| 1 |
/* |
| 2 |
* fpu/mathlib.h - Floating-point math support library |
| 3 |
* |
| 4 |
* Basilisk II (C) 1997-2001 Christian Bauer |
| 5 |
* |
| 6 |
* MC68881/68040 fpu emulation |
| 7 |
* |
| 8 |
* Original UAE FPU, copyright 1996 Herman ten Brugge |
| 9 |
* Rewrite for x86, copyright 1999-2001 Lauri Pesonen |
| 10 |
* New framework, copyright 2000-2001 Gwenole Beauchesne |
| 11 |
* Adapted for JIT compilation (c) Bernd Meyer, 2000-2001 |
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* |
| 13 |
* This program is free software; you can redistribute it and/or modify |
| 14 |
* it under the terms of the GNU General Public License as published by |
| 15 |
* the Free Software Foundation; either version 2 of the License, or |
| 16 |
* (at your option) any later version. |
| 17 |
* |
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* This program is distributed in the hope that it will be useful, |
| 19 |
* but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 20 |
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| 21 |
* GNU General Public License for more details. |
| 22 |
* |
| 23 |
* You should have received a copy of the GNU General Public License |
| 24 |
* along with this program; if not, write to the Free Software |
| 25 |
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA |
| 26 |
*/ |
| 27 |
|
| 28 |
#ifndef FPU_MATHLIB_H |
| 29 |
#define FPU_MATHLIB_H |
| 30 |
|
| 31 |
/* NOTE: this file shall be included only from fpu/fpu_*.cpp */ |
| 32 |
#undef PUBLIC |
| 33 |
#define PUBLIC extern |
| 34 |
|
| 35 |
#undef PRIVATE |
| 36 |
#define PRIVATE static |
| 37 |
|
| 38 |
#undef FFPU |
| 39 |
#define FFPU /**/ |
| 40 |
|
| 41 |
#undef FPU |
| 42 |
#define FPU fpu. |
| 43 |
|
| 44 |
// Define the following macro if branches are expensive. If so, |
| 45 |
// integer-based isnan() and isinf() functions are implemented. |
| 46 |
// TODO: move to Makefile.in |
| 47 |
#define BRANCHES_ARE_EXPENSIVE 1 |
| 48 |
|
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// Use ISO C99 extended-precision math functions (glibc 2.1+) |
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#define FPU_USE_ISO_C99 1 |
| 51 |
|
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// NOTE: this is irrelevant on Win32 platforms since the MS libraries |
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// don't support extended-precision floating-point computations |
| 54 |
#ifdef WIN32 |
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#undef FPU_USE_ISO_C99 |
| 56 |
#endif |
| 57 |
|
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// Use faster implementation of math functions, but this could cause |
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// some incorrect results (?) |
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// TODO: actually implement the slower but safer versions |
| 61 |
#define FPU_FAST_MATH 1 |
| 62 |
|
| 63 |
#if FPU_USE_ISO_C99 |
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// NOTE: no prior <math.h> shall be included at this point |
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#define __USE_ISOC99 1 // for glibc 2.2.X and newer |
| 66 |
#define __USE_ISOC9X 1 // for glibc 2.1.X |
| 67 |
#include <math.h> |
| 68 |
#else |
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#include <cmath> |
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using namespace std; |
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#endif |
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|
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/* -------------------------------------------------------------------------- */ |
| 74 |
/* --- Floating-point register types --- */ |
| 75 |
/* -------------------------------------------------------------------------- */ |
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|
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// Single : S 8*E 23*F |
| 78 |
#define FP_SINGLE_EXP_MAX 0xff |
| 79 |
#define FP_SINGLE_EXP_BIAS 0x7f |
| 80 |
|
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// Double : S 11*E 52*F |
| 82 |
#define FP_DOUBLE_EXP_MAX 0x7ff |
| 83 |
#define FP_DOUBLE_EXP_BIAS 0x3ff |
| 84 |
|
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// Extended : S 15*E 64*F |
| 86 |
#define FP_EXTENDED_EXP_MAX 0x7fff |
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#define FP_EXTENDED_EXP_BIAS 0x3fff |
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|
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// Zeroes : E = 0 & F = 0 |
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// Infinities : E = MAX & F = 0 |
| 91 |
// Not-A-Number : E = MAX & F # 0 |
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|
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/* -------------------------------------------------------------------------- */ |
| 94 |
/* --- Floating-point type shapes (IEEE-compliant) --- */ |
| 95 |
/* -------------------------------------------------------------------------- */ |
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|
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// Taken from glibc 2.2.x: ieee754.h |
| 98 |
|
| 99 |
// IEEE-754 float format |
| 100 |
union fpu_single_shape { |
| 101 |
|
| 102 |
fpu_single value; |
| 103 |
|
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/* This is the IEEE 754 single-precision format. */ |
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struct { |
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#ifdef WORDS_BIGENDIAN |
