ardupilot/libraries/AP_InertialSensor/AP_InertialSensor_MPU6000.cpp

/// -*- tab-width: 4; Mode: C++; c-basic-offset: 4; indent-tabs-mode: nil -*-
#include <FastSerial.h>

#include "AP_InertialSensor_MPU6000.h"

#include <SPI.h>
#if defined(ARDUINO) && ARDUINO >= 100
	#include "Arduino.h"
#else
	#include <wiring.h>
#endif

// MPU 6000 registers
#define MPUREG_XG_OFFS_TC				0x00
#define MPUREG_YG_OFFS_TC				0x01
#define MPUREG_ZG_OFFS_TC				0x02
#define MPUREG_X_FINE_GAIN				0x03
#define MPUREG_Y_FINE_GAIN				0x04
#define MPUREG_Z_FINE_GAIN				0x05
#define MPUREG_XA_OFFS_H				0x06	// X axis accelerometer offset (high byte)
#define MPUREG_XA_OFFS_L				0x07	// X axis accelerometer offset (low byte)
#define MPUREG_YA_OFFS_H				0x08	// Y axis accelerometer offset (high byte)
#define MPUREG_YA_OFFS_L				0x09	// Y axis accelerometer offset (low byte)
#define MPUREG_ZA_OFFS_H				0x0A	// Z axis accelerometer offset (high byte)
#define MPUREG_ZA_OFFS_L				0x0B	// Z axis accelerometer offset (low byte)
#define MPUREG_PRODUCT_ID 				0x0C	// Product ID Register
#define MPUREG_XG_OFFS_USRH 			0x13	// X axis gyro offset (high byte)
#define MPUREG_XG_OFFS_USRL 			0x14	// X axis gyro offset (low byte)
#define MPUREG_YG_OFFS_USRH 			0x15	// Y axis gyro offset (high byte)
#define MPUREG_YG_OFFS_USRL 			0x16	// Y axis gyro offset (low byte)
#define MPUREG_ZG_OFFS_USRH 			0x17	// Z axis gyro offset (high byte)
#define MPUREG_ZG_OFFS_USRL 			0x18	// Z axis gyro offset (low byte)
#define MPUREG_SMPLRT_DIV				0x19	// sample rate.  Fsample= 1Khz/(<this value>+1) = 200Hz
#	define MPUREG_SMPLRT_1000HZ				0x00
#	define MPUREG_SMPLRT_500HZ				0x01
#	define MPUREG_SMPLRT_250HZ				0x03
#	define MPUREG_SMPLRT_200HZ				0x04
#	define MPUREG_SMPLRT_100HZ				0x09
#	define MPUREG_SMPLRT_50HZ				0x13
#define MPUREG_CONFIG						0x1A
#define MPUREG_GYRO_CONFIG					0x1B
// bit definitions for MPUREG_GYRO_CONFIG
#	define BITS_GYRO_FS_250DPS				0x00
#	define BITS_GYRO_FS_500DPS				0x08
#	define BITS_GYRO_FS_1000DPS				0x10
#	define BITS_GYRO_FS_2000DPS				0x18
#	define BITS_GYRO_FS_MASK				0x18	// only bits 3 and 4 are used for gyro full scale so use this to mask off other bits
#	define BITS_GYRO_ZGYRO_SELFTEST			0x20
#	define BITS_GYRO_YGYRO_SELFTEST			0x40
#	define BITS_GYRO_XGYRO_SELFTEST			0x80
#define MPUREG_ACCEL_CONFIG				0x1C
#define MPUREG_MOT_THR					0x1F	// detection threshold for Motion interrupt generation.  Motion is detected when the absolute value of any of the accelerometer measurements exceeds this
#define MPUREG_MOT_DUR					0x20	// duration counter threshold for Motion interrupt generation. The duration counter ticks at 1 kHz, therefore MOT_DUR has a unit of 1 LSB = 1 ms
#define MPUREG_ZRMOT_THR				0x21	// detection threshold for Zero Motion interrupt generation.
#define MPUREG_ZRMOT_DUR				0x22	// duration counter threshold for Zero Motion interrupt generation. The duration counter ticks at 16 Hz, therefore ZRMOT_DUR has a unit of 1 LSB = 64 ms.
#define MPUREG_FIFO_EN					0x23
#define MPUREG_INT_PIN_CFG				0x37
#	define BIT_INT_RD_CLEAR					0x10	// clear the interrupt when any read occurs
#define MPUREG_INT_ENABLE				0x38
// bit definitions for MPUREG_INT_ENABLE
#	define BIT_RAW_RDY_EN					0x01
#	define BIT_DMP_INT_EN					0x02	// enabling this bit (DMP_INT_EN) also enables RAW_RDY_EN it seems
#	define BIT_UNKNOWN_INT_EN				0x04
#	define BIT_I2C_MST_INT_EN				0x08
#	define BIT_FIFO_OFLOW_EN				0x10
#	define BIT_ZMOT_EN						0x20
#	define BIT_MOT_EN						0x40
#	define BIT_FF_EN						0x80
#define MPUREG_INT_STATUS				0x3A
// bit definitions for MPUREG_INT_STATUS (same bit pattern as above because this register shows what interrupt actually fired)
#	define BIT_RAW_RDY_INT					0x01
#	define BIT_DMP_INT						0x02
#	define BIT_UNKNOWN_INT					0x04
#	define BIT_I2C_MST_INT					0x08
#	define BIT_FIFO_OFLOW_INT				0x10
#	define BIT_ZMOT_INT						0x20
#	define BIT_MOT_INT						0x40
#	define BIT_FF_INT						0x80
#define MPUREG_ACCEL_XOUT_H				0x3B
#define MPUREG_ACCEL_XOUT_L				0x3C
#define MPUREG_ACCEL_YOUT_H				0x3D
#define MPUREG_ACCEL_YOUT_L				0x3E
#define MPUREG_ACCEL_ZOUT_H				0x3F
#define MPUREG_ACCEL_ZOUT_L				0x40
#define MPUREG_TEMP_OUT_H				0x41
#define MPUREG_TEMP_OUT_L				0x42
#define MPUREG_GYRO_XOUT_H				0x43
#define MPUREG_GYRO_XOUT_L				0x44
#define MPUREG_GYRO_YOUT_H				0x45
#define MPUREG_GYRO_YOUT_L				0x46
#define MPUREG_GYRO_ZOUT_H				0x47
#define MPUREG_GYRO_ZOUT_L				0x48
#define MPUREG_USER_CTRL				0x6A
// bit definitions for MPUREG_USER_CTRL
#	define BIT_USER_CTRL_SIG_COND_RESET		0x01		// resets signal paths and results registers for all sensors (gyros, accel, temp)
#	define BIT_USER_CTRL_I2C_MST_RESET		0x02		// reset I2C Master (only applicable if I2C_MST_EN bit is set)
#	define BIT_USER_CTRL_FIFO_RESET			0x04		// Reset (i.e. clear) FIFO buffer
#	define BIT_USER_CTRL_DMP_RESET			0x08		// Reset DMP
#	define BIT_USER_CTRL_I2C_IF_DIS			0x10		// Disable primary I2C interface and enable SPI interface
#	define BIT_USER_CTRL_I2C_MST_EN			0x20		// Enable MPU to act as the I2C Master to external slave sensors
#	define BIT_USER_CTRL_FIFO_EN			0x40		// Enable FIFO operations
#	define BIT_USER_CTRL_DMP_EN				0x80		// Enable DMP operations
#define MPUREG_PWR_MGMT_1				0x6B
#	define BIT_PWR_MGMT_1_CLK_INTERNAL		0x00		// clock set to internal 8Mhz oscillator
#	define BIT_PWR_MGMT_1_CLK_XGYRO			0x01		// PLL with X axis gyroscope reference
#	define BIT_PWR_MGMT_1_CLK_YGYRO			0x02		// PLL with Y axis gyroscope reference
#	define BIT_PWR_MGMT_1_CLK_ZGYRO			0x03		// PLL with Z axis gyroscope reference
#	define BIT_PWR_MGMT_1_CLK_EXT32KHZ		0x04		// PLL with external 32.768kHz reference
#	define BIT_PWR_MGMT_1_CLK_EXT19MHZ		0x05		// PLL with external 19.2MHz reference
#	define BIT_PWR_MGMT_1_CLK_STOP			0x07		// Stops the clock and keeps the timing generator in reset
#	define BIT_PWR_MGMT_1_TEMP_DIS			0x08		// disable temperature sensor
#	define BIT_PWR_MGMT_1_CYCLE				0x20		// put sensor into cycle mode.  cycles between sleep mode and waking up to take a single sample of data from active sensors at a rate determined by LP_WAKE_CTRL
#	define BIT_PWR_MGMT_1_SLEEP				0x40		// put sensor into low power sleep mode
#	define BIT_PWR_MGMT_1_DEVICE_RESET		0x80		// reset entire device
#define MPUREG_PWR_MGMT_2				0x6C		// allows the user to configure the frequency of wake-ups in Accelerometer Only Low Power Mode
#define MPUREG_BANK_SEL					0x6D		// DMP bank selection register (used to indirectly access DMP registers)
#define MPUREG_MEM_START_ADDR			0x6E		// DMP memory start address (used to indirectly write to dmp memory)
#define MPUREG_MEM_R_W					0x6F		// DMP related register
#define MPUREG_DMP_CFG_1				0x70		// DMP related register
#define MPUREG_DMP_CFG_2				0x71		// DMP related register
#define MPUREG_FIFO_COUNTH				0x72
#define MPUREG_FIFO_COUNTL				0x73
#define MPUREG_FIFO_R_W					0x74
#define MPUREG_WHOAMI					0x75


