa + xb + xc + xd    
+ * ya' = ya + yb + yc + yd    
+ * xc' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1)    
+ * yc' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1)    
+ * xb' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2)    
+ * yb' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2)    
+ * xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3)    
+ * yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3)    
+ * 
    
+ *    
+ *    
+ * Complex Inverse Fast Fourier Transform:    
+ * \par    
+ * CIFFT uses same twiddle factor table as CFFT with modifications in the design equation as shown below.    
+ *    
+ * \par    
+ *  Modified Butterfly CIFFT equations:    
+ * 
    
+ * xa' = xa + xb + xc + xd    
+ * ya' = ya + yb + yc + yd    
+ * xc' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1)    
+ * yc' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1)    
+ * xb' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2)    
+ * yb' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2)    
+ * xd' = (xa+yb-xc-yd)* co3 - (ya-xb-yc+xd)* (si3)    
+ * yd' = (ya-xb-yc+xd)* co3 + (xa+yb-xc-yd)* (si3)    
+ * 
    
+ *    
+ * \par Instance Structure    
+ * A separate instance structure must be defined for each Instance but the twiddle factors and bit reversal tables can be reused.    
+ * There are separate instance structure declarations for each of the 3 supported data types.    
+ *    
+ * \par Initialization Functions    
+ * There is also an associated initialization function for each data type.    
+ * The initialization function performs the following operations:    
+ * - Sets the values of the internal structure fields.    
+ * - Initializes twiddle factor table and bit reversal table pointers    
+ * \par    
+ * Use of the initialization function is optional.    
+ * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.    
+ * To place an instance structure into a const data section, the instance structure must be manually initialized.    
+ * Manually initialize the instance structure as follows:    
+ * 
    
+ *arm_cfft_radix4_instance_f32 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor, onebyfftLen};    
+ *arm_cfft_radix4_instance_q31 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor};    
+ *arm_cfft_radix4_instance_q15 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor};    
+ * 
    
+ * \par    
+ * where fftLen length of CFFT/CIFFT; ifftFlag Flag for selection of CFFT or CIFFT(Set ifftFlag to calculate CIFFT otherwise calculates CFFT);    
+ * bitReverseFlag Flag for selection of output order(Set bitReverseFlag to output in normal order otherwise output in bit reversed order);     
+ * pTwiddlepoints to array of twiddle coefficients; pBitRevTable points to the array of bit reversal table.    
+ * twidCoefModifier modifier for twiddle factor table which supports all FFT lengths with same table;     
+ * pBitRevTable modifier for bit reversal table which supports all FFT lengths with same table.    
+ * onebyfftLen value of 1/fftLen to calculate CIFFT;    
+ *   
+ * \par Fixed-Point Behavior    
+ * Care must be taken when using the fixed-point versions of the CFFT/CIFFT function.    
+ * Refer to the function specific documentation below for usage guidelines.    
+ */
+
+
+/**    
+ * @addtogroup Radix4_CFFT_CIFFT    
+ * @{    
+ */
+
+/**    
+ * @details    
+ * @brief Processing function for the floating-point Radix-4 CFFT/CIFFT.   
+ * @param[in]      *S    points to an instance of the floating-point Radix-4 CFFT/CIFFT structure.   
+ * @param[in, out] *pSrc points to the complex data buffer of size 2*fftLen. Processing occurs in-place.   
+ * @return none.   
+ */
+
+void arm_cfft_radix4_f32(
+  const arm_cfft_radix4_instance_f32 * S,
+  float32_t * pSrc)
+{
+
+  if(S->ifftFlag == 1u)
+  {
+    /*  Complex IFFT radix-4  */
+    arm_radix4_butterfly_inverse_f32(pSrc, S->fftLen, S->pTwiddle,
+                                     S->twidCoefModifier, S->onebyfftLen);
+  }
+  else
+  {
+    /*  Complex FFT radix-4  */
+    arm_radix4_butterfly_f32(pSrc, S->fftLen, S->pTwiddle,
+                             S->twidCoefModifier);
+  }
+
+  if(S->bitReverseFlag == 1u)
+  {
+    /*  Bit Reversal */
+    arm_bitreversal_f32(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable);
+  }
+
+}
+
+
+/**    
+ * @} end of Radix4_CFFT_CIFFT group    
+ */
+
+
+/* ----------------------------------------------------------------------    
+** Internal helper function used by the FFTs    
+** ------------------------------------------------------------------- */
+
+/*    
+ * @brief  Core function for the floating-point CFFT butterfly process.   
+ * @param[in, out] *pSrc            points to the in-place buffer of floating-point data type.   
+ * @param[in]      fftLen           length of the FFT.   
+ * @param[in]      *pCoef           points to the twiddle coefficient buffer.   
+ * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.   
+ * @return none.   
+ */
+
+void arm_radix4_butterfly_f32(
+  float32_t * pSrc,
+  uint16_t fftLen,
+  float32_t * pCoef,
+  uint16_t twidCoefModifier)
+{
+
+  float32_t co1, co2, co3, si1, si2, si3;
+  uint32_t ia1, ia2, ia3;
+  uint32_t i0, i1, i2, i3;
+  uint32_t n1, n2, j, k;
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  float32_t xaIn, yaIn, xbIn, ybIn, xcIn, ycIn, xdIn, ydIn;
+  float32_t Xaplusc, Xbplusd, Yaplusc, Ybplusd, Xaminusc, Xbminusd, Yaminusc,
+    Ybminusd;
+  float32_t Xb12C_out, Yb12C_out, Xc12C_out, Yc12C_out, Xd12C_out, Yd12C_out;
+  float32_t Xb12_out, Yb12_out, Xc12_out, Yc12_out, Xd12_out, Yd12_out;
+  float32_t *ptr1;
+
+  /*  Initializations for the first stage */
+  n2 = fftLen;
+  n1 = n2;
+
+  /* n2 = fftLen/4 */
+  n2 >>= 2u;
+  i0 = 0u;
+  ia1 = 0u;
+
+  j = n2;
+
+  /*  Calculation of first stage */
+  do
+  {
+    /*  index calculation for the input as, */
+    /*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
+    i1 = i0 + n2;
+    i2 = i1 + n2;
+    i3 = i2 + n2;
+
+    xaIn = pSrc[(2u * i0)];
+    yaIn = pSrc[(2u * i0) + 1u];
+
+    xcIn = pSrc[(2u * i2)];
+    ycIn = pSrc[(2u * i2) + 1u];
+
+    xbIn = pSrc[(2u * i1)];
+    ybIn = pSrc[(2u * i1) + 1u];
+
+    xdIn = pSrc[(2u * i3)];
+    ydIn = pSrc[(2u * i3) + 1u];
+
+    /* xa + xc */
+    Xaplusc = xaIn + xcIn;
+    /* xb + xd */
+    Xbplusd = xbIn + xdIn;
+    /* ya + yc */
+    Yaplusc = yaIn + ycIn;
+    /* yb + yd */
+    Ybplusd = ybIn + ydIn;
+
+    /*  index calculation for the coefficients */
+    ia2 = ia1 + ia1;
+    co2 = pCoef[ia2 * 2u];
+    si2 = pCoef[(ia2 * 2u) + 1u];
+
+    /* xa - xc */
+    Xaminusc = xaIn - xcIn;
+    /* xb - xd */
+    Xbminusd = xbIn - xdIn;
+    /* ya - yc */
+    Yaminusc = yaIn - ycIn;
+    /* yb + yd */
+    Ybminusd = ybIn - ydIn;
+
+    /* xa' = xa + xb + xc + xd */
+    pSrc[(2u * i0)] = Xaplusc + Xbplusd;
+    /* ya' = ya + yb + yc + yd */
+    pSrc[(2u * i0) + 1u] = Yaplusc + Ybplusd;
+
+    /* (xa - xc) + (yb - yd) */
+    Xb12C_out = (Xaminusc + Ybminusd);
+    /* (ya - yc) + (xb - xd) */
+    Yb12C_out = (Yaminusc - Xbminusd);
+    /* (xa + xc) - (xb + xd) */
+    Xc12C_out = (Xaplusc - Xbplusd);
+    /* (ya + yc) - (yb + yd) */
+    Yc12C_out = (Yaplusc - Ybplusd);
+    /* (xa - xc) - (yb - yd) */
+    Xd12C_out = (Xaminusc - Ybminusd);
+    /* (ya - yc) + (xb - xd) */
+    Yd12C_out = (Xbminusd + Yaminusc);
+
+    co1 = pCoef[ia1 * 2u];
+    si1 = pCoef[(ia1 * 2u) + 1u];
+
+    /*  index calculation for the coefficients */
+    ia3 = ia2 + ia1;
+    co3 = pCoef[ia3 * 2u];
+    si3 = pCoef[(ia3 * 2u) + 1u];
+
+    Xb12_out = Xb12C_out * co1;
+    Yb12_out = Yb12C_out * co1;
+    Xc12_out = Xc12C_out * co2;
+    Yc12_out = Yc12C_out * co2;
+    Xd12_out = Xd12C_out * co3;
+    Yd12_out = Yd12C_out * co3;
+
+    /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
+    Xb12_out += Yb12C_out * si1;
+    /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
+    Yb12_out -= Xb12C_out * si1;
+    /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
+    Xc12_out += Yc12C_out * si2;
+    /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
+    Yc12_out -= Xc12C_out * si2;
+    /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
+    Xd12_out += Yd12C_out * si3;
+    /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
+    Yd12_out -= Xd12C_out * si3;
+
+
+    /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
+    pSrc[2u * i1] = Xc12_out;
+
+    /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
+    pSrc[(2u * i1) + 1u] = Yc12_out;
+
+    /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
+    pSrc[2u * i2] = Xb12_out;
+
+    /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
+    pSrc[(2u * i2) + 1u] = Yb12_out;
+
+    /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
+    pSrc[2u * i3] = Xd12_out;
+
+    /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
+    pSrc[(2u * i3) + 1u] = Yd12_out;
+
+    /*  Twiddle coefficients index modifier */
+    ia1 = ia1 + twidCoefModifier;
+
+    /*  Updating input index */
+    i0 = i0 + 1u;
+
+  }
+  while(--j);
+
+  twidCoefModifier <<= 2u;
+
+  /*  Calculation of second stage to excluding last stage */
+  for (k = fftLen / 4; k > 4u; k >>= 2u)
+  {
+    /*  Initializations for the first stage */
+    n1 = n2;
+    n2 >>= 2u;
+    ia1 = 0u;
+
+    /*  Calculation of first stage */
+    for (j = 0u; j <= (n2 - 1u); j++)
+    {
+      /*  index calculation for the coefficients */
+      ia2 = ia1 + ia1;
+      ia3 = ia2 + ia1;
+      co1 = pCoef[ia1 * 2u];
+      si1 = pCoef[(ia1 * 2u) + 1u];
+      co2 = pCoef[ia2 * 2u];
+      si2 = pCoef[(ia2 * 2u) + 1u];
+      co3 = pCoef[ia3 * 2u];
+      si3 = pCoef[(ia3 * 2u) + 1u];
+
+      /*  Twiddle coefficients index modifier */
+      ia1 = ia1 + twidCoefModifier;
+
+      for (i0 = j; i0 < fftLen; i0 += n1)
+      {
+        /*  index calculation for the input as, */
+        /*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
+        i1 = i0 + n2;
+        i2 = i1 + n2;
+        i3 = i2 + n2;
+
+        xaIn = pSrc[(2u * i0)];
+        yaIn = pSrc[(2u * i0) + 1u];
+
+        xbIn = pSrc[(2u * i1)];
+        ybIn = pSrc[(2u * i1) + 1u];
+
+        xcIn = pSrc[(2u * i2)];
+        ycIn = pSrc[(2u * i2) + 1u];
+
+        xdIn = pSrc[(2u * i3)];
+        ydIn = pSrc[(2u * i3) + 1u];
+
+        /* xa - xc */
+        Xaminusc = xaIn - xcIn;
+        /* (xb - xd) */
+        Xbminusd = xbIn - xdIn;
+        /* ya - yc */
+        Yaminusc = yaIn - ycIn;
+        /* (yb - yd) */
+        Ybminusd = ybIn - ydIn;
+
+        /* xa + xc */
+        Xaplusc = xaIn + xcIn;
+        /* xb + xd */
+        Xbplusd = xbIn + xdIn;
+        /* ya + yc */
+        Yaplusc = yaIn + ycIn;
+        /* yb + yd */
+        Ybplusd = ybIn + ydIn;
+
+        /* (xa - xc) + (yb - yd) */
+        Xb12C_out = (Xaminusc + Ybminusd);
+        /* (ya - yc) -  (xb - xd) */
+        Yb12C_out = (Yaminusc - Xbminusd);
+        /* xa + xc -(xb + xd) */
+        Xc12C_out = (Xaplusc - Xbplusd);
+        /* (ya + yc) - (yb + yd) */
+        Yc12C_out = (Yaplusc - Ybplusd);
+        /* (xa - xc) - (yb - yd) */
+        Xd12C_out = (Xaminusc - Ybminusd);
+        /* (ya - yc) +  (xb - xd) */
+        Yd12C_out = (Xbminusd + Yaminusc);
+
+        pSrc[(2u * i0)] = Xaplusc + Xbplusd;
+        pSrc[(2u * i0) + 1u] = Yaplusc + Ybplusd;
+
+        Xb12_out = Xb12C_out * co1;
+        Yb12_out = Yb12C_out * co1;
+        Xc12_out = Xc12C_out * co2;
+        Yc12_out = Yc12C_out * co2;
+        Xd12_out = Xd12C_out * co3;
+        Yd12_out = Yd12C_out * co3;
+
+        /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
+        Xb12_out += Yb12C_out * si1;
+        /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
+        Yb12_out -= Xb12C_out * si1;
+        /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
+        Xc12_out += Yc12C_out * si2;
+        /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
+        Yc12_out -= Xc12C_out * si2;
+        /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
+        Xd12_out += Yd12C_out * si3;
+        /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
+        Yd12_out -= Xd12C_out * si3;
+
+        /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
+        pSrc[2u * i1] = Xc12_out;
+
+        /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
+        pSrc[(2u * i1) + 1u] = Yc12_out;
+
+        /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
+        pSrc[2u * i2] = Xb12_out;
+
+        /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
+        pSrc[(2u * i2) + 1u] = Yb12_out;
+
+        /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
+        pSrc[2u * i3] = Xd12_out;
+
+        /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
+        pSrc[(2u * i3) + 1u] = Yd12_out;
+
+      }
+    }
+    twidCoefModifier <<= 2u;
+  }
+
+  j = fftLen >> 2;
+  ptr1 = &pSrc[0];
+
+  /*  Calculations of last stage */
+  do
+  {
+
+    xaIn = ptr1[0];
+    xcIn = ptr1[4];
+    yaIn = ptr1[1];
+    ycIn = ptr1[5];
+
+    /* xa + xc */
+    Xaplusc = xaIn + xcIn;
+
+    xbIn = ptr1[2];
+
+    /* xa - xc */
+    Xaminusc = xaIn - xcIn;
+
+    xdIn = ptr1[6];
+
+    /* ya + yc */
+    Yaplusc = yaIn + ycIn;
+
+    ybIn = ptr1[3];
+
+    /* ya - yc */
+    Yaminusc = yaIn - ycIn;
+
+    ydIn = ptr1[7];
+
+    /* xb + xd */
+    Xbplusd = xbIn + xdIn;
+
+    /* yb + yd */
+    Ybplusd = ybIn + ydIn;
+
+    /* xa' = xa + xb + xc + xd */
+    ptr1[0] = (Xaplusc + Xbplusd);
+
+    /* (xb-xd) */
+    Xbminusd = xbIn - xdIn;
+
+    /* ya' = ya + yb + yc + yd */
+    ptr1[1] = (Yaplusc + Ybplusd);
+
+    /* (yb-yd) */
+    Ybminusd = ybIn - ydIn;
+
+    /* xc' = (xa-xb+xc-xd) */
+    ptr1[2] = (Xaplusc - Xbplusd);
+    /* yc' = (ya-yb+yc-yd) */
+    ptr1[3] = (Yaplusc - Ybplusd);
+    /* xb' = (xa+yb-xc-yd) */
+    ptr1[4] = (Xaminusc + Ybminusd);
+    /* yb' = (ya-xb-yc+xd) */
+    ptr1[5] = (Yaminusc - Xbminusd);
+    /* xd' = (xa-yb-xc+yd)) */
+    ptr1[6] = (Xaminusc - Ybminusd);
+    /* yd' = (ya+xb-yc-xd) */
+    ptr1[7] = (Xbminusd + Yaminusc);
+
+    /* increment pointer by 8 */
+    ptr1 = ptr1 + 8u;
+
+  } while(--j);
+
+#else
+
+  float32_t t1, t2, r1, r2, s1, s2;
+
+  /* Run the below code for Cortex-M0 */
+
+  /*  Initializations for the fft calculation */
+  n2 = fftLen;
+  n1 = n2;
+  for (k = fftLen; k > 1u; k >>= 2u)
+  {
+    /*  Initializations for the fft calculation */
+    n1 = n2;
+    n2 >>= 2u;
+    ia1 = 0u;
+
+    /*  FFT Calculation */
+    for (j = 0u; j <= (n2 - 1u); j++)
+    {
+      /*  index calculation for the coefficients */
+      ia2 = ia1 + ia1;
+      ia3 = ia2 + ia1;
+      co1 = pCoef[ia1 * 2u];
+      si1 = pCoef[(ia1 * 2u) + 1u];
+      co2 = pCoef[ia2 * 2u];
+      si2 = pCoef[(ia2 * 2u) + 1u];
+      co3 = pCoef[ia3 * 2u];
+      si3 = pCoef[(ia3 * 2u) + 1u];
+
+      /*  Twiddle coefficients index modifier */
+      ia1 = ia1 + twidCoefModifier;
+
+      for (i0 = j; i0 < fftLen; i0 += n1)
+      {
+        /*  index calculation for the input as, */
+        /*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
+        i1 = i0 + n2;
+        i2 = i1 + n2;
+        i3 = i2 + n2;
+
+        /* xa + xc */
+        r1 = pSrc[(2u * i0)] + pSrc[(2u * i2)];
+
+        /* xa - xc */
+        r2 = pSrc[(2u * i0)] - pSrc[(2u * i2)];
+
+        /* ya + yc */
+        s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
+
+        /* ya - yc */
+        s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
+
+        /* xb + xd */
+        t1 = pSrc[2u * i1] + pSrc[2u * i3];
+
+        /* xa' = xa + xb + xc + xd */
+        pSrc[2u * i0] = r1 + t1;
+
+        /* xa + xc -(xb + xd) */
+        r1 = r1 - t1;
+
+        /* yb + yd */
+        t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
+
+        /* ya' = ya + yb + yc + yd */
+        pSrc[(2u * i0) + 1u] = s1 + t2;
+
+        /* (ya + yc) - (yb + yd) */
+        s1 = s1 - t2;
+
+        /* (yb - yd) */
+        t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
+
+        /* (xb - xd) */
+        t2 = pSrc[2u * i1] - pSrc[2u * i3];
+
+        /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
+        pSrc[2u * i1] = (r1 * co2) + (s1 * si2);
+
+        /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
+        pSrc[(2u * i1) + 1u] = (s1 * co2) - (r1 * si2);
+
+        /* (xa - xc) + (yb - yd) */
+        r1 = r2 + t1;
+
+        /* (xa - xc) - (yb - yd) */
+        r2 = r2 - t1;
+
+        /* (ya - yc) -  (xb - xd) */
+        s1 = s2 - t2;
+
+        /* (ya - yc) +  (xb - xd) */
+        s2 = s2 + t2;
+
+        /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
+        pSrc[2u * i2] = (r1 * co1) + (s1 * si1);
+
+        /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
+        pSrc[(2u * i2) + 1u] = (s1 * co1) - (r1 * si1);
+
+        /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
+        pSrc[2u * i3] = (r2 * co3) + (s2 * si3);
+
+        /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
+        pSrc[(2u * i3) + 1u] = (s2 * co3) - (r2 * si3);
+      }
+    }
+    twidCoefModifier <<= 2u;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
+
+/*    
+ * @brief  Core function for the floating-point CIFFT butterfly process.   
+ * @param[in, out] *pSrc            points to the in-place buffer of floating-point data type.   
+ * @param[in]      fftLen           length of the FFT.   
+ * @param[in]      *pCoef           points to twiddle coefficient buffer.   
+ * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.   
+ * @param[in]      onebyfftLen      value of 1/fftLen.   
+ * @return none.   
+ */
+
+void arm_radix4_butterfly_inverse_f32(
+  float32_t * pSrc,
+  uint16_t fftLen,
+  float32_t * pCoef,
+  uint16_t twidCoefModifier,
+  float32_t onebyfftLen)
+{
+  float32_t co1, co2, co3, si1, si2, si3;
+  uint32_t ia1, ia2, ia3;
+  uint32_t i0, i1, i2, i3;
+  uint32_t n1, n2, j, k;
+
+#ifndef ARM_MATH_CM0
+
+  float32_t xaIn, yaIn, xbIn, ybIn, xcIn, ycIn, xdIn, ydIn;
+  float32_t Xaplusc, Xbplusd, Yaplusc, Ybplusd, Xaminusc, Xbminusd, Yaminusc,
+    Ybminusd;
+  float32_t Xb12C_out, Yb12C_out, Xc12C_out, Yc12C_out, Xd12C_out, Yd12C_out;
+  float32_t Xb12_out, Yb12_out, Xc12_out, Yc12_out, Xd12_out, Yd12_out;
+  float32_t *ptr1;
+
+
+  /*  Initializations for the first stage */
+  n2 = fftLen;
+  n1 = n2;
+
+  /* n2 = fftLen/4 */
+  n2 >>= 2u;
+  i0 = 0u;
+  ia1 = 0u;
+
+  j = n2;
+
+  /*  Calculation of first stage */
+  do
+  {
+    /*  index calculation for the input as, */
+    /*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
+    i1 = i0 + n2;
+    i2 = i1 + n2;
+    i3 = i2 + n2;
+
+    /*  Butterfly implementation */
+    xaIn = pSrc[(2u * i0)];
+    yaIn = pSrc[(2u * i0) + 1u];
+
+    xcIn = pSrc[(2u * i2)];
+    ycIn = pSrc[(2u * i2) + 1u];
+
+    xbIn = pSrc[(2u * i1)];
+    ybIn = pSrc[(2u * i1) + 1u];
+
+    xdIn = pSrc[(2u * i3)];
+    ydIn = pSrc[(2u * i3) + 1u];
+
+    /* xa + xc */
+    Xaplusc = xaIn + xcIn;
+    /* xb + xd */
+    Xbplusd = xbIn + xdIn;
+    /* ya + yc */
+    Yaplusc = yaIn + ycIn;
+    /* yb + yd */
+    Ybplusd = ybIn + ydIn;
+
+    /*  index calculation for the coefficients */
+    ia2 = ia1 + ia1;
+    co2 = pCoef[ia2 * 2u];
+    si2 = pCoef[(ia2 * 2u) + 1u];
+
+    /* xa - xc */
+    Xaminusc = xaIn - xcIn;
+    /* xb - xd */
+    Xbminusd = xbIn - xdIn;
+    /* ya - yc */
+    Yaminusc = yaIn - ycIn;
+    /* yb - yd */
+    Ybminusd = ybIn - ydIn;
+
+    /* xa' = xa + xb + xc + xd */
+    pSrc[(2u * i0)] = Xaplusc + Xbplusd;
+
+    /* ya' = ya + yb + yc + yd */
+    pSrc[(2u * i0) + 1u] = Yaplusc + Ybplusd;
+
+    /* (xa - xc) - (yb - yd) */
+    Xb12C_out = (Xaminusc - Ybminusd);
+    /* (ya - yc) + (xb - xd) */
+    Yb12C_out = (Yaminusc + Xbminusd);
+    /* (xa + xc) - (xb + xd) */
+    Xc12C_out = (Xaplusc - Xbplusd);
+    /* (ya + yc) - (yb + yd) */
+    Yc12C_out = (Yaplusc - Ybplusd);
+    /* (xa - xc) + (yb - yd) */
+    Xd12C_out = (Xaminusc + Ybminusd);
+    /* (ya - yc) - (xb - xd) */
+    Yd12C_out = (Yaminusc - Xbminusd);
+
+    co1 = pCoef[ia1 * 2u];
+    si1 = pCoef[(ia1 * 2u) + 1u];
+
+    /*  index calculation for the coefficients */
+    ia3 = ia2 + ia1;
+    co3 = pCoef[ia3 * 2u];
+    si3 = pCoef[(ia3 * 2u) + 1u];
+
+    Xb12_out = Xb12C_out * co1;
+    Yb12_out = Yb12C_out * co1;
+    Xc12_out = Xc12C_out * co2;
+    Yc12_out = Yc12C_out * co2;
+    Xd12_out = Xd12C_out * co3;
+    Yd12_out = Yd12C_out * co3;
+
+    /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
+    Xb12_out -= Yb12C_out * si1;
+    /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
+    Yb12_out += Xb12C_out * si1;
+    /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
+    Xc12_out -= Yc12C_out * si2;
+    /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
+    Yc12_out += Xc12C_out * si2;
+    /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
+    Xd12_out -= Yd12C_out * si3;
+    /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
+    Yd12_out += Xd12C_out * si3;
+
+    /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
+    pSrc[2u * i1] = Xc12_out;
+
+    /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
+    pSrc[(2u * i1) + 1u] = Yc12_out;
+
+    /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
+    pSrc[2u * i2] = Xb12_out;
+
+    /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
+    pSrc[(2u * i2) + 1u] = Yb12_out;
+
+    /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
+    pSrc[2u * i3] = Xd12_out;
+
+    /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
+    pSrc[(2u * i3) + 1u] = Yd12_out;
+
+    /*  Twiddle coefficients index modifier */
+    ia1 = ia1 + twidCoefModifier;
+
+    /*  Updating input index */
+    i0 = i0 + 1u;
+
+  } while(--j);
+
+  twidCoefModifier <<= 2u;
+
+  /*  Calculation of second stage to excluding last stage */
+  for (k = fftLen / 4; k > 4u; k >>= 2u)
+  {
+    /*  Initializations for the first stage */
+    n1 = n2;
+    n2 >>= 2u;
+    ia1 = 0u;
+
+    /*  Calculation of first stage */
+    for (j = 0u; j <= (n2 - 1u); j++)
+    {
+      /*  index calculation for the coefficients */
+      ia2 = ia1 + ia1;
+      ia3 = ia2 + ia1;
+      co1 = pCoef[ia1 * 2u];
+      si1 = pCoef[(ia1 * 2u) + 1u];
+      co2 = pCoef[ia2 * 2u];
+      si2 = pCoef[(ia2 * 2u) + 1u];
+      co3 = pCoef[ia3 * 2u];
+      si3 = pCoef[(ia3 * 2u) + 1u];
+
+      /*  Twiddle coefficients index modifier */
+      ia1 = ia1 + twidCoefModifier;
+
+      for (i0 = j; i0 < fftLen; i0 += n1)
+      {
+        /*  index calculation for the input as, */
+        /*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
+        i1 = i0 + n2;
+        i2 = i1 + n2;
+        i3 = i2 + n2;
+
+        xaIn = pSrc[(2u * i0)];
+        yaIn = pSrc[(2u * i0) + 1u];
+
+        xbIn = pSrc[(2u * i1)];
+        ybIn = pSrc[(2u * i1) + 1u];
+
+        xcIn = pSrc[(2u * i2)];
+        ycIn = pSrc[(2u * i2) + 1u];
+
+        xdIn = pSrc[(2u * i3)];
+        ydIn = pSrc[(2u * i3) + 1u];
+
+        /* xa - xc */
+        Xaminusc = xaIn - xcIn;
+        /* (xb - xd) */
+        Xbminusd = xbIn - xdIn;
+        /* ya - yc */
+        Yaminusc = yaIn - ycIn;
+        /* (yb - yd) */
+        Ybminusd = ybIn - ydIn;
+
+        /* xa + xc */
+        Xaplusc = xaIn + xcIn;
+        /* xb + xd */
+        Xbplusd = xbIn + xdIn;
+        /* ya + yc */
+        Yaplusc = yaIn + ycIn;
+        /* yb + yd */
+        Ybplusd = ybIn + ydIn;
+
+        /* (xa - xc) - (yb - yd) */
+        Xb12C_out = (Xaminusc - Ybminusd);
+        /* (ya - yc) +  (xb - xd) */
+        Yb12C_out = (Yaminusc + Xbminusd);
+        /* xa + xc -(xb + xd) */
+        Xc12C_out = (Xaplusc - Xbplusd);
+        /* (ya + yc) - (yb + yd) */
+        Yc12C_out = (Yaplusc - Ybplusd);
+        /* (xa - xc) + (yb - yd) */
+        Xd12C_out = (Xaminusc + Ybminusd);
+        /* (ya - yc) -  (xb - xd) */
+        Yd12C_out = (Yaminusc - Xbminusd);
+
+        pSrc[(2u * i0)] = Xaplusc + Xbplusd;
+        pSrc[(2u * i0) + 1u] = Yaplusc + Ybplusd;
+
+        Xb12_out = Xb12C_out * co1;
+        Yb12_out = Yb12C_out * co1;
+        Xc12_out = Xc12C_out * co2;
+        Yc12_out = Yc12C_out * co2;
+        Xd12_out = Xd12C_out * co3;
+        Yd12_out = Yd12C_out * co3;
+
+        /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
+        Xb12_out -= Yb12C_out * si1;
+        /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
+        Yb12_out += Xb12C_out * si1;
+        /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
+        Xc12_out -= Yc12C_out * si2;
+        /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
+        Yc12_out += Xc12C_out * si2;
+        /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
+        Xd12_out -= Yd12C_out * si3;
+        /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
+        Yd12_out += Xd12C_out * si3;
+
+        /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
+        pSrc[2u * i1] = Xc12_out;
+
+        /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
+        pSrc[(2u * i1) + 1u] = Yc12_out;
+
+        /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
+        pSrc[2u * i2] = Xb12_out;
+
+        /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
+        pSrc[(2u * i2) + 1u] = Yb12_out;
+
+        /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
+        pSrc[2u * i3] = Xd12_out;
+
+        /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
+        pSrc[(2u * i3) + 1u] = Yd12_out;
+
+      }
+    }
+    twidCoefModifier <<= 2u;
+  }
+  /*  Initializations of last stage */
+
+  j = fftLen >> 2;
+  ptr1 = &pSrc[0];
+
+  /*  Calculations of last stage */
+  do
+  {
+
+    xaIn = ptr1[0];
+    xcIn = ptr1[4];
+    yaIn = ptr1[1];
+    ycIn = ptr1[5];
+
+    /*  Butterfly implementation */
+    /* xa + xc */
+    Xaplusc = xaIn + xcIn;
+
+    xbIn = ptr1[2];
+
+    /* xa - xc */
+    Xaminusc = xaIn - xcIn;
+
+    xdIn = ptr1[6];
+
+    /* ya + yc */
+    Yaplusc = yaIn + ycIn;
+
+    ybIn = ptr1[3];
+
+    /* ya - yc */
+    Yaminusc = yaIn - ycIn;
+
+    ydIn = ptr1[7];
+
+    /* xc + xd */
+    Xbplusd = xbIn + xdIn;
+
+    /* yb + yd */
+    Ybplusd = ybIn + ydIn;
+
+    /* xa' = xa + xb + xc + xd */
+    ptr1[0] = (Xaplusc + Xbplusd) * onebyfftLen;
+
+    /* (xb-xd) */
+    Xbminusd = xbIn - xdIn;
+
+    /* ya' = ya + yb + yc + yd */
+    ptr1[1] = (Yaplusc + Ybplusd) * onebyfftLen;
+
+    /* (yb-yd) */
+    Ybminusd = ybIn - ydIn;
+
+    /* xc' = (xa-xb+xc-xd) * onebyfftLen */
+    ptr1[2] = (Xaplusc - Xbplusd) * onebyfftLen;
+
+    /* yc' = (ya-yb+yc-yd) * onebyfftLen  */
+    ptr1[3] = (Yaplusc - Ybplusd) * onebyfftLen;
+
+    /* xb' = (xa-yb-xc+yd) * onebyfftLen */
+    ptr1[4] = (Xaminusc - Ybminusd) * onebyfftLen;
+
+    /* yb' = (ya+xb-yc-xd) * onebyfftLen */
+    ptr1[5] = (Yaminusc + Xbminusd) * onebyfftLen;
+
+    /* xd' = (xa-yb-xc+yd) * onebyfftLen */
+    ptr1[6] = (Xaminusc + Ybminusd) * onebyfftLen;
+
+    /* yd' = (ya-xb-yc+xd) * onebyfftLen */
+    ptr1[7] = (Yaminusc - Xbminusd) * onebyfftLen;
+
+    /* increment source pointer by 8 for next calculations */
+    ptr1 = ptr1 + 8u;
+
+  } while(--j);
+
+#else
+
+  float32_t t1, t2, r1, r2, s1, s2;
+
+  /* Run the below code for Cortex-M0 */
+
+  /*  Initializations for the first stage */
+  n2 = fftLen;
+  n1 = n2;
+
+  /*  Calculation of first stage */
+  for (k = fftLen; k > 4u; k >>= 2u)
+  {
+    /*  Initializations for the first stage */
+    n1 = n2;
+    n2 >>= 2u;
+    ia1 = 0u;
+
+    /*  Calculation of first stage */
+    for (j = 0u; j <= (n2 - 1u); j++)
+    {
+      /*  index calculation for the coefficients */
+      ia2 = ia1 + ia1;
+      ia3 = ia2 + ia1;
+      co1 = pCoef[ia1 * 2u];
+      si1 = pCoef[(ia1 * 2u) + 1u];
+      co2 = pCoef[ia2 * 2u];
+      si2 = pCoef[(ia2 * 2u) + 1u];
+      co3 = pCoef[ia3 * 2u];
+      si3 = pCoef[(ia3 * 2u) + 1u];
+
+      /*  Twiddle coefficients index modifier */
+      ia1 = ia1 + twidCoefModifier;
+
+      for (i0 = j; i0 < fftLen; i0 += n1)
+      {
+        /*  index calculation for the input as, */
+        /*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
+        i1 = i0 + n2;
+        i2 = i1 + n2;
+        i3 = i2 + n2;
+
+        /* xa + xc */
+        r1 = pSrc[(2u * i0)] + pSrc[(2u * i2)];
+
+        /* xa - xc */
+        r2 = pSrc[(2u * i0)] - pSrc[(2u * i2)];
+
+        /* ya + yc */
+        s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
+
+        /* ya - yc */
+        s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
+
+        /* xb + xd */
+        t1 = pSrc[2u * i1] + pSrc[2u * i3];
+
+        /* xa' = xa + xb + xc + xd */
+        pSrc[2u * i0] = r1 + t1;
+
+        /* xa + xc -(xb + xd) */
+        r1 = r1 - t1;
+
+        /* yb + yd */
+        t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
+
+        /* ya' = ya + yb + yc + yd */
+        pSrc[(2u * i0) + 1u] = s1 + t2;
+
+        /* (ya + yc) - (yb + yd) */
+        s1 = s1 - t2;
+
+        /* (yb - yd) */
+        t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
+
+        /* (xb - xd) */
+        t2 = pSrc[2u * i1] - pSrc[2u * i3];
+
+        /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
+        pSrc[2u * i1] = (r1 * co2) - (s1 * si2);
+
+        /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
+        pSrc[(2u * i1) + 1u] = (s1 * co2) + (r1 * si2);
+
+        /* (xa - xc) - (yb - yd) */
+        r1 = r2 - t1;
+
+        /* (xa - xc) + (yb - yd) */
+        r2 = r2 + t1;
+
+        /* (ya - yc) +  (xb - xd) */
+        s1 = s2 + t2;
+
+        /* (ya - yc) -  (xb - xd) */
+        s2 = s2 - t2;
+
+        /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
+        pSrc[2u * i2] = (r1 * co1) - (s1 * si1);
+
+        /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
+        pSrc[(2u * i2) + 1u] = (s1 * co1) + (r1 * si1);
+
+        /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
+        pSrc[2u * i3] = (r2 * co3) - (s2 * si3);
+
+        /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
+        pSrc[(2u * i3) + 1u] = (s2 * co3) + (r2 * si3);
+      }
+    }
+    twidCoefModifier <<= 2u;
+  }
+  /*  Initializations of last stage */
+  n1 = n2;
+  n2 >>= 2u;
+
+  /*  Calculations of last stage */
+  for (i0 = 0u; i0 <= (fftLen - n1); i0 += n1)
+  {
+    /*  index calculation for the input as, */
+    /*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
+    i1 = i0 + n2;
+    i2 = i1 + n2;
+    i3 = i2 + n2;
+
+    /*  Butterfly implementation */
+    /* xa + xc */
+    r1 = pSrc[2u * i0] + pSrc[2u * i2];
+
+    /* xa - xc */
+    r2 = pSrc[2u * i0] - pSrc[2u * i2];
+
+    /* ya + yc */
+    s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
+
+    /* ya - yc */
+    s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
+
+    /* xc + xd */
+    t1 = pSrc[2u * i1] + pSrc[2u * i3];
+
+    /* xa' = xa + xb + xc + xd */
+    pSrc[2u * i0] = (r1 + t1) * onebyfftLen;
+
+    /* (xa + xb) - (xc + xd) */
+    r1 = r1 - t1;
+
+    /* yb + yd */
+    t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
+
+    /* ya' = ya + yb + yc + yd */
+    pSrc[(2u * i0) + 1u] = (s1 + t2) * onebyfftLen;
+
+    /* (ya + yc) - (yb + yd) */
+    s1 = s1 - t2;
+
+    /* (yb-yd) */
+    t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
+
+    /* (xb-xd) */
+    t2 = pSrc[2u * i1] - pSrc[2u * i3];
+
+    /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
+    pSrc[2u * i1] = r1 * onebyfftLen;
+
+    /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
+    pSrc[(2u * i1) + 1u] = s1 * onebyfftLen;
+
+
+    /* (xa - xc) - (yb-yd) */
+    r1 = r2 - t1;
+
+    /* (xa - xc) + (yb-yd) */
+    r2 = r2 + t1;
+
+    /* (ya - yc) + (xb-xd) */
+    s1 = s2 + t2;
+
+    /* (ya - yc) - (xb-xd) */
+    s2 = s2 - t2;
+
+    /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
+    pSrc[2u * i2] = r1 * onebyfftLen;
+
+    /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
+    pSrc[(2u * i2) + 1u] = s1 * onebyfftLen;
+
+    /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
+    pSrc[2u * i3] = r2 * onebyfftLen;
+
+    /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
+    pSrc[(2u * i3) + 1u] = s2 * onebyfftLen;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_init_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_init_f32.c
new file mode 100644
index 0000000000..f354e1dde1
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_init_f32.c
@@ -0,0 +1,161 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_cfft_radix4_init_f32.c    
+*    
+* Description:	Radix-4 Decimation in Frequency Floating-point CFFT & CIFFT Initialization function    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+* 	 incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+
+#include "arm_math.h"
+#include "arm_common_tables.h"
+
+/**    
+ * @ingroup groupTransforms    
+ */
+
+/**    
+ * @addtogroup Radix4_CFFT_CIFFT    
+ * @{    
+ */
+
+/**    
+* @brief  Initialization function for the floating-point CFFT/CIFFT.   
+* @param[in,out] *S             points to an instance of the floating-point CFFT/CIFFT structure.   
+* @param[in]     fftLen         length of the FFT.   
+* @param[in]     ifftFlag       flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform.   
+* @param[in]     bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.   
+* @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if fftLen is not a supported value.   
+*    
+* \par Description:   
+* \par    
+* The parameter ifftFlag controls whether a forward or inverse transform is computed.    
+* Set(=1) ifftFlag for calculation of CIFFT otherwise  CFFT is calculated   
+* \par    
+* The parameter bitReverseFlag controls whether output is in normal order or bit reversed order.    
+* Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order.    
+* \par    
+* The parameter fftLen	Specifies length of CFFT/CIFFT process. Supported FFT Lengths are 16, 64, 256, 1024.    
+* \par    
+* This Function also initializes Twiddle factor table pointer and Bit reversal table pointer.    
+*/
+
+arm_status arm_cfft_radix4_init_f32(
+  arm_cfft_radix4_instance_f32 * S,
+  uint16_t fftLen,
+  uint8_t ifftFlag,
+  uint8_t bitReverseFlag)
+{
+  /*  Initialise the default arm status */
+  arm_status status = ARM_MATH_SUCCESS;
+
+  /*  Initialise the FFT length */
+  S->fftLen = fftLen;
+
+  /*  Initialise the Twiddle coefficient pointer */
+  S->pTwiddle = (float32_t *) twiddleCoef;
+
+  /*  Initialise the Flag for selection of CFFT or CIFFT */
+  S->ifftFlag = ifftFlag;
+
+  /*  Initialise the Flag for calculation Bit reversal or not */
+  S->bitReverseFlag = bitReverseFlag;
+
+  /*  Initializations of structure parameters depending on the FFT length */
+  switch (S->fftLen)
+  {
+
+  case 4096u:
+    /*  Initializations of structure parameters for 4096 point FFT */
+
+    /*  Initialise the twiddle coef modifier value */
+    S->twidCoefModifier = 1u;
+    /*  Initialise the bit reversal table modifier */
+    S->bitRevFactor = 1u;
+    /*  Initialise the bit reversal table pointer */
+    S->pBitRevTable = (uint16_t *) armBitRevTable;
+    /*  Initialise the 1/fftLen Value */
+    S->onebyfftLen = 0.000244140625;
+    break;
+
+  case 1024u:
+    /*  Initializations of structure parameters for 1024 point FFT */
+
+    /*  Initialise the twiddle coef modifier value */
+    S->twidCoefModifier = 4u;
+    /*  Initialise the bit reversal table modifier */
+    S->bitRevFactor = 4u;
+    /*  Initialise the bit reversal table pointer */
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[3];
+    /*  Initialise the 1/fftLen Value */
+    S->onebyfftLen = 0.0009765625f;
+    break;
+
+
+  case 256u:
+    /*  Initializations of structure parameters for 256 point FFT */
+    S->twidCoefModifier = 16u;
+    S->bitRevFactor = 16u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[15];
+    S->onebyfftLen = 0.00390625f;
+    break;
+
+  case 64u:
+    /*  Initializations of structure parameters for 64 point FFT */
+    S->twidCoefModifier = 64u;
+    S->bitRevFactor = 64u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[63];
+    S->onebyfftLen = 0.015625f;
+    break;
+
+  case 16u:
+    /*  Initializations of structure parameters for 16 point FFT */
+    S->twidCoefModifier = 256u;
+    S->bitRevFactor = 256u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[255];
+    S->onebyfftLen = 0.0625f;
+    break;
+
+
+  default:
+    /*  Reporting argument error if fftSize is not valid value */
+    status = ARM_MATH_ARGUMENT_ERROR;
+    break;
+  }
+
+  return (status);
+}
+
+/**    
+ * @} end of Radix4_CFFT_CIFFT group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_init_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_init_q15.c
new file mode 100644
index 0000000000..5ace3483d8
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_init_q15.c
@@ -0,0 +1,149 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_cfft_radix4_init_q15.c    
+*    
+* Description:	Radix-4 Decimation in Frequency Q15 FFT & IFFT initialization function    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+* 	 incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+#include "arm_common_tables.h"
+
+/**    
+ * @ingroup groupTransforms    
+ */
+
+
+/**    
+ * @addtogroup Radix4_CFFT_CIFFT    
+ * @{    
+ */
+
+
+/**    
+* @brief Initialization function for the Q15 CFFT/CIFFT.   
+* @param[in,out] *S             points to an instance of the Q15 CFFT/CIFFT structure.   
+* @param[in]     fftLen         length of the FFT.   
+* @param[in]     ifftFlag       flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform.   
+* @param[in]     bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.   
+* @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if fftLen is not a supported value.   
+*    
+* \par Description:   
+* \par    
+* The parameter ifftFlag controls whether a forward or inverse transform is computed.    
+* Set(=1) ifftFlag for calculation of CIFFT otherwise  CFFT is calculated   
+* \par    
+* The parameter bitReverseFlag controls whether output is in normal order or bit reversed order.    
+* Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order.    
+* \par    
+* The parameter fftLen	Specifies length of CFFT/CIFFT process. Supported FFT Lengths are 16, 64, 256, 1024.    
+* \par    
+* This Function also initializes Twiddle factor table pointer and Bit reversal table pointer.    
+*/
+
+arm_status arm_cfft_radix4_init_q15(
+  arm_cfft_radix4_instance_q15 * S,
+  uint16_t fftLen,
+  uint8_t ifftFlag,
+  uint8_t bitReverseFlag)
+{
+  /*  Initialise the default arm status */
+  arm_status status = ARM_MATH_SUCCESS;
+  /*  Initialise the FFT length */
+  S->fftLen = fftLen;
+  /*  Initialise the Twiddle coefficient pointer */
+  S->pTwiddle = (q15_t *) twiddleCoefQ15;
+  /*  Initialise the Flag for selection of CFFT or CIFFT */
+  S->ifftFlag = ifftFlag;
+  /*  Initialise the Flag for calculation Bit reversal or not */
+  S->bitReverseFlag = bitReverseFlag;
+
+  /*  Initializations of structure parameters depending on the FFT length */
+  switch (S->fftLen)
+  {
+  case 4096u:
+    /*  Initializations of structure parameters for 4096 point FFT */
+
+    /*  Initialise the twiddle coef modifier value */
+    S->twidCoefModifier = 1u;
+    /*  Initialise the bit reversal table modifier */
+    S->bitRevFactor = 1u;
+    /*  Initialise the bit reversal table pointer */
+    S->pBitRevTable = (uint16_t *) armBitRevTable;
+
+    break;
+
+  case 1024u:
+    /*  Initializations of structure parameters for 1024 point FFT */
+    S->twidCoefModifier = 4u;
+    S->bitRevFactor = 4u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[3];
+
+    break;
+
+  case 256u:
+    /*  Initializations of structure parameters for 256 point FFT */
+    S->twidCoefModifier = 16u;
+    S->bitRevFactor = 16u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[15];
+
+    break;
+
+  case 64u:
+    /*  Initializations of structure parameters for 64 point FFT */
+    S->twidCoefModifier = 64u;
+    S->bitRevFactor = 64u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[63];
+
+    break;
+
+  case 16u:
+    /*  Initializations of structure parameters for 16 point FFT */
+    S->twidCoefModifier = 256u;
+    S->bitRevFactor = 256u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[255];
+
+    break;
+
+  default:
+    /*  Reporting argument error if fftSize is not valid value */
+    status = ARM_MATH_ARGUMENT_ERROR;
+    break;
+  }
+
+  return (status);
+}
+
+/**    
+ * @} end of Radix4_CFFT_CIFFT group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_init_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_init_q31.c
new file mode 100644
index 0000000000..6614994f74
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_init_q31.c
@@ -0,0 +1,145 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_cfft_radix4_init_q31.c    
+*    
+* Description:	Radix-4 Decimation in Frequency Q31 FFT & IFFT initialization function    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+* 	 incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+#include "arm_common_tables.h"
+
+/**    
+ * @ingroup groupTransforms    
+ */
+
+/**    
+ * @addtogroup Radix4_CFFT_CIFFT    
+ * @{    
+ */
+
+/**    
+*    
+* @brief  Initialization function for the Q31 CFFT/CIFFT.   
+* @param[in,out] *S             points to an instance of the Q31 CFFT/CIFFT structure.   
+* @param[in]     fftLen         length of the FFT.   
+* @param[in]     ifftFlag       flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform.   
+* @param[in]     bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.   
+* @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if fftLen is not a supported value.   
+*    
+* \par Description:   
+* \par    
+* The parameter ifftFlag controls whether a forward or inverse transform is computed.    
+* Set(=1) ifftFlag for calculation of CIFFT otherwise  CFFT is calculated   
+* \par    
+* The parameter bitReverseFlag controls whether output is in normal order or bit reversed order.    
+* Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order.    
+* \par    
+* The parameter fftLen	Specifies length of CFFT/CIFFT process. Supported FFT Lengths are 16, 64, 256, 1024.    
+* \par    
+* This Function also initializes Twiddle factor table pointer and Bit reversal table pointer.    
+*/
+
+arm_status arm_cfft_radix4_init_q31(
+  arm_cfft_radix4_instance_q31 * S,
+  uint16_t fftLen,
+  uint8_t ifftFlag,
+  uint8_t bitReverseFlag)
+{
+  /*  Initialise the default arm status */
+  arm_status status = ARM_MATH_SUCCESS;
+  /*  Initialise the FFT length */
+  S->fftLen = fftLen;
+  /*  Initialise the Twiddle coefficient pointer */
+  S->pTwiddle = (q31_t *) twiddleCoefQ31;
+  /*  Initialise the Flag for selection of CFFT or CIFFT */
+  S->ifftFlag = ifftFlag;
+  /*  Initialise the Flag for calculation Bit reversal or not */
+  S->bitReverseFlag = bitReverseFlag;
+
+  /*  Initializations of Instance structure depending on the FFT length */
+  switch (S->fftLen)
+  {
+    /*  Initializations of structure parameters for 4096 point FFT */
+  case 4096u:
+    /*  Initialise the twiddle coef modifier value */
+    S->twidCoefModifier = 1u;
+    /*  Initialise the bit reversal table modifier */
+    S->bitRevFactor = 1u;
+    /*  Initialise the bit reversal table pointer */
+    S->pBitRevTable = (uint16_t *) armBitRevTable;
+    break;
+
+    /*  Initializations of structure parameters for 1024 point FFT */
+  case 1024u:
+    /*  Initialise the twiddle coef modifier value */
+    S->twidCoefModifier = 4u;
+    /*  Initialise the bit reversal table modifier */
+    S->bitRevFactor = 4u;
+    /*  Initialise the bit reversal table pointer */
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[3];
+    break;
+
+  case 256u:
+    /*  Initializations of structure parameters for 256 point FFT */
+    S->twidCoefModifier = 16u;
+    S->bitRevFactor = 16u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[15];
+    break;
+
+  case 64u:
+    /*  Initializations of structure parameters for 64 point FFT */
+    S->twidCoefModifier = 64u;
+    S->bitRevFactor = 64u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[63];
+    break;
+
+  case 16u:
+    /*  Initializations of structure parameters for 16 point FFT */
+    S->twidCoefModifier = 256u;
+    S->bitRevFactor = 256u;
+    S->pBitRevTable = (uint16_t *) & armBitRevTable[255];
+    break;
+
+  default:
+    /*  Reporting argument error if fftSize is not valid value */
+    status = ARM_MATH_ARGUMENT_ERROR;
+    break;
+  }
+
+  return (status);
+}
+
+/**    
+ * @} end of Radix4_CFFT_CIFFT group    
+ */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_q15.c
new file mode 100644
index 0000000000..01d476e6c4
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_q15.c
@@ -0,0 +1,1896 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_cfft_radix4_q15.c    
+*    
+* Description:	This file has function definition of Radix-4 FFT & IFFT function and    
+*				In-place bit reversal using bit reversal table    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+* 	 incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupTransforms    
+ */
+
+/**    
+ * @addtogroup Radix4_CFFT_CIFFT    
+ * @{    
+ */
+
+
+/**    
+ * @details    
+ * @brief Processing function for the Q15 CFFT/CIFFT.   
+ * @param[in]      *S    points to an instance of the Q15 CFFT/CIFFT structure.   
+ * @param[in, out] *pSrc points to the complex data buffer. Processing occurs in-place.   
+ * @return none.   
+ *     
+ * \par Input and output formats:    
+ * \par    
+ * Internally input is downscaled by 2 for every stage to avoid saturations inside CFFT/CIFFT process.   
+ * Hence the output format is different for different FFT sizes.    
+ * The input and output formats for different FFT sizes and number of bits to upscale are mentioned in the tables below for CFFT and CIFFT:   
+ * \par   
+ * \image html CFFTQ15.gif "Input and Output Formats for Q15 CFFT"    
+ * \image html CIFFTQ15.gif "Input and Output Formats for Q15 CIFFT"    
+ */
+
+void arm_cfft_radix4_q15(
+  const arm_cfft_radix4_instance_q15 * S,
+  q15_t * pSrc)
+{
+  if(S->ifftFlag == 1u)
+  {
+    /*  Complex IFFT radix-4  */
+    arm_radix4_butterfly_inverse_q15(pSrc, S->fftLen, S->pTwiddle,
+                                     S->twidCoefModifier);
+  }
+  else
+  {
+    /*  Complex FFT radix-4  */
+    arm_radix4_butterfly_q15(pSrc, S->fftLen, S->pTwiddle,
+                             S->twidCoefModifier);
+  }
+
+  if(S->bitReverseFlag == 1u)
+  {
+    /*  Bit Reversal */
+    arm_bitreversal_q15(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable);
+  }
+
+}
+
+/**    
+ * @} end of Radix4_CFFT_CIFFT group    
+ */
+
+/*    
+* Radix-4 FFT algorithm used is :    
+*    
+* Input real and imaginary data:    
+* x(n) = xa + j * ya    
+* x(n+N/4 ) = xb + j * yb    
+* x(n+N/2 ) = xc + j * yc    
+* x(n+3N 4) = xd + j * yd    
+*    
+*    
+* Output real and imaginary data:    
+* x(4r) = xa'+ j * ya'    
+* x(4r+1) = xb'+ j * yb'    
+* x(4r+2) = xc'+ j * yc'    
+* x(4r+3) = xd'+ j * yd'    
+*    
+*    
+* Twiddle factors for radix-4 FFT:    
+* Wn = co1 + j * (- si1)    
+* W2n = co2 + j * (- si2)    
+* W3n = co3 + j * (- si3)    
+    
+* The real and imaginary output values for the radix-4 butterfly are    
+* xa' = xa + xb + xc + xd    
+* ya' = ya + yb + yc + yd    
+* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1)    
+* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1)    
+* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2)    
+* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2)    
+* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3)    
+* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3)    
+*    
+*/
+
+/**    
+ * @brief  Core function for the Q15 CFFT butterfly process.   
+ * @param[in, out] *pSrc16          points to the in-place buffer of Q15 data type.   
+ * @param[in]      fftLen           length of the FFT.   
+ * @param[in]      *pCoef16         points to twiddle coefficient buffer.   
+ * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.   
+ * @return none.   
+ */
+
+void arm_radix4_butterfly_q15(
+  q15_t * pSrc16,
+  uint32_t fftLen,
+  q15_t * pCoef16,
+  uint32_t twidCoefModifier)
+{
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q31_t R, S, T, U;
+  q31_t C1, C2, C3, out1, out2;
+  uint32_t n1, n2, ic, i0, i1, i2, i3, j, k;
+  q15_t in;
+
+  q15_t *ptr1;
+
+
+
+  q31_t xaya, xbyb, xcyc, xdyd;
+
+  /* Total process is divided into three stages */
+
+  /* process first stage, middle stages, & last stage */
+
+  /*  Initializations for the first stage */
+  n2 = fftLen;
+  n1 = n2;
+
+  /* n2 = fftLen/4 */
+  n2 >>= 2u;
+
+  /* Index for twiddle coefficient */
+  ic = 0u;
+
+  /* Index for input read and output write */
+  i0 = 0u;
+  j = n2;
+
+  /* Input is in 1.15(q15) format */
+
+  /*  start of first stage process */
+  do
+  {
+    /*  Butterfly implementation */
+
+    /*  index calculation for the input as, */
+    /*  pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
+    i1 = i0 + n2;
+    i2 = i1 + n2;
+    i3 = i2 + n2;
+
+    /*  Reading i0, i0+fftLen/2 inputs */
+    /* Read ya (real), xa(imag) input */
+    T = _SIMD32_OFFSET(pSrc16 + (2u * i0));
+    in = ((int16_t) (T & 0xFFFF)) >> 2;
+    T = ((T >> 2) & 0xFFFF0000) | (in & 0xFFFF);
+
+    /* Read yc (real), xc(imag) input */
+    S = _SIMD32_OFFSET(pSrc16 + (2u * i2));
+    in = ((int16_t) (S & 0xFFFF)) >> 2;
+    S = ((S >> 2) & 0xFFFF0000) | (in & 0xFFFF);
+
+    /* R = packed((ya + yc), (xa + xc) ) */
+    R = __QADD16(T, S);
+
+    /* S = packed((ya - yc), (xa - xc) ) */
+    S = __QSUB16(T, S);
+
+    /*  Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
+    /* Read yb (real), xb(imag) input */
+    T = _SIMD32_OFFSET(pSrc16 + (2u * i1));
+    in = ((int16_t) (T & 0xFFFF)) >> 2;
+    T = ((T >> 2) & 0xFFFF0000) | (in & 0xFFFF);
+
+    /* Read yd (real), xd(imag) input */
+    U = _SIMD32_OFFSET(pSrc16 + (2u * i3));
+    in = ((int16_t) (U & 0xFFFF)) >> 2;
+    U = ((U >> 2) & 0xFFFF0000) | (in & 0xFFFF);
+
+    /* T = packed((yb + yd), (xb + xd) ) */
+    T = __QADD16(T, U);
+
+    /*  writing the butterfly processed i0 sample */
+    /* xa' = xa + xb + xc + xd */
+    /* ya' = ya + yb + yc + yd */
+    _SIMD32_OFFSET(pSrc16 + (2u * i0)) = __SHADD16(R, T);
+
+    /* R = packed((ya + yc) - (yb + yd), (xa + xc)- (xb + xd)) */
+    R = __QSUB16(R, T);
+
+    /* co2 & si2 are read from SIMD Coefficient pointer */
+    C2 = _SIMD32_OFFSET(pCoef16 + (4u * ic));
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    /* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
+    out1 = __SMUAD(C2, R) >> 16u;
+    /* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
+    out2 = __SMUSDX(C2, R);
+
+#else
+
+    /* xc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
+    out1 = __SMUSDX(R, C2) >> 16u;
+    /* yc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
+    out2 = __SMUAD(C2, R);
+
+#endif /*      #ifndef ARM_MATH_BIG_ENDIAN     */
+
+    /*  Reading i0+fftLen/4 */
+    /* T = packed(yb, xb) */
+    T = _SIMD32_OFFSET(pSrc16 + (2u * i1));
+    in = ((int16_t) (T & 0xFFFF)) >> 2;
+    T = ((T >> 2) & 0xFFFF0000) | (in & 0xFFFF);
+
+    /* writing the butterfly processed i0 + fftLen/4 sample */
+    /* writing output(xc', yc') in little endian format */
+    _SIMD32_OFFSET(pSrc16 + (2u * i1)) =
+      (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
+
+    /*  Butterfly calculations */
+    /* U = packed(yd, xd) */
+    U = _SIMD32_OFFSET(pSrc16 + (2u * i3));
+    in = ((int16_t) (U & 0xFFFF)) >> 2;
+    U = ((U >> 2) & 0xFFFF0000) | (in & 0xFFFF);
+
+    /* T = packed(yb-yd, xb-xd) */
+    T = __QSUB16(T, U);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    /* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
+    R = __QASX(S, T);
+    /* S = packed((ya-yc) - (xb- xd),  (xa-xc) + (yb-yd)) */
+    S = __QSAX(S, T);
+
+#else
+
+    /* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
+    R = __QSAX(S, T);
+    /* S = packed((ya-yc) - (xb- xd),  (xa-xc) + (yb-yd)) */
+    S = __QASX(S, T);
+
+#endif /*      #ifndef ARM_MATH_BIG_ENDIAN     */
+
+    /* co1 & si1 are read from SIMD Coefficient pointer */
+    C1 = _SIMD32_OFFSET(pCoef16 + (2u * ic));
+    /*  Butterfly process for the i0+fftLen/2 sample */
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    /* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
+    out1 = __SMUAD(C1, S) >> 16u;
+    /* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
+    out2 = __SMUSDX(C1, S);
+
+#else
+
+    /* xb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
+    out1 = __SMUSDX(S, C1) >> 16u;
+    /* yb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
+    out2 = __SMUAD(C1, S);
+
+#endif /*      #ifndef ARM_MATH_BIG_ENDIAN     */
+
+    /* writing output(xb', yb') in little endian format */
+    _SIMD32_OFFSET(pSrc16 + (2u * i2)) =
+      ((out2) & 0xFFFF0000) | ((out1) & 0x0000FFFF);
+
+
+    /* co3 & si3 are read from SIMD Coefficient pointer */
+    C3 = _SIMD32_OFFSET(pCoef16 + (6u * ic));
+    /*  Butterfly process for the i0+3fftLen/4 sample */
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    /* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */
+    out1 = __SMUAD(C3, R) >> 16u;
+    /* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */
+    out2 = __SMUSDX(C3, R);
+
+#else
+
+    /* xd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */
+    out1 = __SMUSDX(R, C3) >> 16u;
+    /* yd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */
+    out2 = __SMUAD(C3, R);
+
+#endif /*      #ifndef ARM_MATH_BIG_ENDIAN     */
+
+    /* writing output(xd', yd') in little endian format */
+    _SIMD32_OFFSET(pSrc16 + (2u * i3)) =
+      ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
+
+    /*  Twiddle coefficients index modifier */
+    ic = ic + twidCoefModifier;
+
+    /*  Updating input index */
+    i0 = i0 + 1u;
+
+  } while(--j);
+  /* data is in 4.11(q11) format */
+
+  /* end of first stage process */
+
+
+  /* start of middle stage process */
+
+  /*  Twiddle coefficients index modifier */
+  twidCoefModifier <<= 2u;
+
+  /*  Calculation of Middle stage */
+  for (k = fftLen / 4u; k > 4u; k >>= 2u)
+  {
+    /*  Initializations for the middle stage */
+    n1 = n2;
+    n2 >>= 2u;
+    ic = 0u;
+
+    for (j = 0u; j <= (n2 - 1u); j++)
+    {
+      /*  index calculation for the coefficients */
+      C1 = _SIMD32_OFFSET(pCoef16 + (2u * ic));
+      C2 = _SIMD32_OFFSET(pCoef16 + (4u * ic));
+      C3 = _SIMD32_OFFSET(pCoef16 + (6u * ic));
+
+      /*  Twiddle coefficients index modifier */
+      ic = ic + twidCoefModifier;
+
+      /*  Butterfly implementation */
+      for (i0 = j; i0 < fftLen; i0 += n1)
+      {
+        /*  index calculation for the input as, */
+        /*  pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
+        i1 = i0 + n2;
+        i2 = i1 + n2;
+        i3 = i2 + n2;
+
+        /*  Reading i0, i0+fftLen/2 inputs */
+        /* Read ya (real), xa(imag) input */
+        T = _SIMD32_OFFSET(pSrc16 + (2u * i0));
+
+        /* Read yc (real), xc(imag) input */
+        S = _SIMD32_OFFSET(pSrc16 + (2u * i2));
+
+        /* R = packed( (ya + yc), (xa + xc)) */
+        R = __QADD16(T, S);
+
+        /* S = packed((ya - yc), (xa - xc)) */
+        S = __QSUB16(T, S);
+
+        /*  Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
+        /* Read yb (real), xb(imag) input */
+        T = _SIMD32_OFFSET(pSrc16 + (2u * i1));
+
+        /* Read yd (real), xd(imag) input */
+        U = _SIMD32_OFFSET(pSrc16 + (2u * i3));
+
+        /* T = packed( (yb + yd), (xb + xd)) */
+        T = __QADD16(T, U);
+
+        /*  writing the butterfly processed i0 sample */
+
+        /* xa' = xa + xb + xc + xd */
+        /* ya' = ya + yb + yc + yd */
+        out1 = __SHADD16(R, T);
+        in = ((int16_t) (out1 & 0xFFFF)) >> 1;
+        out1 = ((out1 >> 1) & 0xFFFF0000) | (in & 0xFFFF);
+        _SIMD32_OFFSET(pSrc16 + (2u * i0)) = out1;
+
+        /* R = packed( (ya + yc) - (yb + yd), (xa + xc) - (xb + xd)) */
+        R = __SHSUB16(R, T);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+        /* (ya-yb+yc-yd)* (si2) + (xa-xb+xc-xd)* co2 */
+        out1 = __SMUAD(C2, R) >> 16u;
+
+        /* (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
+        out2 = __SMUSDX(C2, R);
+
+#else
+
+        /* (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
+        out1 = __SMUSDX(R, C2) >> 16u;
+
+        /* (ya-yb+yc-yd)* (si2) + (xa-xb+xc-xd)* co2 */
+        out2 = __SMUAD(C2, R);
+
+#endif /*      #ifndef ARM_MATH_BIG_ENDIAN     */
+
+        /*  Reading i0+3fftLen/4 */
+        /* Read yb (real), xb(imag) input */
+        T = _SIMD32_OFFSET(pSrc16 + (2u * i1));
+
+        /*  writing the butterfly processed i0 + fftLen/4 sample */
+        /* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
+        /* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
+        _SIMD32_OFFSET(pSrc16 + (2u * i1)) =
+          ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
+
+        /*  Butterfly calculations */
+
+        /* Read yd (real), xd(imag) input */
+        U = _SIMD32_OFFSET(pSrc16 + (2u * i3));
+
+        /* T = packed(yb-yd, xb-xd) */
+        T = __QSUB16(T, U);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+        /* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
+        R = __SHASX(S, T);
+
+        /* S = packed((ya-yc) - (xb- xd),  (xa-xc) + (yb-yd)) */
+        S = __SHSAX(S, T);
+
+
+        /*  Butterfly process for the i0+fftLen/2 sample */
+        out1 = __SMUAD(C1, S) >> 16u;
+        out2 = __SMUSDX(C1, S);
+
+#else
+
+        /* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
+        R = __SHSAX(S, T);
+
+        /* S = packed((ya-yc) - (xb- xd),  (xa-xc) + (yb-yd)) */
+        S = __SHASX(S, T);
+
+
+        /*  Butterfly process for the i0+fftLen/2 sample */
+        out1 = __SMUSDX(S, C1) >> 16u;
+        out2 = __SMUAD(C1, S);
+
+#endif /*      #ifndef ARM_MATH_BIG_ENDIAN     */
+
+        /* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
+        /* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
+        _SIMD32_OFFSET(pSrc16 + (2u * i2)) =
+          ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
+
+        /*  Butterfly process for the i0+3fftLen/4 sample */
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+        out1 = __SMUAD(C3, R) >> 16u;
+        out2 = __SMUSDX(C3, R);
+
+#else
+
+        out1 = __SMUSDX(R, C3) >> 16u;
+        out2 = __SMUAD(C3, R);
+
+#endif /*      #ifndef ARM_MATH_BIG_ENDIAN     */
+
+        /* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */
+        /* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */
+        _SIMD32_OFFSET(pSrc16 + (2u * i3)) =
+          ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
+      }
+    }
+    /*  Twiddle coefficients index modifier */
+    twidCoefModifier <<= 2u;
+  }
+  /* end of middle stage process */
+
+
+  /* data is in 10.6(q6) format for the 1024 point */
+  /* data is in 8.8(q8) format for the 256 point */
+  /* data is in 6.10(q10) format for the 64 point */
+  /* data is in 4.12(q12) format for the 16 point */
+
+  /*  Initializations for the last stage */
+  j = fftLen >> 2;
+
+  ptr1 = &pSrc16[0];
+
+  /* start of last stage process */
+
+  /*  Butterfly implementation */
+  do
+  {
+    /* Read xa (real), ya(imag) input */
+    xaya = *__SIMD32(ptr1)++;
+
+    /* Read xb (real), yb(imag) input */
+    xbyb = *__SIMD32(ptr1)++;
+
+    /* Read xc (real), yc(imag) input */
+    xcyc = *__SIMD32(ptr1)++;
+
+    /* Read xd (real), yd(imag) input */
+    xdyd = *__SIMD32(ptr1)++;
+
+    /* R = packed((ya + yc), (xa + xc)) */
+    R = __QADD16(xaya, xcyc);
+
+    /* T = packed((yb + yd), (xb + xd)) */
+    T = __QADD16(xbyb, xdyd);
+
+    /* pointer updation for writing */
+    ptr1 = ptr1 - 8u;
+
+
+    /* xa' = xa + xb + xc + xd */
+    /* ya' = ya + yb + yc + yd */
+    *__SIMD32(ptr1)++ = __SHADD16(R, T);
+
+    /* T = packed((yb + yd), (xb + xd)) */
+    T = __QADD16(xbyb, xdyd);
+
+    /* xc' = (xa-xb+xc-xd) */
+    /* yc' = (ya-yb+yc-yd) */
+    *__SIMD32(ptr1)++ = __SHSUB16(R, T);
+
+    /* S = packed((ya - yc), (xa - xc)) */
+    S = __QSUB16(xaya, xcyc);
+
+    /* Read yd (real), xd(imag) input */
+    /* T = packed( (yb - yd), (xb - xd))  */
+    U = __QSUB16(xbyb, xdyd);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    /* xb' = (xa+yb-xc-yd) */
+    /* yb' = (ya-xb-yc+xd) */
+    *__SIMD32(ptr1)++ = __SHSAX(S, U);
+
+
+    /* xd' = (xa-yb-xc+yd) */
+    /* yd' = (ya+xb-yc-xd) */
+    *__SIMD32(ptr1)++ = __SHASX(S, U);
+
+#else
+
+    /* xb' = (xa+yb-xc-yd) */
+    /* yb' = (ya-xb-yc+xd) */
+    *__SIMD32(ptr1)++ = __SHASX(S, U);
+
+
+    /* xd' = (xa-yb-xc+yd) */
+    /* yd' = (ya+xb-yc-xd) */
+    *__SIMD32(ptr1)++ = __SHSAX(S, U);
+
+#endif /*      #ifndef ARM_MATH_BIG_ENDIAN     */
+
+  } while(--j);
+
+  /* end of last stage process */
+
+  /* output is in 11.5(q5) format for the 1024 point */
+  /* output is in 9.7(q7) format for the 256 point   */
+  /* output is in 7.9(q9) format for the 64 point  */
+  /* output is in 5.11(q11) format for the 16 point  */
+
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  q15_t R0, R1, S0, S1, T0, T1, U0, U1;
+  q15_t Co1, Si1, Co2, Si2, Co3, Si3, out1, out2;
+  uint32_t n1, n2, ic, i0, i1, i2, i3, j, k;
+
+  /* Total process is divided into three stages */
+
+  /* process first stage, middle stages, & last stage */
+
+  /*  Initializations for the first stage */
+  n2 = fftLen;
+  n1 = n2;
+
+  /* n2 = fftLen/4 */
+  n2 >>= 2u;
+
+  /* Index for twiddle coefficient */
+  ic = 0u;
+
+  /* Index for input read and output write */
+  i0 = 0u;
+  j = n2;
+
+  /* Input is in 1.15(q15) format */
+
+  /*  start of first stage process */
+  do
+  {
+    /*  Butterfly implementation */
+
+    /*  index calculation for the input as, */
+    /*  pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
+    i1 = i0 + n2;
+    i2 = i1 + n2;
+    i3 = i2 + n2;
+
+    /*  Reading i0, i0+fftLen/2 inputs */
+
+    /* input is down scale by 4 to avoid overflow */
+    /* Read ya (real), xa(imag) input */
+    T0 = pSrc16[i0 * 2u] >> 2u;
+    T1 = pSrc16[(i0 * 2u) + 1u] >> 2u;
+
+    /* input is down scale by 4 to avoid overflow */
+    /* Read yc (real), xc(imag) input */
+    S0 = pSrc16[i2 * 2u] >> 2u;
+    S1 = pSrc16[(i2 * 2u) + 1u] >> 2u;
+
+    /* R0 = (ya + yc) */
+    R0 = __SSAT(T0 + S0, 16u);
+    /* R1 = (xa + xc) */
+    R1 = __SSAT(T1 + S1, 16u);
+
+    /* S0 = (ya - yc) */
+    S0 = __SSAT(T0 - S0, 16);
+    /* S1 = (xa - xc) */
+    S1 = __SSAT(T1 - S1, 16);
+
+    /*  Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
+    /* input is down scale by 4 to avoid overflow */
+    /* Read yb (real), xb(imag) input */
+    T0 = pSrc16[i1 * 2u] >> 2u;
+    T1 = pSrc16[(i1 * 2u) + 1u] >> 2u;
+
+    /* input is down scale by 4 to avoid overflow */
+    /* Read yd (real), xd(imag) input */
+    U0 = pSrc16[i3 * 2u] >> 2u;
+    U1 = pSrc16[(i3 * 2u) + 1] >> 2u;
+
+    /* T0 = (yb + yd) */
+    T0 = __SSAT(T0 + U0, 16u);
+    /* T1 = (xb + xd) */
+    T1 = __SSAT(T1 + U1, 16u);
+
+    /*  writing the butterfly processed i0 sample */
+    /* ya' = ya + yb + yc + yd */
+    /* xa' = xa + xb + xc + xd */
+    pSrc16[i0 * 2u] = (R0 >> 1u) + (T0 >> 1u);
+    pSrc16[(i0 * 2u) + 1u] = (R1 >> 1u) + (T1 >> 1u);
+
+    /* R0 = (ya + yc) - (yb + yd) */
+    /* R1 = (xa + xc) - (xb + xd) */
+    R0 = __SSAT(R0 - T0, 16u);
+    R1 = __SSAT(R1 - T1, 16u);
+
+    /* co2 & si2 are read from Coefficient pointer */
+    Co2 = pCoef16[2u * ic * 2u];
+    Si2 = pCoef16[(2u * ic * 2u) + 1];
+
+    /* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
+    out1 = (short) ((Co2 * R0 + Si2 * R1) >> 16u);
+    /* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
+    out2 = (short) ((-Si2 * R0 + Co2 * R1) >> 16u);
+
+    /*  Reading i0+fftLen/4 */
+    /* input is down scale by 4 to avoid overflow */
+    /* T0 = yb, T1 =  xb */
+    T0 = pSrc16[i1 * 2u] >> 2;
+    T1 = pSrc16[(i1 * 2u) + 1] >> 2;
+
+    /* writing the butterfly processed i0 + fftLen/4 sample */
+    /* writing output(xc', yc') in little endian format */
+    pSrc16[i1 * 2u] = out1;
+    pSrc16[(i1 * 2u) + 1] = out2;
+
+    /*  Butterfly calculations */
+    /* input is down scale by 4 to avoid overflow */
+    /* U0 = yd, U1 = xd */
+    U0 = pSrc16[i3 * 2u] >> 2;
+    U1 = pSrc16[(i3 * 2u) + 1] >> 2;
+    /* T0 = yb-yd */
+    T0 = __SSAT(T0 - U0, 16);
+    /* T1 = xb-xd */
+    T1 = __SSAT(T1 - U1, 16);
+
+    /* R1 = (ya-yc) + (xb- xd),  R0 = (xa-xc) - (yb-yd)) */
+    R0 = (short) __SSAT((q31_t) (S0 - T1), 16);
+    R1 = (short) __SSAT((q31_t) (S1 + T0), 16);
+
+    /* S1 = (ya-yc) - (xb- xd), S0 = (xa-xc) + (yb-yd)) */
+    S0 = (short) __SSAT(((q31_t) S0 + T1), 16u);
+    S1 = (short) __SSAT(((q31_t) S1 - T0), 16u);
+
+    /* co1 & si1 are read from Coefficient pointer */
+    Co1 = pCoef16[ic * 2u];
+    Si1 = pCoef16[(ic * 2u) + 1];
+    /*  Butterfly process for the i0+fftLen/2 sample */
+    /* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
+    out1 = (short) ((Si1 * S1 + Co1 * S0) >> 16);
+    /* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
+    out2 = (short) ((-Si1 * S0 + Co1 * S1) >> 16);
+
+    /* writing output(xb', yb') in little endian format */
+    pSrc16[i2 * 2u] = out1;
+    pSrc16[(i2 * 2u) + 1] = out2;
+
+    /* Co3 & si3 are read from Coefficient pointer */
+    Co3 = pCoef16[3u * (ic * 2u)];
+    Si3 = pCoef16[(3u * (ic * 2u)) + 1];
+    /*  Butterfly process for the i0+3fftLen/4 sample */
+    /* xd' = (xa-yb-xc+yd)* Co3 + (ya+xb-yc-xd)* (si3) */
+    out1 = (short) ((Si3 * R1 + Co3 * R0) >> 16u);
+    /* yd' = (ya+xb-yc-xd)* Co3 - (xa-yb-xc+yd)* (si3) */
+    out2 = (short) ((-Si3 * R0 + Co3 * R1) >> 16u);
+    /* writing output(xd', yd') in little endian format */
+    pSrc16[i3 * 2u] = out1;
+    pSrc16[(i3 * 2u) + 1] = out2;
+
+    /*  Twiddle coefficients index modifier */
+    ic = ic + twidCoefModifier;
+
+    /*  Updating input index */
+    i0 = i0 + 1u;
+
+  } while(--j);
+  /* data is in 4.11(q11) format */
+
+  /* end of first stage process */
+
+
+  /* start of middle stage process */
+
+  /*  Twiddle coefficients index modifier */
+  twidCoefModifier <<= 2u;
+
+  /*  Calculation of Middle stage */
+  for (k = fftLen / 4u; k > 4u; k >>= 2u)
+  {
+    /*  Initializations for the middle stage */
+    n1 = n2;
+    n2 >>= 2u;
+    ic = 0u;
+
+    for (j = 0u; j <= (n2 - 1u); j++)
+    {
+      /*  index calculation for the coefficients */
+      Co1 = pCoef16[ic * 2u];
+      Si1 = pCoef16[(ic * 2u) + 1u];
+      Co2 = pCoef16[2u * (ic * 2u)];
+      Si2 = pCoef16[(2u * (ic * 2u)) + 1u];
+      Co3 = pCoef16[3u * (ic * 2u)];
+      Si3 = pCoef16[(3u * (ic * 2u)) + 1u];
+
+      /*  Twiddle coefficients index modifier */
+      ic = ic + twidCoefModifier;
+
+      /*  Butterfly implementation */
+      for (i0 = j; i0 < fftLen; i0 += n1)
+      {
+        /*  index calculation for the input as, */
+        /*  pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
+        i1 = i0 + n2;
+        i2 = i1 + n2;
+        i3 = i2 + n2;
+
+        /*  Reading i0, i0+fftLen/2 inputs */
+        /* Read ya (real), xa(imag) input */
+        T0 = pSrc16[i0 * 2u];
+        T1 = pSrc16[(i0 * 2u) + 1u];
+
+        /* Read yc (real), xc(imag) input */
+        S0 = pSrc16[i2 * 2u];
+        S1 = pSrc16[(i2 * 2u) + 1u];
+
+        /* R0 = (ya + yc), R1 = (xa + xc) */
+        R0 = __SSAT(T0 + S0, 16);
+        R1 = __SSAT(T1 + S1, 16);
+
+        /* S0 = (ya - yc), S1 =(xa - xc) */
+        S0 = __SSAT(T0 - S0, 16);
+        S1 = __SSAT(T1 - S1, 16);
+
+        /*  Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
+        /* Read yb (real), xb(imag) input */
+        T0 = pSrc16[i1 * 2u];
+        T1 = pSrc16[(i1 * 2u) + 1u];
+
+        /* Read yd (real), xd(imag) input */
+        U0 = pSrc16[i3 * 2u];
+        U1 = pSrc16[(i3 * 2u) + 1u];
+
+
+        /* T0 = (yb + yd), T1 = (xb + xd) */
+        T0 = __SSAT(T0 + U0, 16);
+        T1 = __SSAT(T1 + U1, 16);
+
+        /*  writing the butterfly processed i0 sample */
+
+        /* xa' = xa + xb + xc + xd */
+        /* ya' = ya + yb + yc + yd */
+        out1 = ((R0 >> 1u) + (T0 >> 1u)) >> 1u;
+        out2 = ((R1 >> 1u) + (T1 >> 1u)) >> 1u;
+
+        pSrc16[i0 * 2u] = out1;
+        pSrc16[(2u * i0) + 1u] = out2;
+
+        /* R0 = (ya + yc) - (yb + yd), R1 = (xa + xc) - (xb + xd) */
+        R0 = (R0 >> 1u) - (T0 >> 1u);
+        R1 = (R1 >> 1u) - (T1 >> 1u);
+
+        /* (ya-yb+yc-yd)* (si2) + (xa-xb+xc-xd)* co2 */
+        out1 = (short) ((Co2 * R0 + Si2 * R1) >> 16u);
+
+        /* (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
+        out2 = (short) ((-Si2 * R0 + Co2 * R1) >> 16u);
+
+        /*  Reading i0+3fftLen/4 */
+        /* Read yb (real), xb(imag) input */
+        T0 = pSrc16[i1 * 2u];
+        T1 = pSrc16[(i1 * 2u) + 1u];
+
+        /*  writing the butterfly processed i0 + fftLen/4 sample */
+        /* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
+        /* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
+        pSrc16[i1 * 2u] = out1;
+        pSrc16[(i1 * 2u) + 1u] = out2;
+
+        /*  Butterfly calculations */
+
+        /* Read yd (real), xd(imag) input */
+        U0 = pSrc16[i3 * 2u];
+        U1 = pSrc16[(i3 * 2u) + 1u];
+
+        /* T0 = yb-yd, T1 = xb-xd */
+        T0 = __SSAT(T0 - U0, 16);
+        T1 = __SSAT(T1 - U1, 16);
+
+        /* R0 = (ya-yc) + (xb- xd), R1 = (xa-xc) - (yb-yd)) */
+        R0 = (S0 >> 1u) - (T1 >> 1u);
+        R1 = (S1 >> 1u) + (T0 >> 1u);
+
+        /* S0 = (ya-yc) - (xb- xd), S1 = (xa-xc) + (yb-yd)) */
+        S0 = (S0 >> 1u) + (T1 >> 1u);
+        S1 = (S1 >> 1u) - (T0 >> 1u);
+
+        /*  Butterfly process for the i0+fftLen/2 sample */
+        out1 = (short) ((Co1 * S0 + Si1 * S1) >> 16u);
+
+        out2 = (short) ((-Si1 * S0 + Co1 * S1) >> 16u);
+
+        /* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
+        /* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
+        pSrc16[i2 * 2u] = out1;
+        pSrc16[(i2 * 2u) + 1u] = out2;
+
+        /*  Butterfly process for the i0+3fftLen/4 sample */
+        out1 = (short) ((Si3 * R1 + Co3 * R0) >> 16u);
+
+        out2 = (short) ((-Si3 * R0 + Co3 * R1) >> 16u);
+        /* xd' = (xa-yb-xc+yd)* Co3 + (ya+xb-yc-xd)* (si3) */
+        /* yd' = (ya+xb-yc-xd)* Co3 - (xa-yb-xc+yd)* (si3) */
+        pSrc16[i3 * 2u] = out1;
+        pSrc16[(i3 * 2u) + 1u] = out2;
+      }
+    }
+    /*  Twiddle coefficients index modifier */
+    twidCoefModifier <<= 2u;
+  }
+  /* end of middle stage process */
+
+
+  /* data is in 10.6(q6) format for the 1024 point */
+  /* data is in 8.8(q8) format for the 256 point */
+  /* data is in 6.10(q10) format for the 64 point */
+  /* data is in 4.12(q12) format for the 16 point */
+
+  /*  Initializations for the last stage */
+  n1 = n2;
+  n2 >>= 2u;
+
+  /* start of last stage process */
+
+  /*  Butterfly implementation */
+  for (i0 = 0u; i0 <= (fftLen - n1); i0 += n1)
+  {
+    /*  index calculation for the input as, */
+    /*  pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
+    i1 = i0 + n2;
+    i2 = i1 + n2;
+    i3 = i2 + n2;
+
+    /*  Reading i0, i0+fftLen/2 inputs */
+    /* Read ya (real), xa(imag) input */
+    T0 = pSrc16[i0 * 2u];
+    T1 = pSrc16[(i0 * 2u) + 1u];
+
+    /* Read yc (real), xc(imag) input */
+    S0 = pSrc16[i2 * 2u];
+    S1 = pSrc16[(i2 * 2u) + 1u];
+
+    /* R0 = (ya + yc), R1 = (xa + xc) */
+    R0 = __SSAT(T0 + S0, 16u);
+    R1 = __SSAT(T1 + S1, 16u);
+
+    /* S0 = (ya - yc), S1 = (xa - xc) */
+    S0 = __SSAT(T0 - S0, 16u);
+    S1 = __SSAT(T1 - S1, 16u);
+
+    /*  Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
+    /* Read yb (real), xb(imag) input */
+    T0 = pSrc16[i1 * 2u];
+    T1 = pSrc16[(i1 * 2u) + 1u];
+    /* Read yd (real), xd(imag) input */
+    U0 = pSrc16[i3 * 2u];
+    U1 = pSrc16[(i3 * 2u) + 1u];
+
+    /* T0 = (yb + yd), T1 = (xb + xd)) */
+    T0 = __SSAT(T0 + U0, 16u);
+    T1 = __SSAT(T1 + U1, 16u);
+
+    /*  writing the butterfly processed i0 sample */
+    /* xa' = xa + xb + xc + xd */
+    /* ya' = ya + yb + yc + yd */
+    pSrc16[i0 * 2u] = (R0 >> 1u) + (T0 >> 1u);
+    pSrc16[(i0 * 2u) + 1u] = (R1 >> 1u) + (T1 >> 1u);
+
+    /* R0 = (ya + yc) - (yb + yd), R1 = (xa + xc) - (xb + xd) */
+    R0 = (R0 >> 1u) - (T0 >> 1u);
+    R1 = (R1 >> 1u) - (T1 >> 1u);
+    /* Read yb (real), xb(imag) input */
+    T0 = pSrc16[i1 * 2u];
+    T1 = pSrc16[(i1 * 2u) + 1u];
+
+    /*  writing the butterfly processed i0 + fftLen/4 sample */
+    /* xc' = (xa-xb+xc-xd) */
+    /* yc' = (ya-yb+yc-yd) */
+    pSrc16[i1 * 2u] = R0;
+    pSrc16[(i1 * 2u) + 1u] = R1;
+
+    /* Read yd (real), xd(imag) input */
+    U0 = pSrc16[i3 * 2u];
+    U1 = pSrc16[(i3 * 2u) + 1u];
+    /* T0 = (yb - yd), T1 = (xb - xd)  */
+    T0 = __SSAT(T0 - U0, 16u);
+    T1 = __SSAT(T1 - U1, 16u);
+
+    /*  writing the butterfly processed i0 + fftLen/2 sample */
+    /* xb' = (xa+yb-xc-yd) */
+    /* yb' = (ya-xb-yc+xd) */
+    pSrc16[i2 * 2u] = (S0 >> 1u) + (T1 >> 1u);
+    pSrc16[(i2 * 2u) + 1u] = (S1 >> 1u) - (T0 >> 1u);
+
+    /*  writing the butterfly processed i0 + 3fftLen/4 sample */
+    /* xd' = (xa-yb-xc+yd) */
+    /* yd' = (ya+xb-yc-xd) */
+    pSrc16[i3 * 2u] = (S0 >> 1u) - (T1 >> 1u);
+    pSrc16[(i3 * 2u) + 1u] = (S1 >> 1u) + (T0 >> 1u);
+
+  }
+
+  /* end of last stage process */
+
+  /* output is in 11.5(q5) format for the 1024 point */
+  /* output is in 9.7(q7) format for the 256 point   */
+  /* output is in 7.9(q9) format for the 64 point  */
+  /* output is in 5.11(q11) format for the 16 point  */
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
+
+
+/**    
+ * @brief  Core function for the Q15 CIFFT butterfly process.   
+ * @param[in, out] *pSrc16          points to the in-place buffer of Q15 data type.   
+ * @param[in]      fftLen           length of the FFT.   
+ * @param[in]      *pCoef16         points to twiddle coefficient buffer.   
+ * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.   
+ * @return none.   
+ */
+
+/*    
+* Radix-4 IFFT algorithm used is :    
+*    
+* CIFFT uses same twiddle coefficients as CFFT function    
+*  x[k] = x[n] + (j)k * x[n + fftLen/4] + (-1)k * x[n+fftLen/2] + (-j)k * x[n+3*fftLen/4]    
+*    
+*    
+* IFFT is implemented with following changes in equations from FFT    
+*    
+* Input real and imaginary data:    
+* x(n) = xa + j * ya    
+* x(n+N/4 ) = xb + j * yb    
+* x(n+N/2 ) = xc + j * yc    
+* x(n+3N 4) = xd + j * yd    
+*    
+*    
+* Output real and imaginary data:    
+* x(4r) = xa'+ j * ya'    
+* x(4r+1) = xb'+ j * yb'    
+* x(4r+2) = xc'+ j * yc'    
+* x(4r+3) = xd'+ j * yd'    
+*    
+*    
+* Twiddle factors for radix-4 IFFT:    
+* Wn = co1 + j * (si1)    
+* W2n = co2 + j * (si2)    
+* W3n = co3 + j * (si3)    
+    
+* The real and imaginary output values for the radix-4 butterfly are    
+* xa' = xa + xb + xc + xd    
+* ya' = ya + yb + yc + yd    
+* xb' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1)    
+* yb' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1)    
+* xc' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2)    
+* yc' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2)    
+* xd' = (xa+yb-xc-yd)* co3 - (ya-xb-yc+xd)* (si3)    
+* yd' = (ya-xb-yc+xd)* co3 + (xa+yb-xc-yd)* (si3)    
+*    
+*/
+
+void arm_radix4_butterfly_inverse_q15(
+  q15_t * pSrc16,
+  uint32_t fftLen,
+  q15_t * pCoef16,
+  uint32_t twidCoefModifier)
+{
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q31_t R, S, T, U;
+  q31_t C1, C2, C3, out1, out2;
+  uint32_t n1, n2, ic, i0, i1, i2, i3, j, k;
+  q15_t in;
+
+  q15_t *ptr1;
+
+
+
+  q31_t xaya, xbyb, xcyc, xdyd;
+
+  /* Total process is divided into three stages */
+
+  /* process first stage, middle stages, & last stage */
+
+  /*  Initializations for the first stage */
+  n2 = fftLen;
+  n1 = n2;
+
+  /* n2 = fftLen/4 */
+  n2 >>= 2u;
+
+  /* Index for twiddle coefficient */
+  ic = 0u;
+
+  /* Index for input read and output write */
+  i0 = 0u;
+  j = n2;
+
+  /* Input is in 1.15(q15) format */
+
+  /*  start of first stage process */
+  do
+  {
+    /*  Butterfly implementation */
+
+    /*  index calculation for the input as, */
+    /*  pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
+    i1 = i0 + n2;
+    i2 = i1 + n2;
+    i3 = i2 + n2;
+
+    /*  Reading i0, i0+fftLen/2 inputs */
+    /* Read ya (real), xa(imag) input */
+    T = _SIMD32_OFFSET(pSrc16 + (2u * i0));
+    in = ((int16_t) (T & 0xFFFF)) >> 2;
+    T = ((T >> 2) & 0xFFFF0000) | (in & 0xFFFF);
+
+    /* Read yc (real), xc(imag) input */
+    S = _SIMD32_OFFSET(pSrc16 + (2u * i2));
+    in = ((int16_t) (S & 0xFFFF)) >> 2;
+    S = ((S >> 2) & 0xFFFF0000) | (in & 0xFFFF);
+
+    /* R = packed((ya + yc), (xa + xc) ) */
+    R = __QADD16(T, S);
+
+    /* S = packed((ya - yc), (xa - xc) ) */
+    S = __QSUB16(T, S);
+
+    /*  Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
+    /* Read yb (real), xb(imag) input */
+    T = _SIMD32_OFFSET(pSrc16 + (2u * i1));
+    in = ((int16_t) (T & 0xFFFF)) >> 2;
+    T = ((T >> 2) & 0xFFFF0000) | (in & 0xFFFF);
+
+    /* Read yd (real), xd(imag) input */
+    U = _SIMD32_OFFSET(pSrc16 + (2u * i3));
+    in = ((int16_t) (U & 0xFFFF)) >> 2;
+    U = ((U >> 2) & 0xFFFF0000) | (in & 0xFFFF);
+
+    /* T = packed((yb + yd), (xb + xd) ) */
+    T = __QADD16(T, U);
+
+    /*  writing the butterfly processed i0 sample */
+    /* xa' = xa + xb + xc + xd */
+    /* ya' = ya + yb + yc + yd */
+    _SIMD32_OFFSET(pSrc16 + (2u * i0)) = __SHADD16(R, T);
+
+    /* R = packed((ya + yc) - (yb + yd), (xa + xc)- (xb + xd)) */
+    R = __QSUB16(R, T);
+
+    /* co2 & si2 are read from SIMD Coefficient pointer */
+    C2 = _SIMD32_OFFSET(pCoef16 + (4u * ic));
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    /* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
+    out1 = __SMUSD(C2, R) >> 16u;
+    /* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
+    out2 = __SMUADX(C2, R);
+
+#else
+
+    /* xc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
+    out1 = __SMUADX(C2, R) >> 16u;
+    /* yc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
+    out2 = __SMUSD(__QSUB16(0, C2), R);
+
+#endif /*      #ifndef ARM_MATH_BIG_ENDIAN     */
+
+    /*  Reading i0+fftLen/4 */
+    /* T = packed(yb, xb) */
+    T = _SIMD32_OFFSET(pSrc16 + (2u * i1));
+    in = ((int16_t) (T & 0xFFFF)) >> 2;
+    T = ((T >> 2) & 0xFFFF0000) | (in & 0xFFFF);
+
+    /* writing the butterfly processed i0 + fftLen/4 sample */
+    /* writing output(xc', yc') in little endian format */
+    _SIMD32_OFFSET(pSrc16 + (2u * i1)) =
+      (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
+
+    /*  Butterfly calculations */
+    /* U = packed(yd, xd) */
+    U = _SIMD32_OFFSET(pSrc16 + (2u * i3));
+    in = ((int16_t) (U & 0xFFFF)) >> 2;
+    U = ((U >> 2) & 0xFFFF0000) | (in & 0xFFFF);
+
+    /* T = packed(yb-yd, xb-xd) */
+    T = __QSUB16(T, U);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    /* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
+    R = __QSAX(S, T);
+    /* S = packed((ya-yc) + (xb- xd),  (xa-xc) - (yb-yd)) */
+    S = __QASX(S, T);
+
+#else
+
+    /* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
+    R = __QASX(S, T);
+    /* S = packed((ya-yc) - (xb- xd),  (xa-xc) + (yb-yd)) */
+    S = __QSAX(S, T);
+
+#endif /*      #ifndef ARM_MATH_BIG_ENDIAN     */
+
+    /* co1 & si1 are read from SIMD Coefficient pointer */
+    C1 = _SIMD32_OFFSET(pCoef16 + (2u * ic));
+    /*  Butterfly process for the i0+fftLen/2 sample */
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    /* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
+    out1 = __SMUSD(C1, S) >> 16u;
+    /* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
+    out2 = __SMUADX(C1, S);
+
+#else
+
+    /* xb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
+    out1 = __SMUADX(C1, S) >> 16u;
+    /* yb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
+    out2 = __SMUSD(__QSUB16(0, C1), S);
+
+#endif /*      #ifndef ARM_MATH_BIG_ENDIAN     */
+
+    /* writing output(xb', yb') in little endian format */
+    _SIMD32_OFFSET(pSrc16 + (2u * i2)) =
+      ((out2) & 0xFFFF0000) | ((out1) & 0x0000FFFF);
+
+
+    /* co3 & si3 are read from SIMD Coefficient pointer */
+    C3 = _SIMD32_OFFSET(pCoef16 + (6u * ic));
+    /*  Butterfly process for the i0+3fftLen/4 sample */
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    /* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */
+    out1 = __SMUSD(C3, R) >> 16u;
+    /* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */
+    out2 = __SMUADX(C3, R);
+
+#else
+
+    /* xd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */
+    out1 = __SMUADX(C3, R) >> 16u;
+    /* yd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */
+    out2 = __SMUSD(__QSUB16(0, C3), R);
+
+#endif /*      #ifndef ARM_MATH_BIG_ENDIAN     */
+
+    /* writing output(xd', yd') in little endian format */
+    _SIMD32_OFFSET(pSrc16 + (2u * i3)) =
+      ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
+
+    /*  Twiddle coefficients index modifier */
+    ic = ic + twidCoefModifier;
+
+    /*  Updating input index */
+    i0 = i0 + 1u;
+
+  } while(--j);
+  /* data is in 4.11(q11) format */
+
+  /* end of first stage process */
+
+
+  /* start of middle stage process */
+
+  /*  Twiddle coefficients index modifier */
+  twidCoefModifier <<= 2u;
+
+  /*  Calculation of Middle stage */
+  for (k = fftLen / 4u; k > 4u; k >>= 2u)
+  {
+    /*  Initializations for the middle stage */
+    n1 = n2;
+    n2 >>= 2u;
+    ic = 0u;
+
+    for (j = 0u; j <= (n2 - 1u); j++)
+    {
+      /*  index calculation for the coefficients */
+      C1 = _SIMD32_OFFSET(pCoef16 + (2u * ic));
+      C2 = _SIMD32_OFFSET(pCoef16 + (4u * ic));
+      C3 = _SIMD32_OFFSET(pCoef16 + (6u * ic));
+
+      /*  Twiddle coefficients index modifier */
+      ic = ic + twidCoefModifier;
+
+      /*  Butterfly implementation */
+      for (i0 = j; i0 < fftLen; i0 += n1)
+      {
+        /*  index calculation for the input as, */
+        /*  pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
+        i1 = i0 + n2;
+        i2 = i1 + n2;
+        i3 = i2 + n2;
+
+        /*  Reading i0, i0+fftLen/2 inputs */
+        /* Read ya (real), xa(imag) input */
+        T = _SIMD32_OFFSET(pSrc16 + (2u * i0));
+
+        /* Read yc (real), xc(imag) input */
+        S = _SIMD32_OFFSET(pSrc16 + (2u * i2));
+
+        /* R = packed( (ya + yc), (xa + xc)) */
+        R = __QADD16(T, S);
+
+        /* S = packed((ya - yc), (xa - xc)) */
+        S = __QSUB16(T, S);
+
+        /*  Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
+        /* Read yb (real), xb(imag) input */
+        T = _SIMD32_OFFSET(pSrc16 + (2u * i1));
+
+        /* Read yd (real), xd(imag) input */
+        U = _SIMD32_OFFSET(pSrc16 + (2u * i3));
+
+        /* T = packed( (yb + yd), (xb + xd)) */
+        T = __QADD16(T, U);
+
+        /*  writing the butterfly processed i0 sample */
+
+        /* xa' = xa + xb + xc + xd */
+        /* ya' = ya + yb + yc + yd */
+        out1 = __SHADD16(R, T);
+        in = ((int16_t) (out1 & 0xFFFF)) >> 1;
+        out1 = ((out1 >> 1) & 0xFFFF0000) | (in & 0xFFFF);
+        _SIMD32_OFFSET(pSrc16 + (2u * i0)) = out1;
+
+        /* R = packed( (ya + yc) - (yb + yd), (xa + xc) - (xb + xd)) */
+        R = __SHSUB16(R, T);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+        /* (ya-yb+yc-yd)* (si2) + (xa-xb+xc-xd)* co2 */
+        out1 = __SMUSD(C2, R) >> 16u;
+
+        /* (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
+        out2 = __SMUADX(C2, R);
+
+#else
+
+        /* (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
+        out1 = __SMUADX(R, C2) >> 16u;
+
+        /* (ya-yb+yc-yd)* (si2) + (xa-xb+xc-xd)* co2 */
+        out2 = __SMUSD(__QSUB16(0, C2), R);
+
+#endif /*      #ifndef ARM_MATH_BIG_ENDIAN     */
+
+        /*  Reading i0+3fftLen/4 */
+        /* Read yb (real), xb(imag) input */
+        T = _SIMD32_OFFSET(pSrc16 + (2u * i1));
+
+        /*  writing the butterfly processed i0 + fftLen/4 sample */
+        /* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
+        /* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
+        _SIMD32_OFFSET(pSrc16 + (2u * i1)) =
+          ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
+
+        /*  Butterfly calculations */
+
+        /* Read yd (real), xd(imag) input */
+        U = _SIMD32_OFFSET(pSrc16 + (2u * i3));
+
+        /* T = packed(yb-yd, xb-xd) */
+        T = __QSUB16(T, U);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+        /* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
+        R = __SHSAX(S, T);
+
+        /* S = packed((ya-yc) - (xb- xd),  (xa-xc) + (yb-yd)) */
+        S = __SHASX(S, T);
+
+
+        /*  Butterfly process for the i0+fftLen/2 sample */
+        out1 = __SMUSD(C1, S) >> 16u;
+        out2 = __SMUADX(C1, S);
+
+#else
+
+        /* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
+        R = __SHASX(S, T);
+
+        /* S = packed((ya-yc) - (xb- xd),  (xa-xc) + (yb-yd)) */
+        S = __SHSAX(S, T);
+
+
+        /*  Butterfly process for the i0+fftLen/2 sample */
+        out1 = __SMUADX(S, C1) >> 16u;
+        out2 = __SMUSD(__QSUB16(0, C1), S);
+
+#endif /*      #ifndef ARM_MATH_BIG_ENDIAN     */
+
+        /* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
+        /* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
+        _SIMD32_OFFSET(pSrc16 + (2u * i2)) =
+          ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
+
+        /*  Butterfly process for the i0+3fftLen/4 sample */
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+        out1 = __SMUSD(C3, R) >> 16u;
+        out2 = __SMUADX(C3, R);
+
+#else
+
+        out1 = __SMUADX(C3, R) >> 16u;
+        out2 = __SMUSD(__QSUB16(0, C3), R);
+
+#endif /*      #ifndef ARM_MATH_BIG_ENDIAN     */
+
+        /* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */
+        /* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */
+        _SIMD32_OFFSET(pSrc16 + (2u * i3)) =
+          ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
+      }
+    }
+    /*  Twiddle coefficients index modifier */
+    twidCoefModifier <<= 2u;
+  }
+  /* end of middle stage process */
+
+  /* data is in 10.6(q6) format for the 1024 point */
+  /* data is in 8.8(q8) format for the 256 point */
+  /* data is in 6.10(q10) format for the 64 point */
+  /* data is in 4.12(q12) format for the 16 point */
+
+  /*  Initializations for the last stage */
+  j = fftLen >> 2;
+
+  ptr1 = &pSrc16[0];
+
+  /* start of last stage process */
+
+  /*  Butterfly implementation */
+  do
+  {
+    /* Read xa (real), ya(imag) input */
+    xaya = *__SIMD32(ptr1)++;
+
+    /* Read xb (real), yb(imag) input */
+    xbyb = *__SIMD32(ptr1)++;
+
+    /* Read xc (real), yc(imag) input */
+    xcyc = *__SIMD32(ptr1)++;
+
+    /* Read xd (real), yd(imag) input */
+    xdyd = *__SIMD32(ptr1)++;
+
+    /* R = packed((ya + yc), (xa + xc)) */
+    R = __QADD16(xaya, xcyc);
+
+    /* T = packed((yb + yd), (xb + xd)) */
+    T = __QADD16(xbyb, xdyd);
+
+    /* pointer updation for writing */
+    ptr1 = ptr1 - 8u;
+
+
+    /* xa' = xa + xb + xc + xd */
+    /* ya' = ya + yb + yc + yd */
+    *__SIMD32(ptr1)++ = __SHADD16(R, T);
+
+    /* T = packed((yb + yd), (xb + xd)) */
+    T = __QADD16(xbyb, xdyd);
+
+    /* xc' = (xa-xb+xc-xd) */
+    /* yc' = (ya-yb+yc-yd) */
+    *__SIMD32(ptr1)++ = __SHSUB16(R, T);
+
+    /* S = packed((ya - yc), (xa - xc)) */
+    S = __QSUB16(xaya, xcyc);
+
+    /* Read yd (real), xd(imag) input */
+    /* T = packed( (yb - yd), (xb - xd))  */
+    U = __QSUB16(xbyb, xdyd);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    /* xb' = (xa+yb-xc-yd) */
+    /* yb' = (ya-xb-yc+xd) */
+    *__SIMD32(ptr1)++ = __SHASX(S, U);
+
+
+    /* xd' = (xa-yb-xc+yd) */
+    /* yd' = (ya+xb-yc-xd) */
+    *__SIMD32(ptr1)++ = __SHSAX(S, U);
+
+#else
+
+    /* xb' = (xa+yb-xc-yd) */
+    /* yb' = (ya-xb-yc+xd) */
+    *__SIMD32(ptr1)++ = __SHSAX(S, U);
+
+
+    /* xd' = (xa-yb-xc+yd) */
+    /* yd' = (ya+xb-yc-xd) */
+    *__SIMD32(ptr1)++ = __SHASX(S, U);
+
+
+#endif /*      #ifndef ARM_MATH_BIG_ENDIAN     */
+
+  } while(--j);
+
+  /* end of last stage  process */
+
+  /* output is in 11.5(q5) format for the 1024 point */
+  /* output is in 9.7(q7) format for the 256 point   */
+  /* output is in 7.9(q9) format for the 64 point  */
+  /* output is in 5.11(q11) format for the 16 point  */
+
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  q15_t R0, R1, S0, S1, T0, T1, U0, U1;
+  q15_t Co1, Si1, Co2, Si2, Co3, Si3, out1, out2;
+  uint32_t n1, n2, ic, i0, i1, i2, i3, j, k;
+
+  /* Total process is divided into three stages */
+
+  /* process first stage, middle stages, & last stage */
+
+  /*  Initializations for the first stage */
+  n2 = fftLen;
+  n1 = n2;
+
+  /* n2 = fftLen/4 */
+  n2 >>= 2u;
+
+  /* Index for twiddle coefficient */
+  ic = 0u;
+
+  /* Index for input read and output write */
+  i0 = 0u;
+
+  j = n2;
+
+  /* Input is in 1.15(q15) format */
+
+  /*  Start of first stage process */
+  do
+  {
+    /*  Butterfly implementation */
+
+    /*  index calculation for the input as, */
+    /*  pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
+    i1 = i0 + n2;
+    i2 = i1 + n2;
+    i3 = i2 + n2;
+
+    /*  Reading i0, i0+fftLen/2 inputs */
+    /* input is down scale by 4 to avoid overflow */
+    /* Read ya (real), xa(imag) input */
+    T0 = pSrc16[i0 * 2u] >> 2u;
+    T1 = pSrc16[(i0 * 2u) + 1u] >> 2u;
+    /* input is down scale by 4 to avoid overflow */
+    /* Read yc (real), xc(imag) input */
+    S0 = pSrc16[i2 * 2u] >> 2u;
+    S1 = pSrc16[(i2 * 2u) + 1u] >> 2u;
+
+    /* R0 = (ya + yc), R1 = (xa + xc) */
+    R0 = __SSAT(T0 + S0, 16u);
+    R1 = __SSAT(T1 + S1, 16u);
+    /* S0 = (ya - yc), S1 = (xa - xc) */
+    S0 = __SSAT(T0 - S0, 16u);
+    S1 = __SSAT(T1 - S1, 16u);
+
+    /*  Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
+    /* input is down scale by 4 to avoid overflow */
+    /* Read yb (real), xb(imag) input */
+    T0 = pSrc16[i1 * 2u] >> 2u;
+    T1 = pSrc16[(i1 * 2u) + 1u] >> 2u;
+    /* Read yd (real), xd(imag) input */
+    /* input is down scale by 4 to avoid overflow */
+    U0 = pSrc16[i3 * 2u] >> 2u;
+    U1 = pSrc16[(i3 * 2u) + 1u] >> 2u;
+
+    /* T0 = (yb + yd), T1 = (xb + xd) */
+    T0 = __SSAT(T0 + U0, 16u);
+    T1 = __SSAT(T1 + U1, 16u);
+
+    /*  writing the butterfly processed i0 sample */
+    /* xa' = xa + xb + xc + xd */
+    /* ya' = ya + yb + yc + yd */
+    pSrc16[i0 * 2u] = (R0 >> 1u) + (T0 >> 1u);
+    pSrc16[(i0 * 2u) + 1u] = (R1 >> 1u) + (T1 >> 1u);
+
+    /* R0 = (ya + yc) - (yb + yd), R1 = (xa + xc)- (xb + xd) */
+    R0 = __SSAT(R0 - T0, 16u);
+    R1 = __SSAT(R1 - T1, 16u);
+    /* co2 & si2 are read from Coefficient pointer */
+    Co2 = pCoef16[2u * ic * 2u];
+    Si2 = pCoef16[(2u * ic * 2u) + 1u];
+    /* xc' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2) */
+    out1 = (short) ((Co2 * R0 - Si2 * R1) >> 16u);
+    /* yc' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2) */
+    out2 = (short) ((Si2 * R0 + Co2 * R1) >> 16u);
+
+    /*  Reading i0+fftLen/4 */
+    /* input is down scale by 4 to avoid overflow */
+    /* T0 = yb, T1 = xb */
+    T0 = pSrc16[i1 * 2u] >> 2u;
+    T1 = pSrc16[(i1 * 2u) + 1u] >> 2u;
+
+    /* writing the butterfly processed i0 + fftLen/4 sample */
+    /* writing output(xc', yc') in little endian format */
+    pSrc16[i1 * 2u] = out1;
+    pSrc16[(i1 * 2u) + 1u] = out2;
+
+    /*  Butterfly calculations */
+    /* input is down scale by 4 to avoid overflow */
+    /* U0 = yd, U1 = xd) */
+    U0 = pSrc16[i3 * 2u] >> 2u;
+    U1 = pSrc16[(i3 * 2u) + 1u] >> 2u;
+
+    /* T0 = yb-yd, T1 = xb-xd) */
+    T0 = __SSAT(T0 - U0, 16u);
+    T1 = __SSAT(T1 - U1, 16u);
+    /* R0 = (ya-yc) - (xb- xd) , R1 = (xa-xc) + (yb-yd) */
+    R0 = (short) __SSAT((q31_t) (S0 + T1), 16);
+    R1 = (short) __SSAT((q31_t) (S1 - T0), 16);
+    /* S = (ya-yc) + (xb- xd), S1 = (xa-xc) - (yb-yd) */
+    S0 = (short) __SSAT((q31_t) (S0 - T1), 16);
+    S1 = (short) __SSAT((q31_t) (S1 + T0), 16);
+
+    /* co1 & si1 are read from Coefficient pointer */
+    Co1 = pCoef16[ic * 2u];
+    Si1 = pCoef16[(ic * 2u) + 1u];
+    /*  Butterfly process for the i0+fftLen/2 sample */
+    /* xb' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1) */
+    out1 = (short) ((Co1 * S0 - Si1 * S1) >> 16u);
+    /* yb' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1) */
+    out2 = (short) ((Si1 * S0 + Co1 * S1) >> 16u);
+    /* writing output(xb', yb') in little endian format */
+    pSrc16[i2 * 2u] = out1;
+    pSrc16[(i2 * 2u) + 1u] = out2;
+
+    /* Co3 & si3 are read from Coefficient pointer */
+    Co3 = pCoef16[3u * ic * 2u];
+    Si3 = pCoef16[(3u * ic * 2u) + 1u];
+    /*  Butterfly process for the i0+3fftLen/4 sample */
+    /* xd' = (xa+yb-xc-yd)* Co3 - (ya-xb-yc+xd)* (si3) */
+    out1 = (short) ((Co3 * R0 - Si3 * R1) >> 16u);
+    /* yd' = (ya-xb-yc+xd)* Co3 + (xa+yb-xc-yd)* (si3) */
+    out2 = (short) ((Si3 * R0 + Co3 * R1) >> 16u);
+    /* writing output(xd', yd') in little endian format */
+    pSrc16[i3 * 2u] = out1;
+    pSrc16[(i3 * 2u) + 1u] = out2;
+
+    /*  Twiddle coefficients index modifier */
+    ic = ic + twidCoefModifier;
+
+    /*  Updating input index */
+    i0 = i0 + 1u;
+
+  } while(--j);
+
+  /*  End of first stage process */
+
+  /* data is in 4.11(q11) format */
+
+
+  /*  Start of Middle stage process */
+
+  /*  Twiddle coefficients index modifier */
+  twidCoefModifier <<= 2u;
+
+  /*  Calculation of Middle stage */
+  for (k = fftLen / 4u; k > 4u; k >>= 2u)
+  {
+    /*  Initializations for the middle stage */
+    n1 = n2;
+    n2 >>= 2u;
+    ic = 0u;
+
+    for (j = 0u; j <= (n2 - 1u); j++)
+    {
+      /*  index calculation for the coefficients */
+      Co1 = pCoef16[ic * 2u];
+      Si1 = pCoef16[(ic * 2u) + 1u];
+      Co2 = pCoef16[2u * ic * 2u];
+      Si2 = pCoef16[2u * ic * 2u + 1u];
+      Co3 = pCoef16[3u * ic * 2u];
+      Si3 = pCoef16[(3u * ic * 2u) + 1u];
+
+      /*  Twiddle coefficients index modifier */
+      ic = ic + twidCoefModifier;
+
+      /*  Butterfly implementation */
+      for (i0 = j; i0 < fftLen; i0 += n1)
+      {
+        /*  index calculation for the input as, */
+        /*  pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
+        i1 = i0 + n2;
+        i2 = i1 + n2;
+        i3 = i2 + n2;
+
+        /*  Reading i0, i0+fftLen/2 inputs */
+        /* Read ya (real), xa(imag) input */
+        T0 = pSrc16[i0 * 2u];
+        T1 = pSrc16[(i0 * 2u) + 1u];
+
+        /* Read yc (real), xc(imag) input */
+        S0 = pSrc16[i2 * 2u];
+        S1 = pSrc16[(i2 * 2u) + 1u];
+
+
+        /* R0 = (ya + yc), R1 = (xa + xc) */
+        R0 = __SSAT(T0 + S0, 16u);
+        R1 = __SSAT(T1 + S1, 16u);
+        /* S0 = (ya - yc), S1 = (xa - xc) */
+        S0 = __SSAT(T0 - S0, 16u);
+        S1 = __SSAT(T1 - S1, 16u);
+
+        /*  Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
+        /* Read yb (real), xb(imag) input */
+        T0 = pSrc16[i1 * 2u];
+        T1 = pSrc16[(i1 * 2u) + 1u];
+
+        /* Read yd (real), xd(imag) input */
+        U0 = pSrc16[i3 * 2u];
+        U1 = pSrc16[(i3 * 2u) + 1u];
+
+        /* T0 = (yb + yd), T1 = (xb + xd) */
+        T0 = __SSAT(T0 + U0, 16u);
+        T1 = __SSAT(T1 + U1, 16u);
+
+        /*  writing the butterfly processed i0 sample */
+        /* xa' = xa + xb + xc + xd */
+        /* ya' = ya + yb + yc + yd */
+        pSrc16[i0 * 2u] = ((R0 >> 1u) + (T0 >> 1u)) >> 1u;
+        pSrc16[(i0 * 2u) + 1u] = ((R1 >> 1u) + (T1 >> 1u)) >> 1u;
+
+        /* R0 = (ya + yc) - (yb + yd), R1 = (xa + xc) - (xb + xd) */
+        R0 = (R0 >> 1u) - (T0 >> 1u);
+        R1 = (R1 >> 1u) - (T1 >> 1u);
+
+        /* (ya-yb+yc-yd)* (si2) - (xa-xb+xc-xd)* co2 */
+        out1 = (short) ((Co2 * R0 - Si2 * R1) >> 16);
+        /* (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2) */
+        out2 = (short) ((Si2 * R0 + Co2 * R1) >> 16);
+
+        /*  Reading i0+3fftLen/4 */
+        /* Read yb (real), xb(imag) input */
+        T0 = pSrc16[i1 * 2u];
+        T1 = pSrc16[(i1 * 2u) + 1u];
+
+        /*  writing the butterfly processed i0 + fftLen/4 sample */
+        /* xc' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2) */
+        /* yc' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2) */
+        pSrc16[i1 * 2u] = out1;
+        pSrc16[(i1 * 2u) + 1u] = out2;
+
+        /*  Butterfly calculations */
+        /* Read yd (real), xd(imag) input */
+        U0 = pSrc16[i3 * 2u];
+        U1 = pSrc16[(i3 * 2u) + 1u];
+
+        /* T0 = yb-yd, T1 = xb-xd) */
+        T0 = __SSAT(T0 - U0, 16u);
+        T1 = __SSAT(T1 - U1, 16u);
+
+        /* R0 = (ya-yc) - (xb- xd) , R1 = (xa-xc) + (yb-yd) */
+        R0 = (S0 >> 1u) + (T1 >> 1u);
+        R1 = (S1 >> 1u) - (T0 >> 1u);
+
+        /* S1 = (ya-yc) + (xb- xd), S1 = (xa-xc) - (yb-yd) */
+        S0 = (S0 >> 1u) - (T1 >> 1u);
+        S1 = (S1 >> 1u) + (T0 >> 1u);
+
+        /*  Butterfly process for the i0+fftLen/2 sample */
+        out1 = (short) ((Co1 * S0 - Si1 * S1) >> 16u);
+        out2 = (short) ((Si1 * S0 + Co1 * S1) >> 16u);
+        /* xb' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1) */
+        /* yb' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1) */
+        pSrc16[i2 * 2u] = out1;
+        pSrc16[(i2 * 2u) + 1u] = out2;
+
+        /*  Butterfly process for the i0+3fftLen/4 sample */
+        out1 = (short) ((Co3 * R0 - Si3 * R1) >> 16u);
+
+        out2 = (short) ((Si3 * R0 + Co3 * R1) >> 16u);
+        /* xd' = (xa+yb-xc-yd)* Co3 - (ya-xb-yc+xd)* (si3) */
+        /* yd' = (ya-xb-yc+xd)* Co3 + (xa+yb-xc-yd)* (si3) */
+        pSrc16[i3 * 2u] = out1;
+        pSrc16[(i3 * 2u) + 1u] = out2;
+
+
+      }
+    }
+    /*  Twiddle coefficients index modifier */
+    twidCoefModifier <<= 2u;
+  }
+  /*  End of Middle stages process */
+
+
+  /* data is in 10.6(q6) format for the 1024 point */
+  /* data is in 8.8(q8) format for the 256 point   */
+  /* data is in 6.10(q10) format for the 64 point  */
+  /* data is in 4.12(q12) format for the 16 point  */
+
+  /* start of last stage process */
+
+
+  /*  Initializations for the last stage */
+  n1 = n2;
+  n2 >>= 2u;
+
+  /*  Butterfly implementation */
+  for (i0 = 0u; i0 <= (fftLen - n1); i0 += n1)
+  {
+    /*  index calculation for the input as, */
+    /*  pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
+    i1 = i0 + n2;
+    i2 = i1 + n2;
+    i3 = i2 + n2;
+
+    /*  Reading i0, i0+fftLen/2 inputs */
+    /* Read ya (real), xa(imag) input */
+    T0 = pSrc16[i0 * 2u];
+    T1 = pSrc16[(i0 * 2u) + 1u];
+    /* Read yc (real), xc(imag) input */
+    S0 = pSrc16[i2 * 2u];
+    S1 = pSrc16[(i2 * 2u) + 1u];
+
+    /* R0 = (ya + yc), R1 = (xa + xc) */
+    R0 = __SSAT(T0 + S0, 16u);
+    R1 = __SSAT(T1 + S1, 16u);
+    /* S0 = (ya - yc), S1 = (xa - xc) */
+    S0 = __SSAT(T0 - S0, 16u);
+    S1 = __SSAT(T1 - S1, 16u);
+
+    /*  Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
+    /* Read yb (real), xb(imag) input */
+    T0 = pSrc16[i1 * 2u];
+    T1 = pSrc16[(i1 * 2u) + 1u];
+    /* Read yd (real), xd(imag) input */
+    U0 = pSrc16[i3 * 2u];
+    U1 = pSrc16[(i3 * 2u) + 1u];
+
+    /* T0 = (yb + yd), T1 = (xb + xd) */
+    T0 = __SSAT(T0 + U0, 16u);
+    T1 = __SSAT(T1 + U1, 16u);
+
+    /*  writing the butterfly processed i0 sample */
+    /* xa' = xa + xb + xc + xd */
+    /* ya' = ya + yb + yc + yd */
+    pSrc16[i0 * 2u] = (R0 >> 1u) + (T0 >> 1u);
+    pSrc16[(i0 * 2u) + 1u] = (R1 >> 1u) + (T1 >> 1u);
+
+    /* R0 = (ya + yc) - (yb + yd), R1 = (xa + xc) - (xb + xd) */
+    R0 = (R0 >> 1u) - (T0 >> 1u);
+    R1 = (R1 >> 1u) - (T1 >> 1u);
+
+    /* Read yb (real), xb(imag) input */
+    T0 = pSrc16[i1 * 2u];
+    T1 = pSrc16[(i1 * 2u) + 1u];
+
+    /*  writing the butterfly processed i0 + fftLen/4 sample */
+    /* xc' = (xa-xb+xc-xd) */
+    /* yc' = (ya-yb+yc-yd) */
+    pSrc16[i1 * 2u] = R0;
+    pSrc16[(i1 * 2u) + 1u] = R1;
+
+    /* Read yd (real), xd(imag) input */
+    U0 = pSrc16[i3 * 2u];
+    U1 = pSrc16[(i3 * 2u) + 1u];
+    /* T0 = (yb - yd), T1 = (xb - xd) */
+    T0 = __SSAT(T0 - U0, 16u);
+    T1 = __SSAT(T1 - U1, 16u);
+
+    /*  writing the butterfly processed i0 + fftLen/2 sample */
+    /* xb' = (xa-yb-xc+yd) */
+    /* yb' = (ya+xb-yc-xd) */
+    pSrc16[i2 * 2u] = (S0 >> 1u) - (T1 >> 1u);
+    pSrc16[(i2 * 2u) + 1u] = (S1 >> 1u) + (T0 >> 1u);
+
+
+    /*  writing the butterfly processed i0 + 3fftLen/4 sample */
+    /* xd' = (xa+yb-xc-yd) */
+    /* yd' = (ya-xb-yc+xd) */
+    pSrc16[i3 * 2u] = (S0 >> 1u) + (T1 >> 1u);
+    pSrc16[(i3 * 2u) + 1u] = (S1 >> 1u) - (T0 >> 1u);
+  }
+  /* end of last stage  process */
+
+  /* output is in 11.5(q5) format for the 1024 point */
+  /* output is in 9.7(q7) format for the 256 point   */
+  /* output is in 7.9(q9) format for the 64 point  */
+  /* output is in 5.11(q11) format for the 16 point  */
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_q31.c
new file mode 100644
index 0000000000..3a5c523dff
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_q31.c
@@ -0,0 +1,891 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_cfft_radix4_q31.c    
+*    
+* Description:	This file has function definition of Radix-4 FFT & IFFT function and    
+*				In-place bit reversal using bit reversal table    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.5  2010/04/26     
+* 	 incorporated review comments and updated with latest CMSIS layer    
+*    
+* Version 0.0.3  2010/03/10     
+*    Initial version    
+* -------------------------------------------------------------------- */
+#include "arm_math.h"
+
+
+/**    
+ * @ingroup groupTransforms    
+ */
+
+/**    
+ * @addtogroup Radix4_CFFT_CIFFT    
+ * @{    
+ */
+
+/**    
+ * @details    
+ * @brief Processing function for the Q31 CFFT/CIFFT.    
+ * @param[in]      *S    points to an instance of the Q31 CFFT/CIFFT structure.   
+ * @param[in, out] *pSrc points to the complex data buffer of size 2*fftLen. Processing occurs in-place.   
+ * @return none.    
+ *     
+ * \par Input and output formats:    
+ * \par    
+ * Internally input is downscaled by 2 for every stage to avoid saturations inside CFFT/CIFFT process.   
+ * Hence the output format is different for different FFT sizes.    
+ * The input and output formats for different FFT sizes and number of bits to upscale are mentioned in the tables below for CFFT and CIFFT:   
+ * \par   
+ * \image html CFFTQ31.gif "Input and Output Formats for Q31 CFFT"    
+ * \image html CIFFTQ31.gif "Input and Output Formats for Q31 CIFFT"    
+ *    
+ */
+
+void arm_cfft_radix4_q31(
+  const arm_cfft_radix4_instance_q31 * S,
+  q31_t * pSrc)
+{
+  if(S->ifftFlag == 1u)
+  {
+    /* Complex IFFT radix-4 */
+    arm_radix4_butterfly_inverse_q31(pSrc, S->fftLen, S->pTwiddle,
+                                     S->twidCoefModifier);
+  }
+  else
+  {
+    /* Complex FFT radix-4 */
+    arm_radix4_butterfly_q31(pSrc, S->fftLen, S->pTwiddle,
+                             S->twidCoefModifier);
+  }
+
+
+  if(S->bitReverseFlag == 1u)
+  {
+    /*  Bit Reversal */
+    arm_bitreversal_q31(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable);
+  }
+
+}
+
+/**    
+ * @} end of Radix4_CFFT_CIFFT group    
+ */
+
+/*    
+* Radix-4 FFT algorithm used is :    
+*    
+* Input real and imaginary data:    
+* x(n) = xa + j * ya    
+* x(n+N/4 ) = xb + j * yb    
+* x(n+N/2 ) = xc + j * yc    
+* x(n+3N 4) = xd + j * yd    
+*    
+*    
+* Output real and imaginary data:    
+* x(4r) = xa'+ j * ya'    
+* x(4r+1) = xb'+ j * yb'    
+* x(4r+2) = xc'+ j * yc'    
+* x(4r+3) = xd'+ j * yd'    
+*    
+*    
+* Twiddle factors for radix-4 FFT:    
+* Wn = co1 + j * (- si1)    
+* W2n = co2 + j * (- si2)    
+* W3n = co3 + j * (- si3)    
+*    
+*  Butterfly implementation:    
+* xa' = xa + xb + xc + xd    
+* ya' = ya + yb + yc + yd    
+* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1)    
+* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1)    
+* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2)    
+* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2)    
+* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3)    
+* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3)    
+*    
+*/
+
+/**    
+ * @brief  Core function for the Q31 CFFT butterfly process.   
+ * @param[in, out] *pSrc            points to the in-place buffer of Q31 data type.   
+ * @param[in]      fftLen           length of the FFT.   
+ * @param[in]      *pCoef           points to twiddle coefficient buffer.   
+ * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.   
+ * @return none.   
+ */
+
+void arm_radix4_butterfly_q31(
+  q31_t * pSrc,
+  uint32_t fftLen,
+  q31_t * pCoef,
+  uint32_t twidCoefModifier)
+{
+  uint32_t n1, n2, ia1, ia2, ia3, i0, i1, i2, i3, j, k;
+  q31_t t1, t2, r1, r2, s1, s2, co1, co2, co3, si1, si2, si3;
+
+  q31_t xa, xb, xc, xd;
+  q31_t ya, yb, yc, yd;
+  q31_t xa_out, xb_out, xc_out, xd_out;
+  q31_t ya_out, yb_out, yc_out, yd_out;
+
+  q31_t *ptr1;
+  q63_t xaya, xbyb, xcyc, xdyd;
+  /* Total process is divided into three stages */
+
+  /* process first stage, middle stages, & last stage */
+
+
+  /* start of first stage process */
+
+  /*  Initializations for the first stage */
+  n2 = fftLen;
+  n1 = n2;
+  /* n2 = fftLen/4 */
+  n2 >>= 2u;
+  i0 = 0u;
+  ia1 = 0u;
+
+  j = n2;
+
+  /*  Calculation of first stage */
+  do
+  {
+    /*  index calculation for the input as, */
+    /*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2u], pSrc[i0 + 3fftLen/4] */
+    i1 = i0 + n2;
+    i2 = i1 + n2;
+    i3 = i2 + n2;
+
+    /* input is in 1.31(q31) format and provide 4 guard bits for the input */
+
+    /*  Butterfly implementation */
+    /* xa + xc */
+    r1 = (pSrc[(2u * i0)] >> 4u) + (pSrc[(2u * i2)] >> 4u);
+    /* xa - xc */
+    r2 = (pSrc[2u * i0] >> 4u) - (pSrc[2u * i2] >> 4u);
+
+    /* xb + xd */
+    t1 = (pSrc[2u * i1] >> 4u) + (pSrc[2u * i3] >> 4u);
+
+    /* ya + yc */
+    s1 = (pSrc[(2u * i0) + 1u] >> 4u) + (pSrc[(2u * i2) + 1u] >> 4u);
+    /* ya - yc */
+    s2 = (pSrc[(2u * i0) + 1u] >> 4u) - (pSrc[(2u * i2) + 1u] >> 4u);
+
+    /* xa' = xa + xb + xc + xd */
+    pSrc[2u * i0] = (r1 + t1);
+    /* (xa + xc) - (xb + xd) */
+    r1 = r1 - t1;
+    /* yb + yd */
+    t2 = (pSrc[(2u * i1) + 1u] >> 4u) + (pSrc[(2u * i3) + 1u] >> 4u);
+
+    /* ya' = ya + yb + yc + yd */
+    pSrc[(2u * i0) + 1u] = (s1 + t2);
+
+    /* (ya + yc) - (yb + yd) */
+    s1 = s1 - t2;
+
+    /* yb - yd */
+    t1 = (pSrc[(2u * i1) + 1u] >> 4u) - (pSrc[(2u * i3) + 1u] >> 4u);
+    /* xb - xd */
+    t2 = (pSrc[2u * i1] >> 4u) - (pSrc[2u * i3] >> 4u);
+
+    /*  index calculation for the coefficients */
+    ia2 = 2u * ia1;
+    co2 = pCoef[ia2 * 2u];
+    si2 = pCoef[(ia2 * 2u) + 1u];
+
+    /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
+    pSrc[2u * i1] = (((int32_t) (((q63_t) r1 * co2) >> 32)) +
+                     ((int32_t) (((q63_t) s1 * si2) >> 32))) << 1u;
+
+    /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
+    pSrc[(2u * i1) + 1u] = (((int32_t) (((q63_t) s1 * co2) >> 32)) -
+                            ((int32_t) (((q63_t) r1 * si2) >> 32))) << 1u;
+
+    /* (xa - xc) + (yb - yd) */
+    r1 = r2 + t1;
+    /* (xa - xc) - (yb - yd) */
+    r2 = r2 - t1;
+
+    /* (ya - yc) - (xb - xd) */
+    s1 = s2 - t2;
+    /* (ya - yc) + (xb - xd) */
+    s2 = s2 + t2;
+
+    co1 = pCoef[ia1 * 2u];
+    si1 = pCoef[(ia1 * 2u) + 1u];
+
+    /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
+    pSrc[2u * i2] = (((int32_t) (((q63_t) r1 * co1) >> 32)) +
+                     ((int32_t) (((q63_t) s1 * si1) >> 32))) << 1u;
+
+    /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
+    pSrc[(2u * i2) + 1u] = (((int32_t) (((q63_t) s1 * co1) >> 32)) -
+                            ((int32_t) (((q63_t) r1 * si1) >> 32))) << 1u;
+
+    /*  index calculation for the coefficients */
+    ia3 = 3u * ia1;
+    co3 = pCoef[ia3 * 2u];
+    si3 = pCoef[(ia3 * 2u) + 1u];
+
+    /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
+    pSrc[2u * i3] = (((int32_t) (((q63_t) r2 * co3) >> 32)) +
+                     ((int32_t) (((q63_t) s2 * si3) >> 32))) << 1u;
+
+    /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
+    pSrc[(2u * i3) + 1u] = (((int32_t) (((q63_t) s2 * co3) >> 32)) -
+                            ((int32_t) (((q63_t) r2 * si3) >> 32))) << 1u;
+
+    /*  Twiddle coefficients index modifier */
+    ia1 = ia1 + twidCoefModifier;
+
+    /*  Updating input index */
+    i0 = i0 + 1u;
+
+  } while(--j);
+
+  /* end of first stage process */
+
+  /* data is in 5.27(q27) format */
+
+
+  /* start of Middle stages process */
+
+
+  /* each stage in middle stages provides two down scaling of the input */
+
+  twidCoefModifier <<= 2u;
+
+
+  for (k = fftLen / 4u; k > 4u; k >>= 2u)
+  {
+    /*  Initializations for the first stage */
+    n1 = n2;
+    n2 >>= 2u;
+    ia1 = 0u;
+
+    /*  Calculation of first stage */
+    for (j = 0u; j <= (n2 - 1u); j++)
+    {
+      /*  index calculation for the coefficients */
+      ia2 = ia1 + ia1;
+      ia3 = ia2 + ia1;
+      co1 = pCoef[ia1 * 2u];
+      si1 = pCoef[(ia1 * 2u) + 1u];
+      co2 = pCoef[ia2 * 2u];
+      si2 = pCoef[(ia2 * 2u) + 1u];
+      co3 = pCoef[ia3 * 2u];
+      si3 = pCoef[(ia3 * 2u) + 1u];
+      /*  Twiddle coefficients index modifier */
+      ia1 = ia1 + twidCoefModifier;
+
+      for (i0 = j; i0 < fftLen; i0 += n1)
+      {
+        /*  index calculation for the input as, */
+        /*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2u], pSrc[i0 + 3fftLen/4] */
+        i1 = i0 + n2;
+        i2 = i1 + n2;
+        i3 = i2 + n2;
+
+        /*  Butterfly implementation */
+        /* xa + xc */
+        r1 = pSrc[2u * i0] + pSrc[2u * i2];
+        /* xa - xc */
+        r2 = pSrc[2u * i0] - pSrc[2u * i2];
+
+        /* ya + yc */
+        s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
+        /* ya - yc */
+        s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
+
+        /* xb + xd */
+        t1 = pSrc[2u * i1] + pSrc[2u * i3];
+
+        /* xa' = xa + xb + xc + xd */
+        pSrc[2u * i0] = (r1 + t1) >> 2u;
+        /* xa + xc -(xb + xd) */
+        r1 = r1 - t1;
+
+        /* yb + yd */
+        t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
+        /* ya' = ya + yb + yc + yd */
+        pSrc[(2u * i0) + 1u] = (s1 + t2) >> 2u;
+
+        /* (ya + yc) - (yb + yd) */
+        s1 = s1 - t2;
+
+        /* (yb - yd) */
+        t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
+        /* (xb - xd) */
+        t2 = pSrc[2u * i1] - pSrc[2u * i3];
+
+        /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
+        pSrc[2u * i1] = (((int32_t) (((q63_t) r1 * co2) >> 32)) +
+                         ((int32_t) (((q63_t) s1 * si2) >> 32))) >> 1u;
+
+        /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
+        pSrc[(2u * i1) + 1u] = (((int32_t) (((q63_t) s1 * co2) >> 32)) -
+                                ((int32_t) (((q63_t) r1 * si2) >> 32))) >> 1u;
+
+        /* (xa - xc) + (yb - yd) */
+        r1 = r2 + t1;
+        /* (xa - xc) - (yb - yd) */
+        r2 = r2 - t1;
+
+        /* (ya - yc) -  (xb - xd) */
+        s1 = s2 - t2;
+        /* (ya - yc) +  (xb - xd) */
+        s2 = s2 + t2;
+
+        /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
+        pSrc[2u * i2] = (((int32_t) (((q63_t) r1 * co1) >> 32)) +
+                         ((int32_t) (((q63_t) s1 * si1) >> 32))) >> 1u;
+
+        /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
+        pSrc[(2u * i2) + 1u] = (((int32_t) (((q63_t) s1 * co1) >> 32)) -
+                                ((int32_t) (((q63_t) r1 * si1) >> 32))) >> 1u;
+
+        /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
+        pSrc[2u * i3] = (((int32_t) (((q63_t) r2 * co3) >> 32)) +
+                         ((int32_t) (((q63_t) s2 * si3) >> 32))) >> 1u;
+
+        /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
+        pSrc[(2u * i3) + 1u] = (((int32_t) (((q63_t) s2 * co3) >> 32)) -
+                                ((int32_t) (((q63_t) r2 * si3) >> 32))) >> 1u;
+      }
+    }
+    twidCoefModifier <<= 2u;
+  }
+
+  /* End of Middle stages process */
+
+  /* data is in 11.21(q21) format for the 1024 point as there are 3 middle stages */
+  /* data is in 9.23(q23) format for the 256 point as there are 2 middle stages */
+  /* data is in 7.25(q25) format for the 64 point as there are 1 middle stage */
+  /* data is in 5.27(q27) format for the 16 point as there are no middle stages */
+
+
+  /* start of Last stage process */
+  /*  Initializations for the last stage */
+  j = fftLen >> 2;
+  ptr1 = &pSrc[0];
+
+  /*  Calculations of last stage */
+  do
+  {
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    /* Read xa (real), ya(imag) input */
+    xaya = *__SIMD64(ptr1)++;
+    xa = (q31_t) xaya;
+    ya = (q31_t) (xaya >> 32);
+
+    /* Read xb (real), yb(imag) input */
+    xbyb = *__SIMD64(ptr1)++;
+    xb = (q31_t) xbyb;
+    yb = (q31_t) (xbyb >> 32);
+
+    /* Read xc (real), yc(imag) input */
+    xcyc = *__SIMD64(ptr1)++;
+    xc = (q31_t) xcyc;
+    yc = (q31_t) (xcyc >> 32);
+
+    /* Read xc (real), yc(imag) input */
+    xdyd = *__SIMD64(ptr1)++;
+    xd = (q31_t) xdyd;
+    yd = (q31_t) (xdyd >> 32);
+
+#else
+
+    /* Read xa (real), ya(imag) input */
+    xaya = *__SIMD64(ptr1)++;
+    ya = (q31_t) xaya;
+    xa = (q31_t) (xaya >> 32);
+
+    /* Read xb (real), yb(imag) input */
+    xbyb = *__SIMD64(ptr1)++;
+    yb = (q31_t) xbyb;
+    xb = (q31_t) (xbyb >> 32);
+
+    /* Read xc (real), yc(imag) input */
+    xcyc = *__SIMD64(ptr1)++;
+    yc = (q31_t) xcyc;
+    xc = (q31_t) (xcyc >> 32);
+
+    /* Read xc (real), yc(imag) input */
+    xdyd = *__SIMD64(ptr1)++;
+    yd = (q31_t) xdyd;
+    xd = (q31_t) (xdyd >> 32);
+
+
+#endif
+
+    /* xa' = xa + xb + xc + xd */
+    xa_out = xa + xb + xc + xd;
+
+    /* ya' = ya + yb + yc + yd */
+    ya_out = ya + yb + yc + yd;
+
+    /* pointer updation for writing */
+    ptr1 = ptr1 - 8u;
+
+    /* writing xa' and ya' */
+    *ptr1++ = xa_out;
+    *ptr1++ = ya_out;
+
+    xc_out = (xa - xb + xc - xd);
+    yc_out = (ya - yb + yc - yd);
+
+    /* writing xc' and yc' */
+    *ptr1++ = xc_out;
+    *ptr1++ = yc_out;
+
+    xb_out = (xa + yb - xc - yd);
+    yb_out = (ya - xb - yc + xd);
+
+    /* writing xb' and yb' */
+    *ptr1++ = xb_out;
+    *ptr1++ = yb_out;
+
+    xd_out = (xa - yb - xc + yd);
+    yd_out = (ya + xb - yc - xd);
+
+    /* writing xd' and yd' */
+    *ptr1++ = xd_out;
+    *ptr1++ = yd_out;
+
+
+  } while(--j);
+
+  /* output is in 11.21(q21) format for the 1024 point */
+  /* output is in 9.23(q23) format for the 256 point */
+  /* output is in 7.25(q25) format for the 64 point */
+  /* output is in 5.27(q27) format for the 16 point */
+
+  /* End of last stage process */
+
+}
+
+
+/**    
+ * @brief  Core function for the Q31 CIFFT butterfly process.   
+ * @param[in, out] *pSrc            points to the in-place buffer of Q31 data type.   
+ * @param[in]      fftLen           length of the FFT.   
+ * @param[in]      *pCoef           points to twiddle coefficient buffer.   
+ * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.   
+ * @return none.   
+ */
+
+
+/*    
+* Radix-4 IFFT algorithm used is :    
+*    
+* CIFFT uses same twiddle coefficients as CFFT Function    
+*  x[k] = x[n] + (j)k * x[n + fftLen/4] + (-1)k * x[n+fftLen/2] + (-j)k * x[n+3*fftLen/4]    
+*    
+*    
+* IFFT is implemented with following changes in equations from FFT    
+*    
+* Input real and imaginary data:    
+* x(n) = xa + j * ya    
+* x(n+N/4 ) = xb + j * yb    
+* x(n+N/2 ) = xc + j * yc    
+* x(n+3N 4) = xd + j * yd    
+*    
+*    
+* Output real and imaginary data:    
+* x(4r) = xa'+ j * ya'    
+* x(4r+1) = xb'+ j * yb'    
+* x(4r+2) = xc'+ j * yc'    
+* x(4r+3) = xd'+ j * yd'    
+*    
+*    
+* Twiddle factors for radix-4 IFFT:    
+* Wn = co1 + j * (si1)    
+* W2n = co2 + j * (si2)    
+* W3n = co3 + j * (si3)    
+    
+* The real and imaginary output values for the radix-4 butterfly are    
+* xa' = xa + xb + xc + xd    
+* ya' = ya + yb + yc + yd    
+* xb' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1)    
+* yb' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1)    
+* xc' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2)    
+* yc' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2)    
+* xd' = (xa+yb-xc-yd)* co3 - (ya-xb-yc+xd)* (si3)    
+* yd' = (ya-xb-yc+xd)* co3 + (xa+yb-xc-yd)* (si3)    
+*    
+*/
+
+void arm_radix4_butterfly_inverse_q31(
+  q31_t * pSrc,
+  uint32_t fftLen,
+  q31_t * pCoef,
+  uint32_t twidCoefModifier)
+{
+  uint32_t n1, n2, ia1, ia2, ia3, i0, i1, i2, i3, j, k;
+  q31_t t1, t2, r1, r2, s1, s2, co1, co2, co3, si1, si2, si3;
+  q31_t xa, xb, xc, xd;
+  q31_t ya, yb, yc, yd;
+  q31_t xa_out, xb_out, xc_out, xd_out;
+  q31_t ya_out, yb_out, yc_out, yd_out;
+
+  q31_t *ptr1;
+  q63_t xaya, xbyb, xcyc, xdyd;
+
+  /* input is be 1.31(q31) format for all FFT sizes */
+  /* Total process is divided into three stages */
+  /* process first stage, middle stages, & last stage */
+
+  /* Start of first stage process */
+
+  /* Initializations for the first stage */
+  n2 = fftLen;
+  n1 = n2;
+  /* n2 = fftLen/4 */
+  n2 >>= 2u;
+  i0 = 0u;
+  ia1 = 0u;
+
+  j = n2;
+
+  do
+  {
+
+    /* input is in 1.31(q31) format and provide 4 guard bits for the input */
+
+    /*  index calculation for the input as, */
+    /*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2u], pSrc[i0 + 3fftLen/4] */
+    i1 = i0 + n2;
+    i2 = i1 + n2;
+    i3 = i2 + n2;
+
+    /*  Butterfly implementation */
+    /* xa + xc */
+    r1 = (pSrc[2u * i0] >> 4u) + (pSrc[2u * i2] >> 4u);
+    /* xa - xc */
+    r2 = (pSrc[2u * i0] >> 4u) - (pSrc[2u * i2] >> 4u);
+
+    /* xb + xd */
+    t1 = (pSrc[2u * i1] >> 4u) + (pSrc[2u * i3] >> 4u);
+
+    /* ya + yc */
+    s1 = (pSrc[(2u * i0) + 1u] >> 4u) + (pSrc[(2u * i2) + 1u] >> 4u);
+    /* ya - yc */
+    s2 = (pSrc[(2u * i0) + 1u] >> 4u) - (pSrc[(2u * i2) + 1u] >> 4u);
+
+    /* xa' = xa + xb + xc + xd */
+    pSrc[2u * i0] = (r1 + t1);
+    /* (xa + xc) - (xb + xd) */
+    r1 = r1 - t1;
+    /* yb + yd */
+    t2 = (pSrc[(2u * i1) + 1u] >> 4u) + (pSrc[(2u * i3) + 1u] >> 4u);
+    /* ya' = ya + yb + yc + yd */
+    pSrc[(2u * i0) + 1u] = (s1 + t2);
+
+    /* (ya + yc) - (yb + yd) */
+    s1 = s1 - t2;
+
+    /* yb - yd */
+    t1 = (pSrc[(2u * i1) + 1u] >> 4u) - (pSrc[(2u * i3) + 1u] >> 4u);
+    /* xb - xd */
+    t2 = (pSrc[2u * i1] >> 4u) - (pSrc[2u * i3] >> 4u);
+
+    /*  index calculation for the coefficients */
+    ia2 = 2u * ia1;
+    co2 = pCoef[ia2 * 2u];
+    si2 = pCoef[(ia2 * 2u) + 1u];
+
+    /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
+    pSrc[2u * i1] = (((int32_t) (((q63_t) r1 * co2) >> 32)) -
+                     ((int32_t) (((q63_t) s1 * si2) >> 32))) << 1u;
+
+    /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
+    pSrc[2u * i1 + 1u] = (((int32_t) (((q63_t) s1 * co2) >> 32)) +
+                          ((int32_t) (((q63_t) r1 * si2) >> 32))) << 1u;
+
+    /* (xa - xc) - (yb - yd) */
+    r1 = r2 - t1;
+    /* (xa - xc) + (yb - yd) */
+    r2 = r2 + t1;
+
+    /* (ya - yc) + (xb - xd) */
+    s1 = s2 + t2;
+    /* (ya - yc) - (xb - xd) */
+    s2 = s2 - t2;
+
+    co1 = pCoef[ia1 * 2u];
+    si1 = pCoef[(ia1 * 2u) + 1u];
+
+    /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
+    pSrc[2u * i2] = (((int32_t) (((q63_t) r1 * co1) >> 32)) -
+                     ((int32_t) (((q63_t) s1 * si1) >> 32))) << 1u;
+
+    /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
+    pSrc[(2u * i2) + 1u] = (((int32_t) (((q63_t) s1 * co1) >> 32)) +
+                            ((int32_t) (((q63_t) r1 * si1) >> 32))) << 1u;
+
+    /*  index calculation for the coefficients */
+    ia3 = 3u * ia1;
+    co3 = pCoef[ia3 * 2u];
+    si3 = pCoef[(ia3 * 2u) + 1u];
+
+    /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
+    pSrc[2u * i3] = (((int32_t) (((q63_t) r2 * co3) >> 32)) -
+                     ((int32_t) (((q63_t) s2 * si3) >> 32))) << 1u;
+
+    /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
+    pSrc[(2u * i3) + 1u] = (((int32_t) (((q63_t) s2 * co3) >> 32)) +
+                            ((int32_t) (((q63_t) r2 * si3) >> 32))) << 1u;
+
+    /*  Twiddle coefficients index modifier */
+    ia1 = ia1 + twidCoefModifier;
+
+    /*  Updating input index */
+    i0 = i0 + 1u;
+
+  } while(--j);
+
+  /* data is in 5.27(q27) format */
+  /* each stage provides two down scaling of the input */
+
+
+  /* Start of Middle stages process */
+
+  twidCoefModifier <<= 2u;
+
+  /*  Calculation of second stage to excluding last stage */
+  for (k = fftLen / 4u; k > 4u; k >>= 2u)
+  {
+    /*  Initializations for the first stage */
+    n1 = n2;
+    n2 >>= 2u;
+    ia1 = 0u;
+
+    for (j = 0; j <= (n2 - 1u); j++)
+    {
+      /*  index calculation for the coefficients */
+      ia2 = ia1 + ia1;
+      ia3 = ia2 + ia1;
+      co1 = pCoef[ia1 * 2u];
+      si1 = pCoef[(ia1 * 2u) + 1u];
+      co2 = pCoef[ia2 * 2u];
+      si2 = pCoef[(ia2 * 2u) + 1u];
+      co3 = pCoef[ia3 * 2u];
+      si3 = pCoef[(ia3 * 2u) + 1u];
+      /*  Twiddle coefficients index modifier */
+      ia1 = ia1 + twidCoefModifier;
+
+      for (i0 = j; i0 < fftLen; i0 += n1)
+      {
+        /*  index calculation for the input as, */
+        /*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2u], pSrc[i0 + 3fftLen/4] */
+        i1 = i0 + n2;
+        i2 = i1 + n2;
+        i3 = i2 + n2;
+
+        /*  Butterfly implementation */
+        /* xa + xc */
+        r1 = pSrc[2u * i0] + pSrc[2u * i2];
+        /* xa - xc */
+        r2 = pSrc[2u * i0] - pSrc[2u * i2];
+
+        /* ya + yc */
+        s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
+        /* ya - yc */
+        s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
+
+        /* xb + xd */
+        t1 = pSrc[2u * i1] + pSrc[2u * i3];
+
+        /* xa' = xa + xb + xc + xd */
+        pSrc[2u * i0] = (r1 + t1) >> 2u;
+        /* xa + xc -(xb + xd) */
+        r1 = r1 - t1;
+        /* yb + yd */
+        t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
+        /* ya' = ya + yb + yc + yd */
+        pSrc[(2u * i0) + 1u] = (s1 + t2) >> 2u;
+
+        /* (ya + yc) - (yb + yd) */
+        s1 = s1 - t2;
+
+        /* (yb - yd) */
+        t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
+        /* (xb - xd) */
+        t2 = pSrc[2u * i1] - pSrc[2u * i3];
+
+        /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
+        pSrc[2u * i1] = (((int32_t) (((q63_t) r1 * co2) >> 32u)) -
+                         ((int32_t) (((q63_t) s1 * si2) >> 32u))) >> 1u;
+
+        /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
+        pSrc[(2u * i1) + 1u] =
+          (((int32_t) (((q63_t) s1 * co2) >> 32u)) +
+           ((int32_t) (((q63_t) r1 * si2) >> 32u))) >> 1u;
+
+        /* (xa - xc) - (yb - yd) */
+        r1 = r2 - t1;
+        /* (xa - xc) + (yb - yd) */
+        r2 = r2 + t1;
+
+        /* (ya - yc) +  (xb - xd) */
+        s1 = s2 + t2;
+        /* (ya - yc) -  (xb - xd) */
+        s2 = s2 - t2;
+
+        /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
+        pSrc[2u * i2] = (((int32_t) (((q63_t) r1 * co1) >> 32)) -
+                         ((int32_t) (((q63_t) s1 * si1) >> 32))) >> 1u;
+
+        /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
+        pSrc[(2u * i2) + 1u] = (((int32_t) (((q63_t) s1 * co1) >> 32)) +
+                                ((int32_t) (((q63_t) r1 * si1) >> 32))) >> 1u;
+
+        /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
+        pSrc[(2u * i3)] = (((int32_t) (((q63_t) r2 * co3) >> 32)) -
+                           ((int32_t) (((q63_t) s2 * si3) >> 32))) >> 1u;
+
+        /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
+        pSrc[(2u * i3) + 1u] = (((int32_t) (((q63_t) s2 * co3) >> 32)) +
+                                ((int32_t) (((q63_t) r2 * si3) >> 32))) >> 1u;
+      }
+    }
+    twidCoefModifier <<= 2u;
+  }
+
+  /* End of Middle stages process */
+
+  /* data is in 11.21(q21) format for the 1024 point as there are 3 middle stages */
+  /* data is in 9.23(q23) format for the 256 point as there are 2 middle stages */
+  /* data is in 7.25(q25) format for the 64 point as there are 1 middle stage */
+  /* data is in 5.27(q27) format for the 16 point as there are no middle stages */
+
+
+  /* Start of last stage process */
+
+
+  /*  Initializations for the last stage */
+  j = fftLen >> 2;
+  ptr1 = &pSrc[0];
+
+  /*  Calculations of last stage */
+  do
+  {
+#ifndef ARM_MATH_BIG_ENDIAN
+    /* Read xa (real), ya(imag) input */
+    xaya = *__SIMD64(ptr1)++;
+    xa = (q31_t) xaya;
+    ya = (q31_t) (xaya >> 32);
+
+    /* Read xb (real), yb(imag) input */
+    xbyb = *__SIMD64(ptr1)++;
+    xb = (q31_t) xbyb;
+    yb = (q31_t) (xbyb >> 32);
+
+    /* Read xc (real), yc(imag) input */
+    xcyc = *__SIMD64(ptr1)++;
+    xc = (q31_t) xcyc;
+    yc = (q31_t) (xcyc >> 32);
+
+    /* Read xc (real), yc(imag) input */
+    xdyd = *__SIMD64(ptr1)++;
+    xd = (q31_t) xdyd;
+    yd = (q31_t) (xdyd >> 32);
+
+#else
+
+    /* Read xa (real), ya(imag) input */
+    xaya = *__SIMD64(ptr1)++;
+    ya = (q31_t) xaya;
+    xa = (q31_t) (xaya >> 32);
+
+    /* Read xb (real), yb(imag) input */
+    xbyb = *__SIMD64(ptr1)++;
+    yb = (q31_t) xbyb;
+    xb = (q31_t) (xbyb >> 32);
+
+    /* Read xc (real), yc(imag) input */
+    xcyc = *__SIMD64(ptr1)++;
+    yc = (q31_t) xcyc;
+    xc = (q31_t) (xcyc >> 32);
+
+    /* Read xc (real), yc(imag) input */
+    xdyd = *__SIMD64(ptr1)++;
+    yd = (q31_t) xdyd;
+    xd = (q31_t) (xdyd >> 32);
+
+
+#endif
+
+    /* xa' = xa + xb + xc + xd */
+    xa_out = xa + xb + xc + xd;
+
+    /* ya' = ya + yb + yc + yd */
+    ya_out = ya + yb + yc + yd;
+
+    /* pointer updation for writing */
+    ptr1 = ptr1 - 8u;
+
+    /* writing xa' and ya' */
+    *ptr1++ = xa_out;
+    *ptr1++ = ya_out;
+
+    xc_out = (xa - xb + xc - xd);
+    yc_out = (ya - yb + yc - yd);
+
+    /* writing xc' and yc' */
+    *ptr1++ = xc_out;
+    *ptr1++ = yc_out;
+
+    xb_out = (xa - yb - xc + yd);
+    yb_out = (ya + xb - yc - xd);
+
+    /* writing xb' and yb' */
+    *ptr1++ = xb_out;
+    *ptr1++ = yb_out;
+
+    xd_out = (xa + yb - xc - yd);
+    yd_out = (ya - xb - yc + xd);
+
+    /* writing xd' and yd' */
+    *ptr1++ = xd_out;
+    *ptr1++ = yd_out;
+
+
+  } while(--j);
+
+  /* output is in 11.21(q21) format for the 1024 point */
+  /* output is in 9.23(q23) format for the 256 point */
+  /* output is in 7.25(q25) format for the 64 point */
+  /* output is in 5.27(q27) format for the 16 point */
+
+  /* End of last stage process */
+}
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_dct4_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_dct4_f32.c
new file mode 100644
index 0000000000..fb79e31726
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_dct4_f32.c
@@ -0,0 +1,453 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_dct4_f32.c    
+*    
+* Description:	Processing function of DCT4 & IDCT4 F32.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupTransforms    
+ */
+
+/**    
+ * @defgroup DCT4_IDCT4 DCT Type IV Functions    
+ * Representation of signals by minimum number of values is important for storage and transmission.    
+ * The possibility of large discontinuity between the beginning and end of a period of a signal    
+ * in DFT can be avoided by extending the signal so that it is even-symmetric.    
+ * Discrete Cosine Transform (DCT) is constructed such that its energy is heavily concentrated in the lower part of the    
+ * spectrum and is very widely used in signal and image coding applications.    
+ * The family of DCTs (DCT type- 1,2,3,4) is the outcome of different combinations of homogeneous boundary conditions.    
+ * DCT has an excellent energy-packing capability, hence has many applications and in data compression in particular.    
+ *    
+ * DCT is essentially the Discrete Fourier Transform(DFT) of an even-extended real signal.    
+ * Reordering of the input data makes the computation of DCT just a problem of    
+ * computing the DFT of a real signal with a few additional operations.    
+ * This approach provides regular, simple, and very efficient DCT algorithms for practical hardware and software implementations.    
+ *     
+ * DCT type-II can be implemented using Fast fourier transform (FFT) internally, as the transform is applied on real values, Real FFT can be used.    
+ * DCT4 is implemented using DCT2 as their implementations are similar except with some added pre-processing and post-processing.    
+ * DCT2 implementation can be described in the following steps:    
+ * - Re-ordering input    
+ * - Calculating Real FFT    
+ * - Multiplication of weights and Real FFT output and getting real part from the product.    
+ *    
+ * This process is explained by the block diagram below:    
+ * \image html DCT4.gif "Discrete Cosine Transform - type-IV"    
+ *    
+ * \par Algorithm:    
+ * The N-point type-IV DCT is defined as a real, linear transformation by the formula:    
+ * \image html DCT4Equation.gif    
+ * where k = 0,1,2,.....N-1    
+ *\par    
+ * Its inverse is defined as follows:    
+ * \image html IDCT4Equation.gif    
+ * where n = 0,1,2,.....N-1    
+ *\par    
+ * The DCT4 matrices become involutory (i.e. they are self-inverse) by multiplying with an overall scale factor of sqrt(2/N).    
+ * The symmetry of the transform matrix indicates that the fast algorithms for the forward    
+ * and inverse transform computation are identical.    
+ * Note that the implementation of Inverse DCT4 and DCT4 is same, hence same process function can be used for both.    
+ *    
+ * \par Lengths supported by the transform:    
+ *  As DCT4 internally uses Real FFT, it supports all the lengths supported by arm_rfft_f32().    
+ * The library provides separate functions for Q15, Q31, and floating-point data types.    
+ * \par Instance Structure    
+ * The instances for Real FFT and FFT, cosine values table and twiddle factor table are stored in an instance data structure.    
+ * A separate instance structure must be defined for each transform.    
+ * There are separate instance structure declarations for each of the 3 supported data types.    
+ *    
+ * \par Initialization Functions    
+ * There is also an associated initialization function for each data type.    
+ * The initialization function performs the following operations:    
+ * - Sets the values of the internal structure fields.    
+ * - Initializes Real FFT as its process function is used internally in DCT4, by calling arm_rfft_init_f32().    
+ * \par    
+ * Use of the initialization function is optional.    
+ * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.    
+ * To place an instance structure into a const data section, the instance structure must be manually initialized.    
+ * Manually initialize the instance structure as follows:    
+ * 
    
+ *arm_dct4_instance_f32 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};    
+ *arm_dct4_instance_q31 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};   
+ *arm_dct4_instance_q15 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};   
+ * 
   
+ * where \c N is the length of the DCT4; \c Nby2 is half of the length of the DCT4;   
+ * \c normalize is normalizing factor used and is equal to sqrt(2/N);    
+ * \c pTwiddle points to the twiddle factor table;   
+ * \c pCosFactor points to the cosFactor table;   
+ * \c pRfft points to the real FFT instance;   
+ * \c pCfft points to the complex FFT instance;   
+ * The CFFT and RFFT structures also needs to be initialized, refer to arm_cfft_radix4_f32()   
+ * and arm_rfft_f32() respectively for details regarding static initialization.   
+ *   
+ * \par Fixed-Point Behavior    
+ * Care must be taken when using the fixed-point versions of the DCT4 transform functions.    
+ * In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.    
+ * Refer to the function specific documentation below for usage guidelines.    
+ */
+
+ /**    
+ * @addtogroup DCT4_IDCT4    
+ * @{    
+ */
+
+/**    
+ * @brief Processing function for the floating-point DCT4/IDCT4.   
+ * @param[in]       *S             points to an instance of the floating-point DCT4/IDCT4 structure.   
+ * @param[in]       *pState        points to state buffer.   
+ * @param[in,out]   *pInlineBuffer points to the in-place input and output buffer.   
+ * @return none.   
+ */
+
+void arm_dct4_f32(
+  const arm_dct4_instance_f32 * S,
+  float32_t * pState,
+  float32_t * pInlineBuffer)
+{
+  uint32_t i;                                    /* Loop counter */
+  float32_t *weights = S->pTwiddle;              /* Pointer to the Weights table */
+  float32_t *cosFact = S->pCosFactor;            /* Pointer to the cos factors table */
+  float32_t *pS1, *pS2, *pbuff;                  /* Temporary pointers for input buffer and pState buffer */
+  float32_t in;                                  /* Temporary variable */
+
+
+  /* DCT4 computation involves DCT2 (which is calculated using RFFT)    
+   * along with some pre-processing and post-processing.    
+   * Computational procedure is explained as follows:    
+   * (a) Pre-processing involves multiplying input with cos factor,    
+   *     r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n))    
+   *              where,    
+   *                 r(n) -- output of preprocessing    
+   *                 u(n) -- input to preprocessing(actual Source buffer)    
+   * (b) Calculation of DCT2 using FFT is divided into three steps:    
+   *                  Step1: Re-ordering of even and odd elements of input.    
+   *                  Step2: Calculating FFT of the re-ordered input.    
+   *                  Step3: Taking the real part of the product of FFT output and weights.    
+   * (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation:    
+   *                   Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)    
+   *                        where,    
+   *                           Y4 -- DCT4 output,   Y2 -- DCT2 output    
+   * (d) Multiplying the output with the normalizing factor sqrt(2/N).    
+   */
+
+        /*-------- Pre-processing ------------*/
+  /* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */
+  arm_scale_f32(pInlineBuffer, 2.0f, pInlineBuffer, S->N);
+  arm_mult_f32(pInlineBuffer, cosFact, pInlineBuffer, S->N);
+
+  /* ----------------------------------------------------------------    
+   * Step1: Re-ordering of even and odd elements as,    
+   *             pState[i] =  pInlineBuffer[2*i] and    
+   *             pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2    
+   ---------------------------------------------------------------------*/
+
+  /* pS1 initialized to pState */
+  pS1 = pState;
+
+  /* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */
+  pS2 = pState + (S->N - 1u);
+
+  /* pbuff initialized to input buffer */
+  pbuff = pInlineBuffer;
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */
+  i = (uint32_t) S->Nby2 >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  do
+  {
+    /* Re-ordering of even and odd elements */
+    /* pState[i] =  pInlineBuffer[2*i] */
+    *pS1++ = *pbuff++;
+    /* pState[N-i-1] = pInlineBuffer[2*i+1] */
+    *pS2-- = *pbuff++;
+
+    *pS1++ = *pbuff++;
+    *pS2-- = *pbuff++;
+
+    *pS1++ = *pbuff++;
+    *pS2-- = *pbuff++;
+
+    *pS1++ = *pbuff++;
+    *pS2-- = *pbuff++;
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+  /* pbuff initialized to input buffer */
+  pbuff = pInlineBuffer;
+
+  /* pS1 initialized to pState */
+  pS1 = pState;
+
+  /* Initializing the loop counter to N/4 instead of N for loop unrolling */
+  i = (uint32_t) S->N >> 2u;
+
+  /* Processing with loop unrolling 4 times as N is always multiple of 4.    
+   * Compute 4 outputs at a time */
+  do
+  {
+    /* Writing the re-ordered output back to inplace input buffer */
+    *pbuff++ = *pS1++;
+    *pbuff++ = *pS1++;
+    *pbuff++ = *pS1++;
+    *pbuff++ = *pS1++;
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+
+  /* ---------------------------------------------------------    
+   *     Step2: Calculate RFFT for N-point input    
+   * ---------------------------------------------------------- */
+  /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
+  arm_rfft_f32(S->pRfft, pInlineBuffer, pState);
+
+        /*----------------------------------------------------------------------    
+	 *  Step3: Multiply the FFT output with the weights.    
+	 *----------------------------------------------------------------------*/
+  arm_cmplx_mult_cmplx_f32(pState, weights, pState, S->N);
+
+  /* ----------- Post-processing ---------- */
+  /* DCT-IV can be obtained from DCT-II by the equation,    
+   *       Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)    
+   *       Hence, Y4(0) = Y2(0)/2  */
+  /* Getting only real part from the output and Converting to DCT-IV */
+
+  /* Initializing the loop counter to N >> 2 for loop unrolling by 4 */
+  i = ((uint32_t) S->N - 1u) >> 2u;
+
+  /* pbuff initialized to input buffer. */
+  pbuff = pInlineBuffer;
+
+  /* pS1 initialized to pState */
+  pS1 = pState;
+
+  /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
+  in = *pS1++ * (float32_t) 0.5;
+  /* input buffer acts as inplace, so output values are stored in the input itself. */
+  *pbuff++ = in;
+
+  /* pState pointer is incremented twice as the real values are located alternatively in the array */
+  pS1++;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  do
+  {
+    /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
+    /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
+    in = *pS1++ - in;
+    *pbuff++ = in;
+    /* points to the next real value */
+    pS1++;
+
+    in = *pS1++ - in;
+    *pbuff++ = in;
+    pS1++;
+
+    in = *pS1++ - in;
+    *pbuff++ = in;
+    pS1++;
+
+    in = *pS1++ - in;
+    *pbuff++ = in;
+    pS1++;
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  i = ((uint32_t) S->N - 1u) % 0x4u;
+
+  while(i > 0u)
+  {
+    /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
+    /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
+    in = *pS1++ - in;
+    *pbuff++ = in;
+    /* points to the next real value */
+    pS1++;
+
+    /* Decrement the loop counter */
+    i--;
+  }
+
+
+        /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
+
+  /* Initializing the loop counter to N/4 instead of N for loop unrolling */
+  i = (uint32_t) S->N >> 2u;
+
+  /* pbuff initialized to the pInlineBuffer(now contains the output values) */
+  pbuff = pInlineBuffer;
+
+  /* Processing with loop unrolling 4 times as N is always multiple of 4.  Compute 4 outputs at a time */
+  do
+  {
+    /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
+    in = *pbuff;
+    *pbuff++ = in * S->normalize;
+
+    in = *pbuff;
+    *pbuff++ = in * S->normalize;
+
+    in = *pbuff;
+    *pbuff++ = in * S->normalize;
+
+    in = *pbuff;
+    *pbuff++ = in * S->normalize;
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initializing the loop counter to N/2 */
+  i = (uint32_t) S->Nby2;
+
+  do
+  {
+    /* Re-ordering of even and odd elements */
+    /* pState[i] =  pInlineBuffer[2*i] */
+    *pS1++ = *pbuff++;
+    /* pState[N-i-1] = pInlineBuffer[2*i+1] */
+    *pS2-- = *pbuff++;
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+  /* pbuff initialized to input buffer */
+  pbuff = pInlineBuffer;
+
+  /* pS1 initialized to pState */
+  pS1 = pState;
+
+  /* Initializing the loop counter */
+  i = (uint32_t) S->N;
+
+  do
+  {
+    /* Writing the re-ordered output back to inplace input buffer */
+    *pbuff++ = *pS1++;
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+
+  /* ---------------------------------------------------------    
+   *     Step2: Calculate RFFT for N-point input    
+   * ---------------------------------------------------------- */
+  /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
+  arm_rfft_f32(S->pRfft, pInlineBuffer, pState);
+
+        /*----------------------------------------------------------------------    
+	 *  Step3: Multiply the FFT output with the weights.    
+	 *----------------------------------------------------------------------*/
+  arm_cmplx_mult_cmplx_f32(pState, weights, pState, S->N);
+
+  /* ----------- Post-processing ---------- */
+  /* DCT-IV can be obtained from DCT-II by the equation,    
+   *       Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)    
+   *       Hence, Y4(0) = Y2(0)/2  */
+  /* Getting only real part from the output and Converting to DCT-IV */
+
+  /* pbuff initialized to input buffer. */
+  pbuff = pInlineBuffer;
+
+  /* pS1 initialized to pState */
+  pS1 = pState;
+
+  /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
+  in = *pS1++ * (float32_t) 0.5;
+  /* input buffer acts as inplace, so output values are stored in the input itself. */
+  *pbuff++ = in;
+
+  /* pState pointer is incremented twice as the real values are located alternatively in the array */
+  pS1++;
+
+  /* Initializing the loop counter */
+  i = ((uint32_t) S->N - 1u);
+
+  do
+  {
+    /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
+    /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
+    in = *pS1++ - in;
+    *pbuff++ = in;
+    /* points to the next real value */
+    pS1++;
+
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+
+        /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
+
+  /* Initializing the loop counter */
+  i = (uint32_t) S->N;
+
+  /* pbuff initialized to the pInlineBuffer(now contains the output values) */
+  pbuff = pInlineBuffer;
+
+  do
+  {
+    /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
+    in = *pbuff;
+    *pbuff++ = in * S->normalize;
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+   * @} end of DCT4_IDCT4 group    
+   */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_dct4_init_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_dct4_init_f32.c
new file mode 100644
index 0000000000..b5f91ea325
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_dct4_init_f32.c
@@ -0,0 +1,16511 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_dct4_init_f32.c    
+*    
+* Description:	Initialization function of DCT-4 & IDCT4 F32    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupTransforms    
+ */
+
+/**    
+ * @addtogroup DCT4_IDCT4    
+ * @{    
+ */
+
+/*    
+* @brief  Weights Table    
+*/
+
+/**    
+* \par    
+* Weights tables are generated using the formula : 
weights[n] = e^(-j*n*pi/(2*N))
    
+* \par    
+* C command to generate the table    
+* 
    
+* for(i = 0; i< N; i++)    
+* {    
+*    weights[2*i]= cos(i*c);    
+*    weights[(2*i)+1]= -sin(i * c);    
+* } 
    
+* \par    
+* Where N is the Number of weights to be calculated and c is pi/(2*N)    
+* \par    
+* In the tables below the real and imaginary values are placed alternatively, hence the    
+* array length is 2*N.    
+*/
+
+static const float32_t Weights_128[256] = {
+  1.000000000000000000f, 0.000000000000000000f, 0.999924701839144500f,
+  -0.012271538285719925f,
+  0.999698818696204250f, -0.024541228522912288f, 0.999322384588349540f,
+  -0.036807222941358832f,
+  0.998795456205172410f, -0.049067674327418015f, 0.998118112900149180f,
+  -0.061320736302208578f,
+  0.997290456678690210f, -0.073564563599667426f, 0.996312612182778000f,
+  -0.085797312344439894f,
+  0.995184726672196930f, -0.098017140329560604f, 0.993906970002356060f,
+  -0.110222207293883060f,
+  0.992479534598709970f, -0.122410675199216200f, 0.990902635427780010f,
+  -0.134580708507126170f,
+  0.989176509964781010f, -0.146730474455361750f, 0.987301418157858430f,
+  -0.158858143333861450f,
+  0.985277642388941220f, -0.170961888760301220f, 0.983105487431216290f,
+  -0.183039887955140950f,
+  0.980785280403230430f, -0.195090322016128250f, 0.978317370719627650f,
+  -0.207111376192218560f,
+  0.975702130038528570f, -0.219101240156869800f, 0.972939952205560180f,
+  -0.231058108280671110f,
+  0.970031253194543970f, -0.242980179903263870f, 0.966976471044852070f,
+  -0.254865659604514570f,
+  0.963776065795439840f, -0.266712757474898370f, 0.960430519415565790f,
+  -0.278519689385053060f,
+  0.956940335732208820f, -0.290284677254462330f, 0.953306040354193860f,
+  -0.302005949319228080f,
+  0.949528180593036670f, -0.313681740398891520f, 0.945607325380521280f,
+  -0.325310292162262930f,
+  0.941544065183020810f, -0.336889853392220050f, 0.937339011912574960f,
+  -0.348418680249434560f,
+  0.932992798834738960f, -0.359895036534988110f, 0.928506080473215590f,
+  -0.371317193951837540f,
+  0.923879532511286740f, -0.382683432365089780f, 0.919113851690057770f,
+  -0.393992040061048100f,
+  0.914209755703530690f, -0.405241314004989860f, 0.909167983090522380f,
+  -0.416429560097637150f,
+  0.903989293123443340f, -0.427555093430282080f, 0.898674465693953820f,
+  -0.438616238538527660f,
+  0.893224301195515320f, -0.449611329654606540f, 0.887639620402853930f,
+  -0.460538710958240010f,
+  0.881921264348355050f, -0.471396736825997640f, 0.876070094195406600f,
+  -0.482183772079122720f,
+  0.870086991108711460f, -0.492898192229784040f, 0.863972856121586810f,
+  -0.503538383725717580f,
+  0.857728610000272120f, -0.514102744193221660f, 0.851355193105265200f,
+  -0.524589682678468950f,
+  0.844853565249707120f, -0.534997619887097150f, 0.838224705554838080f,
+  -0.545324988422046460f,
+  0.831469612302545240f, -0.555570233019602180f, 0.824589302785025290f,
+  -0.565731810783613120f,
+  0.817584813151583710f, -0.575808191417845340f, 0.810457198252594770f,
+  -0.585797857456438860f,
+  0.803207531480644940f, -0.595699304492433360f, 0.795836904608883570f,
+  -0.605511041404325550f,
+  0.788346427626606340f, -0.615231590580626820f, 0.780737228572094490f,
+  -0.624859488142386340f,
+  0.773010453362736990f, -0.634393284163645490f, 0.765167265622458960f,
+  -0.643831542889791390f,
+  0.757208846506484570f, -0.653172842953776760f, 0.749136394523459370f,
+  -0.662415777590171780f,
+  0.740951125354959110f, -0.671558954847018330f, 0.732654271672412820f,
+  -0.680600997795453020f,
+  0.724247082951467000f, -0.689540544737066830f, 0.715730825283818590f,
+  -0.698376249408972920f,
+  0.707106781186547570f, -0.707106781186547460f, 0.698376249408972920f,
+  -0.715730825283818590f,
+  0.689540544737066940f, -0.724247082951466890f, 0.680600997795453130f,
+  -0.732654271672412820f,
+  0.671558954847018330f, -0.740951125354959110f, 0.662415777590171780f,
+  -0.749136394523459260f,
+  0.653172842953776760f, -0.757208846506484460f, 0.643831542889791500f,
+  -0.765167265622458960f,
+  0.634393284163645490f, -0.773010453362736990f, 0.624859488142386450f,
+  -0.780737228572094380f,
+  0.615231590580626820f, -0.788346427626606230f, 0.605511041404325550f,
+  -0.795836904608883460f,
+  0.595699304492433470f, -0.803207531480644830f, 0.585797857456438860f,
+  -0.810457198252594770f,
+  0.575808191417845340f, -0.817584813151583710f, 0.565731810783613230f,
+  -0.824589302785025290f,
+  0.555570233019602290f, -0.831469612302545240f, 0.545324988422046460f,
+  -0.838224705554837970f,
+  0.534997619887097260f, -0.844853565249707010f, 0.524589682678468840f,
+  -0.851355193105265200f,
+  0.514102744193221660f, -0.857728610000272120f, 0.503538383725717580f,
+  -0.863972856121586700f,
+  0.492898192229784090f, -0.870086991108711350f, 0.482183772079122830f,
+  -0.876070094195406600f,
+  0.471396736825997810f, -0.881921264348354940f, 0.460538710958240010f,
+  -0.887639620402853930f,
+  0.449611329654606600f, -0.893224301195515320f, 0.438616238538527710f,
+  -0.898674465693953820f,
+  0.427555093430282200f, -0.903989293123443340f, 0.416429560097637320f,
+  -0.909167983090522270f,
+  0.405241314004989860f, -0.914209755703530690f, 0.393992040061048100f,
+  -0.919113851690057770f,
+  0.382683432365089840f, -0.923879532511286740f, 0.371317193951837600f,
+  -0.928506080473215480f,
+  0.359895036534988280f, -0.932992798834738850f, 0.348418680249434510f,
+  -0.937339011912574960f,
+  0.336889853392220050f, -0.941544065183020810f, 0.325310292162262980f,
+  -0.945607325380521280f,
+  0.313681740398891570f, -0.949528180593036670f, 0.302005949319228200f,
+  -0.953306040354193750f,
+  0.290284677254462330f, -0.956940335732208940f, 0.278519689385053060f,
+  -0.960430519415565790f,
+  0.266712757474898420f, -0.963776065795439840f, 0.254865659604514630f,
+  -0.966976471044852070f,
+  0.242980179903263980f, -0.970031253194543970f, 0.231058108280671280f,
+  -0.972939952205560070f,
+  0.219101240156869770f, -0.975702130038528570f, 0.207111376192218560f,
+  -0.978317370719627650f,
+  0.195090322016128330f, -0.980785280403230430f, 0.183039887955141060f,
+  -0.983105487431216290f,
+  0.170961888760301360f, -0.985277642388941220f, 0.158858143333861390f,
+  -0.987301418157858430f,
+  0.146730474455361750f, -0.989176509964781010f, 0.134580708507126220f,
+  -0.990902635427780010f,
+  0.122410675199216280f, -0.992479534598709970f, 0.110222207293883180f,
+  -0.993906970002356060f,
+  0.098017140329560770f, -0.995184726672196820f, 0.085797312344439880f,
+  -0.996312612182778000f,
+  0.073564563599667454f, -0.997290456678690210f, 0.061320736302208648f,
+  -0.998118112900149180f,
+  0.049067674327418126f, -0.998795456205172410f, 0.036807222941358991f,
+  -0.999322384588349540f,
+  0.024541228522912264f, -0.999698818696204250f, 0.012271538285719944f,
+  -0.999924701839144500f
+};
+
+static const float32_t Weights_512[1024] = {
+  1.000000000000000000f, 0.000000000000000000f, 0.999995293809576190f,
+  -0.003067956762965976f,
+  0.999981175282601110f, -0.006135884649154475f, 0.999957644551963900f,
+  -0.009203754782059819f,
+  0.999924701839144500f, -0.012271538285719925f, 0.999882347454212560f,
+  -0.015339206284988100f,
+  0.999830581795823400f, -0.018406729905804820f, 0.999769405351215280f,
+  -0.021474080275469508f,
+  0.999698818696204250f, -0.024541228522912288f, 0.999618822495178640f,
+  -0.027608145778965740f,
+  0.999529417501093140f, -0.030674803176636626f, 0.999430604555461730f,
+  -0.033741171851377580f,
+  0.999322384588349540f, -0.036807222941358832f, 0.999204758618363890f,
+  -0.039872927587739811f,
+  0.999077727752645360f, -0.042938256934940820f, 0.998941293186856870f,
+  -0.046003182130914623f,
+  0.998795456205172410f, -0.049067674327418015f, 0.998640218180265270f,
+  -0.052131704680283324f,
+  0.998475580573294770f, -0.055195244349689934f, 0.998301544933892890f,
+  -0.058258264500435752f,
+  0.998118112900149180f, -0.061320736302208578f, 0.997925286198596000f,
+  -0.064382630929857465f,
+  0.997723066644191640f, -0.067443919563664051f, 0.997511456140303450f,
+  -0.070504573389613856f,
+  0.997290456678690210f, -0.073564563599667426f, 0.997060070339482960f,
+  -0.076623861392031492f,
+  0.996820299291165670f, -0.079682437971430126f, 0.996571145790554840f,
+  -0.082740264549375692f,
+  0.996312612182778000f, -0.085797312344439894f, 0.996044700901251970f,
+  -0.088853552582524600f,
+  0.995767414467659820f, -0.091908956497132724f, 0.995480755491926940f,
+  -0.094963495329638992f,
+  0.995184726672196930f, -0.098017140329560604f, 0.994879330794805620f,
+  -0.101069862754827820f,
+  0.994564570734255420f, -0.104121633872054590f, 0.994240449453187900f,
+  -0.107172424956808840f,
+  0.993906970002356060f, -0.110222207293883060f, 0.993564135520595300f,
+  -0.113270952177564350f,
+  0.993211949234794500f, -0.116318630911904750f, 0.992850414459865100f,
+  -0.119365214810991350f,
+  0.992479534598709970f, -0.122410675199216200f, 0.992099313142191800f,
+  -0.125454983411546230f,
+  0.991709753669099530f, -0.128498110793793170f, 0.991310859846115440f,
+  -0.131540028702883120f,
+  0.990902635427780010f, -0.134580708507126170f, 0.990485084256457090f,
+  -0.137620121586486040f,
+  0.990058210262297120f, -0.140658239332849210f, 0.989622017463200890f,
+  -0.143695033150294470f,
+  0.989176509964781010f, -0.146730474455361750f, 0.988721691960323780f,
+  -0.149764534677321510f,
+  0.988257567730749460f, -0.152797185258443440f, 0.987784141644572180f,
+  -0.155828397654265230f,
+  0.987301418157858430f, -0.158858143333861450f, 0.986809401814185530f,
+  -0.161886393780111830f,
+  0.986308097244598670f, -0.164913120489969890f, 0.985797509167567480f,
+  -0.167938294974731170f,
+  0.985277642388941220f, -0.170961888760301220f, 0.984748501801904210f,
+  -0.173983873387463820f,
+  0.984210092386929030f, -0.177004220412148750f, 0.983662419211730250f,
+  -0.180022901405699510f,
+  0.983105487431216290f, -0.183039887955140950f, 0.982539302287441240f,
+  -0.186055151663446630f,
+  0.981963869109555240f, -0.189068664149806190f, 0.981379193313754560f,
+  -0.192080397049892440f,
+  0.980785280403230430f, -0.195090322016128250f, 0.980182135968117430f,
+  -0.198098410717953560f,
+  0.979569765685440520f, -0.201104634842091900f, 0.978948175319062200f,
+  -0.204108966092816870f,
+  0.978317370719627650f, -0.207111376192218560f, 0.977677357824509930f,
+  -0.210111836880469610f,
+  0.977028142657754390f, -0.213110319916091360f, 0.976369731330021140f,
+  -0.216106797076219520f,
+  0.975702130038528570f, -0.219101240156869800f, 0.975025345066994120f,
+  -0.222093620973203510f,
+  0.974339382785575860f, -0.225083911359792830f, 0.973644249650811980f,
+  -0.228072083170885730f,
+  0.972939952205560180f, -0.231058108280671110f, 0.972226497078936270f,
+  -0.234041958583543430f,
+  0.971503890986251780f, -0.237023605994367200f, 0.970772140728950350f,
+  -0.240003022448741500f,
+  0.970031253194543970f, -0.242980179903263870f, 0.969281235356548530f,
+  -0.245955050335794590f,
+  0.968522094274417380f, -0.248927605745720150f, 0.967753837093475510f,
+  -0.251897818154216970f,
+  0.966976471044852070f, -0.254865659604514570f, 0.966190003445412500f,
+  -0.257831102162158990f,
+  0.965394441697689400f, -0.260794117915275510f, 0.964589793289812760f,
+  -0.263754678974831350f,
+  0.963776065795439840f, -0.266712757474898370f, 0.962953266873683880f,
+  -0.269668325572915090f,
+  0.962121404269041580f, -0.272621355449948980f, 0.961280485811320640f,
+  -0.275571819310958140f,
+  0.960430519415565790f, -0.278519689385053060f, 0.959571513081984520f,
+  -0.281464937925757940f,
+  0.958703474895871600f, -0.284407537211271880f, 0.957826413027532910f,
+  -0.287347459544729510f,
+  0.956940335732208820f, -0.290284677254462330f, 0.956045251349996410f,
+  -0.293219162694258630f,
+  0.955141168305770780f, -0.296150888243623790f, 0.954228095109105670f,
+  -0.299079826308040480f,
+  0.953306040354193860f, -0.302005949319228080f, 0.952375012719765880f,
+  -0.304929229735402370f,
+  0.951435020969008340f, -0.307849640041534870f, 0.950486073949481700f,
+  -0.310767152749611470f,
+  0.949528180593036670f, -0.313681740398891520f, 0.948561349915730270f,
+  -0.316593375556165850f,
+  0.947585591017741090f, -0.319502030816015690f, 0.946600913083283530f,
+  -0.322407678801069850f,
+  0.945607325380521280f, -0.325310292162262930f, 0.944604837261480260f,
+  -0.328209843579092500f,
+  0.943593458161960390f, -0.331106305759876430f, 0.942573197601446870f,
+  -0.333999651442009380f,
+  0.941544065183020810f, -0.336889853392220050f, 0.940506070593268300f,
+  -0.339776884406826850f,
+  0.939459223602189920f, -0.342660717311994380f, 0.938403534063108060f,
+  -0.345541324963989090f,
+  0.937339011912574960f, -0.348418680249434560f, 0.936265667170278260f,
+  -0.351292756085567090f,
+  0.935183509938947610f, -0.354163525420490340f, 0.934092550404258980f,
+  -0.357030961233429980f,
+  0.932992798834738960f, -0.359895036534988110f, 0.931884265581668150f,
+  -0.362755724367397230f,
+  0.930766961078983710f, -0.365612997804773850f, 0.929640895843181330f,
+  -0.368466829953372320f,
+  0.928506080473215590f, -0.371317193951837540f, 0.927362525650401110f,
+  -0.374164062971457930f,
+  0.926210242138311380f, -0.377007410216418260f, 0.925049240782677580f,
+  -0.379847208924051160f,
+  0.923879532511286740f, -0.382683432365089780f, 0.922701128333878630f,
+  -0.385516053843918850f,
+  0.921514039342042010f, -0.388345046698826250f, 0.920318276709110590f,
+  -0.391170384302253870f,
+  0.919113851690057770f, -0.393992040061048100f, 0.917900775621390500f,
+  -0.396809987416710310f,
+  0.916679059921042700f, -0.399624199845646790f, 0.915448716088267830f,
+  -0.402434650859418430f,
+  0.914209755703530690f, -0.405241314004989860f, 0.912962190428398210f,
+  -0.408044162864978690f,
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+  -0.996571145790554840f,
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+  -0.997060070339482960f,
+  0.073564563599667454f, -0.997290456678690210f, 0.070504573389614009f,
+  -0.997511456140303450f,
+  0.067443919563664106f, -0.997723066644191640f, 0.064382630929857410f,
+  -0.997925286198596000f,
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+  -0.998301544933892890f,
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+  -0.998640218180265270f,
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+  -0.998941293186856870f,
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+  -0.999204758618363890f,
+  0.036807222941358991f, -0.999322384588349540f, 0.033741171851377642f,
+  -0.999430604555461730f,
+  0.030674803176636581f, -0.999529417501093140f, 0.027608145778965820f,
+  -0.999618822495178640f,
+  0.024541228522912264f, -0.999698818696204250f, 0.021474080275469605f,
+  -0.999769405351215280f,
+  0.018406729905804820f, -0.999830581795823400f, 0.015339206284988220f,
+  -0.999882347454212560f,
+  0.012271538285719944f, -0.999924701839144500f, 0.009203754782059960f,
+  -0.999957644551963900f,
+  0.006135884649154515f, -0.999981175282601110f, 0.003067956762966138f,
+  -0.999995293809576190f
+};
+
+static const float32_t Weights_2048[4096] = {
+  1.000000000000000000f, 0.000000000000000000f, 0.999999705862882230f,
+  -0.000766990318742704f,
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+  -0.002300969151425805f,
+  0.999995293809576190f, -0.003067956762965976f, 0.999992646580707190f,
+  -0.003834942569706228f,
+  0.999989411081928400f, -0.004601926120448571f, 0.999985587315143200f,
+  -0.005368906963996343f,
+  0.999981175282601110f, -0.006135884649154475f, 0.999976174986897610f,
+  -0.006902858724729756f,
+  0.999970586430974140f, -0.007669828739531097f, 0.999964409618118280f,
+  -0.008436794242369799f,
+  0.999957644551963900f, -0.009203754782059819f, 0.999950291236490480f,
+  -0.009970709907418031f,
+  0.999942349676023910f, -0.010737659167264491f, 0.999933819875236000f,
+  -0.011504602110422714f,
+  0.999924701839144500f, -0.012271538285719925f, 0.999914995573113470f,
+  -0.013038467241987334f,
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+  -0.014572301692779064f,
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+  -0.016106101853537287f,
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+  -0.017639864115082053f,
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+  -0.019173584868322623f,
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+  -0.020707260504265895f,
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+  -0.022240887414024961f,
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+  -0.023774461988827555f,
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+  -0.025307980620024571f,
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+  -0.054429407010919133f,
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+  -0.055961049218520569f,
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+  -0.999999705862882230f
+};
+
+static const float32_t Weights_8192[16384] = {
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+  0.017639864115082195, -0.999844405492175240, 0.017448146028360704,
+    -0.999847769513025900,
+  0.017256427300120978, -0.999851096772332190, 0.017064707937411529,
+    -0.999854387269971890,
+  0.016872987947281773, -0.999857641005823860, 0.016681267336780482,
+    -0.999860857979768540,
+  0.016489546112956454, -0.999864038191687680, 0.016297824282859176,
+    -0.999867181641464380,
+  0.016106101853537263, -0.999870288328982950, 0.015914378832040249,
+    -0.999873358254129260,
+  0.015722655225417017, -0.999876391416790410, 0.015530931040716478,
+    -0.999879387816854930,
+  0.015339206284988220, -0.999882347454212560, 0.015147480965280975,
+    -0.999885270328754520,
+  0.014955755088644378, -0.999888156440373320, 0.014764028662127416,
+    -0.999891005788962950,
+  0.014572301692779104, -0.999893818374418490, 0.014380574187649138,
+    -0.999896594196636680,
+  0.014188846153786343, -0.999899333255515390, 0.013997117598240459,
+    -0.999902035550953920,
+  0.013805388528060349, -0.999904701082852900, 0.013613658950295789,
+    -0.999907329851114300,
+  0.013421928871995907, -0.999909921855641540, 0.013230198300209845,
+    -0.999912477096339240,
+  0.013038467241987433, -0.999914995573113470, 0.012846735704377631,
+    -0.999917477285871770,
+  0.012655003694430301, -0.999919922234522750, 0.012463271219194662,
+    -0.999922330418976490,
+  0.012271538285719944, -0.999924701839144500, 0.012079804901056066,
+    -0.999927036494939640,
+  0.011888071072252072, -0.999929334386276070, 0.011696336806357907,
+    -0.999931595513069200,
+  0.011504602110422875, -0.999933819875236000, 0.011312866991496287,
+    -0.999936007472694620,
+  0.011121131456628141, -0.999938158305364590, 0.010929395512867561,
+    -0.999940272373166960,
+  0.010737659167264572, -0.999942349676023910, 0.010545922426868548,
+    -0.999944390213859060,
+  0.010354185298728884, -0.999946393986597460, 0.010162447789895645,
+    -0.999948360994165400,
+  0.009970709907418029, -0.999950291236490480, 0.009778971658346134,
+    -0.999952184713501780,
+  0.009587233049729183, -0.999954041425129780, 0.009395494088617302,
+    -0.999955861371306100,
+  0.009203754782059960, -0.999957644551963900, 0.009012015137106642,
+    -0.999959390967037450,
+  0.008820275160807512, -0.999961100616462820, 0.008628534860211857,
+    -0.999962773500176930,
+  0.008436794242369860, -0.999964409618118280, 0.008245053314331058,
+    -0.999966008970226920,
+  0.008053312083144991, -0.999967571556443780, 0.007861570555861883,
+    -0.999969097376711580,
+  0.007669828739531077, -0.999970586430974140, 0.007478086641202815,
+    -0.999972038719176730,
+  0.007286344267926684, -0.999973454241265940, 0.007094601626752279,
+    -0.999974832997189810,
+  0.006902858724729877, -0.999976174986897610, 0.006711115568908869,
+    -0.999977480210339940,
+  0.006519372166339549, -0.999978748667468830, 0.006327628524071549,
+    -0.999979980358237650,
+  0.006135884649154515, -0.999981175282601110, 0.005944140548638765,
+    -0.999982333440515350,
+  0.005752396229573737, -0.999983454831937730, 0.005560651699009764,
+    -0.999984539456826970,
+  0.005368906963996303, -0.999985587315143200, 0.005177162031583702,
+    -0.999986598406848000,
+  0.004985416908821652, -0.999987572731904080, 0.004793671602759852,
+    -0.999988510290275690,
+  0.004601926120448672, -0.999989411081928400, 0.004410180468937601,
+    -0.999990275106828920,
+  0.004218434655277024, -0.999991102364945590, 0.004026688686516664,
+    -0.999991892856248010,
+  0.003834942569706248, -0.999992646580707190, 0.003643196311896179,
+    -0.999993363538295150,
+  0.003451449920135975, -0.999994043728985820, 0.003259703401476044,
+    -0.999994687152754080,
+  0.003067956762966138, -0.999995293809576190, 0.002876210011656010,
+    -0.999995863699429940,
+  0.002684463154596083, -0.999996396822294350, 0.002492716198835898,
+    -0.999996893178149880,
+  0.002300969151425887, -0.999997352766978210, 0.002109222019415816,
+    -0.999997775588762350,
+  0.001917474809855460, -0.999998161643486980, 0.001725727529795258,
+    -0.999998510931137790,
+  0.001533980186284766, -0.999998823451701880, 0.001342232786374430,
+    -0.999999099205167830,
+  0.001150485337113809, -0.999999338191525530, 0.000958737845553352,
+    -0.999999540410766110,
+  0.000766990318742846, -0.999999705862882230, 0.000575242763732077,
+    -0.999999834547867670,
+  0.000383495187571497, -0.999999926465717890, 0.000191747597310674,
+    -0.999999981616429330,
+
+};
+
+/**    
+* \par    
+* cosFactor tables are generated using the formula : 
cos_factors[n] = 2 * cos((2n+1)*pi/(4*N))
    
+* \par    
+* C command to generate the table    
+* \par    
+* 
 for(i = 0; i< N; i++)    
+* {    
+*    cos_factors[i]= 2 * cos((2*i+1)*c/2);    
+* } 
    
+* \par    
+* where N is the number of factors to generate and c is pi/(2*N)    
+*/
+static const float32_t cos_factors_128[128] = {
+  0.999981175282601110f, 0.999830581795823400f, 0.999529417501093140f,
+  0.999077727752645360f,
+  0.998475580573294770f, 0.997723066644191640f, 0.996820299291165670f,
+  0.995767414467659820f,
+  0.994564570734255420f, 0.993211949234794500f, 0.991709753669099530f,
+  0.990058210262297120f,
+  0.988257567730749460f, 0.986308097244598670f, 0.984210092386929030f,
+  0.981963869109555240f,
+  0.979569765685440520f, 0.977028142657754390f, 0.974339382785575860f,
+  0.971503890986251780f,
+  0.968522094274417380f, 0.965394441697689400f, 0.962121404269041580f,
+  0.958703474895871600f,
+  0.955141168305770780f, 0.951435020969008340f, 0.947585591017741090f,
+  0.943593458161960390f,
+  0.939459223602189920f, 0.935183509938947610f, 0.930766961078983710f,
+  0.926210242138311380f,
+  0.921514039342042010f, 0.916679059921042700f, 0.911706032005429880f,
+  0.906595704514915330f,
+  0.901348847046022030f, 0.895966249756185220f, 0.890448723244757880f,
+  0.884797098430937790f,
+  0.879012226428633530f, 0.873094978418290090f, 0.867046245515692650f,
+  0.860866938637767310f,
+  0.854557988365400530f, 0.848120344803297230f, 0.841554977436898440f,
+  0.834862874986380010f,
+  0.828045045257755800f, 0.821102514991104650f, 0.814036329705948410f,
+  0.806847553543799330f,
+  0.799537269107905010f, 0.792106577300212390f, 0.784556597155575240f,
+  0.776888465673232440f,
+  0.769103337645579700f, 0.761202385484261780f, 0.753186799043612520f,
+  0.745057785441466060f,
+  0.736816568877369900f, 0.728464390448225200f, 0.720002507961381650f,
+  0.711432195745216430f,
+  0.702754744457225300f, 0.693971460889654000f, 0.685083667772700360f,
+  0.676092703575316030f,
+  0.666999922303637470f, 0.657806693297078640f, 0.648514401022112550f,
+  0.639124444863775730f,
+  0.629638238914927100f, 0.620057211763289210f, 0.610382806276309480f,
+  0.600616479383868970f,
+  0.590759701858874280f, 0.580813958095764530f, 0.570780745886967370f,
+  0.560661576197336030f,
+  0.550457972936604810f, 0.540171472729892970f, 0.529803624686294830f,
+  0.519355990165589530f,
+  0.508830142543106990f, 0.498227666972781870f, 0.487550160148436050f,
+  0.476799230063322250f,
+  0.465976495767966130f, 0.455083587126343840f, 0.444122144570429260f,
+  0.433093818853152010f,
+  0.422000270799799790f, 0.410843171057903910f, 0.399624199845646790f,
+  0.388345046698826300f,
+  0.377007410216418310f, 0.365612997804773960f, 0.354163525420490510f,
+  0.342660717311994380f,
+  0.331106305759876430f, 0.319502030816015750f, 0.307849640041534980f,
+  0.296150888243623960f,
+  0.284407537211271820f, 0.272621355449948980f, 0.260794117915275570f,
+  0.248927605745720260f,
+  0.237023605994367340f, 0.225083911359792780f, 0.213110319916091360f,
+  0.201104634842091960f,
+  0.189068664149806280f, 0.177004220412148860f, 0.164913120489970090f,
+  0.152797185258443410f,
+  0.140658239332849240f, 0.128498110793793220f, 0.116318630911904880f,
+  0.104121633872054730f,
+  0.091908956497132696f, 0.079682437971430126f, 0.067443919563664106f,
+  0.055195244349690031f,
+  0.042938256934940959f, 0.030674803176636581f, 0.018406729905804820f,
+  0.006135884649154515f
+};
+
+static const float32_t cos_factors_512[512] = {
+  0.999998823451701880f, 0.999989411081928400f, 0.999970586430974140f,
+  0.999942349676023910f,
+  0.999904701082852900f, 0.999857641005823860f, 0.999801169887884260f,
+  0.999735288260561680f,
+  0.999659996743959220f, 0.999575296046749220f, 0.999481186966166950f,
+  0.999377670388002850f,
+  0.999264747286594420f, 0.999142418724816910f, 0.999010685854073380f,
+  0.998869549914283560f,
+  0.998719012233872940f, 0.998559074229759310f, 0.998389737407340160f,
+  0.998211003360478190f,
+  0.998022873771486240f, 0.997825350411111640f, 0.997618435138519550f,
+  0.997402129901275300f,
+  0.997176436735326190f, 0.996941357764982160f, 0.996696895202896060f,
+  0.996443051350042630f,
+  0.996179828595696980f, 0.995907229417411720f, 0.995625256380994310f,
+  0.995333912140482280f,
+  0.995033199438118630f, 0.994723121104325700f, 0.994403680057679100f,
+  0.994074879304879370f,
+  0.993736721940724600f, 0.993389211148080650f, 0.993032350197851410f,
+  0.992666142448948020f,
+  0.992290591348257370f, 0.991905700430609330f, 0.991511473318743900f,
+  0.991107913723276890f,
+  0.990695025442664630f, 0.990272812363169110f, 0.989841278458820530f,
+  0.989400427791380380f,
+  0.988950264510302990f, 0.988490792852696590f, 0.988022017143283530f,
+  0.987543941794359230f,
+  0.987056571305750970f, 0.986559910264775410f, 0.986053963346195440f,
+  0.985538735312176060f,
+  0.985014231012239840f, 0.984480455383220930f, 0.983937413449218920f,
+  0.983385110321551180f,
+  0.982823551198705240f, 0.982252741366289370f, 0.981672686196983110f,
+  0.981083391150486710f,
+  0.980484861773469380f, 0.979877103699517640f, 0.979260122649082020f,
+  0.978633924429423210f,
+  0.977998514934557140f, 0.977353900145199960f, 0.976700086128711840f,
+  0.976037079039039020f,
+  0.975364885116656980f, 0.974683510688510670f, 0.973992962167955830f,
+  0.973293246054698250f,
+  0.972584368934732210f, 0.971866337480279400f, 0.971139158449725090f,
+  0.970402838687555500f,
+  0.969657385124292450f, 0.968902804776428870f, 0.968139104746362440f,
+  0.967366292222328510f,
+  0.966584374478333120f, 0.965793358874083680f, 0.964993252854920320f,
+  0.964184063951745830f,
+  0.963365799780954050f, 0.962538468044359160f, 0.961702076529122540f,
+  0.960856633107679660f,
+  0.960002145737665960f, 0.959138622461841890f, 0.958266071408017670f,
+  0.957384500788975860f,
+  0.956493918902395100f, 0.955594334130771110f, 0.954685754941338340f,
+  0.953768189885990330f,
+  0.952841647601198720f, 0.951906136807932350f, 0.950961666311575080f,
+  0.950008245001843000f,
+  0.949045881852700560f, 0.948074585922276230f, 0.947094366352777220f,
+  0.946105232370403450f,
+  0.945107193285260610f, 0.944100258491272660f, 0.943084437466093490f,
+  0.942059739771017310f,
+  0.941026175050889260f, 0.939983753034014050f, 0.938932483532064600f,
+  0.937872376439989890f,
+  0.936803441735921560f, 0.935725689481080370f, 0.934639129819680780f,
+  0.933543772978836170f,
+  0.932439629268462360f, 0.931326709081180430f, 0.930205022892219070f,
+  0.929074581259315860f,
+  0.927935394822617890f, 0.926787474304581750f, 0.925630830509872720f,
+  0.924465474325262600f,
+  0.923291416719527640f, 0.922108668743345180f, 0.920917241529189520f,
+  0.919717146291227360f,
+  0.918508394325212250f, 0.917290997008377910f, 0.916064965799331720f,
+  0.914830312237946200f,
+  0.913587047945250810f, 0.912335184623322750f, 0.911074734055176360f,
+  0.909805708104652220f,
+  0.908528118716306120f, 0.907241977915295820f, 0.905947297807268460f,
+  0.904644090578246240f,
+  0.903332368494511820f, 0.902012143902493180f, 0.900683429228646970f,
+  0.899346236979341570f,
+  0.898000579740739880f, 0.896646470178680150f, 0.895283921038557580f,
+  0.893912945145203250f,
+  0.892533555402764580f, 0.891145764794583180f, 0.889749586383072780f,
+  0.888345033309596350f,
+  0.886932118794342190f, 0.885510856136199950f, 0.884081258712634990f,
+  0.882643339979562790f,
+  0.881197113471222090f, 0.879742592800047410f, 0.878279791656541580f,
+  0.876808723809145650f,
+  0.875329403104110890f, 0.873841843465366860f, 0.872346058894391540f,
+  0.870842063470078980f,
+  0.869329871348606840f, 0.867809496763303320f, 0.866280954024512990f,
+  0.864744257519462380f,
+  0.863199421712124160f, 0.861646461143081300f, 0.860085390429390140f,
+  0.858516224264442740f,
+  0.856938977417828760f, 0.855353664735196030f, 0.853760301138111410f,
+  0.852158901623919830f,
+  0.850549481265603480f, 0.848932055211639610f, 0.847306638685858320f,
+  0.845673246987299070f,
+  0.844031895490066410f, 0.842382599643185850f, 0.840725374970458070f,
+  0.839060237070312740f,
+  0.837387201615661940f, 0.835706284353752600f, 0.834017501106018130f,
+  0.832320867767929680f,
+  0.830616400308846310f, 0.828904114771864870f, 0.827184027273669130f,
+  0.825456154004377550f,
+  0.823720511227391430f, 0.821977115279241550f, 0.820225982569434690f,
+  0.818467129580298660f,
+  0.816700572866827850f, 0.814926329056526620f, 0.813144414849253590f,
+  0.811354847017063730f,
+  0.809557642404051260f, 0.807752817926190360f, 0.805940390571176280f,
+  0.804120377398265810f,
+  0.802292795538115720f, 0.800457662192622820f, 0.798614994634760820f,
+  0.796764810208418830f,
+  0.794907126328237010f, 0.793041960479443640f, 0.791169330217690200f,
+  0.789289253168885650f,
+  0.787401747029031430f, 0.785506829564053930f, 0.783604518609638200f,
+  0.781694832071059390f,
+  0.779777787923014550f, 0.777853404209453150f, 0.775921699043407690f,
+  0.773982690606822900f,
+  0.772036397150384520f, 0.770082836993347900f, 0.768122028523365420f,
+  0.766153990196312920f,
+  0.764178740536116670f, 0.762196298134578900f, 0.760206681651202420f,
+  0.758209909813015280f,
+  0.756206001414394540f, 0.754194975316889170f, 0.752176850449042810f,
+  0.750151645806215070f,
+  0.748119380450403600f, 0.746080073510063780f, 0.744033744179929290f,
+  0.741980411720831070f,
+  0.739920095459516200f, 0.737852814788465980f, 0.735778589165713590f,
+  0.733697438114660370f,
+  0.731609381223892630f, 0.729514438146997010f, 0.727412628602375770f,
+  0.725303972373060770f,
+  0.723188489306527460f, 0.721066199314508110f, 0.718937122372804490f,
+  0.716801278521099540f,
+  0.714658687862769090f, 0.712509370564692320f, 0.710353346857062420f,
+  0.708190637033195400f,
+  0.706021261449339740f, 0.703845240524484940f, 0.701662594740168570f,
+  0.699473344640283770f,
+  0.697277510830886630f, 0.695075113980000880f, 0.692866174817424740f,
+  0.690650714134534720f,
+  0.688428752784090550f, 0.686200311680038700f, 0.683965411797315510f,
+  0.681724074171649820f,
+  0.679476319899365080f, 0.677222170137180450f, 0.674961646102012040f,
+  0.672694769070772970f,
+  0.670421560380173090f, 0.668142041426518560f, 0.665856233665509720f,
+  0.663564158612039880f,
+  0.661265837839992270f, 0.658961292982037320f, 0.656650545729429050f,
+  0.654333617831800550f,
+  0.652010531096959500f, 0.649681307390683190f, 0.647345968636512060f,
+  0.645004536815544040f,
+  0.642657033966226860f, 0.640303482184151670f, 0.637943903621844170f,
+  0.635578320488556230f,
+  0.633206755050057190f, 0.630829229628424470f, 0.628445766601832710f,
+  0.626056388404343520f,
+  0.623661117525694640f, 0.621259976511087660f, 0.618852987960976320f,
+  0.616440174530853650f,
+  0.614021558931038490f, 0.611597163926462020f, 0.609167012336453210f,
+  0.606731127034524480f,
+  0.604289530948156070f, 0.601842247058580030f, 0.599389298400564540f,
+  0.596930708062196500f,
+  0.594466499184664540f, 0.591996694962040990f, 0.589521318641063940f,
+  0.587040393520918080f,
+  0.584553942953015330f, 0.582061990340775550f, 0.579564559139405740f,
+  0.577061672855679550f,
+  0.574553355047715760f, 0.572039629324757050f, 0.569520519346947250f,
+  0.566996048825108680f,
+  0.564466241520519500f, 0.561931121244689470f, 0.559390711859136140f,
+  0.556845037275160100f,
+  0.554294121453620110f, 0.551737988404707450f, 0.549176662187719770f,
+  0.546610166910834860f,
+  0.544038526730883930f, 0.541461765853123560f, 0.538879908531008420f,
+  0.536292979065963180f,
+  0.533701001807152960f, 0.531104001151255000f, 0.528502001542228480f,
+  0.525895027471084740f,
+  0.523283103475656430f, 0.520666254140367270f, 0.518044504095999340f,
+  0.515417878019463150f,
+  0.512786400633563070f, 0.510150096706766700f, 0.507508991052970870f,
+  0.504863108531267480f,
+  0.502212474045710900f, 0.499557112545081890f, 0.496897049022654640f,
+  0.494232308515959730f,
+  0.491562916106550060f, 0.488888896919763230f, 0.486210276124486530f,
+  0.483527078932918740f,
+  0.480839330600333900f, 0.478147056424843120f, 0.475450281747155870f,
+  0.472749031950342900f,
+  0.470043332459595620f, 0.467333208741988530f, 0.464618686306237820f,
+  0.461899790702462840f,
+  0.459176547521944150f, 0.456448982396883860f, 0.453717121000163930f,
+  0.450980989045103810f,
+  0.448240612285220000f, 0.445496016513981740f, 0.442747227564570130f,
+  0.439994271309633260f,
+  0.437237173661044200f, 0.434475960569655710f, 0.431710658025057370f,
+  0.428941292055329550f,
+  0.426167888726799620f, 0.423390474143796100f, 0.420609074448402510f,
+  0.417823715820212380f,
+  0.415034424476081630f, 0.412241226669883000f, 0.409444148692257590f,
+  0.406643216870369140f,
+  0.403838457567654130f, 0.401029897183575790f, 0.398217562153373620f,
+  0.395401478947816300f,
+  0.392581674072951530f, 0.389758174069856410f, 0.386931005514388690f,
+  0.384100195016935040f,
+  0.381265769222162490f, 0.378427754808765620f, 0.375586178489217330f,
+  0.372741067009515810f,
+  0.369892447148934270f, 0.367040345719767240f, 0.364184789567079840f,
+  0.361325805568454340f,
+  0.358463420633736540f, 0.355597661704783960f, 0.352728555755210730f,
+  0.349856129790135030f,
+  0.346980410845923680f, 0.344101425989938980f, 0.341219202320282410f,
+  0.338333766965541290f,
+  0.335445147084531660f, 0.332553369866044220f, 0.329658462528587550f,
+  0.326760452320131790f,
+  0.323859366517852960f, 0.320955232427875210f, 0.318048077385015060f,
+  0.315137928752522440f,
+  0.312224813921825050f, 0.309308760312268780f, 0.306389795370861080f,
+  0.303467946572011370f,
+  0.300543241417273400f, 0.297615707435086310f, 0.294685372180514330f,
+  0.291752263234989370f,
+  0.288816408206049480f, 0.285877834727080730f, 0.282936570457055390f,
+  0.279992643080273380f,
+  0.277046080306099950f, 0.274096909868706330f, 0.271145159526808070f,
+  0.268190857063403180f,
+  0.265234030285511900f, 0.262274707023913590f, 0.259312915132886350f,
+  0.256348682489942910f,
+  0.253382036995570270f, 0.250413006572965280f, 0.247441619167773440f,
+  0.244467902747824210f,
+  0.241491885302869300f, 0.238513594844318500f, 0.235533059404975460f,
+  0.232550307038775330f,
+  0.229565365820518870f, 0.226578263845610110f, 0.223589029229790020f,
+  0.220597690108873650f,
+  0.217604274638483670f, 0.214608810993786920f, 0.211611327369227610f,
+  0.208611851978263460f,
+  0.205610413053099320f, 0.202607038844421110f, 0.199601757621131050f,
+  0.196594597670080220f,
+  0.193585587295803750f, 0.190574754820252800f, 0.187562128582529740f,
+  0.184547736938619640f,
+  0.181531608261125130f, 0.178513770938997590f, 0.175494253377271400f,
+  0.172473083996796030f,
+  0.169450291233967930f, 0.166425903540464220f, 0.163399949382973230f,
+  0.160372457242928400f,
+  0.157343455616238280f, 0.154312973013020240f, 0.151281037957330250f,
+  0.148247678986896200f,
+  0.145212924652847520f, 0.142176803519448000f, 0.139139344163826280f,
+  0.136100575175706200f,
+  0.133060525157139180f, 0.130019222722233350f, 0.126976696496885980f,
+  0.123932975118512200f,
+  0.120888087235777220f, 0.117842061508325020f, 0.114794926606510250f,
+  0.111746711211126660f,
+  0.108697444013138670f, 0.105647153713410700f, 0.102595869022436280f,
+  0.099543618660069444f,
+  0.096490431355252607f, 0.093436335845747912f, 0.090381360877865011f,
+  0.087325535206192226f,
+  0.084268887593324127f, 0.081211446809592386f, 0.078153241632794315f,
+  0.075094300847921291f,
+  0.072034653246889416f, 0.068974327628266732f, 0.065913352797003930f,
+  0.062851757564161420f,
+  0.059789570746640007f, 0.056726821166907783f, 0.053663537652730679f,
+  0.050599749036899337f,
+  0.047535484156959261f, 0.044470771854938744f, 0.041405640977076712f,
+  0.038340120373552791f,
+  0.035274238898213947f, 0.032208025408304704f, 0.029141508764193740f,
+  0.026074717829104040f,
+  0.023007681468839410f, 0.019940428551514598f, 0.016872987947281773f,
+  0.013805388528060349f,
+  0.010737659167264572f, 0.007669828739531077f, 0.004601926120448672f,
+  0.001533980186284766f
+};
+
+static const float32_t cos_factors_2048[2048] = {
+  0.999999926465717890f, 0.999999338191525530f, 0.999998161643486980f,
+  0.999996396822294350f,
+  0.999994043728985820f, 0.999991102364945590f, 0.999987572731904080f,
+  0.999983454831937730f,
+  0.999978748667468830f, 0.999973454241265940f, 0.999967571556443780f,
+  0.999961100616462820f,
+  0.999954041425129780f, 0.999946393986597460f, 0.999938158305364590f,
+  0.999929334386276070f,
+  0.999919922234522750f, 0.999909921855641540f, 0.999899333255515390f,
+  0.999888156440373320f,
+  0.999876391416790410f, 0.999864038191687680f, 0.999851096772332190f,
+  0.999837567166337090f,
+  0.999823449381661570f, 0.999808743426610520f, 0.999793449309835270f,
+  0.999777567040332940f,
+  0.999761096627446610f, 0.999744038080865430f, 0.999726391410624470f,
+  0.999708156627104880f,
+  0.999689333741033640f, 0.999669922763483760f, 0.999649923705874240f,
+  0.999629336579970110f,
+  0.999608161397882110f, 0.999586398172067070f, 0.999564046915327740f,
+  0.999541107640812940f,
+  0.999517580362016990f, 0.999493465092780590f, 0.999468761847290050f,
+  0.999443470640077770f,
+  0.999417591486021720f, 0.999391124400346050f, 0.999364069398620550f,
+  0.999336426496761240f,
+  0.999308195711029470f, 0.999279377058032710f, 0.999249970554724420f,
+  0.999219976218403530f,
+  0.999189394066714920f, 0.999158224117649430f, 0.999126466389543390f,
+  0.999094120901079070f,
+  0.999061187671284600f, 0.999027666719533690f, 0.998993558065545680f,
+  0.998958861729386080f,
+  0.998923577731465780f, 0.998887706092541290f, 0.998851246833715180f,
+  0.998814199976435390f,
+  0.998776565542495610f, 0.998738343554035230f, 0.998699534033539280f,
+  0.998660137003838490f,
+  0.998620152488108870f, 0.998579580509872500f, 0.998538421092996730f,
+  0.998496674261694640f,
+  0.998454340040524800f, 0.998411418454391300f, 0.998367909528543820f,
+  0.998323813288577560f,
+  0.998279129760433200f, 0.998233858970396850f, 0.998188000945100300f,
+  0.998141555711520520f,
+  0.998094523296980010f, 0.998046903729146840f, 0.997998697036034390f,
+  0.997949903246001190f,
+  0.997900522387751620f, 0.997850554490335110f, 0.997799999583146470f,
+  0.997748857695925690f,
+  0.997697128858758500f, 0.997644813102075420f, 0.997591910456652630f,
+  0.997538420953611340f,
+  0.997484344624417930f, 0.997429681500884180f, 0.997374431615167150f,
+  0.997318594999768600f,
+  0.997262171687536170f, 0.997205161711661850f, 0.997147565105683480f,
+  0.997089381903483400f,
+  0.997030612139289450f, 0.996971255847674320f, 0.996911313063555740f,
+  0.996850783822196610f,
+  0.996789668159204560f, 0.996727966110532490f, 0.996665677712478160f,
+  0.996602803001684130f,
+  0.996539342015137940f, 0.996475294790172160f, 0.996410661364464100f,
+  0.996345441776035900f,
+  0.996279636063254650f, 0.996213244264832040f, 0.996146266419824620f,
+  0.996078702567633980f,
+  0.996010552748005870f, 0.995941817001031350f, 0.995872495367145730f,
+  0.995802587887129160f,
+  0.995732094602106430f, 0.995661015553546910f, 0.995589350783264600f,
+  0.995517100333418110f,
+  0.995444264246510340f, 0.995370842565388990f, 0.995296835333246090f,
+  0.995222242593618360f,
+  0.995147064390386470f, 0.995071300767776170f, 0.994994951770357020f,
+  0.994918017443043200f,
+  0.994840497831093180f, 0.994762392980109930f, 0.994683702936040250f,
+  0.994604427745175660f,
+  0.994524567454151740f, 0.994444122109948040f, 0.994363091759888570f,
+  0.994281476451641550f,
+  0.994199276233218910f, 0.994116491152977070f, 0.994033121259616400f,
+  0.993949166602181130f,
+  0.993864627230059750f, 0.993779503192984580f, 0.993693794541031790f,
+  0.993607501324621610f,
+  0.993520623594518090f, 0.993433161401829360f, 0.993345114798006910f,
+  0.993256483834846440f,
+  0.993167268564487230f, 0.993077469039412300f, 0.992987085312448390f,
+  0.992896117436765980f,
+  0.992804565465879140f, 0.992712429453645460f, 0.992619709454266140f,
+  0.992526405522286100f,
+  0.992432517712593660f, 0.992338046080420420f, 0.992242990681341700f,
+  0.992147351571276090f,
+  0.992051128806485720f, 0.991954322443575950f, 0.991856932539495470f,
+  0.991758959151536110f,
+  0.991660402337333210f, 0.991561262154865290f, 0.991461538662453790f,
+  0.991361231918763460f,
+  0.991260341982802440f, 0.991158868913921350f, 0.991056812771814340f,
+  0.990954173616518500f,
+  0.990850951508413620f, 0.990747146508222710f, 0.990642758677011570f,
+  0.990537788076188750f,
+  0.990432234767505970f, 0.990326098813057330f, 0.990219380275280000f,
+  0.990112079216953770f,
+  0.990004195701200910f, 0.989895729791486660f, 0.989786681551618640f,
+  0.989677051045747210f,
+  0.989566838338365120f, 0.989456043494307710f, 0.989344666578752640f,
+  0.989232707657220050f,
+  0.989120166795572690f, 0.989007044060015270f, 0.988893339517095130f,
+  0.988779053233701520f,
+  0.988664185277066230f, 0.988548735714763200f, 0.988432704614708340f,
+  0.988316092045159690f,
+  0.988198898074717610f, 0.988081122772324070f, 0.987962766207263420f,
+  0.987843828449161740f,
+  0.987724309567986960f, 0.987604209634049160f, 0.987483528717999710f,
+  0.987362266890832400f,
+  0.987240424223882250f, 0.987118000788826280f, 0.986994996657682980f,
+  0.986871411902812470f,
+  0.986747246596916590f, 0.986622500813038480f, 0.986497174624562880f,
+  0.986371268105216030f,
+  0.986244781329065460f, 0.986117714370520090f, 0.985990067304330140f,
+  0.985861840205586980f,
+  0.985733033149723490f, 0.985603646212513400f, 0.985473679470071810f,
+  0.985343132998854790f,
+  0.985212006875659350f, 0.985080301177623800f, 0.984948015982227030f,
+  0.984815151367289140f,
+  0.984681707410970940f, 0.984547684191773960f, 0.984413081788540700f,
+  0.984277900280454370f,
+  0.984142139747038570f, 0.984005800268157870f, 0.983868881924017220f,
+  0.983731384795162090f,
+  0.983593308962478650f, 0.983454654507193270f, 0.983315421510872810f,
+  0.983175610055424420f,
+  0.983035220223095640f, 0.982894252096474070f, 0.982752705758487830f,
+  0.982610581292404750f,
+  0.982467878781833170f, 0.982324598310721280f, 0.982180739963357090f,
+  0.982036303824369020f,
+  0.981891289978725100f, 0.981745698511732990f, 0.981599529509040720f,
+  0.981452783056635520f,
+  0.981305459240844670f, 0.981157558148334830f, 0.981009079866112630f,
+  0.980860024481523870f,
+  0.980710392082253970f, 0.980560182756327840f, 0.980409396592109910f,
+  0.980258033678303550f,
+  0.980106094103951770f, 0.979953577958436740f, 0.979800485331479790f,
+  0.979646816313141210f,
+  0.979492570993820810f, 0.979337749464256780f, 0.979182351815526930f,
+  0.979026378139047580f,
+  0.978869828526574120f, 0.978712703070200420f, 0.978555001862359550f,
+  0.978396724995823090f,
+  0.978237872563701090f, 0.978078444659442380f, 0.977918441376834370f,
+  0.977757862810002760f,
+  0.977596709053411890f, 0.977434980201864260f, 0.977272676350500860f,
+  0.977109797594800880f,
+  0.976946344030581670f, 0.976782315753998650f, 0.976617712861545640f,
+  0.976452535450054060f,
+  0.976286783616693630f, 0.976120457458971910f, 0.975953557074734300f,
+  0.975786082562163930f,
+  0.975618034019781750f, 0.975449411546446380f, 0.975280215241354220f,
+  0.975110445204038890f,
+  0.974940101534371830f, 0.974769184332561770f, 0.974597693699155050f,
+  0.974425629735034990f,
+  0.974252992541422500f, 0.974079782219875680f, 0.973905998872289570f,
+  0.973731642600896400f,
+  0.973556713508265560f, 0.973381211697303290f, 0.973205137271252800f,
+  0.973028490333694210f,
+  0.972851270988544180f, 0.972673479340056430f, 0.972495115492821190f,
+  0.972316179551765300f,
+  0.972136671622152230f, 0.971956591809581720f, 0.971775940219990140f,
+  0.971594716959650160f,
+  0.971412922135170940f, 0.971230555853497380f, 0.971047618221911100f,
+  0.970864109348029470f,
+  0.970680029339806130f, 0.970495378305530560f, 0.970310156353828110f,
+  0.970124363593660280f,
+  0.969938000134323960f, 0.969751066085452140f, 0.969563561557013180f,
+  0.969375486659311280f,
+  0.969186841502985950f, 0.968997626199012420f, 0.968807840858700970f,
+  0.968617485593697540f,
+  0.968426560515983190f, 0.968235065737874320f, 0.968043001372022260f,
+  0.967850367531413620f,
+  0.967657164329369880f, 0.967463391879547550f, 0.967269050295937790f,
+  0.967074139692867040f,
+  0.966878660184995910f, 0.966682611887320080f, 0.966485994915169840f,
+  0.966288809384209690f,
+  0.966091055410438830f, 0.965892733110190860f, 0.965693842600133690f,
+  0.965494383997269500f,
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+  0.354522137752887430f,
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+  0.351651783631154680f,
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+  0.340137538973531880f,
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+  0.334361099166798900f,
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+  0.331468144962440920f,
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+  0.328572070853663690f,
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+  0.325672904099419900f,
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+  0.314045856820250820f,
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+  0.296517158507877410f,
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+  0.293585779885591310f,
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+  0.207486540966020700f,
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+  0.177381647230260200f,
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+  0.174361506905093830f,
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+  0.171339725423019260f,
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+  0.168316331226194910f,
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+  0.165291352771957970f,
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+  0.162264818532558110f,
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+  0.159236756994887850f,
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+  0.156207196660216040f,
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+  0.153176166043917870f,
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+  0.150143693675208330f,
+  0.149385353653779810f, 0.148626925752796540f, 0.147868410418422360f,
+  0.147109808096871850f,
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+  0.144074537864995330f,
+  0.143315507302571590f, 0.142556392431327340f, 0.141797193697830530f,
+  0.141037911548697770f,
+  0.140278546430595420f, 0.139519098790238600f, 0.138759569074390380f,
+  0.137999957729862760f,
+  0.137240265203515700f, 0.136480491942256310f, 0.135720638393040080f,
+  0.134960705002868830f,
+  0.134200692218792020f, 0.133440600487905820f, 0.132680430257352130f,
+  0.131920181974319760f,
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+  0.128878417262776660f,
+  0.128117785426777150f, 0.127357078222385570f, 0.126596296097105960f,
+  0.125835439498487020f,
+  0.125074508874121300f, 0.124313504671644300f, 0.123552427338735370f,
+  0.122791277323116900f,
+  0.122030055072553410f, 0.121268761034852550f, 0.120507395657864240f,
+  0.119745959389479630f,
+  0.118984452677632520f, 0.118222875970297250f, 0.117461229715489990f,
+  0.116699514361267840f,
+  0.115937730355727850f, 0.115175878147008180f, 0.114413958183287050f,
+  0.113651970912781920f,
+  0.112889916783750470f, 0.112127796244489750f, 0.111365609743335190f,
+  0.110603357728661910f,
+  0.109841040648882680f, 0.109078658952449240f, 0.108316213087851300f,
+  0.107553703503615710f,
+  0.106791130648307380f, 0.106028494970528530f, 0.105265796918917650f,
+  0.104503036942150550f,
+  0.103740215488939480f, 0.102977333008032250f, 0.102214389948213370f,
+  0.101451386758302160f,
+  0.100688323887153970f, 0.099925201783659226f, 0.099162020896742573f,
+  0.098398781675363881f,
+  0.097635484568517339f, 0.096872130025230527f, 0.096108718494565468f,
+  0.095345250425617742f,
+  0.094581726267515473f, 0.093818146469420494f, 0.093054511480527333f,
+  0.092290821750062355f,
+  0.091527077727284981f, 0.090763279861485704f, 0.089999428601987341f,
+  0.089235524398144139f,
+  0.088471567699340822f, 0.087707558954993645f, 0.086943498614549489f,
+  0.086179387127484922f,
+  0.085415224943307277f, 0.084651012511553700f, 0.083886750281790226f,
+  0.083122438703613077f,
+  0.082358078226646619f, 0.081593669300544638f, 0.080829212374989468f,
+  0.080064707899690932f,
+  0.079300156324387569f, 0.078535558098845590f, 0.077770913672857989f,
+  0.077006223496245585f,
+  0.076241488018856149f, 0.075476707690563416f, 0.074711882961268378f,
+  0.073947014280897269f,
+  0.073182102099402888f, 0.072417146866763538f, 0.071652149032982254f,
+  0.070887109048087787f,
+  0.070122027362133646f, 0.069356904425197236f, 0.068591740687380900f,
+  0.067826536598810966f,
+  0.067061292609636836f, 0.066296009170032283f, 0.065530686730193397f,
+  0.064765325740339871f,
+  0.063999926650714078f, 0.063234489911580136f, 0.062469015973224969f,
+  0.061703505285957416f,
+  0.060937958300107238f, 0.060172375466026218f, 0.059406757234087247f,
+  0.058641104054683348f,
+  0.057875416378229017f, 0.057109694655158132f, 0.056343939335925283f,
+  0.055578150871004817f,
+  0.054812329710889909f, 0.054046476306093640f, 0.053280591107148056f,
+  0.052514674564603257f,
+  0.051748727129028414f, 0.050982749251010900f, 0.050216741381155325f,
+  0.049450703970084824f,
+  0.048684637468439020f, 0.047918542326875327f, 0.047152418996068000f,
+  0.046386267926707213f,
+  0.045620089569500123f, 0.044853884375169933f, 0.044087652794454979f,
+  0.043321395278109784f,
+  0.042555112276904117f, 0.041788804241622082f, 0.041022471623063397f,
+  0.040256114872041358f,
+  0.039489734439384118f, 0.038723330775933762f, 0.037956904332545366f,
+  0.037190455560088091f,
+  0.036423984909444228f, 0.035657492831508264f, 0.034890979777187955f,
+  0.034124446197403423f,
+  0.033357892543086159f, 0.032591319265180385f, 0.031824726814640963f,
+  0.031058115642434700f,
+  0.030291486199539423f, 0.029524838936943035f, 0.028758174305644590f,
+  0.027991492756653365f,
+  0.027224794740987910f, 0.026458080709677145f, 0.025691351113759395f,
+  0.024924606404281485f,
+  0.024157847032300020f, 0.023391073448879338f, 0.022624286105092803f,
+  0.021857485452021874f,
+  0.021090671940755180f, 0.020323846022389572f, 0.019557008148029204f,
+  0.018790158768784596f,
+  0.018023298335773701f, 0.017256427300120978f, 0.016489546112956454f,
+  0.015722655225417017f,
+  0.014955755088644378f, 0.014188846153786343f, 0.013421928871995907f,
+  0.012655003694430301f,
+  0.011888071072252072f, 0.011121131456628141f, 0.010354185298728884f,
+  0.009587233049729183f,
+  0.008820275160807512f, 0.008053312083144991f, 0.007286344267926684f,
+  0.006519372166339549f,
+  0.005752396229573737f, 0.004985416908821652f, 0.004218434655277024f,
+  0.003451449920135975f,
+  0.002684463154596083f, 0.001917474809855460f, 0.001150485337113809f,
+  0.000383495187571497f
+};
+
+static const float32_t cos_factors_8192[8192] = {
+  1.999999990808214700, 1.999999917273932200, 1.999999770205369800,
+    1.999999549602533100,
+  1.999999255465430200, 1.999998887794072000, 1.999998446588471700,
+    1.999997931848645600,
+  1.999997343574612800, 1.999996681766395000, 1.999995946424016200,
+    1.999995137547503600,
+  1.999994255136887000, 1.999993299192198700, 1.999992269713474200,
+    1.999991166700750800,
+  1.999989990154069600, 1.999988740073473500, 1.999987416459008600,
+    1.999986019310723500,
+  1.999984548628669600, 1.999983004412901000, 1.999981386663474400,
+    1.999979695380449400,
+  1.999977930563888100, 1.999976092213855400, 1.999974180330418700,
+    1.999972194913648900,
+  1.999970135963618400, 1.999968003480403000, 1.999965797464081200,
+    1.999963517914734100,
+  1.999961164832445800, 1.999958738217302300, 1.999956238069392900,
+    1.999953664388809800,
+  1.999951017175647600, 1.999948296430003500, 1.999945502151977600,
+    1.999942634341672600,
+  1.999939692999193900, 1.999936678124649700, 1.999933589718150700,
+    1.999930427779810900,
+  1.999927192309745900, 1.999923883308075200, 1.999920500774920300,
+    1.999917044710405500,
+  1.999913515114657900, 1.999909911987807200, 1.999906235329986100,
+    1.999902485141329400,
+  1.999898661421975400, 1.999894764172064600, 1.999890793391740000,
+    1.999886749081147800,
+  1.999882631240436700, 1.999878439869758200, 1.999874174969266300,
+    1.999869836539117700,
+  1.999865424579472000, 1.999860939090491600, 1.999856380072341000,
+    1.999851747525188200,
+  1.999847041449203300, 1.999842261844559700, 1.999837408711432600,
+    1.999832482050000900,
+  1.999827481860445300, 1.999822408142949900, 1.999817260897701400,
+    1.999812040124888700,
+  1.999806745824704000, 1.999801377997341800, 1.999795936642999600,
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+  0.171403583349815180, 0.171021495946926340, 0.170639402256066410,
+    0.170257302291283000,
+  0.169875196066625710, 0.169493083596143100, 0.169110964893883830,
+    0.168728839973898290,
+  0.168346708850235140, 0.167964571536945220, 0.167582428048078130,
+    0.167200278397683750,
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+    0.165671618461853270,
+  0.165289438214587970, 0.164907251890102520, 0.164525059502448390,
+    0.164142861065678550,
+  0.163760656593844480, 0.163378446100999640, 0.162996229601196390,
+    0.162614007108487250,
+  0.162231778636926370, 0.161849544200566300, 0.161467303813461580,
+    0.161085057489665670,
+  0.160702805243232240, 0.160320547088216470, 0.159938283038672050,
+    0.159556013108654580,
+  0.159173737312218650, 0.158791455663418930, 0.158409168176311760,
+    0.158026874864951870,
+  0.157644575743395960, 0.157262270825699210, 0.156879960125918730,
+    0.156497643658110590,
+  0.156115321436331000, 0.155732993474637760, 0.155350659787087090,
+    0.154968320387737170,
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+    0.153438905953493550,
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+    0.151909401255095250,
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+    0.150379807192309620,
+  0.149997394818874590, 0.149614976930463660, 0.149232553541138180,
+    0.148850124664957870,
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+    0.147320354572913260,
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+    0.145790497816099230,
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+    0.144260555294492000,
+  0.143878056368811510, 0.143495552153146630, 0.143113042661560050,
+    0.142730527908116440,
+  0.142348007906879320, 0.141965482671912420, 0.141582952217280980,
+    0.141200416557048680,
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+    0.139670222141414250,
+  0.139287660664154770, 0.138905094065686600, 0.138522522360074780,
+    0.138139945561386200,
+  0.137757363683686740, 0.137374776741042340, 0.136992184747520560,
+    0.136609587717187310,
+  0.136226985664110460, 0.135844378602356760, 0.135461766545993150,
+    0.135079149509088060,
+  0.134696527505708320, 0.134313900549922760, 0.133931268655799020,
+    0.133548631837404950,
+  0.133165990108809860, 0.132783343484081580, 0.132400691977289760,
+    0.132018035602502530,
+  0.131635374373789940, 0.131252708305220960, 0.130870037410864640,
+    0.130487361704791580,
+  0.130104681201070800, 0.129721995913773260, 0.129339305856968730,
+    0.128956611044727220,
+  0.128573911491120210, 0.128191207210217570, 0.127808498216091110,
+    0.127425784522811530,
+  0.127043066144449680, 0.126660343095077900, 0.126277615388766920,
+    0.125894883039589430,
+  0.125512146061616980, 0.125129404468921260, 0.124746658275575490,
+    0.124363907495651240,
+  0.123981152143222060, 0.123598392232359880, 0.123215627777138580,
+    0.122832858791630880,
+  0.122450085289909640, 0.122067307286049230, 0.121684524794122440,
+    0.121301737828203960,
+  0.120918946402367330, 0.120536150530686250, 0.120153350227235940,
+    0.119770545506089950,
+  0.119387736381323830, 0.119004922867011920, 0.118622104977228730,
+    0.118239282726050290,
+  0.117856456127550970, 0.117473625195807100, 0.117090789944893860,
+    0.116707950388886520,
+  0.116325106541861910, 0.115942258417895240, 0.115559406031063570,
+    0.115176549395442460,
+  0.114793688525109290, 0.114410823434140360, 0.114027954136612060,
+    0.113645080646602280,
+  0.113262202978187320, 0.112879321145445350, 0.112496435162453430,
+    0.112113545043288730,
+  0.111730650802029900, 0.111347752452754000, 0.110964850009539970,
+    0.110581943486465610,
+  0.110199032897608850, 0.109816118257049110, 0.109433199578864170,
+    0.109050276877133770,
+  0.108667350165936400, 0.108284419459350770, 0.107901484771457020,
+    0.107518546116333660,
+  0.107135603508061170, 0.106752656960718350, 0.106369706488385940,
+    0.105986752105143480,
+  0.105603793825070680, 0.105220831662248700, 0.104837865630757090,
+    0.104454895744677270,
+  0.104071922018089540, 0.103688944465074300, 0.103305963099713400,
+    0.102922977936087120,
+  0.102539988988277600, 0.102156996270365800, 0.101773999796432830,
+    0.101390999580561250,
+  0.101007995636832020, 0.100624987979327970, 0.100241976622130760,
+    0.099858961579322170,
+  0.099475942864985456, 0.099092920493202258, 0.098709894478056073,
+    0.098326864833628791,
+  0.097943831574004214, 0.097560794713264939, 0.097177754265493674,
+    0.096794710244774623,
+  0.096411662665190329, 0.096028611540825232, 0.095645556885762609,
+    0.095262498714085819,
+  0.094879437039879722, 0.094496371877227495, 0.094113303240214247,
+    0.093730231142923864,
+  0.093347155599440373, 0.092964076623849271, 0.092580994230234359,
+    0.092197908432681386,
+  0.091814819245274432, 0.091431726682099479, 0.091048630757241303,
+    0.090665531484784803,
+  0.090282428878816323, 0.089899322953420582, 0.089516213722684160,
+    0.089133101200692441,
+  0.088749985401530951, 0.088366866339286629, 0.087983744028044805,
+    0.087600618481892656,
+  0.087217489714916191, 0.086834357741201490, 0.086451222574836131,
+    0.086068084229906014,
+  0.085684942720498897, 0.085301798060701386, 0.084918650264600160,
+    0.084535499346283349,
+  0.084152345319837438, 0.083769188199350780, 0.083386027998910095,
+    0.083002864732603973,
+  0.082619698414519799, 0.082236529058745025, 0.081853356679368619,
+    0.081470181290477811,
+  0.081087002906161790, 0.080703821540508452, 0.080320637207605849,
+    0.079937449921543474,
+  0.079554259696409127, 0.079171066546292510, 0.078787870485282088,
+    0.078404671527466441,
+  0.078021469686935602, 0.077638264977777913, 0.077255057414083589,
+    0.076871847009941652,
+  0.076488633779441206, 0.076105417736672773, 0.075722198895725248,
+    0.075338977270689375,
+  0.074955752875654230, 0.074572525724710764, 0.074189295831948693,
+    0.073806063211457842,
+  0.073422827877329483, 0.073039589843653177, 0.072656349124520389,
+    0.072273105734021334,
+  0.071889859686246352, 0.071506610995287156, 0.071123359675233852,
+    0.070740105740178361,
+  0.070356849204211397, 0.069973590081423773, 0.069590328385907715,
+    0.069207064131753759,
+  0.068823797333054326, 0.068440528003900616, 0.068057256158383886,
+    0.067673981810596848,
+  0.067290704974630494, 0.066907425664577733, 0.066524143894529736,
+    0.066140859678579578,
+  0.065757573030819083, 0.065374283965340146, 0.064990992496236119,
+    0.064607698637598646,
+  0.064224402403521202, 0.063841103808096086, 0.063457802865415636,
+    0.063074499589573618,
+  0.062691193994662109, 0.062307886094775049, 0.061924575904005130,
+    0.061541263436445129,
+  0.061157948706189229, 0.060774631727329942, 0.060391312513961619,
+    0.060007991080177375,
+  0.059624667440070382, 0.059241341607735261, 0.058858013597264912,
+    0.058474683422754095,
+  0.058091351098295878, 0.057708016637985186, 0.057324680055915692,
+    0.056941341366181127,
+  0.056558000582876661, 0.056174657720095743, 0.055791312791933681,
+    0.055407965812484541,
+  0.055024616795842439, 0.054641265756102911, 0.054257912707359794,
+    0.053874557663708772,
+  0.053491200639244271, 0.053107841648060788, 0.052724480704254229,
+    0.052341117821918783,
+  0.051957753015150501, 0.051574386298044173, 0.051191017684694640,
+    0.050807647189198162,
+  0.050424274825649297, 0.050040900608144430, 0.049657524550778251,
+    0.049274146667647289,
+  0.048890766972846805, 0.048507385480472134, 0.048124002204620014,
+    0.047740617159385448,
+  0.047357230358865306, 0.046973841817155179, 0.046590451548350717,
+    0.046207059566548990,
+  0.045823665885845313, 0.045440270520336883, 0.045056873484119603,
+    0.044673474791289434,
+  0.044290074455943754, 0.043906672492178188, 0.043523268914090238,
+    0.043139863735776100,
+  0.042756456971332048, 0.042373048634855741, 0.041989638740443119,
+    0.041606227302191955,
+  0.041222814334198304, 0.040839399850560058, 0.040455983865373815,
+    0.040072566392736257,
+  0.039689147446745419, 0.039305727041497644, 0.038922305191091085,
+    0.038538881909622631,
+  0.038155457211189216, 0.037772031109889144, 0.037388603619819022,
+    0.037005174755077273,
+  0.036621744529761024, 0.036238312957967478, 0.035854880053795196,
+    0.035471445831341021,
+  0.035088010304703626, 0.034704573487980395, 0.034321135395268765,
+    0.033937696040667535,
+  0.033554255438273790, 0.033170813602186440, 0.032787370546502645,
+    0.032403926285321405,
+  0.032020480832740429, 0.031637034202857461, 0.031253586409771626,
+    0.030870137467580314,
+  0.030486687390382738, 0.030103236192276818, 0.029719783887360508,
+    0.029336330489733147,
+  0.028952876013492331, 0.028569420472737472, 0.028185963881566689,
+    0.027802506254078142,
+  0.027419047604371360, 0.027035587946544135, 0.026652127294696067,
+    0.026268665662925468,
+  0.025885203065330677, 0.025501739516011413, 0.025118275029065638,
+    0.024734809618593138,
+  0.024351343298691951, 0.023967876083461924, 0.023584407987001611,
+    0.023200939023409587,
+  0.022817469206785804, 0.022433998551228459, 0.022050527070837558,
+    0.021667054779711814,
+  0.021283581691949955, 0.020900107821652084, 0.020516633182916549,
+    0.020133157789843505,
+  0.019749681656531803, 0.019366204797080316, 0.018982727225589285,
+    0.018599248956157190,
+  0.018215770002884327, 0.017832290379869671, 0.017448810101212228,
+    0.017065329181012358,
+  0.016681847633368677, 0.016298365472381587, 0.015914882712149747,
+    0.015531399366773606,
+  0.015147915450352307, 0.014764430976985016, 0.014380945960772247,
+    0.013997460415812761,
+  0.013613974356207112, 0.013230487796054543, 0.012847000749454314,
+    0.012463513230507034,
+  0.012080025253311559, 0.011696536831968529, 0.011313047980577277,
+    0.010929558713237145,
+  0.010546069044048827, 0.010162578987111254, 0.009779088556525145,
+    0.009395597766389905,
+  0.009012106630804949, 0.008628615163871038, 0.008245123379687167,
+    0.007861631292354124,
+  0.007478138915970929, 0.007094646264638386, 0.006711153352455981,
+    0.006327660193523208,
+  0.005944166801940901, 0.005560673191808128, 0.005177179377225743,
+    0.004793685372293270,
+  0.004410191191110246, 0.004026696847777542, 0.003643202356394263,
+    0.003259707731061291,
+  0.002876212985878184, 0.002492718134944503, 0.002109223192361147,
+    0.001725728172227238,
+  0.001342233088643682, 0.000958737955710053, 0.000575242787525925,
+    0.000191747598192208,
+
+};
+
+/**    
+ * @brief  Initialization function for the floating-point DCT4/IDCT4.   
+ * @param[in,out] *S         points to an instance of floating-point DCT4/IDCT4 structure.   
+ * @param[in]     *S_RFFT    points to an instance of floating-point RFFT/RIFFT structure.   
+ * @param[in]     *S_CFFT    points to an instance of floating-point CFFT/CIFFT structure.   
+ * @param[in]     N			 length of the DCT4.   
+ * @param[in]     Nby2       half of the length of the DCT4.   
+ * @param[in]     normalize  normalizing factor.   
+ * @return        arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if fftLenReal is not a supported transform length.   
+ * \par Normalizing factor:    
+ * The normalizing factor is sqrt(2/N), which depends on the size of transform N.    
+ * Floating-point normalizing factors are mentioned in the table below for different DCT sizes:    
+ * \image html dct4NormalizingF32Table.gif    
+ */
+
+arm_status arm_dct4_init_f32(
+  arm_dct4_instance_f32 * S,
+  arm_rfft_instance_f32 * S_RFFT,
+  arm_cfft_radix4_instance_f32 * S_CFFT,
+  uint16_t N,
+  uint16_t Nby2,
+  float32_t normalize)
+{
+  /*  Initialize the default arm status */
+  arm_status status = ARM_MATH_SUCCESS;
+
+  /* Initializing the pointer array with the weight table base addresses of different lengths */
+  float32_t *twiddlePtr[4] =
+    { (float32_t *) Weights_128, (float32_t *) Weights_512,
+    (float32_t *) Weights_2048, (float32_t *) Weights_8192
+  };
+
+  /* Initializing the pointer array with the cos factor table base addresses of different lengths */
+  float32_t *pCosFactor[4] =
+    { (float32_t *) cos_factors_128, (float32_t *) cos_factors_512,
+    (float32_t *) cos_factors_2048, (float32_t *) cos_factors_8192
+  };
+
+  /* Initialize the DCT4 length */
+  S->N = N;
+
+  /* Initialize the half of DCT4 length */
+  S->Nby2 = Nby2;
+
+  /* Initialize the DCT4 Normalizing factor */
+  S->normalize = normalize;
+
+  /* Initialize Real FFT Instance */
+  S->pRfft = S_RFFT;
+
+  /* Initialize Complex FFT Instance */
+  S->pCfft = S_CFFT;
+
+  switch (N)
+  {
+    /* Initialize the table modifier values */
+  case 8192u:
+    S->pTwiddle = twiddlePtr[3];
+    S->pCosFactor = pCosFactor[3];
+    break;
+  case 2048u:
+    S->pTwiddle = twiddlePtr[2];
+    S->pCosFactor = pCosFactor[2];
+    break;
+  case 512u:
+    S->pTwiddle = twiddlePtr[1];
+    S->pCosFactor = pCosFactor[1];
+    break;
+  case 128u:
+    S->pTwiddle = twiddlePtr[0];
+    S->pCosFactor = pCosFactor[0];
+    break;
+  default:
+    status = ARM_MATH_ARGUMENT_ERROR;
+  }
+
+  /* Initialize the RFFT/RIFFT */
+  arm_rfft_init_f32(S->pRfft, S->pCfft, S->N, 0u, 1u);
+
+  /* return the status of DCT4 Init function */
+  return (status);
+}
+
+/**    
+   * @} end of DCT4_IDCT4 group    
+   */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_dct4_init_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_dct4_init_q15.c
new file mode 100644
index 0000000000..c6452fe98a
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_dct4_init_q15.c
@@ -0,0 +1,4276 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_dct4_init_q15.c    
+*    
+* Description:	Initialization function of DCT-4 & IDCT4 Q15    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupTransforms    
+ */
+
+/**    
+ * @addtogroup DCT4_IDCT4    
+ * @{    
+ */
+
+/*    
+* @brief  Weights Table    
+*/
+
+/**    
+* \par    
+* Weights tables are generated using the formula : 
weights[n] = e^(-j*n*pi/(2*N))
    
+* \par    
+* C command to generate the table    
+* 
    
+* for(i = 0; i< N; i++)    
+* {    
+*   weights[2*i]= cos(i*c);    
+*   weights[(2*i)+1]= -sin(i * c);    
+* } 
    
