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npy_math_private.h
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npy_math_private.h
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/*
*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* from: @(#)fdlibm.h 5.1 93/09/24
* $FreeBSD$
*/
#ifndef _NPY_MATH_PRIVATE_H_
#define _NPY_MATH_PRIVATE_H_
#include <Python.h>
#ifdef __cplusplus
#include <cmath>
#include <complex>
using std::isgreater;
using std::isless;
#else
#include <math.h>
#endif
#include "npy_config.h"
#include "npy_fpmath.h"
#include "numpy/npy_math.h"
#include "numpy/npy_endian.h"
#include "numpy/npy_common.h"
/*
* The original fdlibm code used statements like:
* n0 = ((*(int*)&one)>>29)^1; * index of high word *
* ix0 = *(n0+(int*)&x); * high word of x *
* ix1 = *((1-n0)+(int*)&x); * low word of x *
* to dig two 32 bit words out of the 64 bit IEEE floating point
* value. That is non-ANSI, and, moreover, the gcc instruction
* scheduler gets it wrong. We instead use the following macros.
* Unlike the original code, we determine the endianness at compile
* time, not at run time; I don't see much benefit to selecting
* endianness at run time.
*/
/*
* A union which permits us to convert between a double and two 32 bit
* ints.
*/
/* XXX: not really, but we already make this assumption elsewhere. Will have to
* fix this at some point */
#define IEEE_WORD_ORDER NPY_BYTE_ORDER
#if IEEE_WORD_ORDER == NPY_BIG_ENDIAN
typedef union
{
double value;
struct
{
npy_uint32 msw;
npy_uint32 lsw;
} parts;
} ieee_double_shape_type;
#endif
#if IEEE_WORD_ORDER == NPY_LITTLE_ENDIAN
typedef union
{
double value;
struct
{
npy_uint32 lsw;
npy_uint32 msw;
} parts;
} ieee_double_shape_type;
#endif
/* Get two 32 bit ints from a double. */
#define EXTRACT_WORDS(ix0,ix1,d) \
do { \
ieee_double_shape_type ew_u; \
ew_u.value = (d); \
(ix0) = ew_u.parts.msw; \
(ix1) = ew_u.parts.lsw; \
} while (0)
/* Get the more significant 32 bit int from a double. */
#define GET_HIGH_WORD(i,d) \
do { \
ieee_double_shape_type gh_u; \
gh_u.value = (d); \
(i) = gh_u.parts.msw; \
} while (0)
/* Get the less significant 32 bit int from a double. */
#define GET_LOW_WORD(i,d) \
do { \
ieee_double_shape_type gl_u; \
gl_u.value = (d); \
(i) = gl_u.parts.lsw; \
} while (0)
/* Set the more significant 32 bits of a double from an int. */
#define SET_HIGH_WORD(d,v) \
do { \
ieee_double_shape_type sh_u; \
sh_u.value = (d); \
sh_u.parts.msw = (v); \
(d) = sh_u.value; \
} while (0)
/* Set the less significant 32 bits of a double from an int. */
#define SET_LOW_WORD(d,v) \
do { \
ieee_double_shape_type sl_u; \
sl_u.value = (d); \
sl_u.parts.lsw = (v); \
(d) = sl_u.value; \
} while (0)
/* Set a double from two 32 bit ints. */
#define INSERT_WORDS(d,ix0,ix1) \
do { \
ieee_double_shape_type iw_u; \
iw_u.parts.msw = (ix0); \
iw_u.parts.lsw = (ix1); \
(d) = iw_u.value; \
} while (0)
/*
* A union which permits us to convert between a float and a 32 bit
* int.