// Configuration bits MPU 3000 and MPU 6000 (not revised)?
#define BITS_DLPF_CFG_256HZ_NOLPF2		0x00
#define BITS_DLPF_CFG_188HZ				0x01
#define BITS_DLPF_CFG_98HZ				0x02
#define BITS_DLPF_CFG_42HZ				0x03
#define BITS_DLPF_CFG_20HZ				0x04
#define BITS_DLPF_CFG_10HZ				0x05
#define BITS_DLPF_CFG_5HZ				0x06
#define BITS_DLPF_CFG_2100HZ_NOLPF		0x07
#define BITS_DLPF_CFG_MASK				0x07

											// Product ID Description for MPU6000
											// high 4 bits 	low 4 bits
											// Product Name	Product Revision
#define MPU6000ES_REV_C4 			0x14 	// 0001			0100
#define MPU6000ES_REV_C5 			0x15 	// 0001			0101
#define MPU6000ES_REV_D6 			0x16	// 0001			0110
#define MPU6000ES_REV_D7 			0x17	// 0001			0111
#define MPU6000ES_REV_D8 			0x18	// 0001			1000	
#define MPU6000_REV_C4 				0x54	// 0101			0100 
#define MPU6000_REV_C5 				0x55	// 0101			0101
#define MPU6000_REV_D6 				0x56	// 0101			0110	
#define MPU6000_REV_D7 				0x57	// 0101			0111
#define MPU6000_REV_D8 				0x58	// 0101			1000
#define MPU6000_REV_D9 				0x59	// 0101			1001

// DMP output rate constants
#define MPU6000_200HZ				0x00    // default value
#define MPU6000_100HZ				0x01
#define MPU6000_66HZ				0x02
#define MPU6000_50HZ				0x03

// DMP FIFO constants
#define FIFO_PACKET_SIZE 18            // Default quaternion FIFO size (4*4) + Footer(2)
#define GYRO_BIAS_FROM_GRAVITY_RATE 4  // Rate of the gyro bias from gravity correction (200Hz/4) => 50Hz
#define DEFAULT_ACCEL_FUSION_GAIN	0x80	// Default gain for accel fusion (with gyros)


uint8_t AP_InertialSensor_MPU6000::_cs_pin;

/* 
   RS-MPU-6000A-00.pdf, page 33, section 4.25 lists LSB sensitivity of
   gyro as 16.4 LSB/DPS at scale factor of +/- 2000dps (FS_SEL==3)
 */
const float AP_InertialSensor_MPU6000::_gyro_scale = (0.0174532 / 16.4);

/* 
   RS-MPU-6000A-00.pdf, page 31, section 4.23 lists LSB sensitivity of
   accel as 4096 LSB/mg at scale factor of +/- 8g (AFS_SEL==2)

   See note below about accel scaling of engineering sample MPU6k
   variants however
 */
const float AP_InertialSensor_MPU6000::_accel_scale = 9.81 / 4096.0;

/* pch: I believe the accel and gyro indicies are correct
 *      but somone else should please confirm.
 */
const uint8_t AP_InertialSensor_MPU6000::_gyro_data_index[3]  = { 5, 4, 6 };
const int8_t  AP_InertialSensor_MPU6000::_gyro_data_sign[3]   = { 1, 1, -1 };

const uint8_t AP_InertialSensor_MPU6000::_accel_data_index[3] = { 1, 0, 2 };
const int8_t  AP_InertialSensor_MPU6000::_accel_data_sign[3]  = { 1, 1, -1 };

const uint8_t AP_InertialSensor_MPU6000::_temp_data_index = 3;

static volatile uint8_t _new_data;

static uint8_t _product_id;

