diff --git a/Doc/library/sys.rst b/Doc/library/sys.rst index 4928d1357b2..51c85d43e82 100644 --- a/Doc/library/sys.rst +++ b/Doc/library/sys.rst @@ -266,6 +266,19 @@ always available. The information in the table is simplified. +.. data:: float_repr_style + + A string indicating how the :func:`repr` function behaves for + floats. If the string has value ``'short'`` then for a finite + float ``x``, ``repr(x)`` aims to produce a short string with the + property that ``float(repr(x)) == x``. This is the usual behaviour + in Python 3.1 and later. Otherwise, ``float_repr_style`` has value + ``'legacy'`` and ``repr(x)`` behaves in the same way as it did in + versions of Python prior to 3.1. + + .. versionadded:: 3.1 + + .. function:: getcheckinterval() Return the interpreter's "check interval"; see :func:`setcheckinterval`. diff --git a/Doc/license.rst b/Doc/license.rst index 7ae9f567510..eb266a7b34a 100644 --- a/Doc/license.rst +++ b/Doc/license.rst @@ -657,3 +657,35 @@ The :mod:`select` and contains the following notice for the kqueue interface:: 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. + + +strtod and dtoa +--------------- + +The file :file:`Python/dtoa.c`, which supplies C functions dtoa and +strtod for conversion of C doubles to and from strings, is derived +from the file of the same name by David M. Gay, currently available +from http://www.netlib.org/fp/. The original file, as retrieved on +March 16, 2009, contains the following copyright and licensing +notice:: + + /**************************************************************** + * + * The author of this software is David M. Gay. + * + * Copyright (c) 1991, 2000, 2001 by Lucent Technologies. + * + * Permission to use, copy, modify, and distribute this software for any + * purpose without fee is hereby granted, provided that this entire notice + * is included in all copies of any software which is or includes a copy + * or modification of this software and in all copies of the supporting + * documentation for such software. + * + * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED + * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY + * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY + * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE. + * + ***************************************************************/ + + diff --git a/Include/Python.h b/Include/Python.h index 76b950321dc..5b45b38d4e3 100644 --- a/Include/Python.h +++ b/Include/Python.h @@ -118,6 +118,7 @@ #include "pystrtod.h" #include "pystrcmp.h" +#include "dtoa.h" /* _Py_Mangle is defined in compile.c */ PyAPI_FUNC(PyObject*) _Py_Mangle(PyObject *p, PyObject *name); diff --git a/Include/dtoa.h b/Include/dtoa.h new file mode 100644 index 00000000000..9b434b77b6e --- /dev/null +++ b/Include/dtoa.h @@ -0,0 +1,15 @@ +#ifndef PY_NO_SHORT_FLOAT_REPR +#ifdef __cplusplus +extern "C" { +#endif + +PyAPI_FUNC(double) _Py_dg_strtod(const char *str, char **ptr); +PyAPI_FUNC(char *) _Py_dg_dtoa(double d, int mode, int ndigits, + int *decpt, int *sign, char **rve); +PyAPI_FUNC(void) _Py_dg_freedtoa(char *s); + + +#ifdef __cplusplus +} +#endif +#endif diff --git a/Include/pymacconfig.h b/Include/pymacconfig.h index a8679af498f..7b204316d1d 100644 --- a/Include/pymacconfig.h +++ b/Include/pymacconfig.h @@ -17,6 +17,9 @@ # undef SIZEOF_VOID_P # undef SIZEOF__BOOL # undef WORDS_BIGENDIAN +# undef DOUBLE_IS_ARM_MIXED_ENDIAN_IEEE754 +# undef DOUBLE_IS_BIG_ENDIAN_IEEE754 +# undef DOUBLE_IS_LITTLE_ENDIAN_IEEE754 # undef VA_LIST_IS_ARRAY # if defined(__LP64__) && defined(__x86_64__) @@ -65,6 +68,9 @@ #ifdef __BIG_ENDIAN__ #define WORDS_BIGENDIAN 1 +#define DOUBLE_IS_BIG_ENDIAN_IEEE754 +#else +#define DOUBLE_IS_LITTLE_ENDIAN_IEEE754 #endif /* __BIG_ENDIAN */ diff --git a/Include/pymath.h b/Include/pymath.h index 6ad174d6455..8872e8a9977 100644 --- a/Include/pymath.h +++ b/Include/pymath.h @@ -92,6 +92,11 @@ PyAPI_FUNC(double) _Py_force_double(double); # endif #endif +#ifdef HAVE_GCC_ASM_FOR_X87 +PyAPI_FUNC(unsigned short) _Py_get_387controlword(void); +PyAPI_FUNC(void) _Py_set_387controlword(unsigned short); +#endif + /* Py_IS_NAN(X) * Return 1 if float or double arg is a NaN, else 0. * Caution: diff --git a/Include/pyport.h b/Include/pyport.h index bf75d89982d..ed435697d33 100644 --- a/Include/pyport.h +++ b/Include/pyport.h @@ -465,6 +465,53 @@ extern "C" { errno = 0; \ } while(0) +/* The functions _Py_dg_strtod and _Py_dg_dtoa in Python/dtoa.c require that + the FPU is using 53-bit precision. Here are macros that force this. See + Python/pystrtod.c for an example of their use. */ + +#ifdef USING_X87_FPU +#define _Py_SET_53BIT_PRECISION_HEADER \ + unsigned short old_387controlword, new_387controlword +#define _Py_SET_53BIT_PRECISION_START \ + do { \ + old_387controlword = _Py_get_387controlword(); \ + new_387controlword = (old_387controlword & ~0x0f00) | 0x0200; \ + if (new_387controlword != old_387controlword) \ + _Py_set_387controlword(new_387controlword); \ + } while (0) +#define _Py_SET_53BIT_PRECISION_END \ + if (new_387controlword != old_387controlword) \ + _Py_set_387controlword(old_387controlword) +#else +#define _Py_SET_53BIT_PRECISION_HEADER +#define _Py_SET_53BIT_PRECISION_START +#define _Py_SET_53BIT_PRECISION_END +#endif + +/* If we can't guarantee 53-bit precision, don't use the code + in Python/dtoa.c, but fall back to standard code. This + means that repr of a float will be long (17 sig digits). + + Realistically, there are two things that could go wrong: + + (1) doubles aren't IEEE 754 doubles, or + (2) we're on x86 with the rounding precision set to 64-bits + (extended precision), and we don't know how to change + the rounding precision. + */ + +#if !defined(DOUBLE_IS_LITTLE_ENDIAN_IEEE754) && \ + !defined(DOUBLE_IS_BIG_ENDIAN_IEEE754) && \ + !defined(DOUBLE_IS_ARM_MIXED_ENDIAN_IEEE754) +#define PY_NO_SHORT_FLOAT_REPR +#endif + +/* double rounding is symptomatic of use of extended precision on x86 */ +#ifdef X87_DOUBLE_ROUNDING +#define PY_NO_SHORT_FLOAT_REPR +#endif + + /* Py_DEPRECATED(version) * Declare a variable, type, or function deprecated. * Usage: diff --git a/Lib/test/formatfloat_testcases.txt b/Lib/test/formatfloat_testcases.txt new file mode 100644 index 00000000000..3abe9384332 --- /dev/null +++ b/Lib/test/formatfloat_testcases.txt @@ -0,0 +1,354 @@ +-- 'f' code formatting, with explicit precision (>= 0). Output always +-- has the given number of places after the point; zeros are added if +-- necessary to make this true. + +-- zeros +%.0f 0 -> 0 +%.1f 0 -> 0.0 +%.2f 0 -> 0.00 +%.3f 0 -> 0.000 +%.50f 0 -> 0.00000000000000000000000000000000000000000000000000 + +-- precision 0; result should never include a . +%.0f 1.5 -> 2 +%.0f 2.5 -> 2 +%.0f 3.5 -> 4 +%.0f 0.0 -> 0 +%.0f 0.1 -> 0 +%.0f 0.001 -> 0 +%.0f 10.0 -> 10 +%.0f 10.1 -> 10 +%.0f 10.01 -> 10 +%.0f 123.456 -> 123 +%.0f 1234.56 -> 1235 +%.0f 1e49 -> 9999999999999999464902769475481793196872414789632 +-- %.0f 1e50 -> 100000000000000007629769841091887003294964970946560 +%.0f 9.9999999999999987e+49 -> 99999999999999986860582406952576489172979654066176 + +-- precision 1 +%.1f 0.0001 -> 0.0 +%.1f 0.001 -> 0.0 +%.1f 0.01 -> 0.0 +%.1f 0.04 -> 0.0 +%.1f 0.06 -> 0.1 +%.1f 0.25 -> 0.2 +%.1f 0.75 -> 0.8 +%.1f 1.4 -> 1.4 +%.1f 1.5 -> 1.5 +%.1f 10.0 -> 10.0 +%.1f 1000.03 -> 1000.0 +%.1f 1234.5678 -> 1234.6 +%.1f 1234.7499 -> 1234.7 +%.1f 1234.75 -> 1234.8 + +-- precision 2 +%.2f 0.0001 -> 0.00 +%.2f 0.001 -> 0.00 +%.2f 0.004999 -> 0.00 +%.2f 0.005001 -> 0.01 +%.2f 0.01 -> 0.01 +%.2f 0.125 -> 0.12 +%.2f 0.375 -> 0.38 +%.2f 1234500 -> 1234500.00 +%.2f 1234560 -> 1234560.00 +%.2f 1234567 -> 1234567.00 +%.2f 1234567.8 -> 1234567.80 +%.2f 1234567.89 -> 1234567.89 +%.2f 1234567.891 -> 1234567.89 +%.2f 1234567.8912 -> 1234567.89 + +-- alternate form always includes a decimal point. This only +-- makes a difference when the precision is 0. +%#.0f 0 -> 0. +%#.1f 0 -> 0.0 +%#.0f 1.5 -> 2. +%#.0f 2.5 -> 2. +%#.0f 10.1 -> 10. +%#.0f 1234.56 -> 1235. +%#.1f 1.4 -> 1.4 +%#.2f 0.375 -> 0.38 + +-- if precision is omitted it defaults to 6 +%f 0 -> 0.000000 +%f 1230000 -> 1230000.000000 +%f 1234567 -> 1234567.000000 +%f 123.4567 -> 123.456700 +%f 1.23456789 -> 1.234568 +%f 0.00012 -> 0.000120 +%f 0.000123 -> 0.000123 +%f 0.00012345 -> 0.000123 +%f 0.000001 -> 0.000001 +%f 0.0000005001 -> 0.000001 +%f 0.0000004999 -> 0.000000 + +-- 'e' code formatting with explicit precision (>= 0). Output should +-- always have exactly the number of places after the point that were +-- requested. + +-- zeros +%.0e 0 -> 0e+00 +%.1e 0 -> 0.0e+00 +%.2e 0 -> 0.00e+00 +%.10e 0 -> 0.0000000000e+00 +%.50e 0 -> 0.00000000000000000000000000000000000000000000000000e+00 + +-- precision 0. no decimal point in the output +%.0e 0.01 -> 1e-02 +%.0e 0.1 -> 1e-01 +%.0e 1 -> 1e+00 +%.0e 10 -> 1e+01 +%.0e 100 -> 1e+02 +%.0e 0.012 -> 1e-02 +%.0e 0.12 -> 1e-01 +%.0e 1.2 -> 1e+00 +%.0e 12 -> 1e+01 +%.0e 120 -> 1e+02 +%.0e 123.456 -> 1e+02 +%.0e 0.000123456 -> 1e-04 +%.0e 123456000 -> 1e+08 +%.0e 0.5 -> 5e-01 +%.0e 1.4 -> 1e+00 +%.0e 1.5 -> 2e+00 +%.0e 1.6 -> 2e+00 +%.0e 2.4999999 -> 2e+00 +%.0e 2.5 -> 2e+00 +%.0e 2.5000001 -> 3e+00 +%.0e 3.499999999999 -> 3e+00 +%.0e 3.5 -> 4e+00 +%.0e 4.5 -> 4e+00 +%.0e 5.5 -> 6e+00 +%.0e 6.5 -> 6e+00 +%.0e 7.5 -> 8e+00 +%.0e 8.5 -> 8e+00 +%.0e 9.4999 -> 9e+00 +%.0e 9.5 -> 1e+01 +%.0e 10.5 -> 1e+01 +%.0e 14.999 -> 1e+01 +%.0e 15 -> 2e+01 + +-- precision 1 +%.1e 0.0001 -> 1.0e-04 +%.1e 0.001 -> 1.0e-03 +%.1e 0.01 -> 1.0e-02 +%.1e 0.1 -> 1.0e-01 +%.1e 1 -> 1.0e+00 +%.1e 10 -> 1.0e+01 +%.1e 100 -> 1.0e+02 +%.1e 120 -> 1.2e+02 +%.1e 123 -> 1.2e+02 +%.1e 123.4 -> 1.2e+02 + +-- precision 2 +%.2e 0.00013 -> 1.30e-04 +%.2e 0.000135 -> 1.35e-04 +%.2e 0.0001357 -> 1.36e-04 +%.2e 0.0001 -> 1.00e-04 +%.2e 0.001 -> 1.00e-03 +%.2e 0.01 -> 1.00e-02 +%.2e 0.1 -> 1.00e-01 +%.2e 1 -> 1.00e+00 +%.2e 10 -> 1.00e+01 +%.2e 100 -> 1.00e+02 +%.2e 1000 -> 1.00e+03 +%.2e 1500 -> 1.50e+03 +%.2e 1590 -> 1.59e+03 +%.2e 1598 -> 1.60e+03 +%.2e 1598.7 -> 1.60e+03 +%.2e 1598.76 -> 1.60e+03 +%.2e 9999 -> 1.00e+04 + +-- omitted precision defaults to 6 +%e 0 -> 0.000000e+00 +%e 165 -> 1.650000e+02 +%e 1234567 -> 1.234567e+06 +%e 12345678 -> 1.234568e+07 +%e 1.1 -> 1.100000e+00 + +-- alternate form always contains a decimal point. This only makes +-- a difference when precision is 0. + +%#.0e 0.01 -> 1.e-02 +%#.0e 0.1 -> 1.e-01 +%#.0e 1 -> 1.e+00 +%#.0e 10 -> 1.e+01 +%#.0e 100 -> 1.e+02 +%#.0e 0.012 -> 1.e-02 +%#.0e 0.12 -> 1.e-01 +%#.0e 1.2 -> 1.e+00 +%#.0e 12 -> 1.e+01 +%#.0e 120 -> 1.e+02 +%#.0e 123.456 -> 1.e+02 +%#.0e 0.000123456 -> 1.e-04 +%#.0e 123456000 -> 1.e+08 +%#.0e 0.5 -> 5.e-01 +%#.0e 1.4 -> 1.e+00 +%#.0e 1.5 -> 2.e+00 +%#.0e 1.6 -> 2.e+00 +%#.0e 2.4999999 -> 2.e+00 +%#.0e 2.5 -> 2.e+00 +%#.0e 2.5000001 -> 3.e+00 +%#.0e 3.499999999999 -> 3.e+00 +%#.0e 3.5 -> 4.e+00 +%#.0e 4.5 -> 4.e+00 +%#.0e 5.5 -> 6.e+00 +%#.0e 6.5 -> 6.e+00 +%#.0e 7.5 -> 8.e+00 +%#.0e 8.5 -> 8.e+00 +%#.0e 9.4999 -> 9.e+00 +%#.0e 9.5 -> 1.e+01 +%#.0e 10.5 -> 1.e+01 +%#.0e 14.999 -> 1.e+01 +%#.0e 15 -> 2.e+01 +%#.1e 123.4 -> 1.2e+02 +%#.2e 0.0001357 -> 1.36e-04 + +-- 'g' code formatting. + +-- zeros +%.0g 0 -> 0 +%.1g 0 -> 0 +%.2g 0 -> 0 +%.3g 0 -> 0 +%.4g 0 -> 0 +%.10g 0 -> 0 +%.50g 0 -> 0 +%.100g 0 -> 0 + +-- precision 0 doesn't make a lot of sense for the 'g' code (what does +-- it mean to have no significant digits?); in practice, it's interpreted +-- as identical to precision 1 +%.0g 1000 -> 1e+03 +%.0g 100 -> 1e+02 +%.0g 10 -> 1e+01 +%.0g 1 -> 1 +%.0g 0.1 -> 0.1 +%.0g 0.01 -> 0.01 +%.0g 1e-3 -> 0.001 +%.0g 1e-4 -> 0.0001 +%.0g 1e-5 -> 1e-05 +%.0g 1e-6 -> 1e-06 +%.0g 12 -> 1e+01 +%.0g 120 -> 1e+02 +%.0g 1.2 -> 1 +%.0g 0.12 -> 0.1 +%.0g 0.012 -> 0.01 +%.0g 0.0012 -> 0.001 +%.0g 0.00012 -> 0.0001 +%.0g 0.000012 -> 1e-05 +%.0g 0.0000012 -> 1e-06 + +-- precision 1 identical to precision 