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unsigned int negative:1; |
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unsigned int exponent:8; |
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unsigned int mantissa:23; |
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#else |
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unsigned int mantissa:23; |
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unsigned int exponent:8; |
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unsigned int negative:1; |
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#endif |
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} ieee; |
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|
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/* This format makes it easier to see if a NaN is a signalling NaN. */ |
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struct { |
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#ifdef WORDS_BIGENDIAN |
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unsigned int negative:1; |
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unsigned int exponent:8; |
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unsigned int quiet_nan:1; |
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unsigned int mantissa:22; |
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#else |
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unsigned int mantissa:22; |
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unsigned int quiet_nan:1; |
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unsigned int exponent:8; |
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unsigned int negative:1; |
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#endif |
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} ieee_nan; |
| 131 |
}; |
| 132 |
|
| 133 |
// IEEE-754 double format |
| 134 |
union fpu_double_shape { |
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fpu_double value; |
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|
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/* This is the IEEE 754 double-precision format. */ |
| 138 |
struct { |
| 139 |
#ifdef WORDS_BIGENDIAN |
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unsigned int negative:1; |
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unsigned int exponent:11; |
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/* Together these comprise the mantissa. */ |
| 143 |
unsigned int mantissa0:20; |
| 144 |
unsigned int mantissa1:32; |
| 145 |
#else |
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# if HOST_FLOAT_WORDS_BIG_ENDIAN |
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unsigned int mantissa0:20; |
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unsigned int exponent:11; |
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unsigned int negative:1; |
| 150 |
unsigned int mantissa1:32; |
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# else |
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/* Together these comprise the mantissa. */ |
| 153 |
unsigned int mantissa1:32; |
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unsigned int mantissa0:20; |
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unsigned int exponent:11; |
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unsigned int negative:1; |
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# endif |
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#endif |
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} ieee; |
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|
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/* This format makes it easier to see if a NaN is a signalling NaN. */ |
| 162 |
struct { |
| 163 |
#ifdef WORDS_BIGENDIAN |
| 164 |
unsigned int negative:1; |
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unsigned int exponent:11; |
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unsigned int quiet_nan:1; |
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/* Together these comprise the mantissa. */ |
| 168 |
unsigned int mantissa0:19; |
| 169 |
unsigned int mantissa1:32; |
| 170 |
#else |
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# if HOST_FLOAT_WORDS_BIG_ENDIAN |
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unsigned int mantissa0:19; |
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unsigned int quiet_nan:1; |
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unsigned int exponent:11; |
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unsigned int negative:1; |
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unsigned int mantissa1:32; |
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# else |
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/* Together these comprise the mantissa. */ |
| 179 |
unsigned int mantissa1:32; |
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unsigned int mantissa0:19; |
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unsigned int quiet_nan:1; |
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unsigned int exponent:11; |
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unsigned int negative:1; |
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# endif |
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#endif |
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} ieee_nan; |
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|
| 188 |
/* This format is used to extract the sign_exponent and mantissa parts only */ |
| 189 |
