1 /* Software floating-point emulation. Common operations. 2 Copyright (C) 1997-2014 Free Software Foundation, Inc. 3 This file is part of the GNU C Library. 4 Contributed by Richard Henderson (rth@cygnus.com), 5 Jakub Jelinek (jj@ultra.linux.cz), 6 David S. Miller (davem@redhat.com) and 7 Peter Maydell (pmaydell@chiark.greenend.org.uk). 8 9 The GNU C Library is free software; you can redistribute it and/or 10 modify it under the terms of the GNU Lesser General Public 11 License as published by the Free Software Foundation; either 12 version 2.1 of the License, or (at your option) any later version. 13 14 In addition to the permissions in the GNU Lesser General Public 15 License, the Free Software Foundation gives you unlimited 16 permission to link the compiled version of this file into 17 combinations with other programs, and to distribute those 18 combinations without any restriction coming from the use of this 19 file. (The Lesser General Public License restrictions do apply in 20 other respects; for example, they cover modification of the file, 21 and distribution when not linked into a combine executable.) 22 23 The GNU C Library is distributed in the hope that it will be useful, 24 but WITHOUT ANY WARRANTY; without even the implied warranty of 25 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 26 Lesser General Public License for more details. 27 28 You should have received a copy of the GNU Lesser General Public 29 License along with the GNU C Library; if not, see 30 <http://www.gnu.org/licenses/>. */ 31 32 #define _FP_DECL(wc, X) \ 33 _FP_I_TYPE X##_c __attribute__ ((unused)); \ 34 _FP_I_TYPE X##_s __attribute__ ((unused)); \ 35 _FP_I_TYPE X##_e __attribute__ ((unused)); \ 36 _FP_FRAC_DECL_##wc (X) 37 38 /* Test whether the qNaN bit denotes a signaling NaN. */ 39 #define _FP_FRAC_SNANP(fs, X) \ 40 ((_FP_QNANNEGATEDP) \ 41 ? (_FP_FRAC_HIGH_RAW_##fs (X) & _FP_QNANBIT_##fs) \ 42 : !(_FP_FRAC_HIGH_RAW_##fs (X) & _FP_QNANBIT_##fs)) 43 #define _FP_FRAC_SNANP_SEMIRAW(fs, X) \ 44 ((_FP_QNANNEGATEDP) \ 45 ? (_FP_FRAC_HIGH_##fs (X) & _FP_QNANBIT_SH_##fs) \ 46 : !(_FP_FRAC_HIGH_##fs (X) & _FP_QNANBIT_SH_##fs)) 47 48 /* Finish truly unpacking a native fp value by classifying the kind 49 of fp value and normalizing both the exponent and the fraction. */ 50 51 #define _FP_UNPACK_CANONICAL(fs, wc, X) \ 52 do \ 53 { \ 54 switch (X##_e) \ 55 { \ 56 default: \ 57 _FP_FRAC_HIGH_RAW_##fs (X) |= _FP_IMPLBIT_##fs; \ 58 _FP_FRAC_SLL_##wc (X, _FP_WORKBITS); \ 59 X##_e -= _FP_EXPBIAS_##fs; \ 60 X##_c = FP_CLS_NORMAL; \ 61 break; \ 62 \ 63 case 0: \ 64 if (_FP_FRAC_ZEROP_##wc (X)) \ 65 X##_c = FP_CLS_ZERO; \ 66 else if (FP_DENORM_ZERO) \ 67 { \ 68 X##_c = FP_CLS_ZERO; \ 69 _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \ 70 FP_SET_EXCEPTION (FP_EX_DENORM); \ 