*/
typedef union
{
float value;
/* FIXME: Assumes 32 bit int. */
npy_uint32 word;
} ieee_float_shape_type;
/* Get a 32 bit int from a float. */
#define GET_FLOAT_WORD(i,d) \
do { \
ieee_float_shape_type gf_u; \
gf_u.value = (d); \
(i) = gf_u.word; \
} while (0)
/* Set a float from a 32 bit int. */
#define SET_FLOAT_WORD(d,i) \
do { \
ieee_float_shape_type sf_u; \
sf_u.word = (i); \
(d) = sf_u.value; \
} while (0)
#ifdef NPY_USE_C99_COMPLEX
#include <complex.h>
#endif
/*
* Long double support
*/
#if defined(HAVE_LDOUBLE_INTEL_EXTENDED_12_BYTES_LE)
/*
* Intel extended 80 bits precision. Bit representation is
* | junk | s |eeeeeeeeeeeeeee|mmmmmmmm................mmmmmmm|
* | 16 bits| 1 bit | 15 bits | 64 bits |
* | a[2] | a[1] | a[0] |
*
* 16 stronger bits of a[2] are junk
*/
typedef npy_uint32 IEEEl2bitsrep_part;
union IEEEl2bitsrep {
npy_longdouble e;
IEEEl2bitsrep_part a[3];
};
#define LDBL_MANL_INDEX 0
#define LDBL_MANL_MASK 0xFFFFFFFF
#define LDBL_MANL_SHIFT 0
#define LDBL_MANH_INDEX 1
#define LDBL_MANH_MASK 0xFFFFFFFF
#define LDBL_MANH_SHIFT 0
#define LDBL_EXP_INDEX 2
#define LDBL_EXP_MASK 0x7FFF
#define LDBL_EXP_SHIFT 0
#define LDBL_SIGN_INDEX 2
#define LDBL_SIGN_MASK 0x8000
#define LDBL_SIGN_SHIFT 15
#define LDBL_NBIT 0x80000000
typedef npy_uint32 ldouble_man_t;
typedef npy_uint32 ldouble_exp_t;
typedef npy_uint32 ldouble_sign_t;
#elif defined(HAVE_LDOUBLE_INTEL_EXTENDED_16_BYTES_LE)
/*
* Intel extended 80 bits precision, 16 bytes alignment.. Bit representation is
* | junk | s |eeeeeeeeeeeeeee|mmmmmmmm................mmmmmmm|
* | 16 bits| 1 bit | 15 bits | 64 bits |
* | a[2] | a[1] | a[0] |
*
* a[3] and 16 stronger bits of a[2] are junk
*/
typedef npy_uint32 IEEEl2bitsrep_part;
union IEEEl2bitsrep {
npy_longdouble e;
IEEEl2bitsrep_part a[4];
};
#define LDBL_MANL_INDEX 0
#define LDBL_MANL_MASK 0xFFFFFFFF
#define LDBL_MANL_SHIFT 0
#define LDBL_MANH_INDEX 1
#define LDBL_MANH_MASK 0xFFFFFFFF
#define LDBL_MANH_SHIFT 0
#define LDBL_EXP_INDEX 2
#define LDBL_EXP_MASK 0x7FFF
#define LDBL_EXP_SHIFT 0
#define LDBL_SIGN_INDEX 2
#define LDBL_SIGN_MASK 0x8000
#define LDBL_SIGN_SHIFT 15
#define LDBL_NBIT 0x800000000
typedef npy_uint32 ldouble_man_t;
typedef npy_uint32 ldouble_exp_t;
typedef npy_uint32 ldouble_sign_t;
#elif defined(HAVE_LDOUBLE_MOTOROLA_EXTENDED_12_BYTES_BE)
/*
* Motorola extended 80 bits precision. Bit representation is
* | s |eeeeeeeeeeeeeee| junk |mmmmmmmm................mmmmmmm|
* | 1 bit | 15 bits | 16 bits| 64 bits |
* | a[0] | a[1] | a[2] |
*
* 16 low bits of a[0] are junk
*/
typedef npy_uint32 IEEEl2bitsrep_part;
union IEEEl2bitsrep {
npy_longdouble e;
IEEEl2bitsrep_part a[3];
};
#define LDBL_MANL_INDEX 2
#define LDBL_MANL_MASK 0xFFFFFFFF
#define LDBL_MANL_SHIFT 0
#define LDBL_MANH_INDEX 1
#define LDBL_MANH_MASK 0xFFFFFFFF
#define LDBL_MANH_SHIFT 0
#define LDBL_EXP_INDEX 0
#define LDBL_EXP_MASK 0x7FFF0000
#define LDBL_EXP_SHIFT 16
#define LDBL_SIGN_INDEX 0
#define LDBL_SIGN_MASK 0x80000000
#define LDBL_SIGN_SHIFT 31
#define LDBL_NBIT 0x80000000
typedef npy_uint32 ldouble_man_t;
typedef npy_uint32 ldouble_exp_t;
typedef npy_uint32 ldouble_sign_t;
#elif defined(HAVE_LDOUBLE_IEEE_DOUBLE_BE)
/* 64 bits IEEE double precision aligned on 16 bytes: used by ppc arch on
