Loading...
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 | /* Software floating-point emulation.
Definitions for IEEE Extended Precision.
Copyright (C) 1999 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Jakub Jelinek (jj@ultra.linux.cz).
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Library General Public License as
published by the Free Software Foundation; either version 2 of the
License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Library General Public License for more details.
You should have received a copy of the GNU Library General Public
License along with the GNU C Library; see the file COPYING.LIB. If
not, write to the Free Software Foundation, Inc.,
59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */
#ifndef __MATH_EMU_EXTENDED_H__
#define __MATH_EMU_EXTENDED_H__
#if _FP_W_TYPE_SIZE < 32
#error "Here's a nickel, kid. Go buy yourself a real computer."
#endif
#if _FP_W_TYPE_SIZE < 64
#define _FP_FRACTBITS_E (4*_FP_W_TYPE_SIZE)
#else
#define _FP_FRACTBITS_E (2*_FP_W_TYPE_SIZE)
#endif
#define _FP_FRACBITS_E 64
#define _FP_FRACXBITS_E (_FP_FRACTBITS_E - _FP_FRACBITS_E)
#define _FP_WFRACBITS_E (_FP_WORKBITS + _FP_FRACBITS_E)
#define _FP_WFRACXBITS_E (_FP_FRACTBITS_E - _FP_WFRACBITS_E)
#define _FP_EXPBITS_E 15
#define _FP_EXPBIAS_E 16383
#define _FP_EXPMAX_E 32767
#define _FP_QNANBIT_E \
((_FP_W_TYPE)1 << (_FP_FRACBITS_E-2) % _FP_W_TYPE_SIZE)
#define _FP_IMPLBIT_E \
((_FP_W_TYPE)1 << (_FP_FRACBITS_E-1) % _FP_W_TYPE_SIZE)
#define _FP_OVERFLOW_E \
((_FP_W_TYPE)1 << (_FP_WFRACBITS_E % _FP_W_TYPE_SIZE))
#if _FP_W_TYPE_SIZE < 64
union _FP_UNION_E
{
long double flt;
struct
{
#if __BYTE_ORDER == __BIG_ENDIAN
unsigned long pad1 : _FP_W_TYPE_SIZE;
unsigned long pad2 : (_FP_W_TYPE_SIZE - 1 - _FP_EXPBITS_E);
unsigned long sign : 1;
unsigned long exp : _FP_EXPBITS_E;
unsigned long frac1 : _FP_W_TYPE_SIZE;
unsigned long frac0 : _FP_W_TYPE_SIZE;
#else
unsigned long frac0 : _FP_W_TYPE_SIZE;
unsigned long frac1 : _FP_W_TYPE_SIZE;
unsigned exp : _FP_EXPBITS_E;
unsigned sign : 1;
#endif /* not bigendian */
} bits __attribute__((packed));
};
#define FP_DECL_E(X) _FP_DECL(4,X)
#define FP_UNPACK_RAW_E(X, val) \
do { \
union _FP_UNION_E _flo; _flo.flt = (val); \
\
X##_f[2] = 0; X##_f[3] = 0; \
X##_f[0] = _flo.bits.frac0; \
X##_f[1] = _flo.bits.frac1; \