71 } \ 72 else \ 73 { \ 74 /* A denormalized number. */ \ 75 _FP_I_TYPE _FP_UNPACK_CANONICAL_shift; \ 76 _FP_FRAC_CLZ_##wc (_FP_UNPACK_CANONICAL_shift, \ 77 X); \ 78 _FP_UNPACK_CANONICAL_shift -= _FP_FRACXBITS_##fs; \ 79 _FP_FRAC_SLL_##wc (X, (_FP_UNPACK_CANONICAL_shift \ 80 + _FP_WORKBITS)); \ 81 X##_e -= (_FP_EXPBIAS_##fs - 1 \ 82 + _FP_UNPACK_CANONICAL_shift); \ 83 X##_c = FP_CLS_NORMAL; \ 84 FP_SET_EXCEPTION (FP_EX_DENORM); \ 85 } \ 86 break; \ 87 \ 88 case _FP_EXPMAX_##fs: \ 89 if (_FP_FRAC_ZEROP_##wc (X)) \ 90 X##_c = FP_CLS_INF; \ 91 else \ 92 { \ 93 X##_c = FP_CLS_NAN; \ 94 /* Check for signaling NaN. */ \ 95 if (_FP_FRAC_SNANP (fs, X)) \ 96 FP_SET_EXCEPTION (FP_EX_INVALID \ 97 | FP_EX_INVALID_SNAN); \ 98 } \ 99 break; \ 100 } \ 101 } \ 102 while (0) 103 104 /* Finish unpacking an fp value in semi-raw mode: the mantissa is 105 shifted by _FP_WORKBITS but the implicit MSB is not inserted and 106 other classification is not done. */ 107 #define _FP_UNPACK_SEMIRAW(fs, wc, X) _FP_FRAC_SLL_##wc (X, _FP_WORKBITS) 108 109 /* Check whether a raw or semi-raw input value should be flushed to 110 zero, and flush it to zero if so. */ 111 #define _FP_CHECK_FLUSH_ZERO(fs, wc, X) \ 112 do \ 113 { \ 114 if (FP_DENORM_ZERO \ 115 && X##_e == 0 \ 116 && !_FP_FRAC_ZEROP_##wc (X)) \ 117 { \ 118 _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \ 119 FP_SET_EXCEPTION (FP_EX_DENORM); \ 120 } \ 121 } \ 122 while (0) 123 124 /* A semi-raw value has overflowed to infinity. Adjust the mantissa 125 and exponent appropriately. */ 126 #define _FP_OVERFLOW_SEMIRAW(fs, wc, X) \ 127 do \ 128 { \ 129 if (FP_ROUNDMODE == FP_RND_NEAREST \ 130 || (FP_ROUNDMODE == FP_RND_PINF && !X##_s) \ 131 || (FP_ROUNDMODE == FP_RND_MINF && X##_s)) \ 132 { \ 133 X##_e = _FP_EXPMAX_##fs; \ 134 _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \ 135 } \ 136 else \ 137 { \ 138 X##_e = _FP_EXPMAX_##fs - 1; \ 139 _FP_FRAC_SET_##wc (X, _FP_MAXFRAC_##wc); \ 140 } \ 141 FP_SET_EXCEPTION (FP_EX_INEXACT); \ 142 FP_SET_EXCEPTION (FP_EX_OVERFLOW); \ 143 } \ 144 while (0) 145 146 /* Check for a semi-raw value being a signaling NaN and raise the 147 invalid exception if so. */ 148 #define _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X) \ 149 do \ 150 { \ 151 if (X##_e == _FP_EXPMAX_##fs \ 152 && !_FP_FRAC_ZEROP_##wc (X) \ 153 && _FP_FRAC_SNANP_SEMIRAW (fs, X)) \ 154 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_SNAN); \ 155 } \ 156 while (0) 157 158 /* Choose a NaN result from an operation on two semi-raw NaN 159 values. */ 160 #define _FP_CHOOSENAN_SEMIRAW(fs, wc, R, X, Y, OP) \ 161 do \ 162 { \ 163 /* _FP_CHOOSENAN expects raw values, so shift as required. */ \ 164 _FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \ 165 _FP_FRAC_SRL_##wc (Y, _FP_WORKBITS); \ 166 _FP_CHOOSENAN (fs, wc, R, X, Y, OP); \ 167 _FP_FRAC_SLL_##wc (R, _FP_WORKBITS); \ 168 } \ 169 while (0) 170 171 /* Make the fractional part a quiet NaN, preserving the payload 172 if possible, otherwise make it the canonical quiet NaN and set 173 the sign bit accordingly. */ 174 #define _FP_SETQNAN(fs, wc, X) \ 175 do \ 176 { \ 177 if (_FP_QNANNEGATEDP) \ 178 { \ 179 _FP_FRAC_HIGH_RAW_##fs (X) &= _FP_QNANBIT_##fs - 1; \ 180 if (_FP_FRAC_ZEROP_##wc (X)) \ 181 { \ 182 X##_s = _FP_NANSIGN_##fs; \ 183 _FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \ 184 } \ 185 } \ 186 else \ 187 _FP_FRAC_HIGH_RAW_##fs (X) |= _FP_QNANBIT_##fs; \ 188 } \ 189 while (0) 190 #define _FP_SETQNAN_SEMIRAW(fs, wc, X) \ 191 do \ 192 { \ 193 if (_FP_QNANNEGATEDP) \ 194 { \ 195 _FP_FRAC_HIGH_##fs (X) &= _FP_QNANBIT_SH_##fs - 1; \ 196 if (_FP_FRAC_ZEROP_##wc (X)) \ 197 { \ 198 X##_s = _FP_NANSIGN_##fs; \ 199 _FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \ 200 _FP_FRAC_SLL_##wc (X, _FP_WORKBITS); \ 201 } \ 202 } \ 203 else \ 204 _FP_FRAC_HIGH_##fs (X) |= _FP_QNANBIT_SH_##fs; \ 205 } \ 206 while (0) 207 208 /* Test whether a biased exponent is normal (not zero or maximum). */ 209 #define _FP_EXP_NORMAL(fs, wc, X) (((X##_e + 1) & _FP_EXPMAX_##fs) > 1) 210 211 /* Prepare to pack an fp value in semi-raw mode: the mantissa is 212 rounded and shifted right, with the rounding possibly increasing 213 the exponent (including changing a finite value to infinity). */ 214 #define _FP_PACK_SEMIRAW(fs, wc, X) \ 215 do \ 216 { \ 217 int _FP_PACK_SEMIRAW_is_tiny \ 218 = X##_e == 0 && !_FP_FRAC_ZEROP_##wc (X); \ 219 if (_FP_TININESS_AFTER_ROUNDING \ 220 && _FP_PACK_SEMIRAW_is_tiny) \ 221 { \ 222 FP_DECL_##fs (_FP_PACK_SEMIRAW_T); \ 223 _FP_FRAC_COPY_##wc (_FP_PACK_SEMIRAW_T, X); \ 224 _FP_PACK_SEMIRAW_T##_s = X##_s; \ 225 _FP_PACK_SEMIRAW_T##_e = X##_e; \ 226 _FP_FRAC_SLL_##wc (_FP_PACK_SEMIRAW_T, 1); \ 227 _FP_ROUND (wc, _FP_PACK_SEMIRAW_T); \ 228 if (_FP_FRAC_OVERP_##wc (fs, _FP_PACK_SEMIRAW_T)) \ 229 _FP_PACK_SEMIRAW_is_tiny = 0; \ 230 } \ 231 _FP_ROUND (wc, X); \ 232 if (_FP_PACK_SEMIRAW_is_tiny) \ 233 { \ 234 if ((FP_CUR_EXCEPTIONS & FP_EX_INEXACT) \ 235 || (FP_TRAPPING_EXCEPTIONS & FP_EX_UNDERFLOW)) \ 236 FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \ 237 } \ 238 if (_FP_FRAC_HIGH_##fs (X) \ 239 & (_FP_OVERFLOW_##fs >> 1)) \ 240 { \ 241 _FP_FRAC_HIGH_##fs (X) &= ~(_FP_OVERFLOW_##fs >> 1); \ 242 X##_e++; \ 243 if (X##_e == _FP_EXPMAX_##fs) \ 244 _FP_OVERFLOW_SEMIRAW (fs, wc, X); \ 245 } \ 246 _FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \ 247 if (X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \ 248 { \ 249 if (!