// DMP related static variables
bool AP_InertialSensor_MPU6000::_dmp_initialised = false;
uint8_t AP_InertialSensor_MPU6000::_received_packet[DMP_FIFO_BUFFER_SIZE];    // FIFO packet buffer
uint8_t AP_InertialSensor_MPU6000::_fifoCountH;			// high byte of number of elements in fifo buffer
uint8_t AP_InertialSensor_MPU6000::_fifoCountL;			// low byte of number of elements in fifo buffer
Quaternion AP_InertialSensor_MPU6000::quaternion;			// holds the 4 quaternions representing attitude taken directly from the DMP

AP_InertialSensor_MPU6000::AP_InertialSensor_MPU6000( uint8_t cs_pin )
{
  _cs_pin = cs_pin; /* can't use initializer list,  is static */
  _gyro.x = 0;
  _gyro.y = 0;
  _gyro.z = 0;
  _accel.x = 0;
  _accel.y = 0;
  _accel.z = 0;
  _temp = 0;
  _initialised = false;
  _dmp_initialised = false;
}

uint16_t AP_InertialSensor_MPU6000::init( AP_PeriodicProcess * scheduler )
{
    if (_initialised) return _product_id;
    _initialised = true;
    scheduler->suspend_timer();
    hardware_init();
    scheduler->resume_timer();
    scheduler->register_process( &AP_InertialSensor_MPU6000::read );
	return _product_id;
}

// accumulation in ISR - must be read with interrupts disabled
// the sum of the values since last read
static volatile int32_t _sum[7];

// how many values we've accumulated since last read
static volatile uint16_t _count;


/*================ AP_INERTIALSENSOR PUBLIC INTERFACE ==================== */

bool AP_InertialSensor_MPU6000::update( void )
{
	int32_t sum[7];
	uint16_t count;
	float count_scale;

	// wait for at least 1 sample
	while (_count == 0) /* nop */;

	// disable interrupts for mininum time
	cli();
	for (int i=0; i<7; i++) {
		sum[i] = _sum[i];
		_sum[i] = 0;
	}
	count = _count;
	_count = 0;
	sei();

	count_scale = 1.0 / count;

	_gyro.x = _gyro_scale * _gyro_data_sign[0] * sum[_gyro_data_index[0]] * count_scale;
	_gyro.y = _gyro_scale * _gyro_data_sign[1] * sum[_gyro_data_index[1]] * count_scale;
	_gyro.z = _gyro_scale * _gyro_data_sign[2] * sum[_gyro_data_index[2]] * count_scale;

	_accel.x = _accel_scale * _accel_data_sign[0] * sum[_accel_data_index[0]] * count_scale;
	_accel.y = _accel_scale * _accel_data_sign[1] * sum[_accel_data_index[1]] * count_scale;
	_accel.z = _accel_scale * _accel_data_sign[2] * sum[_accel_data_index[2]] * count_scale;

	_temp    = _temp_to_celsius(sum[_temp_data_index] * count_scale);

	return true;
}

bool AP_InertialSensor_MPU6000::new_data_available( void )
{
    return _count != 0;
}

float AP_InertialSensor_MPU6000::gx() { return _gyro.x; }
float AP_InertialSensor_MPU6000::gy() { return _gyro.y; }
float AP_InertialSensor_MPU6000::gz() { return _gyro.z; }

void AP_InertialSensor_MPU6000::get_gyros( float * g )
{
  g[0] = _gyro.x;
  g[1] = _gyro.y;
  g[2] = _gyro.z;
}

float AP_InertialSensor_MPU6000::ax() { return _accel.x; }
float AP_InertialSensor_MPU6000::ay() { return _accel.y; }
float AP_InertialSensor_MPU6000::az() { return _accel.z; }

void AP_InertialSensor_MPU6000::get_accels( float * a )
{
  a[0] = _accel.x;
  a[1] = _accel.y;
  a[2] = _accel.z;
}

void AP_InertialSensor_MPU6000::get_sensors( float * sensors )
{
  sensors[0] = _gyro.x;
  sensors[1] = _gyro.y;
  sensors[2] = _gyro.z;
  sensors[3] = _accel.x;
  sensors[4] = _accel.y;
  sensors[5] = _accel.z;
}

float AP_InertialSensor_MPU6000::temperature() { return _temp; }

uint32_t AP_InertialSensor_MPU6000::sample_time()
{
  uint32_t us = micros();
  uint32_t delta = us - _last_sample_micros;
  reset_sample_time();
  return delta;
}

void AP_InertialSensor_MPU6000::reset_sample_time()
{
    _last_sample_micros = micros();
}

/*================ HARDWARE FUNCTIONS ==================== */

static int16_t spi_transfer_16(void)
{
	uint8_t byte_H, byte_L;
	byte_H = SPI.transfer(0);
	byte_L = SPI.transfer(0);
	return (((int16_t)byte_H)<<8) | byte_L;
}

/*
  this is called from a timer interrupt to read data from the MPU6000
  and add it to _sum[]
 */
void AP_InertialSensor_MPU6000::read(uint32_t )
{
    if (_new_data == 0) {
        // no new data is ready from the MPU6000
        return;
    }
    _new_data = 0;

    // now read the data
    digitalWrite(_cs_pin, LOW);
    byte addr = MPUREG_ACCEL_XOUT_H | 0x80;
    SPI.transfer(addr);
    for (uint8_t i=0; i<7; i++) {
        _sum[i] += spi_transfer_16();
    }

    _count++;
    if (_count == 0) {
        // rollover - v unlikely
        memset((void*)_sum, 0, sizeof(_sum));
    }

    digitalWrite(_cs_pin, HIGH);

	// should also read FIFO data if enabled
	if( _dmp_initialised ) {
		if( FIFO_ready() ) {
			FIFO_getPacket();
		}
	}
}

uint8_t AP_InertialSensor_MPU6000::register_read( uint8_t reg )
{
  uint8_t dump;
  uint8_t return_value;
  uint8_t addr = reg | 0x80; // Set most significant bit

  digitalWrite(_cs_pin, LOW);

  dump = SPI.transfer(addr);
  return_value = SPI.transfer(0);

  digitalWrite(_cs_pin, HIGH);

  return return_value;
}

void AP_InertialSensor_MPU6000::register_write(uint8_t reg, uint8_t val)
{
  uint8_t dump;
  digitalWrite(_cs_pin, LOW);
  dump = SPI.transfer(reg);
  dump = SPI.transfer(val);
  digitalWrite(_cs_pin, HIGH);
}