X##_e = _flo.bits.exp; \
X##_s = _flo.bits.sign; \
if (!X##_e && (X##_f[1] || X##_f[0]) \
&& !(X##_f[1] & _FP_IMPLBIT_E)) \
{ \
X##_e++; \
FP_SET_EXCEPTION(FP_EX_DENORM); \
} \
} while (0)
#define FP_UNPACK_RAW_EP(X, val) \
do { \
union _FP_UNION_E *_flo = \
(union _FP_UNION_E *)(val); \
\
X##_f[2] = 0; X##_f[3] = 0; \
X##_f[0] = _flo->bits.frac0; \
X##_f[1] = _flo->bits.frac1; \
X##_e = _flo->bits.exp; \
X##_s = _flo->bits.sign; \
if (!X##_e && (X##_f[1] || X##_f[0]) \
&& !(X##_f[1] & _FP_IMPLBIT_E)) \
{ \
X##_e++; \
FP_SET_EXCEPTION(FP_EX_DENORM); \
} \
} while (0)
#define FP_PACK_RAW_E(val, X) \
do { \
union _FP_UNION_E _flo; \
\
if (X##_e) X##_f[1] |= _FP_IMPLBIT_E; \
else X##_f[1] &= ~(_FP_IMPLBIT_E); \
_flo.bits.frac0 = X##_f[0]; \
_flo.bits.frac1 = X##_f[1]; \
_flo.bits.exp = X##_e; \
_flo.bits.sign = X##_s; \
\
(val) = _flo.flt; \
} while (0)
#define FP_PACK_RAW_EP(val, X) \
do { \
if (!FP_INHIBIT_RESULTS) \
{ \
union _FP_UNION_E *_flo = \
(union _FP_UNION_E *)(val); \
\
if (X##_e) X##_f[1] |= _FP_IMPLBIT_E; \
else X##_f[1] &= ~(_FP_IMPLBIT_E); \
_flo->bits.frac0 = X##_f[0]; \
_flo->bits.frac1 = X##_f[1]; \
_flo->bits.exp = X##_e; \
_flo->bits.sign = X##_s; \
} \
} while (0)
#define FP_UNPACK_E(X,val) \
do { \
FP_UNPACK_RAW_E(X,val); \
_FP_UNPACK_CANONICAL(E,4,X); \
} while (0)
#define FP_UNPACK_EP(X,val) \
do { \
FP_UNPACK_RAW_2_P(X,val); \
_FP_UNPACK_CANONICAL(E,4,X); \
} while (0)
#define FP_PACK_E(val,X) \
do { \
_FP_PACK_CANONICAL(E,4,X); \
FP_PACK_RAW_E(val,X); \
} while (0)
#define FP_PACK_EP(val,X) \
do { \
_FP_PACK_CANONICAL(E,4,X); \
FP_PACK_RAW_EP(val,X); \
} while (0)
#define FP_ISSIGNAN_E(X) _FP_ISSIGNAN(E,4,X)
#define FP_NEG_E(R,X) _FP_NEG(E,4,R,X)
#define FP_ADD_E(R,X,Y) _FP_ADD(E,4,R,X,Y)
#define FP_SUB_E(R,X,Y) _FP_SUB(E,4,R,X,Y)
#define FP_MUL_E(R,X,Y) _FP_MUL(E,4,R,X,Y)
#define FP_DIV_E(R,X,Y) _FP_DIV(E,4,R,X,Y)
#define FP_SQRT_E(R,X) _FP_SQRT(E,4,R,X)
/*
* Square root algorithms:
* We have just one right now, maybe Newton approximation
* should be added for those machines where division is fast.
* This has special _E version because standard _4 square
* root would not work (it has to start normally with the
* second word and not the first), but as we have to do it
* anyway, we optimize it by doing most of the calculations
* in two UWtype registers instead of four.