0 +%.1g 1000 -> 1e+03 +%.1g 100 -> 1e+02 +%.1g 10 -> 1e+01 +%.1g 1 -> 1 +%.1g 0.1 -> 0.1 +%.1g 0.01 -> 0.01 +%.1g 1e-3 -> 0.001 +%.1g 1e-4 -> 0.0001 +%.1g 1e-5 -> 1e-05 +%.1g 1e-6 -> 1e-06 +%.1g 12 -> 1e+01 +%.1g 120 -> 1e+02 +%.1g 1.2 -> 1 +%.1g 0.12 -> 0.1 +%.1g 0.012 -> 0.01 +%.1g 0.0012 -> 0.001 +%.1g 0.00012 -> 0.0001 +%.1g 0.000012 -> 1e-05 +%.1g 0.0000012 -> 1e-06 + +-- precision 2 +%.2g 1000 -> 1e+03 +%.2g 100 -> 1e+02 +%.2g 10 -> 10 +%.2g 1 -> 1 +%.2g 0.1 -> 0.1 +%.2g 0.01 -> 0.01 +%.2g 0.001 -> 0.001 +%.2g 1e-4 -> 0.0001 +%.2g 1e-5 -> 1e-05 +%.2g 1e-6 -> 1e-06 +%.2g 1234 -> 1.2e+03 +%.2g 123 -> 1.2e+02 +%.2g 12.3 -> 12 +%.2g 1.23 -> 1.2 +%.2g 0.123 -> 0.12 +%.2g 0.0123 -> 0.012 +%.2g 0.00123 -> 0.0012 +%.2g 0.000123 -> 0.00012 +%.2g 0.0000123 -> 1.2e-05 + +-- alternate g formatting: always include decimal point and +-- exactly significant digits. +%#.0g 0 -> 0. +%#.1g 0 -> 0. +%#.2g 0 -> 0.0 +%#.3g 0 -> 0.00 +%#.4g 0 -> 0.000 + +%#.0g 0.2 -> 0.2 +%#.1g 0.2 -> 0.2 +%#.2g 0.2 -> 0.20 +%#.3g 0.2 -> 0.200 +%#.4g 0.2 -> 0.2000 +%#.10g 0.2 -> 0.2000000000 + +%#.0g 2 -> 2. +%#.1g 2 -> 2. +%#.2g 2 -> 2.0 +%#.3g 2 -> 2.00 +%#.4g 2 -> 2.000 + +%#.0g 20 -> 2.e+01 +%#.1g 20 -> 2.e+01 +%#.2g 20 -> 20. +%#.3g 20 -> 20.0 +%#.4g 20 -> 20.00 + +%#.0g 234.56 -> 2.e+02 +%#.1g 234.56 -> 2.e+02 +%#.2g 234.56 -> 2.3e+02 +%#.3g 234.56 -> 235. +%#.4g 234.56 -> 234.6 +%#.5g 234.56 -> 234.56 +%#.6g 234.56 -> 234.560 + +-- for repr formatting see the separate test_short_repr test in +-- test_float.py. Not all platforms use short repr for floats. + +-- str formatting. Result always includes decimal point and at +-- least one digit after the point, or an exponent. +%s 0 -> 0.0 +%s 1 -> 1.0 + +%s 0.01 -> 0.01 +%s 0.02 -> 0.02 +%s 0.03 -> 0.03 +%s 0.04 -> 0.04 +%s 0.05 -> 0.05 + +-- str truncates to 12 significant digits +%s 1.234123412341 -> 1.23412341234 +%s 1.23412341234 -> 1.23412341234 +%s 1.2341234123 -> 1.2341234123 + +-- values >= 1e11 get an exponent +%s 10 -> 10.0 +%s 100 -> 100.0 +%s 1e10 -> 10000000000.0 +%s 9.999e10 -> 99990000000.0 +%s 99999999999 -> 99999999999.0 +%s 1e11 -> 1e+11 +%s 1e12 -> 1e+12 + +-- as do values < 1e-4 +%s 1e-3 -> 0.001 +%s 1.001e-4 -> 0.0001001 +%s 1.000000000001e-4 -> 0.0001 +%s 1.00000000001e-4 -> 0.000100000000001 +%s 1.0000000001e-4 -> 0.00010000000001 +%s 1e-4 -> 0.0001 +%s 0.999999999999e-4 -> 9.99999999999e-05 +%s 0.999e-4 -> 9.99e-05 +%s 1e-5 -> 1e-05 diff --git a/Makefile.pre.in b/Makefile.pre.in index 0ad7ee06ce0..0e7831fc497 100644 --- a/Makefile.pre.in +++ b/Makefile.pre.in @@ -305,6 +305,7 @@ PYTHON_OBJS= \ Python/getopt.o \ Python/pystrcmp.o \ Python/pystrtod.o \ + Python/dtoa.o \ Python/formatter_unicode.o \ Python/$(DYNLOADFILE) \ $(LIBOBJS) \ @@ -621,6 +622,7 @@ PYTHON_HEADERS= \ Include/complexobject.h \ Include/descrobject.h \ Include/dictobject.h \ + Include/dtoa.h \ Include/enumobject.h \ Include/errcode.h \ Include/eval.h \ diff --git a/Misc/ACKS b/Misc/ACKS index be09f8a48a5..53d7259c878 100644 --- a/Misc/ACKS +++ b/Misc/ACKS @@ -160,6 +160,7 @@ Scott David Daniels Ben Darnell Jonathan Dasteel John DeGood +Ned Deily Vincent Delft Arnaud Delobelle Erik Demaine diff --git a/Misc/NEWS b/Misc/NEWS index 866a5b557b7..f9c8adaacd3 100644 --- a/Misc/NEWS +++ b/Misc/NEWS @@ -12,6 +12,45 @@ What's New in Python 3.1 beta 1? Core and Builtins ----------------- +- The repr function switches to exponential notation at 1e16, not 1e17 + as it did before. This change applies to both 'short' and legacy + float repr styles. For the new repr style, it avoids misleading + output in some cases: an example is repr(2e16+8), which gives + '2.000000000000001e+16'; without this change it would have produced + '20000000000000010.0' instead. + +- Similarly, the str function switches to exponential notation at + 1e11, not 1e12. This avoids printing 13 significant digits in + situations where only 12 of them are correct. Example problem + value: str(1e11 + 0.5). (This minor issue has existed in 2.x for a + long time.) + +- On x86, SSE2 instructions for floating-point are automatically + detected and, where possible, enabled on platforms using the gcc + compiler. As a consequence, some arithmetic operations may have + different (more accurate!) results on some platforms, and + cross-platform consistency of Python arithmetic should be improved. + This applies particularly to Linux/x86. + +- Issue #1580: On most platforms, use a 'short' float repr: for a + finite float x, repr(x) now outputs a string based on the shortest + sequence of decimal digits that rounds to x. Previous behaviour was + to output 17 significant digits and then strip trailing zeros. + + There's a new sys attribute sys.float_repr_style, which takes + the value 'short' to indicate that we're using short float repr, + and 'legacy' if the short float repr isn't available for one + reason or another. + + The float repr change involves incorporating David Gay's 'perfect + rounding' code into the Python core (it's in Python/dtoa.c). As a + secondary consequence, all string-to-float and float-to-string + conversions (including all float formatting operations) will be + correctly rounded on these platforms. + + See issue 1580 discussions for details of platforms for which + this change does not apply. + - Issue #5759: float() didn't call __float__ on str subclasses. - The string.maketrans() function is deprecated; there is a new static method diff --git a/PC/pyconfig.h b/PC/pyconfig.h index 04abc1f6166..2041784b8bf 100644 --- a/PC/pyconfig.h +++ b/PC/pyconfig.h @@ -752,4 +752,8 @@ Py_NO_ENABLE_SHARED to find out. Also support MS_NO_COREDLL for b/w compat */ socket handles greater than FD_SETSIZE */ #define Py_SOCKET_FD_CAN_BE_GE_FD_SETSIZE +/* Define if C doubles are 64-bit IEEE 754 binary format, stored with the + least significant byte first */ +#define DOUBLE_IS_LITTLE_ENDIAN_IEEE754 1 + #endif /* !Py_CONFIG_H */ diff --git a/PCbuild/pythoncore.vcproj b/PCbuild/pythoncore.vcproj index f8ba1f1ecc3..617b15c19c0 100644 --- a/PCbuild/pythoncore.vcproj +++ b/PCbuild/pythoncore.vcproj @@ -894,6 +894,10 @@ RelativePath="..\Include\pystrtod.h" > + + @@ -1746,6 +1750,10 @@ RelativePath="..\Python\pystrtod.c" > + + diff --git a/Python/dtoa.c b/Python/dtoa.c new file mode 100644 index 00000000000..645e976e432 --- /dev/null +++ b/Python/dtoa.c @@ -0,0 +1,2646 @@ +/**************************************************************** + * + * The author of this software is David M. Gay. + * + * Copyright (c) 1991, 2000, 2001 by Lucent Technologies. + * + * Permission to use, copy, modify, and distribute this software for any + * purpose without fee is hereby granted, provided that this entire notice + * is included in all copies of any software which is or includes a copy + * or modification of this software and in all copies of the supporting + * documentation for such software. + * + * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED + * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY + * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY + * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE. + * + ***************************************************************/ + +/**************************************************************** + * This is dtoa.c by David M. Gay, downloaded from + * http://www.netlib.org/fp/dtoa.c on April 15, 2009 and modified for + * inclusion into the Python core by Mark E. T. Dickinson and Eric V. Smith. + * The major modifications are as follows: + * + * 0. The original code has been specialized to Python's needs by removing + * many of the #ifdef'd sections. In particular, code to support VAX and + * IBM floating-point formats, hex NaNs, hex floats, locale-aware + * treatment of the decimal point, and setting of the inexact flag have + * been removed. + * + * 1. We use PyMem_Malloc and PyMem_Free in place of malloc and free. + * + * 2. The public functions strtod, dtoa and freedtoa all now have + * a _Py_dg_ prefix. + * + * 3. Instead of assuming that PyMem_Malloc always succeeds, we thread + * PyMem_Malloc failures through the code. The functions + * + * Balloc, multadd, s2b, i2b, mult, pow5mult, lshift, diff, d2b + * + * of return type *Bigint all return NULL to indicate a malloc failure. + * Similarly, rv_alloc and nrv_alloc (return type char *) return NULL on + * failure. bigcomp now has return type int (it used to be void) and + * returns -1 on failure and 0 otherwise. _Py_dg_dtoa returns NULL + * on failure. _Py_dg_strtod indicates failure due to malloc failure + * by returning -1.0, setting errno=ENOMEM and *se to s00. + * + * 4. The static variable dtoa_result has been removed. Callers of + * _Py_dg_dtoa are expected to call _Py_dg_freedtoa to free + * the memory allocated by _Py_dg_dtoa. + * + * 5. The code has been reformatted to better fit with Python's + * C style guide (PEP 7). + * + ***************************************************************/ + +/* Please send bug reports for the original dtoa.c code to David M. Gay (dmg + * at acm dot org, with " at " changed at "@" and " dot " changed to "."). + * Please report bugs for this modified version using the Python issue tracker + * (http://bugs.python.org). */ + +/* On a machine with IEEE extended-precision registers, it is + * necessary to specify double-precision (53-bit) rounding precision + * before invoking strtod or dtoa. If the machine uses (the equivalent + * of) Intel 80x87 arithmetic, the call + * _control87(PC_53, MCW_PC); + * does this with many compilers. Whether this or another call is + * appropriate depends on the compiler; for this to work, it may be + * necessary to #include "float.h" or another system-dependent header + * file. + */ + +/* strtod for IEEE-, VAX-, and IBM-arithmetic machines. + * + * This strtod returns a nearest machine number to the input decimal + * string (or sets errno to ERANGE). With IEEE arithmetic, ties are + * broken by the IEEE round-even rule. Otherwise ties are broken by + * biased rounding (add half and chop). + * + * Inspired loosely by William D. Clinger's paper "How to Read Floating + * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101]. + * + * Modifications: + * + * 1. We only require IEEE, IBM, or VAX double-precision + * arithmetic (not IEEE double-extended). + * 2. We get by with floating-point arithmetic in a case that + * Clinger missed -- when we're computing d * 10^n + * for a small integer d and the integer n is not too + * much larger than 22 (the maximum integer k for which + * we can represent 10^k exactly), we may be able to + * compute (d*10^k) * 10^(e-k) with just one roundoff. + * 3. Rather than a bit-at-a-time adjustment of the binary + * result in the hard case, we use floating-point + * arithmetic to determine the adjustment to within + * one bit; only in really hard cases do we need to + * compute a second residual. + * 4. Because of 3., we don't need a large table of powers of 10 + * for ten-to-e (just some small tables, e.g. of 10^k + * for 0 <= k <= 22). + */ + +/* Linking of Python's #defines to Gay's #defines starts here. */ + +#include "Python.h" + +/* if PY_NO_SHORT_FLOAT_REPR is defined, then don't even try to compile + the following code */ +#ifndef PY_NO_SHORT_FLOAT_REPR + +#include "float.h" + +#define MALLOC PyMem_Malloc +#define FREE PyMem_Free + +/* This code should also work for ARM mixed-endian format on little-endian + machines, where doubles have byte order 45670123 (in increasing address + order, 0 being the least significant byte). */ +#ifdef DOUBLE_IS_LITTLE_ENDIAN_IEEE754 +# define IEEE_8087 +#endif +#if defined(DOUBLE_IS_BIG_ENDIAN_IEEE754) || \ + defined(DOUBLE_IS_ARM_MIXED_ENDIAN_IEEE754) +# define IEEE_MC68k +#endif +#if defined(IEEE_8087) + defined(IEEE_MC68k) != 1 +#error "Exactly one of IEEE_8087 or IEEE_MC68k should be defined." +#endif + +/* The code below assumes that the endianness of integers matches the + endianness of the two 32-bit words of a double. Check this. */ +#if defined(WORDS_BIGENDIAN) && (defined(DOUBLE_IS_LITTLE_ENDIAN_IEEE754) || \ + defined(DOUBLE_IS_ARM_MIXED_ENDIAN_IEEE754)) +#error "doubles and ints have incompatible endianness" +#endif + +#if !defined(WORDS_BIGENDIAN) && defined(DOUBLE_IS_BIG_ENDIAN_IEEE754) +#error "doubles and ints have incompatible endianness" +#endif + + +#if defined(HAVE_UINT32_T) && defined(HAVE_INT32_T) +typedef PY_UINT32_T ULong; +typedef PY_INT32_T Long; +#else +#error "Failed to find an exact-width 32-bit integer type" +#endif + +#if defined(HAVE_UINT64_T) +#define ULLong PY_UINT64_T +#else +#undef ULLong +#endif + +#undef DEBUG +#ifdef Py_DEBUG +#define DEBUG +#endif + +/* End Python #define linking */ + +#ifdef DEBUG +#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);} +#endif + +#ifndef PRIVATE_MEM +#define PRIVATE_MEM 2304 +#endif +#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double)) +static double private_mem[PRIVATE_mem], *pmem_next = private_mem; + +#ifdef __cplusplus +extern "C" { +#endif + +typedef union { double d; ULong L[2]; } U; + +#ifdef IEEE_8087 +#define word0(x) (x)->L[1] +#define word1(x) (x)->L[0] +#else +#define word0(x) (x)->L[0] +#define word1(x) (x)->L[1] +#endif +#define dval(x) (x)->d + +#ifndef STRTOD_DIGLIM +#define STRTOD_DIGLIM 40 +#endif + +#ifdef DIGLIM_DEBUG +extern int strtod_diglim; +#else +#define strtod_diglim STRTOD_DIGLIM +#endif + +/* The following definition of Storeinc is appropriate for MIPS processors. + * An alternative that might be better on some machines is + * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff) + */ +#if defined(IEEE_8087) +#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \ + ((unsigned short *)a)[0] = (unsigned short)c, a++) +#else +#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \ + ((unsigned short *)a)[1] = (unsigned short)c, a++) +#endif + +/* #define P DBL_MANT_DIG */ +/* Ten_pmax = floor(P*log(2)/log(5)) */ +/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */ +/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */ +/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */ + +#define Exp_shift 20 +#define Exp_shift1 20 +#define Exp_msk1 0x100000 +#define Exp_msk11 0x100000 +#define Exp_mask 0x7ff00000 +#define P 53 +#define Nbits 53 +#define Bias 1023 +#define Emax 1023 +#define Emin (-1022) +#define Exp_1 0x3ff00000 +#define Exp_11 0x3ff00000 +#define Ebits 11 +#define Frac_mask 0xfffff +#define Frac_mask1 0xfffff +#define Ten_pmax 22 +#define Bletch 0x10 +#define Bndry_mask 0xfffff +#define Bndry_mask1 0xfffff +#define LSB 1 +#define Sign_bit 0x80000000 +#define Log2P 1 +#define Tiny0 0 +#define Tiny1 1 +#define Quick_max 14 +#define Int_max 14 + +#ifndef Flt_Rounds +#ifdef FLT_ROUNDS +#define Flt_Rounds FLT_ROUNDS +#else +#define Flt_Rounds 1 +#endif +#endif /*Flt_Rounds*/ + +#define Rounding Flt_Rounds + +#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1)) +#define Big1 0xffffffff + +#ifndef NAN_WORD0 +#define NAN_WORD0 0x7ff80000 +#endif + +#ifndef NAN_WORD1 +#define NAN_WORD1 0 +#endif + + +/* struct BCinfo is used to pass information from _Py_dg_strtod to bigcomp */ + +typedef struct BCinfo BCinfo; +struct +BCinfo { + int dp0, dp1, dplen, dsign, e0, inexact; + int nd, nd0, rounding, scale, uflchk; +}; + +#define FFFFFFFF 0xffffffffUL + +#define Kmax 7 + +/* struct Bigint is used to represent arbitrary-precision integers. These + integers are stored in sign-magnitude format, with the magnitude stored as + an array of base 2**32 digits. Bigints are always normalized: if x is a + Bigint then x->wds >= 1, and either x->wds == 1 or x[wds-1] is nonzero. + + The Bigint fields are as follows: + + - next is a header used by Balloc and Bfree to keep track of lists + of freed Bigints; it's also used for the linked list of + powers of 5 of the form 5**2**i used by pow5mult. + - k indicates which pool this Bigint was allocated from + - maxwds is the maximum number of words space was allocated for + (usually maxwds == 2**k) + - sign is 1 for negative Bigints, 0 for positive. The sign is unused + (ignored on inputs, set to 0 on outputs) in almost all operations + involving Bigints: a notable exception is the diff function, which + ignores signs on inputs but sets the sign of the output correctly. + - wds is the actual number of significant words + - x contains the vector of words (digits) for this Bigint, from least + significant (x[0]) to most significant (x[wds-1]). +*/ + +struct +Bigint { + struct Bigint *next; + int k, maxwds, sign, wds; + ULong x[1]; +}; + +typedef struct Bigint Bigint; + +/* Memory management: memory is allocated from, and returned to, Kmax+1 pools + of memory, where pool k (0 <= k <= Kmax) is for Bigints b with b->maxwds == + 1 << k. These pools are maintained as linked lists, with freelist[k] + pointing to the head of the list for pool k. + + On allocation, if there's no free slot in the appropriate pool, MALLOC is + called to get more memory. This memory is not returned to the system until + Python quits. There's also a private memory pool that's allocated from + in preference to using MALLOC. + + For Bigints with more than (1 << Kmax) digits (which implies at least 1233 + decimal digits), memory is directly allocated using MALLOC, and freed using + FREE. + + XXX: it would be easy to bypass this memory-management system and + translate each call to Balloc into a call to PyMem_Malloc, and each + Bfree to PyMem_Free. Investigate whether this has any significant + performance on impact. */ + +static Bigint *freelist[Kmax+1]; + +/* Allocate space for a Bigint with up to 1<next; + else { + x = 1 << k; + len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1) + /sizeof(double); + if (pmem_next - private_mem + len <= PRIVATE_mem) { + rv = (Bigint*)pmem_next; + pmem_next += len; + } + else { + rv = (Bigint*)MALLOC(len*sizeof(double)); + if (rv == NULL) + return NULL; + } + rv->k = k; + rv->maxwds = x; + } + rv->sign = rv->wds = 0; + return rv; +} + +/* Free a Bigint allocated with Balloc */ + +static void +Bfree(Bigint *v) +{ + if (v) { + if (v->k > Kmax) + FREE((void*)v); + else { + v->next = freelist[v->k]; + freelist[v->k] = v; + } + } +} + +#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \ + y->wds*sizeof(Long) + 2*sizeof(int)) + +/* Multiply a Bigint b by m and add a. Either modifies b in place and returns + a pointer to the modified b, or Bfrees b and returns a pointer to a copy. + On failure, return NULL. In this case, b will have been already freed. */ + +static Bigint * +multadd(Bigint *b, int m, int a) /* multiply by m and add a */ +{ + int i, wds; +#ifdef ULLong + ULong *x; + ULLong carry, y; +#else + ULong carry, *x, y; + ULong xi, z; +#endif + Bigint *b1; + + wds = b->wds; + x = b->x; + i = 0; + carry = a; + do { +#ifdef ULLong + y = *x * (ULLong)m + carry; + carry = y >> 32; + *x++ = y & FFFFFFFF; +#else + xi = *x; + y = (xi & 0xffff) * m + carry; + z = (xi >> 16) * m + (y >> 16); + carry = z >> 16; + *x++ = (z << 16) + (y & 0xffff); +#endif + } + while(++i < wds); + if (carry) { + if (wds >= b->maxwds) { + b1 = Balloc(b->k+1); + if (b1 == NULL){ + Bfree(b); + return NULL; + } + Bcopy(b1, b); + Bfree(b); + b = b1; + } + b->x[wds++] = (ULong)carry; + b->wds = wds; + } + return b; +} + +/* convert a string s containing nd decimal digits (possibly containing a + decimal separator at position nd0, which is ignored) to a Bigint. This + function carries on where the parsing code in _Py_dg_strtod leaves off: on + entry, y9 contains the result of converting the first 9 digits. Returns + NULL on failure. */ + +static Bigint * +s2b(const char *s, int nd0, int nd, ULong y9, int dplen) +{ + Bigint *b; + int i, k; + Long x, y; + + x = (nd + 8) / 9; + for(k = 0, y = 1; x > y; y <<= 1, k++) ; + b = Balloc(k); + if (b == NULL) + return NULL; + b->x[0] = y9; + b->wds = 1; + + i = 9; + if (9 < nd0) { + s += 9; + do { + b = multadd(b, 10, *s++ - '0'); + if (b == NULL) + return NULL; + } while(++i < nd0); + s += dplen; + } + else + s += dplen + 9; + for(; i < nd; i++) { + b = multadd(b, 10, *s++ - '0'); + if (b == NULL) + return NULL; + } + return b; +} + +/* count leading 0 bits in the 32-bit integer x. */ + +static int +hi0bits(ULong x) +{ + int k = 0; + + if (!(x & 0xffff0000)) { + k = 16; + x <<= 16; + } + if (!(x & 0xff000000)) { + k += 8; + x <<= 8; + } + if (!(x & 0xf0000000)) { + k += 4; + x <<= 4; + } + if (!(x & 0xc0000000)) { + k += 2; + x <<= 2; + } + if (!(x & 0x80000000)) { + k++; + if (!(x & 0x40000000)) + return 32; + } + return k; +} + +/* count trailing 0 bits in the 32-bit integer y, and shift y right by that + number of bits. */ + +static int +lo0bits(ULong *y) +{ + int k; + ULong x = *y; + + if (x & 7) { + if (x & 1) + return 0; + if (x & 2) { + *y = x >> 1; + return 1; + } + *y = x >> 2; + return 2; + } + k = 0; + if (!(x & 0xffff)) { + k = 16; + x >>= 16; + } + if (!(x & 0xff)) { + k += 8; + x >>= 8; + } + if (!(x & 0xf)) { + k += 4; + x >>= 4; + } + if (!(x & 0x3)) { + k += 2; + x >>= 2; + } + if (!(x & 1)) { + k++; + x >>= 1; + if (!x) + return 32; + } + *y = x; + return k; +} + +/* convert a small nonnegative integer to a Bigint */ + +static Bigint * +i2b(int i) +{ + Bigint *b; + + b = Balloc(1); + if (b == NULL) + return NULL; + b->x[0] = i; + b->wds = 1; + return b; +} + +/* multiply two Bigints. Returns a new Bigint, or NULL on failure. Ignores + the signs of a and b. */ + +static Bigint * +mult(Bigint *a, Bigint *b) +{ + Bigint *c; + int k, wa, wb, wc; + ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0; + ULong y; +#ifdef ULLong + ULLong carry, z; +#else + ULong carry, z; + ULong z2; +#endif + + if (a->wds < b->wds) { + c = a; + a = b; + b = c; + } + k = a->k; + wa = a->wds; + wb = b->wds; + wc = wa + wb; + if (wc > a->maxwds) + k++; + c = Balloc(k); + if (c == NULL) + return NULL; + for(x = c->x, xa = x + wc; x < xa; x++) + *x = 0; + xa = a->x; + xae = xa + wa; + xb = b->x; + xbe = xb + wb; + xc0 = c->x; +#ifdef ULLong + for(; xb < xbe; xc0++) { + if ((y = *xb++)) { + x = xa; + xc = xc0; + carry = 0; + do { + z = *x++ * (ULLong)y + *xc + carry; + carry = z >> 32; + *xc++ = z & FFFFFFFF; + } + while(x < xae); + *xc = (ULong)carry; + } + } +#else + for(; xb < xbe; xb++, xc0++) { + if (y = *xb & 0xffff) { + x = xa; + xc = xc0; + carry = 0; + do { + z = (*x & 0xffff) * y + (*xc & 0xffff) + carry; + carry = z >> 16; + z2 = (*x++ >> 16) * y + (*xc >> 16) + carry; + carry = z2 >> 16; + Storeinc(xc, z2, z); + } + while(x < xae); + *xc = carry; + } + if (y = *xb >> 16) { + x = xa; + xc = xc0; + carry = 0; + z2 = *xc; + do { + z = (*x & 0xffff) * y + (*xc >> 16) + carry; + carry = z >> 16; + Storeinc(xc, z, z2); + z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry; + carry = z2 >> 16; + } + while(x < xae); + *xc = z2; + } + } +#endif + for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ; + c->wds = wc; + return c; +} + +/* p5s is a linked list of powers of 5 of the form 5**(2**i), i >= 2 */ + +static Bigint *p5s; + +/* multiply the Bigint b by 5**k. Returns a pointer to the result, or NULL on + failure; if the returned pointer is distinct from b then the original + Bigint b will have been Bfree'd. Ignores the sign of b. */ + +static Bigint * +pow5mult(Bigint *b, int k) +{ + Bigint *b1, *p5, *p51; + int i; + static int p05[3] = { 5, 25, 125 }; + + if ((i = k & 3)) { + b = multadd(b, p05[i-1], 0); + if (b == NULL) + return NULL; + } + + if (!(k >>= 2)) + return b; + p5 = p5s; + if (!p5) { + /* first time */ + p5 = i2b(625); + if (p5 == NULL) { + Bfree(b); + return NULL; + } + p5s = p5; + p5->next = 0; + } + for(;;) { + if (k & 1) { + b1 = mult(b, p5); + Bfree(b); + b = b1; + if (b == NULL) + return NULL; + } + if (!