+* \par    
+* where N is the Number of weights to be calculated and c is pi/(2*N)    
+* \par    
+* Converted the output to q15 format by multiplying with 2^31 and saturated if required.    
+* \par    
+* In the tables below the real and imaginary values are placed alternatively, hence the    
+* array length is 2*N.    
+*/
+
+static const q15_t ALIGN4 WeightsQ15_128[256] = {
+  0x7fff, 0x0, 0x7ffd, 0xfe6e, 0x7ff6, 0xfcdc, 0x7fe9, 0xfb4a,
+  0x7fd8, 0xf9b9, 0x7fc2, 0xf827, 0x7fa7, 0xf696, 0x7f87, 0xf505,
+  0x7f62, 0xf375, 0x7f38, 0xf1e5, 0x7f09, 0xf055, 0x7ed5, 0xeec7,
+  0x7e9d, 0xed38, 0x7e5f, 0xebab, 0x7e1d, 0xea1e, 0x7dd6, 0xe893,
+  0x7d8a, 0xe708, 0x7d39, 0xe57e, 0x7ce3, 0xe3f5, 0x7c89, 0xe26d,
+  0x7c29, 0xe0e7, 0x7bc5, 0xdf61, 0x7b5d, 0xdddd, 0x7aef, 0xdc5a,
+  0x7a7d, 0xdad8, 0x7a05, 0xd958, 0x798a, 0xd7da, 0x7909, 0xd65d,
+  0x7884, 0xd4e1, 0x77fa, 0xd368, 0x776c, 0xd1ef, 0x76d9, 0xd079,
+  0x7641, 0xcf05, 0x75a5, 0xcd92, 0x7504, 0xcc22, 0x745f, 0xcab3,
+  0x73b5, 0xc946, 0x7307, 0xc7dc, 0x7255, 0xc674, 0x719e, 0xc50e,
+  0x70e2, 0xc3aa, 0x7023, 0xc248, 0x6f5f, 0xc0e9, 0x6e96, 0xbf8d,
+  0x6dca, 0xbe32, 0x6cf9, 0xbcdb, 0x6c24, 0xbb86, 0x6b4a, 0xba33,
+  0x6a6d, 0xb8e4, 0x698c, 0xb797, 0x68a6, 0xb64c, 0x67bd, 0xb505,
+  0x66cf, 0xb3c1, 0x65dd, 0xb27f, 0x64e8, 0xb141, 0x63ef, 0xb005,
+  0x62f2, 0xaecd, 0x61f1, 0xad97, 0x60ec, 0xac65, 0x5fe3, 0xab36,
+  0x5ed7, 0xaa0b, 0x5dc7, 0xa8e3, 0x5cb4, 0xa7be, 0x5b9d, 0xa69c,
+  0x5a82, 0xa57e, 0x5964, 0xa463, 0x5842, 0xa34c, 0x571d, 0xa239,
+  0x55f5, 0xa129, 0x54ca, 0xa01d, 0x539b, 0x9f14, 0x5269, 0x9e0f,
+  0x5133, 0x9d0e, 0x4ffb, 0x9c11, 0x4ebf, 0x9b18, 0x4d81, 0x9a23,
+  0x4c3f, 0x9931, 0x4afb, 0x9843, 0x49b4, 0x975a, 0x4869, 0x9674,
+  0x471c, 0x9593, 0x45cd, 0x94b6, 0x447a, 0x93dc, 0x4325, 0x9307,
+  0x41ce, 0x9236, 0x4073, 0x916a, 0x3f17, 0x90a1, 0x3db8, 0x8fdd,
+  0x3c56, 0x8f1e, 0x3af2, 0x8e62, 0x398c, 0x8dab, 0x3824, 0x8cf9,
+  0x36ba, 0x8c4b, 0x354d, 0x8ba1, 0x33de, 0x8afc, 0x326e, 0x8a5b,
+  0x30fb, 0x89bf, 0x2f87, 0x8927, 0x2e11, 0x8894, 0x2c98, 0x8806,
+  0x2b1f, 0x877c, 0x29a3, 0x86f7, 0x2826, 0x8676, 0x26a8, 0x85fb,
+  0x2528, 0x8583, 0x23a6, 0x8511, 0x2223, 0x84a3, 0x209f, 0x843b,
+  0x1f19, 0x83d7, 0x1d93, 0x8377, 0x1c0b, 0x831d, 0x1a82, 0x82c7,
+  0x18f8, 0x8276, 0x176d, 0x822a, 0x15e2, 0x81e3, 0x1455, 0x81a1,
+  0x12c8, 0x8163, 0x1139, 0x812b, 0xfab, 0x80f7, 0xe1b, 0x80c8,
+  0xc8b, 0x809e, 0xafb, 0x8079, 0x96a, 0x8059, 0x7d9, 0x803e,
+  0x647, 0x8028, 0x4b6, 0x8017, 0x324, 0x800a, 0x192, 0x8003,
+};
+
+static const q15_t ALIGN4 WeightsQ15_512[1024] = {
+  0x7fff, 0x0, 0x7fff, 0xff9c, 0x7fff, 0xff37, 0x7ffe, 0xfed3,
+  0x7ffd, 0xfe6e, 0x7ffc, 0xfe0a, 0x7ffa, 0xfda5, 0x7ff8, 0xfd41,
+  0x7ff6, 0xfcdc, 0x7ff3, 0xfc78, 0x7ff0, 0xfc13, 0x7fed, 0xfbaf,
+  0x7fe9, 0xfb4a, 0x7fe5, 0xfae6, 0x7fe1, 0xfa81, 0x7fdd, 0xfa1d,
+  0x7fd8, 0xf9b9, 0x7fd3, 0xf954, 0x7fce, 0xf8f0, 0x7fc8, 0xf88b,
+  0x7fc2, 0xf827, 0x7fbc, 0xf7c3, 0x7fb5, 0xf75e, 0x7fae, 0xf6fa,
+  0x7fa7, 0xf696, 0x7f9f, 0xf632, 0x7f97, 0xf5cd, 0x7f8f, 0xf569,
+  0x7f87, 0xf505, 0x7f7e, 0xf4a1, 0x7f75, 0xf43d, 0x7f6b, 0xf3d9,
+  0x7f62, 0xf375, 0x7f58, 0xf311, 0x7f4d, 0xf2ad, 0x7f43, 0xf249,
+  0x7f38, 0xf1e5, 0x7f2d, 0xf181, 0x7f21, 0xf11d, 0x7f15, 0xf0b9,
+  0x7f09, 0xf055, 0x7efd, 0xeff2, 0x7ef0, 0xef8e, 0x7ee3, 0xef2a,
+  0x7ed5, 0xeec7, 0x7ec8, 0xee63, 0x7eba, 0xedff, 0x7eab, 0xed9c,
+  0x7e9d, 0xed38, 0x7e8e, 0xecd5, 0x7e7f, 0xec72, 0x7e6f, 0xec0e,
+  0x7e5f, 0xebab, 0x7e4f, 0xeb48, 0x7e3f, 0xeae5, 0x7e2e, 0xea81,
+  0x7e1d, 0xea1e, 0x7e0c, 0xe9bb, 0x7dfa, 0xe958, 0x7de8, 0xe8f6,
+  0x7dd6, 0xe893, 0x7dc3, 0xe830, 0x7db0, 0xe7cd, 0x7d9d, 0xe76a,
+  0x7d8a, 0xe708, 0x7d76, 0xe6a5, 0x7d62, 0xe643, 0x7d4e, 0xe5e0,
+  0x7d39, 0xe57e, 0x7d24, 0xe51c, 0x7d0f, 0xe4b9, 0x7cf9, 0xe457,
+  0x7ce3, 0xe3f5, 0x7ccd, 0xe393, 0x7cb7, 0xe331, 0x7ca0, 0xe2cf,
+  0x7c89, 0xe26d, 0x7c71, 0xe20b, 0x7c5a, 0xe1aa, 0x7c42, 0xe148,
+  0x7c29, 0xe0e7, 0x7c11, 0xe085, 0x7bf8, 0xe024, 0x7bdf, 0xdfc2,
+  0x7bc5, 0xdf61, 0x7bac, 0xdf00, 0x7b92, 0xde9f, 0x7b77, 0xde3e,
+  0x7b5d, 0xdddd, 0x7b42, 0xdd7c, 0x7b26, 0xdd1b, 0x7b0b, 0xdcbb,
+  0x7aef, 0xdc5a, 0x7ad3, 0xdbf9, 0x7ab6, 0xdb99, 0x7a9a, 0xdb39,
+  0x7a7d, 0xdad8, 0x7a5f, 0xda78, 0x7a42, 0xda18, 0x7a24, 0xd9b8,
+  0x7a05, 0xd958, 0x79e7, 0xd8f9, 0x79c8, 0xd899, 0x79a9, 0xd839,
+  0x798a, 0xd7da, 0x796a, 0xd77a, 0x794a, 0xd71b, 0x792a, 0xd6bc,
+  0x7909, 0xd65d, 0x78e8, 0xd5fe, 0x78c7, 0xd59f, 0x78a6, 0xd540,
+  0x7884, 0xd4e1, 0x7862, 0xd483, 0x7840, 0xd424, 0x781d, 0xd3c6,
+  0x77fa, 0xd368, 0x77d7, 0xd309, 0x77b4, 0xd2ab, 0x7790, 0xd24d,
+  0x776c, 0xd1ef, 0x7747, 0xd192, 0x7723, 0xd134, 0x76fe, 0xd0d7,
+  0x76d9, 0xd079, 0x76b3, 0xd01c, 0x768e, 0xcfbf, 0x7668, 0xcf62,
+  0x7641, 0xcf05, 0x761b, 0xcea8, 0x75f4, 0xce4b, 0x75cc, 0xcdef,
+  0x75a5, 0xcd92, 0x757d, 0xcd36, 0x7555, 0xccda, 0x752d, 0xcc7e,
+  0x7504, 0xcc22, 0x74db, 0xcbc6, 0x74b2, 0xcb6a, 0x7489, 0xcb0e,
+  0x745f, 0xcab3, 0x7435, 0xca58, 0x740b, 0xc9fc, 0x73e0, 0xc9a1,
+  0x73b5, 0xc946, 0x738a, 0xc8ec, 0x735f, 0xc891, 0x7333, 0xc836,
+  0x7307, 0xc7dc, 0x72db, 0xc782, 0x72af, 0xc728, 0x7282, 0xc6ce,
+  0x7255, 0xc674, 0x7227, 0xc61a, 0x71fa, 0xc5c0, 0x71cc, 0xc567,
+  0x719e, 0xc50e, 0x716f, 0xc4b4, 0x7141, 0xc45b, 0x7112, 0xc403,
+  0x70e2, 0xc3aa, 0x70b3, 0xc351, 0x7083, 0xc2f9, 0x7053, 0xc2a0,
+  0x7023, 0xc248, 0x6ff2, 0xc1f0, 0x6fc1, 0xc198, 0x6f90, 0xc141,
+  0x6f5f, 0xc0e9, 0x6f2d, 0xc092, 0x6efb, 0xc03b, 0x6ec9, 0xbfe3,
+  0x6e96, 0xbf8d, 0x6e63, 0xbf36, 0x6e30, 0xbedf, 0x6dfd, 0xbe89,
+  0x6dca, 0xbe32, 0x6d96, 0xbddc, 0x6d62, 0xbd86, 0x6d2d, 0xbd30,
+  0x6cf9, 0xbcdb, 0x6cc4, 0xbc85, 0x6c8f, 0xbc30, 0x6c59, 0xbbdb,
+  0x6c24, 0xbb86, 0x6bee, 0xbb31, 0x6bb8, 0xbadc, 0x6b81, 0xba88,
+  0x6b4a, 0xba33, 0x6b13, 0xb9df, 0x6adc, 0xb98b, 0x6aa5, 0xb937,
+  0x6a6d, 0xb8e4, 0x6a35, 0xb890, 0x69fd, 0xb83d, 0x69c4, 0xb7ea,
+  0x698c, 0xb797, 0x6953, 0xb744, 0x6919, 0xb6f1, 0x68e0, 0xb69f,
+  0x68a6, 0xb64c, 0x686c, 0xb5fa, 0x6832, 0xb5a8, 0x67f7, 0xb557,
+  0x67bd, 0xb505, 0x6782, 0xb4b4, 0x6746, 0xb462, 0x670b, 0xb411,
+  0x66cf, 0xb3c1, 0x6693, 0xb370, 0x6657, 0xb31f, 0x661a, 0xb2cf,
+  0x65dd, 0xb27f, 0x65a0, 0xb22f, 0x6563, 0xb1df, 0x6526, 0xb190,
+  0x64e8, 0xb141, 0x64aa, 0xb0f1, 0x646c, 0xb0a2, 0x642d, 0xb054,
+  0x63ef, 0xb005, 0x63b0, 0xafb7, 0x6371, 0xaf69, 0x6331, 0xaf1b,
+  0x62f2, 0xaecd, 0x62b2, 0xae7f, 0x6271, 0xae32, 0x6231, 0xade4,
+  0x61f1, 0xad97, 0x61b0, 0xad4b, 0x616f, 0xacfe, 0x612d, 0xacb2,
+  0x60ec, 0xac65, 0x60aa, 0xac19, 0x6068, 0xabcd, 0x6026, 0xab82,
+  0x5fe3, 0xab36, 0x5fa0, 0xaaeb, 0x5f5e, 0xaaa0, 0x5f1a, 0xaa55,
+  0x5ed7, 0xaa0b, 0x5e93, 0xa9c0, 0x5e50, 0xa976, 0x5e0b, 0xa92c,
+  0x5dc7, 0xa8e3, 0x5d83, 0xa899, 0x5d3e, 0xa850, 0x5cf9, 0xa807,
+  0x5cb4, 0xa7be, 0x5c6e, 0xa775, 0x5c29, 0xa72c, 0x5be3, 0xa6e4,
+  0x5b9d, 0xa69c, 0x5b56, 0xa654, 0x5b10, 0xa60d, 0x5ac9, 0xa5c5,
+  0x5a82, 0xa57e, 0x5a3b, 0xa537, 0x59f3, 0xa4f0, 0x59ac, 0xa4aa,
+  0x5964, 0xa463, 0x591c, 0xa41d, 0x58d4, 0xa3d7, 0x588b, 0xa392,
+  0x5842, 0xa34c, 0x57f9, 0xa307, 0x57b0, 0xa2c2, 0x5767, 0xa27d,
+  0x571d, 0xa239, 0x56d4, 0xa1f5, 0x568a, 0xa1b0, 0x5640, 0xa16d,
+  0x55f5, 0xa129, 0x55ab, 0xa0e6, 0x5560, 0xa0a2, 0x5515, 0xa060,
+  0x54ca, 0xa01d, 0x547e, 0x9fda, 0x5433, 0x9f98, 0x53e7, 0x9f56,
+  0x539b, 0x9f14, 0x534e, 0x9ed3, 0x5302, 0x9e91, 0x52b5, 0x9e50,
+  0x5269, 0x9e0f, 0x521c, 0x9dcf, 0x51ce, 0x9d8f, 0x5181, 0x9d4e,
+  0x5133, 0x9d0e, 0x50e5, 0x9ccf, 0x5097, 0x9c8f, 0x5049, 0x9c50,
+  0x4ffb, 0x9c11, 0x4fac, 0x9bd3, 0x4f5e, 0x9b94, 0x4f0f, 0x9b56,
+  0x4ebf, 0x9b18, 0x4e70, 0x9ada, 0x4e21, 0x9a9d, 0x4dd1, 0x9a60,
+  0x4d81, 0x9a23, 0x4d31, 0x99e6, 0x4ce1, 0x99a9, 0x4c90, 0x996d,
+  0x4c3f, 0x9931, 0x4bef, 0x98f5, 0x4b9e, 0x98ba, 0x4b4c, 0x987e,
+  0x4afb, 0x9843, 0x4aa9, 0x9809, 0x4a58, 0x97ce, 0x4a06, 0x9794,
+  0x49b4, 0x975a, 0x4961, 0x9720, 0x490f, 0x96e7, 0x48bc, 0x96ad,
+  0x4869, 0x9674, 0x4816, 0x963c, 0x47c3, 0x9603, 0x4770, 0x95cb,
+  0x471c, 0x9593, 0x46c9, 0x955b, 0x4675, 0x9524, 0x4621, 0x94ed,
+  0x45cd, 0x94b6, 0x4578, 0x947f, 0x4524, 0x9448, 0x44cf, 0x9412,
+  0x447a, 0x93dc, 0x4425, 0x93a7, 0x43d0, 0x9371, 0x437b, 0x933c,
+  0x4325, 0x9307, 0x42d0, 0x92d3, 0x427a, 0x929e, 0x4224, 0x926a,
+  0x41ce, 0x9236, 0x4177, 0x9203, 0x4121, 0x91d0, 0x40ca, 0x919d,
+  0x4073, 0x916a, 0x401d, 0x9137, 0x3fc5, 0x9105, 0x3f6e, 0x90d3,
+  0x3f17, 0x90a1, 0x3ebf, 0x9070, 0x3e68, 0x903f, 0x3e10, 0x900e,
+  0x3db8, 0x8fdd, 0x3d60, 0x8fad, 0x3d07, 0x8f7d, 0x3caf, 0x8f4d,
+  0x3c56, 0x8f1e, 0x3bfd, 0x8eee, 0x3ba5, 0x8ebf, 0x3b4c, 0x8e91,
+  0x3af2, 0x8e62, 0x3a99, 0x8e34, 0x3a40, 0x8e06, 0x39e6, 0x8dd9,
+  0x398c, 0x8dab, 0x3932, 0x8d7e, 0x38d8, 0x8d51, 0x387e, 0x8d25,
+  0x3824, 0x8cf9, 0x37ca, 0x8ccd, 0x376f, 0x8ca1, 0x3714, 0x8c76,
+  0x36ba, 0x8c4b, 0x365f, 0x8c20, 0x3604, 0x8bf5, 0x35a8, 0x8bcb,
+  0x354d, 0x8ba1, 0x34f2, 0x8b77, 0x3496, 0x8b4e, 0x343a, 0x8b25,
+  0x33de, 0x8afc, 0x3382, 0x8ad3, 0x3326, 0x8aab, 0x32ca, 0x8a83,
+  0x326e, 0x8a5b, 0x3211, 0x8a34, 0x31b5, 0x8a0c, 0x3158, 0x89e5,
+  0x30fb, 0x89bf, 0x309e, 0x8998, 0x3041, 0x8972, 0x2fe4, 0x894d,
+  0x2f87, 0x8927, 0x2f29, 0x8902, 0x2ecc, 0x88dd, 0x2e6e, 0x88b9,
+  0x2e11, 0x8894, 0x2db3, 0x8870, 0x2d55, 0x884c, 0x2cf7, 0x8829,
+  0x2c98, 0x8806, 0x2c3a, 0x87e3, 0x2bdc, 0x87c0, 0x2b7d, 0x879e,
+  0x2b1f, 0x877c, 0x2ac0, 0x875a, 0x2a61, 0x8739, 0x2a02, 0x8718,
+  0x29a3, 0x86f7, 0x2944, 0x86d6, 0x28e5, 0x86b6, 0x2886, 0x8696,
+  0x2826, 0x8676, 0x27c7, 0x8657, 0x2767, 0x8638, 0x2707, 0x8619,
+  0x26a8, 0x85fb, 0x2648, 0x85dc, 0x25e8, 0x85be, 0x2588, 0x85a1,
+  0x2528, 0x8583, 0x24c7, 0x8566, 0x2467, 0x854a, 0x2407, 0x852d,
+  0x23a6, 0x8511, 0x2345, 0x84f5, 0x22e5, 0x84da, 0x2284, 0x84be,
+  0x2223, 0x84a3, 0x21c2, 0x8489, 0x2161, 0x846e, 0x2100, 0x8454,
+  0x209f, 0x843b, 0x203e, 0x8421, 0x1fdc, 0x8408, 0x1f7b, 0x83ef,
+  0x1f19, 0x83d7, 0x1eb8, 0x83be, 0x1e56, 0x83a6, 0x1df5, 0x838f,
+  0x1d93, 0x8377, 0x1d31, 0x8360, 0x1ccf, 0x8349, 0x1c6d, 0x8333,
+  0x1c0b, 0x831d, 0x1ba9, 0x8307, 0x1b47, 0x82f1, 0x1ae4, 0x82dc,
+  0x1a82, 0x82c7, 0x1a20, 0x82b2, 0x19bd, 0x829e, 0x195b, 0x828a,
+  0x18f8, 0x8276, 0x1896, 0x8263, 0x1833, 0x8250, 0x17d0, 0x823d,
+  0x176d, 0x822a, 0x170a, 0x8218, 0x16a8, 0x8206, 0x1645, 0x81f4,
+  0x15e2, 0x81e3, 0x157f, 0x81d2, 0x151b, 0x81c1, 0x14b8, 0x81b1,
+  0x1455, 0x81a1, 0x13f2, 0x8191, 0x138e, 0x8181, 0x132b, 0x8172,
+  0x12c8, 0x8163, 0x1264, 0x8155, 0x1201, 0x8146, 0x119d, 0x8138,
+  0x1139, 0x812b, 0x10d6, 0x811d, 0x1072, 0x8110, 0x100e, 0x8103,
+  0xfab, 0x80f7, 0xf47, 0x80eb, 0xee3, 0x80df, 0xe7f, 0x80d3,
+  0xe1b, 0x80c8, 0xdb7, 0x80bd, 0xd53, 0x80b3, 0xcef, 0x80a8,
+  0xc8b, 0x809e, 0xc27, 0x8095, 0xbc3, 0x808b, 0xb5f, 0x8082,
+  0xafb, 0x8079, 0xa97, 0x8071, 0xa33, 0x8069, 0x9ce, 0x8061,
+  0x96a, 0x8059, 0x906, 0x8052, 0x8a2, 0x804b, 0x83d, 0x8044,
+  0x7d9, 0x803e, 0x775, 0x8038, 0x710, 0x8032, 0x6ac, 0x802d,
+  0x647, 0x8028, 0x5e3, 0x8023, 0x57f, 0x801f, 0x51a, 0x801b,
+  0x4b6, 0x8017, 0x451, 0x8013, 0x3ed, 0x8010, 0x388, 0x800d,
+  0x324, 0x800a, 0x2bf, 0x8008, 0x25b, 0x8006, 0x1f6, 0x8004,
+  0x192, 0x8003, 0x12d, 0x8002, 0xc9, 0x8001, 0x64, 0x8001,
+};
+
+static const q15_t ALIGN4 WeightsQ15_2048[4096] = {
+  0x7fff, 0x0, 0x7fff, 0xffe7, 0x7fff, 0xffce, 0x7fff, 0xffb5,
+  0x7fff, 0xff9c, 0x7fff, 0xff83, 0x7fff, 0xff6a, 0x7fff, 0xff51,
+  0x7fff, 0xff37, 0x7fff, 0xff1e, 0x7fff, 0xff05, 0x7ffe, 0xfeec,
+  0x7ffe, 0xfed3, 0x7ffe, 0xfeba, 0x7ffe, 0xfea1, 0x7ffd, 0xfe88,
+  0x7ffd, 0xfe6e, 0x7ffd, 0xfe55, 0x7ffc, 0xfe3c, 0x7ffc, 0xfe23,
+  0x7ffc, 0xfe0a, 0x7ffb, 0xfdf1, 0x7ffb, 0xfdd8, 0x7ffa, 0xfdbe,
+  0x7ffa, 0xfda5, 0x7ff9, 0xfd8c, 0x7ff9, 0xfd73, 0x7ff8, 0xfd5a,
+  0x7ff8, 0xfd41, 0x7ff7, 0xfd28, 0x7ff7, 0xfd0f, 0x7ff6, 0xfcf5,
+  0x7ff6, 0xfcdc, 0x7ff5, 0xfcc3, 0x7ff4, 0xfcaa, 0x7ff4, 0xfc91,
+  0x7ff3, 0xfc78, 0x7ff2, 0xfc5f, 0x7ff2, 0xfc46, 0x7ff1, 0xfc2c,
+  0x7ff0, 0xfc13, 0x7fef, 0xfbfa, 0x7fee, 0xfbe1, 0x7fee, 0xfbc8,
+  0x7fed, 0xfbaf, 0x7fec, 0xfb96, 0x7feb, 0xfb7d, 0x7fea, 0xfb64,
+  0x7fe9, 0xfb4a, 0x7fe8, 0xfb31, 0x7fe7, 0xfb18, 0x7fe6, 0xfaff,
+  0x7fe5, 0xfae6, 0x7fe4, 0xfacd, 0x7fe3, 0xfab4, 0x7fe2, 0xfa9b,
+  0x7fe1, 0xfa81, 0x7fe0, 0xfa68, 0x7fdf, 0xfa4f, 0x7fde, 0xfa36,
+  0x7fdd, 0xfa1d, 0x7fdc, 0xfa04, 0x7fda, 0xf9eb, 0x7fd9, 0xf9d2,
+  0x7fd8, 0xf9b9, 0x7fd7, 0xf9a0, 0x7fd6, 0xf986, 0x7fd4, 0xf96d,
+  0x7fd3, 0xf954, 0x7fd2, 0xf93b, 0x7fd0, 0xf922, 0x7fcf, 0xf909,
+  0x7fce, 0xf8f0, 0x7fcc, 0xf8d7, 0x7fcb, 0xf8be, 0x7fc9, 0xf8a5,
+  0x7fc8, 0xf88b, 0x7fc6, 0xf872, 0x7fc5, 0xf859, 0x7fc3, 0xf840,
+  0x7fc2, 0xf827, 0x7fc0, 0xf80e, 0x7fbf, 0xf7f5, 0x7fbd, 0xf7dc,
+  0x7fbc, 0xf7c3, 0x7fba, 0xf7aa, 0x7fb8, 0xf791, 0x7fb7, 0xf778,
+  0x7fb5, 0xf75e, 0x7fb3, 0xf745, 0x7fb1, 0xf72c, 0x7fb0, 0xf713,
+  0x7fae, 0xf6fa, 0x7fac, 0xf6e1, 0x7faa, 0xf6c8, 0x7fa9, 0xf6af,
+  0x7fa7, 0xf696, 0x7fa5, 0xf67d, 0x7fa3, 0xf664, 0x7fa1, 0xf64b,
+  0x7f9f, 0xf632, 0x7f9d, 0xf619, 0x7f9b, 0xf600, 0x7f99, 0xf5e7,
+  0x7f97, 0xf5cd, 0x7f95, 0xf5b4, 0x7f93, 0xf59b, 0x7f91, 0xf582,
+  0x7f8f, 0xf569, 0x7f8d, 0xf550, 0x7f8b, 0xf537, 0x7f89, 0xf51e,
+  0x7f87, 0xf505, 0x7f85, 0xf4ec, 0x7f82, 0xf4d3, 0x7f80, 0xf4ba,
+  0x7f7e, 0xf4a1, 0x7f7c, 0xf488, 0x7f79, 0xf46f, 0x7f77, 0xf456,
+  0x7f75, 0xf43d, 0x7f72, 0xf424, 0x7f70, 0xf40b, 0x7f6e, 0xf3f2,
+  0x7f6b, 0xf3d9, 0x7f69, 0xf3c0, 0x7f67, 0xf3a7, 0x7f64, 0xf38e,
+  0x7f62, 0xf375, 0x7f5f, 0xf35c, 0x7f5d, 0xf343, 0x7f5a, 0xf32a,
+  0x7f58, 0xf311, 0x7f55, 0xf2f8, 0x7f53, 0xf2df, 0x7f50, 0xf2c6,
+  0x7f4d, 0xf2ad, 0x7f4b, 0xf294, 0x7f48, 0xf27b, 0x7f45, 0xf262,
+  0x7f43, 0xf249, 0x7f40, 0xf230, 0x7f3d, 0xf217, 0x7f3b, 0xf1fe,
+  0x7f38, 0xf1e5, 0x7f35, 0xf1cc, 0x7f32, 0xf1b3, 0x7f2f, 0xf19a,
+  0x7f2d, 0xf181, 0x7f2a, 0xf168, 0x7f27, 0xf14f, 0x7f24, 0xf136,
+  0x7f21, 0xf11d, 0x7f1e, 0xf104, 0x7f1b, 0xf0eb, 0x7f18, 0xf0d2,
+  0x7f15, 0xf0b9, 0x7f12, 0xf0a0, 0x7f0f, 0xf087, 0x7f0c, 0xf06e,
+  0x7f09, 0xf055, 0x7f06, 0xf03c, 0x7f03, 0xf023, 0x7f00, 0xf00b,
+  0x7efd, 0xeff2, 0x7ef9, 0xefd9, 0x7ef6, 0xefc0, 0x7ef3, 0xefa7,
+  0x7ef0, 0xef8e, 0x7eed, 0xef75, 0x7ee9, 0xef5c, 0x7ee6, 0xef43,
+  0x7ee3, 0xef2a, 0x7edf, 0xef11, 0x7edc, 0xeef8, 0x7ed9, 0xeedf,
+  0x7ed5, 0xeec7, 0x7ed2, 0xeeae, 0x7ecf, 0xee95, 0x7ecb, 0xee7c,
+  0x7ec8, 0xee63, 0x7ec4, 0xee4a, 0x7ec1, 0xee31, 0x7ebd, 0xee18,
+  0x7eba, 0xedff, 0x7eb6, 0xede7, 0x7eb3, 0xedce, 0x7eaf, 0xedb5,
+  0x7eab, 0xed9c, 0x7ea8, 0xed83, 0x7ea4, 0xed6a, 0x7ea1, 0xed51,
+  0x7e9d, 0xed38, 0x7e99, 0xed20, 0x7e95, 0xed07, 0x7e92, 0xecee,
+  0x7e8e, 0xecd5, 0x7e8a, 0xecbc, 0x7e86, 0xeca3, 0x7e83, 0xec8a,
+  0x7e7f, 0xec72, 0x7e7b, 0xec59, 0x7e77, 0xec40, 0x7e73, 0xec27,
+  0x7e6f, 0xec0e, 0x7e6b, 0xebf5, 0x7e67, 0xebdd, 0x7e63, 0xebc4,
+  0x7e5f, 0xebab, 0x7e5b, 0xeb92, 0x7e57, 0xeb79, 0x7e53, 0xeb61,
+  0x7e4f, 0xeb48, 0x7e4b, 0xeb2f, 0x7e47, 0xeb16, 0x7e43, 0xeafd,
+  0x7e3f, 0xeae5, 0x7e3b, 0xeacc, 0x7e37, 0xeab3, 0x7e32, 0xea9a,
+  0x7e2e, 0xea81, 0x7e2a, 0xea69, 0x7e26, 0xea50, 0x7e21, 0xea37,
+  0x7e1d, 0xea1e, 0x7e19, 0xea06, 0x7e14, 0xe9ed, 0x7e10, 0xe9d4,
+  0x7e0c, 0xe9bb, 0x7e07, 0xe9a3, 0x7e03, 0xe98a, 0x7dff, 0xe971,
+  0x7dfa, 0xe958, 0x7df6, 0xe940, 0x7df1, 0xe927, 0x7ded, 0xe90e,
+  0x7de8, 0xe8f6, 0x7de4, 0xe8dd, 0x7ddf, 0xe8c4, 0x7dda, 0xe8ab,
+  0x7dd6, 0xe893, 0x7dd1, 0xe87a, 0x7dcd, 0xe861, 0x7dc8, 0xe849,
+  0x7dc3, 0xe830, 0x7dbf, 0xe817, 0x7dba, 0xe7fe, 0x7db5, 0xe7e6,
+  0x7db0, 0xe7cd, 0x7dac, 0xe7b4, 0x7da7, 0xe79c, 0x7da2, 0xe783,
+  0x7d9d, 0xe76a, 0x7d98, 0xe752, 0x7d94, 0xe739, 0x7d8f, 0xe720,
+  0x7d8a, 0xe708, 0x7d85, 0xe6ef, 0x7d80, 0xe6d6, 0x7d7b, 0xe6be,
+  0x7d76, 0xe6a5, 0x7d71, 0xe68d, 0x7d6c, 0xe674, 0x7d67, 0xe65b,
+  0x7d62, 0xe643, 0x7d5d, 0xe62a, 0x7d58, 0xe611, 0x7d53, 0xe5f9,
+  0x7d4e, 0xe5e0, 0x7d49, 0xe5c8, 0x7d43, 0xe5af, 0x7d3e, 0xe596,
+  0x7d39, 0xe57e, 0x7d34, 0xe565, 0x7d2f, 0xe54d, 0x7d29, 0xe534,
+  0x7d24, 0xe51c, 0x7d1f, 0xe503, 0x7d19, 0xe4ea, 0x7d14, 0xe4d2,
+  0x7d0f, 0xe4b9, 0x7d09, 0xe4a1, 0x7d04, 0xe488, 0x7cff, 0xe470,
+  0x7cf9, 0xe457, 0x7cf4, 0xe43f, 0x7cee, 0xe426, 0x7ce9, 0xe40e,
+  0x7ce3, 0xe3f5, 0x7cde, 0xe3dc, 0x7cd8, 0xe3c4, 0x7cd3, 0xe3ab,
+  0x7ccd, 0xe393, 0x7cc8, 0xe37a, 0x7cc2, 0xe362, 0x7cbc, 0xe349,
+  0x7cb7, 0xe331, 0x7cb1, 0xe318, 0x7cab, 0xe300, 0x7ca6, 0xe2e8,
+  0x7ca0, 0xe2cf, 0x7c9a, 0xe2b7, 0x7c94, 0xe29e, 0x7c8f, 0xe286,
+  0x7c89, 0xe26d, 0x7c83, 0xe255, 0x7c7d, 0xe23c, 0x7c77, 0xe224,
+  0x7c71, 0xe20b, 0x7c6c, 0xe1f3, 0x7c66, 0xe1db, 0x7c60, 0xe1c2,
+  0x7c5a, 0xe1aa, 0x7c54, 0xe191, 0x7c4e, 0xe179, 0x7c48, 0xe160,
+  0x7c42, 0xe148, 0x7c3c, 0xe130, 0x7c36, 0xe117, 0x7c30, 0xe0ff,
+  0x7c29, 0xe0e7, 0x7c23, 0xe0ce, 0x7c1d, 0xe0b6, 0x7c17, 0xe09d,
+  0x7c11, 0xe085, 0x7c0b, 0xe06d, 0x7c05, 0xe054, 0x7bfe, 0xe03c,
+  0x7bf8, 0xe024, 0x7bf2, 0xe00b, 0x7beb, 0xdff3, 0x7be5, 0xdfdb,
+  0x7bdf, 0xdfc2, 0x7bd9, 0xdfaa, 0x7bd2, 0xdf92, 0x7bcc, 0xdf79,
+  0x7bc5, 0xdf61, 0x7bbf, 0xdf49, 0x7bb9, 0xdf30, 0x7bb2, 0xdf18,
+  0x7bac, 0xdf00, 0x7ba5, 0xdee8, 0x7b9f, 0xdecf, 0x7b98, 0xdeb7,
+  0x7b92, 0xde9f, 0x7b8b, 0xde87, 0x7b84, 0xde6e, 0x7b7e, 0xde56,
+  0x7b77, 0xde3e, 0x7b71, 0xde26, 0x7b6a, 0xde0d, 0x7b63, 0xddf5,
+  0x7b5d, 0xdddd, 0x7b56, 0xddc5, 0x7b4f, 0xddac, 0x7b48, 0xdd94,
+  0x7b42, 0xdd7c, 0x7b3b, 0xdd64, 0x7b34, 0xdd4c, 0x7b2d, 0xdd33,
+  0x7b26, 0xdd1b, 0x7b1f, 0xdd03, 0x7b19, 0xdceb, 0x7b12, 0xdcd3,
+  0x7b0b, 0xdcbb, 0x7b04, 0xdca2, 0x7afd, 0xdc8a, 0x7af6, 0xdc72,
+  0x7aef, 0xdc5a, 0x7ae8, 0xdc42, 0x7ae1, 0xdc2a, 0x7ada, 0xdc12,
+  0x7ad3, 0xdbf9, 0x7acc, 0xdbe1, 0x7ac5, 0xdbc9, 0x7abd, 0xdbb1,
+  0x7ab6, 0xdb99, 0x7aaf, 0xdb81, 0x7aa8, 0xdb69, 0x7aa1, 0xdb51,
+  0x7a9a, 0xdb39, 0x7a92, 0xdb21, 0x7a8b, 0xdb09, 0x7a84, 0xdaf1,
+  0x7a7d, 0xdad8, 0x7a75, 0xdac0, 0x7a6e, 0xdaa8, 0x7a67, 0xda90,
+  0x7a5f, 0xda78, 0x7a58, 0xda60, 0x7a50, 0xda48, 0x7a49, 0xda30,
+  0x7a42, 0xda18, 0x7a3a, 0xda00, 0x7a33, 0xd9e8, 0x7a2b, 0xd9d0,
+  0x7a24, 0xd9b8, 0x7a1c, 0xd9a0, 0x7a15, 0xd988, 0x7a0d, 0xd970,
+  0x7a05, 0xd958, 0x79fe, 0xd940, 0x79f6, 0xd928, 0x79ef, 0xd911,
+  0x79e7, 0xd8f9, 0x79df, 0xd8e1, 0x79d8, 0xd8c9, 0x79d0, 0xd8b1,
+  0x79c8, 0xd899, 0x79c0, 0xd881, 0x79b9, 0xd869, 0x79b1, 0xd851,
+  0x79a9, 0xd839, 0x79a1, 0xd821, 0x7999, 0xd80a, 0x7992, 0xd7f2,
+  0x798a, 0xd7da, 0x7982, 0xd7c2, 0x797a, 0xd7aa, 0x7972, 0xd792,
+  0x796a, 0xd77a, 0x7962, 0xd763, 0x795a, 0xd74b, 0x7952, 0xd733,
+  0x794a, 0xd71b, 0x7942, 0xd703, 0x793a, 0xd6eb, 0x7932, 0xd6d4,
+  0x792a, 0xd6bc, 0x7922, 0xd6a4, 0x7919, 0xd68c, 0x7911, 0xd675,
+  0x7909, 0xd65d, 0x7901, 0xd645, 0x78f9, 0xd62d, 0x78f1, 0xd615,
+  0x78e8, 0xd5fe, 0x78e0, 0xd5e6, 0x78d8, 0xd5ce, 0x78cf, 0xd5b7,
+  0x78c7, 0xd59f, 0x78bf, 0xd587, 0x78b6, 0xd56f, 0x78ae, 0xd558,
+  0x78a6, 0xd540, 0x789d, 0xd528, 0x7895, 0xd511, 0x788c, 0xd4f9,
+  0x7884, 0xd4e1, 0x787c, 0xd4ca, 0x7873, 0xd4b2, 0x786b, 0xd49a,
+  0x7862, 0xd483, 0x7859, 0xd46b, 0x7851, 0xd453, 0x7848, 0xd43c,
+  0x7840, 0xd424, 0x7837, 0xd40d, 0x782e, 0xd3f5, 0x7826, 0xd3dd,
+  0x781d, 0xd3c6, 0x7814, 0xd3ae, 0x780c, 0xd397, 0x7803, 0xd37f,
+  0x77fa, 0xd368, 0x77f1, 0xd350, 0x77e9, 0xd338, 0x77e0, 0xd321,
+  0x77d7, 0xd309, 0x77ce, 0xd2f2, 0x77c5, 0xd2da, 0x77bc, 0xd2c3,
+  0x77b4, 0xd2ab, 0x77ab, 0xd294, 0x77a2, 0xd27c, 0x7799, 0xd265,
+  0x7790, 0xd24d, 0x7787, 0xd236, 0x777e, 0xd21e, 0x7775, 0xd207,
+  0x776c, 0xd1ef, 0x7763, 0xd1d8, 0x775a, 0xd1c1, 0x7751, 0xd1a9,
+  0x7747, 0xd192, 0x773e, 0xd17a, 0x7735, 0xd163, 0x772c, 0xd14b,
+  0x7723, 0xd134, 0x771a, 0xd11d, 0x7710, 0xd105, 0x7707, 0xd0ee,
+  0x76fe, 0xd0d7, 0x76f5, 0xd0bf, 0x76eb, 0xd0a8, 0x76e2, 0xd091,
+  0x76d9, 0xd079, 0x76cf, 0xd062, 0x76c6, 0xd04b, 0x76bd, 0xd033,
+  0x76b3, 0xd01c, 0x76aa, 0xd005, 0x76a0, 0xcfed, 0x7697, 0xcfd6,
+  0x768e, 0xcfbf, 0x7684, 0xcfa7, 0x767b, 0xcf90, 0x7671, 0xcf79,
+  0x7668, 0xcf62, 0x765e, 0xcf4a, 0x7654, 0xcf33, 0x764b, 0xcf1c,
+  0x7641, 0xcf05, 0x7638, 0xceee, 0x762e, 0xced6, 0x7624, 0xcebf,
+  0x761b, 0xcea8, 0x7611, 0xce91, 0x7607, 0xce7a, 0x75fd, 0xce62,
+  0x75f4, 0xce4b, 0x75ea, 0xce34, 0x75e0, 0xce1d, 0x75d6, 0xce06,
+  0x75cc, 0xcdef, 0x75c3, 0xcdd8, 0x75b9, 0xcdc0, 0x75af, 0xcda9,
+  0x75a5, 0xcd92, 0x759b, 0xcd7b, 0x7591, 0xcd64, 0x7587, 0xcd4d,
+  0x757d, 0xcd36, 0x7573, 0xcd1f, 0x7569, 0xcd08, 0x755f, 0xccf1,
+  0x7555, 0xccda, 0x754b, 0xccc3, 0x7541, 0xccac, 0x7537, 0xcc95,
+  0x752d, 0xcc7e, 0x7523, 0xcc67, 0x7519, 0xcc50, 0x750f, 0xcc39,
+  0x7504, 0xcc22, 0x74fa, 0xcc0b, 0x74f0, 0xcbf4, 0x74e6, 0xcbdd,
+  0x74db, 0xcbc6, 0x74d1, 0xcbaf, 0x74c7, 0xcb98, 0x74bd, 0xcb81,
+  0x74b2, 0xcb6a, 0x74a8, 0xcb53, 0x749e, 0xcb3c, 0x7493, 0xcb25,
+  0x7489, 0xcb0e, 0x747e, 0xcaf8, 0x7474, 0xcae1, 0x746a, 0xcaca,
+  0x745f, 0xcab3, 0x7455, 0xca9c, 0x744a, 0xca85, 0x7440, 0xca6e,
+  0x7435, 0xca58, 0x742b, 0xca41, 0x7420, 0xca2a, 0x7415, 0xca13,
+  0x740b, 0xc9fc, 0x7400, 0xc9e6, 0x73f6, 0xc9cf, 0x73eb, 0xc9b8,
+  0x73e0, 0xc9a1, 0x73d6, 0xc98b, 0x73cb, 0xc974, 0x73c0, 0xc95d,
+  0x73b5, 0xc946, 0x73ab, 0xc930, 0x73a0, 0xc919, 0x7395, 0xc902,
+  0x738a, 0xc8ec, 0x737f, 0xc8d5, 0x7375, 0xc8be, 0x736a, 0xc8a8,
+  0x735f, 0xc891, 0x7354, 0xc87a, 0x7349, 0xc864, 0x733e, 0xc84d,
+  0x7333, 0xc836, 0x7328, 0xc820, 0x731d, 0xc809, 0x7312, 0xc7f3,
+  0x7307, 0xc7dc, 0x72fc, 0xc7c5, 0x72f1, 0xc7af, 0x72e6, 0xc798,
+  0x72db, 0xc782, 0x72d0, 0xc76b, 0x72c5, 0xc755, 0x72ba, 0xc73e,
+  0x72af, 0xc728, 0x72a3, 0xc711, 0x7298, 0xc6fa, 0x728d, 0xc6e4,
+  0x7282, 0xc6ce, 0x7276, 0xc6b7, 0x726b, 0xc6a1, 0x7260, 0xc68a,
+  0x7255, 0xc674, 0x7249, 0xc65d, 0x723e, 0xc647, 0x7233, 0xc630,
+  0x7227, 0xc61a, 0x721c, 0xc603, 0x7211, 0xc5ed, 0x7205, 0xc5d7,
+  0x71fa, 0xc5c0, 0x71ee, 0xc5aa, 0x71e3, 0xc594, 0x71d7, 0xc57d,
+  0x71cc, 0xc567, 0x71c0, 0xc551, 0x71b5, 0xc53a, 0x71a9, 0xc524,
+  0x719e, 0xc50e, 0x7192, 0xc4f7, 0x7186, 0xc4e1, 0x717b, 0xc4cb,
+  0x716f, 0xc4b4, 0x7164, 0xc49e, 0x7158, 0xc488, 0x714c, 0xc472,
+  0x7141, 0xc45b, 0x7135, 0xc445, 0x7129, 0xc42f, 0x711d, 0xc419,
+  0x7112, 0xc403, 0x7106, 0xc3ec, 0x70fa, 0xc3d6, 0x70ee, 0xc3c0,
+  0x70e2, 0xc3aa, 0x70d6, 0xc394, 0x70cb, 0xc37d, 0x70bf, 0xc367,
+  0x70b3, 0xc351, 0x70a7, 0xc33b, 0x709b, 0xc325, 0x708f, 0xc30f,
+  0x7083, 0xc2f9, 0x7077, 0xc2e3, 0x706b, 0xc2cd, 0x705f, 0xc2b7,
+  0x7053, 0xc2a0, 0x7047, 0xc28a, 0x703b, 0xc274, 0x702f, 0xc25e,
+  0x7023, 0xc248, 0x7016, 0xc232, 0x700a, 0xc21c, 0x6ffe, 0xc206,
+  0x6ff2, 0xc1f0, 0x6fe6, 0xc1da, 0x6fda, 0xc1c4, 0x6fcd, 0xc1ae,
+  0x6fc1, 0xc198, 0x6fb5, 0xc183, 0x6fa9, 0xc16d, 0x6f9c, 0xc157,
+  0x6f90, 0xc141, 0x6f84, 0xc12b, 0x6f77, 0xc115, 0x6f6b, 0xc0ff,
+  0x6f5f, 0xc0e9, 0x6f52, 0xc0d3, 0x6f46, 0xc0bd, 0x6f39, 0xc0a8,
+  0x6f2d, 0xc092, 0x6f20, 0xc07c, 0x6f14, 0xc066, 0x6f07, 0xc050,
+  0x6efb, 0xc03b, 0x6eee, 0xc025, 0x6ee2, 0xc00f, 0x6ed5, 0xbff9,
+  0x6ec9, 0xbfe3, 0x6ebc, 0xbfce, 0x6eaf, 0xbfb8, 0x6ea3, 0xbfa2,
+  0x6e96, 0xbf8d, 0x6e89, 0xbf77, 0x6e7d, 0xbf61, 0x6e70, 0xbf4b,
+  0x6e63, 0xbf36, 0x6e57, 0xbf20, 0x6e4a, 0xbf0a, 0x6e3d, 0xbef5,
+  0x6e30, 0xbedf, 0x6e24, 0xbeca, 0x6e17, 0xbeb4, 0x6e0a, 0xbe9e,
+  0x6dfd, 0xbe89, 0x6df0, 0xbe73, 0x6de3, 0xbe5e, 0x6dd6, 0xbe48,
+  0x6dca, 0xbe32, 0x6dbd, 0xbe1d, 0x6db0, 0xbe07, 0x6da3, 0xbdf2,
+  0x6d96, 0xbddc, 0x6d89, 0xbdc7, 0x6d7c, 0xbdb1, 0x6d6f, 0xbd9c,
+  0x6d62, 0xbd86, 0x6d55, 0xbd71, 0x6d48, 0xbd5b, 0x6d3a, 0xbd46,
+  0x6d2d, 0xbd30, 0x6d20, 0xbd1b, 0x6d13, 0xbd06, 0x6d06, 0xbcf0,
+  0x6cf9, 0xbcdb, 0x6cec, 0xbcc5, 0x6cde, 0xbcb0, 0x6cd1, 0xbc9b,
+  0x6cc4, 0xbc85, 0x6cb7, 0xbc70, 0x6ca9, 0xbc5b, 0x6c9c, 0xbc45,
+  0x6c8f, 0xbc30, 0x6c81, 0xbc1b, 0x6c74, 0xbc05, 0x6c67, 0xbbf0,
+  0x6c59, 0xbbdb, 0x6c4c, 0xbbc5, 0x6c3f, 0xbbb0, 0x6c31, 0xbb9b,
+  0x6c24, 0xbb86, 0x6c16, 0xbb70, 0x6c09, 0xbb5b, 0x6bfb, 0xbb46,
+  0x6bee, 0xbb31, 0x6be0, 0xbb1c, 0x6bd3, 0xbb06, 0x6bc5, 0xbaf1,
+  0x6bb8, 0xbadc, 0x6baa, 0xbac7, 0x6b9c, 0xbab2, 0x6b8f, 0xba9d,
+  0x6b81, 0xba88, 0x6b73, 0xba73, 0x6b66, 0xba5d, 0x6b58, 0xba48,
+  0x6b4a, 0xba33, 0x6b3d, 0xba1e, 0x6b2f, 0xba09, 0x6b21, 0xb9f4,
+  0x6b13, 0xb9df, 0x6b06, 0xb9ca, 0x6af8, 0xb9b5, 0x6aea, 0xb9a0,
+  0x6adc, 0xb98b, 0x6ace, 0xb976, 0x6ac1, 0xb961, 0x6ab3, 0xb94c,
+  0x6aa5, 0xb937, 0x6a97, 0xb922, 0x6a89, 0xb90d, 0x6a7b, 0xb8f8,
+  0x6a6d, 0xb8e4, 0x6a5f, 0xb8cf, 0x6a51, 0xb8ba, 0x6a43, 0xb8a5,
+  0x6a35, 0xb890, 0x6a27, 0xb87b, 0x6a19, 0xb866, 0x6a0b, 0xb852,
+  0x69fd, 0xb83d, 0x69ef, 0xb828, 0x69e1, 0xb813, 0x69d3, 0xb7fe,
+  0x69c4, 0xb7ea, 0x69b6, 0xb7d5, 0x69a8, 0xb7c0, 0x699a, 0xb7ab,
+  0x698c, 0xb797, 0x697d, 0xb782, 0x696f, 0xb76d, 0x6961, 0xb758,
+  0x6953, 0xb744, 0x6944, 0xb72f, 0x6936, 0xb71a, 0x6928, 0xb706,
+  0x6919, 0xb6f1, 0x690b, 0xb6dd, 0x68fd, 0xb6c8, 0x68ee, 0xb6b3,
+  0x68e0, 0xb69f, 0x68d1, 0xb68a, 0x68c3, 0xb676, 0x68b5, 0xb661,
+  0x68a6, 0xb64c, 0x6898, 0xb638, 0x6889, 0xb623, 0x687b, 0xb60f,
+  0x686c, 0xb5fa, 0x685e, 0xb5e6, 0x684f, 0xb5d1, 0x6840, 0xb5bd,
+  0x6832, 0xb5a8, 0x6823, 0xb594, 0x6815, 0xb57f, 0x6806, 0xb56b,
+  0x67f7, 0xb557, 0x67e9, 0xb542, 0x67da, 0xb52e, 0x67cb, 0xb519,
+  0x67bd, 0xb505, 0x67ae, 0xb4f1, 0x679f, 0xb4dc, 0x6790, 0xb4c8,
+  0x6782, 0xb4b4, 0x6773, 0xb49f, 0x6764, 0xb48b, 0x6755, 0xb477,
+  0x6746, 0xb462, 0x6737, 0xb44e, 0x6729, 0xb43a, 0x671a, 0xb426,
+  0x670b, 0xb411, 0x66fc, 0xb3fd, 0x66ed, 0xb3e9, 0x66de, 0xb3d5,
+  0x66cf, 0xb3c1, 0x66c0, 0xb3ac, 0x66b1, 0xb398, 0x66a2, 0xb384,
+  0x6693, 0xb370, 0x6684, 0xb35c, 0x6675, 0xb348, 0x6666, 0xb334,
+  0x6657, 0xb31f, 0x6648, 0xb30b, 0x6639, 0xb2f7, 0x6629, 0xb2e3,
+  0x661a, 0xb2cf, 0x660b, 0xb2bb, 0x65fc, 0xb2a7, 0x65ed, 0xb293,
+  0x65dd, 0xb27f, 0x65ce, 0xb26b, 0x65bf, 0xb257, 0x65b0, 0xb243,
+  0x65a0, 0xb22f, 0x6591, 0xb21b, 0x6582, 0xb207, 0x6573, 0xb1f3,
+  0x6563, 0xb1df, 0x6554, 0xb1cc, 0x6545, 0xb1b8, 0x6535, 0xb1a4,
+  0x6526, 0xb190, 0x6516, 0xb17c, 0x6507, 0xb168, 0x64f7, 0xb154,
+  0x64e8, 0xb141, 0x64d9, 0xb12d, 0x64c9, 0xb119, 0x64ba, 0xb105,
+  0x64aa, 0xb0f1, 0x649b, 0xb0de, 0x648b, 0xb0ca, 0x647b, 0xb0b6,
+  0x646c, 0xb0a2, 0x645c, 0xb08f, 0x644d, 0xb07b, 0x643d, 0xb067,
+  0x642d, 0xb054, 0x641e, 0xb040, 0x640e, 0xb02c, 0x63fe, 0xb019,
+  0x63ef, 0xb005, 0x63df, 0xaff1, 0x63cf, 0xafde, 0x63c0, 0xafca,
+  0x63b0, 0xafb7, 0x63a0, 0xafa3, 0x6390, 0xaf90, 0x6380, 0xaf7c,
+  0x6371, 0xaf69, 0x6361, 0xaf55, 0x6351, 0xaf41, 0x6341, 0xaf2e,
+  0x6331, 0xaf1b, 0x6321, 0xaf07, 0x6311, 0xaef4, 0x6301, 0xaee0,
+  0x62f2, 0xaecd, 0x62e2, 0xaeb9, 0x62d2, 0xaea6, 0x62c2, 0xae92,
+  0x62b2, 0xae7f, 0x62a2, 0xae6c, 0x6292, 0xae58, 0x6282, 0xae45,
+  0x6271, 0xae32, 0x6261, 0xae1e, 0x6251, 0xae0b, 0x6241, 0xadf8,
+  0x6231, 0xade4, 0x6221, 0xadd1, 0x6211, 0xadbe, 0x6201, 0xadab,
+  0x61f1, 0xad97, 0x61e0, 0xad84, 0x61d0, 0xad71, 0x61c0, 0xad5e,
+  0x61b0, 0xad4b, 0x619f, 0xad37, 0x618f, 0xad24, 0x617f, 0xad11,
+  0x616f, 0xacfe, 0x615e, 0xaceb, 0x614e, 0xacd8, 0x613e, 0xacc5,
+  0x612d, 0xacb2, 0x611d, 0xac9e, 0x610d, 0xac8b, 0x60fc, 0xac78,
+  0x60ec, 0xac65, 0x60db, 0xac52, 0x60cb, 0xac3f, 0x60ba, 0xac2c,
+  0x60aa, 0xac19, 0x6099, 0xac06, 0x6089, 0xabf3, 0x6078, 0xabe0,
+  0x6068, 0xabcd, 0x6057, 0xabbb, 0x6047, 0xaba8, 0x6036, 0xab95,
+  0x6026, 0xab82, 0x6015, 0xab6f, 0x6004, 0xab5c, 0x5ff4, 0xab49,
+  0x5fe3, 0xab36, 0x5fd3, 0xab24, 0x5fc2, 0xab11, 0x5fb1, 0xaafe,
+  0x5fa0, 0xaaeb, 0x5f90, 0xaad8, 0x5f7f, 0xaac6, 0x5f6e, 0xaab3,
+  0x5f5e, 0xaaa0, 0x5f4d, 0xaa8e, 0x5f3c, 0xaa7b, 0x5f2b, 0xaa68,
+  0x5f1a, 0xaa55, 0x5f0a, 0xaa43, 0x5ef9, 0xaa30, 0x5ee8, 0xaa1d,
+  0x5ed7, 0xaa0b, 0x5ec6, 0xa9f8, 0x5eb5, 0xa9e6, 0x5ea4, 0xa9d3,
+  0x5e93, 0xa9c0, 0x5e82, 0xa9ae, 0x5e71, 0xa99b, 0x5e60, 0xa989,
+  0x5e50, 0xa976, 0x5e3f, 0xa964, 0x5e2d, 0xa951, 0x5e1c, 0xa93f,
+  0x5e0b, 0xa92c, 0x5dfa, 0xa91a, 0x5de9, 0xa907, 0x5dd8, 0xa8f5,
+  0x5dc7, 0xa8e3, 0x5db6, 0xa8d0, 0x5da5, 0xa8be, 0x5d94, 0xa8ab,
+  0x5d83, 0xa899, 0x5d71, 0xa887, 0x5d60, 0xa874, 0x5d4f, 0xa862,
+  0x5d3e, 0xa850, 0x5d2d, 0xa83d, 0x5d1b, 0xa82b, 0x5d0a, 0xa819,
+  0x5cf9, 0xa807, 0x5ce8, 0xa7f4, 0x5cd6, 0xa7e2, 0x5cc5, 0xa7d0,
+  0x5cb4, 0xa7be, 0x5ca2, 0xa7ab, 0x5c91, 0xa799, 0x5c80, 0xa787,
+  0x5c6e, 0xa775, 0x5c5d, 0xa763, 0x5c4b, 0xa751, 0x5c3a, 0xa73f,
+  0x5c29, 0xa72c, 0x5c17, 0xa71a, 0x5c06, 0xa708, 0x5bf4, 0xa6f6,
+  0x5be3, 0xa6e4, 0x5bd1, 0xa6d2, 0x5bc0, 0xa6c0, 0x5bae, 0xa6ae,
+  0x5b9d, 0xa69c, 0x5b8b, 0xa68a, 0x5b79, 0xa678, 0x5b68, 0xa666,
+  0x5b56, 0xa654, 0x5b45, 0xa642, 0x5b33, 0xa630, 0x5b21, 0xa61f,
+  0x5b10, 0xa60d, 0x5afe, 0xa5fb, 0x5aec, 0xa5e9, 0x5adb, 0xa5d7,
+  0x5ac9, 0xa5c5, 0x5ab7, 0xa5b3, 0x5aa5, 0xa5a2, 0x5a94, 0xa590,
+  0x5a82, 0xa57e, 0x5a70, 0xa56c, 0x5a5e, 0xa55b, 0x5a4d, 0xa549,
+  0x5a3b, 0xa537, 0x5a29, 0xa525, 0x5a17, 0xa514, 0x5a05, 0xa502,
+  0x59f3, 0xa4f0, 0x59e1, 0xa4df, 0x59d0, 0xa4cd, 0x59be, 0xa4bb,
+  0x59ac, 0xa4aa, 0x599a, 0xa498, 0x5988, 0xa487, 0x5976, 0xa475,
+  0x5964, 0xa463, 0x5952, 0xa452, 0x5940, 0xa440, 0x592e, 0xa42f,
+  0x591c, 0xa41d, 0x590a, 0xa40c, 0x58f8, 0xa3fa, 0x58e6, 0xa3e9,
+  0x58d4, 0xa3d7, 0x58c1, 0xa3c6, 0x58af, 0xa3b5, 0x589d, 0xa3a3,
+  0x588b, 0xa392, 0x5879, 0xa380, 0x5867, 0xa36f, 0x5855, 0xa35e,
+  0x5842, 0xa34c, 0x5830, 0xa33b, 0x581e, 0xa32a, 0x580c, 0xa318,
+  0x57f9, 0xa307, 0x57e7, 0xa2f6, 0x57d5, 0xa2e5, 0x57c3, 0xa2d3,
+  0x57b0, 0xa2c2, 0x579e, 0xa2b1, 0x578c, 0xa2a0, 0x5779, 0xa28f,
+  0x5767, 0xa27d, 0x5755, 0xa26c, 0x5742, 0xa25b, 0x5730, 0xa24a,
+  0x571d, 0xa239, 0x570b, 0xa228, 0x56f9, 0xa217, 0x56e6, 0xa206,
+  0x56d4, 0xa1f5, 0x56c1, 0xa1e4, 0x56af, 0xa1d3, 0x569c, 0xa1c1,
+  0x568a, 0xa1b0, 0x5677, 0xa1a0, 0x5665, 0xa18f, 0x5652, 0xa17e,
+  0x5640, 0xa16d, 0x562d, 0xa15c, 0x561a, 0xa14b, 0x5608, 0xa13a,
+  0x55f5, 0xa129, 0x55e3, 0xa118, 0x55d0, 0xa107, 0x55bd, 0xa0f6,
+  0x55ab, 0xa0e6, 0x5598, 0xa0d5, 0x5585, 0xa0c4, 0x5572, 0xa0b3,
+  0x5560, 0xa0a2, 0x554d, 0xa092, 0x553a, 0xa081, 0x5528, 0xa070,
+  0x5515, 0xa060, 0x5502, 0xa04f, 0x54ef, 0xa03e, 0x54dc, 0xa02d,
+  0x54ca, 0xa01d, 0x54b7, 0xa00c, 0x54a4, 0x9ffc, 0x5491, 0x9feb,
+  0x547e, 0x9fda, 0x546b, 0x9fca, 0x5458, 0x9fb9, 0x5445, 0x9fa9,
+  0x5433, 0x9f98, 0x5420, 0x9f88, 0x540d, 0x9f77, 0x53fa, 0x9f67,
+  0x53e7, 0x9f56, 0x53d4, 0x9f46, 0x53c1, 0x9f35, 0x53ae, 0x9f25,
+  0x539b, 0x9f14, 0x5388, 0x9f04, 0x5375, 0x9ef3, 0x5362, 0x9ee3,
+  0x534e, 0x9ed3, 0x533b, 0x9ec2, 0x5328, 0x9eb2, 0x5315, 0x9ea2,
+  0x5302, 0x9e91, 0x52ef, 0x9e81, 0x52dc, 0x9e71, 0x52c9, 0x9e61,
+  0x52b5, 0x9e50, 0x52a2, 0x9e40, 0x528f, 0x9e30, 0x527c, 0x9e20,
+  0x5269, 0x9e0f, 0x5255, 0x9dff, 0x5242, 0x9def, 0x522f, 0x9ddf,
+  0x521c, 0x9dcf, 0x5208, 0x9dbf, 0x51f5, 0x9daf, 0x51e2, 0x9d9f,
+  0x51ce, 0x9d8f, 0x51bb, 0x9d7e, 0x51a8, 0x9d6e, 0x5194, 0x9d5e,
+  0x5181, 0x9d4e, 0x516e, 0x9d3e, 0x515a, 0x9d2e, 0x5147, 0x9d1e,
+  0x5133, 0x9d0e, 0x5120, 0x9cff, 0x510c, 0x9cef, 0x50f9, 0x9cdf,
+  0x50e5, 0x9ccf, 0x50d2, 0x9cbf, 0x50bf, 0x9caf, 0x50ab, 0x9c9f,
+  0x5097, 0x9c8f, 0x5084, 0x9c80, 0x5070, 0x9c70, 0x505d, 0x9c60,
+  0x5049, 0x9c50, 0x5036, 0x9c40, 0x5022, 0x9c31, 0x500f, 0x9c21,
+  0x4ffb, 0x9c11, 0x4fe7, 0x9c02, 0x4fd4, 0x9bf2, 0x4fc0, 0x9be2,
+  0x4fac, 0x9bd3, 0x4f99, 0x9bc3, 0x4f85, 0x9bb3, 0x4f71, 0x9ba4,
+  0x4f5e, 0x9b94, 0x4f4a, 0x9b85, 0x4f36, 0x9b75, 0x4f22, 0x9b65,
+  0x4f0f, 0x9b56, 0x4efb, 0x9b46, 0x4ee7, 0x9b37, 0x4ed3, 0x9b27,
+  0x4ebf, 0x9b18, 0x4eac, 0x9b09, 0x4e98, 0x9af9, 0x4e84, 0x9aea,
+  0x4e70, 0x9ada, 0x4e5c, 0x9acb, 0x4e48, 0x9abb, 0x4e34, 0x9aac,
+  0x4e21, 0x9a9d, 0x4e0d, 0x9a8d, 0x4df9, 0x9a7e, 0x4de5, 0x9a6f,
+  0x4dd1, 0x9a60, 0x4dbd, 0x9a50, 0x4da9, 0x9a41, 0x4d95, 0x9a32,
+  0x4d81, 0x9a23, 0x4d6d, 0x9a13, 0x4d59, 0x9a04, 0x4d45, 0x99f5,
+  0x4d31, 0x99e6, 0x4d1d, 0x99d7, 0x4d09, 0x99c7, 0x4cf5, 0x99b8,
+  0x4ce1, 0x99a9, 0x4ccc, 0x999a, 0x4cb8, 0x998b, 0x4ca4, 0x997c,
+  0x4c90, 0x996d, 0x4c7c, 0x995e, 0x4c68, 0x994f, 0x4c54, 0x9940,
+  0x4c3f, 0x9931, 0x4c2b, 0x9922, 0x4c17, 0x9913, 0x4c03, 0x9904,
+  0x4bef, 0x98f5, 0x4bda, 0x98e6, 0x4bc6, 0x98d7, 0x4bb2, 0x98c9,
+  0x4b9e, 0x98ba, 0x4b89, 0x98ab, 0x4b75, 0x989c, 0x4b61, 0x988d,
+  0x4b4c, 0x987e, 0x4b38, 0x9870, 0x4b24, 0x9861, 0x4b0f, 0x9852,
+  0x4afb, 0x9843, 0x4ae7, 0x9835, 0x4ad2, 0x9826, 0x4abe, 0x9817,
+  0x4aa9, 0x9809, 0x4a95, 0x97fa, 0x4a81, 0x97eb, 0x4a6c, 0x97dd,
+  0x4a58, 0x97ce, 0x4a43, 0x97c0, 0x4a2f, 0x97b1, 0x4a1a, 0x97a2,
+  0x4a06, 0x9794, 0x49f1, 0x9785, 0x49dd, 0x9777, 0x49c8, 0x9768,
+  0x49b4, 0x975a, 0x499f, 0x974b, 0x498a, 0x973d, 0x4976, 0x972f,
+  0x4961, 0x9720, 0x494d, 0x9712, 0x4938, 0x9703, 0x4923, 0x96f5,
+  0x490f, 0x96e7, 0x48fa, 0x96d8, 0x48e6, 0x96ca, 0x48d1, 0x96bc,
+  0x48bc, 0x96ad, 0x48a8, 0x969f, 0x4893, 0x9691, 0x487e, 0x9683,
+  0x4869, 0x9674, 0x4855, 0x9666, 0x4840, 0x9658, 0x482b, 0x964a,
+  0x4816, 0x963c, 0x4802, 0x962d, 0x47ed, 0x961f, 0x47d8, 0x9611,
+  0x47c3, 0x9603, 0x47ae, 0x95f5, 0x479a, 0x95e7, 0x4785, 0x95d9,
+  0x4770, 0x95cb, 0x475b, 0x95bd, 0x4746, 0x95af, 0x4731, 0x95a1,
+  0x471c, 0x9593, 0x4708, 0x9585, 0x46f3, 0x9577, 0x46de, 0x9569,
+  0x46c9, 0x955b, 0x46b4, 0x954d, 0x469f, 0x953f, 0x468a, 0x9532,
+  0x4675, 0x9524, 0x4660, 0x9516, 0x464b, 0x9508, 0x4636, 0x94fa,
+  0x4621, 0x94ed, 0x460c, 0x94df, 0x45f7, 0x94d1, 0x45e2, 0x94c3,
+  0x45cd, 0x94b6, 0x45b8, 0x94a8, 0x45a3, 0x949a, 0x458d, 0x948d,
+  0x4578, 0x947f, 0x4563, 0x9471, 0x454e, 0x9464, 0x4539, 0x9456,
+  0x4524, 0x9448, 0x450f, 0x943b, 0x44fa, 0x942d, 0x44e4, 0x9420,
+  0x44cf, 0x9412, 0x44ba, 0x9405, 0x44a5, 0x93f7, 0x4490, 0x93ea,
+  0x447a, 0x93dc, 0x4465, 0x93cf, 0x4450, 0x93c1, 0x443b, 0x93b4,
+  0x4425, 0x93a7, 0x4410, 0x9399, 0x43fb, 0x938c, 0x43e5, 0x937f,
+  0x43d0, 0x9371, 0x43bb, 0x9364, 0x43a5, 0x9357, 0x4390, 0x9349,
+  0x437b, 0x933c, 0x4365, 0x932f, 0x4350, 0x9322, 0x433b, 0x9314,
+  0x4325, 0x9307, 0x4310, 0x92fa, 0x42fa, 0x92ed, 0x42e5, 0x92e0,
+  0x42d0, 0x92d3, 0x42ba, 0x92c6, 0x42a5, 0x92b8, 0x428f, 0x92ab,
+  0x427a, 0x929e, 0x4264, 0x9291, 0x424f, 0x9284, 0x4239, 0x9277,
+  0x4224, 0x926a, 0x420e, 0x925d, 0x41f9, 0x9250, 0x41e3, 0x9243,
+  0x41ce, 0x9236, 0x41b8, 0x922a, 0x41a2, 0x921d, 0x418d, 0x9210,
+  0x4177, 0x9203, 0x4162, 0x91f6, 0x414c, 0x91e9, 0x4136, 0x91dc,
+  0x4121, 0x91d0, 0x410b, 0x91c3, 0x40f6, 0x91b6, 0x40e0, 0x91a9,
+  0x40ca, 0x919d, 0x40b5, 0x9190, 0x409f, 0x9183, 0x4089, 0x9177,
+  0x4073, 0x916a, 0x405e, 0x915d, 0x4048, 0x9151, 0x4032, 0x9144,
+  0x401d, 0x9137, 0x4007, 0x912b, 0x3ff1, 0x911e, 0x3fdb, 0x9112,
+  0x3fc5, 0x9105, 0x3fb0, 0x90f9, 0x3f9a, 0x90ec, 0x3f84, 0x90e0,
+  0x3f6e, 0x90d3, 0x3f58, 0x90c7, 0x3f43, 0x90ba, 0x3f2d, 0x90ae,
+  0x3f17, 0x90a1, 0x3f01, 0x9095, 0x3eeb, 0x9089, 0x3ed5, 0x907c,
+  0x3ebf, 0x9070, 0x3ea9, 0x9064, 0x3e93, 0x9057, 0x3e7d, 0x904b,
+  0x3e68, 0x903f, 0x3e52, 0x9033, 0x3e3c, 0x9026, 0x3e26, 0x901a,
+  0x3e10, 0x900e, 0x3dfa, 0x9002, 0x3de4, 0x8ff6, 0x3dce, 0x8fea,
+  0x3db8, 0x8fdd, 0x3da2, 0x8fd1, 0x3d8c, 0x8fc5, 0x3d76, 0x8fb9,
+  0x3d60, 0x8fad, 0x3d49, 0x8fa1, 0x3d33, 0x8f95, 0x3d1d, 0x8f89,
+  0x3d07, 0x8f7d, 0x3cf1, 0x8f71, 0x3cdb, 0x8f65, 0x3cc5, 0x8f59,
+  0x3caf, 0x8f4d, 0x3c99, 0x8f41, 0x3c83, 0x8f35, 0x3c6c, 0x8f2a,
+  0x3c56, 0x8f1e, 0x3c40, 0x8f12, 0x3c2a, 0x8f06, 0x3c14, 0x8efa,
+  0x3bfd, 0x8eee, 0x3be7, 0x8ee3, 0x3bd1, 0x8ed7, 0x3bbb, 0x8ecb,
+  0x3ba5, 0x8ebf, 0x3b8e, 0x8eb4, 0x3b78, 0x8ea8, 0x3b62, 0x8e9c,
+  0x3b4c, 0x8e91, 0x3b35, 0x8e85, 0x3b1f, 0x8e7a, 0x3b09, 0x8e6e,
+  0x3af2, 0x8e62, 0x3adc, 0x8e57, 0x3ac6, 0x8e4b, 0x3aaf, 0x8e40,
+  0x3a99, 0x8e34, 0x3a83, 0x8e29, 0x3a6c, 0x8e1d, 0x3a56, 0x8e12,
+  0x3a40, 0x8e06, 0x3a29, 0x8dfb, 0x3a13, 0x8def, 0x39fd, 0x8de4,
+  0x39e6, 0x8dd9, 0x39d0, 0x8dcd, 0x39b9, 0x8dc2, 0x39a3, 0x8db7,
+  0x398c, 0x8dab, 0x3976, 0x8da0, 0x395f, 0x8d95, 0x3949, 0x8d8a,
+  0x3932, 0x8d7e, 0x391c, 0x8d73, 0x3906, 0x8d68, 0x38ef, 0x8d5d,
+  0x38d8, 0x8d51, 0x38c2, 0x8d46, 0x38ab, 0x8d3b, 0x3895, 0x8d30,
+  0x387e, 0x8d25, 0x3868, 0x8d1a, 0x3851, 0x8d0f, 0x383b, 0x8d04,
+  0x3824, 0x8cf9, 0x380d, 0x8cee, 0x37f7, 0x8ce3, 0x37e0, 0x8cd8,
+  0x37ca, 0x8ccd, 0x37b3, 0x8cc2, 0x379c, 0x8cb7, 0x3786, 0x8cac,
+  0x376f, 0x8ca1, 0x3758, 0x8c96, 0x3742, 0x8c8b, 0x372b, 0x8c81,
+  0x3714, 0x8c76, 0x36fe, 0x8c6b, 0x36e7, 0x8c60, 0x36d0, 0x8c55,
+  0x36ba, 0x8c4b, 0x36a3, 0x8c40, 0x368c, 0x8c35, 0x3675, 0x8c2a,
+  0x365f, 0x8c20, 0x3648, 0x8c15, 0x3631, 0x8c0a, 0x361a, 0x8c00,
+  0x3604, 0x8bf5, 0x35ed, 0x8beb, 0x35d6, 0x8be0, 0x35bf, 0x8bd5,
+  0x35a8, 0x8bcb, 0x3592, 0x8bc0, 0x357b, 0x8bb6, 0x3564, 0x8bab,
+  0x354d, 0x8ba1, 0x3536, 0x8b96, 0x351f, 0x8b8c, 0x3508, 0x8b82,
+  0x34f2, 0x8b77, 0x34db, 0x8b6d, 0x34c4, 0x8b62, 0x34ad, 0x8b58,
+  0x3496, 0x8b4e, 0x347f, 0x8b43, 0x3468, 0x8b39, 0x3451, 0x8b2f,
+  0x343a, 0x8b25, 0x3423, 0x8b1a, 0x340c, 0x8b10, 0x33f5, 0x8b06,
+  0x33de, 0x8afc, 0x33c7, 0x8af1, 0x33b0, 0x8ae7, 0x3399, 0x8add,
+  0x3382, 0x8ad3, 0x336b, 0x8ac9, 0x3354, 0x8abf, 0x333d, 0x8ab5,
+  0x3326, 0x8aab, 0x330f, 0x8aa1, 0x32f8, 0x8a97, 0x32e1, 0x8a8d,
+  0x32ca, 0x8a83, 0x32b3, 0x8a79, 0x329c, 0x8a6f, 0x3285, 0x8a65,
+  0x326e, 0x8a5b, 0x3257, 0x8a51, 0x3240, 0x8a47, 0x3228, 0x8a3d,
+  0x3211, 0x8a34, 0x31fa, 0x8a2a, 0x31e3, 0x8a20, 0x31cc, 0x8a16,
+  0x31b5, 0x8a0c, 0x319e, 0x8a03, 0x3186, 0x89f9, 0x316f, 0x89ef,
+  0x3158, 0x89e5, 0x3141, 0x89dc, 0x312a, 0x89d2, 0x3112, 0x89c8,
+  0x30fb, 0x89bf, 0x30e4, 0x89b5, 0x30cd, 0x89ac, 0x30b6, 0x89a2,
+  0x309e, 0x8998, 0x3087, 0x898f, 0x3070, 0x8985, 0x3059, 0x897c,
+  0x3041, 0x8972, 0x302a, 0x8969, 0x3013, 0x8960, 0x2ffb, 0x8956,
+  0x2fe4, 0x894d, 0x2fcd, 0x8943, 0x2fb5, 0x893a, 0x2f9e, 0x8931,
+  0x2f87, 0x8927, 0x2f6f, 0x891e, 0x2f58, 0x8915, 0x2f41, 0x890b,
+  0x2f29, 0x8902, 0x2f12, 0x88f9, 0x2efb, 0x88f0, 0x2ee3, 0x88e6,
+  0x2ecc, 0x88dd, 0x2eb5, 0x88d4, 0x2e9d, 0x88cb, 0x2e86, 0x88c2,
+  0x2e6e, 0x88b9, 0x2e57, 0x88af, 0x2e3f, 0x88a6, 0x2e28, 0x889d,
+  0x2e11, 0x8894, 0x2df9, 0x888b, 0x2de2, 0x8882, 0x2dca, 0x8879,
+  0x2db3, 0x8870, 0x2d9b, 0x8867, 0x2d84, 0x885e, 0x2d6c, 0x8855,
+  0x2d55, 0x884c, 0x2d3d, 0x8844, 0x2d26, 0x883b, 0x2d0e, 0x8832,
+  0x2cf7, 0x8829, 0x2cdf, 0x8820, 0x2cc8, 0x8817, 0x2cb0, 0x880f,
+  0x2c98, 0x8806, 0x2c81, 0x87fd, 0x2c69, 0x87f4, 0x2c52, 0x87ec,
+  0x2c3a, 0x87e3, 0x2c23, 0x87da, 0x2c0b, 0x87d2, 0x2bf3, 0x87c9,
+  0x2bdc, 0x87c0, 0x2bc4, 0x87b8, 0x2bad, 0x87af, 0x2b95, 0x87a7,
+  0x2b7d, 0x879e, 0x2b66, 0x8795, 0x2b4e, 0x878d, 0x2b36, 0x8784,
+  0x2b1f, 0x877c, 0x2b07, 0x8774, 0x2aef, 0x876b, 0x2ad8, 0x8763,
+  0x2ac0, 0x875a, 0x2aa8, 0x8752, 0x2a91, 0x874a, 0x2a79, 0x8741,
+  0x2a61, 0x8739, 0x2a49, 0x8731, 0x2a32, 0x8728, 0x2a1a, 0x8720,
+  0x2a02, 0x8718, 0x29eb, 0x870f, 0x29d3, 0x8707, 0x29bb, 0x86ff,
+  0x29a3, 0x86f7, 0x298b, 0x86ef, 0x2974, 0x86e7, 0x295c, 0x86de,
+  0x2944, 0x86d6, 0x292c, 0x86ce, 0x2915, 0x86c6, 0x28fd, 0x86be,
+  0x28e5, 0x86b6, 0x28cd, 0x86ae, 0x28b5, 0x86a6, 0x289d, 0x869e,
+  0x2886, 0x8696, 0x286e, 0x868e, 0x2856, 0x8686, 0x283e, 0x867e,
+  0x2826, 0x8676, 0x280e, 0x866e, 0x27f6, 0x8667, 0x27df, 0x865f,
+  0x27c7, 0x8657, 0x27af, 0x864f, 0x2797, 0x8647, 0x277f, 0x8640,
+  0x2767, 0x8638, 0x274f, 0x8630, 0x2737, 0x8628, 0x271f, 0x8621,
+  0x2707, 0x8619, 0x26ef, 0x8611, 0x26d8, 0x860a, 0x26c0, 0x8602,
+  0x26a8, 0x85fb, 0x2690, 0x85f3, 0x2678, 0x85eb, 0x2660, 0x85e4,
+  0x2648, 0x85dc, 0x2630, 0x85d5, 0x2618, 0x85cd, 0x2600, 0x85c6,
+  0x25e8, 0x85be, 0x25d0, 0x85b7, 0x25b8, 0x85b0, 0x25a0, 0x85a8,
+  0x2588, 0x85a1, 0x2570, 0x8599, 0x2558, 0x8592, 0x2540, 0x858b,
+  0x2528, 0x8583, 0x250f, 0x857c, 0x24f7, 0x8575, 0x24df, 0x856e,
+  0x24c7, 0x8566, 0x24af, 0x855f, 0x2497, 0x8558, 0x247f, 0x8551,
+  0x2467, 0x854a, 0x244f, 0x8543, 0x2437, 0x853b, 0x241f, 0x8534,
+  0x2407, 0x852d, 0x23ee, 0x8526, 0x23d6, 0x851f, 0x23be, 0x8518,
+  0x23a6, 0x8511, 0x238e, 0x850a, 0x2376, 0x8503, 0x235e, 0x84fc,
+  0x2345, 0x84f5, 0x232d, 0x84ee, 0x2315, 0x84e7, 0x22fd, 0x84e1,
+  0x22e5, 0x84da, 0x22cd, 0x84d3, 0x22b4, 0x84cc, 0x229c, 0x84c5,
+  0x2284, 0x84be, 0x226c, 0x84b8, 0x2254, 0x84b1, 0x223b, 0x84aa,
+  0x2223, 0x84a3, 0x220b, 0x849d, 0x21f3, 0x8496, 0x21da, 0x848f,
+  0x21c2, 0x8489, 0x21aa, 0x8482, 0x2192, 0x847c, 0x2179, 0x8475,
+  0x2161, 0x846e, 0x2149, 0x8468, 0x2131, 0x8461, 0x2118, 0x845b,
+  0x2100, 0x8454, 0x20e8, 0x844e, 0x20d0, 0x8447, 0x20b7, 0x8441,
+  0x209f, 0x843b, 0x2087, 0x8434, 0x206e, 0x842e, 0x2056, 0x8427,
+  0x203e, 0x8421, 0x2025, 0x841b, 0x200d, 0x8415, 0x1ff5, 0x840e,
+  0x1fdc, 0x8408, 0x1fc4, 0x8402, 0x1fac, 0x83fb, 0x1f93, 0x83f5,
+  0x1f7b, 0x83ef, 0x1f63, 0x83e9, 0x1f4a, 0x83e3, 0x1f32, 0x83dd,
+  0x1f19, 0x83d7, 0x1f01, 0x83d0, 0x1ee9, 0x83ca, 0x1ed0, 0x83c4,
+  0x1eb8, 0x83be, 0x1ea0, 0x83b8, 0x1e87, 0x83b2, 0x1e6f, 0x83ac,
+  0x1e56, 0x83a6, 0x1e3e, 0x83a0, 0x1e25, 0x839a, 0x1e0d, 0x8394,
+  0x1df5, 0x838f, 0x1ddc, 0x8389, 0x1dc4, 0x8383, 0x1dab, 0x837d,
+  0x1d93, 0x8377, 0x1d7a, 0x8371, 0x1d62, 0x836c, 0x1d49, 0x8366,
+  0x1d31, 0x8360, 0x1d18, 0x835a, 0x1d00, 0x8355, 0x1ce8, 0x834f,
+  0x1ccf, 0x8349, 0x1cb7, 0x8344, 0x1c9e, 0x833e, 0x1c86, 0x8338,
+  0x1c6d, 0x8333, 0x1c55, 0x832d, 0x1c3c, 0x8328, 0x1c24, 0x8322,
+  0x1c0b, 0x831d, 0x1bf2, 0x8317, 0x1bda, 0x8312, 0x1bc1, 0x830c,
+  0x1ba9, 0x8307, 0x1b90, 0x8301, 0x1b78, 0x82fc, 0x1b5f, 0x82f7,
+  0x1b47, 0x82f1, 0x1b2e, 0x82ec, 0x1b16, 0x82e7, 0x1afd, 0x82e1,
+  0x1ae4, 0x82dc, 0x1acc, 0x82d7, 0x1ab3, 0x82d1, 0x1a9b, 0x82cc,
+  0x1a82, 0x82c7, 0x1a6a, 0x82c2, 0x1a51, 0x82bd, 0x1a38, 0x82b7,
+  0x1a20, 0x82b2, 0x1a07, 0x82ad, 0x19ef, 0x82a8, 0x19d6, 0x82a3,
+  0x19bd, 0x829e, 0x19a5, 0x8299, 0x198c, 0x8294, 0x1973, 0x828f,
+  0x195b, 0x828a, 0x1942, 0x8285, 0x192a, 0x8280, 0x1911, 0x827b,
+  0x18f8, 0x8276, 0x18e0, 0x8271, 0x18c7, 0x826c, 0x18ae, 0x8268,
+  0x1896, 0x8263, 0x187d, 0x825e, 0x1864, 0x8259, 0x184c, 0x8254,
+  0x1833, 0x8250, 0x181a, 0x824b, 0x1802, 0x8246, 0x17e9, 0x8241,
+  0x17d0, 0x823d, 0x17b7, 0x8238, 0x179f, 0x8233, 0x1786, 0x822f,
+  0x176d, 0x822a, 0x1755, 0x8226, 0x173c, 0x8221, 0x1723, 0x821c,
+  0x170a, 0x8218, 0x16f2, 0x8213, 0x16d9, 0x820f, 0x16c0, 0x820a,
+  0x16a8, 0x8206, 0x168f, 0x8201, 0x1676, 0x81fd, 0x165d, 0x81f9,
+  0x1645, 0x81f4, 0x162c, 0x81f0, 0x1613, 0x81ec, 0x15fa, 0x81e7,
+  0x15e2, 0x81e3, 0x15c9, 0x81df, 0x15b0, 0x81da, 0x1597, 0x81d6,
+  0x157f, 0x81d2, 0x1566, 0x81ce, 0x154d, 0x81c9, 0x1534, 0x81c5,
+  0x151b, 0x81c1, 0x1503, 0x81bd, 0x14ea, 0x81b9, 0x14d1, 0x81b5,
+  0x14b8, 0x81b1, 0x149f, 0x81ad, 0x1487, 0x81a9, 0x146e, 0x81a5,
+  0x1455, 0x81a1, 0x143c, 0x819d, 0x1423, 0x8199, 0x140b, 0x8195,
+  0x13f2, 0x8191, 0x13d9, 0x818d, 0x13c0, 0x8189, 0x13a7, 0x8185,
+  0x138e, 0x8181, 0x1376, 0x817d, 0x135d, 0x817a, 0x1344, 0x8176,
+  0x132b, 0x8172, 0x1312, 0x816e, 0x12f9, 0x816b, 0x12e0, 0x8167,
+  0x12c8, 0x8163, 0x12af, 0x815f, 0x1296, 0x815c, 0x127d, 0x8158,
+  0x1264, 0x8155, 0x124b, 0x8151, 0x1232, 0x814d, 0x1219, 0x814a,
+  0x1201, 0x8146, 0x11e8, 0x8143, 0x11cf, 0x813f, 0x11b6, 0x813c,
+  0x119d, 0x8138, 0x1184, 0x8135, 0x116b, 0x8131, 0x1152, 0x812e,
+  0x1139, 0x812b, 0x1121, 0x8127, 0x1108, 0x8124, 0x10ef, 0x8121,
+  0x10d6, 0x811d, 0x10bd, 0x811a, 0x10a4, 0x8117, 0x108b, 0x8113,
+  0x1072, 0x8110, 0x1059, 0x810d, 0x1040, 0x810a, 0x1027, 0x8107,
+  0x100e, 0x8103, 0xff5, 0x8100, 0xfdd, 0x80fd, 0xfc4, 0x80fa,
+  0xfab, 0x80f7, 0xf92, 0x80f4, 0xf79, 0x80f1, 0xf60, 0x80ee,
+  0xf47, 0x80eb, 0xf2e, 0x80e8, 0xf15, 0x80e5, 0xefc, 0x80e2,
+  0xee3, 0x80df, 0xeca, 0x80dc, 0xeb1, 0x80d9, 0xe98, 0x80d6,
+  0xe7f, 0x80d3, 0xe66, 0x80d1, 0xe4d, 0x80ce, 0xe34, 0x80cb,
+  0xe1b, 0x80c8, 0xe02, 0x80c5, 0xde9, 0x80c3, 0xdd0, 0x80c0,
+  0xdb7, 0x80bd, 0xd9e, 0x80bb, 0xd85, 0x80b8, 0xd6c, 0x80b5,
+  0xd53, 0x80b3, 0xd3a, 0x80b0, 0xd21, 0x80ad, 0xd08, 0x80ab,
+  0xcef, 0x80a8, 0xcd6, 0x80a6, 0xcbd, 0x80a3, 0xca4, 0x80a1,
+  0xc8b, 0x809e, 0xc72, 0x809c, 0xc59, 0x8099, 0xc40, 0x8097,
+  0xc27, 0x8095, 0xc0e, 0x8092, 0xbf5, 0x8090, 0xbdc, 0x808e,
+  0xbc3, 0x808b, 0xbaa, 0x8089, 0xb91, 0x8087, 0xb78, 0x8084,
+  0xb5f, 0x8082, 0xb46, 0x8080, 0xb2d, 0x807e, 0xb14, 0x807b,
+  0xafb, 0x8079, 0xae2, 0x8077, 0xac9, 0x8075, 0xab0, 0x8073,
+  0xa97, 0x8071, 0xa7e, 0x806f, 0xa65, 0x806d, 0xa4c, 0x806b,
+  0xa33, 0x8069, 0xa19, 0x8067, 0xa00, 0x8065, 0x9e7, 0x8063,
+  0x9ce, 0x8061, 0x9b5, 0x805f, 0x99c, 0x805d, 0x983, 0x805b,
+  0x96a, 0x8059, 0x951, 0x8057, 0x938, 0x8056, 0x91f, 0x8054,
+  0x906, 0x8052, 0x8ed, 0x8050, 0x8d4, 0x804f, 0x8bb, 0x804d,
+  0x8a2, 0x804b, 0x888, 0x8049, 0x86f, 0x8048, 0x856, 0x8046,
+  0x83d, 0x8044, 0x824, 0x8043, 0x80b, 0x8041, 0x7f2, 0x8040,
+  0x7d9, 0x803e, 0x7c0, 0x803d, 0x7a7, 0x803b, 0x78e, 0x803a,
+  0x775, 0x8038, 0x75b, 0x8037, 0x742, 0x8035, 0x729, 0x8034,
+  0x710, 0x8032, 0x6f7, 0x8031, 0x6de, 0x8030, 0x6c5, 0x802e,
+  0x6ac, 0x802d, 0x693, 0x802c, 0x67a, 0x802a, 0x660, 0x8029,
+  0x647, 0x8028, 0x62e, 0x8027, 0x615, 0x8026, 0x5fc, 0x8024,
+  0x5e3, 0x8023, 0x5ca, 0x8022, 0x5b1, 0x8021, 0x598, 0x8020,
+  0x57f, 0x801f, 0x565, 0x801e, 0x54c, 0x801d, 0x533, 0x801c,
+  0x51a, 0x801b, 0x501, 0x801a, 0x4e8, 0x8019, 0x4cf, 0x8018,
+  0x4b6, 0x8017, 0x49c, 0x8016, 0x483, 0x8015, 0x46a, 0x8014,
+  0x451, 0x8013, 0x438, 0x8012, 0x41f, 0x8012, 0x406, 0x8011,
+  0x3ed, 0x8010, 0x3d4, 0x800f, 0x3ba, 0x800e, 0x3a1, 0x800e,
+  0x388, 0x800d, 0x36f, 0x800c, 0x356, 0x800c, 0x33d, 0x800b,
+  0x324, 0x800a, 0x30b, 0x800a, 0x2f1, 0x8009, 0x2d8, 0x8009,
+  0x2bf, 0x8008, 0x2a6, 0x8008, 0x28d, 0x8007, 0x274, 0x8007,
+  0x25b, 0x8006, 0x242, 0x8006, 0x228, 0x8005, 0x20f, 0x8005,
+  0x1f6, 0x8004, 0x1dd, 0x8004, 0x1c4, 0x8004, 0x1ab, 0x8003,
+  0x192, 0x8003, 0x178, 0x8003, 0x15f, 0x8002, 0x146, 0x8002,
+  0x12d, 0x8002, 0x114, 0x8002, 0xfb, 0x8001, 0xe2, 0x8001,
+  0xc9, 0x8001, 0xaf, 0x8001, 0x96, 0x8001, 0x7d, 0x8001,
+  0x64, 0x8001, 0x4b, 0x8001, 0x32, 0x8001, 0x19, 0x8001,
+};
+
+static const q15_t ALIGN4 WeightsQ15_8192[16384] = {
+  0x7fff, 0x0, 0x7fff, 0xfffa, 0x7fff, 0xfff4, 0x7fff, 0xffee,
+  0x7fff, 0xffe7, 0x7fff, 0xffe1, 0x7fff, 0xffdb, 0x7fff, 0xffd5,
+  0x7fff, 0xffce, 0x7fff, 0xffc8, 0x7fff, 0xffc2, 0x7fff, 0xffbb,
+  0x7fff, 0xffb5, 0x7fff, 0xffaf, 0x7fff, 0xffa9, 0x7fff, 0xffa2,
+  0x7fff, 0xff9c, 0x7fff, 0xff96, 0x7fff, 0xff8f, 0x7fff, 0xff89,
+  0x7fff, 0xff83, 0x7fff, 0xff7d, 0x7fff, 0xff76, 0x7fff, 0xff70,
+  0x7fff, 0xff6a, 0x7fff, 0xff63, 0x7fff, 0xff5d, 0x7fff, 0xff57,
+  0x7fff, 0xff51, 0x7fff, 0xff4a, 0x7fff, 0xff44, 0x7fff, 0xff3e,
+  0x7fff, 0xff37, 0x7fff, 0xff31, 0x7fff, 0xff2b, 0x7fff, 0xff25,
+  0x7fff, 0xff1e, 0x7fff, 0xff18, 0x7fff, 0xff12, 0x7fff, 0xff0b,
+  0x7fff, 0xff05, 0x7ffe, 0xfeff, 0x7ffe, 0xfef9, 0x7ffe, 0xfef2,
+  0x7ffe, 0xfeec, 0x7ffe, 0xfee6, 0x7ffe, 0xfedf, 0x7ffe, 0xfed9,
+  0x7ffe, 0xfed3, 0x7ffe, 0xfecd, 0x7ffe, 0xfec6, 0x7ffe, 0xfec0,
+  0x7ffe, 0xfeba, 0x7ffe, 0xfeb3, 0x7ffe, 0xfead, 0x7ffe, 0xfea7,
+  0x7ffe, 0xfea1, 0x7ffe, 0xfe9a, 0x7ffd, 0xfe94, 0x7ffd, 0xfe8e,
+  0x7ffd, 0xfe88, 0x7ffd, 0xfe81, 0x7ffd, 0xfe7b, 0x7ffd, 0xfe75,
+  0x7ffd, 0xfe6e, 0x7ffd, 0xfe68, 0x7ffd, 0xfe62, 0x7ffd, 0xfe5c,
+  0x7ffd, 0xfe55, 0x7ffd, 0xfe4f, 0x7ffd, 0xfe49, 0x7ffc, 0xfe42,
+  0x7ffc, 0xfe3c, 0x7ffc, 0xfe36, 0x7ffc, 0xfe30, 0x7ffc, 0xfe29,
+  0x7ffc, 0xfe23, 0x7ffc, 0xfe1d, 0x7ffc, 0xfe16, 0x7ffc, 0xfe10,
+  0x7ffc, 0xfe0a, 0x7ffc, 0xfe04, 0x7ffb, 0xfdfd, 0x7ffb, 0xfdf7,
+  0x7ffb, 0xfdf1, 0x7ffb, 0xfdea, 0x7ffb, 0xfde4, 0x7ffb, 0xfdde,
+  0x7ffb, 0xfdd8, 0x7ffb, 0xfdd1, 0x7ffb, 0xfdcb, 0x7ffb, 0xfdc5,
+  0x7ffa, 0xfdbe, 0x7ffa, 0xfdb8, 0x7ffa, 0xfdb2, 0x7ffa, 0xfdac,
+  0x7ffa, 0xfda5, 0x7ffa, 0xfd9f, 0x7ffa, 0xfd99, 0x7ffa, 0xfd93,
+  0x7ff9, 0xfd8c, 0x7ff9, 0xfd86, 0x7ff9, 0xfd80, 0x7ff9, 0xfd79,
+  0x7ff9, 0xfd73, 0x7ff9, 0xfd6d, 0x7ff9, 0xfd67, 0x7ff9, 0xfd60,
+  0x7ff8, 0xfd5a, 0x7ff8, 0xfd54, 0x7ff8, 0xfd4d, 0x7ff8, 0xfd47,
+  0x7ff8, 0xfd41, 0x7ff8, 0xfd3b, 0x7ff8, 0xfd34, 0x7ff8, 0xfd2e,
+  0x7ff7, 0xfd28, 0x7ff7, 0xfd21, 0x7ff7, 0xfd1b, 0x7ff7, 0xfd15,
+  0x7ff7, 0xfd0f, 0x7ff7, 0xfd08, 0x7ff7, 0xfd02, 0x7ff6, 0xfcfc,
+  0x7ff6, 0xfcf5, 0x7ff6, 0xfcef, 0x7ff6, 0xfce9, 0x7ff6, 0xfce3,
+  0x7ff6, 0xfcdc, 0x7ff5, 0xfcd6, 0x7ff5, 0xfcd0, 0x7ff5, 0xfcc9,
+  0x7ff5, 0xfcc3, 0x7ff5, 0xfcbd, 0x7ff5, 0xfcb7, 0x7ff5, 0xfcb0,
+  0x7ff4, 0xfcaa, 0x7ff4, 0xfca4, 0x7ff4, 0xfc9e, 0x7ff4, 0xfc97,
+  0x7ff4, 0xfc91, 0x7ff4, 0xfc8b, 0x7ff3, 0xfc84, 0x7ff3, 0xfc7e,
+  0x7ff3, 0xfc78, 0x7ff3, 0xfc72, 0x7ff3, 0xfc6b, 0x7ff2, 0xfc65,
+  0x7ff2, 0xfc5f, 0x7ff2, 0xfc58, 0x7ff2, 0xfc52, 0x7ff2, 0xfc4c,
+  0x7ff2, 0xfc46, 0x7ff1, 0xfc3f, 0x7ff1, 0xfc39, 0x7ff1, 0xfc33,
+  0x7ff1, 0xfc2c, 0x7ff1, 0xfc26, 0x7ff0, 0xfc20, 0x7ff0, 0xfc1a,
+  0x7ff0, 0xfc13, 0x7ff0, 0xfc0d, 0x7ff0, 0xfc07, 0x7fef, 0xfc01,
+  0x7fef, 0xfbfa, 0x7fef, 0xfbf4, 0x7fef, 0xfbee, 0x7fef, 0xfbe7,
+  0x7fee, 0xfbe1, 0x7fee, 0xfbdb, 0x7fee, 0xfbd5, 0x7fee, 0xfbce,
+  0x7fee, 0xfbc8, 0x7fed, 0xfbc2, 0x7fed, 0xfbbb, 0x7fed, 0xfbb5,
+  0x7fed, 0xfbaf, 0x7fed, 0xfba9, 0x7fec, 0xfba2, 0x7fec, 0xfb9c,
+  0x7fec, 0xfb96, 0x7fec, 0xfb8f, 0x7fec, 0xfb89, 0x7feb, 0xfb83,
+  0x7feb, 0xfb7d, 0x7feb, 0xfb76, 0x7feb, 0xfb70, 0x7fea, 0xfb6a,
+  0x7fea, 0xfb64, 0x7fea, 0xfb5d, 0x7fea, 0xfb57, 0x7fea, 0xfb51,
+  0x7fe9, 0xfb4a, 0x7fe9, 0xfb44, 0x7fe9, 0xfb3e, 0x7fe9, 0xfb38,
+  0x7fe8, 0xfb31, 0x7fe8, 0xfb2b, 0x7fe8, 0xfb25, 0x7fe8, 0xfb1e,
+  0x7fe7, 0xfb18, 0x7fe7, 0xfb12, 0x7fe7, 0xfb0c, 0x7fe7, 0xfb05,
+  0x7fe6, 0xfaff, 0x7fe6, 0xfaf9, 0x7fe6, 0xfaf3, 0x7fe6, 0xfaec,
+  0x7fe5, 0xfae6, 0x7fe5, 0xfae0, 0x7fe5, 0xfad9, 0x7fe5, 0xfad3,
+  0x7fe4, 0xfacd, 0x7fe4, 0xfac7, 0x7fe4, 0xfac0, 0x7fe4, 0xfaba,
+  0x7fe3, 0xfab4, 0x7fe3, 0xfaad, 0x7fe3, 0xfaa7, 0x7fe3, 0xfaa1,
+  0x7fe2, 0xfa9b, 0x7fe2, 0xfa94, 0x7fe2, 0xfa8e, 0x7fe2, 0xfa88,
+  0x7fe1, 0xfa81, 0x7fe1, 0xfa7b, 0x7fe1, 0xfa75, 0x7fe0, 0xfa6f,
+  0x7fe0, 0xfa68, 0x7fe0, 0xfa62, 0x7fe0, 0xfa5c, 0x7fdf, 0xfa56,
+  0x7fdf, 0xfa4f, 0x7fdf, 0xfa49, 0x7fdf, 0xfa43, 0x7fde, 0xfa3c,
+  0x7fde, 0xfa36, 0x7fde, 0xfa30, 0x7fdd, 0xfa2a, 0x7fdd, 0xfa23,
+  0x7fdd, 0xfa1d, 0x7fdd, 0xfa17, 0x7fdc, 0xfa11, 0x7fdc, 0xfa0a,
+  0x7fdc, 0xfa04, 0x7fdb, 0xf9fe, 0x7fdb, 0xf9f7, 0x7fdb, 0xf9f1,
+  0x7fda, 0xf9eb, 0x7fda, 0xf9e5, 0x7fda, 0xf9de, 0x7fda, 0xf9d8,
+  0x7fd9, 0xf9d2, 0x7fd9, 0xf9cb, 0x7fd9, 0xf9c5, 0x7fd8, 0xf9bf,
+  0x7fd8, 0xf9b9, 0x7fd8, 0xf9b2, 0x7fd7, 0xf9ac, 0x7fd7, 0xf9a6,
+  0x7fd7, 0xf9a0, 0x7fd6, 0xf999, 0x7fd6, 0xf993, 0x7fd6, 0xf98d,
+  0x7fd6, 0xf986, 0x7fd5, 0xf980, 0x7fd5, 0xf97a, 0x7fd5, 0xf974,
+  0x7fd4, 0xf96d, 0x7fd4, 0xf967, 0x7fd4, 0xf961, 0x7fd3, 0xf95b,
+  0x7fd3, 0xf954, 0x7fd3, 0xf94e, 0x7fd2, 0xf948, 0x7fd2, 0xf941,
+  0x7fd2, 0xf93b, 0x7fd1, 0xf935, 0x7fd1, 0xf92f, 0x7fd1, 0xf928,
+  0x7fd0, 0xf922, 0x7fd0, 0xf91c, 0x7fd0, 0xf916, 0x7fcf, 0xf90f,
+  0x7fcf, 0xf909, 0x7fcf, 0xf903, 0x7fce, 0xf8fc, 0x7fce, 0xf8f6,
+  0x7fce, 0xf8f0, 0x7fcd, 0xf8ea, 0x7fcd, 0xf8e3, 0x7fcd, 0xf8dd,
+  0x7fcc, 0xf8d7, 0x7fcc, 0xf8d0, 0x7fcb, 0xf8ca, 0x7fcb, 0xf8c4,
+  0x7fcb, 0xf8be, 0x7fca, 0xf8b7, 0x7fca, 0xf8b1, 0x7fca, 0xf8ab,
+  0x7fc9, 0xf8a5, 0x7fc9, 0xf89e, 0x7fc9, 0xf898, 0x7fc8, 0xf892,
+  0x7fc8, 0xf88b, 0x7fc7, 0xf885, 0x7fc7, 0xf87f, 0x7fc7, 0xf879,
+  0x7fc6, 0xf872, 0x7fc6, 0xf86c, 0x7fc6, 0xf866, 0x7fc5, 0xf860,
+  0x7fc5, 0xf859, 0x7fc5, 0xf853, 0x7fc4, 0xf84d, 0x7fc4, 0xf846,
+  0x7fc3, 0xf840, 0x7fc3, 0xf83a, 0x7fc3, 0xf834, 0x7fc2, 0xf82d,
+  0x7fc2, 0xf827, 0x7fc1, 0xf821, 0x7fc1, 0xf81b, 0x7fc1, 0xf814,
+  0x7fc0, 0xf80e, 0x7fc0, 0xf808, 0x7fc0, 0xf802, 0x7fbf, 0xf7fb,
+  0x7fbf, 0xf7f5, 0x7fbe, 0xf7ef, 0x7fbe, 0xf7e8, 0x7fbe, 0xf7e2,
+  0x7fbd, 0xf7dc, 0x7fbd, 0xf7d6, 0x7fbc, 0xf7cf, 0x7fbc, 0xf7c9,
+  0x7fbc, 0xf7c3, 0x7fbb, 0xf7bd, 0x7fbb, 0xf7b6, 0x7fba, 0xf7b0,
+  0x7fba, 0xf7aa, 0x7fb9, 0xf7a3, 0x7fb9, 0xf79d, 0x7fb9, 0xf797,
+  0x7fb8, 0xf791, 0x7fb8, 0xf78a, 0x7fb7, 0xf784, 0x7fb7, 0xf77e,
+  0x7fb7, 0xf778, 0x7fb6, 0xf771, 0x7fb6, 0xf76b, 0x7fb5, 0xf765,
+  0x7fb5, 0xf75e, 0x7fb4, 0xf758, 0x7fb4, 0xf752, 0x7fb4, 0xf74c,
+  0x7fb3, 0xf745, 0x7fb3, 0xf73f, 0x7fb2, 0xf739, 0x7fb2, 0xf733,
+  0x7fb1, 0xf72c, 0x7fb1, 0xf726, 0x7fb1, 0xf720, 0x7fb0, 0xf71a,
+  0x7fb0, 0xf713, 0x7faf, 0xf70d, 0x7faf, 0xf707, 0x7fae, 0xf700,
+  0x7fae, 0xf6fa, 0x7fae, 0xf6f4, 0x7fad, 0xf6ee, 0x7fad, 0xf6e7,
+  0x7fac, 0xf6e1, 0x7fac, 0xf6db, 0x7fab, 0xf6d5, 0x7fab, 0xf6ce,
+  0x7faa, 0xf6c8, 0x7faa, 0xf6c2, 0x7fa9, 0xf6bc, 0x7fa9, 0xf6b5,
+  0x7fa9, 0xf6af, 0x7fa8, 0xf6a9, 0x7fa8, 0xf6a2, 0x7fa7, 0xf69c,
+  0x7fa7, 0xf696, 0x7fa6, 0xf690, 0x7fa6, 0xf689, 0x7fa5, 0xf683,
+  0x7fa5, 0xf67d, 0x7fa4, 0xf677, 0x7fa4, 0xf670, 0x7fa3, 0xf66a,
+  0x7fa3, 0xf664, 0x7fa3, 0xf65e, 0x7fa2, 0xf657, 0x7fa2, 0xf651,
+  0x7fa1, 0xf64b, 0x7fa1, 0xf644, 0x7fa0, 0xf63e, 0x7fa0, 0xf638,
+  0x7f9f, 0xf632, 0x7f9f, 0xf62b, 0x7f9e, 0xf625, 0x7f9e, 0xf61f,
+  0x7f9d, 0xf619, 0x7f9d, 0xf612, 0x7f9c, 0xf60c, 0x7f9c, 0xf606,
+  0x7f9b, 0xf600, 0x7f9b, 0xf5f9, 0x7f9a, 0xf5f3, 0x7f9a, 0xf5ed,
+  0x7f99, 0xf5e7, 0x7f99, 0xf5e0, 0x7f98, 0xf5da, 0x7f98, 0xf5d4,
+  0x7f97, 0xf5cd, 0x7f97, 0xf5c7, 0x7f96, 0xf5c1, 0x7f96, 0xf5bb,
+  0x7f95, 0xf5b4, 0x7f95, 0xf5ae, 0x7f94, 0xf5a8, 0x7f94, 0xf5a2,
+  0x7f93, 0xf59b, 0x7f93, 0xf595, 0x7f92, 0xf58f, 0x7f92, 0xf589,
+  0x7f91, 0xf582, 0x7f91, 0xf57c, 0x7f90, 0xf576, 0x7f90, 0xf570,
+  0x7f8f, 0xf569, 0x7f8f, 0xf563, 0x7f8e, 0xf55d, 0x7f8e, 0xf556,
+  0x7f8d, 0xf550, 0x7f8d, 0xf54a, 0x7f8c, 0xf544, 0x7f8b, 0xf53d,
+  0x7f8b, 0xf537, 0x7f8a, 0xf531, 0x7f8a, 0xf52b, 0x7f89, 0xf524,
+  0x7f89, 0xf51e, 0x7f88, 0xf518, 0x7f88, 0xf512, 0x7f87, 0xf50b,
+  0x7f87, 0xf505, 0x7f86, 0xf4ff, 0x7f86, 0xf4f9, 0x7f85, 0xf4f2,
+  0x7f85, 0xf4ec, 0x7f84, 0xf4e6, 0x7f83, 0xf4e0, 0x7f83, 0xf4d9,
+  0x7f82, 0xf4d3, 0x7f82, 0xf4cd, 0x7f81, 0xf4c6, 0x7f81, 0xf4c0,
+  0x7f80, 0xf4ba, 0x7f80, 0xf4b4, 0x7f7f, 0xf4ad, 0x7f7e, 0xf4a7,
+  0x7f7e, 0xf4a1, 0x7f7d, 0xf49b, 0x7f7d, 0xf494, 0x7f7c, 0xf48e,
+  0x7f7c, 0xf488, 0x7f7b, 0xf482, 0x7f7b, 0xf47b, 0x7f7a, 0xf475,
+  0x7f79, 0xf46f, 0x7f79, 0xf469, 0x7f78, 0xf462, 0x7f78, 0xf45c,
+  0x7f77, 0xf456, 0x7f77, 0xf450, 0x7f76, 0xf449, 0x7f75, 0xf443,
+  0x7f75, 0xf43d, 0x7f74, 0xf437, 0x7f74, 0xf430, 0x7f73, 0xf42a,
+  0x7f72, 0xf424, 0x7f72, 0xf41e, 0x7f71, 0xf417, 0x7f71, 0xf411,
+  0x7f70, 0xf40b, 0x7f70, 0xf405, 0x7f6f, 0xf3fe, 0x7f6e, 0xf3f8,
+  0x7f6e, 0xf3f2, 0x7f6d, 0xf3ec, 0x7f6d, 0xf3e5, 0x7f6c, 0xf3df,
+  0x7f6b, 0xf3d9, 0x7f6b, 0xf3d2, 0x7f6a, 0xf3cc, 0x7f6a, 0xf3c6,
+  0x7f69, 0xf3c0, 0x7f68, 0xf3b9, 0x7f68, 0xf3b3, 0x7f67, 0xf3ad,
+  0x7f67, 0xf3a7, 0x7f66, 0xf3a0, 0x7f65, 0xf39a, 0x7f65, 0xf394,
+  0x7f64, 0xf38e, 0x7f64, 0xf387, 0x7f63, 0xf381, 0x7f62, 0xf37b,
+  0x7f62, 0xf375, 0x7f61, 0xf36e, 0x7f60, 0xf368, 0x7f60, 0xf362,
+  0x7f5f, 0xf35c, 0x7f5f, 0xf355, 0x7f5e, 0xf34f, 0x7f5d, 0xf349,
+  0x7f5d, 0xf343, 0x7f5c, 0xf33c, 0x7f5b, 0xf336, 0x7f5b, 0xf330,
+  0x7f5a, 0xf32a, 0x7f5a, 0xf323, 0x7f59, 0xf31d, 0x7f58, 0xf317,
+  0x7f58, 0xf311, 0x7f57, 0xf30a, 0x7f56, 0xf304, 0x7f56, 0xf2fe,
+  0x7f55, 0xf2f8, 0x7f55, 0xf2f1, 0x7f54, 0xf2eb, 0x7f53, 0xf2e5,
+  0x7f53, 0xf2df, 0x7f52, 0xf2d8, 0x7f51, 0xf2d2, 0x7f51, 0xf2cc,
+  0x7f50, 0xf2c6, 0x7f4f, 0xf2bf, 0x7f4f, 0xf2b9, 0x7f4e, 0xf2b3,
+  0x7f4d, 0xf2ad, 0x7f4d, 0xf2a6, 0x7f4c, 0xf2a0, 0x7f4b, 0xf29a,
+  0x7f4b, 0xf294, 0x7f4a, 0xf28d, 0x7f49, 0xf287, 0x7f49, 0xf281,
+  0x7f48, 0xf27b, 0x7f47, 0xf274, 0x7f47, 0xf26e, 0x7f46, 0xf268,
+  0x7f45, 0xf262, 0x7f45, 0xf25b, 0x7f44, 0xf255, 0x7f43, 0xf24f,
+  0x7f43, 0xf249, 0x7f42, 0xf242, 0x7f41, 0xf23c, 0x7f41, 0xf236,
+  0x7f40, 0xf230, 0x7f3f, 0xf229, 0x7f3f, 0xf223, 0x7f3e, 0xf21d,
+  0x7f3d, 0xf217, 0x7f3d, 0xf210, 0x7f3c, 0xf20a, 0x7f3b, 0xf204,
+  0x7f3b, 0xf1fe, 0x7f3a, 0xf1f7, 0x7f39, 0xf1f1, 0x7f39, 0xf1eb,
+  0x7f38, 0xf1e5, 0x7f37, 0xf1de, 0x7f36, 0xf1d8, 0x7f36, 0xf1d2,
+  0x7f35, 0xf1cc, 0x7f34, 0xf1c6, 0x7f34, 0xf1bf, 0x7f33, 0xf1b9,
+  0x7f32, 0xf1b3, 0x7f32, 0xf1ad, 0x7f31, 0xf1a6, 0x7f30, 0xf1a0,
+  0x7f2f, 0xf19a, 0x7f2f, 0xf194, 0x7f2e, 0xf18d, 0x7f2d, 0xf187,
+  0x7f2d, 0xf181, 0x7f2c, 0xf17b, 0x7f2b, 0xf174, 0x7f2a, 0xf16e,
+  0x7f2a, 0xf168, 0x7f29, 0xf162, 0x7f28, 0xf15b, 0x7f28, 0xf155,
+  0x7f27, 0xf14f, 0x7f26, 0xf149, 0x7f25, 0xf142, 0x7f25, 0xf13c,
+  0x7f24, 0xf136, 0x7f23, 0xf130, 0x7f23, 0xf129, 0x7f22, 0xf123,
+  0x7f21, 0xf11d, 0x7f20, 0xf117, 0x7f20, 0xf110, 0x7f1f, 0xf10a,
+  0x7f1e, 0xf104, 0x7f1d, 0xf0fe, 0x7f1d, 0xf0f8, 0x7f1c, 0xf0f1,
+  0x7f1b, 0xf0eb, 0x7f1a, 0xf0e5, 0x7f1a, 0xf0df, 0x7f19, 0xf0d8,
+  0x7f18, 0xf0d2, 0x7f17, 0xf0cc, 0x7f17, 0xf0c6, 0x7f16, 0xf0bf,
+  0x7f15, 0xf0b9, 0x7f14, 0xf0b3, 0x7f14, 0xf0ad, 0x7f13, 0xf0a6,
+  0x7f12, 0xf0a0, 0x7f11, 0xf09a, 0x7f11, 0xf094, 0x7f10, 0xf08d,
+  0x7f0f, 0xf087, 0x7f0e, 0xf081, 0x7f0e, 0xf07b, 0x7f0d, 0xf075,
+  0x7f0c, 0xf06e, 0x7f0b, 0xf068, 0x7f0b, 0xf062, 0x7f0a, 0xf05c,
+  0x7f09, 0xf055, 0x7f08, 0xf04f, 0x7f08, 0xf049, 0x7f07, 0xf043,
+  0x7f06, 0xf03c, 0x7f05, 0xf036, 0x7f04, 0xf030, 0x7f04, 0xf02a,
+  0x7f03, 0xf023, 0x7f02, 0xf01d, 0x7f01, 0xf017, 0x7f01, 0xf011,
+  0x7f00, 0xf00b, 0x7eff, 0xf004, 0x7efe, 0xeffe, 0x7efd, 0xeff8,
+  0x7efd, 0xeff2, 0x7efc, 0xefeb, 0x7efb, 0xefe5, 0x7efa, 0xefdf,
+  0x7ef9, 0xefd9, 0x7ef9, 0xefd2, 0x7ef8, 0xefcc, 0x7ef7, 0xefc6,
+  0x7ef6, 0xefc0, 0x7ef5, 0xefb9, 0x7ef5, 0xefb3, 0x7ef4, 0xefad,
+  0x7ef3, 0xefa7, 0x7ef2, 0xefa1, 0x7ef1, 0xef9a, 0x7ef1, 0xef94,
+  0x7ef0, 0xef8e, 0x7eef, 0xef88, 0x7eee, 0xef81, 0x7eed, 0xef7b,
+  0x7eed, 0xef75, 0x7eec, 0xef6f, 0x7eeb, 0xef68, 0x7eea, 0xef62,
+  0x7ee9, 0xef5c, 0x7ee9, 0xef56, 0x7ee8, 0xef50, 0x7ee7, 0xef49,
+  0x7ee6, 0xef43, 0x7ee5, 0xef3d, 0x7ee4, 0xef37, 0x7ee4, 0xef30,
+  0x7ee3, 0xef2a, 0x7ee2, 0xef24, 0x7ee1, 0xef1e, 0x7ee0, 0xef18,
+  0x7edf, 0xef11, 0x7edf, 0xef0b, 0x7ede, 0xef05, 0x7edd, 0xeeff,
+  0x7edc, 0xeef8, 0x7edb, 0xeef2, 0x7eda, 0xeeec, 0x7eda, 0xeee6,
+  0x7ed9, 0xeedf, 0x7ed8, 0xeed9, 0x7ed7, 0xeed3, 0x7ed6, 0xeecd,
+  0x7ed5, 0xeec7, 0x7ed5, 0xeec0, 0x7ed4, 0xeeba, 0x7ed3, 0xeeb4,
+  0x7ed2, 0xeeae, 0x7ed1, 0xeea7, 0x7ed0, 0xeea1, 0x7ecf, 0xee9b,
+  0x7ecf, 0xee95, 0x7ece, 0xee8f, 0x7ecd, 0xee88, 0x7ecc, 0xee82,
+  0x7ecb, 0xee7c, 0x7eca, 0xee76, 0x7ec9, 0xee6f, 0x7ec9, 0xee69,
+  0x7ec8, 0xee63, 0x7ec7, 0xee5d, 0x7ec6, 0xee57, 0x7ec5, 0xee50,
+  0x7ec4, 0xee4a, 0x7ec3, 0xee44, 0x7ec3, 0xee3e, 0x7ec2, 0xee37,
+  0x7ec1, 0xee31, 0x7ec0, 0xee2b, 0x7ebf, 0xee25, 0x7ebe, 0xee1f,
+  0x7ebd, 0xee18, 0x7ebc, 0xee12, 0x7ebb, 0xee0c, 0x7ebb, 0xee06,
+  0x7eba, 0xedff, 0x7eb9, 0xedf9, 0x7eb8, 0xedf3, 0x7eb7, 0xeded,
+  0x7eb6, 0xede7, 0x7eb5, 0xede0, 0x7eb4, 0xedda, 0x7eb4, 0xedd4,
+  0x7eb3, 0xedce, 0x7eb2, 0xedc7, 0x7eb1, 0xedc1, 0x7eb0, 0xedbb,
+  0x7eaf, 0xedb5, 0x7eae, 0xedaf, 0x7ead, 0xeda8, 0x7eac, 0xeda2,
+  0x7eab, 0xed9c, 0x7eab, 0xed96, 0x7eaa, 0xed8f, 0x7ea9, 0xed89,
+  0x7ea8, 0xed83, 0x7ea7, 0xed7d, 0x7ea6, 0xed77, 0x7ea5, 0xed70,
+  0x7ea4, 0xed6a, 0x7ea3, 0xed64, 0x7ea2, 0xed5e, 0x7ea1, 0xed58,
+  0x7ea1, 0xed51, 0x7ea0, 0xed4b, 0x7e9f, 0xed45, 0x7e9e, 0xed3f,
+  0x7e9d, 0xed38, 0x7e9c, 0xed32, 0x7e9b, 0xed2c, 0x7e9a, 0xed26,
+  0x7e99, 0xed20, 0x7e98, 0xed19, 0x7e97, 0xed13, 0x7e96, 0xed0d,
+  0x7e95, 0xed07, 0x7e94, 0xed01, 0x7e94, 0xecfa, 0x7e93, 0xecf4,
+  0x7e92, 0xecee, 0x7e91, 0xece8, 0x7e90, 0xece1, 0x7e8f, 0xecdb,
+  0x7e8e, 0xecd5, 0x7e8d, 0xeccf, 0x7e8c, 0xecc9, 0x7e8b, 0xecc2,
+  0x7e8a, 0xecbc, 0x7e89, 0xecb6, 0x7e88, 0xecb0, 0x7e87, 0xecaa,
+  0x7e86, 0xeca3, 0x7e85, 0xec9d, 0x7e84, 0xec97, 0x7e84, 0xec91,
+  0x7e83, 0xec8a, 0x7e82, 0xec84, 0x7e81, 0xec7e, 0x7e80, 0xec78,
+  0x7e7f, 0xec72, 0x7e7e, 0xec6b, 0x7e7d, 0xec65, 0x7e7c, 0xec5f,
+  0x7e7b, 0xec59, 0x7e7a, 0xec53, 0x7e79, 0xec4c, 0x7e78, 0xec46,
+  0x7e77, 0xec40, 0x7e76, 0xec3a, 0x7e75, 0xec34, 0x7e74, 0xec2d,
+  0x7e73, 0xec27, 0x7e72, 0xec21, 0x7e71, 0xec1b, 0x7e70, 0xec15,
+  0x7e6f, 0xec0e, 0x7e6e, 0xec08, 0x7e6d, 0xec02, 0x7e6c, 0xebfc,
+  0x7e6b, 0xebf5, 0x7e6a, 0xebef, 0x7e69, 0xebe9, 0x7e68, 0xebe3,
+  0x7e67, 0xebdd, 0x7e66, 0xebd6, 0x7e65, 0xebd0, 0x7e64, 0xebca,
+  0x7e63, 0xebc4, 0x7e62, 0xebbe, 0x7e61, 0xebb7, 0x7e60, 0xebb1,
+  0x7e5f, 0xebab, 0x7e5e, 0xeba5, 0x7e5d, 0xeb9f, 0x7e5c, 0xeb98,
+  0x7e5b, 0xeb92, 0x7e5a, 0xeb8c, 0x7e59, 0xeb86, 0x7e58, 0xeb80,
+  0x7e57, 0xeb79, 0x7e56, 0xeb73, 0x7e55, 0xeb6d, 0x7e54, 0xeb67,
+  0x7e53, 0xeb61, 0x7e52, 0xeb5a, 0x7e51, 0xeb54, 0x7e50, 0xeb4e,
+  0x7e4f, 0xeb48, 0x7e4e, 0xeb42, 0x7e4d, 0xeb3b, 0x7e4c, 0xeb35,
+  0x7e4b, 0xeb2f, 0x7e4a, 0xeb29, 0x7e49, 0xeb23, 0x7e48, 0xeb1c,
+  0x7e47, 0xeb16, 0x7e46, 0xeb10, 0x7e45, 0xeb0a, 0x7e44, 0xeb04,
+  0x7e43, 0xeafd, 0x7e42, 0xeaf7, 0x7e41, 0xeaf1, 0x7e40, 0xeaeb,
+  0x7e3f, 0xeae5, 0x7e3e, 0xeade, 0x7e3d, 0xead8, 0x7e3c, 0xead2,
+  0x7e3b, 0xeacc, 0x7e3a, 0xeac6, 0x7e39, 0xeabf, 0x7e38, 0xeab9,
+  0x7e37, 0xeab3, 0x7e35, 0xeaad, 0x7e34, 0xeaa7, 0x7e33, 0xeaa0,
+  0x7e32, 0xea9a, 0x7e31, 0xea94, 0x7e30, 0xea8e, 0x7e2f, 0xea88,
+  0x7e2e, 0xea81, 0x7e2d, 0xea7b, 0x7e2c, 0xea75, 0x7e2b, 0xea6f,
+  0x7e2a, 0xea69, 0x7e29, 0xea63, 0x7e28, 0xea5c, 0x7e27, 0xea56,
+  0x7e26, 0xea50, 0x7e25, 0xea4a, 0x7e24, 0xea44, 0x7e22, 0xea3d,
+  0x7e21, 0xea37, 0x7e20, 0xea31, 0x7e1f, 0xea2b, 0x7e1e, 0xea25,
+  0x7e1d, 0xea1e, 0x7e1c, 0xea18, 0x7e1b, 0xea12, 0x7e1a, 0xea0c,
+  0x7e19, 0xea06, 0x7e18, 0xe9ff, 0x7e17, 0xe9f9, 0x7e16, 0xe9f3,
+  0x7e14, 0xe9ed, 0x7e13, 0xe9e7, 0x7e12, 0xe9e1, 0x7e11, 0xe9da,
+  0x7e10, 0xe9d4, 0x7e0f, 0xe9ce, 0x7e0e, 0xe9c8, 0x7e0d, 0xe9c2,
+  0x7e0c, 0xe9bb, 0x7e0b, 0xe9b5, 0x7e0a, 0xe9af, 0x7e08, 0xe9a9,
+  0x7e07, 0xe9a3, 0x7e06, 0xe99c, 0x7e05, 0xe996, 0x7e04, 0xe990,
+  0x7e03, 0xe98a, 0x7e02, 0xe984, 0x7e01, 0xe97e, 0x7e00, 0xe977,
+  0x7dff, 0xe971, 0x7dfd, 0xe96b, 0x7dfc, 0xe965, 0x7dfb, 0xe95f,
+  0x7dfa, 0xe958, 0x7df9, 0xe952, 0x7df8, 0xe94c, 0x7df7, 0xe946,
+  0x7df6, 0xe940, 0x7df5, 0xe93a, 0x7df3, 0xe933, 0x7df2, 0xe92d,
+  0x7df1, 0xe927, 0x7df0, 0xe921, 0x7def, 0xe91b, 0x7dee, 0xe914,
+  0x7ded, 0xe90e, 0x7dec, 0xe908, 0x7dea, 0xe902, 0x7de9, 0xe8fc,
+  0x7de8, 0xe8f6, 0x7de7, 0xe8ef, 0x7de6, 0xe8e9, 0x7de5, 0xe8e3,
+  0x7de4, 0xe8dd, 0x7de2, 0xe8d7, 0x7de1, 0xe8d0, 0x7de0, 0xe8ca,
+  0x7ddf, 0xe8c4, 0x7dde, 0xe8be, 0x7ddd, 0xe8b8, 0x7ddc, 0xe8b2,
+  0x7dda, 0xe8ab, 0x7dd9, 0xe8a5, 0x7dd8, 0xe89f, 0x7dd7, 0xe899,
+  0x7dd6, 0xe893, 0x7dd5, 0xe88c, 0x7dd4, 0xe886, 0x7dd2, 0xe880,
+  0x7dd1, 0xe87a, 0x7dd0, 0xe874, 0x7dcf, 0xe86e, 0x7dce, 0xe867,
+  0x7dcd, 0xe861, 0x7dcc, 0xe85b, 0x7dca, 0xe855, 0x7dc9, 0xe84f,
+  0x7dc8, 0xe849, 0x7dc7, 0xe842, 0x7dc6, 0xe83c, 0x7dc5, 0xe836,
+  0x7dc3, 0xe830, 0x7dc2, 0xe82a, 0x7dc1, 0xe823, 0x7dc0, 0xe81d,
+  0x7dbf, 0xe817, 0x7dbd, 0xe811, 0x7dbc, 0xe80b, 0x7dbb, 0xe805,
+  0x7dba, 0xe7fe, 0x7db9, 0xe7f8, 0x7db8, 0xe7f2, 0x7db6, 0xe7ec,
+  0x7db5, 0xe7e6, 0x7db4, 0xe7e0, 0x7db3, 0xe7d9, 0x7db2, 0xe7d3,
+  0x7db0, 0xe7cd, 0x7daf, 0xe7c7, 0x7dae, 0xe7c1, 0x7dad, 0xe7bb,
+  0x7dac, 0xe7b4, 0x7dab, 0xe7ae, 0x7da9, 0xe7a8, 0x7da8, 0xe7a2,
+  0x7da7, 0xe79c, 0x7da6, 0xe796, 0x7da5, 0xe78f, 0x7da3, 0xe789,
+  0x7da2, 0xe783, 0x7da1, 0xe77d, 0x7da0, 0xe777, 0x7d9f, 0xe771,
+  0x7d9d, 0xe76a, 0x7d9c, 0xe764, 0x7d9b, 0xe75e, 0x7d9a, 0xe758,
+  0x7d98, 0xe752, 0x7d97, 0xe74c, 0x7d96, 0xe745, 0x7d95, 0xe73f,
+  0x7d94, 0xe739, 0x7d92, 0xe733, 0x7d91, 0xe72d, 0x7d90, 0xe727,
+  0x7d8f, 0xe720, 0x7d8e, 0xe71a, 0x7d8c, 0xe714, 0x7d8b, 0xe70e,
+  0x7d8a, 0xe708, 0x7d89, 0xe702, 0x7d87, 0xe6fb, 0x7d86, 0xe6f5,
+  0x7d85, 0xe6ef, 0x7d84, 0xe6e9, 0x7d82, 0xe6e3, 0x7d81, 0xe6dd,
+  0x7d80, 0xe6d6, 0x7d7f, 0xe6d0, 0x7d7e, 0xe6ca, 0x7d7c, 0xe6c4,
+  0x7d7b, 0xe6be, 0x7d7a, 0xe6b8, 0x7d79, 0xe6b2, 0x7d77, 0xe6ab,
+  0x7d76, 0xe6a5, 0x7d75, 0xe69f, 0x7d74, 0xe699, 0x7d72, 0xe693,
+  0x7d71, 0xe68d, 0x7d70, 0xe686, 0x7d6f, 0xe680, 0x7d6d, 0xe67a,
+  0x7d6c, 0xe674, 0x7d6b, 0xe66e, 0x7d6a, 0xe668, 0x7d68, 0xe661,
+  0x7d67, 0xe65b, 0x7d66, 0xe655, 0x7d65, 0xe64f, 0x7d63, 0xe649,
+  0x7d62, 0xe643, 0x7d61, 0xe63d, 0x7d60, 0xe636, 0x7d5e, 0xe630,
+  0x7d5d, 0xe62a, 0x7d5c, 0xe624, 0x7d5a, 0xe61e, 0x7d59, 0xe618,
+  0x7d58, 0xe611, 0x7d57, 0xe60b, 0x7d55, 0xe605, 0x7d54, 0xe5ff,
+  0x7d53, 0xe5f9, 0x7d52, 0xe5f3, 0x7d50, 0xe5ed, 0x7d4f, 0xe5e6,
+  0x7d4e, 0xe5e0, 0x7d4c, 0xe5da, 0x7d4b, 0xe5d4, 0x7d4a, 0xe5ce,
+  0x7d49, 0xe5c8, 0x7d47, 0xe5c2, 0x7d46, 0xe5bb, 0x7d45, 0xe5b5,
+  0x7d43, 0xe5af, 0x7d42, 0xe5a9, 0x7d41, 0xe5a3, 0x7d3f, 0xe59d,
+  0x7d3e, 0xe596, 0x7d3d, 0xe590, 0x7d3c, 0xe58a, 0x7d3a, 0xe584,
+  0x7d39, 0xe57e, 0x7d38, 0xe578, 0x7d36, 0xe572, 0x7d35, 0xe56b,
+  0x7d34, 0xe565, 0x7d32, 0xe55f, 0x7d31, 0xe559, 0x7d30, 0xe553,
+  0x7d2f, 0xe54d, 0x7d2d, 0xe547, 0x7d2c, 0xe540, 0x7d2b, 0xe53a,
+  0x7d29, 0xe534, 0x7d28, 0xe52e, 0x7d27, 0xe528, 0x7d25, 0xe522,
+  0x7d24, 0xe51c, 0x7d23, 0xe515, 0x7d21, 0xe50f, 0x7d20, 0xe509,
+  0x7d1f, 0xe503, 0x7d1d, 0xe4fd, 0x7d1c, 0xe4f7, 0x7d1b, 0xe4f1,
+  0x7d19, 0xe4ea, 0x7d18, 0xe4e4, 0x7d17, 0xe4de, 0x7d15, 0xe4d8,
+  0x7d14, 0xe4d2, 0x7d13, 0xe4cc, 0x7d11, 0xe4c6, 0x7d10, 0xe4bf,
+  0x7d0f, 0xe4b9, 0x7d0d, 0xe4b3, 0x7d0c, 0xe4ad, 0x7d0b, 0xe4a7,
+  0x7d09, 0xe4a1, 0x7d08, 0xe49b, 0x7d07, 0xe494, 0x7d05, 0xe48e,
+  0x7d04, 0xe488, 0x7d03, 0xe482, 0x7d01, 0xe47c, 0x7d00, 0xe476,
+  0x7cff, 0xe470, 0x7cfd, 0xe46a, 0x7cfc, 0xe463, 0x7cfb, 0xe45d,
+  0x7cf9, 0xe457, 0x7cf8, 0xe451, 0x7cf6, 0xe44b, 0x7cf5, 0xe445,
+  0x7cf4, 0xe43f, 0x7cf2, 0xe438, 0x7cf1, 0xe432, 0x7cf0, 0xe42c,
+  0x7cee, 0xe426, 0x7ced, 0xe420, 0x7cec, 0xe41a, 0x7cea, 0xe414,
+  0x7ce9, 0xe40e, 0x7ce7, 0xe407, 0x7ce6, 0xe401, 0x7ce5, 0xe3fb,
+  0x7ce3, 0xe3f5, 0x7ce2, 0xe3ef, 0x7ce1, 0xe3e9, 0x7cdf, 0xe3e3,
+  0x7cde, 0xe3dc, 0x7cdc, 0xe3d6, 0x7cdb, 0xe3d0, 0x7cda, 0xe3ca,
+  0x7cd8, 0xe3c4, 0x7cd7, 0xe3be, 0x7cd5, 0xe3b8, 0x7cd4, 0xe3b2,
+  0x7cd3, 0xe3ab, 0x7cd1, 0xe3a5, 0x7cd0, 0xe39f, 0x7ccf, 0xe399,
+  0x7ccd, 0xe393, 0x7ccc, 0xe38d, 0x7cca, 0xe387, 0x7cc9, 0xe381,
+  0x7cc8, 0xe37a, 0x7cc6, 0xe374, 0x7cc5, 0xe36e, 0x7cc3, 0xe368,
+  0x7cc2, 0xe362, 0x7cc1, 0xe35c, 0x7cbf, 0xe356, 0x7cbe, 0xe350,
+  0x7cbc, 0xe349, 0x7cbb, 0xe343, 0x7cb9, 0xe33d, 0x7cb8, 0xe337,
+  0x7cb7, 0xe331, 0x7cb5, 0xe32b, 0x7cb4, 0xe325, 0x7cb2, 0xe31f,
+  0x7cb1, 0xe318, 0x7cb0, 0xe312, 0x7cae, 0xe30c, 0x7cad, 0xe306,
+  0x7cab, 0xe300, 0x7caa, 0xe2fa, 0x7ca8, 0xe2f4, 0x7ca7, 0xe2ee,
+  0x7ca6, 0xe2e8, 0x7ca4, 0xe2e1, 0x7ca3, 0xe2db, 0x7ca1, 0xe2d5,
+  0x7ca0, 0xe2cf, 0x7c9e, 0xe2c9, 0x7c9d, 0xe2c3, 0x7c9c, 0xe2bd,
+  0x7c9a, 0xe2b7, 0x7c99, 0xe2b0, 0x7c97, 0xe2aa, 0x7c96, 0xe2a4,
+  0x7c94, 0xe29e, 0x7c93, 0xe298, 0x7c91, 0xe292, 0x7c90, 0xe28c,
+  0x7c8f, 0xe286, 0x7c8d, 0xe280, 0x7c8c, 0xe279, 0x7c8a, 0xe273,
+  0x7c89, 0xe26d, 0x7c87, 0xe267, 0x7c86, 0xe261, 0x7c84, 0xe25b,
+  0x7c83, 0xe255, 0x7c82, 0xe24f, 0x7c80, 0xe249, 0x7c7f, 0xe242,
+  0x7c7d, 0xe23c, 0x7c7c, 0xe236, 0x7c7a, 0xe230, 0x7c79, 0xe22a,
+  0x7c77, 0xe224, 0x7c76, 0xe21e, 0x7c74, 0xe218, 0x7c73, 0xe212,
+  0x7c71, 0xe20b, 0x7c70, 0xe205, 0x7c6e, 0xe1ff, 0x7c6d, 0xe1f9,
+  0x7c6c, 0xe1f3, 0x7c6a, 0xe1ed, 0x7c69, 0xe1e7, 0x7c67, 0xe1e1,
+  0x7c66, 0xe1db, 0x7c64, 0xe1d4, 0x7c63, 0xe1ce, 0x7c61, 0xe1c8,
+  0x7c60, 0xe1c2, 0x7c5e, 0xe1bc, 0x7c5d, 0xe1b6, 0x7c5b, 0xe1b0,
+  0x7c5a, 0xe1aa, 0x7c58, 0xe1a4, 0x7c57, 0xe19e, 0x7c55, 0xe197,
+  0x7c54, 0xe191, 0x7c52, 0xe18b, 0x7c51, 0xe185, 0x7c4f, 0xe17f,
+  0x7c4e, 0xe179, 0x7c4c, 0xe173, 0x7c4b, 0xe16d, 0x7c49, 0xe167,
+  0x7c48, 0xe160, 0x7c46, 0xe15a, 0x7c45, 0xe154, 0x7c43, 0xe14e,
+  0x7c42, 0xe148, 0x7c40, 0xe142, 0x7c3f, 0xe13c, 0x7c3d, 0xe136,
+  0x7c3c, 0xe130, 0x7c3a, 0xe12a, 0x7c39, 0xe123, 0x7c37, 0xe11d,
+  0x7c36, 0xe117, 0x7c34, 0xe111, 0x7c33, 0xe10b, 0x7c31, 0xe105,
+  0x7c30, 0xe0ff, 0x7c2e, 0xe0f9, 0x7c2d, 0xe0f3, 0x7c2b, 0xe0ed,
+  0x7c29, 0xe0e7, 0x7c28, 0xe0e0, 0x7c26, 0xe0da, 0x7c25, 0xe0d4,
+  0x7c23, 0xe0ce, 0x7c22, 0xe0c8, 0x7c20, 0xe0c2, 0x7c1f, 0xe0bc,
+  0x7c1d, 0xe0b6, 0x7c1c, 0xe0b0, 0x7c1a, 0xe0aa, 0x7c19, 0xe0a3,
+  0x7c17, 0xe09d, 0x7c16, 0xe097, 0x7c14, 0xe091, 0x7c12, 0xe08b,
+  0x7c11, 0xe085, 0x7c0f, 0xe07f, 0x7c0e, 0xe079, 0x7c0c, 0xe073,
+  0x7c0b, 0xe06d, 0x7c09, 0xe067, 0x7c08, 0xe061, 0x7c06, 0xe05a,
+  0x7c05, 0xe054, 0x7c03, 0xe04e, 0x7c01, 0xe048, 0x7c00, 0xe042,
+  0x7bfe, 0xe03c, 0x7bfd, 0xe036, 0x7bfb, 0xe030, 0x7bfa, 0xe02a,
+  0x7bf8, 0xe024, 0x7bf6, 0xe01e, 0x7bf5, 0xe017, 0x7bf3, 0xe011,
+  0x7bf2, 0xe00b, 0x7bf0, 0xe005, 0x7bef, 0xdfff, 0x7bed, 0xdff9,
+  0x7beb, 0xdff3, 0x7bea, 0xdfed, 0x7be8, 0xdfe7, 0x7be7, 0xdfe1,
+  0x7be5, 0xdfdb, 0x7be4, 0xdfd5, 0x7be2, 0xdfce, 0x7be0, 0xdfc8,
+  0x7bdf, 0xdfc2, 0x7bdd, 0xdfbc, 0x7bdc, 0xdfb6, 0x7bda, 0xdfb0,
+  0x7bd9, 0xdfaa, 0x7bd7, 0xdfa4, 0x7bd5, 0xdf9e, 0x7bd4, 0xdf98,
+  0x7bd2, 0xdf92, 0x7bd1, 0xdf8c, 0x7bcf, 0xdf86, 0x7bcd, 0xdf7f,
+  0x7bcc, 0xdf79, 0x7bca, 0xdf73, 0x7bc9, 0xdf6d, 0x7bc7, 0xdf67,
+  0x7bc5, 0xdf61, 0x7bc4, 0xdf5b, 0x7bc2, 0xdf55, 0x7bc1, 0xdf4f,
+  0x7bbf, 0xdf49, 0x7bbd, 0xdf43, 0x7bbc, 0xdf3d, 0x7bba, 0xdf37,
+  0x7bb9, 0xdf30, 0x7bb7, 0xdf2a, 0x7bb5, 0xdf24, 0x7bb4, 0xdf1e,
+  0x7bb2, 0xdf18, 0x7bb0, 0xdf12, 0x7baf, 0xdf0c, 0x7bad, 0xdf06,
+  0x7bac, 0xdf00, 0x7baa, 0xdefa, 0x7ba8, 0xdef4, 0x7ba7, 0xdeee,
+  0x7ba5, 0xdee8, 0x7ba3, 0xdee2, 0x7ba2, 0xdedb, 0x7ba0, 0xded5,
+  0x7b9f, 0xdecf, 0x7b9d, 0xdec9, 0x7b9b, 0xdec3, 0x7b9a, 0xdebd,
+  0x7b98, 0xdeb7, 0x7b96, 0xdeb1, 0x7b95, 0xdeab, 0x7b93, 0xdea5,
+  0x7b92, 0xde9f, 0x7b90, 0xde99, 0x7b8e, 0xde93, 0x7b8d, 0xde8d,
+  0x7b8b, 0xde87, 0x7b89, 0xde80, 0x7b88, 0xde7a, 0x7b86, 0xde74,
+  0x7b84, 0xde6e, 0x7b83, 0xde68, 0x7b81, 0xde62, 0x7b7f, 0xde5c,
+  0x7b7e, 0xde56, 0x7b7c, 0xde50, 0x7b7a, 0xde4a, 0x7b79, 0xde44,
+  0x7b77, 0xde3e, 0x7b76, 0xde38, 0x7b74, 0xde32, 0x7b72, 0xde2c,
+  0x7b71, 0xde26, 0x7b6f, 0xde1f, 0x7b6d, 0xde19, 0x7b6c, 0xde13,
+  0x7b6a, 0xde0d, 0x7b68, 0xde07, 0x7b67, 0xde01, 0x7b65, 0xddfb,
+  0x7b63, 0xddf5, 0x7b62, 0xddef, 0x7b60, 0xdde9, 0x7b5e, 0xdde3,
+  0x7b5d, 0xdddd, 0x7b5b, 0xddd7, 0x7b59, 0xddd1, 0x7b57, 0xddcb,
+  0x7b56, 0xddc5, 0x7b54, 0xddbf, 0x7b52, 0xddb9, 0x7b51, 0xddb2,
+  0x7b4f, 0xddac, 0x7b4d, 0xdda6, 0x7b4c, 0xdda0, 0x7b4a, 0xdd9a,
+  0x7b48, 0xdd94, 0x7b47, 0xdd8e, 0x7b45, 0xdd88, 0x7b43, 0xdd82,
+  0x7b42, 0xdd7c, 0x7b40, 0xdd76, 0x7b3e, 0xdd70, 0x7b3c, 0xdd6a,
+  0x7b3b, 0xdd64, 0x7b39, 0xdd5e, 0x7b37, 0xdd58, 0x7b36, 0xdd52,
+  0x7b34, 0xdd4c, 0x7b32, 0xdd46, 0x7b31, 0xdd40, 0x7b2f, 0xdd39,
+  0x7b2d, 0xdd33, 0x7b2b, 0xdd2d, 0x7b2a, 0xdd27, 0x7b28, 0xdd21,
+  0x7b26, 0xdd1b, 0x7b25, 0xdd15, 0x7b23, 0xdd0f, 0x7b21, 0xdd09,
+  0x7b1f, 0xdd03, 0x7b1e, 0xdcfd, 0x7b1c, 0xdcf7, 0x7b1a, 0xdcf1,
+  0x7b19, 0xdceb, 0x7b17, 0xdce5, 0x7b15, 0xdcdf, 0x7b13, 0xdcd9,
+  0x7b12, 0xdcd3, 0x7b10, 0xdccd, 0x7b0e, 0xdcc7, 0x7b0c, 0xdcc1,
+  0x7b0b, 0xdcbb, 0x7b09, 0xdcb5, 0x7b07, 0xdcae, 0x7b06, 0xdca8,
+  0x7b04, 0xdca2, 0x7b02, 0xdc9c, 0x7b00, 0xdc96, 0x7aff, 0xdc90,
+  0x7afd, 0xdc8a, 0x7afb, 0xdc84, 0x7af9, 0xdc7e, 0x7af8, 0xdc78,
+  0x7af6, 0xdc72, 0x7af4, 0xdc6c, 0x7af2, 0xdc66, 0x7af1, 0xdc60,
+  0x7aef, 0xdc5a, 0x7aed, 0xdc54, 0x7aeb, 0xdc4e, 0x7aea, 0xdc48,
+  0x7ae8, 0xdc42, 0x7ae6, 0xdc3c, 0x7ae4, 0xdc36, 0x7ae3, 0xdc30,
+  0x7ae1, 0xdc2a, 0x7adf, 0xdc24, 0x7add, 0xdc1e, 0x7adc, 0xdc18,
+  0x7ada, 0xdc12, 0x7ad8, 0xdc0c, 0x7ad6, 0xdc06, 0x7ad5, 0xdbff,
+  0x7ad3, 0xdbf9, 0x7ad1, 0xdbf3, 0x7acf, 0xdbed, 0x7acd, 0xdbe7,
+  0x7acc, 0xdbe1, 0x7aca, 0xdbdb, 0x7ac8, 0xdbd5, 0x7ac6, 0xdbcf,
+  0x7ac5, 0xdbc9, 0x7ac3, 0xdbc3, 0x7ac1, 0xdbbd, 0x7abf, 0xdbb7,
+  0x7abd, 0xdbb1, 0x7abc, 0xdbab, 0x7aba, 0xdba5, 0x7ab8, 0xdb9f,
+  0x7ab6, 0xdb99, 0x7ab5, 0xdb93, 0x7ab3, 0xdb8d, 0x7ab1, 0xdb87,
+  0x7aaf, 0xdb81, 0x7aad, 0xdb7b, 0x7aac, 0xdb75, 0x7aaa, 0xdb6f,
+  0x7aa8, 0xdb69, 0x7aa6, 0xdb63, 0x7aa4, 0xdb5d, 0x7aa3, 0xdb57,
+  0x7aa1, 0xdb51, 0x7a9f, 0xdb4b, 0x7a9d, 0xdb45, 0x7a9b, 0xdb3f,
+  0x7a9a, 0xdb39, 0x7a98, 0xdb33, 0x7a96, 0xdb2d, 0x7a94, 0xdb27,
+  0x7a92, 0xdb21, 0x7a91, 0xdb1b, 0x7a8f, 0xdb15, 0x7a8d, 0xdb0f,
+  0x7a8b, 0xdb09, 0x7a89, 0xdb03, 0x7a87, 0xdafd, 0x7a86, 0xdaf7,
+  0x7a84, 0xdaf1, 0x7a82, 0xdaea, 0x7a80, 0xdae4, 0x7a7e, 0xdade,
+  0x7a7d, 0xdad8, 0x7a7b, 0xdad2, 0x7a79, 0xdacc, 0x7a77, 0xdac6,
+  0x7a75, 0xdac0, 0x7a73, 0xdaba, 0x7a72, 0xdab4, 0x7a70, 0xdaae,
+  0x7a6e, 0xdaa8, 0x7a6c, 0xdaa2, 0x7a6a, 0xda9c, 0x7a68, 0xda96,
+  0x7a67, 0xda90, 0x7a65, 0xda8a, 0x7a63, 0xda84, 0x7a61, 0xda7e,
+  0x7a5f, 0xda78, 0x7a5d, 0xda72, 0x7a5c, 0xda6c, 0x7a5a, 0xda66,
+  0x7a58, 0xda60, 0x7a56, 0xda5a, 0x7a54, 0xda54, 0x7a52, 0xda4e,
+  0x7a50, 0xda48, 0x7a4f, 0xda42, 0x7a4d, 0xda3c, 0x7a4b, 0xda36,
+  0x7a49, 0xda30, 0x7a47, 0xda2a, 0x7a45, 0xda24, 0x7a43, 0xda1e,
+  0x7a42, 0xda18, 0x7a40, 0xda12, 0x7a3e, 0xda0c, 0x7a3c, 0xda06,
+  0x7a3a, 0xda00, 0x7a38, 0xd9fa, 0x7a36, 0xd9f4, 0x7a35, 0xd9ee,
+  0x7a33, 0xd9e8, 0x7a31, 0xd9e2, 0x7a2f, 0xd9dc, 0x7a2d, 0xd9d6,
+  0x7a2b, 0xd9d0, 0x7a29, 0xd9ca, 0x7a27, 0xd9c4, 0x7a26, 0xd9be,
+  0x7a24, 0xd9b8, 0x7a22, 0xd9b2, 0x7a20, 0xd9ac, 0x7a1e, 0xd9a6,
+  0x7a1c, 0xd9a0, 0x7a1a, 0xd99a, 0x7a18, 0xd994, 0x7a16, 0xd98e,
+  0x7a15, 0xd988, 0x7a13, 0xd982, 0x7a11, 0xd97c, 0x7a0f, 0xd976,
+  0x7a0d, 0xd970, 0x7a0b, 0xd96a, 0x7a09, 0xd964, 0x7a07, 0xd95e,
+  0x7a05, 0xd958, 0x7a04, 0xd952, 0x7a02, 0xd94c, 0x7a00, 0xd946,
+  0x79fe, 0xd940, 0x79fc, 0xd93a, 0x79fa, 0xd934, 0x79f8, 0xd92e,
+  0x79f6, 0xd928, 0x79f4, 0xd922, 0x79f2, 0xd91c, 0x79f0, 0xd917,
+  0x79ef, 0xd911, 0x79ed, 0xd90b, 0x79eb, 0xd905, 0x79e9, 0xd8ff,
+  0x79e7, 0xd8f9, 0x79e5, 0xd8f3, 0x79e3, 0xd8ed, 0x79e1, 0xd8e7,
+  0x79df, 0xd8e1, 0x79dd, 0xd8db, 0x79db, 0xd8d5, 0x79d9, 0xd8cf,
+  0x79d8, 0xd8c9, 0x79d6, 0xd8c3, 0x79d4, 0xd8bd, 0x79d2, 0xd8b7,
+  0x79d0, 0xd8b1, 0x79ce, 0xd8ab, 0x79cc, 0xd8a5, 0x79ca, 0xd89f,
+  0x79c8, 0xd899, 0x79c6, 0xd893, 0x79c4, 0xd88d, 0x79c2, 0xd887,
+  0x79c0, 0xd881, 0x79be, 0xd87b, 0x79bc, 0xd875, 0x79bb, 0xd86f,
+  0x79b9, 0xd869, 0x79b7, 0xd863, 0x79b5, 0xd85d, 0x79b3, 0xd857,
+  0x79b1, 0xd851, 0x79af, 0xd84b, 0x79ad, 0xd845, 0x79ab, 0xd83f,
+  0x79a9, 0xd839, 0x79a7, 0xd833, 0x79a5, 0xd82d, 0x79a3, 0xd827,
+  0x79a1, 0xd821, 0x799f, 0xd81b, 0x799d, 0xd815, 0x799b, 0xd80f,
+  0x7999, 0xd80a, 0x7997, 0xd804, 0x7995, 0xd7fe, 0x7993, 0xd7f8,
+  0x7992, 0xd7f2, 0x7990, 0xd7ec, 0x798e, 0xd7e6, 0x798c, 0xd7e0,
+  0x798a, 0xd7da, 0x7988, 0xd7d4, 0x7986, 0xd7ce, 0x7984, 0xd7c8,
+  0x7982, 0xd7c2, 0x7980, 0xd7bc, 0x797e, 0xd7b6, 0x797c, 0xd7b0,
+  0x797a, 0xd7aa, 0x7978, 0xd7a4, 0x7976, 0xd79e, 0x7974, 0xd798,
+  0x7972, 0xd792, 0x7970, 0xd78c, 0x796e, 0xd786, 0x796c, 0xd780,
+  0x796a, 0xd77a, 0x7968, 0xd774, 0x7966, 0xd76e, 0x7964, 0xd768,
+  0x7962, 0xd763, 0x7960, 0xd75d, 0x795e, 0xd757, 0x795c, 0xd751,
+  0x795a, 0xd74b, 0x7958, 0xd745, 0x7956, 0xd73f, 0x7954, 0xd739,
+  0x7952, 0xd733, 0x7950, 0xd72d, 0x794e, 0xd727, 0x794c, 0xd721,
+  0x794a, 0xd71b, 0x7948, 0xd715, 0x7946, 0xd70f, 0x7944, 0xd709,
+  0x7942, 0xd703, 0x7940, 0xd6fd, 0x793e, 0xd6f7, 0x793c, 0xd6f1,
+  0x793a, 0xd6eb, 0x7938, 0xd6e5, 0x7936, 0xd6e0, 0x7934, 0xd6da,
+  0x7932, 0xd6d4, 0x7930, 0xd6ce, 0x792e, 0xd6c8, 0x792c, 0xd6c2,
+  0x792a, 0xd6bc, 0x7928, 0xd6b6, 0x7926, 0xd6b0, 0x7924, 0xd6aa,
+  0x7922, 0xd6a4, 0x7920, 0xd69e, 0x791e, 0xd698, 0x791c, 0xd692,
+  0x7919, 0xd68c, 0x7917, 0xd686, 0x7915, 0xd680, 0x7913, 0xd67a,
+  0x7911, 0xd675, 0x790f, 0xd66f, 0x790d, 0xd669, 0x790b, 0xd663,
+  0x7909, 0xd65d, 0x7907, 0xd657, 0x7905, 0xd651, 0x7903, 0xd64b,
+  0x7901, 0xd645, 0x78ff, 0xd63f, 0x78fd, 0xd639, 0x78fb, 0xd633,
+  0x78f9, 0xd62d, 0x78f7, 0xd627, 0x78f5, 0xd621, 0x78f3, 0xd61b,
+  0x78f1, 0xd615, 0x78ee, 0xd610, 0x78ec, 0xd60a, 0x78ea, 0xd604,
+  0x78e8, 0xd5fe, 0x78e6, 0xd5f8, 0x78e4, 0xd5f2, 0x78e2, 0xd5ec,
+  0x78e0, 0xd5e6, 0x78de, 0xd5e0, 0x78dc, 0xd5da, 0x78da, 0xd5d4,
+  0x78d8, 0xd5ce, 0x78d6, 0xd5c8, 0x78d4, 0xd5c2, 0x78d2, 0xd5bc,
+  0x78cf, 0xd5b7, 0x78cd, 0xd5b1, 0x78cb, 0xd5ab, 0x78c9, 0xd5a5,
+  0x78c7, 0xd59f, 0x78c5, 0xd599, 0x78c3, 0xd593, 0x78c1, 0xd58d,
+  0x78bf, 0xd587, 0x78bd, 0xd581, 0x78bb, 0xd57b, 0x78b9, 0xd575,
+  0x78b6, 0xd56f, 0x78b4, 0xd569, 0x78b2, 0xd564, 0x78b0, 0xd55e,
+  0x78ae, 0xd558, 0x78ac, 0xd552, 0x78aa, 0xd54c, 0x78a8, 0xd546,
+  0x78a6, 0xd540, 0x78a4, 0xd53a, 0x78a2, 0xd534, 0x789f, 0xd52e,
+  0x789d, 0xd528, 0x789b, 0xd522, 0x7899, 0xd51c, 0x7897, 0xd517,
+  0x7895, 0xd511, 0x7893, 0xd50b, 0x7891, 0xd505, 0x788f, 0xd4ff,
+  0x788c, 0xd4f9, 0x788a, 0xd4f3, 0x7888, 0xd4ed, 0x7886, 0xd4e7,
+  0x7884, 0xd4e1, 0x7882, 0xd4db, 0x7880, 0xd4d5, 0x787e, 0xd4d0,
+  0x787c, 0xd4ca, 0x7879, 0xd4c4, 0x7877, 0xd4be, 0x7875, 0xd4b8,
+  0x7873, 0xd4b2, 0x7871, 0xd4ac, 0x786f, 0xd4a6, 0x786d, 0xd4a0,
+  0x786b, 0xd49a, 0x7868, 0xd494, 0x7866, 0xd48f, 0x7864, 0xd489,
+  0x7862, 0xd483, 0x7860, 0xd47d, 0x785e, 0xd477, 0x785c, 0xd471,
+  0x7859, 0xd46b, 0x7857, 0xd465, 0x7855, 0xd45f, 0x7853, 0xd459,
+  0x7851, 0xd453, 0x784f, 0xd44e, 0x784d, 0xd448, 0x784a, 0xd442,
+  0x7848, 0xd43c, 0x7846, 0xd436, 0x7844, 0xd430, 0x7842, 0xd42a,
+  0x7840, 0xd424, 0x783e, 0xd41e, 0x783b, 0xd418, 0x7839, 0xd412,
+  0x7837, 0xd40d, 0x7835, 0xd407, 0x7833, 0xd401, 0x7831, 0xd3fb,
+  0x782e, 0xd3f5, 0x782c, 0xd3ef, 0x782a, 0xd3e9, 0x7828, 0xd3e3,
+  0x7826, 0xd3dd, 0x7824, 0xd3d7, 0x7821, 0xd3d2, 0x781f, 0xd3cc,
+  0x781d, 0xd3c6, 0x781b, 0xd3c0, 0x7819, 0xd3ba, 0x7817, 0xd3b4,
+  0x7814, 0xd3ae, 0x7812, 0xd3a8, 0x7810, 0xd3a2, 0x780e, 0xd39d,
+  0x780c, 0xd397, 0x780a, 0xd391, 0x7807, 0xd38b, 0x7805, 0xd385,
+  0x7803, 0xd37f, 0x7801, 0xd379, 0x77ff, 0xd373, 0x77fc, 0xd36d,
+  0x77fa, 0xd368, 0x77f8, 0xd362, 0x77f6, 0xd35c, 0x77f4, 0xd356,
+  0x77f1, 0xd350, 0x77ef, 0xd34a, 0x77ed, 0xd344, 0x77eb, 0xd33e,
+  0x77e9, 0xd338, 0x77e6, 0xd333, 0x77e4, 0xd32d, 0x77e2, 0xd327,
+  0x77e0, 0xd321, 0x77de, 0xd31b, 0x77db, 0xd315, 0x77d9, 0xd30f,
+  0x77d7, 0xd309, 0x77d5, 0xd303, 0x77d3, 0xd2fe, 0x77d0, 0xd2f8,
+  0x77ce, 0xd2f2, 0x77cc, 0xd2ec, 0x77ca, 0xd2e6, 0x77c8, 0xd2e0,
+  0x77c5, 0xd2da, 0x77c3, 0xd2d4, 0x77c1, 0xd2cf, 0x77bf, 0xd2c9,
+  0x77bc, 0xd2c3, 0x77ba, 0xd2bd, 0x77b8, 0xd2b7, 0x77b6, 0xd2b1,
+  0x77b4, 0xd2ab, 0x77b1, 0xd2a5, 0x77af, 0xd2a0, 0x77ad, 0xd29a,
+  0x77ab, 0xd294, 0x77a8, 0xd28e, 0x77a6, 0xd288, 0x77a4, 0xd282,
+  0x77a2, 0xd27c, 0x77a0, 0xd276, 0x779d, 0xd271, 0x779b, 0xd26b,
+  0x7799, 0xd265, 0x7797, 0xd25f, 0x7794, 0xd259, 0x7792, 0xd253,
+  0x7790, 0xd24d, 0x778e, 0xd247, 0x778b, 0xd242, 0x7789, 0xd23c,
+  0x7787, 0xd236, 0x7785, 0xd230, 0x7782, 0xd22a, 0x7780, 0xd224,
+  0x777e, 0xd21e, 0x777c, 0xd219, 0x7779, 0xd213, 0x7777, 0xd20d,
+  0x7775, 0xd207, 0x7773, 0xd201, 0x7770, 0xd1fb, 0x776e, 0xd1f5,
+  0x776c, 0xd1ef, 0x776a, 0xd1ea, 0x7767, 0xd1e4, 0x7765, 0xd1de,
+  0x7763, 0xd1d8, 0x7760, 0xd1d2, 0x775e, 0xd1cc, 0x775c, 0xd1c6,
+  0x775a, 0xd1c1, 0x7757, 0xd1bb, 0x7755, 0xd1b5, 0x7753, 0xd1af,
+  0x7751, 0xd1a9, 0x774e, 0xd1a3, 0x774c, 0xd19d, 0x774a, 0xd198,
+  0x7747, 0xd192, 0x7745, 0xd18c, 0x7743, 0xd186, 0x7741, 0xd180,
+  0x773e, 0xd17a, 0x773c, 0xd174, 0x773a, 0xd16f, 0x7738, 0xd169,
+  0x7735, 0xd163, 0x7733, 0xd15d, 0x7731, 0xd157, 0x772e, 0xd151,
+  0x772c, 0xd14b, 0x772a, 0xd146, 0x7727, 0xd140, 0x7725, 0xd13a,
+  0x7723, 0xd134, 0x7721, 0xd12e, 0x771e, 0xd128, 0x771c, 0xd123,
+  0x771a, 0xd11d, 0x7717, 0xd117, 0x7715, 0xd111, 0x7713, 0xd10b,
+  0x7710, 0xd105, 0x770e, 0xd0ff, 0x770c, 0xd0fa, 0x770a, 0xd0f4,
+  0x7707, 0xd0ee, 0x7705, 0xd0e8, 0x7703, 0xd0e2, 0x7700, 0xd0dc,
+  0x76fe, 0xd0d7, 0x76fc, 0xd0d1, 0x76f9, 0xd0cb, 0x76f7, 0xd0c5,
+  0x76f5, 0xd0bf, 0x76f2, 0xd0b9, 0x76f0, 0xd0b4, 0x76ee, 0xd0ae,
+  0x76eb, 0xd0a8, 0x76e9, 0xd0a2, 0x76e7, 0xd09c, 0x76e4, 0xd096,
+  0x76e2, 0xd091, 0x76e0, 0xd08b, 0x76dd, 0xd085, 0x76db, 0xd07f,
+  0x76d9, 0xd079, 0x76d6, 0xd073, 0x76d4, 0xd06e, 0x76d2, 0xd068,
+  0x76cf, 0xd062, 0x76cd, 0xd05c, 0x76cb, 0xd056, 0x76c8, 0xd050,
+  0x76c6, 0xd04b, 0x76c4, 0xd045, 0x76c1, 0xd03f, 0x76bf, 0xd039,
+  0x76bd, 0xd033, 0x76ba, 0xd02d, 0x76b8, 0xd028, 0x76b6, 0xd022,
+  0x76b3, 0xd01c, 0x76b1, 0xd016, 0x76af, 0xd010, 0x76ac, 0xd00a,
+  0x76aa, 0xd005, 0x76a8, 0xcfff, 0x76a5, 0xcff9, 0x76a3, 0xcff3,
+  0x76a0, 0xcfed, 0x769e, 0xcfe7, 0x769c, 0xcfe2, 0x7699, 0xcfdc,
+  0x7697, 0xcfd6, 0x7695, 0xcfd0, 0x7692, 0xcfca, 0x7690, 0xcfc5,
+  0x768e, 0xcfbf, 0x768b, 0xcfb9, 0x7689, 0xcfb3, 0x7686, 0xcfad,
+  0x7684, 0xcfa7, 0x7682, 0xcfa2, 0x767f, 0xcf9c, 0x767d, 0xcf96,
+  0x767b, 0xcf90, 0x7678, 0xcf8a, 0x7676, 0xcf85, 0x7673, 0xcf7f,
+  0x7671, 0xcf79, 0x766f, 0xcf73, 0x766c, 0xcf6d, 0x766a, 0xcf67,
+  0x7668, 0xcf62, 0x7665, 0xcf5c, 0x7663, 0xcf56, 0x7660, 0xcf50,
+  0x765e, 0xcf4a, 0x765c, 0xcf45, 0x7659, 0xcf3f, 0x7657, 0xcf39,
+  0x7654, 0xcf33, 0x7652, 0xcf2d, 0x7650, 0xcf28, 0x764d, 0xcf22,
+  0x764b, 0xcf1c, 0x7648, 0xcf16, 0x7646, 0xcf10, 0x7644, 0xcf0b,
+  0x7641, 0xcf05, 0x763f, 0xceff, 0x763c, 0xcef9, 0x763a, 0xcef3,
+  0x7638, 0xceee, 0x7635, 0xcee8, 0x7633, 0xcee2, 0x7630, 0xcedc,
+  0x762e, 0xced6, 0x762b, 0xced1, 0x7629, 0xcecb, 0x7627, 0xcec5,
+  0x7624, 0xcebf, 0x7622, 0xceb9, 0x761f, 0xceb4, 0x761d, 0xceae,
+  0x761b, 0xcea8, 0x7618, 0xcea2, 0x7616, 0xce9c, 0x7613, 0xce97,
+  0x7611, 0xce91, 0x760e, 0xce8b, 0x760c, 0xce85, 0x760a, 0xce7f,
+  0x7607, 0xce7a, 0x7605, 0xce74, 0x7602, 0xce6e, 0x7600, 0xce68,
+  0x75fd, 0xce62, 0x75fb, 0xce5d, 0x75f9, 0xce57, 0x75f6, 0xce51,
+  0x75f4, 0xce4b, 0x75f1, 0xce45, 0x75ef, 0xce40, 0x75ec, 0xce3a,
+  0x75ea, 0xce34, 0x75e7, 0xce2e, 0x75e5, 0xce28, 0x75e3, 0xce23,
+  0x75e0, 0xce1d, 0x75de, 0xce17, 0x75db, 0xce11, 0x75d9, 0xce0c,
+  0x75d6, 0xce06, 0x75d4, 0xce00, 0x75d1, 0xcdfa, 0x75cf, 0xcdf4,
+  0x75cc, 0xcdef, 0x75ca, 0xcde9, 0x75c8, 0xcde3, 0x75c5, 0xcddd,
+  0x75c3, 0xcdd8, 0x75c0, 0xcdd2, 0x75be, 0xcdcc, 0x75bb, 0xcdc6,
+  0x75b9, 0xcdc0, 0x75b6, 0xcdbb, 0x75b4, 0xcdb5, 0x75b1, 0xcdaf,
+  0x75af, 0xcda9, 0x75ac, 0xcda3, 0x75aa, 0xcd9e, 0x75a7, 0xcd98,
+  0x75a5, 0xcd92, 0x75a3, 0xcd8c, 0x75a0, 0xcd87, 0x759e, 0xcd81,
+  0x759b, 0xcd7b, 0x7599, 0xcd75, 0x7596, 0xcd70, 0x7594, 0xcd6a,
+  0x7591, 0xcd64, 0x758f, 0xcd5e, 0x758c, 0xcd58, 0x758a, 0xcd53,
+  0x7587, 0xcd4d, 0x7585, 0xcd47, 0x7582, 0xcd41, 0x7580, 0xcd3c,
+  0x757d, 0xcd36, 0x757b, 0xcd30, 0x7578, 0xcd2a, 0x7576, 0xcd25,
+  0x7573, 0xcd1f, 0x7571, 0xcd19, 0x756e, 0xcd13, 0x756c, 0xcd0d,
+  0x7569, 0xcd08, 0x7567, 0xcd02, 0x7564, 0xccfc, 0x7562, 0xccf6,
+  0x755f, 0xccf1, 0x755d, 0xcceb, 0x755a, 0xcce5, 0x7558, 0xccdf,
+  0x7555, 0xccda, 0x7553, 0xccd4, 0x7550, 0xccce, 0x754e, 0xccc8,
+  0x754b, 0xccc3, 0x7549, 0xccbd, 0x7546, 0xccb7, 0x7544, 0xccb1,
+  0x7541, 0xccac, 0x753f, 0xcca6, 0x753c, 0xcca0, 0x753a, 0xcc9a,
+  0x7537, 0xcc95, 0x7535, 0xcc8f, 0x7532, 0xcc89, 0x752f, 0xcc83,
+  0x752d, 0xcc7e, 0x752a, 0xcc78, 0x7528, 0xcc72, 0x7525, 0xcc6c,
+  0x7523, 0xcc67, 0x7520, 0xcc61, 0x751e, 0xcc5b, 0x751b, 0xcc55,
+  0x7519, 0xcc50, 0x7516, 0xcc4a, 0x7514, 0xcc44, 0x7511, 0xcc3e,
+  0x750f, 0xcc39, 0x750c, 0xcc33, 0x7509, 0xcc2d, 0x7507, 0xcc27,
+  0x7504, 0xcc22, 0x7502, 0xcc1c, 0x74ff, 0xcc16, 0x74fd, 0xcc10,
+  0x74fa, 0xcc0b, 0x74f8, 0xcc05, 0x74f5, 0xcbff, 0x74f2, 0xcbf9,
+  0x74f0, 0xcbf4, 0x74ed, 0xcbee, 0x74eb, 0xcbe8, 0x74e8, 0xcbe2,
+  0x74e6, 0xcbdd, 0x74e3, 0xcbd7, 0x74e1, 0xcbd1, 0x74de, 0xcbcb,
+  0x74db, 0xcbc6, 0x74d9, 0xcbc0, 0x74d6, 0xcbba, 0x74d4, 0xcbb5,
+  0x74d1, 0xcbaf, 0x74cf, 0xcba9, 0x74cc, 0xcba3, 0x74c9, 0xcb9e,
+  0x74c7, 0xcb98, 0x74c4, 0xcb92, 0x74c2, 0xcb8c, 0x74bf, 0xcb87,
+  0x74bd, 0xcb81, 0x74ba, 0xcb7b, 0x74b7, 0xcb75, 0x74b5, 0xcb70,
+  0x74b2, 0xcb6a, 0x74b0, 0xcb64, 0x74ad, 0xcb5f, 0x74ab, 0xcb59,
+  0x74a8, 0xcb53, 0x74a5, 0xcb4d, 0x74a3, 0xcb48, 0x74a0, 0xcb42,
+  0x749e, 0xcb3c, 0x749b, 0xcb36, 0x7498, 0xcb31, 0x7496, 0xcb2b,
+  0x7493, 0xcb25, 0x7491, 0xcb20, 0x748e, 0xcb1a, 0x748b, 0xcb14,
+  0x7489, 0xcb0e, 0x7486, 0xcb09, 0x7484, 0xcb03, 0x7481, 0xcafd,
+  0x747e, 0xcaf8, 0x747c, 0xcaf2, 0x7479, 0xcaec, 0x7477, 0xcae6,
+  0x7474, 0xcae1, 0x7471, 0xcadb, 0x746f, 0xcad5, 0x746c, 0xcad0,
+  0x746a, 0xcaca, 0x7467, 0xcac4, 0x7464, 0xcabe, 0x7462, 0xcab9,
+  0x745f, 0xcab3, 0x745c, 0xcaad, 0x745a, 0xcaa8, 0x7457, 0xcaa2,
+  0x7455, 0xca9c, 0x7452, 0xca96, 0x744f, 0xca91, 0x744d, 0xca8b,
+  0x744a, 0xca85, 0x7448, 0xca80, 0x7445, 0xca7a, 0x7442, 0xca74,
+  0x7440, 0xca6e, 0x743d, 0xca69, 0x743a, 0xca63, 0x7438, 0xca5d,
+  0x7435, 0xca58, 0x7432, 0xca52, 0x7430, 0xca4c, 0x742d, 0xca46,
+  0x742b, 0xca41, 0x7428, 0xca3b, 0x7425, 0xca35, 0x7423, 0xca30,
+  0x7420, 0xca2a, 0x741d, 0xca24, 0x741b, 0xca1f, 0x7418, 0xca19,
+  0x7415, 0xca13, 0x7413, 0xca0d, 0x7410, 0xca08, 0x740d, 0xca02,
+  0x740b, 0xc9fc, 0x7408, 0xc9f7, 0x7406, 0xc9f1, 0x7403, 0xc9eb,
+  0x7400, 0xc9e6, 0x73fe, 0xc9e0, 0x73fb, 0xc9da, 0x73f8, 0xc9d5,
+  0x73f6, 0xc9cf, 0x73f3, 0xc9c9, 0x73f0, 0xc9c3, 0x73ee, 0xc9be,
+  0x73eb, 0xc9b8, 0x73e8, 0xc9b2, 0x73e6, 0xc9ad, 0x73e3, 0xc9a7,
+  0x73e0, 0xc9a1, 0x73de, 0xc99c, 0x73db, 0xc996, 0x73d8, 0xc990,
+  0x73d6, 0xc98b, 0x73d3, 0xc985, 0x73d0, 0xc97f, 0x73ce, 0xc97a,
+  0x73cb, 0xc974, 0x73c8, 0xc96e, 0x73c6, 0xc968, 0x73c3, 0xc963,
+  0x73c0, 0xc95d, 0x73bd, 0xc957, 0x73bb, 0xc952, 0x73b8, 0xc94c,
+  0x73b5, 0xc946, 0x73b3, 0xc941, 0x73b0, 0xc93b, 0x73ad, 0xc935,
+  0x73ab, 0xc930, 0x73a8, 0xc92a, 0x73a5, 0xc924, 0x73a3, 0xc91f,
+  0x73a0, 0xc919, 0x739d, 0xc913, 0x739b, 0xc90e, 0x7398, 0xc908,
+  0x7395, 0xc902, 0x7392, 0xc8fd, 0x7390, 0xc8f7, 0x738d, 0xc8f1,
+  0x738a, 0xc8ec, 0x7388, 0xc8e6, 0x7385, 0xc8e0, 0x7382, 0xc8db,
+  0x737f, 0xc8d5, 0x737d, 0xc8cf, 0x737a, 0xc8ca, 0x7377, 0xc8c4,
+  0x7375, 0xc8be, 0x7372, 0xc8b9, 0x736f, 0xc8b3, 0x736c, 0xc8ad,
+  0x736a, 0xc8a8, 0x7367, 0xc8a2, 0x7364, 0xc89c, 0x7362, 0xc897,
+  0x735f, 0xc891, 0x735c, 0xc88b, 0x7359, 0xc886, 0x7357, 0xc880,
+  0x7354, 0xc87a, 0x7351, 0xc875, 0x734f, 0xc86f, 0x734c, 0xc869,
+  0x7349, 0xc864, 0x7346, 0xc85e, 0x7344, 0xc858, 0x7341, 0xc853,
+  0x733e, 0xc84d, 0x733b, 0xc847, 0x7339, 0xc842, 0x7336, 0xc83c,
+  0x7333, 0xc836, 0x7330, 0xc831, 0x732e, 0xc82b, 0x732b, 0xc825,
+  0x7328, 0xc820, 0x7326, 0xc81a, 0x7323, 0xc814, 0x7320, 0xc80f,
+  0x731d, 0xc809, 0x731b, 0xc803, 0x7318, 0xc7fe, 0x7315, 0xc7f8,
+  0x7312, 0xc7f3, 0x7310, 0xc7ed, 0x730d, 0xc7e7, 0x730a, 0xc7e2,
+  0x7307, 0xc7dc, 0x7305, 0xc7d6, 0x7302, 0xc7d1, 0x72ff, 0xc7cb,
+  0x72fc, 0xc7c5, 0x72f9, 0xc7c0, 0x72f7, 0xc7ba, 0x72f4, 0xc7b4,
+  0x72f1, 0xc7af, 0x72ee, 0xc7a9, 0x72ec, 0xc7a3, 0x72e9, 0xc79e,
+  0x72e6, 0xc798, 0x72e3, 0xc793, 0x72e1, 0xc78d, 0x72de, 0xc787,
+  0x72db, 0xc782, 0x72d8, 0xc77c, 0x72d5, 0xc776, 0x72d3, 0xc771,
+  0x72d0, 0xc76b, 0x72cd, 0xc765, 0x72ca, 0xc760, 0x72c8, 0xc75a,
+  0x72c5, 0xc755, 0x72c2, 0xc74f, 0x72bf, 0xc749, 0x72bc, 0xc744,
+  0x72ba, 0xc73e, 0x72b7, 0xc738, 0x72b4, 0xc733, 0x72b1, 0xc72d,
+  0x72af, 0xc728, 0x72ac, 0xc722, 0x72a9, 0xc71c, 0x72a6, 0xc717,
+  0x72a3, 0xc711, 0x72a1, 0xc70b, 0x729e, 0xc706, 0x729b, 0xc700,
+  0x7298, 0xc6fa, 0x7295, 0xc6f5, 0x7293, 0xc6ef, 0x7290, 0xc6ea,
+  0x728d, 0xc6e4, 0x728a, 0xc6de, 0x7287, 0xc6d9, 0x7285, 0xc6d3,
+  0x7282, 0xc6ce, 0x727f, 0xc6c8, 0x727c, 0xc6c2, 0x7279, 0xc6bd,
+  0x7276, 0xc6b7, 0x7274, 0xc6b1, 0x7271, 0xc6ac, 0x726e, 0xc6a6,
+  0x726b, 0xc6a1, 0x7268, 0xc69b, 0x7266, 0xc695, 0x7263, 0xc690,
+  0x7260, 0xc68a, 0x725d, 0xc684, 0x725a, 0xc67f, 0x7257, 0xc679,
+  0x7255, 0xc674, 0x7252, 0xc66e, 0x724f, 0xc668, 0x724c, 0xc663,
+  0x7249, 0xc65d, 0x7247, 0xc658, 0x7244, 0xc652, 0x7241, 0xc64c,
+  0x723e, 0xc647, 0x723b, 0xc641, 0x7238, 0xc63c, 0x7236, 0xc636,
+  0x7233, 0xc630, 0x7230, 0xc62b, 0x722d, 0xc625, 0x722a, 0xc620,
+  0x7227, 0xc61a, 0x7224, 0xc614, 0x7222, 0xc60f, 0x721f, 0xc609,
+  0x721c, 0xc603, 0x7219, 0xc5fe, 0x7216, 0xc5f8, 0x7213, 0xc5f3,
+  0x7211, 0xc5ed, 0x720e, 0xc5e7, 0x720b, 0xc5e2, 0x7208, 0xc5dc,
+  0x7205, 0xc5d7, 0x7202, 0xc5d1, 0x71ff, 0xc5cc, 0x71fd, 0xc5c6,
+  0x71fa, 0xc5c0, 0x71f7, 0xc5bb, 0x71f4, 0xc5b5, 0x71f1, 0xc5b0,
+  0x71ee, 0xc5aa, 0x71eb, 0xc5a4, 0x71e9, 0xc59f, 0x71e6, 0xc599,
+  0x71e3, 0xc594, 0x71e0, 0xc58e, 0x71dd, 0xc588, 0x71da, 0xc583,
+  0x71d7, 0xc57d, 0x71d4, 0xc578, 0x71d2, 0xc572, 0x71cf, 0xc56c,
+  0x71cc, 0xc567, 0x71c9, 0xc561, 0x71c6, 0xc55c, 0x71c3, 0xc556,
+  0x71c0, 0xc551, 0x71bd, 0xc54b, 0x71bb, 0xc545, 0x71b8, 0xc540,
+  0x71b5, 0xc53a, 0x71b2, 0xc535, 0x71af, 0xc52f, 0x71ac, 0xc529,
+  0x71a9, 0xc524, 0x71a6, 0xc51e, 0x71a3, 0xc519, 0x71a1, 0xc513,
+  0x719e, 0xc50e, 0x719b, 0xc508, 0x7198, 0xc502, 0x7195, 0xc4fd,
+  0x7192, 0xc4f7, 0x718f, 0xc4f2, 0x718c, 0xc4ec, 0x7189, 0xc4e7,
+  0x7186, 0xc4e1, 0x7184, 0xc4db, 0x7181, 0xc4d6, 0x717e, 0xc4d0,
+  0x717b, 0xc4cb, 0x7178, 0xc4c5, 0x7175, 0xc4c0, 0x7172, 0xc4ba,
+  0x716f, 0xc4b4, 0x716c, 0xc4af, 0x7169, 0xc4a9, 0x7167, 0xc4a4,
+  0x7164, 0xc49e, 0x7161, 0xc499, 0x715e, 0xc493, 0x715b, 0xc48d,
+  0x7158, 0xc488, 0x7155, 0xc482, 0x7152, 0xc47d, 0x714f, 0xc477,
+  0x714c, 0xc472, 0x7149, 0xc46c, 0x7146, 0xc467, 0x7143, 0xc461,
+  0x7141, 0xc45b, 0x713e, 0xc456, 0x713b, 0xc450, 0x7138, 0xc44b,
+  0x7135, 0xc445, 0x7132, 0xc440, 0x712f, 0xc43a, 0x712c, 0xc434,
+  0x7129, 0xc42f, 0x7126, 0xc429, 0x7123, 0xc424, 0x7120, 0xc41e,
+  0x711d, 0xc419, 0x711a, 0xc413, 0x7117, 0xc40e, 0x7114, 0xc408,
+  0x7112, 0xc403, 0x710f, 0xc3fd, 0x710c, 0xc3f7, 0x7109, 0xc3f2,
+  0x7106, 0xc3ec, 0x7103, 0xc3e7, 0x7100, 0xc3e1, 0x70fd, 0xc3dc,
+  0x70fa, 0xc3d6, 0x70f7, 0xc3d1, 0x70f4, 0xc3cb, 0x70f1, 0xc3c5,
+  0x70ee, 0xc3c0, 0x70eb, 0xc3ba, 0x70e8, 0xc3b5, 0x70e5, 0xc3af,
+  0x70e2, 0xc3aa, 0x70df, 0xc3a4, 0x70dc, 0xc39f, 0x70d9, 0xc399,
+  0x70d6, 0xc394, 0x70d3, 0xc38e, 0x70d1, 0xc389, 0x70ce, 0xc383,
+  0x70cb, 0xc37d, 0x70c8, 0xc378, 0x70c5, 0xc372, 0x70c2, 0xc36d,
+  0x70bf, 0xc367, 0x70bc, 0xc362, 0x70b9, 0xc35c, 0x70b6, 0xc357,
+  0x70b3, 0xc351, 0x70b0, 0xc34c, 0x70ad, 0xc346, 0x70aa, 0xc341,
+  0x70a7, 0xc33b, 0x70a4, 0xc336, 0x70a1, 0xc330, 0x709e, 0xc32a,
+  0x709b, 0xc325, 0x7098, 0xc31f, 0x7095, 0xc31a, 0x7092, 0xc314,
+  0x708f, 0xc30f, 0x708c, 0xc309, 0x7089, 0xc304, 0x7086, 0xc2fe,
+  0x7083, 0xc2f9, 0x7080, 0xc2f3, 0x707d, 0xc2ee, 0x707a, 0xc2e8,
+  0x7077, 0xc2e3, 0x7074, 0xc2dd, 0x7071, 0xc2d8, 0x706e, 0xc2d2,
+  0x706b, 0xc2cd, 0x7068, 0xc2c7, 0x7065, 0xc2c2, 0x7062, 0xc2bc,
+  0x705f, 0xc2b7, 0x705c, 0xc2b1, 0x7059, 0xc2ab, 0x7056, 0xc2a6,
+  0x7053, 0xc2a0, 0x7050, 0xc29b, 0x704d, 0xc295, 0x704a, 0xc290,
+  0x7047, 0xc28a, 0x7044, 0xc285, 0x7041, 0xc27f, 0x703e, 0xc27a,
+  0x703b, 0xc274, 0x7038, 0xc26f, 0x7035, 0xc269, 0x7032, 0xc264,
+  0x702f, 0xc25e, 0x702c, 0xc259, 0x7029, 0xc253, 0x7026, 0xc24e,
+  0x7023, 0xc248, 0x7020, 0xc243, 0x701d, 0xc23d, 0x7019, 0xc238,
+  0x7016, 0xc232, 0x7013, 0xc22d, 0x7010, 0xc227, 0x700d, 0xc222,
+  0x700a, 0xc21c, 0x7007, 0xc217, 0x7004, 0xc211, 0x7001, 0xc20c,
+  0x6ffe, 0xc206, 0x6ffb, 0xc201, 0x6ff8, 0xc1fb, 0x6ff5, 0xc1f6,
+  0x6ff2, 0xc1f0, 0x6fef, 0xc1eb, 0x6fec, 0xc1e5, 0x6fe9, 0xc1e0,
+  0x6fe6, 0xc1da, 0x6fe3, 0xc1d5, 0x6fe0, 0xc1cf, 0x6fdd, 0xc1ca,
+  0x6fda, 0xc1c4, 0x6fd6, 0xc1bf, 0x6fd3, 0xc1b9, 0x6fd0, 0xc1b4,
+  0x6fcd, 0xc1ae, 0x6fca, 0xc1a9, 0x6fc7, 0xc1a3, 0x6fc4, 0xc19e,
+  0x6fc1, 0xc198, 0x6fbe, 0xc193, 0x6fbb, 0xc18d, 0x6fb8, 0xc188,
+  0x6fb5, 0xc183, 0x6fb2, 0xc17d, 0x6faf, 0xc178, 0x6fac, 0xc172,
+  0x6fa9, 0xc16d, 0x6fa5, 0xc167, 0x6fa2, 0xc162, 0x6f9f, 0xc15c,
+  0x6f9c, 0xc157, 0x6f99, 0xc151, 0x6f96, 0xc14c, 0x6f93, 0xc146,
+  0x6f90, 0xc141, 0x6f8d, 0xc13b, 0x6f8a, 0xc136, 0x6f87, 0xc130,
+  0x6f84, 0xc12b, 0x6f81, 0xc125, 0x6f7d, 0xc120, 0x6f7a, 0xc11a,
+  0x6f77, 0xc115, 0x6f74, 0xc10f, 0x6f71, 0xc10a, 0x6f6e, 0xc105,
+  0x6f6b, 0xc0ff, 0x6f68, 0xc0fa, 0x6f65, 0xc0f4, 0x6f62, 0xc0ef,
+  0x6f5f, 0xc0e9, 0x6f5b, 0xc0e4, 0x6f58, 0xc0de, 0x6f55, 0xc0d9,
+  0x6f52, 0xc0d3, 0x6f4f, 0xc0ce, 0x6f4c, 0xc0c8, 0x6f49, 0xc0c3,
+  0x6f46, 0xc0bd, 0x6f43, 0xc0b8, 0x6f3f, 0xc0b3, 0x6f3c, 0xc0ad,
+  0x6f39, 0xc0a8, 0x6f36, 0xc0a2, 0x6f33, 0xc09d, 0x6f30, 0xc097,
+  0x6f2d, 0xc092, 0x6f2a, 0xc08c, 0x6f27, 0xc087, 0x6f23, 0xc081,
+  0x6f20, 0xc07c, 0x6f1d, 0xc077, 0x6f1a, 0xc071, 0x6f17, 0xc06c,
+  0x6f14, 0xc066, 0x6f11, 0xc061, 0x6f0e, 0xc05b, 0x6f0b, 0xc056,
+  0x6f07, 0xc050, 0x6f04, 0xc04b, 0x6f01, 0xc045, 0x6efe, 0xc040,
+  0x6efb, 0xc03b, 0x6ef8, 0xc035, 0x6ef5, 0xc030, 0x6ef1, 0xc02a,
+  0x6eee, 0xc025, 0x6eeb, 0xc01f, 0x6ee8, 0xc01a, 0x6ee5, 0xc014,
+  0x6ee2, 0xc00f, 0x6edf, 0xc00a, 0x6edc, 0xc004, 0x6ed8, 0xbfff,
+  0x6ed5, 0xbff9, 0x6ed2, 0xbff4, 0x6ecf, 0xbfee, 0x6ecc, 0xbfe9,
+  0x6ec9, 0xbfe3, 0x6ec6, 0xbfde, 0x6ec2, 0xbfd9, 0x6ebf, 0xbfd3,
+  0x6ebc, 0xbfce, 0x6eb9, 0xbfc8, 0x6eb6, 0xbfc3, 0x6eb3, 0xbfbd,
+  0x6eaf, 0xbfb8, 0x6eac, 0xbfb3, 0x6ea9, 0xbfad, 0x6ea6, 0xbfa8,
+  0x6ea3, 0xbfa2, 0x6ea0, 0xbf9d, 0x6e9c, 0xbf97, 0x6e99, 0xbf92,
+  0x6e96, 0xbf8d, 0x6e93, 0xbf87, 0x6e90, 0xbf82, 0x6e8d, 0xbf7c,
+  0x6e89, 0xbf77, 0x6e86, 0xbf71, 0x6e83, 0xbf6c, 0x6e80, 0xbf67,
+  0x6e7d, 0xbf61, 0x6e7a, 0xbf5c, 0x6e76, 0xbf56, 0x6e73, 0xbf51,
+  0x6e70, 0xbf4b, 0x6e6d, 0xbf46, 0x6e6a, 0xbf41, 0x6e67, 0xbf3b,
+  0x6e63, 0xbf36, 0x6e60, 0xbf30, 0x6e5d, 0xbf2b, 0x6e5a, 0xbf26,
+  0x6e57, 0xbf20, 0x6e53, 0xbf1b, 0x6e50, 0xbf15, 0x6e4d, 0xbf10,
+  0x6e4a, 0xbf0a, 0x6e47, 0xbf05, 0x6e44, 0xbf00, 0x6e40, 0xbefa,
+  0x6e3d, 0xbef5, 0x6e3a, 0xbeef, 0x6e37, 0xbeea, 0x6e34, 0xbee5,
+  0x6e30, 0xbedf, 0x6e2d, 0xbeda, 0x6e2a, 0xbed4, 0x6e27, 0xbecf,
+  0x6e24, 0xbeca, 0x6e20, 0xbec4, 0x6e1d, 0xbebf, 0x6e1a, 0xbeb9,
+  0x6e17, 0xbeb4, 0x6e14, 0xbeae, 0x6e10, 0xbea9, 0x6e0d, 0xbea4,
+  0x6e0a, 0xbe9e, 0x6e07, 0xbe99, 0x6e04, 0xbe93, 0x6e00, 0xbe8e,
+  0x6dfd, 0xbe89, 0x6dfa, 0xbe83, 0x6df7, 0xbe7e, 0x6df3, 0xbe78,
+  0x6df0, 0xbe73, 0x6ded, 0xbe6e, 0x6dea, 0xbe68, 0x6de7, 0xbe63,
+  0x6de3, 0xbe5e, 0x6de0, 0xbe58, 0x6ddd, 0xbe53, 0x6dda, 0xbe4d,
+  0x6dd6, 0xbe48, 0x6dd3, 0xbe43, 0x6dd0, 0xbe3d, 0x6dcd, 0xbe38,
+  0x6dca, 0xbe32, 0x6dc6, 0xbe2d, 0x6dc3, 0xbe28, 0x6dc0, 0xbe22,
+  0x6dbd, 0xbe1d, 0x6db9, 0xbe17, 0x6db6, 0xbe12, 0x6db3, 0xbe0d,
+  0x6db0, 0xbe07, 0x6dac, 0xbe02, 0x6da9, 0xbdfd, 0x6da6, 0xbdf7,
+  0x6da3, 0xbdf2, 0x6d9f, 0xbdec, 0x6d9c, 0xbde7, 0x6d99, 0xbde2,
+  0x6d96, 0xbddc, 0x6d92, 0xbdd7, 0x6d8f, 0xbdd1, 0x6d8c, 0xbdcc,
+  0x6d89, 0xbdc7, 0x6d85, 0xbdc1, 0x6d82, 0xbdbc, 0x6d7f, 0xbdb7,
+  0x6d7c, 0xbdb1, 0x6d78, 0xbdac, 0x6d75, 0xbda6, 0x6d72, 0xbda1,
+  0x6d6f, 0xbd9c, 0x6d6b, 0xbd96, 0x6d68, 0xbd91, 0x6d65, 0xbd8c,
+  0x6d62, 0xbd86, 0x6d5e, 0xbd81, 0x6d5b, 0xbd7c, 0x6d58, 0xbd76,
+  0x6d55, 0xbd71, 0x6d51, 0xbd6b, 0x6d4e, 0xbd66, 0x6d4b, 0xbd61,
+  0x6d48, 0xbd5b, 0x6d44, 0xbd56, 0x6d41, 0xbd51, 0x6d3e, 0xbd4b,
+  0x6d3a, 0xbd46, 0x6d37, 0xbd40, 0x6d34, 0xbd3b, 0x6d31, 0xbd36,
+  0x6d2d, 0xbd30, 0x6d2a, 0xbd2b, 0x6d27, 0xbd26, 0x6d23, 0xbd20,
+  0x6d20, 0xbd1b, 0x6d1d, 0xbd16, 0x6d1a, 0xbd10, 0x6d16, 0xbd0b,
+  0x6d13, 0xbd06, 0x6d10, 0xbd00, 0x6d0c, 0xbcfb, 0x6d09, 0xbcf5,
+  0x6d06, 0xbcf0, 0x6d03, 0xbceb, 0x6cff, 0xbce5, 0x6cfc, 0xbce0,
+  0x6cf9, 0xbcdb, 0x6cf5, 0xbcd5, 0x6cf2, 0xbcd0, 0x6cef, 0xbccb,
+  0x6cec, 0xbcc5, 0x6ce8, 0xbcc0, 0x6ce5, 0xbcbb, 0x6ce2, 0xbcb5,
+  0x6cde, 0xbcb0, 0x6cdb, 0xbcab, 0x6cd8, 0xbca5, 0x6cd4, 0xbca0,
+  0x6cd1, 0xbc9b, 0x6cce, 0xbc95, 0x6cca, 0xbc90, 0x6cc7, 0xbc8b,
+  0x6cc4, 0xbc85, 0x6cc1, 0xbc80, 0x6cbd, 0xbc7b, 0x6cba, 0xbc75,
+  0x6cb7, 0xbc70, 0x6cb3, 0xbc6b, 0x6cb0, 0xbc65, 0x6cad, 0xbc60,
+  0x6ca9, 0xbc5b, 0x6ca6, 0xbc55, 0x6ca3, 0xbc50, 0x6c9f, 0xbc4b,
+  0x6c9c, 0xbc45, 0x6c99, 0xbc40, 0x6c95, 0xbc3b, 0x6c92, 0xbc35,
+  0x6c8f, 0xbc30, 0x6c8b, 0xbc2b, 0x6c88, 0xbc25, 0x6c85, 0xbc20,
+  0x6c81, 0xbc1b, 0x6c7e, 0xbc15, 0x6c7b, 0xbc10, 0x6c77, 0xbc0b,
+  0x6c74, 0xbc05, 0x6c71, 0xbc00, 0x6c6d, 0xbbfb, 0x6c6a, 0xbbf5,
+  0x6c67, 0xbbf0, 0x6c63, 0xbbeb, 0x6c60, 0xbbe5, 0x6c5d, 0xbbe0,
+  0x6c59, 0xbbdb, 0x6c56, 0xbbd5, 0x6c53, 0xbbd0, 0x6c4f, 0xbbcb,
+  0x6c4c, 0xbbc5, 0x6c49, 0xbbc0, 0x6c45, 0xbbbb, 0x6c42, 0xbbb5,
+  0x6c3f, 0xbbb0, 0x6c3b, 0xbbab, 0x6c38, 0xbba6, 0x6c34, 0xbba0,
+  0x6c31, 0xbb9b, 0x6c2e, 0xbb96, 0x6c2a, 0xbb90, 0x6c27, 0xbb8b,
+  0x6c24, 0xbb86, 0x6c20, 0xbb80, 0x6c1d, 0xbb7b, 0x6c1a, 0xbb76,
+  0x6c16, 0xbb70, 0x6c13, 0xbb6b, 0x6c0f, 0xbb66, 0x6c0c, 0xbb61,
+  0x6c09, 0xbb5b, 0x6c05, 0xbb56, 0x6c02, 0xbb51, 0x6bff, 0xbb4b,
+  0x6bfb, 0xbb46, 0x6bf8, 0xbb41, 0x6bf5, 0xbb3b, 0x6bf1, 0xbb36,
+  0x6bee, 0xbb31, 0x6bea, 0xbb2c, 0x6be7, 0xbb26, 0x6be4, 0xbb21,
+  0x6be0, 0xbb1c, 0x6bdd, 0xbb16, 0x6bd9, 0xbb11, 0x6bd6, 0xbb0c,
+  0x6bd3, 0xbb06, 0x6bcf, 0xbb01, 0x6bcc, 0xbafc, 0x6bc9, 0xbaf7,
+  0x6bc5, 0xbaf1, 0x6bc2, 0xbaec, 0x6bbe, 0xbae7, 0x6bbb, 0xbae1,
+  0x6bb8, 0xbadc, 0x6bb4, 0xbad7, 0x6bb1, 0xbad2, 0x6bad, 0xbacc,
+  0x6baa, 0xbac7, 0x6ba7, 0xbac2, 0x6ba3, 0xbabc, 0x6ba0, 0xbab7,
+  0x6b9c, 0xbab2, 0x6b99, 0xbaad, 0x6b96, 0xbaa7, 0x6b92, 0xbaa2,
+  0x6b8f, 0xba9d, 0x6b8b, 0xba97, 0x6b88, 0xba92, 0x6b85, 0xba8d,
+  0x6b81, 0xba88, 0x6b7e, 0xba82, 0x6b7a, 0xba7d, 0x6b77, 0xba78,
+  0x6b73, 0xba73, 0x6b70, 0xba6d, 0x6b6d, 0xba68, 0x6b69, 0xba63,
+  0x6b66, 0xba5d, 0x6b62, 0xba58, 0x6b5f, 0xba53, 0x6b5c, 0xba4e,
+  0x6b58, 0xba48, 0x6b55, 0xba43, 0x6b51, 0xba3e, 0x6b4e, 0xba39,
+  0x6b4a, 0xba33, 0x6b47, 0xba2e, 0x6b44, 0xba29, 0x6b40, 0xba23,
+  0x6b3d, 0xba1e, 0x6b39, 0xba19, 0x6b36, 0xba14, 0x6b32, 0xba0e,
+  0x6b2f, 0xba09, 0x6b2c, 0xba04, 0x6b28, 0xb9ff, 0x6b25, 0xb9f9,
+  0x6b21, 0xb9f4, 0x6b1e, 0xb9ef, 0x6b1a, 0xb9ea, 0x6b17, 0xb9e4,
+  0x6b13, 0xb9df, 0x6b10, 0xb9da, 0x6b0d, 0xb9d5, 0x6b09, 0xb9cf,
+  0x6b06, 0xb9ca, 0x6b02, 0xb9c5, 0x6aff, 0xb9c0, 0x6afb, 0xb9ba,
+  0x6af8, 0xb9b5, 0x6af4, 0xb9b0, 0x6af1, 0xb9ab, 0x6aee, 0xb9a5,
+  0x6aea, 0xb9a0, 0x6ae7, 0xb99b, 0x6ae3, 0xb996, 0x6ae0, 0xb990,
+  0x6adc, 0xb98b, 0x6ad9, 0xb986, 0x6ad5, 0xb981, 0x6ad2, 0xb97b,
+  0x6ace, 0xb976, 0x6acb, 0xb971, 0x6ac8, 0xb96c, 0x6ac4, 0xb966,
+  0x6ac1, 0xb961, 0x6abd, 0xb95c, 0x6aba, 0xb957, 0x6ab6, 0xb951,
+  0x6ab3, 0xb94c, 0x6aaf, 0xb947, 0x6aac, 0xb942, 0x6aa8, 0xb93c,
+  0x6aa5, 0xb937, 0x6aa1, 0xb932, 0x6a9e, 0xb92d, 0x6a9a, 0xb928,
+  0x6a97, 0xb922, 0x6a93, 0xb91d, 0x6a90, 0xb918, 0x6a8c, 0xb913,
+  0x6a89, 0xb90d, 0x6a86, 0xb908, 0x6a82, 0xb903, 0x6a7f, 0xb8fe,
+  0x6a7b, 0xb8f8, 0x6a78, 0xb8f3, 0x6a74, 0xb8ee, 0x6a71, 0xb8e9,
+  0x6a6d, 0xb8e4, 0x6a6a, 0xb8de, 0x6a66, 0xb8d9, 0x6a63, 0xb8d4,
+  0x6a5f, 0xb8cf, 0x6a5c, 0xb8c9, 0x6a58, 0xb8c4, 0x6a55, 0xb8bf,
+  0x6a51, 0xb8ba, 0x6a4e, 0xb8b5, 0x6a4a, 0xb8af, 0x6a47, 0xb8aa,
+  0x6a43, 0xb8a5, 0x6a40, 0xb8a0, 0x6a3c, 0xb89b, 0x6a39, 0xb895,
+  0x6a35, 0xb890, 0x6a32, 0xb88b, 0x6a2e, 0xb886, 0x6a2b, 0xb880,
+  0x6a27, 0xb87b, 0x6a24, 0xb876, 0x6a20, 0xb871, 0x6a1d, 0xb86c,
+  0x6a19, 0xb866, 0x6a16, 0xb861, 0x6a12, 0xb85c, 0x6a0e, 0xb857,
+  0x6a0b, 0xb852, 0x6a07, 0xb84c, 0x6a04, 0xb847, 0x6a00, 0xb842,
+  0x69fd, 0xb83d, 0x69f9, 0xb838, 0x69f6, 0xb832, 0x69f2, 0xb82d,
+  0x69ef, 0xb828, 0x69eb, 0xb823, 0x69e8, 0xb81e, 0x69e4, 0xb818,
+  0x69e1, 0xb813, 0x69dd, 0xb80e, 0x69da, 0xb809, 0x69d6, 0xb804,
+  0x69d3, 0xb7fe, 0x69cf, 0xb7f9, 0x69cb, 0xb7f4, 0x69c8, 0xb7ef,
+  0x69c4, 0xb7ea, 0x69c1, 0xb7e4, 0x69bd, 0xb7df, 0x69ba, 0xb7da,
+  0x69b6, 0xb7d5, 0x69b3, 0xb7d0, 0x69af, 0xb7ca, 0x69ac, 0xb7c5,
+  0x69a8, 0xb7c0, 0x69a5, 0xb7bb, 0x69a1, 0xb7b6, 0x699d, 0xb7b1,
+  0x699a, 0xb7ab, 0x6996, 0xb7a6, 0x6993, 0xb7a1, 0x698f, 0xb79c,
+  0x698c, 0xb797, 0x6988, 0xb791, 0x6985, 0xb78c, 0x6981, 0xb787,
+  0x697d, 0xb782, 0x697a, 0xb77d, 0x6976, 0xb778, 0x6973, 0xb772,
+  0x696f, 0xb76d, 0x696c, 0xb768, 0x6968, 0xb763, 0x6964, 0xb75e,
+  0x6961, 0xb758, 0x695d, 0xb753, 0x695a, 0xb74e, 0x6956, 0xb749,
+  0x6953, 0xb744, 0x694f, 0xb73f, 0x694b, 0xb739, 0x6948, 0xb734,
+  0x6944, 0xb72f, 0x6941, 0xb72a, 0x693d, 0xb725, 0x693a, 0xb720,
+  0x6936, 0xb71a, 0x6932, 0xb715, 0x692f, 0xb710, 0x692b, 0xb70b,
+  0x6928, 0xb706, 0x6924, 0xb701, 0x6921, 0xb6fb, 0x691d, 0xb6f6,
+  0x6919, 0xb6f1, 0x6916, 0xb6ec, 0x6912, 0xb6e7, 0x690f, 0xb6e2,
+  0x690b, 0xb6dd, 0x6907, 0xb6d7, 0x6904, 0xb6d2, 0x6900, 0xb6cd,
+  0x68fd, 0xb6c8, 0x68f9, 0xb6c3, 0x68f5, 0xb6be, 0x68f2, 0xb6b8,
+  0x68ee, 0xb6b3, 0x68eb, 0xb6ae, 0x68e7, 0xb6a9, 0x68e3, 0xb6a4,
+  0x68e0, 0xb69f, 0x68dc, 0xb69a, 0x68d9, 0xb694, 0x68d5, 0xb68f,
+  0x68d1, 0xb68a, 0x68ce, 0xb685, 0x68ca, 0xb680, 0x68c7, 0xb67b,
+  0x68c3, 0xb676, 0x68bf, 0xb670, 0x68bc, 0xb66b, 0x68b8, 0xb666,
+  0x68b5, 0xb661, 0x68b1, 0xb65c, 0x68ad, 0xb657, 0x68aa, 0xb652,
+  0x68a6, 0xb64c, 0x68a3, 0xb647, 0x689f, 0xb642, 0x689b, 0xb63d,
+  0x6898, 0xb638, 0x6894, 0xb633, 0x6890, 0xb62e, 0x688d, 0xb628,
+  0x6889, 0xb623, 0x6886, 0xb61e, 0x6882, 0xb619, 0x687e, 0xb614,
+  0x687b, 0xb60f, 0x6877, 0xb60a, 0x6873, 0xb605, 0x6870, 0xb5ff,
+  0x686c, 0xb5fa, 0x6868, 0xb5f5, 0x6865, 0xb5f0, 0x6861, 0xb5eb,
+  0x685e, 0xb5e6, 0x685a, 0xb5e1, 0x6856, 0xb5dc, 0x6853, 0xb5d6,
+  0x684f, 0xb5d1, 0x684b, 0xb5cc, 0x6848, 0xb5c7, 0x6844, 0xb5c2,
+  0x6840, 0xb5bd, 0x683d, 0xb5b8, 0x6839, 0xb5b3, 0x6835, 0xb5ae,
+  0x6832, 0xb5a8, 0x682e, 0xb5a3, 0x682b, 0xb59e, 0x6827, 0xb599,
+  0x6823, 0xb594, 0x6820, 0xb58f, 0x681c, 0xb58a, 0x6818, 0xb585,
+  0x6815, 0xb57f, 0x6811, 0xb57a, 0x680d, 0xb575, 0x680a, 0xb570,
+  0x6806, 0xb56b, 0x6802, 0xb566, 0x67ff, 0xb561, 0x67fb, 0xb55c,
+  0x67f7, 0xb557, 0x67f4, 0xb552, 0x67f0, 0xb54c, 0x67ec, 0xb547,
+  0x67e9, 0xb542, 0x67e5, 0xb53d, 0x67e1, 0xb538, 0x67de, 0xb533,
+  0x67da, 0xb52e, 0x67d6, 0xb529, 0x67d3, 0xb524, 0x67cf, 0xb51f,
+  0x67cb, 0xb519, 0x67c8, 0xb514, 0x67c4, 0xb50f, 0x67c0, 0xb50a,
+  0x67bd, 0xb505, 0x67b9, 0xb500, 0x67b5, 0xb4fb, 0x67b2, 0xb4f6,
+  0x67ae, 0xb4f1, 0x67aa, 0xb4ec, 0x67a6, 0xb4e7, 0x67a3, 0xb4e1,
+  0x679f, 0xb4dc, 0x679b, 0xb4d7, 0x6798, 0xb4d2, 0x6794, 0xb4cd,
+  0x6790, 0xb4c8, 0x678d, 0xb4c3, 0x6789, 0xb4be, 0x6785, 0xb4b9,
+  0x6782, 0xb4b4, 0x677e, 0xb4af, 0x677a, 0xb4aa, 0x6776, 0xb4a4,
+  0x6773, 0xb49f, 0x676f, 0xb49a, 0x676b, 0xb495, 0x6768, 0xb490,
+  0x6764, 0xb48b, 0x6760, 0xb486, 0x675d, 0xb481, 0x6759, 0xb47c,
+  0x6755, 0xb477, 0x6751, 0xb472, 0x674e, 0xb46d, 0x674a, 0xb468,
+  0x6746, 0xb462, 0x6743, 0xb45d, 0x673f, 0xb458, 0x673b, 0xb453,
+  0x6737, 0xb44e, 0x6734, 0xb449, 0x6730, 0xb444, 0x672c, 0xb43f,
+  0x6729, 0xb43a, 0x6725, 0xb435, 0x6721, 0xb430, 0x671d, 0xb42b,
+  0x671a, 0xb426, 0x6716, 0xb421, 0x6712, 0xb41c, 0x670e, 0xb417,
+  0x670b, 0xb411, 0x6707, 0xb40c, 0x6703, 0xb407, 0x6700, 0xb402,
+  0x66fc, 0xb3fd, 0x66f8, 0xb3f8, 0x66f4, 0xb3f3, 0x66f1, 0xb3ee,
+  0x66ed, 0xb3e9, 0x66e9, 0xb3e4, 0x66e5, 0xb3df, 0x66e2, 0xb3da,
+  0x66de, 0xb3d5, 0x66da, 0xb3d0, 0x66d6, 0xb3cb, 0x66d3, 0xb3c6,
+  0x66cf, 0xb3c1, 0x66cb, 0xb3bc, 0x66c8, 0xb3b7, 0x66c4, 0xb3b1,
+  0x66c0, 0xb3ac, 0x66bc, 0xb3a7, 0x66b9, 0xb3a2, 0x66b5, 0xb39d,
+  0x66b1, 0xb398, 0x66ad, 0xb393, 0x66aa, 0xb38e, 0x66a6, 0xb389,
+  0x66a2, 0xb384, 0x669e, 0xb37f, 0x669b, 0xb37a, 0x6697, 0xb375,
+  0x6693, 0xb370, 0x668f, 0xb36b, 0x668b, 0xb366, 0x6688, 0xb361,
+  0x6684, 0xb35c, 0x6680, 0xb357, 0x667c, 0xb352, 0x6679, 0xb34d,
+  0x6675, 0xb348, 0x6671, 0xb343, 0x666d, 0xb33e, 0x666a, 0xb339,
+  0x6666, 0xb334, 0x6662, 0xb32f, 0x665e, 0xb32a, 0x665b, 0xb325,
+  0x6657, 0xb31f, 0x6653, 0xb31a, 0x664f, 0xb315, 0x664b, 0xb310,
+  0x6648, 0xb30b, 0x6644, 0xb306, 0x6640, 0xb301, 0x663c, 0xb2fc,
+  0x6639, 0xb2f7, 0x6635, 0xb2f2, 0x6631, 0xb2ed, 0x662d, 0xb2e8,
+  0x6629, 0xb2e3, 0x6626, 0xb2de, 0x6622, 0xb2d9, 0x661e, 0xb2d4,
+  0x661a, 0xb2cf, 0x6616, 0xb2ca, 0x6613, 0xb2c5, 0x660f, 0xb2c0,
+  0x660b, 0xb2bb, 0x6607, 0xb2b6, 0x6603, 0xb2b1, 0x6600, 0xb2ac,
+  0x65fc, 0xb2a7, 0x65f8, 0xb2a2, 0x65f4, 0xb29d, 0x65f0, 0xb298,
+  0x65ed, 0xb293, 0x65e9, 0xb28e, 0x65e5, 0xb289, 0x65e1, 0xb284,
+  0x65dd, 0xb27f, 0x65da, 0xb27a, 0x65d6, 0xb275, 0x65d2, 0xb270,
+  0x65ce, 0xb26b, 0x65ca, 0xb266, 0x65c7, 0xb261, 0x65c3, 0xb25c,
+  0x65bf, 0xb257, 0x65bb, 0xb252, 0x65b7, 0xb24d, 0x65b4, 0xb248,
+  0x65b0, 0xb243, 0x65ac, 0xb23e, 0x65a8, 0xb239, 0x65a4, 0xb234,
+  0x65a0, 0xb22f, 0x659d, 0xb22a, 0x6599, 0xb225, 0x6595, 0xb220,
+  0x6591, 0xb21b, 0x658d, 0xb216, 0x658a, 0xb211, 0x6586, 0xb20c,
+  0x6582, 0xb207, 0x657e, 0xb202, 0x657a, 0xb1fd, 0x6576, 0xb1f8,
+  0x6573, 0xb1f3, 0x656f, 0xb1ee, 0x656b, 0xb1e9, 0x6567, 0xb1e4,
+  0x6563, 0xb1df, 0x655f, 0xb1da, 0x655c, 0xb1d6, 0x6558, 0xb1d1,
+  0x6554, 0xb1cc, 0x6550, 0xb1c7, 0x654c, 0xb1c2, 0x6548, 0xb1bd,
+  0x6545, 0xb1b8, 0x6541, 0xb1b3, 0x653d, 0xb1ae, 0x6539, 0xb1a9,
+  0x6535, 0xb1a4, 0x6531, 0xb19f, 0x652d, 0xb19a, 0x652a, 0xb195,
+  0x6526, 0xb190, 0x6522, 0xb18b, 0x651e, 0xb186, 0x651a, 0xb181,
+  0x6516, 0xb17c, 0x6513, 0xb177, 0x650f, 0xb172, 0x650b, 0xb16d,
+  0x6507, 0xb168, 0x6503, 0xb163, 0x64ff, 0xb15e, 0x64fb, 0xb159,
+  0x64f7, 0xb154, 0x64f4, 0xb14f, 0x64f0, 0xb14a, 0x64ec, 0xb146,
+  0x64e8, 0xb141, 0x64e4, 0xb13c, 0x64e0, 0xb137, 0x64dc, 0xb132,
+  0x64d9, 0xb12d, 0x64d5, 0xb128, 0x64d1, 0xb123, 0x64cd, 0xb11e,
+  0x64c9, 0xb119, 0x64c5, 0xb114, 0x64c1, 0xb10f, 0x64bd, 0xb10a,
+  0x64ba, 0xb105, 0x64b6, 0xb100, 0x64b2, 0xb0fb, 0x64ae, 0xb0f6,
+  0x64aa, 0xb0f1, 0x64a6, 0xb0ec, 0x64a2, 0xb0e8, 0x649e, 0xb0e3,
+  0x649b, 0xb0de, 0x6497, 0xb0d9, 0x6493, 0xb0d4, 0x648f, 0xb0cf,
+  0x648b, 0xb0ca, 0x6487, 0xb0c5, 0x6483, 0xb0c0, 0x647f, 0xb0bb,
+  0x647b, 0xb0b6, 0x6478, 0xb0b1, 0x6474, 0xb0ac, 0x6470, 0xb0a7,
+  0x646c, 0xb0a2, 0x6468, 0xb09e, 0x6464, 0xb099, 0x6460, 0xb094,
+  0x645c, 0xb08f, 0x6458, 0xb08a, 0x6454, 0xb085, 0x6451, 0xb080,
+  0x644d, 0xb07b, 0x6449, 0xb076, 0x6445, 0xb071, 0x6441, 0xb06c,
+  0x643d, 0xb067, 0x6439, 0xb062, 0x6435, 0xb05e, 0x6431, 0xb059,
+  0x642d, 0xb054, 0x6429, 0xb04f, 0x6426, 0xb04a, 0x6422, 0xb045,
+  0x641e, 0xb040, 0x641a, 0xb03b, 0x6416, 0xb036, 0x6412, 0xb031,
+  0x640e, 0xb02c, 0x640a, 0xb027, 0x6406, 0xb023, 0x6402, 0xb01e,
+  0x63fe, 0xb019, 0x63fa, 0xb014, 0x63f7, 0xb00f, 0x63f3, 0xb00a,
+  0x63ef, 0xb005, 0x63eb, 0xb000, 0x63e7, 0xaffb, 0x63e3, 0xaff6,
+  0x63df, 0xaff1, 0x63db, 0xafed, 0x63d7, 0xafe8, 0x63d3, 0xafe3,
+  0x63cf, 0xafde, 0x63cb, 0xafd9, 0x63c7, 0xafd4, 0x63c3, 0xafcf,
+  0x63c0, 0xafca, 0x63bc, 0xafc5, 0x63b8, 0xafc1, 0x63b4, 0xafbc,
+  0x63b0, 0xafb7, 0x63ac, 0xafb2, 0x63a8, 0xafad, 0x63a4, 0xafa8,
+  0x63a0, 0xafa3, 0x639c, 0xaf9e, 0x6398, 0xaf99, 0x6394, 0xaf94,
+  0x6390, 0xaf90, 0x638c, 0xaf8b, 0x6388, 0xaf86, 0x6384, 0xaf81,
+  0x6380, 0xaf7c, 0x637c, 0xaf77, 0x6378, 0xaf72, 0x6375, 0xaf6d,
+  0x6371, 0xaf69, 0x636d, 0xaf64, 0x6369, 0xaf5f, 0x6365, 0xaf5a,
+  0x6361, 0xaf55, 0x635d, 0xaf50, 0x6359, 0xaf4b, 0x6355, 0xaf46,
+  0x6351, 0xaf41, 0x634d, 0xaf3d, 0x6349, 0xaf38, 0x6345, 0xaf33,
+  0x6341, 0xaf2e, 0x633d, 0xaf29, 0x6339, 0xaf24, 0x6335, 0xaf1f,
+  0x6331, 0xaf1b, 0x632d, 0xaf16, 0x6329, 0xaf11, 0x6325, 0xaf0c,
+  0x6321, 0xaf07, 0x631d, 0xaf02, 0x6319, 0xaefd, 0x6315, 0xaef8,
+  0x6311, 0xaef4, 0x630d, 0xaeef, 0x6309, 0xaeea, 0x6305, 0xaee5,
+  0x6301, 0xaee0, 0x62fd, 0xaedb, 0x62f9, 0xaed6, 0x62f5, 0xaed2,
+  0x62f2, 0xaecd, 0x62ee, 0xaec8, 0x62ea, 0xaec3, 0x62e6, 0xaebe,
+  0x62e2, 0xaeb9, 0x62de, 0xaeb4, 0x62da, 0xaeb0, 0x62d6, 0xaeab,
+  0x62d2, 0xaea6, 0x62ce, 0xaea1, 0x62ca, 0xae9c, 0x62c6, 0xae97,
+  0x62c2, 0xae92, 0x62be, 0xae8e, 0x62ba, 0xae89, 0x62b6, 0xae84,
+  0x62b2, 0xae7f, 0x62ae, 0xae7a, 0x62aa, 0xae75, 0x62a6, 0xae71,
+  0x62a2, 0xae6c, 0x629e, 0xae67, 0x629a, 0xae62, 0x6296, 0xae5d,
+  0x6292, 0xae58, 0x628e, 0xae54, 0x628a, 0xae4f, 0x6286, 0xae4a,
+  0x6282, 0xae45, 0x627e, 0xae40, 0x627a, 0xae3b, 0x6275, 0xae37,
+  0x6271, 0xae32, 0x626d, 0xae2d, 0x6269, 0xae28, 0x6265, 0xae23,
+  0x6261, 0xae1e, 0x625d, 0xae1a, 0x6259, 0xae15, 0x6255, 0xae10,
+  0x6251, 0xae0b, 0x624d, 0xae06, 0x6249, 0xae01, 0x6245, 0xadfd,
+  0x6241, 0xadf8, 0x623d, 0xadf3, 0x6239, 0xadee, 0x6235, 0xade9,
+  0x6231, 0xade4, 0x622d, 0xade0, 0x6229, 0xaddb, 0x6225, 0xadd6,
+  0x6221, 0xadd1, 0x621d, 0xadcc, 0x6219, 0xadc8, 0x6215, 0xadc3,
+  0x6211, 0xadbe, 0x620d, 0xadb9, 0x6209, 0xadb4, 0x6205, 0xadaf,
+  0x6201, 0xadab, 0x61fd, 0xada6, 0x61f9, 0xada1, 0x61f5, 0xad9c,
+  0x61f1, 0xad97, 0x61ec, 0xad93, 0x61e8, 0xad8e, 0x61e4, 0xad89,
+  0x61e0, 0xad84, 0x61dc, 0xad7f, 0x61d8, 0xad7b, 0x61d4, 0xad76,
+  0x61d0, 0xad71, 0x61cc, 0xad6c, 0x61c8, 0xad67, 0x61c4, 0xad63,
+  0x61c0, 0xad5e, 0x61bc, 0xad59, 0x61b8, 0xad54, 0x61b4, 0xad4f,
+  0x61b0, 0xad4b, 0x61ac, 0xad46, 0x61a8, 0xad41, 0x61a3, 0xad3c,
+  0x619f, 0xad37, 0x619b, 0xad33, 0x6197, 0xad2e, 0x6193, 0xad29,
+  0x618f, 0xad24, 0x618b, 0xad1f, 0x6187, 0xad1b, 0x6183, 0xad16,
+  0x617f, 0xad11, 0x617b, 0xad0c, 0x6177, 0xad08, 0x6173, 0xad03,
+  0x616f, 0xacfe, 0x616b, 0xacf9, 0x6166, 0xacf4, 0x6162, 0xacf0,
+  0x615e, 0xaceb, 0x615a, 0xace6, 0x6156, 0xace1, 0x6152, 0xacdd,
+  0x614e, 0xacd8, 0x614a, 0xacd3, 0x6146, 0xacce, 0x6142, 0xacc9,
+  0x613e, 0xacc5, 0x613a, 0xacc0, 0x6135, 0xacbb, 0x6131, 0xacb6,
+  0x612d, 0xacb2, 0x6129, 0xacad, 0x6125, 0xaca8, 0x6121, 0xaca3,
+  0x611d, 0xac9e, 0x6119, 0xac9a, 0x6115, 0xac95, 0x6111, 0xac90,
+  0x610d, 0xac8b, 0x6108, 0xac87, 0x6104, 0xac82, 0x6100, 0xac7d,
+  0x60fc, 0xac78, 0x60f8, 0xac74, 0x60f4, 0xac6f, 0x60f0, 0xac6a,
+  0x60ec, 0xac65, 0x60e8, 0xac61, 0x60e4, 0xac5c, 0x60df, 0xac57,
+  0x60db, 0xac52, 0x60d7, 0xac4e, 0x60d3, 0xac49, 0x60cf, 0xac44,
+  0x60cb, 0xac3f, 0x60c7, 0xac3b, 0x60c3, 0xac36, 0x60bf, 0xac31,
+  0x60ba, 0xac2c, 0x60b6, 0xac28, 0x60b2, 0xac23, 0x60ae, 0xac1e,
+  0x60aa, 0xac19, 0x60a6, 0xac15, 0x60a2, 0xac10, 0x609e, 0xac0b,
+  0x6099, 0xac06, 0x6095, 0xac02, 0x6091, 0xabfd, 0x608d, 0xabf8,
+  0x6089, 0xabf3, 0x6085, 0xabef, 0x6081, 0xabea, 0x607d, 0xabe5,
+  0x6078, 0xabe0, 0x6074, 0xabdc, 0x6070, 0xabd7, 0x606c, 0xabd2,
+  0x6068, 0xabcd, 0x6064, 0xabc9, 0x6060, 0xabc4, 0x605c, 0xabbf,
+  0x6057, 0xabbb, 0x6053, 0xabb6, 0x604f, 0xabb1, 0x604b, 0xabac,
+  0x6047, 0xaba8, 0x6043, 0xaba3, 0x603f, 0xab9e, 0x603a, 0xab99,
+  0x6036, 0xab95, 0x6032, 0xab90, 0x602e, 0xab8b, 0x602a, 0xab87,
+  0x6026, 0xab82, 0x6022, 0xab7d, 0x601d, 0xab78, 0x6019, 0xab74,
+  0x6015, 0xab6f, 0x6011, 0xab6a, 0x600d, 0xab66, 0x6009, 0xab61,
+  0x6004, 0xab5c, 0x6000, 0xab57, 0x5ffc, 0xab53, 0x5ff8, 0xab4e,
+  0x5ff4, 0xab49, 0x5ff0, 0xab45, 0x5fec, 0xab40, 0x5fe7, 0xab3b,
+  0x5fe3, 0xab36, 0x5fdf, 0xab32, 0x5fdb, 0xab2d, 0x5fd7, 0xab28,
+  0x5fd3, 0xab24, 0x5fce, 0xab1f, 0x5fca, 0xab1a, 0x5fc6, 0xab16,
+  0x5fc2, 0xab11, 0x5fbe, 0xab0c, 0x5fba, 0xab07, 0x5fb5, 0xab03,
+  0x5fb1, 0xaafe, 0x5fad, 0xaaf9, 0x5fa9, 0xaaf5, 0x5fa5, 0xaaf0,
+  0x5fa0, 0xaaeb, 0x5f9c, 0xaae7, 0x5f98, 0xaae2, 0x5f94, 0xaadd,
+  0x5f90, 0xaad8, 0x5f8c, 0xaad4, 0x5f87, 0xaacf, 0x5f83, 0xaaca,
+  0x5f7f, 0xaac6, 0x5f7b, 0xaac1, 0x5f77, 0xaabc, 0x5f72, 0xaab8,
+  0x5f6e, 0xaab3, 0x5f6a, 0xaaae, 0x5f66, 0xaaaa, 0x5f62, 0xaaa5,
+  0x5f5e, 0xaaa0, 0x5f59, 0xaa9c, 0x5f55, 0xaa97, 0x5f51, 0xaa92,
+  0x5f4d, 0xaa8e, 0x5f49, 0xaa89, 0x5f44, 0xaa84, 0x5f40, 0xaa7f,
+  0x5f3c, 0xaa7b, 0x5f38, 0xaa76, 0x5f34, 0xaa71, 0x5f2f, 0xaa6d,
+  0x5f2b, 0xaa68, 0x5f27, 0xaa63, 0x5f23, 0xaa5f, 0x5f1f, 0xaa5a,
+  0x5f1a, 0xaa55, 0x5f16, 0xaa51, 0x5f12, 0xaa4c, 0x5f0e, 0xaa47,
+  0x5f0a, 0xaa43, 0x5f05, 0xaa3e, 0x5f01, 0xaa39, 0x5efd, 0xaa35,
+  0x5ef9, 0xaa30, 0x5ef5, 0xaa2b, 0x5ef0, 0xaa27, 0x5eec, 0xaa22,
+  0x5ee8, 0xaa1d, 0x5ee4, 0xaa19, 0x5edf, 0xaa14, 0x5edb, 0xaa10,
+  0x5ed7, 0xaa0b, 0x5ed3, 0xaa06, 0x5ecf, 0xaa02, 0x5eca, 0xa9fd,
+  0x5ec6, 0xa9f8, 0x5ec2, 0xa9f4, 0x5ebe, 0xa9ef, 0x5eb9, 0xa9ea,
+  0x5eb5, 0xa9e6, 0x5eb1, 0xa9e1, 0x5ead, 0xa9dc, 0x5ea9, 0xa9d8,
+  0x5ea4, 0xa9d3, 0x5ea0, 0xa9ce, 0x5e9c, 0xa9ca, 0x5e98, 0xa9c5,
+  0x5e93, 0xa9c0, 0x5e8f, 0xa9bc, 0x5e8b, 0xa9b7, 0x5e87, 0xa9b3,
+  0x5e82, 0xa9ae, 0x5e7e, 0xa9a9, 0x5e7a, 0xa9a5, 0x5e76, 0xa9a0,
+  0x5e71, 0xa99b, 0x5e6d, 0xa997, 0x5e69, 0xa992, 0x5e65, 0xa98d,
+  0x5e60, 0xa989, 0x5e5c, 0xa984, 0x5e58, 0xa980, 0x5e54, 0xa97b,
+  0x5e50, 0xa976, 0x5e4b, 0xa972, 0x5e47, 0xa96d, 0x5e43, 0xa968,
+  0x5e3f, 0xa964, 0x5e3a, 0xa95f, 0x5e36, 0xa95b, 0x5e32, 0xa956,
+  0x5e2d, 0xa951, 0x5e29, 0xa94d, 0x5e25, 0xa948, 0x5e21, 0xa943,
+  0x5e1c, 0xa93f, 0x5e18, 0xa93a, 0x5e14, 0xa936, 0x5e10, 0xa931,
+  0x5e0b, 0xa92c, 0x5e07, 0xa928, 0x5e03, 0xa923, 0x5dff, 0xa91e,
+  0x5dfa, 0xa91a, 0x5df6, 0xa915, 0x5df2, 0xa911, 0x5dee, 0xa90c,
+  0x5de9, 0xa907, 0x5de5, 0xa903, 0x5de1, 0xa8fe, 0x5ddc, 0xa8fa,
+  0x5dd8, 0xa8f5, 0x5dd4, 0xa8f0, 0x5dd0, 0xa8ec, 0x5dcb, 0xa8e7,
+  0x5dc7, 0xa8e3, 0x5dc3, 0xa8de, 0x5dbf, 0xa8d9, 0x5dba, 0xa8d5,
+  0x5db6, 0xa8d0, 0x5db2, 0xa8cc, 0x5dad, 0xa8c7, 0x5da9, 0xa8c2,
+  0x5da5, 0xa8be, 0x5da1, 0xa8b9, 0x5d9c, 0xa8b5, 0x5d98, 0xa8b0,
+  0x5d94, 0xa8ab, 0x5d8f, 0xa8a7, 0x5d8b, 0xa8a2, 0x5d87, 0xa89e,
+  0x5d83, 0xa899, 0x5d7e, 0xa894, 0x5d7a, 0xa890, 0x5d76, 0xa88b,
+  0x5d71, 0xa887, 0x5d6d, 0xa882, 0x5d69, 0xa87d, 0x5d65, 0xa879,
+  0x5d60, 0xa874, 0x5d5c, 0xa870, 0x5d58, 0xa86b, 0x5d53, 0xa867,
+  0x5d4f, 0xa862, 0x5d4b, 0xa85d, 0x5d46, 0xa859, 0x5d42, 0xa854,
+  0x5d3e, 0xa850, 0x5d3a, 0xa84b, 0x5d35, 0xa847, 0x5d31, 0xa842,
+  0x5d2d, 0xa83d, 0x5d28, 0xa839, 0x5d24, 0xa834, 0x5d20, 0xa830,
+  0x5d1b, 0xa82b, 0x5d17, 0xa827, 0x5d13, 0xa822, 0x5d0e, 0xa81d,
+  0x5d0a, 0xa819, 0x5d06, 0xa814, 0x5d01, 0xa810, 0x5cfd, 0xa80b,
+  0x5cf9, 0xa807, 0x5cf5, 0xa802, 0x5cf0, 0xa7fd, 0x5cec, 0xa7f9,
+  0x5ce8, 0xa7f4, 0x5ce3, 0xa7f0, 0x5cdf, 0xa7eb, 0x5cdb, 0xa7e7,
+  0x5cd6, 0xa7e2, 0x5cd2, 0xa7de, 0x5cce, 0xa7d9, 0x5cc9, 0xa7d4,
+  0x5cc5, 0xa7d0, 0x5cc1, 0xa7cb, 0x5cbc, 0xa7c7, 0x5cb8, 0xa7c2,
+  0x5cb4, 0xa7be, 0x5caf, 0xa7b9, 0x5cab, 0xa7b5, 0x5ca7, 0xa7b0,
+  0x5ca2, 0xa7ab, 0x5c9e, 0xa7a7, 0x5c9a, 0xa7a2, 0x5c95, 0xa79e,
+  0x5c91, 0xa799, 0x5c8d, 0xa795, 0x5c88, 0xa790, 0x5c84, 0xa78c,
+  0x5c80, 0xa787, 0x5c7b, 0xa783, 0x5c77, 0xa77e, 0x5c73, 0xa779,
+  0x5c6e, 0xa775, 0x5c6a, 0xa770, 0x5c66, 0xa76c, 0x5c61, 0xa767,
+  0x5c5d, 0xa763, 0x5c58, 0xa75e, 0x5c54, 0xa75a, 0x5c50, 0xa755,
+  0x5c4b, 0xa751, 0x5c47, 0xa74c, 0x5c43, 0xa748, 0x5c3e, 0xa743,
+  0x5c3a, 0xa73f, 0x5c36, 0xa73a, 0x5c31, 0xa735, 0x5c2d, 0xa731,
+  0x5c29, 0xa72c, 0x5c24, 0xa728, 0x5c20, 0xa723, 0x5c1b, 0xa71f,
+  0x5c17, 0xa71a, 0x5c13, 0xa716, 0x5c0e, 0xa711, 0x5c0a, 0xa70d,
+  0x5c06, 0xa708, 0x5c01, 0xa704, 0x5bfd, 0xa6ff, 0x5bf9, 0xa6fb,
+  0x5bf4, 0xa6f6, 0x5bf0, 0xa6f2, 0x5beb, 0xa6ed, 0x5be7, 0xa6e9,
+  0x5be3, 0xa6e4, 0x5bde, 0xa6e0, 0x5bda, 0xa6db, 0x5bd6, 0xa6d7,
+  0x5bd1, 0xa6d2, 0x5bcd, 0xa6ce, 0x5bc8, 0xa6c9, 0x5bc4, 0xa6c5,
+  0x5bc0, 0xa6c0, 0x5bbb, 0xa6bc, 0x5bb7, 0xa6b7, 0x5bb2, 0xa6b3,
+  0x5bae, 0xa6ae, 0x5baa, 0xa6aa, 0x5ba5, 0xa6a5, 0x5ba1, 0xa6a1,
+  0x5b9d, 0xa69c, 0x5b98, 0xa698, 0x5b94, 0xa693, 0x5b8f, 0xa68f,
+  0x5b8b, 0xa68a, 0x5b87, 0xa686, 0x5b82, 0xa681, 0x5b7e, 0xa67d,
+  0x5b79, 0xa678, 0x5b75, 0xa674, 0x5b71, 0xa66f, 0x5b6c, 0xa66b,
+  0x5b68, 0xa666, 0x5b63, 0xa662, 0x5b5f, 0xa65d, 0x5b5b, 0xa659,
+  0x5b56, 0xa654, 0x5b52, 0xa650, 0x5b4d, 0xa64b, 0x5b49, 0xa647,
+  0x5b45, 0xa642, 0x5b40, 0xa63e, 0x5b3c, 0xa639, 0x5b37, 0xa635,
+  0x5b33, 0xa630, 0x5b2f, 0xa62c, 0x5b2a, 0xa627, 0x5b26, 0xa623,
+  0x5b21, 0xa61f, 0x5b1d, 0xa61a, 0x5b19, 0xa616, 0x5b14, 0xa611,
+  0x5b10, 0xa60d, 0x5b0b, 0xa608, 0x5b07, 0xa604, 0x5b02, 0xa5ff,
+  0x5afe, 0xa5fb, 0x5afa, 0xa5f6, 0x5af5, 0xa5f2, 0x5af1, 0xa5ed,
+  0x5aec, 0xa5e9, 0x5ae8, 0xa5e4, 0x5ae4, 0xa5e0, 0x5adf, 0xa5dc,
+  0x5adb, 0xa5d7, 0x5ad6, 0xa5d3, 0x5ad2, 0xa5ce, 0x5acd, 0xa5ca,
+  0x5ac9, 0xa5c5, 0x5ac5, 0xa5c1, 0x5ac0, 0xa5bc, 0x5abc, 0xa5b8,
+  0x5ab7, 0xa5b3, 0x5ab3, 0xa5af, 0x5aae, 0xa5aa, 0x5aaa, 0xa5a6,
+  0x5aa5, 0xa5a2, 0x5aa1, 0xa59d, 0x5a9d, 0xa599, 0x5a98, 0xa594,
+  0x5a94, 0xa590, 0x5a8f, 0xa58b, 0x5a8b, 0xa587, 0x5a86, 0xa582,
+  0x5a82, 0xa57e, 0x5a7e, 0xa57a, 0x5a79, 0xa575, 0x5a75, 0xa571,
+  0x5a70, 0xa56c, 0x5a6c, 0xa568, 0x5a67, 0xa563, 0x5a63, 0xa55f,
+  0x5a5e, 0xa55b, 0x5a5a, 0xa556, 0x5a56, 0xa552, 0x5a51, 0xa54d,
+  0x5a4d, 0xa549, 0x5a48, 0xa544, 0x5a44, 0xa540, 0x5a3f, 0xa53b,
+  0x5a3b, 0xa537, 0x5a36, 0xa533, 0x5a32, 0xa52e, 0x5a2d, 0xa52a,
+  0x5a29, 0xa525, 0x5a24, 0xa521, 0x5a20, 0xa51c, 0x5a1c, 0xa518,
+  0x5a17, 0xa514, 0x5a13, 0xa50f, 0x5a0e, 0xa50b, 0x5a0a, 0xa506,
+  0x5a05, 0xa502, 0x5a01, 0xa4fe, 0x59fc, 0xa4f9, 0x59f8, 0xa4f5,
+  0x59f3, 0xa4f0, 0x59ef, 0xa4ec, 0x59ea, 0xa4e7, 0x59e6, 0xa4e3,
+  0x59e1, 0xa4df, 0x59dd, 0xa4da, 0x59d9, 0xa4d6, 0x59d4, 0xa4d1,
+  0x59d0, 0xa4cd, 0x59cb, 0xa4c9, 0x59c7, 0xa4c4, 0x59c2, 0xa4c0,
+  0x59be, 0xa4bb, 0x59b9, 0xa4b7, 0x59b5, 0xa4b3, 0x59b0, 0xa4ae,
+  0x59ac, 0xa4aa, 0x59a7, 0xa4a5, 0x59a3, 0xa4a1, 0x599e, 0xa49d,
+  0x599a, 0xa498, 0x5995, 0xa494, 0x5991, 0xa48f, 0x598c, 0xa48b,
+  0x5988, 0xa487, 0x5983, 0xa482, 0x597f, 0xa47e, 0x597a, 0xa479,
+  0x5976, 0xa475, 0x5971, 0xa471, 0x596d, 0xa46c, 0x5968, 0xa468,
+  0x5964, 0xa463, 0x595f, 0xa45f, 0x595b, 0xa45b, 0x5956, 0xa456,
+  0x5952, 0xa452, 0x594d, 0xa44e, 0x5949, 0xa449, 0x5944, 0xa445,
+  0x5940, 0xa440, 0x593b, 0xa43c, 0x5937, 0xa438, 0x5932, 0xa433,
+  0x592e, 0xa42f, 0x5929, 0xa42a, 0x5925, 0xa426, 0x5920, 0xa422,
+  0x591c, 0xa41d, 0x5917, 0xa419, 0x5913, 0xa415, 0x590e, 0xa410,
+  0x590a, 0xa40c, 0x5905, 0xa407, 0x5901, 0xa403, 0x58fc, 0xa3ff,
+  0x58f8, 0xa3fa, 0x58f3, 0xa3f6, 0x58ef, 0xa3f2, 0x58ea, 0xa3ed,
+  0x58e6, 0xa3e9, 0x58e1, 0xa3e5, 0x58dd, 0xa3e0, 0x58d8, 0xa3dc,
+  0x58d4, 0xa3d7, 0x58cf, 0xa3d3, 0x58cb, 0xa3cf, 0x58c6, 0xa3ca,
+  0x58c1, 0xa3c6, 0x58bd, 0xa3c2, 0x58b8, 0xa3bd, 0x58b4, 0xa3b9,
+  0x58af, 0xa3b5, 0x58ab, 0xa3b0, 0x58a6, 0xa3ac, 0x58a2, 0xa3a8,
+  0x589d, 0xa3a3, 0x5899, 0xa39f, 0x5894, 0xa39a, 0x5890, 0xa396,
+  0x588b, 0xa392, 0x5887, 0xa38d, 0x5882, 0xa389, 0x587d, 0xa385,
+  0x5879, 0xa380, 0x5874, 0xa37c, 0x5870, 0xa378, 0x586b, 0xa373,
+  0x5867, 0xa36f, 0x5862, 0xa36b, 0x585e, 0xa366, 0x5859, 0xa362,
+  0x5855, 0xa35e, 0x5850, 0xa359, 0x584b, 0xa355, 0x5847, 0xa351,
+  0x5842, 0xa34c, 0x583e, 0xa348, 0x5839, 0xa344, 0x5835, 0xa33f,
+  0x5830, 0xa33b, 0x582c, 0xa337, 0x5827, 0xa332, 0x5822, 0xa32e,
+  0x581e, 0xa32a, 0x5819, 0xa325, 0x5815, 0xa321, 0x5810, 0xa31d,
+  0x580c, 0xa318, 0x5807, 0xa314, 0x5803, 0xa310, 0x57fe, 0xa30b,
+  0x57f9, 0xa307, 0x57f5, 0xa303, 0x57f0, 0xa2ff, 0x57ec, 0xa2fa,
+  0x57e7, 0xa2f6, 0x57e3, 0xa2f2, 0x57de, 0xa2ed, 0x57d9, 0xa2e9,
+  0x57d5, 0xa2e5, 0x57d0, 0xa2e0, 0x57cc, 0xa2dc, 0x57c7, 0xa2d8,
+  0x57c3, 0xa2d3, 0x57be, 0xa2cf, 0x57b9, 0xa2cb, 0x57b5, 0xa2c6,
+  0x57b0, 0xa2c2, 0x57ac, 0xa2be, 0x57a7, 0xa2ba, 0x57a3, 0xa2b5,
+  0x579e, 0xa2b1, 0x5799, 0xa2ad, 0x5795, 0xa2a8, 0x5790, 0xa2a4,
+  0x578c, 0xa2a0, 0x5787, 0xa29b, 0x5783, 0xa297, 0x577e, 0xa293,
+  0x5779, 0xa28f, 0x5775, 0xa28a, 0x5770, 0xa286, 0x576c, 0xa282,
+  0x5767, 0xa27d, 0x5762, 0xa279, 0x575e, 0xa275, 0x5759, 0xa271,
+  0x5755, 0xa26c, 0x5750, 0xa268, 0x574b, 0xa264, 0x5747, 0xa25f,
+  0x5742, 0xa25b, 0x573e, 0xa257, 0x5739, 0xa253, 0x5734, 0xa24e,
+  0x5730, 0xa24a, 0x572b, 0xa246, 0x5727, 0xa241, 0x5722, 0xa23d,
+  0x571d, 0xa239, 0x5719, 0xa235, 0x5714, 0xa230, 0x5710, 0xa22c,
+  0x570b, 0xa228, 0x5706, 0xa224, 0x5702, 0xa21f, 0x56fd, 0xa21b,
+  0x56f9, 0xa217, 0x56f4, 0xa212, 0x56ef, 0xa20e, 0x56eb, 0xa20a,
+  0x56e6, 0xa206, 0x56e2, 0xa201, 0x56dd, 0xa1fd, 0x56d8, 0xa1f9,
+  0x56d4, 0xa1f5, 0x56cf, 0xa1f0, 0x56ca, 0xa1ec, 0x56c6, 0xa1e8,
+  0x56c1, 0xa1e4, 0x56bd, 0xa1df, 0x56b8, 0xa1db, 0x56b3, 0xa1d7,
+  0x56af, 0xa1d3, 0x56aa, 0xa1ce, 0x56a5, 0xa1ca, 0x56a1, 0xa1c6,
+  0x569c, 0xa1c1, 0x5698, 0xa1bd, 0x5693, 0xa1b9, 0x568e, 0xa1b5,
+  0x568a, 0xa1b0, 0x5685, 0xa1ac, 0x5680, 0xa1a8, 0x567c, 0xa1a4,
+  0x5677, 0xa1a0, 0x5673, 0xa19b, 0x566e, 0xa197, 0x5669, 0xa193,
+  0x5665, 0xa18f, 0x5660, 0xa18a, 0x565b, 0xa186, 0x5657, 0xa182,
+  0x5652, 0xa17e, 0x564d, 0xa179, 0x5649, 0xa175, 0x5644, 0xa171,
+  0x5640, 0xa16d, 0x563b, 0xa168, 0x5636, 0xa164, 0x5632, 0xa160,
+  0x562d, 0xa15c, 0x5628, 0xa157, 0x5624, 0xa153, 0x561f, 0xa14f,
+  0x561a, 0xa14b, 0x5616, 0xa147, 0x5611, 0xa142, 0x560c, 0xa13e,
+  0x5608, 0xa13a, 0x5603, 0xa136, 0x55fe, 0xa131, 0x55fa, 0xa12d,
+  0x55f5, 0xa129, 0x55f0, 0xa125, 0x55ec, 0xa121, 0x55e7, 0xa11c,
+  0x55e3, 0xa118, 0x55de, 0xa114, 0x55d9, 0xa110, 0x55d5, 0xa10b,
+  0x55d0, 0xa107, 0x55cb, 0xa103, 0x55c7, 0xa0ff, 0x55c2, 0xa0fb,
+  0x55bd, 0xa0f6, 0x55b9, 0xa0f2, 0x55b4, 0xa0ee, 0x55af, 0xa0ea,
+  0x55ab, 0xa0e6, 0x55a6, 0xa0e1, 0x55a1, 0xa0dd, 0x559d, 0xa0d9,
+  0x5598, 0xa0d5, 0x5593, 0xa0d1, 0x558f, 0xa0cc, 0x558a, 0xa0c8,
+  0x5585, 0xa0c4, 0x5581, 0xa0c0, 0x557c, 0xa0bc, 0x5577, 0xa0b7,
+  0x5572, 0xa0b3, 0x556e, 0xa0af, 0x5569, 0xa0ab, 0x5564, 0xa0a7,
+  0x5560, 0xa0a2, 0x555b, 0xa09e, 0x5556, 0xa09a, 0x5552, 0xa096,
+  0x554d, 0xa092, 0x5548, 0xa08e, 0x5544, 0xa089, 0x553f, 0xa085,
+  0x553a, 0xa081, 0x5536, 0xa07d, 0x5531, 0xa079, 0x552c, 0xa074,
+  0x5528, 0xa070, 0x5523, 0xa06c, 0x551e, 0xa068, 0x5519, 0xa064,
+  0x5515, 0xa060, 0x5510, 0xa05b, 0x550b, 0xa057, 0x5507, 0xa053,
+  0x5502, 0xa04f, 0x54fd, 0xa04b, 0x54f9, 0xa046, 0x54f4, 0xa042,
+  0x54ef, 0xa03e, 0x54ea, 0xa03a, 0x54e6, 0xa036, 0x54e1, 0xa032,
+  0x54dc, 0xa02d, 0x54d8, 0xa029, 0x54d3, 0xa025, 0x54ce, 0xa021,
+  0x54ca, 0xa01d, 0x54c5, 0xa019, 0x54c0, 0xa014, 0x54bb, 0xa010,
+  0x54b7, 0xa00c, 0x54b2, 0xa008, 0x54ad, 0xa004, 0x54a9, 0xa000,
+  0x54a4, 0x9ffc, 0x549f, 0x9ff7, 0x549a, 0x9ff3, 0x5496, 0x9fef,
+  0x5491, 0x9feb, 0x548c, 0x9fe7, 0x5488, 0x9fe3, 0x5483, 0x9fde,
+  0x547e, 0x9fda, 0x5479, 0x9fd6, 0x5475, 0x9fd2, 0x5470, 0x9fce,
+  0x546b, 0x9fca, 0x5467, 0x9fc6, 0x5462, 0x9fc1, 0x545d, 0x9fbd,
+  0x5458, 0x9fb9, 0x5454, 0x9fb5, 0x544f, 0x9fb1, 0x544a, 0x9fad,
+  0x5445, 0x9fa9, 0x5441, 0x9fa4, 0x543c, 0x9fa0, 0x5437, 0x9f9c,
+  0x5433, 0x9f98, 0x542e, 0x9f94, 0x5429, 0x9f90, 0x5424, 0x9f8c,
+  0x5420, 0x9f88, 0x541b, 0x9f83, 0x5416, 0x9f7f, 0x5411, 0x9f7b,
+  0x540d, 0x9f77, 0x5408, 0x9f73, 0x5403, 0x9f6f, 0x53fe, 0x9f6b,
+  0x53fa, 0x9f67, 0x53f5, 0x9f62, 0x53f0, 0x9f5e, 0x53eb, 0x9f5a,
+  0x53e7, 0x9f56, 0x53e2, 0x9f52, 0x53dd, 0x9f4e, 0x53d8, 0x9f4a,
+  0x53d4, 0x9f46, 0x53cf, 0x9f41, 0x53ca, 0x9f3d, 0x53c5, 0x9f39,
+  0x53c1, 0x9f35, 0x53bc, 0x9f31, 0x53b7, 0x9f2d, 0x53b2, 0x9f29,
+  0x53ae, 0x9f25, 0x53a9, 0x9f21, 0x53a4, 0x9f1c, 0x539f, 0x9f18,
+  0x539b, 0x9f14, 0x5396, 0x9f10, 0x5391, 0x9f0c, 0x538c, 0x9f08,
+  0x5388, 0x9f04, 0x5383, 0x9f00, 0x537e, 0x9efc, 0x5379, 0x9ef8,
+  0x5375, 0x9ef3, 0x5370, 0x9eef, 0x536b, 0x9eeb, 0x5366, 0x9ee7,
+  0x5362, 0x9ee3, 0x535d, 0x9edf, 0x5358, 0x9edb, 0x5353, 0x9ed7,
+  0x534e, 0x9ed3, 0x534a, 0x9ecf, 0x5345, 0x9ecb, 0x5340, 0x9ec6,
+  0x533b, 0x9ec2, 0x5337, 0x9ebe, 0x5332, 0x9eba, 0x532d, 0x9eb6,
+  0x5328, 0x9eb2, 0x5323, 0x9eae, 0x531f, 0x9eaa, 0x531a, 0x9ea6,
+  0x5315, 0x9ea2, 0x5310, 0x9e9e, 0x530c, 0x9e9a, 0x5307, 0x9e95,
+  0x5302, 0x9e91, 0x52fd, 0x9e8d, 0x52f8, 0x9e89, 0x52f4, 0x9e85,
+  0x52ef, 0x9e81, 0x52ea, 0x9e7d, 0x52e5, 0x9e79, 0x52e1, 0x9e75,
+  0x52dc, 0x9e71, 0x52d7, 0x9e6d, 0x52d2, 0x9e69, 0x52cd, 0x9e65,
+  0x52c9, 0x9e61, 0x52c4, 0x9e5d, 0x52bf, 0x9e58, 0x52ba, 0x9e54,
+  0x52b5, 0x9e50, 0x52b1, 0x9e4c, 0x52ac, 0x9e48, 0x52a7, 0x9e44,
+  0x52a2, 0x9e40, 0x529d, 0x9e3c, 0x5299, 0x9e38, 0x5294, 0x9e34,
+  0x528f, 0x9e30, 0x528a, 0x9e2c, 0x5285, 0x9e28, 0x5281, 0x9e24,
+  0x527c, 0x9e20, 0x5277, 0x9e1c, 0x5272, 0x9e18, 0x526d, 0x9e14,
+  0x5269, 0x9e0f, 0x5264, 0x9e0b, 0x525f, 0x9e07, 0x525a, 0x9e03,
+  0x5255, 0x9dff, 0x5251, 0x9dfb, 0x524c, 0x9df7, 0x5247, 0x9df3,
+  0x5242, 0x9def, 0x523d, 0x9deb, 0x5238, 0x9de7, 0x5234, 0x9de3,
+  0x522f, 0x9ddf, 0x522a, 0x9ddb, 0x5225, 0x9dd7, 0x5220, 0x9dd3,
+  0x521c, 0x9dcf, 0x5217, 0x9dcb, 0x5212, 0x9dc7, 0x520d, 0x9dc3,
+  0x5208, 0x9dbf, 0x5203, 0x9dbb, 0x51ff, 0x9db7, 0x51fa, 0x9db3,
+  0x51f5, 0x9daf, 0x51f0, 0x9dab, 0x51eb, 0x9da7, 0x51e6, 0x9da3,
+  0x51e2, 0x9d9f, 0x51dd, 0x9d9b, 0x51d8, 0x9d97, 0x51d3, 0x9d93,
+  0x51ce, 0x9d8f, 0x51c9, 0x9d8b, 0x51c5, 0x9d86, 0x51c0, 0x9d82,
+  0x51bb, 0x9d7e, 0x51b6, 0x9d7a, 0x51b1, 0x9d76, 0x51ac, 0x9d72,
+  0x51a8, 0x9d6e, 0x51a3, 0x9d6a, 0x519e, 0x9d66, 0x5199, 0x9d62,
+  0x5194, 0x9d5e, 0x518f, 0x9d5a, 0x518b, 0x9d56, 0x5186, 0x9d52,
+  0x5181, 0x9d4e, 0x517c, 0x9d4a, 0x5177, 0x9d46, 0x5172, 0x9d42,
+  0x516e, 0x9d3e, 0x5169, 0x9d3a, 0x5164, 0x9d36, 0x515f, 0x9d32,
+  0x515a, 0x9d2e, 0x5155, 0x9d2a, 0x5150, 0x9d26, 0x514c, 0x9d22,
+  0x5147, 0x9d1e, 0x5142, 0x9d1a, 0x513d, 0x9d16, 0x5138, 0x9d12,
+  0x5133, 0x9d0e, 0x512e, 0x9d0b, 0x512a, 0x9d07, 0x5125, 0x9d03,
+  0x5120, 0x9cff, 0x511b, 0x9cfb, 0x5116, 0x9cf7, 0x5111, 0x9cf3,
+  0x510c, 0x9cef, 0x5108, 0x9ceb, 0x5103, 0x9ce7, 0x50fe, 0x9ce3,
+  0x50f9, 0x9cdf, 0x50f4, 0x9cdb, 0x50ef, 0x9cd7, 0x50ea, 0x9cd3,
+  0x50e5, 0x9ccf, 0x50e1, 0x9ccb, 0x50dc, 0x9cc7, 0x50d7, 0x9cc3,
+  0x50d2, 0x9cbf, 0x50cd, 0x9cbb, 0x50c8, 0x9cb7, 0x50c3, 0x9cb3,
+  0x50bf, 0x9caf, 0x50ba, 0x9cab, 0x50b5, 0x9ca7, 0x50b0, 0x9ca3,
+  0x50ab, 0x9c9f, 0x50a6, 0x9c9b, 0x50a1, 0x9c97, 0x509c, 0x9c93,
+  0x5097, 0x9c8f, 0x5093, 0x9c8b, 0x508e, 0x9c88, 0x5089, 0x9c84,
+  0x5084, 0x9c80, 0x507f, 0x9c7c, 0x507a, 0x9c78, 0x5075, 0x9c74,
+  0x5070, 0x9c70, 0x506c, 0x9c6c, 0x5067, 0x9c68, 0x5062, 0x9c64,
+  0x505d, 0x9c60, 0x5058, 0x9c5c, 0x5053, 0x9c58, 0x504e, 0x9c54,
+  0x5049, 0x9c50, 0x5044, 0x9c4c, 0x503f, 0x9c48, 0x503b, 0x9c44,
+  0x5036, 0x9c40, 0x5031, 0x9c3d, 0x502c, 0x9c39, 0x5027, 0x9c35,
+  0x5022, 0x9c31, 0x501d, 0x9c2d, 0x5018, 0x9c29, 0x5013, 0x9c25,
+  0x500f, 0x9c21, 0x500a, 0x9c1d, 0x5005, 0x9c19, 0x5000, 0x9c15,
+  0x4ffb, 0x9c11, 0x4ff6, 0x9c0d, 0x4ff1, 0x9c09, 0x4fec, 0x9c06,
+  0x4fe7, 0x9c02, 0x4fe2, 0x9bfe, 0x4fdd, 0x9bfa, 0x4fd9, 0x9bf6,
+  0x4fd4, 0x9bf2, 0x4fcf, 0x9bee, 0x4fca, 0x9bea, 0x4fc5, 0x9be6,
+  0x4fc0, 0x9be2, 0x4fbb, 0x9bde, 0x4fb6, 0x9bda, 0x4fb1, 0x9bd7,
+  0x4fac, 0x9bd3, 0x4fa7, 0x9bcf, 0x4fa2, 0x9bcb, 0x4f9e, 0x9bc7,
+  0x4f99, 0x9bc3, 0x4f94, 0x9bbf, 0x4f8f, 0x9bbb, 0x4f8a, 0x9bb7,
+  0x4f85, 0x9bb3, 0x4f80, 0x9baf, 0x4f7b, 0x9bac, 0x4f76, 0x9ba8,
+  0x4f71, 0x9ba4, 0x4f6c, 0x9ba0, 0x4f67, 0x9b9c, 0x4f62, 0x9b98,
+  0x4f5e, 0x9b94, 0x4f59, 0x9b90, 0x4f54, 0x9b8c, 0x4f4f, 0x9b88,
+  0x4f4a, 0x9b85, 0x4f45, 0x9b81, 0x4f40, 0x9b7d, 0x4f3b, 0x9b79,
+  0x4f36, 0x9b75, 0x4f31, 0x9b71, 0x4f2c, 0x9b6d, 0x4f27, 0x9b69,
+  0x4f22, 0x9b65, 0x4f1d, 0x9b62, 0x4f18, 0x9b5e, 0x4f14, 0x9b5a,
+  0x4f0f, 0x9b56, 0x4f0a, 0x9b52, 0x4f05, 0x9b4e, 0x4f00, 0x9b4a,
+  0x4efb, 0x9b46, 0x4ef6, 0x9b43, 0x4ef1, 0x9b3f, 0x4eec, 0x9b3b,
+  0x4ee7, 0x9b37, 0x4ee2, 0x9b33, 0x4edd, 0x9b2f, 0x4ed8, 0x9b2b,
+  0x4ed3, 0x9b27, 0x4ece, 0x9b24, 0x4ec9, 0x9b20, 0x4ec4, 0x9b1c,
+  0x4ebf, 0x9b18, 0x4eba, 0x9b14, 0x4eb6, 0x9b10, 0x4eb1, 0x9b0c,
+  0x4eac, 0x9b09, 0x4ea7, 0x9b05, 0x4ea2, 0x9b01, 0x4e9d, 0x9afd,
+  0x4e98, 0x9af9, 0x4e93, 0x9af5, 0x4e8e, 0x9af1, 0x4e89, 0x9aed,
+  0x4e84, 0x9aea, 0x4e7f, 0x9ae6, 0x4e7a, 0x9ae2, 0x4e75, 0x9ade,
+  0x4e70, 0x9ada, 0x4e6b, 0x9ad6, 0x4e66, 0x9ad3, 0x4e61, 0x9acf,
+  0x4e5c, 0x9acb, 0x4e57, 0x9ac7, 0x4e52, 0x9ac3, 0x4e4d, 0x9abf,
+  0x4e48, 0x9abb, 0x4e43, 0x9ab8, 0x4e3e, 0x9ab4, 0x4e39, 0x9ab0,
+  0x4e34, 0x9aac, 0x4e2f, 0x9aa8, 0x4e2a, 0x9aa4, 0x4e26, 0x9aa1,
+  0x4e21, 0x9a9d, 0x4e1c, 0x9a99, 0x4e17, 0x9a95, 0x4e12, 0x9a91,
+  0x4e0d, 0x9a8d, 0x4e08, 0x9a8a, 0x4e03, 0x9a86, 0x4dfe, 0x9a82,
+  0x4df9, 0x9a7e, 0x4df4, 0x9a7a, 0x4def, 0x9a76, 0x4dea, 0x9a73,
+  0x4de5, 0x9a6f, 0x4de0, 0x9a6b, 0x4ddb, 0x9a67, 0x4dd6, 0x9a63,
+  0x4dd1, 0x9a60, 0x4dcc, 0x9a5c, 0x4dc7, 0x9a58, 0x4dc2, 0x9a54,
+  0x4dbd, 0x9a50, 0x4db8, 0x9a4c, 0x4db3, 0x9a49, 0x4dae, 0x9a45,
+  0x4da9, 0x9a41, 0x4da4, 0x9a3d, 0x4d9f, 0x9a39, 0x4d9a, 0x9a36,
+  0x4d95, 0x9a32, 0x4d90, 0x9a2e, 0x4d8b, 0x9a2a, 0x4d86, 0x9a26,
+  0x4d81, 0x9a23, 0x4d7c, 0x9a1f, 0x4d77, 0x9a1b, 0x4d72, 0x9a17,
+  0x4d6d, 0x9a13, 0x4d68, 0x9a10, 0x4d63, 0x9a0c, 0x4d5e, 0x9a08,
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+  0x4d45, 0x99f5, 0x4d40, 0x99f1, 0x4d3b, 0x99ed, 0x4d36, 0x99ea,
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+  0x33de, 0x8afc, 0x33d9, 0x8af9, 0x33d3, 0x8af7, 0x33cd, 0x8af4,
+  0x33c7, 0x8af1, 0x33c2, 0x8aef, 0x33bc, 0x8aec, 0x33b6, 0x8aea,
+  0x33b0, 0x8ae7, 0x33ab, 0x8ae5, 0x33a5, 0x8ae2, 0x339f, 0x8ae0,
+  0x3399, 0x8add, 0x3394, 0x8adb, 0x338e, 0x8ad8, 0x3388, 0x8ad6,
+  0x3382, 0x8ad3, 0x337d, 0x8ad1, 0x3377, 0x8ace, 0x3371, 0x8acb,
+  0x336b, 0x8ac9, 0x3366, 0x8ac6, 0x3360, 0x8ac4, 0x335a, 0x8ac1,
+  0x3354, 0x8abf, 0x334f, 0x8abc, 0x3349, 0x8aba, 0x3343, 0x8ab7,
+  0x333d, 0x8ab5, 0x3338, 0x8ab2, 0x3332, 0x8ab0, 0x332c, 0x8aad,
+  0x3326, 0x8aab, 0x3321, 0x8aa8, 0x331b, 0x8aa6, 0x3315, 0x8aa3,
+  0x330f, 0x8aa1, 0x330a, 0x8a9e, 0x3304, 0x8a9c, 0x32fe, 0x8a99,
+  0x32f8, 0x8a97, 0x32f3, 0x8a94, 0x32ed, 0x8a92, 0x32e7, 0x8a8f,
+  0x32e1, 0x8a8d, 0x32db, 0x8a8a, 0x32d6, 0x8a88, 0x32d0, 0x8a85,
+  0x32ca, 0x8a83, 0x32c4, 0x8a80, 0x32bf, 0x8a7e, 0x32b9, 0x8a7b,
+  0x32b3, 0x8a79, 0x32ad, 0x8a76, 0x32a8, 0x8a74, 0x32a2, 0x8a71,
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+  0x3285, 0x8a65, 0x327f, 0x8a62, 0x3279, 0x8a60, 0x3274, 0x8a5d,
+  0x326e, 0x8a5b, 0x3268, 0x8a59, 0x3262, 0x8a56, 0x325d, 0x8a54,
+  0x3257, 0x8a51, 0x3251, 0x8a4f, 0x324b, 0x8a4c, 0x3245, 0x8a4a,
+  0x3240, 0x8a47, 0x323a, 0x8a45, 0x3234, 0x8a42, 0x322e, 0x8a40,
+  0x3228, 0x8a3d, 0x3223, 0x8a3b, 0x321d, 0x8a38, 0x3217, 0x8a36,
+  0x3211, 0x8a34, 0x320c, 0x8a31, 0x3206, 0x8a2f, 0x3200, 0x8a2c,
+  0x31fa, 0x8a2a, 0x31f4, 0x8a27, 0x31ef, 0x8a25, 0x31e9, 0x8a22,
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+  0x31cc, 0x8a16, 0x31c6, 0x8a14, 0x31c0, 0x8a11, 0x31bb, 0x8a0f,
+  0x31b5, 0x8a0c, 0x31af, 0x8a0a, 0x31a9, 0x8a07, 0x31a3, 0x8a05,
+  0x319e, 0x8a03, 0x3198, 0x8a00, 0x3192, 0x89fe, 0x318c, 0x89fb,
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+  0x23ee, 0x8526, 0x23e8, 0x8524, 0x23e2, 0x8523, 0x23dc, 0x8521,
+  0x23d6, 0x851f, 0x23d0, 0x851d, 0x23ca, 0x851c, 0x23c4, 0x851a,
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+  0x23a6, 0x8511, 0x23a0, 0x850f, 0x239a, 0x850e, 0x2394, 0x850c,
+  0x238e, 0x850a, 0x2388, 0x8508, 0x2382, 0x8507, 0x237c, 0x8505,
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+  0x232d, 0x84ee, 0x2327, 0x84ed, 0x2321, 0x84eb, 0x231b, 0x84e9,
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+  0x22fd, 0x84e1, 0x22f7, 0x84df, 0x22f1, 0x84dd, 0x22eb, 0x84db,
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+  0x22cd, 0x84d3, 0x22c7, 0x84d1, 0x22c0, 0x84cf, 0x22ba, 0x84ce,
+  0x22b4, 0x84cc, 0x22ae, 0x84ca, 0x22a8, 0x84c9, 0x22a2, 0x84c7,
+  0x229c, 0x84c5, 0x2296, 0x84c4, 0x2290, 0x84c2, 0x228a, 0x84c0,
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+  0x21aa, 0x8482, 0x21a4, 0x8481, 0x219e, 0x847f, 0x2198, 0x847d,
+  0x2192, 0x847c, 0x218c, 0x847a, 0x2186, 0x8478, 0x2180, 0x8477,
+  0x2179, 0x8475, 0x2173, 0x8473, 0x216d, 0x8472, 0x2167, 0x8470,
+  0x2161, 0x846e, 0x215b, 0x846d, 0x2155, 0x846b, 0x214f, 0x846a,
+  0x2149, 0x8468, 0x2143, 0x8466, 0x213d, 0x8465, 0x2137, 0x8463,
+  0x2131, 0x8461, 0x212b, 0x8460, 0x2125, 0x845e, 0x211e, 0x845d,
+  0x2118, 0x845b, 0x2112, 0x8459, 0x210c, 0x8458, 0x2106, 0x8456,
+  0x2100, 0x8454, 0x20fa, 0x8453, 0x20f4, 0x8451, 0x20ee, 0x8450,
+  0x20e8, 0x844e, 0x20e2, 0x844c, 0x20dc, 0x844b, 0x20d6, 0x8449,
+  0x20d0, 0x8447, 0x20c9, 0x8446, 0x20c3, 0x8444, 0x20bd, 0x8443,
+  0x20b7, 0x8441, 0x20b1, 0x843f, 0x20ab, 0x843e, 0x20a5, 0x843c,
+  0x209f, 0x843b, 0x2099, 0x8439, 0x2093, 0x8437, 0x208d, 0x8436,
+  0x2087, 0x8434, 0x2081, 0x8433, 0x207a, 0x8431, 0x2074, 0x842f,
+  0x206e, 0x842e, 0x2068, 0x842c, 0x2062, 0x842b, 0x205c, 0x8429,
+  0x2056, 0x8427, 0x2050, 0x8426, 0x204a, 0x8424, 0x2044, 0x8423,
+  0x203e, 0x8421, 0x2038, 0x8420, 0x2032, 0x841e, 0x202b, 0x841c,
+  0x2025, 0x841b, 0x201f, 0x8419, 0x2019, 0x8418, 0x2013, 0x8416,
+  0x200d, 0x8415, 0x2007, 0x8413, 0x2001, 0x8411, 0x1ffb, 0x8410,
+  0x1ff5, 0x840e, 0x1fef, 0x840d, 0x1fe9, 0x840b, 0x1fe2, 0x840a,
+  0x1fdc, 0x8408, 0x1fd6, 0x8406, 0x1fd0, 0x8405, 0x1fca, 0x8403,
+  0x1fc4, 0x8402, 0x1fbe, 0x8400, 0x1fb8, 0x83ff, 0x1fb2, 0x83fd,
+  0x1fac, 0x83fb, 0x1fa6, 0x83fa, 0x1f9f, 0x83f8, 0x1f99, 0x83f7,
+  0x1f93, 0x83f5, 0x1f8d, 0x83f4, 0x1f87, 0x83f2, 0x1f81, 0x83f1,
+  0x1f7b, 0x83ef, 0x1f75, 0x83ee, 0x1f6f, 0x83ec, 0x1f69, 0x83ea,
+  0x1f63, 0x83e9, 0x1f5d, 0x83e7, 0x1f56, 0x83e6, 0x1f50, 0x83e4,
+  0x1f4a, 0x83e3, 0x1f44, 0x83e1, 0x1f3e, 0x83e0, 0x1f38, 0x83de,
+  0x1f32, 0x83dd, 0x1f2c, 0x83db, 0x1f26, 0x83da, 0x1f20, 0x83d8,
+  0x1f19, 0x83d7, 0x1f13, 0x83d5, 0x1f0d, 0x83d3, 0x1f07, 0x83d2,
+  0x1f01, 0x83d0, 0x1efb, 0x83cf, 0x1ef5, 0x83cd, 0x1eef, 0x83cc,
+  0x1ee9, 0x83ca, 0x1ee3, 0x83c9, 0x1edd, 0x83c7, 0x1ed6, 0x83c6,
+  0x1ed0, 0x83c4, 0x1eca, 0x83c3, 0x1ec4, 0x83c1, 0x1ebe, 0x83c0,
+  0x1eb8, 0x83be, 0x1eb2, 0x83bd, 0x1eac, 0x83bb, 0x1ea6, 0x83ba,
+  0x1ea0, 0x83b8, 0x1e99, 0x83b7, 0x1e93, 0x83b5, 0x1e8d, 0x83b4,
+  0x1e87, 0x83b2, 0x1e81, 0x83b1, 0x1e7b, 0x83af, 0x1e75, 0x83ae,
+  0x1e6f, 0x83ac, 0x1e69, 0x83ab, 0x1e62, 0x83a9, 0x1e5c, 0x83a8,
+  0x1e56, 0x83a6, 0x1e50, 0x83a5, 0x1e4a, 0x83a3, 0x1e44, 0x83a2,
+  0x1e3e, 0x83a0, 0x1e38, 0x839f, 0x1e32, 0x839d, 0x1e2c, 0x839c,
+  0x1e25, 0x839a, 0x1e1f, 0x8399, 0x1e19, 0x8397, 0x1e13, 0x8396,
+  0x1e0d, 0x8394, 0x1e07, 0x8393, 0x1e01, 0x8392, 0x1dfb, 0x8390,
+  0x1df5, 0x838f, 0x1dee, 0x838d, 0x1de8, 0x838c, 0x1de2, 0x838a,
+  0x1ddc, 0x8389, 0x1dd6, 0x8387, 0x1dd0, 0x8386, 0x1dca, 0x8384,
+  0x1dc4, 0x8383, 0x1dbe, 0x8381, 0x1db7, 0x8380, 0x1db1, 0x837e,
+  0x1dab, 0x837d, 0x1da5, 0x837c, 0x1d9f, 0x837a, 0x1d99, 0x8379,
+  0x1d93, 0x8377, 0x1d8d, 0x8376, 0x1d87, 0x8374, 0x1d80, 0x8373,
+  0x1d7a, 0x8371, 0x1d74, 0x8370, 0x1d6e, 0x836f, 0x1d68, 0x836d,
+  0x1d62, 0x836c, 0x1d5c, 0x836a, 0x1d56, 0x8369, 0x1d50, 0x8367,
+  0x1d49, 0x8366, 0x1d43, 0x8364, 0x1d3d, 0x8363, 0x1d37, 0x8362,
+  0x1d31, 0x8360, 0x1d2b, 0x835f, 0x1d25, 0x835d, 0x1d1f, 0x835c,
+  0x1d18, 0x835a, 0x1d12, 0x8359, 0x1d0c, 0x8358, 0x1d06, 0x8356,
+  0x1d00, 0x8355, 0x1cfa, 0x8353, 0x1cf4, 0x8352, 0x1cee, 0x8350,
+  0x1ce8, 0x834f, 0x1ce1, 0x834e, 0x1cdb, 0x834c, 0x1cd5, 0x834b,
+  0x1ccf, 0x8349, 0x1cc9, 0x8348, 0x1cc3, 0x8347, 0x1cbd, 0x8345,
+  0x1cb7, 0x8344, 0x1cb0, 0x8342, 0x1caa, 0x8341, 0x1ca4, 0x833f,
+  0x1c9e, 0x833e, 0x1c98, 0x833d, 0x1c92, 0x833b, 0x1c8c, 0x833a,
+  0x1c86, 0x8338, 0x1c7f, 0x8337, 0x1c79, 0x8336, 0x1c73, 0x8334,
+  0x1c6d, 0x8333, 0x1c67, 0x8331, 0x1c61, 0x8330, 0x1c5b, 0x832f,
+  0x1c55, 0x832d, 0x1c4e, 0x832c, 0x1c48, 0x832b, 0x1c42, 0x8329,
+  0x1c3c, 0x8328, 0x1c36, 0x8326, 0x1c30, 0x8325, 0x1c2a, 0x8324,
+  0x1c24, 0x8322, 0x1c1d, 0x8321, 0x1c17, 0x831f, 0x1c11, 0x831e,
+  0x1c0b, 0x831d, 0x1c05, 0x831b, 0x1bff, 0x831a, 0x1bf9, 0x8319,
+  0x1bf2, 0x8317, 0x1bec, 0x8316, 0x1be6, 0x8314, 0x1be0, 0x8313,
+  0x1bda, 0x8312, 0x1bd4, 0x8310, 0x1bce, 0x830f, 0x1bc8, 0x830e,
+  0x1bc1, 0x830c, 0x1bbb, 0x830b, 0x1bb5, 0x830a, 0x1baf, 0x8308,
+  0x1ba9, 0x8307, 0x1ba3, 0x8305, 0x1b9d, 0x8304, 0x1b96, 0x8303,
+  0x1b90, 0x8301, 0x1b8a, 0x8300, 0x1b84, 0x82ff, 0x1b7e, 0x82fd,
+  0x1b78, 0x82fc, 0x1b72, 0x82fb, 0x1b6c, 0x82f9, 0x1b65, 0x82f8,
+  0x1b5f, 0x82f7, 0x1b59, 0x82f5, 0x1b53, 0x82f4, 0x1b4d, 0x82f3,
+  0x1b47, 0x82f1, 0x1b41, 0x82f0, 0x1b3a, 0x82ef, 0x1b34, 0x82ed,
+  0x1b2e, 0x82ec, 0x1b28, 0x82eb, 0x1b22, 0x82e9, 0x1b1c, 0x82e8,
+  0x1b16, 0x82e7, 0x1b0f, 0x82e5, 0x1b09, 0x82e4, 0x1b03, 0x82e3,
+  0x1afd, 0x82e1, 0x1af7, 0x82e0, 0x1af1, 0x82df, 0x1aeb, 0x82dd,
+  0x1ae4, 0x82dc, 0x1ade, 0x82db, 0x1ad8, 0x82d9, 0x1ad2, 0x82d8,
+  0x1acc, 0x82d7, 0x1ac6, 0x82d5, 0x1ac0, 0x82d4, 0x1ab9, 0x82d3,
+  0x1ab3, 0x82d1, 0x1aad, 0x82d0, 0x1aa7, 0x82cf, 0x1aa1, 0x82ce,
+  0x1a9b, 0x82cc, 0x1a95, 0x82cb, 0x1a8e, 0x82ca, 0x1a88, 0x82c8,
+  0x1a82, 0x82c7, 0x1a7c, 0x82c6, 0x1a76, 0x82c4, 0x1a70, 0x82c3,
+  0x1a6a, 0x82c2, 0x1a63, 0x82c1, 0x1a5d, 0x82bf, 0x1a57, 0x82be,
+  0x1a51, 0x82bd, 0x1a4b, 0x82bb, 0x1a45, 0x82ba, 0x1a3e, 0x82b9,
+  0x1a38, 0x82b7, 0x1a32, 0x82b6, 0x1a2c, 0x82b5, 0x1a26, 0x82b4,
+  0x1a20, 0x82b2, 0x1a1a, 0x82b1, 0x1a13, 0x82b0, 0x1a0d, 0x82ae,
+  0x1a07, 0x82ad, 0x1a01, 0x82ac, 0x19fb, 0x82ab, 0x19f5, 0x82a9,
+  0x19ef, 0x82a8, 0x19e8, 0x82a7, 0x19e2, 0x82a6, 0x19dc, 0x82a4,
+  0x19d6, 0x82a3, 0x19d0, 0x82a2, 0x19ca, 0x82a0, 0x19c3, 0x829f,
+  0x19bd, 0x829e, 0x19b7, 0x829d, 0x19b1, 0x829b, 0x19ab, 0x829a,
+  0x19a5, 0x8299, 0x199f, 0x8298, 0x1998, 0x8296, 0x1992, 0x8295,
+  0x198c, 0x8294, 0x1986, 0x8293, 0x1980, 0x8291, 0x197a, 0x8290,
+  0x1973, 0x828f, 0x196d, 0x828e, 0x1967, 0x828c, 0x1961, 0x828b,
+  0x195b, 0x828a, 0x1955, 0x8289, 0x194e, 0x8287, 0x1948, 0x8286,
+  0x1942, 0x8285, 0x193c, 0x8284, 0x1936, 0x8282, 0x1930, 0x8281,
+  0x192a, 0x8280, 0x1923, 0x827f, 0x191d, 0x827e, 0x1917, 0x827c,
+  0x1911, 0x827b, 0x190b, 0x827a, 0x1905, 0x8279, 0x18fe, 0x8277,
+  0x18f8, 0x8276, 0x18f2, 0x8275, 0x18ec, 0x8274, 0x18e6, 0x8272,
+  0x18e0, 0x8271, 0x18d9, 0x8270, 0x18d3, 0x826f, 0x18cd, 0x826e,
+  0x18c7, 0x826c, 0x18c1, 0x826b, 0x18bb, 0x826a, 0x18b4, 0x8269,
+  0x18ae, 0x8268, 0x18a8, 0x8266, 0x18a2, 0x8265, 0x189c, 0x8264,
+  0x1896, 0x8263, 0x188f, 0x8261, 0x1889, 0x8260, 0x1883, 0x825f,
+  0x187d, 0x825e, 0x1877, 0x825d, 0x1871, 0x825b, 0x186a, 0x825a,
+  0x1864, 0x8259, 0x185e, 0x8258, 0x1858, 0x8257, 0x1852, 0x8255,
+  0x184c, 0x8254, 0x1845, 0x8253, 0x183f, 0x8252, 0x1839, 0x8251,
+  0x1833, 0x8250, 0x182d, 0x824e, 0x1827, 0x824d, 0x1820, 0x824c,
+  0x181a, 0x824b, 0x1814, 0x824a, 0x180e, 0x8248, 0x1808, 0x8247,
+  0x1802, 0x8246, 0x17fb, 0x8245, 0x17f5, 0x8244, 0x17ef, 0x8243,
+  0x17e9, 0x8241, 0x17e3, 0x8240, 0x17dd, 0x823f, 0x17d6, 0x823e,
+  0x17d0, 0x823d, 0x17ca, 0x823b, 0x17c4, 0x823a, 0x17be, 0x8239,
+  0x17b7, 0x8238, 0x17b1, 0x8237, 0x17ab, 0x8236, 0x17a5, 0x8234,
+  0x179f, 0x8233, 0x1799, 0x8232, 0x1792, 0x8231, 0x178c, 0x8230,
+  0x1786, 0x822f, 0x1780, 0x822e, 0x177a, 0x822c, 0x1774, 0x822b,
+  0x176d, 0x822a, 0x1767, 0x8229, 0x1761, 0x8228, 0x175b, 0x8227,
+  0x1755, 0x8226, 0x174e, 0x8224, 0x1748, 0x8223, 0x1742, 0x8222,
+  0x173c, 0x8221, 0x1736, 0x8220, 0x1730, 0x821f, 0x1729, 0x821e,
+  0x1723, 0x821c, 0x171d, 0x821b, 0x1717, 0x821a, 0x1711, 0x8219,
+  0x170a, 0x8218, 0x1704, 0x8217, 0x16fe, 0x8216, 0x16f8, 0x8214,
+  0x16f2, 0x8213, 0x16ec, 0x8212, 0x16e5, 0x8211, 0x16df, 0x8210,
+  0x16d9, 0x820f, 0x16d3, 0x820e, 0x16cd, 0x820d, 0x16c6, 0x820b,
+  0x16c0, 0x820a, 0x16ba, 0x8209, 0x16b4, 0x8208, 0x16ae, 0x8207,
+  0x16a8, 0x8206, 0x16a1, 0x8205, 0x169b, 0x8204, 0x1695, 0x8203,
+  0x168f, 0x8201, 0x1689, 0x8200, 0x1682, 0x81ff, 0x167c, 0x81fe,
+  0x1676, 0x81fd, 0x1670, 0x81fc, 0x166a, 0x81fb, 0x1664, 0x81fa,
+  0x165d, 0x81f9, 0x1657, 0x81f8, 0x1651, 0x81f6, 0x164b, 0x81f5,
+  0x1645, 0x81f4, 0x163e, 0x81f3, 0x1638, 0x81f2, 0x1632, 0x81f1,
+  0x162c, 0x81f0, 0x1626, 0x81ef, 0x161f, 0x81ee, 0x1619, 0x81ed,
+  0x1613, 0x81ec, 0x160d, 0x81ea, 0x1607, 0x81e9, 0x1601, 0x81e8,
+  0x15fa, 0x81e7, 0x15f4, 0x81e6, 0x15ee, 0x81e5, 0x15e8, 0x81e4,
+  0x15e2, 0x81e3, 0x15db, 0x81e2, 0x15d5, 0x81e1, 0x15cf, 0x81e0,
+  0x15c9, 0x81df, 0x15c3, 0x81de, 0x15bc, 0x81dc, 0x15b6, 0x81db,
+  0x15b0, 0x81da, 0x15aa, 0x81d9, 0x15a4, 0x81d8, 0x159d, 0x81d7,
+  0x1597, 0x81d6, 0x1591, 0x81d5, 0x158b, 0x81d4, 0x1585, 0x81d3,
+  0x157f, 0x81d2, 0x1578, 0x81d1, 0x1572, 0x81d0, 0x156c, 0x81cf,
+  0x1566, 0x81ce, 0x1560, 0x81cd, 0x1559, 0x81cc, 0x1553, 0x81cb,
+  0x154d, 0x81c9, 0x1547, 0x81c8, 0x1541, 0x81c7, 0x153a, 0x81c6,
+  0x1534, 0x81c5, 0x152e, 0x81c4, 0x1528, 0x81c3, 0x1522, 0x81c2,
+  0x151b, 0x81c1, 0x1515, 0x81c0, 0x150f, 0x81bf, 0x1509, 0x81be,
+  0x1503, 0x81bd, 0x14fc, 0x81bc, 0x14f6, 0x81bb, 0x14f0, 0x81ba,
+  0x14ea, 0x81b9, 0x14e4, 0x81b8, 0x14dd, 0x81b7, 0x14d7, 0x81b6,
+  0x14d1, 0x81b5, 0x14cb, 0x81b4, 0x14c5, 0x81b3, 0x14be, 0x81b2,
+  0x14b8, 0x81b1, 0x14b2, 0x81b0, 0x14ac, 0x81af, 0x14a6, 0x81ae,
+  0x149f, 0x81ad, 0x1499, 0x81ac, 0x1493, 0x81ab, 0x148d, 0x81aa,
+  0x1487, 0x81a9, 0x1480, 0x81a8, 0x147a, 0x81a7, 0x1474, 0x81a6,
+  0x146e, 0x81a5, 0x1468, 0x81a4, 0x1461, 0x81a3, 0x145b, 0x81a2,
+  0x1455, 0x81a1, 0x144f, 0x81a0, 0x1449, 0x819f, 0x1442, 0x819e,
+  0x143c, 0x819d, 0x1436, 0x819c, 0x1430, 0x819b, 0x142a, 0x819a,
+  0x1423, 0x8199, 0x141d, 0x8198, 0x1417, 0x8197, 0x1411, 0x8196,
+  0x140b, 0x8195, 0x1404, 0x8194, 0x13fe, 0x8193, 0x13f8, 0x8192,
+  0x13f2, 0x8191, 0x13eb, 0x8190, 0x13e5, 0x818f, 0x13df, 0x818e,
+  0x13d9, 0x818d, 0x13d3, 0x818c, 0x13cc, 0x818b, 0x13c6, 0x818a,
+  0x13c0, 0x8189, 0x13ba, 0x8188, 0x13b4, 0x8187, 0x13ad, 0x8186,
+  0x13a7, 0x8185, 0x13a1, 0x8184, 0x139b, 0x8183, 0x1395, 0x8182,
+  0x138e, 0x8181, 0x1388, 0x8180, 0x1382, 0x817f, 0x137c, 0x817e,
+  0x1376, 0x817d, 0x136f, 0x817c, 0x1369, 0x817c, 0x1363, 0x817b,
+  0x135d, 0x817a, 0x1356, 0x8179, 0x1350, 0x8178, 0x134a, 0x8177,
+  0x1344, 0x8176, 0x133e, 0x8175, 0x1337, 0x8174, 0x1331, 0x8173,
+  0x132b, 0x8172, 0x1325, 0x8171, 0x131f, 0x8170, 0x1318, 0x816f,
+  0x1312, 0x816e, 0x130c, 0x816d, 0x1306, 0x816c, 0x12ff, 0x816c,
+  0x12f9, 0x816b, 0x12f3, 0x816a, 0x12ed, 0x8169, 0x12e7, 0x8168,
+  0x12e0, 0x8167, 0x12da, 0x8166, 0x12d4, 0x8165, 0x12ce, 0x8164,
+  0x12c8, 0x8163, 0x12c1, 0x8162, 0x12bb, 0x8161, 0x12b5, 0x8160,
+  0x12af, 0x815f, 0x12a8, 0x815f, 0x12a2, 0x815e, 0x129c, 0x815d,
+  0x1296, 0x815c, 0x1290, 0x815b, 0x1289, 0x815a, 0x1283, 0x8159,
+  0x127d, 0x8158, 0x1277, 0x8157, 0x1271, 0x8156, 0x126a, 0x8155,
+  0x1264, 0x8155, 0x125e, 0x8154, 0x1258, 0x8153, 0x1251, 0x8152,
+  0x124b, 0x8151, 0x1245, 0x8150, 0x123f, 0x814f, 0x1239, 0x814e,
+  0x1232, 0x814d, 0x122c, 0x814c, 0x1226, 0x814c, 0x1220, 0x814b,
+  0x1219, 0x814a, 0x1213, 0x8149, 0x120d, 0x8148, 0x1207, 0x8147,
+  0x1201, 0x8146, 0x11fa, 0x8145, 0x11f4, 0x8145, 0x11ee, 0x8144,
+  0x11e8, 0x8143, 0x11e1, 0x8142, 0x11db, 0x8141, 0x11d5, 0x8140,
+  0x11cf, 0x813f, 0x11c9, 0x813e, 0x11c2, 0x813d, 0x11bc, 0x813d,
+  0x11b6, 0x813c, 0x11b0, 0x813b, 0x11a9, 0x813a, 0x11a3, 0x8139,
+  0x119d, 0x8138, 0x1197, 0x8137, 0x1191, 0x8137, 0x118a, 0x8136,
+  0x1184, 0x8135, 0x117e, 0x8134, 0x1178, 0x8133, 0x1171, 0x8132,
+  0x116b, 0x8131, 0x1165, 0x8131, 0x115f, 0x8130, 0x1159, 0x812f,
+  0x1152, 0x812e, 0x114c, 0x812d, 0x1146, 0x812c, 0x1140, 0x812b,
+  0x1139, 0x812b, 0x1133, 0x812a, 0x112d, 0x8129, 0x1127, 0x8128,
+  0x1121, 0x8127, 0x111a, 0x8126, 0x1114, 0x8126, 0x110e, 0x8125,
+  0x1108, 0x8124, 0x1101, 0x8123, 0x10fb, 0x8122, 0x10f5, 0x8121,
+  0x10ef, 0x8121, 0x10e8, 0x8120, 0x10e2, 0x811f, 0x10dc, 0x811e,
+  0x10d6, 0x811d, 0x10d0, 0x811c, 0x10c9, 0x811c, 0x10c3, 0x811b,
+  0x10bd, 0x811a, 0x10b7, 0x8119, 0x10b0, 0x8118, 0x10aa, 0x8117,
+  0x10a4, 0x8117, 0x109e, 0x8116, 0x1098, 0x8115, 0x1091, 0x8114,
+  0x108b, 0x8113, 0x1085, 0x8113, 0x107f, 0x8112, 0x1078, 0x8111,
+  0x1072, 0x8110, 0x106c, 0x810f, 0x1066, 0x810f, 0x105f, 0x810e,
+  0x1059, 0x810d, 0x1053, 0x810c, 0x104d, 0x810b, 0x1047, 0x810b,
+  0x1040, 0x810a, 0x103a, 0x8109, 0x1034, 0x8108, 0x102e, 0x8107,
+  0x1027, 0x8107, 0x1021, 0x8106, 0x101b, 0x8105, 0x1015, 0x8104,
+  0x100e, 0x8103, 0x1008, 0x8103, 0x1002, 0x8102, 0xffc, 0x8101,
+  0xff5, 0x8100, 0xfef, 0x80ff, 0xfe9, 0x80ff, 0xfe3, 0x80fe,
+  0xfdd, 0x80fd, 0xfd6, 0x80fc, 0xfd0, 0x80fc, 0xfca, 0x80fb,
+  0xfc4, 0x80fa, 0xfbd, 0x80f9, 0xfb7, 0x80f8, 0xfb1, 0x80f8,
+  0xfab, 0x80f7, 0xfa4, 0x80f6, 0xf9e, 0x80f5, 0xf98, 0x80f5,
+  0xf92, 0x80f4, 0xf8b, 0x80f3, 0xf85, 0x80f2, 0xf7f, 0x80f2,
+  0xf79, 0x80f1, 0xf73, 0x80f0, 0xf6c, 0x80ef, 0xf66, 0x80ef,
+  0xf60, 0x80ee, 0xf5a, 0x80ed, 0xf53, 0x80ec, 0xf4d, 0x80ec,
+  0xf47, 0x80eb, 0xf41, 0x80ea, 0xf3a, 0x80e9, 0xf34, 0x80e9,
+  0xf2e, 0x80e8, 0xf28, 0x80e7, 0xf21, 0x80e6, 0xf1b, 0x80e6,
+  0xf15, 0x80e5, 0xf0f, 0x80e4, 0xf08, 0x80e3, 0xf02, 0x80e3,
+  0xefc, 0x80e2, 0xef6, 0x80e1, 0xef0, 0x80e0, 0xee9, 0x80e0,
+  0xee3, 0x80df, 0xedd, 0x80de, 0xed7, 0x80dd, 0xed0, 0x80dd,
+  0xeca, 0x80dc, 0xec4, 0x80db, 0xebe, 0x80db, 0xeb7, 0x80da,
+  0xeb1, 0x80d9, 0xeab, 0x80d8, 0xea5, 0x80d8, 0xe9e, 0x80d7,
+  0xe98, 0x80d6, 0xe92, 0x80d6, 0xe8c, 0x80d5, 0xe85, 0x80d4,
+  0xe7f, 0x80d3, 0xe79, 0x80d3, 0xe73, 0x80d2, 0xe6c, 0x80d1,
+  0xe66, 0x80d1, 0xe60, 0x80d0, 0xe5a, 0x80cf, 0xe53, 0x80ce,
+  0xe4d, 0x80ce, 0xe47, 0x80cd, 0xe41, 0x80cc, 0xe3a, 0x80cc,
+  0xe34, 0x80cb, 0xe2e, 0x80ca, 0xe28, 0x80ca, 0xe22, 0x80c9,
+  0xe1b, 0x80c8, 0xe15, 0x80c7, 0xe0f, 0x80c7, 0xe09, 0x80c6,
+  0xe02, 0x80c5, 0xdfc, 0x80c5, 0xdf6, 0x80c4, 0xdf0, 0x80c3,
+  0xde9, 0x80c3, 0xde3, 0x80c2, 0xddd, 0x80c1, 0xdd7, 0x80c1,
+  0xdd0, 0x80c0, 0xdca, 0x80bf, 0xdc4, 0x80bf, 0xdbe, 0x80be,
+  0xdb7, 0x80bd, 0xdb1, 0x80bd, 0xdab, 0x80bc, 0xda5, 0x80bb,
+  0xd9e, 0x80bb, 0xd98, 0x80ba, 0xd92, 0x80b9, 0xd8c, 0x80b9,
+  0xd85, 0x80b8, 0xd7f, 0x80b7, 0xd79, 0x80b7, 0xd73, 0x80b6,
+  0xd6c, 0x80b5, 0xd66, 0x80b5, 0xd60, 0x80b4, 0xd5a, 0x80b3,
+  0xd53, 0x80b3, 0xd4d, 0x80b2, 0xd47, 0x80b1, 0xd41, 0x80b1,
+  0xd3a, 0x80b0, 0xd34, 0x80af, 0xd2e, 0x80af, 0xd28, 0x80ae,
+  0xd21, 0x80ad, 0xd1b, 0x80ad, 0xd15, 0x80ac, 0xd0f, 0x80ab,
+  0xd08, 0x80ab, 0xd02, 0x80aa, 0xcfc, 0x80aa, 0xcf6, 0x80a9,
+  0xcef, 0x80a8, 0xce9, 0x80a8, 0xce3, 0x80a7, 0xcdd, 0x80a6,
+  0xcd6, 0x80a6, 0xcd0, 0x80a5, 0xcca, 0x80a5, 0xcc4, 0x80a4,
+  0xcbd, 0x80a3, 0xcb7, 0x80a3, 0xcb1, 0x80a2, 0xcab, 0x80a1,
+  0xca4, 0x80a1, 0xc9e, 0x80a0, 0xc98, 0x80a0, 0xc92, 0x809f,
+  0xc8b, 0x809e, 0xc85, 0x809e, 0xc7f, 0x809d, 0xc79, 0x809c,
+  0xc72, 0x809c, 0xc6c, 0x809b, 0xc66, 0x809b, 0xc60, 0x809a,
+  0xc59, 0x8099, 0xc53, 0x8099, 0xc4d, 0x8098, 0xc47, 0x8098,
+  0xc40, 0x8097, 0xc3a, 0x8096, 0xc34, 0x8096, 0xc2e, 0x8095,
+  0xc27, 0x8095, 0xc21, 0x8094, 0xc1b, 0x8093, 0xc14, 0x8093,
+  0xc0e, 0x8092, 0xc08, 0x8092, 0xc02, 0x8091, 0xbfb, 0x8090,
+  0xbf5, 0x8090, 0xbef, 0x808f, 0xbe9, 0x808f, 0xbe2, 0x808e,
+  0xbdc, 0x808e, 0xbd6, 0x808d, 0xbd0, 0x808c, 0xbc9, 0x808c,
+  0xbc3, 0x808b, 0xbbd, 0x808b, 0xbb7, 0x808a, 0xbb0, 0x8089,
+  0xbaa, 0x8089, 0xba4, 0x8088, 0xb9e, 0x8088, 0xb97, 0x8087,
+  0xb91, 0x8087, 0xb8b, 0x8086, 0xb85, 0x8085, 0xb7e, 0x8085,
+  0xb78, 0x8084, 0xb72, 0x8084, 0xb6c, 0x8083, 0xb65, 0x8083,
+  0xb5f, 0x8082, 0xb59, 0x8082, 0xb53, 0x8081, 0xb4c, 0x8080,
+  0xb46, 0x8080, 0xb40, 0x807f, 0xb3a, 0x807f, 0xb33, 0x807e,
+  0xb2d, 0x807e, 0xb27, 0x807d, 0xb20, 0x807d, 0xb1a, 0x807c,
+  0xb14, 0x807b, 0xb0e, 0x807b, 0xb07, 0x807a, 0xb01, 0x807a,
+  0xafb, 0x8079, 0xaf5, 0x8079, 0xaee, 0x8078, 0xae8, 0x8078,
+  0xae2, 0x8077, 0xadc, 0x8077, 0xad5, 0x8076, 0xacf, 0x8076,
+  0xac9, 0x8075, 0xac3, 0x8075, 0xabc, 0x8074, 0xab6, 0x8073,
+  0xab0, 0x8073, 0xaaa, 0x8072, 0xaa3, 0x8072, 0xa9d, 0x8071,
+  0xa97, 0x8071, 0xa90, 0x8070, 0xa8a, 0x8070, 0xa84, 0x806f,
+  0xa7e, 0x806f, 0xa77, 0x806e, 0xa71, 0x806e, 0xa6b, 0x806d,
+  0xa65, 0x806d, 0xa5e, 0x806c, 0xa58, 0x806c, 0xa52, 0x806b,
+  0xa4c, 0x806b, 0xa45, 0x806a, 0xa3f, 0x806a, 0xa39, 0x8069,
+  0xa33, 0x8069, 0xa2c, 0x8068, 0xa26, 0x8068, 0xa20, 0x8067,
+  0xa19, 0x8067, 0xa13, 0x8066, 0xa0d, 0x8066, 0xa07, 0x8065,
+  0xa00, 0x8065, 0x9fa, 0x8064, 0x9f4, 0x8064, 0x9ee, 0x8063,
+  0x9e7, 0x8063, 0x9e1, 0x8062, 0x9db, 0x8062, 0x9d5, 0x8061,
+  0x9ce, 0x8061, 0x9c8, 0x8060, 0x9c2, 0x8060, 0x9bc, 0x805f,
+  0x9b5, 0x805f, 0x9af, 0x805e, 0x9a9, 0x805e, 0x9a2, 0x805d,
+  0x99c, 0x805d, 0x996, 0x805d, 0x990, 0x805c, 0x989, 0x805c,
+  0x983, 0x805b, 0x97d, 0x805b, 0x977, 0x805a, 0x970, 0x805a,
+  0x96a, 0x8059, 0x964, 0x8059, 0x95e, 0x8058, 0x957, 0x8058,
+  0x951, 0x8057, 0x94b, 0x8057, 0x944, 0x8057, 0x93e, 0x8056,
+  0x938, 0x8056, 0x932, 0x8055, 0x92b, 0x8055, 0x925, 0x8054,
+  0x91f, 0x8054, 0x919, 0x8053, 0x912, 0x8053, 0x90c, 0x8052,
+  0x906, 0x8052, 0x900, 0x8052, 0x8f9, 0x8051, 0x8f3, 0x8051,
+  0x8ed, 0x8050, 0x8e6, 0x8050, 0x8e0, 0x804f, 0x8da, 0x804f,
+  0x8d4, 0x804f, 0x8cd, 0x804e, 0x8c7, 0x804e, 0x8c1, 0x804d,
+  0x8bb, 0x804d, 0x8b4, 0x804c, 0x8ae, 0x804c, 0x8a8, 0x804c,
+  0x8a2, 0x804b, 0x89b, 0x804b, 0x895, 0x804a, 0x88f, 0x804a,
+  0x888, 0x8049, 0x882, 0x8049, 0x87c, 0x8049, 0x876, 0x8048,
+  0x86f, 0x8048, 0x869, 0x8047, 0x863, 0x8047, 0x85d, 0x8047,
+  0x856, 0x8046, 0x850, 0x8046, 0x84a, 0x8045, 0x843, 0x8045,
+  0x83d, 0x8044, 0x837, 0x8044, 0x831, 0x8044, 0x82a, 0x8043,
+  0x824, 0x8043, 0x81e, 0x8042, 0x818, 0x8042, 0x811, 0x8042,
+  0x80b, 0x8041, 0x805, 0x8041, 0x7fe, 0x8040, 0x7f8, 0x8040,
+  0x7f2, 0x8040, 0x7ec, 0x803f, 0x7e5, 0x803f, 0x7df, 0x803f,
+  0x7d9, 0x803e, 0x7d3, 0x803e, 0x7cc, 0x803d, 0x7c6, 0x803d,
+  0x7c0, 0x803d, 0x7ba, 0x803c, 0x7b3, 0x803c, 0x7ad, 0x803b,
+  0x7a7, 0x803b, 0x7a0, 0x803b, 0x79a, 0x803a, 0x794, 0x803a,
+  0x78e, 0x803a, 0x787, 0x8039, 0x781, 0x8039, 0x77b, 0x8039,
+  0x775, 0x8038, 0x76e, 0x8038, 0x768, 0x8037, 0x762, 0x8037,
+  0x75b, 0x8037, 0x755, 0x8036, 0x74f, 0x8036, 0x749, 0x8036,
+  0x742, 0x8035, 0x73c, 0x8035, 0x736, 0x8035, 0x730, 0x8034,
+  0x729, 0x8034, 0x723, 0x8033, 0x71d, 0x8033, 0x716, 0x8033,
+  0x710, 0x8032, 0x70a, 0x8032, 0x704, 0x8032, 0x6fd, 0x8031,
+  0x6f7, 0x8031, 0x6f1, 0x8031, 0x6ea, 0x8030, 0x6e4, 0x8030,
+  0x6de, 0x8030, 0x6d8, 0x802f, 0x6d1, 0x802f, 0x6cb, 0x802f,
+  0x6c5, 0x802e, 0x6bf, 0x802e, 0x6b8, 0x802e, 0x6b2, 0x802d,
+  0x6ac, 0x802d, 0x6a5, 0x802d, 0x69f, 0x802c, 0x699, 0x802c,
+  0x693, 0x802c, 0x68c, 0x802b, 0x686, 0x802b, 0x680, 0x802b,
+  0x67a, 0x802a, 0x673, 0x802a, 0x66d, 0x802a, 0x667, 0x802a,
+  0x660, 0x8029, 0x65a, 0x8029, 0x654, 0x8029, 0x64e, 0x8028,
+  0x647, 0x8028, 0x641, 0x8028, 0x63b, 0x8027, 0x635, 0x8027,
+  0x62e, 0x8027, 0x628, 0x8026, 0x622, 0x8026, 0x61b, 0x8026,
+  0x615, 0x8026, 0x60f, 0x8025, 0x609, 0x8025, 0x602, 0x8025,
+  0x5fc, 0x8024, 0x5f6, 0x8024, 0x5ef, 0x8024, 0x5e9, 0x8023,
+  0x5e3, 0x8023, 0x5dd, 0x8023, 0x5d6, 0x8023, 0x5d0, 0x8022,
+  0x5ca, 0x8022, 0x5c4, 0x8022, 0x5bd, 0x8021, 0x5b7, 0x8021,
+  0x5b1, 0x8021, 0x5aa, 0x8021, 0x5a4, 0x8020, 0x59e, 0x8020,
+  0x598, 0x8020, 0x591, 0x8020, 0x58b, 0x801f, 0x585, 0x801f,
+  0x57f, 0x801f, 0x578, 0x801e, 0x572, 0x801e, 0x56c, 0x801e,
+  0x565, 0x801e, 0x55f, 0x801d, 0x559, 0x801d, 0x553, 0x801d,
+  0x54c, 0x801d, 0x546, 0x801c, 0x540, 0x801c, 0x539, 0x801c,
+  0x533, 0x801c, 0x52d, 0x801b, 0x527, 0x801b, 0x520, 0x801b,
+  0x51a, 0x801b, 0x514, 0x801a, 0x50d, 0x801a, 0x507, 0x801a,
+  0x501, 0x801a, 0x4fb, 0x8019, 0x4f4, 0x8019, 0x4ee, 0x8019,
+  0x4e8, 0x8019, 0x4e2, 0x8018, 0x4db, 0x8018, 0x4d5, 0x8018,
+  0x4cf, 0x8018, 0x4c8, 0x8017, 0x4c2, 0x8017, 0x4bc, 0x8017,
+  0x4b6, 0x8017, 0x4af, 0x8016, 0x4a9, 0x8016, 0x4a3, 0x8016,
+  0x49c, 0x8016, 0x496, 0x8016, 0x490, 0x8015, 0x48a, 0x8015,
+  0x483, 0x8015, 0x47d, 0x8015, 0x477, 0x8014, 0x471, 0x8014,
+  0x46a, 0x8014, 0x464, 0x8014, 0x45e, 0x8014, 0x457, 0x8013,
+  0x451, 0x8013, 0x44b, 0x8013, 0x445, 0x8013, 0x43e, 0x8013,
+  0x438, 0x8012, 0x432, 0x8012, 0x42b, 0x8012, 0x425, 0x8012,
+  0x41f, 0x8012, 0x419, 0x8011, 0x412, 0x8011, 0x40c, 0x8011,
+  0x406, 0x8011, 0x3ff, 0x8011, 0x3f9, 0x8010, 0x3f3, 0x8010,
+  0x3ed, 0x8010, 0x3e6, 0x8010, 0x3e0, 0x8010, 0x3da, 0x800f,
+  0x3d4, 0x800f, 0x3cd, 0x800f, 0x3c7, 0x800f, 0x3c1, 0x800f,
+  0x3ba, 0x800e, 0x3b4, 0x800e, 0x3ae, 0x800e, 0x3a8, 0x800e,
+  0x3a1, 0x800e, 0x39b, 0x800e, 0x395, 0x800d, 0x38e, 0x800d,
+  0x388, 0x800d, 0x382, 0x800d, 0x37c, 0x800d, 0x375, 0x800c,
+  0x36f, 0x800c, 0x369, 0x800c, 0x362, 0x800c, 0x35c, 0x800c,
+  0x356, 0x800c, 0x350, 0x800b, 0x349, 0x800b, 0x343, 0x800b,
+  0x33d, 0x800b, 0x337, 0x800b, 0x330, 0x800b, 0x32a, 0x800b,
+  0x324, 0x800a, 0x31d, 0x800a, 0x317, 0x800a, 0x311, 0x800a,
+  0x30b, 0x800a, 0x304, 0x800a, 0x2fe, 0x8009, 0x2f8, 0x8009,
+  0x2f1, 0x8009, 0x2eb, 0x8009, 0x2e5, 0x8009, 0x2df, 0x8009,
+  0x2d8, 0x8009, 0x2d2, 0x8008, 0x2cc, 0x8008, 0x2c5, 0x8008,
+  0x2bf, 0x8008, 0x2b9, 0x8008, 0x2b3, 0x8008, 0x2ac, 0x8008,
+  0x2a6, 0x8008, 0x2a0, 0x8007, 0x299, 0x8007, 0x293, 0x8007,
+  0x28d, 0x8007, 0x287, 0x8007, 0x280, 0x8007, 0x27a, 0x8007,
+  0x274, 0x8007, 0x26d, 0x8006, 0x267, 0x8006, 0x261, 0x8006,
+  0x25b, 0x8006, 0x254, 0x8006, 0x24e, 0x8006, 0x248, 0x8006,
+  0x242, 0x8006, 0x23b, 0x8005, 0x235, 0x8005, 0x22f, 0x8005,
+  0x228, 0x8005, 0x222, 0x8005, 0x21c, 0x8005, 0x216, 0x8005,
+  0x20f, 0x8005, 0x209, 0x8005, 0x203, 0x8005, 0x1fc, 0x8004,
+  0x1f6, 0x8004, 0x1f0, 0x8004, 0x1ea, 0x8004, 0x1e3, 0x8004,
+  0x1dd, 0x8004, 0x1d7, 0x8004, 0x1d0, 0x8004, 0x1ca, 0x8004,
+  0x1c4, 0x8004, 0x1be, 0x8004, 0x1b7, 0x8003, 0x1b1, 0x8003,
+  0x1ab, 0x8003, 0x1a4, 0x8003, 0x19e, 0x8003, 0x198, 0x8003,
+  0x192, 0x8003, 0x18b, 0x8003, 0x185, 0x8003, 0x17f, 0x8003,
+  0x178, 0x8003, 0x172, 0x8003, 0x16c, 0x8003, 0x166, 0x8002,
+  0x15f, 0x8002, 0x159, 0x8002, 0x153, 0x8002, 0x14d, 0x8002,
+  0x146, 0x8002, 0x140, 0x8002, 0x13a, 0x8002, 0x133, 0x8002,
+  0x12d, 0x8002, 0x127, 0x8002, 0x121, 0x8002, 0x11a, 0x8002,
+  0x114, 0x8002, 0x10e, 0x8002, 0x107, 0x8002, 0x101, 0x8002,
+  0xfb, 0x8001, 0xf5, 0x8001, 0xee, 0x8001, 0xe8, 0x8001,
+  0xe2, 0x8001, 0xdb, 0x8001, 0xd5, 0x8001, 0xcf, 0x8001,
+  0xc9, 0x8001, 0xc2, 0x8001, 0xbc, 0x8001, 0xb6, 0x8001,
+  0xaf, 0x8001, 0xa9, 0x8001, 0xa3, 0x8001, 0x9d, 0x8001,
+  0x96, 0x8001, 0x90, 0x8001, 0x8a, 0x8001, 0x83, 0x8001,
+  0x7d, 0x8001, 0x77, 0x8001, 0x71, 0x8001, 0x6a, 0x8001,
+  0x64, 0x8001, 0x5e, 0x8001, 0x57, 0x8001, 0x51, 0x8001,
+  0x4b, 0x8001, 0x45, 0x8001, 0x3e, 0x8001, 0x38, 0x8001,
+  0x32, 0x8001, 0x2b, 0x8001, 0x25, 0x8001, 0x1f, 0x8001,
+  0x19, 0x8001, 0x12, 0x8001, 0xc, 0x8001, 0x6, 0x8001,
+};
+
+
+/**    
+* \par    
+* cosFactor tables are generated using the formula : 
 cos_factors[n] = 2 * cos((2n+1)*pi/(4*N)) 
    
+* \par    
+* C command to generate the table    
+* 
    
+* for(i = 0; i< N; i++)    
+* {    
+*   cos_factors[i]= 2 * cos((2*i+1)*c/2);    
+* } 
    
+* \par    
+* where N is the number of factors to generate and c is pi/(2*N)    
+* \par    
+* Then converted to q15 format by multiplying with 2^31 and saturated if required.    
+    
+*/
+
+static const q15_t ALIGN4 cos_factorsQ15_128[128] = {
+  0x7fff, 0x7ffa, 0x7ff0, 0x7fe1, 0x7fce, 0x7fb5, 0x7f97, 0x7f75,
+  0x7f4d, 0x7f21, 0x7ef0, 0x7eba, 0x7e7f, 0x7e3f, 0x7dfa, 0x7db0,
+  0x7d62, 0x7d0f, 0x7cb7, 0x7c5a, 0x7bf8, 0x7b92, 0x7b26, 0x7ab6,
+  0x7a42, 0x79c8, 0x794a, 0x78c7, 0x7840, 0x77b4, 0x7723, 0x768e,
+  0x75f4, 0x7555, 0x74b2, 0x740b, 0x735f, 0x72af, 0x71fa, 0x7141,
+  0x7083, 0x6fc1, 0x6efb, 0x6e30, 0x6d62, 0x6c8f, 0x6bb8, 0x6adc,
+  0x69fd, 0x6919, 0x6832, 0x6746, 0x6657, 0x6563, 0x646c, 0x6371,
+  0x6271, 0x616f, 0x6068, 0x5f5e, 0x5e50, 0x5d3e, 0x5c29, 0x5b10,
+  0x59f3, 0x58d4, 0x57b0, 0x568a, 0x5560, 0x5433, 0x5302, 0x51ce,
+  0x5097, 0x4f5e, 0x4e21, 0x4ce1, 0x4b9e, 0x4a58, 0x490f, 0x47c3,
+  0x4675, 0x4524, 0x43d0, 0x427a, 0x4121, 0x3fc5, 0x3e68, 0x3d07,
+  0x3ba5, 0x3a40, 0x38d8, 0x376f, 0x3604, 0x3496, 0x3326, 0x31b5,
+  0x3041, 0x2ecc, 0x2d55, 0x2bdc, 0x2a61, 0x28e5, 0x2767, 0x25e8,
+  0x2467, 0x22e5, 0x2161, 0x1fdc, 0x1e56, 0x1ccf, 0x1b47, 0x19bd,
+  0x1833, 0x16a8, 0x151b, 0x138e, 0x1201, 0x1072, 0xee3, 0xd53,
+  0xbc3, 0xa33, 0x8a2, 0x710, 0x57f, 0x3ed, 0x25b, 0xc9
+};
+
+static const q15_t ALIGN4 cos_factorsQ15_512[512] = {
+  0x7fff, 0x7fff, 0x7fff, 0x7ffe, 0x7ffc, 0x7ffb, 0x7ff9, 0x7ff7,
+  0x7ff4, 0x7ff2, 0x7fee, 0x7feb, 0x7fe7, 0x7fe3, 0x7fdf, 0x7fda,
+  0x7fd6, 0x7fd0, 0x7fcb, 0x7fc5, 0x7fbf, 0x7fb8, 0x7fb1, 0x7faa,
+  0x7fa3, 0x7f9b, 0x7f93, 0x7f8b, 0x7f82, 0x7f79, 0x7f70, 0x7f67,
+  0x7f5d, 0x7f53, 0x7f48, 0x7f3d, 0x7f32, 0x7f27, 0x7f1b, 0x7f0f,
+  0x7f03, 0x7ef6, 0x7ee9, 0x7edc, 0x7ecf, 0x7ec1, 0x7eb3, 0x7ea4,
+  0x7e95, 0x7e86, 0x7e77, 0x7e67, 0x7e57, 0x7e47, 0x7e37, 0x7e26,
+  0x7e14, 0x7e03, 0x7df1, 0x7ddf, 0x7dcd, 0x7dba, 0x7da7, 0x7d94,
+  0x7d80, 0x7d6c, 0x7d58, 0x7d43, 0x7d2f, 0x7d19, 0x7d04, 0x7cee,
+  0x7cd8, 0x7cc2, 0x7cab, 0x7c94, 0x7c7d, 0x7c66, 0x7c4e, 0x7c36,
+  0x7c1d, 0x7c05, 0x7beb, 0x7bd2, 0x7bb9, 0x7b9f, 0x7b84, 0x7b6a,
+  0x7b4f, 0x7b34, 0x7b19, 0x7afd, 0x7ae1, 0x7ac5, 0x7aa8, 0x7a8b,
+  0x7a6e, 0x7a50, 0x7a33, 0x7a15, 0x79f6, 0x79d8, 0x79b9, 0x7999,
+  0x797a, 0x795a, 0x793a, 0x7919, 0x78f9, 0x78d8, 0x78b6, 0x7895,
+  0x7873, 0x7851, 0x782e, 0x780c, 0x77e9, 0x77c5, 0x77a2, 0x777e,
+  0x775a, 0x7735, 0x7710, 0x76eb, 0x76c6, 0x76a0, 0x767b, 0x7654,
+  0x762e, 0x7607, 0x75e0, 0x75b9, 0x7591, 0x7569, 0x7541, 0x7519,
+  0x74f0, 0x74c7, 0x749e, 0x7474, 0x744a, 0x7420, 0x73f6, 0x73cb,
+  0x73a0, 0x7375, 0x7349, 0x731d, 0x72f1, 0x72c5, 0x7298, 0x726b,
+  0x723e, 0x7211, 0x71e3, 0x71b5, 0x7186, 0x7158, 0x7129, 0x70fa,
+  0x70cb, 0x709b, 0x706b, 0x703b, 0x700a, 0x6fda, 0x6fa9, 0x6f77,
+  0x6f46, 0x6f14, 0x6ee2, 0x6eaf, 0x6e7d, 0x6e4a, 0x6e17, 0x6de3,
+  0x6db0, 0x6d7c, 0x6d48, 0x6d13, 0x6cde, 0x6ca9, 0x6c74, 0x6c3f,
+  0x6c09, 0x6bd3, 0x6b9c, 0x6b66, 0x6b2f, 0x6af8, 0x6ac1, 0x6a89,
+  0x6a51, 0x6a19, 0x69e1, 0x69a8, 0x696f, 0x6936, 0x68fd, 0x68c3,
+  0x6889, 0x684f, 0x6815, 0x67da, 0x679f, 0x6764, 0x6729, 0x66ed,
+  0x66b1, 0x6675, 0x6639, 0x65fc, 0x65bf, 0x6582, 0x6545, 0x6507,
+  0x64c9, 0x648b, 0x644d, 0x640e, 0x63cf, 0x6390, 0x6351, 0x6311,
+  0x62d2, 0x6292, 0x6251, 0x6211, 0x61d0, 0x618f, 0x614e, 0x610d,
+  0x60cb, 0x6089, 0x6047, 0x6004, 0x5fc2, 0x5f7f, 0x5f3c, 0x5ef9,
+  0x5eb5, 0x5e71, 0x5e2d, 0x5de9, 0x5da5, 0x5d60, 0x5d1b, 0x5cd6,
+  0x5c91, 0x5c4b, 0x5c06, 0x5bc0, 0x5b79, 0x5b33, 0x5aec, 0x5aa5,
+  0x5a5e, 0x5a17, 0x59d0, 0x5988, 0x5940, 0x58f8, 0x58af, 0x5867,
+  0x581e, 0x57d5, 0x578c, 0x5742, 0x56f9, 0x56af, 0x5665, 0x561a,
+  0x55d0, 0x5585, 0x553a, 0x54ef, 0x54a4, 0x5458, 0x540d, 0x53c1,
+  0x5375, 0x5328, 0x52dc, 0x528f, 0x5242, 0x51f5, 0x51a8, 0x515a,
+  0x510c, 0x50bf, 0x5070, 0x5022, 0x4fd4, 0x4f85, 0x4f36, 0x4ee7,
+  0x4e98, 0x4e48, 0x4df9, 0x4da9, 0x4d59, 0x4d09, 0x4cb8, 0x4c68,
+  0x4c17, 0x4bc6, 0x4b75, 0x4b24, 0x4ad2, 0x4a81, 0x4a2f, 0x49dd,
+  0x498a, 0x4938, 0x48e6, 0x4893, 0x4840, 0x47ed, 0x479a, 0x4746,
+  0x46f3, 0x469f, 0x464b, 0x45f7, 0x45a3, 0x454e, 0x44fa, 0x44a5,
+  0x4450, 0x43fb, 0x43a5, 0x4350, 0x42fa, 0x42a5, 0x424f, 0x41f9,
+  0x41a2, 0x414c, 0x40f6, 0x409f, 0x4048, 0x3ff1, 0x3f9a, 0x3f43,
+  0x3eeb, 0x3e93, 0x3e3c, 0x3de4, 0x3d8c, 0x3d33, 0x3cdb, 0x3c83,
+  0x3c2a, 0x3bd1, 0x3b78, 0x3b1f, 0x3ac6, 0x3a6c, 0x3a13, 0x39b9,
+  0x395f, 0x3906, 0x38ab, 0x3851, 0x37f7, 0x379c, 0x3742, 0x36e7,
+  0x368c, 0x3631, 0x35d6, 0x357b, 0x351f, 0x34c4, 0x3468, 0x340c,
+  0x33b0, 0x3354, 0x32f8, 0x329c, 0x3240, 0x31e3, 0x3186, 0x312a,
+  0x30cd, 0x3070, 0x3013, 0x2fb5, 0x2f58, 0x2efb, 0x2e9d, 0x2e3f,
+  0x2de2, 0x2d84, 0x2d26, 0x2cc8, 0x2c69, 0x2c0b, 0x2bad, 0x2b4e,
+  0x2aef, 0x2a91, 0x2a32, 0x29d3, 0x2974, 0x2915, 0x28b5, 0x2856,
+  0x27f6, 0x2797, 0x2737, 0x26d8, 0x2678, 0x2618, 0x25b8, 0x2558,
+  0x24f7, 0x2497, 0x2437, 0x23d6, 0x2376, 0x2315, 0x22b4, 0x2254,
+  0x21f3, 0x2192, 0x2131, 0x20d0, 0x206e, 0x200d, 0x1fac, 0x1f4a,
+  0x1ee9, 0x1e87, 0x1e25, 0x1dc4, 0x1d62, 0x1d00, 0x1c9e, 0x1c3c,
+  0x1bda, 0x1b78, 0x1b16, 0x1ab3, 0x1a51, 0x19ef, 0x198c, 0x192a,
+  0x18c7, 0x1864, 0x1802, 0x179f, 0x173c, 0x16d9, 0x1676, 0x1613,
+  0x15b0, 0x154d, 0x14ea, 0x1487, 0x1423, 0x13c0, 0x135d, 0x12f9,
+  0x1296, 0x1232, 0x11cf, 0x116b, 0x1108, 0x10a4, 0x1040, 0xfdd,
+  0xf79, 0xf15, 0xeb1, 0xe4d, 0xde9, 0xd85, 0xd21, 0xcbd,
+  0xc59, 0xbf5, 0xb91, 0xb2d, 0xac9, 0xa65, 0xa00, 0x99c,
+  0x938, 0x8d4, 0x86f, 0x80b, 0x7a7, 0x742, 0x6de, 0x67a,
+  0x615, 0x5b1, 0x54c, 0x4e8, 0x483, 0x41f, 0x3ba, 0x356,
+  0x2f1, 0x28d, 0x228, 0x1c4, 0x15f, 0xfb, 0x96, 0x32,
+};
+
+static const q15_t ALIGN4 cos_factorsQ15_2048[2048] = {
+  0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff,
+  0x7fff, 0x7fff, 0x7ffe, 0x7ffe, 0x7ffe, 0x7ffe, 0x7ffd, 0x7ffd,
+  0x7ffd, 0x7ffd, 0x7ffc, 0x7ffc, 0x7ffb, 0x7ffb, 0x7ffb, 0x7ffa,
+  0x7ffa, 0x7ff9, 0x7ff9, 0x7ff8, 0x7ff8, 0x7ff7, 0x7ff7, 0x7ff6,
+  0x7ff5, 0x7ff5, 0x7ff4, 0x7ff3, 0x7ff3, 0x7ff2, 0x7ff1, 0x7ff0,
+  0x7ff0, 0x7fef, 0x7fee, 0x7fed, 0x7fec, 0x7fec, 0x7feb, 0x7fea,
+  0x7fe9, 0x7fe8, 0x7fe7, 0x7fe6, 0x7fe5, 0x7fe4, 0x7fe3, 0x7fe2,
+  0x7fe1, 0x7fe0, 0x7fdf, 0x7fdd, 0x7fdc, 0x7fdb, 0x7fda, 0x7fd9,
+  0x7fd7, 0x7fd6, 0x7fd5, 0x7fd4, 0x7fd2, 0x7fd1, 0x7fd0, 0x7fce,
+  0x7fcd, 0x7fcb, 0x7fca, 0x7fc9, 0x7fc7, 0x7fc6, 0x7fc4, 0x7fc3,
+  0x7fc1, 0x7fc0, 0x7fbe, 0x7fbc, 0x7fbb, 0x7fb9, 0x7fb7, 0x7fb6,
+  0x7fb4, 0x7fb2, 0x7fb1, 0x7faf, 0x7fad, 0x7fab, 0x7fa9, 0x7fa8,
+  0x7fa6, 0x7fa4, 0x7fa2, 0x7fa0, 0x7f9e, 0x7f9c, 0x7f9a, 0x7f98,
+  0x7f96, 0x7f94, 0x7f92, 0x7f90, 0x7f8e, 0x7f8c, 0x7f8a, 0x7f88,
+  0x7f86, 0x7f83, 0x7f81, 0x7f7f, 0x7f7d, 0x7f7b, 0x7f78, 0x7f76,
+  0x7f74, 0x7f71, 0x7f6f, 0x7f6d, 0x7f6a, 0x7f68, 0x7f65, 0x7f63,
+  0x7f60, 0x7f5e, 0x7f5b, 0x7f59, 0x7f56, 0x7f54, 0x7f51, 0x7f4f,
+  0x7f4c, 0x7f49, 0x7f47, 0x7f44, 0x7f41, 0x7f3f, 0x7f3c, 0x7f39,
+  0x7f36, 0x7f34, 0x7f31, 0x7f2e, 0x7f2b, 0x7f28, 0x7f25, 0x7f23,
+  0x7f20, 0x7f1d, 0x7f1a, 0x7f17, 0x7f14, 0x7f11, 0x7f0e, 0x7f0b,
+  0x7f08, 0x7f04, 0x7f01, 0x7efe, 0x7efb, 0x7ef8, 0x7ef5, 0x7ef1,
+  0x7eee, 0x7eeb, 0x7ee8, 0x7ee4, 0x7ee1, 0x7ede, 0x7eda, 0x7ed7,
+  0x7ed4, 0x7ed0, 0x7ecd, 0x7ec9, 0x7ec6, 0x7ec3, 0x7ebf, 0x7ebb,
+  0x7eb8, 0x7eb4, 0x7eb1, 0x7ead, 0x7eaa, 0x7ea6, 0x7ea2, 0x7e9f,
+  0x7e9b, 0x7e97, 0x7e94, 0x7e90, 0x7e8c, 0x7e88, 0x7e84, 0x7e81,
+  0x7e7d, 0x7e79, 0x7e75, 0x7e71, 0x7e6d, 0x7e69, 0x7e65, 0x7e61,
+  0x7e5d, 0x7e59, 0x7e55, 0x7e51, 0x7e4d, 0x7e49, 0x7e45, 0x7e41,
+  0x7e3d, 0x7e39, 0x7e34, 0x7e30, 0x7e2c, 0x7e28, 0x7e24, 0x7e1f,
+  0x7e1b, 0x7e17, 0x7e12, 0x7e0e, 0x7e0a, 0x7e05, 0x7e01, 0x7dfc,
+  0x7df8, 0x7df3, 0x7def, 0x7dea, 0x7de6, 0x7de1, 0x7ddd, 0x7dd8,
+  0x7dd4, 0x7dcf, 0x7dca, 0x7dc6, 0x7dc1, 0x7dbc, 0x7db8, 0x7db3,
+  0x7dae, 0x7da9, 0x7da5, 0x7da0, 0x7d9b, 0x7d96, 0x7d91, 0x7d8c,
+  0x7d87, 0x7d82, 0x7d7e, 0x7d79, 0x7d74, 0x7d6f, 0x7d6a, 0x7d65,
+  0x7d60, 0x7d5a, 0x7d55, 0x7d50, 0x7d4b, 0x7d46, 0x7d41, 0x7d3c,
+  0x7d36, 0x7d31, 0x7d2c, 0x7d27, 0x7d21, 0x7d1c, 0x7d17, 0x7d11,
+  0x7d0c, 0x7d07, 0x7d01, 0x7cfc, 0x7cf6, 0x7cf1, 0x7cec, 0x7ce6,
+  0x7ce1, 0x7cdb, 0x7cd5, 0x7cd0, 0x7cca, 0x7cc5, 0x7cbf, 0x7cb9,
+  0x7cb4, 0x7cae, 0x7ca8, 0x7ca3, 0x7c9d, 0x7c97, 0x7c91, 0x7c8c,
+  0x7c86, 0x7c80, 0x7c7a, 0x7c74, 0x7c6e, 0x7c69, 0x7c63, 0x7c5d,
+  0x7c57, 0x7c51, 0x7c4b, 0x7c45, 0x7c3f, 0x7c39, 0x7c33, 0x7c2d,
+  0x7c26, 0x7c20, 0x7c1a, 0x7c14, 0x7c0e, 0x7c08, 0x7c01, 0x7bfb,
+  0x7bf5, 0x7bef, 0x7be8, 0x7be2, 0x7bdc, 0x7bd5, 0x7bcf, 0x7bc9,
+  0x7bc2, 0x7bbc, 0x7bb5, 0x7baf, 0x7ba8, 0x7ba2, 0x7b9b, 0x7b95,
+  0x7b8e, 0x7b88, 0x7b81, 0x7b7a, 0x7b74, 0x7b6d, 0x7b67, 0x7b60,
+  0x7b59, 0x7b52, 0x7b4c, 0x7b45, 0x7b3e, 0x7b37, 0x7b31, 0x7b2a,
+  0x7b23, 0x7b1c, 0x7b15, 0x7b0e, 0x7b07, 0x7b00, 0x7af9, 0x7af2,
+  0x7aeb, 0x7ae4, 0x7add, 0x7ad6, 0x7acf, 0x7ac8, 0x7ac1, 0x7aba,
+  0x7ab3, 0x7aac, 0x7aa4, 0x7a9d, 0x7a96, 0x7a8f, 0x7a87, 0x7a80,
+  0x7a79, 0x7a72, 0x7a6a, 0x7a63, 0x7a5c, 0x7a54, 0x7a4d, 0x7a45,
+  0x7a3e, 0x7a36, 0x7a2f, 0x7a27, 0x7a20, 0x7a18, 0x7a11, 0x7a09,
+  0x7a02, 0x79fa, 0x79f2, 0x79eb, 0x79e3, 0x79db, 0x79d4, 0x79cc,
+  0x79c4, 0x79bc, 0x79b5, 0x79ad, 0x79a5, 0x799d, 0x7995, 0x798e,
+  0x7986, 0x797e, 0x7976, 0x796e, 0x7966, 0x795e, 0x7956, 0x794e,
+  0x7946, 0x793e, 0x7936, 0x792e, 0x7926, 0x791e, 0x7915, 0x790d,
+  0x7905, 0x78fd, 0x78f5, 0x78ec, 0x78e4, 0x78dc, 0x78d4, 0x78cb,
+  0x78c3, 0x78bb, 0x78b2, 0x78aa, 0x78a2, 0x7899, 0x7891, 0x7888,
+  0x7880, 0x7877, 0x786f, 0x7866, 0x785e, 0x7855, 0x784d, 0x7844,
+  0x783b, 0x7833, 0x782a, 0x7821, 0x7819, 0x7810, 0x7807, 0x77ff,
+  0x77f6, 0x77ed, 0x77e4, 0x77db, 0x77d3, 0x77ca, 0x77c1, 0x77b8,
+  0x77af, 0x77a6, 0x779d, 0x7794, 0x778b, 0x7782, 0x7779, 0x7770,
+  0x7767, 0x775e, 0x7755, 0x774c, 0x7743, 0x773a, 0x7731, 0x7727,
+  0x771e, 0x7715, 0x770c, 0x7703, 0x76f9, 0x76f0, 0x76e7, 0x76dd,
+  0x76d4, 0x76cb, 0x76c1, 0x76b8, 0x76af, 0x76a5, 0x769c, 0x7692,
+  0x7689, 0x767f, 0x7676, 0x766c, 0x7663, 0x7659, 0x7650, 0x7646,
+  0x763c, 0x7633, 0x7629, 0x761f, 0x7616, 0x760c, 0x7602, 0x75f9,
+  0x75ef, 0x75e5, 0x75db, 0x75d1, 0x75c8, 0x75be, 0x75b4, 0x75aa,
+  0x75a0, 0x7596, 0x758c, 0x7582, 0x7578, 0x756e, 0x7564, 0x755a,
+  0x7550, 0x7546, 0x753c, 0x7532, 0x7528, 0x751e, 0x7514, 0x7509,
+  0x74ff, 0x74f5, 0x74eb, 0x74e1, 0x74d6, 0x74cc, 0x74c2, 0x74b7,
+  0x74ad, 0x74a3, 0x7498, 0x748e, 0x7484, 0x7479, 0x746f, 0x7464,
+  0x745a, 0x744f, 0x7445, 0x743a, 0x7430, 0x7425, 0x741b, 0x7410,
+  0x7406, 0x73fb, 0x73f0, 0x73e6, 0x73db, 0x73d0, 0x73c6, 0x73bb,
+  0x73b0, 0x73a5, 0x739b, 0x7390, 0x7385, 0x737a, 0x736f, 0x7364,
+  0x7359, 0x734f, 0x7344, 0x7339, 0x732e, 0x7323, 0x7318, 0x730d,
+  0x7302, 0x72f7, 0x72ec, 0x72e1, 0x72d5, 0x72ca, 0x72bf, 0x72b4,
+  0x72a9, 0x729e, 0x7293, 0x7287, 0x727c, 0x7271, 0x7266, 0x725a,
+  0x724f, 0x7244, 0x7238, 0x722d, 0x7222, 0x7216, 0x720b, 0x71ff,
+  0x71f4, 0x71e9, 0x71dd, 0x71d2, 0x71c6, 0x71bb, 0x71af, 0x71a3,
+  0x7198, 0x718c, 0x7181, 0x7175, 0x7169, 0x715e, 0x7152, 0x7146,
+  0x713b, 0x712f, 0x7123, 0x7117, 0x710c, 0x7100, 0x70f4, 0x70e8,
+  0x70dc, 0x70d1, 0x70c5, 0x70b9, 0x70ad, 0x70a1, 0x7095, 0x7089,
+  0x707d, 0x7071, 0x7065, 0x7059, 0x704d, 0x7041, 0x7035, 0x7029,
+  0x701d, 0x7010, 0x7004, 0x6ff8, 0x6fec, 0x6fe0, 0x6fd3, 0x6fc7,
+  0x6fbb, 0x6faf, 0x6fa2, 0x6f96, 0x6f8a, 0x6f7d, 0x6f71, 0x6f65,
+  0x6f58, 0x6f4c, 0x6f3f, 0x6f33, 0x6f27, 0x6f1a, 0x6f0e, 0x6f01,
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+  0x3819, 0x3802, 0x37ec, 0x37d5, 0x37be, 0x37a8, 0x3791, 0x377a,
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+  0x281a, 0x2802, 0x27eb, 0x27d3, 0x27bb, 0x27a3, 0x278b, 0x2773,
+  0x275b, 0x2743, 0x272b, 0x2713, 0x26fb, 0x26e4, 0x26cc, 0x26b4,
+  0x269c, 0x2684, 0x266c, 0x2654, 0x263c, 0x2624, 0x260c, 0x25f4,
+  0x25dc, 0x25c4, 0x25ac, 0x2594, 0x257c, 0x2564, 0x254c, 0x2534,
+  0x251c, 0x2503, 0x24eb, 0x24d3, 0x24bb, 0x24a3, 0x248b, 0x2473,
+  0x245b, 0x2443, 0x242b, 0x2413, 0x23fa, 0x23e2, 0x23ca, 0x23b2,
+  0x239a, 0x2382, 0x236a, 0x2352, 0x2339, 0x2321, 0x2309, 0x22f1,
+  0x22d9, 0x22c0, 0x22a8, 0x2290, 0x2278, 0x2260, 0x2247, 0x222f,
+  0x2217, 0x21ff, 0x21e7, 0x21ce, 0x21b6, 0x219e, 0x2186, 0x216d,
+  0x2155, 0x213d, 0x2125, 0x210c, 0x20f4, 0x20dc, 0x20c3, 0x20ab,
+  0x2093, 0x207a, 0x2062, 0x204a, 0x2032, 0x2019, 0x2001, 0x1fe9,
+  0x1fd0, 0x1fb8, 0x1f9f, 0x1f87, 0x1f6f, 0x1f56, 0x1f3e, 0x1f26,
+  0x1f0d, 0x1ef5, 0x1edd, 0x1ec4, 0x1eac, 0x1e93, 0x1e7b, 0x1e62,
+  0x1e4a, 0x1e32, 0x1e19, 0x1e01, 0x1de8, 0x1dd0, 0x1db7, 0x1d9f,
+  0x1d87, 0x1d6e, 0x1d56, 0x1d3d, 0x1d25, 0x1d0c, 0x1cf4, 0x1cdb,
+  0x1cc3, 0x1caa, 0x1c92, 0x1c79, 0x1c61, 0x1c48, 0x1c30, 0x1c17,
+  0x1bff, 0x1be6, 0x1bce, 0x1bb5, 0x1b9d, 0x1b84, 0x1b6c, 0x1b53,
+  0x1b3a, 0x1b22, 0x1b09, 0x1af1, 0x1ad8, 0x1ac0, 0x1aa7, 0x1a8e,
+  0x1a76, 0x1a5d, 0x1a45, 0x1a2c, 0x1a13, 0x19fb, 0x19e2, 0x19ca,
+  0x19b1, 0x1998, 0x1980, 0x1967, 0x194e, 0x1936, 0x191d, 0x1905,
+  0x18ec, 0x18d3, 0x18bb, 0x18a2, 0x1889, 0x1871, 0x1858, 0x183f,
+  0x1827, 0x180e, 0x17f5, 0x17dd, 0x17c4, 0x17ab, 0x1792, 0x177a,
+  0x1761, 0x1748, 0x1730, 0x1717, 0x16fe, 0x16e5, 0x16cd, 0x16b4,
+  0x169b, 0x1682, 0x166a, 0x1651, 0x1638, 0x161f, 0x1607, 0x15ee,
+  0x15d5, 0x15bc, 0x15a4, 0x158b, 0x1572, 0x1559, 0x1541, 0x1528,
+  0x150f, 0x14f6, 0x14dd, 0x14c5, 0x14ac, 0x1493, 0x147a, 0x1461,
+  0x1449, 0x1430, 0x1417, 0x13fe, 0x13e5, 0x13cc, 0x13b4, 0x139b,
+  0x1382, 0x1369, 0x1350, 0x1337, 0x131f, 0x1306, 0x12ed, 0x12d4,
+  0x12bb, 0x12a2, 0x1289, 0x1271, 0x1258, 0x123f, 0x1226, 0x120d,
+  0x11f4, 0x11db, 0x11c2, 0x11a9, 0x1191, 0x1178, 0x115f, 0x1146,
+  0x112d, 0x1114, 0x10fb, 0x10e2, 0x10c9, 0x10b0, 0x1098, 0x107f,
+  0x1066, 0x104d, 0x1034, 0x101b, 0x1002, 0xfe9, 0xfd0, 0xfb7,
+  0xf9e, 0xf85, 0xf6c, 0xf53, 0xf3a, 0xf21, 0xf08, 0xef0,
+  0xed7, 0xebe, 0xea5, 0xe8c, 0xe73, 0xe5a, 0xe41, 0xe28,
+  0xe0f, 0xdf6, 0xddd, 0xdc4, 0xdab, 0xd92, 0xd79, 0xd60,
+  0xd47, 0xd2e, 0xd15, 0xcfc, 0xce3, 0xcca, 0xcb1, 0xc98,
+  0xc7f, 0xc66, 0xc4d, 0xc34, 0xc1b, 0xc02, 0xbe9, 0xbd0,
+  0xbb7, 0xb9e, 0xb85, 0xb6c, 0xb53, 0xb3a, 0xb20, 0xb07,
+  0xaee, 0xad5, 0xabc, 0xaa3, 0xa8a, 0xa71, 0xa58, 0xa3f,
+  0xa26, 0xa0d, 0x9f4, 0x9db, 0x9c2, 0x9a9, 0x990, 0x977,
+  0x95e, 0x944, 0x92b, 0x912, 0x8f9, 0x8e0, 0x8c7, 0x8ae,
+  0x895, 0x87c, 0x863, 0x84a, 0x831, 0x818, 0x7fe, 0x7e5,
+  0x7cc, 0x7b3, 0x79a, 0x781, 0x768, 0x74f, 0x736, 0x71d,
+  0x704, 0x6ea, 0x6d1, 0x6b8, 0x69f, 0x686, 0x66d, 0x654,
+  0x63b, 0x622, 0x609, 0x5ef, 0x5d6, 0x5bd, 0x5a4, 0x58b,
+  0x572, 0x559, 0x540, 0x527, 0x50d, 0x4f4, 0x4db, 0x4c2,
+  0x4a9, 0x490, 0x477, 0x45e, 0x445, 0x42b, 0x412, 0x3f9,
+  0x3e0, 0x3c7, 0x3ae, 0x395, 0x37c, 0x362, 0x349, 0x330,
+  0x317, 0x2fe, 0x2e5, 0x2cc, 0x2b3, 0x299, 0x280, 0x267,
+  0x24e, 0x235, 0x21c, 0x203, 0x1ea, 0x1d0, 0x1b7, 0x19e,
+  0x185, 0x16c, 0x153, 0x13a, 0x121, 0x107, 0xee, 0xd5,
+  0xbc, 0xa3, 0x8a, 0x71, 0x57, 0x3e, 0x25, 0xc,
+
+};
+
+static const q15_t ALIGN4 cos_factorsQ15_8192[8192] = {
+  0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff,
+  0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff,
+  0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff,
+  0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff,
+  0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff,
+  0x7fff, 0x7ffe, 0x7ffe, 0x7ffe, 0x7ffe, 0x7ffe, 0x7ffe, 0x7ffe,
+  0x7ffe, 0x7ffe, 0x7ffe, 0x7ffe, 0x7ffe, 0x7ffe, 0x7ffe, 0x7ffe,
+  0x7ffe, 0x7ffe, 0x7ffd, 0x7ffd, 0x7ffd, 0x7ffd, 0x7ffd, 0x7ffd,
+  0x7ffd, 0x7ffd, 0x7ffd, 0x7ffd, 0x7ffd, 0x7ffd, 0x7ffd, 0x7ffc,
+  0x7ffc, 0x7ffc, 0x7ffc, 0x7ffc, 0x7ffc, 0x7ffc, 0x7ffc, 0x7ffc,
+  0x7ffc, 0x7ffb, 0x7ffb, 0x7ffb, 0x7ffb, 0x7ffb, 0x7ffb, 0x7ffb,
+  0x7ffb, 0x7ffb, 0x7ffb, 0x7ffa, 0x7ffa, 0x7ffa, 0x7ffa, 0x7ffa,
+  0x7ffa, 0x7ffa, 0x7ffa, 0x7ffa, 0x7ff9, 0x7ff9, 0x7ff9, 0x7ff9,
+  0x7ff9, 0x7ff9, 0x7ff9, 0x7ff9, 0x7ff8, 0x7ff8, 0x7ff8, 0x7ff8,
+  0x7ff8, 0x7ff8, 0x7ff8, 0x7ff7, 0x7ff7, 0x7ff7, 0x7ff7, 0x7ff7,
+  0x7ff7, 0x7ff7, 0x7ff6, 0x7ff6, 0x7ff6, 0x7ff6, 0x7ff6, 0x7ff6,
+  0x7ff6, 0x7ff5, 0x7ff5, 0x7ff5, 0x7ff5, 0x7ff5, 0x7ff5, 0x7ff4,
+  0x7ff4, 0x7ff4, 0x7ff4, 0x7ff4, 0x7ff4, 0x7ff3, 0x7ff3, 0x7ff3,
+  0x7ff3, 0x7ff3, 0x7ff3, 0x7ff2, 0x7ff2, 0x7ff2, 0x7ff2, 0x7ff2,
+  0x7ff1, 0x7ff1, 0x7ff1, 0x7ff1, 0x7ff1, 0x7ff1, 0x7ff0, 0x7ff0,
+  0x7ff0, 0x7ff0, 0x7ff0, 0x7fef, 0x7fef, 0x7fef, 0x7fef, 0x7fef,
+  0x7fee, 0x7fee, 0x7fee, 0x7fee, 0x7fee, 0x7fed, 0x7fed, 0x7fed,
+  0x7fed, 0x7fed, 0x7fec, 0x7fec, 0x7fec, 0x7fec, 0x7feb, 0x7feb,
+  0x7feb, 0x7feb, 0x7feb, 0x7fea, 0x7fea, 0x7fea, 0x7fea, 0x7fe9,
+  0x7fe9, 0x7fe9, 0x7fe9, 0x7fe8, 0x7fe8, 0x7fe8, 0x7fe8, 0x7fe8,
+  0x7fe7, 0x7fe7, 0x7fe7, 0x7fe7, 0x7fe6, 0x7fe6, 0x7fe6, 0x7fe6,
+  0x7fe5, 0x7fe5, 0x7fe5, 0x7fe5, 0x7fe4, 0x7fe4, 0x7fe4, 0x7fe4,
+  0x7fe3, 0x7fe3, 0x7fe3, 0x7fe2, 0x7fe2, 0x7fe2, 0x7fe2, 0x7fe1,
+  0x7fe1, 0x7fe1, 0x7fe1, 0x7fe0, 0x7fe0, 0x7fe0, 0x7fdf, 0x7fdf,
+  0x7fdf, 0x7fdf, 0x7fde, 0x7fde, 0x7fde, 0x7fde, 0x7fdd, 0x7fdd,
+  0x7fdd, 0x7fdc, 0x7fdc, 0x7fdc, 0x7fdb, 0x7fdb, 0x7fdb, 0x7fdb,
+  0x7fda, 0x7fda, 0x7fda, 0x7fd9, 0x7fd9, 0x7fd9, 0x7fd8, 0x7fd8,
+  0x7fd8, 0x7fd8, 0x7fd7, 0x7fd7, 0x7fd7, 0x7fd6, 0x7fd6, 0x7fd6,
+  0x7fd5, 0x7fd5, 0x7fd5, 0x7fd4, 0x7fd4, 0x7fd4, 0x7fd3, 0x7fd3,
+  0x7fd3, 0x7fd2, 0x7fd2, 0x7fd2, 0x7fd1, 0x7fd1, 0x7fd1, 0x7fd0,
+  0x7fd0, 0x7fd0, 0x7fcf, 0x7fcf, 0x7fcf, 0x7fce, 0x7fce, 0x7fce,
+  0x7fcd, 0x7fcd, 0x7fcd, 0x7fcc, 0x7fcc, 0x7fcc, 0x7fcb, 0x7fcb,
+  0x7fcb, 0x7fca, 0x7fca, 0x7fc9, 0x7fc9, 0x7fc9, 0x7fc8, 0x7fc8,
+  0x7fc8, 0x7fc7, 0x7fc7, 0x7fc7, 0x7fc6, 0x7fc6, 0x7fc5, 0x7fc5,
+  0x7fc5, 0x7fc4, 0x7fc4, 0x7fc4, 0x7fc3, 0x7fc3, 0x7fc2, 0x7fc2,
+  0x7fc2, 0x7fc1, 0x7fc1, 0x7fc0, 0x7fc0, 0x7fc0, 0x7fbf, 0x7fbf,
+  0x7fbf, 0x7fbe, 0x7fbe, 0x7fbd, 0x7fbd, 0x7fbd, 0x7fbc, 0x7fbc,
+  0x7fbb, 0x7fbb, 0x7fbb, 0x7fba, 0x7fba, 0x7fb9, 0x7fb9, 0x7fb8,
+  0x7fb8, 0x7fb8, 0x7fb7, 0x7fb7, 0x7fb6, 0x7fb6, 0x7fb6, 0x7fb5,
+  0x7fb5, 0x7fb4, 0x7fb4, 0x7fb3, 0x7fb3, 0x7fb3, 0x7fb2, 0x7fb2,
+  0x7fb1, 0x7fb1, 0x7fb0, 0x7fb0, 0x7faf, 0x7faf, 0x7faf, 0x7fae,
+  0x7fae, 0x7fad, 0x7fad, 0x7fac, 0x7fac, 0x7fac, 0x7fab, 0x7fab,
+  0x7faa, 0x7faa, 0x7fa9, 0x7fa9, 0x7fa8, 0x7fa8, 0x7fa7, 0x7fa7,
+  0x7fa6, 0x7fa6, 0x7fa6, 0x7fa5, 0x7fa5, 0x7fa4, 0x7fa4, 0x7fa3,
+  0x7fa3, 0x7fa2, 0x7fa2, 0x7fa1, 0x7fa1, 0x7fa0, 0x7fa0, 0x7f9f,
+  0x7f9f, 0x7f9e, 0x7f9e, 0x7f9d, 0x7f9d, 0x7f9c, 0x7f9c, 0x7f9c,
+  0x7f9b, 0x7f9b, 0x7f9a, 0x7f9a, 0x7f99, 0x7f99, 0x7f98, 0x7f98,
+  0x7f97, 0x7f97, 0x7f96, 0x7f96, 0x7f95, 0x7f95, 0x7f94, 0x7f94,
+  0x7f93, 0x7f92, 0x7f92, 0x7f91, 0x7f91, 0x7f90, 0x7f90, 0x7f8f,
+  0x7f8f, 0x7f8e, 0x7f8e, 0x7f8d, 0x7f8d, 0x7f8c, 0x7f8c, 0x7f8b,
+  0x7f8b, 0x7f8a, 0x7f8a, 0x7f89, 0x7f89, 0x7f88, 0x7f87, 0x7f87,
+  0x7f86, 0x7f86, 0x7f85, 0x7f85, 0x7f84, 0x7f84, 0x7f83, 0x7f83,
+  0x7f82, 0x7f81, 0x7f81, 0x7f80, 0x7f80, 0x7f7f, 0x7f7f, 0x7f7e,
+  0x7f7e, 0x7f7d, 0x7f7c, 0x7f7c, 0x7f7b, 0x7f7b, 0x7f7a, 0x7f7a,
+  0x7f79, 0x7f79, 0x7f78, 0x7f77, 0x7f77, 0x7f76, 0x7f76, 0x7f75,
+  0x7f75, 0x7f74, 0x7f73, 0x7f73, 0x7f72, 0x7f72, 0x7f71, 0x7f70,
+  0x7f70, 0x7f6f, 0x7f6f, 0x7f6e, 0x7f6d, 0x7f6d, 0x7f6c, 0x7f6c,
+  0x7f6b, 0x7f6b, 0x7f6a, 0x7f69, 0x7f69, 0x7f68, 0x7f68, 0x7f67,
+  0x7f66, 0x7f66, 0x7f65, 0x7f64, 0x7f64, 0x7f63, 0x7f63, 0x7f62,
+  0x7f61, 0x7f61, 0x7f60, 0x7f60, 0x7f5f, 0x7f5e, 0x7f5e, 0x7f5d,
+  0x7f5c, 0x7f5c, 0x7f5b, 0x7f5b, 0x7f5a, 0x7f59, 0x7f59, 0x7f58,
+  0x7f57, 0x7f57, 0x7f56, 0x7f55, 0x7f55, 0x7f54, 0x7f54, 0x7f53,
+  0x7f52, 0x7f52, 0x7f51, 0x7f50, 0x7f50, 0x7f4f, 0x7f4e, 0x7f4e,
+  0x7f4d, 0x7f4c, 0x7f4c, 0x7f4b, 0x7f4a, 0x7f4a, 0x7f49, 0x7f48,
+  0x7f48, 0x7f47, 0x7f46, 0x7f46, 0x7f45, 0x7f44, 0x7f44, 0x7f43,
+  0x7f42, 0x7f42, 0x7f41, 0x7f40, 0x7f40, 0x7f3f, 0x7f3e, 0x7f3e,
+  0x7f3d, 0x7f3c, 0x7f3c, 0x7f3b, 0x7f3a, 0x7f3a, 0x7f39, 0x7f38,
+  0x7f37, 0x7f37, 0x7f36, 0x7f35, 0x7f35, 0x7f34, 0x7f33, 0x7f33,
+  0x7f32, 0x7f31, 0x7f31, 0x7f30, 0x7f2f, 0x7f2e, 0x7f2e, 0x7f2d,
+  0x7f2c, 0x7f2c, 0x7f2b, 0x7f2a, 0x7f29, 0x7f29, 0x7f28, 0x7f27,
+  0x7f27, 0x7f26, 0x7f25, 0x7f24, 0x7f24, 0x7f23, 0x7f22, 0x7f21,
+  0x7f21, 0x7f20, 0x7f1f, 0x7f1f, 0x7f1e, 0x7f1d, 0x7f1c, 0x7f1c,
+  0x7f1b, 0x7f1a, 0x7f19, 0x7f19, 0x7f18, 0x7f17, 0x7f16, 0x7f16,
+  0x7f15, 0x7f14, 0x7f13, 0x7f13, 0x7f12, 0x7f11, 0x7f10, 0x7f10,
+  0x7f0f, 0x7f0e, 0x7f0d, 0x7f0d, 0x7f0c, 0x7f0b, 0x7f0a, 0x7f09,
+  0x7f09, 0x7f08, 0x7f07, 0x7f06, 0x7f06, 0x7f05, 0x7f04, 0x7f03,
+  0x7f02, 0x7f02, 0x7f01, 0x7f00, 0x7eff, 0x7eff, 0x7efe, 0x7efd,
+  0x7efc, 0x7efb, 0x7efb, 0x7efa, 0x7ef9, 0x7ef8, 0x7ef7, 0x7ef7,
+  0x7ef6, 0x7ef5, 0x7ef4, 0x7ef3, 0x7ef3, 0x7ef2, 0x7ef1, 0x7ef0,
+  0x7eef, 0x7eef, 0x7eee, 0x7eed, 0x7eec, 0x7eeb, 0x7eeb, 0x7eea,
+  0x7ee9, 0x7ee8, 0x7ee7, 0x7ee6, 0x7ee6, 0x7ee5, 0x7ee4, 0x7ee3,
+  0x7ee2, 0x7ee2, 0x7ee1, 0x7ee0, 0x7edf, 0x7ede, 0x7edd, 0x7edd,
+  0x7edc, 0x7edb, 0x7eda, 0x7ed9, 0x7ed8, 0x7ed8, 0x7ed7, 0x7ed6,
+  0x7ed5, 0x7ed4, 0x7ed3, 0x7ed2, 0x7ed2, 0x7ed1, 0x7ed0, 0x7ecf,
+  0x7ece, 0x7ecd, 0x7ecc, 0x7ecc, 0x7ecb, 0x7eca, 0x7ec9, 0x7ec8,
+  0x7ec7, 0x7ec6, 0x7ec6, 0x7ec5, 0x7ec4, 0x7ec3, 0x7ec2, 0x7ec1,
+  0x7ec0, 0x7ebf, 0x7ebf, 0x7ebe, 0x7ebd, 0x7ebc, 0x7ebb, 0x7eba,
+  0x7eb9, 0x7eb8, 0x7eb8, 0x7eb7, 0x7eb6, 0x7eb5, 0x7eb4, 0x7eb3,
+  0x7eb2, 0x7eb1, 0x7eb0, 0x7eaf, 0x7eaf, 0x7eae, 0x7ead, 0x7eac,
+  0x7eab, 0x7eaa, 0x7ea9, 0x7ea8, 0x7ea7, 0x7ea6, 0x7ea6, 0x7ea5,
+  0x7ea4, 0x7ea3, 0x7ea2, 0x7ea1, 0x7ea0, 0x7e9f, 0x7e9e, 0x7e9d,
+  0x7e9c, 0x7e9b, 0x7e9b, 0x7e9a, 0x7e99, 0x7e98, 0x7e97, 0x7e96,
+  0x7e95, 0x7e94, 0x7e93, 0x7e92, 0x7e91, 0x7e90, 0x7e8f, 0x7e8e,
+  0x7e8d, 0x7e8d, 0x7e8c, 0x7e8b, 0x7e8a, 0x7e89, 0x7e88, 0x7e87,
+  0x7e86, 0x7e85, 0x7e84, 0x7e83, 0x7e82, 0x7e81, 0x7e80, 0x7e7f,
+  0x7e7e, 0x7e7d, 0x7e7c, 0x7e7b, 0x7e7a, 0x7e79, 0x7e78, 0x7e77,
+  0x7e77, 0x7e76, 0x7e75, 0x7e74, 0x7e73, 0x7e72, 0x7e71, 0x7e70,
+  0x7e6f, 0x7e6e, 0x7e6d, 0x7e6c, 0x7e6b, 0x7e6a, 0x7e69, 0x7e68,
+  0x7e67, 0x7e66, 0x7e65, 0x7e64, 0x7e63, 0x7e62, 0x7e61, 0x7e60,
+  0x7e5f, 0x7e5e, 0x7e5d, 0x7e5c, 0x7e5b, 0x7e5a, 0x7e59, 0x7e58,
+  0x7e57, 0x7e56, 0x7e55, 0x7e54, 0x7e53, 0x7e52, 0x7e51, 0x7e50,
+  0x7e4f, 0x7e4e, 0x7e4d, 0x7e4c, 0x7e4b, 0x7e4a, 0x7e49, 0x7e48,
+  0x7e47, 0x7e46, 0x7e45, 0x7e43, 0x7e42, 0x7e41, 0x7e40, 0x7e3f,
+  0x7e3e, 0x7e3d, 0x7e3c, 0x7e3b, 0x7e3a, 0x7e39, 0x7e38, 0x7e37,
+  0x7e36, 0x7e35, 0x7e34, 0x7e33, 0x7e32, 0x7e31, 0x7e30, 0x7e2f,
+  0x7e2e, 0x7e2d, 0x7e2b, 0x7e2a, 0x7e29, 0x7e28, 0x7e27, 0x7e26,
+  0x7e25, 0x7e24, 0x7e23, 0x7e22, 0x7e21, 0x7e20, 0x7e1f, 0x7e1e,
+  0x7e1d, 0x7e1b, 0x7e1a, 0x7e19, 0x7e18, 0x7e17, 0x7e16, 0x7e15,
+  0x7e14, 0x7e13, 0x7e12, 0x7e11, 0x7e10, 0x7e0e, 0x7e0d, 0x7e0c,
+  0x7e0b, 0x7e0a, 0x7e09, 0x7e08, 0x7e07, 0x7e06, 0x7e05, 0x7e04,
+  0x7e02, 0x7e01, 0x7e00, 0x7dff, 0x7dfe, 0x7dfd, 0x7dfc, 0x7dfb,
+  0x7dfa, 0x7df8, 0x7df7, 0x7df6, 0x7df5, 0x7df4, 0x7df3, 0x7df2,
+  0x7df1, 0x7def, 0x7dee, 0x7ded, 0x7dec, 0x7deb, 0x7dea, 0x7de9,
+  0x7de8, 0x7de6, 0x7de5, 0x7de4, 0x7de3, 0x7de2, 0x7de1, 0x7de0,
+  0x7dde, 0x7ddd, 0x7ddc, 0x7ddb, 0x7dda, 0x7dd9, 0x7dd8, 0x7dd6,
+  0x7dd5, 0x7dd4, 0x7dd3, 0x7dd2, 0x7dd1, 0x7dd0, 0x7dce, 0x7dcd,
+  0x7dcc, 0x7dcb, 0x7dca, 0x7dc9, 0x7dc7, 0x7dc6, 0x7dc5, 0x7dc4,
+  0x7dc3, 0x7dc2, 0x7dc0, 0x7dbf, 0x7dbe, 0x7dbd, 0x7dbc, 0x7dbb,
+  0x7db9, 0x7db8, 0x7db7, 0x7db6, 0x7db5, 0x7db3, 0x7db2, 0x7db1,
+  0x7db0, 0x7daf, 0x7dae, 0x7dac, 0x7dab, 0x7daa, 0x7da9, 0x7da8,
+  0x7da6, 0x7da5, 0x7da4, 0x7da3, 0x7da2, 0x7da0, 0x7d9f, 0x7d9e,
+  0x7d9d, 0x7d9c, 0x7d9a, 0x7d99, 0x7d98, 0x7d97, 0x7d95, 0x7d94,
+  0x7d93, 0x7d92, 0x7d91, 0x7d8f, 0x7d8e, 0x7d8d, 0x7d8c, 0x7d8a,
+  0x7d89, 0x7d88, 0x7d87, 0x7d86, 0x7d84, 0x7d83, 0x7d82, 0x7d81,
+  0x7d7f, 0x7d7e, 0x7d7d, 0x7d7c, 0x7d7a, 0x7d79, 0x7d78, 0x7d77,
+  0x7d75, 0x7d74, 0x7d73, 0x7d72, 0x7d70, 0x7d6f, 0x7d6e, 0x7d6d,
+  0x7d6b, 0x7d6a, 0x7d69, 0x7d68, 0x7d66, 0x7d65, 0x7d64, 0x7d63,
+  0x7d61, 0x7d60, 0x7d5f, 0x7d5e, 0x7d5c, 0x7d5b, 0x7d5a, 0x7d59,
+  0x7d57, 0x7d56, 0x7d55, 0x7d53, 0x7d52, 0x7d51, 0x7d50, 0x7d4e,
+  0x7d4d, 0x7d4c, 0x7d4a, 0x7d49, 0x7d48, 0x7d47, 0x7d45, 0x7d44,
+  0x7d43, 0x7d41, 0x7d40, 0x7d3f, 0x7d3e, 0x7d3c, 0x7d3b, 0x7d3a,
+  0x7d38, 0x7d37, 0x7d36, 0x7d34, 0x7d33, 0x7d32, 0x7d31, 0x7d2f,
+  0x7d2e, 0x7d2d, 0x7d2b, 0x7d2a, 0x7d29, 0x7d27, 0x7d26, 0x7d25,
+  0x7d23, 0x7d22, 0x7d21, 0x7d1f, 0x7d1e, 0x7d1d, 0x7d1b, 0x7d1a,
+  0x7d19, 0x7d17, 0x7d16, 0x7d15, 0x7d13, 0x7d12, 0x7d11, 0x7d0f,
+  0x7d0e, 0x7d0d, 0x7d0b, 0x7d0a, 0x7d09, 0x7d07, 0x7d06, 0x7d05,
+  0x7d03, 0x7d02, 0x7d01, 0x7cff, 0x7cfe, 0x7cfd, 0x7cfb, 0x7cfa,
+  0x7cf9, 0x7cf7, 0x7cf6, 0x7cf4, 0x7cf3, 0x7cf2, 0x7cf0, 0x7cef,
+  0x7cee, 0x7cec, 0x7ceb, 0x7ce9, 0x7ce8, 0x7ce7, 0x7ce5, 0x7ce4,
+  0x7ce3, 0x7ce1, 0x7ce0, 0x7cde, 0x7cdd, 0x7cdc, 0x7cda, 0x7cd9,
+  0x7cd8, 0x7cd6, 0x7cd5, 0x7cd3, 0x7cd2, 0x7cd1, 0x7ccf, 0x7cce,
+  0x7ccc, 0x7ccb, 0x7cca, 0x7cc8, 0x7cc7, 0x7cc5, 0x7cc4, 0x7cc3,
+  0x7cc1, 0x7cc0, 0x7cbe, 0x7cbd, 0x7cbc, 0x7cba, 0x7cb9, 0x7cb7,
+  0x7cb6, 0x7cb5, 0x7cb3, 0x7cb2, 0x7cb0, 0x7caf, 0x7cad, 0x7cac,
+  0x7cab, 0x7ca9, 0x7ca8, 0x7ca6, 0x7ca5, 0x7ca3, 0x7ca2, 0x7ca1,
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+  0x5b77, 0x5b73, 0x5b6e, 0x5b6a, 0x5b66, 0x5b61, 0x5b5d, 0x5b58,
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+  0x5aa3, 0x5a9f, 0x5a9a, 0x5a96, 0x5a92, 0x5a8d, 0x5a89, 0x5a84,
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+  0x5986, 0x5981, 0x597d, 0x5978, 0x5974, 0x596f, 0x596b, 0x5966,
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+  0x54ed, 0x54e8, 0x54e3, 0x54df, 0x54da, 0x54d5, 0x54d1, 0x54cc,
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+  0x53be, 0x53ba, 0x53b5, 0x53b0, 0x53ab, 0x53a7, 0x53a2, 0x539d,
+  0x5398, 0x5394, 0x538f, 0x538a, 0x5385, 0x5380, 0x537c, 0x5377,
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+  0x534c, 0x5347, 0x5343, 0x533e, 0x5339, 0x5334, 0x532f, 0x532b,
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+  0x52d9, 0x52d5, 0x52d0, 0x52cb, 0x52c6, 0x52c1, 0x52bd, 0x52b8,
+  0x52b3, 0x52ae, 0x52a9, 0x52a5, 0x52a0, 0x529b, 0x5296, 0x5291,
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+  0x5266, 0x5261, 0x525d, 0x5258, 0x5253, 0x524e, 0x5249, 0x5244,
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+  0x51f3, 0x51ee, 0x51e9, 0x51e4, 0x51df, 0x51da, 0x51d6, 0x51d1,
+  0x51cc, 0x51c7, 0x51c2, 0x51bd, 0x51b9, 0x51b4, 0x51af, 0x51aa,
+  0x51a5, 0x51a0, 0x519c, 0x5197, 0x5192, 0x518d, 0x5188, 0x5183,
+  0x517e, 0x517a, 0x5175, 0x5170, 0x516b, 0x5166, 0x5161, 0x515d,
+  0x5158, 0x5153, 0x514e, 0x5149, 0x5144, 0x513f, 0x513b, 0x5136,
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+  0x50e3, 0x50de, 0x50d9, 0x50d4, 0x50d0, 0x50cb, 0x50c6, 0x50c1,
+  0x50bc, 0x50b7, 0x50b2, 0x50ad, 0x50a9, 0x50a4, 0x509f, 0x509a,
+  0x5095, 0x5090, 0x508b, 0x5086, 0x5082, 0x507d, 0x5078, 0x5073,
+  0x506e, 0x5069, 0x5064, 0x505f, 0x505a, 0x5056, 0x5051, 0x504c,
+  0x5047, 0x5042, 0x503d, 0x5038, 0x5033, 0x502e, 0x5029, 0x5025,
+  0x5020, 0x501b, 0x5016, 0x5011, 0x500c, 0x5007, 0x5002, 0x4ffd,
+  0x4ff8, 0x4ff4, 0x4fef, 0x4fea, 0x4fe5, 0x4fe0, 0x4fdb, 0x4fd6,
+  0x4fd1, 0x4fcc, 0x4fc7, 0x4fc2, 0x4fbe, 0x4fb9, 0x4fb4, 0x4faf,
+  0x4faa, 0x4fa5, 0x4fa0, 0x4f9b, 0x4f96, 0x4f91, 0x4f8c, 0x4f87,
+  0x4f82, 0x4f7e, 0x4f79, 0x4f74, 0x4f6f, 0x4f6a, 0x4f65, 0x4f60,
+  0x4f5b, 0x4f56, 0x4f51, 0x4f4c, 0x4f47, 0x4f42, 0x4f3d, 0x4f39,
+  0x4f34, 0x4f2f, 0x4f2a, 0x4f25, 0x4f20, 0x4f1b, 0x4f16, 0x4f11,
+  0x4f0c, 0x4f07, 0x4f02, 0x4efd, 0x4ef8, 0x4ef3, 0x4eee, 0x4ee9,
+  0x4ee5, 0x4ee0, 0x4edb, 0x4ed6, 0x4ed1, 0x4ecc, 0x4ec7, 0x4ec2,
+  0x4ebd, 0x4eb8, 0x4eb3, 0x4eae, 0x4ea9, 0x4ea4, 0x4e9f, 0x4e9a,
+  0x4e95, 0x4e90, 0x4e8b, 0x4e86, 0x4e81, 0x4e7c, 0x4e78, 0x4e73,
+  0x4e6e, 0x4e69, 0x4e64, 0x4e5f, 0x4e5a, 0x4e55, 0x4e50, 0x4e4b,
+  0x4e46, 0x4e41, 0x4e3c, 0x4e37, 0x4e32, 0x4e2d, 0x4e28, 0x4e23,
+  0x4e1e, 0x4e19, 0x4e14, 0x4e0f, 0x4e0a, 0x4e05, 0x4e00, 0x4dfb,
+  0x4df6, 0x4df1, 0x4dec, 0x4de7, 0x4de2, 0x4ddd, 0x4dd8, 0x4dd3,
+  0x4dce, 0x4dc9, 0x4dc4, 0x4dbf, 0x4dba, 0x4db5, 0x4db0, 0x4dab,
+  0x4da6, 0x4da1, 0x4d9c, 0x4d97, 0x4d92, 0x4d8d, 0x4d88, 0x4d83,
+  0x4d7e, 0x4d79, 0x4d74, 0x4d6f, 0x4d6a, 0x4d65, 0x4d60, 0x4d5b,
+  0x4d56, 0x4d51, 0x4d4c, 0x4d47, 0x4d42, 0x4d3d, 0x4d38, 0x4d33,
+  0x4d2e, 0x4d29, 0x4d24, 0x4d1f, 0x4d1a, 0x4d15, 0x4d10, 0x4d0b,
+  0x4d06, 0x4d01, 0x4cfc, 0x4cf7, 0x4cf2, 0x4ced, 0x4ce8, 0x4ce3,
+  0x4cde, 0x4cd9, 0x4cd4, 0x4ccf, 0x4cca, 0x4cc5, 0x4cc0, 0x4cbb,
+  0x4cb6, 0x4cb1, 0x4cac, 0x4ca7, 0x4ca2, 0x4c9d, 0x4c98, 0x4c93,
+  0x4c8e, 0x4c88, 0x4c83, 0x4c7e, 0x4c79, 0x4c74, 0x4c6f, 0x4c6a,
+  0x4c65, 0x4c60, 0x4c5b, 0x4c56, 0x4c51, 0x4c4c, 0x4c47, 0x4c42,
+  0x4c3d, 0x4c38, 0x4c33, 0x4c2e, 0x4c29, 0x4c24, 0x4c1f, 0x4c1a,
+  0x4c14, 0x4c0f, 0x4c0a, 0x4c05, 0x4c00, 0x4bfb, 0x4bf6, 0x4bf1,
+  0x4bec, 0x4be7, 0x4be2, 0x4bdd, 0x4bd8, 0x4bd3, 0x4bce, 0x4bc9,
+  0x4bc4, 0x4bbe, 0x4bb9, 0x4bb4, 0x4baf, 0x4baa, 0x4ba5, 0x4ba0,
+  0x4b9b, 0x4b96, 0x4b91, 0x4b8c, 0x4b87, 0x4b82, 0x4b7d, 0x4b77,
+  0x4b72, 0x4b6d, 0x4b68, 0x4b63, 0x4b5e, 0x4b59, 0x4b54, 0x4b4f,
+  0x4b4a, 0x4b45, 0x4b40, 0x4b3b, 0x4b35, 0x4b30, 0x4b2b, 0x4b26,
+  0x4b21, 0x4b1c, 0x4b17, 0x4b12, 0x4b0d, 0x4b08, 0x4b03, 0x4afd,
+  0x4af8, 0x4af3, 0x4aee, 0x4ae9, 0x4ae4, 0x4adf, 0x4ada, 0x4ad5,
+  0x4ad0, 0x4acb, 0x4ac5, 0x4ac0, 0x4abb, 0x4ab6, 0x4ab1, 0x4aac,
+  0x4aa7, 0x4aa2, 0x4a9d, 0x4a97, 0x4a92, 0x4a8d, 0x4a88, 0x4a83,
+  0x4a7e, 0x4a79, 0x4a74, 0x4a6f, 0x4a6a, 0x4a64, 0x4a5f, 0x4a5a,
+  0x4a55, 0x4a50, 0x4a4b, 0x4a46, 0x4a41, 0x4a3b, 0x4a36, 0x4a31,
+  0x4a2c, 0x4a27, 0x4a22, 0x4a1d, 0x4a18, 0x4a12, 0x4a0d, 0x4a08,
+  0x4a03, 0x49fe, 0x49f9, 0x49f4, 0x49ef, 0x49e9, 0x49e4, 0x49df,
+  0x49da, 0x49d5, 0x49d0, 0x49cb, 0x49c6, 0x49c0, 0x49bb, 0x49b6,
+  0x49b1, 0x49ac, 0x49a7, 0x49a2, 0x499c, 0x4997, 0x4992, 0x498d,
+  0x4988, 0x4983, 0x497e, 0x4978, 0x4973, 0x496e, 0x4969, 0x4964,
+  0x495f, 0x495a, 0x4954, 0x494f, 0x494a, 0x4945, 0x4940, 0x493b,
+  0x4936, 0x4930, 0x492b, 0x4926, 0x4921, 0x491c, 0x4917, 0x4911,
+  0x490c, 0x4907, 0x4902, 0x48fd, 0x48f8, 0x48f2, 0x48ed, 0x48e8,
+  0x48e3, 0x48de, 0x48d9, 0x48d3, 0x48ce, 0x48c9, 0x48c4, 0x48bf,
+  0x48ba, 0x48b4, 0x48af, 0x48aa, 0x48a5, 0x48a0, 0x489b, 0x4895,
+  0x4890, 0x488b, 0x4886, 0x4881, 0x487c, 0x4876, 0x4871, 0x486c,
+  0x4867, 0x4862, 0x485c, 0x4857, 0x4852, 0x484d, 0x4848, 0x4843,
+  0x483d, 0x4838, 0x4833, 0x482e, 0x4829, 0x4823, 0x481e, 0x4819,
+  0x4814, 0x480f, 0x4809, 0x4804, 0x47ff, 0x47fa, 0x47f5, 0x47ef,
+  0x47ea, 0x47e5, 0x47e0, 0x47db, 0x47d5, 0x47d0, 0x47cb, 0x47c6,
+  0x47c1, 0x47bb, 0x47b6, 0x47b1, 0x47ac, 0x47a7, 0x47a1, 0x479c,
+  0x4797, 0x4792, 0x478d, 0x4787, 0x4782, 0x477d, 0x4778, 0x4773,
+  0x476d, 0x4768, 0x4763, 0x475e, 0x4758, 0x4753, 0x474e, 0x4749,
+  0x4744, 0x473e, 0x4739, 0x4734, 0x472f, 0x4729, 0x4724, 0x471f,
+  0x471a, 0x4715, 0x470f, 0x470a, 0x4705, 0x4700, 0x46fa, 0x46f5,
+  0x46f0, 0x46eb, 0x46e6, 0x46e0, 0x46db, 0x46d6, 0x46d1, 0x46cb,
+  0x46c6, 0x46c1, 0x46bc, 0x46b6, 0x46b1, 0x46ac, 0x46a7, 0x46a1,
+  0x469c, 0x4697, 0x4692, 0x468d, 0x4687, 0x4682, 0x467d, 0x4678,
+  0x4672, 0x466d, 0x4668, 0x4663, 0x465d, 0x4658, 0x4653, 0x464e,
+  0x4648, 0x4643, 0x463e, 0x4639, 0x4633, 0x462e, 0x4629, 0x4624,
+  0x461e, 0x4619, 0x4614, 0x460e, 0x4609, 0x4604, 0x45ff, 0x45f9,
+  0x45f4, 0x45ef, 0x45ea, 0x45e4, 0x45df, 0x45da, 0x45d5, 0x45cf,
+  0x45ca, 0x45c5, 0x45c0, 0x45ba, 0x45b5, 0x45b0, 0x45aa, 0x45a5,
+  0x45a0, 0x459b, 0x4595, 0x4590, 0x458b, 0x4586, 0x4580, 0x457b,
+  0x4576, 0x4570, 0x456b, 0x4566, 0x4561, 0x455b, 0x4556, 0x4551,
+  0x454b, 0x4546, 0x4541, 0x453c, 0x4536, 0x4531, 0x452c, 0x4526,
+  0x4521, 0x451c, 0x4517, 0x4511, 0x450c, 0x4507, 0x4501, 0x44fc,
+  0x44f7, 0x44f2, 0x44ec, 0x44e7, 0x44e2, 0x44dc, 0x44d7, 0x44d2,
+  0x44cd, 0x44c7, 0x44c2, 0x44bd, 0x44b7, 0x44b2, 0x44ad, 0x44a7,
+  0x44a2, 0x449d, 0x4497, 0x4492, 0x448d, 0x4488, 0x4482, 0x447d,
+  0x4478, 0x4472, 0x446d, 0x4468, 0x4462, 0x445d, 0x4458, 0x4452,
+  0x444d, 0x4448, 0x4443, 0x443d, 0x4438, 0x4433, 0x442d, 0x4428,
+  0x4423, 0x441d, 0x4418, 0x4413, 0x440d, 0x4408, 0x4403, 0x43fd,
+  0x43f8, 0x43f3, 0x43ed, 0x43e8, 0x43e3, 0x43dd, 0x43d8, 0x43d3,
+  0x43cd, 0x43c8, 0x43c3, 0x43bd, 0x43b8, 0x43b3, 0x43ad, 0x43a8,
+  0x43a3, 0x439d, 0x4398, 0x4393, 0x438d, 0x4388, 0x4383, 0x437d,
+  0x4378, 0x4373, 0x436d, 0x4368, 0x4363, 0x435d, 0x4358, 0x4353,
+  0x434d, 0x4348, 0x4343, 0x433d, 0x4338, 0x4333, 0x432d, 0x4328,
+  0x4323, 0x431d, 0x4318, 0x4313, 0x430d, 0x4308, 0x4302, 0x42fd,
+  0x42f8, 0x42f2, 0x42ed, 0x42e8, 0x42e2, 0x42dd, 0x42d8, 0x42d2,
+  0x42cd, 0x42c8, 0x42c2, 0x42bd, 0x42b7, 0x42b2, 0x42ad, 0x42a7,
+  0x42a2, 0x429d, 0x4297, 0x4292, 0x428d, 0x4287, 0x4282, 0x427c,
+  0x4277, 0x4272, 0x426c, 0x4267, 0x4262, 0x425c, 0x4257, 0x4251,
+  0x424c, 0x4247, 0x4241, 0x423c, 0x4237, 0x4231, 0x422c, 0x4226,
+  0x4221, 0x421c, 0x4216, 0x4211, 0x420c, 0x4206, 0x4201, 0x41fb,
+  0x41f6, 0x41f1, 0x41eb, 0x41e6, 0x41e0, 0x41db, 0x41d6, 0x41d0,
+  0x41cb, 0x41c6, 0x41c0, 0x41bb, 0x41b5, 0x41b0, 0x41ab, 0x41a5,
+  0x41a0, 0x419a, 0x4195, 0x4190, 0x418a, 0x4185, 0x417f, 0x417a,
+  0x4175, 0x416f, 0x416a, 0x4164, 0x415f, 0x415a, 0x4154, 0x414f,
+  0x4149, 0x4144, 0x413f, 0x4139, 0x4134, 0x412e, 0x4129, 0x4124,
+  0x411e, 0x4119, 0x4113, 0x410e, 0x4108, 0x4103, 0x40fe, 0x40f8,
+  0x40f3, 0x40ed, 0x40e8, 0x40e3, 0x40dd, 0x40d8, 0x40d2, 0x40cd,
+  0x40c8, 0x40c2, 0x40bd, 0x40b7, 0x40b2, 0x40ac, 0x40a7, 0x40a2,
+  0x409c, 0x4097, 0x4091, 0x408c, 0x4086, 0x4081, 0x407c, 0x4076,
+  0x4071, 0x406b, 0x4066, 0x4060, 0x405b, 0x4056, 0x4050, 0x404b,
+  0x4045, 0x4040, 0x403a, 0x4035, 0x4030, 0x402a, 0x4025, 0x401f,
+  0x401a, 0x4014, 0x400f, 0x4009, 0x4004, 0x3fff, 0x3ff9, 0x3ff4,
+  0x3fee, 0x3fe9, 0x3fe3, 0x3fde, 0x3fd8, 0x3fd3, 0x3fce, 0x3fc8,
+  0x3fc3, 0x3fbd, 0x3fb8, 0x3fb2, 0x3fad, 0x3fa7, 0x3fa2, 0x3f9d,
+  0x3f97, 0x3f92, 0x3f8c, 0x3f87, 0x3f81, 0x3f7c, 0x3f76, 0x3f71,
+  0x3f6b, 0x3f66, 0x3f61, 0x3f5b, 0x3f56, 0x3f50, 0x3f4b, 0x3f45,
+  0x3f40, 0x3f3a, 0x3f35, 0x3f2f, 0x3f2a, 0x3f24, 0x3f1f, 0x3f1a,
+  0x3f14, 0x3f0f, 0x3f09, 0x3f04, 0x3efe, 0x3ef9, 0x3ef3, 0x3eee,
+  0x3ee8, 0x3ee3, 0x3edd, 0x3ed8, 0x3ed2, 0x3ecd, 0x3ec7, 0x3ec2,
+  0x3ebd, 0x3eb7, 0x3eb2, 0x3eac, 0x3ea7, 0x3ea1, 0x3e9c, 0x3e96,
+  0x3e91, 0x3e8b, 0x3e86, 0x3e80, 0x3e7b, 0x3e75, 0x3e70, 0x3e6a,
+  0x3e65, 0x3e5f, 0x3e5a, 0x3e54, 0x3e4f, 0x3e49, 0x3e44, 0x3e3e,
+  0x3e39, 0x3e33, 0x3e2e, 0x3e28, 0x3e23, 0x3e1d, 0x3e18, 0x3e12,
+  0x3e0d, 0x3e07, 0x3e02, 0x3dfc, 0x3df7, 0x3df1, 0x3dec, 0x3de6,
+  0x3de1, 0x3ddb, 0x3dd6, 0x3dd0, 0x3dcb, 0x3dc5, 0x3dc0, 0x3dba,
+  0x3db5, 0x3daf, 0x3daa, 0x3da4, 0x3d9f, 0x3d99, 0x3d94, 0x3d8e,
+  0x3d89, 0x3d83, 0x3d7e, 0x3d78, 0x3d73, 0x3d6d, 0x3d68, 0x3d62,
+  0x3d5d, 0x3d57, 0x3d52, 0x3d4c, 0x3d47, 0x3d41, 0x3d3c, 0x3d36,
+  0x3d31, 0x3d2b, 0x3d26, 0x3d20, 0x3d1b, 0x3d15, 0x3d10, 0x3d0a,
+  0x3d04, 0x3cff, 0x3cf9, 0x3cf4, 0x3cee, 0x3ce9, 0x3ce3, 0x3cde,
+  0x3cd8, 0x3cd3, 0x3ccd, 0x3cc8, 0x3cc2, 0x3cbd, 0x3cb7, 0x3cb2,
+  0x3cac, 0x3ca7, 0x3ca1, 0x3c9b, 0x3c96, 0x3c90, 0x3c8b, 0x3c85,
+  0x3c80, 0x3c7a, 0x3c75, 0x3c6f, 0x3c6a, 0x3c64, 0x3c5f, 0x3c59,
+  0x3c53, 0x3c4e, 0x3c48, 0x3c43, 0x3c3d, 0x3c38, 0x3c32, 0x3c2d,
+  0x3c27, 0x3c22, 0x3c1c, 0x3c16, 0x3c11, 0x3c0b, 0x3c06, 0x3c00,
+  0x3bfb, 0x3bf5, 0x3bf0, 0x3bea, 0x3be5, 0x3bdf, 0x3bd9, 0x3bd4,
+  0x3bce, 0x3bc9, 0x3bc3, 0x3bbe, 0x3bb8, 0x3bb3, 0x3bad, 0x3ba7,
+  0x3ba2, 0x3b9c, 0x3b97, 0x3b91, 0x3b8c, 0x3b86, 0x3b80, 0x3b7b,
+  0x3b75, 0x3b70, 0x3b6a, 0x3b65, 0x3b5f, 0x3b5a, 0x3b54, 0x3b4e,
+  0x3b49, 0x3b43, 0x3b3e, 0x3b38, 0x3b33, 0x3b2d, 0x3b27, 0x3b22,
+  0x3b1c, 0x3b17, 0x3b11, 0x3b0c, 0x3b06, 0x3b00, 0x3afb, 0x3af5,
+  0x3af0, 0x3aea, 0x3ae4, 0x3adf, 0x3ad9, 0x3ad4, 0x3ace, 0x3ac9,
+  0x3ac3, 0x3abd, 0x3ab8, 0x3ab2, 0x3aad, 0x3aa7, 0x3aa2, 0x3a9c,
+  0x3a96, 0x3a91, 0x3a8b, 0x3a86, 0x3a80, 0x3a7a, 0x3a75, 0x3a6f,
+  0x3a6a, 0x3a64, 0x3a5e, 0x3a59, 0x3a53, 0x3a4e, 0x3a48, 0x3a42,
+  0x3a3d, 0x3a37, 0x3a32, 0x3a2c, 0x3a26, 0x3a21, 0x3a1b, 0x3a16,
+  0x3a10, 0x3a0b, 0x3a05, 0x39ff, 0x39fa, 0x39f4, 0x39ee, 0x39e9,
+  0x39e3, 0x39de, 0x39d8, 0x39d2, 0x39cd, 0x39c7, 0x39c2, 0x39bc,
+  0x39b6, 0x39b1, 0x39ab, 0x39a6, 0x39a0, 0x399a, 0x3995, 0x398f,
+  0x398a, 0x3984, 0x397e, 0x3979, 0x3973, 0x396d, 0x3968, 0x3962,
+  0x395d, 0x3957, 0x3951, 0x394c, 0x3946, 0x3941, 0x393b, 0x3935,
+  0x3930, 0x392a, 0x3924, 0x391f, 0x3919, 0x3914, 0x390e, 0x3908,
+  0x3903, 0x38fd, 0x38f7, 0x38f2, 0x38ec, 0x38e7, 0x38e1, 0x38db,
+  0x38d6, 0x38d0, 0x38ca, 0x38c5, 0x38bf, 0x38ba, 0x38b4, 0x38ae,
+  0x38a9, 0x38a3, 0x389d, 0x3898, 0x3892, 0x388c, 0x3887, 0x3881,
+  0x387c, 0x3876, 0x3870, 0x386b, 0x3865, 0x385f, 0x385a, 0x3854,
+  0x384e, 0x3849, 0x3843, 0x383d, 0x3838, 0x3832, 0x382d, 0x3827,
+  0x3821, 0x381c, 0x3816, 0x3810, 0x380b, 0x3805, 0x37ff, 0x37fa,
+  0x37f4, 0x37ee, 0x37e9, 0x37e3, 0x37dd, 0x37d8, 0x37d2, 0x37cc,
+  0x37c7, 0x37c1, 0x37bc, 0x37b6, 0x37b0, 0x37ab, 0x37a5, 0x379f,
+  0x379a, 0x3794, 0x378e, 0x3789, 0x3783, 0x377d, 0x3778, 0x3772,
+  0x376c, 0x3767, 0x3761, 0x375b, 0x3756, 0x3750, 0x374a, 0x3745,
+  0x373f, 0x3739, 0x3734, 0x372e, 0x3728, 0x3723, 0x371d, 0x3717,
+  0x3712, 0x370c, 0x3706, 0x3701, 0x36fb, 0x36f5, 0x36f0, 0x36ea,
+  0x36e4, 0x36df, 0x36d9, 0x36d3, 0x36ce, 0x36c8, 0x36c2, 0x36bc,
+  0x36b7, 0x36b1, 0x36ab, 0x36a6, 0x36a0, 0x369a, 0x3695, 0x368f,
+  0x3689, 0x3684, 0x367e, 0x3678, 0x3673, 0x366d, 0x3667, 0x3662,
+  0x365c, 0x3656, 0x3650, 0x364b, 0x3645, 0x363f, 0x363a, 0x3634,
+  0x362e, 0x3629, 0x3623, 0x361d, 0x3618, 0x3612, 0x360c, 0x3606,
+  0x3601, 0x35fb, 0x35f5, 0x35f0, 0x35ea, 0x35e4, 0x35df, 0x35d9,
+  0x35d3, 0x35cd, 0x35c8, 0x35c2, 0x35bc, 0x35b7, 0x35b1, 0x35ab,
+  0x35a6, 0x35a0, 0x359a, 0x3594, 0x358f, 0x3589, 0x3583, 0x357e,
+  0x3578, 0x3572, 0x356c, 0x3567, 0x3561, 0x355b, 0x3556, 0x3550,
+  0x354a, 0x3544, 0x353f, 0x3539, 0x3533, 0x352e, 0x3528, 0x3522,
+  0x351c, 0x3517, 0x3511, 0x350b, 0x3506, 0x3500, 0x34fa, 0x34f4,
+  0x34ef, 0x34e9, 0x34e3, 0x34de, 0x34d8, 0x34d2, 0x34cc, 0x34c7,
+  0x34c1, 0x34bb, 0x34b6, 0x34b0, 0x34aa, 0x34a4, 0x349f, 0x3499,
+  0x3493, 0x348d, 0x3488, 0x3482, 0x347c, 0x3476, 0x3471, 0x346b,
+  0x3465, 0x3460, 0x345a, 0x3454, 0x344e, 0x3449, 0x3443, 0x343d,
+  0x3437, 0x3432, 0x342c, 0x3426, 0x3420, 0x341b, 0x3415, 0x340f,
+  0x340a, 0x3404, 0x33fe, 0x33f8, 0x33f3, 0x33ed, 0x33e7, 0x33e1,
+  0x33dc, 0x33d6, 0x33d0, 0x33ca, 0x33c5, 0x33bf, 0x33b9, 0x33b3,
+  0x33ae, 0x33a8, 0x33a2, 0x339c, 0x3397, 0x3391, 0x338b, 0x3385,
+  0x3380, 0x337a, 0x3374, 0x336e, 0x3369, 0x3363, 0x335d, 0x3357,
+  0x3352, 0x334c, 0x3346, 0x3340, 0x333b, 0x3335, 0x332f, 0x3329,
+  0x3324, 0x331e, 0x3318, 0x3312, 0x330c, 0x3307, 0x3301, 0x32fb,
+  0x32f5, 0x32f0, 0x32ea, 0x32e4, 0x32de, 0x32d9, 0x32d3, 0x32cd,
+  0x32c7, 0x32c2, 0x32bc, 0x32b6, 0x32b0, 0x32aa, 0x32a5, 0x329f,
+  0x3299, 0x3293, 0x328e, 0x3288, 0x3282, 0x327c, 0x3276, 0x3271,
+  0x326b, 0x3265, 0x325f, 0x325a, 0x3254, 0x324e, 0x3248, 0x3243,
+  0x323d, 0x3237, 0x3231, 0x322b, 0x3226, 0x3220, 0x321a, 0x3214,
+  0x320e, 0x3209, 0x3203, 0x31fd, 0x31f7, 0x31f2, 0x31ec, 0x31e6,
+  0x31e0, 0x31da, 0x31d5, 0x31cf, 0x31c9, 0x31c3, 0x31bd, 0x31b8,
+  0x31b2, 0x31ac, 0x31a6, 0x31a1, 0x319b, 0x3195, 0x318f, 0x3189,
+  0x3184, 0x317e, 0x3178, 0x3172, 0x316c, 0x3167, 0x3161, 0x315b,
+  0x3155, 0x314f, 0x314a, 0x3144, 0x313e, 0x3138, 0x3132, 0x312d,
+  0x3127, 0x3121, 0x311b, 0x3115, 0x3110, 0x310a, 0x3104, 0x30fe,
+  0x30f8, 0x30f3, 0x30ed, 0x30e7, 0x30e1, 0x30db, 0x30d6, 0x30d0,
+  0x30ca, 0x30c4, 0x30be, 0x30b8, 0x30b3, 0x30ad, 0x30a7, 0x30a1,
+  0x309b, 0x3096, 0x3090, 0x308a, 0x3084, 0x307e, 0x3079, 0x3073,
+  0x306d, 0x3067, 0x3061, 0x305b, 0x3056, 0x3050, 0x304a, 0x3044,
+  0x303e, 0x3039, 0x3033, 0x302d, 0x3027, 0x3021, 0x301b, 0x3016,
+  0x3010, 0x300a, 0x3004, 0x2ffe, 0x2ff8, 0x2ff3, 0x2fed, 0x2fe7,
+  0x2fe1, 0x2fdb, 0x2fd6, 0x2fd0, 0x2fca, 0x2fc4, 0x2fbe, 0x2fb8,
+  0x2fb3, 0x2fad, 0x2fa7, 0x2fa1, 0x2f9b, 0x2f95, 0x2f90, 0x2f8a,
+  0x2f84, 0x2f7e, 0x2f78, 0x2f72, 0x2f6d, 0x2f67, 0x2f61, 0x2f5b,
+  0x2f55, 0x2f4f, 0x2f4a, 0x2f44, 0x2f3e, 0x2f38, 0x2f32, 0x2f2c,
+  0x2f27, 0x2f21, 0x2f1b, 0x2f15, 0x2f0f, 0x2f09, 0x2f03, 0x2efe,
+  0x2ef8, 0x2ef2, 0x2eec, 0x2ee6, 0x2ee0, 0x2edb, 0x2ed5, 0x2ecf,
+  0x2ec9, 0x2ec3, 0x2ebd, 0x2eb7, 0x2eb2, 0x2eac, 0x2ea6, 0x2ea0,
+  0x2e9a, 0x2e94, 0x2e8e, 0x2e89, 0x2e83, 0x2e7d, 0x2e77, 0x2e71,
+  0x2e6b, 0x2e65, 0x2e60, 0x2e5a, 0x2e54, 0x2e4e, 0x2e48, 0x2e42,
+  0x2e3c, 0x2e37, 0x2e31, 0x2e2b, 0x2e25, 0x2e1f, 0x2e19, 0x2e13,
+  0x2e0e, 0x2e08, 0x2e02, 0x2dfc, 0x2df6, 0x2df0, 0x2dea, 0x2de5,
+  0x2ddf, 0x2dd9, 0x2dd3, 0x2dcd, 0x2dc7, 0x2dc1, 0x2dbb, 0x2db6,
+  0x2db0, 0x2daa, 0x2da4, 0x2d9e, 0x2d98, 0x2d92, 0x2d8d, 0x2d87,
+  0x2d81, 0x2d7b, 0x2d75, 0x2d6f, 0x2d69, 0x2d63, 0x2d5e, 0x2d58,
+  0x2d52, 0x2d4c, 0x2d46, 0x2d40, 0x2d3a, 0x2d34, 0x2d2f, 0x2d29,
+  0x2d23, 0x2d1d, 0x2d17, 0x2d11, 0x2d0b, 0x2d05, 0x2cff, 0x2cfa,
+  0x2cf4, 0x2cee, 0x2ce8, 0x2ce2, 0x2cdc, 0x2cd6, 0x2cd0, 0x2ccb,
+  0x2cc5, 0x2cbf, 0x2cb9, 0x2cb3, 0x2cad, 0x2ca7, 0x2ca1, 0x2c9b,
+  0x2c96, 0x2c90, 0x2c8a, 0x2c84, 0x2c7e, 0x2c78, 0x2c72, 0x2c6c,
+  0x2c66, 0x2c61, 0x2c5b, 0x2c55, 0x2c4f, 0x2c49, 0x2c43, 0x2c3d,
+  0x2c37, 0x2c31, 0x2c2b, 0x2c26, 0x2c20, 0x2c1a, 0x2c14, 0x2c0e,
+  0x2c08, 0x2c02, 0x2bfc, 0x2bf6, 0x2bf0, 0x2beb, 0x2be5, 0x2bdf,
+  0x2bd9, 0x2bd3, 0x2bcd, 0x2bc7, 0x2bc1, 0x2bbb, 0x2bb5, 0x2bb0,
+  0x2baa, 0x2ba4, 0x2b9e, 0x2b98, 0x2b92, 0x2b8c, 0x2b86, 0x2b80,
+  0x2b7a, 0x2b74, 0x2b6f, 0x2b69, 0x2b63, 0x2b5d, 0x2b57, 0x2b51,
+  0x2b4b, 0x2b45, 0x2b3f, 0x2b39, 0x2b33, 0x2b2d, 0x2b28, 0x2b22,
+  0x2b1c, 0x2b16, 0x2b10, 0x2b0a, 0x2b04, 0x2afe, 0x2af8, 0x2af2,
+  0x2aec, 0x2ae6, 0x2ae1, 0x2adb, 0x2ad5, 0x2acf, 0x2ac9, 0x2ac3,
+  0x2abd, 0x2ab7, 0x2ab1, 0x2aab, 0x2aa5, 0x2a9f, 0x2a99, 0x2a94,
+  0x2a8e, 0x2a88, 0x2a82, 0x2a7c, 0x2a76, 0x2a70, 0x2a6a, 0x2a64,
+  0x2a5e, 0x2a58, 0x2a52, 0x2a4c, 0x2a47, 0x2a41, 0x2a3b, 0x2a35,
+  0x2a2f, 0x2a29, 0x2a23, 0x2a1d, 0x2a17, 0x2a11, 0x2a0b, 0x2a05,
+  0x29ff, 0x29f9, 0x29f3, 0x29ee, 0x29e8, 0x29e2, 0x29dc, 0x29d6,
+  0x29d0, 0x29ca, 0x29c4, 0x29be, 0x29b8, 0x29b2, 0x29ac, 0x29a6,
+  0x29a0, 0x299a, 0x2994, 0x298e, 0x2989, 0x2983, 0x297d, 0x2977,
+  0x2971, 0x296b, 0x2965, 0x295f, 0x2959, 0x2953, 0x294d, 0x2947,
+  0x2941, 0x293b, 0x2935, 0x292f, 0x2929, 0x2923, 0x291d, 0x2918,
+  0x2912, 0x290c, 0x2906, 0x2900, 0x28fa, 0x28f4, 0x28ee, 0x28e8,
+  0x28e2, 0x28dc, 0x28d6, 0x28d0, 0x28ca, 0x28c4, 0x28be, 0x28b8,
+  0x28b2, 0x28ac, 0x28a6, 0x28a0, 0x289a, 0x2895, 0x288f, 0x2889,
+  0x2883, 0x287d, 0x2877, 0x2871, 0x286b, 0x2865, 0x285f, 0x2859,
+  0x2853, 0x284d, 0x2847, 0x2841, 0x283b, 0x2835, 0x282f, 0x2829,
+  0x2823, 0x281d, 0x2817, 0x2811, 0x280b, 0x2805, 0x27ff, 0x27f9,
+  0x27f3, 0x27ee, 0x27e8, 0x27e2, 0x27dc, 0x27d6, 0x27d0, 0x27ca,
+  0x27c4, 0x27be, 0x27b8, 0x27b2, 0x27ac, 0x27a6, 0x27a0, 0x279a,
+  0x2794, 0x278e, 0x2788, 0x2782, 0x277c, 0x2776, 0x2770, 0x276a,
+  0x2764, 0x275e, 0x2758, 0x2752, 0x274c, 0x2746, 0x2740, 0x273a,
+  0x2734, 0x272e, 0x2728, 0x2722, 0x271c, 0x2716, 0x2710, 0x270a,
+  0x2704, 0x26fe, 0x26f8, 0x26f2, 0x26ec, 0x26e7, 0x26e1, 0x26db,
+  0x26d5, 0x26cf, 0x26c9, 0x26c3, 0x26bd, 0x26b7, 0x26b1, 0x26ab,
+  0x26a5, 0x269f, 0x2699, 0x2693, 0x268d, 0x2687, 0x2681, 0x267b,
+  0x2675, 0x266f, 0x2669, 0x2663, 0x265d, 0x2657, 0x2651, 0x264b,
+  0x2645, 0x263f, 0x2639, 0x2633, 0x262d, 0x2627, 0x2621, 0x261b,
+  0x2615, 0x260f, 0x2609, 0x2603, 0x25fd, 0x25f7, 0x25f1, 0x25eb,
+  0x25e5, 0x25df, 0x25d9, 0x25d3, 0x25cd, 0x25c7, 0x25c1, 0x25bb,
+  0x25b5, 0x25af, 0x25a9, 0x25a3, 0x259d, 0x2597, 0x2591, 0x258b,
+  0x2585, 0x257f, 0x2579, 0x2573, 0x256d, 0x2567, 0x2561, 0x255b,
+  0x2555, 0x254f, 0x2549, 0x2543, 0x253d, 0x2537, 0x2531, 0x252b,
+  0x2525, 0x251f, 0x2519, 0x2513, 0x250c, 0x2506, 0x2500, 0x24fa,
+  0x24f4, 0x24ee, 0x24e8, 0x24e2, 0x24dc, 0x24d6, 0x24d0, 0x24ca,
+  0x24c4, 0x24be, 0x24b8, 0x24b2, 0x24ac, 0x24a6, 0x24a0, 0x249a,
+  0x2494, 0x248e, 0x2488, 0x2482, 0x247c, 0x2476, 0x2470, 0x246a,
+  0x2464, 0x245e, 0x2458, 0x2452, 0x244c, 0x2446, 0x2440, 0x243a,
+  0x2434, 0x242e, 0x2428, 0x2422, 0x241c, 0x2416, 0x2410, 0x240a,
+  0x2404, 0x23fd, 0x23f7, 0x23f1, 0x23eb, 0x23e5, 0x23df, 0x23d9,
+  0x23d3, 0x23cd, 0x23c7, 0x23c1, 0x23bb, 0x23b5, 0x23af, 0x23a9,
+  0x23a3, 0x239d, 0x2397, 0x2391, 0x238b, 0x2385, 0x237f, 0x2379,
+  0x2373, 0x236d, 0x2367, 0x2361, 0x235b, 0x2355, 0x234e, 0x2348,
+  0x2342, 0x233c, 0x2336, 0x2330, 0x232a, 0x2324, 0x231e, 0x2318,
+  0x2312, 0x230c, 0x2306, 0x2300, 0x22fa, 0x22f4, 0x22ee, 0x22e8,
+  0x22e2, 0x22dc, 0x22d6, 0x22d0, 0x22ca, 0x22c4, 0x22bd, 0x22b7,
+  0x22b1, 0x22ab, 0x22a5, 0x229f, 0x2299, 0x2293, 0x228d, 0x2287,
+  0x2281, 0x227b, 0x2275, 0x226f, 0x2269, 0x2263, 0x225d, 0x2257,
+  0x2251, 0x224a, 0x2244, 0x223e, 0x2238, 0x2232, 0x222c, 0x2226,
+  0x2220, 0x221a, 0x2214, 0x220e, 0x2208, 0x2202, 0x21fc, 0x21f6,
+  0x21f0, 0x21ea, 0x21e4, 0x21dd, 0x21d7, 0x21d1, 0x21cb, 0x21c5,
+  0x21bf, 0x21b9, 0x21b3, 0x21ad, 0x21a7, 0x21a1, 0x219b, 0x2195,
+  0x218f, 0x2189, 0x2183, 0x217c, 0x2176, 0x2170, 0x216a, 0x2164,
+  0x215e, 0x2158, 0x2152, 0x214c, 0x2146, 0x2140, 0x213a, 0x2134,
+  0x212e, 0x2128, 0x2121, 0x211b, 0x2115, 0x210f, 0x2109, 0x2103,
+  0x20fd, 0x20f7, 0x20f1, 0x20eb, 0x20e5, 0x20df, 0x20d9, 0x20d3,
+  0x20cc, 0x20c6, 0x20c0, 0x20ba, 0x20b4, 0x20ae, 0x20a8, 0x20a2,
+  0x209c, 0x2096, 0x2090, 0x208a, 0x2084, 0x207e, 0x2077, 0x2071,
+  0x206b, 0x2065, 0x205f, 0x2059, 0x2053, 0x204d, 0x2047, 0x2041,
+  0x203b, 0x2035, 0x202e, 0x2028, 0x2022, 0x201c, 0x2016, 0x2010,
+  0x200a, 0x2004, 0x1ffe, 0x1ff8, 0x1ff2, 0x1fec, 0x1fe5, 0x1fdf,
+  0x1fd9, 0x1fd3, 0x1fcd, 0x1fc7, 0x1fc1, 0x1fbb, 0x1fb5, 0x1faf,
+  0x1fa9, 0x1fa3, 0x1f9c, 0x1f96, 0x1f90, 0x1f8a, 0x1f84, 0x1f7e,
+  0x1f78, 0x1f72, 0x1f6c, 0x1f66, 0x1f60, 0x1f59, 0x1f53, 0x1f4d,
+  0x1f47, 0x1f41, 0x1f3b, 0x1f35, 0x1f2f, 0x1f29, 0x1f23, 0x1f1d,
+  0x1f16, 0x1f10, 0x1f0a, 0x1f04, 0x1efe, 0x1ef8, 0x1ef2, 0x1eec,
+  0x1ee6, 0x1ee0, 0x1ed9, 0x1ed3, 0x1ecd, 0x1ec7, 0x1ec1, 0x1ebb,
+  0x1eb5, 0x1eaf, 0x1ea9, 0x1ea3, 0x1e9c, 0x1e96, 0x1e90, 0x1e8a,
+  0x1e84, 0x1e7e, 0x1e78, 0x1e72, 0x1e6c, 0x1e66, 0x1e5f, 0x1e59,
+  0x1e53, 0x1e4d, 0x1e47, 0x1e41, 0x1e3b, 0x1e35, 0x1e2f, 0x1e29,
+  0x1e22, 0x1e1c, 0x1e16, 0x1e10, 0x1e0a, 0x1e04, 0x1dfe, 0x1df8,
+  0x1df2, 0x1deb, 0x1de5, 0x1ddf, 0x1dd9, 0x1dd3, 0x1dcd, 0x1dc7,
+  0x1dc1, 0x1dbb, 0x1db4, 0x1dae, 0x1da8, 0x1da2, 0x1d9c, 0x1d96,
+  0x1d90, 0x1d8a, 0x1d84, 0x1d7d, 0x1d77, 0x1d71, 0x1d6b, 0x1d65,
+  0x1d5f, 0x1d59, 0x1d53, 0x1d4c, 0x1d46, 0x1d40, 0x1d3a, 0x1d34,
+  0x1d2e, 0x1d28, 0x1d22, 0x1d1c, 0x1d15, 0x1d0f, 0x1d09, 0x1d03,
+  0x1cfd, 0x1cf7, 0x1cf1, 0x1ceb, 0x1ce4, 0x1cde, 0x1cd8, 0x1cd2,
+  0x1ccc, 0x1cc6, 0x1cc0, 0x1cba, 0x1cb3, 0x1cad, 0x1ca7, 0x1ca1,
+  0x1c9b, 0x1c95, 0x1c8f, 0x1c89, 0x1c83, 0x1c7c, 0x1c76, 0x1c70,
+  0x1c6a, 0x1c64, 0x1c5e, 0x1c58, 0x1c51, 0x1c4b, 0x1c45, 0x1c3f,
+  0x1c39, 0x1c33, 0x1c2d, 0x1c27, 0x1c20, 0x1c1a, 0x1c14, 0x1c0e,
+  0x1c08, 0x1c02, 0x1bfc, 0x1bf6, 0x1bef, 0x1be9, 0x1be3, 0x1bdd,
+  0x1bd7, 0x1bd1, 0x1bcb, 0x1bc4, 0x1bbe, 0x1bb8, 0x1bb2, 0x1bac,
+  0x1ba6, 0x1ba0, 0x1b9a, 0x1b93, 0x1b8d, 0x1b87, 0x1b81, 0x1b7b,
+  0x1b75, 0x1b6f, 0x1b68, 0x1b62, 0x1b5c, 0x1b56, 0x1b50, 0x1b4a,
+  0x1b44, 0x1b3d, 0x1b37, 0x1b31, 0x1b2b, 0x1b25, 0x1b1f, 0x1b19,
+  0x1b13, 0x1b0c, 0x1b06, 0x1b00, 0x1afa, 0x1af4, 0x1aee, 0x1ae8,
+  0x1ae1, 0x1adb, 0x1ad5, 0x1acf, 0x1ac9, 0x1ac3, 0x1abd, 0x1ab6,
+  0x1ab0, 0x1aaa, 0x1aa4, 0x1a9e, 0x1a98, 0x1a91, 0x1a8b, 0x1a85,
+  0x1a7f, 0x1a79, 0x1a73, 0x1a6d, 0x1a66, 0x1a60, 0x1a5a, 0x1a54,
+  0x1a4e, 0x1a48, 0x1a42, 0x1a3b, 0x1a35, 0x1a2f, 0x1a29, 0x1a23,
+  0x1a1d, 0x1a17, 0x1a10, 0x1a0a, 0x1a04, 0x19fe, 0x19f8, 0x19f2,
+  0x19eb, 0x19e5, 0x19df, 0x19d9, 0x19d3, 0x19cd, 0x19c7, 0x19c0,
+  0x19ba, 0x19b4, 0x19ae, 0x19a8, 0x19a2, 0x199b, 0x1995, 0x198f,
+  0x1989, 0x1983, 0x197d, 0x1977, 0x1970, 0x196a, 0x1964, 0x195e,
+  0x1958, 0x1952, 0x194b, 0x1945, 0x193f, 0x1939, 0x1933, 0x192d,
+  0x1926, 0x1920, 0x191a, 0x1914, 0x190e, 0x1908, 0x1901, 0x18fb,
+  0x18f5, 0x18ef, 0x18e9, 0x18e3, 0x18dc, 0x18d6, 0x18d0, 0x18ca,
+  0x18c4, 0x18be, 0x18b8, 0x18b1, 0x18ab, 0x18a5, 0x189f, 0x1899,
+  0x1893, 0x188c, 0x1886, 0x1880, 0x187a, 0x1874, 0x186e, 0x1867,
+  0x1861, 0x185b, 0x1855, 0x184f, 0x1848, 0x1842, 0x183c, 0x1836,
+  0x1830, 0x182a, 0x1823, 0x181d, 0x1817, 0x1811, 0x180b, 0x1805,
+  0x17fe, 0x17f8, 0x17f2, 0x17ec, 0x17e6, 0x17e0, 0x17d9, 0x17d3,
+  0x17cd, 0x17c7, 0x17c1, 0x17bb, 0x17b4, 0x17ae, 0x17a8, 0x17a2,
+  0x179c, 0x1795, 0x178f, 0x1789, 0x1783, 0x177d, 0x1777, 0x1770,
+  0x176a, 0x1764, 0x175e, 0x1758, 0x1752, 0x174b, 0x1745, 0x173f,
+  0x1739, 0x1733, 0x172c, 0x1726, 0x1720, 0x171a, 0x1714, 0x170e,
+  0x1707, 0x1701, 0x16fb, 0x16f5, 0x16ef, 0x16e8, 0x16e2, 0x16dc,
+  0x16d6, 0x16d0, 0x16ca, 0x16c3, 0x16bd, 0x16b7, 0x16b1, 0x16ab,
+  0x16a4, 0x169e, 0x1698, 0x1692, 0x168c, 0x1686, 0x167f, 0x1679,
+  0x1673, 0x166d, 0x1667, 0x1660, 0x165a, 0x1654, 0x164e, 0x1648,
+  0x1642, 0x163b, 0x1635, 0x162f, 0x1629, 0x1623, 0x161c, 0x1616,
+  0x1610, 0x160a, 0x1604, 0x15fd, 0x15f7, 0x15f1, 0x15eb, 0x15e5,
+  0x15de, 0x15d8, 0x15d2, 0x15cc, 0x15c6, 0x15c0, 0x15b9, 0x15b3,
+  0x15ad, 0x15a7, 0x15a1, 0x159a, 0x1594, 0x158e, 0x1588, 0x1582,
+  0x157b, 0x1575, 0x156f, 0x1569, 0x1563, 0x155c, 0x1556, 0x1550,
+  0x154a, 0x1544, 0x153d, 0x1537, 0x1531, 0x152b, 0x1525, 0x151e,
+  0x1518, 0x1512, 0x150c, 0x1506, 0x14ff, 0x14f9, 0x14f3, 0x14ed,
+  0x14e7, 0x14e0, 0x14da, 0x14d4, 0x14ce, 0x14c8, 0x14c1, 0x14bb,
+  0x14b5, 0x14af, 0x14a9, 0x14a2, 0x149c, 0x1496, 0x1490, 0x148a,
+  0x1483, 0x147d, 0x1477, 0x1471, 0x146b, 0x1464, 0x145e, 0x1458,
+  0x1452, 0x144c, 0x1445, 0x143f, 0x1439, 0x1433, 0x142d, 0x1426,
+  0x1420, 0x141a, 0x1414, 0x140e, 0x1407, 0x1401, 0x13fb, 0x13f5,
+  0x13ef, 0x13e8, 0x13e2, 0x13dc, 0x13d6, 0x13d0, 0x13c9, 0x13c3,
+  0x13bd, 0x13b7, 0x13b1, 0x13aa, 0x13a4, 0x139e, 0x1398, 0x1391,
+  0x138b, 0x1385, 0x137f, 0x1379, 0x1372, 0x136c, 0x1366, 0x1360,
+  0x135a, 0x1353, 0x134d, 0x1347, 0x1341, 0x133b, 0x1334, 0x132e,
+  0x1328, 0x1322, 0x131b, 0x1315, 0x130f, 0x1309, 0x1303, 0x12fc,
+  0x12f6, 0x12f0, 0x12ea, 0x12e4, 0x12dd, 0x12d7, 0x12d1, 0x12cb,
+  0x12c4, 0x12be, 0x12b8, 0x12b2, 0x12ac, 0x12a5, 0x129f, 0x1299,
+  0x1293, 0x128d, 0x1286, 0x1280, 0x127a, 0x1274, 0x126d, 0x1267,
+  0x1261, 0x125b, 0x1255, 0x124e, 0x1248, 0x1242, 0x123c, 0x1235,
+  0x122f, 0x1229, 0x1223, 0x121d, 0x1216, 0x1210, 0x120a, 0x1204,
+  0x11fd, 0x11f7, 0x11f1, 0x11eb, 0x11e5, 0x11de, 0x11d8, 0x11d2,
+  0x11cc, 0x11c5, 0x11bf, 0x11b9, 0x11b3, 0x11ad, 0x11a6, 0x11a0,
+  0x119a, 0x1194, 0x118d, 0x1187, 0x1181, 0x117b, 0x1175, 0x116e,
+  0x1168, 0x1162, 0x115c, 0x1155, 0x114f, 0x1149, 0x1143, 0x113d,
+  0x1136, 0x1130, 0x112a, 0x1124, 0x111d, 0x1117, 0x1111, 0x110b,
+  0x1105, 0x10fe, 0x10f8, 0x10f2, 0x10ec, 0x10e5, 0x10df, 0x10d9,
+  0x10d3, 0x10cc, 0x10c6, 0x10c0, 0x10ba, 0x10b4, 0x10ad, 0x10a7,
+  0x10a1, 0x109b, 0x1094, 0x108e, 0x1088, 0x1082, 0x107b, 0x1075,
+  0x106f, 0x1069, 0x1063, 0x105c, 0x1056, 0x1050, 0x104a, 0x1043,
+  0x103d, 0x1037, 0x1031, 0x102a, 0x1024, 0x101e, 0x1018, 0x1012,
+  0x100b, 0x1005, 0xfff, 0xff9, 0xff2, 0xfec, 0xfe6, 0xfe0,
+  0xfd9, 0xfd3, 0xfcd, 0xfc7, 0xfc0, 0xfba, 0xfb4, 0xfae,
+  0xfa8, 0xfa1, 0xf9b, 0xf95, 0xf8f, 0xf88, 0xf82, 0xf7c,
+  0xf76, 0xf6f, 0xf69, 0xf63, 0xf5d, 0xf56, 0xf50, 0xf4a,
+  0xf44, 0xf3e, 0xf37, 0xf31, 0xf2b, 0xf25, 0xf1e, 0xf18,
+  0xf12, 0xf0c, 0xf05, 0xeff, 0xef9, 0xef3, 0xeec, 0xee6,
+  0xee0, 0xeda, 0xed3, 0xecd, 0xec7, 0xec1, 0xeba, 0xeb4,
+  0xeae, 0xea8, 0xea1, 0xe9b, 0xe95, 0xe8f, 0xe89, 0xe82,
+  0xe7c, 0xe76, 0xe70, 0xe69, 0xe63, 0xe5d, 0xe57, 0xe50,
+  0xe4a, 0xe44, 0xe3e, 0xe37, 0xe31, 0xe2b, 0xe25, 0xe1e,
+  0xe18, 0xe12, 0xe0c, 0xe05, 0xdff, 0xdf9, 0xdf3, 0xdec,
+  0xde6, 0xde0, 0xdda, 0xdd3, 0xdcd, 0xdc7, 0xdc1, 0xdba,
+  0xdb4, 0xdae, 0xda8, 0xda1, 0xd9b, 0xd95, 0xd8f, 0xd88,
+  0xd82, 0xd7c, 0xd76, 0xd6f, 0xd69, 0xd63, 0xd5d, 0xd56,
+  0xd50, 0xd4a, 0xd44, 0xd3d, 0xd37, 0xd31, 0xd2b, 0xd24,
+  0xd1e, 0xd18, 0xd12, 0xd0b, 0xd05, 0xcff, 0xcf9, 0xcf2,
+  0xcec, 0xce6, 0xce0, 0xcd9, 0xcd3, 0xccd, 0xcc7, 0xcc0,
+  0xcba, 0xcb4, 0xcae, 0xca7, 0xca1, 0xc9b, 0xc95, 0xc8e,
+  0xc88, 0xc82, 0xc7c, 0xc75, 0xc6f, 0xc69, 0xc63, 0xc5c,
+  0xc56, 0xc50, 0xc4a, 0xc43, 0xc3d, 0xc37, 0xc31, 0xc2a,
+  0xc24, 0xc1e, 0xc18, 0xc11, 0xc0b, 0xc05, 0xbff, 0xbf8,
+  0xbf2, 0xbec, 0xbe6, 0xbdf, 0xbd9, 0xbd3, 0xbcd, 0xbc6,
+  0xbc0, 0xbba, 0xbb4, 0xbad, 0xba7, 0xba1, 0xb9b, 0xb94,
+  0xb8e, 0xb88, 0xb81, 0xb7b, 0xb75, 0xb6f, 0xb68, 0xb62,
+  0xb5c, 0xb56, 0xb4f, 0xb49, 0xb43, 0xb3d, 0xb36, 0xb30,
+  0xb2a, 0xb24, 0xb1d, 0xb17, 0xb11, 0xb0b, 0xb04, 0xafe,
+  0xaf8, 0xaf2, 0xaeb, 0xae5, 0xadf, 0xad8, 0xad2, 0xacc,
+  0xac6, 0xabf, 0xab9, 0xab3, 0xaad, 0xaa6, 0xaa0, 0xa9a,
+  0xa94, 0xa8d, 0xa87, 0xa81, 0xa7b, 0xa74, 0xa6e, 0xa68,
+  0xa62, 0xa5b, 0xa55, 0xa4f, 0xa48, 0xa42, 0xa3c, 0xa36,
+  0xa2f, 0xa29, 0xa23, 0xa1d, 0xa16, 0xa10, 0xa0a, 0xa04,
+  0x9fd, 0x9f7, 0x9f1, 0x9eb, 0x9e4, 0x9de, 0x9d8, 0x9d1,
+  0x9cb, 0x9c5, 0x9bf, 0x9b8, 0x9b2, 0x9ac, 0x9a6, 0x99f,
+  0x999, 0x993, 0x98d, 0x986, 0x980, 0x97a, 0x973, 0x96d,
+  0x967, 0x961, 0x95a, 0x954, 0x94e, 0x948, 0x941, 0x93b,
+  0x935, 0x92f, 0x928, 0x922, 0x91c, 0x915, 0x90f, 0x909,
+  0x903, 0x8fc, 0x8f6, 0x8f0, 0x8ea, 0x8e3, 0x8dd, 0x8d7,
+  0x8d1, 0x8ca, 0x8c4, 0x8be, 0x8b7, 0x8b1, 0x8ab, 0x8a5,
+  0x89e, 0x898, 0x892, 0x88c, 0x885, 0x87f, 0x879, 0x872,
+  0x86c, 0x866, 0x860, 0x859, 0x853, 0x84d, 0x847, 0x840,
+  0x83a, 0x834, 0x82e, 0x827, 0x821, 0x81b, 0x814, 0x80e,
+  0x808, 0x802, 0x7fb, 0x7f5, 0x7ef, 0x7e9, 0x7e2, 0x7dc,
+  0x7d6, 0x7cf, 0x7c9, 0x7c3, 0x7bd, 0x7b6, 0x7b0, 0x7aa,
+  0x7a4, 0x79d, 0x797, 0x791, 0x78a, 0x784, 0x77e, 0x778,
+  0x771, 0x76b, 0x765, 0x75f, 0x758, 0x752, 0x74c, 0x745,
+  0x73f, 0x739, 0x733, 0x72c, 0x726, 0x720, 0x71a, 0x713,
+  0x70d, 0x707, 0x700, 0x6fa, 0x6f4, 0x6ee, 0x6e7, 0x6e1,
+  0x6db, 0x6d5, 0x6ce, 0x6c8, 0x6c2, 0x6bb, 0x6b5, 0x6af,
+  0x6a9, 0x6a2, 0x69c, 0x696, 0x690, 0x689, 0x683, 0x67d,
+  0x676, 0x670, 0x66a, 0x664, 0x65d, 0x657, 0x651, 0x64a,
+  0x644, 0x63e, 0x638, 0x631, 0x62b, 0x625, 0x61f, 0x618,
+  0x612, 0x60c, 0x605, 0x5ff, 0x5f9, 0x5f3, 0x5ec, 0x5e6,
+  0x5e0, 0x5da, 0x5d3, 0x5cd, 0x5c7, 0x5c0, 0x5ba, 0x5b4,
+  0x5ae, 0x5a7, 0x5a1, 0x59b, 0x594, 0x58e, 0x588, 0x582,
+  0x57b, 0x575, 0x56f, 0x569, 0x562, 0x55c, 0x556, 0x54f,
+  0x549, 0x543, 0x53d, 0x536, 0x530, 0x52a, 0x523, 0x51d,
+  0x517, 0x511, 0x50a, 0x504, 0x4fe, 0x4f8, 0x4f1, 0x4eb,
+  0x4e5, 0x4de, 0x4d8, 0x4d2, 0x4cc, 0x4c5, 0x4bf, 0x4b9,
+  0x4b2, 0x4ac, 0x4a6, 0x4a0, 0x499, 0x493, 0x48d, 0x487,
+  0x480, 0x47a, 0x474, 0x46d, 0x467, 0x461, 0x45b, 0x454,
+  0x44e, 0x448, 0x441, 0x43b, 0x435, 0x42f, 0x428, 0x422,
+  0x41c, 0x415, 0x40f, 0x409, 0x403, 0x3fc, 0x3f6, 0x3f0,
+  0x3ea, 0x3e3, 0x3dd, 0x3d7, 0x3d0, 0x3ca, 0x3c4, 0x3be,
+  0x3b7, 0x3b1, 0x3ab, 0x3a4, 0x39e, 0x398, 0x392, 0x38b,
+  0x385, 0x37f, 0x378, 0x372, 0x36c, 0x366, 0x35f, 0x359,
+  0x353, 0x34c, 0x346, 0x340, 0x33a, 0x333, 0x32d, 0x327,
+  0x321, 0x31a, 0x314, 0x30e, 0x307, 0x301, 0x2fb, 0x2f5,
+  0x2ee, 0x2e8, 0x2e2, 0x2db, 0x2d5, 0x2cf, 0x2c9, 0x2c2,
+  0x2bc, 0x2b6, 0x2af, 0x2a9, 0x2a3, 0x29d, 0x296, 0x290,
+  0x28a, 0x283, 0x27d, 0x277, 0x271, 0x26a, 0x264, 0x25e,
+  0x258, 0x251, 0x24b, 0x245, 0x23e, 0x238, 0x232, 0x22c,
+  0x225, 0x21f, 0x219, 0x212, 0x20c, 0x206, 0x200, 0x1f9,
+  0x1f3, 0x1ed, 0x1e6, 0x1e0, 0x1da, 0x1d4, 0x1cd, 0x1c7,
+  0x1c1, 0x1ba, 0x1b4, 0x1ae, 0x1a8, 0x1a1, 0x19b, 0x195,
+  0x18e, 0x188, 0x182, 0x17c, 0x175, 0x16f, 0x169, 0x162,
+  0x15c, 0x156, 0x150, 0x149, 0x143, 0x13d, 0x137, 0x130,
+  0x12a, 0x124, 0x11d, 0x117, 0x111, 0x10b, 0x104, 0xfe,
+  0xf8, 0xf1, 0xeb, 0xe5, 0xdf, 0xd8, 0xd2, 0xcc,
+  0xc5, 0xbf, 0xb9, 0xb3, 0xac, 0xa6, 0xa0, 0x99,
+  0x93, 0x8d, 0x87, 0x80, 0x7a, 0x74, 0x6d, 0x67,
+  0x61, 0x5b, 0x54, 0x4e, 0x48, 0x41, 0x3b, 0x35,
+  0x2f, 0x28, 0x22, 0x1c, 0x15, 0xf, 0x9, 0x3,
+};
+
+/**    
+ * @brief  Initialization function for the Q15 DCT4/IDCT4.   
+ * @param[in,out] *S         points to an instance of Q15 DCT4/IDCT4 structure.   
+ * @param[in]     *S_RFFT    points to an instance of Q15 RFFT/RIFFT structure.   
+ * @param[in]     *S_CFFT    points to an instance of Q15 CFFT/CIFFT structure.   
+ * @param[in]     N          length of the DCT4.   
+ * @param[in]     Nby2       half of the length of the DCT4.   
+ * @param[in]     normalize  normalizing factor.   
+ * @return  	  arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if N is not a supported transform length.   
+ * \par Normalizing factor:    
+ * The normalizing factor is sqrt(2/N), which depends on the size of transform N.    
+ * Normalizing factors in 1.15 format are mentioned in the table below for different DCT sizes:    
+ * \image html dct4NormalizingQ15Table.gif    
+ */
+
+arm_status arm_dct4_init_q15(
+  arm_dct4_instance_q15 * S,
+  arm_rfft_instance_q15 * S_RFFT,
+  arm_cfft_radix4_instance_q15 * S_CFFT,
+  uint16_t N,
+  uint16_t Nby2,
+  q15_t normalize)
+{
+  /*  Initialise the default arm status */
+  arm_status status = ARM_MATH_SUCCESS;
+
+  /* Initializing the pointer array with the weight table base addresses of different lengths */
+  q15_t *twiddlePtr[4] = { (q15_t *) WeightsQ15_128, (q15_t *) WeightsQ15_512,
+    (q15_t *) WeightsQ15_2048, (q15_t *) WeightsQ15_8192
+  };
+
+  /* Initializing the pointer array with the cos factor table base addresses of different lengths */
+  q15_t *pCosFactor[4] =
+    { (q15_t *) cos_factorsQ15_128, (q15_t *) cos_factorsQ15_512,
+    (q15_t *) cos_factorsQ15_2048, (q15_t *) cos_factorsQ15_8192
+  };
+
+  /* Initialize the DCT4 length */
+  S->N = N;
+
+  /* Initialize the half of DCT4 length */
+  S->Nby2 = Nby2;
+
+  /* Initialize the DCT4 Normalizing factor */
+  S->normalize = normalize;
+
+  /* Initialize Real FFT Instance */
+  S->pRfft = S_RFFT;
+
+  /* Initialize Complex FFT Instance */
+  S->pCfft = S_CFFT;
+
+  switch (N)
+  {
+    /* Initialize the table modifier values */
+  case 8192u:
+    S->pTwiddle = twiddlePtr[3];
+    S->pCosFactor = pCosFactor[3];
+    break;
+  case 2048u:
+    S->pTwiddle = twiddlePtr[2];
+    S->pCosFactor = pCosFactor[2];
+    break;
+  case 512u:
+    S->pTwiddle = twiddlePtr[1];
+    S->pCosFactor = pCosFactor[1];
+    break;
+  case 128u:
+    S->pTwiddle = twiddlePtr[0];
+    S->pCosFactor = pCosFactor[0];
+    break;
+  default:
+    status = ARM_MATH_ARGUMENT_ERROR;
+  }
+
+  /* Initialize the RFFT/RIFFT */
+  arm_rfft_init_q15(S->pRfft, S->pCfft, S->N, 0u, 1u);
+
+  /* return the status of DCT4 Init function */
+  return (status);
+}
+
+/**    
+   * @} end of DCT4_IDCT4 group    
+   */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_dct4_init_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_dct4_init_q31.c
new file mode 100644
index 0000000000..211cdadf38
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_dct4_init_q31.c
@@ -0,0 +1,8356 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_dct4_init_q31.c    
+*    
+* Description:	Initialization function of DCT-4 & IDCT4 Q31    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupTransforms    
+ */
+
+/**    
+ * @addtogroup DCT4_IDCT4    
+ * @{    
+ */
+
+/*    
+* @brief  Weights Table    
+*/
+
+/**    
+* \par    
+* Weights tables are generated using the formula : 
weights[n] = e^(-j*n*pi/(2*N))
    
+* \par    
+* C command to generate the table    
+* 
    
+* for(i = 0; i< N; i++)    
+* {    
+*   weights[2*i]= cos(i*c);    
+*   weights[(2*i)+1]= -sin(i * c);    
+* } 
    