struct { |
| 190 |
#if HOST_FLOAT_WORDS_BIG_ENDIAN |
| 191 |
unsigned int msw:32; |
| 192 |
unsigned int lsw:32; |
| 193 |
#else |
| 194 |
unsigned int lsw:32; |
| 195 |
unsigned int msw:32; |
| 196 |
#endif |
| 197 |
} parts; |
| 198 |
}; |
| 199 |
|
| 200 |
#ifdef USE_LONG_DOUBLE |
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// IEEE-854 long double format |
| 202 |
union fpu_extended_shape { |
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fpu_extended value; |
| 204 |
|
| 205 |
/* This is the IEEE 854 double-extended-precision format. */ |
| 206 |
struct { |
| 207 |
#ifdef WORDS_BIGENDIAN |
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unsigned int negative:1; |
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unsigned int exponent:15; |
| 210 |
unsigned int empty:16; |
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unsigned int mantissa0:32; |
| 212 |
unsigned int mantissa1:32; |
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#else |
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# if HOST_FLOAT_WORDS_BIG_ENDIAN |
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unsigned int exponent:15; |
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unsigned int negative:1; |
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unsigned int empty:16; |
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unsigned int mantissa0:32; |
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unsigned int mantissa1:32; |
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# else |
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unsigned int mantissa1:32; |
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unsigned int mantissa0:32; |
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unsigned int exponent:15; |
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unsigned int negative:1; |
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unsigned int empty:16; |
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# endif |
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#endif |
| 228 |
} ieee; |
| 229 |
|
| 230 |
/* This is for NaNs in the IEEE 854 double-extended-precision format. */ |
| 231 |
struct { |
| 232 |
#ifdef WORDS_BIGENDIAN |
| 233 |
unsigned int negative:1; |
| 234 |
unsigned int exponent:15; |
| 235 |
unsigned int empty:16; |
| 236 |
unsigned int one:1; |
| 237 |
unsigned int quiet_nan:1; |
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unsigned int mantissa0:30; |
| 239 |
unsigned int mantissa1:32; |
| 240 |
#else |
| 241 |
# if HOST_FLOAT_WORDS_BIG_ENDIAN |
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unsigned int exponent:15; |
| 243 |
unsigned int negative:1; |
| 244 |
unsigned int empty:16; |
| 245 |
unsigned int mantissa0:30; |
| 246 |
unsigned int quiet_nan:1; |
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unsigned int one:1; |
| 248 |
unsigned int mantissa1:32; |
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# else |
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unsigned int mantissa1:32; |
| 251 |
unsigned int mantissa0:30; |
| 252 |
unsigned int quiet_nan:1; |
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unsigned int one:1; |
| 254 |
unsigned int exponent:15; |
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unsigned int negative:1; |
| 256 |
unsigned int empty:16; |
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# endif |
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#endif |
| 259 |
} ieee_nan; |
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|
| 261 |
/* This format is used to extract the sign_exponent and mantissa parts only */ |
| 262 |
struct { |
| 263 |
#if HOST_FLOAT_WORDS_BIG_ENDIAN |
| 264 |
unsigned int sign_exponent:16; |
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unsigned int empty:16; |
| 266 |
unsigned int msw:32; |
| 267 |
unsigned int lsw:32; |
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#else |
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unsigned int lsw:32; |
| 270 |
unsigned int msw:32; |
| 271 |
unsigned int sign_exponent:16; |
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unsigned int empty:16; |
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#endif |
| 274 |
} parts; |
| 275 |
}; |
| 276 |
#endif |
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|
| 278 |
#ifdef USE_QUAD_DOUBLE |
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// IEEE-854 quad double format |
| 280 |
union fpu_extended_shape { |
| 281 |
fpu_extended value; |
| 282 |
|
| 283 |
/* This is the IEEE 854 quad-precision format. */ |
| 284 |
struct { |
| 285 |
#ifdef WORDS_BIGENDIAN |
| 286 |
unsigned int negative:1; |
| 287 |
unsigned int exponent:15; |
| 288 |
unsigned int mantissa0:16; |
| 289 |
unsigned int mantissa1:32; |
| 290 |
unsigned int mantissa2:32; |
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unsigned int mantissa3:32; |
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#else |
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unsigned int mantissa3:32; |
| 294 |
unsigned int mantissa2:32; |
| 295 |
unsigned int mantissa1:32; |
| 296 |
unsigned int mantissa0:16; |
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unsigned int exponent:15; |
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unsigned int negative:1; |
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#endif |
| 300 |
} ieee; |
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|
| 302 |
/* This is for NaNs in the IEEE 854 quad-precision format. */ |