(k >>= 1)) + break; + p51 = p5->next; + if (!p51) { + p51 = mult(p5,p5); + if (p51 == NULL) { + Bfree(b); + return NULL; + } + p51->next = 0; + p5->next = p51; + } + p5 = p51; + } + return b; +} + +/* shift a Bigint b left by k bits. Return a pointer to the shifted result, + or NULL on failure. If the returned pointer is distinct from b then the + original b will have been Bfree'd. Ignores the sign of b. */ + +static Bigint * +lshift(Bigint *b, int k) +{ + int i, k1, n, n1; + Bigint *b1; + ULong *x, *x1, *xe, z; + + n = k >> 5; + k1 = b->k; + n1 = n + b->wds + 1; + for(i = b->maxwds; n1 > i; i <<= 1) + k1++; + b1 = Balloc(k1); + if (b1 == NULL) { + Bfree(b); + return NULL; + } + x1 = b1->x; + for(i = 0; i < n; i++) + *x1++ = 0; + x = b->x; + xe = x + b->wds; + if (k &= 0x1f) { + k1 = 32 - k; + z = 0; + do { + *x1++ = *x << k | z; + z = *x++ >> k1; + } + while(x < xe); + if ((*x1 = z)) + ++n1; + } + else do + *x1++ = *x++; + while(x < xe); + b1->wds = n1 - 1; + Bfree(b); + return b1; +} + +/* Do a three-way compare of a and b, returning -1 if a < b, 0 if a == b and + 1 if a > b. Ignores signs of a and b. */ + +static int +cmp(Bigint *a, Bigint *b) +{ + ULong *xa, *xa0, *xb, *xb0; + int i, j; + + i = a->wds; + j = b->wds; +#ifdef DEBUG + if (i > 1 && !a->x[i-1]) + Bug("cmp called with a->x[a->wds-1] == 0"); + if (j > 1 && !b->x[j-1]) + Bug("cmp called with b->x[b->wds-1] == 0"); +#endif + if (i -= j) + return i; + xa0 = a->x; + xa = xa0 + j; + xb0 = b->x; + xb = xb0 + j; + for(;;) { + if (*--xa != *--xb) + return *xa < *xb ? -1 : 1; + if (xa <= xa0) + break; + } + return 0; +} + +/* Take the difference of Bigints a and b, returning a new Bigint. Returns + NULL on failure. The signs of a and b are ignored, but the sign of the + result is set appropriately. */ + +static Bigint * +diff(Bigint *a, Bigint *b) +{ + Bigint *c; + int i, wa, wb; + ULong *xa, *xae, *xb, *xbe, *xc; +#ifdef ULLong + ULLong borrow, y; +#else + ULong borrow, y; + ULong z; +#endif + + i = cmp(a,b); + if (!i) { + c = Balloc(0); + if (c == NULL) + return NULL; + c->wds = 1; + c->x[0] = 0; + return c; + } + if (i < 0) { + c = a; + a = b; + b = c; + i = 1; + } + else + i = 0; + c = Balloc(a->k); + if (c == NULL) + return NULL; + c->sign = i; + wa = a->wds; + xa = a->x; + xae = xa + wa; + wb = b->wds; + xb = b->x; + xbe = xb + wb; + xc = c->x; + borrow = 0; +#ifdef ULLong + do { + y = (ULLong)*xa++ - *xb++ - borrow; + borrow = y >> 32 & (ULong)1; + *xc++ = y & FFFFFFFF; + } + while(xb < xbe); + while(xa < xae) { + y = *xa++ - borrow; + borrow = y >> 32 & (ULong)1; + *xc++ = y & FFFFFFFF; + } +#else + do { + y = (*xa & 0xffff) - (*xb & 0xffff) - borrow; + borrow = (y & 0x10000) >> 16; + z = (*xa++ >> 16) - (*xb++ >> 16) - borrow; + borrow = (z & 0x10000) >> 16; + Storeinc(xc, z, y); + } + while(xb < xbe); + while(xa < xae) { + y = (*xa & 0xffff) - borrow; + borrow = (y & 0x10000) >> 16; + z = (*xa++ >> 16) - borrow; + borrow = (z & 0x10000) >> 16; + Storeinc(xc, z, y); + } +#endif + while(!*--xc) + wa--; + c->wds = wa; + return c; +} + +/* Given a positive normal double x, return the difference between x and the next + double up. Doesn't give correct results for subnormals. */ + +static double +ulp(U *x) +{ + Long L; + U u; + + L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1; + word0(&u) = L; + word1(&u) = 0; + return dval(&u); +} + +/* Convert a Bigint to a double plus an exponent */ + +static double +b2d(Bigint *a, int *e) +{ + ULong *xa, *xa0, w, y, z; + int k; + U d; + + xa0 = a->x; + xa = xa0 + a->wds; + y = *--xa; +#ifdef DEBUG + if (!y) Bug("zero y in b2d"); +#endif + k = hi0bits(y); + *e = 32 - k; + if (k < Ebits) { + word0(&d) = Exp_1 | y >> (Ebits - k); + w = xa > xa0 ? *--xa : 0; + word1(&d) = y << ((32-Ebits) + k) | w >> (Ebits - k); + goto ret_d; + } + z = xa > xa0 ? *--xa : 0; + if (k -= Ebits) { + word0(&d) = Exp_1 | y << k | z >> (32 - k); + y = xa > xa0 ? *--xa : 0; + word1(&d) = z << k | y >> (32 - k); + } + else { + word0(&d) = Exp_1 | y; + word1(&d) = z; + } + ret_d: + return dval(&d); +} + +/* Convert a double to a Bigint plus an exponent. Return NULL on failure. + + Given a finite nonzero double d, return an odd Bigint b and exponent *e + such that fabs(d) = b * 2**e. On return, *bbits gives the number of + significant bits of e; that is, 2**(*bbits-1) <= b < 2**(*bbits). + + If d is zero, then b == 0, *e == -1010, *bbits = 0. + */ + + +static Bigint * +d2b(U *d, int *e, int *bits) +{ + Bigint *b; + int de, k; + ULong *x, y, z; + int i; + + b = Balloc(1); + if (b == NULL) + return NULL; + x = b->x; + + z = word0(d) & Frac_mask; + word0(d) &= 0x7fffffff; /* clear sign bit, which we ignore */ + if ((de = (int)(word0(d) >> Exp_shift))) + z |= Exp_msk1; + if ((y = word1(d))) { + if ((k = lo0bits(&y))) { + x[0] = y | z << (32 - k); + z >>= k; + } + else + x[0] = y; + i = + b->wds = (x[1] = z) ? 2 : 1; + } + else { + k = lo0bits(&z); + x[0] = z; + i = + b->wds = 1; + k += 32; + } + if (de) { + *e = de - Bias - (P-1) + k; + *bits = P - k; + } + else { + *e = de - Bias - (P-1) + 1 + k; + *bits = 32*i - hi0bits(x[i-1]); + } + return b; +} + +/* Compute the ratio of two Bigints, as a double. The result may have an + error of up to 2.5 ulps. */ + +static double +ratio(Bigint *a, Bigint *b) +{ + U da, db; + int k, ka, kb; + + dval(&da) = b2d(a, &ka); + dval(&db) = b2d(b, &kb); + k = ka - kb + 32*(a->wds - b->wds); + if (k > 0) + word0(&da) += k*Exp_msk1; + else { + k = -k; + word0(&db) += k*Exp_msk1; + } + return dval(&da) / dval(&db); +} + +static const double +tens[] = { + 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, + 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, + 1e20, 1e21, 1e22 +}; + +static const double +bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 }; +static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, + 9007199254740992.*9007199254740992.e-256 + /* = 2^106 * 1e-256 */ +}; +/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */ +/* flag unnecessarily. It leads to a song and dance at the end of strtod. */ +#define Scale_Bit 0x10 +#define n_bigtens 5 + +/* case insensitive string match, for recognising 'inf[inity]' and + 'nan' strings. */ + +static int +match(const char **sp, char *t) +{ + int c, d; + const char *s = *sp; + + while((d = *t++)) { + if ((c = *++s) >= 'A' && c <= 'Z') + c += 'a' - 'A'; + if (c != d) + return 0; + } + *sp = s + 1; + return 1; +} + +#define ULbits 32 +#define kshift 5 +#define kmask 31 + + +static int +dshift(Bigint *b, int p2) +{ + int rv = hi0bits(b->x[b->wds-1]) - 4; + if (p2 > 0) + rv -= p2; + return rv & kmask; +} + +/* special case of Bigint division. The quotient is always in the range 0 <= + quotient < 10, and on entry the divisor S is normalized so that its top 4 + bits (28--31) are zero and bit 27 is set. */ + +static int +quorem(Bigint *b, Bigint *S) +{ + int n; + ULong *bx, *bxe, q, *sx, *sxe; +#ifdef ULLong + ULLong borrow, carry, y, ys; +#else + ULong borrow, carry, y, ys; + ULong si, z, zs; +#endif + + n = S->wds; +#ifdef DEBUG + /*debug*/ if (b->wds > n) + /*debug*/ Bug("oversize b in quorem"); +#endif + if (b->wds < n) + return 0; + sx = S->x; + sxe = sx + --n; + bx = b->x; + bxe = bx + n; + q = *bxe / (*sxe + 1); /* ensure q <= true quotient */ +#ifdef DEBUG + /*debug*/ if (q > 9) + /*debug*/ Bug("oversized quotient in quorem"); +#endif + if (q) { + borrow = 0; + carry = 0; + do { +#ifdef ULLong + ys = *sx++ * (ULLong)q + carry; + carry = ys >> 32; + y = *bx - (ys & FFFFFFFF) - borrow; + borrow = y >> 32 & (ULong)1; + *bx++ = y & FFFFFFFF; +#else + si = *sx++; + ys = (si & 0xffff) * q + carry; + zs = (si >> 16) * q + (ys >> 16); + carry = zs >> 16; + y = (*bx & 0xffff) - (ys & 0xffff) - borrow; + borrow = (y & 0x10000) >> 16; + z = (*bx >> 16) - (zs & 0xffff) - borrow; + borrow = (z & 0x10000) >> 16; + Storeinc(bx, z, y); +#endif + } + while(sx <= sxe); + if (!*bxe) { + bx = b->x; + while(--bxe > bx && !*bxe) + --n; + b->wds = n; + } + } + if (cmp(b, S) >= 0) { + q++; + borrow = 0; + carry = 0; + bx = b->x; + sx = S->x; + do { +#ifdef ULLong + ys = *sx++ + carry; + carry = ys >> 32; + y = *bx - (ys & FFFFFFFF) - borrow; + borrow = y >> 32 & (ULong)1; + *bx++ = y & FFFFFFFF; +#else + si = *sx++; + ys = (si & 0xffff) + carry; + zs = (si >> 16) + (ys >> 16); + carry = zs >> 16; + y = (*bx & 0xffff) - (ys & 0xffff) - borrow; + borrow = (y & 0x10000) >> 16; + z = (*bx >> 16) - (zs & 0xffff) - borrow; + borrow = (z & 0x10000) >> 16; + Storeinc(bx, z, y); +#endif + } + while(sx <= sxe); + bx = b->x; + bxe = bx + n; + if (!*bxe) { + while(--bxe > bx && !*bxe) + --n; + b->wds = n; + } + } + return q; +} + + +/* return 0 on success, -1 on failure */ + +static int +bigcomp(U *rv, const char *s0, BCinfo *bc) +{ + Bigint *b, *d; + int b2, bbits, d2, dd, dig, dsign, i, j, nd, nd0, p2, p5, speccase; + + dsign = bc->dsign; + nd = bc->nd; + nd0 = bc->nd0; + p5 = nd + bc->e0 - 1; + speccase = 0; + if (rv->d == 0.) { /* special case: value near underflow-to-zero */ + /* threshold was rounded to zero */ + b = i2b(1); + if (b == NULL) + return -1; + p2 = Emin - P + 1; + bbits = 1; + word0(rv) = (P+2) << Exp_shift; + i = 0; + { + speccase = 1; + --p2; + dsign = 0; + goto have_i; + } + } + else + { + b = d2b(rv, &p2, &bbits); + if (b == NULL) + return -1; + } + p2 -= bc->scale; + /* floor(log2(rv)) == bbits - 1 + p2 */ + /* Check for denormal case. */ + i = P - bbits; + if (i > (j = P - Emin - 1 + p2)) { + i = j; + } + { + b = lshift(b, ++i); + if (b == NULL) + return -1; + b->x[0] |= 1; + } + have_i: + p2 -= p5 + i; + d = i2b(1); + if (d == NULL) { + Bfree(b); + return -1; + } + /* Arrange for convenient computation of quotients: + * shift left if necessary so divisor has 4 leading 0 bits. + */ + if (p5 > 0) { + d = pow5mult(d, p5); + if (d == NULL) { + Bfree(b); + return -1; + } + } + else if (p5 < 0) { + b = pow5mult(b, -p5); + if (b == NULL) { + Bfree(d); + return -1; + } + } + if (p2 > 0) { + b2 = p2; + d2 = 0; + } + else { + b2 = 0; + d2 = -p2; + } + i = dshift(d, d2); + if ((b2 += i) > 0) { + b = lshift(b, b2); + if (b == NULL) { + Bfree(d); + return -1; + } + } + if ((d2 += i) > 0) { + d = lshift(d, d2); + if (d == NULL) { + Bfree(b); + return -1; + } + } + + /* Now b/d = exactly half-way between the two floating-point values */ + /* on either side of the input string. Compute first digit of b/d. */ + + if (!(dig = quorem(b,d))) { + b = multadd(b, 10, 0); /* very unlikely */ + if (b == NULL) { + Bfree(d); + return -1; + } + dig = quorem(b,d); + } + + /* Compare b/d with s0 */ + + assert(nd > 0); + dd = 9999; /* silence gcc compiler warning */ + for(i = 0; i < nd0; ) { + if ((dd = s0[i++] - '0' - dig)) + goto ret; + if (!b->x[0] && b->wds == 1) { + if (i < nd) + dd = 1; + goto ret; + } + b = multadd(b, 10, 0); + if (b == NULL) { + Bfree(d); + return -1; + } + dig = quorem(b,d); + } + for(j = bc->dp1; i++ < nd;) { + if ((dd = s0[j++] - '0' - dig)) + goto ret; + if (!b->x[0] && b->wds == 1) { + if (i < nd) + dd = 1; + goto ret; + } + b = multadd(b, 10, 0); + if (b == NULL) { + Bfree(d); + return -1; + } + dig = quorem(b,d); + } + if (b->x[0] || b->wds > 1) + dd = -1; + ret: + Bfree(b); + Bfree(d); + if (speccase) { + if (dd <= 0) + rv->d = 0.; + } + else if (dd < 0) { + if (!dsign) /* does not happen for round-near */ + retlow1: + dval(rv) -= ulp(rv); + } + else if (dd > 0) { + if (dsign) { + rethi1: + dval(rv) += ulp(rv); + } + } + else { + /* Exact half-way case: apply round-even rule. */ + if (word1(rv) & 1) { + if (dsign) + goto rethi1; + goto retlow1; + } + } + + return 0; +} + +double +_Py_dg_strtod(const char *s00, char **se) +{ + int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, e, e1, error; + int esign, i, j, k, nd, nd0, nf, nz, nz0, sign; + const char *s, *s0, *s1; + double aadj, aadj1; + Long L; + U aadj2, adj, rv, rv0; + ULong y, z; + BCinfo bc; + Bigint *bb, *bb1, *bd, *bd0, *bs, *delta; + + sign = nz0 = nz = bc.dplen = bc.uflchk = 0; + dval(&rv) = 0.; + for(s = s00;;s++) switch(*s) { + case '-': + sign = 1; + /* no break */ + case '+': + if (*++s) + goto break2; + /* no break */ + case 0: + goto ret0; + case '\t': + case '\n': + case '\v': + case '\f': + case '\r': + case ' ': + continue; + default: + goto break2; + } + break2: + if (*s == '0') { + nz0 = 1; + while(*++s == '0') ; + if (!