1 /* Software floating-point emulation. 2 Definitions for IEEE Extended Precision. 3 Copyright (C) 1999-2014 Free Software Foundation, Inc. 4 This file is part of the GNU C Library. 5 Contributed by Jakub Jelinek (jj@ultra.linux.cz). 6 7 The GNU C Library is free software; you can redistribute it and/or 8 modify it under the terms of the GNU Lesser General Public 9 License as published by the Free Software Foundation; either 10 version 2.1 of the License, or (at your option) any later version. 11 12 In addition to the permissions in the GNU Lesser General Public 13 License, the Free Software Foundation gives you unlimited 14 permission to link the compiled version of this file into 15 combinations with other programs, and to distribute those 16 combinations without any restriction coming from the use of this 17 file. (The Lesser General Public License restrictions do apply in 18 other respects; for example, they cover modification of the file, 19 and distribution when not linked into a combine executable.) 20 21 The GNU C Library is distributed in the hope that it will be useful, 22 but WITHOUT ANY WARRANTY; without even the implied warranty of 23 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 24 Lesser General Public License for more details. 25 26 You should have received a copy of the GNU Lesser General Public 27 License along with the GNU C Library; if not, see 28 <http://www.gnu.org/licenses/>. */ 29 30 #if _FP_W_TYPE_SIZE < 32 31 # error "Here's a nickel, kid. Go buy yourself a real computer." 32 #endif 33 34 #if _FP_W_TYPE_SIZE < 64 35 # define _FP_FRACTBITS_E (4*_FP_W_TYPE_SIZE) 36 # define _FP_FRACTBITS_DW_E (8*_FP_W_TYPE_SIZE) 37 #else 38 # define _FP_FRACTBITS_E (2*_FP_W_TYPE_SIZE) 39 # define _FP_FRACTBITS_DW_E (4*_FP_W_TYPE_SIZE) 40 #endif 41 42 #define _FP_FRACBITS_E 64 43 #define _FP_FRACXBITS_E (_FP_FRACTBITS_E - _FP_FRACBITS_E) 44 #define _FP_WFRACBITS_E (_FP_WORKBITS + _FP_FRACBITS_E) 45 #define _FP_WFRACXBITS_E (_FP_FRACTBITS_E - _FP_WFRACBITS_E) 46 #define _FP_EXPBITS_E 15 47 #define _FP_EXPBIAS_E 16383 48 #define _FP_EXPMAX_E 32767 49 50 #define _FP_QNANBIT_E \ 51 ((_FP_W_TYPE) 1 << (_FP_FRACBITS_E-2) % _FP_W_TYPE_SIZE) 52 #define _FP_QNANBIT_SH_E \ 53 ((_FP_W_TYPE) 1 << (_FP_FRACBITS_E-2+_FP_WORKBITS) % _FP_W_TYPE_SIZE) 54 #define _FP_IMPLBIT_E \ 55 ((_FP_W_TYPE) 1 << (_FP_FRACBITS_E-1) % _FP_W_TYPE_SIZE) 56 #define _FP_IMPLBIT_SH_E \ 57 ((_FP_W_TYPE) 1 << (_FP_FRACBITS_E-1+_FP_WORKBITS) % _FP_W_TYPE_SIZE) 58 #define _FP_OVERFLOW_E \ 59 ((_FP_W_TYPE) 1 << (_FP_WFRACBITS_E % _FP_W_TYPE_SIZE)) 60 61 #define _FP_WFRACBITS_DW_E (2 * _FP_WFRACBITS_E) 62 #define _FP_WFRACXBITS_DW_E (_FP_FRACTBITS_DW_E - _FP_WFRACBITS_DW_E) 