| 303 |
struct { |
| 304 |
#ifdef WORDS_BIGENDIAN |
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unsigned int negative:1; |
| 306 |
unsigned int exponent:15; |
| 307 |
unsigned int quiet_nan:1; |
| 308 |
unsigned int mantissa0:15; |
| 309 |
unsigned int mantissa1:30; |
| 310 |
unsigned int mantissa2:32; |
| 311 |
unsigned int mantissa3:32; |
| 312 |
#else |
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unsigned int mantissa3:32; |
| 314 |
unsigned int mantissa2:32; |
| 315 |
unsigned int mantissa1:32; |
| 316 |
unsigned int mantissa0:15; |
| 317 |
unsigned int quiet_nan:1; |
| 318 |
unsigned int exponent:15; |
| 319 |
unsigned int negative:1; |
| 320 |
#endif |
| 321 |
} ieee_nan; |
| 322 |
|
| 323 |
/* This format is used to extract the sign_exponent and mantissa parts only */ |
| 324 |
#if HOST_FLOAT_WORDS_BIG_ENDIAN |
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struct { |
| 326 |
uae_u64 msw; |
| 327 |
uae_u64 lsw; |
| 328 |
} parts64; |
| 329 |
struct { |
| 330 |
uae_u32 w0; |
| 331 |
uae_u32 w1; |
| 332 |
uae_u32 w2; |
| 333 |
uae_u32 w3; |
| 334 |
} parts32; |
| 335 |
#else |
| 336 |
struct { |
| 337 |
uae_u64 lsw; |
| 338 |
uae_u64 msw; |
| 339 |
} parts64; |
| 340 |
struct { |
| 341 |
uae_u32 w3; |
| 342 |
uae_u32 w2; |
| 343 |
uae_u32 w1; |
| 344 |
uae_u32 w0; |
| 345 |
} parts32; |
| 346 |
#endif |
| 347 |
}; |
| 348 |
#endif |
| 349 |
|
| 350 |
// Declare and initialize a pointer to a shape of the requested FP type |
| 351 |
#define fp_declare_init_shape(psvar, rfvar, ftype) \ |
| 352 |
fpu_ ## ftype ## _shape * psvar = (fpu_ ## ftype ## _shape *)( &rfvar ) |
| 353 |
|
| 354 |
/* -------------------------------------------------------------------------- */ |
| 355 |
/* --- Extra Math Functions --- */ |
| 356 |
/* --- (most of them had to be defined before including <fpu/flags.h>) --- */ |
| 357 |
/* -------------------------------------------------------------------------- */ |
| 358 |
|
| 359 |
#undef isnan |
| 360 |
#if 0 && defined(HAVE_ISNANL) |
| 361 |
# define isnan(x) isnanl((x)) |
| 362 |
#else |
| 363 |
# define isnan(x) fp_do_isnan((x)) |
| 364 |
#endif |
| 365 |
|
| 366 |
PRIVATE inline bool FFPU fp_do_isnan(fpu_register const & r) |
| 367 |
{ |
| 368 |
#ifdef BRANCHES_ARE_EXPENSIVE |
| 369 |
#ifndef USE_LONG_DOUBLE |
| 370 |
fp_declare_init_shape(sxp, r, double); |
| 371 |
uae_s32 hx = sxp->parts.msw; |
| 372 |
uae_s32 lx = sxp->parts.lsw; |
| 373 |
hx &= 0x7fffffff; |
| 374 |
hx |= (uae_u32)(lx | (-lx)) >> 31; |
| 375 |
hx = 0x7ff00000 - hx; |
| 376 |
return (int)(((uae_u32)hx) >> 31); |
| 377 |
#elif USE_QUAD_DOUBLE |
| 378 |
fp_declare_init_shape(sxp, r, extended); |
| 379 |
uae_s64 hx = sxp->parts64.msw; |
| 380 |
uae_s64 lx = sxp->parts64.lsw; |
| 381 |
hx &= 0x7fffffffffffffffLL; |
| 382 |
hx |= (uae_u64)(lx | (-lx)) >> 63; |
| 383 |
hx = 0x7fff000000000000LL - hx; |
| 384 |
return (int)((uae_u64)hx >> 63); |
| 385 |
#else |
| 386 |
fp_declare_init_shape(sxp, r, extended); |
| 387 |
uae_s32 se = sxp->parts.sign_exponent; |
| 388 |
uae_s32 hx = sxp->parts.msw; |
| 389 |
uae_s32 lx = sxp->parts.lsw; |
| 390 |
se = (se & 0x7fff) << 1; |
| 391 |
lx |= hx & 0x7fffffff; |
| 392 |
se |= (uae_u32)(lx | (-lx)) >> 31; |
| 393 |
se = 0xfffe - se; |
| 394 |
// TODO: check whether rshift count is 16 or 31 |
| 395 |
return (int)(((uae_u32)(se)) >> 16); |
| 396 |
#endif |
| 397 |
#else |
| 398 |
#if USE_LONG_DOUBLE || USE_QUAD_DOUBLE |
| 399 |
fp_declare_init_shape(sxp, r, extended); |
| 400 |
return (sxp->ieee_nan.exponent == FP_EXTENDED_EXP_MAX) |
| 401 |
#else |
| 402 |
fp_declare_init_shape(sxp, r, double); |
| 403 |
return (sxp->ieee_nan.exponent == FP_DOUBLE_EXP_MAX) |
| 404 |
#endif |
| 405 |
&& (sxp->ieee_nan.mantissa0 != 0) |
| 406 |
&& (sxp->ieee_nan.mantissa1 != 0) |
| 407 |
#ifdef USE_QUAD_DOUBLE |
| 408 |
&& (sxp->ieee_nan.mantissa2 != 0) |
| 409 |
&& (sxp->ieee_nan.mantissa3 != 0) |
| 410 |
#endif |
| 411 |
; |
| 412 |
#endif |
| 413 |
} |
| 414 |
|
| 415 |
#undef isinf |
| 416 |
#if 0 && defined(HAVE_ISINFL) |
| 417 |
# define isinf(x) isinfl((x)) |
| 418 |
#else |
| 419 |
# define isinf(x) fp_do_isinf((x)) |
| 420 |
#endif |
| 421 |
|
| 422 |
PRIVATE inline bool FFPU fp_do_isinf(fpu_register const & r) |
| 423 |
{ |
| 424 |
#ifdef BRANCHES_ARE_EXPENSIVE |
| 425 |
#ifndef USE_LONG_DOUBLE |
| 426 |
fp_declare_init_shape(sxp, r, double); |
| 427 |
uae_s32 hx = sxp->parts.msw; |
| 428 |
uae_s32 lx = sxp->parts.lsw; |
| 429 |
lx |= (hx & 0x7fffffff) ^ 0x7ff00000; |
| 430 |
lx |= -lx; |
| 431 |
return ~(lx >> 31) & (hx >> 30); |
| 432 |
#elif USE_QUAD_DOUBLE |
| 433 |
fp_declare_init_shape(sxp, r, extended); |
| 434 |
uae_s64 hx = sxp->parts64.msw; |
| 435 |
uae_s64 lx = sxp->parts64.lsw; |
| 436 |
lx |= (hx & 0x7fffffffffffffffLL) ^ 0x7fff000000000000LL; |
| 437 |
lx |= -lx; |
| 438 |
return ~(lx >> 63) & (hx >> 62); |
| 439 |
#else |
| 440 |
fp_declare_init_shape(sxp, r, extended); |
| 441 |
uae_s32 se = sxp->parts.sign_exponent; |
| 442 |
uae_s32 hx = sxp->parts.msw; |
| 443 |
uae_s32 lx = sxp->parts.lsw; |
| 444 |
/* This additional ^ 0x80000000 is necessary because in Intel's |
| 445 |
internal representation of the implicit one is explicit. |
| 446 |
NOTE: anyway, this is equivalent to & 0x7fffffff in that case. */ |
| 447 |
#ifdef __i386__ |
| 448 |
lx |= (hx ^ 0x80000000) | ((se & 0x7fff) ^ 0x7fff); |
| 449 |
#else |
| 450 |
lx |= (hx & 0x7fffffff) | ((se & 0x7fff) ^ 0x7fff); |
| 451 |
#endif |
| 452 |
lx |= -lx; |
| 453 |
se &= 0x8000; |
| 454 |
return ~(lx >> 31) & (1 - (se >> 14)); |