*/
#define _FP_SQRT_MEAT_E(R, S, T, X, q) \
do { \
q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \
_FP_FRAC_SRL_4(X, (_FP_WORKBITS)); \
while (q) \
{ \
T##_f[1] = S##_f[1] + q; \
if (T##_f[1] <= X##_f[1]) \
{ \
S##_f[1] = T##_f[1] + q; \
X##_f[1] -= T##_f[1]; \
R##_f[1] += q; \
} \
_FP_FRAC_SLL_2(X, 1); \
q >>= 1; \
} \
q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \
while (q) \
{ \
T##_f[0] = S##_f[0] + q; \
T##_f[1] = S##_f[1]; \
if (T##_f[1] < X##_f[1] || \
(T##_f[1] == X##_f[1] && \
T##_f[0] <= X##_f[0])) \
{ \
S##_f[0] = T##_f[0] + q; \
S##_f[1] += (T##_f[0] > S##_f[0]); \
_FP_FRAC_DEC_2(X, T); \
R##_f[0] += q; \
} \
_FP_FRAC_SLL_2(X, 1); \
q >>= 1; \
} \
_FP_FRAC_SLL_4(R, (_FP_WORKBITS)); \
if (X##_f[0] | X##_f[1]) \
{ \
if (S##_f[1] < X##_f[1] || \
(S##_f[1] == X##_f[1] && \
S##_f[0] < X##_f[0])) \
R##_f[0] |= _FP_WORK_ROUND; \
R##_f[0] |= _FP_WORK_STICKY; \
} \
} while (0)
#define FP_CMP_E(r,X,Y,un) _FP_CMP(E,4,r,X,Y,un)
#define FP_CMP_EQ_E(r,X,Y) _FP_CMP_EQ(E,4,r,X,Y)
#define FP_TO_INT_E(r,X,rsz,rsg) _FP_TO_INT(E,4,r,X,rsz,rsg)
#define FP_TO_INT_ROUND_E(r,X,rsz,rsg) _FP_TO_INT_ROUND(E,4,r,X,rsz,rsg)
#define FP_FROM_INT_E(X,r,rs,rt) _FP_FROM_INT(E,4,X,r,rs,rt)
#define _FP_FRAC_HIGH_E(X) (X##_f[2])
#define _FP_FRAC_HIGH_RAW_E(X) (X##_f[1])
#else /* not _FP_W_TYPE_SIZE < 64 */
union _FP_UNION_E
{
long double flt /* __attribute__((mode(TF))) */ ;
struct {
#if __BYTE_ORDER == __BIG_ENDIAN
unsigned long pad : (_FP_W_TYPE_SIZE - 1 - _FP_EXPBITS_E);
unsigned sign : 1;
unsigned exp : _FP_EXPBITS_E;
unsigned long frac : _FP_W_TYPE_SIZE;
#else
unsigned long frac : _FP_W_TYPE_SIZE;
unsigned exp : _FP_EXPBITS_E;
unsigned sign : 1;
#endif
} bits;
};
#define FP_DECL_E(X) _FP_DECL(2,X)
#define FP_UNPACK_RAW_E(X, val) \
do { \
union _FP_UNION_E _flo; _flo.flt = (val); \
\
X##_f0 = _flo.bits.frac; \
X##_f1 = 0; \
X##_e = _flo.bits.exp; \
X##_s = _flo.bits.sign; \
if (!X##_e && X##_f0 && !(X##_f0 & _FP_IMPLBIT_E)) \
{ \
X##_e++; \
FP_SET_EXCEPTION(FP_EX_DENORM); \
} \
} while (0)
#define FP_UNPACK_RAW_EP(X, val) \
do { \
union _FP_UNION_E *_flo = \
(union _FP_UNION_E *)(val); \
\
X##_f0 = _flo->bits.frac; \
X##_f1 = 0; \
X##_e = _flo->bits.exp; \
X##_s = _flo->bits.sign; \
if (!X##_e && X##_f0 && !(X##_f0 & _FP_IMPLBIT_E)) \
{ \
X##_e++; \
FP_SET_EXCEPTION(FP_EX_DENORM); \
} \
} while (0)
#define FP_PACK_RAW_E(val, X) \
do { \
union _FP_UNION_E _flo; \