63 #define _FP_HIGHBIT_DW_E \ 64 ((_FP_W_TYPE) 1 << (_FP_WFRACBITS_DW_E - 1) % _FP_W_TYPE_SIZE) 65 66 typedef float XFtype __attribute__ ((mode (XF))); 67 68 #if _FP_W_TYPE_SIZE < 64 69 70 union _FP_UNION_E 71 { 72 XFtype flt; 73 struct _FP_STRUCT_LAYOUT 74 { 75 # if __BYTE_ORDER == __BIG_ENDIAN 76 unsigned long pad1 : _FP_W_TYPE_SIZE; 77 unsigned long pad2 : (_FP_W_TYPE_SIZE - 1 - _FP_EXPBITS_E); 78 unsigned long sign : 1; 79 unsigned long exp : _FP_EXPBITS_E; 80 unsigned long frac1 : _FP_W_TYPE_SIZE; 81 unsigned long frac0 : _FP_W_TYPE_SIZE; 82 # else 83 unsigned long frac0 : _FP_W_TYPE_SIZE; 84 unsigned long frac1 : _FP_W_TYPE_SIZE; 85 unsigned exp : _FP_EXPBITS_E; 86 unsigned sign : 1; 87 # endif /* not bigendian */ 88 } bits __attribute__ ((packed)); 89 }; 90 91 92 # define FP_DECL_E(X) _FP_DECL (4, X) 93 94 # define FP_UNPACK_RAW_E(X, val) \ 95 do \ 96 { \ 97 union _FP_UNION_E _flo; \ 98 _flo.flt = (val); \ 99 \ 100 X##_f[2] = 0; \ 101 X##_f[3] = 0; \ 102 X##_f[0] = _flo.bits.frac0; \ 103 X##_f[1] = _flo.bits.frac1; \ 104 X##_e = _flo.bits.exp; \ 105 X##_s = _flo.bits.sign; \ 106 } \ 107 while (0) 108 109 # define FP_UNPACK_RAW_EP(X, val) \ 110 do \ 111 { \ 112 union _FP_UNION_E *_flo = (union _FP_UNION_E *) (val); \ 113 \ 114 X##_f[2] = 0; \ 115 X##_f[3] = 0; \ 116 X##_f[0] = _flo->bits.frac0; \ 117 X##_f[1] = _flo->bits.frac1; \ 118 X##_e = _flo->bits.exp; \ 119 X##_s = _flo->bits.sign; \ 120 } \ 121 while (0) 122 123 # define FP_PACK_RAW_E(val, X) \ 124 do \ 125 { \ 126 union _FP_UNION_E _flo; \ 127 \ 128 if (X##_e) \ 129 X##_f[1] |= _FP_IMPLBIT_E; \ 130 else \ 131 X##_f[1] &= ~(_FP_IMPLBIT_E); \ 132 _flo.bits.frac0 = X##_f[0]; \ 133 _flo.bits.frac1 = X##_f[1]; \ 134 _flo.bits.exp = X##_e; \ 135 _flo.bits.sign = X##_s; \ 136 \ 137 (val) = _flo.flt; \ 138 } \ 139 while (0) 140 141 # define FP_PACK_RAW_EP(val, X) \ 142 do \ 143 { \ 144 if (!FP_INHIBIT_RESULTS) \ 145 { \ 146 union _FP_UNION_E *_flo = (union _FP_UNION_E *) (val); \ 147 \ 148 if (X##_e) \ 149 X##_f[1] |= _FP_IMPLBIT_E; \ 150 else \ 151 X##_f[1] &= ~(_FP_IMPLBIT_E); \ 152 _flo->bits.frac0 = X##_f[0]; \ 153 _flo->bits.frac1 = X##_f[1]; \ 154 _flo->bits.exp = X##_e; \ 155 _flo->bits.sign = X##_s; \ 156 } \ 157 } \ 158 while (0) 159 160 # define FP_UNPACK_E(X, val) \ 161 do \ 162 { \ 163 FP_UNPACK_RAW_E (X, val); \ 164 _FP_UNPACK_CANONICAL (E, 4, X); \ 165 } \ 166 while (0) 167 168 # define FP_UNPACK_EP(X, val) \ 169 do \ 170 { \ 171 FP_UNPACK_RAW_EP (X, val); \ 172 _FP_UNPACK_CANONICAL (E, 4, X); \ 173 } \ 174 while (0) 175 176 # define FP_UNPACK_SEMIRAW_E(X, val) \ 177 do \ 178 { \ 179 FP_UNPACK_RAW_E (X, val); \ 180 _FP_UNPACK_SEMIRAW (E, 4, X); \ 181 } \ 182 while (0) 183 184 # define FP_UNPACK_SEMIRAW_EP(X, val) \ 185 do \ 186 { \ 187 FP_UNPACK_RAW_EP (X, val); \ 188 _FP_UNPACK_SEMIRAW (E, 4, X); \ 189 } \ 190 while (0) 191 192 # define FP_PACK_E(val, X) \ 193 do \ 194 { \ 195 _FP_PACK_CANONICAL (E, 4, X); \ 196 FP_PACK_RAW_E (val, X); \ 197 } \ 198 while (0) 199 200 # define FP_PACK_EP(val, X) \ 201 do \ 202 { \ 203 _FP_PACK_CANONICAL (E, 4, X); \ 204 FP_PACK_RAW_EP (val, X); \ 205 } \ 206 while (0) 207 208 # define FP_PACK_SEMIRAW_E(val, X) \ 209 do \ 210 { \ 211 _FP_PACK_SEMIRAW (E, 4, X); \ 212 FP_PACK_RAW_E (val, X); \ 213 } \ 214 while (0) 215 216 # define FP_PACK_SEMIRAW_EP(val, X) \ 217 do \ 218 { \ 219 _FP_PACK_SEMIRAW (E, 4, X); \ 220 FP_PACK_RAW_EP (val, X); \ 221 } \ 222 while (0) 223 224 # define FP_ISSIGNAN_E(X) _FP_ISSIGNAN (E, 4, X) 225 # define FP_NEG_E(R, X) _FP_NEG (E, 4, R, X) 226 # define FP_ADD_E(R, X, Y) _FP_ADD (E, 4, R, X, Y) 227 # define FP_SUB_E(R, X, Y) _FP_SUB (E, 4, R, X, Y) 228 # define FP_MUL_E(R, X, Y) _FP_MUL (E, 4, R, X, Y) 229 # define FP_DIV_E(R, X, Y) _FP_DIV (E, 4, R, X, Y) 230 # define FP_SQRT_E(R, X) _FP_SQRT (E, 4, R, X) 231 # define FP_FMA_E(R, X, Y, Z) _FP_FMA (E, 4, 8, R, X, Y, Z) 232 233 /* 234 * Square root algorithms: 235 * We have just one right now, maybe Newton approximation 236 * should be added for those machines where division is fast. 237 * This has special _E version because standard _4 square 238 * root would not work (it has to start normally with the 239 * second word and not the first), but as we have to do it 240 * anyway, we optimize it by doing most of the calculations 241 * in two UWtype registers instead of four. 242 */ 243 244 # define _FP_SQRT_MEAT_E(R, S, T, X, q) \ 245 do \ 246 { \ 247 q = (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE - 1); \ 248 _FP_FRAC_SRL_4 (X, (_FP_WORKBITS)); \ 249 while (q) \ 250 { \ 251 T##_f[1] = S##_f[1] + q; \ 252 if (T##_f[1] <= X##_f[1]) \ 253 { \ 254 S##_f[1] = T##_f[1] + q; \ 255 X##_f[1] -= T##_f[1]; \ 256 R##_f[1] += q; \ 257 } \ 258 _FP_FRAC_SLL_2 (X, 1); \ 259 q >>= 1; \ 260 } \ 261 q = (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE - 1); \ 262 while (q) \ 263 { \ 264 T##_f[0] = S##_f[0] + q; \ 265 T##_f[1] = S##_f[1]; \ 266 if (T##_f[1] < X##_f[1] \ 267 || (T##_f[1] == X##_f[1] \ 268 && T##_f[0] <= X##_f[0])) \ 269 { \ 270 S##_f[0] = T##_f[0] + q; \ 271 S##_f[1] += (T##_f[0] > S##_f[0]); \ 272 _FP_FRAC_DEC_2 (X, T); \ 273 R##_f[0] += q; \ 274 } \ 275 _FP_FRAC_SLL_2 (X, 1); \ 276 q >>= 1; \ 277 } \ 278 _FP_FRAC_SLL_4 (R, (_FP_WORKBITS)); \ 279 if (X##_f[0] | X##_f[1]) \ 280 { \ 281 if (S##_f[1] < X##_f[1] \ 282 || (S##_f[1] == X##_f[1] \ 283 && S##_f[0] < X##_f[0])) \ 284 