// MPU6000 new data interrupt on INT6
void AP_InertialSensor_MPU6000::data_interrupt(void)
{
    // tell the timer routine that there is data to be read
    _new_data = 1;
}

void AP_InertialSensor_MPU6000::hardware_init()
{
    // MPU6000 chip select setup
    pinMode(_cs_pin, OUTPUT);
    digitalWrite(_cs_pin, HIGH);
    delay(1);

    // Chip reset
    register_write(MPUREG_PWR_MGMT_1, BIT_PWR_MGMT_1_DEVICE_RESET);
    delay(100);
    // Wake up device and select GyroZ clock (better performance)
    register_write(MPUREG_PWR_MGMT_1, BIT_PWR_MGMT_1_CLK_ZGYRO);
    delay(1);

	register_write(MPUREG_PWR_MGMT_2, 0x00);	// only used for wake-up in accelerometer only low power mode
	delay(1);

    // Disable I2C bus (recommended on datasheet)
    register_write(MPUREG_USER_CTRL, BIT_USER_CTRL_I2C_IF_DIS);
    delay(1);
    // SAMPLE RATE
    register_write(MPUREG_SMPLRT_DIV, MPUREG_SMPLRT_200HZ);     // Sample rate = 200Hz    Fsample= 1Khz/(4+1) = 200Hz
    delay(1);
    // FS & DLPF   FS=2000º/s, DLPF = 98Hz (low pass filter)
    register_write(MPUREG_CONFIG, BITS_DLPF_CFG_98HZ);
    delay(1);
    register_write(MPUREG_GYRO_CONFIG, BITS_GYRO_FS_2000DPS);  // Gyro scale 2000º/s
    delay(1);
	
	_product_id = register_read(MPUREG_PRODUCT_ID); // read the product ID rev c has 1/2 the sensitivity of rev d
	//Serial.printf("Product_ID= 0x%x\n", (unsigned) _product_id);
	
	if ((_product_id == MPU6000ES_REV_C4) || (_product_id == MPU6000ES_REV_C5) ||
		(_product_id == MPU6000_REV_C4)   || (_product_id == MPU6000_REV_C5)){
		// Accel scale 8g (4096 LSB/g)
		// Rev C has different scaling than rev D
		register_write(MPUREG_ACCEL_CONFIG,1<<3);
	} else {
		// Accel scale 8g (4096 LSB/g)
		register_write(MPUREG_ACCEL_CONFIG,2<<3);
	}
    delay(1);

    register_write(MPUREG_INT_ENABLE, BIT_RAW_RDY_EN);			// configure interrupt to fire when new data arrives
    delay(1);
    register_write(MPUREG_INT_PIN_CFG, BIT_INT_RD_CLEAR);		// clear interrupt on any read
    delay(1);

    attachInterrupt(6,data_interrupt,RISING);

	// initialise DMP.  Should we only do this when we know we want to use the DMP for attitude sensing as well?
	dmp_init();
}

float AP_InertialSensor_MPU6000::_temp_to_celsius ( uint16_t regval )
{
    /* TODO */
    return 20.0;
}

// return the MPU6k gyro drift rate in radian/s/s
// note that this is much better than the oilpan gyros
float AP_InertialSensor_MPU6000::get_gyro_drift_rate(void)
{
    // 0.5 degrees/second/minute
    return ToRad(0.5/60);
}

// Update gyro offsets with new values.  Offsets provided in as scaled deg/sec values
void AP_InertialSensor_MPU6000::set_gyro_offsets_scaled(float offX, float offY, float offZ)
{
	int16_t offsetX = offX / _gyro_scale * _gyro_data_sign[0];
	int16_t offsetY = offY / _gyro_scale * _gyro_data_sign[1];
	int16_t offsetZ = offZ / _gyro_scale * _gyro_data_sign[2];

	set_gyro_offsets(offsetX, offsetY, offsetZ);
}

// Update gyro offsets with new values. New offset values are substracted to actual offset values.
// offset values in gyro LSB units (as read from registers)
void AP_InertialSensor_MPU6000::set_gyro_offsets(int16_t offsetX, int16_t offsetY, int16_t offsetZ)
{
	int16_t aux_int;

	if (offsetX != 0){
		// Read actual value
		aux_int = (register_read(MPUREG_XG_OFFS_USRH)<<8) | register_read(MPUREG_XG_OFFS_USRL);
		aux_int -= offsetX<<1;   // Adjust to internal units
		// Write to MPU registers
		register_write(MPUREG_XG_OFFS_USRH, (aux_int>>8)&0xFF);
		register_write(MPUREG_XG_OFFS_USRL, aux_int&0xFF);
	}
	if (offsetY != 0){
		aux_int = (register_read(MPUREG_YG_OFFS_USRH)<<8) | register_read(MPUREG_YG_OFFS_USRL);
		aux_int -= offsetY<<1;   // Adjust to internal units
		// Write to MPU registers
		register_write(MPUREG_YG_OFFS_USRH, (aux_int>>8)&0xFF);
		register_write(MPUREG_YG_OFFS_USRL, aux_int&0xFF);
	}
	if (offsetZ != 0){
		aux_int = (register_read(MPUREG_ZG_OFFS_USRH)<<8) | register_read(MPUREG_ZG_OFFS_USRL);
		aux_int -= offsetZ<<1;   // Adjust to internal units
		// Write to MPU registers
		register_write(MPUREG_ZG_OFFS_USRH, (aux_int>>8)&0xFF);
		register_write(MPUREG_ZG_OFFS_USRL, aux_int&0xFF);
	}
}

// Update accel offsets with new values.  Offsets provided in as scaled values (Gs?)
void AP_InertialSensor_MPU6000::set_accel_offsets_scaled(float offX, float offY, float offZ)
{
	int16_t offsetX = offX / _accel_scale * _accel_data_sign[0];
	int16_t offsetY = offY / _accel_scale * _accel_data_sign[1];
	int16_t offsetZ = offZ / _accel_scale * _accel_data_sign[2];

	set_accel_offsets(offsetX, offsetY, offsetZ);
}

// set_accel_offsets - adds an offset to acceleromter readings
// This is useful for dynamic acceleration correction (for example centripetal force correction)
// and for the initial offset calibration
// Input, accel offsets for X,Y and Z in LSB units (as read from raw values)
void AP_InertialSensor_MPU6000::set_accel_offsets(int16_t offsetX, int16_t offsetY, int16_t offsetZ)
{
	int aux_int;
	uint8_t regs[2];