+* \par    
+* where N is the Number of weights to be calculated and c is pi/(2*N)    
+* \par    
+* Convert the output to q31 format by multiplying with 2^31 and saturated if required.    
+* \par    
+* In the tables below the real and imaginary values are placed alternatively, hence the    
+* array length is 2*N.    
+*/
+
+static const q31_t WeightsQ31_128[256] = {
+  0x7fffffff, 0x0, 0x7ffd885a, 0xfe6de2e0, 0x7ff62182, 0xfcdbd541, 0x7fe9cbc0,
+  0xfb49e6a3,
+  0x7fd8878e, 0xf9b82684, 0x7fc25596, 0xf826a462, 0x7fa736b4, 0xf6956fb7,
+  0x7f872bf3, 0xf50497fb,
+  0x7f62368f, 0xf3742ca2, 0x7f3857f6, 0xf1e43d1c, 0x7f0991c4, 0xf054d8d5,
+  0x7ed5e5c6, 0xeec60f31,
+  0x7e9d55fc, 0xed37ef91, 0x7e5fe493, 0xebaa894f, 0x7e1d93ea, 0xea1debbb,
+  0x7dd6668f, 0xe8922622,
+  0x7d8a5f40, 0xe70747c4, 0x7d3980ec, 0xe57d5fda, 0x7ce3ceb2, 0xe3f47d96,
+  0x7c894bde, 0xe26cb01b,
+  0x7c29fbee, 0xe0e60685, 0x7bc5e290, 0xdf608fe4, 0x7b5d039e, 0xdddc5b3b,
+  0x7aef6323, 0xdc597781,
+  0x7a7d055b, 0xdad7f3a2, 0x7a05eead, 0xd957de7a, 0x798a23b1, 0xd7d946d8,
+  0x7909a92d, 0xd65c3b7b,
+  0x78848414, 0xd4e0cb15, 0x77fab989, 0xd3670446, 0x776c4edb, 0xd1eef59e,
+  0x76d94989, 0xd078ad9e,
+  0x7641af3d, 0xcf043ab3, 0x75a585cf, 0xcd91ab39, 0x7504d345, 0xcc210d79,
+  0x745f9dd1, 0xcab26fa9,
+  0x73b5ebd1, 0xc945dfec, 0x7307c3d0, 0xc7db6c50, 0x72552c85, 0xc67322ce,
+  0x719e2cd2, 0xc50d1149,
+  0x70e2cbc6, 0xc3a94590, 0x7023109a, 0xc247cd5a, 0x6f5f02b2, 0xc0e8b648,
+  0x6e96a99d, 0xbf8c0de3,
+  0x6dca0d14, 0xbe31e19b, 0x6cf934fc, 0xbcda3ecb, 0x6c242960, 0xbb8532b0,
+  0x6b4af279, 0xba32ca71,
+  0x6a6d98a4, 0xb8e31319, 0x698c246c, 0xb796199b, 0x68a69e81, 0xb64beacd,
+  0x67bd0fbd, 0xb5049368,
+  0x66cf8120, 0xb3c0200c, 0x65ddfbd3, 0xb27e9d3c, 0x64e88926, 0xb140175b,
+  0x63ef3290, 0xb0049ab3,
+  0x62f201ac, 0xaecc336c, 0x61f1003f, 0xad96ed92, 0x60ec3830, 0xac64d510,
+  0x5fe3b38d, 0xab35f5b5,
+  0x5ed77c8a, 0xaa0a5b2e, 0x5dc79d7c, 0xa8e21106, 0x5cb420e0, 0xa7bd22ac,
+  0x5b9d1154, 0xa69b9b68,
+  0x5a82799a, 0xa57d8666, 0x59646498, 0xa462eeac, 0x5842dd54, 0xa34bdf20,
+  0x571deefa, 0xa2386284,
+  0x55f5a4d2, 0xa1288376, 0x54ca0a4b, 0xa01c4c73, 0x539b2af0, 0x9f13c7d0,
+  0x5269126e, 0x9e0effc1,
+  0x5133cc94, 0x9d0dfe54, 0x4ffb654d, 0x9c10cd70, 0x4ebfe8a5, 0x9b1776da,
+  0x4d8162c4, 0x9a22042d,
+  0x4c3fdff4, 0x99307ee0, 0x4afb6c98, 0x9842f043, 0x49b41533, 0x9759617f,
+  0x4869e665, 0x9673db94,
+  0x471cece7, 0x9592675c, 0x45cd358f, 0x94b50d87, 0x447acd50, 0x93dbd6a0,
+  0x4325c135, 0x9306cb04,
+  0x41ce1e65, 0x9235f2ec, 0x4073f21d, 0x91695663, 0x3f1749b8, 0x90a0fd4e,
+  0x3db832a6, 0x8fdcef66,
+  0x3c56ba70, 0x8f1d343a, 0x3af2eeb7, 0x8e61d32e, 0x398cdd32, 0x8daad37b,
+  0x382493b0, 0x8cf83c30,
+  0x36ba2014, 0x8c4a142f, 0x354d9057, 0x8ba0622f, 0x33def287, 0x8afb2cbb,
+  0x326e54c7, 0x8a5a7a31,
+  0x30fbc54d, 0x89be50c3, 0x2f875262, 0x8926b677, 0x2e110a62, 0x8893b125,
+  0x2c98fbba, 0x88054677,
+  0x2b1f34eb, 0x877b7bec, 0x29a3c485, 0x86f656d3, 0x2826b928, 0x8675dc4f,
+  0x26a82186, 0x85fa1153,
+  0x25280c5e, 0x8582faa5, 0x23a6887f, 0x85109cdd, 0x2223a4c5, 0x84a2fc62,
+  0x209f701c, 0x843a1d70,
+  0x1f19f97b, 0x83d60412, 0x1d934fe5, 0x8376b422, 0x1c0b826a, 0x831c314e,
+  0x1a82a026, 0x82c67f14,
+  0x18f8b83c, 0x8275a0c0, 0x176dd9de, 0x82299971, 0x15e21445, 0x81e26c16,
+  0x145576b1, 0x81a01b6d,
+  0x12c8106f, 0x8162aa04, 0x1139f0cf, 0x812a1a3a, 0xfab272b, 0x80f66e3c,
+  0xe1bc2e4, 0x80c7a80a,
+  0xc8bd35e, 0x809dc971, 0xafb6805, 0x8078d40d, 0x96a9049, 0x8058c94c,
+  0x7d95b9e, 0x803daa6a,
+  0x647d97c, 0x80277872, 0x4b6195d, 0x80163440, 0x3242abf, 0x8009de7e,
+  0x1921d20, 0x800277a6,
+};
+
+static const q31_t WeightsQ31_512[1024] = {
+  0x7fffffff, 0x0, 0x7fffd886, 0xff9b781d, 0x7fff6216, 0xff36f078, 0x7ffe9cb2,
+  0xfed2694f,
+  0x7ffd885a, 0xfe6de2e0, 0x7ffc250f, 0xfe095d69, 0x7ffa72d1, 0xfda4d929,
+  0x7ff871a2, 0xfd40565c,
+  0x7ff62182, 0xfcdbd541, 0x7ff38274, 0xfc775616, 0x7ff09478, 0xfc12d91a,
+  0x7fed5791, 0xfbae5e89,
+  0x7fe9cbc0, 0xfb49e6a3, 0x7fe5f108, 0xfae571a4, 0x7fe1c76b, 0xfa80ffcb,
+  0x7fdd4eec, 0xfa1c9157,
+  0x7fd8878e, 0xf9b82684, 0x7fd37153, 0xf953bf91, 0x7fce0c3e, 0xf8ef5cbb,
+  0x7fc85854, 0xf88afe42,
+  0x7fc25596, 0xf826a462, 0x7fbc040a, 0xf7c24f59, 0x7fb563b3, 0xf75dff66,
+  0x7fae7495, 0xf6f9b4c6,
+  0x7fa736b4, 0xf6956fb7, 0x7f9faa15, 0xf6313077, 0x7f97cebd, 0xf5ccf743,
+  0x7f8fa4b0, 0xf568c45b,
+  0x7f872bf3, 0xf50497fb, 0x7f7e648c, 0xf4a07261, 0x7f754e80, 0xf43c53cb,
+  0x7f6be9d4, 0xf3d83c77,
+  0x7f62368f, 0xf3742ca2, 0x7f5834b7, 0xf310248a, 0x7f4de451, 0xf2ac246e,
+  0x7f434563, 0xf2482c8a,
+  0x7f3857f6, 0xf1e43d1c, 0x7f2d1c0e, 0xf1805662, 0x7f2191b4, 0xf11c789a,
+  0x7f15b8ee, 0xf0b8a401,
+  0x7f0991c4, 0xf054d8d5, 0x7efd1c3c, 0xeff11753, 0x7ef05860, 0xef8d5fb8,
+  0x7ee34636, 0xef29b243,
+  0x7ed5e5c6, 0xeec60f31, 0x7ec8371a, 0xee6276bf, 0x7eba3a39, 0xedfee92b,
+  0x7eabef2c, 0xed9b66b2,
+  0x7e9d55fc, 0xed37ef91, 0x7e8e6eb2, 0xecd48407, 0x7e7f3957, 0xec71244f,
+  0x7e6fb5f4, 0xec0dd0a8,
+  0x7e5fe493, 0xebaa894f, 0x7e4fc53e, 0xeb474e81, 0x7e3f57ff, 0xeae4207a,
+  0x7e2e9cdf, 0xea80ff7a,
+  0x7e1d93ea, 0xea1debbb, 0x7e0c3d29, 0xe9bae57d, 0x7dfa98a8, 0xe957ecfb,
+  0x7de8a670, 0xe8f50273,
+  0x7dd6668f, 0xe8922622, 0x7dc3d90d, 0xe82f5844, 0x7db0fdf8, 0xe7cc9917,
+  0x7d9dd55a, 0xe769e8d8,
+  0x7d8a5f40, 0xe70747c4, 0x7d769bb5, 0xe6a4b616, 0x7d628ac6, 0xe642340d,
+  0x7d4e2c7f, 0xe5dfc1e5,
+  0x7d3980ec, 0xe57d5fda, 0x7d24881b, 0xe51b0e2a, 0x7d0f4218, 0xe4b8cd11,
+  0x7cf9aef0, 0xe4569ccb,
+  0x7ce3ceb2, 0xe3f47d96, 0x7ccda169, 0xe3926fad, 0x7cb72724, 0xe330734d,
+  0x7ca05ff1, 0xe2ce88b3,
+  0x7c894bde, 0xe26cb01b, 0x7c71eaf9, 0xe20ae9c1, 0x7c5a3d50, 0xe1a935e2,
+  0x7c4242f2, 0xe14794ba,
+  0x7c29fbee, 0xe0e60685, 0x7c116853, 0xe0848b7f, 0x7bf88830, 0xe02323e5,
+  0x7bdf5b94, 0xdfc1cff3,
+  0x7bc5e290, 0xdf608fe4, 0x7bac1d31, 0xdeff63f4, 0x7b920b89, 0xde9e4c60,
+  0x7b77ada8, 0xde3d4964,
+  0x7b5d039e, 0xdddc5b3b, 0x7b420d7a, 0xdd7b8220, 0x7b26cb4f, 0xdd1abe51,
+  0x7b0b3d2c, 0xdcba1008,
+  0x7aef6323, 0xdc597781, 0x7ad33d45, 0xdbf8f4f8, 0x7ab6cba4, 0xdb9888a8,
+  0x7a9a0e50, 0xdb3832cd,
+  0x7a7d055b, 0xdad7f3a2, 0x7a5fb0d8, 0xda77cb63, 0x7a4210d8, 0xda17ba4a,
+  0x7a24256f, 0xd9b7c094,
+  0x7a05eead, 0xd957de7a, 0x79e76ca7, 0xd8f81439, 0x79c89f6e, 0xd898620c,
+  0x79a98715, 0xd838c82d,
+  0x798a23b1, 0xd7d946d8, 0x796a7554, 0xd779de47, 0x794a7c12, 0xd71a8eb5,
+  0x792a37fe, 0xd6bb585e,
+  0x7909a92d, 0xd65c3b7b, 0x78e8cfb2, 0xd5fd3848, 0x78c7aba2, 0xd59e4eff,
+  0x78a63d11, 0xd53f7fda,
+  0x78848414, 0xd4e0cb15, 0x786280bf, 0xd48230e9, 0x78403329, 0xd423b191,
+  0x781d9b65, 0xd3c54d47,
+  0x77fab989, 0xd3670446, 0x77d78daa, 0xd308d6c7, 0x77b417df, 0xd2aac504,
+  0x7790583e, 0xd24ccf39,
+  0x776c4edb, 0xd1eef59e, 0x7747fbce, 0xd191386e, 0x77235f2d, 0xd13397e2,
+  0x76fe790e, 0xd0d61434,
+  0x76d94989, 0xd078ad9e, 0x76b3d0b4, 0xd01b6459, 0x768e0ea6, 0xcfbe389f,
+  0x76680376, 0xcf612aaa,
+  0x7641af3d, 0xcf043ab3, 0x761b1211, 0xcea768f2, 0x75f42c0b, 0xce4ab5a2,
+  0x75ccfd42, 0xcdee20fc,
+  0x75a585cf, 0xcd91ab39, 0x757dc5ca, 0xcd355491, 0x7555bd4c, 0xccd91d3d,
+  0x752d6c6c, 0xcc7d0578,
+  0x7504d345, 0xcc210d79, 0x74dbf1ef, 0xcbc53579, 0x74b2c884, 0xcb697db0,
+  0x7489571c, 0xcb0de658,
+  0x745f9dd1, 0xcab26fa9, 0x74359cbd, 0xca5719db, 0x740b53fb, 0xc9fbe527,
+  0x73e0c3a3, 0xc9a0d1c5,
+  0x73b5ebd1, 0xc945dfec, 0x738acc9e, 0xc8eb0fd6, 0x735f6626, 0xc89061ba,
+  0x7333b883, 0xc835d5d0,
+  0x7307c3d0, 0xc7db6c50, 0x72db8828, 0xc7812572, 0x72af05a7, 0xc727016d,
+  0x72823c67, 0xc6cd0079,
+  0x72552c85, 0xc67322ce, 0x7227d61c, 0xc61968a2, 0x71fa3949, 0xc5bfd22e,
+  0x71cc5626, 0xc5665fa9,
+  0x719e2cd2, 0xc50d1149, 0x716fbd68, 0xc4b3e746, 0x71410805, 0xc45ae1d7,
+  0x71120cc5, 0xc4020133,
+  0x70e2cbc6, 0xc3a94590, 0x70b34525, 0xc350af26, 0x708378ff, 0xc2f83e2a,
+  0x70536771, 0xc29ff2d4,
+  0x7023109a, 0xc247cd5a, 0x6ff27497, 0xc1efcdf3, 0x6fc19385, 0xc197f4d4,
+  0x6f906d84, 0xc1404233,
+  0x6f5f02b2, 0xc0e8b648, 0x6f2d532c, 0xc0915148, 0x6efb5f12, 0xc03a1368,
+  0x6ec92683, 0xbfe2fcdf,
+  0x6e96a99d, 0xbf8c0de3, 0x6e63e87f, 0xbf3546a8, 0x6e30e34a, 0xbedea765,
+  0x6dfd9a1c, 0xbe88304f,
+  0x6dca0d14, 0xbe31e19b, 0x6d963c54, 0xbddbbb7f, 0x6d6227fa, 0xbd85be30,
+  0x6d2dd027, 0xbd2fe9e2,
+  0x6cf934fc, 0xbcda3ecb, 0x6cc45698, 0xbc84bd1f, 0x6c8f351c, 0xbc2f6513,
+  0x6c59d0a9, 0xbbda36dd,
+  0x6c242960, 0xbb8532b0, 0x6bee3f62, 0xbb3058c0, 0x6bb812d1, 0xbadba943,
+  0x6b81a3cd, 0xba87246d,
+  0x6b4af279, 0xba32ca71, 0x6b13fef5, 0xb9de9b83, 0x6adcc964, 0xb98a97d8,
+  0x6aa551e9, 0xb936bfa4,
+  0x6a6d98a4, 0xb8e31319, 0x6a359db9, 0xb88f926d, 0x69fd614a, 0xb83c3dd1,
+  0x69c4e37a, 0xb7e9157a,
+  0x698c246c, 0xb796199b, 0x69532442, 0xb7434a67, 0x6919e320, 0xb6f0a812,
+  0x68e06129, 0xb69e32cd,
+  0x68a69e81, 0xb64beacd, 0x686c9b4b, 0xb5f9d043, 0x683257ab, 0xb5a7e362,
+  0x67f7d3c5, 0xb556245e,
+  0x67bd0fbd, 0xb5049368, 0x67820bb7, 0xb4b330b3, 0x6746c7d8, 0xb461fc70,
+  0x670b4444, 0xb410f6d3,
+  0x66cf8120, 0xb3c0200c, 0x66937e91, 0xb36f784f, 0x66573cbb, 0xb31effcc,
+  0x661abbc5, 0xb2ceb6b5,
+  0x65ddfbd3, 0xb27e9d3c, 0x65a0fd0b, 0xb22eb392, 0x6563bf92, 0xb1def9e9,
+  0x6526438f, 0xb18f7071,
+  0x64e88926, 0xb140175b, 0x64aa907f, 0xb0f0eeda, 0x646c59bf, 0xb0a1f71d,
+  0x642de50d, 0xb0533055,
+  0x63ef3290, 0xb0049ab3, 0x63b0426d, 0xafb63667, 0x637114cc, 0xaf6803a2,
+  0x6331a9d4, 0xaf1a0293,
+  0x62f201ac, 0xaecc336c, 0x62b21c7b, 0xae7e965b, 0x6271fa69, 0xae312b92,
+  0x62319b9d, 0xade3f33e,
+  0x61f1003f, 0xad96ed92, 0x61b02876, 0xad4a1aba, 0x616f146c, 0xacfd7ae8,
+  0x612dc447, 0xacb10e4b,
+  0x60ec3830, 0xac64d510, 0x60aa7050, 0xac18cf69, 0x60686ccf, 0xabccfd83,
+  0x60262dd6, 0xab815f8d,
+  0x5fe3b38d, 0xab35f5b5, 0x5fa0fe1f, 0xaaeac02c, 0x5f5e0db3, 0xaa9fbf1e,
+  0x5f1ae274, 0xaa54f2ba,
+  0x5ed77c8a, 0xaa0a5b2e, 0x5e93dc1f, 0xa9bff8a8, 0x5e50015d, 0xa975cb57,
+  0x5e0bec6e, 0xa92bd367,
+  0x5dc79d7c, 0xa8e21106, 0x5d8314b1, 0xa8988463, 0x5d3e5237, 0xa84f2daa,
+  0x5cf95638, 0xa8060d08,
+  0x5cb420e0, 0xa7bd22ac, 0x5c6eb258, 0xa7746ec0, 0x5c290acc, 0xa72bf174,
+  0x5be32a67, 0xa6e3aaf2,
+  0x5b9d1154, 0xa69b9b68, 0x5b56bfbd, 0xa653c303, 0x5b1035cf, 0xa60c21ee,
+  0x5ac973b5, 0xa5c4b855,
+  0x5a82799a, 0xa57d8666, 0x5a3b47ab, 0xa5368c4b, 0x59f3de12, 0xa4efca31,
+  0x59ac3cfd, 0xa4a94043,
+  0x59646498, 0xa462eeac, 0x591c550e, 0xa41cd599, 0x58d40e8c, 0xa3d6f534,
+  0x588b9140, 0xa3914da8,
+  0x5842dd54, 0xa34bdf20, 0x57f9f2f8, 0xa306a9c8, 0x57b0d256, 0xa2c1adc9,
+  0x57677b9d, 0xa27ceb4f,
+  0x571deefa, 0xa2386284, 0x56d42c99, 0xa1f41392, 0x568a34a9, 0xa1affea3,
+  0x56400758, 0xa16c23e1,
+  0x55f5a4d2, 0xa1288376, 0x55ab0d46, 0xa0e51d8c, 0x556040e2, 0xa0a1f24d,
+  0x55153fd4, 0xa05f01e1,
+  0x54ca0a4b, 0xa01c4c73, 0x547ea073, 0x9fd9d22a, 0x5433027d, 0x9f979331,
+  0x53e73097, 0x9f558fb0,
+  0x539b2af0, 0x9f13c7d0, 0x534ef1b5, 0x9ed23bb9, 0x53028518, 0x9e90eb94,
+  0x52b5e546, 0x9e4fd78a,
+  0x5269126e, 0x9e0effc1, 0x521c0cc2, 0x9dce6463, 0x51ced46e, 0x9d8e0597,
+  0x518169a5, 0x9d4de385,
+  0x5133cc94, 0x9d0dfe54, 0x50e5fd6d, 0x9cce562c, 0x5097fc5e, 0x9c8eeb34,
+  0x5049c999, 0x9c4fbd93,
+  0x4ffb654d, 0x9c10cd70, 0x4faccfab, 0x9bd21af3, 0x4f5e08e3, 0x9b93a641,
+  0x4f0f1126, 0x9b556f81,
+  0x4ebfe8a5, 0x9b1776da, 0x4e708f8f, 0x9ad9bc71, 0x4e210617, 0x9a9c406e,
+  0x4dd14c6e, 0x9a5f02f5,
+  0x4d8162c4, 0x9a22042d, 0x4d31494b, 0x99e5443b, 0x4ce10034, 0x99a8c345,
+  0x4c9087b1, 0x996c816f,
+  0x4c3fdff4, 0x99307ee0, 0x4bef092d, 0x98f4bbbc, 0x4b9e0390, 0x98b93828,
+  0x4b4ccf4d, 0x987df449,
+  0x4afb6c98, 0x9842f043, 0x4aa9dba2, 0x98082c3b, 0x4a581c9e, 0x97cda855,
+  0x4a062fbd, 0x979364b5,
+  0x49b41533, 0x9759617f, 0x4961cd33, 0x971f9ed7, 0x490f57ee, 0x96e61ce0,
+  0x48bcb599, 0x96acdbbe,
+  0x4869e665, 0x9673db94, 0x4816ea86, 0x963b1c86, 0x47c3c22f, 0x96029eb6,
+  0x47706d93, 0x95ca6247,
+  0x471cece7, 0x9592675c, 0x46c9405c, 0x955aae17, 0x46756828, 0x9523369c,
+  0x4621647d, 0x94ec010b,
+  0x45cd358f, 0x94b50d87, 0x4578db93, 0x947e5c33, 0x452456bd, 0x9447ed2f,
+  0x44cfa740, 0x9411c09e,
+  0x447acd50, 0x93dbd6a0, 0x4425c923, 0x93a62f57, 0x43d09aed, 0x9370cae4,
+  0x437b42e1, 0x933ba968,
+  0x4325c135, 0x9306cb04, 0x42d0161e, 0x92d22fd9, 0x427a41d0, 0x929dd806,
+  0x42244481, 0x9269c3ac,
+  0x41ce1e65, 0x9235f2ec, 0x4177cfb1, 0x920265e4, 0x4121589b, 0x91cf1cb6,
+  0x40cab958, 0x919c1781,
+  0x4073f21d, 0x91695663, 0x401d0321, 0x9136d97d, 0x3fc5ec98, 0x9104a0ee,
+  0x3f6eaeb8, 0x90d2acd4,
+  0x3f1749b8, 0x90a0fd4e, 0x3ebfbdcd, 0x906f927c, 0x3e680b2c, 0x903e6c7b,
+  0x3e10320d, 0x900d8b69,
+  0x3db832a6, 0x8fdcef66, 0x3d600d2c, 0x8fac988f, 0x3d07c1d6, 0x8f7c8701,
+  0x3caf50da, 0x8f4cbadb,
+  0x3c56ba70, 0x8f1d343a, 0x3bfdfecd, 0x8eedf33b, 0x3ba51e29, 0x8ebef7fb,
+  0x3b4c18ba, 0x8e904298,
+  0x3af2eeb7, 0x8e61d32e, 0x3a99a057, 0x8e33a9da, 0x3a402dd2, 0x8e05c6b7,
+  0x39e6975e, 0x8dd829e4,
+  0x398cdd32, 0x8daad37b, 0x3932ff87, 0x8d7dc399, 0x38d8fe93, 0x8d50fa59,
+  0x387eda8e, 0x8d2477d8,
+  0x382493b0, 0x8cf83c30, 0x37ca2a30, 0x8ccc477d, 0x376f9e46, 0x8ca099da,
+  0x3714f02a, 0x8c753362,
+  0x36ba2014, 0x8c4a142f, 0x365f2e3b, 0x8c1f3c5d, 0x36041ad9, 0x8bf4ac05,
+  0x35a8e625, 0x8bca6343,
+  0x354d9057, 0x8ba0622f, 0x34f219a8, 0x8b76a8e4, 0x34968250, 0x8b4d377c,
+  0x343aca87, 0x8b240e11,
+  0x33def287, 0x8afb2cbb, 0x3382fa88, 0x8ad29394, 0x3326e2c3, 0x8aaa42b4,
+  0x32caab6f, 0x8a823a36,
+  0x326e54c7, 0x8a5a7a31, 0x3211df04, 0x8a3302be, 0x31b54a5e, 0x8a0bd3f5,
+  0x3158970e, 0x89e4edef,
+  0x30fbc54d, 0x89be50c3, 0x309ed556, 0x8997fc8a, 0x3041c761, 0x8971f15a,
+  0x2fe49ba7, 0x894c2f4c,
+  0x2f875262, 0x8926b677, 0x2f29ebcc, 0x890186f2, 0x2ecc681e, 0x88dca0d3,
+  0x2e6ec792, 0x88b80432,
+  0x2e110a62, 0x8893b125, 0x2db330c7, 0x886fa7c2, 0x2d553afc, 0x884be821,
+  0x2cf72939, 0x88287256,
+  0x2c98fbba, 0x88054677, 0x2c3ab2b9, 0x87e2649b, 0x2bdc4e6f, 0x87bfccd7,
+  0x2b7dcf17, 0x879d7f41,
+  0x2b1f34eb, 0x877b7bec, 0x2ac08026, 0x8759c2ef, 0x2a61b101, 0x8738545e,
+  0x2a02c7b8, 0x8717304e,
+  0x29a3c485, 0x86f656d3, 0x2944a7a2, 0x86d5c802, 0x28e5714b, 0x86b583ee,
+  0x288621b9, 0x86958aac,
+  0x2826b928, 0x8675dc4f, 0x27c737d3, 0x865678eb, 0x27679df4, 0x86376092,
+  0x2707ebc7, 0x86189359,
+  0x26a82186, 0x85fa1153, 0x26483f6c, 0x85dbda91, 0x25e845b6, 0x85bdef28,
+  0x2588349d, 0x85a04f28,
+  0x25280c5e, 0x8582faa5, 0x24c7cd33, 0x8565f1b0, 0x24677758, 0x8549345c,
+  0x24070b08, 0x852cc2bb,
+  0x23a6887f, 0x85109cdd, 0x2345eff8, 0x84f4c2d4, 0x22e541af, 0x84d934b1,
+  0x22847de0, 0x84bdf286,
+  0x2223a4c5, 0x84a2fc62, 0x21c2b69c, 0x84885258, 0x2161b3a0, 0x846df477,
+  0x21009c0c, 0x8453e2cf,
+  0x209f701c, 0x843a1d70, 0x203e300d, 0x8420a46c, 0x1fdcdc1b, 0x840777d0,
+  0x1f7b7481, 0x83ee97ad,
+  0x1f19f97b, 0x83d60412, 0x1eb86b46, 0x83bdbd0e, 0x1e56ca1e, 0x83a5c2b0,
+  0x1df5163f, 0x838e1507,
+  0x1d934fe5, 0x8376b422, 0x1d31774d, 0x835fa00f, 0x1ccf8cb3, 0x8348d8dc,
+  0x1c6d9053, 0x83325e97,
+  0x1c0b826a, 0x831c314e, 0x1ba96335, 0x83065110, 0x1b4732ef, 0x82f0bde8,
+  0x1ae4f1d6, 0x82db77e5,
+  0x1a82a026, 0x82c67f14, 0x1a203e1b, 0x82b1d381, 0x19bdcbf3, 0x829d753a,
+  0x195b49ea, 0x8289644b,
+  0x18f8b83c, 0x8275a0c0, 0x18961728, 0x82622aa6, 0x183366e9, 0x824f0208,
+  0x17d0a7bc, 0x823c26f3,
+  0x176dd9de, 0x82299971, 0x170afd8d, 0x82175990, 0x16a81305, 0x82056758,
+  0x16451a83, 0x81f3c2d7,
+  0x15e21445, 0x81e26c16, 0x157f0086, 0x81d16321, 0x151bdf86, 0x81c0a801,
+  0x14b8b17f, 0x81b03ac2,
+  0x145576b1, 0x81a01b6d, 0x13f22f58, 0x81904a0c, 0x138edbb1, 0x8180c6a9,
+  0x132b7bf9, 0x8171914e,
+  0x12c8106f, 0x8162aa04, 0x1264994e, 0x815410d4, 0x120116d5, 0x8145c5c7,
+  0x119d8941, 0x8137c8e6,
+  0x1139f0cf, 0x812a1a3a, 0x10d64dbd, 0x811cb9ca, 0x1072a048, 0x810fa7a0,
+  0x100ee8ad, 0x8102e3c4,
+  0xfab272b, 0x80f66e3c, 0xf475bff, 0x80ea4712, 0xee38766, 0x80de6e4c,
+  0xe7fa99e, 0x80d2e3f2,
+  0xe1bc2e4, 0x80c7a80a, 0xdb7d376, 0x80bcba9d, 0xd53db92, 0x80b21baf,
+  0xcefdb76, 0x80a7cb49,
+  0xc8bd35e, 0x809dc971, 0xc27c389, 0x8094162c, 0xbc3ac35, 0x808ab180,
+  0xb5f8d9f, 0x80819b74,
+  0xafb6805, 0x8078d40d, 0xa973ba5, 0x80705b50, 0xa3308bd, 0x80683143,
+  0x9cecf89, 0x806055eb,
+  0x96a9049, 0x8058c94c, 0x9064b3a, 0x80518b6b, 0x8a2009a, 0x804a9c4d,
+  0x83db0a7, 0x8043fbf6,
+  0x7d95b9e, 0x803daa6a, 0x77501be, 0x8037a7ac, 0x710a345, 0x8031f3c2,
+  0x6ac406f, 0x802c8ead,
+  0x647d97c, 0x80277872, 0x5e36ea9, 0x8022b114, 0x57f0035, 0x801e3895,
+  0x51a8e5c, 0x801a0ef8,
+  0x4b6195d, 0x80163440, 0x451a177, 0x8012a86f, 0x3ed26e6, 0x800f6b88,
+  0x388a9ea, 0x800c7d8c,
+  0x3242abf, 0x8009de7e, 0x2bfa9a4, 0x80078e5e, 0x25b26d7, 0x80058d2f,
+  0x1f6a297, 0x8003daf1,
+  0x1921d20, 0x800277a6, 0x12d96b1, 0x8001634e, 0xc90f88, 0x80009dea,
+  0x6487e3, 0x8000277a,
+};
+
+static const q31_t WeightsQ31_2048[4096] = {
+  0x7fffffff, 0x0, 0x7ffffd88, 0xffe6de05, 0x7ffff621, 0xffcdbc0b, 0x7fffe9cb,
+  0xffb49a12,
+  0x7fffd886, 0xff9b781d, 0x7fffc251, 0xff82562c, 0x7fffa72c, 0xff69343f,
+  0x7fff8719, 0xff501258,
+  0x7fff6216, 0xff36f078, 0x7fff3824, 0xff1dcea0, 0x7fff0943, 0xff04acd0,
+  0x7ffed572, 0xfeeb8b0a,
+  0x7ffe9cb2, 0xfed2694f, 0x7ffe5f03, 0xfeb947a0, 0x7ffe1c65, 0xfea025fd,
+  0x7ffdd4d7, 0xfe870467,
+  0x7ffd885a, 0xfe6de2e0, 0x7ffd36ee, 0xfe54c169, 0x7ffce093, 0xfe3ba002,
+  0x7ffc8549, 0xfe227eac,
+  0x7ffc250f, 0xfe095d69, 0x7ffbbfe6, 0xfdf03c3a, 0x7ffb55ce, 0xfdd71b1e,
+  0x7ffae6c7, 0xfdbdfa18,
+  0x7ffa72d1, 0xfda4d929, 0x7ff9f9ec, 0xfd8bb850, 0x7ff97c18, 0xfd729790,
+  0x7ff8f954, 0xfd5976e9,
+  0x7ff871a2, 0xfd40565c, 0x7ff7e500, 0xfd2735ea, 0x7ff75370, 0xfd0e1594,
+  0x7ff6bcf0, 0xfcf4f55c,
+  0x7ff62182, 0xfcdbd541, 0x7ff58125, 0xfcc2b545, 0x7ff4dbd9, 0xfca9956a,
+  0x7ff4319d, 0xfc9075af,
+  0x7ff38274, 0xfc775616, 0x7ff2ce5b, 0xfc5e36a0, 0x7ff21553, 0xfc45174e,
+  0x7ff1575d, 0xfc2bf821,
+  0x7ff09478, 0xfc12d91a, 0x7fefcca4, 0xfbf9ba39, 0x7feeffe1, 0xfbe09b80,
+  0x7fee2e30, 0xfbc77cf0,
+  0x7fed5791, 0xfbae5e89, 0x7fec7c02, 0xfb95404d, 0x7feb9b85, 0xfb7c223d,
+  0x7feab61a, 0xfb630459,
+  0x7fe9cbc0, 0xfb49e6a3, 0x7fe8dc78, 0xfb30c91b, 0x7fe7e841, 0xfb17abc2,
+  0x7fe6ef1c, 0xfafe8e9b,
+  0x7fe5f108, 0xfae571a4, 0x7fe4ee06, 0xfacc54e0, 0x7fe3e616, 0xfab3384f,
+  0x7fe2d938, 0xfa9a1bf3,
+  0x7fe1c76b, 0xfa80ffcb, 0x7fe0b0b1, 0xfa67e3da, 0x7fdf9508, 0xfa4ec821,
+  0x7fde7471, 0xfa35ac9f,
+  0x7fdd4eec, 0xfa1c9157, 0x7fdc247a, 0xfa037648, 0x7fdaf519, 0xf9ea5b75,
+  0x7fd9c0ca, 0xf9d140de,
+  0x7fd8878e, 0xf9b82684, 0x7fd74964, 0xf99f0c68, 0x7fd6064c, 0xf985f28a,
+  0x7fd4be46, 0xf96cd8ed,
+  0x7fd37153, 0xf953bf91, 0x7fd21f72, 0xf93aa676, 0x7fd0c8a3, 0xf9218d9e,
+  0x7fcf6ce8, 0xf908750a,
+  0x7fce0c3e, 0xf8ef5cbb, 0x7fcca6a7, 0xf8d644b2, 0x7fcb3c23, 0xf8bd2cef,
+  0x7fc9ccb2, 0xf8a41574,
+  0x7fc85854, 0xf88afe42, 0x7fc6df08, 0xf871e759, 0x7fc560cf, 0xf858d0bb,
+  0x7fc3dda9, 0xf83fba68,
+  0x7fc25596, 0xf826a462, 0x7fc0c896, 0xf80d8ea9, 0x7fbf36aa, 0xf7f4793e,
+  0x7fbd9fd0, 0xf7db6423,
+  0x7fbc040a, 0xf7c24f59, 0x7fba6357, 0xf7a93ae0, 0x7fb8bdb8, 0xf79026b9,
+  0x7fb7132b, 0xf77712e5,
+  0x7fb563b3, 0xf75dff66, 0x7fb3af4e, 0xf744ec3b, 0x7fb1f5fc, 0xf72bd967,
+  0x7fb037bf, 0xf712c6ea,
+  0x7fae7495, 0xf6f9b4c6, 0x7facac7f, 0xf6e0a2fa, 0x7faadf7c, 0xf6c79188,
+  0x7fa90d8e, 0xf6ae8071,
+  0x7fa736b4, 0xf6956fb7, 0x7fa55aee, 0xf67c5f59, 0x7fa37a3c, 0xf6634f59,
+  0x7fa1949e, 0xf64a3fb8,
+  0x7f9faa15, 0xf6313077, 0x7f9dbaa0, 0xf6182196, 0x7f9bc640, 0xf5ff1318,
+  0x7f99ccf4, 0xf5e604fc,
+  0x7f97cebd, 0xf5ccf743, 0x7f95cb9a, 0xf5b3e9f0, 0x7f93c38c, 0xf59add02,
+  0x7f91b694, 0xf581d07b,
+  0x7f8fa4b0, 0xf568c45b, 0x7f8d8de1, 0xf54fb8a4, 0x7f8b7227, 0xf536ad56,
+  0x7f895182, 0xf51da273,
+  0x7f872bf3, 0xf50497fb, 0x7f850179, 0xf4eb8def, 0x7f82d214, 0xf4d28451,
+  0x7f809dc5, 0xf4b97b21,
+  0x7f7e648c, 0xf4a07261, 0x7f7c2668, 0xf4876a10, 0x7f79e35a, 0xf46e6231,
+  0x7f779b62, 0xf4555ac5,
+  0x7f754e80, 0xf43c53cb, 0x7f72fcb4, 0xf4234d45, 0x7f70a5fe, 0xf40a4735,
+  0x7f6e4a5e, 0xf3f1419a,
+  0x7f6be9d4, 0xf3d83c77, 0x7f698461, 0xf3bf37cb, 0x7f671a05, 0xf3a63398,
+  0x7f64aabf, 0xf38d2fe0,
+  0x7f62368f, 0xf3742ca2, 0x7f5fbd77, 0xf35b29e0, 0x7f5d3f75, 0xf342279b,
+  0x7f5abc8a, 0xf32925d3,
+  0x7f5834b7, 0xf310248a, 0x7f55a7fa, 0xf2f723c1, 0x7f531655, 0xf2de2379,
+  0x7f507fc7, 0xf2c523b2,
+  0x7f4de451, 0xf2ac246e, 0x7f4b43f2, 0xf29325ad, 0x7f489eaa, 0xf27a2771,
+  0x7f45f47b, 0xf26129ba,
+  0x7f434563, 0xf2482c8a, 0x7f409164, 0xf22f2fe1, 0x7f3dd87c, 0xf21633c0,
+  0x7f3b1aad, 0xf1fd3829,
+  0x7f3857f6, 0xf1e43d1c, 0x7f359057, 0xf1cb429a, 0x7f32c3d1, 0xf1b248a5,
+  0x7f2ff263, 0xf1994f3d,
+  0x7f2d1c0e, 0xf1805662, 0x7f2a40d2, 0xf1675e17, 0x7f2760af, 0xf14e665c,
+  0x7f247ba5, 0xf1356f32,
+  0x7f2191b4, 0xf11c789a, 0x7f1ea2dc, 0xf1038295, 0x7f1baf1e, 0xf0ea8d24,
+  0x7f18b679, 0xf0d19848,
+  0x7f15b8ee, 0xf0b8a401, 0x7f12b67c, 0xf09fb051, 0x7f0faf25, 0xf086bd39,
+  0x7f0ca2e7, 0xf06dcaba,
+  0x7f0991c4, 0xf054d8d5, 0x7f067bba, 0xf03be78a, 0x7f0360cb, 0xf022f6da,
+  0x7f0040f6, 0xf00a06c8,
+  0x7efd1c3c, 0xeff11753, 0x7ef9f29d, 0xefd8287c, 0x7ef6c418, 0xefbf3a45,
+  0x7ef390ae, 0xefa64cae,
+  0x7ef05860, 0xef8d5fb8, 0x7eed1b2c, 0xef747365, 0x7ee9d914, 0xef5b87b5,
+  0x7ee69217, 0xef429caa,
+  0x7ee34636, 0xef29b243, 0x7edff570, 0xef10c883, 0x7edc9fc6, 0xeef7df6a,
+  0x7ed94538, 0xeedef6f9,
+  0x7ed5e5c6, 0xeec60f31, 0x7ed28171, 0xeead2813, 0x7ecf1837, 0xee9441a0,
+  0x7ecbaa1a, 0xee7b5bd9,
+  0x7ec8371a, 0xee6276bf, 0x7ec4bf36, 0xee499253, 0x7ec14270, 0xee30ae96,
+  0x7ebdc0c6, 0xee17cb88,
+  0x7eba3a39, 0xedfee92b, 0x7eb6aeca, 0xede60780, 0x7eb31e78, 0xedcd2687,
+  0x7eaf8943, 0xedb44642,
+  0x7eabef2c, 0xed9b66b2, 0x7ea85033, 0xed8287d7, 0x7ea4ac58, 0xed69a9b3,
+  0x7ea1039b, 0xed50cc46,
+  0x7e9d55fc, 0xed37ef91, 0x7e99a37c, 0xed1f1396, 0x7e95ec1a, 0xed063856,
+  0x7e922fd6, 0xeced5dd0,
+  0x7e8e6eb2, 0xecd48407, 0x7e8aa8ac, 0xecbbaafb, 0x7e86ddc6, 0xeca2d2ad,
+  0x7e830dff, 0xec89fb1e,
+  0x7e7f3957, 0xec71244f, 0x7e7b5fce, 0xec584e41, 0x7e778166, 0xec3f78f6,
+  0x7e739e1d, 0xec26a46d,
+  0x7e6fb5f4, 0xec0dd0a8, 0x7e6bc8eb, 0xebf4fda8, 0x7e67d703, 0xebdc2b6e,
+  0x7e63e03b, 0xebc359fb,
+  0x7e5fe493, 0xebaa894f, 0x7e5be40c, 0xeb91b96c, 0x7e57dea7, 0xeb78ea52,
+  0x7e53d462, 0xeb601c04,
+  0x7e4fc53e, 0xeb474e81, 0x7e4bb13c, 0xeb2e81ca, 0x7e47985b, 0xeb15b5e1,
+  0x7e437a9c, 0xeafceac6,
+  0x7e3f57ff, 0xeae4207a, 0x7e3b3083, 0xeacb56ff, 0x7e37042a, 0xeab28e56,
+  0x7e32d2f4, 0xea99c67e,
+  0x7e2e9cdf, 0xea80ff7a, 0x7e2a61ed, 0xea683949, 0x7e26221f, 0xea4f73ee,
+  0x7e21dd73, 0xea36af69,
+  0x7e1d93ea, 0xea1debbb, 0x7e194584, 0xea0528e5, 0x7e14f242, 0xe9ec66e8,
+  0x7e109a24, 0xe9d3a5c5,
+  0x7e0c3d29, 0xe9bae57d, 0x7e07db52, 0xe9a22610, 0x7e0374a0, 0xe9896781,
+  0x7dff0911, 0xe970a9ce,
+  0x7dfa98a8, 0xe957ecfb, 0x7df62362, 0xe93f3107, 0x7df1a942, 0xe92675f4,
+  0x7ded2a47, 0xe90dbbc2,
+  0x7de8a670, 0xe8f50273, 0x7de41dc0, 0xe8dc4a07, 0x7ddf9034, 0xe8c39280,
+  0x7ddafdce, 0xe8aadbde,
+  0x7dd6668f, 0xe8922622, 0x7dd1ca75, 0xe879714d, 0x7dcd2981, 0xe860bd61,
+  0x7dc883b4, 0xe8480a5d,
+  0x7dc3d90d, 0xe82f5844, 0x7dbf298d, 0xe816a716, 0x7dba7534, 0xe7fdf6d4,
+  0x7db5bc02, 0xe7e5477f,
+  0x7db0fdf8, 0xe7cc9917, 0x7dac3b15, 0xe7b3eb9f, 0x7da77359, 0xe79b3f16,
+  0x7da2a6c6, 0xe782937e,
+  0x7d9dd55a, 0xe769e8d8, 0x7d98ff17, 0xe7513f25, 0x7d9423fc, 0xe7389665,
+  0x7d8f4409, 0xe71fee99,
+  0x7d8a5f40, 0xe70747c4, 0x7d85759f, 0xe6eea1e4, 0x7d808728, 0xe6d5fcfc,
+  0x7d7b93da, 0xe6bd590d,
+  0x7d769bb5, 0xe6a4b616, 0x7d719eba, 0xe68c141a, 0x7d6c9ce9, 0xe6737319,
+  0x7d679642, 0xe65ad315,
+  0x7d628ac6, 0xe642340d, 0x7d5d7a74, 0xe6299604, 0x7d58654d, 0xe610f8f9,
+  0x7d534b50, 0xe5f85cef,
+  0x7d4e2c7f, 0xe5dfc1e5, 0x7d4908d9, 0xe5c727dd, 0x7d43e05e, 0xe5ae8ed8,
+  0x7d3eb30f, 0xe595f6d7,
+  0x7d3980ec, 0xe57d5fda, 0x7d3449f5, 0xe564c9e3, 0x7d2f0e2b, 0xe54c34f3,
+  0x7d29cd8c, 0xe533a10a,
+  0x7d24881b, 0xe51b0e2a, 0x7d1f3dd6, 0xe5027c53, 0x7d19eebf, 0xe4e9eb87,
+  0x7d149ad5, 0xe4d15bc6,
+  0x7d0f4218, 0xe4b8cd11, 0x7d09e489, 0xe4a03f69, 0x7d048228, 0xe487b2d0,
+  0x7cff1af5, 0xe46f2745,
+  0x7cf9aef0, 0xe4569ccb, 0x7cf43e1a, 0xe43e1362, 0x7ceec873, 0xe4258b0a,
+  0x7ce94dfb, 0xe40d03c6,
+  0x7ce3ceb2, 0xe3f47d96, 0x7cde4a98, 0xe3dbf87a, 0x7cd8c1ae, 0xe3c37474,
+  0x7cd333f3, 0xe3aaf184,
+  0x7ccda169, 0xe3926fad, 0x7cc80a0f, 0xe379eeed, 0x7cc26de5, 0xe3616f48,
+  0x7cbcccec, 0xe348f0bd,
+  0x7cb72724, 0xe330734d, 0x7cb17c8d, 0xe317f6fa, 0x7cabcd28, 0xe2ff7bc3,
+  0x7ca618f3, 0xe2e701ac,
+  0x7ca05ff1, 0xe2ce88b3, 0x7c9aa221, 0xe2b610da, 0x7c94df83, 0xe29d9a23,
+  0x7c8f1817, 0xe285248d,
+  0x7c894bde, 0xe26cb01b, 0x7c837ad8, 0xe2543ccc, 0x7c7da505, 0xe23bcaa2,
+  0x7c77ca65, 0xe223599e,
+  0x7c71eaf9, 0xe20ae9c1, 0x7c6c06c0, 0xe1f27b0b, 0x7c661dbc, 0xe1da0d7e,
+  0x7c602fec, 0xe1c1a11b,
+  0x7c5a3d50, 0xe1a935e2, 0x7c5445e9, 0xe190cbd4, 0x7c4e49b7, 0xe17862f3,
+  0x7c4848ba, 0xe15ffb3f,
+  0x7c4242f2, 0xe14794ba, 0x7c3c3860, 0xe12f2f63, 0x7c362904, 0xe116cb3d,
+  0x7c3014de, 0xe0fe6848,
+  0x7c29fbee, 0xe0e60685, 0x7c23de35, 0xe0cda5f5, 0x7c1dbbb3, 0xe0b54698,
+  0x7c179467, 0xe09ce871,
+  0x7c116853, 0xe0848b7f, 0x7c0b3777, 0xe06c2fc4, 0x7c0501d2, 0xe053d541,
+  0x7bfec765, 0xe03b7bf6,
+  0x7bf88830, 0xe02323e5, 0x7bf24434, 0xe00acd0e, 0x7bebfb70, 0xdff27773,
+  0x7be5ade6, 0xdfda2314,
+  0x7bdf5b94, 0xdfc1cff3, 0x7bd9047c, 0xdfa97e0f, 0x7bd2a89e, 0xdf912d6b,
+  0x7bcc47fa, 0xdf78de07,
+  0x7bc5e290, 0xdf608fe4, 0x7bbf7860, 0xdf484302, 0x7bb9096b, 0xdf2ff764,
+  0x7bb295b0, 0xdf17ad0a,
+  0x7bac1d31, 0xdeff63f4, 0x7ba59fee, 0xdee71c24, 0x7b9f1de6, 0xdeced59b,
+  0x7b989719, 0xdeb69059,
+  0x7b920b89, 0xde9e4c60, 0x7b8b7b36, 0xde8609b1, 0x7b84e61f, 0xde6dc84b,
+  0x7b7e4c45, 0xde558831,
+  0x7b77ada8, 0xde3d4964, 0x7b710a49, 0xde250be3, 0x7b6a6227, 0xde0ccfb1,
+  0x7b63b543, 0xddf494ce,
+  0x7b5d039e, 0xdddc5b3b, 0x7b564d36, 0xddc422f8, 0x7b4f920e, 0xddabec08,
+  0x7b48d225, 0xdd93b66a,
+  0x7b420d7a, 0xdd7b8220, 0x7b3b4410, 0xdd634f2b, 0x7b3475e5, 0xdd4b1d8c,
+  0x7b2da2fa, 0xdd32ed43,
+  0x7b26cb4f, 0xdd1abe51, 0x7b1feee5, 0xdd0290b8, 0x7b190dbc, 0xdcea6478,
+  0x7b1227d3, 0xdcd23993,
+  0x7b0b3d2c, 0xdcba1008, 0x7b044dc7, 0xdca1e7da, 0x7afd59a4, 0xdc89c109,
+  0x7af660c2, 0xdc719b96,
+  0x7aef6323, 0xdc597781, 0x7ae860c7, 0xdc4154cd, 0x7ae159ae, 0xdc293379,
+  0x7ada4dd8, 0xdc111388,
+  0x7ad33d45, 0xdbf8f4f8, 0x7acc27f7, 0xdbe0d7cd, 0x7ac50dec, 0xdbc8bc06,
+  0x7abdef25, 0xdbb0a1a4,
+  0x7ab6cba4, 0xdb9888a8, 0x7aafa367, 0xdb807114, 0x7aa8766f, 0xdb685ae9,
+  0x7aa144bc, 0xdb504626,
+  0x7a9a0e50, 0xdb3832cd, 0x7a92d329, 0xdb2020e0, 0x7a8b9348, 0xdb08105e,
+  0x7a844eae, 0xdaf00149,
+  0x7a7d055b, 0xdad7f3a2, 0x7a75b74f, 0xdabfe76a, 0x7a6e648a, 0xdaa7dca1,
+  0x7a670d0d, 0xda8fd349,
+  0x7a5fb0d8, 0xda77cb63, 0x7a584feb, 0xda5fc4ef, 0x7a50ea47, 0xda47bfee,
+  0x7a497feb, 0xda2fbc61,
+  0x7a4210d8, 0xda17ba4a, 0x7a3a9d0f, 0xd9ffb9a9, 0x7a332490, 0xd9e7ba7f,
+  0x7a2ba75a, 0xd9cfbccd,
+  0x7a24256f, 0xd9b7c094, 0x7a1c9ece, 0xd99fc5d4, 0x7a151378, 0xd987cc90,
+  0x7a0d836d, 0xd96fd4c7,
+  0x7a05eead, 0xd957de7a, 0x79fe5539, 0xd93fe9ab, 0x79f6b711, 0xd927f65b,
+  0x79ef1436, 0xd910048a,
+  0x79e76ca7, 0xd8f81439, 0x79dfc064, 0xd8e0256a, 0x79d80f6f, 0xd8c8381d,
+  0x79d059c8, 0xd8b04c52,
+  0x79c89f6e, 0xd898620c, 0x79c0e062, 0xd880794b, 0x79b91ca4, 0xd868920f,
+  0x79b15435, 0xd850ac5a,
+  0x79a98715, 0xd838c82d, 0x79a1b545, 0xd820e589, 0x7999dec4, 0xd809046e,
+  0x79920392, 0xd7f124dd,
+  0x798a23b1, 0xd7d946d8, 0x79823f20, 0xd7c16a5f, 0x797a55e0, 0xd7a98f73,
+  0x797267f2, 0xd791b616,
+  0x796a7554, 0xd779de47, 0x79627e08, 0xd7620808, 0x795a820e, 0xd74a335b,
+  0x79528167, 0xd732603f,
+  0x794a7c12, 0xd71a8eb5, 0x79427210, 0xd702bec0, 0x793a6361, 0xd6eaf05f,
+  0x79325006, 0xd6d32393,
+  0x792a37fe, 0xd6bb585e, 0x79221b4b, 0xd6a38ec0, 0x7919f9ec, 0xd68bc6ba,
+  0x7911d3e2, 0xd674004e,
+  0x7909a92d, 0xd65c3b7b, 0x790179cd, 0xd6447844, 0x78f945c3, 0xd62cb6a8,
+  0x78f10d0f, 0xd614f6a9,
+  0x78e8cfb2, 0xd5fd3848, 0x78e08dab, 0xd5e57b85, 0x78d846fb, 0xd5cdc062,
+  0x78cffba3, 0xd5b606e0,
+  0x78c7aba2, 0xd59e4eff, 0x78bf56f9, 0xd58698c0, 0x78b6fda8, 0xd56ee424,
+  0x78ae9fb0, 0xd557312d,
+  0x78a63d11, 0xd53f7fda, 0x789dd5cb, 0xd527d02e, 0x789569df, 0xd5102228,
+  0x788cf94c, 0xd4f875ca,
+  0x78848414, 0xd4e0cb15, 0x787c0a36, 0xd4c92209, 0x78738bb3, 0xd4b17aa8,
+  0x786b088c, 0xd499d4f2,
+  0x786280bf, 0xd48230e9, 0x7859f44f, 0xd46a8e8d, 0x7851633b, 0xd452eddf,
+  0x7848cd83, 0xd43b4ee0,
+  0x78403329, 0xd423b191, 0x7837942b, 0xd40c15f3, 0x782ef08b, 0xd3f47c06,
+  0x78264849, 0xd3dce3cd,
+  0x781d9b65, 0xd3c54d47, 0x7814e9df, 0xd3adb876, 0x780c33b8, 0xd396255a,
+  0x780378f1, 0xd37e93f4,
+  0x77fab989, 0xd3670446, 0x77f1f581, 0xd34f764f, 0x77e92cd9, 0xd337ea12,
+  0x77e05f91, 0xd3205f8f,
+  0x77d78daa, 0xd308d6c7, 0x77ceb725, 0xd2f14fba, 0x77c5dc01, 0xd2d9ca6a,
+  0x77bcfc3f, 0xd2c246d8,
+  0x77b417df, 0xd2aac504, 0x77ab2ee2, 0xd29344f0, 0x77a24148, 0xd27bc69c,
+  0x77994f11, 0xd2644a0a,
+  0x7790583e, 0xd24ccf39, 0x77875cce, 0xd235562b, 0x777e5cc3, 0xd21ddee2,
+  0x7775581d, 0xd206695d,
+  0x776c4edb, 0xd1eef59e, 0x776340ff, 0xd1d783a6, 0x775a2e89, 0xd1c01375,
+  0x77511778, 0xd1a8a50d,
+  0x7747fbce, 0xd191386e, 0x773edb8b, 0xd179cd99, 0x7735b6af, 0xd1626490,
+  0x772c8d3a, 0xd14afd52,
+  0x77235f2d, 0xd13397e2, 0x771a2c88, 0xd11c343f, 0x7710f54c, 0xd104d26b,
+  0x7707b979, 0xd0ed7267,
+  0x76fe790e, 0xd0d61434, 0x76f5340e, 0xd0beb7d2, 0x76ebea77, 0xd0a75d42,
+  0x76e29c4b, 0xd0900486,
+  0x76d94989, 0xd078ad9e, 0x76cff232, 0xd061588b, 0x76c69647, 0xd04a054e,
+  0x76bd35c7, 0xd032b3e7,
+  0x76b3d0b4, 0xd01b6459, 0x76aa670d, 0xd00416a3, 0x76a0f8d2, 0xcfeccac7,
+  0x76978605, 0xcfd580c6,
+  0x768e0ea6, 0xcfbe389f, 0x768492b4, 0xcfa6f255, 0x767b1231, 0xcf8fade9,
+  0x76718d1c, 0xcf786b5a,
+  0x76680376, 0xcf612aaa, 0x765e7540, 0xcf49ebda, 0x7654e279, 0xcf32aeeb,
+  0x764b4b23, 0xcf1b73de,
+  0x7641af3d, 0xcf043ab3, 0x76380ec8, 0xceed036b, 0x762e69c4, 0xced5ce08,
+  0x7624c031, 0xcebe9a8a,
+  0x761b1211, 0xcea768f2, 0x76115f63, 0xce903942, 0x7607a828, 0xce790b79,
+  0x75fdec60, 0xce61df99,
+  0x75f42c0b, 0xce4ab5a2, 0x75ea672a, 0xce338d97, 0x75e09dbd, 0xce1c6777,
+  0x75d6cfc5, 0xce054343,
+  0x75ccfd42, 0xcdee20fc, 0x75c32634, 0xcdd700a4, 0x75b94a9c, 0xcdbfe23a,
+  0x75af6a7b, 0xcda8c5c1,
+  0x75a585cf, 0xcd91ab39, 0x759b9c9b, 0xcd7a92a2, 0x7591aedd, 0xcd637bfe,
+  0x7587bc98, 0xcd4c674d,
+  0x757dc5ca, 0xcd355491, 0x7573ca75, 0xcd1e43ca, 0x7569ca99, 0xcd0734f9,
+  0x755fc635, 0xccf0281f,
+  0x7555bd4c, 0xccd91d3d, 0x754bafdc, 0xccc21455, 0x75419de7, 0xccab0d65,
+  0x7537876c, 0xcc940871,
+  0x752d6c6c, 0xcc7d0578, 0x75234ce8, 0xcc66047b, 0x751928e0, 0xcc4f057c,
+  0x750f0054, 0xcc38087b,
+  0x7504d345, 0xcc210d79, 0x74faa1b3, 0xcc0a1477, 0x74f06b9e, 0xcbf31d75,
+  0x74e63108, 0xcbdc2876,
+  0x74dbf1ef, 0xcbc53579, 0x74d1ae55, 0xcbae447f, 0x74c7663a, 0xcb97558a,
+  0x74bd199f, 0xcb80689a,
+  0x74b2c884, 0xcb697db0, 0x74a872e8, 0xcb5294ce, 0x749e18cd, 0xcb3badf3,
+  0x7493ba34, 0xcb24c921,
+  0x7489571c, 0xcb0de658, 0x747eef85, 0xcaf7059a, 0x74748371, 0xcae026e8,
+  0x746a12df, 0xcac94a42,
+  0x745f9dd1, 0xcab26fa9, 0x74552446, 0xca9b971e, 0x744aa63f, 0xca84c0a3,
+  0x744023bc, 0xca6dec37,
+  0x74359cbd, 0xca5719db, 0x742b1144, 0xca404992, 0x74208150, 0xca297b5a,
+  0x7415ece2, 0xca12af37,
+  0x740b53fb, 0xc9fbe527, 0x7400b69a, 0xc9e51d2d, 0x73f614c0, 0xc9ce5748,
+  0x73eb6e6e, 0xc9b7937a,
+  0x73e0c3a3, 0xc9a0d1c5, 0x73d61461, 0xc98a1227, 0x73cb60a8, 0xc97354a4,
+  0x73c0a878, 0xc95c993a,
+  0x73b5ebd1, 0xc945dfec, 0x73ab2ab4, 0xc92f28ba, 0x73a06522, 0xc91873a5,
+  0x73959b1b, 0xc901c0ae,
+  0x738acc9e, 0xc8eb0fd6, 0x737ff9ae, 0xc8d4611d, 0x73752249, 0xc8bdb485,
+  0x736a4671, 0xc8a70a0e,
+  0x735f6626, 0xc89061ba, 0x73548168, 0xc879bb89, 0x73499838, 0xc863177b,
+  0x733eaa96, 0xc84c7593,
+  0x7333b883, 0xc835d5d0, 0x7328c1ff, 0xc81f3834, 0x731dc70a, 0xc8089cbf,
+  0x7312c7a5, 0xc7f20373,
+  0x7307c3d0, 0xc7db6c50, 0x72fcbb8c, 0xc7c4d757, 0x72f1aed9, 0xc7ae4489,
+  0x72e69db7, 0xc797b3e7,
+  0x72db8828, 0xc7812572, 0x72d06e2b, 0xc76a992a, 0x72c54fc1, 0xc7540f11,
+  0x72ba2cea, 0xc73d8727,
+  0x72af05a7, 0xc727016d, 0x72a3d9f7, 0xc7107de4, 0x7298a9dd, 0xc6f9fc8d,
+  0x728d7557, 0xc6e37d69,
+  0x72823c67, 0xc6cd0079, 0x7276ff0d, 0xc6b685bd, 0x726bbd48, 0xc6a00d37,
+  0x7260771b, 0xc68996e7,
+  0x72552c85, 0xc67322ce, 0x7249dd86, 0xc65cb0ed, 0x723e8a20, 0xc6464144,
+  0x72333251, 0xc62fd3d6,
+  0x7227d61c, 0xc61968a2, 0x721c7580, 0xc602ffaa, 0x7211107e, 0xc5ec98ee,
+  0x7205a716, 0xc5d6346f,
+  0x71fa3949, 0xc5bfd22e, 0x71eec716, 0xc5a9722c, 0x71e35080, 0xc593146a,
+  0x71d7d585, 0xc57cb8e9,
+  0x71cc5626, 0xc5665fa9, 0x71c0d265, 0xc55008ab, 0x71b54a41, 0xc539b3f1,
+  0x71a9bdba, 0xc523617a,
+  0x719e2cd2, 0xc50d1149, 0x71929789, 0xc4f6c35d, 0x7186fdde, 0xc4e077b8,
+  0x717b5fd3, 0xc4ca2e5b,
+  0x716fbd68, 0xc4b3e746, 0x7164169d, 0xc49da27a, 0x71586b74, 0xc4875ff9,
+  0x714cbbeb, 0xc4711fc2,
+  0x71410805, 0xc45ae1d7, 0x71354fc0, 0xc444a639, 0x7129931f, 0xc42e6ce8,
+  0x711dd220, 0xc41835e6,
+  0x71120cc5, 0xc4020133, 0x7106430e, 0xc3ebced0, 0x70fa74fc, 0xc3d59ebe,
+  0x70eea28e, 0xc3bf70fd,
+  0x70e2cbc6, 0xc3a94590, 0x70d6f0a4, 0xc3931c76, 0x70cb1128, 0xc37cf5b0,
+  0x70bf2d53, 0xc366d140,
+  0x70b34525, 0xc350af26, 0x70a7589f, 0xc33a8f62, 0x709b67c0, 0xc32471f7,
+  0x708f728b, 0xc30e56e4,
+  0x708378ff, 0xc2f83e2a, 0x70777b1c, 0xc2e227cb, 0x706b78e3, 0xc2cc13c7,
+  0x705f7255, 0xc2b6021f,
+  0x70536771, 0xc29ff2d4, 0x70475839, 0xc289e5e7, 0x703b44ad, 0xc273db58,
+  0x702f2ccd, 0xc25dd329,
+  0x7023109a, 0xc247cd5a, 0x7016f014, 0xc231c9ec, 0x700acb3c, 0xc21bc8e1,
+  0x6ffea212, 0xc205ca38,
+  0x6ff27497, 0xc1efcdf3, 0x6fe642ca, 0xc1d9d412, 0x6fda0cae, 0xc1c3dc97,
+  0x6fcdd241, 0xc1ade781,
+  0x6fc19385, 0xc197f4d4, 0x6fb5507a, 0xc182048d, 0x6fa90921, 0xc16c16b0,
+  0x6f9cbd79, 0xc1562b3d,
+  0x6f906d84, 0xc1404233, 0x6f841942, 0xc12a5b95, 0x6f77c0b3, 0xc1147764,
+  0x6f6b63d8, 0xc0fe959f,
+  0x6f5f02b2, 0xc0e8b648, 0x6f529d40, 0xc0d2d960, 0x6f463383, 0xc0bcfee7,
+  0x6f39c57d, 0xc0a726df,
+  0x6f2d532c, 0xc0915148, 0x6f20dc92, 0xc07b7e23, 0x6f1461b0, 0xc065ad70,
+  0x6f07e285, 0xc04fdf32,
+  0x6efb5f12, 0xc03a1368, 0x6eeed758, 0xc0244a14, 0x6ee24b57, 0xc00e8336,
+  0x6ed5bb10, 0xbff8bece,
+  0x6ec92683, 0xbfe2fcdf, 0x6ebc8db0, 0xbfcd3d69, 0x6eaff099, 0xbfb7806c,
+  0x6ea34f3d, 0xbfa1c5ea,
+  0x6e96a99d, 0xbf8c0de3, 0x6e89ffb9, 0xbf765858, 0x6e7d5193, 0xbf60a54a,
+  0x6e709f2a, 0xbf4af4ba,
+  0x6e63e87f, 0xbf3546a8, 0x6e572d93, 0xbf1f9b16, 0x6e4a6e66, 0xbf09f205,
+  0x6e3daaf8, 0xbef44b74,
+  0x6e30e34a, 0xbedea765, 0x6e24175c, 0xbec905d9, 0x6e174730, 0xbeb366d1,
+  0x6e0a72c5, 0xbe9dca4e,
+  0x6dfd9a1c, 0xbe88304f, 0x6df0bd35, 0xbe7298d7, 0x6de3dc11, 0xbe5d03e6,
+  0x6dd6f6b1, 0xbe47717c,
+  0x6dca0d14, 0xbe31e19b, 0x6dbd1f3c, 0xbe1c5444, 0x6db02d29, 0xbe06c977,
+  0x6da336dc, 0xbdf14135,
+  0x6d963c54, 0xbddbbb7f, 0x6d893d93, 0xbdc63856, 0x6d7c3a98, 0xbdb0b7bb,
+  0x6d6f3365, 0xbd9b39ad,
+  0x6d6227fa, 0xbd85be30, 0x6d551858, 0xbd704542, 0x6d48047e, 0xbd5acee5,
+  0x6d3aec6e, 0xbd455b1a,
+  0x6d2dd027, 0xbd2fe9e2, 0x6d20afac, 0xbd1a7b3d, 0x6d138afb, 0xbd050f2c,
+  0x6d066215, 0xbcefa5b0,
+  0x6cf934fc, 0xbcda3ecb, 0x6cec03af, 0xbcc4da7b, 0x6cdece2f, 0xbcaf78c4,
+  0x6cd1947c, 0xbc9a19a5,
+  0x6cc45698, 0xbc84bd1f, 0x6cb71482, 0xbc6f6333, 0x6ca9ce3b, 0xbc5a0be2,
+  0x6c9c83c3, 0xbc44b72c,
+  0x6c8f351c, 0xbc2f6513, 0x6c81e245, 0xbc1a1598, 0x6c748b3f, 0xbc04c8ba,
+  0x6c67300b, 0xbbef7e7c,
+  0x6c59d0a9, 0xbbda36dd, 0x6c4c6d1a, 0xbbc4f1df, 0x6c3f055d, 0xbbafaf82,
+  0x6c319975, 0xbb9a6fc7,
+  0x6c242960, 0xbb8532b0, 0x6c16b521, 0xbb6ff83c, 0x6c093cb6, 0xbb5ac06d,
+  0x6bfbc021, 0xbb458b43,
+  0x6bee3f62, 0xbb3058c0, 0x6be0ba7b, 0xbb1b28e4, 0x6bd3316a, 0xbb05fbb0,
+  0x6bc5a431, 0xbaf0d125,
+  0x6bb812d1, 0xbadba943, 0x6baa7d49, 0xbac6840c, 0x6b9ce39b, 0xbab16180,
+  0x6b8f45c7, 0xba9c41a0,
+  0x6b81a3cd, 0xba87246d, 0x6b73fdae, 0xba7209e7, 0x6b66536b, 0xba5cf210,
+  0x6b58a503, 0xba47dce8,
+  0x6b4af279, 0xba32ca71, 0x6b3d3bcb, 0xba1dbaaa, 0x6b2f80fb, 0xba08ad95,
+  0x6b21c208, 0xb9f3a332,
+  0x6b13fef5, 0xb9de9b83, 0x6b0637c1, 0xb9c99688, 0x6af86c6c, 0xb9b49442,
+  0x6aea9cf8, 0xb99f94b2,
+  0x6adcc964, 0xb98a97d8, 0x6acef1b2, 0xb9759db6, 0x6ac115e2, 0xb960a64c,
+  0x6ab335f4, 0xb94bb19b,
+  0x6aa551e9, 0xb936bfa4, 0x6a9769c1, 0xb921d067, 0x6a897d7d, 0xb90ce3e6,
+  0x6a7b8d1e, 0xb8f7fa21,
+  0x6a6d98a4, 0xb8e31319, 0x6a5fa010, 0xb8ce2ecf, 0x6a51a361, 0xb8b94d44,
+  0x6a43a29a, 0xb8a46e78,
+  0x6a359db9, 0xb88f926d, 0x6a2794c1, 0xb87ab922, 0x6a1987b0, 0xb865e299,
+  0x6a0b7689, 0xb8510ed4,
+  0x69fd614a, 0xb83c3dd1, 0x69ef47f6, 0xb8276f93, 0x69e12a8c, 0xb812a41a,
+  0x69d3090e, 0xb7fddb67,
+  0x69c4e37a, 0xb7e9157a, 0x69b6b9d3, 0xb7d45255, 0x69a88c19, 0xb7bf91f8,
+  0x699a5a4c, 0xb7aad465,
+  0x698c246c, 0xb796199b, 0x697dea7b, 0xb781619c, 0x696fac78, 0xb76cac69,
+  0x69616a65, 0xb757fa01,
+  0x69532442, 0xb7434a67, 0x6944da10, 0xb72e9d9b, 0x69368bce, 0xb719f39e,
+  0x6928397e, 0xb7054c6f,
+  0x6919e320, 0xb6f0a812, 0x690b88b5, 0xb6dc0685, 0x68fd2a3d, 0xb6c767ca,
+  0x68eec7b9, 0xb6b2cbe2,
+  0x68e06129, 0xb69e32cd, 0x68d1f68f, 0xb6899c8d, 0x68c387e9, 0xb6750921,
+  0x68b5153a, 0xb660788c,
+  0x68a69e81, 0xb64beacd, 0x689823bf, 0xb6375fe5, 0x6889a4f6, 0xb622d7d6,
+  0x687b2224, 0xb60e529f,
+  0x686c9b4b, 0xb5f9d043, 0x685e106c, 0xb5e550c1, 0x684f8186, 0xb5d0d41a,
+  0x6840ee9b, 0xb5bc5a50,
+  0x683257ab, 0xb5a7e362, 0x6823bcb7, 0xb5936f53, 0x68151dbe, 0xb57efe22,
+  0x68067ac3, 0xb56a8fd0,
+  0x67f7d3c5, 0xb556245e, 0x67e928c5, 0xb541bbcd, 0x67da79c3, 0xb52d561e,
+  0x67cbc6c0, 0xb518f351,
+  0x67bd0fbd, 0xb5049368, 0x67ae54ba, 0xb4f03663, 0x679f95b7, 0xb4dbdc42,
+  0x6790d2b6, 0xb4c78507,
+  0x67820bb7, 0xb4b330b3, 0x677340ba, 0xb49edf45, 0x676471c0, 0xb48a90c0,
+  0x67559eca, 0xb4764523,
+  0x6746c7d8, 0xb461fc70, 0x6737ecea, 0xb44db6a8, 0x67290e02, 0xb43973ca,
+  0x671a2b20, 0xb42533d8,
+  0x670b4444, 0xb410f6d3, 0x66fc596f, 0xb3fcbcbb, 0x66ed6aa1, 0xb3e88592,
+  0x66de77dc, 0xb3d45157,
+  0x66cf8120, 0xb3c0200c, 0x66c0866d, 0xb3abf1b2, 0x66b187c3, 0xb397c649,
+  0x66a28524, 0xb3839dd3,
+  0x66937e91, 0xb36f784f, 0x66847408, 0xb35b55bf, 0x6675658c, 0xb3473623,
+  0x6666531d, 0xb333197c,
+  0x66573cbb, 0xb31effcc, 0x66482267, 0xb30ae912, 0x66390422, 0xb2f6d550,
+  0x6629e1ec, 0xb2e2c486,
+  0x661abbc5, 0xb2ceb6b5, 0x660b91af, 0xb2baabde, 0x65fc63a9, 0xb2a6a402,
+  0x65ed31b5, 0xb2929f21,
+  0x65ddfbd3, 0xb27e9d3c, 0x65cec204, 0xb26a9e54, 0x65bf8447, 0xb256a26a,
+  0x65b0429f, 0xb242a97e,
+  0x65a0fd0b, 0xb22eb392, 0x6591b38c, 0xb21ac0a6, 0x65826622, 0xb206d0ba,
+  0x657314cf, 0xb1f2e3d0,
+  0x6563bf92, 0xb1def9e9, 0x6554666d, 0xb1cb1304, 0x6545095f, 0xb1b72f23,
+  0x6535a86b, 0xb1a34e47,
+  0x6526438f, 0xb18f7071, 0x6516dacd, 0xb17b95a0, 0x65076e25, 0xb167bdd7,
+  0x64f7fd98, 0xb153e915,
+  0x64e88926, 0xb140175b, 0x64d910d1, 0xb12c48ab, 0x64c99498, 0xb1187d05,
+  0x64ba147d, 0xb104b46a,
+  0x64aa907f, 0xb0f0eeda, 0x649b08a0, 0xb0dd2c56, 0x648b7ce0, 0xb0c96ce0,
+  0x647bed3f, 0xb0b5b077,
+  0x646c59bf, 0xb0a1f71d, 0x645cc260, 0xb08e40d2, 0x644d2722, 0xb07a8d97,
+  0x643d8806, 0xb066dd6d,
+  0x642de50d, 0xb0533055, 0x641e3e38, 0xb03f864f, 0x640e9386, 0xb02bdf5c,
+  0x63fee4f8, 0xb0183b7d,
+  0x63ef3290, 0xb0049ab3, 0x63df7c4d, 0xaff0fcfe, 0x63cfc231, 0xafdd625f,
+  0x63c0043b, 0xafc9cad7,
+  0x63b0426d, 0xafb63667, 0x63a07cc7, 0xafa2a50f, 0x6390b34a, 0xaf8f16d1,
+  0x6380e5f6, 0xaf7b8bac,
+  0x637114cc, 0xaf6803a2, 0x63613fcd, 0xaf547eb3, 0x635166f9, 0xaf40fce1,
+  0x63418a50, 0xaf2d7e2b,
+  0x6331a9d4, 0xaf1a0293, 0x6321c585, 0xaf068a1a, 0x6311dd64, 0xaef314c0,
+  0x6301f171, 0xaedfa285,
+  0x62f201ac, 0xaecc336c, 0x62e20e17, 0xaeb8c774, 0x62d216b3, 0xaea55e9e,
+  0x62c21b7e, 0xae91f8eb,
+  0x62b21c7b, 0xae7e965b, 0x62a219aa, 0xae6b36f0, 0x6292130c, 0xae57daab,
+  0x628208a1, 0xae44818b,
+  0x6271fa69, 0xae312b92, 0x6261e866, 0xae1dd8c0, 0x6251d298, 0xae0a8916,
+  0x6241b8ff, 0xadf73c96,
+  0x62319b9d, 0xade3f33e, 0x62217a72, 0xadd0ad12, 0x6211557e, 0xadbd6a10,
+  0x62012cc2, 0xadaa2a3b,
+  0x61f1003f, 0xad96ed92, 0x61e0cff5, 0xad83b416, 0x61d09be5, 0xad707dc8,
+  0x61c06410, 0xad5d4aaa,
+  0x61b02876, 0xad4a1aba, 0x619fe918, 0xad36edfc, 0x618fa5f7, 0xad23c46e,
+  0x617f5f12, 0xad109e12,
+  0x616f146c, 0xacfd7ae8, 0x615ec603, 0xacea5af2, 0x614e73da, 0xacd73e30,
+  0x613e1df0, 0xacc424a3,
+  0x612dc447, 0xacb10e4b, 0x611d66de, 0xac9dfb29, 0x610d05b7, 0xac8aeb3e,
+  0x60fca0d2, 0xac77de8b,
+  0x60ec3830, 0xac64d510, 0x60dbcbd1, 0xac51cecf, 0x60cb5bb7, 0xac3ecbc7,
+  0x60bae7e1, 0xac2bcbfa,
+  0x60aa7050, 0xac18cf69, 0x6099f505, 0xac05d613, 0x60897601, 0xabf2dffb,
+  0x6078f344, 0xabdfed1f,
+  0x60686ccf, 0xabccfd83, 0x6057e2a2, 0xabba1125, 0x604754bf, 0xaba72807,
+  0x6036c325, 0xab944229,
+  0x60262dd6, 0xab815f8d, 0x601594d1, 0xab6e8032, 0x6004f819, 0xab5ba41a,
+  0x5ff457ad, 0xab48cb46,
+  0x5fe3b38d, 0xab35f5b5, 0x5fd30bbc, 0xab23236a, 0x5fc26038, 0xab105464,
+  0x5fb1b104, 0xaafd88a4,
+  0x5fa0fe1f, 0xaaeac02c, 0x5f90478a, 0xaad7fafb, 0x5f7f8d46, 0xaac53912,
+  0x5f6ecf53, 0xaab27a73,
+  0x5f5e0db3, 0xaa9fbf1e, 0x5f4d4865, 0xaa8d0713, 0x5f3c7f6b, 0xaa7a5253,
+  0x5f2bb2c5, 0xaa67a0e0,
+  0x5f1ae274, 0xaa54f2ba, 0x5f0a0e77, 0xaa4247e1, 0x5ef936d1, 0xaa2fa056,
+  0x5ee85b82, 0xaa1cfc1a,
+  0x5ed77c8a, 0xaa0a5b2e, 0x5ec699e9, 0xa9f7bd92, 0x5eb5b3a2, 0xa9e52347,
+  0x5ea4c9b3, 0xa9d28c4e,
+  0x5e93dc1f, 0xa9bff8a8, 0x5e82eae5, 0xa9ad6855, 0x5e71f606, 0xa99adb56,
+  0x5e60fd84, 0xa98851ac,
+  0x5e50015d, 0xa975cb57, 0x5e3f0194, 0xa9634858, 0x5e2dfe29, 0xa950c8b0,
+  0x5e1cf71c, 0xa93e4c5f,
+  0x5e0bec6e, 0xa92bd367, 0x5dfade20, 0xa9195dc7, 0x5de9cc33, 0xa906eb82,
+  0x5dd8b6a7, 0xa8f47c97,
+  0x5dc79d7c, 0xa8e21106, 0x5db680b4, 0xa8cfa8d2, 0x5da5604f, 0xa8bd43fa,
+  0x5d943c4e, 0xa8aae280,
+  0x5d8314b1, 0xa8988463, 0x5d71e979, 0xa88629a5, 0x5d60baa7, 0xa873d246,
+  0x5d4f883b, 0xa8617e48,
+  0x5d3e5237, 0xa84f2daa, 0x5d2d189a, 0xa83ce06e, 0x5d1bdb65, 0xa82a9693,
+  0x5d0a9a9a, 0xa818501c,
+  0x5cf95638, 0xa8060d08, 0x5ce80e41, 0xa7f3cd59, 0x5cd6c2b5, 0xa7e1910f,
+  0x5cc57394, 0xa7cf582a,
+  0x5cb420e0, 0xa7bd22ac, 0x5ca2ca99, 0xa7aaf094, 0x5c9170bf, 0xa798c1e5,
+  0x5c801354, 0xa786969e,
+  0x5c6eb258, 0xa7746ec0, 0x5c5d4dcc, 0xa7624a4d, 0x5c4be5b0, 0xa7502943,
+  0x5c3a7a05, 0xa73e0ba5,
+  0x5c290acc, 0xa72bf174, 0x5c179806, 0xa719daae, 0x5c0621b2, 0xa707c757,
+  0x5bf4a7d2, 0xa6f5b76d,
+  0x5be32a67, 0xa6e3aaf2, 0x5bd1a971, 0xa6d1a1e7, 0x5bc024f0, 0xa6bf9c4b,
+  0x5bae9ce7, 0xa6ad9a21,
+  0x5b9d1154, 0xa69b9b68, 0x5b8b8239, 0xa689a022, 0x5b79ef96, 0xa677a84e,
+  0x5b68596d, 0xa665b3ee,
+  0x5b56bfbd, 0xa653c303, 0x5b452288, 0xa641d58c, 0x5b3381ce, 0xa62feb8b,
+  0x5b21dd90, 0xa61e0501,
+  0x5b1035cf, 0xa60c21ee, 0x5afe8a8b, 0xa5fa4252, 0x5aecdbc5, 0xa5e8662f,
+  0x5adb297d, 0xa5d68d85,
+  0x5ac973b5, 0xa5c4b855, 0x5ab7ba6c, 0xa5b2e6a0, 0x5aa5fda5, 0xa5a11866,
+  0x5a943d5e, 0xa58f4da8,
+  0x5a82799a, 0xa57d8666, 0x5a70b258, 0xa56bc2a2, 0x5a5ee79a, 0xa55a025b,
+  0x5a4d1960, 0xa5484594,
+  0x5a3b47ab, 0xa5368c4b, 0x5a29727b, 0xa524d683, 0x5a1799d1, 0xa513243b,
+  0x5a05bdae, 0xa5017575,
+  0x59f3de12, 0xa4efca31, 0x59e1faff, 0xa4de2270, 0x59d01475, 0xa4cc7e32,
+  0x59be2a74, 0xa4badd78,
+  0x59ac3cfd, 0xa4a94043, 0x599a4c12, 0xa497a693, 0x598857b2, 0xa486106a,
+  0x59765fde, 0xa4747dc7,
+  0x59646498, 0xa462eeac, 0x595265df, 0xa4516319, 0x594063b5, 0xa43fdb10,
+  0x592e5e19, 0xa42e568f,
+  0x591c550e, 0xa41cd599, 0x590a4893, 0xa40b582e, 0x58f838a9, 0xa3f9de4e,
+  0x58e62552, 0xa3e867fa,
+  0x58d40e8c, 0xa3d6f534, 0x58c1f45b, 0xa3c585fb, 0x58afd6bd, 0xa3b41a50,
+  0x589db5b3, 0xa3a2b234,
+  0x588b9140, 0xa3914da8, 0x58796962, 0xa37fecac, 0x58673e1b, 0xa36e8f41,
+  0x58550f6c, 0xa35d3567,
+  0x5842dd54, 0xa34bdf20, 0x5830a7d6, 0xa33a8c6c, 0x581e6ef1, 0xa3293d4b,
+  0x580c32a7, 0xa317f1bf,
+  0x57f9f2f8, 0xa306a9c8, 0x57e7afe4, 0xa2f56566, 0x57d5696d, 0xa2e4249b,
+  0x57c31f92, 0xa2d2e766,
+  0x57b0d256, 0xa2c1adc9, 0x579e81b8, 0xa2b077c5, 0x578c2dba, 0xa29f4559,
+  0x5779d65b, 0xa28e1687,
+  0x57677b9d, 0xa27ceb4f, 0x57551d80, 0xa26bc3b2, 0x5742bc06, 0xa25a9fb1,
+  0x5730572e, 0xa2497f4c,
+  0x571deefa, 0xa2386284, 0x570b8369, 0xa2274959, 0x56f9147e, 0xa21633cd,
+  0x56e6a239, 0xa20521e0,
+  0x56d42c99, 0xa1f41392, 0x56c1b3a1, 0xa1e308e4, 0x56af3750, 0xa1d201d7,
+  0x569cb7a8, 0xa1c0fe6c,
+  0x568a34a9, 0xa1affea3, 0x5677ae54, 0xa19f027c, 0x566524aa, 0xa18e09fa,
+  0x565297ab, 0xa17d151b,
+  0x56400758, 0xa16c23e1, 0x562d73b2, 0xa15b364d, 0x561adcb9, 0xa14a4c5e,
+  0x5608426e, 0xa1396617,
+  0x55f5a4d2, 0xa1288376, 0x55e303e6, 0xa117a47e, 0x55d05faa, 0xa106c92f,
+  0x55bdb81f, 0xa0f5f189,
+  0x55ab0d46, 0xa0e51d8c, 0x55985f20, 0xa0d44d3b, 0x5585adad, 0xa0c38095,
+  0x5572f8ed, 0xa0b2b79b,
+  0x556040e2, 0xa0a1f24d, 0x554d858d, 0xa09130ad, 0x553ac6ee, 0xa08072ba,
+  0x55280505, 0xa06fb876,
+  0x55153fd4, 0xa05f01e1, 0x5502775c, 0xa04e4efc, 0x54efab9c, 0xa03d9fc8,
+  0x54dcdc96, 0xa02cf444,
+  0x54ca0a4b, 0xa01c4c73, 0x54b734ba, 0xa00ba853, 0x54a45be6, 0x9ffb07e7,
+  0x54917fce, 0x9fea6b2f,
+  0x547ea073, 0x9fd9d22a, 0x546bbdd7, 0x9fc93cdb, 0x5458d7f9, 0x9fb8ab41,
+  0x5445eedb, 0x9fa81d5e,
+  0x5433027d, 0x9f979331, 0x542012e1, 0x9f870cbc, 0x540d2005, 0x9f7689ff,
+  0x53fa29ed, 0x9f660afb,
+  0x53e73097, 0x9f558fb0, 0x53d43406, 0x9f45181f, 0x53c13439, 0x9f34a449,
+  0x53ae3131, 0x9f24342f,
+  0x539b2af0, 0x9f13c7d0, 0x53882175, 0x9f035f2e, 0x537514c2, 0x9ef2fa49,
+  0x536204d7, 0x9ee29922,
+  0x534ef1b5, 0x9ed23bb9, 0x533bdb5d, 0x9ec1e210, 0x5328c1d0, 0x9eb18c26,
+  0x5315a50e, 0x9ea139fd,
+  0x53028518, 0x9e90eb94, 0x52ef61ee, 0x9e80a0ee, 0x52dc3b92, 0x9e705a09,
+  0x52c91204, 0x9e6016e8,
+  0x52b5e546, 0x9e4fd78a, 0x52a2b556, 0x9e3f9bf0, 0x528f8238, 0x9e2f641b,
+  0x527c4bea, 0x9e1f300b,
+  0x5269126e, 0x9e0effc1, 0x5255d5c5, 0x9dfed33e, 0x524295f0, 0x9deeaa82,
+  0x522f52ee, 0x9dde858e,
+  0x521c0cc2, 0x9dce6463, 0x5208c36a, 0x9dbe4701, 0x51f576ea, 0x9dae2d68,
+  0x51e22740, 0x9d9e179a,
+  0x51ced46e, 0x9d8e0597, 0x51bb7e75, 0x9d7df75f, 0x51a82555, 0x9d6decf4,
+  0x5194c910, 0x9d5de656,
+  0x518169a5, 0x9d4de385, 0x516e0715, 0x9d3de482, 0x515aa162, 0x9d2de94d,
+  0x5147388c, 0x9d1df1e9,
+  0x5133cc94, 0x9d0dfe54, 0x51205d7b, 0x9cfe0e8f, 0x510ceb40, 0x9cee229c,
+  0x50f975e6, 0x9cde3a7b,
+  0x50e5fd6d, 0x9cce562c, 0x50d281d5, 0x9cbe75b0, 0x50bf031f, 0x9cae9907,
+  0x50ab814d, 0x9c9ec033,
+  0x5097fc5e, 0x9c8eeb34, 0x50847454, 0x9c7f1a0a, 0x5070e92f, 0x9c6f4cb6,
+  0x505d5af1, 0x9c5f8339,
+  0x5049c999, 0x9c4fbd93, 0x50363529, 0x9c3ffbc5, 0x50229da1, 0x9c303dcf,
+  0x500f0302, 0x9c2083b3,
+  0x4ffb654d, 0x9c10cd70, 0x4fe7c483, 0x9c011b08, 0x4fd420a4, 0x9bf16c7a,
+  0x4fc079b1, 0x9be1c1c8,
+  0x4faccfab, 0x9bd21af3, 0x4f992293, 0x9bc277fa, 0x4f857269, 0x9bb2d8de,
+  0x4f71bf2e, 0x9ba33da0,
+  0x4f5e08e3, 0x9b93a641, 0x4f4a4f89, 0x9b8412c1, 0x4f369320, 0x9b748320,
+  0x4f22d3aa, 0x9b64f760,
+  0x4f0f1126, 0x9b556f81, 0x4efb4b96, 0x9b45eb83, 0x4ee782fb, 0x9b366b68,
+  0x4ed3b755, 0x9b26ef2f,
+  0x4ebfe8a5, 0x9b1776da, 0x4eac16eb, 0x9b080268, 0x4e984229, 0x9af891db,
+  0x4e846a60, 0x9ae92533,
+  0x4e708f8f, 0x9ad9bc71, 0x4e5cb1b9, 0x9aca5795, 0x4e48d0dd, 0x9abaf6a1,
+  0x4e34ecfc, 0x9aab9993,
+  0x4e210617, 0x9a9c406e, 0x4e0d1c30, 0x9a8ceb31, 0x4df92f46, 0x9a7d99de,
+  0x4de53f5a, 0x9a6e4c74,
+  0x4dd14c6e, 0x9a5f02f5, 0x4dbd5682, 0x9a4fbd61, 0x4da95d96, 0x9a407bb9,
+  0x4d9561ac, 0x9a313dfc,
+  0x4d8162c4, 0x9a22042d, 0x4d6d60df, 0x9a12ce4b, 0x4d595bfe, 0x9a039c57,
+  0x4d455422, 0x99f46e51,
+  0x4d31494b, 0x99e5443b, 0x4d1d3b7a, 0x99d61e14, 0x4d092ab0, 0x99c6fbde,
+  0x4cf516ee, 0x99b7dd99,
+  0x4ce10034, 0x99a8c345, 0x4ccce684, 0x9999ace3, 0x4cb8c9dd, 0x998a9a74,
+  0x4ca4aa41, 0x997b8bf8,
+  0x4c9087b1, 0x996c816f, 0x4c7c622d, 0x995d7adc, 0x4c6839b7, 0x994e783d,
+  0x4c540e4e, 0x993f7993,
+  0x4c3fdff4, 0x99307ee0, 0x4c2baea9, 0x99218824, 0x4c177a6e, 0x9912955f,
+  0x4c034345, 0x9903a691,
+  0x4bef092d, 0x98f4bbbc, 0x4bdacc28, 0x98e5d4e0, 0x4bc68c36, 0x98d6f1fe,
+  0x4bb24958, 0x98c81316,
+  0x4b9e0390, 0x98b93828, 0x4b89badd, 0x98aa6136, 0x4b756f40, 0x989b8e40,
+  0x4b6120bb, 0x988cbf46,
+  0x4b4ccf4d, 0x987df449, 0x4b387af9, 0x986f2d4a, 0x4b2423be, 0x98606a49,
+  0x4b0fc99d, 0x9851ab46,
+  0x4afb6c98, 0x9842f043, 0x4ae70caf, 0x98343940, 0x4ad2a9e2, 0x9825863d,
+  0x4abe4433, 0x9816d73b,
+  0x4aa9dba2, 0x98082c3b, 0x4a957030, 0x97f9853d, 0x4a8101de, 0x97eae242,
+  0x4a6c90ad, 0x97dc4349,
+  0x4a581c9e, 0x97cda855, 0x4a43a5b0, 0x97bf1165, 0x4a2f2be6, 0x97b07e7a,
+  0x4a1aaf3f, 0x97a1ef94,
+  0x4a062fbd, 0x979364b5, 0x49f1ad61, 0x9784dddc, 0x49dd282a, 0x97765b0a,
+  0x49c8a01b, 0x9767dc41,
+  0x49b41533, 0x9759617f, 0x499f8774, 0x974aeac6, 0x498af6df, 0x973c7817,
+  0x49766373, 0x972e0971,
+  0x4961cd33, 0x971f9ed7, 0x494d341e, 0x97113847, 0x49389836, 0x9702d5c3,
+  0x4923f97b, 0x96f4774b,
+  0x490f57ee, 0x96e61ce0, 0x48fab391, 0x96d7c682, 0x48e60c62, 0x96c97432,
+  0x48d16265, 0x96bb25f0,
+  0x48bcb599, 0x96acdbbe, 0x48a805ff, 0x969e959b, 0x48935397, 0x96905388,
+  0x487e9e64, 0x96821585,
+  0x4869e665, 0x9673db94, 0x48552b9b, 0x9665a5b4, 0x48406e08, 0x965773e7,
+  0x482badab, 0x9649462d,
+  0x4816ea86, 0x963b1c86, 0x48022499, 0x962cf6f2, 0x47ed5be6, 0x961ed574,
+  0x47d8906d, 0x9610b80a,
+  0x47c3c22f, 0x96029eb6, 0x47aef12c, 0x95f48977, 0x479a1d67, 0x95e67850,
+  0x478546de, 0x95d86b3f,
+  0x47706d93, 0x95ca6247, 0x475b9188, 0x95bc5d66, 0x4746b2bc, 0x95ae5c9f,
+  0x4731d131, 0x95a05ff0,
+  0x471cece7, 0x9592675c, 0x470805df, 0x958472e2, 0x46f31c1a, 0x95768283,
+  0x46de2f99, 0x9568963f,
+  0x46c9405c, 0x955aae17, 0x46b44e65, 0x954cca0c, 0x469f59b4, 0x953eea1e,
+  0x468a624a, 0x95310e4e,
+  0x46756828, 0x9523369c, 0x46606b4e, 0x95156308, 0x464b6bbe, 0x95079394,
+  0x46366978, 0x94f9c83f,
+  0x4621647d, 0x94ec010b, 0x460c5cce, 0x94de3df8, 0x45f7526b, 0x94d07f05,
+  0x45e24556, 0x94c2c435,
+  0x45cd358f, 0x94b50d87, 0x45b82318, 0x94a75afd, 0x45a30df0, 0x9499ac95,
+  0x458df619, 0x948c0252,
+  0x4578db93, 0x947e5c33, 0x4563be60, 0x9470ba39, 0x454e9e80, 0x94631c65,
+  0x45397bf4, 0x945582b7,
+  0x452456bd, 0x9447ed2f, 0x450f2edb, 0x943a5bcf, 0x44fa0450, 0x942cce96,
+  0x44e4d71c, 0x941f4585,
+  0x44cfa740, 0x9411c09e, 0x44ba74bd, 0x94043fdf, 0x44a53f93, 0x93f6c34a,
+  0x449007c4, 0x93e94adf,
+  0x447acd50, 0x93dbd6a0, 0x44659039, 0x93ce668b, 0x4450507e, 0x93c0faa3,
+  0x443b0e21, 0x93b392e6,
+  0x4425c923, 0x93a62f57, 0x44108184, 0x9398cff5, 0x43fb3746, 0x938b74c1,
+  0x43e5ea68, 0x937e1dbb,
+  0x43d09aed, 0x9370cae4, 0x43bb48d4, 0x93637c3d, 0x43a5f41e, 0x935631c5,
+  0x43909ccd, 0x9348eb7e,
+  0x437b42e1, 0x933ba968, 0x4365e65b, 0x932e6b84, 0x4350873c, 0x932131d1,
+  0x433b2585, 0x9313fc51,
+  0x4325c135, 0x9306cb04, 0x43105a50, 0x92f99deb, 0x42faf0d4, 0x92ec7505,
+  0x42e584c3, 0x92df5054,
+  0x42d0161e, 0x92d22fd9, 0x42baa4e6, 0x92c51392, 0x42a5311b, 0x92b7fb82,
+  0x428fbabe, 0x92aae7a8,
+  0x427a41d0, 0x929dd806, 0x4264c653, 0x9290cc9b, 0x424f4845, 0x9283c568,
+  0x4239c7aa, 0x9276c26d,
+  0x42244481, 0x9269c3ac, 0x420ebecb, 0x925cc924, 0x41f93689, 0x924fd2d7,
+  0x41e3abbc, 0x9242e0c4,
+  0x41ce1e65, 0x9235f2ec, 0x41b88e84, 0x9229094f, 0x41a2fc1a, 0x921c23ef,
+  0x418d6729, 0x920f42cb,
+  0x4177cfb1, 0x920265e4, 0x416235b2, 0x91f58d3b, 0x414c992f, 0x91e8b8d0,
+  0x4136fa27, 0x91dbe8a4,
+  0x4121589b, 0x91cf1cb6, 0x410bb48c, 0x91c25508, 0x40f60dfb, 0x91b5919a,
+  0x40e064ea, 0x91a8d26d,
+  0x40cab958, 0x919c1781, 0x40b50b46, 0x918f60d6, 0x409f5ab6, 0x9182ae6d,
+  0x4089a7a8, 0x91760047,
+  0x4073f21d, 0x91695663, 0x405e3a16, 0x915cb0c3, 0x40487f94, 0x91500f67,
+  0x4032c297, 0x91437250,
+  0x401d0321, 0x9136d97d, 0x40074132, 0x912a44f0, 0x3ff17cca, 0x911db4a9,
+  0x3fdbb5ec, 0x911128a8,
+  0x3fc5ec98, 0x9104a0ee, 0x3fb020ce, 0x90f81d7b, 0x3f9a5290, 0x90eb9e50,
+  0x3f8481dd, 0x90df236e,
+  0x3f6eaeb8, 0x90d2acd4, 0x3f58d921, 0x90c63a83, 0x3f430119, 0x90b9cc7d,
+  0x3f2d26a0, 0x90ad62c0,
+  0x3f1749b8, 0x90a0fd4e, 0x3f016a61, 0x90949c28, 0x3eeb889c, 0x90883f4d,
+  0x3ed5a46b, 0x907be6be,
+  0x3ebfbdcd, 0x906f927c, 0x3ea9d4c3, 0x90634287, 0x3e93e950, 0x9056f6df,
+  0x3e7dfb73, 0x904aaf86,
+  0x3e680b2c, 0x903e6c7b, 0x3e52187f, 0x90322dbf, 0x3e3c2369, 0x9025f352,
+  0x3e262bee, 0x9019bd36,
+  0x3e10320d, 0x900d8b69, 0x3dfa35c8, 0x90015dee, 0x3de4371f, 0x8ff534c4,
+  0x3dce3614, 0x8fe90fec,
+  0x3db832a6, 0x8fdcef66, 0x3da22cd7, 0x8fd0d333, 0x3d8c24a8, 0x8fc4bb53,
+  0x3d761a19, 0x8fb8a7c7,
+  0x3d600d2c, 0x8fac988f, 0x3d49fde1, 0x8fa08dab, 0x3d33ec39, 0x8f94871d,
+  0x3d1dd835, 0x8f8884e4,
+  0x3d07c1d6, 0x8f7c8701, 0x3cf1a91c, 0x8f708d75, 0x3cdb8e09, 0x8f649840,
+  0x3cc5709e, 0x8f58a761,
+  0x3caf50da, 0x8f4cbadb, 0x3c992ec0, 0x8f40d2ad, 0x3c830a50, 0x8f34eed8,
+  0x3c6ce38a, 0x8f290f5c,
+  0x3c56ba70, 0x8f1d343a, 0x3c408f03, 0x8f115d72, 0x3c2a6142, 0x8f058b04,
+  0x3c143130, 0x8ef9bcf2,
+  0x3bfdfecd, 0x8eedf33b, 0x3be7ca1a, 0x8ee22de0, 0x3bd19318, 0x8ed66ce1,
+  0x3bbb59c7, 0x8ecab040,
+  0x3ba51e29, 0x8ebef7fb, 0x3b8ee03e, 0x8eb34415, 0x3b78a007, 0x8ea7948c,
+  0x3b625d86, 0x8e9be963,
+  0x3b4c18ba, 0x8e904298, 0x3b35d1a5, 0x8e84a02d, 0x3b1f8848, 0x8e790222,
+  0x3b093ca3, 0x8e6d6877,
+  0x3af2eeb7, 0x8e61d32e, 0x3adc9e86, 0x8e564246, 0x3ac64c0f, 0x8e4ab5bf,
+  0x3aaff755, 0x8e3f2d9b,
+  0x3a99a057, 0x8e33a9da, 0x3a834717, 0x8e282a7b, 0x3a6ceb96, 0x8e1caf80,
+  0x3a568dd4, 0x8e1138ea,
+  0x3a402dd2, 0x8e05c6b7, 0x3a29cb91, 0x8dfa58ea, 0x3a136712, 0x8deeef82,
+  0x39fd0056, 0x8de38a80,
+  0x39e6975e, 0x8dd829e4, 0x39d02c2a, 0x8dcccdaf, 0x39b9bebc, 0x8dc175e0,
+  0x39a34f13, 0x8db6227a,
+  0x398cdd32, 0x8daad37b, 0x39766919, 0x8d9f88e5, 0x395ff2c9, 0x8d9442b8,
+  0x39497a43, 0x8d8900f3,
+  0x3932ff87, 0x8d7dc399, 0x391c8297, 0x8d728aa9, 0x39060373, 0x8d675623,
+  0x38ef821c, 0x8d5c2609,
+  0x38d8fe93, 0x8d50fa59, 0x38c278d9, 0x8d45d316, 0x38abf0ef, 0x8d3ab03f,
+  0x389566d6, 0x8d2f91d5,
+  0x387eda8e, 0x8d2477d8, 0x38684c19, 0x8d196249, 0x3851bb77, 0x8d0e5127,
+  0x383b28a9, 0x8d034474,
+  0x382493b0, 0x8cf83c30, 0x380dfc8d, 0x8ced385b, 0x37f76341, 0x8ce238f6,
+  0x37e0c7cc, 0x8cd73e01,
+  0x37ca2a30, 0x8ccc477d, 0x37b38a6d, 0x8cc1556a, 0x379ce885, 0x8cb667c8,
+  0x37864477, 0x8cab7e98,
+  0x376f9e46, 0x8ca099da, 0x3758f5f2, 0x8c95b98f, 0x37424b7b, 0x8c8addb7,
+  0x372b9ee3, 0x8c800652,
+  0x3714f02a, 0x8c753362, 0x36fe3f52, 0x8c6a64e5, 0x36e78c5b, 0x8c5f9ade,
+  0x36d0d746, 0x8c54d54c,
+  0x36ba2014, 0x8c4a142f, 0x36a366c6, 0x8c3f5788, 0x368cab5c, 0x8c349f58,
+  0x3675edd9, 0x8c29eb9f,
+  0x365f2e3b, 0x8c1f3c5d, 0x36486c86, 0x8c149192, 0x3631a8b8, 0x8c09eb40,
+  0x361ae2d3, 0x8bff4966,
+  0x36041ad9, 0x8bf4ac05, 0x35ed50c9, 0x8bea131e, 0x35d684a6, 0x8bdf7eb0,
+  0x35bfb66e, 0x8bd4eebc,
+  0x35a8e625, 0x8bca6343, 0x359213c9, 0x8bbfdc44, 0x357b3f5d, 0x8bb559c1,
+  0x356468e2, 0x8baadbba,
+  0x354d9057, 0x8ba0622f, 0x3536b5be, 0x8b95ed21, 0x351fd918, 0x8b8b7c8f,
+  0x3508fa66, 0x8b81107b,
+  0x34f219a8, 0x8b76a8e4, 0x34db36df, 0x8b6c45cc, 0x34c4520d, 0x8b61e733,
+  0x34ad6b32, 0x8b578d18,
+  0x34968250, 0x8b4d377c, 0x347f9766, 0x8b42e661, 0x3468aa76, 0x8b3899c6,
+  0x3451bb81, 0x8b2e51ab,
+  0x343aca87, 0x8b240e11, 0x3423d78a, 0x8b19cef8, 0x340ce28b, 0x8b0f9462,
+  0x33f5eb89, 0x8b055e4d,
+  0x33def287, 0x8afb2cbb, 0x33c7f785, 0x8af0ffac, 0x33b0fa84, 0x8ae6d720,
+  0x3399fb85, 0x8adcb318,
+  0x3382fa88, 0x8ad29394, 0x336bf78f, 0x8ac87894, 0x3354f29b, 0x8abe6219,
+  0x333debab, 0x8ab45024,
+  0x3326e2c3, 0x8aaa42b4, 0x330fd7e1, 0x8aa039cb, 0x32f8cb07, 0x8a963567,
+  0x32e1bc36, 0x8a8c358b,
+  0x32caab6f, 0x8a823a36, 0x32b398b3, 0x8a784368, 0x329c8402, 0x8a6e5123,
+  0x32856d5e, 0x8a646365,
+  0x326e54c7, 0x8a5a7a31, 0x32573a3f, 0x8a509585, 0x32401dc6, 0x8a46b564,
+  0x3228ff5c, 0x8a3cd9cc,
+  0x3211df04, 0x8a3302be, 0x31fabcbd, 0x8a29303b, 0x31e39889, 0x8a1f6243,
+  0x31cc7269, 0x8a1598d6,
+  0x31b54a5e, 0x8a0bd3f5, 0x319e2067, 0x8a0213a0, 0x3186f487, 0x89f857d8,
+  0x316fc6be, 0x89eea09d,
+  0x3158970e, 0x89e4edef, 0x31416576, 0x89db3fcf, 0x312a31f8, 0x89d1963c,
+  0x3112fc95, 0x89c7f138,
+  0x30fbc54d, 0x89be50c3, 0x30e48c22, 0x89b4b4dd, 0x30cd5115, 0x89ab1d87,
+  0x30b61426, 0x89a18ac0,
+  0x309ed556, 0x8997fc8a, 0x308794a6, 0x898e72e4, 0x30705217, 0x8984edcf,
+  0x30590dab, 0x897b6d4c,
+  0x3041c761, 0x8971f15a, 0x302a7f3a, 0x896879fb, 0x30133539, 0x895f072e,
+  0x2ffbe95d, 0x895598f3,
+  0x2fe49ba7, 0x894c2f4c, 0x2fcd4c19, 0x8942ca39, 0x2fb5fab2, 0x893969b9,
+  0x2f9ea775, 0x89300dce,
+  0x2f875262, 0x8926b677, 0x2f6ffb7a, 0x891d63b5, 0x2f58a2be, 0x89141589,
+  0x2f41482e, 0x890acbf2,
+  0x2f29ebcc, 0x890186f2, 0x2f128d99, 0x88f84687, 0x2efb2d95, 0x88ef0ab4,
+  0x2ee3cbc1, 0x88e5d378,
+  0x2ecc681e, 0x88dca0d3, 0x2eb502ae, 0x88d372c6, 0x2e9d9b70, 0x88ca4951,
+  0x2e863267, 0x88c12475,
+  0x2e6ec792, 0x88b80432, 0x2e575af3, 0x88aee888, 0x2e3fec8b, 0x88a5d177,
+  0x2e287c5a, 0x889cbf01,
+  0x2e110a62, 0x8893b125, 0x2df996a3, 0x888aa7e3, 0x2de2211e, 0x8881a33d,
+  0x2dcaa9d5, 0x8878a332,
+  0x2db330c7, 0x886fa7c2, 0x2d9bb5f6, 0x8866b0ef, 0x2d843964, 0x885dbeb8,
+  0x2d6cbb10, 0x8854d11e,
+  0x2d553afc, 0x884be821, 0x2d3db928, 0x884303c1, 0x2d263596, 0x883a23ff,
+  0x2d0eb046, 0x883148db,
+  0x2cf72939, 0x88287256, 0x2cdfa071, 0x881fa06f, 0x2cc815ee, 0x8816d327,
+  0x2cb089b1, 0x880e0a7f,
+  0x2c98fbba, 0x88054677, 0x2c816c0c, 0x87fc870f, 0x2c69daa6, 0x87f3cc48,
+  0x2c52478a, 0x87eb1621,
+  0x2c3ab2b9, 0x87e2649b, 0x2c231c33, 0x87d9b7b7, 0x2c0b83fa, 0x87d10f75,
+  0x2bf3ea0d, 0x87c86bd5,
+  0x2bdc4e6f, 0x87bfccd7, 0x2bc4b120, 0x87b7327d, 0x2bad1221, 0x87ae9cc5,
+  0x2b957173, 0x87a60bb1,
+  0x2b7dcf17, 0x879d7f41, 0x2b662b0e, 0x8794f774, 0x2b4e8558, 0x878c744d,
+  0x2b36ddf7, 0x8783f5ca,
+  0x2b1f34eb, 0x877b7bec, 0x2b078a36, 0x877306b4, 0x2aefddd8, 0x876a9621,
+  0x2ad82fd2, 0x87622a35,
+  0x2ac08026, 0x8759c2ef, 0x2aa8ced3, 0x87516050, 0x2a911bdc, 0x87490258,
+  0x2a796740, 0x8740a907,
+  0x2a61b101, 0x8738545e, 0x2a49f920, 0x8730045d, 0x2a323f9e, 0x8727b905,
+  0x2a1a847b, 0x871f7255,
+  0x2a02c7b8, 0x8717304e, 0x29eb0957, 0x870ef2f1, 0x29d34958, 0x8706ba3d,
+  0x29bb87bc, 0x86fe8633,
+  0x29a3c485, 0x86f656d3, 0x298bffb2, 0x86ee2c1e, 0x29743946, 0x86e60614,
+  0x295c7140, 0x86dde4b5,
+  0x2944a7a2, 0x86d5c802, 0x292cdc6d, 0x86cdaffa, 0x29150fa1, 0x86c59c9f,
+  0x28fd4140, 0x86bd8df0,
+  0x28e5714b, 0x86b583ee, 0x28cd9fc1, 0x86ad7e99, 0x28b5cca5, 0x86a57df2,
+  0x289df7f8, 0x869d81f8,
+  0x288621b9, 0x86958aac, 0x286e49ea, 0x868d980e, 0x2856708d, 0x8685aa20,
+  0x283e95a1, 0x867dc0e0,
+  0x2826b928, 0x8675dc4f, 0x280edb23, 0x866dfc6e, 0x27f6fb92, 0x8666213c,
+  0x27df1a77, 0x865e4abb,
+  0x27c737d3, 0x865678eb, 0x27af53a6, 0x864eabcb, 0x27976df1, 0x8646e35c,
+  0x277f86b5, 0x863f1f9e,
+  0x27679df4, 0x86376092, 0x274fb3ae, 0x862fa638, 0x2737c7e3, 0x8627f091,
+  0x271fda96, 0x86203f9c,
+  0x2707ebc7, 0x86189359, 0x26effb76, 0x8610ebca, 0x26d809a5, 0x860948ef,
+  0x26c01655, 0x8601aac7,
+  0x26a82186, 0x85fa1153, 0x26902b39, 0x85f27c93, 0x26783370, 0x85eaec88,
+  0x26603a2c, 0x85e36132,
+  0x26483f6c, 0x85dbda91, 0x26304333, 0x85d458a6, 0x26184581, 0x85ccdb70,
+  0x26004657, 0x85c562f1,
+  0x25e845b6, 0x85bdef28, 0x25d0439f, 0x85b68015, 0x25b84012, 0x85af15b9,
+  0x25a03b11, 0x85a7b015,
+  0x2588349d, 0x85a04f28, 0x25702cb7, 0x8598f2f3, 0x2558235f, 0x85919b76,
+  0x25401896, 0x858a48b1,
+  0x25280c5e, 0x8582faa5, 0x250ffeb7, 0x857bb152, 0x24f7efa2, 0x85746cb8,
+  0x24dfdf20, 0x856d2cd7,
+  0x24c7cd33, 0x8565f1b0, 0x24afb9da, 0x855ebb44, 0x2497a517, 0x85578991,
+  0x247f8eec, 0x85505c99,
+  0x24677758, 0x8549345c, 0x244f5e5c, 0x854210db, 0x243743fa, 0x853af214,
+  0x241f2833, 0x8533d809,
+  0x24070b08, 0x852cc2bb, 0x23eeec78, 0x8525b228, 0x23d6cc87, 0x851ea652,
+  0x23beab33, 0x85179f39,
+  0x23a6887f, 0x85109cdd, 0x238e646a, 0x85099f3e, 0x23763ef7, 0x8502a65c,
+  0x235e1826, 0x84fbb239,
+  0x2345eff8, 0x84f4c2d4, 0x232dc66d, 0x84edd82d, 0x23159b88, 0x84e6f244,
+  0x22fd6f48, 0x84e0111b,
+  0x22e541af, 0x84d934b1, 0x22cd12bd, 0x84d25d06, 0x22b4e274, 0x84cb8a1b,
+  0x229cb0d5, 0x84c4bbf0,
+  0x22847de0, 0x84bdf286, 0x226c4996, 0x84b72ddb, 0x225413f8, 0x84b06df2,
+  0x223bdd08, 0x84a9b2ca,
+  0x2223a4c5, 0x84a2fc62, 0x220b6b32, 0x849c4abd, 0x21f3304f, 0x84959dd9,
+  0x21daf41d, 0x848ef5b7,
+  0x21c2b69c, 0x84885258, 0x21aa77cf, 0x8481b3bb, 0x219237b5, 0x847b19e1,
+  0x2179f64f, 0x847484ca,
+  0x2161b3a0, 0x846df477, 0x21496fa7, 0x846768e7, 0x21312a65, 0x8460e21a,
+  0x2118e3dc, 0x845a6012,
+  0x21009c0c, 0x8453e2cf, 0x20e852f6, 0x844d6a50, 0x20d0089c, 0x8446f695,
+  0x20b7bcfe, 0x844087a0,
+  0x209f701c, 0x843a1d70, 0x208721f9, 0x8433b806, 0x206ed295, 0x842d5762,
+  0x205681f1, 0x8426fb84,
+  0x203e300d, 0x8420a46c, 0x2025dcec, 0x841a521a, 0x200d888d, 0x84140490,
+  0x1ff532f2, 0x840dbbcc,
+  0x1fdcdc1b, 0x840777d0, 0x1fc4840a, 0x8401389b, 0x1fac2abf, 0x83fafe2e,
+  0x1f93d03c, 0x83f4c889,
+  0x1f7b7481, 0x83ee97ad, 0x1f63178f, 0x83e86b99, 0x1f4ab968, 0x83e2444d,
+  0x1f325a0b, 0x83dc21cb,
+  0x1f19f97b, 0x83d60412, 0x1f0197b8, 0x83cfeb22, 0x1ee934c3, 0x83c9d6fc,
+  0x1ed0d09d, 0x83c3c7a0,
+  0x1eb86b46, 0x83bdbd0e, 0x1ea004c1, 0x83b7b746, 0x1e879d0d, 0x83b1b649,
+  0x1e6f342c, 0x83abba17,
+  0x1e56ca1e, 0x83a5c2b0, 0x1e3e5ee5, 0x839fd014, 0x1e25f282, 0x8399e244,
+  0x1e0d84f5, 0x8393f940,
+  0x1df5163f, 0x838e1507, 0x1ddca662, 0x8388359b, 0x1dc4355e, 0x83825afb,
+  0x1dabc334, 0x837c8528,
+  0x1d934fe5, 0x8376b422, 0x1d7adb73, 0x8370e7e9, 0x1d6265dd, 0x836b207d,
+  0x1d49ef26, 0x83655ddf,
+  0x1d31774d, 0x835fa00f, 0x1d18fe54, 0x8359e70d, 0x1d00843d, 0x835432d8,
+  0x1ce80906, 0x834e8373,
+  0x1ccf8cb3, 0x8348d8dc, 0x1cb70f43, 0x83433314, 0x1c9e90b8, 0x833d921b,
+  0x1c861113, 0x8337f5f1,
+  0x1c6d9053, 0x83325e97, 0x1c550e7c, 0x832ccc0d, 0x1c3c8b8c, 0x83273e52,
+  0x1c240786, 0x8321b568,
+  0x1c0b826a, 0x831c314e, 0x1bf2fc3a, 0x8316b205, 0x1bda74f6, 0x8311378d,
+  0x1bc1ec9e, 0x830bc1e6,
+  0x1ba96335, 0x83065110, 0x1b90d8bb, 0x8300e50b, 0x1b784d30, 0x82fb7dd8,
+  0x1b5fc097, 0x82f61b77,
+  0x1b4732ef, 0x82f0bde8, 0x1b2ea43a, 0x82eb652b, 0x1b161479, 0x82e61141,
+  0x1afd83ad, 0x82e0c22a,
+  0x1ae4f1d6, 0x82db77e5, 0x1acc5ef6, 0x82d63274, 0x1ab3cb0d, 0x82d0f1d5,
+  0x1a9b361d, 0x82cbb60b,
+  0x1a82a026, 0x82c67f14, 0x1a6a0929, 0x82c14cf1, 0x1a517128, 0x82bc1fa2,
+  0x1a38d823, 0x82b6f727,
+  0x1a203e1b, 0x82b1d381, 0x1a07a311, 0x82acb4b0, 0x19ef0707, 0x82a79ab3,
+  0x19d669fc, 0x82a2858c,
+  0x19bdcbf3, 0x829d753a, 0x19a52ceb, 0x829869be, 0x198c8ce7, 0x82936317,
+  0x1973ebe6, 0x828e6146,
+  0x195b49ea, 0x8289644b, 0x1942a6f3, 0x82846c26, 0x192a0304, 0x827f78d8,
+  0x19115e1c, 0x827a8a61,
+  0x18f8b83c, 0x8275a0c0, 0x18e01167, 0x8270bbf7, 0x18c7699b, 0x826bdc04,
+  0x18aec0db, 0x826700e9,
+  0x18961728, 0x82622aa6, 0x187d6c82, 0x825d593a, 0x1864c0ea, 0x82588ca7,
+  0x184c1461, 0x8253c4eb,
+  0x183366e9, 0x824f0208, 0x181ab881, 0x824a43fe, 0x1802092c, 0x82458acc,
+  0x17e958ea, 0x8240d673,
+  0x17d0a7bc, 0x823c26f3, 0x17b7f5a3, 0x82377c4c, 0x179f429f, 0x8232d67f,
+  0x17868eb3, 0x822e358b,
+  0x176dd9de, 0x82299971, 0x17552422, 0x82250232, 0x173c6d80, 0x82206fcc,
+  0x1723b5f9, 0x821be240,
+  0x170afd8d, 0x82175990, 0x16f2443e, 0x8212d5b9, 0x16d98a0c, 0x820e56be,
+  0x16c0cef9, 0x8209dc9e,
+  0x16a81305, 0x82056758, 0x168f5632, 0x8200f6ef, 0x1676987f, 0x81fc8b60,
+  0x165dd9f0, 0x81f824ae,
+  0x16451a83, 0x81f3c2d7, 0x162c5a3b, 0x81ef65dc, 0x16139918, 0x81eb0dbe,
+  0x15fad71b, 0x81e6ba7c,
+  0x15e21445, 0x81e26c16, 0x15c95097, 0x81de228d, 0x15b08c12, 0x81d9dde1,
+  0x1597c6b7, 0x81d59e13,
+  0x157f0086, 0x81d16321, 0x15663982, 0x81cd2d0c, 0x154d71aa, 0x81c8fbd6,
+  0x1534a901, 0x81c4cf7d,
+  0x151bdf86, 0x81c0a801, 0x1503153a, 0x81bc8564, 0x14ea4a1f, 0x81b867a5,
+  0x14d17e36, 0x81b44ec4,
+  0x14b8b17f, 0x81b03ac2, 0x149fe3fc, 0x81ac2b9e, 0x148715ae, 0x81a82159,
+  0x146e4694, 0x81a41bf4,
+  0x145576b1, 0x81a01b6d, 0x143ca605, 0x819c1fc5, 0x1423d492, 0x819828fd,
+  0x140b0258, 0x81943715,
+  0x13f22f58, 0x81904a0c, 0x13d95b93, 0x818c61e3, 0x13c0870a, 0x81887e9a,
+  0x13a7b1bf, 0x8184a032,
+  0x138edbb1, 0x8180c6a9, 0x137604e2, 0x817cf201, 0x135d2d53, 0x8179223a,
+  0x13445505, 0x81755754,
+  0x132b7bf9, 0x8171914e, 0x1312a230, 0x816dd02a, 0x12f9c7aa, 0x816a13e6,
+  0x12e0ec6a, 0x81665c84,
+  0x12c8106f, 0x8162aa04, 0x12af33ba, 0x815efc65, 0x1296564d, 0x815b53a8,
+  0x127d7829, 0x8157afcd,
+  0x1264994e, 0x815410d4, 0x124bb9be, 0x815076bd, 0x1232d979, 0x814ce188,
+  0x1219f880, 0x81495136,
+  0x120116d5, 0x8145c5c7, 0x11e83478, 0x81423f3a, 0x11cf516a, 0x813ebd90,
+  0x11b66dad, 0x813b40ca,
+  0x119d8941, 0x8137c8e6, 0x1184a427, 0x813455e6, 0x116bbe60, 0x8130e7c9,
+  0x1152d7ed, 0x812d7e8f,
+  0x1139f0cf, 0x812a1a3a, 0x11210907, 0x8126bac8, 0x11082096, 0x8123603a,
+  0x10ef377d, 0x81200a90,
+  0x10d64dbd, 0x811cb9ca, 0x10bd6356, 0x81196de9, 0x10a4784b, 0x811626ec,
+  0x108b8c9b, 0x8112e4d4,
+  0x1072a048, 0x810fa7a0, 0x1059b352, 0x810c6f52, 0x1040c5bb, 0x81093be8,
+  0x1027d784, 0x81060d63,
+  0x100ee8ad, 0x8102e3c4, 0xff5f938, 0x80ffbf0a, 0xfdd0926, 0x80fc9f35,
+  0xfc41876, 0x80f98446,
+  0xfab272b, 0x80f66e3c, 0xf923546, 0x80f35d19, 0xf7942c7, 0x80f050db,
+  0xf604faf, 0x80ed4984,
+  0xf475bff, 0x80ea4712, 0xf2e67b8, 0x80e74987, 0xf1572dc, 0x80e450e2,
+  0xefc7d6b, 0x80e15d24,
+  0xee38766, 0x80de6e4c, 0xeca90ce, 0x80db845b, 0xeb199a4, 0x80d89f51,
+  0xe98a1e9, 0x80d5bf2e,
+  0xe7fa99e, 0x80d2e3f2, 0xe66b0c3, 0x80d00d9d, 0xe4db75b, 0x80cd3c2f,
+  0xe34bd66, 0x80ca6fa9,
+  0xe1bc2e4, 0x80c7a80a, 0xe02c7d7, 0x80c4e553, 0xde9cc40, 0x80c22784,
+  0xdd0d01f, 0x80bf6e9c,
+  0xdb7d376, 0x80bcba9d, 0xd9ed646, 0x80ba0b85, 0xd85d88f, 0x80b76156,
+  0xd6cda53, 0x80b4bc0e,
+  0xd53db92, 0x80b21baf, 0xd3adc4e, 0x80af8039, 0xd21dc87, 0x80ace9ab,
+  0xd08dc3f, 0x80aa5806,
+  0xcefdb76, 0x80a7cb49, 0xcd6da2d, 0x80a54376, 0xcbdd865, 0x80a2c08b,
+  0xca4d620, 0x80a04289,
+  0xc8bd35e, 0x809dc971, 0xc72d020, 0x809b5541, 0xc59cc68, 0x8098e5fb,
+  0xc40c835, 0x80967b9f,
+  0xc27c389, 0x8094162c, 0xc0ebe66, 0x8091b5a2, 0xbf5b8cb, 0x808f5a02,
+  0xbdcb2bb, 0x808d034c,
+  0xbc3ac35, 0x808ab180, 0xbaaa53b, 0x8088649e, 0xb919dcf, 0x80861ca6,
+  0xb7895f0, 0x8083d998,
+  0xb5f8d9f, 0x80819b74, 0xb4684df, 0x807f623b, 0xb2d7baf, 0x807d2dec,
+  0xb147211, 0x807afe87,
+  0xafb6805, 0x8078d40d, 0xae25d8d, 0x8076ae7e, 0xac952aa, 0x80748dd9,
+  0xab0475c, 0x8072721f,
+  0xa973ba5, 0x80705b50, 0xa7e2f85, 0x806e496c, 0xa6522fe, 0x806c3c74,
+  0xa4c1610, 0x806a3466,
+  0xa3308bd, 0x80683143, 0xa19fb04, 0x8066330c, 0xa00ece8, 0x806439c0,
+  0x9e7de6a, 0x80624560,
+  0x9cecf89, 0x806055eb, 0x9b5c048, 0x805e6b62, 0x99cb0a7, 0x805c85c4,
+  0x983a0a7, 0x805aa512,
+  0x96a9049, 0x8058c94c, 0x9517f8f, 0x8056f272, 0x9386e78, 0x80552084,
+  0x91f5d06, 0x80535381,
+  0x9064b3a, 0x80518b6b, 0x8ed3916, 0x804fc841, 0x8d42699, 0x804e0a04,
+  0x8bb13c5, 0x804c50b2,
+  0x8a2009a, 0x804a9c4d, 0x888ed1b, 0x8048ecd5, 0x86fd947, 0x80474248,
+  0x856c520, 0x80459ca9,
+  0x83db0a7, 0x8043fbf6, 0x8249bdd, 0x80426030, 0x80b86c2, 0x8040c956,
+  0x7f27157, 0x803f376a,
+  0x7d95b9e, 0x803daa6a, 0x7c04598, 0x803c2257, 0x7a72f45, 0x803a9f31,
+  0x78e18a7, 0x803920f8,
+  0x77501be, 0x8037a7ac, 0x75bea8c, 0x8036334e, 0x742d311, 0x8034c3dd,
+  0x729bb4e, 0x80335959,
+  0x710a345, 0x8031f3c2, 0x6f78af6, 0x80309318, 0x6de7262, 0x802f375d,
+  0x6c5598a, 0x802de08e,
+  0x6ac406f, 0x802c8ead, 0x6932713, 0x802b41ba, 0x67a0d76, 0x8029f9b4,
+  0x660f398, 0x8028b69c,
+  0x647d97c, 0x80277872, 0x62ebf22, 0x80263f36, 0x615a48b, 0x80250ae7,
+  0x5fc89b8, 0x8023db86,
+  0x5e36ea9, 0x8022b114, 0x5ca5361, 0x80218b8f, 0x5b137df, 0x80206af8,
+  0x5981c26, 0x801f4f4f,
+  0x57f0035, 0x801e3895, 0x565e40d, 0x801d26c8, 0x54cc7b1, 0x801c19ea,
+  0x533ab20, 0x801b11fa,
+  0x51a8e5c, 0x801a0ef8, 0x5017165, 0x801910e4, 0x4e8543e, 0x801817bf,
+  0x4cf36e5, 0x80172388,
+  0x4b6195d, 0x80163440, 0x49cfba7, 0x801549e6, 0x483ddc3, 0x8014647b,
+  0x46abfb3, 0x801383fe,
+  0x451a177, 0x8012a86f, 0x4388310, 0x8011d1d0, 0x41f6480, 0x8011001f,
+  0x40645c7, 0x8010335c,
+  0x3ed26e6, 0x800f6b88, 0x3d407df, 0x800ea8a3, 0x3bae8b2, 0x800deaad,
+  0x3a1c960, 0x800d31a5,
+  0x388a9ea, 0x800c7d8c, 0x36f8a51, 0x800bce63, 0x3566a96, 0x800b2427,
+  0x33d4abb, 0x800a7edb,
+  0x3242abf, 0x8009de7e, 0x30b0aa4, 0x80094310, 0x2f1ea6c, 0x8008ac90,
+  0x2d8ca16, 0x80081b00,
+  0x2bfa9a4, 0x80078e5e, 0x2a68917, 0x800706ac, 0x28d6870, 0x800683e8,
+  0x27447b0, 0x80060614,
+  0x25b26d7, 0x80058d2f, 0x24205e8, 0x80051939, 0x228e4e2, 0x8004aa32,
+  0x20fc3c6, 0x8004401a,
+  0x1f6a297, 0x8003daf1, 0x1dd8154, 0x80037ab7, 0x1c45ffe, 0x80031f6d,
+  0x1ab3e97, 0x8002c912,
+  0x1921d20, 0x800277a6, 0x178fb99, 0x80022b29, 0x15fda03, 0x8001e39b,
+  0x146b860, 0x8001a0fd,
+  0x12d96b1, 0x8001634e, 0x11474f6, 0x80012a8e, 0xfb5330, 0x8000f6bd,
+  0xe23160, 0x8000c7dc,
+  0xc90f88, 0x80009dea, 0xafeda8, 0x800078e7, 0x96cbc1, 0x800058d4, 0x7da9d4,
+  0x80003daf,
+  0x6487e3, 0x8000277a, 0x4b65ee, 0x80001635, 0x3243f5, 0x800009df, 0x1921fb,
+  0x80000278,
+};
+
+static const q31_t WeightsQ31_8192[16384] = {
+  0x7fffffff, 0x0, 0x7fffffd9, 0xfff9b781, 0x7fffff62, 0xfff36f02, 0x7ffffe9d,
+    0xffed2684,
+  0x7ffffd88, 0xffe6de05, 0x7ffffc25, 0xffe09586, 0x7ffffa73, 0xffda4d08,
+    0x7ffff872, 0xffd40489,
+  0x7ffff621, 0xffcdbc0b, 0x7ffff382, 0xffc7738c, 0x7ffff094, 0xffc12b0e,
+    0x7fffed57, 0xffbae290,
+  0x7fffe9cb, 0xffb49a12, 0x7fffe5f0, 0xffae5195, 0x7fffe1c6, 0xffa80917,
+    0x7fffdd4d, 0xffa1c09a,
+  0x7fffd886, 0xff9b781d, 0x7fffd36f, 0xff952fa0, 0x7fffce09, 0xff8ee724,
+    0x7fffc854, 0xff889ea7,
+  0x7fffc251, 0xff82562c, 0x7fffbbfe, 0xff7c0db0, 0x7fffb55c, 0xff75c535,
+    0x7fffae6c, 0xff6f7cba,
+  0x7fffa72c, 0xff69343f, 0x7fff9f9e, 0xff62ebc5, 0x7fff97c1, 0xff5ca34b,
+    0x7fff8f94, 0xff565ad1,
+  0x7fff8719, 0xff501258, 0x7fff7e4f, 0xff49c9df, 0x7fff7536, 0xff438167,
+    0x7fff6bcd, 0xff3d38ef,
+  0x7fff6216, 0xff36f078, 0x7fff5810, 0xff30a801, 0x7fff4dbb, 0xff2a5f8b,
+    0x7fff4317, 0xff241715,
+  0x7fff3824, 0xff1dcea0, 0x7fff2ce2, 0xff17862b, 0x7fff2151, 0xff113db7,
+    0x7fff1572, 0xff0af543,
+  0x7fff0943, 0xff04acd0, 0x7ffefcc5, 0xfefe645e, 0x7ffeeff8, 0xfef81bec,
+    0x7ffee2dd, 0xfef1d37b,
+  0x7ffed572, 0xfeeb8b0a, 0x7ffec7b9, 0xfee5429a, 0x7ffeb9b0, 0xfedefa2b,
+    0x7ffeab59, 0xfed8b1bd,
+  0x7ffe9cb2, 0xfed2694f, 0x7ffe8dbd, 0xfecc20e2, 0x7ffe7e79, 0xfec5d876,
+    0x7ffe6ee5, 0xfebf900a,
+  0x7ffe5f03, 0xfeb947a0, 0x7ffe4ed2, 0xfeb2ff36, 0x7ffe3e52, 0xfeacb6cc,
+    0x7ffe2d83, 0xfea66e64,
+  0x7ffe1c65, 0xfea025fd, 0x7ffe0af8, 0xfe99dd96, 0x7ffdf93c, 0xfe939530,
+    0x7ffde731, 0xfe8d4ccb,
+  0x7ffdd4d7, 0xfe870467, 0x7ffdc22e, 0xfe80bc04, 0x7ffdaf37, 0xfe7a73a2,
+    0x7ffd9bf0, 0xfe742b41,
+  0x7ffd885a, 0xfe6de2e0, 0x7ffd7476, 0xfe679a81, 0x7ffd6042, 0xfe615223,
+    0x7ffd4bc0, 0xfe5b09c5,
+  0x7ffd36ee, 0xfe54c169, 0x7ffd21ce, 0xfe4e790d, 0x7ffd0c5f, 0xfe4830b3,
+    0x7ffcf6a0, 0xfe41e85a,
+  0x7ffce093, 0xfe3ba002, 0x7ffcca37, 0xfe3557ab, 0x7ffcb38c, 0xfe2f0f55,
+    0x7ffc9c92, 0xfe28c700,
+  0x7ffc8549, 0xfe227eac, 0x7ffc6db1, 0xfe1c365a, 0x7ffc55ca, 0xfe15ee09,
+    0x7ffc3d94, 0xfe0fa5b8,
+  0x7ffc250f, 0xfe095d69, 0x7ffc0c3b, 0xfe03151c, 0x7ffbf319, 0xfdfccccf,
+    0x7ffbd9a7, 0xfdf68484,
+  0x7ffbbfe6, 0xfdf03c3a, 0x7ffba5d7, 0xfde9f3f1, 0x7ffb8b78, 0xfde3aba9,
+    0x7ffb70cb, 0xfddd6363,
+  0x7ffb55ce, 0xfdd71b1e, 0x7ffb3a83, 0xfdd0d2db, 0x7ffb1ee9, 0xfdca8a99,
+    0x7ffb0300, 0xfdc44258,
+  0x7ffae6c7, 0xfdbdfa18, 0x7ffaca40, 0xfdb7b1da, 0x7ffaad6a, 0xfdb1699e,
+    0x7ffa9045, 0xfdab2162,
+  0x7ffa72d1, 0xfda4d929, 0x7ffa550e, 0xfd9e90f0, 0x7ffa36fc, 0xfd9848b9,
+    0x7ffa189c, 0xfd920084,
+  0x7ff9f9ec, 0xfd8bb850, 0x7ff9daed, 0xfd85701e, 0x7ff9bba0, 0xfd7f27ed,
+    0x7ff99c03, 0xfd78dfbd,
+  0x7ff97c18, 0xfd729790, 0x7ff95bdd, 0xfd6c4f64, 0x7ff93b54, 0xfd660739,
+    0x7ff91a7b, 0xfd5fbf10,
+  0x7ff8f954, 0xfd5976e9, 0x7ff8d7de, 0xfd532ec3, 0x7ff8b619, 0xfd4ce69f,
+    0x7ff89405, 0xfd469e7c,
+  0x7ff871a2, 0xfd40565c, 0x7ff84ef0, 0xfd3a0e3d, 0x7ff82bef, 0xfd33c61f,
+    0x7ff8089f, 0xfd2d7e04,
+  0x7ff7e500, 0xfd2735ea, 0x7ff7c113, 0xfd20edd2, 0x7ff79cd6, 0xfd1aa5bc,
+    0x7ff7784a, 0xfd145da7,
+  0x7ff75370, 0xfd0e1594, 0x7ff72e46, 0xfd07cd83, 0x7ff708ce, 0xfd018574,
+    0x7ff6e307, 0xfcfb3d67,
+  0x7ff6bcf0, 0xfcf4f55c, 0x7ff6968b, 0xfceead52, 0x7ff66fd7, 0xfce8654b,
+    0x7ff648d4, 0xfce21d45,
+  0x7ff62182, 0xfcdbd541, 0x7ff5f9e1, 0xfcd58d3f, 0x7ff5d1f1, 0xfccf453f,
+    0x7ff5a9b2, 0xfcc8fd41,
+  0x7ff58125, 0xfcc2b545, 0x7ff55848, 0xfcbc6d4c, 0x7ff52f1d, 0xfcb62554,
+    0x7ff505a2, 0xfcafdd5e,
+  0x7ff4dbd9, 0xfca9956a, 0x7ff4b1c0, 0xfca34d78, 0x7ff48759, 0xfc9d0588,
+    0x7ff45ca3, 0xfc96bd9b,
+  0x7ff4319d, 0xfc9075af, 0x7ff40649, 0xfc8a2dc6, 0x7ff3daa6, 0xfc83e5de,
+    0x7ff3aeb4, 0xfc7d9df9,
+  0x7ff38274, 0xfc775616, 0x7ff355e4, 0xfc710e36, 0x7ff32905, 0xfc6ac657,
+    0x7ff2fbd7, 0xfc647e7b,
+  0x7ff2ce5b, 0xfc5e36a0, 0x7ff2a08f, 0xfc57eec9, 0x7ff27275, 0xfc51a6f3,
+    0x7ff2440b, 0xfc4b5f20,
+  0x7ff21553, 0xfc45174e, 0x7ff1e64c, 0xfc3ecf80, 0x7ff1b6f6, 0xfc3887b3,
+    0x7ff18751, 0xfc323fe9,
+  0x7ff1575d, 0xfc2bf821, 0x7ff1271a, 0xfc25b05c, 0x7ff0f688, 0xfc1f6899,
+    0x7ff0c5a7, 0xfc1920d8,
+  0x7ff09478, 0xfc12d91a, 0x7ff062f9, 0xfc0c915e, 0x7ff0312c, 0xfc0649a5,
+    0x7fefff0f, 0xfc0001ee,
+  0x7fefcca4, 0xfbf9ba39, 0x7fef99ea, 0xfbf37287, 0x7fef66e1, 0xfbed2ad8,
+    0x7fef3388, 0xfbe6e32b,
+  0x7feeffe1, 0xfbe09b80, 0x7feecbec, 0xfbda53d8, 0x7fee97a7, 0xfbd40c33,
+    0x7fee6313, 0xfbcdc490,
+  0x7fee2e30, 0xfbc77cf0, 0x7fedf8ff, 0xfbc13552, 0x7fedc37e, 0xfbbaedb7,
+    0x7fed8daf, 0xfbb4a61f,
+  0x7fed5791, 0xfbae5e89, 0x7fed2123, 0xfba816f6, 0x7fecea67, 0xfba1cf66,
+    0x7fecb35c, 0xfb9b87d8,
+  0x7fec7c02, 0xfb95404d, 0x7fec4459, 0xfb8ef8c5, 0x7fec0c62, 0xfb88b13f,
+    0x7febd41b, 0xfb8269bd,
+  0x7feb9b85, 0xfb7c223d, 0x7feb62a1, 0xfb75dac0, 0x7feb296d, 0xfb6f9345,
+    0x7feaefeb, 0xfb694bce,
+  0x7feab61a, 0xfb630459, 0x7fea7bfa, 0xfb5cbce7, 0x7fea418b, 0xfb567578,
+    0x7fea06cd, 0xfb502e0c,
+  0x7fe9cbc0, 0xfb49e6a3, 0x7fe99064, 0xfb439f3c, 0x7fe954ba, 0xfb3d57d9,
+    0x7fe918c0, 0xfb371078,
+  0x7fe8dc78, 0xfb30c91b, 0x7fe89fe0, 0xfb2a81c0, 0x7fe862fa, 0xfb243a69,
+    0x7fe825c5, 0xfb1df314,
+  0x7fe7e841, 0xfb17abc2, 0x7fe7aa6e, 0xfb116474, 0x7fe76c4c, 0xfb0b1d28,
+    0x7fe72ddb, 0xfb04d5e0,
+  0x7fe6ef1c, 0xfafe8e9b, 0x7fe6b00d, 0xfaf84758, 0x7fe670b0, 0xfaf20019,
+    0x7fe63103, 0xfaebb8dd,
+  0x7fe5f108, 0xfae571a4, 0x7fe5b0be, 0xfadf2a6e, 0x7fe57025, 0xfad8e33c,
+    0x7fe52f3d, 0xfad29c0c,
+  0x7fe4ee06, 0xfacc54e0, 0x7fe4ac81, 0xfac60db7, 0x7fe46aac, 0xfabfc691,
+    0x7fe42889, 0xfab97f6e,
+  0x7fe3e616, 0xfab3384f, 0x7fe3a355, 0xfaacf133, 0x7fe36045, 0xfaa6aa1a,
+    0x7fe31ce6, 0xfaa06305,
+  0x7fe2d938, 0xfa9a1bf3, 0x7fe2953b, 0xfa93d4e4, 0x7fe250ef, 0xfa8d8dd8,
+    0x7fe20c55, 0xfa8746d0,
+  0x7fe1c76b, 0xfa80ffcb, 0x7fe18233, 0xfa7ab8ca, 0x7fe13cac, 0xfa7471cc,
+    0x7fe0f6d6, 0xfa6e2ad1,
+  0x7fe0b0b1, 0xfa67e3da, 0x7fe06a3d, 0xfa619ce7, 0x7fe0237a, 0xfa5b55f7,
+    0x7fdfdc69, 0xfa550f0a,
+  0x7fdf9508, 0xfa4ec821, 0x7fdf4d59, 0xfa48813b, 0x7fdf055a, 0xfa423a59,
+    0x7fdebd0d, 0xfa3bf37a,
+  0x7fde7471, 0xfa35ac9f, 0x7fde2b86, 0xfa2f65c8, 0x7fdde24d, 0xfa291ef4,
+    0x7fdd98c4, 0xfa22d823,
+  0x7fdd4eec, 0xfa1c9157, 0x7fdd04c6, 0xfa164a8e, 0x7fdcba51, 0xfa1003c8,
+    0x7fdc6f8d, 0xfa09bd06,
+  0x7fdc247a, 0xfa037648, 0x7fdbd918, 0xf9fd2f8e, 0x7fdb8d67, 0xf9f6e8d7,
+    0x7fdb4167, 0xf9f0a224,
+  0x7fdaf519, 0xf9ea5b75, 0x7fdaa87c, 0xf9e414ca, 0x7fda5b8f, 0xf9ddce22,
+    0x7fda0e54, 0xf9d7877e,
+  0x7fd9c0ca, 0xf9d140de, 0x7fd972f2, 0xf9cafa42, 0x7fd924ca, 0xf9c4b3a9,
+    0x7fd8d653, 0xf9be6d15,
+  0x7fd8878e, 0xf9b82684, 0x7fd8387a, 0xf9b1dff7, 0x7fd7e917, 0xf9ab996e,
+    0x7fd79965, 0xf9a552e9,
+  0x7fd74964, 0xf99f0c68, 0x7fd6f914, 0xf998c5ea, 0x7fd6a875, 0xf9927f71,
+    0x7fd65788, 0xf98c38fc,
+  0x7fd6064c, 0xf985f28a, 0x7fd5b4c1, 0xf97fac1d, 0x7fd562e7, 0xf97965b4,
+    0x7fd510be, 0xf9731f4e,
+  0x7fd4be46, 0xf96cd8ed, 0x7fd46b80, 0xf9669290, 0x7fd4186a, 0xf9604c37,
+    0x7fd3c506, 0xf95a05e2,
+  0x7fd37153, 0xf953bf91, 0x7fd31d51, 0xf94d7944, 0x7fd2c900, 0xf94732fb,
+    0x7fd27460, 0xf940ecb7,
+  0x7fd21f72, 0xf93aa676, 0x7fd1ca35, 0xf934603a, 0x7fd174a8, 0xf92e1a02,
+    0x7fd11ecd, 0xf927d3ce,
+  0x7fd0c8a3, 0xf9218d9e, 0x7fd0722b, 0xf91b4773, 0x7fd01b63, 0xf915014c,
+    0x7fcfc44d, 0xf90ebb29,
+  0x7fcf6ce8, 0xf908750a, 0x7fcf1533, 0xf9022ef0, 0x7fcebd31, 0xf8fbe8da,
+    0x7fce64df, 0xf8f5a2c9,
+  0x7fce0c3e, 0xf8ef5cbb, 0x7fcdb34f, 0xf8e916b2, 0x7fcd5a11, 0xf8e2d0ae,
+    0x7fcd0083, 0xf8dc8aae,
+  0x7fcca6a7, 0xf8d644b2, 0x7fcc4c7d, 0xf8cffebb, 0x7fcbf203, 0xf8c9b8c8,
+    0x7fcb973b, 0xf8c372d9,
+  0x7fcb3c23, 0xf8bd2cef, 0x7fcae0bd, 0xf8b6e70a, 0x7fca8508, 0xf8b0a129,
+    0x7fca2905, 0xf8aa5b4c,
+  0x7fc9ccb2, 0xf8a41574, 0x7fc97011, 0xf89dcfa1, 0x7fc91320, 0xf89789d2,
+    0x7fc8b5e1, 0xf8914407,
+  0x7fc85854, 0xf88afe42, 0x7fc7fa77, 0xf884b880, 0x7fc79c4b, 0xf87e72c4,
+    0x7fc73dd1, 0xf8782d0c,
+  0x7fc6df08, 0xf871e759, 0x7fc67ff0, 0xf86ba1aa, 0x7fc62089, 0xf8655c00,
+    0x7fc5c0d3, 0xf85f165b,
+  0x7fc560cf, 0xf858d0bb, 0x7fc5007c, 0xf8528b1f, 0x7fc49fda, 0xf84c4588,
+    0x7fc43ee9, 0xf845fff5,
+  0x7fc3dda9, 0xf83fba68, 0x7fc37c1b, 0xf83974df, 0x7fc31a3d, 0xf8332f5b,
+    0x7fc2b811, 0xf82ce9dc,
+  0x7fc25596, 0xf826a462, 0x7fc1f2cc, 0xf8205eec, 0x7fc18fb4, 0xf81a197b,
+    0x7fc12c4d, 0xf813d410,
+  0x7fc0c896, 0xf80d8ea9, 0x7fc06491, 0xf8074947, 0x7fc0003e, 0xf80103ea,
+    0x7fbf9b9b, 0xf7fabe92,
+  0x7fbf36aa, 0xf7f4793e, 0x7fbed16a, 0xf7ee33f0, 0x7fbe6bdb, 0xf7e7eea7,
+    0x7fbe05fd, 0xf7e1a963,
+  0x7fbd9fd0, 0xf7db6423, 0x7fbd3955, 0xf7d51ee9, 0x7fbcd28b, 0xf7ced9b4,
+    0x7fbc6b72, 0xf7c89484,
+  0x7fbc040a, 0xf7c24f59, 0x7fbb9c53, 0xf7bc0a33, 0x7fbb344e, 0xf7b5c512,
+    0x7fbacbfa, 0xf7af7ff6,
+  0x7fba6357, 0xf7a93ae0, 0x7fb9fa65, 0xf7a2f5ce, 0x7fb99125, 0xf79cb0c2,
+    0x7fb92796, 0xf7966bbb,
+  0x7fb8bdb8, 0xf79026b9, 0x7fb8538b, 0xf789e1bc, 0x7fb7e90f, 0xf7839cc4,
+    0x7fb77e45, 0xf77d57d2,
+  0x7fb7132b, 0xf77712e5, 0x7fb6a7c3, 0xf770cdfd, 0x7fb63c0d, 0xf76a891b,
+    0x7fb5d007, 0xf764443d,
+  0x7fb563b3, 0xf75dff66, 0x7fb4f710, 0xf757ba93, 0x7fb48a1e, 0xf75175c6,
+    0x7fb41cdd, 0xf74b30fe,
+  0x7fb3af4e, 0xf744ec3b, 0x7fb34170, 0xf73ea77e, 0x7fb2d343, 0xf73862c6,
+    0x7fb264c7, 0xf7321e14,
+  0x7fb1f5fc, 0xf72bd967, 0x7fb186e3, 0xf72594c0, 0x7fb1177b, 0xf71f501e,
+    0x7fb0a7c4, 0xf7190b81,
+  0x7fb037bf, 0xf712c6ea, 0x7fafc76a, 0xf70c8259, 0x7faf56c7, 0xf7063dcd,
+    0x7faee5d5, 0xf6fff946,
+  0x7fae7495, 0xf6f9b4c6, 0x7fae0305, 0xf6f3704a, 0x7fad9127, 0xf6ed2bd4,
+    0x7fad1efa, 0xf6e6e764,
+  0x7facac7f, 0xf6e0a2fa, 0x7fac39b4, 0xf6da5e95, 0x7fabc69b, 0xf6d41a36,
+    0x7fab5333, 0xf6cdd5dc,
+  0x7faadf7c, 0xf6c79188, 0x7faa6b77, 0xf6c14d3a, 0x7fa9f723, 0xf6bb08f1,
+    0x7fa98280, 0xf6b4c4ae,
+  0x7fa90d8e, 0xf6ae8071, 0x7fa8984e, 0xf6a83c3a, 0x7fa822bf, 0xf6a1f808,
+    0x7fa7ace1, 0xf69bb3dd,
+  0x7fa736b4, 0xf6956fb7, 0x7fa6c039, 0xf68f2b96, 0x7fa6496e, 0xf688e77c,
+    0x7fa5d256, 0xf682a367,
+  0x7fa55aee, 0xf67c5f59, 0x7fa4e338, 0xf6761b50, 0x7fa46b32, 0xf66fd74d,
+    0x7fa3f2df, 0xf6699350,
+  0x7fa37a3c, 0xf6634f59, 0x7fa3014b, 0xf65d0b68, 0x7fa2880b, 0xf656c77c,
+    0x7fa20e7c, 0xf6508397,
+  0x7fa1949e, 0xf64a3fb8, 0x7fa11a72, 0xf643fbdf, 0x7fa09ff7, 0xf63db80b,
+    0x7fa0252e, 0xf637743e,
+  0x7f9faa15, 0xf6313077, 0x7f9f2eae, 0xf62aecb5, 0x7f9eb2f8, 0xf624a8fa,
+    0x7f9e36f4, 0xf61e6545,
+  0x7f9dbaa0, 0xf6182196, 0x7f9d3dfe, 0xf611dded, 0x7f9cc10d, 0xf60b9a4b,
+    0x7f9c43ce, 0xf60556ae,
+  0x7f9bc640, 0xf5ff1318, 0x7f9b4863, 0xf5f8cf87, 0x7f9aca37, 0xf5f28bfd,
+    0x7f9a4bbd, 0xf5ec4879,
+  0x7f99ccf4, 0xf5e604fc, 0x7f994ddc, 0xf5dfc184, 0x7f98ce76, 0xf5d97e13,
+    0x7f984ec1, 0xf5d33aa8,
+  0x7f97cebd, 0xf5ccf743, 0x7f974e6a, 0xf5c6b3e5, 0x7f96cdc9, 0xf5c0708d,
+    0x7f964cd9, 0xf5ba2d3b,
+  0x7f95cb9a, 0xf5b3e9f0, 0x7f954a0d, 0xf5ada6ab, 0x7f94c831, 0xf5a7636c,
+    0x7f944606, 0xf5a12034,
+  0x7f93c38c, 0xf59add02, 0x7f9340c4, 0xf59499d6, 0x7f92bdad, 0xf58e56b1,
+    0x7f923a48, 0xf5881393,
+  0x7f91b694, 0xf581d07b, 0x7f913291, 0xf57b8d69, 0x7f90ae3f, 0xf5754a5e,
+    0x7f90299f, 0xf56f0759,
+  0x7f8fa4b0, 0xf568c45b, 0x7f8f1f72, 0xf5628163, 0x7f8e99e6, 0xf55c3e72,
+    0x7f8e140a, 0xf555fb88,
+  0x7f8d8de1, 0xf54fb8a4, 0x7f8d0768, 0xf54975c6, 0x7f8c80a1, 0xf54332ef,
+    0x7f8bf98b, 0xf53cf01f,
+  0x7f8b7227, 0xf536ad56, 0x7f8aea74, 0xf5306a93, 0x7f8a6272, 0xf52a27d7,
+    0x7f89da21, 0xf523e521,
+  0x7f895182, 0xf51da273, 0x7f88c894, 0xf5175fca, 0x7f883f58, 0xf5111d29,
+    0x7f87b5cd, 0xf50ada8f,
+  0x7f872bf3, 0xf50497fb, 0x7f86a1ca, 0xf4fe556e, 0x7f861753, 0xf4f812e7,
+    0x7f858c8d, 0xf4f1d068,
+  0x7f850179, 0xf4eb8def, 0x7f847616, 0xf4e54b7d, 0x7f83ea64, 0xf4df0912,
+    0x7f835e64, 0xf4d8c6ae,
+  0x7f82d214, 0xf4d28451, 0x7f824577, 0xf4cc41fb, 0x7f81b88a, 0xf4c5ffab,
+    0x7f812b4f, 0xf4bfbd63,
+  0x7f809dc5, 0xf4b97b21, 0x7f800fed, 0xf4b338e7, 0x7f7f81c6, 0xf4acf6b3,
+    0x7f7ef350, 0xf4a6b486,
+  0x7f7e648c, 0xf4a07261, 0x7f7dd579, 0xf49a3042, 0x7f7d4617, 0xf493ee2b,
+    0x7f7cb667, 0xf48dac1a,
+  0x7f7c2668, 0xf4876a10, 0x7f7b961b, 0xf481280e, 0x7f7b057e, 0xf47ae613,
+    0x7f7a7494, 0xf474a41f,
+  0x7f79e35a, 0xf46e6231, 0x7f7951d2, 0xf468204b, 0x7f78bffb, 0xf461de6d,
+    0x7f782dd6, 0xf45b9c95,
+  0x7f779b62, 0xf4555ac5, 0x7f77089f, 0xf44f18fb, 0x7f76758e, 0xf448d739,
+    0x7f75e22e, 0xf442957e,
+  0x7f754e80, 0xf43c53cb, 0x7f74ba83, 0xf436121e, 0x7f742637, 0xf42fd079,
+    0x7f73919d, 0xf4298edc,
+  0x7f72fcb4, 0xf4234d45, 0x7f72677c, 0xf41d0bb6, 0x7f71d1f6, 0xf416ca2e,
+    0x7f713c21, 0xf41088ae,
+  0x7f70a5fe, 0xf40a4735, 0x7f700f8c, 0xf40405c3, 0x7f6f78cb, 0xf3fdc459,
+    0x7f6ee1bc, 0xf3f782f6,
+  0x7f6e4a5e, 0xf3f1419a, 0x7f6db2b1, 0xf3eb0046, 0x7f6d1ab6, 0xf3e4bef9,
+    0x7f6c826d, 0xf3de7db4,
+  0x7f6be9d4, 0xf3d83c77, 0x7f6b50ed, 0xf3d1fb40, 0x7f6ab7b8, 0xf3cbba12,
+    0x7f6a1e34, 0xf3c578eb,
+  0x7f698461, 0xf3bf37cb, 0x7f68ea40, 0xf3b8f6b3, 0x7f684fd0, 0xf3b2b5a3,
+    0x7f67b512, 0xf3ac749a,
+  0x7f671a05, 0xf3a63398, 0x7f667ea9, 0xf39ff29f, 0x7f65e2ff, 0xf399b1ad,
+    0x7f654706, 0xf39370c2,
+  0x7f64aabf, 0xf38d2fe0, 0x7f640e29, 0xf386ef05, 0x7f637144, 0xf380ae31,
+    0x7f62d411, 0xf37a6d66,
+  0x7f62368f, 0xf3742ca2, 0x7f6198bf, 0xf36debe6, 0x7f60faa0, 0xf367ab31,
+    0x7f605c33, 0xf3616a85,
+  0x7f5fbd77, 0xf35b29e0, 0x7f5f1e6c, 0xf354e943, 0x7f5e7f13, 0xf34ea8ae,
+    0x7f5ddf6b, 0xf3486820,
+  0x7f5d3f75, 0xf342279b, 0x7f5c9f30, 0xf33be71d, 0x7f5bfe9d, 0xf335a6a7,
+    0x7f5b5dbb, 0xf32f6639,
+  0x7f5abc8a, 0xf32925d3, 0x7f5a1b0b, 0xf322e575, 0x7f59793e, 0xf31ca51f,
+    0x7f58d721, 0xf31664d1,
+  0x7f5834b7, 0xf310248a, 0x7f5791fd, 0xf309e44c, 0x7f56eef5, 0xf303a416,
+    0x7f564b9f, 0xf2fd63e8,
+  0x7f55a7fa, 0xf2f723c1, 0x7f550407, 0xf2f0e3a3, 0x7f545fc5, 0xf2eaa38d,
+    0x7f53bb34, 0xf2e4637f,
+  0x7f531655, 0xf2de2379, 0x7f527127, 0xf2d7e37b, 0x7f51cbab, 0xf2d1a385,
+    0x7f5125e0, 0xf2cb6398,
+  0x7f507fc7, 0xf2c523b2, 0x7f4fd95f, 0xf2bee3d5, 0x7f4f32a9, 0xf2b8a400,
+    0x7f4e8ba4, 0xf2b26433,
+  0x7f4de451, 0xf2ac246e, 0x7f4d3caf, 0xf2a5e4b1, 0x7f4c94be, 0xf29fa4fd,
+    0x7f4bec7f, 0xf2996551,
+  0x7f4b43f2, 0xf29325ad, 0x7f4a9b16, 0xf28ce612, 0x7f49f1eb, 0xf286a67e,
+    0x7f494872, 0xf28066f4,
+  0x7f489eaa, 0xf27a2771, 0x7f47f494, 0xf273e7f7, 0x7f474a30, 0xf26da885,
+    0x7f469f7d, 0xf267691b,
+  0x7f45f47b, 0xf26129ba, 0x7f45492b, 0xf25aea61, 0x7f449d8c, 0xf254ab11,
+    0x7f43f19f, 0xf24e6bc9,
+  0x7f434563, 0xf2482c8a, 0x7f4298d9, 0xf241ed53, 0x7f41ec01, 0xf23bae24,
+    0x7f413ed9, 0xf2356efe,
+  0x7f409164, 0xf22f2fe1, 0x7f3fe3a0, 0xf228f0cc, 0x7f3f358d, 0xf222b1c0,
+    0x7f3e872c, 0xf21c72bc,
+  0x7f3dd87c, 0xf21633c0, 0x7f3d297e, 0xf20ff4ce, 0x7f3c7a31, 0xf209b5e4,
+    0x7f3bca96, 0xf2037702,
+  0x7f3b1aad, 0xf1fd3829, 0x7f3a6a75, 0xf1f6f959, 0x7f39b9ee, 0xf1f0ba91,
+    0x7f390919, 0xf1ea7bd2,
+  0x7f3857f6, 0xf1e43d1c, 0x7f37a684, 0xf1ddfe6f, 0x7f36f4c3, 0xf1d7bfca,
+    0x7f3642b4, 0xf1d1812e,
+  0x7f359057, 0xf1cb429a, 0x7f34ddab, 0xf1c50410, 0x7f342ab1, 0xf1bec58e,
+    0x7f337768, 0xf1b88715,
+  0x7f32c3d1, 0xf1b248a5, 0x7f320feb, 0xf1ac0a3e, 0x7f315bb7, 0xf1a5cbdf,
+    0x7f30a734, 0xf19f8d89,
+  0x7f2ff263, 0xf1994f3d, 0x7f2f3d44, 0xf19310f9, 0x7f2e87d6, 0xf18cd2be,
+    0x7f2dd219, 0xf186948c,
+  0x7f2d1c0e, 0xf1805662, 0x7f2c65b5, 0xf17a1842, 0x7f2baf0d, 0xf173da2b,
+    0x7f2af817, 0xf16d9c1d,
+  0x7f2a40d2, 0xf1675e17, 0x7f29893f, 0xf161201b, 0x7f28d15d, 0xf15ae228,
+    0x7f28192d, 0xf154a43d,
+  0x7f2760af, 0xf14e665c, 0x7f26a7e2, 0xf1482884, 0x7f25eec7, 0xf141eab5,
+    0x7f25355d, 0xf13bacef,
+  0x7f247ba5, 0xf1356f32, 0x7f23c19e, 0xf12f317e, 0x7f230749, 0xf128f3d4,
+    0x7f224ca6, 0xf122b632,
+  0x7f2191b4, 0xf11c789a, 0x7f20d674, 0xf1163b0b, 0x7f201ae5, 0xf10ffd85,
+    0x7f1f5f08, 0xf109c009,
+  0x7f1ea2dc, 0xf1038295, 0x7f1de662, 0xf0fd452b, 0x7f1d299a, 0xf0f707ca,
+    0x7f1c6c83, 0xf0f0ca72,
+  0x7f1baf1e, 0xf0ea8d24, 0x7f1af16a, 0xf0e44fdf, 0x7f1a3368, 0xf0de12a3,
+    0x7f197518, 0xf0d7d571,
+  0x7f18b679, 0xf0d19848, 0x7f17f78c, 0xf0cb5b28, 0x7f173850, 0xf0c51e12,
+    0x7f1678c6, 0xf0bee105,
+  0x7f15b8ee, 0xf0b8a401, 0x7f14f8c7, 0xf0b26707, 0x7f143852, 0xf0ac2a16,
+    0x7f13778e, 0xf0a5ed2f,
+  0x7f12b67c, 0xf09fb051, 0x7f11f51c, 0xf099737d, 0x7f11336d, 0xf09336b2,
+    0x7f107170, 0xf08cf9f1,
+  0x7f0faf25, 0xf086bd39, 0x7f0eec8b, 0xf080808b, 0x7f0e29a3, 0xf07a43e7,
+    0x7f0d666c, 0xf074074c,
+  0x7f0ca2e7, 0xf06dcaba, 0x7f0bdf14, 0xf0678e32, 0x7f0b1af2, 0xf06151b4,
+    0x7f0a5682, 0xf05b1540,
+  0x7f0991c4, 0xf054d8d5, 0x7f08ccb7, 0xf04e9c73, 0x7f08075c, 0xf048601c,
+    0x7f0741b2, 0xf04223ce,
+  0x7f067bba, 0xf03be78a, 0x7f05b574, 0xf035ab4f, 0x7f04eedf, 0xf02f6f1f,
+    0x7f0427fc, 0xf02932f8,
+  0x7f0360cb, 0xf022f6da, 0x7f02994b, 0xf01cbac7, 0x7f01d17d, 0xf0167ebd,
+    0x7f010961, 0xf01042be,
+  0x7f0040f6, 0xf00a06c8, 0x7eff783d, 0xf003cadc, 0x7efeaf36, 0xeffd8ef9,
+    0x7efde5e0, 0xeff75321,
+  0x7efd1c3c, 0xeff11753, 0x7efc524a, 0xefeadb8e, 0x7efb8809, 0xefe49fd3,
+    0x7efabd7a, 0xefde6423,
+  0x7ef9f29d, 0xefd8287c, 0x7ef92771, 0xefd1ecdf, 0x7ef85bf7, 0xefcbb14c,
+    0x7ef7902f, 0xefc575c3,
+  0x7ef6c418, 0xefbf3a45, 0x7ef5f7b3, 0xefb8fed0, 0x7ef52b00, 0xefb2c365,
+    0x7ef45dfe, 0xefac8804,
+  0x7ef390ae, 0xefa64cae, 0x7ef2c310, 0xefa01161, 0x7ef1f524, 0xef99d61f,
+    0x7ef126e9, 0xef939ae6,
+  0x7ef05860, 0xef8d5fb8, 0x7eef8988, 0xef872494, 0x7eeeba62, 0xef80e97a,
+    0x7eedeaee, 0xef7aae6b,
+  0x7eed1b2c, 0xef747365, 0x7eec4b1b, 0xef6e386a, 0x7eeb7abc, 0xef67fd79,
+    0x7eeaaa0f, 0xef61c292,
+  0x7ee9d914, 0xef5b87b5, 0x7ee907ca, 0xef554ce3, 0x7ee83632, 0xef4f121b,
+    0x7ee7644c, 0xef48d75d,
+  0x7ee69217, 0xef429caa, 0x7ee5bf94, 0xef3c6201, 0x7ee4ecc3, 0xef362762,
+    0x7ee419a3, 0xef2feccd,
+  0x7ee34636, 0xef29b243, 0x7ee2727a, 0xef2377c4, 0x7ee19e6f, 0xef1d3d4e,
+    0x7ee0ca17, 0xef1702e4,
+  0x7edff570, 0xef10c883, 0x7edf207b, 0xef0a8e2d, 0x7ede4b38, 0xef0453e2,
+    0x7edd75a6, 0xeefe19a1,
+  0x7edc9fc6, 0xeef7df6a, 0x7edbc998, 0xeef1a53e, 0x7edaf31c, 0xeeeb6b1c,
+    0x7eda1c51, 0xeee53105,
+  0x7ed94538, 0xeedef6f9, 0x7ed86dd1, 0xeed8bcf7, 0x7ed7961c, 0xeed28300,
+    0x7ed6be18, 0xeecc4913,
+  0x7ed5e5c6, 0xeec60f31, 0x7ed50d26, 0xeebfd55a, 0x7ed43438, 0xeeb99b8d,
+    0x7ed35afb, 0xeeb361cb,
+  0x7ed28171, 0xeead2813, 0x7ed1a798, 0xeea6ee66, 0x7ed0cd70, 0xeea0b4c4,
+    0x7ecff2fb, 0xee9a7b2d,
+  0x7ecf1837, 0xee9441a0, 0x7ece3d25, 0xee8e081e, 0x7ecd61c5, 0xee87cea7,
+    0x7ecc8617, 0xee81953b,
+  0x7ecbaa1a, 0xee7b5bd9, 0x7ecacdd0, 0xee752283, 0x7ec9f137, 0xee6ee937,
+    0x7ec9144f, 0xee68aff6,
+  0x7ec8371a, 0xee6276bf, 0x7ec75996, 0xee5c3d94, 0x7ec67bc5, 0xee560473,
+    0x7ec59da5, 0xee4fcb5e,
+  0x7ec4bf36, 0xee499253, 0x7ec3e07a, 0xee435953, 0x7ec3016f, 0xee3d205e,
+    0x7ec22217, 0xee36e775,
+  0x7ec14270, 0xee30ae96, 0x7ec0627a, 0xee2a75c2, 0x7ebf8237, 0xee243cf9,
+    0x7ebea1a6, 0xee1e043b,
+  0x7ebdc0c6, 0xee17cb88, 0x7ebcdf98, 0xee1192e0, 0x7ebbfe1c, 0xee0b5a43,
+    0x7ebb1c52, 0xee0521b2,
+  0x7eba3a39, 0xedfee92b, 0x7eb957d2, 0xedf8b0b0, 0x7eb8751e, 0xedf2783f,
+    0x7eb7921b, 0xedec3fda,
+  0x7eb6aeca, 0xede60780, 0x7eb5cb2a, 0xeddfcf31, 0x7eb4e73d, 0xedd996ed,
+    0x7eb40301, 0xedd35eb5,
+  0x7eb31e78, 0xedcd2687, 0x7eb239a0, 0xedc6ee65, 0x7eb1547a, 0xedc0b64e,
+    0x7eb06f05, 0xedba7e43,
+  0x7eaf8943, 0xedb44642, 0x7eaea333, 0xedae0e4d, 0x7eadbcd4, 0xeda7d664,
+    0x7eacd627, 0xeda19e85,
+  0x7eabef2c, 0xed9b66b2, 0x7eab07e3, 0xed952eea, 0x7eaa204c, 0xed8ef72e,
+    0x7ea93867, 0xed88bf7d,
+  0x7ea85033, 0xed8287d7, 0x7ea767b2, 0xed7c503d, 0x7ea67ee2, 0xed7618ae,
+    0x7ea595c4, 0xed6fe12b,
+  0x7ea4ac58, 0xed69a9b3, 0x7ea3c29e, 0xed637246, 0x7ea2d896, 0xed5d3ae5,
+    0x7ea1ee3f, 0xed570390,
+  0x7ea1039b, 0xed50cc46, 0x7ea018a8, 0xed4a9507, 0x7e9f2d68, 0xed445dd5,
+    0x7e9e41d9, 0xed3e26ad,
+  0x7e9d55fc, 0xed37ef91, 0x7e9c69d1, 0xed31b881, 0x7e9b7d58, 0xed2b817d,
+    0x7e9a9091, 0xed254a84,
+  0x7e99a37c, 0xed1f1396, 0x7e98b618, 0xed18dcb5, 0x7e97c867, 0xed12a5df,
+    0x7e96da67, 0xed0c6f14,
+  0x7e95ec1a, 0xed063856, 0x7e94fd7e, 0xed0001a3, 0x7e940e94, 0xecf9cafb,
+    0x7e931f5c, 0xecf39460,
+  0x7e922fd6, 0xeced5dd0, 0x7e914002, 0xece7274c, 0x7e904fe0, 0xece0f0d4,
+    0x7e8f5f70, 0xecdaba67,
+  0x7e8e6eb2, 0xecd48407, 0x7e8d7da6, 0xecce4db2, 0x7e8c8c4b, 0xecc81769,
+    0x7e8b9aa3, 0xecc1e12c,
+  0x7e8aa8ac, 0xecbbaafb, 0x7e89b668, 0xecb574d5, 0x7e88c3d5, 0xecaf3ebc,
+    0x7e87d0f5, 0xeca908ae,
+  0x7e86ddc6, 0xeca2d2ad, 0x7e85ea49, 0xec9c9cb7, 0x7e84f67e, 0xec9666cd,
+    0x7e840265, 0xec9030f0,
+  0x7e830dff, 0xec89fb1e, 0x7e82194a, 0xec83c558, 0x7e812447, 0xec7d8f9e,
+    0x7e802ef6, 0xec7759f1,
+  0x7e7f3957, 0xec71244f, 0x7e7e436a, 0xec6aeeba, 0x7e7d4d2f, 0xec64b930,
+    0x7e7c56a5, 0xec5e83b3,
+  0x7e7b5fce, 0xec584e41, 0x7e7a68a9, 0xec5218dc, 0x7e797136, 0xec4be383,
+    0x7e787975, 0xec45ae36,
+  0x7e778166, 0xec3f78f6, 0x7e768908, 0xec3943c1, 0x7e75905d, 0xec330e99,
+    0x7e749764, 0xec2cd97d,
+  0x7e739e1d, 0xec26a46d, 0x7e72a488, 0xec206f69, 0x7e71aaa4, 0xec1a3a72,
+    0x7e70b073, 0xec140587,
+  0x7e6fb5f4, 0xec0dd0a8, 0x7e6ebb27, 0xec079bd6, 0x7e6dc00c, 0xec01670f,
+    0x7e6cc4a2, 0xebfb3256,
+  0x7e6bc8eb, 0xebf4fda8, 0x7e6acce6, 0xebeec907, 0x7e69d093, 0xebe89472,
+    0x7e68d3f2, 0xebe25fea,
+  0x7e67d703, 0xebdc2b6e, 0x7e66d9c6, 0xebd5f6fe, 0x7e65dc3b, 0xebcfc29b,
+    0x7e64de62, 0xebc98e45,
+  0x7e63e03b, 0xebc359fb, 0x7e62e1c6, 0xebbd25bd, 0x7e61e303, 0xebb6f18c,
+    0x7e60e3f2, 0xebb0bd67,
+  0x7e5fe493, 0xebaa894f, 0x7e5ee4e6, 0xeba45543, 0x7e5de4ec, 0xeb9e2144,
+    0x7e5ce4a3, 0xeb97ed52,
+  0x7e5be40c, 0xeb91b96c, 0x7e5ae328, 0xeb8b8593, 0x7e59e1f5, 0xeb8551c6,
+    0x7e58e075, 0xeb7f1e06,
+  0x7e57dea7, 0xeb78ea52, 0x7e56dc8a, 0xeb72b6ac, 0x7e55da20, 0xeb6c8312,
+    0x7e54d768, 0xeb664f84,
+  0x7e53d462, 0xeb601c04, 0x7e52d10e, 0xeb59e890, 0x7e51cd6c, 0xeb53b529,
+    0x7e50c97c, 0xeb4d81ce,
+  0x7e4fc53e, 0xeb474e81, 0x7e4ec0b2, 0xeb411b40, 0x7e4dbbd9, 0xeb3ae80c,
+    0x7e4cb6b1, 0xeb34b4e4,
+  0x7e4bb13c, 0xeb2e81ca, 0x7e4aab78, 0xeb284ebc, 0x7e49a567, 0xeb221bbb,
+    0x7e489f08, 0xeb1be8c8,
+  0x7e47985b, 0xeb15b5e1, 0x7e469160, 0xeb0f8307, 0x7e458a17, 0xeb095039,
+    0x7e448281, 0xeb031d79,
+  0x7e437a9c, 0xeafceac6, 0x7e427269, 0xeaf6b81f, 0x7e4169e9, 0xeaf08586,
+    0x7e40611b, 0xeaea52fa,
+  0x7e3f57ff, 0xeae4207a, 0x7e3e4e95, 0xeaddee08, 0x7e3d44dd, 0xead7bba3,
+    0x7e3c3ad7, 0xead1894b,
+  0x7e3b3083, 0xeacb56ff, 0x7e3a25e2, 0xeac524c1, 0x7e391af3, 0xeabef290,
+    0x7e380fb5, 0xeab8c06c,
+  0x7e37042a, 0xeab28e56, 0x7e35f851, 0xeaac5c4c, 0x7e34ec2b, 0xeaa62a4f,
+    0x7e33dfb6, 0xea9ff860,
+  0x7e32d2f4, 0xea99c67e, 0x7e31c5e3, 0xea9394a9, 0x7e30b885, 0xea8d62e1,
+    0x7e2faad9, 0xea873127,
+  0x7e2e9cdf, 0xea80ff7a, 0x7e2d8e97, 0xea7acdda, 0x7e2c8002, 0xea749c47,
+    0x7e2b711f, 0xea6e6ac2,
+  0x7e2a61ed, 0xea683949, 0x7e29526e, 0xea6207df, 0x7e2842a2, 0xea5bd681,
+    0x7e273287, 0xea55a531,
+  0x7e26221f, 0xea4f73ee, 0x7e251168, 0xea4942b9, 0x7e240064, 0xea431191,
+    0x7e22ef12, 0xea3ce077,
+  0x7e21dd73, 0xea36af69, 0x7e20cb85, 0xea307e6a, 0x7e1fb94a, 0xea2a4d78,
+    0x7e1ea6c1, 0xea241c93,
+  0x7e1d93ea, 0xea1debbb, 0x7e1c80c5, 0xea17baf2, 0x7e1b6d53, 0xea118a35,
+    0x7e1a5992, 0xea0b5987,
+  0x7e194584, 0xea0528e5, 0x7e183128, 0xe9fef852, 0x7e171c7f, 0xe9f8c7cc,
+    0x7e160787, 0xe9f29753,
+  0x7e14f242, 0xe9ec66e8, 0x7e13dcaf, 0xe9e6368b, 0x7e12c6ce, 0xe9e0063c,
+    0x7e11b0a0, 0xe9d9d5fa,
+  0x7e109a24, 0xe9d3a5c5, 0x7e0f835a, 0xe9cd759f, 0x7e0e6c42, 0xe9c74586,
+    0x7e0d54dc, 0xe9c1157a,
+  0x7e0c3d29, 0xe9bae57d, 0x7e0b2528, 0xe9b4b58d, 0x7e0a0cd9, 0xe9ae85ab,
+    0x7e08f43d, 0xe9a855d7,
+  0x7e07db52, 0xe9a22610, 0x7e06c21a, 0xe99bf658, 0x7e05a894, 0xe995c6ad,
+    0x7e048ec1, 0xe98f9710,
+  0x7e0374a0, 0xe9896781, 0x7e025a31, 0xe98337ff, 0x7e013f74, 0xe97d088c,
+    0x7e00246a, 0xe976d926,
+  0x7dff0911, 0xe970a9ce, 0x7dfded6c, 0xe96a7a85, 0x7dfcd178, 0xe9644b49,
+    0x7dfbb537, 0xe95e1c1b,
+  0x7dfa98a8, 0xe957ecfb, 0x7df97bcb, 0xe951bde9, 0x7df85ea0, 0xe94b8ee5,
+    0x7df74128, 0xe9455fef,
+  0x7df62362, 0xe93f3107, 0x7df5054f, 0xe939022d, 0x7df3e6ee, 0xe932d361,
+    0x7df2c83f, 0xe92ca4a4,
+  0x7df1a942, 0xe92675f4, 0x7df089f8, 0xe9204752, 0x7def6a60, 0xe91a18bf,
+    0x7dee4a7a, 0xe913ea39,
+  0x7ded2a47, 0xe90dbbc2, 0x7dec09c6, 0xe9078d59, 0x7deae8f7, 0xe9015efe,
+    0x7de9c7da, 0xe8fb30b1,
+  0x7de8a670, 0xe8f50273, 0x7de784b9, 0xe8eed443, 0x7de662b3, 0xe8e8a621,
+    0x7de54060, 0xe8e2780d,
+  0x7de41dc0, 0xe8dc4a07, 0x7de2fad1, 0xe8d61c10, 0x7de1d795, 0xe8cfee27,
+    0x7de0b40b, 0xe8c9c04c,
+  0x7ddf9034, 0xe8c39280, 0x7dde6c0f, 0xe8bd64c2, 0x7ddd479d, 0xe8b73712,
+    0x7ddc22dc, 0xe8b10971,
+  0x7ddafdce, 0xe8aadbde, 0x7dd9d873, 0xe8a4ae59, 0x7dd8b2ca, 0xe89e80e3,
+    0x7dd78cd3, 0xe898537b,
+  0x7dd6668f, 0xe8922622, 0x7dd53ffc, 0xe88bf8d7, 0x7dd4191d, 0xe885cb9a,
+    0x7dd2f1f0, 0xe87f9e6c,
+  0x7dd1ca75, 0xe879714d, 0x7dd0a2ac, 0xe873443c, 0x7dcf7a96, 0xe86d173a,
+    0x7dce5232, 0xe866ea46,
+  0x7dcd2981, 0xe860bd61, 0x7dcc0082, 0xe85a908a, 0x7dcad736, 0xe85463c2,
+    0x7dc9ad9c, 0xe84e3708,
+  0x7dc883b4, 0xe8480a5d, 0x7dc7597f, 0xe841ddc1, 0x7dc62efc, 0xe83bb133,
+    0x7dc5042b, 0xe83584b4,
+  0x7dc3d90d, 0xe82f5844, 0x7dc2ada2, 0xe8292be3, 0x7dc181e8, 0xe822ff90,
+    0x7dc055e2, 0xe81cd34b,
+  0x7dbf298d, 0xe816a716, 0x7dbdfceb, 0xe8107aef, 0x7dbccffc, 0xe80a4ed7,
+    0x7dbba2bf, 0xe80422ce,
+  0x7dba7534, 0xe7fdf6d4, 0x7db9475c, 0xe7f7cae8, 0x7db81936, 0xe7f19f0c,
+    0x7db6eac3, 0xe7eb733e,
+  0x7db5bc02, 0xe7e5477f, 0x7db48cf4, 0xe7df1bcf, 0x7db35d98, 0xe7d8f02d,
+    0x7db22def, 0xe7d2c49b,
+  0x7db0fdf8, 0xe7cc9917, 0x7dafcdb3, 0xe7c66da3, 0x7dae9d21, 0xe7c0423d,
+    0x7dad6c42, 0xe7ba16e7,
+  0x7dac3b15, 0xe7b3eb9f, 0x7dab099a, 0xe7adc066, 0x7da9d7d2, 0xe7a7953d,
+    0x7da8a5bc, 0xe7a16a22,
+  0x7da77359, 0xe79b3f16, 0x7da640a9, 0xe795141a, 0x7da50dab, 0xe78ee92c,
+    0x7da3da5f, 0xe788be4e,
+  0x7da2a6c6, 0xe782937e, 0x7da172df, 0xe77c68be, 0x7da03eab, 0xe7763e0d,
+    0x7d9f0a29, 0xe770136b,
+  0x7d9dd55a, 0xe769e8d8, 0x7d9ca03e, 0xe763be55, 0x7d9b6ad3, 0xe75d93e0,
+    0x7d9a351c, 0xe757697b,
+  0x7d98ff17, 0xe7513f25, 0x7d97c8c4, 0xe74b14de, 0x7d969224, 0xe744eaa6,
+    0x7d955b37, 0xe73ec07e,
+  0x7d9423fc, 0xe7389665, 0x7d92ec73, 0xe7326c5b, 0x7d91b49e, 0xe72c4260,
+    0x7d907c7a, 0xe7261875,
+  0x7d8f4409, 0xe71fee99, 0x7d8e0b4b, 0xe719c4cd, 0x7d8cd240, 0xe7139b10,
+    0x7d8b98e6, 0xe70d7162,
+  0x7d8a5f40, 0xe70747c4, 0x7d89254c, 0xe7011e35, 0x7d87eb0a, 0xe6faf4b5,
+    0x7d86b07c, 0xe6f4cb45,
+  0x7d85759f, 0xe6eea1e4, 0x7d843a76, 0xe6e87893, 0x7d82fefe, 0xe6e24f51,
+    0x7d81c33a, 0xe6dc261f,
+  0x7d808728, 0xe6d5fcfc, 0x7d7f4ac8, 0xe6cfd3e9, 0x7d7e0e1c, 0xe6c9aae5,
+    0x7d7cd121, 0xe6c381f1,
+  0x7d7b93da, 0xe6bd590d, 0x7d7a5645, 0xe6b73038, 0x7d791862, 0xe6b10772,
+    0x7d77da32, 0xe6aadebc,
+  0x7d769bb5, 0xe6a4b616, 0x7d755cea, 0xe69e8d80, 0x7d741dd2, 0xe69864f9,
+    0x7d72de6d, 0xe6923c82,
+  0x7d719eba, 0xe68c141a, 0x7d705eba, 0xe685ebc2, 0x7d6f1e6c, 0xe67fc37a,
+    0x7d6dddd2, 0xe6799b42,
+  0x7d6c9ce9, 0xe6737319, 0x7d6b5bb4, 0xe66d4b01, 0x7d6a1a31, 0xe66722f7,
+    0x7d68d860, 0xe660fafe,
+  0x7d679642, 0xe65ad315, 0x7d6653d7, 0xe654ab3b, 0x7d65111f, 0xe64e8371,
+    0x7d63ce19, 0xe6485bb7,
+  0x7d628ac6, 0xe642340d, 0x7d614725, 0xe63c0c73, 0x7d600338, 0xe635e4e9,
+    0x7d5ebefc, 0xe62fbd6e,
+  0x7d5d7a74, 0xe6299604, 0x7d5c359e, 0xe6236ea9, 0x7d5af07b, 0xe61d475e,
+    0x7d59ab0a, 0xe6172024,
+  0x7d58654d, 0xe610f8f9, 0x7d571f41, 0xe60ad1de, 0x7d55d8e9, 0xe604aad4,
+    0x7d549243, 0xe5fe83d9,
+  0x7d534b50, 0xe5f85cef, 0x7d520410, 0xe5f23614, 0x7d50bc82, 0xe5ec0f4a,
+    0x7d4f74a7, 0xe5e5e88f,
+  0x7d4e2c7f, 0xe5dfc1e5, 0x7d4ce409, 0xe5d99b4b, 0x7d4b9b46, 0xe5d374c1,
+    0x7d4a5236, 0xe5cd4e47,
+  0x7d4908d9, 0xe5c727dd, 0x7d47bf2e, 0xe5c10184, 0x7d467536, 0xe5badb3a,
+    0x7d452af1, 0xe5b4b501,
+  0x7d43e05e, 0xe5ae8ed8, 0x7d42957e, 0xe5a868bf, 0x7d414a51, 0xe5a242b7,
+    0x7d3ffed7, 0xe59c1cbf,
+  0x7d3eb30f, 0xe595f6d7, 0x7d3d66fa, 0xe58fd0ff, 0x7d3c1a98, 0xe589ab38,
+    0x7d3acde9, 0xe5838581,
+  0x7d3980ec, 0xe57d5fda, 0x7d3833a2, 0xe5773a44, 0x7d36e60b, 0xe57114be,
+    0x7d359827, 0xe56aef49,
+  0x7d3449f5, 0xe564c9e3, 0x7d32fb76, 0xe55ea48f, 0x7d31acaa, 0xe5587f4a,
+    0x7d305d91, 0xe5525a17,
+  0x7d2f0e2b, 0xe54c34f3, 0x7d2dbe77, 0xe5460fe0, 0x7d2c6e76, 0xe53feade,
+    0x7d2b1e28, 0xe539c5ec,
+  0x7d29cd8c, 0xe533a10a, 0x7d287ca4, 0xe52d7c39, 0x7d272b6e, 0xe5275779,
+    0x7d25d9eb, 0xe52132c9,
+  0x7d24881b, 0xe51b0e2a, 0x7d2335fe, 0xe514e99b, 0x7d21e393, 0xe50ec51d,
+    0x7d2090db, 0xe508a0b0,
+  0x7d1f3dd6, 0xe5027c53, 0x7d1dea84, 0xe4fc5807, 0x7d1c96e5, 0xe4f633cc,
+    0x7d1b42f9, 0xe4f00fa1,
+  0x7d19eebf, 0xe4e9eb87, 0x7d189a38, 0xe4e3c77d, 0x7d174564, 0xe4dda385,
+    0x7d15f043, 0xe4d77f9d,
+  0x7d149ad5, 0xe4d15bc6, 0x7d134519, 0xe4cb37ff, 0x7d11ef11, 0xe4c5144a,
+    0x7d1098bb, 0xe4bef0a5,
+  0x7d0f4218, 0xe4b8cd11, 0x7d0deb28, 0xe4b2a98e, 0x7d0c93eb, 0xe4ac861b,
+    0x7d0b3c60, 0xe4a662ba,
+  0x7d09e489, 0xe4a03f69, 0x7d088c64, 0xe49a1c29, 0x7d0733f3, 0xe493f8fb,
+    0x7d05db34, 0xe48dd5dd,
+  0x7d048228, 0xe487b2d0, 0x7d0328cf, 0xe4818fd4, 0x7d01cf29, 0xe47b6ce9,
+    0x7d007535, 0xe4754a0e,
+  0x7cff1af5, 0xe46f2745, 0x7cfdc068, 0xe469048d, 0x7cfc658d, 0xe462e1e6,
+    0x7cfb0a65, 0xe45cbf50,
+  0x7cf9aef0, 0xe4569ccb, 0x7cf8532f, 0xe4507a57, 0x7cf6f720, 0xe44a57f4,
+    0x7cf59ac4, 0xe44435a2,
+  0x7cf43e1a, 0xe43e1362, 0x7cf2e124, 0xe437f132, 0x7cf183e1, 0xe431cf14,
+    0x7cf02651, 0xe42bad07,
+  0x7ceec873, 0xe4258b0a, 0x7ced6a49, 0xe41f6920, 0x7cec0bd1, 0xe4194746,
+    0x7ceaad0c, 0xe413257d,
+  0x7ce94dfb, 0xe40d03c6, 0x7ce7ee9c, 0xe406e220, 0x7ce68ef0, 0xe400c08b,
+    0x7ce52ef7, 0xe3fa9f08,
+  0x7ce3ceb2, 0xe3f47d96, 0x7ce26e1f, 0xe3ee5c35, 0x7ce10d3f, 0xe3e83ae5,
+    0x7cdfac12, 0xe3e219a7,
+  0x7cde4a98, 0xe3dbf87a, 0x7cdce8d1, 0xe3d5d75e, 0x7cdb86bd, 0xe3cfb654,
+    0x7cda245c, 0xe3c9955b,
+  0x7cd8c1ae, 0xe3c37474, 0x7cd75eb3, 0xe3bd539e, 0x7cd5fb6a, 0xe3b732d9,
+    0x7cd497d5, 0xe3b11226,
+  0x7cd333f3, 0xe3aaf184, 0x7cd1cfc4, 0xe3a4d0f4, 0x7cd06b48, 0xe39eb075,
+    0x7ccf067f, 0xe3989008,
+  0x7ccda169, 0xe3926fad, 0x7ccc3c06, 0xe38c4f63, 0x7ccad656, 0xe3862f2a,
+    0x7cc97059, 0xe3800f03,
+  0x7cc80a0f, 0xe379eeed, 0x7cc6a378, 0xe373ceea, 0x7cc53c94, 0xe36daef7,
+    0x7cc3d563, 0xe3678f17,
+  0x7cc26de5, 0xe3616f48, 0x7cc1061a, 0xe35b4f8b, 0x7cbf9e03, 0xe3552fdf,
+    0x7cbe359e, 0xe34f1045,
+  0x7cbcccec, 0xe348f0bd, 0x7cbb63ee, 0xe342d146, 0x7cb9faa2, 0xe33cb1e1,
+    0x7cb8910a, 0xe336928e,
+  0x7cb72724, 0xe330734d, 0x7cb5bcf2, 0xe32a541d, 0x7cb45272, 0xe3243500,
+    0x7cb2e7a6, 0xe31e15f4,
+  0x7cb17c8d, 0xe317f6fa, 0x7cb01127, 0xe311d811, 0x7caea574, 0xe30bb93b,
+    0x7cad3974, 0xe3059a76,
+  0x7cabcd28, 0xe2ff7bc3, 0x7caa608e, 0xe2f95d23, 0x7ca8f3a7, 0xe2f33e94,
+    0x7ca78674, 0xe2ed2017,
+  0x7ca618f3, 0xe2e701ac, 0x7ca4ab26, 0xe2e0e352, 0x7ca33d0c, 0xe2dac50b,
+    0x7ca1cea5, 0xe2d4a6d6,
+  0x7ca05ff1, 0xe2ce88b3, 0x7c9ef0f0, 0xe2c86aa2, 0x7c9d81a3, 0xe2c24ca2,
+    0x7c9c1208, 0xe2bc2eb5,
+  0x7c9aa221, 0xe2b610da, 0x7c9931ec, 0xe2aff311, 0x7c97c16b, 0xe2a9d55a,
+    0x7c96509d, 0xe2a3b7b5,
+  0x7c94df83, 0xe29d9a23, 0x7c936e1b, 0xe2977ca2, 0x7c91fc66, 0xe2915f34,
+    0x7c908a65, 0xe28b41d7,
+  0x7c8f1817, 0xe285248d, 0x7c8da57c, 0xe27f0755, 0x7c8c3294, 0xe278ea30,
+    0x7c8abf5f, 0xe272cd1c,
+  0x7c894bde, 0xe26cb01b, 0x7c87d810, 0xe266932c, 0x7c8663f4, 0xe260764f,
+    0x7c84ef8c, 0xe25a5984,
+  0x7c837ad8, 0xe2543ccc, 0x7c8205d6, 0xe24e2026, 0x7c809088, 0xe2480393,
+    0x7c7f1aed, 0xe241e711,
+  0x7c7da505, 0xe23bcaa2, 0x7c7c2ed0, 0xe235ae46, 0x7c7ab84e, 0xe22f91fc,
+    0x7c794180, 0xe22975c4,
+  0x7c77ca65, 0xe223599e, 0x7c7652fd, 0xe21d3d8b, 0x7c74db48, 0xe217218b,
+    0x7c736347, 0xe211059d,
+  0x7c71eaf9, 0xe20ae9c1, 0x7c70725e, 0xe204cdf8, 0x7c6ef976, 0xe1feb241,
+    0x7c6d8041, 0xe1f8969d,
+  0x7c6c06c0, 0xe1f27b0b, 0x7c6a8cf2, 0xe1ec5f8c, 0x7c6912d7, 0xe1e64420,
+    0x7c679870, 0xe1e028c6,
+  0x7c661dbc, 0xe1da0d7e, 0x7c64a2bb, 0xe1d3f24a, 0x7c63276d, 0xe1cdd727,
+    0x7c61abd3, 0xe1c7bc18,
+  0x7c602fec, 0xe1c1a11b, 0x7c5eb3b8, 0xe1bb8631, 0x7c5d3737, 0xe1b56b59,
+    0x7c5bba6a, 0xe1af5094,
+  0x7c5a3d50, 0xe1a935e2, 0x7c58bfe9, 0xe1a31b42, 0x7c574236, 0xe19d00b6,
+    0x7c55c436, 0xe196e63c,
+  0x7c5445e9, 0xe190cbd4, 0x7c52c74f, 0xe18ab180, 0x7c514869, 0xe184973e,
+    0x7c4fc936, 0xe17e7d0f,
+  0x7c4e49b7, 0xe17862f3, 0x7c4cc9ea, 0xe17248ea, 0x7c4b49d2, 0xe16c2ef4,
+    0x7c49c96c, 0xe1661510,
+  0x7c4848ba, 0xe15ffb3f, 0x7c46c7bb, 0xe159e182, 0x7c45466f, 0xe153c7d7,
+    0x7c43c4d7, 0xe14dae3f,
+  0x7c4242f2, 0xe14794ba, 0x7c40c0c1, 0xe1417b48, 0x7c3f3e42, 0xe13b61e9,
+    0x7c3dbb78, 0xe135489d,
+  0x7c3c3860, 0xe12f2f63, 0x7c3ab4fc, 0xe129163d, 0x7c39314b, 0xe122fd2a,
+    0x7c37ad4e, 0xe11ce42a,
+  0x7c362904, 0xe116cb3d, 0x7c34a46d, 0xe110b263, 0x7c331f8a, 0xe10a999c,
+    0x7c319a5a, 0xe10480e9,
+  0x7c3014de, 0xe0fe6848, 0x7c2e8f15, 0xe0f84fbb, 0x7c2d08ff, 0xe0f23740,
+    0x7c2b829d, 0xe0ec1ed9,
+  0x7c29fbee, 0xe0e60685, 0x7c2874f3, 0xe0dfee44, 0x7c26edab, 0xe0d9d616,
+    0x7c256616, 0xe0d3bdfc,
+  0x7c23de35, 0xe0cda5f5, 0x7c225607, 0xe0c78e01, 0x7c20cd8d, 0xe0c17620,
+    0x7c1f44c6, 0xe0bb5e53,
+  0x7c1dbbb3, 0xe0b54698, 0x7c1c3253, 0xe0af2ef2, 0x7c1aa8a6, 0xe0a9175e,
+    0x7c191ead, 0xe0a2ffde,
+  0x7c179467, 0xe09ce871, 0x7c1609d5, 0xe096d117, 0x7c147ef6, 0xe090b9d1,
+    0x7c12f3cb, 0xe08aa29f,
+  0x7c116853, 0xe0848b7f, 0x7c0fdc8f, 0xe07e7473, 0x7c0e507e, 0xe0785d7b,
+    0x7c0cc421, 0xe0724696,
+  0x7c0b3777, 0xe06c2fc4, 0x7c09aa80, 0xe0661906, 0x7c081d3d, 0xe060025c,
+    0x7c068fae, 0xe059ebc5,
+  0x7c0501d2, 0xe053d541, 0x7c0373a9, 0xe04dbed1, 0x7c01e534, 0xe047a875,
+    0x7c005673, 0xe041922c,
+  0x7bfec765, 0xe03b7bf6, 0x7bfd380a, 0xe03565d5, 0x7bfba863, 0xe02f4fc6,
+    0x7bfa1870, 0xe02939cc,
+  0x7bf88830, 0xe02323e5, 0x7bf6f7a4, 0xe01d0e12, 0x7bf566cb, 0xe016f852,
+    0x7bf3d5a6, 0xe010e2a7,
+  0x7bf24434, 0xe00acd0e, 0x7bf0b276, 0xe004b78a, 0x7bef206b, 0xdffea219,
+    0x7bed8e14, 0xdff88cbc,
+  0x7bebfb70, 0xdff27773, 0x7bea6880, 0xdfec623e, 0x7be8d544, 0xdfe64d1c,
+    0x7be741bb, 0xdfe0380e,
+  0x7be5ade6, 0xdfda2314, 0x7be419c4, 0xdfd40e2e, 0x7be28556, 0xdfcdf95c,
+    0x7be0f09b, 0xdfc7e49d,
+  0x7bdf5b94, 0xdfc1cff3, 0x7bddc641, 0xdfbbbb5c, 0x7bdc30a1, 0xdfb5a6d9,
+    0x7bda9ab5, 0xdfaf926a,
+  0x7bd9047c, 0xdfa97e0f, 0x7bd76df7, 0xdfa369c8, 0x7bd5d726, 0xdf9d5595,
+    0x7bd44008, 0xdf974176,
+  0x7bd2a89e, 0xdf912d6b, 0x7bd110e8, 0xdf8b1974, 0x7bcf78e5, 0xdf850591,
+    0x7bcde095, 0xdf7ef1c2,
+  0x7bcc47fa, 0xdf78de07, 0x7bcaaf12, 0xdf72ca60, 0x7bc915dd, 0xdf6cb6cd,
+    0x7bc77c5d, 0xdf66a34e,
+  0x7bc5e290, 0xdf608fe4, 0x7bc44876, 0xdf5a7c8d, 0x7bc2ae10, 0xdf54694b,
+    0x7bc1135e, 0xdf4e561c,
+  0x7bbf7860, 0xdf484302, 0x7bbddd15, 0xdf422ffd, 0x7bbc417e, 0xdf3c1d0b,
+    0x7bbaa59a, 0xdf360a2d,
+  0x7bb9096b, 0xdf2ff764, 0x7bb76cef, 0xdf29e4af, 0x7bb5d026, 0xdf23d20e,
+    0x7bb43311, 0xdf1dbf82,
+  0x7bb295b0, 0xdf17ad0a, 0x7bb0f803, 0xdf119aa6, 0x7baf5a09, 0xdf0b8856,
+    0x7badbbc3, 0xdf05761b,
+  0x7bac1d31, 0xdeff63f4, 0x7baa7e53, 0xdef951e2, 0x7ba8df28, 0xdef33fe3,
+    0x7ba73fb1, 0xdeed2dfa,
+  0x7ba59fee, 0xdee71c24, 0x7ba3ffde, 0xdee10a63, 0x7ba25f82, 0xdedaf8b7,
+    0x7ba0beda, 0xded4e71f,
+  0x7b9f1de6, 0xdeced59b, 0x7b9d7ca5, 0xdec8c42c, 0x7b9bdb18, 0xdec2b2d1,
+    0x7b9a393f, 0xdebca18b,
+  0x7b989719, 0xdeb69059, 0x7b96f4a8, 0xdeb07f3c, 0x7b9551ea, 0xdeaa6e34,
+    0x7b93aee0, 0xdea45d40,
+  0x7b920b89, 0xde9e4c60, 0x7b9067e7, 0xde983b95, 0x7b8ec3f8, 0xde922adf,
+    0x7b8d1fbd, 0xde8c1a3e,
+  0x7b8b7b36, 0xde8609b1, 0x7b89d662, 0xde7ff938, 0x7b883143, 0xde79e8d5,
+    0x7b868bd7, 0xde73d886,
+  0x7b84e61f, 0xde6dc84b, 0x7b83401b, 0xde67b826, 0x7b8199ca, 0xde61a815,
+    0x7b7ff32e, 0xde5b9819,
+  0x7b7e4c45, 0xde558831, 0x7b7ca510, 0xde4f785f, 0x7b7afd8f, 0xde4968a1,
+    0x7b7955c2, 0xde4358f8,
+  0x7b77ada8, 0xde3d4964, 0x7b760542, 0xde3739e4, 0x7b745c91, 0xde312a7a,
+    0x7b72b393, 0xde2b1b24,
+  0x7b710a49, 0xde250be3, 0x7b6f60b2, 0xde1efcb7, 0x7b6db6d0, 0xde18eda0,
+    0x7b6c0ca2, 0xde12de9e,
+  0x7b6a6227, 0xde0ccfb1, 0x7b68b760, 0xde06c0d9, 0x7b670c4d, 0xde00b216,
+    0x7b6560ee, 0xddfaa367,
+  0x7b63b543, 0xddf494ce, 0x7b62094c, 0xddee8649, 0x7b605d09, 0xdde877da,
+    0x7b5eb079, 0xdde26980,
+  0x7b5d039e, 0xdddc5b3b, 0x7b5b5676, 0xddd64d0a, 0x7b59a902, 0xddd03eef,
+    0x7b57fb42, 0xddca30e9,
+  0x7b564d36, 0xddc422f8, 0x7b549ede, 0xddbe151d, 0x7b52f03a, 0xddb80756,
+    0x7b51414a, 0xddb1f9a4,
+  0x7b4f920e, 0xddabec08, 0x7b4de286, 0xdda5de81, 0x7b4c32b1, 0xdd9fd10f,
+    0x7b4a8291, 0xdd99c3b2,
+  0x7b48d225, 0xdd93b66a, 0x7b47216c, 0xdd8da938, 0x7b457068, 0xdd879c1b,
+    0x7b43bf17, 0xdd818f13,
+  0x7b420d7a, 0xdd7b8220, 0x7b405b92, 0xdd757543, 0x7b3ea95d, 0xdd6f687b,
+    0x7b3cf6dc, 0xdd695bc9,
+  0x7b3b4410, 0xdd634f2b, 0x7b3990f7, 0xdd5d42a3, 0x7b37dd92, 0xdd573631,
+    0x7b3629e1, 0xdd5129d4,
+  0x7b3475e5, 0xdd4b1d8c, 0x7b32c19c, 0xdd451159, 0x7b310d07, 0xdd3f053c,
+    0x7b2f5826, 0xdd38f935,
+  0x7b2da2fa, 0xdd32ed43, 0x7b2bed81, 0xdd2ce166, 0x7b2a37bc, 0xdd26d59f,
+    0x7b2881ac, 0xdd20c9ed,
+  0x7b26cb4f, 0xdd1abe51, 0x7b2514a6, 0xdd14b2ca, 0x7b235db2, 0xdd0ea759,
+    0x7b21a671, 0xdd089bfe,
+  0x7b1feee5, 0xdd0290b8, 0x7b1e370d, 0xdcfc8588, 0x7b1c7ee8, 0xdcf67a6d,
+    0x7b1ac678, 0xdcf06f68,
+  0x7b190dbc, 0xdcea6478, 0x7b1754b3, 0xdce4599e, 0x7b159b5f, 0xdcde4eda,
+    0x7b13e1bf, 0xdcd8442b,
+  0x7b1227d3, 0xdcd23993, 0x7b106d9b, 0xdccc2f0f, 0x7b0eb318, 0xdcc624a2,
+    0x7b0cf848, 0xdcc01a4a,
+  0x7b0b3d2c, 0xdcba1008, 0x7b0981c5, 0xdcb405dc, 0x7b07c612, 0xdcadfbc5,
+    0x7b060a12, 0xdca7f1c5,
+  0x7b044dc7, 0xdca1e7da, 0x7b029130, 0xdc9bde05, 0x7b00d44d, 0xdc95d446,
+    0x7aff171e, 0xdc8fca9c,
+  0x7afd59a4, 0xdc89c109, 0x7afb9bdd, 0xdc83b78b, 0x7af9ddcb, 0xdc7dae23,
+    0x7af81f6c, 0xdc77a4d2,
+  0x7af660c2, 0xdc719b96, 0x7af4a1cc, 0xdc6b9270, 0x7af2e28b, 0xdc658960,
+    0x7af122fd, 0xdc5f8066,
+  0x7aef6323, 0xdc597781, 0x7aeda2fe, 0xdc536eb3, 0x7aebe28d, 0xdc4d65fb,
+    0x7aea21d0, 0xdc475d59,
+  0x7ae860c7, 0xdc4154cd, 0x7ae69f73, 0xdc3b4c57, 0x7ae4ddd2, 0xdc3543f7,
+    0x7ae31be6, 0xdc2f3bad,
+  0x7ae159ae, 0xdc293379, 0x7adf972a, 0xdc232b5c, 0x7addd45b, 0xdc1d2354,
+    0x7adc113f, 0xdc171b63,
+  0x7ada4dd8, 0xdc111388, 0x7ad88a25, 0xdc0b0bc2, 0x7ad6c626, 0xdc050414,
+    0x7ad501dc, 0xdbfefc7b,
+  0x7ad33d45, 0xdbf8f4f8, 0x7ad17863, 0xdbf2ed8c, 0x7acfb336, 0xdbece636,
+    0x7acdedbc, 0xdbe6def6,
+  0x7acc27f7, 0xdbe0d7cd, 0x7aca61e6, 0xdbdad0b9, 0x7ac89b89, 0xdbd4c9bc,
+    0x7ac6d4e0, 0xdbcec2d6,
+  0x7ac50dec, 0xdbc8bc06, 0x7ac346ac, 0xdbc2b54c, 0x7ac17f20, 0xdbbcaea8,
+    0x7abfb749, 0xdbb6a81b,
+  0x7abdef25, 0xdbb0a1a4, 0x7abc26b7, 0xdbaa9b43, 0x7aba5dfc, 0xdba494f9,
+    0x7ab894f6, 0xdb9e8ec6,
+  0x7ab6cba4, 0xdb9888a8, 0x7ab50206, 0xdb9282a2, 0x7ab3381d, 0xdb8c7cb1,
+    0x7ab16de7, 0xdb8676d8,
+  0x7aafa367, 0xdb807114, 0x7aadd89a, 0xdb7a6b68, 0x7aac0d82, 0xdb7465d1,
+    0x7aaa421e, 0xdb6e6052,
+  0x7aa8766f, 0xdb685ae9, 0x7aa6aa74, 0xdb625596, 0x7aa4de2d, 0xdb5c505a,
+    0x7aa3119a, 0xdb564b35,
+  0x7aa144bc, 0xdb504626, 0x7a9f7793, 0xdb4a412e, 0x7a9daa1d, 0xdb443c4c,
+    0x7a9bdc5c, 0xdb3e3781,
+  0x7a9a0e50, 0xdb3832cd, 0x7a983ff7, 0xdb322e30, 0x7a967153, 0xdb2c29a9,
+    0x7a94a264, 0xdb262539,
+  0x7a92d329, 0xdb2020e0, 0x7a9103a2, 0xdb1a1c9d, 0x7a8f33d0, 0xdb141871,
+    0x7a8d63b2, 0xdb0e145c,
+  0x7a8b9348, 0xdb08105e, 0x7a89c293, 0xdb020c77, 0x7a87f192, 0xdafc08a6,
+    0x7a862046, 0xdaf604ec,
+  0x7a844eae, 0xdaf00149, 0x7a827ccb, 0xdae9fdbd, 0x7a80aa9c, 0xdae3fa48,
+    0x7a7ed821, 0xdaddf6ea,
+  0x7a7d055b, 0xdad7f3a2, 0x7a7b3249, 0xdad1f072, 0x7a795eec, 0xdacbed58,
+    0x7a778b43, 0xdac5ea56,
+  0x7a75b74f, 0xdabfe76a, 0x7a73e30f, 0xdab9e495, 0x7a720e84, 0xdab3e1d8,
+    0x7a7039ad, 0xdaaddf31,
+  0x7a6e648a, 0xdaa7dca1, 0x7a6c8f1c, 0xdaa1da29, 0x7a6ab963, 0xda9bd7c7,
+    0x7a68e35e, 0xda95d57d,
+  0x7a670d0d, 0xda8fd349, 0x7a653671, 0xda89d12d, 0x7a635f8a, 0xda83cf28,
+    0x7a618857, 0xda7dcd3a,
+  0x7a5fb0d8, 0xda77cb63, 0x7a5dd90e, 0xda71c9a3, 0x7a5c00f9, 0xda6bc7fa,
+    0x7a5a2898, 0xda65c669,
+  0x7a584feb, 0xda5fc4ef, 0x7a5676f3, 0xda59c38c, 0x7a549db0, 0xda53c240,
+    0x7a52c421, 0xda4dc10b,
+  0x7a50ea47, 0xda47bfee, 0x7a4f1021, 0xda41bee8, 0x7a4d35b0, 0xda3bbdf9,
+    0x7a4b5af3, 0xda35bd22,
+  0x7a497feb, 0xda2fbc61, 0x7a47a498, 0xda29bbb9, 0x7a45c8f9, 0xda23bb27,
+    0x7a43ed0e, 0xda1dbaad,
+  0x7a4210d8, 0xda17ba4a, 0x7a403457, 0xda11b9ff, 0x7a3e578b, 0xda0bb9cb,
+    0x7a3c7a73, 0xda05b9ae,
+  0x7a3a9d0f, 0xd9ffb9a9, 0x7a38bf60, 0xd9f9b9bb, 0x7a36e166, 0xd9f3b9e5,
+    0x7a350321, 0xd9edba26,
+  0x7a332490, 0xd9e7ba7f, 0x7a3145b3, 0xd9e1baef, 0x7a2f668c, 0xd9dbbb77,
+    0x7a2d8719, 0xd9d5bc16,
+  0x7a2ba75a, 0xd9cfbccd, 0x7a29c750, 0xd9c9bd9b, 0x7a27e6fb, 0xd9c3be81,
+    0x7a26065b, 0xd9bdbf7e,
+  0x7a24256f, 0xd9b7c094, 0x7a224437, 0xd9b1c1c0, 0x7a2062b5, 0xd9abc305,
+    0x7a1e80e7, 0xd9a5c461,
+  0x7a1c9ece, 0xd99fc5d4, 0x7a1abc69, 0xd999c75f, 0x7a18d9b9, 0xd993c902,
+    0x7a16f6be, 0xd98dcabd,
+  0x7a151378, 0xd987cc90, 0x7a132fe6, 0xd981ce7a, 0x7a114c09, 0xd97bd07c,
+    0x7a0f67e0, 0xd975d295,
+  0x7a0d836d, 0xd96fd4c7, 0x7a0b9eae, 0xd969d710, 0x7a09b9a4, 0xd963d971,
+    0x7a07d44e, 0xd95ddbea,
+  0x7a05eead, 0xd957de7a, 0x7a0408c1, 0xd951e123, 0x7a02228a, 0xd94be3e3,
+    0x7a003c07, 0xd945e6bb,
+  0x79fe5539, 0xd93fe9ab, 0x79fc6e20, 0xd939ecb3, 0x79fa86bc, 0xd933efd3,
+    0x79f89f0c, 0xd92df30b,
+  0x79f6b711, 0xd927f65b, 0x79f4cecb, 0xd921f9c3, 0x79f2e63a, 0xd91bfd43,
+    0x79f0fd5d, 0xd91600da,
+  0x79ef1436, 0xd910048a, 0x79ed2ac3, 0xd90a0852, 0x79eb4105, 0xd9040c32,
+    0x79e956fb, 0xd8fe1029,
+  0x79e76ca7, 0xd8f81439, 0x79e58207, 0xd8f21861, 0x79e3971c, 0xd8ec1ca1,
+    0x79e1abe6, 0xd8e620fa,
+  0x79dfc064, 0xd8e0256a, 0x79ddd498, 0xd8da29f2, 0x79dbe880, 0xd8d42e93,
+    0x79d9fc1d, 0xd8ce334c,
+  0x79d80f6f, 0xd8c8381d, 0x79d62276, 0xd8c23d06, 0x79d43532, 0xd8bc4207,
+    0x79d247a2, 0xd8b64720,
+  0x79d059c8, 0xd8b04c52, 0x79ce6ba2, 0xd8aa519c, 0x79cc7d31, 0xd8a456ff,
+    0x79ca8e75, 0xd89e5c79,
+  0x79c89f6e, 0xd898620c, 0x79c6b01b, 0xd89267b7, 0x79c4c07e, 0xd88c6d7b,
+    0x79c2d095, 0xd8867356,
+  0x79c0e062, 0xd880794b, 0x79beefe3, 0xd87a7f57, 0x79bcff19, 0xd874857c,
+    0x79bb0e04, 0xd86e8bb9,
+  0x79b91ca4, 0xd868920f, 0x79b72af9, 0xd862987d, 0x79b53903, 0xd85c9f04,
+    0x79b346c2, 0xd856a5a3,
+  0x79b15435, 0xd850ac5a, 0x79af615e, 0xd84ab32a, 0x79ad6e3c, 0xd844ba13,
+    0x79ab7ace, 0xd83ec114,
+  0x79a98715, 0xd838c82d, 0x79a79312, 0xd832cf5f, 0x79a59ec3, 0xd82cd6aa,
+    0x79a3aa29, 0xd826de0d,
+  0x79a1b545, 0xd820e589, 0x799fc015, 0xd81aed1d, 0x799dca9a, 0xd814f4ca,
+    0x799bd4d4, 0xd80efc8f,
+  0x7999dec4, 0xd809046e, 0x7997e868, 0xd8030c64, 0x7995f1c1, 0xd7fd1474,
+    0x7993facf, 0xd7f71c9c,
+  0x79920392, 0xd7f124dd, 0x79900c0a, 0xd7eb2d37, 0x798e1438, 0xd7e535a9,
+    0x798c1c1a, 0xd7df3e34,
+  0x798a23b1, 0xd7d946d8, 0x79882afd, 0xd7d34f94, 0x798631ff, 0xd7cd586a,
+    0x798438b5, 0xd7c76158,
+  0x79823f20, 0xd7c16a5f, 0x79804541, 0xd7bb737f, 0x797e4b16, 0xd7b57cb7,
+    0x797c50a1, 0xd7af8609,
+  0x797a55e0, 0xd7a98f73, 0x79785ad5, 0xd7a398f6, 0x79765f7f, 0xd79da293,
+    0x797463de, 0xd797ac48,
+  0x797267f2, 0xd791b616, 0x79706bbb, 0xd78bbffc, 0x796e6f39, 0xd785c9fc,
+    0x796c726c, 0xd77fd415,
+  0x796a7554, 0xd779de47, 0x796877f1, 0xd773e892, 0x79667a44, 0xd76df2f6,
+    0x79647c4c, 0xd767fd72,
+  0x79627e08, 0xd7620808, 0x79607f7a, 0xd75c12b7, 0x795e80a1, 0xd7561d7f,
+    0x795c817d, 0xd7502860,
+  0x795a820e, 0xd74a335b, 0x79588255, 0xd7443e6e, 0x79568250, 0xd73e499a,
+    0x79548201, 0xd73854e0,
+  0x79528167, 0xd732603f, 0x79508082, 0xd72c6bb6, 0x794e7f52, 0xd7267748,
+    0x794c7dd7, 0xd72082f2,
+  0x794a7c12, 0xd71a8eb5, 0x79487a01, 0xd7149a92, 0x794677a6, 0xd70ea688,
+    0x79447500, 0xd708b297,
+  0x79427210, 0xd702bec0, 0x79406ed4, 0xd6fccb01, 0x793e6b4e, 0xd6f6d75d,
+    0x793c677d, 0xd6f0e3d1,
+  0x793a6361, 0xd6eaf05f, 0x79385efa, 0xd6e4fd06, 0x79365a49, 0xd6df09c6,
+    0x7934554d, 0xd6d916a0,
+  0x79325006, 0xd6d32393, 0x79304a74, 0xd6cd30a0, 0x792e4497, 0xd6c73dc6,
+    0x792c3e70, 0xd6c14b05,
+  0x792a37fe, 0xd6bb585e, 0x79283141, 0xd6b565d0, 0x79262a3a, 0xd6af735c,
+    0x792422e8, 0xd6a98101,
+  0x79221b4b, 0xd6a38ec0, 0x79201363, 0xd69d9c98, 0x791e0b31, 0xd697aa8a,
+    0x791c02b4, 0xd691b895,
+  0x7919f9ec, 0xd68bc6ba, 0x7917f0d9, 0xd685d4f9, 0x7915e77c, 0xd67fe351,
+    0x7913ddd4, 0xd679f1c2,
+  0x7911d3e2, 0xd674004e, 0x790fc9a4, 0xd66e0ef2, 0x790dbf1d, 0xd6681db1,
+    0x790bb44a, 0xd6622c89,
+  0x7909a92d, 0xd65c3b7b, 0x79079dc5, 0xd6564a87, 0x79059212, 0xd65059ac,
+    0x79038615, 0xd64a68eb,
+  0x790179cd, 0xd6447844, 0x78ff6d3b, 0xd63e87b6, 0x78fd605d, 0xd6389742,
+    0x78fb5336, 0xd632a6e8,
+  0x78f945c3, 0xd62cb6a8, 0x78f73806, 0xd626c681, 0x78f529fe, 0xd620d675,
+    0x78f31bac, 0xd61ae682,
+  0x78f10d0f, 0xd614f6a9, 0x78eefe28, 0xd60f06ea, 0x78eceef6, 0xd6091745,
+    0x78eadf79, 0xd60327b9,
+  0x78e8cfb2, 0xd5fd3848, 0x78e6bfa0, 0xd5f748f0, 0x78e4af44, 0xd5f159b3,
+    0x78e29e9d, 0xd5eb6a8f,
+  0x78e08dab, 0xd5e57b85, 0x78de7c6f, 0xd5df8c96, 0x78dc6ae8, 0xd5d99dc0,
+    0x78da5917, 0xd5d3af04,
+  0x78d846fb, 0xd5cdc062, 0x78d63495, 0xd5c7d1db, 0x78d421e4, 0xd5c1e36d,
+    0x78d20ee9, 0xd5bbf519,
+  0x78cffba3, 0xd5b606e0, 0x78cde812, 0xd5b018c0, 0x78cbd437, 0xd5aa2abb,
+    0x78c9c012, 0xd5a43cd0,
+  0x78c7aba2, 0xd59e4eff, 0x78c596e7, 0xd5986148, 0x78c381e2, 0xd59273ab,
+    0x78c16c93, 0xd58c8628,
+  0x78bf56f9, 0xd58698c0, 0x78bd4114, 0xd580ab72, 0x78bb2ae5, 0xd57abe3d,
+    0x78b9146c, 0xd574d124,
+  0x78b6fda8, 0xd56ee424, 0x78b4e69a, 0xd568f73f, 0x78b2cf41, 0xd5630a74,
+    0x78b0b79e, 0xd55d1dc3,
+  0x78ae9fb0, 0xd557312d, 0x78ac8778, 0xd55144b0, 0x78aa6ef5, 0xd54b584f,
+    0x78a85628, 0xd5456c07,
+  0x78a63d11, 0xd53f7fda, 0x78a423af, 0xd53993c7, 0x78a20a03, 0xd533a7cf,
+    0x789ff00c, 0xd52dbbf1,
+  0x789dd5cb, 0xd527d02e, 0x789bbb3f, 0xd521e484, 0x7899a06a, 0xd51bf8f6,
+    0x78978549, 0xd5160d82,
+  0x789569df, 0xd5102228, 0x78934e2a, 0xd50a36e9, 0x7891322a, 0xd5044bc4,
+    0x788f15e0, 0xd4fe60ba,
+  0x788cf94c, 0xd4f875ca, 0x788adc6e, 0xd4f28af5, 0x7888bf45, 0xd4eca03a,
+    0x7886a1d1, 0xd4e6b59a,
+  0x78848414, 0xd4e0cb15, 0x7882660c, 0xd4dae0aa, 0x788047ba, 0xd4d4f65a,
+    0x787e291d, 0xd4cf0c24,
+  0x787c0a36, 0xd4c92209, 0x7879eb05, 0xd4c33809, 0x7877cb89, 0xd4bd4e23,
+    0x7875abc3, 0xd4b76458,
+  0x78738bb3, 0xd4b17aa8, 0x78716b59, 0xd4ab9112, 0x786f4ab4, 0xd4a5a798,
+    0x786d29c5, 0xd49fbe37,
+  0x786b088c, 0xd499d4f2, 0x7868e708, 0xd493ebc8, 0x7866c53a, 0xd48e02b8,
+    0x7864a322, 0xd48819c3,
+  0x786280bf, 0xd48230e9, 0x78605e13, 0xd47c4829, 0x785e3b1c, 0xd4765f85,
+    0x785c17db, 0xd47076fb,
+  0x7859f44f, 0xd46a8e8d, 0x7857d079, 0xd464a639, 0x7855ac5a, 0xd45ebe00,
+    0x785387ef, 0xd458d5e2,
+  0x7851633b, 0xd452eddf, 0x784f3e3c, 0xd44d05f6, 0x784d18f4, 0xd4471e29,
+    0x784af361, 0xd4413677,
+  0x7848cd83, 0xd43b4ee0, 0x7846a75c, 0xd4356763, 0x784480ea, 0xd42f8002,
+    0x78425a2f, 0xd42998bc,
+  0x78403329, 0xd423b191, 0x783e0bd9, 0xd41dca81, 0x783be43e, 0xd417e38c,
+    0x7839bc5a, 0xd411fcb2,
+  0x7837942b, 0xd40c15f3, 0x78356bb2, 0xd4062f4f, 0x783342ef, 0xd40048c6,
+    0x783119e2, 0xd3fa6259,
+  0x782ef08b, 0xd3f47c06, 0x782cc6ea, 0xd3ee95cf, 0x782a9cfe, 0xd3e8afb3,
+    0x782872c8, 0xd3e2c9b2,
+  0x78264849, 0xd3dce3cd, 0x78241d7f, 0xd3d6fe03, 0x7821f26b, 0xd3d11853,
+    0x781fc70d, 0xd3cb32c0,
+  0x781d9b65, 0xd3c54d47, 0x781b6f72, 0xd3bf67ea, 0x78194336, 0xd3b982a8,
+    0x781716b0, 0xd3b39d81,
+  0x7814e9df, 0xd3adb876, 0x7812bcc4, 0xd3a7d385, 0x78108f60, 0xd3a1eeb1,
+    0x780e61b1, 0xd39c09f7,
+  0x780c33b8, 0xd396255a, 0x780a0575, 0xd39040d7, 0x7807d6e9, 0xd38a5c70,
+    0x7805a812, 0xd3847824,
+  0x780378f1, 0xd37e93f4, 0x78014986, 0xd378afdf, 0x77ff19d1, 0xd372cbe6,
+    0x77fce9d2, 0xd36ce808,
+  0x77fab989, 0xd3670446, 0x77f888f6, 0xd361209f, 0x77f65819, 0xd35b3d13,
+    0x77f426f2, 0xd35559a4,
+  0x77f1f581, 0xd34f764f, 0x77efc3c5, 0xd3499317, 0x77ed91c0, 0xd343affa,
+    0x77eb5f71, 0xd33dccf8,
+  0x77e92cd9, 0xd337ea12, 0x77e6f9f6, 0xd3320748, 0x77e4c6c9, 0xd32c2499,
+    0x77e29352, 0xd3264206,
+  0x77e05f91, 0xd3205f8f, 0x77de2b86, 0xd31a7d33, 0x77dbf732, 0xd3149af3,
+    0x77d9c293, 0xd30eb8cf,
+  0x77d78daa, 0xd308d6c7, 0x77d55878, 0xd302f4da, 0x77d322fc, 0xd2fd1309,
+    0x77d0ed35, 0xd2f73154,
+  0x77ceb725, 0xd2f14fba, 0x77cc80cb, 0xd2eb6e3c, 0x77ca4a27, 0xd2e58cdb,
+    0x77c81339, 0xd2dfab95,
+  0x77c5dc01, 0xd2d9ca6a, 0x77c3a47f, 0xd2d3e95c, 0x77c16cb4, 0xd2ce0869,
+    0x77bf349f, 0xd2c82793,
+  0x77bcfc3f, 0xd2c246d8, 0x77bac396, 0xd2bc6639, 0x77b88aa3, 0xd2b685b6,
+    0x77b65166, 0xd2b0a54f,
+  0x77b417df, 0xd2aac504, 0x77b1de0f, 0xd2a4e4d5, 0x77afa3f5, 0xd29f04c2,
+    0x77ad6990, 0xd29924cb,
+  0x77ab2ee2, 0xd29344f0, 0x77a8f3ea, 0xd28d6531, 0x77a6b8a9, 0xd287858e,
+    0x77a47d1d, 0xd281a607,
+  0x77a24148, 0xd27bc69c, 0x77a00529, 0xd275e74d, 0x779dc8c0, 0xd270081b,
+    0x779b8c0e, 0xd26a2904,
+  0x77994f11, 0xd2644a0a, 0x779711cb, 0xd25e6b2b, 0x7794d43b, 0xd2588c69,
+    0x77929661, 0xd252adc3,
+  0x7790583e, 0xd24ccf39, 0x778e19d0, 0xd246f0cb, 0x778bdb19, 0xd241127a,
+    0x77899c19, 0xd23b3444,
+  0x77875cce, 0xd235562b, 0x77851d3a, 0xd22f782f, 0x7782dd5c, 0xd2299a4e,
+    0x77809d35, 0xd223bc8a,
+  0x777e5cc3, 0xd21ddee2, 0x777c1c08, 0xd2180156, 0x7779db03, 0xd21223e7,
+    0x777799b5, 0xd20c4694,
+  0x7775581d, 0xd206695d, 0x7773163b, 0xd2008c43, 0x7770d40f, 0xd1faaf45,
+    0x776e919a, 0xd1f4d263,
+  0x776c4edb, 0xd1eef59e, 0x776a0bd3, 0xd1e918f5, 0x7767c880, 0xd1e33c69,
+    0x776584e5, 0xd1dd5ff9,
+  0x776340ff, 0xd1d783a6, 0x7760fcd0, 0xd1d1a76f, 0x775eb857, 0xd1cbcb54,
+    0x775c7395, 0xd1c5ef56,
+  0x775a2e89, 0xd1c01375, 0x7757e933, 0xd1ba37b0, 0x7755a394, 0xd1b45c08,
+    0x77535dab, 0xd1ae807c,
+  0x77511778, 0xd1a8a50d, 0x774ed0fc, 0xd1a2c9ba, 0x774c8a36, 0xd19cee84,
+    0x774a4327, 0xd197136b,
+  0x7747fbce, 0xd191386e, 0x7745b42c, 0xd18b5d8e, 0x77436c40, 0xd18582ca,
+    0x7741240a, 0xd17fa823,
+  0x773edb8b, 0xd179cd99, 0x773c92c2, 0xd173f32c, 0x773a49b0, 0xd16e18db,
+    0x77380054, 0xd1683ea7,
+  0x7735b6af, 0xd1626490, 0x77336cc0, 0xd15c8a95, 0x77312287, 0xd156b0b7,
+    0x772ed805, 0xd150d6f6,
+  0x772c8d3a, 0xd14afd52, 0x772a4225, 0xd14523cb, 0x7727f6c6, 0xd13f4a60,
+    0x7725ab1f, 0xd1397113,
+  0x77235f2d, 0xd13397e2, 0x772112f2, 0xd12dbece, 0x771ec66e, 0xd127e5d7,
+    0x771c79a0, 0xd1220cfc,
+  0x771a2c88, 0xd11c343f, 0x7717df27, 0xd1165b9f, 0x7715917d, 0xd110831b,
+    0x77134389, 0xd10aaab5,
+  0x7710f54c, 0xd104d26b, 0x770ea6c5, 0xd0fefa3f, 0x770c57f5, 0xd0f9222f,
+    0x770a08dc, 0xd0f34a3d,
+  0x7707b979, 0xd0ed7267, 0x770569cc, 0xd0e79aaf, 0x770319d6, 0xd0e1c313,
+    0x7700c997, 0xd0dbeb95,
+  0x76fe790e, 0xd0d61434, 0x76fc283c, 0xd0d03cf0, 0x76f9d721, 0xd0ca65c9,
+    0x76f785bc, 0xd0c48ebf,
+  0x76f5340e, 0xd0beb7d2, 0x76f2e216, 0xd0b8e102, 0x76f08fd5, 0xd0b30a50,
+    0x76ee3d4b, 0xd0ad33ba,
+  0x76ebea77, 0xd0a75d42, 0x76e9975a, 0xd0a186e7, 0x76e743f4, 0xd09bb0aa,
+    0x76e4f044, 0xd095da89,
+  0x76e29c4b, 0xd0900486, 0x76e04808, 0xd08a2ea0, 0x76ddf37c, 0xd08458d7,
+    0x76db9ea7, 0xd07e832c,
+  0x76d94989, 0xd078ad9e, 0x76d6f421, 0xd072d82d, 0x76d49e70, 0xd06d02da,
+    0x76d24876, 0xd0672da3,
+  0x76cff232, 0xd061588b, 0x76cd9ba5, 0xd05b838f, 0x76cb44cf, 0xd055aeb1,
+    0x76c8edb0, 0xd04fd9f1,
+  0x76c69647, 0xd04a054e, 0x76c43e95, 0xd04430c8, 0x76c1e699, 0xd03e5c60,
+    0x76bf8e55, 0xd0388815,
+  0x76bd35c7, 0xd032b3e7, 0x76badcf0, 0xd02cdfd8, 0x76b883d0, 0xd0270be5,
+    0x76b62a66, 0xd0213810,
+  0x76b3d0b4, 0xd01b6459, 0x76b176b8, 0xd01590bf, 0x76af1c72, 0xd00fbd43,
+    0x76acc1e4, 0xd009e9e4,
+  0x76aa670d, 0xd00416a3, 0x76a80bec, 0xcffe4380, 0x76a5b082, 0xcff8707a,
+    0x76a354cf, 0xcff29d92,
+  0x76a0f8d2, 0xcfeccac7, 0x769e9c8d, 0xcfe6f81a, 0x769c3ffe, 0xcfe1258b,
+    0x7699e326, 0xcfdb531a,
+  0x76978605, 0xcfd580c6, 0x7695289b, 0xcfcfae8f, 0x7692cae8, 0xcfc9dc77,
+    0x76906ceb, 0xcfc40a7c,
+  0x768e0ea6, 0xcfbe389f, 0x768bb017, 0xcfb866e0, 0x7689513f, 0xcfb2953f,
+    0x7686f21e, 0xcfacc3bb,
+  0x768492b4, 0xcfa6f255, 0x76823301, 0xcfa1210d, 0x767fd304, 0xcf9b4fe3,
+    0x767d72bf, 0xcf957ed7,
+  0x767b1231, 0xcf8fade9, 0x7678b159, 0xcf89dd18, 0x76765038, 0xcf840c65,
+    0x7673eecf, 0xcf7e3bd1,
+  0x76718d1c, 0xcf786b5a, 0x766f2b20, 0xcf729b01, 0x766cc8db, 0xcf6ccac6,
+    0x766a664d, 0xcf66faa9,
+  0x76680376, 0xcf612aaa, 0x7665a056, 0xcf5b5ac9, 0x76633ced, 0xcf558b06,
+    0x7660d93b, 0xcf4fbb61,
+  0x765e7540, 0xcf49ebda, 0x765c10fc, 0xcf441c71, 0x7659ac6f, 0xcf3e4d26,
+    0x76574798, 0xcf387dfa,
+  0x7654e279, 0xcf32aeeb, 0x76527d11, 0xcf2cdffa, 0x76501760, 0xcf271128,
+    0x764db166, 0xcf214274,
+  0x764b4b23, 0xcf1b73de, 0x7648e497, 0xcf15a566, 0x76467dc2, 0xcf0fd70c,
+    0x764416a4, 0xcf0a08d0,
+  0x7641af3d, 0xcf043ab3, 0x763f478d, 0xcefe6cb3, 0x763cdf94, 0xcef89ed2,
+    0x763a7752, 0xcef2d110,
+  0x76380ec8, 0xceed036b, 0x7635a5f4, 0xcee735e5, 0x76333cd8, 0xcee1687d,
+    0x7630d372, 0xcedb9b33,
+  0x762e69c4, 0xced5ce08, 0x762bffcd, 0xced000fb, 0x7629958c, 0xceca340c,
+    0x76272b03, 0xcec4673c,
+  0x7624c031, 0xcebe9a8a, 0x76225517, 0xceb8cdf7, 0x761fe9b3, 0xceb30181,
+    0x761d7e06, 0xcead352b,
+  0x761b1211, 0xcea768f2, 0x7618a5d3, 0xcea19cd8, 0x7616394c, 0xce9bd0dd,
+    0x7613cc7c, 0xce960500,
+  0x76115f63, 0xce903942, 0x760ef201, 0xce8a6da2, 0x760c8457, 0xce84a220,
+    0x760a1664, 0xce7ed6bd,
+  0x7607a828, 0xce790b79, 0x760539a3, 0xce734053, 0x7602cad5, 0xce6d754c,
+    0x76005bbf, 0xce67aa63,
+  0x75fdec60, 0xce61df99, 0x75fb7cb8, 0xce5c14ed, 0x75f90cc7, 0xce564a60,
+    0x75f69c8d, 0xce507ff2,
+  0x75f42c0b, 0xce4ab5a2, 0x75f1bb40, 0xce44eb71, 0x75ef4a2c, 0xce3f215f,
+    0x75ecd8cf, 0xce39576c,
+  0x75ea672a, 0xce338d97, 0x75e7f53c, 0xce2dc3e1, 0x75e58305, 0xce27fa49,
+    0x75e31086, 0xce2230d0,
+  0x75e09dbd, 0xce1c6777, 0x75de2aac, 0xce169e3b, 0x75dbb753, 0xce10d51f,
+    0x75d943b0, 0xce0b0c21,
+  0x75d6cfc5, 0xce054343, 0x75d45b92, 0xcdff7a83, 0x75d1e715, 0xcdf9b1e2,
+    0x75cf7250, 0xcdf3e95f,
+  0x75ccfd42, 0xcdee20fc, 0x75ca87ec, 0xcde858b8, 0x75c8124d, 0xcde29092,
+    0x75c59c65, 0xcddcc88b,
+  0x75c32634, 0xcdd700a4, 0x75c0afbb, 0xcdd138db, 0x75be38fa, 0xcdcb7131,
+    0x75bbc1ef, 0xcdc5a9a6,
+  0x75b94a9c, 0xcdbfe23a, 0x75b6d301, 0xcdba1aee, 0x75b45b1d, 0xcdb453c0,
+    0x75b1e2f0, 0xcdae8cb1,
+  0x75af6a7b, 0xcda8c5c1, 0x75acf1bd, 0xcda2fef0, 0x75aa78b6, 0xcd9d383f,
+    0x75a7ff67, 0xcd9771ac,
+  0x75a585cf, 0xcd91ab39, 0x75a30bef, 0xcd8be4e4, 0x75a091c6, 0xcd861eaf,
+    0x759e1755, 0xcd805899,
+  0x759b9c9b, 0xcd7a92a2, 0x75992198, 0xcd74ccca, 0x7596a64d, 0xcd6f0711,
+    0x75942ab9, 0xcd694178,
+  0x7591aedd, 0xcd637bfe, 0x758f32b9, 0xcd5db6a3, 0x758cb64c, 0xcd57f167,
+    0x758a3996, 0xcd522c4a,
+  0x7587bc98, 0xcd4c674d, 0x75853f51, 0xcd46a26f, 0x7582c1c2, 0xcd40ddb0,
+    0x758043ea, 0xcd3b1911,
+  0x757dc5ca, 0xcd355491, 0x757b4762, 0xcd2f9030, 0x7578c8b0, 0xcd29cbee,
+    0x757649b7, 0xcd2407cc,
+  0x7573ca75, 0xcd1e43ca, 0x75714aea, 0xcd187fe6, 0x756ecb18, 0xcd12bc22,
+    0x756c4afc, 0xcd0cf87e,
+  0x7569ca99, 0xcd0734f9, 0x756749ec, 0xcd017193, 0x7564c8f8, 0xccfbae4d,
+    0x756247bb, 0xccf5eb26,
+  0x755fc635, 0xccf0281f, 0x755d4467, 0xccea6538, 0x755ac251, 0xcce4a26f,
+    0x75583ff3, 0xccdedfc7,
+  0x7555bd4c, 0xccd91d3d, 0x75533a5c, 0xccd35ad4, 0x7550b725, 0xcccd988a,
+    0x754e33a4, 0xccc7d65f,
+  0x754bafdc, 0xccc21455, 0x75492bcb, 0xccbc5269, 0x7546a772, 0xccb6909e,
+    0x754422d0, 0xccb0cef2,
+  0x75419de7, 0xccab0d65, 0x753f18b4, 0xcca54bf9, 0x753c933a, 0xcc9f8aac,
+    0x753a0d77, 0xcc99c97e,
+  0x7537876c, 0xcc940871, 0x75350118, 0xcc8e4783, 0x75327a7d, 0xcc8886b5,
+    0x752ff399, 0xcc82c607,
+  0x752d6c6c, 0xcc7d0578, 0x752ae4f8, 0xcc774509, 0x75285d3b, 0xcc7184ba,
+    0x7525d536, 0xcc6bc48b,
+  0x75234ce8, 0xcc66047b, 0x7520c453, 0xcc60448c, 0x751e3b75, 0xcc5a84bc,
+    0x751bb24f, 0xcc54c50c,
+  0x751928e0, 0xcc4f057c, 0x75169f2a, 0xcc49460c, 0x7514152b, 0xcc4386bc,
+    0x75118ae4, 0xcc3dc78b,
+  0x750f0054, 0xcc38087b, 0x750c757d, 0xcc32498a, 0x7509ea5d, 0xcc2c8aba,
+    0x75075ef5, 0xcc26cc09,
+  0x7504d345, 0xcc210d79, 0x7502474d, 0xcc1b4f08, 0x74ffbb0d, 0xcc1590b8,
+    0x74fd2e84, 0xcc0fd287,
+  0x74faa1b3, 0xcc0a1477, 0x74f8149a, 0xcc045686, 0x74f58739, 0xcbfe98b6,
+    0x74f2f990, 0xcbf8db05,
+  0x74f06b9e, 0xcbf31d75, 0x74eddd65, 0xcbed6005, 0x74eb4ee3, 0xcbe7a2b5,
+    0x74e8c01a, 0xcbe1e585,
+  0x74e63108, 0xcbdc2876, 0x74e3a1ae, 0xcbd66b86, 0x74e1120c, 0xcbd0aeb7,
+    0x74de8221, 0xcbcaf208,
+  0x74dbf1ef, 0xcbc53579, 0x74d96175, 0xcbbf790a, 0x74d6d0b2, 0xcbb9bcbb,
+    0x74d43fa8, 0xcbb4008d,
+  0x74d1ae55, 0xcbae447f, 0x74cf1cbb, 0xcba88891, 0x74cc8ad8, 0xcba2ccc4,
+    0x74c9f8ad, 0xcb9d1117,
+  0x74c7663a, 0xcb97558a, 0x74c4d380, 0xcb919a1d, 0x74c2407d, 0xcb8bded1,
+    0x74bfad32, 0xcb8623a5,
+  0x74bd199f, 0xcb80689a, 0x74ba85c4, 0xcb7aadaf, 0x74b7f1a1, 0xcb74f2e4,
+    0x74b55d36, 0xcb6f383a,
+  0x74b2c884, 0xcb697db0, 0x74b03389, 0xcb63c347, 0x74ad9e46, 0xcb5e08fe,
+    0x74ab08bb, 0xcb584ed6,
+  0x74a872e8, 0xcb5294ce, 0x74a5dccd, 0xcb4cdae6, 0x74a3466b, 0xcb47211f,
+    0x74a0afc0, 0xcb416779,
+  0x749e18cd, 0xcb3badf3, 0x749b8193, 0xcb35f48d, 0x7498ea11, 0xcb303b49,
+    0x74965246, 0xcb2a8224,
+  0x7493ba34, 0xcb24c921, 0x749121da, 0xcb1f103e, 0x748e8938, 0xcb19577b,
+    0x748bf04d, 0xcb139ed9,
+  0x7489571c, 0xcb0de658, 0x7486bda2, 0xcb082df8, 0x748423e0, 0xcb0275b8,
+    0x748189d7, 0xcafcbd99,
+  0x747eef85, 0xcaf7059a, 0x747c54ec, 0xcaf14dbd, 0x7479ba0b, 0xcaeb9600,
+    0x74771ee2, 0xcae5de64,
+  0x74748371, 0xcae026e8, 0x7471e7b8, 0xcada6f8d, 0x746f4bb8, 0xcad4b853,
+    0x746caf70, 0xcacf013a,
+  0x746a12df, 0xcac94a42, 0x74677608, 0xcac3936b, 0x7464d8e8, 0xcabddcb4,
+    0x74623b80, 0xcab8261e,
+  0x745f9dd1, 0xcab26fa9, 0x745cffda, 0xcaacb955, 0x745a619b, 0xcaa70322,
+    0x7457c314, 0xcaa14d10,
+  0x74552446, 0xca9b971e, 0x74528530, 0xca95e14e, 0x744fe5d2, 0xca902b9f,
+    0x744d462c, 0xca8a7610,
+  0x744aa63f, 0xca84c0a3, 0x7448060a, 0xca7f0b56, 0x7445658d, 0xca79562b,
+    0x7442c4c8, 0xca73a120,
+  0x744023bc, 0xca6dec37, 0x743d8268, 0xca68376e, 0x743ae0cc, 0xca6282c7,
+    0x74383ee9, 0xca5cce40,
+  0x74359cbd, 0xca5719db, 0x7432fa4b, 0xca516597, 0x74305790, 0xca4bb174,
+    0x742db48e, 0xca45fd72,
+  0x742b1144, 0xca404992, 0x74286db3, 0xca3a95d2, 0x7425c9da, 0xca34e234,
+    0x742325b9, 0xca2f2eb6,
+  0x74208150, 0xca297b5a, 0x741ddca0, 0xca23c820, 0x741b37a9, 0xca1e1506,
+    0x74189269, 0xca18620e,
+  0x7415ece2, 0xca12af37, 0x74134714, 0xca0cfc81, 0x7410a0fe, 0xca0749ec,
+    0x740dfaa0, 0xca019779,
+  0x740b53fb, 0xc9fbe527, 0x7408ad0e, 0xc9f632f6, 0x740605d9, 0xc9f080e7,
+    0x74035e5d, 0xc9eacef9,
+  0x7400b69a, 0xc9e51d2d, 0x73fe0e8f, 0xc9df6b81, 0x73fb663c, 0xc9d9b9f7,
+    0x73f8bda2, 0xc9d4088f,
+  0x73f614c0, 0xc9ce5748, 0x73f36b97, 0xc9c8a622, 0x73f0c226, 0xc9c2f51e,
+    0x73ee186e, 0xc9bd443c,
+  0x73eb6e6e, 0xc9b7937a, 0x73e8c426, 0xc9b1e2db, 0x73e61997, 0xc9ac325d,
+    0x73e36ec1, 0xc9a68200,
+  0x73e0c3a3, 0xc9a0d1c5, 0x73de183e, 0xc99b21ab, 0x73db6c91, 0xc99571b3,
+    0x73d8c09d, 0xc98fc1dc,
+  0x73d61461, 0xc98a1227, 0x73d367de, 0xc9846294, 0x73d0bb13, 0xc97eb322,
+    0x73ce0e01, 0xc97903d2,
+  0x73cb60a8, 0xc97354a4, 0x73c8b307, 0xc96da597, 0x73c6051f, 0xc967f6ac,
+    0x73c356ef, 0xc96247e2,
+  0x73c0a878, 0xc95c993a, 0x73bdf9b9, 0xc956eab4, 0x73bb4ab3, 0xc9513c50,
+    0x73b89b66, 0xc94b8e0d,
+  0x73b5ebd1, 0xc945dfec, 0x73b33bf5, 0xc94031ed, 0x73b08bd1, 0xc93a8410,
+    0x73addb67, 0xc934d654,
+  0x73ab2ab4, 0xc92f28ba, 0x73a879bb, 0xc9297b42, 0x73a5c87a, 0xc923cdec,
+    0x73a316f2, 0xc91e20b8,
+  0x73a06522, 0xc91873a5, 0x739db30b, 0xc912c6b5, 0x739b00ad, 0xc90d19e6,
+    0x73984e07, 0xc9076d39,
+  0x73959b1b, 0xc901c0ae, 0x7392e7e6, 0xc8fc1445, 0x7390346b, 0xc8f667fe,
+    0x738d80a8, 0xc8f0bbd9,
+  0x738acc9e, 0xc8eb0fd6, 0x7388184d, 0xc8e563f5, 0x738563b5, 0xc8dfb836,
+    0x7382aed5, 0xc8da0c99,
+  0x737ff9ae, 0xc8d4611d, 0x737d4440, 0xc8ceb5c4, 0x737a8e8a, 0xc8c90a8d,
+    0x7377d88d, 0xc8c35f78,
+  0x73752249, 0xc8bdb485, 0x73726bbe, 0xc8b809b4, 0x736fb4ec, 0xc8b25f06,
+    0x736cfdd2, 0xc8acb479,
+  0x736a4671, 0xc8a70a0e, 0x73678ec9, 0xc8a15fc6, 0x7364d6da, 0xc89bb5a0,
+    0x73621ea4, 0xc8960b9c,
+  0x735f6626, 0xc89061ba, 0x735cad61, 0xc88ab7fa, 0x7359f456, 0xc8850e5d,
+    0x73573b03, 0xc87f64e2,
+  0x73548168, 0xc879bb89, 0x7351c787, 0xc8741252, 0x734f0d5f, 0xc86e693d,
+    0x734c52ef, 0xc868c04b,
+  0x73499838, 0xc863177b, 0x7346dd3a, 0xc85d6ece, 0x734421f6, 0xc857c642,
+    0x7341666a, 0xc8521dd9,
+  0x733eaa96, 0xc84c7593, 0x733bee7c, 0xc846cd6e, 0x7339321b, 0xc841256d,
+    0x73367572, 0xc83b7d8d,
+  0x7333b883, 0xc835d5d0, 0x7330fb4d, 0xc8302e35, 0x732e3dcf, 0xc82a86bd,
+    0x732b800a, 0xc824df67,
+  0x7328c1ff, 0xc81f3834, 0x732603ac, 0xc8199123, 0x73234512, 0xc813ea35,
+    0x73208632, 0xc80e4369,
+  0x731dc70a, 0xc8089cbf, 0x731b079b, 0xc802f638, 0x731847e5, 0xc7fd4fd4,
+    0x731587e8, 0xc7f7a992,
+  0x7312c7a5, 0xc7f20373, 0x7310071a, 0xc7ec5d76, 0x730d4648, 0xc7e6b79c,
+    0x730a8530, 0xc7e111e5,
+  0x7307c3d0, 0xc7db6c50, 0x73050229, 0xc7d5c6de, 0x7302403c, 0xc7d0218e,
+    0x72ff7e07, 0xc7ca7c61,
+  0x72fcbb8c, 0xc7c4d757, 0x72f9f8c9, 0xc7bf3270, 0x72f735c0, 0xc7b98dab,
+    0x72f47270, 0xc7b3e909,
+  0x72f1aed9, 0xc7ae4489, 0x72eeeafb, 0xc7a8a02c, 0x72ec26d6, 0xc7a2fbf3,
+    0x72e9626a, 0xc79d57db,
+  0x72e69db7, 0xc797b3e7, 0x72e3d8be, 0xc7921015, 0x72e1137d, 0xc78c6c67,
+    0x72de4df6, 0xc786c8db,
+  0x72db8828, 0xc7812572, 0x72d8c213, 0xc77b822b, 0x72d5fbb7, 0xc775df08,
+    0x72d33514, 0xc7703c08,
+  0x72d06e2b, 0xc76a992a, 0x72cda6fb, 0xc764f66f, 0x72cadf83, 0xc75f53d7,
+    0x72c817c6, 0xc759b163,
+  0x72c54fc1, 0xc7540f11, 0x72c28775, 0xc74e6ce2, 0x72bfbee3, 0xc748cad6,
+    0x72bcf60a, 0xc74328ed,
+  0x72ba2cea, 0xc73d8727, 0x72b76383, 0xc737e584, 0x72b499d6, 0xc7324404,
+    0x72b1cfe1, 0xc72ca2a7,
+  0x72af05a7, 0xc727016d, 0x72ac3b25, 0xc7216056, 0x72a9705c, 0xc71bbf62,
+    0x72a6a54d, 0xc7161e92,
+  0x72a3d9f7, 0xc7107de4, 0x72a10e5b, 0xc70add5a, 0x729e4277, 0xc7053cf2,
+    0x729b764d, 0xc6ff9cae,
+  0x7298a9dd, 0xc6f9fc8d, 0x7295dd25, 0xc6f45c8f, 0x72931027, 0xc6eebcb5,
+    0x729042e3, 0xc6e91cfd,
+  0x728d7557, 0xc6e37d69, 0x728aa785, 0xc6ddddf8, 0x7287d96c, 0xc6d83eab,
+    0x72850b0d, 0xc6d29f80,
+  0x72823c67, 0xc6cd0079, 0x727f6d7a, 0xc6c76195, 0x727c9e47, 0xc6c1c2d4,
+    0x7279cecd, 0xc6bc2437,
+  0x7276ff0d, 0xc6b685bd, 0x72742f05, 0xc6b0e767, 0x72715eb8, 0xc6ab4933,
+    0x726e8e23, 0xc6a5ab23,
+  0x726bbd48, 0xc6a00d37, 0x7268ec27, 0xc69a6f6e, 0x72661abf, 0xc694d1c8,
+    0x72634910, 0xc68f3446,
+  0x7260771b, 0xc68996e7, 0x725da4df, 0xc683f9ab, 0x725ad25d, 0xc67e5c93,
+    0x7257ff94, 0xc678bf9f,
+  0x72552c85, 0xc67322ce, 0x7252592f, 0xc66d8620, 0x724f8593, 0xc667e996,
+    0x724cb1b0, 0xc6624d30,
+  0x7249dd86, 0xc65cb0ed, 0x72470916, 0xc65714cd, 0x72443460, 0xc65178d1,
+    0x72415f63, 0xc64bdcf9,
+  0x723e8a20, 0xc6464144, 0x723bb496, 0xc640a5b3, 0x7238dec5, 0xc63b0a46,
+    0x723608af, 0xc6356efc,
+  0x72333251, 0xc62fd3d6, 0x72305bae, 0xc62a38d4, 0x722d84c4, 0xc6249df5,
+    0x722aad93, 0xc61f033a,
+  0x7227d61c, 0xc61968a2, 0x7224fe5f, 0xc613ce2f, 0x7222265b, 0xc60e33df,
+    0x721f4e11, 0xc60899b2,
+  0x721c7580, 0xc602ffaa, 0x72199ca9, 0xc5fd65c5, 0x7216c38c, 0xc5f7cc04,
+    0x7213ea28, 0xc5f23267,
+  0x7211107e, 0xc5ec98ee, 0x720e368d, 0xc5e6ff98, 0x720b5c57, 0xc5e16667,
+    0x720881d9, 0xc5dbcd59,
+  0x7205a716, 0xc5d6346f, 0x7202cc0c, 0xc5d09ba9, 0x71fff0bc, 0xc5cb0307,
+    0x71fd1525, 0xc5c56a89,
+  0x71fa3949, 0xc5bfd22e, 0x71f75d25, 0xc5ba39f8, 0x71f480bc, 0xc5b4a1e5,
+    0x71f1a40c, 0xc5af09f7,
+  0x71eec716, 0xc5a9722c, 0x71ebe9da, 0xc5a3da86, 0x71e90c57, 0xc59e4303,
+    0x71e62e8f, 0xc598aba5,
+  0x71e35080, 0xc593146a, 0x71e0722a, 0xc58d7d54, 0x71dd938f, 0xc587e661,
+    0x71dab4ad, 0xc5824f93,
+  0x71d7d585, 0xc57cb8e9, 0x71d4f617, 0xc5772263, 0x71d21662, 0xc5718c00,
+    0x71cf3667, 0xc56bf5c2,
+  0x71cc5626, 0xc5665fa9, 0x71c9759f, 0xc560c9b3, 0x71c694d2, 0xc55b33e2,
+    0x71c3b3bf, 0xc5559e34,
+  0x71c0d265, 0xc55008ab, 0x71bdf0c5, 0xc54a7346, 0x71bb0edf, 0xc544de05,
+    0x71b82cb3, 0xc53f48e9,
+  0x71b54a41, 0xc539b3f1, 0x71b26788, 0xc5341f1d, 0x71af848a, 0xc52e8a6d,
+    0x71aca145, 0xc528f5e1,
+  0x71a9bdba, 0xc523617a, 0x71a6d9e9, 0xc51dcd37, 0x71a3f5d2, 0xc5183919,
+    0x71a11175, 0xc512a51f,
+  0x719e2cd2, 0xc50d1149, 0x719b47e9, 0xc5077d97, 0x719862b9, 0xc501ea0a,
+    0x71957d44, 0xc4fc56a2,
+  0x71929789, 0xc4f6c35d, 0x718fb187, 0xc4f1303d, 0x718ccb3f, 0xc4eb9d42,
+    0x7189e4b2, 0xc4e60a6b,
+  0x7186fdde, 0xc4e077b8, 0x718416c4, 0xc4dae52a, 0x71812f65, 0xc4d552c1,
+    0x717e47bf, 0xc4cfc07c,
+  0x717b5fd3, 0xc4ca2e5b, 0x717877a1, 0xc4c49c5f, 0x71758f29, 0xc4bf0a87,
+    0x7172a66c, 0xc4b978d4,
+  0x716fbd68, 0xc4b3e746, 0x716cd41e, 0xc4ae55dc, 0x7169ea8f, 0xc4a8c497,
+    0x716700b9, 0xc4a33376,
+  0x7164169d, 0xc49da27a, 0x71612c3c, 0xc49811a3, 0x715e4194, 0xc49280f0,
+    0x715b56a7, 0xc48cf062,
+  0x71586b74, 0xc4875ff9, 0x71557ffa, 0xc481cfb4, 0x7152943b, 0xc47c3f94,
+    0x714fa836, 0xc476af98,
+  0x714cbbeb, 0xc4711fc2, 0x7149cf5a, 0xc46b9010, 0x7146e284, 0xc4660083,
+    0x7143f567, 0xc460711b,
+  0x71410805, 0xc45ae1d7, 0x713e1a5c, 0xc45552b8, 0x713b2c6e, 0xc44fc3be,
+    0x71383e3a, 0xc44a34e9,
+  0x71354fc0, 0xc444a639, 0x71326101, 0xc43f17ad, 0x712f71fb, 0xc4398947,
+    0x712c82b0, 0xc433fb05,
+  0x7129931f, 0xc42e6ce8, 0x7126a348, 0xc428def0, 0x7123b32b, 0xc423511d,
+    0x7120c2c8, 0xc41dc36f,
+  0x711dd220, 0xc41835e6, 0x711ae132, 0xc412a882, 0x7117effe, 0xc40d1b42,
+    0x7114fe84, 0xc4078e28,
+  0x71120cc5, 0xc4020133, 0x710f1ac0, 0xc3fc7462, 0x710c2875, 0xc3f6e7b7,
+    0x710935e4, 0xc3f15b31,
+  0x7106430e, 0xc3ebced0, 0x71034ff2, 0xc3e64294, 0x71005c90, 0xc3e0b67d,
+    0x70fd68e9, 0xc3db2a8b,
+  0x70fa74fc, 0xc3d59ebe, 0x70f780c9, 0xc3d01316, 0x70f48c50, 0xc3ca8793,
+    0x70f19792, 0xc3c4fc36,
+  0x70eea28e, 0xc3bf70fd, 0x70ebad45, 0xc3b9e5ea, 0x70e8b7b5, 0xc3b45afc,
+    0x70e5c1e1, 0xc3aed034,
+  0x70e2cbc6, 0xc3a94590, 0x70dfd566, 0xc3a3bb12, 0x70dcdec0, 0xc39e30b8,
+    0x70d9e7d5, 0xc398a685,
+  0x70d6f0a4, 0xc3931c76, 0x70d3f92d, 0xc38d928d, 0x70d10171, 0xc38808c9,
+    0x70ce096f, 0xc3827f2a,
+  0x70cb1128, 0xc37cf5b0, 0x70c8189b, 0xc3776c5c, 0x70c51fc8, 0xc371e32d,
+    0x70c226b0, 0xc36c5a24,
+  0x70bf2d53, 0xc366d140, 0x70bc33b0, 0xc3614881, 0x70b939c7, 0xc35bbfe8,
+    0x70b63f99, 0xc3563774,
+  0x70b34525, 0xc350af26, 0x70b04a6b, 0xc34b26fc, 0x70ad4f6d, 0xc3459ef9,
+    0x70aa5428, 0xc340171b,
+  0x70a7589f, 0xc33a8f62, 0x70a45ccf, 0xc33507cf, 0x70a160ba, 0xc32f8061,
+    0x709e6460, 0xc329f919,
+  0x709b67c0, 0xc32471f7, 0x70986adb, 0xc31eeaf9, 0x70956db1, 0xc3196422,
+    0x70927041, 0xc313dd70,
+  0x708f728b, 0xc30e56e4, 0x708c7490, 0xc308d07d, 0x70897650, 0xc3034a3c,
+    0x708677ca, 0xc2fdc420,
+  0x708378ff, 0xc2f83e2a, 0x708079ee, 0xc2f2b85a, 0x707d7a98, 0xc2ed32af,
+    0x707a7afd, 0xc2e7ad2a,
+  0x70777b1c, 0xc2e227cb, 0x70747af6, 0xc2dca291, 0x70717a8a, 0xc2d71d7e,
+    0x706e79d9, 0xc2d1988f,
+  0x706b78e3, 0xc2cc13c7, 0x706877a7, 0xc2c68f24, 0x70657626, 0xc2c10aa7,
+    0x70627460, 0xc2bb8650,
+  0x705f7255, 0xc2b6021f, 0x705c7004, 0xc2b07e14, 0x70596d6d, 0xc2aafa2e,
+    0x70566a92, 0xc2a5766e,
+  0x70536771, 0xc29ff2d4, 0x7050640b, 0xc29a6f60, 0x704d6060, 0xc294ec12,
+    0x704a5c6f, 0xc28f68e9,
+  0x70475839, 0xc289e5e7, 0x704453be, 0xc284630a, 0x70414efd, 0xc27ee054,
+    0x703e49f8, 0xc2795dc3,
+  0x703b44ad, 0xc273db58, 0x70383f1d, 0xc26e5913, 0x70353947, 0xc268d6f5,
+    0x7032332d, 0xc26354fc,
+  0x702f2ccd, 0xc25dd329, 0x702c2628, 0xc258517c, 0x70291f3e, 0xc252cff5,
+    0x7026180e, 0xc24d4e95,
+  0x7023109a, 0xc247cd5a, 0x702008e0, 0xc2424c46, 0x701d00e1, 0xc23ccb57,
+    0x7019f89d, 0xc2374a8f,
+  0x7016f014, 0xc231c9ec, 0x7013e746, 0xc22c4970, 0x7010de32, 0xc226c91a,
+    0x700dd4da, 0xc22148ea,
+  0x700acb3c, 0xc21bc8e1, 0x7007c159, 0xc21648fd, 0x7004b731, 0xc210c940,
+    0x7001acc4, 0xc20b49a9,
+  0x6ffea212, 0xc205ca38, 0x6ffb971b, 0xc2004aed, 0x6ff88bde, 0xc1facbc9,
+    0x6ff5805d, 0xc1f54cca,
+  0x6ff27497, 0xc1efcdf3, 0x6fef688b, 0xc1ea4f41, 0x6fec5c3b, 0xc1e4d0b6,
+    0x6fe94fa5, 0xc1df5251,
+  0x6fe642ca, 0xc1d9d412, 0x6fe335ab, 0xc1d455f9, 0x6fe02846, 0xc1ced807,
+    0x6fdd1a9c, 0xc1c95a3c,
+  0x6fda0cae, 0xc1c3dc97, 0x6fd6fe7a, 0xc1be5f18, 0x6fd3f001, 0xc1b8e1bf,
+    0x6fd0e144, 0xc1b3648d,
+  0x6fcdd241, 0xc1ade781, 0x6fcac2fa, 0xc1a86a9c, 0x6fc7b36d, 0xc1a2edde,
+    0x6fc4a39c, 0xc19d7145,
+  0x6fc19385, 0xc197f4d4, 0x6fbe832a, 0xc1927888, 0x6fbb728a, 0xc18cfc63,
+    0x6fb861a4, 0xc1878065,
+  0x6fb5507a, 0xc182048d, 0x6fb23f0b, 0xc17c88dc, 0x6faf2d57, 0xc1770d52,
+    0x6fac1b5f, 0xc17191ee,
+  0x6fa90921, 0xc16c16b0, 0x6fa5f69e, 0xc1669b99, 0x6fa2e3d7, 0xc16120a9,
+    0x6f9fd0cb, 0xc15ba5df,
+  0x6f9cbd79, 0xc1562b3d, 0x6f99a9e3, 0xc150b0c0, 0x6f969608, 0xc14b366b,
+    0x6f9381e9, 0xc145bc3c,
+  0x6f906d84, 0xc1404233, 0x6f8d58db, 0xc13ac852, 0x6f8a43ed, 0xc1354e97,
+    0x6f872eba, 0xc12fd503,
+  0x6f841942, 0xc12a5b95, 0x6f810386, 0xc124e24f, 0x6f7ded84, 0xc11f692f,
+    0x6f7ad73e, 0xc119f036,
+  0x6f77c0b3, 0xc1147764, 0x6f74a9e4, 0xc10efeb8, 0x6f7192cf, 0xc1098634,
+    0x6f6e7b76, 0xc1040dd6,
+  0x6f6b63d8, 0xc0fe959f, 0x6f684bf6, 0xc0f91d8f, 0x6f6533ce, 0xc0f3a5a6,
+    0x6f621b62, 0xc0ee2de3,
+  0x6f5f02b2, 0xc0e8b648, 0x6f5be9bc, 0xc0e33ed4, 0x6f58d082, 0xc0ddc786,
+    0x6f55b703, 0xc0d8505f,
+  0x6f529d40, 0xc0d2d960, 0x6f4f8338, 0xc0cd6287, 0x6f4c68eb, 0xc0c7ebd6,
+    0x6f494e5a, 0xc0c2754b,
+  0x6f463383, 0xc0bcfee7, 0x6f431869, 0xc0b788ab, 0x6f3ffd09, 0xc0b21295,
+    0x6f3ce165, 0xc0ac9ca6,
+  0x6f39c57d, 0xc0a726df, 0x6f36a94f, 0xc0a1b13e, 0x6f338cde, 0xc09c3bc5,
+    0x6f307027, 0xc096c673,
+  0x6f2d532c, 0xc0915148, 0x6f2a35ed, 0xc08bdc44, 0x6f271868, 0xc0866767,
+    0x6f23faa0, 0xc080f2b1,
+  0x6f20dc92, 0xc07b7e23, 0x6f1dbe41, 0xc07609bb, 0x6f1a9faa, 0xc070957b,
+    0x6f1780cf, 0xc06b2162,
+  0x6f1461b0, 0xc065ad70, 0x6f11424c, 0xc06039a6, 0x6f0e22a3, 0xc05ac603,
+    0x6f0b02b6, 0xc0555287,
+  0x6f07e285, 0xc04fdf32, 0x6f04c20f, 0xc04a6c05, 0x6f01a155, 0xc044f8fe,
+    0x6efe8056, 0xc03f8620,
+  0x6efb5f12, 0xc03a1368, 0x6ef83d8a, 0xc034a0d8, 0x6ef51bbe, 0xc02f2e6f,
+    0x6ef1f9ad, 0xc029bc2e,
+  0x6eeed758, 0xc0244a14, 0x6eebb4bf, 0xc01ed821, 0x6ee891e1, 0xc0196656,
+    0x6ee56ebe, 0xc013f4b2,
+  0x6ee24b57, 0xc00e8336, 0x6edf27ac, 0xc00911e1, 0x6edc03bc, 0xc003a0b3,
+    0x6ed8df88, 0xbffe2fad,
+  0x6ed5bb10, 0xbff8bece, 0x6ed29653, 0xbff34e17, 0x6ecf7152, 0xbfeddd88,
+    0x6ecc4c0d, 0xbfe86d20,
+  0x6ec92683, 0xbfe2fcdf, 0x6ec600b5, 0xbfdd8cc6, 0x6ec2daa2, 0xbfd81cd5,
+    0x6ebfb44b, 0xbfd2ad0b,
+  0x6ebc8db0, 0xbfcd3d69, 0x6eb966d1, 0xbfc7cdee, 0x6eb63fad, 0xbfc25e9b,
+    0x6eb31845, 0xbfbcef70,
+  0x6eaff099, 0xbfb7806c, 0x6eacc8a8, 0xbfb21190, 0x6ea9a073, 0xbfaca2dc,
+    0x6ea677fa, 0xbfa7344f,
+  0x6ea34f3d, 0xbfa1c5ea, 0x6ea0263b, 0xbf9c57ac, 0x6e9cfcf5, 0xbf96e997,
+    0x6e99d36b, 0xbf917ba9,
+  0x6e96a99d, 0xbf8c0de3, 0x6e937f8a, 0xbf86a044, 0x6e905534, 0xbf8132ce,
+    0x6e8d2a99, 0xbf7bc57f,
+  0x6e89ffb9, 0xbf765858, 0x6e86d496, 0xbf70eb59, 0x6e83a92f, 0xbf6b7e81,
+    0x6e807d83, 0xbf6611d2,
+  0x6e7d5193, 0xbf60a54a, 0x6e7a255f, 0xbf5b38ea, 0x6e76f8e7, 0xbf55ccb2,
+    0x6e73cc2b, 0xbf5060a2,
+  0x6e709f2a, 0xbf4af4ba, 0x6e6d71e6, 0xbf4588fa, 0x6e6a445d, 0xbf401d61,
+    0x6e671690, 0xbf3ab1f1,
+  0x6e63e87f, 0xbf3546a8, 0x6e60ba2a, 0xbf2fdb88, 0x6e5d8b91, 0xbf2a708f,
+    0x6e5a5cb4, 0xbf2505bf,
+  0x6e572d93, 0xbf1f9b16, 0x6e53fe2e, 0xbf1a3096, 0x6e50ce84, 0xbf14c63d,
+    0x6e4d9e97, 0xbf0f5c0d,
+  0x6e4a6e66, 0xbf09f205, 0x6e473df0, 0xbf048824, 0x6e440d37, 0xbeff1e6c,
+    0x6e40dc39, 0xbef9b4dc,
+  0x6e3daaf8, 0xbef44b74, 0x6e3a7972, 0xbeeee234, 0x6e3747a9, 0xbee9791c,
+    0x6e34159b, 0xbee4102d,
+  0x6e30e34a, 0xbedea765, 0x6e2db0b4, 0xbed93ec6, 0x6e2a7ddb, 0xbed3d64f,
+    0x6e274abe, 0xbece6e00,
+  0x6e24175c, 0xbec905d9, 0x6e20e3b7, 0xbec39ddb, 0x6e1dafce, 0xbebe3605,
+    0x6e1a7ba1, 0xbeb8ce57,
+  0x6e174730, 0xbeb366d1, 0x6e14127b, 0xbeadff74, 0x6e10dd82, 0xbea8983f,
+    0x6e0da845, 0xbea33132,
+  0x6e0a72c5, 0xbe9dca4e, 0x6e073d00, 0xbe986391, 0x6e0406f8, 0xbe92fcfe,
+    0x6e00d0ac, 0xbe8d9692,
+  0x6dfd9a1c, 0xbe88304f, 0x6dfa6348, 0xbe82ca35, 0x6df72c30, 0xbe7d6442,
+    0x6df3f4d4, 0xbe77fe78,
+  0x6df0bd35, 0xbe7298d7, 0x6ded8552, 0xbe6d335e, 0x6dea4d2b, 0xbe67ce0d,
+    0x6de714c0, 0xbe6268e5,
+  0x6de3dc11, 0xbe5d03e6, 0x6de0a31f, 0xbe579f0f, 0x6ddd69e9, 0xbe523a60,
+    0x6dda306f, 0xbe4cd5da,
+  0x6dd6f6b1, 0xbe47717c, 0x6dd3bcaf, 0xbe420d47, 0x6dd0826a, 0xbe3ca93b,
+    0x6dcd47e1, 0xbe374557,
+  0x6dca0d14, 0xbe31e19b, 0x6dc6d204, 0xbe2c7e09, 0x6dc396b0, 0xbe271a9f,
+    0x6dc05b18, 0xbe21b75d,
+  0x6dbd1f3c, 0xbe1c5444, 0x6db9e31d, 0xbe16f154, 0x6db6a6ba, 0xbe118e8c,
+    0x6db36a14, 0xbe0c2bed,
+  0x6db02d29, 0xbe06c977, 0x6daceffb, 0xbe01672a, 0x6da9b28a, 0xbdfc0505,
+    0x6da674d5, 0xbdf6a309,
+  0x6da336dc, 0xbdf14135, 0x6d9ff89f, 0xbdebdf8b, 0x6d9cba1f, 0xbde67e09,
+    0x6d997b5b, 0xbde11cb0,
+  0x6d963c54, 0xbddbbb7f, 0x6d92fd09, 0xbdd65a78, 0x6d8fbd7a, 0xbdd0f999,
+    0x6d8c7da8, 0xbdcb98e3,
+  0x6d893d93, 0xbdc63856, 0x6d85fd39, 0xbdc0d7f2, 0x6d82bc9d, 0xbdbb77b7,
+    0x6d7f7bbc, 0xbdb617a4,
+  0x6d7c3a98, 0xbdb0b7bb, 0x6d78f931, 0xbdab57fa, 0x6d75b786, 0xbda5f862,
+    0x6d727597, 0xbda098f3,
+  0x6d6f3365, 0xbd9b39ad, 0x6d6bf0f0, 0xbd95da91, 0x6d68ae37, 0xbd907b9d,
+    0x6d656b3a, 0xbd8b1cd2,
+  0x6d6227fa, 0xbd85be30, 0x6d5ee477, 0xbd805fb7, 0x6d5ba0b0, 0xbd7b0167,
+    0x6d585ca6, 0xbd75a340,
+  0x6d551858, 0xbd704542, 0x6d51d3c6, 0xbd6ae76d, 0x6d4e8ef2, 0xbd6589c1,
+    0x6d4b49da, 0xbd602c3f,
+  0x6d48047e, 0xbd5acee5, 0x6d44bedf, 0xbd5571b5, 0x6d4178fd, 0xbd5014ad,
+    0x6d3e32d7, 0xbd4ab7cf,
+  0x6d3aec6e, 0xbd455b1a, 0x6d37a5c1, 0xbd3ffe8e, 0x6d345ed1, 0xbd3aa22c,
+    0x6d31179e, 0xbd3545f2,
+  0x6d2dd027, 0xbd2fe9e2, 0x6d2a886e, 0xbd2a8dfb, 0x6d274070, 0xbd25323d,
+    0x6d23f830, 0xbd1fd6a8,
+  0x6d20afac, 0xbd1a7b3d, 0x6d1d66e4, 0xbd151ffb, 0x6d1a1dda, 0xbd0fc4e2,
+    0x6d16d48c, 0xbd0a69f2,
+  0x6d138afb, 0xbd050f2c, 0x6d104126, 0xbcffb48f, 0x6d0cf70f, 0xbcfa5a1b,
+    0x6d09acb4, 0xbcf4ffd1,
+  0x6d066215, 0xbcefa5b0, 0x6d031734, 0xbcea4bb9, 0x6cffcc0f, 0xbce4f1eb,
+    0x6cfc80a7, 0xbcdf9846,
+  0x6cf934fc, 0xbcda3ecb, 0x6cf5e90d, 0xbcd4e579, 0x6cf29cdc, 0xbccf8c50,
+    0x6cef5067, 0xbcca3351,
+  0x6cec03af, 0xbcc4da7b, 0x6ce8b6b4, 0xbcbf81cf, 0x6ce56975, 0xbcba294d,
+    0x6ce21bf4, 0xbcb4d0f4,
+  0x6cdece2f, 0xbcaf78c4, 0x6cdb8027, 0xbcaa20be, 0x6cd831dc, 0xbca4c8e1,
+    0x6cd4e34e, 0xbc9f712e,
+  0x6cd1947c, 0xbc9a19a5, 0x6cce4568, 0xbc94c245, 0x6ccaf610, 0xbc8f6b0f,
+    0x6cc7a676, 0xbc8a1402,
+  0x6cc45698, 0xbc84bd1f, 0x6cc10677, 0xbc7f6665, 0x6cbdb613, 0xbc7a0fd6,
+    0x6cba656c, 0xbc74b96f,
+  0x6cb71482, 0xbc6f6333, 0x6cb3c355, 0xbc6a0d20, 0x6cb071e4, 0xbc64b737,
+    0x6cad2031, 0xbc5f6177,
+  0x6ca9ce3b, 0xbc5a0be2, 0x6ca67c01, 0xbc54b676, 0x6ca32985, 0xbc4f6134,
+    0x6c9fd6c6, 0xbc4a0c1b,
+  0x6c9c83c3, 0xbc44b72c, 0x6c99307e, 0xbc3f6267, 0x6c95dcf6, 0xbc3a0dcc,
+    0x6c92892a, 0xbc34b95b,
+  0x6c8f351c, 0xbc2f6513, 0x6c8be0cb, 0xbc2a10f6, 0x6c888c36, 0xbc24bd02,
+    0x6c85375f, 0xbc1f6938,
+  0x6c81e245, 0xbc1a1598, 0x6c7e8ce8, 0xbc14c221, 0x6c7b3748, 0xbc0f6ed5,
+    0x6c77e165, 0xbc0a1bb3,
+  0x6c748b3f, 0xbc04c8ba, 0x6c7134d7, 0xbbff75ec, 0x6c6dde2b, 0xbbfa2347,
+    0x6c6a873d, 0xbbf4d0cc,
+  0x6c67300b, 0xbbef7e7c, 0x6c63d897, 0xbbea2c55, 0x6c6080e0, 0xbbe4da58,
+    0x6c5d28e6, 0xbbdf8885,
+  0x6c59d0a9, 0xbbda36dd, 0x6c56782a, 0xbbd4e55e, 0x6c531f67, 0xbbcf940a,
+    0x6c4fc662, 0xbbca42df,
+  0x6c4c6d1a, 0xbbc4f1df, 0x6c49138f, 0xbbbfa108, 0x6c45b9c1, 0xbbba505c,
+    0x6c425fb1, 0xbbb4ffda,
+  0x6c3f055d, 0xbbafaf82, 0x6c3baac7, 0xbbaa5f54, 0x6c384fef, 0xbba50f50,
+    0x6c34f4d3, 0xbb9fbf77,
+  0x6c319975, 0xbb9a6fc7, 0x6c2e3dd4, 0xbb952042, 0x6c2ae1f0, 0xbb8fd0e7,
+    0x6c2785ca, 0xbb8a81b6,
+  0x6c242960, 0xbb8532b0, 0x6c20ccb4, 0xbb7fe3d3, 0x6c1d6fc6, 0xbb7a9521,
+    0x6c1a1295, 0xbb754699,
+  0x6c16b521, 0xbb6ff83c, 0x6c13576a, 0xbb6aaa09, 0x6c0ff971, 0xbb655c00,
+    0x6c0c9b35, 0xbb600e21,
+  0x6c093cb6, 0xbb5ac06d, 0x6c05ddf5, 0xbb5572e3, 0x6c027ef1, 0xbb502583,
+    0x6bff1faa, 0xbb4ad84e,
+  0x6bfbc021, 0xbb458b43, 0x6bf86055, 0xbb403e63, 0x6bf50047, 0xbb3af1ad,
+    0x6bf19ff6, 0xbb35a521,
+  0x6bee3f62, 0xbb3058c0, 0x6beade8c, 0xbb2b0c8a, 0x6be77d74, 0xbb25c07d,
+    0x6be41c18, 0xbb20749c,
+  0x6be0ba7b, 0xbb1b28e4, 0x6bdd589a, 0xbb15dd57, 0x6bd9f677, 0xbb1091f5,
+    0x6bd69412, 0xbb0b46bd,
+  0x6bd3316a, 0xbb05fbb0, 0x6bcfce80, 0xbb00b0ce, 0x6bcc6b53, 0xbafb6615,
+    0x6bc907e3, 0xbaf61b88,
+  0x6bc5a431, 0xbaf0d125, 0x6bc2403d, 0xbaeb86ed, 0x6bbedc06, 0xbae63cdf,
+    0x6bbb778d, 0xbae0f2fc,
+  0x6bb812d1, 0xbadba943, 0x6bb4add3, 0xbad65fb5, 0x6bb14892, 0xbad11652,
+    0x6bade30f, 0xbacbcd1a,
+  0x6baa7d49, 0xbac6840c, 0x6ba71741, 0xbac13b29, 0x6ba3b0f7, 0xbabbf270,
+    0x6ba04a6a, 0xbab6a9e3,
+  0x6b9ce39b, 0xbab16180, 0x6b997c8a, 0xbaac1948, 0x6b961536, 0xbaa6d13a,
+    0x6b92ada0, 0xbaa18958,
+  0x6b8f45c7, 0xba9c41a0, 0x6b8bddac, 0xba96fa13, 0x6b88754f, 0xba91b2b1,
+    0x6b850caf, 0xba8c6b79,
+  0x6b81a3cd, 0xba87246d, 0x6b7e3aa9, 0xba81dd8b, 0x6b7ad142, 0xba7c96d4,
+    0x6b776799, 0xba775048,
+  0x6b73fdae, 0xba7209e7, 0x6b709381, 0xba6cc3b1, 0x6b6d2911, 0xba677da6,
+    0x6b69be5f, 0xba6237c5,
+  0x6b66536b, 0xba5cf210, 0x6b62e834, 0xba57ac86, 0x6b5f7cbc, 0xba526726,
+    0x6b5c1101, 0xba4d21f2,
+  0x6b58a503, 0xba47dce8, 0x6b5538c4, 0xba42980a, 0x6b51cc42, 0xba3d5356,
+    0x6b4e5f7f, 0xba380ece,
+  0x6b4af279, 0xba32ca71, 0x6b478530, 0xba2d863e, 0x6b4417a6, 0xba284237,
+    0x6b40a9d9, 0xba22fe5b,
+  0x6b3d3bcb, 0xba1dbaaa, 0x6b39cd7a, 0xba187724, 0x6b365ee7, 0xba1333c9,
+    0x6b32f012, 0xba0df099,
+  0x6b2f80fb, 0xba08ad95, 0x6b2c11a1, 0xba036abb, 0x6b28a206, 0xb9fe280d,
+    0x6b253228, 0xb9f8e58a,
+  0x6b21c208, 0xb9f3a332, 0x6b1e51a7, 0xb9ee6106, 0x6b1ae103, 0xb9e91f04,
+    0x6b17701d, 0xb9e3dd2e,
+  0x6b13fef5, 0xb9de9b83, 0x6b108d8b, 0xb9d95a03, 0x6b0d1bdf, 0xb9d418af,
+    0x6b09a9f1, 0xb9ced786,
+  0x6b0637c1, 0xb9c99688, 0x6b02c54f, 0xb9c455b6, 0x6aff529a, 0xb9bf150e,
+    0x6afbdfa4, 0xb9b9d493,
+  0x6af86c6c, 0xb9b49442, 0x6af4f8f2, 0xb9af541d, 0x6af18536, 0xb9aa1423,
+    0x6aee1138, 0xb9a4d455,
+  0x6aea9cf8, 0xb99f94b2, 0x6ae72876, 0xb99a553a, 0x6ae3b3b2, 0xb99515ee,
+    0x6ae03eac, 0xb98fd6cd,
+  0x6adcc964, 0xb98a97d8, 0x6ad953db, 0xb985590e, 0x6ad5de0f, 0xb9801a70,
+    0x6ad26802, 0xb97adbfd,
+  0x6acef1b2, 0xb9759db6, 0x6acb7b21, 0xb9705f9a, 0x6ac8044e, 0xb96b21aa,
+    0x6ac48d39, 0xb965e3e5,
+  0x6ac115e2, 0xb960a64c, 0x6abd9e49, 0xb95b68de, 0x6aba266e, 0xb9562b9c,
+    0x6ab6ae52, 0xb950ee86,
+  0x6ab335f4, 0xb94bb19b, 0x6aafbd54, 0xb94674dc, 0x6aac4472, 0xb9413848,
+    0x6aa8cb4e, 0xb93bfbe0,
+  0x6aa551e9, 0xb936bfa4, 0x6aa1d841, 0xb9318393, 0x6a9e5e58, 0xb92c47ae,
+    0x6a9ae42e, 0xb9270bf5,
+  0x6a9769c1, 0xb921d067, 0x6a93ef13, 0xb91c9505, 0x6a907423, 0xb91759cf,
+    0x6a8cf8f1, 0xb9121ec5,
+  0x6a897d7d, 0xb90ce3e6, 0x6a8601c8, 0xb907a933, 0x6a8285d1, 0xb9026eac,
+    0x6a7f0999, 0xb8fd3451,
+  0x6a7b8d1e, 0xb8f7fa21, 0x6a781062, 0xb8f2c01d, 0x6a749365, 0xb8ed8646,
+    0x6a711625, 0xb8e84c99,
+  0x6a6d98a4, 0xb8e31319, 0x6a6a1ae2, 0xb8ddd9c5, 0x6a669cdd, 0xb8d8a09d,
+    0x6a631e97, 0xb8d367a0,
+  0x6a5fa010, 0xb8ce2ecf, 0x6a5c2147, 0xb8c8f62b, 0x6a58a23c, 0xb8c3bdb2,
+    0x6a5522ef, 0xb8be8565,
+  0x6a51a361, 0xb8b94d44, 0x6a4e2392, 0xb8b4154f, 0x6a4aa381, 0xb8aedd86,
+    0x6a47232e, 0xb8a9a5e9,
+  0x6a43a29a, 0xb8a46e78, 0x6a4021c4, 0xb89f3733, 0x6a3ca0ad, 0xb89a001a,
+    0x6a391f54, 0xb894c92d,
+  0x6a359db9, 0xb88f926d, 0x6a321bdd, 0xb88a5bd8, 0x6a2e99c0, 0xb885256f,
+    0x6a2b1761, 0xb87fef33,
+  0x6a2794c1, 0xb87ab922, 0x6a2411df, 0xb875833e, 0x6a208ebb, 0xb8704d85,
+    0x6a1d0b57, 0xb86b17f9,
+  0x6a1987b0, 0xb865e299, 0x6a1603c8, 0xb860ad66, 0x6a127f9f, 0xb85b785e,
+    0x6a0efb35, 0xb8564383,
+  0x6a0b7689, 0xb8510ed4, 0x6a07f19b, 0xb84bda51, 0x6a046c6c, 0xb846a5fa,
+    0x6a00e6fc, 0xb84171cf,
+  0x69fd614a, 0xb83c3dd1, 0x69f9db57, 0xb83709ff, 0x69f65523, 0xb831d659,
+    0x69f2cead, 0xb82ca2e0,
+  0x69ef47f6, 0xb8276f93, 0x69ebc0fe, 0xb8223c72, 0x69e839c4, 0xb81d097e,
+    0x69e4b249, 0xb817d6b6,
+  0x69e12a8c, 0xb812a41a, 0x69dda28f, 0xb80d71aa, 0x69da1a50, 0xb8083f67,
+    0x69d691cf, 0xb8030d51,
+  0x69d3090e, 0xb7fddb67, 0x69cf800b, 0xb7f8a9a9, 0x69cbf6c7, 0xb7f37818,
+    0x69c86d41, 0xb7ee46b3,
+  0x69c4e37a, 0xb7e9157a, 0x69c15973, 0xb7e3e46e, 0x69bdcf29, 0xb7deb38f,
+    0x69ba449f, 0xb7d982dc,
+  0x69b6b9d3, 0xb7d45255, 0x69b32ec7, 0xb7cf21fb, 0x69afa378, 0xb7c9f1ce,
+    0x69ac17e9, 0xb7c4c1cd,
+  0x69a88c19, 0xb7bf91f8, 0x69a50007, 0xb7ba6251, 0x69a173b5, 0xb7b532d6,
+    0x699de721, 0xb7b00387,
+  0x699a5a4c, 0xb7aad465, 0x6996cd35, 0xb7a5a570, 0x69933fde, 0xb7a076a7,
+    0x698fb246, 0xb79b480b,
+  0x698c246c, 0xb796199b, 0x69889651, 0xb790eb58, 0x698507f6, 0xb78bbd42,
+    0x69817959, 0xb7868f59,
+  0x697dea7b, 0xb781619c, 0x697a5b5c, 0xb77c340c, 0x6976cbfc, 0xb77706a9,
+    0x69733c5b, 0xb771d972,
+  0x696fac78, 0xb76cac69, 0x696c1c55, 0xb7677f8c, 0x69688bf1, 0xb76252db,
+    0x6964fb4c, 0xb75d2658,
+  0x69616a65, 0xb757fa01, 0x695dd93e, 0xb752cdd8, 0x695a47d6, 0xb74da1db,
+    0x6956b62d, 0xb748760b,
+  0x69532442, 0xb7434a67, 0x694f9217, 0xb73e1ef1, 0x694bffab, 0xb738f3a7,
+    0x69486cfe, 0xb733c88b,
+  0x6944da10, 0xb72e9d9b, 0x694146e1, 0xb72972d8, 0x693db371, 0xb7244842,
+    0x693a1fc0, 0xb71f1dd9,
+  0x69368bce, 0xb719f39e, 0x6932f79b, 0xb714c98e, 0x692f6328, 0xb70f9fac,
+    0x692bce73, 0xb70a75f7,
+  0x6928397e, 0xb7054c6f, 0x6924a448, 0xb7002314, 0x69210ed1, 0xb6faf9e6,
+    0x691d7919, 0xb6f5d0e5,
+  0x6919e320, 0xb6f0a812, 0x69164ce7, 0xb6eb7f6b, 0x6912b66c, 0xb6e656f1,
+    0x690f1fb1, 0xb6e12ea4,
+  0x690b88b5, 0xb6dc0685, 0x6907f178, 0xb6d6de92, 0x690459fb, 0xb6d1b6cd,
+    0x6900c23c, 0xb6cc8f35,
+  0x68fd2a3d, 0xb6c767ca, 0x68f991fd, 0xb6c2408c, 0x68f5f97d, 0xb6bd197c,
+    0x68f260bb, 0xb6b7f298,
+  0x68eec7b9, 0xb6b2cbe2, 0x68eb2e76, 0xb6ada559, 0x68e794f3, 0xb6a87efd,
+    0x68e3fb2e, 0xb6a358ce,
+  0x68e06129, 0xb69e32cd, 0x68dcc6e4, 0xb6990cf9, 0x68d92c5d, 0xb693e752,
+    0x68d59196, 0xb68ec1d9,
+  0x68d1f68f, 0xb6899c8d, 0x68ce5b46, 0xb684776e, 0x68cabfbd, 0xb67f527c,
+    0x68c723f3, 0xb67a2db8,
+  0x68c387e9, 0xb6750921, 0x68bfeb9e, 0xb66fe4b8, 0x68bc4f13, 0xb66ac07c,
+    0x68b8b247, 0xb6659c6d,
+  0x68b5153a, 0xb660788c, 0x68b177ed, 0xb65b54d8, 0x68adda5f, 0xb6563151,
+    0x68aa3c90, 0xb6510df8,
+  0x68a69e81, 0xb64beacd, 0x68a30031, 0xb646c7ce, 0x689f61a1, 0xb641a4fe,
+    0x689bc2d1, 0xb63c825b,
+  0x689823bf, 0xb6375fe5, 0x6894846e, 0xb6323d9d, 0x6890e4dc, 0xb62d1b82,
+    0x688d4509, 0xb627f995,
+  0x6889a4f6, 0xb622d7d6, 0x688604a2, 0xb61db644, 0x6882640e, 0xb61894df,
+    0x687ec339, 0xb61373a9,
+  0x687b2224, 0xb60e529f, 0x687780ce, 0xb60931c4, 0x6873df38, 0xb6041116,
+    0x68703d62, 0xb5fef095,
+  0x686c9b4b, 0xb5f9d043, 0x6868f8f4, 0xb5f4b01e, 0x6865565c, 0xb5ef9026,
+    0x6861b384, 0xb5ea705d,
+  0x685e106c, 0xb5e550c1, 0x685a6d13, 0xb5e03153, 0x6856c979, 0xb5db1212,
+    0x685325a0, 0xb5d5f2ff,
+  0x684f8186, 0xb5d0d41a, 0x684bdd2c, 0xb5cbb563, 0x68483891, 0xb5c696da,
+    0x684493b6, 0xb5c1787e,
+  0x6840ee9b, 0xb5bc5a50, 0x683d493f, 0xb5b73c50, 0x6839a3a4, 0xb5b21e7e,
+    0x6835fdc7, 0xb5ad00d9,
+  0x683257ab, 0xb5a7e362, 0x682eb14e, 0xb5a2c61a, 0x682b0ab1, 0xb59da8ff,
+    0x682763d4, 0xb5988c12,
+  0x6823bcb7, 0xb5936f53, 0x68201559, 0xb58e52c2, 0x681c6dbb, 0xb589365e,
+    0x6818c5dd, 0xb5841a29,
+  0x68151dbe, 0xb57efe22, 0x68117560, 0xb579e248, 0x680dccc1, 0xb574c69d,
+    0x680a23e2, 0xb56fab1f,
+  0x68067ac3, 0xb56a8fd0, 0x6802d164, 0xb56574ae, 0x67ff27c4, 0xb56059bb,
+    0x67fb7de5, 0xb55b3ef5,
+  0x67f7d3c5, 0xb556245e, 0x67f42965, 0xb55109f5, 0x67f07ec5, 0xb54befba,
+    0x67ecd3e5, 0xb546d5ac,
+  0x67e928c5, 0xb541bbcd, 0x67e57d64, 0xb53ca21c, 0x67e1d1c4, 0xb5378899,
+    0x67de25e3, 0xb5326f45,
+  0x67da79c3, 0xb52d561e, 0x67d6cd62, 0xb5283d26, 0x67d320c1, 0xb523245b,
+    0x67cf73e1, 0xb51e0bbf,
+  0x67cbc6c0, 0xb518f351, 0x67c8195f, 0xb513db12, 0x67c46bbe, 0xb50ec300,
+    0x67c0bddd, 0xb509ab1d,
+  0x67bd0fbd, 0xb5049368, 0x67b9615c, 0xb4ff7be1, 0x67b5b2bb, 0xb4fa6489,
+    0x67b203da, 0xb4f54d5f,
+  0x67ae54ba, 0xb4f03663, 0x67aaa559, 0xb4eb1f95, 0x67a6f5b8, 0xb4e608f6,
+    0x67a345d8, 0xb4e0f285,
+  0x679f95b7, 0xb4dbdc42, 0x679be557, 0xb4d6c62e, 0x679834b6, 0xb4d1b048,
+    0x679483d6, 0xb4cc9a90,
+  0x6790d2b6, 0xb4c78507, 0x678d2156, 0xb4c26fad, 0x67896fb6, 0xb4bd5a80,
+    0x6785bdd6, 0xb4b84582,
+  0x67820bb7, 0xb4b330b3, 0x677e5957, 0xb4ae1c12, 0x677aa6b8, 0xb4a9079f,
+    0x6776f3d9, 0xb4a3f35b,
+  0x677340ba, 0xb49edf45, 0x676f8d5b, 0xb499cb5e, 0x676bd9bd, 0xb494b7a6,
+    0x676825de, 0xb48fa41c,
+  0x676471c0, 0xb48a90c0, 0x6760bd62, 0xb4857d93, 0x675d08c4, 0xb4806a95,
+    0x675953e7, 0xb47b57c5,
+  0x67559eca, 0xb4764523, 0x6751e96d, 0xb47132b1, 0x674e33d0, 0xb46c206d,
+    0x674a7df4, 0xb4670e57,
+  0x6746c7d8, 0xb461fc70, 0x6743117c, 0xb45ceab8, 0x673f5ae0, 0xb457d92f,
+    0x673ba405, 0xb452c7d4,
+  0x6737ecea, 0xb44db6a8, 0x67343590, 0xb448a5aa, 0x67307df5, 0xb44394db,
+    0x672cc61c, 0xb43e843b,
+  0x67290e02, 0xb43973ca, 0x672555a9, 0xb4346387, 0x67219d10, 0xb42f5373,
+    0x671de438, 0xb42a438e,
+  0x671a2b20, 0xb42533d8, 0x671671c8, 0xb4202451, 0x6712b831, 0xb41b14f8,
+    0x670efe5a, 0xb41605ce,
+  0x670b4444, 0xb410f6d3, 0x670789ee, 0xb40be807, 0x6703cf58, 0xb406d969,
+    0x67001483, 0xb401cafb,
+  0x66fc596f, 0xb3fcbcbb, 0x66f89e1b, 0xb3f7aeaa, 0x66f4e287, 0xb3f2a0c9,
+    0x66f126b4, 0xb3ed9316,
+  0x66ed6aa1, 0xb3e88592, 0x66e9ae4f, 0xb3e3783d, 0x66e5f1be, 0xb3de6b17,
+    0x66e234ed, 0xb3d95e1f,
+  0x66de77dc, 0xb3d45157, 0x66daba8c, 0xb3cf44be, 0x66d6fcfd, 0xb3ca3854,
+    0x66d33f2e, 0xb3c52c19,
+  0x66cf8120, 0xb3c0200c, 0x66cbc2d2, 0xb3bb142f, 0x66c80445, 0xb3b60881,
+    0x66c44579, 0xb3b0fd02,
+  0x66c0866d, 0xb3abf1b2, 0x66bcc721, 0xb3a6e691, 0x66b90797, 0xb3a1dba0,
+    0x66b547cd, 0xb39cd0dd,
+  0x66b187c3, 0xb397c649, 0x66adc77b, 0xb392bbe5, 0x66aa06f3, 0xb38db1b0,
+    0x66a6462b, 0xb388a7aa,
+  0x66a28524, 0xb3839dd3, 0x669ec3de, 0xb37e942b, 0x669b0259, 0xb3798ab2,
+    0x66974095, 0xb3748169,
+  0x66937e91, 0xb36f784f, 0x668fbc4e, 0xb36a6f64, 0x668bf9cb, 0xb36566a8,
+    0x66883709, 0xb3605e1c,
+  0x66847408, 0xb35b55bf, 0x6680b0c8, 0xb3564d91, 0x667ced49, 0xb3514592,
+    0x6679298a, 0xb34c3dc3,
+  0x6675658c, 0xb3473623, 0x6671a14f, 0xb3422eb2, 0x666ddcd3, 0xb33d2771,
+    0x666a1818, 0xb338205f,
+  0x6666531d, 0xb333197c, 0x66628de4, 0xb32e12c9, 0x665ec86b, 0xb3290c45,
+    0x665b02b3, 0xb32405f1,
+  0x66573cbb, 0xb31effcc, 0x66537685, 0xb319f9d6, 0x664fb010, 0xb314f410,
+    0x664be95b, 0xb30fee79,
+  0x66482267, 0xb30ae912, 0x66445b35, 0xb305e3da, 0x664093c3, 0xb300ded2,
+    0x663ccc12, 0xb2fbd9f9,
+  0x66390422, 0xb2f6d550, 0x66353bf3, 0xb2f1d0d6, 0x66317385, 0xb2eccc8c,
+    0x662daad8, 0xb2e7c871,
+  0x6629e1ec, 0xb2e2c486, 0x662618c1, 0xb2ddc0ca, 0x66224f56, 0xb2d8bd3e,
+    0x661e85ad, 0xb2d3b9e2,
+  0x661abbc5, 0xb2ceb6b5, 0x6616f19e, 0xb2c9b3b8, 0x66132738, 0xb2c4b0ea,
+    0x660f5c93, 0xb2bfae4c,
+  0x660b91af, 0xb2baabde, 0x6607c68c, 0xb2b5a99f, 0x6603fb2a, 0xb2b0a790,
+    0x66002f89, 0xb2aba5b1,
+  0x65fc63a9, 0xb2a6a402, 0x65f8978b, 0xb2a1a282, 0x65f4cb2d, 0xb29ca132,
+    0x65f0fe91, 0xb297a011,
+  0x65ed31b5, 0xb2929f21, 0x65e9649b, 0xb28d9e60, 0x65e59742, 0xb2889dcf,
+    0x65e1c9aa, 0xb2839d6d,
+  0x65ddfbd3, 0xb27e9d3c, 0x65da2dbd, 0xb2799d3a, 0x65d65f69, 0xb2749d68,
+    0x65d290d6, 0xb26f9dc6,
+  0x65cec204, 0xb26a9e54, 0x65caf2f3, 0xb2659f12, 0x65c723a3, 0xb2609fff,
+    0x65c35415, 0xb25ba11d,
+  0x65bf8447, 0xb256a26a, 0x65bbb43b, 0xb251a3e7, 0x65b7e3f1, 0xb24ca594,
+    0x65b41367, 0xb247a771,
+  0x65b0429f, 0xb242a97e, 0x65ac7198, 0xb23dabbb, 0x65a8a052, 0xb238ae28,
+    0x65a4cece, 0xb233b0c5,
+  0x65a0fd0b, 0xb22eb392, 0x659d2b09, 0xb229b68f, 0x659958c9, 0xb224b9bc,
+    0x6595864a, 0xb21fbd19,
+  0x6591b38c, 0xb21ac0a6, 0x658de08f, 0xb215c463, 0x658a0d54, 0xb210c850,
+    0x658639db, 0xb20bcc6d,
+  0x65826622, 0xb206d0ba, 0x657e922b, 0xb201d537, 0x657abdf6, 0xb1fcd9e5,
+    0x6576e982, 0xb1f7dec2,
+  0x657314cf, 0xb1f2e3d0, 0x656f3fde, 0xb1ede90e, 0x656b6aae, 0xb1e8ee7c,
+    0x6567953f, 0xb1e3f41a,
+  0x6563bf92, 0xb1def9e9, 0x655fe9a7, 0xb1d9ffe7, 0x655c137d, 0xb1d50616,
+    0x65583d14, 0xb1d00c75,
+  0x6554666d, 0xb1cb1304, 0x65508f87, 0xb1c619c3, 0x654cb863, 0xb1c120b3,
+    0x6548e101, 0xb1bc27d3,
+  0x6545095f, 0xb1b72f23, 0x65413180, 0xb1b236a4, 0x653d5962, 0xb1ad3e55,
+    0x65398105, 0xb1a84636,
+  0x6535a86b, 0xb1a34e47, 0x6531cf91, 0xb19e5689, 0x652df679, 0xb1995efb,
+    0x652a1d23, 0xb194679e,
+  0x6526438f, 0xb18f7071, 0x652269bc, 0xb18a7974, 0x651e8faa, 0xb18582a8,
+    0x651ab55b, 0xb1808c0c,
+  0x6516dacd, 0xb17b95a0, 0x65130000, 0xb1769f65, 0x650f24f5, 0xb171a95b,
+    0x650b49ac, 0xb16cb380,
+  0x65076e25, 0xb167bdd7, 0x6503925f, 0xb162c85d, 0x64ffb65b, 0xb15dd315,
+    0x64fbda18, 0xb158ddfd,
+  0x64f7fd98, 0xb153e915, 0x64f420d9, 0xb14ef45e, 0x64f043dc, 0xb149ffd7,
+    0x64ec66a0, 0xb1450b81,
+  0x64e88926, 0xb140175b, 0x64e4ab6e, 0xb13b2367, 0x64e0cd78, 0xb1362fa2,
+    0x64dcef44, 0xb1313c0e,
+  0x64d910d1, 0xb12c48ab, 0x64d53220, 0xb1275579, 0x64d15331, 0xb1226277,
+    0x64cd7404, 0xb11d6fa6,
+  0x64c99498, 0xb1187d05, 0x64c5b4ef, 0xb1138a95, 0x64c1d507, 0xb10e9856,
+    0x64bdf4e1, 0xb109a648,
+  0x64ba147d, 0xb104b46a, 0x64b633da, 0xb0ffc2bd, 0x64b252fa, 0xb0fad140,
+    0x64ae71dc, 0xb0f5dff5,
+  0x64aa907f, 0xb0f0eeda, 0x64a6aee4, 0xb0ebfdf0, 0x64a2cd0c, 0xb0e70d37,
+    0x649eeaf5, 0xb0e21cae,
+  0x649b08a0, 0xb0dd2c56, 0x6497260d, 0xb0d83c2f, 0x6493433c, 0xb0d34c39,
+    0x648f602d, 0xb0ce5c74,
+  0x648b7ce0, 0xb0c96ce0, 0x64879955, 0xb0c47d7c, 0x6483b58c, 0xb0bf8e4a,
+    0x647fd185, 0xb0ba9f48,
+  0x647bed3f, 0xb0b5b077, 0x647808bc, 0xb0b0c1d7, 0x647423fb, 0xb0abd368,
+    0x64703efc, 0xb0a6e52a,
+  0x646c59bf, 0xb0a1f71d, 0x64687444, 0xb09d0941, 0x64648e8c, 0xb0981b96,
+    0x6460a895, 0xb0932e1b,
+  0x645cc260, 0xb08e40d2, 0x6458dbed, 0xb08953ba, 0x6454f53d, 0xb08466d3,
+    0x64510e4e, 0xb07f7a1c,
+  0x644d2722, 0xb07a8d97, 0x64493fb8, 0xb075a143, 0x64455810, 0xb070b520,
+    0x6441702a, 0xb06bc92e,
+  0x643d8806, 0xb066dd6d, 0x64399fa5, 0xb061f1de, 0x6435b706, 0xb05d067f,
+    0x6431ce28, 0xb0581b51,
+  0x642de50d, 0xb0533055, 0x6429fbb5, 0xb04e458a, 0x6426121e, 0xb0495af0,
+    0x6422284a, 0xb0447087,
+  0x641e3e38, 0xb03f864f, 0x641a53e8, 0xb03a9c49, 0x6416695a, 0xb035b273,
+    0x64127e8f, 0xb030c8cf,
+  0x640e9386, 0xb02bdf5c, 0x640aa83f, 0xb026f61b, 0x6406bcba, 0xb0220d0a,
+    0x6402d0f8, 0xb01d242b,
+  0x63fee4f8, 0xb0183b7d, 0x63faf8bb, 0xb0135301, 0x63f70c3f, 0xb00e6ab5,
+    0x63f31f86, 0xb009829c,
+  0x63ef3290, 0xb0049ab3, 0x63eb455c, 0xafffb2fc, 0x63e757ea, 0xaffacb76,
+    0x63e36a3a, 0xaff5e421,
+  0x63df7c4d, 0xaff0fcfe, 0x63db8e22, 0xafec160c, 0x63d79fba, 0xafe72f4c,
+    0x63d3b114, 0xafe248bd,
+  0x63cfc231, 0xafdd625f, 0x63cbd310, 0xafd87c33, 0x63c7e3b1, 0xafd39638,
+    0x63c3f415, 0xafceb06f,
+  0x63c0043b, 0xafc9cad7, 0x63bc1424, 0xafc4e571, 0x63b823cf, 0xafc0003c,
+    0x63b4333d, 0xafbb1b39,
+  0x63b0426d, 0xafb63667, 0x63ac5160, 0xafb151c7, 0x63a86015, 0xafac6d58,
+    0x63a46e8d, 0xafa7891b,
+  0x63a07cc7, 0xafa2a50f, 0x639c8ac4, 0xaf9dc135, 0x63989884, 0xaf98dd8d,
+    0x6394a606, 0xaf93fa16,
+  0x6390b34a, 0xaf8f16d1, 0x638cc051, 0xaf8a33bd, 0x6388cd1b, 0xaf8550db,
+    0x6384d9a7, 0xaf806e2b,
+  0x6380e5f6, 0xaf7b8bac, 0x637cf208, 0xaf76a95f, 0x6378fddc, 0xaf71c743,
+    0x63750973, 0xaf6ce55a,
+  0x637114cc, 0xaf6803a2, 0x636d1fe9, 0xaf63221c, 0x63692ac7, 0xaf5e40c7,
+    0x63653569, 0xaf595fa4,
+  0x63613fcd, 0xaf547eb3, 0x635d49f4, 0xaf4f9df4, 0x635953dd, 0xaf4abd66,
+    0x63555d8a, 0xaf45dd0b,
+  0x635166f9, 0xaf40fce1, 0x634d702b, 0xaf3c1ce9, 0x6349791f, 0xaf373d22,
+    0x634581d6, 0xaf325d8e,
+  0x63418a50, 0xaf2d7e2b, 0x633d928d, 0xaf289efa, 0x63399a8d, 0xaf23bffb,
+    0x6335a24f, 0xaf1ee12e,
+  0x6331a9d4, 0xaf1a0293, 0x632db11c, 0xaf15242a, 0x6329b827, 0xaf1045f3,
+    0x6325bef5, 0xaf0b67ed,
+  0x6321c585, 0xaf068a1a, 0x631dcbd9, 0xaf01ac78, 0x6319d1ef, 0xaefccf09,
+    0x6315d7c8, 0xaef7f1cb,
+  0x6311dd64, 0xaef314c0, 0x630de2c3, 0xaeee37e6, 0x6309e7e4, 0xaee95b3f,
+    0x6305ecc9, 0xaee47ec9,
+  0x6301f171, 0xaedfa285, 0x62fdf5db, 0xaedac674, 0x62f9fa09, 0xaed5ea95,
+    0x62f5fdf9, 0xaed10ee7,
+  0x62f201ac, 0xaecc336c, 0x62ee0523, 0xaec75823, 0x62ea085c, 0xaec27d0c,
+    0x62e60b58, 0xaebda227,
+  0x62e20e17, 0xaeb8c774, 0x62de109a, 0xaeb3ecf3, 0x62da12df, 0xaeaf12a4,
+    0x62d614e7, 0xaeaa3888,
+  0x62d216b3, 0xaea55e9e, 0x62ce1841, 0xaea084e6, 0x62ca1992, 0xae9bab60,
+    0x62c61aa7, 0xae96d20c,
+  0x62c21b7e, 0xae91f8eb, 0x62be1c19, 0xae8d1ffb, 0x62ba1c77, 0xae88473e,
+    0x62b61c98, 0xae836eb4,
+  0x62b21c7b, 0xae7e965b, 0x62ae1c23, 0xae79be35, 0x62aa1b8d, 0xae74e641,
+    0x62a61aba, 0xae700e80,
+  0x62a219aa, 0xae6b36f0, 0x629e185e, 0xae665f93, 0x629a16d5, 0xae618869,
+    0x6296150f, 0xae5cb171,
+  0x6292130c, 0xae57daab, 0x628e10cc, 0xae530417, 0x628a0e50, 0xae4e2db6,
+    0x62860b97, 0xae495787,
+  0x628208a1, 0xae44818b, 0x627e056e, 0xae3fabc1, 0x627a01fe, 0xae3ad629,
+    0x6275fe52, 0xae3600c4,
+  0x6271fa69, 0xae312b92, 0x626df643, 0xae2c5691, 0x6269f1e1, 0xae2781c4,
+    0x6265ed42, 0xae22ad29,
+  0x6261e866, 0xae1dd8c0, 0x625de34e, 0xae19048a, 0x6259ddf8, 0xae143086,
+    0x6255d866, 0xae0f5cb5,
+  0x6251d298, 0xae0a8916, 0x624dcc8d, 0xae05b5aa, 0x6249c645, 0xae00e271,
+    0x6245bfc0, 0xadfc0f6a,
+  0x6241b8ff, 0xadf73c96, 0x623db202, 0xadf269f4, 0x6239aac7, 0xaded9785,
+    0x6235a351, 0xade8c548,
+  0x62319b9d, 0xade3f33e, 0x622d93ad, 0xaddf2167, 0x62298b81, 0xadda4fc3,
+    0x62258317, 0xadd57e51,
+  0x62217a72, 0xadd0ad12, 0x621d7190, 0xadcbdc05, 0x62196871, 0xadc70b2c,
+    0x62155f16, 0xadc23a85,
+  0x6211557e, 0xadbd6a10, 0x620d4baa, 0xadb899cf, 0x62094199, 0xadb3c9c0,
+    0x6205374c, 0xadaef9e4,
+  0x62012cc2, 0xadaa2a3b, 0x61fd21fc, 0xada55ac4, 0x61f916f9, 0xada08b80,
+    0x61f50bba, 0xad9bbc70,
+  0x61f1003f, 0xad96ed92, 0x61ecf487, 0xad921ee6, 0x61e8e893, 0xad8d506e,
+    0x61e4dc62, 0xad888229,
+  0x61e0cff5, 0xad83b416, 0x61dcc34c, 0xad7ee636, 0x61d8b666, 0xad7a1889,
+    0x61d4a944, 0xad754b0f,
+  0x61d09be5, 0xad707dc8, 0x61cc8e4b, 0xad6bb0b4, 0x61c88074, 0xad66e3d3,
+    0x61c47260, 0xad621725,
+  0x61c06410, 0xad5d4aaa, 0x61bc5584, 0xad587e61, 0x61b846bc, 0xad53b24c,
+    0x61b437b7, 0xad4ee66a,
+  0x61b02876, 0xad4a1aba, 0x61ac18f9, 0xad454f3e, 0x61a80940, 0xad4083f5,
+    0x61a3f94a, 0xad3bb8df,
+  0x619fe918, 0xad36edfc, 0x619bd8aa, 0xad32234b, 0x6197c800, 0xad2d58ce,
+    0x6193b719, 0xad288e85,
+  0x618fa5f7, 0xad23c46e, 0x618b9498, 0xad1efa8a, 0x618782fd, 0xad1a30d9,
+    0x61837126, 0xad15675c,
+  0x617f5f12, 0xad109e12, 0x617b4cc3, 0xad0bd4fb, 0x61773a37, 0xad070c17,
+    0x61732770, 0xad024366,
+  0x616f146c, 0xacfd7ae8, 0x616b012c, 0xacf8b29e, 0x6166edb0, 0xacf3ea87,
+    0x6162d9f8, 0xacef22a3,
+  0x615ec603, 0xacea5af2, 0x615ab1d3, 0xace59375, 0x61569d67, 0xace0cc2b,
+    0x615288be, 0xacdc0514,
+  0x614e73da, 0xacd73e30, 0x614a5eba, 0xacd27780, 0x6146495d, 0xaccdb103,
+    0x614233c5, 0xacc8eab9,
+  0x613e1df0, 0xacc424a3, 0x613a07e0, 0xacbf5ec0, 0x6135f193, 0xacba9910,
+    0x6131db0b, 0xacb5d394,
+  0x612dc447, 0xacb10e4b, 0x6129ad46, 0xacac4935, 0x6125960a, 0xaca78453,
+    0x61217e92, 0xaca2bfa4,
+  0x611d66de, 0xac9dfb29, 0x61194eee, 0xac9936e1, 0x611536c2, 0xac9472cd,
+    0x61111e5b, 0xac8faeec,
+  0x610d05b7, 0xac8aeb3e, 0x6108ecd8, 0xac8627c4, 0x6104d3bc, 0xac81647e,
+    0x6100ba65, 0xac7ca16b,
+  0x60fca0d2, 0xac77de8b, 0x60f88703, 0xac731bdf, 0x60f46cf9, 0xac6e5967,
+    0x60f052b2, 0xac699722,
+  0x60ec3830, 0xac64d510, 0x60e81d72, 0xac601333, 0x60e40278, 0xac5b5189,
+    0x60dfe743, 0xac569012,
+  0x60dbcbd1, 0xac51cecf, 0x60d7b024, 0xac4d0dc0, 0x60d3943b, 0xac484ce4,
+    0x60cf7817, 0xac438c3c,
+  0x60cb5bb7, 0xac3ecbc7, 0x60c73f1b, 0xac3a0b87, 0x60c32243, 0xac354b7a,
+    0x60bf0530, 0xac308ba0,
+  0x60bae7e1, 0xac2bcbfa, 0x60b6ca56, 0xac270c88, 0x60b2ac8f, 0xac224d4a,
+    0x60ae8e8d, 0xac1d8e40,
+  0x60aa7050, 0xac18cf69, 0x60a651d7, 0xac1410c6, 0x60a23322, 0xac0f5256,
+    0x609e1431, 0xac0a941b,
+  0x6099f505, 0xac05d613, 0x6095d59d, 0xac01183f, 0x6091b5fa, 0xabfc5a9f,
+    0x608d961b, 0xabf79d33,
+  0x60897601, 0xabf2dffb, 0x608555ab, 0xabee22f6, 0x60813519, 0xabe96625,
+    0x607d144c, 0xabe4a988,
+  0x6078f344, 0xabdfed1f, 0x6074d200, 0xabdb30ea, 0x6070b080, 0xabd674e9,
+    0x606c8ec5, 0xabd1b91c,
+  0x60686ccf, 0xabccfd83, 0x60644a9d, 0xabc8421d, 0x6060282f, 0xabc386ec,
+    0x605c0587, 0xabbecbee,
+  0x6057e2a2, 0xabba1125, 0x6053bf82, 0xabb5568f, 0x604f9c27, 0xabb09c2e,
+    0x604b7891, 0xababe200,
+  0x604754bf, 0xaba72807, 0x604330b1, 0xaba26e41, 0x603f0c69, 0xab9db4b0,
+    0x603ae7e5, 0xab98fb52,
+  0x6036c325, 0xab944229, 0x60329e2a, 0xab8f8934, 0x602e78f4, 0xab8ad073,
+    0x602a5383, 0xab8617e6,
+  0x60262dd6, 0xab815f8d, 0x602207ee, 0xab7ca768, 0x601de1ca, 0xab77ef77,
+    0x6019bb6b, 0xab7337bb,
+  0x601594d1, 0xab6e8032, 0x60116dfc, 0xab69c8de, 0x600d46ec, 0xab6511be,
+    0x60091fa0, 0xab605ad2,
+  0x6004f819, 0xab5ba41a, 0x6000d057, 0xab56ed97, 0x5ffca859, 0xab523748,
+    0x5ff88021, 0xab4d812d,
+  0x5ff457ad, 0xab48cb46, 0x5ff02efe, 0xab441593, 0x5fec0613, 0xab3f6015,
+    0x5fe7dcee, 0xab3aaacb,
+  0x5fe3b38d, 0xab35f5b5, 0x5fdf89f2, 0xab3140d4, 0x5fdb601b, 0xab2c8c27,
+    0x5fd73609, 0xab27d7ae,
+  0x5fd30bbc, 0xab23236a, 0x5fcee133, 0xab1e6f5a, 0x5fcab670, 0xab19bb7e,
+    0x5fc68b72, 0xab1507d7,
+  0x5fc26038, 0xab105464, 0x5fbe34c4, 0xab0ba125, 0x5fba0914, 0xab06ee1b,
+    0x5fb5dd29, 0xab023b46,
+  0x5fb1b104, 0xaafd88a4, 0x5fad84a3, 0xaaf8d637, 0x5fa95807, 0xaaf423ff,
+    0x5fa52b31, 0xaaef71fb,
+  0x5fa0fe1f, 0xaaeac02c, 0x5f9cd0d2, 0xaae60e91, 0x5f98a34a, 0xaae15d2a,
+    0x5f947588, 0xaadcabf8,
+  0x5f90478a, 0xaad7fafb, 0x5f8c1951, 0xaad34a32, 0x5f87eade, 0xaace999d,
+    0x5f83bc2f, 0xaac9e93e,
+  0x5f7f8d46, 0xaac53912, 0x5f7b5e22, 0xaac0891c, 0x5f772ec2, 0xaabbd959,
+    0x5f72ff28, 0xaab729cc,
+  0x5f6ecf53, 0xaab27a73, 0x5f6a9f44, 0xaaadcb4f, 0x5f666ef9, 0xaaa91c5f,
+    0x5f623e73, 0xaaa46da4,
+  0x5f5e0db3, 0xaa9fbf1e, 0x5f59dcb8, 0xaa9b10cc, 0x5f55ab82, 0xaa9662af,
+    0x5f517a11, 0xaa91b4c7,
+  0x5f4d4865, 0xaa8d0713, 0x5f49167f, 0xaa885994, 0x5f44e45e, 0xaa83ac4a,
+    0x5f40b202, 0xaa7eff34,
+  0x5f3c7f6b, 0xaa7a5253, 0x5f384c9a, 0xaa75a5a8, 0x5f34198e, 0xaa70f930,
+    0x5f2fe647, 0xaa6c4cee,
+  0x5f2bb2c5, 0xaa67a0e0, 0x5f277f09, 0xaa62f507, 0x5f234b12, 0xaa5e4963,
+    0x5f1f16e0, 0xaa599df4,
+  0x5f1ae274, 0xaa54f2ba, 0x5f16adcc, 0xaa5047b4, 0x5f1278eb, 0xaa4b9ce3,
+    0x5f0e43ce, 0xaa46f248,
+  0x5f0a0e77, 0xaa4247e1, 0x5f05d8e6, 0xaa3d9daf, 0x5f01a31a, 0xaa38f3b1,
+    0x5efd6d13, 0xaa3449e9,
+  0x5ef936d1, 0xaa2fa056, 0x5ef50055, 0xaa2af6f7, 0x5ef0c99f, 0xaa264dce,
+    0x5eec92ae, 0xaa21a4d9,
+  0x5ee85b82, 0xaa1cfc1a, 0x5ee4241c, 0xaa18538f, 0x5edfec7b, 0xaa13ab3a,
+    0x5edbb49f, 0xaa0f0319,
+  0x5ed77c8a, 0xaa0a5b2e, 0x5ed34439, 0xaa05b377, 0x5ecf0baf, 0xaa010bf6,
+    0x5ecad2e9, 0xa9fc64a9,
+  0x5ec699e9, 0xa9f7bd92, 0x5ec260af, 0xa9f316b0, 0x5ebe273b, 0xa9ee7002,
+    0x5eb9ed8b, 0xa9e9c98a,
+  0x5eb5b3a2, 0xa9e52347, 0x5eb1797e, 0xa9e07d39, 0x5ead3f1f, 0xa9dbd761,
+    0x5ea90487, 0xa9d731bd,
+  0x5ea4c9b3, 0xa9d28c4e, 0x5ea08ea6, 0xa9cde715, 0x5e9c535e, 0xa9c94211,
+    0x5e9817dc, 0xa9c49d42,
+  0x5e93dc1f, 0xa9bff8a8, 0x5e8fa028, 0xa9bb5444, 0x5e8b63f7, 0xa9b6b014,
+    0x5e87278b, 0xa9b20c1a,
+  0x5e82eae5, 0xa9ad6855, 0x5e7eae05, 0xa9a8c4c5, 0x5e7a70ea, 0xa9a4216b,
+    0x5e763395, 0xa99f7e46,
+  0x5e71f606, 0xa99adb56, 0x5e6db83d, 0xa996389b, 0x5e697a39, 0xa9919616,
+    0x5e653bfc, 0xa98cf3c6,
+  0x5e60fd84, 0xa98851ac, 0x5e5cbed1, 0xa983afc6, 0x5e587fe5, 0xa97f0e16,
+    0x5e5440be, 0xa97a6c9c,
+  0x5e50015d, 0xa975cb57, 0x5e4bc1c2, 0xa9712a47, 0x5e4781ed, 0xa96c896c,
+    0x5e4341de, 0xa967e8c7,
+  0x5e3f0194, 0xa9634858, 0x5e3ac110, 0xa95ea81d, 0x5e368053, 0xa95a0819,
+    0x5e323f5b, 0xa9556849,
+  0x5e2dfe29, 0xa950c8b0, 0x5e29bcbd, 0xa94c294b, 0x5e257b17, 0xa9478a1c,
+    0x5e213936, 0xa942eb23,
+  0x5e1cf71c, 0xa93e4c5f, 0x5e18b4c8, 0xa939add1, 0x5e147239, 0xa9350f78,
+    0x5e102f71, 0xa9307155,
+  0x5e0bec6e, 0xa92bd367, 0x5e07a932, 0xa92735af, 0x5e0365bb, 0xa922982c,
+    0x5dff220b, 0xa91dfadf,
+  0x5dfade20, 0xa9195dc7, 0x5df699fc, 0xa914c0e6, 0x5df2559e, 0xa9102439,
+    0x5dee1105, 0xa90b87c3,
+  0x5de9cc33, 0xa906eb82, 0x5de58727, 0xa9024f76, 0x5de141e1, 0xa8fdb3a1,
+    0x5ddcfc61, 0xa8f91801,
+  0x5dd8b6a7, 0xa8f47c97, 0x5dd470b3, 0xa8efe162, 0x5dd02a85, 0xa8eb4663,
+    0x5dcbe41d, 0xa8e6ab9a,
+  0x5dc79d7c, 0xa8e21106, 0x5dc356a1, 0xa8dd76a9, 0x5dbf0f8c, 0xa8d8dc81,
+    0x5dbac83d, 0xa8d4428f,
+  0x5db680b4, 0xa8cfa8d2, 0x5db238f1, 0xa8cb0f4b, 0x5dadf0f5, 0xa8c675fb,
+    0x5da9a8bf, 0xa8c1dce0,
+  0x5da5604f, 0xa8bd43fa, 0x5da117a5, 0xa8b8ab4b, 0x5d9ccec2, 0xa8b412d1,
+    0x5d9885a5, 0xa8af7a8e,
+  0x5d943c4e, 0xa8aae280, 0x5d8ff2bd, 0xa8a64aa8, 0x5d8ba8f3, 0xa8a1b306,
+    0x5d875eef, 0xa89d1b99,
+  0x5d8314b1, 0xa8988463, 0x5d7eca39, 0xa893ed63, 0x5d7a7f88, 0xa88f5698,
+    0x5d76349d, 0xa88ac004,
+  0x5d71e979, 0xa88629a5, 0x5d6d9e1b, 0xa881937c, 0x5d695283, 0xa87cfd8a,
+    0x5d6506b2, 0xa87867cd,
+  0x5d60baa7, 0xa873d246, 0x5d5c6e62, 0xa86f3cf6, 0x5d5821e4, 0xa86aa7db,
+    0x5d53d52d, 0xa86612f6,
+  0x5d4f883b, 0xa8617e48, 0x5d4b3b10, 0xa85ce9cf, 0x5d46edac, 0xa858558d,
+    0x5d42a00e, 0xa853c180,
+  0x5d3e5237, 0xa84f2daa, 0x5d3a0426, 0xa84a9a0a, 0x5d35b5db, 0xa84606a0,
+    0x5d316757, 0xa841736c,
+  0x5d2d189a, 0xa83ce06e, 0x5d28c9a3, 0xa8384da6, 0x5d247a72, 0xa833bb14,
+    0x5d202b09, 0xa82f28b9,
+  0x5d1bdb65, 0xa82a9693, 0x5d178b89, 0xa82604a4, 0x5d133b72, 0xa82172eb,
+    0x5d0eeb23, 0xa81ce169,
+  0x5d0a9a9a, 0xa818501c, 0x5d0649d7, 0xa813bf06, 0x5d01f8dc, 0xa80f2e26,
+    0x5cfda7a7, 0xa80a9d7c,
+  0x5cf95638, 0xa8060d08, 0x5cf50490, 0xa8017ccb, 0x5cf0b2af, 0xa7fcecc4,
+    0x5cec6095, 0xa7f85cf3,
+  0x5ce80e41, 0xa7f3cd59, 0x5ce3bbb4, 0xa7ef3df5, 0x5cdf68ed, 0xa7eaaec7,
+    0x5cdb15ed, 0xa7e61fd0,
+  0x5cd6c2b5, 0xa7e1910f, 0x5cd26f42, 0xa7dd0284, 0x5cce1b97, 0xa7d8742f,
+    0x5cc9c7b2, 0xa7d3e611,
+  0x5cc57394, 0xa7cf582a, 0x5cc11f3d, 0xa7caca79, 0x5cbccaac, 0xa7c63cfe,
+    0x5cb875e3, 0xa7c1afb9,
+  0x5cb420e0, 0xa7bd22ac, 0x5cafcba4, 0xa7b895d4, 0x5cab762f, 0xa7b40933,
+    0x5ca72080, 0xa7af7cc8,
+  0x5ca2ca99, 0xa7aaf094, 0x5c9e7478, 0xa7a66497, 0x5c9a1e1e, 0xa7a1d8d0,
+    0x5c95c78b, 0xa79d4d3f,
+  0x5c9170bf, 0xa798c1e5, 0x5c8d19ba, 0xa79436c1, 0x5c88c27c, 0xa78fabd4,
+    0x5c846b05, 0xa78b211e,
+  0x5c801354, 0xa786969e, 0x5c7bbb6b, 0xa7820c55, 0x5c776348, 0xa77d8242,
+    0x5c730aed, 0xa778f866,
+  0x5c6eb258, 0xa7746ec0, 0x5c6a598b, 0xa76fe551, 0x5c660084, 0xa76b5c19,
+    0x5c61a745, 0xa766d317,
+  0x5c5d4dcc, 0xa7624a4d, 0x5c58f41a, 0xa75dc1b8, 0x5c549a30, 0xa759395b,
+    0x5c50400d, 0xa754b134,
+  0x5c4be5b0, 0xa7502943, 0x5c478b1b, 0xa74ba18a, 0x5c43304d, 0xa7471a07,
+    0x5c3ed545, 0xa74292bb,
+  0x5c3a7a05, 0xa73e0ba5, 0x5c361e8c, 0xa73984c7, 0x5c31c2db, 0xa734fe1f,
+    0x5c2d66f0, 0xa73077ae,
+  0x5c290acc, 0xa72bf174, 0x5c24ae70, 0xa7276b70, 0x5c2051db, 0xa722e5a3,
+    0x5c1bf50d, 0xa71e600d,
+  0x5c179806, 0xa719daae, 0x5c133ac6, 0xa7155586, 0x5c0edd4e, 0xa710d095,
+    0x5c0a7f9c, 0xa70c4bda,
+  0x5c0621b2, 0xa707c757, 0x5c01c38f, 0xa703430a, 0x5bfd6534, 0xa6febef4,
+    0x5bf906a0, 0xa6fa3b15,
+  0x5bf4a7d2, 0xa6f5b76d, 0x5bf048cd, 0xa6f133fc, 0x5bebe98e, 0xa6ecb0c2,
+    0x5be78a17, 0xa6e82dbe,
+  0x5be32a67, 0xa6e3aaf2, 0x5bdeca7f, 0xa6df285d, 0x5bda6a5d, 0xa6daa5fe,
+    0x5bd60a03, 0xa6d623d7,
+  0x5bd1a971, 0xa6d1a1e7, 0x5bcd48a6, 0xa6cd202d, 0x5bc8e7a2, 0xa6c89eab,
+    0x5bc48666, 0xa6c41d60,
+  0x5bc024f0, 0xa6bf9c4b, 0x5bbbc343, 0xa6bb1b6e, 0x5bb7615d, 0xa6b69ac8,
+    0x5bb2ff3e, 0xa6b21a59,
+  0x5bae9ce7, 0xa6ad9a21, 0x5baa3a57, 0xa6a91a20, 0x5ba5d78e, 0xa6a49a56,
+    0x5ba1748d, 0xa6a01ac4,
+  0x5b9d1154, 0xa69b9b68, 0x5b98ade2, 0xa6971c44, 0x5b944a37, 0xa6929d57,
+    0x5b8fe654, 0xa68e1ea1,
+  0x5b8b8239, 0xa689a022, 0x5b871de5, 0xa68521da, 0x5b82b958, 0xa680a3ca,
+    0x5b7e5493, 0xa67c25f0,
+  0x5b79ef96, 0xa677a84e, 0x5b758a60, 0xa6732ae3, 0x5b7124f2, 0xa66eadb0,
+    0x5b6cbf4c, 0xa66a30b3,
+  0x5b68596d, 0xa665b3ee, 0x5b63f355, 0xa6613760, 0x5b5f8d06, 0xa65cbb0a,
+    0x5b5b267e, 0xa6583eeb,
+  0x5b56bfbd, 0xa653c303, 0x5b5258c4, 0xa64f4752, 0x5b4df193, 0xa64acbd9,
+    0x5b498a2a, 0xa6465097,
+  0x5b452288, 0xa641d58c, 0x5b40baae, 0xa63d5ab9, 0x5b3c529c, 0xa638e01d,
+    0x5b37ea51, 0xa63465b9,
+  0x5b3381ce, 0xa62feb8b, 0x5b2f1913, 0xa62b7196, 0x5b2ab020, 0xa626f7d7,
+    0x5b2646f4, 0xa6227e50,
+  0x5b21dd90, 0xa61e0501, 0x5b1d73f4, 0xa6198be9, 0x5b190a20, 0xa6151308,
+    0x5b14a014, 0xa6109a5f,
+  0x5b1035cf, 0xa60c21ee, 0x5b0bcb52, 0xa607a9b4, 0x5b07609d, 0xa60331b1,
+    0x5b02f5b0, 0xa5feb9e6,
+  0x5afe8a8b, 0xa5fa4252, 0x5afa1f2e, 0xa5f5caf6, 0x5af5b398, 0xa5f153d2,
+    0x5af147ca, 0xa5ecdce5,
+  0x5aecdbc5, 0xa5e8662f, 0x5ae86f87, 0xa5e3efb1, 0x5ae40311, 0xa5df796b,
+    0x5adf9663, 0xa5db035c,
+  0x5adb297d, 0xa5d68d85, 0x5ad6bc5f, 0xa5d217e6, 0x5ad24f09, 0xa5cda27e,
+    0x5acde17b, 0xa5c92d4e,
+  0x5ac973b5, 0xa5c4b855, 0x5ac505b7, 0xa5c04395, 0x5ac09781, 0xa5bbcf0b,
+    0x5abc2912, 0xa5b75aba,
+  0x5ab7ba6c, 0xa5b2e6a0, 0x5ab34b8e, 0xa5ae72be, 0x5aaedc78, 0xa5a9ff14,
+    0x5aaa6d2b, 0xa5a58ba1,
+  0x5aa5fda5, 0xa5a11866, 0x5aa18de7, 0xa59ca563, 0x5a9d1df1, 0xa5983297,
+    0x5a98adc4, 0xa593c004,
+  0x5a943d5e, 0xa58f4da8, 0x5a8fccc1, 0xa58adb84, 0x5a8b5bec, 0xa5866997,
+    0x5a86eadf, 0xa581f7e3,
+  0x5a82799a, 0xa57d8666, 0x5a7e081d, 0xa5791521, 0x5a799669, 0xa574a414,
+    0x5a75247c, 0xa570333f,
+  0x5a70b258, 0xa56bc2a2, 0x5a6c3ffc, 0xa567523c, 0x5a67cd69, 0xa562e20f,
+    0x5a635a9d, 0xa55e7219,
+  0x5a5ee79a, 0xa55a025b, 0x5a5a745f, 0xa55592d5, 0x5a5600ec, 0xa5512388,
+    0x5a518d42, 0xa54cb472,
+  0x5a4d1960, 0xa5484594, 0x5a48a546, 0xa543d6ee, 0x5a4430f5, 0xa53f687f,
+    0x5a3fbc6b, 0xa53afa49,
+  0x5a3b47ab, 0xa5368c4b, 0x5a36d2b2, 0xa5321e85, 0x5a325d82, 0xa52db0f7,
+    0x5a2de81a, 0xa52943a1,
+  0x5a29727b, 0xa524d683, 0x5a24fca4, 0xa520699d, 0x5a208695, 0xa51bfcef,
+    0x5a1c104f, 0xa5179079,
+  0x5a1799d1, 0xa513243b, 0x5a13231b, 0xa50eb836, 0x5a0eac2e, 0xa50a4c68,
+    0x5a0a350a, 0xa505e0d2,
+  0x5a05bdae, 0xa5017575, 0x5a01461a, 0xa4fd0a50, 0x59fcce4f, 0xa4f89f63,
+    0x59f8564c, 0xa4f434ae,
+  0x59f3de12, 0xa4efca31, 0x59ef65a1, 0xa4eb5fec, 0x59eaecf8, 0xa4e6f5e0,
+    0x59e67417, 0xa4e28c0c,
+  0x59e1faff, 0xa4de2270, 0x59dd81b0, 0xa4d9b90c, 0x59d90829, 0xa4d54fe0,
+    0x59d48e6a, 0xa4d0e6ed,
+  0x59d01475, 0xa4cc7e32, 0x59cb9a47, 0xa4c815af, 0x59c71fe3, 0xa4c3ad64,
+    0x59c2a547, 0xa4bf4552,
+  0x59be2a74, 0xa4badd78, 0x59b9af69, 0xa4b675d6, 0x59b53427, 0xa4b20e6d,
+    0x59b0b8ae, 0xa4ada73c,
+  0x59ac3cfd, 0xa4a94043, 0x59a7c115, 0xa4a4d982, 0x59a344f6, 0xa4a072fa,
+    0x599ec8a0, 0xa49c0cab,
+  0x599a4c12, 0xa497a693, 0x5995cf4d, 0xa49340b4, 0x59915250, 0xa48edb0e,
+    0x598cd51d, 0xa48a75a0,
+  0x598857b2, 0xa486106a, 0x5983da10, 0xa481ab6d, 0x597f5c36, 0xa47d46a8,
+    0x597ade26, 0xa478e21b,
+  0x59765fde, 0xa4747dc7, 0x5971e15f, 0xa47019ac, 0x596d62a9, 0xa46bb5c9,
+    0x5968e3bc, 0xa467521e,
+  0x59646498, 0xa462eeac, 0x595fe53c, 0xa45e8b73, 0x595b65aa, 0xa45a2872,
+    0x5956e5e0, 0xa455c5a9,
+  0x595265df, 0xa4516319, 0x594de5a7, 0xa44d00c2, 0x59496538, 0xa4489ea3,
+    0x5944e492, 0xa4443cbd,
+  0x594063b5, 0xa43fdb10, 0x593be2a0, 0xa43b799a, 0x59376155, 0xa437185e,
+    0x5932dfd3, 0xa432b75a,
+  0x592e5e19, 0xa42e568f, 0x5929dc29, 0xa429f5fd, 0x59255a02, 0xa42595a3,
+    0x5920d7a3, 0xa4213581,
+  0x591c550e, 0xa41cd599, 0x5917d242, 0xa41875e9, 0x59134f3e, 0xa4141672,
+    0x590ecc04, 0xa40fb733,
+  0x590a4893, 0xa40b582e, 0x5905c4eb, 0xa406f960, 0x5901410c, 0xa4029acc,
+    0x58fcbcf6, 0xa3fe3c71,
+  0x58f838a9, 0xa3f9de4e, 0x58f3b426, 0xa3f58064, 0x58ef2f6b, 0xa3f122b2,
+    0x58eaaa7a, 0xa3ecc53a,
+  0x58e62552, 0xa3e867fa, 0x58e19ff3, 0xa3e40af3, 0x58dd1a5d, 0xa3dfae25,
+    0x58d89490, 0xa3db5190,
+  0x58d40e8c, 0xa3d6f534, 0x58cf8852, 0xa3d29910, 0x58cb01e1, 0xa3ce3d25,
+    0x58c67b39, 0xa3c9e174,
+  0x58c1f45b, 0xa3c585fb, 0x58bd6d45, 0xa3c12abb, 0x58b8e5f9, 0xa3bccfb3,
+    0x58b45e76, 0xa3b874e5,
+  0x58afd6bd, 0xa3b41a50, 0x58ab4ecc, 0xa3afbff3, 0x58a6c6a5, 0xa3ab65d0,
+    0x58a23e48, 0xa3a70be6,
+  0x589db5b3, 0xa3a2b234, 0x58992ce9, 0xa39e58bb, 0x5894a3e7, 0xa399ff7c,
+    0x58901aaf, 0xa395a675,
+  0x588b9140, 0xa3914da8, 0x5887079a, 0xa38cf513, 0x58827dbe, 0xa3889cb8,
+    0x587df3ab, 0xa3844495,
+  0x58796962, 0xa37fecac, 0x5874dee2, 0xa37b94fb, 0x5870542c, 0xa3773d84,
+    0x586bc93f, 0xa372e646,
+  0x58673e1b, 0xa36e8f41, 0x5862b2c1, 0xa36a3875, 0x585e2730, 0xa365e1e2,
+    0x58599b69, 0xa3618b88,
+  0x58550f6c, 0xa35d3567, 0x58508338, 0xa358df80, 0x584bf6cd, 0xa35489d1,
+    0x58476a2c, 0xa350345c,
+  0x5842dd54, 0xa34bdf20, 0x583e5047, 0xa3478a1d, 0x5839c302, 0xa3433554,
+    0x58353587, 0xa33ee0c3,
+  0x5830a7d6, 0xa33a8c6c, 0x582c19ef, 0xa336384e, 0x58278bd1, 0xa331e469,
+    0x5822fd7c, 0xa32d90be,
+  0x581e6ef1, 0xa3293d4b, 0x5819e030, 0xa324ea13, 0x58155139, 0xa3209713,
+    0x5810c20b, 0xa31c444c,
+  0x580c32a7, 0xa317f1bf, 0x5807a30d, 0xa3139f6b, 0x5803133c, 0xa30f4d51,
+    0x57fe8335, 0xa30afb70,
+  0x57f9f2f8, 0xa306a9c8, 0x57f56284, 0xa3025859, 0x57f0d1da, 0xa2fe0724,
+    0x57ec40fa, 0xa2f9b629,
+  0x57e7afe4, 0xa2f56566, 0x57e31e97, 0xa2f114dd, 0x57de8d15, 0xa2ecc48e,
+    0x57d9fb5c, 0xa2e87477,
+  0x57d5696d, 0xa2e4249b, 0x57d0d747, 0xa2dfd4f7, 0x57cc44ec, 0xa2db858e,
+    0x57c7b25a, 0xa2d7365d,
+  0x57c31f92, 0xa2d2e766, 0x57be8c94, 0xa2ce98a9, 0x57b9f960, 0xa2ca4a25,
+    0x57b565f6, 0xa2c5fbda,
+  0x57b0d256, 0xa2c1adc9, 0x57ac3e80, 0xa2bd5ff2, 0x57a7aa73, 0xa2b91254,
+    0x57a31631, 0xa2b4c4f0,
+  0x579e81b8, 0xa2b077c5, 0x5799ed0a, 0xa2ac2ad3, 0x57955825, 0xa2a7de1c,
+    0x5790c30a, 0xa2a3919e,
+  0x578c2dba, 0xa29f4559, 0x57879833, 0xa29af94e, 0x57830276, 0xa296ad7d,
+    0x577e6c84, 0xa29261e5,
+  0x5779d65b, 0xa28e1687, 0x57753ffc, 0xa289cb63, 0x5770a968, 0xa2858078,
+    0x576c129d, 0xa28135c7,
+  0x57677b9d, 0xa27ceb4f, 0x5762e467, 0xa278a111, 0x575e4cfa, 0xa274570d,
+    0x5759b558, 0xa2700d43,
+  0x57551d80, 0xa26bc3b2, 0x57508572, 0xa2677a5b, 0x574bed2f, 0xa263313e,
+    0x574754b5, 0xa25ee85b,
+  0x5742bc06, 0xa25a9fb1, 0x573e2320, 0xa2565741, 0x57398a05, 0xa2520f0b,
+    0x5734f0b5, 0xa24dc70f,
+  0x5730572e, 0xa2497f4c, 0x572bbd71, 0xa24537c3, 0x5727237f, 0xa240f074,
+    0x57228957, 0xa23ca95f,
+  0x571deefa, 0xa2386284, 0x57195466, 0xa2341be3, 0x5714b99d, 0xa22fd57b,
+    0x57101e9e, 0xa22b8f4d,
+  0x570b8369, 0xa2274959, 0x5706e7ff, 0xa223039f, 0x57024c5f, 0xa21ebe1f,
+    0x56fdb08a, 0xa21a78d9,
+  0x56f9147e, 0xa21633cd, 0x56f4783d, 0xa211eefb, 0x56efdbc7, 0xa20daa62,
+    0x56eb3f1a, 0xa2096604,
+  0x56e6a239, 0xa20521e0, 0x56e20521, 0xa200ddf5, 0x56dd67d4, 0xa1fc9a45,
+    0x56d8ca51, 0xa1f856ce,
+  0x56d42c99, 0xa1f41392, 0x56cf8eab, 0xa1efd08f, 0x56caf088, 0xa1eb8dc7,
+    0x56c6522f, 0xa1e74b38,
+  0x56c1b3a1, 0xa1e308e4, 0x56bd14dd, 0xa1dec6ca, 0x56b875e4, 0xa1da84e9,
+    0x56b3d6b5, 0xa1d64343,
+  0x56af3750, 0xa1d201d7, 0x56aa97b7, 0xa1cdc0a5, 0x56a5f7e7, 0xa1c97fad,
+    0x56a157e3, 0xa1c53ef0,
+  0x569cb7a8, 0xa1c0fe6c, 0x56981739, 0xa1bcbe22, 0x56937694, 0xa1b87e13,
+    0x568ed5b9, 0xa1b43e3e,
+  0x568a34a9, 0xa1affea3, 0x56859364, 0xa1abbf42, 0x5680f1ea, 0xa1a7801b,
+    0x567c503a, 0xa1a3412f,
+  0x5677ae54, 0xa19f027c, 0x56730c3a, 0xa19ac404, 0x566e69ea, 0xa19685c7,
+    0x5669c765, 0xa19247c3,
+  0x566524aa, 0xa18e09fa, 0x566081ba, 0xa189cc6b, 0x565bde95, 0xa1858f16,
+    0x56573b3b, 0xa18151fb,
+  0x565297ab, 0xa17d151b, 0x564df3e6, 0xa178d875, 0x56494fec, 0xa1749c09,
+    0x5644abbc, 0xa1705fd8,
+  0x56400758, 0xa16c23e1, 0x563b62be, 0xa167e824, 0x5636bdef, 0xa163aca2,
+    0x563218eb, 0xa15f715a,
+  0x562d73b2, 0xa15b364d, 0x5628ce43, 0xa156fb79, 0x5624289f, 0xa152c0e1,
+    0x561f82c7, 0xa14e8682,
+  0x561adcb9, 0xa14a4c5e, 0x56163676, 0xa1461275, 0x56118ffe, 0xa141d8c5,
+    0x560ce950, 0xa13d9f51,
+  0x5608426e, 0xa1396617, 0x56039b57, 0xa1352d17, 0x55fef40a, 0xa130f451,
+    0x55fa4c89, 0xa12cbbc7,
+  0x55f5a4d2, 0xa1288376, 0x55f0fce7, 0xa1244b61, 0x55ec54c6, 0xa1201385,
+    0x55e7ac71, 0xa11bdbe4,
+  0x55e303e6, 0xa117a47e, 0x55de5b27, 0xa1136d52, 0x55d9b232, 0xa10f3661,
+    0x55d50909, 0xa10affab,
+  0x55d05faa, 0xa106c92f, 0x55cbb617, 0xa10292ed, 0x55c70c4f, 0xa0fe5ce6,
+    0x55c26251, 0xa0fa271a,
+  0x55bdb81f, 0xa0f5f189, 0x55b90db8, 0xa0f1bc32, 0x55b4631d, 0xa0ed8715,
+    0x55afb84c, 0xa0e95234,
+  0x55ab0d46, 0xa0e51d8c, 0x55a6620c, 0xa0e0e920, 0x55a1b69d, 0xa0dcb4ee,
+    0x559d0af9, 0xa0d880f7,
+  0x55985f20, 0xa0d44d3b, 0x5593b312, 0xa0d019b9, 0x558f06d0, 0xa0cbe672,
+    0x558a5a58, 0xa0c7b366,
+  0x5585adad, 0xa0c38095, 0x558100cc, 0xa0bf4dfe, 0x557c53b6, 0xa0bb1ba2,
+    0x5577a66c, 0xa0b6e981,
+  0x5572f8ed, 0xa0b2b79b, 0x556e4b39, 0xa0ae85ef, 0x55699d51, 0xa0aa547e,
+    0x5564ef34, 0xa0a62348,
+  0x556040e2, 0xa0a1f24d, 0x555b925c, 0xa09dc18d, 0x5556e3a1, 0xa0999107,
+    0x555234b1, 0xa09560bc,
+  0x554d858d, 0xa09130ad, 0x5548d634, 0xa08d00d8, 0x554426a7, 0xa088d13e,
+    0x553f76e4, 0xa084a1de,
+  0x553ac6ee, 0xa08072ba, 0x553616c2, 0xa07c43d1, 0x55316663, 0xa0781522,
+    0x552cb5ce, 0xa073e6af,
+  0x55280505, 0xa06fb876, 0x55235408, 0xa06b8a78, 0x551ea2d6, 0xa0675cb6,
+    0x5519f16f, 0xa0632f2e,
+  0x55153fd4, 0xa05f01e1, 0x55108e05, 0xa05ad4cf, 0x550bdc01, 0xa056a7f9,
+    0x550729c9, 0xa0527b5d,
+  0x5502775c, 0xa04e4efc, 0x54fdc4ba, 0xa04a22d7, 0x54f911e5, 0xa045f6ec,
+    0x54f45edb, 0xa041cb3c,
+  0x54efab9c, 0xa03d9fc8, 0x54eaf829, 0xa039748e, 0x54e64482, 0xa0354990,
+    0x54e190a6, 0xa0311ecd,
+  0x54dcdc96, 0xa02cf444, 0x54d82852, 0xa028c9f7, 0x54d373d9, 0xa0249fe5,
+    0x54cebf2c, 0xa020760e,
+  0x54ca0a4b, 0xa01c4c73, 0x54c55535, 0xa0182312, 0x54c09feb, 0xa013f9ed,
+    0x54bbea6d, 0xa00fd102,
+  0x54b734ba, 0xa00ba853, 0x54b27ed3, 0xa0077fdf, 0x54adc8b8, 0xa00357a7,
+    0x54a91269, 0x9fff2fa9,
+  0x54a45be6, 0x9ffb07e7, 0x549fa52e, 0x9ff6e060, 0x549aee42, 0x9ff2b914,
+    0x54963722, 0x9fee9204,
+  0x54917fce, 0x9fea6b2f, 0x548cc845, 0x9fe64495, 0x54881089, 0x9fe21e36,
+    0x54835898, 0x9fddf812,
+  0x547ea073, 0x9fd9d22a, 0x5479e81a, 0x9fd5ac7d, 0x54752f8d, 0x9fd1870c,
+    0x547076cc, 0x9fcd61d6,
+  0x546bbdd7, 0x9fc93cdb, 0x546704ae, 0x9fc5181b, 0x54624b50, 0x9fc0f397,
+    0x545d91bf, 0x9fbccf4f,
+  0x5458d7f9, 0x9fb8ab41, 0x54541e00, 0x9fb4876f, 0x544f63d2, 0x9fb063d9,
+    0x544aa971, 0x9fac407e,
+  0x5445eedb, 0x9fa81d5e, 0x54413412, 0x9fa3fa79, 0x543c7914, 0x9f9fd7d1,
+    0x5437bde3, 0x9f9bb563,
+  0x5433027d, 0x9f979331, 0x542e46e4, 0x9f93713b, 0x54298b17, 0x9f8f4f80,
+    0x5424cf16, 0x9f8b2e00,
+  0x542012e1, 0x9f870cbc, 0x541b5678, 0x9f82ebb4, 0x541699db, 0x9f7ecae7,
+    0x5411dd0a, 0x9f7aaa55,
+  0x540d2005, 0x9f7689ff, 0x540862cd, 0x9f7269e5, 0x5403a561, 0x9f6e4a06,
+    0x53fee7c1, 0x9f6a2a63,
+  0x53fa29ed, 0x9f660afb, 0x53f56be5, 0x9f61ebcf, 0x53f0adaa, 0x9f5dccde,
+    0x53ebef3a, 0x9f59ae29,
+  0x53e73097, 0x9f558fb0, 0x53e271c0, 0x9f517173, 0x53ddb2b6, 0x9f4d5371,
+    0x53d8f378, 0x9f4935aa,
+  0x53d43406, 0x9f45181f, 0x53cf7460, 0x9f40fad0, 0x53cab486, 0x9f3cddbd,
+    0x53c5f479, 0x9f38c0e5,
+  0x53c13439, 0x9f34a449, 0x53bc73c4, 0x9f3087e9, 0x53b7b31c, 0x9f2c6bc5,
+    0x53b2f240, 0x9f284fdc,
+  0x53ae3131, 0x9f24342f, 0x53a96fee, 0x9f2018bd, 0x53a4ae77, 0x9f1bfd88,
+    0x539feccd, 0x9f17e28e,
+  0x539b2af0, 0x9f13c7d0, 0x539668de, 0x9f0fad4e, 0x5391a699, 0x9f0b9307,
+    0x538ce421, 0x9f0778fd,
+  0x53882175, 0x9f035f2e, 0x53835e95, 0x9eff459b, 0x537e9b82, 0x9efb2c44,
+    0x5379d83c, 0x9ef71328,
+  0x537514c2, 0x9ef2fa49, 0x53705114, 0x9eeee1a5, 0x536b8d33, 0x9eeac93e,
+    0x5366c91f, 0x9ee6b112,
+  0x536204d7, 0x9ee29922, 0x535d405c, 0x9ede816e, 0x53587bad, 0x9eda69f6,
+    0x5353b6cb, 0x9ed652ba,
+  0x534ef1b5, 0x9ed23bb9, 0x534a2c6c, 0x9ece24f5, 0x534566f0, 0x9eca0e6d,
+    0x5340a140, 0x9ec5f820,
+  0x533bdb5d, 0x9ec1e210, 0x53371547, 0x9ebdcc3b, 0x53324efd, 0x9eb9b6a3,
+    0x532d8880, 0x9eb5a146,
+  0x5328c1d0, 0x9eb18c26, 0x5323faec, 0x9ead7742, 0x531f33d5, 0x9ea96299,
+    0x531a6c8b, 0x9ea54e2d,
+  0x5315a50e, 0x9ea139fd, 0x5310dd5d, 0x9e9d2608, 0x530c1579, 0x9e991250,
+    0x53074d62, 0x9e94fed4,
+  0x53028518, 0x9e90eb94, 0x52fdbc9a, 0x9e8cd890, 0x52f8f3e9, 0x9e88c5c9,
+    0x52f42b05, 0x9e84b33d,
+  0x52ef61ee, 0x9e80a0ee, 0x52ea98a4, 0x9e7c8eda, 0x52e5cf27, 0x9e787d03,
+    0x52e10576, 0x9e746b68,
+  0x52dc3b92, 0x9e705a09, 0x52d7717b, 0x9e6c48e7, 0x52d2a732, 0x9e683800,
+    0x52cddcb5, 0x9e642756,
+  0x52c91204, 0x9e6016e8, 0x52c44721, 0x9e5c06b6, 0x52bf7c0b, 0x9e57f6c0,
+    0x52bab0c2, 0x9e53e707,
+  0x52b5e546, 0x9e4fd78a, 0x52b11996, 0x9e4bc849, 0x52ac4db4, 0x9e47b944,
+    0x52a7819f, 0x9e43aa7c,
+  0x52a2b556, 0x9e3f9bf0, 0x529de8db, 0x9e3b8da0, 0x52991c2d, 0x9e377f8c,
+    0x52944f4c, 0x9e3371b5,
+  0x528f8238, 0x9e2f641b, 0x528ab4f1, 0x9e2b56bc, 0x5285e777, 0x9e27499a,
+    0x528119ca, 0x9e233cb4,
+  0x527c4bea, 0x9e1f300b, 0x52777dd7, 0x9e1b239e, 0x5272af92, 0x9e17176d,
+    0x526de11a, 0x9e130b79,
+  0x5269126e, 0x9e0effc1, 0x52644390, 0x9e0af446, 0x525f7480, 0x9e06e907,
+    0x525aa53c, 0x9e02de04,
+  0x5255d5c5, 0x9dfed33e, 0x5251061c, 0x9dfac8b4, 0x524c3640, 0x9df6be67,
+    0x52476631, 0x9df2b456,
+  0x524295f0, 0x9deeaa82, 0x523dc57b, 0x9deaa0ea, 0x5238f4d4, 0x9de6978f,
+    0x523423fb, 0x9de28e70,
+  0x522f52ee, 0x9dde858e, 0x522a81af, 0x9dda7ce9, 0x5225b03d, 0x9dd6747f,
+    0x5220de99, 0x9dd26c53,
+  0x521c0cc2, 0x9dce6463, 0x52173ab8, 0x9dca5caf, 0x5212687b, 0x9dc65539,
+    0x520d960c, 0x9dc24dfe,
+  0x5208c36a, 0x9dbe4701, 0x5203f096, 0x9dba4040, 0x51ff1d8f, 0x9db639bb,
+    0x51fa4a56, 0x9db23373,
+  0x51f576ea, 0x9dae2d68, 0x51f0a34b, 0x9daa279a, 0x51ebcf7a, 0x9da62208,
+    0x51e6fb76, 0x9da21cb2,
+  0x51e22740, 0x9d9e179a, 0x51dd52d7, 0x9d9a12be, 0x51d87e3c, 0x9d960e1f,
+    0x51d3a96f, 0x9d9209bd,
+  0x51ced46e, 0x9d8e0597, 0x51c9ff3c, 0x9d8a01ae, 0x51c529d7, 0x9d85fe02,
+    0x51c0543f, 0x9d81fa92,
+  0x51bb7e75, 0x9d7df75f, 0x51b6a879, 0x9d79f469, 0x51b1d24a, 0x9d75f1b0,
+    0x51acfbe9, 0x9d71ef34,
+  0x51a82555, 0x9d6decf4, 0x51a34e8f, 0x9d69eaf1, 0x519e7797, 0x9d65e92b,
+    0x5199a06d, 0x9d61e7a2,
+  0x5194c910, 0x9d5de656, 0x518ff180, 0x9d59e546, 0x518b19bf, 0x9d55e473,
+    0x518641cb, 0x9d51e3dd,
+  0x518169a5, 0x9d4de385, 0x517c914c, 0x9d49e368, 0x5177b8c2, 0x9d45e389,
+    0x5172e005, 0x9d41e3e7,
+  0x516e0715, 0x9d3de482, 0x51692df4, 0x9d39e559, 0x516454a0, 0x9d35e66e,
+    0x515f7b1a, 0x9d31e7bf,
+  0x515aa162, 0x9d2de94d, 0x5155c778, 0x9d29eb19, 0x5150ed5c, 0x9d25ed21,
+    0x514c130d, 0x9d21ef66,
+  0x5147388c, 0x9d1df1e9, 0x51425dd9, 0x9d19f4a8, 0x513d82f4, 0x9d15f7a4,
+    0x5138a7dd, 0x9d11fadd,
+  0x5133cc94, 0x9d0dfe54, 0x512ef119, 0x9d0a0207, 0x512a156b, 0x9d0605f7,
+    0x5125398c, 0x9d020a25,
+  0x51205d7b, 0x9cfe0e8f, 0x511b8137, 0x9cfa1337, 0x5116a4c1, 0x9cf6181c,
+    0x5111c81a, 0x9cf21d3d,
+  0x510ceb40, 0x9cee229c, 0x51080e35, 0x9cea2838, 0x510330f7, 0x9ce62e11,
+    0x50fe5388, 0x9ce23427,
+  0x50f975e6, 0x9cde3a7b, 0x50f49813, 0x9cda410b, 0x50efba0d, 0x9cd647d9,
+    0x50eadbd6, 0x9cd24ee4,
+  0x50e5fd6d, 0x9cce562c, 0x50e11ed2, 0x9cca5db1, 0x50dc4005, 0x9cc66573,
+    0x50d76106, 0x9cc26d73,
+  0x50d281d5, 0x9cbe75b0, 0x50cda272, 0x9cba7e2a, 0x50c8c2de, 0x9cb686e1,
+    0x50c3e317, 0x9cb28fd5,
+  0x50bf031f, 0x9cae9907, 0x50ba22f5, 0x9caaa276, 0x50b5429a, 0x9ca6ac23,
+    0x50b0620c, 0x9ca2b60c,
+  0x50ab814d, 0x9c9ec033, 0x50a6a05c, 0x9c9aca97, 0x50a1bf39, 0x9c96d539,
+    0x509cdde4, 0x9c92e017,
+  0x5097fc5e, 0x9c8eeb34, 0x50931aa6, 0x9c8af68d, 0x508e38bd, 0x9c870224,
+    0x508956a1, 0x9c830df8,
+  0x50847454, 0x9c7f1a0a, 0x507f91d5, 0x9c7b2659, 0x507aaf25, 0x9c7732e5,
+    0x5075cc43, 0x9c733faf,
+  0x5070e92f, 0x9c6f4cb6, 0x506c05ea, 0x9c6b59fa, 0x50672273, 0x9c67677c,
+    0x50623ecb, 0x9c63753c,
+  0x505d5af1, 0x9c5f8339, 0x505876e5, 0x9c5b9173, 0x505392a8, 0x9c579feb,
+    0x504eae39, 0x9c53aea0,
+  0x5049c999, 0x9c4fbd93, 0x5044e4c7, 0x9c4bccc3, 0x503fffc4, 0x9c47dc31,
+    0x503b1a8f, 0x9c43ebdc,
+  0x50363529, 0x9c3ffbc5, 0x50314f91, 0x9c3c0beb, 0x502c69c8, 0x9c381c4f,
+    0x502783cd, 0x9c342cf0,
+  0x50229da1, 0x9c303dcf, 0x501db743, 0x9c2c4eec, 0x5018d0b4, 0x9c286046,
+    0x5013e9f4, 0x9c2471de,
+  0x500f0302, 0x9c2083b3, 0x500a1bdf, 0x9c1c95c6, 0x5005348a, 0x9c18a816,
+    0x50004d04, 0x9c14baa4,
+  0x4ffb654d, 0x9c10cd70, 0x4ff67d64, 0x9c0ce07a, 0x4ff1954b, 0x9c08f3c1,
+    0x4fecacff, 0x9c050745,
+  0x4fe7c483, 0x9c011b08, 0x4fe2dbd5, 0x9bfd2f08, 0x4fddf2f6, 0x9bf94346,
+    0x4fd909e5, 0x9bf557c1,
+  0x4fd420a4, 0x9bf16c7a, 0x4fcf3731, 0x9bed8171, 0x4fca4d8d, 0x9be996a6,
+    0x4fc563b7, 0x9be5ac18,
+  0x4fc079b1, 0x9be1c1c8, 0x4fbb8f79, 0x9bddd7b6, 0x4fb6a510, 0x9bd9ede2,
+    0x4fb1ba76, 0x9bd6044b,
+  0x4faccfab, 0x9bd21af3, 0x4fa7e4af, 0x9bce31d8, 0x4fa2f981, 0x9bca48fa,
+    0x4f9e0e22, 0x9bc6605b,
+  0x4f992293, 0x9bc277fa, 0x4f9436d2, 0x9bbe8fd6, 0x4f8f4ae0, 0x9bbaa7f0,
+    0x4f8a5ebd, 0x9bb6c048,
+  0x4f857269, 0x9bb2d8de, 0x4f8085e4, 0x9baef1b2, 0x4f7b992d, 0x9bab0ac3,
+    0x4f76ac46, 0x9ba72413,
+  0x4f71bf2e, 0x9ba33da0, 0x4f6cd1e5, 0x9b9f576b, 0x4f67e46a, 0x9b9b7174,
+    0x4f62f6bf, 0x9b978bbc,
+  0x4f5e08e3, 0x9b93a641, 0x4f591ad6, 0x9b8fc104, 0x4f542c98, 0x9b8bdc05,
+    0x4f4f3e29, 0x9b87f744,
+  0x4f4a4f89, 0x9b8412c1, 0x4f4560b8, 0x9b802e7b, 0x4f4071b6, 0x9b7c4a74,
+    0x4f3b8284, 0x9b7866ab,
+  0x4f369320, 0x9b748320, 0x4f31a38c, 0x9b709fd3, 0x4f2cb3c7, 0x9b6cbcc4,
+    0x4f27c3d1, 0x9b68d9f3,
+  0x4f22d3aa, 0x9b64f760, 0x4f1de352, 0x9b61150b, 0x4f18f2c9, 0x9b5d32f4,
+    0x4f140210, 0x9b59511c,
+  0x4f0f1126, 0x9b556f81, 0x4f0a200b, 0x9b518e24, 0x4f052ec0, 0x9b4dad06,
+    0x4f003d43, 0x9b49cc26,
+  0x4efb4b96, 0x9b45eb83, 0x4ef659b8, 0x9b420b1f, 0x4ef167aa, 0x9b3e2af9,
+    0x4eec756b, 0x9b3a4b11,
+  0x4ee782fb, 0x9b366b68, 0x4ee2905a, 0x9b328bfc, 0x4edd9d89, 0x9b2eaccf,
+    0x4ed8aa87, 0x9b2acde0,
+  0x4ed3b755, 0x9b26ef2f, 0x4ecec3f2, 0x9b2310bc, 0x4ec9d05e, 0x9b1f3288,
+    0x4ec4dc99, 0x9b1b5492,
+  0x4ebfe8a5, 0x9b1776da, 0x4ebaf47f, 0x9b139960, 0x4eb60029, 0x9b0fbc24,
+    0x4eb10ba2, 0x9b0bdf27,
+  0x4eac16eb, 0x9b080268, 0x4ea72203, 0x9b0425e8, 0x4ea22ceb, 0x9b0049a5,
+    0x4e9d37a3, 0x9afc6da1,
+  0x4e984229, 0x9af891db, 0x4e934c80, 0x9af4b654, 0x4e8e56a5, 0x9af0db0b,
+    0x4e89609b, 0x9aed0000,
+  0x4e846a60, 0x9ae92533, 0x4e7f73f4, 0x9ae54aa5, 0x4e7a7d58, 0x9ae17056,
+    0x4e75868c, 0x9add9644,
+  0x4e708f8f, 0x9ad9bc71, 0x4e6b9862, 0x9ad5e2dd, 0x4e66a105, 0x9ad20987,
+    0x4e61a977, 0x9ace306f,
+  0x4e5cb1b9, 0x9aca5795, 0x4e57b9ca, 0x9ac67efb, 0x4e52c1ab, 0x9ac2a69e,
+    0x4e4dc95c, 0x9abece80,
+  0x4e48d0dd, 0x9abaf6a1, 0x4e43d82d, 0x9ab71eff, 0x4e3edf4d, 0x9ab3479d,
+    0x4e39e63d, 0x9aaf7079,
+  0x4e34ecfc, 0x9aab9993, 0x4e2ff38b, 0x9aa7c2ec, 0x4e2af9ea, 0x9aa3ec83,
+    0x4e260019, 0x9aa01659,
+  0x4e210617, 0x9a9c406e, 0x4e1c0be6, 0x9a986ac1, 0x4e171184, 0x9a949552,
+    0x4e1216f2, 0x9a90c022,
+  0x4e0d1c30, 0x9a8ceb31, 0x4e08213e, 0x9a89167e, 0x4e03261b, 0x9a85420a,
+    0x4dfe2ac9, 0x9a816dd5,
+  0x4df92f46, 0x9a7d99de, 0x4df43393, 0x9a79c625, 0x4def37b0, 0x9a75f2ac,
+    0x4dea3b9d, 0x9a721f71,
+  0x4de53f5a, 0x9a6e4c74, 0x4de042e7, 0x9a6a79b6, 0x4ddb4644, 0x9a66a737,
+    0x4dd64971, 0x9a62d4f7,
+  0x4dd14c6e, 0x9a5f02f5, 0x4dcc4f3b, 0x9a5b3132, 0x4dc751d8, 0x9a575fae,
+    0x4dc25445, 0x9a538e68,
+  0x4dbd5682, 0x9a4fbd61, 0x4db8588f, 0x9a4bec99, 0x4db35a6c, 0x9a481c0f,
+    0x4dae5c19, 0x9a444bc5,
+  0x4da95d96, 0x9a407bb9, 0x4da45ee3, 0x9a3cabeb, 0x4d9f6001, 0x9a38dc5d,
+    0x4d9a60ee, 0x9a350d0d,
+  0x4d9561ac, 0x9a313dfc, 0x4d90623a, 0x9a2d6f2a, 0x4d8b6298, 0x9a29a097,
+    0x4d8662c6, 0x9a25d243,
+  0x4d8162c4, 0x9a22042d, 0x4d7c6293, 0x9a1e3656, 0x4d776231, 0x9a1a68be,
+    0x4d7261a0, 0x9a169b65,
+  0x4d6d60df, 0x9a12ce4b, 0x4d685fef, 0x9a0f016f, 0x4d635ece, 0x9a0b34d3,
+    0x4d5e5d7e, 0x9a076875,
+  0x4d595bfe, 0x9a039c57, 0x4d545a4f, 0x99ffd077, 0x4d4f5870, 0x99fc04d6,
+    0x4d4a5661, 0x99f83974,
+  0x4d455422, 0x99f46e51, 0x4d4051b4, 0x99f0a36d, 0x4d3b4f16, 0x99ecd8c8,
+    0x4d364c48, 0x99e90e62,
+  0x4d31494b, 0x99e5443b, 0x4d2c461e, 0x99e17a53, 0x4d2742c2, 0x99ddb0aa,
+    0x4d223f36, 0x99d9e73f,
+  0x4d1d3b7a, 0x99d61e14, 0x4d18378f, 0x99d25528, 0x4d133374, 0x99ce8c7b,
+    0x4d0e2f2a, 0x99cac40d,
+  0x4d092ab0, 0x99c6fbde, 0x4d042607, 0x99c333ee, 0x4cff212e, 0x99bf6c3d,
+    0x4cfa1c26, 0x99bba4cb,
+  0x4cf516ee, 0x99b7dd99, 0x4cf01187, 0x99b416a5, 0x4ceb0bf0, 0x99b04ff0,
+    0x4ce6062a, 0x99ac897b,
+  0x4ce10034, 0x99a8c345, 0x4cdbfa0f, 0x99a4fd4d, 0x4cd6f3bb, 0x99a13795,
+    0x4cd1ed37, 0x999d721c,
+  0x4ccce684, 0x9999ace3, 0x4cc7dfa1, 0x9995e7e8, 0x4cc2d88f, 0x9992232d,
+    0x4cbdd14e, 0x998e5eb1,
+  0x4cb8c9dd, 0x998a9a74, 0x4cb3c23d, 0x9986d676, 0x4caeba6e, 0x998312b7,
+    0x4ca9b26f, 0x997f4f38,
+  0x4ca4aa41, 0x997b8bf8, 0x4c9fa1e4, 0x9977c8f7, 0x4c9a9958, 0x99740635,
+    0x4c95909c, 0x997043b2,
+  0x4c9087b1, 0x996c816f, 0x4c8b7e97, 0x9968bf6b, 0x4c86754e, 0x9964fda7,
+    0x4c816bd5, 0x99613c22,
+  0x4c7c622d, 0x995d7adc, 0x4c775856, 0x9959b9d5, 0x4c724e50, 0x9955f90d,
+    0x4c6d441b, 0x99523885,
+  0x4c6839b7, 0x994e783d, 0x4c632f23, 0x994ab833, 0x4c5e2460, 0x9946f869,
+    0x4c59196f, 0x994338df,
+  0x4c540e4e, 0x993f7993, 0x4c4f02fe, 0x993bba87, 0x4c49f77f, 0x9937fbbb,
+    0x4c44ebd1, 0x99343d2e,
+  0x4c3fdff4, 0x99307ee0, 0x4c3ad3e7, 0x992cc0d2, 0x4c35c7ac, 0x99290303,
+    0x4c30bb42, 0x99254574,
+  0x4c2baea9, 0x99218824, 0x4c26a1e1, 0x991dcb13, 0x4c2194e9, 0x991a0e42,
+    0x4c1c87c3, 0x991651b1,
+  0x4c177a6e, 0x9912955f, 0x4c126cea, 0x990ed94c, 0x4c0d5f37, 0x990b1d79,
+    0x4c085156, 0x990761e5,
+  0x4c034345, 0x9903a691, 0x4bfe3505, 0x98ffeb7d, 0x4bf92697, 0x98fc30a8,
+    0x4bf417f9, 0x98f87612,
+  0x4bef092d, 0x98f4bbbc, 0x4be9fa32, 0x98f101a6, 0x4be4eb08, 0x98ed47cf,
+    0x4bdfdbaf, 0x98e98e38,
+  0x4bdacc28, 0x98e5d4e0, 0x4bd5bc72, 0x98e21bc8, 0x4bd0ac8d, 0x98de62f0,
+    0x4bcb9c79, 0x98daaa57,
+  0x4bc68c36, 0x98d6f1fe, 0x4bc17bc5, 0x98d339e4, 0x4bbc6b25, 0x98cf820b,
+    0x4bb75a56, 0x98cbca70,
+  0x4bb24958, 0x98c81316, 0x4bad382c, 0x98c45bfb, 0x4ba826d1, 0x98c0a520,
+    0x4ba31548, 0x98bcee84,
+  0x4b9e0390, 0x98b93828, 0x4b98f1a9, 0x98b5820c, 0x4b93df93, 0x98b1cc30,
+    0x4b8ecd4f, 0x98ae1693,
+  0x4b89badd, 0x98aa6136, 0x4b84a83b, 0x98a6ac19, 0x4b7f956b, 0x98a2f73c,
+    0x4b7a826d, 0x989f429e,
+  0x4b756f40, 0x989b8e40, 0x4b705be4, 0x9897da22, 0x4b6b485a, 0x98942643,
+    0x4b6634a2, 0x989072a5,
+  0x4b6120bb, 0x988cbf46, 0x4b5c0ca5, 0x98890c27, 0x4b56f861, 0x98855948,
+    0x4b51e3ee, 0x9881a6a9,
+  0x4b4ccf4d, 0x987df449, 0x4b47ba7e, 0x987a422a, 0x4b42a580, 0x9876904a,
+    0x4b3d9053, 0x9872deaa,
+  0x4b387af9, 0x986f2d4a, 0x4b336570, 0x986b7c2a, 0x4b2e4fb8, 0x9867cb4a,
+    0x4b2939d2, 0x98641aa9,
+  0x4b2423be, 0x98606a49, 0x4b1f0d7b, 0x985cba28, 0x4b19f70a, 0x98590a48,
+    0x4b14e06b, 0x98555aa7,
+  0x4b0fc99d, 0x9851ab46, 0x4b0ab2a1, 0x984dfc26, 0x4b059b77, 0x984a4d45,
+    0x4b00841f, 0x98469ea4,
+  0x4afb6c98, 0x9842f043, 0x4af654e3, 0x983f4223, 0x4af13d00, 0x983b9442,
+    0x4aec24ee, 0x9837e6a1,
+  0x4ae70caf, 0x98343940, 0x4ae1f441, 0x98308c1f, 0x4adcdba5, 0x982cdf3f,
+    0x4ad7c2da, 0x9829329e,
+  0x4ad2a9e2, 0x9825863d, 0x4acd90bb, 0x9821da1d, 0x4ac87767, 0x981e2e3c,
+    0x4ac35de4, 0x981a829c,
+  0x4abe4433, 0x9816d73b, 0x4ab92a54, 0x98132c1b, 0x4ab41046, 0x980f813b,
+    0x4aaef60b, 0x980bd69b,
+  0x4aa9dba2, 0x98082c3b, 0x4aa4c10b, 0x9804821b, 0x4a9fa645, 0x9800d83c,
+    0x4a9a8b52, 0x97fd2e9c,
+  0x4a957030, 0x97f9853d, 0x4a9054e1, 0x97f5dc1e, 0x4a8b3963, 0x97f2333f,
+    0x4a861db8, 0x97ee8aa0,
+  0x4a8101de, 0x97eae242, 0x4a7be5d7, 0x97e73a23, 0x4a76c9a2, 0x97e39245,
+    0x4a71ad3e, 0x97dfeaa7,
+  0x4a6c90ad, 0x97dc4349, 0x4a6773ee, 0x97d89c2c, 0x4a625701, 0x97d4f54f,
+    0x4a5d39e6, 0x97d14eb2,
+  0x4a581c9e, 0x97cda855, 0x4a52ff27, 0x97ca0239, 0x4a4de182, 0x97c65c5c,
+    0x4a48c3b0, 0x97c2b6c1,
+  0x4a43a5b0, 0x97bf1165, 0x4a3e8782, 0x97bb6c4a, 0x4a396926, 0x97b7c76f,
+    0x4a344a9d, 0x97b422d4,
+  0x4a2f2be6, 0x97b07e7a, 0x4a2a0d01, 0x97acda60, 0x4a24edee, 0x97a93687,
+    0x4a1fcead, 0x97a592ed,
+  0x4a1aaf3f, 0x97a1ef94, 0x4a158fa3, 0x979e4c7c, 0x4a106fda, 0x979aa9a4,
+    0x4a0b4fe2, 0x9797070c,
+  0x4a062fbd, 0x979364b5, 0x4a010f6b, 0x978fc29e, 0x49fbeeea, 0x978c20c8,
+    0x49f6ce3c, 0x97887f32,
+  0x49f1ad61, 0x9784dddc, 0x49ec8c57, 0x97813cc7, 0x49e76b21, 0x977d9bf2,
+    0x49e249bc, 0x9779fb5e,
+  0x49dd282a, 0x97765b0a, 0x49d8066b, 0x9772baf7, 0x49d2e47e, 0x976f1b24,
+    0x49cdc263, 0x976b7b92,
+  0x49c8a01b, 0x9767dc41, 0x49c37da5, 0x97643d2f, 0x49be5b02, 0x97609e5f,
+    0x49b93832, 0x975cffcf,
+  0x49b41533, 0x9759617f, 0x49aef208, 0x9755c370, 0x49a9ceaf, 0x975225a1,
+    0x49a4ab28, 0x974e8813,
+  0x499f8774, 0x974aeac6, 0x499a6393, 0x97474db9, 0x49953f84, 0x9743b0ed,
+    0x49901b48, 0x97401462,
+  0x498af6df, 0x973c7817, 0x4985d248, 0x9738dc0d, 0x4980ad84, 0x97354043,
+    0x497b8892, 0x9731a4ba,
+  0x49766373, 0x972e0971, 0x49713e27, 0x972a6e6a, 0x496c18ae, 0x9726d3a3,
+    0x4966f307, 0x9723391c,
+  0x4961cd33, 0x971f9ed7, 0x495ca732, 0x971c04d2, 0x49578103, 0x97186b0d,
+    0x49525aa7, 0x9714d18a,
+  0x494d341e, 0x97113847, 0x49480d68, 0x970d9f45, 0x4942e684, 0x970a0683,
+    0x493dbf74, 0x97066e03,
+  0x49389836, 0x9702d5c3, 0x493370cb, 0x96ff3dc4, 0x492e4933, 0x96fba605,
+    0x4929216e, 0x96f80e88,
+  0x4923f97b, 0x96f4774b, 0x491ed15c, 0x96f0e04f, 0x4919a90f, 0x96ed4994,
+    0x49148095, 0x96e9b319,
+  0x490f57ee, 0x96e61ce0, 0x490a2f1b, 0x96e286e7, 0x4905061a, 0x96def12f,
+    0x48ffdcec, 0x96db5bb8,
+  0x48fab391, 0x96d7c682, 0x48f58a09, 0x96d4318d, 0x48f06054, 0x96d09cd8,
+    0x48eb3672, 0x96cd0865,
+  0x48e60c62, 0x96c97432, 0x48e0e227, 0x96c5e040, 0x48dbb7be, 0x96c24c8f,
+    0x48d68d28, 0x96beb91f,
+  0x48d16265, 0x96bb25f0, 0x48cc3775, 0x96b79302, 0x48c70c59, 0x96b40055,
+    0x48c1e10f, 0x96b06de9,
+  0x48bcb599, 0x96acdbbe, 0x48b789f5, 0x96a949d3, 0x48b25e25, 0x96a5b82a,
+    0x48ad3228, 0x96a226c2,
+  0x48a805ff, 0x969e959b, 0x48a2d9a8, 0x969b04b4, 0x489dad25, 0x9697740f,
+    0x48988074, 0x9693e3ab,
+  0x48935397, 0x96905388, 0x488e268e, 0x968cc3a5, 0x4888f957, 0x96893404,
+    0x4883cbf4, 0x9685a4a4,
+  0x487e9e64, 0x96821585, 0x487970a7, 0x967e86a7, 0x487442be, 0x967af80a,
+    0x486f14a8, 0x967769af,
+  0x4869e665, 0x9673db94, 0x4864b7f5, 0x96704dba, 0x485f8959, 0x966cc022,
+    0x485a5a90, 0x966932cb,
+  0x48552b9b, 0x9665a5b4, 0x484ffc79, 0x966218df, 0x484acd2a, 0x965e8c4b,
+    0x48459daf, 0x965afff9,
+  0x48406e08, 0x965773e7, 0x483b3e33, 0x9653e817, 0x48360e32, 0x96505c88,
+    0x4830de05, 0x964cd139,
+  0x482badab, 0x9649462d, 0x48267d24, 0x9645bb61, 0x48214c71, 0x964230d7,
+    0x481c1b92, 0x963ea68d,
+  0x4816ea86, 0x963b1c86, 0x4811b94d, 0x963792bf, 0x480c87e8, 0x96340939,
+    0x48075657, 0x96307ff5,
+  0x48022499, 0x962cf6f2, 0x47fcf2af, 0x96296e31, 0x47f7c099, 0x9625e5b0,
+    0x47f28e56, 0x96225d71,
+  0x47ed5be6, 0x961ed574, 0x47e8294a, 0x961b4db7, 0x47e2f682, 0x9617c63c,
+    0x47ddc38e, 0x96143f02,
+  0x47d8906d, 0x9610b80a, 0x47d35d20, 0x960d3153, 0x47ce29a7, 0x9609aadd,
+    0x47c8f601, 0x960624a9,
+  0x47c3c22f, 0x96029eb6, 0x47be8e31, 0x95ff1904, 0x47b95a06, 0x95fb9394,
+    0x47b425af, 0x95f80e65,
+  0x47aef12c, 0x95f48977, 0x47a9bc7d, 0x95f104cb, 0x47a487a2, 0x95ed8061,
+    0x479f529a, 0x95e9fc38,
+  0x479a1d67, 0x95e67850, 0x4794e807, 0x95e2f4a9, 0x478fb27b, 0x95df7145,
+    0x478a7cc2, 0x95dbee21,
+  0x478546de, 0x95d86b3f, 0x478010cd, 0x95d4e89f, 0x477ada91, 0x95d16640,
+    0x4775a428, 0x95cde423,
+  0x47706d93, 0x95ca6247, 0x476b36d3, 0x95c6e0ac, 0x4765ffe6, 0x95c35f53,
+    0x4760c8cd, 0x95bfde3c,
+  0x475b9188, 0x95bc5d66, 0x47565a17, 0x95b8dcd2, 0x4751227a, 0x95b55c7f,
+    0x474beab1, 0x95b1dc6e,
+  0x4746b2bc, 0x95ae5c9f, 0x47417a9b, 0x95aadd11, 0x473c424e, 0x95a75dc4,
+    0x473709d5, 0x95a3deb9,
+  0x4731d131, 0x95a05ff0, 0x472c9860, 0x959ce169, 0x47275f63, 0x95996323,
+    0x4722263b, 0x9595e51e,
+  0x471cece7, 0x9592675c, 0x4717b367, 0x958ee9db, 0x471279ba, 0x958b6c9b,
+    0x470d3fe3, 0x9587ef9e,
+  0x470805df, 0x958472e2, 0x4702cbaf, 0x9580f667, 0x46fd9154, 0x957d7a2f,
+    0x46f856cd, 0x9579fe38,
+  0x46f31c1a, 0x95768283, 0x46ede13b, 0x9573070f, 0x46e8a631, 0x956f8bdd,
+    0x46e36afb, 0x956c10ed,
+  0x46de2f99, 0x9568963f, 0x46d8f40b, 0x95651bd2, 0x46d3b852, 0x9561a1a8,
+    0x46ce7c6d, 0x955e27bf,
+  0x46c9405c, 0x955aae17, 0x46c40420, 0x955734b2, 0x46bec7b8, 0x9553bb8e,
+    0x46b98b24, 0x955042ac,
+  0x46b44e65, 0x954cca0c, 0x46af117a, 0x954951ae, 0x46a9d464, 0x9545d992,
+    0x46a49722, 0x954261b7,
+  0x469f59b4, 0x953eea1e, 0x469a1c1b, 0x953b72c7, 0x4694de56, 0x9537fbb2,
+    0x468fa066, 0x953484df,
+  0x468a624a, 0x95310e4e, 0x46852403, 0x952d97fe, 0x467fe590, 0x952a21f1,
+    0x467aa6f2, 0x9526ac25,
+  0x46756828, 0x9523369c, 0x46702933, 0x951fc154, 0x466aea12, 0x951c4c4e,
+    0x4665aac6, 0x9518d78a,
+  0x46606b4e, 0x95156308, 0x465b2bab, 0x9511eec8, 0x4655ebdd, 0x950e7aca,
+    0x4650abe3, 0x950b070e,
+  0x464b6bbe, 0x95079394, 0x46462b6d, 0x9504205c, 0x4640eaf2, 0x9500ad66,
+    0x463baa4a, 0x94fd3ab1,
+  0x46366978, 0x94f9c83f, 0x4631287a, 0x94f6560f, 0x462be751, 0x94f2e421,
+    0x4626a5fd, 0x94ef7275,
+  0x4621647d, 0x94ec010b, 0x461c22d2, 0x94e88fe3, 0x4616e0fc, 0x94e51efd,
+    0x46119efa, 0x94e1ae59,
+  0x460c5cce, 0x94de3df8, 0x46071a76, 0x94dacdd8, 0x4601d7f3, 0x94d75dfa,
+    0x45fc9545, 0x94d3ee5f,
+  0x45f7526b, 0x94d07f05, 0x45f20f67, 0x94cd0fee, 0x45eccc37, 0x94c9a119,
+    0x45e788dc, 0x94c63286,
+  0x45e24556, 0x94c2c435, 0x45dd01a5, 0x94bf5627, 0x45d7bdc9, 0x94bbe85a,
+    0x45d279c2, 0x94b87ad0,
+  0x45cd358f, 0x94b50d87, 0x45c7f132, 0x94b1a081, 0x45c2acaa, 0x94ae33be,
+    0x45bd67f6, 0x94aac73c,
+  0x45b82318, 0x94a75afd, 0x45b2de0e, 0x94a3eeff, 0x45ad98da, 0x94a08344,
+    0x45a8537a, 0x949d17cc,
+  0x45a30df0, 0x9499ac95, 0x459dc83b, 0x949641a1, 0x4598825a, 0x9492d6ef,
+    0x45933c4f, 0x948f6c7f,
+  0x458df619, 0x948c0252, 0x4588afb8, 0x94889867, 0x4583692c, 0x94852ebe,
+    0x457e2275, 0x9481c557,
+  0x4578db93, 0x947e5c33, 0x45739487, 0x947af351, 0x456e4d4f, 0x94778ab1,
+    0x456905ed, 0x94742254,
+  0x4563be60, 0x9470ba39, 0x455e76a8, 0x946d5260, 0x45592ec6, 0x9469eaca,
+    0x4553e6b8, 0x94668376,
+  0x454e9e80, 0x94631c65, 0x4549561d, 0x945fb596, 0x45440d90, 0x945c4f09,
+    0x453ec4d7, 0x9458e8bf,
+  0x45397bf4, 0x945582b7, 0x453432e6, 0x94521cf1, 0x452ee9ae, 0x944eb76e,
+    0x4529a04b, 0x944b522d,
+  0x452456bd, 0x9447ed2f, 0x451f0d04, 0x94448873, 0x4519c321, 0x944123fa,
+    0x45147913, 0x943dbfc3,
+  0x450f2edb, 0x943a5bcf, 0x4509e478, 0x9436f81d, 0x450499eb, 0x943394ad,
+    0x44ff4f32, 0x94303180,
+  0x44fa0450, 0x942cce96, 0x44f4b943, 0x94296bee, 0x44ef6e0b, 0x94260989,
+    0x44ea22a9, 0x9422a766,
+  0x44e4d71c, 0x941f4585, 0x44df8b64, 0x941be3e8, 0x44da3f83, 0x9418828c,
+    0x44d4f376, 0x94152174,
+  0x44cfa740, 0x9411c09e, 0x44ca5adf, 0x940e600a, 0x44c50e53, 0x940affb9,
+    0x44bfc19d, 0x94079fab,
+  0x44ba74bd, 0x94043fdf, 0x44b527b2, 0x9400e056, 0x44afda7d, 0x93fd810f,
+    0x44aa8d1d, 0x93fa220b,
+  0x44a53f93, 0x93f6c34a, 0x449ff1df, 0x93f364cb, 0x449aa400, 0x93f0068f,
+    0x449555f7, 0x93eca896,
+  0x449007c4, 0x93e94adf, 0x448ab967, 0x93e5ed6b, 0x44856adf, 0x93e2903a,
+    0x44801c2d, 0x93df334c,
+  0x447acd50, 0x93dbd6a0, 0x44757e4a, 0x93d87a36, 0x44702f19, 0x93d51e10,
+    0x446adfbe, 0x93d1c22c,
+  0x44659039, 0x93ce668b, 0x44604089, 0x93cb0b2d, 0x445af0b0, 0x93c7b011,
+    0x4455a0ac, 0x93c45539,
+  0x4450507e, 0x93c0faa3, 0x444b0026, 0x93bda04f, 0x4445afa4, 0x93ba463f,
+    0x44405ef8, 0x93b6ec71,
+  0x443b0e21, 0x93b392e6, 0x4435bd21, 0x93b0399e, 0x44306bf6, 0x93ace099,
+    0x442b1aa2, 0x93a987d6,
+  0x4425c923, 0x93a62f57, 0x4420777b, 0x93a2d71a, 0x441b25a8, 0x939f7f20,
+    0x4415d3ab, 0x939c2769,
+  0x44108184, 0x9398cff5, 0x440b2f34, 0x939578c3, 0x4405dcb9, 0x939221d5,
+    0x44008a14, 0x938ecb29,
+  0x43fb3746, 0x938b74c1, 0x43f5e44d, 0x93881e9b, 0x43f0912b, 0x9384c8b8,
+    0x43eb3ddf, 0x93817318,
+  0x43e5ea68, 0x937e1dbb, 0x43e096c8, 0x937ac8a1, 0x43db42fe, 0x937773ca,
+    0x43d5ef0a, 0x93741f35,
+  0x43d09aed, 0x9370cae4, 0x43cb46a5, 0x936d76d6, 0x43c5f234, 0x936a230a,
+    0x43c09d99, 0x9366cf82,
+  0x43bb48d4, 0x93637c3d, 0x43b5f3e5, 0x9360293a, 0x43b09ecc, 0x935cd67b,
+    0x43ab498a, 0x935983ff,
+  0x43a5f41e, 0x935631c5, 0x43a09e89, 0x9352dfcf, 0x439b48c9, 0x934f8e1c,
+    0x4395f2e0, 0x934c3cab,
+  0x43909ccd, 0x9348eb7e, 0x438b4691, 0x93459a94, 0x4385f02a, 0x934249ed,
+    0x4380999b, 0x933ef989,
+  0x437b42e1, 0x933ba968, 0x4375ebfe, 0x9338598a, 0x437094f1, 0x933509f0,
+    0x436b3dbb, 0x9331ba98,
+  0x4365e65b, 0x932e6b84, 0x43608ed2, 0x932b1cb2, 0x435b371f, 0x9327ce24,
+    0x4355df42, 0x93247fd9,
+  0x4350873c, 0x932131d1, 0x434b2f0c, 0x931de40c, 0x4345d6b3, 0x931a968b,
+    0x43407e31, 0x9317494c,
+  0x433b2585, 0x9313fc51, 0x4335ccaf, 0x9310af99, 0x433073b0, 0x930d6324,
+    0x432b1a87, 0x930a16f3,
+  0x4325c135, 0x9306cb04, 0x432067ba, 0x93037f59, 0x431b0e15, 0x930033f1,
+    0x4315b447, 0x92fce8cc,
+  0x43105a50, 0x92f99deb, 0x430b002f, 0x92f6534c, 0x4305a5e5, 0x92f308f1,
+    0x43004b71, 0x92efbeda,
+  0x42faf0d4, 0x92ec7505, 0x42f5960e, 0x92e92b74, 0x42f03b1e, 0x92e5e226,
+    0x42eae005, 0x92e2991c,
+  0x42e584c3, 0x92df5054, 0x42e02958, 0x92dc07d0, 0x42dacdc3, 0x92d8bf90,
+    0x42d57205, 0x92d57792,
+  0x42d0161e, 0x92d22fd9, 0x42caba0e, 0x92cee862, 0x42c55dd4, 0x92cba12f,
+    0x42c00172, 0x92c85a3f,
+  0x42baa4e6, 0x92c51392, 0x42b54831, 0x92c1cd29, 0x42afeb53, 0x92be8703,
+    0x42aa8e4b, 0x92bb4121,
+  0x42a5311b, 0x92b7fb82, 0x429fd3c1, 0x92b4b626, 0x429a763f, 0x92b1710e,
+    0x42951893, 0x92ae2c3a,
+  0x428fbabe, 0x92aae7a8, 0x428a5cc0, 0x92a7a35a, 0x4284fe99, 0x92a45f50,
+    0x427fa049, 0x92a11b89,
+  0x427a41d0, 0x929dd806, 0x4274e32e, 0x929a94c6, 0x426f8463, 0x929751c9,
+    0x426a256f, 0x92940f10,
+  0x4264c653, 0x9290cc9b, 0x425f670d, 0x928d8a69, 0x425a079e, 0x928a487a,
+    0x4254a806, 0x928706cf,
+  0x424f4845, 0x9283c568, 0x4249e85c, 0x92808444, 0x42448849, 0x927d4363,
+    0x423f280e, 0x927a02c7,
+  0x4239c7aa, 0x9276c26d, 0x4234671d, 0x92738258, 0x422f0667, 0x92704286,
+    0x4229a588, 0x926d02f7,
+  0x42244481, 0x9269c3ac, 0x421ee350, 0x926684a5, 0x421981f7, 0x926345e1,
+    0x42142075, 0x92600761,
+  0x420ebecb, 0x925cc924, 0x42095cf7, 0x92598b2b, 0x4203fafb, 0x92564d76,
+    0x41fe98d6, 0x92531005,
+  0x41f93689, 0x924fd2d7, 0x41f3d413, 0x924c95ec, 0x41ee7174, 0x92495946,
+    0x41e90eac, 0x92461ce3,
+  0x41e3abbc, 0x9242e0c4, 0x41de48a3, 0x923fa4e8, 0x41d8e561, 0x923c6950,
+    0x41d381f7, 0x92392dfc,
+  0x41ce1e65, 0x9235f2ec, 0x41c8baa9, 0x9232b81f, 0x41c356c5, 0x922f7d96,
+    0x41bdf2b9, 0x922c4351,
+  0x41b88e84, 0x9229094f, 0x41b32a26, 0x9225cf91, 0x41adc5a0, 0x92229617,
+    0x41a860f1, 0x921f5ce1,
+  0x41a2fc1a, 0x921c23ef, 0x419d971b, 0x9218eb40, 0x419831f3, 0x9215b2d5,
+    0x4192cca2, 0x92127aae,
+  0x418d6729, 0x920f42cb, 0x41880188, 0x920c0b2c, 0x41829bbe, 0x9208d3d0,
+    0x417d35cb, 0x92059cb8,
+  0x4177cfb1, 0x920265e4, 0x4172696e, 0x91ff2f54, 0x416d0302, 0x91fbf908,
+    0x41679c6f, 0x91f8c300,
+  0x416235b2, 0x91f58d3b, 0x415ccece, 0x91f257bb, 0x415767c1, 0x91ef227e,
+    0x4152008c, 0x91ebed85,
+  0x414c992f, 0x91e8b8d0, 0x414731a9, 0x91e5845f, 0x4141c9fb, 0x91e25032,
+    0x413c6225, 0x91df1c49,
+  0x4136fa27, 0x91dbe8a4, 0x41319200, 0x91d8b542, 0x412c29b1, 0x91d58225,
+    0x4126c13a, 0x91d24f4c,
+  0x4121589b, 0x91cf1cb6, 0x411befd3, 0x91cbea65, 0x411686e4, 0x91c8b857,
+    0x41111dcc, 0x91c5868e,
+  0x410bb48c, 0x91c25508, 0x41064b24, 0x91bf23c7, 0x4100e194, 0x91bbf2c9,
+    0x40fb77dc, 0x91b8c210,
+  0x40f60dfb, 0x91b5919a, 0x40f0a3f3, 0x91b26169, 0x40eb39c3, 0x91af317c,
+    0x40e5cf6a, 0x91ac01d2,
+  0x40e064ea, 0x91a8d26d, 0x40dafa41, 0x91a5a34c, 0x40d58f71, 0x91a2746f,
+    0x40d02478, 0x919f45d6,
+  0x40cab958, 0x919c1781, 0x40c54e0f, 0x9198e970, 0x40bfe29f, 0x9195bba3,
+    0x40ba7706, 0x91928e1a,
+  0x40b50b46, 0x918f60d6, 0x40af9f5e, 0x918c33d5, 0x40aa334e, 0x91890719,
+    0x40a4c716, 0x9185daa1,
+  0x409f5ab6, 0x9182ae6d, 0x4099ee2e, 0x917f827d, 0x4094817f, 0x917c56d1,
+    0x408f14a7, 0x91792b6a,
+  0x4089a7a8, 0x91760047, 0x40843a81, 0x9172d567, 0x407ecd32, 0x916faacc,
+    0x40795fbc, 0x916c8076,
+  0x4073f21d, 0x91695663, 0x406e8457, 0x91662c95, 0x40691669, 0x9163030b,
+    0x4063a854, 0x915fd9c5,
+  0x405e3a16, 0x915cb0c3, 0x4058cbb1, 0x91598806, 0x40535d24, 0x91565f8d,
+    0x404dee70, 0x91533758,
+  0x40487f94, 0x91500f67, 0x40431090, 0x914ce7bb, 0x403da165, 0x9149c053,
+    0x40383212, 0x9146992f,
+  0x4032c297, 0x91437250, 0x402d52f5, 0x91404bb5, 0x4027e32b, 0x913d255e,
+    0x4022733a, 0x9139ff4b,
+  0x401d0321, 0x9136d97d, 0x401792e0, 0x9133b3f3, 0x40122278, 0x91308eae,
+    0x400cb1e9, 0x912d69ad,
+  0x40074132, 0x912a44f0, 0x4001d053, 0x91272078, 0x3ffc5f4d, 0x9123fc44,
+    0x3ff6ee1f, 0x9120d854,
+  0x3ff17cca, 0x911db4a9, 0x3fec0b4e, 0x911a9142, 0x3fe699aa, 0x91176e1f,
+    0x3fe127df, 0x91144b41,
+  0x3fdbb5ec, 0x911128a8, 0x3fd643d2, 0x910e0653, 0x3fd0d191, 0x910ae442,
+    0x3fcb5f28, 0x9107c276,
+  0x3fc5ec98, 0x9104a0ee, 0x3fc079e0, 0x91017faa, 0x3fbb0702, 0x90fe5eab,
+    0x3fb593fb, 0x90fb3df1,
+  0x3fb020ce, 0x90f81d7b, 0x3faaad79, 0x90f4fd4a, 0x3fa539fd, 0x90f1dd5d,
+    0x3f9fc65a, 0x90eebdb4,
+  0x3f9a5290, 0x90eb9e50, 0x3f94de9e, 0x90e87f31, 0x3f8f6a85, 0x90e56056,
+    0x3f89f645, 0x90e241bf,
+  0x3f8481dd, 0x90df236e, 0x3f7f0d4f, 0x90dc0560, 0x3f799899, 0x90d8e798,
+    0x3f7423bc, 0x90d5ca13,
+  0x3f6eaeb8, 0x90d2acd4, 0x3f69398d, 0x90cf8fd9, 0x3f63c43b, 0x90cc7322,
+    0x3f5e4ec2, 0x90c956b1,
+  0x3f58d921, 0x90c63a83, 0x3f53635a, 0x90c31e9b, 0x3f4ded6b, 0x90c002f7,
+    0x3f487755, 0x90bce797,
+  0x3f430119, 0x90b9cc7d, 0x3f3d8ab5, 0x90b6b1a6, 0x3f38142a, 0x90b39715,
+    0x3f329d79, 0x90b07cc8,
+  0x3f2d26a0, 0x90ad62c0, 0x3f27afa1, 0x90aa48fd, 0x3f22387a, 0x90a72f7e,
+    0x3f1cc12c, 0x90a41644,
+  0x3f1749b8, 0x90a0fd4e, 0x3f11d21d, 0x909de49e, 0x3f0c5a5a, 0x909acc32,
+    0x3f06e271, 0x9097b40a,
+  0x3f016a61, 0x90949c28, 0x3efbf22a, 0x9091848a, 0x3ef679cc, 0x908e6d31,
+    0x3ef10148, 0x908b561c,
+  0x3eeb889c, 0x90883f4d, 0x3ee60fca, 0x908528c2, 0x3ee096d1, 0x9082127c,
+    0x3edb1db1, 0x907efc7a,
+  0x3ed5a46b, 0x907be6be, 0x3ed02afd, 0x9078d146, 0x3ecab169, 0x9075bc13,
+    0x3ec537ae, 0x9072a725,
+  0x3ebfbdcd, 0x906f927c, 0x3eba43c4, 0x906c7e17, 0x3eb4c995, 0x906969f8,
+    0x3eaf4f40, 0x9066561d,
+  0x3ea9d4c3, 0x90634287, 0x3ea45a21, 0x90602f35, 0x3e9edf57, 0x905d1c29,
+    0x3e996467, 0x905a0962,
+  0x3e93e950, 0x9056f6df, 0x3e8e6e12, 0x9053e4a1, 0x3e88f2ae, 0x9050d2a9,
+    0x3e837724, 0x904dc0f5,
+  0x3e7dfb73, 0x904aaf86, 0x3e787f9b, 0x90479e5c, 0x3e73039d, 0x90448d76,
+    0x3e6d8778, 0x90417cd6,
+  0x3e680b2c, 0x903e6c7b, 0x3e628ebb, 0x903b5c64, 0x3e5d1222, 0x90384c93,
+    0x3e579564, 0x90353d06,
+  0x3e52187f, 0x90322dbf, 0x3e4c9b73, 0x902f1ebc, 0x3e471e41, 0x902c0fff,
+    0x3e41a0e8, 0x90290186,
+  0x3e3c2369, 0x9025f352, 0x3e36a5c4, 0x9022e564, 0x3e3127f9, 0x901fd7ba,
+    0x3e2baa07, 0x901cca55,
+  0x3e262bee, 0x9019bd36, 0x3e20adaf, 0x9016b05b, 0x3e1b2f4a, 0x9013a3c5,
+    0x3e15b0bf, 0x90109775,
+  0x3e10320d, 0x900d8b69, 0x3e0ab336, 0x900a7fa3, 0x3e053437, 0x90077422,
+    0x3dffb513, 0x900468e5,
+  0x3dfa35c8, 0x90015dee, 0x3df4b657, 0x8ffe533c, 0x3def36c0, 0x8ffb48cf,
+    0x3de9b703, 0x8ff83ea7,
+  0x3de4371f, 0x8ff534c4, 0x3ddeb716, 0x8ff22b26, 0x3dd936e6, 0x8fef21ce,
+    0x3dd3b690, 0x8fec18ba,
+  0x3dce3614, 0x8fe90fec, 0x3dc8b571, 0x8fe60763, 0x3dc334a9, 0x8fe2ff1f,
+    0x3dbdb3ba, 0x8fdff720,
+  0x3db832a6, 0x8fdcef66, 0x3db2b16b, 0x8fd9e7f2, 0x3dad300b, 0x8fd6e0c2,
+    0x3da7ae84, 0x8fd3d9d8,
+  0x3da22cd7, 0x8fd0d333, 0x3d9cab04, 0x8fcdccd3, 0x3d97290b, 0x8fcac6b9,
+    0x3d91a6ed, 0x8fc7c0e3,
+  0x3d8c24a8, 0x8fc4bb53, 0x3d86a23d, 0x8fc1b608, 0x3d811fac, 0x8fbeb103,
+    0x3d7b9cf6, 0x8fbbac42,
+  0x3d761a19, 0x8fb8a7c7, 0x3d709717, 0x8fb5a391, 0x3d6b13ee, 0x8fb29fa0,
+    0x3d6590a0, 0x8faf9bf5,
+  0x3d600d2c, 0x8fac988f, 0x3d5a8992, 0x8fa9956e, 0x3d5505d2, 0x8fa69293,
+    0x3d4f81ec, 0x8fa38ffc,
+  0x3d49fde1, 0x8fa08dab, 0x3d4479b0, 0x8f9d8ba0, 0x3d3ef559, 0x8f9a89da,
+    0x3d3970dc, 0x8f978859,
+  0x3d33ec39, 0x8f94871d, 0x3d2e6771, 0x8f918627, 0x3d28e282, 0x8f8e8576,
+    0x3d235d6f, 0x8f8b850a,
+  0x3d1dd835, 0x8f8884e4, 0x3d1852d6, 0x8f858503, 0x3d12cd51, 0x8f828568,
+    0x3d0d47a6, 0x8f7f8612,
+  0x3d07c1d6, 0x8f7c8701, 0x3d023be0, 0x8f798836, 0x3cfcb5c4, 0x8f7689b0,
+    0x3cf72f83, 0x8f738b70,
+  0x3cf1a91c, 0x8f708d75, 0x3cec2290, 0x8f6d8fbf, 0x3ce69bde, 0x8f6a924f,
+    0x3ce11507, 0x8f679525,
+  0x3cdb8e09, 0x8f649840, 0x3cd606e7, 0x8f619ba0, 0x3cd07f9f, 0x8f5e9f46,
+    0x3ccaf831, 0x8f5ba331,
+  0x3cc5709e, 0x8f58a761, 0x3cbfe8e5, 0x8f55abd8, 0x3cba6107, 0x8f52b093,
+    0x3cb4d904, 0x8f4fb595,
+  0x3caf50da, 0x8f4cbadb, 0x3ca9c88c, 0x8f49c067, 0x3ca44018, 0x8f46c639,
+    0x3c9eb77f, 0x8f43cc50,
+  0x3c992ec0, 0x8f40d2ad, 0x3c93a5dc, 0x8f3dd950, 0x3c8e1cd3, 0x8f3ae038,
+    0x3c8893a4, 0x8f37e765,
+  0x3c830a50, 0x8f34eed8, 0x3c7d80d6, 0x8f31f691, 0x3c77f737, 0x8f2efe8f,
+    0x3c726d73, 0x8f2c06d3,
+  0x3c6ce38a, 0x8f290f5c, 0x3c67597b, 0x8f26182b, 0x3c61cf48, 0x8f232140,
+    0x3c5c44ee, 0x8f202a9a,
+  0x3c56ba70, 0x8f1d343a, 0x3c512fcc, 0x8f1a3e1f, 0x3c4ba504, 0x8f17484b,
+    0x3c461a16, 0x8f1452bb,
+  0x3c408f03, 0x8f115d72, 0x3c3b03ca, 0x8f0e686e, 0x3c35786d, 0x8f0b73b0,
+    0x3c2fecea, 0x8f087f37,
+  0x3c2a6142, 0x8f058b04, 0x3c24d575, 0x8f029717, 0x3c1f4983, 0x8effa370,
+    0x3c19bd6c, 0x8efcb00e,
+  0x3c143130, 0x8ef9bcf2, 0x3c0ea4cf, 0x8ef6ca1c, 0x3c091849, 0x8ef3d78b,
+    0x3c038b9e, 0x8ef0e540,
+  0x3bfdfecd, 0x8eedf33b, 0x3bf871d8, 0x8eeb017c, 0x3bf2e4be, 0x8ee81002,
+    0x3bed577e, 0x8ee51ece,
+  0x3be7ca1a, 0x8ee22de0, 0x3be23c91, 0x8edf3d38, 0x3bdcaee3, 0x8edc4cd5,
+    0x3bd72110, 0x8ed95cb8,
+  0x3bd19318, 0x8ed66ce1, 0x3bcc04fb, 0x8ed37d50, 0x3bc676b9, 0x8ed08e05,
+    0x3bc0e853, 0x8ecd9eff,
+  0x3bbb59c7, 0x8ecab040, 0x3bb5cb17, 0x8ec7c1c6, 0x3bb03c42, 0x8ec4d392,
+    0x3baaad48, 0x8ec1e5a4,
+  0x3ba51e29, 0x8ebef7fb, 0x3b9f8ee5, 0x8ebc0a99, 0x3b99ff7d, 0x8eb91d7c,
+    0x3b946ff0, 0x8eb630a6,
+  0x3b8ee03e, 0x8eb34415, 0x3b895068, 0x8eb057ca, 0x3b83c06c, 0x8ead6bc5,
+    0x3b7e304c, 0x8eaa8006,
+  0x3b78a007, 0x8ea7948c, 0x3b730f9e, 0x8ea4a959, 0x3b6d7f10, 0x8ea1be6c,
+    0x3b67ee5d, 0x8e9ed3c4,
+  0x3b625d86, 0x8e9be963, 0x3b5ccc8a, 0x8e98ff47, 0x3b573b69, 0x8e961571,
+    0x3b51aa24, 0x8e932be2,
+  0x3b4c18ba, 0x8e904298, 0x3b46872c, 0x8e8d5994, 0x3b40f579, 0x8e8a70d7,
+    0x3b3b63a1, 0x8e87885f,
+  0x3b35d1a5, 0x8e84a02d, 0x3b303f84, 0x8e81b841, 0x3b2aad3f, 0x8e7ed09b,
+    0x3b251ad6, 0x8e7be93c,
+  0x3b1f8848, 0x8e790222, 0x3b19f595, 0x8e761b4e, 0x3b1462be, 0x8e7334c1,
+    0x3b0ecfc3, 0x8e704e79,
+  0x3b093ca3, 0x8e6d6877, 0x3b03a95e, 0x8e6a82bc, 0x3afe15f6, 0x8e679d47,
+    0x3af88269, 0x8e64b817,
+  0x3af2eeb7, 0x8e61d32e, 0x3aed5ae1, 0x8e5eee8b, 0x3ae7c6e7, 0x8e5c0a2e,
+    0x3ae232c9, 0x8e592617,
+  0x3adc9e86, 0x8e564246, 0x3ad70a1f, 0x8e535ebb, 0x3ad17593, 0x8e507b76,
+    0x3acbe0e3, 0x8e4d9878,
+  0x3ac64c0f, 0x8e4ab5bf, 0x3ac0b717, 0x8e47d34d, 0x3abb21fb, 0x8e44f121,
+    0x3ab58cba, 0x8e420f3b,
+  0x3aaff755, 0x8e3f2d9b, 0x3aaa61cc, 0x8e3c4c41, 0x3aa4cc1e, 0x8e396b2e,
+    0x3a9f364d, 0x8e368a61,
+  0x3a99a057, 0x8e33a9da, 0x3a940a3e, 0x8e30c999, 0x3a8e7400, 0x8e2de99e,
+    0x3a88dd9d, 0x8e2b09e9,
+  0x3a834717, 0x8e282a7b, 0x3a7db06d, 0x8e254b53, 0x3a78199f, 0x8e226c71,
+    0x3a7282ac, 0x8e1f8dd6,
+  0x3a6ceb96, 0x8e1caf80, 0x3a67545b, 0x8e19d171, 0x3a61bcfd, 0x8e16f3a9,
+    0x3a5c257a, 0x8e141626,
+  0x3a568dd4, 0x8e1138ea, 0x3a50f609, 0x8e0e5bf4, 0x3a4b5e1b, 0x8e0b7f44,
+    0x3a45c608, 0x8e08a2db,
+  0x3a402dd2, 0x8e05c6b7, 0x3a3a9577, 0x8e02eadb, 0x3a34fcf9, 0x8e000f44,
+    0x3a2f6457, 0x8dfd33f4,
+  0x3a29cb91, 0x8dfa58ea, 0x3a2432a7, 0x8df77e27, 0x3a1e9999, 0x8df4a3a9,
+    0x3a190068, 0x8df1c973,
+  0x3a136712, 0x8deeef82, 0x3a0dcd99, 0x8dec15d8, 0x3a0833fc, 0x8de93c74,
+    0x3a029a3b, 0x8de66357,
+  0x39fd0056, 0x8de38a80, 0x39f7664e, 0x8de0b1ef, 0x39f1cc21, 0x8dddd9a5,
+    0x39ec31d1, 0x8ddb01a1,
+  0x39e6975e, 0x8dd829e4, 0x39e0fcc6, 0x8dd5526d, 0x39db620b, 0x8dd27b3c,
+    0x39d5c72c, 0x8dcfa452,
+  0x39d02c2a, 0x8dcccdaf, 0x39ca9104, 0x8dc9f751, 0x39c4f5ba, 0x8dc7213b,
+    0x39bf5a4d, 0x8dc44b6a,
+  0x39b9bebc, 0x8dc175e0, 0x39b42307, 0x8dbea09d, 0x39ae872f, 0x8dbbcba0,
+    0x39a8eb33, 0x8db8f6ea,
+  0x39a34f13, 0x8db6227a, 0x399db2d0, 0x8db34e50, 0x3998166a, 0x8db07a6d,
+    0x399279e0, 0x8dada6d1,
+  0x398cdd32, 0x8daad37b, 0x39874061, 0x8da8006c, 0x3981a36d, 0x8da52da3,
+    0x397c0655, 0x8da25b21,
+  0x39766919, 0x8d9f88e5, 0x3970cbba, 0x8d9cb6f0, 0x396b2e38, 0x8d99e541,
+    0x39659092, 0x8d9713d9,
+  0x395ff2c9, 0x8d9442b8, 0x395a54dd, 0x8d9171dd, 0x3954b6cd, 0x8d8ea148,
+    0x394f1899, 0x8d8bd0fb,
+  0x39497a43, 0x8d8900f3, 0x3943dbc9, 0x8d863133, 0x393e3d2c, 0x8d8361b9,
+    0x39389e6b, 0x8d809286,
+  0x3932ff87, 0x8d7dc399, 0x392d6080, 0x8d7af4f3, 0x3927c155, 0x8d782694,
+    0x39222208, 0x8d75587b,
+  0x391c8297, 0x8d728aa9, 0x3916e303, 0x8d6fbd1d, 0x3911434b, 0x8d6cefd9,
+    0x390ba371, 0x8d6a22db,
+  0x39060373, 0x8d675623, 0x39006352, 0x8d6489b3, 0x38fac30e, 0x8d61bd89,
+    0x38f522a6, 0x8d5ef1a5,
+  0x38ef821c, 0x8d5c2609, 0x38e9e16e, 0x8d595ab3, 0x38e4409e, 0x8d568fa4,
+    0x38de9faa, 0x8d53c4db,
+  0x38d8fe93, 0x8d50fa59, 0x38d35d59, 0x8d4e301f, 0x38cdbbfc, 0x8d4b662a,
+    0x38c81a7c, 0x8d489c7d,
+  0x38c278d9, 0x8d45d316, 0x38bcd713, 0x8d4309f6, 0x38b7352a, 0x8d40411d,
+    0x38b1931e, 0x8d3d788b,
+  0x38abf0ef, 0x8d3ab03f, 0x38a64e9d, 0x8d37e83a, 0x38a0ac29, 0x8d35207d,
+    0x389b0991, 0x8d325905,
+  0x389566d6, 0x8d2f91d5, 0x388fc3f8, 0x8d2ccaec, 0x388a20f8, 0x8d2a0449,
+    0x38847dd5, 0x8d273ded,
+  0x387eda8e, 0x8d2477d8, 0x38793725, 0x8d21b20a, 0x38739399, 0x8d1eec83,
+    0x386defeb, 0x8d1c2742,
+  0x38684c19, 0x8d196249, 0x3862a825, 0x8d169d96, 0x385d040d, 0x8d13d92a,
+    0x38575fd4, 0x8d111505,
+  0x3851bb77, 0x8d0e5127, 0x384c16f7, 0x8d0b8d90, 0x38467255, 0x8d08ca40,
+    0x3840cd90, 0x8d060737,
+  0x383b28a9, 0x8d034474, 0x3835839f, 0x8d0081f9, 0x382fde72, 0x8cfdbfc4,
+    0x382a3922, 0x8cfafdd7,
+  0x382493b0, 0x8cf83c30, 0x381eee1b, 0x8cf57ad0, 0x38194864, 0x8cf2b9b8,
+    0x3813a28a, 0x8ceff8e6,
+  0x380dfc8d, 0x8ced385b, 0x3808566e, 0x8cea7818, 0x3802b02c, 0x8ce7b81b,
+    0x37fd09c8, 0x8ce4f865,
+  0x37f76341, 0x8ce238f6, 0x37f1bc97, 0x8cdf79ce, 0x37ec15cb, 0x8cdcbaee,
+    0x37e66edd, 0x8cd9fc54,
+  0x37e0c7cc, 0x8cd73e01, 0x37db2099, 0x8cd47ff6, 0x37d57943, 0x8cd1c231,
+    0x37cfd1cb, 0x8ccf04b3,
+  0x37ca2a30, 0x8ccc477d, 0x37c48273, 0x8cc98a8e, 0x37beda93, 0x8cc6cde5,
+    0x37b93292, 0x8cc41184,
+  0x37b38a6d, 0x8cc1556a, 0x37ade227, 0x8cbe9996, 0x37a839be, 0x8cbbde0a,
+    0x37a29132, 0x8cb922c6,
+  0x379ce885, 0x8cb667c8, 0x37973fb5, 0x8cb3ad11, 0x379196c3, 0x8cb0f2a1,
+    0x378bedae, 0x8cae3879,
+  0x37864477, 0x8cab7e98, 0x37809b1e, 0x8ca8c4fd, 0x377af1a3, 0x8ca60baa,
+    0x37754806, 0x8ca3529f,
+  0x376f9e46, 0x8ca099da, 0x3769f464, 0x8c9de15c, 0x37644a60, 0x8c9b2926,
+    0x375ea03a, 0x8c987137,
+  0x3758f5f2, 0x8c95b98f, 0x37534b87, 0x8c93022e, 0x374da0fa, 0x8c904b14,
+    0x3747f64c, 0x8c8d9442,
+  0x37424b7b, 0x8c8addb7, 0x373ca088, 0x8c882773, 0x3736f573, 0x8c857176,
+    0x37314a3c, 0x8c82bbc0,
+  0x372b9ee3, 0x8c800652, 0x3725f367, 0x8c7d512b, 0x372047ca, 0x8c7a9c4b,
+    0x371a9c0b, 0x8c77e7b3,
+  0x3714f02a, 0x8c753362, 0x370f4427, 0x8c727f58, 0x37099802, 0x8c6fcb95,
+    0x3703ebbb, 0x8c6d181a,
+  0x36fe3f52, 0x8c6a64e5, 0x36f892c7, 0x8c67b1f9, 0x36f2e61a, 0x8c64ff53,
+    0x36ed394b, 0x8c624cf5,
+  0x36e78c5b, 0x8c5f9ade, 0x36e1df48, 0x8c5ce90e, 0x36dc3214, 0x8c5a3786,
+    0x36d684be, 0x8c578645,
+  0x36d0d746, 0x8c54d54c, 0x36cb29ac, 0x8c522499, 0x36c57bf0, 0x8c4f742f,
+    0x36bfce13, 0x8c4cc40b,
+  0x36ba2014, 0x8c4a142f, 0x36b471f3, 0x8c47649a, 0x36aec3b0, 0x8c44b54d,
+    0x36a9154c, 0x8c420647,
+  0x36a366c6, 0x8c3f5788, 0x369db81e, 0x8c3ca911, 0x36980954, 0x8c39fae1,
+    0x36925a69, 0x8c374cf9,
+  0x368cab5c, 0x8c349f58, 0x3686fc2e, 0x8c31f1ff, 0x36814cde, 0x8c2f44ed,
+    0x367b9d6c, 0x8c2c9822,
+  0x3675edd9, 0x8c29eb9f, 0x36703e24, 0x8c273f63, 0x366a8e4d, 0x8c24936f,
+    0x3664de55, 0x8c21e7c2,
+  0x365f2e3b, 0x8c1f3c5d, 0x36597e00, 0x8c1c913f, 0x3653cda3, 0x8c19e669,
+    0x364e1d25, 0x8c173bda,
+  0x36486c86, 0x8c149192, 0x3642bbc4, 0x8c11e792, 0x363d0ae2, 0x8c0f3dda,
+    0x363759de, 0x8c0c9469,
+  0x3631a8b8, 0x8c09eb40, 0x362bf771, 0x8c07425e, 0x36264609, 0x8c0499c4,
+    0x3620947f, 0x8c01f171,
+  0x361ae2d3, 0x8bff4966, 0x36153107, 0x8bfca1a3, 0x360f7f19, 0x8bf9fa27,
+    0x3609cd0a, 0x8bf752f2,
+  0x36041ad9, 0x8bf4ac05, 0x35fe6887, 0x8bf20560, 0x35f8b614, 0x8bef5f02,
+    0x35f3037f, 0x8becb8ec,
+  0x35ed50c9, 0x8bea131e, 0x35e79df2, 0x8be76d97, 0x35e1eafa, 0x8be4c857,
+    0x35dc37e0, 0x8be22360,
+  0x35d684a6, 0x8bdf7eb0, 0x35d0d14a, 0x8bdcda47, 0x35cb1dcc, 0x8bda3626,
+    0x35c56a2e, 0x8bd7924d,
+  0x35bfb66e, 0x8bd4eebc, 0x35ba028e, 0x8bd24b72, 0x35b44e8c, 0x8bcfa870,
+    0x35ae9a69, 0x8bcd05b5,
+  0x35a8e625, 0x8bca6343, 0x35a331c0, 0x8bc7c117, 0x359d7d39, 0x8bc51f34,
+    0x3597c892, 0x8bc27d98,
+  0x359213c9, 0x8bbfdc44, 0x358c5ee0, 0x8bbd3b38, 0x3586a9d5, 0x8bba9a73,
+    0x3580f4aa, 0x8bb7f9f6,
+  0x357b3f5d, 0x8bb559c1, 0x357589f0, 0x8bb2b9d4, 0x356fd461, 0x8bb01a2e,
+    0x356a1eb2, 0x8bad7ad0,
+  0x356468e2, 0x8baadbba, 0x355eb2f0, 0x8ba83cec, 0x3558fcde, 0x8ba59e65,
+    0x355346ab, 0x8ba30026,
+  0x354d9057, 0x8ba0622f, 0x3547d9e2, 0x8b9dc480, 0x3542234c, 0x8b9b2718,
+    0x353c6c95, 0x8b9889f8,
+  0x3536b5be, 0x8b95ed21, 0x3530fec6, 0x8b935090, 0x352b47ad, 0x8b90b448,
+    0x35259073, 0x8b8e1848,
+  0x351fd918, 0x8b8b7c8f, 0x351a219c, 0x8b88e11e, 0x35146a00, 0x8b8645f5,
+    0x350eb243, 0x8b83ab14,
+  0x3508fa66, 0x8b81107b, 0x35034267, 0x8b7e7629, 0x34fd8a48, 0x8b7bdc20,
+    0x34f7d208, 0x8b79425e,
+  0x34f219a8, 0x8b76a8e4, 0x34ec6127, 0x8b740fb3, 0x34e6a885, 0x8b7176c8,
+    0x34e0efc2, 0x8b6ede26,
+  0x34db36df, 0x8b6c45cc, 0x34d57ddc, 0x8b69adba, 0x34cfc4b7, 0x8b6715ef,
+    0x34ca0b73, 0x8b647e6d,
+  0x34c4520d, 0x8b61e733, 0x34be9887, 0x8b5f5040, 0x34b8dee1, 0x8b5cb995,
+    0x34b3251a, 0x8b5a2333,
+  0x34ad6b32, 0x8b578d18, 0x34a7b12a, 0x8b54f745, 0x34a1f702, 0x8b5261ba,
+    0x349c3cb9, 0x8b4fcc77,
+  0x34968250, 0x8b4d377c, 0x3490c7c6, 0x8b4aa2ca, 0x348b0d1c, 0x8b480e5f,
+    0x34855251, 0x8b457a3c,
+  0x347f9766, 0x8b42e661, 0x3479dc5b, 0x8b4052ce, 0x3474212f, 0x8b3dbf83,
+    0x346e65e3, 0x8b3b2c80,
+  0x3468aa76, 0x8b3899c6, 0x3462eee9, 0x8b360753, 0x345d333c, 0x8b337528,
+    0x3457776f, 0x8b30e345,
+  0x3451bb81, 0x8b2e51ab, 0x344bff73, 0x8b2bc058, 0x34464345, 0x8b292f4e,
+    0x344086f6, 0x8b269e8b,
+  0x343aca87, 0x8b240e11, 0x34350df8, 0x8b217ddf, 0x342f5149, 0x8b1eedf4,
+    0x3429947a, 0x8b1c5e52,
+  0x3423d78a, 0x8b19cef8, 0x341e1a7b, 0x8b173fe6, 0x34185d4b, 0x8b14b11d,
+    0x34129ffb, 0x8b12229b,
+  0x340ce28b, 0x8b0f9462, 0x340724fb, 0x8b0d0670, 0x3401674a, 0x8b0a78c7,
+    0x33fba97a, 0x8b07eb66,
+  0x33f5eb89, 0x8b055e4d, 0x33f02d79, 0x8b02d17c, 0x33ea6f48, 0x8b0044f3,
+    0x33e4b0f8, 0x8afdb8b3,
+  0x33def287, 0x8afb2cbb, 0x33d933f7, 0x8af8a10b, 0x33d37546, 0x8af615a3,
+    0x33cdb676, 0x8af38a83,
+  0x33c7f785, 0x8af0ffac, 0x33c23875, 0x8aee751c, 0x33bc7944, 0x8aebead5,
+    0x33b6b9f4, 0x8ae960d6,
+  0x33b0fa84, 0x8ae6d720, 0x33ab3af4, 0x8ae44db1, 0x33a57b44, 0x8ae1c48b,
+    0x339fbb74, 0x8adf3bad,
+  0x3399fb85, 0x8adcb318, 0x33943b75, 0x8ada2aca, 0x338e7b46, 0x8ad7a2c5,
+    0x3388baf7, 0x8ad51b08,
+  0x3382fa88, 0x8ad29394, 0x337d39f9, 0x8ad00c67, 0x3377794b, 0x8acd8583,
+    0x3371b87d, 0x8acafee8,
+  0x336bf78f, 0x8ac87894, 0x33663682, 0x8ac5f289, 0x33607554, 0x8ac36cc6,
+    0x335ab407, 0x8ac0e74c,
+  0x3354f29b, 0x8abe6219, 0x334f310e, 0x8abbdd30, 0x33496f62, 0x8ab9588e,
+    0x3343ad97, 0x8ab6d435,
+  0x333debab, 0x8ab45024, 0x333829a1, 0x8ab1cc5c, 0x33326776, 0x8aaf48db,
+    0x332ca52c, 0x8aacc5a4,
+  0x3326e2c3, 0x8aaa42b4, 0x33212039, 0x8aa7c00d, 0x331b5d91, 0x8aa53daf,
+    0x33159ac8, 0x8aa2bb99,
+  0x330fd7e1, 0x8aa039cb, 0x330a14da, 0x8a9db845, 0x330451b3, 0x8a9b3708,
+    0x32fe8e6d, 0x8a98b614,
+  0x32f8cb07, 0x8a963567, 0x32f30782, 0x8a93b504, 0x32ed43de, 0x8a9134e8,
+    0x32e7801a, 0x8a8eb516,
+  0x32e1bc36, 0x8a8c358b, 0x32dbf834, 0x8a89b649, 0x32d63412, 0x8a873750,
+    0x32d06fd0, 0x8a84b89e,
+  0x32caab6f, 0x8a823a36, 0x32c4e6ef, 0x8a7fbc16, 0x32bf2250, 0x8a7d3e3e,
+    0x32b95d91, 0x8a7ac0af,
+  0x32b398b3, 0x8a784368, 0x32add3b6, 0x8a75c66a, 0x32a80e99, 0x8a7349b4,
+    0x32a2495d, 0x8a70cd47,
+  0x329c8402, 0x8a6e5123, 0x3296be88, 0x8a6bd547, 0x3290f8ef, 0x8a6959b3,
+    0x328b3336, 0x8a66de68,
+  0x32856d5e, 0x8a646365, 0x327fa767, 0x8a61e8ab, 0x3279e151, 0x8a5f6e3a,
+    0x32741b1c, 0x8a5cf411,
+  0x326e54c7, 0x8a5a7a31, 0x32688e54, 0x8a580099, 0x3262c7c1, 0x8a55874a,
+    0x325d0110, 0x8a530e43,
+  0x32573a3f, 0x8a509585, 0x3251734f, 0x8a4e1d10, 0x324bac40, 0x8a4ba4e3,
+    0x3245e512, 0x8a492cff,
+  0x32401dc6, 0x8a46b564, 0x323a565a, 0x8a443e11, 0x32348ecf, 0x8a41c706,
+    0x322ec725, 0x8a3f5045,
+  0x3228ff5c, 0x8a3cd9cc, 0x32233775, 0x8a3a639b, 0x321d6f6e, 0x8a37edb3,
+    0x3217a748, 0x8a357814,
+  0x3211df04, 0x8a3302be, 0x320c16a1, 0x8a308db0, 0x32064e1e, 0x8a2e18eb,
+    0x3200857d, 0x8a2ba46e,
+  0x31fabcbd, 0x8a29303b, 0x31f4f3df, 0x8a26bc50, 0x31ef2ae1, 0x8a2448ad,
+    0x31e961c5, 0x8a21d554,
+  0x31e39889, 0x8a1f6243, 0x31ddcf30, 0x8a1cef7a, 0x31d805b7, 0x8a1a7cfb,
+    0x31d23c1f, 0x8a180ac4,
+  0x31cc7269, 0x8a1598d6, 0x31c6a894, 0x8a132731, 0x31c0dea1, 0x8a10b5d4,
+    0x31bb148f, 0x8a0e44c0,
+  0x31b54a5e, 0x8a0bd3f5, 0x31af800e, 0x8a096373, 0x31a9b5a0, 0x8a06f339,
+    0x31a3eb13, 0x8a048348,
+  0x319e2067, 0x8a0213a0, 0x3198559d, 0x89ffa441, 0x31928ab4, 0x89fd352b,
+    0x318cbfad, 0x89fac65d,
+  0x3186f487, 0x89f857d8, 0x31812943, 0x89f5e99c, 0x317b5de0, 0x89f37ba9,
+    0x3175925e, 0x89f10dff,
+  0x316fc6be, 0x89eea09d, 0x3169fb00, 0x89ec3384, 0x31642f23, 0x89e9c6b4,
+    0x315e6328, 0x89e75a2d,
+  0x3158970e, 0x89e4edef, 0x3152cad5, 0x89e281fa, 0x314cfe7f, 0x89e0164d,
+    0x31473209, 0x89ddaae9,
+  0x31416576, 0x89db3fcf, 0x313b98c4, 0x89d8d4fd, 0x3135cbf4, 0x89d66a74,
+    0x312fff05, 0x89d40033,
+  0x312a31f8, 0x89d1963c, 0x312464cd, 0x89cf2c8e, 0x311e9783, 0x89ccc328,
+    0x3118ca1b, 0x89ca5a0c,
+  0x3112fc95, 0x89c7f138, 0x310d2ef0, 0x89c588ae, 0x3107612e, 0x89c3206c,
+    0x3101934d, 0x89c0b873,
+  0x30fbc54d, 0x89be50c3, 0x30f5f730, 0x89bbe95c, 0x30f028f4, 0x89b9823e,
+    0x30ea5a9a, 0x89b71b69,
+  0x30e48c22, 0x89b4b4dd, 0x30debd8c, 0x89b24e9a, 0x30d8eed8, 0x89afe8a0,
+    0x30d32006, 0x89ad82ef,
+  0x30cd5115, 0x89ab1d87, 0x30c78206, 0x89a8b868, 0x30c1b2da, 0x89a65391,
+    0x30bbe38f, 0x89a3ef04,
+  0x30b61426, 0x89a18ac0, 0x30b0449f, 0x899f26c5, 0x30aa74fa, 0x899cc313,
+    0x30a4a537, 0x899a5faa,
+  0x309ed556, 0x8997fc8a, 0x30990557, 0x899599b3, 0x3093353a, 0x89933725,
+    0x308d64ff, 0x8990d4e0,
+  0x308794a6, 0x898e72e4, 0x3081c42f, 0x898c1131, 0x307bf39b, 0x8989afc8,
+    0x307622e8, 0x89874ea7,
+  0x30705217, 0x8984edcf, 0x306a8129, 0x89828d41, 0x3064b01d, 0x89802cfc,
+    0x305edef3, 0x897dccff,
+  0x30590dab, 0x897b6d4c, 0x30533c45, 0x89790de2, 0x304d6ac1, 0x8976aec1,
+    0x30479920, 0x89744fe9,
+  0x3041c761, 0x8971f15a, 0x303bf584, 0x896f9315, 0x30362389, 0x896d3518,
+    0x30305171, 0x896ad765,
+  0x302a7f3a, 0x896879fb, 0x3024ace6, 0x89661cda, 0x301eda75, 0x8963c002,
+    0x301907e6, 0x89616373,
+  0x30133539, 0x895f072e, 0x300d626e, 0x895cab31, 0x30078f86, 0x895a4f7e,
+    0x3001bc80, 0x8957f414,
+  0x2ffbe95d, 0x895598f3, 0x2ff6161c, 0x89533e1c, 0x2ff042bd, 0x8950e38e,
+    0x2fea6f41, 0x894e8948,
+  0x2fe49ba7, 0x894c2f4c, 0x2fdec7f0, 0x8949d59a, 0x2fd8f41b, 0x89477c30,
+    0x2fd32028, 0x89452310,
+  0x2fcd4c19, 0x8942ca39, 0x2fc777eb, 0x894071ab, 0x2fc1a3a0, 0x893e1967,
+    0x2fbbcf38, 0x893bc16b,
+  0x2fb5fab2, 0x893969b9, 0x2fb0260f, 0x89371250, 0x2faa514f, 0x8934bb31,
+    0x2fa47c71, 0x8932645b,
+  0x2f9ea775, 0x89300dce, 0x2f98d25d, 0x892db78a, 0x2f92fd26, 0x892b6190,
+    0x2f8d27d3, 0x89290bdf,
+  0x2f875262, 0x8926b677, 0x2f817cd4, 0x89246159, 0x2f7ba729, 0x89220c84,
+    0x2f75d160, 0x891fb7f8,
+  0x2f6ffb7a, 0x891d63b5, 0x2f6a2577, 0x891b0fbc, 0x2f644f56, 0x8918bc0c,
+    0x2f5e7919, 0x891668a6,
+  0x2f58a2be, 0x89141589, 0x2f52cc46, 0x8911c2b5, 0x2f4cf5b0, 0x890f702b,
+    0x2f471efe, 0x890d1dea,
+  0x2f41482e, 0x890acbf2, 0x2f3b7141, 0x89087a44, 0x2f359a37, 0x890628df,
+    0x2f2fc310, 0x8903d7c4,
+  0x2f29ebcc, 0x890186f2, 0x2f24146b, 0x88ff3669, 0x2f1e3ced, 0x88fce62a,
+    0x2f186551, 0x88fa9634,
+  0x2f128d99, 0x88f84687, 0x2f0cb5c3, 0x88f5f724, 0x2f06ddd1, 0x88f3a80b,
+    0x2f0105c1, 0x88f1593b,
+  0x2efb2d95, 0x88ef0ab4, 0x2ef5554b, 0x88ecbc77, 0x2eef7ce5, 0x88ea6e83,
+    0x2ee9a461, 0x88e820d9,
+  0x2ee3cbc1, 0x88e5d378, 0x2eddf304, 0x88e38660, 0x2ed81a29, 0x88e13992,
+    0x2ed24132, 0x88deed0e,
+  0x2ecc681e, 0x88dca0d3, 0x2ec68eed, 0x88da54e1, 0x2ec0b5a0, 0x88d8093a,
+    0x2ebadc35, 0x88d5bddb,
+  0x2eb502ae, 0x88d372c6, 0x2eaf290a, 0x88d127fb, 0x2ea94f49, 0x88cedd79,
+    0x2ea3756b, 0x88cc9340,
+  0x2e9d9b70, 0x88ca4951, 0x2e97c159, 0x88c7ffac, 0x2e91e725, 0x88c5b650,
+    0x2e8c0cd4, 0x88c36d3e,
+  0x2e863267, 0x88c12475, 0x2e8057dd, 0x88bedbf6, 0x2e7a7d36, 0x88bc93c0,
+    0x2e74a272, 0x88ba4bd4,
+  0x2e6ec792, 0x88b80432, 0x2e68ec95, 0x88b5bcd9, 0x2e63117c, 0x88b375ca,
+    0x2e5d3646, 0x88b12f04,
+  0x2e575af3, 0x88aee888, 0x2e517f84, 0x88aca255, 0x2e4ba3f8, 0x88aa5c6c,
+    0x2e45c850, 0x88a816cd,
+  0x2e3fec8b, 0x88a5d177, 0x2e3a10aa, 0x88a38c6b, 0x2e3434ac, 0x88a147a9,
+    0x2e2e5891, 0x889f0330,
+  0x2e287c5a, 0x889cbf01, 0x2e22a007, 0x889a7b1b, 0x2e1cc397, 0x88983780,
+    0x2e16e70b, 0x8895f42d,
+  0x2e110a62, 0x8893b125, 0x2e0b2d9d, 0x88916e66, 0x2e0550bb, 0x888f2bf1,
+    0x2dff73bd, 0x888ce9c5,
+  0x2df996a3, 0x888aa7e3, 0x2df3b96c, 0x8888664b, 0x2deddc19, 0x888624fd,
+    0x2de7feaa, 0x8883e3f8,
+  0x2de2211e, 0x8881a33d, 0x2ddc4376, 0x887f62cb, 0x2dd665b2, 0x887d22a4,
+    0x2dd087d1, 0x887ae2c6,
+  0x2dcaa9d5, 0x8878a332, 0x2dc4cbbc, 0x887663e7, 0x2dbeed86, 0x887424e7,
+    0x2db90f35, 0x8871e630,
+  0x2db330c7, 0x886fa7c2, 0x2dad523d, 0x886d699f, 0x2da77397, 0x886b2bc5,
+    0x2da194d5, 0x8868ee35,
+  0x2d9bb5f6, 0x8866b0ef, 0x2d95d6fc, 0x886473f2, 0x2d8ff7e5, 0x88623740,
+    0x2d8a18b3, 0x885ffad7,
+  0x2d843964, 0x885dbeb8, 0x2d7e59f9, 0x885b82e3, 0x2d787a72, 0x88594757,
+    0x2d729acf, 0x88570c16,
+  0x2d6cbb10, 0x8854d11e, 0x2d66db35, 0x88529670, 0x2d60fb3e, 0x88505c0b,
+    0x2d5b1b2b, 0x884e21f1,
+  0x2d553afc, 0x884be821, 0x2d4f5ab1, 0x8849ae9a, 0x2d497a4a, 0x8847755d,
+    0x2d4399c7, 0x88453c6a,
+  0x2d3db928, 0x884303c1, 0x2d37d86d, 0x8840cb61, 0x2d31f797, 0x883e934c,
+    0x2d2c16a4, 0x883c5b81,
+  0x2d263596, 0x883a23ff, 0x2d20546b, 0x8837ecc7, 0x2d1a7325, 0x8835b5d9,
+    0x2d1491c4, 0x88337f35,
+  0x2d0eb046, 0x883148db, 0x2d08ceac, 0x882f12cb, 0x2d02ecf7, 0x882cdd04,
+    0x2cfd0b26, 0x882aa788,
+  0x2cf72939, 0x88287256, 0x2cf14731, 0x88263d6d, 0x2ceb650d, 0x882408ce,
+    0x2ce582cd, 0x8821d47a,
+  0x2cdfa071, 0x881fa06f, 0x2cd9bdfa, 0x881d6cae, 0x2cd3db67, 0x881b3937,
+    0x2ccdf8b8, 0x8819060a,
+  0x2cc815ee, 0x8816d327, 0x2cc23308, 0x8814a08f, 0x2cbc5006, 0x88126e40,
+    0x2cb66ce9, 0x88103c3b,
+  0x2cb089b1, 0x880e0a7f, 0x2caaa65c, 0x880bd90e, 0x2ca4c2ed, 0x8809a7e7,
+    0x2c9edf61, 0x8807770a,
+  0x2c98fbba, 0x88054677, 0x2c9317f8, 0x8803162e, 0x2c8d341a, 0x8800e62f,
+    0x2c875021, 0x87feb67a,
+  0x2c816c0c, 0x87fc870f, 0x2c7b87dc, 0x87fa57ee, 0x2c75a390, 0x87f82917,
+    0x2c6fbf29, 0x87f5fa8b,
+  0x2c69daa6, 0x87f3cc48, 0x2c63f609, 0x87f19e4f, 0x2c5e114f, 0x87ef70a0,
+    0x2c582c7b, 0x87ed433c,
+  0x2c52478a, 0x87eb1621, 0x2c4c627f, 0x87e8e950, 0x2c467d58, 0x87e6bcca,
+    0x2c409816, 0x87e4908e,
+  0x2c3ab2b9, 0x87e2649b, 0x2c34cd40, 0x87e038f3, 0x2c2ee7ad, 0x87de0d95,
+    0x2c2901fd, 0x87dbe281,
+  0x2c231c33, 0x87d9b7b7, 0x2c1d364e, 0x87d78d38, 0x2c17504d, 0x87d56302,
+    0x2c116a31, 0x87d33916,
+  0x2c0b83fa, 0x87d10f75, 0x2c059da7, 0x87cee61e, 0x2bffb73a, 0x87ccbd11,
+    0x2bf9d0b1, 0x87ca944e,
+  0x2bf3ea0d, 0x87c86bd5, 0x2bee034e, 0x87c643a6, 0x2be81c74, 0x87c41bc2,
+    0x2be2357f, 0x87c1f427,
+  0x2bdc4e6f, 0x87bfccd7, 0x2bd66744, 0x87bda5d1, 0x2bd07ffe, 0x87bb7f16,
+    0x2bca989d, 0x87b958a4,
+  0x2bc4b120, 0x87b7327d, 0x2bbec989, 0x87b50c9f, 0x2bb8e1d7, 0x87b2e70c,
+    0x2bb2fa0a, 0x87b0c1c4,
+  0x2bad1221, 0x87ae9cc5, 0x2ba72a1e, 0x87ac7811, 0x2ba14200, 0x87aa53a6,
+    0x2b9b59c7, 0x87a82f87,
+  0x2b957173, 0x87a60bb1, 0x2b8f8905, 0x87a3e825, 0x2b89a07b, 0x87a1c4e4,
+    0x2b83b7d7, 0x879fa1ed,
+  0x2b7dcf17, 0x879d7f41, 0x2b77e63d, 0x879b5cde, 0x2b71fd48, 0x87993ac6,
+    0x2b6c1438, 0x879718f8,
+  0x2b662b0e, 0x8794f774, 0x2b6041c9, 0x8792d63b, 0x2b5a5868, 0x8790b54c,
+    0x2b546eee, 0x878e94a7,
+  0x2b4e8558, 0x878c744d, 0x2b489ba8, 0x878a543d, 0x2b42b1dd, 0x87883477,
+    0x2b3cc7f7, 0x878614fb,
+  0x2b36ddf7, 0x8783f5ca, 0x2b30f3dc, 0x8781d6e3, 0x2b2b09a6, 0x877fb846,
+    0x2b251f56, 0x877d99f4,
+  0x2b1f34eb, 0x877b7bec, 0x2b194a66, 0x87795e2f, 0x2b135fc6, 0x877740bb,
+    0x2b0d750b, 0x87752392,
+  0x2b078a36, 0x877306b4, 0x2b019f46, 0x8770ea20, 0x2afbb43c, 0x876ecdd6,
+    0x2af5c917, 0x876cb1d6,
+  0x2aefddd8, 0x876a9621, 0x2ae9f27e, 0x87687ab7, 0x2ae4070a, 0x87665f96,
+    0x2ade1b7c, 0x876444c1,
+  0x2ad82fd2, 0x87622a35, 0x2ad2440f, 0x87600ff4, 0x2acc5831, 0x875df5fd,
+    0x2ac66c39, 0x875bdc51,
+  0x2ac08026, 0x8759c2ef, 0x2aba93f9, 0x8757a9d8, 0x2ab4a7b1, 0x8755910b,
+    0x2aaebb50, 0x87537888,
+  0x2aa8ced3, 0x87516050, 0x2aa2e23d, 0x874f4862, 0x2a9cf58c, 0x874d30bf,
+    0x2a9708c1, 0x874b1966,
+  0x2a911bdc, 0x87490258, 0x2a8b2edc, 0x8746eb94, 0x2a8541c3, 0x8744d51b,
+    0x2a7f548e, 0x8742beec,
+  0x2a796740, 0x8740a907, 0x2a7379d8, 0x873e936d, 0x2a6d8c55, 0x873c7e1e,
+    0x2a679eb8, 0x873a6919,
+  0x2a61b101, 0x8738545e, 0x2a5bc330, 0x87363fee, 0x2a55d545, 0x87342bc9,
+    0x2a4fe740, 0x873217ee,
+  0x2a49f920, 0x8730045d, 0x2a440ae7, 0x872df117, 0x2a3e1c93, 0x872bde1c,
+    0x2a382e25, 0x8729cb6b,
+  0x2a323f9e, 0x8727b905, 0x2a2c50fc, 0x8725a6e9, 0x2a266240, 0x87239518,
+    0x2a20736a, 0x87218391,
+  0x2a1a847b, 0x871f7255, 0x2a149571, 0x871d6163, 0x2a0ea64d, 0x871b50bc,
+    0x2a08b710, 0x87194060,
+  0x2a02c7b8, 0x8717304e, 0x29fcd847, 0x87152087, 0x29f6e8bb, 0x8713110a,
+    0x29f0f916, 0x871101d8,
+  0x29eb0957, 0x870ef2f1, 0x29e5197e, 0x870ce454, 0x29df298b, 0x870ad602,
+    0x29d9397f, 0x8708c7fa,
+  0x29d34958, 0x8706ba3d, 0x29cd5918, 0x8704acca, 0x29c768be, 0x87029fa3,
+    0x29c1784a, 0x870092c5,
+  0x29bb87bc, 0x86fe8633, 0x29b59715, 0x86fc79eb, 0x29afa654, 0x86fa6dee,
+    0x29a9b579, 0x86f8623b,
+  0x29a3c485, 0x86f656d3, 0x299dd377, 0x86f44bb6, 0x2997e24f, 0x86f240e3,
+    0x2991f10e, 0x86f0365c,
+  0x298bffb2, 0x86ee2c1e, 0x29860e3e, 0x86ec222c, 0x29801caf, 0x86ea1884,
+    0x297a2b07, 0x86e80f27,
+  0x29743946, 0x86e60614, 0x296e476b, 0x86e3fd4c, 0x29685576, 0x86e1f4cf,
+    0x29626368, 0x86dfec9d,
+  0x295c7140, 0x86dde4b5, 0x29567eff, 0x86dbdd18, 0x29508ca4, 0x86d9d5c6,
+    0x294a9a30, 0x86d7cebf,
+  0x2944a7a2, 0x86d5c802, 0x293eb4fb, 0x86d3c190, 0x2938c23a, 0x86d1bb69,
+    0x2932cf60, 0x86cfb58c,
+  0x292cdc6d, 0x86cdaffa, 0x2926e960, 0x86cbaab3, 0x2920f63a, 0x86c9a5b7,
+    0x291b02fa, 0x86c7a106,
+  0x29150fa1, 0x86c59c9f, 0x290f1c2f, 0x86c39883, 0x290928a3, 0x86c194b2,
+    0x290334ff, 0x86bf912c,
+  0x28fd4140, 0x86bd8df0, 0x28f74d69, 0x86bb8b00, 0x28f15978, 0x86b9885a,
+    0x28eb656e, 0x86b785ff,
+  0x28e5714b, 0x86b583ee, 0x28df7d0e, 0x86b38229, 0x28d988b8, 0x86b180ae,
+    0x28d3944a, 0x86af7f7e,
+  0x28cd9fc1, 0x86ad7e99, 0x28c7ab20, 0x86ab7dff, 0x28c1b666, 0x86a97db0,
+    0x28bbc192, 0x86a77dab,
+  0x28b5cca5, 0x86a57df2, 0x28afd7a0, 0x86a37e83, 0x28a9e281, 0x86a17f5f,
+    0x28a3ed49, 0x869f8086,
+  0x289df7f8, 0x869d81f8, 0x2898028e, 0x869b83b4, 0x28920d0a, 0x869985bc,
+    0x288c176e, 0x8697880f,
+  0x288621b9, 0x86958aac, 0x28802beb, 0x86938d94, 0x287a3604, 0x869190c7,
+    0x28744004, 0x868f9445,
+  0x286e49ea, 0x868d980e, 0x286853b8, 0x868b9c22, 0x28625d6d, 0x8689a081,
+    0x285c670a, 0x8687a52b,
+  0x2856708d, 0x8685aa20, 0x285079f7, 0x8683af5f, 0x284a8349, 0x8681b4ea,
+    0x28448c81, 0x867fbabf,
+  0x283e95a1, 0x867dc0e0, 0x28389ea8, 0x867bc74b, 0x2832a796, 0x8679ce01,
+    0x282cb06c, 0x8677d503,
+  0x2826b928, 0x8675dc4f, 0x2820c1cc, 0x8673e3e6, 0x281aca57, 0x8671ebc8,
+    0x2814d2c9, 0x866ff3f6,
+  0x280edb23, 0x866dfc6e, 0x2808e364, 0x866c0531, 0x2802eb8c, 0x866a0e3f,
+    0x27fcf39c, 0x86681798,
+  0x27f6fb92, 0x8666213c, 0x27f10371, 0x86642b2c, 0x27eb0b36, 0x86623566,
+    0x27e512e3, 0x86603feb,
+  0x27df1a77, 0x865e4abb, 0x27d921f3, 0x865c55d7, 0x27d32956, 0x865a613d,
+    0x27cd30a1, 0x86586cee,
+  0x27c737d3, 0x865678eb, 0x27c13eec, 0x86548532, 0x27bb45ed, 0x865291c4,
+    0x27b54cd6, 0x86509ea2,
+  0x27af53a6, 0x864eabcb, 0x27a95a5d, 0x864cb93e, 0x27a360fc, 0x864ac6fd,
+    0x279d6783, 0x8648d507,
+  0x27976df1, 0x8646e35c, 0x27917447, 0x8644f1fc, 0x278b7a84, 0x864300e7,
+    0x278580a9, 0x8641101d,
+  0x277f86b5, 0x863f1f9e, 0x27798caa, 0x863d2f6b, 0x27739285, 0x863b3f82,
+    0x276d9849, 0x86394fe5,
+  0x27679df4, 0x86376092, 0x2761a387, 0x8635718b, 0x275ba901, 0x863382cf,
+    0x2755ae64, 0x8631945e,
+  0x274fb3ae, 0x862fa638, 0x2749b8e0, 0x862db85e, 0x2743bdf9, 0x862bcace,
+    0x273dc2fa, 0x8629dd8a,
+  0x2737c7e3, 0x8627f091, 0x2731ccb4, 0x862603e3, 0x272bd16d, 0x86241780,
+    0x2725d60e, 0x86222b68,
+  0x271fda96, 0x86203f9c, 0x2719df06, 0x861e541a, 0x2713e35f, 0x861c68e4,
+    0x270de79f, 0x861a7df9,
+  0x2707ebc7, 0x86189359, 0x2701efd7, 0x8616a905, 0x26fbf3ce, 0x8614befb,
+    0x26f5f7ae, 0x8612d53d,
+  0x26effb76, 0x8610ebca, 0x26e9ff26, 0x860f02a3, 0x26e402bd, 0x860d19c6,
+    0x26de063d, 0x860b3135,
+  0x26d809a5, 0x860948ef, 0x26d20cf5, 0x860760f4, 0x26cc102d, 0x86057944,
+    0x26c6134d, 0x860391e0,
+  0x26c01655, 0x8601aac7, 0x26ba1945, 0x85ffc3f9, 0x26b41c1d, 0x85fddd76,
+    0x26ae1edd, 0x85fbf73f,
+  0x26a82186, 0x85fa1153, 0x26a22416, 0x85f82bb2, 0x269c268f, 0x85f6465c,
+    0x269628f0, 0x85f46152,
+  0x26902b39, 0x85f27c93, 0x268a2d6b, 0x85f09820, 0x26842f84, 0x85eeb3f7,
+    0x267e3186, 0x85ecd01a,
+  0x26783370, 0x85eaec88, 0x26723543, 0x85e90942, 0x266c36fe, 0x85e72647,
+    0x266638a1, 0x85e54397,
+  0x26603a2c, 0x85e36132, 0x265a3b9f, 0x85e17f19, 0x26543cfb, 0x85df9d4b,
+    0x264e3e40, 0x85ddbbc9,
+  0x26483f6c, 0x85dbda91, 0x26424082, 0x85d9f9a5, 0x263c417f, 0x85d81905,
+    0x26364265, 0x85d638b0,
+  0x26304333, 0x85d458a6, 0x262a43ea, 0x85d278e7, 0x26244489, 0x85d09974,
+    0x261e4511, 0x85ceba4d,
+  0x26184581, 0x85ccdb70, 0x261245da, 0x85cafcdf, 0x260c461b, 0x85c91e9a,
+    0x26064645, 0x85c740a0,
+  0x26004657, 0x85c562f1, 0x25fa4652, 0x85c3858d, 0x25f44635, 0x85c1a875,
+    0x25ee4601, 0x85bfcba9,
+  0x25e845b6, 0x85bdef28, 0x25e24553, 0x85bc12f2, 0x25dc44d9, 0x85ba3707,
+    0x25d64447, 0x85b85b68,
+  0x25d0439f, 0x85b68015, 0x25ca42de, 0x85b4a50d, 0x25c44207, 0x85b2ca50,
+    0x25be4118, 0x85b0efdf,
+  0x25b84012, 0x85af15b9, 0x25b23ef5, 0x85ad3bdf, 0x25ac3dc0, 0x85ab6250,
+    0x25a63c74, 0x85a9890d,
+  0x25a03b11, 0x85a7b015, 0x259a3997, 0x85a5d768, 0x25943806, 0x85a3ff07,
+    0x258e365d, 0x85a226f2,
+  0x2588349d, 0x85a04f28, 0x258232c6, 0x859e77a9, 0x257c30d8, 0x859ca076,
+    0x25762ed3, 0x859ac98f,
+  0x25702cb7, 0x8598f2f3, 0x256a2a83, 0x85971ca2, 0x25642839, 0x8595469d,
+    0x255e25d7, 0x859370e4,
+  0x2558235f, 0x85919b76, 0x255220cf, 0x858fc653, 0x254c1e28, 0x858df17c,
+    0x25461b6b, 0x858c1cf1,
+  0x25401896, 0x858a48b1, 0x253a15aa, 0x858874bd, 0x253412a8, 0x8586a114,
+    0x252e0f8e, 0x8584cdb7,
+  0x25280c5e, 0x8582faa5, 0x25220916, 0x858127df, 0x251c05b8, 0x857f5564,
+    0x25160243, 0x857d8335,
+  0x250ffeb7, 0x857bb152, 0x2509fb14, 0x8579dfba, 0x2503f75a, 0x85780e6e,
+    0x24fdf389, 0x85763d6d,
+  0x24f7efa2, 0x85746cb8, 0x24f1eba4, 0x85729c4e, 0x24ebe78f, 0x8570cc30,
+    0x24e5e363, 0x856efc5e,
+  0x24dfdf20, 0x856d2cd7, 0x24d9dac7, 0x856b5d9c, 0x24d3d657, 0x85698ead,
+    0x24cdd1d0, 0x8567c009,
+  0x24c7cd33, 0x8565f1b0, 0x24c1c87f, 0x856423a4, 0x24bbc3b4, 0x856255e3,
+    0x24b5bed2, 0x8560886d,
+  0x24afb9da, 0x855ebb44, 0x24a9b4cb, 0x855cee66, 0x24a3afa6, 0x855b21d3,
+    0x249daa6a, 0x8559558c,
+  0x2497a517, 0x85578991, 0x24919fae, 0x8555bde2, 0x248b9a2f, 0x8553f27e,
+    0x24859498, 0x85522766,
+  0x247f8eec, 0x85505c99, 0x24798928, 0x854e9219, 0x2473834f, 0x854cc7e3,
+    0x246d7d5e, 0x854afdfa,
+  0x24677758, 0x8549345c, 0x2461713a, 0x85476b0a, 0x245b6b07, 0x8545a204,
+    0x245564bd, 0x8543d949,
+  0x244f5e5c, 0x854210db, 0x244957e5, 0x854048b7, 0x24435158, 0x853e80e0,
+    0x243d4ab4, 0x853cb954,
+  0x243743fa, 0x853af214, 0x24313d2a, 0x85392b20, 0x242b3644, 0x85376477,
+    0x24252f47, 0x85359e1a,
+  0x241f2833, 0x8533d809, 0x2419210a, 0x85321244, 0x241319ca, 0x85304cca,
+    0x240d1274, 0x852e879d,
+  0x24070b08, 0x852cc2bb, 0x24010385, 0x852afe24, 0x23fafbec, 0x852939da,
+    0x23f4f43e, 0x852775db,
+  0x23eeec78, 0x8525b228, 0x23e8e49d, 0x8523eec1, 0x23e2dcac, 0x85222ba5,
+    0x23dcd4a4, 0x852068d6,
+  0x23d6cc87, 0x851ea652, 0x23d0c453, 0x851ce41a, 0x23cabc09, 0x851b222e,
+    0x23c4b3a9, 0x8519608d,
+  0x23beab33, 0x85179f39, 0x23b8a2a7, 0x8515de30, 0x23b29a05, 0x85141d73,
+    0x23ac914d, 0x85125d02,
+  0x23a6887f, 0x85109cdd, 0x23a07f9a, 0x850edd03, 0x239a76a0, 0x850d1d75,
+    0x23946d90, 0x850b5e34,
+  0x238e646a, 0x85099f3e, 0x23885b2e, 0x8507e094, 0x238251dd, 0x85062235,
+    0x237c4875, 0x85046423,
+  0x23763ef7, 0x8502a65c, 0x23703564, 0x8500e8e2, 0x236a2bba, 0x84ff2bb3,
+    0x236421fb, 0x84fd6ed0,
+  0x235e1826, 0x84fbb239, 0x23580e3b, 0x84f9f5ee, 0x2352043b, 0x84f839ee,
+    0x234bfa24, 0x84f67e3b,
+  0x2345eff8, 0x84f4c2d4, 0x233fe5b6, 0x84f307b8, 0x2339db5e, 0x84f14ce8,
+    0x2333d0f1, 0x84ef9265,
+  0x232dc66d, 0x84edd82d, 0x2327bbd5, 0x84ec1e41, 0x2321b126, 0x84ea64a1,
+    0x231ba662, 0x84e8ab4d,
+  0x23159b88, 0x84e6f244, 0x230f9098, 0x84e53988, 0x23098593, 0x84e38118,
+    0x23037a78, 0x84e1c8f3,
+  0x22fd6f48, 0x84e0111b, 0x22f76402, 0x84de598f, 0x22f158a7, 0x84dca24e,
+    0x22eb4d36, 0x84daeb5a,
+  0x22e541af, 0x84d934b1, 0x22df3613, 0x84d77e54, 0x22d92a61, 0x84d5c844,
+    0x22d31e9a, 0x84d4127f,
+  0x22cd12bd, 0x84d25d06, 0x22c706cb, 0x84d0a7da, 0x22c0fac4, 0x84cef2f9,
+    0x22baeea7, 0x84cd3e64,
+  0x22b4e274, 0x84cb8a1b, 0x22aed62c, 0x84c9d61f, 0x22a8c9cf, 0x84c8226e,
+    0x22a2bd5d, 0x84c66f09,
+  0x229cb0d5, 0x84c4bbf0, 0x2296a437, 0x84c30924, 0x22909785, 0x84c156a3,
+    0x228a8abd, 0x84bfa46e,
+  0x22847de0, 0x84bdf286, 0x227e70ed, 0x84bc40e9, 0x227863e5, 0x84ba8f98,
+    0x227256c8, 0x84b8de94,
+  0x226c4996, 0x84b72ddb, 0x22663c4e, 0x84b57d6f, 0x22602ef1, 0x84b3cd4f,
+    0x225a217f, 0x84b21d7a,
+  0x225413f8, 0x84b06df2, 0x224e065c, 0x84aebeb6, 0x2247f8aa, 0x84ad0fc6,
+    0x2241eae3, 0x84ab6122,
+  0x223bdd08, 0x84a9b2ca, 0x2235cf17, 0x84a804be, 0x222fc111, 0x84a656fe,
+    0x2229b2f6, 0x84a4a98a,
+  0x2223a4c5, 0x84a2fc62, 0x221d9680, 0x84a14f87, 0x22178826, 0x849fa2f7,
+    0x221179b7, 0x849df6b4,
+  0x220b6b32, 0x849c4abd, 0x22055c99, 0x849a9f12, 0x21ff4dea, 0x8498f3b3,
+    0x21f93f27, 0x849748a0,
+  0x21f3304f, 0x84959dd9, 0x21ed2162, 0x8493f35e, 0x21e71260, 0x84924930,
+    0x21e10349, 0x84909f4e,
+  0x21daf41d, 0x848ef5b7, 0x21d4e4dc, 0x848d4c6d, 0x21ced586, 0x848ba36f,
+    0x21c8c61c, 0x8489fabe,
+  0x21c2b69c, 0x84885258, 0x21bca708, 0x8486aa3e, 0x21b6975f, 0x84850271,
+    0x21b087a1, 0x84835af0,
+  0x21aa77cf, 0x8481b3bb, 0x21a467e7, 0x84800cd2, 0x219e57eb, 0x847e6636,
+    0x219847da, 0x847cbfe5,
+  0x219237b5, 0x847b19e1, 0x218c277a, 0x84797429, 0x2186172b, 0x8477cebd,
+    0x218006c8, 0x8476299e,
+  0x2179f64f, 0x847484ca, 0x2173e5c2, 0x8472e043, 0x216dd521, 0x84713c08,
+    0x2167c46b, 0x846f9819,
+  0x2161b3a0, 0x846df477, 0x215ba2c0, 0x846c5120, 0x215591cc, 0x846aae16,
+    0x214f80c4, 0x84690b58,
+  0x21496fa7, 0x846768e7, 0x21435e75, 0x8465c6c1, 0x213d4d2f, 0x846424e8,
+    0x21373bd4, 0x8462835b,
+  0x21312a65, 0x8460e21a, 0x212b18e1, 0x845f4126, 0x21250749, 0x845da07e,
+    0x211ef59d, 0x845c0022,
+  0x2118e3dc, 0x845a6012, 0x2112d206, 0x8458c04f, 0x210cc01d, 0x845720d8,
+    0x2106ae1e, 0x845581ad,
+  0x21009c0c, 0x8453e2cf, 0x20fa89e5, 0x8452443d, 0x20f477aa, 0x8450a5f7,
+    0x20ee655a, 0x844f07fd,
+  0x20e852f6, 0x844d6a50, 0x20e2407e, 0x844bccef, 0x20dc2df2, 0x844a2fda,
+    0x20d61b51, 0x84489311,
+  0x20d0089c, 0x8446f695, 0x20c9f5d3, 0x84455a66, 0x20c3e2f5, 0x8443be82,
+    0x20bdd003, 0x844222eb,
+  0x20b7bcfe, 0x844087a0, 0x20b1a9e4, 0x843eeca2, 0x20ab96b5, 0x843d51f0,
+    0x20a58373, 0x843bb78a,
+  0x209f701c, 0x843a1d70, 0x20995cb2, 0x843883a3, 0x20934933, 0x8436ea23,
+    0x208d35a0, 0x843550ee,
+  0x208721f9, 0x8433b806, 0x20810e3e, 0x84321f6b, 0x207afa6f, 0x8430871b,
+    0x2074e68c, 0x842eef18,
+  0x206ed295, 0x842d5762, 0x2068be8a, 0x842bbff8, 0x2062aa6b, 0x842a28da,
+    0x205c9638, 0x84289209,
+  0x205681f1, 0x8426fb84, 0x20506d96, 0x8425654b, 0x204a5927, 0x8423cf5f,
+    0x204444a4, 0x842239bf,
+  0x203e300d, 0x8420a46c, 0x20381b63, 0x841f0f65, 0x203206a4, 0x841d7aaa,
+    0x202bf1d2, 0x841be63c,
+  0x2025dcec, 0x841a521a, 0x201fc7f2, 0x8418be45, 0x2019b2e4, 0x84172abc,
+    0x20139dc2, 0x84159780,
+  0x200d888d, 0x84140490, 0x20077344, 0x841271ec, 0x20015de7, 0x8410df95,
+    0x1ffb4876, 0x840f4d8a,
+  0x1ff532f2, 0x840dbbcc, 0x1fef1d59, 0x840c2a5a, 0x1fe907ae, 0x840a9935,
+    0x1fe2f1ee, 0x8409085c,
+  0x1fdcdc1b, 0x840777d0, 0x1fd6c634, 0x8405e790, 0x1fd0b03a, 0x8404579d,
+    0x1fca9a2b, 0x8402c7f6,
+  0x1fc4840a, 0x8401389b, 0x1fbe6dd4, 0x83ffa98d, 0x1fb8578b, 0x83fe1acc,
+    0x1fb2412f, 0x83fc8c57,
+  0x1fac2abf, 0x83fafe2e, 0x1fa6143b, 0x83f97052, 0x1f9ffda4, 0x83f7e2c3,
+    0x1f99e6fa, 0x83f65580,
+  0x1f93d03c, 0x83f4c889, 0x1f8db96a, 0x83f33bdf, 0x1f87a285, 0x83f1af82,
+    0x1f818b8d, 0x83f02371,
+  0x1f7b7481, 0x83ee97ad, 0x1f755d61, 0x83ed0c35, 0x1f6f462f, 0x83eb810a,
+    0x1f692ee9, 0x83e9f62b,
+  0x1f63178f, 0x83e86b99, 0x1f5d0022, 0x83e6e153, 0x1f56e8a2, 0x83e5575a,
+    0x1f50d10e, 0x83e3cdad,
+  0x1f4ab968, 0x83e2444d, 0x1f44a1ad, 0x83e0bb3a, 0x1f3e89e0, 0x83df3273,
+    0x1f3871ff, 0x83dda9f9,
+  0x1f325a0b, 0x83dc21cb, 0x1f2c4204, 0x83da99ea, 0x1f2629ea, 0x83d91255,
+    0x1f2011bc, 0x83d78b0d,
+  0x1f19f97b, 0x83d60412, 0x1f13e127, 0x83d47d63, 0x1f0dc8c0, 0x83d2f701,
+    0x1f07b045, 0x83d170eb,
+  0x1f0197b8, 0x83cfeb22, 0x1efb7f17, 0x83ce65a6, 0x1ef56664, 0x83cce076,
+    0x1eef4d9d, 0x83cb5b93,
+  0x1ee934c3, 0x83c9d6fc, 0x1ee31bd6, 0x83c852b2, 0x1edd02d6, 0x83c6ceb5,
+    0x1ed6e9c3, 0x83c54b04,
+  0x1ed0d09d, 0x83c3c7a0, 0x1ecab763, 0x83c24488, 0x1ec49e17, 0x83c0c1be,
+    0x1ebe84b8, 0x83bf3f3f,
+  0x1eb86b46, 0x83bdbd0e, 0x1eb251c1, 0x83bc3b29, 0x1eac3829, 0x83bab991,
+    0x1ea61e7e, 0x83b93845,
+  0x1ea004c1, 0x83b7b746, 0x1e99eaf0, 0x83b63694, 0x1e93d10c, 0x83b4b62e,
+    0x1e8db716, 0x83b33616,
+  0x1e879d0d, 0x83b1b649, 0x1e8182f1, 0x83b036ca, 0x1e7b68c2, 0x83aeb797,
+    0x1e754e80, 0x83ad38b1,
+  0x1e6f342c, 0x83abba17, 0x1e6919c4, 0x83aa3bca, 0x1e62ff4a, 0x83a8bdca,
+    0x1e5ce4be, 0x83a74017,
+  0x1e56ca1e, 0x83a5c2b0, 0x1e50af6c, 0x83a44596, 0x1e4a94a7, 0x83a2c8c9,
+    0x1e4479cf, 0x83a14c48,
+  0x1e3e5ee5, 0x839fd014, 0x1e3843e8, 0x839e542d, 0x1e3228d9, 0x839cd893,
+    0x1e2c0db6, 0x839b5d45,
+  0x1e25f282, 0x8399e244, 0x1e1fd73a, 0x83986790, 0x1e19bbe0, 0x8396ed29,
+    0x1e13a074, 0x8395730e,
+  0x1e0d84f5, 0x8393f940, 0x1e076963, 0x83927fbf, 0x1e014dbf, 0x8391068a,
+    0x1dfb3208, 0x838f8da2,
+  0x1df5163f, 0x838e1507, 0x1deefa63, 0x838c9cb9, 0x1de8de75, 0x838b24b8,
+    0x1de2c275, 0x8389ad03,
+  0x1ddca662, 0x8388359b, 0x1dd68a3c, 0x8386be80, 0x1dd06e04, 0x838547b2,
+    0x1dca51ba, 0x8383d130,
+  0x1dc4355e, 0x83825afb, 0x1dbe18ef, 0x8380e513, 0x1db7fc6d, 0x837f6f78,
+    0x1db1dfda, 0x837dfa2a,
+  0x1dabc334, 0x837c8528, 0x1da5a67c, 0x837b1074, 0x1d9f89b1, 0x83799c0c,
+    0x1d996cd4, 0x837827f0,
+  0x1d934fe5, 0x8376b422, 0x1d8d32e4, 0x837540a1, 0x1d8715d0, 0x8373cd6c,
+    0x1d80f8ab, 0x83725a84,
+  0x1d7adb73, 0x8370e7e9, 0x1d74be29, 0x836f759b, 0x1d6ea0cc, 0x836e039a,
+    0x1d68835e, 0x836c91e5,
+  0x1d6265dd, 0x836b207d, 0x1d5c484b, 0x8369af63, 0x1d562aa6, 0x83683e95,
+    0x1d500cef, 0x8366ce14,
+  0x1d49ef26, 0x83655ddf, 0x1d43d14b, 0x8363edf8, 0x1d3db35e, 0x83627e5d,
+    0x1d37955e, 0x83610f10,
+  0x1d31774d, 0x835fa00f, 0x1d2b592a, 0x835e315b, 0x1d253af5, 0x835cc2f4,
+    0x1d1f1cae, 0x835b54da,
+  0x1d18fe54, 0x8359e70d, 0x1d12dfe9, 0x8358798c, 0x1d0cc16c, 0x83570c59,
+    0x1d06a2dd, 0x83559f72,
+  0x1d00843d, 0x835432d8, 0x1cfa658a, 0x8352c68c, 0x1cf446c5, 0x83515a8c,
+    0x1cee27ef, 0x834feed9,
+  0x1ce80906, 0x834e8373, 0x1ce1ea0c, 0x834d185a, 0x1cdbcb00, 0x834bad8e,
+    0x1cd5abe3, 0x834a430e,
+  0x1ccf8cb3, 0x8348d8dc, 0x1cc96d72, 0x83476ef6, 0x1cc34e1f, 0x8346055e,
+    0x1cbd2eba, 0x83449c12,
+  0x1cb70f43, 0x83433314, 0x1cb0efbb, 0x8341ca62, 0x1caad021, 0x834061fd,
+    0x1ca4b075, 0x833ef9e6,
+  0x1c9e90b8, 0x833d921b, 0x1c9870e9, 0x833c2a9d, 0x1c925109, 0x833ac36c,
+    0x1c8c3116, 0x83395c88,
+  0x1c861113, 0x8337f5f1, 0x1c7ff0fd, 0x83368fa7, 0x1c79d0d6, 0x833529aa,
+    0x1c73b09d, 0x8333c3fa,
+  0x1c6d9053, 0x83325e97, 0x1c676ff8, 0x8330f981, 0x1c614f8b, 0x832f94b8,
+    0x1c5b2f0c, 0x832e303c,
+  0x1c550e7c, 0x832ccc0d, 0x1c4eedda, 0x832b682b, 0x1c48cd27, 0x832a0496,
+    0x1c42ac62, 0x8328a14d,
+  0x1c3c8b8c, 0x83273e52, 0x1c366aa5, 0x8325dba4, 0x1c3049ac, 0x83247943,
+    0x1c2a28a2, 0x8323172f,
+  0x1c240786, 0x8321b568, 0x1c1de659, 0x832053ee, 0x1c17c51b, 0x831ef2c1,
+    0x1c11a3cb, 0x831d91e1,
+  0x1c0b826a, 0x831c314e, 0x1c0560f8, 0x831ad109, 0x1bff3f75, 0x83197110,
+    0x1bf91de0, 0x83181164,
+  0x1bf2fc3a, 0x8316b205, 0x1becda83, 0x831552f4, 0x1be6b8ba, 0x8313f42f,
+    0x1be096e0, 0x831295b7,
+  0x1bda74f6, 0x8311378d, 0x1bd452f9, 0x830fd9af, 0x1bce30ec, 0x830e7c1f,
+    0x1bc80ece, 0x830d1edc,
+  0x1bc1ec9e, 0x830bc1e6, 0x1bbbca5e, 0x830a653c, 0x1bb5a80c, 0x830908e0,
+    0x1baf85a9, 0x8307acd1,
+  0x1ba96335, 0x83065110, 0x1ba340b0, 0x8304f59b, 0x1b9d1e1a, 0x83039a73,
+    0x1b96fb73, 0x83023f98,
+  0x1b90d8bb, 0x8300e50b, 0x1b8ab5f2, 0x82ff8acb, 0x1b849317, 0x82fe30d7,
+    0x1b7e702c, 0x82fcd731,
+  0x1b784d30, 0x82fb7dd8, 0x1b722a23, 0x82fa24cc, 0x1b6c0705, 0x82f8cc0d,
+    0x1b65e3d7, 0x82f7739c,
+  0x1b5fc097, 0x82f61b77, 0x1b599d46, 0x82f4c3a0, 0x1b5379e5, 0x82f36c15,
+    0x1b4d5672, 0x82f214d8,
+  0x1b4732ef, 0x82f0bde8, 0x1b410f5b, 0x82ef6745, 0x1b3aebb6, 0x82ee10ef,
+    0x1b34c801, 0x82ecbae7,
+  0x1b2ea43a, 0x82eb652b, 0x1b288063, 0x82ea0fbd, 0x1b225c7b, 0x82e8ba9c,
+    0x1b1c3883, 0x82e765c8,
+  0x1b161479, 0x82e61141, 0x1b0ff05f, 0x82e4bd07, 0x1b09cc34, 0x82e3691b,
+    0x1b03a7f9, 0x82e2157c,
+  0x1afd83ad, 0x82e0c22a, 0x1af75f50, 0x82df6f25, 0x1af13ae3, 0x82de1c6d,
+    0x1aeb1665, 0x82dcca02,
+  0x1ae4f1d6, 0x82db77e5, 0x1adecd37, 0x82da2615, 0x1ad8a887, 0x82d8d492,
+    0x1ad283c7, 0x82d7835c,
+  0x1acc5ef6, 0x82d63274, 0x1ac63a14, 0x82d4e1d8, 0x1ac01522, 0x82d3918a,
+    0x1ab9f020, 0x82d24189,
+  0x1ab3cb0d, 0x82d0f1d5, 0x1aada5e9, 0x82cfa26f, 0x1aa780b6, 0x82ce5356,
+    0x1aa15b71, 0x82cd048a,
+  0x1a9b361d, 0x82cbb60b, 0x1a9510b7, 0x82ca67d9, 0x1a8eeb42, 0x82c919f5,
+    0x1a88c5bc, 0x82c7cc5e,
+  0x1a82a026, 0x82c67f14, 0x1a7c7a7f, 0x82c53217, 0x1a7654c8, 0x82c3e568,
+    0x1a702f01, 0x82c29906,
+  0x1a6a0929, 0x82c14cf1, 0x1a63e341, 0x82c00129, 0x1a5dbd49, 0x82beb5af,
+    0x1a579741, 0x82bd6a82,
+  0x1a517128, 0x82bc1fa2, 0x1a4b4aff, 0x82bad50f, 0x1a4524c6, 0x82b98aca,
+    0x1a3efe7c, 0x82b840d2,
+  0x1a38d823, 0x82b6f727, 0x1a32b1b9, 0x82b5adca, 0x1a2c8b3f, 0x82b464ba,
+    0x1a2664b5, 0x82b31bf7,
+  0x1a203e1b, 0x82b1d381, 0x1a1a1771, 0x82b08b59, 0x1a13f0b6, 0x82af437e,
+    0x1a0dc9ec, 0x82adfbf0,
+  0x1a07a311, 0x82acb4b0, 0x1a017c27, 0x82ab6dbd, 0x19fb552c, 0x82aa2717,
+    0x19f52e22, 0x82a8e0bf,
+  0x19ef0707, 0x82a79ab3, 0x19e8dfdc, 0x82a654f6, 0x19e2b8a2, 0x82a50f85,
+    0x19dc9157, 0x82a3ca62,
+  0x19d669fc, 0x82a2858c, 0x19d04292, 0x82a14104, 0x19ca1b17, 0x829ffcc8,
+    0x19c3f38d, 0x829eb8db,
+  0x19bdcbf3, 0x829d753a, 0x19b7a449, 0x829c31e7, 0x19b17c8f, 0x829aeee1,
+    0x19ab54c5, 0x8299ac29,
+  0x19a52ceb, 0x829869be, 0x199f0502, 0x829727a0, 0x1998dd09, 0x8295e5cf,
+    0x1992b4ff, 0x8294a44c,
+  0x198c8ce7, 0x82936317, 0x198664be, 0x8292222e, 0x19803c86, 0x8290e194,
+    0x197a143e, 0x828fa146,
+  0x1973ebe6, 0x828e6146, 0x196dc37e, 0x828d2193, 0x19679b07, 0x828be22e,
+    0x19617280, 0x828aa316,
+  0x195b49ea, 0x8289644b, 0x19552144, 0x828825ce, 0x194ef88e, 0x8286e79e,
+    0x1948cfc8, 0x8285a9bb,
+  0x1942a6f3, 0x82846c26, 0x193c7e0f, 0x82832edf, 0x1936551b, 0x8281f1e4,
+    0x19302c17, 0x8280b538,
+  0x192a0304, 0x827f78d8, 0x1923d9e1, 0x827e3cc6, 0x191db0af, 0x827d0102,
+    0x1917876d, 0x827bc58a,
+  0x19115e1c, 0x827a8a61, 0x190b34bb, 0x82794f84, 0x19050b4b, 0x827814f6,
+    0x18fee1cb, 0x8276dab4,
+  0x18f8b83c, 0x8275a0c0, 0x18f28e9e, 0x8274671a, 0x18ec64f0, 0x82732dc0,
+    0x18e63b33, 0x8271f4b5,
+  0x18e01167, 0x8270bbf7, 0x18d9e78b, 0x826f8386, 0x18d3bda0, 0x826e4b62,
+    0x18cd93a5, 0x826d138d,
+  0x18c7699b, 0x826bdc04, 0x18c13f82, 0x826aa4c9, 0x18bb155a, 0x82696ddc,
+    0x18b4eb22, 0x8268373c,
+  0x18aec0db, 0x826700e9, 0x18a89685, 0x8265cae4, 0x18a26c20, 0x8264952d,
+    0x189c41ab, 0x82635fc2,
+  0x18961728, 0x82622aa6, 0x188fec95, 0x8260f5d7, 0x1889c1f3, 0x825fc155,
+    0x18839742, 0x825e8d21,
+  0x187d6c82, 0x825d593a, 0x187741b2, 0x825c25a1, 0x187116d4, 0x825af255,
+    0x186aebe6, 0x8259bf57,
+  0x1864c0ea, 0x82588ca7, 0x185e95de, 0x82575a44, 0x18586ac3, 0x8256282e,
+    0x18523f9a, 0x8254f666,
+  0x184c1461, 0x8253c4eb, 0x1845e919, 0x825293be, 0x183fbdc3, 0x825162df,
+    0x1839925d, 0x8250324d,
+  0x183366e9, 0x824f0208, 0x182d3b65, 0x824dd211, 0x18270fd3, 0x824ca268,
+    0x1820e431, 0x824b730c,
+  0x181ab881, 0x824a43fe, 0x18148cc2, 0x8249153d, 0x180e60f4, 0x8247e6ca,
+    0x18083518, 0x8246b8a4,
+  0x1802092c, 0x82458acc, 0x17fbdd32, 0x82445d41, 0x17f5b129, 0x82433004,
+    0x17ef8511, 0x82420315,
+  0x17e958ea, 0x8240d673, 0x17e32cb5, 0x823faa1e, 0x17dd0070, 0x823e7e18,
+    0x17d6d41d, 0x823d525e,
+  0x17d0a7bc, 0x823c26f3, 0x17ca7b4c, 0x823afbd5, 0x17c44ecd, 0x8239d104,
+    0x17be223f, 0x8238a681,
+  0x17b7f5a3, 0x82377c4c, 0x17b1c8f8, 0x82365264, 0x17ab9c3e, 0x823528ca,
+    0x17a56f76, 0x8233ff7e,
+  0x179f429f, 0x8232d67f, 0x179915ba, 0x8231adce, 0x1792e8c6, 0x8230856a,
+    0x178cbbc4, 0x822f5d54,
+  0x17868eb3, 0x822e358b, 0x17806194, 0x822d0e10, 0x177a3466, 0x822be6e3,
+    0x17740729, 0x822ac004,
+  0x176dd9de, 0x82299971, 0x1767ac85, 0x8228732d, 0x17617f1d, 0x82274d36,
+    0x175b51a7, 0x8226278d,
+  0x17552422, 0x82250232, 0x174ef68f, 0x8223dd24, 0x1748c8ee, 0x8222b863,
+    0x17429b3e, 0x822193f1,
+  0x173c6d80, 0x82206fcc, 0x17363fb4, 0x821f4bf5, 0x173011d9, 0x821e286b,
+    0x1729e3f0, 0x821d052f,
+  0x1723b5f9, 0x821be240, 0x171d87f3, 0x821abfa0, 0x171759df, 0x82199d4d,
+    0x17112bbd, 0x82187b47,
+  0x170afd8d, 0x82175990, 0x1704cf4f, 0x82163826, 0x16fea102, 0x82151709,
+    0x16f872a7, 0x8213f63a,
+  0x16f2443e, 0x8212d5b9, 0x16ec15c7, 0x8211b586, 0x16e5e741, 0x821095a0,
+    0x16dfb8ae, 0x820f7608,
+  0x16d98a0c, 0x820e56be, 0x16d35b5c, 0x820d37c1, 0x16cd2c9f, 0x820c1912,
+    0x16c6fdd3, 0x820afab1,
+  0x16c0cef9, 0x8209dc9e, 0x16baa011, 0x8208bed8, 0x16b4711b, 0x8207a160,
+    0x16ae4217, 0x82068435,
+  0x16a81305, 0x82056758, 0x16a1e3e5, 0x82044ac9, 0x169bb4b7, 0x82032e88,
+    0x1695857b, 0x82021294,
+  0x168f5632, 0x8200f6ef, 0x168926da, 0x81ffdb96, 0x1682f774, 0x81fec08c,
+    0x167cc801, 0x81fda5cf,
+  0x1676987f, 0x81fc8b60, 0x167068f0, 0x81fb713f, 0x166a3953, 0x81fa576c,
+    0x166409a8, 0x81f93de6,
+  0x165dd9f0, 0x81f824ae, 0x1657aa29, 0x81f70bc3, 0x16517a55, 0x81f5f327,
+    0x164b4a73, 0x81f4dad8,
+  0x16451a83, 0x81f3c2d7, 0x163eea86, 0x81f2ab24, 0x1638ba7a, 0x81f193be,
+    0x16328a61, 0x81f07ca6,
+  0x162c5a3b, 0x81ef65dc, 0x16262a06, 0x81ee4f60, 0x161ff9c4, 0x81ed3932,
+    0x1619c975, 0x81ec2351,
+  0x16139918, 0x81eb0dbe, 0x160d68ad, 0x81e9f879, 0x16073834, 0x81e8e381,
+    0x160107ae, 0x81e7ced8,
+  0x15fad71b, 0x81e6ba7c, 0x15f4a679, 0x81e5a66e, 0x15ee75cb, 0x81e492ad,
+    0x15e8450e, 0x81e37f3b,
+  0x15e21445, 0x81e26c16, 0x15dbe36d, 0x81e1593f, 0x15d5b288, 0x81e046b6,
+    0x15cf8196, 0x81df347b,
+  0x15c95097, 0x81de228d, 0x15c31f89, 0x81dd10ee, 0x15bcee6f, 0x81dbff9c,
+    0x15b6bd47, 0x81daee98,
+  0x15b08c12, 0x81d9dde1, 0x15aa5acf, 0x81d8cd79, 0x15a4297f, 0x81d7bd5e,
+    0x159df821, 0x81d6ad92,
+  0x1597c6b7, 0x81d59e13, 0x1591953e, 0x81d48ee1, 0x158b63b9, 0x81d37ffe,
+    0x15853226, 0x81d27169,
+  0x157f0086, 0x81d16321, 0x1578ced9, 0x81d05527, 0x15729d1f, 0x81cf477b,
+    0x156c6b57, 0x81ce3a1d,
+  0x15663982, 0x81cd2d0c, 0x156007a0, 0x81cc204a, 0x1559d5b1, 0x81cb13d5,
+    0x1553a3b4, 0x81ca07af,
+  0x154d71aa, 0x81c8fbd6, 0x15473f94, 0x81c7f04b, 0x15410d70, 0x81c6e50d,
+    0x153adb3f, 0x81c5da1e,
+  0x1534a901, 0x81c4cf7d, 0x152e76b5, 0x81c3c529, 0x1528445d, 0x81c2bb23,
+    0x152211f8, 0x81c1b16b,
+  0x151bdf86, 0x81c0a801, 0x1515ad06, 0x81bf9ee5, 0x150f7a7a, 0x81be9617,
+    0x150947e1, 0x81bd8d97,
+  0x1503153a, 0x81bc8564, 0x14fce287, 0x81bb7d7f, 0x14f6afc7, 0x81ba75e9,
+    0x14f07cf9, 0x81b96ea0,
+  0x14ea4a1f, 0x81b867a5, 0x14e41738, 0x81b760f8, 0x14dde445, 0x81b65a99,
+    0x14d7b144, 0x81b55488,
+  0x14d17e36, 0x81b44ec4, 0x14cb4b1c, 0x81b3494f, 0x14c517f4, 0x81b24427,
+    0x14bee4c0, 0x81b13f4e,
+  0x14b8b17f, 0x81b03ac2, 0x14b27e32, 0x81af3684, 0x14ac4ad7, 0x81ae3294,
+    0x14a61770, 0x81ad2ef2,
+  0x149fe3fc, 0x81ac2b9e, 0x1499b07c, 0x81ab2898, 0x14937cee, 0x81aa25e0,
+    0x148d4954, 0x81a92376,
+  0x148715ae, 0x81a82159, 0x1480e1fa, 0x81a71f8b, 0x147aae3a, 0x81a61e0b,
+    0x14747a6d, 0x81a51cd8,
+  0x146e4694, 0x81a41bf4, 0x146812ae, 0x81a31b5d, 0x1461debc, 0x81a21b14,
+    0x145baabd, 0x81a11b1a,
+  0x145576b1, 0x81a01b6d, 0x144f4299, 0x819f1c0e, 0x14490e74, 0x819e1cfd,
+    0x1442da43, 0x819d1e3a,
+  0x143ca605, 0x819c1fc5, 0x143671bb, 0x819b219e, 0x14303d65, 0x819a23c5,
+    0x142a0902, 0x8199263a,
+  0x1423d492, 0x819828fd, 0x141da016, 0x81972c0e, 0x14176b8e, 0x81962f6d,
+    0x141136f9, 0x8195331a,
+  0x140b0258, 0x81943715, 0x1404cdaa, 0x81933b5e, 0x13fe98f1, 0x81923ff4,
+    0x13f8642a, 0x819144d9,
+  0x13f22f58, 0x81904a0c, 0x13ebfa79, 0x818f4f8d, 0x13e5c58e, 0x818e555c,
+    0x13df9097, 0x818d5b78,
+  0x13d95b93, 0x818c61e3, 0x13d32683, 0x818b689c, 0x13ccf167, 0x818a6fa3,
+    0x13c6bc3f, 0x818976f8,
+  0x13c0870a, 0x81887e9a, 0x13ba51ca, 0x8187868b, 0x13b41c7d, 0x81868eca,
+    0x13ade724, 0x81859757,
+  0x13a7b1bf, 0x8184a032, 0x13a17c4d, 0x8183a95b, 0x139b46d0, 0x8182b2d1,
+    0x13951146, 0x8181bc96,
+  0x138edbb1, 0x8180c6a9, 0x1388a60f, 0x817fd10a, 0x13827062, 0x817edbb9,
+    0x137c3aa8, 0x817de6b6,
+  0x137604e2, 0x817cf201, 0x136fcf10, 0x817bfd9b, 0x13699933, 0x817b0982,
+    0x13636349, 0x817a15b7,
+  0x135d2d53, 0x8179223a, 0x1356f752, 0x81782f0b, 0x1350c144, 0x81773c2b,
+    0x134a8b2b, 0x81764998,
+  0x13445505, 0x81755754, 0x133e1ed4, 0x8174655d, 0x1337e897, 0x817373b5,
+    0x1331b24e, 0x8172825a,
+  0x132b7bf9, 0x8171914e, 0x13254599, 0x8170a090, 0x131f0f2c, 0x816fb020,
+    0x1318d8b4, 0x816ebffe,
+  0x1312a230, 0x816dd02a, 0x130c6ba0, 0x816ce0a4, 0x13063505, 0x816bf16c,
+    0x12fffe5d, 0x816b0282,
+  0x12f9c7aa, 0x816a13e6, 0x12f390ec, 0x81692599, 0x12ed5a21, 0x81683799,
+    0x12e7234b, 0x816749e8,
+  0x12e0ec6a, 0x81665c84, 0x12dab57c, 0x81656f6f, 0x12d47e83, 0x816482a8,
+    0x12ce477f, 0x8163962f,
+  0x12c8106f, 0x8162aa04, 0x12c1d953, 0x8161be27, 0x12bba22b, 0x8160d298,
+    0x12b56af9, 0x815fe758,
+  0x12af33ba, 0x815efc65, 0x12a8fc70, 0x815e11c1, 0x12a2c51b, 0x815d276a,
+    0x129c8dba, 0x815c3d62,
+  0x1296564d, 0x815b53a8, 0x12901ed5, 0x815a6a3c, 0x1289e752, 0x8159811e,
+    0x1283afc3, 0x8158984e,
+  0x127d7829, 0x8157afcd, 0x12774083, 0x8156c799, 0x127108d2, 0x8155dfb4,
+    0x126ad116, 0x8154f81d,
+  0x1264994e, 0x815410d4, 0x125e617b, 0x815329d9, 0x1258299c, 0x8152432c,
+    0x1251f1b3, 0x81515ccd,
+  0x124bb9be, 0x815076bd, 0x124581bd, 0x814f90fb, 0x123f49b2, 0x814eab86,
+    0x1239119b, 0x814dc660,
+  0x1232d979, 0x814ce188, 0x122ca14b, 0x814bfcff, 0x12266913, 0x814b18c3,
+    0x122030cf, 0x814a34d6,
+  0x1219f880, 0x81495136, 0x1213c026, 0x81486de5, 0x120d87c1, 0x81478ae2,
+    0x12074f50, 0x8146a82e,
+  0x120116d5, 0x8145c5c7, 0x11fade4e, 0x8144e3ae, 0x11f4a5bd, 0x814401e4,
+    0x11ee6d20, 0x81432068,
+  0x11e83478, 0x81423f3a, 0x11e1fbc5, 0x81415e5a, 0x11dbc307, 0x81407dc9,
+    0x11d58a3e, 0x813f9d86,
+  0x11cf516a, 0x813ebd90, 0x11c9188b, 0x813ddde9, 0x11c2dfa2, 0x813cfe91,
+    0x11bca6ad, 0x813c1f86,
+  0x11b66dad, 0x813b40ca, 0x11b034a2, 0x813a625b, 0x11a9fb8d, 0x8139843b,
+    0x11a3c26c, 0x8138a66a,
+  0x119d8941, 0x8137c8e6, 0x1197500a, 0x8136ebb1, 0x119116c9, 0x81360ec9,
+    0x118add7d, 0x81353230,
+  0x1184a427, 0x813455e6, 0x117e6ac5, 0x813379e9, 0x11783159, 0x81329e3b,
+    0x1171f7e2, 0x8131c2db,
+  0x116bbe60, 0x8130e7c9, 0x116584d3, 0x81300d05, 0x115f4b3c, 0x812f3290,
+    0x1159119a, 0x812e5868,
+  0x1152d7ed, 0x812d7e8f, 0x114c9e35, 0x812ca505, 0x11466473, 0x812bcbc8,
+    0x11402aa6, 0x812af2da,
+  0x1139f0cf, 0x812a1a3a, 0x1133b6ed, 0x812941e8, 0x112d7d00, 0x812869e4,
+    0x11274309, 0x8127922f,
+  0x11210907, 0x8126bac8, 0x111acefb, 0x8125e3af, 0x111494e4, 0x81250ce4,
+    0x110e5ac2, 0x81243668,
+  0x11082096, 0x8123603a, 0x1101e65f, 0x81228a5a, 0x10fbac1e, 0x8121b4c8,
+    0x10f571d3, 0x8120df85,
+  0x10ef377d, 0x81200a90, 0x10e8fd1c, 0x811f35e9, 0x10e2c2b2, 0x811e6191,
+    0x10dc883c, 0x811d8d86,
+  0x10d64dbd, 0x811cb9ca, 0x10d01333, 0x811be65d, 0x10c9d89e, 0x811b133d,
+    0x10c39dff, 0x811a406c,
+  0x10bd6356, 0x81196de9, 0x10b728a3, 0x81189bb4, 0x10b0ede5, 0x8117c9ce,
+    0x10aab31d, 0x8116f836,
+  0x10a4784b, 0x811626ec, 0x109e3d6e, 0x811555f1, 0x10980287, 0x81148544,
+    0x1091c796, 0x8113b4e5,
+  0x108b8c9b, 0x8112e4d4, 0x10855195, 0x81121512, 0x107f1686, 0x8111459e,
+    0x1078db6c, 0x81107678,
+  0x1072a048, 0x810fa7a0, 0x106c651a, 0x810ed917, 0x106629e1, 0x810e0adc,
+    0x105fee9f, 0x810d3cf0,
+  0x1059b352, 0x810c6f52, 0x105377fc, 0x810ba202, 0x104d3c9b, 0x810ad500,
+    0x10470130, 0x810a084d,
+  0x1040c5bb, 0x81093be8, 0x103a8a3d, 0x81086fd1, 0x10344eb4, 0x8107a409,
+    0x102e1321, 0x8106d88f,
+  0x1027d784, 0x81060d63, 0x10219bdd, 0x81054286, 0x101b602d, 0x810477f7,
+    0x10152472, 0x8103adb6,
+  0x100ee8ad, 0x8102e3c4, 0x1008acdf, 0x81021a20, 0x10027107, 0x810150ca,
+    0xffc3524, 0x810087c3,
+  0xff5f938, 0x80ffbf0a, 0xfefbd42, 0x80fef69f, 0xfe98143, 0x80fe2e83,
+    0xfe34539, 0x80fd66b5,
+  0xfdd0926, 0x80fc9f35, 0xfd6cd08, 0x80fbd804, 0xfd090e1, 0x80fb1121,
+    0xfca54b1, 0x80fa4a8c,
+  0xfc41876, 0x80f98446, 0xfbddc32, 0x80f8be4e, 0xfb79fe4, 0x80f7f8a4,
+    0xfb1638d, 0x80f73349,
+  0xfab272b, 0x80f66e3c, 0xfa4eac0, 0x80f5a97e, 0xf9eae4c, 0x80f4e50e,
+    0xf9871ce, 0x80f420ec,
+  0xf923546, 0x80f35d19, 0xf8bf8b4, 0x80f29994, 0xf85bc19, 0x80f1d65d,
+    0xf7f7f75, 0x80f11375,
+  0xf7942c7, 0x80f050db, 0xf73060f, 0x80ef8e90, 0xf6cc94e, 0x80eecc93,
+    0xf668c83, 0x80ee0ae4,
+  0xf604faf, 0x80ed4984, 0xf5a12d1, 0x80ec8872, 0xf53d5ea, 0x80ebc7ae,
+    0xf4d98f9, 0x80eb0739,
+  0xf475bff, 0x80ea4712, 0xf411efb, 0x80e9873a, 0xf3ae1ee, 0x80e8c7b0,
+    0xf34a4d8, 0x80e80874,
+  0xf2e67b8, 0x80e74987, 0xf282a8f, 0x80e68ae8, 0xf21ed5d, 0x80e5cc98,
+    0xf1bb021, 0x80e50e96,
+  0xf1572dc, 0x80e450e2, 0xf0f358e, 0x80e3937d, 0xf08f836, 0x80e2d666,
+    0xf02bad5, 0x80e2199e,
+  0xefc7d6b, 0x80e15d24, 0xef63ff7, 0x80e0a0f8, 0xef0027b, 0x80dfe51b,
+    0xee9c4f5, 0x80df298c,
+  0xee38766, 0x80de6e4c, 0xedd49ce, 0x80ddb35a, 0xed70c2c, 0x80dcf8b7,
+    0xed0ce82, 0x80dc3e62,
+  0xeca90ce, 0x80db845b, 0xec45311, 0x80dacaa3, 0xebe154b, 0x80da1139,
+    0xeb7d77c, 0x80d9581e,
+  0xeb199a4, 0x80d89f51, 0xeab5bc3, 0x80d7e6d3, 0xea51dd8, 0x80d72ea3,
+    0xe9edfe5, 0x80d676c1,
+  0xe98a1e9, 0x80d5bf2e, 0xe9263e3, 0x80d507e9, 0xe8c25d5, 0x80d450f3,
+    0xe85e7be, 0x80d39a4b,
+  0xe7fa99e, 0x80d2e3f2, 0xe796b74, 0x80d22de7, 0xe732d42, 0x80d1782a,
+    0xe6cef07, 0x80d0c2bc,
+  0xe66b0c3, 0x80d00d9d, 0xe607277, 0x80cf58cc, 0xe5a3421, 0x80cea449,
+    0xe53f5c2, 0x80cdf015,
+  0xe4db75b, 0x80cd3c2f, 0xe4778eb, 0x80cc8898, 0xe413a72, 0x80cbd54f,
+    0xe3afbf0, 0x80cb2255,
+  0xe34bd66, 0x80ca6fa9, 0xe2e7ed2, 0x80c9bd4c, 0xe284036, 0x80c90b3d,
+    0xe220191, 0x80c8597c,
+  0xe1bc2e4, 0x80c7a80a, 0xe15842e, 0x80c6f6e7, 0xe0f456f, 0x80c64612,
+    0xe0906a7, 0x80c5958b,
+  0xe02c7d7, 0x80c4e553, 0xdfc88fe, 0x80c4356a, 0xdf64a1c, 0x80c385cf,
+    0xdf00b32, 0x80c2d682,
+  0xde9cc40, 0x80c22784, 0xde38d44, 0x80c178d4, 0xddd4e40, 0x80c0ca73,
+    0xdd70f34, 0x80c01c60,
+  0xdd0d01f, 0x80bf6e9c, 0xdca9102, 0x80bec127, 0xdc451dc, 0x80be13ff,
+    0xdbe12ad, 0x80bd6727,
+  0xdb7d376, 0x80bcba9d, 0xdb19437, 0x80bc0e61, 0xdab54ef, 0x80bb6274,
+    0xda5159f, 0x80bab6d5,
+  0xd9ed646, 0x80ba0b85, 0xd9896e5, 0x80b96083, 0xd92577b, 0x80b8b5d0,
+    0xd8c1809, 0x80b80b6c,
+  0xd85d88f, 0x80b76156, 0xd7f990c, 0x80b6b78e, 0xd795982, 0x80b60e15,
+    0xd7319ee, 0x80b564ea,
+  0xd6cda53, 0x80b4bc0e, 0xd669aaf, 0x80b41381, 0xd605b03, 0x80b36b42,
+    0xd5a1b4f, 0x80b2c351,
+  0xd53db92, 0x80b21baf, 0xd4d9bcd, 0x80b1745c, 0xd475c00, 0x80b0cd57,
+    0xd411c2b, 0x80b026a1,
+  0xd3adc4e, 0x80af8039, 0xd349c68, 0x80aeda20, 0xd2e5c7b, 0x80ae3455,
+    0xd281c85, 0x80ad8ed9,
+  0xd21dc87, 0x80ace9ab, 0xd1b9c81, 0x80ac44cc, 0xd155c73, 0x80aba03b,
+    0xd0f1c5d, 0x80aafbf9,
+  0xd08dc3f, 0x80aa5806, 0xd029c18, 0x80a9b461, 0xcfc5bea, 0x80a9110b,
+    0xcf61bb4, 0x80a86e03,
+  0xcefdb76, 0x80a7cb49, 0xce99b2f, 0x80a728df, 0xce35ae1, 0x80a686c2,
+    0xcdd1a8b, 0x80a5e4f5,
+  0xcd6da2d, 0x80a54376, 0xcd099c7, 0x80a4a245, 0xcca5959, 0x80a40163,
+    0xcc418e3, 0x80a360d0,
+  0xcbdd865, 0x80a2c08b, 0xcb797e0, 0x80a22095, 0xcb15752, 0x80a180ed,
+    0xcab16bd, 0x80a0e194,
+  0xca4d620, 0x80a04289, 0xc9e957b, 0x809fa3cd, 0xc9854cf, 0x809f0560,
+    0xc92141a, 0x809e6741,
+  0xc8bd35e, 0x809dc971, 0xc85929a, 0x809d2bef, 0xc7f51cf, 0x809c8ebc,
+    0xc7910fb, 0x809bf1d7,
+  0xc72d020, 0x809b5541, 0xc6c8f3e, 0x809ab8fa, 0xc664e53, 0x809a1d01,
+    0xc600d61, 0x80998157,
+  0xc59cc68, 0x8098e5fb, 0xc538b66, 0x80984aee, 0xc4d4a5d, 0x8097b030,
+    0xc47094d, 0x809715c0,
+  0xc40c835, 0x80967b9f, 0xc3a8715, 0x8095e1cc, 0xc3445ee, 0x80954848,
+    0xc2e04c0, 0x8094af13,
+  0xc27c389, 0x8094162c, 0xc21824c, 0x80937d93, 0xc1b4107, 0x8092e54a,
+    0xc14ffba, 0x80924d4f,
+  0xc0ebe66, 0x8091b5a2, 0xc087d0a, 0x80911e44, 0xc023ba7, 0x80908735,
+    0xbfbfa3d, 0x808ff074,
+  0xbf5b8cb, 0x808f5a02, 0xbef7752, 0x808ec3df, 0xbe935d2, 0x808e2e0a,
+    0xbe2f44a, 0x808d9884,
+  0xbdcb2bb, 0x808d034c, 0xbd67124, 0x808c6e63, 0xbd02f87, 0x808bd9c9,
+    0xbc9ede2, 0x808b457d,
+  0xbc3ac35, 0x808ab180, 0xbbd6a82, 0x808a1dd2, 0xbb728c7, 0x80898a72,
+    0xbb0e705, 0x8088f761,
+  0xbaaa53b, 0x8088649e, 0xba4636b, 0x8087d22a, 0xb9e2193, 0x80874005,
+    0xb97dfb5, 0x8086ae2e,
+  0xb919dcf, 0x80861ca6, 0xb8b5be1, 0x80858b6c, 0xb8519ed, 0x8084fa82,
+    0xb7ed7f2, 0x808469e5,
+  0xb7895f0, 0x8083d998, 0xb7253e6, 0x80834999, 0xb6c11d5, 0x8082b9e9,
+    0xb65cfbe, 0x80822a87,
+  0xb5f8d9f, 0x80819b74, 0xb594b7a, 0x80810cb0, 0xb53094d, 0x80807e3a,
+    0xb4cc719, 0x807ff013,
+  0xb4684df, 0x807f623b, 0xb40429d, 0x807ed4b1, 0xb3a0055, 0x807e4776,
+    0xb33be05, 0x807dba89,
+  0xb2d7baf, 0x807d2dec, 0xb273952, 0x807ca19c, 0xb20f6ee, 0x807c159c,
+    0xb1ab483, 0x807b89ea,
+  0xb147211, 0x807afe87, 0xb0e2f98, 0x807a7373, 0xb07ed19, 0x8079e8ad,
+    0xb01aa92, 0x80795e36,
+  0xafb6805, 0x8078d40d, 0xaf52571, 0x80784a33, 0xaeee2d7, 0x8077c0a8,
+    0xae8a036, 0x8077376c,
+  0xae25d8d, 0x8076ae7e, 0xadc1adf, 0x807625df, 0xad5d829, 0x80759d8e,
+    0xacf956d, 0x8075158c,
+  0xac952aa, 0x80748dd9, 0xac30fe1, 0x80740675, 0xabccd11, 0x80737f5f,
+    0xab68a3a, 0x8072f898,
+  0xab0475c, 0x8072721f, 0xaaa0478, 0x8071ebf6, 0xaa3c18e, 0x8071661a,
+    0xa9d7e9d, 0x8070e08e,
+  0xa973ba5, 0x80705b50, 0xa90f8a7, 0x806fd661, 0xa8ab5a2, 0x806f51c1,
+    0xa847297, 0x806ecd6f,
+  0xa7e2f85, 0x806e496c, 0xa77ec6d, 0x806dc5b8, 0xa71a94f, 0x806d4253,
+    0xa6b662a, 0x806cbf3c,
+  0xa6522fe, 0x806c3c74, 0xa5edfcc, 0x806bb9fa, 0xa589c94, 0x806b37cf,
+    0xa525955, 0x806ab5f3,
+  0xa4c1610, 0x806a3466, 0xa45d2c5, 0x8069b327, 0xa3f8f73, 0x80693237,
+    0xa394c1b, 0x8068b196,
+  0xa3308bd, 0x80683143, 0xa2cc558, 0x8067b13f, 0xa2681ed, 0x8067318a,
+    0xa203e7c, 0x8066b224,
+  0xa19fb04, 0x8066330c, 0xa13b787, 0x8065b443, 0xa0d7403, 0x806535c9,
+    0xa073079, 0x8064b79d,
+  0xa00ece8, 0x806439c0, 0x9faa952, 0x8063bc32, 0x9f465b5, 0x80633ef3,
+    0x9ee2213, 0x8062c202,
+  0x9e7de6a, 0x80624560, 0x9e19abb, 0x8061c90c, 0x9db5706, 0x80614d08,
+    0x9d5134b, 0x8060d152,
+  0x9cecf89, 0x806055eb, 0x9c88bc2, 0x805fdad2, 0x9c247f5, 0x805f6009,
+    0x9bc0421, 0x805ee58e,
+  0x9b5c048, 0x805e6b62, 0x9af7c69, 0x805df184, 0x9a93884, 0x805d77f5,
+    0x9a2f498, 0x805cfeb5,
+  0x99cb0a7, 0x805c85c4, 0x9966cb0, 0x805c0d21, 0x99028b3, 0x805b94ce,
+    0x989e4b0, 0x805b1cc8,
+  0x983a0a7, 0x805aa512, 0x97d5c99, 0x805a2daa, 0x9771884, 0x8059b692,
+    0x970d46a, 0x80593fc7,
+  0x96a9049, 0x8058c94c, 0x9644c23, 0x8058531f, 0x95e07f8, 0x8057dd41,
+    0x957c3c6, 0x805767b2,
+  0x9517f8f, 0x8056f272, 0x94b3b52, 0x80567d80, 0x944f70f, 0x805608dd,
+    0x93eb2c6, 0x80559489,
+  0x9386e78, 0x80552084, 0x9322a24, 0x8054accd, 0x92be5ca, 0x80543965,
+    0x925a16b, 0x8053c64c,
+  0x91f5d06, 0x80535381, 0x919189c, 0x8052e106, 0x912d42c, 0x80526ed9,
+    0x90c8fb6, 0x8051fcfb,
+  0x9064b3a, 0x80518b6b, 0x90006ba, 0x80511a2b, 0x8f9c233, 0x8050a939,
+    0x8f37da7, 0x80503896,
+  0x8ed3916, 0x804fc841, 0x8e6f47f, 0x804f583c, 0x8e0afe2, 0x804ee885,
+    0x8da6b40, 0x804e791d,
+  0x8d42699, 0x804e0a04, 0x8cde1ec, 0x804d9b39, 0x8c79d3a, 0x804d2cbd,
+    0x8c15882, 0x804cbe90,
+  0x8bb13c5, 0x804c50b2, 0x8b4cf02, 0x804be323, 0x8ae8a3a, 0x804b75e2,
+    0x8a8456d, 0x804b08f0,
+  0x8a2009a, 0x804a9c4d, 0x89bbbc3, 0x804a2ff9, 0x89576e5, 0x8049c3f3,
+    0x88f3203, 0x8049583d,
+  0x888ed1b, 0x8048ecd5, 0x882a82e, 0x804881bb, 0x87c633c, 0x804816f1,
+    0x8761e44, 0x8047ac75,
+  0x86fd947, 0x80474248, 0x8699445, 0x8046d86a, 0x8634f3e, 0x80466edb,
+    0x85d0a32, 0x8046059b,
+  0x856c520, 0x80459ca9, 0x850800a, 0x80453406, 0x84a3aee, 0x8044cbb2,
+    0x843f5cd, 0x804463ad,
+  0x83db0a7, 0x8043fbf6, 0x8376b7c, 0x8043948e, 0x831264c, 0x80432d75,
+    0x82ae117, 0x8042c6ab,
+  0x8249bdd, 0x80426030, 0x81e569d, 0x8041fa03, 0x8181159, 0x80419425,
+    0x811cc10, 0x80412e96,
+  0x80b86c2, 0x8040c956, 0x805416e, 0x80406465, 0x7fefc16, 0x803fffc2,
+    0x7f8b6b9, 0x803f9b6f,
+  0x7f27157, 0x803f376a, 0x7ec2bf0, 0x803ed3b3, 0x7e5e685, 0x803e704c,
+    0x7dfa114, 0x803e0d34,
+  0x7d95b9e, 0x803daa6a, 0x7d31624, 0x803d47ef, 0x7ccd0a5, 0x803ce5c3,
+    0x7c68b21, 0x803c83e5,
+  0x7c04598, 0x803c2257, 0x7ba000b, 0x803bc117, 0x7b3ba78, 0x803b6026,
+    0x7ad74e1, 0x803aff84,
+  0x7a72f45, 0x803a9f31, 0x7a0e9a5, 0x803a3f2d, 0x79aa400, 0x8039df77,
+    0x7945e56, 0x80398010,
+  0x78e18a7, 0x803920f8, 0x787d2f4, 0x8038c22f, 0x7818d3c, 0x803863b5,
+    0x77b4780, 0x80380589,
+  0x77501be, 0x8037a7ac, 0x76ebbf9, 0x80374a1f, 0x768762e, 0x8036ece0,
+    0x762305f, 0x80368fef,
+  0x75bea8c, 0x8036334e, 0x755a4b4, 0x8035d6fb, 0x74f5ed7, 0x80357af8,
+    0x74918f6, 0x80351f43,
+  0x742d311, 0x8034c3dd, 0x73c8d27, 0x803468c5, 0x7364738, 0x80340dfd,
+    0x7300145, 0x8033b383,
+  0x729bb4e, 0x80335959, 0x7237552, 0x8032ff7d, 0x71d2f52, 0x8032a5ef,
+    0x716e94e, 0x80324cb1,
+  0x710a345, 0x8031f3c2, 0x70a5d37, 0x80319b21, 0x7041726, 0x803142cf,
+    0x6fdd110, 0x8030eacd,
+  0x6f78af6, 0x80309318, 0x6f144d7, 0x80303bb3, 0x6eafeb4, 0x802fe49d,
+    0x6e4b88d, 0x802f8dd5,
+  0x6de7262, 0x802f375d, 0x6d82c32, 0x802ee133, 0x6d1e5fe, 0x802e8b58,
+    0x6cb9fc6, 0x802e35cb,
+  0x6c5598a, 0x802de08e, 0x6bf1349, 0x802d8ba0, 0x6b8cd05, 0x802d3700,
+    0x6b286bc, 0x802ce2af,
+  0x6ac406f, 0x802c8ead, 0x6a5fa1e, 0x802c3afa, 0x69fb3c9, 0x802be796,
+    0x6996d70, 0x802b9480,
+  0x6932713, 0x802b41ba, 0x68ce0b2, 0x802aef42, 0x6869a4c, 0x802a9d19,
+    0x68053e3, 0x802a4b3f,
+  0x67a0d76, 0x8029f9b4, 0x673c704, 0x8029a878, 0x66d808f, 0x8029578b,
+    0x6673a16, 0x802906ec,
+  0x660f398, 0x8028b69c, 0x65aad17, 0x8028669b, 0x6546692, 0x802816e9,
+    0x64e2009, 0x8027c786,
+  0x647d97c, 0x80277872, 0x64192eb, 0x802729ad, 0x63b4c57, 0x8026db36,
+    0x63505be, 0x80268d0e,
+  0x62ebf22, 0x80263f36, 0x6287882, 0x8025f1ac, 0x62231de, 0x8025a471,
+    0x61beb36, 0x80255784,
+  0x615a48b, 0x80250ae7, 0x60f5ddc, 0x8024be99, 0x6091729, 0x80247299,
+    0x602d072, 0x802426e8,
+  0x5fc89b8, 0x8023db86, 0x5f642fa, 0x80239073, 0x5effc38, 0x802345af,
+    0x5e9b572, 0x8022fb3a,
+  0x5e36ea9, 0x8022b114, 0x5dd27dd, 0x8022673c, 0x5d6e10c, 0x80221db3,
+    0x5d09a38, 0x8021d47a,
+  0x5ca5361, 0x80218b8f, 0x5c40c86, 0x802142f3, 0x5bdc5a7, 0x8020faa6,
+    0x5b77ec5, 0x8020b2a7,
+  0x5b137df, 0x80206af8, 0x5aaf0f6, 0x80202397, 0x5a4aa09, 0x801fdc86,
+    0x59e6319, 0x801f95c3,
+  0x5981c26, 0x801f4f4f, 0x591d52f, 0x801f092a, 0x58b8e34, 0x801ec354,
+    0x5854736, 0x801e7dcd,
+  0x57f0035, 0x801e3895, 0x578b930, 0x801df3ab, 0x5727228, 0x801daf11,
+    0x56c2b1c, 0x801d6ac5,
+  0x565e40d, 0x801d26c8, 0x55f9cfb, 0x801ce31a, 0x55955e6, 0x801c9fbb,
+    0x5530ecd, 0x801c5cab,
+  0x54cc7b1, 0x801c19ea, 0x5468092, 0x801bd777, 0x540396f, 0x801b9554,
+    0x539f249, 0x801b537f,
+  0x533ab20, 0x801b11fa, 0x52d63f4, 0x801ad0c3, 0x5271cc4, 0x801a8fdb,
+    0x520d592, 0x801a4f42,
+  0x51a8e5c, 0x801a0ef8, 0x5144723, 0x8019cefd, 0x50dffe7, 0x80198f50,
+    0x507b8a8, 0x80194ff3,
+  0x5017165, 0x801910e4, 0x4fb2a20, 0x8018d225, 0x4f4e2d8, 0x801893b4,
+    0x4ee9b8c, 0x80185592,
+  0x4e8543e, 0x801817bf, 0x4e20cec, 0x8017da3b, 0x4dbc597, 0x80179d06,
+    0x4d57e40, 0x80176020,
+  0x4cf36e5, 0x80172388, 0x4c8ef88, 0x8016e740, 0x4c2a827, 0x8016ab46,
+    0x4bc60c4, 0x80166f9c,
+  0x4b6195d, 0x80163440, 0x4afd1f4, 0x8015f933, 0x4a98a88, 0x8015be75,
+    0x4a34319, 0x80158406,
+  0x49cfba7, 0x801549e6, 0x496b432, 0x80151015, 0x4906cbb, 0x8014d693,
+    0x48a2540, 0x80149d5f,
+  0x483ddc3, 0x8014647b, 0x47d9643, 0x80142be5, 0x4774ec1, 0x8013f39e,
+    0x471073b, 0x8013bba7,
+  0x46abfb3, 0x801383fe, 0x4647828, 0x80134ca4, 0x45e309a, 0x80131599,
+    0x457e90a, 0x8012dedd,
+  0x451a177, 0x8012a86f, 0x44b59e1, 0x80127251, 0x4451249, 0x80123c82,
+    0x43ecaae, 0x80120701,
+  0x4388310, 0x8011d1d0, 0x4323b70, 0x80119ced, 0x42bf3cd, 0x80116859,
+    0x425ac28, 0x80113414,
+  0x41f6480, 0x8011001f, 0x4191cd5, 0x8010cc78, 0x412d528, 0x8010991f,
+    0x40c8d79, 0x80106616,
+  0x40645c7, 0x8010335c, 0x3fffe12, 0x801000f1, 0x3f9b65b, 0x800fced4,
+    0x3f36ea2, 0x800f9d07,
+  0x3ed26e6, 0x800f6b88, 0x3e6df28, 0x800f3a59, 0x3e09767, 0x800f0978,
+    0x3da4fa4, 0x800ed8e6,
+  0x3d407df, 0x800ea8a3, 0x3cdc017, 0x800e78af, 0x3c7784d, 0x800e490a,
+    0x3c13080, 0x800e19b4,
+  0x3bae8b2, 0x800deaad, 0x3b4a0e0, 0x800dbbf5, 0x3ae590d, 0x800d8d8b,
+    0x3a81137, 0x800d5f71,
+  0x3a1c960, 0x800d31a5, 0x39b8185, 0x800d0429, 0x39539a9, 0x800cd6fb,
+    0x38ef1ca, 0x800caa1c,
+  0x388a9ea, 0x800c7d8c, 0x3826207, 0x800c514c, 0x37c1a22, 0x800c255a,
+    0x375d23a, 0x800bf9b7,
+  0x36f8a51, 0x800bce63, 0x3694265, 0x800ba35d, 0x362fa78, 0x800b78a7,
+    0x35cb288, 0x800b4e40,
+  0x3566a96, 0x800b2427, 0x35022a2, 0x800afa5e, 0x349daac, 0x800ad0e3,
+    0x34392b4, 0x800aa7b8,
+  0x33d4abb, 0x800a7edb, 0x33702bf, 0x800a564e, 0x330bac1, 0x800a2e0f,
+    0x32a72c1, 0x800a061f,
+  0x3242abf, 0x8009de7e, 0x31de2bb, 0x8009b72c, 0x3179ab5, 0x80099029,
+    0x31152ae, 0x80096975,
+  0x30b0aa4, 0x80094310, 0x304c299, 0x80091cf9, 0x2fe7a8c, 0x8008f732,
+    0x2f8327d, 0x8008d1ba,
+  0x2f1ea6c, 0x8008ac90, 0x2eba259, 0x800887b6, 0x2e55a44, 0x8008632a,
+    0x2df122e, 0x80083eed,
+  0x2d8ca16, 0x80081b00, 0x2d281fc, 0x8007f761, 0x2cc39e1, 0x8007d411,
+    0x2c5f1c3, 0x8007b110,
+  0x2bfa9a4, 0x80078e5e, 0x2b96184, 0x80076bfb, 0x2b31961, 0x800749e7,
+    0x2acd13d, 0x80072822,
+  0x2a68917, 0x800706ac, 0x2a040f0, 0x8006e585, 0x299f8c7, 0x8006c4ac,
+    0x293b09c, 0x8006a423,
+  0x28d6870, 0x800683e8, 0x2872043, 0x800663fd, 0x280d813, 0x80064460,
+    0x27a8fe2, 0x80062513,
+  0x27447b0, 0x80060614, 0x26dff7c, 0x8005e764, 0x267b747, 0x8005c904,
+    0x2616f10, 0x8005aaf2,
+  0x25b26d7, 0x80058d2f, 0x254de9e, 0x80056fbb, 0x24e9662, 0x80055296,
+    0x2484e26, 0x800535c0,
+  0x24205e8, 0x80051939, 0x23bbda8, 0x8004fd00, 0x2357567, 0x8004e117,
+    0x22f2d25, 0x8004c57d,
+  0x228e4e2, 0x8004aa32, 0x2229c9d, 0x80048f35, 0x21c5457, 0x80047488,
+    0x2160c0f, 0x80045a29,
+  0x20fc3c6, 0x8004401a, 0x2097b7c, 0x80042659, 0x2033331, 0x80040ce7,
+    0x1fceae4, 0x8003f3c5,
+  0x1f6a297, 0x8003daf1, 0x1f05a48, 0x8003c26c, 0x1ea11f7, 0x8003aa36,
+    0x1e3c9a6, 0x8003924f,
+  0x1dd8154, 0x80037ab7, 0x1d73900, 0x8003636e, 0x1d0f0ab, 0x80034c74,
+    0x1caa855, 0x800335c9,
+  0x1c45ffe, 0x80031f6d, 0x1be17a6, 0x80030960, 0x1b7cf4d, 0x8002f3a1,
+    0x1b186f3, 0x8002de32,
+  0x1ab3e97, 0x8002c912, 0x1a4f63b, 0x8002b440, 0x19eaddd, 0x80029fbe,
+    0x198657f, 0x80028b8a,
+  0x1921d20, 0x800277a6, 0x18bd4bf, 0x80026410, 0x1858c5e, 0x800250c9,
+    0x17f43fc, 0x80023dd2,
+  0x178fb99, 0x80022b29, 0x172b335, 0x800218cf, 0x16c6ad0, 0x800206c4,
+    0x166226a, 0x8001f508,
+  0x15fda03, 0x8001e39b, 0x159919c, 0x8001d27d, 0x1534934, 0x8001c1ae,
+    0x14d00ca, 0x8001b12e,
+  0x146b860, 0x8001a0fd, 0x1406ff6, 0x8001911b, 0x13a278a, 0x80018187,
+    0x133df1e, 0x80017243,
+  0x12d96b1, 0x8001634e, 0x1274e43, 0x800154a7, 0x12105d5, 0x80014650,
+    0x11abd66, 0x80013847,
+  0x11474f6, 0x80012a8e, 0x10e2c85, 0x80011d23, 0x107e414, 0x80011008,
+    0x1019ba2, 0x8001033b,
+  0xfb5330, 0x8000f6bd, 0xf50abd, 0x8000ea8e, 0xeec249, 0x8000deaf, 0xe879d5,
+    0x8000d31e,
+  0xe23160, 0x8000c7dc, 0xdbe8eb, 0x8000bce9, 0xd5a075, 0x8000b245, 0xcf57ff,
+    0x8000a7f0,
+  0xc90f88, 0x80009dea, 0xc2c711, 0x80009433, 0xbc7e99, 0x80008aca, 0xb63621,
+    0x800081b1,
+  0xafeda8, 0x800078e7, 0xa9a52f, 0x8000706c, 0xa35cb5, 0x8000683f, 0x9d143b,
+    0x80006062,
+  0x96cbc1, 0x800058d4, 0x908346, 0x80005194, 0x8a3acb, 0x80004aa4, 0x83f250,
+    0x80004402,
+  0x7da9d4, 0x80003daf, 0x776159, 0x800037ac, 0x7118dc, 0x800031f7, 0x6ad060,
+    0x80002c91,
+  0x6487e3, 0x8000277a, 0x5e3f66, 0x800022b3, 0x57f6e9, 0x80001e3a, 0x51ae6b,
+    0x80001a10,
+  0x4b65ee, 0x80001635, 0x451d70, 0x800012a9, 0x3ed4f2, 0x80000f6c, 0x388c74,
+    0x80000c7e,
+  0x3243f5, 0x800009df, 0x2bfb77, 0x8000078e, 0x25b2f8, 0x8000058d, 0x1f6a7a,
+    0x800003db,
+  0x1921fb, 0x80000278, 0x12d97c, 0x80000163, 0xc90fe, 0x8000009e, 0x6487f,
+    0x80000027,
+
+};
+
+/**    
+* \par    
+* cosFactor tables are generated using the formula : 
cos_factors[n] = 2 * cos((2n+1)*pi/(4*N))
    