* Mac OS X */
/*
* IEEE double precision. Bit representation is
* | s |eeeeeeeeeee|mmmmmmmm................mmmmmmm|
* |1 bit| 11 bits | 52 bits |
* | a[0] | a[1] |
*/
typedef npy_uint32 IEEEl2bitsrep_part;
union IEEEl2bitsrep {
npy_longdouble e;
IEEEl2bitsrep_part a[2];
};
#define LDBL_MANL_INDEX 1
#define LDBL_MANL_MASK 0xFFFFFFFF
#define LDBL_MANL_SHIFT 0
#define LDBL_MANH_INDEX 0
#define LDBL_MANH_MASK 0x000FFFFF
#define LDBL_MANH_SHIFT 0
#define LDBL_EXP_INDEX 0
#define LDBL_EXP_MASK 0x7FF00000
#define LDBL_EXP_SHIFT 20
#define LDBL_SIGN_INDEX 0
#define LDBL_SIGN_MASK 0x80000000
#define LDBL_SIGN_SHIFT 31
#define LDBL_NBIT 0
typedef npy_uint32 ldouble_man_t;
typedef npy_uint32 ldouble_exp_t;
typedef npy_uint32 ldouble_sign_t;
#elif defined(HAVE_LDOUBLE_IEEE_DOUBLE_LE)
/* 64 bits IEEE double precision, Little Endian. */
/*
* IEEE double precision. Bit representation is
* | s |eeeeeeeeeee|mmmmmmmm................mmmmmmm|
* |1 bit| 11 bits | 52 bits |
* | a[1] | a[0] |
*/
typedef npy_uint32 IEEEl2bitsrep_part;
union IEEEl2bitsrep {
npy_longdouble e;
IEEEl2bitsrep_part a[2];
};
#define LDBL_MANL_INDEX 0
#define LDBL_MANL_MASK 0xFFFFFFFF
#define LDBL_MANL_SHIFT 0
#define LDBL_MANH_INDEX 1
#define LDBL_MANH_MASK 0x000FFFFF
#define LDBL_MANH_SHIFT 0
#define LDBL_EXP_INDEX 1
#define LDBL_EXP_MASK 0x7FF00000
#define LDBL_EXP_SHIFT 20
#define LDBL_SIGN_INDEX 1
#define LDBL_SIGN_MASK 0x80000000
#define LDBL_SIGN_SHIFT 31
#define LDBL_NBIT 0x00000080
typedef npy_uint32 ldouble_man_t;
typedef npy_uint32 ldouble_exp_t;
typedef npy_uint32 ldouble_sign_t;
#elif defined(HAVE_LDOUBLE_IEEE_QUAD_BE)
/*
* IEEE quad precision, Big Endian. Bit representation is
* | s |eeeeeeeeeee|mmmmmmmm................mmmmmmm|
* |1 bit| 15 bits | 112 bits |
* | a[0] | a[1] |
*/
typedef npy_uint64 IEEEl2bitsrep_part;
union IEEEl2bitsrep {
npy_longdouble e;
IEEEl2bitsrep_part a[2];
};
#define LDBL_MANL_INDEX 1
#define LDBL_MANL_MASK 0xFFFFFFFFFFFFFFFF
#define LDBL_MANL_SHIFT 0
#define LDBL_MANH_INDEX 0
#define LDBL_MANH_MASK 0x0000FFFFFFFFFFFF
#define LDBL_MANH_SHIFT 0
#define LDBL_EXP_INDEX 0
#define LDBL_EXP_MASK 0x7FFF000000000000
#define LDBL_EXP_SHIFT 48
#define LDBL_SIGN_INDEX 0
#define LDBL_SIGN_MASK 0x8000000000000000
#define LDBL_SIGN_SHIFT 63
#define LDBL_NBIT 0
typedef npy_uint64 ldouble_man_t;
typedef npy_uint64 ldouble_exp_t;
typedef npy_uint32 ldouble_sign_t;
#elif defined(HAVE_LDOUBLE_IEEE_QUAD_LE)
/*
* IEEE quad precision, Little Endian. Bit representation is
* | s |eeeeeeeeeee|mmmmmmmm................mmmmmmm|
* |1 bit| 15 bits | 112 bits |
* | a[1] | a[0] |
*/
typedef npy_uint64 IEEEl2bitsrep_part;
union IEEEl2bitsrep {
npy_longdouble e;
IEEEl2bitsrep_part a[2];
};
#define LDBL_MANL_INDEX 0
#define LDBL_MANL_MASK 0xFFFFFFFFFFFFFFFF
#define LDBL_MANL_SHIFT 0
#define LDBL_MANH_INDEX 1
#define LDBL_MANH_MASK 0x0000FFFFFFFFFFFF
#define LDBL_MANH_SHIFT 0
#define LDBL_EXP_INDEX 1
#define LDBL_EXP_MASK 0x7FFF000000000000
#define LDBL_EXP_SHIFT 48
#define LDBL_SIGN_INDEX 1
#define LDBL_SIGN_MASK 0x8000000000000000
#define LDBL_SIGN_SHIFT 63
#define LDBL_NBIT 0
typedef npy_uint64 ldouble_man_t;
typedef npy_uint64 ldouble_exp_t;
typedef npy_uint32 ldouble_sign_t;
#endif
#if !defined(HAVE_LDOUBLE_IBM_DOUBLE_DOUBLE_BE) && \