	// Write accel offsets to DMP memory...
	// TO-DO: why don't we write to main accel offset registries? i.e. MPUREG_XA_OFFS_H
	aux_int = offsetX>>1;			// Transform to internal units
	regs[0]=(aux_int>>8)&0xFF;
	regs[1]=aux_int&0xFF;
	dmp_register_write(0x01,0x08,2,regs);		// key KEY_D_1_8  Accel X offset

	aux_int = offsetY>>1;
	regs[0]=(aux_int>>8)&0xFF;
	regs[1]=aux_int&0xFF;
	dmp_register_write(0x01,0x0A,2,regs);		// key KEY_D_1_10  Accel Y offset

	aux_int = offsetZ>>1;
	regs[0]=(aux_int>>8)&0xFF;
	regs[1]=aux_int&0xFF;
	dmp_register_write(0x01,0x02,2,regs);		// key KEY_D_1_2  Accel Z offset
}

// dmp_register_write - method to write to dmp's registers
//    the dmp is logically separated from the main mpu6000.  To write a block of memory to the DMP's memory you
//    write the "bank" and starting address into two of the main MPU's registers, then write the data one byte 
//    at a time into the MPUREG_MEM_R_W register
void AP_InertialSensor_MPU6000::dmp_register_write(uint8_t bank, uint8_t address, uint8_t num_bytes, uint8_t data[])
{
  uint8_t dump;

  register_write(MPUREG_BANK_SEL,bank);
  register_write(MPUREG_MEM_START_ADDR,address);
  digitalWrite(_cs_pin, LOW);
  dump = SPI.transfer(MPUREG_MEM_R_W);
  for( uint8_t i=0; i<num_bytes; i++ ) {
    dump = SPI.transfer(data[i]);
  }
  digitalWrite(_cs_pin, HIGH);
}

// MPU6000 DMP initialization
void AP_InertialSensor_MPU6000::dmp_init()
{
  uint8_t regs[4];	// for writing to dmp

  // ensure we only initialise once
  if( _dmp_initialised ) {
	return;
  }

  // load initial values into DMP memory
  dmp_load_mem();

  dmp_set_gyro_calibration();
  dmp_set_accel_calibration();
  dmp_apply_endian_accel();
  dmp_set_mpu_sensors();
  dmp_set_bias_none();
  dmp_set_fifo_interrupt();
  dmp_send_quaternion();                        // By default we only send the quaternion to the FIFO (18 bytes packet size)
  dmp_set_fifo_rate(MPU6000_200HZ);   			// 200Hz DMP output rate

  register_write(MPUREG_INT_ENABLE, BIT_RAW_RDY_EN | BIT_DMP_INT_EN );	// configure interrupts to fire only when new data arrives from DMP (in fifo buffer)

  // Randy: no idea what this does
  register_write(MPUREG_DMP_CFG_1, 0x03);		//MPUREG_DMP_CFG_1, 0x03
  register_write(MPUREG_DMP_CFG_2, 0x00);		//MPUREG_DMP_CFG_2, 0x00

  //inv_state_change_fifo
  regs[0] = 0xFF;
  regs[1] = 0xFF;
  dmp_register_write(0x01, 0xB2, 0x02, regs);	// D_1_178

  // ?? FIFO ??
  regs[0] = 0x09;
  regs[1] = 0x23;
  regs[2] = 0xA1;
  regs[3] = 0x35;
  dmp_register_write(0x01, 0x90, 0x04, regs);	// D_1_144

  //register_write(MPUREG_USER_CTRL, BIT_USER_CTRL_FIFO_RESET);		//MPUREG_USER_CTRL, BIT_FIFO_RST
  FIFO_reset();

  FIFO_ready();

  //register_write(MPUREG_USER_CTRL, 0x00);		// MPUREG_USER_CTRL, 0.  TO-DO: is all this setting of USER_CTRL really necessary?

  register_write(MPUREG_USER_CTRL, BIT_USER_CTRL_FIFO_RESET);		//MPUREG_USER_CTRL, BIT_FIFO_RST.  TO-DO: replace this call with FIFO_reset()?
  register_write(MPUREG_USER_CTRL, 0x00);		// MPUREG_USER_CTRL: 0
  register_write(MPUREG_USER_CTRL, BIT_USER_CTRL_DMP_EN | BIT_USER_CTRL_FIFO_EN | BIT_USER_CTRL_DMP_RESET);

  // Set the gain of the accel in the sensor fusion
  dmp_set_sensor_fusion_accel_gain(DEFAULT_ACCEL_FUSION_GAIN);   // default value

  // dmp initialisation complete
  _dmp_initialised = true;
}

// dmp_reset - reset dmp (required for changes in gains or offsets to take effect)
void AP_InertialSensor_MPU6000::dmp_reset()
{
	//uint8_t tmp = register_read(MPUREG_USER_CTRL);
	//tmp |= BIT_USER_CTRL_DMP_RESET;
	//register_write(MPUREG_USER_CTRL,tmp);
	register_write(MPUREG_USER_CTRL, BIT_USER_CTRL_FIFO_RESET);		//MPUREG_USER_CTRL, BIT_FIFO_RST.  TO-DO: replace this call with FIFO_reset()?
	register_write(MPUREG_USER_CTRL, 0x00);		// MPUREG_USER_CTRL: 0
	register_write(MPUREG_USER_CTRL, BIT_USER_CTRL_DMP_EN | BIT_USER_CTRL_FIFO_EN | BIT_USER_CTRL_DMP_RESET);
}

// New data packet in FIFO?
bool AP_InertialSensor_MPU6000::FIFO_ready()
{
	_fifoCountH = register_read(MPUREG_FIFO_COUNTH);
	_fifoCountL = register_read(MPUREG_FIFO_COUNTL);
	if(_fifoCountL == FIFO_PACKET_SIZE){
		return 1;
	}
	else{
		//We should not reach this point or maybe we have more than one packet (we should manage this!)
		FIFO_reset();
		return 0;
	}
}

// FIFO_reset - reset/clear FIFO buffer used to capture attitude information from DMP
void AP_InertialSensor_MPU6000::FIFO_reset()
{
	uint8_t temp;
	temp = register_read(MPUREG_USER_CTRL);
	temp = temp | BIT_USER_CTRL_FIFO_RESET;		// FIFO RESET BIT
	register_write(MPUREG_USER_CTRL, temp);
	_new_data = 0;								// clear new data flag
}

// FIFO_getPacket - read an attitude packet from FIFO buffer
// TO-DO: interpret results instead of just dumping into a buffer
void AP_InertialSensor_MPU6000::FIFO_getPacket()
{
	uint8_t i;
	int16_t q_long[4];
	uint8_t dump;
	uint8_t addr = MPUREG_FIFO_R_W | 0x80;	// Set most significant bit to indicate a read
	digitalWrite(_cs_pin, LOW);				// enable the device
	dump = SPI.transfer(addr);				// send address we want to read from
	for(i = 0; i < _fifoCountL; i++){
		_received_packet[i] = SPI.transfer(0);	// request value
	}
	digitalWrite(_cs_pin, HIGH);				// disable device