+* \par    
+* C command to generate the table    
+* 
    
+* for(i = 0; i< N; i++)    
+* {    
+*   cos_factors[i]= 2 * cos((2*i+1)*c/2);    
+* } 
    
+* \par    
+* where N is the number of factors to generate and c is pi/(2*N)    
+* \par    
+* Then converted to q31 format by multiplying with 2^31 and saturated if required.    
+*/
+
+
+static const q31_t cos_factorsQ31_128[128] = {
+  0x7fff6216, 0x7ffa72d1, 0x7ff09478, 0x7fe1c76b, 0x7fce0c3e, 0x7fb563b3,
+  0x7f97cebd, 0x7f754e80,
+  0x7f4de451, 0x7f2191b4, 0x7ef05860, 0x7eba3a39, 0x7e7f3957, 0x7e3f57ff,
+  0x7dfa98a8, 0x7db0fdf8,
+  0x7d628ac6, 0x7d0f4218, 0x7cb72724, 0x7c5a3d50, 0x7bf88830, 0x7b920b89,
+  0x7b26cb4f, 0x7ab6cba4,
+  0x7a4210d8, 0x79c89f6e, 0x794a7c12, 0x78c7aba2, 0x78403329, 0x77b417df,
+  0x77235f2d, 0x768e0ea6,
+  0x75f42c0b, 0x7555bd4c, 0x74b2c884, 0x740b53fb, 0x735f6626, 0x72af05a7,
+  0x71fa3949, 0x71410805,
+  0x708378ff, 0x6fc19385, 0x6efb5f12, 0x6e30e34a, 0x6d6227fa, 0x6c8f351c,
+  0x6bb812d1, 0x6adcc964,
+  0x69fd614a, 0x6919e320, 0x683257ab, 0x6746c7d8, 0x66573cbb, 0x6563bf92,
+  0x646c59bf, 0x637114cc,
+  0x6271fa69, 0x616f146c, 0x60686ccf, 0x5f5e0db3, 0x5e50015d, 0x5d3e5237,
+  0x5c290acc, 0x5b1035cf,
+  0x59f3de12, 0x58d40e8c, 0x57b0d256, 0x568a34a9, 0x556040e2, 0x5433027d,
+  0x53028518, 0x51ced46e,
+  0x5097fc5e, 0x4f5e08e3, 0x4e210617, 0x4ce10034, 0x4b9e0390, 0x4a581c9e,
+  0x490f57ee, 0x47c3c22f,
+  0x46756828, 0x452456bd, 0x43d09aed, 0x427a41d0, 0x4121589b, 0x3fc5ec98,
+  0x3e680b2c, 0x3d07c1d6,
+  0x3ba51e29, 0x3a402dd2, 0x38d8fe93, 0x376f9e46, 0x36041ad9, 0x34968250,
+  0x3326e2c3, 0x31b54a5e,
+  0x3041c761, 0x2ecc681e, 0x2d553afc, 0x2bdc4e6f, 0x2a61b101, 0x28e5714b,
+  0x27679df4, 0x25e845b6,
+  0x24677758, 0x22e541af, 0x2161b3a0, 0x1fdcdc1b, 0x1e56ca1e, 0x1ccf8cb3,
+  0x1b4732ef, 0x19bdcbf3,
+  0x183366e9, 0x16a81305, 0x151bdf86, 0x138edbb1, 0x120116d5, 0x1072a048,
+  0xee38766, 0xd53db92,
+  0xbc3ac35, 0xa3308bd, 0x8a2009a, 0x710a345, 0x57f0035, 0x3ed26e6, 0x25b26d7,
+  0xc90f88,
+};
+
+static const q31_t cos_factorsQ31_512[512] = {
+  0x7ffff621, 0x7fffa72c, 0x7fff0943, 0x7ffe1c65, 0x7ffce093, 0x7ffb55ce,
+  0x7ff97c18, 0x7ff75370,
+  0x7ff4dbd9, 0x7ff21553, 0x7feeffe1, 0x7feb9b85, 0x7fe7e841, 0x7fe3e616,
+  0x7fdf9508, 0x7fdaf519,
+  0x7fd6064c, 0x7fd0c8a3, 0x7fcb3c23, 0x7fc560cf, 0x7fbf36aa, 0x7fb8bdb8,
+  0x7fb1f5fc, 0x7faadf7c,
+  0x7fa37a3c, 0x7f9bc640, 0x7f93c38c, 0x7f8b7227, 0x7f82d214, 0x7f79e35a,
+  0x7f70a5fe, 0x7f671a05,
+  0x7f5d3f75, 0x7f531655, 0x7f489eaa, 0x7f3dd87c, 0x7f32c3d1, 0x7f2760af,
+  0x7f1baf1e, 0x7f0faf25,
+  0x7f0360cb, 0x7ef6c418, 0x7ee9d914, 0x7edc9fc6, 0x7ecf1837, 0x7ec14270,
+  0x7eb31e78, 0x7ea4ac58,
+  0x7e95ec1a, 0x7e86ddc6, 0x7e778166, 0x7e67d703, 0x7e57dea7, 0x7e47985b,
+  0x7e37042a, 0x7e26221f,
+  0x7e14f242, 0x7e0374a0, 0x7df1a942, 0x7ddf9034, 0x7dcd2981, 0x7dba7534,
+  0x7da77359, 0x7d9423fc,
+  0x7d808728, 0x7d6c9ce9, 0x7d58654d, 0x7d43e05e, 0x7d2f0e2b, 0x7d19eebf,
+  0x7d048228, 0x7ceec873,
+  0x7cd8c1ae, 0x7cc26de5, 0x7cabcd28, 0x7c94df83, 0x7c7da505, 0x7c661dbc,
+  0x7c4e49b7, 0x7c362904,
+  0x7c1dbbb3, 0x7c0501d2, 0x7bebfb70, 0x7bd2a89e, 0x7bb9096b, 0x7b9f1de6,
+  0x7b84e61f, 0x7b6a6227,
+  0x7b4f920e, 0x7b3475e5, 0x7b190dbc, 0x7afd59a4, 0x7ae159ae, 0x7ac50dec,
+  0x7aa8766f, 0x7a8b9348,
+  0x7a6e648a, 0x7a50ea47, 0x7a332490, 0x7a151378, 0x79f6b711, 0x79d80f6f,
+  0x79b91ca4, 0x7999dec4,
+  0x797a55e0, 0x795a820e, 0x793a6361, 0x7919f9ec, 0x78f945c3, 0x78d846fb,
+  0x78b6fda8, 0x789569df,
+  0x78738bb3, 0x7851633b, 0x782ef08b, 0x780c33b8, 0x77e92cd9, 0x77c5dc01,
+  0x77a24148, 0x777e5cc3,
+  0x775a2e89, 0x7735b6af, 0x7710f54c, 0x76ebea77, 0x76c69647, 0x76a0f8d2,
+  0x767b1231, 0x7654e279,
+  0x762e69c4, 0x7607a828, 0x75e09dbd, 0x75b94a9c, 0x7591aedd, 0x7569ca99,
+  0x75419de7, 0x751928e0,
+  0x74f06b9e, 0x74c7663a, 0x749e18cd, 0x74748371, 0x744aa63f, 0x74208150,
+  0x73f614c0, 0x73cb60a8,
+  0x73a06522, 0x73752249, 0x73499838, 0x731dc70a, 0x72f1aed9, 0x72c54fc1,
+  0x7298a9dd, 0x726bbd48,
+  0x723e8a20, 0x7211107e, 0x71e35080, 0x71b54a41, 0x7186fdde, 0x71586b74,
+  0x7129931f, 0x70fa74fc,
+  0x70cb1128, 0x709b67c0, 0x706b78e3, 0x703b44ad, 0x700acb3c, 0x6fda0cae,
+  0x6fa90921, 0x6f77c0b3,
+  0x6f463383, 0x6f1461b0, 0x6ee24b57, 0x6eaff099, 0x6e7d5193, 0x6e4a6e66,
+  0x6e174730, 0x6de3dc11,
+  0x6db02d29, 0x6d7c3a98, 0x6d48047e, 0x6d138afb, 0x6cdece2f, 0x6ca9ce3b,
+  0x6c748b3f, 0x6c3f055d,
+  0x6c093cb6, 0x6bd3316a, 0x6b9ce39b, 0x6b66536b, 0x6b2f80fb, 0x6af86c6c,
+  0x6ac115e2, 0x6a897d7d,
+  0x6a51a361, 0x6a1987b0, 0x69e12a8c, 0x69a88c19, 0x696fac78, 0x69368bce,
+  0x68fd2a3d, 0x68c387e9,
+  0x6889a4f6, 0x684f8186, 0x68151dbe, 0x67da79c3, 0x679f95b7, 0x676471c0,
+  0x67290e02, 0x66ed6aa1,
+  0x66b187c3, 0x6675658c, 0x66390422, 0x65fc63a9, 0x65bf8447, 0x65826622,
+  0x6545095f, 0x65076e25,
+  0x64c99498, 0x648b7ce0, 0x644d2722, 0x640e9386, 0x63cfc231, 0x6390b34a,
+  0x635166f9, 0x6311dd64,
+  0x62d216b3, 0x6292130c, 0x6251d298, 0x6211557e, 0x61d09be5, 0x618fa5f7,
+  0x614e73da, 0x610d05b7,
+  0x60cb5bb7, 0x60897601, 0x604754bf, 0x6004f819, 0x5fc26038, 0x5f7f8d46,
+  0x5f3c7f6b, 0x5ef936d1,
+  0x5eb5b3a2, 0x5e71f606, 0x5e2dfe29, 0x5de9cc33, 0x5da5604f, 0x5d60baa7,
+  0x5d1bdb65, 0x5cd6c2b5,
+  0x5c9170bf, 0x5c4be5b0, 0x5c0621b2, 0x5bc024f0, 0x5b79ef96, 0x5b3381ce,
+  0x5aecdbc5, 0x5aa5fda5,
+  0x5a5ee79a, 0x5a1799d1, 0x59d01475, 0x598857b2, 0x594063b5, 0x58f838a9,
+  0x58afd6bd, 0x58673e1b,
+  0x581e6ef1, 0x57d5696d, 0x578c2dba, 0x5742bc06, 0x56f9147e, 0x56af3750,
+  0x566524aa, 0x561adcb9,
+  0x55d05faa, 0x5585adad, 0x553ac6ee, 0x54efab9c, 0x54a45be6, 0x5458d7f9,
+  0x540d2005, 0x53c13439,
+  0x537514c2, 0x5328c1d0, 0x52dc3b92, 0x528f8238, 0x524295f0, 0x51f576ea,
+  0x51a82555, 0x515aa162,
+  0x510ceb40, 0x50bf031f, 0x5070e92f, 0x50229da1, 0x4fd420a4, 0x4f857269,
+  0x4f369320, 0x4ee782fb,
+  0x4e984229, 0x4e48d0dd, 0x4df92f46, 0x4da95d96, 0x4d595bfe, 0x4d092ab0,
+  0x4cb8c9dd, 0x4c6839b7,
+  0x4c177a6e, 0x4bc68c36, 0x4b756f40, 0x4b2423be, 0x4ad2a9e2, 0x4a8101de,
+  0x4a2f2be6, 0x49dd282a,
+  0x498af6df, 0x49389836, 0x48e60c62, 0x48935397, 0x48406e08, 0x47ed5be6,
+  0x479a1d67, 0x4746b2bc,
+  0x46f31c1a, 0x469f59b4, 0x464b6bbe, 0x45f7526b, 0x45a30df0, 0x454e9e80,
+  0x44fa0450, 0x44a53f93,
+  0x4450507e, 0x43fb3746, 0x43a5f41e, 0x4350873c, 0x42faf0d4, 0x42a5311b,
+  0x424f4845, 0x41f93689,
+  0x41a2fc1a, 0x414c992f, 0x40f60dfb, 0x409f5ab6, 0x40487f94, 0x3ff17cca,
+  0x3f9a5290, 0x3f430119,
+  0x3eeb889c, 0x3e93e950, 0x3e3c2369, 0x3de4371f, 0x3d8c24a8, 0x3d33ec39,
+  0x3cdb8e09, 0x3c830a50,
+  0x3c2a6142, 0x3bd19318, 0x3b78a007, 0x3b1f8848, 0x3ac64c0f, 0x3a6ceb96,
+  0x3a136712, 0x39b9bebc,
+  0x395ff2c9, 0x39060373, 0x38abf0ef, 0x3851bb77, 0x37f76341, 0x379ce885,
+  0x37424b7b, 0x36e78c5b,
+  0x368cab5c, 0x3631a8b8, 0x35d684a6, 0x357b3f5d, 0x351fd918, 0x34c4520d,
+  0x3468aa76, 0x340ce28b,
+  0x33b0fa84, 0x3354f29b, 0x32f8cb07, 0x329c8402, 0x32401dc6, 0x31e39889,
+  0x3186f487, 0x312a31f8,
+  0x30cd5115, 0x30705217, 0x30133539, 0x2fb5fab2, 0x2f58a2be, 0x2efb2d95,
+  0x2e9d9b70, 0x2e3fec8b,
+  0x2de2211e, 0x2d843964, 0x2d263596, 0x2cc815ee, 0x2c69daa6, 0x2c0b83fa,
+  0x2bad1221, 0x2b4e8558,
+  0x2aefddd8, 0x2a911bdc, 0x2a323f9e, 0x29d34958, 0x29743946, 0x29150fa1,
+  0x28b5cca5, 0x2856708d,
+  0x27f6fb92, 0x27976df1, 0x2737c7e3, 0x26d809a5, 0x26783370, 0x26184581,
+  0x25b84012, 0x2558235f,
+  0x24f7efa2, 0x2497a517, 0x243743fa, 0x23d6cc87, 0x23763ef7, 0x23159b88,
+  0x22b4e274, 0x225413f8,
+  0x21f3304f, 0x219237b5, 0x21312a65, 0x20d0089c, 0x206ed295, 0x200d888d,
+  0x1fac2abf, 0x1f4ab968,
+  0x1ee934c3, 0x1e879d0d, 0x1e25f282, 0x1dc4355e, 0x1d6265dd, 0x1d00843d,
+  0x1c9e90b8, 0x1c3c8b8c,
+  0x1bda74f6, 0x1b784d30, 0x1b161479, 0x1ab3cb0d, 0x1a517128, 0x19ef0707,
+  0x198c8ce7, 0x192a0304,
+  0x18c7699b, 0x1864c0ea, 0x1802092c, 0x179f429f, 0x173c6d80, 0x16d98a0c,
+  0x1676987f, 0x16139918,
+  0x15b08c12, 0x154d71aa, 0x14ea4a1f, 0x148715ae, 0x1423d492, 0x13c0870a,
+  0x135d2d53, 0x12f9c7aa,
+  0x1296564d, 0x1232d979, 0x11cf516a, 0x116bbe60, 0x11082096, 0x10a4784b,
+  0x1040c5bb, 0xfdd0926,
+  0xf7942c7, 0xf1572dc, 0xeb199a4, 0xe4db75b, 0xde9cc40, 0xd85d88f, 0xd21dc87,
+  0xcbdd865,
+  0xc59cc68, 0xbf5b8cb, 0xb919dcf, 0xb2d7baf, 0xac952aa, 0xa6522fe, 0xa00ece8,
+  0x99cb0a7,
+  0x9386e78, 0x8d42699, 0x86fd947, 0x80b86c2, 0x7a72f45, 0x742d311, 0x6de7262,
+  0x67a0d76,
+  0x615a48b, 0x5b137df, 0x54cc7b1, 0x4e8543e, 0x483ddc3, 0x41f6480, 0x3bae8b2,
+  0x3566a96,
+  0x2f1ea6c, 0x28d6870, 0x228e4e2, 0x1c45ffe, 0x15fda03, 0xfb5330, 0x96cbc1,
+  0x3243f5,
+};
+
+static const q31_t cos_factorsQ31_2048[2048] = {
+  0x7fffff62, 0x7ffffa73, 0x7ffff094, 0x7fffe1c6, 0x7fffce09, 0x7fffb55c,
+  0x7fff97c1, 0x7fff7536,
+  0x7fff4dbb, 0x7fff2151, 0x7ffeeff8, 0x7ffeb9b0, 0x7ffe7e79, 0x7ffe3e52,
+  0x7ffdf93c, 0x7ffdaf37,
+  0x7ffd6042, 0x7ffd0c5f, 0x7ffcb38c, 0x7ffc55ca, 0x7ffbf319, 0x7ffb8b78,
+  0x7ffb1ee9, 0x7ffaad6a,
+  0x7ffa36fc, 0x7ff9bba0, 0x7ff93b54, 0x7ff8b619, 0x7ff82bef, 0x7ff79cd6,
+  0x7ff708ce, 0x7ff66fd7,
+  0x7ff5d1f1, 0x7ff52f1d, 0x7ff48759, 0x7ff3daa6, 0x7ff32905, 0x7ff27275,
+  0x7ff1b6f6, 0x7ff0f688,
+  0x7ff0312c, 0x7fef66e1, 0x7fee97a7, 0x7fedc37e, 0x7fecea67, 0x7fec0c62,
+  0x7feb296d, 0x7fea418b,
+  0x7fe954ba, 0x7fe862fa, 0x7fe76c4c, 0x7fe670b0, 0x7fe57025, 0x7fe46aac,
+  0x7fe36045, 0x7fe250ef,
+  0x7fe13cac, 0x7fe0237a, 0x7fdf055a, 0x7fdde24d, 0x7fdcba51, 0x7fdb8d67,
+  0x7fda5b8f, 0x7fd924ca,
+  0x7fd7e917, 0x7fd6a875, 0x7fd562e7, 0x7fd4186a, 0x7fd2c900, 0x7fd174a8,
+  0x7fd01b63, 0x7fcebd31,
+  0x7fcd5a11, 0x7fcbf203, 0x7fca8508, 0x7fc91320, 0x7fc79c4b, 0x7fc62089,
+  0x7fc49fda, 0x7fc31a3d,
+  0x7fc18fb4, 0x7fc0003e, 0x7fbe6bdb, 0x7fbcd28b, 0x7fbb344e, 0x7fb99125,
+  0x7fb7e90f, 0x7fb63c0d,
+  0x7fb48a1e, 0x7fb2d343, 0x7fb1177b, 0x7faf56c7, 0x7fad9127, 0x7fabc69b,
+  0x7fa9f723, 0x7fa822bf,
+  0x7fa6496e, 0x7fa46b32, 0x7fa2880b, 0x7fa09ff7, 0x7f9eb2f8, 0x7f9cc10d,
+  0x7f9aca37, 0x7f98ce76,
+  0x7f96cdc9, 0x7f94c831, 0x7f92bdad, 0x7f90ae3f, 0x7f8e99e6, 0x7f8c80a1,
+  0x7f8a6272, 0x7f883f58,
+  0x7f861753, 0x7f83ea64, 0x7f81b88a, 0x7f7f81c6, 0x7f7d4617, 0x7f7b057e,
+  0x7f78bffb, 0x7f76758e,
+  0x7f742637, 0x7f71d1f6, 0x7f6f78cb, 0x7f6d1ab6, 0x7f6ab7b8, 0x7f684fd0,
+  0x7f65e2ff, 0x7f637144,
+  0x7f60faa0, 0x7f5e7f13, 0x7f5bfe9d, 0x7f59793e, 0x7f56eef5, 0x7f545fc5,
+  0x7f51cbab, 0x7f4f32a9,
+  0x7f4c94be, 0x7f49f1eb, 0x7f474a30, 0x7f449d8c, 0x7f41ec01, 0x7f3f358d,
+  0x7f3c7a31, 0x7f39b9ee,
+  0x7f36f4c3, 0x7f342ab1, 0x7f315bb7, 0x7f2e87d6, 0x7f2baf0d, 0x7f28d15d,
+  0x7f25eec7, 0x7f230749,
+  0x7f201ae5, 0x7f1d299a, 0x7f1a3368, 0x7f173850, 0x7f143852, 0x7f11336d,
+  0x7f0e29a3, 0x7f0b1af2,
+  0x7f08075c, 0x7f04eedf, 0x7f01d17d, 0x7efeaf36, 0x7efb8809, 0x7ef85bf7,
+  0x7ef52b00, 0x7ef1f524,
+  0x7eeeba62, 0x7eeb7abc, 0x7ee83632, 0x7ee4ecc3, 0x7ee19e6f, 0x7ede4b38,
+  0x7edaf31c, 0x7ed7961c,
+  0x7ed43438, 0x7ed0cd70, 0x7ecd61c5, 0x7ec9f137, 0x7ec67bc5, 0x7ec3016f,
+  0x7ebf8237, 0x7ebbfe1c,
+  0x7eb8751e, 0x7eb4e73d, 0x7eb1547a, 0x7eadbcd4, 0x7eaa204c, 0x7ea67ee2,
+  0x7ea2d896, 0x7e9f2d68,
+  0x7e9b7d58, 0x7e97c867, 0x7e940e94, 0x7e904fe0, 0x7e8c8c4b, 0x7e88c3d5,
+  0x7e84f67e, 0x7e812447,
+  0x7e7d4d2f, 0x7e797136, 0x7e75905d, 0x7e71aaa4, 0x7e6dc00c, 0x7e69d093,
+  0x7e65dc3b, 0x7e61e303,
+  0x7e5de4ec, 0x7e59e1f5, 0x7e55da20, 0x7e51cd6c, 0x7e4dbbd9, 0x7e49a567,
+  0x7e458a17, 0x7e4169e9,
+  0x7e3d44dd, 0x7e391af3, 0x7e34ec2b, 0x7e30b885, 0x7e2c8002, 0x7e2842a2,
+  0x7e240064, 0x7e1fb94a,
+  0x7e1b6d53, 0x7e171c7f, 0x7e12c6ce, 0x7e0e6c42, 0x7e0a0cd9, 0x7e05a894,
+  0x7e013f74, 0x7dfcd178,
+  0x7df85ea0, 0x7df3e6ee, 0x7def6a60, 0x7deae8f7, 0x7de662b3, 0x7de1d795,
+  0x7ddd479d, 0x7dd8b2ca,
+  0x7dd4191d, 0x7dcf7a96, 0x7dcad736, 0x7dc62efc, 0x7dc181e8, 0x7dbccffc,
+  0x7db81936, 0x7db35d98,
+  0x7dae9d21, 0x7da9d7d2, 0x7da50dab, 0x7da03eab, 0x7d9b6ad3, 0x7d969224,
+  0x7d91b49e, 0x7d8cd240,
+  0x7d87eb0a, 0x7d82fefe, 0x7d7e0e1c, 0x7d791862, 0x7d741dd2, 0x7d6f1e6c,
+  0x7d6a1a31, 0x7d65111f,
+  0x7d600338, 0x7d5af07b, 0x7d55d8e9, 0x7d50bc82, 0x7d4b9b46, 0x7d467536,
+  0x7d414a51, 0x7d3c1a98,
+  0x7d36e60b, 0x7d31acaa, 0x7d2c6e76, 0x7d272b6e, 0x7d21e393, 0x7d1c96e5,
+  0x7d174564, 0x7d11ef11,
+  0x7d0c93eb, 0x7d0733f3, 0x7d01cf29, 0x7cfc658d, 0x7cf6f720, 0x7cf183e1,
+  0x7cec0bd1, 0x7ce68ef0,
+  0x7ce10d3f, 0x7cdb86bd, 0x7cd5fb6a, 0x7cd06b48, 0x7ccad656, 0x7cc53c94,
+  0x7cbf9e03, 0x7cb9faa2,
+  0x7cb45272, 0x7caea574, 0x7ca8f3a7, 0x7ca33d0c, 0x7c9d81a3, 0x7c97c16b,
+  0x7c91fc66, 0x7c8c3294,
+  0x7c8663f4, 0x7c809088, 0x7c7ab84e, 0x7c74db48, 0x7c6ef976, 0x7c6912d7,
+  0x7c63276d, 0x7c5d3737,
+  0x7c574236, 0x7c514869, 0x7c4b49d2, 0x7c45466f, 0x7c3f3e42, 0x7c39314b,
+  0x7c331f8a, 0x7c2d08ff,
+  0x7c26edab, 0x7c20cd8d, 0x7c1aa8a6, 0x7c147ef6, 0x7c0e507e, 0x7c081d3d,
+  0x7c01e534, 0x7bfba863,
+  0x7bf566cb, 0x7bef206b, 0x7be8d544, 0x7be28556, 0x7bdc30a1, 0x7bd5d726,
+  0x7bcf78e5, 0x7bc915dd,
+  0x7bc2ae10, 0x7bbc417e, 0x7bb5d026, 0x7baf5a09, 0x7ba8df28, 0x7ba25f82,
+  0x7b9bdb18, 0x7b9551ea,
+  0x7b8ec3f8, 0x7b883143, 0x7b8199ca, 0x7b7afd8f, 0x7b745c91, 0x7b6db6d0,
+  0x7b670c4d, 0x7b605d09,
+  0x7b59a902, 0x7b52f03a, 0x7b4c32b1, 0x7b457068, 0x7b3ea95d, 0x7b37dd92,
+  0x7b310d07, 0x7b2a37bc,
+  0x7b235db2, 0x7b1c7ee8, 0x7b159b5f, 0x7b0eb318, 0x7b07c612, 0x7b00d44d,
+  0x7af9ddcb, 0x7af2e28b,
+  0x7aebe28d, 0x7ae4ddd2, 0x7addd45b, 0x7ad6c626, 0x7acfb336, 0x7ac89b89,
+  0x7ac17f20, 0x7aba5dfc,
+  0x7ab3381d, 0x7aac0d82, 0x7aa4de2d, 0x7a9daa1d, 0x7a967153, 0x7a8f33d0,
+  0x7a87f192, 0x7a80aa9c,
+  0x7a795eec, 0x7a720e84, 0x7a6ab963, 0x7a635f8a, 0x7a5c00f9, 0x7a549db0,
+  0x7a4d35b0, 0x7a45c8f9,
+  0x7a3e578b, 0x7a36e166, 0x7a2f668c, 0x7a27e6fb, 0x7a2062b5, 0x7a18d9b9,
+  0x7a114c09, 0x7a09b9a4,
+  0x7a02228a, 0x79fa86bc, 0x79f2e63a, 0x79eb4105, 0x79e3971c, 0x79dbe880,
+  0x79d43532, 0x79cc7d31,
+  0x79c4c07e, 0x79bcff19, 0x79b53903, 0x79ad6e3c, 0x79a59ec3, 0x799dca9a,
+  0x7995f1c1, 0x798e1438,
+  0x798631ff, 0x797e4b16, 0x79765f7f, 0x796e6f39, 0x79667a44, 0x795e80a1,
+  0x79568250, 0x794e7f52,
+  0x794677a6, 0x793e6b4e, 0x79365a49, 0x792e4497, 0x79262a3a, 0x791e0b31,
+  0x7915e77c, 0x790dbf1d,
+  0x79059212, 0x78fd605d, 0x78f529fe, 0x78eceef6, 0x78e4af44, 0x78dc6ae8,
+  0x78d421e4, 0x78cbd437,
+  0x78c381e2, 0x78bb2ae5, 0x78b2cf41, 0x78aa6ef5, 0x78a20a03, 0x7899a06a,
+  0x7891322a, 0x7888bf45,
+  0x788047ba, 0x7877cb89, 0x786f4ab4, 0x7866c53a, 0x785e3b1c, 0x7855ac5a,
+  0x784d18f4, 0x784480ea,
+  0x783be43e, 0x783342ef, 0x782a9cfe, 0x7821f26b, 0x78194336, 0x78108f60,
+  0x7807d6e9, 0x77ff19d1,
+  0x77f65819, 0x77ed91c0, 0x77e4c6c9, 0x77dbf732, 0x77d322fc, 0x77ca4a27,
+  0x77c16cb4, 0x77b88aa3,
+  0x77afa3f5, 0x77a6b8a9, 0x779dc8c0, 0x7794d43b, 0x778bdb19, 0x7782dd5c,
+  0x7779db03, 0x7770d40f,
+  0x7767c880, 0x775eb857, 0x7755a394, 0x774c8a36, 0x77436c40, 0x773a49b0,
+  0x77312287, 0x7727f6c6,
+  0x771ec66e, 0x7715917d, 0x770c57f5, 0x770319d6, 0x76f9d721, 0x76f08fd5,
+  0x76e743f4, 0x76ddf37c,
+  0x76d49e70, 0x76cb44cf, 0x76c1e699, 0x76b883d0, 0x76af1c72, 0x76a5b082,
+  0x769c3ffe, 0x7692cae8,
+  0x7689513f, 0x767fd304, 0x76765038, 0x766cc8db, 0x76633ced, 0x7659ac6f,
+  0x76501760, 0x76467dc2,
+  0x763cdf94, 0x76333cd8, 0x7629958c, 0x761fe9b3, 0x7616394c, 0x760c8457,
+  0x7602cad5, 0x75f90cc7,
+  0x75ef4a2c, 0x75e58305, 0x75dbb753, 0x75d1e715, 0x75c8124d, 0x75be38fa,
+  0x75b45b1d, 0x75aa78b6,
+  0x75a091c6, 0x7596a64d, 0x758cb64c, 0x7582c1c2, 0x7578c8b0, 0x756ecb18,
+  0x7564c8f8, 0x755ac251,
+  0x7550b725, 0x7546a772, 0x753c933a, 0x75327a7d, 0x75285d3b, 0x751e3b75,
+  0x7514152b, 0x7509ea5d,
+  0x74ffbb0d, 0x74f58739, 0x74eb4ee3, 0x74e1120c, 0x74d6d0b2, 0x74cc8ad8,
+  0x74c2407d, 0x74b7f1a1,
+  0x74ad9e46, 0x74a3466b, 0x7498ea11, 0x748e8938, 0x748423e0, 0x7479ba0b,
+  0x746f4bb8, 0x7464d8e8,
+  0x745a619b, 0x744fe5d2, 0x7445658d, 0x743ae0cc, 0x74305790, 0x7425c9da,
+  0x741b37a9, 0x7410a0fe,
+  0x740605d9, 0x73fb663c, 0x73f0c226, 0x73e61997, 0x73db6c91, 0x73d0bb13,
+  0x73c6051f, 0x73bb4ab3,
+  0x73b08bd1, 0x73a5c87a, 0x739b00ad, 0x7390346b, 0x738563b5, 0x737a8e8a,
+  0x736fb4ec, 0x7364d6da,
+  0x7359f456, 0x734f0d5f, 0x734421f6, 0x7339321b, 0x732e3dcf, 0x73234512,
+  0x731847e5, 0x730d4648,
+  0x7302403c, 0x72f735c0, 0x72ec26d6, 0x72e1137d, 0x72d5fbb7, 0x72cadf83,
+  0x72bfbee3, 0x72b499d6,
+  0x72a9705c, 0x729e4277, 0x72931027, 0x7287d96c, 0x727c9e47, 0x72715eb8,
+  0x72661abf, 0x725ad25d,
+  0x724f8593, 0x72443460, 0x7238dec5, 0x722d84c4, 0x7222265b, 0x7216c38c,
+  0x720b5c57, 0x71fff0bc,
+  0x71f480bc, 0x71e90c57, 0x71dd938f, 0x71d21662, 0x71c694d2, 0x71bb0edf,
+  0x71af848a, 0x71a3f5d2,
+  0x719862b9, 0x718ccb3f, 0x71812f65, 0x71758f29, 0x7169ea8f, 0x715e4194,
+  0x7152943b, 0x7146e284,
+  0x713b2c6e, 0x712f71fb, 0x7123b32b, 0x7117effe, 0x710c2875, 0x71005c90,
+  0x70f48c50, 0x70e8b7b5,
+  0x70dcdec0, 0x70d10171, 0x70c51fc8, 0x70b939c7, 0x70ad4f6d, 0x70a160ba,
+  0x70956db1, 0x70897650,
+  0x707d7a98, 0x70717a8a, 0x70657626, 0x70596d6d, 0x704d6060, 0x70414efd,
+  0x70353947, 0x70291f3e,
+  0x701d00e1, 0x7010de32, 0x7004b731, 0x6ff88bde, 0x6fec5c3b, 0x6fe02846,
+  0x6fd3f001, 0x6fc7b36d,
+  0x6fbb728a, 0x6faf2d57, 0x6fa2e3d7, 0x6f969608, 0x6f8a43ed, 0x6f7ded84,
+  0x6f7192cf, 0x6f6533ce,
+  0x6f58d082, 0x6f4c68eb, 0x6f3ffd09, 0x6f338cde, 0x6f271868, 0x6f1a9faa,
+  0x6f0e22a3, 0x6f01a155,
+  0x6ef51bbe, 0x6ee891e1, 0x6edc03bc, 0x6ecf7152, 0x6ec2daa2, 0x6eb63fad,
+  0x6ea9a073, 0x6e9cfcf5,
+  0x6e905534, 0x6e83a92f, 0x6e76f8e7, 0x6e6a445d, 0x6e5d8b91, 0x6e50ce84,
+  0x6e440d37, 0x6e3747a9,
+  0x6e2a7ddb, 0x6e1dafce, 0x6e10dd82, 0x6e0406f8, 0x6df72c30, 0x6dea4d2b,
+  0x6ddd69e9, 0x6dd0826a,
+  0x6dc396b0, 0x6db6a6ba, 0x6da9b28a, 0x6d9cba1f, 0x6d8fbd7a, 0x6d82bc9d,
+  0x6d75b786, 0x6d68ae37,
+  0x6d5ba0b0, 0x6d4e8ef2, 0x6d4178fd, 0x6d345ed1, 0x6d274070, 0x6d1a1dda,
+  0x6d0cf70f, 0x6cffcc0f,
+  0x6cf29cdc, 0x6ce56975, 0x6cd831dc, 0x6ccaf610, 0x6cbdb613, 0x6cb071e4,
+  0x6ca32985, 0x6c95dcf6,
+  0x6c888c36, 0x6c7b3748, 0x6c6dde2b, 0x6c6080e0, 0x6c531f67, 0x6c45b9c1,
+  0x6c384fef, 0x6c2ae1f0,
+  0x6c1d6fc6, 0x6c0ff971, 0x6c027ef1, 0x6bf50047, 0x6be77d74, 0x6bd9f677,
+  0x6bcc6b53, 0x6bbedc06,
+  0x6bb14892, 0x6ba3b0f7, 0x6b961536, 0x6b88754f, 0x6b7ad142, 0x6b6d2911,
+  0x6b5f7cbc, 0x6b51cc42,
+  0x6b4417a6, 0x6b365ee7, 0x6b28a206, 0x6b1ae103, 0x6b0d1bdf, 0x6aff529a,
+  0x6af18536, 0x6ae3b3b2,
+  0x6ad5de0f, 0x6ac8044e, 0x6aba266e, 0x6aac4472, 0x6a9e5e58, 0x6a907423,
+  0x6a8285d1, 0x6a749365,
+  0x6a669cdd, 0x6a58a23c, 0x6a4aa381, 0x6a3ca0ad, 0x6a2e99c0, 0x6a208ebb,
+  0x6a127f9f, 0x6a046c6c,
+  0x69f65523, 0x69e839c4, 0x69da1a50, 0x69cbf6c7, 0x69bdcf29, 0x69afa378,
+  0x69a173b5, 0x69933fde,
+  0x698507f6, 0x6976cbfc, 0x69688bf1, 0x695a47d6, 0x694bffab, 0x693db371,
+  0x692f6328, 0x69210ed1,
+  0x6912b66c, 0x690459fb, 0x68f5f97d, 0x68e794f3, 0x68d92c5d, 0x68cabfbd,
+  0x68bc4f13, 0x68adda5f,
+  0x689f61a1, 0x6890e4dc, 0x6882640e, 0x6873df38, 0x6865565c, 0x6856c979,
+  0x68483891, 0x6839a3a4,
+  0x682b0ab1, 0x681c6dbb, 0x680dccc1, 0x67ff27c4, 0x67f07ec5, 0x67e1d1c4,
+  0x67d320c1, 0x67c46bbe,
+  0x67b5b2bb, 0x67a6f5b8, 0x679834b6, 0x67896fb6, 0x677aa6b8, 0x676bd9bd,
+  0x675d08c4, 0x674e33d0,
+  0x673f5ae0, 0x67307df5, 0x67219d10, 0x6712b831, 0x6703cf58, 0x66f4e287,
+  0x66e5f1be, 0x66d6fcfd,
+  0x66c80445, 0x66b90797, 0x66aa06f3, 0x669b0259, 0x668bf9cb, 0x667ced49,
+  0x666ddcd3, 0x665ec86b,
+  0x664fb010, 0x664093c3, 0x66317385, 0x66224f56, 0x66132738, 0x6603fb2a,
+  0x65f4cb2d, 0x65e59742,
+  0x65d65f69, 0x65c723a3, 0x65b7e3f1, 0x65a8a052, 0x659958c9, 0x658a0d54,
+  0x657abdf6, 0x656b6aae,
+  0x655c137d, 0x654cb863, 0x653d5962, 0x652df679, 0x651e8faa, 0x650f24f5,
+  0x64ffb65b, 0x64f043dc,
+  0x64e0cd78, 0x64d15331, 0x64c1d507, 0x64b252fa, 0x64a2cd0c, 0x6493433c,
+  0x6483b58c, 0x647423fb,
+  0x64648e8c, 0x6454f53d, 0x64455810, 0x6435b706, 0x6426121e, 0x6416695a,
+  0x6406bcba, 0x63f70c3f,
+  0x63e757ea, 0x63d79fba, 0x63c7e3b1, 0x63b823cf, 0x63a86015, 0x63989884,
+  0x6388cd1b, 0x6378fddc,
+  0x63692ac7, 0x635953dd, 0x6349791f, 0x63399a8d, 0x6329b827, 0x6319d1ef,
+  0x6309e7e4, 0x62f9fa09,
+  0x62ea085c, 0x62da12df, 0x62ca1992, 0x62ba1c77, 0x62aa1b8d, 0x629a16d5,
+  0x628a0e50, 0x627a01fe,
+  0x6269f1e1, 0x6259ddf8, 0x6249c645, 0x6239aac7, 0x62298b81, 0x62196871,
+  0x62094199, 0x61f916f9,
+  0x61e8e893, 0x61d8b666, 0x61c88074, 0x61b846bc, 0x61a80940, 0x6197c800,
+  0x618782fd, 0x61773a37,
+  0x6166edb0, 0x61569d67, 0x6146495d, 0x6135f193, 0x6125960a, 0x611536c2,
+  0x6104d3bc, 0x60f46cf9,
+  0x60e40278, 0x60d3943b, 0x60c32243, 0x60b2ac8f, 0x60a23322, 0x6091b5fa,
+  0x60813519, 0x6070b080,
+  0x6060282f, 0x604f9c27, 0x603f0c69, 0x602e78f4, 0x601de1ca, 0x600d46ec,
+  0x5ffca859, 0x5fec0613,
+  0x5fdb601b, 0x5fcab670, 0x5fba0914, 0x5fa95807, 0x5f98a34a, 0x5f87eade,
+  0x5f772ec2, 0x5f666ef9,
+  0x5f55ab82, 0x5f44e45e, 0x5f34198e, 0x5f234b12, 0x5f1278eb, 0x5f01a31a,
+  0x5ef0c99f, 0x5edfec7b,
+  0x5ecf0baf, 0x5ebe273b, 0x5ead3f1f, 0x5e9c535e, 0x5e8b63f7, 0x5e7a70ea,
+  0x5e697a39, 0x5e587fe5,
+  0x5e4781ed, 0x5e368053, 0x5e257b17, 0x5e147239, 0x5e0365bb, 0x5df2559e,
+  0x5de141e1, 0x5dd02a85,
+  0x5dbf0f8c, 0x5dadf0f5, 0x5d9ccec2, 0x5d8ba8f3, 0x5d7a7f88, 0x5d695283,
+  0x5d5821e4, 0x5d46edac,
+  0x5d35b5db, 0x5d247a72, 0x5d133b72, 0x5d01f8dc, 0x5cf0b2af, 0x5cdf68ed,
+  0x5cce1b97, 0x5cbccaac,
+  0x5cab762f, 0x5c9a1e1e, 0x5c88c27c, 0x5c776348, 0x5c660084, 0x5c549a30,
+  0x5c43304d, 0x5c31c2db,
+  0x5c2051db, 0x5c0edd4e, 0x5bfd6534, 0x5bebe98e, 0x5bda6a5d, 0x5bc8e7a2,
+  0x5bb7615d, 0x5ba5d78e,
+  0x5b944a37, 0x5b82b958, 0x5b7124f2, 0x5b5f8d06, 0x5b4df193, 0x5b3c529c,
+  0x5b2ab020, 0x5b190a20,
+  0x5b07609d, 0x5af5b398, 0x5ae40311, 0x5ad24f09, 0x5ac09781, 0x5aaedc78,
+  0x5a9d1df1, 0x5a8b5bec,
+  0x5a799669, 0x5a67cd69, 0x5a5600ec, 0x5a4430f5, 0x5a325d82, 0x5a208695,
+  0x5a0eac2e, 0x59fcce4f,
+  0x59eaecf8, 0x59d90829, 0x59c71fe3, 0x59b53427, 0x59a344f6, 0x59915250,
+  0x597f5c36, 0x596d62a9,
+  0x595b65aa, 0x59496538, 0x59376155, 0x59255a02, 0x59134f3e, 0x5901410c,
+  0x58ef2f6b, 0x58dd1a5d,
+  0x58cb01e1, 0x58b8e5f9, 0x58a6c6a5, 0x5894a3e7, 0x58827dbe, 0x5870542c,
+  0x585e2730, 0x584bf6cd,
+  0x5839c302, 0x58278bd1, 0x58155139, 0x5803133c, 0x57f0d1da, 0x57de8d15,
+  0x57cc44ec, 0x57b9f960,
+  0x57a7aa73, 0x57955825, 0x57830276, 0x5770a968, 0x575e4cfa, 0x574bed2f,
+  0x57398a05, 0x5727237f,
+  0x5714b99d, 0x57024c5f, 0x56efdbc7, 0x56dd67d4, 0x56caf088, 0x56b875e4,
+  0x56a5f7e7, 0x56937694,
+  0x5680f1ea, 0x566e69ea, 0x565bde95, 0x56494fec, 0x5636bdef, 0x5624289f,
+  0x56118ffe, 0x55fef40a,
+  0x55ec54c6, 0x55d9b232, 0x55c70c4f, 0x55b4631d, 0x55a1b69d, 0x558f06d0,
+  0x557c53b6, 0x55699d51,
+  0x5556e3a1, 0x554426a7, 0x55316663, 0x551ea2d6, 0x550bdc01, 0x54f911e5,
+  0x54e64482, 0x54d373d9,
+  0x54c09feb, 0x54adc8b8, 0x549aee42, 0x54881089, 0x54752f8d, 0x54624b50,
+  0x544f63d2, 0x543c7914,
+  0x54298b17, 0x541699db, 0x5403a561, 0x53f0adaa, 0x53ddb2b6, 0x53cab486,
+  0x53b7b31c, 0x53a4ae77,
+  0x5391a699, 0x537e9b82, 0x536b8d33, 0x53587bad, 0x534566f0, 0x53324efd,
+  0x531f33d5, 0x530c1579,
+  0x52f8f3e9, 0x52e5cf27, 0x52d2a732, 0x52bf7c0b, 0x52ac4db4, 0x52991c2d,
+  0x5285e777, 0x5272af92,
+  0x525f7480, 0x524c3640, 0x5238f4d4, 0x5225b03d, 0x5212687b, 0x51ff1d8f,
+  0x51ebcf7a, 0x51d87e3c,
+  0x51c529d7, 0x51b1d24a, 0x519e7797, 0x518b19bf, 0x5177b8c2, 0x516454a0,
+  0x5150ed5c, 0x513d82f4,
+  0x512a156b, 0x5116a4c1, 0x510330f7, 0x50efba0d, 0x50dc4005, 0x50c8c2de,
+  0x50b5429a, 0x50a1bf39,
+  0x508e38bd, 0x507aaf25, 0x50672273, 0x505392a8, 0x503fffc4, 0x502c69c8,
+  0x5018d0b4, 0x5005348a,
+  0x4ff1954b, 0x4fddf2f6, 0x4fca4d8d, 0x4fb6a510, 0x4fa2f981, 0x4f8f4ae0,
+  0x4f7b992d, 0x4f67e46a,
+  0x4f542c98, 0x4f4071b6, 0x4f2cb3c7, 0x4f18f2c9, 0x4f052ec0, 0x4ef167aa,
+  0x4edd9d89, 0x4ec9d05e,
+  0x4eb60029, 0x4ea22ceb, 0x4e8e56a5, 0x4e7a7d58, 0x4e66a105, 0x4e52c1ab,
+  0x4e3edf4d, 0x4e2af9ea,
+  0x4e171184, 0x4e03261b, 0x4def37b0, 0x4ddb4644, 0x4dc751d8, 0x4db35a6c,
+  0x4d9f6001, 0x4d8b6298,
+  0x4d776231, 0x4d635ece, 0x4d4f5870, 0x4d3b4f16, 0x4d2742c2, 0x4d133374,
+  0x4cff212e, 0x4ceb0bf0,
+  0x4cd6f3bb, 0x4cc2d88f, 0x4caeba6e, 0x4c9a9958, 0x4c86754e, 0x4c724e50,
+  0x4c5e2460, 0x4c49f77f,
+  0x4c35c7ac, 0x4c2194e9, 0x4c0d5f37, 0x4bf92697, 0x4be4eb08, 0x4bd0ac8d,
+  0x4bbc6b25, 0x4ba826d1,
+  0x4b93df93, 0x4b7f956b, 0x4b6b485a, 0x4b56f861, 0x4b42a580, 0x4b2e4fb8,
+  0x4b19f70a, 0x4b059b77,
+  0x4af13d00, 0x4adcdba5, 0x4ac87767, 0x4ab41046, 0x4a9fa645, 0x4a8b3963,
+  0x4a76c9a2, 0x4a625701,
+  0x4a4de182, 0x4a396926, 0x4a24edee, 0x4a106fda, 0x49fbeeea, 0x49e76b21,
+  0x49d2e47e, 0x49be5b02,
+  0x49a9ceaf, 0x49953f84, 0x4980ad84, 0x496c18ae, 0x49578103, 0x4942e684,
+  0x492e4933, 0x4919a90f,
+  0x4905061a, 0x48f06054, 0x48dbb7be, 0x48c70c59, 0x48b25e25, 0x489dad25,
+  0x4888f957, 0x487442be,
+  0x485f8959, 0x484acd2a, 0x48360e32, 0x48214c71, 0x480c87e8, 0x47f7c099,
+  0x47e2f682, 0x47ce29a7,
+  0x47b95a06, 0x47a487a2, 0x478fb27b, 0x477ada91, 0x4765ffe6, 0x4751227a,
+  0x473c424e, 0x47275f63,
+  0x471279ba, 0x46fd9154, 0x46e8a631, 0x46d3b852, 0x46bec7b8, 0x46a9d464,
+  0x4694de56, 0x467fe590,
+  0x466aea12, 0x4655ebdd, 0x4640eaf2, 0x462be751, 0x4616e0fc, 0x4601d7f3,
+  0x45eccc37, 0x45d7bdc9,
+  0x45c2acaa, 0x45ad98da, 0x4598825a, 0x4583692c, 0x456e4d4f, 0x45592ec6,
+  0x45440d90, 0x452ee9ae,
+  0x4519c321, 0x450499eb, 0x44ef6e0b, 0x44da3f83, 0x44c50e53, 0x44afda7d,
+  0x449aa400, 0x44856adf,
+  0x44702f19, 0x445af0b0, 0x4445afa4, 0x44306bf6, 0x441b25a8, 0x4405dcb9,
+  0x43f0912b, 0x43db42fe,
+  0x43c5f234, 0x43b09ecc, 0x439b48c9, 0x4385f02a, 0x437094f1, 0x435b371f,
+  0x4345d6b3, 0x433073b0,
+  0x431b0e15, 0x4305a5e5, 0x42f03b1e, 0x42dacdc3, 0x42c55dd4, 0x42afeb53,
+  0x429a763f, 0x4284fe99,
+  0x426f8463, 0x425a079e, 0x42448849, 0x422f0667, 0x421981f7, 0x4203fafb,
+  0x41ee7174, 0x41d8e561,
+  0x41c356c5, 0x41adc5a0, 0x419831f3, 0x41829bbe, 0x416d0302, 0x415767c1,
+  0x4141c9fb, 0x412c29b1,
+  0x411686e4, 0x4100e194, 0x40eb39c3, 0x40d58f71, 0x40bfe29f, 0x40aa334e,
+  0x4094817f, 0x407ecd32,
+  0x40691669, 0x40535d24, 0x403da165, 0x4027e32b, 0x40122278, 0x3ffc5f4d,
+  0x3fe699aa, 0x3fd0d191,
+  0x3fbb0702, 0x3fa539fd, 0x3f8f6a85, 0x3f799899, 0x3f63c43b, 0x3f4ded6b,
+  0x3f38142a, 0x3f22387a,
+  0x3f0c5a5a, 0x3ef679cc, 0x3ee096d1, 0x3ecab169, 0x3eb4c995, 0x3e9edf57,
+  0x3e88f2ae, 0x3e73039d,
+  0x3e5d1222, 0x3e471e41, 0x3e3127f9, 0x3e1b2f4a, 0x3e053437, 0x3def36c0,
+  0x3dd936e6, 0x3dc334a9,
+  0x3dad300b, 0x3d97290b, 0x3d811fac, 0x3d6b13ee, 0x3d5505d2, 0x3d3ef559,
+  0x3d28e282, 0x3d12cd51,
+  0x3cfcb5c4, 0x3ce69bde, 0x3cd07f9f, 0x3cba6107, 0x3ca44018, 0x3c8e1cd3,
+  0x3c77f737, 0x3c61cf48,
+  0x3c4ba504, 0x3c35786d, 0x3c1f4983, 0x3c091849, 0x3bf2e4be, 0x3bdcaee3,
+  0x3bc676b9, 0x3bb03c42,
+  0x3b99ff7d, 0x3b83c06c, 0x3b6d7f10, 0x3b573b69, 0x3b40f579, 0x3b2aad3f,
+  0x3b1462be, 0x3afe15f6,
+  0x3ae7c6e7, 0x3ad17593, 0x3abb21fb, 0x3aa4cc1e, 0x3a8e7400, 0x3a78199f,
+  0x3a61bcfd, 0x3a4b5e1b,
+  0x3a34fcf9, 0x3a1e9999, 0x3a0833fc, 0x39f1cc21, 0x39db620b, 0x39c4f5ba,
+  0x39ae872f, 0x3998166a,
+  0x3981a36d, 0x396b2e38, 0x3954b6cd, 0x393e3d2c, 0x3927c155, 0x3911434b,
+  0x38fac30e, 0x38e4409e,
+  0x38cdbbfc, 0x38b7352a, 0x38a0ac29, 0x388a20f8, 0x38739399, 0x385d040d,
+  0x38467255, 0x382fde72,
+  0x38194864, 0x3802b02c, 0x37ec15cb, 0x37d57943, 0x37beda93, 0x37a839be,
+  0x379196c3, 0x377af1a3,
+  0x37644a60, 0x374da0fa, 0x3736f573, 0x372047ca, 0x37099802, 0x36f2e61a,
+  0x36dc3214, 0x36c57bf0,
+  0x36aec3b0, 0x36980954, 0x36814cde, 0x366a8e4d, 0x3653cda3, 0x363d0ae2,
+  0x36264609, 0x360f7f19,
+  0x35f8b614, 0x35e1eafa, 0x35cb1dcc, 0x35b44e8c, 0x359d7d39, 0x3586a9d5,
+  0x356fd461, 0x3558fcde,
+  0x3542234c, 0x352b47ad, 0x35146a00, 0x34fd8a48, 0x34e6a885, 0x34cfc4b7,
+  0x34b8dee1, 0x34a1f702,
+  0x348b0d1c, 0x3474212f, 0x345d333c, 0x34464345, 0x342f5149, 0x34185d4b,
+  0x3401674a, 0x33ea6f48,
+  0x33d37546, 0x33bc7944, 0x33a57b44, 0x338e7b46, 0x3377794b, 0x33607554,
+  0x33496f62, 0x33326776,
+  0x331b5d91, 0x330451b3, 0x32ed43de, 0x32d63412, 0x32bf2250, 0x32a80e99,
+  0x3290f8ef, 0x3279e151,
+  0x3262c7c1, 0x324bac40, 0x32348ecf, 0x321d6f6e, 0x32064e1e, 0x31ef2ae1,
+  0x31d805b7, 0x31c0dea1,
+  0x31a9b5a0, 0x31928ab4, 0x317b5de0, 0x31642f23, 0x314cfe7f, 0x3135cbf4,
+  0x311e9783, 0x3107612e,
+  0x30f028f4, 0x30d8eed8, 0x30c1b2da, 0x30aa74fa, 0x3093353a, 0x307bf39b,
+  0x3064b01d, 0x304d6ac1,
+  0x30362389, 0x301eda75, 0x30078f86, 0x2ff042bd, 0x2fd8f41b, 0x2fc1a3a0,
+  0x2faa514f, 0x2f92fd26,
+  0x2f7ba729, 0x2f644f56, 0x2f4cf5b0, 0x2f359a37, 0x2f1e3ced, 0x2f06ddd1,
+  0x2eef7ce5, 0x2ed81a29,
+  0x2ec0b5a0, 0x2ea94f49, 0x2e91e725, 0x2e7a7d36, 0x2e63117c, 0x2e4ba3f8,
+  0x2e3434ac, 0x2e1cc397,
+  0x2e0550bb, 0x2deddc19, 0x2dd665b2, 0x2dbeed86, 0x2da77397, 0x2d8ff7e5,
+  0x2d787a72, 0x2d60fb3e,
+  0x2d497a4a, 0x2d31f797, 0x2d1a7325, 0x2d02ecf7, 0x2ceb650d, 0x2cd3db67,
+  0x2cbc5006, 0x2ca4c2ed,
+  0x2c8d341a, 0x2c75a390, 0x2c5e114f, 0x2c467d58, 0x2c2ee7ad, 0x2c17504d,
+  0x2bffb73a, 0x2be81c74,
+  0x2bd07ffe, 0x2bb8e1d7, 0x2ba14200, 0x2b89a07b, 0x2b71fd48, 0x2b5a5868,
+  0x2b42b1dd, 0x2b2b09a6,
+  0x2b135fc6, 0x2afbb43c, 0x2ae4070a, 0x2acc5831, 0x2ab4a7b1, 0x2a9cf58c,
+  0x2a8541c3, 0x2a6d8c55,
+  0x2a55d545, 0x2a3e1c93, 0x2a266240, 0x2a0ea64d, 0x29f6e8bb, 0x29df298b,
+  0x29c768be, 0x29afa654,
+  0x2997e24f, 0x29801caf, 0x29685576, 0x29508ca4, 0x2938c23a, 0x2920f63a,
+  0x290928a3, 0x28f15978,
+  0x28d988b8, 0x28c1b666, 0x28a9e281, 0x28920d0a, 0x287a3604, 0x28625d6d,
+  0x284a8349, 0x2832a796,
+  0x281aca57, 0x2802eb8c, 0x27eb0b36, 0x27d32956, 0x27bb45ed, 0x27a360fc,
+  0x278b7a84, 0x27739285,
+  0x275ba901, 0x2743bdf9, 0x272bd16d, 0x2713e35f, 0x26fbf3ce, 0x26e402bd,
+  0x26cc102d, 0x26b41c1d,
+  0x269c268f, 0x26842f84, 0x266c36fe, 0x26543cfb, 0x263c417f, 0x26244489,
+  0x260c461b, 0x25f44635,
+  0x25dc44d9, 0x25c44207, 0x25ac3dc0, 0x25943806, 0x257c30d8, 0x25642839,
+  0x254c1e28, 0x253412a8,
+  0x251c05b8, 0x2503f75a, 0x24ebe78f, 0x24d3d657, 0x24bbc3b4, 0x24a3afa6,
+  0x248b9a2f, 0x2473834f,
+  0x245b6b07, 0x24435158, 0x242b3644, 0x241319ca, 0x23fafbec, 0x23e2dcac,
+  0x23cabc09, 0x23b29a05,
+  0x239a76a0, 0x238251dd, 0x236a2bba, 0x2352043b, 0x2339db5e, 0x2321b126,
+  0x23098593, 0x22f158a7,
+  0x22d92a61, 0x22c0fac4, 0x22a8c9cf, 0x22909785, 0x227863e5, 0x22602ef1,
+  0x2247f8aa, 0x222fc111,
+  0x22178826, 0x21ff4dea, 0x21e71260, 0x21ced586, 0x21b6975f, 0x219e57eb,
+  0x2186172b, 0x216dd521,
+  0x215591cc, 0x213d4d2f, 0x21250749, 0x210cc01d, 0x20f477aa, 0x20dc2df2,
+  0x20c3e2f5, 0x20ab96b5,
+  0x20934933, 0x207afa6f, 0x2062aa6b, 0x204a5927, 0x203206a4, 0x2019b2e4,
+  0x20015de7, 0x1fe907ae,
+  0x1fd0b03a, 0x1fb8578b, 0x1f9ffda4, 0x1f87a285, 0x1f6f462f, 0x1f56e8a2,
+  0x1f3e89e0, 0x1f2629ea,
+  0x1f0dc8c0, 0x1ef56664, 0x1edd02d6, 0x1ec49e17, 0x1eac3829, 0x1e93d10c,
+  0x1e7b68c2, 0x1e62ff4a,
+  0x1e4a94a7, 0x1e3228d9, 0x1e19bbe0, 0x1e014dbf, 0x1de8de75, 0x1dd06e04,
+  0x1db7fc6d, 0x1d9f89b1,
+  0x1d8715d0, 0x1d6ea0cc, 0x1d562aa6, 0x1d3db35e, 0x1d253af5, 0x1d0cc16c,
+  0x1cf446c5, 0x1cdbcb00,
+  0x1cc34e1f, 0x1caad021, 0x1c925109, 0x1c79d0d6, 0x1c614f8b, 0x1c48cd27,
+  0x1c3049ac, 0x1c17c51b,
+  0x1bff3f75, 0x1be6b8ba, 0x1bce30ec, 0x1bb5a80c, 0x1b9d1e1a, 0x1b849317,
+  0x1b6c0705, 0x1b5379e5,
+  0x1b3aebb6, 0x1b225c7b, 0x1b09cc34, 0x1af13ae3, 0x1ad8a887, 0x1ac01522,
+  0x1aa780b6, 0x1a8eeb42,
+  0x1a7654c8, 0x1a5dbd49, 0x1a4524c6, 0x1a2c8b3f, 0x1a13f0b6, 0x19fb552c,
+  0x19e2b8a2, 0x19ca1b17,
+  0x19b17c8f, 0x1998dd09, 0x19803c86, 0x19679b07, 0x194ef88e, 0x1936551b,
+  0x191db0af, 0x19050b4b,
+  0x18ec64f0, 0x18d3bda0, 0x18bb155a, 0x18a26c20, 0x1889c1f3, 0x187116d4,
+  0x18586ac3, 0x183fbdc3,
+  0x18270fd3, 0x180e60f4, 0x17f5b129, 0x17dd0070, 0x17c44ecd, 0x17ab9c3e,
+  0x1792e8c6, 0x177a3466,
+  0x17617f1d, 0x1748c8ee, 0x173011d9, 0x171759df, 0x16fea102, 0x16e5e741,
+  0x16cd2c9f, 0x16b4711b,
+  0x169bb4b7, 0x1682f774, 0x166a3953, 0x16517a55, 0x1638ba7a, 0x161ff9c4,
+  0x16073834, 0x15ee75cb,
+  0x15d5b288, 0x15bcee6f, 0x15a4297f, 0x158b63b9, 0x15729d1f, 0x1559d5b1,
+  0x15410d70, 0x1528445d,
+  0x150f7a7a, 0x14f6afc7, 0x14dde445, 0x14c517f4, 0x14ac4ad7, 0x14937cee,
+  0x147aae3a, 0x1461debc,
+  0x14490e74, 0x14303d65, 0x14176b8e, 0x13fe98f1, 0x13e5c58e, 0x13ccf167,
+  0x13b41c7d, 0x139b46d0,
+  0x13827062, 0x13699933, 0x1350c144, 0x1337e897, 0x131f0f2c, 0x13063505,
+  0x12ed5a21, 0x12d47e83,
+  0x12bba22b, 0x12a2c51b, 0x1289e752, 0x127108d2, 0x1258299c, 0x123f49b2,
+  0x12266913, 0x120d87c1,
+  0x11f4a5bd, 0x11dbc307, 0x11c2dfa2, 0x11a9fb8d, 0x119116c9, 0x11783159,
+  0x115f4b3c, 0x11466473,
+  0x112d7d00, 0x111494e4, 0x10fbac1e, 0x10e2c2b2, 0x10c9d89e, 0x10b0ede5,
+  0x10980287, 0x107f1686,
+  0x106629e1, 0x104d3c9b, 0x10344eb4, 0x101b602d, 0x10027107, 0xfe98143,
+  0xfd090e1, 0xfb79fe4,
+  0xf9eae4c, 0xf85bc19, 0xf6cc94e, 0xf53d5ea, 0xf3ae1ee, 0xf21ed5d, 0xf08f836,
+  0xef0027b,
+  0xed70c2c, 0xebe154b, 0xea51dd8, 0xe8c25d5, 0xe732d42, 0xe5a3421, 0xe413a72,
+  0xe284036,
+  0xe0f456f, 0xdf64a1c, 0xddd4e40, 0xdc451dc, 0xdab54ef, 0xd92577b, 0xd795982,
+  0xd605b03,
+  0xd475c00, 0xd2e5c7b, 0xd155c73, 0xcfc5bea, 0xce35ae1, 0xcca5959, 0xcb15752,
+  0xc9854cf,
+  0xc7f51cf, 0xc664e53, 0xc4d4a5d, 0xc3445ee, 0xc1b4107, 0xc023ba7, 0xbe935d2,
+  0xbd02f87,
+  0xbb728c7, 0xb9e2193, 0xb8519ed, 0xb6c11d5, 0xb53094d, 0xb3a0055, 0xb20f6ee,
+  0xb07ed19,
+  0xaeee2d7, 0xad5d829, 0xabccd11, 0xaa3c18e, 0xa8ab5a2, 0xa71a94f, 0xa589c94,
+  0xa3f8f73,
+  0xa2681ed, 0xa0d7403, 0x9f465b5, 0x9db5706, 0x9c247f5, 0x9a93884, 0x99028b3,
+  0x9771884,
+  0x95e07f8, 0x944f70f, 0x92be5ca, 0x912d42c, 0x8f9c233, 0x8e0afe2, 0x8c79d3a,
+  0x8ae8a3a,
+  0x89576e5, 0x87c633c, 0x8634f3e, 0x84a3aee, 0x831264c, 0x8181159, 0x7fefc16,
+  0x7e5e685,
+  0x7ccd0a5, 0x7b3ba78, 0x79aa400, 0x7818d3c, 0x768762e, 0x74f5ed7, 0x7364738,
+  0x71d2f52,
+  0x7041726, 0x6eafeb4, 0x6d1e5fe, 0x6b8cd05, 0x69fb3c9, 0x6869a4c, 0x66d808f,
+  0x6546692,
+  0x63b4c57, 0x62231de, 0x6091729, 0x5effc38, 0x5d6e10c, 0x5bdc5a7, 0x5a4aa09,
+  0x58b8e34,
+  0x5727228, 0x55955e6, 0x540396f, 0x5271cc4, 0x50dffe7, 0x4f4e2d8, 0x4dbc597,
+  0x4c2a827,
+  0x4a98a88, 0x4906cbb, 0x4774ec1, 0x45e309a, 0x4451249, 0x42bf3cd, 0x412d528,
+  0x3f9b65b,
+  0x3e09767, 0x3c7784d, 0x3ae590d, 0x39539a9, 0x37c1a22, 0x362fa78, 0x349daac,
+  0x330bac1,
+  0x3179ab5, 0x2fe7a8c, 0x2e55a44, 0x2cc39e1, 0x2b31961, 0x299f8c7, 0x280d813,
+  0x267b747,
+  0x24e9662, 0x2357567, 0x21c5457, 0x2033331, 0x1ea11f7, 0x1d0f0ab, 0x1b7cf4d,
+  0x19eaddd,
+  0x1858c5e, 0x16c6ad0, 0x1534934, 0x13a278a, 0x12105d5, 0x107e414, 0xeec249,
+  0xd5a075,
+  0xbc7e99, 0xa35cb5, 0x8a3acb, 0x7118dc, 0x57f6e9, 0x3ed4f2, 0x25b2f8,
+  0xc90fe,
+
+};
+
+static const q31_t cos_factorsQ31_8192[8192] = {
+  0x7ffffff6, 0x7fffffa7, 0x7fffff09, 0x7ffffe1c, 0x7ffffce1, 0x7ffffb56,
+    0x7ffff97c, 0x7ffff753,
+  0x7ffff4dc, 0x7ffff215, 0x7fffef00, 0x7fffeb9b, 0x7fffe7e8, 0x7fffe3e5,
+    0x7fffdf94, 0x7fffdaf3,
+  0x7fffd604, 0x7fffd0c6, 0x7fffcb39, 0x7fffc55c, 0x7fffbf31, 0x7fffb8b7,
+    0x7fffb1ee, 0x7fffaad6,
+  0x7fffa36f, 0x7fff9bb9, 0x7fff93b4, 0x7fff8b61, 0x7fff82be, 0x7fff79cc,
+    0x7fff708b, 0x7fff66fc,
+  0x7fff5d1d, 0x7fff52ef, 0x7fff4873, 0x7fff3da8, 0x7fff328d, 0x7fff2724,
+    0x7fff1b6b, 0x7fff0f64,
+  0x7fff030e, 0x7ffef669, 0x7ffee975, 0x7ffedc31, 0x7ffece9f, 0x7ffec0be,
+    0x7ffeb28e, 0x7ffea40f,
+  0x7ffe9542, 0x7ffe8625, 0x7ffe76b9, 0x7ffe66fe, 0x7ffe56f5, 0x7ffe469c,
+    0x7ffe35f4, 0x7ffe24fe,
+  0x7ffe13b8, 0x7ffe0224, 0x7ffdf040, 0x7ffdde0e, 0x7ffdcb8d, 0x7ffdb8bc,
+    0x7ffda59d, 0x7ffd922f,
+  0x7ffd7e72, 0x7ffd6a66, 0x7ffd560b, 0x7ffd4161, 0x7ffd2c68, 0x7ffd1720,
+    0x7ffd0189, 0x7ffceba4,
+  0x7ffcd56f, 0x7ffcbeeb, 0x7ffca819, 0x7ffc90f7, 0x7ffc7987, 0x7ffc61c7,
+    0x7ffc49b9, 0x7ffc315b,
+  0x7ffc18af, 0x7ffbffb4, 0x7ffbe66a, 0x7ffbccd0, 0x7ffbb2e8, 0x7ffb98b1,
+    0x7ffb7e2b, 0x7ffb6356,
+  0x7ffb4833, 0x7ffb2cc0, 0x7ffb10fe, 0x7ffaf4ed, 0x7ffad88e, 0x7ffabbdf,
+    0x7ffa9ee2, 0x7ffa8195,
+  0x7ffa63fa, 0x7ffa460f, 0x7ffa27d6, 0x7ffa094e, 0x7ff9ea76, 0x7ff9cb50,
+    0x7ff9abdb, 0x7ff98c17,
+  0x7ff96c04, 0x7ff94ba2, 0x7ff92af1, 0x7ff909f2, 0x7ff8e8a3, 0x7ff8c705,
+    0x7ff8a519, 0x7ff882dd,
+  0x7ff86053, 0x7ff83d79, 0x7ff81a51, 0x7ff7f6da, 0x7ff7d313, 0x7ff7aefe,
+    0x7ff78a9a, 0x7ff765e7,
+  0x7ff740e5, 0x7ff71b94, 0x7ff6f5f4, 0x7ff6d005, 0x7ff6a9c8, 0x7ff6833b,
+    0x7ff65c5f, 0x7ff63535,
+  0x7ff60dbb, 0x7ff5e5f3, 0x7ff5bddc, 0x7ff59576, 0x7ff56cc0, 0x7ff543bc,
+    0x7ff51a69, 0x7ff4f0c7,
+  0x7ff4c6d6, 0x7ff49c96, 0x7ff47208, 0x7ff4472a, 0x7ff41bfd, 0x7ff3f082,
+    0x7ff3c4b7, 0x7ff3989e,
+  0x7ff36c36, 0x7ff33f7e, 0x7ff31278, 0x7ff2e523, 0x7ff2b77f, 0x7ff2898c,
+    0x7ff25b4a, 0x7ff22cb9,
+  0x7ff1fdd9, 0x7ff1ceab, 0x7ff19f2d, 0x7ff16f61, 0x7ff13f45, 0x7ff10edb,
+    0x7ff0de22, 0x7ff0ad19,
+  0x7ff07bc2, 0x7ff04a1c, 0x7ff01827, 0x7fefe5e4, 0x7fefb351, 0x7fef806f,
+    0x7fef4d3e, 0x7fef19bf,
+  0x7feee5f0, 0x7feeb1d3, 0x7fee7d67, 0x7fee48ac, 0x7fee13a1, 0x7fedde48,
+    0x7feda8a0, 0x7fed72aa,
+  0x7fed3c64, 0x7fed05cf, 0x7fecceec, 0x7fec97b9, 0x7fec6038, 0x7fec2867,
+    0x7febf048, 0x7febb7da,
+  0x7feb7f1d, 0x7feb4611, 0x7feb0cb6, 0x7fead30c, 0x7fea9914, 0x7fea5ecc,
+    0x7fea2436, 0x7fe9e950,
+  0x7fe9ae1c, 0x7fe97299, 0x7fe936c7, 0x7fe8faa6, 0x7fe8be36, 0x7fe88177,
+    0x7fe84469, 0x7fe8070d,
+  0x7fe7c961, 0x7fe78b67, 0x7fe74d1e, 0x7fe70e85, 0x7fe6cf9e, 0x7fe69068,
+    0x7fe650e3, 0x7fe61110,
+  0x7fe5d0ed, 0x7fe5907b, 0x7fe54fbb, 0x7fe50eac, 0x7fe4cd4d, 0x7fe48ba0,
+    0x7fe449a4, 0x7fe40759,
+  0x7fe3c4bf, 0x7fe381d7, 0x7fe33e9f, 0x7fe2fb19, 0x7fe2b743, 0x7fe2731f,
+    0x7fe22eac, 0x7fe1e9ea,
+  0x7fe1a4d9, 0x7fe15f79, 0x7fe119cb, 0x7fe0d3cd, 0x7fe08d81, 0x7fe046e5,
+    0x7fdffffb, 0x7fdfb8c2,
+  0x7fdf713a, 0x7fdf2963, 0x7fdee13e, 0x7fde98c9, 0x7fde5006, 0x7fde06f3,
+    0x7fddbd92, 0x7fdd73e2,
+  0x7fdd29e3, 0x7fdcdf95, 0x7fdc94f9, 0x7fdc4a0d, 0x7fdbfed3, 0x7fdbb349,
+    0x7fdb6771, 0x7fdb1b4a,
+  0x7fdaced4, 0x7fda820f, 0x7fda34fc, 0x7fd9e799, 0x7fd999e8, 0x7fd94be8,
+    0x7fd8fd98, 0x7fd8aefa,
+  0x7fd8600e, 0x7fd810d2, 0x7fd7c147, 0x7fd7716e, 0x7fd72146, 0x7fd6d0cf,
+    0x7fd68009, 0x7fd62ef4,
+  0x7fd5dd90, 0x7fd58bdd, 0x7fd539dc, 0x7fd4e78c, 0x7fd494ed, 0x7fd441ff,
+    0x7fd3eec2, 0x7fd39b36,
+  0x7fd3475c, 0x7fd2f332, 0x7fd29eba, 0x7fd249f3, 0x7fd1f4dd, 0x7fd19f78,
+    0x7fd149c5, 0x7fd0f3c2,
+  0x7fd09d71, 0x7fd046d1, 0x7fcfefe2, 0x7fcf98a4, 0x7fcf4117, 0x7fcee93c,
+    0x7fce9112, 0x7fce3898,
+  0x7fcddfd0, 0x7fcd86b9, 0x7fcd2d54, 0x7fccd39f, 0x7fcc799c, 0x7fcc1f4a,
+    0x7fcbc4a9, 0x7fcb69b9,
+  0x7fcb0e7a, 0x7fcab2ed, 0x7fca5710, 0x7fc9fae5, 0x7fc99e6b, 0x7fc941a2,
+    0x7fc8e48b, 0x7fc88724,
+  0x7fc8296f, 0x7fc7cb6b, 0x7fc76d18, 0x7fc70e76, 0x7fc6af86, 0x7fc65046,
+    0x7fc5f0b8, 0x7fc590db,
+  0x7fc530af, 0x7fc4d035, 0x7fc46f6b, 0x7fc40e53, 0x7fc3acec, 0x7fc34b36,
+    0x7fc2e931, 0x7fc286de,
+  0x7fc2243b, 0x7fc1c14a, 0x7fc15e0a, 0x7fc0fa7b, 0x7fc0969e, 0x7fc03271,
+    0x7fbfcdf6, 0x7fbf692c,
+  0x7fbf0414, 0x7fbe9eac, 0x7fbe38f6, 0x7fbdd2f0, 0x7fbd6c9c, 0x7fbd05fa,
+    0x7fbc9f08, 0x7fbc37c8,
+  0x7fbbd039, 0x7fbb685b, 0x7fbb002e, 0x7fba97b2, 0x7fba2ee8, 0x7fb9c5cf,
+    0x7fb95c67, 0x7fb8f2b0,
+  0x7fb888ab, 0x7fb81e57, 0x7fb7b3b4, 0x7fb748c2, 0x7fb6dd81, 0x7fb671f2,
+    0x7fb60614, 0x7fb599e7,
+  0x7fb52d6b, 0x7fb4c0a1, 0x7fb45387, 0x7fb3e61f, 0x7fb37869, 0x7fb30a63,
+    0x7fb29c0f, 0x7fb22d6c,
+  0x7fb1be7a, 0x7fb14f39, 0x7fb0dfaa, 0x7fb06fcb, 0x7fafff9e, 0x7faf8f23,
+    0x7faf1e58, 0x7faead3f,
+  0x7fae3bd7, 0x7fadca20, 0x7fad581b, 0x7face5c6, 0x7fac7323, 0x7fac0031,
+    0x7fab8cf1, 0x7fab1962,
+  0x7faaa584, 0x7faa3157, 0x7fa9bcdb, 0x7fa94811, 0x7fa8d2f8, 0x7fa85d90,
+    0x7fa7e7d9, 0x7fa771d4,
+  0x7fa6fb80, 0x7fa684dd, 0x7fa60dec, 0x7fa596ac, 0x7fa51f1d, 0x7fa4a73f,
+    0x7fa42f12, 0x7fa3b697,
+  0x7fa33dcd, 0x7fa2c4b5, 0x7fa24b4d, 0x7fa1d197, 0x7fa15792, 0x7fa0dd3f,
+    0x7fa0629c, 0x7f9fe7ab,
+  0x7f9f6c6b, 0x7f9ef0dd, 0x7f9e7500, 0x7f9df8d4, 0x7f9d7c59, 0x7f9cff90,
+    0x7f9c8278, 0x7f9c0511,
+  0x7f9b875b, 0x7f9b0957, 0x7f9a8b04, 0x7f9a0c62, 0x7f998d72, 0x7f990e33,
+    0x7f988ea5, 0x7f980ec8,
+  0x7f978e9d, 0x7f970e23, 0x7f968d5b, 0x7f960c43, 0x7f958add, 0x7f950929,
+    0x7f948725, 0x7f9404d3,
+  0x7f938232, 0x7f92ff43, 0x7f927c04, 0x7f91f878, 0x7f91749c, 0x7f90f072,
+    0x7f906bf9, 0x7f8fe731,
+  0x7f8f621b, 0x7f8edcb6, 0x7f8e5702, 0x7f8dd0ff, 0x7f8d4aae, 0x7f8cc40f,
+    0x7f8c3d20, 0x7f8bb5e3,
+  0x7f8b2e57, 0x7f8aa67d, 0x7f8a1e54, 0x7f8995dc, 0x7f890d15, 0x7f888400,
+    0x7f87fa9c, 0x7f8770ea,
+  0x7f86e6e9, 0x7f865c99, 0x7f85d1fa, 0x7f85470d, 0x7f84bbd1, 0x7f843047,
+    0x7f83a46e, 0x7f831846,
+  0x7f828bcf, 0x7f81ff0a, 0x7f8171f6, 0x7f80e494, 0x7f8056e3, 0x7f7fc8e3,
+    0x7f7f3a95, 0x7f7eabf8,
+  0x7f7e1d0c, 0x7f7d8dd2, 0x7f7cfe49, 0x7f7c6e71, 0x7f7bde4b, 0x7f7b4dd6,
+    0x7f7abd13, 0x7f7a2c01,
+  0x7f799aa0, 0x7f7908f0, 0x7f7876f2, 0x7f77e4a6, 0x7f77520a, 0x7f76bf21,
+    0x7f762be8, 0x7f759861,
+  0x7f75048b, 0x7f747067, 0x7f73dbf4, 0x7f734732, 0x7f72b222, 0x7f721cc3,
+    0x7f718715, 0x7f70f119,
+  0x7f705ace, 0x7f6fc435, 0x7f6f2d4d, 0x7f6e9617, 0x7f6dfe91, 0x7f6d66be,
+    0x7f6cce9b, 0x7f6c362a,
+  0x7f6b9d6b, 0x7f6b045d, 0x7f6a6b00, 0x7f69d154, 0x7f69375a, 0x7f689d12,
+    0x7f68027b, 0x7f676795,
+  0x7f66cc61, 0x7f6630de, 0x7f65950c, 0x7f64f8ec, 0x7f645c7d, 0x7f63bfc0,
+    0x7f6322b4, 0x7f62855a,
+  0x7f61e7b1, 0x7f6149b9, 0x7f60ab73, 0x7f600cdf, 0x7f5f6dfb, 0x7f5ecec9,
+    0x7f5e2f49, 0x7f5d8f7a,
+  0x7f5cef5c, 0x7f5c4ef0, 0x7f5bae36, 0x7f5b0d2c, 0x7f5a6bd5, 0x7f59ca2e,
+    0x7f592839, 0x7f5885f6,
+  0x7f57e364, 0x7f574083, 0x7f569d54, 0x7f55f9d6, 0x7f55560a, 0x7f54b1ef,
+    0x7f540d86, 0x7f5368ce,
+  0x7f52c3c8, 0x7f521e73, 0x7f5178cf, 0x7f50d2dd, 0x7f502c9d, 0x7f4f860e,
+    0x7f4edf30, 0x7f4e3804,
+  0x7f4d9089, 0x7f4ce8c0, 0x7f4c40a8, 0x7f4b9842, 0x7f4aef8d, 0x7f4a468a,
+    0x7f499d38, 0x7f48f398,
+  0x7f4849a9, 0x7f479f6c, 0x7f46f4e0, 0x7f464a06, 0x7f459edd, 0x7f44f365,
+    0x7f44479f, 0x7f439b8b,
+  0x7f42ef28, 0x7f424277, 0x7f419577, 0x7f40e828, 0x7f403a8b, 0x7f3f8ca0,
+    0x7f3ede66, 0x7f3e2fde,
+  0x7f3d8107, 0x7f3cd1e2, 0x7f3c226e, 0x7f3b72ab, 0x7f3ac29b, 0x7f3a123b,
+    0x7f39618e, 0x7f38b091,
+  0x7f37ff47, 0x7f374dad, 0x7f369bc6, 0x7f35e990, 0x7f35370b, 0x7f348438,
+    0x7f33d116, 0x7f331da6,
+  0x7f3269e8, 0x7f31b5db, 0x7f31017f, 0x7f304cd6, 0x7f2f97dd, 0x7f2ee296,
+    0x7f2e2d01, 0x7f2d771e,
+  0x7f2cc0eb, 0x7f2c0a6b, 0x7f2b539c, 0x7f2a9c7e, 0x7f29e512, 0x7f292d58,
+    0x7f28754f, 0x7f27bcf8,
+  0x7f270452, 0x7f264b5e, 0x7f25921c, 0x7f24d88b, 0x7f241eab, 0x7f23647e,
+    0x7f22aa01, 0x7f21ef37,
+  0x7f21341e, 0x7f2078b6, 0x7f1fbd00, 0x7f1f00fc, 0x7f1e44a9, 0x7f1d8808,
+    0x7f1ccb18, 0x7f1c0dda,
+  0x7f1b504e, 0x7f1a9273, 0x7f19d44a, 0x7f1915d2, 0x7f18570c, 0x7f1797f8,
+    0x7f16d895, 0x7f1618e4,
+  0x7f1558e4, 0x7f149896, 0x7f13d7fa, 0x7f13170f, 0x7f1255d6, 0x7f11944f,
+    0x7f10d279, 0x7f101054,
+  0x7f0f4de2, 0x7f0e8b21, 0x7f0dc811, 0x7f0d04b3, 0x7f0c4107, 0x7f0b7d0d,
+    0x7f0ab8c4, 0x7f09f42d,
+  0x7f092f47, 0x7f086a13, 0x7f07a491, 0x7f06dec0, 0x7f0618a1, 0x7f055233,
+    0x7f048b78, 0x7f03c46d,
+  0x7f02fd15, 0x7f02356e, 0x7f016d79, 0x7f00a535, 0x7effdca4, 0x7eff13c3,
+    0x7efe4a95, 0x7efd8118,
+  0x7efcb74d, 0x7efbed33, 0x7efb22cb, 0x7efa5815, 0x7ef98d11, 0x7ef8c1be,
+    0x7ef7f61d, 0x7ef72a2d,
+  0x7ef65def, 0x7ef59163, 0x7ef4c489, 0x7ef3f760, 0x7ef329e9, 0x7ef25c24,
+    0x7ef18e10, 0x7ef0bfae,
+  0x7eeff0fe, 0x7eef21ff, 0x7eee52b2, 0x7eed8317, 0x7eecb32d, 0x7eebe2f6,
+    0x7eeb1270, 0x7eea419b,
+  0x7ee97079, 0x7ee89f08, 0x7ee7cd49, 0x7ee6fb3b, 0x7ee628df, 0x7ee55635,
+    0x7ee4833d, 0x7ee3aff6,
+  0x7ee2dc61, 0x7ee2087e, 0x7ee1344d, 0x7ee05fcd, 0x7edf8aff, 0x7edeb5e3,
+    0x7edde079, 0x7edd0ac0,
+  0x7edc34b9, 0x7edb5e64, 0x7eda87c0, 0x7ed9b0ce, 0x7ed8d98e, 0x7ed80200,
+    0x7ed72a24, 0x7ed651f9,
+  0x7ed57980, 0x7ed4a0b9, 0x7ed3c7a3, 0x7ed2ee40, 0x7ed2148e, 0x7ed13a8e,
+    0x7ed0603f, 0x7ecf85a3,
+  0x7eceaab8, 0x7ecdcf7f, 0x7eccf3f8, 0x7ecc1822, 0x7ecb3bff, 0x7eca5f8d,
+    0x7ec982cd, 0x7ec8a5bf,
+  0x7ec7c862, 0x7ec6eab7, 0x7ec60cbe, 0x7ec52e77, 0x7ec44fe2, 0x7ec370fe,
+    0x7ec291cd, 0x7ec1b24d,
+  0x7ec0d27f, 0x7ebff263, 0x7ebf11f8, 0x7ebe313f, 0x7ebd5039, 0x7ebc6ee4,
+    0x7ebb8d40, 0x7ebaab4f,
+  0x7eb9c910, 0x7eb8e682, 0x7eb803a6, 0x7eb7207c, 0x7eb63d04, 0x7eb5593d,
+    0x7eb47529, 0x7eb390c6,
+  0x7eb2ac15, 0x7eb1c716, 0x7eb0e1c9, 0x7eaffc2e, 0x7eaf1645, 0x7eae300d,
+    0x7ead4987, 0x7eac62b3,
+  0x7eab7b91, 0x7eaa9421, 0x7ea9ac63, 0x7ea8c457, 0x7ea7dbfc, 0x7ea6f353,
+    0x7ea60a5d, 0x7ea52118,
+  0x7ea43785, 0x7ea34da4, 0x7ea26374, 0x7ea178f7, 0x7ea08e2b, 0x7e9fa312,
+    0x7e9eb7aa, 0x7e9dcbf4,
+  0x7e9cdff0, 0x7e9bf39e, 0x7e9b06fe, 0x7e9a1a10, 0x7e992cd4, 0x7e983f49,
+    0x7e975171, 0x7e96634a,
+  0x7e9574d6, 0x7e948613, 0x7e939702, 0x7e92a7a3, 0x7e91b7f6, 0x7e90c7fb,
+    0x7e8fd7b2, 0x7e8ee71b,
+  0x7e8df636, 0x7e8d0502, 0x7e8c1381, 0x7e8b21b1, 0x7e8a2f94, 0x7e893d28,
+    0x7e884a6f, 0x7e875767,
+  0x7e866411, 0x7e85706d, 0x7e847c7c, 0x7e83883c, 0x7e8293ae, 0x7e819ed2,
+    0x7e80a9a8, 0x7e7fb430,
+  0x7e7ebe6a, 0x7e7dc856, 0x7e7cd1f4, 0x7e7bdb44, 0x7e7ae446, 0x7e79ecf9,
+    0x7e78f55f, 0x7e77fd77,
+  0x7e770541, 0x7e760cbd, 0x7e7513ea, 0x7e741aca, 0x7e73215c, 0x7e7227a0,
+    0x7e712d96, 0x7e70333d,
+  0x7e6f3897, 0x7e6e3da3, 0x7e6d4261, 0x7e6c46d1, 0x7e6b4af2, 0x7e6a4ec6,
+    0x7e69524c, 0x7e685584,
+  0x7e67586e, 0x7e665b0a, 0x7e655d58, 0x7e645f58, 0x7e63610a, 0x7e62626e,
+    0x7e616384, 0x7e60644c,
+  0x7e5f64c7, 0x7e5e64f3, 0x7e5d64d1, 0x7e5c6461, 0x7e5b63a4, 0x7e5a6298,
+    0x7e59613f, 0x7e585f97,
+  0x7e575da2, 0x7e565b5f, 0x7e5558ce, 0x7e5455ef, 0x7e5352c1, 0x7e524f46,
+    0x7e514b7e, 0x7e504767,
+  0x7e4f4302, 0x7e4e3e4f, 0x7e4d394f, 0x7e4c3400, 0x7e4b2e64, 0x7e4a287a,
+    0x7e492241, 0x7e481bbb,
+  0x7e4714e7, 0x7e460dc5, 0x7e450656, 0x7e43fe98, 0x7e42f68c, 0x7e41ee33,
+    0x7e40e58c, 0x7e3fdc97,
+  0x7e3ed353, 0x7e3dc9c3, 0x7e3cbfe4, 0x7e3bb5b7, 0x7e3aab3c, 0x7e39a074,
+    0x7e38955e, 0x7e3789fa,
+  0x7e367e48, 0x7e357248, 0x7e3465fa, 0x7e33595e, 0x7e324c75, 0x7e313f3e,
+    0x7e3031b9, 0x7e2f23e6,
+  0x7e2e15c5, 0x7e2d0756, 0x7e2bf89a, 0x7e2ae990, 0x7e29da38, 0x7e28ca92,
+    0x7e27ba9e, 0x7e26aa5d,
+  0x7e2599cd, 0x7e2488f0, 0x7e2377c5, 0x7e22664c, 0x7e215486, 0x7e204271,
+    0x7e1f300f, 0x7e1e1d5f,
+  0x7e1d0a61, 0x7e1bf716, 0x7e1ae37c, 0x7e19cf95, 0x7e18bb60, 0x7e17a6dd,
+    0x7e16920d, 0x7e157cee,
+  0x7e146782, 0x7e1351c9, 0x7e123bc1, 0x7e11256c, 0x7e100ec8, 0x7e0ef7d7,
+    0x7e0de099, 0x7e0cc90c,
+  0x7e0bb132, 0x7e0a990a, 0x7e098095, 0x7e0867d1, 0x7e074ec0, 0x7e063561,
+    0x7e051bb4, 0x7e0401ba,
+  0x7e02e772, 0x7e01ccdc, 0x7e00b1f9, 0x7dff96c7, 0x7dfe7b48, 0x7dfd5f7b,
+    0x7dfc4361, 0x7dfb26f9,
+  0x7dfa0a43, 0x7df8ed3f, 0x7df7cfee, 0x7df6b24f, 0x7df59462, 0x7df47628,
+    0x7df357a0, 0x7df238ca,
+  0x7df119a7, 0x7deffa35, 0x7deeda77, 0x7dedba6a, 0x7dec9a10, 0x7deb7968,
+    0x7dea5872, 0x7de9372f,
+  0x7de8159e, 0x7de6f3c0, 0x7de5d193, 0x7de4af1a, 0x7de38c52, 0x7de2693d,
+    0x7de145da, 0x7de02229,
+  0x7ddefe2b, 0x7dddd9e0, 0x7ddcb546, 0x7ddb905f, 0x7dda6b2a, 0x7dd945a8,
+    0x7dd81fd8, 0x7dd6f9ba,
+  0x7dd5d34f, 0x7dd4ac96, 0x7dd38590, 0x7dd25e3c, 0x7dd1369a, 0x7dd00eab,
+    0x7dcee66e, 0x7dcdbde3,
+  0x7dcc950b, 0x7dcb6be6, 0x7dca4272, 0x7dc918b1, 0x7dc7eea3, 0x7dc6c447,
+    0x7dc5999d, 0x7dc46ea6,
+  0x7dc34361, 0x7dc217cf, 0x7dc0ebef, 0x7dbfbfc1, 0x7dbe9346, 0x7dbd667d,
+    0x7dbc3967, 0x7dbb0c03,
+  0x7db9de52, 0x7db8b053, 0x7db78207, 0x7db6536d, 0x7db52485, 0x7db3f550,
+    0x7db2c5cd, 0x7db195fd,
+  0x7db065df, 0x7daf3574, 0x7dae04bb, 0x7dacd3b5, 0x7daba261, 0x7daa70c0,
+    0x7da93ed1, 0x7da80c95,
+  0x7da6da0b, 0x7da5a733, 0x7da4740e, 0x7da3409c, 0x7da20cdc, 0x7da0d8cf,
+    0x7d9fa474, 0x7d9e6fcb,
+  0x7d9d3ad6, 0x7d9c0592, 0x7d9ad001, 0x7d999a23, 0x7d9863f7, 0x7d972d7e,
+    0x7d95f6b7, 0x7d94bfa3,
+  0x7d938841, 0x7d925092, 0x7d911896, 0x7d8fe04c, 0x7d8ea7b4, 0x7d8d6ecf,
+    0x7d8c359d, 0x7d8afc1d,
+  0x7d89c250, 0x7d888835, 0x7d874dcd, 0x7d861317, 0x7d84d814, 0x7d839cc4,
+    0x7d826126, 0x7d81253a,
+  0x7d7fe902, 0x7d7eac7c, 0x7d7d6fa8, 0x7d7c3287, 0x7d7af519, 0x7d79b75d,
+    0x7d787954, 0x7d773afd,
+  0x7d75fc59, 0x7d74bd68, 0x7d737e29, 0x7d723e9d, 0x7d70fec4, 0x7d6fbe9d,
+    0x7d6e7e29, 0x7d6d3d67,
+  0x7d6bfc58, 0x7d6abafc, 0x7d697952, 0x7d68375b, 0x7d66f517, 0x7d65b285,
+    0x7d646fa6, 0x7d632c79,
+  0x7d61e8ff, 0x7d60a538, 0x7d5f6124, 0x7d5e1cc2, 0x7d5cd813, 0x7d5b9316,
+    0x7d5a4dcc, 0x7d590835,
+  0x7d57c251, 0x7d567c1f, 0x7d5535a0, 0x7d53eed3, 0x7d52a7ba, 0x7d516053,
+    0x7d50189e, 0x7d4ed09d,
+  0x7d4d884e, 0x7d4c3fb1, 0x7d4af6c8, 0x7d49ad91, 0x7d48640d, 0x7d471a3c,
+    0x7d45d01d, 0x7d4485b1,
+  0x7d433af8, 0x7d41eff1, 0x7d40a49e, 0x7d3f58fd, 0x7d3e0d0e, 0x7d3cc0d3,
+    0x7d3b744a, 0x7d3a2774,
+  0x7d38da51, 0x7d378ce0, 0x7d363f23, 0x7d34f118, 0x7d33a2bf, 0x7d32541a,
+    0x7d310527, 0x7d2fb5e7,
+  0x7d2e665a, 0x7d2d1680, 0x7d2bc659, 0x7d2a75e4, 0x7d292522, 0x7d27d413,
+    0x7d2682b6, 0x7d25310d,
+  0x7d23df16, 0x7d228cd2, 0x7d213a41, 0x7d1fe762, 0x7d1e9437, 0x7d1d40be,
+    0x7d1becf8, 0x7d1a98e5,
+  0x7d194485, 0x7d17efd8, 0x7d169add, 0x7d154595, 0x7d13f001, 0x7d129a1f,
+    0x7d1143ef, 0x7d0fed73,
+  0x7d0e96aa, 0x7d0d3f93, 0x7d0be82f, 0x7d0a907e, 0x7d093880, 0x7d07e035,
+    0x7d06879d, 0x7d052eb8,
+  0x7d03d585, 0x7d027c05, 0x7d012239, 0x7cffc81f, 0x7cfe6db8, 0x7cfd1304,
+    0x7cfbb803, 0x7cfa5cb4,
+  0x7cf90119, 0x7cf7a531, 0x7cf648fb, 0x7cf4ec79, 0x7cf38fa9, 0x7cf2328c,
+    0x7cf0d522, 0x7cef776b,
+  0x7cee1967, 0x7cecbb16, 0x7ceb5c78, 0x7ce9fd8d, 0x7ce89e55, 0x7ce73ed0,
+    0x7ce5defd, 0x7ce47ede,
+  0x7ce31e72, 0x7ce1bdb8, 0x7ce05cb2, 0x7cdefb5e, 0x7cdd99be, 0x7cdc37d0,
+    0x7cdad596, 0x7cd9730e,
+  0x7cd8103a, 0x7cd6ad18, 0x7cd549aa, 0x7cd3e5ee, 0x7cd281e5, 0x7cd11d90,
+    0x7ccfb8ed, 0x7cce53fe,
+  0x7ccceec1, 0x7ccb8937, 0x7cca2361, 0x7cc8bd3d, 0x7cc756cd, 0x7cc5f010,
+    0x7cc48905, 0x7cc321ae,
+  0x7cc1ba09, 0x7cc05218, 0x7cbee9da, 0x7cbd814f, 0x7cbc1877, 0x7cbaaf51,
+    0x7cb945df, 0x7cb7dc20,
+  0x7cb67215, 0x7cb507bc, 0x7cb39d16, 0x7cb23223, 0x7cb0c6e4, 0x7caf5b57,
+    0x7cadef7e, 0x7cac8358,
+  0x7cab16e4, 0x7ca9aa24, 0x7ca83d17, 0x7ca6cfbd, 0x7ca56216, 0x7ca3f423,
+    0x7ca285e2, 0x7ca11755,
+  0x7c9fa87a, 0x7c9e3953, 0x7c9cc9df, 0x7c9b5a1e, 0x7c99ea10, 0x7c9879b6,
+    0x7c97090e, 0x7c95981a,
+  0x7c9426d8, 0x7c92b54a, 0x7c91436f, 0x7c8fd148, 0x7c8e5ed3, 0x7c8cec12,
+    0x7c8b7903, 0x7c8a05a8,
+  0x7c889200, 0x7c871e0c, 0x7c85a9ca, 0x7c84353c, 0x7c82c060, 0x7c814b39,
+    0x7c7fd5c4, 0x7c7e6002,
+  0x7c7ce9f4, 0x7c7b7399, 0x7c79fcf1, 0x7c7885fc, 0x7c770eba, 0x7c75972c,
+    0x7c741f51, 0x7c72a729,
+  0x7c712eb5, 0x7c6fb5f3, 0x7c6e3ce5, 0x7c6cc38a, 0x7c6b49e3, 0x7c69cfee,
+    0x7c6855ad, 0x7c66db1f,
+  0x7c656045, 0x7c63e51e, 0x7c6269aa, 0x7c60ede9, 0x7c5f71db, 0x7c5df581,
+    0x7c5c78da, 0x7c5afbe6,
+  0x7c597ea6, 0x7c580119, 0x7c56833f, 0x7c550519, 0x7c5386a6, 0x7c5207e6,
+    0x7c5088d9, 0x7c4f0980,
+  0x7c4d89da, 0x7c4c09e8, 0x7c4a89a8, 0x7c49091c, 0x7c478844, 0x7c46071f,
+    0x7c4485ad, 0x7c4303ee,
+  0x7c4181e3, 0x7c3fff8b, 0x7c3e7ce7, 0x7c3cf9f5, 0x7c3b76b8, 0x7c39f32d,
+    0x7c386f56, 0x7c36eb33,
+  0x7c3566c2, 0x7c33e205, 0x7c325cfc, 0x7c30d7a6, 0x7c2f5203, 0x7c2dcc14,
+    0x7c2c45d8, 0x7c2abf4f,
+  0x7c29387a, 0x7c27b158, 0x7c2629ea, 0x7c24a22f, 0x7c231a28, 0x7c2191d4,
+    0x7c200933, 0x7c1e8046,
+  0x7c1cf70c, 0x7c1b6d86, 0x7c19e3b3, 0x7c185994, 0x7c16cf28, 0x7c15446f,
+    0x7c13b96a, 0x7c122e19,
+  0x7c10a27b, 0x7c0f1690, 0x7c0d8a59, 0x7c0bfdd5, 0x7c0a7105, 0x7c08e3e8,
+    0x7c07567f, 0x7c05c8c9,
+  0x7c043ac7, 0x7c02ac78, 0x7c011ddd, 0x7bff8ef5, 0x7bfdffc1, 0x7bfc7041,
+    0x7bfae073, 0x7bf9505a,
+  0x7bf7bff4, 0x7bf62f41, 0x7bf49e42, 0x7bf30cf6, 0x7bf17b5e, 0x7befe97a,
+    0x7bee5749, 0x7becc4cc,
+  0x7beb3202, 0x7be99eec, 0x7be80b89, 0x7be677da, 0x7be4e3df, 0x7be34f97,
+    0x7be1bb02, 0x7be02621,
+  0x7bde90f4, 0x7bdcfb7b, 0x7bdb65b5, 0x7bd9cfa2, 0x7bd83944, 0x7bd6a298,
+    0x7bd50ba1, 0x7bd3745d,
+  0x7bd1dccc, 0x7bd044f0, 0x7bceacc7, 0x7bcd1451, 0x7bcb7b8f, 0x7bc9e281,
+    0x7bc84927, 0x7bc6af80,
+  0x7bc5158c, 0x7bc37b4d, 0x7bc1e0c1, 0x7bc045e9, 0x7bbeaac4, 0x7bbd0f53,
+    0x7bbb7396, 0x7bb9d78c,
+  0x7bb83b36, 0x7bb69e94, 0x7bb501a5, 0x7bb3646a, 0x7bb1c6e3, 0x7bb02910,
+    0x7bae8af0, 0x7bacec84,
+  0x7bab4dcc, 0x7ba9aec7, 0x7ba80f76, 0x7ba66fd9, 0x7ba4cfef, 0x7ba32fba,
+    0x7ba18f38, 0x7b9fee69,
+  0x7b9e4d4f, 0x7b9cabe8, 0x7b9b0a35, 0x7b996836, 0x7b97c5ea, 0x7b962352,
+    0x7b94806e, 0x7b92dd3e,
+  0x7b9139c2, 0x7b8f95f9, 0x7b8df1e4, 0x7b8c4d83, 0x7b8aa8d6, 0x7b8903dc,
+    0x7b875e96, 0x7b85b904,
+  0x7b841326, 0x7b826cfc, 0x7b80c686, 0x7b7f1fc3, 0x7b7d78b4, 0x7b7bd159,
+    0x7b7a29b2, 0x7b7881be,
+  0x7b76d97f, 0x7b7530f3, 0x7b73881b, 0x7b71def7, 0x7b703587, 0x7b6e8bcb,
+    0x7b6ce1c2, 0x7b6b376e,
+  0x7b698ccd, 0x7b67e1e0, 0x7b6636a7, 0x7b648b22, 0x7b62df51, 0x7b613334,
+    0x7b5f86ca, 0x7b5dda15,
+  0x7b5c2d13, 0x7b5a7fc6, 0x7b58d22c, 0x7b572446, 0x7b557614, 0x7b53c796,
+    0x7b5218cc, 0x7b5069b6,
+  0x7b4eba53, 0x7b4d0aa5, 0x7b4b5aab, 0x7b49aa64, 0x7b47f9d2, 0x7b4648f3,
+    0x7b4497c9, 0x7b42e652,
+  0x7b413490, 0x7b3f8281, 0x7b3dd026, 0x7b3c1d80, 0x7b3a6a8d, 0x7b38b74e,
+    0x7b3703c3, 0x7b354fed,
+  0x7b339bca, 0x7b31e75b, 0x7b3032a0, 0x7b2e7d9a, 0x7b2cc847, 0x7b2b12a8,
+    0x7b295cbe, 0x7b27a687,
+  0x7b25f004, 0x7b243936, 0x7b22821b, 0x7b20cab5, 0x7b1f1302, 0x7b1d5b04,
+    0x7b1ba2b9, 0x7b19ea23,
+  0x7b183141, 0x7b167813, 0x7b14be99, 0x7b1304d3, 0x7b114ac1, 0x7b0f9063,
+    0x7b0dd5b9, 0x7b0c1ac4,
+  0x7b0a5f82, 0x7b08a3f5, 0x7b06e81b, 0x7b052bf6, 0x7b036f85, 0x7b01b2c8,
+    0x7afff5bf, 0x7afe386a,
+  0x7afc7aca, 0x7afabcdd, 0x7af8fea5, 0x7af74021, 0x7af58151, 0x7af3c235,
+    0x7af202cd, 0x7af0431a,
+  0x7aee831a, 0x7aecc2cf, 0x7aeb0238, 0x7ae94155, 0x7ae78026, 0x7ae5beac,
+    0x7ae3fce6, 0x7ae23ad4,
+  0x7ae07876, 0x7adeb5cc, 0x7adcf2d6, 0x7adb2f95, 0x7ad96c08, 0x7ad7a82f,
+    0x7ad5e40a, 0x7ad41f9a,
+  0x7ad25ade, 0x7ad095d6, 0x7aced082, 0x7acd0ae3, 0x7acb44f8, 0x7ac97ec1,
+    0x7ac7b83e, 0x7ac5f170,
+  0x7ac42a55, 0x7ac262ef, 0x7ac09b3e, 0x7abed341, 0x7abd0af7, 0x7abb4263,
+    0x7ab97982, 0x7ab7b056,
+  0x7ab5e6de, 0x7ab41d1b, 0x7ab2530b, 0x7ab088b0, 0x7aaebe0a, 0x7aacf318,
+    0x7aab27da, 0x7aa95c50,
+  0x7aa7907b, 0x7aa5c45a, 0x7aa3f7ed, 0x7aa22b35, 0x7aa05e31, 0x7a9e90e1,
+    0x7a9cc346, 0x7a9af55f,
+  0x7a99272d, 0x7a9758af, 0x7a9589e5, 0x7a93bad0, 0x7a91eb6f, 0x7a901bc2,
+    0x7a8e4bca, 0x7a8c7b87,
+  0x7a8aaaf7, 0x7a88da1c, 0x7a8708f6, 0x7a853784, 0x7a8365c6, 0x7a8193bd,
+    0x7a7fc168, 0x7a7deec8,
+  0x7a7c1bdc, 0x7a7a48a4, 0x7a787521, 0x7a76a153, 0x7a74cd38, 0x7a72f8d3,
+    0x7a712422, 0x7a6f4f25,
+  0x7a6d79dd, 0x7a6ba449, 0x7a69ce6a, 0x7a67f83f, 0x7a6621c9, 0x7a644b07,
+    0x7a6273fa, 0x7a609ca1,
+  0x7a5ec4fc, 0x7a5ced0d, 0x7a5b14d1, 0x7a593c4b, 0x7a576379, 0x7a558a5b,
+    0x7a53b0f2, 0x7a51d73d,
+  0x7a4ffd3d, 0x7a4e22f2, 0x7a4c485b, 0x7a4a6d78, 0x7a48924b, 0x7a46b6d1,
+    0x7a44db0d, 0x7a42fefd,
+  0x7a4122a1, 0x7a3f45fa, 0x7a3d6908, 0x7a3b8bca, 0x7a39ae41, 0x7a37d06d,
+    0x7a35f24d, 0x7a3413e2,
+  0x7a32352b, 0x7a305629, 0x7a2e76dc, 0x7a2c9743, 0x7a2ab75f, 0x7a28d72f,
+    0x7a26f6b4, 0x7a2515ee,
+  0x7a2334dd, 0x7a215380, 0x7a1f71d7, 0x7a1d8fe4, 0x7a1bada5, 0x7a19cb1b,
+    0x7a17e845, 0x7a160524,
+  0x7a1421b8, 0x7a123e01, 0x7a1059fe, 0x7a0e75b0, 0x7a0c9117, 0x7a0aac32,
+    0x7a08c702, 0x7a06e187,
+  0x7a04fbc1, 0x7a0315af, 0x7a012f52, 0x79ff48aa, 0x79fd61b6, 0x79fb7a77,
+    0x79f992ed, 0x79f7ab18,
+  0x79f5c2f8, 0x79f3da8c, 0x79f1f1d5, 0x79f008d3, 0x79ee1f86, 0x79ec35ed,
+    0x79ea4c09, 0x79e861da,
+  0x79e67760, 0x79e48c9b, 0x79e2a18a, 0x79e0b62e, 0x79deca87, 0x79dcde95,
+    0x79daf258, 0x79d905d0,
+  0x79d718fc, 0x79d52bdd, 0x79d33e73, 0x79d150be, 0x79cf62be, 0x79cd7473,
+    0x79cb85dc, 0x79c996fb,
+  0x79c7a7ce, 0x79c5b856, 0x79c3c893, 0x79c1d885, 0x79bfe82c, 0x79bdf788,
+    0x79bc0698, 0x79ba155e,
+  0x79b823d8, 0x79b63207, 0x79b43fec, 0x79b24d85, 0x79b05ad3, 0x79ae67d6,
+    0x79ac748e, 0x79aa80fb,
+  0x79a88d1d, 0x79a698f4, 0x79a4a480, 0x79a2afc1, 0x79a0bab6, 0x799ec561,
+    0x799ccfc1, 0x799ad9d5,
+  0x7998e39f, 0x7996ed1e, 0x7994f651, 0x7992ff3a, 0x799107d8, 0x798f102a,
+    0x798d1832, 0x798b1fef,
+  0x79892761, 0x79872e87, 0x79853563, 0x79833bf4, 0x7981423a, 0x797f4835,
+    0x797d4de5, 0x797b534a,
+  0x79795864, 0x79775d33, 0x797561b8, 0x797365f1, 0x797169df, 0x796f6d83,
+    0x796d70dc, 0x796b73e9,
+  0x796976ac, 0x79677924, 0x79657b51, 0x79637d33, 0x79617eca, 0x795f8017,
+    0x795d8118, 0x795b81cf,
+  0x7959823b, 0x7957825c, 0x79558232, 0x795381bd, 0x795180fe, 0x794f7ff3,
+    0x794d7e9e, 0x794b7cfe,
+  0x79497b13, 0x794778dd, 0x7945765d, 0x79437391, 0x7941707b, 0x793f6d1a,
+    0x793d696f, 0x793b6578,
+  0x79396137, 0x79375cab, 0x793557d4, 0x793352b2, 0x79314d46, 0x792f478f,
+    0x792d418d, 0x792b3b40,
+  0x792934a9, 0x79272dc7, 0x7925269a, 0x79231f22, 0x79211760, 0x791f0f53,
+    0x791d06fb, 0x791afe59,
+  0x7918f56c, 0x7916ec34, 0x7914e2b2, 0x7912d8e4, 0x7910cecc, 0x790ec46a,
+    0x790cb9bd, 0x790aaec5,
+  0x7908a382, 0x790697f5, 0x79048c1d, 0x79027ffa, 0x7900738d, 0x78fe66d5,
+    0x78fc59d3, 0x78fa4c86,
+  0x78f83eee, 0x78f6310c, 0x78f422df, 0x78f21467, 0x78f005a5, 0x78edf698,
+    0x78ebe741, 0x78e9d79f,
+  0x78e7c7b2, 0x78e5b77b, 0x78e3a6f9, 0x78e1962d, 0x78df8516, 0x78dd73b5,
+    0x78db6209, 0x78d95012,
+  0x78d73dd1, 0x78d52b46, 0x78d31870, 0x78d1054f, 0x78cef1e4, 0x78ccde2e,
+    0x78caca2e, 0x78c8b5e3,
+  0x78c6a14e, 0x78c48c6e, 0x78c27744, 0x78c061cf, 0x78be4c10, 0x78bc3606,
+    0x78ba1fb2, 0x78b80913,
+  0x78b5f22a, 0x78b3daf7, 0x78b1c379, 0x78afabb0, 0x78ad939d, 0x78ab7b40,
+    0x78a96298, 0x78a749a6,
+  0x78a53069, 0x78a316e2, 0x78a0fd11, 0x789ee2f5, 0x789cc88f, 0x789aadde,
+    0x789892e3, 0x7896779d,
+  0x78945c0d, 0x78924033, 0x7890240e, 0x788e07a0, 0x788beae6, 0x7889cde2,
+    0x7887b094, 0x788592fc,
+  0x78837519, 0x788156ec, 0x787f3875, 0x787d19b3, 0x787afaa7, 0x7878db50,
+    0x7876bbb0, 0x78749bc5,
+  0x78727b8f, 0x78705b10, 0x786e3a46, 0x786c1932, 0x7869f7d3, 0x7867d62a,
+    0x7865b437, 0x786391fa,
+  0x78616f72, 0x785f4ca1, 0x785d2984, 0x785b061e, 0x7858e26e, 0x7856be73,
+    0x78549a2e, 0x7852759e,
+  0x785050c5, 0x784e2ba1, 0x784c0633, 0x7849e07b, 0x7847ba79, 0x7845942c,
+    0x78436d96, 0x784146b5,
+  0x783f1f8a, 0x783cf815, 0x783ad055, 0x7838a84c, 0x78367ff8, 0x7834575a,
+    0x78322e72, 0x78300540,
+  0x782ddbc4, 0x782bb1fd, 0x782987ed, 0x78275d92, 0x782532ed, 0x782307fe,
+    0x7820dcc5, 0x781eb142,
+  0x781c8575, 0x781a595d, 0x78182cfc, 0x78160051, 0x7813d35b, 0x7811a61b,
+    0x780f7892, 0x780d4abe,
+  0x780b1ca0, 0x7808ee38, 0x7806bf86, 0x7804908a, 0x78026145, 0x780031b5,
+    0x77fe01db, 0x77fbd1b6,
+  0x77f9a148, 0x77f77090, 0x77f53f8e, 0x77f30e42, 0x77f0dcac, 0x77eeaacc,
+    0x77ec78a2, 0x77ea462e,
+  0x77e81370, 0x77e5e068, 0x77e3ad17, 0x77e1797b, 0x77df4595, 0x77dd1165,
+    0x77dadcec, 0x77d8a828,
+  0x77d6731a, 0x77d43dc3, 0x77d20822, 0x77cfd236, 0x77cd9c01, 0x77cb6582,
+    0x77c92eb9, 0x77c6f7a6,
+  0x77c4c04a, 0x77c288a3, 0x77c050b2, 0x77be1878, 0x77bbdff4, 0x77b9a726,
+    0x77b76e0e, 0x77b534ac,
+  0x77b2fb00, 0x77b0c10b, 0x77ae86cc, 0x77ac4c43, 0x77aa1170, 0x77a7d653,
+    0x77a59aec, 0x77a35f3c,
+  0x77a12342, 0x779ee6fe, 0x779caa70, 0x779a6d99, 0x77983077, 0x7795f30c,
+    0x7793b557, 0x77917759,
+  0x778f3910, 0x778cfa7e, 0x778abba2, 0x77887c7d, 0x77863d0d, 0x7783fd54,
+    0x7781bd52, 0x777f7d05,
+  0x777d3c6f, 0x777afb8f, 0x7778ba65, 0x777678f2, 0x77743735, 0x7771f52e,
+    0x776fb2de, 0x776d7044,
+  0x776b2d60, 0x7768ea33, 0x7766a6bc, 0x776462fb, 0x77621ef1, 0x775fda9d,
+    0x775d95ff, 0x775b5118,
+  0x77590be7, 0x7756c66c, 0x775480a8, 0x77523a9b, 0x774ff443, 0x774dada2,
+    0x774b66b8, 0x77491f84,
+  0x7746d806, 0x7744903f, 0x7742482e, 0x773fffd4, 0x773db730, 0x773b6e42,
+    0x7739250b, 0x7736db8b,
+  0x773491c0, 0x773247ad, 0x772ffd50, 0x772db2a9, 0x772b67b9, 0x77291c7f,
+    0x7726d0fc, 0x7724852f,
+  0x77223919, 0x771fecb9, 0x771da010, 0x771b531d, 0x771905e1, 0x7716b85b,
+    0x77146a8c, 0x77121c74,
+  0x770fce12, 0x770d7f66, 0x770b3072, 0x7708e133, 0x770691ab, 0x770441da,
+    0x7701f1c0, 0x76ffa15c,
+  0x76fd50ae, 0x76faffb8, 0x76f8ae78, 0x76f65cee, 0x76f40b1b, 0x76f1b8ff,
+    0x76ef6699, 0x76ed13ea,
+  0x76eac0f2, 0x76e86db0, 0x76e61a25, 0x76e3c650, 0x76e17233, 0x76df1dcb,
+    0x76dcc91b, 0x76da7421,
+  0x76d81ede, 0x76d5c952, 0x76d3737c, 0x76d11d5d, 0x76cec6f5, 0x76cc7043,
+    0x76ca1948, 0x76c7c204,
+  0x76c56a77, 0x76c312a0, 0x76c0ba80, 0x76be6217, 0x76bc0965, 0x76b9b069,
+    0x76b75724, 0x76b4fd96,
+  0x76b2a3bf, 0x76b0499e, 0x76adef34, 0x76ab9481, 0x76a93985, 0x76a6de40,
+    0x76a482b1, 0x76a226da,
+  0x769fcab9, 0x769d6e4f, 0x769b119b, 0x7698b49f, 0x76965759, 0x7693f9ca,
+    0x76919bf3, 0x768f3dd2,
+  0x768cdf67, 0x768a80b4, 0x768821b8, 0x7685c272, 0x768362e4, 0x7681030c,
+    0x767ea2eb, 0x767c4281,
+  0x7679e1ce, 0x767780d2, 0x76751f8d, 0x7672bdfe, 0x76705c27, 0x766dfa07,
+    0x766b979d, 0x766934eb,
+  0x7666d1ef, 0x76646eab, 0x76620b1d, 0x765fa747, 0x765d4327, 0x765adebe,
+    0x76587a0d, 0x76561512,
+  0x7653afce, 0x76514a42, 0x764ee46c, 0x764c7e4d, 0x764a17e6, 0x7647b135,
+    0x76454a3c, 0x7642e2f9,
+  0x76407b6e, 0x763e139a, 0x763bab7c, 0x76394316, 0x7636da67, 0x7634716f,
+    0x7632082e, 0x762f9ea4,
+  0x762d34d1, 0x762acab6, 0x76286051, 0x7625f5a3, 0x76238aad, 0x76211f6e,
+    0x761eb3e6, 0x761c4815,
+  0x7619dbfb, 0x76176f98, 0x761502ed, 0x761295f9, 0x761028bb, 0x760dbb35,
+    0x760b4d67, 0x7608df4f,
+  0x760670ee, 0x76040245, 0x76019353, 0x75ff2418, 0x75fcb495, 0x75fa44c8,
+    0x75f7d4b3, 0x75f56455,
+  0x75f2f3ae, 0x75f082bf, 0x75ee1187, 0x75eba006, 0x75e92e3c, 0x75e6bc2a,
+    0x75e449ce, 0x75e1d72b,
+  0x75df643e, 0x75dcf109, 0x75da7d8b, 0x75d809c4, 0x75d595b4, 0x75d3215c,
+    0x75d0acbc, 0x75ce37d2,
+  0x75cbc2a0, 0x75c94d25, 0x75c6d762, 0x75c46156, 0x75c1eb01, 0x75bf7464,
+    0x75bcfd7e, 0x75ba864f,
+  0x75b80ed8, 0x75b59718, 0x75b31f0f, 0x75b0a6be, 0x75ae2e25, 0x75abb542,
+    0x75a93c18, 0x75a6c2a4,
+  0x75a448e8, 0x75a1cee4, 0x759f5496, 0x759cda01, 0x759a5f22, 0x7597e3fc,
+    0x7595688c, 0x7592ecd4,
+  0x759070d4, 0x758df48b, 0x758b77fa, 0x7588fb20, 0x75867dfd, 0x75840093,
+    0x758182df, 0x757f04e3,
+  0x757c869f, 0x757a0812, 0x7577893d, 0x75750a1f, 0x75728ab9, 0x75700b0a,
+    0x756d8b13, 0x756b0ad3,
+  0x75688a4b, 0x7566097b, 0x75638862, 0x75610701, 0x755e8557, 0x755c0365,
+    0x7559812b, 0x7556fea8,
+  0x75547bdd, 0x7551f8c9, 0x754f756e, 0x754cf1c9, 0x754a6ddd, 0x7547e9a8,
+    0x7545652a, 0x7542e065,
+  0x75405b57, 0x753dd600, 0x753b5061, 0x7538ca7b, 0x7536444b, 0x7533bdd4,
+    0x75313714, 0x752eb00c,
+  0x752c28bb, 0x7529a122, 0x75271941, 0x75249118, 0x752208a7, 0x751f7fed,
+    0x751cf6eb, 0x751a6da0,
+  0x7517e40e, 0x75155a33, 0x7512d010, 0x751045a5, 0x750dbaf2, 0x750b2ff6,
+    0x7508a4b2, 0x75061926,
+  0x75038d52, 0x75010136, 0x74fe74d1, 0x74fbe825, 0x74f95b30, 0x74f6cdf3,
+    0x74f4406d, 0x74f1b2a0,
+  0x74ef248b, 0x74ec962d, 0x74ea0787, 0x74e7789a, 0x74e4e964, 0x74e259e6,
+    0x74dfca20, 0x74dd3a11,
+  0x74daa9bb, 0x74d8191d, 0x74d58836, 0x74d2f708, 0x74d06591, 0x74cdd3d2,
+    0x74cb41cc, 0x74c8af7d,
+  0x74c61ce6, 0x74c38a07, 0x74c0f6e0, 0x74be6372, 0x74bbcfbb, 0x74b93bbc,
+    0x74b6a775, 0x74b412e6,
+  0x74b17e0f, 0x74aee8f0, 0x74ac5389, 0x74a9bddb, 0x74a727e4, 0x74a491a5,
+    0x74a1fb1e, 0x749f6450,
+  0x749ccd39, 0x749a35db, 0x74979e34, 0x74950646, 0x74926e10, 0x748fd592,
+    0x748d3ccb, 0x748aa3be,
+  0x74880a68, 0x748570ca, 0x7482d6e4, 0x74803cb7, 0x747da242, 0x747b0784,
+    0x74786c7f, 0x7475d132,
+  0x7473359e, 0x747099c1, 0x746dfd9d, 0x746b6131, 0x7468c47c, 0x74662781,
+    0x74638a3d, 0x7460ecb2,
+  0x745e4ede, 0x745bb0c3, 0x74591261, 0x745673b6, 0x7453d4c4, 0x7451358a,
+    0x744e9608, 0x744bf63e,
+  0x7449562d, 0x7446b5d4, 0x74441533, 0x7441744b, 0x743ed31b, 0x743c31a3,
+    0x74398fe3, 0x7436eddc,
+  0x74344b8d, 0x7431a8f6, 0x742f0618, 0x742c62f2, 0x7429bf84, 0x74271bcf,
+    0x742477d2, 0x7421d38e,
+  0x741f2f01, 0x741c8a2d, 0x7419e512, 0x74173faf, 0x74149a04, 0x7411f412,
+    0x740f4dd8, 0x740ca756,
+  0x740a008d, 0x7407597d, 0x7404b224, 0x74020a85, 0x73ff629d, 0x73fcba6e,
+    0x73fa11f8, 0x73f7693a,
+  0x73f4c034, 0x73f216e7, 0x73ef6d53, 0x73ecc377, 0x73ea1953, 0x73e76ee8,
+    0x73e4c435, 0x73e2193b,
+  0x73df6df9, 0x73dcc270, 0x73da16a0, 0x73d76a88, 0x73d4be28, 0x73d21182,
+    0x73cf6493, 0x73ccb75d,
+  0x73ca09e0, 0x73c75c1c, 0x73c4ae10, 0x73c1ffbc, 0x73bf5121, 0x73bca23f,
+    0x73b9f315, 0x73b743a4,
+  0x73b493ec, 0x73b1e3ec, 0x73af33a5, 0x73ac8316, 0x73a9d240, 0x73a72123,
+    0x73a46fbf, 0x73a1be13,
+  0x739f0c20, 0x739c59e5, 0x7399a763, 0x7396f49a, 0x73944189, 0x73918e32,
+    0x738eda93, 0x738c26ac,
+  0x7389727f, 0x7386be0a, 0x7384094e, 0x7381544a, 0x737e9f00, 0x737be96e,
+    0x73793395, 0x73767d74,
+  0x7373c70d, 0x7371105e, 0x736e5968, 0x736ba22b, 0x7368eaa6, 0x736632db,
+    0x73637ac8, 0x7360c26e,
+  0x735e09cd, 0x735b50e4, 0x735897b5, 0x7355de3e, 0x73532481, 0x73506a7c,
+    0x734db030, 0x734af59d,
+  0x73483ac2, 0x73457fa1, 0x7342c438, 0x73400889, 0x733d4c92, 0x733a9054,
+    0x7337d3d0, 0x73351704,
+  0x733259f1, 0x732f9c97, 0x732cdef6, 0x732a210d, 0x732762de, 0x7324a468,
+    0x7321e5ab, 0x731f26a7,
+  0x731c675b, 0x7319a7c9, 0x7316e7f0, 0x731427cf, 0x73116768, 0x730ea6ba,
+    0x730be5c5, 0x73092489,
+  0x73066306, 0x7303a13b, 0x7300df2a, 0x72fe1cd2, 0x72fb5a34, 0x72f8974e,
+    0x72f5d421, 0x72f310ad,
+  0x72f04cf3, 0x72ed88f1, 0x72eac4a9, 0x72e8001a, 0x72e53b44, 0x72e27627,
+    0x72dfb0c3, 0x72dceb18,
+  0x72da2526, 0x72d75eee, 0x72d4986f, 0x72d1d1a9, 0x72cf0a9c, 0x72cc4348,
+    0x72c97bad, 0x72c6b3cc,
+  0x72c3eba4, 0x72c12335, 0x72be5a7f, 0x72bb9183, 0x72b8c83f, 0x72b5feb5,
+    0x72b334e4, 0x72b06acd,
+  0x72ada06f, 0x72aad5c9, 0x72a80ade, 0x72a53fab, 0x72a27432, 0x729fa872,
+    0x729cdc6b, 0x729a101e,
+  0x7297438a, 0x729476af, 0x7291a98e, 0x728edc26, 0x728c0e77, 0x72894082,
+    0x72867245, 0x7283a3c3,
+  0x7280d4f9, 0x727e05e9, 0x727b3693, 0x727866f6, 0x72759712, 0x7272c6e7,
+    0x726ff676, 0x726d25bf,
+  0x726a54c1, 0x7267837c, 0x7264b1f0, 0x7261e01e, 0x725f0e06, 0x725c3ba7,
+    0x72596901, 0x72569615,
+  0x7253c2e3, 0x7250ef6a, 0x724e1baa, 0x724b47a4, 0x72487357, 0x72459ec4,
+    0x7242c9ea, 0x723ff4ca,
+  0x723d1f63, 0x723a49b6, 0x723773c3, 0x72349d89, 0x7231c708, 0x722ef041,
+    0x722c1934, 0x722941e0,
+  0x72266a46, 0x72239266, 0x7220ba3f, 0x721de1d1, 0x721b091d, 0x72183023,
+    0x721556e3, 0x72127d5c,
+  0x720fa38e, 0x720cc97b, 0x7209ef21, 0x72071480, 0x7204399a, 0x72015e6d,
+    0x71fe82f9, 0x71fba740,
+  0x71f8cb40, 0x71f5eefa, 0x71f3126d, 0x71f0359a, 0x71ed5881, 0x71ea7b22,
+    0x71e79d7c, 0x71e4bf90,
+  0x71e1e15e, 0x71df02e5, 0x71dc2427, 0x71d94522, 0x71d665d6, 0x71d38645,
+    0x71d0a66d, 0x71cdc650,
+  0x71cae5ec, 0x71c80542, 0x71c52451, 0x71c2431b, 0x71bf619e, 0x71bc7fdb,
+    0x71b99dd2, 0x71b6bb83,
+  0x71b3d8ed, 0x71b0f612, 0x71ae12f0, 0x71ab2f89, 0x71a84bdb, 0x71a567e7,
+    0x71a283ad, 0x719f9f2c,
+  0x719cba66, 0x7199d55a, 0x7196f008, 0x71940a6f, 0x71912490, 0x718e3e6c,
+    0x718b5801, 0x71887151,
+  0x71858a5a, 0x7182a31d, 0x717fbb9a, 0x717cd3d2, 0x7179ebc3, 0x7177036e,
+    0x71741ad3, 0x717131f3,
+  0x716e48cc, 0x716b5f5f, 0x716875ad, 0x71658bb4, 0x7162a175, 0x715fb6f1,
+    0x715ccc26, 0x7159e116,
+  0x7156f5c0, 0x71540a24, 0x71511e42, 0x714e321a, 0x714b45ac, 0x714858f8,
+    0x71456bfe, 0x71427ebf,
+  0x713f9139, 0x713ca36e, 0x7139b55d, 0x7136c706, 0x7133d869, 0x7130e987,
+    0x712dfa5e, 0x712b0af0,
+  0x71281b3c, 0x71252b42, 0x71223b02, 0x711f4a7d, 0x711c59b2, 0x711968a1,
+    0x7116774a, 0x711385ad,
+  0x711093cb, 0x710da1a3, 0x710aaf35, 0x7107bc82, 0x7104c989, 0x7101d64a,
+    0x70fee2c5, 0x70fbeefb,
+  0x70f8faeb, 0x70f60695, 0x70f311fa, 0x70f01d19, 0x70ed27f2, 0x70ea3286,
+    0x70e73cd4, 0x70e446dc,
+  0x70e1509f, 0x70de5a1c, 0x70db6353, 0x70d86c45, 0x70d574f1, 0x70d27d58,
+    0x70cf8579, 0x70cc8d54,
+  0x70c994ea, 0x70c69c3a, 0x70c3a345, 0x70c0aa0a, 0x70bdb08a, 0x70bab6c4,
+    0x70b7bcb8, 0x70b4c267,
+  0x70b1c7d1, 0x70aeccf5, 0x70abd1d3, 0x70a8d66c, 0x70a5dac0, 0x70a2dece,
+    0x709fe296, 0x709ce619,
+  0x7099e957, 0x7096ec4f, 0x7093ef01, 0x7090f16e, 0x708df396, 0x708af579,
+    0x7087f715, 0x7084f86d,
+  0x7081f97f, 0x707efa4c, 0x707bfad3, 0x7078fb15, 0x7075fb11, 0x7072fac9,
+    0x706ffa3a, 0x706cf967,
+  0x7069f84e, 0x7066f6f0, 0x7063f54c, 0x7060f363, 0x705df135, 0x705aeec1,
+    0x7057ec08, 0x7054e90a,
+  0x7051e5c7, 0x704ee23e, 0x704bde70, 0x7048da5d, 0x7045d604, 0x7042d166,
+    0x703fcc83, 0x703cc75b,
+  0x7039c1ed, 0x7036bc3b, 0x7033b643, 0x7030b005, 0x702da983, 0x702aa2bb,
+    0x70279baf, 0x7024945d,
+  0x70218cc6, 0x701e84e9, 0x701b7cc8, 0x70187461, 0x70156bb5, 0x701262c4,
+    0x700f598e, 0x700c5013,
+  0x70094653, 0x70063c4e, 0x70033203, 0x70002774, 0x6ffd1c9f, 0x6ffa1185,
+    0x6ff70626, 0x6ff3fa82,
+  0x6ff0ee99, 0x6fede26b, 0x6fead5f8, 0x6fe7c940, 0x6fe4bc43, 0x6fe1af01,
+    0x6fdea17a, 0x6fdb93ae,
+  0x6fd8859d, 0x6fd57746, 0x6fd268ab, 0x6fcf59cb, 0x6fcc4aa6, 0x6fc93b3c,
+    0x6fc62b8d, 0x6fc31b99,
+  0x6fc00b60, 0x6fbcfae2, 0x6fb9ea20, 0x6fb6d918, 0x6fb3c7cb, 0x6fb0b63a,
+    0x6fada464, 0x6faa9248,
+  0x6fa77fe8, 0x6fa46d43, 0x6fa15a59, 0x6f9e472b, 0x6f9b33b7, 0x6f981fff,
+    0x6f950c01, 0x6f91f7bf,
+  0x6f8ee338, 0x6f8bce6c, 0x6f88b95c, 0x6f85a407, 0x6f828e6c, 0x6f7f788d,
+    0x6f7c626a, 0x6f794c01,
+  0x6f763554, 0x6f731e62, 0x6f70072b, 0x6f6cefb0, 0x6f69d7f0, 0x6f66bfeb,
+    0x6f63a7a1, 0x6f608f13,
+  0x6f5d7640, 0x6f5a5d28, 0x6f5743cb, 0x6f542a2a, 0x6f511044, 0x6f4df61a,
+    0x6f4adbab, 0x6f47c0f7,
+  0x6f44a5ff, 0x6f418ac2, 0x6f3e6f40, 0x6f3b537a, 0x6f38376f, 0x6f351b1f,
+    0x6f31fe8b, 0x6f2ee1b2,
+  0x6f2bc495, 0x6f28a733, 0x6f25898d, 0x6f226ba2, 0x6f1f4d72, 0x6f1c2efe,
+    0x6f191045, 0x6f15f148,
+  0x6f12d206, 0x6f0fb280, 0x6f0c92b6, 0x6f0972a6, 0x6f065253, 0x6f0331ba,
+    0x6f0010de, 0x6efcefbd,
+  0x6ef9ce57, 0x6ef6acad, 0x6ef38abe, 0x6ef0688b, 0x6eed4614, 0x6eea2358,
+    0x6ee70058, 0x6ee3dd13,
+  0x6ee0b98a, 0x6edd95bd, 0x6eda71ab, 0x6ed74d55, 0x6ed428ba, 0x6ed103db,
+    0x6ecddeb8, 0x6ecab950,
+  0x6ec793a4, 0x6ec46db4, 0x6ec1477f, 0x6ebe2106, 0x6ebafa49, 0x6eb7d347,
+    0x6eb4ac02, 0x6eb18477,
+  0x6eae5ca9, 0x6eab3496, 0x6ea80c3f, 0x6ea4e3a4, 0x6ea1bac4, 0x6e9e91a1,
+    0x6e9b6839, 0x6e983e8d,
+  0x6e95149c, 0x6e91ea67, 0x6e8ebfef, 0x6e8b9532, 0x6e886a30, 0x6e853eeb,
+    0x6e821361, 0x6e7ee794,
+  0x6e7bbb82, 0x6e788f2c, 0x6e756291, 0x6e7235b3, 0x6e6f0890, 0x6e6bdb2a,
+    0x6e68ad7f, 0x6e657f90,
+  0x6e62515d, 0x6e5f22e6, 0x6e5bf42b, 0x6e58c52c, 0x6e5595e9, 0x6e526662,
+    0x6e4f3696, 0x6e4c0687,
+  0x6e48d633, 0x6e45a59c, 0x6e4274c1, 0x6e3f43a1, 0x6e3c123e, 0x6e38e096,
+    0x6e35aeab, 0x6e327c7b,
+  0x6e2f4a08, 0x6e2c1750, 0x6e28e455, 0x6e25b115, 0x6e227d92, 0x6e1f49cb,
+    0x6e1c15c0, 0x6e18e171,
+  0x6e15acde, 0x6e127807, 0x6e0f42ec, 0x6e0c0d8e, 0x6e08d7eb, 0x6e05a205,
+    0x6e026bda, 0x6dff356c,
+  0x6dfbfeba, 0x6df8c7c4, 0x6df5908b, 0x6df2590d, 0x6def214c, 0x6debe947,
+    0x6de8b0fe, 0x6de57871,
+  0x6de23fa0, 0x6ddf068c, 0x6ddbcd34, 0x6dd89398, 0x6dd559b9, 0x6dd21f95,
+    0x6dcee52e, 0x6dcbaa83,
+  0x6dc86f95, 0x6dc53462, 0x6dc1f8ec, 0x6dbebd33, 0x6dbb8135, 0x6db844f4,
+    0x6db5086f, 0x6db1cba7,
+  0x6dae8e9b, 0x6dab514b, 0x6da813b8, 0x6da4d5e1, 0x6da197c6, 0x6d9e5968,
+    0x6d9b1ac6, 0x6d97dbe0,
+  0x6d949cb7, 0x6d915d4a, 0x6d8e1d9a, 0x6d8adda6, 0x6d879d6e, 0x6d845cf3,
+    0x6d811c35, 0x6d7ddb33,
+  0x6d7a99ed, 0x6d775864, 0x6d741697, 0x6d70d487, 0x6d6d9233, 0x6d6a4f9c,
+    0x6d670cc1, 0x6d63c9a3,
+  0x6d608641, 0x6d5d429c, 0x6d59feb3, 0x6d56ba87, 0x6d537617, 0x6d503164,
+    0x6d4cec6e, 0x6d49a734,
+  0x6d4661b7, 0x6d431bf6, 0x6d3fd5f2, 0x6d3c8fab, 0x6d394920, 0x6d360252,
+    0x6d32bb40, 0x6d2f73eb,
+  0x6d2c2c53, 0x6d28e477, 0x6d259c58, 0x6d2253f6, 0x6d1f0b50, 0x6d1bc267,
+    0x6d18793b, 0x6d152fcc,
+  0x6d11e619, 0x6d0e9c23, 0x6d0b51e9, 0x6d08076d, 0x6d04bcad, 0x6d0171aa,
+    0x6cfe2663, 0x6cfadada,
+  0x6cf78f0d, 0x6cf442fd, 0x6cf0f6aa, 0x6cedaa13, 0x6cea5d3a, 0x6ce7101d,
+    0x6ce3c2bd, 0x6ce0751a,
+  0x6cdd2733, 0x6cd9d90a, 0x6cd68a9d, 0x6cd33bed, 0x6ccfecfa, 0x6ccc9dc4,
+    0x6cc94e4b, 0x6cc5fe8f,
+  0x6cc2ae90, 0x6cbf5e4d, 0x6cbc0dc8, 0x6cb8bcff, 0x6cb56bf4, 0x6cb21aa5,
+    0x6caec913, 0x6cab773e,
+  0x6ca82527, 0x6ca4d2cc, 0x6ca1802e, 0x6c9e2d4d, 0x6c9ada29, 0x6c9786c2,
+    0x6c943318, 0x6c90df2c,
+  0x6c8d8afc, 0x6c8a3689, 0x6c86e1d3, 0x6c838cdb, 0x6c80379f, 0x6c7ce220,
+    0x6c798c5f, 0x6c76365b,
+  0x6c72e013, 0x6c6f8989, 0x6c6c32bc, 0x6c68dbac, 0x6c658459, 0x6c622cc4,
+    0x6c5ed4eb, 0x6c5b7cd0,
+  0x6c582472, 0x6c54cbd1, 0x6c5172ed, 0x6c4e19c6, 0x6c4ac05d, 0x6c4766b0,
+    0x6c440cc1, 0x6c40b28f,
+  0x6c3d581b, 0x6c39fd63, 0x6c36a269, 0x6c33472c, 0x6c2febad, 0x6c2c8fea,
+    0x6c2933e5, 0x6c25d79d,
+  0x6c227b13, 0x6c1f1e45, 0x6c1bc136, 0x6c1863e3, 0x6c15064e, 0x6c11a876,
+    0x6c0e4a5b, 0x6c0aebfe,
+  0x6c078d5e, 0x6c042e7b, 0x6c00cf56, 0x6bfd6fee, 0x6bfa1044, 0x6bf6b056,
+    0x6bf35027, 0x6befefb5,
+  0x6bec8f00, 0x6be92e08, 0x6be5ccce, 0x6be26b52, 0x6bdf0993, 0x6bdba791,
+    0x6bd8454d, 0x6bd4e2c6,
+  0x6bd17ffd, 0x6bce1cf1, 0x6bcab9a3, 0x6bc75613, 0x6bc3f23f, 0x6bc08e2a,
+    0x6bbd29d2, 0x6bb9c537,
+  0x6bb6605a, 0x6bb2fb3b, 0x6baf95d9, 0x6bac3034, 0x6ba8ca4e, 0x6ba56425,
+    0x6ba1fdb9, 0x6b9e970b,
+  0x6b9b301b, 0x6b97c8e8, 0x6b946173, 0x6b90f9bc, 0x6b8d91c2, 0x6b8a2986,
+    0x6b86c107, 0x6b835846,
+  0x6b7fef43, 0x6b7c85fe, 0x6b791c76, 0x6b75b2ac, 0x6b7248a0, 0x6b6ede51,
+    0x6b6b73c0, 0x6b6808ed,
+  0x6b649dd8, 0x6b613280, 0x6b5dc6e6, 0x6b5a5b0a, 0x6b56eeec, 0x6b53828b,
+    0x6b5015e9, 0x6b4ca904,
+  0x6b493bdd, 0x6b45ce73, 0x6b4260c8, 0x6b3ef2da, 0x6b3b84ab, 0x6b381639,
+    0x6b34a785, 0x6b31388e,
+  0x6b2dc956, 0x6b2a59dc, 0x6b26ea1f, 0x6b237a21, 0x6b2009e0, 0x6b1c995d,
+    0x6b192898, 0x6b15b791,
+  0x6b124648, 0x6b0ed4bd, 0x6b0b62f0, 0x6b07f0e1, 0x6b047e90, 0x6b010bfd,
+    0x6afd9928, 0x6afa2610,
+  0x6af6b2b7, 0x6af33f1c, 0x6aefcb3f, 0x6aec5720, 0x6ae8e2bf, 0x6ae56e1c,
+    0x6ae1f937, 0x6ade8410,
+  0x6adb0ea8, 0x6ad798fd, 0x6ad42311, 0x6ad0ace2, 0x6acd3672, 0x6ac9bfc0,
+    0x6ac648cb, 0x6ac2d195,
+  0x6abf5a1e, 0x6abbe264, 0x6ab86a68, 0x6ab4f22b, 0x6ab179ac, 0x6aae00eb,
+    0x6aaa87e8, 0x6aa70ea4,
+  0x6aa3951d, 0x6aa01b55, 0x6a9ca14b, 0x6a992700, 0x6a95ac72, 0x6a9231a3,
+    0x6a8eb692, 0x6a8b3b3f,
+  0x6a87bfab, 0x6a8443d5, 0x6a80c7bd, 0x6a7d4b64, 0x6a79cec8, 0x6a7651ec,
+    0x6a72d4cd, 0x6a6f576d,
+  0x6a6bd9cb, 0x6a685be8, 0x6a64ddc2, 0x6a615f5c, 0x6a5de0b3, 0x6a5a61c9,
+    0x6a56e29e, 0x6a536331,
+  0x6a4fe382, 0x6a4c6391, 0x6a48e360, 0x6a4562ec, 0x6a41e237, 0x6a3e6140,
+    0x6a3ae008, 0x6a375e8f,
+  0x6a33dcd4, 0x6a305ad7, 0x6a2cd899, 0x6a295619, 0x6a25d358, 0x6a225055,
+    0x6a1ecd11, 0x6a1b498c,
+  0x6a17c5c5, 0x6a1441bc, 0x6a10bd72, 0x6a0d38e7, 0x6a09b41a, 0x6a062f0c,
+    0x6a02a9bc, 0x69ff242b,
+  0x69fb9e59, 0x69f81845, 0x69f491f0, 0x69f10b5a, 0x69ed8482, 0x69e9fd69,
+    0x69e6760f, 0x69e2ee73,
+  0x69df6696, 0x69dbde77, 0x69d85618, 0x69d4cd77, 0x69d14494, 0x69cdbb71,
+    0x69ca320c, 0x69c6a866,
+  0x69c31e7f, 0x69bf9456, 0x69bc09ec, 0x69b87f41, 0x69b4f455, 0x69b16928,
+    0x69adddb9, 0x69aa5209,
+  0x69a6c618, 0x69a339e6, 0x699fad73, 0x699c20be, 0x699893c9, 0x69950692,
+    0x6991791a, 0x698deb61,
+  0x698a5d67, 0x6986cf2c, 0x698340af, 0x697fb1f2, 0x697c22f3, 0x697893b4,
+    0x69750433, 0x69717472,
+  0x696de46f, 0x696a542b, 0x6966c3a6, 0x696332e1, 0x695fa1da, 0x695c1092,
+    0x69587f09, 0x6954ed40,
+  0x69515b35, 0x694dc8e9, 0x694a365c, 0x6946a38f, 0x69431080, 0x693f7d31,
+    0x693be9a0, 0x693855cf,
+  0x6934c1bd, 0x69312d6a, 0x692d98d6, 0x692a0401, 0x69266eeb, 0x6922d995,
+    0x691f43fd, 0x691bae25,
+  0x6918180c, 0x691481b2, 0x6910eb17, 0x690d543b, 0x6909bd1f, 0x690625c2,
+    0x69028e24, 0x68fef645,
+  0x68fb5e25, 0x68f7c5c5, 0x68f42d24, 0x68f09442, 0x68ecfb20, 0x68e961bd,
+    0x68e5c819, 0x68e22e34,
+  0x68de940f, 0x68daf9a9, 0x68d75f02, 0x68d3c41b, 0x68d028f2, 0x68cc8d8a,
+    0x68c8f1e0, 0x68c555f6,
+  0x68c1b9cc, 0x68be1d61, 0x68ba80b5, 0x68b6e3c8, 0x68b3469b, 0x68afa92e,
+    0x68ac0b7f, 0x68a86d91,
+  0x68a4cf61, 0x68a130f1, 0x689d9241, 0x6899f350, 0x6896541f, 0x6892b4ad,
+    0x688f14fa, 0x688b7507,
+  0x6887d4d4, 0x68843460, 0x688093ab, 0x687cf2b6, 0x68795181, 0x6875b00b,
+    0x68720e55, 0x686e6c5e,
+  0x686aca27, 0x686727b0, 0x686384f8, 0x685fe200, 0x685c3ec7, 0x68589b4e,
+    0x6854f795, 0x6851539b,
+  0x684daf61, 0x684a0ae6, 0x6846662c, 0x6842c131, 0x683f1bf5, 0x683b7679,
+    0x6837d0bd, 0x68342ac1,
+  0x68308485, 0x682cde08, 0x6829374b, 0x6825904d, 0x6821e910, 0x681e4192,
+    0x681a99d4, 0x6816f1d6,
+  0x68134997, 0x680fa118, 0x680bf85a, 0x68084f5a, 0x6804a61b, 0x6800fc9c,
+    0x67fd52dc, 0x67f9a8dd,
+  0x67f5fe9d, 0x67f2541d, 0x67eea95d, 0x67eafe5d, 0x67e7531c, 0x67e3a79c,
+    0x67dffbdc, 0x67dc4fdb,
+  0x67d8a39a, 0x67d4f71a, 0x67d14a59, 0x67cd9d58, 0x67c9f017, 0x67c64297,
+    0x67c294d6, 0x67bee6d5,
+  0x67bb3894, 0x67b78a13, 0x67b3db53, 0x67b02c52, 0x67ac7d11, 0x67a8cd91,
+    0x67a51dd0, 0x67a16dcf,
+  0x679dbd8f, 0x679a0d0f, 0x67965c4e, 0x6792ab4e, 0x678efa0e, 0x678b488e,
+    0x678796ce, 0x6783e4cf,
+  0x6780328f, 0x677c8010, 0x6778cd50, 0x67751a51, 0x67716713, 0x676db394,
+    0x6769ffd5, 0x67664bd7,
+  0x67629799, 0x675ee31b, 0x675b2e5e, 0x67577960, 0x6753c423, 0x67500ea7,
+    0x674c58ea, 0x6748a2ee,
+  0x6744ecb2, 0x67413636, 0x673d7f7b, 0x6739c880, 0x67361145, 0x673259ca,
+    0x672ea210, 0x672aea17,
+  0x672731dd, 0x67237964, 0x671fc0ac, 0x671c07b4, 0x67184e7c, 0x67149504,
+    0x6710db4d, 0x670d2157,
+  0x67096721, 0x6705acab, 0x6701f1f6, 0x66fe3701, 0x66fa7bcd, 0x66f6c059,
+    0x66f304a6, 0x66ef48b3,
+  0x66eb8c80, 0x66e7d00f, 0x66e4135d, 0x66e0566c, 0x66dc993c, 0x66d8dbcd,
+    0x66d51e1d, 0x66d1602f,
+  0x66cda201, 0x66c9e393, 0x66c624e7, 0x66c265fa, 0x66bea6cf, 0x66bae764,
+    0x66b727ba, 0x66b367d0,
+  0x66afa7a7, 0x66abe73f, 0x66a82697, 0x66a465b0, 0x66a0a489, 0x669ce324,
+    0x6699217f, 0x66955f9b,
+  0x66919d77, 0x668ddb14, 0x668a1872, 0x66865591, 0x66829270, 0x667ecf11,
+    0x667b0b72, 0x66774793,
+  0x66738376, 0x666fbf19, 0x666bfa7d, 0x666835a2, 0x66647088, 0x6660ab2f,
+    0x665ce596, 0x66591fbf,
+  0x665559a8, 0x66519352, 0x664dccbd, 0x664a05e9, 0x66463ed6, 0x66427784,
+    0x663eaff2, 0x663ae822,
+  0x66372012, 0x663357c4, 0x662f8f36, 0x662bc66a, 0x6627fd5e, 0x66243413,
+    0x66206a8a, 0x661ca0c1,
+  0x6618d6b9, 0x66150c73, 0x661141ed, 0x660d7729, 0x6609ac25, 0x6605e0e3,
+    0x66021561, 0x65fe49a1,
+  0x65fa7da2, 0x65f6b164, 0x65f2e4e7, 0x65ef182b, 0x65eb4b30, 0x65e77df6,
+    0x65e3b07e, 0x65dfe2c6,
+  0x65dc14d0, 0x65d8469b, 0x65d47827, 0x65d0a975, 0x65ccda83, 0x65c90b53,
+    0x65c53be4, 0x65c16c36,
+  0x65bd9c49, 0x65b9cc1e, 0x65b5fbb4, 0x65b22b0b, 0x65ae5a23, 0x65aa88fd,
+    0x65a6b798, 0x65a2e5f4,
+  0x659f1412, 0x659b41f1, 0x65976f91, 0x65939cf3, 0x658fca15, 0x658bf6fa,
+    0x6588239f, 0x65845006,
+  0x65807c2f, 0x657ca818, 0x6578d3c4, 0x6574ff30, 0x65712a5e, 0x656d554d,
+    0x65697ffe, 0x6565aa71,
+  0x6561d4a4, 0x655dfe99, 0x655a2850, 0x655651c8, 0x65527b02, 0x654ea3fd,
+    0x654accba, 0x6546f538,
+  0x65431d77, 0x653f4579, 0x653b6d3b, 0x653794c0, 0x6533bc06, 0x652fe30d,
+    0x652c09d6, 0x65283061,
+  0x652456ad, 0x65207cbb, 0x651ca28a, 0x6518c81b, 0x6514ed6e, 0x65111283,
+    0x650d3759, 0x65095bf0,
+  0x6505804a, 0x6501a465, 0x64fdc841, 0x64f9ebe0, 0x64f60f40, 0x64f23262,
+    0x64ee5546, 0x64ea77eb,
+  0x64e69a52, 0x64e2bc7b, 0x64dede66, 0x64db0012, 0x64d72180, 0x64d342b0,
+    0x64cf63a2, 0x64cb8456,
+  0x64c7a4cb, 0x64c3c502, 0x64bfe4fc, 0x64bc04b6, 0x64b82433, 0x64b44372,
+    0x64b06273, 0x64ac8135,
+  0x64a89fba, 0x64a4be00, 0x64a0dc08, 0x649cf9d2, 0x6499175e, 0x649534ac,
+    0x649151bc, 0x648d6e8e,
+  0x64898b22, 0x6485a778, 0x6481c390, 0x647ddf6a, 0x6479fb06, 0x64761664,
+    0x64723184, 0x646e4c66,
+  0x646a670a, 0x64668170, 0x64629b98, 0x645eb582, 0x645acf2e, 0x6456e89d,
+    0x645301cd, 0x644f1ac0,
+  0x644b3375, 0x64474bec, 0x64436425, 0x643f7c20, 0x643b93dd, 0x6437ab5d,
+    0x6433c29f, 0x642fd9a3,
+  0x642bf069, 0x642806f1, 0x64241d3c, 0x64203348, 0x641c4917, 0x64185ea9,
+    0x641473fc, 0x64108912,
+  0x640c9dea, 0x6408b284, 0x6404c6e1, 0x6400db00, 0x63fceee1, 0x63f90285,
+    0x63f515eb, 0x63f12913,
+  0x63ed3bfd, 0x63e94eaa, 0x63e5611a, 0x63e1734b, 0x63dd853f, 0x63d996f6,
+    0x63d5a86f, 0x63d1b9aa,
+  0x63cdcaa8, 0x63c9db68, 0x63c5ebeb, 0x63c1fc30, 0x63be0c37, 0x63ba1c01,
+    0x63b62b8e, 0x63b23add,
+  0x63ae49ee, 0x63aa58c2, 0x63a66759, 0x63a275b2, 0x639e83cd, 0x639a91ac,
+    0x63969f4c, 0x6392acaf,
+  0x638eb9d5, 0x638ac6be, 0x6386d369, 0x6382dfd6, 0x637eec07, 0x637af7fa,
+    0x637703af, 0x63730f27,
+  0x636f1a62, 0x636b2560, 0x63673020, 0x63633aa3, 0x635f44e8, 0x635b4ef0,
+    0x635758bb, 0x63536249,
+  0x634f6b99, 0x634b74ad, 0x63477d82, 0x6343861b, 0x633f8e76, 0x633b9695,
+    0x63379e76, 0x6333a619,
+  0x632fad80, 0x632bb4a9, 0x6327bb96, 0x6323c245, 0x631fc8b7, 0x631bceeb,
+    0x6317d4e3, 0x6313da9e,
+  0x630fe01b, 0x630be55b, 0x6307ea5e, 0x6303ef25, 0x62fff3ae, 0x62fbf7fa,
+    0x62f7fc08, 0x62f3ffda,
+  0x62f0036f, 0x62ec06c7, 0x62e809e2, 0x62e40cbf, 0x62e00f60, 0x62dc11c4,
+    0x62d813eb, 0x62d415d4,
+  0x62d01781, 0x62cc18f1, 0x62c81a24, 0x62c41b1a, 0x62c01bd3, 0x62bc1c4f,
+    0x62b81c8f, 0x62b41c91,
+  0x62b01c57, 0x62ac1bdf, 0x62a81b2b, 0x62a41a3a, 0x62a0190c, 0x629c17a1,
+    0x629815fa, 0x62941415,
+  0x629011f4, 0x628c0f96, 0x62880cfb, 0x62840a23, 0x6280070f, 0x627c03be,
+    0x62780030, 0x6273fc65,
+  0x626ff85e, 0x626bf41a, 0x6267ef99, 0x6263eadc, 0x625fe5e1, 0x625be0ab,
+    0x6257db37, 0x6253d587,
+  0x624fcf9a, 0x624bc970, 0x6247c30a, 0x6243bc68, 0x623fb588, 0x623bae6c,
+    0x6237a714, 0x62339f7e,
+  0x622f97ad, 0x622b8f9e, 0x62278754, 0x62237ecc, 0x621f7608, 0x621b6d08,
+    0x621763cb, 0x62135a51,
+  0x620f509b, 0x620b46a9, 0x62073c7a, 0x6203320e, 0x61ff2766, 0x61fb1c82,
+    0x61f71161, 0x61f30604,
+  0x61eefa6b, 0x61eaee95, 0x61e6e282, 0x61e2d633, 0x61dec9a8, 0x61dabce0,
+    0x61d6afdd, 0x61d2a29c,
+  0x61ce9520, 0x61ca8767, 0x61c67971, 0x61c26b40, 0x61be5cd2, 0x61ba4e28,
+    0x61b63f41, 0x61b2301e,
+  0x61ae20bf, 0x61aa1124, 0x61a6014d, 0x61a1f139, 0x619de0e9, 0x6199d05d,
+    0x6195bf94, 0x6191ae90,
+  0x618d9d4f, 0x61898bd2, 0x61857a19, 0x61816824, 0x617d55f2, 0x61794385,
+    0x617530db, 0x61711df5,
+  0x616d0ad3, 0x6168f775, 0x6164e3db, 0x6160d005, 0x615cbbf3, 0x6158a7a4,
+    0x6154931a, 0x61507e54,
+  0x614c6951, 0x61485413, 0x61443e98, 0x614028e2, 0x613c12f0, 0x6137fcc1,
+    0x6133e657, 0x612fcfb0,
+  0x612bb8ce, 0x6127a1b0, 0x61238a56, 0x611f72c0, 0x611b5aee, 0x611742e0,
+    0x61132a96, 0x610f1210,
+  0x610af94f, 0x6106e051, 0x6102c718, 0x60feada3, 0x60fa93f2, 0x60f67a05,
+    0x60f25fdd, 0x60ee4579,
+  0x60ea2ad8, 0x60e60ffd, 0x60e1f4e5, 0x60ddd991, 0x60d9be02, 0x60d5a237,
+    0x60d18631, 0x60cd69ee,
+  0x60c94d70, 0x60c530b6, 0x60c113c1, 0x60bcf690, 0x60b8d923, 0x60b4bb7a,
+    0x60b09d96, 0x60ac7f76,
+  0x60a8611b, 0x60a44284, 0x60a023b1, 0x609c04a3, 0x6097e559, 0x6093c5d3,
+    0x608fa612, 0x608b8616,
+  0x608765dd, 0x6083456a, 0x607f24ba, 0x607b03d0, 0x6076e2a9, 0x6072c148,
+    0x606e9faa, 0x606a7dd2,
+  0x60665bbd, 0x6062396e, 0x605e16e2, 0x6059f41c, 0x6055d11a, 0x6051addc,
+    0x604d8a63, 0x604966af,
+  0x604542bf, 0x60411e94, 0x603cfa2e, 0x6038d58c, 0x6034b0af, 0x60308b97,
+    0x602c6643, 0x602840b4,
+  0x60241ae9, 0x601ff4e3, 0x601bcea2, 0x6017a826, 0x6013816e, 0x600f5a7b,
+    0x600b334d, 0x60070be4,
+  0x6002e43f, 0x5ffebc5f, 0x5ffa9444, 0x5ff66bee, 0x5ff2435d, 0x5fee1a90,
+    0x5fe9f188, 0x5fe5c845,
+  0x5fe19ec7, 0x5fdd750e, 0x5fd94b19, 0x5fd520ea, 0x5fd0f67f, 0x5fcccbd9,
+    0x5fc8a0f8, 0x5fc475dc,
+  0x5fc04a85, 0x5fbc1ef3, 0x5fb7f326, 0x5fb3c71e, 0x5faf9adb, 0x5fab6e5d,
+    0x5fa741a3, 0x5fa314af,
+  0x5f9ee780, 0x5f9aba16, 0x5f968c70, 0x5f925e90, 0x5f8e3075, 0x5f8a021f,
+    0x5f85d38e, 0x5f81a4c2,
+  0x5f7d75bb, 0x5f794679, 0x5f7516fd, 0x5f70e745, 0x5f6cb753, 0x5f688726,
+    0x5f6456be, 0x5f60261b,
+  0x5f5bf53d, 0x5f57c424, 0x5f5392d1, 0x5f4f6143, 0x5f4b2f7a, 0x5f46fd76,
+    0x5f42cb37, 0x5f3e98be,
+  0x5f3a660a, 0x5f36331b, 0x5f31fff1, 0x5f2dcc8d, 0x5f2998ee, 0x5f256515,
+    0x5f213100, 0x5f1cfcb1,
+  0x5f18c827, 0x5f149363, 0x5f105e64, 0x5f0c292a, 0x5f07f3b6, 0x5f03be07,
+    0x5eff881d, 0x5efb51f9,
+  0x5ef71b9b, 0x5ef2e501, 0x5eeeae2d, 0x5eea771f, 0x5ee63fd6, 0x5ee20853,
+    0x5eddd094, 0x5ed9989c,
+  0x5ed56069, 0x5ed127fb, 0x5eccef53, 0x5ec8b671, 0x5ec47d54, 0x5ec043fc,
+    0x5ebc0a6a, 0x5eb7d09e,
+  0x5eb39697, 0x5eaf5c56, 0x5eab21da, 0x5ea6e724, 0x5ea2ac34, 0x5e9e7109,
+    0x5e9a35a4, 0x5e95fa05,
+  0x5e91be2b, 0x5e8d8217, 0x5e8945c8, 0x5e85093f, 0x5e80cc7c, 0x5e7c8f7f,
+    0x5e785247, 0x5e7414d5,
+  0x5e6fd729, 0x5e6b9943, 0x5e675b22, 0x5e631cc7, 0x5e5ede32, 0x5e5a9f62,
+    0x5e566059, 0x5e522115,
+  0x5e4de197, 0x5e49a1df, 0x5e4561ed, 0x5e4121c0, 0x5e3ce15a, 0x5e38a0b9,
+    0x5e345fde, 0x5e301ec9,
+  0x5e2bdd7a, 0x5e279bf1, 0x5e235a2e, 0x5e1f1830, 0x5e1ad5f9, 0x5e169388,
+    0x5e1250dc, 0x5e0e0df7,
+  0x5e09cad7, 0x5e05877e, 0x5e0143ea, 0x5dfd001d, 0x5df8bc15, 0x5df477d4,
+    0x5df03359, 0x5debeea3,
+  0x5de7a9b4, 0x5de3648b, 0x5ddf1f28, 0x5ddad98b, 0x5dd693b4, 0x5dd24da3,
+    0x5dce0759, 0x5dc9c0d4,
+  0x5dc57a16, 0x5dc1331d, 0x5dbcebeb, 0x5db8a480, 0x5db45cda, 0x5db014fa,
+    0x5dabcce1, 0x5da7848e,
+  0x5da33c01, 0x5d9ef33b, 0x5d9aaa3a, 0x5d966100, 0x5d92178d, 0x5d8dcddf,
+    0x5d8983f8, 0x5d8539d7,
+  0x5d80ef7c, 0x5d7ca4e8, 0x5d785a1a, 0x5d740f12, 0x5d6fc3d1, 0x5d6b7856,
+    0x5d672ca2, 0x5d62e0b4,
+  0x5d5e948c, 0x5d5a482a, 0x5d55fb90, 0x5d51aebb, 0x5d4d61ad, 0x5d491465,
+    0x5d44c6e4, 0x5d40792a,
+  0x5d3c2b35, 0x5d37dd08, 0x5d338ea0, 0x5d2f4000, 0x5d2af125, 0x5d26a212,
+    0x5d2252c5, 0x5d1e033e,
+  0x5d19b37e, 0x5d156385, 0x5d111352, 0x5d0cc2e5, 0x5d087240, 0x5d042161,
+    0x5cffd048, 0x5cfb7ef7,
+  0x5cf72d6b, 0x5cf2dba7, 0x5cee89a9, 0x5cea3772, 0x5ce5e501, 0x5ce19258,
+    0x5cdd3f75, 0x5cd8ec58,
+  0x5cd49903, 0x5cd04574, 0x5ccbf1ab, 0x5cc79daa, 0x5cc3496f, 0x5cbef4fc,
+    0x5cbaa04f, 0x5cb64b68,
+  0x5cb1f649, 0x5cada0f0, 0x5ca94b5e, 0x5ca4f594, 0x5ca09f8f, 0x5c9c4952,
+    0x5c97f2dc, 0x5c939c2c,
+  0x5c8f4544, 0x5c8aee22, 0x5c8696c7, 0x5c823f34, 0x5c7de767, 0x5c798f61,
+    0x5c753722, 0x5c70deaa,
+  0x5c6c85f9, 0x5c682d0f, 0x5c63d3eb, 0x5c5f7a8f, 0x5c5b20fa, 0x5c56c72c,
+    0x5c526d25, 0x5c4e12e5,
+  0x5c49b86d, 0x5c455dbb, 0x5c4102d0, 0x5c3ca7ad, 0x5c384c50, 0x5c33f0bb,
+    0x5c2f94ec, 0x5c2b38e5,
+  0x5c26dca5, 0x5c22802c, 0x5c1e237b, 0x5c19c690, 0x5c15696d, 0x5c110c11,
+    0x5c0cae7c, 0x5c0850ae,
+  0x5c03f2a8, 0x5bff9469, 0x5bfb35f1, 0x5bf6d740, 0x5bf27857, 0x5bee1935,
+    0x5be9b9da, 0x5be55a46,
+  0x5be0fa7a, 0x5bdc9a75, 0x5bd83a37, 0x5bd3d9c1, 0x5bcf7912, 0x5bcb182b,
+    0x5bc6b70b, 0x5bc255b2,
+  0x5bbdf421, 0x5bb99257, 0x5bb53054, 0x5bb0ce19, 0x5bac6ba6, 0x5ba808f9,
+    0x5ba3a615, 0x5b9f42f7,
+  0x5b9adfa2, 0x5b967c13, 0x5b92184d, 0x5b8db44d, 0x5b895016, 0x5b84eba6,
+    0x5b8086fd, 0x5b7c221c,
+  0x5b77bd02, 0x5b7357b0, 0x5b6ef226, 0x5b6a8c63, 0x5b662668, 0x5b61c035,
+    0x5b5d59c9, 0x5b58f324,
+  0x5b548c48, 0x5b502533, 0x5b4bbde6, 0x5b475660, 0x5b42eea2, 0x5b3e86ac,
+    0x5b3a1e7e, 0x5b35b617,
+  0x5b314d78, 0x5b2ce4a1, 0x5b287b91, 0x5b241249, 0x5b1fa8c9, 0x5b1b3f11,
+    0x5b16d521, 0x5b126af8,
+  0x5b0e0098, 0x5b0995ff, 0x5b052b2e, 0x5b00c025, 0x5afc54e3, 0x5af7e96a,
+    0x5af37db8, 0x5aef11cf,
+  0x5aeaa5ad, 0x5ae63953, 0x5ae1ccc1, 0x5add5ff7, 0x5ad8f2f5, 0x5ad485bb,
+    0x5ad01849, 0x5acbaa9f,
+  0x5ac73cbd, 0x5ac2cea3, 0x5abe6050, 0x5ab9f1c6, 0x5ab58304, 0x5ab1140a,
+    0x5aaca4d8, 0x5aa8356f,
+  0x5aa3c5cd, 0x5a9f55f3, 0x5a9ae5e2, 0x5a967598, 0x5a920517, 0x5a8d945d,
+    0x5a89236c, 0x5a84b243,
+  0x5a8040e3, 0x5a7bcf4a, 0x5a775d7a, 0x5a72eb71, 0x5a6e7931, 0x5a6a06ba,
+    0x5a65940a, 0x5a612123,
+  0x5a5cae04, 0x5a583aad, 0x5a53c71e, 0x5a4f5358, 0x5a4adf5a, 0x5a466b24,
+    0x5a41f6b7, 0x5a3d8212,
+  0x5a390d35, 0x5a349821, 0x5a3022d5, 0x5a2bad51, 0x5a273796, 0x5a22c1a3,
+    0x5a1e4b79, 0x5a19d517,
+  0x5a155e7d, 0x5a10e7ac, 0x5a0c70a3, 0x5a07f963, 0x5a0381eb, 0x59ff0a3c,
+    0x59fa9255, 0x59f61a36,
+  0x59f1a1e0, 0x59ed2953, 0x59e8b08e, 0x59e43792, 0x59dfbe5e, 0x59db44f3,
+    0x59d6cb50, 0x59d25176,
+  0x59cdd765, 0x59c95d1c, 0x59c4e29c, 0x59c067e4, 0x59bbecf5, 0x59b771cf,
+    0x59b2f671, 0x59ae7add,
+  0x59a9ff10, 0x59a5830d, 0x59a106d2, 0x599c8a60, 0x59980db6, 0x599390d5,
+    0x598f13bd, 0x598a966e,
+  0x598618e8, 0x59819b2a, 0x597d1d35, 0x59789f09, 0x597420a6, 0x596fa20b,
+    0x596b233a, 0x5966a431,
+  0x596224f1, 0x595da57a, 0x595925cc, 0x5954a5e6, 0x595025ca, 0x594ba576,
+    0x594724ec, 0x5942a42a,
+  0x593e2331, 0x5939a202, 0x5935209b, 0x59309efd, 0x592c1d28, 0x59279b1c,
+    0x592318d9, 0x591e9660,
+  0x591a13af, 0x591590c7, 0x59110da8, 0x590c8a53, 0x590806c6, 0x59038302,
+    0x58feff08, 0x58fa7ad7,
+  0x58f5f66e, 0x58f171cf, 0x58ececf9, 0x58e867ed, 0x58e3e2a9, 0x58df5d2e,
+    0x58dad77d, 0x58d65195,
+  0x58d1cb76, 0x58cd4520, 0x58c8be94, 0x58c437d1, 0x58bfb0d7, 0x58bb29a6,
+    0x58b6a23e, 0x58b21aa0,
+  0x58ad92cb, 0x58a90ac0, 0x58a4827d, 0x589ffa04, 0x589b7155, 0x5896e86f,
+    0x58925f52, 0x588dd5fe,
+  0x58894c74, 0x5884c2b3, 0x588038bb, 0x587bae8d, 0x58772429, 0x5872998e,
+    0x586e0ebc, 0x586983b4,
+  0x5864f875, 0x58606d00, 0x585be154, 0x58575571, 0x5852c958, 0x584e3d09,
+    0x5849b083, 0x584523c7,
+  0x584096d4, 0x583c09ab, 0x58377c4c, 0x5832eeb6, 0x582e60e9, 0x5829d2e6,
+    0x582544ad, 0x5820b63e,
+  0x581c2798, 0x581798bb, 0x581309a9, 0x580e7a60, 0x5809eae1, 0x58055b2b,
+    0x5800cb3f, 0x57fc3b1d,
+  0x57f7aac5, 0x57f31a36, 0x57ee8971, 0x57e9f876, 0x57e56744, 0x57e0d5dd,
+    0x57dc443f, 0x57d7b26b,
+  0x57d32061, 0x57ce8e20, 0x57c9fbaa, 0x57c568fd, 0x57c0d61a, 0x57bc4301,
+    0x57b7afb2, 0x57b31c2d,
+  0x57ae8872, 0x57a9f480, 0x57a56059, 0x57a0cbfb, 0x579c3768, 0x5797a29e,
+    0x57930d9e, 0x578e7869,
+  0x5789e2fd, 0x57854d5b, 0x5780b784, 0x577c2176, 0x57778b32, 0x5772f4b9,
+    0x576e5e09, 0x5769c724,
+  0x57653009, 0x576098b7, 0x575c0130, 0x57576973, 0x5752d180, 0x574e3957,
+    0x5749a0f9, 0x57450864,
+  0x57406f9a, 0x573bd69a, 0x57373d64, 0x5732a3f8, 0x572e0a56, 0x5729707f,
+    0x5724d672, 0x57203c2f,
+  0x571ba1b7, 0x57170708, 0x57126c24, 0x570dd10a, 0x570935bb, 0x57049a36,
+    0x56fffe7b, 0x56fb628b,
+  0x56f6c664, 0x56f22a09, 0x56ed8d77, 0x56e8f0b0, 0x56e453b4, 0x56dfb681,
+    0x56db1919, 0x56d67b7c,
+  0x56d1dda9, 0x56cd3fa1, 0x56c8a162, 0x56c402ef, 0x56bf6446, 0x56bac567,
+    0x56b62653, 0x56b18709,
+  0x56ace78a, 0x56a847d6, 0x56a3a7ec, 0x569f07cc, 0x569a6777, 0x5695c6ed,
+    0x5691262d, 0x568c8538,
+  0x5687e40e, 0x568342ae, 0x567ea118, 0x5679ff4e, 0x56755d4e, 0x5670bb19,
+    0x566c18ae, 0x5667760e,
+  0x5662d339, 0x565e302e, 0x56598cee, 0x5654e979, 0x565045cf, 0x564ba1f0,
+    0x5646fddb, 0x56425991,
+  0x563db512, 0x5639105d, 0x56346b74, 0x562fc655, 0x562b2101, 0x56267b78,
+    0x5621d5ba, 0x561d2fc6,
+  0x5618899e, 0x5613e340, 0x560f3cae, 0x560a95e6, 0x5605eee9, 0x560147b7,
+    0x55fca050, 0x55f7f8b4,
+  0x55f350e3, 0x55eea8dd, 0x55ea00a2, 0x55e55832, 0x55e0af8d, 0x55dc06b3,
+    0x55d75da4, 0x55d2b460,
+  0x55ce0ae7, 0x55c96139, 0x55c4b757, 0x55c00d3f, 0x55bb62f3, 0x55b6b871,
+    0x55b20dbb, 0x55ad62d0,
+  0x55a8b7b0, 0x55a40c5b, 0x559f60d1, 0x559ab513, 0x55960920, 0x55915cf8,
+    0x558cb09b, 0x55880409,
+  0x55835743, 0x557eaa48, 0x5579fd18, 0x55754fb3, 0x5570a21a, 0x556bf44c,
+    0x55674649, 0x55629812,
+  0x555de9a6, 0x55593b05, 0x55548c30, 0x554fdd26, 0x554b2de7, 0x55467e74,
+    0x5541cecc, 0x553d1ef0,
+  0x55386edf, 0x5533be99, 0x552f0e1f, 0x552a5d70, 0x5525ac8d, 0x5520fb75,
+    0x551c4a29, 0x551798a8,
+  0x5512e6f3, 0x550e3509, 0x550982eb, 0x5504d099, 0x55001e12, 0x54fb6b56,
+    0x54f6b866, 0x54f20542,
+  0x54ed51e9, 0x54e89e5c, 0x54e3ea9a, 0x54df36a5, 0x54da827a, 0x54d5ce1c,
+    0x54d11989, 0x54cc64c2,
+  0x54c7afc6, 0x54c2fa96, 0x54be4532, 0x54b98f9a, 0x54b4d9cd, 0x54b023cc,
+    0x54ab6d97, 0x54a6b72e,
+  0x54a20090, 0x549d49bf, 0x549892b9, 0x5493db7f, 0x548f2410, 0x548a6c6e,
+    0x5485b497, 0x5480fc8c,
+  0x547c444d, 0x54778bda, 0x5472d333, 0x546e1a58, 0x54696149, 0x5464a805,
+    0x545fee8e, 0x545b34e3,
+  0x54567b03, 0x5451c0f0, 0x544d06a8, 0x54484c2d, 0x5443917d, 0x543ed699,
+    0x543a1b82, 0x54356037,
+  0x5430a4b7, 0x542be904, 0x54272d1d, 0x54227102, 0x541db4b3, 0x5418f830,
+    0x54143b79, 0x540f7e8e,
+  0x540ac170, 0x5406041d, 0x54014697, 0x53fc88dd, 0x53f7caef, 0x53f30cce,
+    0x53ee4e78, 0x53e98fef,
+  0x53e4d132, 0x53e01242, 0x53db531d, 0x53d693c5, 0x53d1d439, 0x53cd147a,
+    0x53c85486, 0x53c3945f,
+  0x53bed405, 0x53ba1377, 0x53b552b5, 0x53b091bf, 0x53abd096, 0x53a70f39,
+    0x53a24da9, 0x539d8be5,
+  0x5398c9ed, 0x539407c2, 0x538f4564, 0x538a82d1, 0x5385c00c, 0x5380fd12,
+    0x537c39e6, 0x53777685,
+  0x5372b2f2, 0x536def2a, 0x53692b30, 0x53646701, 0x535fa2a0, 0x535ade0b,
+    0x53561942, 0x53515447,
+  0x534c8f17, 0x5347c9b5, 0x5343041f, 0x533e3e55, 0x53397859, 0x5334b229,
+    0x532febc5, 0x532b252f,
+  0x53265e65, 0x53219767, 0x531cd037, 0x531808d3, 0x5313413c, 0x530e7972,
+    0x5309b174, 0x5304e943,
+  0x530020df, 0x52fb5848, 0x52f68f7e, 0x52f1c680, 0x52ecfd4f, 0x52e833ec,
+    0x52e36a55, 0x52dea08a,
+  0x52d9d68d, 0x52d50c5d, 0x52d041f9, 0x52cb7763, 0x52c6ac99, 0x52c1e19d,
+    0x52bd166d, 0x52b84b0a,
+  0x52b37f74, 0x52aeb3ac, 0x52a9e7b0, 0x52a51b81, 0x52a04f1f, 0x529b828a,
+    0x5296b5c3, 0x5291e8c8,
+  0x528d1b9b, 0x52884e3a, 0x528380a7, 0x527eb2e0, 0x5279e4e7, 0x527516bb,
+    0x5270485c, 0x526b79ca,
+  0x5266ab06, 0x5261dc0e, 0x525d0ce4, 0x52583d87, 0x52536df7, 0x524e9e34,
+    0x5249ce3f, 0x5244fe17,
+  0x52402dbc, 0x523b5d2e, 0x52368c6e, 0x5231bb7b, 0x522cea55, 0x522818fc,
+    0x52234771, 0x521e75b3,
+  0x5219a3c3, 0x5214d1a0, 0x520fff4a, 0x520b2cc2, 0x52065a07, 0x52018719,
+    0x51fcb3f9, 0x51f7e0a6,
+  0x51f30d21, 0x51ee3969, 0x51e9657e, 0x51e49162, 0x51dfbd12, 0x51dae890,
+    0x51d613dc, 0x51d13ef5,
+  0x51cc69db, 0x51c79490, 0x51c2bf11, 0x51bde960, 0x51b9137d, 0x51b43d68,
+    0x51af6720, 0x51aa90a5,
+  0x51a5b9f9, 0x51a0e31a, 0x519c0c08, 0x519734c4, 0x51925d4e, 0x518d85a6,
+    0x5188adcb, 0x5183d5be,
+  0x517efd7f, 0x517a250d, 0x51754c69, 0x51707393, 0x516b9a8b, 0x5166c150,
+    0x5161e7e4, 0x515d0e45,
+  0x51583473, 0x51535a70, 0x514e803b, 0x5149a5d3, 0x5144cb39, 0x513ff06d,
+    0x513b156f, 0x51363a3f,
+  0x51315edd, 0x512c8348, 0x5127a782, 0x5122cb8a, 0x511def5f, 0x51191302,
+    0x51143674, 0x510f59b3,
+  0x510a7cc1, 0x51059f9c, 0x5100c246, 0x50fbe4bd, 0x50f70703, 0x50f22916,
+    0x50ed4af8, 0x50e86ca8,
+  0x50e38e25, 0x50deaf71, 0x50d9d08b, 0x50d4f173, 0x50d0122a, 0x50cb32ae,
+    0x50c65301, 0x50c17322,
+  0x50bc9311, 0x50b7b2ce, 0x50b2d259, 0x50adf1b3, 0x50a910db, 0x50a42fd1,
+    0x509f4e95, 0x509a6d28,
+  0x50958b88, 0x5090a9b8, 0x508bc7b5, 0x5086e581, 0x5082031b, 0x507d2083,
+    0x50783dba, 0x50735abf,
+  0x506e7793, 0x50699435, 0x5064b0a5, 0x505fcce4, 0x505ae8f1, 0x505604cd,
+    0x50512077, 0x504c3bef,
+  0x50475736, 0x5042724c, 0x503d8d30, 0x5038a7e2, 0x5033c263, 0x502edcb2,
+    0x5029f6d1, 0x502510bd,
+  0x50202a78, 0x501b4402, 0x50165d5a, 0x50117681, 0x500c8f77, 0x5007a83b,
+    0x5002c0cd, 0x4ffdd92f,
+  0x4ff8f15f, 0x4ff4095e, 0x4fef212b, 0x4fea38c7, 0x4fe55032, 0x4fe0676c,
+    0x4fdb7e74, 0x4fd6954b,
+  0x4fd1abf0, 0x4fccc265, 0x4fc7d8a8, 0x4fc2eeba, 0x4fbe049b, 0x4fb91a4b,
+    0x4fb42fc9, 0x4faf4517,
+  0x4faa5a33, 0x4fa56f1e, 0x4fa083d8, 0x4f9b9861, 0x4f96acb8, 0x4f91c0df,
+    0x4f8cd4d4, 0x4f87e899,
+  0x4f82fc2c, 0x4f7e0f8f, 0x4f7922c0, 0x4f7435c0, 0x4f6f488f, 0x4f6a5b2e,
+    0x4f656d9b, 0x4f607fd7,
+  0x4f5b91e3, 0x4f56a3bd, 0x4f51b566, 0x4f4cc6df, 0x4f47d827, 0x4f42e93d,
+    0x4f3dfa23, 0x4f390ad8,
+  0x4f341b5c, 0x4f2f2baf, 0x4f2a3bd2, 0x4f254bc3, 0x4f205b84, 0x4f1b6b14,
+    0x4f167a73, 0x4f1189a1,
+  0x4f0c989f, 0x4f07a76b, 0x4f02b608, 0x4efdc473, 0x4ef8d2ad, 0x4ef3e0b7,
+    0x4eeeee90, 0x4ee9fc39,
+  0x4ee509b1, 0x4ee016f8, 0x4edb240e, 0x4ed630f4, 0x4ed13da9, 0x4ecc4a2e,
+    0x4ec75682, 0x4ec262a5,
+  0x4ebd6e98, 0x4eb87a5a, 0x4eb385ec, 0x4eae914d, 0x4ea99c7d, 0x4ea4a77d,
+    0x4e9fb24d, 0x4e9abcec,
+  0x4e95c75b, 0x4e90d199, 0x4e8bdba6, 0x4e86e583, 0x4e81ef30, 0x4e7cf8ac,
+    0x4e7801f8, 0x4e730b14,
+  0x4e6e13ff, 0x4e691cba, 0x4e642544, 0x4e5f2d9e, 0x4e5a35c7, 0x4e553dc1,
+    0x4e50458a, 0x4e4b4d22,
+  0x4e46548b, 0x4e415bc3, 0x4e3c62cb, 0x4e3769a2, 0x4e32704a, 0x4e2d76c1,
+    0x4e287d08, 0x4e23831e,
+  0x4e1e8905, 0x4e198ebb, 0x4e149441, 0x4e0f9997, 0x4e0a9ebd, 0x4e05a3b2,
+    0x4e00a878, 0x4dfbad0d,
+  0x4df6b173, 0x4df1b5a8, 0x4decb9ad, 0x4de7bd82, 0x4de2c127, 0x4dddc49c,
+    0x4dd8c7e1, 0x4dd3caf6,
+  0x4dcecdda, 0x4dc9d08f, 0x4dc4d314, 0x4dbfd569, 0x4dbad78e, 0x4db5d983,
+    0x4db0db48, 0x4dabdcdd,
+  0x4da6de43, 0x4da1df78, 0x4d9ce07d, 0x4d97e153, 0x4d92e1f9, 0x4d8de26f,
+    0x4d88e2b5, 0x4d83e2cb,
+  0x4d7ee2b1, 0x4d79e268, 0x4d74e1ef, 0x4d6fe146, 0x4d6ae06d, 0x4d65df64,
+    0x4d60de2c, 0x4d5bdcc4,
+  0x4d56db2d, 0x4d51d965, 0x4d4cd76e, 0x4d47d547, 0x4d42d2f1, 0x4d3dd06b,
+    0x4d38cdb5, 0x4d33cad0,
+  0x4d2ec7bb, 0x4d29c476, 0x4d24c102, 0x4d1fbd5e, 0x4d1ab98b, 0x4d15b588,
+    0x4d10b155, 0x4d0bacf3,
+  0x4d06a862, 0x4d01a3a0, 0x4cfc9eb0, 0x4cf79990, 0x4cf29440, 0x4ced8ec1,
+    0x4ce88913, 0x4ce38335,
+  0x4cde7d28, 0x4cd976eb, 0x4cd4707f, 0x4ccf69e3, 0x4cca6318, 0x4cc55c1e,
+    0x4cc054f4, 0x4cbb4d9b,
+  0x4cb64613, 0x4cb13e5b, 0x4cac3674, 0x4ca72e5e, 0x4ca22619, 0x4c9d1da4,
+    0x4c981500, 0x4c930c2d,
+  0x4c8e032a, 0x4c88f9f8, 0x4c83f097, 0x4c7ee707, 0x4c79dd48, 0x4c74d359,
+    0x4c6fc93b, 0x4c6abeef,
+  0x4c65b473, 0x4c60a9c8, 0x4c5b9eed, 0x4c5693e4, 0x4c5188ac, 0x4c4c7d44,
+    0x4c4771ae, 0x4c4265e8,
+  0x4c3d59f3, 0x4c384dd0, 0x4c33417d, 0x4c2e34fb, 0x4c29284b, 0x4c241b6b,
+    0x4c1f0e5c, 0x4c1a011f,
+  0x4c14f3b2, 0x4c0fe617, 0x4c0ad84c, 0x4c05ca53, 0x4c00bc2b, 0x4bfbadd4,
+    0x4bf69f4e, 0x4bf19099,
+  0x4bec81b5, 0x4be772a3, 0x4be26362, 0x4bdd53f2, 0x4bd84453, 0x4bd33485,
+    0x4bce2488, 0x4bc9145d,
+  0x4bc40403, 0x4bbef37b, 0x4bb9e2c3, 0x4bb4d1dd, 0x4bafc0c8, 0x4baaaf85,
+    0x4ba59e12, 0x4ba08c72,
+  0x4b9b7aa2, 0x4b9668a4, 0x4b915677, 0x4b8c441c, 0x4b873192, 0x4b821ed9,
+    0x4b7d0bf2, 0x4b77f8dc,
+  0x4b72e598, 0x4b6dd225, 0x4b68be84, 0x4b63aab4, 0x4b5e96b6, 0x4b598289,
+    0x4b546e2d, 0x4b4f59a4,
+  0x4b4a44eb, 0x4b453005, 0x4b401aef, 0x4b3b05ac, 0x4b35f03a, 0x4b30da9a,
+    0x4b2bc4cb, 0x4b26aece,
+  0x4b2198a2, 0x4b1c8248, 0x4b176bc0, 0x4b12550a, 0x4b0d3e25, 0x4b082712,
+    0x4b030fd1, 0x4afdf861,
+  0x4af8e0c3, 0x4af3c8f7, 0x4aeeb0fd, 0x4ae998d4, 0x4ae4807d, 0x4adf67f8,
+    0x4ada4f45, 0x4ad53664,
+  0x4ad01d54, 0x4acb0417, 0x4ac5eaab, 0x4ac0d111, 0x4abbb749, 0x4ab69d53,
+    0x4ab1832f, 0x4aac68dc,
+  0x4aa74e5c, 0x4aa233ae, 0x4a9d18d1, 0x4a97fdc7, 0x4a92e28e, 0x4a8dc728,
+    0x4a88ab93, 0x4a838fd1,
+  0x4a7e73e0, 0x4a7957c2, 0x4a743b76, 0x4a6f1efc, 0x4a6a0253, 0x4a64e57d,
+    0x4a5fc879, 0x4a5aab48,
+  0x4a558de8, 0x4a50705a, 0x4a4b529f, 0x4a4634b6, 0x4a41169f, 0x4a3bf85a,
+    0x4a36d9e7, 0x4a31bb47,
+  0x4a2c9c79, 0x4a277d7d, 0x4a225e53, 0x4a1d3efc, 0x4a181f77, 0x4a12ffc4,
+    0x4a0ddfe4, 0x4a08bfd5,
+  0x4a039f9a, 0x49fe7f30, 0x49f95e99, 0x49f43dd4, 0x49ef1ce2, 0x49e9fbc2,
+    0x49e4da74, 0x49dfb8f9,
+  0x49da9750, 0x49d5757a, 0x49d05376, 0x49cb3145, 0x49c60ee6, 0x49c0ec59,
+    0x49bbc9a0, 0x49b6a6b8,
+  0x49b183a3, 0x49ac6061, 0x49a73cf1, 0x49a21954, 0x499cf589, 0x4997d191,
+    0x4992ad6c, 0x498d8919,
+  0x49886499, 0x49833fec, 0x497e1b11, 0x4978f609, 0x4973d0d3, 0x496eab70,
+    0x496985e0, 0x49646023,
+  0x495f3a38, 0x495a1420, 0x4954eddb, 0x494fc768, 0x494aa0c9, 0x494579fc,
+    0x49405302, 0x493b2bdb,
+  0x49360486, 0x4930dd05, 0x492bb556, 0x49268d7a, 0x49216571, 0x491c3d3b,
+    0x491714d8, 0x4911ec47,
+  0x490cc38a, 0x49079aa0, 0x49027188, 0x48fd4844, 0x48f81ed2, 0x48f2f534,
+    0x48edcb68, 0x48e8a170,
+  0x48e3774a, 0x48de4cf8, 0x48d92278, 0x48d3f7cc, 0x48ceccf3, 0x48c9a1ed,
+    0x48c476b9, 0x48bf4b59,
+  0x48ba1fcd, 0x48b4f413, 0x48afc82c, 0x48aa9c19, 0x48a56fd9, 0x48a0436c,
+    0x489b16d2, 0x4895ea0b,
+  0x4890bd18, 0x488b8ff8, 0x488662ab, 0x48813531, 0x487c078b, 0x4876d9b8,
+    0x4871abb8, 0x486c7d8c,
+  0x48674f33, 0x486220ad, 0x485cf1fa, 0x4857c31b, 0x48529410, 0x484d64d7,
+    0x48483572, 0x484305e1,
+  0x483dd623, 0x4838a638, 0x48337621, 0x482e45dd, 0x4829156d, 0x4823e4d0,
+    0x481eb407, 0x48198311,
+  0x481451ef, 0x480f20a0, 0x4809ef25, 0x4804bd7e, 0x47ff8baa, 0x47fa59a9,
+    0x47f5277d, 0x47eff523,
+  0x47eac29e, 0x47e58fec, 0x47e05d0e, 0x47db2a03, 0x47d5f6cc, 0x47d0c369,
+    0x47cb8fd9, 0x47c65c1d,
+  0x47c12835, 0x47bbf421, 0x47b6bfe0, 0x47b18b74, 0x47ac56da, 0x47a72215,
+    0x47a1ed24, 0x479cb806,
+  0x479782bc, 0x47924d46, 0x478d17a4, 0x4787e1d6, 0x4782abdb, 0x477d75b5,
+    0x47783f62, 0x477308e3,
+  0x476dd239, 0x47689b62, 0x4763645f, 0x475e2d30, 0x4758f5d5, 0x4753be4e,
+    0x474e869b, 0x47494ebc,
+  0x474416b1, 0x473ede7a, 0x4739a617, 0x47346d89, 0x472f34ce, 0x4729fbe7,
+    0x4724c2d5, 0x471f8996,
+  0x471a502c, 0x47151696, 0x470fdcd4, 0x470aa2e6, 0x470568cd, 0x47002e87,
+    0x46faf416, 0x46f5b979,
+  0x46f07eb0, 0x46eb43bc, 0x46e6089b, 0x46e0cd4f, 0x46db91d8, 0x46d65634,
+    0x46d11a65, 0x46cbde6a,
+  0x46c6a244, 0x46c165f1, 0x46bc2974, 0x46b6ecca, 0x46b1aff5, 0x46ac72f4,
+    0x46a735c8, 0x46a1f870,
+  0x469cbaed, 0x46977d3e, 0x46923f63, 0x468d015d, 0x4687c32c, 0x468284cf,
+    0x467d4646, 0x46780792,
+  0x4672c8b3, 0x466d89a8, 0x46684a71, 0x46630b0f, 0x465dcb82, 0x46588bc9,
+    0x46534be5, 0x464e0bd6,
+  0x4648cb9b, 0x46438b35, 0x463e4aa3, 0x463909e7, 0x4633c8fe, 0x462e87eb,
+    0x462946ac, 0x46240542,
+  0x461ec3ad, 0x461981ec, 0x46144001, 0x460efde9, 0x4609bba7, 0x4604793a,
+    0x45ff36a1, 0x45f9f3dd,
+  0x45f4b0ee, 0x45ef6dd4, 0x45ea2a8f, 0x45e4e71f, 0x45dfa383, 0x45da5fbc,
+    0x45d51bcb, 0x45cfd7ae,
+  0x45ca9366, 0x45c54ef3, 0x45c00a55, 0x45bac58c, 0x45b58098, 0x45b03b79,
+    0x45aaf630, 0x45a5b0bb,
+  0x45a06b1b, 0x459b2550, 0x4595df5a, 0x45909939, 0x458b52ee, 0x45860c77,
+    0x4580c5d6, 0x457b7f0a,
+  0x45763813, 0x4570f0f1, 0x456ba9a4, 0x4566622c, 0x45611a8a, 0x455bd2bc,
+    0x45568ac4, 0x455142a2,
+  0x454bfa54, 0x4546b1dc, 0x45416939, 0x453c206b, 0x4536d773, 0x45318e4f,
+    0x452c4502, 0x4526fb89,
+  0x4521b1e6, 0x451c6818, 0x45171e20, 0x4511d3fd, 0x450c89af, 0x45073f37,
+    0x4501f494, 0x44fca9c6,
+  0x44f75ecf, 0x44f213ac, 0x44ecc85f, 0x44e77ce7, 0x44e23145, 0x44dce579,
+    0x44d79982, 0x44d24d60,
+  0x44cd0114, 0x44c7b49e, 0x44c267fd, 0x44bd1b32, 0x44b7ce3c, 0x44b2811c,
+    0x44ad33d2, 0x44a7e65d,
+  0x44a298be, 0x449d4af5, 0x4497fd01, 0x4492aee3, 0x448d609b, 0x44881228,
+    0x4482c38b, 0x447d74c4,
+  0x447825d2, 0x4472d6b7, 0x446d8771, 0x44683801, 0x4462e866, 0x445d98a2,
+    0x445848b3, 0x4452f89b,
+  0x444da858, 0x444857ea, 0x44430753, 0x443db692, 0x443865a7, 0x44331491,
+    0x442dc351, 0x442871e8,
+  0x44232054, 0x441dce96, 0x44187caf, 0x44132a9d, 0x440dd861, 0x440885fc,
+    0x4403336c, 0x43fde0b2,
+  0x43f88dcf, 0x43f33ac1, 0x43ede78a, 0x43e89429, 0x43e3409d, 0x43ddece8,
+    0x43d8990a, 0x43d34501,
+  0x43cdf0ce, 0x43c89c72, 0x43c347eb, 0x43bdf33b, 0x43b89e62, 0x43b3495e,
+    0x43adf431, 0x43a89ed9,
+  0x43a34959, 0x439df3ae, 0x43989dda, 0x439347dc, 0x438df1b4, 0x43889b63,
+    0x438344e8, 0x437dee43,
+  0x43789775, 0x4373407d, 0x436de95b, 0x43689210, 0x43633a9c, 0x435de2fd,
+    0x43588b36, 0x43533344,
+  0x434ddb29, 0x434882e5, 0x43432a77, 0x433dd1e0, 0x4338791f, 0x43332035,
+    0x432dc721, 0x43286de4,
+  0x4323147d, 0x431dbaed, 0x43186133, 0x43130751, 0x430dad44, 0x4308530f,
+    0x4302f8b0, 0x42fd9e28,
+  0x42f84376, 0x42f2e89b, 0x42ed8d97, 0x42e83269, 0x42e2d713, 0x42dd7b93,
+    0x42d81fe9, 0x42d2c417,
+  0x42cd681b, 0x42c80bf6, 0x42c2afa8, 0x42bd5331, 0x42b7f690, 0x42b299c7,
+    0x42ad3cd4, 0x42a7dfb8,
+  0x42a28273, 0x429d2505, 0x4297c76e, 0x429269ae, 0x428d0bc4, 0x4287adb2,
+    0x42824f76, 0x427cf112,
+  0x42779285, 0x427233ce, 0x426cd4ef, 0x426775e6, 0x426216b5, 0x425cb75a,
+    0x425757d7, 0x4251f82b,
+  0x424c9856, 0x42473858, 0x4241d831, 0x423c77e1, 0x42371769, 0x4231b6c7,
+    0x422c55fd, 0x4226f50a,
+  0x422193ee, 0x421c32a9, 0x4216d13c, 0x42116fa5, 0x420c0de6, 0x4206abfe,
+    0x420149ee, 0x41fbe7b5,
+  0x41f68553, 0x41f122c8, 0x41ebc015, 0x41e65d39, 0x41e0fa35, 0x41db9707,
+    0x41d633b1, 0x41d0d033,
+  0x41cb6c8c, 0x41c608bc, 0x41c0a4c4, 0x41bb40a3, 0x41b5dc5a, 0x41b077e8,
+    0x41ab134e, 0x41a5ae8b,
+  0x41a049a0, 0x419ae48c, 0x41957f4f, 0x419019eb, 0x418ab45d, 0x41854ea8,
+    0x417fe8ca, 0x417a82c3,
+  0x41751c94, 0x416fb63d, 0x416a4fbd, 0x4164e916, 0x415f8245, 0x415a1b4d,
+    0x4154b42c, 0x414f4ce2,
+  0x4149e571, 0x41447dd7, 0x413f1615, 0x4139ae2b, 0x41344618, 0x412edddd,
+    0x4129757b, 0x41240cef,
+  0x411ea43c, 0x41193b61, 0x4113d25d, 0x410e6931, 0x4108ffdd, 0x41039661,
+    0x40fe2cbd, 0x40f8c2f1,
+  0x40f358fc, 0x40edeee0, 0x40e8849b, 0x40e31a2f, 0x40ddaf9b, 0x40d844de,
+    0x40d2d9f9, 0x40cd6eed,
+  0x40c803b8, 0x40c2985c, 0x40bd2cd8, 0x40b7c12b, 0x40b25557, 0x40ace95b,
+    0x40a77d37, 0x40a210eb,
+  0x409ca477, 0x409737dc, 0x4091cb18, 0x408c5e2d, 0x4086f11a, 0x408183df,
+    0x407c167c, 0x4076a8f1,
+  0x40713b3f, 0x406bcd65, 0x40665f63, 0x4060f13a, 0x405b82e9, 0x40561470,
+    0x4050a5cf, 0x404b3707,
+  0x4045c817, 0x404058ff, 0x403ae9c0, 0x40357a59, 0x40300acb, 0x402a9b15,
+    0x40252b37, 0x401fbb32,
+  0x401a4b05, 0x4014dab1, 0x400f6a35, 0x4009f992, 0x400488c7, 0x3fff17d5,
+    0x3ff9a6bb, 0x3ff4357a,
+  0x3feec411, 0x3fe95281, 0x3fe3e0c9, 0x3fde6eeb, 0x3fd8fce4, 0x3fd38ab6,
+    0x3fce1861, 0x3fc8a5e5,
+  0x3fc33341, 0x3fbdc076, 0x3fb84d83, 0x3fb2da6a, 0x3fad6729, 0x3fa7f3c0,
+    0x3fa28031, 0x3f9d0c7a,
+  0x3f97989c, 0x3f922496, 0x3f8cb06a, 0x3f873c16, 0x3f81c79b, 0x3f7c52f9,
+    0x3f76de30, 0x3f71693f,
+  0x3f6bf428, 0x3f667ee9, 0x3f610983, 0x3f5b93f6, 0x3f561e42, 0x3f50a867,
+    0x3f4b3265, 0x3f45bc3c,
+  0x3f4045ec, 0x3f3acf75, 0x3f3558d7, 0x3f2fe211, 0x3f2a6b25, 0x3f24f412,
+    0x3f1f7cd8, 0x3f1a0577,
+  0x3f148def, 0x3f0f1640, 0x3f099e6b, 0x3f04266e, 0x3efeae4a, 0x3ef93600,
+    0x3ef3bd8f, 0x3eee44f7,
+  0x3ee8cc38, 0x3ee35352, 0x3eddda46, 0x3ed86113, 0x3ed2e7b9, 0x3ecd6e38,
+    0x3ec7f491, 0x3ec27ac2,
+  0x3ebd00cd, 0x3eb786b2, 0x3eb20c6f, 0x3eac9206, 0x3ea71777, 0x3ea19cc1,
+    0x3e9c21e4, 0x3e96a6e0,
+  0x3e912bb6, 0x3e8bb065, 0x3e8634ee, 0x3e80b950, 0x3e7b3d8c, 0x3e75c1a1,
+    0x3e70458f, 0x3e6ac957,
+  0x3e654cf8, 0x3e5fd073, 0x3e5a53c8, 0x3e54d6f6, 0x3e4f59fe, 0x3e49dcdf,
+    0x3e445f99, 0x3e3ee22e,
+  0x3e39649c, 0x3e33e6e3, 0x3e2e6904, 0x3e28eaff, 0x3e236cd4, 0x3e1dee82,
+    0x3e18700a, 0x3e12f16b,
+  0x3e0d72a6, 0x3e07f3bb, 0x3e0274aa, 0x3dfcf572, 0x3df77615, 0x3df1f691,
+    0x3dec76e6, 0x3de6f716,
+  0x3de1771f, 0x3ddbf703, 0x3dd676c0, 0x3dd0f656, 0x3dcb75c7, 0x3dc5f512,
+    0x3dc07436, 0x3dbaf335,
+  0x3db5720d, 0x3daff0c0, 0x3daa6f4c, 0x3da4edb2, 0x3d9f6bf2, 0x3d99ea0d,
+    0x3d946801, 0x3d8ee5cf,
+  0x3d896377, 0x3d83e0f9, 0x3d7e5e56, 0x3d78db8c, 0x3d73589d, 0x3d6dd587,
+    0x3d68524c, 0x3d62ceeb,
+  0x3d5d4b64, 0x3d57c7b7, 0x3d5243e4, 0x3d4cbfeb, 0x3d473bcd, 0x3d41b789,
+    0x3d3c331f, 0x3d36ae8f,
+  0x3d3129da, 0x3d2ba4fe, 0x3d261ffd, 0x3d209ad7, 0x3d1b158a, 0x3d159018,
+    0x3d100a80, 0x3d0a84c3,
+  0x3d04fee0, 0x3cff78d7, 0x3cf9f2a9, 0x3cf46c55, 0x3ceee5db, 0x3ce95f3c,
+    0x3ce3d877, 0x3cde518d,
+  0x3cd8ca7d, 0x3cd34347, 0x3ccdbbed, 0x3cc8346c, 0x3cc2acc6, 0x3cbd24fb,
+    0x3cb79d0a, 0x3cb214f4,
+  0x3cac8cb8, 0x3ca70457, 0x3ca17bd0, 0x3c9bf324, 0x3c966a53, 0x3c90e15c,
+    0x3c8b5840, 0x3c85cefe,
+  0x3c804598, 0x3c7abc0c, 0x3c75325a, 0x3c6fa883, 0x3c6a1e87, 0x3c649466,
+    0x3c5f0a20, 0x3c597fb4,
+  0x3c53f523, 0x3c4e6a6d, 0x3c48df91, 0x3c435491, 0x3c3dc96b, 0x3c383e20,
+    0x3c32b2b0, 0x3c2d271b,
+  0x3c279b61, 0x3c220f81, 0x3c1c837d, 0x3c16f753, 0x3c116b04, 0x3c0bde91,
+    0x3c0651f8, 0x3c00c53a,
+  0x3bfb3857, 0x3bf5ab50, 0x3bf01e23, 0x3bea90d1, 0x3be5035a, 0x3bdf75bf,
+    0x3bd9e7fe, 0x3bd45a19,
+  0x3bcecc0e, 0x3bc93ddf, 0x3bc3af8b, 0x3bbe2112, 0x3bb89274, 0x3bb303b1,
+    0x3bad74c9, 0x3ba7e5bd,
+  0x3ba2568c, 0x3b9cc736, 0x3b9737bb, 0x3b91a81c, 0x3b8c1857, 0x3b86886e,
+    0x3b80f861, 0x3b7b682e,
+  0x3b75d7d7, 0x3b70475c, 0x3b6ab6bb, 0x3b6525f6, 0x3b5f950c, 0x3b5a03fe,
+    0x3b5472cb, 0x3b4ee173,
+  0x3b494ff7, 0x3b43be57, 0x3b3e2c91, 0x3b389aa8, 0x3b330899, 0x3b2d7666,
+    0x3b27e40f, 0x3b225193,
+  0x3b1cbef3, 0x3b172c2e, 0x3b119945, 0x3b0c0637, 0x3b067305, 0x3b00dfaf,
+    0x3afb4c34, 0x3af5b894,
+  0x3af024d1, 0x3aea90e9, 0x3ae4fcdc, 0x3adf68ac, 0x3ad9d457, 0x3ad43fdd,
+    0x3aceab40, 0x3ac9167e,
+  0x3ac38198, 0x3abdec8d, 0x3ab8575f, 0x3ab2c20c, 0x3aad2c95, 0x3aa796fa,
+    0x3aa2013a, 0x3a9c6b57,
+  0x3a96d54f, 0x3a913f23, 0x3a8ba8d3, 0x3a86125f, 0x3a807bc7, 0x3a7ae50a,
+    0x3a754e2a, 0x3a6fb726,
+  0x3a6a1ffd, 0x3a6488b1, 0x3a5ef140, 0x3a5959ab, 0x3a53c1f3, 0x3a4e2a16,
+    0x3a489216, 0x3a42f9f2,
+  0x3a3d61a9, 0x3a37c93d, 0x3a3230ad, 0x3a2c97f9, 0x3a26ff21, 0x3a216625,
+    0x3a1bcd05, 0x3a1633c1,
+  0x3a109a5a, 0x3a0b00cf, 0x3a056720, 0x39ffcd4d, 0x39fa3356, 0x39f4993c,
+    0x39eefefe, 0x39e9649c,
+  0x39e3ca17, 0x39de2f6d, 0x39d894a0, 0x39d2f9b0, 0x39cd5e9b, 0x39c7c363,
+    0x39c22808, 0x39bc8c89,
+  0x39b6f0e6, 0x39b1551f, 0x39abb935, 0x39a61d28, 0x39a080f6, 0x399ae4a2,
+    0x39954829, 0x398fab8e,
+  0x398a0ece, 0x398471ec, 0x397ed4e5, 0x397937bc, 0x39739a6e, 0x396dfcfe,
+    0x39685f6a, 0x3962c1b2,
+  0x395d23d7, 0x395785d9, 0x3951e7b8, 0x394c4973, 0x3946ab0a, 0x39410c7f,
+    0x393b6dd0, 0x3935cefd,
+  0x39303008, 0x392a90ef, 0x3924f1b3, 0x391f5254, 0x3919b2d1, 0x3914132b,
+    0x390e7362, 0x3908d376,
+  0x39033367, 0x38fd9334, 0x38f7f2de, 0x38f25266, 0x38ecb1ca, 0x38e7110a,
+    0x38e17028, 0x38dbcf23,
+  0x38d62dfb, 0x38d08caf, 0x38caeb41, 0x38c549af, 0x38bfa7fb, 0x38ba0623,
+    0x38b46429, 0x38aec20b,
+  0x38a91fcb, 0x38a37d67, 0x389ddae1, 0x38983838, 0x3892956c, 0x388cf27d,
+    0x38874f6b, 0x3881ac36,
+  0x387c08de, 0x38766564, 0x3870c1c6, 0x386b1e06, 0x38657a23, 0x385fd61d,
+    0x385a31f5, 0x38548daa,
+  0x384ee93b, 0x384944ab, 0x38439ff7, 0x383dfb21, 0x38385628, 0x3832b10d,
+    0x382d0bce, 0x3827666d,
+  0x3821c0ea, 0x381c1b44, 0x3816757b, 0x3810cf90, 0x380b2982, 0x38058351,
+    0x37ffdcfe, 0x37fa3688,
+  0x37f48ff0, 0x37eee936, 0x37e94259, 0x37e39b59, 0x37ddf437, 0x37d84cf2,
+    0x37d2a58b, 0x37ccfe02,
+  0x37c75656, 0x37c1ae87, 0x37bc0697, 0x37b65e84, 0x37b0b64e, 0x37ab0df6,
+    0x37a5657c, 0x379fbce0,
+  0x379a1421, 0x37946b40, 0x378ec23d, 0x37891917, 0x37836fcf, 0x377dc665,
+    0x37781cd9, 0x3772732a,
+  0x376cc959, 0x37671f66, 0x37617551, 0x375bcb1a, 0x375620c1, 0x37507645,
+    0x374acba7, 0x374520e7,
+  0x373f7606, 0x3739cb02, 0x37341fdc, 0x372e7493, 0x3728c929, 0x37231d9d,
+    0x371d71ef, 0x3717c61f,
+  0x37121a2d, 0x370c6e19, 0x3706c1e2, 0x3701158a, 0x36fb6910, 0x36f5bc75,
+    0x36f00fb7, 0x36ea62d7,
+  0x36e4b5d6, 0x36df08b2, 0x36d95b6d, 0x36d3ae06, 0x36ce007d, 0x36c852d2,
+    0x36c2a506, 0x36bcf718,
+  0x36b74908, 0x36b19ad6, 0x36abec82, 0x36a63e0d, 0x36a08f76, 0x369ae0bd,
+    0x369531e3, 0x368f82e7,
+  0x3689d3c9, 0x3684248a, 0x367e7529, 0x3678c5a7, 0x36731602, 0x366d663d,
+    0x3667b655, 0x3662064c,
+  0x365c5622, 0x3656a5d6, 0x3650f569, 0x364b44da, 0x36459429, 0x363fe357,
+    0x363a3264, 0x3634814f,
+  0x362ed019, 0x36291ec1, 0x36236d48, 0x361dbbad, 0x361809f1, 0x36125814,
+    0x360ca615, 0x3606f3f5,
+  0x360141b4, 0x35fb8f52, 0x35f5dcce, 0x35f02a28, 0x35ea7762, 0x35e4c47a,
+    0x35df1171, 0x35d95e47,
+  0x35d3aafc, 0x35cdf78f, 0x35c84401, 0x35c29052, 0x35bcdc82, 0x35b72891,
+    0x35b1747e, 0x35abc04b,
+  0x35a60bf6, 0x35a05781, 0x359aa2ea, 0x3594ee32, 0x358f3959, 0x3589845f,
+    0x3583cf44, 0x357e1a08,
+  0x357864ab, 0x3572af2d, 0x356cf98e, 0x356743ce, 0x35618ded, 0x355bd7eb,
+    0x355621c9, 0x35506b85,
+  0x354ab520, 0x3544fe9b, 0x353f47f5, 0x3539912e, 0x3533da46, 0x352e233d,
+    0x35286c14, 0x3522b4c9,
+  0x351cfd5e, 0x351745d2, 0x35118e26, 0x350bd658, 0x35061e6a, 0x3500665c,
+    0x34faae2c, 0x34f4f5dc,
+  0x34ef3d6b, 0x34e984da, 0x34e3cc28, 0x34de1355, 0x34d85a62, 0x34d2a14e,
+    0x34cce819, 0x34c72ec4,
+  0x34c1754e, 0x34bbbbb8, 0x34b60202, 0x34b0482a, 0x34aa8e33, 0x34a4d41a,
+    0x349f19e2, 0x34995f88,
+  0x3493a50f, 0x348dea75, 0x34882fba, 0x348274e0, 0x347cb9e4, 0x3476fec9,
+    0x3471438d, 0x346b8830,
+  0x3465ccb4, 0x34601117, 0x345a5559, 0x3454997c, 0x344edd7e, 0x34492160,
+    0x34436521, 0x343da8c3,
+  0x3437ec44, 0x34322fa5, 0x342c72e6, 0x3426b606, 0x3420f907, 0x341b3be7,
+    0x34157ea7, 0x340fc147,
+  0x340a03c7, 0x34044626, 0x33fe8866, 0x33f8ca86, 0x33f30c85, 0x33ed4e65,
+    0x33e79024, 0x33e1d1c4,
+  0x33dc1343, 0x33d654a2, 0x33d095e2, 0x33cad701, 0x33c51801, 0x33bf58e1,
+    0x33b999a0, 0x33b3da40,
+  0x33ae1ac0, 0x33a85b20, 0x33a29b60, 0x339cdb81, 0x33971b81, 0x33915b62,
+    0x338b9b22, 0x3385dac4,
+  0x33801a45, 0x337a59a6, 0x337498e8, 0x336ed80a, 0x3369170c, 0x336355ef,
+    0x335d94b2, 0x3357d355,
+  0x335211d8, 0x334c503c, 0x33468e80, 0x3340cca5, 0x333b0aaa, 0x3335488f,
+    0x332f8655, 0x3329c3fb,
+  0x33240182, 0x331e3ee9, 0x33187c31, 0x3312b959, 0x330cf661, 0x3307334a,
+    0x33017014, 0x32fbacbe,
+  0x32f5e948, 0x32f025b4, 0x32ea61ff, 0x32e49e2c, 0x32deda39, 0x32d91626,
+    0x32d351f5, 0x32cd8da4,
+  0x32c7c933, 0x32c204a3, 0x32bc3ff4, 0x32b67b26, 0x32b0b638, 0x32aaf12b,
+    0x32a52bff, 0x329f66b4,
+  0x3299a149, 0x3293dbbf, 0x328e1616, 0x3288504e, 0x32828a67, 0x327cc460,
+    0x3276fe3a, 0x327137f6,
+  0x326b7192, 0x3265ab0f, 0x325fe46c, 0x325a1dab, 0x325456cb, 0x324e8fcc,
+    0x3248c8ad, 0x32430170,
+  0x323d3a14, 0x32377298, 0x3231aafe, 0x322be345, 0x32261b6c, 0x32205375,
+    0x321a8b5f, 0x3214c32a,
+  0x320efad6, 0x32093263, 0x320369d2, 0x31fda121, 0x31f7d852, 0x31f20f64,
+    0x31ec4657, 0x31e67d2b,
+  0x31e0b3e0, 0x31daea77, 0x31d520ef, 0x31cf5748, 0x31c98d83, 0x31c3c39e,
+    0x31bdf99b, 0x31b82f7a,
+  0x31b2653a, 0x31ac9adb, 0x31a6d05d, 0x31a105c1, 0x319b3b06, 0x3195702d,
+    0x318fa535, 0x3189da1e,
+  0x31840ee9, 0x317e4395, 0x31787823, 0x3172ac92, 0x316ce0e3, 0x31671515,
+    0x31614929, 0x315b7d1e,
+  0x3155b0f5, 0x314fe4ae, 0x314a1848, 0x31444bc3, 0x313e7f21, 0x3138b260,
+    0x3132e580, 0x312d1882,
+  0x31274b66, 0x31217e2c, 0x311bb0d3, 0x3115e35c, 0x311015c6, 0x310a4813,
+    0x31047a41, 0x30feac51,
+  0x30f8de42, 0x30f31016, 0x30ed41cb, 0x30e77362, 0x30e1a4db, 0x30dbd636,
+    0x30d60772, 0x30d03891,
+  0x30ca6991, 0x30c49a74, 0x30becb38, 0x30b8fbde, 0x30b32c66, 0x30ad5cd0,
+    0x30a78d1c, 0x30a1bd4a,
+  0x309bed5a, 0x30961d4c, 0x30904d20, 0x308a7cd6, 0x3084ac6e, 0x307edbe9,
+    0x30790b45, 0x30733a83,
+  0x306d69a4, 0x306798a7, 0x3061c78b, 0x305bf652, 0x305624fb, 0x30505387,
+    0x304a81f4, 0x3044b044,
+  0x303ede76, 0x30390c8a, 0x30333a80, 0x302d6859, 0x30279614, 0x3021c3b1,
+    0x301bf131, 0x30161e93,
+  0x30104bd7, 0x300a78fe, 0x3004a607, 0x2ffed2f2, 0x2ff8ffc0, 0x2ff32c70,
+    0x2fed5902, 0x2fe78577,
+  0x2fe1b1cf, 0x2fdbde09, 0x2fd60a25, 0x2fd03624, 0x2fca6206, 0x2fc48dc9,
+    0x2fbeb970, 0x2fb8e4f9,
+  0x2fb31064, 0x2fad3bb3, 0x2fa766e3, 0x2fa191f7, 0x2f9bbced, 0x2f95e7c5,
+    0x2f901280, 0x2f8a3d1e,
+  0x2f84679f, 0x2f7e9202, 0x2f78bc48, 0x2f72e671, 0x2f6d107c, 0x2f673a6a,
+    0x2f61643b, 0x2f5b8def,
+  0x2f55b785, 0x2f4fe0ff, 0x2f4a0a5b, 0x2f44339a, 0x2f3e5cbb, 0x2f3885c0,
+    0x2f32aea8, 0x2f2cd772,
+  0x2f27001f, 0x2f2128af, 0x2f1b5122, 0x2f157979, 0x2f0fa1b2, 0x2f09c9ce,
+    0x2f03f1cd, 0x2efe19ae,
+  0x2ef84173, 0x2ef2691b, 0x2eec90a7, 0x2ee6b815, 0x2ee0df66, 0x2edb069a,
+    0x2ed52db1, 0x2ecf54ac,
+  0x2ec97b89, 0x2ec3a24a, 0x2ebdc8ee, 0x2eb7ef75, 0x2eb215df, 0x2eac3c2d,
+    0x2ea6625d, 0x2ea08871,
+  0x2e9aae68, 0x2e94d443, 0x2e8efa00, 0x2e891fa1, 0x2e834525, 0x2e7d6a8d,
+    0x2e778fd8, 0x2e71b506,
+  0x2e6bda17, 0x2e65ff0c, 0x2e6023e5, 0x2e5a48a0, 0x2e546d3f, 0x2e4e91c2,
+    0x2e48b628, 0x2e42da71,
+  0x2e3cfe9e, 0x2e3722ae, 0x2e3146a2, 0x2e2b6a79, 0x2e258e34, 0x2e1fb1d3,
+    0x2e19d554, 0x2e13f8ba,
+  0x2e0e1c03, 0x2e083f30, 0x2e026240, 0x2dfc8534, 0x2df6a80b, 0x2df0cac6,
+    0x2deaed65, 0x2de50fe8,
+  0x2ddf324e, 0x2dd95498, 0x2dd376c5, 0x2dcd98d7, 0x2dc7bacc, 0x2dc1dca4,
+    0x2dbbfe61, 0x2db62001,
+  0x2db04186, 0x2daa62ee, 0x2da4843a, 0x2d9ea569, 0x2d98c67d, 0x2d92e774,
+    0x2d8d084f, 0x2d87290f,
+  0x2d8149b2, 0x2d7b6a39, 0x2d758aa4, 0x2d6faaf3, 0x2d69cb26, 0x2d63eb3d,
+    0x2d5e0b38, 0x2d582b17,
+  0x2d524ada, 0x2d4c6a81, 0x2d468a0c, 0x2d40a97b, 0x2d3ac8ce, 0x2d34e805,
+    0x2d2f0721, 0x2d292620,
+  0x2d234504, 0x2d1d63cc, 0x2d178278, 0x2d11a108, 0x2d0bbf7d, 0x2d05ddd5,
+    0x2cfffc12, 0x2cfa1a33,
+  0x2cf43839, 0x2cee5622, 0x2ce873f0, 0x2ce291a2, 0x2cdcaf39, 0x2cd6ccb4,
+    0x2cd0ea13, 0x2ccb0756,
+  0x2cc5247e, 0x2cbf418b, 0x2cb95e7b, 0x2cb37b51, 0x2cad980a, 0x2ca7b4a8,
+    0x2ca1d12a, 0x2c9bed91,
+  0x2c9609dd, 0x2c90260d, 0x2c8a4221, 0x2c845e1a, 0x2c7e79f7, 0x2c7895b9,
+    0x2c72b160, 0x2c6ccceb,
+  0x2c66e85b, 0x2c6103af, 0x2c5b1ee8, 0x2c553a06, 0x2c4f5508, 0x2c496fef,
+    0x2c438abb, 0x2c3da56b,
+  0x2c37c000, 0x2c31da7a, 0x2c2bf4d8, 0x2c260f1c, 0x2c202944, 0x2c1a4351,
+    0x2c145d42, 0x2c0e7719,
+  0x2c0890d4, 0x2c02aa74, 0x2bfcc3f9, 0x2bf6dd63, 0x2bf0f6b1, 0x2beb0fe5,
+    0x2be528fd, 0x2bdf41fb,
+  0x2bd95add, 0x2bd373a4, 0x2bcd8c51, 0x2bc7a4e2, 0x2bc1bd58, 0x2bbbd5b3,
+    0x2bb5edf4, 0x2bb00619,
+  0x2baa1e23, 0x2ba43613, 0x2b9e4de7, 0x2b9865a1, 0x2b927d3f, 0x2b8c94c3,
+    0x2b86ac2c, 0x2b80c37a,
+  0x2b7adaae, 0x2b74f1c6, 0x2b6f08c4, 0x2b691fa6, 0x2b63366f, 0x2b5d4d1c,
+    0x2b5763ae, 0x2b517a26,
+  0x2b4b9083, 0x2b45a6c6, 0x2b3fbced, 0x2b39d2fa, 0x2b33e8ed, 0x2b2dfec5,
+    0x2b281482, 0x2b222a24,
+  0x2b1c3fac, 0x2b165519, 0x2b106a6c, 0x2b0a7fa4, 0x2b0494c2, 0x2afea9c5,
+    0x2af8bead, 0x2af2d37b,
+  0x2aece82f, 0x2ae6fcc8, 0x2ae11146, 0x2adb25aa, 0x2ad539f4, 0x2acf4e23,
+    0x2ac96238, 0x2ac37633,
+  0x2abd8a13, 0x2ab79dd8, 0x2ab1b184, 0x2aabc515, 0x2aa5d88b, 0x2a9febe8,
+    0x2a99ff2a, 0x2a941252,
+  0x2a8e255f, 0x2a883853, 0x2a824b2c, 0x2a7c5deb, 0x2a76708f, 0x2a70831a,
+    0x2a6a958a, 0x2a64a7e0,
+  0x2a5eba1c, 0x2a58cc3e, 0x2a52de46, 0x2a4cf033, 0x2a470207, 0x2a4113c0,
+    0x2a3b2560, 0x2a3536e5,
+  0x2a2f4850, 0x2a2959a1, 0x2a236ad9, 0x2a1d7bf6, 0x2a178cf9, 0x2a119de2,
+    0x2a0baeb2, 0x2a05bf67,
+  0x29ffd003, 0x29f9e084, 0x29f3f0ec, 0x29ee013a, 0x29e8116e, 0x29e22188,
+    0x29dc3188, 0x29d6416f,
+  0x29d0513b, 0x29ca60ee, 0x29c47087, 0x29be8007, 0x29b88f6c, 0x29b29eb8,
+    0x29acadea, 0x29a6bd02,
+  0x29a0cc01, 0x299adae6, 0x2994e9b1, 0x298ef863, 0x298906fb, 0x2983157a,
+    0x297d23df, 0x2977322a,
+  0x2971405b, 0x296b4e74, 0x29655c72, 0x295f6a57, 0x29597823, 0x295385d5,
+    0x294d936d, 0x2947a0ec,
+  0x2941ae52, 0x293bbb9e, 0x2935c8d1, 0x292fd5ea, 0x2929e2ea, 0x2923efd0,
+    0x291dfc9d, 0x29180951,
+  0x291215eb, 0x290c226c, 0x29062ed4, 0x29003b23, 0x28fa4758, 0x28f45374,
+    0x28ee5f76, 0x28e86b5f,
+  0x28e27730, 0x28dc82e6, 0x28d68e84, 0x28d09a09, 0x28caa574, 0x28c4b0c6,
+    0x28bebbff, 0x28b8c71f,
+  0x28b2d226, 0x28acdd13, 0x28a6e7e8, 0x28a0f2a3, 0x289afd46, 0x289507cf,
+    0x288f123f, 0x28891c97,
+  0x288326d5, 0x287d30fa, 0x28773b07, 0x287144fa, 0x286b4ed5, 0x28655896,
+    0x285f623f, 0x28596bce,
+  0x28537545, 0x284d7ea3, 0x284787e8, 0x28419114, 0x283b9a28, 0x2835a322,
+    0x282fac04, 0x2829b4cd,
+  0x2823bd7d, 0x281dc615, 0x2817ce93, 0x2811d6f9, 0x280bdf46, 0x2805e77b,
+    0x27ffef97, 0x27f9f79a,
+  0x27f3ff85, 0x27ee0756, 0x27e80f10, 0x27e216b0, 0x27dc1e38, 0x27d625a8,
+    0x27d02cff, 0x27ca343d,
+  0x27c43b63, 0x27be4270, 0x27b84965, 0x27b25041, 0x27ac5705, 0x27a65db0,
+    0x27a06443, 0x279a6abd,
+  0x2794711f, 0x278e7768, 0x27887d99, 0x278283b2, 0x277c89b3, 0x27768f9b,
+    0x2770956a, 0x276a9b21,
+  0x2764a0c0, 0x275ea647, 0x2758abb6, 0x2752b10c, 0x274cb64a, 0x2746bb6f,
+    0x2740c07d, 0x273ac572,
+  0x2734ca4f, 0x272ecf14, 0x2728d3c0, 0x2722d855, 0x271cdcd1, 0x2716e136,
+    0x2710e582, 0x270ae9b6,
+  0x2704edd2, 0x26fef1d5, 0x26f8f5c1, 0x26f2f995, 0x26ecfd51, 0x26e700f5,
+    0x26e10480, 0x26db07f4,
+  0x26d50b50, 0x26cf0e94, 0x26c911c0, 0x26c314d4, 0x26bd17d0, 0x26b71ab4,
+    0x26b11d80, 0x26ab2034,
+  0x26a522d1, 0x269f2556, 0x269927c3, 0x26932a18, 0x268d2c55, 0x26872e7b,
+    0x26813088, 0x267b327e,
+  0x2675345d, 0x266f3623, 0x266937d2, 0x26633969, 0x265d3ae9, 0x26573c50,
+    0x26513da1, 0x264b3ed9,
+  0x26453ffa, 0x263f4103, 0x263941f5, 0x263342cf, 0x262d4392, 0x2627443d,
+    0x262144d0, 0x261b454c,
+  0x261545b0, 0x260f45fd, 0x26094633, 0x26034651, 0x25fd4657, 0x25f74646,
+    0x25f1461e, 0x25eb45de,
+  0x25e54587, 0x25df4519, 0x25d94493, 0x25d343f6, 0x25cd4341, 0x25c74276,
+    0x25c14192, 0x25bb4098,
+  0x25b53f86, 0x25af3e5d, 0x25a93d1d, 0x25a33bc6, 0x259d3a57, 0x259738d1,
+    0x25913734, 0x258b3580,
+  0x258533b5, 0x257f31d2, 0x25792fd8, 0x25732dc8, 0x256d2ba0, 0x25672961,
+    0x2561270b, 0x255b249e,
+  0x2555221a, 0x254f1f7e, 0x25491ccc, 0x25431a03, 0x253d1723, 0x2537142c,
+    0x2531111e, 0x252b0df9,
+  0x25250abd, 0x251f076a, 0x25190400, 0x25130080, 0x250cfce8, 0x2506f93a,
+    0x2500f574, 0x24faf198,
+  0x24f4eda6, 0x24eee99c, 0x24e8e57c, 0x24e2e144, 0x24dcdcf6, 0x24d6d892,
+    0x24d0d416, 0x24cacf84,
+  0x24c4cadb, 0x24bec61c, 0x24b8c146, 0x24b2bc59, 0x24acb756, 0x24a6b23b,
+    0x24a0ad0b, 0x249aa7c4,
+  0x2494a266, 0x248e9cf1, 0x24889766, 0x248291c5, 0x247c8c0d, 0x2476863e,
+    0x24708059, 0x246a7a5e,
+  0x2464744c, 0x245e6e23, 0x245867e4, 0x2452618f, 0x244c5b24, 0x244654a1,
+    0x24404e09, 0x243a475a,
+  0x24344095, 0x242e39ba, 0x242832c8, 0x24222bc0, 0x241c24a1, 0x24161d6d,
+    0x24101622, 0x240a0ec1,
+  0x24040749, 0x23fdffbc, 0x23f7f818, 0x23f1f05e, 0x23ebe88e, 0x23e5e0a7,
+    0x23dfd8ab, 0x23d9d098,
+  0x23d3c86f, 0x23cdc031, 0x23c7b7dc, 0x23c1af71, 0x23bba6f0, 0x23b59e59,
+    0x23af95ac, 0x23a98ce8,
+  0x23a3840f, 0x239d7b20, 0x2397721b, 0x23916900, 0x238b5fcf, 0x23855688,
+    0x237f4d2b, 0x237943b9,
+  0x23733a30, 0x236d3092, 0x236726dd, 0x23611d13, 0x235b1333, 0x2355093e,
+    0x234eff32, 0x2348f511,
+  0x2342eada, 0x233ce08d, 0x2336d62a, 0x2330cbb2, 0x232ac124, 0x2324b680,
+    0x231eabc7, 0x2318a0f8,
+  0x23129613, 0x230c8b19, 0x23068009, 0x230074e3, 0x22fa69a8, 0x22f45e57,
+    0x22ee52f1, 0x22e84775,
+  0x22e23be4, 0x22dc303d, 0x22d62480, 0x22d018ae, 0x22ca0cc7, 0x22c400ca,
+    0x22bdf4b8, 0x22b7e890,
+  0x22b1dc53, 0x22abd001, 0x22a5c399, 0x229fb71b, 0x2299aa89, 0x22939de1,
+    0x228d9123, 0x22878451,
+  0x22817769, 0x227b6a6c, 0x22755d59, 0x226f5032, 0x226942f5, 0x226335a2,
+    0x225d283b, 0x22571abe,
+  0x22510d2d, 0x224aff86, 0x2244f1c9, 0x223ee3f8, 0x2238d612, 0x2232c816,
+    0x222cba06, 0x2226abe0,
+  0x22209da5, 0x221a8f56, 0x221480f1, 0x220e7277, 0x220863e8, 0x22025544,
+    0x21fc468b, 0x21f637be,
+  0x21f028db, 0x21ea19e3, 0x21e40ad7, 0x21ddfbb5, 0x21d7ec7f, 0x21d1dd34,
+    0x21cbcdd3, 0x21c5be5e,
+  0x21bfaed5, 0x21b99f36, 0x21b38f83, 0x21ad7fba, 0x21a76fdd, 0x21a15fec,
+    0x219b4fe5, 0x21953fca,
+  0x218f2f9a, 0x21891f55, 0x21830efc, 0x217cfe8e, 0x2176ee0b, 0x2170dd74,
+    0x216accc8, 0x2164bc08,
+  0x215eab33, 0x21589a49, 0x2152894b, 0x214c7838, 0x21466710, 0x214055d4,
+    0x213a4484, 0x2134331f,
+  0x212e21a6, 0x21281018, 0x2121fe76, 0x211becbf, 0x2115daf4, 0x210fc914,
+    0x2109b720, 0x2103a518,
+  0x20fd92fb, 0x20f780ca, 0x20f16e84, 0x20eb5c2b, 0x20e549bd, 0x20df373a,
+    0x20d924a4, 0x20d311f9,
+  0x20ccff3a, 0x20c6ec66, 0x20c0d97f, 0x20bac683, 0x20b4b373, 0x20aea04f,
+    0x20a88d17, 0x20a279ca,
+  0x209c666a, 0x209652f5, 0x20903f6c, 0x208a2bcf, 0x2084181e, 0x207e0459,
+    0x2077f080, 0x2071dc93,
+  0x206bc892, 0x2065b47d, 0x205fa054, 0x20598c17, 0x205377c6, 0x204d6361,
+    0x20474ee8, 0x20413a5b,
+  0x203b25bb, 0x20351106, 0x202efc3e, 0x2028e761, 0x2022d271, 0x201cbd6d,
+    0x2016a856, 0x2010932a,
+  0x200a7deb, 0x20046898, 0x1ffe5331, 0x1ff83db6, 0x1ff22828, 0x1fec1286,
+    0x1fe5fcd0, 0x1fdfe707,
+  0x1fd9d12a, 0x1fd3bb39, 0x1fcda535, 0x1fc78f1d, 0x1fc178f1, 0x1fbb62b2,
+    0x1fb54c60, 0x1faf35f9,
+  0x1fa91f80, 0x1fa308f2, 0x1f9cf252, 0x1f96db9d, 0x1f90c4d5, 0x1f8aadfa,
+    0x1f84970b, 0x1f7e8009,
+  0x1f7868f4, 0x1f7251ca, 0x1f6c3a8e, 0x1f66233e, 0x1f600bdb, 0x1f59f465,
+    0x1f53dcdb, 0x1f4dc53d,
+  0x1f47ad8d, 0x1f4195c9, 0x1f3b7df2, 0x1f356608, 0x1f2f4e0a, 0x1f2935f9,
+    0x1f231dd5, 0x1f1d059e,
+  0x1f16ed54, 0x1f10d4f6, 0x1f0abc85, 0x1f04a401, 0x1efe8b6a, 0x1ef872c0,
+    0x1ef25a03, 0x1eec4132,
+  0x1ee6284f, 0x1ee00f58, 0x1ed9f64f, 0x1ed3dd32, 0x1ecdc402, 0x1ec7aac0,
+    0x1ec1916a, 0x1ebb7802,
+  0x1eb55e86, 0x1eaf44f8, 0x1ea92b56, 0x1ea311a2, 0x1e9cf7db, 0x1e96de01,
+    0x1e90c414, 0x1e8aaa14,
+  0x1e849001, 0x1e7e75dc, 0x1e785ba3, 0x1e724158, 0x1e6c26fa, 0x1e660c8a,
+    0x1e5ff206, 0x1e59d770,
+  0x1e53bcc7, 0x1e4da20c, 0x1e47873d, 0x1e416c5d, 0x1e3b5169, 0x1e353663,
+    0x1e2f1b4a, 0x1e29001e,
+  0x1e22e4e0, 0x1e1cc990, 0x1e16ae2c, 0x1e1092b6, 0x1e0a772e, 0x1e045b93,
+    0x1dfe3fe6, 0x1df82426,
+  0x1df20853, 0x1debec6f, 0x1de5d077, 0x1ddfb46e, 0x1dd99851, 0x1dd37c23,
+    0x1dcd5fe2, 0x1dc7438e,
+  0x1dc12729, 0x1dbb0ab0, 0x1db4ee26, 0x1daed189, 0x1da8b4da, 0x1da29819,
+    0x1d9c7b45, 0x1d965e5f,
+  0x1d904167, 0x1d8a245c, 0x1d840740, 0x1d7dea11, 0x1d77ccd0, 0x1d71af7d,
+    0x1d6b9217, 0x1d6574a0,
+  0x1d5f5716, 0x1d59397a, 0x1d531bcc, 0x1d4cfe0d, 0x1d46e03a, 0x1d40c256,
+    0x1d3aa460, 0x1d348658,
+  0x1d2e683e, 0x1d284a12, 0x1d222bd3, 0x1d1c0d83, 0x1d15ef21, 0x1d0fd0ad,
+    0x1d09b227, 0x1d03938f,
+  0x1cfd74e5, 0x1cf7562a, 0x1cf1375c, 0x1ceb187d, 0x1ce4f98c, 0x1cdeda89,
+    0x1cd8bb74, 0x1cd29c4d,
+  0x1ccc7d15, 0x1cc65dca, 0x1cc03e6e, 0x1cba1f01, 0x1cb3ff81, 0x1caddff0,
+    0x1ca7c04d, 0x1ca1a099,
+  0x1c9b80d3, 0x1c9560fb, 0x1c8f4112, 0x1c892117, 0x1c83010a, 0x1c7ce0ec,
+    0x1c76c0bc, 0x1c70a07b,
+  0x1c6a8028, 0x1c645fc3, 0x1c5e3f4d, 0x1c581ec6, 0x1c51fe2d, 0x1c4bdd83,
+    0x1c45bcc7, 0x1c3f9bf9,
+  0x1c397b1b, 0x1c335a2b, 0x1c2d3929, 0x1c271816, 0x1c20f6f2, 0x1c1ad5bc,
+    0x1c14b475, 0x1c0e931d,
+  0x1c0871b4, 0x1c025039, 0x1bfc2ead, 0x1bf60d0f, 0x1befeb60, 0x1be9c9a1,
+    0x1be3a7cf, 0x1bdd85ed,
+  0x1bd763fa, 0x1bd141f5, 0x1bcb1fdf, 0x1bc4fdb8, 0x1bbedb80, 0x1bb8b937,
+    0x1bb296dc, 0x1bac7471,
+  0x1ba651f5, 0x1ba02f67, 0x1b9a0cc8, 0x1b93ea19, 0x1b8dc758, 0x1b87a487,
+    0x1b8181a4, 0x1b7b5eb0,
+  0x1b753bac, 0x1b6f1897, 0x1b68f570, 0x1b62d239, 0x1b5caef1, 0x1b568b98,
+    0x1b50682e, 0x1b4a44b3,
+  0x1b442127, 0x1b3dfd8b, 0x1b37d9de, 0x1b31b620, 0x1b2b9251, 0x1b256e71,
+    0x1b1f4a81, 0x1b192680,
+  0x1b13026e, 0x1b0cde4c, 0x1b06ba19, 0x1b0095d5, 0x1afa7180, 0x1af44d1b,
+    0x1aee28a6, 0x1ae8041f,
+  0x1ae1df88, 0x1adbbae1, 0x1ad59629, 0x1acf7160, 0x1ac94c87, 0x1ac3279d,
+    0x1abd02a3, 0x1ab6dd98,
+  0x1ab0b87d, 0x1aaa9352, 0x1aa46e16, 0x1a9e48c9, 0x1a98236c, 0x1a91fdff,
+    0x1a8bd881, 0x1a85b2f3,
+  0x1a7f8d54, 0x1a7967a6, 0x1a7341e6, 0x1a6d1c17, 0x1a66f637, 0x1a60d047,
+    0x1a5aaa47, 0x1a548436,
+  0x1a4e5e15, 0x1a4837e4, 0x1a4211a3, 0x1a3beb52, 0x1a35c4f0, 0x1a2f9e7e,
+    0x1a2977fc, 0x1a23516a,
+  0x1a1d2ac8, 0x1a170416, 0x1a10dd53, 0x1a0ab681, 0x1a048f9e, 0x19fe68ac,
+    0x19f841a9, 0x19f21a96,
+  0x19ebf374, 0x19e5cc41, 0x19dfa4fe, 0x19d97dac, 0x19d35649, 0x19cd2ed7,
+    0x19c70754, 0x19c0dfc2,
+  0x19bab820, 0x19b4906e, 0x19ae68ac, 0x19a840da, 0x19a218f9, 0x199bf107,
+    0x1995c906, 0x198fa0f5,
+  0x198978d4, 0x198350a4, 0x197d2864, 0x19770014, 0x1970d7b4, 0x196aaf45,
+    0x196486c6, 0x195e5e37,
+  0x19583599, 0x19520ceb, 0x194be42d, 0x1945bb60, 0x193f9283, 0x19396997,
+    0x1933409b, 0x192d178f,
+  0x1926ee74, 0x1920c54a, 0x191a9c10, 0x191472c6, 0x190e496d, 0x19082005,
+    0x1901f68d, 0x18fbcd06,
+  0x18f5a36f, 0x18ef79c9, 0x18e95014, 0x18e3264f, 0x18dcfc7b, 0x18d6d297,
+    0x18d0a8a4, 0x18ca7ea2,
+  0x18c45491, 0x18be2a70, 0x18b80040, 0x18b1d601, 0x18ababb2, 0x18a58154,
+    0x189f56e8, 0x18992c6b,
+  0x189301e0, 0x188cd746, 0x1886ac9c, 0x188081e4, 0x187a571c, 0x18742c45,
+    0x186e015f, 0x1867d66a,
+  0x1861ab66, 0x185b8053, 0x18555530, 0x184f29ff, 0x1848febf, 0x1842d370,
+    0x183ca812, 0x18367ca5,
+  0x18305129, 0x182a259e, 0x1823fa04, 0x181dce5b, 0x1817a2a4, 0x181176dd,
+    0x180b4b08, 0x18051f24,
+  0x17fef331, 0x17f8c72f, 0x17f29b1e, 0x17ec6eff, 0x17e642d1, 0x17e01694,
+    0x17d9ea49, 0x17d3bdee,
+  0x17cd9186, 0x17c7650e, 0x17c13888, 0x17bb0bf3, 0x17b4df4f, 0x17aeb29d,
+    0x17a885dc, 0x17a2590d,
+  0x179c2c2f, 0x1795ff42, 0x178fd247, 0x1789a53d, 0x17837825, 0x177d4afe,
+    0x17771dc9, 0x1770f086,
+  0x176ac333, 0x176495d3, 0x175e6864, 0x17583ae7, 0x17520d5b, 0x174bdfc1,
+    0x1745b218, 0x173f8461,
+  0x1739569c, 0x173328c8, 0x172cfae6, 0x1726ccf6, 0x17209ef8, 0x171a70eb,
+    0x171442d0, 0x170e14a7,
+  0x1707e670, 0x1701b82a, 0x16fb89d6, 0x16f55b74, 0x16ef2d04, 0x16e8fe86,
+    0x16e2cff9, 0x16dca15f,
+  0x16d672b6, 0x16d043ff, 0x16ca153a, 0x16c3e667, 0x16bdb787, 0x16b78898,
+    0x16b1599b, 0x16ab2a90,
+  0x16a4fb77, 0x169ecc50, 0x16989d1b, 0x16926dd8, 0x168c3e87, 0x16860f29,
+    0x167fdfbc, 0x1679b042,
+  0x167380ba, 0x166d5123, 0x1667217f, 0x1660f1ce, 0x165ac20e, 0x16549241,
+    0x164e6266, 0x1648327d,
+  0x16420286, 0x163bd282, 0x1635a270, 0x162f7250, 0x16294222, 0x162311e7,
+    0x161ce19e, 0x1616b148,
+  0x161080e4, 0x160a5072, 0x16041ff3, 0x15fdef66, 0x15f7becc, 0x15f18e24,
+    0x15eb5d6e, 0x15e52cab,
+  0x15defbdb, 0x15d8cafd, 0x15d29a11, 0x15cc6918, 0x15c63812, 0x15c006fe,
+    0x15b9d5dd, 0x15b3a4ae,
+  0x15ad7372, 0x15a74228, 0x15a110d2, 0x159adf6e, 0x1594adfc, 0x158e7c7d,
+    0x15884af1, 0x15821958,
+  0x157be7b1, 0x1575b5fe, 0x156f843c, 0x1569526e, 0x15632093, 0x155ceeaa,
+    0x1556bcb4, 0x15508ab1,
+  0x154a58a1, 0x15442683, 0x153df459, 0x1537c221, 0x15318fdd, 0x152b5d8b,
+    0x15252b2c, 0x151ef8c0,
+  0x1518c648, 0x151293c2, 0x150c612f, 0x15062e8f, 0x14fffbe2, 0x14f9c928,
+    0x14f39662, 0x14ed638e,
+  0x14e730ae, 0x14e0fdc0, 0x14dacac6, 0x14d497bf, 0x14ce64ab, 0x14c8318a,
+    0x14c1fe5c, 0x14bbcb22,
+  0x14b597da, 0x14af6486, 0x14a93125, 0x14a2fdb8, 0x149cca3e, 0x149696b7,
+    0x14906323, 0x148a2f82,
+  0x1483fbd5, 0x147dc81c, 0x14779455, 0x14716082, 0x146b2ca3, 0x1464f8b7,
+    0x145ec4be, 0x145890b9,
+  0x14525ca7, 0x144c2888, 0x1445f45d, 0x143fc026, 0x14398be2, 0x14335792,
+    0x142d2335, 0x1426eecb,
+  0x1420ba56, 0x141a85d3, 0x14145145, 0x140e1caa, 0x1407e803, 0x1401b34f,
+    0x13fb7e8f, 0x13f549c3,
+  0x13ef14ea, 0x13e8e005, 0x13e2ab14, 0x13dc7616, 0x13d6410d, 0x13d00bf7,
+    0x13c9d6d4, 0x13c3a1a6,
+  0x13bd6c6b, 0x13b73725, 0x13b101d2, 0x13aacc73, 0x13a49707, 0x139e6190,
+    0x13982c0d, 0x1391f67d,
+  0x138bc0e1, 0x13858b3a, 0x137f5586, 0x13791fc6, 0x1372e9fb, 0x136cb423,
+    0x13667e3f, 0x13604850,
+  0x135a1254, 0x1353dc4c, 0x134da639, 0x1347701a, 0x134139ee, 0x133b03b7,
+    0x1334cd74, 0x132e9725,
+  0x132860ca, 0x13222a64, 0x131bf3f2, 0x1315bd73, 0x130f86ea, 0x13095054,
+    0x130319b3, 0x12fce305,
+  0x12f6ac4d, 0x12f07588, 0x12ea3eb8, 0x12e407dc, 0x12ddd0f4, 0x12d79a01,
+    0x12d16303, 0x12cb2bf8,
+  0x12c4f4e2, 0x12bebdc1, 0x12b88693, 0x12b24f5b, 0x12ac1817, 0x12a5e0c7,
+    0x129fa96c, 0x12997205,
+  0x12933a93, 0x128d0315, 0x1286cb8c, 0x128093f7, 0x127a5c57, 0x127424ac,
+    0x126decf5, 0x1267b533,
+  0x12617d66, 0x125b458d, 0x12550da9, 0x124ed5ba, 0x12489dbf, 0x124265b9,
+    0x123c2da8, 0x1235f58b,
+  0x122fbd63, 0x12298530, 0x12234cf2, 0x121d14a9, 0x1216dc54, 0x1210a3f5,
+    0x120a6b8a, 0x12043314,
+  0x11fdfa93, 0x11f7c207, 0x11f18970, 0x11eb50cd, 0x11e51820, 0x11dedf68,
+    0x11d8a6a4, 0x11d26dd6,
+  0x11cc34fc, 0x11c5fc18, 0x11bfc329, 0x11b98a2e, 0x11b35129, 0x11ad1819,
+    0x11a6defe, 0x11a0a5d8,
+  0x119a6ca7, 0x1194336b, 0x118dfa25, 0x1187c0d3, 0x11818777, 0x117b4e10,
+    0x1175149e, 0x116edb22,
+  0x1168a19b, 0x11626809, 0x115c2e6c, 0x1155f4c4, 0x114fbb12, 0x11498156,
+    0x1143478e, 0x113d0dbc,
+  0x1136d3df, 0x113099f8, 0x112a6006, 0x11242609, 0x111dec02, 0x1117b1f0,
+    0x111177d4, 0x110b3dad,
+  0x1105037c, 0x10fec940, 0x10f88efa, 0x10f254a9, 0x10ec1a4e, 0x10e5dfe8,
+    0x10dfa578, 0x10d96afe,
+  0x10d33079, 0x10ccf5ea, 0x10c6bb50, 0x10c080ac, 0x10ba45fe, 0x10b40b45,
+    0x10add082, 0x10a795b5,
+  0x10a15ade, 0x109b1ffc, 0x1094e510, 0x108eaa1a, 0x10886f19, 0x1082340f,
+    0x107bf8fa, 0x1075bddb,
+  0x106f82b2, 0x1069477f, 0x10630c41, 0x105cd0fa, 0x105695a8, 0x10505a4d,
+    0x104a1ee7, 0x1043e377,
+  0x103da7fd, 0x10376c79, 0x103130ec, 0x102af554, 0x1024b9b2, 0x101e7e06,
+    0x10184251, 0x10120691,
+  0x100bcac7, 0x10058ef4, 0xfff5317, 0xff91730, 0xff2db3e, 0xfec9f44,
+    0xfe6633f, 0xfe02730,
+  0xfd9eb18, 0xfd3aef6, 0xfcd72ca, 0xfc73695, 0xfc0fa55, 0xfbabe0c, 0xfb481ba,
+    0xfae455d,
+  0xfa808f7, 0xfa1cc87, 0xf9b900e, 0xf95538b, 0xf8f16fe, 0xf88da68, 0xf829dc8,
+    0xf7c611f,
+  0xf76246c, 0xf6fe7af, 0xf69aae9, 0xf636e1a, 0xf5d3141, 0xf56f45e, 0xf50b773,
+    0xf4a7a7d,
+  0xf443d7e, 0xf3e0076, 0xf37c365, 0xf318649, 0xf2b4925, 0xf250bf7, 0xf1ecec0,
+    0xf189180,
+  0xf125436, 0xf0c16e3, 0xf05d987, 0xeff9c21, 0xef95eb2, 0xef3213a, 0xeece3b9,
+    0xee6a62f,
+  0xee0689b, 0xeda2afe, 0xed3ed58, 0xecdafa9, 0xec771f1, 0xec1342f, 0xebaf665,
+    0xeb4b891,
+  0xeae7ab4, 0xea83ccf, 0xea1fee0, 0xe9bc0e8, 0xe9582e7, 0xe8f44dd, 0xe8906cb,
+    0xe82c8af,
+  0xe7c8a8a, 0xe764c5c, 0xe700e26, 0xe69cfe6, 0xe63919e, 0xe5d534d, 0xe5714f3,
+    0xe50d690,
+  0xe4a9824, 0xe4459af, 0xe3e1b32, 0xe37dcac, 0xe319e1d, 0xe2b5f85, 0xe2520e5,
+    0xe1ee23c,
+  0xe18a38a, 0xe1264cf, 0xe0c260c, 0xe05e740, 0xdffa86b, 0xdf9698e, 0xdf32aa8,
+    0xdecebba,
+  0xde6acc3, 0xde06dc3, 0xdda2ebb, 0xdd3efab, 0xdcdb091, 0xdc77170, 0xdc13245,
+    0xdbaf313,
+  0xdb4b3d7, 0xdae7494, 0xda83548, 0xda1f5f3, 0xd9bb696, 0xd957731, 0xd8f37c3,
+    0xd88f84d,
+  0xd82b8cf, 0xd7c7948, 0xd7639b9, 0xd6ffa22, 0xd69ba82, 0xd637ada, 0xd5d3b2a,
+    0xd56fb71,
+  0xd50bbb1, 0xd4a7be8, 0xd443c17, 0xd3dfc3e, 0xd37bc5c, 0xd317c73, 0xd2b3c81,
+    0xd24fc87,
+  0xd1ebc85, 0xd187c7b, 0xd123c69, 0xd0bfc4f, 0xd05bc2d, 0xcff7c02, 0xcf93bd0,
+    0xcf2fb96,
+  0xcecbb53, 0xce67b09, 0xce03ab7, 0xcd9fa5d, 0xcd3b9fb, 0xccd7991, 0xcc7391f,
+    0xcc0f8a5,
+  0xcbab824, 0xcb4779a, 0xcae3709, 0xca7f670, 0xca1b5cf, 0xc9b7526, 0xc953475,
+    0xc8ef3bd,
+  0xc88b2fd, 0xc827235, 0xc7c3166, 0xc75f08f, 0xc6fafb0, 0xc696ec9, 0xc632ddb,
+    0xc5cece5,
+  0xc56abe8, 0xc506ae3, 0xc4a29d6, 0xc43e8c2, 0xc3da7a6, 0xc376683, 0xc312558,
+    0xc2ae425,
+  0xc24a2eb, 0xc1e61aa, 0xc182061, 0xc11df11, 0xc0b9db9, 0xc055c5a, 0xbff1af3,
+    0xbf8d985,
+  0xbf29810, 0xbec5693, 0xbe6150f, 0xbdfd383, 0xbd991f0, 0xbd35056, 0xbcd0eb5,
+    0xbc6cd0c,
+  0xbc08b5c, 0xbba49a5, 0xbb407e7, 0xbadc621, 0xba78454, 0xba14280, 0xb9b00a5,
+    0xb94bec2,
+  0xb8e7cd9, 0xb883ae8, 0xb81f8f0, 0xb7bb6f2, 0xb7574ec, 0xb6f32df, 0xb68f0cb,
+    0xb62aeaf,
+  0xb5c6c8d, 0xb562a64, 0xb4fe834, 0xb49a5fd, 0xb4363bf, 0xb3d217a, 0xb36df2e,
+    0xb309cdb,
+  0xb2a5a81, 0xb241820, 0xb1dd5b9, 0xb17934b, 0xb1150d5, 0xb0b0e59, 0xb04cbd6,
+    0xafe894d,
+  0xaf846bc, 0xaf20425, 0xaebc187, 0xae57ee2, 0xadf3c37, 0xad8f985, 0xad2b6cc,
+    0xacc740c,
+  0xac63146, 0xabfee79, 0xab9aba6, 0xab368cc, 0xaad25eb, 0xaa6e304, 0xaa0a016,
+    0xa9a5d22,
+  0xa941a27, 0xa8dd725, 0xa87941d, 0xa81510f, 0xa7b0dfa, 0xa74cadf, 0xa6e87bd,
+    0xa684495,
+  0xa620166, 0xa5bbe31, 0xa557af5, 0xa4f37b3, 0xa48f46b, 0xa42b11d, 0xa3c6dc8,
+    0xa362a6d,
+  0xa2fe70b, 0xa29a3a3, 0xa236035, 0xa1d1cc1, 0xa16d946, 0xa1095c6, 0xa0a523f,
+    0xa040eb1,
+  0x9fdcb1e, 0x9f78784, 0x9f143e5, 0x9eb003f, 0x9e4bc93, 0x9de78e1, 0x9d83529,
+    0x9d1f16b,
+  0x9cbada7, 0x9c569dc, 0x9bf260c, 0x9b8e236, 0x9b29e59, 0x9ac5a77, 0x9a6168f,
+    0x99fd2a0,
+  0x9998eac, 0x9934ab2, 0x98d06b2, 0x986c2ac, 0x9807ea1, 0x97a3a8f, 0x973f678,
+    0x96db25a,
+  0x9676e37, 0x9612a0e, 0x95ae5e0, 0x954a1ab, 0x94e5d71, 0x9481931, 0x941d4eb,
+    0x93b90a0,
+  0x9354c4f, 0x92f07f8, 0x928c39b, 0x9227f39, 0x91c3ad2, 0x915f664, 0x90fb1f1,
+    0x9096d79,
+  0x90328fb, 0x8fce477, 0x8f69fee, 0x8f05b5f, 0x8ea16cb, 0x8e3d231, 0x8dd8d92,
+    0x8d748ed,
+  0x8d10443, 0x8cabf93, 0x8c47ade, 0x8be3624, 0x8b7f164, 0x8b1ac9f, 0x8ab67d4,
+    0x8a52304,
+  0x89ede2f, 0x8989955, 0x8925475, 0x88c0f90, 0x885caa5, 0x87f85b5, 0x87940c1,
+    0x872fbc6,
+  0x86cb6c7, 0x86671c2, 0x8602cb9, 0x859e7aa, 0x853a296, 0x84d5d7d, 0x847185e,
+    0x840d33b,
+  0x83a8e12, 0x83448e5, 0x82e03b2, 0x827be7a, 0x821793e, 0x81b33fc, 0x814eeb5,
+    0x80ea969,
+  0x8086419, 0x8021ec3, 0x7fbd968, 0x7f59409, 0x7ef4ea4, 0x7e9093b, 0x7e2c3cd,
+    0x7dc7e5a,
+  0x7d638e2, 0x7cff365, 0x7c9ade4, 0x7c3685d, 0x7bd22d2, 0x7b6dd42, 0x7b097ad,
+    0x7aa5214,
+  0x7a40c76, 0x79dc6d3, 0x797812b, 0x7913b7f, 0x78af5ce, 0x784b019, 0x77e6a5e,
+    0x77824a0,
+  0x771dedc, 0x76b9914, 0x7655347, 0x75f0d76, 0x758c7a1, 0x75281c6, 0x74c3be7,
+    0x745f604,
+  0x73fb01c, 0x7396a30, 0x733243f, 0x72cde4a, 0x7269851, 0x7205253, 0x71a0c50,
+    0x713c64a,
+  0x70d803f, 0x7073a2f, 0x700f41b, 0x6faae03, 0x6f467e7, 0x6ee21c6, 0x6e7dba1,
+    0x6e19578,
+  0x6db4f4a, 0x6d50919, 0x6cec2e3, 0x6c87ca9, 0x6c2366a, 0x6bbf028, 0x6b5a9e1,
+    0x6af6396,
+  0x6a91d47, 0x6a2d6f4, 0x69c909d, 0x6964a42, 0x69003e3, 0x689bd80, 0x6837718,
+    0x67d30ad,
+  0x676ea3d, 0x670a3ca, 0x66a5d53, 0x66416d8, 0x65dd058, 0x65789d5, 0x651434e,
+    0x64afcc3,
+  0x644b634, 0x63e6fa2, 0x638290b, 0x631e271, 0x62b9bd3, 0x6255531, 0x61f0e8b,
+    0x618c7e1,
+  0x6128134, 0x60c3a83, 0x605f3ce, 0x5ffad15, 0x5f96659, 0x5f31f99, 0x5ecd8d6,
+    0x5e6920e,
+  0x5e04b43, 0x5da0475, 0x5d3bda3, 0x5cd76cd, 0x5c72ff4, 0x5c0e917, 0x5baa237,
+    0x5b45b53,
+  0x5ae146b, 0x5a7cd80, 0x5a18692, 0x59b3fa0, 0x594f8aa, 0x58eb1b2, 0x5886ab5,
+    0x58223b6,
+  0x57bdcb3, 0x57595ac, 0x56f4ea2, 0x5690795, 0x562c085, 0x55c7971, 0x556325a,
+    0x54feb3f,
+  0x549a422, 0x5435d01, 0x53d15dd, 0x536ceb5, 0x530878a, 0x52a405d, 0x523f92c,
+    0x51db1f7,
+  0x5176ac0, 0x5112385, 0x50adc48, 0x5049507, 0x4fe4dc3, 0x4f8067c, 0x4f1bf32,
+    0x4eb77e5,
+  0x4e53095, 0x4dee942, 0x4d8a1ec, 0x4d25a93, 0x4cc1337, 0x4c5cbd8, 0x4bf8476,
+    0x4b93d11,
+  0x4b2f5a9, 0x4acae3e, 0x4a666d1, 0x4a01f60, 0x499d7ed, 0x4939077, 0x48d48fe,
+    0x4870182,
+  0x480ba04, 0x47a7282, 0x4742afe, 0x46de377, 0x4679bee, 0x4615461, 0x45b0cd2,
+    0x454c541,
+  0x44e7dac, 0x4483615, 0x441ee7c, 0x43ba6df, 0x4355f40, 0x42f179f, 0x428cffb,
+    0x4228854,
+  0x41c40ab, 0x415f8ff, 0x40fb151, 0x40969a0, 0x40321ed, 0x3fcda37, 0x3f6927f,
+    0x3f04ac4,
+  0x3ea0307, 0x3e3bb48, 0x3dd7386, 0x3d72bc2, 0x3d0e3fb, 0x3ca9c32, 0x3c45467,
+    0x3be0c99,
+  0x3b7c4c9, 0x3b17cf7, 0x3ab3523, 0x3a4ed4c, 0x39ea573, 0x3985d97, 0x39215ba,
+    0x38bcdda,
+  0x38585f8, 0x37f3e14, 0x378f62e, 0x372ae46, 0x36c665b, 0x3661e6f, 0x35fd680,
+    0x3598e8f,
+  0x353469c, 0x34cfea8, 0x346b6b1, 0x3406eb8, 0x33a26bd, 0x333dec0, 0x32d96c1,
+    0x3274ec0,
+  0x32106bd, 0x31abeb9, 0x31476b2, 0x30e2ea9, 0x307e69f, 0x3019e93, 0x2fb5684,
+    0x2f50e74,
+  0x2eec663, 0x2e87e4f, 0x2e2363a, 0x2dbee22, 0x2d5a609, 0x2cf5def, 0x2c915d2,
+    0x2c2cdb4,
+  0x2bc8594, 0x2b63d73, 0x2aff54f, 0x2a9ad2a, 0x2a36504, 0x29d1cdc, 0x296d4b2,
+    0x2908c87,
+  0x28a445a, 0x283fc2b, 0x27db3fb, 0x2776bc9, 0x2712396, 0x26adb62, 0x264932b,
+    0x25e4af4,
+  0x25802bb, 0x251ba80, 0x24b7244, 0x2452a07, 0x23ee1c8, 0x2389988, 0x2325147,
+    0x22c0904,
+  0x225c0bf, 0x21f787a, 0x2193033, 0x212e7eb, 0x20c9fa1, 0x2065757, 0x2000f0b,
+    0x1f9c6be,
+  0x1f37e6f, 0x1ed3620, 0x1e6edcf, 0x1e0a57d, 0x1da5d2a, 0x1d414d6, 0x1cdcc80,
+    0x1c7842a,
+  0x1c13bd2, 0x1baf37a, 0x1b4ab20, 0x1ae62c5, 0x1a81a69, 0x1a1d20c, 0x19b89ae,
+    0x1954150,
+  0x18ef8f0, 0x188b08f, 0x182682d, 0x17c1fcb, 0x175d767, 0x16f8f03, 0x169469d,
+    0x162fe37,
+  0x15cb5d0, 0x1566d68, 0x15024ff, 0x149dc96, 0x143942b, 0x13d4bc0, 0x1370354,
+    0x130bae7,
+  0x12a727a, 0x1242a0c, 0x11de19d, 0x117992e, 0x11150be, 0x10b084d, 0x104bfdb,
+    0xfe7769,
+  0xf82ef6, 0xf1e683, 0xeb9e0f, 0xe5559b, 0xdf0d26, 0xd8c4b0, 0xd27c3a,
+    0xcc33c3,
+  0xc5eb4c, 0xbfa2d5, 0xb95a5d, 0xb311e4, 0xacc96b, 0xa680f2, 0xa03878,
+    0x99effe,
+  0x93a784, 0x8d5f09, 0x87168e, 0x80ce12, 0x7a8597, 0x743d1a, 0x6df49e,
+    0x67ac21,
+  0x6163a5, 0x5b1b27, 0x54d2aa, 0x4e8a2c, 0x4841af, 0x41f931, 0x3bb0b3,
+    0x356835,
+  0x2f1fb6, 0x28d738, 0x228eb9, 0x1c463b, 0x15fdbc, 0xfb53d, 0x96cbe, 0x3243f,
+
+};
+
+/**    
+ * @brief  Initialization function for the Q31 DCT4/IDCT4.   
+ * @param[in,out] *S         points to an instance of Q31 DCT4/IDCT4 structure.   
+ * @param[in]     *S_RFFT    points to an instance of Q31 RFFT/RIFFT structure   
+ * @param[in]     *S_CFFT    points to an instance of Q31 CFFT/CIFFT structure   
+ * @param[in]     N          length of the DCT4.   
+ * @param[in]     Nby2       half of the length of the DCT4.   
+ * @param[in]     normalize  normalizing factor.   
+ * @return		  arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if N is not a supported transform length.   
+ * \par Normalizing factor:    
+ * The normalizing factor is sqrt(2/N), which depends on the size of transform N.    
+ * Normalizing factors in 1.31 format are mentioned in the table below for different DCT sizes:    
+ * \image html dct4NormalizingQ31Table.gif    
+ */
+
+arm_status arm_dct4_init_q31(
+  arm_dct4_instance_q31 * S,
+  arm_rfft_instance_q31 * S_RFFT,
+  arm_cfft_radix4_instance_q31 * S_CFFT,
+  uint16_t N,
+  uint16_t Nby2,
+  q31_t normalize)
+{
+  /*  Initialise the default arm status */
+  arm_status status = ARM_MATH_SUCCESS;
+
+  /* Initializing the pointer array with the weight table base addresses of different lengths */
+  q31_t *twiddlePtr[4] = { (q31_t *) WeightsQ31_128, (q31_t *) WeightsQ31_512,
+    (q31_t *) WeightsQ31_2048, (q31_t *) WeightsQ31_8192
+  };
+
+  /* Initializing the pointer array with the cos factor table base addresses of different lengths */
+  q31_t *pCosFactor[4] =
+    { (q31_t *) cos_factorsQ31_128, (q31_t *) cos_factorsQ31_512,
+    (q31_t *) cos_factorsQ31_2048, (q31_t *) cos_factorsQ31_8192
+  };
+
+  /* Initialize the DCT4 length */
+  S->N = N;
+
+  /* Initialize the half of DCT4 length */
+  S->Nby2 = Nby2;
+
+  /* Initialize the DCT4 Normalizing factor */
+  S->normalize = normalize;
+
+  /* Initialize Real FFT Instance */
+  S->pRfft = S_RFFT;
+
+  /* Initialize Complex FFT Instance */
+  S->pCfft = S_CFFT;
+
+  switch (N)
+  {
+    /* Initialize the table modifier values */
+  case 8192u:
+    S->pTwiddle = twiddlePtr[3];
+    S->pCosFactor = pCosFactor[3];
+    break;
+  case 2048u:
+    S->pTwiddle = twiddlePtr[2];
+    S->pCosFactor = pCosFactor[2];
+    break;
+  case 512u:
+    S->pTwiddle = twiddlePtr[1];
+    S->pCosFactor = pCosFactor[1];
+    break;
+  case 128u:
+    S->pTwiddle = twiddlePtr[0];
+    S->pCosFactor = pCosFactor[0];
+    break;
+  default:
+    status = ARM_MATH_ARGUMENT_ERROR;
+  }
+
+  /* Initialize the RFFT/RIFFT Function */
+  arm_rfft_init_q31(S->pRfft, S->pCfft, S->N, 0, 1);
+
+  /* return the status of DCT4 Init function */
+  return (status);
+}
+
+/**    
+   * @} end of DCT4_IDCT4 group    
+   */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_dct4_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_dct4_q15.c
new file mode 100644
index 0000000000..feaa2ae3c0
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_dct4_q15.c
@@ -0,0 +1,386 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_dct4_q15.c    
+*    
+* Description:	Processing function of DCT4 & IDCT4 Q15.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @addtogroup DCT4_IDCT4    
+ * @{    
+ */
+
+/**    
+ * @brief Processing function for the Q15 DCT4/IDCT4.   
+ * @param[in]       *S             points to an instance of the Q15 DCT4 structure.   
+ * @param[in]       *pState        points to state buffer.   
+ * @param[in,out]   *pInlineBuffer points to the in-place input and output buffer.   
+ * @return none.   
+ *     
+ * \par Input an output formats:    
+ * Internally inputs are downscaled in the RFFT process function to avoid overflows.    
+ * Number of bits downscaled, depends on the size of the transform.    
+ * The input and output formats for different DCT sizes and number of bits to upscale are mentioned in the table below:     
+ *    
+ * \image html dct4FormatsQ15Table.gif    
+ */
+
+void arm_dct4_q15(
+  const arm_dct4_instance_q15 * S,
+  q15_t * pState,
+  q15_t * pInlineBuffer)
+{
+  uint32_t i;                                    /* Loop counter */
+  q15_t *weights = S->pTwiddle;                  /* Pointer to the Weights table */
+  q15_t *cosFact = S->pCosFactor;                /* Pointer to the cos factors table */
+  q15_t *pS1, *pS2, *pbuff;                      /* Temporary pointers for input buffer and pState buffer */
+  q15_t in;                                      /* Temporary variable */
+
+
+  /* DCT4 computation involves DCT2 (which is calculated using RFFT)    
+   * along with some pre-processing and post-processing.    
+   * Computational procedure is explained as follows:    
+   * (a) Pre-processing involves multiplying input with cos factor,    
+   *     r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n))    
+   *              where,    
+   *                 r(n) -- output of preprocessing    
+   *                 u(n) -- input to preprocessing(actual Source buffer)    
+   * (b) Calculation of DCT2 using FFT is divided into three steps:    
+   *                  Step1: Re-ordering of even and odd elements of input.    
+   *                  Step2: Calculating FFT of the re-ordered input.    
+   *                  Step3: Taking the real part of the product of FFT output and weights.    
+   * (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation:    
+   *                   Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)    
+   *                        where,    
+   *                           Y4 -- DCT4 output,   Y2 -- DCT2 output    
+   * (d) Multiplying the output with the normalizing factor sqrt(2/N).    
+   */
+
+        /*-------- Pre-processing ------------*/
+  /* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */
+  arm_mult_q15(pInlineBuffer, cosFact, pInlineBuffer, S->N);
+  arm_shift_q15(pInlineBuffer, 1, pInlineBuffer, S->N);
+
+  /* ----------------------------------------------------------------    
+   * Step1: Re-ordering of even and odd elements as    
+   *             pState[i] =  pInlineBuffer[2*i] and    
+   *             pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2    
+   ---------------------------------------------------------------------*/
+
+  /* pS1 initialized to pState */
+  pS1 = pState;
+
+  /* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */
+  pS2 = pState + (S->N - 1u);
+
+  /* pbuff initialized to input buffer */
+  pbuff = pInlineBuffer;
+
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */
+  i = (uint32_t) S->Nby2 >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  do
+  {
+    /* Re-ordering of even and odd elements */
+    /* pState[i] =  pInlineBuffer[2*i] */
+    *pS1++ = *pbuff++;
+    /* pState[N-i-1] = pInlineBuffer[2*i+1] */
+    *pS2-- = *pbuff++;
+
+    *pS1++ = *pbuff++;
+    *pS2-- = *pbuff++;
+
+    *pS1++ = *pbuff++;
+    *pS2-- = *pbuff++;
+
+    *pS1++ = *pbuff++;
+    *pS2-- = *pbuff++;
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+  /* pbuff initialized to input buffer */
+  pbuff = pInlineBuffer;
+
+  /* pS1 initialized to pState */
+  pS1 = pState;
+
+  /* Initializing the loop counter to N/4 instead of N for loop unrolling */
+  i = (uint32_t) S->N >> 2u;
+
+  /* Processing with loop unrolling 4 times as N is always multiple of 4.    
+   * Compute 4 outputs at a time */
+  do
+  {
+    /* Writing the re-ordered output back to inplace input buffer */
+    *pbuff++ = *pS1++;
+    *pbuff++ = *pS1++;
+    *pbuff++ = *pS1++;
+    *pbuff++ = *pS1++;
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+
+  /* ---------------------------------------------------------    
+   *     Step2: Calculate RFFT for N-point input    
+   * ---------------------------------------------------------- */
+  /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
+  arm_rfft_q15(S->pRfft, pInlineBuffer, pState);
+
+ /*----------------------------------------------------------------------    
+  *  Step3: Multiply the FFT output with the weights.    
+  *----------------------------------------------------------------------*/
+  arm_cmplx_mult_cmplx_q15(pState, weights, pState, S->N);
+
+  /* The output of complex multiplication is in 3.13 format.    
+   * Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.15 format by shifting left by 2 bits. */
+  arm_shift_q15(pState, 2, pState, S->N * 2);
+
+  /* ----------- Post-processing ---------- */
+  /* DCT-IV can be obtained from DCT-II by the equation,    
+   *       Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)    
+   *       Hence, Y4(0) = Y2(0)/2  */
+  /* Getting only real part from the output and Converting to DCT-IV */
+
+  /* Initializing the loop counter to N >> 2 for loop unrolling by 4 */
+  i = ((uint32_t) S->N - 1u) >> 2u;
+
+  /* pbuff initialized to input buffer. */
+  pbuff = pInlineBuffer;
+
+  /* pS1 initialized to pState */
+  pS1 = pState;
+
+  /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
+  in = *pS1++ >> 1u;
+  /* input buffer acts as inplace, so output values are stored in the input itself. */
+  *pbuff++ = in;
+
+  /* pState pointer is incremented twice as the real values are located alternatively in the array */
+  pS1++;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  do
+  {
+    /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
+    /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
+    in = *pS1++ - in;
+    *pbuff++ = in;
+    /* points to the next real value */
+    pS1++;
+
+    in = *pS1++ - in;
+    *pbuff++ = in;
+    pS1++;
+
+    in = *pS1++ - in;
+    *pbuff++ = in;
+    pS1++;
+
+    in = *pS1++ - in;
+    *pbuff++ = in;
+    pS1++;
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  i = ((uint32_t) S->N - 1u) % 0x4u;
+
+  while(i > 0u)
+  {
+    /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
+    /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
+    in = *pS1++ - in;
+    *pbuff++ = in;
+    /* points to the next real value */
+    pS1++;
+
+    /* Decrement the loop counter */
+    i--;
+  }
+
+
+   /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
+
+  /* Initializing the loop counter to N/4 instead of N for loop unrolling */
+  i = (uint32_t) S->N >> 2u;
+
+  /* pbuff initialized to the pInlineBuffer(now contains the output values) */
+  pbuff = pInlineBuffer;
+
+  /* Processing with loop unrolling 4 times as N is always multiple of 4.  Compute 4 outputs at a time */
+  do
+  {
+    /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
+    in = *pbuff;
+    *pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15));
+
+    in = *pbuff;
+    *pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15));
+
+    in = *pbuff;
+    *pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15));
+
+    in = *pbuff;
+    *pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15));
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initializing the loop counter to N/2 */
+  i = (uint32_t) S->Nby2;
+
+  do
+  {
+    /* Re-ordering of even and odd elements */
+    /* pState[i] =  pInlineBuffer[2*i] */
+    *pS1++ = *pbuff++;
+    /* pState[N-i-1] = pInlineBuffer[2*i+1] */
+    *pS2-- = *pbuff++;
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+  /* pbuff initialized to input buffer */
+  pbuff = pInlineBuffer;
+
+  /* pS1 initialized to pState */
+  pS1 = pState;
+
+  /* Initializing the loop counter */
+  i = (uint32_t) S->N;
+
+  do
+  {
+    /* Writing the re-ordered output back to inplace input buffer */
+    *pbuff++ = *pS1++;
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+
+  /* ---------------------------------------------------------    
+   *     Step2: Calculate RFFT for N-point input    
+   * ---------------------------------------------------------- */
+  /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
+  arm_rfft_q15(S->pRfft, pInlineBuffer, pState);
+
+ /*----------------------------------------------------------------------    
+  *  Step3: Multiply the FFT output with the weights.    
+  *----------------------------------------------------------------------*/
+  arm_cmplx_mult_cmplx_q15(pState, weights, pState, S->N);
+
+  /* The output of complex multiplication is in 3.13 format.    
+   * Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.15 format by shifting left by 2 bits. */
+  arm_shift_q15(pState, 2, pState, S->N * 2);
+
+  /* ----------- Post-processing ---------- */
+  /* DCT-IV can be obtained from DCT-II by the equation,    
+   *       Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)    
+   *       Hence, Y4(0) = Y2(0)/2  */
+  /* Getting only real part from the output and Converting to DCT-IV */
+
+  /* Initializing the loop counter */
+  i = ((uint32_t) S->N - 1u);
+
+  /* pbuff initialized to input buffer. */
+  pbuff = pInlineBuffer;
+
+  /* pS1 initialized to pState */
+  pS1 = pState;
+
+  /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
+  in = *pS1++ >> 1u;
+  /* input buffer acts as inplace, so output values are stored in the input itself. */
+  *pbuff++ = in;
+
+  /* pState pointer is incremented twice as the real values are located alternatively in the array */
+  pS1++;
+
+  do
+  {
+    /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
+    /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
+    in = *pS1++ - in;
+    *pbuff++ = in;
+    /* points to the next real value */
+    pS1++;
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+   /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
+
+  /* Initializing the loop counter */
+  i = (uint32_t) S->N;
+
+  /* pbuff initialized to the pInlineBuffer(now contains the output values) */
+  pbuff = pInlineBuffer;
+
+  do
+  {
+    /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
+    in = *pbuff;
+    *pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15));
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+   * @} end of DCT4_IDCT4 group    
+   */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_dct4_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_dct4_q31.c
new file mode 100644
index 0000000000..887cfb385d
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_dct4_q31.c
@@ -0,0 +1,387 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_dct4_q31.c    
+*    
+* Description:	Processing function of DCT4 & IDCT4 Q31.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @addtogroup DCT4_IDCT4    
+ * @{    
+ */
+
+/**    
+ * @brief Processing function for the Q31 DCT4/IDCT4.   
+ * @param[in]       *S             points to an instance of the Q31 DCT4 structure.   
+ * @param[in]       *pState        points to state buffer.   
+ * @param[in,out]   *pInlineBuffer points to the in-place input and output buffer.   
+ * @return none.   
+ * \par Input an output formats:    
+ * Input samples need to be downscaled by 1 bit to avoid saturations in the Q31 DCT process,    
+ * as the conversion from DCT2 to DCT4 involves one subtraction.    
+ * Internally inputs are downscaled in the RFFT process function to avoid overflows.    
+ * Number of bits downscaled, depends on the size of the transform.    
+ * The input and output formats for different DCT sizes and number of bits to upscale are mentioned in the table below:     
+ *    
+ * \image html dct4FormatsQ31Table.gif    
+ */
+
+void arm_dct4_q31(
+  const arm_dct4_instance_q31 * S,
+  q31_t * pState,
+  q31_t * pInlineBuffer)
+{
+  uint16_t i;                                    /* Loop counter */
+  q31_t *weights = S->pTwiddle;                  /* Pointer to the Weights table */
+  q31_t *cosFact = S->pCosFactor;                /* Pointer to the cos factors table */
+  q31_t *pS1, *pS2, *pbuff;                      /* Temporary pointers for input buffer and pState buffer */
+  q31_t in;                                      /* Temporary variable */
+
+
+  /* DCT4 computation involves DCT2 (which is calculated using RFFT)    
+   * along with some pre-processing and post-processing.    
+   * Computational procedure is explained as follows:    
+   * (a) Pre-processing involves multiplying input with cos factor,    
+   *     r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n))    
+   *              where,    
+   *                 r(n) -- output of preprocessing    
+   *                 u(n) -- input to preprocessing(actual Source buffer)    
+   * (b) Calculation of DCT2 using FFT is divided into three steps:    
+   *                  Step1: Re-ordering of even and odd elements of input.    
+   *                  Step2: Calculating FFT of the re-ordered input.    
+   *                  Step3: Taking the real part of the product of FFT output and weights.    
+   * (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation:    
+   *                   Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)    
+   *                        where,    
+   *                           Y4 -- DCT4 output,   Y2 -- DCT2 output    
+   * (d) Multiplying the output with the normalizing factor sqrt(2/N).    
+   */
+
+        /*-------- Pre-processing ------------*/
+  /* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */
+  arm_mult_q31(pInlineBuffer, cosFact, pInlineBuffer, S->N);
+  arm_shift_q31(pInlineBuffer, 1, pInlineBuffer, S->N);
+
+  /* ----------------------------------------------------------------    
+   * Step1: Re-ordering of even and odd elements as    
+   *             pState[i] =  pInlineBuffer[2*i] and    
+   *             pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2    
+   ---------------------------------------------------------------------*/
+
+  /* pS1 initialized to pState */
+  pS1 = pState;
+
+  /* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */
+  pS2 = pState + (S->N - 1u);
+
+  /* pbuff initialized to input buffer */
+  pbuff = pInlineBuffer;
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */
+  i = S->Nby2 >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  do
+  {
+    /* Re-ordering of even and odd elements */
+    /* pState[i] =  pInlineBuffer[2*i] */
+    *pS1++ = *pbuff++;
+    /* pState[N-i-1] = pInlineBuffer[2*i+1] */
+    *pS2-- = *pbuff++;
+
+    *pS1++ = *pbuff++;
+    *pS2-- = *pbuff++;
+
+    *pS1++ = *pbuff++;
+    *pS2-- = *pbuff++;
+
+    *pS1++ = *pbuff++;
+    *pS2-- = *pbuff++;
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+  /* pbuff initialized to input buffer */
+  pbuff = pInlineBuffer;
+
+  /* pS1 initialized to pState */
+  pS1 = pState;
+
+  /* Initializing the loop counter to N/4 instead of N for loop unrolling */
+  i = S->N >> 2u;
+
+  /* Processing with loop unrolling 4 times as N is always multiple of 4.    
+   * Compute 4 outputs at a time */
+  do
+  {
+    /* Writing the re-ordered output back to inplace input buffer */
+    *pbuff++ = *pS1++;
+    *pbuff++ = *pS1++;
+    *pbuff++ = *pS1++;
+    *pbuff++ = *pS1++;
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+
+  /* ---------------------------------------------------------    
+   *     Step2: Calculate RFFT for N-point input    
+   * ---------------------------------------------------------- */
+  /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
+  arm_rfft_q31(S->pRfft, pInlineBuffer, pState);
+
+  /*----------------------------------------------------------------------    
+   *  Step3: Multiply the FFT output with the weights.    
+   *----------------------------------------------------------------------*/
+  arm_cmplx_mult_cmplx_q31(pState, weights, pState, S->N);
+
+  /* The output of complex multiplication is in 3.29 format.    
+   * Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.31 format by shifting left by 2 bits. */
+  arm_shift_q31(pState, 2, pState, S->N * 2);
+
+  /* ----------- Post-processing ---------- */
+  /* DCT-IV can be obtained from DCT-II by the equation,    
+   *       Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)    
+   *       Hence, Y4(0) = Y2(0)/2  */
+  /* Getting only real part from the output and Converting to DCT-IV */
+
+  /* Initializing the loop counter to N >> 2 for loop unrolling by 4 */
+  i = (S->N - 1u) >> 2u;
+
+  /* pbuff initialized to input buffer. */
+  pbuff = pInlineBuffer;
+
+  /* pS1 initialized to pState */
+  pS1 = pState;
+
+  /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
+  in = *pS1++ >> 1u;
+  /* input buffer acts as inplace, so output values are stored in the input itself. */
+  *pbuff++ = in;
+
+  /* pState pointer is incremented twice as the real values are located alternatively in the array */
+  pS1++;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  do
+  {
+    /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
+    /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
+    in = *pS1++ - in;
+    *pbuff++ = in;
+    /* points to the next real value */
+    pS1++;
+
+    in = *pS1++ - in;
+    *pbuff++ = in;
+    pS1++;
+
+    in = *pS1++ - in;
+    *pbuff++ = in;
+    pS1++;
+
+    in = *pS1++ - in;
+    *pbuff++ = in;
+    pS1++;
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  i = (S->N - 1u) % 0x4u;
+
+  while(i > 0u)
+  {
+    /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
+    /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
+    in = *pS1++ - in;
+    *pbuff++ = in;
+    /* points to the next real value */
+    pS1++;
+
+    /* Decrement the loop counter */
+    i--;
+  }
+
+
+        /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
+
+  /* Initializing the loop counter to N/4 instead of N for loop unrolling */
+  i = S->N >> 2u;
+
+  /* pbuff initialized to the pInlineBuffer(now contains the output values) */
+  pbuff = pInlineBuffer;
+
+  /* Processing with loop unrolling 4 times as N is always multiple of 4.  Compute 4 outputs at a time */
+  do
+  {
+    /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
+    in = *pbuff;
+    *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));
+
+    in = *pbuff;
+    *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));
+
+    in = *pbuff;
+    *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));
+
+    in = *pbuff;
+    *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initializing the loop counter to N/2 */
+  i = S->Nby2;
+
+  do
+  {
+    /* Re-ordering of even and odd elements */
+    /* pState[i] =  pInlineBuffer[2*i] */
+    *pS1++ = *pbuff++;
+    /* pState[N-i-1] = pInlineBuffer[2*i+1] */
+    *pS2-- = *pbuff++;
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+  /* pbuff initialized to input buffer */
+  pbuff = pInlineBuffer;
+
+  /* pS1 initialized to pState */
+  pS1 = pState;
+
+  /* Initializing the loop counter */
+  i = S->N;
+
+  do
+  {
+    /* Writing the re-ordered output back to inplace input buffer */
+    *pbuff++ = *pS1++;
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+
+  /* ---------------------------------------------------------    
+   *     Step2: Calculate RFFT for N-point input    
+   * ---------------------------------------------------------- */
+  /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
+  arm_rfft_q31(S->pRfft, pInlineBuffer, pState);
+
+  /*----------------------------------------------------------------------    
+   *  Step3: Multiply the FFT output with the weights.    
+   *----------------------------------------------------------------------*/
+  arm_cmplx_mult_cmplx_q31(pState, weights, pState, S->N);
+
+  /* The output of complex multiplication is in 3.29 format.    
+   * Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.31 format by shifting left by 2 bits. */
+  arm_shift_q31(pState, 2, pState, S->N * 2);
+
+  /* ----------- Post-processing ---------- */
+  /* DCT-IV can be obtained from DCT-II by the equation,    
+   *       Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)    
+   *       Hence, Y4(0) = Y2(0)/2  */
+  /* Getting only real part from the output and Converting to DCT-IV */
+
+  /* pbuff initialized to input buffer. */
+  pbuff = pInlineBuffer;
+
+  /* pS1 initialized to pState */
+  pS1 = pState;
+
+  /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
+  in = *pS1++ >> 1u;
+  /* input buffer acts as inplace, so output values are stored in the input itself. */
+  *pbuff++ = in;
+
+  /* pState pointer is incremented twice as the real values are located alternatively in the array */
+  pS1++;
+
+  /* Initializing the loop counter */
+  i = (S->N - 1u);
+
+  while(i > 0u)
+  {
+    /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
+    /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
+    in = *pS1++ - in;
+    *pbuff++ = in;
+    /* points to the next real value */
+    pS1++;
+
+    /* Decrement the loop counter */
+    i--;
+  }
+
+
+        /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
+
+  /* Initializing the loop counter */
+  i = S->N;
+
+  /* pbuff initialized to the pInlineBuffer(now contains the output values) */
+  pbuff = pInlineBuffer;
+
+  do
+  {
+    /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
+    in = *pbuff;
+    *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+   * @} end of DCT4_IDCT4 group    
+   */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_rfft_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_rfft_f32.c
new file mode 100644
index 0000000000..2043a4e0df
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_rfft_f32.c
@@ -0,0 +1,382 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_rfft_f32.c    
+*    
+* Description:	RFFT & RIFFT Floating point process function    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupTransforms    
+ */
+
+/**    
+ * @defgroup RFFT_RIFFT Real FFT Functions    
+ *    
+ * \par    
+ * Complex FFT/IFFT typically assumes complex input and output. However many applications use real valued data in time domain.     
+ * Real FFT/IFFT efficiently process real valued sequences with the advantage of requirement of low memory and with less complexity.    
+ *    
+ * \par    
+ * This set of functions implements Real Fast Fourier Transforms(RFFT) and Real Inverse Fast Fourier Transform(RIFFT)    
+ * for Q15, Q31, and floating-point data types.      
+ *    
+ *    
+ * \par Algorithm:    
+ *    
+ * Real Fast Fourier Transform:    
+ * \par    
+ * Real FFT of N-point is calculated using CFFT of N/2-point and Split RFFT process as shown below figure.    
+ * \par    
+ * \image html RFFT.gif "Real Fast Fourier Transform"    
+ * \par    
+ * The RFFT functions operate on blocks of input and output data and each call to the function processes    
+ * fftLenR samples through the transform.  pSrc  points to input array containing fftLenR values.    
+ * pDst  points to output array containing 2*fftLenR values. \n   
+ * Input for real FFT is in the order of     
+ * 
{real[0], real[1], real[2], real[3], ..}
    