| 455 |
#endif |
| 456 |
#else |
| 457 |
#if USE_LONG_DOUBLE || USE_QUAD_DOUBLE |
| 458 |
fp_declare_init_shape(sxp, r, extended); |
| 459 |
return (sxp->ieee_nan.exponent == FP_EXTENDED_EXP_MAX) |
| 460 |
#else |
| 461 |
fp_declare_init_shape(sxp, r, double); |
| 462 |
return (sxp->ieee_nan.exponent == FP_DOUBLE_EXP_MAX) |
| 463 |
#endif |
| 464 |
&& (sxp->ieee_nan.mantissa0 == 0) |
| 465 |
&& (sxp->ieee_nan.mantissa1 == 0) |
| 466 |
#ifdef USE_QUAD_DOUBLE |
| 467 |
&& (sxp->ieee_nan.mantissa2 == 0) |
| 468 |
&& (sxp->ieee_nan.mantissa3 == 0) |
| 469 |
#endif |
| 470 |
; |
| 471 |
#endif |
| 472 |
} |
| 473 |
|
| 474 |
#undef isneg |
| 475 |
#define isneg(x) fp_do_isneg((x)) |
| 476 |
|
| 477 |
PRIVATE inline bool FFPU fp_do_isneg(fpu_register const & r) |
| 478 |
{ |
| 479 |
#if USE_LONG_DOUBLE || USE_QUAD_DOUBLE |
| 480 |
fp_declare_init_shape(sxp, r, extended); |
| 481 |
#else |
| 482 |
fp_declare_init_shape(sxp, r, double); |
| 483 |
#endif |
| 484 |
return sxp->ieee.negative; |
| 485 |
} |
| 486 |
|
| 487 |
#undef iszero |
| 488 |
#define iszero(x) fp_do_iszero((x)) |
| 489 |
|
| 490 |
PRIVATE inline bool FFPU fp_do_iszero(fpu_register const & r) |
| 491 |
{ |
| 492 |
// TODO: BRANCHES_ARE_EXPENSIVE |
| 493 |
#if USE_LONG_DOUBLE || USE_QUAD_DOUBLE |
| 494 |
fp_declare_init_shape(sxp, r, extended); |
| 495 |
#else |
| 496 |
fp_declare_init_shape(sxp, r, double); |
| 497 |
#endif |
| 498 |
return (sxp->ieee.exponent == 0) |
| 499 |
&& (sxp->ieee.mantissa0 == 0) |
| 500 |
&& (sxp->ieee.mantissa1 == 0) |
| 501 |
#ifdef USE_QUAD_DOUBLE |
| 502 |
&& (sxp->ieee.mantissa2 == 0) |
| 503 |
&& (sxp->ieee.mantissa3 == 0) |
| 504 |
#endif |
| 505 |
; |
| 506 |
} |
| 507 |
|
| 508 |
PRIVATE inline void FFPU get_dest_flags(fpu_register const & r) |
| 509 |
{ |
| 510 |
fl_dest.negative = isneg(r); |
| 511 |
fl_dest.zero = iszero(r); |
| 512 |
fl_dest.infinity = isinf(r); |
| 513 |
fl_dest.nan = isnan(r); |
| 514 |
fl_dest.in_range = !fl_dest.zero && !fl_dest.infinity && !fl_dest.nan; |
| 515 |
} |
| 516 |
|
| 517 |
PRIVATE inline void FFPU get_source_flags(fpu_register const & r) |
| 518 |
{ |
| 519 |
fl_source.negative = isneg(r); |
| 520 |
fl_source.zero = iszero(r); |
| 521 |
fl_source.infinity = isinf(r); |
| 522 |
fl_source.nan = isnan(r); |
| 523 |
fl_source.in_range = !fl_source.zero && !fl_source.infinity && !fl_source.nan; |
| 524 |
} |
| 525 |
|
| 526 |
PRIVATE inline void FFPU make_nan(fpu_register & r) |
| 527 |
{ |
| 528 |
// FIXME: is that correct ? |
| 529 |
#if USE_LONG_DOUBLE || USE_QUAD_DOUBLE |
| 530 |
fp_declare_init_shape(sxp, r, extended); |
| 531 |
sxp->ieee.exponent = FP_EXTENDED_EXP_MAX; |
| 532 |
sxp->ieee.mantissa0 = 0xffffffff; |
| 533 |
#else |
| 534 |
fp_declare_init_shape(sxp, r, double); |
| 535 |
sxp->ieee.exponent = FP_DOUBLE_EXP_MAX; |
| 536 |
sxp->ieee.mantissa0 = 0xfffff; |
| 537 |
#endif |
| 538 |
sxp->ieee.mantissa1 = 0xffffffff; |
| 539 |
#ifdef USE_QUAD_DOUBLE |
| 540 |
sxp->ieee.mantissa2 = 0xffffffff; |
| 541 |
sxp->ieee.mantissa3 = 0xffffffff; |
| 542 |
#endif |
| 543 |
} |
| 544 |
|
| 545 |
PRIVATE inline void FFPU make_zero_positive(fpu_register & r) |
| 546 |
{ |
| 547 |
#if 1 |
| 548 |
r = +0.0; |
| 549 |
#else |
| 550 |
#if USE_LONG_DOUBLE || USE_QUAD_DOUBLE |
| 551 |
fp_declare_init_shape(sxp, r, extended); |
| 552 |
#else |
| 553 |
fp_declare_init_shape(sxp, r, double); |
| 554 |
#endif |
| 555 |
sxp->ieee.negative = 0; |
| 556 |
sxp->ieee.exponent = 0; |
| 557 |
sxp->ieee.mantissa0 = 0; |
| 558 |
sxp->ieee.mantissa1 = 0; |
| 559 |
#ifdef USE_QUAD_DOUBLE |
| 560 |
sxp->ieee.mantissa2 = 0; |
| 561 |
sxp->ieee.mantissa3 = 0; |
| 562 |
#endif |
| 563 |
#endif |
| 564 |
} |
| 565 |
|
| 566 |
PRIVATE inline void FFPU make_zero_negative(fpu_register & r) |
| 567 |
{ |
| 568 |
#if 1 |
| 569 |
r = -0.0; |
| 570 |
#else |
| 571 |
#if USE_LONG_DOUBLE || USE_QUAD_DOUBLE |
| 572 |
fp_declare_init_shape(sxp, r, extended); |
| 573 |
#else |
| 574 |
fp_declare_init_shape(sxp, r, double); |
| 575 |
#endif |
| 576 |
sxp->ieee.negative = 1; |
| 577 |
sxp->ieee.exponent = 0; |
| 578 |
sxp->ieee.mantissa0 = 0; |
| 579 |
sxp->ieee.mantissa1 = 0; |
| 580 |
#ifdef USE_QUAD_DOUBLE |
| 581 |
sxp->ieee.mantissa2 = 0; |
| 582 |
sxp->ieee.mantissa3 = 0; |
| 583 |
#endif |
| 584 |
#endif |
| 585 |
} |
| 586 |
|
| 587 |
PRIVATE inline void FFPU make_inf_positive(fpu_register & r) |
| 588 |
{ |
| 589 |
#if USE_LONG_DOUBLE || USE_QUAD_DOUBLE |
| 590 |
fp_declare_init_shape(sxp, r, extended); |
| 591 |
sxp->ieee_nan.exponent = FP_EXTENDED_EXP_MAX; |
| 592 |
#else |
| 593 |
fp_declare_init_shape(sxp, r, double); |
| 594 |
sxp->ieee_nan.exponent = FP_DOUBLE_EXP_MAX; |
| 595 |
#endif |
| 596 |
sxp->ieee_nan.negative = 0; |
| 597 |
sxp->ieee_nan.mantissa0 = 0; |
| 598 |
sxp->ieee_nan.mantissa1 = 0; |
| 599 |
#ifdef USE_QUAD_DOUBLE |
| 600 |
sxp->ieee_nan.mantissa2 = 0; |
| 601 |
sxp->ieee_nan.mantissa3 = 0; |
| 602 |
#endif |
| 603 |
} |
| 604 |
|
| 605 |
PRIVATE inline void FFPU make_inf_negative(fpu_register & r) |
| 606 |
{ |
| 607 |
#if USE_LONG_DOUBLE || USE_QUAD_DOUBLE |
| 608 |
fp_declare_init_shape(sxp, r, extended); |
| 609 |
sxp->ieee_nan.exponent = FP_EXTENDED_EXP_MAX; |
| 610 |
#else |
| 611 |
fp_declare_init_shape(sxp, r, double); |
| 612 |
sxp->ieee_nan.exponent = FP_DOUBLE_EXP_MAX; |
| 613 |
#endif |
| 614 |
sxp->ieee_nan.negative = 1; |
| 615 |
sxp->ieee_nan.mantissa0 = 0; |
| 616 |
sxp->ieee_nan.mantissa1 = 0; |
| 617 |
#ifdef USE_QUAD_DOUBLE |
| 618 |
sxp->ieee_nan.mantissa2 = 0; |
| 619 |
