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amath/src/real/prim.h

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/*-
* Copyright (c) 2014-2017 Carsten Sonne Larsen <cs@innolan.net>
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
* Project homepage:
* http://amath.innolan.net
*
*/
#ifndef AMATH_LIB_REAL_PRIM_H
#define AMATH_LIB_REAL_PRIM_H
/**
* @file prim.h
* @brief Primitives in math library for handling real numbers.
*
* The library is based on fdlib by Sun Microsystems.
* The original library can be downloaded at:
* http://www.netlib.org/fdlibm/
*
* or from mirror site:
* http://www.hensa.ac.uk/
*
* All headers and dates are preserved.
*
*/
// ---------------------------------------------------------------------------
// ------------------------- High precision constants ------------------------
// ---------------------------------------------------------------------------
double __kernel_cos(double x, double y);
double __kernel_sin(double x, double y, int iy);
double __kernel_tan(double x, double y, int iy);
int __kernel_rem_pio2(double* x, double* y, int e0, int nx, int prec, const int* ipio2);
/* Detect ARM CPUs */
#if !defined(__IEEE_LITTLE_ENDIAN) && !defined(__IEEE_BIG_ENDIAN)
#if defined(__arm__) || defined(__ARM_ARCH_2__) || \
defined(__ARM_ARCH_3__) || defined(__ARM_ARCH_3M__) || \
defined(__ARM_ARCH_4T__) || defined(__TARGET_ARM_4T) || \
defined(__ARM_ARCH_5__) || defined(__ARM_ARCH_5E__) || \
defined(__ARM_ARCH_5T__) || defined(__ARM_ARCH_5TE__) || \
defined(__ARM_ARCH_6__) || defined(__ARM_ARCH_6J__) || \
defined(__ARM_ARCH_6K__) || defined(__ARM_ARCH_6Z__) || \
defined(__ARM_ARCH_6ZK__) || defined(__ARM_ARCH_6T2__) || \
defined(__ARM_ARCH_7__) || defined(__ARM_ARCH_7A__) || \
defined(__ARM_ARCH_7R__) || defined(__ARM_ARCH_7M__) || \
defined(__ARM_ARCH_7S_) || defined(__ARM_ARCH_5TEJ__) || \
defined(_M_ARM) || defined(ARMCPU) || \
defined(__aarch64__)
#define __IEEE_LITTLE_ENDIAN
#endif
#endif
/* Detect Motorola CPUs */
#if !defined(__IEEE_LITTLE_ENDIAN) && !defined(__IEEE_BIG_ENDIAN)
#if defined(mc68000) || defined(__mc68000) || defined(_M68000) || \
defined(mc68020) || defined(__mc68020) || defined(_M68020) || \
defined(mc68030) || defined(__mc68030) || defined(_M68030) || \
defined(mc68040) || defined(__mc68040) || defined(_M68040) || \
defined(mc68060) || defined(__mc68060) || defined(_M68060) || \
defined(__m68k__)
#define __IEEE_BIG_ENDIAN
#endif
#endif
/* Detect Intel CPUs */
#if !defined(__IEEE_LITTLE_ENDIAN) && !defined(__IEEE_BIG_ENDIAN)
#if defined(i386) || defined(__i386) || defined(__i386__) || \
defined(i386) || defined(__i486) || defined(__i486__) || \
defined(i386) || defined(__i586) || defined(__i586__) || \
defined(i386) || defined(__i686) || defined(__i686__) || \
defined(x86) || defined(intel) || defined(i86pc) || \
defined(_M_IX86) || defined(_M_AMD64) || defined(__x86_64__) || \
defined(INTELCPU)
#define __IEEE_LITTLE_ENDIAN
#endif
#endif
/* Detect other LE CPUs */
#if !defined(__IEEE_LITTLE_ENDIAN) && !defined(__IEEE_BIG_ENDIAN)
#if defined(__alpha) || defined(__osf__)
#define __IEEE_LITTLE_ENDIAN
#endif
#endif
/* Detect other BE CPUs */
#if !defined(__IEEE_LITTLE_ENDIAN) && !defined(__IEEE_BIG_ENDIAN)
#if defined(PPCCPU) || defined(__PPC__) || \
defined(__powerpc__) || defined(__powerpc64__)
#define __IEEE_BIG_ENDIAN
#endif
#endif
#ifndef __IEEE_BIG_ENDIAN
#ifndef __IEEE_LITTLE_ENDIAN
#error Must define endianness
#endif
#endif
// ---------------------------------------------------------------------------
// -------------- Endianness implementation for IEEE arithmetic --------------
// ---------------------------------------------------------------------------
/**
* @brief 32 bit unsigned integer.
*
*/
typedef unsigned int uword;
/**
* @brief 32 bit signed integer.
*
*/
typedef signed int sword;
#ifdef __IEEE_BIG_ENDIAN
/**
* @brief A union which permits us to convert between a double and two 32 bit ints.
*
* Big endian version.
*
*/
typedef union
{
double value;
struct
{
uword msw;
uword lsw;
} parts;
} ieee_double_shape_type;
#endif
#ifdef __IEEE_LITTLE_ENDIAN
/**
* @brief A union which permits us to convert between a double and two 32 bit ints.
*
* Little endian version.
*
*/
typedef union
{
double value;
struct
{
uword lsw;
uword msw;
} parts;
} ieee_double_shape_type;
#endif
// ---------------------------------------------------------------------------
// ---------- Endianness implementation for 64 bit IEEE arithmetic -----------
// ---------------------------------------------------------------------------
/**
* @brief 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)
/**
* @brief 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)
/**
* @brief 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)
/**
* @brief 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)
/**
* @brief 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)
/**
* @brief 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)
// ---------------------------------------------------------------------------
// ---------- Endianness implementation for 32 bit IEEE arithmetic -----------
// ---------------------------------------------------------------------------
/**
* @brief A union which permits us to convert between a float and a 32 bit int.
*
*/
typedef union
{
float value;
uword word;
} ieee_float_shape_type;
/**
* @brief 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)
/**
* @brief 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)
// ---------------------------------------------------------------------------
// ------------------- End of real primitive definitions ---------------------
// ---------------------------------------------------------------------------
#endif
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