\
if (X##_e) X##_f0 |= _FP_IMPLBIT_E; \
else X##_f0 &= ~(_FP_IMPLBIT_E); \
_flo.bits.frac = X##_f0; \
_flo.bits.exp = X##_e; \
_flo.bits.sign = X##_s; \
\
(val) = _flo.flt; \
} while (0)
#define FP_PACK_RAW_EP(fs, val, X) \
do { \
if (!FP_INHIBIT_RESULTS) \
{ \
union _FP_UNION_E *_flo = \
(union _FP_UNION_E *)(val); \
\
if (X##_e) X##_f0 |= _FP_IMPLBIT_E; \
else X##_f0 &= ~(_FP_IMPLBIT_E); \
_flo->bits.frac = X##_f0; \
_flo->bits.exp = X##_e; \
_flo->bits.sign = X##_s; \
} \
} while (0)
#define FP_UNPACK_E(X,val) \
do { \
FP_UNPACK_RAW_E(X,val); \
_FP_UNPACK_CANONICAL(E,2,X); \
} while (0)
#define FP_UNPACK_EP(X,val) \
do { \
FP_UNPACK_RAW_EP(X,val); \
_FP_UNPACK_CANONICAL(E,2,X); \
} while (0)
#define FP_PACK_E(val,X) \
do { \
_FP_PACK_CANONICAL(E,2,X); \
FP_PACK_RAW_E(val,X); \
} while (0)
#define FP_PACK_EP(val,X) \
do { \
_FP_PACK_CANONICAL(E,2,X); \
FP_PACK_RAW_EP(val,X); \
} while (0)
#define FP_ISSIGNAN_E(X) _FP_ISSIGNAN(E,2,X)
#define FP_NEG_E(R,X) _FP_NEG(E,2,R,X)
#define FP_ADD_E(R,X,Y) _FP_ADD(E,2,R,X,Y)
#define FP_SUB_E(R,X,Y) _FP_SUB(E,2,R,X,Y)
#define FP_MUL_E(R,X,Y) _FP_MUL(E,2,R,X,Y)
#define FP_DIV_E(R,X,Y) _FP_DIV(E,2,R,X,Y)
#define FP_SQRT_E(R,X) _FP_SQRT(E,2,R,X)
/*
* Square root algorithms:
* We have just one right now, maybe Newton approximation
* should be added for those machines where division is fast.
* We optimize it by doing most of the calculations
* in one UWtype registers instead of two, although we don't
* have to.
*/
#define _FP_SQRT_MEAT_E(R, S, T, X, q) \
do { \
q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \
_FP_FRAC_SRL_2(X, (_FP_WORKBITS)); \
while (q) \
{ \
T##_f0 = S##_f0 + q; \
if (T##_f0 <= X##_f0) \
{ \
S##_f0 = T##_f0 + q; \
X##_f0 -= T##_f0; \
R##_f0 += q; \
} \
_FP_FRAC_SLL_1(X, 1); \
q >>= 1; \
} \
_FP_FRAC_SLL_2(R, (_FP_WORKBITS)); \
if (X##_f0) \
{ \
if (S##_f0 < X##_f0) \
R##_f0 |= _FP_WORK_ROUND; \
R##_f0 |= _FP_WORK_STICKY; \
} \
} while (0)
#define FP_CMP_E(r,X,Y,un) _FP_CMP(E,2,r,X,Y,un)
#define FP_CMP_EQ_E(r,X,Y) _FP_CMP_EQ(E,2,r,X,Y)
#define FP_TO_INT_E(r,X,rsz,rsg) _FP_TO_INT(E,2,r,X,rsz,rsg)
#define FP_TO_INT_ROUND_E(r,X,rsz,rsg) _FP_TO_INT_ROUND(E,2,r,X,rsz,rsg)
#define FP_FROM_INT_E(X,r,rs,rt) _FP_FROM_INT(E,2,X,r,rs,rt)
#define _FP_FRAC_HIGH_E(X) (X##_f1)
#define _FP_FRAC_HIGH_RAW_E(X) (X##_f0)
#endif /* not _FP_W_TYPE_SIZE < 64 */
#endif /* __MATH_EMU_EXTENDED_H__ */
|