sxp->ieee_nan.mantissa3 = 0; |
| 620 |
#endif |
| 621 |
} |
| 622 |
|
| 623 |
PRIVATE inline fpu_register FFPU fast_fgetexp(fpu_register const & r) |
| 624 |
{ |
| 625 |
#if USE_LONG_DOUBLE || USE_QUAD_DOUBLE |
| 626 |
fp_declare_init_shape(sxp, r, extended); |
| 627 |
return (sxp->ieee.exponent - FP_EXTENDED_EXP_BIAS); |
| 628 |
#else |
| 629 |
fp_declare_init_shape(sxp, r, double); |
| 630 |
return (sxp->ieee.exponent - FP_DOUBLE_EXP_BIAS); |
| 631 |
#endif |
| 632 |
} |
| 633 |
|
| 634 |
// Normalize to range 1..2 |
| 635 |
PRIVATE inline void FFPU fast_remove_exponent(fpu_register & r) |
| 636 |
{ |
| 637 |
#if USE_LONG_DOUBLE || USE_QUAD_DOUBLE |
| 638 |
fp_declare_init_shape(sxp, r, extended); |
| 639 |
sxp->ieee.exponent = FP_EXTENDED_EXP_BIAS; |
| 640 |
#else |
| 641 |
fp_declare_init_shape(sxp, r, double); |
| 642 |
sxp->ieee.exponent = FP_DOUBLE_EXP_BIAS; |
| 643 |
#endif |
| 644 |
} |
| 645 |
|
| 646 |
// The sign of the quotient is the exclusive-OR of the sign bits |
| 647 |
// of the source and destination operands. |
| 648 |
PRIVATE inline uae_u32 FFPU get_quotient_sign(fpu_register const & ra, fpu_register const & rb) |
| 649 |
{ |
| 650 |
#if USE_LONG_DOUBLE || USE_QUAD_DOUBLE |
| 651 |
fp_declare_init_shape(sap, ra, extended); |
| 652 |
fp_declare_init_shape(sbp, rb, extended); |
| 653 |
#else |
| 654 |
fp_declare_init_shape(sap, ra, double); |
| 655 |
fp_declare_init_shape(sbp, rb, double); |
| 656 |
#endif |
| 657 |
return ((sap->ieee.negative ^ sbp->ieee.negative) ? FPSR_QUOTIENT_SIGN : 0); |
| 658 |
} |
| 659 |
|
| 660 |
/* -------------------------------------------------------------------------- */ |
| 661 |
/* --- Math functions --- */ |
| 662 |
/* -------------------------------------------------------------------------- */ |
| 663 |
|
| 664 |
#if FPU_USE_ISO_C99 && (USE_LONG_DOUBLE || USE_QUAD_DOUBLE) |
| 665 |
# ifdef HAVE_LOGL |
| 666 |
# define fp_log logl |
| 667 |
# endif |
| 668 |
# ifdef HAVE_LOG10L |
| 669 |
# define fp_log10 log10l |
| 670 |
# endif |
| 671 |
# ifdef HAVE_EXPL |
| 672 |
# define fp_exp expl |
| 673 |
# endif |
| 674 |
# ifdef HAVE_POWL |
| 675 |
# define fp_pow powl |
| 676 |
# endif |
| 677 |
# ifdef HAVE_FABSL |
| 678 |
# define fp_fabs fabsl |
| 679 |
# endif |
| 680 |
# ifdef HAVE_SQRTL |
| 681 |
# define fp_sqrt sqrtl |
| 682 |
# endif |
| 683 |
# ifdef HAVE_SINL |
| 684 |
# define fp_sin sinl |
| 685 |
# endif |
| 686 |
# ifdef HAVE_COSL |
| 687 |
# define fp_cos cosl |
| 688 |
# endif |
| 689 |
# ifdef HAVE_TANL |
| 690 |
# define fp_tan tanl |
| 691 |
# endif |
| 692 |
# ifdef HAVE_SINHL |
| 693 |
# define fp_sinh sinhl |
| 694 |
# endif |
| 695 |
# ifdef HAVE_COSHL |
| 696 |
# define fp_cosh coshl |
| 697 |
# endif |
| 698 |
# ifdef HAVE_TANHL |
| 699 |
# define fp_tanh tanhl |
| 700 |
# endif |
| 701 |
# ifdef HAVE_ASINL |
| 702 |
# define fp_asin asinl |
| 703 |
# endif |
| 704 |
# ifdef HAVE_ACOSL |
| 705 |
# define fp_acos acosl |
| 706 |
# endif |
| 707 |
# ifdef HAVE_ATANL |
| 708 |
# define fp_atan atanl |
| 709 |
# endif |
| 710 |
# ifdef HAVE_ASINHL |
| 711 |
# define fp_asinh asinhl |
| 712 |
# endif |
| 713 |
# ifdef HAVE_ACOSHL |
| 714 |
# define fp_acosh acoshl |
| 715 |
# endif |
| 716 |
# ifdef HAVE_ATANHL |
| 717 |
# define fp_atanh atanhl |
| 718 |
# endif |
| 719 |
# ifdef HAVE_FLOORL |
| 720 |
# define fp_floor floorl |
| 721 |
# endif |
| 722 |
# ifdef HAVE_CEILL |
| 723 |
# define fp_ceil ceill |
| 724 |
# endif |
| 725 |
#endif |
| 726 |
|
| 727 |
#ifndef fp_log |
| 728 |
# define fp_log log |
| 729 |
#endif |
| 730 |
#ifndef fp_log10 |
| 731 |
# define fp_log10 log10 |
| 732 |
#endif |
| 733 |
#ifndef fp_exp |
| 734 |
# define fp_exp exp |
| 735 |
#endif |
| 736 |
#ifndef fp_pow |
| 737 |
# define fp_pow pow |
| 738 |
#endif |
| 739 |
#ifndef fp_fabs |
| 740 |
# define fp_fabs fabs |
| 741 |
#endif |
| 742 |
#ifndef fp_sqrt |
| 743 |
# define fp_sqrt sqrt |
| 744 |
#endif |
| 745 |
#ifndef fp_sin |
| 746 |
# define fp_sin sin |
| 747 |
#endif |
| 748 |
#ifndef fp_cos |
| 749 |
# define fp_cos cos |
| 750 |
#endif |
| 751 |
#ifndef fp_tan |
| 752 |
# define fp_tan tan |
| 753 |
#endif |
| 754 |
#ifndef fp_sinh |
| 755 |
# define fp_sinh sinh |
| 756 |
#endif |
| 757 |
#ifndef fp_cosh |
| 758 |
# define fp_cosh cosh |
| 759 |
#endif |
| 760 |
#ifndef fp_tanh |
| 761 |
# define fp_tanh tanh |
| 762 |
#endif |
| 763 |
#ifndef fp_asin |
| 764 |
# define fp_asin asin |
| 765 |
#endif |
| 766 |
#ifndef fp_acos |
| 767 |
# define fp_acos acos |
| 768 |
#endif |
| 769 |
#ifndef fp_atan |
| 770 |
# define fp_atan atan |
| 771 |
#endif |
| 772 |
#ifndef fp_asinh |
| 773 |
# define fp_asinh asinh |
| 774 |
#endif |
| 775 |
#ifndef fp_acosh |
| 776 |
# define fp_acosh acosh |
| 777 |
#endif |
| 778 |
#ifndef fp_atanh |
| 779 |
# define fp_atanh atanh |
| 780 |
#endif |
| 781 |
#ifndef fp_floor |
| 782 |
# define fp_floor floor |
| 783 |
#endif |
| 784 |
#ifndef fp_ceil |
| 785 |
# define fp_ceil ceil |
| 786 |
#endif |
| 787 |
|
| 788 |
#if defined(FPU_IEEE) && defined(USE_X87_ASSEMBLY) |
| 789 |
// Assembly optimized support functions. Taken from glibc 2.2.2 |
| 790 |
|
| 791 |
#undef fp_log |
| 792 |
#define fp_log fp_do_log |
| 793 |
|
| 794 |
#ifndef FPU_FAST_MATH |
| 795 |
// FIXME: unimplemented |
| 796 |
PRIVATE fpu_extended fp_do_log(fpu_extended x); |
| 797 |
#else |
| 798 |
PRIVATE inline fpu_extended fp_do_log(fpu_extended x) |
| 799 |
{ |
| 800 |
fpu_extended value; |
| 801 |
__asm__ __volatile__("fldln2; fxch; fyl2x" : "=t" (value) : "0" (x) : "st(1)"); |
| 802 |