+ * Output for real FFT is complex and are in the order of    
+ * 
{real(0), imag(0), real(1), imag(1), ...}
     
+ *    
+ * Real Inverse Fast Fourier Transform:    
+ * \par    
+ * Real IFFT of N-point is calculated using Split RIFFT process and CFFT of N/2-point as shown below figure.    
+ * \par    
+ * \image html RIFFT.gif "Real Inverse Fast Fourier Transform"    
+ * \par    
+ * The RIFFT functions operate on blocks of input and output data and each call to the function processes    
+ * 2*fftLenR samples through the transform.  pSrc  points to input array containing 2*fftLenR values.    
+ * pDst  points to output array containing fftLenR values. \n    
+ * Input for real IFFT is complex and are in the order of   
+ * 
{real(0), imag(0), real(1), imag(1), ...}
   
+ *  Output for real IFFT is real and in the order of     
+ * 
{real[0], real[1], real[2], real[3], ..}
   
+ *    
+ * \par Lengths supported by the transform:   
+ * \par    
+ * Real FFT/IFFT supports the lengths [128, 512, 2048], as it internally uses CFFT/CIFFT.    
+ *    
+ * \par Instance Structure    
+ * A separate instance structure must be defined for each Instance but the twiddle factors can be reused.    
+ * There are separate instance structure declarations for each of the 3 supported data types.    
+ *    
+ * \par Initialization Functions    
+ * There is also an associated initialization function for each data type.    
+ * The initialization function performs the following operations:    
+ * - Sets the values of the internal structure fields.    
+ * - Initializes twiddle factor tables.   
+ * - Initializes CFFT data structure fields.     
+ * \par    
+ * Use of the initialization function is optional.    
+ * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.    
+ * To place an instance structure into a const data section, the instance structure must be manually initialized.    
+ * Manually initialize the instance structure as follows:    
+ * 
    
+ *arm_rfft_instance_f32 S = {fftLenReal, fftLenBy2, ifftFlagR, bitReverseFlagR, twidCoefRModifier, pTwiddleAReal, pTwiddleBReal, pCfft};    
+ *arm_rfft_instance_q31 S = {fftLenReal, fftLenBy2, ifftFlagR, bitReverseFlagR, twidCoefRModifier, pTwiddleAReal, pTwiddleBReal, pCfft};    
+ *arm_rfft_instance_q15 S = {fftLenReal, fftLenBy2, ifftFlagR, bitReverseFlagR, twidCoefRModifier, pTwiddleAReal, pTwiddleBReal, pCfft};    
+ * 
    
+ * where fftLenReal length of RFFT/RIFFT; fftLenBy2 length of CFFT/CIFFT.     
+ * ifftFlagR Flag for selection of RFFT or RIFFT(Set ifftFlagR to calculate RIFFT otherwise calculates RFFT);    
+ * bitReverseFlagR Flag for selection of output order(Set bitReverseFlagR to output in normal order otherwise output in bit reversed order);     
+ * twidCoefRModifier modifier for twiddle factor table which supports 128, 512, 2048 RFFT lengths with same table;    
+ * pTwiddleARealpoints to A array of twiddle coefficients; pTwiddleBRealpoints to B array of twiddle coefficients;    
+ * pCfft points to the CFFT Instance structure. The CFFT structure also needs to be initialized, refer to arm_cfft_radix4_f32() for details regarding    
+ * static initialization of cfft structure.    
+ *    
+ * \par Fixed-Point Behavior    
+ * Care must be taken when using the fixed-point versions of the RFFT/RIFFT function.    
+ * Refer to the function specific documentation below for usage guidelines.    
+ */
+
+/*--------------------------------------------------------------------    
+ *		Internal functions prototypes    
+ *--------------------------------------------------------------------*/
+
+void arm_split_rfft_f32(
+  float32_t * pSrc,
+  uint32_t fftLen,
+  float32_t * pATable,
+  float32_t * pBTable,
+  float32_t * pDst,
+  uint32_t modifier);
+void arm_split_rifft_f32(
+  float32_t * pSrc,
+  uint32_t fftLen,
+  float32_t * pATable,
+  float32_t * pBTable,
+  float32_t * pDst,
+  uint32_t modifier);
+
+/**    
+ * @addtogroup RFFT_RIFFT    
+ * @{    
+ */
+
+/**    
+ * @brief Processing function for the floating-point RFFT/RIFFT.   
+ * @param[in]  *S    points to an instance of the floating-point RFFT/RIFFT structure.   
+ * @param[in]  *pSrc points to the input buffer.   
+ * @param[out] *pDst points to the output buffer.   
+ * @return none.   
+ */
+
+void arm_rfft_f32(
+  const arm_rfft_instance_f32 * S,
+  float32_t * pSrc,
+  float32_t * pDst)
+{
+  const arm_cfft_radix4_instance_f32 *S_CFFT = S->pCfft;
+
+
+  /* Calculation of Real IFFT of input */
+  if(S->ifftFlagR == 1u)
+  {
+    /*  Real IFFT core process */
+    arm_split_rifft_f32(pSrc, S->fftLenBy2, S->pTwiddleAReal,
+                        S->pTwiddleBReal, pDst, S->twidCoefRModifier);
+
+
+    /* Complex radix-4 IFFT process */
+    arm_radix4_butterfly_inverse_f32(pDst, S_CFFT->fftLen,
+                                     S_CFFT->pTwiddle,
+                                     S_CFFT->twidCoefModifier,
+                                     S_CFFT->onebyfftLen);
+
+    /* Bit reversal process */
+    if(S->bitReverseFlagR == 1u)
+    {
+      arm_bitreversal_f32(pDst, S_CFFT->fftLen,
+                          S_CFFT->bitRevFactor, S_CFFT->pBitRevTable);
+    }
+  }
+  else
+  {
+
+    /* Calculation of RFFT of input */
+
+    /* Complex radix-4 FFT process */
+    arm_radix4_butterfly_f32(pSrc, S_CFFT->fftLen,
+                             S_CFFT->pTwiddle, S_CFFT->twidCoefModifier);
+
+    /* Bit reversal process */
+    if(S->bitReverseFlagR == 1u)
+    {
+      arm_bitreversal_f32(pSrc, S_CFFT->fftLen,
+                          S_CFFT->bitRevFactor, S_CFFT->pBitRevTable);
+    }
+
+
+    /*  Real FFT core process */
+    arm_split_rfft_f32(pSrc, S->fftLenBy2, S->pTwiddleAReal,
+                       S->pTwiddleBReal, pDst, S->twidCoefRModifier);
+  }
+
+}
+
+/**    
+   * @} end of RFFT_RIFFT group    
+   */
+
+/**    
+ * @brief  Core Real FFT process    
+ * @param[in]   *pSrc 				points to the input buffer.    
+ * @param[in]   fftLen  			length of FFT.    
+ * @param[in]   *pATable 			points to the twiddle Coef A buffer.    
+ * @param[in]   *pBTable 			points to the twiddle Coef B buffer.    
+ * @param[out]  *pDst 				points to the output buffer.    
+ * @param[in]   modifier 	        twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.   
+ * @return none.    
+ */
+
+void arm_split_rfft_f32(
+  float32_t * pSrc,
+  uint32_t fftLen,
+  float32_t * pATable,
+  float32_t * pBTable,
+  float32_t * pDst,
+  uint32_t modifier)
+{
+  uint32_t i;                                    /* Loop Counter */
+  float32_t outR, outI;                          /* Temporary variables for output */
+  float32_t *pCoefA, *pCoefB;                    /* Temporary pointers for twiddle factors */
+  float32_t CoefA1, CoefA2, CoefB1;              /* Temporary variables for twiddle coefficients */
+  float32_t *pDst1 = &pDst[2], *pDst2 = &pDst[(4u * fftLen) - 1u];      /* temp pointers for output buffer */
+  float32_t *pSrc1 = &pSrc[2], *pSrc2 = &pSrc[(2u * fftLen) - 1u];      /* temp pointers for input buffer */
+
+  /* Init coefficient pointers */
+  pCoefA = &pATable[modifier * 2u];
+  pCoefB = &pBTable[modifier * 2u];
+
+  i = fftLen - 1u;
+
+  while(i > 0u)
+  {
+    /*    
+       outR = (pSrc[2 * i] * pATable[2 * i] - pSrc[2 * i + 1] * pATable[2 * i + 1]    
+       + pSrc[2 * n - 2 * i] * pBTable[2 * i] +    
+       pSrc[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);    
+     */
+
+    /* outI = (pIn[2 * i + 1] * pATable[2 * i] + pIn[2 * i] * pATable[2 * i + 1] +    
+       pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -    
+       pIn[2 * n - 2 * i + 1] * pBTable[2 * i]); */
+
+    /* read pATable[2 * i] */
+    CoefA1 = *pCoefA++;
+    /* pATable[2 * i + 1] */
+    CoefA2 = *pCoefA;
+
+    /* pSrc[2 * i] * pATable[2 * i] */
+    outR = *pSrc1 * CoefA1;
+    /* pSrc[2 * i] * CoefA2 */
+    outI = *pSrc1++ * CoefA2;
+
+    /* (pSrc[2 * i + 1] + pSrc[2 * fftLen - 2 * i + 1]) * CoefA2 */
+    outR -= (*pSrc1 + *pSrc2) * CoefA2;
+    /* pSrc[2 * i + 1] * CoefA1 */
+    outI += *pSrc1++ * CoefA1;
+
+    CoefB1 = *pCoefB;
+
+    /* pSrc[2 * fftLen - 2 * i + 1] * CoefB1 */
+    outI -= *pSrc2-- * CoefB1;
+    /* pSrc[2 * fftLen - 2 * i] * CoefA2 */
+    outI -= *pSrc2 * CoefA2;
+
+    /* pSrc[2 * fftLen - 2 * i] * CoefB1 */
+    outR += *pSrc2-- * CoefB1;
+
+    /* write output */
+    *pDst1++ = outR;
+    *pDst1++ = outI;
+
+    /* write complex conjugate output */
+    *pDst2-- = -outI;
+    *pDst2-- = outR;
+
+    /* update coefficient pointer */
+    pCoefB = pCoefB + (modifier * 2u);
+    pCoefA = pCoefA + ((modifier * 2u) - 1u);
+
+    i--;
+
+  }
+
+  pDst[2u * fftLen] = pSrc[0] - pSrc[1];
+  pDst[(2u * fftLen) + 1u] = 0.0f;
+
+  pDst[0] = pSrc[0] + pSrc[1];
+  pDst[1] = 0.0f;
+
+}
+
+
+/**    
+ * @brief  Core Real IFFT process    
+ * @param[in]   *pSrc 				points to the input buffer.    
+ * @param[in]   fftLen  			length of FFT.   
+ * @param[in]   *pATable 			points to the twiddle Coef A buffer.   
+ * @param[in]   *pBTable 			points to the twiddle Coef B buffer.   
+ * @param[out]  *pDst 				points to the output buffer.   
+ * @param[in]   modifier 	        twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.    
+ * @return none.    
+ */
+
+void arm_split_rifft_f32(
+  float32_t * pSrc,
+  uint32_t fftLen,
+  float32_t * pATable,
+  float32_t * pBTable,
+  float32_t * pDst,
+  uint32_t modifier)
+{
+  float32_t outR, outI;                          /* Temporary variables for output */
+  float32_t *pCoefA, *pCoefB;                    /* Temporary pointers for twiddle factors */
+  float32_t CoefA1, CoefA2, CoefB1;              /* Temporary variables for twiddle coefficients */
+  float32_t *pSrc1 = &pSrc[0], *pSrc2 = &pSrc[(2u * fftLen) + 1u];
+
+  pCoefA = &pATable[0];
+  pCoefB = &pBTable[0];
+
+  while(fftLen > 0u)
+  {
+    /*    
+       outR = (pIn[2 * i] * pATable[2 * i] + pIn[2 * i + 1] * pATable[2 * i + 1] +    
+       pIn[2 * n - 2 * i] * pBTable[2 * i] -    
+       pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);    
+
+       outI = (pIn[2 * i + 1] * pATable[2 * i] - pIn[2 * i] * pATable[2 * i + 1] -    
+       pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -    
+       pIn[2 * n - 2 * i + 1] * pBTable[2 * i]);    
+
+     */
+
+    CoefA1 = *pCoefA++;
+    CoefA2 = *pCoefA;
+
+    /* outR = (pSrc[2 * i] * CoefA1 */
+    outR = *pSrc1 * CoefA1;
+
+    /* - pSrc[2 * i] * CoefA2 */
+    outI = -(*pSrc1++) * CoefA2;
+
+    /* (pSrc[2 * i + 1] + pSrc[2 * fftLen - 2 * i + 1]) * CoefA2 */
+    outR += (*pSrc1 + *pSrc2) * CoefA2;
+
+    /* pSrc[2 * i + 1] * CoefA1 */
+    outI += (*pSrc1++) * CoefA1;
+
+    CoefB1 = *pCoefB;
+
+    /* - pSrc[2 * fftLen - 2 * i + 1] * CoefB1 */
+    outI -= *pSrc2-- * CoefB1;
+
+    /* pSrc[2 * fftLen - 2 * i] * CoefB1 */
+    outR += *pSrc2 * CoefB1;
+
+    /* pSrc[2 * fftLen - 2 * i] * CoefA2 */
+    outI += *pSrc2-- * CoefA2;
+
+    /* write output */
+    *pDst++ = outR;
+    *pDst++ = outI;
+
+    /* update coefficient pointer */
+    pCoefB = pCoefB + (modifier * 2u);
+    pCoefA = pCoefA + ((modifier * 2u) - 1u);
+
+    /* Decrement loop count */
+    fftLen--;
+  }
+
+}
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_rfft_init_f32.c b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_rfft_init_f32.c
new file mode 100644
index 0000000000..7a54df6e21
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_rfft_init_f32.c
@@ -0,0 +1,8369 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_rfft_init_f32.c    
+*    
+* Description:	RFFT & RIFFT Floating point initialisation function    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupTransforms    
+ */
+
+/**    
+ * @addtogroup RFFT_RIFFT    
+ * @{    
+ */
+
+/**    
+* \par    
+* Generation of realCoefA array:    
+* \par    
+* 	n = 4096    
+* 
for (i = 0; i < n; i++)    
+*  {    
+*    pATable[2 * i] = 0.5 * (1.0 - sin (2 * PI / (double) (2 * n) * (double) i));    
+*    pATable[2 * i + 1] = 0.5 * (-1.0 * cos (2 * PI / (double) (2 * n) * (double) i));    
+*  } 
    
+*/
+
+
+
+static const float32_t realCoefA[8192] = {
+  0.500000000000000f, -0.500000000000000f, 0.499616503715515f,
+    -0.499999850988388f,
+  0.499233007431030f, -0.499999403953552f, 0.498849511146545f,
+    -0.499998688697815f,
+  0.498466014862061f, -0.499997645616531f, 0.498082518577576f,
+    -0.499996334314346f,
+  0.497699022293091f, -0.499994695186615f, 0.497315555810928f,
+    -0.499992787837982f,
+  0.496932059526443f, -0.499990582466125f, 0.496548563241959f,
+    -0.499988079071045f,
+  0.496165096759796f, -0.499985307455063f, 0.495781600475311f,
+    -0.499982208013535f,
+  0.495398133993149f, -0.499978810548782f, 0.495014637708664f,
+    -0.499975144863129f,
+  0.494631171226501f, -0.499971181154251f, 0.494247704744339f,
+    -0.499966919422150f,
+  0.493864238262177f, -0.499962359666824f, 0.493480771780014f,
+    -0.499957501888275f,
+  0.493097305297852f, -0.499952346086502f, 0.492713838815689f,
+    -0.499946922063828f,
+  0.492330402135849f, -0.499941170215607f, 0.491946935653687f,
+    -0.499935150146484f,
+  0.491563498973846f, -0.499928832054138f, 0.491180062294006f,
+    -0.499922215938568f,
+  0.490796625614166f, -0.499915301799774f, 0.490413218736649f,
+    -0.499908089637756f,
+  0.490029782056808f, -0.499900579452515f, 0.489646375179291f,
+    -0.499892801046371f,
+  0.489262968301773f, -0.499884694814682f, 0.488879561424255f,
+    -0.499876320362091f,
+  0.488496154546738f, -0.499867647886276f, 0.488112777471542f,
+    -0.499858677387238f,
+  0.487729400396347f, -0.499849408864975f, 0.487346023321152f,
+    -0.499839842319489f,
+  0.486962646245956f, -0.499830007553101f, 0.486579269170761f,
+    -0.499819844961166f,
+  0.486195921897888f, -0.499809414148331f, 0.485812574625015f,
+    -0.499798685312271f,
+  0.485429257154465f, -0.499787658452988f, 0.485045909881592f,
+    -0.499776333570480f,
+  0.484662592411041f, -0.499764710664749f, 0.484279274940491f,
+    -0.499752789735794f,
+  0.483895987272263f, -0.499740600585938f, 0.483512699604034f,
+    -0.499728083610535f,
+  0.483129411935806f, -0.499715298414230f, 0.482746154069901f,
+    -0.499702215194702f,
+  0.482362866401672f, -0.499688833951950f, 0.481979638338089f,
+    -0.499675154685974f,
+  0.481596380472183f, -0.499661177396774f, 0.481213152408600f,
+    -0.499646931886673f,
+  0.480829954147339f, -0.499632388353348f, 0.480446726083755f,
+    -0.499617516994476f,
+  0.480063527822495f, -0.499602377414703f, 0.479680359363556f,
+    -0.499586939811707f,
+  0.479297190904617f, -0.499571204185486f, 0.478914022445679f,
+    -0.499555170536041f,
+  0.478530883789063f, -0.499538868665695f, 0.478147745132446f,
+    -0.499522238969803f,
+  0.477764606475830f, -0.499505341053009f, 0.477381497621536f,
+    -0.499488145112991f,
+  0.476998418569565f, -0.499470651149750f, 0.476615339517593f,
+    -0.499452859163284f,
+  0.476232260465622f, -0.499434769153595f, 0.475849211215973f,
+    -0.499416410923004f,
+  0.475466161966324f, -0.499397724866867f, 0.475083142518997f,
+    -0.499378770589828f,
+  0.474700123071671f, -0.499359518289566f, 0.474317133426666f,
+    -0.499339967966080f,
+  0.473934143781662f, -0.499320119619370f, 0.473551183938980f,
+    -0.499299973249435f,
+  0.473168224096298f, -0.499279528856277f, 0.472785294055939f,
+    -0.499258816242218f,
+  0.472402364015579f, -0.499237775802612f, 0.472019463777542f,
+    -0.499216467142105f,
+  0.471636593341827f, -0.499194860458374f, 0.471253722906113f,
+    -0.499172955751419f,
+  0.470870882272720f, -0.499150782823563f, 0.470488041639328f,
+    -0.499128282070160f,
+  0.470105201005936f, -0.499105513095856f, 0.469722419977188f,
+    -0.499082416296005f,
+  0.469339638948441f, -0.499059051275253f, 0.468956857919693f,
+    -0.499035388231277f,
+  0.468574106693268f, -0.499011427164078f, 0.468191385269165f,
+    -0.498987197875977f,
+  0.467808693647385f, -0.498962640762329f, 0.467426002025604f,
+    -0.498937815427780f,
+  0.467043310403824f, -0.498912662267685f, 0.466660678386688f,
+    -0.498887240886688f,
+  0.466278046369553f, -0.498861521482468f, 0.465895414352417f,
+    -0.498835533857346f,
+  0.465512841939926f, -0.498809218406677f, 0.465130269527435f,
+    -0.498782604932785f,
+  0.464747726917267f, -0.498755723237991f, 0.464365184307098f,
+    -0.498728543519974f,
+  0.463982671499252f, -0.498701065778732f, 0.463600188493729f,
+    -0.498673290014267f,
+  0.463217705488205f, -0.498645216226578f, 0.462835282087326f,
+    -0.498616874217987f,
+  0.462452858686447f, -0.498588204383850f, 0.462070435285568f,
+    -0.498559266328812f,
+  0.461688071489334f, -0.498530030250549f, 0.461305707693100f,
+    -0.498500496149063f,
+  0.460923373699188f, -0.498470664024353f, 0.460541069507599f,
+    -0.498440563678741f,
+  0.460158795118332f, -0.498410135507584f, 0.459776520729065f,
+    -0.498379439115524f,
+  0.459394276142120f, -0.498348444700241f, 0.459012061357498f,
+    -0.498317152261734f,
+  0.458629876375198f, -0.498285561800003f, 0.458247691392899f,
+    -0.498253703117371f,
+  0.457865566015244f, -0.498221516609192f, 0.457483440637589f,
+    -0.498189061880112f,
+  0.457101345062256f, -0.498156309127808f, 0.456719279289246f,
+    -0.498123258352280f,
+  0.456337243318558f, -0.498089909553528f, 0.455955207347870f,
+    -0.498056292533875f,
+  0.455573230981827f, -0.498022347688675f, 0.455191254615784f,
+    -0.497988134622574f,
+  0.454809308052063f, -0.497953623533249f, 0.454427421092987f,
+    -0.497918814420700f,
+  0.454045534133911f, -0.497883707284927f, 0.453663676977158f,
+    -0.497848302125931f,
+  0.453281819820404f, -0.497812628746033f, 0.452900022268295f,
+    -0.497776657342911f,
+  0.452518254518509f, -0.497740387916565f, 0.452136516571045f,
+    -0.497703820466995f,
+  0.451754778623581f, -0.497666954994202f, 0.451373100280762f,
+    -0.497629791498184f,
+  0.450991421937943f, -0.497592359781265f, 0.450609803199768f,
+    -0.497554630041122f,
+  0.450228184461594f, -0.497516602277756f, 0.449846625328064f,
+    -0.497478276491165f,
+  0.449465066194534f, -0.497439652681351f, 0.449083566665649f,
+    -0.497400760650635f,
+  0.448702067136765f, -0.497361570596695f, 0.448320597410202f,
+    -0.497322082519531f,
+  0.447939187288284f, -0.497282296419144f, 0.447557777166367f,
+    -0.497242212295532f,
+  0.447176426649094f, -0.497201830148697f, 0.446795076131821f,
+    -0.497161179780960f,
+  0.446413785219193f, -0.497120231389999f, 0.446032524108887f,
+    -0.497078984975815f,
+  0.445651292800903f, -0.497037440538406f, 0.445270061492920f,
+    -0.496995598077774f,
+  0.444888889789581f, -0.496953487396240f, 0.444507747888565f,
+    -0.496911078691483f,
+  0.444126635789871f, -0.496868371963501f, 0.443745553493500f,
+    -0.496825367212296f,
+  0.443364530801773f, -0.496782064437866f, 0.442983508110046f,
+    -0.496738493442535f,
+  0.442602545022964f, -0.496694594621658f, 0.442221581935883f,
+    -0.496650427579880f,
+  0.441840678453445f, -0.496605962514877f, 0.441459804773331f,
+    -0.496561229228973f,
+  0.441078960895538f, -0.496516168117523f, 0.440698176622391f,
+    -0.496470838785172f,
+  0.440317392349243f, -0.496425211429596f, 0.439936667680740f,
+    -0.496379286050797f,
+  0.439555943012238f, -0.496333062648773f, 0.439175277948380f,
+    -0.496286571025848f,
+  0.438794672489166f, -0.496239781379700f, 0.438414067029953f,
+    -0.496192663908005f,
+  0.438033521175385f, -0.496145308017731f, 0.437653005123138f,
+    -0.496097624301910f,
+  0.437272518873215f, -0.496049642562866f, 0.436892062425613f,
+    -0.496001392602921f,
+  0.436511665582657f, -0.495952844619751f, 0.436131268739700f,
+    -0.495903998613358f,
+  0.435750931501389f, -0.495854884386063f, 0.435370653867722f,
+    -0.495805442333221f,
+  0.434990376234055f, -0.495755732059479f, 0.434610158205032f,
+    -0.495705723762512f,
+  0.434229999780655f, -0.495655417442322f, 0.433849841356277f,
+    -0.495604842901230f,
+  0.433469742536545f, -0.495553970336914f, 0.433089673519135f,
+    -0.495502769947052f,
+  0.432709634304047f, -0.495451331138611f, 0.432329654693604f,
+    -0.495399564504623f,
+  0.431949704885483f, -0.495347499847412f, 0.431569814682007f,
+    -0.495295166969299f,
+  0.431189924478531f, -0.495242536067963f, 0.430810123682022f,
+    -0.495189607143402f,
+  0.430430322885513f, -0.495136409997940f, 0.430050581693649f,
+    -0.495082914829254f,
+  0.429670870304108f, -0.495029091835022f, 0.429291218519211f,
+    -0.494975030422211f,
+  0.428911596536636f, -0.494920641183853f, 0.428532034158707f,
+    -0.494865983724594f,
+  0.428152471780777f, -0.494810998439789f, 0.427772998809814f,
+    -0.494755744934082f,
+  0.427393525838852f, -0.494700223207474f, 0.427014142274857f,
+    -0.494644373655319f,
+  0.426634758710861f, -0.494588255882263f, 0.426255434751511f,
+    -0.494531840085983f,
+  0.425876170396805f, -0.494475126266479f, 0.425496935844421f,
+    -0.494418144226074f,
+  0.425117731094360f, -0.494360834360123f, 0.424738585948944f,
+    -0.494303256273270f,
+  0.424359470605850f, -0.494245409965515f, 0.423980414867401f,
+    -0.494187235832214f,
+  0.423601418733597f, -0.494128793478012f, 0.423222452402115f,
+    -0.494070053100586f,
+  0.422843515872955f, -0.494011014699936f, 0.422464638948441f,
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+  0.494631171226501f, 0.499971181154251f, 0.495014637708664f,
+    0.499975144863129f,
+  0.495398133993149f, 0.499978810548782f, 0.495781600475311f,
+    0.499982208013535f,
+  0.496165096759796f, 0.499985307455063f, 0.496548563241959f,
+    0.499988079071045f,
+  0.496932059526443f, 0.499990582466125f, 0.497315555810928f,
+    0.499992787837982f,
+  0.497699022293091f, 0.499994695186615f, 0.498082518577576f,
+    0.499996334314346f,
+  0.498466014862061f, 0.499997645616531f, 0.498849511146545f,
+    0.499998688697815f,
+  0.499233007431030f, 0.499999403953552f, 0.499616503715515f,
+    0.499999850988388f,
+};
+
+
+/**    
+* \par   
+* Generation of realCoefB array:    
+* \par   
+* n = 4096    
+* 
for (i = 0; i < n; i++)    
+* {    
+*    pBTable[2 * i] = 0.5 * (1.0 + sin (2 * PI / (double) (2 * n) * (double) i));    
+*    pBTable[2 * i + 1] = 0.5 * (1.0 * cos (2 * PI / (double) (2 * n) * (double) i));    
+*  } 
    
+*    
+*/
+static const float32_t realCoefB[8192] = {
+  0.500000000000000f, 0.500000000000000f, 0.500383496284485f,
+    0.499999850988388f,
+  0.500766992568970f, 0.499999403953552f, 0.501150488853455f,
+    0.499998688697815f,
+  0.501533985137939f, 0.499997645616531f, 0.501917481422424f,
+    0.499996334314346f,
+  0.502300977706909f, 0.499994695186615f, 0.502684473991394f,
+    0.499992787837982f,
+  0.503067970275879f, 0.499990582466125f, 0.503451406955719f,
+    0.499988079071045f,
+  0.503834903240204f, 0.499985307455063f, 0.504218399524689f,
+    0.499982208013535f,
+  0.504601895809174f, 0.499978810548782f, 0.504985332489014f,
+    0.499975144863129f,
+  0.505368828773499f, 0.499971181154251f, 0.505752325057983f,
+    0.499966919422150f,
+  0.506135761737823f, 0.499962359666824f, 0.506519258022308f,
+    0.499957501888275f,
+  0.506902694702148f, 0.499952346086502f, 0.507286131381989f,
+    0.499946922063828f,
+  0.507669627666473f, 0.499941170215607f, 0.508053064346313f,
+    0.499935150146484f,
+  0.508436501026154f, 0.499928832054138f, 0.508819937705994f,
+    0.499922215938568f,
+  0.509203374385834f, 0.499915301799774f, 0.509586811065674f,
+    0.499908089637756f,
+  0.509970188140869f, 0.499900579452515f, 0.510353624820709f,
+    0.499892801046371f,
+  0.510737061500549f, 0.499884694814682f, 0.511120438575745f,
+    0.499876320362091f,
+  0.511503815650940f, 0.499867647886276f, 0.511887252330780f,
+    0.499858677387238f,
+  0.512270629405975f, 0.499849408864975f, 0.512654006481171f,
+    0.499839842319489f,
+  0.513037383556366f, 0.499830007553101f, 0.513420701026917f,
+    0.499819844961166f,
+  0.513804078102112f, 0.499809414148331f, 0.514187395572662f,
+    0.499798685312271f,
+  0.514570772647858f, 0.499787658452988f, 0.514954090118408f,
+    0.499776333570480f,
+  0.515337407588959f, 0.499764710664749f, 0.515720725059509f,
+    0.499752789735794f,
+  0.516103982925415f, 0.499740600585938f, 0.516487300395966f,
+    0.499728083610535f,
+  0.516870558261871f, 0.499715298414230f, 0.517253875732422f,
+    0.499702215194702f,
+  0.517637133598328f, 0.499688833951950f, 0.518020391464233f,
+    0.499675154685974f,
+  0.518403589725494f, 0.499661177396774f, 0.518786847591400f,
+    0.499646931886673f,
+  0.519170045852661f, 0.499632388353348f, 0.519553244113922f,
+    0.499617516994476f,
+  0.519936442375183f, 0.499602377414703f, 0.520319640636444f,
+    0.499586939811707f,
+  0.520702838897705f, 0.499571204185486f, 0.521085977554321f,
+    0.499555170536041f,
+  0.521469116210938f, 0.499538868665695f, 0.521852254867554f,
+    0.499522238969803f,
+  0.522235393524170f, 0.499505341053009f, 0.522618472576141f,
+    0.499488145112991f,
+  0.523001611232758f, 0.499470651149750f, 0.523384690284729f,
+    0.499452859163284f,
+  0.523767769336700f, 0.499434769153595f, 0.524150788784027f,
+    0.499416410923004f,
+  0.524533808231354f, 0.499397724866867f, 0.524916887283325f,
+    0.499378770589828f,
+  0.525299847126007f, 0.499359518289566f, 0.525682866573334f,
+    0.499339967966080f,
+  0.526065826416016f, 0.499320119619370f, 0.526448845863342f,
+    0.499299973249435f,
+  0.526831746101379f, 0.499279528856277f, 0.527214705944061f,
+    0.499258816242218f,
+  0.527597606182098f, 0.499237775802612f, 0.527980506420136f,
+    0.499216467142105f,
+  0.528363406658173f, 0.499194860458374f, 0.528746306896210f,
+    0.499172955751419f,
+  0.529129147529602f, 0.499150782823563f, 0.529511988162994f,
+    0.499128282070160f,
+  0.529894769191742f, 0.499105513095856f, 0.530277609825134f,
+    0.499082416296005f,
+  0.530660390853882f, 0.499059051275253f, 0.531043112277985f,
+    0.499035388231277f,
+  0.531425893306732f, 0.499011427164078f, 0.531808614730835f,
+    0.498987197875977f,
+  0.532191336154938f, 0.498962640762329f, 0.532573997974396f,
+    0.498937815427780f,
+  0.532956659793854f, 0.498912662267685f, 0.533339321613312f,
+    0.498887240886688f,
+  0.533721983432770f, 0.498861521482468f, 0.534104585647583f,
+    0.498835533857346f,
+  0.534487187862396f, 0.498809218406677f, 0.534869730472565f,
+    0.498782604932785f,
+  0.535252273082733f, 0.498755723237991f, 0.535634815692902f,
+    0.498728543519974f,
+  0.536017298698425f, 0.498701065778732f, 0.536399841308594f,
+    0.498673290014267f,
+  0.536782264709473f, 0.498645216226578f, 0.537164747714996f,
+    0.498616874217987f,
+  0.537547171115875f, 0.498588204383850f, 0.537929534912109f,
+    0.498559266328812f,
+  0.538311958312988f, 0.498530030250549f, 0.538694262504578f,
+    0.498500496149063f,
+  0.539076626300812f, 0.498470664024353f, 0.539458930492401f,
+    0.498440563678741f,
+  0.539841234683990f, 0.498410135507584f, 0.540223479270935f,
+    0.498379439115524f,
+  0.540605723857880f, 0.498348444700241f, 0.540987968444824f,
+    0.498317152261734f,
+  0.541370153427124f, 0.498285561800003f, 0.541752278804779f,
+    0.498253703117371f,
+  0.542134463787079f, 0.498221516609192f, 0.542516589164734f,
+    0.498189061880112f,
+  0.542898654937744f, 0.498156309127808f, 0.543280720710754f,
+    0.498123258352280f,
+  0.543662786483765f, 0.498089909553528f, 0.544044792652130f,
+    0.498056292533875f,
+  0.544426798820496f, 0.498022347688675f, 0.544808745384216f,
+    0.497988134622574f,
+  0.545190691947937f, 0.497953623533249f, 0.545572578907013f,
+    0.497918814420700f,
+  0.545954465866089f, 0.497883707284927f, 0.546336352825165f,
+    0.497848302125931f,
+  0.546718180179596f, 0.497812628746033f, 0.547099947929382f,
+    0.497776657342911f,
+  0.547481775283813f, 0.497740387916565f, 0.547863483428955f,
+    0.497703820466995f,
+  0.548245191574097f, 0.497666954994202f, 0.548626899719238f,
+    0.497629791498184f,
+  0.549008548259735f, 0.497592359781265f, 0.549390196800232f,
+    0.497554630041122f,
+  0.549771785736084f, 0.497516602277756f, 0.550153374671936f,
+    0.497478276491165f,
+  0.550534904003143f, 0.497439652681351f, 0.550916433334351f,
+    0.497400760650635f,
+  0.551297962665558f, 0.497361570596695f, 0.551679372787476f,
+    0.497322082519531f,
+  0.552060842514038f, 0.497282296419144f, 0.552442193031311f,
+    0.497242212295532f,
+  0.552823603153229f, 0.497201830148697f, 0.553204894065857f,
+    0.497161179780960f,
+  0.553586184978485f, 0.497120231389999f, 0.553967475891113f,
+    0.497078984975815f,
+  0.554348707199097f, 0.497037440538406f, 0.554729938507080f,
+    0.496995598077774f,
+  0.555111110210419f, 0.496953487396240f, 0.555492222309113f,
+    0.496911078691483f,
+  0.555873334407806f, 0.496868371963501f, 0.556254446506500f,
+    0.496825367212296f,
+  0.556635499000549f, 0.496782064437866f, 0.557016491889954f,
+    0.496738493442535f,
+  0.557397484779358f, 0.496694594621658f, 0.557778418064117f,
+    0.496650427579880f,
+  0.558159291744232f, 0.496605962514877f, 0.558540165424347f,
+    0.496561229228973f,
+  0.558921039104462f, 0.496516168117523f, 0.559301853179932f,
+    0.496470838785172f,
+  0.559682607650757f, 0.496425211429596f, 0.560063362121582f,
+    0.496379286050797f,
+  0.560444056987762f, 0.496333062648773f, 0.560824692249298f,
+    0.496286571025848f,
+  0.561205327510834f, 0.496239781379700f, 0.561585903167725f,
+    0.496192663908005f,
+  0.561966478824615f, 0.496145308017731f, 0.562346994876862f,
+    0.496097624301910f,
+  0.562727510929108f, 0.496049642562866f, 0.563107967376709f,
+    0.496001392602921f,
+  0.563488364219666f, 0.495952844619751f, 0.563868701457977f,
+    0.495903998613358f,
+  0.564249038696289f, 0.495854884386063f, 0.564629375934601f,
+    0.495805442333221f,
+  0.565009593963623f, 0.495755732059479f, 0.565389811992645f,
+    0.495705723762512f,
+  0.565770030021667f, 0.495655417442322f, 0.566150128841400f,
+    0.495604842901230f,
+  0.566530287265778f, 0.495553970336914f, 0.566910326480865f,
+    0.495502769947052f,
+  0.567290365695953f, 0.495451331138611f, 0.567670345306396f,
+    0.495399564504623f,
+  0.568050265312195f, 0.495347499847412f, 0.568430185317993f,
+    0.495295166969299f,
+  0.568810045719147f, 0.495242536067963f, 0.569189906120300f,
+    0.495189607143402f,
+  0.569569647312164f, 0.495136409997940f, 0.569949388504028f,
+    0.495082914829254f,
+  0.570329129695892f, 0.495029091835022f, 0.570708811283112f,
+    0.494975030422211f,
+  0.571088373661041f, 0.494920641183853f, 0.571467995643616f,
+    0.494865983724594f,
+  0.571847498416901f, 0.494810998439789f, 0.572227001190186f,
+    0.494755744934082f,
+  0.572606444358826f, 0.494700223207474f, 0.572985887527466f,
+    0.494644373655319f,
+  0.573365211486816f, 0.494588255882263f, 0.573744535446167f,
+    0.494531840085983f,
+  0.574123859405518f, 0.494475126266479f, 0.574503064155579f,
+    0.494418144226074f,
+  0.574882268905640f, 0.494360834360123f, 0.575261414051056f,
+    0.494303256273270f,
+  0.575640499591827f, 0.494245409965515f, 0.576019585132599f,
+    0.494187235832214f,
+  0.576398611068726f, 0.494128793478012f, 0.576777577400208f,
+    0.494070053100586f,
+  0.577156484127045f, 0.494011014699936f, 0.577535390853882f,
+    0.493951678276062f,
+  0.577914178371429f, 0.493892073631287f, 0.578292965888977f,
+    0.493832170963287f,
+  0.578671753406525f, 0.493771970272064f, 0.579050421714783f,
+    0.493711471557617f,
+  0.579429090023041f, 0.493650704622269f, 0.579807698726654f,
+    0.493589639663696f,
+  0.580186247825623f, 0.493528276681900f, 0.580564737319946f,
+    0.493466645479202f,
+  0.580943167209625f, 0.493404686450958f, 0.581321597099304f,
+    0.493342459201813f,
+  0.581699967384338f, 0.493279963731766f, 0.582078278064728f,
+    0.493217140436172f,
+  0.582456588745117f, 0.493154048919678f, 0.582834780216217f,
+    0.493090659379959f,
+  0.583212971687317f, 0.493026971817017f, 0.583591103553772f,
+    0.492963016033173f,
+  0.583969175815582f, 0.492898762226105f, 0.584347188472748f,
+    0.492834210395813f,
+  0.584725141525269f, 0.492769360542297f, 0.585103094577789f,
+    0.492704242467880f,
+  0.585480928421021f, 0.492638826370239f, 0.585858762264252f,
+    0.492573112249374f,
+  0.586236536502838f, 0.492507129907608f, 0.586614251136780f,
+    0.492440819740295f,
+  0.586991965770721f, 0.492374241352081f, 0.587369561195374f,
+    0.492307394742966f,
+  0.587747097015381f, 0.492240220308304f, 0.588124632835388f,
+    0.492172777652740f,
+  0.588502109050751f, 0.492105036973953f, 0.588879525661469f,
+    0.492037028074265f,
+  0.589256882667542f, 0.491968721151352f, 0.589634180068970f,
+    0.491900116205215f,
+  0.590011477470398f, 0.491831213235855f, 0.590388655662537f,
+    0.491762012243271f,
+  0.590765833854675f, 0.491692543029785f, 0.591142892837524f,
+    0.491622805595398f,
+  0.591519951820374f, 0.491552740335464f, 0.591896951198578f,
+    0.491482406854630f,
+  0.592273890972137f, 0.491411775350571f, 0.592650771141052f,
+    0.491340845823288f,
+  0.593027591705322f, 0.491269648075104f, 0.593404352664948f,
+    0.491198152303696f,
+  0.593781054019928f, 0.491126358509064f, 0.594157755374908f,
+    0.491054296493530f,
+  0.594534337520599f, 0.490981936454773f, 0.594910860061646f,
+    0.490909278392792f,
+  0.595287382602692f, 0.490836352109909f, 0.595663845539093f,
+    0.490763127803802f,
+  0.596040189266205f, 0.490689605474472f, 0.596416532993317f,
+    0.490615785121918f,
+  0.596792817115784f, 0.490541696548462f, 0.597168982028961f,
+    0.490467309951782f,
+  0.597545146942139f, 0.490392625331879f, 0.597921252250671f,
+    0.490317672491074f,
+  0.598297297954559f, 0.490242421627045f, 0.598673284053802f,
+    0.490166902542114f,
+  0.599049210548401f, 0.490091055631638f, 0.599425077438354f,
+    0.490014940500259f,
+  0.599800884723663f, 0.489938557147980f, 0.600176632404327f,
+    0.489861875772476f,
+  0.600552320480347f, 0.489784896373749f, 0.600927948951721f,
+    0.489707618951797f,
+  0.601303517818451f, 0.489630073308945f, 0.601679027080536f,
+    0.489552229642868f,
+  0.602054476737976f, 0.489474087953568f, 0.602429866790771f,
+    0.489395678043365f,
+  0.602805197238922f, 0.489316970109940f, 0.603180468082428f,
+    0.489237964153290f,
+  0.603555679321289f, 0.489158689975739f, 0.603930830955505f,
+    0.489079117774963f,
+  0.604305922985077f, 0.488999247550964f, 0.604680955410004f,
+    0.488919109106064f,
+  0.605055928230286f, 0.488838672637939f, 0.605430841445923f,
+    0.488757967948914f,
+  0.605805635452271f, 0.488676935434341f, 0.606180429458618f,
+    0.488595664501190f,
+  0.606555163860321f, 0.488514065742493f, 0.606929838657379f,
+    0.488432198762894f,
+  0.607304394245148f, 0.488350033760071f, 0.607678949832916f,
+    0.488267600536346f,
+  0.608053386211395f, 0.488184869289398f, 0.608427822589874f,
+    0.488101840019226f,
+  0.608802139759064f, 0.488018542528152f, 0.609176397323608f,
+    0.487934947013855f,
+  0.609550595283508f, 0.487851053476334f, 0.609924793243408f,
+    0.487766891717911f,
+  0.610298871994019f, 0.487682431936264f, 0.610672831535339f,
+    0.487597703933716f,
+  0.611046791076660f, 0.487512677907944f, 0.611420691013336f,
+    0.487427353858948f,
+  0.611794531345367f, 0.487341761589050f, 0.612168252468109f,
+    0.487255871295929f,
+  0.612541973590851f, 0.487169682979584f, 0.612915575504303f,
+    0.487083226442337f,
+  0.613289117813110f, 0.486996471881866f, 0.613662600517273f,
+    0.486909449100494f,
+  0.614036023616791f, 0.486822128295898f, 0.614409387111664f,
+    0.486734509468079f,
+  0.614782691001892f, 0.486646622419357f, 0.615155875682831f,
+    0.486558437347412f,
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+    -0.499999850988388f,
+};
+
+
+
+/**    
+* @brief  Initialization function for the floating-point RFFT/RIFFT.   
+* @param[in,out] *S             points to an instance of the floating-point RFFT/RIFFT structure.   
+* @param[in,out] *S_CFFT        points to an instance of the floating-point CFFT/CIFFT structure.   
+* @param[in]     fftLenReal     length of the FFT.   
+* @param[in]     ifftFlagR      flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform.   
+* @param[in]     bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.   
+* @return		The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if fftLenReal is not a supported value.   
+*    
+* \par Description:   
+* \par   
+* The parameter fftLenReal	Specifies length of RFFT/RIFFT Process. Supported FFT Lengths are 128, 512, 2048.    
+* \par    
+* The parameter ifftFlagR controls whether a forward or inverse transform is computed.    
+* Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated.    
+* \par    
+* The parameter bitReverseFlag controls whether output is in normal order or bit reversed order.    
+* Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order.   
+* \par    
+* This function also initializes Twiddle factor table.     
+*/
+
+arm_status arm_rfft_init_f32(
+  arm_rfft_instance_f32 * S,
+  arm_cfft_radix4_instance_f32 * S_CFFT,
+  uint32_t fftLenReal,
+  uint32_t ifftFlagR,
+  uint32_t bitReverseFlag)
+{
+
+  /*  Initialise the default arm status */
+  arm_status status = ARM_MATH_SUCCESS;
+
+  /*  Initialize the Real FFT length */
+  S->fftLenReal = (uint16_t) fftLenReal;
+
+  /*  Initialize the Complex FFT length */
+  S->fftLenBy2 = (uint16_t) fftLenReal / 2u;
+
+  /*  Initialize the Twiddle coefficientA pointer */
+  S->pTwiddleAReal = (float32_t *) realCoefA;
+
+  /*  Initialize the Twiddle coefficientB pointer */
+  S->pTwiddleBReal = (float32_t *) realCoefB;
+
+  /*  Initialize the Flag for selection of RFFT or RIFFT */
+  S->ifftFlagR = (uint8_t) ifftFlagR;
+
+  /*  Initialize the Flag for calculation Bit reversal or not */
+  S->bitReverseFlagR = (uint8_t) bitReverseFlag;
+
+  /*  Initializations of structure parameters depending on the FFT length */
+  switch (S->fftLenReal)
+  {
+    /* Init table modifier value */
+  case 8192u:
+    S->twidCoefRModifier = 1u;
+    break;
+  case 2048u:
+    S->twidCoefRModifier = 4u;
+    break;
+  case 512u:
+    S->twidCoefRModifier = 16u;
+    break;
+  case 128u:
+    S->twidCoefRModifier = 64u;
+    break;
+  default:
+    /*  Reporting argument error if rfftSize is not valid value */
+    status = ARM_MATH_ARGUMENT_ERROR;
+    break;
+  }
+
+  /* Init Complex FFT Instance */
+  S->pCfft = S_CFFT;
+
+  if(S->ifftFlagR)
+  {
+    /* Initializes the CIFFT Module for fftLenreal/2 length */
+    arm_cfft_radix4_init_f32(S->pCfft, S->fftLenBy2, 1u, 0u);
+  }
+  else
+  {
+    /* Initializes the CFFT Module for fftLenreal/2 length */
+    arm_cfft_radix4_init_f32(S->pCfft, S->fftLenBy2, 0u, 0u);
+  }
+
+  /* return the status of RFFT Init function */
+  return (status);
+
+}
+
+  /**    
+   * @} end of RFFT_RIFFT group    
+   */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_rfft_init_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_rfft_init_q15.c
new file mode 100644
index 0000000000..50b9d994d0
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_rfft_init_q15.c
@@ -0,0 +1,2229 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_rfft_init_q15.c    
+*    
+* Description:	RFFT & RIFFT Q15 initialisation function    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupTransforms    
+ */
+
+/**    
+ * @addtogroup RFFT_RIFFT    
+ * @{    
+ */
+
+
+
+/**    
+* \par    
+* Generation floating point real_CoefA array:    
+* \par    
+* n = 4096    
+* 
for (i = 0; i < n; i++)    
+*  {    
+*    pATable[2 * i] = 0.5 * (1.0 - sin (2 * PI / (double) (2 * n) * (double) i));    
+*    pATable[2 * i + 1] = 0.5 * (-1.0 * cos (2 * PI / (double) (2 * n) * (double) i));    
+*  } 
    
+* \par    
+* Convert to fixed point Q15 format    
+*       round(pATable[i] * pow(2, 15))    
+*/
+
+
+static const q15_t ALIGN4 realCoefAQ15[8192] = {
+  0x4000, 0xc000, 0x3ff3, 0xc000, 0x3fe7, 0xc000, 0x3fda, 0xc000,
+  0x3fce, 0xc000, 0x3fc1, 0xc000, 0x3fb5, 0xc000, 0x3fa8, 0xc000,
+  0x3f9b, 0xc000, 0x3f8f, 0xc000, 0x3f82, 0xc000, 0x3f76, 0xc001,
+  0x3f69, 0xc001, 0x3f5d, 0xc001, 0x3f50, 0xc001, 0x3f44, 0xc001,
+  0x3f37, 0xc001, 0x3f2a, 0xc001, 0x3f1e, 0xc002, 0x3f11, 0xc002,
+  0x3f05, 0xc002, 0x3ef8, 0xc002, 0x3eec, 0xc002, 0x3edf, 0xc003,
+  0x3ed2, 0xc003, 0x3ec6, 0xc003, 0x3eb9, 0xc003, 0x3ead, 0xc004,
+  0x3ea0, 0xc004, 0x3e94, 0xc004, 0x3e87, 0xc004, 0x3e7a, 0xc005,
+  0x3e6e, 0xc005, 0x3e61, 0xc005, 0x3e55, 0xc006, 0x3e48, 0xc006,
+  0x3e3c, 0xc006, 0x3e2f, 0xc007, 0x3e23, 0xc007, 0x3e16, 0xc007,
+  0x3e09, 0xc008, 0x3dfd, 0xc008, 0x3df0, 0xc009, 0x3de4, 0xc009,
+  0x3dd7, 0xc009, 0x3dcb, 0xc00a, 0x3dbe, 0xc00a, 0x3db2, 0xc00b,
+  0x3da5, 0xc00b, 0x3d98, 0xc00c, 0x3d8c, 0xc00c, 0x3d7f, 0xc00d,
+  0x3d73, 0xc00d, 0x3d66, 0xc00e, 0x3d5a, 0xc00e, 0x3d4d, 0xc00f,
+  0x3d40, 0xc00f, 0x3d34, 0xc010, 0x3d27, 0xc010, 0x3d1b, 0xc011,
+  0x3d0e, 0xc011, 0x3d02, 0xc012, 0x3cf5, 0xc013, 0x3ce9, 0xc013,
+  0x3cdc, 0xc014, 0x3cd0, 0xc014, 0x3cc3, 0xc015, 0x3cb6, 0xc016,
+  0x3caa, 0xc016, 0x3c9d, 0xc017, 0x3c91, 0xc018, 0x3c84, 0xc018,
+  0x3c78, 0xc019, 0x3c6b, 0xc01a, 0x3c5f, 0xc01a, 0x3c52, 0xc01b,
+  0x3c45, 0xc01c, 0x3c39, 0xc01d, 0x3c2c, 0xc01d, 0x3c20, 0xc01e,
+  0x3c13, 0xc01f, 0x3c07, 0xc020, 0x3bfa, 0xc020, 0x3bee, 0xc021,
+  0x3be1, 0xc022, 0x3bd5, 0xc023, 0x3bc8, 0xc024, 0x3bbc, 0xc024,
+  0x3baf, 0xc025, 0x3ba2, 0xc026, 0x3b96, 0xc027, 0x3b89, 0xc028,
+  0x3b7d, 0xc029, 0x3b70, 0xc02a, 0x3b64, 0xc02b, 0x3b57, 0xc02b,
+  0x3b4b, 0xc02c, 0x3b3e, 0xc02d, 0x3b32, 0xc02e, 0x3b25, 0xc02f,
+  0x3b19, 0xc030, 0x3b0c, 0xc031, 0x3b00, 0xc032, 0x3af3, 0xc033,
+  0x3ae6, 0xc034, 0x3ada, 0xc035, 0x3acd, 0xc036, 0x3ac1, 0xc037,
+  0x3ab4, 0xc038, 0x3aa8, 0xc039, 0x3a9b, 0xc03a, 0x3a8f, 0xc03b,
+  0x3a82, 0xc03c, 0x3a76, 0xc03d, 0x3a69, 0xc03f, 0x3a5d, 0xc040,
+  0x3a50, 0xc041, 0x3a44, 0xc042, 0x3a37, 0xc043, 0x3a2b, 0xc044,
+  0x3a1e, 0xc045, 0x3a12, 0xc047, 0x3a05, 0xc048, 0x39f9, 0xc049,
+  0x39ec, 0xc04a, 0x39e0, 0xc04b, 0x39d3, 0xc04c, 0x39c7, 0xc04e,
+  0x39ba, 0xc04f, 0x39ae, 0xc050, 0x39a1, 0xc051, 0x3995, 0xc053,
+  0x3988, 0xc054, 0x397c, 0xc055, 0x396f, 0xc056, 0x3963, 0xc058,
+  0x3956, 0xc059, 0x394a, 0xc05a, 0x393d, 0xc05c, 0x3931, 0xc05d,
+  0x3924, 0xc05e, 0x3918, 0xc060, 0x390b, 0xc061, 0x38ff, 0xc062,
+  0x38f2, 0xc064, 0x38e6, 0xc065, 0x38d9, 0xc067, 0x38cd, 0xc068,
+  0x38c0, 0xc069, 0x38b4, 0xc06b, 0x38a7, 0xc06c, 0x389b, 0xc06e,
+  0x388e, 0xc06f, 0x3882, 0xc071, 0x3875, 0xc072, 0x3869, 0xc074,
+  0x385c, 0xc075, 0x3850, 0xc077, 0x3843, 0xc078, 0x3837, 0xc07a,
+  0x382a, 0xc07b, 0x381e, 0xc07d, 0x3811, 0xc07e, 0x3805, 0xc080,
+  0x37f9, 0xc081, 0x37ec, 0xc083, 0x37e0, 0xc085, 0x37d3, 0xc086,
+  0x37c7, 0xc088, 0x37ba, 0xc089, 0x37ae, 0xc08b, 0x37a1, 0xc08d,
+  0x3795, 0xc08e, 0x3788, 0xc090, 0x377c, 0xc092, 0x376f, 0xc093,
+  0x3763, 0xc095, 0x3757, 0xc097, 0x374a, 0xc098, 0x373e, 0xc09a,
+  0x3731, 0xc09c, 0x3725, 0xc09e, 0x3718, 0xc09f, 0x370c, 0xc0a1,
+  0x36ff, 0xc0a3, 0x36f3, 0xc0a5, 0x36e7, 0xc0a6, 0x36da, 0xc0a8,
+  0x36ce, 0xc0aa, 0x36c1, 0xc0ac, 0x36b5, 0xc0ae, 0x36a8, 0xc0af,
+  0x369c, 0xc0b1, 0x3690, 0xc0b3, 0x3683, 0xc0b5, 0x3677, 0xc0b7,
+  0x366a, 0xc0b9, 0x365e, 0xc0bb, 0x3651, 0xc0bd, 0x3645, 0xc0be,
+  0x3639, 0xc0c0, 0x362c, 0xc0c2, 0x3620, 0xc0c4, 0x3613, 0xc0c6,
+  0x3607, 0xc0c8, 0x35fa, 0xc0ca, 0x35ee, 0xc0cc, 0x35e2, 0xc0ce,
+  0x35d5, 0xc0d0, 0x35c9, 0xc0d2, 0x35bc, 0xc0d4, 0x35b0, 0xc0d6,
+  0x35a4, 0xc0d8, 0x3597, 0xc0da, 0x358b, 0xc0dc, 0x357e, 0xc0de,
+  0x3572, 0xc0e0, 0x3566, 0xc0e2, 0x3559, 0xc0e4, 0x354d, 0xc0e7,
+  0x3540, 0xc0e9, 0x3534, 0xc0eb, 0x3528, 0xc0ed, 0x351b, 0xc0ef,
+  0x350f, 0xc0f1, 0x3503, 0xc0f3, 0x34f6, 0xc0f6, 0x34ea, 0xc0f8,
+  0x34dd, 0xc0fa, 0x34d1, 0xc0fc, 0x34c5, 0xc0fe, 0x34b8, 0xc100,
+  0x34ac, 0xc103, 0x34a0, 0xc105, 0x3493, 0xc107, 0x3487, 0xc109,
+  0x347b, 0xc10c, 0x346e, 0xc10e, 0x3462, 0xc110, 0x3455, 0xc113,
+  0x3449, 0xc115, 0x343d, 0xc117, 0x3430, 0xc119, 0x3424, 0xc11c,
+  0x3418, 0xc11e, 0x340b, 0xc120, 0x33ff, 0xc123, 0x33f3, 0xc125,
+  0x33e6, 0xc128, 0x33da, 0xc12a, 0x33ce, 0xc12c, 0x33c1, 0xc12f,
+  0x33b5, 0xc131, 0x33a9, 0xc134, 0x339c, 0xc136, 0x3390, 0xc138,
+  0x3384, 0xc13b, 0x3377, 0xc13d, 0x336b, 0xc140, 0x335f, 0xc142,
+  0x3352, 0xc145, 0x3346, 0xc147, 0x333a, 0xc14a, 0x332d, 0xc14c,
+  0x3321, 0xc14f, 0x3315, 0xc151, 0x3308, 0xc154, 0x32fc, 0xc156,
+  0x32f0, 0xc159, 0x32e4, 0xc15b, 0x32d7, 0xc15e, 0x32cb, 0xc161,
+  0x32bf, 0xc163, 0x32b2, 0xc166, 0x32a6, 0xc168, 0x329a, 0xc16b,
+  0x328e, 0xc16e, 0x3281, 0xc170, 0x3275, 0xc173, 0x3269, 0xc176,
+  0x325c, 0xc178, 0x3250, 0xc17b, 0x3244, 0xc17e, 0x3238, 0xc180,
+  0x322b, 0xc183, 0x321f, 0xc186, 0x3213, 0xc189, 0x3207, 0xc18b,
+  0x31fa, 0xc18e, 0x31ee, 0xc191, 0x31e2, 0xc194, 0x31d5, 0xc196,
+  0x31c9, 0xc199, 0x31bd, 0xc19c, 0x31b1, 0xc19f, 0x31a4, 0xc1a2,
+  0x3198, 0xc1a4, 0x318c, 0xc1a7, 0x3180, 0xc1aa, 0x3174, 0xc1ad,
+  0x3167, 0xc1b0, 0x315b, 0xc1b3, 0x314f, 0xc1b6, 0x3143, 0xc1b8,
+  0x3136, 0xc1bb, 0x312a, 0xc1be, 0x311e, 0xc1c1, 0x3112, 0xc1c4,
+  0x3105, 0xc1c7, 0x30f9, 0xc1ca, 0x30ed, 0xc1cd, 0x30e1, 0xc1d0,
+  0x30d5, 0xc1d3, 0x30c8, 0xc1d6, 0x30bc, 0xc1d9, 0x30b0, 0xc1dc,
+  0x30a4, 0xc1df, 0x3098, 0xc1e2, 0x308b, 0xc1e5, 0x307f, 0xc1e8,
+  0x3073, 0xc1eb, 0x3067, 0xc1ee, 0x305b, 0xc1f1, 0x304e, 0xc1f4,
+  0x3042, 0xc1f7, 0x3036, 0xc1fa, 0x302a, 0xc1fd, 0x301e, 0xc201,
+  0x3012, 0xc204, 0x3005, 0xc207, 0x2ff9, 0xc20a, 0x2fed, 0xc20d,
+  0x2fe1, 0xc210, 0x2fd5, 0xc213, 0x2fc9, 0xc217, 0x2fbc, 0xc21a,
+  0x2fb0, 0xc21d, 0x2fa4, 0xc220, 0x2f98, 0xc223, 0x2f8c, 0xc227,
+  0x2f80, 0xc22a, 0x2f74, 0xc22d, 0x2f67, 0xc230, 0x2f5b, 0xc234,
+  0x2f4f, 0xc237, 0x2f43, 0xc23a, 0x2f37, 0xc23e, 0x2f2b, 0xc241,
+  0x2f1f, 0xc244, 0x2f13, 0xc247, 0x2f06, 0xc24b, 0x2efa, 0xc24e,
+  0x2eee, 0xc251, 0x2ee2, 0xc255, 0x2ed6, 0xc258, 0x2eca, 0xc25c,
+  0x2ebe, 0xc25f, 0x2eb2, 0xc262, 0x2ea6, 0xc266, 0x2e99, 0xc269,
+  0x2e8d, 0xc26d, 0x2e81, 0xc270, 0x2e75, 0xc273, 0x2e69, 0xc277,
+  0x2e5d, 0xc27a, 0x2e51, 0xc27e, 0x2e45, 0xc281, 0x2e39, 0xc285,
+  0x2e2d, 0xc288, 0x2e21, 0xc28c, 0x2e15, 0xc28f, 0x2e09, 0xc293,
+  0x2dfc, 0xc296, 0x2df0, 0xc29a, 0x2de4, 0xc29d, 0x2dd8, 0xc2a1,
+  0x2dcc, 0xc2a5, 0x2dc0, 0xc2a8, 0x2db4, 0xc2ac, 0x2da8, 0xc2af,
+  0x2d9c, 0xc2b3, 0x2d90, 0xc2b7, 0x2d84, 0xc2ba, 0x2d78, 0xc2be,
+  0x2d6c, 0xc2c1, 0x2d60, 0xc2c5, 0x2d54, 0xc2c9, 0x2d48, 0xc2cc,
+  0x2d3c, 0xc2d0, 0x2d30, 0xc2d4, 0x2d24, 0xc2d8, 0x2d18, 0xc2db,
+  0x2d0c, 0xc2df, 0x2d00, 0xc2e3, 0x2cf4, 0xc2e6, 0x2ce8, 0xc2ea,
+  0x2cdc, 0xc2ee, 0x2cd0, 0xc2f2, 0x2cc4, 0xc2f5, 0x2cb8, 0xc2f9,
+  0x2cac, 0xc2fd, 0x2ca0, 0xc301, 0x2c94, 0xc305, 0x2c88, 0xc308,
+  0x2c7c, 0xc30c, 0x2c70, 0xc310, 0x2c64, 0xc314, 0x2c58, 0xc318,
+  0x2c4c, 0xc31c, 0x2c40, 0xc320, 0x2c34, 0xc323, 0x2c28, 0xc327,
+  0x2c1c, 0xc32b, 0x2c10, 0xc32f, 0x2c05, 0xc333, 0x2bf9, 0xc337,
+  0x2bed, 0xc33b, 0x2be1, 0xc33f, 0x2bd5, 0xc343, 0x2bc9, 0xc347,
+  0x2bbd, 0xc34b, 0x2bb1, 0xc34f, 0x2ba5, 0xc353, 0x2b99, 0xc357,
+  0x2b8d, 0xc35b, 0x2b81, 0xc35f, 0x2b75, 0xc363, 0x2b6a, 0xc367,
+  0x2b5e, 0xc36b, 0x2b52, 0xc36f, 0x2b46, 0xc373, 0x2b3a, 0xc377,
+  0x2b2e, 0xc37b, 0x2b22, 0xc37f, 0x2b16, 0xc383, 0x2b0a, 0xc387,
+  0x2aff, 0xc38c, 0x2af3, 0xc390, 0x2ae7, 0xc394, 0x2adb, 0xc398,
+  0x2acf, 0xc39c, 0x2ac3, 0xc3a0, 0x2ab7, 0xc3a5, 0x2aac, 0xc3a9,
+  0x2aa0, 0xc3ad, 0x2a94, 0xc3b1, 0x2a88, 0xc3b5, 0x2a7c, 0xc3ba,
+  0x2a70, 0xc3be, 0x2a65, 0xc3c2, 0x2a59, 0xc3c6, 0x2a4d, 0xc3ca,
+  0x2a41, 0xc3cf, 0x2a35, 0xc3d3, 0x2a29, 0xc3d7, 0x2a1e, 0xc3dc,
+  0x2a12, 0xc3e0, 0x2a06, 0xc3e4, 0x29fa, 0xc3e9, 0x29ee, 0xc3ed,
+  0x29e3, 0xc3f1, 0x29d7, 0xc3f6, 0x29cb, 0xc3fa, 0x29bf, 0xc3fe,
+  0x29b4, 0xc403, 0x29a8, 0xc407, 0x299c, 0xc40b, 0x2990, 0xc410,
+  0x2984, 0xc414, 0x2979, 0xc419, 0x296d, 0xc41d, 0x2961, 0xc422,
+  0x2955, 0xc426, 0x294a, 0xc42a, 0x293e, 0xc42f, 0x2932, 0xc433,
+  0x2926, 0xc438, 0x291b, 0xc43c, 0x290f, 0xc441, 0x2903, 0xc445,
+  0x28f7, 0xc44a, 0x28ec, 0xc44e, 0x28e0, 0xc453, 0x28d4, 0xc457,
+  0x28c9, 0xc45c, 0x28bd, 0xc461, 0x28b1, 0xc465, 0x28a5, 0xc46a,
+  0x289a, 0xc46e, 0x288e, 0xc473, 0x2882, 0xc478, 0x2877, 0xc47c,
+  0x286b, 0xc481, 0x285f, 0xc485, 0x2854, 0xc48a, 0x2848, 0xc48f,
+  0x283c, 0xc493, 0x2831, 0xc498, 0x2825, 0xc49d, 0x2819, 0xc4a1,
+  0x280e, 0xc4a6, 0x2802, 0xc4ab, 0x27f6, 0xc4b0, 0x27eb, 0xc4b4,
+  0x27df, 0xc4b9, 0x27d3, 0xc4be, 0x27c8, 0xc4c2, 0x27bc, 0xc4c7,
+  0x27b1, 0xc4cc, 0x27a5, 0xc4d1, 0x2799, 0xc4d6, 0x278e, 0xc4da,
+  0x2782, 0xc4df, 0x2777, 0xc4e4, 0x276b, 0xc4e9, 0x275f, 0xc4ee,
+  0x2754, 0xc4f2, 0x2748, 0xc4f7, 0x273d, 0xc4fc, 0x2731, 0xc501,
+  0x2725, 0xc506, 0x271a, 0xc50b, 0x270e, 0xc510, 0x2703, 0xc515,
+  0x26f7, 0xc51a, 0x26ec, 0xc51e, 0x26e0, 0xc523, 0x26d4, 0xc528,
+  0x26c9, 0xc52d, 0x26bd, 0xc532, 0x26b2, 0xc537, 0x26a6, 0xc53c,
+  0x269b, 0xc541, 0x268f, 0xc546, 0x2684, 0xc54b, 0x2678, 0xc550,
+  0x266d, 0xc555, 0x2661, 0xc55a, 0x2656, 0xc55f, 0x264a, 0xc564,
+  0x263f, 0xc569, 0x2633, 0xc56e, 0x2628, 0xc573, 0x261c, 0xc578,
+  0x2611, 0xc57e, 0x2605, 0xc583, 0x25fa, 0xc588, 0x25ee, 0xc58d,
+  0x25e3, 0xc592, 0x25d7, 0xc597, 0x25cc, 0xc59c, 0x25c0, 0xc5a1,
+  0x25b5, 0xc5a7, 0x25a9, 0xc5ac, 0x259e, 0xc5b1, 0x2592, 0xc5b6,
+  0x2587, 0xc5bb, 0x257c, 0xc5c1, 0x2570, 0xc5c6, 0x2565, 0xc5cb,
+  0x2559, 0xc5d0, 0x254e, 0xc5d5, 0x2542, 0xc5db, 0x2537, 0xc5e0,
+  0x252c, 0xc5e5, 0x2520, 0xc5ea, 0x2515, 0xc5f0, 0x2509, 0xc5f5,
+  0x24fe, 0xc5fa, 0x24f3, 0xc600, 0x24e7, 0xc605, 0x24dc, 0xc60a,
+  0x24d0, 0xc610, 0x24c5, 0xc615, 0x24ba, 0xc61a, 0x24ae, 0xc620,
+  0x24a3, 0xc625, 0x2498, 0xc62a, 0x248c, 0xc630, 0x2481, 0xc635,
+  0x2476, 0xc63b, 0x246a, 0xc640, 0x245f, 0xc645, 0x2454, 0xc64b,
+  0x2448, 0xc650, 0x243d, 0xc656, 0x2432, 0xc65b, 0x2426, 0xc661,
+  0x241b, 0xc666, 0x2410, 0xc66c, 0x2404, 0xc671, 0x23f9, 0xc677,
+  0x23ee, 0xc67c, 0x23e2, 0xc682, 0x23d7, 0xc687, 0x23cc, 0xc68d,
+  0x23c1, 0xc692, 0x23b5, 0xc698, 0x23aa, 0xc69d, 0x239f, 0xc6a3,
+  0x2394, 0xc6a8, 0x2388, 0xc6ae, 0x237d, 0xc6b4, 0x2372, 0xc6b9,
+  0x2367, 0xc6bf, 0x235b, 0xc6c5, 0x2350, 0xc6ca, 0x2345, 0xc6d0,
+  0x233a, 0xc6d5, 0x232e, 0xc6db, 0x2323, 0xc6e1, 0x2318, 0xc6e6,
+  0x230d, 0xc6ec, 0x2301, 0xc6f2, 0x22f6, 0xc6f7, 0x22eb, 0xc6fd,
+  0x22e0, 0xc703, 0x22d5, 0xc709, 0x22ca, 0xc70e, 0x22be, 0xc714,
+  0x22b3, 0xc71a, 0x22a8, 0xc720, 0x229d, 0xc725, 0x2292, 0xc72b,
+  0x2287, 0xc731, 0x227b, 0xc737, 0x2270, 0xc73d, 0x2265, 0xc742,
+  0x225a, 0xc748, 0x224f, 0xc74e, 0x2244, 0xc754, 0x2239, 0xc75a,
+  0x222d, 0xc75f, 0x2222, 0xc765, 0x2217, 0xc76b, 0x220c, 0xc771,
+  0x2201, 0xc777, 0x21f6, 0xc77d, 0x21eb, 0xc783, 0x21e0, 0xc789,
+  0x21d5, 0xc78f, 0x21ca, 0xc795, 0x21be, 0xc79a, 0x21b3, 0xc7a0,
+  0x21a8, 0xc7a6, 0x219d, 0xc7ac, 0x2192, 0xc7b2, 0x2187, 0xc7b8,
+  0x217c, 0xc7be, 0x2171, 0xc7c4, 0x2166, 0xc7ca, 0x215b, 0xc7d0,
+  0x2150, 0xc7d6, 0x2145, 0xc7dc, 0x213a, 0xc7e2, 0x212f, 0xc7e8,
+  0x2124, 0xc7ee, 0x2119, 0xc7f5, 0x210e, 0xc7fb, 0x2103, 0xc801,
+  0x20f8, 0xc807, 0x20ed, 0xc80d, 0x20e2, 0xc813, 0x20d7, 0xc819,
+  0x20cc, 0xc81f, 0x20c1, 0xc825, 0x20b6, 0xc82b, 0x20ab, 0xc832,
+  0x20a0, 0xc838, 0x2095, 0xc83e, 0x208a, 0xc844, 0x207f, 0xc84a,
+  0x2074, 0xc850, 0x2069, 0xc857, 0x205e, 0xc85d, 0x2054, 0xc863,
+  0x2049, 0xc869, 0x203e, 0xc870, 0x2033, 0xc876, 0x2028, 0xc87c,
+  0x201d, 0xc882, 0x2012, 0xc889, 0x2007, 0xc88f, 0x1ffc, 0xc895,
+  0x1ff1, 0xc89b, 0x1fe7, 0xc8a2, 0x1fdc, 0xc8a8, 0x1fd1, 0xc8ae,
+  0x1fc6, 0xc8b5, 0x1fbb, 0xc8bb, 0x1fb0, 0xc8c1, 0x1fa5, 0xc8c8,
+  0x1f9b, 0xc8ce, 0x1f90, 0xc8d4, 0x1f85, 0xc8db, 0x1f7a, 0xc8e1,
+  0x1f6f, 0xc8e8, 0x1f65, 0xc8ee, 0x1f5a, 0xc8f4, 0x1f4f, 0xc8fb,
+  0x1f44, 0xc901, 0x1f39, 0xc908, 0x1f2f, 0xc90e, 0x1f24, 0xc915,
+  0x1f19, 0xc91b, 0x1f0e, 0xc921, 0x1f03, 0xc928, 0x1ef9, 0xc92e,
+  0x1eee, 0xc935, 0x1ee3, 0xc93b, 0x1ed8, 0xc942, 0x1ece, 0xc948,
+  0x1ec3, 0xc94f, 0x1eb8, 0xc955, 0x1ead, 0xc95c, 0x1ea3, 0xc963,
+  0x1e98, 0xc969, 0x1e8d, 0xc970, 0x1e83, 0xc976, 0x1e78, 0xc97d,
+  0x1e6d, 0xc983, 0x1e62, 0xc98a, 0x1e58, 0xc991, 0x1e4d, 0xc997,
+  0x1e42, 0xc99e, 0x1e38, 0xc9a4, 0x1e2d, 0xc9ab, 0x1e22, 0xc9b2,
+  0x1e18, 0xc9b8, 0x1e0d, 0xc9bf, 0x1e02, 0xc9c6, 0x1df8, 0xc9cc,
+  0x1ded, 0xc9d3, 0x1de2, 0xc9da, 0x1dd8, 0xc9e0, 0x1dcd, 0xc9e7,
+  0x1dc3, 0xc9ee, 0x1db8, 0xc9f5, 0x1dad, 0xc9fb, 0x1da3, 0xca02,
+  0x1d98, 0xca09, 0x1d8e, 0xca10, 0x1d83, 0xca16, 0x1d78, 0xca1d,
+  0x1d6e, 0xca24, 0x1d63, 0xca2b, 0x1d59, 0xca32, 0x1d4e, 0xca38,
+  0x1d44, 0xca3f, 0x1d39, 0xca46, 0x1d2e, 0xca4d, 0x1d24, 0xca54,
+  0x1d19, 0xca5b, 0x1d0f, 0xca61, 0x1d04, 0xca68, 0x1cfa, 0xca6f,
+  0x1cef, 0xca76, 0x1ce5, 0xca7d, 0x1cda, 0xca84, 0x1cd0, 0xca8b,
+  0x1cc5, 0xca92, 0x1cbb, 0xca99, 0x1cb0, 0xca9f, 0x1ca6, 0xcaa6,
+  0x1c9b, 0xcaad, 0x1c91, 0xcab4, 0x1c86, 0xcabb, 0x1c7c, 0xcac2,
+  0x1c72, 0xcac9, 0x1c67, 0xcad0, 0x1c5d, 0xcad7, 0x1c52, 0xcade,
+  0x1c48, 0xcae5, 0x1c3d, 0xcaec, 0x1c33, 0xcaf3, 0x1c29, 0xcafa,
+  0x1c1e, 0xcb01, 0x1c14, 0xcb08, 0x1c09, 0xcb0f, 0x1bff, 0xcb16,
+  0x1bf5, 0xcb1e, 0x1bea, 0xcb25, 0x1be0, 0xcb2c, 0x1bd5, 0xcb33,
+  0x1bcb, 0xcb3a, 0x1bc1, 0xcb41, 0x1bb6, 0xcb48, 0x1bac, 0xcb4f,
+  0x1ba2, 0xcb56, 0x1b97, 0xcb5e, 0x1b8d, 0xcb65, 0x1b83, 0xcb6c,
+  0x1b78, 0xcb73, 0x1b6e, 0xcb7a, 0x1b64, 0xcb81, 0x1b59, 0xcb89,
+  0x1b4f, 0xcb90, 0x1b45, 0xcb97, 0x1b3b, 0xcb9e, 0x1b30, 0xcba5,
+  0x1b26, 0xcbad, 0x1b1c, 0xcbb4, 0x1b11, 0xcbbb, 0x1b07, 0xcbc2,
+  0x1afd, 0xcbca, 0x1af3, 0xcbd1, 0x1ae8, 0xcbd8, 0x1ade, 0xcbe0,
+  0x1ad4, 0xcbe7, 0x1aca, 0xcbee, 0x1abf, 0xcbf5, 0x1ab5, 0xcbfd,
+  0x1aab, 0xcc04, 0x1aa1, 0xcc0b, 0x1a97, 0xcc13, 0x1a8c, 0xcc1a,
+  0x1a82, 0xcc21, 0x1a78, 0xcc29, 0x1a6e, 0xcc30, 0x1a64, 0xcc38,
+  0x1a5a, 0xcc3f, 0x1a4f, 0xcc46, 0x1a45, 0xcc4e, 0x1a3b, 0xcc55,
+  0x1a31, 0xcc5d, 0x1a27, 0xcc64, 0x1a1d, 0xcc6b, 0x1a13, 0xcc73,
+  0x1a08, 0xcc7a, 0x19fe, 0xcc82, 0x19f4, 0xcc89, 0x19ea, 0xcc91,
+  0x19e0, 0xcc98, 0x19d6, 0xcca0, 0x19cc, 0xcca7, 0x19c2, 0xccaf,
+  0x19b8, 0xccb6, 0x19ae, 0xccbe, 0x19a4, 0xccc5, 0x199a, 0xcccd,
+  0x198f, 0xccd4, 0x1985, 0xccdc, 0x197b, 0xcce3, 0x1971, 0xcceb,
+  0x1967, 0xccf3, 0x195d, 0xccfa, 0x1953, 0xcd02, 0x1949, 0xcd09,
+  0x193f, 0xcd11, 0x1935, 0xcd19, 0x192b, 0xcd20, 0x1921, 0xcd28,
+  0x1917, 0xcd30, 0x190d, 0xcd37, 0x1903, 0xcd3f, 0x18f9, 0xcd46,
+  0x18ef, 0xcd4e, 0x18e6, 0xcd56, 0x18dc, 0xcd5d, 0x18d2, 0xcd65,
+  0x18c8, 0xcd6d, 0x18be, 0xcd75, 0x18b4, 0xcd7c, 0x18aa, 0xcd84,
+  0x18a0, 0xcd8c, 0x1896, 0xcd93, 0x188c, 0xcd9b, 0x1882, 0xcda3,
+  0x1878, 0xcdab, 0x186f, 0xcdb2, 0x1865, 0xcdba, 0x185b, 0xcdc2,
+  0x1851, 0xcdca, 0x1847, 0xcdd2, 0x183d, 0xcdd9, 0x1833, 0xcde1,
+  0x182a, 0xcde9, 0x1820, 0xcdf1, 0x1816, 0xcdf9, 0x180c, 0xce01,
+  0x1802, 0xce08, 0x17f8, 0xce10, 0x17ef, 0xce18, 0x17e5, 0xce20,
+  0x17db, 0xce28, 0x17d1, 0xce30, 0x17c8, 0xce38, 0x17be, 0xce40,
+  0x17b4, 0xce47, 0x17aa, 0xce4f, 0x17a0, 0xce57, 0x1797, 0xce5f,
+  0x178d, 0xce67, 0x1783, 0xce6f, 0x177a, 0xce77, 0x1770, 0xce7f,
+  0x1766, 0xce87, 0x175c, 0xce8f, 0x1753, 0xce97, 0x1749, 0xce9f,
+  0x173f, 0xcea7, 0x1736, 0xceaf, 0x172c, 0xceb7, 0x1722, 0xcebf,
+  0x1719, 0xcec7, 0x170f, 0xcecf, 0x1705, 0xced7, 0x16fc, 0xcedf,
+  0x16f2, 0xcee7, 0x16e8, 0xceef, 0x16df, 0xcef7, 0x16d5, 0xceff,
+  0x16cb, 0xcf07, 0x16c2, 0xcf10, 0x16b8, 0xcf18, 0x16af, 0xcf20,
+  0x16a5, 0xcf28, 0x169b, 0xcf30, 0x1692, 0xcf38, 0x1688, 0xcf40,
+  0x167f, 0xcf48, 0x1675, 0xcf51, 0x166c, 0xcf59, 0x1662, 0xcf61,
+  0x1659, 0xcf69, 0x164f, 0xcf71, 0x1645, 0xcf79, 0x163c, 0xcf82,
+  0x1632, 0xcf8a, 0x1629, 0xcf92, 0x161f, 0xcf9a, 0x1616, 0xcfa3,
+  0x160c, 0xcfab, 0x1603, 0xcfb3, 0x15f9, 0xcfbb, 0x15f0, 0xcfc4,
+  0x15e6, 0xcfcc, 0x15dd, 0xcfd4, 0x15d4, 0xcfdc, 0x15ca, 0xcfe5,
+  0x15c1, 0xcfed, 0x15b7, 0xcff5, 0x15ae, 0xcffe, 0x15a4, 0xd006,
+  0x159b, 0xd00e, 0x1592, 0xd016, 0x1588, 0xd01f, 0x157f, 0xd027,
+  0x1575, 0xd030, 0x156c, 0xd038, 0x1563, 0xd040, 0x1559, 0xd049,
+  0x1550, 0xd051, 0x1547, 0xd059, 0x153d, 0xd062, 0x1534, 0xd06a,
+  0x152a, 0xd073, 0x1521, 0xd07b, 0x1518, 0xd083, 0x150e, 0xd08c,
+  0x1505, 0xd094, 0x14fc, 0xd09d, 0x14f3, 0xd0a5, 0x14e9, 0xd0ae,
+  0x14e0, 0xd0b6, 0x14d7, 0xd0bf, 0x14cd, 0xd0c7, 0x14c4, 0xd0d0,
+  0x14bb, 0xd0d8, 0x14b2, 0xd0e0, 0x14a8, 0xd0e9, 0x149f, 0xd0f2,
+  0x1496, 0xd0fa, 0x148d, 0xd103, 0x1483, 0xd10b, 0x147a, 0xd114,
+  0x1471, 0xd11c, 0x1468, 0xd125, 0x145f, 0xd12d, 0x1455, 0xd136,
+  0x144c, 0xd13e, 0x1443, 0xd147, 0x143a, 0xd150, 0x1431, 0xd158,
+  0x1428, 0xd161, 0x141e, 0xd169, 0x1415, 0xd172, 0x140c, 0xd17b,
+  0x1403, 0xd183, 0x13fa, 0xd18c, 0x13f1, 0xd195, 0x13e8, 0xd19d,
+  0x13df, 0xd1a6, 0x13d5, 0xd1af, 0x13cc, 0xd1b7, 0x13c3, 0xd1c0,
+  0x13ba, 0xd1c9, 0x13b1, 0xd1d1, 0x13a8, 0xd1da, 0x139f, 0xd1e3,
+  0x1396, 0xd1eb, 0x138d, 0xd1f4, 0x1384, 0xd1fd, 0x137b, 0xd206,
+  0x1372, 0xd20e, 0x1369, 0xd217, 0x1360, 0xd220, 0x1357, 0xd229,
+  0x134e, 0xd231, 0x1345, 0xd23a, 0x133c, 0xd243, 0x1333, 0xd24c,
+  0x132a, 0xd255, 0x1321, 0xd25d, 0x1318, 0xd266, 0x130f, 0xd26f,
+  0x1306, 0xd278, 0x12fd, 0xd281, 0x12f4, 0xd28a, 0x12eb, 0xd292,
+  0x12e2, 0xd29b, 0x12d9, 0xd2a4, 0x12d1, 0xd2ad, 0x12c8, 0xd2b6,
+  0x12bf, 0xd2bf, 0x12b6, 0xd2c8, 0x12ad, 0xd2d1, 0x12a4, 0xd2d9,
+  0x129b, 0xd2e2, 0x1292, 0xd2eb, 0x128a, 0xd2f4, 0x1281, 0xd2fd,
+  0x1278, 0xd306, 0x126f, 0xd30f, 0x1266, 0xd318, 0x125d, 0xd321,
+  0x1255, 0xd32a, 0x124c, 0xd333, 0x1243, 0xd33c, 0x123a, 0xd345,
+  0x1231, 0xd34e, 0x1229, 0xd357, 0x1220, 0xd360, 0x1217, 0xd369,
+  0x120e, 0xd372, 0x1206, 0xd37b, 0x11fd, 0xd384, 0x11f4, 0xd38d,
+  0x11eb, 0xd396, 0x11e3, 0xd39f, 0x11da, 0xd3a8, 0x11d1, 0xd3b1,
+  0x11c9, 0xd3ba, 0x11c0, 0xd3c3, 0x11b7, 0xd3cc, 0x11af, 0xd3d5,
+  0x11a6, 0xd3df, 0x119d, 0xd3e8, 0x1195, 0xd3f1, 0x118c, 0xd3fa,
+  0x1183, 0xd403, 0x117b, 0xd40c, 0x1172, 0xd415, 0x1169, 0xd41e,
+  0x1161, 0xd428, 0x1158, 0xd431, 0x1150, 0xd43a, 0x1147, 0xd443,
+  0x113e, 0xd44c, 0x1136, 0xd455, 0x112d, 0xd45f, 0x1125, 0xd468,
+  0x111c, 0xd471, 0x1114, 0xd47a, 0x110b, 0xd483, 0x1103, 0xd48d,
+  0x10fa, 0xd496, 0x10f2, 0xd49f, 0x10e9, 0xd4a8, 0x10e0, 0xd4b2,
+  0x10d8, 0xd4bb, 0x10d0, 0xd4c4, 0x10c7, 0xd4cd, 0x10bf, 0xd4d7,
+  0x10b6, 0xd4e0, 0x10ae, 0xd4e9, 0x10a5, 0xd4f3, 0x109d, 0xd4fc,
+  0x1094, 0xd505, 0x108c, 0xd50e, 0x1083, 0xd518, 0x107b, 0xd521,
+  0x1073, 0xd52a, 0x106a, 0xd534, 0x1062, 0xd53d, 0x1059, 0xd547,
+  0x1051, 0xd550, 0x1049, 0xd559, 0x1040, 0xd563, 0x1038, 0xd56c,
+  0x1030, 0xd575, 0x1027, 0xd57f, 0x101f, 0xd588, 0x1016, 0xd592,
+  0x100e, 0xd59b, 0x1006, 0xd5a4, 0xffe, 0xd5ae, 0xff5, 0xd5b7,
+  0xfed, 0xd5c1, 0xfe5, 0xd5ca, 0xfdc, 0xd5d4, 0xfd4, 0xd5dd,
+  0xfcc, 0xd5e6, 0xfc4, 0xd5f0, 0xfbb, 0xd5f9, 0xfb3, 0xd603,
+  0xfab, 0xd60c, 0xfa3, 0xd616, 0xf9a, 0xd61f, 0xf92, 0xd629,
+  0xf8a, 0xd632, 0xf82, 0xd63c, 0xf79, 0xd645, 0xf71, 0xd64f,
+  0xf69, 0xd659, 0xf61, 0xd662, 0xf59, 0xd66c, 0xf51, 0xd675,
+  0xf48, 0xd67f, 0xf40, 0xd688, 0xf38, 0xd692, 0xf30, 0xd69b,
+  0xf28, 0xd6a5, 0xf20, 0xd6af, 0xf18, 0xd6b8, 0xf10, 0xd6c2,
+  0xf07, 0xd6cb, 0xeff, 0xd6d5, 0xef7, 0xd6df, 0xeef, 0xd6e8,
+  0xee7, 0xd6f2, 0xedf, 0xd6fc, 0xed7, 0xd705, 0xecf, 0xd70f,
+  0xec7, 0xd719, 0xebf, 0xd722, 0xeb7, 0xd72c, 0xeaf, 0xd736,
+  0xea7, 0xd73f, 0xe9f, 0xd749, 0xe97, 0xd753, 0xe8f, 0xd75c,
+  0xe87, 0xd766, 0xe7f, 0xd770, 0xe77, 0xd77a, 0xe6f, 0xd783,
+  0xe67, 0xd78d, 0xe5f, 0xd797, 0xe57, 0xd7a0, 0xe4f, 0xd7aa,
+  0xe47, 0xd7b4, 0xe40, 0xd7be, 0xe38, 0xd7c8, 0xe30, 0xd7d1,
+  0xe28, 0xd7db, 0xe20, 0xd7e5, 0xe18, 0xd7ef, 0xe10, 0xd7f8,
+  0xe08, 0xd802, 0xe01, 0xd80c, 0xdf9, 0xd816, 0xdf1, 0xd820,
+  0xde9, 0xd82a, 0xde1, 0xd833, 0xdd9, 0xd83d, 0xdd2, 0xd847,
+  0xdca, 0xd851, 0xdc2, 0xd85b, 0xdba, 0xd865, 0xdb2, 0xd86f,
+  0xdab, 0xd878, 0xda3, 0xd882, 0xd9b, 0xd88c, 0xd93, 0xd896,
+  0xd8c, 0xd8a0, 0xd84, 0xd8aa, 0xd7c, 0xd8b4, 0xd75, 0xd8be,
+  0xd6d, 0xd8c8, 0xd65, 0xd8d2, 0xd5d, 0xd8dc, 0xd56, 0xd8e6,
+  0xd4e, 0xd8ef, 0xd46, 0xd8f9, 0xd3f, 0xd903, 0xd37, 0xd90d,
+  0xd30, 0xd917, 0xd28, 0xd921, 0xd20, 0xd92b, 0xd19, 0xd935,
+  0xd11, 0xd93f, 0xd09, 0xd949, 0xd02, 0xd953, 0xcfa, 0xd95d,
+  0xcf3, 0xd967, 0xceb, 0xd971, 0xce3, 0xd97b, 0xcdc, 0xd985,
+  0xcd4, 0xd98f, 0xccd, 0xd99a, 0xcc5, 0xd9a4, 0xcbe, 0xd9ae,
+  0xcb6, 0xd9b8, 0xcaf, 0xd9c2, 0xca7, 0xd9cc, 0xca0, 0xd9d6,
+  0xc98, 0xd9e0, 0xc91, 0xd9ea, 0xc89, 0xd9f4, 0xc82, 0xd9fe,
+  0xc7a, 0xda08, 0xc73, 0xda13, 0xc6b, 0xda1d, 0xc64, 0xda27,
+  0xc5d, 0xda31, 0xc55, 0xda3b, 0xc4e, 0xda45, 0xc46, 0xda4f,
+  0xc3f, 0xda5a, 0xc38, 0xda64, 0xc30, 0xda6e, 0xc29, 0xda78,
+  0xc21, 0xda82, 0xc1a, 0xda8c, 0xc13, 0xda97, 0xc0b, 0xdaa1,
+  0xc04, 0xdaab, 0xbfd, 0xdab5, 0xbf5, 0xdabf, 0xbee, 0xdaca,
+  0xbe7, 0xdad4, 0xbe0, 0xdade, 0xbd8, 0xdae8, 0xbd1, 0xdaf3,
+  0xbca, 0xdafd, 0xbc2, 0xdb07, 0xbbb, 0xdb11, 0xbb4, 0xdb1c,
+  0xbad, 0xdb26, 0xba5, 0xdb30, 0xb9e, 0xdb3b, 0xb97, 0xdb45,
+  0xb90, 0xdb4f, 0xb89, 0xdb59, 0xb81, 0xdb64, 0xb7a, 0xdb6e,
+  0xb73, 0xdb78, 0xb6c, 0xdb83, 0xb65, 0xdb8d, 0xb5e, 0xdb97,
+  0xb56, 0xdba2, 0xb4f, 0xdbac, 0xb48, 0xdbb6, 0xb41, 0xdbc1,
+  0xb3a, 0xdbcb, 0xb33, 0xdbd5, 0xb2c, 0xdbe0, 0xb25, 0xdbea,
+  0xb1e, 0xdbf5, 0xb16, 0xdbff, 0xb0f, 0xdc09, 0xb08, 0xdc14,
+  0xb01, 0xdc1e, 0xafa, 0xdc29, 0xaf3, 0xdc33, 0xaec, 0xdc3d,
+  0xae5, 0xdc48, 0xade, 0xdc52, 0xad7, 0xdc5d, 0xad0, 0xdc67,
+  0xac9, 0xdc72, 0xac2, 0xdc7c, 0xabb, 0xdc86, 0xab4, 0xdc91,
+  0xaad, 0xdc9b, 0xaa6, 0xdca6, 0xa9f, 0xdcb0, 0xa99, 0xdcbb,
+  0xa92, 0xdcc5, 0xa8b, 0xdcd0, 0xa84, 0xdcda, 0xa7d, 0xdce5,
+  0xa76, 0xdcef, 0xa6f, 0xdcfa, 0xa68, 0xdd04, 0xa61, 0xdd0f,
+  0xa5b, 0xdd19, 0xa54, 0xdd24, 0xa4d, 0xdd2e, 0xa46, 0xdd39,
+  0xa3f, 0xdd44, 0xa38, 0xdd4e, 0xa32, 0xdd59, 0xa2b, 0xdd63,
+  0xa24, 0xdd6e, 0xa1d, 0xdd78, 0xa16, 0xdd83, 0xa10, 0xdd8e,
+  0xa09, 0xdd98, 0xa02, 0xdda3, 0x9fb, 0xddad, 0x9f5, 0xddb8,
+  0x9ee, 0xddc3, 0x9e7, 0xddcd, 0x9e0, 0xddd8, 0x9da, 0xdde2,
+  0x9d3, 0xdded, 0x9cc, 0xddf8, 0x9c6, 0xde02, 0x9bf, 0xde0d,
+  0x9b8, 0xde18, 0x9b2, 0xde22, 0x9ab, 0xde2d, 0x9a4, 0xde38,
+  0x99e, 0xde42, 0x997, 0xde4d, 0x991, 0xde58, 0x98a, 0xde62,
+  0x983, 0xde6d, 0x97d, 0xde78, 0x976, 0xde83, 0x970, 0xde8d,
+  0x969, 0xde98, 0x963, 0xdea3, 0x95c, 0xdead, 0x955, 0xdeb8,
+  0x94f, 0xdec3, 0x948, 0xdece, 0x942, 0xded8, 0x93b, 0xdee3,
+  0x935, 0xdeee, 0x92e, 0xdef9, 0x928, 0xdf03, 0x921, 0xdf0e,
+  0x91b, 0xdf19, 0x915, 0xdf24, 0x90e, 0xdf2f, 0x908, 0xdf39,
+  0x901, 0xdf44, 0x8fb, 0xdf4f, 0x8f4, 0xdf5a, 0x8ee, 0xdf65,
+  0x8e8, 0xdf6f, 0x8e1, 0xdf7a, 0x8db, 0xdf85, 0x8d4, 0xdf90,
+  0x8ce, 0xdf9b, 0x8c8, 0xdfa5, 0x8c1, 0xdfb0, 0x8bb, 0xdfbb,
+  0x8b5, 0xdfc6, 0x8ae, 0xdfd1, 0x8a8, 0xdfdc, 0x8a2, 0xdfe7,
+  0x89b, 0xdff1, 0x895, 0xdffc, 0x88f, 0xe007, 0x889, 0xe012,
+  0x882, 0xe01d, 0x87c, 0xe028, 0x876, 0xe033, 0x870, 0xe03e,
+  0x869, 0xe049, 0x863, 0xe054, 0x85d, 0xe05e, 0x857, 0xe069,
+  0x850, 0xe074, 0x84a, 0xe07f, 0x844, 0xe08a, 0x83e, 0xe095,
+  0x838, 0xe0a0, 0x832, 0xe0ab, 0x82b, 0xe0b6, 0x825, 0xe0c1,
+  0x81f, 0xe0cc, 0x819, 0xe0d7, 0x813, 0xe0e2, 0x80d, 0xe0ed,
+  0x807, 0xe0f8, 0x801, 0xe103, 0x7fb, 0xe10e, 0x7f5, 0xe119,
+  0x7ee, 0xe124, 0x7e8, 0xe12f, 0x7e2, 0xe13a, 0x7dc, 0xe145,
+  0x7d6, 0xe150, 0x7d0, 0xe15b, 0x7ca, 0xe166, 0x7c4, 0xe171,
+  0x7be, 0xe17c, 0x7b8, 0xe187, 0x7b2, 0xe192, 0x7ac, 0xe19d,
+  0x7a6, 0xe1a8, 0x7a0, 0xe1b3, 0x79a, 0xe1be, 0x795, 0xe1ca,
+  0x78f, 0xe1d5, 0x789, 0xe1e0, 0x783, 0xe1eb, 0x77d, 0xe1f6,
+  0x777, 0xe201, 0x771, 0xe20c, 0x76b, 0xe217, 0x765, 0xe222,
+  0x75f, 0xe22d, 0x75a, 0xe239, 0x754, 0xe244, 0x74e, 0xe24f,
+  0x748, 0xe25a, 0x742, 0xe265, 0x73d, 0xe270, 0x737, 0xe27b,
+  0x731, 0xe287, 0x72b, 0xe292, 0x725, 0xe29d, 0x720, 0xe2a8,
+  0x71a, 0xe2b3, 0x714, 0xe2be, 0x70e, 0xe2ca, 0x709, 0xe2d5,
+  0x703, 0xe2e0, 0x6fd, 0xe2eb, 0x6f7, 0xe2f6, 0x6f2, 0xe301,
+  0x6ec, 0xe30d, 0x6e6, 0xe318, 0x6e1, 0xe323, 0x6db, 0xe32e,
+  0x6d5, 0xe33a, 0x6d0, 0xe345, 0x6ca, 0xe350, 0x6c5, 0xe35b,
+  0x6bf, 0xe367, 0x6b9, 0xe372, 0x6b4, 0xe37d, 0x6ae, 0xe388,
+  0x6a8, 0xe394, 0x6a3, 0xe39f, 0x69d, 0xe3aa, 0x698, 0xe3b5,
+  0x692, 0xe3c1, 0x68d, 0xe3cc, 0x687, 0xe3d7, 0x682, 0xe3e2,
+  0x67c, 0xe3ee, 0x677, 0xe3f9, 0x671, 0xe404, 0x66c, 0xe410,
+  0x666, 0xe41b, 0x661, 0xe426, 0x65b, 0xe432, 0x656, 0xe43d,
+  0x650, 0xe448, 0x64b, 0xe454, 0x645, 0xe45f, 0x640, 0xe46a,
+  0x63b, 0xe476, 0x635, 0xe481, 0x630, 0xe48c, 0x62a, 0xe498,
+  0x625, 0xe4a3, 0x620, 0xe4ae, 0x61a, 0xe4ba, 0x615, 0xe4c5,
+  0x610, 0xe4d0, 0x60a, 0xe4dc, 0x605, 0xe4e7, 0x600, 0xe4f3,
+  0x5fa, 0xe4fe, 0x5f5, 0xe509, 0x5f0, 0xe515, 0x5ea, 0xe520,
+  0x5e5, 0xe52c, 0x5e0, 0xe537, 0x5db, 0xe542, 0x5d5, 0xe54e,
+  0x5d0, 0xe559, 0x5cb, 0xe565, 0x5c6, 0xe570, 0x5c1, 0xe57c,
+  0x5bb, 0xe587, 0x5b6, 0xe592, 0x5b1, 0xe59e, 0x5ac, 0xe5a9,
+  0x5a7, 0xe5b5, 0x5a1, 0xe5c0, 0x59c, 0xe5cc, 0x597, 0xe5d7,
+  0x592, 0xe5e3, 0x58d, 0xe5ee, 0x588, 0xe5fa, 0x583, 0xe605,
+  0x57e, 0xe611, 0x578, 0xe61c, 0x573, 0xe628, 0x56e, 0xe633,
+  0x569, 0xe63f, 0x564, 0xe64a, 0x55f, 0xe656, 0x55a, 0xe661,
+  0x555, 0xe66d, 0x550, 0xe678, 0x54b, 0xe684, 0x546, 0xe68f,
+  0x541, 0xe69b, 0x53c, 0xe6a6, 0x537, 0xe6b2, 0x532, 0xe6bd,
+  0x52d, 0xe6c9, 0x528, 0xe6d4, 0x523, 0xe6e0, 0x51e, 0xe6ec,
+  0x51a, 0xe6f7, 0x515, 0xe703, 0x510, 0xe70e, 0x50b, 0xe71a,
+  0x506, 0xe725, 0x501, 0xe731, 0x4fc, 0xe73d, 0x4f7, 0xe748,
+  0x4f2, 0xe754, 0x4ee, 0xe75f, 0x4e9, 0xe76b, 0x4e4, 0xe777,
+  0x4df, 0xe782, 0x4da, 0xe78e, 0x4d6, 0xe799, 0x4d1, 0xe7a5,
+  0x4cc, 0xe7b1, 0x4c7, 0xe7bc, 0x4c2, 0xe7c8, 0x4be, 0xe7d3,
+  0x4b9, 0xe7df, 0x4b4, 0xe7eb, 0x4b0, 0xe7f6, 0x4ab, 0xe802,
+  0x4a6, 0xe80e, 0x4a1, 0xe819, 0x49d, 0xe825, 0x498, 0xe831,
+  0x493, 0xe83c, 0x48f, 0xe848, 0x48a, 0xe854, 0x485, 0xe85f,
+  0x481, 0xe86b, 0x47c, 0xe877, 0x478, 0xe882, 0x473, 0xe88e,
+  0x46e, 0xe89a, 0x46a, 0xe8a5, 0x465, 0xe8b1, 0x461, 0xe8bd,
+  0x45c, 0xe8c9, 0x457, 0xe8d4, 0x453, 0xe8e0, 0x44e, 0xe8ec,
+  0x44a, 0xe8f7, 0x445, 0xe903, 0x441, 0xe90f, 0x43c, 0xe91b,
+  0x438, 0xe926, 0x433, 0xe932, 0x42f, 0xe93e, 0x42a, 0xe94a,
+  0x426, 0xe955, 0x422, 0xe961, 0x41d, 0xe96d, 0x419, 0xe979,
+  0x414, 0xe984, 0x410, 0xe990, 0x40b, 0xe99c, 0x407, 0xe9a8,
+  0x403, 0xe9b4, 0x3fe, 0xe9bf, 0x3fa, 0xe9cb, 0x3f6, 0xe9d7,
+  0x3f1, 0xe9e3, 0x3ed, 0xe9ee, 0x3e9, 0xe9fa, 0x3e4, 0xea06,
+  0x3e0, 0xea12, 0x3dc, 0xea1e, 0x3d7, 0xea29, 0x3d3, 0xea35,
+  0x3cf, 0xea41, 0x3ca, 0xea4d, 0x3c6, 0xea59, 0x3c2, 0xea65,
+  0x3be, 0xea70, 0x3ba, 0xea7c, 0x3b5, 0xea88, 0x3b1, 0xea94,
+  0x3ad, 0xeaa0, 0x3a9, 0xeaac, 0x3a5, 0xeab7, 0x3a0, 0xeac3,
+  0x39c, 0xeacf, 0x398, 0xeadb, 0x394, 0xeae7, 0x390, 0xeaf3,
+  0x38c, 0xeaff, 0x387, 0xeb0a, 0x383, 0xeb16, 0x37f, 0xeb22,
+  0x37b, 0xeb2e, 0x377, 0xeb3a, 0x373, 0xeb46, 0x36f, 0xeb52,
+  0x36b, 0xeb5e, 0x367, 0xeb6a, 0x363, 0xeb75, 0x35f, 0xeb81,
+  0x35b, 0xeb8d, 0x357, 0xeb99, 0x353, 0xeba5, 0x34f, 0xebb1,
+  0x34b, 0xebbd, 0x347, 0xebc9, 0x343, 0xebd5, 0x33f, 0xebe1,
+  0x33b, 0xebed, 0x337, 0xebf9, 0x333, 0xec05, 0x32f, 0xec10,
+  0x32b, 0xec1c, 0x327, 0xec28, 0x323, 0xec34, 0x320, 0xec40,
+  0x31c, 0xec4c, 0x318, 0xec58, 0x314, 0xec64, 0x310, 0xec70,
+  0x30c, 0xec7c, 0x308, 0xec88, 0x305, 0xec94, 0x301, 0xeca0,
+  0x2fd, 0xecac, 0x2f9, 0xecb8, 0x2f5, 0xecc4, 0x2f2, 0xecd0,
+  0x2ee, 0xecdc, 0x2ea, 0xece8, 0x2e6, 0xecf4, 0x2e3, 0xed00,
+  0x2df, 0xed0c, 0x2db, 0xed18, 0x2d8, 0xed24, 0x2d4, 0xed30,
+  0x2d0, 0xed3c, 0x2cc, 0xed48, 0x2c9, 0xed54, 0x2c5, 0xed60,
+  0x2c1, 0xed6c, 0x2be, 0xed78, 0x2ba, 0xed84, 0x2b7, 0xed90,
+  0x2b3, 0xed9c, 0x2af, 0xeda8, 0x2ac, 0xedb4, 0x2a8, 0xedc0,
+  0x2a5, 0xedcc, 0x2a1, 0xedd8, 0x29d, 0xede4, 0x29a, 0xedf0,
+  0x296, 0xedfc, 0x293, 0xee09, 0x28f, 0xee15, 0x28c, 0xee21,
+  0x288, 0xee2d, 0x285, 0xee39, 0x281, 0xee45, 0x27e, 0xee51,
+  0x27a, 0xee5d, 0x277, 0xee69, 0x273, 0xee75, 0x270, 0xee81,
+  0x26d, 0xee8d, 0x269, 0xee99, 0x266, 0xeea6, 0x262, 0xeeb2,
+  0x25f, 0xeebe, 0x25c, 0xeeca, 0x258, 0xeed6, 0x255, 0xeee2,
+  0x251, 0xeeee, 0x24e, 0xeefa, 0x24b, 0xef06, 0x247, 0xef13,
+  0x244, 0xef1f, 0x241, 0xef2b, 0x23e, 0xef37, 0x23a, 0xef43,
+  0x237, 0xef4f, 0x234, 0xef5b, 0x230, 0xef67, 0x22d, 0xef74,
+  0x22a, 0xef80, 0x227, 0xef8c, 0x223, 0xef98, 0x220, 0xefa4,
+  0x21d, 0xefb0, 0x21a, 0xefbc, 0x217, 0xefc9, 0x213, 0xefd5,
+  0x210, 0xefe1, 0x20d, 0xefed, 0x20a, 0xeff9, 0x207, 0xf005,
+  0x204, 0xf012, 0x201, 0xf01e, 0x1fd, 0xf02a, 0x1fa, 0xf036,
+  0x1f7, 0xf042, 0x1f4, 0xf04e, 0x1f1, 0xf05b, 0x1ee, 0xf067,
+  0x1eb, 0xf073, 0x1e8, 0xf07f, 0x1e5, 0xf08b, 0x1e2, 0xf098,
+  0x1df, 0xf0a4, 0x1dc, 0xf0b0, 0x1d9, 0xf0bc, 0x1d6, 0xf0c8,
+  0x1d3, 0xf0d5, 0x1d0, 0xf0e1, 0x1cd, 0xf0ed, 0x1ca, 0xf0f9,
+  0x1c7, 0xf105, 0x1c4, 0xf112, 0x1c1, 0xf11e, 0x1be, 0xf12a,
+  0x1bb, 0xf136, 0x1b8, 0xf143, 0x1b6, 0xf14f, 0x1b3, 0xf15b,
+  0x1b0, 0xf167, 0x1ad, 0xf174, 0x1aa, 0xf180, 0x1a7, 0xf18c,
+  0x1a4, 0xf198, 0x1a2, 0xf1a4, 0x19f, 0xf1b1, 0x19c, 0xf1bd,
+  0x199, 0xf1c9, 0x196, 0xf1d5, 0x194, 0xf1e2, 0x191, 0xf1ee,
+  0x18e, 0xf1fa, 0x18b, 0xf207, 0x189, 0xf213, 0x186, 0xf21f,
+  0x183, 0xf22b, 0x180, 0xf238, 0x17e, 0xf244, 0x17b, 0xf250,
+  0x178, 0xf25c, 0x176, 0xf269, 0x173, 0xf275, 0x170, 0xf281,
+  0x16e, 0xf28e, 0x16b, 0xf29a, 0x168, 0xf2a6, 0x166, 0xf2b2,
+  0x163, 0xf2bf, 0x161, 0xf2cb, 0x15e, 0xf2d7, 0x15b, 0xf2e4,
+  0x159, 0xf2f0, 0x156, 0xf2fc, 0x154, 0xf308, 0x151, 0xf315,
+  0x14f, 0xf321, 0x14c, 0xf32d, 0x14a, 0xf33a, 0x147, 0xf346,
+  0x145, 0xf352, 0x142, 0xf35f, 0x140, 0xf36b, 0x13d, 0xf377,
+  0x13b, 0xf384, 0x138, 0xf390, 0x136, 0xf39c, 0x134, 0xf3a9,
+  0x131, 0xf3b5, 0x12f, 0xf3c1, 0x12c, 0xf3ce, 0x12a, 0xf3da,
+  0x128, 0xf3e6, 0x125, 0xf3f3, 0x123, 0xf3ff, 0x120, 0xf40b,
+  0x11e, 0xf418, 0x11c, 0xf424, 0x119, 0xf430, 0x117, 0xf43d,
+  0x115, 0xf449, 0x113, 0xf455, 0x110, 0xf462, 0x10e, 0xf46e,
+  0x10c, 0xf47b, 0x109, 0xf487, 0x107, 0xf493, 0x105, 0xf4a0,
+  0x103, 0xf4ac, 0x100, 0xf4b8, 0xfe, 0xf4c5, 0xfc, 0xf4d1,
+  0xfa, 0xf4dd, 0xf8, 0xf4ea, 0xf6, 0xf4f6, 0xf3, 0xf503,
+  0xf1, 0xf50f, 0xef, 0xf51b, 0xed, 0xf528, 0xeb, 0xf534,
+  0xe9, 0xf540, 0xe7, 0xf54d, 0xe4, 0xf559, 0xe2, 0xf566,
+  0xe0, 0xf572, 0xde, 0xf57e, 0xdc, 0xf58b, 0xda, 0xf597,
+  0xd8, 0xf5a4, 0xd6, 0xf5b0, 0xd4, 0xf5bc, 0xd2, 0xf5c9,
+  0xd0, 0xf5d5, 0xce, 0xf5e2, 0xcc, 0xf5ee, 0xca, 0xf5fa,
+  0xc8, 0xf607, 0xc6, 0xf613, 0xc4, 0xf620, 0xc2, 0xf62c,
+  0xc0, 0xf639, 0xbe, 0xf645, 0xbd, 0xf651, 0xbb, 0xf65e,
+  0xb9, 0xf66a, 0xb7, 0xf677, 0xb5, 0xf683, 0xb3, 0xf690,
+  0xb1, 0xf69c, 0xaf, 0xf6a8, 0xae, 0xf6b5, 0xac, 0xf6c1,
+  0xaa, 0xf6ce, 0xa8, 0xf6da, 0xa6, 0xf6e7, 0xa5, 0xf6f3,
+  0xa3, 0xf6ff, 0xa1, 0xf70c, 0x9f, 0xf718, 0x9e, 0xf725,
+  0x9c, 0xf731, 0x9a, 0xf73e, 0x98, 0xf74a, 0x97, 0xf757,
+  0x95, 0xf763, 0x93, 0xf76f, 0x92, 0xf77c, 0x90, 0xf788,
+  0x8e, 0xf795, 0x8d, 0xf7a1, 0x8b, 0xf7ae, 0x89, 0xf7ba,
+  0x88, 0xf7c7, 0x86, 0xf7d3, 0x85, 0xf7e0, 0x83, 0xf7ec,
+  0x81, 0xf7f9, 0x80, 0xf805, 0x7e, 0xf811, 0x7d, 0xf81e,
+  0x7b, 0xf82a, 0x7a, 0xf837, 0x78, 0xf843, 0x77, 0xf850,
+  0x75, 0xf85c, 0x74, 0xf869, 0x72, 0xf875, 0x71, 0xf882,
+  0x6f, 0xf88e, 0x6e, 0xf89b, 0x6c, 0xf8a7, 0x6b, 0xf8b4,
+  0x69, 0xf8c0, 0x68, 0xf8cd, 0x67, 0xf8d9, 0x65, 0xf8e6,
+  0x64, 0xf8f2, 0x62, 0xf8ff, 0x61, 0xf90b, 0x60, 0xf918,
+  0x5e, 0xf924, 0x5d, 0xf931, 0x5c, 0xf93d, 0x5a, 0xf94a,
+  0x59, 0xf956, 0x58, 0xf963, 0x56, 0xf96f, 0x55, 0xf97c,
+  0x54, 0xf988, 0x53, 0xf995, 0x51, 0xf9a1, 0x50, 0xf9ae,
+  0x4f, 0xf9ba, 0x4e, 0xf9c7, 0x4c, 0xf9d3, 0x4b, 0xf9e0,
+  0x4a, 0xf9ec, 0x49, 0xf9f9, 0x48, 0xfa05, 0x47, 0xfa12,
+  0x45, 0xfa1e, 0x44, 0xfa2b, 0x43, 0xfa37, 0x42, 0xfa44,
+  0x41, 0xfa50, 0x40, 0xfa5d, 0x3f, 0xfa69, 0x3d, 0xfa76,
+  0x3c, 0xfa82, 0x3b, 0xfa8f, 0x3a, 0xfa9b, 0x39, 0xfaa8,
+  0x38, 0xfab4, 0x37, 0xfac1, 0x36, 0xfacd, 0x35, 0xfada,
+  0x34, 0xfae6, 0x33, 0xfaf3, 0x32, 0xfb00, 0x31, 0xfb0c,
+  0x30, 0xfb19, 0x2f, 0xfb25, 0x2e, 0xfb32, 0x2d, 0xfb3e,
+  0x2c, 0xfb4b, 0x2b, 0xfb57, 0x2b, 0xfb64, 0x2a, 0xfb70,
+  0x29, 0xfb7d, 0x28, 0xfb89, 0x27, 0xfb96, 0x26, 0xfba2,
+  0x25, 0xfbaf, 0x24, 0xfbbc, 0x24, 0xfbc8, 0x23, 0xfbd5,
+  0x22, 0xfbe1, 0x21, 0xfbee, 0x20, 0xfbfa, 0x20, 0xfc07,
+  0x1f, 0xfc13, 0x1e, 0xfc20, 0x1d, 0xfc2c, 0x1d, 0xfc39,
+  0x1c, 0xfc45, 0x1b, 0xfc52, 0x1a, 0xfc5f, 0x1a, 0xfc6b,
+  0x19, 0xfc78, 0x18, 0xfc84, 0x18, 0xfc91, 0x17, 0xfc9d,
+  0x16, 0xfcaa, 0x16, 0xfcb6, 0x15, 0xfcc3, 0x14, 0xfcd0,
+  0x14, 0xfcdc, 0x13, 0xfce9, 0x13, 0xfcf5, 0x12, 0xfd02,
+  0x11, 0xfd0e, 0x11, 0xfd1b, 0x10, 0xfd27, 0x10, 0xfd34,
+  0xf, 0xfd40, 0xf, 0xfd4d, 0xe, 0xfd5a, 0xe, 0xfd66,
+  0xd, 0xfd73, 0xd, 0xfd7f, 0xc, 0xfd8c, 0xc, 0xfd98,
+  0xb, 0xfda5, 0xb, 0xfdb2, 0xa, 0xfdbe, 0xa, 0xfdcb,
+  0x9, 0xfdd7, 0x9, 0xfde4, 0x9, 0xfdf0, 0x8, 0xfdfd,
+  0x8, 0xfe09, 0x7, 0xfe16, 0x7, 0xfe23, 0x7, 0xfe2f,
+  0x6, 0xfe3c, 0x6, 0xfe48, 0x6, 0xfe55, 0x5, 0xfe61,
+  0x5, 0xfe6e, 0x5, 0xfe7a, 0x4, 0xfe87, 0x4, 0xfe94,
+  0x4, 0xfea0, 0x4, 0xfead, 0x3, 0xfeb9, 0x3, 0xfec6,
+  0x3, 0xfed2, 0x3, 0xfedf, 0x2, 0xfeec, 0x2, 0xfef8,
+  0x2, 0xff05, 0x2, 0xff11, 0x2, 0xff1e, 0x1, 0xff2a,
+  0x1, 0xff37, 0x1, 0xff44, 0x1, 0xff50, 0x1, 0xff5d,
+  0x1, 0xff69, 0x1, 0xff76, 0x0, 0xff82, 0x0, 0xff8f,
+  0x0, 0xff9b, 0x0, 0xffa8, 0x0, 0xffb5, 0x0, 0xffc1,
+  0x0, 0xffce, 0x0, 0xffda, 0x0, 0xffe7, 0x0, 0xfff3,
+  0x0, 0x0, 0x0, 0xd, 0x0, 0x19, 0x0, 0x26,
+  0x0, 0x32, 0x0, 0x3f, 0x0, 0x4b, 0x0, 0x58,
+  0x0, 0x65, 0x0, 0x71, 0x0, 0x7e, 0x1, 0x8a,
+  0x1, 0x97, 0x1, 0xa3, 0x1, 0xb0, 0x1, 0xbc,
+  0x1, 0xc9, 0x1, 0xd6, 0x2, 0xe2, 0x2, 0xef,
+  0x2, 0xfb, 0x2, 0x108, 0x2, 0x114, 0x3, 0x121,
+  0x3, 0x12e, 0x3, 0x13a, 0x3, 0x147, 0x4, 0x153,
+  0x4, 0x160, 0x4, 0x16c, 0x4, 0x179, 0x5, 0x186,
+  0x5, 0x192, 0x5, 0x19f, 0x6, 0x1ab, 0x6, 0x1b8,
+  0x6, 0x1c4, 0x7, 0x1d1, 0x7, 0x1dd, 0x7, 0x1ea,
+  0x8, 0x1f7, 0x8, 0x203, 0x9, 0x210, 0x9, 0x21c,
+  0x9, 0x229, 0xa, 0x235, 0xa, 0x242, 0xb, 0x24e,
+  0xb, 0x25b, 0xc, 0x268, 0xc, 0x274, 0xd, 0x281,
+  0xd, 0x28d, 0xe, 0x29a, 0xe, 0x2a6, 0xf, 0x2b3,
+  0xf, 0x2c0, 0x10, 0x2cc, 0x10, 0x2d9, 0x11, 0x2e5,
+  0x11, 0x2f2, 0x12, 0x2fe, 0x13, 0x30b, 0x13, 0x317,
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+  0x16, 0x356, 0x17, 0x363, 0x18, 0x36f, 0x18, 0x37c,
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+  0x1f, 0x3ed, 0x20, 0x3f9, 0x20, 0x406, 0x21, 0x412,
+  0x22, 0x41f, 0x23, 0x42b, 0x24, 0x438, 0x24, 0x444,
+  0x25, 0x451, 0x26, 0x45e, 0x27, 0x46a, 0x28, 0x477,
+  0x29, 0x483, 0x2a, 0x490, 0x2b, 0x49c, 0x2b, 0x4a9,
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+  0x34, 0x51a, 0x35, 0x526, 0x36, 0x533, 0x37, 0x53f,
+  0x38, 0x54c, 0x39, 0x558, 0x3a, 0x565, 0x3b, 0x571,
+  0x3c, 0x57e, 0x3d, 0x58a, 0x3f, 0x597, 0x40, 0x5a3,
+  0x41, 0x5b0, 0x42, 0x5bc, 0x43, 0x5c9, 0x44, 0x5d5,
+  0x45, 0x5e2, 0x47, 0x5ee, 0x48, 0x5fb, 0x49, 0x607,
+  0x4a, 0x614, 0x4b, 0x620, 0x4c, 0x62d, 0x4e, 0x639,
+  0x4f, 0x646, 0x50, 0x652, 0x51, 0x65f, 0x53, 0x66b,
+  0x54, 0x678, 0x55, 0x684, 0x56, 0x691, 0x58, 0x69d,
+  0x59, 0x6aa, 0x5a, 0x6b6, 0x5c, 0x6c3, 0x5d, 0x6cf,
+  0x5e, 0x6dc, 0x60, 0x6e8, 0x61, 0x6f5, 0x62, 0x701,
+  0x64, 0x70e, 0x65, 0x71a, 0x67, 0x727, 0x68, 0x733,
+  0x69, 0x740, 0x6b, 0x74c, 0x6c, 0x759, 0x6e, 0x765,
+  0x6f, 0x772, 0x71, 0x77e, 0x72, 0x78b, 0x74, 0x797,
+  0x75, 0x7a4, 0x77, 0x7b0, 0x78, 0x7bd, 0x7a, 0x7c9,
+  0x7b, 0x7d6, 0x7d, 0x7e2, 0x7e, 0x7ef, 0x80, 0x7fb,
+  0x81, 0x807, 0x83, 0x814, 0x85, 0x820, 0x86, 0x82d,
+  0x88, 0x839, 0x89, 0x846, 0x8b, 0x852, 0x8d, 0x85f,
+  0x8e, 0x86b, 0x90, 0x878, 0x92, 0x884, 0x93, 0x891,
+  0x95, 0x89d, 0x97, 0x8a9, 0x98, 0x8b6, 0x9a, 0x8c2,
+  0x9c, 0x8cf, 0x9e, 0x8db, 0x9f, 0x8e8, 0xa1, 0x8f4,
+  0xa3, 0x901, 0xa5, 0x90d, 0xa6, 0x919, 0xa8, 0x926,
+  0xaa, 0x932, 0xac, 0x93f, 0xae, 0x94b, 0xaf, 0x958,
+  0xb1, 0x964, 0xb3, 0x970, 0xb5, 0x97d, 0xb7, 0x989,
+  0xb9, 0x996, 0xbb, 0x9a2, 0xbd, 0x9af, 0xbe, 0x9bb,
+  0xc0, 0x9c7, 0xc2, 0x9d4, 0xc4, 0x9e0, 0xc6, 0x9ed,
+  0xc8, 0x9f9, 0xca, 0xa06, 0xcc, 0xa12, 0xce, 0xa1e,
+  0xd0, 0xa2b, 0xd2, 0xa37, 0xd4, 0xa44, 0xd6, 0xa50,
+  0xd8, 0xa5c, 0xda, 0xa69, 0xdc, 0xa75, 0xde, 0xa82,
+  0xe0, 0xa8e, 0xe2, 0xa9a, 0xe4, 0xaa7, 0xe7, 0xab3,
+  0xe9, 0xac0, 0xeb, 0xacc, 0xed, 0xad8, 0xef, 0xae5,
+  0xf1, 0xaf1, 0xf3, 0xafd, 0xf6, 0xb0a, 0xf8, 0xb16,
+  0xfa, 0xb23, 0xfc, 0xb2f, 0xfe, 0xb3b, 0x100, 0xb48,
+  0x103, 0xb54, 0x105, 0xb60, 0x107, 0xb6d, 0x109, 0xb79,
+  0x10c, 0xb85, 0x10e, 0xb92, 0x110, 0xb9e, 0x113, 0xbab,
+  0x115, 0xbb7, 0x117, 0xbc3, 0x119, 0xbd0, 0x11c, 0xbdc,
+  0x11e, 0xbe8, 0x120, 0xbf5, 0x123, 0xc01, 0x125, 0xc0d,
+  0x128, 0xc1a, 0x12a, 0xc26, 0x12c, 0xc32, 0x12f, 0xc3f,
+  0x131, 0xc4b, 0x134, 0xc57, 0x136, 0xc64, 0x138, 0xc70,
+  0x13b, 0xc7c, 0x13d, 0xc89, 0x140, 0xc95, 0x142, 0xca1,
+  0x145, 0xcae, 0x147, 0xcba, 0x14a, 0xcc6, 0x14c, 0xcd3,
+  0x14f, 0xcdf, 0x151, 0xceb, 0x154, 0xcf8, 0x156, 0xd04,
+  0x159, 0xd10, 0x15b, 0xd1c, 0x15e, 0xd29, 0x161, 0xd35,
+  0x163, 0xd41, 0x166, 0xd4e, 0x168, 0xd5a, 0x16b, 0xd66,
+  0x16e, 0xd72, 0x170, 0xd7f, 0x173, 0xd8b, 0x176, 0xd97,
+  0x178, 0xda4, 0x17b, 0xdb0, 0x17e, 0xdbc, 0x180, 0xdc8,
+  0x183, 0xdd5, 0x186, 0xde1, 0x189, 0xded, 0x18b, 0xdf9,
+  0x18e, 0xe06, 0x191, 0xe12, 0x194, 0xe1e, 0x196, 0xe2b,
+  0x199, 0xe37, 0x19c, 0xe43, 0x19f, 0xe4f, 0x1a2, 0xe5c,
+  0x1a4, 0xe68, 0x1a7, 0xe74, 0x1aa, 0xe80, 0x1ad, 0xe8c,
+  0x1b0, 0xe99, 0x1b3, 0xea5, 0x1b6, 0xeb1, 0x1b8, 0xebd,
+  0x1bb, 0xeca, 0x1be, 0xed6, 0x1c1, 0xee2, 0x1c4, 0xeee,
+  0x1c7, 0xefb, 0x1ca, 0xf07, 0x1cd, 0xf13, 0x1d0, 0xf1f,
+  0x1d3, 0xf2b, 0x1d6, 0xf38, 0x1d9, 0xf44, 0x1dc, 0xf50,
+  0x1df, 0xf5c, 0x1e2, 0xf68, 0x1e5, 0xf75, 0x1e8, 0xf81,
+  0x1eb, 0xf8d, 0x1ee, 0xf99, 0x1f1, 0xfa5, 0x1f4, 0xfb2,
+  0x1f7, 0xfbe, 0x1fa, 0xfca, 0x1fd, 0xfd6, 0x201, 0xfe2,
+  0x204, 0xfee, 0x207, 0xffb, 0x20a, 0x1007, 0x20d, 0x1013,
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+  0x21d, 0x1050, 0x220, 0x105c, 0x223, 0x1068, 0x227, 0x1074,
+  0x22a, 0x1080, 0x22d, 0x108c, 0x230, 0x1099, 0x234, 0x10a5,
+  0x237, 0x10b1, 0x23a, 0x10bd, 0x23e, 0x10c9, 0x241, 0x10d5,
+  0x244, 0x10e1, 0x247, 0x10ed, 0x24b, 0x10fa, 0x24e, 0x1106,
+  0x251, 0x1112, 0x255, 0x111e, 0x258, 0x112a, 0x25c, 0x1136,
+  0x25f, 0x1142, 0x262, 0x114e, 0x266, 0x115a, 0x269, 0x1167,
+  0x26d, 0x1173, 0x270, 0x117f, 0x273, 0x118b, 0x277, 0x1197,
+  0x27a, 0x11a3, 0x27e, 0x11af, 0x281, 0x11bb, 0x285, 0x11c7,
+  0x288, 0x11d3, 0x28c, 0x11df, 0x28f, 0x11eb, 0x293, 0x11f7,
+  0x296, 0x1204, 0x29a, 0x1210, 0x29d, 0x121c, 0x2a1, 0x1228,
+  0x2a5, 0x1234, 0x2a8, 0x1240, 0x2ac, 0x124c, 0x2af, 0x1258,
+  0x2b3, 0x1264, 0x2b7, 0x1270, 0x2ba, 0x127c, 0x2be, 0x1288,
+  0x2c1, 0x1294, 0x2c5, 0x12a0, 0x2c9, 0x12ac, 0x2cc, 0x12b8,
+  0x2d0, 0x12c4, 0x2d4, 0x12d0, 0x2d8, 0x12dc, 0x2db, 0x12e8,
+  0x2df, 0x12f4, 0x2e3, 0x1300, 0x2e6, 0x130c, 0x2ea, 0x1318,
+  0x2ee, 0x1324, 0x2f2, 0x1330, 0x2f5, 0x133c, 0x2f9, 0x1348,
+  0x2fd, 0x1354, 0x301, 0x1360, 0x305, 0x136c, 0x308, 0x1378,
+  0x30c, 0x1384, 0x310, 0x1390, 0x314, 0x139c, 0x318, 0x13a8,
+  0x31c, 0x13b4, 0x320, 0x13c0, 0x323, 0x13cc, 0x327, 0x13d8,
+  0x32b, 0x13e4, 0x32f, 0x13f0, 0x333, 0x13fb, 0x337, 0x1407,
+  0x33b, 0x1413, 0x33f, 0x141f, 0x343, 0x142b, 0x347, 0x1437,
+  0x34b, 0x1443, 0x34f, 0x144f, 0x353, 0x145b, 0x357, 0x1467,
+  0x35b, 0x1473, 0x35f, 0x147f, 0x363, 0x148b, 0x367, 0x1496,
+  0x36b, 0x14a2, 0x36f, 0x14ae, 0x373, 0x14ba, 0x377, 0x14c6,
+  0x37b, 0x14d2, 0x37f, 0x14de, 0x383, 0x14ea, 0x387, 0x14f6,
+  0x38c, 0x1501, 0x390, 0x150d, 0x394, 0x1519, 0x398, 0x1525,
+  0x39c, 0x1531, 0x3a0, 0x153d, 0x3a5, 0x1549, 0x3a9, 0x1554,
+  0x3ad, 0x1560, 0x3b1, 0x156c, 0x3b5, 0x1578, 0x3ba, 0x1584,
+  0x3be, 0x1590, 0x3c2, 0x159b, 0x3c6, 0x15a7, 0x3ca, 0x15b3,
+  0x3cf, 0x15bf, 0x3d3, 0x15cb, 0x3d7, 0x15d7, 0x3dc, 0x15e2,
+  0x3e0, 0x15ee, 0x3e4, 0x15fa, 0x3e9, 0x1606, 0x3ed, 0x1612,
+  0x3f1, 0x161d, 0x3f6, 0x1629, 0x3fa, 0x1635, 0x3fe, 0x1641,
+  0x403, 0x164c, 0x407, 0x1658, 0x40b, 0x1664, 0x410, 0x1670,
+  0x414, 0x167c, 0x419, 0x1687, 0x41d, 0x1693, 0x422, 0x169f,
+  0x426, 0x16ab, 0x42a, 0x16b6, 0x42f, 0x16c2, 0x433, 0x16ce,
+  0x438, 0x16da, 0x43c, 0x16e5, 0x441, 0x16f1, 0x445, 0x16fd,
+  0x44a, 0x1709, 0x44e, 0x1714, 0x453, 0x1720, 0x457, 0x172c,
+  0x45c, 0x1737, 0x461, 0x1743, 0x465, 0x174f, 0x46a, 0x175b,
+  0x46e, 0x1766, 0x473, 0x1772, 0x478, 0x177e, 0x47c, 0x1789,
+  0x481, 0x1795, 0x485, 0x17a1, 0x48a, 0x17ac, 0x48f, 0x17b8,
+  0x493, 0x17c4, 0x498, 0x17cf, 0x49d, 0x17db, 0x4a1, 0x17e7,
+  0x4a6, 0x17f2, 0x4ab, 0x17fe, 0x4b0, 0x180a, 0x4b4, 0x1815,
+  0x4b9, 0x1821, 0x4be, 0x182d, 0x4c2, 0x1838, 0x4c7, 0x1844,
+  0x4cc, 0x184f, 0x4d1, 0x185b, 0x4d6, 0x1867, 0x4da, 0x1872,
+  0x4df, 0x187e, 0x4e4, 0x1889, 0x4e9, 0x1895, 0x4ee, 0x18a1,
+  0x4f2, 0x18ac, 0x4f7, 0x18b8, 0x4fc, 0x18c3, 0x501, 0x18cf,
+  0x506, 0x18db, 0x50b, 0x18e6, 0x510, 0x18f2, 0x515, 0x18fd,
+  0x51a, 0x1909, 0x51e, 0x1914, 0x523, 0x1920, 0x528, 0x192c,
+  0x52d, 0x1937, 0x532, 0x1943, 0x537, 0x194e, 0x53c, 0x195a,
+  0x541, 0x1965, 0x546, 0x1971, 0x54b, 0x197c, 0x550, 0x1988,
+  0x555, 0x1993, 0x55a, 0x199f, 0x55f, 0x19aa, 0x564, 0x19b6,
+  0x569, 0x19c1, 0x56e, 0x19cd, 0x573, 0x19d8, 0x578, 0x19e4,
+  0x57e, 0x19ef, 0x583, 0x19fb, 0x588, 0x1a06, 0x58d, 0x1a12,
+  0x592, 0x1a1d, 0x597, 0x1a29, 0x59c, 0x1a34, 0x5a1, 0x1a40,
+  0x5a7, 0x1a4b, 0x5ac, 0x1a57, 0x5b1, 0x1a62, 0x5b6, 0x1a6e,
+  0x5bb, 0x1a79, 0x5c1, 0x1a84, 0x5c6, 0x1a90, 0x5cb, 0x1a9b,
+  0x5d0, 0x1aa7, 0x5d5, 0x1ab2, 0x5db, 0x1abe, 0x5e0, 0x1ac9,
+  0x5e5, 0x1ad4, 0x5ea, 0x1ae0, 0x5f0, 0x1aeb, 0x5f5, 0x1af7,
+  0x5fa, 0x1b02, 0x600, 0x1b0d, 0x605, 0x1b19, 0x60a, 0x1b24,
+  0x610, 0x1b30, 0x615, 0x1b3b, 0x61a, 0x1b46, 0x620, 0x1b52,
+  0x625, 0x1b5d, 0x62a, 0x1b68, 0x630, 0x1b74, 0x635, 0x1b7f,
+  0x63b, 0x1b8a, 0x640, 0x1b96, 0x645, 0x1ba1, 0x64b, 0x1bac,
+  0x650, 0x1bb8, 0x656, 0x1bc3, 0x65b, 0x1bce, 0x661, 0x1bda,
+  0x666, 0x1be5, 0x66c, 0x1bf0, 0x671, 0x1bfc, 0x677, 0x1c07,
+  0x67c, 0x1c12, 0x682, 0x1c1e, 0x687, 0x1c29, 0x68d, 0x1c34,
+  0x692, 0x1c3f, 0x698, 0x1c4b, 0x69d, 0x1c56, 0x6a3, 0x1c61,
+  0x6a8, 0x1c6c, 0x6ae, 0x1c78, 0x6b4, 0x1c83, 0x6b9, 0x1c8e,
+  0x6bf, 0x1c99, 0x6c5, 0x1ca5, 0x6ca, 0x1cb0, 0x6d0, 0x1cbb,
+  0x6d5, 0x1cc6, 0x6db, 0x1cd2, 0x6e1, 0x1cdd, 0x6e6, 0x1ce8,
+  0x6ec, 0x1cf3, 0x6f2, 0x1cff, 0x6f7, 0x1d0a, 0x6fd, 0x1d15,
+  0x703, 0x1d20, 0x709, 0x1d2b, 0x70e, 0x1d36, 0x714, 0x1d42,
+  0x71a, 0x1d4d, 0x720, 0x1d58, 0x725, 0x1d63, 0x72b, 0x1d6e,
+  0x731, 0x1d79, 0x737, 0x1d85, 0x73d, 0x1d90, 0x742, 0x1d9b,
+  0x748, 0x1da6, 0x74e, 0x1db1, 0x754, 0x1dbc, 0x75a, 0x1dc7,
+  0x75f, 0x1dd3, 0x765, 0x1dde, 0x76b, 0x1de9, 0x771, 0x1df4,
+  0x777, 0x1dff, 0x77d, 0x1e0a, 0x783, 0x1e15, 0x789, 0x1e20,
+  0x78f, 0x1e2b, 0x795, 0x1e36, 0x79a, 0x1e42, 0x7a0, 0x1e4d,
+  0x7a6, 0x1e58, 0x7ac, 0x1e63, 0x7b2, 0x1e6e, 0x7b8, 0x1e79,
+  0x7be, 0x1e84, 0x7c4, 0x1e8f, 0x7ca, 0x1e9a, 0x7d0, 0x1ea5,
+  0x7d6, 0x1eb0, 0x7dc, 0x1ebb, 0x7e2, 0x1ec6, 0x7e8, 0x1ed1,
+  0x7ee, 0x1edc, 0x7f5, 0x1ee7, 0x7fb, 0x1ef2, 0x801, 0x1efd,
+  0x807, 0x1f08, 0x80d, 0x1f13, 0x813, 0x1f1e, 0x819, 0x1f29,
+  0x81f, 0x1f34, 0x825, 0x1f3f, 0x82b, 0x1f4a, 0x832, 0x1f55,
+  0x838, 0x1f60, 0x83e, 0x1f6b, 0x844, 0x1f76, 0x84a, 0x1f81,
+  0x850, 0x1f8c, 0x857, 0x1f97, 0x85d, 0x1fa2, 0x863, 0x1fac,
+  0x869, 0x1fb7, 0x870, 0x1fc2, 0x876, 0x1fcd, 0x87c, 0x1fd8,
+  0x882, 0x1fe3, 0x889, 0x1fee, 0x88f, 0x1ff9, 0x895, 0x2004,
+  0x89b, 0x200f, 0x8a2, 0x2019, 0x8a8, 0x2024, 0x8ae, 0x202f,
+  0x8b5, 0x203a, 0x8bb, 0x2045, 0x8c1, 0x2050, 0x8c8, 0x205b,
+  0x8ce, 0x2065, 0x8d4, 0x2070, 0x8db, 0x207b, 0x8e1, 0x2086,
+  0x8e8, 0x2091, 0x8ee, 0x209b, 0x8f4, 0x20a6, 0x8fb, 0x20b1,
+  0x901, 0x20bc, 0x908, 0x20c7, 0x90e, 0x20d1, 0x915, 0x20dc,
+  0x91b, 0x20e7, 0x921, 0x20f2, 0x928, 0x20fd, 0x92e, 0x2107,
+  0x935, 0x2112, 0x93b, 0x211d, 0x942, 0x2128, 0x948, 0x2132,
+  0x94f, 0x213d, 0x955, 0x2148, 0x95c, 0x2153, 0x963, 0x215d,
+  0x969, 0x2168, 0x970, 0x2173, 0x976, 0x217d, 0x97d, 0x2188,
+  0x983, 0x2193, 0x98a, 0x219e, 0x991, 0x21a8, 0x997, 0x21b3,
+  0x99e, 0x21be, 0x9a4, 0x21c8, 0x9ab, 0x21d3, 0x9b2, 0x21de,
+  0x9b8, 0x21e8, 0x9bf, 0x21f3, 0x9c6, 0x21fe, 0x9cc, 0x2208,
+  0x9d3, 0x2213, 0x9da, 0x221e, 0x9e0, 0x2228, 0x9e7, 0x2233,
+  0x9ee, 0x223d, 0x9f5, 0x2248, 0x9fb, 0x2253, 0xa02, 0x225d,
+  0xa09, 0x2268, 0xa10, 0x2272, 0xa16, 0x227d, 0xa1d, 0x2288,
+  0xa24, 0x2292, 0xa2b, 0x229d, 0xa32, 0x22a7, 0xa38, 0x22b2,
+  0xa3f, 0x22bc, 0xa46, 0x22c7, 0xa4d, 0x22d2, 0xa54, 0x22dc,
+  0xa5b, 0x22e7, 0xa61, 0x22f1, 0xa68, 0x22fc, 0xa6f, 0x2306,
+  0xa76, 0x2311, 0xa7d, 0x231b, 0xa84, 0x2326, 0xa8b, 0x2330,
+  0xa92, 0x233b, 0xa99, 0x2345, 0xa9f, 0x2350, 0xaa6, 0x235a,
+  0xaad, 0x2365, 0xab4, 0x236f, 0xabb, 0x237a, 0xac2, 0x2384,
+  0xac9, 0x238e, 0xad0, 0x2399, 0xad7, 0x23a3, 0xade, 0x23ae,
+  0xae5, 0x23b8, 0xaec, 0x23c3, 0xaf3, 0x23cd, 0xafa, 0x23d7,
+  0xb01, 0x23e2, 0xb08, 0x23ec, 0xb0f, 0x23f7, 0xb16, 0x2401,
+  0xb1e, 0x240b, 0xb25, 0x2416, 0xb2c, 0x2420, 0xb33, 0x242b,
+  0xb3a, 0x2435, 0xb41, 0x243f, 0xb48, 0x244a, 0xb4f, 0x2454,
+  0xb56, 0x245e, 0xb5e, 0x2469, 0xb65, 0x2473, 0xb6c, 0x247d,
+  0xb73, 0x2488, 0xb7a, 0x2492, 0xb81, 0x249c, 0xb89, 0x24a7,
+  0xb90, 0x24b1, 0xb97, 0x24bb, 0xb9e, 0x24c5, 0xba5, 0x24d0,
+  0xbad, 0x24da, 0xbb4, 0x24e4, 0xbbb, 0x24ef, 0xbc2, 0x24f9,
+  0xbca, 0x2503, 0xbd1, 0x250d, 0xbd8, 0x2518, 0xbe0, 0x2522,
+  0xbe7, 0x252c, 0xbee, 0x2536, 0xbf5, 0x2541, 0xbfd, 0x254b,
+  0xc04, 0x2555, 0xc0b, 0x255f, 0xc13, 0x2569, 0xc1a, 0x2574,
+  0xc21, 0x257e, 0xc29, 0x2588, 0xc30, 0x2592, 0xc38, 0x259c,
+  0xc3f, 0x25a6, 0xc46, 0x25b1, 0xc4e, 0x25bb, 0xc55, 0x25c5,
+  0xc5d, 0x25cf, 0xc64, 0x25d9, 0xc6b, 0x25e3, 0xc73, 0x25ed,
+  0xc7a, 0x25f8, 0xc82, 0x2602, 0xc89, 0x260c, 0xc91, 0x2616,
+  0xc98, 0x2620, 0xca0, 0x262a, 0xca7, 0x2634, 0xcaf, 0x263e,
+  0xcb6, 0x2648, 0xcbe, 0x2652, 0xcc5, 0x265c, 0xccd, 0x2666,
+  0xcd4, 0x2671, 0xcdc, 0x267b, 0xce3, 0x2685, 0xceb, 0x268f,
+  0xcf3, 0x2699, 0xcfa, 0x26a3, 0xd02, 0x26ad, 0xd09, 0x26b7,
+  0xd11, 0x26c1, 0xd19, 0x26cb, 0xd20, 0x26d5, 0xd28, 0x26df,
+  0xd30, 0x26e9, 0xd37, 0x26f3, 0xd3f, 0x26fd, 0xd46, 0x2707,
+  0xd4e, 0x2711, 0xd56, 0x271a, 0xd5d, 0x2724, 0xd65, 0x272e,
+  0xd6d, 0x2738, 0xd75, 0x2742, 0xd7c, 0x274c, 0xd84, 0x2756,
+  0xd8c, 0x2760, 0xd93, 0x276a, 0xd9b, 0x2774, 0xda3, 0x277e,
+  0xdab, 0x2788, 0xdb2, 0x2791, 0xdba, 0x279b, 0xdc2, 0x27a5,
+  0xdca, 0x27af, 0xdd2, 0x27b9, 0xdd9, 0x27c3, 0xde1, 0x27cd,
+  0xde9, 0x27d6, 0xdf1, 0x27e0, 0xdf9, 0x27ea, 0xe01, 0x27f4,
+  0xe08, 0x27fe, 0xe10, 0x2808, 0xe18, 0x2811, 0xe20, 0x281b,
+  0xe28, 0x2825, 0xe30, 0x282f, 0xe38, 0x2838, 0xe40, 0x2842,
+  0xe47, 0x284c, 0xe4f, 0x2856, 0xe57, 0x2860, 0xe5f, 0x2869,
+  0xe67, 0x2873, 0xe6f, 0x287d, 0xe77, 0x2886, 0xe7f, 0x2890,
+  0xe87, 0x289a, 0xe8f, 0x28a4, 0xe97, 0x28ad, 0xe9f, 0x28b7,
+  0xea7, 0x28c1, 0xeaf, 0x28ca, 0xeb7, 0x28d4, 0xebf, 0x28de,
+  0xec7, 0x28e7, 0xecf, 0x28f1, 0xed7, 0x28fb, 0xedf, 0x2904,
+  0xee7, 0x290e, 0xeef, 0x2918, 0xef7, 0x2921, 0xeff, 0x292b,
+  0xf07, 0x2935, 0xf10, 0x293e, 0xf18, 0x2948, 0xf20, 0x2951,
+  0xf28, 0x295b, 0xf30, 0x2965, 0xf38, 0x296e, 0xf40, 0x2978,
+  0xf48, 0x2981, 0xf51, 0x298b, 0xf59, 0x2994, 0xf61, 0x299e,
+  0xf69, 0x29a7, 0xf71, 0x29b1, 0xf79, 0x29bb, 0xf82, 0x29c4,
+  0xf8a, 0x29ce, 0xf92, 0x29d7, 0xf9a, 0x29e1, 0xfa3, 0x29ea,
+  0xfab, 0x29f4, 0xfb3, 0x29fd, 0xfbb, 0x2a07, 0xfc4, 0x2a10,
+  0xfcc, 0x2a1a, 0xfd4, 0x2a23, 0xfdc, 0x2a2c, 0xfe5, 0x2a36,
+  0xfed, 0x2a3f, 0xff5, 0x2a49, 0xffe, 0x2a52, 0x1006, 0x2a5c,
+  0x100e, 0x2a65, 0x1016, 0x2a6e, 0x101f, 0x2a78, 0x1027, 0x2a81,
+  0x1030, 0x2a8b, 0x1038, 0x2a94, 0x1040, 0x2a9d, 0x1049, 0x2aa7,
+  0x1051, 0x2ab0, 0x1059, 0x2ab9, 0x1062, 0x2ac3, 0x106a, 0x2acc,
+  0x1073, 0x2ad6, 0x107b, 0x2adf, 0x1083, 0x2ae8, 0x108c, 0x2af2,
+  0x1094, 0x2afb, 0x109d, 0x2b04, 0x10a5, 0x2b0d, 0x10ae, 0x2b17,
+  0x10b6, 0x2b20, 0x10bf, 0x2b29, 0x10c7, 0x2b33, 0x10d0, 0x2b3c,
+  0x10d8, 0x2b45, 0x10e0, 0x2b4e, 0x10e9, 0x2b58, 0x10f2, 0x2b61,
+  0x10fa, 0x2b6a, 0x1103, 0x2b73, 0x110b, 0x2b7d, 0x1114, 0x2b86,
+  0x111c, 0x2b8f, 0x1125, 0x2b98, 0x112d, 0x2ba1, 0x1136, 0x2bab,
+  0x113e, 0x2bb4, 0x1147, 0x2bbd, 0x1150, 0x2bc6, 0x1158, 0x2bcf,
+  0x1161, 0x2bd8, 0x1169, 0x2be2, 0x1172, 0x2beb, 0x117b, 0x2bf4,
+  0x1183, 0x2bfd, 0x118c, 0x2c06, 0x1195, 0x2c0f, 0x119d, 0x2c18,
+  0x11a6, 0x2c21, 0x11af, 0x2c2b, 0x11b7, 0x2c34, 0x11c0, 0x2c3d,
+  0x11c9, 0x2c46, 0x11d1, 0x2c4f, 0x11da, 0x2c58, 0x11e3, 0x2c61,
+  0x11eb, 0x2c6a, 0x11f4, 0x2c73, 0x11fd, 0x2c7c, 0x1206, 0x2c85,
+  0x120e, 0x2c8e, 0x1217, 0x2c97, 0x1220, 0x2ca0, 0x1229, 0x2ca9,
+  0x1231, 0x2cb2, 0x123a, 0x2cbb, 0x1243, 0x2cc4, 0x124c, 0x2ccd,
+  0x1255, 0x2cd6, 0x125d, 0x2cdf, 0x1266, 0x2ce8, 0x126f, 0x2cf1,
+  0x1278, 0x2cfa, 0x1281, 0x2d03, 0x128a, 0x2d0c, 0x1292, 0x2d15,
+  0x129b, 0x2d1e, 0x12a4, 0x2d27, 0x12ad, 0x2d2f, 0x12b6, 0x2d38,
+  0x12bf, 0x2d41, 0x12c8, 0x2d4a, 0x12d1, 0x2d53, 0x12d9, 0x2d5c,
+  0x12e2, 0x2d65, 0x12eb, 0x2d6e, 0x12f4, 0x2d76, 0x12fd, 0x2d7f,
+  0x1306, 0x2d88, 0x130f, 0x2d91, 0x1318, 0x2d9a, 0x1321, 0x2da3,
+  0x132a, 0x2dab, 0x1333, 0x2db4, 0x133c, 0x2dbd, 0x1345, 0x2dc6,
+  0x134e, 0x2dcf, 0x1357, 0x2dd7, 0x1360, 0x2de0, 0x1369, 0x2de9,
+  0x1372, 0x2df2, 0x137b, 0x2dfa, 0x1384, 0x2e03, 0x138d, 0x2e0c,
+  0x1396, 0x2e15, 0x139f, 0x2e1d, 0x13a8, 0x2e26, 0x13b1, 0x2e2f,
+  0x13ba, 0x2e37, 0x13c3, 0x2e40, 0x13cc, 0x2e49, 0x13d5, 0x2e51,
+  0x13df, 0x2e5a, 0x13e8, 0x2e63, 0x13f1, 0x2e6b, 0x13fa, 0x2e74,
+  0x1403, 0x2e7d, 0x140c, 0x2e85, 0x1415, 0x2e8e, 0x141e, 0x2e97,
+  0x1428, 0x2e9f, 0x1431, 0x2ea8, 0x143a, 0x2eb0, 0x1443, 0x2eb9,
+  0x144c, 0x2ec2, 0x1455, 0x2eca, 0x145f, 0x2ed3, 0x1468, 0x2edb,
+  0x1471, 0x2ee4, 0x147a, 0x2eec, 0x1483, 0x2ef5, 0x148d, 0x2efd,
+  0x1496, 0x2f06, 0x149f, 0x2f0e, 0x14a8, 0x2f17, 0x14b2, 0x2f20,
+  0x14bb, 0x2f28, 0x14c4, 0x2f30, 0x14cd, 0x2f39, 0x14d7, 0x2f41,
+  0x14e0, 0x2f4a, 0x14e9, 0x2f52, 0x14f3, 0x2f5b, 0x14fc, 0x2f63,
+  0x1505, 0x2f6c, 0x150e, 0x2f74, 0x1518, 0x2f7d, 0x1521, 0x2f85,
+  0x152a, 0x2f8d, 0x1534, 0x2f96, 0x153d, 0x2f9e, 0x1547, 0x2fa7,
+  0x1550, 0x2faf, 0x1559, 0x2fb7, 0x1563, 0x2fc0, 0x156c, 0x2fc8,
+  0x1575, 0x2fd0, 0x157f, 0x2fd9, 0x1588, 0x2fe1, 0x1592, 0x2fea,
+  0x159b, 0x2ff2, 0x15a4, 0x2ffa, 0x15ae, 0x3002, 0x15b7, 0x300b,
+  0x15c1, 0x3013, 0x15ca, 0x301b, 0x15d4, 0x3024, 0x15dd, 0x302c,
+  0x15e6, 0x3034, 0x15f0, 0x303c, 0x15f9, 0x3045, 0x1603, 0x304d,
+  0x160c, 0x3055, 0x1616, 0x305d, 0x161f, 0x3066, 0x1629, 0x306e,
+  0x1632, 0x3076, 0x163c, 0x307e, 0x1645, 0x3087, 0x164f, 0x308f,
+  0x1659, 0x3097, 0x1662, 0x309f, 0x166c, 0x30a7, 0x1675, 0x30af,
+  0x167f, 0x30b8, 0x1688, 0x30c0, 0x1692, 0x30c8, 0x169b, 0x30d0,
+  0x16a5, 0x30d8, 0x16af, 0x30e0, 0x16b8, 0x30e8, 0x16c2, 0x30f0,
+  0x16cb, 0x30f9, 0x16d5, 0x3101, 0x16df, 0x3109, 0x16e8, 0x3111,
+  0x16f2, 0x3119, 0x16fc, 0x3121, 0x1705, 0x3129, 0x170f, 0x3131,
+  0x1719, 0x3139, 0x1722, 0x3141, 0x172c, 0x3149, 0x1736, 0x3151,
+  0x173f, 0x3159, 0x1749, 0x3161, 0x1753, 0x3169, 0x175c, 0x3171,
+  0x1766, 0x3179, 0x1770, 0x3181, 0x177a, 0x3189, 0x1783, 0x3191,
+  0x178d, 0x3199, 0x1797, 0x31a1, 0x17a0, 0x31a9, 0x17aa, 0x31b1,
+  0x17b4, 0x31b9, 0x17be, 0x31c0, 0x17c8, 0x31c8, 0x17d1, 0x31d0,
+  0x17db, 0x31d8, 0x17e5, 0x31e0, 0x17ef, 0x31e8, 0x17f8, 0x31f0,
+  0x1802, 0x31f8, 0x180c, 0x31ff, 0x1816, 0x3207, 0x1820, 0x320f,
+  0x182a, 0x3217, 0x1833, 0x321f, 0x183d, 0x3227, 0x1847, 0x322e,
+  0x1851, 0x3236, 0x185b, 0x323e, 0x1865, 0x3246, 0x186f, 0x324e,
+  0x1878, 0x3255, 0x1882, 0x325d, 0x188c, 0x3265, 0x1896, 0x326d,
+  0x18a0, 0x3274, 0x18aa, 0x327c, 0x18b4, 0x3284, 0x18be, 0x328b,
+  0x18c8, 0x3293, 0x18d2, 0x329b, 0x18dc, 0x32a3, 0x18e6, 0x32aa,
+  0x18ef, 0x32b2, 0x18f9, 0x32ba, 0x1903, 0x32c1, 0x190d, 0x32c9,
+  0x1917, 0x32d0, 0x1921, 0x32d8, 0x192b, 0x32e0, 0x1935, 0x32e7,
+  0x193f, 0x32ef, 0x1949, 0x32f7, 0x1953, 0x32fe, 0x195d, 0x3306,
+  0x1967, 0x330d, 0x1971, 0x3315, 0x197b, 0x331d, 0x1985, 0x3324,
+  0x198f, 0x332c, 0x199a, 0x3333, 0x19a4, 0x333b, 0x19ae, 0x3342,
+  0x19b8, 0x334a, 0x19c2, 0x3351, 0x19cc, 0x3359, 0x19d6, 0x3360,
+  0x19e0, 0x3368, 0x19ea, 0x336f, 0x19f4, 0x3377, 0x19fe, 0x337e,
+  0x1a08, 0x3386, 0x1a13, 0x338d, 0x1a1d, 0x3395, 0x1a27, 0x339c,
+  0x1a31, 0x33a3, 0x1a3b, 0x33ab, 0x1a45, 0x33b2, 0x1a4f, 0x33ba,
+  0x1a5a, 0x33c1, 0x1a64, 0x33c8, 0x1a6e, 0x33d0, 0x1a78, 0x33d7,
+  0x1a82, 0x33df, 0x1a8c, 0x33e6, 0x1a97, 0x33ed, 0x1aa1, 0x33f5,
+  0x1aab, 0x33fc, 0x1ab5, 0x3403, 0x1abf, 0x340b, 0x1aca, 0x3412,
+  0x1ad4, 0x3419, 0x1ade, 0x3420, 0x1ae8, 0x3428, 0x1af3, 0x342f,
+  0x1afd, 0x3436, 0x1b07, 0x343e, 0x1b11, 0x3445, 0x1b1c, 0x344c,
+  0x1b26, 0x3453, 0x1b30, 0x345b, 0x1b3b, 0x3462, 0x1b45, 0x3469,
+  0x1b4f, 0x3470, 0x1b59, 0x3477, 0x1b64, 0x347f, 0x1b6e, 0x3486,
+  0x1b78, 0x348d, 0x1b83, 0x3494, 0x1b8d, 0x349b, 0x1b97, 0x34a2,
+  0x1ba2, 0x34aa, 0x1bac, 0x34b1, 0x1bb6, 0x34b8, 0x1bc1, 0x34bf,
+  0x1bcb, 0x34c6, 0x1bd5, 0x34cd, 0x1be0, 0x34d4, 0x1bea, 0x34db,
+  0x1bf5, 0x34e2, 0x1bff, 0x34ea, 0x1c09, 0x34f1, 0x1c14, 0x34f8,
+  0x1c1e, 0x34ff, 0x1c29, 0x3506, 0x1c33, 0x350d, 0x1c3d, 0x3514,
+  0x1c48, 0x351b, 0x1c52, 0x3522, 0x1c5d, 0x3529, 0x1c67, 0x3530,
+  0x1c72, 0x3537, 0x1c7c, 0x353e, 0x1c86, 0x3545, 0x1c91, 0x354c,
+  0x1c9b, 0x3553, 0x1ca6, 0x355a, 0x1cb0, 0x3561, 0x1cbb, 0x3567,
+  0x1cc5, 0x356e, 0x1cd0, 0x3575, 0x1cda, 0x357c, 0x1ce5, 0x3583,
+  0x1cef, 0x358a, 0x1cfa, 0x3591, 0x1d04, 0x3598, 0x1d0f, 0x359f,
+  0x1d19, 0x35a5, 0x1d24, 0x35ac, 0x1d2e, 0x35b3, 0x1d39, 0x35ba,
+  0x1d44, 0x35c1, 0x1d4e, 0x35c8, 0x1d59, 0x35ce, 0x1d63, 0x35d5,
+  0x1d6e, 0x35dc, 0x1d78, 0x35e3, 0x1d83, 0x35ea, 0x1d8e, 0x35f0,
+  0x1d98, 0x35f7, 0x1da3, 0x35fe, 0x1dad, 0x3605, 0x1db8, 0x360b,
+  0x1dc3, 0x3612, 0x1dcd, 0x3619, 0x1dd8, 0x3620, 0x1de2, 0x3626,
+  0x1ded, 0x362d, 0x1df8, 0x3634, 0x1e02, 0x363a, 0x1e0d, 0x3641,
+  0x1e18, 0x3648, 0x1e22, 0x364e, 0x1e2d, 0x3655, 0x1e38, 0x365c,
+  0x1e42, 0x3662, 0x1e4d, 0x3669, 0x1e58, 0x366f, 0x1e62, 0x3676,
+  0x1e6d, 0x367d, 0x1e78, 0x3683, 0x1e83, 0x368a, 0x1e8d, 0x3690,
+  0x1e98, 0x3697, 0x1ea3, 0x369d, 0x1ead, 0x36a4, 0x1eb8, 0x36ab,
+  0x1ec3, 0x36b1, 0x1ece, 0x36b8, 0x1ed8, 0x36be, 0x1ee3, 0x36c5,
+  0x1eee, 0x36cb, 0x1ef9, 0x36d2, 0x1f03, 0x36d8, 0x1f0e, 0x36df,
+  0x1f19, 0x36e5, 0x1f24, 0x36eb, 0x1f2f, 0x36f2, 0x1f39, 0x36f8,
+  0x1f44, 0x36ff, 0x1f4f, 0x3705, 0x1f5a, 0x370c, 0x1f65, 0x3712,
+  0x1f6f, 0x3718, 0x1f7a, 0x371f, 0x1f85, 0x3725, 0x1f90, 0x372c,
+  0x1f9b, 0x3732, 0x1fa5, 0x3738, 0x1fb0, 0x373f, 0x1fbb, 0x3745,
+  0x1fc6, 0x374b, 0x1fd1, 0x3752, 0x1fdc, 0x3758, 0x1fe7, 0x375e,
+  0x1ff1, 0x3765, 0x1ffc, 0x376b, 0x2007, 0x3771, 0x2012, 0x3777,
+  0x201d, 0x377e, 0x2028, 0x3784, 0x2033, 0x378a, 0x203e, 0x3790,
+  0x2049, 0x3797, 0x2054, 0x379d, 0x205e, 0x37a3, 0x2069, 0x37a9,
+  0x2074, 0x37b0, 0x207f, 0x37b6, 0x208a, 0x37bc, 0x2095, 0x37c2,
+  0x20a0, 0x37c8, 0x20ab, 0x37ce, 0x20b6, 0x37d5, 0x20c1, 0x37db,
+  0x20cc, 0x37e1, 0x20d7, 0x37e7, 0x20e2, 0x37ed, 0x20ed, 0x37f3,
+  0x20f8, 0x37f9, 0x2103, 0x37ff, 0x210e, 0x3805, 0x2119, 0x380b,
+  0x2124, 0x3812, 0x212f, 0x3818, 0x213a, 0x381e, 0x2145, 0x3824,
+  0x2150, 0x382a, 0x215b, 0x3830, 0x2166, 0x3836, 0x2171, 0x383c,
+  0x217c, 0x3842, 0x2187, 0x3848, 0x2192, 0x384e, 0x219d, 0x3854,
+  0x21a8, 0x385a, 0x21b3, 0x3860, 0x21be, 0x3866, 0x21ca, 0x386b,
+  0x21d5, 0x3871, 0x21e0, 0x3877, 0x21eb, 0x387d, 0x21f6, 0x3883,
+  0x2201, 0x3889, 0x220c, 0x388f, 0x2217, 0x3895, 0x2222, 0x389b,
+  0x222d, 0x38a1, 0x2239, 0x38a6, 0x2244, 0x38ac, 0x224f, 0x38b2,
+  0x225a, 0x38b8, 0x2265, 0x38be, 0x2270, 0x38c3, 0x227b, 0x38c9,
+  0x2287, 0x38cf, 0x2292, 0x38d5, 0x229d, 0x38db, 0x22a8, 0x38e0,
+  0x22b3, 0x38e6, 0x22be, 0x38ec, 0x22ca, 0x38f2, 0x22d5, 0x38f7,
+  0x22e0, 0x38fd, 0x22eb, 0x3903, 0x22f6, 0x3909, 0x2301, 0x390e,
+  0x230d, 0x3914, 0x2318, 0x391a, 0x2323, 0x391f, 0x232e, 0x3925,
+  0x233a, 0x392b, 0x2345, 0x3930, 0x2350, 0x3936, 0x235b, 0x393b,
+  0x2367, 0x3941, 0x2372, 0x3947, 0x237d, 0x394c, 0x2388, 0x3952,
+  0x2394, 0x3958, 0x239f, 0x395d, 0x23aa, 0x3963, 0x23b5, 0x3968,
+  0x23c1, 0x396e, 0x23cc, 0x3973, 0x23d7, 0x3979, 0x23e2, 0x397e,
+  0x23ee, 0x3984, 0x23f9, 0x3989, 0x2404, 0x398f, 0x2410, 0x3994,
+  0x241b, 0x399a, 0x2426, 0x399f, 0x2432, 0x39a5, 0x243d, 0x39aa,
+  0x2448, 0x39b0, 0x2454, 0x39b5, 0x245f, 0x39bb, 0x246a, 0x39c0,
+  0x2476, 0x39c5, 0x2481, 0x39cb, 0x248c, 0x39d0, 0x2498, 0x39d6,
+  0x24a3, 0x39db, 0x24ae, 0x39e0, 0x24ba, 0x39e6, 0x24c5, 0x39eb,
+  0x24d0, 0x39f0, 0x24dc, 0x39f6, 0x24e7, 0x39fb, 0x24f3, 0x3a00,
+  0x24fe, 0x3a06, 0x2509, 0x3a0b, 0x2515, 0x3a10, 0x2520, 0x3a16,
+  0x252c, 0x3a1b, 0x2537, 0x3a20, 0x2542, 0x3a25, 0x254e, 0x3a2b,
+  0x2559, 0x3a30, 0x2565, 0x3a35, 0x2570, 0x3a3a, 0x257c, 0x3a3f,
+  0x2587, 0x3a45, 0x2592, 0x3a4a, 0x259e, 0x3a4f, 0x25a9, 0x3a54,
+  0x25b5, 0x3a59, 0x25c0, 0x3a5f, 0x25cc, 0x3a64, 0x25d7, 0x3a69,
+  0x25e3, 0x3a6e, 0x25ee, 0x3a73, 0x25fa, 0x3a78, 0x2605, 0x3a7d,
+  0x2611, 0x3a82, 0x261c, 0x3a88, 0x2628, 0x3a8d, 0x2633, 0x3a92,
+  0x263f, 0x3a97, 0x264a, 0x3a9c, 0x2656, 0x3aa1, 0x2661, 0x3aa6,
+  0x266d, 0x3aab, 0x2678, 0x3ab0, 0x2684, 0x3ab5, 0x268f, 0x3aba,
+  0x269b, 0x3abf, 0x26a6, 0x3ac4, 0x26b2, 0x3ac9, 0x26bd, 0x3ace,
+  0x26c9, 0x3ad3, 0x26d4, 0x3ad8, 0x26e0, 0x3add, 0x26ec, 0x3ae2,
+  0x26f7, 0x3ae6, 0x2703, 0x3aeb, 0x270e, 0x3af0, 0x271a, 0x3af5,
+  0x2725, 0x3afa, 0x2731, 0x3aff, 0x273d, 0x3b04, 0x2748, 0x3b09,
+  0x2754, 0x3b0e, 0x275f, 0x3b12, 0x276b, 0x3b17, 0x2777, 0x3b1c,
+  0x2782, 0x3b21, 0x278e, 0x3b26, 0x2799, 0x3b2a, 0x27a5, 0x3b2f,
+  0x27b1, 0x3b34, 0x27bc, 0x3b39, 0x27c8, 0x3b3e, 0x27d3, 0x3b42,
+  0x27df, 0x3b47, 0x27eb, 0x3b4c, 0x27f6, 0x3b50, 0x2802, 0x3b55,
+  0x280e, 0x3b5a, 0x2819, 0x3b5f, 0x2825, 0x3b63, 0x2831, 0x3b68,
+  0x283c, 0x3b6d, 0x2848, 0x3b71, 0x2854, 0x3b76, 0x285f, 0x3b7b,
+  0x286b, 0x3b7f, 0x2877, 0x3b84, 0x2882, 0x3b88, 0x288e, 0x3b8d,
+  0x289a, 0x3b92, 0x28a5, 0x3b96, 0x28b1, 0x3b9b, 0x28bd, 0x3b9f,
+  0x28c9, 0x3ba4, 0x28d4, 0x3ba9, 0x28e0, 0x3bad, 0x28ec, 0x3bb2,
+  0x28f7, 0x3bb6, 0x2903, 0x3bbb, 0x290f, 0x3bbf, 0x291b, 0x3bc4,
+  0x2926, 0x3bc8, 0x2932, 0x3bcd, 0x293e, 0x3bd1, 0x294a, 0x3bd6,
+  0x2955, 0x3bda, 0x2961, 0x3bde, 0x296d, 0x3be3, 0x2979, 0x3be7,
+  0x2984, 0x3bec, 0x2990, 0x3bf0, 0x299c, 0x3bf5, 0x29a8, 0x3bf9,
+  0x29b4, 0x3bfd, 0x29bf, 0x3c02, 0x29cb, 0x3c06, 0x29d7, 0x3c0a,
+  0x29e3, 0x3c0f, 0x29ee, 0x3c13, 0x29fa, 0x3c17, 0x2a06, 0x3c1c,
+  0x2a12, 0x3c20, 0x2a1e, 0x3c24, 0x2a29, 0x3c29, 0x2a35, 0x3c2d,
+  0x2a41, 0x3c31, 0x2a4d, 0x3c36, 0x2a59, 0x3c3a, 0x2a65, 0x3c3e,
+  0x2a70, 0x3c42, 0x2a7c, 0x3c46, 0x2a88, 0x3c4b, 0x2a94, 0x3c4f,
+  0x2aa0, 0x3c53, 0x2aac, 0x3c57, 0x2ab7, 0x3c5b, 0x2ac3, 0x3c60,
+  0x2acf, 0x3c64, 0x2adb, 0x3c68, 0x2ae7, 0x3c6c, 0x2af3, 0x3c70,
+  0x2aff, 0x3c74, 0x2b0a, 0x3c79, 0x2b16, 0x3c7d, 0x2b22, 0x3c81,
+  0x2b2e, 0x3c85, 0x2b3a, 0x3c89, 0x2b46, 0x3c8d, 0x2b52, 0x3c91,
+  0x2b5e, 0x3c95, 0x2b6a, 0x3c99, 0x2b75, 0x3c9d, 0x2b81, 0x3ca1,
+  0x2b8d, 0x3ca5, 0x2b99, 0x3ca9, 0x2ba5, 0x3cad, 0x2bb1, 0x3cb1,
+  0x2bbd, 0x3cb5, 0x2bc9, 0x3cb9, 0x2bd5, 0x3cbd, 0x2be1, 0x3cc1,
+  0x2bed, 0x3cc5, 0x2bf9, 0x3cc9, 0x2c05, 0x3ccd, 0x2c10, 0x3cd1,
+  0x2c1c, 0x3cd5, 0x2c28, 0x3cd9, 0x2c34, 0x3cdd, 0x2c40, 0x3ce0,
+  0x2c4c, 0x3ce4, 0x2c58, 0x3ce8, 0x2c64, 0x3cec, 0x2c70, 0x3cf0,
+  0x2c7c, 0x3cf4, 0x2c88, 0x3cf8, 0x2c94, 0x3cfb, 0x2ca0, 0x3cff,
+  0x2cac, 0x3d03, 0x2cb8, 0x3d07, 0x2cc4, 0x3d0b, 0x2cd0, 0x3d0e,
+  0x2cdc, 0x3d12, 0x2ce8, 0x3d16, 0x2cf4, 0x3d1a, 0x2d00, 0x3d1d,
+  0x2d0c, 0x3d21, 0x2d18, 0x3d25, 0x2d24, 0x3d28, 0x2d30, 0x3d2c,
+  0x2d3c, 0x3d30, 0x2d48, 0x3d34, 0x2d54, 0x3d37, 0x2d60, 0x3d3b,
+  0x2d6c, 0x3d3f, 0x2d78, 0x3d42, 0x2d84, 0x3d46, 0x2d90, 0x3d49,
+  0x2d9c, 0x3d4d, 0x2da8, 0x3d51, 0x2db4, 0x3d54, 0x2dc0, 0x3d58,
+  0x2dcc, 0x3d5b, 0x2dd8, 0x3d5f, 0x2de4, 0x3d63, 0x2df0, 0x3d66,
+  0x2dfc, 0x3d6a, 0x2e09, 0x3d6d, 0x2e15, 0x3d71, 0x2e21, 0x3d74,
+  0x2e2d, 0x3d78, 0x2e39, 0x3d7b, 0x2e45, 0x3d7f, 0x2e51, 0x3d82,
+  0x2e5d, 0x3d86, 0x2e69, 0x3d89, 0x2e75, 0x3d8d, 0x2e81, 0x3d90,
+  0x2e8d, 0x3d93, 0x2e99, 0x3d97, 0x2ea6, 0x3d9a, 0x2eb2, 0x3d9e,
+  0x2ebe, 0x3da1, 0x2eca, 0x3da4, 0x2ed6, 0x3da8, 0x2ee2, 0x3dab,
+  0x2eee, 0x3daf, 0x2efa, 0x3db2, 0x2f06, 0x3db5, 0x2f13, 0x3db9,
+  0x2f1f, 0x3dbc, 0x2f2b, 0x3dbf, 0x2f37, 0x3dc2, 0x2f43, 0x3dc6,
+  0x2f4f, 0x3dc9, 0x2f5b, 0x3dcc, 0x2f67, 0x3dd0, 0x2f74, 0x3dd3,
+  0x2f80, 0x3dd6, 0x2f8c, 0x3dd9, 0x2f98, 0x3ddd, 0x2fa4, 0x3de0,
+  0x2fb0, 0x3de3, 0x2fbc, 0x3de6, 0x2fc9, 0x3de9, 0x2fd5, 0x3ded,
+  0x2fe1, 0x3df0, 0x2fed, 0x3df3, 0x2ff9, 0x3df6, 0x3005, 0x3df9,
+  0x3012, 0x3dfc, 0x301e, 0x3dff, 0x302a, 0x3e03, 0x3036, 0x3e06,
+  0x3042, 0x3e09, 0x304e, 0x3e0c, 0x305b, 0x3e0f, 0x3067, 0x3e12,
+  0x3073, 0x3e15, 0x307f, 0x3e18, 0x308b, 0x3e1b, 0x3098, 0x3e1e,
+  0x30a4, 0x3e21, 0x30b0, 0x3e24, 0x30bc, 0x3e27, 0x30c8, 0x3e2a,
+  0x30d5, 0x3e2d, 0x30e1, 0x3e30, 0x30ed, 0x3e33, 0x30f9, 0x3e36,
+  0x3105, 0x3e39, 0x3112, 0x3e3c, 0x311e, 0x3e3f, 0x312a, 0x3e42,
+  0x3136, 0x3e45, 0x3143, 0x3e48, 0x314f, 0x3e4a, 0x315b, 0x3e4d,
+  0x3167, 0x3e50, 0x3174, 0x3e53, 0x3180, 0x3e56, 0x318c, 0x3e59,
+  0x3198, 0x3e5c, 0x31a4, 0x3e5e, 0x31b1, 0x3e61, 0x31bd, 0x3e64,
+  0x31c9, 0x3e67, 0x31d5, 0x3e6a, 0x31e2, 0x3e6c, 0x31ee, 0x3e6f,
+  0x31fa, 0x3e72, 0x3207, 0x3e75, 0x3213, 0x3e77, 0x321f, 0x3e7a,
+  0x322b, 0x3e7d, 0x3238, 0x3e80, 0x3244, 0x3e82, 0x3250, 0x3e85,
+  0x325c, 0x3e88, 0x3269, 0x3e8a, 0x3275, 0x3e8d, 0x3281, 0x3e90,
+  0x328e, 0x3e92, 0x329a, 0x3e95, 0x32a6, 0x3e98, 0x32b2, 0x3e9a,
+  0x32bf, 0x3e9d, 0x32cb, 0x3e9f, 0x32d7, 0x3ea2, 0x32e4, 0x3ea5,
+  0x32f0, 0x3ea7, 0x32fc, 0x3eaa, 0x3308, 0x3eac, 0x3315, 0x3eaf,
+  0x3321, 0x3eb1, 0x332d, 0x3eb4, 0x333a, 0x3eb6, 0x3346, 0x3eb9,
+  0x3352, 0x3ebb, 0x335f, 0x3ebe, 0x336b, 0x3ec0, 0x3377, 0x3ec3,
+  0x3384, 0x3ec5, 0x3390, 0x3ec8, 0x339c, 0x3eca, 0x33a9, 0x3ecc,
+  0x33b5, 0x3ecf, 0x33c1, 0x3ed1, 0x33ce, 0x3ed4, 0x33da, 0x3ed6,
+  0x33e6, 0x3ed8, 0x33f3, 0x3edb, 0x33ff, 0x3edd, 0x340b, 0x3ee0,
+  0x3418, 0x3ee2, 0x3424, 0x3ee4, 0x3430, 0x3ee7, 0x343d, 0x3ee9,
+  0x3449, 0x3eeb, 0x3455, 0x3eed, 0x3462, 0x3ef0, 0x346e, 0x3ef2,
+  0x347b, 0x3ef4, 0x3487, 0x3ef7, 0x3493, 0x3ef9, 0x34a0, 0x3efb,
+  0x34ac, 0x3efd, 0x34b8, 0x3f00, 0x34c5, 0x3f02, 0x34d1, 0x3f04,
+  0x34dd, 0x3f06, 0x34ea, 0x3f08, 0x34f6, 0x3f0a, 0x3503, 0x3f0d,
+  0x350f, 0x3f0f, 0x351b, 0x3f11, 0x3528, 0x3f13, 0x3534, 0x3f15,
+  0x3540, 0x3f17, 0x354d, 0x3f19, 0x3559, 0x3f1c, 0x3566, 0x3f1e,
+  0x3572, 0x3f20, 0x357e, 0x3f22, 0x358b, 0x3f24, 0x3597, 0x3f26,
+  0x35a4, 0x3f28, 0x35b0, 0x3f2a, 0x35bc, 0x3f2c, 0x35c9, 0x3f2e,
+  0x35d5, 0x3f30, 0x35e2, 0x3f32, 0x35ee, 0x3f34, 0x35fa, 0x3f36,
+  0x3607, 0x3f38, 0x3613, 0x3f3a, 0x3620, 0x3f3c, 0x362c, 0x3f3e,
+  0x3639, 0x3f40, 0x3645, 0x3f42, 0x3651, 0x3f43, 0x365e, 0x3f45,
+  0x366a, 0x3f47, 0x3677, 0x3f49, 0x3683, 0x3f4b, 0x3690, 0x3f4d,
+  0x369c, 0x3f4f, 0x36a8, 0x3f51, 0x36b5, 0x3f52, 0x36c1, 0x3f54,
+  0x36ce, 0x3f56, 0x36da, 0x3f58, 0x36e7, 0x3f5a, 0x36f3, 0x3f5b,
+  0x36ff, 0x3f5d, 0x370c, 0x3f5f, 0x3718, 0x3f61, 0x3725, 0x3f62,
+  0x3731, 0x3f64, 0x373e, 0x3f66, 0x374a, 0x3f68, 0x3757, 0x3f69,
+  0x3763, 0x3f6b, 0x376f, 0x3f6d, 0x377c, 0x3f6e, 0x3788, 0x3f70,
+  0x3795, 0x3f72, 0x37a1, 0x3f73, 0x37ae, 0x3f75, 0x37ba, 0x3f77,
+  0x37c7, 0x3f78, 0x37d3, 0x3f7a, 0x37e0, 0x3f7b, 0x37ec, 0x3f7d,
+  0x37f9, 0x3f7f, 0x3805, 0x3f80, 0x3811, 0x3f82, 0x381e, 0x3f83,
+  0x382a, 0x3f85, 0x3837, 0x3f86, 0x3843, 0x3f88, 0x3850, 0x3f89,
+  0x385c, 0x3f8b, 0x3869, 0x3f8c, 0x3875, 0x3f8e, 0x3882, 0x3f8f,
+  0x388e, 0x3f91, 0x389b, 0x3f92, 0x38a7, 0x3f94, 0x38b4, 0x3f95,
+  0x38c0, 0x3f97, 0x38cd, 0x3f98, 0x38d9, 0x3f99, 0x38e6, 0x3f9b,
+  0x38f2, 0x3f9c, 0x38ff, 0x3f9e, 0x390b, 0x3f9f, 0x3918, 0x3fa0,
+  0x3924, 0x3fa2, 0x3931, 0x3fa3, 0x393d, 0x3fa4, 0x394a, 0x3fa6,
+  0x3956, 0x3fa7, 0x3963, 0x3fa8, 0x396f, 0x3faa, 0x397c, 0x3fab,
+  0x3988, 0x3fac, 0x3995, 0x3fad, 0x39a1, 0x3faf, 0x39ae, 0x3fb0,
+  0x39ba, 0x3fb1, 0x39c7, 0x3fb2, 0x39d3, 0x3fb4, 0x39e0, 0x3fb5,
+  0x39ec, 0x3fb6, 0x39f9, 0x3fb7, 0x3a05, 0x3fb8, 0x3a12, 0x3fb9,
+  0x3a1e, 0x3fbb, 0x3a2b, 0x3fbc, 0x3a37, 0x3fbd, 0x3a44, 0x3fbe,
+  0x3a50, 0x3fbf, 0x3a5d, 0x3fc0, 0x3a69, 0x3fc1, 0x3a76, 0x3fc3,
+  0x3a82, 0x3fc4, 0x3a8f, 0x3fc5, 0x3a9b, 0x3fc6, 0x3aa8, 0x3fc7,
+  0x3ab4, 0x3fc8, 0x3ac1, 0x3fc9, 0x3acd, 0x3fca, 0x3ada, 0x3fcb,
+  0x3ae6, 0x3fcc, 0x3af3, 0x3fcd, 0x3b00, 0x3fce, 0x3b0c, 0x3fcf,
+  0x3b19, 0x3fd0, 0x3b25, 0x3fd1, 0x3b32, 0x3fd2, 0x3b3e, 0x3fd3,
+  0x3b4b, 0x3fd4, 0x3b57, 0x3fd5, 0x3b64, 0x3fd5, 0x3b70, 0x3fd6,
+  0x3b7d, 0x3fd7, 0x3b89, 0x3fd8, 0x3b96, 0x3fd9, 0x3ba2, 0x3fda,
+  0x3baf, 0x3fdb, 0x3bbc, 0x3fdc, 0x3bc8, 0x3fdc, 0x3bd5, 0x3fdd,
+  0x3be1, 0x3fde, 0x3bee, 0x3fdf, 0x3bfa, 0x3fe0, 0x3c07, 0x3fe0,
+  0x3c13, 0x3fe1, 0x3c20, 0x3fe2, 0x3c2c, 0x3fe3, 0x3c39, 0x3fe3,
+  0x3c45, 0x3fe4, 0x3c52, 0x3fe5, 0x3c5f, 0x3fe6, 0x3c6b, 0x3fe6,
+  0x3c78, 0x3fe7, 0x3c84, 0x3fe8, 0x3c91, 0x3fe8, 0x3c9d, 0x3fe9,
+  0x3caa, 0x3fea, 0x3cb6, 0x3fea, 0x3cc3, 0x3feb, 0x3cd0, 0x3fec,
+  0x3cdc, 0x3fec, 0x3ce9, 0x3fed, 0x3cf5, 0x3fed, 0x3d02, 0x3fee,
+  0x3d0e, 0x3fef, 0x3d1b, 0x3fef, 0x3d27, 0x3ff0, 0x3d34, 0x3ff0,
+  0x3d40, 0x3ff1, 0x3d4d, 0x3ff1, 0x3d5a, 0x3ff2, 0x3d66, 0x3ff2,
+  0x3d73, 0x3ff3, 0x3d7f, 0x3ff3, 0x3d8c, 0x3ff4, 0x3d98, 0x3ff4,
+  0x3da5, 0x3ff5, 0x3db2, 0x3ff5, 0x3dbe, 0x3ff6, 0x3dcb, 0x3ff6,
+  0x3dd7, 0x3ff7, 0x3de4, 0x3ff7, 0x3df0, 0x3ff7, 0x3dfd, 0x3ff8,
+  0x3e09, 0x3ff8, 0x3e16, 0x3ff9, 0x3e23, 0x3ff9, 0x3e2f, 0x3ff9,
+  0x3e3c, 0x3ffa, 0x3e48, 0x3ffa, 0x3e55, 0x3ffa, 0x3e61, 0x3ffb,
+  0x3e6e, 0x3ffb, 0x3e7a, 0x3ffb, 0x3e87, 0x3ffc, 0x3e94, 0x3ffc,
+  0x3ea0, 0x3ffc, 0x3ead, 0x3ffc, 0x3eb9, 0x3ffd, 0x3ec6, 0x3ffd,
+  0x3ed2, 0x3ffd, 0x3edf, 0x3ffd, 0x3eec, 0x3ffe, 0x3ef8, 0x3ffe,
+  0x3f05, 0x3ffe, 0x3f11, 0x3ffe, 0x3f1e, 0x3ffe, 0x3f2a, 0x3fff,
+  0x3f37, 0x3fff, 0x3f44, 0x3fff, 0x3f50, 0x3fff, 0x3f5d, 0x3fff,
+  0x3f69, 0x3fff, 0x3f76, 0x3fff, 0x3f82, 0x4000, 0x3f8f, 0x4000,
+  0x3f9b, 0x4000, 0x3fa8, 0x4000, 0x3fb5, 0x4000, 0x3fc1, 0x4000,
+  0x3fce, 0x4000, 0x3fda, 0x4000, 0x3fe7, 0x4000, 0x3ff3, 0x4000,
+};
+
+/**    
+* \par   
+* Generation of real_CoefB array:    
+* \par    
+* n = 4096    
+* 
for (i = 0; i < n; i++)    
+*  {    
+*    pBTable[2 * i] = 0.5 * (1.0 + sin (2 * PI / (double) (2 * n) * (double) i));    
+*    pBTable[2 * i + 1] = 0.5 * (1.0 * cos (2 * PI / (double) (2 * n) * (double) i));    
+*  } 
   
+* \par    
+* Convert to fixed point Q15 format    
+*       round(pBTable[i] * pow(2, 15))    
+*    
+*/
+
+static const q15_t ALIGN4 realCoefBQ15[8192] = {
+  0x4000, 0x4000, 0x400d, 0x4000, 0x4019, 0x4000, 0x4026, 0x4000,
+  0x4032, 0x4000, 0x403f, 0x4000, 0x404b, 0x4000, 0x4058, 0x4000,
+  0x4065, 0x4000, 0x4071, 0x4000, 0x407e, 0x4000, 0x408a, 0x3fff,
+  0x4097, 0x3fff, 0x40a3, 0x3fff, 0x40b0, 0x3fff, 0x40bc, 0x3fff,
+  0x40c9, 0x3fff, 0x40d6, 0x3fff, 0x40e2, 0x3ffe, 0x40ef, 0x3ffe,
+  0x40fb, 0x3ffe, 0x4108, 0x3ffe, 0x4114, 0x3ffe, 0x4121, 0x3ffd,
+  0x412e, 0x3ffd, 0x413a, 0x3ffd, 0x4147, 0x3ffd, 0x4153, 0x3ffc,
+  0x4160, 0x3ffc, 0x416c, 0x3ffc, 0x4179, 0x3ffc, 0x4186, 0x3ffb,
+  0x4192, 0x3ffb, 0x419f, 0x3ffb, 0x41ab, 0x3ffa, 0x41b8, 0x3ffa,
+  0x41c4, 0x3ffa, 0x41d1, 0x3ff9, 0x41dd, 0x3ff9, 0x41ea, 0x3ff9,
+  0x41f7, 0x3ff8, 0x4203, 0x3ff8, 0x4210, 0x3ff7, 0x421c, 0x3ff7,
+  0x4229, 0x3ff7, 0x4235, 0x3ff6, 0x4242, 0x3ff6, 0x424e, 0x3ff5,
+  0x425b, 0x3ff5, 0x4268, 0x3ff4, 0x4274, 0x3ff4, 0x4281, 0x3ff3,
+  0x428d, 0x3ff3, 0x429a, 0x3ff2, 0x42a6, 0x3ff2, 0x42b3, 0x3ff1,
+  0x42c0, 0x3ff1, 0x42cc, 0x3ff0, 0x42d9, 0x3ff0, 0x42e5, 0x3fef,
+  0x42f2, 0x3fef, 0x42fe, 0x3fee, 0x430b, 0x3fed, 0x4317, 0x3fed,
+  0x4324, 0x3fec, 0x4330, 0x3fec, 0x433d, 0x3feb, 0x434a, 0x3fea,
+  0x4356, 0x3fea, 0x4363, 0x3fe9, 0x436f, 0x3fe8, 0x437c, 0x3fe8,
+  0x4388, 0x3fe7, 0x4395, 0x3fe6, 0x43a1, 0x3fe6, 0x43ae, 0x3fe5,
+  0x43bb, 0x3fe4, 0x43c7, 0x3fe3, 0x43d4, 0x3fe3, 0x43e0, 0x3fe2,
+  0x43ed, 0x3fe1, 0x43f9, 0x3fe0, 0x4406, 0x3fe0, 0x4412, 0x3fdf,
+  0x441f, 0x3fde, 0x442b, 0x3fdd, 0x4438, 0x3fdc, 0x4444, 0x3fdc,
+  0x4451, 0x3fdb, 0x445e, 0x3fda, 0x446a, 0x3fd9, 0x4477, 0x3fd8,
+  0x4483, 0x3fd7, 0x4490, 0x3fd6, 0x449c, 0x3fd5, 0x44a9, 0x3fd5,
+  0x44b5, 0x3fd4, 0x44c2, 0x3fd3, 0x44ce, 0x3fd2, 0x44db, 0x3fd1,
+  0x44e7, 0x3fd0, 0x44f4, 0x3fcf, 0x4500, 0x3fce, 0x450d, 0x3fcd,
+  0x451a, 0x3fcc, 0x4526, 0x3fcb, 0x4533, 0x3fca, 0x453f, 0x3fc9,
+  0x454c, 0x3fc8, 0x4558, 0x3fc7, 0x4565, 0x3fc6, 0x4571, 0x3fc5,
+  0x457e, 0x3fc4, 0x458a, 0x3fc3, 0x4597, 0x3fc1, 0x45a3, 0x3fc0,
+  0x45b0, 0x3fbf, 0x45bc, 0x3fbe, 0x45c9, 0x3fbd, 0x45d5, 0x3fbc,
+  0x45e2, 0x3fbb, 0x45ee, 0x3fb9, 0x45fb, 0x3fb8, 0x4607, 0x3fb7,
+  0x4614, 0x3fb6, 0x4620, 0x3fb5, 0x462d, 0x3fb4, 0x4639, 0x3fb2,
+  0x4646, 0x3fb1, 0x4652, 0x3fb0, 0x465f, 0x3faf, 0x466b, 0x3fad,
+  0x4678, 0x3fac, 0x4684, 0x3fab, 0x4691, 0x3faa, 0x469d, 0x3fa8,
+  0x46aa, 0x3fa7, 0x46b6, 0x3fa6, 0x46c3, 0x3fa4, 0x46cf, 0x3fa3,
+  0x46dc, 0x3fa2, 0x46e8, 0x3fa0, 0x46f5, 0x3f9f, 0x4701, 0x3f9e,
+  0x470e, 0x3f9c, 0x471a, 0x3f9b, 0x4727, 0x3f99, 0x4733, 0x3f98,
+  0x4740, 0x3f97, 0x474c, 0x3f95, 0x4759, 0x3f94, 0x4765, 0x3f92,
+  0x4772, 0x3f91, 0x477e, 0x3f8f, 0x478b, 0x3f8e, 0x4797, 0x3f8c,
+  0x47a4, 0x3f8b, 0x47b0, 0x3f89, 0x47bd, 0x3f88, 0x47c9, 0x3f86,
+  0x47d6, 0x3f85, 0x47e2, 0x3f83, 0x47ef, 0x3f82, 0x47fb, 0x3f80,
+  0x4807, 0x3f7f, 0x4814, 0x3f7d, 0x4820, 0x3f7b, 0x482d, 0x3f7a,
+  0x4839, 0x3f78, 0x4846, 0x3f77, 0x4852, 0x3f75, 0x485f, 0x3f73,
+  0x486b, 0x3f72, 0x4878, 0x3f70, 0x4884, 0x3f6e, 0x4891, 0x3f6d,
+  0x489d, 0x3f6b, 0x48a9, 0x3f69, 0x48b6, 0x3f68, 0x48c2, 0x3f66,
+  0x48cf, 0x3f64, 0x48db, 0x3f62, 0x48e8, 0x3f61, 0x48f4, 0x3f5f,
+  0x4901, 0x3f5d, 0x490d, 0x3f5b, 0x4919, 0x3f5a, 0x4926, 0x3f58,
+  0x4932, 0x3f56, 0x493f, 0x3f54, 0x494b, 0x3f52, 0x4958, 0x3f51,
+  0x4964, 0x3f4f, 0x4970, 0x3f4d, 0x497d, 0x3f4b, 0x4989, 0x3f49,
+  0x4996, 0x3f47, 0x49a2, 0x3f45, 0x49af, 0x3f43, 0x49bb, 0x3f42,
+  0x49c7, 0x3f40, 0x49d4, 0x3f3e, 0x49e0, 0x3f3c, 0x49ed, 0x3f3a,
+  0x49f9, 0x3f38, 0x4a06, 0x3f36, 0x4a12, 0x3f34, 0x4a1e, 0x3f32,
+  0x4a2b, 0x3f30, 0x4a37, 0x3f2e, 0x4a44, 0x3f2c, 0x4a50, 0x3f2a,
+  0x4a5c, 0x3f28, 0x4a69, 0x3f26, 0x4a75, 0x3f24, 0x4a82, 0x3f22,
+  0x4a8e, 0x3f20, 0x4a9a, 0x3f1e, 0x4aa7, 0x3f1c, 0x4ab3, 0x3f19,
+  0x4ac0, 0x3f17, 0x4acc, 0x3f15, 0x4ad8, 0x3f13, 0x4ae5, 0x3f11,
+  0x4af1, 0x3f0f, 0x4afd, 0x3f0d, 0x4b0a, 0x3f0a, 0x4b16, 0x3f08,
+  0x4b23, 0x3f06, 0x4b2f, 0x3f04, 0x4b3b, 0x3f02, 0x4b48, 0x3f00,
+  0x4b54, 0x3efd, 0x4b60, 0x3efb, 0x4b6d, 0x3ef9, 0x4b79, 0x3ef7,
+  0x4b85, 0x3ef4, 0x4b92, 0x3ef2, 0x4b9e, 0x3ef0, 0x4bab, 0x3eed,
+  0x4bb7, 0x3eeb, 0x4bc3, 0x3ee9, 0x4bd0, 0x3ee7, 0x4bdc, 0x3ee4,
+  0x4be8, 0x3ee2, 0x4bf5, 0x3ee0, 0x4c01, 0x3edd, 0x4c0d, 0x3edb,
+  0x4c1a, 0x3ed8, 0x4c26, 0x3ed6, 0x4c32, 0x3ed4, 0x4c3f, 0x3ed1,
+  0x4c4b, 0x3ecf, 0x4c57, 0x3ecc, 0x4c64, 0x3eca, 0x4c70, 0x3ec8,
+  0x4c7c, 0x3ec5, 0x4c89, 0x3ec3, 0x4c95, 0x3ec0, 0x4ca1, 0x3ebe,
+  0x4cae, 0x3ebb, 0x4cba, 0x3eb9, 0x4cc6, 0x3eb6, 0x4cd3, 0x3eb4,
+  0x4cdf, 0x3eb1, 0x4ceb, 0x3eaf, 0x4cf8, 0x3eac, 0x4d04, 0x3eaa,
+  0x4d10, 0x3ea7, 0x4d1c, 0x3ea5, 0x4d29, 0x3ea2, 0x4d35, 0x3e9f,
+  0x4d41, 0x3e9d, 0x4d4e, 0x3e9a, 0x4d5a, 0x3e98, 0x4d66, 0x3e95,
+  0x4d72, 0x3e92, 0x4d7f, 0x3e90, 0x4d8b, 0x3e8d, 0x4d97, 0x3e8a,
+  0x4da4, 0x3e88, 0x4db0, 0x3e85, 0x4dbc, 0x3e82, 0x4dc8, 0x3e80,
+  0x4dd5, 0x3e7d, 0x4de1, 0x3e7a, 0x4ded, 0x3e77, 0x4df9, 0x3e75,
+  0x4e06, 0x3e72, 0x4e12, 0x3e6f, 0x4e1e, 0x3e6c, 0x4e2b, 0x3e6a,
+  0x4e37, 0x3e67, 0x4e43, 0x3e64, 0x4e4f, 0x3e61, 0x4e5c, 0x3e5e,
+  0x4e68, 0x3e5c, 0x4e74, 0x3e59, 0x4e80, 0x3e56, 0x4e8c, 0x3e53,
+  0x4e99, 0x3e50, 0x4ea5, 0x3e4d, 0x4eb1, 0x3e4a, 0x4ebd, 0x3e48,
+  0x4eca, 0x3e45, 0x4ed6, 0x3e42, 0x4ee2, 0x3e3f, 0x4eee, 0x3e3c,
+  0x4efb, 0x3e39, 0x4f07, 0x3e36, 0x4f13, 0x3e33, 0x4f1f, 0x3e30,
+  0x4f2b, 0x3e2d, 0x4f38, 0x3e2a, 0x4f44, 0x3e27, 0x4f50, 0x3e24,
+  0x4f5c, 0x3e21, 0x4f68, 0x3e1e, 0x4f75, 0x3e1b, 0x4f81, 0x3e18,
+  0x4f8d, 0x3e15, 0x4f99, 0x3e12, 0x4fa5, 0x3e0f, 0x4fb2, 0x3e0c,
+  0x4fbe, 0x3e09, 0x4fca, 0x3e06, 0x4fd6, 0x3e03, 0x4fe2, 0x3dff,
+  0x4fee, 0x3dfc, 0x4ffb, 0x3df9, 0x5007, 0x3df6, 0x5013, 0x3df3,
+  0x501f, 0x3df0, 0x502b, 0x3ded, 0x5037, 0x3de9, 0x5044, 0x3de6,
+  0x5050, 0x3de3, 0x505c, 0x3de0, 0x5068, 0x3ddd, 0x5074, 0x3dd9,
+  0x5080, 0x3dd6, 0x508c, 0x3dd3, 0x5099, 0x3dd0, 0x50a5, 0x3dcc,
+  0x50b1, 0x3dc9, 0x50bd, 0x3dc6, 0x50c9, 0x3dc2, 0x50d5, 0x3dbf,
+  0x50e1, 0x3dbc, 0x50ed, 0x3db9, 0x50fa, 0x3db5, 0x5106, 0x3db2,
+  0x5112, 0x3daf, 0x511e, 0x3dab, 0x512a, 0x3da8, 0x5136, 0x3da4,
+  0x5142, 0x3da1, 0x514e, 0x3d9e, 0x515a, 0x3d9a, 0x5167, 0x3d97,
+  0x5173, 0x3d93, 0x517f, 0x3d90, 0x518b, 0x3d8d, 0x5197, 0x3d89,
+  0x51a3, 0x3d86, 0x51af, 0x3d82, 0x51bb, 0x3d7f, 0x51c7, 0x3d7b,
+  0x51d3, 0x3d78, 0x51df, 0x3d74, 0x51eb, 0x3d71, 0x51f7, 0x3d6d,
+  0x5204, 0x3d6a, 0x5210, 0x3d66, 0x521c, 0x3d63, 0x5228, 0x3d5f,
+  0x5234, 0x3d5b, 0x5240, 0x3d58, 0x524c, 0x3d54, 0x5258, 0x3d51,
+  0x5264, 0x3d4d, 0x5270, 0x3d49, 0x527c, 0x3d46, 0x5288, 0x3d42,
+  0x5294, 0x3d3f, 0x52a0, 0x3d3b, 0x52ac, 0x3d37, 0x52b8, 0x3d34,
+  0x52c4, 0x3d30, 0x52d0, 0x3d2c, 0x52dc, 0x3d28, 0x52e8, 0x3d25,
+  0x52f4, 0x3d21, 0x5300, 0x3d1d, 0x530c, 0x3d1a, 0x5318, 0x3d16,
+  0x5324, 0x3d12, 0x5330, 0x3d0e, 0x533c, 0x3d0b, 0x5348, 0x3d07,
+  0x5354, 0x3d03, 0x5360, 0x3cff, 0x536c, 0x3cfb, 0x5378, 0x3cf8,
+  0x5384, 0x3cf4, 0x5390, 0x3cf0, 0x539c, 0x3cec, 0x53a8, 0x3ce8,
+  0x53b4, 0x3ce4, 0x53c0, 0x3ce0, 0x53cc, 0x3cdd, 0x53d8, 0x3cd9,
+  0x53e4, 0x3cd5, 0x53f0, 0x3cd1, 0x53fb, 0x3ccd, 0x5407, 0x3cc9,
+  0x5413, 0x3cc5, 0x541f, 0x3cc1, 0x542b, 0x3cbd, 0x5437, 0x3cb9,
+  0x5443, 0x3cb5, 0x544f, 0x3cb1, 0x545b, 0x3cad, 0x5467, 0x3ca9,
+  0x5473, 0x3ca5, 0x547f, 0x3ca1, 0x548b, 0x3c9d, 0x5496, 0x3c99,
+  0x54a2, 0x3c95, 0x54ae, 0x3c91, 0x54ba, 0x3c8d, 0x54c6, 0x3c89,
+  0x54d2, 0x3c85, 0x54de, 0x3c81, 0x54ea, 0x3c7d, 0x54f6, 0x3c79,
+  0x5501, 0x3c74, 0x550d, 0x3c70, 0x5519, 0x3c6c, 0x5525, 0x3c68,
+  0x5531, 0x3c64, 0x553d, 0x3c60, 0x5549, 0x3c5b, 0x5554, 0x3c57,
+  0x5560, 0x3c53, 0x556c, 0x3c4f, 0x5578, 0x3c4b, 0x5584, 0x3c46,
+  0x5590, 0x3c42, 0x559b, 0x3c3e, 0x55a7, 0x3c3a, 0x55b3, 0x3c36,
+  0x55bf, 0x3c31, 0x55cb, 0x3c2d, 0x55d7, 0x3c29, 0x55e2, 0x3c24,
+  0x55ee, 0x3c20, 0x55fa, 0x3c1c, 0x5606, 0x3c17, 0x5612, 0x3c13,
+  0x561d, 0x3c0f, 0x5629, 0x3c0a, 0x5635, 0x3c06, 0x5641, 0x3c02,
+  0x564c, 0x3bfd, 0x5658, 0x3bf9, 0x5664, 0x3bf5, 0x5670, 0x3bf0,
+  0x567c, 0x3bec, 0x5687, 0x3be7, 0x5693, 0x3be3, 0x569f, 0x3bde,
+  0x56ab, 0x3bda, 0x56b6, 0x3bd6, 0x56c2, 0x3bd1, 0x56ce, 0x3bcd,
+  0x56da, 0x3bc8, 0x56e5, 0x3bc4, 0x56f1, 0x3bbf, 0x56fd, 0x3bbb,
+  0x5709, 0x3bb6, 0x5714, 0x3bb2, 0x5720, 0x3bad, 0x572c, 0x3ba9,
+  0x5737, 0x3ba4, 0x5743, 0x3b9f, 0x574f, 0x3b9b, 0x575b, 0x3b96,
+  0x5766, 0x3b92, 0x5772, 0x3b8d, 0x577e, 0x3b88, 0x5789, 0x3b84,
+  0x5795, 0x3b7f, 0x57a1, 0x3b7b, 0x57ac, 0x3b76, 0x57b8, 0x3b71,
+  0x57c4, 0x3b6d, 0x57cf, 0x3b68, 0x57db, 0x3b63, 0x57e7, 0x3b5f,
+  0x57f2, 0x3b5a, 0x57fe, 0x3b55, 0x580a, 0x3b50, 0x5815, 0x3b4c,
+  0x5821, 0x3b47, 0x582d, 0x3b42, 0x5838, 0x3b3e, 0x5844, 0x3b39,
+  0x584f, 0x3b34, 0x585b, 0x3b2f, 0x5867, 0x3b2a, 0x5872, 0x3b26,
+  0x587e, 0x3b21, 0x5889, 0x3b1c, 0x5895, 0x3b17, 0x58a1, 0x3b12,
+  0x58ac, 0x3b0e, 0x58b8, 0x3b09, 0x58c3, 0x3b04, 0x58cf, 0x3aff,
+  0x58db, 0x3afa, 0x58e6, 0x3af5, 0x58f2, 0x3af0, 0x58fd, 0x3aeb,
+  0x5909, 0x3ae6, 0x5914, 0x3ae2, 0x5920, 0x3add, 0x592c, 0x3ad8,
+  0x5937, 0x3ad3, 0x5943, 0x3ace, 0x594e, 0x3ac9, 0x595a, 0x3ac4,
+  0x5965, 0x3abf, 0x5971, 0x3aba, 0x597c, 0x3ab5, 0x5988, 0x3ab0,
+  0x5993, 0x3aab, 0x599f, 0x3aa6, 0x59aa, 0x3aa1, 0x59b6, 0x3a9c,
+  0x59c1, 0x3a97, 0x59cd, 0x3a92, 0x59d8, 0x3a8d, 0x59e4, 0x3a88,
+  0x59ef, 0x3a82, 0x59fb, 0x3a7d, 0x5a06, 0x3a78, 0x5a12, 0x3a73,
+  0x5a1d, 0x3a6e, 0x5a29, 0x3a69, 0x5a34, 0x3a64, 0x5a40, 0x3a5f,
+  0x5a4b, 0x3a59, 0x5a57, 0x3a54, 0x5a62, 0x3a4f, 0x5a6e, 0x3a4a,
+  0x5a79, 0x3a45, 0x5a84, 0x3a3f, 0x5a90, 0x3a3a, 0x5a9b, 0x3a35,
+  0x5aa7, 0x3a30, 0x5ab2, 0x3a2b, 0x5abe, 0x3a25, 0x5ac9, 0x3a20,
+  0x5ad4, 0x3a1b, 0x5ae0, 0x3a16, 0x5aeb, 0x3a10, 0x5af7, 0x3a0b,
+  0x5b02, 0x3a06, 0x5b0d, 0x3a00, 0x5b19, 0x39fb, 0x5b24, 0x39f6,
+  0x5b30, 0x39f0, 0x5b3b, 0x39eb, 0x5b46, 0x39e6, 0x5b52, 0x39e0,
+  0x5b5d, 0x39db, 0x5b68, 0x39d6, 0x5b74, 0x39d0, 0x5b7f, 0x39cb,
+  0x5b8a, 0x39c5, 0x5b96, 0x39c0, 0x5ba1, 0x39bb, 0x5bac, 0x39b5,
+  0x5bb8, 0x39b0, 0x5bc3, 0x39aa, 0x5bce, 0x39a5, 0x5bda, 0x399f,
+  0x5be5, 0x399a, 0x5bf0, 0x3994, 0x5bfc, 0x398f, 0x5c07, 0x3989,
+  0x5c12, 0x3984, 0x5c1e, 0x397e, 0x5c29, 0x3979, 0x5c34, 0x3973,
+  0x5c3f, 0x396e, 0x5c4b, 0x3968, 0x5c56, 0x3963, 0x5c61, 0x395d,
+  0x5c6c, 0x3958, 0x5c78, 0x3952, 0x5c83, 0x394c, 0x5c8e, 0x3947,
+  0x5c99, 0x3941, 0x5ca5, 0x393b, 0x5cb0, 0x3936, 0x5cbb, 0x3930,
+  0x5cc6, 0x392b, 0x5cd2, 0x3925, 0x5cdd, 0x391f, 0x5ce8, 0x391a,
+  0x5cf3, 0x3914, 0x5cff, 0x390e, 0x5d0a, 0x3909, 0x5d15, 0x3903,
+  0x5d20, 0x38fd, 0x5d2b, 0x38f7, 0x5d36, 0x38f2, 0x5d42, 0x38ec,
+  0x5d4d, 0x38e6, 0x5d58, 0x38e0, 0x5d63, 0x38db, 0x5d6e, 0x38d5,
+  0x5d79, 0x38cf, 0x5d85, 0x38c9, 0x5d90, 0x38c3, 0x5d9b, 0x38be,
+  0x5da6, 0x38b8, 0x5db1, 0x38b2, 0x5dbc, 0x38ac, 0x5dc7, 0x38a6,
+  0x5dd3, 0x38a1, 0x5dde, 0x389b, 0x5de9, 0x3895, 0x5df4, 0x388f,
+  0x5dff, 0x3889, 0x5e0a, 0x3883, 0x5e15, 0x387d, 0x5e20, 0x3877,
+  0x5e2b, 0x3871, 0x5e36, 0x386b, 0x5e42, 0x3866, 0x5e4d, 0x3860,
+  0x5e58, 0x385a, 0x5e63, 0x3854, 0x5e6e, 0x384e, 0x5e79, 0x3848,
+  0x5e84, 0x3842, 0x5e8f, 0x383c, 0x5e9a, 0x3836, 0x5ea5, 0x3830,
+  0x5eb0, 0x382a, 0x5ebb, 0x3824, 0x5ec6, 0x381e, 0x5ed1, 0x3818,
+  0x5edc, 0x3812, 0x5ee7, 0x380b, 0x5ef2, 0x3805, 0x5efd, 0x37ff,
+  0x5f08, 0x37f9, 0x5f13, 0x37f3, 0x5f1e, 0x37ed, 0x5f29, 0x37e7,
+  0x5f34, 0x37e1, 0x5f3f, 0x37db, 0x5f4a, 0x37d5, 0x5f55, 0x37ce,
+  0x5f60, 0x37c8, 0x5f6b, 0x37c2, 0x5f76, 0x37bc, 0x5f81, 0x37b6,
+  0x5f8c, 0x37b0, 0x5f97, 0x37a9, 0x5fa2, 0x37a3, 0x5fac, 0x379d,
+  0x5fb7, 0x3797, 0x5fc2, 0x3790, 0x5fcd, 0x378a, 0x5fd8, 0x3784,
+  0x5fe3, 0x377e, 0x5fee, 0x3777, 0x5ff9, 0x3771, 0x6004, 0x376b,
+  0x600f, 0x3765, 0x6019, 0x375e, 0x6024, 0x3758, 0x602f, 0x3752,
+  0x603a, 0x374b, 0x6045, 0x3745, 0x6050, 0x373f, 0x605b, 0x3738,
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+  0x7797, 0x1fb7, 0x779d, 0x1fac, 0x77a3, 0x1fa2, 0x77a9, 0x1f97,
+  0x77b0, 0x1f8c, 0x77b6, 0x1f81, 0x77bc, 0x1f76, 0x77c2, 0x1f6b,
+  0x77c8, 0x1f60, 0x77ce, 0x1f55, 0x77d5, 0x1f4a, 0x77db, 0x1f3f,
+  0x77e1, 0x1f34, 0x77e7, 0x1f29, 0x77ed, 0x1f1e, 0x77f3, 0x1f13,
+  0x77f9, 0x1f08, 0x77ff, 0x1efd, 0x7805, 0x1ef2, 0x780b, 0x1ee7,
+  0x7812, 0x1edc, 0x7818, 0x1ed1, 0x781e, 0x1ec6, 0x7824, 0x1ebb,
+  0x782a, 0x1eb0, 0x7830, 0x1ea5, 0x7836, 0x1e9a, 0x783c, 0x1e8f,
+  0x7842, 0x1e84, 0x7848, 0x1e79, 0x784e, 0x1e6e, 0x7854, 0x1e63,
+  0x785a, 0x1e58, 0x7860, 0x1e4d, 0x7866, 0x1e42, 0x786b, 0x1e36,
+  0x7871, 0x1e2b, 0x7877, 0x1e20, 0x787d, 0x1e15, 0x7883, 0x1e0a,
+  0x7889, 0x1dff, 0x788f, 0x1df4, 0x7895, 0x1de9, 0x789b, 0x1dde,
+  0x78a1, 0x1dd3, 0x78a6, 0x1dc7, 0x78ac, 0x1dbc, 0x78b2, 0x1db1,
+  0x78b8, 0x1da6, 0x78be, 0x1d9b, 0x78c3, 0x1d90, 0x78c9, 0x1d85,
+  0x78cf, 0x1d79, 0x78d5, 0x1d6e, 0x78db, 0x1d63, 0x78e0, 0x1d58,
+  0x78e6, 0x1d4d, 0x78ec, 0x1d42, 0x78f2, 0x1d36, 0x78f7, 0x1d2b,
+  0x78fd, 0x1d20, 0x7903, 0x1d15, 0x7909, 0x1d0a, 0x790e, 0x1cff,
+  0x7914, 0x1cf3, 0x791a, 0x1ce8, 0x791f, 0x1cdd, 0x7925, 0x1cd2,
+  0x792b, 0x1cc6, 0x7930, 0x1cbb, 0x7936, 0x1cb0, 0x793b, 0x1ca5,
+  0x7941, 0x1c99, 0x7947, 0x1c8e, 0x794c, 0x1c83, 0x7952, 0x1c78,
+  0x7958, 0x1c6c, 0x795d, 0x1c61, 0x7963, 0x1c56, 0x7968, 0x1c4b,
+  0x796e, 0x1c3f, 0x7973, 0x1c34, 0x7979, 0x1c29, 0x797e, 0x1c1e,
+  0x7984, 0x1c12, 0x7989, 0x1c07, 0x798f, 0x1bfc, 0x7994, 0x1bf0,
+  0x799a, 0x1be5, 0x799f, 0x1bda, 0x79a5, 0x1bce, 0x79aa, 0x1bc3,
+  0x79b0, 0x1bb8, 0x79b5, 0x1bac, 0x79bb, 0x1ba1, 0x79c0, 0x1b96,
+  0x79c5, 0x1b8a, 0x79cb, 0x1b7f, 0x79d0, 0x1b74, 0x79d6, 0x1b68,
+  0x79db, 0x1b5d, 0x79e0, 0x1b52, 0x79e6, 0x1b46, 0x79eb, 0x1b3b,
+  0x79f0, 0x1b30, 0x79f6, 0x1b24, 0x79fb, 0x1b19, 0x7a00, 0x1b0d,
+  0x7a06, 0x1b02, 0x7a0b, 0x1af7, 0x7a10, 0x1aeb, 0x7a16, 0x1ae0,
+  0x7a1b, 0x1ad4, 0x7a20, 0x1ac9, 0x7a25, 0x1abe, 0x7a2b, 0x1ab2,
+  0x7a30, 0x1aa7, 0x7a35, 0x1a9b, 0x7a3a, 0x1a90, 0x7a3f, 0x1a84,
+  0x7a45, 0x1a79, 0x7a4a, 0x1a6e, 0x7a4f, 0x1a62, 0x7a54, 0x1a57,
+  0x7a59, 0x1a4b, 0x7a5f, 0x1a40, 0x7a64, 0x1a34, 0x7a69, 0x1a29,
+  0x7a6e, 0x1a1d, 0x7a73, 0x1a12, 0x7a78, 0x1a06, 0x7a7d, 0x19fb,
+  0x7a82, 0x19ef, 0x7a88, 0x19e4, 0x7a8d, 0x19d8, 0x7a92, 0x19cd,
+  0x7a97, 0x19c1, 0x7a9c, 0x19b6, 0x7aa1, 0x19aa, 0x7aa6, 0x199f,
+  0x7aab, 0x1993, 0x7ab0, 0x1988, 0x7ab5, 0x197c, 0x7aba, 0x1971,
+  0x7abf, 0x1965, 0x7ac4, 0x195a, 0x7ac9, 0x194e, 0x7ace, 0x1943,
+  0x7ad3, 0x1937, 0x7ad8, 0x192c, 0x7add, 0x1920, 0x7ae2, 0x1914,
+  0x7ae6, 0x1909, 0x7aeb, 0x18fd, 0x7af0, 0x18f2, 0x7af5, 0x18e6,
+  0x7afa, 0x18db, 0x7aff, 0x18cf, 0x7b04, 0x18c3, 0x7b09, 0x18b8,
+  0x7b0e, 0x18ac, 0x7b12, 0x18a1, 0x7b17, 0x1895, 0x7b1c, 0x1889,
+  0x7b21, 0x187e, 0x7b26, 0x1872, 0x7b2a, 0x1867, 0x7b2f, 0x185b,
+  0x7b34, 0x184f, 0x7b39, 0x1844, 0x7b3e, 0x1838, 0x7b42, 0x182d,
+  0x7b47, 0x1821, 0x7b4c, 0x1815, 0x7b50, 0x180a, 0x7b55, 0x17fe,
+  0x7b5a, 0x17f2, 0x7b5f, 0x17e7, 0x7b63, 0x17db, 0x7b68, 0x17cf,
+  0x7b6d, 0x17c4, 0x7b71, 0x17b8, 0x7b76, 0x17ac, 0x7b7b, 0x17a1,
+  0x7b7f, 0x1795, 0x7b84, 0x1789, 0x7b88, 0x177e, 0x7b8d, 0x1772,
+  0x7b92, 0x1766, 0x7b96, 0x175b, 0x7b9b, 0x174f, 0x7b9f, 0x1743,
+  0x7ba4, 0x1737, 0x7ba9, 0x172c, 0x7bad, 0x1720, 0x7bb2, 0x1714,
+  0x7bb6, 0x1709, 0x7bbb, 0x16fd, 0x7bbf, 0x16f1, 0x7bc4, 0x16e5,
+  0x7bc8, 0x16da, 0x7bcd, 0x16ce, 0x7bd1, 0x16c2, 0x7bd6, 0x16b6,
+  0x7bda, 0x16ab, 0x7bde, 0x169f, 0x7be3, 0x1693, 0x7be7, 0x1687,
+  0x7bec, 0x167c, 0x7bf0, 0x1670, 0x7bf5, 0x1664, 0x7bf9, 0x1658,
+  0x7bfd, 0x164c, 0x7c02, 0x1641, 0x7c06, 0x1635, 0x7c0a, 0x1629,
+  0x7c0f, 0x161d, 0x7c13, 0x1612, 0x7c17, 0x1606, 0x7c1c, 0x15fa,
+  0x7c20, 0x15ee, 0x7c24, 0x15e2, 0x7c29, 0x15d7, 0x7c2d, 0x15cb,
+  0x7c31, 0x15bf, 0x7c36, 0x15b3, 0x7c3a, 0x15a7, 0x7c3e, 0x159b,
+  0x7c42, 0x1590, 0x7c46, 0x1584, 0x7c4b, 0x1578, 0x7c4f, 0x156c,
+  0x7c53, 0x1560, 0x7c57, 0x1554, 0x7c5b, 0x1549, 0x7c60, 0x153d,
+  0x7c64, 0x1531, 0x7c68, 0x1525, 0x7c6c, 0x1519, 0x7c70, 0x150d,
+  0x7c74, 0x1501, 0x7c79, 0x14f6, 0x7c7d, 0x14ea, 0x7c81, 0x14de,
+  0x7c85, 0x14d2, 0x7c89, 0x14c6, 0x7c8d, 0x14ba, 0x7c91, 0x14ae,
+  0x7c95, 0x14a2, 0x7c99, 0x1496, 0x7c9d, 0x148b, 0x7ca1, 0x147f,
+  0x7ca5, 0x1473, 0x7ca9, 0x1467, 0x7cad, 0x145b, 0x7cb1, 0x144f,
+  0x7cb5, 0x1443, 0x7cb9, 0x1437, 0x7cbd, 0x142b, 0x7cc1, 0x141f,
+  0x7cc5, 0x1413, 0x7cc9, 0x1407, 0x7ccd, 0x13fb, 0x7cd1, 0x13f0,
+  0x7cd5, 0x13e4, 0x7cd9, 0x13d8, 0x7cdd, 0x13cc, 0x7ce0, 0x13c0,
+  0x7ce4, 0x13b4, 0x7ce8, 0x13a8, 0x7cec, 0x139c, 0x7cf0, 0x1390,
+  0x7cf4, 0x1384, 0x7cf8, 0x1378, 0x7cfb, 0x136c, 0x7cff, 0x1360,
+  0x7d03, 0x1354, 0x7d07, 0x1348, 0x7d0b, 0x133c, 0x7d0e, 0x1330,
+  0x7d12, 0x1324, 0x7d16, 0x1318, 0x7d1a, 0x130c, 0x7d1d, 0x1300,
+  0x7d21, 0x12f4, 0x7d25, 0x12e8, 0x7d28, 0x12dc, 0x7d2c, 0x12d0,
+  0x7d30, 0x12c4, 0x7d34, 0x12b8, 0x7d37, 0x12ac, 0x7d3b, 0x12a0,
+  0x7d3f, 0x1294, 0x7d42, 0x1288, 0x7d46, 0x127c, 0x7d49, 0x1270,
+  0x7d4d, 0x1264, 0x7d51, 0x1258, 0x7d54, 0x124c, 0x7d58, 0x1240,
+  0x7d5b, 0x1234, 0x7d5f, 0x1228, 0x7d63, 0x121c, 0x7d66, 0x1210,
+  0x7d6a, 0x1204, 0x7d6d, 0x11f7, 0x7d71, 0x11eb, 0x7d74, 0x11df,
+  0x7d78, 0x11d3, 0x7d7b, 0x11c7, 0x7d7f, 0x11bb, 0x7d82, 0x11af,
+  0x7d86, 0x11a3, 0x7d89, 0x1197, 0x7d8d, 0x118b, 0x7d90, 0x117f,
+  0x7d93, 0x1173, 0x7d97, 0x1167, 0x7d9a, 0x115a, 0x7d9e, 0x114e,
+  0x7da1, 0x1142, 0x7da4, 0x1136, 0x7da8, 0x112a, 0x7dab, 0x111e,
+  0x7daf, 0x1112, 0x7db2, 0x1106, 0x7db5, 0x10fa, 0x7db9, 0x10ed,
+  0x7dbc, 0x10e1, 0x7dbf, 0x10d5, 0x7dc2, 0x10c9, 0x7dc6, 0x10bd,
+  0x7dc9, 0x10b1, 0x7dcc, 0x10a5, 0x7dd0, 0x1099, 0x7dd3, 0x108c,
+  0x7dd6, 0x1080, 0x7dd9, 0x1074, 0x7ddd, 0x1068, 0x7de0, 0x105c,
+  0x7de3, 0x1050, 0x7de6, 0x1044, 0x7de9, 0x1037, 0x7ded, 0x102b,
+  0x7df0, 0x101f, 0x7df3, 0x1013, 0x7df6, 0x1007, 0x7df9, 0xffb,
+  0x7dfc, 0xfee, 0x7dff, 0xfe2, 0x7e03, 0xfd6, 0x7e06, 0xfca,
+  0x7e09, 0xfbe, 0x7e0c, 0xfb2, 0x7e0f, 0xfa5, 0x7e12, 0xf99,
+  0x7e15, 0xf8d, 0x7e18, 0xf81, 0x7e1b, 0xf75, 0x7e1e, 0xf68,
+  0x7e21, 0xf5c, 0x7e24, 0xf50, 0x7e27, 0xf44, 0x7e2a, 0xf38,
+  0x7e2d, 0xf2b, 0x7e30, 0xf1f, 0x7e33, 0xf13, 0x7e36, 0xf07,
+  0x7e39, 0xefb, 0x7e3c, 0xeee, 0x7e3f, 0xee2, 0x7e42, 0xed6,
+  0x7e45, 0xeca, 0x7e48, 0xebd, 0x7e4a, 0xeb1, 0x7e4d, 0xea5,
+  0x7e50, 0xe99, 0x7e53, 0xe8c, 0x7e56, 0xe80, 0x7e59, 0xe74,
+  0x7e5c, 0xe68, 0x7e5e, 0xe5c, 0x7e61, 0xe4f, 0x7e64, 0xe43,
+  0x7e67, 0xe37, 0x7e6a, 0xe2b, 0x7e6c, 0xe1e, 0x7e6f, 0xe12,
+  0x7e72, 0xe06, 0x7e75, 0xdf9, 0x7e77, 0xded, 0x7e7a, 0xde1,
+  0x7e7d, 0xdd5, 0x7e80, 0xdc8, 0x7e82, 0xdbc, 0x7e85, 0xdb0,
+  0x7e88, 0xda4, 0x7e8a, 0xd97, 0x7e8d, 0xd8b, 0x7e90, 0xd7f,
+  0x7e92, 0xd72, 0x7e95, 0xd66, 0x7e98, 0xd5a, 0x7e9a, 0xd4e,
+  0x7e9d, 0xd41, 0x7e9f, 0xd35, 0x7ea2, 0xd29, 0x7ea5, 0xd1c,
+  0x7ea7, 0xd10, 0x7eaa, 0xd04, 0x7eac, 0xcf8, 0x7eaf, 0xceb,
+  0x7eb1, 0xcdf, 0x7eb4, 0xcd3, 0x7eb6, 0xcc6, 0x7eb9, 0xcba,
+  0x7ebb, 0xcae, 0x7ebe, 0xca1, 0x7ec0, 0xc95, 0x7ec3, 0xc89,
+  0x7ec5, 0xc7c, 0x7ec8, 0xc70, 0x7eca, 0xc64, 0x7ecc, 0xc57,
+  0x7ecf, 0xc4b, 0x7ed1, 0xc3f, 0x7ed4, 0xc32, 0x7ed6, 0xc26,
+  0x7ed8, 0xc1a, 0x7edb, 0xc0d, 0x7edd, 0xc01, 0x7ee0, 0xbf5,
+  0x7ee2, 0xbe8, 0x7ee4, 0xbdc, 0x7ee7, 0xbd0, 0x7ee9, 0xbc3,
+  0x7eeb, 0xbb7, 0x7eed, 0xbab, 0x7ef0, 0xb9e, 0x7ef2, 0xb92,
+  0x7ef4, 0xb85, 0x7ef7, 0xb79, 0x7ef9, 0xb6d, 0x7efb, 0xb60,
+  0x7efd, 0xb54, 0x7f00, 0xb48, 0x7f02, 0xb3b, 0x7f04, 0xb2f,
+  0x7f06, 0xb23, 0x7f08, 0xb16, 0x7f0a, 0xb0a, 0x7f0d, 0xafd,
+  0x7f0f, 0xaf1, 0x7f11, 0xae5, 0x7f13, 0xad8, 0x7f15, 0xacc,
+  0x7f17, 0xac0, 0x7f19, 0xab3, 0x7f1c, 0xaa7, 0x7f1e, 0xa9a,
+  0x7f20, 0xa8e, 0x7f22, 0xa82, 0x7f24, 0xa75, 0x7f26, 0xa69,
+  0x7f28, 0xa5c, 0x7f2a, 0xa50, 0x7f2c, 0xa44, 0x7f2e, 0xa37,
+  0x7f30, 0xa2b, 0x7f32, 0xa1e, 0x7f34, 0xa12, 0x7f36, 0xa06,
+  0x7f38, 0x9f9, 0x7f3a, 0x9ed, 0x7f3c, 0x9e0, 0x7f3e, 0x9d4,
+  0x7f40, 0x9c7, 0x7f42, 0x9bb, 0x7f43, 0x9af, 0x7f45, 0x9a2,
+  0x7f47, 0x996, 0x7f49, 0x989, 0x7f4b, 0x97d, 0x7f4d, 0x970,
+  0x7f4f, 0x964, 0x7f51, 0x958, 0x7f52, 0x94b, 0x7f54, 0x93f,
+  0x7f56, 0x932, 0x7f58, 0x926, 0x7f5a, 0x919, 0x7f5b, 0x90d,
+  0x7f5d, 0x901, 0x7f5f, 0x8f4, 0x7f61, 0x8e8, 0x7f62, 0x8db,
+  0x7f64, 0x8cf, 0x7f66, 0x8c2, 0x7f68, 0x8b6, 0x7f69, 0x8a9,
+  0x7f6b, 0x89d, 0x7f6d, 0x891, 0x7f6e, 0x884, 0x7f70, 0x878,
+  0x7f72, 0x86b, 0x7f73, 0x85f, 0x7f75, 0x852, 0x7f77, 0x846,
+  0x7f78, 0x839, 0x7f7a, 0x82d, 0x7f7b, 0x820, 0x7f7d, 0x814,
+  0x7f7f, 0x807, 0x7f80, 0x7fb, 0x7f82, 0x7ef, 0x7f83, 0x7e2,
+  0x7f85, 0x7d6, 0x7f86, 0x7c9, 0x7f88, 0x7bd, 0x7f89, 0x7b0,
+  0x7f8b, 0x7a4, 0x7f8c, 0x797, 0x7f8e, 0x78b, 0x7f8f, 0x77e,
+  0x7f91, 0x772, 0x7f92, 0x765, 0x7f94, 0x759, 0x7f95, 0x74c,
+  0x7f97, 0x740, 0x7f98, 0x733, 0x7f99, 0x727, 0x7f9b, 0x71a,
+  0x7f9c, 0x70e, 0x7f9e, 0x701, 0x7f9f, 0x6f5, 0x7fa0, 0x6e8,
+  0x7fa2, 0x6dc, 0x7fa3, 0x6cf, 0x7fa4, 0x6c3, 0x7fa6, 0x6b6,
+  0x7fa7, 0x6aa, 0x7fa8, 0x69d, 0x7faa, 0x691, 0x7fab, 0x684,
+  0x7fac, 0x678, 0x7fad, 0x66b, 0x7faf, 0x65f, 0x7fb0, 0x652,
+  0x7fb1, 0x646, 0x7fb2, 0x639, 0x7fb4, 0x62d, 0x7fb5, 0x620,
+  0x7fb6, 0x614, 0x7fb7, 0x607, 0x7fb8, 0x5fb, 0x7fb9, 0x5ee,
+  0x7fbb, 0x5e2, 0x7fbc, 0x5d5, 0x7fbd, 0x5c9, 0x7fbe, 0x5bc,
+  0x7fbf, 0x5b0, 0x7fc0, 0x5a3, 0x7fc1, 0x597, 0x7fc3, 0x58a,
+  0x7fc4, 0x57e, 0x7fc5, 0x571, 0x7fc6, 0x565, 0x7fc7, 0x558,
+  0x7fc8, 0x54c, 0x7fc9, 0x53f, 0x7fca, 0x533, 0x7fcb, 0x526,
+  0x7fcc, 0x51a, 0x7fcd, 0x50d, 0x7fce, 0x500, 0x7fcf, 0x4f4,
+  0x7fd0, 0x4e7, 0x7fd1, 0x4db, 0x7fd2, 0x4ce, 0x7fd3, 0x4c2,
+  0x7fd4, 0x4b5, 0x7fd5, 0x4a9, 0x7fd5, 0x49c, 0x7fd6, 0x490,
+  0x7fd7, 0x483, 0x7fd8, 0x477, 0x7fd9, 0x46a, 0x7fda, 0x45e,
+  0x7fdb, 0x451, 0x7fdc, 0x444, 0x7fdc, 0x438, 0x7fdd, 0x42b,
+  0x7fde, 0x41f, 0x7fdf, 0x412, 0x7fe0, 0x406, 0x7fe0, 0x3f9,
+  0x7fe1, 0x3ed, 0x7fe2, 0x3e0, 0x7fe3, 0x3d4, 0x7fe3, 0x3c7,
+  0x7fe4, 0x3bb, 0x7fe5, 0x3ae, 0x7fe6, 0x3a1, 0x7fe6, 0x395,
+  0x7fe7, 0x388, 0x7fe8, 0x37c, 0x7fe8, 0x36f, 0x7fe9, 0x363,
+  0x7fea, 0x356, 0x7fea, 0x34a, 0x7feb, 0x33d, 0x7fec, 0x330,
+  0x7fec, 0x324, 0x7fed, 0x317, 0x7fed, 0x30b, 0x7fee, 0x2fe,
+  0x7fef, 0x2f2, 0x7fef, 0x2e5, 0x7ff0, 0x2d9, 0x7ff0, 0x2cc,
+  0x7ff1, 0x2c0, 0x7ff1, 0x2b3, 0x7ff2, 0x2a6, 0x7ff2, 0x29a,
+  0x7ff3, 0x28d, 0x7ff3, 0x281, 0x7ff4, 0x274, 0x7ff4, 0x268,
+  0x7ff5, 0x25b, 0x7ff5, 0x24e, 0x7ff6, 0x242, 0x7ff6, 0x235,
+  0x7ff7, 0x229, 0x7ff7, 0x21c, 0x7ff7, 0x210, 0x7ff8, 0x203,
+  0x7ff8, 0x1f7, 0x7ff9, 0x1ea, 0x7ff9, 0x1dd, 0x7ff9, 0x1d1,
+  0x7ffa, 0x1c4, 0x7ffa, 0x1b8, 0x7ffa, 0x1ab, 0x7ffb, 0x19f,
+  0x7ffb, 0x192, 0x7ffb, 0x186, 0x7ffc, 0x179, 0x7ffc, 0x16c,
+  0x7ffc, 0x160, 0x7ffc, 0x153, 0x7ffd, 0x147, 0x7ffd, 0x13a,
+  0x7ffd, 0x12e, 0x7ffd, 0x121, 0x7ffe, 0x114, 0x7ffe, 0x108,
+  0x7ffe, 0xfb, 0x7ffe, 0xef, 0x7ffe, 0xe2, 0x7fff, 0xd6,
+  0x7fff, 0xc9, 0x7fff, 0xbc, 0x7fff, 0xb0, 0x7fff, 0xa3,
+  0x7fff, 0x97, 0x7fff, 0x8a, 0x7fff, 0x7e, 0x7fff, 0x71,
+  0x7fff, 0x65, 0x7fff, 0x58, 0x7fff, 0x4b, 0x7fff, 0x3f,
+  0x7fff, 0x32, 0x7fff, 0x26, 0x7fff, 0x19, 0x7fff, 0xd,
+  0x7fff, 0x0, 0x7fff, 0xfff3, 0x7fff, 0xffe7, 0x7fff, 0xffda,
+  0x7fff, 0xffce, 0x7fff, 0xffc1, 0x7fff, 0xffb5, 0x7fff, 0xffa8,
+  0x7fff, 0xff9b, 0x7fff, 0xff8f, 0x7fff, 0xff82, 0x7fff, 0xff76,
+  0x7fff, 0xff69, 0x7fff, 0xff5d, 0x7fff, 0xff50, 0x7fff, 0xff44,
+  0x7fff, 0xff37, 0x7fff, 0xff2a, 0x7ffe, 0xff1e, 0x7ffe, 0xff11,
+  0x7ffe, 0xff05, 0x7ffe, 0xfef8, 0x7ffe, 0xfeec, 0x7ffd, 0xfedf,
+  0x7ffd, 0xfed2, 0x7ffd, 0xfec6, 0x7ffd, 0xfeb9, 0x7ffc, 0xfead,
+  0x7ffc, 0xfea0, 0x7ffc, 0xfe94, 0x7ffc, 0xfe87, 0x7ffb, 0xfe7a,
+  0x7ffb, 0xfe6e, 0x7ffb, 0xfe61, 0x7ffa, 0xfe55, 0x7ffa, 0xfe48,
+  0x7ffa, 0xfe3c, 0x7ff9, 0xfe2f, 0x7ff9, 0xfe23, 0x7ff9, 0xfe16,
+  0x7ff8, 0xfe09, 0x7ff8, 0xfdfd, 0x7ff7, 0xfdf0, 0x7ff7, 0xfde4,
+  0x7ff7, 0xfdd7, 0x7ff6, 0xfdcb, 0x7ff6, 0xfdbe, 0x7ff5, 0xfdb2,
+  0x7ff5, 0xfda5, 0x7ff4, 0xfd98, 0x7ff4, 0xfd8c, 0x7ff3, 0xfd7f,
+  0x7ff3, 0xfd73, 0x7ff2, 0xfd66, 0x7ff2, 0xfd5a, 0x7ff1, 0xfd4d,
+  0x7ff1, 0xfd40, 0x7ff0, 0xfd34, 0x7ff0, 0xfd27, 0x7fef, 0xfd1b,
+  0x7fef, 0xfd0e, 0x7fee, 0xfd02, 0x7fed, 0xfcf5, 0x7fed, 0xfce9,
+  0x7fec, 0xfcdc, 0x7fec, 0xfcd0, 0x7feb, 0xfcc3, 0x7fea, 0xfcb6,
+  0x7fea, 0xfcaa, 0x7fe9, 0xfc9d, 0x7fe8, 0xfc91, 0x7fe8, 0xfc84,
+  0x7fe7, 0xfc78, 0x7fe6, 0xfc6b, 0x7fe6, 0xfc5f, 0x7fe5, 0xfc52,
+  0x7fe4, 0xfc45, 0x7fe3, 0xfc39, 0x7fe3, 0xfc2c, 0x7fe2, 0xfc20,
+  0x7fe1, 0xfc13, 0x7fe0, 0xfc07, 0x7fe0, 0xfbfa, 0x7fdf, 0xfbee,
+  0x7fde, 0xfbe1, 0x7fdd, 0xfbd5, 0x7fdc, 0xfbc8, 0x7fdc, 0xfbbc,
+  0x7fdb, 0xfbaf, 0x7fda, 0xfba2, 0x7fd9, 0xfb96, 0x7fd8, 0xfb89,
+  0x7fd7, 0xfb7d, 0x7fd6, 0xfb70, 0x7fd5, 0xfb64, 0x7fd5, 0xfb57,
+  0x7fd4, 0xfb4b, 0x7fd3, 0xfb3e, 0x7fd2, 0xfb32, 0x7fd1, 0xfb25,
+  0x7fd0, 0xfb19, 0x7fcf, 0xfb0c, 0x7fce, 0xfb00, 0x7fcd, 0xfaf3,
+  0x7fcc, 0xfae6, 0x7fcb, 0xfada, 0x7fca, 0xfacd, 0x7fc9, 0xfac1,
+  0x7fc8, 0xfab4, 0x7fc7, 0xfaa8, 0x7fc6, 0xfa9b, 0x7fc5, 0xfa8f,
+  0x7fc4, 0xfa82, 0x7fc3, 0xfa76, 0x7fc1, 0xfa69, 0x7fc0, 0xfa5d,
+  0x7fbf, 0xfa50, 0x7fbe, 0xfa44, 0x7fbd, 0xfa37, 0x7fbc, 0xfa2b,
+  0x7fbb, 0xfa1e, 0x7fb9, 0xfa12, 0x7fb8, 0xfa05, 0x7fb7, 0xf9f9,
+  0x7fb6, 0xf9ec, 0x7fb5, 0xf9e0, 0x7fb4, 0xf9d3, 0x7fb2, 0xf9c7,
+  0x7fb1, 0xf9ba, 0x7fb0, 0xf9ae, 0x7faf, 0xf9a1, 0x7fad, 0xf995,
+  0x7fac, 0xf988, 0x7fab, 0xf97c, 0x7faa, 0xf96f, 0x7fa8, 0xf963,
+  0x7fa7, 0xf956, 0x7fa6, 0xf94a, 0x7fa4, 0xf93d, 0x7fa3, 0xf931,
+  0x7fa2, 0xf924, 0x7fa0, 0xf918, 0x7f9f, 0xf90b, 0x7f9e, 0xf8ff,
+  0x7f9c, 0xf8f2, 0x7f9b, 0xf8e6, 0x7f99, 0xf8d9, 0x7f98, 0xf8cd,
+  0x7f97, 0xf8c0, 0x7f95, 0xf8b4, 0x7f94, 0xf8a7, 0x7f92, 0xf89b,
+  0x7f91, 0xf88e, 0x7f8f, 0xf882, 0x7f8e, 0xf875, 0x7f8c, 0xf869,
+  0x7f8b, 0xf85c, 0x7f89, 0xf850, 0x7f88, 0xf843, 0x7f86, 0xf837,
+  0x7f85, 0xf82a, 0x7f83, 0xf81e, 0x7f82, 0xf811, 0x7f80, 0xf805,
+  0x7f7f, 0xf7f9, 0x7f7d, 0xf7ec, 0x7f7b, 0xf7e0, 0x7f7a, 0xf7d3,
+  0x7f78, 0xf7c7, 0x7f77, 0xf7ba, 0x7f75, 0xf7ae, 0x7f73, 0xf7a1,
+  0x7f72, 0xf795, 0x7f70, 0xf788, 0x7f6e, 0xf77c, 0x7f6d, 0xf76f,
+  0x7f6b, 0xf763, 0x7f69, 0xf757, 0x7f68, 0xf74a, 0x7f66, 0xf73e,
+  0x7f64, 0xf731, 0x7f62, 0xf725, 0x7f61, 0xf718, 0x7f5f, 0xf70c,
+  0x7f5d, 0xf6ff, 0x7f5b, 0xf6f3, 0x7f5a, 0xf6e7, 0x7f58, 0xf6da,
+  0x7f56, 0xf6ce, 0x7f54, 0xf6c1, 0x7f52, 0xf6b5, 0x7f51, 0xf6a8,
+  0x7f4f, 0xf69c, 0x7f4d, 0xf690, 0x7f4b, 0xf683, 0x7f49, 0xf677,
+  0x7f47, 0xf66a, 0x7f45, 0xf65e, 0x7f43, 0xf651, 0x7f42, 0xf645,
+  0x7f40, 0xf639, 0x7f3e, 0xf62c, 0x7f3c, 0xf620, 0x7f3a, 0xf613,
+  0x7f38, 0xf607, 0x7f36, 0xf5fa, 0x7f34, 0xf5ee, 0x7f32, 0xf5e2,
+  0x7f30, 0xf5d5, 0x7f2e, 0xf5c9, 0x7f2c, 0xf5bc, 0x7f2a, 0xf5b0,
+  0x7f28, 0xf5a4, 0x7f26, 0xf597, 0x7f24, 0xf58b, 0x7f22, 0xf57e,
+  0x7f20, 0xf572, 0x7f1e, 0xf566, 0x7f1c, 0xf559, 0x7f19, 0xf54d,
+  0x7f17, 0xf540, 0x7f15, 0xf534, 0x7f13, 0xf528, 0x7f11, 0xf51b,
+  0x7f0f, 0xf50f, 0x7f0d, 0xf503, 0x7f0a, 0xf4f6, 0x7f08, 0xf4ea,
+  0x7f06, 0xf4dd, 0x7f04, 0xf4d1, 0x7f02, 0xf4c5, 0x7f00, 0xf4b8,
+  0x7efd, 0xf4ac, 0x7efb, 0xf4a0, 0x7ef9, 0xf493, 0x7ef7, 0xf487,
+  0x7ef4, 0xf47b, 0x7ef2, 0xf46e, 0x7ef0, 0xf462, 0x7eed, 0xf455,
+  0x7eeb, 0xf449, 0x7ee9, 0xf43d, 0x7ee7, 0xf430, 0x7ee4, 0xf424,
+  0x7ee2, 0xf418, 0x7ee0, 0xf40b, 0x7edd, 0xf3ff, 0x7edb, 0xf3f3,
+  0x7ed8, 0xf3e6, 0x7ed6, 0xf3da, 0x7ed4, 0xf3ce, 0x7ed1, 0xf3c1,
+  0x7ecf, 0xf3b5, 0x7ecc, 0xf3a9, 0x7eca, 0xf39c, 0x7ec8, 0xf390,
+  0x7ec5, 0xf384, 0x7ec3, 0xf377, 0x7ec0, 0xf36b, 0x7ebe, 0xf35f,
+  0x7ebb, 0xf352, 0x7eb9, 0xf346, 0x7eb6, 0xf33a, 0x7eb4, 0xf32d,
+  0x7eb1, 0xf321, 0x7eaf, 0xf315, 0x7eac, 0xf308, 0x7eaa, 0xf2fc,
+  0x7ea7, 0xf2f0, 0x7ea5, 0xf2e4, 0x7ea2, 0xf2d7, 0x7e9f, 0xf2cb,
+  0x7e9d, 0xf2bf, 0x7e9a, 0xf2b2, 0x7e98, 0xf2a6, 0x7e95, 0xf29a,
+  0x7e92, 0xf28e, 0x7e90, 0xf281, 0x7e8d, 0xf275, 0x7e8a, 0xf269,
+  0x7e88, 0xf25c, 0x7e85, 0xf250, 0x7e82, 0xf244, 0x7e80, 0xf238,
+  0x7e7d, 0xf22b, 0x7e7a, 0xf21f, 0x7e77, 0xf213, 0x7e75, 0xf207,
+  0x7e72, 0xf1fa, 0x7e6f, 0xf1ee, 0x7e6c, 0xf1e2, 0x7e6a, 0xf1d5,
+  0x7e67, 0xf1c9, 0x7e64, 0xf1bd, 0x7e61, 0xf1b1, 0x7e5e, 0xf1a4,
+  0x7e5c, 0xf198, 0x7e59, 0xf18c, 0x7e56, 0xf180, 0x7e53, 0xf174,
+  0x7e50, 0xf167, 0x7e4d, 0xf15b, 0x7e4a, 0xf14f, 0x7e48, 0xf143,
+  0x7e45, 0xf136, 0x7e42, 0xf12a, 0x7e3f, 0xf11e, 0x7e3c, 0xf112,
+  0x7e39, 0xf105, 0x7e36, 0xf0f9, 0x7e33, 0xf0ed, 0x7e30, 0xf0e1,
+  0x7e2d, 0xf0d5, 0x7e2a, 0xf0c8, 0x7e27, 0xf0bc, 0x7e24, 0xf0b0,
+  0x7e21, 0xf0a4, 0x7e1e, 0xf098, 0x7e1b, 0xf08b, 0x7e18, 0xf07f,
+  0x7e15, 0xf073, 0x7e12, 0xf067, 0x7e0f, 0xf05b, 0x7e0c, 0xf04e,
+  0x7e09, 0xf042, 0x7e06, 0xf036, 0x7e03, 0xf02a, 0x7dff, 0xf01e,
+  0x7dfc, 0xf012, 0x7df9, 0xf005, 0x7df6, 0xeff9, 0x7df3, 0xefed,
+  0x7df0, 0xefe1, 0x7ded, 0xefd5, 0x7de9, 0xefc9, 0x7de6, 0xefbc,
+  0x7de3, 0xefb0, 0x7de0, 0xefa4, 0x7ddd, 0xef98, 0x7dd9, 0xef8c,
+  0x7dd6, 0xef80, 0x7dd3, 0xef74, 0x7dd0, 0xef67, 0x7dcc, 0xef5b,
+  0x7dc9, 0xef4f, 0x7dc6, 0xef43, 0x7dc2, 0xef37, 0x7dbf, 0xef2b,
+  0x7dbc, 0xef1f, 0x7db9, 0xef13, 0x7db5, 0xef06, 0x7db2, 0xeefa,
+  0x7daf, 0xeeee, 0x7dab, 0xeee2, 0x7da8, 0xeed6, 0x7da4, 0xeeca,
+  0x7da1, 0xeebe, 0x7d9e, 0xeeb2, 0x7d9a, 0xeea6, 0x7d97, 0xee99,
+  0x7d93, 0xee8d, 0x7d90, 0xee81, 0x7d8d, 0xee75, 0x7d89, 0xee69,
+  0x7d86, 0xee5d, 0x7d82, 0xee51, 0x7d7f, 0xee45, 0x7d7b, 0xee39,
+  0x7d78, 0xee2d, 0x7d74, 0xee21, 0x7d71, 0xee15, 0x7d6d, 0xee09,
+  0x7d6a, 0xedfc, 0x7d66, 0xedf0, 0x7d63, 0xede4, 0x7d5f, 0xedd8,
+  0x7d5b, 0xedcc, 0x7d58, 0xedc0, 0x7d54, 0xedb4, 0x7d51, 0xeda8,
+  0x7d4d, 0xed9c, 0x7d49, 0xed90, 0x7d46, 0xed84, 0x7d42, 0xed78,
+  0x7d3f, 0xed6c, 0x7d3b, 0xed60, 0x7d37, 0xed54, 0x7d34, 0xed48,
+  0x7d30, 0xed3c, 0x7d2c, 0xed30, 0x7d28, 0xed24, 0x7d25, 0xed18,
+  0x7d21, 0xed0c, 0x7d1d, 0xed00, 0x7d1a, 0xecf4, 0x7d16, 0xece8,
+  0x7d12, 0xecdc, 0x7d0e, 0xecd0, 0x7d0b, 0xecc4, 0x7d07, 0xecb8,
+  0x7d03, 0xecac, 0x7cff, 0xeca0, 0x7cfb, 0xec94, 0x7cf8, 0xec88,
+  0x7cf4, 0xec7c, 0x7cf0, 0xec70, 0x7cec, 0xec64, 0x7ce8, 0xec58,
+  0x7ce4, 0xec4c, 0x7ce0, 0xec40, 0x7cdd, 0xec34, 0x7cd9, 0xec28,
+  0x7cd5, 0xec1c, 0x7cd1, 0xec10, 0x7ccd, 0xec05, 0x7cc9, 0xebf9,
+  0x7cc5, 0xebed, 0x7cc1, 0xebe1, 0x7cbd, 0xebd5, 0x7cb9, 0xebc9,
+  0x7cb5, 0xebbd, 0x7cb1, 0xebb1, 0x7cad, 0xeba5, 0x7ca9, 0xeb99,
+  0x7ca5, 0xeb8d, 0x7ca1, 0xeb81, 0x7c9d, 0xeb75, 0x7c99, 0xeb6a,
+  0x7c95, 0xeb5e, 0x7c91, 0xeb52, 0x7c8d, 0xeb46, 0x7c89, 0xeb3a,
+  0x7c85, 0xeb2e, 0x7c81, 0xeb22, 0x7c7d, 0xeb16, 0x7c79, 0xeb0a,
+  0x7c74, 0xeaff, 0x7c70, 0xeaf3, 0x7c6c, 0xeae7, 0x7c68, 0xeadb,
+  0x7c64, 0xeacf, 0x7c60, 0xeac3, 0x7c5b, 0xeab7, 0x7c57, 0xeaac,
+  0x7c53, 0xeaa0, 0x7c4f, 0xea94, 0x7c4b, 0xea88, 0x7c46, 0xea7c,
+  0x7c42, 0xea70, 0x7c3e, 0xea65, 0x7c3a, 0xea59, 0x7c36, 0xea4d,
+  0x7c31, 0xea41, 0x7c2d, 0xea35, 0x7c29, 0xea29, 0x7c24, 0xea1e,
+  0x7c20, 0xea12, 0x7c1c, 0xea06, 0x7c17, 0xe9fa, 0x7c13, 0xe9ee,
+  0x7c0f, 0xe9e3, 0x7c0a, 0xe9d7, 0x7c06, 0xe9cb, 0x7c02, 0xe9bf,
+  0x7bfd, 0xe9b4, 0x7bf9, 0xe9a8, 0x7bf5, 0xe99c, 0x7bf0, 0xe990,
+  0x7bec, 0xe984, 0x7be7, 0xe979, 0x7be3, 0xe96d, 0x7bde, 0xe961,
+  0x7bda, 0xe955, 0x7bd6, 0xe94a, 0x7bd1, 0xe93e, 0x7bcd, 0xe932,
+  0x7bc8, 0xe926, 0x7bc4, 0xe91b, 0x7bbf, 0xe90f, 0x7bbb, 0xe903,
+  0x7bb6, 0xe8f7, 0x7bb2, 0xe8ec, 0x7bad, 0xe8e0, 0x7ba9, 0xe8d4,
+  0x7ba4, 0xe8c9, 0x7b9f, 0xe8bd, 0x7b9b, 0xe8b1, 0x7b96, 0xe8a5,
+  0x7b92, 0xe89a, 0x7b8d, 0xe88e, 0x7b88, 0xe882, 0x7b84, 0xe877,
+  0x7b7f, 0xe86b, 0x7b7b, 0xe85f, 0x7b76, 0xe854, 0x7b71, 0xe848,
+  0x7b6d, 0xe83c, 0x7b68, 0xe831, 0x7b63, 0xe825, 0x7b5f, 0xe819,
+  0x7b5a, 0xe80e, 0x7b55, 0xe802, 0x7b50, 0xe7f6, 0x7b4c, 0xe7eb,
+  0x7b47, 0xe7df, 0x7b42, 0xe7d3, 0x7b3e, 0xe7c8, 0x7b39, 0xe7bc,
+  0x7b34, 0xe7b1, 0x7b2f, 0xe7a5, 0x7b2a, 0xe799, 0x7b26, 0xe78e,
+  0x7b21, 0xe782, 0x7b1c, 0xe777, 0x7b17, 0xe76b, 0x7b12, 0xe75f,
+  0x7b0e, 0xe754, 0x7b09, 0xe748, 0x7b04, 0xe73d, 0x7aff, 0xe731,
+  0x7afa, 0xe725, 0x7af5, 0xe71a, 0x7af0, 0xe70e, 0x7aeb, 0xe703,
+  0x7ae6, 0xe6f7, 0x7ae2, 0xe6ec, 0x7add, 0xe6e0, 0x7ad8, 0xe6d4,
+  0x7ad3, 0xe6c9, 0x7ace, 0xe6bd, 0x7ac9, 0xe6b2, 0x7ac4, 0xe6a6,
+  0x7abf, 0xe69b, 0x7aba, 0xe68f, 0x7ab5, 0xe684, 0x7ab0, 0xe678,
+  0x7aab, 0xe66d, 0x7aa6, 0xe661, 0x7aa1, 0xe656, 0x7a9c, 0xe64a,
+  0x7a97, 0xe63f, 0x7a92, 0xe633, 0x7a8d, 0xe628, 0x7a88, 0xe61c,
+  0x7a82, 0xe611, 0x7a7d, 0xe605, 0x7a78, 0xe5fa, 0x7a73, 0xe5ee,
+  0x7a6e, 0xe5e3, 0x7a69, 0xe5d7, 0x7a64, 0xe5cc, 0x7a5f, 0xe5c0,
+  0x7a59, 0xe5b5, 0x7a54, 0xe5a9, 0x7a4f, 0xe59e, 0x7a4a, 0xe592,
+  0x7a45, 0xe587, 0x7a3f, 0xe57c, 0x7a3a, 0xe570, 0x7a35, 0xe565,
+  0x7a30, 0xe559, 0x7a2b, 0xe54e, 0x7a25, 0xe542, 0x7a20, 0xe537,
+  0x7a1b, 0xe52c, 0x7a16, 0xe520, 0x7a10, 0xe515, 0x7a0b, 0xe509,
+  0x7a06, 0xe4fe, 0x7a00, 0xe4f3, 0x79fb, 0xe4e7, 0x79f6, 0xe4dc,
+  0x79f0, 0xe4d0, 0x79eb, 0xe4c5, 0x79e6, 0xe4ba, 0x79e0, 0xe4ae,
+  0x79db, 0xe4a3, 0x79d6, 0xe498, 0x79d0, 0xe48c, 0x79cb, 0xe481,
+  0x79c5, 0xe476, 0x79c0, 0xe46a, 0x79bb, 0xe45f, 0x79b5, 0xe454,
+  0x79b0, 0xe448, 0x79aa, 0xe43d, 0x79a5, 0xe432, 0x799f, 0xe426,
+  0x799a, 0xe41b, 0x7994, 0xe410, 0x798f, 0xe404, 0x7989, 0xe3f9,
+  0x7984, 0xe3ee, 0x797e, 0xe3e2, 0x7979, 0xe3d7, 0x7973, 0xe3cc,
+  0x796e, 0xe3c1, 0x7968, 0xe3b5, 0x7963, 0xe3aa, 0x795d, 0xe39f,
+  0x7958, 0xe394, 0x7952, 0xe388, 0x794c, 0xe37d, 0x7947, 0xe372,
+  0x7941, 0xe367, 0x793b, 0xe35b, 0x7936, 0xe350, 0x7930, 0xe345,
+  0x792b, 0xe33a, 0x7925, 0xe32e, 0x791f, 0xe323, 0x791a, 0xe318,
+  0x7914, 0xe30d, 0x790e, 0xe301, 0x7909, 0xe2f6, 0x7903, 0xe2eb,
+  0x78fd, 0xe2e0, 0x78f7, 0xe2d5, 0x78f2, 0xe2ca, 0x78ec, 0xe2be,
+  0x78e6, 0xe2b3, 0x78e0, 0xe2a8, 0x78db, 0xe29d, 0x78d5, 0xe292,
+  0x78cf, 0xe287, 0x78c9, 0xe27b, 0x78c3, 0xe270, 0x78be, 0xe265,
+  0x78b8, 0xe25a, 0x78b2, 0xe24f, 0x78ac, 0xe244, 0x78a6, 0xe239,
+  0x78a1, 0xe22d, 0x789b, 0xe222, 0x7895, 0xe217, 0x788f, 0xe20c,
+  0x7889, 0xe201, 0x7883, 0xe1f6, 0x787d, 0xe1eb, 0x7877, 0xe1e0,
+  0x7871, 0xe1d5, 0x786b, 0xe1ca, 0x7866, 0xe1be, 0x7860, 0xe1b3,
+  0x785a, 0xe1a8, 0x7854, 0xe19d, 0x784e, 0xe192, 0x7848, 0xe187,
+  0x7842, 0xe17c, 0x783c, 0xe171, 0x7836, 0xe166, 0x7830, 0xe15b,
+  0x782a, 0xe150, 0x7824, 0xe145, 0x781e, 0xe13a, 0x7818, 0xe12f,
+  0x7812, 0xe124, 0x780b, 0xe119, 0x7805, 0xe10e, 0x77ff, 0xe103,
+  0x77f9, 0xe0f8, 0x77f3, 0xe0ed, 0x77ed, 0xe0e2, 0x77e7, 0xe0d7,
+  0x77e1, 0xe0cc, 0x77db, 0xe0c1, 0x77d5, 0xe0b6, 0x77ce, 0xe0ab,
+  0x77c8, 0xe0a0, 0x77c2, 0xe095, 0x77bc, 0xe08a, 0x77b6, 0xe07f,
+  0x77b0, 0xe074, 0x77a9, 0xe069, 0x77a3, 0xe05e, 0x779d, 0xe054,
+  0x7797, 0xe049, 0x7790, 0xe03e, 0x778a, 0xe033, 0x7784, 0xe028,
+  0x777e, 0xe01d, 0x7777, 0xe012, 0x7771, 0xe007, 0x776b, 0xdffc,
+  0x7765, 0xdff1, 0x775e, 0xdfe7, 0x7758, 0xdfdc, 0x7752, 0xdfd1,
+  0x774b, 0xdfc6, 0x7745, 0xdfbb, 0x773f, 0xdfb0, 0x7738, 0xdfa5,
+  0x7732, 0xdf9b, 0x772c, 0xdf90, 0x7725, 0xdf85, 0x771f, 0xdf7a,
+  0x7718, 0xdf6f, 0x7712, 0xdf65, 0x770c, 0xdf5a, 0x7705, 0xdf4f,
+  0x76ff, 0xdf44, 0x76f8, 0xdf39, 0x76f2, 0xdf2f, 0x76eb, 0xdf24,
+  0x76e5, 0xdf19, 0x76df, 0xdf0e, 0x76d8, 0xdf03, 0x76d2, 0xdef9,
+  0x76cb, 0xdeee, 0x76c5, 0xdee3, 0x76be, 0xded8, 0x76b8, 0xdece,
+  0x76b1, 0xdec3, 0x76ab, 0xdeb8, 0x76a4, 0xdead, 0x769d, 0xdea3,
+  0x7697, 0xde98, 0x7690, 0xde8d, 0x768a, 0xde83, 0x7683, 0xde78,
+  0x767d, 0xde6d, 0x7676, 0xde62, 0x766f, 0xde58, 0x7669, 0xde4d,
+  0x7662, 0xde42, 0x765c, 0xde38, 0x7655, 0xde2d, 0x764e, 0xde22,
+  0x7648, 0xde18, 0x7641, 0xde0d, 0x763a, 0xde02, 0x7634, 0xddf8,
+  0x762d, 0xdded, 0x7626, 0xdde2, 0x7620, 0xddd8, 0x7619, 0xddcd,
+  0x7612, 0xddc3, 0x760b, 0xddb8, 0x7605, 0xddad, 0x75fe, 0xdda3,
+  0x75f7, 0xdd98, 0x75f0, 0xdd8e, 0x75ea, 0xdd83, 0x75e3, 0xdd78,
+  0x75dc, 0xdd6e, 0x75d5, 0xdd63, 0x75ce, 0xdd59, 0x75c8, 0xdd4e,
+  0x75c1, 0xdd44, 0x75ba, 0xdd39, 0x75b3, 0xdd2e, 0x75ac, 0xdd24,
+  0x75a5, 0xdd19, 0x759f, 0xdd0f, 0x7598, 0xdd04, 0x7591, 0xdcfa,
+  0x758a, 0xdcef, 0x7583, 0xdce5, 0x757c, 0xdcda, 0x7575, 0xdcd0,
+  0x756e, 0xdcc5, 0x7567, 0xdcbb, 0x7561, 0xdcb0, 0x755a, 0xdca6,
+  0x7553, 0xdc9b, 0x754c, 0xdc91, 0x7545, 0xdc86, 0x753e, 0xdc7c,
+  0x7537, 0xdc72, 0x7530, 0xdc67, 0x7529, 0xdc5d, 0x7522, 0xdc52,
+  0x751b, 0xdc48, 0x7514, 0xdc3d, 0x750d, 0xdc33, 0x7506, 0xdc29,
+  0x74ff, 0xdc1e, 0x74f8, 0xdc14, 0x74f1, 0xdc09, 0x74ea, 0xdbff,
+  0x74e2, 0xdbf5, 0x74db, 0xdbea, 0x74d4, 0xdbe0, 0x74cd, 0xdbd5,
+  0x74c6, 0xdbcb, 0x74bf, 0xdbc1, 0x74b8, 0xdbb6, 0x74b1, 0xdbac,
+  0x74aa, 0xdba2, 0x74a2, 0xdb97, 0x749b, 0xdb8d, 0x7494, 0xdb83,
+  0x748d, 0xdb78, 0x7486, 0xdb6e, 0x747f, 0xdb64, 0x7477, 0xdb59,
+  0x7470, 0xdb4f, 0x7469, 0xdb45, 0x7462, 0xdb3b, 0x745b, 0xdb30,
+  0x7453, 0xdb26, 0x744c, 0xdb1c, 0x7445, 0xdb11, 0x743e, 0xdb07,
+  0x7436, 0xdafd, 0x742f, 0xdaf3, 0x7428, 0xdae8, 0x7420, 0xdade,
+  0x7419, 0xdad4, 0x7412, 0xdaca, 0x740b, 0xdabf, 0x7403, 0xdab5,
+  0x73fc, 0xdaab, 0x73f5, 0xdaa1, 0x73ed, 0xda97, 0x73e6, 0xda8c,
+  0x73df, 0xda82, 0x73d7, 0xda78, 0x73d0, 0xda6e, 0x73c8, 0xda64,
+  0x73c1, 0xda5a, 0x73ba, 0xda4f, 0x73b2, 0xda45, 0x73ab, 0xda3b,
+  0x73a3, 0xda31, 0x739c, 0xda27, 0x7395, 0xda1d, 0x738d, 0xda13,
+  0x7386, 0xda08, 0x737e, 0xd9fe, 0x7377, 0xd9f4, 0x736f, 0xd9ea,
+  0x7368, 0xd9e0, 0x7360, 0xd9d6, 0x7359, 0xd9cc, 0x7351, 0xd9c2,
+  0x734a, 0xd9b8, 0x7342, 0xd9ae, 0x733b, 0xd9a4, 0x7333, 0xd99a,
+  0x732c, 0xd98f, 0x7324, 0xd985, 0x731d, 0xd97b, 0x7315, 0xd971,
+  0x730d, 0xd967, 0x7306, 0xd95d, 0x72fe, 0xd953, 0x72f7, 0xd949,
+  0x72ef, 0xd93f, 0x72e7, 0xd935, 0x72e0, 0xd92b, 0x72d8, 0xd921,
+  0x72d0, 0xd917, 0x72c9, 0xd90d, 0x72c1, 0xd903, 0x72ba, 0xd8f9,
+  0x72b2, 0xd8ef, 0x72aa, 0xd8e6, 0x72a3, 0xd8dc, 0x729b, 0xd8d2,
+  0x7293, 0xd8c8, 0x728b, 0xd8be, 0x7284, 0xd8b4, 0x727c, 0xd8aa,
+  0x7274, 0xd8a0, 0x726d, 0xd896, 0x7265, 0xd88c, 0x725d, 0xd882,
+  0x7255, 0xd878, 0x724e, 0xd86f, 0x7246, 0xd865, 0x723e, 0xd85b,
+  0x7236, 0xd851, 0x722e, 0xd847, 0x7227, 0xd83d, 0x721f, 0xd833,
+  0x7217, 0xd82a, 0x720f, 0xd820, 0x7207, 0xd816, 0x71ff, 0xd80c,
+  0x71f8, 0xd802, 0x71f0, 0xd7f8, 0x71e8, 0xd7ef, 0x71e0, 0xd7e5,
+  0x71d8, 0xd7db, 0x71d0, 0xd7d1, 0x71c8, 0xd7c8, 0x71c0, 0xd7be,
+  0x71b9, 0xd7b4, 0x71b1, 0xd7aa, 0x71a9, 0xd7a0, 0x71a1, 0xd797,
+  0x7199, 0xd78d, 0x7191, 0xd783, 0x7189, 0xd77a, 0x7181, 0xd770,
+  0x7179, 0xd766, 0x7171, 0xd75c, 0x7169, 0xd753, 0x7161, 0xd749,
+  0x7159, 0xd73f, 0x7151, 0xd736, 0x7149, 0xd72c, 0x7141, 0xd722,
+  0x7139, 0xd719, 0x7131, 0xd70f, 0x7129, 0xd705, 0x7121, 0xd6fc,
+  0x7119, 0xd6f2, 0x7111, 0xd6e8, 0x7109, 0xd6df, 0x7101, 0xd6d5,
+  0x70f9, 0xd6cb, 0x70f0, 0xd6c2, 0x70e8, 0xd6b8, 0x70e0, 0xd6af,
+  0x70d8, 0xd6a5, 0x70d0, 0xd69b, 0x70c8, 0xd692, 0x70c0, 0xd688,
+  0x70b8, 0xd67f, 0x70af, 0xd675, 0x70a7, 0xd66c, 0x709f, 0xd662,
+  0x7097, 0xd659, 0x708f, 0xd64f, 0x7087, 0xd645, 0x707e, 0xd63c,
+  0x7076, 0xd632, 0x706e, 0xd629, 0x7066, 0xd61f, 0x705d, 0xd616,
+  0x7055, 0xd60c, 0x704d, 0xd603, 0x7045, 0xd5f9, 0x703c, 0xd5f0,
+  0x7034, 0xd5e6, 0x702c, 0xd5dd, 0x7024, 0xd5d4, 0x701b, 0xd5ca,
+  0x7013, 0xd5c1, 0x700b, 0xd5b7, 0x7002, 0xd5ae, 0x6ffa, 0xd5a4,
+  0x6ff2, 0xd59b, 0x6fea, 0xd592, 0x6fe1, 0xd588, 0x6fd9, 0xd57f,
+  0x6fd0, 0xd575, 0x6fc8, 0xd56c, 0x6fc0, 0xd563, 0x6fb7, 0xd559,
+  0x6faf, 0xd550, 0x6fa7, 0xd547, 0x6f9e, 0xd53d, 0x6f96, 0xd534,
+  0x6f8d, 0xd52a, 0x6f85, 0xd521, 0x6f7d, 0xd518, 0x6f74, 0xd50e,
+  0x6f6c, 0xd505, 0x6f63, 0xd4fc, 0x6f5b, 0xd4f3, 0x6f52, 0xd4e9,
+  0x6f4a, 0xd4e0, 0x6f41, 0xd4d7, 0x6f39, 0xd4cd, 0x6f30, 0xd4c4,
+  0x6f28, 0xd4bb, 0x6f20, 0xd4b2, 0x6f17, 0xd4a8, 0x6f0e, 0xd49f,
+  0x6f06, 0xd496, 0x6efd, 0xd48d, 0x6ef5, 0xd483, 0x6eec, 0xd47a,
+  0x6ee4, 0xd471, 0x6edb, 0xd468, 0x6ed3, 0xd45f, 0x6eca, 0xd455,
+  0x6ec2, 0xd44c, 0x6eb9, 0xd443, 0x6eb0, 0xd43a, 0x6ea8, 0xd431,
+  0x6e9f, 0xd428, 0x6e97, 0xd41e, 0x6e8e, 0xd415, 0x6e85, 0xd40c,
+  0x6e7d, 0xd403, 0x6e74, 0xd3fa, 0x6e6b, 0xd3f1, 0x6e63, 0xd3e8,
+  0x6e5a, 0xd3df, 0x6e51, 0xd3d5, 0x6e49, 0xd3cc, 0x6e40, 0xd3c3,
+  0x6e37, 0xd3ba, 0x6e2f, 0xd3b1, 0x6e26, 0xd3a8, 0x6e1d, 0xd39f,
+  0x6e15, 0xd396, 0x6e0c, 0xd38d, 0x6e03, 0xd384, 0x6dfa, 0xd37b,
+  0x6df2, 0xd372, 0x6de9, 0xd369, 0x6de0, 0xd360, 0x6dd7, 0xd357,
+  0x6dcf, 0xd34e, 0x6dc6, 0xd345, 0x6dbd, 0xd33c, 0x6db4, 0xd333,
+  0x6dab, 0xd32a, 0x6da3, 0xd321, 0x6d9a, 0xd318, 0x6d91, 0xd30f,
+  0x6d88, 0xd306, 0x6d7f, 0xd2fd, 0x6d76, 0xd2f4, 0x6d6e, 0xd2eb,
+  0x6d65, 0xd2e2, 0x6d5c, 0xd2d9, 0x6d53, 0xd2d1, 0x6d4a, 0xd2c8,
+  0x6d41, 0xd2bf, 0x6d38, 0xd2b6, 0x6d2f, 0xd2ad, 0x6d27, 0xd2a4,
+  0x6d1e, 0xd29b, 0x6d15, 0xd292, 0x6d0c, 0xd28a, 0x6d03, 0xd281,
+  0x6cfa, 0xd278, 0x6cf1, 0xd26f, 0x6ce8, 0xd266, 0x6cdf, 0xd25d,
+  0x6cd6, 0xd255, 0x6ccd, 0xd24c, 0x6cc4, 0xd243, 0x6cbb, 0xd23a,
+  0x6cb2, 0xd231, 0x6ca9, 0xd229, 0x6ca0, 0xd220, 0x6c97, 0xd217,
+  0x6c8e, 0xd20e, 0x6c85, 0xd206, 0x6c7c, 0xd1fd, 0x6c73, 0xd1f4,
+  0x6c6a, 0xd1eb, 0x6c61, 0xd1e3, 0x6c58, 0xd1da, 0x6c4f, 0xd1d1,
+  0x6c46, 0xd1c9, 0x6c3d, 0xd1c0, 0x6c34, 0xd1b7, 0x6c2b, 0xd1af,
+  0x6c21, 0xd1a6, 0x6c18, 0xd19d, 0x6c0f, 0xd195, 0x6c06, 0xd18c,
+  0x6bfd, 0xd183, 0x6bf4, 0xd17b, 0x6beb, 0xd172, 0x6be2, 0xd169,
+  0x6bd8, 0xd161, 0x6bcf, 0xd158, 0x6bc6, 0xd150, 0x6bbd, 0xd147,
+  0x6bb4, 0xd13e, 0x6bab, 0xd136, 0x6ba1, 0xd12d, 0x6b98, 0xd125,
+  0x6b8f, 0xd11c, 0x6b86, 0xd114, 0x6b7d, 0xd10b, 0x6b73, 0xd103,
+  0x6b6a, 0xd0fa, 0x6b61, 0xd0f2, 0x6b58, 0xd0e9, 0x6b4e, 0xd0e0,
+  0x6b45, 0xd0d8, 0x6b3c, 0xd0d0, 0x6b33, 0xd0c7, 0x6b29, 0xd0bf,
+  0x6b20, 0xd0b6, 0x6b17, 0xd0ae, 0x6b0d, 0xd0a5, 0x6b04, 0xd09d,
+  0x6afb, 0xd094, 0x6af2, 0xd08c, 0x6ae8, 0xd083, 0x6adf, 0xd07b,
+  0x6ad6, 0xd073, 0x6acc, 0xd06a, 0x6ac3, 0xd062, 0x6ab9, 0xd059,
+  0x6ab0, 0xd051, 0x6aa7, 0xd049, 0x6a9d, 0xd040, 0x6a94, 0xd038,
+  0x6a8b, 0xd030, 0x6a81, 0xd027, 0x6a78, 0xd01f, 0x6a6e, 0xd016,
+  0x6a65, 0xd00e, 0x6a5c, 0xd006, 0x6a52, 0xcffe, 0x6a49, 0xcff5,
+  0x6a3f, 0xcfed, 0x6a36, 0xcfe5, 0x6a2c, 0xcfdc, 0x6a23, 0xcfd4,
+  0x6a1a, 0xcfcc, 0x6a10, 0xcfc4, 0x6a07, 0xcfbb, 0x69fd, 0xcfb3,
+  0x69f4, 0xcfab, 0x69ea, 0xcfa3, 0x69e1, 0xcf9a, 0x69d7, 0xcf92,
+  0x69ce, 0xcf8a, 0x69c4, 0xcf82, 0x69bb, 0xcf79, 0x69b1, 0xcf71,
+  0x69a7, 0xcf69, 0x699e, 0xcf61, 0x6994, 0xcf59, 0x698b, 0xcf51,
+  0x6981, 0xcf48, 0x6978, 0xcf40, 0x696e, 0xcf38, 0x6965, 0xcf30,
+  0x695b, 0xcf28, 0x6951, 0xcf20, 0x6948, 0xcf18, 0x693e, 0xcf10,
+  0x6935, 0xcf07, 0x692b, 0xceff, 0x6921, 0xcef7, 0x6918, 0xceef,
+  0x690e, 0xcee7, 0x6904, 0xcedf, 0x68fb, 0xced7, 0x68f1, 0xcecf,
+  0x68e7, 0xcec7, 0x68de, 0xcebf, 0x68d4, 0xceb7, 0x68ca, 0xceaf,
+  0x68c1, 0xcea7, 0x68b7, 0xce9f, 0x68ad, 0xce97, 0x68a4, 0xce8f,
+  0x689a, 0xce87, 0x6890, 0xce7f, 0x6886, 0xce77, 0x687d, 0xce6f,
+  0x6873, 0xce67, 0x6869, 0xce5f, 0x6860, 0xce57, 0x6856, 0xce4f,
+  0x684c, 0xce47, 0x6842, 0xce40, 0x6838, 0xce38, 0x682f, 0xce30,
+  0x6825, 0xce28, 0x681b, 0xce20, 0x6811, 0xce18, 0x6808, 0xce10,
+  0x67fe, 0xce08, 0x67f4, 0xce01, 0x67ea, 0xcdf9, 0x67e0, 0xcdf1,
+  0x67d6, 0xcde9, 0x67cd, 0xcde1, 0x67c3, 0xcdd9, 0x67b9, 0xcdd2,
+  0x67af, 0xcdca, 0x67a5, 0xcdc2, 0x679b, 0xcdba, 0x6791, 0xcdb2,
+  0x6788, 0xcdab, 0x677e, 0xcda3, 0x6774, 0xcd9b, 0x676a, 0xcd93,
+  0x6760, 0xcd8c, 0x6756, 0xcd84, 0x674c, 0xcd7c, 0x6742, 0xcd75,
+  0x6738, 0xcd6d, 0x672e, 0xcd65, 0x6724, 0xcd5d, 0x671a, 0xcd56,
+  0x6711, 0xcd4e, 0x6707, 0xcd46, 0x66fd, 0xcd3f, 0x66f3, 0xcd37,
+  0x66e9, 0xcd30, 0x66df, 0xcd28, 0x66d5, 0xcd20, 0x66cb, 0xcd19,
+  0x66c1, 0xcd11, 0x66b7, 0xcd09, 0x66ad, 0xcd02, 0x66a3, 0xccfa,
+  0x6699, 0xccf3, 0x668f, 0xcceb, 0x6685, 0xcce3, 0x667b, 0xccdc,
+  0x6671, 0xccd4, 0x6666, 0xcccd, 0x665c, 0xccc5, 0x6652, 0xccbe,
+  0x6648, 0xccb6, 0x663e, 0xccaf, 0x6634, 0xcca7, 0x662a, 0xcca0,
+  0x6620, 0xcc98, 0x6616, 0xcc91, 0x660c, 0xcc89, 0x6602, 0xcc82,
+  0x65f8, 0xcc7a, 0x65ed, 0xcc73, 0x65e3, 0xcc6b, 0x65d9, 0xcc64,
+  0x65cf, 0xcc5d, 0x65c5, 0xcc55, 0x65bb, 0xcc4e, 0x65b1, 0xcc46,
+  0x65a6, 0xcc3f, 0x659c, 0xcc38, 0x6592, 0xcc30, 0x6588, 0xcc29,
+  0x657e, 0xcc21, 0x6574, 0xcc1a, 0x6569, 0xcc13, 0x655f, 0xcc0b,
+  0x6555, 0xcc04, 0x654b, 0xcbfd, 0x6541, 0xcbf5, 0x6536, 0xcbee,
+  0x652c, 0xcbe7, 0x6522, 0xcbe0, 0x6518, 0xcbd8, 0x650d, 0xcbd1,
+  0x6503, 0xcbca, 0x64f9, 0xcbc2, 0x64ef, 0xcbbb, 0x64e4, 0xcbb4,
+  0x64da, 0xcbad, 0x64d0, 0xcba5, 0x64c5, 0xcb9e, 0x64bb, 0xcb97,
+  0x64b1, 0xcb90, 0x64a7, 0xcb89, 0x649c, 0xcb81, 0x6492, 0xcb7a,
+  0x6488, 0xcb73, 0x647d, 0xcb6c, 0x6473, 0xcb65, 0x6469, 0xcb5e,
+  0x645e, 0xcb56, 0x6454, 0xcb4f, 0x644a, 0xcb48, 0x643f, 0xcb41,
+  0x6435, 0xcb3a, 0x642b, 0xcb33, 0x6420, 0xcb2c, 0x6416, 0xcb25,
+  0x640b, 0xcb1e, 0x6401, 0xcb16, 0x63f7, 0xcb0f, 0x63ec, 0xcb08,
+  0x63e2, 0xcb01, 0x63d7, 0xcafa, 0x63cd, 0xcaf3, 0x63c3, 0xcaec,
+  0x63b8, 0xcae5, 0x63ae, 0xcade, 0x63a3, 0xcad7, 0x6399, 0xcad0,
+  0x638e, 0xcac9, 0x6384, 0xcac2, 0x637a, 0xcabb, 0x636f, 0xcab4,
+  0x6365, 0xcaad, 0x635a, 0xcaa6, 0x6350, 0xca9f, 0x6345, 0xca99,
+  0x633b, 0xca92, 0x6330, 0xca8b, 0x6326, 0xca84, 0x631b, 0xca7d,
+  0x6311, 0xca76, 0x6306, 0xca6f, 0x62fc, 0xca68, 0x62f1, 0xca61,
+  0x62e7, 0xca5b, 0x62dc, 0xca54, 0x62d2, 0xca4d, 0x62c7, 0xca46,
+  0x62bc, 0xca3f, 0x62b2, 0xca38, 0x62a7, 0xca32, 0x629d, 0xca2b,
+  0x6292, 0xca24, 0x6288, 0xca1d, 0x627d, 0xca16, 0x6272, 0xca10,
+  0x6268, 0xca09, 0x625d, 0xca02, 0x6253, 0xc9fb, 0x6248, 0xc9f5,
+  0x623d, 0xc9ee, 0x6233, 0xc9e7, 0x6228, 0xc9e0, 0x621e, 0xc9da,
+  0x6213, 0xc9d3, 0x6208, 0xc9cc, 0x61fe, 0xc9c6, 0x61f3, 0xc9bf,
+  0x61e8, 0xc9b8, 0x61de, 0xc9b2, 0x61d3, 0xc9ab, 0x61c8, 0xc9a4,
+  0x61be, 0xc99e, 0x61b3, 0xc997, 0x61a8, 0xc991, 0x619e, 0xc98a,
+  0x6193, 0xc983, 0x6188, 0xc97d, 0x617d, 0xc976, 0x6173, 0xc970,
+  0x6168, 0xc969, 0x615d, 0xc963, 0x6153, 0xc95c, 0x6148, 0xc955,
+  0x613d, 0xc94f, 0x6132, 0xc948, 0x6128, 0xc942, 0x611d, 0xc93b,
+  0x6112, 0xc935, 0x6107, 0xc92e, 0x60fd, 0xc928, 0x60f2, 0xc921,
+  0x60e7, 0xc91b, 0x60dc, 0xc915, 0x60d1, 0xc90e, 0x60c7, 0xc908,
+  0x60bc, 0xc901, 0x60b1, 0xc8fb, 0x60a6, 0xc8f4, 0x609b, 0xc8ee,
+  0x6091, 0xc8e8, 0x6086, 0xc8e1, 0x607b, 0xc8db, 0x6070, 0xc8d4,
+  0x6065, 0xc8ce, 0x605b, 0xc8c8, 0x6050, 0xc8c1, 0x6045, 0xc8bb,
+  0x603a, 0xc8b5, 0x602f, 0xc8ae, 0x6024, 0xc8a8, 0x6019, 0xc8a2,
+  0x600f, 0xc89b, 0x6004, 0xc895, 0x5ff9, 0xc88f, 0x5fee, 0xc889,
+  0x5fe3, 0xc882, 0x5fd8, 0xc87c, 0x5fcd, 0xc876, 0x5fc2, 0xc870,
+  0x5fb7, 0xc869, 0x5fac, 0xc863, 0x5fa2, 0xc85d, 0x5f97, 0xc857,
+  0x5f8c, 0xc850, 0x5f81, 0xc84a, 0x5f76, 0xc844, 0x5f6b, 0xc83e,
+  0x5f60, 0xc838, 0x5f55, 0xc832, 0x5f4a, 0xc82b, 0x5f3f, 0xc825,
+  0x5f34, 0xc81f, 0x5f29, 0xc819, 0x5f1e, 0xc813, 0x5f13, 0xc80d,
+  0x5f08, 0xc807, 0x5efd, 0xc801, 0x5ef2, 0xc7fb, 0x5ee7, 0xc7f5,
+  0x5edc, 0xc7ee, 0x5ed1, 0xc7e8, 0x5ec6, 0xc7e2, 0x5ebb, 0xc7dc,
+  0x5eb0, 0xc7d6, 0x5ea5, 0xc7d0, 0x5e9a, 0xc7ca, 0x5e8f, 0xc7c4,
+  0x5e84, 0xc7be, 0x5e79, 0xc7b8, 0x5e6e, 0xc7b2, 0x5e63, 0xc7ac,
+  0x5e58, 0xc7a6, 0x5e4d, 0xc7a0, 0x5e42, 0xc79a, 0x5e36, 0xc795,
+  0x5e2b, 0xc78f, 0x5e20, 0xc789, 0x5e15, 0xc783, 0x5e0a, 0xc77d,
+  0x5dff, 0xc777, 0x5df4, 0xc771, 0x5de9, 0xc76b, 0x5dde, 0xc765,
+  0x5dd3, 0xc75f, 0x5dc7, 0xc75a, 0x5dbc, 0xc754, 0x5db1, 0xc74e,
+  0x5da6, 0xc748, 0x5d9b, 0xc742, 0x5d90, 0xc73d, 0x5d85, 0xc737,
+  0x5d79, 0xc731, 0x5d6e, 0xc72b, 0x5d63, 0xc725, 0x5d58, 0xc720,
+  0x5d4d, 0xc71a, 0x5d42, 0xc714, 0x5d36, 0xc70e, 0x5d2b, 0xc709,
+  0x5d20, 0xc703, 0x5d15, 0xc6fd, 0x5d0a, 0xc6f7, 0x5cff, 0xc6f2,
+  0x5cf3, 0xc6ec, 0x5ce8, 0xc6e6, 0x5cdd, 0xc6e1, 0x5cd2, 0xc6db,
+  0x5cc6, 0xc6d5, 0x5cbb, 0xc6d0, 0x5cb0, 0xc6ca, 0x5ca5, 0xc6c5,
+  0x5c99, 0xc6bf, 0x5c8e, 0xc6b9, 0x5c83, 0xc6b4, 0x5c78, 0xc6ae,
+  0x5c6c, 0xc6a8, 0x5c61, 0xc6a3, 0x5c56, 0xc69d, 0x5c4b, 0xc698,
+  0x5c3f, 0xc692, 0x5c34, 0xc68d, 0x5c29, 0xc687, 0x5c1e, 0xc682,
+  0x5c12, 0xc67c, 0x5c07, 0xc677, 0x5bfc, 0xc671, 0x5bf0, 0xc66c,
+  0x5be5, 0xc666, 0x5bda, 0xc661, 0x5bce, 0xc65b, 0x5bc3, 0xc656,
+  0x5bb8, 0xc650, 0x5bac, 0xc64b, 0x5ba1, 0xc645, 0x5b96, 0xc640,
+  0x5b8a, 0xc63b, 0x5b7f, 0xc635, 0x5b74, 0xc630, 0x5b68, 0xc62a,
+  0x5b5d, 0xc625, 0x5b52, 0xc620, 0x5b46, 0xc61a, 0x5b3b, 0xc615,
+  0x5b30, 0xc610, 0x5b24, 0xc60a, 0x5b19, 0xc605, 0x5b0d, 0xc600,
+  0x5b02, 0xc5fa, 0x5af7, 0xc5f5, 0x5aeb, 0xc5f0, 0x5ae0, 0xc5ea,
+  0x5ad4, 0xc5e5, 0x5ac9, 0xc5e0, 0x5abe, 0xc5db, 0x5ab2, 0xc5d5,
+  0x5aa7, 0xc5d0, 0x5a9b, 0xc5cb, 0x5a90, 0xc5c6, 0x5a84, 0xc5c1,
+  0x5a79, 0xc5bb, 0x5a6e, 0xc5b6, 0x5a62, 0xc5b1, 0x5a57, 0xc5ac,
+  0x5a4b, 0xc5a7, 0x5a40, 0xc5a1, 0x5a34, 0xc59c, 0x5a29, 0xc597,
+  0x5a1d, 0xc592, 0x5a12, 0xc58d, 0x5a06, 0xc588, 0x59fb, 0xc583,
+  0x59ef, 0xc57e, 0x59e4, 0xc578, 0x59d8, 0xc573, 0x59cd, 0xc56e,
+  0x59c1, 0xc569, 0x59b6, 0xc564, 0x59aa, 0xc55f, 0x599f, 0xc55a,
+  0x5993, 0xc555, 0x5988, 0xc550, 0x597c, 0xc54b, 0x5971, 0xc546,
+  0x5965, 0xc541, 0x595a, 0xc53c, 0x594e, 0xc537, 0x5943, 0xc532,
+  0x5937, 0xc52d, 0x592c, 0xc528, 0x5920, 0xc523, 0x5914, 0xc51e,
+  0x5909, 0xc51a, 0x58fd, 0xc515, 0x58f2, 0xc510, 0x58e6, 0xc50b,
+  0x58db, 0xc506, 0x58cf, 0xc501, 0x58c3, 0xc4fc, 0x58b8, 0xc4f7,
+  0x58ac, 0xc4f2, 0x58a1, 0xc4ee, 0x5895, 0xc4e9, 0x5889, 0xc4e4,
+  0x587e, 0xc4df, 0x5872, 0xc4da, 0x5867, 0xc4d6, 0x585b, 0xc4d1,
+  0x584f, 0xc4cc, 0x5844, 0xc4c7, 0x5838, 0xc4c2, 0x582d, 0xc4be,
+  0x5821, 0xc4b9, 0x5815, 0xc4b4, 0x580a, 0xc4b0, 0x57fe, 0xc4ab,
+  0x57f2, 0xc4a6, 0x57e7, 0xc4a1, 0x57db, 0xc49d, 0x57cf, 0xc498,
+  0x57c4, 0xc493, 0x57b8, 0xc48f, 0x57ac, 0xc48a, 0x57a1, 0xc485,
+  0x5795, 0xc481, 0x5789, 0xc47c, 0x577e, 0xc478, 0x5772, 0xc473,
+  0x5766, 0xc46e, 0x575b, 0xc46a, 0x574f, 0xc465, 0x5743, 0xc461,
+  0x5737, 0xc45c, 0x572c, 0xc457, 0x5720, 0xc453, 0x5714, 0xc44e,
+  0x5709, 0xc44a, 0x56fd, 0xc445, 0x56f1, 0xc441, 0x56e5, 0xc43c,
+  0x56da, 0xc438, 0x56ce, 0xc433, 0x56c2, 0xc42f, 0x56b6, 0xc42a,
+  0x56ab, 0xc426, 0x569f, 0xc422, 0x5693, 0xc41d, 0x5687, 0xc419,
+  0x567c, 0xc414, 0x5670, 0xc410, 0x5664, 0xc40b, 0x5658, 0xc407,
+  0x564c, 0xc403, 0x5641, 0xc3fe, 0x5635, 0xc3fa, 0x5629, 0xc3f6,
+  0x561d, 0xc3f1, 0x5612, 0xc3ed, 0x5606, 0xc3e9, 0x55fa, 0xc3e4,
+  0x55ee, 0xc3e0, 0x55e2, 0xc3dc, 0x55d7, 0xc3d7, 0x55cb, 0xc3d3,
+  0x55bf, 0xc3cf, 0x55b3, 0xc3ca, 0x55a7, 0xc3c6, 0x559b, 0xc3c2,
+  0x5590, 0xc3be, 0x5584, 0xc3ba, 0x5578, 0xc3b5, 0x556c, 0xc3b1,
+  0x5560, 0xc3ad, 0x5554, 0xc3a9, 0x5549, 0xc3a5, 0x553d, 0xc3a0,
+  0x5531, 0xc39c, 0x5525, 0xc398, 0x5519, 0xc394, 0x550d, 0xc390,
+  0x5501, 0xc38c, 0x54f6, 0xc387, 0x54ea, 0xc383, 0x54de, 0xc37f,
+  0x54d2, 0xc37b, 0x54c6, 0xc377, 0x54ba, 0xc373, 0x54ae, 0xc36f,
+  0x54a2, 0xc36b, 0x5496, 0xc367, 0x548b, 0xc363, 0x547f, 0xc35f,
+  0x5473, 0xc35b, 0x5467, 0xc357, 0x545b, 0xc353, 0x544f, 0xc34f,
+  0x5443, 0xc34b, 0x5437, 0xc347, 0x542b, 0xc343, 0x541f, 0xc33f,
+  0x5413, 0xc33b, 0x5407, 0xc337, 0x53fb, 0xc333, 0x53f0, 0xc32f,
+  0x53e4, 0xc32b, 0x53d8, 0xc327, 0x53cc, 0xc323, 0x53c0, 0xc320,
+  0x53b4, 0xc31c, 0x53a8, 0xc318, 0x539c, 0xc314, 0x5390, 0xc310,
+  0x5384, 0xc30c, 0x5378, 0xc308, 0x536c, 0xc305, 0x5360, 0xc301,
+  0x5354, 0xc2fd, 0x5348, 0xc2f9, 0x533c, 0xc2f5, 0x5330, 0xc2f2,
+  0x5324, 0xc2ee, 0x5318, 0xc2ea, 0x530c, 0xc2e6, 0x5300, 0xc2e3,
+  0x52f4, 0xc2df, 0x52e8, 0xc2db, 0x52dc, 0xc2d8, 0x52d0, 0xc2d4,
+  0x52c4, 0xc2d0, 0x52b8, 0xc2cc, 0x52ac, 0xc2c9, 0x52a0, 0xc2c5,
+  0x5294, 0xc2c1, 0x5288, 0xc2be, 0x527c, 0xc2ba, 0x5270, 0xc2b7,
+  0x5264, 0xc2b3, 0x5258, 0xc2af, 0x524c, 0xc2ac, 0x5240, 0xc2a8,
+  0x5234, 0xc2a5, 0x5228, 0xc2a1, 0x521c, 0xc29d, 0x5210, 0xc29a,
+  0x5204, 0xc296, 0x51f7, 0xc293, 0x51eb, 0xc28f, 0x51df, 0xc28c,
+  0x51d3, 0xc288, 0x51c7, 0xc285, 0x51bb, 0xc281, 0x51af, 0xc27e,
+  0x51a3, 0xc27a, 0x5197, 0xc277, 0x518b, 0xc273, 0x517f, 0xc270,
+  0x5173, 0xc26d, 0x5167, 0xc269, 0x515a, 0xc266, 0x514e, 0xc262,
+  0x5142, 0xc25f, 0x5136, 0xc25c, 0x512a, 0xc258, 0x511e, 0xc255,
+  0x5112, 0xc251, 0x5106, 0xc24e, 0x50fa, 0xc24b, 0x50ed, 0xc247,
+  0x50e1, 0xc244, 0x50d5, 0xc241, 0x50c9, 0xc23e, 0x50bd, 0xc23a,
+  0x50b1, 0xc237, 0x50a5, 0xc234, 0x5099, 0xc230, 0x508c, 0xc22d,
+  0x5080, 0xc22a, 0x5074, 0xc227, 0x5068, 0xc223, 0x505c, 0xc220,
+  0x5050, 0xc21d, 0x5044, 0xc21a, 0x5037, 0xc217, 0x502b, 0xc213,
+  0x501f, 0xc210, 0x5013, 0xc20d, 0x5007, 0xc20a, 0x4ffb, 0xc207,
+  0x4fee, 0xc204, 0x4fe2, 0xc201, 0x4fd6, 0xc1fd, 0x4fca, 0xc1fa,
+  0x4fbe, 0xc1f7, 0x4fb2, 0xc1f4, 0x4fa5, 0xc1f1, 0x4f99, 0xc1ee,
+  0x4f8d, 0xc1eb, 0x4f81, 0xc1e8, 0x4f75, 0xc1e5, 0x4f68, 0xc1e2,
+  0x4f5c, 0xc1df, 0x4f50, 0xc1dc, 0x4f44, 0xc1d9, 0x4f38, 0xc1d6,
+  0x4f2b, 0xc1d3, 0x4f1f, 0xc1d0, 0x4f13, 0xc1cd, 0x4f07, 0xc1ca,
+  0x4efb, 0xc1c7, 0x4eee, 0xc1c4, 0x4ee2, 0xc1c1, 0x4ed6, 0xc1be,
+  0x4eca, 0xc1bb, 0x4ebd, 0xc1b8, 0x4eb1, 0xc1b6, 0x4ea5, 0xc1b3,
+  0x4e99, 0xc1b0, 0x4e8c, 0xc1ad, 0x4e80, 0xc1aa, 0x4e74, 0xc1a7,
+  0x4e68, 0xc1a4, 0x4e5c, 0xc1a2, 0x4e4f, 0xc19f, 0x4e43, 0xc19c,
+  0x4e37, 0xc199, 0x4e2b, 0xc196, 0x4e1e, 0xc194, 0x4e12, 0xc191,
+  0x4e06, 0xc18e, 0x4df9, 0xc18b, 0x4ded, 0xc189, 0x4de1, 0xc186,
+  0x4dd5, 0xc183, 0x4dc8, 0xc180, 0x4dbc, 0xc17e, 0x4db0, 0xc17b,
+  0x4da4, 0xc178, 0x4d97, 0xc176, 0x4d8b, 0xc173, 0x4d7f, 0xc170,
+  0x4d72, 0xc16e, 0x4d66, 0xc16b, 0x4d5a, 0xc168, 0x4d4e, 0xc166,
+  0x4d41, 0xc163, 0x4d35, 0xc161, 0x4d29, 0xc15e, 0x4d1c, 0xc15b,
+  0x4d10, 0xc159, 0x4d04, 0xc156, 0x4cf8, 0xc154, 0x4ceb, 0xc151,
+  0x4cdf, 0xc14f, 0x4cd3, 0xc14c, 0x4cc6, 0xc14a, 0x4cba, 0xc147,
+  0x4cae, 0xc145, 0x4ca1, 0xc142, 0x4c95, 0xc140, 0x4c89, 0xc13d,
+  0x4c7c, 0xc13b, 0x4c70, 0xc138, 0x4c64, 0xc136, 0x4c57, 0xc134,
+  0x4c4b, 0xc131, 0x4c3f, 0xc12f, 0x4c32, 0xc12c, 0x4c26, 0xc12a,
+  0x4c1a, 0xc128, 0x4c0d, 0xc125, 0x4c01, 0xc123, 0x4bf5, 0xc120,
+  0x4be8, 0xc11e, 0x4bdc, 0xc11c, 0x4bd0, 0xc119, 0x4bc3, 0xc117,
+  0x4bb7, 0xc115, 0x4bab, 0xc113, 0x4b9e, 0xc110, 0x4b92, 0xc10e,
+  0x4b85, 0xc10c, 0x4b79, 0xc109, 0x4b6d, 0xc107, 0x4b60, 0xc105,
+  0x4b54, 0xc103, 0x4b48, 0xc100, 0x4b3b, 0xc0fe, 0x4b2f, 0xc0fc,
+  0x4b23, 0xc0fa, 0x4b16, 0xc0f8, 0x4b0a, 0xc0f6, 0x4afd, 0xc0f3,
+  0x4af1, 0xc0f1, 0x4ae5, 0xc0ef, 0x4ad8, 0xc0ed, 0x4acc, 0xc0eb,
+  0x4ac0, 0xc0e9, 0x4ab3, 0xc0e7, 0x4aa7, 0xc0e4, 0x4a9a, 0xc0e2,
+  0x4a8e, 0xc0e0, 0x4a82, 0xc0de, 0x4a75, 0xc0dc, 0x4a69, 0xc0da,
+  0x4a5c, 0xc0d8, 0x4a50, 0xc0d6, 0x4a44, 0xc0d4, 0x4a37, 0xc0d2,
+  0x4a2b, 0xc0d0, 0x4a1e, 0xc0ce, 0x4a12, 0xc0cc, 0x4a06, 0xc0ca,
+  0x49f9, 0xc0c8, 0x49ed, 0xc0c6, 0x49e0, 0xc0c4, 0x49d4, 0xc0c2,
+  0x49c7, 0xc0c0, 0x49bb, 0xc0be, 0x49af, 0xc0bd, 0x49a2, 0xc0bb,
+  0x4996, 0xc0b9, 0x4989, 0xc0b7, 0x497d, 0xc0b5, 0x4970, 0xc0b3,
+  0x4964, 0xc0b1, 0x4958, 0xc0af, 0x494b, 0xc0ae, 0x493f, 0xc0ac,
+  0x4932, 0xc0aa, 0x4926, 0xc0a8, 0x4919, 0xc0a6, 0x490d, 0xc0a5,
+  0x4901, 0xc0a3, 0x48f4, 0xc0a1, 0x48e8, 0xc09f, 0x48db, 0xc09e,
+  0x48cf, 0xc09c, 0x48c2, 0xc09a, 0x48b6, 0xc098, 0x48a9, 0xc097,
+  0x489d, 0xc095, 0x4891, 0xc093, 0x4884, 0xc092, 0x4878, 0xc090,
+  0x486b, 0xc08e, 0x485f, 0xc08d, 0x4852, 0xc08b, 0x4846, 0xc089,
+  0x4839, 0xc088, 0x482d, 0xc086, 0x4820, 0xc085, 0x4814, 0xc083,
+  0x4807, 0xc081, 0x47fb, 0xc080, 0x47ef, 0xc07e, 0x47e2, 0xc07d,
+  0x47d6, 0xc07b, 0x47c9, 0xc07a, 0x47bd, 0xc078, 0x47b0, 0xc077,
+  0x47a4, 0xc075, 0x4797, 0xc074, 0x478b, 0xc072, 0x477e, 0xc071,
+  0x4772, 0xc06f, 0x4765, 0xc06e, 0x4759, 0xc06c, 0x474c, 0xc06b,
+  0x4740, 0xc069, 0x4733, 0xc068, 0x4727, 0xc067, 0x471a, 0xc065,
+  0x470e, 0xc064, 0x4701, 0xc062, 0x46f5, 0xc061, 0x46e8, 0xc060,
+  0x46dc, 0xc05e, 0x46cf, 0xc05d, 0x46c3, 0xc05c, 0x46b6, 0xc05a,
+  0x46aa, 0xc059, 0x469d, 0xc058, 0x4691, 0xc056, 0x4684, 0xc055,
+  0x4678, 0xc054, 0x466b, 0xc053, 0x465f, 0xc051, 0x4652, 0xc050,
+  0x4646, 0xc04f, 0x4639, 0xc04e, 0x462d, 0xc04c, 0x4620, 0xc04b,
+  0x4614, 0xc04a, 0x4607, 0xc049, 0x45fb, 0xc048, 0x45ee, 0xc047,
+  0x45e2, 0xc045, 0x45d5, 0xc044, 0x45c9, 0xc043, 0x45bc, 0xc042,
+  0x45b0, 0xc041, 0x45a3, 0xc040, 0x4597, 0xc03f, 0x458a, 0xc03d,
+  0x457e, 0xc03c, 0x4571, 0xc03b, 0x4565, 0xc03a, 0x4558, 0xc039,
+  0x454c, 0xc038, 0x453f, 0xc037, 0x4533, 0xc036, 0x4526, 0xc035,
+  0x451a, 0xc034, 0x450d, 0xc033, 0x4500, 0xc032, 0x44f4, 0xc031,
+  0x44e7, 0xc030, 0x44db, 0xc02f, 0x44ce, 0xc02e, 0x44c2, 0xc02d,
+  0x44b5, 0xc02c, 0x44a9, 0xc02b, 0x449c, 0xc02b, 0x4490, 0xc02a,
+  0x4483, 0xc029, 0x4477, 0xc028, 0x446a, 0xc027, 0x445e, 0xc026,
+  0x4451, 0xc025, 0x4444, 0xc024, 0x4438, 0xc024, 0x442b, 0xc023,
+  0x441f, 0xc022, 0x4412, 0xc021, 0x4406, 0xc020, 0x43f9, 0xc020,
+  0x43ed, 0xc01f, 0x43e0, 0xc01e, 0x43d4, 0xc01d, 0x43c7, 0xc01d,
+  0x43bb, 0xc01c, 0x43ae, 0xc01b, 0x43a1, 0xc01a, 0x4395, 0xc01a,
+  0x4388, 0xc019, 0x437c, 0xc018, 0x436f, 0xc018, 0x4363, 0xc017,
+  0x4356, 0xc016, 0x434a, 0xc016, 0x433d, 0xc015, 0x4330, 0xc014,
+  0x4324, 0xc014, 0x4317, 0xc013, 0x430b, 0xc013, 0x42fe, 0xc012,
+  0x42f2, 0xc011, 0x42e5, 0xc011, 0x42d9, 0xc010, 0x42cc, 0xc010,
+  0x42c0, 0xc00f, 0x42b3, 0xc00f, 0x42a6, 0xc00e, 0x429a, 0xc00e,
+  0x428d, 0xc00d, 0x4281, 0xc00d, 0x4274, 0xc00c, 0x4268, 0xc00c,
+  0x425b, 0xc00b, 0x424e, 0xc00b, 0x4242, 0xc00a, 0x4235, 0xc00a,
+  0x4229, 0xc009, 0x421c, 0xc009, 0x4210, 0xc009, 0x4203, 0xc008,
+  0x41f7, 0xc008, 0x41ea, 0xc007, 0x41dd, 0xc007, 0x41d1, 0xc007,
+  0x41c4, 0xc006, 0x41b8, 0xc006, 0x41ab, 0xc006, 0x419f, 0xc005,
+  0x4192, 0xc005, 0x4186, 0xc005, 0x4179, 0xc004, 0x416c, 0xc004,
+  0x4160, 0xc004, 0x4153, 0xc004, 0x4147, 0xc003, 0x413a, 0xc003,
+  0x412e, 0xc003, 0x4121, 0xc003, 0x4114, 0xc002, 0x4108, 0xc002,
+  0x40fb, 0xc002, 0x40ef, 0xc002, 0x40e2, 0xc002, 0x40d6, 0xc001,
+  0x40c9, 0xc001, 0x40bc, 0xc001, 0x40b0, 0xc001, 0x40a3, 0xc001,
+  0x4097, 0xc001, 0x408a, 0xc001, 0x407e, 0xc000, 0x4071, 0xc000,
+  0x4065, 0xc000, 0x4058, 0xc000, 0x404b, 0xc000, 0x403f, 0xc000,
+  0x4032, 0xc000, 0x4026, 0xc000, 0x4019, 0xc000, 0x400d, 0xc000,
+};
+
+/**    
+* @brief  Initialization function for the Q15 RFFT/RIFFT.   
+* @param[in, out] *S             points to an instance of the Q15 RFFT/RIFFT structure.   
+* @param[in]      *S_CFFT        points to an instance of the Q15 CFFT/CIFFT structure.   
+* @param[in]      fftLenReal     length of the FFT.   
+* @param[in]      ifftFlagR      flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform.   
+* @param[in]      bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.   
+* @return		The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if fftLenReal is not a supported value.   
+*    
+* \par Description:   
+* \par   
+* The parameter fftLenReal	Specifies length of RFFT/RIFFT Process. Supported FFT Lengths are 128, 512, 2048.    
+* \par    
+* The parameter ifftFlagR controls whether a forward or inverse transform is computed.    
+* Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated.    
+* \par    
+* The parameter bitReverseFlag controls whether output is in normal order or bit reversed order.    
+* Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order.   
+* \par    
+* This function also initializes Twiddle factor table.     
+*/
+
+arm_status arm_rfft_init_q15(
+  arm_rfft_instance_q15 * S,
+  arm_cfft_radix4_instance_q15 * S_CFFT,
+  uint32_t fftLenReal,
+  uint32_t ifftFlagR,
+  uint32_t bitReverseFlag)
+{
+
+  /*  Initialise the default arm status */
+  arm_status status = ARM_MATH_SUCCESS;
+
+  /*  Initialize the Real FFT length */
+  S->fftLenReal = (uint16_t) fftLenReal;
+
+  /*  Initialize the Complex FFT length */
+  S->fftLenBy2 = (uint16_t) fftLenReal / 2u;
+
+  /*  Initialize the Twiddle coefficientA pointer */
+  S->pTwiddleAReal = (q15_t *) realCoefAQ15;
+
+  /*  Initialize the Twiddle coefficientB pointer */
+  S->pTwiddleBReal = (q15_t *) realCoefBQ15;
+
+  /*  Initialize the Flag for selection of RFFT or RIFFT */
+  S->ifftFlagR = (uint8_t) ifftFlagR;
+
+  /*  Initialize the Flag for calculation Bit reversal or not */
+  S->bitReverseFlagR = (uint8_t) bitReverseFlag;
+
+  /*  Initialization of coef modifier depending on the FFT length */
+  switch (S->fftLenReal)
+  {
+  case 8192:
+    S->twidCoefRModifier = 1u;
+    break;
+  case 2048u:
+    S->twidCoefRModifier = 4u;
+    break;
+  case 512u:
+    S->twidCoefRModifier = 16u;
+    break;
+  case 128u:
+    S->twidCoefRModifier = 64u;
+    break;
+  default:
+    /*  Reporting argument error if rfftSize is not valid value */
+    status = ARM_MATH_ARGUMENT_ERROR;
+    break;
+  }
+
+  /* Init Complex FFT Instance */
+  S->pCfft = S_CFFT;
+
+  if(S->ifftFlagR)
+  {
+    /* Initializes the CIFFT Module for fftLenreal/2 length */
+    arm_cfft_radix4_init_q15(S->pCfft, S->fftLenBy2, 1u, 1u);
+  }
+  else
+  {
+    /* Initializes the CFFT Module for fftLenreal/2 length */
+    arm_cfft_radix4_init_q15(S->pCfft, S->fftLenBy2, 0u, 1u);
+  }
+
+  /* return the status of RFFT Init function */
+  return (status);
+
+}
+
+  /**    
+   * @} end of RFFT_RIFFT group    
+   */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_rfft_init_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_rfft_init_q31.c
new file mode 100644
index 0000000000..400fe586c3
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_rfft_init_q31.c
@@ -0,0 +1,4274 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_rfft_init_q31.c    
+*    
+* Description:	RFFT & RIFFT Q31 initialisation function    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupTransforms    
+ */
+
+/**    
+ * @addtogroup RFFT_RIFFT    
+ * @{    
+ */
+
+/**    
+* \par    
+* Generation floating point realCoefAQ31 array:    
+* \par    
+* n = 4096    
+* 
for (i = 0; i < n; i++)    
+* {    
+*    pATable[2 * i] = 0.5 * (1.0 - sin (2 * PI / (double) (2 * n) * (double) i));    
+*    pATable[2 * i + 1] = 0.5 * (-1.0 * cos (2 * PI / (double) (2 * n) * (double) i));    
+* }
    