	// we are using 16 bits resolution
	q_long[0] = (int16_t) ((((uint16_t) _received_packet[0]) << 8) + ((uint16_t) _received_packet[1]));
	q_long[1] = (int16_t) ((((uint16_t) _received_packet[4]) << 8) + ((uint16_t) _received_packet[5]));
	q_long[2] = (int16_t) ((((uint16_t) _received_packet[8]) << 8) + ((uint16_t) _received_packet[9]));
	q_long[3] = (int16_t) ((((uint16_t) _received_packet[12]) << 8) + ((uint16_t) _received_packet[13]));
	// Take care of sign
	for (i = 0; i < 4; i++ ){
		if(q_long[i] > 32767){
			q_long[i] -= 65536;
		}
	}
	quaternion.q1 = ((float)q_long[0]) / 16384.0f;   // convert from fixed point to float
	quaternion.q2 = ((float)q_long[2]) / 16384.0f;   // convert from fixed point to float
	quaternion.q3 = ((float)q_long[1]) / 16384.0f;   // convert from fixed point to float
	quaternion.q4 = ((float)-q_long[3]) / 16384.0f;   // convert from fixed point to float
}

// dmp_set_gyro_calibration - apply default gyro calibration FS=2000dps and default orientation
void AP_InertialSensor_MPU6000::dmp_set_gyro_calibration()
{
	uint8_t regs[4];
	regs[0]=0x4C;
	regs[1]=0xCD;
	regs[2]=0x6C;
	dmp_register_write(0x03, 0x7B, 0x03, regs);		//FCFG_1 inv_set_gyro_calibration
	regs[0]=0x36;
	regs[1]=0x56;
	regs[2]=0x76;
	dmp_register_write(0x03, 0xAB, 0x03, regs);		//FCFG_3 inv_set_gyro_calibration
	regs[0]=0x02;
	regs[1]=0xCB;
	regs[2]=0x47;
	regs[3]=0xA2;
	dmp_register_write(0x00, 0x68, 0x04, regs);		//D_0_104 inv_set_gyro_calibration
	regs[0]=0x00;
	regs[1]=0x05;
	regs[2]=0x8B;
	regs[3]=0xC1;
	dmp_register_write(0x02, 0x18, 0x04, regs);		//D_0_24 inv_set_gyro_calibration
}

// dmp_set_accel_calibration - apply default accel calibration scale=8g and default orientation
void AP_InertialSensor_MPU6000::dmp_set_accel_calibration()
{
	uint8_t regs[6];
	regs[0]=0x00;
	regs[1]=0x00;
	regs[2]=0x00;
	regs[3]=0x00;
	dmp_register_write(0x01, 0x0C, 0x04, regs);		//D_1_152 inv_set_accel_calibration
	regs[0]=0x0C;
	regs[1]=0xC9;
	regs[2]=0x2C;
	regs[3]=0x97;
	regs[4]=0x97;
	regs[5]=0x97;
	dmp_register_write(0x03, 0x7F, 0x06, regs);		//FCFG_2 inv_set_accel_calibration
	regs[0]=0x26;
	regs[1]=0x46;
	regs[2]=0x66;
	dmp_register_write(0x03, 0x89, 0x03, regs);		//FCFG_7 inv_set_accel_calibration
	// accel range, 0x20,0x00 => 2g, 0x10,0x00=>4g    regs= (1073741824/accel_scale*65536)
	//regs[0]=0x20;	// 2g
	regs[0]=0x08;		// 8g
	regs[1]=0x00;
	dmp_register_write(0x00, 0x6C, 0x02, regs);		//D_0_108 inv_set_accel_calibration
}

// dmp_apply_endian_accel - set byte order of accelerometer values?
void AP_InertialSensor_MPU6000::dmp_apply_endian_accel()
{
	uint8_t regs[4];
	regs[0]=0x00;
	regs[1]=0x00;
	regs[2]=0x40;
	regs[3]=0x00;
	dmp_register_write(0x01, 0xEC, 0x04, regs);   //D_1_236 inv_apply_endian_accel
}

// dmp_set_mpu_sensors - to configure for SIX_AXIS output
void AP_InertialSensor_MPU6000::dmp_set_mpu_sensors()
{
	uint8_t regs[6];
	regs[0]=0x0C;
	regs[1]=0xC9;
	regs[2]=0x2C;
	regs[3]=0x97;
	regs[4]=0x97;
	regs[5]=0x97;
	dmp_register_write(0x03, 0x7F, 0x06, regs);   //FCFG_2  inv_set_mpu_sensors(INV_SIX_AXIS_GYRO_ACCEL);
}

// dmp_set_bias_from_no_motion - turn on bias from no motion
void AP_InertialSensor_MPU6000::dmp_set_bias_from_no_motion()
{
	uint8_t regs[4];
	regs[0]=0x0D;
	regs[1]=0x35;
	regs[2]=0x5D;
	dmp_register_write(0x04, 0x02, 0x03, regs);   //CFG_MOTION_BIAS inv_turn_on_bias_from_no_motion
	regs[0]=0x87;
	regs[1]=0x2D;
	regs[2]=0x35;
	regs[3]=0x3D;
	dmp_register_write(0x04, 0x09, 0x04, regs);   //FCFG_5 inv_set_bias_update( INV_BIAS_FROM_NO_MOTION );
}

// dmp_set_bias_none - turn off internal bias correction (we will use this and we handle the gyro bias correction externally)
void AP_InertialSensor_MPU6000::dmp_set_bias_none()
{
	uint8_t regs[4];
	regs[0]=0x98;
	regs[1]=0x98;
	regs[2]=0x98;
	dmp_register_write(0x04, 0x02, 0x03, regs);   //CFG_MOTION_BIAS inv_turn_off_bias_from_no_motion
	regs[0]=0x87;
	regs[1]=0x2D;
	regs[2]=0x35;
	regs[3]=0x3D;
	dmp_register_write(0x04, 0x09, 0x04, regs);   //FCFG_5 inv_set_bias_update( INV_BIAS_FROM_NO_MOTION );
}

// dmp_set_fifo_interrupt
void AP_InertialSensor_MPU6000::dmp_set_fifo_interrupt()
{
	uint8_t regs[1];
	regs[0]=0xFE;
	dmp_register_write(0x07, 0x86, 0x01, regs);   //CFG_6 inv_set_fifo_interupt
}

// dmp_send_quaternion - send quaternion data to FIFO
void AP_InertialSensor_MPU6000::dmp_send_quaternion()
{
	uint8_t regs[5];
	regs[0]=0xF1;
	regs[1]=0x20;
	regs[2]=0x28;
	regs[3]=0x30;
	regs[4]=0x38;
	dmp_register_write(0x07, 0x41, 0x05, regs);   //CFG_8 inv_send_quaternion
	regs[0]=0x30;
	dmp_register_write(0x07, 0x7E, 0x01, regs);   //CFG_16 inv_set_footer
}