return value; |
| 803 |
} |
| 804 |
#endif |
| 805 |
|
| 806 |
#undef fp_log10 |
| 807 |
#define fp_log10 fp_do_log10 |
| 808 |
|
| 809 |
#ifndef FPU_FAST_MATH |
| 810 |
// FIXME: unimplemented |
| 811 |
PRIVATE fpu_extended fp_do_log10(fpu_extended x); |
| 812 |
#else |
| 813 |
PRIVATE inline fpu_extended fp_do_log10(fpu_extended x) |
| 814 |
{ |
| 815 |
fpu_extended value; |
| 816 |
__asm__ __volatile__("fldlg2; fxch; fyl2x" : "=t" (value) : "0" (x) : "st(1)"); |
| 817 |
return value; |
| 818 |
} |
| 819 |
#endif |
| 820 |
|
| 821 |
#undef fp_exp |
| 822 |
#define fp_exp fp_do_exp |
| 823 |
|
| 824 |
#ifndef FPU_FAST_MATH |
| 825 |
// FIXME: unimplemented |
| 826 |
PRIVATE fpu_extended fp_do_exp(fpu_extended x); |
| 827 |
#else |
| 828 |
PRIVATE inline fpu_extended fp_do_exp(fpu_extended x) |
| 829 |
{ |
| 830 |
fpu_extended value, exponent; |
| 831 |
__asm__ __volatile__("fldl2e # e^x = 2^(x * log2(e))\n\t" |
| 832 |
"fmul %%st(1) # x * log2(e)\n\t" |
| 833 |
"fst %%st(1)\n\t" |
| 834 |
"frndint # int(x * log2(e))\n\t" |
| 835 |
"fxch\n\t" |
| 836 |
"fsub %%st(1) # fract(x * log2(e))\n\t" |
| 837 |
"f2xm1 # 2^(fract(x * log2(e))) - 1\n\t" |
| 838 |
: "=t" (value), "=u" (exponent) : "0" (x)); |
| 839 |
value += 1.0; |
| 840 |
__asm__ __volatile__("fscale" : "=t" (value) : "0" (value), "u" (exponent)); |
| 841 |
return value; |
| 842 |
} |
| 843 |
#endif |
| 844 |
|
| 845 |
#undef fp_pow |
| 846 |
#define fp_pow fp_do_pow |
| 847 |
|
| 848 |
PRIVATE fpu_extended fp_do_pow(fpu_extended x, fpu_extended y); |
| 849 |
|
| 850 |
#undef fp_fabs |
| 851 |
#define fp_fabs fp_do_fabs |
| 852 |
|
| 853 |
PRIVATE inline fpu_extended fp_do_fabs(fpu_extended x) |
| 854 |
{ |
| 855 |
fpu_extended value; |
| 856 |
__asm__ __volatile__("fabs" : "=t" (value) : "0" (x)); |
| 857 |
return value; |
| 858 |
} |
| 859 |
|
| 860 |
#undef fp_sqrt |
| 861 |
#define fp_sqrt fp_do_sqrt |
| 862 |
|
| 863 |
PRIVATE inline fpu_extended fp_do_sqrt(fpu_extended x) |
| 864 |
{ |
| 865 |
fpu_extended value; |
| 866 |
__asm__ __volatile__("fsqrt" : "=t" (value) : "0" (x)); |
| 867 |
return value; |
| 868 |
} |
| 869 |
|
| 870 |
#undef fp_sin |
| 871 |
#define fp_sin fp_do_sin |
| 872 |
|
| 873 |
PRIVATE inline fpu_extended fp_do_sin(fpu_extended x) |
| 874 |
{ |
| 875 |
fpu_extended value; |
| 876 |
__asm__ __volatile__("fsin" : "=t" (value) : "0" (x)); |
| 877 |
return value; |
| 878 |
} |
| 879 |
|
| 880 |
#undef fp_cos |
| 881 |
#define fp_cos fp_do_cos |
| 882 |
|
| 883 |
PRIVATE inline fpu_extended fp_do_cos(fpu_extended x) |
| 884 |
{ |
| 885 |
fpu_extended value; |
| 886 |
__asm__ __volatile__("fcos" : "=t" (value) : "0" (x)); |
| 887 |
return value; |
| 888 |
} |
| 889 |
|
| 890 |
#undef fp_tan |
| 891 |
#define fp_tan fp_do_tan |
| 892 |
|
| 893 |
PRIVATE inline fpu_extended fp_do_tan(fpu_extended x) |
| 894 |
{ |
| 895 |
fpu_extended value; |
| 896 |
__asm__ __volatile__("fptan" : "=t" (value) : "0" (x)); |
| 897 |
return value; |
| 898 |
} |
| 899 |
|
| 900 |
#undef fp_expm1 |
| 901 |
#define fp_expm1 fp_do_expm1 |
| 902 |
|
| 903 |
// Returns: exp(X) - 1.0 |
| 904 |
PRIVATE inline fpu_extended fp_do_expm1(fpu_extended x) |
| 905 |
{ |
| 906 |
fpu_extended value, exponent, temp; |
| 907 |
__asm__ __volatile__("fldl2e # e^x - 1 = 2^(x * log2(e)) - 1\n\t" |
| 908 |
"fmul %%st(1) # x * log2(e)\n\t" |
| 909 |
"fst %%st(1)\n\t" |
| 910 |
"frndint # int(x * log2(e))\n\t" |
| 911 |
"fxch\n\t" |
| 912 |
"fsub %%st(1) # fract(x * log2(e))\n\t" |
| 913 |
"f2xm1 # 2^(fract(x * log2(e))) - 1\n\t" |
| 914 |
"fscale # 2^(x * log2(e)) - 2^(int(x * log2(e)))\n\t" |
| 915 |
: "=t" (value), "=u" (exponent) : "0" (x)); |
| 916 |
__asm__ __volatile__("fscale" : "=t" (temp) : "0" (1.0), "u" (exponent)); |
| 917 |
temp -= 1.0; |
| 918 |
return temp + value ? temp + value : x; |
| 919 |
} |
| 920 |
|
| 921 |
#undef fp_sgn1 |
| 922 |
#define fp_sgn1 fp_do_sgn1 |
| 923 |
|
| 924 |
PRIVATE inline fpu_extended fp_do_sgn1(fpu_extended x) |
| 925 |
{ |
| 926 |
#if USE_LONG_DOUBLE || USE_QUAD_DOUBLE |
| 927 |
fp_declare_init_shape(sxp, x, extended); |
| 928 |
sxp->ieee_nan.exponent = FP_EXTENDED_EXP_MAX; |
| 929 |
sxp->ieee_nan.one = 1; |
| 930 |
#else |
| 931 |
fp_declare_init_shape(sxp, x, double); |
| 932 |
sxp->ieee_nan.exponent = FP_DOUBLE_EXP_MAX; |
| 933 |
#endif |
| 934 |
sxp->ieee_nan.quiet_nan = 0; |
| 935 |
sxp->ieee_nan.mantissa0 = 0; |
| 936 |
sxp->ieee_nan.mantissa1 = 0; |
| 937 |
return x; |
| 938 |
} |
| 939 |
|
| 940 |
#undef fp_sinh |
| 941 |
#define fp_sinh fp_do_sinh |
| 942 |
|
| 943 |
#ifndef FPU_FAST_MATH |
| 944 |
// FIXME: unimplemented |
| 945 |
PRIVATE fpu_extended fp_do_sinh(fpu_extended x); |
| 946 |
#else |
| 947 |
PRIVATE inline fpu_extended fp_do_sinh(fpu_extended x) |
| 948 |
{ |
| 949 |
fpu_extended exm1 = fp_expm1(fp_fabs(x)); |
| 950 |
return 0.5 * (exm1 / (exm1 + 1.0) + exm1) * fp_sgn1(x); |
| 951 |
} |
| 952 |
#endif |
| 953 |
|
| 954 |
#undef fp_cosh |
| 955 |
#define fp_cosh fp_do_cosh |
| 956 |
|
| 957 |
#ifndef FPU_FAST_MATH |
| 958 |
// FIXME: unimplemented |
| 959 |
PRIVATE fpu_extended fp_do_cosh(fpu_extended x); |
| 960 |
#else |
| 961 |
PRIVATE inline fpu_extended fp_do_cosh(fpu_extended x) |
| 962 |
{ |
| 963 |
fpu_extended ex = fp_exp(x); |
| 964 |
return 0.5 * (ex + 1.0 / ex); |
| 965 |
} |
| 966 |
#endif |
| 967 |
|
| 968 |
#undef fp_tanh |
| 969 |
#define fp_tanh fp_do_tanh |
| 970 |
|
| 971 |
#ifndef FPU_FAST_MATH |
| 972 |
// FIXME: unimplemented |
| 973 |
PRIVATE fpu_extended fp_do_tanh(fpu_extended x); |