R##_f[0] |= _FP_WORK_ROUND; \ 285 R##_f[0] |= _FP_WORK_STICKY; \ 286 } \ 287 } \ 288 while (0) 289 290 # define FP_CMP_E(r, X, Y, un) _FP_CMP (E, 4, r, X, Y, un) 291 # define FP_CMP_EQ_E(r, X, Y) _FP_CMP_EQ (E, 4, r, X, Y) 292 # define FP_CMP_UNORD_E(r, X, Y) _FP_CMP_UNORD (E, 4, r, X, Y) 293 294 # define FP_TO_INT_E(r, X, rsz, rsg) _FP_TO_INT (E, 4, r, X, rsz, rsg) 295 # define FP_FROM_INT_E(X, r, rs, rt) _FP_FROM_INT (E, 4, X, r, rs, rt) 296 297 # define _FP_FRAC_HIGH_E(X) (X##_f[2]) 298 # define _FP_FRAC_HIGH_RAW_E(X) (X##_f[1]) 299 300 # define _FP_FRAC_HIGH_DW_E(X) (X##_f[4]) 301 302 #else /* not _FP_W_TYPE_SIZE < 64 */ 303 union _FP_UNION_E 304 { 305 XFtype flt; 306 struct _FP_STRUCT_LAYOUT 307 { 308 # if __BYTE_ORDER == __BIG_ENDIAN 309 _FP_W_TYPE pad : (_FP_W_TYPE_SIZE - 1 - _FP_EXPBITS_E); 310 unsigned sign : 1; 311 unsigned exp : _FP_EXPBITS_E; 312 _FP_W_TYPE frac : _FP_W_TYPE_SIZE; 313 # else 314 _FP_W_TYPE frac : _FP_W_TYPE_SIZE; 315 unsigned exp : _FP_EXPBITS_E; 316 unsigned sign : 1; 317 # endif 318 } bits; 319 }; 320 321 # define FP_DECL_E(X) _FP_DECL (2, X) 322 323 # define FP_UNPACK_RAW_E(X, val) \ 324 do \ 325 { \ 326 union _FP_UNION_E _flo; \ 327 _flo.flt = (val); \ 328 \ 329 X##_f0 = _flo.bits.frac; \ 330 X##_f1 = 0; \ 331 X##_e = _flo.bits.exp; \ 332 X##_s = _flo.bits.sign; \ 333 } \ 334 while (0) 335 336 # define FP_UNPACK_RAW_EP(X, val) \ 337 do \ 338 { \ 339 union _FP_UNION_E *_flo = (union _FP_UNION_E *) (val); \ 340 \ 341 X##_f0 = _flo->bits.frac; \ 342 X##_f1 = 0; \ 343 X##_e = _flo->bits.exp; \ 344 X##_s = _flo->bits.sign; \ 345 } \ 346 while (0) 347 348 # define FP_PACK_RAW_E(val, X) \ 349 do \ 350 { \ 351 union _FP_UNION_E _flo; \ 352 \ 353 if (X##_e) \ 354 X##_f0 |= _FP_IMPLBIT_E; \ 355 else \ 356 X##_f0 &= ~(_FP_IMPLBIT_E); \ 357 _flo.bits.frac = X##_f0; \ 358 _flo.bits.exp = X##_e; \ 359 _flo.bits.sign = X##_s; \ 360 \ 361 (val) = _flo.flt; \ 362 } \ 363 while (0) 364 365 # define FP_PACK_RAW_EP(fs, val, X) \ 366 do \ 367 { \ 368 if (!FP_INHIBIT_RESULTS) \ 369 { \ 370 union _FP_UNION_E *_flo = (union _FP_UNION_E *) (val); \ 371 \ 372 if (X##_e) \ 373 X##_f0 |= _FP_IMPLBIT_E; \ 374 else \ 375 X##_f0 &= ~(_FP_IMPLBIT_E); \ 376 _flo->bits.frac = X##_f0; \ 377 _flo->bits.exp = X##_e; \ 378 _flo->bits.sign = X##_s; \ 379 } \ 380 } \ 381 while (0) 382 383 384 # define FP_UNPACK_E(X, val) \ 385 do \ 386 { \ 387 FP_UNPACK_RAW_E (X, val); \ 388 _FP_UNPACK_CANONICAL (E, 2, X); \ 389 } \ 390 while (0) 391 392 # define FP_UNPACK_EP(X, val) \ 393 do \ 394 { \ 395 FP_UNPACK_RAW_EP (X, val); \ 396 _FP_UNPACK_CANONICAL (E, 2, X); \ 397 } \ 398 while (0) 399 400 # define FP_UNPACK_SEMIRAW_E(X, val) \ 401 do \ 402 { \ 403 FP_UNPACK_RAW_E (X, val); \ 404 _FP_UNPACK_SEMIRAW (E, 2, X); \ 405 } \ 406 while (0) 407 408 # define FP_UNPACK_SEMIRAW_EP(X, val) \ 409 do \ 410 { \ 411 FP_UNPACK_RAW_EP (X, val); \ 412 _FP_UNPACK_SEMIRAW (E, 2, X); \ 413 } \ 414 while (0) 415 416 # define FP_PACK_E(val, X) \ 417 do \ 418 { \ 419 _FP_PACK_CANONICAL (E, 2, X); \ 420 FP_PACK_RAW_E (val, X); \ 421 } \ 422 while (0) 423 424 # define FP_PACK_EP(val, X) \ 425 do \ 426 { \ 427 _FP_PACK_CANONICAL (E, 2, X); \ 428 FP_PACK_RAW_EP (val, X); \ 429 } \ 430 while (0) 431 432 # define FP_PACK_SEMIRAW_E(val, X) \ 433 do \ 434 { \ 435 _FP_PACK_SEMIRAW (E, 2, X); \ 436 FP_PACK_RAW_E (val, X); \ 437 } \ 438 while (0) 439 440 # define FP_PACK_SEMIRAW_EP(val, X) \ 441 do \ 442 { \ 443 _FP_PACK_SEMIRAW (E, 2, X); \ 444 FP_PACK_RAW_EP (val, X); \ 445 } \ 446 while (0) 447 448 # define FP_ISSIGNAN_E(X) _FP_ISSIGNAN (E, 2, X) 449 # define FP_NEG_E(R, X) _FP_NEG (E, 2, R, X) 450 # define FP_ADD_E(R, X, Y) _FP_ADD (E, 2, R, X, Y) 451 # define FP_SUB_E(R, X, Y) _FP_SUB (E, 2, R, X, Y) 452 # define FP_MUL_E(R, X, Y) _FP_MUL (E, 2, R, X, Y) 453 # define FP_DIV_E(R, X, Y) _FP_DIV (E, 2, R, X, Y) 454 # define FP_SQRT_E(R, X) _FP_SQRT (E, 2, R, X) 455 # define FP_FMA_E(R, X, Y, Z) _FP_FMA (E, 2, 4, R, X, Y, Z) 456 457 /* 458 * Square root algorithms: 459 * We have just one right now, maybe Newton approximation 460 * should be added for those machines where division is fast. 461 * We optimize it by doing most of the calculations 462 * in one UWtype registers instead of two, although we don't 463 * have to. 464 */ 465 # define _FP_SQRT_MEAT_E(R, S, T, X, q) \ 466 do \ 467 { \ 468 q = (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE - 1); \ 469 _FP_FRAC_SRL_2 (X, (_FP_WORKBITS)); \ 470 while (q) \ 471 { \ 472 T##_f0 = S##_f0 + q; \ 473 if (T##_f0 <= X##_f0) \ 474 { \ 475 S##_f0 = T##_f0 + q; \ 476 X##_f0 -= T##_f0; \ 477 R##_f0 += q; \ 478 } \ 479 _FP_FRAC_SLL_1 (X, 1); \ 480 q >>= 1; \ 481 } \ 482 _FP_FRAC_SLL_2 (R, (_FP_WORKBITS)); \ 483 if (X##_f0) \ 484 { \ 485 if (S##_f0 < X##_f0) \ 486 R##_f0 |= _FP_WORK_ROUND; \ 487 R##_f0 |= _FP_WORK_STICKY; \ 488 } \ 489 } \ 490 while (0) 491 492 # define FP_CMP_E(r, X, Y, un) _FP_CMP (E, 2, r, X, Y, un) 493 # define FP_CMP_EQ_E(r, X, Y) _FP_CMP_EQ (E, 2, r, X, Y) 494 # define FP_CMP_UNORD_E(r, X, Y) _FP_CMP_UNORD (E, 2, r, X, Y) 495 496 # define FP_TO_INT_E(r, X, rsz, rsg) _FP_TO_INT (E, 2, r, X, rsz, rsg) 497 # define FP_FROM_INT_E(X, r, rs, rt) _FP_FROM_INT (E, 2, X, r, rs, rt) 498 499 # define _FP_FRAC_HIGH_E(X) (X##_f1) 500 # define _FP_FRAC_HIGH_RAW_E(X) (X##_f0) 501 502 # define _FP_FRAC_HIGH_DW_E(X) (X##_f[2]) 503 504 #endif /* not _FP_W_TYPE_SIZE < 64 */ 505