+* \par    
+* Convert to fixed point Q31 format    
+*     round(pATable[i] * pow(2, 31))    
+*/
+
+
+static const q31_t realCoefAQ31[8192] = {
+  0x40000000, 0xc0000000, 0x3ff36f02, 0xc000013c,
+  0x3fe6de05, 0xc00004ef, 0x3fda4d09, 0xc0000b1a,
+  0x3fcdbc0f, 0xc00013bd, 0x3fc12b16, 0xc0001ed8,
+  0x3fb49a1f, 0xc0002c6a, 0x3fa8092c, 0xc0003c74,
+  0x3f9b783c, 0xc0004ef5, 0x3f8ee750, 0xc00063ee,
+  0x3f825668, 0xc0007b5f, 0x3f75c585, 0xc0009547,
+  0x3f6934a8, 0xc000b1a7, 0x3f5ca3d0, 0xc000d07e,
+  0x3f5012fe, 0xc000f1ce, 0x3f438234, 0xc0011594,
+  0x3f36f170, 0xc0013bd3, 0x3f2a60b4, 0xc0016489,
+  0x3f1dd001, 0xc0018fb6, 0x3f113f56, 0xc001bd5c,
+  0x3f04aeb5, 0xc001ed78, 0x3ef81e1d, 0xc002200d,
+  0x3eeb8d8f, 0xc0025519, 0x3edefd0c, 0xc0028c9c,
+  0x3ed26c94, 0xc002c697, 0x3ec5dc28, 0xc003030a,
+  0x3eb94bc8, 0xc00341f4, 0x3eacbb74, 0xc0038356,
+  0x3ea02b2e, 0xc003c72f, 0x3e939af5, 0xc0040d80,
+  0x3e870aca, 0xc0045648, 0x3e7a7aae, 0xc004a188,
+  0x3e6deaa1, 0xc004ef3f, 0x3e615aa3, 0xc0053f6e,
+  0x3e54cab5, 0xc0059214, 0x3e483ad8, 0xc005e731,
+  0x3e3bab0b, 0xc0063ec6, 0x3e2f1b50, 0xc00698d3,
+  0x3e228ba7, 0xc006f556, 0x3e15fc11, 0xc0075452,
+  0x3e096c8d, 0xc007b5c4, 0x3dfcdd1d, 0xc00819ae,
+  0x3df04dc0, 0xc008800f, 0x3de3be78, 0xc008e8e8,
+  0x3dd72f45, 0xc0095438, 0x3dcaa027, 0xc009c1ff,
+  0x3dbe111e, 0xc00a323d, 0x3db1822c, 0xc00aa4f3,
+  0x3da4f351, 0xc00b1a20, 0x3d98648d, 0xc00b91c4,
+  0x3d8bd5e1, 0xc00c0be0, 0x3d7f474d, 0xc00c8872,
+  0x3d72b8d2, 0xc00d077c, 0x3d662a70, 0xc00d88fd,
+  0x3d599c28, 0xc00e0cf5, 0x3d4d0df9, 0xc00e9364,
+  0x3d407fe6, 0xc00f1c4a, 0x3d33f1ed, 0xc00fa7a8,
+  0x3d276410, 0xc010357c, 0x3d1ad650, 0xc010c5c7,
+  0x3d0e48ab, 0xc011588a, 0x3d01bb24, 0xc011edc3,
+  0x3cf52dbb, 0xc0128574, 0x3ce8a06f, 0xc0131f9b,
+  0x3cdc1342, 0xc013bc39, 0x3ccf8634, 0xc0145b4e,
+  0x3cc2f945, 0xc014fcda, 0x3cb66c77, 0xc015a0dd,
+  0x3ca9dfc8, 0xc0164757, 0x3c9d533b, 0xc016f047,
+  0x3c90c6cf, 0xc0179bae, 0x3c843a85, 0xc018498c,
+  0x3c77ae5e, 0xc018f9e1, 0x3c6b2259, 0xc019acac,
+  0x3c5e9678, 0xc01a61ee, 0x3c520aba, 0xc01b19a7,
+  0x3c457f21, 0xc01bd3d6, 0x3c38f3ac, 0xc01c907c,
+  0x3c2c685d, 0xc01d4f99, 0x3c1fdd34, 0xc01e112b,
+  0x3c135231, 0xc01ed535, 0x3c06c754, 0xc01f9bb5,
+  0x3bfa3c9f, 0xc02064ab, 0x3bedb212, 0xc0213018,
+  0x3be127ac, 0xc021fdfb, 0x3bd49d70, 0xc022ce54,
+  0x3bc8135c, 0xc023a124, 0x3bbb8973, 0xc024766a,
+  0x3baeffb3, 0xc0254e27, 0x3ba2761e, 0xc0262859,
+  0x3b95ecb4, 0xc0270502, 0x3b896375, 0xc027e421,
+  0x3b7cda63, 0xc028c5b6, 0x3b70517d, 0xc029a9c1,
+  0x3b63c8c4, 0xc02a9042, 0x3b574039, 0xc02b7939,
+  0x3b4ab7db, 0xc02c64a6, 0x3b3e2fac, 0xc02d5289,
+  0x3b31a7ac, 0xc02e42e2, 0x3b251fdc, 0xc02f35b1,
+  0x3b18983b, 0xc0302af5, 0x3b0c10cb, 0xc03122b0,
+  0x3aff898c, 0xc0321ce0, 0x3af3027e, 0xc0331986,
+  0x3ae67ba2, 0xc03418a2, 0x3ad9f4f8, 0xc0351a33,
+  0x3acd6e81, 0xc0361e3a, 0x3ac0e83d, 0xc03724b6,
+  0x3ab4622d, 0xc0382da8, 0x3aa7dc52, 0xc0393910,
+  0x3a9b56ab, 0xc03a46ed, 0x3a8ed139, 0xc03b573f,
+  0x3a824bfd, 0xc03c6a07, 0x3a75c6f8, 0xc03d7f44,
+  0x3a694229, 0xc03e96f6, 0x3a5cbd91, 0xc03fb11d,
+  0x3a503930, 0xc040cdba, 0x3a43b508, 0xc041eccc,
+  0x3a373119, 0xc0430e53, 0x3a2aad62, 0xc044324f,
+  0x3a1e29e5, 0xc04558c0, 0x3a11a6a3, 0xc04681a6,
+  0x3a05239a, 0xc047ad01, 0x39f8a0cd, 0xc048dad1,
+  0x39ec1e3b, 0xc04a0b16, 0x39df9be6, 0xc04b3dcf,
+  0x39d319cc, 0xc04c72fe, 0x39c697f0, 0xc04daaa1,
+  0x39ba1651, 0xc04ee4b8, 0x39ad94f0, 0xc0502145,
+  0x39a113cd, 0xc0516045, 0x399492ea, 0xc052a1bb,
+  0x39881245, 0xc053e5a5, 0x397b91e1, 0xc0552c03,
+  0x396f11bc, 0xc05674d6, 0x396291d9, 0xc057c01d,
+  0x39561237, 0xc0590dd8, 0x394992d7, 0xc05a5e07,
+  0x393d13b8, 0xc05bb0ab, 0x393094dd, 0xc05d05c3,
+  0x39241645, 0xc05e5d4e, 0x391797f0, 0xc05fb74e,
+  0x390b19e0, 0xc06113c2, 0x38fe9c15, 0xc06272aa,
+  0x38f21e8e, 0xc063d405, 0x38e5a14d, 0xc06537d4,
+  0x38d92452, 0xc0669e18, 0x38cca79e, 0xc06806ce,
+  0x38c02b31, 0xc06971f9, 0x38b3af0c, 0xc06adf97,
+  0x38a7332e, 0xc06c4fa8, 0x389ab799, 0xc06dc22e,
+  0x388e3c4d, 0xc06f3726, 0x3881c14b, 0xc070ae92,
+  0x38754692, 0xc0722871, 0x3868cc24, 0xc073a4c3,
+  0x385c5201, 0xc0752389, 0x384fd829, 0xc076a4c2,
+  0x38435e9d, 0xc078286e, 0x3836e55d, 0xc079ae8c,
+  0x382a6c6a, 0xc07b371e, 0x381df3c5, 0xc07cc223,
+  0x38117b6d, 0xc07e4f9b, 0x38050364, 0xc07fdf85,
+  0x37f88ba9, 0xc08171e2, 0x37ec143e, 0xc08306b2,
+  0x37df9d22, 0xc0849df4, 0x37d32657, 0xc08637a9,
+  0x37c6afdc, 0xc087d3d0, 0x37ba39b3, 0xc089726a,
+  0x37adc3db, 0xc08b1376, 0x37a14e55, 0xc08cb6f5,
+  0x3794d922, 0xc08e5ce5, 0x37886442, 0xc0900548,
+  0x377befb5, 0xc091b01d, 0x376f7b7d, 0xc0935d64,
+  0x37630799, 0xc0950d1d, 0x3756940a, 0xc096bf48,
+  0x374a20d0, 0xc09873e4, 0x373daded, 0xc09a2af3,
+  0x37313b60, 0xc09be473, 0x3724c92a, 0xc09da065,
+  0x3718574b, 0xc09f5ec8, 0x370be5c4, 0xc0a11f9d,
+  0x36ff7496, 0xc0a2e2e3, 0x36f303c0, 0xc0a4a89b,
+  0x36e69344, 0xc0a670c4, 0x36da2321, 0xc0a83b5e,
+  0x36cdb359, 0xc0aa086a, 0x36c143ec, 0xc0abd7e6,
+  0x36b4d4d9, 0xc0ada9d4, 0x36a86623, 0xc0af7e33,
+  0x369bf7c9, 0xc0b15502, 0x368f89cb, 0xc0b32e42,
+  0x36831c2b, 0xc0b509f3, 0x3676aee8, 0xc0b6e815,
+  0x366a4203, 0xc0b8c8a7, 0x365dd57d, 0xc0baabaa,
+  0x36516956, 0xc0bc911d, 0x3644fd8f, 0xc0be7901,
+  0x36389228, 0xc0c06355, 0x362c2721, 0xc0c25019,
+  0x361fbc7b, 0xc0c43f4d, 0x36135237, 0xc0c630f2,
+  0x3606e854, 0xc0c82506, 0x35fa7ed4, 0xc0ca1b8a,
+  0x35ee15b7, 0xc0cc147f, 0x35e1acfd, 0xc0ce0fe3,
+  0x35d544a7, 0xc0d00db6, 0x35c8dcb6, 0xc0d20dfa,
+  0x35bc7529, 0xc0d410ad, 0x35b00e02, 0xc0d615cf,
+  0x35a3a740, 0xc0d81d61, 0x359740e5, 0xc0da2762,
+  0x358adaf0, 0xc0dc33d2, 0x357e7563, 0xc0de42b2,
+  0x3572103d, 0xc0e05401, 0x3565ab80, 0xc0e267be,
+  0x3559472b, 0xc0e47deb, 0x354ce33f, 0xc0e69686,
+  0x35407fbd, 0xc0e8b190, 0x35341ca5, 0xc0eacf09,
+  0x3527b9f7, 0xc0eceef1, 0x351b57b5, 0xc0ef1147,
+  0x350ef5de, 0xc0f1360b, 0x35029473, 0xc0f35d3e,
+  0x34f63374, 0xc0f586df, 0x34e9d2e3, 0xc0f7b2ee,
+  0x34dd72be, 0xc0f9e16b, 0x34d11308, 0xc0fc1257,
+  0x34c4b3c0, 0xc0fe45b0, 0x34b854e7, 0xc1007b77,
+  0x34abf67e, 0xc102b3ac, 0x349f9884, 0xc104ee4f,
+  0x34933afa, 0xc1072b5f, 0x3486dde1, 0xc1096add,
+  0x347a8139, 0xc10bacc8, 0x346e2504, 0xc10df120,
+  0x3461c940, 0xc11037e6, 0x34556def, 0xc1128119,
+  0x34491311, 0xc114ccb9, 0x343cb8a7, 0xc1171ac6,
+  0x34305eb0, 0xc1196b3f, 0x3424052f, 0xc11bbe26,
+  0x3417ac22, 0xc11e1379, 0x340b538b, 0xc1206b39,
+  0x33fefb6a, 0xc122c566, 0x33f2a3bf, 0xc12521ff,
+  0x33e64c8c, 0xc1278104, 0x33d9f5cf, 0xc129e276,
+  0x33cd9f8b, 0xc12c4653, 0x33c149bf, 0xc12eac9d,
+  0x33b4f46c, 0xc1311553, 0x33a89f92, 0xc1338075,
+  0x339c4b32, 0xc135ee02, 0x338ff74d, 0xc1385dfb,
+  0x3383a3e2, 0xc13ad060, 0x337750f2, 0xc13d4530,
+  0x336afe7e, 0xc13fbc6c, 0x335eac86, 0xc1423613,
+  0x33525b0b, 0xc144b225, 0x33460a0d, 0xc14730a3,
+  0x3339b98d, 0xc149b18b, 0x332d698a, 0xc14c34df,
+  0x33211a07, 0xc14eba9d, 0x3314cb02, 0xc15142c6,
+  0x33087c7d, 0xc153cd5a, 0x32fc2e77, 0xc1565a58,
+  0x32efe0f2, 0xc158e9c1, 0x32e393ef, 0xc15b7b94,
+  0x32d7476c, 0xc15e0fd1, 0x32cafb6b, 0xc160a678,
+  0x32beafed, 0xc1633f8a, 0x32b264f2, 0xc165db05,
+  0x32a61a7a, 0xc16878eb, 0x3299d085, 0xc16b193a,
+  0x328d8715, 0xc16dbbf3, 0x32813e2a, 0xc1706115,
+  0x3274f5c3, 0xc17308a1, 0x3268ade3, 0xc175b296,
+  0x325c6688, 0xc1785ef4, 0x32501fb5, 0xc17b0dbb,
+  0x3243d968, 0xc17dbeec, 0x323793a3, 0xc1807285,
+  0x322b4e66, 0xc1832888, 0x321f09b1, 0xc185e0f3,
+  0x3212c585, 0xc1889bc6, 0x320681e3, 0xc18b5903,
+  0x31fa3ecb, 0xc18e18a7, 0x31edfc3d, 0xc190dab4,
+  0x31e1ba3a, 0xc1939f29, 0x31d578c2, 0xc1966606,
+  0x31c937d6, 0xc1992f4c, 0x31bcf777, 0xc19bfaf9,
+  0x31b0b7a4, 0xc19ec90d, 0x31a4785e, 0xc1a1998a,
+  0x319839a6, 0xc1a46c6e, 0x318bfb7d, 0xc1a741b9,
+  0x317fbde2, 0xc1aa196c, 0x317380d6, 0xc1acf386,
+  0x31674459, 0xc1afd007, 0x315b086d, 0xc1b2aef0,
+  0x314ecd11, 0xc1b5903f, 0x31429247, 0xc1b873f5,
+  0x3136580d, 0xc1bb5a11, 0x312a1e66, 0xc1be4294,
+  0x311de551, 0xc1c12d7e, 0x3111accf, 0xc1c41ace,
+  0x310574e0, 0xc1c70a84, 0x30f93d86, 0xc1c9fca0,
+  0x30ed06bf, 0xc1ccf122, 0x30e0d08d, 0xc1cfe80a,
+  0x30d49af1, 0xc1d2e158, 0x30c865ea, 0xc1d5dd0c,
+  0x30bc317a, 0xc1d8db25, 0x30affda0, 0xc1dbdba3,
+  0x30a3ca5d, 0xc1dede87, 0x309797b2, 0xc1e1e3d0,
+  0x308b659f, 0xc1e4eb7e, 0x307f3424, 0xc1e7f591,
+  0x30730342, 0xc1eb0209, 0x3066d2fa, 0xc1ee10e5,
+  0x305aa34c, 0xc1f12227, 0x304e7438, 0xc1f435cc,
+  0x304245c0, 0xc1f74bd6, 0x303617e2, 0xc1fa6445,
+  0x3029eaa1, 0xc1fd7f17, 0x301dbdfb, 0xc2009c4e,
+  0x301191f3, 0xc203bbe8, 0x30056687, 0xc206dde6,
+  0x2ff93bba, 0xc20a0248, 0x2fed118a, 0xc20d290d,
+  0x2fe0e7f9, 0xc2105236, 0x2fd4bf08, 0xc2137dc2,
+  0x2fc896b5, 0xc216abb1, 0x2fbc6f03, 0xc219dc03,
+  0x2fb047f2, 0xc21d0eb8, 0x2fa42181, 0xc22043d0,
+  0x2f97fbb2, 0xc2237b4b, 0x2f8bd685, 0xc226b528,
+  0x2f7fb1fa, 0xc229f167, 0x2f738e12, 0xc22d3009,
+  0x2f676ace, 0xc230710d, 0x2f5b482d, 0xc233b473,
+  0x2f4f2630, 0xc236fa3b, 0x2f4304d8, 0xc23a4265,
+  0x2f36e426, 0xc23d8cf1, 0x2f2ac419, 0xc240d9de,
+  0x2f1ea4b2, 0xc244292c, 0x2f1285f2, 0xc2477adc,
+  0x2f0667d9, 0xc24aceed, 0x2efa4a67, 0xc24e255e,
+  0x2eee2d9d, 0xc2517e31, 0x2ee2117c, 0xc254d965,
+  0x2ed5f604, 0xc25836f9, 0x2ec9db35, 0xc25b96ee,
+  0x2ebdc110, 0xc25ef943, 0x2eb1a796, 0xc2625df8,
+  0x2ea58ec6, 0xc265c50e, 0x2e9976a1, 0xc2692e83,
+  0x2e8d5f29, 0xc26c9a58, 0x2e81485c, 0xc270088e,
+  0x2e75323c, 0xc2737922, 0x2e691cc9, 0xc276ec16,
+  0x2e5d0804, 0xc27a616a, 0x2e50f3ed, 0xc27dd91c,
+  0x2e44e084, 0xc281532e, 0x2e38cdcb, 0xc284cf9f,
+  0x2e2cbbc1, 0xc2884e6e, 0x2e20aa67, 0xc28bcf9c,
+  0x2e1499bd, 0xc28f5329, 0x2e0889c4, 0xc292d914,
+  0x2dfc7a7c, 0xc296615d, 0x2df06be6, 0xc299ec05,
+  0x2de45e03, 0xc29d790a, 0x2dd850d2, 0xc2a1086d,
+  0x2dcc4454, 0xc2a49a2e, 0x2dc0388a, 0xc2a82e4d,
+  0x2db42d74, 0xc2abc4c9, 0x2da82313, 0xc2af5da2,
+  0x2d9c1967, 0xc2b2f8d8, 0x2d901070, 0xc2b6966c,
+  0x2d84082f, 0xc2ba365c, 0x2d7800a5, 0xc2bdd8a9,
+  0x2d6bf9d1, 0xc2c17d52, 0x2d5ff3b5, 0xc2c52459,
+  0x2d53ee51, 0xc2c8cdbb, 0x2d47e9a5, 0xc2cc7979,
+  0x2d3be5b1, 0xc2d02794, 0x2d2fe277, 0xc2d3d80a,
+  0x2d23dff7, 0xc2d78add, 0x2d17de31, 0xc2db400a,
+  0x2d0bdd25, 0xc2def794, 0x2cffdcd4, 0xc2e2b178,
+  0x2cf3dd3f, 0xc2e66db8, 0x2ce7de66, 0xc2ea2c53,
+  0x2cdbe04a, 0xc2eded49, 0x2ccfe2ea, 0xc2f1b099,
+  0x2cc3e648, 0xc2f57644, 0x2cb7ea63, 0xc2f93e4a,
+  0x2cabef3d, 0xc2fd08a9, 0x2c9ff4d6, 0xc300d563,
+  0x2c93fb2e, 0xc304a477, 0x2c880245, 0xc30875e5,
+  0x2c7c0a1d, 0xc30c49ad, 0x2c7012b5, 0xc3101fce,
+  0x2c641c0e, 0xc313f848, 0x2c582629, 0xc317d31c,
+  0x2c4c3106, 0xc31bb049, 0x2c403ca5, 0xc31f8fcf,
+  0x2c344908, 0xc32371ae, 0x2c28562d, 0xc32755e5,
+  0x2c1c6417, 0xc32b3c75, 0x2c1072c4, 0xc32f255e,
+  0x2c048237, 0xc333109e, 0x2bf8926f, 0xc336fe37,
+  0x2beca36c, 0xc33aee27, 0x2be0b52f, 0xc33ee070,
+  0x2bd4c7ba, 0xc342d510, 0x2bc8db0b, 0xc346cc07,
+  0x2bbcef23, 0xc34ac556, 0x2bb10404, 0xc34ec0fc,
+  0x2ba519ad, 0xc352bef9, 0x2b99301f, 0xc356bf4d,
+  0x2b8d475b, 0xc35ac1f7, 0x2b815f60, 0xc35ec6f8,
+  0x2b75782f, 0xc362ce50, 0x2b6991ca, 0xc366d7fd,
+  0x2b5dac2f, 0xc36ae401, 0x2b51c760, 0xc36ef25b,
+  0x2b45e35d, 0xc373030a, 0x2b3a0027, 0xc377160f,
+  0x2b2e1dbe, 0xc37b2b6a, 0x2b223c22, 0xc37f4319,
+  0x2b165b54, 0xc3835d1e, 0x2b0a7b54, 0xc3877978,
+  0x2afe9c24, 0xc38b9827, 0x2af2bdc3, 0xc38fb92a,
+  0x2ae6e031, 0xc393dc82, 0x2adb0370, 0xc398022f,
+  0x2acf277f, 0xc39c2a2f, 0x2ac34c60, 0xc3a05484,
+  0x2ab77212, 0xc3a4812c, 0x2aab9896, 0xc3a8b028,
+  0x2a9fbfed, 0xc3ace178, 0x2a93e817, 0xc3b1151b,
+  0x2a881114, 0xc3b54b11, 0x2a7c3ae5, 0xc3b9835a,
+  0x2a70658a, 0xc3bdbdf6, 0x2a649105, 0xc3c1fae5,
+  0x2a58bd54, 0xc3c63a26, 0x2a4cea79, 0xc3ca7bba,
+  0x2a411874, 0xc3cebfa0, 0x2a354746, 0xc3d305d8,
+  0x2a2976ef, 0xc3d74e62, 0x2a1da770, 0xc3db993e,
+  0x2a11d8c8, 0xc3dfe66c, 0x2a060af9, 0xc3e435ea,
+  0x29fa3e03, 0xc3e887bb, 0x29ee71e6, 0xc3ecdbdc,
+  0x29e2a6a3, 0xc3f1324e, 0x29d6dc3b, 0xc3f58b10,
+  0x29cb12ad, 0xc3f9e624, 0x29bf49fa, 0xc3fe4388,
+  0x29b38223, 0xc402a33c, 0x29a7bb28, 0xc4070540,
+  0x299bf509, 0xc40b6994, 0x29902fc7, 0xc40fd037,
+  0x29846b63, 0xc414392b, 0x2978a7dd, 0xc418a46d,
+  0x296ce535, 0xc41d11ff, 0x2961236c, 0xc42181e0,
+  0x29556282, 0xc425f410, 0x2949a278, 0xc42a688f,
+  0x293de34e, 0xc42edf5c, 0x29322505, 0xc4335877,
+  0x2926679c, 0xc437d3e1, 0x291aab16, 0xc43c5199,
+  0x290eef71, 0xc440d19e, 0x290334af, 0xc44553f2,
+  0x28f77acf, 0xc449d892, 0x28ebc1d3, 0xc44e5f80,
+  0x28e009ba, 0xc452e8bc, 0x28d45286, 0xc4577444,
+  0x28c89c37, 0xc45c0219, 0x28bce6cd, 0xc460923b,
+  0x28b13248, 0xc46524a9, 0x28a57ea9, 0xc469b963,
+  0x2899cbf1, 0xc46e5069, 0x288e1a20, 0xc472e9bc,
+  0x28826936, 0xc477855a, 0x2876b934, 0xc47c2344,
+  0x286b0a1a, 0xc480c379, 0x285f5be9, 0xc48565f9,
+  0x2853aea1, 0xc48a0ac4, 0x28480243, 0xc48eb1db,
+  0x283c56cf, 0xc4935b3c, 0x2830ac45, 0xc49806e7,
+  0x282502a7, 0xc49cb4dd, 0x281959f4, 0xc4a1651c,
+  0x280db22d, 0xc4a617a6, 0x28020b52, 0xc4aacc7a,
+  0x27f66564, 0xc4af8397, 0x27eac063, 0xc4b43cfd,
+  0x27df1c50, 0xc4b8f8ad, 0x27d3792b, 0xc4bdb6a6,
+  0x27c7d6f4, 0xc4c276e8, 0x27bc35ad, 0xc4c73972,
+  0x27b09555, 0xc4cbfe45, 0x27a4f5ed, 0xc4d0c560,
+  0x27995776, 0xc4d58ec3, 0x278db9ef, 0xc4da5a6f,
+  0x27821d59, 0xc4df2862, 0x277681b6, 0xc4e3f89c,
+  0x276ae704, 0xc4e8cb1e, 0x275f4d45, 0xc4ed9fe7,
+  0x2753b479, 0xc4f276f7, 0x27481ca1, 0xc4f7504e,
+  0x273c85bc, 0xc4fc2bec, 0x2730efcc, 0xc50109d0,
+  0x27255ad1, 0xc505e9fb, 0x2719c6cb, 0xc50acc6b,
+  0x270e33bb, 0xc50fb121, 0x2702a1a1, 0xc514981d,
+  0x26f7107e, 0xc519815f, 0x26eb8052, 0xc51e6ce6,
+  0x26dff11d, 0xc5235ab2, 0x26d462e1, 0xc5284ac3,
+  0x26c8d59c, 0xc52d3d18, 0x26bd4951, 0xc53231b3,
+  0x26b1bdff, 0xc5372891, 0x26a633a6, 0xc53c21b4,
+  0x269aaa48, 0xc5411d1b, 0x268f21e5, 0xc5461ac6,
+  0x26839a7c, 0xc54b1ab4, 0x26781410, 0xc5501ce5,
+  0x266c8e9f, 0xc555215a, 0x26610a2a, 0xc55a2812,
+  0x265586b3, 0xc55f310d, 0x264a0438, 0xc5643c4a,
+  0x263e82bc, 0xc56949ca, 0x2633023e, 0xc56e598c,
+  0x262782be, 0xc5736b90, 0x261c043d, 0xc5787fd6,
+  0x261086bc, 0xc57d965d, 0x26050a3b, 0xc582af26,
+  0x25f98ebb, 0xc587ca31, 0x25ee143b, 0xc58ce77c,
+  0x25e29abc, 0xc5920708, 0x25d72240, 0xc59728d5,
+  0x25cbaac5, 0xc59c4ce3, 0x25c0344d, 0xc5a17330,
+  0x25b4bed8, 0xc5a69bbe, 0x25a94a67, 0xc5abc68c,
+  0x259dd6f9, 0xc5b0f399, 0x25926490, 0xc5b622e6,
+  0x2586f32c, 0xc5bb5472, 0x257b82cd, 0xc5c0883d,
+  0x25701374, 0xc5c5be47, 0x2564a521, 0xc5caf690,
+  0x255937d5, 0xc5d03118, 0x254dcb8f, 0xc5d56ddd,
+  0x25426051, 0xc5daace1, 0x2536f61b, 0xc5dfee22,
+  0x252b8cee, 0xc5e531a1, 0x252024c9, 0xc5ea775e,
+  0x2514bdad, 0xc5efbf58, 0x2509579b, 0xc5f5098f,
+  0x24fdf294, 0xc5fa5603, 0x24f28e96, 0xc5ffa4b3,
+  0x24e72ba4, 0xc604f5a0, 0x24dbc9bd, 0xc60a48c9,
+  0x24d068e2, 0xc60f9e2e, 0x24c50914, 0xc614f5cf,
+  0x24b9aa52, 0xc61a4fac, 0x24ae4c9d, 0xc61fabc4,
+  0x24a2eff6, 0xc6250a18, 0x2497945d, 0xc62a6aa6,
+  0x248c39d3, 0xc62fcd6f, 0x2480e057, 0xc6353273,
+  0x247587eb, 0xc63a99b1, 0x246a308f, 0xc6400329,
+  0x245eda43, 0xc6456edb, 0x24538507, 0xc64adcc7,
+  0x244830dd, 0xc6504ced, 0x243cddc4, 0xc655bf4c,
+  0x24318bbe, 0xc65b33e4, 0x24263ac9, 0xc660aab5,
+  0x241aeae8, 0xc66623be, 0x240f9c1a, 0xc66b9f01,
+  0x24044e60, 0xc6711c7b, 0x23f901ba, 0xc6769c2e,
+  0x23edb628, 0xc67c1e18, 0x23e26bac, 0xc681a23a,
+  0x23d72245, 0xc6872894, 0x23cbd9f4, 0xc68cb124,
+  0x23c092b9, 0xc6923bec, 0x23b54c95, 0xc697c8eb,
+  0x23aa0788, 0xc69d5820, 0x239ec393, 0xc6a2e98b,
+  0x239380b6, 0xc6a87d2d, 0x23883ef2, 0xc6ae1304,
+  0x237cfe47, 0xc6b3ab12, 0x2371beb5, 0xc6b94554,
+  0x2366803c, 0xc6bee1cd, 0x235b42df, 0xc6c4807a,
+  0x2350069b, 0xc6ca215c, 0x2344cb73, 0xc6cfc472,
+  0x23399167, 0xc6d569be, 0x232e5876, 0xc6db113d,
+  0x232320a2, 0xc6e0baf0, 0x2317e9eb, 0xc6e666d7,
+  0x230cb451, 0xc6ec14f2, 0x23017fd5, 0xc6f1c540,
+  0x22f64c77, 0xc6f777c1, 0x22eb1a37, 0xc6fd2c75,
+  0x22dfe917, 0xc702e35c, 0x22d4b916, 0xc7089c75,
+  0x22c98a35, 0xc70e57c0, 0x22be5c74, 0xc714153e,
+  0x22b32fd4, 0xc719d4ed, 0x22a80456, 0xc71f96ce,
+  0x229cd9f8, 0xc7255ae0, 0x2291b0bd, 0xc72b2123,
+  0x228688a4, 0xc730e997, 0x227b61af, 0xc736b43c,
+  0x22703bdc, 0xc73c8111, 0x2265172e, 0xc7425016,
+  0x2259f3a3, 0xc748214c, 0x224ed13d, 0xc74df4b1,
+  0x2243affc, 0xc753ca46, 0x22388fe1, 0xc759a20a,
+  0x222d70eb, 0xc75f7bfe, 0x2222531c, 0xc7655820,
+  0x22173674, 0xc76b3671, 0x220c1af3, 0xc77116f0,
+  0x22010099, 0xc776f99d, 0x21f5e768, 0xc77cde79,
+  0x21eacf5f, 0xc782c582, 0x21dfb87f, 0xc788aeb9,
+  0x21d4a2c8, 0xc78e9a1d, 0x21c98e3b, 0xc79487ae,
+  0x21be7ad8, 0xc79a776c, 0x21b368a0, 0xc7a06957,
+  0x21a85793, 0xc7a65d6e, 0x219d47b1, 0xc7ac53b1,
+  0x219238fb, 0xc7b24c20, 0x21872b72, 0xc7b846ba,
+  0x217c1f15, 0xc7be4381, 0x217113e5, 0xc7c44272,
+  0x216609e3, 0xc7ca438f, 0x215b0110, 0xc7d046d6,
+  0x214ff96a, 0xc7d64c47, 0x2144f2f3, 0xc7dc53e3,
+  0x2139edac, 0xc7e25daa, 0x212ee995, 0xc7e8699a,
+  0x2123e6ad, 0xc7ee77b3, 0x2118e4f6, 0xc7f487f6,
+  0x210de470, 0xc7fa9a62, 0x2102e51c, 0xc800aef7,
+  0x20f7e6f9, 0xc806c5b5, 0x20ecea09, 0xc80cde9b,
+  0x20e1ee4b, 0xc812f9a9, 0x20d6f3c1, 0xc81916df,
+  0x20cbfa6a, 0xc81f363d, 0x20c10247, 0xc82557c3,
+  0x20b60b58, 0xc82b7b70, 0x20ab159e, 0xc831a143,
+  0x20a0211a, 0xc837c93e, 0x20952dcb, 0xc83df35f,
+  0x208a3bb2, 0xc8441fa6, 0x207f4acf, 0xc84a4e14,
+  0x20745b24, 0xc8507ea7, 0x20696cb0, 0xc856b160,
+  0x205e7f74, 0xc85ce63e, 0x2053936f, 0xc8631d42,
+  0x2048a8a4, 0xc869566a, 0x203dbf11, 0xc86f91b7,
+  0x2032d6b8, 0xc875cf28, 0x2027ef99, 0xc87c0ebd,
+  0x201d09b4, 0xc8825077, 0x2012250a, 0xc8889454,
+  0x2007419b, 0xc88eda54, 0x1ffc5f67, 0xc8952278,
+  0x1ff17e70, 0xc89b6cbf, 0x1fe69eb4, 0xc8a1b928,
+  0x1fdbc036, 0xc8a807b4, 0x1fd0e2f5, 0xc8ae5862,
+  0x1fc606f1, 0xc8b4ab32, 0x1fbb2c2c, 0xc8bb0023,
+  0x1fb052a5, 0xc8c15736, 0x1fa57a5d, 0xc8c7b06b,
+  0x1f9aa354, 0xc8ce0bc0, 0x1f8fcd8b, 0xc8d46936,
+  0x1f84f902, 0xc8dac8cd, 0x1f7a25ba, 0xc8e12a84,
+  0x1f6f53b3, 0xc8e78e5b, 0x1f6482ed, 0xc8edf452,
+  0x1f59b369, 0xc8f45c68, 0x1f4ee527, 0xc8fac69e,
+  0x1f441828, 0xc90132f2, 0x1f394c6b, 0xc907a166,
+  0x1f2e81f3, 0xc90e11f7, 0x1f23b8be, 0xc91484a8,
+  0x1f18f0ce, 0xc91af976, 0x1f0e2a22, 0xc9217062,
+  0x1f0364bc, 0xc927e96b, 0x1ef8a09b, 0xc92e6492,
+  0x1eedddc0, 0xc934e1d6, 0x1ee31c2b, 0xc93b6137,
+  0x1ed85bdd, 0xc941e2b4, 0x1ecd9cd7, 0xc948664d,
+  0x1ec2df18, 0xc94eec03, 0x1eb822a1, 0xc95573d4,
+  0x1ead6773, 0xc95bfdc1, 0x1ea2ad8d, 0xc96289c9,
+  0x1e97f4f1, 0xc96917ec, 0x1e8d3d9e, 0xc96fa82a,
+  0x1e828796, 0xc9763a83, 0x1e77d2d8, 0xc97ccef5,
+  0x1e6d1f65, 0xc9836582, 0x1e626d3e, 0xc989fe29,
+  0x1e57bc62, 0xc99098e9, 0x1e4d0cd2, 0xc99735c2,
+  0x1e425e8f, 0xc99dd4b4, 0x1e37b199, 0xc9a475bf,
+  0x1e2d05f1, 0xc9ab18e3, 0x1e225b96, 0xc9b1be1e,
+  0x1e17b28a, 0xc9b86572, 0x1e0d0acc, 0xc9bf0edd,
+  0x1e02645d, 0xc9c5ba60, 0x1df7bf3e, 0xc9cc67fa,
+  0x1ded1b6e, 0xc9d317ab, 0x1de278ef, 0xc9d9c973,
+  0x1dd7d7c1, 0xc9e07d51, 0x1dcd37e4, 0xc9e73346,
+  0x1dc29958, 0xc9edeb50, 0x1db7fc1e, 0xc9f4a570,
+  0x1dad6036, 0xc9fb61a5, 0x1da2c5a2, 0xca021fef,
+  0x1d982c60, 0xca08e04f, 0x1d8d9472, 0xca0fa2c3,
+  0x1d82fdd8, 0xca16674b, 0x1d786892, 0xca1d2de7,
+  0x1d6dd4a2, 0xca23f698, 0x1d634206, 0xca2ac15b,
+  0x1d58b0c0, 0xca318e32, 0x1d4e20d0, 0xca385d1d,
+  0x1d439236, 0xca3f2e19, 0x1d3904f4, 0xca460129,
+  0x1d2e7908, 0xca4cd64b, 0x1d23ee74, 0xca53ad7e,
+  0x1d196538, 0xca5a86c4, 0x1d0edd55, 0xca61621b,
+  0x1d0456ca, 0xca683f83, 0x1cf9d199, 0xca6f1efc,
+  0x1cef4dc2, 0xca760086, 0x1ce4cb44, 0xca7ce420,
+  0x1cda4a21, 0xca83c9ca, 0x1ccfca59, 0xca8ab184,
+  0x1cc54bec, 0xca919b4e, 0x1cbacedb, 0xca988727,
+  0x1cb05326, 0xca9f750f, 0x1ca5d8cd, 0xcaa66506,
+  0x1c9b5fd2, 0xcaad570c, 0x1c90e834, 0xcab44b1f,
+  0x1c8671f3, 0xcabb4141, 0x1c7bfd11, 0xcac23971,
+  0x1c71898d, 0xcac933ae, 0x1c671768, 0xcad02ff8,
+  0x1c5ca6a2, 0xcad72e4f, 0x1c52373c, 0xcade2eb3,
+  0x1c47c936, 0xcae53123, 0x1c3d5c91, 0xcaec35a0,
+  0x1c32f14d, 0xcaf33c28, 0x1c28876a, 0xcafa44bc,
+  0x1c1e1ee9, 0xcb014f5b, 0x1c13b7c9, 0xcb085c05,
+  0x1c09520d, 0xcb0f6aba, 0x1bfeedb3, 0xcb167b79,
+  0x1bf48abd, 0xcb1d8e43, 0x1bea292b, 0xcb24a316,
+  0x1bdfc8fc, 0xcb2bb9f4, 0x1bd56a32, 0xcb32d2da,
+  0x1bcb0cce, 0xcb39edca, 0x1bc0b0ce, 0xcb410ac3,
+  0x1bb65634, 0xcb4829c4, 0x1babfd01, 0xcb4f4acd,
+  0x1ba1a534, 0xcb566ddf, 0x1b974ece, 0xcb5d92f8,
+  0x1b8cf9cf, 0xcb64ba19, 0x1b82a638, 0xcb6be341,
+  0x1b785409, 0xcb730e70, 0x1b6e0342, 0xcb7a3ba5,
+  0x1b63b3e5, 0xcb816ae1, 0x1b5965f1, 0xcb889c23,
+  0x1b4f1967, 0xcb8fcf6b, 0x1b44ce46, 0xcb9704b9,
+  0x1b3a8491, 0xcb9e3c0b, 0x1b303c46, 0xcba57563,
+  0x1b25f566, 0xcbacb0bf, 0x1b1baff2, 0xcbb3ee20,
+  0x1b116beb, 0xcbbb2d85, 0x1b072950, 0xcbc26eee,
+  0x1afce821, 0xcbc9b25a, 0x1af2a860, 0xcbd0f7ca,
+  0x1ae86a0d, 0xcbd83f3d, 0x1ade2d28, 0xcbdf88b3,
+  0x1ad3f1b1, 0xcbe6d42b, 0x1ac9b7a9, 0xcbee21a5,
+  0x1abf7f11, 0xcbf57121, 0x1ab547e8, 0xcbfcc29f,
+  0x1aab122f, 0xcc04161e, 0x1aa0dde7, 0xcc0b6b9e,
+  0x1a96ab0f, 0xcc12c31f, 0x1a8c79a9, 0xcc1a1ca0,
+  0x1a8249b4, 0xcc217822, 0x1a781b31, 0xcc28d5a3,
+  0x1a6dee21, 0xcc303524, 0x1a63c284, 0xcc3796a5,
+  0x1a599859, 0xcc3efa25, 0x1a4f6fa3, 0xcc465fa3,
+  0x1a454860, 0xcc4dc720, 0x1a3b2292, 0xcc55309b,
+  0x1a30fe38, 0xcc5c9c14, 0x1a26db54, 0xcc64098b,
+  0x1a1cb9e5, 0xcc6b78ff, 0x1a1299ec, 0xcc72ea70,
+  0x1a087b69, 0xcc7a5dde, 0x19fe5e5e, 0xcc81d349,
+  0x19f442c9, 0xcc894aaf, 0x19ea28ac, 0xcc90c412,
+  0x19e01006, 0xcc983f70, 0x19d5f8d9, 0xcc9fbcca,
+  0x19cbe325, 0xcca73c1e, 0x19c1cee9, 0xccaebd6e,
+  0x19b7bc27, 0xccb640b8, 0x19adaadf, 0xccbdc5fc,
+  0x19a39b11, 0xccc54d3a, 0x19998cbe, 0xccccd671,
+  0x198f7fe6, 0xccd461a2, 0x19857489, 0xccdbeecc,
+  0x197b6aa8, 0xcce37def, 0x19716243, 0xcceb0f0a,
+  0x19675b5a, 0xccf2a21d, 0x195d55ef, 0xccfa3729,
+  0x19535201, 0xcd01ce2b, 0x19494f90, 0xcd096725,
+  0x193f4e9e, 0xcd110216, 0x19354f2a, 0xcd189efe,
+  0x192b5135, 0xcd203ddc, 0x192154bf, 0xcd27deb0,
+  0x191759c9, 0xcd2f817b, 0x190d6053, 0xcd37263a,
+  0x1903685d, 0xcd3eccef, 0x18f971e8, 0xcd467599,
+  0x18ef7cf4, 0xcd4e2037, 0x18e58982, 0xcd55ccca,
+  0x18db9792, 0xcd5d7b50, 0x18d1a724, 0xcd652bcb,
+  0x18c7b838, 0xcd6cde39, 0x18bdcad0, 0xcd74929a,
+  0x18b3deeb, 0xcd7c48ee, 0x18a9f48a, 0xcd840134,
+  0x18a00bae, 0xcd8bbb6d, 0x18962456, 0xcd937798,
+  0x188c3e83, 0xcd9b35b4, 0x18825a35, 0xcda2f5c2,
+  0x1878776d, 0xcdaab7c0, 0x186e962b, 0xcdb27bb0,
+  0x1864b670, 0xcdba4190, 0x185ad83c, 0xcdc20960,
+  0x1850fb8e, 0xcdc9d320, 0x18472069, 0xcdd19ed0,
+  0x183d46cc, 0xcdd96c6f, 0x18336eb7, 0xcde13bfd,
+  0x1829982b, 0xcde90d79, 0x181fc328, 0xcdf0e0e4,
+  0x1815efae, 0xcdf8b63d, 0x180c1dbf, 0xce008d84,
+  0x18024d59, 0xce0866b8, 0x17f87e7f, 0xce1041d9,
+  0x17eeb130, 0xce181ee8, 0x17e4e56c, 0xce1ffde2,
+  0x17db1b34, 0xce27dec9, 0x17d15288, 0xce2fc19c,
+  0x17c78b68, 0xce37a65b, 0x17bdc5d6, 0xce3f8d05,
+  0x17b401d1, 0xce47759a, 0x17aa3f5a, 0xce4f6019,
+  0x17a07e70, 0xce574c84, 0x1796bf16, 0xce5f3ad8,
+  0x178d014a, 0xce672b16, 0x1783450d, 0xce6f1d3d,
+  0x17798a60, 0xce77114e, 0x176fd143, 0xce7f0748,
+  0x176619b6, 0xce86ff2a, 0x175c63ba, 0xce8ef8f4,
+  0x1752af4f, 0xce96f4a7, 0x1748fc75, 0xce9ef241,
+  0x173f4b2e, 0xcea6f1c2, 0x17359b78, 0xceaef32b,
+  0x172bed55, 0xceb6f67a, 0x172240c5, 0xcebefbb0,
+  0x171895c9, 0xcec702cb, 0x170eec60, 0xcecf0bcd,
+  0x1705448b, 0xced716b4, 0x16fb9e4b, 0xcedf2380,
+  0x16f1f99f, 0xcee73231, 0x16e85689, 0xceef42c7,
+  0x16deb508, 0xcef75541, 0x16d5151d, 0xceff699f,
+  0x16cb76c9, 0xcf077fe1, 0x16c1da0b, 0xcf0f9805,
+  0x16b83ee4, 0xcf17b20d, 0x16aea555, 0xcf1fcdf8,
+  0x16a50d5d, 0xcf27ebc5, 0x169b76fe, 0xcf300b74,
+  0x1691e237, 0xcf382d05, 0x16884f09, 0xcf405077,
+  0x167ebd74, 0xcf4875ca, 0x16752d79, 0xcf509cfe,
+  0x166b9f18, 0xcf58c613, 0x16621251, 0xcf60f108,
+  0x16588725, 0xcf691ddd, 0x164efd94, 0xcf714c91,
+  0x1645759f, 0xcf797d24, 0x163bef46, 0xcf81af97,
+  0x16326a88, 0xcf89e3e8, 0x1628e767, 0xcf921a17,
+  0x161f65e4, 0xcf9a5225, 0x1615e5fd, 0xcfa28c10,
+  0x160c67b4, 0xcfaac7d8, 0x1602eb0a, 0xcfb3057d,
+  0x15f96ffd, 0xcfbb4500, 0x15eff690, 0xcfc3865e,
+  0x15e67ec1, 0xcfcbc999, 0x15dd0892, 0xcfd40eaf,
+  0x15d39403, 0xcfdc55a1, 0x15ca2115, 0xcfe49e6d,
+  0x15c0afc6, 0xcfece915, 0x15b74019, 0xcff53597,
+  0x15add20d, 0xcffd83f4, 0x15a465a3, 0xd005d42a,
+  0x159afadb, 0xd00e2639, 0x159191b5, 0xd0167a22,
+  0x15882a32, 0xd01ecfe4, 0x157ec452, 0xd027277e,
+  0x15756016, 0xd02f80f1, 0x156bfd7d, 0xd037dc3b,
+  0x15629c89, 0xd040395d, 0x15593d3a, 0xd0489856,
+  0x154fdf8f, 0xd050f926, 0x15468389, 0xd0595bcd,
+  0x153d292a, 0xd061c04a, 0x1533d070, 0xd06a269d,
+  0x152a795d, 0xd0728ec6, 0x152123f0, 0xd07af8c4,
+  0x1517d02b, 0xd0836497, 0x150e7e0d, 0xd08bd23f,
+  0x15052d97, 0xd09441bb, 0x14fbdec9, 0xd09cb30b,
+  0x14f291a4, 0xd0a5262f, 0x14e94627, 0xd0ad9b26,
+  0x14dffc54, 0xd0b611f1, 0x14d6b42b, 0xd0be8a8d,
+  0x14cd6dab, 0xd0c704fd, 0x14c428d6, 0xd0cf813e,
+  0x14bae5ab, 0xd0d7ff51, 0x14b1a42c, 0xd0e07f36,
+  0x14a86458, 0xd0e900ec, 0x149f2630, 0xd0f18472,
+  0x1495e9b3, 0xd0fa09c9, 0x148caee4, 0xd10290f0,
+  0x148375c1, 0xd10b19e7, 0x147a3e4b, 0xd113a4ad,
+  0x14710883, 0xd11c3142, 0x1467d469, 0xd124bfa6,
+  0x145ea1fd, 0xd12d4fd9, 0x14557140, 0xd135e1d9,
+  0x144c4232, 0xd13e75a8, 0x144314d3, 0xd1470b44,
+  0x1439e923, 0xd14fa2ad, 0x1430bf24, 0xd1583be2,
+  0x142796d5, 0xd160d6e5, 0x141e7037, 0xd16973b3,
+  0x14154b4a, 0xd172124d, 0x140c280e, 0xd17ab2b3,
+  0x14030684, 0xd18354e4, 0x13f9e6ad, 0xd18bf8e0,
+  0x13f0c887, 0xd1949ea6, 0x13e7ac15, 0xd19d4636,
+  0x13de9156, 0xd1a5ef90, 0x13d5784a, 0xd1ae9ab4,
+  0x13cc60f2, 0xd1b747a0, 0x13c34b4f, 0xd1bff656,
+  0x13ba3760, 0xd1c8a6d4, 0x13b12526, 0xd1d1591a,
+  0x13a814a2, 0xd1da0d28, 0x139f05d3, 0xd1e2c2fd,
+  0x1395f8ba, 0xd1eb7a9a, 0x138ced57, 0xd1f433fd,
+  0x1383e3ab, 0xd1fcef27, 0x137adbb6, 0xd205ac17,
+  0x1371d579, 0xd20e6acc, 0x1368d0f3, 0xd2172b48,
+  0x135fce26, 0xd21fed88, 0x1356cd11, 0xd228b18d,
+  0x134dcdb4, 0xd2317756, 0x1344d011, 0xd23a3ee4,
+  0x133bd427, 0xd2430835, 0x1332d9f7, 0xd24bd34a,
+  0x1329e181, 0xd254a021, 0x1320eac6, 0xd25d6ebc,
+  0x1317f5c6, 0xd2663f19, 0x130f0280, 0xd26f1138,
+  0x130610f7, 0xd277e518, 0x12fd2129, 0xd280babb,
+  0x12f43318, 0xd289921e, 0x12eb46c3, 0xd2926b41,
+  0x12e25c2b, 0xd29b4626, 0x12d97350, 0xd2a422ca,
+  0x12d08c33, 0xd2ad012e, 0x12c7a6d4, 0xd2b5e151,
+  0x12bec333, 0xd2bec333, 0x12b5e151, 0xd2c7a6d4,
+  0x12ad012e, 0xd2d08c33, 0x12a422ca, 0xd2d97350,
+  0x129b4626, 0xd2e25c2b, 0x12926b41, 0xd2eb46c3,
+  0x1289921e, 0xd2f43318, 0x1280babb, 0xd2fd2129,
+  0x1277e518, 0xd30610f7, 0x126f1138, 0xd30f0280,
+  0x12663f19, 0xd317f5c6, 0x125d6ebc, 0xd320eac6,
+  0x1254a021, 0xd329e181, 0x124bd34a, 0xd332d9f7,
+  0x12430835, 0xd33bd427, 0x123a3ee4, 0xd344d011,
+  0x12317756, 0xd34dcdb4, 0x1228b18d, 0xd356cd11,
+  0x121fed88, 0xd35fce26, 0x12172b48, 0xd368d0f3,
+  0x120e6acc, 0xd371d579, 0x1205ac17, 0xd37adbb6,
+  0x11fcef27, 0xd383e3ab, 0x11f433fd, 0xd38ced57,
+  0x11eb7a9a, 0xd395f8ba, 0x11e2c2fd, 0xd39f05d3,
+  0x11da0d28, 0xd3a814a2, 0x11d1591a, 0xd3b12526,
+  0x11c8a6d4, 0xd3ba3760, 0x11bff656, 0xd3c34b4f,
+  0x11b747a0, 0xd3cc60f2, 0x11ae9ab4, 0xd3d5784a,
+  0x11a5ef90, 0xd3de9156, 0x119d4636, 0xd3e7ac15,
+  0x11949ea6, 0xd3f0c887, 0x118bf8e0, 0xd3f9e6ad,
+  0x118354e4, 0xd4030684, 0x117ab2b3, 0xd40c280e,
+  0x1172124d, 0xd4154b4a, 0x116973b3, 0xd41e7037,
+  0x1160d6e5, 0xd42796d5, 0x11583be2, 0xd430bf24,
+  0x114fa2ad, 0xd439e923, 0x11470b44, 0xd44314d3,
+  0x113e75a8, 0xd44c4232, 0x1135e1d9, 0xd4557140,
+  0x112d4fd9, 0xd45ea1fd, 0x1124bfa6, 0xd467d469,
+  0x111c3142, 0xd4710883, 0x1113a4ad, 0xd47a3e4b,
+  0x110b19e7, 0xd48375c1, 0x110290f0, 0xd48caee4,
+  0x10fa09c9, 0xd495e9b3, 0x10f18472, 0xd49f2630,
+  0x10e900ec, 0xd4a86458, 0x10e07f36, 0xd4b1a42c,
+  0x10d7ff51, 0xd4bae5ab, 0x10cf813e, 0xd4c428d6,
+  0x10c704fd, 0xd4cd6dab, 0x10be8a8d, 0xd4d6b42b,
+  0x10b611f1, 0xd4dffc54, 0x10ad9b26, 0xd4e94627,
+  0x10a5262f, 0xd4f291a4, 0x109cb30b, 0xd4fbdec9,
+  0x109441bb, 0xd5052d97, 0x108bd23f, 0xd50e7e0d,
+  0x10836497, 0xd517d02b, 0x107af8c4, 0xd52123f0,
+  0x10728ec6, 0xd52a795d, 0x106a269d, 0xd533d070,
+  0x1061c04a, 0xd53d292a, 0x10595bcd, 0xd5468389,
+  0x1050f926, 0xd54fdf8f, 0x10489856, 0xd5593d3a,
+  0x1040395d, 0xd5629c89, 0x1037dc3b, 0xd56bfd7d,
+  0x102f80f1, 0xd5756016, 0x1027277e, 0xd57ec452,
+  0x101ecfe4, 0xd5882a32, 0x10167a22, 0xd59191b5,
+  0x100e2639, 0xd59afadb, 0x1005d42a, 0xd5a465a3,
+  0xffd83f4, 0xd5add20d, 0xff53597, 0xd5b74019,
+  0xfece915, 0xd5c0afc6, 0xfe49e6d, 0xd5ca2115,
+  0xfdc55a1, 0xd5d39403, 0xfd40eaf, 0xd5dd0892,
+  0xfcbc999, 0xd5e67ec1, 0xfc3865e, 0xd5eff690,
+  0xfbb4500, 0xd5f96ffd, 0xfb3057d, 0xd602eb0a,
+  0xfaac7d8, 0xd60c67b4, 0xfa28c10, 0xd615e5fd,
+  0xf9a5225, 0xd61f65e4, 0xf921a17, 0xd628e767,
+  0xf89e3e8, 0xd6326a88, 0xf81af97, 0xd63bef46,
+  0xf797d24, 0xd645759f, 0xf714c91, 0xd64efd94,
+  0xf691ddd, 0xd6588725, 0xf60f108, 0xd6621251,
+  0xf58c613, 0xd66b9f18, 0xf509cfe, 0xd6752d79,
+  0xf4875ca, 0xd67ebd74, 0xf405077, 0xd6884f09,
+  0xf382d05, 0xd691e237, 0xf300b74, 0xd69b76fe,
+  0xf27ebc5, 0xd6a50d5d, 0xf1fcdf8, 0xd6aea555,
+  0xf17b20d, 0xd6b83ee4, 0xf0f9805, 0xd6c1da0b,
+  0xf077fe1, 0xd6cb76c9, 0xeff699f, 0xd6d5151d,
+  0xef75541, 0xd6deb508, 0xeef42c7, 0xd6e85689,
+  0xee73231, 0xd6f1f99f, 0xedf2380, 0xd6fb9e4b,
+  0xed716b4, 0xd705448b, 0xecf0bcd, 0xd70eec60,
+  0xec702cb, 0xd71895c9, 0xebefbb0, 0xd72240c5,
+  0xeb6f67a, 0xd72bed55, 0xeaef32b, 0xd7359b78,
+  0xea6f1c2, 0xd73f4b2e, 0xe9ef241, 0xd748fc75,
+  0xe96f4a7, 0xd752af4f, 0xe8ef8f4, 0xd75c63ba,
+  0xe86ff2a, 0xd76619b6, 0xe7f0748, 0xd76fd143,
+  0xe77114e, 0xd7798a60, 0xe6f1d3d, 0xd783450d,
+  0xe672b16, 0xd78d014a, 0xe5f3ad8, 0xd796bf16,
+  0xe574c84, 0xd7a07e70, 0xe4f6019, 0xd7aa3f5a,
+  0xe47759a, 0xd7b401d1, 0xe3f8d05, 0xd7bdc5d6,
+  0xe37a65b, 0xd7c78b68, 0xe2fc19c, 0xd7d15288,
+  0xe27dec9, 0xd7db1b34, 0xe1ffde2, 0xd7e4e56c,
+  0xe181ee8, 0xd7eeb130, 0xe1041d9, 0xd7f87e7f,
+  0xe0866b8, 0xd8024d59, 0xe008d84, 0xd80c1dbf,
+  0xdf8b63d, 0xd815efae, 0xdf0e0e4, 0xd81fc328,
+  0xde90d79, 0xd829982b, 0xde13bfd, 0xd8336eb7,
+  0xdd96c6f, 0xd83d46cc, 0xdd19ed0, 0xd8472069,
+  0xdc9d320, 0xd850fb8e, 0xdc20960, 0xd85ad83c,
+  0xdba4190, 0xd864b670, 0xdb27bb0, 0xd86e962b,
+  0xdaab7c0, 0xd878776d, 0xda2f5c2, 0xd8825a35,
+  0xd9b35b4, 0xd88c3e83, 0xd937798, 0xd8962456,
+  0xd8bbb6d, 0xd8a00bae, 0xd840134, 0xd8a9f48a,
+  0xd7c48ee, 0xd8b3deeb, 0xd74929a, 0xd8bdcad0,
+  0xd6cde39, 0xd8c7b838, 0xd652bcb, 0xd8d1a724,
+  0xd5d7b50, 0xd8db9792, 0xd55ccca, 0xd8e58982,
+  0xd4e2037, 0xd8ef7cf4, 0xd467599, 0xd8f971e8,
+  0xd3eccef, 0xd903685d, 0xd37263a, 0xd90d6053,
+  0xd2f817b, 0xd91759c9, 0xd27deb0, 0xd92154bf,
+  0xd203ddc, 0xd92b5135, 0xd189efe, 0xd9354f2a,
+  0xd110216, 0xd93f4e9e, 0xd096725, 0xd9494f90,
+  0xd01ce2b, 0xd9535201, 0xcfa3729, 0xd95d55ef,
+  0xcf2a21d, 0xd9675b5a, 0xceb0f0a, 0xd9716243,
+  0xce37def, 0xd97b6aa8, 0xcdbeecc, 0xd9857489,
+  0xcd461a2, 0xd98f7fe6, 0xcccd671, 0xd9998cbe,
+  0xcc54d3a, 0xd9a39b11, 0xcbdc5fc, 0xd9adaadf,
+  0xcb640b8, 0xd9b7bc27, 0xcaebd6e, 0xd9c1cee9,
+  0xca73c1e, 0xd9cbe325, 0xc9fbcca, 0xd9d5f8d9,
+  0xc983f70, 0xd9e01006, 0xc90c412, 0xd9ea28ac,
+  0xc894aaf, 0xd9f442c9, 0xc81d349, 0xd9fe5e5e,
+  0xc7a5dde, 0xda087b69, 0xc72ea70, 0xda1299ec,
+  0xc6b78ff, 0xda1cb9e5, 0xc64098b, 0xda26db54,
+  0xc5c9c14, 0xda30fe38, 0xc55309b, 0xda3b2292,
+  0xc4dc720, 0xda454860, 0xc465fa3, 0xda4f6fa3,
+  0xc3efa25, 0xda599859, 0xc3796a5, 0xda63c284,
+  0xc303524, 0xda6dee21, 0xc28d5a3, 0xda781b31,
+  0xc217822, 0xda8249b4, 0xc1a1ca0, 0xda8c79a9,
+  0xc12c31f, 0xda96ab0f, 0xc0b6b9e, 0xdaa0dde7,
+  0xc04161e, 0xdaab122f, 0xbfcc29f, 0xdab547e8,
+  0xbf57121, 0xdabf7f11, 0xbee21a5, 0xdac9b7a9,
+  0xbe6d42b, 0xdad3f1b1, 0xbdf88b3, 0xdade2d28,
+  0xbd83f3d, 0xdae86a0d, 0xbd0f7ca, 0xdaf2a860,
+  0xbc9b25a, 0xdafce821, 0xbc26eee, 0xdb072950,
+  0xbbb2d85, 0xdb116beb, 0xbb3ee20, 0xdb1baff2,
+  0xbacb0bf, 0xdb25f566, 0xba57563, 0xdb303c46,
+  0xb9e3c0b, 0xdb3a8491, 0xb9704b9, 0xdb44ce46,
+  0xb8fcf6b, 0xdb4f1967, 0xb889c23, 0xdb5965f1,
+  0xb816ae1, 0xdb63b3e5, 0xb7a3ba5, 0xdb6e0342,
+  0xb730e70, 0xdb785409, 0xb6be341, 0xdb82a638,
+  0xb64ba19, 0xdb8cf9cf, 0xb5d92f8, 0xdb974ece,
+  0xb566ddf, 0xdba1a534, 0xb4f4acd, 0xdbabfd01,
+  0xb4829c4, 0xdbb65634, 0xb410ac3, 0xdbc0b0ce,
+  0xb39edca, 0xdbcb0cce, 0xb32d2da, 0xdbd56a32,
+  0xb2bb9f4, 0xdbdfc8fc, 0xb24a316, 0xdbea292b,
+  0xb1d8e43, 0xdbf48abd, 0xb167b79, 0xdbfeedb3,
+  0xb0f6aba, 0xdc09520d, 0xb085c05, 0xdc13b7c9,
+  0xb014f5b, 0xdc1e1ee9, 0xafa44bc, 0xdc28876a,
+  0xaf33c28, 0xdc32f14d, 0xaec35a0, 0xdc3d5c91,
+  0xae53123, 0xdc47c936, 0xade2eb3, 0xdc52373c,
+  0xad72e4f, 0xdc5ca6a2, 0xad02ff8, 0xdc671768,
+  0xac933ae, 0xdc71898d, 0xac23971, 0xdc7bfd11,
+  0xabb4141, 0xdc8671f3, 0xab44b1f, 0xdc90e834,
+  0xaad570c, 0xdc9b5fd2, 0xaa66506, 0xdca5d8cd,
+  0xa9f750f, 0xdcb05326, 0xa988727, 0xdcbacedb,
+  0xa919b4e, 0xdcc54bec, 0xa8ab184, 0xdccfca59,
+  0xa83c9ca, 0xdcda4a21, 0xa7ce420, 0xdce4cb44,
+  0xa760086, 0xdcef4dc2, 0xa6f1efc, 0xdcf9d199,
+  0xa683f83, 0xdd0456ca, 0xa61621b, 0xdd0edd55,
+  0xa5a86c4, 0xdd196538, 0xa53ad7e, 0xdd23ee74,
+  0xa4cd64b, 0xdd2e7908, 0xa460129, 0xdd3904f4,
+  0xa3f2e19, 0xdd439236, 0xa385d1d, 0xdd4e20d0,
+  0xa318e32, 0xdd58b0c0, 0xa2ac15b, 0xdd634206,
+  0xa23f698, 0xdd6dd4a2, 0xa1d2de7, 0xdd786892,
+  0xa16674b, 0xdd82fdd8, 0xa0fa2c3, 0xdd8d9472,
+  0xa08e04f, 0xdd982c60, 0xa021fef, 0xdda2c5a2,
+  0x9fb61a5, 0xddad6036, 0x9f4a570, 0xddb7fc1e,
+  0x9edeb50, 0xddc29958, 0x9e73346, 0xddcd37e4,
+  0x9e07d51, 0xddd7d7c1, 0x9d9c973, 0xdde278ef,
+  0x9d317ab, 0xdded1b6e, 0x9cc67fa, 0xddf7bf3e,
+  0x9c5ba60, 0xde02645d, 0x9bf0edd, 0xde0d0acc,
+  0x9b86572, 0xde17b28a, 0x9b1be1e, 0xde225b96,
+  0x9ab18e3, 0xde2d05f1, 0x9a475bf, 0xde37b199,
+  0x99dd4b4, 0xde425e8f, 0x99735c2, 0xde4d0cd2,
+  0x99098e9, 0xde57bc62, 0x989fe29, 0xde626d3e,
+  0x9836582, 0xde6d1f65, 0x97ccef5, 0xde77d2d8,
+  0x9763a83, 0xde828796, 0x96fa82a, 0xde8d3d9e,
+  0x96917ec, 0xde97f4f1, 0x96289c9, 0xdea2ad8d,
+  0x95bfdc1, 0xdead6773, 0x95573d4, 0xdeb822a1,
+  0x94eec03, 0xdec2df18, 0x948664d, 0xdecd9cd7,
+  0x941e2b4, 0xded85bdd, 0x93b6137, 0xdee31c2b,
+  0x934e1d6, 0xdeedddc0, 0x92e6492, 0xdef8a09b,
+  0x927e96b, 0xdf0364bc, 0x9217062, 0xdf0e2a22,
+  0x91af976, 0xdf18f0ce, 0x91484a8, 0xdf23b8be,
+  0x90e11f7, 0xdf2e81f3, 0x907a166, 0xdf394c6b,
+  0x90132f2, 0xdf441828, 0x8fac69e, 0xdf4ee527,
+  0x8f45c68, 0xdf59b369, 0x8edf452, 0xdf6482ed,
+  0x8e78e5b, 0xdf6f53b3, 0x8e12a84, 0xdf7a25ba,
+  0x8dac8cd, 0xdf84f902, 0x8d46936, 0xdf8fcd8b,
+  0x8ce0bc0, 0xdf9aa354, 0x8c7b06b, 0xdfa57a5d,
+  0x8c15736, 0xdfb052a5, 0x8bb0023, 0xdfbb2c2c,
+  0x8b4ab32, 0xdfc606f1, 0x8ae5862, 0xdfd0e2f5,
+  0x8a807b4, 0xdfdbc036, 0x8a1b928, 0xdfe69eb4,
+  0x89b6cbf, 0xdff17e70, 0x8952278, 0xdffc5f67,
+  0x88eda54, 0xe007419b, 0x8889454, 0xe012250a,
+  0x8825077, 0xe01d09b4, 0x87c0ebd, 0xe027ef99,
+  0x875cf28, 0xe032d6b8, 0x86f91b7, 0xe03dbf11,
+  0x869566a, 0xe048a8a4, 0x8631d42, 0xe053936f,
+  0x85ce63e, 0xe05e7f74, 0x856b160, 0xe0696cb0,
+  0x8507ea7, 0xe0745b24, 0x84a4e14, 0xe07f4acf,
+  0x8441fa6, 0xe08a3bb2, 0x83df35f, 0xe0952dcb,
+  0x837c93e, 0xe0a0211a, 0x831a143, 0xe0ab159e,
+  0x82b7b70, 0xe0b60b58, 0x82557c3, 0xe0c10247,
+  0x81f363d, 0xe0cbfa6a, 0x81916df, 0xe0d6f3c1,
+  0x812f9a9, 0xe0e1ee4b, 0x80cde9b, 0xe0ecea09,
+  0x806c5b5, 0xe0f7e6f9, 0x800aef7, 0xe102e51c,
+  0x7fa9a62, 0xe10de470, 0x7f487f6, 0xe118e4f6,
+  0x7ee77b3, 0xe123e6ad, 0x7e8699a, 0xe12ee995,
+  0x7e25daa, 0xe139edac, 0x7dc53e3, 0xe144f2f3,
+  0x7d64c47, 0xe14ff96a, 0x7d046d6, 0xe15b0110,
+  0x7ca438f, 0xe16609e3, 0x7c44272, 0xe17113e5,
+  0x7be4381, 0xe17c1f15, 0x7b846ba, 0xe1872b72,
+  0x7b24c20, 0xe19238fb, 0x7ac53b1, 0xe19d47b1,
+  0x7a65d6e, 0xe1a85793, 0x7a06957, 0xe1b368a0,
+  0x79a776c, 0xe1be7ad8, 0x79487ae, 0xe1c98e3b,
+  0x78e9a1d, 0xe1d4a2c8, 0x788aeb9, 0xe1dfb87f,
+  0x782c582, 0xe1eacf5f, 0x77cde79, 0xe1f5e768,
+  0x776f99d, 0xe2010099, 0x77116f0, 0xe20c1af3,
+  0x76b3671, 0xe2173674, 0x7655820, 0xe222531c,
+  0x75f7bfe, 0xe22d70eb, 0x759a20a, 0xe2388fe1,
+  0x753ca46, 0xe243affc, 0x74df4b1, 0xe24ed13d,
+  0x748214c, 0xe259f3a3, 0x7425016, 0xe265172e,
+  0x73c8111, 0xe2703bdc, 0x736b43c, 0xe27b61af,
+  0x730e997, 0xe28688a4, 0x72b2123, 0xe291b0bd,
+  0x7255ae0, 0xe29cd9f8, 0x71f96ce, 0xe2a80456,
+  0x719d4ed, 0xe2b32fd4, 0x714153e, 0xe2be5c74,
+  0x70e57c0, 0xe2c98a35, 0x7089c75, 0xe2d4b916,
+  0x702e35c, 0xe2dfe917, 0x6fd2c75, 0xe2eb1a37,
+  0x6f777c1, 0xe2f64c77, 0x6f1c540, 0xe3017fd5,
+  0x6ec14f2, 0xe30cb451, 0x6e666d7, 0xe317e9eb,
+  0x6e0baf0, 0xe32320a2, 0x6db113d, 0xe32e5876,
+  0x6d569be, 0xe3399167, 0x6cfc472, 0xe344cb73,
+  0x6ca215c, 0xe350069b, 0x6c4807a, 0xe35b42df,
+  0x6bee1cd, 0xe366803c, 0x6b94554, 0xe371beb5,
+  0x6b3ab12, 0xe37cfe47, 0x6ae1304, 0xe3883ef2,
+  0x6a87d2d, 0xe39380b6, 0x6a2e98b, 0xe39ec393,
+  0x69d5820, 0xe3aa0788, 0x697c8eb, 0xe3b54c95,
+  0x6923bec, 0xe3c092b9, 0x68cb124, 0xe3cbd9f4,
+  0x6872894, 0xe3d72245, 0x681a23a, 0xe3e26bac,
+  0x67c1e18, 0xe3edb628, 0x6769c2e, 0xe3f901ba,
+  0x6711c7b, 0xe4044e60, 0x66b9f01, 0xe40f9c1a,
+  0x66623be, 0xe41aeae8, 0x660aab5, 0xe4263ac9,
+  0x65b33e4, 0xe4318bbe, 0x655bf4c, 0xe43cddc4,
+  0x6504ced, 0xe44830dd, 0x64adcc7, 0xe4538507,
+  0x6456edb, 0xe45eda43, 0x6400329, 0xe46a308f,
+  0x63a99b1, 0xe47587eb, 0x6353273, 0xe480e057,
+  0x62fcd6f, 0xe48c39d3, 0x62a6aa6, 0xe497945d,
+  0x6250a18, 0xe4a2eff6, 0x61fabc4, 0xe4ae4c9d,
+  0x61a4fac, 0xe4b9aa52, 0x614f5cf, 0xe4c50914,
+  0x60f9e2e, 0xe4d068e2, 0x60a48c9, 0xe4dbc9bd,
+  0x604f5a0, 0xe4e72ba4, 0x5ffa4b3, 0xe4f28e96,
+  0x5fa5603, 0xe4fdf294, 0x5f5098f, 0xe509579b,
+  0x5efbf58, 0xe514bdad, 0x5ea775e, 0xe52024c9,
+  0x5e531a1, 0xe52b8cee, 0x5dfee22, 0xe536f61b,
+  0x5daace1, 0xe5426051, 0x5d56ddd, 0xe54dcb8f,
+  0x5d03118, 0xe55937d5, 0x5caf690, 0xe564a521,
+  0x5c5be47, 0xe5701374, 0x5c0883d, 0xe57b82cd,
+  0x5bb5472, 0xe586f32c, 0x5b622e6, 0xe5926490,
+  0x5b0f399, 0xe59dd6f9, 0x5abc68c, 0xe5a94a67,
+  0x5a69bbe, 0xe5b4bed8, 0x5a17330, 0xe5c0344d,
+  0x59c4ce3, 0xe5cbaac5, 0x59728d5, 0xe5d72240,
+  0x5920708, 0xe5e29abc, 0x58ce77c, 0xe5ee143b,
+  0x587ca31, 0xe5f98ebb, 0x582af26, 0xe6050a3b,
+  0x57d965d, 0xe61086bc, 0x5787fd6, 0xe61c043d,
+  0x5736b90, 0xe62782be, 0x56e598c, 0xe633023e,
+  0x56949ca, 0xe63e82bc, 0x5643c4a, 0xe64a0438,
+  0x55f310d, 0xe65586b3, 0x55a2812, 0xe6610a2a,
+  0x555215a, 0xe66c8e9f, 0x5501ce5, 0xe6781410,
+  0x54b1ab4, 0xe6839a7c, 0x5461ac6, 0xe68f21e5,
+  0x5411d1b, 0xe69aaa48, 0x53c21b4, 0xe6a633a6,
+  0x5372891, 0xe6b1bdff, 0x53231b3, 0xe6bd4951,
+  0x52d3d18, 0xe6c8d59c, 0x5284ac3, 0xe6d462e1,
+  0x5235ab2, 0xe6dff11d, 0x51e6ce6, 0xe6eb8052,
+  0x519815f, 0xe6f7107e, 0x514981d, 0xe702a1a1,
+  0x50fb121, 0xe70e33bb, 0x50acc6b, 0xe719c6cb,
+  0x505e9fb, 0xe7255ad1, 0x50109d0, 0xe730efcc,
+  0x4fc2bec, 0xe73c85bc, 0x4f7504e, 0xe7481ca1,
+  0x4f276f7, 0xe753b479, 0x4ed9fe7, 0xe75f4d45,
+  0x4e8cb1e, 0xe76ae704, 0x4e3f89c, 0xe77681b6,
+  0x4df2862, 0xe7821d59, 0x4da5a6f, 0xe78db9ef,
+  0x4d58ec3, 0xe7995776, 0x4d0c560, 0xe7a4f5ed,
+  0x4cbfe45, 0xe7b09555, 0x4c73972, 0xe7bc35ad,
+  0x4c276e8, 0xe7c7d6f4, 0x4bdb6a6, 0xe7d3792b,
+  0x4b8f8ad, 0xe7df1c50, 0x4b43cfd, 0xe7eac063,
+  0x4af8397, 0xe7f66564, 0x4aacc7a, 0xe8020b52,
+  0x4a617a6, 0xe80db22d, 0x4a1651c, 0xe81959f4,
+  0x49cb4dd, 0xe82502a7, 0x49806e7, 0xe830ac45,
+  0x4935b3c, 0xe83c56cf, 0x48eb1db, 0xe8480243,
+  0x48a0ac4, 0xe853aea1, 0x48565f9, 0xe85f5be9,
+  0x480c379, 0xe86b0a1a, 0x47c2344, 0xe876b934,
+  0x477855a, 0xe8826936, 0x472e9bc, 0xe88e1a20,
+  0x46e5069, 0xe899cbf1, 0x469b963, 0xe8a57ea9,
+  0x46524a9, 0xe8b13248, 0x460923b, 0xe8bce6cd,
+  0x45c0219, 0xe8c89c37, 0x4577444, 0xe8d45286,
+  0x452e8bc, 0xe8e009ba, 0x44e5f80, 0xe8ebc1d3,
+  0x449d892, 0xe8f77acf, 0x44553f2, 0xe90334af,
+  0x440d19e, 0xe90eef71, 0x43c5199, 0xe91aab16,
+  0x437d3e1, 0xe926679c, 0x4335877, 0xe9322505,
+  0x42edf5c, 0xe93de34e, 0x42a688f, 0xe949a278,
+  0x425f410, 0xe9556282, 0x42181e0, 0xe961236c,
+  0x41d11ff, 0xe96ce535, 0x418a46d, 0xe978a7dd,
+  0x414392b, 0xe9846b63, 0x40fd037, 0xe9902fc7,
+  0x40b6994, 0xe99bf509, 0x4070540, 0xe9a7bb28,
+  0x402a33c, 0xe9b38223, 0x3fe4388, 0xe9bf49fa,
+  0x3f9e624, 0xe9cb12ad, 0x3f58b10, 0xe9d6dc3b,
+  0x3f1324e, 0xe9e2a6a3, 0x3ecdbdc, 0xe9ee71e6,
+  0x3e887bb, 0xe9fa3e03, 0x3e435ea, 0xea060af9,
+  0x3dfe66c, 0xea11d8c8, 0x3db993e, 0xea1da770,
+  0x3d74e62, 0xea2976ef, 0x3d305d8, 0xea354746,
+  0x3cebfa0, 0xea411874, 0x3ca7bba, 0xea4cea79,
+  0x3c63a26, 0xea58bd54, 0x3c1fae5, 0xea649105,
+  0x3bdbdf6, 0xea70658a, 0x3b9835a, 0xea7c3ae5,
+  0x3b54b11, 0xea881114, 0x3b1151b, 0xea93e817,
+  0x3ace178, 0xea9fbfed, 0x3a8b028, 0xeaab9896,
+  0x3a4812c, 0xeab77212, 0x3a05484, 0xeac34c60,
+  0x39c2a2f, 0xeacf277f, 0x398022f, 0xeadb0370,
+  0x393dc82, 0xeae6e031, 0x38fb92a, 0xeaf2bdc3,
+  0x38b9827, 0xeafe9c24, 0x3877978, 0xeb0a7b54,
+  0x3835d1e, 0xeb165b54, 0x37f4319, 0xeb223c22,
+  0x37b2b6a, 0xeb2e1dbe, 0x377160f, 0xeb3a0027,
+  0x373030a, 0xeb45e35d, 0x36ef25b, 0xeb51c760,
+  0x36ae401, 0xeb5dac2f, 0x366d7fd, 0xeb6991ca,
+  0x362ce50, 0xeb75782f, 0x35ec6f8, 0xeb815f60,
+  0x35ac1f7, 0xeb8d475b, 0x356bf4d, 0xeb99301f,
+  0x352bef9, 0xeba519ad, 0x34ec0fc, 0xebb10404,
+  0x34ac556, 0xebbcef23, 0x346cc07, 0xebc8db0b,
+  0x342d510, 0xebd4c7ba, 0x33ee070, 0xebe0b52f,
+  0x33aee27, 0xebeca36c, 0x336fe37, 0xebf8926f,
+  0x333109e, 0xec048237, 0x32f255e, 0xec1072c4,
+  0x32b3c75, 0xec1c6417, 0x32755e5, 0xec28562d,
+  0x32371ae, 0xec344908, 0x31f8fcf, 0xec403ca5,
+  0x31bb049, 0xec4c3106, 0x317d31c, 0xec582629,
+  0x313f848, 0xec641c0e, 0x3101fce, 0xec7012b5,
+  0x30c49ad, 0xec7c0a1d, 0x30875e5, 0xec880245,
+  0x304a477, 0xec93fb2e, 0x300d563, 0xec9ff4d6,
+  0x2fd08a9, 0xecabef3d, 0x2f93e4a, 0xecb7ea63,
+  0x2f57644, 0xecc3e648, 0x2f1b099, 0xeccfe2ea,
+  0x2eded49, 0xecdbe04a, 0x2ea2c53, 0xece7de66,
+  0x2e66db8, 0xecf3dd3f, 0x2e2b178, 0xecffdcd4,
+  0x2def794, 0xed0bdd25, 0x2db400a, 0xed17de31,
+  0x2d78add, 0xed23dff7, 0x2d3d80a, 0xed2fe277,
+  0x2d02794, 0xed3be5b1, 0x2cc7979, 0xed47e9a5,
+  0x2c8cdbb, 0xed53ee51, 0x2c52459, 0xed5ff3b5,
+  0x2c17d52, 0xed6bf9d1, 0x2bdd8a9, 0xed7800a5,
+  0x2ba365c, 0xed84082f, 0x2b6966c, 0xed901070,
+  0x2b2f8d8, 0xed9c1967, 0x2af5da2, 0xeda82313,
+  0x2abc4c9, 0xedb42d74, 0x2a82e4d, 0xedc0388a,
+  0x2a49a2e, 0xedcc4454, 0x2a1086d, 0xedd850d2,
+  0x29d790a, 0xede45e03, 0x299ec05, 0xedf06be6,
+  0x296615d, 0xedfc7a7c, 0x292d914, 0xee0889c4,
+  0x28f5329, 0xee1499bd, 0x28bcf9c, 0xee20aa67,
+  0x2884e6e, 0xee2cbbc1, 0x284cf9f, 0xee38cdcb,
+  0x281532e, 0xee44e084, 0x27dd91c, 0xee50f3ed,
+  0x27a616a, 0xee5d0804, 0x276ec16, 0xee691cc9,
+  0x2737922, 0xee75323c, 0x270088e, 0xee81485c,
+  0x26c9a58, 0xee8d5f29, 0x2692e83, 0xee9976a1,
+  0x265c50e, 0xeea58ec6, 0x2625df8, 0xeeb1a796,
+  0x25ef943, 0xeebdc110, 0x25b96ee, 0xeec9db35,
+  0x25836f9, 0xeed5f604, 0x254d965, 0xeee2117c,
+  0x2517e31, 0xeeee2d9d, 0x24e255e, 0xeefa4a67,
+  0x24aceed, 0xef0667d9, 0x2477adc, 0xef1285f2,
+  0x244292c, 0xef1ea4b2, 0x240d9de, 0xef2ac419,
+  0x23d8cf1, 0xef36e426, 0x23a4265, 0xef4304d8,
+  0x236fa3b, 0xef4f2630, 0x233b473, 0xef5b482d,
+  0x230710d, 0xef676ace, 0x22d3009, 0xef738e12,
+  0x229f167, 0xef7fb1fa, 0x226b528, 0xef8bd685,
+  0x2237b4b, 0xef97fbb2, 0x22043d0, 0xefa42181,
+  0x21d0eb8, 0xefb047f2, 0x219dc03, 0xefbc6f03,
+  0x216abb1, 0xefc896b5, 0x2137dc2, 0xefd4bf08,
+  0x2105236, 0xefe0e7f9, 0x20d290d, 0xefed118a,
+  0x20a0248, 0xeff93bba, 0x206dde6, 0xf0056687,
+  0x203bbe8, 0xf01191f3, 0x2009c4e, 0xf01dbdfb,
+  0x1fd7f17, 0xf029eaa1, 0x1fa6445, 0xf03617e2,
+  0x1f74bd6, 0xf04245c0, 0x1f435cc, 0xf04e7438,
+  0x1f12227, 0xf05aa34c, 0x1ee10e5, 0xf066d2fa,
+  0x1eb0209, 0xf0730342, 0x1e7f591, 0xf07f3424,
+  0x1e4eb7e, 0xf08b659f, 0x1e1e3d0, 0xf09797b2,
+  0x1dede87, 0xf0a3ca5d, 0x1dbdba3, 0xf0affda0,
+  0x1d8db25, 0xf0bc317a, 0x1d5dd0c, 0xf0c865ea,
+  0x1d2e158, 0xf0d49af1, 0x1cfe80a, 0xf0e0d08d,
+  0x1ccf122, 0xf0ed06bf, 0x1c9fca0, 0xf0f93d86,
+  0x1c70a84, 0xf10574e0, 0x1c41ace, 0xf111accf,
+  0x1c12d7e, 0xf11de551, 0x1be4294, 0xf12a1e66,
+  0x1bb5a11, 0xf136580d, 0x1b873f5, 0xf1429247,
+  0x1b5903f, 0xf14ecd11, 0x1b2aef0, 0xf15b086d,
+  0x1afd007, 0xf1674459, 0x1acf386, 0xf17380d6,
+  0x1aa196c, 0xf17fbde2, 0x1a741b9, 0xf18bfb7d,
+  0x1a46c6e, 0xf19839a6, 0x1a1998a, 0xf1a4785e,
+  0x19ec90d, 0xf1b0b7a4, 0x19bfaf9, 0xf1bcf777,
+  0x1992f4c, 0xf1c937d6, 0x1966606, 0xf1d578c2,
+  0x1939f29, 0xf1e1ba3a, 0x190dab4, 0xf1edfc3d,
+  0x18e18a7, 0xf1fa3ecb, 0x18b5903, 0xf20681e3,
+  0x1889bc6, 0xf212c585, 0x185e0f3, 0xf21f09b1,
+  0x1832888, 0xf22b4e66, 0x1807285, 0xf23793a3,
+  0x17dbeec, 0xf243d968, 0x17b0dbb, 0xf2501fb5,
+  0x1785ef4, 0xf25c6688, 0x175b296, 0xf268ade3,
+  0x17308a1, 0xf274f5c3, 0x1706115, 0xf2813e2a,
+  0x16dbbf3, 0xf28d8715, 0x16b193a, 0xf299d085,
+  0x16878eb, 0xf2a61a7a, 0x165db05, 0xf2b264f2,
+  0x1633f8a, 0xf2beafed, 0x160a678, 0xf2cafb6b,
+  0x15e0fd1, 0xf2d7476c, 0x15b7b94, 0xf2e393ef,
+  0x158e9c1, 0xf2efe0f2, 0x1565a58, 0xf2fc2e77,
+  0x153cd5a, 0xf3087c7d, 0x15142c6, 0xf314cb02,
+  0x14eba9d, 0xf3211a07, 0x14c34df, 0xf32d698a,
+  0x149b18b, 0xf339b98d, 0x14730a3, 0xf3460a0d,
+  0x144b225, 0xf3525b0b, 0x1423613, 0xf35eac86,
+  0x13fbc6c, 0xf36afe7e, 0x13d4530, 0xf37750f2,
+  0x13ad060, 0xf383a3e2, 0x1385dfb, 0xf38ff74d,
+  0x135ee02, 0xf39c4b32, 0x1338075, 0xf3a89f92,
+  0x1311553, 0xf3b4f46c, 0x12eac9d, 0xf3c149bf,
+  0x12c4653, 0xf3cd9f8b, 0x129e276, 0xf3d9f5cf,
+  0x1278104, 0xf3e64c8c, 0x12521ff, 0xf3f2a3bf,
+  0x122c566, 0xf3fefb6a, 0x1206b39, 0xf40b538b,
+  0x11e1379, 0xf417ac22, 0x11bbe26, 0xf424052f,
+  0x1196b3f, 0xf4305eb0, 0x1171ac6, 0xf43cb8a7,
+  0x114ccb9, 0xf4491311, 0x1128119, 0xf4556def,
+  0x11037e6, 0xf461c940, 0x10df120, 0xf46e2504,
+  0x10bacc8, 0xf47a8139, 0x1096add, 0xf486dde1,
+  0x1072b5f, 0xf4933afa, 0x104ee4f, 0xf49f9884,
+  0x102b3ac, 0xf4abf67e, 0x1007b77, 0xf4b854e7,
+  0xfe45b0, 0xf4c4b3c0, 0xfc1257, 0xf4d11308,
+  0xf9e16b, 0xf4dd72be, 0xf7b2ee, 0xf4e9d2e3,
+  0xf586df, 0xf4f63374, 0xf35d3e, 0xf5029473,
+  0xf1360b, 0xf50ef5de, 0xef1147, 0xf51b57b5,
+  0xeceef1, 0xf527b9f7, 0xeacf09, 0xf5341ca5,
+  0xe8b190, 0xf5407fbd, 0xe69686, 0xf54ce33f,
+  0xe47deb, 0xf559472b, 0xe267be, 0xf565ab80,
+  0xe05401, 0xf572103d, 0xde42b2, 0xf57e7563,
+  0xdc33d2, 0xf58adaf0, 0xda2762, 0xf59740e5,
+  0xd81d61, 0xf5a3a740, 0xd615cf, 0xf5b00e02,
+  0xd410ad, 0xf5bc7529, 0xd20dfa, 0xf5c8dcb6,
+  0xd00db6, 0xf5d544a7, 0xce0fe3, 0xf5e1acfd,
+  0xcc147f, 0xf5ee15b7, 0xca1b8a, 0xf5fa7ed4,
+  0xc82506, 0xf606e854, 0xc630f2, 0xf6135237,
+  0xc43f4d, 0xf61fbc7b, 0xc25019, 0xf62c2721,
+  0xc06355, 0xf6389228, 0xbe7901, 0xf644fd8f,
+  0xbc911d, 0xf6516956, 0xbaabaa, 0xf65dd57d,
+  0xb8c8a7, 0xf66a4203, 0xb6e815, 0xf676aee8,
+  0xb509f3, 0xf6831c2b, 0xb32e42, 0xf68f89cb,
+  0xb15502, 0xf69bf7c9, 0xaf7e33, 0xf6a86623,
+  0xada9d4, 0xf6b4d4d9, 0xabd7e6, 0xf6c143ec,
+  0xaa086a, 0xf6cdb359, 0xa83b5e, 0xf6da2321,
+  0xa670c4, 0xf6e69344, 0xa4a89b, 0xf6f303c0,
+  0xa2e2e3, 0xf6ff7496, 0xa11f9d, 0xf70be5c4,
+  0x9f5ec8, 0xf718574b, 0x9da065, 0xf724c92a,
+  0x9be473, 0xf7313b60, 0x9a2af3, 0xf73daded,
+  0x9873e4, 0xf74a20d0, 0x96bf48, 0xf756940a,
+  0x950d1d, 0xf7630799, 0x935d64, 0xf76f7b7d,
+  0x91b01d, 0xf77befb5, 0x900548, 0xf7886442,
+  0x8e5ce5, 0xf794d922, 0x8cb6f5, 0xf7a14e55,
+  0x8b1376, 0xf7adc3db, 0x89726a, 0xf7ba39b3,
+  0x87d3d0, 0xf7c6afdc, 0x8637a9, 0xf7d32657,
+  0x849df4, 0xf7df9d22, 0x8306b2, 0xf7ec143e,
+  0x8171e2, 0xf7f88ba9, 0x7fdf85, 0xf8050364,
+  0x7e4f9b, 0xf8117b6d, 0x7cc223, 0xf81df3c5,
+  0x7b371e, 0xf82a6c6a, 0x79ae8c, 0xf836e55d,
+  0x78286e, 0xf8435e9d, 0x76a4c2, 0xf84fd829,
+  0x752389, 0xf85c5201, 0x73a4c3, 0xf868cc24,
+  0x722871, 0xf8754692, 0x70ae92, 0xf881c14b,
+  0x6f3726, 0xf88e3c4d, 0x6dc22e, 0xf89ab799,
+  0x6c4fa8, 0xf8a7332e, 0x6adf97, 0xf8b3af0c,
+  0x6971f9, 0xf8c02b31, 0x6806ce, 0xf8cca79e,
+  0x669e18, 0xf8d92452, 0x6537d4, 0xf8e5a14d,
+  0x63d405, 0xf8f21e8e, 0x6272aa, 0xf8fe9c15,
+  0x6113c2, 0xf90b19e0, 0x5fb74e, 0xf91797f0,
+  0x5e5d4e, 0xf9241645, 0x5d05c3, 0xf93094dd,
+  0x5bb0ab, 0xf93d13b8, 0x5a5e07, 0xf94992d7,
+  0x590dd8, 0xf9561237, 0x57c01d, 0xf96291d9,
+  0x5674d6, 0xf96f11bc, 0x552c03, 0xf97b91e1,
+  0x53e5a5, 0xf9881245, 0x52a1bb, 0xf99492ea,
+  0x516045, 0xf9a113cd, 0x502145, 0xf9ad94f0,
+  0x4ee4b8, 0xf9ba1651, 0x4daaa1, 0xf9c697f0,
+  0x4c72fe, 0xf9d319cc, 0x4b3dcf, 0xf9df9be6,
+  0x4a0b16, 0xf9ec1e3b, 0x48dad1, 0xf9f8a0cd,
+  0x47ad01, 0xfa05239a, 0x4681a6, 0xfa11a6a3,
+  0x4558c0, 0xfa1e29e5, 0x44324f, 0xfa2aad62,
+  0x430e53, 0xfa373119, 0x41eccc, 0xfa43b508,
+  0x40cdba, 0xfa503930, 0x3fb11d, 0xfa5cbd91,
+  0x3e96f6, 0xfa694229, 0x3d7f44, 0xfa75c6f8,
+  0x3c6a07, 0xfa824bfd, 0x3b573f, 0xfa8ed139,
+  0x3a46ed, 0xfa9b56ab, 0x393910, 0xfaa7dc52,
+  0x382da8, 0xfab4622d, 0x3724b6, 0xfac0e83d,
+  0x361e3a, 0xfacd6e81, 0x351a33, 0xfad9f4f8,
+  0x3418a2, 0xfae67ba2, 0x331986, 0xfaf3027e,
+  0x321ce0, 0xfaff898c, 0x3122b0, 0xfb0c10cb,
+  0x302af5, 0xfb18983b, 0x2f35b1, 0xfb251fdc,
+  0x2e42e2, 0xfb31a7ac, 0x2d5289, 0xfb3e2fac,
+  0x2c64a6, 0xfb4ab7db, 0x2b7939, 0xfb574039,
+  0x2a9042, 0xfb63c8c4, 0x29a9c1, 0xfb70517d,
+  0x28c5b6, 0xfb7cda63, 0x27e421, 0xfb896375,
+  0x270502, 0xfb95ecb4, 0x262859, 0xfba2761e,
+  0x254e27, 0xfbaeffb3, 0x24766a, 0xfbbb8973,
+  0x23a124, 0xfbc8135c, 0x22ce54, 0xfbd49d70,
+  0x21fdfb, 0xfbe127ac, 0x213018, 0xfbedb212,
+  0x2064ab, 0xfbfa3c9f, 0x1f9bb5, 0xfc06c754,
+  0x1ed535, 0xfc135231, 0x1e112b, 0xfc1fdd34,
+  0x1d4f99, 0xfc2c685d, 0x1c907c, 0xfc38f3ac,
+  0x1bd3d6, 0xfc457f21, 0x1b19a7, 0xfc520aba,
+  0x1a61ee, 0xfc5e9678, 0x19acac, 0xfc6b2259,
+  0x18f9e1, 0xfc77ae5e, 0x18498c, 0xfc843a85,
+  0x179bae, 0xfc90c6cf, 0x16f047, 0xfc9d533b,
+  0x164757, 0xfca9dfc8, 0x15a0dd, 0xfcb66c77,
+  0x14fcda, 0xfcc2f945, 0x145b4e, 0xfccf8634,
+  0x13bc39, 0xfcdc1342, 0x131f9b, 0xfce8a06f,
+  0x128574, 0xfcf52dbb, 0x11edc3, 0xfd01bb24,
+  0x11588a, 0xfd0e48ab, 0x10c5c7, 0xfd1ad650,
+  0x10357c, 0xfd276410, 0xfa7a8, 0xfd33f1ed,
+  0xf1c4a, 0xfd407fe6, 0xe9364, 0xfd4d0df9,
+  0xe0cf5, 0xfd599c28, 0xd88fd, 0xfd662a70,
+  0xd077c, 0xfd72b8d2, 0xc8872, 0xfd7f474d,
+  0xc0be0, 0xfd8bd5e1, 0xb91c4, 0xfd98648d,
+  0xb1a20, 0xfda4f351, 0xaa4f3, 0xfdb1822c,
+  0xa323d, 0xfdbe111e, 0x9c1ff, 0xfdcaa027,
+  0x95438, 0xfdd72f45, 0x8e8e8, 0xfde3be78,
+  0x8800f, 0xfdf04dc0, 0x819ae, 0xfdfcdd1d,
+  0x7b5c4, 0xfe096c8d, 0x75452, 0xfe15fc11,
+  0x6f556, 0xfe228ba7, 0x698d3, 0xfe2f1b50,
+  0x63ec6, 0xfe3bab0b, 0x5e731, 0xfe483ad8,
+  0x59214, 0xfe54cab5, 0x53f6e, 0xfe615aa3,
+  0x4ef3f, 0xfe6deaa1, 0x4a188, 0xfe7a7aae,
+  0x45648, 0xfe870aca, 0x40d80, 0xfe939af5,
+  0x3c72f, 0xfea02b2e, 0x38356, 0xfeacbb74,
+  0x341f4, 0xfeb94bc8, 0x3030a, 0xfec5dc28,
+  0x2c697, 0xfed26c94, 0x28c9c, 0xfedefd0c,
+  0x25519, 0xfeeb8d8f, 0x2200d, 0xfef81e1d,
+  0x1ed78, 0xff04aeb5, 0x1bd5c, 0xff113f56,
+  0x18fb6, 0xff1dd001, 0x16489, 0xff2a60b4,
+  0x13bd3, 0xff36f170, 0x11594, 0xff438234,
+  0xf1ce, 0xff5012fe, 0xd07e, 0xff5ca3d0,
+  0xb1a7, 0xff6934a8, 0x9547, 0xff75c585,
+  0x7b5f, 0xff825668, 0x63ee, 0xff8ee750,
+  0x4ef5, 0xff9b783c, 0x3c74, 0xffa8092c,
+  0x2c6a, 0xffb49a1f, 0x1ed8, 0xffc12b16,
+  0x13bd, 0xffcdbc0f, 0xb1a, 0xffda4d09,
+  0x4ef, 0xffe6de05, 0x13c, 0xfff36f02,
+  0x0, 0x0, 0x13c, 0xc90fe,
+  0x4ef, 0x1921fb, 0xb1a, 0x25b2f7,
+  0x13bd, 0x3243f1, 0x1ed8, 0x3ed4ea,
+  0x2c6a, 0x4b65e1, 0x3c74, 0x57f6d4,
+  0x4ef5, 0x6487c4, 0x63ee, 0x7118b0,
+  0x7b5f, 0x7da998, 0x9547, 0x8a3a7b,
+  0xb1a7, 0x96cb58, 0xd07e, 0xa35c30,
+  0xf1ce, 0xafed02, 0x11594, 0xbc7dcc,
+  0x13bd3, 0xc90e90, 0x16489, 0xd59f4c,
+  0x18fb6, 0xe22fff, 0x1bd5c, 0xeec0aa,
+  0x1ed78, 0xfb514b, 0x2200d, 0x107e1e3,
+  0x25519, 0x1147271, 0x28c9c, 0x12102f4,
+  0x2c697, 0x12d936c, 0x3030a, 0x13a23d8,
+  0x341f4, 0x146b438, 0x38356, 0x153448c,
+  0x3c72f, 0x15fd4d2, 0x40d80, 0x16c650b,
+  0x45648, 0x178f536, 0x4a188, 0x1858552,
+  0x4ef3f, 0x192155f, 0x53f6e, 0x19ea55d,
+  0x59214, 0x1ab354b, 0x5e731, 0x1b7c528,
+  0x63ec6, 0x1c454f5, 0x698d3, 0x1d0e4b0,
+  0x6f556, 0x1dd7459, 0x75452, 0x1ea03ef,
+  0x7b5c4, 0x1f69373, 0x819ae, 0x20322e3,
+  0x8800f, 0x20fb240, 0x8e8e8, 0x21c4188,
+  0x95438, 0x228d0bb, 0x9c1ff, 0x2355fd9,
+  0xa323d, 0x241eee2, 0xaa4f3, 0x24e7dd4,
+  0xb1a20, 0x25b0caf, 0xb91c4, 0x2679b73,
+  0xc0be0, 0x2742a1f, 0xc8872, 0x280b8b3,
+  0xd077c, 0x28d472e, 0xd88fd, 0x299d590,
+  0xe0cf5, 0x2a663d8, 0xe9364, 0x2b2f207,
+  0xf1c4a, 0x2bf801a, 0xfa7a8, 0x2cc0e13,
+  0x10357c, 0x2d89bf0, 0x10c5c7, 0x2e529b0,
+  0x11588a, 0x2f1b755, 0x11edc3, 0x2fe44dc,
+  0x128574, 0x30ad245, 0x131f9b, 0x3175f91,
+  0x13bc39, 0x323ecbe, 0x145b4e, 0x33079cc,
+  0x14fcda, 0x33d06bb, 0x15a0dd, 0x3499389,
+  0x164757, 0x3562038, 0x16f047, 0x362acc5,
+  0x179bae, 0x36f3931, 0x18498c, 0x37bc57b,
+  0x18f9e1, 0x38851a2, 0x19acac, 0x394dda7,
+  0x1a61ee, 0x3a16988, 0x1b19a7, 0x3adf546,
+  0x1bd3d6, 0x3ba80df, 0x1c907c, 0x3c70c54,
+  0x1d4f99, 0x3d397a3, 0x1e112b, 0x3e022cc,
+  0x1ed535, 0x3ecadcf, 0x1f9bb5, 0x3f938ac,
+  0x2064ab, 0x405c361, 0x213018, 0x4124dee,
+  0x21fdfb, 0x41ed854, 0x22ce54, 0x42b6290,
+  0x23a124, 0x437eca4, 0x24766a, 0x444768d,
+  0x254e27, 0x451004d, 0x262859, 0x45d89e2,
+  0x270502, 0x46a134c, 0x27e421, 0x4769c8b,
+  0x28c5b6, 0x483259d, 0x29a9c1, 0x48fae83,
+  0x2a9042, 0x49c373c, 0x2b7939, 0x4a8bfc7,
+  0x2c64a6, 0x4b54825, 0x2d5289, 0x4c1d054,
+  0x2e42e2, 0x4ce5854, 0x2f35b1, 0x4dae024,
+  0x302af5, 0x4e767c5, 0x3122b0, 0x4f3ef35,
+  0x321ce0, 0x5007674, 0x331986, 0x50cfd82,
+  0x3418a2, 0x519845e, 0x351a33, 0x5260b08,
+  0x361e3a, 0x532917f, 0x3724b6, 0x53f17c3,
+  0x382da8, 0x54b9dd3, 0x393910, 0x55823ae,
+  0x3a46ed, 0x564a955, 0x3b573f, 0x5712ec7,
+  0x3c6a07, 0x57db403, 0x3d7f44, 0x58a3908,
+  0x3e96f6, 0x596bdd7, 0x3fb11d, 0x5a3426f,
+  0x40cdba, 0x5afc6d0, 0x41eccc, 0x5bc4af8,
+  0x430e53, 0x5c8cee7, 0x44324f, 0x5d5529e,
+  0x4558c0, 0x5e1d61b, 0x4681a6, 0x5ee595d,
+  0x47ad01, 0x5fadc66, 0x48dad1, 0x6075f33,
+  0x4a0b16, 0x613e1c5, 0x4b3dcf, 0x620641a,
+  0x4c72fe, 0x62ce634, 0x4daaa1, 0x6396810,
+  0x4ee4b8, 0x645e9af, 0x502145, 0x6526b10,
+  0x516045, 0x65eec33, 0x52a1bb, 0x66b6d16,
+  0x53e5a5, 0x677edbb, 0x552c03, 0x6846e1f,
+  0x5674d6, 0x690ee44, 0x57c01d, 0x69d6e27,
+  0x590dd8, 0x6a9edc9, 0x5a5e07, 0x6b66d29,
+  0x5bb0ab, 0x6c2ec48, 0x5d05c3, 0x6cf6b23,
+  0x5e5d4e, 0x6dbe9bb, 0x5fb74e, 0x6e86810,
+  0x6113c2, 0x6f4e620, 0x6272aa, 0x70163eb,
+  0x63d405, 0x70de172, 0x6537d4, 0x71a5eb3,
+  0x669e18, 0x726dbae, 0x6806ce, 0x7335862,
+  0x6971f9, 0x73fd4cf, 0x6adf97, 0x74c50f4,
+  0x6c4fa8, 0x758ccd2, 0x6dc22e, 0x7654867,
+  0x6f3726, 0x771c3b3, 0x70ae92, 0x77e3eb5,
+  0x722871, 0x78ab96e, 0x73a4c3, 0x79733dc,
+  0x752389, 0x7a3adff, 0x76a4c2, 0x7b027d7,
+  0x78286e, 0x7bca163, 0x79ae8c, 0x7c91aa3,
+  0x7b371e, 0x7d59396, 0x7cc223, 0x7e20c3b,
+  0x7e4f9b, 0x7ee8493, 0x7fdf85, 0x7fafc9c,
+  0x8171e2, 0x8077457, 0x8306b2, 0x813ebc2,
+  0x849df4, 0x82062de, 0x8637a9, 0x82cd9a9,
+  0x87d3d0, 0x8395024, 0x89726a, 0x845c64d,
+  0x8b1376, 0x8523c25, 0x8cb6f5, 0x85eb1ab,
+  0x8e5ce5, 0x86b26de, 0x900548, 0x8779bbe,
+  0x91b01d, 0x884104b, 0x935d64, 0x8908483,
+  0x950d1d, 0x89cf867, 0x96bf48, 0x8a96bf6,
+  0x9873e4, 0x8b5df30, 0x9a2af3, 0x8c25213,
+  0x9be473, 0x8cec4a0, 0x9da065, 0x8db36d6,
+  0x9f5ec8, 0x8e7a8b5, 0xa11f9d, 0x8f41a3c,
+  0xa2e2e3, 0x9008b6a, 0xa4a89b, 0x90cfc40,
+  0xa670c4, 0x9196cbc, 0xa83b5e, 0x925dcdf,
+  0xaa086a, 0x9324ca7, 0xabd7e6, 0x93ebc14,
+  0xada9d4, 0x94b2b27, 0xaf7e33, 0x95799dd,
+  0xb15502, 0x9640837, 0xb32e42, 0x9707635,
+  0xb509f3, 0x97ce3d5, 0xb6e815, 0x9895118,
+  0xb8c8a7, 0x995bdfd, 0xbaabaa, 0x9a22a83,
+  0xbc911d, 0x9ae96aa, 0xbe7901, 0x9bb0271,
+  0xc06355, 0x9c76dd8, 0xc25019, 0x9d3d8df,
+  0xc43f4d, 0x9e04385, 0xc630f2, 0x9ecadc9,
+  0xc82506, 0x9f917ac, 0xca1b8a, 0xa05812c,
+  0xcc147f, 0xa11ea49, 0xce0fe3, 0xa1e5303,
+  0xd00db6, 0xa2abb59, 0xd20dfa, 0xa37234a,
+  0xd410ad, 0xa438ad7, 0xd615cf, 0xa4ff1fe,
+  0xd81d61, 0xa5c58c0, 0xda2762, 0xa68bf1b,
+  0xdc33d2, 0xa752510, 0xde42b2, 0xa818a9d,
+  0xe05401, 0xa8defc3, 0xe267be, 0xa9a5480,
+  0xe47deb, 0xaa6b8d5, 0xe69686, 0xab31cc1,
+  0xe8b190, 0xabf8043, 0xeacf09, 0xacbe35b,
+  0xeceef1, 0xad84609, 0xef1147, 0xae4a84b,
+  0xf1360b, 0xaf10a22, 0xf35d3e, 0xafd6b8d,
+  0xf586df, 0xb09cc8c, 0xf7b2ee, 0xb162d1d,
+  0xf9e16b, 0xb228d42, 0xfc1257, 0xb2eecf8,
+  0xfe45b0, 0xb3b4c40, 0x1007b77, 0xb47ab19,
+  0x102b3ac, 0xb540982, 0x104ee4f, 0xb60677c,
+  0x1072b5f, 0xb6cc506, 0x1096add, 0xb79221f,
+  0x10bacc8, 0xb857ec7, 0x10df120, 0xb91dafc,
+  0x11037e6, 0xb9e36c0, 0x1128119, 0xbaa9211,
+  0x114ccb9, 0xbb6ecef, 0x1171ac6, 0xbc34759,
+  0x1196b3f, 0xbcfa150, 0x11bbe26, 0xbdbfad1,
+  0x11e1379, 0xbe853de, 0x1206b39, 0xbf4ac75,
+  0x122c566, 0xc010496, 0x12521ff, 0xc0d5c41,
+  0x1278104, 0xc19b374, 0x129e276, 0xc260a31,
+  0x12c4653, 0xc326075, 0x12eac9d, 0xc3eb641,
+  0x1311553, 0xc4b0b94, 0x1338075, 0xc57606e,
+  0x135ee02, 0xc63b4ce, 0x1385dfb, 0xc7008b3,
+  0x13ad060, 0xc7c5c1e, 0x13d4530, 0xc88af0e,
+  0x13fbc6c, 0xc950182, 0x1423613, 0xca1537a,
+  0x144b225, 0xcada4f5, 0x14730a3, 0xcb9f5f3,
+  0x149b18b, 0xcc64673, 0x14c34df, 0xcd29676,
+  0x14eba9d, 0xcdee5f9, 0x15142c6, 0xceb34fe,
+  0x153cd5a, 0xcf78383, 0x1565a58, 0xd03d189,
+  0x158e9c1, 0xd101f0e, 0x15b7b94, 0xd1c6c11,
+  0x15e0fd1, 0xd28b894, 0x160a678, 0xd350495,
+  0x1633f8a, 0xd415013, 0x165db05, 0xd4d9b0e,
+  0x16878eb, 0xd59e586, 0x16b193a, 0xd662f7b,
+  0x16dbbf3, 0xd7278eb, 0x1706115, 0xd7ec1d6,
+  0x17308a1, 0xd8b0a3d, 0x175b296, 0xd97521d,
+  0x1785ef4, 0xda39978, 0x17b0dbb, 0xdafe04b,
+  0x17dbeec, 0xdbc2698, 0x1807285, 0xdc86c5d,
+  0x1832888, 0xdd4b19a, 0x185e0f3, 0xde0f64f,
+  0x1889bc6, 0xded3a7b, 0x18b5903, 0xdf97e1d,
+  0x18e18a7, 0xe05c135, 0x190dab4, 0xe1203c3,
+  0x1939f29, 0xe1e45c6, 0x1966606, 0xe2a873e,
+  0x1992f4c, 0xe36c82a, 0x19bfaf9, 0xe430889,
+  0x19ec90d, 0xe4f485c, 0x1a1998a, 0xe5b87a2,
+  0x1a46c6e, 0xe67c65a, 0x1a741b9, 0xe740483,
+  0x1aa196c, 0xe80421e, 0x1acf386, 0xe8c7f2a,
+  0x1afd007, 0xe98bba7, 0x1b2aef0, 0xea4f793,
+  0x1b5903f, 0xeb132ef, 0x1b873f5, 0xebd6db9,
+  0x1bb5a11, 0xec9a7f3, 0x1be4294, 0xed5e19a,
+  0x1c12d7e, 0xee21aaf, 0x1c41ace, 0xeee5331,
+  0x1c70a84, 0xefa8b20, 0x1c9fca0, 0xf06c27a,
+  0x1ccf122, 0xf12f941, 0x1cfe80a, 0xf1f2f73,
+  0x1d2e158, 0xf2b650f, 0x1d5dd0c, 0xf379a16,
+  0x1d8db25, 0xf43ce86, 0x1dbdba3, 0xf500260,
+  0x1dede87, 0xf5c35a3, 0x1e1e3d0, 0xf68684e,
+  0x1e4eb7e, 0xf749a61, 0x1e7f591, 0xf80cbdc,
+  0x1eb0209, 0xf8cfcbe, 0x1ee10e5, 0xf992d06,
+  0x1f12227, 0xfa55cb4, 0x1f435cc, 0xfb18bc8,
+  0x1f74bd6, 0xfbdba40, 0x1fa6445, 0xfc9e81e,
+  0x1fd7f17, 0xfd6155f, 0x2009c4e, 0xfe24205,
+  0x203bbe8, 0xfee6e0d, 0x206dde6, 0xffa9979,
+  0x20a0248, 0x1006c446, 0x20d290d, 0x1012ee76,
+  0x2105236, 0x101f1807, 0x2137dc2, 0x102b40f8,
+  0x216abb1, 0x1037694b, 0x219dc03, 0x104390fd,
+  0x21d0eb8, 0x104fb80e, 0x22043d0, 0x105bde7f,
+  0x2237b4b, 0x1068044e, 0x226b528, 0x1074297b,
+  0x229f167, 0x10804e06, 0x22d3009, 0x108c71ee,
+  0x230710d, 0x10989532, 0x233b473, 0x10a4b7d3,
+  0x236fa3b, 0x10b0d9d0, 0x23a4265, 0x10bcfb28,
+  0x23d8cf1, 0x10c91bda, 0x240d9de, 0x10d53be7,
+  0x244292c, 0x10e15b4e, 0x2477adc, 0x10ed7a0e,
+  0x24aceed, 0x10f99827, 0x24e255e, 0x1105b599,
+  0x2517e31, 0x1111d263, 0x254d965, 0x111dee84,
+  0x25836f9, 0x112a09fc, 0x25b96ee, 0x113624cb,
+  0x25ef943, 0x11423ef0, 0x2625df8, 0x114e586a,
+  0x265c50e, 0x115a713a, 0x2692e83, 0x1166895f,
+  0x26c9a58, 0x1172a0d7, 0x270088e, 0x117eb7a4,
+  0x2737922, 0x118acdc4, 0x276ec16, 0x1196e337,
+  0x27a616a, 0x11a2f7fc, 0x27dd91c, 0x11af0c13,
+  0x281532e, 0x11bb1f7c, 0x284cf9f, 0x11c73235,
+  0x2884e6e, 0x11d3443f, 0x28bcf9c, 0x11df5599,
+  0x28f5329, 0x11eb6643, 0x292d914, 0x11f7763c,
+  0x296615d, 0x12038584, 0x299ec05, 0x120f941a,
+  0x29d790a, 0x121ba1fd, 0x2a1086d, 0x1227af2e,
+  0x2a49a2e, 0x1233bbac, 0x2a82e4d, 0x123fc776,
+  0x2abc4c9, 0x124bd28c, 0x2af5da2, 0x1257dced,
+  0x2b2f8d8, 0x1263e699, 0x2b6966c, 0x126fef90,
+  0x2ba365c, 0x127bf7d1, 0x2bdd8a9, 0x1287ff5b,
+  0x2c17d52, 0x1294062f, 0x2c52459, 0x12a00c4b,
+  0x2c8cdbb, 0x12ac11af, 0x2cc7979, 0x12b8165b,
+  0x2d02794, 0x12c41a4f, 0x2d3d80a, 0x12d01d89,
+  0x2d78add, 0x12dc2009, 0x2db400a, 0x12e821cf,
+  0x2def794, 0x12f422db, 0x2e2b178, 0x1300232c,
+  0x2e66db8, 0x130c22c1, 0x2ea2c53, 0x1318219a,
+  0x2eded49, 0x13241fb6, 0x2f1b099, 0x13301d16,
+  0x2f57644, 0x133c19b8, 0x2f93e4a, 0x1348159d,
+  0x2fd08a9, 0x135410c3, 0x300d563, 0x13600b2a,
+  0x304a477, 0x136c04d2, 0x30875e5, 0x1377fdbb,
+  0x30c49ad, 0x1383f5e3, 0x3101fce, 0x138fed4b,
+  0x313f848, 0x139be3f2, 0x317d31c, 0x13a7d9d7,
+  0x31bb049, 0x13b3cefa, 0x31f8fcf, 0x13bfc35b,
+  0x32371ae, 0x13cbb6f8, 0x32755e5, 0x13d7a9d3,
+  0x32b3c75, 0x13e39be9, 0x32f255e, 0x13ef8d3c,
+  0x333109e, 0x13fb7dc9, 0x336fe37, 0x14076d91,
+  0x33aee27, 0x14135c94, 0x33ee070, 0x141f4ad1,
+  0x342d510, 0x142b3846, 0x346cc07, 0x143724f5,
+  0x34ac556, 0x144310dd, 0x34ec0fc, 0x144efbfc,
+  0x352bef9, 0x145ae653, 0x356bf4d, 0x1466cfe1,
+  0x35ac1f7, 0x1472b8a5, 0x35ec6f8, 0x147ea0a0,
+  0x362ce50, 0x148a87d1, 0x366d7fd, 0x14966e36,
+  0x36ae401, 0x14a253d1, 0x36ef25b, 0x14ae38a0,
+  0x373030a, 0x14ba1ca3, 0x377160f, 0x14c5ffd9,
+  0x37b2b6a, 0x14d1e242, 0x37f4319, 0x14ddc3de,
+  0x3835d1e, 0x14e9a4ac, 0x3877978, 0x14f584ac,
+  0x38b9827, 0x150163dc, 0x38fb92a, 0x150d423d,
+  0x393dc82, 0x15191fcf, 0x398022f, 0x1524fc90,
+  0x39c2a2f, 0x1530d881, 0x3a05484, 0x153cb3a0,
+  0x3a4812c, 0x15488dee, 0x3a8b028, 0x1554676a,
+  0x3ace178, 0x15604013, 0x3b1151b, 0x156c17e9,
+  0x3b54b11, 0x1577eeec, 0x3b9835a, 0x1583c51b,
+  0x3bdbdf6, 0x158f9a76, 0x3c1fae5, 0x159b6efb,
+  0x3c63a26, 0x15a742ac, 0x3ca7bba, 0x15b31587,
+  0x3cebfa0, 0x15bee78c, 0x3d305d8, 0x15cab8ba,
+  0x3d74e62, 0x15d68911, 0x3db993e, 0x15e25890,
+  0x3dfe66c, 0x15ee2738, 0x3e435ea, 0x15f9f507,
+  0x3e887bb, 0x1605c1fd, 0x3ecdbdc, 0x16118e1a,
+  0x3f1324e, 0x161d595d, 0x3f58b10, 0x162923c5,
+  0x3f9e624, 0x1634ed53, 0x3fe4388, 0x1640b606,
+  0x402a33c, 0x164c7ddd, 0x4070540, 0x165844d8,
+  0x40b6994, 0x16640af7, 0x40fd037, 0x166fd039,
+  0x414392b, 0x167b949d, 0x418a46d, 0x16875823,
+  0x41d11ff, 0x16931acb, 0x42181e0, 0x169edc94,
+  0x425f410, 0x16aa9d7e, 0x42a688f, 0x16b65d88,
+  0x42edf5c, 0x16c21cb2, 0x4335877, 0x16cddafb,
+  0x437d3e1, 0x16d99864, 0x43c5199, 0x16e554ea,
+  0x440d19e, 0x16f1108f, 0x44553f2, 0x16fccb51,
+  0x449d892, 0x17088531, 0x44e5f80, 0x17143e2d,
+  0x452e8bc, 0x171ff646, 0x4577444, 0x172bad7a,
+  0x45c0219, 0x173763c9, 0x460923b, 0x17431933,
+  0x46524a9, 0x174ecdb8, 0x469b963, 0x175a8157,
+  0x46e5069, 0x1766340f, 0x472e9bc, 0x1771e5e0,
+  0x477855a, 0x177d96ca, 0x47c2344, 0x178946cc,
+  0x480c379, 0x1794f5e6, 0x48565f9, 0x17a0a417,
+  0x48a0ac4, 0x17ac515f, 0x48eb1db, 0x17b7fdbd,
+  0x4935b3c, 0x17c3a931, 0x49806e7, 0x17cf53bb,
+  0x49cb4dd, 0x17dafd59, 0x4a1651c, 0x17e6a60c,
+  0x4a617a6, 0x17f24dd3, 0x4aacc7a, 0x17fdf4ae,
+  0x4af8397, 0x18099a9c, 0x4b43cfd, 0x18153f9d,
+  0x4b8f8ad, 0x1820e3b0, 0x4bdb6a6, 0x182c86d5,
+  0x4c276e8, 0x1838290c, 0x4c73972, 0x1843ca53,
+  0x4cbfe45, 0x184f6aab, 0x4d0c560, 0x185b0a13,
+  0x4d58ec3, 0x1866a88a, 0x4da5a6f, 0x18724611,
+  0x4df2862, 0x187de2a7, 0x4e3f89c, 0x18897e4a,
+  0x4e8cb1e, 0x189518fc, 0x4ed9fe7, 0x18a0b2bb,
+  0x4f276f7, 0x18ac4b87, 0x4f7504e, 0x18b7e35f,
+  0x4fc2bec, 0x18c37a44, 0x50109d0, 0x18cf1034,
+  0x505e9fb, 0x18daa52f, 0x50acc6b, 0x18e63935,
+  0x50fb121, 0x18f1cc45, 0x514981d, 0x18fd5e5f,
+  0x519815f, 0x1908ef82, 0x51e6ce6, 0x19147fae,
+  0x5235ab2, 0x19200ee3, 0x5284ac3, 0x192b9d1f,
+  0x52d3d18, 0x19372a64, 0x53231b3, 0x1942b6af,
+  0x5372891, 0x194e4201, 0x53c21b4, 0x1959cc5a,
+  0x5411d1b, 0x196555b8, 0x5461ac6, 0x1970de1b,
+  0x54b1ab4, 0x197c6584, 0x5501ce5, 0x1987ebf0,
+  0x555215a, 0x19937161, 0x55a2812, 0x199ef5d6,
+  0x55f310d, 0x19aa794d, 0x5643c4a, 0x19b5fbc8,
+  0x56949ca, 0x19c17d44, 0x56e598c, 0x19ccfdc2,
+  0x5736b90, 0x19d87d42, 0x5787fd6, 0x19e3fbc3,
+  0x57d965d, 0x19ef7944, 0x582af26, 0x19faf5c5,
+  0x587ca31, 0x1a067145, 0x58ce77c, 0x1a11ebc5,
+  0x5920708, 0x1a1d6544, 0x59728d5, 0x1a28ddc0,
+  0x59c4ce3, 0x1a34553b, 0x5a17330, 0x1a3fcbb3,
+  0x5a69bbe, 0x1a4b4128, 0x5abc68c, 0x1a56b599,
+  0x5b0f399, 0x1a622907, 0x5b622e6, 0x1a6d9b70,
+  0x5bb5472, 0x1a790cd4, 0x5c0883d, 0x1a847d33,
+  0x5c5be47, 0x1a8fec8c, 0x5caf690, 0x1a9b5adf,
+  0x5d03118, 0x1aa6c82b, 0x5d56ddd, 0x1ab23471,
+  0x5daace1, 0x1abd9faf, 0x5dfee22, 0x1ac909e5,
+  0x5e531a1, 0x1ad47312, 0x5ea775e, 0x1adfdb37,
+  0x5efbf58, 0x1aeb4253, 0x5f5098f, 0x1af6a865,
+  0x5fa5603, 0x1b020d6c, 0x5ffa4b3, 0x1b0d716a,
+  0x604f5a0, 0x1b18d45c, 0x60a48c9, 0x1b243643,
+  0x60f9e2e, 0x1b2f971e, 0x614f5cf, 0x1b3af6ec,
+  0x61a4fac, 0x1b4655ae, 0x61fabc4, 0x1b51b363,
+  0x6250a18, 0x1b5d100a, 0x62a6aa6, 0x1b686ba3,
+  0x62fcd6f, 0x1b73c62d, 0x6353273, 0x1b7f1fa9,
+  0x63a99b1, 0x1b8a7815, 0x6400329, 0x1b95cf71,
+  0x6456edb, 0x1ba125bd, 0x64adcc7, 0x1bac7af9,
+  0x6504ced, 0x1bb7cf23, 0x655bf4c, 0x1bc3223c,
+  0x65b33e4, 0x1bce7442, 0x660aab5, 0x1bd9c537,
+  0x66623be, 0x1be51518, 0x66b9f01, 0x1bf063e6,
+  0x6711c7b, 0x1bfbb1a0, 0x6769c2e, 0x1c06fe46,
+  0x67c1e18, 0x1c1249d8, 0x681a23a, 0x1c1d9454,
+  0x6872894, 0x1c28ddbb, 0x68cb124, 0x1c34260c,
+  0x6923bec, 0x1c3f6d47, 0x697c8eb, 0x1c4ab36b,
+  0x69d5820, 0x1c55f878, 0x6a2e98b, 0x1c613c6d,
+  0x6a87d2d, 0x1c6c7f4a, 0x6ae1304, 0x1c77c10e,
+  0x6b3ab12, 0x1c8301b9, 0x6b94554, 0x1c8e414b,
+  0x6bee1cd, 0x1c997fc4, 0x6c4807a, 0x1ca4bd21,
+  0x6ca215c, 0x1caff965, 0x6cfc472, 0x1cbb348d,
+  0x6d569be, 0x1cc66e99, 0x6db113d, 0x1cd1a78a,
+  0x6e0baf0, 0x1cdcdf5e, 0x6e666d7, 0x1ce81615,
+  0x6ec14f2, 0x1cf34baf, 0x6f1c540, 0x1cfe802b,
+  0x6f777c1, 0x1d09b389, 0x6fd2c75, 0x1d14e5c9,
+  0x702e35c, 0x1d2016e9, 0x7089c75, 0x1d2b46ea,
+  0x70e57c0, 0x1d3675cb, 0x714153e, 0x1d41a38c,
+  0x719d4ed, 0x1d4cd02c, 0x71f96ce, 0x1d57fbaa,
+  0x7255ae0, 0x1d632608, 0x72b2123, 0x1d6e4f43,
+  0x730e997, 0x1d79775c, 0x736b43c, 0x1d849e51,
+  0x73c8111, 0x1d8fc424, 0x7425016, 0x1d9ae8d2,
+  0x748214c, 0x1da60c5d, 0x74df4b1, 0x1db12ec3,
+  0x753ca46, 0x1dbc5004, 0x759a20a, 0x1dc7701f,
+  0x75f7bfe, 0x1dd28f15, 0x7655820, 0x1dddace4,
+  0x76b3671, 0x1de8c98c, 0x77116f0, 0x1df3e50d,
+  0x776f99d, 0x1dfeff67, 0x77cde79, 0x1e0a1898,
+  0x782c582, 0x1e1530a1, 0x788aeb9, 0x1e204781,
+  0x78e9a1d, 0x1e2b5d38, 0x79487ae, 0x1e3671c5,
+  0x79a776c, 0x1e418528, 0x7a06957, 0x1e4c9760,
+  0x7a65d6e, 0x1e57a86d, 0x7ac53b1, 0x1e62b84f,
+  0x7b24c20, 0x1e6dc705, 0x7b846ba, 0x1e78d48e,
+  0x7be4381, 0x1e83e0eb, 0x7c44272, 0x1e8eec1b,
+  0x7ca438f, 0x1e99f61d, 0x7d046d6, 0x1ea4fef0,
+  0x7d64c47, 0x1eb00696, 0x7dc53e3, 0x1ebb0d0d,
+  0x7e25daa, 0x1ec61254, 0x7e8699a, 0x1ed1166b,
+  0x7ee77b3, 0x1edc1953, 0x7f487f6, 0x1ee71b0a,
+  0x7fa9a62, 0x1ef21b90, 0x800aef7, 0x1efd1ae4,
+  0x806c5b5, 0x1f081907, 0x80cde9b, 0x1f1315f7,
+  0x812f9a9, 0x1f1e11b5, 0x81916df, 0x1f290c3f,
+  0x81f363d, 0x1f340596, 0x82557c3, 0x1f3efdb9,
+  0x82b7b70, 0x1f49f4a8, 0x831a143, 0x1f54ea62,
+  0x837c93e, 0x1f5fdee6, 0x83df35f, 0x1f6ad235,
+  0x8441fa6, 0x1f75c44e, 0x84a4e14, 0x1f80b531,
+  0x8507ea7, 0x1f8ba4dc, 0x856b160, 0x1f969350,
+  0x85ce63e, 0x1fa1808c, 0x8631d42, 0x1fac6c91,
+  0x869566a, 0x1fb7575c, 0x86f91b7, 0x1fc240ef,
+  0x875cf28, 0x1fcd2948, 0x87c0ebd, 0x1fd81067,
+  0x8825077, 0x1fe2f64c, 0x8889454, 0x1feddaf6,
+  0x88eda54, 0x1ff8be65, 0x8952278, 0x2003a099,
+  0x89b6cbf, 0x200e8190, 0x8a1b928, 0x2019614c,
+  0x8a807b4, 0x20243fca, 0x8ae5862, 0x202f1d0b,
+  0x8b4ab32, 0x2039f90f, 0x8bb0023, 0x2044d3d4,
+  0x8c15736, 0x204fad5b, 0x8c7b06b, 0x205a85a3,
+  0x8ce0bc0, 0x20655cac, 0x8d46936, 0x20703275,
+  0x8dac8cd, 0x207b06fe, 0x8e12a84, 0x2085da46,
+  0x8e78e5b, 0x2090ac4d, 0x8edf452, 0x209b7d13,
+  0x8f45c68, 0x20a64c97, 0x8fac69e, 0x20b11ad9,
+  0x90132f2, 0x20bbe7d8, 0x907a166, 0x20c6b395,
+  0x90e11f7, 0x20d17e0d, 0x91484a8, 0x20dc4742,
+  0x91af976, 0x20e70f32, 0x9217062, 0x20f1d5de,
+  0x927e96b, 0x20fc9b44, 0x92e6492, 0x21075f65,
+  0x934e1d6, 0x21122240, 0x93b6137, 0x211ce3d5,
+  0x941e2b4, 0x2127a423, 0x948664d, 0x21326329,
+  0x94eec03, 0x213d20e8, 0x95573d4, 0x2147dd5f,
+  0x95bfdc1, 0x2152988d, 0x96289c9, 0x215d5273,
+  0x96917ec, 0x21680b0f, 0x96fa82a, 0x2172c262,
+  0x9763a83, 0x217d786a, 0x97ccef5, 0x21882d28,
+  0x9836582, 0x2192e09b, 0x989fe29, 0x219d92c2,
+  0x99098e9, 0x21a8439e, 0x99735c2, 0x21b2f32e,
+  0x99dd4b4, 0x21bda171, 0x9a475bf, 0x21c84e67,
+  0x9ab18e3, 0x21d2fa0f, 0x9b1be1e, 0x21dda46a,
+  0x9b86572, 0x21e84d76, 0x9bf0edd, 0x21f2f534,
+  0x9c5ba60, 0x21fd9ba3, 0x9cc67fa, 0x220840c2,
+  0x9d317ab, 0x2212e492, 0x9d9c973, 0x221d8711,
+  0x9e07d51, 0x2228283f, 0x9e73346, 0x2232c81c,
+  0x9edeb50, 0x223d66a8, 0x9f4a570, 0x224803e2,
+  0x9fb61a5, 0x22529fca, 0xa021fef, 0x225d3a5e,
+  0xa08e04f, 0x2267d3a0, 0xa0fa2c3, 0x22726b8e,
+  0xa16674b, 0x227d0228, 0xa1d2de7, 0x2287976e,
+  0xa23f698, 0x22922b5e, 0xa2ac15b, 0x229cbdfa,
+  0xa318e32, 0x22a74f40, 0xa385d1d, 0x22b1df30,
+  0xa3f2e19, 0x22bc6dca, 0xa460129, 0x22c6fb0c,
+  0xa4cd64b, 0x22d186f8, 0xa53ad7e, 0x22dc118c,
+  0xa5a86c4, 0x22e69ac8, 0xa61621b, 0x22f122ab,
+  0xa683f83, 0x22fba936, 0xa6f1efc, 0x23062e67,
+  0xa760086, 0x2310b23e, 0xa7ce420, 0x231b34bc,
+  0xa83c9ca, 0x2325b5df, 0xa8ab184, 0x233035a7,
+  0xa919b4e, 0x233ab414, 0xa988727, 0x23453125,
+  0xa9f750f, 0x234facda, 0xaa66506, 0x235a2733,
+  0xaad570c, 0x2364a02e, 0xab44b1f, 0x236f17cc,
+  0xabb4141, 0x23798e0d, 0xac23971, 0x238402ef,
+  0xac933ae, 0x238e7673, 0xad02ff8, 0x2398e898,
+  0xad72e4f, 0x23a3595e, 0xade2eb3, 0x23adc8c4,
+  0xae53123, 0x23b836ca, 0xaec35a0, 0x23c2a36f,
+  0xaf33c28, 0x23cd0eb3, 0xafa44bc, 0x23d77896,
+  0xb014f5b, 0x23e1e117, 0xb085c05, 0x23ec4837,
+  0xb0f6aba, 0x23f6adf3, 0xb167b79, 0x2401124d,
+  0xb1d8e43, 0x240b7543, 0xb24a316, 0x2415d6d5,
+  0xb2bb9f4, 0x24203704, 0xb32d2da, 0x242a95ce,
+  0xb39edca, 0x2434f332, 0xb410ac3, 0x243f4f32,
+  0xb4829c4, 0x2449a9cc, 0xb4f4acd, 0x245402ff,
+  0xb566ddf, 0x245e5acc, 0xb5d92f8, 0x2468b132,
+  0xb64ba19, 0x24730631, 0xb6be341, 0x247d59c8,
+  0xb730e70, 0x2487abf7, 0xb7a3ba5, 0x2491fcbe,
+  0xb816ae1, 0x249c4c1b, 0xb889c23, 0x24a69a0f,
+  0xb8fcf6b, 0x24b0e699, 0xb9704b9, 0x24bb31ba,
+  0xb9e3c0b, 0x24c57b6f, 0xba57563, 0x24cfc3ba,
+  0xbacb0bf, 0x24da0a9a, 0xbb3ee20, 0x24e4500e,
+  0xbbb2d85, 0x24ee9415, 0xbc26eee, 0x24f8d6b0,
+  0xbc9b25a, 0x250317df, 0xbd0f7ca, 0x250d57a0,
+  0xbd83f3d, 0x251795f3, 0xbdf88b3, 0x2521d2d8,
+  0xbe6d42b, 0x252c0e4f, 0xbee21a5, 0x25364857,
+  0xbf57121, 0x254080ef, 0xbfcc29f, 0x254ab818,
+  0xc04161e, 0x2554edd1, 0xc0b6b9e, 0x255f2219,
+  0xc12c31f, 0x256954f1, 0xc1a1ca0, 0x25738657,
+  0xc217822, 0x257db64c, 0xc28d5a3, 0x2587e4cf,
+  0xc303524, 0x259211df, 0xc3796a5, 0x259c3d7c,
+  0xc3efa25, 0x25a667a7, 0xc465fa3, 0x25b0905d,
+  0xc4dc720, 0x25bab7a0, 0xc55309b, 0x25c4dd6e,
+  0xc5c9c14, 0x25cf01c8, 0xc64098b, 0x25d924ac,
+  0xc6b78ff, 0x25e3461b, 0xc72ea70, 0x25ed6614,
+  0xc7a5dde, 0x25f78497, 0xc81d349, 0x2601a1a2,
+  0xc894aaf, 0x260bbd37, 0xc90c412, 0x2615d754,
+  0xc983f70, 0x261feffa, 0xc9fbcca, 0x262a0727,
+  0xca73c1e, 0x26341cdb, 0xcaebd6e, 0x263e3117,
+  0xcb640b8, 0x264843d9, 0xcbdc5fc, 0x26525521,
+  0xcc54d3a, 0x265c64ef, 0xcccd671, 0x26667342,
+  0xcd461a2, 0x2670801a, 0xcdbeecc, 0x267a8b77,
+  0xce37def, 0x26849558, 0xceb0f0a, 0x268e9dbd,
+  0xcf2a21d, 0x2698a4a6, 0xcfa3729, 0x26a2aa11,
+  0xd01ce2b, 0x26acadff, 0xd096725, 0x26b6b070,
+  0xd110216, 0x26c0b162, 0xd189efe, 0x26cab0d6,
+  0xd203ddc, 0x26d4aecb, 0xd27deb0, 0x26deab41,
+  0xd2f817b, 0x26e8a637, 0xd37263a, 0x26f29fad,
+  0xd3eccef, 0x26fc97a3, 0xd467599, 0x27068e18,
+  0xd4e2037, 0x2710830c, 0xd55ccca, 0x271a767e,
+  0xd5d7b50, 0x2724686e, 0xd652bcb, 0x272e58dc,
+  0xd6cde39, 0x273847c8, 0xd74929a, 0x27423530,
+  0xd7c48ee, 0x274c2115, 0xd840134, 0x27560b76,
+  0xd8bbb6d, 0x275ff452, 0xd937798, 0x2769dbaa,
+  0xd9b35b4, 0x2773c17d, 0xda2f5c2, 0x277da5cb,
+  0xdaab7c0, 0x27878893, 0xdb27bb0, 0x279169d5,
+  0xdba4190, 0x279b4990, 0xdc20960, 0x27a527c4,
+  0xdc9d320, 0x27af0472, 0xdd19ed0, 0x27b8df97,
+  0xdd96c6f, 0x27c2b934, 0xde13bfd, 0x27cc9149,
+  0xde90d79, 0x27d667d5, 0xdf0e0e4, 0x27e03cd8,
+  0xdf8b63d, 0x27ea1052, 0xe008d84, 0x27f3e241,
+  0xe0866b8, 0x27fdb2a7, 0xe1041d9, 0x28078181,
+  0xe181ee8, 0x28114ed0, 0xe1ffde2, 0x281b1a94,
+  0xe27dec9, 0x2824e4cc, 0xe2fc19c, 0x282ead78,
+  0xe37a65b, 0x28387498, 0xe3f8d05, 0x28423a2a,
+  0xe47759a, 0x284bfe2f, 0xe4f6019, 0x2855c0a6,
+  0xe574c84, 0x285f8190, 0xe5f3ad8, 0x286940ea,
+  0xe672b16, 0x2872feb6, 0xe6f1d3d, 0x287cbaf3,
+  0xe77114e, 0x288675a0, 0xe7f0748, 0x28902ebd,
+  0xe86ff2a, 0x2899e64a, 0xe8ef8f4, 0x28a39c46,
+  0xe96f4a7, 0x28ad50b1, 0xe9ef241, 0x28b7038b,
+  0xea6f1c2, 0x28c0b4d2, 0xeaef32b, 0x28ca6488,
+  0xeb6f67a, 0x28d412ab, 0xebefbb0, 0x28ddbf3b,
+  0xec702cb, 0x28e76a37, 0xecf0bcd, 0x28f113a0,
+  0xed716b4, 0x28fabb75, 0xedf2380, 0x290461b5,
+  0xee73231, 0x290e0661, 0xeef42c7, 0x2917a977,
+  0xef75541, 0x29214af8, 0xeff699f, 0x292aeae3,
+  0xf077fe1, 0x29348937, 0xf0f9805, 0x293e25f5,
+  0xf17b20d, 0x2947c11c, 0xf1fcdf8, 0x29515aab,
+  0xf27ebc5, 0x295af2a3, 0xf300b74, 0x29648902,
+  0xf382d05, 0x296e1dc9, 0xf405077, 0x2977b0f7,
+  0xf4875ca, 0x2981428c, 0xf509cfe, 0x298ad287,
+  0xf58c613, 0x299460e8, 0xf60f108, 0x299dedaf,
+  0xf691ddd, 0x29a778db, 0xf714c91, 0x29b1026c,
+  0xf797d24, 0x29ba8a61, 0xf81af97, 0x29c410ba,
+  0xf89e3e8, 0x29cd9578, 0xf921a17, 0x29d71899,
+  0xf9a5225, 0x29e09a1c, 0xfa28c10, 0x29ea1a03,
+  0xfaac7d8, 0x29f3984c, 0xfb3057d, 0x29fd14f6,
+  0xfbb4500, 0x2a069003, 0xfc3865e, 0x2a100970,
+  0xfcbc999, 0x2a19813f, 0xfd40eaf, 0x2a22f76e,
+  0xfdc55a1, 0x2a2c6bfd, 0xfe49e6d, 0x2a35deeb,
+  0xfece915, 0x2a3f503a, 0xff53597, 0x2a48bfe7,
+  0xffd83f4, 0x2a522df3, 0x1005d42a, 0x2a5b9a5d,
+  0x100e2639, 0x2a650525, 0x10167a22, 0x2a6e6e4b,
+  0x101ecfe4, 0x2a77d5ce, 0x1027277e, 0x2a813bae,
+  0x102f80f1, 0x2a8a9fea, 0x1037dc3b, 0x2a940283,
+  0x1040395d, 0x2a9d6377, 0x10489856, 0x2aa6c2c6,
+  0x1050f926, 0x2ab02071, 0x10595bcd, 0x2ab97c77,
+  0x1061c04a, 0x2ac2d6d6, 0x106a269d, 0x2acc2f90,
+  0x10728ec6, 0x2ad586a3, 0x107af8c4, 0x2adedc10,
+  0x10836497, 0x2ae82fd5, 0x108bd23f, 0x2af181f3,
+  0x109441bb, 0x2afad269, 0x109cb30b, 0x2b042137,
+  0x10a5262f, 0x2b0d6e5c, 0x10ad9b26, 0x2b16b9d9,
+  0x10b611f1, 0x2b2003ac, 0x10be8a8d, 0x2b294bd5,
+  0x10c704fd, 0x2b329255, 0x10cf813e, 0x2b3bd72a,
+  0x10d7ff51, 0x2b451a55, 0x10e07f36, 0x2b4e5bd4,
+  0x10e900ec, 0x2b579ba8, 0x10f18472, 0x2b60d9d0,
+  0x10fa09c9, 0x2b6a164d, 0x110290f0, 0x2b73511c,
+  0x110b19e7, 0x2b7c8a3f, 0x1113a4ad, 0x2b85c1b5,
+  0x111c3142, 0x2b8ef77d, 0x1124bfa6, 0x2b982b97,
+  0x112d4fd9, 0x2ba15e03, 0x1135e1d9, 0x2baa8ec0,
+  0x113e75a8, 0x2bb3bdce, 0x11470b44, 0x2bbceb2d,
+  0x114fa2ad, 0x2bc616dd, 0x11583be2, 0x2bcf40dc,
+  0x1160d6e5, 0x2bd8692b, 0x116973b3, 0x2be18fc9,
+  0x1172124d, 0x2beab4b6, 0x117ab2b3, 0x2bf3d7f2,
+  0x118354e4, 0x2bfcf97c, 0x118bf8e0, 0x2c061953,
+  0x11949ea6, 0x2c0f3779, 0x119d4636, 0x2c1853eb,
+  0x11a5ef90, 0x2c216eaa, 0x11ae9ab4, 0x2c2a87b6,
+  0x11b747a0, 0x2c339f0e, 0x11bff656, 0x2c3cb4b1,
+  0x11c8a6d4, 0x2c45c8a0, 0x11d1591a, 0x2c4edada,
+  0x11da0d28, 0x2c57eb5e, 0x11e2c2fd, 0x2c60fa2d,
+  0x11eb7a9a, 0x2c6a0746, 0x11f433fd, 0x2c7312a9,
+  0x11fcef27, 0x2c7c1c55, 0x1205ac17, 0x2c85244a,
+  0x120e6acc, 0x2c8e2a87, 0x12172b48, 0x2c972f0d,
+  0x121fed88, 0x2ca031da, 0x1228b18d, 0x2ca932ef,
+  0x12317756, 0x2cb2324c, 0x123a3ee4, 0x2cbb2fef,
+  0x12430835, 0x2cc42bd9, 0x124bd34a, 0x2ccd2609,
+  0x1254a021, 0x2cd61e7f, 0x125d6ebc, 0x2cdf153a,
+  0x12663f19, 0x2ce80a3a, 0x126f1138, 0x2cf0fd80,
+  0x1277e518, 0x2cf9ef09, 0x1280babb, 0x2d02ded7,
+  0x1289921e, 0x2d0bcce8, 0x12926b41, 0x2d14b93d,
+  0x129b4626, 0x2d1da3d5, 0x12a422ca, 0x2d268cb0,
+  0x12ad012e, 0x2d2f73cd, 0x12b5e151, 0x2d38592c,
+  0x12bec333, 0x2d413ccd, 0x12c7a6d4, 0x2d4a1eaf,
+  0x12d08c33, 0x2d52fed2, 0x12d97350, 0x2d5bdd36,
+  0x12e25c2b, 0x2d64b9da, 0x12eb46c3, 0x2d6d94bf,
+  0x12f43318, 0x2d766de2, 0x12fd2129, 0x2d7f4545,
+  0x130610f7, 0x2d881ae8, 0x130f0280, 0x2d90eec8,
+  0x1317f5c6, 0x2d99c0e7, 0x1320eac6, 0x2da29144,
+  0x1329e181, 0x2dab5fdf, 0x1332d9f7, 0x2db42cb6,
+  0x133bd427, 0x2dbcf7cb, 0x1344d011, 0x2dc5c11c,
+  0x134dcdb4, 0x2dce88aa, 0x1356cd11, 0x2dd74e73,
+  0x135fce26, 0x2de01278, 0x1368d0f3, 0x2de8d4b8,
+  0x1371d579, 0x2df19534, 0x137adbb6, 0x2dfa53e9,
+  0x1383e3ab, 0x2e0310d9, 0x138ced57, 0x2e0bcc03,
+  0x1395f8ba, 0x2e148566, 0x139f05d3, 0x2e1d3d03,
+  0x13a814a2, 0x2e25f2d8, 0x13b12526, 0x2e2ea6e6,
+  0x13ba3760, 0x2e37592c, 0x13c34b4f, 0x2e4009aa,
+  0x13cc60f2, 0x2e48b860, 0x13d5784a, 0x2e51654c,
+  0x13de9156, 0x2e5a1070, 0x13e7ac15, 0x2e62b9ca,
+  0x13f0c887, 0x2e6b615a, 0x13f9e6ad, 0x2e740720,
+  0x14030684, 0x2e7cab1c, 0x140c280e, 0x2e854d4d,
+  0x14154b4a, 0x2e8dedb3, 0x141e7037, 0x2e968c4d,
+  0x142796d5, 0x2e9f291b, 0x1430bf24, 0x2ea7c41e,
+  0x1439e923, 0x2eb05d53, 0x144314d3, 0x2eb8f4bc,
+  0x144c4232, 0x2ec18a58, 0x14557140, 0x2eca1e27,
+  0x145ea1fd, 0x2ed2b027, 0x1467d469, 0x2edb405a,
+  0x14710883, 0x2ee3cebe, 0x147a3e4b, 0x2eec5b53,
+  0x148375c1, 0x2ef4e619, 0x148caee4, 0x2efd6f10,
+  0x1495e9b3, 0x2f05f637, 0x149f2630, 0x2f0e7b8e,
+  0x14a86458, 0x2f16ff14, 0x14b1a42c, 0x2f1f80ca,
+  0x14bae5ab, 0x2f2800af, 0x14c428d6, 0x2f307ec2,
+  0x14cd6dab, 0x2f38fb03, 0x14d6b42b, 0x2f417573,
+  0x14dffc54, 0x2f49ee0f, 0x14e94627, 0x2f5264da,
+  0x14f291a4, 0x2f5ad9d1, 0x14fbdec9, 0x2f634cf5,
+  0x15052d97, 0x2f6bbe45, 0x150e7e0d, 0x2f742dc1,
+  0x1517d02b, 0x2f7c9b69, 0x152123f0, 0x2f85073c,
+  0x152a795d, 0x2f8d713a, 0x1533d070, 0x2f95d963,
+  0x153d292a, 0x2f9e3fb6, 0x15468389, 0x2fa6a433,
+  0x154fdf8f, 0x2faf06da, 0x15593d3a, 0x2fb767aa,
+  0x15629c89, 0x2fbfc6a3, 0x156bfd7d, 0x2fc823c5,
+  0x15756016, 0x2fd07f0f, 0x157ec452, 0x2fd8d882,
+  0x15882a32, 0x2fe1301c, 0x159191b5, 0x2fe985de,
+  0x159afadb, 0x2ff1d9c7, 0x15a465a3, 0x2ffa2bd6,
+  0x15add20d, 0x30027c0c, 0x15b74019, 0x300aca69,
+  0x15c0afc6, 0x301316eb, 0x15ca2115, 0x301b6193,
+  0x15d39403, 0x3023aa5f, 0x15dd0892, 0x302bf151,
+  0x15e67ec1, 0x30343667, 0x15eff690, 0x303c79a2,
+  0x15f96ffd, 0x3044bb00, 0x1602eb0a, 0x304cfa83,
+  0x160c67b4, 0x30553828, 0x1615e5fd, 0x305d73f0,
+  0x161f65e4, 0x3065addb, 0x1628e767, 0x306de5e9,
+  0x16326a88, 0x30761c18, 0x163bef46, 0x307e5069,
+  0x1645759f, 0x308682dc, 0x164efd94, 0x308eb36f,
+  0x16588725, 0x3096e223, 0x16621251, 0x309f0ef8,
+  0x166b9f18, 0x30a739ed, 0x16752d79, 0x30af6302,
+  0x167ebd74, 0x30b78a36, 0x16884f09, 0x30bfaf89,
+  0x1691e237, 0x30c7d2fb, 0x169b76fe, 0x30cff48c,
+  0x16a50d5d, 0x30d8143b, 0x16aea555, 0x30e03208,
+  0x16b83ee4, 0x30e84df3, 0x16c1da0b, 0x30f067fb,
+  0x16cb76c9, 0x30f8801f, 0x16d5151d, 0x31009661,
+  0x16deb508, 0x3108aabf, 0x16e85689, 0x3110bd39,
+  0x16f1f99f, 0x3118cdcf, 0x16fb9e4b, 0x3120dc80,
+  0x1705448b, 0x3128e94c, 0x170eec60, 0x3130f433,
+  0x171895c9, 0x3138fd35, 0x172240c5, 0x31410450,
+  0x172bed55, 0x31490986, 0x17359b78, 0x31510cd5,
+  0x173f4b2e, 0x31590e3e, 0x1748fc75, 0x31610dbf,
+  0x1752af4f, 0x31690b59, 0x175c63ba, 0x3171070c,
+  0x176619b6, 0x317900d6, 0x176fd143, 0x3180f8b8,
+  0x17798a60, 0x3188eeb2, 0x1783450d, 0x3190e2c3,
+  0x178d014a, 0x3198d4ea, 0x1796bf16, 0x31a0c528,
+  0x17a07e70, 0x31a8b37c, 0x17aa3f5a, 0x31b09fe7,
+  0x17b401d1, 0x31b88a66, 0x17bdc5d6, 0x31c072fb,
+  0x17c78b68, 0x31c859a5, 0x17d15288, 0x31d03e64,
+  0x17db1b34, 0x31d82137, 0x17e4e56c, 0x31e0021e,
+  0x17eeb130, 0x31e7e118, 0x17f87e7f, 0x31efbe27,
+  0x18024d59, 0x31f79948, 0x180c1dbf, 0x31ff727c,
+  0x1815efae, 0x320749c3, 0x181fc328, 0x320f1f1c,
+  0x1829982b, 0x3216f287, 0x18336eb7, 0x321ec403,
+  0x183d46cc, 0x32269391, 0x18472069, 0x322e6130,
+  0x1850fb8e, 0x32362ce0, 0x185ad83c, 0x323df6a0,
+  0x1864b670, 0x3245be70, 0x186e962b, 0x324d8450,
+  0x1878776d, 0x32554840, 0x18825a35, 0x325d0a3e,
+  0x188c3e83, 0x3264ca4c, 0x18962456, 0x326c8868,
+  0x18a00bae, 0x32744493, 0x18a9f48a, 0x327bfecc,
+  0x18b3deeb, 0x3283b712, 0x18bdcad0, 0x328b6d66,
+  0x18c7b838, 0x329321c7, 0x18d1a724, 0x329ad435,
+  0x18db9792, 0x32a284b0, 0x18e58982, 0x32aa3336,
+  0x18ef7cf4, 0x32b1dfc9, 0x18f971e8, 0x32b98a67,
+  0x1903685d, 0x32c13311, 0x190d6053, 0x32c8d9c6,
+  0x191759c9, 0x32d07e85, 0x192154bf, 0x32d82150,
+  0x192b5135, 0x32dfc224, 0x19354f2a, 0x32e76102,
+  0x193f4e9e, 0x32eefdea, 0x19494f90, 0x32f698db,
+  0x19535201, 0x32fe31d5, 0x195d55ef, 0x3305c8d7,
+  0x19675b5a, 0x330d5de3, 0x19716243, 0x3314f0f6,
+  0x197b6aa8, 0x331c8211, 0x19857489, 0x33241134,
+  0x198f7fe6, 0x332b9e5e, 0x19998cbe, 0x3333298f,
+  0x19a39b11, 0x333ab2c6, 0x19adaadf, 0x33423a04,
+  0x19b7bc27, 0x3349bf48, 0x19c1cee9, 0x33514292,
+  0x19cbe325, 0x3358c3e2, 0x19d5f8d9, 0x33604336,
+  0x19e01006, 0x3367c090, 0x19ea28ac, 0x336f3bee,
+  0x19f442c9, 0x3376b551, 0x19fe5e5e, 0x337e2cb7,
+  0x1a087b69, 0x3385a222, 0x1a1299ec, 0x338d1590,
+  0x1a1cb9e5, 0x33948701, 0x1a26db54, 0x339bf675,
+  0x1a30fe38, 0x33a363ec, 0x1a3b2292, 0x33aacf65,
+  0x1a454860, 0x33b238e0, 0x1a4f6fa3, 0x33b9a05d,
+  0x1a599859, 0x33c105db, 0x1a63c284, 0x33c8695b,
+  0x1a6dee21, 0x33cfcadc, 0x1a781b31, 0x33d72a5d,
+  0x1a8249b4, 0x33de87de, 0x1a8c79a9, 0x33e5e360,
+  0x1a96ab0f, 0x33ed3ce1, 0x1aa0dde7, 0x33f49462,
+  0x1aab122f, 0x33fbe9e2, 0x1ab547e8, 0x34033d61,
+  0x1abf7f11, 0x340a8edf, 0x1ac9b7a9, 0x3411de5b,
+  0x1ad3f1b1, 0x34192bd5, 0x1ade2d28, 0x3420774d,
+  0x1ae86a0d, 0x3427c0c3, 0x1af2a860, 0x342f0836,
+  0x1afce821, 0x34364da6, 0x1b072950, 0x343d9112,
+  0x1b116beb, 0x3444d27b, 0x1b1baff2, 0x344c11e0,
+  0x1b25f566, 0x34534f41, 0x1b303c46, 0x345a8a9d,
+  0x1b3a8491, 0x3461c3f5, 0x1b44ce46, 0x3468fb47,
+  0x1b4f1967, 0x34703095, 0x1b5965f1, 0x347763dd,
+  0x1b63b3e5, 0x347e951f, 0x1b6e0342, 0x3485c45b,
+  0x1b785409, 0x348cf190, 0x1b82a638, 0x34941cbf,
+  0x1b8cf9cf, 0x349b45e7, 0x1b974ece, 0x34a26d08,
+  0x1ba1a534, 0x34a99221, 0x1babfd01, 0x34b0b533,
+  0x1bb65634, 0x34b7d63c, 0x1bc0b0ce, 0x34bef53d,
+  0x1bcb0cce, 0x34c61236, 0x1bd56a32, 0x34cd2d26,
+  0x1bdfc8fc, 0x34d4460c, 0x1bea292b, 0x34db5cea,
+  0x1bf48abd, 0x34e271bd, 0x1bfeedb3, 0x34e98487,
+  0x1c09520d, 0x34f09546, 0x1c13b7c9, 0x34f7a3fb,
+  0x1c1e1ee9, 0x34feb0a5, 0x1c28876a, 0x3505bb44,
+  0x1c32f14d, 0x350cc3d8, 0x1c3d5c91, 0x3513ca60,
+  0x1c47c936, 0x351acedd, 0x1c52373c, 0x3521d14d,
+  0x1c5ca6a2, 0x3528d1b1, 0x1c671768, 0x352fd008,
+  0x1c71898d, 0x3536cc52, 0x1c7bfd11, 0x353dc68f,
+  0x1c8671f3, 0x3544bebf, 0x1c90e834, 0x354bb4e1,
+  0x1c9b5fd2, 0x3552a8f4, 0x1ca5d8cd, 0x35599afa,
+  0x1cb05326, 0x35608af1, 0x1cbacedb, 0x356778d9,
+  0x1cc54bec, 0x356e64b2, 0x1ccfca59, 0x35754e7c,
+  0x1cda4a21, 0x357c3636, 0x1ce4cb44, 0x35831be0,
+  0x1cef4dc2, 0x3589ff7a, 0x1cf9d199, 0x3590e104,
+  0x1d0456ca, 0x3597c07d, 0x1d0edd55, 0x359e9de5,
+  0x1d196538, 0x35a5793c, 0x1d23ee74, 0x35ac5282,
+  0x1d2e7908, 0x35b329b5, 0x1d3904f4, 0x35b9fed7,
+  0x1d439236, 0x35c0d1e7, 0x1d4e20d0, 0x35c7a2e3,
+  0x1d58b0c0, 0x35ce71ce, 0x1d634206, 0x35d53ea5,
+  0x1d6dd4a2, 0x35dc0968, 0x1d786892, 0x35e2d219,
+  0x1d82fdd8, 0x35e998b5, 0x1d8d9472, 0x35f05d3d,
+  0x1d982c60, 0x35f71fb1, 0x1da2c5a2, 0x35fde011,
+  0x1dad6036, 0x36049e5b, 0x1db7fc1e, 0x360b5a90,
+  0x1dc29958, 0x361214b0, 0x1dcd37e4, 0x3618ccba,
+  0x1dd7d7c1, 0x361f82af, 0x1de278ef, 0x3626368d,
+  0x1ded1b6e, 0x362ce855, 0x1df7bf3e, 0x36339806,
+  0x1e02645d, 0x363a45a0, 0x1e0d0acc, 0x3640f123,
+  0x1e17b28a, 0x36479a8e, 0x1e225b96, 0x364e41e2,
+  0x1e2d05f1, 0x3654e71d, 0x1e37b199, 0x365b8a41,
+  0x1e425e8f, 0x36622b4c, 0x1e4d0cd2, 0x3668ca3e,
+  0x1e57bc62, 0x366f6717, 0x1e626d3e, 0x367601d7,
+  0x1e6d1f65, 0x367c9a7e, 0x1e77d2d8, 0x3683310b,
+  0x1e828796, 0x3689c57d, 0x1e8d3d9e, 0x369057d6,
+  0x1e97f4f1, 0x3696e814, 0x1ea2ad8d, 0x369d7637,
+  0x1ead6773, 0x36a4023f, 0x1eb822a1, 0x36aa8c2c,
+  0x1ec2df18, 0x36b113fd, 0x1ecd9cd7, 0x36b799b3,
+  0x1ed85bdd, 0x36be1d4c, 0x1ee31c2b, 0x36c49ec9,
+  0x1eedddc0, 0x36cb1e2a, 0x1ef8a09b, 0x36d19b6e,
+  0x1f0364bc, 0x36d81695, 0x1f0e2a22, 0x36de8f9e,
+  0x1f18f0ce, 0x36e5068a, 0x1f23b8be, 0x36eb7b58,
+  0x1f2e81f3, 0x36f1ee09, 0x1f394c6b, 0x36f85e9a,
+  0x1f441828, 0x36fecd0e, 0x1f4ee527, 0x37053962,
+  0x1f59b369, 0x370ba398, 0x1f6482ed, 0x37120bae,
+  0x1f6f53b3, 0x371871a5, 0x1f7a25ba, 0x371ed57c,
+  0x1f84f902, 0x37253733, 0x1f8fcd8b, 0x372b96ca,
+  0x1f9aa354, 0x3731f440, 0x1fa57a5d, 0x37384f95,
+  0x1fb052a5, 0x373ea8ca, 0x1fbb2c2c, 0x3744ffdd,
+  0x1fc606f1, 0x374b54ce, 0x1fd0e2f5, 0x3751a79e,
+  0x1fdbc036, 0x3757f84c, 0x1fe69eb4, 0x375e46d8,
+  0x1ff17e70, 0x37649341, 0x1ffc5f67, 0x376add88,
+  0x2007419b, 0x377125ac, 0x2012250a, 0x37776bac,
+  0x201d09b4, 0x377daf89, 0x2027ef99, 0x3783f143,
+  0x2032d6b8, 0x378a30d8, 0x203dbf11, 0x37906e49,
+  0x2048a8a4, 0x3796a996, 0x2053936f, 0x379ce2be,
+  0x205e7f74, 0x37a319c2, 0x20696cb0, 0x37a94ea0,
+  0x20745b24, 0x37af8159, 0x207f4acf, 0x37b5b1ec,
+  0x208a3bb2, 0x37bbe05a, 0x20952dcb, 0x37c20ca1,
+  0x20a0211a, 0x37c836c2, 0x20ab159e, 0x37ce5ebd,
+  0x20b60b58, 0x37d48490, 0x20c10247, 0x37daa83d,
+  0x20cbfa6a, 0x37e0c9c3, 0x20d6f3c1, 0x37e6e921,
+  0x20e1ee4b, 0x37ed0657, 0x20ecea09, 0x37f32165,
+  0x20f7e6f9, 0x37f93a4b, 0x2102e51c, 0x37ff5109,
+  0x210de470, 0x3805659e, 0x2118e4f6, 0x380b780a,
+  0x2123e6ad, 0x3811884d, 0x212ee995, 0x38179666,
+  0x2139edac, 0x381da256, 0x2144f2f3, 0x3823ac1d,
+  0x214ff96a, 0x3829b3b9, 0x215b0110, 0x382fb92a,
+  0x216609e3, 0x3835bc71, 0x217113e5, 0x383bbd8e,
+  0x217c1f15, 0x3841bc7f, 0x21872b72, 0x3847b946,
+  0x219238fb, 0x384db3e0, 0x219d47b1, 0x3853ac4f,
+  0x21a85793, 0x3859a292, 0x21b368a0, 0x385f96a9,
+  0x21be7ad8, 0x38658894, 0x21c98e3b, 0x386b7852,
+  0x21d4a2c8, 0x387165e3, 0x21dfb87f, 0x38775147,
+  0x21eacf5f, 0x387d3a7e, 0x21f5e768, 0x38832187,
+  0x22010099, 0x38890663, 0x220c1af3, 0x388ee910,
+  0x22173674, 0x3894c98f, 0x2222531c, 0x389aa7e0,
+  0x222d70eb, 0x38a08402, 0x22388fe1, 0x38a65df6,
+  0x2243affc, 0x38ac35ba, 0x224ed13d, 0x38b20b4f,
+  0x2259f3a3, 0x38b7deb4, 0x2265172e, 0x38bdafea,
+  0x22703bdc, 0x38c37eef, 0x227b61af, 0x38c94bc4,
+  0x228688a4, 0x38cf1669, 0x2291b0bd, 0x38d4dedd,
+  0x229cd9f8, 0x38daa520, 0x22a80456, 0x38e06932,
+  0x22b32fd4, 0x38e62b13, 0x22be5c74, 0x38ebeac2,
+  0x22c98a35, 0x38f1a840, 0x22d4b916, 0x38f7638b,
+  0x22dfe917, 0x38fd1ca4, 0x22eb1a37, 0x3902d38b,
+  0x22f64c77, 0x3908883f, 0x23017fd5, 0x390e3ac0,
+  0x230cb451, 0x3913eb0e, 0x2317e9eb, 0x39199929,
+  0x232320a2, 0x391f4510, 0x232e5876, 0x3924eec3,
+  0x23399167, 0x392a9642, 0x2344cb73, 0x39303b8e,
+  0x2350069b, 0x3935dea4, 0x235b42df, 0x393b7f86,
+  0x2366803c, 0x39411e33, 0x2371beb5, 0x3946baac,
+  0x237cfe47, 0x394c54ee, 0x23883ef2, 0x3951ecfc,
+  0x239380b6, 0x395782d3, 0x239ec393, 0x395d1675,
+  0x23aa0788, 0x3962a7e0, 0x23b54c95, 0x39683715,
+  0x23c092b9, 0x396dc414, 0x23cbd9f4, 0x39734edc,
+  0x23d72245, 0x3978d76c, 0x23e26bac, 0x397e5dc6,
+  0x23edb628, 0x3983e1e8, 0x23f901ba, 0x398963d2,
+  0x24044e60, 0x398ee385, 0x240f9c1a, 0x399460ff,
+  0x241aeae8, 0x3999dc42, 0x24263ac9, 0x399f554b,
+  0x24318bbe, 0x39a4cc1c, 0x243cddc4, 0x39aa40b4,
+  0x244830dd, 0x39afb313, 0x24538507, 0x39b52339,
+  0x245eda43, 0x39ba9125, 0x246a308f, 0x39bffcd7,
+  0x247587eb, 0x39c5664f, 0x2480e057, 0x39cacd8d,
+  0x248c39d3, 0x39d03291, 0x2497945d, 0x39d5955a,
+  0x24a2eff6, 0x39daf5e8, 0x24ae4c9d, 0x39e0543c,
+  0x24b9aa52, 0x39e5b054, 0x24c50914, 0x39eb0a31,
+  0x24d068e2, 0x39f061d2, 0x24dbc9bd, 0x39f5b737,
+  0x24e72ba4, 0x39fb0a60, 0x24f28e96, 0x3a005b4d,
+  0x24fdf294, 0x3a05a9fd, 0x2509579b, 0x3a0af671,
+  0x2514bdad, 0x3a1040a8, 0x252024c9, 0x3a1588a2,
+  0x252b8cee, 0x3a1ace5f, 0x2536f61b, 0x3a2011de,
+  0x25426051, 0x3a25531f, 0x254dcb8f, 0x3a2a9223,
+  0x255937d5, 0x3a2fcee8, 0x2564a521, 0x3a350970,
+  0x25701374, 0x3a3a41b9, 0x257b82cd, 0x3a3f77c3,
+  0x2586f32c, 0x3a44ab8e, 0x25926490, 0x3a49dd1a,
+  0x259dd6f9, 0x3a4f0c67, 0x25a94a67, 0x3a543974,
+  0x25b4bed8, 0x3a596442, 0x25c0344d, 0x3a5e8cd0,
+  0x25cbaac5, 0x3a63b31d, 0x25d72240, 0x3a68d72b,
+  0x25e29abc, 0x3a6df8f8, 0x25ee143b, 0x3a731884,
+  0x25f98ebb, 0x3a7835cf, 0x26050a3b, 0x3a7d50da,
+  0x261086bc, 0x3a8269a3, 0x261c043d, 0x3a87802a,
+  0x262782be, 0x3a8c9470, 0x2633023e, 0x3a91a674,
+  0x263e82bc, 0x3a96b636, 0x264a0438, 0x3a9bc3b6,
+  0x265586b3, 0x3aa0cef3, 0x26610a2a, 0x3aa5d7ee,
+  0x266c8e9f, 0x3aaadea6, 0x26781410, 0x3aafe31b,
+  0x26839a7c, 0x3ab4e54c, 0x268f21e5, 0x3ab9e53a,
+  0x269aaa48, 0x3abee2e5, 0x26a633a6, 0x3ac3de4c,
+  0x26b1bdff, 0x3ac8d76f, 0x26bd4951, 0x3acdce4d,
+  0x26c8d59c, 0x3ad2c2e8, 0x26d462e1, 0x3ad7b53d,
+  0x26dff11d, 0x3adca54e, 0x26eb8052, 0x3ae1931a,
+  0x26f7107e, 0x3ae67ea1, 0x2702a1a1, 0x3aeb67e3,
+  0x270e33bb, 0x3af04edf, 0x2719c6cb, 0x3af53395,
+  0x27255ad1, 0x3afa1605, 0x2730efcc, 0x3afef630,
+  0x273c85bc, 0x3b03d414, 0x27481ca1, 0x3b08afb2,
+  0x2753b479, 0x3b0d8909, 0x275f4d45, 0x3b126019,
+  0x276ae704, 0x3b1734e2, 0x277681b6, 0x3b1c0764,
+  0x27821d59, 0x3b20d79e, 0x278db9ef, 0x3b25a591,
+  0x27995776, 0x3b2a713d, 0x27a4f5ed, 0x3b2f3aa0,
+  0x27b09555, 0x3b3401bb, 0x27bc35ad, 0x3b38c68e,
+  0x27c7d6f4, 0x3b3d8918, 0x27d3792b, 0x3b42495a,
+  0x27df1c50, 0x3b470753, 0x27eac063, 0x3b4bc303,
+  0x27f66564, 0x3b507c69, 0x28020b52, 0x3b553386,
+  0x280db22d, 0x3b59e85a, 0x281959f4, 0x3b5e9ae4,
+  0x282502a7, 0x3b634b23, 0x2830ac45, 0x3b67f919,
+  0x283c56cf, 0x3b6ca4c4, 0x28480243, 0x3b714e25,
+  0x2853aea1, 0x3b75f53c, 0x285f5be9, 0x3b7a9a07,
+  0x286b0a1a, 0x3b7f3c87, 0x2876b934, 0x3b83dcbc,
+  0x28826936, 0x3b887aa6, 0x288e1a20, 0x3b8d1644,
+  0x2899cbf1, 0x3b91af97, 0x28a57ea9, 0x3b96469d,
+  0x28b13248, 0x3b9adb57, 0x28bce6cd, 0x3b9f6dc5,
+  0x28c89c37, 0x3ba3fde7, 0x28d45286, 0x3ba88bbc,
+  0x28e009ba, 0x3bad1744, 0x28ebc1d3, 0x3bb1a080,
+  0x28f77acf, 0x3bb6276e, 0x290334af, 0x3bbaac0e,
+  0x290eef71, 0x3bbf2e62, 0x291aab16, 0x3bc3ae67,
+  0x2926679c, 0x3bc82c1f, 0x29322505, 0x3bcca789,
+  0x293de34e, 0x3bd120a4, 0x2949a278, 0x3bd59771,
+  0x29556282, 0x3bda0bf0, 0x2961236c, 0x3bde7e20,
+  0x296ce535, 0x3be2ee01, 0x2978a7dd, 0x3be75b93,
+  0x29846b63, 0x3bebc6d5, 0x29902fc7, 0x3bf02fc9,
+  0x299bf509, 0x3bf4966c, 0x29a7bb28, 0x3bf8fac0,
+  0x29b38223, 0x3bfd5cc4, 0x29bf49fa, 0x3c01bc78,
+  0x29cb12ad, 0x3c0619dc, 0x29d6dc3b, 0x3c0a74f0,
+  0x29e2a6a3, 0x3c0ecdb2, 0x29ee71e6, 0x3c132424,
+  0x29fa3e03, 0x3c177845, 0x2a060af9, 0x3c1bca16,
+  0x2a11d8c8, 0x3c201994, 0x2a1da770, 0x3c2466c2,
+  0x2a2976ef, 0x3c28b19e, 0x2a354746, 0x3c2cfa28,
+  0x2a411874, 0x3c314060, 0x2a4cea79, 0x3c358446,
+  0x2a58bd54, 0x3c39c5da, 0x2a649105, 0x3c3e051b,
+  0x2a70658a, 0x3c42420a, 0x2a7c3ae5, 0x3c467ca6,
+  0x2a881114, 0x3c4ab4ef, 0x2a93e817, 0x3c4eeae5,
+  0x2a9fbfed, 0x3c531e88, 0x2aab9896, 0x3c574fd8,
+  0x2ab77212, 0x3c5b7ed4, 0x2ac34c60, 0x3c5fab7c,
+  0x2acf277f, 0x3c63d5d1, 0x2adb0370, 0x3c67fdd1,
+  0x2ae6e031, 0x3c6c237e, 0x2af2bdc3, 0x3c7046d6,
+  0x2afe9c24, 0x3c7467d9, 0x2b0a7b54, 0x3c788688,
+  0x2b165b54, 0x3c7ca2e2, 0x2b223c22, 0x3c80bce7,
+  0x2b2e1dbe, 0x3c84d496, 0x2b3a0027, 0x3c88e9f1,
+  0x2b45e35d, 0x3c8cfcf6, 0x2b51c760, 0x3c910da5,
+  0x2b5dac2f, 0x3c951bff, 0x2b6991ca, 0x3c992803,
+  0x2b75782f, 0x3c9d31b0, 0x2b815f60, 0x3ca13908,
+  0x2b8d475b, 0x3ca53e09, 0x2b99301f, 0x3ca940b3,
+  0x2ba519ad, 0x3cad4107, 0x2bb10404, 0x3cb13f04,
+  0x2bbcef23, 0x3cb53aaa, 0x2bc8db0b, 0x3cb933f9,
+  0x2bd4c7ba, 0x3cbd2af0, 0x2be0b52f, 0x3cc11f90,
+  0x2beca36c, 0x3cc511d9, 0x2bf8926f, 0x3cc901c9,
+  0x2c048237, 0x3cccef62, 0x2c1072c4, 0x3cd0daa2,
+  0x2c1c6417, 0x3cd4c38b, 0x2c28562d, 0x3cd8aa1b,
+  0x2c344908, 0x3cdc8e52, 0x2c403ca5, 0x3ce07031,
+  0x2c4c3106, 0x3ce44fb7, 0x2c582629, 0x3ce82ce4,
+  0x2c641c0e, 0x3cec07b8, 0x2c7012b5, 0x3cefe032,
+  0x2c7c0a1d, 0x3cf3b653, 0x2c880245, 0x3cf78a1b,
+  0x2c93fb2e, 0x3cfb5b89, 0x2c9ff4d6, 0x3cff2a9d,
+  0x2cabef3d, 0x3d02f757, 0x2cb7ea63, 0x3d06c1b6,
+  0x2cc3e648, 0x3d0a89bc, 0x2ccfe2ea, 0x3d0e4f67,
+  0x2cdbe04a, 0x3d1212b7, 0x2ce7de66, 0x3d15d3ad,
+  0x2cf3dd3f, 0x3d199248, 0x2cffdcd4, 0x3d1d4e88,
+  0x2d0bdd25, 0x3d21086c, 0x2d17de31, 0x3d24bff6,
+  0x2d23dff7, 0x3d287523, 0x2d2fe277, 0x3d2c27f6,
+  0x2d3be5b1, 0x3d2fd86c, 0x2d47e9a5, 0x3d338687,
+  0x2d53ee51, 0x3d373245, 0x2d5ff3b5, 0x3d3adba7,
+  0x2d6bf9d1, 0x3d3e82ae, 0x2d7800a5, 0x3d422757,
+  0x2d84082f, 0x3d45c9a4, 0x2d901070, 0x3d496994,
+  0x2d9c1967, 0x3d4d0728, 0x2da82313, 0x3d50a25e,
+  0x2db42d74, 0x3d543b37, 0x2dc0388a, 0x3d57d1b3,
+  0x2dcc4454, 0x3d5b65d2, 0x2dd850d2, 0x3d5ef793,
+  0x2de45e03, 0x3d6286f6, 0x2df06be6, 0x3d6613fb,
+  0x2dfc7a7c, 0x3d699ea3, 0x2e0889c4, 0x3d6d26ec,
+  0x2e1499bd, 0x3d70acd7, 0x2e20aa67, 0x3d743064,
+  0x2e2cbbc1, 0x3d77b192, 0x2e38cdcb, 0x3d7b3061,
+  0x2e44e084, 0x3d7eacd2, 0x2e50f3ed, 0x3d8226e4,
+  0x2e5d0804, 0x3d859e96, 0x2e691cc9, 0x3d8913ea,
+  0x2e75323c, 0x3d8c86de, 0x2e81485c, 0x3d8ff772,
+  0x2e8d5f29, 0x3d9365a8, 0x2e9976a1, 0x3d96d17d,
+  0x2ea58ec6, 0x3d9a3af2, 0x2eb1a796, 0x3d9da208,
+  0x2ebdc110, 0x3da106bd, 0x2ec9db35, 0x3da46912,
+  0x2ed5f604, 0x3da7c907, 0x2ee2117c, 0x3dab269b,
+  0x2eee2d9d, 0x3dae81cf, 0x2efa4a67, 0x3db1daa2,
+  0x2f0667d9, 0x3db53113, 0x2f1285f2, 0x3db88524,
+  0x2f1ea4b2, 0x3dbbd6d4, 0x2f2ac419, 0x3dbf2622,
+  0x2f36e426, 0x3dc2730f, 0x2f4304d8, 0x3dc5bd9b,
+  0x2f4f2630, 0x3dc905c5, 0x2f5b482d, 0x3dcc4b8d,
+  0x2f676ace, 0x3dcf8ef3, 0x2f738e12, 0x3dd2cff7,
+  0x2f7fb1fa, 0x3dd60e99, 0x2f8bd685, 0x3dd94ad8,
+  0x2f97fbb2, 0x3ddc84b5, 0x2fa42181, 0x3ddfbc30,
+  0x2fb047f2, 0x3de2f148, 0x2fbc6f03, 0x3de623fd,
+  0x2fc896b5, 0x3de9544f, 0x2fd4bf08, 0x3dec823e,
+  0x2fe0e7f9, 0x3defadca, 0x2fed118a, 0x3df2d6f3,
+  0x2ff93bba, 0x3df5fdb8, 0x30056687, 0x3df9221a,
+  0x301191f3, 0x3dfc4418, 0x301dbdfb, 0x3dff63b2,
+  0x3029eaa1, 0x3e0280e9, 0x303617e2, 0x3e059bbb,
+  0x304245c0, 0x3e08b42a, 0x304e7438, 0x3e0bca34,
+  0x305aa34c, 0x3e0eddd9, 0x3066d2fa, 0x3e11ef1b,
+  0x30730342, 0x3e14fdf7, 0x307f3424, 0x3e180a6f,
+  0x308b659f, 0x3e1b1482, 0x309797b2, 0x3e1e1c30,
+  0x30a3ca5d, 0x3e212179, 0x30affda0, 0x3e24245d,
+  0x30bc317a, 0x3e2724db, 0x30c865ea, 0x3e2a22f4,
+  0x30d49af1, 0x3e2d1ea8, 0x30e0d08d, 0x3e3017f6,
+  0x30ed06bf, 0x3e330ede, 0x30f93d86, 0x3e360360,
+  0x310574e0, 0x3e38f57c, 0x3111accf, 0x3e3be532,
+  0x311de551, 0x3e3ed282, 0x312a1e66, 0x3e41bd6c,
+  0x3136580d, 0x3e44a5ef, 0x31429247, 0x3e478c0b,
+  0x314ecd11, 0x3e4a6fc1, 0x315b086d, 0x3e4d5110,
+  0x31674459, 0x3e502ff9, 0x317380d6, 0x3e530c7a,
+  0x317fbde2, 0x3e55e694, 0x318bfb7d, 0x3e58be47,
+  0x319839a6, 0x3e5b9392, 0x31a4785e, 0x3e5e6676,
+  0x31b0b7a4, 0x3e6136f3, 0x31bcf777, 0x3e640507,
+  0x31c937d6, 0x3e66d0b4, 0x31d578c2, 0x3e6999fa,
+  0x31e1ba3a, 0x3e6c60d7, 0x31edfc3d, 0x3e6f254c,
+  0x31fa3ecb, 0x3e71e759, 0x320681e3, 0x3e74a6fd,
+  0x3212c585, 0x3e77643a, 0x321f09b1, 0x3e7a1f0d,
+  0x322b4e66, 0x3e7cd778, 0x323793a3, 0x3e7f8d7b,
+  0x3243d968, 0x3e824114, 0x32501fb5, 0x3e84f245,
+  0x325c6688, 0x3e87a10c, 0x3268ade3, 0x3e8a4d6a,
+  0x3274f5c3, 0x3e8cf75f, 0x32813e2a, 0x3e8f9eeb,
+  0x328d8715, 0x3e92440d, 0x3299d085, 0x3e94e6c6,
+  0x32a61a7a, 0x3e978715, 0x32b264f2, 0x3e9a24fb,
+  0x32beafed, 0x3e9cc076, 0x32cafb6b, 0x3e9f5988,
+  0x32d7476c, 0x3ea1f02f, 0x32e393ef, 0x3ea4846c,
+  0x32efe0f2, 0x3ea7163f, 0x32fc2e77, 0x3ea9a5a8,
+  0x33087c7d, 0x3eac32a6, 0x3314cb02, 0x3eaebd3a,
+  0x33211a07, 0x3eb14563, 0x332d698a, 0x3eb3cb21,
+  0x3339b98d, 0x3eb64e75, 0x33460a0d, 0x3eb8cf5d,
+  0x33525b0b, 0x3ebb4ddb, 0x335eac86, 0x3ebdc9ed,
+  0x336afe7e, 0x3ec04394, 0x337750f2, 0x3ec2bad0,
+  0x3383a3e2, 0x3ec52fa0, 0x338ff74d, 0x3ec7a205,
+  0x339c4b32, 0x3eca11fe, 0x33a89f92, 0x3ecc7f8b,
+  0x33b4f46c, 0x3eceeaad, 0x33c149bf, 0x3ed15363,
+  0x33cd9f8b, 0x3ed3b9ad, 0x33d9f5cf, 0x3ed61d8a,
+  0x33e64c8c, 0x3ed87efc, 0x33f2a3bf, 0x3edade01,
+  0x33fefb6a, 0x3edd3a9a, 0x340b538b, 0x3edf94c7,
+  0x3417ac22, 0x3ee1ec87, 0x3424052f, 0x3ee441da,
+  0x34305eb0, 0x3ee694c1, 0x343cb8a7, 0x3ee8e53a,
+  0x34491311, 0x3eeb3347, 0x34556def, 0x3eed7ee7,
+  0x3461c940, 0x3eefc81a, 0x346e2504, 0x3ef20ee0,
+  0x347a8139, 0x3ef45338, 0x3486dde1, 0x3ef69523,
+  0x34933afa, 0x3ef8d4a1, 0x349f9884, 0x3efb11b1,
+  0x34abf67e, 0x3efd4c54, 0x34b854e7, 0x3eff8489,
+  0x34c4b3c0, 0x3f01ba50, 0x34d11308, 0x3f03eda9,
+  0x34dd72be, 0x3f061e95, 0x34e9d2e3, 0x3f084d12,
+  0x34f63374, 0x3f0a7921, 0x35029473, 0x3f0ca2c2,
+  0x350ef5de, 0x3f0ec9f5, 0x351b57b5, 0x3f10eeb9,
+  0x3527b9f7, 0x3f13110f, 0x35341ca5, 0x3f1530f7,
+  0x35407fbd, 0x3f174e70, 0x354ce33f, 0x3f19697a,
+  0x3559472b, 0x3f1b8215, 0x3565ab80, 0x3f1d9842,
+  0x3572103d, 0x3f1fabff, 0x357e7563, 0x3f21bd4e,
+  0x358adaf0, 0x3f23cc2e, 0x359740e5, 0x3f25d89e,
+  0x35a3a740, 0x3f27e29f, 0x35b00e02, 0x3f29ea31,
+  0x35bc7529, 0x3f2bef53, 0x35c8dcb6, 0x3f2df206,
+  0x35d544a7, 0x3f2ff24a, 0x35e1acfd, 0x3f31f01d,
+  0x35ee15b7, 0x3f33eb81, 0x35fa7ed4, 0x3f35e476,
+  0x3606e854, 0x3f37dafa, 0x36135237, 0x3f39cf0e,
+  0x361fbc7b, 0x3f3bc0b3, 0x362c2721, 0x3f3dafe7,
+  0x36389228, 0x3f3f9cab, 0x3644fd8f, 0x3f4186ff,
+  0x36516956, 0x3f436ee3, 0x365dd57d, 0x3f455456,
+  0x366a4203, 0x3f473759, 0x3676aee8, 0x3f4917eb,
+  0x36831c2b, 0x3f4af60d, 0x368f89cb, 0x3f4cd1be,
+  0x369bf7c9, 0x3f4eaafe, 0x36a86623, 0x3f5081cd,
+  0x36b4d4d9, 0x3f52562c, 0x36c143ec, 0x3f54281a,
+  0x36cdb359, 0x3f55f796, 0x36da2321, 0x3f57c4a2,
+  0x36e69344, 0x3f598f3c, 0x36f303c0, 0x3f5b5765,
+  0x36ff7496, 0x3f5d1d1d, 0x370be5c4, 0x3f5ee063,
+  0x3718574b, 0x3f60a138, 0x3724c92a, 0x3f625f9b,
+  0x37313b60, 0x3f641b8d, 0x373daded, 0x3f65d50d,
+  0x374a20d0, 0x3f678c1c, 0x3756940a, 0x3f6940b8,
+  0x37630799, 0x3f6af2e3, 0x376f7b7d, 0x3f6ca29c,
+  0x377befb5, 0x3f6e4fe3, 0x37886442, 0x3f6ffab8,
+  0x3794d922, 0x3f71a31b, 0x37a14e55, 0x3f73490b,
+  0x37adc3db, 0x3f74ec8a, 0x37ba39b3, 0x3f768d96,
+  0x37c6afdc, 0x3f782c30, 0x37d32657, 0x3f79c857,
+  0x37df9d22, 0x3f7b620c, 0x37ec143e, 0x3f7cf94e,
+  0x37f88ba9, 0x3f7e8e1e, 0x38050364, 0x3f80207b,
+  0x38117b6d, 0x3f81b065, 0x381df3c5, 0x3f833ddd,
+  0x382a6c6a, 0x3f84c8e2, 0x3836e55d, 0x3f865174,
+  0x38435e9d, 0x3f87d792, 0x384fd829, 0x3f895b3e,
+  0x385c5201, 0x3f8adc77, 0x3868cc24, 0x3f8c5b3d,
+  0x38754692, 0x3f8dd78f, 0x3881c14b, 0x3f8f516e,
+  0x388e3c4d, 0x3f90c8da, 0x389ab799, 0x3f923dd2,
+  0x38a7332e, 0x3f93b058, 0x38b3af0c, 0x3f952069,
+  0x38c02b31, 0x3f968e07, 0x38cca79e, 0x3f97f932,
+  0x38d92452, 0x3f9961e8, 0x38e5a14d, 0x3f9ac82c,
+  0x38f21e8e, 0x3f9c2bfb, 0x38fe9c15, 0x3f9d8d56,
+  0x390b19e0, 0x3f9eec3e, 0x391797f0, 0x3fa048b2,
+  0x39241645, 0x3fa1a2b2, 0x393094dd, 0x3fa2fa3d,
+  0x393d13b8, 0x3fa44f55, 0x394992d7, 0x3fa5a1f9,
+  0x39561237, 0x3fa6f228, 0x396291d9, 0x3fa83fe3,
+  0x396f11bc, 0x3fa98b2a, 0x397b91e1, 0x3faad3fd,
+  0x39881245, 0x3fac1a5b, 0x399492ea, 0x3fad5e45,
+  0x39a113cd, 0x3fae9fbb, 0x39ad94f0, 0x3fafdebb,
+  0x39ba1651, 0x3fb11b48, 0x39c697f0, 0x3fb2555f,
+  0x39d319cc, 0x3fb38d02, 0x39df9be6, 0x3fb4c231,
+  0x39ec1e3b, 0x3fb5f4ea, 0x39f8a0cd, 0x3fb7252f,
+  0x3a05239a, 0x3fb852ff, 0x3a11a6a3, 0x3fb97e5a,
+  0x3a1e29e5, 0x3fbaa740, 0x3a2aad62, 0x3fbbcdb1,
+  0x3a373119, 0x3fbcf1ad, 0x3a43b508, 0x3fbe1334,
+  0x3a503930, 0x3fbf3246, 0x3a5cbd91, 0x3fc04ee3,
+  0x3a694229, 0x3fc1690a, 0x3a75c6f8, 0x3fc280bc,
+  0x3a824bfd, 0x3fc395f9, 0x3a8ed139, 0x3fc4a8c1,
+  0x3a9b56ab, 0x3fc5b913, 0x3aa7dc52, 0x3fc6c6f0,
+  0x3ab4622d, 0x3fc7d258, 0x3ac0e83d, 0x3fc8db4a,
+  0x3acd6e81, 0x3fc9e1c6, 0x3ad9f4f8, 0x3fcae5cd,
+  0x3ae67ba2, 0x3fcbe75e, 0x3af3027e, 0x3fcce67a,
+  0x3aff898c, 0x3fcde320, 0x3b0c10cb, 0x3fcedd50,
+  0x3b18983b, 0x3fcfd50b, 0x3b251fdc, 0x3fd0ca4f,
+  0x3b31a7ac, 0x3fd1bd1e, 0x3b3e2fac, 0x3fd2ad77,
+  0x3b4ab7db, 0x3fd39b5a, 0x3b574039, 0x3fd486c7,
+  0x3b63c8c4, 0x3fd56fbe, 0x3b70517d, 0x3fd6563f,
+  0x3b7cda63, 0x3fd73a4a, 0x3b896375, 0x3fd81bdf,
+  0x3b95ecb4, 0x3fd8fafe, 0x3ba2761e, 0x3fd9d7a7,
+  0x3baeffb3, 0x3fdab1d9, 0x3bbb8973, 0x3fdb8996,
+  0x3bc8135c, 0x3fdc5edc, 0x3bd49d70, 0x3fdd31ac,
+  0x3be127ac, 0x3fde0205, 0x3bedb212, 0x3fdecfe8,
+  0x3bfa3c9f, 0x3fdf9b55, 0x3c06c754, 0x3fe0644b,
+  0x3c135231, 0x3fe12acb, 0x3c1fdd34, 0x3fe1eed5,
+  0x3c2c685d, 0x3fe2b067, 0x3c38f3ac, 0x3fe36f84,
+  0x3c457f21, 0x3fe42c2a, 0x3c520aba, 0x3fe4e659,
+  0x3c5e9678, 0x3fe59e12, 0x3c6b2259, 0x3fe65354,
+  0x3c77ae5e, 0x3fe7061f, 0x3c843a85, 0x3fe7b674,
+  0x3c90c6cf, 0x3fe86452, 0x3c9d533b, 0x3fe90fb9,
+  0x3ca9dfc8, 0x3fe9b8a9, 0x3cb66c77, 0x3fea5f23,
+  0x3cc2f945, 0x3feb0326, 0x3ccf8634, 0x3feba4b2,
+  0x3cdc1342, 0x3fec43c7, 0x3ce8a06f, 0x3fece065,
+  0x3cf52dbb, 0x3fed7a8c, 0x3d01bb24, 0x3fee123d,
+  0x3d0e48ab, 0x3feea776, 0x3d1ad650, 0x3fef3a39,
+  0x3d276410, 0x3fefca84, 0x3d33f1ed, 0x3ff05858,
+  0x3d407fe6, 0x3ff0e3b6, 0x3d4d0df9, 0x3ff16c9c,
+  0x3d599c28, 0x3ff1f30b, 0x3d662a70, 0x3ff27703,
+  0x3d72b8d2, 0x3ff2f884, 0x3d7f474d, 0x3ff3778e,
+  0x3d8bd5e1, 0x3ff3f420, 0x3d98648d, 0x3ff46e3c,
+  0x3da4f351, 0x3ff4e5e0, 0x3db1822c, 0x3ff55b0d,
+  0x3dbe111e, 0x3ff5cdc3, 0x3dcaa027, 0x3ff63e01,
+  0x3dd72f45, 0x3ff6abc8, 0x3de3be78, 0x3ff71718,
+  0x3df04dc0, 0x3ff77ff1, 0x3dfcdd1d, 0x3ff7e652,
+  0x3e096c8d, 0x3ff84a3c, 0x3e15fc11, 0x3ff8abae,
+  0x3e228ba7, 0x3ff90aaa, 0x3e2f1b50, 0x3ff9672d,
+  0x3e3bab0b, 0x3ff9c13a, 0x3e483ad8, 0x3ffa18cf,
+  0x3e54cab5, 0x3ffa6dec, 0x3e615aa3, 0x3ffac092,
+  0x3e6deaa1, 0x3ffb10c1, 0x3e7a7aae, 0x3ffb5e78,
+  0x3e870aca, 0x3ffba9b8, 0x3e939af5, 0x3ffbf280,
+  0x3ea02b2e, 0x3ffc38d1, 0x3eacbb74, 0x3ffc7caa,
+  0x3eb94bc8, 0x3ffcbe0c, 0x3ec5dc28, 0x3ffcfcf6,
+  0x3ed26c94, 0x3ffd3969, 0x3edefd0c, 0x3ffd7364,
+  0x3eeb8d8f, 0x3ffdaae7, 0x3ef81e1d, 0x3ffddff3,
+  0x3f04aeb5, 0x3ffe1288, 0x3f113f56, 0x3ffe42a4,
+  0x3f1dd001, 0x3ffe704a, 0x3f2a60b4, 0x3ffe9b77,
+  0x3f36f170, 0x3ffec42d, 0x3f438234, 0x3ffeea6c,
+  0x3f5012fe, 0x3fff0e32, 0x3f5ca3d0, 0x3fff2f82,
+  0x3f6934a8, 0x3fff4e59, 0x3f75c585, 0x3fff6ab9,
+  0x3f825668, 0x3fff84a1, 0x3f8ee750, 0x3fff9c12,
+  0x3f9b783c, 0x3fffb10b, 0x3fa8092c, 0x3fffc38c,
+  0x3fb49a1f, 0x3fffd396, 0x3fc12b16, 0x3fffe128,
+  0x3fcdbc0f, 0x3fffec43, 0x3fda4d09, 0x3ffff4e6,
+  0x3fe6de05, 0x3ffffb11, 0x3ff36f02, 0x3ffffec4,
+};
+
+
+/**    
+* \par   
+* Generation of realCoefBQ31 array:    
+* \par    
+*  n = 4096        
+* 
for (i = 0; i < n; i++)    
+* {    
+*    pBTable[2 * i] = 0.5 * (1.0 + sin (2 * PI / (double) (2 * n) * (double) i));    
+*    pBTable[2 * i + 1] = 0.5 * (1.0 * cos (2 * PI / (double) (2 * n) * (double) i));    
+* } 
    
+* \par    
+* Convert to fixed point Q31 format    
+*     round(pBTable[i] * pow(2, 31))    
+*    
+*/
+
+static const q31_t realCoefBQ31[8192] = {
+  0x40000000, 0x40000000, 0x400c90fe, 0x3ffffec4,
+  0x401921fb, 0x3ffffb11, 0x4025b2f7, 0x3ffff4e6,
+  0x403243f1, 0x3fffec43, 0x403ed4ea, 0x3fffe128,
+  0x404b65e1, 0x3fffd396, 0x4057f6d4, 0x3fffc38c,
+  0x406487c4, 0x3fffb10b, 0x407118b0, 0x3fff9c12,
+  0x407da998, 0x3fff84a1, 0x408a3a7b, 0x3fff6ab9,
+  0x4096cb58, 0x3fff4e59, 0x40a35c30, 0x3fff2f82,
+  0x40afed02, 0x3fff0e32, 0x40bc7dcc, 0x3ffeea6c,
+  0x40c90e90, 0x3ffec42d, 0x40d59f4c, 0x3ffe9b77,
+  0x40e22fff, 0x3ffe704a, 0x40eec0aa, 0x3ffe42a4,
+  0x40fb514b, 0x3ffe1288, 0x4107e1e3, 0x3ffddff3,
+  0x41147271, 0x3ffdaae7, 0x412102f4, 0x3ffd7364,
+  0x412d936c, 0x3ffd3969, 0x413a23d8, 0x3ffcfcf6,
+  0x4146b438, 0x3ffcbe0c, 0x4153448c, 0x3ffc7caa,
+  0x415fd4d2, 0x3ffc38d1, 0x416c650b, 0x3ffbf280,
+  0x4178f536, 0x3ffba9b8, 0x41858552, 0x3ffb5e78,
+  0x4192155f, 0x3ffb10c1, 0x419ea55d, 0x3ffac092,
+  0x41ab354b, 0x3ffa6dec, 0x41b7c528, 0x3ffa18cf,
+  0x41c454f5, 0x3ff9c13a, 0x41d0e4b0, 0x3ff9672d,
+  0x41dd7459, 0x3ff90aaa, 0x41ea03ef, 0x3ff8abae,
+  0x41f69373, 0x3ff84a3c, 0x420322e3, 0x3ff7e652,
+  0x420fb240, 0x3ff77ff1, 0x421c4188, 0x3ff71718,
+  0x4228d0bb, 0x3ff6abc8, 0x42355fd9, 0x3ff63e01,
+  0x4241eee2, 0x3ff5cdc3, 0x424e7dd4, 0x3ff55b0d,
+  0x425b0caf, 0x3ff4e5e0, 0x42679b73, 0x3ff46e3c,
+  0x42742a1f, 0x3ff3f420, 0x4280b8b3, 0x3ff3778e,
+  0x428d472e, 0x3ff2f884, 0x4299d590, 0x3ff27703,
+  0x42a663d8, 0x3ff1f30b, 0x42b2f207, 0x3ff16c9c,
+  0x42bf801a, 0x3ff0e3b6, 0x42cc0e13, 0x3ff05858,
+  0x42d89bf0, 0x3fefca84, 0x42e529b0, 0x3fef3a39,
+  0x42f1b755, 0x3feea776, 0x42fe44dc, 0x3fee123d,
+  0x430ad245, 0x3fed7a8c, 0x43175f91, 0x3fece065,
+  0x4323ecbe, 0x3fec43c7, 0x433079cc, 0x3feba4b2,
+  0x433d06bb, 0x3feb0326, 0x43499389, 0x3fea5f23,
+  0x43562038, 0x3fe9b8a9, 0x4362acc5, 0x3fe90fb9,
+  0x436f3931, 0x3fe86452, 0x437bc57b, 0x3fe7b674,
+  0x438851a2, 0x3fe7061f, 0x4394dda7, 0x3fe65354,
+  0x43a16988, 0x3fe59e12, 0x43adf546, 0x3fe4e659,
+  0x43ba80df, 0x3fe42c2a, 0x43c70c54, 0x3fe36f84,
+  0x43d397a3, 0x3fe2b067, 0x43e022cc, 0x3fe1eed5,
+  0x43ecadcf, 0x3fe12acb, 0x43f938ac, 0x3fe0644b,
+  0x4405c361, 0x3fdf9b55, 0x44124dee, 0x3fdecfe8,
+  0x441ed854, 0x3fde0205, 0x442b6290, 0x3fdd31ac,
+  0x4437eca4, 0x3fdc5edc, 0x4444768d, 0x3fdb8996,
+  0x4451004d, 0x3fdab1d9, 0x445d89e2, 0x3fd9d7a7,
+  0x446a134c, 0x3fd8fafe, 0x44769c8b, 0x3fd81bdf,
+  0x4483259d, 0x3fd73a4a, 0x448fae83, 0x3fd6563f,
+  0x449c373c, 0x3fd56fbe, 0x44a8bfc7, 0x3fd486c7,
+  0x44b54825, 0x3fd39b5a, 0x44c1d054, 0x3fd2ad77,
+  0x44ce5854, 0x3fd1bd1e, 0x44dae024, 0x3fd0ca4f,
+  0x44e767c5, 0x3fcfd50b, 0x44f3ef35, 0x3fcedd50,
+  0x45007674, 0x3fcde320, 0x450cfd82, 0x3fcce67a,
+  0x4519845e, 0x3fcbe75e, 0x45260b08, 0x3fcae5cd,
+  0x4532917f, 0x3fc9e1c6, 0x453f17c3, 0x3fc8db4a,
+  0x454b9dd3, 0x3fc7d258, 0x455823ae, 0x3fc6c6f0,
+  0x4564a955, 0x3fc5b913, 0x45712ec7, 0x3fc4a8c1,
+  0x457db403, 0x3fc395f9, 0x458a3908, 0x3fc280bc,
+  0x4596bdd7, 0x3fc1690a, 0x45a3426f, 0x3fc04ee3,
+  0x45afc6d0, 0x3fbf3246, 0x45bc4af8, 0x3fbe1334,
+  0x45c8cee7, 0x3fbcf1ad, 0x45d5529e, 0x3fbbcdb1,
+  0x45e1d61b, 0x3fbaa740, 0x45ee595d, 0x3fb97e5a,
+  0x45fadc66, 0x3fb852ff, 0x46075f33, 0x3fb7252f,
+  0x4613e1c5, 0x3fb5f4ea, 0x4620641a, 0x3fb4c231,
+  0x462ce634, 0x3fb38d02, 0x46396810, 0x3fb2555f,
+  0x4645e9af, 0x3fb11b48, 0x46526b10, 0x3fafdebb,
+  0x465eec33, 0x3fae9fbb, 0x466b6d16, 0x3fad5e45,
+  0x4677edbb, 0x3fac1a5b, 0x46846e1f, 0x3faad3fd,
+  0x4690ee44, 0x3fa98b2a, 0x469d6e27, 0x3fa83fe3,
+  0x46a9edc9, 0x3fa6f228, 0x46b66d29, 0x3fa5a1f9,
+  0x46c2ec48, 0x3fa44f55, 0x46cf6b23, 0x3fa2fa3d,
+  0x46dbe9bb, 0x3fa1a2b2, 0x46e86810, 0x3fa048b2,
+  0x46f4e620, 0x3f9eec3e, 0x470163eb, 0x3f9d8d56,
+  0x470de172, 0x3f9c2bfb, 0x471a5eb3, 0x3f9ac82c,
+  0x4726dbae, 0x3f9961e8, 0x47335862, 0x3f97f932,
+  0x473fd4cf, 0x3f968e07, 0x474c50f4, 0x3f952069,
+  0x4758ccd2, 0x3f93b058, 0x47654867, 0x3f923dd2,
+  0x4771c3b3, 0x3f90c8da, 0x477e3eb5, 0x3f8f516e,
+  0x478ab96e, 0x3f8dd78f, 0x479733dc, 0x3f8c5b3d,
+  0x47a3adff, 0x3f8adc77, 0x47b027d7, 0x3f895b3e,
+  0x47bca163, 0x3f87d792, 0x47c91aa3, 0x3f865174,
+  0x47d59396, 0x3f84c8e2, 0x47e20c3b, 0x3f833ddd,
+  0x47ee8493, 0x3f81b065, 0x47fafc9c, 0x3f80207b,
+  0x48077457, 0x3f7e8e1e, 0x4813ebc2, 0x3f7cf94e,
+  0x482062de, 0x3f7b620c, 0x482cd9a9, 0x3f79c857,
+  0x48395024, 0x3f782c30, 0x4845c64d, 0x3f768d96,
+  0x48523c25, 0x3f74ec8a, 0x485eb1ab, 0x3f73490b,
+  0x486b26de, 0x3f71a31b, 0x48779bbe, 0x3f6ffab8,
+  0x4884104b, 0x3f6e4fe3, 0x48908483, 0x3f6ca29c,
+  0x489cf867, 0x3f6af2e3, 0x48a96bf6, 0x3f6940b8,
+  0x48b5df30, 0x3f678c1c, 0x48c25213, 0x3f65d50d,
+  0x48cec4a0, 0x3f641b8d, 0x48db36d6, 0x3f625f9b,
+  0x48e7a8b5, 0x3f60a138, 0x48f41a3c, 0x3f5ee063,
+  0x49008b6a, 0x3f5d1d1d, 0x490cfc40, 0x3f5b5765,
+  0x49196cbc, 0x3f598f3c, 0x4925dcdf, 0x3f57c4a2,
+  0x49324ca7, 0x3f55f796, 0x493ebc14, 0x3f54281a,
+  0x494b2b27, 0x3f52562c, 0x495799dd, 0x3f5081cd,
+  0x49640837, 0x3f4eaafe, 0x49707635, 0x3f4cd1be,
+  0x497ce3d5, 0x3f4af60d, 0x49895118, 0x3f4917eb,
+  0x4995bdfd, 0x3f473759, 0x49a22a83, 0x3f455456,
+  0x49ae96aa, 0x3f436ee3, 0x49bb0271, 0x3f4186ff,
+  0x49c76dd8, 0x3f3f9cab, 0x49d3d8df, 0x3f3dafe7,
+  0x49e04385, 0x3f3bc0b3, 0x49ecadc9, 0x3f39cf0e,
+  0x49f917ac, 0x3f37dafa, 0x4a05812c, 0x3f35e476,
+  0x4a11ea49, 0x3f33eb81, 0x4a1e5303, 0x3f31f01d,
+  0x4a2abb59, 0x3f2ff24a, 0x4a37234a, 0x3f2df206,
+  0x4a438ad7, 0x3f2bef53, 0x4a4ff1fe, 0x3f29ea31,
+  0x4a5c58c0, 0x3f27e29f, 0x4a68bf1b, 0x3f25d89e,
+  0x4a752510, 0x3f23cc2e, 0x4a818a9d, 0x3f21bd4e,
+  0x4a8defc3, 0x3f1fabff, 0x4a9a5480, 0x3f1d9842,
+  0x4aa6b8d5, 0x3f1b8215, 0x4ab31cc1, 0x3f19697a,
+  0x4abf8043, 0x3f174e70, 0x4acbe35b, 0x3f1530f7,
+  0x4ad84609, 0x3f13110f, 0x4ae4a84b, 0x3f10eeb9,
+  0x4af10a22, 0x3f0ec9f5, 0x4afd6b8d, 0x3f0ca2c2,
+  0x4b09cc8c, 0x3f0a7921, 0x4b162d1d, 0x3f084d12,
+  0x4b228d42, 0x3f061e95, 0x4b2eecf8, 0x3f03eda9,
+  0x4b3b4c40, 0x3f01ba50, 0x4b47ab19, 0x3eff8489,
+  0x4b540982, 0x3efd4c54, 0x4b60677c, 0x3efb11b1,
+  0x4b6cc506, 0x3ef8d4a1, 0x4b79221f, 0x3ef69523,
+  0x4b857ec7, 0x3ef45338, 0x4b91dafc, 0x3ef20ee0,
+  0x4b9e36c0, 0x3eefc81a, 0x4baa9211, 0x3eed7ee7,
+  0x4bb6ecef, 0x3eeb3347, 0x4bc34759, 0x3ee8e53a,
+  0x4bcfa150, 0x3ee694c1, 0x4bdbfad1, 0x3ee441da,
+  0x4be853de, 0x3ee1ec87, 0x4bf4ac75, 0x3edf94c7,
+  0x4c010496, 0x3edd3a9a, 0x4c0d5c41, 0x3edade01,
+  0x4c19b374, 0x3ed87efc, 0x4c260a31, 0x3ed61d8a,
+  0x4c326075, 0x3ed3b9ad, 0x4c3eb641, 0x3ed15363,
+  0x4c4b0b94, 0x3eceeaad, 0x4c57606e, 0x3ecc7f8b,
+  0x4c63b4ce, 0x3eca11fe, 0x4c7008b3, 0x3ec7a205,
+  0x4c7c5c1e, 0x3ec52fa0, 0x4c88af0e, 0x3ec2bad0,
+  0x4c950182, 0x3ec04394, 0x4ca1537a, 0x3ebdc9ed,
+  0x4cada4f5, 0x3ebb4ddb, 0x4cb9f5f3, 0x3eb8cf5d,
+  0x4cc64673, 0x3eb64e75, 0x4cd29676, 0x3eb3cb21,
+  0x4cdee5f9, 0x3eb14563, 0x4ceb34fe, 0x3eaebd3a,
+  0x4cf78383, 0x3eac32a6, 0x4d03d189, 0x3ea9a5a8,
+  0x4d101f0e, 0x3ea7163f, 0x4d1c6c11, 0x3ea4846c,
+  0x4d28b894, 0x3ea1f02f, 0x4d350495, 0x3e9f5988,
+  0x4d415013, 0x3e9cc076, 0x4d4d9b0e, 0x3e9a24fb,
+  0x4d59e586, 0x3e978715, 0x4d662f7b, 0x3e94e6c6,
+  0x4d7278eb, 0x3e92440d, 0x4d7ec1d6, 0x3e8f9eeb,
+  0x4d8b0a3d, 0x3e8cf75f, 0x4d97521d, 0x3e8a4d6a,
+  0x4da39978, 0x3e87a10c, 0x4dafe04b, 0x3e84f245,
+  0x4dbc2698, 0x3e824114, 0x4dc86c5d, 0x3e7f8d7b,
+  0x4dd4b19a, 0x3e7cd778, 0x4de0f64f, 0x3e7a1f0d,
+  0x4ded3a7b, 0x3e77643a, 0x4df97e1d, 0x3e74a6fd,
+  0x4e05c135, 0x3e71e759, 0x4e1203c3, 0x3e6f254c,
+  0x4e1e45c6, 0x3e6c60d7, 0x4e2a873e, 0x3e6999fa,
+  0x4e36c82a, 0x3e66d0b4, 0x4e430889, 0x3e640507,
+  0x4e4f485c, 0x3e6136f3, 0x4e5b87a2, 0x3e5e6676,
+  0x4e67c65a, 0x3e5b9392, 0x4e740483, 0x3e58be47,
+  0x4e80421e, 0x3e55e694, 0x4e8c7f2a, 0x3e530c7a,
+  0x4e98bba7, 0x3e502ff9, 0x4ea4f793, 0x3e4d5110,
+  0x4eb132ef, 0x3e4a6fc1, 0x4ebd6db9, 0x3e478c0b,
+  0x4ec9a7f3, 0x3e44a5ef, 0x4ed5e19a, 0x3e41bd6c,
+  0x4ee21aaf, 0x3e3ed282, 0x4eee5331, 0x3e3be532,
+  0x4efa8b20, 0x3e38f57c, 0x4f06c27a, 0x3e360360,
+  0x4f12f941, 0x3e330ede, 0x4f1f2f73, 0x3e3017f6,
+  0x4f2b650f, 0x3e2d1ea8, 0x4f379a16, 0x3e2a22f4,
+  0x4f43ce86, 0x3e2724db, 0x4f500260, 0x3e24245d,
+  0x4f5c35a3, 0x3e212179, 0x4f68684e, 0x3e1e1c30,
+  0x4f749a61, 0x3e1b1482, 0x4f80cbdc, 0x3e180a6f,
+  0x4f8cfcbe, 0x3e14fdf7, 0x4f992d06, 0x3e11ef1b,
+  0x4fa55cb4, 0x3e0eddd9, 0x4fb18bc8, 0x3e0bca34,
+  0x4fbdba40, 0x3e08b42a, 0x4fc9e81e, 0x3e059bbb,
+  0x4fd6155f, 0x3e0280e9, 0x4fe24205, 0x3dff63b2,
+  0x4fee6e0d, 0x3dfc4418, 0x4ffa9979, 0x3df9221a,
+  0x5006c446, 0x3df5fdb8, 0x5012ee76, 0x3df2d6f3,
+  0x501f1807, 0x3defadca, 0x502b40f8, 0x3dec823e,
+  0x5037694b, 0x3de9544f, 0x504390fd, 0x3de623fd,
+  0x504fb80e, 0x3de2f148, 0x505bde7f, 0x3ddfbc30,
+  0x5068044e, 0x3ddc84b5, 0x5074297b, 0x3dd94ad8,
+  0x50804e06, 0x3dd60e99, 0x508c71ee, 0x3dd2cff7,
+  0x50989532, 0x3dcf8ef3, 0x50a4b7d3, 0x3dcc4b8d,
+  0x50b0d9d0, 0x3dc905c5, 0x50bcfb28, 0x3dc5bd9b,
+  0x50c91bda, 0x3dc2730f, 0x50d53be7, 0x3dbf2622,
+  0x50e15b4e, 0x3dbbd6d4, 0x50ed7a0e, 0x3db88524,
+  0x50f99827, 0x3db53113, 0x5105b599, 0x3db1daa2,
+  0x5111d263, 0x3dae81cf, 0x511dee84, 0x3dab269b,
+  0x512a09fc, 0x3da7c907, 0x513624cb, 0x3da46912,
+  0x51423ef0, 0x3da106bd, 0x514e586a, 0x3d9da208,
+  0x515a713a, 0x3d9a3af2, 0x5166895f, 0x3d96d17d,
+  0x5172a0d7, 0x3d9365a8, 0x517eb7a4, 0x3d8ff772,
+  0x518acdc4, 0x3d8c86de, 0x5196e337, 0x3d8913ea,
+  0x51a2f7fc, 0x3d859e96, 0x51af0c13, 0x3d8226e4,
+  0x51bb1f7c, 0x3d7eacd2, 0x51c73235, 0x3d7b3061,
+  0x51d3443f, 0x3d77b192, 0x51df5599, 0x3d743064,
+  0x51eb6643, 0x3d70acd7, 0x51f7763c, 0x3d6d26ec,
+  0x52038584, 0x3d699ea3, 0x520f941a, 0x3d6613fb,
+  0x521ba1fd, 0x3d6286f6, 0x5227af2e, 0x3d5ef793,
+  0x5233bbac, 0x3d5b65d2, 0x523fc776, 0x3d57d1b3,
+  0x524bd28c, 0x3d543b37, 0x5257dced, 0x3d50a25e,
+  0x5263e699, 0x3d4d0728, 0x526fef90, 0x3d496994,
+  0x527bf7d1, 0x3d45c9a4, 0x5287ff5b, 0x3d422757,
+  0x5294062f, 0x3d3e82ae, 0x52a00c4b, 0x3d3adba7,
+  0x52ac11af, 0x3d373245, 0x52b8165b, 0x3d338687,
+  0x52c41a4f, 0x3d2fd86c, 0x52d01d89, 0x3d2c27f6,
+  0x52dc2009, 0x3d287523, 0x52e821cf, 0x3d24bff6,
+  0x52f422db, 0x3d21086c, 0x5300232c, 0x3d1d4e88,
+  0x530c22c1, 0x3d199248, 0x5318219a, 0x3d15d3ad,
+  0x53241fb6, 0x3d1212b7, 0x53301d16, 0x3d0e4f67,
+  0x533c19b8, 0x3d0a89bc, 0x5348159d, 0x3d06c1b6,
+  0x535410c3, 0x3d02f757, 0x53600b2a, 0x3cff2a9d,
+  0x536c04d2, 0x3cfb5b89, 0x5377fdbb, 0x3cf78a1b,
+  0x5383f5e3, 0x3cf3b653, 0x538fed4b, 0x3cefe032,
+  0x539be3f2, 0x3cec07b8, 0x53a7d9d7, 0x3ce82ce4,
+  0x53b3cefa, 0x3ce44fb7, 0x53bfc35b, 0x3ce07031,
+  0x53cbb6f8, 0x3cdc8e52, 0x53d7a9d3, 0x3cd8aa1b,
+  0x53e39be9, 0x3cd4c38b, 0x53ef8d3c, 0x3cd0daa2,
+  0x53fb7dc9, 0x3cccef62, 0x54076d91, 0x3cc901c9,
+  0x54135c94, 0x3cc511d9, 0x541f4ad1, 0x3cc11f90,
+  0x542b3846, 0x3cbd2af0, 0x543724f5, 0x3cb933f9,
+  0x544310dd, 0x3cb53aaa, 0x544efbfc, 0x3cb13f04,
+  0x545ae653, 0x3cad4107, 0x5466cfe1, 0x3ca940b3,
+  0x5472b8a5, 0x3ca53e09, 0x547ea0a0, 0x3ca13908,
+  0x548a87d1, 0x3c9d31b0, 0x54966e36, 0x3c992803,
+  0x54a253d1, 0x3c951bff, 0x54ae38a0, 0x3c910da5,
+  0x54ba1ca3, 0x3c8cfcf6, 0x54c5ffd9, 0x3c88e9f1,
+  0x54d1e242, 0x3c84d496, 0x54ddc3de, 0x3c80bce7,
+  0x54e9a4ac, 0x3c7ca2e2, 0x54f584ac, 0x3c788688,
+  0x550163dc, 0x3c7467d9, 0x550d423d, 0x3c7046d6,
+  0x55191fcf, 0x3c6c237e, 0x5524fc90, 0x3c67fdd1,
+  0x5530d881, 0x3c63d5d1, 0x553cb3a0, 0x3c5fab7c,
+  0x55488dee, 0x3c5b7ed4, 0x5554676a, 0x3c574fd8,
+  0x55604013, 0x3c531e88, 0x556c17e9, 0x3c4eeae5,
+  0x5577eeec, 0x3c4ab4ef, 0x5583c51b, 0x3c467ca6,
+  0x558f9a76, 0x3c42420a, 0x559b6efb, 0x3c3e051b,
+  0x55a742ac, 0x3c39c5da, 0x55b31587, 0x3c358446,
+  0x55bee78c, 0x3c314060, 0x55cab8ba, 0x3c2cfa28,
+  0x55d68911, 0x3c28b19e, 0x55e25890, 0x3c2466c2,
+  0x55ee2738, 0x3c201994, 0x55f9f507, 0x3c1bca16,
+  0x5605c1fd, 0x3c177845, 0x56118e1a, 0x3c132424,
+  0x561d595d, 0x3c0ecdb2, 0x562923c5, 0x3c0a74f0,
+  0x5634ed53, 0x3c0619dc, 0x5640b606, 0x3c01bc78,
+  0x564c7ddd, 0x3bfd5cc4, 0x565844d8, 0x3bf8fac0,
+  0x56640af7, 0x3bf4966c, 0x566fd039, 0x3bf02fc9,
+  0x567b949d, 0x3bebc6d5, 0x56875823, 0x3be75b93,
+  0x56931acb, 0x3be2ee01, 0x569edc94, 0x3bde7e20,
+  0x56aa9d7e, 0x3bda0bf0, 0x56b65d88, 0x3bd59771,
+  0x56c21cb2, 0x3bd120a4, 0x56cddafb, 0x3bcca789,
+  0x56d99864, 0x3bc82c1f, 0x56e554ea, 0x3bc3ae67,
+  0x56f1108f, 0x3bbf2e62, 0x56fccb51, 0x3bbaac0e,
+  0x57088531, 0x3bb6276e, 0x57143e2d, 0x3bb1a080,
+  0x571ff646, 0x3bad1744, 0x572bad7a, 0x3ba88bbc,
+  0x573763c9, 0x3ba3fde7, 0x57431933, 0x3b9f6dc5,
+  0x574ecdb8, 0x3b9adb57, 0x575a8157, 0x3b96469d,
+  0x5766340f, 0x3b91af97, 0x5771e5e0, 0x3b8d1644,
+  0x577d96ca, 0x3b887aa6, 0x578946cc, 0x3b83dcbc,
+  0x5794f5e6, 0x3b7f3c87, 0x57a0a417, 0x3b7a9a07,
+  0x57ac515f, 0x3b75f53c, 0x57b7fdbd, 0x3b714e25,
+  0x57c3a931, 0x3b6ca4c4, 0x57cf53bb, 0x3b67f919,
+  0x57dafd59, 0x3b634b23, 0x57e6a60c, 0x3b5e9ae4,
+  0x57f24dd3, 0x3b59e85a, 0x57fdf4ae, 0x3b553386,
+  0x58099a9c, 0x3b507c69, 0x58153f9d, 0x3b4bc303,
+  0x5820e3b0, 0x3b470753, 0x582c86d5, 0x3b42495a,
+  0x5838290c, 0x3b3d8918, 0x5843ca53, 0x3b38c68e,
+  0x584f6aab, 0x3b3401bb, 0x585b0a13, 0x3b2f3aa0,
+  0x5866a88a, 0x3b2a713d, 0x58724611, 0x3b25a591,
+  0x587de2a7, 0x3b20d79e, 0x58897e4a, 0x3b1c0764,
+  0x589518fc, 0x3b1734e2, 0x58a0b2bb, 0x3b126019,
+  0x58ac4b87, 0x3b0d8909, 0x58b7e35f, 0x3b08afb2,
+  0x58c37a44, 0x3b03d414, 0x58cf1034, 0x3afef630,
+  0x58daa52f, 0x3afa1605, 0x58e63935, 0x3af53395,
+  0x58f1cc45, 0x3af04edf, 0x58fd5e5f, 0x3aeb67e3,
+  0x5908ef82, 0x3ae67ea1, 0x59147fae, 0x3ae1931a,
+  0x59200ee3, 0x3adca54e, 0x592b9d1f, 0x3ad7b53d,
+  0x59372a64, 0x3ad2c2e8, 0x5942b6af, 0x3acdce4d,
+  0x594e4201, 0x3ac8d76f, 0x5959cc5a, 0x3ac3de4c,
+  0x596555b8, 0x3abee2e5, 0x5970de1b, 0x3ab9e53a,
+  0x597c6584, 0x3ab4e54c, 0x5987ebf0, 0x3aafe31b,
+  0x59937161, 0x3aaadea6, 0x599ef5d6, 0x3aa5d7ee,
+  0x59aa794d, 0x3aa0cef3, 0x59b5fbc8, 0x3a9bc3b6,
+  0x59c17d44, 0x3a96b636, 0x59ccfdc2, 0x3a91a674,
+  0x59d87d42, 0x3a8c9470, 0x59e3fbc3, 0x3a87802a,
+  0x59ef7944, 0x3a8269a3, 0x59faf5c5, 0x3a7d50da,
+  0x5a067145, 0x3a7835cf, 0x5a11ebc5, 0x3a731884,
+  0x5a1d6544, 0x3a6df8f8, 0x5a28ddc0, 0x3a68d72b,
+  0x5a34553b, 0x3a63b31d, 0x5a3fcbb3, 0x3a5e8cd0,
+  0x5a4b4128, 0x3a596442, 0x5a56b599, 0x3a543974,
+  0x5a622907, 0x3a4f0c67, 0x5a6d9b70, 0x3a49dd1a,
+  0x5a790cd4, 0x3a44ab8e, 0x5a847d33, 0x3a3f77c3,
+  0x5a8fec8c, 0x3a3a41b9, 0x5a9b5adf, 0x3a350970,
+  0x5aa6c82b, 0x3a2fcee8, 0x5ab23471, 0x3a2a9223,
+  0x5abd9faf, 0x3a25531f, 0x5ac909e5, 0x3a2011de,
+  0x5ad47312, 0x3a1ace5f, 0x5adfdb37, 0x3a1588a2,
+  0x5aeb4253, 0x3a1040a8, 0x5af6a865, 0x3a0af671,
+  0x5b020d6c, 0x3a05a9fd, 0x5b0d716a, 0x3a005b4d,
+  0x5b18d45c, 0x39fb0a60, 0x5b243643, 0x39f5b737,
+  0x5b2f971e, 0x39f061d2, 0x5b3af6ec, 0x39eb0a31,
+  0x5b4655ae, 0x39e5b054, 0x5b51b363, 0x39e0543c,
+  0x5b5d100a, 0x39daf5e8, 0x5b686ba3, 0x39d5955a,
+  0x5b73c62d, 0x39d03291, 0x5b7f1fa9, 0x39cacd8d,
+  0x5b8a7815, 0x39c5664f, 0x5b95cf71, 0x39bffcd7,
+  0x5ba125bd, 0x39ba9125, 0x5bac7af9, 0x39b52339,
+  0x5bb7cf23, 0x39afb313, 0x5bc3223c, 0x39aa40b4,
+  0x5bce7442, 0x39a4cc1c, 0x5bd9c537, 0x399f554b,
+  0x5be51518, 0x3999dc42, 0x5bf063e6, 0x399460ff,
+  0x5bfbb1a0, 0x398ee385, 0x5c06fe46, 0x398963d2,
+  0x5c1249d8, 0x3983e1e8, 0x5c1d9454, 0x397e5dc6,
+  0x5c28ddbb, 0x3978d76c, 0x5c34260c, 0x39734edc,
+  0x5c3f6d47, 0x396dc414, 0x5c4ab36b, 0x39683715,
+  0x5c55f878, 0x3962a7e0, 0x5c613c6d, 0x395d1675,
+  0x5c6c7f4a, 0x395782d3, 0x5c77c10e, 0x3951ecfc,
+  0x5c8301b9, 0x394c54ee, 0x5c8e414b, 0x3946baac,
+  0x5c997fc4, 0x39411e33, 0x5ca4bd21, 0x393b7f86,
+  0x5caff965, 0x3935dea4, 0x5cbb348d, 0x39303b8e,
+  0x5cc66e99, 0x392a9642, 0x5cd1a78a, 0x3924eec3,
+  0x5cdcdf5e, 0x391f4510, 0x5ce81615, 0x39199929,
+  0x5cf34baf, 0x3913eb0e, 0x5cfe802b, 0x390e3ac0,
+  0x5d09b389, 0x3908883f, 0x5d14e5c9, 0x3902d38b,
+  0x5d2016e9, 0x38fd1ca4, 0x5d2b46ea, 0x38f7638b,
+  0x5d3675cb, 0x38f1a840, 0x5d41a38c, 0x38ebeac2,
+  0x5d4cd02c, 0x38e62b13, 0x5d57fbaa, 0x38e06932,
+  0x5d632608, 0x38daa520, 0x5d6e4f43, 0x38d4dedd,
+  0x5d79775c, 0x38cf1669, 0x5d849e51, 0x38c94bc4,
+  0x5d8fc424, 0x38c37eef, 0x5d9ae8d2, 0x38bdafea,
+  0x5da60c5d, 0x38b7deb4, 0x5db12ec3, 0x38b20b4f,
+  0x5dbc5004, 0x38ac35ba, 0x5dc7701f, 0x38a65df6,
+  0x5dd28f15, 0x38a08402, 0x5dddace4, 0x389aa7e0,
+  0x5de8c98c, 0x3894c98f, 0x5df3e50d, 0x388ee910,
+  0x5dfeff67, 0x38890663, 0x5e0a1898, 0x38832187,
+  0x5e1530a1, 0x387d3a7e, 0x5e204781, 0x38775147,
+  0x5e2b5d38, 0x387165e3, 0x5e3671c5, 0x386b7852,
+  0x5e418528, 0x38658894, 0x5e4c9760, 0x385f96a9,
+  0x5e57a86d, 0x3859a292, 0x5e62b84f, 0x3853ac4f,
+  0x5e6dc705, 0x384db3e0, 0x5e78d48e, 0x3847b946,
+  0x5e83e0eb, 0x3841bc7f, 0x5e8eec1b, 0x383bbd8e,
+  0x5e99f61d, 0x3835bc71, 0x5ea4fef0, 0x382fb92a,
+  0x5eb00696, 0x3829b3b9, 0x5ebb0d0d, 0x3823ac1d,
+  0x5ec61254, 0x381da256, 0x5ed1166b, 0x38179666,
+  0x5edc1953, 0x3811884d, 0x5ee71b0a, 0x380b780a,
+  0x5ef21b90, 0x3805659e, 0x5efd1ae4, 0x37ff5109,
+  0x5f081907, 0x37f93a4b, 0x5f1315f7, 0x37f32165,
+  0x5f1e11b5, 0x37ed0657, 0x5f290c3f, 0x37e6e921,
+  0x5f340596, 0x37e0c9c3, 0x5f3efdb9, 0x37daa83d,
+  0x5f49f4a8, 0x37d48490, 0x5f54ea62, 0x37ce5ebd,
+  0x5f5fdee6, 0x37c836c2, 0x5f6ad235, 0x37c20ca1,
+  0x5f75c44e, 0x37bbe05a, 0x5f80b531, 0x37b5b1ec,
+  0x5f8ba4dc, 0x37af8159, 0x5f969350, 0x37a94ea0,
+  0x5fa1808c, 0x37a319c2, 0x5fac6c91, 0x379ce2be,
+  0x5fb7575c, 0x3796a996, 0x5fc240ef, 0x37906e49,
+  0x5fcd2948, 0x378a30d8, 0x5fd81067, 0x3783f143,
+  0x5fe2f64c, 0x377daf89, 0x5feddaf6, 0x37776bac,
+  0x5ff8be65, 0x377125ac, 0x6003a099, 0x376add88,
+  0x600e8190, 0x37649341, 0x6019614c, 0x375e46d8,
+  0x60243fca, 0x3757f84c, 0x602f1d0b, 0x3751a79e,
+  0x6039f90f, 0x374b54ce, 0x6044d3d4, 0x3744ffdd,
+  0x604fad5b, 0x373ea8ca, 0x605a85a3, 0x37384f95,
+  0x60655cac, 0x3731f440, 0x60703275, 0x372b96ca,
+  0x607b06fe, 0x37253733, 0x6085da46, 0x371ed57c,
+  0x6090ac4d, 0x371871a5, 0x609b7d13, 0x37120bae,
+  0x60a64c97, 0x370ba398, 0x60b11ad9, 0x37053962,
+  0x60bbe7d8, 0x36fecd0e, 0x60c6b395, 0x36f85e9a,
+  0x60d17e0d, 0x36f1ee09, 0x60dc4742, 0x36eb7b58,
+  0x60e70f32, 0x36e5068a, 0x60f1d5de, 0x36de8f9e,
+  0x60fc9b44, 0x36d81695, 0x61075f65, 0x36d19b6e,
+  0x61122240, 0x36cb1e2a, 0x611ce3d5, 0x36c49ec9,
+  0x6127a423, 0x36be1d4c, 0x61326329, 0x36b799b3,
+  0x613d20e8, 0x36b113fd, 0x6147dd5f, 0x36aa8c2c,
+  0x6152988d, 0x36a4023f, 0x615d5273, 0x369d7637,
+  0x61680b0f, 0x3696e814, 0x6172c262, 0x369057d6,
+  0x617d786a, 0x3689c57d, 0x61882d28, 0x3683310b,
+  0x6192e09b, 0x367c9a7e, 0x619d92c2, 0x367601d7,
+  0x61a8439e, 0x366f6717, 0x61b2f32e, 0x3668ca3e,
+  0x61bda171, 0x36622b4c, 0x61c84e67, 0x365b8a41,
+  0x61d2fa0f, 0x3654e71d, 0x61dda46a, 0x364e41e2,
+  0x61e84d76, 0x36479a8e, 0x61f2f534, 0x3640f123,
+  0x61fd9ba3, 0x363a45a0, 0x620840c2, 0x36339806,
+  0x6212e492, 0x362ce855, 0x621d8711, 0x3626368d,
+  0x6228283f, 0x361f82af, 0x6232c81c, 0x3618ccba,
+  0x623d66a8, 0x361214b0, 0x624803e2, 0x360b5a90,
+  0x62529fca, 0x36049e5b, 0x625d3a5e, 0x35fde011,
+  0x6267d3a0, 0x35f71fb1, 0x62726b8e, 0x35f05d3d,
+  0x627d0228, 0x35e998b5, 0x6287976e, 0x35e2d219,
+  0x62922b5e, 0x35dc0968, 0x629cbdfa, 0x35d53ea5,
+  0x62a74f40, 0x35ce71ce, 0x62b1df30, 0x35c7a2e3,
+  0x62bc6dca, 0x35c0d1e7, 0x62c6fb0c, 0x35b9fed7,
+  0x62d186f8, 0x35b329b5, 0x62dc118c, 0x35ac5282,
+  0x62e69ac8, 0x35a5793c, 0x62f122ab, 0x359e9de5,
+  0x62fba936, 0x3597c07d, 0x63062e67, 0x3590e104,
+  0x6310b23e, 0x3589ff7a, 0x631b34bc, 0x35831be0,
+  0x6325b5df, 0x357c3636, 0x633035a7, 0x35754e7c,
+  0x633ab414, 0x356e64b2, 0x63453125, 0x356778d9,
+  0x634facda, 0x35608af1, 0x635a2733, 0x35599afa,
+  0x6364a02e, 0x3552a8f4, 0x636f17cc, 0x354bb4e1,
+  0x63798e0d, 0x3544bebf, 0x638402ef, 0x353dc68f,
+  0x638e7673, 0x3536cc52, 0x6398e898, 0x352fd008,
+  0x63a3595e, 0x3528d1b1, 0x63adc8c4, 0x3521d14d,
+  0x63b836ca, 0x351acedd, 0x63c2a36f, 0x3513ca60,
+  0x63cd0eb3, 0x350cc3d8, 0x63d77896, 0x3505bb44,
+  0x63e1e117, 0x34feb0a5, 0x63ec4837, 0x34f7a3fb,
+  0x63f6adf3, 0x34f09546, 0x6401124d, 0x34e98487,
+  0x640b7543, 0x34e271bd, 0x6415d6d5, 0x34db5cea,
+  0x64203704, 0x34d4460c, 0x642a95ce, 0x34cd2d26,
+  0x6434f332, 0x34c61236, 0x643f4f32, 0x34bef53d,
+  0x6449a9cc, 0x34b7d63c, 0x645402ff, 0x34b0b533,
+  0x645e5acc, 0x34a99221, 0x6468b132, 0x34a26d08,
+  0x64730631, 0x349b45e7, 0x647d59c8, 0x34941cbf,
+  0x6487abf7, 0x348cf190, 0x6491fcbe, 0x3485c45b,
+  0x649c4c1b, 0x347e951f, 0x64a69a0f, 0x347763dd,
+  0x64b0e699, 0x34703095, 0x64bb31ba, 0x3468fb47,
+  0x64c57b6f, 0x3461c3f5, 0x64cfc3ba, 0x345a8a9d,
+  0x64da0a9a, 0x34534f41, 0x64e4500e, 0x344c11e0,
+  0x64ee9415, 0x3444d27b, 0x64f8d6b0, 0x343d9112,
+  0x650317df, 0x34364da6, 0x650d57a0, 0x342f0836,
+  0x651795f3, 0x3427c0c3, 0x6521d2d8, 0x3420774d,
+  0x652c0e4f, 0x34192bd5, 0x65364857, 0x3411de5b,
+  0x654080ef, 0x340a8edf, 0x654ab818, 0x34033d61,
+  0x6554edd1, 0x33fbe9e2, 0x655f2219, 0x33f49462,
+  0x656954f1, 0x33ed3ce1, 0x65738657, 0x33e5e360,
+  0x657db64c, 0x33de87de, 0x6587e4cf, 0x33d72a5d,
+  0x659211df, 0x33cfcadc, 0x659c3d7c, 0x33c8695b,
+  0x65a667a7, 0x33c105db, 0x65b0905d, 0x33b9a05d,
+  0x65bab7a0, 0x33b238e0, 0x65c4dd6e, 0x33aacf65,
+  0x65cf01c8, 0x33a363ec, 0x65d924ac, 0x339bf675,
+  0x65e3461b, 0x33948701, 0x65ed6614, 0x338d1590,
+  0x65f78497, 0x3385a222, 0x6601a1a2, 0x337e2cb7,
+  0x660bbd37, 0x3376b551, 0x6615d754, 0x336f3bee,
+  0x661feffa, 0x3367c090, 0x662a0727, 0x33604336,
+  0x66341cdb, 0x3358c3e2, 0x663e3117, 0x33514292,
+  0x664843d9, 0x3349bf48, 0x66525521, 0x33423a04,
+  0x665c64ef, 0x333ab2c6, 0x66667342, 0x3333298f,
+  0x6670801a, 0x332b9e5e, 0x667a8b77, 0x33241134,
+  0x66849558, 0x331c8211, 0x668e9dbd, 0x3314f0f6,
+  0x6698a4a6, 0x330d5de3, 0x66a2aa11, 0x3305c8d7,
+  0x66acadff, 0x32fe31d5, 0x66b6b070, 0x32f698db,
+  0x66c0b162, 0x32eefdea, 0x66cab0d6, 0x32e76102,
+  0x66d4aecb, 0x32dfc224, 0x66deab41, 0x32d82150,
+  0x66e8a637, 0x32d07e85, 0x66f29fad, 0x32c8d9c6,
+  0x66fc97a3, 0x32c13311, 0x67068e18, 0x32b98a67,
+  0x6710830c, 0x32b1dfc9, 0x671a767e, 0x32aa3336,
+  0x6724686e, 0x32a284b0, 0x672e58dc, 0x329ad435,
+  0x673847c8, 0x329321c7, 0x67423530, 0x328b6d66,
+  0x674c2115, 0x3283b712, 0x67560b76, 0x327bfecc,
+  0x675ff452, 0x32744493, 0x6769dbaa, 0x326c8868,
+  0x6773c17d, 0x3264ca4c, 0x677da5cb, 0x325d0a3e,
+  0x67878893, 0x32554840, 0x679169d5, 0x324d8450,
+  0x679b4990, 0x3245be70, 0x67a527c4, 0x323df6a0,
+  0x67af0472, 0x32362ce0, 0x67b8df97, 0x322e6130,
+  0x67c2b934, 0x32269391, 0x67cc9149, 0x321ec403,
+  0x67d667d5, 0x3216f287, 0x67e03cd8, 0x320f1f1c,
+  0x67ea1052, 0x320749c3, 0x67f3e241, 0x31ff727c,
+  0x67fdb2a7, 0x31f79948, 0x68078181, 0x31efbe27,
+  0x68114ed0, 0x31e7e118, 0x681b1a94, 0x31e0021e,
+  0x6824e4cc, 0x31d82137, 0x682ead78, 0x31d03e64,
+  0x68387498, 0x31c859a5, 0x68423a2a, 0x31c072fb,
+  0x684bfe2f, 0x31b88a66, 0x6855c0a6, 0x31b09fe7,
+  0x685f8190, 0x31a8b37c, 0x686940ea, 0x31a0c528,
+  0x6872feb6, 0x3198d4ea, 0x687cbaf3, 0x3190e2c3,
+  0x688675a0, 0x3188eeb2, 0x68902ebd, 0x3180f8b8,
+  0x6899e64a, 0x317900d6, 0x68a39c46, 0x3171070c,
+  0x68ad50b1, 0x31690b59, 0x68b7038b, 0x31610dbf,
+  0x68c0b4d2, 0x31590e3e, 0x68ca6488, 0x31510cd5,
+  0x68d412ab, 0x31490986, 0x68ddbf3b, 0x31410450,
+  0x68e76a37, 0x3138fd35, 0x68f113a0, 0x3130f433,
+  0x68fabb75, 0x3128e94c, 0x690461b5, 0x3120dc80,
+  0x690e0661, 0x3118cdcf, 0x6917a977, 0x3110bd39,
+  0x69214af8, 0x3108aabf, 0x692aeae3, 0x31009661,
+  0x69348937, 0x30f8801f, 0x693e25f5, 0x30f067fb,
+  0x6947c11c, 0x30e84df3, 0x69515aab, 0x30e03208,
+  0x695af2a3, 0x30d8143b, 0x69648902, 0x30cff48c,
+  0x696e1dc9, 0x30c7d2fb, 0x6977b0f7, 0x30bfaf89,
+  0x6981428c, 0x30b78a36, 0x698ad287, 0x30af6302,
+  0x699460e8, 0x30a739ed, 0x699dedaf, 0x309f0ef8,
+  0x69a778db, 0x3096e223, 0x69b1026c, 0x308eb36f,
+  0x69ba8a61, 0x308682dc, 0x69c410ba, 0x307e5069,
+  0x69cd9578, 0x30761c18, 0x69d71899, 0x306de5e9,
+  0x69e09a1c, 0x3065addb, 0x69ea1a03, 0x305d73f0,
+  0x69f3984c, 0x30553828, 0x69fd14f6, 0x304cfa83,
+  0x6a069003, 0x3044bb00, 0x6a100970, 0x303c79a2,
+  0x6a19813f, 0x30343667, 0x6a22f76e, 0x302bf151,
+  0x6a2c6bfd, 0x3023aa5f, 0x6a35deeb, 0x301b6193,
+  0x6a3f503a, 0x301316eb, 0x6a48bfe7, 0x300aca69,
+  0x6a522df3, 0x30027c0c, 0x6a5b9a5d, 0x2ffa2bd6,
+  0x6a650525, 0x2ff1d9c7, 0x6a6e6e4b, 0x2fe985de,
+  0x6a77d5ce, 0x2fe1301c, 0x6a813bae, 0x2fd8d882,
+  0x6a8a9fea, 0x2fd07f0f, 0x6a940283, 0x2fc823c5,
+  0x6a9d6377, 0x2fbfc6a3, 0x6aa6c2c6, 0x2fb767aa,
+  0x6ab02071, 0x2faf06da, 0x6ab97c77, 0x2fa6a433,
+  0x6ac2d6d6, 0x2f9e3fb6, 0x6acc2f90, 0x2f95d963,
+  0x6ad586a3, 0x2f8d713a, 0x6adedc10, 0x2f85073c,
+  0x6ae82fd5, 0x2f7c9b69, 0x6af181f3, 0x2f742dc1,
+  0x6afad269, 0x2f6bbe45, 0x6b042137, 0x2f634cf5,
+  0x6b0d6e5c, 0x2f5ad9d1, 0x6b16b9d9, 0x2f5264da,
+  0x6b2003ac, 0x2f49ee0f, 0x6b294bd5, 0x2f417573,
+  0x6b329255, 0x2f38fb03, 0x6b3bd72a, 0x2f307ec2,
+  0x6b451a55, 0x2f2800af, 0x6b4e5bd4, 0x2f1f80ca,
+  0x6b579ba8, 0x2f16ff14, 0x6b60d9d0, 0x2f0e7b8e,
+  0x6b6a164d, 0x2f05f637, 0x6b73511c, 0x2efd6f10,
+  0x6b7c8a3f, 0x2ef4e619, 0x6b85c1b5, 0x2eec5b53,
+  0x6b8ef77d, 0x2ee3cebe, 0x6b982b97, 0x2edb405a,
+  0x6ba15e03, 0x2ed2b027, 0x6baa8ec0, 0x2eca1e27,
+  0x6bb3bdce, 0x2ec18a58, 0x6bbceb2d, 0x2eb8f4bc,
+  0x6bc616dd, 0x2eb05d53, 0x6bcf40dc, 0x2ea7c41e,
+  0x6bd8692b, 0x2e9f291b, 0x6be18fc9, 0x2e968c4d,
+  0x6beab4b6, 0x2e8dedb3, 0x6bf3d7f2, 0x2e854d4d,
+  0x6bfcf97c, 0x2e7cab1c, 0x6c061953, 0x2e740720,
+  0x6c0f3779, 0x2e6b615a, 0x6c1853eb, 0x2e62b9ca,
+  0x6c216eaa, 0x2e5a1070, 0x6c2a87b6, 0x2e51654c,
+  0x6c339f0e, 0x2e48b860, 0x6c3cb4b1, 0x2e4009aa,
+  0x6c45c8a0, 0x2e37592c, 0x6c4edada, 0x2e2ea6e6,
+  0x6c57eb5e, 0x2e25f2d8, 0x6c60fa2d, 0x2e1d3d03,
+  0x6c6a0746, 0x2e148566, 0x6c7312a9, 0x2e0bcc03,
+  0x6c7c1c55, 0x2e0310d9, 0x6c85244a, 0x2dfa53e9,
+  0x6c8e2a87, 0x2df19534, 0x6c972f0d, 0x2de8d4b8,
+  0x6ca031da, 0x2de01278, 0x6ca932ef, 0x2dd74e73,
+  0x6cb2324c, 0x2dce88aa, 0x6cbb2fef, 0x2dc5c11c,
+  0x6cc42bd9, 0x2dbcf7cb, 0x6ccd2609, 0x2db42cb6,
+  0x6cd61e7f, 0x2dab5fdf, 0x6cdf153a, 0x2da29144,
+  0x6ce80a3a, 0x2d99c0e7, 0x6cf0fd80, 0x2d90eec8,
+  0x6cf9ef09, 0x2d881ae8, 0x6d02ded7, 0x2d7f4545,
+  0x6d0bcce8, 0x2d766de2, 0x6d14b93d, 0x2d6d94bf,
+  0x6d1da3d5, 0x2d64b9da, 0x6d268cb0, 0x2d5bdd36,
+  0x6d2f73cd, 0x2d52fed2, 0x6d38592c, 0x2d4a1eaf,
+  0x6d413ccd, 0x2d413ccd, 0x6d4a1eaf, 0x2d38592c,
+  0x6d52fed2, 0x2d2f73cd, 0x6d5bdd36, 0x2d268cb0,
+  0x6d64b9da, 0x2d1da3d5, 0x6d6d94bf, 0x2d14b93d,
+  0x6d766de2, 0x2d0bcce8, 0x6d7f4545, 0x2d02ded7,
+  0x6d881ae8, 0x2cf9ef09, 0x6d90eec8, 0x2cf0fd80,
+  0x6d99c0e7, 0x2ce80a3a, 0x6da29144, 0x2cdf153a,
+  0x6dab5fdf, 0x2cd61e7f, 0x6db42cb6, 0x2ccd2609,
+  0x6dbcf7cb, 0x2cc42bd9, 0x6dc5c11c, 0x2cbb2fef,
+  0x6dce88aa, 0x2cb2324c, 0x6dd74e73, 0x2ca932ef,
+  0x6de01278, 0x2ca031da, 0x6de8d4b8, 0x2c972f0d,
+  0x6df19534, 0x2c8e2a87, 0x6dfa53e9, 0x2c85244a,
+  0x6e0310d9, 0x2c7c1c55, 0x6e0bcc03, 0x2c7312a9,
+  0x6e148566, 0x2c6a0746, 0x6e1d3d03, 0x2c60fa2d,
+  0x6e25f2d8, 0x2c57eb5e, 0x6e2ea6e6, 0x2c4edada,
+  0x6e37592c, 0x2c45c8a0, 0x6e4009aa, 0x2c3cb4b1,
+  0x6e48b860, 0x2c339f0e, 0x6e51654c, 0x2c2a87b6,
+  0x6e5a1070, 0x2c216eaa, 0x6e62b9ca, 0x2c1853eb,
+  0x6e6b615a, 0x2c0f3779, 0x6e740720, 0x2c061953,
+  0x6e7cab1c, 0x2bfcf97c, 0x6e854d4d, 0x2bf3d7f2,
+  0x6e8dedb3, 0x2beab4b6, 0x6e968c4d, 0x2be18fc9,
+  0x6e9f291b, 0x2bd8692b, 0x6ea7c41e, 0x2bcf40dc,
+  0x6eb05d53, 0x2bc616dd, 0x6eb8f4bc, 0x2bbceb2d,
+  0x6ec18a58, 0x2bb3bdce, 0x6eca1e27, 0x2baa8ec0,
+  0x6ed2b027, 0x2ba15e03, 0x6edb405a, 0x2b982b97,
+  0x6ee3cebe, 0x2b8ef77d, 0x6eec5b53, 0x2b85c1b5,
+  0x6ef4e619, 0x2b7c8a3f, 0x6efd6f10, 0x2b73511c,
+  0x6f05f637, 0x2b6a164d, 0x6f0e7b8e, 0x2b60d9d0,
+  0x6f16ff14, 0x2b579ba8, 0x6f1f80ca, 0x2b4e5bd4,
+  0x6f2800af, 0x2b451a55, 0x6f307ec2, 0x2b3bd72a,
+  0x6f38fb03, 0x2b329255, 0x6f417573, 0x2b294bd5,
+  0x6f49ee0f, 0x2b2003ac, 0x6f5264da, 0x2b16b9d9,
+  0x6f5ad9d1, 0x2b0d6e5c, 0x6f634cf5, 0x2b042137,
+  0x6f6bbe45, 0x2afad269, 0x6f742dc1, 0x2af181f3,
+  0x6f7c9b69, 0x2ae82fd5, 0x6f85073c, 0x2adedc10,
+  0x6f8d713a, 0x2ad586a3, 0x6f95d963, 0x2acc2f90,
+  0x6f9e3fb6, 0x2ac2d6d6, 0x6fa6a433, 0x2ab97c77,
+  0x6faf06da, 0x2ab02071, 0x6fb767aa, 0x2aa6c2c6,
+  0x6fbfc6a3, 0x2a9d6377, 0x6fc823c5, 0x2a940283,
+  0x6fd07f0f, 0x2a8a9fea, 0x6fd8d882, 0x2a813bae,
+  0x6fe1301c, 0x2a77d5ce, 0x6fe985de, 0x2a6e6e4b,
+  0x6ff1d9c7, 0x2a650525, 0x6ffa2bd6, 0x2a5b9a5d,
+  0x70027c0c, 0x2a522df3, 0x700aca69, 0x2a48bfe7,
+  0x701316eb, 0x2a3f503a, 0x701b6193, 0x2a35deeb,
+  0x7023aa5f, 0x2a2c6bfd, 0x702bf151, 0x2a22f76e,
+  0x70343667, 0x2a19813f, 0x703c79a2, 0x2a100970,
+  0x7044bb00, 0x2a069003, 0x704cfa83, 0x29fd14f6,
+  0x70553828, 0x29f3984c, 0x705d73f0, 0x29ea1a03,
+  0x7065addb, 0x29e09a1c, 0x706de5e9, 0x29d71899,
+  0x70761c18, 0x29cd9578, 0x707e5069, 0x29c410ba,
+  0x708682dc, 0x29ba8a61, 0x708eb36f, 0x29b1026c,
+  0x7096e223, 0x29a778db, 0x709f0ef8, 0x299dedaf,
+  0x70a739ed, 0x299460e8, 0x70af6302, 0x298ad287,
+  0x70b78a36, 0x2981428c, 0x70bfaf89, 0x2977b0f7,
+  0x70c7d2fb, 0x296e1dc9, 0x70cff48c, 0x29648902,
+  0x70d8143b, 0x295af2a3, 0x70e03208, 0x29515aab,
+  0x70e84df3, 0x2947c11c, 0x70f067fb, 0x293e25f5,
+  0x70f8801f, 0x29348937, 0x71009661, 0x292aeae3,
+  0x7108aabf, 0x29214af8, 0x7110bd39, 0x2917a977,
+  0x7118cdcf, 0x290e0661, 0x7120dc80, 0x290461b5,
+  0x7128e94c, 0x28fabb75, 0x7130f433, 0x28f113a0,
+  0x7138fd35, 0x28e76a37, 0x71410450, 0x28ddbf3b,
+  0x71490986, 0x28d412ab, 0x71510cd5, 0x28ca6488,
+  0x71590e3e, 0x28c0b4d2, 0x71610dbf, 0x28b7038b,
+  0x71690b59, 0x28ad50b1, 0x7171070c, 0x28a39c46,
+  0x717900d6, 0x2899e64a, 0x7180f8b8, 0x28902ebd,
+  0x7188eeb2, 0x288675a0, 0x7190e2c3, 0x287cbaf3,
+  0x7198d4ea, 0x2872feb6, 0x71a0c528, 0x286940ea,
+  0x71a8b37c, 0x285f8190, 0x71b09fe7, 0x2855c0a6,
+  0x71b88a66, 0x284bfe2f, 0x71c072fb, 0x28423a2a,
+  0x71c859a5, 0x28387498, 0x71d03e64, 0x282ead78,
+  0x71d82137, 0x2824e4cc, 0x71e0021e, 0x281b1a94,
+  0x71e7e118, 0x28114ed0, 0x71efbe27, 0x28078181,
+  0x71f79948, 0x27fdb2a7, 0x71ff727c, 0x27f3e241,
+  0x720749c3, 0x27ea1052, 0x720f1f1c, 0x27e03cd8,
+  0x7216f287, 0x27d667d5, 0x721ec403, 0x27cc9149,
+  0x72269391, 0x27c2b934, 0x722e6130, 0x27b8df97,
+  0x72362ce0, 0x27af0472, 0x723df6a0, 0x27a527c4,
+  0x7245be70, 0x279b4990, 0x724d8450, 0x279169d5,
+  0x72554840, 0x27878893, 0x725d0a3e, 0x277da5cb,
+  0x7264ca4c, 0x2773c17d, 0x726c8868, 0x2769dbaa,
+  0x72744493, 0x275ff452, 0x727bfecc, 0x27560b76,
+  0x7283b712, 0x274c2115, 0x728b6d66, 0x27423530,
+  0x729321c7, 0x273847c8, 0x729ad435, 0x272e58dc,
+  0x72a284b0, 0x2724686e, 0x72aa3336, 0x271a767e,
+  0x72b1dfc9, 0x2710830c, 0x72b98a67, 0x27068e18,
+  0x72c13311, 0x26fc97a3, 0x72c8d9c6, 0x26f29fad,
+  0x72d07e85, 0x26e8a637, 0x72d82150, 0x26deab41,
+  0x72dfc224, 0x26d4aecb, 0x72e76102, 0x26cab0d6,
+  0x72eefdea, 0x26c0b162, 0x72f698db, 0x26b6b070,
+  0x72fe31d5, 0x26acadff, 0x7305c8d7, 0x26a2aa11,
+  0x730d5de3, 0x2698a4a6, 0x7314f0f6, 0x268e9dbd,
+  0x731c8211, 0x26849558, 0x73241134, 0x267a8b77,
+  0x732b9e5e, 0x2670801a, 0x7333298f, 0x26667342,
+  0x733ab2c6, 0x265c64ef, 0x73423a04, 0x26525521,
+  0x7349bf48, 0x264843d9, 0x73514292, 0x263e3117,
+  0x7358c3e2, 0x26341cdb, 0x73604336, 0x262a0727,
+  0x7367c090, 0x261feffa, 0x736f3bee, 0x2615d754,
+  0x7376b551, 0x260bbd37, 0x737e2cb7, 0x2601a1a2,
+  0x7385a222, 0x25f78497, 0x738d1590, 0x25ed6614,
+  0x73948701, 0x25e3461b, 0x739bf675, 0x25d924ac,
+  0x73a363ec, 0x25cf01c8, 0x73aacf65, 0x25c4dd6e,
+  0x73b238e0, 0x25bab7a0, 0x73b9a05d, 0x25b0905d,
+  0x73c105db, 0x25a667a7, 0x73c8695b, 0x259c3d7c,
+  0x73cfcadc, 0x259211df, 0x73d72a5d, 0x2587e4cf,
+  0x73de87de, 0x257db64c, 0x73e5e360, 0x25738657,
+  0x73ed3ce1, 0x256954f1, 0x73f49462, 0x255f2219,
+  0x73fbe9e2, 0x2554edd1, 0x74033d61, 0x254ab818,
+  0x740a8edf, 0x254080ef, 0x7411de5b, 0x25364857,
+  0x74192bd5, 0x252c0e4f, 0x7420774d, 0x2521d2d8,
+  0x7427c0c3, 0x251795f3, 0x742f0836, 0x250d57a0,
+  0x74364da6, 0x250317df, 0x743d9112, 0x24f8d6b0,
+  0x7444d27b, 0x24ee9415, 0x744c11e0, 0x24e4500e,
+  0x74534f41, 0x24da0a9a, 0x745a8a9d, 0x24cfc3ba,
+  0x7461c3f5, 0x24c57b6f, 0x7468fb47, 0x24bb31ba,
+  0x74703095, 0x24b0e699, 0x747763dd, 0x24a69a0f,
+  0x747e951f, 0x249c4c1b, 0x7485c45b, 0x2491fcbe,
+  0x748cf190, 0x2487abf7, 0x74941cbf, 0x247d59c8,
+  0x749b45e7, 0x24730631, 0x74a26d08, 0x2468b132,
+  0x74a99221, 0x245e5acc, 0x74b0b533, 0x245402ff,
+  0x74b7d63c, 0x2449a9cc, 0x74bef53d, 0x243f4f32,
+  0x74c61236, 0x2434f332, 0x74cd2d26, 0x242a95ce,
+  0x74d4460c, 0x24203704, 0x74db5cea, 0x2415d6d5,
+  0x74e271bd, 0x240b7543, 0x74e98487, 0x2401124d,
+  0x74f09546, 0x23f6adf3, 0x74f7a3fb, 0x23ec4837,
+  0x74feb0a5, 0x23e1e117, 0x7505bb44, 0x23d77896,
+  0x750cc3d8, 0x23cd0eb3, 0x7513ca60, 0x23c2a36f,
+  0x751acedd, 0x23b836ca, 0x7521d14d, 0x23adc8c4,
+  0x7528d1b1, 0x23a3595e, 0x752fd008, 0x2398e898,
+  0x7536cc52, 0x238e7673, 0x753dc68f, 0x238402ef,
+  0x7544bebf, 0x23798e0d, 0x754bb4e1, 0x236f17cc,
+  0x7552a8f4, 0x2364a02e, 0x75599afa, 0x235a2733,
+  0x75608af1, 0x234facda, 0x756778d9, 0x23453125,
+  0x756e64b2, 0x233ab414, 0x75754e7c, 0x233035a7,
+  0x757c3636, 0x2325b5df, 0x75831be0, 0x231b34bc,
+  0x7589ff7a, 0x2310b23e, 0x7590e104, 0x23062e67,
+  0x7597c07d, 0x22fba936, 0x759e9de5, 0x22f122ab,
+  0x75a5793c, 0x22e69ac8, 0x75ac5282, 0x22dc118c,
+  0x75b329b5, 0x22d186f8, 0x75b9fed7, 0x22c6fb0c,
+  0x75c0d1e7, 0x22bc6dca, 0x75c7a2e3, 0x22b1df30,
+  0x75ce71ce, 0x22a74f40, 0x75d53ea5, 0x229cbdfa,
+  0x75dc0968, 0x22922b5e, 0x75e2d219, 0x2287976e,
+  0x75e998b5, 0x227d0228, 0x75f05d3d, 0x22726b8e,
+  0x75f71fb1, 0x2267d3a0, 0x75fde011, 0x225d3a5e,
+  0x76049e5b, 0x22529fca, 0x760b5a90, 0x224803e2,
+  0x761214b0, 0x223d66a8, 0x7618ccba, 0x2232c81c,
+  0x761f82af, 0x2228283f, 0x7626368d, 0x221d8711,
+  0x762ce855, 0x2212e492, 0x76339806, 0x220840c2,
+  0x763a45a0, 0x21fd9ba3, 0x7640f123, 0x21f2f534,
+  0x76479a8e, 0x21e84d76, 0x764e41e2, 0x21dda46a,
+  0x7654e71d, 0x21d2fa0f, 0x765b8a41, 0x21c84e67,
+  0x76622b4c, 0x21bda171, 0x7668ca3e, 0x21b2f32e,
+  0x766f6717, 0x21a8439e, 0x767601d7, 0x219d92c2,
+  0x767c9a7e, 0x2192e09b, 0x7683310b, 0x21882d28,
+  0x7689c57d, 0x217d786a, 0x769057d6, 0x2172c262,
+  0x7696e814, 0x21680b0f, 0x769d7637, 0x215d5273,
+  0x76a4023f, 0x2152988d, 0x76aa8c2c, 0x2147dd5f,
+  0x76b113fd, 0x213d20e8, 0x76b799b3, 0x21326329,
+  0x76be1d4c, 0x2127a423, 0x76c49ec9, 0x211ce3d5,
+  0x76cb1e2a, 0x21122240, 0x76d19b6e, 0x21075f65,
+  0x76d81695, 0x20fc9b44, 0x76de8f9e, 0x20f1d5de,
+  0x76e5068a, 0x20e70f32, 0x76eb7b58, 0x20dc4742,
+  0x76f1ee09, 0x20d17e0d, 0x76f85e9a, 0x20c6b395,
+  0x76fecd0e, 0x20bbe7d8, 0x77053962, 0x20b11ad9,
+  0x770ba398, 0x20a64c97, 0x77120bae, 0x209b7d13,
+  0x771871a5, 0x2090ac4d, 0x771ed57c, 0x2085da46,
+  0x77253733, 0x207b06fe, 0x772b96ca, 0x20703275,
+  0x7731f440, 0x20655cac, 0x77384f95, 0x205a85a3,
+  0x773ea8ca, 0x204fad5b, 0x7744ffdd, 0x2044d3d4,
+  0x774b54ce, 0x2039f90f, 0x7751a79e, 0x202f1d0b,
+  0x7757f84c, 0x20243fca, 0x775e46d8, 0x2019614c,
+  0x77649341, 0x200e8190, 0x776add88, 0x2003a099,
+  0x777125ac, 0x1ff8be65, 0x77776bac, 0x1feddaf6,
+  0x777daf89, 0x1fe2f64c, 0x7783f143, 0x1fd81067,
+  0x778a30d8, 0x1fcd2948, 0x77906e49, 0x1fc240ef,
+  0x7796a996, 0x1fb7575c, 0x779ce2be, 0x1fac6c91,
+  0x77a319c2, 0x1fa1808c, 0x77a94ea0, 0x1f969350,
+  0x77af8159, 0x1f8ba4dc, 0x77b5b1ec, 0x1f80b531,
+  0x77bbe05a, 0x1f75c44e, 0x77c20ca1, 0x1f6ad235,
+  0x77c836c2, 0x1f5fdee6, 0x77ce5ebd, 0x1f54ea62,
+  0x77d48490, 0x1f49f4a8, 0x77daa83d, 0x1f3efdb9,
+  0x77e0c9c3, 0x1f340596, 0x77e6e921, 0x1f290c3f,
+  0x77ed0657, 0x1f1e11b5, 0x77f32165, 0x1f1315f7,
+  0x77f93a4b, 0x1f081907, 0x77ff5109, 0x1efd1ae4,
+  0x7805659e, 0x1ef21b90, 0x780b780a, 0x1ee71b0a,
+  0x7811884d, 0x1edc1953, 0x78179666, 0x1ed1166b,
+  0x781da256, 0x1ec61254, 0x7823ac1d, 0x1ebb0d0d,
+  0x7829b3b9, 0x1eb00696, 0x782fb92a, 0x1ea4fef0,
+  0x7835bc71, 0x1e99f61d, 0x783bbd8e, 0x1e8eec1b,
+  0x7841bc7f, 0x1e83e0eb, 0x7847b946, 0x1e78d48e,
+  0x784db3e0, 0x1e6dc705, 0x7853ac4f, 0x1e62b84f,
+  0x7859a292, 0x1e57a86d, 0x785f96a9, 0x1e4c9760,
+  0x78658894, 0x1e418528, 0x786b7852, 0x1e3671c5,
+  0x787165e3, 0x1e2b5d38, 0x78775147, 0x1e204781,
+  0x787d3a7e, 0x1e1530a1, 0x78832187, 0x1e0a1898,
+  0x78890663, 0x1dfeff67, 0x788ee910, 0x1df3e50d,
+  0x7894c98f, 0x1de8c98c, 0x789aa7e0, 0x1dddace4,
+  0x78a08402, 0x1dd28f15, 0x78a65df6, 0x1dc7701f,
+  0x78ac35ba, 0x1dbc5004, 0x78b20b4f, 0x1db12ec3,
+  0x78b7deb4, 0x1da60c5d, 0x78bdafea, 0x1d9ae8d2,
+  0x78c37eef, 0x1d8fc424, 0x78c94bc4, 0x1d849e51,
+  0x78cf1669, 0x1d79775c, 0x78d4dedd, 0x1d6e4f43,
+  0x78daa520, 0x1d632608, 0x78e06932, 0x1d57fbaa,
+  0x78e62b13, 0x1d4cd02c, 0x78ebeac2, 0x1d41a38c,
+  0x78f1a840, 0x1d3675cb, 0x78f7638b, 0x1d2b46ea,
+  0x78fd1ca4, 0x1d2016e9, 0x7902d38b, 0x1d14e5c9,
+  0x7908883f, 0x1d09b389, 0x790e3ac0, 0x1cfe802b,
+  0x7913eb0e, 0x1cf34baf, 0x79199929, 0x1ce81615,
+  0x791f4510, 0x1cdcdf5e, 0x7924eec3, 0x1cd1a78a,
+  0x792a9642, 0x1cc66e99, 0x79303b8e, 0x1cbb348d,
+  0x7935dea4, 0x1caff965, 0x793b7f86, 0x1ca4bd21,
+  0x79411e33, 0x1c997fc4, 0x7946baac, 0x1c8e414b,
+  0x794c54ee, 0x1c8301b9, 0x7951ecfc, 0x1c77c10e,
+  0x795782d3, 0x1c6c7f4a, 0x795d1675, 0x1c613c6d,
+  0x7962a7e0, 0x1c55f878, 0x79683715, 0x1c4ab36b,
+  0x796dc414, 0x1c3f6d47, 0x79734edc, 0x1c34260c,
+  0x7978d76c, 0x1c28ddbb, 0x797e5dc6, 0x1c1d9454,
+  0x7983e1e8, 0x1c1249d8, 0x798963d2, 0x1c06fe46,
+  0x798ee385, 0x1bfbb1a0, 0x799460ff, 0x1bf063e6,
+  0x7999dc42, 0x1be51518, 0x799f554b, 0x1bd9c537,
+  0x79a4cc1c, 0x1bce7442, 0x79aa40b4, 0x1bc3223c,
+  0x79afb313, 0x1bb7cf23, 0x79b52339, 0x1bac7af9,
+  0x79ba9125, 0x1ba125bd, 0x79bffcd7, 0x1b95cf71,
+  0x79c5664f, 0x1b8a7815, 0x79cacd8d, 0x1b7f1fa9,
+  0x79d03291, 0x1b73c62d, 0x79d5955a, 0x1b686ba3,
+  0x79daf5e8, 0x1b5d100a, 0x79e0543c, 0x1b51b363,
+  0x79e5b054, 0x1b4655ae, 0x79eb0a31, 0x1b3af6ec,
+  0x79f061d2, 0x1b2f971e, 0x79f5b737, 0x1b243643,
+  0x79fb0a60, 0x1b18d45c, 0x7a005b4d, 0x1b0d716a,
+  0x7a05a9fd, 0x1b020d6c, 0x7a0af671, 0x1af6a865,
+  0x7a1040a8, 0x1aeb4253, 0x7a1588a2, 0x1adfdb37,
+  0x7a1ace5f, 0x1ad47312, 0x7a2011de, 0x1ac909e5,
+  0x7a25531f, 0x1abd9faf, 0x7a2a9223, 0x1ab23471,
+  0x7a2fcee8, 0x1aa6c82b, 0x7a350970, 0x1a9b5adf,
+  0x7a3a41b9, 0x1a8fec8c, 0x7a3f77c3, 0x1a847d33,
+  0x7a44ab8e, 0x1a790cd4, 0x7a49dd1a, 0x1a6d9b70,
+  0x7a4f0c67, 0x1a622907, 0x7a543974, 0x1a56b599,
+  0x7a596442, 0x1a4b4128, 0x7a5e8cd0, 0x1a3fcbb3,
+  0x7a63b31d, 0x1a34553b, 0x7a68d72b, 0x1a28ddc0,
+  0x7a6df8f8, 0x1a1d6544, 0x7a731884, 0x1a11ebc5,
+  0x7a7835cf, 0x1a067145, 0x7a7d50da, 0x19faf5c5,
+  0x7a8269a3, 0x19ef7944, 0x7a87802a, 0x19e3fbc3,
+  0x7a8c9470, 0x19d87d42, 0x7a91a674, 0x19ccfdc2,
+  0x7a96b636, 0x19c17d44, 0x7a9bc3b6, 0x19b5fbc8,
+  0x7aa0cef3, 0x19aa794d, 0x7aa5d7ee, 0x199ef5d6,
+  0x7aaadea6, 0x19937161, 0x7aafe31b, 0x1987ebf0,
+  0x7ab4e54c, 0x197c6584, 0x7ab9e53a, 0x1970de1b,
+  0x7abee2e5, 0x196555b8, 0x7ac3de4c, 0x1959cc5a,
+  0x7ac8d76f, 0x194e4201, 0x7acdce4d, 0x1942b6af,
+  0x7ad2c2e8, 0x19372a64, 0x7ad7b53d, 0x192b9d1f,
+  0x7adca54e, 0x19200ee3, 0x7ae1931a, 0x19147fae,
+  0x7ae67ea1, 0x1908ef82, 0x7aeb67e3, 0x18fd5e5f,
+  0x7af04edf, 0x18f1cc45, 0x7af53395, 0x18e63935,
+  0x7afa1605, 0x18daa52f, 0x7afef630, 0x18cf1034,
+  0x7b03d414, 0x18c37a44, 0x7b08afb2, 0x18b7e35f,
+  0x7b0d8909, 0x18ac4b87, 0x7b126019, 0x18a0b2bb,
+  0x7b1734e2, 0x189518fc, 0x7b1c0764, 0x18897e4a,
+  0x7b20d79e, 0x187de2a7, 0x7b25a591, 0x18724611,
+  0x7b2a713d, 0x1866a88a, 0x7b2f3aa0, 0x185b0a13,
+  0x7b3401bb, 0x184f6aab, 0x7b38c68e, 0x1843ca53,
+  0x7b3d8918, 0x1838290c, 0x7b42495a, 0x182c86d5,
+  0x7b470753, 0x1820e3b0, 0x7b4bc303, 0x18153f9d,
+  0x7b507c69, 0x18099a9c, 0x7b553386, 0x17fdf4ae,
+  0x7b59e85a, 0x17f24dd3, 0x7b5e9ae4, 0x17e6a60c,
+  0x7b634b23, 0x17dafd59, 0x7b67f919, 0x17cf53bb,
+  0x7b6ca4c4, 0x17c3a931, 0x7b714e25, 0x17b7fdbd,
+  0x7b75f53c, 0x17ac515f, 0x7b7a9a07, 0x17a0a417,
+  0x7b7f3c87, 0x1794f5e6, 0x7b83dcbc, 0x178946cc,
+  0x7b887aa6, 0x177d96ca, 0x7b8d1644, 0x1771e5e0,
+  0x7b91af97, 0x1766340f, 0x7b96469d, 0x175a8157,
+  0x7b9adb57, 0x174ecdb8, 0x7b9f6dc5, 0x17431933,
+  0x7ba3fde7, 0x173763c9, 0x7ba88bbc, 0x172bad7a,
+  0x7bad1744, 0x171ff646, 0x7bb1a080, 0x17143e2d,
+  0x7bb6276e, 0x17088531, 0x7bbaac0e, 0x16fccb51,
+  0x7bbf2e62, 0x16f1108f, 0x7bc3ae67, 0x16e554ea,
+  0x7bc82c1f, 0x16d99864, 0x7bcca789, 0x16cddafb,
+  0x7bd120a4, 0x16c21cb2, 0x7bd59771, 0x16b65d88,
+  0x7bda0bf0, 0x16aa9d7e, 0x7bde7e20, 0x169edc94,
+  0x7be2ee01, 0x16931acb, 0x7be75b93, 0x16875823,
+  0x7bebc6d5, 0x167b949d, 0x7bf02fc9, 0x166fd039,
+  0x7bf4966c, 0x16640af7, 0x7bf8fac0, 0x165844d8,
+  0x7bfd5cc4, 0x164c7ddd, 0x7c01bc78, 0x1640b606,
+  0x7c0619dc, 0x1634ed53, 0x7c0a74f0, 0x162923c5,
+  0x7c0ecdb2, 0x161d595d, 0x7c132424, 0x16118e1a,
+  0x7c177845, 0x1605c1fd, 0x7c1bca16, 0x15f9f507,
+  0x7c201994, 0x15ee2738, 0x7c2466c2, 0x15e25890,
+  0x7c28b19e, 0x15d68911, 0x7c2cfa28, 0x15cab8ba,
+  0x7c314060, 0x15bee78c, 0x7c358446, 0x15b31587,
+  0x7c39c5da, 0x15a742ac, 0x7c3e051b, 0x159b6efb,
+  0x7c42420a, 0x158f9a76, 0x7c467ca6, 0x1583c51b,
+  0x7c4ab4ef, 0x1577eeec, 0x7c4eeae5, 0x156c17e9,
+  0x7c531e88, 0x15604013, 0x7c574fd8, 0x1554676a,
+  0x7c5b7ed4, 0x15488dee, 0x7c5fab7c, 0x153cb3a0,
+  0x7c63d5d1, 0x1530d881, 0x7c67fdd1, 0x1524fc90,
+  0x7c6c237e, 0x15191fcf, 0x7c7046d6, 0x150d423d,
+  0x7c7467d9, 0x150163dc, 0x7c788688, 0x14f584ac,
+  0x7c7ca2e2, 0x14e9a4ac, 0x7c80bce7, 0x14ddc3de,
+  0x7c84d496, 0x14d1e242, 0x7c88e9f1, 0x14c5ffd9,
+  0x7c8cfcf6, 0x14ba1ca3, 0x7c910da5, 0x14ae38a0,
+  0x7c951bff, 0x14a253d1, 0x7c992803, 0x14966e36,
+  0x7c9d31b0, 0x148a87d1, 0x7ca13908, 0x147ea0a0,
+  0x7ca53e09, 0x1472b8a5, 0x7ca940b3, 0x1466cfe1,
+  0x7cad4107, 0x145ae653, 0x7cb13f04, 0x144efbfc,
+  0x7cb53aaa, 0x144310dd, 0x7cb933f9, 0x143724f5,
+  0x7cbd2af0, 0x142b3846, 0x7cc11f90, 0x141f4ad1,
+  0x7cc511d9, 0x14135c94, 0x7cc901c9, 0x14076d91,
+  0x7cccef62, 0x13fb7dc9, 0x7cd0daa2, 0x13ef8d3c,
+  0x7cd4c38b, 0x13e39be9, 0x7cd8aa1b, 0x13d7a9d3,
+  0x7cdc8e52, 0x13cbb6f8, 0x7ce07031, 0x13bfc35b,
+  0x7ce44fb7, 0x13b3cefa, 0x7ce82ce4, 0x13a7d9d7,
+  0x7cec07b8, 0x139be3f2, 0x7cefe032, 0x138fed4b,
+  0x7cf3b653, 0x1383f5e3, 0x7cf78a1b, 0x1377fdbb,
+  0x7cfb5b89, 0x136c04d2, 0x7cff2a9d, 0x13600b2a,
+  0x7d02f757, 0x135410c3, 0x7d06c1b6, 0x1348159d,
+  0x7d0a89bc, 0x133c19b8, 0x7d0e4f67, 0x13301d16,
+  0x7d1212b7, 0x13241fb6, 0x7d15d3ad, 0x1318219a,
+  0x7d199248, 0x130c22c1, 0x7d1d4e88, 0x1300232c,
+  0x7d21086c, 0x12f422db, 0x7d24bff6, 0x12e821cf,
+  0x7d287523, 0x12dc2009, 0x7d2c27f6, 0x12d01d89,
+  0x7d2fd86c, 0x12c41a4f, 0x7d338687, 0x12b8165b,
+  0x7d373245, 0x12ac11af, 0x7d3adba7, 0x12a00c4b,
+  0x7d3e82ae, 0x1294062f, 0x7d422757, 0x1287ff5b,
+  0x7d45c9a4, 0x127bf7d1, 0x7d496994, 0x126fef90,
+  0x7d4d0728, 0x1263e699, 0x7d50a25e, 0x1257dced,
+  0x7d543b37, 0x124bd28c, 0x7d57d1b3, 0x123fc776,
+  0x7d5b65d2, 0x1233bbac, 0x7d5ef793, 0x1227af2e,
+  0x7d6286f6, 0x121ba1fd, 0x7d6613fb, 0x120f941a,
+  0x7d699ea3, 0x12038584, 0x7d6d26ec, 0x11f7763c,
+  0x7d70acd7, 0x11eb6643, 0x7d743064, 0x11df5599,
+  0x7d77b192, 0x11d3443f, 0x7d7b3061, 0x11c73235,
+  0x7d7eacd2, 0x11bb1f7c, 0x7d8226e4, 0x11af0c13,
+  0x7d859e96, 0x11a2f7fc, 0x7d8913ea, 0x1196e337,
+  0x7d8c86de, 0x118acdc4, 0x7d8ff772, 0x117eb7a4,
+  0x7d9365a8, 0x1172a0d7, 0x7d96d17d, 0x1166895f,
+  0x7d9a3af2, 0x115a713a, 0x7d9da208, 0x114e586a,
+  0x7da106bd, 0x11423ef0, 0x7da46912, 0x113624cb,
+  0x7da7c907, 0x112a09fc, 0x7dab269b, 0x111dee84,
+  0x7dae81cf, 0x1111d263, 0x7db1daa2, 0x1105b599,
+  0x7db53113, 0x10f99827, 0x7db88524, 0x10ed7a0e,
+  0x7dbbd6d4, 0x10e15b4e, 0x7dbf2622, 0x10d53be7,
+  0x7dc2730f, 0x10c91bda, 0x7dc5bd9b, 0x10bcfb28,
+  0x7dc905c5, 0x10b0d9d0, 0x7dcc4b8d, 0x10a4b7d3,
+  0x7dcf8ef3, 0x10989532, 0x7dd2cff7, 0x108c71ee,
+  0x7dd60e99, 0x10804e06, 0x7dd94ad8, 0x1074297b,
+  0x7ddc84b5, 0x1068044e, 0x7ddfbc30, 0x105bde7f,
+  0x7de2f148, 0x104fb80e, 0x7de623fd, 0x104390fd,
+  0x7de9544f, 0x1037694b, 0x7dec823e, 0x102b40f8,
+  0x7defadca, 0x101f1807, 0x7df2d6f3, 0x1012ee76,
+  0x7df5fdb8, 0x1006c446, 0x7df9221a, 0xffa9979,
+  0x7dfc4418, 0xfee6e0d, 0x7dff63b2, 0xfe24205,
+  0x7e0280e9, 0xfd6155f, 0x7e059bbb, 0xfc9e81e,
+  0x7e08b42a, 0xfbdba40, 0x7e0bca34, 0xfb18bc8,
+  0x7e0eddd9, 0xfa55cb4, 0x7e11ef1b, 0xf992d06,
+  0x7e14fdf7, 0xf8cfcbe, 0x7e180a6f, 0xf80cbdc,
+  0x7e1b1482, 0xf749a61, 0x7e1e1c30, 0xf68684e,
+  0x7e212179, 0xf5c35a3, 0x7e24245d, 0xf500260,
+  0x7e2724db, 0xf43ce86, 0x7e2a22f4, 0xf379a16,
+  0x7e2d1ea8, 0xf2b650f, 0x7e3017f6, 0xf1f2f73,
+  0x7e330ede, 0xf12f941, 0x7e360360, 0xf06c27a,
+  0x7e38f57c, 0xefa8b20, 0x7e3be532, 0xeee5331,
+  0x7e3ed282, 0xee21aaf, 0x7e41bd6c, 0xed5e19a,
+  0x7e44a5ef, 0xec9a7f3, 0x7e478c0b, 0xebd6db9,
+  0x7e4a6fc1, 0xeb132ef, 0x7e4d5110, 0xea4f793,
+  0x7e502ff9, 0xe98bba7, 0x7e530c7a, 0xe8c7f2a,
+  0x7e55e694, 0xe80421e, 0x7e58be47, 0xe740483,
+  0x7e5b9392, 0xe67c65a, 0x7e5e6676, 0xe5b87a2,
+  0x7e6136f3, 0xe4f485c, 0x7e640507, 0xe430889,
+  0x7e66d0b4, 0xe36c82a, 0x7e6999fa, 0xe2a873e,
+  0x7e6c60d7, 0xe1e45c6, 0x7e6f254c, 0xe1203c3,
+  0x7e71e759, 0xe05c135, 0x7e74a6fd, 0xdf97e1d,
+  0x7e77643a, 0xded3a7b, 0x7e7a1f0d, 0xde0f64f,
+  0x7e7cd778, 0xdd4b19a, 0x7e7f8d7b, 0xdc86c5d,
+  0x7e824114, 0xdbc2698, 0x7e84f245, 0xdafe04b,
+  0x7e87a10c, 0xda39978, 0x7e8a4d6a, 0xd97521d,
+  0x7e8cf75f, 0xd8b0a3d, 0x7e8f9eeb, 0xd7ec1d6,
+  0x7e92440d, 0xd7278eb, 0x7e94e6c6, 0xd662f7b,
+  0x7e978715, 0xd59e586, 0x7e9a24fb, 0xd4d9b0e,
+  0x7e9cc076, 0xd415013, 0x7e9f5988, 0xd350495,
+  0x7ea1f02f, 0xd28b894, 0x7ea4846c, 0xd1c6c11,
+  0x7ea7163f, 0xd101f0e, 0x7ea9a5a8, 0xd03d189,
+  0x7eac32a6, 0xcf78383, 0x7eaebd3a, 0xceb34fe,
+  0x7eb14563, 0xcdee5f9, 0x7eb3cb21, 0xcd29676,
+  0x7eb64e75, 0xcc64673, 0x7eb8cf5d, 0xcb9f5f3,
+  0x7ebb4ddb, 0xcada4f5, 0x7ebdc9ed, 0xca1537a,
+  0x7ec04394, 0xc950182, 0x7ec2bad0, 0xc88af0e,
+  0x7ec52fa0, 0xc7c5c1e, 0x7ec7a205, 0xc7008b3,
+  0x7eca11fe, 0xc63b4ce, 0x7ecc7f8b, 0xc57606e,
+  0x7eceeaad, 0xc4b0b94, 0x7ed15363, 0xc3eb641,
+  0x7ed3b9ad, 0xc326075, 0x7ed61d8a, 0xc260a31,
+  0x7ed87efc, 0xc19b374, 0x7edade01, 0xc0d5c41,
+  0x7edd3a9a, 0xc010496, 0x7edf94c7, 0xbf4ac75,
+  0x7ee1ec87, 0xbe853de, 0x7ee441da, 0xbdbfad1,
+  0x7ee694c1, 0xbcfa150, 0x7ee8e53a, 0xbc34759,
+  0x7eeb3347, 0xbb6ecef, 0x7eed7ee7, 0xbaa9211,
+  0x7eefc81a, 0xb9e36c0, 0x7ef20ee0, 0xb91dafc,
+  0x7ef45338, 0xb857ec7, 0x7ef69523, 0xb79221f,
+  0x7ef8d4a1, 0xb6cc506, 0x7efb11b1, 0xb60677c,
+  0x7efd4c54, 0xb540982, 0x7eff8489, 0xb47ab19,
+  0x7f01ba50, 0xb3b4c40, 0x7f03eda9, 0xb2eecf8,
+  0x7f061e95, 0xb228d42, 0x7f084d12, 0xb162d1d,
+  0x7f0a7921, 0xb09cc8c, 0x7f0ca2c2, 0xafd6b8d,
+  0x7f0ec9f5, 0xaf10a22, 0x7f10eeb9, 0xae4a84b,
+  0x7f13110f, 0xad84609, 0x7f1530f7, 0xacbe35b,
+  0x7f174e70, 0xabf8043, 0x7f19697a, 0xab31cc1,
+  0x7f1b8215, 0xaa6b8d5, 0x7f1d9842, 0xa9a5480,
+  0x7f1fabff, 0xa8defc3, 0x7f21bd4e, 0xa818a9d,
+  0x7f23cc2e, 0xa752510, 0x7f25d89e, 0xa68bf1b,
+  0x7f27e29f, 0xa5c58c0, 0x7f29ea31, 0xa4ff1fe,
+  0x7f2bef53, 0xa438ad7, 0x7f2df206, 0xa37234a,
+  0x7f2ff24a, 0xa2abb59, 0x7f31f01d, 0xa1e5303,
+  0x7f33eb81, 0xa11ea49, 0x7f35e476, 0xa05812c,
+  0x7f37dafa, 0x9f917ac, 0x7f39cf0e, 0x9ecadc9,
+  0x7f3bc0b3, 0x9e04385, 0x7f3dafe7, 0x9d3d8df,
+  0x7f3f9cab, 0x9c76dd8, 0x7f4186ff, 0x9bb0271,
+  0x7f436ee3, 0x9ae96aa, 0x7f455456, 0x9a22a83,
+  0x7f473759, 0x995bdfd, 0x7f4917eb, 0x9895118,
+  0x7f4af60d, 0x97ce3d5, 0x7f4cd1be, 0x9707635,
+  0x7f4eaafe, 0x9640837, 0x7f5081cd, 0x95799dd,
+  0x7f52562c, 0x94b2b27, 0x7f54281a, 0x93ebc14,
+  0x7f55f796, 0x9324ca7, 0x7f57c4a2, 0x925dcdf,
+  0x7f598f3c, 0x9196cbc, 0x7f5b5765, 0x90cfc40,
+  0x7f5d1d1d, 0x9008b6a, 0x7f5ee063, 0x8f41a3c,
+  0x7f60a138, 0x8e7a8b5, 0x7f625f9b, 0x8db36d6,
+  0x7f641b8d, 0x8cec4a0, 0x7f65d50d, 0x8c25213,
+  0x7f678c1c, 0x8b5df30, 0x7f6940b8, 0x8a96bf6,
+  0x7f6af2e3, 0x89cf867, 0x7f6ca29c, 0x8908483,
+  0x7f6e4fe3, 0x884104b, 0x7f6ffab8, 0x8779bbe,
+  0x7f71a31b, 0x86b26de, 0x7f73490b, 0x85eb1ab,
+  0x7f74ec8a, 0x8523c25, 0x7f768d96, 0x845c64d,
+  0x7f782c30, 0x8395024, 0x7f79c857, 0x82cd9a9,
+  0x7f7b620c, 0x82062de, 0x7f7cf94e, 0x813ebc2,
+  0x7f7e8e1e, 0x8077457, 0x7f80207b, 0x7fafc9c,
+  0x7f81b065, 0x7ee8493, 0x7f833ddd, 0x7e20c3b,
+  0x7f84c8e2, 0x7d59396, 0x7f865174, 0x7c91aa3,
+  0x7f87d792, 0x7bca163, 0x7f895b3e, 0x7b027d7,
+  0x7f8adc77, 0x7a3adff, 0x7f8c5b3d, 0x79733dc,
+  0x7f8dd78f, 0x78ab96e, 0x7f8f516e, 0x77e3eb5,
+  0x7f90c8da, 0x771c3b3, 0x7f923dd2, 0x7654867,
+  0x7f93b058, 0x758ccd2, 0x7f952069, 0x74c50f4,
+  0x7f968e07, 0x73fd4cf, 0x7f97f932, 0x7335862,
+  0x7f9961e8, 0x726dbae, 0x7f9ac82c, 0x71a5eb3,
+  0x7f9c2bfb, 0x70de172, 0x7f9d8d56, 0x70163eb,
+  0x7f9eec3e, 0x6f4e620, 0x7fa048b2, 0x6e86810,
+  0x7fa1a2b2, 0x6dbe9bb, 0x7fa2fa3d, 0x6cf6b23,
+  0x7fa44f55, 0x6c2ec48, 0x7fa5a1f9, 0x6b66d29,
+  0x7fa6f228, 0x6a9edc9, 0x7fa83fe3, 0x69d6e27,
+  0x7fa98b2a, 0x690ee44, 0x7faad3fd, 0x6846e1f,
+  0x7fac1a5b, 0x677edbb, 0x7fad5e45, 0x66b6d16,
+  0x7fae9fbb, 0x65eec33, 0x7fafdebb, 0x6526b10,
+  0x7fb11b48, 0x645e9af, 0x7fb2555f, 0x6396810,
+  0x7fb38d02, 0x62ce634, 0x7fb4c231, 0x620641a,
+  0x7fb5f4ea, 0x613e1c5, 0x7fb7252f, 0x6075f33,
+  0x7fb852ff, 0x5fadc66, 0x7fb97e5a, 0x5ee595d,
+  0x7fbaa740, 0x5e1d61b, 0x7fbbcdb1, 0x5d5529e,
+  0x7fbcf1ad, 0x5c8cee7, 0x7fbe1334, 0x5bc4af8,
+  0x7fbf3246, 0x5afc6d0, 0x7fc04ee3, 0x5a3426f,
+  0x7fc1690a, 0x596bdd7, 0x7fc280bc, 0x58a3908,
+  0x7fc395f9, 0x57db403, 0x7fc4a8c1, 0x5712ec7,
+  0x7fc5b913, 0x564a955, 0x7fc6c6f0, 0x55823ae,
+  0x7fc7d258, 0x54b9dd3, 0x7fc8db4a, 0x53f17c3,
+  0x7fc9e1c6, 0x532917f, 0x7fcae5cd, 0x5260b08,
+  0x7fcbe75e, 0x519845e, 0x7fcce67a, 0x50cfd82,
+  0x7fcde320, 0x5007674, 0x7fcedd50, 0x4f3ef35,
+  0x7fcfd50b, 0x4e767c5, 0x7fd0ca4f, 0x4dae024,
+  0x7fd1bd1e, 0x4ce5854, 0x7fd2ad77, 0x4c1d054,
+  0x7fd39b5a, 0x4b54825, 0x7fd486c7, 0x4a8bfc7,
+  0x7fd56fbe, 0x49c373c, 0x7fd6563f, 0x48fae83,
+  0x7fd73a4a, 0x483259d, 0x7fd81bdf, 0x4769c8b,
+  0x7fd8fafe, 0x46a134c, 0x7fd9d7a7, 0x45d89e2,
+  0x7fdab1d9, 0x451004d, 0x7fdb8996, 0x444768d,
+  0x7fdc5edc, 0x437eca4, 0x7fdd31ac, 0x42b6290,
+  0x7fde0205, 0x41ed854, 0x7fdecfe8, 0x4124dee,
+  0x7fdf9b55, 0x405c361, 0x7fe0644b, 0x3f938ac,
+  0x7fe12acb, 0x3ecadcf, 0x7fe1eed5, 0x3e022cc,
+  0x7fe2b067, 0x3d397a3, 0x7fe36f84, 0x3c70c54,
+  0x7fe42c2a, 0x3ba80df, 0x7fe4e659, 0x3adf546,
+  0x7fe59e12, 0x3a16988, 0x7fe65354, 0x394dda7,
+  0x7fe7061f, 0x38851a2, 0x7fe7b674, 0x37bc57b,
+  0x7fe86452, 0x36f3931, 0x7fe90fb9, 0x362acc5,
+  0x7fe9b8a9, 0x3562038, 0x7fea5f23, 0x3499389,
+  0x7feb0326, 0x33d06bb, 0x7feba4b2, 0x33079cc,
+  0x7fec43c7, 0x323ecbe, 0x7fece065, 0x3175f91,
+  0x7fed7a8c, 0x30ad245, 0x7fee123d, 0x2fe44dc,
+  0x7feea776, 0x2f1b755, 0x7fef3a39, 0x2e529b0,
+  0x7fefca84, 0x2d89bf0, 0x7ff05858, 0x2cc0e13,
+  0x7ff0e3b6, 0x2bf801a, 0x7ff16c9c, 0x2b2f207,
+  0x7ff1f30b, 0x2a663d8, 0x7ff27703, 0x299d590,
+  0x7ff2f884, 0x28d472e, 0x7ff3778e, 0x280b8b3,
+  0x7ff3f420, 0x2742a1f, 0x7ff46e3c, 0x2679b73,
+  0x7ff4e5e0, 0x25b0caf, 0x7ff55b0d, 0x24e7dd4,
+  0x7ff5cdc3, 0x241eee2, 0x7ff63e01, 0x2355fd9,
+  0x7ff6abc8, 0x228d0bb, 0x7ff71718, 0x21c4188,
+  0x7ff77ff1, 0x20fb240, 0x7ff7e652, 0x20322e3,
+  0x7ff84a3c, 0x1f69373, 0x7ff8abae, 0x1ea03ef,
+  0x7ff90aaa, 0x1dd7459, 0x7ff9672d, 0x1d0e4b0,
+  0x7ff9c13a, 0x1c454f5, 0x7ffa18cf, 0x1b7c528,
+  0x7ffa6dec, 0x1ab354b, 0x7ffac092, 0x19ea55d,
+  0x7ffb10c1, 0x192155f, 0x7ffb5e78, 0x1858552,
+  0x7ffba9b8, 0x178f536, 0x7ffbf280, 0x16c650b,
+  0x7ffc38d1, 0x15fd4d2, 0x7ffc7caa, 0x153448c,
+  0x7ffcbe0c, 0x146b438, 0x7ffcfcf6, 0x13a23d8,
+  0x7ffd3969, 0x12d936c, 0x7ffd7364, 0x12102f4,
+  0x7ffdaae7, 0x1147271, 0x7ffddff3, 0x107e1e3,
+  0x7ffe1288, 0xfb514b, 0x7ffe42a4, 0xeec0aa,
+  0x7ffe704a, 0xe22fff, 0x7ffe9b77, 0xd59f4c,
+  0x7ffec42d, 0xc90e90, 0x7ffeea6c, 0xbc7dcc,
+  0x7fff0e32, 0xafed02, 0x7fff2f82, 0xa35c30,
+  0x7fff4e59, 0x96cb58, 0x7fff6ab9, 0x8a3a7b,
+  0x7fff84a1, 0x7da998, 0x7fff9c12, 0x7118b0,
+  0x7fffb10b, 0x6487c4, 0x7fffc38c, 0x57f6d4,
+  0x7fffd396, 0x4b65e1, 0x7fffe128, 0x3ed4ea,
+  0x7fffec43, 0x3243f1, 0x7ffff4e6, 0x25b2f7,
+  0x7ffffb11, 0x1921fb, 0x7ffffec4, 0xc90fe,
+  0x7fffffff, 0x0, 0x7ffffec4, 0xfff36f02,
+  0x7ffffb11, 0xffe6de05, 0x7ffff4e6, 0xffda4d09,
+  0x7fffec43, 0xffcdbc0f, 0x7fffe128, 0xffc12b16,
+  0x7fffd396, 0xffb49a1f, 0x7fffc38c, 0xffa8092c,
+  0x7fffb10b, 0xff9b783c, 0x7fff9c12, 0xff8ee750,
+  0x7fff84a1, 0xff825668, 0x7fff6ab9, 0xff75c585,
+  0x7fff4e59, 0xff6934a8, 0x7fff2f82, 0xff5ca3d0,
+  0x7fff0e32, 0xff5012fe, 0x7ffeea6c, 0xff438234,
+  0x7ffec42d, 0xff36f170, 0x7ffe9b77, 0xff2a60b4,
+  0x7ffe704a, 0xff1dd001, 0x7ffe42a4, 0xff113f56,
+  0x7ffe1288, 0xff04aeb5, 0x7ffddff3, 0xfef81e1d,
+  0x7ffdaae7, 0xfeeb8d8f, 0x7ffd7364, 0xfedefd0c,
+  0x7ffd3969, 0xfed26c94, 0x7ffcfcf6, 0xfec5dc28,
+  0x7ffcbe0c, 0xfeb94bc8, 0x7ffc7caa, 0xfeacbb74,
+  0x7ffc38d1, 0xfea02b2e, 0x7ffbf280, 0xfe939af5,
+  0x7ffba9b8, 0xfe870aca, 0x7ffb5e78, 0xfe7a7aae,
+  0x7ffb10c1, 0xfe6deaa1, 0x7ffac092, 0xfe615aa3,
+  0x7ffa6dec, 0xfe54cab5, 0x7ffa18cf, 0xfe483ad8,
+  0x7ff9c13a, 0xfe3bab0b, 0x7ff9672d, 0xfe2f1b50,
+  0x7ff90aaa, 0xfe228ba7, 0x7ff8abae, 0xfe15fc11,
+  0x7ff84a3c, 0xfe096c8d, 0x7ff7e652, 0xfdfcdd1d,
+  0x7ff77ff1, 0xfdf04dc0, 0x7ff71718, 0xfde3be78,
+  0x7ff6abc8, 0xfdd72f45, 0x7ff63e01, 0xfdcaa027,
+  0x7ff5cdc3, 0xfdbe111e, 0x7ff55b0d, 0xfdb1822c,
+  0x7ff4e5e0, 0xfda4f351, 0x7ff46e3c, 0xfd98648d,
+  0x7ff3f420, 0xfd8bd5e1, 0x7ff3778e, 0xfd7f474d,
+  0x7ff2f884, 0xfd72b8d2, 0x7ff27703, 0xfd662a70,
+  0x7ff1f30b, 0xfd599c28, 0x7ff16c9c, 0xfd4d0df9,
+  0x7ff0e3b6, 0xfd407fe6, 0x7ff05858, 0xfd33f1ed,
+  0x7fefca84, 0xfd276410, 0x7fef3a39, 0xfd1ad650,
+  0x7feea776, 0xfd0e48ab, 0x7fee123d, 0xfd01bb24,
+  0x7fed7a8c, 0xfcf52dbb, 0x7fece065, 0xfce8a06f,
+  0x7fec43c7, 0xfcdc1342, 0x7feba4b2, 0xfccf8634,
+  0x7feb0326, 0xfcc2f945, 0x7fea5f23, 0xfcb66c77,
+  0x7fe9b8a9, 0xfca9dfc8, 0x7fe90fb9, 0xfc9d533b,
+  0x7fe86452, 0xfc90c6cf, 0x7fe7b674, 0xfc843a85,
+  0x7fe7061f, 0xfc77ae5e, 0x7fe65354, 0xfc6b2259,
+  0x7fe59e12, 0xfc5e9678, 0x7fe4e659, 0xfc520aba,
+  0x7fe42c2a, 0xfc457f21, 0x7fe36f84, 0xfc38f3ac,
+  0x7fe2b067, 0xfc2c685d, 0x7fe1eed5, 0xfc1fdd34,
+  0x7fe12acb, 0xfc135231, 0x7fe0644b, 0xfc06c754,
+  0x7fdf9b55, 0xfbfa3c9f, 0x7fdecfe8, 0xfbedb212,
+  0x7fde0205, 0xfbe127ac, 0x7fdd31ac, 0xfbd49d70,
+  0x7fdc5edc, 0xfbc8135c, 0x7fdb8996, 0xfbbb8973,
+  0x7fdab1d9, 0xfbaeffb3, 0x7fd9d7a7, 0xfba2761e,
+  0x7fd8fafe, 0xfb95ecb4, 0x7fd81bdf, 0xfb896375,
+  0x7fd73a4a, 0xfb7cda63, 0x7fd6563f, 0xfb70517d,
+  0x7fd56fbe, 0xfb63c8c4, 0x7fd486c7, 0xfb574039,
+  0x7fd39b5a, 0xfb4ab7db, 0x7fd2ad77, 0xfb3e2fac,
+  0x7fd1bd1e, 0xfb31a7ac, 0x7fd0ca4f, 0xfb251fdc,
+  0x7fcfd50b, 0xfb18983b, 0x7fcedd50, 0xfb0c10cb,
+  0x7fcde320, 0xfaff898c, 0x7fcce67a, 0xfaf3027e,
+  0x7fcbe75e, 0xfae67ba2, 0x7fcae5cd, 0xfad9f4f8,
+  0x7fc9e1c6, 0xfacd6e81, 0x7fc8db4a, 0xfac0e83d,
+  0x7fc7d258, 0xfab4622d, 0x7fc6c6f0, 0xfaa7dc52,
+  0x7fc5b913, 0xfa9b56ab, 0x7fc4a8c1, 0xfa8ed139,
+  0x7fc395f9, 0xfa824bfd, 0x7fc280bc, 0xfa75c6f8,
+  0x7fc1690a, 0xfa694229, 0x7fc04ee3, 0xfa5cbd91,
+  0x7fbf3246, 0xfa503930, 0x7fbe1334, 0xfa43b508,
+  0x7fbcf1ad, 0xfa373119, 0x7fbbcdb1, 0xfa2aad62,
+  0x7fbaa740, 0xfa1e29e5, 0x7fb97e5a, 0xfa11a6a3,
+  0x7fb852ff, 0xfa05239a, 0x7fb7252f, 0xf9f8a0cd,
+  0x7fb5f4ea, 0xf9ec1e3b, 0x7fb4c231, 0xf9df9be6,
+  0x7fb38d02, 0xf9d319cc, 0x7fb2555f, 0xf9c697f0,
+  0x7fb11b48, 0xf9ba1651, 0x7fafdebb, 0xf9ad94f0,
+  0x7fae9fbb, 0xf9a113cd, 0x7fad5e45, 0xf99492ea,
+  0x7fac1a5b, 0xf9881245, 0x7faad3fd, 0xf97b91e1,
+  0x7fa98b2a, 0xf96f11bc, 0x7fa83fe3, 0xf96291d9,
+  0x7fa6f228, 0xf9561237, 0x7fa5a1f9, 0xf94992d7,
+  0x7fa44f55, 0xf93d13b8, 0x7fa2fa3d, 0xf93094dd,
+  0x7fa1a2b2, 0xf9241645, 0x7fa048b2, 0xf91797f0,
+  0x7f9eec3e, 0xf90b19e0, 0x7f9d8d56, 0xf8fe9c15,
+  0x7f9c2bfb, 0xf8f21e8e, 0x7f9ac82c, 0xf8e5a14d,
+  0x7f9961e8, 0xf8d92452, 0x7f97f932, 0xf8cca79e,
+  0x7f968e07, 0xf8c02b31, 0x7f952069, 0xf8b3af0c,
+  0x7f93b058, 0xf8a7332e, 0x7f923dd2, 0xf89ab799,
+  0x7f90c8da, 0xf88e3c4d, 0x7f8f516e, 0xf881c14b,
+  0x7f8dd78f, 0xf8754692, 0x7f8c5b3d, 0xf868cc24,
+  0x7f8adc77, 0xf85c5201, 0x7f895b3e, 0xf84fd829,
+  0x7f87d792, 0xf8435e9d, 0x7f865174, 0xf836e55d,
+  0x7f84c8e2, 0xf82a6c6a, 0x7f833ddd, 0xf81df3c5,
+  0x7f81b065, 0xf8117b6d, 0x7f80207b, 0xf8050364,
+  0x7f7e8e1e, 0xf7f88ba9, 0x7f7cf94e, 0xf7ec143e,
+  0x7f7b620c, 0xf7df9d22, 0x7f79c857, 0xf7d32657,
+  0x7f782c30, 0xf7c6afdc, 0x7f768d96, 0xf7ba39b3,
+  0x7f74ec8a, 0xf7adc3db, 0x7f73490b, 0xf7a14e55,
+  0x7f71a31b, 0xf794d922, 0x7f6ffab8, 0xf7886442,
+  0x7f6e4fe3, 0xf77befb5, 0x7f6ca29c, 0xf76f7b7d,
+  0x7f6af2e3, 0xf7630799, 0x7f6940b8, 0xf756940a,
+  0x7f678c1c, 0xf74a20d0, 0x7f65d50d, 0xf73daded,
+  0x7f641b8d, 0xf7313b60, 0x7f625f9b, 0xf724c92a,
+  0x7f60a138, 0xf718574b, 0x7f5ee063, 0xf70be5c4,
+  0x7f5d1d1d, 0xf6ff7496, 0x7f5b5765, 0xf6f303c0,
+  0x7f598f3c, 0xf6e69344, 0x7f57c4a2, 0xf6da2321,
+  0x7f55f796, 0xf6cdb359, 0x7f54281a, 0xf6c143ec,
+  0x7f52562c, 0xf6b4d4d9, 0x7f5081cd, 0xf6a86623,
+  0x7f4eaafe, 0xf69bf7c9, 0x7f4cd1be, 0xf68f89cb,
+  0x7f4af60d, 0xf6831c2b, 0x7f4917eb, 0xf676aee8,
+  0x7f473759, 0xf66a4203, 0x7f455456, 0xf65dd57d,
+  0x7f436ee3, 0xf6516956, 0x7f4186ff, 0xf644fd8f,
+  0x7f3f9cab, 0xf6389228, 0x7f3dafe7, 0xf62c2721,
+  0x7f3bc0b3, 0xf61fbc7b, 0x7f39cf0e, 0xf6135237,
+  0x7f37dafa, 0xf606e854, 0x7f35e476, 0xf5fa7ed4,
+  0x7f33eb81, 0xf5ee15b7, 0x7f31f01d, 0xf5e1acfd,
+  0x7f2ff24a, 0xf5d544a7, 0x7f2df206, 0xf5c8dcb6,
+  0x7f2bef53, 0xf5bc7529, 0x7f29ea31, 0xf5b00e02,
+  0x7f27e29f, 0xf5a3a740, 0x7f25d89e, 0xf59740e5,
+  0x7f23cc2e, 0xf58adaf0, 0x7f21bd4e, 0xf57e7563,
+  0x7f1fabff, 0xf572103d, 0x7f1d9842, 0xf565ab80,
+  0x7f1b8215, 0xf559472b, 0x7f19697a, 0xf54ce33f,
+  0x7f174e70, 0xf5407fbd, 0x7f1530f7, 0xf5341ca5,
+  0x7f13110f, 0xf527b9f7, 0x7f10eeb9, 0xf51b57b5,
+  0x7f0ec9f5, 0xf50ef5de, 0x7f0ca2c2, 0xf5029473,
+  0x7f0a7921, 0xf4f63374, 0x7f084d12, 0xf4e9d2e3,
+  0x7f061e95, 0xf4dd72be, 0x7f03eda9, 0xf4d11308,
+  0x7f01ba50, 0xf4c4b3c0, 0x7eff8489, 0xf4b854e7,
+  0x7efd4c54, 0xf4abf67e, 0x7efb11b1, 0xf49f9884,
+  0x7ef8d4a1, 0xf4933afa, 0x7ef69523, 0xf486dde1,
+  0x7ef45338, 0xf47a8139, 0x7ef20ee0, 0xf46e2504,
+  0x7eefc81a, 0xf461c940, 0x7eed7ee7, 0xf4556def,
+  0x7eeb3347, 0xf4491311, 0x7ee8e53a, 0xf43cb8a7,
+  0x7ee694c1, 0xf4305eb0, 0x7ee441da, 0xf424052f,
+  0x7ee1ec87, 0xf417ac22, 0x7edf94c7, 0xf40b538b,
+  0x7edd3a9a, 0xf3fefb6a, 0x7edade01, 0xf3f2a3bf,
+  0x7ed87efc, 0xf3e64c8c, 0x7ed61d8a, 0xf3d9f5cf,
+  0x7ed3b9ad, 0xf3cd9f8b, 0x7ed15363, 0xf3c149bf,
+  0x7eceeaad, 0xf3b4f46c, 0x7ecc7f8b, 0xf3a89f92,
+  0x7eca11fe, 0xf39c4b32, 0x7ec7a205, 0xf38ff74d,
+  0x7ec52fa0, 0xf383a3e2, 0x7ec2bad0, 0xf37750f2,
+  0x7ec04394, 0xf36afe7e, 0x7ebdc9ed, 0xf35eac86,
+  0x7ebb4ddb, 0xf3525b0b, 0x7eb8cf5d, 0xf3460a0d,
+  0x7eb64e75, 0xf339b98d, 0x7eb3cb21, 0xf32d698a,
+  0x7eb14563, 0xf3211a07, 0x7eaebd3a, 0xf314cb02,
+  0x7eac32a6, 0xf3087c7d, 0x7ea9a5a8, 0xf2fc2e77,
+  0x7ea7163f, 0xf2efe0f2, 0x7ea4846c, 0xf2e393ef,
+  0x7ea1f02f, 0xf2d7476c, 0x7e9f5988, 0xf2cafb6b,
+  0x7e9cc076, 0xf2beafed, 0x7e9a24fb, 0xf2b264f2,
+  0x7e978715, 0xf2a61a7a, 0x7e94e6c6, 0xf299d085,
+  0x7e92440d, 0xf28d8715, 0x7e8f9eeb, 0xf2813e2a,
+  0x7e8cf75f, 0xf274f5c3, 0x7e8a4d6a, 0xf268ade3,
+  0x7e87a10c, 0xf25c6688, 0x7e84f245, 0xf2501fb5,
+  0x7e824114, 0xf243d968, 0x7e7f8d7b, 0xf23793a3,
+  0x7e7cd778, 0xf22b4e66, 0x7e7a1f0d, 0xf21f09b1,
+  0x7e77643a, 0xf212c585, 0x7e74a6fd, 0xf20681e3,
+  0x7e71e759, 0xf1fa3ecb, 0x7e6f254c, 0xf1edfc3d,
+  0x7e6c60d7, 0xf1e1ba3a, 0x7e6999fa, 0xf1d578c2,
+  0x7e66d0b4, 0xf1c937d6, 0x7e640507, 0xf1bcf777,
+  0x7e6136f3, 0xf1b0b7a4, 0x7e5e6676, 0xf1a4785e,
+  0x7e5b9392, 0xf19839a6, 0x7e58be47, 0xf18bfb7d,
+  0x7e55e694, 0xf17fbde2, 0x7e530c7a, 0xf17380d6,
+  0x7e502ff9, 0xf1674459, 0x7e4d5110, 0xf15b086d,
+  0x7e4a6fc1, 0xf14ecd11, 0x7e478c0b, 0xf1429247,
+  0x7e44a5ef, 0xf136580d, 0x7e41bd6c, 0xf12a1e66,
+  0x7e3ed282, 0xf11de551, 0x7e3be532, 0xf111accf,
+  0x7e38f57c, 0xf10574e0, 0x7e360360, 0xf0f93d86,
+  0x7e330ede, 0xf0ed06bf, 0x7e3017f6, 0xf0e0d08d,
+  0x7e2d1ea8, 0xf0d49af1, 0x7e2a22f4, 0xf0c865ea,
+  0x7e2724db, 0xf0bc317a, 0x7e24245d, 0xf0affda0,
+  0x7e212179, 0xf0a3ca5d, 0x7e1e1c30, 0xf09797b2,
+  0x7e1b1482, 0xf08b659f, 0x7e180a6f, 0xf07f3424,
+  0x7e14fdf7, 0xf0730342, 0x7e11ef1b, 0xf066d2fa,
+  0x7e0eddd9, 0xf05aa34c, 0x7e0bca34, 0xf04e7438,
+  0x7e08b42a, 0xf04245c0, 0x7e059bbb, 0xf03617e2,
+  0x7e0280e9, 0xf029eaa1, 0x7dff63b2, 0xf01dbdfb,
+  0x7dfc4418, 0xf01191f3, 0x7df9221a, 0xf0056687,
+  0x7df5fdb8, 0xeff93bba, 0x7df2d6f3, 0xefed118a,
+  0x7defadca, 0xefe0e7f9, 0x7dec823e, 0xefd4bf08,
+  0x7de9544f, 0xefc896b5, 0x7de623fd, 0xefbc6f03,
+  0x7de2f148, 0xefb047f2, 0x7ddfbc30, 0xefa42181,
+  0x7ddc84b5, 0xef97fbb2, 0x7dd94ad8, 0xef8bd685,
+  0x7dd60e99, 0xef7fb1fa, 0x7dd2cff7, 0xef738e12,
+  0x7dcf8ef3, 0xef676ace, 0x7dcc4b8d, 0xef5b482d,
+  0x7dc905c5, 0xef4f2630, 0x7dc5bd9b, 0xef4304d8,
+  0x7dc2730f, 0xef36e426, 0x7dbf2622, 0xef2ac419,
+  0x7dbbd6d4, 0xef1ea4b2, 0x7db88524, 0xef1285f2,
+  0x7db53113, 0xef0667d9, 0x7db1daa2, 0xeefa4a67,
+  0x7dae81cf, 0xeeee2d9d, 0x7dab269b, 0xeee2117c,
+  0x7da7c907, 0xeed5f604, 0x7da46912, 0xeec9db35,
+  0x7da106bd, 0xeebdc110, 0x7d9da208, 0xeeb1a796,
+  0x7d9a3af2, 0xeea58ec6, 0x7d96d17d, 0xee9976a1,
+  0x7d9365a8, 0xee8d5f29, 0x7d8ff772, 0xee81485c,
+  0x7d8c86de, 0xee75323c, 0x7d8913ea, 0xee691cc9,
+  0x7d859e96, 0xee5d0804, 0x7d8226e4, 0xee50f3ed,
+  0x7d7eacd2, 0xee44e084, 0x7d7b3061, 0xee38cdcb,
+  0x7d77b192, 0xee2cbbc1, 0x7d743064, 0xee20aa67,
+  0x7d70acd7, 0xee1499bd, 0x7d6d26ec, 0xee0889c4,
+  0x7d699ea3, 0xedfc7a7c, 0x7d6613fb, 0xedf06be6,
+  0x7d6286f6, 0xede45e03, 0x7d5ef793, 0xedd850d2,
+  0x7d5b65d2, 0xedcc4454, 0x7d57d1b3, 0xedc0388a,
+  0x7d543b37, 0xedb42d74, 0x7d50a25e, 0xeda82313,
+  0x7d4d0728, 0xed9c1967, 0x7d496994, 0xed901070,
+  0x7d45c9a4, 0xed84082f, 0x7d422757, 0xed7800a5,
+  0x7d3e82ae, 0xed6bf9d1, 0x7d3adba7, 0xed5ff3b5,
+  0x7d373245, 0xed53ee51, 0x7d338687, 0xed47e9a5,
+  0x7d2fd86c, 0xed3be5b1, 0x7d2c27f6, 0xed2fe277,
+  0x7d287523, 0xed23dff7, 0x7d24bff6, 0xed17de31,
+  0x7d21086c, 0xed0bdd25, 0x7d1d4e88, 0xecffdcd4,
+  0x7d199248, 0xecf3dd3f, 0x7d15d3ad, 0xece7de66,
+  0x7d1212b7, 0xecdbe04a, 0x7d0e4f67, 0xeccfe2ea,
+  0x7d0a89bc, 0xecc3e648, 0x7d06c1b6, 0xecb7ea63,
+  0x7d02f757, 0xecabef3d, 0x7cff2a9d, 0xec9ff4d6,
+  0x7cfb5b89, 0xec93fb2e, 0x7cf78a1b, 0xec880245,
+  0x7cf3b653, 0xec7c0a1d, 0x7cefe032, 0xec7012b5,
+  0x7cec07b8, 0xec641c0e, 0x7ce82ce4, 0xec582629,
+  0x7ce44fb7, 0xec4c3106, 0x7ce07031, 0xec403ca5,
+  0x7cdc8e52, 0xec344908, 0x7cd8aa1b, 0xec28562d,
+  0x7cd4c38b, 0xec1c6417, 0x7cd0daa2, 0xec1072c4,
+  0x7cccef62, 0xec048237, 0x7cc901c9, 0xebf8926f,
+  0x7cc511d9, 0xebeca36c, 0x7cc11f90, 0xebe0b52f,
+  0x7cbd2af0, 0xebd4c7ba, 0x7cb933f9, 0xebc8db0b,
+  0x7cb53aaa, 0xebbcef23, 0x7cb13f04, 0xebb10404,
+  0x7cad4107, 0xeba519ad, 0x7ca940b3, 0xeb99301f,
+  0x7ca53e09, 0xeb8d475b, 0x7ca13908, 0xeb815f60,
+  0x7c9d31b0, 0xeb75782f, 0x7c992803, 0xeb6991ca,
+  0x7c951bff, 0xeb5dac2f, 0x7c910da5, 0xeb51c760,
+  0x7c8cfcf6, 0xeb45e35d, 0x7c88e9f1, 0xeb3a0027,
+  0x7c84d496, 0xeb2e1dbe, 0x7c80bce7, 0xeb223c22,
+  0x7c7ca2e2, 0xeb165b54, 0x7c788688, 0xeb0a7b54,
+  0x7c7467d9, 0xeafe9c24, 0x7c7046d6, 0xeaf2bdc3,
+  0x7c6c237e, 0xeae6e031, 0x7c67fdd1, 0xeadb0370,
+  0x7c63d5d1, 0xeacf277f, 0x7c5fab7c, 0xeac34c60,
+  0x7c5b7ed4, 0xeab77212, 0x7c574fd8, 0xeaab9896,
+  0x7c531e88, 0xea9fbfed, 0x7c4eeae5, 0xea93e817,
+  0x7c4ab4ef, 0xea881114, 0x7c467ca6, 0xea7c3ae5,
+  0x7c42420a, 0xea70658a, 0x7c3e051b, 0xea649105,
+  0x7c39c5da, 0xea58bd54, 0x7c358446, 0xea4cea79,
+  0x7c314060, 0xea411874, 0x7c2cfa28, 0xea354746,
+  0x7c28b19e, 0xea2976ef, 0x7c2466c2, 0xea1da770,
+  0x7c201994, 0xea11d8c8, 0x7c1bca16, 0xea060af9,
+  0x7c177845, 0xe9fa3e03, 0x7c132424, 0xe9ee71e6,
+  0x7c0ecdb2, 0xe9e2a6a3, 0x7c0a74f0, 0xe9d6dc3b,
+  0x7c0619dc, 0xe9cb12ad, 0x7c01bc78, 0xe9bf49fa,
+  0x7bfd5cc4, 0xe9b38223, 0x7bf8fac0, 0xe9a7bb28,
+  0x7bf4966c, 0xe99bf509, 0x7bf02fc9, 0xe9902fc7,
+  0x7bebc6d5, 0xe9846b63, 0x7be75b93, 0xe978a7dd,
+  0x7be2ee01, 0xe96ce535, 0x7bde7e20, 0xe961236c,
+  0x7bda0bf0, 0xe9556282, 0x7bd59771, 0xe949a278,
+  0x7bd120a4, 0xe93de34e, 0x7bcca789, 0xe9322505,
+  0x7bc82c1f, 0xe926679c, 0x7bc3ae67, 0xe91aab16,
+  0x7bbf2e62, 0xe90eef71, 0x7bbaac0e, 0xe90334af,
+  0x7bb6276e, 0xe8f77acf, 0x7bb1a080, 0xe8ebc1d3,
+  0x7bad1744, 0xe8e009ba, 0x7ba88bbc, 0xe8d45286,
+  0x7ba3fde7, 0xe8c89c37, 0x7b9f6dc5, 0xe8bce6cd,
+  0x7b9adb57, 0xe8b13248, 0x7b96469d, 0xe8a57ea9,
+  0x7b91af97, 0xe899cbf1, 0x7b8d1644, 0xe88e1a20,
+  0x7b887aa6, 0xe8826936, 0x7b83dcbc, 0xe876b934,
+  0x7b7f3c87, 0xe86b0a1a, 0x7b7a9a07, 0xe85f5be9,
+  0x7b75f53c, 0xe853aea1, 0x7b714e25, 0xe8480243,
+  0x7b6ca4c4, 0xe83c56cf, 0x7b67f919, 0xe830ac45,
+  0x7b634b23, 0xe82502a7, 0x7b5e9ae4, 0xe81959f4,
+  0x7b59e85a, 0xe80db22d, 0x7b553386, 0xe8020b52,
+  0x7b507c69, 0xe7f66564, 0x7b4bc303, 0xe7eac063,
+  0x7b470753, 0xe7df1c50, 0x7b42495a, 0xe7d3792b,
+  0x7b3d8918, 0xe7c7d6f4, 0x7b38c68e, 0xe7bc35ad,
+  0x7b3401bb, 0xe7b09555, 0x7b2f3aa0, 0xe7a4f5ed,
+  0x7b2a713d, 0xe7995776, 0x7b25a591, 0xe78db9ef,
+  0x7b20d79e, 0xe7821d59, 0x7b1c0764, 0xe77681b6,
+  0x7b1734e2, 0xe76ae704, 0x7b126019, 0xe75f4d45,
+  0x7b0d8909, 0xe753b479, 0x7b08afb2, 0xe7481ca1,
+  0x7b03d414, 0xe73c85bc, 0x7afef630, 0xe730efcc,
+  0x7afa1605, 0xe7255ad1, 0x7af53395, 0xe719c6cb,
+  0x7af04edf, 0xe70e33bb, 0x7aeb67e3, 0xe702a1a1,
+  0x7ae67ea1, 0xe6f7107e, 0x7ae1931a, 0xe6eb8052,
+  0x7adca54e, 0xe6dff11d, 0x7ad7b53d, 0xe6d462e1,
+  0x7ad2c2e8, 0xe6c8d59c, 0x7acdce4d, 0xe6bd4951,
+  0x7ac8d76f, 0xe6b1bdff, 0x7ac3de4c, 0xe6a633a6,
+  0x7abee2e5, 0xe69aaa48, 0x7ab9e53a, 0xe68f21e5,
+  0x7ab4e54c, 0xe6839a7c, 0x7aafe31b, 0xe6781410,
+  0x7aaadea6, 0xe66c8e9f, 0x7aa5d7ee, 0xe6610a2a,
+  0x7aa0cef3, 0xe65586b3, 0x7a9bc3b6, 0xe64a0438,
+  0x7a96b636, 0xe63e82bc, 0x7a91a674, 0xe633023e,
+  0x7a8c9470, 0xe62782be, 0x7a87802a, 0xe61c043d,
+  0x7a8269a3, 0xe61086bc, 0x7a7d50da, 0xe6050a3b,
+  0x7a7835cf, 0xe5f98ebb, 0x7a731884, 0xe5ee143b,
+  0x7a6df8f8, 0xe5e29abc, 0x7a68d72b, 0xe5d72240,
+  0x7a63b31d, 0xe5cbaac5, 0x7a5e8cd0, 0xe5c0344d,
+  0x7a596442, 0xe5b4bed8, 0x7a543974, 0xe5a94a67,
+  0x7a4f0c67, 0xe59dd6f9, 0x7a49dd1a, 0xe5926490,
+  0x7a44ab8e, 0xe586f32c, 0x7a3f77c3, 0xe57b82cd,
+  0x7a3a41b9, 0xe5701374, 0x7a350970, 0xe564a521,
+  0x7a2fcee8, 0xe55937d5, 0x7a2a9223, 0xe54dcb8f,
+  0x7a25531f, 0xe5426051, 0x7a2011de, 0xe536f61b,
+  0x7a1ace5f, 0xe52b8cee, 0x7a1588a2, 0xe52024c9,
+  0x7a1040a8, 0xe514bdad, 0x7a0af671, 0xe509579b,
+  0x7a05a9fd, 0xe4fdf294, 0x7a005b4d, 0xe4f28e96,
+  0x79fb0a60, 0xe4e72ba4, 0x79f5b737, 0xe4dbc9bd,
+  0x79f061d2, 0xe4d068e2, 0x79eb0a31, 0xe4c50914,
+  0x79e5b054, 0xe4b9aa52, 0x79e0543c, 0xe4ae4c9d,
+  0x79daf5e8, 0xe4a2eff6, 0x79d5955a, 0xe497945d,
+  0x79d03291, 0xe48c39d3, 0x79cacd8d, 0xe480e057,
+  0x79c5664f, 0xe47587eb, 0x79bffcd7, 0xe46a308f,
+  0x79ba9125, 0xe45eda43, 0x79b52339, 0xe4538507,
+  0x79afb313, 0xe44830dd, 0x79aa40b4, 0xe43cddc4,
+  0x79a4cc1c, 0xe4318bbe, 0x799f554b, 0xe4263ac9,
+  0x7999dc42, 0xe41aeae8, 0x799460ff, 0xe40f9c1a,
+  0x798ee385, 0xe4044e60, 0x798963d2, 0xe3f901ba,
+  0x7983e1e8, 0xe3edb628, 0x797e5dc6, 0xe3e26bac,
+  0x7978d76c, 0xe3d72245, 0x79734edc, 0xe3cbd9f4,
+  0x796dc414, 0xe3c092b9, 0x79683715, 0xe3b54c95,
+  0x7962a7e0, 0xe3aa0788, 0x795d1675, 0xe39ec393,
+  0x795782d3, 0xe39380b6, 0x7951ecfc, 0xe3883ef2,
+  0x794c54ee, 0xe37cfe47, 0x7946baac, 0xe371beb5,
+  0x79411e33, 0xe366803c, 0x793b7f86, 0xe35b42df,
+  0x7935dea4, 0xe350069b, 0x79303b8e, 0xe344cb73,
+  0x792a9642, 0xe3399167, 0x7924eec3, 0xe32e5876,
+  0x791f4510, 0xe32320a2, 0x79199929, 0xe317e9eb,
+  0x7913eb0e, 0xe30cb451, 0x790e3ac0, 0xe3017fd5,
+  0x7908883f, 0xe2f64c77, 0x7902d38b, 0xe2eb1a37,
+  0x78fd1ca4, 0xe2dfe917, 0x78f7638b, 0xe2d4b916,
+  0x78f1a840, 0xe2c98a35, 0x78ebeac2, 0xe2be5c74,
+  0x78e62b13, 0xe2b32fd4, 0x78e06932, 0xe2a80456,
+  0x78daa520, 0xe29cd9f8, 0x78d4dedd, 0xe291b0bd,
+  0x78cf1669, 0xe28688a4, 0x78c94bc4, 0xe27b61af,
+  0x78c37eef, 0xe2703bdc, 0x78bdafea, 0xe265172e,
+  0x78b7deb4, 0xe259f3a3, 0x78b20b4f, 0xe24ed13d,
+  0x78ac35ba, 0xe243affc, 0x78a65df6, 0xe2388fe1,
+  0x78a08402, 0xe22d70eb, 0x789aa7e0, 0xe222531c,
+  0x7894c98f, 0xe2173674, 0x788ee910, 0xe20c1af3,
+  0x78890663, 0xe2010099, 0x78832187, 0xe1f5e768,
+  0x787d3a7e, 0xe1eacf5f, 0x78775147, 0xe1dfb87f,
+  0x787165e3, 0xe1d4a2c8, 0x786b7852, 0xe1c98e3b,
+  0x78658894, 0xe1be7ad8, 0x785f96a9, 0xe1b368a0,
+  0x7859a292, 0xe1a85793, 0x7853ac4f, 0xe19d47b1,
+  0x784db3e0, 0xe19238fb, 0x7847b946, 0xe1872b72,
+  0x7841bc7f, 0xe17c1f15, 0x783bbd8e, 0xe17113e5,
+  0x7835bc71, 0xe16609e3, 0x782fb92a, 0xe15b0110,
+  0x7829b3b9, 0xe14ff96a, 0x7823ac1d, 0xe144f2f3,
+  0x781da256, 0xe139edac, 0x78179666, 0xe12ee995,
+  0x7811884d, 0xe123e6ad, 0x780b780a, 0xe118e4f6,
+  0x7805659e, 0xe10de470, 0x77ff5109, 0xe102e51c,
+  0x77f93a4b, 0xe0f7e6f9, 0x77f32165, 0xe0ecea09,
+  0x77ed0657, 0xe0e1ee4b, 0x77e6e921, 0xe0d6f3c1,
+  0x77e0c9c3, 0xe0cbfa6a, 0x77daa83d, 0xe0c10247,
+  0x77d48490, 0xe0b60b58, 0x77ce5ebd, 0xe0ab159e,
+  0x77c836c2, 0xe0a0211a, 0x77c20ca1, 0xe0952dcb,
+  0x77bbe05a, 0xe08a3bb2, 0x77b5b1ec, 0xe07f4acf,
+  0x77af8159, 0xe0745b24, 0x77a94ea0, 0xe0696cb0,
+  0x77a319c2, 0xe05e7f74, 0x779ce2be, 0xe053936f,
+  0x7796a996, 0xe048a8a4, 0x77906e49, 0xe03dbf11,
+  0x778a30d8, 0xe032d6b8, 0x7783f143, 0xe027ef99,
+  0x777daf89, 0xe01d09b4, 0x77776bac, 0xe012250a,
+  0x777125ac, 0xe007419b, 0x776add88, 0xdffc5f67,
+  0x77649341, 0xdff17e70, 0x775e46d8, 0xdfe69eb4,
+  0x7757f84c, 0xdfdbc036, 0x7751a79e, 0xdfd0e2f5,
+  0x774b54ce, 0xdfc606f1, 0x7744ffdd, 0xdfbb2c2c,
+  0x773ea8ca, 0xdfb052a5, 0x77384f95, 0xdfa57a5d,
+  0x7731f440, 0xdf9aa354, 0x772b96ca, 0xdf8fcd8b,
+  0x77253733, 0xdf84f902, 0x771ed57c, 0xdf7a25ba,
+  0x771871a5, 0xdf6f53b3, 0x77120bae, 0xdf6482ed,
+  0x770ba398, 0xdf59b369, 0x77053962, 0xdf4ee527,
+  0x76fecd0e, 0xdf441828, 0x76f85e9a, 0xdf394c6b,
+  0x76f1ee09, 0xdf2e81f3, 0x76eb7b58, 0xdf23b8be,
+  0x76e5068a, 0xdf18f0ce, 0x76de8f9e, 0xdf0e2a22,
+  0x76d81695, 0xdf0364bc, 0x76d19b6e, 0xdef8a09b,
+  0x76cb1e2a, 0xdeedddc0, 0x76c49ec9, 0xdee31c2b,
+  0x76be1d4c, 0xded85bdd, 0x76b799b3, 0xdecd9cd7,
+  0x76b113fd, 0xdec2df18, 0x76aa8c2c, 0xdeb822a1,
+  0x76a4023f, 0xdead6773, 0x769d7637, 0xdea2ad8d,
+  0x7696e814, 0xde97f4f1, 0x769057d6, 0xde8d3d9e,
+  0x7689c57d, 0xde828796, 0x7683310b, 0xde77d2d8,
+  0x767c9a7e, 0xde6d1f65, 0x767601d7, 0xde626d3e,
+  0x766f6717, 0xde57bc62, 0x7668ca3e, 0xde4d0cd2,
+  0x76622b4c, 0xde425e8f, 0x765b8a41, 0xde37b199,
+  0x7654e71d, 0xde2d05f1, 0x764e41e2, 0xde225b96,
+  0x76479a8e, 0xde17b28a, 0x7640f123, 0xde0d0acc,
+  0x763a45a0, 0xde02645d, 0x76339806, 0xddf7bf3e,
+  0x762ce855, 0xdded1b6e, 0x7626368d, 0xdde278ef,
+  0x761f82af, 0xddd7d7c1, 0x7618ccba, 0xddcd37e4,
+  0x761214b0, 0xddc29958, 0x760b5a90, 0xddb7fc1e,
+  0x76049e5b, 0xddad6036, 0x75fde011, 0xdda2c5a2,
+  0x75f71fb1, 0xdd982c60, 0x75f05d3d, 0xdd8d9472,
+  0x75e998b5, 0xdd82fdd8, 0x75e2d219, 0xdd786892,
+  0x75dc0968, 0xdd6dd4a2, 0x75d53ea5, 0xdd634206,
+  0x75ce71ce, 0xdd58b0c0, 0x75c7a2e3, 0xdd4e20d0,
+  0x75c0d1e7, 0xdd439236, 0x75b9fed7, 0xdd3904f4,
+  0x75b329b5, 0xdd2e7908, 0x75ac5282, 0xdd23ee74,
+  0x75a5793c, 0xdd196538, 0x759e9de5, 0xdd0edd55,
+  0x7597c07d, 0xdd0456ca, 0x7590e104, 0xdcf9d199,
+  0x7589ff7a, 0xdcef4dc2, 0x75831be0, 0xdce4cb44,
+  0x757c3636, 0xdcda4a21, 0x75754e7c, 0xdccfca59,
+  0x756e64b2, 0xdcc54bec, 0x756778d9, 0xdcbacedb,
+  0x75608af1, 0xdcb05326, 0x75599afa, 0xdca5d8cd,
+  0x7552a8f4, 0xdc9b5fd2, 0x754bb4e1, 0xdc90e834,
+  0x7544bebf, 0xdc8671f3, 0x753dc68f, 0xdc7bfd11,
+  0x7536cc52, 0xdc71898d, 0x752fd008, 0xdc671768,
+  0x7528d1b1, 0xdc5ca6a2, 0x7521d14d, 0xdc52373c,
+  0x751acedd, 0xdc47c936, 0x7513ca60, 0xdc3d5c91,
+  0x750cc3d8, 0xdc32f14d, 0x7505bb44, 0xdc28876a,
+  0x74feb0a5, 0xdc1e1ee9, 0x74f7a3fb, 0xdc13b7c9,
+  0x74f09546, 0xdc09520d, 0x74e98487, 0xdbfeedb3,
+  0x74e271bd, 0xdbf48abd, 0x74db5cea, 0xdbea292b,
+  0x74d4460c, 0xdbdfc8fc, 0x74cd2d26, 0xdbd56a32,
+  0x74c61236, 0xdbcb0cce, 0x74bef53d, 0xdbc0b0ce,
+  0x74b7d63c, 0xdbb65634, 0x74b0b533, 0xdbabfd01,
+  0x74a99221, 0xdba1a534, 0x74a26d08, 0xdb974ece,
+  0x749b45e7, 0xdb8cf9cf, 0x74941cbf, 0xdb82a638,
+  0x748cf190, 0xdb785409, 0x7485c45b, 0xdb6e0342,
+  0x747e951f, 0xdb63b3e5, 0x747763dd, 0xdb5965f1,
+  0x74703095, 0xdb4f1967, 0x7468fb47, 0xdb44ce46,
+  0x7461c3f5, 0xdb3a8491, 0x745a8a9d, 0xdb303c46,
+  0x74534f41, 0xdb25f566, 0x744c11e0, 0xdb1baff2,
+  0x7444d27b, 0xdb116beb, 0x743d9112, 0xdb072950,
+  0x74364da6, 0xdafce821, 0x742f0836, 0xdaf2a860,
+  0x7427c0c3, 0xdae86a0d, 0x7420774d, 0xdade2d28,
+  0x74192bd5, 0xdad3f1b1, 0x7411de5b, 0xdac9b7a9,
+  0x740a8edf, 0xdabf7f11, 0x74033d61, 0xdab547e8,
+  0x73fbe9e2, 0xdaab122f, 0x73f49462, 0xdaa0dde7,
+  0x73ed3ce1, 0xda96ab0f, 0x73e5e360, 0xda8c79a9,
+  0x73de87de, 0xda8249b4, 0x73d72a5d, 0xda781b31,
+  0x73cfcadc, 0xda6dee21, 0x73c8695b, 0xda63c284,
+  0x73c105db, 0xda599859, 0x73b9a05d, 0xda4f6fa3,
+  0x73b238e0, 0xda454860, 0x73aacf65, 0xda3b2292,
+  0x73a363ec, 0xda30fe38, 0x739bf675, 0xda26db54,
+  0x73948701, 0xda1cb9e5, 0x738d1590, 0xda1299ec,
+  0x7385a222, 0xda087b69, 0x737e2cb7, 0xd9fe5e5e,
+  0x7376b551, 0xd9f442c9, 0x736f3bee, 0xd9ea28ac,
+  0x7367c090, 0xd9e01006, 0x73604336, 0xd9d5f8d9,
+  0x7358c3e2, 0xd9cbe325, 0x73514292, 0xd9c1cee9,
+  0x7349bf48, 0xd9b7bc27, 0x73423a04, 0xd9adaadf,
+  0x733ab2c6, 0xd9a39b11, 0x7333298f, 0xd9998cbe,
+  0x732b9e5e, 0xd98f7fe6, 0x73241134, 0xd9857489,
+  0x731c8211, 0xd97b6aa8, 0x7314f0f6, 0xd9716243,
+  0x730d5de3, 0xd9675b5a, 0x7305c8d7, 0xd95d55ef,
+  0x72fe31d5, 0xd9535201, 0x72f698db, 0xd9494f90,
+  0x72eefdea, 0xd93f4e9e, 0x72e76102, 0xd9354f2a,
+  0x72dfc224, 0xd92b5135, 0x72d82150, 0xd92154bf,
+  0x72d07e85, 0xd91759c9, 0x72c8d9c6, 0xd90d6053,
+  0x72c13311, 0xd903685d, 0x72b98a67, 0xd8f971e8,
+  0x72b1dfc9, 0xd8ef7cf4, 0x72aa3336, 0xd8e58982,
+  0x72a284b0, 0xd8db9792, 0x729ad435, 0xd8d1a724,
+  0x729321c7, 0xd8c7b838, 0x728b6d66, 0xd8bdcad0,
+  0x7283b712, 0xd8b3deeb, 0x727bfecc, 0xd8a9f48a,
+  0x72744493, 0xd8a00bae, 0x726c8868, 0xd8962456,
+  0x7264ca4c, 0xd88c3e83, 0x725d0a3e, 0xd8825a35,
+  0x72554840, 0xd878776d, 0x724d8450, 0xd86e962b,
+  0x7245be70, 0xd864b670, 0x723df6a0, 0xd85ad83c,
+  0x72362ce0, 0xd850fb8e, 0x722e6130, 0xd8472069,
+  0x72269391, 0xd83d46cc, 0x721ec403, 0xd8336eb7,
+  0x7216f287, 0xd829982b, 0x720f1f1c, 0xd81fc328,
+  0x720749c3, 0xd815efae, 0x71ff727c, 0xd80c1dbf,
+  0x71f79948, 0xd8024d59, 0x71efbe27, 0xd7f87e7f,
+  0x71e7e118, 0xd7eeb130, 0x71e0021e, 0xd7e4e56c,
+  0x71d82137, 0xd7db1b34, 0x71d03e64, 0xd7d15288,
+  0x71c859a5, 0xd7c78b68, 0x71c072fb, 0xd7bdc5d6,
+  0x71b88a66, 0xd7b401d1, 0x71b09fe7, 0xd7aa3f5a,
+  0x71a8b37c, 0xd7a07e70, 0x71a0c528, 0xd796bf16,
+  0x7198d4ea, 0xd78d014a, 0x7190e2c3, 0xd783450d,
+  0x7188eeb2, 0xd7798a60, 0x7180f8b8, 0xd76fd143,
+  0x717900d6, 0xd76619b6, 0x7171070c, 0xd75c63ba,
+  0x71690b59, 0xd752af4f, 0x71610dbf, 0xd748fc75,
+  0x71590e3e, 0xd73f4b2e, 0x71510cd5, 0xd7359b78,
+  0x71490986, 0xd72bed55, 0x71410450, 0xd72240c5,
+  0x7138fd35, 0xd71895c9, 0x7130f433, 0xd70eec60,
+  0x7128e94c, 0xd705448b, 0x7120dc80, 0xd6fb9e4b,
+  0x7118cdcf, 0xd6f1f99f, 0x7110bd39, 0xd6e85689,
+  0x7108aabf, 0xd6deb508, 0x71009661, 0xd6d5151d,
+  0x70f8801f, 0xd6cb76c9, 0x70f067fb, 0xd6c1da0b,
+  0x70e84df3, 0xd6b83ee4, 0x70e03208, 0xd6aea555,
+  0x70d8143b, 0xd6a50d5d, 0x70cff48c, 0xd69b76fe,
+  0x70c7d2fb, 0xd691e237, 0x70bfaf89, 0xd6884f09,
+  0x70b78a36, 0xd67ebd74, 0x70af6302, 0xd6752d79,
+  0x70a739ed, 0xd66b9f18, 0x709f0ef8, 0xd6621251,
+  0x7096e223, 0xd6588725, 0x708eb36f, 0xd64efd94,
+  0x708682dc, 0xd645759f, 0x707e5069, 0xd63bef46,
+  0x70761c18, 0xd6326a88, 0x706de5e9, 0xd628e767,
+  0x7065addb, 0xd61f65e4, 0x705d73f0, 0xd615e5fd,
+  0x70553828, 0xd60c67b4, 0x704cfa83, 0xd602eb0a,
+  0x7044bb00, 0xd5f96ffd, 0x703c79a2, 0xd5eff690,
+  0x70343667, 0xd5e67ec1, 0x702bf151, 0xd5dd0892,
+  0x7023aa5f, 0xd5d39403, 0x701b6193, 0xd5ca2115,
+  0x701316eb, 0xd5c0afc6, 0x700aca69, 0xd5b74019,
+  0x70027c0c, 0xd5add20d, 0x6ffa2bd6, 0xd5a465a3,
+  0x6ff1d9c7, 0xd59afadb, 0x6fe985de, 0xd59191b5,
+  0x6fe1301c, 0xd5882a32, 0x6fd8d882, 0xd57ec452,
+  0x6fd07f0f, 0xd5756016, 0x6fc823c5, 0xd56bfd7d,
+  0x6fbfc6a3, 0xd5629c89, 0x6fb767aa, 0xd5593d3a,
+  0x6faf06da, 0xd54fdf8f, 0x6fa6a433, 0xd5468389,
+  0x6f9e3fb6, 0xd53d292a, 0x6f95d963, 0xd533d070,
+  0x6f8d713a, 0xd52a795d, 0x6f85073c, 0xd52123f0,
+  0x6f7c9b69, 0xd517d02b, 0x6f742dc1, 0xd50e7e0d,
+  0x6f6bbe45, 0xd5052d97, 0x6f634cf5, 0xd4fbdec9,
+  0x6f5ad9d1, 0xd4f291a4, 0x6f5264da, 0xd4e94627,
+  0x6f49ee0f, 0xd4dffc54, 0x6f417573, 0xd4d6b42b,
+  0x6f38fb03, 0xd4cd6dab, 0x6f307ec2, 0xd4c428d6,
+  0x6f2800af, 0xd4bae5ab, 0x6f1f80ca, 0xd4b1a42c,
+  0x6f16ff14, 0xd4a86458, 0x6f0e7b8e, 0xd49f2630,
+  0x6f05f637, 0xd495e9b3, 0x6efd6f10, 0xd48caee4,
+  0x6ef4e619, 0xd48375c1, 0x6eec5b53, 0xd47a3e4b,
+  0x6ee3cebe, 0xd4710883, 0x6edb405a, 0xd467d469,
+  0x6ed2b027, 0xd45ea1fd, 0x6eca1e27, 0xd4557140,
+  0x6ec18a58, 0xd44c4232, 0x6eb8f4bc, 0xd44314d3,
+  0x6eb05d53, 0xd439e923, 0x6ea7c41e, 0xd430bf24,
+  0x6e9f291b, 0xd42796d5, 0x6e968c4d, 0xd41e7037,
+  0x6e8dedb3, 0xd4154b4a, 0x6e854d4d, 0xd40c280e,
+  0x6e7cab1c, 0xd4030684, 0x6e740720, 0xd3f9e6ad,
+  0x6e6b615a, 0xd3f0c887, 0x6e62b9ca, 0xd3e7ac15,
+  0x6e5a1070, 0xd3de9156, 0x6e51654c, 0xd3d5784a,
+  0x6e48b860, 0xd3cc60f2, 0x6e4009aa, 0xd3c34b4f,
+  0x6e37592c, 0xd3ba3760, 0x6e2ea6e6, 0xd3b12526,
+  0x6e25f2d8, 0xd3a814a2, 0x6e1d3d03, 0xd39f05d3,
+  0x6e148566, 0xd395f8ba, 0x6e0bcc03, 0xd38ced57,
+  0x6e0310d9, 0xd383e3ab, 0x6dfa53e9, 0xd37adbb6,
+  0x6df19534, 0xd371d579, 0x6de8d4b8, 0xd368d0f3,
+  0x6de01278, 0xd35fce26, 0x6dd74e73, 0xd356cd11,
+  0x6dce88aa, 0xd34dcdb4, 0x6dc5c11c, 0xd344d011,
+  0x6dbcf7cb, 0xd33bd427, 0x6db42cb6, 0xd332d9f7,
+  0x6dab5fdf, 0xd329e181, 0x6da29144, 0xd320eac6,
+  0x6d99c0e7, 0xd317f5c6, 0x6d90eec8, 0xd30f0280,
+  0x6d881ae8, 0xd30610f7, 0x6d7f4545, 0xd2fd2129,
+  0x6d766de2, 0xd2f43318, 0x6d6d94bf, 0xd2eb46c3,
+  0x6d64b9da, 0xd2e25c2b, 0x6d5bdd36, 0xd2d97350,
+  0x6d52fed2, 0xd2d08c33, 0x6d4a1eaf, 0xd2c7a6d4,
+  0x6d413ccd, 0xd2bec333, 0x6d38592c, 0xd2b5e151,
+  0x6d2f73cd, 0xd2ad012e, 0x6d268cb0, 0xd2a422ca,
+  0x6d1da3d5, 0xd29b4626, 0x6d14b93d, 0xd2926b41,
+  0x6d0bcce8, 0xd289921e, 0x6d02ded7, 0xd280babb,
+  0x6cf9ef09, 0xd277e518, 0x6cf0fd80, 0xd26f1138,
+  0x6ce80a3a, 0xd2663f19, 0x6cdf153a, 0xd25d6ebc,
+  0x6cd61e7f, 0xd254a021, 0x6ccd2609, 0xd24bd34a,
+  0x6cc42bd9, 0xd2430835, 0x6cbb2fef, 0xd23a3ee4,
+  0x6cb2324c, 0xd2317756, 0x6ca932ef, 0xd228b18d,
+  0x6ca031da, 0xd21fed88, 0x6c972f0d, 0xd2172b48,
+  0x6c8e2a87, 0xd20e6acc, 0x6c85244a, 0xd205ac17,
+  0x6c7c1c55, 0xd1fcef27, 0x6c7312a9, 0xd1f433fd,
+  0x6c6a0746, 0xd1eb7a9a, 0x6c60fa2d, 0xd1e2c2fd,
+  0x6c57eb5e, 0xd1da0d28, 0x6c4edada, 0xd1d1591a,
+  0x6c45c8a0, 0xd1c8a6d4, 0x6c3cb4b1, 0xd1bff656,
+  0x6c339f0e, 0xd1b747a0, 0x6c2a87b6, 0xd1ae9ab4,
+  0x6c216eaa, 0xd1a5ef90, 0x6c1853eb, 0xd19d4636,
+  0x6c0f3779, 0xd1949ea6, 0x6c061953, 0xd18bf8e0,
+  0x6bfcf97c, 0xd18354e4, 0x6bf3d7f2, 0xd17ab2b3,
+  0x6beab4b6, 0xd172124d, 0x6be18fc9, 0xd16973b3,
+  0x6bd8692b, 0xd160d6e5, 0x6bcf40dc, 0xd1583be2,
+  0x6bc616dd, 0xd14fa2ad, 0x6bbceb2d, 0xd1470b44,
+  0x6bb3bdce, 0xd13e75a8, 0x6baa8ec0, 0xd135e1d9,
+  0x6ba15e03, 0xd12d4fd9, 0x6b982b97, 0xd124bfa6,
+  0x6b8ef77d, 0xd11c3142, 0x6b85c1b5, 0xd113a4ad,
+  0x6b7c8a3f, 0xd10b19e7, 0x6b73511c, 0xd10290f0,
+  0x6b6a164d, 0xd0fa09c9, 0x6b60d9d0, 0xd0f18472,
+  0x6b579ba8, 0xd0e900ec, 0x6b4e5bd4, 0xd0e07f36,
+  0x6b451a55, 0xd0d7ff51, 0x6b3bd72a, 0xd0cf813e,
+  0x6b329255, 0xd0c704fd, 0x6b294bd5, 0xd0be8a8d,
+  0x6b2003ac, 0xd0b611f1, 0x6b16b9d9, 0xd0ad9b26,
+  0x6b0d6e5c, 0xd0a5262f, 0x6b042137, 0xd09cb30b,
+  0x6afad269, 0xd09441bb, 0x6af181f3, 0xd08bd23f,
+  0x6ae82fd5, 0xd0836497, 0x6adedc10, 0xd07af8c4,
+  0x6ad586a3, 0xd0728ec6, 0x6acc2f90, 0xd06a269d,
+  0x6ac2d6d6, 0xd061c04a, 0x6ab97c77, 0xd0595bcd,
+  0x6ab02071, 0xd050f926, 0x6aa6c2c6, 0xd0489856,
+  0x6a9d6377, 0xd040395d, 0x6a940283, 0xd037dc3b,
+  0x6a8a9fea, 0xd02f80f1, 0x6a813bae, 0xd027277e,
+  0x6a77d5ce, 0xd01ecfe4, 0x6a6e6e4b, 0xd0167a22,
+  0x6a650525, 0xd00e2639, 0x6a5b9a5d, 0xd005d42a,
+  0x6a522df3, 0xcffd83f4, 0x6a48bfe7, 0xcff53597,
+  0x6a3f503a, 0xcfece915, 0x6a35deeb, 0xcfe49e6d,
+  0x6a2c6bfd, 0xcfdc55a1, 0x6a22f76e, 0xcfd40eaf,
+  0x6a19813f, 0xcfcbc999, 0x6a100970, 0xcfc3865e,
+  0x6a069003, 0xcfbb4500, 0x69fd14f6, 0xcfb3057d,
+  0x69f3984c, 0xcfaac7d8, 0x69ea1a03, 0xcfa28c10,
+  0x69e09a1c, 0xcf9a5225, 0x69d71899, 0xcf921a17,
+  0x69cd9578, 0xcf89e3e8, 0x69c410ba, 0xcf81af97,
+  0x69ba8a61, 0xcf797d24, 0x69b1026c, 0xcf714c91,
+  0x69a778db, 0xcf691ddd, 0x699dedaf, 0xcf60f108,
+  0x699460e8, 0xcf58c613, 0x698ad287, 0xcf509cfe,
+  0x6981428c, 0xcf4875ca, 0x6977b0f7, 0xcf405077,
+  0x696e1dc9, 0xcf382d05, 0x69648902, 0xcf300b74,
+  0x695af2a3, 0xcf27ebc5, 0x69515aab, 0xcf1fcdf8,
+  0x6947c11c, 0xcf17b20d, 0x693e25f5, 0xcf0f9805,
+  0x69348937, 0xcf077fe1, 0x692aeae3, 0xceff699f,
+  0x69214af8, 0xcef75541, 0x6917a977, 0xceef42c7,
+  0x690e0661, 0xcee73231, 0x690461b5, 0xcedf2380,
+  0x68fabb75, 0xced716b4, 0x68f113a0, 0xcecf0bcd,
+  0x68e76a37, 0xcec702cb, 0x68ddbf3b, 0xcebefbb0,
+  0x68d412ab, 0xceb6f67a, 0x68ca6488, 0xceaef32b,
+  0x68c0b4d2, 0xcea6f1c2, 0x68b7038b, 0xce9ef241,
+  0x68ad50b1, 0xce96f4a7, 0x68a39c46, 0xce8ef8f4,
+  0x6899e64a, 0xce86ff2a, 0x68902ebd, 0xce7f0748,
+  0x688675a0, 0xce77114e, 0x687cbaf3, 0xce6f1d3d,
+  0x6872feb6, 0xce672b16, 0x686940ea, 0xce5f3ad8,
+  0x685f8190, 0xce574c84, 0x6855c0a6, 0xce4f6019,
+  0x684bfe2f, 0xce47759a, 0x68423a2a, 0xce3f8d05,
+  0x68387498, 0xce37a65b, 0x682ead78, 0xce2fc19c,
+  0x6824e4cc, 0xce27dec9, 0x681b1a94, 0xce1ffde2,
+  0x68114ed0, 0xce181ee8, 0x68078181, 0xce1041d9,
+  0x67fdb2a7, 0xce0866b8, 0x67f3e241, 0xce008d84,
+  0x67ea1052, 0xcdf8b63d, 0x67e03cd8, 0xcdf0e0e4,
+  0x67d667d5, 0xcde90d79, 0x67cc9149, 0xcde13bfd,
+  0x67c2b934, 0xcdd96c6f, 0x67b8df97, 0xcdd19ed0,
+  0x67af0472, 0xcdc9d320, 0x67a527c4, 0xcdc20960,
+  0x679b4990, 0xcdba4190, 0x679169d5, 0xcdb27bb0,
+  0x67878893, 0xcdaab7c0, 0x677da5cb, 0xcda2f5c2,
+  0x6773c17d, 0xcd9b35b4, 0x6769dbaa, 0xcd937798,
+  0x675ff452, 0xcd8bbb6d, 0x67560b76, 0xcd840134,
+  0x674c2115, 0xcd7c48ee, 0x67423530, 0xcd74929a,
+  0x673847c8, 0xcd6cde39, 0x672e58dc, 0xcd652bcb,
+  0x6724686e, 0xcd5d7b50, 0x671a767e, 0xcd55ccca,
+  0x6710830c, 0xcd4e2037, 0x67068e18, 0xcd467599,
+  0x66fc97a3, 0xcd3eccef, 0x66f29fad, 0xcd37263a,
+  0x66e8a637, 0xcd2f817b, 0x66deab41, 0xcd27deb0,
+  0x66d4aecb, 0xcd203ddc, 0x66cab0d6, 0xcd189efe,
+  0x66c0b162, 0xcd110216, 0x66b6b070, 0xcd096725,
+  0x66acadff, 0xcd01ce2b, 0x66a2aa11, 0xccfa3729,
+  0x6698a4a6, 0xccf2a21d, 0x668e9dbd, 0xcceb0f0a,
+  0x66849558, 0xcce37def, 0x667a8b77, 0xccdbeecc,
+  0x6670801a, 0xccd461a2, 0x66667342, 0xccccd671,
+  0x665c64ef, 0xccc54d3a, 0x66525521, 0xccbdc5fc,
+  0x664843d9, 0xccb640b8, 0x663e3117, 0xccaebd6e,
+  0x66341cdb, 0xcca73c1e, 0x662a0727, 0xcc9fbcca,
+  0x661feffa, 0xcc983f70, 0x6615d754, 0xcc90c412,
+  0x660bbd37, 0xcc894aaf, 0x6601a1a2, 0xcc81d349,
+  0x65f78497, 0xcc7a5dde, 0x65ed6614, 0xcc72ea70,
+  0x65e3461b, 0xcc6b78ff, 0x65d924ac, 0xcc64098b,
+  0x65cf01c8, 0xcc5c9c14, 0x65c4dd6e, 0xcc55309b,
+  0x65bab7a0, 0xcc4dc720, 0x65b0905d, 0xcc465fa3,
+  0x65a667a7, 0xcc3efa25, 0x659c3d7c, 0xcc3796a5,
+  0x659211df, 0xcc303524, 0x6587e4cf, 0xcc28d5a3,
+  0x657db64c, 0xcc217822, 0x65738657, 0xcc1a1ca0,
+  0x656954f1, 0xcc12c31f, 0x655f2219, 0xcc0b6b9e,
+  0x6554edd1, 0xcc04161e, 0x654ab818, 0xcbfcc29f,
+  0x654080ef, 0xcbf57121, 0x65364857, 0xcbee21a5,
+  0x652c0e4f, 0xcbe6d42b, 0x6521d2d8, 0xcbdf88b3,
+  0x651795f3, 0xcbd83f3d, 0x650d57a0, 0xcbd0f7ca,
+  0x650317df, 0xcbc9b25a, 0x64f8d6b0, 0xcbc26eee,
+  0x64ee9415, 0xcbbb2d85, 0x64e4500e, 0xcbb3ee20,
+  0x64da0a9a, 0xcbacb0bf, 0x64cfc3ba, 0xcba57563,
+  0x64c57b6f, 0xcb9e3c0b, 0x64bb31ba, 0xcb9704b9,
+  0x64b0e699, 0xcb8fcf6b, 0x64a69a0f, 0xcb889c23,
+  0x649c4c1b, 0xcb816ae1, 0x6491fcbe, 0xcb7a3ba5,
+  0x6487abf7, 0xcb730e70, 0x647d59c8, 0xcb6be341,
+  0x64730631, 0xcb64ba19, 0x6468b132, 0xcb5d92f8,
+  0x645e5acc, 0xcb566ddf, 0x645402ff, 0xcb4f4acd,
+  0x6449a9cc, 0xcb4829c4, 0x643f4f32, 0xcb410ac3,
+  0x6434f332, 0xcb39edca, 0x642a95ce, 0xcb32d2da,
+  0x64203704, 0xcb2bb9f4, 0x6415d6d5, 0xcb24a316,
+  0x640b7543, 0xcb1d8e43, 0x6401124d, 0xcb167b79,
+  0x63f6adf3, 0xcb0f6aba, 0x63ec4837, 0xcb085c05,
+  0x63e1e117, 0xcb014f5b, 0x63d77896, 0xcafa44bc,
+  0x63cd0eb3, 0xcaf33c28, 0x63c2a36f, 0xcaec35a0,
+  0x63b836ca, 0xcae53123, 0x63adc8c4, 0xcade2eb3,
+  0x63a3595e, 0xcad72e4f, 0x6398e898, 0xcad02ff8,
+  0x638e7673, 0xcac933ae, 0x638402ef, 0xcac23971,
+  0x63798e0d, 0xcabb4141, 0x636f17cc, 0xcab44b1f,
+  0x6364a02e, 0xcaad570c, 0x635a2733, 0xcaa66506,
+  0x634facda, 0xca9f750f, 0x63453125, 0xca988727,
+  0x633ab414, 0xca919b4e, 0x633035a7, 0xca8ab184,
+  0x6325b5df, 0xca83c9ca, 0x631b34bc, 0xca7ce420,
+  0x6310b23e, 0xca760086, 0x63062e67, 0xca6f1efc,
+  0x62fba936, 0xca683f83, 0x62f122ab, 0xca61621b,
+  0x62e69ac8, 0xca5a86c4, 0x62dc118c, 0xca53ad7e,
+  0x62d186f8, 0xca4cd64b, 0x62c6fb0c, 0xca460129,
+  0x62bc6dca, 0xca3f2e19, 0x62b1df30, 0xca385d1d,
+  0x62a74f40, 0xca318e32, 0x629cbdfa, 0xca2ac15b,
+  0x62922b5e, 0xca23f698, 0x6287976e, 0xca1d2de7,
+  0x627d0228, 0xca16674b, 0x62726b8e, 0xca0fa2c3,
+  0x6267d3a0, 0xca08e04f, 0x625d3a5e, 0xca021fef,
+  0x62529fca, 0xc9fb61a5, 0x624803e2, 0xc9f4a570,
+  0x623d66a8, 0xc9edeb50, 0x6232c81c, 0xc9e73346,
+  0x6228283f, 0xc9e07d51, 0x621d8711, 0xc9d9c973,
+  0x6212e492, 0xc9d317ab, 0x620840c2, 0xc9cc67fa,
+  0x61fd9ba3, 0xc9c5ba60, 0x61f2f534, 0xc9bf0edd,
+  0x61e84d76, 0xc9b86572, 0x61dda46a, 0xc9b1be1e,
+  0x61d2fa0f, 0xc9ab18e3, 0x61c84e67, 0xc9a475bf,
+  0x61bda171, 0xc99dd4b4, 0x61b2f32e, 0xc99735c2,
+  0x61a8439e, 0xc99098e9, 0x619d92c2, 0xc989fe29,
+  0x6192e09b, 0xc9836582, 0x61882d28, 0xc97ccef5,
+  0x617d786a, 0xc9763a83, 0x6172c262, 0xc96fa82a,
+  0x61680b0f, 0xc96917ec, 0x615d5273, 0xc96289c9,
+  0x6152988d, 0xc95bfdc1, 0x6147dd5f, 0xc95573d4,
+  0x613d20e8, 0xc94eec03, 0x61326329, 0xc948664d,
+  0x6127a423, 0xc941e2b4, 0x611ce3d5, 0xc93b6137,
+  0x61122240, 0xc934e1d6, 0x61075f65, 0xc92e6492,
+  0x60fc9b44, 0xc927e96b, 0x60f1d5de, 0xc9217062,
+  0x60e70f32, 0xc91af976, 0x60dc4742, 0xc91484a8,
+  0x60d17e0d, 0xc90e11f7, 0x60c6b395, 0xc907a166,
+  0x60bbe7d8, 0xc90132f2, 0x60b11ad9, 0xc8fac69e,
+  0x60a64c97, 0xc8f45c68, 0x609b7d13, 0xc8edf452,
+  0x6090ac4d, 0xc8e78e5b, 0x6085da46, 0xc8e12a84,
+  0x607b06fe, 0xc8dac8cd, 0x60703275, 0xc8d46936,
+  0x60655cac, 0xc8ce0bc0, 0x605a85a3, 0xc8c7b06b,
+  0x604fad5b, 0xc8c15736, 0x6044d3d4, 0xc8bb0023,
+  0x6039f90f, 0xc8b4ab32, 0x602f1d0b, 0xc8ae5862,
+  0x60243fca, 0xc8a807b4, 0x6019614c, 0xc8a1b928,
+  0x600e8190, 0xc89b6cbf, 0x6003a099, 0xc8952278,
+  0x5ff8be65, 0xc88eda54, 0x5feddaf6, 0xc8889454,
+  0x5fe2f64c, 0xc8825077, 0x5fd81067, 0xc87c0ebd,
+  0x5fcd2948, 0xc875cf28, 0x5fc240ef, 0xc86f91b7,
+  0x5fb7575c, 0xc869566a, 0x5fac6c91, 0xc8631d42,
+  0x5fa1808c, 0xc85ce63e, 0x5f969350, 0xc856b160,
+  0x5f8ba4dc, 0xc8507ea7, 0x5f80b531, 0xc84a4e14,
+  0x5f75c44e, 0xc8441fa6, 0x5f6ad235, 0xc83df35f,
+  0x5f5fdee6, 0xc837c93e, 0x5f54ea62, 0xc831a143,
+  0x5f49f4a8, 0xc82b7b70, 0x5f3efdb9, 0xc82557c3,
+  0x5f340596, 0xc81f363d, 0x5f290c3f, 0xc81916df,
+  0x5f1e11b5, 0xc812f9a9, 0x5f1315f7, 0xc80cde9b,
+  0x5f081907, 0xc806c5b5, 0x5efd1ae4, 0xc800aef7,
+  0x5ef21b90, 0xc7fa9a62, 0x5ee71b0a, 0xc7f487f6,
+  0x5edc1953, 0xc7ee77b3, 0x5ed1166b, 0xc7e8699a,
+  0x5ec61254, 0xc7e25daa, 0x5ebb0d0d, 0xc7dc53e3,
+  0x5eb00696, 0xc7d64c47, 0x5ea4fef0, 0xc7d046d6,
+  0x5e99f61d, 0xc7ca438f, 0x5e8eec1b, 0xc7c44272,
+  0x5e83e0eb, 0xc7be4381, 0x5e78d48e, 0xc7b846ba,
+  0x5e6dc705, 0xc7b24c20, 0x5e62b84f, 0xc7ac53b1,
+  0x5e57a86d, 0xc7a65d6e, 0x5e4c9760, 0xc7a06957,
+  0x5e418528, 0xc79a776c, 0x5e3671c5, 0xc79487ae,
+  0x5e2b5d38, 0xc78e9a1d, 0x5e204781, 0xc788aeb9,
+  0x5e1530a1, 0xc782c582, 0x5e0a1898, 0xc77cde79,
+  0x5dfeff67, 0xc776f99d, 0x5df3e50d, 0xc77116f0,
+  0x5de8c98c, 0xc76b3671, 0x5dddace4, 0xc7655820,
+  0x5dd28f15, 0xc75f7bfe, 0x5dc7701f, 0xc759a20a,
+  0x5dbc5004, 0xc753ca46, 0x5db12ec3, 0xc74df4b1,
+  0x5da60c5d, 0xc748214c, 0x5d9ae8d2, 0xc7425016,
+  0x5d8fc424, 0xc73c8111, 0x5d849e51, 0xc736b43c,
+  0x5d79775c, 0xc730e997, 0x5d6e4f43, 0xc72b2123,
+  0x5d632608, 0xc7255ae0, 0x5d57fbaa, 0xc71f96ce,
+  0x5d4cd02c, 0xc719d4ed, 0x5d41a38c, 0xc714153e,
+  0x5d3675cb, 0xc70e57c0, 0x5d2b46ea, 0xc7089c75,
+  0x5d2016e9, 0xc702e35c, 0x5d14e5c9, 0xc6fd2c75,
+  0x5d09b389, 0xc6f777c1, 0x5cfe802b, 0xc6f1c540,
+  0x5cf34baf, 0xc6ec14f2, 0x5ce81615, 0xc6e666d7,
+  0x5cdcdf5e, 0xc6e0baf0, 0x5cd1a78a, 0xc6db113d,
+  0x5cc66e99, 0xc6d569be, 0x5cbb348d, 0xc6cfc472,
+  0x5caff965, 0xc6ca215c, 0x5ca4bd21, 0xc6c4807a,
+  0x5c997fc4, 0xc6bee1cd, 0x5c8e414b, 0xc6b94554,
+  0x5c8301b9, 0xc6b3ab12, 0x5c77c10e, 0xc6ae1304,
+  0x5c6c7f4a, 0xc6a87d2d, 0x5c613c6d, 0xc6a2e98b,
+  0x5c55f878, 0xc69d5820, 0x5c4ab36b, 0xc697c8eb,
+  0x5c3f6d47, 0xc6923bec, 0x5c34260c, 0xc68cb124,
+  0x5c28ddbb, 0xc6872894, 0x5c1d9454, 0xc681a23a,
+  0x5c1249d8, 0xc67c1e18, 0x5c06fe46, 0xc6769c2e,
+  0x5bfbb1a0, 0xc6711c7b, 0x5bf063e6, 0xc66b9f01,
+  0x5be51518, 0xc66623be, 0x5bd9c537, 0xc660aab5,
+  0x5bce7442, 0xc65b33e4, 0x5bc3223c, 0xc655bf4c,
+  0x5bb7cf23, 0xc6504ced, 0x5bac7af9, 0xc64adcc7,
+  0x5ba125bd, 0xc6456edb, 0x5b95cf71, 0xc6400329,
+  0x5b8a7815, 0xc63a99b1, 0x5b7f1fa9, 0xc6353273,
+  0x5b73c62d, 0xc62fcd6f, 0x5b686ba3, 0xc62a6aa6,
+  0x5b5d100a, 0xc6250a18, 0x5b51b363, 0xc61fabc4,
+  0x5b4655ae, 0xc61a4fac, 0x5b3af6ec, 0xc614f5cf,
+  0x5b2f971e, 0xc60f9e2e, 0x5b243643, 0xc60a48c9,
+  0x5b18d45c, 0xc604f5a0, 0x5b0d716a, 0xc5ffa4b3,
+  0x5b020d6c, 0xc5fa5603, 0x5af6a865, 0xc5f5098f,
+  0x5aeb4253, 0xc5efbf58, 0x5adfdb37, 0xc5ea775e,
+  0x5ad47312, 0xc5e531a1, 0x5ac909e5, 0xc5dfee22,
+  0x5abd9faf, 0xc5daace1, 0x5ab23471, 0xc5d56ddd,
+  0x5aa6c82b, 0xc5d03118, 0x5a9b5adf, 0xc5caf690,
+  0x5a8fec8c, 0xc5c5be47, 0x5a847d33, 0xc5c0883d,
+  0x5a790cd4, 0xc5bb5472, 0x5a6d9b70, 0xc5b622e6,
+  0x5a622907, 0xc5b0f399, 0x5a56b599, 0xc5abc68c,
+  0x5a4b4128, 0xc5a69bbe, 0x5a3fcbb3, 0xc5a17330,
+  0x5a34553b, 0xc59c4ce3, 0x5a28ddc0, 0xc59728d5,
+  0x5a1d6544, 0xc5920708, 0x5a11ebc5, 0xc58ce77c,
+  0x5a067145, 0xc587ca31, 0x59faf5c5, 0xc582af26,
+  0x59ef7944, 0xc57d965d, 0x59e3fbc3, 0xc5787fd6,
+  0x59d87d42, 0xc5736b90, 0x59ccfdc2, 0xc56e598c,
+  0x59c17d44, 0xc56949ca, 0x59b5fbc8, 0xc5643c4a,
+  0x59aa794d, 0xc55f310d, 0x599ef5d6, 0xc55a2812,
+  0x59937161, 0xc555215a, 0x5987ebf0, 0xc5501ce5,
+  0x597c6584, 0xc54b1ab4, 0x5970de1b, 0xc5461ac6,
+  0x596555b8, 0xc5411d1b, 0x5959cc5a, 0xc53c21b4,
+  0x594e4201, 0xc5372891, 0x5942b6af, 0xc53231b3,
+  0x59372a64, 0xc52d3d18, 0x592b9d1f, 0xc5284ac3,
+  0x59200ee3, 0xc5235ab2, 0x59147fae, 0xc51e6ce6,
+  0x5908ef82, 0xc519815f, 0x58fd5e5f, 0xc514981d,
+  0x58f1cc45, 0xc50fb121, 0x58e63935, 0xc50acc6b,
+  0x58daa52f, 0xc505e9fb, 0x58cf1034, 0xc50109d0,
+  0x58c37a44, 0xc4fc2bec, 0x58b7e35f, 0xc4f7504e,
+  0x58ac4b87, 0xc4f276f7, 0x58a0b2bb, 0xc4ed9fe7,
+  0x589518fc, 0xc4e8cb1e, 0x58897e4a, 0xc4e3f89c,
+  0x587de2a7, 0xc4df2862, 0x58724611, 0xc4da5a6f,
+  0x5866a88a, 0xc4d58ec3, 0x585b0a13, 0xc4d0c560,
+  0x584f6aab, 0xc4cbfe45, 0x5843ca53, 0xc4c73972,
+  0x5838290c, 0xc4c276e8, 0x582c86d5, 0xc4bdb6a6,
+  0x5820e3b0, 0xc4b8f8ad, 0x58153f9d, 0xc4b43cfd,
+  0x58099a9c, 0xc4af8397, 0x57fdf4ae, 0xc4aacc7a,
+  0x57f24dd3, 0xc4a617a6, 0x57e6a60c, 0xc4a1651c,
+  0x57dafd59, 0xc49cb4dd, 0x57cf53bb, 0xc49806e7,
+  0x57c3a931, 0xc4935b3c, 0x57b7fdbd, 0xc48eb1db,
+  0x57ac515f, 0xc48a0ac4, 0x57a0a417, 0xc48565f9,
+  0x5794f5e6, 0xc480c379, 0x578946cc, 0xc47c2344,
+  0x577d96ca, 0xc477855a, 0x5771e5e0, 0xc472e9bc,
+  0x5766340f, 0xc46e5069, 0x575a8157, 0xc469b963,
+  0x574ecdb8, 0xc46524a9, 0x57431933, 0xc460923b,
+  0x573763c9, 0xc45c0219, 0x572bad7a, 0xc4577444,
+  0x571ff646, 0xc452e8bc, 0x57143e2d, 0xc44e5f80,
+  0x57088531, 0xc449d892, 0x56fccb51, 0xc44553f2,
+  0x56f1108f, 0xc440d19e, 0x56e554ea, 0xc43c5199,
+  0x56d99864, 0xc437d3e1, 0x56cddafb, 0xc4335877,
+  0x56c21cb2, 0xc42edf5c, 0x56b65d88, 0xc42a688f,
+  0x56aa9d7e, 0xc425f410, 0x569edc94, 0xc42181e0,
+  0x56931acb, 0xc41d11ff, 0x56875823, 0xc418a46d,
+  0x567b949d, 0xc414392b, 0x566fd039, 0xc40fd037,
+  0x56640af7, 0xc40b6994, 0x565844d8, 0xc4070540,
+  0x564c7ddd, 0xc402a33c, 0x5640b606, 0xc3fe4388,
+  0x5634ed53, 0xc3f9e624, 0x562923c5, 0xc3f58b10,
+  0x561d595d, 0xc3f1324e, 0x56118e1a, 0xc3ecdbdc,
+  0x5605c1fd, 0xc3e887bb, 0x55f9f507, 0xc3e435ea,
+  0x55ee2738, 0xc3dfe66c, 0x55e25890, 0xc3db993e,
+  0x55d68911, 0xc3d74e62, 0x55cab8ba, 0xc3d305d8,
+  0x55bee78c, 0xc3cebfa0, 0x55b31587, 0xc3ca7bba,
+  0x55a742ac, 0xc3c63a26, 0x559b6efb, 0xc3c1fae5,
+  0x558f9a76, 0xc3bdbdf6, 0x5583c51b, 0xc3b9835a,
+  0x5577eeec, 0xc3b54b11, 0x556c17e9, 0xc3b1151b,
+  0x55604013, 0xc3ace178, 0x5554676a, 0xc3a8b028,
+  0x55488dee, 0xc3a4812c, 0x553cb3a0, 0xc3a05484,
+  0x5530d881, 0xc39c2a2f, 0x5524fc90, 0xc398022f,
+  0x55191fcf, 0xc393dc82, 0x550d423d, 0xc38fb92a,
+  0x550163dc, 0xc38b9827, 0x54f584ac, 0xc3877978,
+  0x54e9a4ac, 0xc3835d1e, 0x54ddc3de, 0xc37f4319,
+  0x54d1e242, 0xc37b2b6a, 0x54c5ffd9, 0xc377160f,
+  0x54ba1ca3, 0xc373030a, 0x54ae38a0, 0xc36ef25b,
+  0x54a253d1, 0xc36ae401, 0x54966e36, 0xc366d7fd,
+  0x548a87d1, 0xc362ce50, 0x547ea0a0, 0xc35ec6f8,
+  0x5472b8a5, 0xc35ac1f7, 0x5466cfe1, 0xc356bf4d,
+  0x545ae653, 0xc352bef9, 0x544efbfc, 0xc34ec0fc,
+  0x544310dd, 0xc34ac556, 0x543724f5, 0xc346cc07,
+  0x542b3846, 0xc342d510, 0x541f4ad1, 0xc33ee070,
+  0x54135c94, 0xc33aee27, 0x54076d91, 0xc336fe37,
+  0x53fb7dc9, 0xc333109e, 0x53ef8d3c, 0xc32f255e,
+  0x53e39be9, 0xc32b3c75, 0x53d7a9d3, 0xc32755e5,
+  0x53cbb6f8, 0xc32371ae, 0x53bfc35b, 0xc31f8fcf,
+  0x53b3cefa, 0xc31bb049, 0x53a7d9d7, 0xc317d31c,
+  0x539be3f2, 0xc313f848, 0x538fed4b, 0xc3101fce,
+  0x5383f5e3, 0xc30c49ad, 0x5377fdbb, 0xc30875e5,
+  0x536c04d2, 0xc304a477, 0x53600b2a, 0xc300d563,
+  0x535410c3, 0xc2fd08a9, 0x5348159d, 0xc2f93e4a,
+  0x533c19b8, 0xc2f57644, 0x53301d16, 0xc2f1b099,
+  0x53241fb6, 0xc2eded49, 0x5318219a, 0xc2ea2c53,
+  0x530c22c1, 0xc2e66db8, 0x5300232c, 0xc2e2b178,
+  0x52f422db, 0xc2def794, 0x52e821cf, 0xc2db400a,
+  0x52dc2009, 0xc2d78add, 0x52d01d89, 0xc2d3d80a,
+  0x52c41a4f, 0xc2d02794, 0x52b8165b, 0xc2cc7979,
+  0x52ac11af, 0xc2c8cdbb, 0x52a00c4b, 0xc2c52459,
+  0x5294062f, 0xc2c17d52, 0x5287ff5b, 0xc2bdd8a9,
+  0x527bf7d1, 0xc2ba365c, 0x526fef90, 0xc2b6966c,
+  0x5263e699, 0xc2b2f8d8, 0x5257dced, 0xc2af5da2,
+  0x524bd28c, 0xc2abc4c9, 0x523fc776, 0xc2a82e4d,
+  0x5233bbac, 0xc2a49a2e, 0x5227af2e, 0xc2a1086d,
+  0x521ba1fd, 0xc29d790a, 0x520f941a, 0xc299ec05,
+  0x52038584, 0xc296615d, 0x51f7763c, 0xc292d914,
+  0x51eb6643, 0xc28f5329, 0x51df5599, 0xc28bcf9c,
+  0x51d3443f, 0xc2884e6e, 0x51c73235, 0xc284cf9f,
+  0x51bb1f7c, 0xc281532e, 0x51af0c13, 0xc27dd91c,
+  0x51a2f7fc, 0xc27a616a, 0x5196e337, 0xc276ec16,
+  0x518acdc4, 0xc2737922, 0x517eb7a4, 0xc270088e,
+  0x5172a0d7, 0xc26c9a58, 0x5166895f, 0xc2692e83,
+  0x515a713a, 0xc265c50e, 0x514e586a, 0xc2625df8,
+  0x51423ef0, 0xc25ef943, 0x513624cb, 0xc25b96ee,
+  0x512a09fc, 0xc25836f9, 0x511dee84, 0xc254d965,
+  0x5111d263, 0xc2517e31, 0x5105b599, 0xc24e255e,
+  0x50f99827, 0xc24aceed, 0x50ed7a0e, 0xc2477adc,
+  0x50e15b4e, 0xc244292c, 0x50d53be7, 0xc240d9de,
+  0x50c91bda, 0xc23d8cf1, 0x50bcfb28, 0xc23a4265,
+  0x50b0d9d0, 0xc236fa3b, 0x50a4b7d3, 0xc233b473,
+  0x50989532, 0xc230710d, 0x508c71ee, 0xc22d3009,
+  0x50804e06, 0xc229f167, 0x5074297b, 0xc226b528,
+  0x5068044e, 0xc2237b4b, 0x505bde7f, 0xc22043d0,
+  0x504fb80e, 0xc21d0eb8, 0x504390fd, 0xc219dc03,
+  0x5037694b, 0xc216abb1, 0x502b40f8, 0xc2137dc2,
+  0x501f1807, 0xc2105236, 0x5012ee76, 0xc20d290d,
+  0x5006c446, 0xc20a0248, 0x4ffa9979, 0xc206dde6,
+  0x4fee6e0d, 0xc203bbe8, 0x4fe24205, 0xc2009c4e,
+  0x4fd6155f, 0xc1fd7f17, 0x4fc9e81e, 0xc1fa6445,
+  0x4fbdba40, 0xc1f74bd6, 0x4fb18bc8, 0xc1f435cc,
+  0x4fa55cb4, 0xc1f12227, 0x4f992d06, 0xc1ee10e5,
+  0x4f8cfcbe, 0xc1eb0209, 0x4f80cbdc, 0xc1e7f591,
+  0x4f749a61, 0xc1e4eb7e, 0x4f68684e, 0xc1e1e3d0,
+  0x4f5c35a3, 0xc1dede87, 0x4f500260, 0xc1dbdba3,
+  0x4f43ce86, 0xc1d8db25, 0x4f379a16, 0xc1d5dd0c,
+  0x4f2b650f, 0xc1d2e158, 0x4f1f2f73, 0xc1cfe80a,
+  0x4f12f941, 0xc1ccf122, 0x4f06c27a, 0xc1c9fca0,
+  0x4efa8b20, 0xc1c70a84, 0x4eee5331, 0xc1c41ace,
+  0x4ee21aaf, 0xc1c12d7e, 0x4ed5e19a, 0xc1be4294,
+  0x4ec9a7f3, 0xc1bb5a11, 0x4ebd6db9, 0xc1b873f5,
+  0x4eb132ef, 0xc1b5903f, 0x4ea4f793, 0xc1b2aef0,
+  0x4e98bba7, 0xc1afd007, 0x4e8c7f2a, 0xc1acf386,
+  0x4e80421e, 0xc1aa196c, 0x4e740483, 0xc1a741b9,
+  0x4e67c65a, 0xc1a46c6e, 0x4e5b87a2, 0xc1a1998a,
+  0x4e4f485c, 0xc19ec90d, 0x4e430889, 0xc19bfaf9,
+  0x4e36c82a, 0xc1992f4c, 0x4e2a873e, 0xc1966606,
+  0x4e1e45c6, 0xc1939f29, 0x4e1203c3, 0xc190dab4,
+  0x4e05c135, 0xc18e18a7, 0x4df97e1d, 0xc18b5903,
+  0x4ded3a7b, 0xc1889bc6, 0x4de0f64f, 0xc185e0f3,
+  0x4dd4b19a, 0xc1832888, 0x4dc86c5d, 0xc1807285,
+  0x4dbc2698, 0xc17dbeec, 0x4dafe04b, 0xc17b0dbb,
+  0x4da39978, 0xc1785ef4, 0x4d97521d, 0xc175b296,
+  0x4d8b0a3d, 0xc17308a1, 0x4d7ec1d6, 0xc1706115,
+  0x4d7278eb, 0xc16dbbf3, 0x4d662f7b, 0xc16b193a,
+  0x4d59e586, 0xc16878eb, 0x4d4d9b0e, 0xc165db05,
+  0x4d415013, 0xc1633f8a, 0x4d350495, 0xc160a678,
+  0x4d28b894, 0xc15e0fd1, 0x4d1c6c11, 0xc15b7b94,
+  0x4d101f0e, 0xc158e9c1, 0x4d03d189, 0xc1565a58,
+  0x4cf78383, 0xc153cd5a, 0x4ceb34fe, 0xc15142c6,
+  0x4cdee5f9, 0xc14eba9d, 0x4cd29676, 0xc14c34df,
+  0x4cc64673, 0xc149b18b, 0x4cb9f5f3, 0xc14730a3,
+  0x4cada4f5, 0xc144b225, 0x4ca1537a, 0xc1423613,
+  0x4c950182, 0xc13fbc6c, 0x4c88af0e, 0xc13d4530,
+  0x4c7c5c1e, 0xc13ad060, 0x4c7008b3, 0xc1385dfb,
+  0x4c63b4ce, 0xc135ee02, 0x4c57606e, 0xc1338075,
+  0x4c4b0b94, 0xc1311553, 0x4c3eb641, 0xc12eac9d,
+  0x4c326075, 0xc12c4653, 0x4c260a31, 0xc129e276,
+  0x4c19b374, 0xc1278104, 0x4c0d5c41, 0xc12521ff,
+  0x4c010496, 0xc122c566, 0x4bf4ac75, 0xc1206b39,
+  0x4be853de, 0xc11e1379, 0x4bdbfad1, 0xc11bbe26,
+  0x4bcfa150, 0xc1196b3f, 0x4bc34759, 0xc1171ac6,
+  0x4bb6ecef, 0xc114ccb9, 0x4baa9211, 0xc1128119,
+  0x4b9e36c0, 0xc11037e6, 0x4b91dafc, 0xc10df120,
+  0x4b857ec7, 0xc10bacc8, 0x4b79221f, 0xc1096add,
+  0x4b6cc506, 0xc1072b5f, 0x4b60677c, 0xc104ee4f,
+  0x4b540982, 0xc102b3ac, 0x4b47ab19, 0xc1007b77,
+  0x4b3b4c40, 0xc0fe45b0, 0x4b2eecf8, 0xc0fc1257,
+  0x4b228d42, 0xc0f9e16b, 0x4b162d1d, 0xc0f7b2ee,
+  0x4b09cc8c, 0xc0f586df, 0x4afd6b8d, 0xc0f35d3e,
+  0x4af10a22, 0xc0f1360b, 0x4ae4a84b, 0xc0ef1147,
+  0x4ad84609, 0xc0eceef1, 0x4acbe35b, 0xc0eacf09,
+  0x4abf8043, 0xc0e8b190, 0x4ab31cc1, 0xc0e69686,
+  0x4aa6b8d5, 0xc0e47deb, 0x4a9a5480, 0xc0e267be,
+  0x4a8defc3, 0xc0e05401, 0x4a818a9d, 0xc0de42b2,
+  0x4a752510, 0xc0dc33d2, 0x4a68bf1b, 0xc0da2762,
+  0x4a5c58c0, 0xc0d81d61, 0x4a4ff1fe, 0xc0d615cf,
+  0x4a438ad7, 0xc0d410ad, 0x4a37234a, 0xc0d20dfa,
+  0x4a2abb59, 0xc0d00db6, 0x4a1e5303, 0xc0ce0fe3,
+  0x4a11ea49, 0xc0cc147f, 0x4a05812c, 0xc0ca1b8a,
+  0x49f917ac, 0xc0c82506, 0x49ecadc9, 0xc0c630f2,
+  0x49e04385, 0xc0c43f4d, 0x49d3d8df, 0xc0c25019,
+  0x49c76dd8, 0xc0c06355, 0x49bb0271, 0xc0be7901,
+  0x49ae96aa, 0xc0bc911d, 0x49a22a83, 0xc0baabaa,
+  0x4995bdfd, 0xc0b8c8a7, 0x49895118, 0xc0b6e815,
+  0x497ce3d5, 0xc0b509f3, 0x49707635, 0xc0b32e42,
+  0x49640837, 0xc0b15502, 0x495799dd, 0xc0af7e33,
+  0x494b2b27, 0xc0ada9d4, 0x493ebc14, 0xc0abd7e6,
+  0x49324ca7, 0xc0aa086a, 0x4925dcdf, 0xc0a83b5e,
+  0x49196cbc, 0xc0a670c4, 0x490cfc40, 0xc0a4a89b,
+  0x49008b6a, 0xc0a2e2e3, 0x48f41a3c, 0xc0a11f9d,
+  0x48e7a8b5, 0xc09f5ec8, 0x48db36d6, 0xc09da065,
+  0x48cec4a0, 0xc09be473, 0x48c25213, 0xc09a2af3,
+  0x48b5df30, 0xc09873e4, 0x48a96bf6, 0xc096bf48,
+  0x489cf867, 0xc0950d1d, 0x48908483, 0xc0935d64,
+  0x4884104b, 0xc091b01d, 0x48779bbe, 0xc0900548,
+  0x486b26de, 0xc08e5ce5, 0x485eb1ab, 0xc08cb6f5,
+  0x48523c25, 0xc08b1376, 0x4845c64d, 0xc089726a,
+  0x48395024, 0xc087d3d0, 0x482cd9a9, 0xc08637a9,
+  0x482062de, 0xc0849df4, 0x4813ebc2, 0xc08306b2,
+  0x48077457, 0xc08171e2, 0x47fafc9c, 0xc07fdf85,
+  0x47ee8493, 0xc07e4f9b, 0x47e20c3b, 0xc07cc223,
+  0x47d59396, 0xc07b371e, 0x47c91aa3, 0xc079ae8c,
+  0x47bca163, 0xc078286e, 0x47b027d7, 0xc076a4c2,
+  0x47a3adff, 0xc0752389, 0x479733dc, 0xc073a4c3,
+  0x478ab96e, 0xc0722871, 0x477e3eb5, 0xc070ae92,
+  0x4771c3b3, 0xc06f3726, 0x47654867, 0xc06dc22e,
+  0x4758ccd2, 0xc06c4fa8, 0x474c50f4, 0xc06adf97,
+  0x473fd4cf, 0xc06971f9, 0x47335862, 0xc06806ce,
+  0x4726dbae, 0xc0669e18, 0x471a5eb3, 0xc06537d4,
+  0x470de172, 0xc063d405, 0x470163eb, 0xc06272aa,
+  0x46f4e620, 0xc06113c2, 0x46e86810, 0xc05fb74e,
+  0x46dbe9bb, 0xc05e5d4e, 0x46cf6b23, 0xc05d05c3,
+  0x46c2ec48, 0xc05bb0ab, 0x46b66d29, 0xc05a5e07,
+  0x46a9edc9, 0xc0590dd8, 0x469d6e27, 0xc057c01d,
+  0x4690ee44, 0xc05674d6, 0x46846e1f, 0xc0552c03,
+  0x4677edbb, 0xc053e5a5, 0x466b6d16, 0xc052a1bb,
+  0x465eec33, 0xc0516045, 0x46526b10, 0xc0502145,
+  0x4645e9af, 0xc04ee4b8, 0x46396810, 0xc04daaa1,
+  0x462ce634, 0xc04c72fe, 0x4620641a, 0xc04b3dcf,
+  0x4613e1c5, 0xc04a0b16, 0x46075f33, 0xc048dad1,
+  0x45fadc66, 0xc047ad01, 0x45ee595d, 0xc04681a6,
+  0x45e1d61b, 0xc04558c0, 0x45d5529e, 0xc044324f,
+  0x45c8cee7, 0xc0430e53, 0x45bc4af8, 0xc041eccc,
+  0x45afc6d0, 0xc040cdba, 0x45a3426f, 0xc03fb11d,
+  0x4596bdd7, 0xc03e96f6, 0x458a3908, 0xc03d7f44,
+  0x457db403, 0xc03c6a07, 0x45712ec7, 0xc03b573f,
+  0x4564a955, 0xc03a46ed, 0x455823ae, 0xc0393910,
+  0x454b9dd3, 0xc0382da8, 0x453f17c3, 0xc03724b6,
+  0x4532917f, 0xc0361e3a, 0x45260b08, 0xc0351a33,
+  0x4519845e, 0xc03418a2, 0x450cfd82, 0xc0331986,
+  0x45007674, 0xc0321ce0, 0x44f3ef35, 0xc03122b0,
+  0x44e767c5, 0xc0302af5, 0x44dae024, 0xc02f35b1,
+  0x44ce5854, 0xc02e42e2, 0x44c1d054, 0xc02d5289,
+  0x44b54825, 0xc02c64a6, 0x44a8bfc7, 0xc02b7939,
+  0x449c373c, 0xc02a9042, 0x448fae83, 0xc029a9c1,
+  0x4483259d, 0xc028c5b6, 0x44769c8b, 0xc027e421,
+  0x446a134c, 0xc0270502, 0x445d89e2, 0xc0262859,
+  0x4451004d, 0xc0254e27, 0x4444768d, 0xc024766a,
+  0x4437eca4, 0xc023a124, 0x442b6290, 0xc022ce54,
+  0x441ed854, 0xc021fdfb, 0x44124dee, 0xc0213018,
+  0x4405c361, 0xc02064ab, 0x43f938ac, 0xc01f9bb5,
+  0x43ecadcf, 0xc01ed535, 0x43e022cc, 0xc01e112b,
+  0x43d397a3, 0xc01d4f99, 0x43c70c54, 0xc01c907c,
+  0x43ba80df, 0xc01bd3d6, 0x43adf546, 0xc01b19a7,
+  0x43a16988, 0xc01a61ee, 0x4394dda7, 0xc019acac,
+  0x438851a2, 0xc018f9e1, 0x437bc57b, 0xc018498c,
+  0x436f3931, 0xc0179bae, 0x4362acc5, 0xc016f047,
+  0x43562038, 0xc0164757, 0x43499389, 0xc015a0dd,
+  0x433d06bb, 0xc014fcda, 0x433079cc, 0xc0145b4e,
+  0x4323ecbe, 0xc013bc39, 0x43175f91, 0xc0131f9b,
+  0x430ad245, 0xc0128574, 0x42fe44dc, 0xc011edc3,
+  0x42f1b755, 0xc011588a, 0x42e529b0, 0xc010c5c7,
+  0x42d89bf0, 0xc010357c, 0x42cc0e13, 0xc00fa7a8,
+  0x42bf801a, 0xc00f1c4a, 0x42b2f207, 0xc00e9364,
+  0x42a663d8, 0xc00e0cf5, 0x4299d590, 0xc00d88fd,
+  0x428d472e, 0xc00d077c, 0x4280b8b3, 0xc00c8872,
+  0x42742a1f, 0xc00c0be0, 0x42679b73, 0xc00b91c4,
+  0x425b0caf, 0xc00b1a20, 0x424e7dd4, 0xc00aa4f3,
+  0x4241eee2, 0xc00a323d, 0x42355fd9, 0xc009c1ff,
+  0x4228d0bb, 0xc0095438, 0x421c4188, 0xc008e8e8,
+  0x420fb240, 0xc008800f, 0x420322e3, 0xc00819ae,
+  0x41f69373, 0xc007b5c4, 0x41ea03ef, 0xc0075452,
+  0x41dd7459, 0xc006f556, 0x41d0e4b0, 0xc00698d3,
+  0x41c454f5, 0xc0063ec6, 0x41b7c528, 0xc005e731,
+  0x41ab354b, 0xc0059214, 0x419ea55d, 0xc0053f6e,
+  0x4192155f, 0xc004ef3f, 0x41858552, 0xc004a188,
+  0x4178f536, 0xc0045648, 0x416c650b, 0xc0040d80,
+  0x415fd4d2, 0xc003c72f, 0x4153448c, 0xc0038356,
+  0x4146b438, 0xc00341f4, 0x413a23d8, 0xc003030a,
+  0x412d936c, 0xc002c697, 0x412102f4, 0xc0028c9c,
+  0x41147271, 0xc0025519, 0x4107e1e3, 0xc002200d,
+  0x40fb514b, 0xc001ed78, 0x40eec0aa, 0xc001bd5c,
+  0x40e22fff, 0xc0018fb6, 0x40d59f4c, 0xc0016489,
+  0x40c90e90, 0xc0013bd3, 0x40bc7dcc, 0xc0011594,
+  0x40afed02, 0xc000f1ce, 0x40a35c30, 0xc000d07e,
+  0x4096cb58, 0xc000b1a7, 0x408a3a7b, 0xc0009547,
+  0x407da998, 0xc0007b5f, 0x407118b0, 0xc00063ee,
+  0x406487c4, 0xc0004ef5, 0x4057f6d4, 0xc0003c74,
+  0x404b65e1, 0xc0002c6a, 0x403ed4ea, 0xc0001ed8,
+  0x403243f1, 0xc00013bd, 0x4025b2f7, 0xc0000b1a,
+  0x401921fb, 0xc00004ef, 0x400c90fe, 0xc000013c,
+};
+
+/**    
+* @brief  Initialization function for the Q31 RFFT/RIFFT.   
+* @param[in, out] *S             points to an instance of the Q31 RFFT/RIFFT structure.   
+* @param[in, out] *S_CFFT        points to an instance of the Q31 CFFT/CIFFT structure.   
+* @param[in]      fftLenReal     length of the FFT.   
+* @param[in]      ifftFlagR      flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform.   
+* @param[in]      bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.   
+* @return		The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if fftLenReal is not a supported value.   
+*    
+* \par Description:   
+* \par   
+* The parameter fftLenReal	Specifies length of RFFT/RIFFT Process. Supported FFT Lengths are 128, 512, 2048.    
+* \par    
+* The parameter ifftFlagR controls whether a forward or inverse transform is computed.    
+* Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated.    
+* \par    
+* The parameter bitReverseFlag controls whether output is in normal order or bit reversed order.    
+* Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order.   
+* \par    
+* This function also initializes Twiddle factor table.    
+*/
+
+arm_status arm_rfft_init_q31(
+  arm_rfft_instance_q31 * S,
+  arm_cfft_radix4_instance_q31 * S_CFFT,
+  uint32_t fftLenReal,
+  uint32_t ifftFlagR,
+  uint32_t bitReverseFlag)
+{
+  /*  Initialise the default arm status */
+  arm_status status = ARM_MATH_SUCCESS;
+
+  /*  Initialize the Real FFT length */
+  S->fftLenReal = (uint16_t) fftLenReal;
+
+  /*  Initialize the Complex FFT length */
+  S->fftLenBy2 = (uint16_t) fftLenReal / 2u;
+
+  /*  Initialize the Twiddle coefficientA pointer */
+  S->pTwiddleAReal = (q31_t *) realCoefAQ31;
+
+  /*  Initialize the Twiddle coefficientB pointer */
+  S->pTwiddleBReal = (q31_t *) realCoefBQ31;
+
+  /*  Initialize the Flag for selection of RFFT or RIFFT */
+  S->ifftFlagR = (uint8_t) ifftFlagR;
+
+  /*  Initialize the Flag for calculation Bit reversal or not */
+  S->bitReverseFlagR = (uint8_t) bitReverseFlag;
+
+  /*  Initialization of coef modifier depending on the FFT length */
+  switch (S->fftLenReal)
+  {
+  case 8192:
+    S->twidCoefRModifier = 1u;
+    break;
+  case 2048u:
+    S->twidCoefRModifier = 4u;
+    break;
+  case 512u:
+    S->twidCoefRModifier = 16u;
+    break;
+  case 128u:
+    S->twidCoefRModifier = 64u;
+    break;
+  default:
+    /*  Reporting argument error if rfftSize is not valid value */
+    status = ARM_MATH_ARGUMENT_ERROR;
+    break;
+  }
+
+  /* Init Complex FFT Instance */
+  S->pCfft = S_CFFT;
+
+  if(S->ifftFlagR)
+  {
+    /* Initializes the CIFFT Module for fftLenreal/2 length */
+    arm_cfft_radix4_init_q31(S->pCfft, (uint16_t) S->fftLenBy2, 1u, 1u);
+  }
+  else
+  {
+    /* Initializes the CFFT Module for fftLenreal/2 length */
+    arm_cfft_radix4_init_q31(S->pCfft, (uint16_t) S->fftLenBy2, 0u, 1u);
+  }
+
+  /* return the status of RFFT Init function */
+  return (status);
+
+}
+
+  /**    
+   * @} end of RFFT_RIFFT group    
+   */
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_rfft_q15.c b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_rfft_q15.c
new file mode 100644
index 0000000000..c0c201277e
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_rfft_q15.c
@@ -0,0 +1,460 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_rfft_q15.c    
+*    
+* Description:	RFFT & RIFFT Q15 process function    
+*    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+
+#include "arm_math.h"
+
+/*--------------------------------------------------------------------    
+*		Internal functions prototypes    
+--------------------------------------------------------------------*/
+
+void arm_split_rfft_q15(
+  q15_t * pSrc,
+  uint32_t fftLen,
+  q15_t * pATable,
+  q15_t * pBTable,
+  q15_t * pDst,
+  uint32_t modifier);
+
+void arm_split_rifft_q15(
+  q15_t * pSrc,
+  uint32_t fftLen,
+  q15_t * pATable,
+  q15_t * pBTable,
+  q15_t * pDst,
+  uint32_t modifier);
+
+/**    
+ * @addtogroup RFFT_RIFFT    
+ * @{    
+ */
+
+/**    
+ * @brief Processing function for the Q15 RFFT/RIFFT.   
+ * @param[in]  *S    points to an instance of the Q15 RFFT/RIFFT structure.   
+ * @param[in]  *pSrc points to the input buffer.   
+ * @param[out] *pDst points to the output buffer.   
+ * @return none.   
+ *    
+ * \par Input an output formats:   
+ * \par    
+ * Internally input is downscaled by 2 for every stage to avoid saturations inside CFFT/CIFFT process.    
+ * Hence the output format is different for different RFFT sizes.    
+ * The input and output formats for different RFFT sizes and number of bits to upscale are mentioned in the tables below for RFFT and RIFFT:   
+ * \par    
+ * \image html RFFTQ15.gif "Input and Output Formats for Q15 RFFT"    
+ * \par    
+ * \image html RIFFTQ15.gif "Input and Output Formats for Q15 RIFFT"    
+ */
+
+void arm_rfft_q15(
+  const arm_rfft_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst)
+{
+  const arm_cfft_radix4_instance_q15 *S_CFFT = S->pCfft;
+
+  /* Calculation of RIFFT of input */
+  if(S->ifftFlagR == 1u)
+  {
+    /*  Real IFFT core process */
+    arm_split_rifft_q15(pSrc, S->fftLenBy2, S->pTwiddleAReal,
+                        S->pTwiddleBReal, pDst, S->twidCoefRModifier);
+
+    /* Complex readix-4 IFFT process */
+    arm_radix4_butterfly_inverse_q15(pDst, S_CFFT->fftLen,
+                                     S_CFFT->pTwiddle,
+                                     S_CFFT->twidCoefModifier);
+
+    /* Bit reversal process */
+    if(S->bitReverseFlagR == 1u)
+    {
+      arm_bitreversal_q15(pDst, S_CFFT->fftLen,
+                          S_CFFT->bitRevFactor, S_CFFT->pBitRevTable);
+    }
+  }
+  else
+  {
+    /* Calculation of RFFT of input */
+
+    /* Complex readix-4 FFT process */
+    arm_radix4_butterfly_q15(pSrc, S_CFFT->fftLen,
+                             S_CFFT->pTwiddle, S_CFFT->twidCoefModifier);
+
+    /* Bit reversal process */
+    if(S->bitReverseFlagR == 1u)
+    {
+      arm_bitreversal_q15(pSrc, S_CFFT->fftLen,
+                          S_CFFT->bitRevFactor, S_CFFT->pBitRevTable);
+    }
+
+    arm_split_rfft_q15(pSrc, S->fftLenBy2, S->pTwiddleAReal,
+                       S->pTwiddleBReal, pDst, S->twidCoefRModifier);
+  }
+
+}
+
+  /**    
+   * @} end of RFFT_RIFFT group    
+   */
+
+/**    
+ * @brief  Core Real FFT process    
+ * @param  *pSrc 				points to the input buffer.   
+ * @param  fftLen  				length of FFT.   
+ * @param  *pATable 			points to the A twiddle Coef buffer.    
+ * @param  *pBTable 			points to the B twiddle Coef buffer.   
+ * @param  *pDst 				points to the output buffer.   
+ * @param  modifier 	        twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.   
+ * @return none.    
+ * The function implements a Real FFT    
+ */
+
+void arm_split_rfft_q15(
+  q15_t * pSrc,
+  uint32_t fftLen,
+  q15_t * pATable,
+  q15_t * pBTable,
+  q15_t * pDst,
+  uint32_t modifier)
+{
+  uint32_t i;                                    /* Loop Counter */
+  q31_t outR, outI;                              /* Temporary variables for output */
+  q15_t *pCoefA, *pCoefB;                        /* Temporary pointers for twiddle factors */
+  q15_t *pSrc1, *pSrc2;
+
+
+//  pSrc[2u * fftLen] = pSrc[0]; 
+//  pSrc[(2u * fftLen) + 1u] = pSrc[1]; 
+
+  pCoefA = &pATable[modifier * 2u];
+  pCoefB = &pBTable[modifier * 2u];
+
+  pSrc1 = &pSrc[2];
+  pSrc2 = &pSrc[(2u * fftLen) - 2u];
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  i = 1u;
+
+  while(i < fftLen)
+  {
+    /*    
+       outR = (pSrc[2 * i] * pATable[2 * i] - pSrc[2 * i + 1] * pATable[2 * i + 1]    
+       + pSrc[2 * n - 2 * i] * pBTable[2 * i] +    
+       pSrc[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);    
+     */
+
+    /* outI = (pIn[2 * i + 1] * pATable[2 * i] + pIn[2 * i] * pATable[2 * i + 1] +    
+       pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -    
+       pIn[2 * n - 2 * i + 1] * pBTable[2 * i]); */
+
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    /* pSrc[2 * i] * pATable[2 * i] - pSrc[2 * i + 1] * pATable[2 * i + 1] */
+    outR = __SMUSD(*__SIMD32(pSrc1), *__SIMD32(pCoefA));
+
+#else
+
+    /* -(pSrc[2 * i + 1] * pATable[2 * i + 1] - pSrc[2 * i] * pATable[2 * i]) */
+    outR = -(__SMUSD(*__SIMD32(pSrc1), *__SIMD32(pCoefA)));
+
+#endif /*      #ifndef ARM_MATH_BIG_ENDIAN     */
+
+    /* pSrc[2 * n - 2 * i] * pBTable[2 * i] +    
+       pSrc[2 * n - 2 * i + 1] * pBTable[2 * i + 1]) */
+    outR = __SMLAD(*__SIMD32(pSrc2), *__SIMD32(pCoefB), outR) >> 15u;
+
+    /* pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -    
+       pIn[2 * n - 2 * i + 1] * pBTable[2 * i] */
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    outI = __SMUSDX(*__SIMD32(pSrc2)--, *__SIMD32(pCoefB));
+
+#else
+
+    outI = __SMUSDX(*__SIMD32(pCoefB), *__SIMD32(pSrc2)--);
+
+#endif /*      #ifndef ARM_MATH_BIG_ENDIAN     */
+
+    /* (pIn[2 * i + 1] * pATable[2 * i] + pIn[2 * i] * pATable[2 * i + 1] */
+    outI = __SMLADX(*__SIMD32(pSrc1)++, *__SIMD32(pCoefA), outI);
+
+    /* write output */
+    pDst[2u * i] = (q15_t) outR;
+    pDst[(2u * i) + 1u] = outI >> 15u;
+
+    /* write complex conjugate output */
+    pDst[(4u * fftLen) - (2u * i)] = (q15_t) outR;
+    pDst[((4u * fftLen) - (2u * i)) + 1u] = -(outI >> 15u);
+
+    /* update coefficient pointer */
+    pCoefB = pCoefB + (2u * modifier);
+    pCoefA = pCoefA + (2u * modifier);
+
+    i++;
+
+  }
+
+  pDst[2u * fftLen] = pSrc[0] - pSrc[1];
+  pDst[(2u * fftLen) + 1u] = 0;
+
+  pDst[0] = pSrc[0] + pSrc[1];
+  pDst[1] = 0;
+
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  i = 1u;
+
+  while(i < fftLen)
+  {
+    /*    
+       outR = (pSrc[2 * i] * pATable[2 * i] - pSrc[2 * i + 1] * pATable[2 * i + 1]    
+       + pSrc[2 * n - 2 * i] * pBTable[2 * i] +    
+       pSrc[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);    
+     */
+
+    outR = *pSrc1 * *pCoefA;
+    outR = outR - (*(pSrc1 + 1) * *(pCoefA + 1));
+    outR = outR + (*pSrc2 * *pCoefB);
+    outR = (outR + (*(pSrc2 + 1) * *(pCoefB + 1))) >> 15;
+
+
+    /* outI = (pIn[2 * i + 1] * pATable[2 * i] + pIn[2 * i] * pATable[2 * i + 1] +    
+       pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -    
+       pIn[2 * n - 2 * i + 1] * pBTable[2 * i]);   
+     */
+
+    outI = *pSrc2 * *(pCoefB + 1);
+    outI = outI - (*(pSrc2 + 1) * *pCoefB);
+    outI = outI + (*(pSrc1 + 1) * *pCoefA);
+    outI = outI + (*pSrc1 * *(pCoefA + 1));
+
+    /* update input pointers */
+    pSrc1 += 2u;
+    pSrc2 -= 2u;
+
+    /* write output */
+    pDst[2u * i] = (q15_t) outR;
+    pDst[(2u * i) + 1u] = outI >> 15u;
+
+    /* write complex conjugate output */
+    pDst[(4u * fftLen) - (2u * i)] = (q15_t) outR;
+    pDst[((4u * fftLen) - (2u * i)) + 1u] = -(outI >> 15u);
+
+    /* update coefficient pointer */
+    pCoefB = pCoefB + (2u * modifier);
+    pCoefA = pCoefA + (2u * modifier);
+
+    i++;
+
+  }
+
+  pDst[2u * fftLen] = pSrc[0] - pSrc[1];
+  pDst[(2u * fftLen) + 1u] = 0;
+
+  pDst[0] = pSrc[0] + pSrc[1];
+  pDst[1] = 0;
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
+
+
+/**    
+ * @brief  Core Real IFFT process    
+ * @param[in]   *pSrc 				points to the input buffer.    
+ * @param[in]   fftLen  		    length of FFT.   
+ * @param[in]   *pATable 			points to the twiddle Coef A buffer.   
+ * @param[in]   *pBTable 			points to the twiddle Coef B buffer.    
+ * @param[out]  *pDst 				points to the output buffer.   
+ * @param[in]   modifier 	        twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.   
+ * @return none.    
+ * The function implements a Real IFFT    
+ */
+void arm_split_rifft_q15(
+  q15_t * pSrc,
+  uint32_t fftLen,
+  q15_t * pATable,
+  q15_t * pBTable,
+  q15_t * pDst,
+  uint32_t modifier)
+{
+  uint32_t i;                                    /* Loop Counter */
+  q31_t outR, outI;                              /* Temporary variables for output */
+  q15_t *pCoefA, *pCoefB;                        /* Temporary pointers for twiddle factors */
+  q15_t *pSrc1, *pSrc2;
+  q15_t *pDst1 = &pDst[0];
+
+  pCoefA = &pATable[0];
+  pCoefB = &pBTable[0];
+
+  pSrc1 = &pSrc[0];
+  pSrc2 = &pSrc[2u * fftLen];
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  i = fftLen;
+
+  while(i > 0u)
+  {
+
+    /*    
+       outR = (pIn[2 * i] * pATable[2 * i] + pIn[2 * i + 1] * pATable[2 * i + 1] +    
+       pIn[2 * n - 2 * i] * pBTable[2 * i] -    
+       pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);    
+
+       outI = (pIn[2 * i + 1] * pATable[2 * i] - pIn[2 * i] * pATable[2 * i + 1] -    
+       pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -    
+       pIn[2 * n - 2 * i + 1] * pBTable[2 * i]);    
+
+     */
+
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    /* pIn[2 * n - 2 * i] * pBTable[2 * i] -    
+       pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1]) */
+    outR = __SMUSD(*__SIMD32(pSrc2), *__SIMD32(pCoefB));
+
+#else
+
+    /* -(-pIn[2 * n - 2 * i] * pBTable[2 * i] +  
+       pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1])) */
+    outR = -(__SMUSD(*__SIMD32(pSrc2), *__SIMD32(pCoefB)));
+
+#endif /*      #ifndef ARM_MATH_BIG_ENDIAN     */
+
+    /* pIn[2 * i] * pATable[2 * i] + pIn[2 * i + 1] * pATable[2 * i + 1] +    
+       pIn[2 * n - 2 * i] * pBTable[2 * i] */
+    outR = __SMLAD(*__SIMD32(pSrc1), *__SIMD32(pCoefA), outR) >> 15u;
+
+    /*    
+       -pIn[2 * n - 2 * i] * pBTable[2 * i + 1] +    
+       pIn[2 * n - 2 * i + 1] * pBTable[2 * i] */
+    outI = __SMUADX(*__SIMD32(pSrc2)--, *__SIMD32(pCoefB));
+
+    /* pIn[2 * i + 1] * pATable[2 * i] - pIn[2 * i] * pATable[2 * i + 1] */
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    outI = __SMLSDX(*__SIMD32(pCoefA), *__SIMD32(pSrc1)++, -outI);
+
+#else
+
+    outI = __SMLSDX(*__SIMD32(pSrc1)++, *__SIMD32(pCoefA), -outI);
+
+#endif /*      #ifndef ARM_MATH_BIG_ENDIAN     */
+    /* write output */
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    *__SIMD32(pDst1)++ = __PKHBT(outR, (outI >> 15u), 16);
+
+#else
+
+    *__SIMD32(pDst1)++ = __PKHBT((outI >> 15u), outR, 16);
+
+#endif /*      #ifndef ARM_MATH_BIG_ENDIAN     */
+
+    /* update coefficient pointer */
+    pCoefB = pCoefB + (2u * modifier);
+    pCoefA = pCoefA + (2u * modifier);
+
+    i--;
+
+  }
+
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  i = fftLen;
+
+  while(i > 0u)
+  {
+
+    /*    
+       outR = (pIn[2 * i] * pATable[2 * i] + pIn[2 * i + 1] * pATable[2 * i + 1] +    
+       pIn[2 * n - 2 * i] * pBTable[2 * i] -    
+       pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);    
+     */
+
+    outR = *pSrc2 * *pCoefB;
+    outR = outR - (*(pSrc2 + 1) * *(pCoefB + 1));
+    outR = outR + (*pSrc1 * *pCoefA);
+    outR = (outR + (*(pSrc1 + 1) * *(pCoefA + 1))) >> 15;
+
+    /*   
+       outI = (pIn[2 * i + 1] * pATable[2 * i] - pIn[2 * i] * pATable[2 * i + 1] -   
+       pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -   
+       pIn[2 * n - 2 * i + 1] * pBTable[2 * i]);   
+     */
+
+    outI = *(pSrc1 + 1) * *pCoefA;
+    outI = outI - (*pSrc1 * *(pCoefA + 1));
+    outI = outI - (*pSrc2 * *(pCoefB + 1));
+    outI = outI - (*(pSrc2 + 1) * *(pCoefB));
+
+    /* update input pointers */
+    pSrc1 += 2u;
+    pSrc2 -= 2u;
+
+    /* write output */
+    *pDst1++ = (q15_t) outR;
+    *pDst1++ = (q15_t) (outI >> 15);
+
+    /* update coefficient pointer */
+    pCoefB = pCoefB + (2u * modifier);
+    pCoefA = pCoefA + (2u * modifier);
+
+    i--;
+
+  }
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_rfft_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_rfft_q31.c
new file mode 100644
index 0000000000..afcb470416
--- /dev/null
+++ b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_rfft_q31.c
@@ -0,0 +1,326 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision: 	V1.1.0  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_rfft_q31.c    
+*    
+* Description:	RFFT & RIFFT Q31 process function    
+*    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/*--------------------------------------------------------------------    
+*		Internal functions prototypes    
+--------------------------------------------------------------------*/
+
+void arm_split_rfft_q31(
+  q31_t * pSrc,
+  uint32_t fftLen,
+  q31_t * pATable,
+  q31_t * pBTable,
+  q31_t * pDst,
+  uint32_t modifier);
+
+void arm_split_rifft_q31(
+  q31_t * pSrc,
+  uint32_t fftLen,
+  q31_t * pATable,
+  q31_t * pBTable,
+  q31_t * pDst,
+  uint32_t modifier);
+
+/**    
+ * @addtogroup RFFT_RIFFT    
+ * @{    
+ */
+
+/**    
+ * @brief Processing function for the Q31 RFFT/RIFFT.   
+ * @param[in]  *S    points to an instance of the Q31 RFFT/RIFFT structure.   
+ * @param[in]  *pSrc points to the input buffer.   
+ * @param[out] *pDst points to the output buffer.   
+ * @return none.   
+ *    
+ * \par Input an output formats:   
+ * \par    
+ * Internally input is downscaled by 2 for every stage to avoid saturations inside CFFT/CIFFT process.   
+ * Hence the output format is different for different RFFT sizes.    
+ * The input and output formats for different RFFT sizes and number of bits to upscale are mentioned in the tables below for RFFT and RIFFT:   
+ * \par    
+ * \image html RFFTQ31.gif "Input and Output Formats for Q31 RFFT"    
+ *    
+ * \par    
+ * \image html RIFFTQ31.gif "Input and Output Formats for Q31 RIFFT"    
+ */
+
+void arm_rfft_q31(
+  const arm_rfft_instance_q31 * S,
+  q31_t * pSrc,
+  q31_t * pDst)
+{
+  const arm_cfft_radix4_instance_q31 *S_CFFT = S->pCfft;
+
+  /* Calculation of RIFFT of input */
+  if(S->ifftFlagR == 1u)
+  {
+    /*  Real IFFT core process */
+    arm_split_rifft_q31(pSrc, S->fftLenBy2, S->pTwiddleAReal,
+                        S->pTwiddleBReal, pDst, S->twidCoefRModifier);
+
+    /* Complex readix-4 IFFT process */
+    arm_radix4_butterfly_inverse_q31(pDst, S_CFFT->fftLen,
+                                     S_CFFT->pTwiddle,
+                                     S_CFFT->twidCoefModifier);
+    /* Bit reversal process */
+    if(S->bitReverseFlagR == 1u)
+    {
+      arm_bitreversal_q31(pDst, S_CFFT->fftLen,
+                          S_CFFT->bitRevFactor, S_CFFT->pBitRevTable);
+    }
+  }
+  else
+  {
+    /* Calculation of RFFT of input */
+
+    /* Complex readix-4 FFT process */
+    arm_radix4_butterfly_q31(pSrc, S_CFFT->fftLen,
+                             S_CFFT->pTwiddle, S_CFFT->twidCoefModifier);
+
+    /* Bit reversal process */
+    if(S->bitReverseFlagR == 1u)
+    {
+      arm_bitreversal_q31(pSrc, S_CFFT->fftLen,
+                          S_CFFT->bitRevFactor, S_CFFT->pBitRevTable);
+    }
+
+    /*  Real FFT core process */
+    arm_split_rfft_q31(pSrc, S->fftLenBy2, S->pTwiddleAReal,
+                       S->pTwiddleBReal, pDst, S->twidCoefRModifier);
+  }
+
+}
+
+
+  /**    
+   * @} end of RFFT_RIFFT group    
+   */
+
+/**    
+ * @brief  Core Real FFT process    
+ * @param[in]   *pSrc 				points to the input buffer.    
+ * @param[in]   fftLen  			length of FFT.   
+ * @param[in]   *pATable 			points to the twiddle Coef A buffer.    
+ * @param[in]   *pBTable 			points to the twiddle Coef B buffer.    
+ * @param[out]  *pDst 				points to the output buffer.    
+ * @param[in]   modifier 	        twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.   
+ * @return none.    
+ */
+
+void arm_split_rfft_q31(
+  q31_t * pSrc,
+  uint32_t fftLen,
+  q31_t * pATable,
+  q31_t * pBTable,
+  q31_t * pDst,
+  uint32_t modifier)
+{
+  uint32_t i;                                    /* Loop Counter */
+  q31_t outR, outI;                              /* Temporary variables for output */
+  q31_t *pCoefA, *pCoefB;                        /* Temporary pointers for twiddle factors */
+  q31_t CoefA1, CoefA2, CoefB1;                  /* Temporary variables for twiddle coefficients */
+  q31_t *pOut1 = &pDst[2], *pOut2 = &pDst[(4u * fftLen) - 1u];
+  q31_t *pIn1 = &pSrc[2], *pIn2 = &pSrc[(2u * fftLen) - 1u];
+
+  /* Init coefficient pointers */
+  pCoefA = &pATable[modifier * 2u];
+  pCoefB = &pBTable[modifier * 2u];
+
+  i = fftLen - 1u;
+
+  while(i > 0u)
+  {
+    /*    
+       outR = (pSrc[2 * i] * pATable[2 * i] - pSrc[2 * i + 1] * pATable[2 * i + 1]    
+       + pSrc[2 * n - 2 * i] * pBTable[2 * i] +    
+       pSrc[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);    
+     */
+
+    /* outI = (pIn[2 * i + 1] * pATable[2 * i] + pIn[2 * i] * pATable[2 * i + 1] +    
+       pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -    
+       pIn[2 * n - 2 * i + 1] * pBTable[2 * i]); */
+
+    CoefA1 = *pCoefA++;
+    CoefA2 = *pCoefA;
+
+    /* outR = (pSrc[2 * i] * pATable[2 * i] */
+    outR = ((int32_t) (((q63_t) * pIn1 * CoefA1) >> 32));
+
+    /* outI = pIn[2 * i] * pATable[2 * i + 1] */
+    outI = ((int32_t) (((q63_t) * pIn1++ * CoefA2) >> 32));
+
+    /* - pSrc[2 * i + 1] * pATable[2 * i + 1] */
+    outR =
+      (q31_t) ((((q63_t) outR << 32) + ((q63_t) * pIn1 * (-CoefA2))) >> 32);
+
+    /* (pIn[2 * i + 1] * pATable[2 * i] */
+    outI =
+      (q31_t) ((((q63_t) outI << 32) + ((q63_t) * pIn1++ * (CoefA1))) >> 32);
+
+    /* pSrc[2 * n - 2 * i] * pBTable[2 * i]  */
+    outR =
+      (q31_t) ((((q63_t) outR << 32) + ((q63_t) * pIn2 * (-CoefA2))) >> 32);
+    CoefB1 = *pCoefB;
+
+    /* pIn[2 * n - 2 * i] * pBTable[2 * i + 1] */
+    outI =
+      (q31_t) ((((q63_t) outI << 32) + ((q63_t) * pIn2-- * (-CoefB1))) >> 32);
+
+    /* pSrc[2 * n - 2 * i + 1] * pBTable[2 * i + 1] */
+    outR =
+      (q31_t) ((((q63_t) outR << 32) + ((q63_t) * pIn2 * (CoefB1))) >> 32);
+
+    /* pIn[2 * n - 2 * i + 1] * pBTable[2 * i] */
+    outI =
+      (q31_t) ((((q63_t) outI << 32) + ((q63_t) * pIn2-- * (-CoefA2))) >> 32);
+
+    /* write output */
+    *pOut1++ = (outR << 1u);
+    *pOut1++ = (outI << 1u);
+
+    /* write complex conjugate output */
+    *pOut2-- = -(outI << 1u);
+    *pOut2-- = (outR << 1u);
+
+    /* update coefficient pointer */
+    pCoefB = pCoefB + (modifier * 2u);
+    pCoefA = pCoefA + ((modifier * 2u) - 1u);
+
+    i--;
+
+  }
+
+  pDst[2u * fftLen] = pSrc[0] - pSrc[1];
+  pDst[(2u * fftLen) + 1u] = 0;
+
+  pDst[0] = pSrc[0] + pSrc[1];
+  pDst[1] = 0;
+
+}
+
+
+/**    
+ * @brief  Core Real IFFT process    
+ * @param[in]   *pSrc 				points to the input buffer.   
+ * @param[in]   fftLen  			length of FFT.    
+ * @param[in]   *pATable 			points to the twiddle Coef A buffer.   
+ * @param[in]   *pBTable 			points to the twiddle Coef B buffer.    
+ * @param[out]  *pDst 				points to the output buffer.   
+ * @param[in]   modifier 	        twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.   
+ * @return none.    
+ */
+
+void arm_split_rifft_q31(
+  q31_t * pSrc,
+  uint32_t fftLen,
+  q31_t * pATable,
+  q31_t * pBTable,
+  q31_t * pDst,
+  uint32_t modifier)
+{
+  q31_t outR, outI;                              /* Temporary variables for output */
+  q31_t *pCoefA, *pCoefB;                        /* Temporary pointers for twiddle factors */
+  q31_t CoefA1, CoefA2, CoefB1;                  /* Temporary variables for twiddle coefficients */
+  q31_t *pIn1 = &pSrc[0], *pIn2 = &pSrc[(2u * fftLen) + 1u];
+
+  pCoefA = &pATable[0];
+  pCoefB = &pBTable[0];
+
+  while(fftLen > 0u)
+  {
+    /*    
+       outR = (pIn[2 * i] * pATable[2 * i] + pIn[2 * i + 1] * pATable[2 * i + 1] +    
+       pIn[2 * n - 2 * i] * pBTable[2 * i] -    
+       pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);    
+
+       outI = (pIn[2 * i + 1] * pATable[2 * i] - pIn[2 * i] * pATable[2 * i + 1] -    
+       pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -    
+       pIn[2 * n - 2 * i + 1] * pBTable[2 * i]);    
+
+     */
+    CoefA1 = *pCoefA++;
+    CoefA2 = *pCoefA;
+
+    /* outR = (pIn[2 * i] * pATable[2 * i] */
+    outR = ((int32_t) (((q63_t) * pIn1 * CoefA1) >> 32));
+
+    /* - pIn[2 * i] * pATable[2 * i + 1] */
+    outI = -((int32_t) (((q63_t) * pIn1++ * CoefA2) >> 32));
+
+    /* pIn[2 * i + 1] * pATable[2 * i + 1] */
+    outR =
+      (q31_t) ((((q63_t) outR << 32) + ((q63_t) * pIn1 * (CoefA2))) >> 32);
+
+    /* pIn[2 * i + 1] * pATable[2 * i] */
+    outI =
+      (q31_t) ((((q63_t) outI << 32) + ((q63_t) * pIn1++ * (CoefA1))) >> 32);
+
+    /* pIn[2 * n - 2 * i] * pBTable[2 * i] */
+    outR =
+      (q31_t) ((((q63_t) outR << 32) + ((q63_t) * pIn2 * (CoefA2))) >> 32);
+
+    CoefB1 = *pCoefB;
+
+    /* pIn[2 * n - 2 * i] * pBTable[2 * i + 1] */
+    outI =
+      (q31_t) ((((q63_t) outI << 32) - ((q63_t) * pIn2-- * (CoefB1))) >> 32);
+
+    /* pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1] */
+    outR =
+      (q31_t) ((((q63_t) outR << 32) + ((q63_t) * pIn2 * (CoefB1))) >> 32);
+
+    /* pIn[2 * n - 2 * i + 1] * pBTable[2 * i] */
+    outI =
+      (q31_t) ((((q63_t) outI << 32) + ((q63_t) * pIn2-- * (CoefA2))) >> 32);
+
+    /* write output */
+    *pDst++ = (outR << 1u);
+    *pDst++ = (outI << 1u);
+
+    /* update coefficient pointer */
+    pCoefB = pCoefB + (modifier * 2u);
+    pCoefA = pCoefA + ((modifier * 2u) - 1u);
+
+    /* Decrement loop count */
+    fftLen--;
+
+  }
+
+
+}
diff --git a/apps/mathlib/CMSIS/Device/ARM/ARMCM3/Include/ARMCM3.h b/apps/mathlib/CMSIS/Device/ARM/ARMCM3/Include/ARMCM3.h
new file mode 100644
index 0000000000..8f39acd9dd
--- /dev/null
+++ b/apps/mathlib/CMSIS/Device/ARM/ARMCM3/Include/ARMCM3.h
@@ -0,0 +1,264 @@
+/**************************************************************************//**
+ * @file     ARMCM3.h
+ * @brief    CMSIS Core Peripheral Access Layer Header File for
+ *           ARMCM3 Device Series
+ * @version  V1.07
+ * @date     30. January 2012
+ *
+ * @note
+ * Copyright (C) 2012 ARM Limited. All rights reserved.
+ *
+ * @par
+ * ARM Limited (ARM) is supplying this software for use with Cortex-M 
+ * processor based microcontrollers.  This file can be freely distributed 
+ * within development tools that are supporting such ARM based processors. 
+ *
+ * @par
+ * THIS SOFTWARE IS PROVIDED "AS IS".  NO WARRANTIES, WHETHER EXPRESS, IMPLIED
+ * OR STATUTORY, INCLUDING, BUT NOT LIMITED TO, IMPLIED WARRANTIES OF
+ * MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE APPLY TO THIS SOFTWARE.
+ * ARM SHALL NOT, IN ANY CIRCUMSTANCES, BE LIABLE FOR SPECIAL, INCIDENTAL, OR
+ * CONSEQUENTIAL DAMAGES, FOR ANY REASON WHATSOEVER.
+ *
+ ******************************************************************************/
+
+#ifndef ARMCM3_H
+#define ARMCM3_H
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+
+/* -------------------------  Interrupt Number Definition  ------------------------ */
+
+typedef enum IRQn
+{
+/* -------------------  Cortex-M3 Processor Exceptions Numbers  ------------------- */
+  NonMaskableInt_IRQn           = -14,      /*!<  2 Non Maskable Interrupt          */
+  HardFault_IRQn                = -13,      /*!<  3 HardFault Interrupt             */
+  MemoryManagement_IRQn         = -12,      /*!<  4 Memory Management Interrupt     */
+  BusFault_IRQn                 = -11,      /*!<  5 Bus Fault Interrupt             */
+  UsageFault_IRQn               = -10,      /*!<  6 Usage Fault Interrupt           */
+  SVCall_IRQn                   =  -5,      /*!< 11 SV Call Interrupt               */
+  DebugMonitor_IRQn             =  -4,      /*!< 12 Debug Monitor Interrupt         */
+  PendSV_IRQn                   =  -2,      /*!< 14 Pend SV Interrupt               */
+  SysTick_IRQn                  =  -1,      /*!< 15 System Tick Interrupt           */
+
+/* ----------------------  ARMCM3 Specific Interrupt Numbers  --------------------- */
+  WDT_IRQn                      =   0,      /*!< Watchdog Timer Interrupt           */
+  RTC_IRQn                      =   1,      /*!< Real Time Clock Interrupt          */
+  TIM0_IRQn                     =   2,      /*!< Timer0 / Timer1 Interrupt          */
+  TIM2_IRQn                     =   3,      /*!< Timer2 / Timer3 Interrupt          */
+  MCIA_IRQn                     =   4,      /*!< MCIa Interrupt                     */
+  MCIB_IRQn                     =   5,      /*!< MCIb Interrupt                     */
+  UART0_IRQn                    =   6,      /*!< UART0 Interrupt                    */
+  UART1_IRQn                    =   7,      /*!< UART1 Interrupt                    */
+  UART2_IRQn                    =   8,      /*!< UART2 Interrupt                    */
+  UART4_IRQn                    =   9,      /*!< UART4 Interrupt                    */
+  AACI_IRQn                     =  10,      /*!< AACI / AC97 Interrupt              */
+  CLCD_IRQn                     =  11,      /*!< CLCD Combined Interrupt            */
+  ENET_IRQn                     =  12,      /*!< Ethernet Interrupt                 */
+  USBDC_IRQn                    =  13,      /*!< USB Device Interrupt               */
+  USBHC_IRQn                    =  14,      /*!< USB Host Controller Interrupt      */
+  CHLCD_IRQn                    =  15,      /*!< Character LCD Interrupt            */
+  FLEXRAY_IRQn                  =  16,      /*!< Flexray Interrupt                  */
+  CAN_IRQn                      =  17,      /*!< CAN Interrupt                      */
+  LIN_IRQn                      =  18,      /*!< LIN Interrupt                      */
+  I2C_IRQn                      =  19,      /*!< I2C ADC/DAC Interrupt              */
+  CPU_CLCD_IRQn                 =  28,      /*!< CPU CLCD Combined Interrupt        */
+  UART3_IRQn                    =  30,      /*!< UART3 Interrupt                    */
+  SPI_IRQn                      =  31,      /*!< SPI Touchscreen Interrupt          */
+} IRQn_Type;
+
+
+/* ================================================================================ */
+/* ================      Processor and Core Peripheral Section     ================ */
+/* ================================================================================ */
+
+/* --------  Configuration of the Cortex-M4 Processor and Core Peripherals  ------- */
+#define __CM3_REV                 0x0201    /*!< Core revision r2p1                              */
+#define __MPU_PRESENT             1         /*!< MPU present or not                              */
+#define __NVIC_PRIO_BITS          3         /*!< Number of Bits used for Priority Levels         */
+#define __Vendor_SysTickConfig    0         /*!< Set to 1 if different SysTick Config is used    */
+
+#include                        /* Processor and core peripherals                    */
+/* NuttX */
+//#include "system_ARMCM3.h"                  /* System Header                                     */
+
+
+/* ================================================================================ */
+/* ================       Device Specific Peripheral Section       ================ */
+/* ================================================================================ */
+
+/* -------------------  Start of section using anonymous unions  ------------------ */
+#if defined(__CC_ARM)
+  #pragma push
+  #pragma anon_unions
+#elif defined(__ICCARM__)
+  #pragma language=extended
+#elif defined(__GNUC__)
+  /* anonymous unions are enabled by default */
+#elif defined(__TMS470__)
+/* anonymous unions are enabled by default */
+#elif defined(__TASKING__)
+  #pragma warning 586
+#else
+  #warning Not supported compiler type
+#endif
+
+
+
+/* ================================================================================ */
+/* ================            CPU FPGA System (CPU_SYS)           ================ */
+/* ================================================================================ */
+typedef struct
+{
+  __I  uint32_t ID;               /* Offset: 0x000 (R/ )  Board and FPGA Identifier */
+  __IO uint32_t MEMCFG;           /* Offset: 0x004 (R/W)  Remap and Alias Memory Control */
+  __I  uint32_t SW;               /* Offset: 0x008 (R/ )  Switch States */
+  __IO uint32_t LED;              /* Offset: 0x00C (R/W)  LED Output States */
+  __I  uint32_t TS;               /* Offset: 0x010 (R/ )  Touchscreen Register */
+  __IO uint32_t CTRL1;            /* Offset: 0x014 (R/W)  Misc Control Functions */
+       uint32_t RESERVED0[2];
+  __IO uint32_t CLKCFG;           /* Offset: 0x020 (R/W)  System Clock Configuration */
+  __IO uint32_t WSCFG;            /* Offset: 0x024 (R/W)  Flash Waitstate Configuration */
+  __IO uint32_t CPUCFG;           /* Offset: 0x028 (R/W)  Processor Configuration */
+       uint32_t RESERVED1[3];
+  __IO uint32_t BASE;             /* Offset: 0x038 (R/W)  ROM Table base Address */
+  __IO uint32_t ID2;              /* Offset: 0x03C (R/W)  Secondary Identification Register */
+} ARM_CPU_SYS_TypeDef;
+
+
+/* ================================================================================ */
+/* ================            DUT FPGA System (DUT_SYS)           ================ */
+/* ================================================================================ */
+typedef struct
+{
+  __I  uint32_t ID;               /* Offset: 0x000 (R/ )  Board and FPGA Identifier */
+  __IO uint32_t PERCFG;           /* Offset: 0x004 (R/W)  Peripheral Control Signals */
+  __I  uint32_t SW;               /* Offset: 0x008 (R/ )  Switch States */
+  __IO uint32_t LED;              /* Offset: 0x00C (R/W)  LED Output States */
+  __IO uint32_t SEG7;             /* Offset: 0x010 (R/W)  7-segment LED Output States */
+  __I  uint32_t CNT25MHz;         /* Offset: 0x014 (R/ )  Freerunning counter incrementing at 25MHz */
+  __I  uint32_t CNT100Hz;         /* Offset: 0x018 (R/ )  Freerunning counter incrementing at 100Hz */
+} ARM_DUT_SYS_TypeDef;
+
+
+/* ================================================================================ */
+/* ================                   Timer (TIM)                  ================ */
+/* ================================================================================ */
+typedef struct
+{
+  __IO uint32_t Timer1Load;       /* Offset: 0x000 (R/W)  Timer 1 Load */
+  __I  uint32_t Timer1Value;      /* Offset: 0x004 (R/ )  Timer 1 Counter Current Value */
+  __IO uint32_t Timer1Control;    /* Offset: 0x008 (R/W)  Timer 1 Control */
+  __O  uint32_t Timer1IntClr;     /* Offset: 0x00C ( /W)  Timer 1 Interrupt Clear */
+  __I  uint32_t Timer1RIS;        /* Offset: 0x010 (R/ )  Timer 1 Raw Interrupt Status */
+  __I  uint32_t Timer1MIS;        /* Offset: 0x014 (R/ )  Timer 1 Masked Interrupt Status */
+  __IO uint32_t Timer1BGLoad;     /* Offset: 0x018 (R/W)  Background Load Register */
+       uint32_t RESERVED0[1];
+  __IO uint32_t Timer2Load;       /* Offset: 0x020 (R/W)  Timer 2 Load */
+  __I  uint32_t Timer2Value;      /* Offset: 0x024 (R/ )  Timer 2 Counter Current Value */
+  __IO uint32_t Timer2Control;    /* Offset: 0x028 (R/W)  Timer 2 Control */
+  __O  uint32_t Timer2IntClr;     /* Offset: 0x02C ( /W)  Timer 2 Interrupt Clear */
+  __I  uint32_t Timer2RIS;        /* Offset: 0x030 (R/ )  Timer 2 Raw Interrupt Status */
+  __I  uint32_t Timer2MIS;        /* Offset: 0x034 (R/ )  Timer 2 Masked Interrupt Status */
+  __IO uint32_t Timer2BGLoad;     /* Offset: 0x038 (R/W)  Background Load Register */
+} ARM_TIM_TypeDef;
+
+
+/* ================================================================================ */
+/* ============== Universal Asyncronous Receiver / Transmitter (UART) ============= */
+/* ================================================================================ */
+typedef struct
+{
+  __IO uint32_t DR;               /* Offset: 0x000 (R/W)  Data */ 
+  union {
+  __I  uint32_t RSR;              /* Offset: 0x000 (R/ )  Receive Status */
+  __O  uint32_t ECR;              /* Offset: 0x000 ( /W)  Error Clear */
+  };
+       uint32_t RESERVED0[4];
+  __IO uint32_t FR;               /* Offset: 0x018 (R/W)  Flags */
+       uint32_t RESERVED1[1];
+  __IO uint32_t ILPR;             /* Offset: 0x020 (R/W)  IrDA Low-power Counter */
+  __IO uint32_t IBRD;             /* Offset: 0x024 (R/W)  Interger Baud Rate */
+  __IO uint32_t FBRD;             /* Offset: 0x028 (R/W)  Fractional Baud Rate */
+  __IO uint32_t LCR_H;            /* Offset: 0x02C (R/W)  Line Control */
+  __IO uint32_t CR;               /* Offset: 0x030 (R/W)  Control */
+  __IO uint32_t IFLS;             /* Offset: 0x034 (R/W)  Interrupt FIFO Level Select */
+  __IO uint32_t IMSC;             /* Offset: 0x038 (R/W)  Interrupt Mask Set / Clear */
+  __IO uint32_t RIS;              /* Offset: 0x03C (R/W)  Raw Interrupt Status */
+  __IO uint32_t MIS;              /* Offset: 0x040 (R/W)  Masked Interrupt Status */
+  __O  uint32_t ICR;              /* Offset: 0x044 ( /W)  Interrupt Clear */
+  __IO uint32_t DMACR;            /* Offset: 0x048 (R/W)  DMA Control */
+} ARM_UART_TypeDef;
+
+
+/* --------------------  End of section using anonymous unions  ------------------- */
+#if defined(__CC_ARM)
+  #pragma pop
+#elif defined(__ICCARM__)
+  /* leave anonymous unions enabled */
+#elif defined(__GNUC__)
+  /* anonymous unions are enabled by default */
+#elif defined(__TMS470__)
+  /* anonymous unions are enabled by default */
+#elif defined(__TASKING__)
+  #pragma warning restore
+#else
+  #warning Not supported compiler type
+#endif
+
+
+
+
+/* ================================================================================ */
+/* ================              Peripheral memory map             ================ */
+/* ================================================================================ */
+/* --------------------------  CPU FPGA memory map  ------------------------------- */
+#define ARM_FLASH_BASE            (0x00000000UL)
+#define ARM_RAM_BASE              (0x20000000UL)
+#define ARM_RAM_FPGA_BASE         (0x1EFF0000UL)
+#define ARM_CPU_CFG_BASE          (0xDFFF0000UL)
+
+#define ARM_CPU_SYS_BASE          (ARM_CPU_CFG_BASE  + 0x00000)
+#define ARM_UART3_BASE            (ARM_CPU_CFG_BASE  + 0x05000)
+
+/* --------------------------  DUT FPGA memory map  ------------------------------- */
+#define ARM_APB_BASE              (0x40000000UL)
+#define ARM_AHB_BASE              (0x4FF00000UL)
+#define ARM_DMC_BASE              (0x60000000UL)
+#define ARM_SMC_BASE              (0xA0000000UL)
+
+#define ARM_TIM0_BASE             (ARM_APB_BASE      + 0x02000)
+#define ARM_TIM2_BASE             (ARM_APB_BASE      + 0x03000)
+#define ARM_DUT_SYS_BASE          (ARM_APB_BASE      + 0x04000)
+#define ARM_UART0_BASE            (ARM_APB_BASE      + 0x06000)
+#define ARM_UART1_BASE            (ARM_APB_BASE      + 0x07000)
+#define ARM_UART2_BASE            (ARM_APB_BASE      + 0x08000)
+#define ARM_UART4_BASE            (ARM_APB_BASE      + 0x09000)
+
+
+/* ================================================================================ */
+/* ================             Peripheral declaration             ================ */
+/* ================================================================================ */
+/* --------------------------  CPU FPGA Peripherals  ------------------------------ */
+#define ARM_CPU_SYS               ((ARM_CPU_SYS_TypeDef *)  ARM_CPU_SYS_BASE)
+#define ARM_UART3                 ((   ARM_UART_TypeDef *)    ARM_UART3_BASE)
+
+/* --------------------------  DUT FPGA Peripherals  ------------------------------ */
+#define ARM_DUT_SYS               ((ARM_DUT_SYS_TypeDef *)  ARM_DUT_SYS_BASE)
+#define ARM_TIM0                  ((    ARM_TIM_TypeDef *)     ARM_TIM0_BASE)
+#define ARM_TIM2                  ((    ARM_TIM_TypeDef *)     ARM_TIM2_BASE)
+#define ARM_UART0                 ((   ARM_UART_TypeDef *)    ARM_UART0_BASE)
+#define ARM_UART1                 ((   ARM_UART_TypeDef *)    ARM_UART1_BASE)
+#define ARM_UART2                 ((   ARM_UART_TypeDef *)    ARM_UART2_BASE)
+#define ARM_UART4                 ((   ARM_UART_TypeDef *)    ARM_UART4_BASE)
+
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif  /* ARMCM3_H */
diff --git a/apps/mathlib/CMSIS/Device/ARM/ARMCM4/Include/ARMCM4.h b/apps/mathlib/CMSIS/Device/ARM/ARMCM4/Include/ARMCM4.h
new file mode 100644
index 0000000000..181b7e4335
--- /dev/null
+++ b/apps/mathlib/CMSIS/Device/ARM/ARMCM4/Include/ARMCM4.h
@@ -0,0 +1,265 @@
+/**************************************************************************//**
+ * @file     ARMCM4.h
+ * @brief    CMSIS Core Peripheral Access Layer Header File for
+ *           ARMCM4 Device Series
+ * @version  V1.07
+ * @date     30. January 2012
+ *
+ * @note
+ * Copyright (C) 2012 ARM Limited. All rights reserved.
+ *
+ * @par
+ * ARM Limited (ARM) is supplying this software for use with Cortex-M 
+ * processor based microcontrollers.  This file can be freely distributed 
+ * within development tools that are supporting such ARM based processors. 
+ *
+ * @par
+ * THIS SOFTWARE IS PROVIDED "AS IS".  NO WARRANTIES, WHETHER EXPRESS, IMPLIED
+ * OR STATUTORY, INCLUDING, BUT NOT LIMITED TO, IMPLIED WARRANTIES OF
+ * MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE APPLY TO THIS SOFTWARE.
+ * ARM SHALL NOT, IN ANY CIRCUMSTANCES, BE LIABLE FOR SPECIAL, INCIDENTAL, OR
+ * CONSEQUENTIAL DAMAGES, FOR ANY REASON WHATSOEVER.
+ *
+ ******************************************************************************/
+
+#ifndef ARMCM4_H
+#define ARMCM4_H
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+
+/* -------------------------  Interrupt Number Definition  ------------------------ */
+
+typedef enum IRQn
+{
+/* -------------------  Cortex-M4 Processor Exceptions Numbers  ------------------- */
+  NonMaskableInt_IRQn           = -14,      /*!<  2 Non Maskable Interrupt          */
+  HardFault_IRQn                = -13,      /*!<  3 HardFault Interrupt             */
+  MemoryManagement_IRQn         = -12,      /*!<  4 Memory Management Interrupt     */
+  BusFault_IRQn                 = -11,      /*!<  5 Bus Fault Interrupt             */
+  UsageFault_IRQn               = -10,      /*!<  6 Usage Fault Interrupt           */
+  SVCall_IRQn                   =  -5,      /*!< 11 SV Call Interrupt               */
+  DebugMonitor_IRQn             =  -4,      /*!< 12 Debug Monitor Interrupt         */
+  PendSV_IRQn                   =  -2,      /*!< 14 Pend SV Interrupt               */
+  SysTick_IRQn                  =  -1,      /*!< 15 System Tick Interrupt           */
+
+/* ----------------------  ARMCM4 Specific Interrupt Numbers  --------------------- */
+  WDT_IRQn                      =   0,      /*!< Watchdog Timer Interrupt           */
+  RTC_IRQn                      =   1,      /*!< Real Time Clock Interrupt          */
+  TIM0_IRQn                     =   2,      /*!< Timer0 / Timer1 Interrupt          */
+  TIM2_IRQn                     =   3,      /*!< Timer2 / Timer3 Interrupt          */
+  MCIA_IRQn                     =   4,      /*!< MCIa Interrupt                     */
+  MCIB_IRQn                     =   5,      /*!< MCIb Interrupt                     */
+  UART0_IRQn                    =   6,      /*!< UART0 Interrupt                    */
+  UART1_IRQn                    =   7,      /*!< UART1 Interrupt                    */
+  UART2_IRQn                    =   8,      /*!< UART2 Interrupt                    */
+  UART4_IRQn                    =   9,      /*!< UART4 Interrupt                    */
+  AACI_IRQn                     =  10,      /*!< AACI / AC97 Interrupt              */
+  CLCD_IRQn                     =  11,      /*!< CLCD Combined Interrupt            */
+  ENET_IRQn                     =  12,      /*!< Ethernet Interrupt                 */
+  USBDC_IRQn                    =  13,      /*!< USB Device Interrupt               */
+  USBHC_IRQn                    =  14,      /*!< USB Host Controller Interrupt      */
+  CHLCD_IRQn                    =  15,      /*!< Character LCD Interrupt            */
+  FLEXRAY_IRQn                  =  16,      /*!< Flexray Interrupt                  */
+  CAN_IRQn                      =  17,      /*!< CAN Interrupt                      */
+  LIN_IRQn                      =  18,      /*!< LIN Interrupt                      */
+  I2C_IRQn                      =  19,      /*!< I2C ADC/DAC Interrupt              */
+  CPU_CLCD_IRQn                 =  28,      /*!< CPU CLCD Combined Interrupt        */
+  UART3_IRQn                    =  30,      /*!< UART3 Interrupt                    */
+  SPI_IRQn                      =  31,      /*!< SPI Touchscreen Interrupt          */
+} IRQn_Type;
+
+
+/* ================================================================================ */
+/* ================      Processor and Core Peripheral Section     ================ */
+/* ================================================================================ */
+
+/* --------  Configuration of the Cortex-M4 Processor and Core Peripherals  ------- */
+#define __CM4_REV                 0x0001    /*!< Core revision r0p1                              */
+#define __MPU_PRESENT             1         /*!< MPU present or not                              */
+#define __NVIC_PRIO_BITS          3         /*!< Number of Bits used for Priority Levels         */
+#define __Vendor_SysTickConfig    0         /*!< Set to 1 if different SysTick Config is used    */
+#define __FPU_PRESENT             1         /*!< FPU present or not                              */
+
+#include                        /* Processor and core peripherals                    */
+/* NuttX */
+//#include "system_ARMCM4.h"                  /* System Header                                     */
+
+
+/* ================================================================================ */
+/* ================       Device Specific Peripheral Section       ================ */
+/* ================================================================================ */
+
+/* -------------------  Start of section using anonymous unions  ------------------ */
+#if defined(__CC_ARM)
+  #pragma push
+  #pragma anon_unions
+#elif defined(__ICCARM__)
+  #pragma language=extended
+#elif defined(__GNUC__)
+  /* anonymous unions are enabled by default */
+#elif defined(__TMS470__)
+/* anonymous unions are enabled by default */
+#elif defined(__TASKING__)
+  #pragma warning 586
+#else
+  #warning Not supported compiler type
+#endif
+
+
+
+/* ================================================================================ */
+/* ================            CPU FPGA System (CPU_SYS)           ================ */
+/* ================================================================================ */
+typedef struct
+{
+  __I  uint32_t ID;               /* Offset: 0x000 (R/ )  Board and FPGA Identifier */
+  __IO uint32_t MEMCFG;           /* Offset: 0x004 (R/W)  Remap and Alias Memory Control */
+  __I  uint32_t SW;               /* Offset: 0x008 (R/ )  Switch States */
+  __IO uint32_t LED;              /* Offset: 0x00C (R/W)  LED Output States */
+  __I  uint32_t TS;               /* Offset: 0x010 (R/ )  Touchscreen Register */
+  __IO uint32_t CTRL1;            /* Offset: 0x014 (R/W)  Misc Control Functions */
+       uint32_t RESERVED0[2];
+  __IO uint32_t CLKCFG;           /* Offset: 0x020 (R/W)  System Clock Configuration */
+  __IO uint32_t WSCFG;            /* Offset: 0x024 (R/W)  Flash Waitstate Configuration */
+  __IO uint32_t CPUCFG;           /* Offset: 0x028 (R/W)  Processor Configuration */
+       uint32_t RESERVED1[3];
+  __IO uint32_t BASE;             /* Offset: 0x038 (R/W)  ROM Table base Address */
+  __IO uint32_t ID2;              /* Offset: 0x03C (R/W)  Secondary Identification Register */
+} ARM_CPU_SYS_TypeDef;
+
+
+/* ================================================================================ */
+/* ================            DUT FPGA System (DUT_SYS)           ================ */
+/* ================================================================================ */
+typedef struct
+{
+  __I  uint32_t ID;               /* Offset: 0x000 (R/ )  Board and FPGA Identifier */
+  __IO uint32_t PERCFG;           /* Offset: 0x004 (R/W)  Peripheral Control Signals */
+  __I  uint32_t SW;               /* Offset: 0x008 (R/ )  Switch States */
+  __IO uint32_t LED;              /* Offset: 0x00C (R/W)  LED Output States */
+  __IO uint32_t SEG7;             /* Offset: 0x010 (R/W)  7-segment LED Output States */
+  __I  uint32_t CNT25MHz;         /* Offset: 0x014 (R/ )  Freerunning counter incrementing at 25MHz */
+  __I  uint32_t CNT100Hz;         /* Offset: 0x018 (R/ )  Freerunning counter incrementing at 100Hz */
+} ARM_DUT_SYS_TypeDef;
+
+
+/* ================================================================================ */
+/* ================                   Timer (TIM)                  ================ */
+/* ================================================================================ */
+typedef struct
+{
+  __IO uint32_t Timer1Load;       /* Offset: 0x000 (R/W)  Timer 1 Load */
+  __I  uint32_t Timer1Value;      /* Offset: 0x004 (R/ )  Timer 1 Counter Current Value */
+  __IO uint32_t Timer1Control;    /* Offset: 0x008 (R/W)  Timer 1 Control */
+  __O  uint32_t Timer1IntClr;     /* Offset: 0x00C ( /W)  Timer 1 Interrupt Clear */
+  __I  uint32_t Timer1RIS;        /* Offset: 0x010 (R/ )  Timer 1 Raw Interrupt Status */
+  __I  uint32_t Timer1MIS;        /* Offset: 0x014 (R/ )  Timer 1 Masked Interrupt Status */
+  __IO uint32_t Timer1BGLoad;     /* Offset: 0x018 (R/W)  Background Load Register */
+       uint32_t RESERVED0[1];
+  __IO uint32_t Timer2Load;       /* Offset: 0x020 (R/W)  Timer 2 Load */
+  __I  uint32_t Timer2Value;      /* Offset: 0x024 (R/ )  Timer 2 Counter Current Value */
+  __IO uint32_t Timer2Control;    /* Offset: 0x028 (R/W)  Timer 2 Control */
+  __O  uint32_t Timer2IntClr;     /* Offset: 0x02C ( /W)  Timer 2 Interrupt Clear */
+  __I  uint32_t Timer2RIS;        /* Offset: 0x030 (R/ )  Timer 2 Raw Interrupt Status */
+  __I  uint32_t Timer2MIS;        /* Offset: 0x034 (R/ )  Timer 2 Masked Interrupt Status */
+  __IO uint32_t Timer2BGLoad;     /* Offset: 0x038 (R/W)  Background Load Register */
+} ARM_TIM_TypeDef;
+
+
+/* ================================================================================ */
+/* ============== Universal Asyncronous Receiver / Transmitter (UART) ============= */
+/* ================================================================================ */
+typedef struct
+{
+  __IO uint32_t DR;               /* Offset: 0x000 (R/W)  Data */ 
+  union {
+  __I  uint32_t RSR;              /* Offset: 0x000 (R/ )  Receive Status */
+  __O  uint32_t ECR;              /* Offset: 0x000 ( /W)  Error Clear */
+  };
+       uint32_t RESERVED0[4];
+  __IO uint32_t FR;               /* Offset: 0x018 (R/W)  Flags */
+       uint32_t RESERVED1[1];
+  __IO uint32_t ILPR;             /* Offset: 0x020 (R/W)  IrDA Low-power Counter */
+  __IO uint32_t IBRD;             /* Offset: 0x024 (R/W)  Interger Baud Rate */
+  __IO uint32_t FBRD;             /* Offset: 0x028 (R/W)  Fractional Baud Rate */
+  __IO uint32_t LCR_H;            /* Offset: 0x02C (R/W)  Line Control */
+  __IO uint32_t CR;               /* Offset: 0x030 (R/W)  Control */
+  __IO uint32_t IFLS;             /* Offset: 0x034 (R/W)  Interrupt FIFO Level Select */
+  __IO uint32_t IMSC;             /* Offset: 0x038 (R/W)  Interrupt Mask Set / Clear */
+  __IO uint32_t RIS;              /* Offset: 0x03C (R/W)  Raw Interrupt Status */
+  __IO uint32_t MIS;              /* Offset: 0x040 (R/W)  Masked Interrupt Status */
+  __O  uint32_t ICR;              /* Offset: 0x044 ( /W)  Interrupt Clear */
+  __IO uint32_t DMACR;            /* Offset: 0x048 (R/W)  DMA Control */
+} ARM_UART_TypeDef;
+
+
+/* --------------------  End of section using anonymous unions  ------------------- */
+#if defined(__CC_ARM)
+  #pragma pop
+#elif defined(__ICCARM__)
+  /* leave anonymous unions enabled */
+#elif defined(__GNUC__)
+  /* anonymous unions are enabled by default */
+#elif defined(__TMS470__)
+  /* anonymous unions are enabled by default */
+#elif defined(__TASKING__)
+  #pragma warning restore
+#else
+  #warning Not supported compiler type
+#endif
+
+
+
+
+/* ================================================================================ */
+/* ================              Peripheral memory map             ================ */
+/* ================================================================================ */
+/* --------------------------  CPU FPGA memory map  ------------------------------- */
+#define ARM_FLASH_BASE            (0x00000000UL)
+#define ARM_RAM_BASE              (0x20000000UL)
+#define ARM_RAM_FPGA_BASE         (0x1EFF0000UL)
+#define ARM_CPU_CFG_BASE          (0xDFFF0000UL)
+
+#define ARM_CPU_SYS_BASE          (ARM_CPU_CFG_BASE  + 0x00000)
+#define ARM_UART3_BASE            (ARM_CPU_CFG_BASE  + 0x05000)
+
+/* --------------------------  DUT FPGA memory map  ------------------------------- */
+#define ARM_APB_BASE              (0x40000000UL)
+#define ARM_AHB_BASE              (0x4FF00000UL)
+#define ARM_DMC_BASE              (0x60000000UL)
+#define ARM_SMC_BASE              (0xA0000000UL)
+
+#define ARM_TIM0_BASE             (ARM_APB_BASE      + 0x02000)
+#define ARM_TIM2_BASE             (ARM_APB_BASE      + 0x03000)
+#define ARM_DUT_SYS_BASE          (ARM_APB_BASE      + 0x04000)
+#define ARM_UART0_BASE            (ARM_APB_BASE      + 0x06000)
+#define ARM_UART1_BASE            (ARM_APB_BASE      + 0x07000)
+#define ARM_UART2_BASE            (ARM_APB_BASE      + 0x08000)
+#define ARM_UART4_BASE            (ARM_APB_BASE      + 0x09000)
+
+
+/* ================================================================================ */
+/* ================             Peripheral declaration             ================ */
+/* ================================================================================ */
+/* --------------------------  CPU FPGA Peripherals  ------------------------------ */
+#define ARM_CPU_SYS               ((ARM_CPU_SYS_TypeDef *)  ARM_CPU_SYS_BASE)
+#define ARM_UART3                 ((   ARM_UART_TypeDef *)    ARM_UART3_BASE)
+
+/* --------------------------  DUT FPGA Peripherals  ------------------------------ */
+#define ARM_DUT_SYS               ((ARM_DUT_SYS_TypeDef *)  ARM_DUT_SYS_BASE)
+#define ARM_TIM0                  ((    ARM_TIM_TypeDef *)     ARM_TIM0_BASE)
+#define ARM_TIM2                  ((    ARM_TIM_TypeDef *)     ARM_TIM2_BASE)
+#define ARM_UART0                 ((   ARM_UART_TypeDef *)    ARM_UART0_BASE)
+#define ARM_UART1                 ((   ARM_UART_TypeDef *)    ARM_UART1_BASE)
+#define ARM_UART2                 ((   ARM_UART_TypeDef *)    ARM_UART2_BASE)
+#define ARM_UART4                 ((   ARM_UART_TypeDef *)    ARM_UART4_BASE)
+
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif  /* ARMCM4_H */
diff --git a/apps/mathlib/CMSIS/Include/arm_common_tables.h b/apps/mathlib/CMSIS/Include/arm_common_tables.h
new file mode 100644
index 0000000000..5fd6ff4af9
--- /dev/null
+++ b/apps/mathlib/CMSIS/Include/arm_common_tables.h
@@ -0,0 +1,38 @@
+/* ---------------------------------------------------------------------- 
+* Copyright (C) 2010 ARM Limited. All rights reserved. 
+* 
+* $Date:        11. November 2010  
+* $Revision: 	V1.0.2  
+* 
+* Project: 	    CMSIS DSP Library 
+* Title:	    arm_common_tables.h 
+* 
+* Description:	This file has extern declaration for common tables like Bitreverse, reciprocal etc which are used across different functions 
+* 
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Version 1.0.2 2010/11/11 
+*    Documentation updated.  
+* 
+* Version 1.0.1 2010/10/05  
+*    Production release and review comments incorporated. 
+* 
+* Version 1.0.0 2010/09/20  
+*    Production release and review comments incorporated. 
+* -------------------------------------------------------------------- */
+
+#ifndef _ARM_COMMON_TABLES_H
+#define _ARM_COMMON_TABLES_H
+
+#include "arm_math.h"
+
+extern const uint16_t armBitRevTable[1024];
+extern const q15_t armRecipTableQ15[64];
+extern const q31_t armRecipTableQ31[64];
+extern const q31_t realCoefAQ31[1024];
+extern const q31_t realCoefBQ31[1024];
+extern const float32_t twiddleCoef[6144];
+extern const q31_t twiddleCoefQ31[6144];
+extern const q15_t twiddleCoefQ15[6144];
+
+#endif /*  ARM_COMMON_TABLES_H */
diff --git a/apps/mathlib/CMSIS/Include/arm_math.h b/apps/mathlib/CMSIS/Include/arm_math.h
new file mode 100644
index 0000000000..fabd98be7a
--- /dev/null
+++ b/apps/mathlib/CMSIS/Include/arm_math.h
@@ -0,0 +1,7569 @@
+/* ----------------------------------------------------------------------   
+ * Copyright (C) 2010-2011 ARM Limited. All rights reserved.   
+ *   
+ * $Date:        15. February 2012  
+ * $Revision: 	V1.1.0  
+ *   
+ * Project: 	    CMSIS DSP Library   
+ * Title:	     	arm_math.h
+ *   
+ * Description:	 Public header file for CMSIS DSP Library
+ *   
+ * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+ *  
+ * Version 1.1.0 2012/02/15 
+ *    Updated with more optimizations, bug fixes and minor API changes.  
+ *  
+ * Version 1.0.10 2011/7/15 
+ *    Big Endian support added and Merged M0 and M3/M4 Source code.  
+ *   
+ * Version 1.0.3 2010/11/29  
+ *    Re-organized the CMSIS folders and updated documentation.   
+ *    
+ * Version 1.0.2 2010/11/11   
+ *    Documentation updated.    
+ *   
+ * Version 1.0.1 2010/10/05    
+ *    Production release and review comments incorporated.   
+ *   
+ * Version 1.0.0 2010/09/20    
+ *    Production release and review comments incorporated.   
+ * -------------------------------------------------------------------- */
+
+/**
+   \mainpage CMSIS DSP Software Library
+   *
+   * Introduction
+   *
+   * This user manual describes the CMSIS DSP software library, 
+   * a suite of common signal processing functions for use on Cortex-M processor based devices.
+   *
+   * The library is divided into a number of functions each covering a specific category:  
+   * - Basic math functions
+   * - Fast math functions
+   * - Complex math functions
+   * - Filters
+   * - Matrix functions
+   * - Transforms
+   * - Motor control functions
+   * - Statistical functions
+   * - Support functions
+   * - Interpolation functions
+   *
+   * The library has separate functions for operating on 8-bit integers, 16-bit integers,
+   * 32-bit integer and 32-bit floating-point values. 
+   *
+   * Pre-processor Macros 
+   * 
+   * Each library project have differant pre-processor macros. 
+   * 
+   * - UNALIGNED_SUPPORT_DISABLE: 
+   * 
+   * Define macro UNALIGNED_SUPPORT_DISABLE, If the silicon does not support unaligned memory access    
+   * 
+   * - ARM_MATH_BIG_ENDIAN: 
+   * 
+   * Define macro ARM_MATH_BIG_ENDIAN to build the library for big endian targets. By default library builds for little endian targets. 
+   * 
+   * - ARM_MATH_MATRIX_CHECK: 
+   * 
+   * Define macro ARM_MATH_MATRIX_CHECK for checking on the input and output sizes of matrices 
+   * 
+   * - ARM_MATH_ROUNDING: 
+   * 
+   * Define macro ARM_MATH_ROUNDING for rounding on support functions
+   *
+   * - ARM_MATH_CMx:
+   *
+   * Define macro ARM_MATH_CM4 for building the library on Cortex-M4 target, ARM_MATH_CM3 for building library on Cortex-M3 target
+   * and ARM_MATH_CM0 for building library on cortex-M0 target.
+   * 
+   * - __FPU_PRESENT:
+   *
+   * Initialize macro __FPU_PRESENT = 1 when building on FPU supported Targets. Enable this macro for M4bf and M4lf libraries 
+   *
+   * Toolchain Support
+   *
+   * The library has been developed and tested with MDK-ARM version 4.23. 
+   * The library is being tested in GCC and IAR toolchains and updates on this activity will be made available shortly.
+   *
+   * Using the Library
+   *
+   * The library installer contains prebuilt versions of the libraries in the Lib folder.
+   * - arm_cortexM4lf_math.lib (Little endian and Floating Point Unit on Cortex-M4)
+   * - arm_cortexM4bf_math.lib (Big endian and Floating Point Unit on Cortex-M4)
+   * - arm_cortexM4l_math.lib (Little endian on Cortex-M4)
+   * - arm_cortexM4b_math.lib (Big endian on Cortex-M4)
+   * - arm_cortexM3l_math.lib (Little endian on Cortex-M3)
+   * - arm_cortexM3b_math.lib (Big endian on Cortex-M3)
+   * - arm_cortexM0l_math.lib (Little endian on Cortex-M0)
+   * - arm_cortexM0b_math.lib (Big endian on Cortex-M3)
+   *
+   * The library functions are declared in the public file arm_math.h which is placed in the Include folder.
+   * Simply include this file and link the appropriate library in the application and begin calling the library functions. The Library supports single 
+   * public header file  arm_math.h for Cortex-M4/M3/M0 with little endian and big endian. Same header file will be used for floating point unit(FPU) variants. 
+   * Define the appropriate pre processor MACRO ARM_MATH_CM4 or  ARM_MATH_CM3 or 
+   * ARM_MATH_CM0 depending on the target processor in the application.
+   *
+   * Examples
+   *
+   * The library ships with a number of examples which demonstrate how to use the library functions.
+   *
+   * Building the Library
+   *
+   * The library installer contains project files to re build libraries on MDK Tool chain in the CMSIS\\DSP_Lib\\Source\\ARM folder.
+   * - arm_cortexM0b_math.uvproj
+   * - arm_cortexM0l_math.uvproj
+   * - arm_cortexM3b_math.uvproj
+   * - arm_cortexM3l_math.uvproj  
+   * - arm_cortexM4b_math.uvproj
+   * - arm_cortexM4l_math.uvproj
+   * - arm_cortexM4bf_math.uvproj
+   * - arm_cortexM4lf_math.uvproj
+   *
+   *
+   * The project can be built by opening the appropriate project in MDK-ARM 4.23 chain and defining the optional pre processor MACROs detailed above.
+   *
+   * Copyright Notice
+   *
+   * Copyright (C) 2010 ARM Limited. All rights reserved.
+   */
+
+
+/**
+ * @defgroup groupMath Basic Math Functions
+ */
+
+/**
+ * @defgroup groupFastMath Fast Math Functions
+ * This set of functions provides a fast approximation to sine, cosine, and square root.
+ * As compared to most of the other functions in the CMSIS math library, the fast math functions
+ * operate on individual values and not arrays.
+ * There are separate functions for Q15, Q31, and floating-point data.
+ *
+ */
+
+/**
+ * @defgroup groupCmplxMath Complex Math Functions
+ * This set of functions operates on complex data vectors.
+ * The data in the complex arrays is stored in an interleaved fashion
+ * (real, imag, real, imag, ...).
+ * In the API functions, the number of samples in a complex array refers
+ * to the number of complex values; the array contains twice this number of
+ * real values.
+ */
+
+/**
+ * @defgroup groupFilters Filtering Functions
+ */
+
+/**
+ * @defgroup groupMatrix Matrix Functions
+ *
+ * This set of functions provides basic matrix math operations.
+ * The functions operate on matrix data structures.  For example,
+ * the type
+ * definition for the floating-point matrix structure is shown
+ * below:
+ * 
+ *     typedef struct
+ *     {
+ *       uint16_t numRows;     // number of rows of the matrix.
+ *       uint16_t numCols;     // number of columns of the matrix.
+ *       float32_t *pData;     // points to the data of the matrix.
+ *     } arm_matrix_instance_f32;
+ * 