// dmp_send_gyro - send gyro data to FIFO
void AP_InertialSensor_MPU6000::dmp_send_gyro()
{
	uint8_t regs[4];
	regs[0]=0xF1;
	regs[1]=0x28;
	regs[2]=0x30;
	regs[3]=0x38;
	dmp_register_write(0x07, 0x47, 0x04, regs);   //CFG_9 inv_send_gyro
}

// dmp_send_accel - send accel data to FIFO
void AP_InertialSensor_MPU6000::dmp_send_accel()
{
	uint8_t regs[54];
	regs[0]=0xF1;
	regs[1]=0x28;
	regs[2]=0x30;
	regs[3]=0x38;
	dmp_register_write(0x07, 0x6C, 0x04, regs);   //CFG_12 inv_send_accel
}

// This functions defines the rate at wich attitude data is send to FIFO
// Rate: 0 => SAMPLE_RATE(ex:200Hz), 1=> SAMPLE_RATE/2 (ex:100Hz), 2=> SAMPLE_RATE/3 (ex:66Hz)
// rate constant definitions in MPU6000.h
void AP_InertialSensor_MPU6000::dmp_set_fifo_rate(uint8_t rate)
{
	uint8_t regs[2];
	regs[0]=0x00;
	regs[1]=rate;
	dmp_register_write(0x02, 0x16, 0x02, regs);		//D_0_22 inv_set_fifo_rate
}

// This function defines the weight of the accel on the sensor fusion
// default value is 0x80
// The official invensense name is inv_key_0_96 (??)
void AP_InertialSensor_MPU6000::dmp_set_sensor_fusion_accel_gain(uint8_t gain)
{
	uint8_t dump;
	//inv_key_0_96
	register_write(MPUREG_BANK_SEL,0x00);
	register_write(MPUREG_MEM_START_ADDR, 0x60);
	digitalWrite(_cs_pin, LOW);
	dump = SPI.transfer(MPUREG_MEM_R_W);
	dump = SPI.transfer(0x00);
	dump = SPI.transfer(gain);  // Original : 0x80    To test: 0x40,  0x20 (too less)
	dump = SPI.transfer(0x00);
	dump = SPI.transfer(0x00);
	digitalWrite(_cs_pin, HIGH);
}

// Load initial memory values into DMP memory banks
void AP_InertialSensor_MPU6000::dmp_load_mem()
{
	uint8_t dump;

	for(int i = 0; i < 7; i++) {
		register_write(MPUREG_BANK_SEL,i);      //MPUREG_BANK_SEL
		for(uint8_t j = 0; j < 16; j++){
			uint8_t start_addy = j * 0x10;
			register_write(MPUREG_MEM_START_ADDR,start_addy);
			digitalWrite(_cs_pin, LOW);
			dump = SPI.transfer(MPUREG_MEM_R_W);
			for(int k = 0; k < 16; k++){
				unsigned char byteToSend = pgm_read_byte(&(dmpMem[i][j][k]));
				dump = SPI.transfer((uint8_t) byteToSend);
			}
			digitalWrite(_cs_pin, HIGH);
		}
	}

	register_write(MPUREG_BANK_SEL,7);      //MPUREG_BANK_SEL
	for(uint8_t j = 0; j < 8; j++){
		uint8_t start_addy = j * 0x10;
		register_write(MPUREG_MEM_START_ADDR,start_addy);
		digitalWrite(_cs_pin, LOW);
		dump = SPI.transfer(MPUREG_MEM_R_W);
		for(int k = 0; k < 16; k++){
			unsigned char byteToSend = pgm_read_byte(&(dmpMem[7][j][k]));
			dump = SPI.transfer((uint8_t) byteToSend);
		}
		digitalWrite(_cs_pin, HIGH);
	}

	register_write(MPUREG_MEM_START_ADDR,0x80);
	digitalWrite(_cs_pin, LOW);
	dump = SPI.transfer(MPUREG_MEM_R_W);
	for(int k = 0; k < 9; k++){
		unsigned char byteToSend = pgm_read_byte(&(dmpMem[7][8][k]));
		dump = SPI.transfer((uint8_t) byteToSend);
	}
	digitalWrite(_cs_pin, HIGH);
}