!defined(HAVE_LDOUBLE_IBM_DOUBLE_DOUBLE_LE)
/* Get the sign bit of x. x should be of type IEEEl2bitsrep */
#define GET_LDOUBLE_SIGN(x) \
(((x).a[LDBL_SIGN_INDEX] & LDBL_SIGN_MASK) >> LDBL_SIGN_SHIFT)
/* Set the sign bit of x to v. x should be of type IEEEl2bitsrep */
#define SET_LDOUBLE_SIGN(x, v) \
((x).a[LDBL_SIGN_INDEX] = \
((x).a[LDBL_SIGN_INDEX] & ~LDBL_SIGN_MASK) | \
(((IEEEl2bitsrep_part)(v) << LDBL_SIGN_SHIFT) & LDBL_SIGN_MASK))
/* Get the exp bits of x. x should be of type IEEEl2bitsrep */
#define GET_LDOUBLE_EXP(x) \
(((x).a[LDBL_EXP_INDEX] & LDBL_EXP_MASK) >> LDBL_EXP_SHIFT)
/* Set the exp bit of x to v. x should be of type IEEEl2bitsrep */
#define SET_LDOUBLE_EXP(x, v) \
((x).a[LDBL_EXP_INDEX] = \
((x).a[LDBL_EXP_INDEX] & ~LDBL_EXP_MASK) | \
(((IEEEl2bitsrep_part)(v) << LDBL_EXP_SHIFT) & LDBL_EXP_MASK))
/* Get the manl bits of x. x should be of type IEEEl2bitsrep */
#define GET_LDOUBLE_MANL(x) \
(((x).a[LDBL_MANL_INDEX] & LDBL_MANL_MASK) >> LDBL_MANL_SHIFT)
/* Set the manl bit of x to v. x should be of type IEEEl2bitsrep */
#define SET_LDOUBLE_MANL(x, v) \
((x).a[LDBL_MANL_INDEX] = \
((x).a[LDBL_MANL_INDEX] & ~LDBL_MANL_MASK) | \
(((IEEEl2bitsrep_part)(v) << LDBL_MANL_SHIFT) & LDBL_MANL_MASK))
/* Get the manh bits of x. x should be of type IEEEl2bitsrep */
#define GET_LDOUBLE_MANH(x) \
(((x).a[LDBL_MANH_INDEX] & LDBL_MANH_MASK) >> LDBL_MANH_SHIFT)
/* Set the manh bit of x to v. x should be of type IEEEl2bitsrep */
#define SET_LDOUBLE_MANH(x, v) \
((x).a[LDBL_MANH_INDEX] = \
((x).a[LDBL_MANH_INDEX] & ~LDBL_MANH_MASK) | \
(((IEEEl2bitsrep_part)(v) << LDBL_MANH_SHIFT) & LDBL_MANH_MASK))
#endif /* !HAVE_LDOUBLE_DOUBLE_DOUBLE_* */
/*
* Those unions are used to convert a pointer of npy_cdouble to native C99
* complex or our own complex type independently on whether C99 complex
* support is available
*/
#ifdef NPY_USE_C99_COMPLEX
/*
* Microsoft C defines _MSC_VER
* Intel compiler does not use MSVC complex types, but defines _MSC_VER by
* default.
* since c++17 msvc is no longer support them.
*/
#if !defined(__cplusplus) && defined(_MSC_VER) && !defined(__INTEL_COMPILER)
typedef union {
npy_cdouble npy_z;
_Dcomplex c99_z;
} __npy_cdouble_to_c99_cast;
typedef union {
npy_cfloat npy_z;
_Fcomplex c99_z;
} __npy_cfloat_to_c99_cast;
typedef union {
npy_clongdouble npy_z;
_Lcomplex c99_z;
} __npy_clongdouble_to_c99_cast;
#else /* !_MSC_VER */
typedef union {
npy_cdouble npy_z;
#ifdef __cplusplus
std::complex<double> c99_z;
#else
complex double c99_z;
#endif
} __npy_cdouble_to_c99_cast;
typedef union {
npy_cfloat npy_z;
#ifdef __cplusplus
std::complex<float> c99_z;
#else
complex float c99_z;
#endif
} __npy_cfloat_to_c99_cast;
typedef union {
npy_clongdouble npy_z;
#ifdef __cplusplus
std::complex<long double> c99_z;
#else
complex long double c99_z;
#endif
} __npy_clongdouble_to_c99_cast;
#endif /* !_MSC_VER */
#else /* !NPY_USE_C99_COMPLEX */
typedef union {
npy_cdouble npy_z;
npy_cdouble c99_z;
} __npy_cdouble_to_c99_cast;
typedef union {
npy_cfloat npy_z;
npy_cfloat c99_z;
} __npy_cfloat_to_c99_cast;
typedef union {
npy_clongdouble npy_z;
npy_clongdouble c99_z;
} __npy_clongdouble_to_c99_cast;
#endif /* !NPY_USE_C99_COMPLEX */
#endif /* !_NPY_MATH_PRIVATE_H_ */