+ * There are similar definitions for Q15 and Q31 data types.
+ *
+ * The structure specifies the size of the matrix and then points to
+ * an array of data.  The array is of size numRows X numCols
+ * and the values are arranged in row order.  That is, the
+ * matrix element (i, j) is stored at:
+ * 
+ *     pData[i*numCols + j]
+ * 

+ *
+ * \par Init Functions
+ * There is an associated initialization function for each type of matrix
+ * data structure.
+ * The initialization function sets the values of the internal structure fields.
+ * Refer to the function arm_mat_init_f32(), arm_mat_init_q31()
+ * and arm_mat_init_q15() for floating-point, Q31 and Q15 types,  respectively.
+ *
+ * \par
+ * Use of the initialization function is optional. However, if initialization function is used
+ * then the instance structure cannot be placed into a const data section.
+ * To place the instance structure in a const data
+ * section, manually initialize the data structure.  For example:
+ * 
+ * arm_matrix_instance_f32 S = {nRows, nColumns, pData};
+ * arm_matrix_instance_q31 S = {nRows, nColumns, pData};
+ * arm_matrix_instance_q15 S = {nRows, nColumns, pData};
+ * 

+ * where nRows specifies the number of rows, nColumns
+ * specifies the number of columns, and pData points to the
+ * data array.
+ *
+ * \par Size Checking
+ * By default all of the matrix functions perform size checking on the input and
+ * output matrices.  For example, the matrix addition function verifies that the
+ * two input matrices and the output matrix all have the same number of rows and
+ * columns.  If the size check fails the functions return:
+ * 
+ *     ARM_MATH_SIZE_MISMATCH
+ * 

+ * Otherwise the functions return
+ * 
+ *     ARM_MATH_SUCCESS
+ * 

+ * There is some overhead associated with this matrix size checking.
+ * The matrix size checking is enabled via the \#define
+ * 
+ *     ARM_MATH_MATRIX_CHECK
+ * 

+ * within the library project settings.  By default this macro is defined
+ * and size checking is enabled.  By changing the project settings and
+ * undefining this macro size checking is eliminated and the functions
+ * run a bit faster.  With size checking disabled the functions always
+ * return ARM_MATH_SUCCESS.
+ */
+
+/**
+ * @defgroup groupTransforms Transform Functions
+ */
+
+/**
+ * @defgroup groupController Controller Functions
+ */
+
+/**
+ * @defgroup groupStats Statistics Functions
+ */
+/**
+ * @defgroup groupSupport Support Functions
+ */
+
+/**
+ * @defgroup groupInterpolation Interpolation Functions
+ * These functions perform 1- and 2-dimensional interpolation of data.
+ * Linear interpolation is used for 1-dimensional data and
+ * bilinear interpolation is used for 2-dimensional data.
+ */
+
+/**
+ * @defgroup groupExamples Examples
+ */
+#ifndef _ARM_MATH_H
+#define _ARM_MATH_H
+
+#define __CMSIS_GENERIC         /* disable NVIC and Systick functions */
+
+/* NuttX */
+#include 
+#ifdef CONFIG_ARCH_CORTEXM4
+# define ARM_MATH_CM4 1
+#endif
+#ifdef CONFIG_ARCH_CORTEXM3
+# define ARM_MATH_CM3 1
+#endif
+#ifdef CONFIG_ARCH_FPU
+# define __FPU_PRESENT 1
+#endif
+
+#if defined (ARM_MATH_CM4)
+#include "core_cm4.h"
+#elif defined (ARM_MATH_CM3)
+#include "core_cm3.h"
+#elif defined (ARM_MATH_CM0)
+#include "core_cm0.h"
+#else
+#include "ARMCM4.h"
+#warning "Define either ARM_MATH_CM4 OR ARM_MATH_CM3...By Default building on ARM_MATH_CM4....."
+#endif
+
+#undef  __CMSIS_GENERIC         /* enable NVIC and Systick functions */
+#include "string.h"
+#include "math.h"
+#ifdef	__cplusplus
+extern "C"
+{
+#endif
+
+
+  /**
+   * @brief Macros required for reciprocal calculation in Normalized LMS
+   */
+
+#define DELTA_Q31 			(0x100)
+#define DELTA_Q15 			0x5
+#define INDEX_MASK 			0x0000003F
+#ifndef PI
+#define PI					3.14159265358979f
+#endif
+
+  /**
+   * @brief Macros required for SINE and COSINE Fast math approximations
+   */
+
+#define TABLE_SIZE			256
+#define TABLE_SPACING_Q31	0x800000
+#define TABLE_SPACING_Q15	0x80
+
+  /**
+   * @brief Macros required for SINE and COSINE Controller functions
+   */
+  /* 1.31(q31) Fixed value of 2/360 */
+  /* -1 to +1 is divided into 360 values so total spacing is (2/360) */
+#define INPUT_SPACING			0xB60B61
+
+  /**
+   * @brief Macro for Unaligned Support
+   */
+#ifndef UNALIGNED_SUPPORT_DISABLE
+    #define ALIGN4
+#else
+  #if defined  (__GNUC__)
+    #define ALIGN4 __attribute__((aligned(4)))
+  #else
+    #define ALIGN4 __align(4)
+  #endif
+#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/
+
+  /**
+   * @brief Error status returned by some functions in the library.
+   */
+
+  typedef enum
+  {
+    ARM_MATH_SUCCESS = 0,                /**< No error */
+    ARM_MATH_ARGUMENT_ERROR = -1,        /**< One or more arguments are incorrect */
+    ARM_MATH_LENGTH_ERROR = -2,          /**< Length of data buffer is incorrect */
+    ARM_MATH_SIZE_MISMATCH = -3,         /**< Size of matrices is not compatible with the operation. */
+    ARM_MATH_NANINF = -4,                /**< Not-a-number (NaN) or infinity is generated */
+    ARM_MATH_SINGULAR = -5,              /**< Generated by matrix inversion if the input matrix is singular and cannot be inverted. */
+    ARM_MATH_TEST_FAILURE = -6           /**< Test Failed  */
+  } arm_status;
+
+  /**
+   * @brief 8-bit fractional data type in 1.7 format.
+   */
+  typedef int8_t q7_t;
+
+  /**
+   * @brief 16-bit fractional data type in 1.15 format.
+   */
+  typedef int16_t q15_t;
+
+  /**
+   * @brief 32-bit fractional data type in 1.31 format.
+   */
+  typedef int32_t q31_t;
+
+  /**
+   * @brief 64-bit fractional data type in 1.63 format.
+   */
+  typedef int64_t q63_t;
+
+  /**
+   * @brief 32-bit floating-point type definition.
+   */
+  typedef float float32_t;
+
+  /**
+   * @brief 64-bit floating-point type definition.
+   */
+  typedef double float64_t;
+
+  /**
+   * @brief definition to read/write two 16 bit values.
+   */
+#if defined  (__GNUC__)
+  #define __SIMD32(addr)         (*( int32_t **) & (addr))
+  #define  _SIMD32_OFFSET(addr)  (*( int32_t * )   (addr))
+#else
+  #define __SIMD32(addr)         (*(__packed                    int32_t **) & (addr))
+  #define  _SIMD32_OFFSET(addr)  (*(__packed                    int32_t * )   (addr))
+#endif 
+
+  #define __SIMD64(addr)  (*(int64_t **) & (addr))
+
+#if defined (ARM_MATH_CM3) || defined (ARM_MATH_CM0)
+  /**
+   * @brief definition to pack two 16 bit values.
+   */
+#define __PKHBT(ARG1, ARG2, ARG3)      ( (((int32_t)(ARG1) <<  0) & (int32_t)0x0000FFFF) | \
+                                         (((int32_t)(ARG2) << ARG3) & (int32_t)0xFFFF0000)  )
+#define __PKHTB(ARG1, ARG2, ARG3)      ( (((int32_t)(ARG1) <<  0) & (int32_t)0xFFFF0000) | \
+                                         (((int32_t)(ARG2) >> ARG3) & (int32_t)0x0000FFFF)  )
+
+#endif
+
+
+   /**
+   * @brief definition to pack four 8 bit values.
+   */
+#ifndef ARM_MATH_BIG_ENDIAN
+
+#define __PACKq7(v0,v1,v2,v3) ( (((int32_t)(v0) <<  0) & (int32_t)0x000000FF) |	\
+                                (((int32_t)(v1) <<  8) & (int32_t)0x0000FF00) |	\
+							    (((int32_t)(v2) << 16) & (int32_t)0x00FF0000) |	\
+							    (((int32_t)(v3) << 24) & (int32_t)0xFF000000)  )
+#else
+
+#define __PACKq7(v0,v1,v2,v3) ( (((int32_t)(v3) <<  0) & (int32_t)0x000000FF) |	\
+                                (((int32_t)(v2) <<  8) & (int32_t)0x0000FF00) |	\
+							    (((int32_t)(v1) << 16) & (int32_t)0x00FF0000) |	\
+							    (((int32_t)(v0) << 24) & (int32_t)0xFF000000)  )
+
+#endif
+
+
+  /**
+   * @brief Clips Q63 to Q31 values.
+   */
+  __STATIC_INLINE q31_t clip_q63_to_q31(
+  q63_t x)
+  {
+    return ((q31_t) (x >> 32) != ((q31_t) x >> 31)) ?
+      ((0x7FFFFFFF ^ ((q31_t) (x >> 63)))) : (q31_t) x;
+  }
+
+  /**
+   * @brief Clips Q63 to Q15 values.
+   */
+  __STATIC_INLINE q15_t clip_q63_to_q15(
+  q63_t x)
+  {
+    return ((q31_t) (x >> 32) != ((q31_t) x >> 31)) ?
+      ((0x7FFF ^ ((q15_t) (x >> 63)))) : (q15_t) (x >> 15);
+  }
+
+  /**
+   * @brief Clips Q31 to Q7 values.
+   */
+  __STATIC_INLINE q7_t clip_q31_to_q7(
+  q31_t x)
+  {
+    return ((q31_t) (x >> 24) != ((q31_t) x >> 23)) ?
+      ((0x7F ^ ((q7_t) (x >> 31)))) : (q7_t) x;
+  }
+
+  /**
+   * @brief Clips Q31 to Q15 values.
+   */
+  __STATIC_INLINE q15_t clip_q31_to_q15(
+  q31_t x)
+  {
+    return ((q31_t) (x >> 16) != ((q31_t) x >> 15)) ?
+      ((0x7FFF ^ ((q15_t) (x >> 31)))) : (q15_t) x;
+  }
+
+  /**
+   * @brief Multiplies 32 X 64 and returns 32 bit result in 2.30 format.
+   */
+
+  __STATIC_INLINE q63_t mult32x64(
+  q63_t x,
+  q31_t y)
+  {
+    return ((((q63_t) (x & 0x00000000FFFFFFFF) * y) >> 32) +
+            (((q63_t) (x >> 32) * y)));
+  }
+
+
+#if defined (ARM_MATH_CM0) && defined ( __CC_ARM   )
+#define __CLZ __clz
+#endif
+
+#if defined (ARM_MATH_CM0) && defined ( __TASKING__ )
+/* No need to redefine __CLZ */
+#endif
+
+#if defined (ARM_MATH_CM0) && ((defined (__ICCARM__)) ||(defined (__GNUC__)) )
+
+  __STATIC_INLINE  uint32_t __CLZ(q31_t data);
+
+
+  __STATIC_INLINE uint32_t __CLZ(q31_t data)
+  {
+    uint32_t count = 0;
+    uint32_t mask = 0x80000000;
+
+    while((data & mask) == 0)
+    {
+      count += 1u;
+      mask = mask >> 1u;
+    }
+
+    return (count);
+
+  }
+
+#endif
+
+  /**
+   * @brief Function to Calculates 1/in(reciprocal) value of Q31 Data type.
+   */
+
+  __STATIC_INLINE uint32_t arm_recip_q31(
+  q31_t in,
+  q31_t * dst,
+  q31_t * pRecipTable)
+  {
+
+    uint32_t out, tempVal;
+    uint32_t index, i;
+    uint32_t signBits;
+
+    if(in > 0)
+    {
+      signBits = __CLZ(in) - 1;
+    }
+    else
+    {
+      signBits = __CLZ(-in) - 1;
+    }
+
+    /* Convert input sample to 1.31 format */
+    in = in << signBits;
+
+    /* calculation of index for initial approximated Val */
+    index = (uint32_t) (in >> 24u);
+    index = (index & INDEX_MASK);
+
+    /* 1.31 with exp 1 */
+    out = pRecipTable[index];
+
+    /* calculation of reciprocal value */
+    /* running approximation for two iterations */
+    for (i = 0u; i < 2u; i++)
+    {
+      tempVal = (q31_t) (((q63_t) in * out) >> 31u);
+      tempVal = 0x7FFFFFFF - tempVal;
+      /*      1.31 with exp 1 */
+      //out = (q31_t) (((q63_t) out * tempVal) >> 30u);
+      out = (q31_t) clip_q63_to_q31(((q63_t) out * tempVal) >> 30u);
+    }
+
+    /* write output */
+    *dst = out;
+
+    /* return num of signbits of out = 1/in value */
+    return (signBits + 1u);
+
+  }
+
+  /**
+   * @brief Function to Calculates 1/in(reciprocal) value of Q15 Data type.
+   */
+  __STATIC_INLINE uint32_t arm_recip_q15(
+  q15_t in,
+  q15_t * dst,
+  q15_t * pRecipTable)
+  {
+
+    uint32_t out = 0, tempVal = 0;
+    uint32_t index = 0, i = 0;
+    uint32_t signBits = 0;
+
+    if(in > 0)
+    {
+      signBits = __CLZ(in) - 17;
+    }
+    else
+    {
+      signBits = __CLZ(-in) - 17;
+    }
+
+    /* Convert input sample to 1.15 format */
+    in = in << signBits;
+
+    /* calculation of index for initial approximated Val */
+    index = in >> 8;
+    index = (index & INDEX_MASK);
+
+    /*      1.15 with exp 1  */
+    out = pRecipTable[index];
+
+    /* calculation of reciprocal value */
+    /* running approximation for two iterations */
+    for (i = 0; i < 2; i++)
+    {
+      tempVal = (q15_t) (((q31_t) in * out) >> 15);
+      tempVal = 0x7FFF - tempVal;
+      /*      1.15 with exp 1 */
+      out = (q15_t) (((q31_t) out * tempVal) >> 14);
+    }
+
+    /* write output */
+    *dst = out;
+
+    /* return num of signbits of out = 1/in value */
+    return (signBits + 1);
+
+  }
+
+
+  /*
+   * @brief C custom defined intrinisic function for only M0 processors
+   */
+#if defined(ARM_MATH_CM0)
+
+  __STATIC_INLINE q31_t __SSAT(
+  q31_t x,
+  uint32_t y)
+  {
+    int32_t posMax, negMin;
+    uint32_t i;
+
+    posMax = 1;
+    for (i = 0; i < (y - 1); i++)
+    {
+      posMax = posMax * 2;
+    }
+
+    if(x > 0)
+    {
+      posMax = (posMax - 1);
+
+      if(x > posMax)
+      {
+        x = posMax;
+      }
+    }
+    else
+    {
+      negMin = -posMax;
+
+      if(x < negMin)
+      {
+        x = negMin;
+      }
+    }
+    return (x);
+
+
+  }
+
+#endif /* end of ARM_MATH_CM0 */
+
+
+
+  /*
+   * @brief C custom defined intrinsic function for M3 and M0 processors
+   */
+#if defined (ARM_MATH_CM3) || defined (ARM_MATH_CM0)
+
+  /*
+   * @brief C custom defined QADD8 for M3 and M0 processors
+   */
+  __STATIC_INLINE q31_t __QADD8(
+  q31_t x,
+  q31_t y)
+  {
+
+    q31_t sum;
+    q7_t r, s, t, u;
+
+    r = (q7_t) x;
+    s = (q7_t) y;
+
+    r = __SSAT((q31_t) (r + s), 8);
+    s = __SSAT(((q31_t) (((x << 16) >> 24) + ((y << 16) >> 24))), 8);
+    t = __SSAT(((q31_t) (((x << 8) >> 24) + ((y << 8) >> 24))), 8);
+    u = __SSAT(((q31_t) ((x >> 24) + (y >> 24))), 8);
+
+    sum =
+      (((q31_t) u << 24) & 0xFF000000) | (((q31_t) t << 16) & 0x00FF0000) |
+      (((q31_t) s << 8) & 0x0000FF00) | (r & 0x000000FF);
+
+    return sum;
+
+  }
+
+  /*
+   * @brief C custom defined QSUB8 for M3 and M0 processors
+   */
+  __STATIC_INLINE q31_t __QSUB8(
+  q31_t x,
+  q31_t y)
+  {
+
+    q31_t sum;
+    q31_t r, s, t, u;
+
+    r = (q7_t) x;
+    s = (q7_t) y;
+
+    r = __SSAT((r - s), 8);
+    s = __SSAT(((q31_t) (((x << 16) >> 24) - ((y << 16) >> 24))), 8) << 8;
+    t = __SSAT(((q31_t) (((x << 8) >> 24) - ((y << 8) >> 24))), 8) << 16;
+    u = __SSAT(((q31_t) ((x >> 24) - (y >> 24))), 8) << 24;
+
+    sum =
+      (u & 0xFF000000) | (t & 0x00FF0000) | (s & 0x0000FF00) | (r &
+                                                                0x000000FF);
+
+    return sum;
+  }
+
+  /*
+   * @brief C custom defined QADD16 for M3 and M0 processors
+   */
+
+  /*
+   * @brief C custom defined QADD16 for M3 and M0 processors
+   */
+  __STATIC_INLINE q31_t __QADD16(
+  q31_t x,
+  q31_t y)
+  {
+
+    q31_t sum;
+    q31_t r, s;
+
+    r = (short) x;
+    s = (short) y;
+
+    r = __SSAT(r + s, 16);
+    s = __SSAT(((q31_t) ((x >> 16) + (y >> 16))), 16) << 16;
+
+    sum = (s & 0xFFFF0000) | (r & 0x0000FFFF);
+
+    return sum;
+
+  }
+
+  /*
+   * @brief C custom defined SHADD16 for M3 and M0 processors
+   */
+  __STATIC_INLINE q31_t __SHADD16(
+  q31_t x,
+  q31_t y)
+  {
+
+    q31_t sum;
+    q31_t r, s;
+
+    r = (short) x;
+    s = (short) y;
+
+    r = ((r >> 1) + (s >> 1));
+    s = ((q31_t) ((x >> 17) + (y >> 17))) << 16;
+
+    sum = (s & 0xFFFF0000) | (r & 0x0000FFFF);
+
+    return sum;
+
+  }
+
+  /*
+   * @brief C custom defined QSUB16 for M3 and M0 processors
+   */
+  __STATIC_INLINE q31_t __QSUB16(
+  q31_t x,
+  q31_t y)
+  {
+
+    q31_t sum;
+    q31_t r, s;
+
+    r = (short) x;
+    s = (short) y;
+
+    r = __SSAT(r - s, 16);
+    s = __SSAT(((q31_t) ((x >> 16) - (y >> 16))), 16) << 16;
+
+    sum = (s & 0xFFFF0000) | (r & 0x0000FFFF);
+
+    return sum;
+  }
+
+  /*
+   * @brief C custom defined SHSUB16 for M3 and M0 processors
+   */
+  __STATIC_INLINE q31_t __SHSUB16(
+  q31_t x,
+  q31_t y)
+  {
+
+    q31_t diff;
+    q31_t r, s;
+
+    r = (short) x;
+    s = (short) y;
+
+    r = ((r >> 1) - (s >> 1));
+    s = (((x >> 17) - (y >> 17)) << 16);
+
+    diff = (s & 0xFFFF0000) | (r & 0x0000FFFF);
+
+    return diff;
+  }
+
+  /*
+   * @brief C custom defined QASX for M3 and M0 processors
+   */
+  __STATIC_INLINE q31_t __QASX(
+  q31_t x,
+  q31_t y)
+  {
+
+    q31_t sum = 0;
+
+    sum =
+      ((sum +
+        clip_q31_to_q15((q31_t) ((short) (x >> 16) + (short) y))) << 16) +
+      clip_q31_to_q15((q31_t) ((short) x - (short) (y >> 16)));
+
+    return sum;
+  }
+
+  /*
+   * @brief C custom defined SHASX for M3 and M0 processors
+   */
+  __STATIC_INLINE q31_t __SHASX(
+  q31_t x,
+  q31_t y)
+  {
+
+    q31_t sum;
+    q31_t r, s;
+
+    r = (short) x;
+    s = (short) y;
+
+    r = ((r >> 1) - (y >> 17));
+    s = (((x >> 17) + (s >> 1)) << 16);
+
+    sum = (s & 0xFFFF0000) | (r & 0x0000FFFF);
+
+    return sum;
+  }
+
+
+  /*
+   * @brief C custom defined QSAX for M3 and M0 processors
+   */
+  __STATIC_INLINE q31_t __QSAX(
+  q31_t x,
+  q31_t y)
+  {
+
+    q31_t sum = 0;
+
+    sum =
+      ((sum +
+        clip_q31_to_q15((q31_t) ((short) (x >> 16) - (short) y))) << 16) +
+      clip_q31_to_q15((q31_t) ((short) x + (short) (y >> 16)));
+
+    return sum;
+  }
+
+  /*
+   * @brief C custom defined SHSAX for M3 and M0 processors
+   */
+  __STATIC_INLINE q31_t __SHSAX(
+  q31_t x,
+  q31_t y)
+  {
+
+    q31_t sum;
+    q31_t r, s;
+
+    r = (short) x;
+    s = (short) y;
+
+    r = ((r >> 1) + (y >> 17));
+    s = (((x >> 17) - (s >> 1)) << 16);
+
+    sum = (s & 0xFFFF0000) | (r & 0x0000FFFF);
+
+    return sum;
+  }
+
+  /*
+   * @brief C custom defined SMUSDX for M3 and M0 processors
+   */
+  __STATIC_INLINE q31_t __SMUSDX(
+  q31_t x,
+  q31_t y)
+  {
+
+    return ((q31_t) (((short) x * (short) (y >> 16)) -
+                     ((short) (x >> 16) * (short) y)));
+  }
+
+  /*
+   * @brief C custom defined SMUADX for M3 and M0 processors
+   */
+  __STATIC_INLINE q31_t __SMUADX(
+  q31_t x,
+  q31_t y)
+  {
+
+    return ((q31_t) (((short) x * (short) (y >> 16)) +
+                     ((short) (x >> 16) * (short) y)));
+  }
+
+  /*
+   * @brief C custom defined QADD for M3 and M0 processors
+   */
+  __STATIC_INLINE q31_t __QADD(
+  q31_t x,
+  q31_t y)
+  {
+    return clip_q63_to_q31((q63_t) x + y);
+  }
+
+  /*
+   * @brief C custom defined QSUB for M3 and M0 processors
+   */
+  __STATIC_INLINE q31_t __QSUB(
+  q31_t x,
+  q31_t y)
+  {
+    return clip_q63_to_q31((q63_t) x - y);
+  }
+
+  /*
+   * @brief C custom defined SMLAD for M3 and M0 processors
+   */
+  __STATIC_INLINE q31_t __SMLAD(
+  q31_t x,
+  q31_t y,
+  q31_t sum)
+  {
+
+    return (sum + ((short) (x >> 16) * (short) (y >> 16)) +
+            ((short) x * (short) y));
+  }
+
+  /*
+   * @brief C custom defined SMLADX for M3 and M0 processors
+   */
+  __STATIC_INLINE q31_t __SMLADX(
+  q31_t x,
+  q31_t y,
+  q31_t sum)
+  {
+
+    return (sum + ((short) (x >> 16) * (short) (y)) +
+            ((short) x * (short) (y >> 16)));
+  }
+
+  /*
+   * @brief C custom defined SMLSDX for M3 and M0 processors
+   */
+  __STATIC_INLINE q31_t __SMLSDX(
+  q31_t x,
+  q31_t y,
+  q31_t sum)
+  {
+
+    return (sum - ((short) (x >> 16) * (short) (y)) +
+            ((short) x * (short) (y >> 16)));
+  }
+
+  /*
+   * @brief C custom defined SMLALD for M3 and M0 processors
+   */
+  __STATIC_INLINE q63_t __SMLALD(
+  q31_t x,
+  q31_t y,
+  q63_t sum)
+  {
+
+    return (sum + ((short) (x >> 16) * (short) (y >> 16)) +
+            ((short) x * (short) y));
+  }
+
+  /*
+   * @brief C custom defined SMLALDX for M3 and M0 processors
+   */
+  __STATIC_INLINE q63_t __SMLALDX(
+  q31_t x,
+  q31_t y,
+  q63_t sum)
+  {
+
+    return (sum + ((short) (x >> 16) * (short) y)) +
+      ((short) x * (short) (y >> 16));
+  }
+
+  /*
+   * @brief C custom defined SMUAD for M3 and M0 processors
+   */
+  __STATIC_INLINE q31_t __SMUAD(
+  q31_t x,
+  q31_t y)
+  {
+
+    return (((x >> 16) * (y >> 16)) +
+            (((x << 16) >> 16) * ((y << 16) >> 16)));
+  }
+
+  /*
+   * @brief C custom defined SMUSD for M3 and M0 processors
+   */
+  __STATIC_INLINE q31_t __SMUSD(
+  q31_t x,
+  q31_t y)
+  {
+
+    return (-((x >> 16) * (y >> 16)) +
+            (((x << 16) >> 16) * ((y << 16) >> 16)));
+  }
+
+
+  /*
+   * @brief C custom defined SXTB16 for M3 and M0 processors
+   */
+  __STATIC_INLINE q31_t __SXTB16(
+  q31_t x)
+  {
+
+    return ((((x << 24) >> 24) & 0x0000FFFF) |
+            (((x << 8) >> 8) & 0xFFFF0000));
+  }
+
+
+#endif /* defined (ARM_MATH_CM3) || defined (ARM_MATH_CM0) */
+
+
+  /**
+   * @brief Instance structure for the Q7 FIR filter.
+   */
+  typedef struct
+  {
+    uint16_t numTaps;        /**< number of filter coefficients in the filter. */
+    q7_t *pState;            /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+    q7_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps.*/
+  } arm_fir_instance_q7;
+
+  /**
+   * @brief Instance structure for the Q15 FIR filter.
+   */
+  typedef struct
+  {
+    uint16_t numTaps;         /**< number of filter coefficients in the filter. */
+    q15_t *pState;            /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+    q15_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps.*/
+  } arm_fir_instance_q15;
+
+  /**
+   * @brief Instance structure for the Q31 FIR filter.
+   */
+  typedef struct
+  {
+    uint16_t numTaps;         /**< number of filter coefficients in the filter. */
+    q31_t *pState;            /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+    q31_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps. */
+  } arm_fir_instance_q31;
+
+  /**
+   * @brief Instance structure for the floating-point FIR filter.
+   */
+  typedef struct
+  {
+    uint16_t numTaps;     /**< number of filter coefficients in the filter. */
+    float32_t *pState;    /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+    float32_t *pCoeffs;   /**< points to the coefficient array. The array is of length numTaps. */
+  } arm_fir_instance_f32;
+
+
+  /**
+   * @brief Processing function for the Q7 FIR filter.
+   * @param[in] *S points to an instance of the Q7 FIR filter structure.
+   * @param[in] *pSrc points to the block of input data.
+   * @param[out] *pDst points to the block of output data.
+   * @param[in] blockSize number of samples to process.
+   * @return none.
+   */
+  void arm_fir_q7(
+  const arm_fir_instance_q7 * S,
+  q7_t * pSrc,
+  q7_t * pDst,
+  uint32_t blockSize);
+
+
+  /**
+   * @brief  Initialization function for the Q7 FIR filter.
+   * @param[in,out] *S points to an instance of the Q7 FIR structure.
+   * @param[in] numTaps  Number of filter coefficients in the filter.
+   * @param[in] *pCoeffs points to the filter coefficients.
+   * @param[in] *pState points to the state buffer.
+   * @param[in] blockSize number of samples that are processed.
+   * @return none
+   */
+  void arm_fir_init_q7(
+  arm_fir_instance_q7 * S,
+  uint16_t numTaps,
+  q7_t * pCoeffs,
+  q7_t * pState,
+  uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the Q15 FIR filter.
+   * @param[in] *S points to an instance of the Q15 FIR structure.
+   * @param[in] *pSrc points to the block of input data.
+   * @param[out] *pDst points to the block of output data.
+   * @param[in] blockSize number of samples to process.
+   * @return none.
+   */
+  void arm_fir_q15(
+  const arm_fir_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Processing function for the fast Q15 FIR filter for Cortex-M3 and Cortex-M4.
+   * @param[in] *S points to an instance of the Q15 FIR filter structure.
+   * @param[in] *pSrc points to the block of input data.
+   * @param[out] *pDst points to the block of output data.
+   * @param[in] blockSize number of samples to process.
+   * @return none.
+   */
+  void arm_fir_fast_q15(
+  const arm_fir_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Initialization function for the Q15 FIR filter.
+   * @param[in,out] *S points to an instance of the Q15 FIR filter structure.
+   * @param[in] numTaps  Number of filter coefficients in the filter. Must be even and greater than or equal to 4.
+   * @param[in] *pCoeffs points to the filter coefficients.
+   * @param[in] *pState points to the state buffer.
+   * @param[in] blockSize number of samples that are processed at a time.
+   * @return The function returns ARM_MATH_SUCCESS if initialization was successful or ARM_MATH_ARGUMENT_ERROR if
+   * numTaps is not a supported value.
+   */
+
+  arm_status arm_fir_init_q15(
+  arm_fir_instance_q15 * S,
+  uint16_t numTaps,
+  q15_t * pCoeffs,
+  q15_t * pState,
+  uint32_t blockSize);
+
+  /**
+   * @brief Processing function for the Q31 FIR filter.
+   * @param[in] *S points to an instance of the Q31 FIR filter structure.
+   * @param[in] *pSrc points to the block of input data.
+   * @param[out] *pDst points to the block of output data.
+   * @param[in] blockSize number of samples to process.
+   * @return none.
+   */
+  void arm_fir_q31(
+  const arm_fir_instance_q31 * S,
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Processing function for the fast Q31 FIR filter for Cortex-M3 and Cortex-M4.
+   * @param[in] *S points to an instance of the Q31 FIR structure.
+   * @param[in] *pSrc points to the block of input data.
+   * @param[out] *pDst points to the block of output data.
+   * @param[in] blockSize number of samples to process.
+   * @return none.
+   */
+  void arm_fir_fast_q31(
+  const arm_fir_instance_q31 * S,
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Initialization function for the Q31 FIR filter.
+   * @param[in,out] *S points to an instance of the Q31 FIR structure.
+   * @param[in] 	numTaps  Number of filter coefficients in the filter.
+   * @param[in] 	*pCoeffs points to the filter coefficients.
+   * @param[in] 	*pState points to the state buffer.
+   * @param[in] 	blockSize number of samples that are processed at a time.
+   * @return 		none.
+   */
+  void arm_fir_init_q31(
+  arm_fir_instance_q31 * S,
+  uint16_t numTaps,
+  q31_t * pCoeffs,
+  q31_t * pState,
+  uint32_t blockSize);
+
+  /**
+   * @brief Processing function for the floating-point FIR filter.
+   * @param[in] *S points to an instance of the floating-point FIR structure.
+   * @param[in] *pSrc points to the block of input data.
+   * @param[out] *pDst points to the block of output data.
+   * @param[in] blockSize number of samples to process.
+   * @return none.
+   */
+  void arm_fir_f32(
+  const arm_fir_instance_f32 * S,
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Initialization function for the floating-point FIR filter.
+   * @param[in,out] *S points to an instance of the floating-point FIR filter structure.
+   * @param[in] 	numTaps  Number of filter coefficients in the filter.
+   * @param[in] 	*pCoeffs points to the filter coefficients.
+   * @param[in] 	*pState points to the state buffer.
+   * @param[in] 	blockSize number of samples that are processed at a time.
+   * @return    	none.
+   */
+  void arm_fir_init_f32(
+  arm_fir_instance_f32 * S,
+  uint16_t numTaps,
+  float32_t * pCoeffs,
+  float32_t * pState,
+  uint32_t blockSize);
+
+
+  /**
+   * @brief Instance structure for the Q15 Biquad cascade filter.
+   */
+  typedef struct
+  {
+    int8_t numStages;         /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
+    q15_t *pState;            /**< Points to the array of state coefficients.  The array is of length 4*numStages. */
+    q15_t *pCoeffs;           /**< Points to the array of coefficients.  The array is of length 5*numStages. */
+    int8_t postShift;         /**< Additional shift, in bits, applied to each output sample. */
+
+  } arm_biquad_casd_df1_inst_q15;
+
+
+  /**
+   * @brief Instance structure for the Q31 Biquad cascade filter.
+   */
+  typedef struct
+  {
+    uint32_t numStages;      /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
+    q31_t *pState;           /**< Points to the array of state coefficients.  The array is of length 4*numStages. */
+    q31_t *pCoeffs;          /**< Points to the array of coefficients.  The array is of length 5*numStages. */
+    uint8_t postShift;       /**< Additional shift, in bits, applied to each output sample. */
+
+  } arm_biquad_casd_df1_inst_q31;
+
+  /**
+   * @brief Instance structure for the floating-point Biquad cascade filter.
+   */
+  typedef struct
+  {
+    uint32_t numStages;         /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
+    float32_t *pState;          /**< Points to the array of state coefficients.  The array is of length 4*numStages. */
+    float32_t *pCoeffs;         /**< Points to the array of coefficients.  The array is of length 5*numStages. */
+
+
+  } arm_biquad_casd_df1_inst_f32;
+
+
+
+  /**
+   * @brief Processing function for the Q15 Biquad cascade filter.
+   * @param[in]  *S points to an instance of the Q15 Biquad cascade structure.
+   * @param[in]  *pSrc points to the block of input data.
+   * @param[out] *pDst points to the block of output data.
+   * @param[in]  blockSize number of samples to process.
+   * @return     none.
+   */
+
+  void arm_biquad_cascade_df1_q15(
+  const arm_biquad_casd_df1_inst_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Initialization function for the Q15 Biquad cascade filter.
+   * @param[in,out] *S           points to an instance of the Q15 Biquad cascade structure.
+   * @param[in]     numStages    number of 2nd order stages in the filter.
+   * @param[in]     *pCoeffs     points to the filter coefficients.
+   * @param[in]     *pState      points to the state buffer.
+   * @param[in]     postShift    Shift to be applied to the output. Varies according to the coefficients format
+   * @return        none
+   */
+
+  void arm_biquad_cascade_df1_init_q15(
+  arm_biquad_casd_df1_inst_q15 * S,
+  uint8_t numStages,
+  q15_t * pCoeffs,
+  q15_t * pState,
+  int8_t postShift);
+
+
+  /**
+   * @brief Fast but less precise processing function for the Q15 Biquad cascade filter for Cortex-M3 and Cortex-M4.
+   * @param[in]  *S points to an instance of the Q15 Biquad cascade structure.
+   * @param[in]  *pSrc points to the block of input data.
+   * @param[out] *pDst points to the block of output data.
+   * @param[in]  blockSize number of samples to process.
+   * @return     none.
+   */
+
+  void arm_biquad_cascade_df1_fast_q15(
+  const arm_biquad_casd_df1_inst_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the Q31 Biquad cascade filter
+   * @param[in]  *S         points to an instance of the Q31 Biquad cascade structure.
+   * @param[in]  *pSrc      points to the block of input data.
+   * @param[out] *pDst      points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   * @return     none.
+   */
+
+  void arm_biquad_cascade_df1_q31(
+  const arm_biquad_casd_df1_inst_q31 * S,
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Fast but less precise processing function for the Q31 Biquad cascade filter for Cortex-M3 and Cortex-M4.
+   * @param[in]  *S         points to an instance of the Q31 Biquad cascade structure.
+   * @param[in]  *pSrc      points to the block of input data.
+   * @param[out] *pDst      points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   * @return     none.
+   */
+
+  void arm_biquad_cascade_df1_fast_q31(
+  const arm_biquad_casd_df1_inst_q31 * S,
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Initialization function for the Q31 Biquad cascade filter.
+   * @param[in,out] *S           points to an instance of the Q31 Biquad cascade structure.
+   * @param[in]     numStages      number of 2nd order stages in the filter.
+   * @param[in]     *pCoeffs     points to the filter coefficients.
+   * @param[in]     *pState      points to the state buffer.
+   * @param[in]     postShift    Shift to be applied to the output. Varies according to the coefficients format
+   * @return        none
+   */
+
+  void arm_biquad_cascade_df1_init_q31(
+  arm_biquad_casd_df1_inst_q31 * S,
+  uint8_t numStages,
+  q31_t * pCoeffs,
+  q31_t * pState,
+  int8_t postShift);
+
+  /**
+   * @brief Processing function for the floating-point Biquad cascade filter.
+   * @param[in]  *S         points to an instance of the floating-point Biquad cascade structure.
+   * @param[in]  *pSrc      points to the block of input data.
+   * @param[out] *pDst      points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   * @return     none.
+   */
+
+  void arm_biquad_cascade_df1_f32(
+  const arm_biquad_casd_df1_inst_f32 * S,
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Initialization function for the floating-point Biquad cascade filter.
+   * @param[in,out] *S           points to an instance of the floating-point Biquad cascade structure.
+   * @param[in]     numStages    number of 2nd order stages in the filter.
+   * @param[in]     *pCoeffs     points to the filter coefficients.
+   * @param[in]     *pState      points to the state buffer.
+   * @return        none
+   */
+
+  void arm_biquad_cascade_df1_init_f32(
+  arm_biquad_casd_df1_inst_f32 * S,
+  uint8_t numStages,
+  float32_t * pCoeffs,
+  float32_t * pState);
+
+
+  /**
+   * @brief Instance structure for the floating-point matrix structure.
+   */
+
+  typedef struct
+  {
+    uint16_t numRows;     /**< number of rows of the matrix.     */
+    uint16_t numCols;     /**< number of columns of the matrix.  */
+    float32_t *pData;     /**< points to the data of the matrix. */
+  } arm_matrix_instance_f32;
+
+  /**
+   * @brief Instance structure for the Q15 matrix structure.
+   */
+
+  typedef struct
+  {
+    uint16_t numRows;     /**< number of rows of the matrix.     */
+    uint16_t numCols;     /**< number of columns of the matrix.  */
+    q15_t *pData;         /**< points to the data of the matrix. */
+
+  } arm_matrix_instance_q15;
+
+  /**
+   * @brief Instance structure for the Q31 matrix structure.
+   */
+
+  typedef struct
+  {
+    uint16_t numRows;     /**< number of rows of the matrix.     */
+    uint16_t numCols;     /**< number of columns of the matrix.  */
+    q31_t *pData;         /**< points to the data of the matrix. */
+
+  } arm_matrix_instance_q31;
+
+
+
+  /**
+   * @brief Floating-point matrix addition.
+   * @param[in]       *pSrcA points to the first input matrix structure
+   * @param[in]       *pSrcB points to the second input matrix structure
+   * @param[out]      *pDst points to output matrix structure
+   * @return     The function returns either
+   * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.
+   */
+
+  arm_status arm_mat_add_f32(
+  const arm_matrix_instance_f32 * pSrcA,
+  const arm_matrix_instance_f32 * pSrcB,
+  arm_matrix_instance_f32 * pDst);
+
+  /**
+   * @brief Q15 matrix addition.
+   * @param[in]       *pSrcA points to the first input matrix structure
+   * @param[in]       *pSrcB points to the second input matrix structure
+   * @param[out]      *pDst points to output matrix structure
+   * @return     The function returns either
+   * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.
+   */
+
+  arm_status arm_mat_add_q15(
+  const arm_matrix_instance_q15 * pSrcA,
+  const arm_matrix_instance_q15 * pSrcB,
+  arm_matrix_instance_q15 * pDst);
+
+  /**
+   * @brief Q31 matrix addition.
+   * @param[in]       *pSrcA points to the first input matrix structure
+   * @param[in]       *pSrcB points to the second input matrix structure
+   * @param[out]      *pDst points to output matrix structure
+   * @return     The function returns either
+   * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.
+   */
+
+  arm_status arm_mat_add_q31(
+  const arm_matrix_instance_q31 * pSrcA,
+  const arm_matrix_instance_q31 * pSrcB,
+  arm_matrix_instance_q31 * pDst);
+
+
+  /**
+   * @brief Floating-point matrix transpose.
+   * @param[in]  *pSrc points to the input matrix
+   * @param[out] *pDst points to the output matrix
+   * @return 	The function returns either  ARM_MATH_SIZE_MISMATCH
+   * or ARM_MATH_SUCCESS based on the outcome of size checking.
+   */
+
+  arm_status arm_mat_trans_f32(
+  const arm_matrix_instance_f32 * pSrc,
+  arm_matrix_instance_f32 * pDst);
+
+
+  /**
+   * @brief Q15 matrix transpose.
+   * @param[in]  *pSrc points to the input matrix
+   * @param[out] *pDst points to the output matrix
+   * @return 	The function returns either  ARM_MATH_SIZE_MISMATCH
+   * or ARM_MATH_SUCCESS based on the outcome of size checking.
+   */
+
+  arm_status arm_mat_trans_q15(
+  const arm_matrix_instance_q15 * pSrc,
+  arm_matrix_instance_q15 * pDst);
+
+  /**
+   * @brief Q31 matrix transpose.
+   * @param[in]  *pSrc points to the input matrix
+   * @param[out] *pDst points to the output matrix
+   * @return 	The function returns either  ARM_MATH_SIZE_MISMATCH
+   * or ARM_MATH_SUCCESS based on the outcome of size checking.
+   */
+
+  arm_status arm_mat_trans_q31(
+  const arm_matrix_instance_q31 * pSrc,
+  arm_matrix_instance_q31 * pDst);
+
+
+  /**
+   * @brief Floating-point matrix multiplication
+   * @param[in]       *pSrcA points to the first input matrix structure
+   * @param[in]       *pSrcB points to the second input matrix structure
+   * @param[out]      *pDst points to output matrix structure
+   * @return     The function returns either
+   * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.
+   */
+
+  arm_status arm_mat_mult_f32(
+  const arm_matrix_instance_f32 * pSrcA,
+  const arm_matrix_instance_f32 * pSrcB,
+  arm_matrix_instance_f32 * pDst);
+
+  /**
+   * @brief Q15 matrix multiplication
+   * @param[in]       *pSrcA points to the first input matrix structure
+   * @param[in]       *pSrcB points to the second input matrix structure
+   * @param[out]      *pDst points to output matrix structure
+   * @return     The function returns either
+   * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.
+   */
+
+  arm_status arm_mat_mult_q15(
+  const arm_matrix_instance_q15 * pSrcA,
+  const arm_matrix_instance_q15 * pSrcB,
+  arm_matrix_instance_q15 * pDst,
+  q15_t * pState);
+
+  /**
+   * @brief Q15 matrix multiplication (fast variant) for Cortex-M3 and Cortex-M4
+   * @param[in]       *pSrcA  points to the first input matrix structure
+   * @param[in]       *pSrcB  points to the second input matrix structure
+   * @param[out]      *pDst   points to output matrix structure
+   * @param[in]		  *pState points to the array for storing intermediate results  
+   * @return     The function returns either
+   * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.
+   */
+
+  arm_status arm_mat_mult_fast_q15(
+  const arm_matrix_instance_q15 * pSrcA,
+  const arm_matrix_instance_q15 * pSrcB,
+  arm_matrix_instance_q15 * pDst,
+  q15_t * pState);
+
+  /**
+   * @brief Q31 matrix multiplication
+   * @param[in]       *pSrcA points to the first input matrix structure
+   * @param[in]       *pSrcB points to the second input matrix structure
+   * @param[out]      *pDst points to output matrix structure
+   * @return     The function returns either
+   * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.
+   */
+
+  arm_status arm_mat_mult_q31(
+  const arm_matrix_instance_q31 * pSrcA,
+  const arm_matrix_instance_q31 * pSrcB,
+  arm_matrix_instance_q31 * pDst);
+
+  /**
+   * @brief Q31 matrix multiplication (fast variant) for Cortex-M3 and Cortex-M4
+   * @param[in]       *pSrcA points to the first input matrix structure
+   * @param[in]       *pSrcB points to the second input matrix structure
+   * @param[out]      *pDst points to output matrix structure
+   * @return     The function returns either
+   * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.
+   */
+
+  arm_status arm_mat_mult_fast_q31(
+  const arm_matrix_instance_q31 * pSrcA,
+  const arm_matrix_instance_q31 * pSrcB,
+  arm_matrix_instance_q31 * pDst);
+
+
+  /**
+   * @brief Floating-point matrix subtraction
+   * @param[in]       *pSrcA points to the first input matrix structure
+   * @param[in]       *pSrcB points to the second input matrix structure
+   * @param[out]      *pDst points to output matrix structure
+   * @return     The function returns either
+   * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.
+   */
+
+  arm_status arm_mat_sub_f32(
+  const arm_matrix_instance_f32 * pSrcA,
+  const arm_matrix_instance_f32 * pSrcB,
+  arm_matrix_instance_f32 * pDst);
+
+  /**
+   * @brief Q15 matrix subtraction
+   * @param[in]       *pSrcA points to the first input matrix structure
+   * @param[in]       *pSrcB points to the second input matrix structure
+   * @param[out]      *pDst points to output matrix structure
+   * @return     The function returns either
+   * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.
+   */
+
+  arm_status arm_mat_sub_q15(
+  const arm_matrix_instance_q15 * pSrcA,
+  const arm_matrix_instance_q15 * pSrcB,
+  arm_matrix_instance_q15 * pDst);
+
+  /**
+   * @brief Q31 matrix subtraction
+   * @param[in]       *pSrcA points to the first input matrix structure
+   * @param[in]       *pSrcB points to the second input matrix structure
+   * @param[out]      *pDst points to output matrix structure
+   * @return     The function returns either
+   * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.
+   */
+
+  arm_status arm_mat_sub_q31(
+  const arm_matrix_instance_q31 * pSrcA,
+  const arm_matrix_instance_q31 * pSrcB,
+  arm_matrix_instance_q31 * pDst);
+
+  /**
+   * @brief Floating-point matrix scaling.
+   * @param[in]  *pSrc points to the input matrix
+   * @param[in]  scale scale factor
+   * @param[out] *pDst points to the output matrix
+   * @return     The function returns either
+   * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.
+   */
+
+  arm_status arm_mat_scale_f32(
+  const arm_matrix_instance_f32 * pSrc,
+  float32_t scale,
+  arm_matrix_instance_f32 * pDst);
+
+  /**
+   * @brief Q15 matrix scaling.
+   * @param[in]       *pSrc points to input matrix
+   * @param[in]       scaleFract fractional portion of the scale factor
+   * @param[in]       shift number of bits to shift the result by
+   * @param[out]      *pDst points to output matrix
+   * @return     The function returns either
+   * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.
+   */
+
+  arm_status arm_mat_scale_q15(
+  const arm_matrix_instance_q15 * pSrc,
+  q15_t scaleFract,
+  int32_t shift,
+  arm_matrix_instance_q15 * pDst);
+
+  /**
+   * @brief Q31 matrix scaling.
+   * @param[in]       *pSrc points to input matrix
+   * @param[in]       scaleFract fractional portion of the scale factor
+   * @param[in]       shift number of bits to shift the result by
+   * @param[out]      *pDst points to output matrix structure
+   * @return     The function returns either
+   * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking.
+   */
+
+  arm_status arm_mat_scale_q31(
+  const arm_matrix_instance_q31 * pSrc,
+  q31_t scaleFract,
+  int32_t shift,
+  arm_matrix_instance_q31 * pDst);
+
+
+  /**
+   * @brief  Q31 matrix initialization.
+   * @param[in,out] *S             points to an instance of the floating-point matrix structure.
+   * @param[in]     nRows          number of rows in the matrix.
+   * @param[in]     nColumns       number of columns in the matrix.
+   * @param[in]     *pData	       points to the matrix data array.
+   * @return        none
+   */
+
+  void arm_mat_init_q31(
+  arm_matrix_instance_q31 * S,
+  uint16_t nRows,
+  uint16_t nColumns,
+  q31_t * pData);
+
+  /**
+   * @brief  Q15 matrix initialization.
+   * @param[in,out] *S             points to an instance of the floating-point matrix structure.
+   * @param[in]     nRows          number of rows in the matrix.
+   * @param[in]     nColumns       number of columns in the matrix.
+   * @param[in]     *pData	       points to the matrix data array.
+   * @return        none
+   */
+
+  void arm_mat_init_q15(
+  arm_matrix_instance_q15 * S,
+  uint16_t nRows,
+  uint16_t nColumns,
+  q15_t * pData);
+
+  /**
+   * @brief  Floating-point matrix initialization.
+   * @param[in,out] *S             points to an instance of the floating-point matrix structure.
+   * @param[in]     nRows          number of rows in the matrix.
+   * @param[in]     nColumns       number of columns in the matrix.
+   * @param[in]     *pData	       points to the matrix data array.
+   * @return        none
+   */
+
+  void arm_mat_init_f32(
+  arm_matrix_instance_f32 * S,
+  uint16_t nRows,
+  uint16_t nColumns,
+  float32_t * pData);
+
+
+
+  /**
+   * @brief Instance structure for the Q15 PID Control.
+   */
+  typedef struct
+  {
+    q15_t A0;    /**< The derived gain, A0 = Kp + Ki + Kd . */
+#ifdef ARM_MATH_CM0
+    q15_t A1;
+    q15_t A2;
+#else
+    q31_t A1;           /**< The derived gain A1 = -Kp - 2Kd | Kd.*/
+#endif
+    q15_t state[3];       /**< The state array of length 3. */
+    q15_t Kp;           /**< The proportional gain. */
+    q15_t Ki;           /**< The integral gain. */
+    q15_t Kd;           /**< The derivative gain. */
+  } arm_pid_instance_q15;
+
+  /**
+   * @brief Instance structure for the Q31 PID Control.
+   */
+  typedef struct
+  {
+    q31_t A0;            /**< The derived gain, A0 = Kp + Ki + Kd . */
+    q31_t A1;            /**< The derived gain, A1 = -Kp - 2Kd. */
+    q31_t A2;            /**< The derived gain, A2 = Kd . */
+    q31_t state[3];      /**< The state array of length 3. */
+    q31_t Kp;            /**< The proportional gain. */
+    q31_t Ki;            /**< The integral gain. */
+    q31_t Kd;            /**< The derivative gain. */
+
+  } arm_pid_instance_q31;
+
+  /**
+   * @brief Instance structure for the floating-point PID Control.
+   */
+  typedef struct
+  {
+    float32_t A0;          /**< The derived gain, A0 = Kp + Ki + Kd . */
+    float32_t A1;          /**< The derived gain, A1 = -Kp - 2Kd. */
+    float32_t A2;          /**< The derived gain, A2 = Kd . */
+    float32_t state[3];    /**< The state array of length 3. */
+    float32_t Kp;               /**< The proportional gain. */
+    float32_t Ki;               /**< The integral gain. */
+    float32_t Kd;               /**< The derivative gain. */
+  } arm_pid_instance_f32;
+
+
+
+  /**
+   * @brief  Initialization function for the floating-point PID Control.
+   * @param[in,out] *S      points to an instance of the PID structure.
+   * @param[in]     resetStateFlag  flag to reset the state. 0 = no change in state 1 = reset the state.
+   * @return none.
+   */
+  void arm_pid_init_f32(
+  arm_pid_instance_f32 * S,
+  int32_t resetStateFlag);
+
+  /**
+   * @brief  Reset function for the floating-point PID Control.
+   * @param[in,out] *S is an instance of the floating-point PID Control structure
+   * @return none
+   */
+  void arm_pid_reset_f32(
+  arm_pid_instance_f32 * S);
+
+
+  /**
+   * @brief  Initialization function for the Q31 PID Control.
+   * @param[in,out] *S points to an instance of the Q15 PID structure.
+   * @param[in]     resetStateFlag  flag to reset the state. 0 = no change in state 1 = reset the state.
+   * @return none.
+   */
+  void arm_pid_init_q31(
+  arm_pid_instance_q31 * S,
+  int32_t resetStateFlag);
+
+
+  /**
+   * @brief  Reset function for the Q31 PID Control.
+   * @param[in,out] *S points to an instance of the Q31 PID Control structure
+   * @return none
+   */
+
+  void arm_pid_reset_q31(
+  arm_pid_instance_q31 * S);
+
+  /**
+   * @brief  Initialization function for the Q15 PID Control.
+   * @param[in,out] *S points to an instance of the Q15 PID structure.
+   * @param[in] resetStateFlag  flag to reset the state. 0 = no change in state 1 = reset the state.
+   * @return none.
+   */
+  void arm_pid_init_q15(
+  arm_pid_instance_q15 * S,
+  int32_t resetStateFlag);
+
+  /**
+   * @brief  Reset function for the Q15 PID Control.
+   * @param[in,out] *S points to an instance of the q15 PID Control structure
+   * @return none
+   */
+  void arm_pid_reset_q15(
+  arm_pid_instance_q15 * S);
+
+
+  /**
+   * @brief Instance structure for the floating-point Linear Interpolate function.
+   */
+  typedef struct
+  {
+    uint32_t nValues;           /**< nValues */
+    float32_t x1;               /**< x1 */
+    float32_t xSpacing;         /**< xSpacing */
+    float32_t *pYData;          /**< pointer to the table of Y values */
+  } arm_linear_interp_instance_f32;
+
+  /**
+   * @brief Instance structure for the floating-point bilinear interpolation function.
+   */
+
+  typedef struct
+  {
+    uint16_t numRows;   /**< number of rows in the data table. */
+    uint16_t numCols;   /**< number of columns in the data table. */
+    float32_t *pData;   /**< points to the data table. */
+  } arm_bilinear_interp_instance_f32;
+
+   /**
+   * @brief Instance structure for the Q31 bilinear interpolation function.
+   */
+
+  typedef struct
+  {
+    uint16_t numRows;   /**< number of rows in the data table. */
+    uint16_t numCols;   /**< number of columns in the data table. */
+    q31_t *pData;       /**< points to the data table. */
+  } arm_bilinear_interp_instance_q31;
+
+   /**
+   * @brief Instance structure for the Q15 bilinear interpolation function.
+   */
+
+  typedef struct
+  {
+    uint16_t numRows;   /**< number of rows in the data table. */
+    uint16_t numCols;   /**< number of columns in the data table. */
+    q15_t *pData;       /**< points to the data table. */
+  } arm_bilinear_interp_instance_q15;
+
+   /**
+   * @brief Instance structure for the Q15 bilinear interpolation function.
+   */
+
+  typedef struct
+  {
+    uint16_t numRows;   /**< number of rows in the data table. */
+    uint16_t numCols;   /**< number of columns in the data table. */
+    q7_t *pData;                /**< points to the data table. */
+  } arm_bilinear_interp_instance_q7;
+
+
+  /**
+   * @brief Q7 vector multiplication.
+   * @param[in]       *pSrcA points to the first input vector
+   * @param[in]       *pSrcB points to the second input vector
+   * @param[out]      *pDst  points to the output vector
+   * @param[in]       blockSize number of samples in each vector
+   * @return none.
+   */
+
+  void arm_mult_q7(
+  q7_t * pSrcA,
+  q7_t * pSrcB,
+  q7_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Q15 vector multiplication.
+   * @param[in]       *pSrcA points to the first input vector
+   * @param[in]       *pSrcB points to the second input vector
+   * @param[out]      *pDst  points to the output vector
+   * @param[in]       blockSize number of samples in each vector
+   * @return none.
+   */
+
+  void arm_mult_q15(
+  q15_t * pSrcA,
+  q15_t * pSrcB,
+  q15_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Q31 vector multiplication.
+   * @param[in]       *pSrcA points to the first input vector
+   * @param[in]       *pSrcB points to the second input vector
+   * @param[out]      *pDst points to the output vector
+   * @param[in]       blockSize number of samples in each vector
+   * @return none.
+   */
+
+  void arm_mult_q31(
+  q31_t * pSrcA,
+  q31_t * pSrcB,
+  q31_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Floating-point vector multiplication.
+   * @param[in]       *pSrcA points to the first input vector
+   * @param[in]       *pSrcB points to the second input vector
+   * @param[out]      *pDst points to the output vector
+   * @param[in]       blockSize number of samples in each vector
+   * @return none.
+   */
+
+  void arm_mult_f32(
+  float32_t * pSrcA,
+  float32_t * pSrcB,
+  float32_t * pDst,
+  uint32_t blockSize);
+
+
+  /**
+   * @brief Instance structure for the Q15 CFFT/CIFFT function.
+   */
+
+  typedef struct
+  {
+    uint16_t fftLen;                 /**< length of the FFT. */
+    uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
+    uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
+    q15_t *pTwiddle;                 /**< points to the twiddle factor table. */
+    uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
+    uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+    uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
+  } arm_cfft_radix4_instance_q15;
+
+  /**
+   * @brief Instance structure for the Q31 CFFT/CIFFT function.
+   */
+
+  typedef struct
+  {
+    uint16_t fftLen;                 /**< length of the FFT. */
+    uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
+    uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
+    q31_t *pTwiddle;                 /**< points to the twiddle factor table. */
+    uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
+    uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+    uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
+  } arm_cfft_radix4_instance_q31;
+
+
+  /**
+   * @brief Instance structure for the floating-point CFFT/CIFFT function.
+   */
+
+  typedef struct
+  {
+    uint16_t fftLen;                   /**< length of the FFT. */
+    uint8_t ifftFlag;                  /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
+    uint8_t bitReverseFlag;            /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
+    float32_t *pTwiddle;               /**< points to the twiddle factor table. */
+    uint16_t *pBitRevTable;            /**< points to the bit reversal table. */
+    uint16_t twidCoefModifier;         /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+    uint16_t bitRevFactor;             /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
+    float32_t onebyfftLen;                 /**< value of 1/fftLen. */
+  } arm_cfft_radix4_instance_f32;
+
+
+  /**
+   * @brief Instance structure for the Q15 CFFT/CIFFT function.
+   */
+
+  typedef struct
+  {
+    uint16_t fftLen;                 /**< length of the FFT. */
+    uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
+    uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
+    q15_t *pTwiddle;                     /**< points to the Sin twiddle factor table. */
+    uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
+    uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+    uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
+  } arm_cfft_radix2_instance_q15;
+
+  /**
+   * @brief Instance structure for the Radix-2 Q31 CFFT/CIFFT function.
+   */
+
+  typedef struct
+  {
+    uint16_t fftLen;                 /**< length of the FFT. */
+    uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
+    uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
+    q31_t *pTwiddle;                     /**< points to the Twiddle factor table. */
+    uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
+    uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+    uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
+  } arm_cfft_radix2_instance_q31;
+
+  /**
+   * @brief Instance structure for the floating-point CFFT/CIFFT function.
+   */
+
+  typedef struct
+  {
+    uint16_t fftLen;                   /**< length of the FFT. */
+    uint8_t ifftFlag;                  /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
+    uint8_t bitReverseFlag;            /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
+    float32_t *pTwiddle;               /**< points to the Twiddle factor table. */
+    uint16_t *pBitRevTable;            /**< points to the bit reversal table. */
+    uint16_t twidCoefModifier;         /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+    uint16_t bitRevFactor;             /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
+    float32_t onebyfftLen;                 /**< value of 1/fftLen. */
+  } arm_cfft_radix2_instance_f32;
+
+
+  /**
+   * @brief Processing function for the Q15 CFFT/CIFFT.
+   * @param[in]      *S    points to an instance of the Q15 CFFT/CIFFT structure.
+   * @param[in, out] *pSrc points to the complex data buffer. Processing occurs in-place.
+   * @return none.
+   */
+
+  void arm_cfft_radix4_q15(
+  const arm_cfft_radix4_instance_q15 * S,
+  q15_t * pSrc);
+
+  /**
+   * @brief Processing function for the Q15 CFFT/CIFFT.
+   * @param[in]      *S    points to an instance of the Q15 CFFT/CIFFT structure.
+   * @param[in, out] *pSrc points to the complex data buffer. Processing occurs in-place.
+   * @return none.
+   */
+
+  void arm_cfft_radix2_q15(
+  const arm_cfft_radix2_instance_q15 * S,
+  q15_t * pSrc);
+
+  /**
+   * @brief Initialization function for the Q15 CFFT/CIFFT.
+   * @param[in,out] *S             points to an instance of the Q15 CFFT/CIFFT structure.
+   * @param[in]     fftLen         length of the FFT.
+   * @param[in]     ifftFlag       flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform.
+   * @param[in]     bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
+   * @return        arm_status     function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if fftLen is not a supported value.
+   */
+
+  arm_status arm_cfft_radix4_init_q15(
+  arm_cfft_radix4_instance_q15 * S,
+  uint16_t fftLen,
+  uint8_t ifftFlag,
+  uint8_t bitReverseFlag);
+
+  /**
+   * @brief Initialization function for the Q15 CFFT/CIFFT.
+   * @param[in,out] *S             points to an instance of the Q15 CFFT/CIFFT structure.
+   * @param[in]     fftLen         length of the FFT.
+   * @param[in]     ifftFlag       flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform.
+   * @param[in]     bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
+   * @return        arm_status     function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if fftLen is not a supported value.
+   */
+
+  arm_status arm_cfft_radix2_init_q15(
+  arm_cfft_radix2_instance_q15 * S,
+  uint16_t fftLen,
+  uint8_t ifftFlag,
+  uint8_t bitReverseFlag);
+
+  /**
+   * @brief Processing function for the Q31 CFFT/CIFFT.
+   * @param[in]      *S    points to an instance of the Q31 CFFT/CIFFT structure.
+   * @param[in, out] *pSrc points to the complex data buffer. Processing occurs in-place.
+   * @return none.
+   */
+
+  void arm_cfft_radix4_q31(
+  const arm_cfft_radix4_instance_q31 * S,
+  q31_t * pSrc);
+
+  /**
+   * @brief  Initialization function for the Q31 CFFT/CIFFT.
+   * @param[in,out] *S             points to an instance of the Q31 CFFT/CIFFT structure.
+   * @param[in]     fftLen         length of the FFT.
+   * @param[in]     ifftFlag       flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform.
+   * @param[in]     bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
+   * @return        arm_status     function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if fftLen is not a supported value.
+   */
+
+  arm_status arm_cfft_radix4_init_q31(
+  arm_cfft_radix4_instance_q31 * S,
+  uint16_t fftLen,
+  uint8_t ifftFlag,
+  uint8_t bitReverseFlag);
+
+  /**
+   * @brief Processing function for the Radix-2 Q31 CFFT/CIFFT.
+   * @param[in]      *S    points to an instance of the Radix-2 Q31 CFFT/CIFFT structure.
+   * @param[in, out] *pSrc points to the complex data buffer. Processing occurs in-place.
+   * @return none.
+   */
+
+  void arm_cfft_radix2_q31(
+  const arm_cfft_radix2_instance_q31 * S,
+  q31_t * pSrc);
+
+  /**
+   * @brief  Initialization function for the Radix-2 Q31 CFFT/CIFFT.
+   * @param[in,out] *S             points to an instance of the Radix-2 Q31 CFFT/CIFFT structure.
+   * @param[in]     fftLen         length of the FFT.
+   * @param[in]     ifftFlag       flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform.
+   * @param[in]     bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
+   * @return        arm_status     function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if fftLen is not a supported value.
+   */
+
+  arm_status arm_cfft_radix2_init_q31(
+  arm_cfft_radix2_instance_q31 * S,
+  uint16_t fftLen,
+  uint8_t ifftFlag,
+  uint8_t bitReverseFlag);
+
+
+
+  /**
+   * @brief Processing function for the floating-point CFFT/CIFFT.
+   * @param[in]      *S    points to an instance of the floating-point CFFT/CIFFT structure.
+   * @param[in, out] *pSrc points to the complex data buffer. Processing occurs in-place.
+   * @return none.
+   */
+
+  void arm_cfft_radix2_f32(
+  const arm_cfft_radix2_instance_f32 * S,
+  float32_t * pSrc);
+
+  /**
+   * @brief  Initialization function for the floating-point CFFT/CIFFT.
+   * @param[in,out] *S             points to an instance of the floating-point CFFT/CIFFT structure.
+   * @param[in]     fftLen         length of the FFT.
+   * @param[in]     ifftFlag       flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform.
+   * @param[in]     bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
+   * @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if fftLen is not a supported value.
+   */
+
+  arm_status arm_cfft_radix2_init_f32(
+  arm_cfft_radix2_instance_f32 * S,
+  uint16_t fftLen,
+  uint8_t ifftFlag,
+  uint8_t bitReverseFlag);
+
+  /**
+   * @brief Processing function for the floating-point CFFT/CIFFT.
+   * @param[in]      *S    points to an instance of the floating-point CFFT/CIFFT structure.
+   * @param[in, out] *pSrc points to the complex data buffer. Processing occurs in-place.
+   * @return none.
+   */
+
+  void arm_cfft_radix4_f32(
+  const arm_cfft_radix4_instance_f32 * S,
+  float32_t * pSrc);
+
+  /**
+   * @brief  Initialization function for the floating-point CFFT/CIFFT.
+   * @param[in,out] *S             points to an instance of the floating-point CFFT/CIFFT structure.
+   * @param[in]     fftLen         length of the FFT.
+   * @param[in]     ifftFlag       flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform.
+   * @param[in]     bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
+   * @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if fftLen is not a supported value.
+   */
+
+  arm_status arm_cfft_radix4_init_f32(
+  arm_cfft_radix4_instance_f32 * S,
+  uint16_t fftLen,
+  uint8_t ifftFlag,
+  uint8_t bitReverseFlag);
+
+
+
+  /*----------------------------------------------------------------------
+   *		Internal functions prototypes FFT function
+   ----------------------------------------------------------------------*/
+
+  /**
+   * @brief  Core function for the floating-point CFFT butterfly process.
+   * @param[in, out] *pSrc            points to the in-place buffer of floating-point data type.
+   * @param[in]      fftLen           length of the FFT.
+   * @param[in]      *pCoef           points to the twiddle coefficient buffer.
+   * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
+   * @return none.
+   */
+
+  void arm_radix4_butterfly_f32(
+  float32_t * pSrc,
+  uint16_t fftLen,
+  float32_t * pCoef,
+  uint16_t twidCoefModifier);
+
+  /**
+   * @brief  Core function for the floating-point CIFFT butterfly process.
+   * @param[in, out] *pSrc            points to the in-place buffer of floating-point data type.
+   * @param[in]      fftLen           length of the FFT.
+   * @param[in]      *pCoef           points to twiddle coefficient buffer.
+   * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
+   * @param[in]      onebyfftLen      value of 1/fftLen.
+   * @return none.
+   */
+
+  void arm_radix4_butterfly_inverse_f32(
+  float32_t * pSrc,
+  uint16_t fftLen,
+  float32_t * pCoef,
+  uint16_t twidCoefModifier,
+  float32_t onebyfftLen);
+
+  /**
+   * @brief  In-place bit reversal function.
+   * @param[in, out] *pSrc        points to the in-place buffer of floating-point data type.
+   * @param[in]      fftSize      length of the FFT.
+   * @param[in]      bitRevFactor bit reversal modifier that supports different size FFTs with the same bit reversal table.
+   * @param[in]      *pBitRevTab  points to the bit reversal table.
+   * @return none.
+   */
+
+  void arm_bitreversal_f32(
+  float32_t * pSrc,
+  uint16_t fftSize,
+  uint16_t bitRevFactor,
+  uint16_t * pBitRevTab);
+
+  /**
+   * @brief  Core function for the Q31 CFFT butterfly process.
+   * @param[in, out] *pSrc            points to the in-place buffer of Q31 data type.
+   * @param[in]      fftLen           length of the FFT.
+   * @param[in]      *pCoef           points to Twiddle coefficient buffer.
+   * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
+   * @return none.
+   */
+
+  void arm_radix4_butterfly_q31(
+  q31_t * pSrc,
+  uint32_t fftLen,
+  q31_t * pCoef,
+  uint32_t twidCoefModifier);
+
+  /**
+   * @brief  Core function for the f32 FFT butterfly process.
+   * @param[in, out] *pSrc            points to the in-place buffer of f32 data type.
+   * @param[in]      fftLen           length of the FFT.
+   * @param[in]      *pCoef        	  points to Twiddle coefficient buffer.
+   * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
+   * @return none.
+   */
+
+  void arm_radix2_butterfly_f32(
+  float32_t * pSrc,
+  uint32_t fftLen,
+  float32_t * pCoef,
+  uint16_t twidCoefModifier);
+
+        /**  
+	 * @brief  Core function for the Radix-2 Q31 CFFT butterfly process. 
+	 * @param[in, out] *pSrc            points to the in-place buffer of Q31 data type. 
+	 * @param[in]      fftLen           length of the FFT. 
+	 * @param[in]      *pCoef         	points to Twiddle coefficient buffer.
+	 * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. 
+	 * @return none. 
+	 */
+
+  void arm_radix2_butterfly_q31(
+  q31_t * pSrc,
+  uint32_t fftLen,
+  q31_t * pCoef,
+  uint16_t twidCoefModifier);
+
+        /**  
+	 * @brief  Core function for the Radix-2 Q15 CFFT butterfly process. 
+	 * @param[in, out] *pSrc            points to the in-place buffer of Q15 data type. 
+	 * @param[in]      fftLen           length of the FFT. 
+	 * @param[in]      *pCoef           points to Twiddle coefficient buffer.
+	 * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. 
+	 * @return none. 
+	 */
+
+  void arm_radix2_butterfly_q15(
+  q15_t * pSrc,
+  uint32_t fftLen,
+  q15_t * pCoef,
+  uint16_t twidCoefModifier);
+
+        /**  
+	 * @brief  Core function for the Radix-2 Q15 CFFT Inverse butterfly process. 
+	 * @param[in, out] *pSrc            points to the in-place buffer of Q15 data type. 
+	 * @param[in]      fftLen           length of the FFT. 
+	 * @param[in]      *pCoef       	points to Twiddle coefficient buffer.
+	 * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. 
+	 * @return none. 
+	 */
+
+  void arm_radix2_butterfly_inverse_q15(
+  q15_t * pSrc,
+  uint32_t fftLen,
+  q15_t * pCoef,
+  uint16_t twidCoefModifier);
+
+        /**  
+	 * @brief  Core function for the Radix-2 Q31 CFFT Inverse butterfly process. 
+	 * @param[in, out] *pSrc            points to the in-place buffer of Q31 data type. 
+	 * @param[in]      fftLen           length of the FFT. 
+	 * @param[in]      *pCoef         	points to Twiddle coefficient buffer.
+	 * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. 
+	 * @return none. 
+	 */
+
+  void arm_radix2_butterfly_inverse_q31(
+  q31_t * pSrc,
+  uint32_t fftLen,
+  q31_t * pCoef,
+  uint16_t twidCoefModifier);
+
+  /**
+   * @brief  Core function for the f32 IFFT butterfly process.
+   * @param[in, out] *pSrc            points to the in-place buffer of f32 data type.
+   * @param[in]      fftLen           length of the FFT.
+   * @param[in]      *pCoef        	  points to Twiddle coefficient buffer.
+   * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
+   * @param[in]		 onebyfftLen	  1/fftLenfth
+   * @return none.
+   */
+
+  void arm_radix2_butterfly_inverse_f32(
+  float32_t * pSrc,
+  uint32_t fftLen,
+  float32_t * pCoef,
+  uint16_t twidCoefModifier,
+  float32_t onebyfftLen);
+
+                                                                /**
+   * @brief  Core function for the Q31 CIFFT butterfly process.
+   * @param[in, out] *pSrc            points to the in-place buffer of Q31 data type.
+   * @param[in]      fftLen           length of the FFT.
+   * @param[in]      *pCoef           points to twiddle coefficient buffer.
+   * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
+   * @return none.
+   */
+
+  void arm_radix4_butterfly_inverse_q31(
+  q31_t * pSrc,
+  uint32_t fftLen,
+  q31_t * pCoef,
+  uint32_t twidCoefModifier);
+
+  /**
+   * @brief  In-place bit reversal function.
+   * @param[in, out] *pSrc        points to the in-place buffer of Q31 data type.
+   * @param[in]      fftLen       length of the FFT.
+   * @param[in]      bitRevFactor bit reversal modifier that supports different size FFTs with the same bit reversal table
+   * @param[in]      *pBitRevTab  points to bit reversal table.
+   * @return none.
+   */
+
+  void arm_bitreversal_q31(
+  q31_t * pSrc,
+  uint32_t fftLen,
+  uint16_t bitRevFactor,
+  uint16_t * pBitRevTab);
+
+  /**
+   * @brief  Core function for the Q15 CFFT butterfly process.
+   * @param[in, out] *pSrc16          points to the in-place buffer of Q15 data type.
+   * @param[in]      fftLen           length of the FFT.
+   * @param[in]      *pCoef16         points to twiddle coefficient buffer.
+   * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
+   * @return none.
+   */
+
+  void arm_radix4_butterfly_q15(
+  q15_t * pSrc16,
+  uint32_t fftLen,
+  q15_t * pCoef16,
+  uint32_t twidCoefModifier);
+
+
+  /**
+   * @brief  Core function for the Q15 CIFFT butterfly process.
+   * @param[in, out] *pSrc16          points to the in-place buffer of Q15 data type.
+   * @param[in]      fftLen           length of the FFT.
+   * @param[in]      *pCoef16         points to twiddle coefficient buffer.
+   * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
+   * @return none.
+   */
+
+  void arm_radix4_butterfly_inverse_q15(
+  q15_t * pSrc16,
+  uint32_t fftLen,
+  q15_t * pCoef16,
+  uint32_t twidCoefModifier);
+
+  /**
+   * @brief  In-place bit reversal function.
+   * @param[in, out] *pSrc        points to the in-place buffer of Q15 data type.
+   * @param[in]      fftLen       length of the FFT.
+   * @param[in]      bitRevFactor bit reversal modifier that supports different size FFTs with the same bit reversal table
+   * @param[in]      *pBitRevTab  points to bit reversal table.
+   * @return none.
+   */
+
+  void arm_bitreversal_q15(
+  q15_t * pSrc,
+  uint32_t fftLen,
+  uint16_t bitRevFactor,
+  uint16_t * pBitRevTab);
+
+
+  /**
+   * @brief Instance structure for the Q15 RFFT/RIFFT function.
+   */
+
+  typedef struct
+  {
+    uint32_t fftLenReal;                      /**< length of the real FFT. */
+    uint32_t fftLenBy2;                       /**< length of the complex FFT. */
+    uint8_t ifftFlagR;                        /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */
+    uint8_t bitReverseFlagR;                      /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */
+    uint32_t twidCoefRModifier;               /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+    q15_t *pTwiddleAReal;                     /**< points to the real twiddle factor table. */
+    q15_t *pTwiddleBReal;                     /**< points to the imag twiddle factor table. */
+    arm_cfft_radix4_instance_q15 *pCfft;          /**< points to the complex FFT instance. */
+  } arm_rfft_instance_q15;
+
+  /**
+   * @brief Instance structure for the Q31 RFFT/RIFFT function.
+   */
+
+  typedef struct
+  {
+    uint32_t fftLenReal;                        /**< length of the real FFT. */
+    uint32_t fftLenBy2;                         /**< length of the complex FFT. */
+    uint8_t ifftFlagR;                          /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */
+    uint8_t bitReverseFlagR;                        /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */
+    uint32_t twidCoefRModifier;                 /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+    q31_t *pTwiddleAReal;                       /**< points to the real twiddle factor table. */
+    q31_t *pTwiddleBReal;                       /**< points to the imag twiddle factor table. */
+    arm_cfft_radix4_instance_q31 *pCfft;        /**< points to the complex FFT instance. */
+  } arm_rfft_instance_q31;
+
+  /**
+   * @brief Instance structure for the floating-point RFFT/RIFFT function.
+   */
+
+  typedef struct
+  {
+    uint32_t fftLenReal;                        /**< length of the real FFT. */
+    uint16_t fftLenBy2;                         /**< length of the complex FFT. */
+    uint8_t ifftFlagR;                          /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */
+    uint8_t bitReverseFlagR;                    /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */
+    uint32_t twidCoefRModifier;                     /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+    float32_t *pTwiddleAReal;                   /**< points to the real twiddle factor table. */
+    float32_t *pTwiddleBReal;                   /**< points to the imag twiddle factor table. */
+    arm_cfft_radix4_instance_f32 *pCfft;        /**< points to the complex FFT instance. */
+  } arm_rfft_instance_f32;
+
+  /**
+   * @brief Processing function for the Q15 RFFT/RIFFT.
+   * @param[in]  *S    points to an instance of the Q15 RFFT/RIFFT structure.
+   * @param[in]  *pSrc points to the input buffer.
+   * @param[out] *pDst points to the output buffer.
+   * @return none.
+   */
+
+  void arm_rfft_q15(
+  const arm_rfft_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst);
+
+  /**
+   * @brief  Initialization function for the Q15 RFFT/RIFFT.
+   * @param[in, out] *S             points to an instance of the Q15 RFFT/RIFFT structure.
+   * @param[in]      *S_CFFT        points to an instance of the Q15 CFFT/CIFFT structure.
+   * @param[in]      fftLenReal     length of the FFT.
+   * @param[in]      ifftFlagR      flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform.
+   * @param[in]      bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
+   * @return		The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if fftLenReal is not a supported value.
+   */
+
+  arm_status arm_rfft_init_q15(
+  arm_rfft_instance_q15 * S,
+  arm_cfft_radix4_instance_q15 * S_CFFT,
+  uint32_t fftLenReal,
+  uint32_t ifftFlagR,
+  uint32_t bitReverseFlag);
+
+  /**
+   * @brief Processing function for the Q31 RFFT/RIFFT.
+   * @param[in]  *S    points to an instance of the Q31 RFFT/RIFFT structure.
+   * @param[in]  *pSrc points to the input buffer.
+   * @param[out] *pDst points to the output buffer.
+   * @return none.
+   */
+
+  void arm_rfft_q31(
+  const arm_rfft_instance_q31 * S,
+  q31_t * pSrc,
+  q31_t * pDst);
+
+  /**
+   * @brief  Initialization function for the Q31 RFFT/RIFFT.
+   * @param[in, out] *S             points to an instance of the Q31 RFFT/RIFFT structure.
+   * @param[in, out] *S_CFFT        points to an instance of the Q31 CFFT/CIFFT structure.
+   * @param[in]      fftLenReal     length of the FFT.
+   * @param[in]      ifftFlagR      flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform.
+   * @param[in]      bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
+   * @return		The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if fftLenReal is not a supported value.
+   */
+
+  arm_status arm_rfft_init_q31(
+  arm_rfft_instance_q31 * S,
+  arm_cfft_radix4_instance_q31 * S_CFFT,
+  uint32_t fftLenReal,
+  uint32_t ifftFlagR,
+  uint32_t bitReverseFlag);
+
+  /**
+   * @brief  Initialization function for the floating-point RFFT/RIFFT.
+   * @param[in,out] *S             points to an instance of the floating-point RFFT/RIFFT structure.
+   * @param[in,out] *S_CFFT        points to an instance of the floating-point CFFT/CIFFT structure.
+   * @param[in]     fftLenReal     length of the FFT.
+   * @param[in]     ifftFlagR      flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform.
+   * @param[in]     bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
+   * @return		The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if fftLenReal is not a supported value.
+   */
+
+  arm_status arm_rfft_init_f32(
+  arm_rfft_instance_f32 * S,
+  arm_cfft_radix4_instance_f32 * S_CFFT,
+  uint32_t fftLenReal,
+  uint32_t ifftFlagR,
+  uint32_t bitReverseFlag);
+
+  /**
+   * @brief Processing function for the floating-point RFFT/RIFFT.
+   * @param[in]  *S    points to an instance of the floating-point RFFT/RIFFT structure.
+   * @param[in]  *pSrc points to the input buffer.
+   * @param[out] *pDst points to the output buffer.
+   * @return none.
+   */
+
+  void arm_rfft_f32(
+  const arm_rfft_instance_f32 * S,
+  float32_t * pSrc,
+  float32_t * pDst);
+
+  /**
+   * @brief Instance structure for the floating-point DCT4/IDCT4 function.
+   */
+
+  typedef struct
+  {
+    uint16_t N;                         /**< length of the DCT4. */
+    uint16_t Nby2;                      /**< half of the length of the DCT4. */
+    float32_t normalize;                /**< normalizing factor. */
+    float32_t *pTwiddle;                /**< points to the twiddle factor table. */
+    float32_t *pCosFactor;              /**< points to the cosFactor table. */
+    arm_rfft_instance_f32 *pRfft;        /**< points to the real FFT instance. */
+    arm_cfft_radix4_instance_f32 *pCfft; /**< points to the complex FFT instance. */
+  } arm_dct4_instance_f32;
+
+  /**
+   * @brief  Initialization function for the floating-point DCT4/IDCT4.
+   * @param[in,out] *S         points to an instance of floating-point DCT4/IDCT4 structure.
+   * @param[in]     *S_RFFT    points to an instance of floating-point RFFT/RIFFT structure.
+   * @param[in]     *S_CFFT    points to an instance of floating-point CFFT/CIFFT structure.
+   * @param[in]     N          length of the DCT4.
+   * @param[in]     Nby2       half of the length of the DCT4.
+   * @param[in]     normalize  normalizing factor.
+   * @return		arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if fftLenReal is not a supported transform length.
+   */
+
+  arm_status arm_dct4_init_f32(
+  arm_dct4_instance_f32 * S,
+  arm_rfft_instance_f32 * S_RFFT,
+  arm_cfft_radix4_instance_f32 * S_CFFT,
+  uint16_t N,
+  uint16_t Nby2,
+  float32_t normalize);
+
+  /**
+   * @brief Processing function for the floating-point DCT4/IDCT4.
+   * @param[in]       *S             points to an instance of the floating-point DCT4/IDCT4 structure.
+   * @param[in]       *pState        points to state buffer.
+   * @param[in,out]   *pInlineBuffer points to the in-place input and output buffer.
+   * @return none.
+   */
+
+  void arm_dct4_f32(
+  const arm_dct4_instance_f32 * S,
+  float32_t * pState,
+  float32_t * pInlineBuffer);
+
+  /**
+   * @brief Instance structure for the Q31 DCT4/IDCT4 function.
+   */
+
+  typedef struct
+  {
+    uint16_t N;                         /**< length of the DCT4. */
+    uint16_t Nby2;                      /**< half of the length of the DCT4. */
+    q31_t normalize;                    /**< normalizing factor. */
+    q31_t *pTwiddle;                    /**< points to the twiddle factor table. */
+    q31_t *pCosFactor;                  /**< points to the cosFactor table. */
+    arm_rfft_instance_q31 *pRfft;        /**< points to the real FFT instance. */
+    arm_cfft_radix4_instance_q31 *pCfft; /**< points to the complex FFT instance. */
+  } arm_dct4_instance_q31;
+
+  /**
+   * @brief  Initialization function for the Q31 DCT4/IDCT4.
+   * @param[in,out] *S         points to an instance of Q31 DCT4/IDCT4 structure.
+   * @param[in]     *S_RFFT    points to an instance of Q31 RFFT/RIFFT structure
+   * @param[in]     *S_CFFT    points to an instance of Q31 CFFT/CIFFT structure
+   * @param[in]     N          length of the DCT4.
+   * @param[in]     Nby2       half of the length of the DCT4.
+   * @param[in]     normalize  normalizing factor.
+   * @return		arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if N is not a supported transform length.
+   */
+
+  arm_status arm_dct4_init_q31(
+  arm_dct4_instance_q31 * S,
+  arm_rfft_instance_q31 * S_RFFT,
+  arm_cfft_radix4_instance_q31 * S_CFFT,
+  uint16_t N,
+  uint16_t Nby2,
+  q31_t normalize);
+
+  /**
+   * @brief Processing function for the Q31 DCT4/IDCT4.
+   * @param[in]       *S             points to an instance of the Q31 DCT4 structure.
+   * @param[in]       *pState        points to state buffer.
+   * @param[in,out]   *pInlineBuffer points to the in-place input and output buffer.
+   * @return none.
+   */
+
+  void arm_dct4_q31(
+  const arm_dct4_instance_q31 * S,
+  q31_t * pState,
+  q31_t * pInlineBuffer);
+
+  /**
+   * @brief Instance structure for the Q15 DCT4/IDCT4 function.
+   */
+
+  typedef struct
+  {
+    uint16_t N;                         /**< length of the DCT4. */
+    uint16_t Nby2;                      /**< half of the length of the DCT4. */
+    q15_t normalize;                    /**< normalizing factor. */
+    q15_t *pTwiddle;                    /**< points to the twiddle factor table. */
+    q15_t *pCosFactor;                  /**< points to the cosFactor table. */
+    arm_rfft_instance_q15 *pRfft;        /**< points to the real FFT instance. */
+    arm_cfft_radix4_instance_q15 *pCfft; /**< points to the complex FFT instance. */
+  } arm_dct4_instance_q15;
+
+  /**
+   * @brief  Initialization function for the Q15 DCT4/IDCT4.
+   * @param[in,out] *S         points to an instance of Q15 DCT4/IDCT4 structure.
+   * @param[in]     *S_RFFT    points to an instance of Q15 RFFT/RIFFT structure.
+   * @param[in]     *S_CFFT    points to an instance of Q15 CFFT/CIFFT structure.
+   * @param[in]     N          length of the DCT4.
+   * @param[in]     Nby2       half of the length of the DCT4.
+   * @param[in]     normalize  normalizing factor.
+   * @return		arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if N is not a supported transform length.
+   */
+
+  arm_status arm_dct4_init_q15(
+  arm_dct4_instance_q15 * S,
+  arm_rfft_instance_q15 * S_RFFT,
+  arm_cfft_radix4_instance_q15 * S_CFFT,
+  uint16_t N,
+  uint16_t Nby2,
+  q15_t normalize);
+
+  /**
+   * @brief Processing function for the Q15 DCT4/IDCT4.
+   * @param[in]       *S             points to an instance of the Q15 DCT4 structure.
+   * @param[in]       *pState        points to state buffer.
+   * @param[in,out]   *pInlineBuffer points to the in-place input and output buffer.
+   * @return none.
+   */
+
+  void arm_dct4_q15(
+  const arm_dct4_instance_q15 * S,
+  q15_t * pState,
+  q15_t * pInlineBuffer);
+
+  /**
+   * @brief Floating-point vector addition.
+   * @param[in]       *pSrcA points to the first input vector
+   * @param[in]       *pSrcB points to the second input vector
+   * @param[out]      *pDst points to the output vector
+   * @param[in]       blockSize number of samples in each vector
+   * @return none.
+   */
+
+  void arm_add_f32(
+  float32_t * pSrcA,
+  float32_t * pSrcB,
+  float32_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Q7 vector addition.
+   * @param[in]       *pSrcA points to the first input vector
+   * @param[in]       *pSrcB points to the second input vector
+   * @param[out]      *pDst points to the output vector
+   * @param[in]       blockSize number of samples in each vector
+   * @return none.
+   */
+
+  void arm_add_q7(
+  q7_t * pSrcA,
+  q7_t * pSrcB,
+  q7_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Q15 vector addition.
+   * @param[in]       *pSrcA points to the first input vector
+   * @param[in]       *pSrcB points to the second input vector
+   * @param[out]      *pDst points to the output vector
+   * @param[in]       blockSize number of samples in each vector
+   * @return none.
+   */
+
+  void arm_add_q15(
+  q15_t * pSrcA,
+  q15_t * pSrcB,
+  q15_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Q31 vector addition.
+   * @param[in]       *pSrcA points to the first input vector
+   * @param[in]       *pSrcB points to the second input vector
+   * @param[out]      *pDst points to the output vector
+   * @param[in]       blockSize number of samples in each vector
+   * @return none.
+   */
+
+  void arm_add_q31(
+  q31_t * pSrcA,
+  q31_t * pSrcB,
+  q31_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Floating-point vector subtraction.
+   * @param[in]       *pSrcA points to the first input vector
+   * @param[in]       *pSrcB points to the second input vector
+   * @param[out]      *pDst points to the output vector
+   * @param[in]       blockSize number of samples in each vector
+   * @return none.
+   */
+
+  void arm_sub_f32(
+  float32_t * pSrcA,
+  float32_t * pSrcB,
+  float32_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Q7 vector subtraction.
+   * @param[in]       *pSrcA points to the first input vector
+   * @param[in]       *pSrcB points to the second input vector
+   * @param[out]      *pDst points to the output vector
+   * @param[in]       blockSize number of samples in each vector
+   * @return none.
+   */
+
+  void arm_sub_q7(
+  q7_t * pSrcA,
+  q7_t * pSrcB,
+  q7_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Q15 vector subtraction.
+   * @param[in]       *pSrcA points to the first input vector
+   * @param[in]       *pSrcB points to the second input vector
+   * @param[out]      *pDst points to the output vector
+   * @param[in]       blockSize number of samples in each vector
+   * @return none.
+   */
+
+  void arm_sub_q15(
+  q15_t * pSrcA,
+  q15_t * pSrcB,
+  q15_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Q31 vector subtraction.
+   * @param[in]       *pSrcA points to the first input vector
+   * @param[in]       *pSrcB points to the second input vector
+   * @param[out]      *pDst points to the output vector
+   * @param[in]       blockSize number of samples in each vector
+   * @return none.
+   */
+
+  void arm_sub_q31(
+  q31_t * pSrcA,
+  q31_t * pSrcB,
+  q31_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Multiplies a floating-point vector by a scalar.
+   * @param[in]       *pSrc points to the input vector
+   * @param[in]       scale scale factor to be applied
+   * @param[out]      *pDst points to the output vector
+   * @param[in]       blockSize number of samples in the vector
+   * @return none.
+   */
+
+  void arm_scale_f32(
+  float32_t * pSrc,
+  float32_t scale,
+  float32_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Multiplies a Q7 vector by a scalar.
+   * @param[in]       *pSrc points to the input vector
+   * @param[in]       scaleFract fractional portion of the scale value
+   * @param[in]       shift number of bits to shift the result by
+   * @param[out]      *pDst points to the output vector
+   * @param[in]       blockSize number of samples in the vector
+   * @return none.
+   */
+
+  void arm_scale_q7(
+  q7_t * pSrc,
+  q7_t scaleFract,
+  int8_t shift,
+  q7_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Multiplies a Q15 vector by a scalar.
+   * @param[in]       *pSrc points to the input vector
+   * @param[in]       scaleFract fractional portion of the scale value
+   * @param[in]       shift number of bits to shift the result by
+   * @param[out]      *pDst points to the output vector
+   * @param[in]       blockSize number of samples in the vector
+   * @return none.
+   */
+
+  void arm_scale_q15(
+  q15_t * pSrc,
+  q15_t scaleFract,
+  int8_t shift,
+  q15_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Multiplies a Q31 vector by a scalar.
+   * @param[in]       *pSrc points to the input vector
+   * @param[in]       scaleFract fractional portion of the scale value
+   * @param[in]       shift number of bits to shift the result by
+   * @param[out]      *pDst points to the output vector
+   * @param[in]       blockSize number of samples in the vector
+   * @return none.
+   */
+
+  void arm_scale_q31(
+  q31_t * pSrc,
+  q31_t scaleFract,
+  int8_t shift,
+  q31_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Q7 vector absolute value.
+   * @param[in]       *pSrc points to the input buffer
+   * @param[out]      *pDst points to the output buffer
+   * @param[in]       blockSize number of samples in each vector
+   * @return none.
+   */
+
+  void arm_abs_q7(
+  q7_t * pSrc,
+  q7_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Floating-point vector absolute value.
+   * @param[in]       *pSrc points to the input buffer
+   * @param[out]      *pDst points to the output buffer
+   * @param[in]       blockSize number of samples in each vector
+   * @return none.
+   */
+
+  void arm_abs_f32(
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Q15 vector absolute value.
+   * @param[in]       *pSrc points to the input buffer
+   * @param[out]      *pDst points to the output buffer
+   * @param[in]       blockSize number of samples in each vector
+   * @return none.
+   */
+
+  void arm_abs_q15(
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Q31 vector absolute value.
+   * @param[in]       *pSrc points to the input buffer
+   * @param[out]      *pDst points to the output buffer
+   * @param[in]       blockSize number of samples in each vector
+   * @return none.
+   */
+
+  void arm_abs_q31(
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Dot product of floating-point vectors.
+   * @param[in]       *pSrcA points to the first input vector
+   * @param[in]       *pSrcB points to the second input vector
+   * @param[in]       blockSize number of samples in each vector
+   * @param[out]      *result output result returned here
+   * @return none.
+   */
+
+  void arm_dot_prod_f32(
+  float32_t * pSrcA,
+  float32_t * pSrcB,
+  uint32_t blockSize,
+  float32_t * result);
+
+  /**
+   * @brief Dot product of Q7 vectors.
+   * @param[in]       *pSrcA points to the first input vector
+   * @param[in]       *pSrcB points to the second input vector
+   * @param[in]       blockSize number of samples in each vector
+   * @param[out]      *result output result returned here
+   * @return none.
+   */
+
+  void arm_dot_prod_q7(
+  q7_t * pSrcA,
+  q7_t * pSrcB,
+  uint32_t blockSize,
+  q31_t * result);
+
+  /**
+   * @brief Dot product of Q15 vectors.
+   * @param[in]       *pSrcA points to the first input vector
+   * @param[in]       *pSrcB points to the second input vector
+   * @param[in]       blockSize number of samples in each vector
+   * @param[out]      *result output result returned here
+   * @return none.
+   */
+
+  void arm_dot_prod_q15(
+  q15_t * pSrcA,
+  q15_t * pSrcB,
+  uint32_t blockSize,
+  q63_t * result);
+
+  /**
+   * @brief Dot product of Q31 vectors.
+   * @param[in]       *pSrcA points to the first input vector
+   * @param[in]       *pSrcB points to the second input vector
+   * @param[in]       blockSize number of samples in each vector
+   * @param[out]      *result output result returned here
+   * @return none.
+   */
+
+  void arm_dot_prod_q31(
+  q31_t * pSrcA,
+  q31_t * pSrcB,
+  uint32_t blockSize,
+  q63_t * result);
+
+  /**
+   * @brief  Shifts the elements of a Q7 vector a specified number of bits.
+   * @param[in]  *pSrc points to the input vector
+   * @param[in]  shiftBits number of bits to shift.  A positive value shifts left; a negative value shifts right.
+   * @param[out]  *pDst points to the output vector
+   * @param[in]  blockSize number of samples in the vector
+   * @return none.
+   */
+
+  void arm_shift_q7(
+  q7_t * pSrc,
+  int8_t shiftBits,
+  q7_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Shifts the elements of a Q15 vector a specified number of bits.
+   * @param[in]  *pSrc points to the input vector
+   * @param[in]  shiftBits number of bits to shift.  A positive value shifts left; a negative value shifts right.
+   * @param[out]  *pDst points to the output vector
+   * @param[in]  blockSize number of samples in the vector
+   * @return none.
+   */
+
+  void arm_shift_q15(
+  q15_t * pSrc,
+  int8_t shiftBits,
+  q15_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Shifts the elements of a Q31 vector a specified number of bits.
+   * @param[in]  *pSrc points to the input vector
+   * @param[in]  shiftBits number of bits to shift.  A positive value shifts left; a negative value shifts right.
+   * @param[out]  *pDst points to the output vector
+   * @param[in]  blockSize number of samples in the vector
+   * @return none.
+   */
+
+  void arm_shift_q31(
+  q31_t * pSrc,
+  int8_t shiftBits,
+  q31_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Adds a constant offset to a floating-point vector.
+   * @param[in]  *pSrc points to the input vector
+   * @param[in]  offset is the offset to be added
+   * @param[out]  *pDst points to the output vector
+   * @param[in]  blockSize number of samples in the vector
+   * @return none.
+   */
+
+  void arm_offset_f32(
+  float32_t * pSrc,
+  float32_t offset,
+  float32_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Adds a constant offset to a Q7 vector.
+   * @param[in]  *pSrc points to the input vector
+   * @param[in]  offset is the offset to be added
+   * @param[out]  *pDst points to the output vector
+   * @param[in]  blockSize number of samples in the vector
+   * @return none.
+   */
+
+  void arm_offset_q7(
+  q7_t * pSrc,
+  q7_t offset,
+  q7_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Adds a constant offset to a Q15 vector.
+   * @param[in]  *pSrc points to the input vector
+   * @param[in]  offset is the offset to be added
+   * @param[out]  *pDst points to the output vector
+   * @param[in]  blockSize number of samples in the vector
+   * @return none.
+   */
+
+  void arm_offset_q15(
+  q15_t * pSrc,
+  q15_t offset,
+  q15_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Adds a constant offset to a Q31 vector.
+   * @param[in]  *pSrc points to the input vector
+   * @param[in]  offset is the offset to be added
+   * @param[out]  *pDst points to the output vector
+   * @param[in]  blockSize number of samples in the vector
+   * @return none.
+   */
+
+  void arm_offset_q31(
+  q31_t * pSrc,
+  q31_t offset,
+  q31_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Negates the elements of a floating-point vector.
+   * @param[in]  *pSrc points to the input vector
+   * @param[out]  *pDst points to the output vector
+   * @param[in]  blockSize number of samples in the vector
+   * @return none.
+   */
+
+  void arm_negate_f32(
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Negates the elements of a Q7 vector.
+   * @param[in]  *pSrc points to the input vector
+   * @param[out]  *pDst points to the output vector
+   * @param[in]  blockSize number of samples in the vector
+   * @return none.
+   */
+
+  void arm_negate_q7(
+  q7_t * pSrc,
+  q7_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Negates the elements of a Q15 vector.
+   * @param[in]  *pSrc points to the input vector
+   * @param[out]  *pDst points to the output vector
+   * @param[in]  blockSize number of samples in the vector
+   * @return none.
+   */
+
+  void arm_negate_q15(
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Negates the elements of a Q31 vector.
+   * @param[in]  *pSrc points to the input vector
+   * @param[out]  *pDst points to the output vector
+   * @param[in]  blockSize number of samples in the vector
+   * @return none.
+   */
+
+  void arm_negate_q31(
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize);
+  /**
+   * @brief  Copies the elements of a floating-point vector. 
+   * @param[in]  *pSrc input pointer
+   * @param[out]  *pDst output pointer
+   * @param[in]  blockSize number of samples to process
+   * @return none.
+   */
+  void arm_copy_f32(
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Copies the elements of a Q7 vector. 
+   * @param[in]  *pSrc input pointer
+   * @param[out]  *pDst output pointer
+   * @param[in]  blockSize number of samples to process
+   * @return none.
+   */
+  void arm_copy_q7(
+  q7_t * pSrc,
+  q7_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Copies the elements of a Q15 vector. 
+   * @param[in]  *pSrc input pointer
+   * @param[out]  *pDst output pointer
+   * @param[in]  blockSize number of samples to process
+   * @return none.
+   */
+  void arm_copy_q15(
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Copies the elements of a Q31 vector. 
+   * @param[in]  *pSrc input pointer
+   * @param[out]  *pDst output pointer
+   * @param[in]  blockSize number of samples to process
+   * @return none.
+   */
+  void arm_copy_q31(
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize);
+  /**
+   * @brief  Fills a constant value into a floating-point vector. 
+   * @param[in]  value input value to be filled
+   * @param[out]  *pDst output pointer
+   * @param[in]  blockSize number of samples to process
+   * @return none.
+   */
+  void arm_fill_f32(
+  float32_t value,
+  float32_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Fills a constant value into a Q7 vector. 
+   * @param[in]  value input value to be filled
+   * @param[out]  *pDst output pointer
+   * @param[in]  blockSize number of samples to process
+   * @return none.
+   */
+  void arm_fill_q7(
+  q7_t value,
+  q7_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Fills a constant value into a Q15 vector. 
+   * @param[in]  value input value to be filled
+   * @param[out]  *pDst output pointer
+   * @param[in]  blockSize number of samples to process
+   * @return none.
+   */
+  void arm_fill_q15(
+  q15_t value,
+  q15_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Fills a constant value into a Q31 vector. 
+   * @param[in]  value input value to be filled
+   * @param[out]  *pDst output pointer
+   * @param[in]  blockSize number of samples to process
+   * @return none.
+   */
+  void arm_fill_q31(
+  q31_t value,
+  q31_t * pDst,
+  uint32_t blockSize);
+
+/**  
+ * @brief Convolution of floating-point sequences.  
+ * @param[in] *pSrcA points to the first input sequence.  
+ * @param[in] srcALen length of the first input sequence.  
+ * @param[in] *pSrcB points to the second input sequence.  
+ * @param[in] srcBLen length of the second input sequence.  
+ * @param[out] *pDst points to the location where the output result is written.  Length srcALen+srcBLen-1.  
+ * @return none.  
+ */
+
+  void arm_conv_f32(
+  float32_t * pSrcA,
+  uint32_t srcALen,
+  float32_t * pSrcB,
+  uint32_t srcBLen,
+  float32_t * pDst);
+
+  
+  /**   
+   * @brief Convolution of Q15 sequences.   
+   * @param[in] *pSrcA points to the first input sequence.   
+   * @param[in] srcALen length of the first input sequence.   
+   * @param[in] *pSrcB points to the second input sequence.   
+   * @param[in] srcBLen length of the second input sequence.   
+   * @param[out] *pDst points to the block of output data  Length srcALen+srcBLen-1.   
+   * @param[in]  *pScratch1 points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.   
+   * @param[in]  *pScratch2 points to scratch buffer of size min(srcALen, srcBLen).   
+   * @return none.   
+   */
+
+
+  void arm_conv_opt_q15(
+  q15_t * pSrcA,
+  uint32_t srcALen,
+  q15_t * pSrcB,
+  uint32_t srcBLen,
+  q15_t * pDst,
+  q15_t * pScratch1,
+  q15_t * pScratch2);
+
+
+/**  
+ * @brief Convolution of Q15 sequences.  
+ * @param[in] *pSrcA points to the first input sequence.  
+ * @param[in] srcALen length of the first input sequence.  
+ * @param[in] *pSrcB points to the second input sequence.  
+ * @param[in] srcBLen length of the second input sequence.  
+ * @param[out] *pDst points to the location where the output result is written.  Length srcALen+srcBLen-1.  
+ * @return none.  
+ */
+
+  void arm_conv_q15(
+  q15_t * pSrcA,
+  uint32_t srcALen,
+  q15_t * pSrcB,
+  uint32_t srcBLen,
+  q15_t * pDst);
+
+  /**
+   * @brief Convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4
+   * @param[in] *pSrcA points to the first input sequence.
+   * @param[in] srcALen length of the first input sequence.
+   * @param[in] *pSrcB points to the second input sequence.
+   * @param[in] srcBLen length of the second input sequence.
+   * @param[out] *pDst points to the block of output data  Length srcALen+srcBLen-1.
+   * @return none.
+   */
+
+  void arm_conv_fast_q15(
+			  q15_t * pSrcA,
+			 uint32_t srcALen,
+			  q15_t * pSrcB,
+			 uint32_t srcBLen,
+			 q15_t * pDst);
+
+  /**
+   * @brief Convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4
+   * @param[in] *pSrcA points to the first input sequence.
+   * @param[in] srcALen length of the first input sequence.
+   * @param[in] *pSrcB points to the second input sequence.
+   * @param[in] srcBLen length of the second input sequence.
+   * @param[out] *pDst points to the block of output data  Length srcALen+srcBLen-1.
+   * @param[in]  *pScratch1 points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.   
+   * @param[in]  *pScratch2 points to scratch buffer of size min(srcALen, srcBLen).   
+   * @return none.   
+   */
+
+  void arm_conv_fast_opt_q15(
+  q15_t * pSrcA,
+  uint32_t srcALen,
+  q15_t * pSrcB,
+  uint32_t srcBLen,
+  q15_t * pDst,
+  q15_t * pScratch1,
+  q15_t * pScratch2);
+
+
+
+  /**
+   * @brief Convolution of Q31 sequences.
+   * @param[in] *pSrcA points to the first input sequence.
+   * @param[in] srcALen length of the first input sequence.
+   * @param[in] *pSrcB points to the second input sequence.
+   * @param[in] srcBLen length of the second input sequence.
+   * @param[out] *pDst points to the block of output data  Length srcALen+srcBLen-1.
+   * @return none.
+   */
+
+  void arm_conv_q31(
+  q31_t * pSrcA,
+  uint32_t srcALen,
+  q31_t * pSrcB,
+  uint32_t srcBLen,
+  q31_t * pDst);
+
+  /**
+   * @brief Convolution of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4
+   * @param[in] *pSrcA points to the first input sequence.
+   * @param[in] srcALen length of the first input sequence.
+   * @param[in] *pSrcB points to the second input sequence.
+   * @param[in] srcBLen length of the second input sequence.
+   * @param[out] *pDst points to the block of output data  Length srcALen+srcBLen-1.
+   * @return none.
+   */
+
+  void arm_conv_fast_q31(
+  q31_t * pSrcA,
+  uint32_t srcALen,
+  q31_t * pSrcB,
+  uint32_t srcBLen,
+  q31_t * pDst);
+
+
+    /**   
+   * @brief Convolution of Q7 sequences.   
+   * @param[in] *pSrcA points to the first input sequence.   
+   * @param[in] srcALen length of the first input sequence.   
+   * @param[in] *pSrcB points to the second input sequence.   
+   * @param[in] srcBLen length of the second input sequence.   
+   * @param[out] *pDst points to the block of output data  Length srcALen+srcBLen-1.   
+   * @param[in]  *pScratch1 points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.   
+   * @param[in]  *pScratch2 points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen).   
+   * @return none.   
+   */
+
+  void arm_conv_opt_q7(
+  q7_t * pSrcA,
+  uint32_t srcALen,
+  q7_t * pSrcB,
+  uint32_t srcBLen,
+  q7_t * pDst,
+  q15_t * pScratch1,
+  q15_t * pScratch2);
+
+
+
+  /**
+   * @brief Convolution of Q7 sequences.
+   * @param[in] *pSrcA points to the first input sequence.
+   * @param[in] srcALen length of the first input sequence.
+   * @param[in] *pSrcB points to the second input sequence.
+   * @param[in] srcBLen length of the second input sequence.
+   * @param[out] *pDst points to the block of output data  Length srcALen+srcBLen-1.
+   * @return none.
+   */
+
+  void arm_conv_q7(
+  q7_t * pSrcA,
+  uint32_t srcALen,
+  q7_t * pSrcB,
+  uint32_t srcBLen,
+  q7_t * pDst);
+
+
+  /**
+   * @brief Partial convolution of floating-point sequences.
+   * @param[in]       *pSrcA points to the first input sequence.
+   * @param[in]       srcALen length of the first input sequence.
+   * @param[in]       *pSrcB points to the second input sequence.
+   * @param[in]       srcBLen length of the second input sequence.
+   * @param[out]      *pDst points to the block of output data
+   * @param[in]       firstIndex is the first output sample to start with.
+   * @param[in]       numPoints is the number of output points to be computed.
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
+   */
+
+  arm_status arm_conv_partial_f32(
+  float32_t * pSrcA,
+  uint32_t srcALen,
+  float32_t * pSrcB,
+  uint32_t srcBLen,
+  float32_t * pDst,
+  uint32_t firstIndex,
+  uint32_t numPoints);
+
+    /**   
+   * @brief Partial convolution of Q15 sequences.   
+   * @param[in]       *pSrcA points to the first input sequence.   
+   * @param[in]       srcALen length of the first input sequence.   
+   * @param[in]       *pSrcB points to the second input sequence.   
+   * @param[in]       srcBLen length of the second input sequence.   
+   * @param[out]      *pDst points to the block of output data   
+   * @param[in]       firstIndex is the first output sample to start with.   
+   * @param[in]       numPoints is the number of output points to be computed.   
+   * @param[in]       * pScratch1 points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.   
+   * @param[in]       * pScratch2 points to scratch buffer of size min(srcALen, srcBLen).   
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].   
+   */
+
+  arm_status arm_conv_partial_opt_q15(
+  q15_t * pSrcA,
+  uint32_t srcALen,
+  q15_t * pSrcB,
+  uint32_t srcBLen,
+  q15_t * pDst,
+  uint32_t firstIndex,
+  uint32_t numPoints,
+  q15_t * pScratch1,
+  q15_t * pScratch2);
+
+
+/**
+   * @brief Partial convolution of Q15 sequences.
+   * @param[in]       *pSrcA points to the first input sequence.
+   * @param[in]       srcALen length of the first input sequence.
+   * @param[in]       *pSrcB points to the second input sequence.
+   * @param[in]       srcBLen length of the second input sequence.
+   * @param[out]      *pDst points to the block of output data
+   * @param[in]       firstIndex is the first output sample to start with.
+   * @param[in]       numPoints is the number of output points to be computed.
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
+   */
+
+  arm_status arm_conv_partial_q15(
+  q15_t * pSrcA,
+  uint32_t srcALen,
+  q15_t * pSrcB,
+  uint32_t srcBLen,
+  q15_t * pDst,
+  uint32_t firstIndex,
+  uint32_t numPoints);
+
+  /**
+   * @brief Partial convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4
+   * @param[in]       *pSrcA points to the first input sequence.
+   * @param[in]       srcALen length of the first input sequence.
+   * @param[in]       *pSrcB points to the second input sequence.
+   * @param[in]       srcBLen length of the second input sequence.
+   * @param[out]      *pDst points to the block of output data
+   * @param[in]       firstIndex is the first output sample to start with.
+   * @param[in]       numPoints is the number of output points to be computed.
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
+   */
+
+  arm_status arm_conv_partial_fast_q15(
+				        q15_t * pSrcA,
+				       uint32_t srcALen,
+				        q15_t * pSrcB,
+				       uint32_t srcBLen,
+				       q15_t * pDst,
+				       uint32_t firstIndex,
+				       uint32_t numPoints);
+
+
+  /**
+   * @brief Partial convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4
+   * @param[in]       *pSrcA points to the first input sequence.
+   * @param[in]       srcALen length of the first input sequence.
+   * @param[in]       *pSrcB points to the second input sequence.
+   * @param[in]       srcBLen length of the second input sequence.
+   * @param[out]      *pDst points to the block of output data
+   * @param[in]       firstIndex is the first output sample to start with.
+   * @param[in]       numPoints is the number of output points to be computed.
+   * @param[in]       * pScratch1 points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.   
+   * @param[in]       * pScratch2 points to scratch buffer of size min(srcALen, srcBLen).   
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].   
+   */
+
+  arm_status arm_conv_partial_fast_opt_q15(
+  q15_t * pSrcA,
+  uint32_t srcALen,
+  q15_t * pSrcB,
+  uint32_t srcBLen,
+  q15_t * pDst,
+  uint32_t firstIndex,
+  uint32_t numPoints,
+  q15_t * pScratch1,
+  q15_t * pScratch2);
+
+
+  /**
+   * @brief Partial convolution of Q31 sequences.
+   * @param[in]       *pSrcA points to the first input sequence.
+   * @param[in]       srcALen length of the first input sequence.
+   * @param[in]       *pSrcB points to the second input sequence.
+   * @param[in]       srcBLen length of the second input sequence.
+   * @param[out]      *pDst points to the block of output data
+   * @param[in]       firstIndex is the first output sample to start with.
+   * @param[in]       numPoints is the number of output points to be computed.
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
+   */
+
+  arm_status arm_conv_partial_q31(
+  q31_t * pSrcA,
+  uint32_t srcALen,
+  q31_t * pSrcB,
+  uint32_t srcBLen,
+  q31_t * pDst,
+  uint32_t firstIndex,
+  uint32_t numPoints);
+
+
+  /**
+   * @brief Partial convolution of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4
+   * @param[in]       *pSrcA points to the first input sequence.
+   * @param[in]       srcALen length of the first input sequence.
+   * @param[in]       *pSrcB points to the second input sequence.
+   * @param[in]       srcBLen length of the second input sequence.
+   * @param[out]      *pDst points to the block of output data
+   * @param[in]       firstIndex is the first output sample to start with.
+   * @param[in]       numPoints is the number of output points to be computed.
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
+   */
+
+  arm_status arm_conv_partial_fast_q31(
+  q31_t * pSrcA,
+  uint32_t srcALen,
+  q31_t * pSrcB,
+  uint32_t srcBLen,
+  q31_t * pDst,
+  uint32_t firstIndex,
+  uint32_t numPoints);
+
+
+  /**   
+   * @brief Partial convolution of Q7 sequences   
+   * @param[in]       *pSrcA points to the first input sequence.   
+   * @param[in]       srcALen length of the first input sequence.   
+   * @param[in]       *pSrcB points to the second input sequence.   
+   * @param[in]       srcBLen length of the second input sequence.   
+   * @param[out]      *pDst points to the block of output data   
+   * @param[in]       firstIndex is the first output sample to start with.   
+   * @param[in]       numPoints is the number of output points to be computed.   
+   * @param[in]  *pScratch1 points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.   
+   * @param[in]  *pScratch2 points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen).   
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].   
+   */
+
+  arm_status arm_conv_partial_opt_q7(
+  q7_t * pSrcA,
+  uint32_t srcALen,
+  q7_t * pSrcB,
+  uint32_t srcBLen,
+  q7_t * pDst,
+  uint32_t firstIndex,
+  uint32_t numPoints,
+  q15_t * pScratch1,
+  q15_t * pScratch2);
+
+
+/**
+   * @brief Partial convolution of Q7 sequences.
+   * @param[in]       *pSrcA points to the first input sequence.
+   * @param[in]       srcALen length of the first input sequence.
+   * @param[in]       *pSrcB points to the second input sequence.
+   * @param[in]       srcBLen length of the second input sequence.
+   * @param[out]      *pDst points to the block of output data
+   * @param[in]       firstIndex is the first output sample to start with.
+   * @param[in]       numPoints is the number of output points to be computed.
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
+   */
+
+  arm_status arm_conv_partial_q7(
+  q7_t * pSrcA,
+  uint32_t srcALen,
+  q7_t * pSrcB,
+  uint32_t srcBLen,
+  q7_t * pDst,
+  uint32_t firstIndex,
+  uint32_t numPoints);
+
+
+
+  /**
+   * @brief Instance structure for the Q15 FIR decimator.
+   */
+
+  typedef struct
+  {
+    uint8_t M;                      /**< decimation factor. */
+    uint16_t numTaps;               /**< number of coefficients in the filter. */
+    q15_t *pCoeffs;                  /**< points to the coefficient array. The array is of length numTaps.*/
+    q15_t *pState;                   /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+  } arm_fir_decimate_instance_q15;
+
+  /**
+   * @brief Instance structure for the Q31 FIR decimator.
+   */
+
+  typedef struct
+  {
+    uint8_t M;                  /**< decimation factor. */
+    uint16_t numTaps;           /**< number of coefficients in the filter. */
+    q31_t *pCoeffs;              /**< points to the coefficient array. The array is of length numTaps.*/
+    q31_t *pState;               /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+
+  } arm_fir_decimate_instance_q31;
+
+  /**
+   * @brief Instance structure for the floating-point FIR decimator.
+   */
+
+  typedef struct
+  {
+    uint8_t M;                          /**< decimation factor. */
+    uint16_t numTaps;                   /**< number of coefficients in the filter. */
+    float32_t *pCoeffs;                  /**< points to the coefficient array. The array is of length numTaps.*/
+    float32_t *pState;                   /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+
+  } arm_fir_decimate_instance_f32;
+
+
+
+  /**
+   * @brief Processing function for the floating-point FIR decimator.
+   * @param[in] *S points to an instance of the floating-point FIR decimator structure.
+   * @param[in] *pSrc points to the block of input data.
+   * @param[out] *pDst points to the block of output data
+   * @param[in] blockSize number of input samples to process per call.
+   * @return none
+   */
+
+  void arm_fir_decimate_f32(
+  const arm_fir_decimate_instance_f32 * S,
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize);
+
+
+  /**
+   * @brief  Initialization function for the floating-point FIR decimator.
+   * @param[in,out] *S points to an instance of the floating-point FIR decimator structure.
+   * @param[in] numTaps  number of coefficients in the filter.
+   * @param[in] M  decimation factor.
+   * @param[in] *pCoeffs points to the filter coefficients.
+   * @param[in] *pState points to the state buffer.
+   * @param[in] blockSize number of input samples to process per call.
+   * @return    The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
+   * blockSize is not a multiple of M.
+   */
+
+  arm_status arm_fir_decimate_init_f32(
+  arm_fir_decimate_instance_f32 * S,
+  uint16_t numTaps,
+  uint8_t M,
+  float32_t * pCoeffs,
+  float32_t * pState,
+  uint32_t blockSize);
+
+  /**
+   * @brief Processing function for the Q15 FIR decimator.
+   * @param[in] *S points to an instance of the Q15 FIR decimator structure.
+   * @param[in] *pSrc points to the block of input data.
+   * @param[out] *pDst points to the block of output data
+   * @param[in] blockSize number of input samples to process per call.
+   * @return none
+   */
+
+  void arm_fir_decimate_q15(
+  const arm_fir_decimate_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Processing function for the Q15 FIR decimator (fast variant) for Cortex-M3 and Cortex-M4.
+   * @param[in] *S points to an instance of the Q15 FIR decimator structure.
+   * @param[in] *pSrc points to the block of input data.
+   * @param[out] *pDst points to the block of output data
+   * @param[in] blockSize number of input samples to process per call.
+   * @return none
+   */
+
+  void arm_fir_decimate_fast_q15(
+  const arm_fir_decimate_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize);
+
+
+
+  /**
+   * @brief  Initialization function for the Q15 FIR decimator.
+   * @param[in,out] *S points to an instance of the Q15 FIR decimator structure.
+   * @param[in] numTaps  number of coefficients in the filter.
+   * @param[in] M  decimation factor.
+   * @param[in] *pCoeffs points to the filter coefficients.
+   * @param[in] *pState points to the state buffer.
+   * @param[in] blockSize number of input samples to process per call.
+   * @return    The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
+   * blockSize is not a multiple of M.
+   */
+
+  arm_status arm_fir_decimate_init_q15(
+  arm_fir_decimate_instance_q15 * S,
+  uint16_t numTaps,
+  uint8_t M,
+  q15_t * pCoeffs,
+  q15_t * pState,
+  uint32_t blockSize);
+
+  /**
+   * @brief Processing function for the Q31 FIR decimator.
+   * @param[in] *S points to an instance of the Q31 FIR decimator structure.
+   * @param[in] *pSrc points to the block of input data.
+   * @param[out] *pDst points to the block of output data
+   * @param[in] blockSize number of input samples to process per call.
+   * @return none
+   */
+
+  void arm_fir_decimate_q31(
+  const arm_fir_decimate_instance_q31 * S,
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Processing function for the Q31 FIR decimator (fast variant) for Cortex-M3 and Cortex-M4.
+   * @param[in] *S points to an instance of the Q31 FIR decimator structure.
+   * @param[in] *pSrc points to the block of input data.
+   * @param[out] *pDst points to the block of output data
+   * @param[in] blockSize number of input samples to process per call.
+   * @return none
+   */
+
+  void arm_fir_decimate_fast_q31(
+  arm_fir_decimate_instance_q31 * S,
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize);
+
+
+  /**
+   * @brief  Initialization function for the Q31 FIR decimator.
+   * @param[in,out] *S points to an instance of the Q31 FIR decimator structure.
+   * @param[in] numTaps  number of coefficients in the filter.
+   * @param[in] M  decimation factor.
+   * @param[in] *pCoeffs points to the filter coefficients.
+   * @param[in] *pState points to the state buffer.
+   * @param[in] blockSize number of input samples to process per call.
+   * @return    The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
+   * blockSize is not a multiple of M.
+   */
+
+  arm_status arm_fir_decimate_init_q31(
+  arm_fir_decimate_instance_q31 * S,
+  uint16_t numTaps,
+  uint8_t M,
+  q31_t * pCoeffs,
+  q31_t * pState,
+  uint32_t blockSize);
+
+
+
+  /**
+   * @brief Instance structure for the Q15 FIR interpolator.
+   */
+
+  typedef struct
+  {
+    uint8_t L;                      /**< upsample factor. */
+    uint16_t phaseLength;           /**< length of each polyphase filter component. */
+    q15_t *pCoeffs;                 /**< points to the coefficient array. The array is of length L*phaseLength. */
+    q15_t *pState;                  /**< points to the state variable array. The array is of length blockSize+phaseLength-1. */
+  } arm_fir_interpolate_instance_q15;
+
+  /**
+   * @brief Instance structure for the Q31 FIR interpolator.
+   */
+
+  typedef struct
+  {
+    uint8_t L;                      /**< upsample factor. */
+    uint16_t phaseLength;           /**< length of each polyphase filter component. */
+    q31_t *pCoeffs;                  /**< points to the coefficient array. The array is of length L*phaseLength. */
+    q31_t *pState;                   /**< points to the state variable array. The array is of length blockSize+phaseLength-1. */
+  } arm_fir_interpolate_instance_q31;
+
+  /**
+   * @brief Instance structure for the floating-point FIR interpolator.
+   */
+
+  typedef struct
+  {
+    uint8_t L;                     /**< upsample factor. */
+    uint16_t phaseLength;          /**< length of each polyphase filter component. */
+    float32_t *pCoeffs;             /**< points to the coefficient array. The array is of length L*phaseLength. */
+    float32_t *pState;              /**< points to the state variable array. The array is of length phaseLength+numTaps-1. */
+  } arm_fir_interpolate_instance_f32;
+
+
+  /**
+   * @brief Processing function for the Q15 FIR interpolator.
+   * @param[in] *S        points to an instance of the Q15 FIR interpolator structure.
+   * @param[in] *pSrc     points to the block of input data.
+   * @param[out] *pDst    points to the block of output data.
+   * @param[in] blockSize number of input samples to process per call.
+   * @return none.
+   */
+
+  void arm_fir_interpolate_q15(
+  const arm_fir_interpolate_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize);
+
+
+  /**
+   * @brief  Initialization function for the Q15 FIR interpolator.
+   * @param[in,out] *S        points to an instance of the Q15 FIR interpolator structure.
+   * @param[in]     L         upsample factor.
+   * @param[in]     numTaps   number of filter coefficients in the filter.
+   * @param[in]     *pCoeffs  points to the filter coefficient buffer.
+   * @param[in]     *pState   points to the state buffer.
+   * @param[in]     blockSize number of input samples to process per call.
+   * @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
+   * the filter length numTaps is not a multiple of the interpolation factor L.
+   */
+
+  arm_status arm_fir_interpolate_init_q15(
+  arm_fir_interpolate_instance_q15 * S,
+  uint8_t L,
+  uint16_t numTaps,
+  q15_t * pCoeffs,
+  q15_t * pState,
+  uint32_t blockSize);
+
+  /**
+   * @brief Processing function for the Q31 FIR interpolator.
+   * @param[in] *S        points to an instance of the Q15 FIR interpolator structure.
+   * @param[in] *pSrc     points to the block of input data.
+   * @param[out] *pDst    points to the block of output data.
+   * @param[in] blockSize number of input samples to process per call.
+   * @return none.
+   */
+
+  void arm_fir_interpolate_q31(
+  const arm_fir_interpolate_instance_q31 * S,
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Initialization function for the Q31 FIR interpolator.
+   * @param[in,out] *S        points to an instance of the Q31 FIR interpolator structure.
+   * @param[in]     L         upsample factor.
+   * @param[in]     numTaps   number of filter coefficients in the filter.
+   * @param[in]     *pCoeffs  points to the filter coefficient buffer.
+   * @param[in]     *pState   points to the state buffer.
+   * @param[in]     blockSize number of input samples to process per call.
+   * @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
+   * the filter length numTaps is not a multiple of the interpolation factor L.
+   */
+
+  arm_status arm_fir_interpolate_init_q31(
+  arm_fir_interpolate_instance_q31 * S,
+  uint8_t L,
+  uint16_t numTaps,
+  q31_t * pCoeffs,
+  q31_t * pState,
+  uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the floating-point FIR interpolator.
+   * @param[in] *S        points to an instance of the floating-point FIR interpolator structure.
+   * @param[in] *pSrc     points to the block of input data.
+   * @param[out] *pDst    points to the block of output data.
+   * @param[in] blockSize number of input samples to process per call.
+   * @return none.
+   */
+
+  void arm_fir_interpolate_f32(
+  const arm_fir_interpolate_instance_f32 * S,
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Initialization function for the floating-point FIR interpolator.
+   * @param[in,out] *S        points to an instance of the floating-point FIR interpolator structure.
+   * @param[in]     L         upsample factor.
+   * @param[in]     numTaps   number of filter coefficients in the filter.
+   * @param[in]     *pCoeffs  points to the filter coefficient buffer.
+   * @param[in]     *pState   points to the state buffer.
+   * @param[in]     blockSize number of input samples to process per call.
+   * @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
+   * the filter length numTaps is not a multiple of the interpolation factor L.
+   */
+
+  arm_status arm_fir_interpolate_init_f32(
+  arm_fir_interpolate_instance_f32 * S,
+  uint8_t L,
+  uint16_t numTaps,
+  float32_t * pCoeffs,
+  float32_t * pState,
+  uint32_t blockSize);
+
+  /**
+   * @brief Instance structure for the high precision Q31 Biquad cascade filter.
+   */
+
+  typedef struct
+  {
+    uint8_t numStages;       /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
+    q63_t *pState;           /**< points to the array of state coefficients.  The array is of length 4*numStages. */
+    q31_t *pCoeffs;          /**< points to the array of coefficients.  The array is of length 5*numStages. */
+    uint8_t postShift;       /**< additional shift, in bits, applied to each output sample. */
+
+  } arm_biquad_cas_df1_32x64_ins_q31;
+
+
+  /**
+   * @param[in]  *S        points to an instance of the high precision Q31 Biquad cascade filter structure.
+   * @param[in]  *pSrc     points to the block of input data.
+   * @param[out] *pDst     points to the block of output data
+   * @param[in]  blockSize number of samples to process.
+   * @return none.
+   */
+
+  void arm_biquad_cas_df1_32x64_q31(
+  const arm_biquad_cas_df1_32x64_ins_q31 * S,
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize);
+
+
+  /**
+   * @param[in,out] *S           points to an instance of the high precision Q31 Biquad cascade filter structure.
+   * @param[in]     numStages    number of 2nd order stages in the filter.
+   * @param[in]     *pCoeffs     points to the filter coefficients.
+   * @param[in]     *pState      points to the state buffer.
+   * @param[in]     postShift    shift to be applied to the output. Varies according to the coefficients format
+   * @return        none
+   */
+
+  void arm_biquad_cas_df1_32x64_init_q31(
+  arm_biquad_cas_df1_32x64_ins_q31 * S,
+  uint8_t numStages,
+  q31_t * pCoeffs,
+  q63_t * pState,
+  uint8_t postShift);
+
+
+
+  /**
+   * @brief Instance structure for the floating-point transposed direct form II Biquad cascade filter.
+   */
+
+  typedef struct
+  {
+    uint8_t numStages;         /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
+    float32_t *pState;         /**< points to the array of state coefficients.  The array is of length 2*numStages. */
+    float32_t *pCoeffs;        /**< points to the array of coefficients.  The array is of length 5*numStages. */
+  } arm_biquad_cascade_df2T_instance_f32;
+
+
+  /**
+   * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter.
+   * @param[in]  *S        points to an instance of the filter data structure.
+   * @param[in]  *pSrc     points to the block of input data.
+   * @param[out] *pDst     points to the block of output data
+   * @param[in]  blockSize number of samples to process.
+   * @return none.
+   */
+
+  void arm_biquad_cascade_df2T_f32(
+  const arm_biquad_cascade_df2T_instance_f32 * S,
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize);
+
+
+  /**
+   * @brief  Initialization function for the floating-point transposed direct form II Biquad cascade filter.
+   * @param[in,out] *S           points to an instance of the filter data structure.
+   * @param[in]     numStages    number of 2nd order stages in the filter.
+   * @param[in]     *pCoeffs     points to the filter coefficients.
+   * @param[in]     *pState      points to the state buffer.
+   * @return        none
+   */
+
+  void arm_biquad_cascade_df2T_init_f32(
+  arm_biquad_cascade_df2T_instance_f32 * S,
+  uint8_t numStages,
+  float32_t * pCoeffs,
+  float32_t * pState);
+
+
+
+  /**
+   * @brief Instance structure for the Q15 FIR lattice filter.
+   */
+
+  typedef struct
+  {
+    uint16_t numStages;                          /**< number of filter stages. */
+    q15_t *pState;                               /**< points to the state variable array. The array is of length numStages. */
+    q15_t *pCoeffs;                              /**< points to the coefficient array. The array is of length numStages. */
+  } arm_fir_lattice_instance_q15;
+
+  /**
+   * @brief Instance structure for the Q31 FIR lattice filter.
+   */
+
+  typedef struct
+  {
+    uint16_t numStages;                          /**< number of filter stages. */
+    q31_t *pState;                               /**< points to the state variable array. The array is of length numStages. */
+    q31_t *pCoeffs;                              /**< points to the coefficient array. The array is of length numStages. */
+  } arm_fir_lattice_instance_q31;
+
+  /**
+   * @brief Instance structure for the floating-point FIR lattice filter.
+   */
+
+  typedef struct
+  {
+    uint16_t numStages;                  /**< number of filter stages. */
+    float32_t *pState;                   /**< points to the state variable array. The array is of length numStages. */
+    float32_t *pCoeffs;                  /**< points to the coefficient array. The array is of length numStages. */
+  } arm_fir_lattice_instance_f32;
+
+  /**
+   * @brief Initialization function for the Q15 FIR lattice filter.
+   * @param[in] *S points to an instance of the Q15 FIR lattice structure.
+   * @param[in] numStages  number of filter stages.
+   * @param[in] *pCoeffs points to the coefficient buffer.  The array is of length numStages. 
+   * @param[in] *pState points to the state buffer.  The array is of length numStages. 
+   * @return none.
+   */
+
+  void arm_fir_lattice_init_q15(
+  arm_fir_lattice_instance_q15 * S,
+  uint16_t numStages,
+  q15_t * pCoeffs,
+  q15_t * pState);
+
+
+  /**
+   * @brief Processing function for the Q15 FIR lattice filter.
+   * @param[in] *S points to an instance of the Q15 FIR lattice structure.
+   * @param[in] *pSrc points to the block of input data.
+   * @param[out] *pDst points to the block of output data.
+   * @param[in] blockSize number of samples to process.
+   * @return none.
+   */
+  void arm_fir_lattice_q15(
+  const arm_fir_lattice_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Initialization function for the Q31 FIR lattice filter.
+   * @param[in] *S points to an instance of the Q31 FIR lattice structure.
+   * @param[in] numStages  number of filter stages.
+   * @param[in] *pCoeffs points to the coefficient buffer.  The array is of length numStages.
+   * @param[in] *pState points to the state buffer.   The array is of length numStages.
+   * @return none.
+   */
+
+  void arm_fir_lattice_init_q31(
+  arm_fir_lattice_instance_q31 * S,
+  uint16_t numStages,
+  q31_t * pCoeffs,
+  q31_t * pState);
+
+
+  /**
+   * @brief Processing function for the Q31 FIR lattice filter.
+   * @param[in]  *S        points to an instance of the Q31 FIR lattice structure.
+   * @param[in]  *pSrc     points to the block of input data.
+   * @param[out] *pDst     points to the block of output data
+   * @param[in]  blockSize number of samples to process.
+   * @return none.
+   */
+
+  void arm_fir_lattice_q31(
+  const arm_fir_lattice_instance_q31 * S,
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize);
+
+/**
+ * @brief Initialization function for the floating-point FIR lattice filter.
+ * @param[in] *S points to an instance of the floating-point FIR lattice structure.
+ * @param[in] numStages  number of filter stages.
+ * @param[in] *pCoeffs points to the coefficient buffer.  The array is of length numStages.
+ * @param[in] *pState points to the state buffer.  The array is of length numStages.
+ * @return none.
+ */
+
+  void arm_fir_lattice_init_f32(
+  arm_fir_lattice_instance_f32 * S,
+  uint16_t numStages,
+  float32_t * pCoeffs,
+  float32_t * pState);
+
+  /**
+   * @brief Processing function for the floating-point FIR lattice filter.
+   * @param[in]  *S        points to an instance of the floating-point FIR lattice structure.
+   * @param[in]  *pSrc     points to the block of input data.
+   * @param[out] *pDst     points to the block of output data
+   * @param[in]  blockSize number of samples to process.
+   * @return none.
+   */
+
+  void arm_fir_lattice_f32(
+  const arm_fir_lattice_instance_f32 * S,
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Instance structure for the Q15 IIR lattice filter.
+   */
+  typedef struct
+  {
+    uint16_t numStages;                         /**< number of stages in the filter. */
+    q15_t *pState;                              /**< points to the state variable array. The array is of length numStages+blockSize. */
+    q15_t *pkCoeffs;                            /**< points to the reflection coefficient array. The array is of length numStages. */
+    q15_t *pvCoeffs;                            /**< points to the ladder coefficient array. The array is of length numStages+1. */
+  } arm_iir_lattice_instance_q15;
+
+  /**
+   * @brief Instance structure for the Q31 IIR lattice filter.
+   */
+  typedef struct
+  {
+    uint16_t numStages;                         /**< number of stages in the filter. */
+    q31_t *pState;                              /**< points to the state variable array. The array is of length numStages+blockSize. */
+    q31_t *pkCoeffs;                            /**< points to the reflection coefficient array. The array is of length numStages. */
+    q31_t *pvCoeffs;                            /**< points to the ladder coefficient array. The array is of length numStages+1. */
+  } arm_iir_lattice_instance_q31;
+
+  /**
+   * @brief Instance structure for the floating-point IIR lattice filter.
+   */
+  typedef struct
+  {
+    uint16_t numStages;                         /**< number of stages in the filter. */
+    float32_t *pState;                          /**< points to the state variable array. The array is of length numStages+blockSize. */
+    float32_t *pkCoeffs;                        /**< points to the reflection coefficient array. The array is of length numStages. */
+    float32_t *pvCoeffs;                        /**< points to the ladder coefficient array. The array is of length numStages+1. */
+  } arm_iir_lattice_instance_f32;
+
+  /**
+   * @brief Processing function for the floating-point IIR lattice filter.
+   * @param[in] *S points to an instance of the floating-point IIR lattice structure.
+   * @param[in] *pSrc points to the block of input data.
+   * @param[out] *pDst points to the block of output data.
+   * @param[in] blockSize number of samples to process.
+   * @return none.
+   */
+
+  void arm_iir_lattice_f32(
+  const arm_iir_lattice_instance_f32 * S,
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Initialization function for the floating-point IIR lattice filter.
+   * @param[in] *S points to an instance of the floating-point IIR lattice structure.
+   * @param[in] numStages number of stages in the filter.
+   * @param[in] *pkCoeffs points to the reflection coefficient buffer.  The array is of length numStages.
+   * @param[in] *pvCoeffs points to the ladder coefficient buffer.  The array is of length numStages+1.
+   * @param[in] *pState points to the state buffer.  The array is of length numStages+blockSize-1.
+   * @param[in] blockSize number of samples to process.
+   * @return none.
+   */
+
+  void arm_iir_lattice_init_f32(
+  arm_iir_lattice_instance_f32 * S,
+  uint16_t numStages,
+  float32_t * pkCoeffs,
+  float32_t * pvCoeffs,
+  float32_t * pState,
+  uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the Q31 IIR lattice filter.
+   * @param[in] *S points to an instance of the Q31 IIR lattice structure.
+   * @param[in] *pSrc points to the block of input data.
+   * @param[out] *pDst points to the block of output data.
+   * @param[in] blockSize number of samples to process.
+   * @return none.
+   */
+
+  void arm_iir_lattice_q31(
+  const arm_iir_lattice_instance_q31 * S,
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize);
+
+
+  /**
+   * @brief Initialization function for the Q31 IIR lattice filter.
+   * @param[in] *S points to an instance of the Q31 IIR lattice structure.
+   * @param[in] numStages number of stages in the filter.
+   * @param[in] *pkCoeffs points to the reflection coefficient buffer.  The array is of length numStages.
+   * @param[in] *pvCoeffs points to the ladder coefficient buffer.  The array is of length numStages+1.
+   * @param[in] *pState points to the state buffer.  The array is of length numStages+blockSize.
+   * @param[in] blockSize number of samples to process.
+   * @return none.
+   */
+
+  void arm_iir_lattice_init_q31(
+  arm_iir_lattice_instance_q31 * S,
+  uint16_t numStages,
+  q31_t * pkCoeffs,
+  q31_t * pvCoeffs,
+  q31_t * pState,
+  uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the Q15 IIR lattice filter.
+   * @param[in] *S points to an instance of the Q15 IIR lattice structure.
+   * @param[in] *pSrc points to the block of input data.
+   * @param[out] *pDst points to the block of output data.
+   * @param[in] blockSize number of samples to process.
+   * @return none.
+   */
+
+  void arm_iir_lattice_q15(
+  const arm_iir_lattice_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize);
+
+
+/**
+ * @brief Initialization function for the Q15 IIR lattice filter.
+ * @param[in] *S points to an instance of the fixed-point Q15 IIR lattice structure.
+ * @param[in] numStages  number of stages in the filter.
+ * @param[in] *pkCoeffs points to reflection coefficient buffer.  The array is of length numStages.
+ * @param[in] *pvCoeffs points to ladder coefficient buffer.  The array is of length numStages+1.
+ * @param[in] *pState points to state buffer.  The array is of length numStages+blockSize.
+ * @param[in] blockSize number of samples to process per call.
+ * @return none.
+ */
+
+  void arm_iir_lattice_init_q15(
+  arm_iir_lattice_instance_q15 * S,
+  uint16_t numStages,
+  q15_t * pkCoeffs,
+  q15_t * pvCoeffs,
+  q15_t * pState,
+  uint32_t blockSize);
+
+  /**
+   * @brief Instance structure for the floating-point LMS filter.
+   */
+
+  typedef struct
+  {
+    uint16_t numTaps;    /**< number of coefficients in the filter. */
+    float32_t *pState;   /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+    float32_t *pCoeffs;  /**< points to the coefficient array. The array is of length numTaps. */
+    float32_t mu;        /**< step size that controls filter coefficient updates. */
+  } arm_lms_instance_f32;
+
+  /**
+   * @brief Processing function for floating-point LMS filter.
+   * @param[in]  *S points to an instance of the floating-point LMS filter structure.
+   * @param[in]  *pSrc points to the block of input data.
+   * @param[in]  *pRef points to the block of reference data.
+   * @param[out] *pOut points to the block of output data.
+   * @param[out] *pErr points to the block of error data.
+   * @param[in]  blockSize number of samples to process.
+   * @return     none.
+   */
+
+  void arm_lms_f32(
+  const arm_lms_instance_f32 * S,
+  float32_t * pSrc,
+  float32_t * pRef,
+  float32_t * pOut,
+  float32_t * pErr,
+  uint32_t blockSize);
+
+  /**
+   * @brief Initialization function for floating-point LMS filter.
+   * @param[in] *S points to an instance of the floating-point LMS filter structure.
+   * @param[in] numTaps  number of filter coefficients.
+   * @param[in] *pCoeffs points to the coefficient buffer.
+   * @param[in] *pState points to state buffer.
+   * @param[in] mu step size that controls filter coefficient updates.
+   * @param[in] blockSize number of samples to process.
+   * @return none.
+   */
+
+  void arm_lms_init_f32(
+  arm_lms_instance_f32 * S,
+  uint16_t numTaps,
+  float32_t * pCoeffs,
+  float32_t * pState,
+  float32_t mu,
+  uint32_t blockSize);
+
+  /**
+   * @brief Instance structure for the Q15 LMS filter.
+   */
+
+  typedef struct
+  {
+    uint16_t numTaps;    /**< number of coefficients in the filter. */
+    q15_t *pState;       /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+    q15_t *pCoeffs;      /**< points to the coefficient array. The array is of length numTaps. */
+    q15_t mu;            /**< step size that controls filter coefficient updates. */
+    uint32_t postShift;  /**< bit shift applied to coefficients. */
+  } arm_lms_instance_q15;
+
+
+  /**
+   * @brief Initialization function for the Q15 LMS filter.
+   * @param[in] *S points to an instance of the Q15 LMS filter structure.
+   * @param[in] numTaps  number of filter coefficients.
+   * @param[in] *pCoeffs points to the coefficient buffer.
+   * @param[in] *pState points to the state buffer.
+   * @param[in] mu step size that controls filter coefficient updates.
+   * @param[in] blockSize number of samples to process.
+   * @param[in] postShift bit shift applied to coefficients.
+   * @return    none.
+   */
+
+  void arm_lms_init_q15(
+  arm_lms_instance_q15 * S,
+  uint16_t numTaps,
+  q15_t * pCoeffs,
+  q15_t * pState,
+  q15_t mu,
+  uint32_t blockSize,
+  uint32_t postShift);
+
+  /**
+   * @brief Processing function for Q15 LMS filter.
+   * @param[in] *S points to an instance of the Q15 LMS filter structure.
+   * @param[in] *pSrc points to the block of input data.
+   * @param[in] *pRef points to the block of reference data.
+   * @param[out] *pOut points to the block of output data.
+   * @param[out] *pErr points to the block of error data.
+   * @param[in] blockSize number of samples to process.
+   * @return none.
+   */
+
+  void arm_lms_q15(
+  const arm_lms_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pRef,
+  q15_t * pOut,
+  q15_t * pErr,
+  uint32_t blockSize);
+
+
+  /**
+   * @brief Instance structure for the Q31 LMS filter.
+   */
+
+  typedef struct
+  {
+    uint16_t numTaps;    /**< number of coefficients in the filter. */
+    q31_t *pState;       /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+    q31_t *pCoeffs;      /**< points to the coefficient array. The array is of length numTaps. */
+    q31_t mu;            /**< step size that controls filter coefficient updates. */
+    uint32_t postShift;  /**< bit shift applied to coefficients. */
+
+  } arm_lms_instance_q31;
+
+  /**
+   * @brief Processing function for Q31 LMS filter.
+   * @param[in]  *S points to an instance of the Q15 LMS filter structure.
+   * @param[in]  *pSrc points to the block of input data.
+   * @param[in]  *pRef points to the block of reference data.
+   * @param[out] *pOut points to the block of output data.
+   * @param[out] *pErr points to the block of error data.
+   * @param[in]  blockSize number of samples to process.
+   * @return     none.
+   */
+
+  void arm_lms_q31(
+  const arm_lms_instance_q31 * S,
+  q31_t * pSrc,
+  q31_t * pRef,
+  q31_t * pOut,
+  q31_t * pErr,
+  uint32_t blockSize);
+
+  /**
+   * @brief Initialization function for Q31 LMS filter.
+   * @param[in] *S points to an instance of the Q31 LMS filter structure.
+   * @param[in] numTaps  number of filter coefficients.
+   * @param[in] *pCoeffs points to coefficient buffer.
+   * @param[in] *pState points to state buffer.
+   * @param[in] mu step size that controls filter coefficient updates.
+   * @param[in] blockSize number of samples to process.
+   * @param[in] postShift bit shift applied to coefficients.
+   * @return none.
+   */
+
+  void arm_lms_init_q31(
+  arm_lms_instance_q31 * S,
+  uint16_t numTaps,
+  q31_t * pCoeffs,
+  q31_t * pState,
+  q31_t mu,
+  uint32_t blockSize,
+  uint32_t postShift);
+
+  /**
+   * @brief Instance structure for the floating-point normalized LMS filter.
+   */
+
+  typedef struct
+  {
+    uint16_t numTaps;     /**< number of coefficients in the filter. */
+    float32_t *pState;    /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+    float32_t *pCoeffs;   /**< points to the coefficient array. The array is of length numTaps. */
+    float32_t mu;        /**< step size that control filter coefficient updates. */
+    float32_t energy;    /**< saves previous frame energy. */
+    float32_t x0;        /**< saves previous input sample. */
+  } arm_lms_norm_instance_f32;
+
+  /**
+   * @brief Processing function for floating-point normalized LMS filter.
+   * @param[in] *S points to an instance of the floating-point normalized LMS filter structure.
+   * @param[in] *pSrc points to the block of input data.
+   * @param[in] *pRef points to the block of reference data.
+   * @param[out] *pOut points to the block of output data.
+   * @param[out] *pErr points to the block of error data.
+   * @param[in] blockSize number of samples to process.
+   * @return none.
+   */
+
+  void arm_lms_norm_f32(
+  arm_lms_norm_instance_f32 * S,
+  float32_t * pSrc,
+  float32_t * pRef,
+  float32_t * pOut,
+  float32_t * pErr,
+  uint32_t blockSize);
+
+  /**
+   * @brief Initialization function for floating-point normalized LMS filter.
+   * @param[in] *S points to an instance of the floating-point LMS filter structure.
+   * @param[in] numTaps  number of filter coefficients.
+   * @param[in] *pCoeffs points to coefficient buffer.
+   * @param[in] *pState points to state buffer.
+   * @param[in] mu step size that controls filter coefficient updates.
+   * @param[in] blockSize number of samples to process.
+   * @return none.
+   */
+
+  void arm_lms_norm_init_f32(
+  arm_lms_norm_instance_f32 * S,
+  uint16_t numTaps,
+  float32_t * pCoeffs,
+  float32_t * pState,
+  float32_t mu,
+  uint32_t blockSize);
+
+
+  /**
+   * @brief Instance structure for the Q31 normalized LMS filter.
+   */
+  typedef struct
+  {
+    uint16_t numTaps;     /**< number of coefficients in the filter. */
+    q31_t *pState;        /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+    q31_t *pCoeffs;       /**< points to the coefficient array. The array is of length numTaps. */
+    q31_t mu;             /**< step size that controls filter coefficient updates. */
+    uint8_t postShift;    /**< bit shift applied to coefficients. */
+    q31_t *recipTable;    /**< points to the reciprocal initial value table. */
+    q31_t energy;         /**< saves previous frame energy. */
+    q31_t x0;             /**< saves previous input sample. */
+  } arm_lms_norm_instance_q31;
+
+  /**
+   * @brief Processing function for Q31 normalized LMS filter.
+   * @param[in] *S points to an instance of the Q31 normalized LMS filter structure.
+   * @param[in] *pSrc points to the block of input data.
+   * @param[in] *pRef points to the block of reference data.
+   * @param[out] *pOut points to the block of output data.
+   * @param[out] *pErr points to the block of error data.
+   * @param[in] blockSize number of samples to process.
+   * @return none.
+   */
+
+  void arm_lms_norm_q31(
+  arm_lms_norm_instance_q31 * S,
+  q31_t * pSrc,
+  q31_t * pRef,
+  q31_t * pOut,
+  q31_t * pErr,
+  uint32_t blockSize);
+
+  /**
+   * @brief Initialization function for Q31 normalized LMS filter.
+   * @param[in] *S points to an instance of the Q31 normalized LMS filter structure.
+   * @param[in] numTaps  number of filter coefficients.
+   * @param[in] *pCoeffs points to coefficient buffer.
+   * @param[in] *pState points to state buffer.
+   * @param[in] mu step size that controls filter coefficient updates.
+   * @param[in] blockSize number of samples to process.
+   * @param[in] postShift bit shift applied to coefficients.
+   * @return none.
+   */
+
+  void arm_lms_norm_init_q31(
+  arm_lms_norm_instance_q31 * S,
+  uint16_t numTaps,
+  q31_t * pCoeffs,
+  q31_t * pState,
+  q31_t mu,
+  uint32_t blockSize,
+  uint8_t postShift);
+
+  /**
+   * @brief Instance structure for the Q15 normalized LMS filter.
+   */
+
+  typedef struct
+  {
+    uint16_t numTaps;    /**< Number of coefficients in the filter. */
+    q15_t *pState;        /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+    q15_t *pCoeffs;       /**< points to the coefficient array. The array is of length numTaps. */
+    q15_t mu;            /**< step size that controls filter coefficient updates. */
+    uint8_t postShift;   /**< bit shift applied to coefficients. */
+    q15_t *recipTable;   /**< Points to the reciprocal initial value table. */
+    q15_t energy;        /**< saves previous frame energy. */
+    q15_t x0;            /**< saves previous input sample. */
+  } arm_lms_norm_instance_q15;
+
+  /**
+   * @brief Processing function for Q15 normalized LMS filter.
+   * @param[in] *S points to an instance of the Q15 normalized LMS filter structure.
+   * @param[in] *pSrc points to the block of input data.
+   * @param[in] *pRef points to the block of reference data.
+   * @param[out] *pOut points to the block of output data.
+   * @param[out] *pErr points to the block of error data.
+   * @param[in] blockSize number of samples to process.
+   * @return none.
+   */
+
+  void arm_lms_norm_q15(
+  arm_lms_norm_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pRef,
+  q15_t * pOut,
+  q15_t * pErr,
+  uint32_t blockSize);
+
+
+  /**
+   * @brief Initialization function for Q15 normalized LMS filter.
+   * @param[in] *S points to an instance of the Q15 normalized LMS filter structure.
+   * @param[in] numTaps  number of filter coefficients.
+   * @param[in] *pCoeffs points to coefficient buffer.
+   * @param[in] *pState points to state buffer.
+   * @param[in] mu step size that controls filter coefficient updates.
+   * @param[in] blockSize number of samples to process.
+   * @param[in] postShift bit shift applied to coefficients.
+   * @return none.
+   */
+
+  void arm_lms_norm_init_q15(
+  arm_lms_norm_instance_q15 * S,
+  uint16_t numTaps,
+  q15_t * pCoeffs,
+  q15_t * pState,
+  q15_t mu,
+  uint32_t blockSize,
+  uint8_t postShift);
+
+  /**
+   * @brief Correlation of floating-point sequences.
+   * @param[in] *pSrcA points to the first input sequence.
+   * @param[in] srcALen length of the first input sequence.
+   * @param[in] *pSrcB points to the second input sequence.
+   * @param[in] srcBLen length of the second input sequence.
+   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
+   * @return none.
+   */
+
+  void arm_correlate_f32(
+  float32_t * pSrcA,
+  uint32_t srcALen,
+  float32_t * pSrcB,
+  uint32_t srcBLen,
+  float32_t * pDst);
+
+
+   /**   
+   * @brief Correlation of Q15 sequences   
+   * @param[in] *pSrcA points to the first input sequence.   
+   * @param[in] srcALen length of the first input sequence.   
+   * @param[in] *pSrcB points to the second input sequence.   
+   * @param[in] srcBLen length of the second input sequence.   
+   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.   
+   * @param[in]  *pScratch points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.   
+   * @return none.   
+   */
+  void arm_correlate_opt_q15(
+  q15_t * pSrcA,
+  uint32_t srcALen,
+  q15_t * pSrcB,
+  uint32_t srcBLen,
+  q15_t * pDst,
+  q15_t * pScratch);
+
+
+  /**
+   * @brief Correlation of Q15 sequences.
+   * @param[in] *pSrcA points to the first input sequence.
+   * @param[in] srcALen length of the first input sequence.
+   * @param[in] *pSrcB points to the second input sequence.
+   * @param[in] srcBLen length of the second input sequence.
+   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
+   * @return none.
+   */
+
+  void arm_correlate_q15(
+  q15_t * pSrcA,
+  uint32_t srcALen,
+  q15_t * pSrcB,
+  uint32_t srcBLen,
+  q15_t * pDst);
+
+  /**
+   * @brief Correlation of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4.
+   * @param[in] *pSrcA points to the first input sequence.
+   * @param[in] srcALen length of the first input sequence.
+   * @param[in] *pSrcB points to the second input sequence.
+   * @param[in] srcBLen length of the second input sequence.
+   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
+   * @return none.
+   */
+
+  void arm_correlate_fast_q15(
+			       q15_t * pSrcA,
+			      uint32_t srcALen,
+			       q15_t * pSrcB,
+			      uint32_t srcBLen,
+			      q15_t * pDst);
+
+
+
+  /**
+   * @brief Correlation of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4.
+   * @param[in] *pSrcA points to the first input sequence.
+   * @param[in] srcALen length of the first input sequence.
+   * @param[in] *pSrcB points to the second input sequence.
+   * @param[in] srcBLen length of the second input sequence.
+   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
+   * @param[in]  *pScratch points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.   
+   * @return none.
+   */
+
+  void arm_correlate_fast_opt_q15(
+  q15_t * pSrcA,
+  uint32_t srcALen,
+  q15_t * pSrcB,
+  uint32_t srcBLen,
+  q15_t * pDst,
+  q15_t * pScratch);
+
+  /**
+   * @brief Correlation of Q31 sequences.
+   * @param[in] *pSrcA points to the first input sequence.
+   * @param[in] srcALen length of the first input sequence.
+   * @param[in] *pSrcB points to the second input sequence.
+   * @param[in] srcBLen length of the second input sequence.
+   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
+   * @return none.
+   */
+
+  void arm_correlate_q31(
+  q31_t * pSrcA,
+  uint32_t srcALen,
+  q31_t * pSrcB,
+  uint32_t srcBLen,
+  q31_t * pDst);
+
+  /**
+   * @brief Correlation of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4
+   * @param[in] *pSrcA points to the first input sequence.
+   * @param[in] srcALen length of the first input sequence.
+   * @param[in] *pSrcB points to the second input sequence.
+   * @param[in] srcBLen length of the second input sequence.
+   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
+   * @return none.
+   */
+
+  void arm_correlate_fast_q31(
+  q31_t * pSrcA,
+  uint32_t srcALen,
+  q31_t * pSrcB,
+  uint32_t srcBLen,
+  q31_t * pDst);
+
+
+
+ /**   
+   * @brief Correlation of Q7 sequences.   
+   * @param[in] *pSrcA points to the first input sequence.   
+   * @param[in] srcALen length of the first input sequence.   
+   * @param[in] *pSrcB points to the second input sequence.   
+   * @param[in] srcBLen length of the second input sequence.   
+   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.   
+   * @param[in]  *pScratch1 points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.   
+   * @param[in]  *pScratch2 points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen).   
+   * @return none.   
+   */
+
+  void arm_correlate_opt_q7(
+  q7_t * pSrcA,
+  uint32_t srcALen,
+  q7_t * pSrcB,
+  uint32_t srcBLen,
+  q7_t * pDst,
+  q15_t * pScratch1,
+  q15_t * pScratch2);
+
+
+  /**
+   * @brief Correlation of Q7 sequences.
+   * @param[in] *pSrcA points to the first input sequence.
+   * @param[in] srcALen length of the first input sequence.
+   * @param[in] *pSrcB points to the second input sequence.
+   * @param[in] srcBLen length of the second input sequence.
+   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
+   * @return none.
+   */
+
+  void arm_correlate_q7(
+  q7_t * pSrcA,
+  uint32_t srcALen,
+  q7_t * pSrcB,
+  uint32_t srcBLen,
+  q7_t * pDst);
+
+
+  /**
+   * @brief Instance structure for the floating-point sparse FIR filter.
+   */
+  typedef struct
+  {
+    uint16_t numTaps;             /**< number of coefficients in the filter. */
+    uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
+    float32_t *pState;            /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
+    float32_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps.*/
+    uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
+    int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
+  } arm_fir_sparse_instance_f32;
+
+  /**
+   * @brief Instance structure for the Q31 sparse FIR filter.
+   */
+
+  typedef struct
+  {
+    uint16_t numTaps;             /**< number of coefficients in the filter. */
+    uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
+    q31_t *pState;                /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
+    q31_t *pCoeffs;               /**< points to the coefficient array. The array is of length numTaps.*/
+    uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
+    int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
+  } arm_fir_sparse_instance_q31;
+
+  /**
+   * @brief Instance structure for the Q15 sparse FIR filter.
+   */
+
+  typedef struct
+  {
+    uint16_t numTaps;             /**< number of coefficients in the filter. */
+    uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
+    q15_t *pState;                /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
+    q15_t *pCoeffs;               /**< points to the coefficient array. The array is of length numTaps.*/
+    uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
+    int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
+  } arm_fir_sparse_instance_q15;
+
+  /**
+   * @brief Instance structure for the Q7 sparse FIR filter.
+   */
+
+  typedef struct
+  {
+    uint16_t numTaps;             /**< number of coefficients in the filter. */
+    uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
+    q7_t *pState;                 /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
+    q7_t *pCoeffs;                /**< points to the coefficient array. The array is of length numTaps.*/
+    uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
+    int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
+  } arm_fir_sparse_instance_q7;
+
+  /**
+   * @brief Processing function for the floating-point sparse FIR filter.
+   * @param[in]  *S          points to an instance of the floating-point sparse FIR structure.
+   * @param[in]  *pSrc       points to the block of input data.
+   * @param[out] *pDst       points to the block of output data
+   * @param[in]  *pScratchIn points to a temporary buffer of size blockSize.
+   * @param[in]  blockSize   number of input samples to process per call.
+   * @return none.
+   */
+
+  void arm_fir_sparse_f32(
+  arm_fir_sparse_instance_f32 * S,
+  float32_t * pSrc,
+  float32_t * pDst,
+  float32_t * pScratchIn,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Initialization function for the floating-point sparse FIR filter.
+   * @param[in,out] *S         points to an instance of the floating-point sparse FIR structure.
+   * @param[in]     numTaps    number of nonzero coefficients in the filter.
+   * @param[in]     *pCoeffs   points to the array of filter coefficients.
+   * @param[in]     *pState    points to the state buffer.
+   * @param[in]     *pTapDelay points to the array of offset times.
+   * @param[in]     maxDelay   maximum offset time supported.
+   * @param[in]     blockSize  number of samples that will be processed per block.
+   * @return none
+   */
+
+  void arm_fir_sparse_init_f32(
+  arm_fir_sparse_instance_f32 * S,
+  uint16_t numTaps,
+  float32_t * pCoeffs,
+  float32_t * pState,
+  int32_t * pTapDelay,
+  uint16_t maxDelay,
+  uint32_t blockSize);
+
+  /**
+   * @brief Processing function for the Q31 sparse FIR filter.
+   * @param[in]  *S          points to an instance of the Q31 sparse FIR structure.
+   * @param[in]  *pSrc       points to the block of input data.
+   * @param[out] *pDst       points to the block of output data
+   * @param[in]  *pScratchIn points to a temporary buffer of size blockSize.
+   * @param[in]  blockSize   number of input samples to process per call.
+   * @return none.
+   */
+
+  void arm_fir_sparse_q31(
+  arm_fir_sparse_instance_q31 * S,
+  q31_t * pSrc,
+  q31_t * pDst,
+  q31_t * pScratchIn,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Initialization function for the Q31 sparse FIR filter.
+   * @param[in,out] *S         points to an instance of the Q31 sparse FIR structure.
+   * @param[in]     numTaps    number of nonzero coefficients in the filter.
+   * @param[in]     *pCoeffs   points to the array of filter coefficients.
+   * @param[in]     *pState    points to the state buffer.
+   * @param[in]     *pTapDelay points to the array of offset times.
+   * @param[in]     maxDelay   maximum offset time supported.
+   * @param[in]     blockSize  number of samples that will be processed per block.
+   * @return none
+   */
+
+  void arm_fir_sparse_init_q31(
+  arm_fir_sparse_instance_q31 * S,
+  uint16_t numTaps,
+  q31_t * pCoeffs,
+  q31_t * pState,
+  int32_t * pTapDelay,
+  uint16_t maxDelay,
+  uint32_t blockSize);
+
+  /**
+   * @brief Processing function for the Q15 sparse FIR filter.
+   * @param[in]  *S           points to an instance of the Q15 sparse FIR structure.
+   * @param[in]  *pSrc        points to the block of input data.
+   * @param[out] *pDst        points to the block of output data
+   * @param[in]  *pScratchIn  points to a temporary buffer of size blockSize.
+   * @param[in]  *pScratchOut points to a temporary buffer of size blockSize.
+   * @param[in]  blockSize    number of input samples to process per call.
+   * @return none.
+   */
+
+  void arm_fir_sparse_q15(
+  arm_fir_sparse_instance_q15 * S,
+  q15_t * pSrc,
+  q15_t * pDst,
+  q15_t * pScratchIn,
+  q31_t * pScratchOut,
+  uint32_t blockSize);
+
+
+  /**
+   * @brief  Initialization function for the Q15 sparse FIR filter.
+   * @param[in,out] *S         points to an instance of the Q15 sparse FIR structure.
+   * @param[in]     numTaps    number of nonzero coefficients in the filter.
+   * @param[in]     *pCoeffs   points to the array of filter coefficients.
+   * @param[in]     *pState    points to the state buffer.
+   * @param[in]     *pTapDelay points to the array of offset times.
+   * @param[in]     maxDelay   maximum offset time supported.
+   * @param[in]     blockSize  number of samples that will be processed per block.
+   * @return none
+   */
+
+  void arm_fir_sparse_init_q15(
+  arm_fir_sparse_instance_q15 * S,
+  uint16_t numTaps,
+  q15_t * pCoeffs,
+  q15_t * pState,
+  int32_t * pTapDelay,
+  uint16_t maxDelay,
+  uint32_t blockSize);
+
+  /**
+   * @brief Processing function for the Q7 sparse FIR filter.
+   * @param[in]  *S           points to an instance of the Q7 sparse FIR structure.
+   * @param[in]  *pSrc        points to the block of input data.
+   * @param[out] *pDst        points to the block of output data
+   * @param[in]  *pScratchIn  points to a temporary buffer of size blockSize.
+   * @param[in]  *pScratchOut points to a temporary buffer of size blockSize.
+   * @param[in]  blockSize    number of input samples to process per call.
+   * @return none.
+   */
+
+  void arm_fir_sparse_q7(
+  arm_fir_sparse_instance_q7 * S,
+  q7_t * pSrc,
+  q7_t * pDst,
+  q7_t * pScratchIn,
+  q31_t * pScratchOut,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Initialization function for the Q7 sparse FIR filter.
+   * @param[in,out] *S         points to an instance of the Q7 sparse FIR structure.
+   * @param[in]     numTaps    number of nonzero coefficients in the filter.
+   * @param[in]     *pCoeffs   points to the array of filter coefficients.
+   * @param[in]     *pState    points to the state buffer.
+   * @param[in]     *pTapDelay points to the array of offset times.
+   * @param[in]     maxDelay   maximum offset time supported.
+   * @param[in]     blockSize  number of samples that will be processed per block.
+   * @return none
+   */
+
+  void arm_fir_sparse_init_q7(
+  arm_fir_sparse_instance_q7 * S,
+  uint16_t numTaps,
+  q7_t * pCoeffs,
+  q7_t * pState,
+  int32_t * pTapDelay,
+  uint16_t maxDelay,
+  uint32_t blockSize);
+
+
+  /*
+   * @brief  Floating-point sin_cos function.
+   * @param[in]  theta    input value in degrees 
+   * @param[out] *pSinVal points to the processed sine output. 
+   * @param[out] *pCosVal points to the processed cos output. 
+   * @return none.
+   */
+
+  void arm_sin_cos_f32(
+  float32_t theta,
+  float32_t * pSinVal,
+  float32_t * pCcosVal);
+
+  /*
+   * @brief  Q31 sin_cos function.
+   * @param[in]  theta    scaled input value in degrees 
+   * @param[out] *pSinVal points to the processed sine output. 
+   * @param[out] *pCosVal points to the processed cosine output. 
+   * @return none.
+   */
+
+  void arm_sin_cos_q31(
+  q31_t theta,
+  q31_t * pSinVal,
+  q31_t * pCosVal);
+
+
+  /**
+   * @brief  Floating-point complex conjugate.
+   * @param[in]  *pSrc points to the input vector
+   * @param[out]  *pDst points to the output vector
+   * @param[in]  numSamples number of complex samples in each vector
+   * @return none.
+   */
+
+  void arm_cmplx_conj_f32(
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t numSamples);
+
+  /**
+   * @brief  Q31 complex conjugate.
+   * @param[in]  *pSrc points to the input vector
+   * @param[out]  *pDst points to the output vector
+   * @param[in]  numSamples number of complex samples in each vector
+   * @return none.
+   */
+
+  void arm_cmplx_conj_q31(
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t numSamples);
+
+  /**
+   * @brief  Q15 complex conjugate.
+   * @param[in]  *pSrc points to the input vector
+   * @param[out]  *pDst points to the output vector
+   * @param[in]  numSamples number of complex samples in each vector
+   * @return none.
+   */
+
+  void arm_cmplx_conj_q15(
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t numSamples);
+
+
+
+  /**
+   * @brief  Floating-point complex magnitude squared
+   * @param[in]  *pSrc points to the complex input vector
+   * @param[out]  *pDst points to the real output vector
+   * @param[in]  numSamples number of complex samples in the input vector
+   * @return none.
+   */
+
+  void arm_cmplx_mag_squared_f32(
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t numSamples);
+
+  /**
+   * @brief  Q31 complex magnitude squared
+   * @param[in]  *pSrc points to the complex input vector
+   * @param[out]  *pDst points to the real output vector
+   * @param[in]  numSamples number of complex samples in the input vector
+   * @return none.
+   */
+
+  void arm_cmplx_mag_squared_q31(
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t numSamples);
+
+  /**
+   * @brief  Q15 complex magnitude squared
+   * @param[in]  *pSrc points to the complex input vector
+   * @param[out]  *pDst points to the real output vector
+   * @param[in]  numSamples number of complex samples in the input vector
+   * @return none.
+   */
+
+  void arm_cmplx_mag_squared_q15(
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t numSamples);
+
+
+ /**
+   * @ingroup groupController
+   */
+
+  /**
+   * @defgroup PID PID Motor Control
+   *
+   * A Proportional Integral Derivative (PID) controller is a generic feedback control 
+   * loop mechanism widely used in industrial control systems.
+   * A PID controller is the most commonly used type of feedback controller.
+   *
+   * This set of functions implements (PID) controllers
+   * for Q15, Q31, and floating-point data types.  The functions operate on a single sample
+   * of data and each call to the function returns a single processed value.
+   * S points to an instance of the PID control data structure.  in
+   * is the input sample value. The functions return the output value.
+   *
+   * \par Algorithm:
+   * 
+   *    y[n] = y[n-1] + A0 * x[n] + A1 * x[n-1] + A2 * x[n-2]
+   *    A0 = Kp + Ki + Kd
+   *    A1 = (-Kp ) - (2 * Kd )
+   *    A2 = Kd  

+   *
+   * \par
+   * where \c Kp is proportional constant, \c Ki is Integral constant and \c Kd is Derivative constant
+   * 
+   * \par 
+   * \image html PID.gif "Proportional Integral Derivative Controller" 
+   *
+   * \par
+   * The PID controller calculates an "error" value as the difference between
+   * the measured output and the reference input.
+   * The controller attempts to minimize the error by adjusting the process control inputs.  
+   * The proportional value determines the reaction to the current error, 
+   * the integral value determines the reaction based on the sum of recent errors, 
+   * and the derivative value determines the reaction based on the rate at which the error has been changing.
+   *
+   * \par Instance Structure 
+   * The Gains A0, A1, A2 and state variables for a PID controller are stored together in an instance data structure. 
+   * A separate instance structure must be defined for each PID Controller. 
+   * There are separate instance structure declarations for each of the 3 supported data types. 
+   * 
+   * \par Reset Functions 
+   * There is also an associated reset function for each data type which clears the state array. 
+   *
+   * \par Initialization Functions 
+   * There is also an associated initialization function for each data type. 
+   * The initialization function performs the following operations: 
+   * - Initializes the Gains A0, A1, A2 from Kp,Ki, Kd gains.
+   * - Zeros out the values in the state buffer.   
+   * 
+   * \par 
+   * Instance structure cannot be placed into a const data section and it is recommended to use the initialization function. 
+   *
+   * \par Fixed-Point Behavior 
+   * Care must be taken when using the fixed-point versions of the PID Controller functions. 
+   * In particular, the overflow and saturation behavior of the accumulator used in each function must be considered. 
+   * Refer to the function specific documentation below for usage guidelines. 
+   */
+
+  /**
+   * @addtogroup PID
+   * @{
+   */
+
+  /**
+   * @brief  Process function for the floating-point PID Control.
+   * @param[in,out] *S is an instance of the floating-point PID Control structure
+   * @param[in] in input sample to process
+   * @return out processed output sample.
+   */
+
+
+  __STATIC_INLINE float32_t arm_pid_f32(
+  arm_pid_instance_f32 * S,
+  float32_t in)
+  {
+    float32_t out;
+
+    /* y[n] = y[n-1] + A0 * x[n] + A1 * x[n-1] + A2 * x[n-2]  */
+    out = (S->A0 * in) +
+      (S->A1 * S->state[0]) + (S->A2 * S->state[1]) + (S->state[2]);
+
+    /* Update state */
+    S->state[1] = S->state[0];
+    S->state[0] = in;
+    S->state[2] = out;
+
+    /* return to application */
+    return (out);
+
+  }
+
+  /**
+   * @brief  Process function for the Q31 PID Control.
+   * @param[in,out] *S points to an instance of the Q31 PID Control structure
+   * @param[in] in input sample to process
+   * @return out processed output sample.
+   *
+   * Scaling and Overflow Behavior: 
+   * \par 
+   * The function is implemented using an internal 64-bit accumulator. 
+   * The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit. 
+   * Thus, if the accumulator result overflows it wraps around rather than clip. 
+   * In order to avoid overflows completely the input signal must be scaled down by 2 bits as there are four additions. 
+   * After all multiply-accumulates are performed, the 2.62 accumulator is truncated to 1.32 format and then saturated to 1.31 format. 
+   */
+
+  __STATIC_INLINE q31_t arm_pid_q31(
+  arm_pid_instance_q31 * S,
+  q31_t in)
+  {
+    q63_t acc;
+    q31_t out;
+
+    /* acc = A0 * x[n]  */
+    acc = (q63_t) S->A0 * in;
+
+    /* acc += A1 * x[n-1] */
+    acc += (q63_t) S->A1 * S->state[0];
+
+    /* acc += A2 * x[n-2]  */
+    acc += (q63_t) S->A2 * S->state[1];
+
+    /* convert output to 1.31 format to add y[n-1] */
+    out = (q31_t) (acc >> 31u);
+
+    /* out += y[n-1] */
+    out += S->state[2];
+
+    /* Update state */
+    S->state[1] = S->state[0];
+    S->state[0] = in;
+    S->state[2] = out;
+
+    /* return to application */
+    return (out);
+
+  }
+
+  /**
+   * @brief  Process function for the Q15 PID Control.
+   * @param[in,out] *S points to an instance of the Q15 PID Control structure
+   * @param[in] in input sample to process
+   * @return out processed output sample.
+   *
+   * Scaling and Overflow Behavior: 
+   * \par 
+   * The function is implemented using a 64-bit internal accumulator. 
+   * Both Gains and state variables are represented in 1.15 format and multiplications yield a 2.30 result. 
+   * The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format. 
+   * There is no risk of internal overflow with this approach and the full precision of intermediate multiplications is preserved. 
+   * After all additions have been performed, the accumulator is truncated to 34.15 format by discarding low 15 bits. 
+   * Lastly, the accumulator is saturated to yield a result in 1.15 format.
+   */
+
+  __STATIC_INLINE q15_t arm_pid_q15(
+  arm_pid_instance_q15 * S,
+  q15_t in)
+  {
+    q63_t acc;
+    q15_t out;
+
+    /* Implementation of PID controller */
+
+#ifdef ARM_MATH_CM0
+
+    /* acc = A0 * x[n]  */
+    acc = ((q31_t) S->A0) * in;
+
+#else
+
+    /* acc = A0 * x[n]  */
+    acc = (q31_t) __SMUAD(S->A0, in);
+
+#endif
+
+#ifdef ARM_MATH_CM0
+
+    /* acc += A1 * x[n-1] + A2 * x[n-2]  */
+    acc += (q31_t) S->A1 * S->state[0];
+    acc += (q31_t) S->A2 * S->state[1];
+
+#else
+
+    /* acc += A1 * x[n-1] + A2 * x[n-2]  */
+    acc = __SMLALD(S->A1, (q31_t) __SIMD32(S->state), acc);
+
+#endif
+
+    /* acc += y[n-1] */
+    acc += (q31_t) S->state[2] << 15;
+
+    /* saturate the output */
+    out = (q15_t) (__SSAT((acc >> 15), 16));
+
+    /* Update state */
+    S->state[1] = S->state[0];
+    S->state[0] = in;
+    S->state[2] = out;
+
+    /* return to application */
+    return (out);
+
+  }
+
+  /**
+   * @} end of PID group
+   */
+
+
+  /**
+   * @brief Floating-point matrix inverse.
+   * @param[in]  *src points to the instance of the input floating-point matrix structure.
+   * @param[out] *dst points to the instance of the output floating-point matrix structure.
+   * @return The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match.
+   * If the input matrix is singular (does not have an inverse), then the algorithm terminates and returns error status ARM_MATH_SINGULAR.
+   */
+
+  arm_status arm_mat_inverse_f32(
+  const arm_matrix_instance_f32 * src,
+  arm_matrix_instance_f32 * dst);
+
+
+
+  /**
+   * @ingroup groupController
+   */
+
+
+  /**
+   * @defgroup clarke Vector Clarke Transform
+   * Forward Clarke transform converts the instantaneous stator phases into a two-coordinate time invariant vector.
+   * Generally the Clarke transform uses three-phase currents Ia, Ib and Ic to calculate currents
+   * in the two-phase orthogonal stator axis Ialpha and Ibeta.
+   * When Ialpha is superposed with Ia as shown in the figure below
+   * \image html clarke.gif Stator current space vector and its components in (a,b).
+   * and Ia + Ib + Ic = 0, in this condition Ialpha and Ibeta
+   * can be calculated using only Ia and Ib.
+   *
+   * The function operates on a single sample of data and each call to the function returns the processed output. 
+   * The library provides separate functions for Q31 and floating-point data types.
+   * \par Algorithm
+   * \image html clarkeFormula.gif
+   * where Ia and Ib are the instantaneous stator phases and
+   * pIalpha and pIbeta are the two coordinates of time invariant vector.
+   * \par Fixed-Point Behavior
+   * Care must be taken when using the Q31 version of the Clarke transform.
+   * In particular, the overflow and saturation behavior of the accumulator used must be considered.
+   * Refer to the function specific documentation below for usage guidelines.
+   */
+
+  /**
+   * @addtogroup clarke
+   * @{
+   */
+
+  /**
+   *
+   * @brief  Floating-point Clarke transform
+   * @param[in]       Ia       input three-phase coordinate a
+   * @param[in]       Ib       input three-phase coordinate b
+   * @param[out]      *pIalpha points to output two-phase orthogonal vector axis alpha
+   * @param[out]      *pIbeta  points to output two-phase orthogonal vector axis beta
+   * @return none.
+   */
+
+  __STATIC_INLINE void arm_clarke_f32(
+  float32_t Ia,
+  float32_t Ib,
+  float32_t * pIalpha,
+  float32_t * pIbeta)
+  {
+    /* Calculate pIalpha using the equation, pIalpha = Ia */
+    *pIalpha = Ia;
+
+    /* Calculate pIbeta using the equation, pIbeta = (1/sqrt(3)) * Ia + (2/sqrt(3)) * Ib */
+    *pIbeta =
+      ((float32_t) 0.57735026919 * Ia + (float32_t) 1.15470053838 * Ib);
+
+  }
+
+  /**
+   * @brief  Clarke transform for Q31 version
+   * @param[in]       Ia       input three-phase coordinate a
+   * @param[in]       Ib       input three-phase coordinate b
+   * @param[out]      *pIalpha points to output two-phase orthogonal vector axis alpha
+   * @param[out]      *pIbeta  points to output two-phase orthogonal vector axis beta
+   * @return none.
+   *
+   * Scaling and Overflow Behavior:
+   * \par
+   * The function is implemented using an internal 32-bit accumulator.
+   * The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
+   * There is saturation on the addition, hence there is no risk of overflow.
+   */
+
+  __STATIC_INLINE void arm_clarke_q31(
+  q31_t Ia,
+  q31_t Ib,
+  q31_t * pIalpha,
+  q31_t * pIbeta)
+  {
+    q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
+
+    /* Calculating pIalpha from Ia by equation pIalpha = Ia */
+    *pIalpha = Ia;
+
+    /* Intermediate product is calculated by (1/(sqrt(3)) * Ia) */
+    product1 = (q31_t) (((q63_t) Ia * 0x24F34E8B) >> 30);
+
+    /* Intermediate product is calculated by (2/sqrt(3) * Ib) */
+    product2 = (q31_t) (((q63_t) Ib * 0x49E69D16) >> 30);
+
+    /* pIbeta is calculated by adding the intermediate products */
+    *pIbeta = __QADD(product1, product2);
+  }
+
+  /**
+   * @} end of clarke group
+   */
+
+  /**
+   * @brief  Converts the elements of the Q7 vector to Q31 vector.
+   * @param[in]  *pSrc     input pointer
+   * @param[out]  *pDst    output pointer
+   * @param[in]  blockSize number of samples to process
+   * @return none.
+   */
+  void arm_q7_to_q31(
+  q7_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize);
+
+
+
+
+  /**
+   * @ingroup groupController
+   */
+
+  /**
+   * @defgroup inv_clarke Vector Inverse Clarke Transform
+   * Inverse Clarke transform converts the two-coordinate time invariant vector into instantaneous stator phases.
+   * 
+   * The function operates on a single sample of data and each call to the function returns the processed output. 
+   * The library provides separate functions for Q31 and floating-point data types.
+   * \par Algorithm
+   * \image html clarkeInvFormula.gif
+   * where pIa and pIb are the instantaneous stator phases and
+   * Ialpha and Ibeta are the two coordinates of time invariant vector.
+   * \par Fixed-Point Behavior
+   * Care must be taken when using the Q31 version of the Clarke transform.
+   * In particular, the overflow and saturation behavior of the accumulator used must be considered.
+   * Refer to the function specific documentation below for usage guidelines.
+   */
+
+  /**
+   * @addtogroup inv_clarke
+   * @{
+   */
+
+   /**
+   * @brief  Floating-point Inverse Clarke transform
+   * @param[in]       Ialpha  input two-phase orthogonal vector axis alpha
+   * @param[in]       Ibeta   input two-phase orthogonal vector axis beta
+   * @param[out]      *pIa    points to output three-phase coordinate a
+   * @param[out]      *pIb    points to output three-phase coordinate b
+   * @return none.
+   */
+
+
+  __STATIC_INLINE void arm_inv_clarke_f32(
+  float32_t Ialpha,
+  float32_t Ibeta,
+  float32_t * pIa,
+  float32_t * pIb)
+  {
+    /* Calculating pIa from Ialpha by equation pIa = Ialpha */
+    *pIa = Ialpha;
+
+    /* Calculating pIb from Ialpha and Ibeta by equation pIb = -(1/2) * Ialpha + (sqrt(3)/2) * Ibeta */
+    *pIb = -0.5 * Ialpha + (float32_t) 0.8660254039 *Ibeta;
+
+  }
+
+  /**
+   * @brief  Inverse Clarke transform for Q31 version 
+   * @param[in]       Ialpha  input two-phase orthogonal vector axis alpha
+   * @param[in]       Ibeta   input two-phase orthogonal vector axis beta
+   * @param[out]      *pIa    points to output three-phase coordinate a
+   * @param[out]      *pIb    points to output three-phase coordinate b
+   * @return none.
+   *
+   * Scaling and Overflow Behavior:
+   * \par
+   * The function is implemented using an internal 32-bit accumulator.
+   * The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
+   * There is saturation on the subtraction, hence there is no risk of overflow.
+   */
+
+  __STATIC_INLINE void arm_inv_clarke_q31(
+  q31_t Ialpha,
+  q31_t Ibeta,
+  q31_t * pIa,
+  q31_t * pIb)
+  {
+    q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
+
+    /* Calculating pIa from Ialpha by equation pIa = Ialpha */
+    *pIa = Ialpha;
+
+    /* Intermediate product is calculated by (1/(2*sqrt(3)) * Ia) */
+    product1 = (q31_t) (((q63_t) (Ialpha) * (0x40000000)) >> 31);
+
+    /* Intermediate product is calculated by (1/sqrt(3) * pIb) */
+    product2 = (q31_t) (((q63_t) (Ibeta) * (0x6ED9EBA1)) >> 31);
+
+    /* pIb is calculated by subtracting the products */
+    *pIb = __QSUB(product2, product1);
+
+  }
+
+  /**
+   * @} end of inv_clarke group
+   */
+
+  /**
+   * @brief  Converts the elements of the Q7 vector to Q15 vector.
+   * @param[in]  *pSrc     input pointer
+   * @param[out] *pDst     output pointer
+   * @param[in]  blockSize number of samples to process
+   * @return none.
+   */
+  void arm_q7_to_q15(
+  q7_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize);
+
+
+
+  /**
+   * @ingroup groupController
+   */
+
+  /**
+   * @defgroup park Vector Park Transform
+   *
+   * Forward Park transform converts the input two-coordinate vector to flux and torque components.
+   * The Park transform can be used to realize the transformation of the Ialpha and the Ibeta currents 
+   * from the stationary to the moving reference frame and control the spatial relationship between 
+   * the stator vector current and rotor flux vector.
+   * If we consider the d axis aligned with the rotor flux, the diagram below shows the 
+   * current vector and the relationship from the two reference frames:
+   * \image html park.gif "Stator current space vector and its component in (a,b) and in the d,q rotating reference frame"
+   *
+   * The function operates on a single sample of data and each call to the function returns the processed output. 
+   * The library provides separate functions for Q31 and floating-point data types.
+   * \par Algorithm
+   * \image html parkFormula.gif
+   * where Ialpha and Ibeta are the stator vector components,  
+   * pId and pIq are rotor vector components and cosVal and sinVal are the 
+   * cosine and sine values of theta (rotor flux position).
+   * \par Fixed-Point Behavior
+   * Care must be taken when using the Q31 version of the Park transform.
+   * In particular, the overflow and saturation behavior of the accumulator used must be considered.
+   * Refer to the function specific documentation below for usage guidelines.
+   */
+
+  /**
+   * @addtogroup park
+   * @{
+   */
+
+  /**
+   * @brief Floating-point Park transform
+   * @param[in]       Ialpha input two-phase vector coordinate alpha
+   * @param[in]       Ibeta  input two-phase vector coordinate beta
+   * @param[out]      *pId   points to output	rotor reference frame d
+   * @param[out]      *pIq   points to output	rotor reference frame q
+   * @param[in]       sinVal sine value of rotation angle theta
+   * @param[in]       cosVal cosine value of rotation angle theta
+   * @return none.
+   *
+   * The function implements the forward Park transform.
+   *
+   */
+
+  __STATIC_INLINE void arm_park_f32(
+  float32_t Ialpha,
+  float32_t Ibeta,
+  float32_t * pId,
+  float32_t * pIq,
+  float32_t sinVal,
+  float32_t cosVal)
+  {
+    /* Calculate pId using the equation, pId = Ialpha * cosVal + Ibeta * sinVal */
+    *pId = Ialpha * cosVal + Ibeta * sinVal;
+
+    /* Calculate pIq using the equation, pIq = - Ialpha * sinVal + Ibeta * cosVal */
+    *pIq = -Ialpha * sinVal + Ibeta * cosVal;
+
+  }
+
+  /**
+   * @brief  Park transform for Q31 version 
+   * @param[in]       Ialpha input two-phase vector coordinate alpha
+   * @param[in]       Ibeta  input two-phase vector coordinate beta
+   * @param[out]      *pId   points to output rotor reference frame d
+   * @param[out]      *pIq   points to output rotor reference frame q
+   * @param[in]       sinVal sine value of rotation angle theta
+   * @param[in]       cosVal cosine value of rotation angle theta
+   * @return none.
+   *
+   * Scaling and Overflow Behavior:
+   * \par
+   * The function is implemented using an internal 32-bit accumulator.
+   * The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
+   * There is saturation on the addition and subtraction, hence there is no risk of overflow.
+   */
+
+
+  __STATIC_INLINE void arm_park_q31(
+  q31_t Ialpha,
+  q31_t Ibeta,
+  q31_t * pId,
+  q31_t * pIq,
+  q31_t sinVal,
+  q31_t cosVal)
+  {
+    q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
+    q31_t product3, product4;                    /* Temporary variables used to store intermediate results */
+
+    /* Intermediate product is calculated by (Ialpha * cosVal) */
+    product1 = (q31_t) (((q63_t) (Ialpha) * (cosVal)) >> 31);
+
+    /* Intermediate product is calculated by (Ibeta * sinVal) */
+    product2 = (q31_t) (((q63_t) (Ibeta) * (sinVal)) >> 31);
+
+
+    /* Intermediate product is calculated by (Ialpha * sinVal) */
+    product3 = (q31_t) (((q63_t) (Ialpha) * (sinVal)) >> 31);
+
+    /* Intermediate product is calculated by (Ibeta * cosVal) */
+    product4 = (q31_t) (((q63_t) (Ibeta) * (cosVal)) >> 31);
+
+    /* Calculate pId by adding the two intermediate products 1 and 2 */
+    *pId = __QADD(product1, product2);
+
+    /* Calculate pIq by subtracting the two intermediate products 3 from 4 */
+    *pIq = __QSUB(product4, product3);
+  }
+
+  /**
+   * @} end of park group
+   */
+
+  /**
+   * @brief  Converts the elements of the Q7 vector to floating-point vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[out]  *pDst is output pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @return none.
+   */
+  void arm_q7_to_float(
+  q7_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize);
+
+
+  /**
+   * @ingroup groupController
+   */
+
+  /**
+   * @defgroup inv_park Vector Inverse Park transform
+   * Inverse Park transform converts the input flux and torque components to two-coordinate vector.
+   *
+   * The function operates on a single sample of data and each call to the function returns the processed output. 
+   * The library provides separate functions for Q31 and floating-point data types.
+   * \par Algorithm
+   * \image html parkInvFormula.gif
+   * where pIalpha and pIbeta are the stator vector components,  
+   * Id and Iq are rotor vector components and cosVal and sinVal are the 
+   * cosine and sine values of theta (rotor flux position).
+   * \par Fixed-Point Behavior
+   * Care must be taken when using the Q31 version of the Park transform.
+   * In particular, the overflow and saturation behavior of the accumulator used must be considered.
+   * Refer to the function specific documentation below for usage guidelines.
+   */
+
+  /**
+   * @addtogroup inv_park
+   * @{
+   */
+
+   /**
+   * @brief  Floating-point Inverse Park transform
+   * @param[in]       Id        input coordinate of rotor reference frame d
+   * @param[in]       Iq        input coordinate of rotor reference frame q
+   * @param[out]      *pIalpha  points to output two-phase orthogonal vector axis alpha
+   * @param[out]      *pIbeta   points to output two-phase orthogonal vector axis beta
+   * @param[in]       sinVal    sine value of rotation angle theta
+   * @param[in]       cosVal    cosine value of rotation angle theta
+   * @return none.
+   */
+
+  __STATIC_INLINE void arm_inv_park_f32(
+  float32_t Id,
+  float32_t Iq,
+  float32_t * pIalpha,
+  float32_t * pIbeta,
+  float32_t sinVal,
+  float32_t cosVal)
+  {
+    /* Calculate pIalpha using the equation, pIalpha = Id * cosVal - Iq * sinVal */
+    *pIalpha = Id * cosVal - Iq * sinVal;
+
+    /* Calculate pIbeta using the equation, pIbeta = Id * sinVal + Iq * cosVal */
+    *pIbeta = Id * sinVal + Iq * cosVal;
+
+  }
+
+
+  /**
+   * @brief  Inverse Park transform for	Q31 version 
+   * @param[in]       Id        input coordinate of rotor reference frame d
+   * @param[in]       Iq        input coordinate of rotor reference frame q
+   * @param[out]      *pIalpha  points to output two-phase orthogonal vector axis alpha
+   * @param[out]      *pIbeta   points to output two-phase orthogonal vector axis beta
+   * @param[in]       sinVal    sine value of rotation angle theta
+   * @param[in]       cosVal    cosine value of rotation angle theta
+   * @return none.
+   *
+   * Scaling and Overflow Behavior:
+   * \par
+   * The function is implemented using an internal 32-bit accumulator.
+   * The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
+   * There is saturation on the addition, hence there is no risk of overflow.
+   */
+
+
+  __STATIC_INLINE void arm_inv_park_q31(
+  q31_t Id,
+  q31_t Iq,
+  q31_t * pIalpha,
+  q31_t * pIbeta,
+  q31_t sinVal,
+  q31_t cosVal)
+  {
+    q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
+    q31_t product3, product4;                    /* Temporary variables used to store intermediate results */
+
+    /* Intermediate product is calculated by (Id * cosVal) */
+    product1 = (q31_t) (((q63_t) (Id) * (cosVal)) >> 31);
+
+    /* Intermediate product is calculated by (Iq * sinVal) */
+    product2 = (q31_t) (((q63_t) (Iq) * (sinVal)) >> 31);
+
+
+    /* Intermediate product is calculated by (Id * sinVal) */
+    product3 = (q31_t) (((q63_t) (Id) * (sinVal)) >> 31);
+
+    /* Intermediate product is calculated by (Iq * cosVal) */
+    product4 = (q31_t) (((q63_t) (Iq) * (cosVal)) >> 31);
+
+    /* Calculate pIalpha by using the two intermediate products 1 and 2 */
+    *pIalpha = __QSUB(product1, product2);
+
+    /* Calculate pIbeta by using the two intermediate products 3 and 4 */
+    *pIbeta = __QADD(product4, product3);
+
+  }
+
+  /**
+   * @} end of Inverse park group
+   */
+
+
+  /**
+   * @brief  Converts the elements of the Q31 vector to floating-point vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[out]  *pDst is output pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @return none.
+   */
+  void arm_q31_to_float(
+  q31_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @ingroup groupInterpolation
+   */
+
+  /**
+   * @defgroup LinearInterpolate Linear Interpolation
+   *
+   * Linear interpolation is a method of curve fitting using linear polynomials.
+   * Linear interpolation works by effectively drawing a straight line between two neighboring samples and returning the appropriate point along that line
+   *
+   * \par 
+   * \image html LinearInterp.gif "Linear interpolation"
+   *
+   * \par
+   * A  Linear Interpolate function calculates an output value(y), for the input(x)
+   * using linear interpolation of the input values x0, x1( nearest input values) and the output values y0 and y1(nearest output values)
+   *
+   * \par Algorithm:
+   * 
+   *       y = y0 + (x - x0) * ((y1 - y0)/(x1-x0))
+   *       where x0, x1 are nearest values of input x
+   *             y0, y1 are nearest values to output y
+   * 

+   *
+   * \par
+   * This set of functions implements Linear interpolation process
+   * for Q7, Q15, Q31, and floating-point data types.  The functions operate on a single
+   * sample of data and each call to the function returns a single processed value.
+   * S points to an instance of the Linear Interpolate function data structure.
+   * x is the input sample value. The functions returns the output value.
+   * 
+   * \par
+   * if x is outside of the table boundary, Linear interpolation returns first value of the table 
+   * if x is below input range and returns last value of table if x is above range.  
+   */
+
+  /**
+   * @addtogroup LinearInterpolate
+   * @{
+   */
+
+  /**
+   * @brief  Process function for the floating-point Linear Interpolation Function.
+   * @param[in,out] *S is an instance of the floating-point Linear Interpolation structure
+   * @param[in] x input sample to process
+   * @return y processed output sample.
+   *
+   */
+
+  __STATIC_INLINE float32_t arm_linear_interp_f32(
+  arm_linear_interp_instance_f32 * S,
+  float32_t x)
+  {
+
+    float32_t y;
+    float32_t x0, x1;                            /* Nearest input values */
+    float32_t y0, y1;                            /* Nearest output values */
+    float32_t xSpacing = S->xSpacing;            /* spacing between input values */
+    int32_t i;                                   /* Index variable */
+    float32_t *pYData = S->pYData;               /* pointer to output table */
+
+    /* Calculation of index */
+    i = (x - S->x1) / xSpacing;
+
+    if(i < 0)
+    {
+      /* Iniatilize output for below specified range as least output value of table */
+      y = pYData[0];
+    }
+    else if(i >= S->nValues)
+    {
+      /* Iniatilize output for above specified range as last output value of table */
+      y = pYData[S->nValues - 1];
+    }
+    else
+    {
+      /* Calculation of nearest input values */
+      x0 = S->x1 + i * xSpacing;
+      x1 = S->x1 + (i + 1) * xSpacing;
+
+      /* Read of nearest output values */
+      y0 = pYData[i];
+      y1 = pYData[i + 1];
+
+      /* Calculation of output */
+      y = y0 + (x - x0) * ((y1 - y0) / (x1 - x0));
+
+    }
+
+    /* returns output value */
+    return (y);
+  }
+
+   /**
+   *
+   * @brief  Process function for the Q31 Linear Interpolation Function.
+   * @param[in] *pYData  pointer to Q31 Linear Interpolation table
+   * @param[in] x input sample to process
+   * @param[in] nValues number of table values
+   * @return y processed output sample.
+   *
+   * \par
+   * Input sample x is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part.
+   * This function can support maximum of table size 2^12.
+   *
+   */
+
+
+  __STATIC_INLINE q31_t arm_linear_interp_q31(
+  q31_t * pYData,
+  q31_t x,
+  uint32_t nValues)
+  {
+    q31_t y;                                     /* output */
+    q31_t y0, y1;                                /* Nearest output values */
+    q31_t fract;                                 /* fractional part */
+    int32_t index;                               /* Index to read nearest output values */
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    index = ((x & 0xFFF00000) >> 20);
+
+    if(index >= (nValues - 1))
+    {
+      return (pYData[nValues - 1]);
+    }
+    else if(index < 0)
+    {
+      return (pYData[0]);
+    }
+    else
+    {
+
+      /* 20 bits for the fractional part */
+      /* shift left by 11 to keep fract in 1.31 format */
+      fract = (x & 0x000FFFFF) << 11;
+
+      /* Read two nearest output values from the index in 1.31(q31) format */
+      y0 = pYData[index];
+      y1 = pYData[index + 1u];
+
+      /* Calculation of y0 * (1-fract) and y is in 2.30 format */
+      y = ((q31_t) ((q63_t) y0 * (0x7FFFFFFF - fract) >> 32));
+
+      /* Calculation of y0 * (1-fract) + y1 *fract and y is in 2.30 format */
+      y += ((q31_t) (((q63_t) y1 * fract) >> 32));
+
+      /* Convert y to 1.31 format */
+      return (y << 1u);
+
+    }
+
+  }
+
+  /**
+   *
+   * @brief  Process function for the Q15 Linear Interpolation Function.
+   * @param[in] *pYData  pointer to Q15 Linear Interpolation table
+   * @param[in] x input sample to process
+   * @param[in] nValues number of table values
+   * @return y processed output sample.
+   *
+   * \par
+   * Input sample x is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part.
+   * This function can support maximum of table size 2^12. 
+   *
+   */
+
+
+  __STATIC_INLINE q15_t arm_linear_interp_q15(
+  q15_t * pYData,
+  q31_t x,
+  uint32_t nValues)
+  {
+    q63_t y;                                     /* output */
+    q15_t y0, y1;                                /* Nearest output values */
+    q31_t fract;                                 /* fractional part */
+    int32_t index;                               /* Index to read nearest output values */
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    index = ((x & 0xFFF00000) >> 20u);
+
+    if(index >= (nValues - 1))
+    {
+      return (pYData[nValues - 1]);
+    }
+    else if(index < 0)
+    {
+      return (pYData[0]);
+    }
+    else
+    {
+      /* 20 bits for the fractional part */
+      /* fract is in 12.20 format */
+      fract = (x & 0x000FFFFF);
+
+      /* Read two nearest output values from the index */
+      y0 = pYData[index];
+      y1 = pYData[index + 1u];
+
+      /* Calculation of y0 * (1-fract) and y is in 13.35 format */
+      y = ((q63_t) y0 * (0xFFFFF - fract));
+
+      /* Calculation of (y0 * (1-fract) + y1 * fract) and y is in 13.35 format */
+      y += ((q63_t) y1 * (fract));
+
+      /* convert y to 1.15 format */
+      return (y >> 20);
+    }
+
+
+  }
+
+  /**
+   *
+   * @brief  Process function for the Q7 Linear Interpolation Function.
+   * @param[in] *pYData  pointer to Q7 Linear Interpolation table
+   * @param[in] x input sample to process
+   * @param[in] nValues number of table values
+   * @return y processed output sample.
+   *
+   * \par
+   * Input sample x is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part.
+   * This function can support maximum of table size 2^12.
+   */
+
+
+  __STATIC_INLINE q7_t arm_linear_interp_q7(
+  q7_t * pYData,
+  q31_t x,
+  uint32_t nValues)
+  {
+    q31_t y;                                     /* output */
+    q7_t y0, y1;                                 /* Nearest output values */
+    q31_t fract;                                 /* fractional part */
+    int32_t index;                               /* Index to read nearest output values */
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    index = ((x & 0xFFF00000) >> 20u);
+
+
+    if(index >= (nValues - 1))
+    {
+      return (pYData[nValues - 1]);
+    }
+    else if(index < 0)
+    {
+      return (pYData[0]);
+    }
+    else
+    {
+
+      /* 20 bits for the fractional part */
+      /* fract is in 12.20 format */
+      fract = (x & 0x000FFFFF);
+
+      /* Read two nearest output values from the index and are in 1.7(q7) format */
+      y0 = pYData[index];
+      y1 = pYData[index + 1u];
+
+      /* Calculation of y0 * (1-fract ) and y is in 13.27(q27) format */
+      y = ((y0 * (0xFFFFF - fract)));
+
+      /* Calculation of y1 * fract + y0 * (1-fract) and y is in 13.27(q27) format */
+      y += (y1 * fract);
+
+      /* convert y to 1.7(q7) format */
+      return (y >> 20u);
+
+    }
+
+  }
+  /**
+   * @} end of LinearInterpolate group
+   */
+
+  /**
+   * @brief  Fast approximation to the trigonometric sine function for floating-point data.
+   * @param[in] x input value in radians.
+   * @return  sin(x).
+   */
+
+  float32_t arm_sin_f32(
+  float32_t x);
+
+  /**
+   * @brief  Fast approximation to the trigonometric sine function for Q31 data.
+   * @param[in] x Scaled input value in radians.
+   * @return  sin(x).
+   */
+
+  q31_t arm_sin_q31(
+  q31_t x);
+
+  /**
+   * @brief  Fast approximation to the trigonometric sine function for Q15 data.
+   * @param[in] x Scaled input value in radians.
+   * @return  sin(x).
+   */
+
+  q15_t arm_sin_q15(
+  q15_t x);
+
+  /**
+   * @brief  Fast approximation to the trigonometric cosine function for floating-point data.
+   * @param[in] x input value in radians.
+   * @return  cos(x).
+   */
+
+  float32_t arm_cos_f32(
+  float32_t x);
+
+  /**
+   * @brief Fast approximation to the trigonometric cosine function for Q31 data.
+   * @param[in] x Scaled input value in radians.
+   * @return  cos(x).
+   */
+
+  q31_t arm_cos_q31(
+  q31_t x);
+
+  /**
+   * @brief  Fast approximation to the trigonometric cosine function for Q15 data.
+   * @param[in] x Scaled input value in radians.
+   * @return  cos(x).
+   */
+
+  q15_t arm_cos_q15(
+  q15_t x);
+
+
+  /**
+   * @ingroup groupFastMath
+   */
+
+
+  /**
+   * @defgroup SQRT Square Root
+   *
+   * Computes the square root of a number.
+   * There are separate functions for Q15, Q31, and floating-point data types.  
+   * The square root function is computed using the Newton-Raphson algorithm.
+   * This is an iterative algorithm of the form:
+   * 
+   *      x1 = x0 - f(x0)/f'(x0)
+   * 

+   * where x1 is the current estimate,
+   * x0 is the previous estimate and
+   * f'(x0) is the derivative of f() evaluated at x0.
+   * For the square root function, the algorithm reduces to:
+   * 
+   *     x0 = in/2                         [initial guess]
+   *     x1 = 1/2 * ( x0 + in / x0)        [each iteration]
+   * 

+   */
+
+
+  /**
+   * @addtogroup SQRT
+   * @{
+   */
+
+  /**
+   * @brief  Floating-point square root function.
+   * @param[in]  in     input value.
+   * @param[out] *pOut  square root of input value.
+   * @return The function returns ARM_MATH_SUCCESS if input value is positive value or ARM_MATH_ARGUMENT_ERROR if
+   * in is negative value and returns zero output for negative values.
+   */
+
+  __STATIC_INLINE arm_status arm_sqrt_f32(
+  float32_t in,
+  float32_t * pOut)
+  {
+    if(in > 0)
+    {
+
+//    #if __FPU_USED
+    #if (__FPU_USED == 1) && defined ( __CC_ARM   )
+        *pOut = __sqrtf(in);
+    #elif (__FPU_USED == 1) && defined ( __TMS_740 )
+        *pOut = __builtin_sqrtf(in);
+    #else
+        *pOut = sqrtf(in);
+    #endif
+
+      return (ARM_MATH_SUCCESS);
+    }
+    else
+    {
+      *pOut = 0.0f;
+      return (ARM_MATH_ARGUMENT_ERROR);
+    }
+
+  }
+
+
+  /**
+   * @brief Q31 square root function.
+   * @param[in]   in    input value.  The range of the input value is [0 +1) or 0x00000000 to 0x7FFFFFFF.
+   * @param[out]  *pOut square root of input value.
+   * @return The function returns ARM_MATH_SUCCESS if input value is positive value or ARM_MATH_ARGUMENT_ERROR if
+   * in is negative value and returns zero output for negative values.
+   */
+  arm_status arm_sqrt_q31(
+  q31_t in,
+  q31_t * pOut);
+
+  /**
+   * @brief  Q15 square root function.
+   * @param[in]   in     input value.  The range of the input value is [0 +1) or 0x0000 to 0x7FFF.
+   * @param[out]  *pOut  square root of input value.
+   * @return The function returns ARM_MATH_SUCCESS if input value is positive value or ARM_MATH_ARGUMENT_ERROR if
+   * in is negative value and returns zero output for negative values.
+   */
+  arm_status arm_sqrt_q15(
+  q15_t in,
+  q15_t * pOut);
+
+  /**
+   * @} end of SQRT group
+   */
+
+
+
+
+
+
+  /**
+   * @brief floating-point Circular write function.
+   */
+
+  __STATIC_INLINE void arm_circularWrite_f32(
+  int32_t * circBuffer,
+  int32_t L,
+  uint16_t * writeOffset,
+  int32_t bufferInc,
+  const int32_t * src,
+  int32_t srcInc,
+  uint32_t blockSize)
+  {
+    uint32_t i = 0u;
+    int32_t wOffset;
+
+    /* Copy the value of Index pointer that points
+     * to the current location where the input samples to be copied */
+    wOffset = *writeOffset;
+
+    /* Loop over the blockSize */
+    i = blockSize;
+
+    while(i > 0u)
+    {
+      /* copy the input sample to the circular buffer */
+      circBuffer[wOffset] = *src;
+
+      /* Update the input pointer */
+      src += srcInc;
+
+      /* Circularly update wOffset.  Watch out for positive and negative value */
+      wOffset += bufferInc;
+      if(wOffset >= L)
+        wOffset -= L;
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Update the index pointer */
+    *writeOffset = wOffset;
+  }
+
+
+
+  /**
+   * @brief floating-point Circular Read function.
+   */
+  __STATIC_INLINE void arm_circularRead_f32(
+  int32_t * circBuffer,
+  int32_t L,
+  int32_t * readOffset,
+  int32_t bufferInc,
+  int32_t * dst,
+  int32_t * dst_base,
+  int32_t dst_length,
+  int32_t dstInc,
+  uint32_t blockSize)
+  {
+    uint32_t i = 0u;
+    int32_t rOffset, dst_end;
+
+    /* Copy the value of Index pointer that points
+     * to the current location from where the input samples to be read */
+    rOffset = *readOffset;
+    dst_end = (int32_t) (dst_base + dst_length);
+
+    /* Loop over the blockSize */
+    i = blockSize;
+
+    while(i > 0u)
+    {
+      /* copy the sample from the circular buffer to the destination buffer */
+      *dst = circBuffer[rOffset];
+
+      /* Update the input pointer */
+      dst += dstInc;
+
+      if(dst == (int32_t *) dst_end)
+      {
+        dst = dst_base;
+      }
+
+      /* Circularly update rOffset.  Watch out for positive and negative value  */
+      rOffset += bufferInc;
+
+      if(rOffset >= L)
+      {
+        rOffset -= L;
+      }
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Update the index pointer */
+    *readOffset = rOffset;
+  }
+
+  /**
+   * @brief Q15 Circular write function.
+   */
+
+  __STATIC_INLINE void arm_circularWrite_q15(
+  q15_t * circBuffer,
+  int32_t L,
+  uint16_t * writeOffset,
+  int32_t bufferInc,
+  const q15_t * src,
+  int32_t srcInc,
+  uint32_t blockSize)
+  {
+    uint32_t i = 0u;
+    int32_t wOffset;
+
+    /* Copy the value of Index pointer that points
+     * to the current location where the input samples to be copied */
+    wOffset = *writeOffset;
+
+    /* Loop over the blockSize */
+    i = blockSize;
+
+    while(i > 0u)
+    {
+      /* copy the input sample to the circular buffer */
+      circBuffer[wOffset] = *src;
+
+      /* Update the input pointer */
+      src += srcInc;
+
+      /* Circularly update wOffset.  Watch out for positive and negative value */
+      wOffset += bufferInc;
+      if(wOffset >= L)
+        wOffset -= L;
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Update the index pointer */
+    *writeOffset = wOffset;
+  }
+
+
+
+  /**
+   * @brief Q15 Circular Read function.
+   */
+  __STATIC_INLINE void arm_circularRead_q15(
+  q15_t * circBuffer,
+  int32_t L,
+  int32_t * readOffset,
+  int32_t bufferInc,
+  q15_t * dst,
+  q15_t * dst_base,
+  int32_t dst_length,
+  int32_t dstInc,
+  uint32_t blockSize)
+  {
+    uint32_t i = 0;
+    int32_t rOffset, dst_end;
+
+    /* Copy the value of Index pointer that points
+     * to the current location from where the input samples to be read */
+    rOffset = *readOffset;
+
+    dst_end = (int32_t) (dst_base + dst_length);
+
+    /* Loop over the blockSize */
+    i = blockSize;
+
+    while(i > 0u)
+    {
+      /* copy the sample from the circular buffer to the destination buffer */
+      *dst = circBuffer[rOffset];
+
+      /* Update the input pointer */
+      dst += dstInc;
+
+      if(dst == (q15_t *) dst_end)
+      {
+        dst = dst_base;
+      }
+
+      /* Circularly update wOffset.  Watch out for positive and negative value */
+      rOffset += bufferInc;
+
+      if(rOffset >= L)
+      {
+        rOffset -= L;
+      }
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Update the index pointer */
+    *readOffset = rOffset;
+  }
+
+
+  /**
+   * @brief Q7 Circular write function.
+   */
+
+  __STATIC_INLINE void arm_circularWrite_q7(
+  q7_t * circBuffer,
+  int32_t L,
+  uint16_t * writeOffset,
+  int32_t bufferInc,
+  const q7_t * src,
+  int32_t srcInc,
+  uint32_t blockSize)
+  {
+    uint32_t i = 0u;
+    int32_t wOffset;
+
+    /* Copy the value of Index pointer that points
+     * to the current location where the input samples to be copied */
+    wOffset = *writeOffset;
+
+    /* Loop over the blockSize */
+    i = blockSize;
+
+    while(i > 0u)
+    {
+      /* copy the input sample to the circular buffer */
+      circBuffer[wOffset] = *src;
+
+      /* Update the input pointer */
+      src += srcInc;
+
+      /* Circularly update wOffset.  Watch out for positive and negative value */
+      wOffset += bufferInc;
+      if(wOffset >= L)
+        wOffset -= L;
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Update the index pointer */
+    *writeOffset = wOffset;
+  }
+
+
+
+  /**
+   * @brief Q7 Circular Read function.
+   */
+  __STATIC_INLINE void arm_circularRead_q7(
+  q7_t * circBuffer,
+  int32_t L,
+  int32_t * readOffset,
+  int32_t bufferInc,
+  q7_t * dst,
+  q7_t * dst_base,
+  int32_t dst_length,
+  int32_t dstInc,
+  uint32_t blockSize)
+  {
+    uint32_t i = 0;
+    int32_t rOffset, dst_end;
+
+    /* Copy the value of Index pointer that points
+     * to the current location from where the input samples to be read */
+    rOffset = *readOffset;
+
+    dst_end = (int32_t) (dst_base + dst_length);
+
+    /* Loop over the blockSize */
+    i = blockSize;
+
+    while(i > 0u)
+    {
+      /* copy the sample from the circular buffer to the destination buffer */
+      *dst = circBuffer[rOffset];
+
+      /* Update the input pointer */
+      dst += dstInc;
+
+      if(dst == (q7_t *) dst_end)
+      {
+        dst = dst_base;
+      }
+
+      /* Circularly update rOffset.  Watch out for positive and negative value */
+      rOffset += bufferInc;
+
+      if(rOffset >= L)
+      {
+        rOffset -= L;
+      }
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Update the index pointer */
+    *readOffset = rOffset;
+  }
+
+
+  /**
+   * @brief  Sum of the squares of the elements of a Q31 vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @param[out]  *pResult is output value.
+   * @return none.
+   */
+
+  void arm_power_q31(
+  q31_t * pSrc,
+  uint32_t blockSize,
+  q63_t * pResult);
+
+  /**
+   * @brief  Sum of the squares of the elements of a floating-point vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @param[out]  *pResult is output value.
+   * @return none.
+   */
+
+  void arm_power_f32(
+  float32_t * pSrc,
+  uint32_t blockSize,
+  float32_t * pResult);
+
+  /**
+   * @brief  Sum of the squares of the elements of a Q15 vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @param[out]  *pResult is output value.
+   * @return none.
+   */
+
+  void arm_power_q15(
+  q15_t * pSrc,
+  uint32_t blockSize,
+  q63_t * pResult);
+
+  /**
+   * @brief  Sum of the squares of the elements of a Q7 vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @param[out]  *pResult is output value.
+   * @return none.
+   */
+
+  void arm_power_q7(
+  q7_t * pSrc,
+  uint32_t blockSize,
+  q31_t * pResult);
+
+  /**
+   * @brief  Mean value of a Q7 vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @param[out]  *pResult is output value.
+   * @return none.
+   */
+
+  void arm_mean_q7(
+  q7_t * pSrc,
+  uint32_t blockSize,
+  q7_t * pResult);
+
+  /**
+   * @brief  Mean value of a Q15 vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @param[out]  *pResult is output value.
+   * @return none.
+   */
+  void arm_mean_q15(
+  q15_t * pSrc,
+  uint32_t blockSize,
+  q15_t * pResult);
+
+  /**
+   * @brief  Mean value of a Q31 vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @param[out]  *pResult is output value.
+   * @return none.
+   */
+  void arm_mean_q31(
+  q31_t * pSrc,
+  uint32_t blockSize,
+  q31_t * pResult);
+
+  /**
+   * @brief  Mean value of a floating-point vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @param[out]  *pResult is output value.
+   * @return none.
+   */
+  void arm_mean_f32(
+  float32_t * pSrc,
+  uint32_t blockSize,
+  float32_t * pResult);
+
+  /**
+   * @brief  Variance of the elements of a floating-point vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @param[out]  *pResult is output value.
+   * @return none.
+   */
+
+  void arm_var_f32(
+  float32_t * pSrc,
+  uint32_t blockSize,
+  float32_t * pResult);
+
+  /**
+   * @brief  Variance of the elements of a Q31 vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @param[out]  *pResult is output value.
+   * @return none.
+   */
+
+  void arm_var_q31(
+  q31_t * pSrc,
+  uint32_t blockSize,
+  q63_t * pResult);
+
+  /**
+   * @brief  Variance of the elements of a Q15 vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @param[out]  *pResult is output value.
+   * @return none.
+   */
+
+  void arm_var_q15(
+  q15_t * pSrc,
+  uint32_t blockSize,
+  q31_t * pResult);
+
+  /**
+   * @brief  Root Mean Square of the elements of a floating-point vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @param[out]  *pResult is output value.
+   * @return none.
+   */
+
+  void arm_rms_f32(
+  float32_t * pSrc,
+  uint32_t blockSize,
+  float32_t * pResult);
+
+  /**
+   * @brief  Root Mean Square of the elements of a Q31 vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @param[out]  *pResult is output value.
+   * @return none.
+   */
+
+  void arm_rms_q31(
+  q31_t * pSrc,
+  uint32_t blockSize,
+  q31_t * pResult);
+
+  /**
+   * @brief  Root Mean Square of the elements of a Q15 vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @param[out]  *pResult is output value.
+   * @return none.
+   */
+
+  void arm_rms_q15(
+  q15_t * pSrc,
+  uint32_t blockSize,
+  q15_t * pResult);
+
+  /**
+   * @brief  Standard deviation of the elements of a floating-point vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @param[out]  *pResult is output value.
+   * @return none.
+   */
+
+  void arm_std_f32(
+  float32_t * pSrc,
+  uint32_t blockSize,
+  float32_t * pResult);
+
+  /**
+   * @brief  Standard deviation of the elements of a Q31 vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @param[out]  *pResult is output value.
+   * @return none.
+   */
+
+  void arm_std_q31(
+  q31_t * pSrc,
+  uint32_t blockSize,
+  q31_t * pResult);
+
+  /**
+   * @brief  Standard deviation of the elements of a Q15 vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @param[out]  *pResult is output value.
+   * @return none.
+   */
+
+  void arm_std_q15(
+  q15_t * pSrc,
+  uint32_t blockSize,
+  q15_t * pResult);
+
+  /**
+   * @brief  Floating-point complex magnitude
+   * @param[in]  *pSrc points to the complex input vector
+   * @param[out]  *pDst points to the real output vector
+   * @param[in]  numSamples number of complex samples in the input vector
+   * @return none.
+   */
+
+  void arm_cmplx_mag_f32(
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t numSamples);
+
+  /**
+   * @brief  Q31 complex magnitude
+   * @param[in]  *pSrc points to the complex input vector
+   * @param[out]  *pDst points to the real output vector
+   * @param[in]  numSamples number of complex samples in the input vector
+   * @return none.
+   */
+
+  void arm_cmplx_mag_q31(
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t numSamples);
+
+  /**
+   * @brief  Q15 complex magnitude
+   * @param[in]  *pSrc points to the complex input vector
+   * @param[out]  *pDst points to the real output vector
+   * @param[in]  numSamples number of complex samples in the input vector
+   * @return none.
+   */
+
+  void arm_cmplx_mag_q15(
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t numSamples);
+
+  /**
+   * @brief  Q15 complex dot product
+   * @param[in]  *pSrcA points to the first input vector
+   * @param[in]  *pSrcB points to the second input vector
+   * @param[in]  numSamples number of complex samples in each vector
+   * @param[out]  *realResult real part of the result returned here
+   * @param[out]  *imagResult imaginary part of the result returned here
+   * @return none.
+   */
+
+  void arm_cmplx_dot_prod_q15(
+  q15_t * pSrcA,
+  q15_t * pSrcB,
+  uint32_t numSamples,
+  q31_t * realResult,
+  q31_t * imagResult);
+
+  /**
+   * @brief  Q31 complex dot product
+   * @param[in]  *pSrcA points to the first input vector
+   * @param[in]  *pSrcB points to the second input vector
+   * @param[in]  numSamples number of complex samples in each vector
+   * @param[out]  *realResult real part of the result returned here
+   * @param[out]  *imagResult imaginary part of the result returned here
+   * @return none.
+   */
+
+  void arm_cmplx_dot_prod_q31(
+  q31_t * pSrcA,
+  q31_t * pSrcB,
+  uint32_t numSamples,
+  q63_t * realResult,
+  q63_t * imagResult);
+
+  /**
+   * @brief  Floating-point complex dot product
+   * @param[in]  *pSrcA points to the first input vector
+   * @param[in]  *pSrcB points to the second input vector
+   * @param[in]  numSamples number of complex samples in each vector
+   * @param[out]  *realResult real part of the result returned here
+   * @param[out]  *imagResult imaginary part of the result returned here
+   * @return none.
+   */
+
+  void arm_cmplx_dot_prod_f32(
+  float32_t * pSrcA,
+  float32_t * pSrcB,
+  uint32_t numSamples,
+  float32_t * realResult,
+  float32_t * imagResult);
+
+  /**
+   * @brief  Q15 complex-by-real multiplication
+   * @param[in]  *pSrcCmplx points to the complex input vector
+   * @param[in]  *pSrcReal points to the real input vector
+   * @param[out]  *pCmplxDst points to the complex output vector
+   * @param[in]  numSamples number of samples in each vector
+   * @return none.
+   */
+
+  void arm_cmplx_mult_real_q15(
+  q15_t * pSrcCmplx,
+  q15_t * pSrcReal,
+  q15_t * pCmplxDst,
+  uint32_t numSamples);
+
+  /**
+   * @brief  Q31 complex-by-real multiplication
+   * @param[in]  *pSrcCmplx points to the complex input vector
+   * @param[in]  *pSrcReal points to the real input vector
+   * @param[out]  *pCmplxDst points to the complex output vector
+   * @param[in]  numSamples number of samples in each vector
+   * @return none.
+   */
+
+  void arm_cmplx_mult_real_q31(
+  q31_t * pSrcCmplx,
+  q31_t * pSrcReal,
+  q31_t * pCmplxDst,
+  uint32_t numSamples);
+
+  /**
+   * @brief  Floating-point complex-by-real multiplication
+   * @param[in]  *pSrcCmplx points to the complex input vector
+   * @param[in]  *pSrcReal points to the real input vector
+   * @param[out]  *pCmplxDst points to the complex output vector
+   * @param[in]  numSamples number of samples in each vector
+   * @return none.
+   */
+
+  void arm_cmplx_mult_real_f32(
+  float32_t * pSrcCmplx,
+  float32_t * pSrcReal,
+  float32_t * pCmplxDst,
+  uint32_t numSamples);
+
+  /**
+   * @brief  Minimum value of a Q7 vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @param[out]  *result is output pointer
+   * @param[in]  index is the array index of the minimum value in the input buffer.
+   * @return none.
+   */
+
+  void arm_min_q7(
+  q7_t * pSrc,
+  uint32_t blockSize,
+  q7_t * result,
+  uint32_t * index);
+
+  /**
+   * @brief  Minimum value of a Q15 vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @param[out]  *pResult is output pointer
+   * @param[in]  *pIndex is the array index of the minimum value in the input buffer.
+   * @return none.
+   */
+
+  void arm_min_q15(
+  q15_t * pSrc,
+  uint32_t blockSize,
+  q15_t * pResult,
+  uint32_t * pIndex);
+
+  /**
+   * @brief  Minimum value of a Q31 vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @param[out]  *pResult is output pointer
+   * @param[out]  *pIndex is the array index of the minimum value in the input buffer.
+   * @return none.
+   */
+  void arm_min_q31(
+  q31_t * pSrc,
+  uint32_t blockSize,
+  q31_t * pResult,
+  uint32_t * pIndex);
+
+  /**
+   * @brief  Minimum value of a floating-point vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @param[out]  *pResult is output pointer
+   * @param[out]  *pIndex is the array index of the minimum value in the input buffer.
+   * @return none.
+   */
+
+  void arm_min_f32(
+  float32_t * pSrc,
+  uint32_t blockSize,
+  float32_t * pResult,
+  uint32_t * pIndex);
+
+/**
+ * @brief Maximum value of a Q7 vector.
+ * @param[in]       *pSrc points to the input buffer
+ * @param[in]       blockSize length of the input vector
+ * @param[out]      *pResult maximum value returned here
+ * @param[out]      *pIndex index of maximum value returned here
+ * @return none.
+ */
+
+  void arm_max_q7(
+  q7_t * pSrc,
+  uint32_t blockSize,
+  q7_t * pResult,
+  uint32_t * pIndex);
+
+/**
+ * @brief Maximum value of a Q15 vector.
+ * @param[in]       *pSrc points to the input buffer
+ * @param[in]       blockSize length of the input vector
+ * @param[out]      *pResult maximum value returned here
+ * @param[out]      *pIndex index of maximum value returned here
+ * @return none.
+ */
+
+  void arm_max_q15(
+  q15_t * pSrc,
+  uint32_t blockSize,
+  q15_t * pResult,
+  uint32_t * pIndex);
+
+/**
+ * @brief Maximum value of a Q31 vector.
+ * @param[in]       *pSrc points to the input buffer
+ * @param[in]       blockSize length of the input vector
+ * @param[out]      *pResult maximum value returned here
+ * @param[out]      *pIndex index of maximum value returned here
+ * @return none.
+ */
+
+  void arm_max_q31(
+  q31_t * pSrc,
+  uint32_t blockSize,
+  q31_t * pResult,
+  uint32_t * pIndex);
+
+/**
+ * @brief Maximum value of a floating-point vector.
+ * @param[in]       *pSrc points to the input buffer
+ * @param[in]       blockSize length of the input vector
+ * @param[out]      *pResult maximum value returned here
+ * @param[out]      *pIndex index of maximum value returned here
+ * @return none.
+ */
+
+  void arm_max_f32(
+  float32_t * pSrc,
+  uint32_t blockSize,
+  float32_t * pResult,
+  uint32_t * pIndex);
+
+  /**
+   * @brief  Q15 complex-by-complex multiplication
+   * @param[in]  *pSrcA points to the first input vector
+   * @param[in]  *pSrcB points to the second input vector
+   * @param[out]  *pDst  points to the output vector
+   * @param[in]  numSamples number of complex samples in each vector
+   * @return none.
+   */
+
+  void arm_cmplx_mult_cmplx_q15(
+  q15_t * pSrcA,
+  q15_t * pSrcB,
+  q15_t * pDst,
+  uint32_t numSamples);
+
+  /**
+   * @brief  Q31 complex-by-complex multiplication
+   * @param[in]  *pSrcA points to the first input vector
+   * @param[in]  *pSrcB points to the second input vector
+   * @param[out]  *pDst  points to the output vector
+   * @param[in]  numSamples number of complex samples in each vector
+   * @return none.
+   */
+
+  void arm_cmplx_mult_cmplx_q31(
+  q31_t * pSrcA,
+  q31_t * pSrcB,
+  q31_t * pDst,
+  uint32_t numSamples);
+
+  /**
+   * @brief  Floating-point complex-by-complex multiplication
+   * @param[in]  *pSrcA points to the first input vector
+   * @param[in]  *pSrcB points to the second input vector
+   * @param[out]  *pDst  points to the output vector
+   * @param[in]  numSamples number of complex samples in each vector
+   * @return none.
+   */
+
+  void arm_cmplx_mult_cmplx_f32(
+  float32_t * pSrcA,
+  float32_t * pSrcB,
+  float32_t * pDst,
+  uint32_t numSamples);
+
+  /**
+   * @brief Converts the elements of the floating-point vector to Q31 vector. 
+   * @param[in]       *pSrc points to the floating-point input vector 
+   * @param[out]      *pDst points to the Q31 output vector
+   * @param[in]       blockSize length of the input vector 
+   * @return none. 
+   */
+  void arm_float_to_q31(
+  float32_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Converts the elements of the floating-point vector to Q15 vector. 
+   * @param[in]       *pSrc points to the floating-point input vector 
+   * @param[out]      *pDst points to the Q15 output vector
+   * @param[in]       blockSize length of the input vector 
+   * @return          none
+   */
+  void arm_float_to_q15(
+  float32_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief Converts the elements of the floating-point vector to Q7 vector. 
+   * @param[in]       *pSrc points to the floating-point input vector 
+   * @param[out]      *pDst points to the Q7 output vector
+   * @param[in]       blockSize length of the input vector 
+   * @return          none
+   */
+  void arm_float_to_q7(
+  float32_t * pSrc,
+  q7_t * pDst,
+  uint32_t blockSize);
+
+
+  /**
+   * @brief  Converts the elements of the Q31 vector to Q15 vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[out]  *pDst is output pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @return none.
+   */
+  void arm_q31_to_q15(
+  q31_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Converts the elements of the Q31 vector to Q7 vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[out]  *pDst is output pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @return none.
+   */
+  void arm_q31_to_q7(
+  q31_t * pSrc,
+  q7_t * pDst,
+  uint32_t blockSize);
+
+  /**
+   * @brief  Converts the elements of the Q15 vector to floating-point vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[out]  *pDst is output pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @return none.
+   */
+  void arm_q15_to_float(
+  q15_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize);
+
+
+  /**
+   * @brief  Converts the elements of the Q15 vector to Q31 vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[out]  *pDst is output pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @return none.
+   */
+  void arm_q15_to_q31(
+  q15_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize);
+
+
+  /**
+   * @brief  Converts the elements of the Q15 vector to Q7 vector.
+   * @param[in]  *pSrc is input pointer
+   * @param[out]  *pDst is output pointer
+   * @param[in]  blockSize is the number of samples to process
+   * @return none.
+   */
+  void arm_q15_to_q7(
+  q15_t * pSrc,
+  q7_t * pDst,
+  uint32_t blockSize);
+
+
+  /**
+   * @ingroup groupInterpolation
+   */
+
+  /**
+   * @defgroup BilinearInterpolate Bilinear Interpolation
+   *
+   * Bilinear interpolation is an extension of linear interpolation applied to a two dimensional grid.
+   * The underlying function f(x, y) is sampled on a regular grid and the interpolation process
+   * determines values between the grid points.
+   * Bilinear interpolation is equivalent to two step linear interpolation, first in the x-dimension and then in the y-dimension.
+   * Bilinear interpolation is often used in image processing to rescale images.
+   * The CMSIS DSP library provides bilinear interpolation functions for Q7, Q15, Q31, and floating-point data types.
+   *
+   * Algorithm
+   * \par
+   * The instance structure used by the bilinear interpolation functions describes a two dimensional data table.
+   * For floating-point, the instance structure is defined as:
+   * 
+   *   typedef struct
+   *   {
+   *     uint16_t numRows;
+   *     uint16_t numCols;
+   *     float32_t *pData;
+   * } arm_bilinear_interp_instance_f32;
+   * 

+   *
+   * \par
+   * where numRows specifies the number of rows in the table;
+   * numCols specifies the number of columns in the table;
+   * and pData points to an array of size numRows*numCols values.
+   * The data table pTable is organized in row order and the supplied data values fall on integer indexes.
+   * That is, table element (x,y) is located at pTable[x + y*numCols] where x and y are integers.
+   *
+   * \par
+   * Let (x, y) specify the desired interpolation point.  Then define:
+   * 
+   *     XF = floor(x)
+   *     YF = floor(y)
+   * 

+   * \par
+   * The interpolated output point is computed as:
+   * 
+   *  f(x, y) = f(XF, YF) * (1-(x-XF)) * (1-(y-YF))
+   *           + f(XF+1, YF) * (x-XF)*(1-(y-YF))
+   *           + f(XF, YF+1) * (1-(x-XF))*(y-YF)
+   *           + f(XF+1, YF+1) * (x-XF)*(y-YF)
+   * 

+   * Note that the coordinates (x, y) contain integer and fractional components.  
+   * The integer components specify which portion of the table to use while the
+   * fractional components control the interpolation processor.
+   *
+   * \par
+   * if (x,y) are outside of the table boundary, Bilinear interpolation returns zero output. 
+   */
+
+  /**
+   * @addtogroup BilinearInterpolate
+   * @{
+   */
+
+  /**
+  *
+  * @brief  Floating-point bilinear interpolation.
+  * @param[in,out] *S points to an instance of the interpolation structure.
+  * @param[in] X interpolation coordinate.
+  * @param[in] Y interpolation coordinate.
+  * @return out interpolated value.
+  */
+
+
+  __STATIC_INLINE float32_t arm_bilinear_interp_f32(
+  const arm_bilinear_interp_instance_f32 * S,
+  float32_t X,
+  float32_t Y)
+  {
+    float32_t out;
+    float32_t f00, f01, f10, f11;
+    float32_t *pData = S->pData;
+    int32_t xIndex, yIndex, index;
+    float32_t xdiff, ydiff;
+    float32_t b1, b2, b3, b4;
+
+    xIndex = (int32_t) X;
+    yIndex = (int32_t) Y;
+
+    /* Care taken for table outside boundary */
+    /* Returns zero output when values are outside table boundary */
+    if(xIndex < 0 || xIndex > (S->numRows - 1) || yIndex < 0
+       || yIndex > (S->numCols - 1))
+    {
+      return (0);
+    }
+
+    /* Calculation of index for two nearest points in X-direction */
+    index = (xIndex - 1) + (yIndex - 1) * S->numCols;
+
+
+    /* Read two nearest points in X-direction */
+    f00 = pData[index];
+    f01 = pData[index + 1];
+
+    /* Calculation of index for two nearest points in Y-direction */
+    index = (xIndex - 1) + (yIndex) * S->numCols;
+
+
+    /* Read two nearest points in Y-direction */
+    f10 = pData[index];
+    f11 = pData[index + 1];
+
+    /* Calculation of intermediate values */
+    b1 = f00;
+    b2 = f01 - f00;
+    b3 = f10 - f00;
+    b4 = f00 - f01 - f10 + f11;
+
+    /* Calculation of fractional part in X */
+    xdiff = X - xIndex;
+
+    /* Calculation of fractional part in Y */
+    ydiff = Y - yIndex;
+
+    /* Calculation of bi-linear interpolated output */
+    out = b1 + b2 * xdiff + b3 * ydiff + b4 * xdiff * ydiff;
+
+    /* return to application */
+    return (out);
+
+  }
+
+  /**
+  *
+  * @brief  Q31 bilinear interpolation.
+  * @param[in,out] *S points to an instance of the interpolation structure.
+  * @param[in] X interpolation coordinate in 12.20 format.
+  * @param[in] Y interpolation coordinate in 12.20 format.
+  * @return out interpolated value.
+  */
+
+  __STATIC_INLINE q31_t arm_bilinear_interp_q31(
+  arm_bilinear_interp_instance_q31 * S,
+  q31_t X,
+  q31_t Y)
+  {
+    q31_t out;                                   /* Temporary output */
+    q31_t acc = 0;                               /* output */
+    q31_t xfract, yfract;                        /* X, Y fractional parts */
+    q31_t x1, x2, y1, y2;                        /* Nearest output values */
+    int32_t rI, cI;                              /* Row and column indices */
+    q31_t *pYData = S->pData;                    /* pointer to output table values */
+    uint32_t nCols = S->numCols;                 /* num of rows */
+
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    rI = ((X & 0xFFF00000) >> 20u);
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    cI = ((Y & 0xFFF00000) >> 20u);
+
+    /* Care taken for table outside boundary */
+    /* Returns zero output when values are outside table boundary */
+    if(rI < 0 || rI > (S->numRows - 1) || cI < 0 || cI > (S->numCols - 1))
+    {
+      return (0);
+    }
+
+    /* 20 bits for the fractional part */
+    /* shift left xfract by 11 to keep 1.31 format */
+    xfract = (X & 0x000FFFFF) << 11u;
+
+    /* Read two nearest output values from the index */
+    x1 = pYData[(rI) + nCols * (cI)];
+    x2 = pYData[(rI) + nCols * (cI) + 1u];
+
+    /* 20 bits for the fractional part */
+    /* shift left yfract by 11 to keep 1.31 format */
+    yfract = (Y & 0x000FFFFF) << 11u;
+
+    /* Read two nearest output values from the index */
+    y1 = pYData[(rI) + nCols * (cI + 1)];
+    y2 = pYData[(rI) + nCols * (cI + 1) + 1u];
+
+    /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 3.29(q29) format */
+    out = ((q31_t) (((q63_t) x1 * (0x7FFFFFFF - xfract)) >> 32));
+    acc = ((q31_t) (((q63_t) out * (0x7FFFFFFF - yfract)) >> 32));
+
+    /* x2 * (xfract) * (1-yfract)  in 3.29(q29) and adding to acc */
+    out = ((q31_t) ((q63_t) x2 * (0x7FFFFFFF - yfract) >> 32));
+    acc += ((q31_t) ((q63_t) out * (xfract) >> 32));
+
+    /* y1 * (1 - xfract) * (yfract)  in 3.29(q29) and adding to acc */
+    out = ((q31_t) ((q63_t) y1 * (0x7FFFFFFF - xfract) >> 32));
+    acc += ((q31_t) ((q63_t) out * (yfract) >> 32));
+
+    /* y2 * (xfract) * (yfract)  in 3.29(q29) and adding to acc */
+    out = ((q31_t) ((q63_t) y2 * (xfract) >> 32));
+    acc += ((q31_t) ((q63_t) out * (yfract) >> 32));
+
+    /* Convert acc to 1.31(q31) format */
+    return (acc << 2u);
+
+  }
+
+  /**
+  * @brief  Q15 bilinear interpolation.
+  * @param[in,out] *S points to an instance of the interpolation structure.
+  * @param[in] X interpolation coordinate in 12.20 format.
+  * @param[in] Y interpolation coordinate in 12.20 format.
+  * @return out interpolated value.
+  */
+
+  __STATIC_INLINE q15_t arm_bilinear_interp_q15(
+  arm_bilinear_interp_instance_q15 * S,
+  q31_t X,
+  q31_t Y)
+  {
+    q63_t acc = 0;                               /* output */
+    q31_t out;                                   /* Temporary output */
+    q15_t x1, x2, y1, y2;                        /* Nearest output values */
+    q31_t xfract, yfract;                        /* X, Y fractional parts */
+    int32_t rI, cI;                              /* Row and column indices */
+    q15_t *pYData = S->pData;                    /* pointer to output table values */
+    uint32_t nCols = S->numCols;                 /* num of rows */
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    rI = ((X & 0xFFF00000) >> 20);
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    cI = ((Y & 0xFFF00000) >> 20);
+
+    /* Care taken for table outside boundary */
+    /* Returns zero output when values are outside table boundary */
+    if(rI < 0 || rI > (S->numRows - 1) || cI < 0 || cI > (S->numCols - 1))
+    {
+      return (0);
+    }
+
+    /* 20 bits for the fractional part */
+    /* xfract should be in 12.20 format */
+    xfract = (X & 0x000FFFFF);
+
+    /* Read two nearest output values from the index */
+    x1 = pYData[(rI) + nCols * (cI)];
+    x2 = pYData[(rI) + nCols * (cI) + 1u];
+
+
+    /* 20 bits for the fractional part */
+    /* yfract should be in 12.20 format */
+    yfract = (Y & 0x000FFFFF);
+
+    /* Read two nearest output values from the index */
+    y1 = pYData[(rI) + nCols * (cI + 1)];
+    y2 = pYData[(rI) + nCols * (cI + 1) + 1u];
+
+    /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 13.51 format */
+
+    /* x1 is in 1.15(q15), xfract in 12.20 format and out is in 13.35 format */
+    /* convert 13.35 to 13.31 by right shifting  and out is in 1.31 */
+    out = (q31_t) (((q63_t) x1 * (0xFFFFF - xfract)) >> 4u);
+    acc = ((q63_t) out * (0xFFFFF - yfract));
+
+    /* x2 * (xfract) * (1-yfract)  in 1.51 and adding to acc */
+    out = (q31_t) (((q63_t) x2 * (0xFFFFF - yfract)) >> 4u);
+    acc += ((q63_t) out * (xfract));
+
+    /* y1 * (1 - xfract) * (yfract)  in 1.51 and adding to acc */
+    out = (q31_t) (((q63_t) y1 * (0xFFFFF - xfract)) >> 4u);
+    acc += ((q63_t) out * (yfract));
+
+    /* y2 * (xfract) * (yfract)  in 1.51 and adding to acc */
+    out = (q31_t) (((q63_t) y2 * (xfract)) >> 4u);
+    acc += ((q63_t) out * (yfract));
+
+    /* acc is in 13.51 format and down shift acc by 36 times */
+    /* Convert out to 1.15 format */
+    return (acc >> 36);
+
+  }
+
+  /**
+  * @brief  Q7 bilinear interpolation.
+  * @param[in,out] *S points to an instance of the interpolation structure.
+  * @param[in] X interpolation coordinate in 12.20 format.
+  * @param[in] Y interpolation coordinate in 12.20 format.
+  * @return out interpolated value.
+  */
+
+  __STATIC_INLINE q7_t arm_bilinear_interp_q7(
+  arm_bilinear_interp_instance_q7 * S,
+  q31_t X,
+  q31_t Y)
+  {
+    q63_t acc = 0;                               /* output */
+    q31_t out;                                   /* Temporary output */
+    q31_t xfract, yfract;                        /* X, Y fractional parts */
+    q7_t x1, x2, y1, y2;                         /* Nearest output values */
+    int32_t rI, cI;                              /* Row and column indices */
+    q7_t *pYData = S->pData;                     /* pointer to output table values */
+    uint32_t nCols = S->numCols;                 /* num of rows */
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    rI = ((X & 0xFFF00000) >> 20);
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    cI = ((Y & 0xFFF00000) >> 20);
+
+    /* Care taken for table outside boundary */
+    /* Returns zero output when values are outside table boundary */
+    if(rI < 0 || rI > (S->numRows - 1) || cI < 0 || cI > (S->numCols - 1))
+    {
+      return (0);
+    }
+
+    /* 20 bits for the fractional part */
+    /* xfract should be in 12.20 format */
+    xfract = (X & 0x000FFFFF);
+
+    /* Read two nearest output values from the index */
+    x1 = pYData[(rI) + nCols * (cI)];
+    x2 = pYData[(rI) + nCols * (cI) + 1u];
+
+
+    /* 20 bits for the fractional part */
+    /* yfract should be in 12.20 format */
+    yfract = (Y & 0x000FFFFF);
+
+    /* Read two nearest output values from the index */
+    y1 = pYData[(rI) + nCols * (cI + 1)];
+    y2 = pYData[(rI) + nCols * (cI + 1) + 1u];
+
+    /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 16.47 format */
+    out = ((x1 * (0xFFFFF - xfract)));
+    acc = (((q63_t) out * (0xFFFFF - yfract)));
+
+    /* x2 * (xfract) * (1-yfract)  in 2.22 and adding to acc */
+    out = ((x2 * (0xFFFFF - yfract)));
+    acc += (((q63_t) out * (xfract)));
+
+    /* y1 * (1 - xfract) * (yfract)  in 2.22 and adding to acc */
+    out = ((y1 * (0xFFFFF - xfract)));
+    acc += (((q63_t) out * (yfract)));
+
+    /* y2 * (xfract) * (yfract)  in 2.22 and adding to acc */
+    out = ((y2 * (yfract)));
+    acc += (((q63_t) out * (xfract)));
+
+    /* acc in 16.47 format and down shift by 40 to convert to 1.7 format */
+    return (acc >> 40);
+
+  }
+
+  /**
+   * @} end of BilinearInterpolate group
+   */
+
+
+
+
+
+
+#ifdef	__cplusplus
+}
+#endif
+
+
+#endif /* _ARM_MATH_H */
+
+
+/**
+ *
+ * End of file.
+ */
diff --git a/apps/mathlib/CMSIS/Include/core_cm3.h b/apps/mathlib/CMSIS/Include/core_cm3.h
new file mode 100644
index 0000000000..733d6be539
--- /dev/null
+++ b/apps/mathlib/CMSIS/Include/core_cm3.h
@@ -0,0 +1,1612 @@
+/**************************************************************************//**
+ * @file     core_cm3.h
+ * @brief    CMSIS Cortex-M3 Core Peripheral Access Layer Header File
+ * @version  V3.01
+ * @date     22. March 2012
+ *
+ * @note
+ * Copyright (C) 2009-2012 ARM Limited. All rights reserved.
+ *
+ * @par
+ * ARM Limited (ARM) is supplying this software for use with Cortex-M
+ * processor based microcontrollers.  This file can be freely distributed
+ * within development tools that are supporting such ARM based processors.
+ *
+ * @par
+ * THIS SOFTWARE IS PROVIDED "AS IS".  NO WARRANTIES, WHETHER EXPRESS, IMPLIED
+ * OR STATUTORY, INCLUDING, BUT NOT LIMITED TO, IMPLIED WARRANTIES OF
+ * MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE APPLY TO THIS SOFTWARE.
+ * ARM SHALL NOT, IN ANY CIRCUMSTANCES, BE LIABLE FOR SPECIAL, INCIDENTAL, OR
+ * CONSEQUENTIAL DAMAGES, FOR ANY REASON WHATSOEVER.
+ *
+ ******************************************************************************/
+#if defined ( __ICCARM__ )
+ #pragma system_include  /* treat file as system include file for MISRA check */
+#endif
+
+#ifdef __cplusplus
+ extern "C" {
+#endif
+
+#ifndef __CORE_CM3_H_GENERIC
+#define __CORE_CM3_H_GENERIC
+
+/** \page CMSIS_MISRA_Exceptions  MISRA-C:2004 Compliance Exceptions
+  CMSIS violates the following MISRA-C:2004 rules:
+
+   \li Required Rule 8.5, object/function definition in header file.

+     Function definitions in header files are used to allow 'inlining'.
+
+   \li Required Rule 18.4, declaration of union type or object of union type: '{...}'.

+     Unions are used for effective representation of core registers.
+
+   \li Advisory Rule 19.7, Function-like macro defined.