// ========= DMP MEMORY ================================

//dmpMem from dmpDefaultMantis.c
unsigned char dmpMem[8][16][16] PROGMEM = {
  {
    {
      0xFB, 0x00, 0x00, 0x3E, 0x00, 0x0B, 0x00, 0x36, 0x00, 0x01, 0x00, 0x02, 0x00, 0x03, 0x00, 0x00    }
    ,
    {
      0x00, 0x65, 0x00, 0x54, 0xFF, 0xEF, 0x00, 0x00, 0xFA, 0x80, 0x00, 0x0B, 0x12, 0x82, 0x00, 0x01    }
    ,
    {
      0x00, 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00    }
    ,
    {
      0x00, 0x28, 0x00, 0x00, 0xFF, 0xFF, 0x45, 0x81, 0xFF, 0xFF, 0xFA, 0x72, 0x00, 0x00, 0x00, 0x00    }
    ,
    {
      0x00, 0x00, 0x03, 0xE8, 0x00, 0x00, 0x00, 0x01, 0x00, 0x01, 0x7F, 0xFF, 0xFF, 0xFE, 0x80, 0x01    }
    ,
    {
      0x00, 0x1B, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00    }
    ,
    {
      0x00, 0x3E, 0x03, 0x30, 0x40, 0x00, 0x00, 0x00, 0x02, 0xCA, 0xE3, 0x09, 0x3E, 0x80, 0x00, 0x00    }
    ,
    {
      0x20, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x40, 0x00, 0x00, 0x00, 0x60, 0x00, 0x00, 0x00    }
    ,
    {
      0x41, 0xFF, 0x00, 0x00, 0x00, 0x00, 0x0B, 0x2A, 0x00, 0x00, 0x16, 0x55, 0x00, 0x00, 0x21, 0x82    }
    ,
    {
      0xFD, 0x87, 0x26, 0x50, 0xFD, 0x80, 0x00, 0x00, 0x00, 0x1F, 0x00, 0x00, 0x00, 0x05, 0x80, 0x00    }
    ,
    {
      0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x02, 0x00, 0x00, 0x00, 0x03, 0x00, 0x00    }
    ,
    {
      0x40, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04, 0x6F, 0x00, 0x02, 0x65, 0x32, 0x00, 0x00, 0x5E, 0xC0    }
    ,
    {
      0x40, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00    }
    ,
    {
      0xFB, 0x8C, 0x6F, 0x5D, 0xFD, 0x5D, 0x08, 0xD9, 0x00, 0x7C, 0x73, 0x3B, 0x00, 0x6C, 0x12, 0xCC    }
    ,
    {
      0x32, 0x00, 0x13, 0x9D, 0x32, 0x00, 0xD0, 0xD6, 0x32, 0x00, 0x08, 0x00, 0x40, 0x00, 0x01, 0xF4    }
    ,
    {
      0xFF, 0xE6, 0x80, 0x79, 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0xD0, 0xD6, 0x00, 0x00, 0x27, 0x10    }
  }
  ,
  {
    {
      0xFB, 0x00, 0x00, 0x00, 0x40, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00    }
    ,
    {
      0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0x00, 0x01, 0x00, 0x00, 0x00    }
    ,
    {
      0x00, 0x00, 0xFA, 0x36, 0xFF, 0xBC, 0x30, 0x8E, 0x00, 0x05, 0xFB, 0xF0, 0xFF, 0xD9, 0x5B, 0xC8    }
    ,
    {
      0xFF, 0xD0, 0x9A, 0xBE, 0x00, 0x00, 0x10, 0xA9, 0xFF, 0xF4, 0x1E, 0xB2, 0x00, 0xCE, 0xBB, 0xF7    }
    ,
    {
      0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x04, 0x00, 0x02, 0x00, 0x02, 0x02, 0x00, 0x00, 0x0C    }
    ,
    {
      0xFF, 0xC2, 0x80, 0x00, 0x00, 0x01, 0x80, 0x00, 0x00, 0xCF, 0x80, 0x00, 0x40, 0x00, 0x00, 0x00    }
    ,
    {
      0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x06, 0x00, 0x00, 0x00, 0x00, 0x14    }
    ,
    {
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    {
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    {
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    {
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    {
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    {
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    {
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    {
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    {
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    {
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    {
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    {
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    {
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    {
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    {
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    {
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    {
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    {
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    {
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    {
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    {
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    {
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    {
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    {
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    {
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    {
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    ,
    {
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    {
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    ,
    {
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    {
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    ,
    {
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    ,
    {
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    ,
    {
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    ,
    {
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    ,
    {
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    ,
    {
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    ,
    {
      0x00, 0x2C, 0x54, 0x7C, 0xF2, 0xB1, 0x8C, 0xB4, 0x99, 0xB9, 0xA3, 0x2D, 0x55, 0x7D, 0x81, 0x91    }
    ,
    {
      0xAC, 0x38, 0xAD, 0x3A, 0xB5, 0x83, 0x91, 0xAC, 0x2D, 0xD9, 0x28, 0xD8, 0x4D, 0xD9, 0x48, 0xD8    }
    ,
    {
      0x6D, 0xD9, 0x68, 0xD8, 0x8C, 0x9D, 0xAE, 0x29, 0xD9, 0x04, 0xAE, 0xD8, 0x51, 0xD9, 0x04, 0xAE    }
    ,
    {
      0xD8, 0x79, 0xD9, 0x04, 0xD8, 0x81, 0xF3, 0x9D, 0xAD, 0x00, 0x8D, 0xAE, 0x19, 0x81, 0xAD, 0xD9    }
    ,
    {
      0x01, 0xD8, 0xF2, 0xAE, 0xDA, 0x26, 0xD8, 0x8E, 0x91, 0x29, 0x83, 0xA7, 0xD9, 0xAD, 0xAD, 0xAD    }
    ,
    {
      0xAD, 0xF3, 0x2A, 0xD8, 0xD8, 0xF1, 0xB0, 0xAC, 0x89, 0x91, 0x3E, 0x5E, 0x76, 0xF3, 0xAC, 0x2E    }
    ,
    {
      0x2E, 0xF1, 0xB1, 0x8C, 0x5A, 0x9C, 0xAC, 0x2C, 0x28, 0x28, 0x28, 0x9C, 0xAC, 0x30, 0x18, 0xA8    }
    ,
    {
      0x98, 0x81, 0x28, 0x34, 0x3C, 0x97, 0x24, 0xA7, 0x28, 0x34, 0x3C, 0x9C, 0x24, 0xF2, 0xB0, 0x89    }
    ,
    {
      0xAC, 0x91, 0x2C, 0x4C, 0x6C, 0x8A, 0x9B, 0x2D, 0xD9, 0xD8, 0xD8, 0x51, 0xD9, 0xD8, 0xD8, 0x79    }
  }
  ,
  {
    {
      0xD9, 0xD8, 0xD8, 0xF1, 0x9E, 0x88, 0xA3, 0x31, 0xDA, 0xD8, 0xD8, 0x91, 0x2D, 0xD9, 0x28, 0xD8    }
    ,
    {
      0x4D, 0xD9, 0x48, 0xD8, 0x6D, 0xD9, 0x68, 0xD8, 0xB1, 0x83, 0x93, 0x35, 0x3D, 0x80, 0x25, 0xDA    }
    ,
    {
      0xD8, 0xD8, 0x85, 0x69, 0xDA, 0xD8, 0xD8, 0xB4, 0x93, 0x81, 0xA3, 0x28, 0x34, 0x3C, 0xF3, 0xAB    }
    ,
    {
      0x8B, 0xF8, 0xA3, 0x91, 0xB6, 0x09, 0xB4, 0xD9, 0xAB, 0xDE, 0xFA, 0xB0, 0x87, 0x9C, 0xB9, 0xA3    }
    ,
    {
      0xDD, 0xF1, 0xA3, 0xA3, 0xA3, 0xA3, 0x95, 0xF1, 0xA3, 0xA3, 0xA3, 0x9D, 0xF1, 0xA3, 0xA3, 0xA3    }
    ,
    {
      0xA3, 0xF2, 0xA3, 0xB4, 0x90, 0x80, 0xF2, 0xA3, 0xA3, 0xA3, 0xA3, 0xA3, 0xA3, 0xA3, 0xA3, 0xA3    }
    ,
    {
      0xA3, 0xB2, 0xA3, 0xA3, 0xA3, 0xA3, 0xA3, 0xA3, 0xB0, 0x87, 0xB5, 0x99, 0xF1, 0xA3, 0xA3, 0xA3    }
    ,
    {
      0x98, 0xF1, 0xA3, 0xA3, 0xA3, 0xA3, 0x97, 0xA3, 0xA3, 0xA3, 0xA3, 0xF3, 0x9B, 0xA3, 0xA3, 0xDC    }
    ,
    {
      0xB9, 0xA7, 0xF1, 0x26, 0x26, 0x26, 0xD8, 0xD8, 0xFF    }
  }
};