*s) + goto ret; + } + s0 = s; + y = z = 0; + for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++) + if (nd < 9) + y = 10*y + c - '0'; + else if (nd < 16) + z = 10*z + c - '0'; + nd0 = nd; + bc.dp0 = bc.dp1 = s - s0; + if (c == '.') { + c = *++s; + bc.dp1 = s - s0; + bc.dplen = bc.dp1 - bc.dp0; + if (!nd) { + for(; c == '0'; c = *++s) + nz++; + if (c > '0' && c <= '9') { + s0 = s; + nf += nz; + nz = 0; + goto have_dig; + } + goto dig_done; + } + for(; c >= '0' && c <= '9'; c = *++s) { + have_dig: + nz++; + if (c -= '0') { + nf += nz; + for(i = 1; i < nz; i++) + if (nd++ < 9) + y *= 10; + else if (nd <= DBL_DIG + 1) + z *= 10; + if (nd++ < 9) + y = 10*y + c; + else if (nd <= DBL_DIG + 1) + z = 10*z + c; + nz = 0; + } + } + } + dig_done: + e = 0; + if (c == 'e' || c == 'E') { + if (!nd && !nz && !nz0) { + goto ret0; + } + s00 = s; + esign = 0; + switch(c = *++s) { + case '-': + esign = 1; + case '+': + c = *++s; + } + if (c >= '0' && c <= '9') { + while(c == '0') + c = *++s; + if (c > '0' && c <= '9') { + L = c - '0'; + s1 = s; + while((c = *++s) >= '0' && c <= '9') + L = 10*L + c - '0'; + if (s - s1 > 8 || L > 19999) + /* Avoid confusion from exponents + * so large that e might overflow. + */ + e = 19999; /* safe for 16 bit ints */ + else + e = (int)L; + if (esign) + e = -e; + } + else + e = 0; + } + else + s = s00; + } + if (!nd) { + if (!nz && !nz0) { + /* Check for Nan and Infinity */ + if (!bc.dplen) + switch(c) { + case 'i': + case 'I': + if (match(&s,"nf")) { + --s; + if (!match(&s,"inity")) + ++s; + word0(&rv) = 0x7ff00000; + word1(&rv) = 0; + goto ret; + } + break; + case 'n': + case 'N': + if (match(&s, "an")) { + word0(&rv) = NAN_WORD0; + word1(&rv) = NAN_WORD1; + goto ret; + } + } + ret0: + s = s00; + sign = 0; + } + goto ret; + } + bc.e0 = e1 = e -= nf; + + /* Now we have nd0 digits, starting at s0, followed by a + * decimal point, followed by nd-nd0 digits. The number we're + * after is the integer represented by those digits times + * 10**e */ + + if (!nd0) + nd0 = nd; + k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1; + dval(&rv) = y; + if (k > 9) { + dval(&rv) = tens[k - 9] * dval(&rv) + z; + } + bd0 = 0; + if (nd <= DBL_DIG + && Flt_Rounds == 1 + ) { + if (!e) + goto ret; + if (e > 0) { + if (e <= Ten_pmax) { + dval(&rv) *= tens[e]; + goto ret; + } + i = DBL_DIG - nd; + if (e <= Ten_pmax + i) { + /* A fancier test would sometimes let us do + * this for larger i values. + */ + e -= i; + dval(&rv) *= tens[i]; + dval(&rv) *= tens[e]; + goto ret; + } + } + else if (e >= -Ten_pmax) { + dval(&rv) /= tens[-e]; + goto ret; + } + } + e1 += nd - k; + + bc.scale = 0; + + /* Get starting approximation = rv * 10**e1 */ + + if (e1 > 0) { + if ((i = e1 & 15)) + dval(&rv) *= tens[i]; + if (e1 &= ~15) { + if (e1 > DBL_MAX_10_EXP) { + ovfl: + errno = ERANGE; + /* Can't trust HUGE_VAL */ + word0(&rv) = Exp_mask; + word1(&rv) = 0; + goto ret; + } + e1 >>= 4; + for(j = 0; e1 > 1; j++, e1 >>= 1) + if (e1 & 1) + dval(&rv) *= bigtens[j]; + /* The last multiplication could overflow. */ + word0(&rv) -= P*Exp_msk1; + dval(&rv) *= bigtens[j]; + if ((z = word0(&rv) & Exp_mask) + > Exp_msk1*(DBL_MAX_EXP+Bias-P)) + goto ovfl; + if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) { + /* set to largest number */ + /* (Can't trust DBL_MAX) */ + word0(&rv) = Big0; + word1(&rv) = Big1; + } + else + word0(&rv) += P*Exp_msk1; + } + } + else if (e1 < 0) { + e1 = -e1; + if ((i = e1 & 15)) + dval(&rv) /= tens[i]; + if (e1 >>= 4) { + if (e1 >= 1 << n_bigtens) + goto undfl; + if (e1 & Scale_Bit) + bc.scale = 2*P; + for(j = 0; e1 > 0; j++, e1 >>= 1) + if (e1 & 1) + dval(&rv) *= tinytens[j]; + if (bc.scale && (j = 2*P + 1 - ((word0(&rv) & Exp_mask) + >> Exp_shift)) > 0) { + /* scaled rv is denormal; clear j low bits */ + if (j >= 32) { + word1(&rv) = 0; + if (j >= 53) + word0(&rv) = (P+2)*Exp_msk1; + else + word0(&rv) &= 0xffffffff << (j-32); + } + else + word1(&rv) &= 0xffffffff << j; + } + if (!dval(&rv)) { + undfl: + dval(&rv) = 0.; + errno = ERANGE; + goto ret; + } + } + } + + /* Now the hard part -- adjusting rv to the correct value.*/ + + /* Put digits into bd: true value = bd * 10^e */ + + bc.nd = nd; + bc.nd0 = nd0; /* Only needed if nd > strtod_diglim, but done here */ + /* to silence an erroneous warning about bc.nd0 */ + /* possibly not being initialized. */ + if (nd > strtod_diglim) { + /* ASSERT(strtod_diglim >= 18); 18 == one more than the */ + /* minimum number of decimal digits to distinguish double values */ + /* in IEEE arithmetic. */ + i = j = 18; + if (i > nd0) + j += bc.dplen; + for(;;) { + if (--j <= bc.dp1 && j >= bc.dp0) + j = bc.dp0 - 1; + if (s0[j] != '0') + break; + --i; + } + e += nd - i; + nd = i; + if (nd0 > nd) + nd0 = nd; + if (nd < 9) { /* must recompute y */ + y = 0; + for(i = 0; i < nd0; ++i) + y = 10*y + s0[i] - '0'; + for(j = bc.dp1; i < nd; ++i) + y = 10*y + s0[j++] - '0'; + } + } + bd0 = s2b(s0, nd0, nd, y, bc.dplen); + if (bd0 == NULL) + goto failed_malloc; + + for(;;) { + bd = Balloc(bd0->k); + if (bd == NULL) { + Bfree(bd0); + goto failed_malloc; + } + Bcopy(bd, bd0); + bb = d2b(&rv, &bbe, &bbbits); /* rv = bb * 2^bbe */ + if (bb == NULL) { + Bfree(bd); + Bfree(bd0); + goto failed_malloc; + } + bs = i2b(1); + if (bs == NULL) { + Bfree(bb); + Bfree(bd); + Bfree(bd0); + goto failed_malloc; + } + + if (e >= 0) { + bb2 = bb5 = 0; + bd2 = bd5 = e; + } + else { + bb2 = bb5 = -e; + bd2 = bd5 = 0; + } + if (bbe >= 0) + bb2 += bbe; + else + bd2 -= bbe; + bs2 = bb2; + j = bbe - bc.scale; + i = j + bbbits - 1; /* logb(rv) */ + if (i < Emin) /* denormal */ + j += P - Emin; + else + j = P + 1 - bbbits; + bb2 += j; + bd2 += j; + bd2 += bc.scale; + i = bb2 < bd2 ? bb2 : bd2; + if (i > bs2) + i = bs2; + if (i > 0) { + bb2 -= i; + bd2 -= i; + bs2 -= i; + } + if (bb5 > 0) { + bs = pow5mult(bs, bb5); + if (bs == NULL) { + Bfree(bb); + Bfree(bd); + Bfree(bd0); + goto failed_malloc; + } + bb1 = mult(bs, bb); + Bfree(bb); + bb = bb1; + if (bb == NULL) { + Bfree(bs); + Bfree(bd); + Bfree(bd0); + goto failed_malloc; + } + } + if (bb2 > 0) { + bb = lshift(bb, bb2); + if (bb == NULL) { + Bfree(bs); + Bfree(bd); + Bfree(bd0); + goto failed_malloc; + } + } + if (bd5 > 0) { + bd = pow5mult(bd, bd5); + if (bd == NULL) { + Bfree(bb); + Bfree(bs); + Bfree(bd0); + goto failed_malloc; + } + } + if (bd2 > 0) { + bd = lshift(bd, bd2); + if (bd == NULL) { + Bfree(bb); + Bfree(bs); + Bfree(bd0); + goto failed_malloc; + } + } + if (bs2 > 0) { + bs = lshift(bs, bs2); + if (bs == NULL) { + Bfree(bb); + Bfree(bd); + Bfree(bd0); + goto failed_malloc; + } + } + delta = diff(bb, bd); + if (delta == NULL) { + Bfree(bb); + Bfree(bs); + Bfree(bd); + Bfree(bd0); + goto failed_malloc; + } + bc.dsign = delta->sign; + delta->sign = 0; + i = cmp(delta, bs); + if (bc.nd > nd && i <= 0) { + if (bc.dsign) + break; /* Must use bigcomp(). */ + { + bc.nd = nd; + i = -1; /* Discarded digits make delta smaller. */ + } + } + + if (i < 0) { + /* Error is less than half an ulp -- check for + * special case of mantissa a power of two. + */ + if (bc.dsign || word1(&rv) || word0(&rv) & Bndry_mask + || (word0(&rv) & Exp_mask) <= (2*P+1)*Exp_msk1 + ) { + break; + } + if (!delta->x[0] && delta->wds <= 1) { + /* exact result */ + break; + } + delta = lshift(delta,Log2P); + if (delta == NULL) { + Bfree(bb); + Bfree(bs); + Bfree(bd); + Bfree(bd0); + goto failed_malloc; + } + if (cmp(delta, bs) > 0) + goto drop_down; + break; + } + if (i == 0) { + /* exactly half-way between */ + if (bc.dsign) { + if ((word0(&rv) & Bndry_mask1) == Bndry_mask1 + && word1(&rv) == ( + (bc.scale && + (y = word0(&rv) & Exp_mask) <= 2*P*Exp_msk1) ? + (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) : + 0xffffffff)) { + /*boundary case -- increment exponent*/ + word0(&rv) = (word0(&rv) & Exp_mask) + + Exp_msk1 + ; + word1(&rv) = 0; + bc.dsign = 0; + break; + } + } + else if (!(word0(&rv) & Bndry_mask) && !word1(&rv)) { + drop_down: + /* boundary case -- decrement exponent */ + if (bc.scale) { + L = word0(&rv) & Exp_mask; + if (L <= (2*P+1)*Exp_msk1) { + if (L > (P+2)*Exp_msk1) + /* round even ==> */ + /* accept rv */ + break; + /* rv = smallest denormal */ + if (bc.nd >nd) { + bc.uflchk = 1; + break; + } + goto undfl; + } + } + L = (word0(&rv) & Exp_mask) - Exp_msk1; + word0(&rv) = L | Bndry_mask1; + word1(&rv) = 0xffffffff; + break; + } + if (!(word1(&rv) & LSB)) + break; + if (bc.dsign) + dval(&rv) += ulp(&rv); + else { + dval(&rv) -= ulp(&rv); + if (!dval(&rv)) { + if (bc.nd >nd) { + bc.uflchk = 1; + break; + } + goto undfl; + } + } + bc.dsign = 1 - bc.dsign; + break; + } + if ((aadj = ratio(delta, bs)) <= 2.) { + if (bc.dsign) + aadj = aadj1 = 1.; + else if (word1(&rv) || word0(&rv) & Bndry_mask) { + if (word1(&rv) == Tiny1 && !word0(&rv)) { + if (bc.nd >nd) { + bc.uflchk = 1; + break; + } + goto undfl; + } + aadj = 1.; + aadj1 = -1.; + } + else { + /* special case -- power of FLT_RADIX to be */ + /* rounded down... */ + + if (aadj < 2./FLT_RADIX) + aadj = 1./FLT_RADIX; + else + aadj *= 0.5; + aadj1 = -aadj; + } + } + else { + aadj *= 0.5; + aadj1 = bc.dsign ? aadj : -aadj; + if (Flt_Rounds == 0) + aadj1 += 0.5; + } + y = word0(&rv) & Exp_mask; + + /* Check for overflow */ + + if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) { + dval(&rv0) = dval(&rv); + word0(&rv) -= P*Exp_msk1; + adj.d = aadj1 * ulp(&rv); + dval(&rv) += adj.d; + if ((word0(&rv) & Exp_mask) >= + Exp_msk1*(DBL_MAX_EXP+Bias-P)) { + if (word0(&rv0) == Big0 && word1(&rv0) == Big1) + goto ovfl; + word0(&rv) = Big0; + word1(&rv) = Big1; + goto cont; + } + else + word0(&rv) += P*Exp_msk1; + } + else { + if (bc.scale && y <= 2*P*Exp_msk1) { + if (aadj <= 0x7fffffff) { + if ((z = (ULong)aadj) <= 0) + z = 1; + aadj = z; + aadj1 = bc.dsign ? aadj : -aadj; + } + dval(&aadj2) = aadj1; + word0(&aadj2) += (2*P+1)*Exp_msk1 - y; + aadj1 = dval(&aadj2); + } + adj.d = aadj1 * ulp(&rv); + dval(&rv) += adj.d; + } + z = word0(&rv) & Exp_mask; + if (bc.nd == nd) { + if (!bc.scale) + if (y == z) { + /* Can we stop now? */ + L = (Long)aadj; + aadj -= L; + /* The tolerances below are conservative. */ + if (bc.dsign || word1(&rv) || word0(&rv) & Bndry_mask) { + if (aadj < .4999999 || aadj > .5000001) + break; + } + else if (aadj < .4999999/FLT_RADIX) + break; + } + } + cont: + Bfree(bb); + Bfree(bd); + Bfree(bs); + Bfree(delta); + } + Bfree(bb); + Bfree(bd); + Bfree(bs); + Bfree(bd0); + Bfree(delta); + if (bc.nd > nd) { + error = bigcomp(&rv, s0, &bc); + if (error) + goto failed_malloc; + } + + if (bc.scale) { + word0(&rv0) = Exp_1 - 2*P*Exp_msk1; + word1(&rv0) = 0; + dval(&rv) *= dval(&rv0); + /* try to avoid the bug of testing an 8087 register value */ + if (!