+     Function-like macros are used to allow more efficient code.
+ */
+
+
+/*******************************************************************************
+ *                 CMSIS definitions
+ ******************************************************************************/
+/** \ingroup Cortex_M3
+  @{
+ */
+
+/*  CMSIS CM3 definitions */
+#define __CM3_CMSIS_VERSION_MAIN  (0x03)                                   /*!< [31:16] CMSIS HAL main version   */
+#define __CM3_CMSIS_VERSION_SUB   (0x01)                                   /*!< [15:0]  CMSIS HAL sub version    */
+#define __CM3_CMSIS_VERSION       ((__CM3_CMSIS_VERSION_MAIN << 16) | \
+                                    __CM3_CMSIS_VERSION_SUB          )     /*!< CMSIS HAL version number         */
+
+#define __CORTEX_M                (0x03)                                   /*!< Cortex-M Core                    */
+
+
+#if   defined ( __CC_ARM )
+  #define __ASM            __asm                                      /*!< asm keyword for ARM Compiler          */
+  #define __INLINE         __inline                                   /*!< inline keyword for ARM Compiler       */
+  #define __STATIC_INLINE  static __inline
+
+#elif defined ( __ICCARM__ )
+  #define __ASM            __asm                                      /*!< asm keyword for IAR Compiler          */
+  #define __INLINE         inline                                     /*!< inline keyword for IAR Compiler. Only available in High optimization mode! */
+  #define __STATIC_INLINE  static inline
+
+#elif defined ( __TMS470__ )
+  #define __ASM            __asm                                      /*!< asm keyword for TI CCS Compiler       */
+  #define __STATIC_INLINE  static inline
+
+#elif defined ( __GNUC__ )
+  #define __ASM            __asm                                      /*!< asm keyword for GNU Compiler          */
+  #define __INLINE         inline                                     /*!< inline keyword for GNU Compiler       */
+  #define __STATIC_INLINE  static inline
+
+#elif defined ( __TASKING__ )
+  #define __ASM            __asm                                      /*!< asm keyword for TASKING Compiler      */
+  #define __INLINE         inline                                     /*!< inline keyword for TASKING Compiler   */
+  #define __STATIC_INLINE  static inline
+
+#endif
+
+/** __FPU_USED indicates whether an FPU is used or not. This core does not support an FPU at all
+*/
+#define __FPU_USED       0
+
+#if defined ( __CC_ARM )
+  #if defined __TARGET_FPU_VFP
+    #warning "Compiler generates FPU instructions for a device without an FPU (check __FPU_PRESENT)"
+  #endif
+
+#elif defined ( __ICCARM__ )
+  #if defined __ARMVFP__
+    #warning "Compiler generates FPU instructions for a device without an FPU (check __FPU_PRESENT)"
+  #endif
+
+#elif defined ( __TMS470__ )
+  #if defined __TI__VFP_SUPPORT____
+    #warning "Compiler generates FPU instructions for a device without an FPU (check __FPU_PRESENT)"
+  #endif
+
+#elif defined ( __GNUC__ )
+  #if defined (__VFP_FP__) && !defined(__SOFTFP__)
+    #warning "Compiler generates FPU instructions for a device without an FPU (check __FPU_PRESENT)"
+  #endif
+
+#elif defined ( __TASKING__ )
+  #if defined __FPU_VFP__
+    #error "Compiler generates FPU instructions for a device without an FPU (check __FPU_PRESENT)"
+  #endif
+#endif
+
+#include                       /* standard types definitions                      */
+#include "core_cmInstr.h"                /* Core Instruction Access                         */
+#include "core_cmFunc.h"                 /* Core Function Access                            */
+
+#endif /* __CORE_CM3_H_GENERIC */
+
+#ifndef __CMSIS_GENERIC
+
+#ifndef __CORE_CM3_H_DEPENDANT
+#define __CORE_CM3_H_DEPENDANT
+
+/* check device defines and use defaults */
+#if defined __CHECK_DEVICE_DEFINES
+  #ifndef __CM3_REV
+    #define __CM3_REV               0x0200
+    #warning "__CM3_REV not defined in device header file; using default!"
+  #endif
+
+  #ifndef __MPU_PRESENT
+    #define __MPU_PRESENT             0
+    #warning "__MPU_PRESENT not defined in device header file; using default!"
+  #endif
+
+  #ifndef __NVIC_PRIO_BITS
+    #define __NVIC_PRIO_BITS          4
+    #warning "__NVIC_PRIO_BITS not defined in device header file; using default!"
+  #endif
+
+  #ifndef __Vendor_SysTickConfig
+    #define __Vendor_SysTickConfig    0
+    #warning "__Vendor_SysTickConfig not defined in device header file; using default!"
+  #endif
+#endif
+
+/* IO definitions (access restrictions to peripheral registers) */
+/**
+    \defgroup CMSIS_glob_defs CMSIS Global Defines
+
+    IO Type Qualifiers are used
+    \li to specify the access to peripheral variables.
+    \li for automatic generation of peripheral register debug information.
+*/
+#ifdef __cplusplus
+  #define   __I     volatile             /*!< Defines 'read only' permissions                 */
+#else
+  #define   __I     volatile const       /*!< Defines 'read only' permissions                 */
+#endif
+#define     __O     volatile             /*!< Defines 'write only' permissions                */
+#define     __IO    volatile             /*!< Defines 'read / write' permissions              */
+
+/*@} end of group Cortex_M3 */
+
+
+
+/*******************************************************************************
+ *                 Register Abstraction
+  Core Register contain:
+  - Core Register
+  - Core NVIC Register
+  - Core SCB Register
+  - Core SysTick Register
+  - Core Debug Register
+  - Core MPU Register
+ ******************************************************************************/
+/** \defgroup CMSIS_core_register Defines and Type Definitions
+    \brief Type definitions and defines for Cortex-M processor based devices.
+*/
+
+/** \ingroup    CMSIS_core_register
+    \defgroup   CMSIS_CORE  Status and Control Registers
+    \brief  Core Register type definitions.
+  @{
+ */
+
+/** \brief  Union type to access the Application Program Status Register (APSR).
+ */
+typedef union
+{
+  struct
+  {
+#if (__CORTEX_M != 0x04)
+    uint32_t _reserved0:27;              /*!< bit:  0..26  Reserved                           */
+#else
+    uint32_t _reserved0:16;              /*!< bit:  0..15  Reserved                           */
+    uint32_t GE:4;                       /*!< bit: 16..19  Greater than or Equal flags        */
+    uint32_t _reserved1:7;               /*!< bit: 20..26  Reserved                           */
+#endif
+    uint32_t Q:1;                        /*!< bit:     27  Saturation condition flag          */
+    uint32_t V:1;                        /*!< bit:     28  Overflow condition code flag       */
+    uint32_t C:1;                        /*!< bit:     29  Carry condition code flag          */
+    uint32_t Z:1;                        /*!< bit:     30  Zero condition code flag           */
+    uint32_t N:1;                        /*!< bit:     31  Negative condition code flag       */
+  } b;                                   /*!< Structure used for bit  access                  */
+  uint32_t w;                            /*!< Type      used for word access                  */
+} APSR_Type;
+
+
+/** \brief  Union type to access the Interrupt Program Status Register (IPSR).
+ */
+typedef union
+{
+  struct
+  {
+    uint32_t ISR:9;                      /*!< bit:  0.. 8  Exception number                   */
+    uint32_t _reserved0:23;              /*!< bit:  9..31  Reserved                           */
+  } b;                                   /*!< Structure used for bit  access                  */
+  uint32_t w;                            /*!< Type      used for word access                  */
+} IPSR_Type;
+
+
+/** \brief  Union type to access the Special-Purpose Program Status Registers (xPSR).
+ */
+typedef union
+{
+  struct
+  {
+    uint32_t ISR:9;                      /*!< bit:  0.. 8  Exception number                   */
+#if (__CORTEX_M != 0x04)
+    uint32_t _reserved0:15;              /*!< bit:  9..23  Reserved                           */
+#else
+    uint32_t _reserved0:7;               /*!< bit:  9..15  Reserved                           */
+    uint32_t GE:4;                       /*!< bit: 16..19  Greater than or Equal flags        */
+    uint32_t _reserved1:4;               /*!< bit: 20..23  Reserved                           */
+#endif
+    uint32_t T:1;                        /*!< bit:     24  Thumb bit        (read 0)          */
+    uint32_t IT:2;                       /*!< bit: 25..26  saved IT state   (read 0)          */
+    uint32_t Q:1;                        /*!< bit:     27  Saturation condition flag          */
+    uint32_t V:1;                        /*!< bit:     28  Overflow condition code flag       */
+    uint32_t C:1;                        /*!< bit:     29  Carry condition code flag          */
+    uint32_t Z:1;                        /*!< bit:     30  Zero condition code flag           */
+    uint32_t N:1;                        /*!< bit:     31  Negative condition code flag       */
+  } b;                                   /*!< Structure used for bit  access                  */
+  uint32_t w;                            /*!< Type      used for word access                  */
+} xPSR_Type;
+
+
+/** \brief  Union type to access the Control Registers (CONTROL).
+ */
+typedef union
+{
+  struct
+  {
+    uint32_t nPRIV:1;                    /*!< bit:      0  Execution privilege in Thread mode */
+    uint32_t SPSEL:1;                    /*!< bit:      1  Stack to be used                   */
+    uint32_t FPCA:1;                     /*!< bit:      2  FP extension active flag           */
+    uint32_t _reserved0:29;              /*!< bit:  3..31  Reserved                           */
+  } b;                                   /*!< Structure used for bit  access                  */
+  uint32_t w;                            /*!< Type      used for word access                  */
+} CONTROL_Type;
+
+/*@} end of group CMSIS_CORE */
+
+
+/** \ingroup    CMSIS_core_register
+    \defgroup   CMSIS_NVIC  Nested Vectored Interrupt Controller (NVIC)
+    \brief      Type definitions for the NVIC Registers
+  @{
+ */
+
+/** \brief  Structure type to access the Nested Vectored Interrupt Controller (NVIC).
+ */
+typedef struct
+{
+  __IO uint32_t ISER[8];                 /*!< Offset: 0x000 (R/W)  Interrupt Set Enable Register           */
+       uint32_t RESERVED0[24];
+  __IO uint32_t ICER[8];                 /*!< Offset: 0x080 (R/W)  Interrupt Clear Enable Register         */
+       uint32_t RSERVED1[24];
+  __IO uint32_t ISPR[8];                 /*!< Offset: 0x100 (R/W)  Interrupt Set Pending Register          */
+       uint32_t RESERVED2[24];
+  __IO uint32_t ICPR[8];                 /*!< Offset: 0x180 (R/W)  Interrupt Clear Pending Register        */
+       uint32_t RESERVED3[24];
+  __IO uint32_t IABR[8];                 /*!< Offset: 0x200 (R/W)  Interrupt Active bit Register           */
+       uint32_t RESERVED4[56];
+  __IO uint8_t  IP[240];                 /*!< Offset: 0x300 (R/W)  Interrupt Priority Register (8Bit wide) */
+       uint32_t RESERVED5[644];
+  __O  uint32_t STIR;                    /*!< Offset: 0xE00 ( /W)  Software Trigger Interrupt Register     */
+}  NVIC_Type;
+
+/* Software Triggered Interrupt Register Definitions */
+#define NVIC_STIR_INTID_Pos                 0                                          /*!< STIR: INTLINESNUM Position */
+#define NVIC_STIR_INTID_Msk                (0x1FFUL << NVIC_STIR_INTID_Pos)            /*!< STIR: INTLINESNUM Mask */
+
+/*@} end of group CMSIS_NVIC */
+
+
+/** \ingroup  CMSIS_core_register
+    \defgroup CMSIS_SCB     System Control Block (SCB)
+    \brief      Type definitions for the System Control Block Registers
+  @{
+ */
+
+/** \brief  Structure type to access the System Control Block (SCB).
+ */
+typedef struct
+{
+  __I  uint32_t CPUID;                   /*!< Offset: 0x000 (R/ )  CPUID Base Register                                   */
+  __IO uint32_t ICSR;                    /*!< Offset: 0x004 (R/W)  Interrupt Control and State Register                  */
+  __IO uint32_t VTOR;                    /*!< Offset: 0x008 (R/W)  Vector Table Offset Register                          */
+  __IO uint32_t AIRCR;                   /*!< Offset: 0x00C (R/W)  Application Interrupt and Reset Control Register      */
+  __IO uint32_t SCR;                     /*!< Offset: 0x010 (R/W)  System Control Register                               */
+  __IO uint32_t CCR;                     /*!< Offset: 0x014 (R/W)  Configuration Control Register                        */
+  __IO uint8_t  SHP[12];                 /*!< Offset: 0x018 (R/W)  System Handlers Priority Registers (4-7, 8-11, 12-15) */
+  __IO uint32_t SHCSR;                   /*!< Offset: 0x024 (R/W)  System Handler Control and State Register             */
+  __IO uint32_t CFSR;                    /*!< Offset: 0x028 (R/W)  Configurable Fault Status Register                    */
+  __IO uint32_t HFSR;                    /*!< Offset: 0x02C (R/W)  HardFault Status Register                             */
+  __IO uint32_t DFSR;                    /*!< Offset: 0x030 (R/W)  Debug Fault Status Register                           */
+  __IO uint32_t MMFAR;                   /*!< Offset: 0x034 (R/W)  MemManage Fault Address Register                      */
+  __IO uint32_t BFAR;                    /*!< Offset: 0x038 (R/W)  BusFault Address Register                             */
+  __IO uint32_t AFSR;                    /*!< Offset: 0x03C (R/W)  Auxiliary Fault Status Register                       */
+  __I  uint32_t PFR[2];                  /*!< Offset: 0x040 (R/ )  Processor Feature Register                            */
+  __I  uint32_t DFR;                     /*!< Offset: 0x048 (R/ )  Debug Feature Register                                */
+  __I  uint32_t ADR;                     /*!< Offset: 0x04C (R/ )  Auxiliary Feature Register                            */
+  __I  uint32_t MMFR[4];                 /*!< Offset: 0x050 (R/ )  Memory Model Feature Register                         */
+  __I  uint32_t ISAR[5];                 /*!< Offset: 0x060 (R/ )  Instruction Set Attributes Register                   */
+       uint32_t RESERVED0[5];
+  __IO uint32_t CPACR;                   /*!< Offset: 0x088 (R/W)  Coprocessor Access Control Register                   */
+} SCB_Type;
+
+/* SCB CPUID Register Definitions */
+#define SCB_CPUID_IMPLEMENTER_Pos          24                                             /*!< SCB CPUID: IMPLEMENTER Position */
+#define SCB_CPUID_IMPLEMENTER_Msk          (0xFFUL << SCB_CPUID_IMPLEMENTER_Pos)          /*!< SCB CPUID: IMPLEMENTER Mask */
+
+#define SCB_CPUID_VARIANT_Pos              20                                             /*!< SCB CPUID: VARIANT Position */
+#define SCB_CPUID_VARIANT_Msk              (0xFUL << SCB_CPUID_VARIANT_Pos)               /*!< SCB CPUID: VARIANT Mask */
+
+#define SCB_CPUID_ARCHITECTURE_Pos         16                                             /*!< SCB CPUID: ARCHITECTURE Position */
+#define SCB_CPUID_ARCHITECTURE_Msk         (0xFUL << SCB_CPUID_ARCHITECTURE_Pos)          /*!< SCB CPUID: ARCHITECTURE Mask */
+
+#define SCB_CPUID_PARTNO_Pos                4                                             /*!< SCB CPUID: PARTNO Position */
+#define SCB_CPUID_PARTNO_Msk               (0xFFFUL << SCB_CPUID_PARTNO_Pos)              /*!< SCB CPUID: PARTNO Mask */
+
+#define SCB_CPUID_REVISION_Pos              0                                             /*!< SCB CPUID: REVISION Position */
+#define SCB_CPUID_REVISION_Msk             (0xFUL << SCB_CPUID_REVISION_Pos)              /*!< SCB CPUID: REVISION Mask */
+
+/* SCB Interrupt Control State Register Definitions */
+#define SCB_ICSR_NMIPENDSET_Pos            31                                             /*!< SCB ICSR: NMIPENDSET Position */
+#define SCB_ICSR_NMIPENDSET_Msk            (1UL << SCB_ICSR_NMIPENDSET_Pos)               /*!< SCB ICSR: NMIPENDSET Mask */
+
+#define SCB_ICSR_PENDSVSET_Pos             28                                             /*!< SCB ICSR: PENDSVSET Position */
+#define SCB_ICSR_PENDSVSET_Msk             (1UL << SCB_ICSR_PENDSVSET_Pos)                /*!< SCB ICSR: PENDSVSET Mask */
+
+#define SCB_ICSR_PENDSVCLR_Pos             27                                             /*!< SCB ICSR: PENDSVCLR Position */
+#define SCB_ICSR_PENDSVCLR_Msk             (1UL << SCB_ICSR_PENDSVCLR_Pos)                /*!< SCB ICSR: PENDSVCLR Mask */
+
+#define SCB_ICSR_PENDSTSET_Pos             26                                             /*!< SCB ICSR: PENDSTSET Position */
+#define SCB_ICSR_PENDSTSET_Msk             (1UL << SCB_ICSR_PENDSTSET_Pos)                /*!< SCB ICSR: PENDSTSET Mask */
+
+#define SCB_ICSR_PENDSTCLR_Pos             25                                             /*!< SCB ICSR: PENDSTCLR Position */
+#define SCB_ICSR_PENDSTCLR_Msk             (1UL << SCB_ICSR_PENDSTCLR_Pos)                /*!< SCB ICSR: PENDSTCLR Mask */
+
+#define SCB_ICSR_ISRPREEMPT_Pos            23                                             /*!< SCB ICSR: ISRPREEMPT Position */
+#define SCB_ICSR_ISRPREEMPT_Msk            (1UL << SCB_ICSR_ISRPREEMPT_Pos)               /*!< SCB ICSR: ISRPREEMPT Mask */
+
+#define SCB_ICSR_ISRPENDING_Pos            22                                             /*!< SCB ICSR: ISRPENDING Position */
+#define SCB_ICSR_ISRPENDING_Msk            (1UL << SCB_ICSR_ISRPENDING_Pos)               /*!< SCB ICSR: ISRPENDING Mask */
+
+#define SCB_ICSR_VECTPENDING_Pos           12                                             /*!< SCB ICSR: VECTPENDING Position */
+#define SCB_ICSR_VECTPENDING_Msk           (0x1FFUL << SCB_ICSR_VECTPENDING_Pos)          /*!< SCB ICSR: VECTPENDING Mask */
+
+#define SCB_ICSR_RETTOBASE_Pos             11                                             /*!< SCB ICSR: RETTOBASE Position */
+#define SCB_ICSR_RETTOBASE_Msk             (1UL << SCB_ICSR_RETTOBASE_Pos)                /*!< SCB ICSR: RETTOBASE Mask */
+
+#define SCB_ICSR_VECTACTIVE_Pos             0                                             /*!< SCB ICSR: VECTACTIVE Position */
+#define SCB_ICSR_VECTACTIVE_Msk            (0x1FFUL << SCB_ICSR_VECTACTIVE_Pos)           /*!< SCB ICSR: VECTACTIVE Mask */
+
+/* SCB Vector Table Offset Register Definitions */
+#if (__CM3_REV < 0x0201)                   /* core r2p1 */
+#define SCB_VTOR_TBLBASE_Pos               29                                             /*!< SCB VTOR: TBLBASE Position */
+#define SCB_VTOR_TBLBASE_Msk               (1UL << SCB_VTOR_TBLBASE_Pos)                  /*!< SCB VTOR: TBLBASE Mask */
+
+#define SCB_VTOR_TBLOFF_Pos                 7                                             /*!< SCB VTOR: TBLOFF Position */
+#define SCB_VTOR_TBLOFF_Msk                (0x3FFFFFUL << SCB_VTOR_TBLOFF_Pos)            /*!< SCB VTOR: TBLOFF Mask */
+#else
+#define SCB_VTOR_TBLOFF_Pos                 7                                             /*!< SCB VTOR: TBLOFF Position */
+#define SCB_VTOR_TBLOFF_Msk                (0x1FFFFFFUL << SCB_VTOR_TBLOFF_Pos)           /*!< SCB VTOR: TBLOFF Mask */
+#endif
+
+/* SCB Application Interrupt and Reset Control Register Definitions */
+#define SCB_AIRCR_VECTKEY_Pos              16                                             /*!< SCB AIRCR: VECTKEY Position */
+#define SCB_AIRCR_VECTKEY_Msk              (0xFFFFUL << SCB_AIRCR_VECTKEY_Pos)            /*!< SCB AIRCR: VECTKEY Mask */
+
+#define SCB_AIRCR_VECTKEYSTAT_Pos          16                                             /*!< SCB AIRCR: VECTKEYSTAT Position */
+#define SCB_AIRCR_VECTKEYSTAT_Msk          (0xFFFFUL << SCB_AIRCR_VECTKEYSTAT_Pos)        /*!< SCB AIRCR: VECTKEYSTAT Mask */
+
+#define SCB_AIRCR_ENDIANESS_Pos            15                                             /*!< SCB AIRCR: ENDIANESS Position */
+#define SCB_AIRCR_ENDIANESS_Msk            (1UL << SCB_AIRCR_ENDIANESS_Pos)               /*!< SCB AIRCR: ENDIANESS Mask */
+
+#define SCB_AIRCR_PRIGROUP_Pos              8                                             /*!< SCB AIRCR: PRIGROUP Position */
+#define SCB_AIRCR_PRIGROUP_Msk             (7UL << SCB_AIRCR_PRIGROUP_Pos)                /*!< SCB AIRCR: PRIGROUP Mask */
+
+#define SCB_AIRCR_SYSRESETREQ_Pos           2                                             /*!< SCB AIRCR: SYSRESETREQ Position */
+#define SCB_AIRCR_SYSRESETREQ_Msk          (1UL << SCB_AIRCR_SYSRESETREQ_Pos)             /*!< SCB AIRCR: SYSRESETREQ Mask */
+
+#define SCB_AIRCR_VECTCLRACTIVE_Pos         1                                             /*!< SCB AIRCR: VECTCLRACTIVE Position */
+#define SCB_AIRCR_VECTCLRACTIVE_Msk        (1UL << SCB_AIRCR_VECTCLRACTIVE_Pos)           /*!< SCB AIRCR: VECTCLRACTIVE Mask */
+
+#define SCB_AIRCR_VECTRESET_Pos             0                                             /*!< SCB AIRCR: VECTRESET Position */
+#define SCB_AIRCR_VECTRESET_Msk            (1UL << SCB_AIRCR_VECTRESET_Pos)               /*!< SCB AIRCR: VECTRESET Mask */
+
+/* SCB System Control Register Definitions */
+#define SCB_SCR_SEVONPEND_Pos               4                                             /*!< SCB SCR: SEVONPEND Position */
+#define SCB_SCR_SEVONPEND_Msk              (1UL << SCB_SCR_SEVONPEND_Pos)                 /*!< SCB SCR: SEVONPEND Mask */
+
+#define SCB_SCR_SLEEPDEEP_Pos               2                                             /*!< SCB SCR: SLEEPDEEP Position */
+#define SCB_SCR_SLEEPDEEP_Msk              (1UL << SCB_SCR_SLEEPDEEP_Pos)                 /*!< SCB SCR: SLEEPDEEP Mask */
+
+#define SCB_SCR_SLEEPONEXIT_Pos             1                                             /*!< SCB SCR: SLEEPONEXIT Position */
+#define SCB_SCR_SLEEPONEXIT_Msk            (1UL << SCB_SCR_SLEEPONEXIT_Pos)               /*!< SCB SCR: SLEEPONEXIT Mask */
+
+/* SCB Configuration Control Register Definitions */
+#define SCB_CCR_STKALIGN_Pos                9                                             /*!< SCB CCR: STKALIGN Position */
+#define SCB_CCR_STKALIGN_Msk               (1UL << SCB_CCR_STKALIGN_Pos)                  /*!< SCB CCR: STKALIGN Mask */
+
+#define SCB_CCR_BFHFNMIGN_Pos               8                                             /*!< SCB CCR: BFHFNMIGN Position */
+#define SCB_CCR_BFHFNMIGN_Msk              (1UL << SCB_CCR_BFHFNMIGN_Pos)                 /*!< SCB CCR: BFHFNMIGN Mask */
+
+#define SCB_CCR_DIV_0_TRP_Pos               4                                             /*!< SCB CCR: DIV_0_TRP Position */
+#define SCB_CCR_DIV_0_TRP_Msk              (1UL << SCB_CCR_DIV_0_TRP_Pos)                 /*!< SCB CCR: DIV_0_TRP Mask */
+
+#define SCB_CCR_UNALIGN_TRP_Pos             3                                             /*!< SCB CCR: UNALIGN_TRP Position */
+#define SCB_CCR_UNALIGN_TRP_Msk            (1UL << SCB_CCR_UNALIGN_TRP_Pos)               /*!< SCB CCR: UNALIGN_TRP Mask */
+
+#define SCB_CCR_USERSETMPEND_Pos            1                                             /*!< SCB CCR: USERSETMPEND Position */
+#define SCB_CCR_USERSETMPEND_Msk           (1UL << SCB_CCR_USERSETMPEND_Pos)              /*!< SCB CCR: USERSETMPEND Mask */
+
+#define SCB_CCR_NONBASETHRDENA_Pos          0                                             /*!< SCB CCR: NONBASETHRDENA Position */
+#define SCB_CCR_NONBASETHRDENA_Msk         (1UL << SCB_CCR_NONBASETHRDENA_Pos)            /*!< SCB CCR: NONBASETHRDENA Mask */
+
+/* SCB System Handler Control and State Register Definitions */
+#define SCB_SHCSR_USGFAULTENA_Pos          18                                             /*!< SCB SHCSR: USGFAULTENA Position */
+#define SCB_SHCSR_USGFAULTENA_Msk          (1UL << SCB_SHCSR_USGFAULTENA_Pos)             /*!< SCB SHCSR: USGFAULTENA Mask */
+
+#define SCB_SHCSR_BUSFAULTENA_Pos          17                                             /*!< SCB SHCSR: BUSFAULTENA Position */
+#define SCB_SHCSR_BUSFAULTENA_Msk          (1UL << SCB_SHCSR_BUSFAULTENA_Pos)             /*!< SCB SHCSR: BUSFAULTENA Mask */
+
+#define SCB_SHCSR_MEMFAULTENA_Pos          16                                             /*!< SCB SHCSR: MEMFAULTENA Position */
+#define SCB_SHCSR_MEMFAULTENA_Msk          (1UL << SCB_SHCSR_MEMFAULTENA_Pos)             /*!< SCB SHCSR: MEMFAULTENA Mask */
+
+#define SCB_SHCSR_SVCALLPENDED_Pos         15                                             /*!< SCB SHCSR: SVCALLPENDED Position */
+#define SCB_SHCSR_SVCALLPENDED_Msk         (1UL << SCB_SHCSR_SVCALLPENDED_Pos)            /*!< SCB SHCSR: SVCALLPENDED Mask */
+
+#define SCB_SHCSR_BUSFAULTPENDED_Pos       14                                             /*!< SCB SHCSR: BUSFAULTPENDED Position */
+#define SCB_SHCSR_BUSFAULTPENDED_Msk       (1UL << SCB_SHCSR_BUSFAULTPENDED_Pos)          /*!< SCB SHCSR: BUSFAULTPENDED Mask */
+
+#define SCB_SHCSR_MEMFAULTPENDED_Pos       13                                             /*!< SCB SHCSR: MEMFAULTPENDED Position */
+#define SCB_SHCSR_MEMFAULTPENDED_Msk       (1UL << SCB_SHCSR_MEMFAULTPENDED_Pos)          /*!< SCB SHCSR: MEMFAULTPENDED Mask */
+
+#define SCB_SHCSR_USGFAULTPENDED_Pos       12                                             /*!< SCB SHCSR: USGFAULTPENDED Position */
+#define SCB_SHCSR_USGFAULTPENDED_Msk       (1UL << SCB_SHCSR_USGFAULTPENDED_Pos)          /*!< SCB SHCSR: USGFAULTPENDED Mask */
+
+#define SCB_SHCSR_SYSTICKACT_Pos           11                                             /*!< SCB SHCSR: SYSTICKACT Position */
+#define SCB_SHCSR_SYSTICKACT_Msk           (1UL << SCB_SHCSR_SYSTICKACT_Pos)              /*!< SCB SHCSR: SYSTICKACT Mask */
+
+#define SCB_SHCSR_PENDSVACT_Pos            10                                             /*!< SCB SHCSR: PENDSVACT Position */
+#define SCB_SHCSR_PENDSVACT_Msk            (1UL << SCB_SHCSR_PENDSVACT_Pos)               /*!< SCB SHCSR: PENDSVACT Mask */
+
+#define SCB_SHCSR_MONITORACT_Pos            8                                             /*!< SCB SHCSR: MONITORACT Position */
+#define SCB_SHCSR_MONITORACT_Msk           (1UL << SCB_SHCSR_MONITORACT_Pos)              /*!< SCB SHCSR: MONITORACT Mask */
+
+#define SCB_SHCSR_SVCALLACT_Pos             7                                             /*!< SCB SHCSR: SVCALLACT Position */
+#define SCB_SHCSR_SVCALLACT_Msk            (1UL << SCB_SHCSR_SVCALLACT_Pos)               /*!< SCB SHCSR: SVCALLACT Mask */
+
+#define SCB_SHCSR_USGFAULTACT_Pos           3                                             /*!< SCB SHCSR: USGFAULTACT Position */
+#define SCB_SHCSR_USGFAULTACT_Msk          (1UL << SCB_SHCSR_USGFAULTACT_Pos)             /*!< SCB SHCSR: USGFAULTACT Mask */
+
+#define SCB_SHCSR_BUSFAULTACT_Pos           1                                             /*!< SCB SHCSR: BUSFAULTACT Position */
+#define SCB_SHCSR_BUSFAULTACT_Msk          (1UL << SCB_SHCSR_BUSFAULTACT_Pos)             /*!< SCB SHCSR: BUSFAULTACT Mask */
+
+#define SCB_SHCSR_MEMFAULTACT_Pos           0                                             /*!< SCB SHCSR: MEMFAULTACT Position */
+#define SCB_SHCSR_MEMFAULTACT_Msk          (1UL << SCB_SHCSR_MEMFAULTACT_Pos)             /*!< SCB SHCSR: MEMFAULTACT Mask */
+
+/* SCB Configurable Fault Status Registers Definitions */
+#define SCB_CFSR_USGFAULTSR_Pos            16                                             /*!< SCB CFSR: Usage Fault Status Register Position */
+#define SCB_CFSR_USGFAULTSR_Msk            (0xFFFFUL << SCB_CFSR_USGFAULTSR_Pos)          /*!< SCB CFSR: Usage Fault Status Register Mask */
+
+#define SCB_CFSR_BUSFAULTSR_Pos             8                                             /*!< SCB CFSR: Bus Fault Status Register Position */
+#define SCB_CFSR_BUSFAULTSR_Msk            (0xFFUL << SCB_CFSR_BUSFAULTSR_Pos)            /*!< SCB CFSR: Bus Fault Status Register Mask */
+
+#define SCB_CFSR_MEMFAULTSR_Pos             0                                             /*!< SCB CFSR: Memory Manage Fault Status Register Position */
+#define SCB_CFSR_MEMFAULTSR_Msk            (0xFFUL << SCB_CFSR_MEMFAULTSR_Pos)            /*!< SCB CFSR: Memory Manage Fault Status Register Mask */
+
+/* SCB Hard Fault Status Registers Definitions */
+#define SCB_HFSR_DEBUGEVT_Pos              31                                             /*!< SCB HFSR: DEBUGEVT Position */
+#define SCB_HFSR_DEBUGEVT_Msk              (1UL << SCB_HFSR_DEBUGEVT_Pos)                 /*!< SCB HFSR: DEBUGEVT Mask */
+
+#define SCB_HFSR_FORCED_Pos                30                                             /*!< SCB HFSR: FORCED Position */
+#define SCB_HFSR_FORCED_Msk                (1UL << SCB_HFSR_FORCED_Pos)                   /*!< SCB HFSR: FORCED Mask */
+
+#define SCB_HFSR_VECTTBL_Pos                1                                             /*!< SCB HFSR: VECTTBL Position */
+#define SCB_HFSR_VECTTBL_Msk               (1UL << SCB_HFSR_VECTTBL_Pos)                  /*!< SCB HFSR: VECTTBL Mask */
+
+/* SCB Debug Fault Status Register Definitions */
+#define SCB_DFSR_EXTERNAL_Pos               4                                             /*!< SCB DFSR: EXTERNAL Position */
+#define SCB_DFSR_EXTERNAL_Msk              (1UL << SCB_DFSR_EXTERNAL_Pos)                 /*!< SCB DFSR: EXTERNAL Mask */
+
+#define SCB_DFSR_VCATCH_Pos                 3                                             /*!< SCB DFSR: VCATCH Position */
+#define SCB_DFSR_VCATCH_Msk                (1UL << SCB_DFSR_VCATCH_Pos)                   /*!< SCB DFSR: VCATCH Mask */
+
+#define SCB_DFSR_DWTTRAP_Pos                2                                             /*!< SCB DFSR: DWTTRAP Position */
+#define SCB_DFSR_DWTTRAP_Msk               (1UL << SCB_DFSR_DWTTRAP_Pos)                  /*!< SCB DFSR: DWTTRAP Mask */
+
+#define SCB_DFSR_BKPT_Pos                   1                                             /*!< SCB DFSR: BKPT Position */
+#define SCB_DFSR_BKPT_Msk                  (1UL << SCB_DFSR_BKPT_Pos)                     /*!< SCB DFSR: BKPT Mask */
+
+#define SCB_DFSR_HALTED_Pos                 0                                             /*!< SCB DFSR: HALTED Position */
+#define SCB_DFSR_HALTED_Msk                (1UL << SCB_DFSR_HALTED_Pos)                   /*!< SCB DFSR: HALTED Mask */
+
+/*@} end of group CMSIS_SCB */
+
+
+/** \ingroup  CMSIS_core_register
+    \defgroup CMSIS_SCnSCB System Controls not in SCB (SCnSCB)
+    \brief      Type definitions for the System Control and ID Register not in the SCB
+  @{
+ */
+
+/** \brief  Structure type to access the System Control and ID Register not in the SCB.
+ */
+typedef struct
+{
+       uint32_t RESERVED0[1];
+  __I  uint32_t ICTR;                    /*!< Offset: 0x004 (R/ )  Interrupt Controller Type Register      */
+#if ((defined __CM3_REV) && (__CM3_REV >= 0x200))
+  __IO uint32_t ACTLR;                   /*!< Offset: 0x008 (R/W)  Auxiliary Control Register      */
+#else
+       uint32_t RESERVED1[1];
+#endif
+} SCnSCB_Type;
+
+/* Interrupt Controller Type Register Definitions */
+#define SCnSCB_ICTR_INTLINESNUM_Pos         0                                          /*!< ICTR: INTLINESNUM Position */
+#define SCnSCB_ICTR_INTLINESNUM_Msk        (0xFUL << SCnSCB_ICTR_INTLINESNUM_Pos)      /*!< ICTR: INTLINESNUM Mask */
+
+/* Auxiliary Control Register Definitions */
+
+#define SCnSCB_ACTLR_DISFOLD_Pos            2                                          /*!< ACTLR: DISFOLD Position */
+#define SCnSCB_ACTLR_DISFOLD_Msk           (1UL << SCnSCB_ACTLR_DISFOLD_Pos)           /*!< ACTLR: DISFOLD Mask */
+
+#define SCnSCB_ACTLR_DISDEFWBUF_Pos         1                                          /*!< ACTLR: DISDEFWBUF Position */
+#define SCnSCB_ACTLR_DISDEFWBUF_Msk        (1UL << SCnSCB_ACTLR_DISDEFWBUF_Pos)        /*!< ACTLR: DISDEFWBUF Mask */
+
+#define SCnSCB_ACTLR_DISMCYCINT_Pos         0                                          /*!< ACTLR: DISMCYCINT Position */
+#define SCnSCB_ACTLR_DISMCYCINT_Msk        (1UL << SCnSCB_ACTLR_DISMCYCINT_Pos)        /*!< ACTLR: DISMCYCINT Mask */
+
+/*@} end of group CMSIS_SCnotSCB */
+
+
+/** \ingroup  CMSIS_core_register
+    \defgroup CMSIS_SysTick     System Tick Timer (SysTick)
+    \brief      Type definitions for the System Timer Registers.
+  @{
+ */
+
+/** \brief  Structure type to access the System Timer (SysTick).
+ */
+typedef struct
+{
+  __IO uint32_t CTRL;                    /*!< Offset: 0x000 (R/W)  SysTick Control and Status Register */
+  __IO uint32_t LOAD;                    /*!< Offset: 0x004 (R/W)  SysTick Reload Value Register       */
+  __IO uint32_t VAL;                     /*!< Offset: 0x008 (R/W)  SysTick Current Value Register      */
+  __I  uint32_t CALIB;                   /*!< Offset: 0x00C (R/ )  SysTick Calibration Register        */
+} SysTick_Type;
+
+/* SysTick Control / Status Register Definitions */
+#define SysTick_CTRL_COUNTFLAG_Pos         16                                             /*!< SysTick CTRL: COUNTFLAG Position */
+#define SysTick_CTRL_COUNTFLAG_Msk         (1UL << SysTick_CTRL_COUNTFLAG_Pos)            /*!< SysTick CTRL: COUNTFLAG Mask */
+
+#define SysTick_CTRL_CLKSOURCE_Pos          2                                             /*!< SysTick CTRL: CLKSOURCE Position */
+#define SysTick_CTRL_CLKSOURCE_Msk         (1UL << SysTick_CTRL_CLKSOURCE_Pos)            /*!< SysTick CTRL: CLKSOURCE Mask */
+
+#define SysTick_CTRL_TICKINT_Pos            1                                             /*!< SysTick CTRL: TICKINT Position */
+#define SysTick_CTRL_TICKINT_Msk           (1UL << SysTick_CTRL_TICKINT_Pos)              /*!< SysTick CTRL: TICKINT Mask */
+
+#define SysTick_CTRL_ENABLE_Pos             0                                             /*!< SysTick CTRL: ENABLE Position */
+#define SysTick_CTRL_ENABLE_Msk            (1UL << SysTick_CTRL_ENABLE_Pos)               /*!< SysTick CTRL: ENABLE Mask */
+
+/* SysTick Reload Register Definitions */
+#define SysTick_LOAD_RELOAD_Pos             0                                             /*!< SysTick LOAD: RELOAD Position */
+#define SysTick_LOAD_RELOAD_Msk            (0xFFFFFFUL << SysTick_LOAD_RELOAD_Pos)        /*!< SysTick LOAD: RELOAD Mask */
+
+/* SysTick Current Register Definitions */
+#define SysTick_VAL_CURRENT_Pos             0                                             /*!< SysTick VAL: CURRENT Position */
+#define SysTick_VAL_CURRENT_Msk            (0xFFFFFFUL << SysTick_VAL_CURRENT_Pos)        /*!< SysTick VAL: CURRENT Mask */
+
+/* SysTick Calibration Register Definitions */
+#define SysTick_CALIB_NOREF_Pos            31                                             /*!< SysTick CALIB: NOREF Position */
+#define SysTick_CALIB_NOREF_Msk            (1UL << SysTick_CALIB_NOREF_Pos)               /*!< SysTick CALIB: NOREF Mask */
+
+#define SysTick_CALIB_SKEW_Pos             30                                             /*!< SysTick CALIB: SKEW Position */
+#define SysTick_CALIB_SKEW_Msk             (1UL << SysTick_CALIB_SKEW_Pos)                /*!< SysTick CALIB: SKEW Mask */
+
+#define SysTick_CALIB_TENMS_Pos             0                                             /*!< SysTick CALIB: TENMS Position */
+#define SysTick_CALIB_TENMS_Msk            (0xFFFFFFUL << SysTick_VAL_CURRENT_Pos)        /*!< SysTick CALIB: TENMS Mask */
+
+/*@} end of group CMSIS_SysTick */
+
+
+/** \ingroup  CMSIS_core_register
+    \defgroup CMSIS_ITM     Instrumentation Trace Macrocell (ITM)
+    \brief      Type definitions for the Instrumentation Trace Macrocell (ITM)
+  @{
+ */
+
+/** \brief  Structure type to access the Instrumentation Trace Macrocell Register (ITM).
+ */
+typedef struct
+{
+  __O  union
+  {
+    __O  uint8_t    u8;                  /*!< Offset: 0x000 ( /W)  ITM Stimulus Port 8-bit                   */
+    __O  uint16_t   u16;                 /*!< Offset: 0x000 ( /W)  ITM Stimulus Port 16-bit                  */
+    __O  uint32_t   u32;                 /*!< Offset: 0x000 ( /W)  ITM Stimulus Port 32-bit                  */
+  }  PORT [32];                          /*!< Offset: 0x000 ( /W)  ITM Stimulus Port Registers               */
+       uint32_t RESERVED0[864];
+  __IO uint32_t TER;                     /*!< Offset: 0xE00 (R/W)  ITM Trace Enable Register                 */
+       uint32_t RESERVED1[15];
+  __IO uint32_t TPR;                     /*!< Offset: 0xE40 (R/W)  ITM Trace Privilege Register              */
+       uint32_t RESERVED2[15];
+  __IO uint32_t TCR;                     /*!< Offset: 0xE80 (R/W)  ITM Trace Control Register                */
+       uint32_t RESERVED3[29];                                  
+  __O  uint32_t IWR;                     /*!< Offset: 0xEF8 ( /W)  ITM Integration Write Register            */
+  __I  uint32_t IRR;                     /*!< Offset: 0xEFC (R/ )  ITM Integration Read Register             */
+  __IO uint32_t IMCR;                    /*!< Offset: 0xF00 (R/W)  ITM Integration Mode Control Register     */
+       uint32_t RESERVED4[43];                                  
+  __O  uint32_t LAR;                     /*!< Offset: 0xFB0 ( /W)  ITM Lock Access Register                  */
+  __I  uint32_t LSR;                     /*!< Offset: 0xFB4 (R/ )  ITM Lock Status Register                  */
+       uint32_t RESERVED5[6];                                   
+  __I  uint32_t PID4;                    /*!< Offset: 0xFD0 (R/ )  ITM Peripheral Identification Register #4 */
+  __I  uint32_t PID5;                    /*!< Offset: 0xFD4 (R/ )  ITM Peripheral Identification Register #5 */
+  __I  uint32_t PID6;                    /*!< Offset: 0xFD8 (R/ )  ITM Peripheral Identification Register #6 */
+  __I  uint32_t PID7;                    /*!< Offset: 0xFDC (R/ )  ITM Peripheral Identification Register #7 */
+  __I  uint32_t PID0;                    /*!< Offset: 0xFE0 (R/ )  ITM Peripheral Identification Register #0 */
+  __I  uint32_t PID1;                    /*!< Offset: 0xFE4 (R/ )  ITM Peripheral Identification Register #1 */
+  __I  uint32_t PID2;                    /*!< Offset: 0xFE8 (R/ )  ITM Peripheral Identification Register #2 */
+  __I  uint32_t PID3;                    /*!< Offset: 0xFEC (R/ )  ITM Peripheral Identification Register #3 */
+  __I  uint32_t CID0;                    /*!< Offset: 0xFF0 (R/ )  ITM Component  Identification Register #0 */
+  __I  uint32_t CID1;                    /*!< Offset: 0xFF4 (R/ )  ITM Component  Identification Register #1 */
+  __I  uint32_t CID2;                    /*!< Offset: 0xFF8 (R/ )  ITM Component  Identification Register #2 */
+  __I  uint32_t CID3;                    /*!< Offset: 0xFFC (R/ )  ITM Component  Identification Register #3 */
+} ITM_Type;
+
+/* ITM Trace Privilege Register Definitions */
+#define ITM_TPR_PRIVMASK_Pos                0                                             /*!< ITM TPR: PRIVMASK Position */
+#define ITM_TPR_PRIVMASK_Msk               (0xFUL << ITM_TPR_PRIVMASK_Pos)                /*!< ITM TPR: PRIVMASK Mask */
+
+/* ITM Trace Control Register Definitions */
+#define ITM_TCR_BUSY_Pos                   23                                             /*!< ITM TCR: BUSY Position */
+#define ITM_TCR_BUSY_Msk                   (1UL << ITM_TCR_BUSY_Pos)                      /*!< ITM TCR: BUSY Mask */
+
+#define ITM_TCR_TraceBusID_Pos             16                                             /*!< ITM TCR: ATBID Position */
+#define ITM_TCR_TraceBusID_Msk             (0x7FUL << ITM_TCR_TraceBusID_Pos)             /*!< ITM TCR: ATBID Mask */
+
+#define ITM_TCR_GTSFREQ_Pos                10                                             /*!< ITM TCR: Global timestamp frequency Position */
+#define ITM_TCR_GTSFREQ_Msk                (3UL << ITM_TCR_GTSFREQ_Pos)                   /*!< ITM TCR: Global timestamp frequency Mask */
+
+#define ITM_TCR_TSPrescale_Pos              8                                             /*!< ITM TCR: TSPrescale Position */
+#define ITM_TCR_TSPrescale_Msk             (3UL << ITM_TCR_TSPrescale_Pos)                /*!< ITM TCR: TSPrescale Mask */
+
+#define ITM_TCR_SWOENA_Pos                  4                                             /*!< ITM TCR: SWOENA Position */
+#define ITM_TCR_SWOENA_Msk                 (1UL << ITM_TCR_SWOENA_Pos)                    /*!< ITM TCR: SWOENA Mask */
+
+#define ITM_TCR_DWTENA_Pos                  3                                             /*!< ITM TCR: DWTENA Position */
+#define ITM_TCR_DWTENA_Msk                 (1UL << ITM_TCR_DWTENA_Pos)                    /*!< ITM TCR: DWTENA Mask */
+
+#define ITM_TCR_SYNCENA_Pos                 2                                             /*!< ITM TCR: SYNCENA Position */
+#define ITM_TCR_SYNCENA_Msk                (1UL << ITM_TCR_SYNCENA_Pos)                   /*!< ITM TCR: SYNCENA Mask */
+
+#define ITM_TCR_TSENA_Pos                   1                                             /*!< ITM TCR: TSENA Position */
+#define ITM_TCR_TSENA_Msk                  (1UL << ITM_TCR_TSENA_Pos)                     /*!< ITM TCR: TSENA Mask */
+
+#define ITM_TCR_ITMENA_Pos                  0                                             /*!< ITM TCR: ITM Enable bit Position */
+#define ITM_TCR_ITMENA_Msk                 (1UL << ITM_TCR_ITMENA_Pos)                    /*!< ITM TCR: ITM Enable bit Mask */
+
+/* ITM Integration Write Register Definitions */
+#define ITM_IWR_ATVALIDM_Pos                0                                             /*!< ITM IWR: ATVALIDM Position */
+#define ITM_IWR_ATVALIDM_Msk               (1UL << ITM_IWR_ATVALIDM_Pos)                  /*!< ITM IWR: ATVALIDM Mask */
+
+/* ITM Integration Read Register Definitions */
+#define ITM_IRR_ATREADYM_Pos                0                                             /*!< ITM IRR: ATREADYM Position */
+#define ITM_IRR_ATREADYM_Msk               (1UL << ITM_IRR_ATREADYM_Pos)                  /*!< ITM IRR: ATREADYM Mask */
+
+/* ITM Integration Mode Control Register Definitions */
+#define ITM_IMCR_INTEGRATION_Pos            0                                             /*!< ITM IMCR: INTEGRATION Position */
+#define ITM_IMCR_INTEGRATION_Msk           (1UL << ITM_IMCR_INTEGRATION_Pos)              /*!< ITM IMCR: INTEGRATION Mask */
+
+/* ITM Lock Status Register Definitions */
+#define ITM_LSR_ByteAcc_Pos                 2                                             /*!< ITM LSR: ByteAcc Position */
+#define ITM_LSR_ByteAcc_Msk                (1UL << ITM_LSR_ByteAcc_Pos)                   /*!< ITM LSR: ByteAcc Mask */
+
+#define ITM_LSR_Access_Pos                  1                                             /*!< ITM LSR: Access Position */
+#define ITM_LSR_Access_Msk                 (1UL << ITM_LSR_Access_Pos)                    /*!< ITM LSR: Access Mask */
+
+#define ITM_LSR_Present_Pos                 0                                             /*!< ITM LSR: Present Position */
+#define ITM_LSR_Present_Msk                (1UL << ITM_LSR_Present_Pos)                   /*!< ITM LSR: Present Mask */
+
+/*@}*/ /* end of group CMSIS_ITM */
+
+
+/** \ingroup  CMSIS_core_register
+    \defgroup CMSIS_DWT     Data Watchpoint and Trace (DWT)
+    \brief      Type definitions for the Data Watchpoint and Trace (DWT)
+  @{
+ */
+
+/** \brief  Structure type to access the Data Watchpoint and Trace Register (DWT).
+ */
+typedef struct
+{
+  __IO uint32_t CTRL;                    /*!< Offset: 0x000 (R/W)  Control Register                          */
+  __IO uint32_t CYCCNT;                  /*!< Offset: 0x004 (R/W)  Cycle Count Register                      */
+  __IO uint32_t CPICNT;                  /*!< Offset: 0x008 (R/W)  CPI Count Register                        */
+  __IO uint32_t EXCCNT;                  /*!< Offset: 0x00C (R/W)  Exception Overhead Count Register         */
+  __IO uint32_t SLEEPCNT;                /*!< Offset: 0x010 (R/W)  Sleep Count Register                      */
+  __IO uint32_t LSUCNT;                  /*!< Offset: 0x014 (R/W)  LSU Count Register                        */
+  __IO uint32_t FOLDCNT;                 /*!< Offset: 0x018 (R/W)  Folded-instruction Count Register         */
+  __I  uint32_t PCSR;                    /*!< Offset: 0x01C (R/ )  Program Counter Sample Register           */
+  __IO uint32_t COMP0;                   /*!< Offset: 0x020 (R/W)  Comparator Register 0                     */
+  __IO uint32_t MASK0;                   /*!< Offset: 0x024 (R/W)  Mask Register 0                           */
+  __IO uint32_t FUNCTION0;               /*!< Offset: 0x028 (R/W)  Function Register 0                       */
+       uint32_t RESERVED0[1];
+  __IO uint32_t COMP1;                   /*!< Offset: 0x030 (R/W)  Comparator Register 1                     */
+  __IO uint32_t MASK1;                   /*!< Offset: 0x034 (R/W)  Mask Register 1                           */
+  __IO uint32_t FUNCTION1;               /*!< Offset: 0x038 (R/W)  Function Register 1                       */
+       uint32_t RESERVED1[1];
+  __IO uint32_t COMP2;                   /*!< Offset: 0x040 (R/W)  Comparator Register 2                     */
+  __IO uint32_t MASK2;                   /*!< Offset: 0x044 (R/W)  Mask Register 2                           */
+  __IO uint32_t FUNCTION2;               /*!< Offset: 0x048 (R/W)  Function Register 2                       */
+       uint32_t RESERVED2[1];
+  __IO uint32_t COMP3;                   /*!< Offset: 0x050 (R/W)  Comparator Register 3                     */
+  __IO uint32_t MASK3;                   /*!< Offset: 0x054 (R/W)  Mask Register 3                           */
+  __IO uint32_t FUNCTION3;               /*!< Offset: 0x058 (R/W)  Function Register 3                       */
+} DWT_Type;
+
+/* DWT Control Register Definitions */
+#define DWT_CTRL_NUMCOMP_Pos               28                                          /*!< DWT CTRL: NUMCOMP Position */
+#define DWT_CTRL_NUMCOMP_Msk               (0xFUL << DWT_CTRL_NUMCOMP_Pos)             /*!< DWT CTRL: NUMCOMP Mask */
+
+#define DWT_CTRL_NOTRCPKT_Pos              27                                          /*!< DWT CTRL: NOTRCPKT Position */
+#define DWT_CTRL_NOTRCPKT_Msk              (0x1UL << DWT_CTRL_NOTRCPKT_Pos)            /*!< DWT CTRL: NOTRCPKT Mask */
+
+#define DWT_CTRL_NOEXTTRIG_Pos             26                                          /*!< DWT CTRL: NOEXTTRIG Position */
+#define DWT_CTRL_NOEXTTRIG_Msk             (0x1UL << DWT_CTRL_NOEXTTRIG_Pos)           /*!< DWT CTRL: NOEXTTRIG Mask */
+
+#define DWT_CTRL_NOCYCCNT_Pos              25                                          /*!< DWT CTRL: NOCYCCNT Position */
+#define DWT_CTRL_NOCYCCNT_Msk              (0x1UL << DWT_CTRL_NOCYCCNT_Pos)            /*!< DWT CTRL: NOCYCCNT Mask */
+
+#define DWT_CTRL_NOPRFCNT_Pos              24                                          /*!< DWT CTRL: NOPRFCNT Position */
+#define DWT_CTRL_NOPRFCNT_Msk              (0x1UL << DWT_CTRL_NOPRFCNT_Pos)            /*!< DWT CTRL: NOPRFCNT Mask */
+
+#define DWT_CTRL_CYCEVTENA_Pos             22                                          /*!< DWT CTRL: CYCEVTENA Position */
+#define DWT_CTRL_CYCEVTENA_Msk             (0x1UL << DWT_CTRL_CYCEVTENA_Pos)           /*!< DWT CTRL: CYCEVTENA Mask */
+
+#define DWT_CTRL_FOLDEVTENA_Pos            21                                          /*!< DWT CTRL: FOLDEVTENA Position */
+#define DWT_CTRL_FOLDEVTENA_Msk            (0x1UL << DWT_CTRL_FOLDEVTENA_Pos)          /*!< DWT CTRL: FOLDEVTENA Mask */
+
+#define DWT_CTRL_LSUEVTENA_Pos             20                                          /*!< DWT CTRL: LSUEVTENA Position */
+#define DWT_CTRL_LSUEVTENA_Msk             (0x1UL << DWT_CTRL_LSUEVTENA_Pos)           /*!< DWT CTRL: LSUEVTENA Mask */
+
+#define DWT_CTRL_SLEEPEVTENA_Pos           19                                          /*!< DWT CTRL: SLEEPEVTENA Position */
+#define DWT_CTRL_SLEEPEVTENA_Msk           (0x1UL << DWT_CTRL_SLEEPEVTENA_Pos)         /*!< DWT CTRL: SLEEPEVTENA Mask */
+
+#define DWT_CTRL_EXCEVTENA_Pos             18                                          /*!< DWT CTRL: EXCEVTENA Position */
+#define DWT_CTRL_EXCEVTENA_Msk             (0x1UL << DWT_CTRL_EXCEVTENA_Pos)           /*!< DWT CTRL: EXCEVTENA Mask */
+
+#define DWT_CTRL_CPIEVTENA_Pos             17                                          /*!< DWT CTRL: CPIEVTENA Position */
+#define DWT_CTRL_CPIEVTENA_Msk             (0x1UL << DWT_CTRL_CPIEVTENA_Pos)           /*!< DWT CTRL: CPIEVTENA Mask */
+
+#define DWT_CTRL_EXCTRCENA_Pos             16                                          /*!< DWT CTRL: EXCTRCENA Position */
+#define DWT_CTRL_EXCTRCENA_Msk             (0x1UL << DWT_CTRL_EXCTRCENA_Pos)           /*!< DWT CTRL: EXCTRCENA Mask */
+
+#define DWT_CTRL_PCSAMPLENA_Pos            12                                          /*!< DWT CTRL: PCSAMPLENA Position */
+#define DWT_CTRL_PCSAMPLENA_Msk            (0x1UL << DWT_CTRL_PCSAMPLENA_Pos)          /*!< DWT CTRL: PCSAMPLENA Mask */
+
+#define DWT_CTRL_SYNCTAP_Pos               10                                          /*!< DWT CTRL: SYNCTAP Position */
+#define DWT_CTRL_SYNCTAP_Msk               (0x3UL << DWT_CTRL_SYNCTAP_Pos)             /*!< DWT CTRL: SYNCTAP Mask */
+
+#define DWT_CTRL_CYCTAP_Pos                 9                                          /*!< DWT CTRL: CYCTAP Position */
+#define DWT_CTRL_CYCTAP_Msk                (0x1UL << DWT_CTRL_CYCTAP_Pos)              /*!< DWT CTRL: CYCTAP Mask */
+
+#define DWT_CTRL_POSTINIT_Pos               5                                          /*!< DWT CTRL: POSTINIT Position */
+#define DWT_CTRL_POSTINIT_Msk              (0xFUL << DWT_CTRL_POSTINIT_Pos)            /*!< DWT CTRL: POSTINIT Mask */
+
+#define DWT_CTRL_POSTPRESET_Pos             1                                          /*!< DWT CTRL: POSTPRESET Position */
+#define DWT_CTRL_POSTPRESET_Msk            (0xFUL << DWT_CTRL_POSTPRESET_Pos)          /*!< DWT CTRL: POSTPRESET Mask */
+
+#define DWT_CTRL_CYCCNTENA_Pos              0                                          /*!< DWT CTRL: CYCCNTENA Position */
+#define DWT_CTRL_CYCCNTENA_Msk             (0x1UL << DWT_CTRL_CYCCNTENA_Pos)           /*!< DWT CTRL: CYCCNTENA Mask */
+
+/* DWT CPI Count Register Definitions */
+#define DWT_CPICNT_CPICNT_Pos               0                                          /*!< DWT CPICNT: CPICNT Position */
+#define DWT_CPICNT_CPICNT_Msk              (0xFFUL << DWT_CPICNT_CPICNT_Pos)           /*!< DWT CPICNT: CPICNT Mask */
+
+/* DWT Exception Overhead Count Register Definitions */
+#define DWT_EXCCNT_EXCCNT_Pos               0                                          /*!< DWT EXCCNT: EXCCNT Position */
+#define DWT_EXCCNT_EXCCNT_Msk              (0xFFUL << DWT_EXCCNT_EXCCNT_Pos)           /*!< DWT EXCCNT: EXCCNT Mask */
+
+/* DWT Sleep Count Register Definitions */
+#define DWT_SLEEPCNT_SLEEPCNT_Pos           0                                          /*!< DWT SLEEPCNT: SLEEPCNT Position */
+#define DWT_SLEEPCNT_SLEEPCNT_Msk          (0xFFUL << DWT_SLEEPCNT_SLEEPCNT_Pos)       /*!< DWT SLEEPCNT: SLEEPCNT Mask */
+
+/* DWT LSU Count Register Definitions */
+#define DWT_LSUCNT_LSUCNT_Pos               0                                          /*!< DWT LSUCNT: LSUCNT Position */
+#define DWT_LSUCNT_LSUCNT_Msk              (0xFFUL << DWT_LSUCNT_LSUCNT_Pos)           /*!< DWT LSUCNT: LSUCNT Mask */
+
+/* DWT Folded-instruction Count Register Definitions */
+#define DWT_FOLDCNT_FOLDCNT_Pos             0                                          /*!< DWT FOLDCNT: FOLDCNT Position */
+#define DWT_FOLDCNT_FOLDCNT_Msk            (0xFFUL << DWT_FOLDCNT_FOLDCNT_Pos)         /*!< DWT FOLDCNT: FOLDCNT Mask */
+
+/* DWT Comparator Mask Register Definitions */
+#define DWT_MASK_MASK_Pos                   0                                          /*!< DWT MASK: MASK Position */
+#define DWT_MASK_MASK_Msk                  (0x1FUL << DWT_MASK_MASK_Pos)               /*!< DWT MASK: MASK Mask */
+
+/* DWT Comparator Function Register Definitions */
+#define DWT_FUNCTION_MATCHED_Pos           24                                          /*!< DWT FUNCTION: MATCHED Position */
+#define DWT_FUNCTION_MATCHED_Msk           (0x1UL << DWT_FUNCTION_MATCHED_Pos)         /*!< DWT FUNCTION: MATCHED Mask */
+
+#define DWT_FUNCTION_DATAVADDR1_Pos        16                                          /*!< DWT FUNCTION: DATAVADDR1 Position */
+#define DWT_FUNCTION_DATAVADDR1_Msk        (0xFUL << DWT_FUNCTION_DATAVADDR1_Pos)      /*!< DWT FUNCTION: DATAVADDR1 Mask */
+
+#define DWT_FUNCTION_DATAVADDR0_Pos        12                                          /*!< DWT FUNCTION: DATAVADDR0 Position */
+#define DWT_FUNCTION_DATAVADDR0_Msk        (0xFUL << DWT_FUNCTION_DATAVADDR0_Pos)      /*!< DWT FUNCTION: DATAVADDR0 Mask */
+
+#define DWT_FUNCTION_DATAVSIZE_Pos         10                                          /*!< DWT FUNCTION: DATAVSIZE Position */
+#define DWT_FUNCTION_DATAVSIZE_Msk         (0x3UL << DWT_FUNCTION_DATAVSIZE_Pos)       /*!< DWT FUNCTION: DATAVSIZE Mask */
+
+#define DWT_FUNCTION_LNK1ENA_Pos            9                                          /*!< DWT FUNCTION: LNK1ENA Position */
+#define DWT_FUNCTION_LNK1ENA_Msk           (0x1UL << DWT_FUNCTION_LNK1ENA_Pos)         /*!< DWT FUNCTION: LNK1ENA Mask */
+
+#define DWT_FUNCTION_DATAVMATCH_Pos         8                                          /*!< DWT FUNCTION: DATAVMATCH Position */
+#define DWT_FUNCTION_DATAVMATCH_Msk        (0x1UL << DWT_FUNCTION_DATAVMATCH_Pos)      /*!< DWT FUNCTION: DATAVMATCH Mask */
+
+#define DWT_FUNCTION_CYCMATCH_Pos           7                                          /*!< DWT FUNCTION: CYCMATCH Position */
+#define DWT_FUNCTION_CYCMATCH_Msk          (0x1UL << DWT_FUNCTION_CYCMATCH_Pos)        /*!< DWT FUNCTION: CYCMATCH Mask */
+
+#define DWT_FUNCTION_EMITRANGE_Pos          5                                          /*!< DWT FUNCTION: EMITRANGE Position */
+#define DWT_FUNCTION_EMITRANGE_Msk         (0x1UL << DWT_FUNCTION_EMITRANGE_Pos)       /*!< DWT FUNCTION: EMITRANGE Mask */
+
+#define DWT_FUNCTION_FUNCTION_Pos           0                                          /*!< DWT FUNCTION: FUNCTION Position */
+#define DWT_FUNCTION_FUNCTION_Msk          (0xFUL << DWT_FUNCTION_FUNCTION_Pos)        /*!< DWT FUNCTION: FUNCTION Mask */
+
+/*@}*/ /* end of group CMSIS_DWT */
+
+
+/** \ingroup  CMSIS_core_register
+    \defgroup CMSIS_TPI     Trace Port Interface (TPI)
+    \brief      Type definitions for the Trace Port Interface (TPI)
+  @{
+ */
+
+/** \brief  Structure type to access the Trace Port Interface Register (TPI).
+ */
+typedef struct
+{
+  __IO uint32_t SSPSR;                   /*!< Offset: 0x000 (R/ )  Supported Parallel Port Size Register     */
+  __IO uint32_t CSPSR;                   /*!< Offset: 0x004 (R/W)  Current Parallel Port Size Register */
+       uint32_t RESERVED0[2];
+  __IO uint32_t ACPR;                    /*!< Offset: 0x010 (R/W)  Asynchronous Clock Prescaler Register */
+       uint32_t RESERVED1[55];
+  __IO uint32_t SPPR;                    /*!< Offset: 0x0F0 (R/W)  Selected Pin Protocol Register */
+       uint32_t RESERVED2[131];
+  __I  uint32_t FFSR;                    /*!< Offset: 0x300 (R/ )  Formatter and Flush Status Register */
+  __IO uint32_t FFCR;                    /*!< Offset: 0x304 (R/W)  Formatter and Flush Control Register */
+  __I  uint32_t FSCR;                    /*!< Offset: 0x308 (R/ )  Formatter Synchronization Counter Register */
+       uint32_t RESERVED3[759];
+  __I  uint32_t TRIGGER;                 /*!< Offset: 0xEE8 (R/ )  TRIGGER */
+  __I  uint32_t FIFO0;                   /*!< Offset: 0xEEC (R/ )  Integration ETM Data */
+  __I  uint32_t ITATBCTR2;               /*!< Offset: 0xEF0 (R/ )  ITATBCTR2 */
+       uint32_t RESERVED4[1];
+  __I  uint32_t ITATBCTR0;               /*!< Offset: 0xEF8 (R/ )  ITATBCTR0 */
+  __I  uint32_t FIFO1;                   /*!< Offset: 0xEFC (R/ )  Integration ITM Data */
+  __IO uint32_t ITCTRL;                  /*!< Offset: 0xF00 (R/W)  Integration Mode Control */
+       uint32_t RESERVED5[39];
+  __IO uint32_t CLAIMSET;                /*!< Offset: 0xFA0 (R/W)  Claim tag set */
+  __IO uint32_t CLAIMCLR;                /*!< Offset: 0xFA4 (R/W)  Claim tag clear */
+       uint32_t RESERVED7[8];
+  __I  uint32_t DEVID;                   /*!< Offset: 0xFC8 (R/ )  TPIU_DEVID */
+  __I  uint32_t DEVTYPE;                 /*!< Offset: 0xFCC (R/ )  TPIU_DEVTYPE */
+} TPI_Type;
+
+/* TPI Asynchronous Clock Prescaler Register Definitions */
+#define TPI_ACPR_PRESCALER_Pos              0                                          /*!< TPI ACPR: PRESCALER Position */
+#define TPI_ACPR_PRESCALER_Msk             (0x1FFFUL << TPI_ACPR_PRESCALER_Pos)        /*!< TPI ACPR: PRESCALER Mask */
+
+/* TPI Selected Pin Protocol Register Definitions */
+#define TPI_SPPR_TXMODE_Pos                 0                                          /*!< TPI SPPR: TXMODE Position */
+#define TPI_SPPR_TXMODE_Msk                (0x3UL << TPI_SPPR_TXMODE_Pos)              /*!< TPI SPPR: TXMODE Mask */
+
+/* TPI Formatter and Flush Status Register Definitions */
+#define TPI_FFSR_FtNonStop_Pos              3                                          /*!< TPI FFSR: FtNonStop Position */
+#define TPI_FFSR_FtNonStop_Msk             (0x1UL << TPI_FFSR_FtNonStop_Pos)           /*!< TPI FFSR: FtNonStop Mask */
+
+#define TPI_FFSR_TCPresent_Pos              2                                          /*!< TPI FFSR: TCPresent Position */
+#define TPI_FFSR_TCPresent_Msk             (0x1UL << TPI_FFSR_TCPresent_Pos)           /*!< TPI FFSR: TCPresent Mask */
+
+#define TPI_FFSR_FtStopped_Pos              1                                          /*!< TPI FFSR: FtStopped Position */
+#define TPI_FFSR_FtStopped_Msk             (0x1UL << TPI_FFSR_FtStopped_Pos)           /*!< TPI FFSR: FtStopped Mask */
+
+#define TPI_FFSR_FlInProg_Pos               0                                          /*!< TPI FFSR: FlInProg Position */
+#define TPI_FFSR_FlInProg_Msk              (0x1UL << TPI_FFSR_FlInProg_Pos)            /*!< TPI FFSR: FlInProg Mask */
+
+/* TPI Formatter and Flush Control Register Definitions */
+#define TPI_FFCR_TrigIn_Pos                 8                                          /*!< TPI FFCR: TrigIn Position */
+#define TPI_FFCR_TrigIn_Msk                (0x1UL << TPI_FFCR_TrigIn_Pos)              /*!< TPI FFCR: TrigIn Mask */
+
+#define TPI_FFCR_EnFCont_Pos                1                                          /*!< TPI FFCR: EnFCont Position */
+#define TPI_FFCR_EnFCont_Msk               (0x1UL << TPI_FFCR_EnFCont_Pos)             /*!< TPI FFCR: EnFCont Mask */
+
+/* TPI TRIGGER Register Definitions */
+#define TPI_TRIGGER_TRIGGER_Pos             0                                          /*!< TPI TRIGGER: TRIGGER Position */
+#define TPI_TRIGGER_TRIGGER_Msk            (0x1UL << TPI_TRIGGER_TRIGGER_Pos)          /*!< TPI TRIGGER: TRIGGER Mask */
+
+/* TPI Integration ETM Data Register Definitions (FIFO0) */
+#define TPI_FIFO0_ITM_ATVALID_Pos          29                                          /*!< TPI FIFO0: ITM_ATVALID Position */
+#define TPI_FIFO0_ITM_ATVALID_Msk          (0x3UL << TPI_FIFO0_ITM_ATVALID_Pos)        /*!< TPI FIFO0: ITM_ATVALID Mask */
+
+#define TPI_FIFO0_ITM_bytecount_Pos        27                                          /*!< TPI FIFO0: ITM_bytecount Position */
+#define TPI_FIFO0_ITM_bytecount_Msk        (0x3UL << TPI_FIFO0_ITM_bytecount_Pos)      /*!< TPI FIFO0: ITM_bytecount Mask */
+
+#define TPI_FIFO0_ETM_ATVALID_Pos          26                                          /*!< TPI FIFO0: ETM_ATVALID Position */
+#define TPI_FIFO0_ETM_ATVALID_Msk          (0x3UL << TPI_FIFO0_ETM_ATVALID_Pos)        /*!< TPI FIFO0: ETM_ATVALID Mask */
+
+#define TPI_FIFO0_ETM_bytecount_Pos        24                                          /*!< TPI FIFO0: ETM_bytecount Position */
+#define TPI_FIFO0_ETM_bytecount_Msk        (0x3UL << TPI_FIFO0_ETM_bytecount_Pos)      /*!< TPI FIFO0: ETM_bytecount Mask */
+
+#define TPI_FIFO0_ETM2_Pos                 16                                          /*!< TPI FIFO0: ETM2 Position */
+#define TPI_FIFO0_ETM2_Msk                 (0xFFUL << TPI_FIFO0_ETM2_Pos)              /*!< TPI FIFO0: ETM2 Mask */
+
+#define TPI_FIFO0_ETM1_Pos                  8                                          /*!< TPI FIFO0: ETM1 Position */
+#define TPI_FIFO0_ETM1_Msk                 (0xFFUL << TPI_FIFO0_ETM1_Pos)              /*!< TPI FIFO0: ETM1 Mask */
+
+#define TPI_FIFO0_ETM0_Pos                  0                                          /*!< TPI FIFO0: ETM0 Position */
+#define TPI_FIFO0_ETM0_Msk                 (0xFFUL << TPI_FIFO0_ETM0_Pos)              /*!< TPI FIFO0: ETM0 Mask */
+
+/* TPI ITATBCTR2 Register Definitions */
+#define TPI_ITATBCTR2_ATREADY_Pos           0                                          /*!< TPI ITATBCTR2: ATREADY Position */
+#define TPI_ITATBCTR2_ATREADY_Msk          (0x1UL << TPI_ITATBCTR2_ATREADY_Pos)        /*!< TPI ITATBCTR2: ATREADY Mask */
+
+/* TPI Integration ITM Data Register Definitions (FIFO1) */
+#define TPI_FIFO1_ITM_ATVALID_Pos          29                                          /*!< TPI FIFO1: ITM_ATVALID Position */
+#define TPI_FIFO1_ITM_ATVALID_Msk          (0x3UL << TPI_FIFO1_ITM_ATVALID_Pos)        /*!< TPI FIFO1: ITM_ATVALID Mask */
+
+#define TPI_FIFO1_ITM_bytecount_Pos        27                                          /*!< TPI FIFO1: ITM_bytecount Position */
+#define TPI_FIFO1_ITM_bytecount_Msk        (0x3UL << TPI_FIFO1_ITM_bytecount_Pos)      /*!< TPI FIFO1: ITM_bytecount Mask */
+
+#define TPI_FIFO1_ETM_ATVALID_Pos          26                                          /*!< TPI FIFO1: ETM_ATVALID Position */
+#define TPI_FIFO1_ETM_ATVALID_Msk          (0x3UL << TPI_FIFO1_ETM_ATVALID_Pos)        /*!< TPI FIFO1: ETM_ATVALID Mask */
+
+#define TPI_FIFO1_ETM_bytecount_Pos        24                                          /*!< TPI FIFO1: ETM_bytecount Position */
+#define TPI_FIFO1_ETM_bytecount_Msk        (0x3UL << TPI_FIFO1_ETM_bytecount_Pos)      /*!< TPI FIFO1: ETM_bytecount Mask */
+
+#define TPI_FIFO1_ITM2_Pos                 16                                          /*!< TPI FIFO1: ITM2 Position */
+#define TPI_FIFO1_ITM2_Msk                 (0xFFUL << TPI_FIFO1_ITM2_Pos)              /*!< TPI FIFO1: ITM2 Mask */
+
+#define TPI_FIFO1_ITM1_Pos                  8                                          /*!< TPI FIFO1: ITM1 Position */
+#define TPI_FIFO1_ITM1_Msk                 (0xFFUL << TPI_FIFO1_ITM1_Pos)              /*!< TPI FIFO1: ITM1 Mask */
+
+#define TPI_FIFO1_ITM0_Pos                  0                                          /*!< TPI FIFO1: ITM0 Position */
+#define TPI_FIFO1_ITM0_Msk                 (0xFFUL << TPI_FIFO1_ITM0_Pos)              /*!< TPI FIFO1: ITM0 Mask */
+
+/* TPI ITATBCTR0 Register Definitions */
+#define TPI_ITATBCTR0_ATREADY_Pos           0                                          /*!< TPI ITATBCTR0: ATREADY Position */
+#define TPI_ITATBCTR0_ATREADY_Msk          (0x1UL << TPI_ITATBCTR0_ATREADY_Pos)        /*!< TPI ITATBCTR0: ATREADY Mask */
+
+/* TPI Integration Mode Control Register Definitions */
+#define TPI_ITCTRL_Mode_Pos                 0                                          /*!< TPI ITCTRL: Mode Position */
+#define TPI_ITCTRL_Mode_Msk                (0x1UL << TPI_ITCTRL_Mode_Pos)              /*!< TPI ITCTRL: Mode Mask */
+
+/* TPI DEVID Register Definitions */
+#define TPI_DEVID_NRZVALID_Pos             11                                          /*!< TPI DEVID: NRZVALID Position */
+#define TPI_DEVID_NRZVALID_Msk             (0x1UL << TPI_DEVID_NRZVALID_Pos)           /*!< TPI DEVID: NRZVALID Mask */
+
+#define TPI_DEVID_MANCVALID_Pos            10                                          /*!< TPI DEVID: MANCVALID Position */
+#define TPI_DEVID_MANCVALID_Msk            (0x1UL << TPI_DEVID_MANCVALID_Pos)          /*!< TPI DEVID: MANCVALID Mask */
+
+#define TPI_DEVID_PTINVALID_Pos             9                                          /*!< TPI DEVID: PTINVALID Position */
+#define TPI_DEVID_PTINVALID_Msk            (0x1UL << TPI_DEVID_PTINVALID_Pos)          /*!< TPI DEVID: PTINVALID Mask */
+
+#define TPI_DEVID_MinBufSz_Pos              6                                          /*!< TPI DEVID: MinBufSz Position */
+#define TPI_DEVID_MinBufSz_Msk             (0x7UL << TPI_DEVID_MinBufSz_Pos)           /*!< TPI DEVID: MinBufSz Mask */
+
+#define TPI_DEVID_AsynClkIn_Pos             5                                          /*!< TPI DEVID: AsynClkIn Position */
+#define TPI_DEVID_AsynClkIn_Msk            (0x1UL << TPI_DEVID_AsynClkIn_Pos)          /*!< TPI DEVID: AsynClkIn Mask */
+
+#define TPI_DEVID_NrTraceInput_Pos          0                                          /*!< TPI DEVID: NrTraceInput Position */
+#define TPI_DEVID_NrTraceInput_Msk         (0x1FUL << TPI_DEVID_NrTraceInput_Pos)      /*!< TPI DEVID: NrTraceInput Mask */
+
+/* TPI DEVTYPE Register Definitions */
+#define TPI_DEVTYPE_SubType_Pos             0                                          /*!< TPI DEVTYPE: SubType Position */
+#define TPI_DEVTYPE_SubType_Msk            (0xFUL << TPI_DEVTYPE_SubType_Pos)          /*!< TPI DEVTYPE: SubType Mask */
+
+#define TPI_DEVTYPE_MajorType_Pos           4                                          /*!< TPI DEVTYPE: MajorType Position */
+#define TPI_DEVTYPE_MajorType_Msk          (0xFUL << TPI_DEVTYPE_MajorType_Pos)        /*!< TPI DEVTYPE: MajorType Mask */
+
+/*@}*/ /* end of group CMSIS_TPI */
+
+
+#if (__MPU_PRESENT == 1)
+/** \ingroup  CMSIS_core_register
+    \defgroup CMSIS_MPU     Memory Protection Unit (MPU)
+    \brief      Type definitions for the Memory Protection Unit (MPU)
+  @{
+ */
+
+/** \brief  Structure type to access the Memory Protection Unit (MPU).
+ */
+typedef struct
+{
+  __I  uint32_t TYPE;                    /*!< Offset: 0x000 (R/ )  MPU Type Register                              */
+  __IO uint32_t CTRL;                    /*!< Offset: 0x004 (R/W)  MPU Control Register                           */
+  __IO uint32_t RNR;                     /*!< Offset: 0x008 (R/W)  MPU Region RNRber Register                     */
+  __IO uint32_t RBAR;                    /*!< Offset: 0x00C (R/W)  MPU Region Base Address Register               */
+  __IO uint32_t RASR;                    /*!< Offset: 0x010 (R/W)  MPU Region Attribute and Size Register         */
+  __IO uint32_t RBAR_A1;                 /*!< Offset: 0x014 (R/W)  MPU Alias 1 Region Base Address Register       */
+  __IO uint32_t RASR_A1;                 /*!< Offset: 0x018 (R/W)  MPU Alias 1 Region Attribute and Size Register */
+  __IO uint32_t RBAR_A2;                 /*!< Offset: 0x01C (R/W)  MPU Alias 2 Region Base Address Register       */
+  __IO uint32_t RASR_A2;                 /*!< Offset: 0x020 (R/W)  MPU Alias 2 Region Attribute and Size Register */
+  __IO uint32_t RBAR_A3;                 /*!< Offset: 0x024 (R/W)  MPU Alias 3 Region Base Address Register       */
+  __IO uint32_t RASR_A3;                 /*!< Offset: 0x028 (R/W)  MPU Alias 3 Region Attribute and Size Register */
+} MPU_Type;
+
+/* MPU Type Register */
+#define MPU_TYPE_IREGION_Pos               16                                             /*!< MPU TYPE: IREGION Position */
+#define MPU_TYPE_IREGION_Msk               (0xFFUL << MPU_TYPE_IREGION_Pos)               /*!< MPU TYPE: IREGION Mask */
+
+#define MPU_TYPE_DREGION_Pos                8                                             /*!< MPU TYPE: DREGION Position */
+#define MPU_TYPE_DREGION_Msk               (0xFFUL << MPU_TYPE_DREGION_Pos)               /*!< MPU TYPE: DREGION Mask */
+
+#define MPU_TYPE_SEPARATE_Pos               0                                             /*!< MPU TYPE: SEPARATE Position */
+#define MPU_TYPE_SEPARATE_Msk              (1UL << MPU_TYPE_SEPARATE_Pos)                 /*!< MPU TYPE: SEPARATE Mask */
+
+/* MPU Control Register */
+#define MPU_CTRL_PRIVDEFENA_Pos             2                                             /*!< MPU CTRL: PRIVDEFENA Position */
+#define MPU_CTRL_PRIVDEFENA_Msk            (1UL << MPU_CTRL_PRIVDEFENA_Pos)               /*!< MPU CTRL: PRIVDEFENA Mask */
+
+#define MPU_CTRL_HFNMIENA_Pos               1                                             /*!< MPU CTRL: HFNMIENA Position */
+#define MPU_CTRL_HFNMIENA_Msk              (1UL << MPU_CTRL_HFNMIENA_Pos)                 /*!< MPU CTRL: HFNMIENA Mask */
+
+#define MPU_CTRL_ENABLE_Pos                 0                                             /*!< MPU CTRL: ENABLE Position */
+#define MPU_CTRL_ENABLE_Msk                (1UL << MPU_CTRL_ENABLE_Pos)                   /*!< MPU CTRL: ENABLE Mask */
+
+/* MPU Region Number Register */
+#define MPU_RNR_REGION_Pos                  0                                             /*!< MPU RNR: REGION Position */
+#define MPU_RNR_REGION_Msk                 (0xFFUL << MPU_RNR_REGION_Pos)                 /*!< MPU RNR: REGION Mask */
+
+/* MPU Region Base Address Register */
+#define MPU_RBAR_ADDR_Pos                   5                                             /*!< MPU RBAR: ADDR Position */
+#define MPU_RBAR_ADDR_Msk                  (0x7FFFFFFUL << MPU_RBAR_ADDR_Pos)             /*!< MPU RBAR: ADDR Mask */
+
+#define MPU_RBAR_VALID_Pos                  4                                             /*!< MPU RBAR: VALID Position */
+#define MPU_RBAR_VALID_Msk                 (1UL << MPU_RBAR_VALID_Pos)                    /*!< MPU RBAR: VALID Mask */
+
+#define MPU_RBAR_REGION_Pos                 0                                             /*!< MPU RBAR: REGION Position */
+#define MPU_RBAR_REGION_Msk                (0xFUL << MPU_RBAR_REGION_Pos)                 /*!< MPU RBAR: REGION Mask */
+
+/* MPU Region Attribute and Size Register */
+#define MPU_RASR_ATTRS_Pos                 16                                             /*!< MPU RASR: MPU Region Attribute field Position */
+#define MPU_RASR_ATTRS_Msk                 (0xFFFFUL << MPU_RASR_ATTRS_Pos)               /*!< MPU RASR: MPU Region Attribute field Mask */
+
+#define MPU_RASR_XN_Pos                    28                                             /*!< MPU RASR: ATTRS.XN Position */
+#define MPU_RASR_XN_Msk                    (1UL << MPU_RASR_XN_Pos)                       /*!< MPU RASR: ATTRS.XN Mask */
+
+#define MPU_RASR_AP_Pos                    24                                             /*!< MPU RASR: ATTRS.AP Position */
+#define MPU_RASR_AP_Msk                    (0x7UL << MPU_RASR_AP_Pos)                     /*!< MPU RASR: ATTRS.AP Mask */
+
+#define MPU_RASR_TEX_Pos                   19                                             /*!< MPU RASR: ATTRS.TEX Position */
+#define MPU_RASR_TEX_Msk                   (0x7UL << MPU_RASR_TEX_Pos)                    /*!< MPU RASR: ATTRS.TEX Mask */
+
+#define MPU_RASR_S_Pos                     18                                             /*!< MPU RASR: ATTRS.S Position */
+#define MPU_RASR_S_Msk                     (1UL << MPU_RASR_S_Pos)                        /*!< MPU RASR: ATTRS.S Mask */
+
+#define MPU_RASR_C_Pos                     17                                             /*!< MPU RASR: ATTRS.C Position */
+#define MPU_RASR_C_Msk                     (1UL << MPU_RASR_C_Pos)                        /*!< MPU RASR: ATTRS.C Mask */
+
+#define MPU_RASR_B_Pos                     16                                             /*!< MPU RASR: ATTRS.B Position */
+#define MPU_RASR_B_Msk                     (1UL << MPU_RASR_B_Pos)                        /*!< MPU RASR: ATTRS.B Mask */
+
+#define MPU_RASR_SRD_Pos                    8                                             /*!< MPU RASR: Sub-Region Disable Position */
+#define MPU_RASR_SRD_Msk                   (0xFFUL << MPU_RASR_SRD_Pos)                   /*!< MPU RASR: Sub-Region Disable Mask */
+
+#define MPU_RASR_SIZE_Pos                   1                                             /*!< MPU RASR: Region Size Field Position */
+#define MPU_RASR_SIZE_Msk                  (0x1FUL << MPU_RASR_SIZE_Pos)                  /*!< MPU RASR: Region Size Field Mask */
+
+#define MPU_RASR_ENABLE_Pos                 0                                             /*!< MPU RASR: Region enable bit Position */
+#define MPU_RASR_ENABLE_Msk                (1UL << MPU_RASR_ENABLE_Pos)                   /*!< MPU RASR: Region enable bit Disable Mask */
+
+/*@} end of group CMSIS_MPU */
+#endif
+
+
+/** \ingroup  CMSIS_core_register
+    \defgroup CMSIS_CoreDebug       Core Debug Registers (CoreDebug)
+    \brief      Type definitions for the Core Debug Registers
+  @{
+ */
+
+/** \brief  Structure type to access the Core Debug Register (CoreDebug).
+ */
+typedef struct
+{
+  __IO uint32_t DHCSR;                   /*!< Offset: 0x000 (R/W)  Debug Halting Control and Status Register    */
+  __O  uint32_t DCRSR;                   /*!< Offset: 0x004 ( /W)  Debug Core Register Selector Register        */
+  __IO uint32_t DCRDR;                   /*!< Offset: 0x008 (R/W)  Debug Core Register Data Register            */
+  __IO uint32_t DEMCR;                   /*!< Offset: 0x00C (R/W)  Debug Exception and Monitor Control Register */
+} CoreDebug_Type;
+
+/* Debug Halting Control and Status Register */
+#define CoreDebug_DHCSR_DBGKEY_Pos         16                                             /*!< CoreDebug DHCSR: DBGKEY Position */
+#define CoreDebug_DHCSR_DBGKEY_Msk         (0xFFFFUL << CoreDebug_DHCSR_DBGKEY_Pos)       /*!< CoreDebug DHCSR: DBGKEY Mask */
+
+#define CoreDebug_DHCSR_S_RESET_ST_Pos     25                                             /*!< CoreDebug DHCSR: S_RESET_ST Position */
+#define CoreDebug_DHCSR_S_RESET_ST_Msk     (1UL << CoreDebug_DHCSR_S_RESET_ST_Pos)        /*!< CoreDebug DHCSR: S_RESET_ST Mask */
+
+#define CoreDebug_DHCSR_S_RETIRE_ST_Pos    24                                             /*!< CoreDebug DHCSR: S_RETIRE_ST Position */
+#define CoreDebug_DHCSR_S_RETIRE_ST_Msk    (1UL << CoreDebug_DHCSR_S_RETIRE_ST_Pos)       /*!< CoreDebug DHCSR: S_RETIRE_ST Mask */
+
+#define CoreDebug_DHCSR_S_LOCKUP_Pos       19                                             /*!< CoreDebug DHCSR: S_LOCKUP Position */
+#define CoreDebug_DHCSR_S_LOCKUP_Msk       (1UL << CoreDebug_DHCSR_S_LOCKUP_Pos)          /*!< CoreDebug DHCSR: S_LOCKUP Mask */
+
+#define CoreDebug_DHCSR_S_SLEEP_Pos        18                                             /*!< CoreDebug DHCSR: S_SLEEP Position */
+#define CoreDebug_DHCSR_S_SLEEP_Msk        (1UL << CoreDebug_DHCSR_S_SLEEP_Pos)           /*!< CoreDebug DHCSR: S_SLEEP Mask */
+
+#define CoreDebug_DHCSR_S_HALT_Pos         17                                             /*!< CoreDebug DHCSR: S_HALT Position */
+#define CoreDebug_DHCSR_S_HALT_Msk         (1UL << CoreDebug_DHCSR_S_HALT_Pos)            /*!< CoreDebug DHCSR: S_HALT Mask */
+
+#define CoreDebug_DHCSR_S_REGRDY_Pos       16                                             /*!< CoreDebug DHCSR: S_REGRDY Position */
+#define CoreDebug_DHCSR_S_REGRDY_Msk       (1UL << CoreDebug_DHCSR_S_REGRDY_Pos)          /*!< CoreDebug DHCSR: S_REGRDY Mask */
+
+#define CoreDebug_DHCSR_C_SNAPSTALL_Pos     5                                             /*!< CoreDebug DHCSR: C_SNAPSTALL Position */
+#define CoreDebug_DHCSR_C_SNAPSTALL_Msk    (1UL << CoreDebug_DHCSR_C_SNAPSTALL_Pos)       /*!< CoreDebug DHCSR: C_SNAPSTALL Mask */
+
+#define CoreDebug_DHCSR_C_MASKINTS_Pos      3                                             /*!< CoreDebug DHCSR: C_MASKINTS Position */
+#define CoreDebug_DHCSR_C_MASKINTS_Msk     (1UL << CoreDebug_DHCSR_C_MASKINTS_Pos)        /*!< CoreDebug DHCSR: C_MASKINTS Mask */
+
+#define CoreDebug_DHCSR_C_STEP_Pos          2                                             /*!< CoreDebug DHCSR: C_STEP Position */
+#define CoreDebug_DHCSR_C_STEP_Msk         (1UL << CoreDebug_DHCSR_C_STEP_Pos)            /*!< CoreDebug DHCSR: C_STEP Mask */
+
+#define CoreDebug_DHCSR_C_HALT_Pos          1                                             /*!< CoreDebug DHCSR: C_HALT Position */
+#define CoreDebug_DHCSR_C_HALT_Msk         (1UL << CoreDebug_DHCSR_C_HALT_Pos)            /*!< CoreDebug DHCSR: C_HALT Mask */
+
+#define CoreDebug_DHCSR_C_DEBUGEN_Pos       0                                             /*!< CoreDebug DHCSR: C_DEBUGEN Position */
+#define CoreDebug_DHCSR_C_DEBUGEN_Msk      (1UL << CoreDebug_DHCSR_C_DEBUGEN_Pos)         /*!< CoreDebug DHCSR: C_DEBUGEN Mask */
+
+/* Debug Core Register Selector Register */
+#define CoreDebug_DCRSR_REGWnR_Pos         16                                             /*!< CoreDebug DCRSR: REGWnR Position */
+#define CoreDebug_DCRSR_REGWnR_Msk         (1UL << CoreDebug_DCRSR_REGWnR_Pos)            /*!< CoreDebug DCRSR: REGWnR Mask */
+
+#define CoreDebug_DCRSR_REGSEL_Pos          0                                             /*!< CoreDebug DCRSR: REGSEL Position */
+#define CoreDebug_DCRSR_REGSEL_Msk         (0x1FUL << CoreDebug_DCRSR_REGSEL_Pos)         /*!< CoreDebug DCRSR: REGSEL Mask */
+
+/* Debug Exception and Monitor Control Register */
+#define CoreDebug_DEMCR_TRCENA_Pos         24                                             /*!< CoreDebug DEMCR: TRCENA Position */
+#define CoreDebug_DEMCR_TRCENA_Msk         (1UL << CoreDebug_DEMCR_TRCENA_Pos)            /*!< CoreDebug DEMCR: TRCENA Mask */
+
+#define CoreDebug_DEMCR_MON_REQ_Pos        19                                             /*!< CoreDebug DEMCR: MON_REQ Position */
+#define CoreDebug_DEMCR_MON_REQ_Msk        (1UL << CoreDebug_DEMCR_MON_REQ_Pos)           /*!< CoreDebug DEMCR: MON_REQ Mask */
+
+#define CoreDebug_DEMCR_MON_STEP_Pos       18                                             /*!< CoreDebug DEMCR: MON_STEP Position */
+#define CoreDebug_DEMCR_MON_STEP_Msk       (1UL << CoreDebug_DEMCR_MON_STEP_Pos)          /*!< CoreDebug DEMCR: MON_STEP Mask */
+
+#define CoreDebug_DEMCR_MON_PEND_Pos       17                                             /*!< CoreDebug DEMCR: MON_PEND Position */
+#define CoreDebug_DEMCR_MON_PEND_Msk       (1UL << CoreDebug_DEMCR_MON_PEND_Pos)          /*!< CoreDebug DEMCR: MON_PEND Mask */
+
+#define CoreDebug_DEMCR_MON_EN_Pos         16                                             /*!< CoreDebug DEMCR: MON_EN Position */
+#define CoreDebug_DEMCR_MON_EN_Msk         (1UL << CoreDebug_DEMCR_MON_EN_Pos)            /*!< CoreDebug DEMCR: MON_EN Mask */
+
+#define CoreDebug_DEMCR_VC_HARDERR_Pos     10                                             /*!< CoreDebug DEMCR: VC_HARDERR Position */
+#define CoreDebug_DEMCR_VC_HARDERR_Msk     (1UL << CoreDebug_DEMCR_VC_HARDERR_Pos)        /*!< CoreDebug DEMCR: VC_HARDERR Mask */
+
+#define CoreDebug_DEMCR_VC_INTERR_Pos       9                                             /*!< CoreDebug DEMCR: VC_INTERR Position */
+#define CoreDebug_DEMCR_VC_INTERR_Msk      (1UL << CoreDebug_DEMCR_VC_INTERR_Pos)         /*!< CoreDebug DEMCR: VC_INTERR Mask */
+
+#define CoreDebug_DEMCR_VC_BUSERR_Pos       8                                             /*!< CoreDebug DEMCR: VC_BUSERR Position */
+#define CoreDebug_DEMCR_VC_BUSERR_Msk      (1UL << CoreDebug_DEMCR_VC_BUSERR_Pos)         /*!< CoreDebug DEMCR: VC_BUSERR Mask */
+
+#define CoreDebug_DEMCR_VC_STATERR_Pos      7                                             /*!< CoreDebug DEMCR: VC_STATERR Position */
+#define CoreDebug_DEMCR_VC_STATERR_Msk     (1UL << CoreDebug_DEMCR_VC_STATERR_Pos)        /*!< CoreDebug DEMCR: VC_STATERR Mask */
+
+#define CoreDebug_DEMCR_VC_CHKERR_Pos       6                                             /*!< CoreDebug DEMCR: VC_CHKERR Position */
+#define CoreDebug_DEMCR_VC_CHKERR_Msk      (1UL << CoreDebug_DEMCR_VC_CHKERR_Pos)         /*!< CoreDebug DEMCR: VC_CHKERR Mask */
+
+#define CoreDebug_DEMCR_VC_NOCPERR_Pos      5                                             /*!< CoreDebug DEMCR: VC_NOCPERR Position */
+#define CoreDebug_DEMCR_VC_NOCPERR_Msk     (1UL << CoreDebug_DEMCR_VC_NOCPERR_Pos)        /*!< CoreDebug DEMCR: VC_NOCPERR Mask */
+
+#define CoreDebug_DEMCR_VC_MMERR_Pos        4                                             /*!< CoreDebug DEMCR: VC_MMERR Position */
+#define CoreDebug_DEMCR_VC_MMERR_Msk       (1UL << CoreDebug_DEMCR_VC_MMERR_Pos)          /*!< CoreDebug DEMCR: VC_MMERR Mask */
+
+#define CoreDebug_DEMCR_VC_CORERESET_Pos    0                                             /*!< CoreDebug DEMCR: VC_CORERESET Position */
+#define CoreDebug_DEMCR_VC_CORERESET_Msk   (1UL << CoreDebug_DEMCR_VC_CORERESET_Pos)      /*!< CoreDebug DEMCR: VC_CORERESET Mask */
+
+/*@} end of group CMSIS_CoreDebug */
+
+
+/** \ingroup    CMSIS_core_register
+    \defgroup   CMSIS_core_base     Core Definitions
+    \brief      Definitions for base addresses, unions, and structures.
+  @{
+ */
+
+/* Memory mapping of Cortex-M3 Hardware */
+#define SCS_BASE            (0xE000E000UL)                            /*!< System Control Space Base Address  */
+#define ITM_BASE            (0xE0000000UL)                            /*!< ITM Base Address                   */
+#define DWT_BASE            (0xE0001000UL)                            /*!< DWT Base Address                   */
+#define TPI_BASE            (0xE0040000UL)                            /*!< TPI Base Address                   */
+#define CoreDebug_BASE      (0xE000EDF0UL)                            /*!< Core Debug Base Address            */
+#define SysTick_BASE        (SCS_BASE +  0x0010UL)                    /*!< SysTick Base Address               */
+#define NVIC_BASE           (SCS_BASE +  0x0100UL)                    /*!< NVIC Base Address                  */
+#define SCB_BASE            (SCS_BASE +  0x0D00UL)                    /*!< System Control Block Base Address  */
+
+#define SCnSCB              ((SCnSCB_Type    *)     SCS_BASE      )   /*!< System control Register not in SCB */
+#define SCB                 ((SCB_Type       *)     SCB_BASE      )   /*!< SCB configuration struct           */
+#define SysTick             ((SysTick_Type   *)     SysTick_BASE  )   /*!< SysTick configuration struct       */
+#define NVIC                ((NVIC_Type      *)     NVIC_BASE     )   /*!< NVIC configuration struct          */
+#define ITM                 ((ITM_Type       *)     ITM_BASE      )   /*!< ITM configuration struct           */
+#define DWT                 ((DWT_Type       *)     DWT_BASE      )   /*!< DWT configuration struct           */
+#define TPI                 ((TPI_Type       *)     TPI_BASE      )   /*!< TPI configuration struct           */
+#define CoreDebug           ((CoreDebug_Type *)     CoreDebug_BASE)   /*!< Core Debug configuration struct    */
+
+#if (__MPU_PRESENT == 1)
+  #define MPU_BASE          (SCS_BASE +  0x0D90UL)                    /*!< Memory Protection Unit             */
+  #define MPU               ((MPU_Type       *)     MPU_BASE      )   /*!< Memory Protection Unit             */
+#endif
+
+/*@} */
+
+
+
+/*******************************************************************************
+ *                Hardware Abstraction Layer
+  Core Function Interface contains:
+  - Core NVIC Functions
+  - Core SysTick Functions
+  - Core Debug Functions
+  - Core Register Access Functions
+ ******************************************************************************/
+/** \defgroup CMSIS_Core_FunctionInterface Functions and Instructions Reference
+*/
+
+
+
+/* ##########################   NVIC functions  #################################### */
+/** \ingroup  CMSIS_Core_FunctionInterface
+    \defgroup CMSIS_Core_NVICFunctions NVIC Functions
+    \brief      Functions that manage interrupts and exceptions via the NVIC.
+    @{
+ */
+
+/** \brief  Set Priority Grouping
+
+  The function sets the priority grouping field using the required unlock sequence.
+  The parameter PriorityGroup is assigned to the field SCB->AIRCR [10:8] PRIGROUP field.
+  Only values from 0..7 are used.
+  In case of a conflict between priority grouping and available
+  priority bits (__NVIC_PRIO_BITS), the smallest possible priority group is set.
+
+    \param [in]      PriorityGroup  Priority grouping field.
+ */
+__STATIC_INLINE void NVIC_SetPriorityGrouping(uint32_t PriorityGroup)
+{
+  uint32_t reg_value;
+  uint32_t PriorityGroupTmp = (PriorityGroup & (uint32_t)0x07);               /* only values 0..7 are used          */
+
+  reg_value  =  SCB->AIRCR;                                                   /* read old register configuration    */
+  reg_value &= ~(SCB_AIRCR_VECTKEY_Msk | SCB_AIRCR_PRIGROUP_Msk);             /* clear bits to change               */
+  reg_value  =  (reg_value                                 |
+                ((uint32_t)0x5FA << SCB_AIRCR_VECTKEY_Pos) |
+                (PriorityGroupTmp << 8));                                     /* Insert write key and priorty group */
+  SCB->AIRCR =  reg_value;
+}
+
+
+/** \brief  Get Priority Grouping
+
+  The function reads the priority grouping field from the NVIC Interrupt Controller.
+
+    \return                Priority grouping field (SCB->AIRCR [10:8] PRIGROUP field).
+ */
+__STATIC_INLINE uint32_t NVIC_GetPriorityGrouping(void)
+{
+  return ((SCB->AIRCR & SCB_AIRCR_PRIGROUP_Msk) >> SCB_AIRCR_PRIGROUP_Pos);   /* read priority grouping field */
+}
+
+
+/** \brief  Enable External Interrupt
+
+    The function enables a device-specific interrupt in the NVIC interrupt controller.
+
+    \param [in]      IRQn  External interrupt number. Value cannot be negative.
+ */
+__STATIC_INLINE void NVIC_EnableIRQ(IRQn_Type IRQn)
+{
+  NVIC->ISER[((uint32_t)(IRQn) >> 5)] = (1 << ((uint32_t)(IRQn) & 0x1F)); /* enable interrupt */
+}
+
+
+/** \brief  Disable External Interrupt
+
+    The function disables a device-specific interrupt in the NVIC interrupt controller.
+
+    \param [in]      IRQn  External interrupt number. Value cannot be negative.
+ */
+__STATIC_INLINE void NVIC_DisableIRQ(IRQn_Type IRQn)
+{
+  NVIC->ICER[((uint32_t)(IRQn) >> 5)] = (1 << ((uint32_t)(IRQn) & 0x1F)); /* disable interrupt */
+}
+
+
+/** \brief  Get Pending Interrupt
+
+    The function reads the pending register in the NVIC and returns the pending bit
+    for the specified interrupt.
+
+    \param [in]      IRQn  Interrupt number.
+
+    \return             0  Interrupt status is not pending.
+    \return             1  Interrupt status is pending.
+ */
+__STATIC_INLINE uint32_t NVIC_GetPendingIRQ(IRQn_Type IRQn)
+{
+  return((uint32_t) ((NVIC->ISPR[(uint32_t)(IRQn) >> 5] & (1 << ((uint32_t)(IRQn) & 0x1F)))?1:0)); /* Return 1 if pending else 0 */
+}
+
+
+/** \brief  Set Pending Interrupt
+
+    The function sets the pending bit of an external interrupt.
+
+    \param [in]      IRQn  Interrupt number. Value cannot be negative.
+ */
+__STATIC_INLINE void NVIC_SetPendingIRQ(IRQn_Type IRQn)
+{
+  NVIC->ISPR[((uint32_t)(IRQn) >> 5)] = (1 << ((uint32_t)(IRQn) & 0x1F)); /* set interrupt pending */
+}
+
+
+/** \brief  Clear Pending Interrupt
+
+    The function clears the pending bit of an external interrupt.
+
+    \param [in]      IRQn  External interrupt number. Value cannot be negative.
+ */
+__STATIC_INLINE void NVIC_ClearPendingIRQ(IRQn_Type IRQn)
+{
+  NVIC->ICPR[((uint32_t)(IRQn) >> 5)] = (1 << ((uint32_t)(IRQn) & 0x1F)); /* Clear pending interrupt */
+}
+
+
+/** \brief  Get Active Interrupt
+
+    The function reads the active register in NVIC and returns the active bit.
+
+    \param [in]      IRQn  Interrupt number.
+
+    \return             0  Interrupt status is not active.
+    \return             1  Interrupt status is active.
+ */
+__STATIC_INLINE uint32_t NVIC_GetActive(IRQn_Type IRQn)
+{
+  return((uint32_t)((NVIC->IABR[(uint32_t)(IRQn) >> 5] & (1 << ((uint32_t)(IRQn) & 0x1F)))?1:0)); /* Return 1 if active else 0 */
+}
+
+
+/** \brief  Set Interrupt Priority
+
+    The function sets the priority of an interrupt.
+
+    \note The priority cannot be set for every core interrupt.
+
+    \param [in]      IRQn  Interrupt number.
+    \param [in]  priority  Priority to set.
+ */
+__STATIC_INLINE void NVIC_SetPriority(IRQn_Type IRQn, uint32_t priority)
+{
+  if(IRQn < 0) {
+    SCB->SHP[((uint32_t)(IRQn) & 0xF)-4] = ((priority << (8 - __NVIC_PRIO_BITS)) & 0xff); } /* set Priority for Cortex-M  System Interrupts */
+  else {
+    NVIC->IP[(uint32_t)(IRQn)] = ((priority << (8 - __NVIC_PRIO_BITS)) & 0xff);    }        /* set Priority for device specific Interrupts  */
+}
+
+
+/** \brief  Get Interrupt Priority
+
+    The function reads the priority of an interrupt. The interrupt
+    number can be positive to specify an external (device specific)
+    interrupt, or negative to specify an internal (core) interrupt.
+
+
+    \param [in]   IRQn  Interrupt number.
+    \return             Interrupt Priority. Value is aligned automatically to the implemented
+                        priority bits of the microcontroller.
+ */
+__STATIC_INLINE uint32_t NVIC_GetPriority(IRQn_Type IRQn)
+{
+
+  if(IRQn < 0) {
+    return((uint32_t)(SCB->SHP[((uint32_t)(IRQn) & 0xF)-4] >> (8 - __NVIC_PRIO_BITS)));  } /* get priority for Cortex-M  system interrupts */
+  else {
+    return((uint32_t)(NVIC->IP[(uint32_t)(IRQn)]           >> (8 - __NVIC_PRIO_BITS)));  } /* get priority for device specific interrupts  */
+}
+
+
+/** \brief  Encode Priority
+
+    The function encodes the priority for an interrupt with the given priority group,
+    preemptive priority value, and subpriority value.
+    In case of a conflict between priority grouping and available
+    priority bits (__NVIC_PRIO_BITS), the samllest possible priority group is set.
+
+    \param [in]     PriorityGroup  Used priority group.
+    \param [in]   PreemptPriority  Preemptive priority value (starting from 0).
+    \param [in]       SubPriority  Subpriority value (starting from 0).
+    \return                        Encoded priority. Value can be used in the function \ref NVIC_SetPriority().
+ */
+__STATIC_INLINE uint32_t NVIC_EncodePriority (uint32_t PriorityGroup, uint32_t PreemptPriority, uint32_t SubPriority)
+{
+  uint32_t PriorityGroupTmp = (PriorityGroup & 0x07);          /* only values 0..7 are used          */
+  uint32_t PreemptPriorityBits;
+  uint32_t SubPriorityBits;
+
+  PreemptPriorityBits = ((7 - PriorityGroupTmp) > __NVIC_PRIO_BITS) ? __NVIC_PRIO_BITS : 7 - PriorityGroupTmp;
+  SubPriorityBits     = ((PriorityGroupTmp + __NVIC_PRIO_BITS) < 7) ? 0 : PriorityGroupTmp - 7 + __NVIC_PRIO_BITS;
+
+  return (
+           ((PreemptPriority & ((1 << (PreemptPriorityBits)) - 1)) << SubPriorityBits) |
+           ((SubPriority     & ((1 << (SubPriorityBits    )) - 1)))
+         );
+}
+
+
+/** \brief  Decode Priority
+
+    The function decodes an interrupt priority value with a given priority group to
+    preemptive priority value and subpriority value.
+    In case of a conflict between priority grouping and available
+    priority bits (__NVIC_PRIO_BITS) the samllest possible priority group is set.
+
+    \param [in]         Priority   Priority value, which can be retrieved with the function \ref NVIC_GetPriority().
+    \param [in]     PriorityGroup  Used priority group.
+    \param [out] pPreemptPriority  Preemptive priority value (starting from 0).
+    \param [out]     pSubPriority  Subpriority value (starting from 0).
+ */
+__STATIC_INLINE void NVIC_DecodePriority (uint32_t Priority, uint32_t PriorityGroup, uint32_t* pPreemptPriority, uint32_t* pSubPriority)
+{
+  uint32_t PriorityGroupTmp = (PriorityGroup & 0x07);          /* only values 0..7 are used          */
+  uint32_t PreemptPriorityBits;
+  uint32_t SubPriorityBits;
+
+  PreemptPriorityBits = ((7 - PriorityGroupTmp) > __NVIC_PRIO_BITS) ? __NVIC_PRIO_BITS : 7 - PriorityGroupTmp;
+  SubPriorityBits     = ((PriorityGroupTmp + __NVIC_PRIO_BITS) < 7) ? 0 : PriorityGroupTmp - 7 + __NVIC_PRIO_BITS;
+
+  *pPreemptPriority = (Priority >> SubPriorityBits) & ((1 << (PreemptPriorityBits)) - 1);
+  *pSubPriority     = (Priority                   ) & ((1 << (SubPriorityBits    )) - 1);
+}
+
+
+/** \brief  System Reset
+
+    The function initiates a system reset request to reset the MCU.
+ */
+__STATIC_INLINE void NVIC_SystemReset(void)
+{
+  __DSB();                                                     /* Ensure all outstanding memory accesses included
+                                                                  buffered write are completed before reset */
+  SCB->AIRCR  = ((0x5FA << SCB_AIRCR_VECTKEY_Pos)      |
+                 (SCB->AIRCR & SCB_AIRCR_PRIGROUP_Msk) |
+                 SCB_AIRCR_SYSRESETREQ_Msk);                   /* Keep priority group unchanged */
+  __DSB();                                                     /* Ensure completion of memory access */
+  while(1);                                                    /* wait until reset */
+}
+
+/*@} end of CMSIS_Core_NVICFunctions */
+
+
+
+/* ##################################    SysTick function  ############################################ */
+/** \ingroup  CMSIS_Core_FunctionInterface
+    \defgroup CMSIS_Core_SysTickFunctions SysTick Functions
+    \brief      Functions that configure the System.
+  @{
+ */
+
+#if (__Vendor_SysTickConfig == 0)
+
+/** \brief  System Tick Configuration
+
+    The function initializes the System Timer and its interrupt, and starts the System Tick Timer.
+    Counter is in free running mode to generate periodic interrupts.
+
+    \param [in]  ticks  Number of ticks between two interrupts.
+
+    \return          0  Function succeeded.
+    \return          1  Function failed.
+
+    \note     When the variable __Vendor_SysTickConfig is set to 1, then the
+    function SysTick_Config is not included. In this case, the file device.h
+    must contain a vendor-specific implementation of this function.
+
+ */
+__STATIC_INLINE uint32_t SysTick_Config(uint32_t ticks)
+{
+  if (ticks > SysTick_LOAD_RELOAD_Msk)  return (1);            /* Reload value impossible */
+
+  SysTick->LOAD  = (ticks & SysTick_LOAD_RELOAD_Msk) - 1;      /* set reload register */
+  NVIC_SetPriority (SysTick_IRQn, (1<<__NVIC_PRIO_BITS) - 1);  /* set Priority for Systick Interrupt */
+  SysTick->VAL   = 0;                                          /* Load the SysTick Counter Value */
+  SysTick->CTRL  = SysTick_CTRL_CLKSOURCE_Msk |
+                   SysTick_CTRL_TICKINT_Msk   |
+                   SysTick_CTRL_ENABLE_Msk;                    /* Enable SysTick IRQ and SysTick Timer */
+  return (0);                                                  /* Function successful */
+}
+
+#endif
+
+/*@} end of CMSIS_Core_SysTickFunctions */
+
+
+
+/* ##################################### Debug In/Output function ########################################### */
+/** \ingroup  CMSIS_Core_FunctionInterface
+    \defgroup CMSIS_core_DebugFunctions ITM Functions
+    \brief   Functions that access the ITM debug interface.
+  @{
+ */
+
+extern volatile int32_t ITM_RxBuffer;                    /*!< External variable to receive characters.                         */
+#define                 ITM_RXBUFFER_EMPTY    0x5AA55AA5 /*!< Value identifying \ref ITM_RxBuffer is ready for next character. */
+
+
+/** \brief  ITM Send Character
+
+    The function transmits a character via the ITM channel 0, and
+    \li Just returns when no debugger is connected that has booked the output.
+    \li Is blocking when a debugger is connected, but the previous character sent has not been transmitted.
+
+    \param [in]     ch  Character to transmit.
+
+    \returns            Character to transmit.
+ */
+__STATIC_INLINE uint32_t ITM_SendChar (uint32_t ch)
+{
+  if ((ITM->TCR & ITM_TCR_ITMENA_Msk)                  &&      /* ITM enabled */
+      (ITM->TER & (1UL << 0)        )                    )     /* ITM Port #0 enabled */
+  {
+    while (ITM->PORT[0].u32 == 0);
+    ITM->PORT[0].u8 = (uint8_t) ch;
+  }
+  return (ch);
+}
+
+
+/** \brief  ITM Receive Character
+
+    The function inputs a character via the external variable \ref ITM_RxBuffer.
+
+    \return             Received character.
+    \return         -1  No character pending.
+ */
+__STATIC_INLINE int32_t ITM_ReceiveChar (void) {
+  int32_t ch = -1;                           /* no character available */
+
+  if (ITM_RxBuffer != ITM_RXBUFFER_EMPTY) {
+    ch = ITM_RxBuffer;
+    ITM_RxBuffer = ITM_RXBUFFER_EMPTY;       /* ready for next character */
+  }
+
+  return (ch);
+}
+
+
+/** \brief  ITM Check Character
+
+    The function checks whether a character is pending for reading in the variable \ref ITM_RxBuffer.
+
+    \return          0  No character available.
+    \return          1  Character available.
+ */
+__STATIC_INLINE int32_t ITM_CheckChar (void) {
+
+  if (ITM_RxBuffer == ITM_RXBUFFER_EMPTY) {
+    return (0);                                 /* no character available */
+  } else {
+    return (1);                                 /*    character available */
+  }
+}
+
+/*@} end of CMSIS_core_DebugFunctions */
+
+#endif /* __CORE_CM3_H_DEPENDANT */
+
+#endif /* __CMSIS_GENERIC */
+
+#ifdef __cplusplus
+}
+#endif
diff --git a/apps/mathlib/CMSIS/Include/core_cm4.h b/apps/mathlib/CMSIS/Include/core_cm4.h
new file mode 100644
index 0000000000..5f3b7d6198
--- /dev/null
+++ b/apps/mathlib/CMSIS/Include/core_cm4.h
@@ -0,0 +1,1757 @@
+/**************************************************************************//**
+ * @file     core_cm4.h
+ * @brief    CMSIS Cortex-M4 Core Peripheral Access Layer Header File
+ * @version  V3.01
+ * @date     22. March 2012
+ *
+ * @note
+ * Copyright (C) 2009-2012 ARM Limited. All rights reserved.
+ *
+ * @par
+ * ARM Limited (ARM) is supplying this software for use with Cortex-M
+ * processor based microcontrollers.  This file can be freely distributed
+ * within development tools that are supporting such ARM based processors.
+ *
+ * @par
+ * THIS SOFTWARE IS PROVIDED "AS IS".  NO WARRANTIES, WHETHER EXPRESS, IMPLIED
+ * OR STATUTORY, INCLUDING, BUT NOT LIMITED TO, IMPLIED WARRANTIES OF
+ * MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE APPLY TO THIS SOFTWARE.
+ * ARM SHALL NOT, IN ANY CIRCUMSTANCES, BE LIABLE FOR SPECIAL, INCIDENTAL, OR
+ * CONSEQUENTIAL DAMAGES, FOR ANY REASON WHATSOEVER.
+ *
+ ******************************************************************************/
+#if defined ( __ICCARM__ )
+ #pragma system_include  /* treat file as system include file for MISRA check */
+#endif
+
+#ifdef __cplusplus
+ extern "C" {
+#endif
+
+#ifndef __CORE_CM4_H_GENERIC
+#define __CORE_CM4_H_GENERIC
+
+/** \page CMSIS_MISRA_Exceptions  MISRA-C:2004 Compliance Exceptions
+  CMSIS violates the following MISRA-C:2004 rules:
+
+   \li Required Rule 8.5, object/function definition in header file.

+     Function definitions in header files are used to allow 'inlining'.
+
+   \li Required Rule 18.4, declaration of union type or object of union type: '{...}'.

+     Unions are used for effective representation of core registers.
+
+   \li Advisory Rule 19.7, Function-like macro defined.

+     Function-like macros are used to allow more efficient code.
+ */
+
+
+/*******************************************************************************
+ *                 CMSIS definitions
+ ******************************************************************************/
+/** \ingroup Cortex_M4
+  @{
+ */
+
+/*  CMSIS CM4 definitions */
+#define __CM4_CMSIS_VERSION_MAIN  (0x03)                                   /*!< [31:16] CMSIS HAL main version   */
+#define __CM4_CMSIS_VERSION_SUB   (0x01)                                   /*!< [15:0]  CMSIS HAL sub version    */
+#define __CM4_CMSIS_VERSION       ((__CM4_CMSIS_VERSION_MAIN << 16) | \
+                                    __CM4_CMSIS_VERSION_SUB          )     /*!< CMSIS HAL version number         */
+
+#define __CORTEX_M                (0x04)                                   /*!< Cortex-M Core                    */
+
+
+#if   defined ( __CC_ARM )
+  #define __ASM            __asm                                      /*!< asm keyword for ARM Compiler          */
+  #define __INLINE         __inline                                   /*!< inline keyword for ARM Compiler       */
+  #define __STATIC_INLINE  static __inline
+
+#elif defined ( __ICCARM__ )
+  #define __ASM            __asm                                      /*!< asm keyword for IAR Compiler          */
+  #define __INLINE         inline                                     /*!< inline keyword for IAR Compiler. Only available in High optimization mode! */
+  #define __STATIC_INLINE  static inline
+
+#elif defined ( __TMS470__ )
+  #define __ASM            __asm                                      /*!< asm keyword for TI CCS Compiler       */
+  #define __STATIC_INLINE  static inline
+
+#elif defined ( __GNUC__ )
+  #define __ASM            __asm                                      /*!< asm keyword for GNU Compiler          */
+  #define __INLINE         inline                                     /*!< inline keyword for GNU Compiler       */
+  #define __STATIC_INLINE  static inline
+
+#elif defined ( __TASKING__ )
+  #define __ASM            __asm                                      /*!< asm keyword for TASKING Compiler      */
+  #define __INLINE         inline                                     /*!< inline keyword for TASKING Compiler   */
+  #define __STATIC_INLINE  static inline
+
+#endif
+
+/** __FPU_USED indicates whether an FPU is used or not. For this, __FPU_PRESENT has to be checked prior to making use of FPU specific registers and functions.
+*/
+#if defined ( __CC_ARM )
+  #if defined __TARGET_FPU_VFP
+    #if (__FPU_PRESENT == 1)
+      #define __FPU_USED       1
+    #else
+      #warning "Compiler generates FPU instructions for a device without an FPU (check __FPU_PRESENT)"
+      #define __FPU_USED       0
+    #endif
+  #else
+    #define __FPU_USED         0
+  #endif
+
+#elif defined ( __ICCARM__ )
+  #if defined __ARMVFP__
+    #if (__FPU_PRESENT == 1)
+      #define __FPU_USED       1
+    #else
+      #warning "Compiler generates FPU instructions for a device without an FPU (check __FPU_PRESENT)"
+      #define __FPU_USED       0
+    #endif
+  #else
+    #define __FPU_USED         0
+  #endif
+
+#elif defined ( __TMS470__ )
+  #if defined __TI_VFP_SUPPORT__
+    #if (__FPU_PRESENT == 1)
+      #define __FPU_USED       1
+    #else
+      #warning "Compiler generates FPU instructions for a device without an FPU (check __FPU_PRESENT)"
+      #define __FPU_USED       0
+    #endif
+  #else
+    #define __FPU_USED         0
+  #endif
+
+#elif defined ( __GNUC__ )
+  #if defined (__VFP_FP__) && !defined(__SOFTFP__)
+    #if (__FPU_PRESENT == 1)
+      #define __FPU_USED       1
+    #else
+      #warning "Compiler generates FPU instructions for a device without an FPU (check __FPU_PRESENT)"
+      #define __FPU_USED       0
+    #endif
+  #else
+    #define __FPU_USED         0
+  #endif
+
+#elif defined ( __TASKING__ )
+  #if defined __FPU_VFP__
+    #if (__FPU_PRESENT == 1)
+      #define __FPU_USED       1
+    #else
+      #error "Compiler generates FPU instructions for a device without an FPU (check __FPU_PRESENT)"
+      #define __FPU_USED       0
+    #endif
+  #else
+    #define __FPU_USED         0
+  #endif
+#endif
+
+#include                       /* standard types definitions                      */
+#include "core_cmInstr.h"                /* Core Instruction Access                         */
+#include "core_cmFunc.h"                 /* Core Function Access                            */
+#include "core_cm4_simd.h"               /* Compiler specific SIMD Intrinsics               */
+
+#endif /* __CORE_CM4_H_GENERIC */
+
+#ifndef __CMSIS_GENERIC
+
+#ifndef __CORE_CM4_H_DEPENDANT
+#define __CORE_CM4_H_DEPENDANT
+
+/* check device defines and use defaults */
+#if defined __CHECK_DEVICE_DEFINES
+  #ifndef __CM4_REV
+    #define __CM4_REV               0x0000
+    #warning "__CM4_REV not defined in device header file; using default!"
+  #endif
+
+  #ifndef __FPU_PRESENT
+    #define __FPU_PRESENT             0
+    #warning "__FPU_PRESENT not defined in device header file; using default!"
+  #endif
+
+  #ifndef __MPU_PRESENT
+    #define __MPU_PRESENT             0
+    #warning "__MPU_PRESENT not defined in device header file; using default!"
+  #endif
+
+  #ifndef __NVIC_PRIO_BITS
+    #define __NVIC_PRIO_BITS          4
+    #warning "__NVIC_PRIO_BITS not defined in device header file; using default!"
+  #endif
+
+  #ifndef __Vendor_SysTickConfig
+    #define __Vendor_SysTickConfig    0
+    #warning "__Vendor_SysTickConfig not defined in device header file; using default!"
+  #endif
+#endif
+
+/* IO definitions (access restrictions to peripheral registers) */
+/**
+    \defgroup CMSIS_glob_defs CMSIS Global Defines
+
+    IO Type Qualifiers are used
+    \li to specify the access to peripheral variables.
+    \li for automatic generation of peripheral register debug information.
+*/
+#ifdef __cplusplus
+  #define   __I     volatile             /*!< Defines 'read only' permissions                 */
+#else
+  #define   __I     volatile const       /*!< Defines 'read only' permissions                 */
+#endif
+#define     __O     volatile             /*!< Defines 'write only' permissions                */
+#define     __IO    volatile             /*!< Defines 'read / write' permissions              */
+
+/*@} end of group Cortex_M4 */
+
+
+
+/*******************************************************************************
+ *                 Register Abstraction
+  Core Register contain:
+  - Core Register
+  - Core NVIC Register
+  - Core SCB Register
+  - Core SysTick Register
+  - Core Debug Register
+  - Core MPU Register
+  - Core FPU Register
+ ******************************************************************************/
+/** \defgroup CMSIS_core_register Defines and Type Definitions
+    \brief Type definitions and defines for Cortex-M processor based devices.
+*/
+
+/** \ingroup    CMSIS_core_register
+    \defgroup   CMSIS_CORE  Status and Control Registers
+    \brief  Core Register type definitions.
+  @{
+ */
+
+/** \brief  Union type to access the Application Program Status Register (APSR).
+ */
+typedef union
+{
+  struct
+  {
+#if (__CORTEX_M != 0x04)
+    uint32_t _reserved0:27;              /*!< bit:  0..26  Reserved                           */
+#else
+    uint32_t _reserved0:16;              /*!< bit:  0..15  Reserved                           */
+    uint32_t GE:4;                       /*!< bit: 16..19  Greater than or Equal flags        */
+    uint32_t _reserved1:7;               /*!< bit: 20..26  Reserved                           */
+#endif
+    uint32_t Q:1;                        /*!< bit:     27  Saturation condition flag          */
+    uint32_t V:1;                        /*!< bit:     28  Overflow condition code flag       */
+    uint32_t C:1;                        /*!< bit:     29  Carry condition code flag          */
+    uint32_t Z:1;                        /*!< bit:     30  Zero condition code flag           */
+    uint32_t N:1;                        /*!< bit:     31  Negative condition code flag       */
+  } b;                                   /*!< Structure used for bit  access                  */
+  uint32_t w;                            /*!< Type      used for word access                  */
+} APSR_Type;
+
+
+/** \brief  Union type to access the Interrupt Program Status Register (IPSR).
+ */
+typedef union
+{
+  struct
+  {
+    uint32_t ISR:9;                      /*!< bit:  0.. 8  Exception number                   */
+    uint32_t _reserved0:23;              /*!< bit:  9..31  Reserved                           */
+  } b;                                   /*!< Structure used for bit  access                  */
+  uint32_t w;                            /*!< Type      used for word access                  */
+} IPSR_Type;
+
+
+/** \brief  Union type to access the Special-Purpose Program Status Registers (xPSR).
+ */
+typedef union
+{
+  struct
+  {
+    uint32_t ISR:9;                      /*!< bit:  0.. 8  Exception number                   */
+#if (__CORTEX_M != 0x04)
+    uint32_t _reserved0:15;              /*!< bit:  9..23  Reserved                           */
+#else
+    uint32_t _reserved0:7;               /*!< bit:  9..15  Reserved                           */
+    uint32_t GE:4;                       /*!< bit: 16..19  Greater than or Equal flags        */
+    uint32_t _reserved1:4;               /*!< bit: 20..23  Reserved                           */
+#endif
+    uint32_t T:1;                        /*!< bit:     24  Thumb bit        (read 0)          */
+    uint32_t IT:2;                       /*!< bit: 25..26  saved IT state   (read 0)          */
+    uint32_t Q:1;                        /*!< bit:     27  Saturation condition flag          */
+    uint32_t V:1;                        /*!< bit:     28  Overflow condition code flag       */
+    uint32_t C:1;                        /*!< bit:     29  Carry condition code flag          */
+    uint32_t Z:1;                        /*!< bit:     30  Zero condition code flag           */
+    uint32_t N:1;                        /*!< bit:     31  Negative condition code flag       */
+  } b;                                   /*!< Structure used for bit  access                  */
+  uint32_t w;                            /*!< Type      used for word access                  */
+} xPSR_Type;
+
+
+/** \brief  Union type to access the Control Registers (CONTROL).
+ */
+typedef union
+{
+  struct
+  {
+    uint32_t nPRIV:1;                    /*!< bit:      0  Execution privilege in Thread mode */
+    uint32_t SPSEL:1;                    /*!< bit:      1  Stack to be used                   */
+    uint32_t FPCA:1;                     /*!< bit:      2  FP extension active flag           */
+    uint32_t _reserved0:29;              /*!< bit:  3..31  Reserved                           */
+  } b;                                   /*!< Structure used for bit  access                  */
+  uint32_t w;                            /*!< Type      used for word access                  */
+} CONTROL_Type;
+
+/*@} end of group CMSIS_CORE */
+
+
+/** \ingroup    CMSIS_core_register
+    \defgroup   CMSIS_NVIC  Nested Vectored Interrupt Controller (NVIC)
+    \brief      Type definitions for the NVIC Registers
+  @{
+ */
+
+/** \brief  Structure type to access the Nested Vectored Interrupt Controller (NVIC).
+ */
+typedef struct
+{
+  __IO uint32_t ISER[8];                 /*!< Offset: 0x000 (R/W)  Interrupt Set Enable Register           */
+       uint32_t RESERVED0[24];
+  __IO uint32_t ICER[8];                 /*!< Offset: 0x080 (R/W)  Interrupt Clear Enable Register         */
+       uint32_t RSERVED1[24];
+  __IO uint32_t ISPR[8];                 /*!< Offset: 0x100 (R/W)  Interrupt Set Pending Register          */
+       uint32_t RESERVED2[24];
+  __IO uint32_t ICPR[8];                 /*!< Offset: 0x180 (R/W)  Interrupt Clear Pending Register        */
+       uint32_t RESERVED3[24];
+  __IO uint32_t IABR[8];                 /*!< Offset: 0x200 (R/W)  Interrupt Active bit Register           */
+       uint32_t RESERVED4[56];
+  __IO uint8_t  IP[240];                 /*!< Offset: 0x300 (R/W)  Interrupt Priority Register (8Bit wide) */
+       uint32_t RESERVED5[644];
+  __O  uint32_t STIR;                    /*!< Offset: 0xE00 ( /W)  Software Trigger Interrupt Register     */
+}  NVIC_Type;
+
+/* Software Triggered Interrupt Register Definitions */
+#define NVIC_STIR_INTID_Pos                 0                                          /*!< STIR: INTLINESNUM Position */
+#define NVIC_STIR_INTID_Msk                (0x1FFUL << NVIC_STIR_INTID_Pos)            /*!< STIR: INTLINESNUM Mask */
+
+/*@} end of group CMSIS_NVIC */
+
+
+/** \ingroup  CMSIS_core_register
+    \defgroup CMSIS_SCB     System Control Block (SCB)
+    \brief      Type definitions for the System Control Block Registers
+  @{
+ */
+
+/** \brief  Structure type to access the System Control Block (SCB).
+ */
+typedef struct
+{
+  __I  uint32_t CPUID;                   /*!< Offset: 0x000 (R/ )  CPUID Base Register                                   */
+  __IO uint32_t ICSR;                    /*!< Offset: 0x004 (R/W)  Interrupt Control and State Register                  */
+  __IO uint32_t VTOR;                    /*!< Offset: 0x008 (R/W)  Vector Table Offset Register                          */
+  __IO uint32_t AIRCR;                   /*!< Offset: 0x00C (R/W)  Application Interrupt and Reset Control Register      */
+  __IO uint32_t SCR;                     /*!< Offset: 0x010 (R/W)  System Control Register                               */
+  __IO uint32_t CCR;                     /*!< Offset: 0x014 (R/W)  Configuration Control Register                        */
+  __IO uint8_t  SHP[12];                 /*!< Offset: 0x018 (R/W)  System Handlers Priority Registers (4-7, 8-11, 12-15) */
+  __IO uint32_t SHCSR;                   /*!< Offset: 0x024 (R/W)  System Handler Control and State Register             */
+  __IO uint32_t CFSR;                    /*!< Offset: 0x028 (R/W)  Configurable Fault Status Register                    */
+  __IO uint32_t HFSR;                    /*!< Offset: 0x02C (R/W)  HardFault Status Register                             */
+  __IO uint32_t DFSR;                    /*!< Offset: 0x030 (R/W)  Debug Fault Status Register                           */
+  __IO uint32_t MMFAR;                   /*!< Offset: 0x034 (R/W)  MemManage Fault Address Register                      */
+  __IO uint32_t BFAR;                    /*!< Offset: 0x038 (R/W)  BusFault Address Register                             */
+  __IO uint32_t AFSR;                    /*!< Offset: 0x03C (R/W)  Auxiliary Fault Status Register                       */
+  __I  uint32_t PFR[2];                  /*!< Offset: 0x040 (R/ )  Processor Feature Register                            */
+  __I  uint32_t DFR;                     /*!< Offset: 0x048 (R/ )  Debug Feature Register                                */
+  __I  uint32_t ADR;                     /*!< Offset: 0x04C (R/ )  Auxiliary Feature Register                            */
+  __I  uint32_t MMFR[4];                 /*!< Offset: 0x050 (R/ )  Memory Model Feature Register                         */
+  __I  uint32_t ISAR[5];                 /*!< Offset: 0x060 (R/ )  Instruction Set Attributes Register                   */
+       uint32_t RESERVED0[5];
+  __IO uint32_t CPACR;                   /*!< Offset: 0x088 (R/W)  Coprocessor Access Control Register                   */
+} SCB_Type;
+
+/* SCB CPUID Register Definitions */
+#define SCB_CPUID_IMPLEMENTER_Pos          24                                             /*!< SCB CPUID: IMPLEMENTER Position */
+#define SCB_CPUID_IMPLEMENTER_Msk          (0xFFUL << SCB_CPUID_IMPLEMENTER_Pos)          /*!< SCB CPUID: IMPLEMENTER Mask */
+
+#define SCB_CPUID_VARIANT_Pos              20                                             /*!< SCB CPUID: VARIANT Position */
+#define SCB_CPUID_VARIANT_Msk              (0xFUL << SCB_CPUID_VARIANT_Pos)               /*!< SCB CPUID: VARIANT Mask */
+
+#define SCB_CPUID_ARCHITECTURE_Pos         16                                             /*!< SCB CPUID: ARCHITECTURE Position */
+#define SCB_CPUID_ARCHITECTURE_Msk         (0xFUL << SCB_CPUID_ARCHITECTURE_Pos)          /*!< SCB CPUID: ARCHITECTURE Mask */
+
+#define SCB_CPUID_PARTNO_Pos                4                                             /*!< SCB CPUID: PARTNO Position */
+#define SCB_CPUID_PARTNO_Msk               (0xFFFUL << SCB_CPUID_PARTNO_Pos)              /*!< SCB CPUID: PARTNO Mask */
+
+#define SCB_CPUID_REVISION_Pos              0                                             /*!< SCB CPUID: REVISION Position */
+#define SCB_CPUID_REVISION_Msk             (0xFUL << SCB_CPUID_REVISION_Pos)              /*!< SCB CPUID: REVISION Mask */
+
+/* SCB Interrupt Control State Register Definitions */
+#define SCB_ICSR_NMIPENDSET_Pos            31                                             /*!< SCB ICSR: NMIPENDSET Position */
+#define SCB_ICSR_NMIPENDSET_Msk            (1UL << SCB_ICSR_NMIPENDSET_Pos)               /*!< SCB ICSR: NMIPENDSET Mask */
+
+#define SCB_ICSR_PENDSVSET_Pos             28                                             /*!< SCB ICSR: PENDSVSET Position */
+#define SCB_ICSR_PENDSVSET_Msk             (1UL << SCB_ICSR_PENDSVSET_Pos)                /*!< SCB ICSR: PENDSVSET Mask */
+
+#define SCB_ICSR_PENDSVCLR_Pos             27                                             /*!< SCB ICSR: PENDSVCLR Position */
+#define SCB_ICSR_PENDSVCLR_Msk             (1UL << SCB_ICSR_PENDSVCLR_Pos)                /*!< SCB ICSR: PENDSVCLR Mask */
+
+#define SCB_ICSR_PENDSTSET_Pos             26                                             /*!< SCB ICSR: PENDSTSET Position */
+#define SCB_ICSR_PENDSTSET_Msk             (1UL << SCB_ICSR_PENDSTSET_Pos)                /*!< SCB ICSR: PENDSTSET Mask */
+
+#define SCB_ICSR_PENDSTCLR_Pos             25                                             /*!< SCB ICSR: PENDSTCLR Position */
+#define SCB_ICSR_PENDSTCLR_Msk             (1UL << SCB_ICSR_PENDSTCLR_Pos)                /*!< SCB ICSR: PENDSTCLR Mask */
+
+#define SCB_ICSR_ISRPREEMPT_Pos            23                                             /*!< SCB ICSR: ISRPREEMPT Position */
+#define SCB_ICSR_ISRPREEMPT_Msk            (1UL << SCB_ICSR_ISRPREEMPT_Pos)               /*!< SCB ICSR: ISRPREEMPT Mask */
+
+#define SCB_ICSR_ISRPENDING_Pos            22                                             /*!< SCB ICSR: ISRPENDING Position */
+#define SCB_ICSR_ISRPENDING_Msk            (1UL << SCB_ICSR_ISRPENDING_Pos)               /*!< SCB ICSR: ISRPENDING Mask */
+
+#define SCB_ICSR_VECTPENDING_Pos           12                                             /*!< SCB ICSR: VECTPENDING Position */
+#define SCB_ICSR_VECTPENDING_Msk           (0x1FFUL << SCB_ICSR_VECTPENDING_Pos)          /*!< SCB ICSR: VECTPENDING Mask */
+
+#define SCB_ICSR_RETTOBASE_Pos             11                                             /*!< SCB ICSR: RETTOBASE Position */
+#define SCB_ICSR_RETTOBASE_Msk             (1UL << SCB_ICSR_RETTOBASE_Pos)                /*!< SCB ICSR: RETTOBASE Mask */
+
+#define SCB_ICSR_VECTACTIVE_Pos             0                                             /*!< SCB ICSR: VECTACTIVE Position */
+#define SCB_ICSR_VECTACTIVE_Msk            (0x1FFUL << SCB_ICSR_VECTACTIVE_Pos)           /*!< SCB ICSR: VECTACTIVE Mask */
+
+/* SCB Vector Table Offset Register Definitions */
+#define SCB_VTOR_TBLOFF_Pos                 7                                             /*!< SCB VTOR: TBLOFF Position */
+#define SCB_VTOR_TBLOFF_Msk                (0x1FFFFFFUL << SCB_VTOR_TBLOFF_Pos)           /*!< SCB VTOR: TBLOFF Mask */
+
+/* SCB Application Interrupt and Reset Control Register Definitions */
+#define SCB_AIRCR_VECTKEY_Pos              16                                             /*!< SCB AIRCR: VECTKEY Position */
+#define SCB_AIRCR_VECTKEY_Msk              (0xFFFFUL << SCB_AIRCR_VECTKEY_Pos)            /*!< SCB AIRCR: VECTKEY Mask */
+
+#define SCB_AIRCR_VECTKEYSTAT_Pos          16                                             /*!< SCB AIRCR: VECTKEYSTAT Position */
+#define SCB_AIRCR_VECTKEYSTAT_Msk          (0xFFFFUL << SCB_AIRCR_VECTKEYSTAT_Pos)        /*!< SCB AIRCR: VECTKEYSTAT Mask */
+
+#define SCB_AIRCR_ENDIANESS_Pos            15                                             /*!< SCB AIRCR: ENDIANESS Position */
+#define SCB_AIRCR_ENDIANESS_Msk            (1UL << SCB_AIRCR_ENDIANESS_Pos)               /*!< SCB AIRCR: ENDIANESS Mask */
+
+#define SCB_AIRCR_PRIGROUP_Pos              8                                             /*!< SCB AIRCR: PRIGROUP Position */
+#define SCB_AIRCR_PRIGROUP_Msk             (7UL << SCB_AIRCR_PRIGROUP_Pos)                /*!< SCB AIRCR: PRIGROUP Mask */
+
+#define SCB_AIRCR_SYSRESETREQ_Pos           2                                             /*!< SCB AIRCR: SYSRESETREQ Position */
+#define SCB_AIRCR_SYSRESETREQ_Msk          (1UL << SCB_AIRCR_SYSRESETREQ_Pos)             /*!< SCB AIRCR: SYSRESETREQ Mask */
+
+#define SCB_AIRCR_VECTCLRACTIVE_Pos         1                                             /*!< SCB AIRCR: VECTCLRACTIVE Position */
+#define SCB_AIRCR_VECTCLRACTIVE_Msk        (1UL << SCB_AIRCR_VECTCLRACTIVE_Pos)           /*!< SCB AIRCR: VECTCLRACTIVE Mask */
+
+#define SCB_AIRCR_VECTRESET_Pos             0                                             /*!< SCB AIRCR: VECTRESET Position */
+#define SCB_AIRCR_VECTRESET_Msk            (1UL << SCB_AIRCR_VECTRESET_Pos)               /*!< SCB AIRCR: VECTRESET Mask */
+
+/* SCB System Control Register Definitions */
+#define SCB_SCR_SEVONPEND_Pos               4                                             /*!< SCB SCR: SEVONPEND Position */
+#define SCB_SCR_SEVONPEND_Msk              (1UL << SCB_SCR_SEVONPEND_Pos)                 /*!< SCB SCR: SEVONPEND Mask */
+
+#define SCB_SCR_SLEEPDEEP_Pos               2                                             /*!< SCB SCR: SLEEPDEEP Position */
+#define SCB_SCR_SLEEPDEEP_Msk              (1UL << SCB_SCR_SLEEPDEEP_Pos)                 /*!< SCB SCR: SLEEPDEEP Mask */
+
+#define SCB_SCR_SLEEPONEXIT_Pos             1                                             /*!< SCB SCR: SLEEPONEXIT Position */
+#define SCB_SCR_SLEEPONEXIT_Msk            (1UL << SCB_SCR_SLEEPONEXIT_Pos)               /*!< SCB SCR: SLEEPONEXIT Mask */
+
+/* SCB Configuration Control Register Definitions */
+#define SCB_CCR_STKALIGN_Pos                9                                             /*!< SCB CCR: STKALIGN Position */
+#define SCB_CCR_STKALIGN_Msk               (1UL << SCB_CCR_STKALIGN_Pos)                  /*!< SCB CCR: STKALIGN Mask */
+
+#define SCB_CCR_BFHFNMIGN_Pos               8                                             /*!< SCB CCR: BFHFNMIGN Position */
+#define SCB_CCR_BFHFNMIGN_Msk              (1UL << SCB_CCR_BFHFNMIGN_Pos)                 /*!< SCB CCR: BFHFNMIGN Mask */
+
+#define SCB_CCR_DIV_0_TRP_Pos               4                                             /*!< SCB CCR: DIV_0_TRP Position */
+#define SCB_CCR_DIV_0_TRP_Msk              (1UL << SCB_CCR_DIV_0_TRP_Pos)                 /*!< SCB CCR: DIV_0_TRP Mask */
+
+#define SCB_CCR_UNALIGN_TRP_Pos             3                                             /*!< SCB CCR: UNALIGN_TRP Position */
+#define SCB_CCR_UNALIGN_TRP_Msk            (1UL << SCB_CCR_UNALIGN_TRP_Pos)               /*!< SCB CCR: UNALIGN_TRP Mask */
+
+#define SCB_CCR_USERSETMPEND_Pos            1                                             /*!< SCB CCR: USERSETMPEND Position */
+#define SCB_CCR_USERSETMPEND_Msk           (1UL << SCB_CCR_USERSETMPEND_Pos)              /*!< SCB CCR: USERSETMPEND Mask */
+
+#define SCB_CCR_NONBASETHRDENA_Pos          0                                             /*!< SCB CCR: NONBASETHRDENA Position */
+#define SCB_CCR_NONBASETHRDENA_Msk         (1UL << SCB_CCR_NONBASETHRDENA_Pos)            /*!< SCB CCR: NONBASETHRDENA Mask */
+
+/* SCB System Handler Control and State Register Definitions */
+#define SCB_SHCSR_USGFAULTENA_Pos          18                                             /*!< SCB SHCSR: USGFAULTENA Position */
+#define SCB_SHCSR_USGFAULTENA_Msk          (1UL << SCB_SHCSR_USGFAULTENA_Pos)             /*!< SCB SHCSR: USGFAULTENA Mask */
+
+#define SCB_SHCSR_BUSFAULTENA_Pos          17                                             /*!< SCB SHCSR: BUSFAULTENA Position */
+#define SCB_SHCSR_BUSFAULTENA_Msk          (1UL << SCB_SHCSR_BUSFAULTENA_Pos)             /*!< SCB SHCSR: BUSFAULTENA Mask */
+
+#define SCB_SHCSR_MEMFAULTENA_Pos          16                                             /*!< SCB SHCSR: MEMFAULTENA Position */
+#define SCB_SHCSR_MEMFAULTENA_Msk          (1UL << SCB_SHCSR_MEMFAULTENA_Pos)             /*!< SCB SHCSR: MEMFAULTENA Mask */
+
+#define SCB_SHCSR_SVCALLPENDED_Pos         15                                             /*!< SCB SHCSR: SVCALLPENDED Position */
+#define SCB_SHCSR_SVCALLPENDED_Msk         (1UL << SCB_SHCSR_SVCALLPENDED_Pos)            /*!< SCB SHCSR: SVCALLPENDED Mask */
+
+#define SCB_SHCSR_BUSFAULTPENDED_Pos       14                                             /*!< SCB SHCSR: BUSFAULTPENDED Position */
+#define SCB_SHCSR_BUSFAULTPENDED_Msk       (1UL << SCB_SHCSR_BUSFAULTPENDED_Pos)          /*!< SCB SHCSR: BUSFAULTPENDED Mask */
+
+#define SCB_SHCSR_MEMFAULTPENDED_Pos       13                                             /*!< SCB SHCSR: MEMFAULTPENDED Position */
+#define SCB_SHCSR_MEMFAULTPENDED_Msk       (1UL << SCB_SHCSR_MEMFAULTPENDED_Pos)          /*!< SCB SHCSR: MEMFAULTPENDED Mask */
+
+#define SCB_SHCSR_USGFAULTPENDED_Pos       12                                             /*!< SCB SHCSR: USGFAULTPENDED Position */
+#define SCB_SHCSR_USGFAULTPENDED_Msk       (1UL << SCB_SHCSR_USGFAULTPENDED_Pos)          /*!< SCB SHCSR: USGFAULTPENDED Mask */
+
+#define SCB_SHCSR_SYSTICKACT_Pos           11                                             /*!< SCB SHCSR: SYSTICKACT Position */
+#define SCB_SHCSR_SYSTICKACT_Msk           (1UL << SCB_SHCSR_SYSTICKACT_Pos)              /*!< SCB SHCSR: SYSTICKACT Mask */
+
+#define SCB_SHCSR_PENDSVACT_Pos            10                                             /*!< SCB SHCSR: PENDSVACT Position */
+#define SCB_SHCSR_PENDSVACT_Msk            (1UL << SCB_SHCSR_PENDSVACT_Pos)               /*!< SCB SHCSR: PENDSVACT Mask */
+
+#define SCB_SHCSR_MONITORACT_Pos            8                                             /*!< SCB SHCSR: MONITORACT Position */
+#define SCB_SHCSR_MONITORACT_Msk           (1UL << SCB_SHCSR_MONITORACT_Pos)              /*!< SCB SHCSR: MONITORACT Mask */
+
+#define SCB_SHCSR_SVCALLACT_Pos             7                                             /*!< SCB SHCSR: SVCALLACT Position */
+#define SCB_SHCSR_SVCALLACT_Msk            (1UL << SCB_SHCSR_SVCALLACT_Pos)               /*!< SCB SHCSR: SVCALLACT Mask */
+
+#define SCB_SHCSR_USGFAULTACT_Pos           3                                             /*!< SCB SHCSR: USGFAULTACT Position */
+#define SCB_SHCSR_USGFAULTACT_Msk          (1UL << SCB_SHCSR_USGFAULTACT_Pos)             /*!< SCB SHCSR: USGFAULTACT Mask */
+
+#define SCB_SHCSR_BUSFAULTACT_Pos           1                                             /*!< SCB SHCSR: BUSFAULTACT Position */
+#define SCB_SHCSR_BUSFAULTACT_Msk          (1UL << SCB_SHCSR_BUSFAULTACT_Pos)             /*!< SCB SHCSR: BUSFAULTACT Mask */
+
+#define SCB_SHCSR_MEMFAULTACT_Pos           0                                             /*!< SCB SHCSR: MEMFAULTACT Position */
+#define SCB_SHCSR_MEMFAULTACT_Msk          (1UL << SCB_SHCSR_MEMFAULTACT_Pos)             /*!< SCB SHCSR: MEMFAULTACT Mask */
+
+/* SCB Configurable Fault Status Registers Definitions */
+#define SCB_CFSR_USGFAULTSR_Pos            16                                             /*!< SCB CFSR: Usage Fault Status Register Position */
+#define SCB_CFSR_USGFAULTSR_Msk            (0xFFFFUL << SCB_CFSR_USGFAULTSR_Pos)          /*!< SCB CFSR: Usage Fault Status Register Mask */
+
+#define SCB_CFSR_BUSFAULTSR_Pos             8                                             /*!< SCB CFSR: Bus Fault Status Register Position */
+#define SCB_CFSR_BUSFAULTSR_Msk            (0xFFUL << SCB_CFSR_BUSFAULTSR_Pos)            /*!< SCB CFSR: Bus Fault Status Register Mask */
+
+#define SCB_CFSR_MEMFAULTSR_Pos             0                                             /*!< SCB CFSR: Memory Manage Fault Status Register Position */
+#define SCB_CFSR_MEMFAULTSR_Msk            (0xFFUL << SCB_CFSR_MEMFAULTSR_Pos)            /*!< SCB CFSR: Memory Manage Fault Status Register Mask */
+
+/* SCB Hard Fault Status Registers Definitions */
+#define SCB_HFSR_DEBUGEVT_Pos              31                                             /*!< SCB HFSR: DEBUGEVT Position */
+#define SCB_HFSR_DEBUGEVT_Msk              (1UL << SCB_HFSR_DEBUGEVT_Pos)                 /*!< SCB HFSR: DEBUGEVT Mask */
+
+#define SCB_HFSR_FORCED_Pos                30                                             /*!< SCB HFSR: FORCED Position */
+#define SCB_HFSR_FORCED_Msk                (1UL << SCB_HFSR_FORCED_Pos)                   /*!< SCB HFSR: FORCED Mask */
+
+#define SCB_HFSR_VECTTBL_Pos                1                                             /*!< SCB HFSR: VECTTBL Position */
+#define SCB_HFSR_VECTTBL_Msk               (1UL << SCB_HFSR_VECTTBL_Pos)                  /*!< SCB HFSR: VECTTBL Mask */
+
+/* SCB Debug Fault Status Register Definitions */
+#define SCB_DFSR_EXTERNAL_Pos               4                                             /*!< SCB DFSR: EXTERNAL Position */
+#define SCB_DFSR_EXTERNAL_Msk              (1UL << SCB_DFSR_EXTERNAL_Pos)                 /*!< SCB DFSR: EXTERNAL Mask */
+
+#define SCB_DFSR_VCATCH_Pos                 3                                             /*!< SCB DFSR: VCATCH Position */
+#define SCB_DFSR_VCATCH_Msk                (1UL << SCB_DFSR_VCATCH_Pos)                   /*!< SCB DFSR: VCATCH Mask */
+
+#define SCB_DFSR_DWTTRAP_Pos                2                                             /*!< SCB DFSR: DWTTRAP Position */
+#define SCB_DFSR_DWTTRAP_Msk               (1UL << SCB_DFSR_DWTTRAP_Pos)                  /*!< SCB DFSR: DWTTRAP Mask */
+
+#define SCB_DFSR_BKPT_Pos                   1                                             /*!< SCB DFSR: BKPT Position */
+#define SCB_DFSR_BKPT_Msk                  (1UL << SCB_DFSR_BKPT_Pos)                     /*!< SCB DFSR: BKPT Mask */
+
+#define SCB_DFSR_HALTED_Pos                 0                                             /*!< SCB DFSR: HALTED Position */
+#define SCB_DFSR_HALTED_Msk                (1UL << SCB_DFSR_HALTED_Pos)                   /*!< SCB DFSR: HALTED Mask */
+
+/*@} end of group CMSIS_SCB */
+
+
+/** \ingroup  CMSIS_core_register
+    \defgroup CMSIS_SCnSCB System Controls not in SCB (SCnSCB)
+    \brief      Type definitions for the System Control and ID Register not in the SCB
+  @{
+ */
+
+/** \brief  Structure type to access the System Control and ID Register not in the SCB.
+ */
+typedef struct
+{
+       uint32_t RESERVED0[1];
+  __I  uint32_t ICTR;                    /*!< Offset: 0x004 (R/ )  Interrupt Controller Type Register      */
+  __IO uint32_t ACTLR;                   /*!< Offset: 0x008 (R/W)  Auxiliary Control Register              */
+} SCnSCB_Type;
+
+/* Interrupt Controller Type Register Definitions */
+#define SCnSCB_ICTR_INTLINESNUM_Pos         0                                          /*!< ICTR: INTLINESNUM Position */
+#define SCnSCB_ICTR_INTLINESNUM_Msk        (0xFUL << SCnSCB_ICTR_INTLINESNUM_Pos)      /*!< ICTR: INTLINESNUM Mask */
+
+/* Auxiliary Control Register Definitions */
+#define SCnSCB_ACTLR_DISOOFP_Pos            9                                          /*!< ACTLR: DISOOFP Position */
+#define SCnSCB_ACTLR_DISOOFP_Msk           (1UL << SCnSCB_ACTLR_DISOOFP_Pos)           /*!< ACTLR: DISOOFP Mask */
+
+#define SCnSCB_ACTLR_DISFPCA_Pos            8                                          /*!< ACTLR: DISFPCA Position */
+#define SCnSCB_ACTLR_DISFPCA_Msk           (1UL << SCnSCB_ACTLR_DISFPCA_Pos)           /*!< ACTLR: DISFPCA Mask */
+
+#define SCnSCB_ACTLR_DISFOLD_Pos            2                                          /*!< ACTLR: DISFOLD Position */
+#define SCnSCB_ACTLR_DISFOLD_Msk           (1UL << SCnSCB_ACTLR_DISFOLD_Pos)           /*!< ACTLR: DISFOLD Mask */
+
+#define SCnSCB_ACTLR_DISDEFWBUF_Pos         1                                          /*!< ACTLR: DISDEFWBUF Position */
+#define SCnSCB_ACTLR_DISDEFWBUF_Msk        (1UL << SCnSCB_ACTLR_DISDEFWBUF_Pos)        /*!< ACTLR: DISDEFWBUF Mask */
+
+#define SCnSCB_ACTLR_DISMCYCINT_Pos         0                                          /*!< ACTLR: DISMCYCINT Position */
+#define SCnSCB_ACTLR_DISMCYCINT_Msk        (1UL << SCnSCB_ACTLR_DISMCYCINT_Pos)        /*!< ACTLR: DISMCYCINT Mask */
+
+/*@} end of group CMSIS_SCnotSCB */
+
+
+/** \ingroup  CMSIS_core_register
+    \defgroup CMSIS_SysTick     System Tick Timer (SysTick)
+    \brief      Type definitions for the System Timer Registers.
+  @{
+ */
+
+/** \brief  Structure type to access the System Timer (SysTick).
+ */
+typedef struct
+{
+  __IO uint32_t CTRL;                    /*!< Offset: 0x000 (R/W)  SysTick Control and Status Register */
+  __IO uint32_t LOAD;                    /*!< Offset: 0x004 (R/W)  SysTick Reload Value Register       */
+  __IO uint32_t VAL;                     /*!< Offset: 0x008 (R/W)  SysTick Current Value Register      */
+  __I  uint32_t CALIB;                   /*!< Offset: 0x00C (R/ )  SysTick Calibration Register        */
+} SysTick_Type;
+
+/* SysTick Control / Status Register Definitions */
+#define SysTick_CTRL_COUNTFLAG_Pos         16                                             /*!< SysTick CTRL: COUNTFLAG Position */
+#define SysTick_CTRL_COUNTFLAG_Msk         (1UL << SysTick_CTRL_COUNTFLAG_Pos)            /*!< SysTick CTRL: COUNTFLAG Mask */
+
+#define SysTick_CTRL_CLKSOURCE_Pos          2                                             /*!< SysTick CTRL: CLKSOURCE Position */
+#define SysTick_CTRL_CLKSOURCE_Msk         (1UL << SysTick_CTRL_CLKSOURCE_Pos)            /*!< SysTick CTRL: CLKSOURCE Mask */
+
+#define SysTick_CTRL_TICKINT_Pos            1                                             /*!< SysTick CTRL: TICKINT Position */
+#define SysTick_CTRL_TICKINT_Msk           (1UL << SysTick_CTRL_TICKINT_Pos)              /*!< SysTick CTRL: TICKINT Mask */
+
+#define SysTick_CTRL_ENABLE_Pos             0                                             /*!< SysTick CTRL: ENABLE Position */
+#define SysTick_CTRL_ENABLE_Msk            (1UL << SysTick_CTRL_ENABLE_Pos)               /*!< SysTick CTRL: ENABLE Mask */
+
+/* SysTick Reload Register Definitions */
+#define SysTick_LOAD_RELOAD_Pos             0                                             /*!< SysTick LOAD: RELOAD Position */
+#define SysTick_LOAD_RELOAD_Msk            (0xFFFFFFUL << SysTick_LOAD_RELOAD_Pos)        /*!< SysTick LOAD: RELOAD Mask */
+
+/* SysTick Current Register Definitions */
+#define SysTick_VAL_CURRENT_Pos             0                                             /*!< SysTick VAL: CURRENT Position */
+#define SysTick_VAL_CURRENT_Msk            (0xFFFFFFUL << SysTick_VAL_CURRENT_Pos)        /*!< SysTick VAL: CURRENT Mask */
+
+/* SysTick Calibration Register Definitions */
+#define SysTick_CALIB_NOREF_Pos            31                                             /*!< SysTick CALIB: NOREF Position */
+#define SysTick_CALIB_NOREF_Msk            (1UL << SysTick_CALIB_NOREF_Pos)               /*!< SysTick CALIB: NOREF Mask */
+
+#define SysTick_CALIB_SKEW_Pos             30                                             /*!< SysTick CALIB: SKEW Position */
+#define SysTick_CALIB_SKEW_Msk             (1UL << SysTick_CALIB_SKEW_Pos)                /*!< SysTick CALIB: SKEW Mask */
+
+#define SysTick_CALIB_TENMS_Pos             0                                             /*!< SysTick CALIB: TENMS Position */
+#define SysTick_CALIB_TENMS_Msk            (0xFFFFFFUL << SysTick_VAL_CURRENT_Pos)        /*!< SysTick CALIB: TENMS Mask */
+
+/*@} end of group CMSIS_SysTick */
+
+
+/** \ingroup  CMSIS_core_register
+    \defgroup CMSIS_ITM     Instrumentation Trace Macrocell (ITM)
+    \brief      Type definitions for the Instrumentation Trace Macrocell (ITM)
+  @{
+ */
+
+/** \brief  Structure type to access the Instrumentation Trace Macrocell Register (ITM).
+ */
+typedef struct
+{
+  __O  union
+  {
+    __O  uint8_t    u8;                  /*!< Offset: 0x000 ( /W)  ITM Stimulus Port 8-bit                   */
+    __O  uint16_t   u16;                 /*!< Offset: 0x000 ( /W)  ITM Stimulus Port 16-bit                  */
+    __O  uint32_t   u32;                 /*!< Offset: 0x000 ( /W)  ITM Stimulus Port 32-bit                  */
+  }  PORT [32];                          /*!< Offset: 0x000 ( /W)  ITM Stimulus Port Registers               */
+       uint32_t RESERVED0[864];
+  __IO uint32_t TER;                     /*!< Offset: 0xE00 (R/W)  ITM Trace Enable Register                 */
+       uint32_t RESERVED1[15];
+  __IO uint32_t TPR;                     /*!< Offset: 0xE40 (R/W)  ITM Trace Privilege Register              */
+       uint32_t RESERVED2[15];
+  __IO uint32_t TCR;                     /*!< Offset: 0xE80 (R/W)  ITM Trace Control Register                */
+       uint32_t RESERVED3[29];                                  
+  __O  uint32_t IWR;                     /*!< Offset: 0xEF8 ( /W)  ITM Integration Write Register            */
+  __I  uint32_t IRR;                     /*!< Offset: 0xEFC (R/ )  ITM Integration Read Register             */
+  __IO uint32_t IMCR;                    /*!< Offset: 0xF00 (R/W)  ITM Integration Mode Control Register     */
+       uint32_t RESERVED4[43];                                  
+  __O  uint32_t LAR;                     /*!< Offset: 0xFB0 ( /W)  ITM Lock Access Register                  */
+  __I  uint32_t LSR;                     /*!< Offset: 0xFB4 (R/ )  ITM Lock Status Register                  */
+       uint32_t RESERVED5[6];                                   
+  __I  uint32_t PID4;                    /*!< Offset: 0xFD0 (R/ )  ITM Peripheral Identification Register #4 */
+  __I  uint32_t PID5;                    /*!< Offset: 0xFD4 (R/ )  ITM Peripheral Identification Register #5 */
+  __I  uint32_t PID6;                    /*!< Offset: 0xFD8 (R/ )  ITM Peripheral Identification Register #6 */
+  __I  uint32_t PID7;                    /*!< Offset: 0xFDC (R/ )  ITM Peripheral Identification Register #7 */
+  __I  uint32_t PID0;                    /*!< Offset: 0xFE0 (R/ )  ITM Peripheral Identification Register #0 */
+  __I  uint32_t PID1;                    /*!< Offset: 0xFE4 (R/ )  ITM Peripheral Identification Register #1 */
+  __I  uint32_t PID2;                    /*!< Offset: 0xFE8 (R/ )  ITM Peripheral Identification Register #2 */
+  __I  uint32_t PID3;                    /*!< Offset: 0xFEC (R/ )  ITM Peripheral Identification Register #3 */
+  __I  uint32_t CID0;                    /*!< Offset: 0xFF0 (R/ )  ITM Component  Identification Register #0 */
+  __I  uint32_t CID1;                    /*!< Offset: 0xFF4 (R/ )  ITM Component  Identification Register #1 */
+  __I  uint32_t CID2;                    /*!< Offset: 0xFF8 (R/ )  ITM Component  Identification Register #2 */
+  __I  uint32_t CID3;                    /*!< Offset: 0xFFC (R/ )  ITM Component  Identification Register #3 */
+} ITM_Type;
+
+/* ITM Trace Privilege Register Definitions */
+#define ITM_TPR_PRIVMASK_Pos                0                                             /*!< ITM TPR: PRIVMASK Position */
+#define ITM_TPR_PRIVMASK_Msk               (0xFUL << ITM_TPR_PRIVMASK_Pos)                /*!< ITM TPR: PRIVMASK Mask */
+
+/* ITM Trace Control Register Definitions */
+#define ITM_TCR_BUSY_Pos                   23                                             /*!< ITM TCR: BUSY Position */
+#define ITM_TCR_BUSY_Msk                   (1UL << ITM_TCR_BUSY_Pos)                      /*!< ITM TCR: BUSY Mask */
+
+#define ITM_TCR_TraceBusID_Pos             16                                             /*!< ITM TCR: ATBID Position */
+#define ITM_TCR_TraceBusID_Msk             (0x7FUL << ITM_TCR_TraceBusID_Pos)             /*!< ITM TCR: ATBID Mask */
+
+#define ITM_TCR_GTSFREQ_Pos                10                                             /*!< ITM TCR: Global timestamp frequency Position */
+#define ITM_TCR_GTSFREQ_Msk                (3UL << ITM_TCR_GTSFREQ_Pos)                   /*!< ITM TCR: Global timestamp frequency Mask */
+
+#define ITM_TCR_TSPrescale_Pos              8                                             /*!< ITM TCR: TSPrescale Position */
+#define ITM_TCR_TSPrescale_Msk             (3UL << ITM_TCR_TSPrescale_Pos)                /*!< ITM TCR: TSPrescale Mask */
+
+#define ITM_TCR_SWOENA_Pos                  4                                             /*!< ITM TCR: SWOENA Position */
+#define ITM_TCR_SWOENA_Msk                 (1UL << ITM_TCR_SWOENA_Pos)                    /*!< ITM TCR: SWOENA Mask */
+
+#define ITM_TCR_DWTENA_Pos                  3                                             /*!< ITM TCR: DWTENA Position */
+#define ITM_TCR_DWTENA_Msk                 (1UL << ITM_TCR_DWTENA_Pos)                    /*!< ITM TCR: DWTENA Mask */
+
+#define ITM_TCR_SYNCENA_Pos                 2                                             /*!< ITM TCR: SYNCENA Position */
+#define ITM_TCR_SYNCENA_Msk                (1UL << ITM_TCR_SYNCENA_Pos)                   /*!< ITM TCR: SYNCENA Mask */
+
+#define ITM_TCR_TSENA_Pos                   1                                             /*!< ITM TCR: TSENA Position */
+#define ITM_TCR_TSENA_Msk                  (1UL << ITM_TCR_TSENA_Pos)                     /*!< ITM TCR: TSENA Mask */
+
+#define ITM_TCR_ITMENA_Pos                  0                                             /*!< ITM TCR: ITM Enable bit Position */
+#define ITM_TCR_ITMENA_Msk                 (1UL << ITM_TCR_ITMENA_Pos)                    /*!< ITM TCR: ITM Enable bit Mask */
+
+/* ITM Integration Write Register Definitions */
+#define ITM_IWR_ATVALIDM_Pos                0                                             /*!< ITM IWR: ATVALIDM Position */
+#define ITM_IWR_ATVALIDM_Msk               (1UL << ITM_IWR_ATVALIDM_Pos)                  /*!< ITM IWR: ATVALIDM Mask */
+
+/* ITM Integration Read Register Definitions */
+#define ITM_IRR_ATREADYM_Pos                0                                             /*!< ITM IRR: ATREADYM Position */
+#define ITM_IRR_ATREADYM_Msk               (1UL << ITM_IRR_ATREADYM_Pos)                  /*!< ITM IRR: ATREADYM Mask */
+
+/* ITM Integration Mode Control Register Definitions */
+#define ITM_IMCR_INTEGRATION_Pos            0                                             /*!< ITM IMCR: INTEGRATION Position */
+#define ITM_IMCR_INTEGRATION_Msk           (1UL << ITM_IMCR_INTEGRATION_Pos)              /*!< ITM IMCR: INTEGRATION Mask */
+
+/* ITM Lock Status Register Definitions */
+#define ITM_LSR_ByteAcc_Pos                 2                                             /*!< ITM LSR: ByteAcc Position */
+#define ITM_LSR_ByteAcc_Msk                (1UL << ITM_LSR_ByteAcc_Pos)                   /*!< ITM LSR: ByteAcc Mask */
+
+#define ITM_LSR_Access_Pos                  1                                             /*!< ITM LSR: Access Position */
+#define ITM_LSR_Access_Msk                 (1UL << ITM_LSR_Access_Pos)                    /*!< ITM LSR: Access Mask */
+
+#define ITM_LSR_Present_Pos                 0                                             /*!< ITM LSR: Present Position */
+#define ITM_LSR_Present_Msk                (1UL << ITM_LSR_Present_Pos)                   /*!< ITM LSR: Present Mask */
+
+/*@}*/ /* end of group CMSIS_ITM */
+
+
+/** \ingroup  CMSIS_core_register
+    \defgroup CMSIS_DWT     Data Watchpoint and Trace (DWT)
+    \brief      Type definitions for the Data Watchpoint and Trace (DWT)
+  @{
+ */
+
+/** \brief  Structure type to access the Data Watchpoint and Trace Register (DWT).
+ */
+typedef struct
+{
+  __IO uint32_t CTRL;                    /*!< Offset: 0x000 (R/W)  Control Register                          */
+  __IO uint32_t CYCCNT;                  /*!< Offset: 0x004 (R/W)  Cycle Count Register                      */
+  __IO uint32_t CPICNT;                  /*!< Offset: 0x008 (R/W)  CPI Count Register                        */
+  __IO uint32_t EXCCNT;                  /*!< Offset: 0x00C (R/W)  Exception Overhead Count Register         */
+  __IO uint32_t SLEEPCNT;                /*!< Offset: 0x010 (R/W)  Sleep Count Register                      */
+  __IO uint32_t LSUCNT;                  /*!< Offset: 0x014 (R/W)  LSU Count Register                        */
+  __IO uint32_t FOLDCNT;                 /*!< Offset: 0x018 (R/W)  Folded-instruction Count Register         */
+  __I  uint32_t PCSR;                    /*!< Offset: 0x01C (R/ )  Program Counter Sample Register           */
+  __IO uint32_t COMP0;                   /*!< Offset: 0x020 (R/W)  Comparator Register 0                     */
+  __IO uint32_t MASK0;                   /*!< Offset: 0x024 (R/W)  Mask Register 0                           */
+  __IO uint32_t FUNCTION0;               /*!< Offset: 0x028 (R/W)  Function Register 0                       */
+       uint32_t RESERVED0[1];
+  __IO uint32_t COMP1;                   /*!< Offset: 0x030 (R/W)  Comparator Register 1                     */
+  __IO uint32_t MASK1;                   /*!< Offset: 0x034 (R/W)  Mask Register 1                           */
+  __IO uint32_t FUNCTION1;               /*!< Offset: 0x038 (R/W)  Function Register 1                       */
+       uint32_t RESERVED1[1];
+  __IO uint32_t COMP2;                   /*!< Offset: 0x040 (R/W)  Comparator Register 2                     */
+  __IO uint32_t MASK2;                   /*!< Offset: 0x044 (R/W)  Mask Register 2                           */
+  __IO uint32_t FUNCTION2;               /*!< Offset: 0x048 (R/W)  Function Register 2                       */
+       uint32_t RESERVED2[1];
+  __IO uint32_t COMP3;                   /*!< Offset: 0x050 (R/W)  Comparator Register 3                     */
+  __IO uint32_t MASK3;                   /*!< Offset: 0x054 (R/W)  Mask Register 3                           */
+  __IO uint32_t FUNCTION3;               /*!< Offset: 0x058 (R/W)  Function Register 3                       */
+} DWT_Type;
+
+/* DWT Control Register Definitions */
+#define DWT_CTRL_NUMCOMP_Pos               28                                          /*!< DWT CTRL: NUMCOMP Position */
+#define DWT_CTRL_NUMCOMP_Msk               (0xFUL << DWT_CTRL_NUMCOMP_Pos)             /*!< DWT CTRL: NUMCOMP Mask */
+
+#define DWT_CTRL_NOTRCPKT_Pos              27                                          /*!< DWT CTRL: NOTRCPKT Position */
+#define DWT_CTRL_NOTRCPKT_Msk              (0x1UL << DWT_CTRL_NOTRCPKT_Pos)            /*!< DWT CTRL: NOTRCPKT Mask */
+
+#define DWT_CTRL_NOEXTTRIG_Pos             26                                          /*!< DWT CTRL: NOEXTTRIG Position */
+#define DWT_CTRL_NOEXTTRIG_Msk             (0x1UL << DWT_CTRL_NOEXTTRIG_Pos)           /*!< DWT CTRL: NOEXTTRIG Mask */
+
+#define DWT_CTRL_NOCYCCNT_Pos              25                                          /*!< DWT CTRL: NOCYCCNT Position */
+#define DWT_CTRL_NOCYCCNT_Msk              (0x1UL << DWT_CTRL_NOCYCCNT_Pos)            /*!< DWT CTRL: NOCYCCNT Mask */
+
+#define DWT_CTRL_NOPRFCNT_Pos              24                                          /*!< DWT CTRL: NOPRFCNT Position */
+#define DWT_CTRL_NOPRFCNT_Msk              (0x1UL << DWT_CTRL_NOPRFCNT_Pos)            /*!< DWT CTRL: NOPRFCNT Mask */
+
+#define DWT_CTRL_CYCEVTENA_Pos             22                                          /*!< DWT CTRL: CYCEVTENA Position */
+#define DWT_CTRL_CYCEVTENA_Msk             (0x1UL << DWT_CTRL_CYCEVTENA_Pos)           /*!< DWT CTRL: CYCEVTENA Mask */
+
+#define DWT_CTRL_FOLDEVTENA_Pos            21                                          /*!< DWT CTRL: FOLDEVTENA Position */
+#define DWT_CTRL_FOLDEVTENA_Msk            (0x1UL << DWT_CTRL_FOLDEVTENA_Pos)          /*!< DWT CTRL: FOLDEVTENA Mask */
+
+#define DWT_CTRL_LSUEVTENA_Pos             20                                          /*!< DWT CTRL: LSUEVTENA Position */
+#define DWT_CTRL_LSUEVTENA_Msk             (0x1UL << DWT_CTRL_LSUEVTENA_Pos)           /*!< DWT CTRL: LSUEVTENA Mask */
+
+#define DWT_CTRL_SLEEPEVTENA_Pos           19                                          /*!< DWT CTRL: SLEEPEVTENA Position */
+#define DWT_CTRL_SLEEPEVTENA_Msk           (0x1UL << DWT_CTRL_SLEEPEVTENA_Pos)         /*!< DWT CTRL: SLEEPEVTENA Mask */
+
+#define DWT_CTRL_EXCEVTENA_Pos             18                                          /*!< DWT CTRL: EXCEVTENA Position */
+#define DWT_CTRL_EXCEVTENA_Msk             (0x1UL << DWT_CTRL_EXCEVTENA_Pos)           /*!< DWT CTRL: EXCEVTENA Mask */
+
+#define DWT_CTRL_CPIEVTENA_Pos             17                                          /*!< DWT CTRL: CPIEVTENA Position */
+#define DWT_CTRL_CPIEVTENA_Msk             (0x1UL << DWT_CTRL_CPIEVTENA_Pos)           /*!< DWT CTRL: CPIEVTENA Mask */
+
+#define DWT_CTRL_EXCTRCENA_Pos             16                                          /*!< DWT CTRL: EXCTRCENA Position */
+#define DWT_CTRL_EXCTRCENA_Msk             (0x1UL << DWT_CTRL_EXCTRCENA_Pos)           /*!< DWT CTRL: EXCTRCENA Mask */
+
+#define DWT_CTRL_PCSAMPLENA_Pos            12                                          /*!< DWT CTRL: PCSAMPLENA Position */
+#define DWT_CTRL_PCSAMPLENA_Msk            (0x1UL << DWT_CTRL_PCSAMPLENA_Pos)          /*!< DWT CTRL: PCSAMPLENA Mask */
+
+#define DWT_CTRL_SYNCTAP_Pos               10                                          /*!< DWT CTRL: SYNCTAP Position */
+#define DWT_CTRL_SYNCTAP_Msk               (0x3UL << DWT_CTRL_SYNCTAP_Pos)             /*!< DWT CTRL: SYNCTAP Mask */
+
+#define DWT_CTRL_CYCTAP_Pos                 9                                          /*!< DWT CTRL: CYCTAP Position */
+#define DWT_CTRL_CYCTAP_Msk                (0x1UL << DWT_CTRL_CYCTAP_Pos)              /*!< DWT CTRL: CYCTAP Mask */
+
+#define DWT_CTRL_POSTINIT_Pos               5                                          /*!< DWT CTRL: POSTINIT Position */
+#define DWT_CTRL_POSTINIT_Msk              (0xFUL << DWT_CTRL_POSTINIT_Pos)            /*!< DWT CTRL: POSTINIT Mask */
+
+#define DWT_CTRL_POSTPRESET_Pos             1                                          /*!< DWT CTRL: POSTPRESET Position */
+#define DWT_CTRL_POSTPRESET_Msk            (0xFUL << DWT_CTRL_POSTPRESET_Pos)          /*!< DWT CTRL: POSTPRESET Mask */
+
+#define DWT_CTRL_CYCCNTENA_Pos              0                                          /*!< DWT CTRL: CYCCNTENA Position */
+#define DWT_CTRL_CYCCNTENA_Msk             (0x1UL << DWT_CTRL_CYCCNTENA_Pos)           /*!< DWT CTRL: CYCCNTENA Mask */
+
+/* DWT CPI Count Register Definitions */
+#define DWT_CPICNT_CPICNT_Pos               0                                          /*!< DWT CPICNT: CPICNT Position */
+#define DWT_CPICNT_CPICNT_Msk              (0xFFUL << DWT_CPICNT_CPICNT_Pos)           /*!< DWT CPICNT: CPICNT Mask */
+
+/* DWT Exception Overhead Count Register Definitions */
+#define DWT_EXCCNT_EXCCNT_Pos               0                                          /*!< DWT EXCCNT: EXCCNT Position */
+#define DWT_EXCCNT_EXCCNT_Msk              (0xFFUL << DWT_EXCCNT_EXCCNT_Pos)           /*!< DWT EXCCNT: EXCCNT Mask */
+
+/* DWT Sleep Count Register Definitions */
+#define DWT_SLEEPCNT_SLEEPCNT_Pos           0                                          /*!< DWT SLEEPCNT: SLEEPCNT Position */
+#define DWT_SLEEPCNT_SLEEPCNT_Msk          (0xFFUL << DWT_SLEEPCNT_SLEEPCNT_Pos)       /*!< DWT SLEEPCNT: SLEEPCNT Mask */
+
+/* DWT LSU Count Register Definitions */
+#define DWT_LSUCNT_LSUCNT_Pos               0                                          /*!< DWT LSUCNT: LSUCNT Position */
+#define DWT_LSUCNT_LSUCNT_Msk              (0xFFUL << DWT_LSUCNT_LSUCNT_Pos)           /*!< DWT LSUCNT: LSUCNT Mask */
+
+/* DWT Folded-instruction Count Register Definitions */
+#define DWT_FOLDCNT_FOLDCNT_Pos             0                                          /*!< DWT FOLDCNT: FOLDCNT Position */
+#define DWT_FOLDCNT_FOLDCNT_Msk            (0xFFUL << DWT_FOLDCNT_FOLDCNT_Pos)         /*!< DWT FOLDCNT: FOLDCNT Mask */
+
+/* DWT Comparator Mask Register Definitions */
+#define DWT_MASK_MASK_Pos                   0                                          /*!< DWT MASK: MASK Position */
+#define DWT_MASK_MASK_Msk                  (0x1FUL << DWT_MASK_MASK_Pos)               /*!< DWT MASK: MASK Mask */
+
+/* DWT Comparator Function Register Definitions */
+#define DWT_FUNCTION_MATCHED_Pos           24                                          /*!< DWT FUNCTION: MATCHED Position */
+#define DWT_FUNCTION_MATCHED_Msk           (0x1UL << DWT_FUNCTION_MATCHED_Pos)         /*!< DWT FUNCTION: MATCHED Mask */
+
+#define DWT_FUNCTION_DATAVADDR1_Pos        16                                          /*!< DWT FUNCTION: DATAVADDR1 Position */
+#define DWT_FUNCTION_DATAVADDR1_Msk        (0xFUL << DWT_FUNCTION_DATAVADDR1_Pos)      /*!< DWT FUNCTION: DATAVADDR1 Mask */
+
+#define DWT_FUNCTION_DATAVADDR0_Pos        12                                          /*!< DWT FUNCTION: DATAVADDR0 Position */
+#define DWT_FUNCTION_DATAVADDR0_Msk        (0xFUL << DWT_FUNCTION_DATAVADDR0_Pos)      /*!< DWT FUNCTION: DATAVADDR0 Mask */
+
+#define DWT_FUNCTION_DATAVSIZE_Pos         10                                          /*!< DWT FUNCTION: DATAVSIZE Position */
+#define DWT_FUNCTION_DATAVSIZE_Msk         (0x3UL << DWT_FUNCTION_DATAVSIZE_Pos)       /*!< DWT FUNCTION: DATAVSIZE Mask */
+
+#define DWT_FUNCTION_LNK1ENA_Pos            9                                          /*!< DWT FUNCTION: LNK1ENA Position */
+#define DWT_FUNCTION_LNK1ENA_Msk           (0x1UL << DWT_FUNCTION_LNK1ENA_Pos)         /*!< DWT FUNCTION: LNK1ENA Mask */
+
+#define DWT_FUNCTION_DATAVMATCH_Pos         8                                          /*!< DWT FUNCTION: DATAVMATCH Position */
+#define DWT_FUNCTION_DATAVMATCH_Msk        (0x1UL << DWT_FUNCTION_DATAVMATCH_Pos)      /*!< DWT FUNCTION: DATAVMATCH Mask */
+
+#define DWT_FUNCTION_CYCMATCH_Pos           7                                          /*!< DWT FUNCTION: CYCMATCH Position */
+#define DWT_FUNCTION_CYCMATCH_Msk          (0x1UL << DWT_FUNCTION_CYCMATCH_Pos)        /*!< DWT FUNCTION: CYCMATCH Mask */
+
+#define DWT_FUNCTION_EMITRANGE_Pos          5                                          /*!< DWT FUNCTION: EMITRANGE Position */
+#define DWT_FUNCTION_EMITRANGE_Msk         (0x1UL << DWT_FUNCTION_EMITRANGE_Pos)       /*!< DWT FUNCTION: EMITRANGE Mask */
+
+#define DWT_FUNCTION_FUNCTION_Pos           0                                          /*!< DWT FUNCTION: FUNCTION Position */
+#define DWT_FUNCTION_FUNCTION_Msk          (0xFUL << DWT_FUNCTION_FUNCTION_Pos)        /*!< DWT FUNCTION: FUNCTION Mask */
+
+/*@}*/ /* end of group CMSIS_DWT */
+
+
+/** \ingroup  CMSIS_core_register
+    \defgroup CMSIS_TPI     Trace Port Interface (TPI)
+    \brief      Type definitions for the Trace Port Interface (TPI)
+  @{
+ */
+
+/** \brief  Structure type to access the Trace Port Interface Register (TPI).
+ */
+typedef struct
+{
+  __IO uint32_t SSPSR;                   /*!< Offset: 0x000 (R/ )  Supported Parallel Port Size Register     */
+  __IO uint32_t CSPSR;                   /*!< Offset: 0x004 (R/W)  Current Parallel Port Size Register */
+       uint32_t RESERVED0[2];
+  __IO uint32_t ACPR;                    /*!< Offset: 0x010 (R/W)  Asynchronous Clock Prescaler Register */
+       uint32_t RESERVED1[55];
+  __IO uint32_t SPPR;                    /*!< Offset: 0x0F0 (R/W)  Selected Pin Protocol Register */
+       uint32_t RESERVED2[131];
+  __I  uint32_t FFSR;                    /*!< Offset: 0x300 (R/ )  Formatter and Flush Status Register */
+  __IO uint32_t FFCR;                    /*!< Offset: 0x304 (R/W)  Formatter and Flush Control Register */
+  __I  uint32_t FSCR;                    /*!< Offset: 0x308 (R/ )  Formatter Synchronization Counter Register */
+       uint32_t RESERVED3[759];
+  __I  uint32_t TRIGGER;                 /*!< Offset: 0xEE8 (R/ )  TRIGGER */
+  __I  uint32_t FIFO0;                   /*!< Offset: 0xEEC (R/ )  Integration ETM Data */
+  __I  uint32_t ITATBCTR2;               /*!< Offset: 0xEF0 (R/ )  ITATBCTR2 */
+       uint32_t RESERVED4[1];
+  __I  uint32_t ITATBCTR0;               /*!< Offset: 0xEF8 (R/ )  ITATBCTR0 */
+  __I  uint32_t FIFO1;                   /*!< Offset: 0xEFC (R/ )  Integration ITM Data */
+  __IO uint32_t ITCTRL;                  /*!< Offset: 0xF00 (R/W)  Integration Mode Control */
+       uint32_t RESERVED5[39];
+  __IO uint32_t CLAIMSET;                /*!< Offset: 0xFA0 (R/W)  Claim tag set */
+  __IO uint32_t CLAIMCLR;                /*!< Offset: 0xFA4 (R/W)  Claim tag clear */
+       uint32_t RESERVED7[8];
+  __I  uint32_t DEVID;                   /*!< Offset: 0xFC8 (R/ )  TPIU_DEVID */
+  __I  uint32_t DEVTYPE;                 /*!< Offset: 0xFCC (R/ )  TPIU_DEVTYPE */
+} TPI_Type;
+
+/* TPI Asynchronous Clock Prescaler Register Definitions */
+#define TPI_ACPR_PRESCALER_Pos              0                                          /*!< TPI ACPR: PRESCALER Position */
+#define TPI_ACPR_PRESCALER_Msk             (0x1FFFUL << TPI_ACPR_PRESCALER_Pos)        /*!< TPI ACPR: PRESCALER Mask */
+
+/* TPI Selected Pin Protocol Register Definitions */
+#define TPI_SPPR_TXMODE_Pos                 0                                          /*!< TPI SPPR: TXMODE Position */
+#define TPI_SPPR_TXMODE_Msk                (0x3UL << TPI_SPPR_TXMODE_Pos)              /*!< TPI SPPR: TXMODE Mask */
+
+/* TPI Formatter and Flush Status Register Definitions */
+#define TPI_FFSR_FtNonStop_Pos              3                                          /*!< TPI FFSR: FtNonStop Position */
+#define TPI_FFSR_FtNonStop_Msk             (0x1UL << TPI_FFSR_FtNonStop_Pos)           /*!< TPI FFSR: FtNonStop Mask */
+
+#define TPI_FFSR_TCPresent_Pos              2                                          /*!< TPI FFSR: TCPresent Position */
+#define TPI_FFSR_TCPresent_Msk             (0x1UL << TPI_FFSR_TCPresent_Pos)           /*!< TPI FFSR: TCPresent Mask */
+
+#define TPI_FFSR_FtStopped_Pos              1                                          /*!< TPI FFSR: FtStopped Position */
+#define TPI_FFSR_FtStopped_Msk             (0x1UL << TPI_FFSR_FtStopped_Pos)           /*!< TPI FFSR: FtStopped Mask */
+
+#define TPI_FFSR_FlInProg_Pos               0                                          /*!< TPI FFSR: FlInProg Position */
+#define TPI_FFSR_FlInProg_Msk              (0x1UL << TPI_FFSR_FlInProg_Pos)            /*!< TPI FFSR: FlInProg Mask */
+
+/* TPI Formatter and Flush Control Register Definitions */
+#define TPI_FFCR_TrigIn_Pos                 8                                          /*!< TPI FFCR: TrigIn Position */
+#define TPI_FFCR_TrigIn_Msk                (0x1UL << TPI_FFCR_TrigIn_Pos)              /*!< TPI FFCR: TrigIn Mask */
+
+#define TPI_FFCR_EnFCont_Pos                1                                          /*!< TPI FFCR: EnFCont Position */
+#define TPI_FFCR_EnFCont_Msk               (0x1UL << TPI_FFCR_EnFCont_Pos)             /*!< TPI FFCR: EnFCont Mask */
+
+/* TPI TRIGGER Register Definitions */
+#define TPI_TRIGGER_TRIGGER_Pos             0                                          /*!< TPI TRIGGER: TRIGGER Position */
+#define TPI_TRIGGER_TRIGGER_Msk            (0x1UL << TPI_TRIGGER_TRIGGER_Pos)          /*!< TPI TRIGGER: TRIGGER Mask */
+
+/* TPI Integration ETM Data Register Definitions (FIFO0) */
+#define TPI_FIFO0_ITM_ATVALID_Pos          29                                          /*!< TPI FIFO0: ITM_ATVALID Position */
+#define TPI_FIFO0_ITM_ATVALID_Msk          (0x3UL << TPI_FIFO0_ITM_ATVALID_Pos)        /*!< TPI FIFO0: ITM_ATVALID Mask */
+
+#define TPI_FIFO0_ITM_bytecount_Pos        27                                          /*!< TPI FIFO0: ITM_bytecount Position */
+#define TPI_FIFO0_ITM_bytecount_Msk        (0x3UL << TPI_FIFO0_ITM_bytecount_Pos)      /*!< TPI FIFO0: ITM_bytecount Mask */
+
+#define TPI_FIFO0_ETM_ATVALID_Pos          26                                          /*!< TPI FIFO0: ETM_ATVALID Position */
+#define TPI_FIFO0_ETM_ATVALID_Msk          (0x3UL << TPI_FIFO0_ETM_ATVALID_Pos)        /*!< TPI FIFO0: ETM_ATVALID Mask */
+
+#define TPI_FIFO0_ETM_bytecount_Pos        24                                          /*!< TPI FIFO0: ETM_bytecount Position */
+#define TPI_FIFO0_ETM_bytecount_Msk        (0x3UL << TPI_FIFO0_ETM_bytecount_Pos)      /*!< TPI FIFO0: ETM_bytecount Mask */
+
+#define TPI_FIFO0_ETM2_Pos                 16                                          /*!< TPI FIFO0: ETM2 Position */
+#define TPI_FIFO0_ETM2_Msk                 (0xFFUL << TPI_FIFO0_ETM2_Pos)              /*!< TPI FIFO0: ETM2 Mask */
+
+#define TPI_FIFO0_ETM1_Pos                  8                                          /*!< TPI FIFO0: ETM1 Position */
+#define TPI_FIFO0_ETM1_Msk                 (0xFFUL << TPI_FIFO0_ETM1_Pos)              /*!< TPI FIFO0: ETM1 Mask */
+
+#define TPI_FIFO0_ETM0_Pos                  0                                          /*!< TPI FIFO0: ETM0 Position */
+#define TPI_FIFO0_ETM0_Msk                 (0xFFUL << TPI_FIFO0_ETM0_Pos)              /*!< TPI FIFO0: ETM0 Mask */
+
+/* TPI ITATBCTR2 Register Definitions */
+#define TPI_ITATBCTR2_ATREADY_Pos           0                                          /*!< TPI ITATBCTR2: ATREADY Position */
+#define TPI_ITATBCTR2_ATREADY_Msk          (0x1UL << TPI_ITATBCTR2_ATREADY_Pos)        /*!< TPI ITATBCTR2: ATREADY Mask */
+
+/* TPI Integration ITM Data Register Definitions (FIFO1) */
+#define TPI_FIFO1_ITM_ATVALID_Pos          29                                          /*!< TPI FIFO1: ITM_ATVALID Position */
+#define TPI_FIFO1_ITM_ATVALID_Msk          (0x3UL << TPI_FIFO1_ITM_ATVALID_Pos)        /*!< TPI FIFO1: ITM_ATVALID Mask */
+
+#define TPI_FIFO1_ITM_bytecount_Pos        27                                          /*!< TPI FIFO1: ITM_bytecount Position */
+#define TPI_FIFO1_ITM_bytecount_Msk        (0x3UL << TPI_FIFO1_ITM_bytecount_Pos)      /*!< TPI FIFO1: ITM_bytecount Mask */
+
+#define TPI_FIFO1_ETM_ATVALID_Pos          26                                          /*!< TPI FIFO1: ETM_ATVALID Position */
+#define TPI_FIFO1_ETM_ATVALID_Msk          (0x3UL << TPI_FIFO1_ETM_ATVALID_Pos)        /*!< TPI FIFO1: ETM_ATVALID Mask */
+
+#define TPI_FIFO1_ETM_bytecount_Pos        24                                          /*!< TPI FIFO1: ETM_bytecount Position */
+#define TPI_FIFO1_ETM_bytecount_Msk        (0x3UL << TPI_FIFO1_ETM_bytecount_Pos)      /*!< TPI FIFO1: ETM_bytecount Mask */
+
+#define TPI_FIFO1_ITM2_Pos                 16                                          /*!< TPI FIFO1: ITM2 Position */
+#define TPI_FIFO1_ITM2_Msk                 (0xFFUL << TPI_FIFO1_ITM2_Pos)              /*!< TPI FIFO1: ITM2 Mask */
+
+#define TPI_FIFO1_ITM1_Pos                  8                                          /*!< TPI FIFO1: ITM1 Position */
+#define TPI_FIFO1_ITM1_Msk                 (0xFFUL << TPI_FIFO1_ITM1_Pos)              /*!< TPI FIFO1: ITM1 Mask */
+
+#define TPI_FIFO1_ITM0_Pos                  0                                          /*!< TPI FIFO1: ITM0 Position */
+#define TPI_FIFO1_ITM0_Msk                 (0xFFUL << TPI_FIFO1_ITM0_Pos)              /*!< TPI FIFO1: ITM0 Mask */
+
+/* TPI ITATBCTR0 Register Definitions */
+#define TPI_ITATBCTR0_ATREADY_Pos           0                                          /*!< TPI ITATBCTR0: ATREADY Position */
+#define TPI_ITATBCTR0_ATREADY_Msk          (0x1UL << TPI_ITATBCTR0_ATREADY_Pos)        /*!< TPI ITATBCTR0: ATREADY Mask */
+
+/* TPI Integration Mode Control Register Definitions */
+#define TPI_ITCTRL_Mode_Pos                 0                                          /*!< TPI ITCTRL: Mode Position */
+#define TPI_ITCTRL_Mode_Msk                (0x1UL << TPI_ITCTRL_Mode_Pos)              /*!< TPI ITCTRL: Mode Mask */
+
+/* TPI DEVID Register Definitions */
+#define TPI_DEVID_NRZVALID_Pos             11                                          /*!< TPI DEVID: NRZVALID Position */
+#define TPI_DEVID_NRZVALID_Msk             (0x1UL << TPI_DEVID_NRZVALID_Pos)           /*!< TPI DEVID: NRZVALID Mask */
+
+#define TPI_DEVID_MANCVALID_Pos            10                                          /*!< TPI DEVID: MANCVALID Position */
+#define TPI_DEVID_MANCVALID_Msk            (0x1UL << TPI_DEVID_MANCVALID_Pos)          /*!< TPI DEVID: MANCVALID Mask */
+
+#define TPI_DEVID_PTINVALID_Pos             9                                          /*!< TPI DEVID: PTINVALID Position */
+#define TPI_DEVID_PTINVALID_Msk            (0x1UL << TPI_DEVID_PTINVALID_Pos)          /*!< TPI DEVID: PTINVALID Mask */
+
+#define TPI_DEVID_MinBufSz_Pos              6                                          /*!< TPI DEVID: MinBufSz Position */
+#define TPI_DEVID_MinBufSz_Msk             (0x7UL << TPI_DEVID_MinBufSz_Pos)           /*!< TPI DEVID: MinBufSz Mask */
+
+#define TPI_DEVID_AsynClkIn_Pos             5                                          /*!< TPI DEVID: AsynClkIn Position */
+#define TPI_DEVID_AsynClkIn_Msk            (0x1UL << TPI_DEVID_AsynClkIn_Pos)          /*!< TPI DEVID: AsynClkIn Mask */
+
+#define TPI_DEVID_NrTraceInput_Pos          0                                          /*!< TPI DEVID: NrTraceInput Position */
+#define TPI_DEVID_NrTraceInput_Msk         (0x1FUL << TPI_DEVID_NrTraceInput_Pos)      /*!< TPI DEVID: NrTraceInput Mask */
+
+/* TPI DEVTYPE Register Definitions */
+#define TPI_DEVTYPE_SubType_Pos             0                                          /*!< TPI DEVTYPE: SubType Position */
+#define TPI_DEVTYPE_SubType_Msk            (0xFUL << TPI_DEVTYPE_SubType_Pos)          /*!< TPI DEVTYPE: SubType Mask */
+
+#define TPI_DEVTYPE_MajorType_Pos           4                                          /*!< TPI DEVTYPE: MajorType Position */
+#define TPI_DEVTYPE_MajorType_Msk          (0xFUL << TPI_DEVTYPE_MajorType_Pos)        /*!< TPI DEVTYPE: MajorType Mask */
+
+/*@}*/ /* end of group CMSIS_TPI */
+
+
+#if (__MPU_PRESENT == 1)
+/** \ingroup  CMSIS_core_register
+    \defgroup CMSIS_MPU     Memory Protection Unit (MPU)
+    \brief      Type definitions for the Memory Protection Unit (MPU)
+  @{
+ */
+
+/** \brief  Structure type to access the Memory Protection Unit (MPU).
+ */
+typedef struct
+{
+  __I  uint32_t TYPE;                    /*!< Offset: 0x000 (R/ )  MPU Type Register                              */
+  __IO uint32_t CTRL;                    /*!< Offset: 0x004 (R/W)  MPU Control Register                           */
+  __IO uint32_t RNR;                     /*!< Offset: 0x008 (R/W)  MPU Region RNRber Register                     */
+  __IO uint32_t RBAR;                    /*!< Offset: 0x00C (R/W)  MPU Region Base Address Register               */
+  __IO uint32_t RASR;                    /*!< Offset: 0x010 (R/W)  MPU Region Attribute and Size Register         */
+  __IO uint32_t RBAR_A1;                 /*!< Offset: 0x014 (R/W)  MPU Alias 1 Region Base Address Register       */
+  __IO uint32_t RASR_A1;                 /*!< Offset: 0x018 (R/W)  MPU Alias 1 Region Attribute and Size Register */
+  __IO uint32_t RBAR_A2;                 /*!< Offset: 0x01C (R/W)  MPU Alias 2 Region Base Address Register       */
+  __IO uint32_t RASR_A2;                 /*!< Offset: 0x020 (R/W)  MPU Alias 2 Region Attribute and Size Register */
+  __IO uint32_t RBAR_A3;                 /*!< Offset: 0x024 (R/W)  MPU Alias 3 Region Base Address Register       */
+  __IO uint32_t RASR_A3;                 /*!< Offset: 0x028 (R/W)  MPU Alias 3 Region Attribute and Size Register */
+} MPU_Type;
+
+/* MPU Type Register */
+#define MPU_TYPE_IREGION_Pos               16                                             /*!< MPU TYPE: IREGION Position */
+#define MPU_TYPE_IREGION_Msk               (0xFFUL << MPU_TYPE_IREGION_Pos)               /*!< MPU TYPE: IREGION Mask */
+
+#define MPU_TYPE_DREGION_Pos                8                                             /*!< MPU TYPE: DREGION Position */
+#define MPU_TYPE_DREGION_Msk               (0xFFUL << MPU_TYPE_DREGION_Pos)               /*!< MPU TYPE: DREGION Mask */
+
+#define MPU_TYPE_SEPARATE_Pos               0                                             /*!< MPU TYPE: SEPARATE Position */
+#define MPU_TYPE_SEPARATE_Msk              (1UL << MPU_TYPE_SEPARATE_Pos)                 /*!< MPU TYPE: SEPARATE Mask */
+
+/* MPU Control Register */
+#define MPU_CTRL_PRIVDEFENA_Pos             2                                             /*!< MPU CTRL: PRIVDEFENA Position */
+#define MPU_CTRL_PRIVDEFENA_Msk            (1UL << MPU_CTRL_PRIVDEFENA_Pos)               /*!< MPU CTRL: PRIVDEFENA Mask */
+
+#define MPU_CTRL_HFNMIENA_Pos               1                                             /*!< MPU CTRL: HFNMIENA Position */
+#define MPU_CTRL_HFNMIENA_Msk              (1UL << MPU_CTRL_HFNMIENA_Pos)                 /*!< MPU CTRL: HFNMIENA Mask */
+
+#define MPU_CTRL_ENABLE_Pos                 0                                             /*!< MPU CTRL: ENABLE Position */
+#define MPU_CTRL_ENABLE_Msk                (1UL << MPU_CTRL_ENABLE_Pos)                   /*!< MPU CTRL: ENABLE Mask */
+
+/* MPU Region Number Register */
+#define MPU_RNR_REGION_Pos                  0                                             /*!< MPU RNR: REGION Position */
+#define MPU_RNR_REGION_Msk                 (0xFFUL << MPU_RNR_REGION_Pos)                 /*!< MPU RNR: REGION Mask */
+
+/* MPU Region Base Address Register */
+#define MPU_RBAR_ADDR_Pos                   5                                             /*!< MPU RBAR: ADDR Position */
+#define MPU_RBAR_ADDR_Msk                  (0x7FFFFFFUL << MPU_RBAR_ADDR_Pos)             /*!< MPU RBAR: ADDR Mask */
+
+#define MPU_RBAR_VALID_Pos                  4                                             /*!< MPU RBAR: VALID Position */
+#define MPU_RBAR_VALID_Msk                 (1UL << MPU_RBAR_VALID_Pos)                    /*!< MPU RBAR: VALID Mask */
+
+#define MPU_RBAR_REGION_Pos                 0                                             /*!< MPU RBAR: REGION Position */
+#define MPU_RBAR_REGION_Msk                (0xFUL << MPU_RBAR_REGION_Pos)                 /*!< MPU RBAR: REGION Mask */
+
+/* MPU Region Attribute and Size Register */
+#define MPU_RASR_ATTRS_Pos                 16                                             /*!< MPU RASR: MPU Region Attribute field Position */
+#define MPU_RASR_ATTRS_Msk                 (0xFFFFUL << MPU_RASR_ATTRS_Pos)               /*!< MPU RASR: MPU Region Attribute field Mask */
+
+#define MPU_RASR_XN_Pos                    28                                             /*!< MPU RASR: ATTRS.XN Position */
+#define MPU_RASR_XN_Msk                    (1UL << MPU_RASR_XN_Pos)                       /*!< MPU RASR: ATTRS.XN Mask */
+
+#define MPU_RASR_AP_Pos                    24                                             /*!< MPU RASR: ATTRS.AP Position */
+#define MPU_RASR_AP_Msk                    (0x7UL << MPU_RASR_AP_Pos)                     /*!< MPU RASR: ATTRS.AP Mask */
+
+#define MPU_RASR_TEX_Pos                   19                                             /*!< MPU RASR: ATTRS.TEX Position */
+#define MPU_RASR_TEX_Msk                   (0x7UL << MPU_RASR_TEX_Pos)                    /*!< MPU RASR: ATTRS.TEX Mask */
+
+#define MPU_RASR_S_Pos                     18                                             /*!< MPU RASR: ATTRS.S Position */
+#define MPU_RASR_S_Msk                     (1UL << MPU_RASR_S_Pos)                        /*!< MPU RASR: ATTRS.S Mask */
+
+#define MPU_RASR_C_Pos                     17                                             /*!< MPU RASR: ATTRS.C Position */
+#define MPU_RASR_C_Msk                     (1UL << MPU_RASR_C_Pos)                        /*!< MPU RASR: ATTRS.C Mask */
+
+#define MPU_RASR_B_Pos                     16                                             /*!< MPU RASR: ATTRS.B Position */
+#define MPU_RASR_B_Msk                     (1UL << MPU_RASR_B_Pos)                        /*!< MPU RASR: ATTRS.B Mask */
+
+#define MPU_RASR_SRD_Pos                    8                                             /*!< MPU RASR: Sub-Region Disable Position */
+#define MPU_RASR_SRD_Msk                   (0xFFUL << MPU_RASR_SRD_Pos)                   /*!< MPU RASR: Sub-Region Disable Mask */
+
+#define MPU_RASR_SIZE_Pos                   1                                             /*!< MPU RASR: Region Size Field Position */
+#define MPU_RASR_SIZE_Msk                  (0x1FUL << MPU_RASR_SIZE_Pos)                  /*!< MPU RASR: Region Size Field Mask */
+
+#define MPU_RASR_ENABLE_Pos                 0                                             /*!< MPU RASR: Region enable bit Position */
+#define MPU_RASR_ENABLE_Msk                (1UL << MPU_RASR_ENABLE_Pos)                   /*!< MPU RASR: Region enable bit Disable Mask */
+
+/*@} end of group CMSIS_MPU */
+#endif
+
+
+#if (__FPU_PRESENT == 1)
+/** \ingroup  CMSIS_core_register
+    \defgroup CMSIS_FPU     Floating Point Unit (FPU)
+    \brief      Type definitions for the Floating Point Unit (FPU)
+  @{
+ */
+
+/** \brief  Structure type to access the Floating Point Unit (FPU).
+ */
+typedef struct
+{
+       uint32_t RESERVED0[1];
+  __IO uint32_t FPCCR;                   /*!< Offset: 0x004 (R/W)  Floating-Point Context Control Register               */
+  __IO uint32_t FPCAR;                   /*!< Offset: 0x008 (R/W)  Floating-Point Context Address Register               */
+  __IO uint32_t FPDSCR;                  /*!< Offset: 0x00C (R/W)  Floating-Point Default Status Control Register        */
+  __I  uint32_t MVFR0;                   /*!< Offset: 0x010 (R/ )  Media and FP Feature Register 0                       */
+  __I  uint32_t MVFR1;                   /*!< Offset: 0x014 (R/ )  Media and FP Feature Register 1                       */
+} FPU_Type;
+
+/* Floating-Point Context Control Register */
+#define FPU_FPCCR_ASPEN_Pos                31                                             /*!< FPCCR: ASPEN bit Position */
+#define FPU_FPCCR_ASPEN_Msk                (1UL << FPU_FPCCR_ASPEN_Pos)                   /*!< FPCCR: ASPEN bit Mask */
+
+#define FPU_FPCCR_LSPEN_Pos                30                                             /*!< FPCCR: LSPEN Position */
+#define FPU_FPCCR_LSPEN_Msk                (1UL << FPU_FPCCR_LSPEN_Pos)                   /*!< FPCCR: LSPEN bit Mask */
+
+#define FPU_FPCCR_MONRDY_Pos                8                                             /*!< FPCCR: MONRDY Position */
+#define FPU_FPCCR_MONRDY_Msk               (1UL << FPU_FPCCR_MONRDY_Pos)                  /*!< FPCCR: MONRDY bit Mask */
+
+#define FPU_FPCCR_BFRDY_Pos                 6                                             /*!< FPCCR: BFRDY Position */
+#define FPU_FPCCR_BFRDY_Msk                (1UL << FPU_FPCCR_BFRDY_Pos)                   /*!< FPCCR: BFRDY bit Mask */
+
+#define FPU_FPCCR_MMRDY_Pos                 5                                             /*!< FPCCR: MMRDY Position */
+#define FPU_FPCCR_MMRDY_Msk                (1UL << FPU_FPCCR_MMRDY_Pos)                   /*!< FPCCR: MMRDY bit Mask */
+
+#define FPU_FPCCR_HFRDY_Pos                 4                                             /*!< FPCCR: HFRDY Position */
+#define FPU_FPCCR_HFRDY_Msk                (1UL << FPU_FPCCR_HFRDY_Pos)                   /*!< FPCCR: HFRDY bit Mask */
+
+#define FPU_FPCCR_THREAD_Pos                3                                             /*!< FPCCR: processor mode bit Position */
+#define FPU_FPCCR_THREAD_Msk               (1UL << FPU_FPCCR_THREAD_Pos)                  /*!< FPCCR: processor mode active bit Mask */
+
+#define FPU_FPCCR_USER_Pos                  1                                             /*!< FPCCR: privilege level bit Position */
+#define FPU_FPCCR_USER_Msk                 (1UL << FPU_FPCCR_USER_Pos)                    /*!< FPCCR: privilege level bit Mask */
+
+#define FPU_FPCCR_LSPACT_Pos                0                                             /*!< FPCCR: Lazy state preservation active bit Position */
+#define FPU_FPCCR_LSPACT_Msk               (1UL << FPU_FPCCR_LSPACT_Pos)                  /*!< FPCCR: Lazy state preservation active bit Mask */
+
+/* Floating-Point Context Address Register */
+#define FPU_FPCAR_ADDRESS_Pos               3                                             /*!< FPCAR: ADDRESS bit Position */
+#define FPU_FPCAR_ADDRESS_Msk              (0x1FFFFFFFUL << FPU_FPCAR_ADDRESS_Pos)        /*!< FPCAR: ADDRESS bit Mask */
+
+/* Floating-Point Default Status Control Register */
+#define FPU_FPDSCR_AHP_Pos                 26                                             /*!< FPDSCR: AHP bit Position */
+#define FPU_FPDSCR_AHP_Msk                 (1UL << FPU_FPDSCR_AHP_Pos)                    /*!< FPDSCR: AHP bit Mask */
+
+#define FPU_FPDSCR_DN_Pos                  25                                             /*!< FPDSCR: DN bit Position */
+#define FPU_FPDSCR_DN_Msk                  (1UL << FPU_FPDSCR_DN_Pos)                     /*!< FPDSCR: DN bit Mask */
+
+#define FPU_FPDSCR_FZ_Pos                  24                                             /*!< FPDSCR: FZ bit Position */
+#define FPU_FPDSCR_FZ_Msk                  (1UL << FPU_FPDSCR_FZ_Pos)                     /*!< FPDSCR: FZ bit Mask */
+
+#define FPU_FPDSCR_RMode_Pos               22                                             /*!< FPDSCR: RMode bit Position */
+#define FPU_FPDSCR_RMode_Msk               (3UL << FPU_FPDSCR_RMode_Pos)                  /*!< FPDSCR: RMode bit Mask */
+
+/* Media and FP Feature Register 0 */
+#define FPU_MVFR0_FP_rounding_modes_Pos    28                                             /*!< MVFR0: FP rounding modes bits Position */
+#define FPU_MVFR0_FP_rounding_modes_Msk    (0xFUL << FPU_MVFR0_FP_rounding_modes_Pos)     /*!< MVFR0: FP rounding modes bits Mask */
+
+#define FPU_MVFR0_Short_vectors_Pos        24                                             /*!< MVFR0: Short vectors bits Position */
+#define FPU_MVFR0_Short_vectors_Msk        (0xFUL << FPU_MVFR0_Short_vectors_Pos)         /*!< MVFR0: Short vectors bits Mask */
+
+#define FPU_MVFR0_Square_root_Pos          20                                             /*!< MVFR0: Square root bits Position */
+#define FPU_MVFR0_Square_root_Msk          (0xFUL << FPU_MVFR0_Square_root_Pos)           /*!< MVFR0: Square root bits Mask */
+
+#define FPU_MVFR0_Divide_Pos               16                                             /*!< MVFR0: Divide bits Position */
+#define FPU_MVFR0_Divide_Msk               (0xFUL << FPU_MVFR0_Divide_Pos)                /*!< MVFR0: Divide bits Mask */
+
+#define FPU_MVFR0_FP_excep_trapping_Pos    12                                             /*!< MVFR0: FP exception trapping bits Position */
+#define FPU_MVFR0_FP_excep_trapping_Msk    (0xFUL << FPU_MVFR0_FP_excep_trapping_Pos)     /*!< MVFR0: FP exception trapping bits Mask */
+
+#define FPU_MVFR0_Double_precision_Pos      8                                             /*!< MVFR0: Double-precision bits Position */
+#define FPU_MVFR0_Double_precision_Msk     (0xFUL << FPU_MVFR0_Double_precision_Pos)      /*!< MVFR0: Double-precision bits Mask */
+
+#define FPU_MVFR0_Single_precision_Pos      4                                             /*!< MVFR0: Single-precision bits Position */
+#define FPU_MVFR0_Single_precision_Msk     (0xFUL << FPU_MVFR0_Single_precision_Pos)      /*!< MVFR0: Single-precision bits Mask */
+
+#define FPU_MVFR0_A_SIMD_registers_Pos      0                                             /*!< MVFR0: A_SIMD registers bits Position */
+#define FPU_MVFR0_A_SIMD_registers_Msk     (0xFUL << FPU_MVFR0_A_SIMD_registers_Pos)      /*!< MVFR0: A_SIMD registers bits Mask */
+
+/* Media and FP Feature Register 1 */
+#define FPU_MVFR1_FP_fused_MAC_Pos         28                                             /*!< MVFR1: FP fused MAC bits Position */
+#define FPU_MVFR1_FP_fused_MAC_Msk         (0xFUL << FPU_MVFR1_FP_fused_MAC_Pos)          /*!< MVFR1: FP fused MAC bits Mask */
+
+#define FPU_MVFR1_FP_HPFP_Pos              24                                             /*!< MVFR1: FP HPFP bits Position */
+#define FPU_MVFR1_FP_HPFP_Msk              (0xFUL << FPU_MVFR1_FP_HPFP_Pos)               /*!< MVFR1: FP HPFP bits Mask */
+
+#define FPU_MVFR1_D_NaN_mode_Pos            4                                             /*!< MVFR1: D_NaN mode bits Position */
+#define FPU_MVFR1_D_NaN_mode_Msk           (0xFUL << FPU_MVFR1_D_NaN_mode_Pos)            /*!< MVFR1: D_NaN mode bits Mask */
+
+#define FPU_MVFR1_FtZ_mode_Pos              0                                             /*!< MVFR1: FtZ mode bits Position */
+#define FPU_MVFR1_FtZ_mode_Msk             (0xFUL << FPU_MVFR1_FtZ_mode_Pos)              /*!< MVFR1: FtZ mode bits Mask */
+
+/*@} end of group CMSIS_FPU */
+#endif
+
+
+/** \ingroup  CMSIS_core_register
+    \defgroup CMSIS_CoreDebug       Core Debug Registers (CoreDebug)
+    \brief      Type definitions for the Core Debug Registers
+  @{
+ */
+
+/** \brief  Structure type to access the Core Debug Register (CoreDebug).
+ */
+typedef struct
+{
+  __IO uint32_t DHCSR;                   /*!< Offset: 0x000 (R/W)  Debug Halting Control and Status Register    */
+  __O  uint32_t DCRSR;                   /*!< Offset: 0x004 ( /W)  Debug Core Register Selector Register        */
+  __IO uint32_t DCRDR;                   /*!< Offset: 0x008 (R/W)  Debug Core Register Data Register            */
+  __IO uint32_t DEMCR;                   /*!< Offset: 0x00C (R/W)  Debug Exception and Monitor Control Register */
+} CoreDebug_Type;
+
+/* Debug Halting Control and Status Register */
+#define CoreDebug_DHCSR_DBGKEY_Pos         16                                             /*!< CoreDebug DHCSR: DBGKEY Position */
+#define CoreDebug_DHCSR_DBGKEY_Msk         (0xFFFFUL << CoreDebug_DHCSR_DBGKEY_Pos)       /*!< CoreDebug DHCSR: DBGKEY Mask */
+
+#define CoreDebug_DHCSR_S_RESET_ST_Pos     25                                             /*!< CoreDebug DHCSR: S_RESET_ST Position */
+#define CoreDebug_DHCSR_S_RESET_ST_Msk     (1UL << CoreDebug_DHCSR_S_RESET_ST_Pos)        /*!< CoreDebug DHCSR: S_RESET_ST Mask */
+
+#define CoreDebug_DHCSR_S_RETIRE_ST_Pos    24                                             /*!< CoreDebug DHCSR: S_RETIRE_ST Position */
+#define CoreDebug_DHCSR_S_RETIRE_ST_Msk    (1UL << CoreDebug_DHCSR_S_RETIRE_ST_Pos)       /*!< CoreDebug DHCSR: S_RETIRE_ST Mask */
+
+#define CoreDebug_DHCSR_S_LOCKUP_Pos       19                                             /*!< CoreDebug DHCSR: S_LOCKUP Position */
+#define CoreDebug_DHCSR_S_LOCKUP_Msk       (1UL << CoreDebug_DHCSR_S_LOCKUP_Pos)          /*!< CoreDebug DHCSR: S_LOCKUP Mask */
+
+#define CoreDebug_DHCSR_S_SLEEP_Pos        18                                             /*!< CoreDebug DHCSR: S_SLEEP Position */
+#define CoreDebug_DHCSR_S_SLEEP_Msk        (1UL << CoreDebug_DHCSR_S_SLEEP_Pos)           /*!< CoreDebug DHCSR: S_SLEEP Mask */
+
+#define CoreDebug_DHCSR_S_HALT_Pos         17                                             /*!< CoreDebug DHCSR: S_HALT Position */
+#define CoreDebug_DHCSR_S_HALT_Msk         (1UL << CoreDebug_DHCSR_S_HALT_Pos)            /*!< CoreDebug DHCSR: S_HALT Mask */
+
+#define CoreDebug_DHCSR_S_REGRDY_Pos       16                                             /*!< CoreDebug DHCSR: S_REGRDY Position */
+#define CoreDebug_DHCSR_S_REGRDY_Msk       (1UL << CoreDebug_DHCSR_S_REGRDY_Pos)          /*!< CoreDebug DHCSR: S_REGRDY Mask */
+
+#define CoreDebug_DHCSR_C_SNAPSTALL_Pos     5                                             /*!< CoreDebug DHCSR: C_SNAPSTALL Position */
+#define CoreDebug_DHCSR_C_SNAPSTALL_Msk    (1UL << CoreDebug_DHCSR_C_SNAPSTALL_Pos)       /*!< CoreDebug DHCSR: C_SNAPSTALL Mask */
+
+#define CoreDebug_DHCSR_C_MASKINTS_Pos      3                                             /*!< CoreDebug DHCSR: C_MASKINTS Position */
+#define CoreDebug_DHCSR_C_MASKINTS_Msk     (1UL << CoreDebug_DHCSR_C_MASKINTS_Pos)        /*!< CoreDebug DHCSR: C_MASKINTS Mask */
+
+#define CoreDebug_DHCSR_C_STEP_Pos          2                                             /*!< CoreDebug DHCSR: C_STEP Position */
+#define CoreDebug_DHCSR_C_STEP_Msk         (1UL << CoreDebug_DHCSR_C_STEP_Pos)            /*!< CoreDebug DHCSR: C_STEP Mask */
+
+#define CoreDebug_DHCSR_C_HALT_Pos          1                                             /*!< CoreDebug DHCSR: C_HALT Position */
+#define CoreDebug_DHCSR_C_HALT_Msk         (1UL << CoreDebug_DHCSR_C_HALT_Pos)            /*!< CoreDebug DHCSR: C_HALT Mask */
+
+#define CoreDebug_DHCSR_C_DEBUGEN_Pos       0                                             /*!< CoreDebug DHCSR: C_DEBUGEN Position */
+#define CoreDebug_DHCSR_C_DEBUGEN_Msk      (1UL << CoreDebug_DHCSR_C_DEBUGEN_Pos)         /*!< CoreDebug DHCSR: C_DEBUGEN Mask */
+
+/* Debug Core Register Selector Register */
+#define CoreDebug_DCRSR_REGWnR_Pos         16                                             /*!< CoreDebug DCRSR: REGWnR Position */
+#define CoreDebug_DCRSR_REGWnR_Msk         (1UL << CoreDebug_DCRSR_REGWnR_Pos)            /*!< CoreDebug DCRSR: REGWnR Mask */
+
+#define CoreDebug_DCRSR_REGSEL_Pos          0                                             /*!< CoreDebug DCRSR: REGSEL Position */
+#define CoreDebug_DCRSR_REGSEL_Msk         (0x1FUL << CoreDebug_DCRSR_REGSEL_Pos)         /*!< CoreDebug DCRSR: REGSEL Mask */
+
+/* Debug Exception and Monitor Control Register */
+#define CoreDebug_DEMCR_TRCENA_Pos         24                                             /*!< CoreDebug DEMCR: TRCENA Position */
+#define CoreDebug_DEMCR_TRCENA_Msk         (1UL << CoreDebug_DEMCR_TRCENA_Pos)            /*!< CoreDebug DEMCR: TRCENA Mask */
+
+#define CoreDebug_DEMCR_MON_REQ_Pos        19                                             /*!< CoreDebug DEMCR: MON_REQ Position */
+#define CoreDebug_DEMCR_MON_REQ_Msk        (1UL << CoreDebug_DEMCR_MON_REQ_Pos)           /*!< CoreDebug DEMCR: MON_REQ Mask */
+
+#define CoreDebug_DEMCR_MON_STEP_Pos       18                                             /*!< CoreDebug DEMCR: MON_STEP Position */
+#define CoreDebug_DEMCR_MON_STEP_Msk       (1UL << CoreDebug_DEMCR_MON_STEP_Pos)          /*!< CoreDebug DEMCR: MON_STEP Mask */
+
+#define CoreDebug_DEMCR_MON_PEND_Pos       17                                             /*!< CoreDebug DEMCR: MON_PEND Position */
+#define CoreDebug_DEMCR_MON_PEND_Msk       (1UL << CoreDebug_DEMCR_MON_PEND_Pos)          /*!< CoreDebug DEMCR: MON_PEND Mask */
+
+#define CoreDebug_DEMCR_MON_EN_Pos         16                                             /*!< CoreDebug DEMCR: MON_EN Position */
+#define CoreDebug_DEMCR_MON_EN_Msk         (1UL << CoreDebug_DEMCR_MON_EN_Pos)            /*!< CoreDebug DEMCR: MON_EN Mask */
+
+#define CoreDebug_DEMCR_VC_HARDERR_Pos     10                                             /*!< CoreDebug DEMCR: VC_HARDERR Position */
+#define CoreDebug_DEMCR_VC_HARDERR_Msk     (1UL << CoreDebug_DEMCR_VC_HARDERR_Pos)        /*!< CoreDebug DEMCR: VC_HARDERR Mask */
+
+#define CoreDebug_DEMCR_VC_INTERR_Pos       9                                             /*!< CoreDebug DEMCR: VC_INTERR Position */
+#define CoreDebug_DEMCR_VC_INTERR_Msk      (1UL << CoreDebug_DEMCR_VC_INTERR_Pos)         /*!< CoreDebug DEMCR: VC_INTERR Mask */
+
+#define CoreDebug_DEMCR_VC_BUSERR_Pos       8                                             /*!< CoreDebug DEMCR: VC_BUSERR Position */
+#define CoreDebug_DEMCR_VC_BUSERR_Msk      (1UL << CoreDebug_DEMCR_VC_BUSERR_Pos)         /*!< CoreDebug DEMCR: VC_BUSERR Mask */
+
+#define CoreDebug_DEMCR_VC_STATERR_Pos      7                                             /*!< CoreDebug DEMCR: VC_STATERR Position */
+#define CoreDebug_DEMCR_VC_STATERR_Msk     (1UL << CoreDebug_DEMCR_VC_STATERR_Pos)        /*!< CoreDebug DEMCR: VC_STATERR Mask */
+
+#define CoreDebug_DEMCR_VC_CHKERR_Pos       6                                             /*!< CoreDebug DEMCR: VC_CHKERR Position */
+#define CoreDebug_DEMCR_VC_CHKERR_Msk      (1UL << CoreDebug_DEMCR_VC_CHKERR_Pos)         /*!< CoreDebug DEMCR: VC_CHKERR Mask */
+
+#define CoreDebug_DEMCR_VC_NOCPERR_Pos      5                                             /*!< CoreDebug DEMCR: VC_NOCPERR Position */
+#define CoreDebug_DEMCR_VC_NOCPERR_Msk     (1UL << CoreDebug_DEMCR_VC_NOCPERR_Pos)        /*!< CoreDebug DEMCR: VC_NOCPERR Mask */
+
+#define CoreDebug_DEMCR_VC_MMERR_Pos        4                                             /*!< CoreDebug DEMCR: VC_MMERR Position */
+#define CoreDebug_DEMCR_VC_MMERR_Msk       (1UL << CoreDebug_DEMCR_VC_MMERR_Pos)          /*!< CoreDebug DEMCR: VC_MMERR Mask */
+
+#define CoreDebug_DEMCR_VC_CORERESET_Pos    0                                             /*!< CoreDebug DEMCR: VC_CORERESET Position */
+#define CoreDebug_DEMCR_VC_CORERESET_Msk   (1UL << CoreDebug_DEMCR_VC_CORERESET_Pos)      /*!< CoreDebug DEMCR: VC_CORERESET Mask */
+
+/*@} end of group CMSIS_CoreDebug */
+
+
+/** \ingroup    CMSIS_core_register
+    \defgroup   CMSIS_core_base     Core Definitions
+    \brief      Definitions for base addresses, unions, and structures.
+  @{
+ */
+
+/* Memory mapping of Cortex-M4 Hardware */
+#define SCS_BASE            (0xE000E000UL)                            /*!< System Control Space Base Address  */
+#define ITM_BASE            (0xE0000000UL)                            /*!< ITM Base Address                   */
+#define DWT_BASE            (0xE0001000UL)                            /*!< DWT Base Address                   */
+#define TPI_BASE            (0xE0040000UL)                            /*!< TPI Base Address                   */
+#define CoreDebug_BASE      (0xE000EDF0UL)                            /*!< Core Debug Base Address            */
+#define SysTick_BASE        (SCS_BASE +  0x0010UL)                    /*!< SysTick Base Address               */
+#define NVIC_BASE           (SCS_BASE +  0x0100UL)                    /*!< NVIC Base Address                  */
+#define SCB_BASE            (SCS_BASE +  0x0D00UL)                    /*!< System Control Block Base Address  */
+
+#define SCnSCB              ((SCnSCB_Type    *)     SCS_BASE      )   /*!< System control Register not in SCB */
+#define SCB                 ((SCB_Type       *)     SCB_BASE      )   /*!< SCB configuration struct           */
+#define SysTick             ((SysTick_Type   *)     SysTick_BASE  )   /*!< SysTick configuration struct       */
+#define NVIC                ((NVIC_Type      *)     NVIC_BASE     )   /*!< NVIC configuration struct          */
+#define ITM                 ((ITM_Type       *)     ITM_BASE      )   /*!< ITM configuration struct           */
+#define DWT                 ((DWT_Type       *)     DWT_BASE      )   /*!< DWT configuration struct           */
+#define TPI                 ((TPI_Type       *)     TPI_BASE      )   /*!< TPI configuration struct           */
+#define CoreDebug           ((CoreDebug_Type *)     CoreDebug_BASE)   /*!< Core Debug configuration struct    */
+
+#if (__MPU_PRESENT == 1)
+  #define MPU_BASE          (SCS_BASE +  0x0D90UL)                    /*!< Memory Protection Unit             */
+  #define MPU               ((MPU_Type       *)     MPU_BASE      )   /*!< Memory Protection Unit             */
+#endif
+
+#if (__FPU_PRESENT == 1)
+  #define FPU_BASE          (SCS_BASE +  0x0F30UL)                    /*!< Floating Point Unit                */
+  #define FPU               ((FPU_Type       *)     FPU_BASE      )   /*!< Floating Point Unit                */
+#endif
+
+/*@} */
+
+
+
+/*******************************************************************************
+ *                Hardware Abstraction Layer
+  Core Function Interface contains:
+  - Core NVIC Functions
+  - Core SysTick Functions
+  - Core Debug Functions
+  - Core Register Access Functions
+ ******************************************************************************/
+/** \defgroup CMSIS_Core_FunctionInterface Functions and Instructions Reference
+*/
+
+
+
+/* ##########################   NVIC functions  #################################### */
+/** \ingroup  CMSIS_Core_FunctionInterface
+    \defgroup CMSIS_Core_NVICFunctions NVIC Functions
+    \brief      Functions that manage interrupts and exceptions via the NVIC.
+    @{
+ */
+
+/** \brief  Set Priority Grouping
+
+  The function sets the priority grouping field using the required unlock sequence.
+  The parameter PriorityGroup is assigned to the field SCB->AIRCR [10:8] PRIGROUP field.
+  Only values from 0..7 are used.
+  In case of a conflict between priority grouping and available
+  priority bits (__NVIC_PRIO_BITS), the smallest possible priority group is set.
+
+    \param [in]      PriorityGroup  Priority grouping field.
+ */
+__STATIC_INLINE void NVIC_SetPriorityGrouping(uint32_t PriorityGroup)
+{
+  uint32_t reg_value;
+  uint32_t PriorityGroupTmp = (PriorityGroup & (uint32_t)0x07);               /* only values 0..7 are used          */
+
+  reg_value  =  SCB->AIRCR;                                                   /* read old register configuration    */
+  reg_value &= ~(SCB_AIRCR_VECTKEY_Msk | SCB_AIRCR_PRIGROUP_Msk);             /* clear bits to change               */
+  reg_value  =  (reg_value                                 |
+                ((uint32_t)0x5FA << SCB_AIRCR_VECTKEY_Pos) |
+                (PriorityGroupTmp << 8));                                     /* Insert write key and priorty group */
+  SCB->AIRCR =  reg_value;
+}
+
+
+/** \brief  Get Priority Grouping
+
+  The function reads the priority grouping field from the NVIC Interrupt Controller.
+
+    \return                Priority grouping field (SCB->AIRCR [10:8] PRIGROUP field).
+ */
+__STATIC_INLINE uint32_t NVIC_GetPriorityGrouping(void)
+{
+  return ((SCB->AIRCR & SCB_AIRCR_PRIGROUP_Msk) >> SCB_AIRCR_PRIGROUP_Pos);   /* read priority grouping field */
+}
+
+
+/** \brief  Enable External Interrupt
+
+    The function enables a device-specific interrupt in the NVIC interrupt controller.
+
+    \param [in]      IRQn  External interrupt number. Value cannot be negative.
+ */
+__STATIC_INLINE void NVIC_EnableIRQ(IRQn_Type IRQn)
+{
+/*  NVIC->ISER[((uint32_t)(IRQn) >> 5)] = (1 << ((uint32_t)(IRQn) & 0x1F));  enable interrupt */
+  NVIC->ISER[(uint32_t)((int32_t)IRQn) >> 5] = (uint32_t)(1 << ((uint32_t)((int32_t)IRQn) & (uint32_t)0x1F)); /* enable interrupt */
+}
+
+
+/** \brief  Disable External Interrupt
+
+    The function disables a device-specific interrupt in the NVIC interrupt controller.
+
+    \param [in]      IRQn  External interrupt number. Value cannot be negative.
+ */
+__STATIC_INLINE void NVIC_DisableIRQ(IRQn_Type IRQn)
+{
+  NVIC->ICER[((uint32_t)(IRQn) >> 5)] = (1 << ((uint32_t)(IRQn) & 0x1F)); /* disable interrupt */
+}
+
+
+/** \brief  Get Pending Interrupt
+
+    The function reads the pending register in the NVIC and returns the pending bit
+    for the specified interrupt.
+
+    \param [in]      IRQn  Interrupt number.
+
+    \return             0  Interrupt status is not pending.
+    \return             1  Interrupt status is pending.
+ */
+__STATIC_INLINE uint32_t NVIC_GetPendingIRQ(IRQn_Type IRQn)
+{
+  return((uint32_t) ((NVIC->ISPR[(uint32_t)(IRQn) >> 5] & (1 << ((uint32_t)(IRQn) & 0x1F)))?1:0)); /* Return 1 if pending else 0 */
+}
+
+
+/** \brief  Set Pending Interrupt
+
+    The function sets the pending bit of an external interrupt.
+
+    \param [in]      IRQn  Interrupt number. Value cannot be negative.
+ */
+__STATIC_INLINE void NVIC_SetPendingIRQ(IRQn_Type IRQn)
+{
+  NVIC->ISPR[((uint32_t)(IRQn) >> 5)] = (1 << ((uint32_t)(IRQn) & 0x1F)); /* set interrupt pending */
+}
+
+
+/** \brief  Clear Pending Interrupt
+
+    The function clears the pending bit of an external interrupt.
+
+    \param [in]      IRQn  External interrupt number. Value cannot be negative.
+ */
+__STATIC_INLINE void NVIC_ClearPendingIRQ(IRQn_Type IRQn)
+{
+  NVIC->ICPR[((uint32_t)(IRQn) >> 5)] = (1 << ((uint32_t)(IRQn) & 0x1F)); /* Clear pending interrupt */
+}
+
+
+/** \brief  Get Active Interrupt
+
+    The function reads the active register in NVIC and returns the active bit.
+
+    \param [in]      IRQn  Interrupt number.
+
+    \return             0  Interrupt status is not active.
+    \return             1  Interrupt status is active.
+ */
+__STATIC_INLINE uint32_t NVIC_GetActive(IRQn_Type IRQn)
+{
+  return((uint32_t)((NVIC->IABR[(uint32_t)(IRQn) >> 5] & (1 << ((uint32_t)(IRQn) & 0x1F)))?1:0)); /* Return 1 if active else 0 */
+}
+
+
+/** \brief  Set Interrupt Priority
+
+    The function sets the priority of an interrupt.
+
+    \note The priority cannot be set for every core interrupt.
+
+    \param [in]      IRQn  Interrupt number.
+    \param [in]  priority  Priority to set.
+ */
+__STATIC_INLINE void NVIC_SetPriority(IRQn_Type IRQn, uint32_t priority)
+{
+  if(IRQn < 0) {
+    SCB->SHP[((uint32_t)(IRQn) & 0xF)-4] = ((priority << (8 - __NVIC_PRIO_BITS)) & 0xff); } /* set Priority for Cortex-M  System Interrupts */
+  else {
+    NVIC->IP[(uint32_t)(IRQn)] = ((priority << (8 - __NVIC_PRIO_BITS)) & 0xff);    }        /* set Priority for device specific Interrupts  */
+}
+
+
+/** \brief  Get Interrupt Priority
+
+    The function reads the priority of an interrupt. The interrupt
+    number can be positive to specify an external (device specific)
+    interrupt, or negative to specify an internal (core) interrupt.
+
+
+    \param [in]   IRQn  Interrupt number.
+    \return             Interrupt Priority. Value is aligned automatically to the implemented
+                        priority bits of the microcontroller.
+ */
+__STATIC_INLINE uint32_t NVIC_GetPriority(IRQn_Type IRQn)
+{
+
+  if(IRQn < 0) {
+    return((uint32_t)(SCB->SHP[((uint32_t)(IRQn) & 0xF)-4] >> (8 - __NVIC_PRIO_BITS)));  } /* get priority for Cortex-M  system interrupts */
+  else {
+    return((uint32_t)(NVIC->IP[(uint32_t)(IRQn)]           >> (8 - __NVIC_PRIO_BITS)));  } /* get priority for device specific interrupts  */
+}
+
+
+/** \brief  Encode Priority
+
+    The function encodes the priority for an interrupt with the given priority group,
+    preemptive priority value, and subpriority value.
+    In case of a conflict between priority grouping and available
+    priority bits (__NVIC_PRIO_BITS), the samllest possible priority group is set.
+
+    \param [in]     PriorityGroup  Used priority group.
+    \param [in]   PreemptPriority  Preemptive priority value (starting from 0).
+    \param [in]       SubPriority  Subpriority value (starting from 0).
+    \return                        Encoded priority. Value can be used in the function \ref NVIC_SetPriority().
+ */
+__STATIC_INLINE uint32_t NVIC_EncodePriority (uint32_t PriorityGroup, uint32_t PreemptPriority, uint32_t SubPriority)
+{
+  uint32_t PriorityGroupTmp = (PriorityGroup & 0x07);          /* only values 0..7 are used          */
+  uint32_t PreemptPriorityBits;
+  uint32_t SubPriorityBits;
+
+  PreemptPriorityBits = ((7 - PriorityGroupTmp) > __NVIC_PRIO_BITS) ? __NVIC_PRIO_BITS : 7 - PriorityGroupTmp;
+  SubPriorityBits     = ((PriorityGroupTmp + __NVIC_PRIO_BITS) < 7) ? 0 : PriorityGroupTmp - 7 + __NVIC_PRIO_BITS;
+
+  return (
+           ((PreemptPriority & ((1 << (PreemptPriorityBits)) - 1)) << SubPriorityBits) |
+           ((SubPriority     & ((1 << (SubPriorityBits    )) - 1)))
+         );
+}
+
+
+/** \brief  Decode Priority
+
+    The function decodes an interrupt priority value with a given priority group to
+    preemptive priority value and subpriority value.
+    In case of a conflict between priority grouping and available
+    priority bits (__NVIC_PRIO_BITS) the samllest possible priority group is set.
+
+    \param [in]         Priority   Priority value, which can be retrieved with the function \ref NVIC_GetPriority().
+    \param [in]     PriorityGroup  Used priority group.
+    \param [out] pPreemptPriority  Preemptive priority value (starting from 0).
+    \param [out]     pSubPriority  Subpriority value (starting from 0).
+ */
+__STATIC_INLINE void NVIC_DecodePriority (uint32_t Priority, uint32_t PriorityGroup, uint32_t* pPreemptPriority, uint32_t* pSubPriority)
+{
+  uint32_t PriorityGroupTmp = (PriorityGroup & 0x07);          /* only values 0..7 are used          */
+  uint32_t PreemptPriorityBits;
+  uint32_t SubPriorityBits;
+
+  PreemptPriorityBits = ((7 - PriorityGroupTmp) > __NVIC_PRIO_BITS) ? __NVIC_PRIO_BITS : 7 - PriorityGroupTmp;
+  SubPriorityBits     = ((PriorityGroupTmp + __NVIC_PRIO_BITS) < 7) ? 0 : PriorityGroupTmp - 7 + __NVIC_PRIO_BITS;
+
+  *pPreemptPriority = (Priority >> SubPriorityBits) & ((1 << (PreemptPriorityBits)) - 1);
+  *pSubPriority     = (Priority                   ) & ((1 << (SubPriorityBits    )) - 1);
+}
+
+
+/** \brief  System Reset
+
+    The function initiates a system reset request to reset the MCU.
+ */
+__STATIC_INLINE void NVIC_SystemReset(void)
+{
+  __DSB();                                                     /* Ensure all outstanding memory accesses included
+                                                                  buffered write are completed before reset */
+  SCB->AIRCR  = ((0x5FA << SCB_AIRCR_VECTKEY_Pos)      |
+                 (SCB->AIRCR & SCB_AIRCR_PRIGROUP_Msk) |
+                 SCB_AIRCR_SYSRESETREQ_Msk);                   /* Keep priority group unchanged */
+  __DSB();                                                     /* Ensure completion of memory access */
+  while(1);                                                    /* wait until reset */
+}
+
+/*@} end of CMSIS_Core_NVICFunctions */
+
+
+
+/* ##################################    SysTick function  ############################################ */
+/** \ingroup  CMSIS_Core_FunctionInterface
+    \defgroup CMSIS_Core_SysTickFunctions SysTick Functions
+    \brief      Functions that configure the System.
+  @{
+ */
+
+#if (__Vendor_SysTickConfig == 0)
+
+/** \brief  System Tick Configuration
+
+    The function initializes the System Timer and its interrupt, and starts the System Tick Timer.
+    Counter is in free running mode to generate periodic interrupts.
+
+    \param [in]  ticks  Number of ticks between two interrupts.
+
+    \return          0  Function succeeded.
+    \return          1  Function failed.
+
+    \note     When the variable __Vendor_SysTickConfig is set to 1, then the
+    function SysTick_Config is not included. In this case, the file device.h
+    must contain a vendor-specific implementation of this function.
+
+ */
+__STATIC_INLINE uint32_t SysTick_Config(uint32_t ticks)
+{
+  if (ticks > SysTick_LOAD_RELOAD_Msk)  return (1);            /* Reload value impossible */
+
+  SysTick->LOAD  = (ticks & SysTick_LOAD_RELOAD_Msk) - 1;      /* set reload register */
+  NVIC_SetPriority (SysTick_IRQn, (1<<__NVIC_PRIO_BITS) - 1);  /* set Priority for Systick Interrupt */
+  SysTick->VAL   = 0;                                          /* Load the SysTick Counter Value */
+  SysTick->CTRL  = SysTick_CTRL_CLKSOURCE_Msk |
+                   SysTick_CTRL_TICKINT_Msk   |
+                   SysTick_CTRL_ENABLE_Msk;                    /* Enable SysTick IRQ and SysTick Timer */
+  return (0);                                                  /* Function successful */
+}
+
+#endif
+
+/*@} end of CMSIS_Core_SysTickFunctions */
+
+
+
+/* ##################################### Debug In/Output function ########################################### */
+/** \ingroup  CMSIS_Core_FunctionInterface
+    \defgroup CMSIS_core_DebugFunctions ITM Functions
+    \brief   Functions that access the ITM debug interface.
+  @{
+ */
+
+extern volatile int32_t ITM_RxBuffer;                    /*!< External variable to receive characters.                         */
+#define                 ITM_RXBUFFER_EMPTY    0x5AA55AA5 /*!< Value identifying \ref ITM_RxBuffer is ready for next character. */
+
+
+/** \brief  ITM Send Character
+
+    The function transmits a character via the ITM channel 0, and
+    \li Just returns when no debugger is connected that has booked the output.
+    \li Is blocking when a debugger is connected, but the previous character sent has not been transmitted.
+
+    \param [in]     ch  Character to transmit.
+
+    \returns            Character to transmit.
+ */
+__STATIC_INLINE uint32_t ITM_SendChar (uint32_t ch)
+{
+  if ((ITM->TCR & ITM_TCR_ITMENA_Msk)                  &&      /* ITM enabled */
+      (ITM->TER & (1UL << 0)        )                    )     /* ITM Port #0 enabled */
+  {
+    while (ITM->PORT[0].u32 == 0);
+    ITM->PORT[0].u8 = (uint8_t) ch;
+  }
+  return (ch);
+}
+
+
+/** \brief  ITM Receive Character
+
+    The function inputs a character via the external variable \ref ITM_RxBuffer.
+
+    \return             Received character.
+    \return         -1  No character pending.
+ */
+__STATIC_INLINE int32_t ITM_ReceiveChar (void) {
+  int32_t ch = -1;                           /* no character available */
+
+  if (ITM_RxBuffer != ITM_RXBUFFER_EMPTY) {
+    ch = ITM_RxBuffer;
+    ITM_RxBuffer = ITM_RXBUFFER_EMPTY;       /* ready for next character */
+  }
+
+  return (ch);
+}
+
+
+/** \brief  ITM Check Character
+
+    The function checks whether a character is pending for reading in the variable \ref ITM_RxBuffer.
+
+    \return          0  No character available.
+    \return          1  Character available.
+ */
+__STATIC_INLINE int32_t ITM_CheckChar (void) {
+
+  if (ITM_RxBuffer == ITM_RXBUFFER_EMPTY) {
+    return (0);                                 /* no character available */
+  } else {
+    return (1);                                 /*    character available */
+  }
+}
+
+/*@} end of CMSIS_core_DebugFunctions */
+
+#endif /* __CORE_CM4_H_DEPENDANT */
+
+#endif /* __CMSIS_GENERIC */
+
+#ifdef __cplusplus
+}
+#endif
diff --git a/apps/mathlib/CMSIS/Include/core_cm4_simd.h b/apps/mathlib/CMSIS/Include/core_cm4_simd.h
new file mode 100644
index 0000000000..b5140073fb
--- /dev/null
+++ b/apps/mathlib/CMSIS/Include/core_cm4_simd.h
@@ -0,0 +1,649 @@
+/**************************************************************************//**
+ * @file     core_cm4_simd.h
+ * @brief    CMSIS Cortex-M4 SIMD Header File
+ * @version  V3.01
+ * @date     06. March 2012
+ *
+ * @note
+ * Copyright (C) 2010-2012 ARM Limited. All rights reserved.
+ *
+ * @par
+ * ARM Limited (ARM) is supplying this software for use with Cortex-M
+ * processor based microcontrollers.  This file can be freely distributed
+ * within development tools that are supporting such ARM based processors.
+ *
+ * @par
+ * THIS SOFTWARE IS PROVIDED "AS IS".  NO WARRANTIES, WHETHER EXPRESS, IMPLIED
+ * OR STATUTORY, INCLUDING, BUT NOT LIMITED TO, IMPLIED WARRANTIES OF
+ * MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE APPLY TO THIS SOFTWARE.
+ * ARM SHALL NOT, IN ANY CIRCUMSTANCES, BE LIABLE FOR SPECIAL, INCIDENTAL, OR
+ * CONSEQUENTIAL DAMAGES, FOR ANY REASON WHATSOEVER.
+ *
+ ******************************************************************************/
+
+#ifdef __cplusplus
+ extern "C" {
+#endif
+
+#ifndef __CORE_CM4_SIMD_H
+#define __CORE_CM4_SIMD_H
+
+
+/*******************************************************************************
+ *                Hardware Abstraction Layer
+ ******************************************************************************/
+
+
+/* ###################  Compiler specific Intrinsics  ########################### */
+/** \defgroup CMSIS_SIMD_intrinsics CMSIS SIMD Intrinsics
+  Access to dedicated SIMD instructions
+  @{
+*/
+
+#if   defined ( __CC_ARM ) /*------------------RealView Compiler -----------------*/
+/* ARM armcc specific functions */
+
+/*------ CM4 SIMD Intrinsics -----------------------------------------------------*/
+#define __SADD8                           __sadd8
+#define __QADD8                           __qadd8
+#define __SHADD8                          __shadd8
+#define __UADD8                           __uadd8
+#define __UQADD8                          __uqadd8
+#define __UHADD8                          __uhadd8
+#define __SSUB8                           __ssub8
+#define __QSUB8                           __qsub8
+#define __SHSUB8                          __shsub8
+#define __USUB8                           __usub8
+#define __UQSUB8                          __uqsub8
+#define __UHSUB8                          __uhsub8
+#define __SADD16                          __sadd16
+#define __QADD16                          __qadd16
+#define __SHADD16                         __shadd16
+#define __UADD16                          __uadd16
+#define __UQADD16                         __uqadd16
+#define __UHADD16                         __uhadd16
+#define __SSUB16                          __ssub16
+#define __QSUB16                          __qsub16
+#define __SHSUB16                         __shsub16
+#define __USUB16                          __usub16
+#define __UQSUB16                         __uqsub16
+#define __UHSUB16                         __uhsub16
+#define __SASX                            __sasx
+#define __QASX                            __qasx
+#define __SHASX                           __shasx
+#define __UASX                            __uasx
+#define __UQASX                           __uqasx
+#define __UHASX                           __uhasx
+#define __SSAX                            __ssax
+#define __QSAX                            __qsax
+#define __SHSAX                           __shsax
+#define __USAX                            __usax
+#define __UQSAX                           __uqsax
+#define __UHSAX                           __uhsax
+#define __USAD8                           __usad8
+#define __USADA8                          __usada8
+#define __SSAT16                          __ssat16
+#define __USAT16                          __usat16
+#define __UXTB16                          __uxtb16
+#define __UXTAB16                         __uxtab16
+#define __SXTB16                          __sxtb16
+#define __SXTAB16                         __sxtab16
+#define __SMUAD                           __smuad
+#define __SMUADX                          __smuadx
+#define __SMLAD                           __smlad
+#define __SMLADX                          __smladx
+#define __SMLALD                          __smlald
+#define __SMLALDX                         __smlaldx
+#define __SMUSD                           __smusd
+#define __SMUSDX                          __smusdx
+#define __SMLSD                           __smlsd
+#define __SMLSDX                          __smlsdx
+#define __SMLSLD                          __smlsld
+#define __SMLSLDX                         __smlsldx
+#define __SEL                             __sel
+#define __QADD                            __qadd
+#define __QSUB                            __qsub
+
+#define __PKHBT(ARG1,ARG2,ARG3)          ( ((((uint32_t)(ARG1))          ) & 0x0000FFFFUL) |  \
+                                           ((((uint32_t)(ARG2)) << (ARG3)) & 0xFFFF0000UL)  )
+
+#define __PKHTB(ARG1,ARG2,ARG3)          ( ((((uint32_t)(ARG1))          ) & 0xFFFF0000UL) |  \
+                                           ((((uint32_t)(ARG2)) >> (ARG3)) & 0x0000FFFFUL)  )
+
+
+/*-- End CM4 SIMD Intrinsics -----------------------------------------------------*/
+
+
+
+#elif defined ( __ICCARM__ ) /*------------------ ICC Compiler -------------------*/
+/* IAR iccarm specific functions */
+
+/*------ CM4 SIMD Intrinsics -----------------------------------------------------*/
+#include 
+
+/*-- End CM4 SIMD Intrinsics -----------------------------------------------------*/
+
+
+
+#elif defined ( __TMS470__ ) /*---------------- TI CCS Compiler ------------------*/
+/* TI CCS specific functions */
+
+/*------ CM4 SIMD Intrinsics -----------------------------------------------------*/
+#include 
+
+/*-- End CM4 SIMD Intrinsics -----------------------------------------------------*/
+
+
+
+#elif defined ( __GNUC__ ) /*------------------ GNU Compiler ---------------------*/
+/* GNU gcc specific functions */
+
+/*------ CM4 SIMD Intrinsics -----------------------------------------------------*/
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __SADD8(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("sadd8 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __QADD8(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("qadd8 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __SHADD8(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("shadd8 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __UADD8(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("uadd8 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __UQADD8(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("uqadd8 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __UHADD8(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("uhadd8 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __SSUB8(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("ssub8 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __QSUB8(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("qsub8 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __SHSUB8(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("shsub8 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __USUB8(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("usub8 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __UQSUB8(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("uqsub8 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __UHSUB8(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("uhsub8 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __SADD16(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("sadd16 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __QADD16(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("qadd16 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __SHADD16(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("shadd16 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __UADD16(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("uadd16 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __UQADD16(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("uqadd16 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __UHADD16(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("uhadd16 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __SSUB16(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("ssub16 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __QSUB16(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("qsub16 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __SHSUB16(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("shsub16 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __USUB16(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("usub16 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __UQSUB16(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("uqsub16 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __UHSUB16(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("uhsub16 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __SASX(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("sasx %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __QASX(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("qasx %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __SHASX(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("shasx %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __UASX(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("uasx %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __UQASX(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("uqasx %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __UHASX(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("uhasx %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __SSAX(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("ssax %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __QSAX(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("qsax %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __SHSAX(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("shsax %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __USAX(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("usax %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __UQSAX(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("uqsax %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __UHSAX(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("uhsax %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __USAD8(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("usad8 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __USADA8(uint32_t op1, uint32_t op2, uint32_t op3)
+{
+  uint32_t result;
+
+  __ASM volatile ("usada8 %0, %1, %2, %3" : "=r" (result) : "r" (op1), "r" (op2), "r" (op3) );
+  return(result);
+}
+
+#define __SSAT16(ARG1,ARG2) \
+({                          \
+  uint32_t __RES, __ARG1 = (ARG1); \
+  __ASM ("ssat16 %0, %1, %2" : "=r" (__RES) :  "I" (ARG2), "r" (__ARG1) ); \
+  __RES; \
+ })
+
+#define __USAT16(ARG1,ARG2) \
+({                          \
+  uint32_t __RES, __ARG1 = (ARG1); \
+  __ASM ("usat16 %0, %1, %2" : "=r" (__RES) :  "I" (ARG2), "r" (__ARG1) ); \
+  __RES; \
+ })
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __UXTB16(uint32_t op1)
+{
+  uint32_t result;
+
+  __ASM volatile ("uxtb16 %0, %1" : "=r" (result) : "r" (op1));
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __UXTAB16(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("uxtab16 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __SXTB16(uint32_t op1)
+{
+  uint32_t result;
+
+  __ASM volatile ("sxtb16 %0, %1" : "=r" (result) : "r" (op1));
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __SXTAB16(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("sxtab16 %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __SMUAD  (uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("smuad %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __SMUADX (uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("smuadx %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __SMLAD (uint32_t op1, uint32_t op2, uint32_t op3)
+{
+  uint32_t result;
+
+  __ASM volatile ("smlad %0, %1, %2, %3" : "=r" (result) : "r" (op1), "r" (op2), "r" (op3) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __SMLADX (uint32_t op1, uint32_t op2, uint32_t op3)
+{
+  uint32_t result;
+
+  __ASM volatile ("smladx %0, %1, %2, %3" : "=r" (result) : "r" (op1), "r" (op2), "r" (op3) );
+  return(result);
+}
+
+#define __SMLALD(ARG1,ARG2,ARG3) \
+({ \
+  uint32_t __ARG1 = (ARG1), __ARG2 = (ARG2), __ARG3_H = (uint32_t)((uint64_t)(ARG3) >> 32), __ARG3_L = (uint32_t)((uint64_t)(ARG3) & 0xFFFFFFFFUL); \
+  __ASM volatile ("smlald %0, %1, %2, %3" : "=r" (__ARG3_L), "=r" (__ARG3_H) : "r" (__ARG1), "r" (__ARG2), "0" (__ARG3_L), "1" (__ARG3_H) ); \
+  (uint64_t)(((uint64_t)__ARG3_H << 32) | __ARG3_L); \
+ })
+
+#define __SMLALDX(ARG1,ARG2,ARG3) \
+({ \
+  uint32_t __ARG1 = (ARG1), __ARG2 = (ARG2), __ARG3_H = (uint32_t)((uint64_t)(ARG3) >> 32), __ARG3_L = (uint32_t)((uint64_t)(ARG3) & 0xFFFFFFFFUL); \
+  __ASM volatile ("smlaldx %0, %1, %2, %3" : "=r" (__ARG3_L), "=r" (__ARG3_H) : "r" (__ARG1), "r" (__ARG2), "0" (__ARG3_L), "1" (__ARG3_H) ); \
+  (uint64_t)(((uint64_t)__ARG3_H << 32) | __ARG3_L); \
+ })
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __SMUSD  (uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("smusd %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __SMUSDX (uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("smusdx %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __SMLSD (uint32_t op1, uint32_t op2, uint32_t op3)
+{
+  uint32_t result;
+
+  __ASM volatile ("smlsd %0, %1, %2, %3" : "=r" (result) : "r" (op1), "r" (op2), "r" (op3) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __SMLSDX (uint32_t op1, uint32_t op2, uint32_t op3)
+{
+  uint32_t result;
+
+  __ASM volatile ("smlsdx %0, %1, %2, %3" : "=r" (result) : "r" (op1), "r" (op2), "r" (op3) );
+  return(result);
+}
+
+#define __SMLSLD(ARG1,ARG2,ARG3) \
+({ \
+  uint32_t __ARG1 = (ARG1), __ARG2 = (ARG2), __ARG3_H = (uint32_t)((ARG3) >> 32), __ARG3_L = (uint32_t)((ARG3) & 0xFFFFFFFFUL); \
+  __ASM volatile ("smlsld %0, %1, %2, %3" : "=r" (__ARG3_L), "=r" (__ARG3_H) : "r" (__ARG1), "r" (__ARG2), "0" (__ARG3_L), "1" (__ARG3_H) ); \
+  (uint64_t)(((uint64_t)__ARG3_H << 32) | __ARG3_L); \
+ })
+
+#define __SMLSLDX(ARG1,ARG2,ARG3) \
+({ \
+  uint32_t __ARG1 = (ARG1), __ARG2 = (ARG2), __ARG3_H = (uint32_t)((ARG3) >> 32), __ARG3_L = (uint32_t)((ARG3) & 0xFFFFFFFFUL); \
+  __ASM volatile ("smlsldx %0, %1, %2, %3" : "=r" (__ARG3_L), "=r" (__ARG3_H) : "r" (__ARG1), "r" (__ARG2), "0" (__ARG3_L), "1" (__ARG3_H) ); \
+  (uint64_t)(((uint64_t)__ARG3_H << 32) | __ARG3_L); \
+ })
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __SEL  (uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("sel %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __QADD(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("qadd %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __QSUB(uint32_t op1, uint32_t op2)
+{
+  uint32_t result;
+
+  __ASM volatile ("qsub %0, %1, %2" : "=r" (result) : "r" (op1), "r" (op2) );
+  return(result);
+}
+
+#define __PKHBT(ARG1,ARG2,ARG3) \
+({                          \
+  uint32_t __RES, __ARG1 = (ARG1), __ARG2 = (ARG2); \
+  __ASM ("pkhbt %0, %1, %2, lsl %3" : "=r" (__RES) :  "r" (__ARG1), "r" (__ARG2), "I" (ARG3)  ); \
+  __RES; \
+ })
+
+#define __PKHTB(ARG1,ARG2,ARG3) \
+({                          \
+  uint32_t __RES, __ARG1 = (ARG1), __ARG2 = (ARG2); \
+  if (ARG3 == 0) \
+    __ASM ("pkhtb %0, %1, %2" : "=r" (__RES) :  "r" (__ARG1), "r" (__ARG2)  ); \
+  else \
+    __ASM ("pkhtb %0, %1, %2, asr %3" : "=r" (__RES) :  "r" (__ARG1), "r" (__ARG2), "I" (ARG3)  ); \
+  __RES; \
+ })
+
+/*-- End CM4 SIMD Intrinsics -----------------------------------------------------*/
+
+
+
+#elif defined ( __TASKING__ ) /*------------------ TASKING Compiler --------------*/
+/* TASKING carm specific functions */
+
+
+/*------ CM4 SIMD Intrinsics -----------------------------------------------------*/
+/* not yet supported */
+/*-- End CM4 SIMD Intrinsics -----------------------------------------------------*/
+
+
+#endif
+
+/*@} end of group CMSIS_SIMD_intrinsics */
+
+
+#endif /* __CORE_CM4_SIMD_H */
+
+#ifdef __cplusplus
+}
+#endif
diff --git a/apps/mathlib/CMSIS/Include/core_cmFunc.h b/apps/mathlib/CMSIS/Include/core_cmFunc.h
new file mode 100644
index 0000000000..adb07b5d34
--- /dev/null
+++ b/apps/mathlib/CMSIS/Include/core_cmFunc.h
@@ -0,0 +1,616 @@
+/**************************************************************************//**
+ * @file     core_cmFunc.h
+ * @brief    CMSIS Cortex-M Core Function Access Header File
+ * @version  V3.01
+ * @date     06. March 2012
+ *
+ * @note
+ * Copyright (C) 2009-2012 ARM Limited. All rights reserved.
+ *
+ * @par
+ * ARM Limited (ARM) is supplying this software for use with Cortex-M
+ * processor based microcontrollers.  This file can be freely distributed
+ * within development tools that are supporting such ARM based processors.
+ *
+ * @par
+ * THIS SOFTWARE IS PROVIDED "AS IS".  NO WARRANTIES, WHETHER EXPRESS, IMPLIED
+ * OR STATUTORY, INCLUDING, BUT NOT LIMITED TO, IMPLIED WARRANTIES OF
+ * MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE APPLY TO THIS SOFTWARE.
+ * ARM SHALL NOT, IN ANY CIRCUMSTANCES, BE LIABLE FOR SPECIAL, INCIDENTAL, OR
+ * CONSEQUENTIAL DAMAGES, FOR ANY REASON WHATSOEVER.
+ *
+ ******************************************************************************/
+
+#ifndef __CORE_CMFUNC_H
+#define __CORE_CMFUNC_H
+
+
+/* ###########################  Core Function Access  ########################### */
+/** \ingroup  CMSIS_Core_FunctionInterface
+    \defgroup CMSIS_Core_RegAccFunctions CMSIS Core Register Access Functions
+  @{
+ */
+
+#if   defined ( __CC_ARM ) /*------------------RealView Compiler -----------------*/
+/* ARM armcc specific functions */
+
+#if (__ARMCC_VERSION < 400677)
+  #error "Please use ARM Compiler Toolchain V4.0.677 or later!"
+#endif
+
+/* intrinsic void __enable_irq();     */
+/* intrinsic void __disable_irq();    */
+
+/** \brief  Get Control Register
+
+    This function returns the content of the Control Register.
+
+    \return               Control Register value
+ */
+__STATIC_INLINE uint32_t __get_CONTROL(void)
+{
+  register uint32_t __regControl         __ASM("control");
+  return(__regControl);
+}
+
+
+/** \brief  Set Control Register
+
+    This function writes the given value to the Control Register.
+
+    \param [in]    control  Control Register value to set
+ */
+__STATIC_INLINE void __set_CONTROL(uint32_t control)
+{
+  register uint32_t __regControl         __ASM("control");
+  __regControl = control;
+}
+
+
+/** \brief  Get IPSR Register
+
+    This function returns the content of the IPSR Register.
+
+    \return               IPSR Register value
+ */
+__STATIC_INLINE uint32_t __get_IPSR(void)
+{
+  register uint32_t __regIPSR          __ASM("ipsr");
+  return(__regIPSR);
+}
+
+
+/** \brief  Get APSR Register
+
+    This function returns the content of the APSR Register.
+
+    \return               APSR Register value
+ */
+__STATIC_INLINE uint32_t __get_APSR(void)
+{
+  register uint32_t __regAPSR          __ASM("apsr");
+  return(__regAPSR);
+}
+
+
+/** \brief  Get xPSR Register
+
+    This function returns the content of the xPSR Register.
+
+    \return               xPSR Register value
+ */
+__STATIC_INLINE uint32_t __get_xPSR(void)
+{
+  register uint32_t __regXPSR          __ASM("xpsr");
+  return(__regXPSR);
+}
+
+
+/** \brief  Get Process Stack Pointer
+
+    This function returns the current value of the Process Stack Pointer (PSP).
+
+    \return               PSP Register value
+ */
+__STATIC_INLINE uint32_t __get_PSP(void)
+{
+  register uint32_t __regProcessStackPointer  __ASM("psp");
+  return(__regProcessStackPointer);
+}
+
+
+/** \brief  Set Process Stack Pointer
+
+    This function assigns the given value to the Process Stack Pointer (PSP).
+
+    \param [in]    topOfProcStack  Process Stack Pointer value to set
+ */
+__STATIC_INLINE void __set_PSP(uint32_t topOfProcStack)
+{
+  register uint32_t __regProcessStackPointer  __ASM("psp");
+  __regProcessStackPointer = topOfProcStack;
+}
+
+
+/** \brief  Get Main Stack Pointer
+
+    This function returns the current value of the Main Stack Pointer (MSP).
+
+    \return               MSP Register value
+ */
+__STATIC_INLINE uint32_t __get_MSP(void)
+{
+  register uint32_t __regMainStackPointer     __ASM("msp");
+  return(__regMainStackPointer);
+}
+
+
+/** \brief  Set Main Stack Pointer
+
+    This function assigns the given value to the Main Stack Pointer (MSP).
+
+    \param [in]    topOfMainStack  Main Stack Pointer value to set
+ */
+__STATIC_INLINE void __set_MSP(uint32_t topOfMainStack)
+{
+  register uint32_t __regMainStackPointer     __ASM("msp");
+  __regMainStackPointer = topOfMainStack;
+}
+
+
+/** \brief  Get Priority Mask
+
+    This function returns the current state of the priority mask bit from the Priority Mask Register.
+
+    \return               Priority Mask value
+ */
+__STATIC_INLINE uint32_t __get_PRIMASK(void)
+{
+  register uint32_t __regPriMask         __ASM("primask");
+  return(__regPriMask);
+}
+
+
+/** \brief  Set Priority Mask
+
+    This function assigns the given value to the Priority Mask Register.
+
+    \param [in]    priMask  Priority Mask
+ */
+__STATIC_INLINE void __set_PRIMASK(uint32_t priMask)
+{
+  register uint32_t __regPriMask         __ASM("primask");
+  __regPriMask = (priMask);
+}
+
+
+#if       (__CORTEX_M >= 0x03)
+
+/** \brief  Enable FIQ
+
+    This function enables FIQ interrupts by clearing the F-bit in the CPSR.
+    Can only be executed in Privileged modes.
+ */
+#define __enable_fault_irq                __enable_fiq
+
+
+/** \brief  Disable FIQ
+
+    This function disables FIQ interrupts by setting the F-bit in the CPSR.
+    Can only be executed in Privileged modes.
+ */
+#define __disable_fault_irq               __disable_fiq
+
+
+/** \brief  Get Base Priority
+
+    This function returns the current value of the Base Priority register.
+
+    \return               Base Priority register value
+ */
+__STATIC_INLINE uint32_t  __get_BASEPRI(void)
+{
+  register uint32_t __regBasePri         __ASM("basepri");
+  return(__regBasePri);
+}
+
+
+/** \brief  Set Base Priority
+
+    This function assigns the given value to the Base Priority register.
+
+    \param [in]    basePri  Base Priority value to set
+ */
+__STATIC_INLINE void __set_BASEPRI(uint32_t basePri)
+{
+  register uint32_t __regBasePri         __ASM("basepri");
+  __regBasePri = (basePri & 0xff);
+}
+
+
+/** \brief  Get Fault Mask
+
+    This function returns the current value of the Fault Mask register.
+
+    \return               Fault Mask register value
+ */
+__STATIC_INLINE uint32_t __get_FAULTMASK(void)
+{
+  register uint32_t __regFaultMask       __ASM("faultmask");
+  return(__regFaultMask);
+}
+
+
+/** \brief  Set Fault Mask
+
+    This function assigns the given value to the Fault Mask register.
+
+    \param [in]    faultMask  Fault Mask value to set
+ */
+__STATIC_INLINE void __set_FAULTMASK(uint32_t faultMask)
+{
+  register uint32_t __regFaultMask       __ASM("faultmask");
+  __regFaultMask = (faultMask & (uint32_t)1);
+}
+
+#endif /* (__CORTEX_M >= 0x03) */
+
+
+#if       (__CORTEX_M == 0x04)
+
+/** \brief  Get FPSCR
+
+    This function returns the current value of the Floating Point Status/Control register.
+
+    \return               Floating Point Status/Control register value
+ */
+__STATIC_INLINE uint32_t __get_FPSCR(void)
+{
+#if (__FPU_PRESENT == 1) && (__FPU_USED == 1)
+  register uint32_t __regfpscr         __ASM("fpscr");
+  return(__regfpscr);
+#else
+   return(0);
+#endif
+}
+
+
+/** \brief  Set FPSCR
+
+    This function assigns the given value to the Floating Point Status/Control register.
+
+    \param [in]    fpscr  Floating Point Status/Control value to set
+ */
+__STATIC_INLINE void __set_FPSCR(uint32_t fpscr)
+{
+#if (__FPU_PRESENT == 1) && (__FPU_USED == 1)
+  register uint32_t __regfpscr         __ASM("fpscr");
+  __regfpscr = (fpscr);
+#endif
+}
+
+#endif /* (__CORTEX_M == 0x04) */
+
+
+#elif defined ( __ICCARM__ ) /*------------------ ICC Compiler -------------------*/
+/* IAR iccarm specific functions */
+
+#include 
+
+
+#elif defined ( __TMS470__ ) /*---------------- TI CCS Compiler ------------------*/
+/* TI CCS specific functions */
+
+#include 
+
+
+#elif defined ( __GNUC__ ) /*------------------ GNU Compiler ---------------------*/
+/* GNU gcc specific functions */
+
+/** \brief  Enable IRQ Interrupts
+
+  This function enables IRQ interrupts by clearing the I-bit in the CPSR.
+  Can only be executed in Privileged modes.
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE void __enable_irq(void)
+{
+  __ASM volatile ("cpsie i");
+}
+
+
+/** \brief  Disable IRQ Interrupts
+
+  This function disables IRQ interrupts by setting the I-bit in the CPSR.
+  Can only be executed in Privileged modes.
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE void __disable_irq(void)
+{
+  __ASM volatile ("cpsid i");
+}
+
+
+/** \brief  Get Control Register
+
+    This function returns the content of the Control Register.
+
+    \return               Control Register value
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __get_CONTROL(void)
+{
+  uint32_t result;
+
+  __ASM volatile ("MRS %0, control" : "=r" (result) );
+  return(result);
+}
+
+
+/** \brief  Set Control Register
+
+    This function writes the given value to the Control Register.
+
+    \param [in]    control  Control Register value to set
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE void __set_CONTROL(uint32_t control)
+{
+  __ASM volatile ("MSR control, %0" : : "r" (control) );
+}
+
+
+/** \brief  Get IPSR Register
+
+    This function returns the content of the IPSR Register.
+
+    \return               IPSR Register value
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __get_IPSR(void)
+{
+  uint32_t result;
+
+  __ASM volatile ("MRS %0, ipsr" : "=r" (result) );
+  return(result);
+}
+
+
+/** \brief  Get APSR Register
+
+    This function returns the content of the APSR Register.
+
+    \return               APSR Register value
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __get_APSR(void)
+{
+  uint32_t result;
+
+  __ASM volatile ("MRS %0, apsr" : "=r" (result) );
+  return(result);
+}
+
+
+/** \brief  Get xPSR Register
+
+    This function returns the content of the xPSR Register.
+
+    \return               xPSR Register value
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __get_xPSR(void)
+{
+  uint32_t result;
+
+  __ASM volatile ("MRS %0, xpsr" : "=r" (result) );
+  return(result);
+}
+
+
+/** \brief  Get Process Stack Pointer
+
+    This function returns the current value of the Process Stack Pointer (PSP).
+
+    \return               PSP Register value
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __get_PSP(void)
+{
+  register uint32_t result;
+
+  __ASM volatile ("MRS %0, psp\n"  : "=r" (result) );
+  return(result);
+}
+
+
+/** \brief  Set Process Stack Pointer
+
+    This function assigns the given value to the Process Stack Pointer (PSP).
+
+    \param [in]    topOfProcStack  Process Stack Pointer value to set
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE void __set_PSP(uint32_t topOfProcStack)
+{
+  __ASM volatile ("MSR psp, %0\n" : : "r" (topOfProcStack) );
+}
+
+
+/** \brief  Get Main Stack Pointer
+
+    This function returns the current value of the Main Stack Pointer (MSP).
+
+    \return               MSP Register value
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __get_MSP(void)
+{
+  register uint32_t result;
+
+  __ASM volatile ("MRS %0, msp\n" : "=r" (result) );
+  return(result);
+}
+
+
+/** \brief  Set Main Stack Pointer
+
+    This function assigns the given value to the Main Stack Pointer (MSP).
+
+    \param [in]    topOfMainStack  Main Stack Pointer value to set
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE void __set_MSP(uint32_t topOfMainStack)
+{
+  __ASM volatile ("MSR msp, %0\n" : : "r" (topOfMainStack) );
+}
+
+
+/** \brief  Get Priority Mask
+
+    This function returns the current state of the priority mask bit from the Priority Mask Register.
+
+    \return               Priority Mask value
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __get_PRIMASK(void)
+{
+  uint32_t result;
+
+  __ASM volatile ("MRS %0, primask" : "=r" (result) );
+  return(result);
+}
+
+
+/** \brief  Set Priority Mask
+
+    This function assigns the given value to the Priority Mask Register.
+
+    \param [in]    priMask  Priority Mask
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE void __set_PRIMASK(uint32_t priMask)
+{
+  __ASM volatile ("MSR primask, %0" : : "r" (priMask) );
+}
+
+
+#if       (__CORTEX_M >= 0x03)
+
+/** \brief  Enable FIQ
+
+    This function enables FIQ interrupts by clearing the F-bit in the CPSR.
+    Can only be executed in Privileged modes.
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE void __enable_fault_irq(void)
+{
+  __ASM volatile ("cpsie f");
+}
+
+
+/** \brief  Disable FIQ
+
+    This function disables FIQ interrupts by setting the F-bit in the CPSR.
+    Can only be executed in Privileged modes.
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE void __disable_fault_irq(void)
+{
+  __ASM volatile ("cpsid f");
+}
+
+
+/** \brief  Get Base Priority
+
+    This function returns the current value of the Base Priority register.
+
+    \return               Base Priority register value
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __get_BASEPRI(void)
+{
+  uint32_t result;
+
+  __ASM volatile ("MRS %0, basepri_max" : "=r" (result) );
+  return(result);
+}
+
+
+/** \brief  Set Base Priority
+
+    This function assigns the given value to the Base Priority register.
+
+    \param [in]    basePri  Base Priority value to set
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE void __set_BASEPRI(uint32_t value)
+{
+  __ASM volatile ("MSR basepri, %0" : : "r" (value) );
+}
+
+
+/** \brief  Get Fault Mask
+
+    This function returns the current value of the Fault Mask register.
+
+    \return               Fault Mask register value
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __get_FAULTMASK(void)
+{
+  uint32_t result;
+
+  __ASM volatile ("MRS %0, faultmask" : "=r" (result) );
+  return(result);
+}
+
+
+/** \brief  Set Fault Mask
+
+    This function assigns the given value to the Fault Mask register.
+
+    \param [in]    faultMask  Fault Mask value to set
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE void __set_FAULTMASK(uint32_t faultMask)
+{
+  __ASM volatile ("MSR faultmask, %0" : : "r" (faultMask) );
+}
+
+#endif /* (__CORTEX_M >= 0x03) */
+
+
+#if       (__CORTEX_M == 0x04)
+
+/** \brief  Get FPSCR
+
+    This function returns the current value of the Floating Point Status/Control register.
+
+    \return               Floating Point Status/Control register value
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __get_FPSCR(void)
+{
+#if (__FPU_PRESENT == 1) && (__FPU_USED == 1)
+  uint32_t result;
+
+  __ASM volatile ("VMRS %0, fpscr" : "=r" (result) );
+  return(result);
+#else
+   return(0);
+#endif
+}
+
+
+/** \brief  Set FPSCR
+
+    This function assigns the given value to the Floating Point Status/Control register.
+
+    \param [in]    fpscr  Floating Point Status/Control value to set
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE void __set_FPSCR(uint32_t fpscr)
+{
+#if (__FPU_PRESENT == 1) && (__FPU_USED == 1)
+  __ASM volatile ("VMSR fpscr, %0" : : "r" (fpscr) );
+#endif
+}
+
+#endif /* (__CORTEX_M == 0x04) */
+
+
+#elif defined ( __TASKING__ ) /*------------------ TASKING Compiler --------------*/
+/* TASKING carm specific functions */
+
+/*
+ * The CMSIS functions have been implemented as intrinsics in the compiler.
+ * Please use "carm -?i" to get an up to date list of all instrinsics,
+ * Including the CMSIS ones.
+ */
+
+#endif
+
+/*@} end of CMSIS_Core_RegAccFunctions */
+
+
+#endif /* __CORE_CMFUNC_H */
diff --git a/apps/mathlib/CMSIS/Include/core_cmInstr.h b/apps/mathlib/CMSIS/Include/core_cmInstr.h
new file mode 100644
index 0000000000..624c175fd5
--- /dev/null
+++ b/apps/mathlib/CMSIS/Include/core_cmInstr.h
@@ -0,0 +1,618 @@
+/**************************************************************************//**
+ * @file     core_cmInstr.h
+ * @brief    CMSIS Cortex-M Core Instruction Access Header File
+ * @version  V3.01
+ * @date     06. March 2012
+ *
+ * @note
+ * Copyright (C) 2009-2012 ARM Limited. All rights reserved.
+ *
+ * @par
+ * ARM Limited (ARM) is supplying this software for use with Cortex-M
+ * processor based microcontrollers.  This file can be freely distributed
+ * within development tools that are supporting such ARM based processors.
+ *
+ * @par
+ * THIS SOFTWARE IS PROVIDED "AS IS".  NO WARRANTIES, WHETHER EXPRESS, IMPLIED
+ * OR STATUTORY, INCLUDING, BUT NOT LIMITED TO, IMPLIED WARRANTIES OF
+ * MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE APPLY TO THIS SOFTWARE.
+ * ARM SHALL NOT, IN ANY CIRCUMSTANCES, BE LIABLE FOR SPECIAL, INCIDENTAL, OR
+ * CONSEQUENTIAL DAMAGES, FOR ANY REASON WHATSOEVER.
+ *
+ ******************************************************************************/
+
+#ifndef __CORE_CMINSTR_H
+#define __CORE_CMINSTR_H
+
+
+/* ##########################  Core Instruction Access  ######################### */
+/** \defgroup CMSIS_Core_InstructionInterface CMSIS Core Instruction Interface
+  Access to dedicated instructions
+  @{
+*/
+
+#if   defined ( __CC_ARM ) /*------------------RealView Compiler -----------------*/
+/* ARM armcc specific functions */
+
+#if (__ARMCC_VERSION < 400677)
+  #error "Please use ARM Compiler Toolchain V4.0.677 or later!"
+#endif
+
+
+/** \brief  No Operation
+
+    No Operation does nothing. This instruction can be used for code alignment purposes.
+ */
+#define __NOP                             __nop
+
+
+/** \brief  Wait For Interrupt
+
+    Wait For Interrupt is a hint instruction that suspends execution
+    until one of a number of events occurs.
+ */
+#define __WFI                             __wfi
+
+
+/** \brief  Wait For Event
+
+    Wait For Event is a hint instruction that permits the processor to enter
+    a low-power state until one of a number of events occurs.
+ */
+#define __WFE                             __wfe
+
+
+/** \brief  Send Event
+
+    Send Event is a hint instruction. It causes an event to be signaled to the CPU.
+ */
+#define __SEV                             __sev
+
+
+/** \brief  Instruction Synchronization Barrier
+
+    Instruction Synchronization Barrier flushes the pipeline in the processor,
+    so that all instructions following the ISB are fetched from cache or
+    memory, after the instruction has been completed.
+ */
+#define __ISB()                           __isb(0xF)
+
+
+/** \brief  Data Synchronization Barrier
+
+    This function acts as a special kind of Data Memory Barrier.
+    It completes when all explicit memory accesses before this instruction complete.
+ */
+#define __DSB()                           __dsb(0xF)
+
+
+/** \brief  Data Memory Barrier
+
+    This function ensures the apparent order of the explicit memory operations before
+    and after the instruction, without ensuring their completion.
+ */
+#define __DMB()                           __dmb(0xF)
+
+
+/** \brief  Reverse byte order (32 bit)
+
+    This function reverses the byte order in integer value.
+
+    \param [in]    value  Value to reverse
+    \return               Reversed value
+ */
+#define __REV                             __rev
+
+
+/** \brief  Reverse byte order (16 bit)
+
+    This function reverses the byte order in two unsigned short values.
+
+    \param [in]    value  Value to reverse
+    \return               Reversed value
+ */
+__attribute__((section(".rev16_text"))) __STATIC_INLINE __ASM uint32_t __REV16(uint32_t value)
+{
+  rev16 r0, r0
+  bx lr
+}
+
+
+/** \brief  Reverse byte order in signed short value
+
+    This function reverses the byte order in a signed short value with sign extension to integer.
+
+    \param [in]    value  Value to reverse
+    \return               Reversed value
+ */
+__attribute__((section(".revsh_text"))) __STATIC_INLINE __ASM int32_t __REVSH(int32_t value)
+{
+  revsh r0, r0
+  bx lr
+}
+
+
+/** \brief  Rotate Right in unsigned value (32 bit)
+
+    This function Rotate Right (immediate) provides the value of the contents of a register rotated by a variable number of bits.
+
+    \param [in]    value  Value to rotate
+    \param [in]    value  Number of Bits to rotate
+    \return               Rotated value
+ */
+#define __ROR                             __ror
+
+
+#if       (__CORTEX_M >= 0x03)
+
+/** \brief  Reverse bit order of value
+
+    This function reverses the bit order of the given value.
+
+    \param [in]    value  Value to reverse
+    \return               Reversed value
+ */
+#define __RBIT                            __rbit
+
+
+/** \brief  LDR Exclusive (8 bit)
+
+    This function performs a exclusive LDR command for 8 bit value.
+
+    \param [in]    ptr  Pointer to data
+    \return             value of type uint8_t at (*ptr)
+ */
+#define __LDREXB(ptr)                     ((uint8_t ) __ldrex(ptr))
+
+
+/** \brief  LDR Exclusive (16 bit)
+
+    This function performs a exclusive LDR command for 16 bit values.
+
+    \param [in]    ptr  Pointer to data
+    \return        value of type uint16_t at (*ptr)
+ */
+#define __LDREXH(ptr)                     ((uint16_t) __ldrex(ptr))
+
+
+/** \brief  LDR Exclusive (32 bit)
+
+    This function performs a exclusive LDR command for 32 bit values.
+
+    \param [in]    ptr  Pointer to data
+    \return        value of type uint32_t at (*ptr)
+ */
+#define __LDREXW(ptr)                     ((uint32_t ) __ldrex(ptr))
+
+
+/** \brief  STR Exclusive (8 bit)
+
+    This function performs a exclusive STR command for 8 bit values.
+
+    \param [in]  value  Value to store
+    \param [in]    ptr  Pointer to location
+    \return          0  Function succeeded
+    \return          1  Function failed
+ */
+#define __STREXB(value, ptr)              __strex(value, ptr)
+
+
+/** \brief  STR Exclusive (16 bit)
+
+    This function performs a exclusive STR command for 16 bit values.
+
+    \param [in]  value  Value to store
+    \param [in]    ptr  Pointer to location
+    \return          0  Function succeeded
+    \return          1  Function failed
+ */
+#define __STREXH(value, ptr)              __strex(value, ptr)
+
+
+/** \brief  STR Exclusive (32 bit)
+
+    This function performs a exclusive STR command for 32 bit values.
+
+    \param [in]  value  Value to store
+    \param [in]    ptr  Pointer to location
+    \return          0  Function succeeded
+    \return          1  Function failed
+ */
+#define __STREXW(value, ptr)              __strex(value, ptr)
+
+
+/** \brief  Remove the exclusive lock
+
+    This function removes the exclusive lock which is created by LDREX.
+
+ */
+#define __CLREX                           __clrex
+
+
+/** \brief  Signed Saturate
+
+    This function saturates a signed value.
+
+    \param [in]  value  Value to be saturated
+    \param [in]    sat  Bit position to saturate to (1..32)
+    \return             Saturated value
+ */
+#define __SSAT                            __ssat
+
+
+/** \brief  Unsigned Saturate
+
+    This function saturates an unsigned value.
+
+    \param [in]  value  Value to be saturated
+    \param [in]    sat  Bit position to saturate to (0..31)
+    \return             Saturated value
+ */
+#define __USAT                            __usat
+
+
+/** \brief  Count leading zeros
+
+    This function counts the number of leading zeros of a data value.
+
+    \param [in]  value  Value to count the leading zeros
+    \return             number of leading zeros in value
+ */
+#define __CLZ                             __clz
+
+#endif /* (__CORTEX_M >= 0x03) */
+
+
+
+#elif defined ( __ICCARM__ ) /*------------------ ICC Compiler -------------------*/
+/* IAR iccarm specific functions */
+
+#include 
+
+
+#elif defined ( __TMS470__ ) /*---------------- TI CCS Compiler ------------------*/
+/* TI CCS specific functions */
+
+#include 
+
+
+#elif defined ( __GNUC__ ) /*------------------ GNU Compiler ---------------------*/
+/* GNU gcc specific functions */
+
+/** \brief  No Operation
+
+    No Operation does nothing. This instruction can be used for code alignment purposes.
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE void __NOP(void)
+{
+  __ASM volatile ("nop");
+}
+
+
+/** \brief  Wait For Interrupt
+
+    Wait For Interrupt is a hint instruction that suspends execution
+    until one of a number of events occurs.
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE void __WFI(void)
+{
+  __ASM volatile ("wfi");
+}
+
+
+/** \brief  Wait For Event
+
+    Wait For Event is a hint instruction that permits the processor to enter
+    a low-power state until one of a number of events occurs.
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE void __WFE(void)
+{
+  __ASM volatile ("wfe");
+}
+
+
+/** \brief  Send Event
+
+    Send Event is a hint instruction. It causes an event to be signaled to the CPU.
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE void __SEV(void)
+{
+  __ASM volatile ("sev");
+}
+
+
+/** \brief  Instruction Synchronization Barrier
+
+    Instruction Synchronization Barrier flushes the pipeline in the processor,
+    so that all instructions following the ISB are fetched from cache or
+    memory, after the instruction has been completed.
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE void __ISB(void)
+{
+  __ASM volatile ("isb");
+}
+
+
+/** \brief  Data Synchronization Barrier
+
+    This function acts as a special kind of Data Memory Barrier.
+    It completes when all explicit memory accesses before this instruction complete.
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE void __DSB(void)
+{
+  __ASM volatile ("dsb");
+}
+
+
+/** \brief  Data Memory Barrier
+
+    This function ensures the apparent order of the explicit memory operations before
+    and after the instruction, without ensuring their completion.
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE void __DMB(void)
+{
+  __ASM volatile ("dmb");
+}
+
+
+/** \brief  Reverse byte order (32 bit)
+
+    This function reverses the byte order in integer value.
+
+    \param [in]    value  Value to reverse
+    \return               Reversed value
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __REV(uint32_t value)
+{
+  uint32_t result;
+
+  __ASM volatile ("rev %0, %1" : "=r" (result) : "r" (value) );
+  return(result);
+}
+
+
+/** \brief  Reverse byte order (16 bit)
+
+    This function reverses the byte order in two unsigned short values.
+
+    \param [in]    value  Value to reverse
+    \return               Reversed value
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __REV16(uint32_t value)
+{
+  uint32_t result;
+
+  __ASM volatile ("rev16 %0, %1" : "=r" (result) : "r" (value) );
+  return(result);
+}
+
+
+/** \brief  Reverse byte order in signed short value
+
+    This function reverses the byte order in a signed short value with sign extension to integer.
+
+    \param [in]    value  Value to reverse
+    \return               Reversed value
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE int32_t __REVSH(int32_t value)
+{
+  uint32_t result;
+
+  __ASM volatile ("revsh %0, %1" : "=r" (result) : "r" (value) );
+  return(result);
+}
+
+
+/** \brief  Rotate Right in unsigned value (32 bit)
+
+    This function Rotate Right (immediate) provides the value of the contents of a register rotated by a variable number of bits.
+
+    \param [in]    value  Value to rotate
+    \param [in]    value  Number of Bits to rotate
+    \return               Rotated value
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __ROR(uint32_t op1, uint32_t op2)
+{
+
+  __ASM volatile ("ror %0, %0, %1" : "+r" (op1) : "r" (op2) );
+  return(op1);
+}
+
+
+#if       (__CORTEX_M >= 0x03)
+
+/** \brief  Reverse bit order of value
+
+    This function reverses the bit order of the given value.
+
+    \param [in]    value  Value to reverse
+    \return               Reversed value
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __RBIT(uint32_t value)
+{
+  uint32_t result;
+
+   __ASM volatile ("rbit %0, %1" : "=r" (result) : "r" (value) );
+   return(result);
+}
+
+
+/** \brief  LDR Exclusive (8 bit)
+
+    This function performs a exclusive LDR command for 8 bit value.
+
+    \param [in]    ptr  Pointer to data
+    \return             value of type uint8_t at (*ptr)
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint8_t __LDREXB(volatile uint8_t *addr)
+{
+    uint8_t result;
+
+   __ASM volatile ("ldrexb %0, [%1]" : "=r" (result) : "r" (addr) );
+   return(result);
+}
+
+
+/** \brief  LDR Exclusive (16 bit)
+
+    This function performs a exclusive LDR command for 16 bit values.
+
+    \param [in]    ptr  Pointer to data
+    \return        value of type uint16_t at (*ptr)
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint16_t __LDREXH(volatile uint16_t *addr)
+{
+    uint16_t result;
+
+   __ASM volatile ("ldrexh %0, [%1]" : "=r" (result) : "r" (addr) );
+   return(result);
+}
+
+
+/** \brief  LDR Exclusive (32 bit)
+
+    This function performs a exclusive LDR command for 32 bit values.
+
+    \param [in]    ptr  Pointer to data
+    \return        value of type uint32_t at (*ptr)
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __LDREXW(volatile uint32_t *addr)
+{
+    uint32_t result;
+
+   __ASM volatile ("ldrex %0, [%1]" : "=r" (result) : "r" (addr) );
+   return(result);
+}
+
+
+/** \brief  STR Exclusive (8 bit)
+
+    This function performs a exclusive STR command for 8 bit values.
+
+    \param [in]  value  Value to store
+    \param [in]    ptr  Pointer to location
+    \return          0  Function succeeded
+    \return          1  Function failed
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __STREXB(uint8_t value, volatile uint8_t *addr)
+{
+   uint32_t result;
+
+   __ASM volatile ("strexb %0, %2, [%1]" : "=&r" (result) : "r" (addr), "r" (value) );
+   return(result);
+}
+
+
+/** \brief  STR Exclusive (16 bit)
+
+    This function performs a exclusive STR command for 16 bit values.
+
+    \param [in]  value  Value to store
+    \param [in]    ptr  Pointer to location
+    \return          0  Function succeeded
+    \return          1  Function failed
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __STREXH(uint16_t value, volatile uint16_t *addr)
+{
+   uint32_t result;
+
+   __ASM volatile ("strexh %0, %2, [%1]" : "=&r" (result) : "r" (addr), "r" (value) );
+   return(result);
+}
+
+
+/** \brief  STR Exclusive (32 bit)
+
+    This function performs a exclusive STR command for 32 bit values.
+
+    \param [in]  value  Value to store
+    \param [in]    ptr  Pointer to location
+    \return          0  Function succeeded
+    \return          1  Function failed
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint32_t __STREXW(uint32_t value, volatile uint32_t *addr)
+{
+   uint32_t result;
+
+   __ASM volatile ("strex %0, %2, [%1]" : "=&r" (result) : "r" (addr), "r" (value) );
+   return(result);
+}
+
+
+/** \brief  Remove the exclusive lock
+
+    This function removes the exclusive lock which is created by LDREX.
+
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE void __CLREX(void)
+{
+  __ASM volatile ("clrex");
+}
+
+
+/** \brief  Signed Saturate
+
+    This function saturates a signed value.
+
+    \param [in]  value  Value to be saturated
+    \param [in]    sat  Bit position to saturate to (1..32)
+    \return             Saturated value
+ */
+#define __SSAT(ARG1,ARG2) \
+({                          \
+  uint32_t __RES, __ARG1 = (ARG1); \
+  __ASM ("ssat %0, %1, %2" : "=r" (__RES) :  "I" (ARG2), "r" (__ARG1) ); \
+  __RES; \
+ })
+
+
+/** \brief  Unsigned Saturate
+
+    This function saturates an unsigned value.
+
+    \param [in]  value  Value to be saturated
+    \param [in]    sat  Bit position to saturate to (0..31)
+    \return             Saturated value
+ */
+#define __USAT(ARG1,ARG2) \
+({                          \
+  uint32_t __RES, __ARG1 = (ARG1); \
+  __ASM ("usat %0, %1, %2" : "=r" (__RES) :  "I" (ARG2), "r" (__ARG1) ); \
+  __RES; \
+ })
+
+
+/** \brief  Count leading zeros
+
+    This function counts the number of leading zeros of a data value.
+
+    \param [in]  value  Value to count the leading zeros
+    \return             number of leading zeros in value
+ */
+__attribute__( ( always_inline ) ) __STATIC_INLINE uint8_t __CLZ(uint32_t value)
+{
+  uint8_t result;
+
+  __ASM volatile ("clz %0, %1" : "=r" (result) : "r" (value) );
+  return(result);
+}
+
+#endif /* (__CORTEX_M >= 0x03) */
+
+
+
+
+#elif defined ( __TASKING__ ) /*------------------ TASKING Compiler --------------*/
+/* TASKING carm specific functions */
+
+/*
+ * The CMSIS functions have been implemented as intrinsics in the compiler.
+ * Please use "carm -?i" to get an up to date list of all intrinsics,
+ * Including the CMSIS ones.
+ */
+
+#endif
+
+/*@}*/ /* end of group CMSIS_Core_InstructionInterface */
+
+#endif /* __CORE_CMINSTR_H */
diff --git a/apps/mathlib/CMSIS/Makefile b/apps/mathlib/CMSIS/Makefile
new file mode 100644
index 0000000000..0b67944709
--- /dev/null
+++ b/apps/mathlib/CMSIS/Makefile
@@ -0,0 +1,54 @@
+############################################################################
+#
+#   Copyright (C) 2012 PX4 Development Team. All rights reserved.
+#
+# Redistribution and use in source and binary forms, with or without
+# modification, are permitted provided that the following conditions
+# are met:
+#
+# 1. Redistributions of source code must retain the above copyright
+#    notice, this list of conditions and the following disclaimer.
+# 2. Redistributions in binary form must reproduce the above copyright
+#    notice, this list of conditions and the following disclaimer in
+#    the documentation and/or other materials provided with the
+#    distribution.
+# 3. Neither the name PX4 nor the names of its contributors may be
+#    used to endorse or promote products derived from this software
+#    without specific prior written permission.
+#
+# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+# FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+# COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+# INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+# BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+# OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+# AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+# ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+# POSSIBILITY OF SUCH DAMAGE.
+#
+############################################################################
+
+#
+# ARM CMSIS DSP library
+#
+
+#
+# Find sources
+#
+DSPLIB_SRCDIR		 = $(dir $(lastword $(MAKEFILE_LIST)))
+CSRCS			:= $(wildcard $(DSPLIB_SRCDIR)/DSP_Lib/Source/*/*.c)
+
+INCLUDES		+= $(DSPLIB_SRCDIR)/Include \
+			   $(DSPLIB_SRCDIR)/Device/ARM/ARMCM4/Include \
+			   $(DSPLIB_SRCDIR)/Device/ARM/ARMCM3/Include
+
+#
+# Override the default visibility for symbols, since the CMSIS DSPLib doesn't
+# have anything we can use to mark exported symbols.
+#
+DEFAULT_VISIBILITY	 = YES
+
+include $(APPDIR)/mk/app.mk
diff --git a/apps/mathlib/Makefile b/apps/mathlib/Makefile
new file mode 100644
index 0000000000..e5fab1e354
--- /dev/null
+++ b/apps/mathlib/Makefile
@@ -0,0 +1,70 @@
+############################################################################
+#
+#   Copyright (C) 2012 PX4 Development Team. All rights reserved.
+#
+# Redistribution and use in source and binary forms, with or without
+# modification, are permitted provided that the following conditions
+# are met:
+#
+# 1. Redistributions of source code must retain the above copyright
+#    notice, this list of conditions and the following disclaimer.
+# 2. Redistributions in binary form must reproduce the above copyright
+#    notice, this list of conditions and the following disclaimer in
+#    the documentation and/or other materials provided with the
+#    distribution.
+# 3. Neither the name PX4 nor the names of its contributors may be
+#    used to endorse or promote products derived from this software
+#    without specific prior written permission.
+#
+# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+# FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+# COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+# INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+# BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+# OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+# AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+# ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+# POSSIBILITY OF SUCH DAMAGE.
+#
+############################################################################
+
+include $(TOPDIR)/.config
+
+#
+# Math library
+#
+CXXSRCS		 = math/test/test.cpp \
+		   math/Vector.cpp \
+		   math/Vector3.cpp \
+		   math/EulerAngles.cpp \
+		   math/Quaternion.cpp \
+		   math/Dcm.cpp \
+		   math/Matrix.cpp
+
+CXXHDRS		 = math/test/test.hpp \
+		   math/Vector.hpp \
+		   math/Vector3.hpp \
+		   math/EulerAngles.hpp \
+		   math/Quaternion.hpp \
+		   math/Dcm.hpp \
+		   math/Matrix.hpp
+
+# XXX this really should be a CONFIG_* test
+ifeq ($(CONFIG_ARCH_CORTEXM4)$(CONFIG_ARCH_FPU),yy)
+INCLUDES	+= math/arm
+CXXSRCS		+= math/arm/Vector.cpp \
+		   math/arm/Matrix.cpp
+CXXHDRS		+= math/arm/Vector.hpp \
+		   math/arm/Matrix.hpp
+else
+INCLUDES	+= math/generic
+CXXSRCS		+= math/generic/Vector.cpp \
+		   math/generic/Matrix.cpp
+CXXHDRS		+= math/generic/Vector.hpp \
+		   math/generic/Matrix.hpp
+endif
+
+include $(APPDIR)/mk/app.mk
diff --git a/apps/mathlib/math/Dcm.cpp b/apps/mathlib/math/Dcm.cpp
new file mode 100644
index 0000000000..59f3d88ab4
--- /dev/null
+++ b/apps/mathlib/math/Dcm.cpp
@@ -0,0 +1,136 @@
+/****************************************************************************
+ *
+ *   Copyright (C) 2012 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+/**
+ * @file Dcm.cpp
+ *
+ * math direction cosine matrix
+ */
+
+#include "math/test/test.hpp"
+
+#include "Dcm.hpp"
+#include "Quaternion.hpp"
+#include "EulerAngles.hpp"
+#include "Vector3.hpp"
+
+namespace math
+{
+
+Dcm::Dcm() :
+	Matrix(Matrix::identity(3))
+{
+}
+
+Dcm::Dcm(const float *data) :
+	Matrix(3, 3, data)
+{
+}
+
+Dcm::Dcm(const Quaternion &q) :
+	Matrix(3, 3)
+{
+	Dcm &dcm = *this;
+	float a = q.getA();
+	float b = q.getB();
+	float c = q.getC();
+	float d = q.getD();
+	float aSq = a * a;
+	float bSq = b * b;
+	float cSq = c * c;
+	float dSq = d * d;
+	dcm(0, 0) = aSq + bSq - cSq - dSq;
+	dcm(0, 1) = 2 * (b * c - a * d);
+	dcm(0, 2) = 2 * (a * c + b * d);
+	dcm(1, 0) = 2 * (b * c + a * d);
+	dcm(1, 1) = aSq - bSq + cSq - dSq;
+	dcm(1, 2) = 2 * (c * d - a * b);
+	dcm(2, 0) = 2 * (b * d - a * c);
+	dcm(2, 1) = 2 * (a * b + c * d);
+	dcm(2, 2) = aSq - bSq - cSq + dSq;
+}
+
+Dcm::Dcm(const EulerAngles &euler) :
+	Matrix(3, 3)
+{
+	Dcm &dcm = *this;
+	float cosPhi = cosf(euler.getPhi());
+	float sinPhi = sinf(euler.getPhi());
+	float cosThe = cosf(euler.getTheta());
+	float sinThe = sinf(euler.getTheta());
+	float cosPsi = cosf(euler.getPsi());
+	float sinPsi = sinf(euler.getPsi());
+
+	dcm(0, 0) = cosThe * cosPsi;
+	dcm(0, 1) = -cosPhi * sinPsi + sinPhi * sinThe * cosPsi;
+	dcm(0, 2) = sinPhi * sinPsi + cosPhi * sinThe * cosPsi;
+
+	dcm(1, 0) = cosThe * sinPsi;
+	dcm(1, 1) = cosPhi * cosPsi + sinPhi * sinThe * sinPsi;
+	dcm(1, 2) = -sinPhi * cosPsi + cosPhi * sinThe * sinPsi;
+
+	dcm(2, 0) = -sinThe;
+	dcm(2, 1) = sinPhi * cosThe;
+	dcm(2, 2) = cosPhi * cosThe;
+}
+
+Dcm::Dcm(const Dcm &right) :
+	Matrix(right)
+{
+}
+
+Dcm::~Dcm()
+{
+}
+
+int __EXPORT dcmTest()
+{
+	printf("Test DCM\t\t: ");
+	Vector3 vB(1, 2, 3);
+	ASSERT(matrixEqual(Dcm(Quaternion(1, 0, 0, 0)),
+			   Matrix::identity(3)));
+	ASSERT(matrixEqual(Dcm(EulerAngles(0, 0, 0)),
+			   Matrix::identity(3)));
+	ASSERT(vectorEqual(Vector3(-2, 1, 3),
+			   Dcm(EulerAngles(0, 0, M_PI_2_F))*vB));
+	ASSERT(vectorEqual(Vector3(3, 2, -1),
+			   Dcm(EulerAngles(0, M_PI_2_F, 0))*vB));
+	ASSERT(vectorEqual(Vector3(1, -3, 2),
+			   Dcm(EulerAngles(M_PI_2_F, 0, 0))*vB));
+	ASSERT(vectorEqual(Vector3(3, 2, -1),
+			   Dcm(EulerAngles(
+				       M_PI_2_F, M_PI_2_F, M_PI_2_F))*vB));
+	printf("PASS\n");
+	return 0;
+}
+} // namespace math
diff --git a/apps/mathlib/math/Dcm.hpp b/apps/mathlib/math/Dcm.hpp
new file mode 100644
index 0000000000..de69a7aa4d
--- /dev/null
+++ b/apps/mathlib/math/Dcm.hpp
@@ -0,0 +1,96 @@
+/****************************************************************************
+ *
+ *   Copyright (C) 2012 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+/**
+ * @file Dcm.hpp
+ *
+ * math direction cosine matrix
+ */
+
+//#pragma once
+
+#include "Vector.hpp"
+#include "Matrix.hpp"
+
+namespace math
+{
+
+class Quaternion;
+class EulerAngles;
+
+/**
+ * This is a Tait Bryan, Body 3-2-1 sequence.
+ * (yaw)-(pitch)-(roll)
+ * The Dcm transforms a vector in the body frame
+ * to the navigation frame, typically represented
+ * as C_nb. C_bn can be obtained through use
+ * of the transpose() method.
+ */
+class __EXPORT Dcm : public Matrix
+{
+public:
+	/**
+	 * default ctor
+	 */
+	Dcm();
+
+	/**
+	 * data ctor
+	 */
+	Dcm(const float *data);
+
+	/**
+	 * quaternion ctor
+	 */
+	Dcm(const Quaternion &q);
+
+	/**
+	 * euler angles ctor
+	 */
+	Dcm(const EulerAngles &euler);
+
+	/**
+	 * copy ctor (deep)
+	 */
+	Dcm(const Dcm &right);
+
+	/**
+	 * dtor
+	 */
+	virtual ~Dcm();
+};
+
+int __EXPORT dcmTest();
+
+} // math
+
diff --git a/apps/mathlib/math/EulerAngles.cpp b/apps/mathlib/math/EulerAngles.cpp
new file mode 100644
index 0000000000..8991d56234
--- /dev/null
+++ b/apps/mathlib/math/EulerAngles.cpp
@@ -0,0 +1,122 @@
+/****************************************************************************
+ *
+ *   Copyright (C) 2012 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+/**
+ * @file Vector.cpp
+ *
+ * math vector
+ */
+
+#include "math/test/test.hpp"
+
+#include "EulerAngles.hpp"
+#include "Quaternion.hpp"
+#include "Dcm.hpp"
+#include "Vector3.hpp"
+
+namespace math
+{
+
+EulerAngles::EulerAngles() :
+	Vector(3)
+{
+	setPhi(0.0f);
+	setTheta(0.0f);
+	setPsi(0.0f);
+}
+
+EulerAngles::EulerAngles(float phi, float theta, float psi) :
+	Vector(3)
+{
+	setPhi(phi);
+	setTheta(theta);
+	setPsi(psi);
+}
+
+EulerAngles::EulerAngles(const Quaternion &q) :
+	Vector(3)
+{
+	(*this) = EulerAngles(Dcm(q));
+}
+
+EulerAngles::EulerAngles(const Dcm &dcm) :
+	Vector(3)
+{
+	setTheta(asinf(-dcm(2, 0)));
+
+	if (fabsf(getTheta() - M_PI_2_F) < 1.0e-3f) {
+		setPhi(0.0f);
+		setPsi(atan2f(dcm(1, 2) - dcm(0, 1),
+			      dcm(0, 2) + dcm(1, 1)) + getPhi());
+
+	} else if (fabsf(getTheta() + M_PI_2_F) < 1.0e-3f) {
+		setPhi(0.0f);
+		setPsi(atan2f(dcm(1, 2) - dcm(0, 1),
+			      dcm(0, 2) + dcm(1, 1)) - getPhi());
+
+	} else {
+		setPhi(atan2f(dcm(2, 1), dcm(2, 2)));
+		setPsi(atan2f(dcm(1, 0), dcm(0, 0)));
+	}
+}
+
+EulerAngles::~EulerAngles()
+{
+}
+
+int __EXPORT eulerAnglesTest()
+{
+	printf("Test EulerAngles\t: ");
+	EulerAngles euler(1, 2, 3);
+
+	// test ctor
+	ASSERT(vectorEqual(Vector3(1, 2, 3), euler));
+	ASSERT(equal(euler.getPhi(), 1));
+	ASSERT(equal(euler.getTheta(), 2));
+	ASSERT(equal(euler.getPsi(), 3));
+
+	// test dcm ctor
+
+	// test assignment
+	euler.setPhi(4);
+	ASSERT(equal(euler.getPhi(), 4));
+	euler.setTheta(5);
+	ASSERT(equal(euler.getTheta(), 5));
+	euler.setPsi(6);
+	ASSERT(equal(euler.getPsi(), 6));
+
+	printf("PASS\n");
+	return 0;
+}
+
+} // namespace math
diff --git a/apps/mathlib/math/EulerAngles.hpp b/apps/mathlib/math/EulerAngles.hpp
new file mode 100644
index 0000000000..399eecfa7d
--- /dev/null
+++ b/apps/mathlib/math/EulerAngles.hpp
@@ -0,0 +1,74 @@
+/****************************************************************************
+ *
+ *   Copyright (C) 2012 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+/**
+ * @file Vector.h
+ *
+ * math vector
+ */
+
+#pragma once
+
+#include "Vector.hpp"
+
+namespace math
+{
+
+class Quaternion;
+class Dcm;
+
+class __EXPORT EulerAngles : public Vector
+{
+public:
+	EulerAngles();
+	EulerAngles(float phi, float theta, float psi);
+	EulerAngles(const Quaternion &q);
+	EulerAngles(const Dcm &dcm);
+	virtual ~EulerAngles();
+
+	// alias
+	void setPhi(float phi) { (*this)(0) = phi; }
+	void setTheta(float theta) { (*this)(1) = theta; }
+	void setPsi(float psi) { (*this)(2) = psi; }
+
+	// const accessors
+	const float &getPhi() const { return (*this)(0); }
+	const float &getTheta() const { return (*this)(1); }
+	const float &getPsi() const { return (*this)(2); }
+
+};
+
+int __EXPORT eulerAnglesTest();
+
+} // math
+
diff --git a/apps/mathlib/math/Matrix.cpp b/apps/mathlib/math/Matrix.cpp
new file mode 100644
index 0000000000..9817323702
--- /dev/null
+++ b/apps/mathlib/math/Matrix.cpp
@@ -0,0 +1,193 @@
+/****************************************************************************
+ *
+ *   Copyright (C) 2012 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+/**
+ * @file Matrix.cpp
+ *
+ * matrix code
+ */
+
+#include "math/test/test.hpp"
+#include 
+
+#include "Matrix.hpp"
+
+namespace math
+{
+
+static const float data_testA[] = {
+	1, 2, 3,
+	4, 5, 6
+};
+static Matrix testA(2, 3, data_testA);
+
+static const float data_testB[] = {
+	0, 1, 3,
+	7, -1, 2
+};
+static Matrix testB(2, 3, data_testB);
+
+static const float data_testC[] = {
+	0, 1,
+	2, 1,
+	3, 2
+};
+static Matrix testC(3, 2, data_testC);
+
+static const float data_testD[] = {
+	0, 1, 2,
+	2, 1, 4,
+	5, 2, 0
+};
+static Matrix testD(3, 3, data_testD);
+
+static const float data_testE[] = {
+	1, -1, 2,
+	0, 2, 3,
+	2, -1, 1
+};
+static Matrix testE(3, 3, data_testE);
+
+static const float data_testF[] = {
+	3.777e006f, 2.915e007f, 0.000e000f,
+	2.938e007f, 2.267e008f, 0.000e000f,
+	0.000e000f, 0.000e000f, 6.033e008f
+};
+static Matrix testF(3, 3, data_testF);
+
+int __EXPORT matrixTest()
+{
+	matrixAddTest();
+	matrixSubTest();
+	matrixMultTest();
+	matrixInvTest();
+	matrixDivTest();
+	return 0;
+}
+
+int matrixAddTest()
+{
+	printf("Test Matrix Add\t\t: ");
+	Matrix r = testA + testB;
+	float data_test[] = {
+		1.0f, 3.0f, 6.0f,
+		11.0f, 4.0f, 8.0f
+	};
+	ASSERT(matrixEqual(Matrix(2, 3, data_test), r));
+	printf("PASS\n");
+	return 0;
+}
+
+int matrixSubTest()
+{
+	printf("Test Matrix Sub\t\t: ");
+	Matrix r = testA - testB;
+	float data_test[] = {
+		1.0f, 1.0f, 0.0f,
+		-3.0f, 6.0f, 4.0f
+	};
+	ASSERT(matrixEqual(Matrix(2, 3, data_test), r));
+	printf("PASS\n");
+	return 0;
+}
+
+int matrixMultTest()
+{
+	printf("Test Matrix Mult\t: ");
+	Matrix r = testC * testB;
+	float data_test[] = {
+		7.0f, -1.0f,  2.0f,
+		7.0f,  1.0f,  8.0f,
+		14.0f,  1.0f, 13.0f
+	};
+	ASSERT(matrixEqual(Matrix(3, 3, data_test), r));
+	printf("PASS\n");
+	return 0;
+}
+
+int matrixInvTest()
+{
+	printf("Test Matrix Inv\t\t: ");
+	Matrix origF = testF;
+	Matrix r = testF.inverse();
+	float data_test[] = {
+		-0.0012518f,  0.0001610f, 0.0000000f,
+		0.0001622f, -0.0000209f, 0.0000000f,
+		0.0000000f,  0.0000000f, 1.6580e-9f
+	};
+	ASSERT(matrixEqual(Matrix(3, 3, data_test), r));
+	// make sure F in unchanged
+	ASSERT(matrixEqual(origF, testF));
+	printf("PASS\n");
+	return 0;
+}
+
+int matrixDivTest()
+{
+	printf("Test Matrix Div\t\t: ");
+	Matrix r = testD / testE;
+	float data_test[] = {
+		0.2222222f, 0.5555556f, -0.1111111f,
+		0.0f,       1.0f,         1.0,
+		-4.1111111f, 1.2222222f,  4.5555556f
+	};
+	ASSERT(matrixEqual(Matrix(3, 3, data_test), r));
+	printf("PASS\n");
+	return 0;
+}
+
+bool matrixEqual(const Matrix &a, const Matrix &b, float eps)
+{
+	if (a.getRows() != b.getRows()) {
+		printf("row number not equal a: %d, b:%d\n", a.getRows(), b.getRows());
+		return false;
+
+	} else if (a.getCols() != b.getCols()) {
+		printf("column number not equal a: %d, b:%d\n", a.getCols(), b.getCols());
+		return false;
+	}
+
+	bool ret = true;
+
+	for (size_t i = 0; i < a.getRows(); i++)
+		for (size_t j = 0; j < a.getCols(); j++) {
+			if (!equal(a(i, j), b(i, j), eps)) {
+				printf("element mismatch (%d, %d)\n", i, j);
+				ret = false;
+			}
+		}
+
+	return ret;
+}
+
+} // namespace math
diff --git a/apps/mathlib/math/Matrix.hpp b/apps/mathlib/math/Matrix.hpp
new file mode 100644
index 0000000000..f19db15eca
--- /dev/null
+++ b/apps/mathlib/math/Matrix.hpp
@@ -0,0 +1,61 @@
+/****************************************************************************
+ *
+ *   Copyright (C) 2012 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+/**
+ * @file Matrix.h
+ *
+ * matrix code
+ */
+
+#pragma once
+
+#include 
+
+#if defined(CONFIG_ARCH_CORTEXM4) && defined(CONFIG_ARCH_FPU)
+#include "arm/Matrix.hpp"
+#else
+#include "generic/Matrix.hpp"
+#endif
+
+namespace math
+{
+class Matrix;
+int matrixTest();
+int matrixAddTest();
+int matrixSubTest();
+int matrixMultTest();
+int matrixInvTest();
+int matrixDivTest();
+int matrixArmTest();
+bool matrixEqual(const Matrix &a, const Matrix &b, float eps = 1.0e-5f);
+} // namespace math
diff --git a/apps/mathlib/math/Quaternion.cpp b/apps/mathlib/math/Quaternion.cpp
new file mode 100644
index 0000000000..68fe85300c
--- /dev/null
+++ b/apps/mathlib/math/Quaternion.cpp
@@ -0,0 +1,181 @@
+/****************************************************************************
+ *
+ *   Copyright (C) 2012 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+/**
+ * @file Quaternion.cpp
+ *
+ * math vector
+ */
+
+#include "math/test/test.hpp"
+
+
+#include "Quaternion.hpp"
+#include "Dcm.hpp"
+#include "EulerAngles.hpp"
+
+namespace math
+{
+
+Quaternion::Quaternion() :
+	Vector(4)
+{
+	setA(1.0f);
+	setB(0.0f);
+	setC(0.0f);
+	setD(0.0f);
+}
+
+Quaternion::Quaternion(float a, float b,
+		       float c, float d) :
+	Vector(4)
+{
+	setA(a);
+	setB(b);
+	setC(c);
+	setD(d);
+}
+
+Quaternion::Quaternion(const float *data) :
+	Vector(4, data)
+{
+}
+
+Quaternion::Quaternion(const Vector &v) :
+	Vector(v)
+{
+}
+
+Quaternion::Quaternion(const Dcm &dcm) :
+	Vector(4)
+{
+	setA(0.5f * sqrtf(1 + dcm(0, 0) +
+			  dcm(1, 1) + dcm(2, 2)));
+	setB((dcm(2, 1) - dcm(1, 2)) /
+	     (4 * getA()));
+	setC((dcm(0, 2) - dcm(2, 0)) /
+	     (4 * getA()));
+	setD((dcm(1, 0) - dcm(0, 1)) /
+	     (4 * getA()));
+}
+
+Quaternion::Quaternion(const EulerAngles &euler) :
+	Vector(4)
+{
+	float cosPhi_2 = cosf(euler.getPhi() / 2.0f);
+	float cosTheta_2 = cosf(euler.getTheta() / 2.0f);
+	float cosPsi_2 = cosf(euler.getPsi() / 2.0f);
+	float sinPhi_2 = sinf(euler.getPhi() / 2.0f);
+	float sinTheta_2 = sinf(euler.getTheta() / 2.0f);
+	float sinPsi_2 = sinf(euler.getPsi() / 2.0f);
+	setA(cosPhi_2 * cosTheta_2 * cosPsi_2 +
+	     sinPhi_2 * sinTheta_2 * sinPsi_2);
+	setB(sinPhi_2 * cosTheta_2 * cosPsi_2 -
+	     cosPhi_2 * sinTheta_2 * sinPsi_2);
+	setC(cosPhi_2 * sinTheta_2 * cosPsi_2 +
+	     sinPhi_2 * cosTheta_2 * sinPsi_2);
+	setD(cosPhi_2 * cosTheta_2 * sinPsi_2 +
+	     sinPhi_2 * sinTheta_2 * cosPsi_2);
+}
+
+Quaternion::Quaternion(const Quaternion &right) :
+	Vector(right)
+{
+}
+
+Quaternion::~Quaternion()
+{
+}
+
+Vector Quaternion::derivative(const Vector &w)
+{
+#ifdef QUATERNION_ASSERT
+	ASSERT(w.getRows() == 3);
+#endif
+	float dataQ[] = {
+		getA(), -getB(), -getC(), -getD(),
+		getB(),  getA(), -getD(),  getC(),
+		getC(),  getD(),  getA(), -getB(),
+		getD(), -getC(),  getB(),  getA()
+	};
+	Vector v(4);
+	v(0) = 0.0f;
+	v(1) = w(0);
+	v(2) = w(1);
+	v(3) = w(2);
+	Matrix Q(4, 4, dataQ);
+	return Q * v * 0.5f;
+}
+
+int __EXPORT quaternionTest()
+{
+	printf("Test Quaternion\t\t: ");
+	// test default ctor
+	Quaternion q;
+	ASSERT(equal(q.getA(), 1));
+	ASSERT(equal(q.getB(), 0));
+	ASSERT(equal(q.getC(), 0));
+	ASSERT(equal(q.getD(), 0));
+	// test float ctor
+	q = Quaternion(0, 1, 0, 0);
+	ASSERT(equal(q.getA(), 0));
+	ASSERT(equal(q.getB(), 1));
+	ASSERT(equal(q.getC(), 0));
+	ASSERT(equal(q.getD(), 0));
+	// test euler ctor
+	q = Quaternion(EulerAngles(0, 0, 0));
+	ASSERT(equal(q.getA(), 1));
+	ASSERT(equal(q.getB(), 0));
+	ASSERT(equal(q.getC(), 0));
+	ASSERT(equal(q.getD(), 0));
+	// test dcm ctor
+	q = Quaternion(Dcm());
+	ASSERT(equal(q.getA(), 1));
+	ASSERT(equal(q.getB(), 0));
+	ASSERT(equal(q.getC(), 0));
+	ASSERT(equal(q.getD(), 0));
+	// TODO test derivative
+	// test accessors
+	q.setA(0.1);
+	q.setB(0.2);
+	q.setC(0.3);
+	q.setD(0.4);
+	ASSERT(equal(q.getA(), 0.1));
+	ASSERT(equal(q.getB(), 0.2));
+	ASSERT(equal(q.getC(), 0.3));
+	ASSERT(equal(q.getD(), 0.4));
+	printf("PASS\n");
+	return 0;
+}
+
+} // namespace math
diff --git a/apps/mathlib/math/Quaternion.hpp b/apps/mathlib/math/Quaternion.hpp
new file mode 100644
index 0000000000..4b4e959d8b
--- /dev/null
+++ b/apps/mathlib/math/Quaternion.hpp
@@ -0,0 +1,115 @@
+/****************************************************************************
+ *
+ *   Copyright (C) 2012 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+/**
+ * @file Quaternion.hpp
+ *
+ * math quaternion lib
+ */
+
+//#pragma once
+
+#include "Vector.hpp"
+#include "Matrix.hpp"
+
+namespace math
+{
+
+class Dcm;
+class EulerAngles;
+
+class __EXPORT Quaternion : public Vector
+{
+public:
+
+	/**
+	 * default ctor
+	 */
+	Quaternion();
+
+	/**
+	 * ctor from floats
+	 */
+	Quaternion(float a, float b, float c, float d);
+
+	/**
+	 * ctor from data
+	 */
+	Quaternion(const float *data);
+
+	/**
+	 * ctor from Vector
+	 */
+	Quaternion(const Vector &v);
+
+	/**
+	 * ctor from EulerAngles
+	 */
+	Quaternion(const EulerAngles &euler);
+
+	/**
+	 * ctor from Dcm
+	 */
+	Quaternion(const Dcm &dcm);
+
+	/**
+	 * deep copy ctor
+	 */
+	Quaternion(const Quaternion &right);
+
+	/**
+	 * dtor
+	 */
+	virtual ~Quaternion();
+
+	/**
+	 * derivative
+	 */
+	Vector derivative(const Vector &w);
+
+	/**
+	 * accessors
+	 */
+	void setA(float a) { (*this)(0) = a; }
+	void setB(float b) { (*this)(1) = b; }
+	void setC(float c) { (*this)(2) = c; }
+	void setD(float d) { (*this)(3) = d; }
+	const float &getA() const { return (*this)(0); }
+	const float &getB() const { return (*this)(1); }
+	const float &getC() const { return (*this)(2); }
+	const float &getD() const { return (*this)(3); }
+};
+
+int __EXPORT quaternionTest();
+} // math
+
diff --git a/apps/mathlib/math/Vector.cpp b/apps/mathlib/math/Vector.cpp
new file mode 100644
index 0000000000..d58e719dbc
--- /dev/null
+++ b/apps/mathlib/math/Vector.cpp
@@ -0,0 +1,100 @@
+/****************************************************************************
+ *
+ *   Copyright (C) 2012 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+/**
+ * @file Vector.cpp
+ *
+ * math vector
+ */
+
+#include "math/test/test.hpp"
+
+#include "Vector.hpp"
+
+namespace math
+{
+
+static const float data_testA[] = {1, 3};
+static const float data_testB[] = {4, 1};
+
+static Vector testA(2, data_testA);
+static Vector testB(2, data_testB);
+
+int __EXPORT vectorTest()
+{
+	vectorAddTest();
+	vectorSubTest();
+	return 0;
+}
+
+int vectorAddTest()
+{
+	printf("Test Vector Add\t\t: ");
+	Vector r = testA + testB;
+	float data_test[] = {5.0f, 4.0f};
+	ASSERT(vectorEqual(Vector(2, data_test), r));
+	printf("PASS\n");
+	return 0;
+}
+
+int vectorSubTest()
+{
+	printf("Test Vector Sub\t\t: ");
+	Vector r(2);
+	r = testA - testB;
+	float data_test[] = { -3.0f, 2.0f};
+	ASSERT(vectorEqual(Vector(2, data_test), r));
+	printf("PASS\n");
+	return 0;
+}
+
+bool vectorEqual(const Vector &a, const Vector &b, float eps)
+{
+	if (a.getRows() != b.getRows()) {
+		printf("row number not equal a: %d, b:%d\n", a.getRows(), b.getRows());
+		return false;
+	}
+
+	bool ret = true;
+
+	for (size_t i = 0; i < a.getRows(); i++) {
+		if (!equal(a(i), b(i), eps)) {
+			printf("element mismatch (%d)\n", i);
+			ret = false;
+		}
+	}
+
+	return ret;
+}
+
+} // namespace math
diff --git a/apps/mathlib/math/Vector.hpp b/apps/mathlib/math/Vector.hpp
new file mode 100644
index 0000000000..73de793d51
--- /dev/null
+++ b/apps/mathlib/math/Vector.hpp
@@ -0,0 +1,57 @@
+/****************************************************************************
+ *
+ *   Copyright (C) 2012 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+/**
+ * @file Vector.h
+ *
+ * math vector
+ */
+
+#pragma once
+
+#include 
+
+#if defined(CONFIG_ARCH_CORTEXM4) && defined(CONFIG_ARCH_FPU)
+#include "arm/Vector.hpp"
+#else
+#include "generic/Vector.hpp"
+#endif
+
+namespace math
+{
+class Vector;
+int __EXPORT vectorTest();
+int __EXPORT vectorAddTest();
+int __EXPORT vectorSubTest();
+bool vectorEqual(const Vector &a, const Vector &b, float eps = 1.0e-5f);
+} // math
diff --git a/apps/mathlib/math/Vector3.cpp b/apps/mathlib/math/Vector3.cpp
new file mode 100644
index 0000000000..9c57506da3
--- /dev/null
+++ b/apps/mathlib/math/Vector3.cpp
@@ -0,0 +1,99 @@
+/****************************************************************************
+ *
+ *   Copyright (C) 2012 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+/**
+ * @file Vector3.cpp
+ *
+ * math vector
+ */
+
+#include "math/test/test.hpp"
+
+#include "Vector3.hpp"
+
+namespace math
+{
+
+Vector3::Vector3() :
+	Vector(3)
+{
+}
+
+Vector3::Vector3(const Vector &right) :
+	Vector(right)
+{
+#ifdef VECTOR_ASSERT
+	ASSERT(right.getRows() == 3);
+#endif
+}
+
+Vector3::Vector3(float x, float y, float z) :
+	Vector(3)
+{
+	setX(x);
+	setY(y);
+	setZ(z);
+}
+
+Vector3::Vector3(const float *data) :
+	Vector(3, data)
+{
+}
+
+Vector3::~Vector3()
+{
+}
+
+Vector3 Vector3::cross(const Vector3 &b)
+{
+	Vector3 &a = *this;
+	Vector3 result;
+	result(0) = a(1) * b(2) - a(2) * b(1);
+	result(1) = a(2) * b(0) - a(0) * b(2);
+	result(2) = a(0) * b(1) - a(1) * b(0);
+	return result;
+}
+
+int __EXPORT vector3Test()
+{
+	printf("Test Vector3\t\t: ");
+	// test float ctor
+	Vector3 v(1, 2, 3);
+	ASSERT(equal(v(0), 1));
+	ASSERT(equal(v(1), 2));
+	ASSERT(equal(v(2), 3));
+	printf("PASS\n");
+	return 0;
+}
+
+} // namespace math
diff --git a/apps/mathlib/math/Vector3.hpp b/apps/mathlib/math/Vector3.hpp
new file mode 100644
index 0000000000..8c36ac1347
--- /dev/null
+++ b/apps/mathlib/math/Vector3.hpp
@@ -0,0 +1,71 @@
+/****************************************************************************
+ *
+ *   Copyright (C) 2012 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+/**
+ * @file Vector3.hpp
+ *
+ * math 3 vector
+ */
+
+#pragma once
+
+#include "Vector.hpp"
+
+namespace math
+{
+
+class __EXPORT Vector3 :
+	public Vector
+{
+public:
+	Vector3();
+	Vector3(const Vector &right);
+	Vector3(float x, float y, float z);
+	Vector3(const float *data);
+	virtual ~Vector3();
+	Vector3 cross(const Vector3 &b);
+
+	/**
+	 * accessors
+	 */
+	void setX(float x) { (*this)(0) = x; }
+	void setY(float y) { (*this)(1) = y; }
+	void setZ(float z) { (*this)(2) = z; }
+	const float &getX() const { return (*this)(0); }
+	const float &getY() const { return (*this)(1); }
+	const float &getZ() const { return (*this)(2); }
+};
+
+int __EXPORT vector3Test();
+} // math
+
diff --git a/apps/mathlib/math/arm/Matrix.cpp b/apps/mathlib/math/arm/Matrix.cpp
new file mode 100644
index 0000000000..21661622ab
--- /dev/null
+++ b/apps/mathlib/math/arm/Matrix.cpp
@@ -0,0 +1,40 @@
+/****************************************************************************
+ *
+ *   Copyright (C) 2012 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+/**
+ * @file Matrix.cpp
+ *
+ * matrix code
+ */
+
+#include "Matrix.hpp"
diff --git a/apps/mathlib/math/arm/Matrix.hpp b/apps/mathlib/math/arm/Matrix.hpp
new file mode 100644
index 0000000000..715fd3a5e8
--- /dev/null
+++ b/apps/mathlib/math/arm/Matrix.hpp
@@ -0,0 +1,292 @@
+/****************************************************************************
+ *
+ *   Copyright (C) 2012 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+/**
+ * @file Matrix.h
+ *
+ * matrix code
+ */
+
+#pragma once
+
+
+#include 
+#include 
+#include 
+#include 
+#include 
+#include 
+
+#include "../Vector.hpp"
+#include "../Matrix.hpp"
+
+// arm specific
+#include "../../CMSIS/Include/arm_math.h"
+
+namespace math
+{
+
+class __EXPORT Matrix
+{
+public:
+	// constructor
+	Matrix(size_t rows, size_t cols) :
+		_matrix() {
+		arm_mat_init_f32(&_matrix,
+				 rows, cols,
+				 (float *)calloc(rows * cols, sizeof(float)));
+	}
+	Matrix(size_t rows, size_t cols, const float *data) :
+		_matrix() {
+		arm_mat_init_f32(&_matrix,
+				 rows, cols,
+				 (float *)malloc(rows * cols * sizeof(float)));
+		memcpy(getData(), data, getSize());
+	}
+	// deconstructor
+	virtual ~Matrix() {
+		delete [] _matrix.pData;
+	}
+	// copy constructor (deep)
+	Matrix(const Matrix &right) :
+		_matrix() {
+		arm_mat_init_f32(&_matrix,
+				 right.getRows(), right.getCols(),
+				 (float *)malloc(right.getRows()*
+						 right.getCols()*sizeof(float)));
+		memcpy(getData(), right.getData(),
+		       getSize());
+	}
+	// assignment
+	inline Matrix &operator=(const Matrix &right) {
+#ifdef MATRIX_ASSERT
+		ASSERT(getRows() == right.getRows());
+		ASSERT(getCols() == right.getCols());
+#endif
+
+		if (this != &right) {
+			memcpy(getData(), right.getData(),
+			       right.getSize());
+		}
+
+		return *this;
+	}
+	// element accessors
+	inline float &operator()(size_t i, size_t j) {
+#ifdef MATRIX_ASSERT
+		ASSERT(i < getRows());
+		ASSERT(j < getCols());
+#endif
+		return getData()[i * getCols() + j];
+	}
+	inline const float &operator()(size_t i, size_t j) const {
+#ifdef MATRIX_ASSERT
+		ASSERT(i < getRows());
+		ASSERT(j < getCols());
+#endif
+		return getData()[i * getCols() + j];
+	}
+	// output
+	inline void print() const {
+		for (size_t i = 0; i < getRows(); i++) {
+			for (size_t j = 0; j < getCols(); j++) {
+				float sig;
+				int exp;
+				float num = (*this)(i, j);
+				float2SigExp(num, sig, exp);
+				printf("%6.3fe%03.3d,", (double)sig, exp);
+			}
+
+			printf("\n");
+		}
+	}
+	// boolean ops
+	inline bool operator==(const Matrix &right) const {
+		for (size_t i = 0; i < getRows(); i++) {
+			for (size_t j = 0; j < getCols(); j++) {
+				if (fabsf((*this)(i, j) - right(i, j)) > 1e-30f)
+					return false;
+			}
+		}
+
+		return true;
+	}
+	// scalar ops
+	inline Matrix operator+(float right) const {
+		Matrix result(getRows(), getCols());
+		arm_offset_f32((float *)getData(), right,
+			       (float *)result.getData(), getRows()*getCols());
+		return result;
+	}
+	inline Matrix operator-(float right) const {
+		Matrix result(getRows(), getCols());
+		arm_offset_f32((float *)getData(), -right,
+			       (float *)result.getData(), getRows()*getCols());
+		return result;
+	}
+	inline Matrix operator*(float right) const {
+		Matrix result(getRows(), getCols());
+		arm_mat_scale_f32(&_matrix, right,
+				  &(result._matrix));
+		return result;
+	}
+	inline Matrix operator/(float right) const {
+		Matrix result(getRows(), getCols());
+		arm_mat_scale_f32(&_matrix, 1.0f / right,
+				  &(result._matrix));
+		return result;
+	}
+	// vector ops
+	inline Vector operator*(const Vector &right) const {
+#ifdef MATRIX_ASSERT
+		ASSERT(getCols() == right.getRows());
+#endif
+		Matrix resultMat = (*this) *
+				   Matrix(right.getRows(), 1, right.getData());
+		return Vector(getRows(), resultMat.getData());
+	}
+	// matrix ops
+	inline Matrix operator+(const Matrix &right) const {
+#ifdef MATRIX_ASSERT
+		ASSERT(getRows() == right.getRows());
+		ASSERT(getCols() == right.getCols());
+#endif
+		Matrix result(getRows(), getCols());
+		arm_mat_add_f32(&_matrix, &(right._matrix),
+				&(result._matrix));
+		return result;
+	}
+	inline Matrix operator-(const Matrix &right) const {
+#ifdef MATRIX_ASSERT
+		ASSERT(getRows() == right.getRows());
+		ASSERT(getCols() == right.getCols());
+#endif
+		Matrix result(getRows(), getCols());
+		arm_mat_sub_f32(&_matrix, &(right._matrix),
+				&(result._matrix));
+		return result;
+	}
+	inline Matrix operator*(const Matrix &right) const {
+#ifdef MATRIX_ASSERT
+		ASSERT(getCols() == right.getRows());
+#endif
+		Matrix result(getRows(), right.getCols());
+		arm_mat_mult_f32(&_matrix, &(right._matrix),
+				 &(result._matrix));
+		return result;
+	}
+	inline Matrix operator/(const Matrix &right) const {
+#ifdef MATRIX_ASSERT
+		ASSERT(right.getRows() == right.getCols());
+		ASSERT(getCols() == right.getCols());
+#endif
+		return (*this) * right.inverse();
+	}
+	// other functions
+	inline Matrix transpose() const {
+		Matrix result(getCols(), getRows());
+		arm_mat_trans_f32(&_matrix, &(result._matrix));
+		return result;
+	}
+	inline void swapRows(size_t a, size_t b) {
+		if (a == b) return;
+
+		for (size_t j = 0; j < getCols(); j++) {
+			float tmp = (*this)(a, j);
+			(*this)(a, j) = (*this)(b, j);
+			(*this)(b, j) = tmp;
+		}
+	}
+	inline void swapCols(size_t a, size_t b) {
+		if (a == b) return;
+
+		for (size_t i = 0; i < getRows(); i++) {
+			float tmp = (*this)(i, a);
+			(*this)(i, a) = (*this)(i, b);
+			(*this)(i, b) = tmp;
+		}
+	}
+	/**
+	 * inverse based on LU factorization with partial pivotting
+	 */
+	Matrix inverse() const {
+#ifdef MATRIX_ASSERT
+		ASSERT(getRows() == getCols());
+#endif
+		Matrix result(getRows(), getCols());
+		Matrix work = (*this);
+		arm_mat_inverse_f32(&(work._matrix),
+				    &(result._matrix));
+		return result;
+	}
+	inline void setAll(const float &val) {
+		for (size_t i = 0; i < getRows(); i++) {
+			for (size_t j = 0; j < getCols(); j++) {
+				(*this)(i, j) = val;
+			}
+		}
+	}
+	inline void set(const float *data) {
+		memcpy(getData(), data, getSize());
+	}
+	inline size_t getRows() const { return _matrix.numRows; }
+	inline size_t getCols() const { return _matrix.numCols; }
+	inline static Matrix identity(size_t size) {
+		Matrix result(size, size);
+
+		for (size_t i = 0; i < size; i++) {
+			result(i, i) = 1.0f;
+		}
+
+		return result;
+	}
+	inline static Matrix zero(size_t size) {
+		Matrix result(size, size);
+		result.setAll(0.0f);
+		return result;
+	}
+	inline static Matrix zero(size_t m, size_t n) {
+		Matrix result(m, n);
+		result.setAll(0.0f);
+		return result;
+	}
+protected:
+	inline size_t getSize() const { return sizeof(float) * getRows() * getCols(); }
+	inline float *getData() { return _matrix.pData; }
+	inline const float *getData() const { return _matrix.pData; }
+	inline void setData(float *data) { _matrix.pData = data; }
+private:
+	arm_matrix_instance_f32 _matrix;
+};
+
+} // namespace math
diff --git a/apps/mathlib/math/arm/Vector.cpp b/apps/mathlib/math/arm/Vector.cpp
new file mode 100644
index 0000000000..7ea6496bb1
--- /dev/null
+++ b/apps/mathlib/math/arm/Vector.cpp
@@ -0,0 +1,40 @@
+/****************************************************************************
+ *
+ *   Copyright (C) 2012 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+/**
+ * @file Vector.cpp
+ *
+ * math vector
+ */
+
+#include "Vector.hpp"
diff --git a/apps/mathlib/math/arm/Vector.hpp b/apps/mathlib/math/arm/Vector.hpp
new file mode 100644
index 0000000000..58d51107d5
--- /dev/null
+++ b/apps/mathlib/math/arm/Vector.hpp
@@ -0,0 +1,220 @@
+/****************************************************************************
+ *
+ *   Copyright (C) 2012 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+/**
+ * @file Vector.h
+ *
+ * math vector
+ */
+
+#pragma once
+
+#include 
+#include 
+#include 
+#include 
+#include 
+#include 
+
+#include "../Vector.hpp"
+#include "../test/test.hpp"
+
+// arm specific
+#include "../../CMSIS/Include/arm_math.h"
+
+namespace math
+{
+
+class __EXPORT Vector
+{
+public:
+	// constructor
+	Vector(size_t rows) :
+		_rows(rows),
+		_data((float *)calloc(rows, sizeof(float))) {
+	}
+	Vector(size_t rows, const float *data) :
+		_rows(rows),
+		_data((float *)malloc(getSize())) {
+		memcpy(getData(), data, getSize());
+	}
+	// deconstructor
+	virtual ~Vector() {
+		delete [] getData();
+	}
+	// copy constructor (deep)
+	Vector(const Vector &right) :
+		_rows(right.getRows()),
+		_data((float *)malloc(getSize())) {
+		memcpy(getData(), right.getData(),
+		       right.getSize());
+	}
+	// assignment
+	inline Vector &operator=(const Vector &right) {
+#ifdef VECTOR_ASSERT
+		ASSERT(getRows() == right.getRows());
+#endif
+
+		if (this != &right) {
+			memcpy(getData(), right.getData(),
+			       right.getSize());
+		}
+
+		return *this;
+	}
+	// element accessors
+	inline float &operator()(size_t i) {
+#ifdef VECTOR_ASSERT
+		ASSERT(i < getRows());
+#endif
+		return getData()[i];
+	}
+	inline const float &operator()(size_t i) const {
+#ifdef VECTOR_ASSERT
+		ASSERT(i < getRows());
+#endif
+		return getData()[i];
+	}
+	// output
+	inline void print() const {
+		for (size_t i = 0; i < getRows(); i++) {
+			float sig;
+			int exp;
+			float num = (*this)(i);
+			float2SigExp(num, sig, exp);
+			printf("%6.3fe%03.3d,", (double)sig, exp);
+		}
+
+		printf("\n");
+	}
+	// boolean ops
+	inline bool operator==(const Vector &right) const {
+		for (size_t i = 0; i < getRows(); i++) {
+			if (fabsf(((*this)(i) - right(i))) > 1e-30f)
+				return false;
+		}
+
+		return true;
+	}
+	// scalar ops
+	inline Vector operator+(float right) const {
+		Vector result(getRows());
+		arm_offset_f32((float *)getData(),
+			       right, result.getData(),
+			       getRows());
+		return result;
+	}
+	inline Vector operator-(float right) const {
+		Vector result(getRows());
+		arm_offset_f32((float *)getData(),
+			       -right, result.getData(),
+			       getRows());
+		return result;
+	}
+	inline Vector operator*(float right) const {
+		Vector result(getRows());
+		arm_scale_f32((float *)getData(),
+			      right, result.getData(),
+			      getRows());
+		return result;
+	}
+	inline Vector operator/(float right) const {
+		Vector result(getRows());
+		arm_scale_f32((float *)getData(),
+			      1.0f / right, result.getData(),
+			      getRows());
+		return result;
+	}
+	// vector ops
+	inline Vector operator+(const Vector &right) const {
+#ifdef VECTOR_ASSERT
+		ASSERT(getRows() == right.getRows());
+#endif
+		Vector result(getRows());
+		arm_add_f32((float *)getData(),
+			    (float *)right.getData(),
+			    result.getData(),
+			    getRows());
+		return result;
+	}
+	inline Vector operator-(const Vector &right) const {
+#ifdef VECTOR_ASSERT
+		ASSERT(getRows() == right.getRows());
+#endif
+		Vector result(getRows());
+		arm_sub_f32((float *)getData(),
+			    (float *)right.getData(),
+			    result.getData(),
+			    getRows());
+		return result;
+	}
+	// other functions
+	inline float dot(const Vector &right) {
+		float result = 0;
+		arm_dot_prod_f32((float *)getData(),
+				 (float *)right.getData(),
+				 getRows(),
+				 &result);
+		return result;
+	}
+	inline float norm() {
+		return sqrtf(dot(*this));
+	}
+	inline Vector unit() {
+		return (*this) / norm();
+	}
+	inline static Vector zero(size_t rows) {
+		Vector result(rows);
+		// calloc returns zeroed memory
+		return result;
+	}
+	inline void setAll(const float &val) {
+		for (size_t i = 0; i < getRows(); i++) {
+			(*this)(i) = val;
+		}
+	}
+	inline void set(const float *data) {
+		memcpy(getData(), data, getSize());
+	}
+	inline size_t getRows() const { return _rows; }
+	inline const float *getData() const { return _data; }
+protected:
+	inline size_t getSize() const { return sizeof(float) * getRows(); }
+	inline float *getData() { return _data; }
+	inline void setData(float *data) { _data = data; }
+private:
+	size_t _rows;
+	float *_data;
+};
+
+} // math
diff --git a/apps/mathlib/math/generic/Matrix.cpp b/apps/mathlib/math/generic/Matrix.cpp
new file mode 100644
index 0000000000..21661622ab
--- /dev/null
+++ b/apps/mathlib/math/generic/Matrix.cpp
@@ -0,0 +1,40 @@
+/****************************************************************************
+ *
+ *   Copyright (C) 2012 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+/**
+ * @file Matrix.cpp
+ *
+ * matrix code
+ */
+
+#include "Matrix.hpp"
diff --git a/apps/mathlib/math/generic/Matrix.hpp b/apps/mathlib/math/generic/Matrix.hpp
new file mode 100644
index 0000000000..5601a3447b
--- /dev/null
+++ b/apps/mathlib/math/generic/Matrix.hpp
@@ -0,0 +1,437 @@
+/****************************************************************************
+ *
+ *   Copyright (C) 2012 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+/**
+ * @file Matrix.h
+ *
+ * matrix code
+ */
+
+#pragma once
+
+
+#include 
+#include 
+#include 
+#include 
+#include 
+#include 
+
+#include "../Vector.hpp"
+#include "../Matrix.hpp"
+
+namespace math
+{
+
+class __EXPORT Matrix
+{
+public:
+	// constructor
+	Matrix(size_t rows, size_t cols) :
+		_rows(rows),
+		_cols(cols),
+		_data((float *)calloc(rows *cols, sizeof(float))) {
+	}
+	Matrix(size_t rows, size_t cols, const float *data) :
+		_rows(rows),
+		_cols(cols),
+		_data((float *)malloc(getSize())) {
+		memcpy(getData(), data, getSize());
+	}
+	// deconstructor
+	virtual ~Matrix() {
+		delete [] getData();
+	}
+	// copy constructor (deep)
+	Matrix(const Matrix &right) :
+		_rows(right.getRows()),
+		_cols(right.getCols()),
+		_data((float *)malloc(getSize())) {
+		memcpy(getData(), right.getData(),
+		       right.getSize());
+	}
+	// assignment
+	inline Matrix &operator=(const Matrix &right) {
+#ifdef MATRIX_ASSERT
+		ASSERT(getRows() == right.getRows());
+		ASSERT(getCols() == right.getCols());
+#endif
+
+		if (this != &right) {
+			memcpy(getData(), right.getData(),
+			       right.getSize());
+		}
+
+		return *this;
+	}
+	// element accessors
+	inline float &operator()(size_t i, size_t j) {
+#ifdef MATRIX_ASSERT
+		ASSERT(i < getRows());
+		ASSERT(j < getCols());
+#endif
+		return getData()[i * getCols() + j];
+	}
+	inline const float &operator()(size_t i, size_t j) const {
+#ifdef MATRIX_ASSERT
+		ASSERT(i < getRows());
+		ASSERT(j < getCols());
+#endif
+		return getData()[i * getCols() + j];
+	}
+	// output
+	inline void print() const {
+		for (size_t i = 0; i < getRows(); i++) {
+			for (size_t j = 0; j < getCols(); j++) {
+				float sig;
+				int exp;
+				float num = (*this)(i, j);
+				float2SigExp(num, sig, exp);
+				printf("%6.3fe%03.3d,", (double)sig, exp);
+			}
+
+			printf("\n");
+		}
+	}
+	// boolean ops
+	inline bool operator==(const Matrix &right) const {
+		for (size_t i = 0; i < getRows(); i++) {
+			for (size_t j = 0; j < getCols(); j++) {
+				if (fabsf((*this)(i, j) - right(i, j)) > 1e-30f)
+					return false;
+			}
+		}
+
+		return true;
+	}
+	// scalar ops
+	inline Matrix operator+(const float &right) const {
+		Matrix result(getRows(), getCols());
+
+		for (size_t i = 0; i < getRows(); i++) {
+			for (size_t j = 0; j < getCols(); j++) {
+				result(i, j) = (*this)(i, j) + right;
+			}
+		}
+
+		return result;
+	}
+	inline Matrix operator-(const float &right) const {
+		Matrix result(getRows(), getCols());
+
+		for (size_t i = 0; i < getRows(); i++) {
+			for (size_t j = 0; j < getCols(); j++) {
+				result(i, j) = (*this)(i, j) - right;
+			}
+		}
+
+		return result;
+	}
+	inline Matrix operator*(const float &right) const {
+		Matrix result(getRows(), getCols());
+
+		for (size_t i = 0; i < getRows(); i++) {
+			for (size_t j = 0; j < getCols(); j++) {
+				result(i, j) = (*this)(i, j) * right;
+			}
+		}
+
+		return result;
+	}
+	inline Matrix operator/(const float &right) const {
+		Matrix result(getRows(), getCols());
+
+		for (size_t i = 0; i < getRows(); i++) {
+			for (size_t j = 0; j < getCols(); j++) {
+				result(i, j) = (*this)(i, j) / right;
+			}
+		}
+
+		return result;
+	}
+	// vector ops
+	inline Vector operator*(const Vector &right) const {
+#ifdef MATRIX_ASSERT
+		ASSERT(getCols() == right.getRows());
+#endif
+		Vector result(getRows());
+
+		for (size_t i = 0; i < getRows(); i++) {
+			for (size_t j = 0; j < getCols(); j++) {
+				result(i) += (*this)(i, j) * right(j);
+			}
+		}
+
+		return result;
+	}
+	// matrix ops
+	inline Matrix operator+(const Matrix &right) const {
+#ifdef MATRIX_ASSERT
+		ASSERT(getRows() == right.getRows());
+		ASSERT(getCols() == right.getCols());
+#endif
+		Matrix result(getRows(), getCols());
+
+		for (size_t i = 0; i < getRows(); i++) {
+			for (size_t j = 0; j < getCols(); j++) {
+				result(i, j) = (*this)(i, j) + right(i, j);
+			}
+		}
+
+		return result;
+	}
+	inline Matrix operator-(const Matrix &right) const {
+#ifdef MATRIX_ASSERT
+		ASSERT(getRows() == right.getRows());
+		ASSERT(getCols() == right.getCols());
+#endif
+		Matrix result(getRows(), getCols());
+
+		for (size_t i = 0; i < getRows(); i++) {
+			for (size_t j = 0; j < getCols(); j++) {
+				result(i, j) = (*this)(i, j) - right(i, j);
+			}
+		}
+
+		return result;
+	}
+	inline Matrix operator*(const Matrix &right) const {
+#ifdef MATRIX_ASSERT
+		ASSERT(getCols() == right.getRows());
+#endif
+		Matrix result(getRows(), right.getCols());
+
+		for (size_t i = 0; i < getRows(); i++) {
+			for (size_t j = 0; j < right.getCols(); j++) {
+				for (size_t k = 0; k < right.getRows(); k++) {
+					result(i, j) += (*this)(i, k) * right(k, j);
+				}
+			}
+		}
+
+		return result;
+	}
+	inline Matrix operator/(const Matrix &right) const {
+#ifdef MATRIX_ASSERT
+		ASSERT(right.getRows() == right.getCols());
+		ASSERT(getCols() == right.getCols());
+#endif
+		return (*this) * right.inverse();
+	}
+	// other functions
+	inline Matrix transpose() const {
+		Matrix result(getCols(), getRows());
+
+		for (size_t i = 0; i < getRows(); i++) {
+			for (size_t j = 0; j < getCols(); j++) {
+				result(j, i) = (*this)(i, j);
+			}
+		}
+
+		return result;
+	}
+	inline void swapRows(size_t a, size_t b) {
+		if (a == b) return;
+
+		for (size_t j = 0; j < getCols(); j++) {
+			float tmp = (*this)(a, j);
+			(*this)(a, j) = (*this)(b, j);
+			(*this)(b, j) = tmp;
+		}
+	}
+	inline void swapCols(size_t a, size_t b) {
+		if (a == b) return;
+
+		for (size_t i = 0; i < getRows(); i++) {
+			float tmp = (*this)(i, a);
+			(*this)(i, a) = (*this)(i, b);
+			(*this)(i, b) = tmp;
+		}
+	}
+	/**
+	 * inverse based on LU factorization with partial pivotting
+	 */
+	Matrix inverse() const {
+#ifdef MATRIX_ASSERT
+		ASSERT(getRows() == getCols());
+#endif
+		size_t N = getRows();
+		Matrix L = identity(N);
+		const Matrix &A = (*this);
+		Matrix U = A;
+		Matrix P = identity(N);
+
+		//printf("A:\n"); A.print();
+
+		// for all diagonal elements
+		for (size_t n = 0; n < N; n++) {
+
+			// if diagonal is zero, swap with row below
+			if (fabsf(U(n, n)) < 1e-8f) {
+				//printf("trying pivot for row %d\n",n);
+				for (size_t i = 0; i < N; i++) {
+					if (i == n) continue;
+
+					//printf("\ttrying row %d\n",i);
+					if (fabsf(U(i, n)) > 1e-8f) {
+						//printf("swapped %d\n",i);
+						U.swapRows(i, n);
+						P.swapRows(i, n);
+					}
+				}
+			}
+
+#ifdef MATRIX_ASSERT
+			//printf("A:\n"); A.print();
+			//printf("U:\n"); U.print();
+			//printf("P:\n"); P.print();
+			//fflush(stdout);
+			ASSERT(fabsf(U(n, n)) > 1e-8f);
+#endif
+
+			// failsafe, return zero matrix
+			if (fabsf(U(n, n)) < 1e-8f) {
+				return Matrix::zero(n);
+			}
+
+			// for all rows below diagonal
+			for (size_t i = (n + 1); i < N; i++) {
+				L(i, n) = U(i, n) / U(n, n);
+
+				// add i-th row and n-th row
+				// multiplied by: -a(i,n)/a(n,n)
+				for (size_t k = n; k < N; k++) {
+					U(i, k) -= L(i, n) * U(n, k);
+				}
+			}
+		}
+
+		//printf("L:\n"); L.print();
+		//printf("U:\n"); U.print();
+
+		// solve LY=P*I for Y by forward subst
+		Matrix Y = P;
+
+		// for all columns of Y
+		for (size_t c = 0; c < N; c++) {
+			// for all rows of L
+			for (size_t i = 0; i < N; i++) {
+				// for all columns of L
+				for (size_t j = 0; j < i; j++) {
+					// for all existing y
+					// subtract the component they
+					// contribute to the solution
+					Y(i, c) -= L(i, j) * Y(j, c);
+				}
+
+				// divide by the factor
+				// on current
+				// term to be solved
+				// Y(i,c) /= L(i,i);
+				// but L(i,i) = 1.0
+			}
+		}
+
+		//printf("Y:\n"); Y.print();
+
+		// solve Ux=y for x by back subst
+		Matrix X = Y;
+
+		// for all columns of X
+		for (size_t c = 0; c < N; c++) {
+			// for all rows of U
+			for (size_t k = 0; k < N; k++) {
+				// have to go in reverse order
+				size_t i = N - 1 - k;
+
+				// for all columns of U
+				for (size_t j = i + 1; j < N; j++) {
+					// for all existing x
+					// subtract the component they
+					// contribute to the solution
+					X(i, c) -= U(i, j) * X(j, c);
+				}
+
+				// divide by the factor
+				// on current
+				// term to be solved
+				X(i, c) /= U(i, i);
+			}
+		}
+
+		//printf("X:\n"); X.print();
+		return X;
+	}
+	inline void setAll(const float &val) {
+		for (size_t i = 0; i < getRows(); i++) {
+			for (size_t j = 0; j < getCols(); j++) {
+				(*this)(i, j) = val;
+			}
+		}
+	}
+	inline void set(const float *data) {
+		memcpy(getData(), data, getSize());
+	}
+	inline size_t getRows() const { return _rows; }
+	inline size_t getCols() const { return _cols; }
+	inline static Matrix identity(size_t size) {
+		Matrix result(size, size);
+
+		for (size_t i = 0; i < size; i++) {
+			result(i, i) = 1.0f;
+		}
+
+		return result;
+	}
+	inline static Matrix zero(size_t size) {
+		Matrix result(size, size);
+		result.setAll(0.0f);
+		return result;
+	}
+	inline static Matrix zero(size_t m, size_t n) {
+		Matrix result(m, n);
+		result.setAll(0.0f);
+		return result;
+	}
+protected:
+	inline size_t getSize() const { return sizeof(float) * getRows() * getCols(); }
+	inline float *getData() { return _data; }
+	inline const float *getData() const { return _data; }
+	inline void setData(float *data) { _data = data; }
+private:
+	size_t _rows;
+	size_t _cols;
+	float *_data;
+};
+
+} // namespace math
diff --git a/apps/mathlib/math/generic/Vector.cpp b/apps/mathlib/math/generic/Vector.cpp
new file mode 100644
index 0000000000..7ea6496bb1
--- /dev/null
+++ b/apps/mathlib/math/generic/Vector.cpp
@@ -0,0 +1,40 @@
+/****************************************************************************
+ *
+ *   Copyright (C) 2012 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+/**
+ * @file Vector.cpp
+ *
+ * math vector
+ */
+
+#include "Vector.hpp"
diff --git a/apps/mathlib/math/generic/Vector.hpp b/apps/mathlib/math/generic/Vector.hpp
new file mode 100644
index 0000000000..1a73637798
--- /dev/null
+++ b/apps/mathlib/math/generic/Vector.hpp
@@ -0,0 +1,227 @@
+/****************************************************************************
+ *
+ *   Copyright (C) 2012 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+/**
+ * @file Vector.h
+ *
+ * math vector
+ */
+
+#pragma once
+
+#include 
+#include 
+#include 
+#include 
+#include 
+#include 
+
+#include "../Vector.hpp"
+
+namespace math
+{
+
+class __EXPORT Vector
+{
+public:
+	// constructor
+	Vector(size_t rows) :
+		_rows(rows),
+		_data((float *)calloc(rows, sizeof(float))) {
+	}
+	Vector(size_t rows, const float *data) :
+		_rows(rows),
+		_data((float *)malloc(getSize())) {
+		memcpy(getData(), data, getSize());
+	}
+	// deconstructor
+	virtual ~Vector() {
+		delete [] getData();
+	}
+	// copy constructor (deep)
+	Vector(const Vector &right) :
+		_rows(right.getRows()),
+		_data((float *)malloc(getSize())) {
+		memcpy(getData(), right.getData(),
+		       right.getSize());
+	}
+	// assignment
+	inline Vector &operator=(const Vector &right) {
+#ifdef VECTOR_ASSERT
+		ASSERT(getRows() == right.getRows());
+#endif
+
+		if (this != &right) {
+			memcpy(getData(), right.getData(),
+			       right.getSize());
+		}
+
+		return *this;
+	}
+	// element accessors
+	inline float &operator()(size_t i) {
+#ifdef VECTOR_ASSERT
+		ASSERT(i < getRows());
+#endif
+		return getData()[i];
+	}
+	inline const float &operator()(size_t i) const {
+#ifdef VECTOR_ASSERT
+		ASSERT(i < getRows());
+#endif
+		return getData()[i];
+	}
+	// output
+	inline void print() const {
+		for (size_t i = 0; i < getRows(); i++) {
+			float sig;
+			int exp;
+			float num = (*this)(i);
+			float2SigExp(num, sig, exp);
+			printf("%6.3fe%03.3d,", (double)sig, exp);
+		}
+
+		printf("\n");
+	}
+	// boolean ops
+	inline bool operator==(const Vector &right) const {
+		for (size_t i = 0; i < getRows(); i++) {
+			if (fabsf(((*this)(i) - right(i))) > 1e-30f)
+				return false;
+		}
+
+		return true;
+	}
+	// scalar ops
+	inline Vector operator+(const float &right) const {
+		Vector result(getRows());
+
+		for (size_t i = 0; i < getRows(); i++) {
+			result(i) = (*this)(i) + right;
+		}
+
+		return result;
+	}
+	inline Vector operator-(const float &right) const {
+		Vector result(getRows());
+
+		for (size_t i = 0; i < getRows(); i++) {
+			result(i) = (*this)(i) - right;
+		}
+
+		return result;
+	}
+	inline Vector operator*(const float &right) const {
+		Vector result(getRows());
+
+		for (size_t i = 0; i < getRows(); i++) {
+			result(i) = (*this)(i) * right;
+		}
+
+		return result;
+	}
+	inline Vector operator/(const float &right) const {
+		Vector result(getRows());
+
+		for (size_t i = 0; i < getRows(); i++) {
+			result(i) = (*this)(i) / right;
+		}
+
+		return result;
+	}
+	// vector ops
+	inline Vector operator+(const Vector &right) const {
+#ifdef VECTOR_ASSERT
+		ASSERT(getRows() == right.getRows());
+#endif
+		Vector result(getRows());
+
+		for (size_t i = 0; i < getRows(); i++) {
+			result(i) = (*this)(i) + right(i);
+		}
+
+		return result;
+	}
+	inline Vector operator-(const Vector &right) const {
+#ifdef VECTOR_ASSERT
+		ASSERT(getRows() == right.getRows());
+#endif
+		Vector result(getRows());
+
+		for (size_t i = 0; i < getRows(); i++) {
+			result(i) = (*this)(i) - right(i);
+		}
+
+		return result;
+	}
+	// other functions
+	inline float dot(const Vector &right) {
+		float result = 0;
+
+		for (size_t i = 0; i < getRows(); i++) {
+			result += (*this)(i) * (*this)(i);
+		}
+
+		return result;
+	}
+	inline float norm() {
+		return sqrtf(dot(*this));
+	}
+	inline Vector unit() {
+		return (*this) / norm();
+	}
+	inline static Vector zero(size_t rows) {
+		Vector result(rows);
+		// calloc returns zeroed memory
+		return result;
+	}
+	inline void setAll(const float &val) {
+		for (size_t i = 0; i < getRows(); i++) {
+			(*this)(i) = val;
+		}
+	}
+	inline void set(const float *data) {
+		memcpy(getData(), data, getSize());
+	}
+	inline size_t getRows() const { return _rows; }
+protected:
+	inline size_t getSize() const { return sizeof(float) * getRows(); }
+	inline float *getData() { return _data; }
+	inline const float *getData() const { return _data; }
+	inline void setData(float *data) { _data = data; }
+private:
+	size_t _rows;
+	float *_data;
+};
+
+} // math
diff --git a/apps/mathlib/math/test/test.cpp b/apps/mathlib/math/test/test.cpp
new file mode 100644
index 0000000000..f5db76d704
--- /dev/null
+++ b/apps/mathlib/math/test/test.cpp
@@ -0,0 +1,93 @@
+/****************************************************************************
+ *
+ *   Copyright (C) 2012 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+/**
+ * @file test.cpp
+ *
+ * Test library code
+ */
+
+#include 
+#include 
+
+#include "test.hpp"
+
+bool __EXPORT equal(float a, float b, float epsilon)
+{
+	float diff = fabsf(a - b);
+
+	if (diff > epsilon) {
+		printf("not equal ->\n\ta: %12.8f\n\tb: %12.8f\n", double(a), double(b));
+		return false;
+
+	} else return true;
+}
+
+void __EXPORT float2SigExp(
+	const float &num,
+	float &sig,
+	int &exp)
+{
+	if (isnan(num) || isinf(num)) {
+		sig = 0.0f;
+		exp = -99;
+		return;
+	}
+
+	if (fabsf(num) < 1.0e-38f) {
+		sig = 0;
+		exp = 0;
+		return;
+	}
+
+	exp = log10f(fabsf(num));
+
+	if (exp > 0) {
+		exp = ceil(exp);
+
+	} else {
+		exp = floor(exp);
+	}
+
+	sig = num;
+
+	// cheap power since it is integer
+	if (exp > 0) {
+		for (int i = 0; i < abs(exp); i++) sig /= 10;
+
+	} else {
+		for (int i = 0; i < abs(exp); i++) sig *= 10;
+	}
+}
+
+
diff --git a/apps/mathlib/math/test/test.hpp b/apps/mathlib/math/test/test.hpp
new file mode 100644
index 0000000000..841c421445
--- /dev/null
+++ b/apps/mathlib/math/test/test.hpp
@@ -0,0 +1,50 @@
+/****************************************************************************
+ *
+ *   Copyright (C) 2012 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+/**
+ * @file test.hpp
+ *
+ * Controller library code
+ */
+
+#pragma once
+
+#include 
+#include 
+#include 
+
+bool equal(float a, float b, float eps = 1e-5);
+void float2SigExp(
+	const float &num,
+	float &sig,
+	int &exp);
diff --git a/apps/mathlib/mathlib.h b/apps/mathlib/mathlib.h
new file mode 100644
index 0000000000..b919d53dbb
--- /dev/null
+++ b/apps/mathlib/mathlib.h
@@ -0,0 +1,55 @@
+/****************************************************************************
+ *
+ *   Copyright (C) 2012 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+/**
+ * @file mathlib.h
+ *
+ * Common header for mathlib exports.
+ */
+
+#ifdef __cplusplus
+
+#include "math/Dcm.hpp"
+#include "math/EulerAngles.hpp"
+#include "math/Matrix.hpp"
+#include "math/Quaternion.hpp"
+#include "math/Vector.hpp"
+#include "math/Vector3.hpp"
+
+#endif
+
+#ifdef CONFIG_ARCH_ARM
+
+#include "CMSIS/Include/arm_math.h"
+
+#endif
\ No newline at end of file
diff --git a/apps/mk/app.mk b/apps/mk/app.mk
index 3948ef354f..1d8b0e44c1 100644
--- a/apps/mk/app.mk
+++ b/apps/mk/app.mk
@@ -69,7 +69,7 @@
 #		  CONFIG_PTHREAD_STACK_DEFAULT)
 #
 # Symbols in the module are private to the module unless deliberately exported
-# using the __EXPORT tag.
+# using the __EXPORT tag, or DEFAULT_VISIBILITY is set
 #
 
 ############################################################################
@@ -101,7 +101,9 @@ INCLUDES	+= $(APPDIR)
 
 ASRCS		?= $(wildcard $(SRCDIR)/*.S)
 CSRCS		?= $(wildcard $(SRCDIR)/*.c)
+CHDRS		?= $(wildcard $(SRCDIR)/*.h)
 CXXSRCS		?= $(wildcard $(SRCDIR)/*.cpp)
+CXXHDRS		?= $(wildcard $(SRCDIR)/*.hpp)
 
 # if APPNAME is not set, this is a library
 ifeq ($(APPNAME),)
@@ -125,8 +127,15 @@ endif
 ############################################################################
 # Adjust compilation flags to implement EXPORT
 #
-CFLAGS		+= -fvisibility=hidden -include $(APPDIR)/systemlib/visibility.h
-CXXFLAGS	+= -fvisibility=hidden -include $(APPDIR)/systemlib/visibility.h
+
+ifeq ($(DEFAULT_VISIBILITY),)
+DEFAULT_VISIBILITY = hidden
+else
+DEFAULT_VISIBILITY = default
+endif
+
+CFLAGS		+= -fvisibility=$(DEFAULT_VISIBILITY) -include $(APPDIR)/systemlib/visibility.h
+CXXFLAGS	+= -fvisibility=$(DEFAULT_VISIBILITY) -include $(APPDIR)/systemlib/visibility.h
 
 ############################################################################
 # Add extra include directories
@@ -179,8 +188,8 @@ all:		.built
 #
 depend:		.depend
 .depend:	$(MAKEFILE_LIST) $(SRCS)
-	@$(MKDEP) --dep-path . $(CC) -- $(CFLAGS) -- $(CSRCS) >Make.dep
-	@$(MKDEP) --dep-path . $(CXX) -- $(CXXFLAGS) -- $(CXXSRCS) >>Make.dep
+	@$(MKDEP) --dep-path . $(CC) -- $(CFLAGS) -- $(CSRCS) $(CHDRS) >Make.dep
+	@$(MKDEP) --dep-path . $(CXX) -- $(CXXFLAGS) -- $(CXXSRCS) $(CXXHDRS) >>Make.dep
 	@touch $@
 
 ifneq ($(APPNAME),)
diff --git a/apps/systemlib/Makefile b/apps/systemlib/Makefile
index 5778c552e2..942116faa3 100644
--- a/apps/systemlib/Makefile
+++ b/apps/systemlib/Makefile
@@ -47,8 +47,6 @@ CSRCS		 = err.c \
 
 #		   ppm_decode.c \
 
-
-
 #
 # XXX this really should be a CONFIG_* test
 #
diff --git a/nuttx/configs/px4fmu/common/Make.defs b/nuttx/configs/px4fmu/common/Make.defs
index ff2e4c5fac..75df4c4c9c 100644
--- a/nuttx/configs/px4fmu/common/Make.defs
+++ b/nuttx/configs/px4fmu/common/Make.defs
@@ -144,7 +144,7 @@ ARCHCWARNINGS		 = $(ARCHWARNINGS) \
 			   -Wnested-externs \
 			   -Wunsuffixed-float-constants
 ARCHWARNINGSXX		 = $(ARCHWARNINGS)
-ARCHDEFINES		 = 
+ARCHDEFINES		 =
 ARCHPICFLAGS		 = -fpic -msingle-pic-base -mpic-register=r10
 
 # this seems to be the only way to add linker flags
diff --git a/nuttx/configs/px4fmu/nsh/appconfig b/nuttx/configs/px4fmu/nsh/appconfig
index 7f1a93df92..fcdf689aab 100644
--- a/nuttx/configs/px4fmu/nsh/appconfig
+++ b/nuttx/configs/px4fmu/nsh/appconfig
@@ -45,6 +45,16 @@ CONFIGURED_APPS += system/readline
 CONFIGURED_APPS += systemlib
 CONFIGURED_APPS += systemlib/mixer
 
+# Math library
+CONFIGURED_APPS += mathlib
+CONFIGURED_APPS += mathlib/CMSIS
+CONFIGURED_APPS += examples/math_demo
+
+# Control library
+CONFIGURED_APPS	+= controllib
+CONFIGURED_APPS += examples/control_demo
+CONFIGURED_APPS += examples/kalman_demo
+
 # System utility commands
 CONFIGURED_APPS += systemcmds/reboot
 CONFIGURED_APPS += systemcmds/perf