| 974 |
#else |
| 975 |
PRIVATE inline fpu_extended fp_do_tanh(fpu_extended x) |
| 976 |
{ |
| 977 |
fpu_extended exm1 = fp_expm1(-fp_fabs(x + x)); |
| 978 |
return exm1 / (exm1 + 2.0) * fp_sgn1(-x); |
| 979 |
} |
| 980 |
#endif |
| 981 |
|
| 982 |
#undef fp_atan2 |
| 983 |
#define fp_atan2 fp_do_atan2 |
| 984 |
|
| 985 |
PRIVATE inline fpu_extended fp_do_atan2(fpu_extended y, fpu_extended x) |
| 986 |
{ |
| 987 |
fpu_extended value; |
| 988 |
__asm__ __volatile__("fpatan" : "=t" (value) : "0" (x), "u" (y) : "st(1)"); |
| 989 |
return value; |
| 990 |
} |
| 991 |
|
| 992 |
#undef fp_asin |
| 993 |
#define fp_asin fp_do_asin |
| 994 |
|
| 995 |
PRIVATE inline fpu_extended fp_do_asin(fpu_extended x) |
| 996 |
{ |
| 997 |
return fp_atan2(x, fp_sqrt(1.0 - x * x)); |
| 998 |
} |
| 999 |
|
| 1000 |
#undef fp_acos |
| 1001 |
#define fp_acos fp_do_acos |
| 1002 |
|
| 1003 |
PRIVATE inline fpu_extended fp_do_acos(fpu_extended x) |
| 1004 |
{ |
| 1005 |
return fp_atan2(fp_sqrt(1.0 - x * x), x); |
| 1006 |
} |
| 1007 |
|
| 1008 |
#undef fp_atan |
| 1009 |
#define fp_atan fp_do_atan |
| 1010 |
|
| 1011 |
PRIVATE inline fpu_extended fp_do_atan(fpu_extended x) |
| 1012 |
{ |
| 1013 |
fpu_extended value; |
| 1014 |
__asm__ __volatile__("fld1; fpatan" : "=t" (value) : "0" (x) : "st(1)"); |
| 1015 |
return value; |
| 1016 |
} |
| 1017 |
|
| 1018 |
#undef fp_log1p |
| 1019 |
#define fp_log1p fp_do_log1p |
| 1020 |
|
| 1021 |
// Returns: ln(1.0 + X) |
| 1022 |
PRIVATE fpu_extended fp_do_log1p(fpu_extended x); |
| 1023 |
|
| 1024 |
#undef fp_asinh |
| 1025 |
#define fp_asinh fp_do_asinh |
| 1026 |
|
| 1027 |
PRIVATE inline fpu_extended fp_do_asinh(fpu_extended x) |
| 1028 |
{ |
| 1029 |
fpu_extended y = fp_fabs(x); |
| 1030 |
return (fp_log1p(y * y / (fp_sqrt(y * y + 1.0) + 1.0) + y) * fp_sgn1(x)); |
| 1031 |
} |
| 1032 |
|
| 1033 |
#undef fp_acosh |
| 1034 |
#define fp_acosh fp_do_acosh |
| 1035 |
|
| 1036 |
PRIVATE inline fpu_extended fp_do_acosh(fpu_extended x) |
| 1037 |
{ |
| 1038 |
return fp_log(x + fp_sqrt(x - 1.0) * fp_sqrt(x + 1.0)); |
| 1039 |
} |
| 1040 |
|
| 1041 |
#undef fp_atanh |
| 1042 |
#define fp_atanh fp_do_atanh |
| 1043 |
|
| 1044 |
PRIVATE inline fpu_extended fp_do_atanh(fpu_extended x) |
| 1045 |
{ |
| 1046 |
fpu_extended y = fp_fabs(x); |
| 1047 |
return -0.5 * fp_log1p(-(y + y) / (1.0 + y)) * fp_sgn1(x); |
| 1048 |
} |
| 1049 |
|
| 1050 |
#undef fp_floor |
| 1051 |
#define fp_floor fp_do_floor |
| 1052 |
|
| 1053 |
PRIVATE inline fpu_extended fp_do_floor(fpu_extended x) |
| 1054 |
{ |
| 1055 |
volatile unsigned int cw; |
| 1056 |
__asm__ __volatile__("fnstcw %0" : "=m" (cw)); |
| 1057 |
volatile unsigned int cw_temp = (cw & 0xf3ff) | 0x0400; // rounding down |
| 1058 |
__asm__ __volatile__("fldcw %0" : : "m" (cw_temp)); |
| 1059 |
fpu_extended value; |
| 1060 |
__asm__ __volatile__("frndint" : "=t" (value) : "0" (x)); |
| 1061 |
__asm__ __volatile__("fldcw %0" : : "m" (cw)); |
| 1062 |
return value; |
| 1063 |
} |
| 1064 |
|
| 1065 |
#undef fp_ceil |
| 1066 |
#define fp_ceil fp_do_ceil |
| 1067 |
|
| 1068 |
PRIVATE inline fpu_extended fp_do_ceil(fpu_extended x) |
| 1069 |
{ |
| 1070 |
volatile unsigned int cw; |
| 1071 |
__asm__ __volatile__("fnstcw %0" : "=m" (cw)); |
| 1072 |
volatile unsigned int cw_temp = (cw & 0xf3ff) | 0x0800; // rounding up |
| 1073 |
__asm__ __volatile__("fldcw %0" : : "m" (cw_temp)); |
| 1074 |
fpu_extended value; |
| 1075 |
__asm__ __volatile__("frndint" : "=t" (value) : "0" (x)); |
| 1076 |
__asm__ __volatile__("fldcw %0" : : "m" (cw)); |
| 1077 |
return value; |
| 1078 |
} |
| 1079 |
|
| 1080 |
#define DEFINE_ROUND_FUNC(rounding_mode_str, rounding_mode) \ |
| 1081 |
PRIVATE inline fpu_extended fp_do_round_to_ ## rounding_mode_str(fpu_extended x) \ |
| 1082 |
{ \ |
| 1083 |
volatile unsigned int cw; \ |
| 1084 |
__asm__ __volatile__("fnstcw %0" : "=m" (cw)); \ |
| 1085 |
volatile unsigned int cw_temp = (cw & 0xf3ff) | (rounding_mode); \ |
| 1086 |
__asm__ __volatile__("fldcw %0" : : "m" (cw_temp)); \ |
| 1087 |
fpu_extended value; \ |
| 1088 |
__asm__ __volatile__("frndint" : "=t" (value) : "0" (x)); \ |
| 1089 |
__asm__ __volatile__("fldcw %0" : : "m" (cw)); \ |
| 1090 |
return value; \ |
| 1091 |
} |
| 1092 |
|
| 1093 |
#undef fp_round_to_minus_infinity |
| 1094 |
#define fp_round_to_minus_infinity fp_do_round_to_minus_infinity |
| 1095 |
|
| 1096 |
DEFINE_ROUND_FUNC(minus_infinity, 0x400) |
| 1097 |
|
| 1098 |
#undef fp_round_to_plus_infinity |
| 1099 |
#define fp_round_to_plus_infinity fp_do_round_to_plus_infinity |
| 1100 |
|
| 1101 |
DEFINE_ROUND_FUNC(plus_infinity, 0x800) |
| 1102 |
|
| 1103 |
#undef fp_round_to_zero |
| 1104 |
#define fp_round_to_zero fp_do_round_to_zero |
| 1105 |
|
| 1106 |
DEFINE_ROUND_FUNC(zero, 0xc00) |
| 1107 |
|
| 1108 |
#undef fp_round_to_nearest |
| 1109 |
#define fp_round_to_nearest fp_do_round_to_nearest |
| 1110 |
|
| 1111 |
DEFINE_ROUND_FUNC(nearest, 0x000) |
| 1112 |
|
| 1113 |
#endif /* USE_X87_ASSEMBLY */ |
| 1114 |
|
| 1115 |
#ifndef fp_round_to_minus_infinity |
| 1116 |
#define fp_round_to_minus_infinity(x) fp_floor(x) |
| 1117 |
#endif |
| 1118 |
|
| 1119 |
#ifndef fp_round_to_plus_infinity |
| 1120 |
#define fp_round_to_plus_infinity(x) fp_ceil(x) |
| 1121 |
#endif |
| 1122 |
|
| 1123 |
#ifndef fp_round_to_zero |
| 1124 |
#define fp_round_to_zero(x) ((int)(x)) |
| 1125 |
#endif |
| 1126 |
|
| 1127 |
#ifndef fp_round_to_nearest |
| 1128 |
#define fp_round_to_nearest(x) ((int)((x) + 0.5)) |
| 1129 |
#endif |
| 1130 |
|
| 1131 |
#endif /* FPU_MATHLIB_H */ |