(word0(&rv) & Exp_mask)) + errno = ERANGE; + } + ret: + if (se) + *se = (char *)s; + return sign ? -dval(&rv) : dval(&rv); + + failed_malloc: + if (se) + *se = (char *)s00; + errno = ENOMEM; + return -1.0; +} + +static char * +rv_alloc(int i) +{ + int j, k, *r; + + j = sizeof(ULong); + for(k = 0; + sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (unsigned)i; + j <<= 1) + k++; + r = (int*)Balloc(k); + if (r == NULL) + return NULL; + *r = k; + return (char *)(r+1); +} + +static char * +nrv_alloc(char *s, char **rve, int n) +{ + char *rv, *t; + + rv = rv_alloc(n); + if (rv == NULL) + return NULL; + t = rv; + while((*t = *s++)) t++; + if (rve) + *rve = t; + return rv; +} + +/* freedtoa(s) must be used to free values s returned by dtoa + * when MULTIPLE_THREADS is #defined. It should be used in all cases, + * but for consistency with earlier versions of dtoa, it is optional + * when MULTIPLE_THREADS is not defined. + */ + +void +_Py_dg_freedtoa(char *s) +{ + Bigint *b = (Bigint *)((int *)s - 1); + b->maxwds = 1 << (b->k = *(int*)b); + Bfree(b); +} + +/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string. + * + * Inspired by "How to Print Floating-Point Numbers Accurately" by + * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126]. + * + * Modifications: + * 1. Rather than iterating, we use a simple numeric overestimate + * to determine k = floor(log10(d)). We scale relevant + * quantities using O(log2(k)) rather than O(k) multiplications. + * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't + * try to generate digits strictly left to right. Instead, we + * compute with fewer bits and propagate the carry if necessary + * when rounding the final digit up. This is often faster. + * 3. Under the assumption that input will be rounded nearest, + * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22. + * That is, we allow equality in stopping tests when the + * round-nearest rule will give the same floating-point value + * as would satisfaction of the stopping test with strict + * inequality. + * 4. We remove common factors of powers of 2 from relevant + * quantities. + * 5. When converting floating-point integers less than 1e16, + * we use floating-point arithmetic rather than resorting + * to multiple-precision integers. + * 6. When asked to produce fewer than 15 digits, we first try + * to get by with floating-point arithmetic; we resort to + * multiple-precision integer arithmetic only if we cannot + * guarantee that the floating-point calculation has given + * the correctly rounded result. For k requested digits and + * "uniformly" distributed input, the probability is + * something like 10^(k-15) that we must resort to the Long + * calculation. + */ + +/* Additional notes (METD): (1) returns NULL on failure. (2) to avoid memory + leakage, a successful call to _Py_dg_dtoa should always be matched by a + call to _Py_dg_freedtoa. */ + +char * +_Py_dg_dtoa(double dd, int mode, int ndigits, + int *decpt, int *sign, char **rve) +{ + /* Arguments ndigits, decpt, sign are similar to those + of ecvt and fcvt; trailing zeros are suppressed from + the returned string. If not null, *rve is set to point + to the end of the return value. If d is +-Infinity or NaN, + then *decpt is set to 9999. + + mode: + 0 ==> shortest string that yields d when read in + and rounded to nearest. + 1 ==> like 0, but with Steele & White stopping rule; + e.g. with IEEE P754 arithmetic , mode 0 gives + 1e23 whereas mode 1 gives 9.999999999999999e22. + 2 ==> max(1,ndigits) significant digits. This gives a + return value similar to that of ecvt, except + that trailing zeros are suppressed. + 3 ==> through ndigits past the decimal point. This + gives a return value similar to that from fcvt, + except that trailing zeros are suppressed, and + ndigits can be negative. + 4,5 ==> similar to 2 and 3, respectively, but (in + round-nearest mode) with the tests of mode 0 to + possibly return a shorter string that rounds to d. + With IEEE arithmetic and compilation with + -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same + as modes 2 and 3 when FLT_ROUNDS != 1. + 6-9 ==> Debugging modes similar to mode - 4: don't try + fast floating-point estimate (if applicable). + + Values of mode other than 0-9 are treated as mode 0. + + Sufficient space is allocated to the return value + to hold the suppressed trailing zeros. + */ + + int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1, + j, j1, k, k0, k_check, leftright, m2, m5, s2, s5, + spec_case, try_quick; + Long L; + int denorm; + ULong x; + Bigint *b, *b1, *delta, *mlo, *mhi, *S; + U d2, eps, u; + double ds; + char *s, *s0; + + /* set pointers to NULL, to silence gcc compiler warnings and make + cleanup easier on error */ + mlo = mhi = b = S = 0; + s0 = 0; + + u.d = dd; + if (word0(&u) & Sign_bit) { + /* set sign for everything, including 0's and NaNs */ + *sign = 1; + word0(&u) &= ~Sign_bit; /* clear sign bit */ + } + else + *sign = 0; + + /* quick return for Infinities, NaNs and zeros */ + if ((word0(&u) & Exp_mask) == Exp_mask) + { + /* Infinity or NaN */ + *decpt = 9999; + if (!word1(&u) && !(word0(&u) & 0xfffff)) + return nrv_alloc("Infinity", rve, 8); + return nrv_alloc("NaN", rve, 3); + } + if (!dval(&u)) { + *decpt = 1; + return nrv_alloc("0", rve, 1); + } + + /* compute k = floor(log10(d)). The computation may leave k + one too large, but should never leave k too small. */ + b = d2b(&u, &be, &bbits); + if (b == NULL) + goto failed_malloc; + if ((i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) { + dval(&d2) = dval(&u); + word0(&d2) &= Frac_mask1; + word0(&d2) |= Exp_11; + + /* log(x) ~=~ log(1.5) + (x-1.5)/1.5 + * log10(x) = log(x) / log(10) + * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10)) + * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2) + * + * This suggests computing an approximation k to log10(d) by + * + * k = (i - Bias)*0.301029995663981 + * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 ); + * + * We want k to be too large rather than too small. + * The error in the first-order Taylor series approximation + * is in our favor, so we just round up the constant enough + * to compensate for any error in the multiplication of + * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077, + * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14, + * adding 1e-13 to the constant term more than suffices. + * Hence we adjust the constant term to 0.1760912590558. + * (We could get a more accurate k by invoking log10, + * but this is probably not worthwhile.) + */ + + i -= Bias; + denorm = 0; + } + else { + /* d is denormalized */ + + i = bbits + be + (Bias + (P-1) - 1); + x = i > 32 ? word0(&u) << (64 - i) | word1(&u) >> (i - 32) + : word1(&u) << (32 - i); + dval(&d2) = x; + word0(&d2) -= 31*Exp_msk1; /* adjust exponent */ + i -= (Bias + (P-1) - 1) + 1; + denorm = 1; + } + ds = (dval(&d2)-1.5)*0.289529654602168 + 0.1760912590558 + + i*0.301029995663981; + k = (int)ds; + if (ds < 0. && ds != k) + k--; /* want k = floor(ds) */ + k_check = 1; + if (k >= 0 && k <= Ten_pmax) { + if (dval(&u) < tens[k]) + k--; + k_check = 0; + } + j = bbits - i - 1; + if (j >= 0) { + b2 = 0; + s2 = j; + } + else { + b2 = -j; + s2 = 0; + } + if (k >= 0) { + b5 = 0; + s5 = k; + s2 += k; + } + else { + b2 -= k; + b5 = -k; + s5 = 0; + } + if (mode < 0 || mode > 9) + mode = 0; + + try_quick = 1; + + if (mode > 5) { + mode -= 4; + try_quick = 0; + } + leftright = 1; + ilim = ilim1 = -1; /* Values for cases 0 and 1; done here to */ + /* silence erroneous "gcc -Wall" warning. */ + switch(mode) { + case 0: + case 1: + i = 18; + ndigits = 0; + break; + case 2: + leftright = 0; + /* no break */ + case 4: + if (ndigits <= 0) + ndigits = 1; + ilim = ilim1 = i = ndigits; + break; + case 3: + leftright = 0; + /* no break */ + case 5: + i = ndigits + k + 1; + ilim = i; + ilim1 = i - 1; + if (i <= 0) + i = 1; + } + s0 = rv_alloc(i); + if (s0 == NULL) + goto failed_malloc; + s = s0; + + + if (ilim >= 0 && ilim <= Quick_max && try_quick) { + + /* Try to get by with floating-point arithmetic. */ + + i = 0; + dval(&d2) = dval(&u); + k0 = k; + ilim0 = ilim; + ieps = 2; /* conservative */ + if (k > 0) { + ds = tens[k&0xf]; + j = k >> 4; + if (j & Bletch) { + /* prevent overflows */ + j &= Bletch - 1; + dval(&u) /= bigtens[n_bigtens-1]; + ieps++; + } + for(; j; j >>= 1, i++) + if (j & 1) { + ieps++; + ds *= bigtens[i]; + } + dval(&u) /= ds; + } + else if ((j1 = -k)) { + dval(&u) *= tens[j1 & 0xf]; + for(j = j1 >> 4; j; j >>= 1, i++) + if (j & 1) { + ieps++; + dval(&u) *= bigtens[i]; + } + } + if (k_check && dval(&u) < 1. && ilim > 0) { + if (ilim1 <= 0) + goto fast_failed; + ilim = ilim1; + k--; + dval(&u) *= 10.; + ieps++; + } + dval(&eps) = ieps*dval(&u) + 7.; + word0(&eps) -= (P-1)*Exp_msk1; + if (ilim == 0) { + S = mhi = 0; + dval(&u) -= 5.; + if (dval(&u) > dval(&eps)) + goto one_digit; + if (dval(&u) < -dval(&eps)) + goto no_digits; + goto fast_failed; + } + if (leftright) { + /* Use Steele & White method of only + * generating digits needed. + */ + dval(&eps) = 0.5/tens[ilim-1] - dval(&eps); + for(i = 0;;) { + L = (Long)dval(&u); + dval(&u) -= L; + *s++ = '0' + (int)L; + if (dval(&u) < dval(&eps)) + goto ret1; + if (1. - dval(&u) < dval(&eps)) + goto bump_up; + if (++i >= ilim) + break; + dval(&eps) *= 10.; + dval(&u) *= 10.; + } + } + else { + /* Generate ilim digits, then fix them up. */ + dval(&eps) *= tens[ilim-1]; + for(i = 1;; i++, dval(&u) *= 10.) { + L = (Long)(dval(&u)); + if (!(dval(&u) -= L)) + ilim = i; + *s++ = '0' + (int)L; + if (i == ilim) { + if (dval(&u) > 0.5 + dval(&eps)) + goto bump_up; + else if (dval(&u) < 0.5 - dval(&eps)) { + while(*--s == '0'); + s++; + goto ret1; + } + break; + } + } + } + fast_failed: + s = s0; + dval(&u) = dval(&d2); + k = k0; + ilim = ilim0; + } + + /* Do we have a "small" integer? */ + + if (be >= 0 && k <= Int_max) { + /* Yes. */ + ds = tens[k]; + if (ndigits < 0 && ilim <= 0) { + S = mhi = 0; + if (ilim < 0 || dval(&u) <= 5*ds) + goto no_digits; + goto one_digit; + } + for(i = 1;; i++, dval(&u) *= 10.) { + L = (Long)(dval(&u) / ds); + dval(&u) -= L*ds; + *s++ = '0' + (int)L; + if (!dval(&u)) { + break; + } + if (i == ilim) { + dval(&u) += dval(&u); + if (dval(&u) > ds || (dval(&u) == ds && L & 1)) { + bump_up: + while(*--s == '9') + if (s == s0) { + k++; + *s = '0'; + break; + } + ++*s++; + } + break; + } + } + goto ret1; + } + + m2 = b2; + m5 = b5; + if (leftright) { + i = + denorm ? be + (Bias + (P-1) - 1 + 1) : + 1 + P - bbits; + b2 += i; + s2 += i; + mhi = i2b(1); + if (mhi == NULL) + goto failed_malloc; + } + if (m2 > 0 && s2 > 0) { + i = m2 < s2 ? m2 : s2; + b2 -= i; + m2 -= i; + s2 -= i; + } + if (b5 > 0) { + if (leftright) { + if (m5 > 0) { + mhi = pow5mult(mhi, m5); + if (mhi == NULL) + goto failed_malloc; + b1 = mult(mhi, b); + Bfree(b); + b = b1; + if (b == NULL) + goto failed_malloc; + } + if ((j = b5 - m5)) { + b = pow5mult(b, j); + if (b == NULL) + goto failed_malloc; + } + } + else { + b = pow5mult(b, b5); + if (b == NULL) + goto failed_malloc; + } + } + S = i2b(1); + if (S == NULL) + goto failed_malloc; + if (s5 > 0) { + S = pow5mult(S, s5); + if (S == NULL) + goto failed_malloc; + } + + /* Check for special case that d is a normalized power of 2. */ + + spec_case = 0; + if ((mode < 2 || leftright) + ) { + if (!word1(&u) && !(word0(&u) & Bndry_mask) + && word0(&u) & (Exp_mask & ~Exp_msk1) + ) { + /* The special case */ + b2 += Log2P; + s2 += Log2P; + spec_case = 1; + } + } + + /* Arrange for convenient computation of quotients: + * shift left if necessary so divisor has 4 leading 0 bits. + * + * Perhaps we should just compute leading 28 bits of S once + * and for all and pass them and a shift to quorem, so it + * can do shifts and ors to compute the numerator for q. + */ + if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f)) + i = 32 - i; +#define iInc 28 + i = dshift(S, s2); + b2 += i; + m2 += i; + s2 += i; + if (b2 > 0) { + b = lshift(b, b2); + if (b == NULL) + goto failed_malloc; + } + if (s2 > 0) { + S = lshift(S, s2); + if (S == NULL) + goto failed_malloc; + } + if (k_check) { + if (cmp(b,S) < 0) { + k--; + b = multadd(b, 10, 0); /* we botched the k estimate */ + if (b == NULL) + goto failed_malloc; + if (leftright) { + mhi = multadd(mhi, 10, 0); + if (mhi == NULL) + goto failed_malloc; + } + ilim = ilim1; + } + } + if (ilim <= 0 && (mode == 3 || mode == 5)) { + if (ilim < 0) { + /* no digits, fcvt style */ + no_digits: + k = -1 - ndigits; + goto ret; + } + else { + S = multadd(S, 5, 0); + if (S == NULL) + goto failed_malloc; + if (cmp(b, S) <= 0) + goto no_digits; + } + one_digit: + *s++ = '1'; + k++; + goto ret; + } + if (leftright) { + if (m2 > 0) { + mhi = lshift(mhi, m2); + if (mhi == NULL) + goto failed_malloc; + } + + /* Compute mlo -- check for special case + * that d is a normalized power of 2. + */ + + mlo = mhi; + if (spec_case) { + mhi = Balloc(mhi->k); + if (mhi == NULL) + goto failed_malloc; + Bcopy(mhi, mlo); + mhi = lshift(mhi, Log2P); + if (mhi == NULL) + goto failed_malloc; + } + + for(i = 1;;i++) { + dig = quorem(b,S) + '0'; + /* Do we yet have the shortest decimal string + * that will round to d? + */ + j = cmp(b, mlo); + delta = diff(S, mhi); + if (delta == NULL) + goto failed_malloc; + j1 = delta->sign ? 1 : cmp(b, delta); + Bfree(delta); + if (j1 == 0 && mode != 1 && !(word1(&u) & 1) + ) { + if (dig == '9') + goto round_9_up; + if (j > 0) + dig++; + *s++ = dig; + goto ret; + } + if (j < 0 || (j == 0 && mode != 1 + && !(word1(&u) & 1) + )) { + if (!b->x[0] && b->wds <= 1) { + goto accept_dig; + } + if (j1 > 0) { + b = lshift(b, 1); + if (b == NULL) + goto failed_malloc; + j1 = cmp(b, S); + if ((j1 > 0 || (j1 == 0 && dig & 1)) + && dig++ == '9') + goto round_9_up; + } + accept_dig: + *s++ = dig; + goto ret; + } + if (j1 > 0) { + if (dig == '9') { /* possible if i == 1 */ + round_9_up: + *s++ = '9'; + goto roundoff; + } + *s++ = dig + 1; + goto ret; + } + *s++ = dig; + if (i == ilim) + break; + b = multadd(b, 10, 0); + if (b == NULL) + goto failed_malloc; + if (mlo == mhi) { + mlo = mhi = multadd(mhi, 10, 0); + if (mlo == NULL) + goto failed_malloc; + } + else { + mlo = multadd(mlo, 10, 0); + if (mlo == NULL) + goto failed_malloc; + mhi = multadd(mhi, 10, 0); + if (mhi == NULL) + goto failed_malloc; + } + } + } + else + for(i = 1;; i++) { + *s++ = dig = quorem(b,S) + '0'; + if (!b->x[0] && b->wds <= 1) { + goto ret; + } + if (i >= ilim) + break; + b = multadd(b, 10, 0); + if (b == NULL) + goto failed_malloc; + } + + /* Round off last digit */ + + b = lshift(b, 1); + if (b == NULL) + goto failed_malloc; + j = cmp(b, S); + if (j > 0 || (j == 0 && dig & 1)) { + roundoff: + while(*--s == '9') + if (s == s0) { + k++; + *s++ = '1'; + goto ret; + } + ++*s++; + } + else { + while(*--s == '0'); + s++; + } + ret: + Bfree(S); + if (mhi) { + if (mlo && mlo != mhi) + Bfree(mlo); + Bfree(mhi); + } + ret1: + Bfree(b); + *s = 0; + *decpt = k + 1; + if (rve) + *rve = s; + return s0; + failed_malloc: + if (S) + Bfree(S); + if (mlo && mlo != mhi) + Bfree(mlo); + if (mhi) + Bfree(mhi); + if (b) + Bfree(b); + if (s0) + _Py_dg_freedtoa(s0); + return NULL; +} +#ifdef __cplusplus +} +#endif + +#endif /* PY_NO_SHORT_FLOAT_REPR */ diff --git a/Python/pymath.c b/Python/pymath.c index 5d09b4c3c78..2e049be8704 100644 --- a/Python/pymath.c +++ b/Python/pymath.c @@ -13,6 +13,28 @@ double _Py_force_double(double x) } #endif +#ifdef USING_X87_FPU +# ifdef HAVE_GCC_ASM_FOR_X87 + +/* inline assembly for getting and setting the 387 FPU control word on + gcc/x86 */ + +unsigned short _Py_get_387controlword(void) { + unsigned short cw; + __asm__ __volatile__ ("fnstcw %0" : "=m" (cw)); + return cw; +} + +void _Py_set_387controlword(unsigned short cw) { + __asm__ __volatile__ ("fldcw %0" : : "m" (cw)); +} + +# else +# error "Unable to get and set x87 control word" +# endif +#endif + + #ifndef HAVE_HYPOT double hypot(double x, double y) { diff --git a/Python/sysmodule.c b/Python/sysmodule.c index 443d8eb0994..262f5a1199e 100644 --- a/Python/sysmodule.c +++ b/Python/sysmodule.c @@ -1025,6 +1025,7 @@ platform -- platform identifier\n\ executable -- pathname of this Python interpreter\n\ prefix -- prefix used to find the Python library\n\ exec_prefix -- prefix used to find the machine-specific Python library\n\ +float_repr_style -- string indicating the style of repr() output for floats\n\ " ) #ifdef MS_WINDOWS @@ -1428,6 +1429,15 @@ _PySys_Init(void) FlagsType.tp_init = NULL; FlagsType.tp_new = NULL; + /* float repr style: 0.03 (short) vs 0.029999999999999999 (legacy) */ +#ifndef PY_NO_SHORT_FLOAT_REPR + SET_SYS_FROM_STRING("float_repr_style", + PyUnicode_FromString("short")); +#else + SET_SYS_FROM_STRING("float_repr_style", + PyUnicode_FromString("legacy")); +#endif + #undef SET_SYS_FROM_STRING if (PyErr_Occurred()) return NULL; diff --git a/configure b/configure index f5d7352bed0..f4ee3109f42 100755 --- a/configure +++ b/configure @@ -1,5 +1,5 @@ #! /bin/sh -# From configure.in Revision: 71261 . +# From configure.in Revision: 71274 . # Guess values for system-dependent variables and create Makefiles. # Generated by GNU Autoconf 2.61 for python 3.1. # @@ -21603,12 +21603,455 @@ echo "${ECHO_T}default LIBC=\"$LIBC\"" >&6; } fi -# ************************************ -# * Check for mathematical functions * -# ************************************ +# ************************************************** +# * Check for various properties of floating point * +# ************************************************** -LIBS_SAVE=$LIBS -LIBS="$LIBS $LIBM" +{ echo "$as_me:$LINENO: checking whether C doubles are little-endian IEEE 754 binary64" >&5 +echo $ECHO_N "checking whether C doubles are little-endian IEEE 754 binary64... $ECHO_C" >&6; } +if test "${ac_cv_little_endian_double+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + +if test "$cross_compiling" = yes; then + ac_cv_little_endian_double=no +else + cat >conftest.$ac_ext <<_ACEOF +/* confdefs.h. */ +_ACEOF +cat confdefs.h >>conftest.$ac_ext +cat >>conftest.$ac_ext <<_ACEOF +/* end confdefs.h. */ + +#include +int main() { + double x = 9006104071832581.0; + if (memcmp(&x, "\x05\x04\x03\x02\x01\xff\x3f\x43", 8) == 0) + return 0; + else + return 1; +} + +_ACEOF +rm -f conftest$ac_exeext +if { (ac_try="$ac_link" +case "(($ac_try" in + *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;; + *) ac_try_echo=$ac_try;; +esac +eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5 + (eval "$ac_link") 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); } && { ac_try='./conftest$ac_exeext' + { (case "(($ac_try" in + *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;; + *) ac_try_echo=$ac_try;; +esac +eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5 + (eval "$ac_try") 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; }; then + ac_cv_little_endian_double=yes +else + echo "$as_me: program exited with status $ac_status" >&5 +echo "$as_me: failed program was:" >&5 +sed 's/^/| /' conftest.$ac_ext >&5 + +( exit $ac_status ) +ac_cv_little_endian_double=no +fi +rm -f core *.core core.conftest.* gmon.out bb.out conftest$ac_exeext conftest.$ac_objext conftest.$ac_ext +fi + + +fi + +{ echo "$as_me:$LINENO: result: $ac_cv_little_endian_double" >&5 +echo "${ECHO_T}$ac_cv_little_endian_double" >&6; } +if test "$ac_cv_little_endian_double" = yes +then + +cat >>confdefs.h <<\_ACEOF +#define DOUBLE_IS_LITTLE_ENDIAN_IEEE754 1 +_ACEOF + +fi + +{ echo "$as_me:$LINENO: checking whether C doubles are big-endian IEEE 754 binary64" >&5 +echo $ECHO_N "checking whether C doubles are big-endian IEEE 754 binary64... $ECHO_C" >&6; } +if test "${ac_cv_big_endian_double+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + +if test "$cross_compiling" = yes; then + ac_cv_big_endian_double=no +else + cat >conftest.$ac_ext <<_ACEOF +/* confdefs.h. */ +_ACEOF +cat confdefs.h >>conftest.$ac_ext +cat >>conftest.$ac_ext <<_ACEOF +/* end confdefs.h. */ + +#include +int main() { + double x = 9006104071832581.0; + if (memcmp(&x, "\x43\x3f\xff\x01\x02\x03\x04\x05", 8) == 0) + return 0; + else + return 1; +} + +_ACEOF +rm -f conftest$ac_exeext +if { (ac_try="$ac_link" +case "(($ac_try" in + *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;; + *) ac_try_echo=$ac_try;; +esac +eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5 + (eval "$ac_link") 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); } && { ac_try='./conftest$ac_exeext' + { (case "(($ac_try" in + *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;; + *) ac_try_echo=$ac_try;; +esac +eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5 + (eval "$ac_try") 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; }; then + ac_cv_big_endian_double=yes +else + echo "$as_me: program exited with status $ac_status" >&5 +echo "$as_me: failed program was:" >&5 +sed 's/^/| /' conftest.$ac_ext >&5 + +( exit $ac_status ) +ac_cv_big_endian_double=no +fi +rm -f core *.core core.conftest.* gmon.out bb.out conftest$ac_exeext conftest.$ac_objext conftest.$ac_ext +fi + + +fi + +{ echo "$as_me:$LINENO: result: $ac_cv_big_endian_double" >&5 +echo "${ECHO_T}$ac_cv_big_endian_double" >&6; } +if test "$ac_cv_big_endian_double" = yes +then + +cat >>confdefs.h <<\_ACEOF +#define DOUBLE_IS_BIG_ENDIAN_IEEE754 1 +_ACEOF + +fi + +# Some ARM platforms use a mixed-endian representation for doubles. +# While Python doesn't currently have full support for these platforms +# (see e.g., issue 1762561), we can at least make sure that float <-> string +# conversions work. +{ echo "$as_me:$LINENO: checking whether C doubles are ARM mixed-endian IEEE 754 binary64" >&5 +echo $ECHO_N "checking whether C doubles are ARM mixed-endian IEEE 754 binary64... $ECHO_C" >&6; } +if test "${ac_cv_mixed_endian_double+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + +if test "$cross_compiling" = yes; then + ac_cv_mixed_endian_double=no +else + cat >conftest.$ac_ext <<_ACEOF +/* confdefs.h. */ +_ACEOF +cat confdefs.h >>conftest.$ac_ext +cat >>conftest.$ac_ext <<_ACEOF +/* end confdefs.h. */ + +#include +int main() { + double x = 9006104071832581.0; + if (memcmp(&x, "\x01\xff\x3f\x43\x05\x04\x03\x02", 8) == 0) + return 0; + else + return 1; +} + +_ACEOF +rm -f conftest$ac_exeext +if { (ac_try="$ac_link" +case "(($ac_try" in + *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;; + *) ac_try_echo=$ac_try;; +esac +eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5 + (eval "$ac_link") 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); } && { ac_try='./conftest$ac_exeext' + { (case "(($ac_try" in + *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;; + *) ac_try_echo=$ac_try;; +esac +eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5 + (eval "$ac_try") 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; }; then + ac_cv_mixed_endian_double=yes +else + echo "$as_me: program exited with status $ac_status" >&5 +echo "$as_me: failed program was:" >&5 +sed 's/^/| /' conftest.$ac_ext >&5 + +( exit $ac_status ) +ac_cv_mixed_endian_double=no +fi +rm -f core *.core core.conftest.* gmon.out bb.out conftest$ac_exeext conftest.$ac_objext conftest.$ac_ext +fi + + +fi + +{ echo "$as_me:$LINENO: result: $ac_cv_mixed_endian_double" >&5 +echo "${ECHO_T}$ac_cv_mixed_endian_double" >&6; } +if test "$ac_cv_mixed_endian_double" = yes +then + +cat >>confdefs.h <<\_ACEOF +#define DOUBLE_IS_ARM_MIXED_ENDIAN_IEEE754 1 +_ACEOF + +fi + +# David Gay's code in Python/dtoa.c requires that the FPU uses 53-bit +# rounding; this is a particular problem on x86, where the x87 FPU has +# a default rounding precision of 64 bits. For gcc/x86, we try to fix +# this by: +# +# (1) using the SSE2 instruction set when available (it usually is +# on modern machines) +# (2) using inline assembler to get and set the x87 FPU control word +# otherwise. +# +# On AMD64 (aka x86-64), gcc automatically enables use of SSE2 +# instructions, so we don't bother trying to detect. + +if test "$GCC" = yes && test -n "`$CC -dM -E - &5 +echo $ECHO_N "checking whether SSE2 instructions are already enabled for math... $ECHO_C" >&6; } + if test -n "`$CC -dM -E - &5 +echo "${ECHO_T}$ac_sse2_enabled" >&6; } + + # if we're not using SSE2 already, we need to either enable it + # (when available), or use inline assembler to get and set the + # 387 control word. + if test $ac_sse2_enabled = no + then + # Check cpuid for SSE2 availability. Bits 25 and 26 of edx tell + # us about SSE and SSE2 respectively. + { echo "$as_me:$LINENO: checking whether SSE2 instructions are available on this CPU" >&5 +echo $ECHO_N "checking whether SSE2 instructions are available on this CPU... $ECHO_C" >&6; } + if test "$cross_compiling" = yes; then + ac_cv_cpu_has_sse2=no +else + cat >conftest.$ac_ext <<_ACEOF +/* confdefs.h. */ +_ACEOF +cat confdefs.h >>conftest.$ac_ext +cat >>conftest.$ac_ext <<_ACEOF +/* end confdefs.h. */ + + int main() { + unsigned int ax, bx, cx, dx, func; + func = 1U; + __asm__ __volatile__ ( + "pushl %%ebx\n\t" /* don't clobber ebx */ + "cpuid\n\t" + "movl %%ebx, %1\n\t" + "popl %%ebx" + : "=a" (ax), "=r" (bx), "=c" (cx), "=d" (dx) + : "a" (func) + : "cc" ); + if ((dx & (1U << 25)) && (dx & (1U << 26))) + return 0; + else + return 1; + } + +_ACEOF +rm -f conftest$ac_exeext +if { (ac_try="$ac_link" +case "(($ac_try" in + *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;; + *) ac_try_echo=$ac_try;; +esac +eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5 + (eval "$ac_link") 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); } && { ac_try='./conftest$ac_exeext' + { (case "(($ac_try" in + *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;; + *) ac_try_echo=$ac_try;; +esac +eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5 + (eval "$ac_try") 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; }; then + ac_cv_cpu_has_sse2=yes +else + echo "$as_me: program exited with status $ac_status" >&5 +echo "$as_me: failed program was:" >&5 +sed 's/^/| /' conftest.$ac_ext >&5 + +( exit $ac_status ) +ac_cv_cpu_has_sse2=no +fi +rm -f core *.core core.conftest.* gmon.out bb.out conftest$ac_exeext conftest.$ac_objext conftest.$ac_ext +fi + + + { echo "$as_me:$LINENO: result: $ac_cv_cpu_has_sse2" >&5 +echo "${ECHO_T}$ac_cv_cpu_has_sse2" >&6; } + + # determine whether gcc accepts options to turn on SSE2 + { echo "$as_me:$LINENO: checking whether $CC accepts -msse2 -mfpmath=sse" >&5 +echo $ECHO_N "checking whether $CC accepts -msse2 -mfpmath=sse... $ECHO_C" >&6; } + ac_save_cc="$CC" + CC="$CC -msse2 -mfpmath=sse" + if test "$cross_compiling" = yes; then + ac_cv_msse2_ok=no +else + cat >conftest.$ac_ext <<_ACEOF +/* confdefs.h. */ +_ACEOF +cat confdefs.h >>conftest.$ac_ext +cat >>conftest.$ac_ext <<_ACEOF +/* end confdefs.h. */ +int main() { return 0; } +_ACEOF +rm -f conftest$ac_exeext +if { (ac_try="$ac_link" +case "(($ac_try" in + *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;; + *) ac_try_echo=$ac_try;; +esac +eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5 + (eval "$ac_link") 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); } && { ac_try='./conftest$ac_exeext' + { (case "(($ac_try" in + *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;; + *) ac_try_echo=$ac_try;; +esac +eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5 + (eval "$ac_try") 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; }; then + ac_cv_msse2_ok=yes +else + echo "$as_me: program exited with status $ac_status" >&5 +echo "$as_me: failed program was:" >&5 +sed 's/^/| /' conftest.$ac_ext >&5 + +( exit $ac_status ) +ac_cv_msse2_ok=no +fi +rm -f core *.core core.conftest.* gmon.out bb.out conftest$ac_exeext conftest.$ac_objext conftest.$ac_ext +fi + + + CC="$ac_save_cc" + { echo "$as_me:$LINENO: result: $ac_cv_msse2_ok" >&5 +echo "${ECHO_T}$ac_cv_msse2_ok" >&6; } + + if test $ac_cv_cpu_has_sse2 = yes && test $ac_cv_msse2_ok = yes + then + BASECFLAGS="$BASECFLAGS -msse2 -mfpmath=sse" + else + # SSE2 doesn't appear to be available. Check that it's okay + # to use gcc inline assembler to get and set x87 control word + +cat >>confdefs.h <<\_ACEOF +#define USING_X87_FPU 1 +_ACEOF + + { echo "$as_me:$LINENO: checking whether we can use gcc inline assembler to get and set x87 control word" >&5 +echo $ECHO_N "checking whether we can use gcc inline assembler to get and set x87 control word... $ECHO_C" >&6; } + cat >conftest.$ac_ext <<_ACEOF +/* confdefs.h. */ +_ACEOF +cat confdefs.h >>conftest.$ac_ext +cat >>conftest.$ac_ext <<_ACEOF +/* end confdefs.h. */ + +int +main () +{ + + unsigned short cw; + __asm__ __volatile__ ("fnstcw %0" : "=m" (cw)); + __asm__ __volatile__ ("fldcw %0" : : "m" (cw)); + + ; + return 0; +} +_ACEOF +rm -f conftest.$ac_objext +if { (ac_try="$ac_compile" +case "(($ac_try" in + *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;; + *) ac_try_echo=$ac_try;; +esac +eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5 + (eval "$ac_compile") 2>conftest.er1 + ac_status=$? + grep -v '^ *+' conftest.er1 >conftest.err + rm -f conftest.er1 + cat conftest.err >&5 + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); } && { + test -z "$ac_c_werror_flag" || + test ! -s conftest.err + } && test -s conftest.$ac_objext; then + have_gcc_asm_for_x87=yes +else + echo "$as_me: failed program was:" >&5 +sed 's/^/| /' conftest.$ac_ext >&5 + + have_gcc_asm_for_x87=no +fi + +rm -f core conftest.err conftest.$ac_objext conftest.$ac_ext + { echo "$as_me:$LINENO: result: $have_gcc_asm_for_x87" >&5 +echo "${ECHO_T}$have_gcc_asm_for_x87" >&6; } + if test "$have_gcc_asm_for_x87" = yes + then + +cat >>confdefs.h <<\_ACEOF +#define HAVE_GCC_ASM_FOR_X87 1 +_ACEOF + + fi + fi + fi +fi # Detect whether system arithmetic is subject to x87-style double # rounding issues. The result of this test has little meaning on non @@ -21617,10 +22060,9 @@ LIBS="$LIBS $LIBM" # 0 otherwise. See http://bugs.python.org/issue2937 for more info. { echo "$as_me:$LINENO: checking for x87-style double rounding" >&5 echo $ECHO_N "checking for x87-style double rounding... $ECHO_C" >&6; } -if test "${ac_cv_x87_double_rounding+set}" = set; then - echo $ECHO_N "(cached) $ECHO_C" >&6 -else - +# $BASECFLAGS may affect the result +ac_save_cc="$CC" +CC="$CC $BASECFLAGS" if test "$cross_compiling" = yes; then ac_cv_x87_double_rounding=no else @@ -21684,8 +22126,7 @@ rm -f core *.core core.conftest.* gmon.out bb.out conftest$ac_exeext conftest.$a fi -fi - +CC="$ac_save_cc" { echo "$as_me:$LINENO: result: $ac_cv_x87_double_rounding" >&5 echo "${ECHO_T}$ac_cv_x87_double_rounding" >&6; } if test "$ac_cv_x87_double_rounding" = yes @@ -21697,6 +22138,13 @@ _ACEOF fi +# ************************************ +# * Check for mathematical functions * +# ************************************ + +LIBS_SAVE=$LIBS +LIBS="$LIBS $LIBM" + # Multiprocessing check for broken sem_getvalue { echo "$as_me:$LINENO: checking for broken sem_getvalue" >&5 echo $ECHO_N "checking for broken sem_getvalue... $ECHO_C" >&6; } diff --git a/configure.in b/configure.in index 40fa044ba86..b3bd00fb270 100644 --- a/configure.in +++ b/configure.in @@ -3065,12 +3065,176 @@ else AC_MSG_ERROR([proper usage is --with-libc=STRING]) fi], [AC_MSG_RESULT(default LIBC="$LIBC")]) -# ************************************ -# * Check for mathematical functions * -# ************************************ +# ************************************************** +# * Check for various properties of floating point * +# ************************************************** -LIBS_SAVE=$LIBS -LIBS="$LIBS $LIBM" +AC_MSG_CHECKING(whether C doubles are little-endian IEEE 754 binary64) +AC_CACHE_VAL(ac_cv_little_endian_double, [ +AC_TRY_RUN([ +#include +int main() { + double x = 9006104071832581.0; + if (memcmp(&x, "\x05\x04\x03\x02\x01\xff\x3f\x43", 8) == 0) + return 0; + else + return 1; +} +], +ac_cv_little_endian_double=yes, +ac_cv_little_endian_double=no, +ac_cv_little_endian_double=no)]) +AC_MSG_RESULT($ac_cv_little_endian_double) +if test "$ac_cv_little_endian_double" = yes +then + AC_DEFINE(DOUBLE_IS_LITTLE_ENDIAN_IEEE754, 1, + [Define if C doubles are 64-bit IEEE 754 binary format, stored + with the least significant byte first]) +fi + +AC_MSG_CHECKING(whether C doubles are big-endian IEEE 754 binary64) +AC_CACHE_VAL(ac_cv_big_endian_double, [ +AC_TRY_RUN([ +#include +int main() { + double x = 9006104071832581.0; + if (memcmp(&x, "\x43\x3f\xff\x01\x02\x03\x04\x05", 8) == 0) + return 0; + else + return 1; +} +], +ac_cv_big_endian_double=yes, +ac_cv_big_endian_double=no, +ac_cv_big_endian_double=no)]) +AC_MSG_RESULT($ac_cv_big_endian_double) +if test "$ac_cv_big_endian_double" = yes +then + AC_DEFINE(DOUBLE_IS_BIG_ENDIAN_IEEE754, 1, + [Define if C doubles are 64-bit IEEE 754 binary format, stored + with the most significant byte first]) +fi + +# Some ARM platforms use a mixed-endian representation for doubles. +# While Python doesn't currently have full support for these platforms +# (see e.g., issue 1762561), we can at least make sure that float <-> string +# conversions work. +AC_MSG_CHECKING(whether C doubles are ARM mixed-endian IEEE 754 binary64) +AC_CACHE_VAL(ac_cv_mixed_endian_double, [ +AC_TRY_RUN([ +#include +int main() { + double x = 9006104071832581.0; + if (memcmp(&x, "\x01\xff\x3f\x43\x05\x04\x03\x02", 8) == 0) + return 0; + else + return 1; +} +], +ac_cv_mixed_endian_double=yes, +ac_cv_mixed_endian_double=no, +ac_cv_mixed_endian_double=no)]) +AC_MSG_RESULT($ac_cv_mixed_endian_double) +if test "$ac_cv_mixed_endian_double" = yes +then + AC_DEFINE(DOUBLE_IS_ARM_MIXED_ENDIAN_IEEE754, 1, + [Define if C doubles are 64-bit IEEE 754 binary format, stored + in ARM mixed-endian order (byte order 45670123)]) +fi + +# David Gay's code in Python/dtoa.c requires that the FPU uses 53-bit +# rounding; this is a particular problem on x86, where the x87 FPU has +# a default rounding precision of 64 bits. For gcc/x86, we try to fix +# this by: +# +# (1) using the SSE2 instruction set when available (it usually is +# on modern machines) +# (2) using inline assembler to get and set the x87 FPU control word +# otherwise. +# +# On AMD64 (aka x86-64), gcc automatically enables use of SSE2 +# instructions, so we don't bother trying to detect. + +if test "$GCC" = yes && test -n "`$CC -dM -E - #include @@ -3101,7 +3267,8 @@ int main() { ], ac_cv_x87_double_rounding=no, ac_cv_x87_double_rounding=yes, -ac_cv_x87_double_rounding=no)]) +ac_cv_x87_double_rounding=no) +CC="$ac_save_cc" AC_MSG_RESULT($ac_cv_x87_double_rounding) if test "$ac_cv_x87_double_rounding" = yes then @@ -3109,6 +3276,13 @@ then [Define if arithmetic is subject to x87-style double rounding issue]) fi +# ************************************ +# * Check for mathematical functions * +# ************************************ + +LIBS_SAVE=$LIBS +LIBS="$LIBS $LIBM" + # Multiprocessing check for broken sem_getvalue AC_MSG_CHECKING(for broken sem_getvalue) AC_TRY_RUN([ diff --git a/pyconfig.h.in b/pyconfig.h.in index 40067f6ef82..72f5fb3959e 100644 --- a/pyconfig.h.in +++ b/pyconfig.h.in @@ -15,6 +15,18 @@ /* Define if you have the Mach cthreads package */ #undef C_THREADS +/* Define if C doubles are 64-bit IEEE 754 binary format, stored in ARM + mixed-endian order (byte order 45670123) */ +#undef DOUBLE_IS_ARM_MIXED_ENDIAN_IEEE754 + +/* Define if C doubles are 64-bit IEEE 754 binary format, stored with the most + significant byte first */ +#undef DOUBLE_IS_BIG_ENDIAN_IEEE754 + +/* Define if C doubles are 64-bit IEEE 754 binary format, stored with the + least significant byte first */ +#undef DOUBLE_IS_LITTLE_ENDIAN_IEEE754 + /* Define if --enable-ipv6 is specified */ #undef ENABLE_IPV6 @@ -232,6 +244,10 @@ /* Define to 1 if you have the `gai_strerror' function. */ #undef HAVE_GAI_STRERROR +/* Define if we can use gcc inline assembler to get and set x87 control word + */ +#undef HAVE_GCC_ASM_FOR_X87 + /* Define if you have the getaddrinfo function. */ #undef HAVE_GETADDRINFO @@ -970,6 +986,10 @@ /* Define if you want to use computed gotos in ceval.c. */ #undef USE_COMPUTED_GOTOS +/* Define on x86 hardware if the x87 FPU is being used for floating-point + arithmetic */ +#undef USING_X87_FPU + /* Define if a va_list is an array of some kind */ #undef VA_LIST_IS_ARRAY