_FP_KEEPNANFRACP) \ 250 { \ 251 _FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \ 252 X##_s = _FP_NANSIGN_##fs; \ 253 } \ 254 else \ 255 _FP_SETQNAN (fs, wc, X); \ 256 } \ 257 } \ 258 while (0) 259 260 /* Before packing the bits back into the native fp result, take care 261 of such mundane things as rounding and overflow. Also, for some 262 kinds of fp values, the original parts may not have been fully 263 extracted -- but that is ok, we can regenerate them now. */ 264 265 #define _FP_PACK_CANONICAL(fs, wc, X) \ 266 do \ 267 { \ 268 switch (X##_c) \ 269 { \ 270 case FP_CLS_NORMAL: \ 271 X##_e += _FP_EXPBIAS_##fs; \ 272 if (X##_e > 0) \ 273 { \ 274 _FP_ROUND (wc, X); \ 275 if (_FP_FRAC_OVERP_##wc (fs, X)) \ 276 { \ 277 _FP_FRAC_CLEAR_OVERP_##wc (fs, X); \ 278 X##_e++; \ 279 } \ 280 _FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \ 281 if (X##_e >= _FP_EXPMAX_##fs) \ 282 { \ 283 /* Overflow. */ \ 284 switch (FP_ROUNDMODE) \ 285 { \ 286 case FP_RND_NEAREST: \ 287 X##_c = FP_CLS_INF; \ 288 break; \ 289 case FP_RND_PINF: \ 290 if (!X##_s) \ 291 X##_c = FP_CLS_INF; \ 292 break; \ 293 case FP_RND_MINF: \ 294 if (X##_s) \ 295 X##_c = FP_CLS_INF; \ 296 break; \ 297 } \ 298 if (X##_c == FP_CLS_INF) \ 299 { \ 300 /* Overflow to infinity. */ \ 301 X##_e = _FP_EXPMAX_##fs; \ 302 _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \ 303 } \ 304 else \ 305 { \ 306 /* Overflow to maximum normal. */ \ 307 X##_e = _FP_EXPMAX_##fs - 1; \ 308 _FP_FRAC_SET_##wc (X, _FP_MAXFRAC_##wc); \ 309 } \ 310 FP_SET_EXCEPTION (FP_EX_OVERFLOW); \ 311 FP_SET_EXCEPTION (FP_EX_INEXACT); \ 312 } \ 313 } \ 314 else \ 315 { \ 316 /* We've got a denormalized number. */ \ 317 int _FP_PACK_CANONICAL_is_tiny = 1; \ 318 if (_FP_TININESS_AFTER_ROUNDING && X##_e == 0) \ 319 { \ 320 FP_DECL_##fs (_FP_PACK_CANONICAL_T); \ 321 _FP_FRAC_COPY_##wc (_FP_PACK_CANONICAL_T, X); \ 322 _FP_PACK_CANONICAL_T##_s = X##_s; \ 323 _FP_PACK_CANONICAL_T##_e = X##_e; \ 324 _FP_ROUND (wc, _FP_PACK_CANONICAL_T); \ 325 if (_FP_FRAC_OVERP_##wc (fs, _FP_PACK_CANONICAL_T)) \ 326 _FP_PACK_CANONICAL_is_tiny = 0; \ 327 } \ 328 X##_e = -X##_e + 1; \ 329 if (X##_e <= _FP_WFRACBITS_##fs) \ 330 { \ 331 _FP_FRAC_SRS_##wc (X, X##_e, _FP_WFRACBITS_##fs); \ 332 _FP_ROUND (wc, X); \ 333 if (_FP_FRAC_HIGH_##fs (X) \ 334 & (_FP_OVERFLOW_##fs >> 1)) \ 335 { \ 336 X##_e = 1; \ 337 _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \ 338 FP_SET_EXCEPTION (FP_EX_INEXACT); \ 339 } \ 340 else \ 341 { \ 342 X##_e = 0; \ 343 _FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \ 344 } \ 345 if (_FP_PACK_CANONICAL_is_tiny \ 346 && ((FP_CUR_EXCEPTIONS & FP_EX_INEXACT) \ 347 || (FP_TRAPPING_EXCEPTIONS \ 348 & FP_EX_UNDERFLOW))) \ 349 FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \ 350 } \ 351 else \ 352 { \ 353 /* Underflow to zero. */ \ 354 X##_e = 0; \ 355 if (!_FP_FRAC_ZEROP_##wc (X)) \ 356 { \ 357 _FP_FRAC_SET_##wc (X, _FP_MINFRAC_##wc); \ 358 _FP_ROUND (wc, X); \ 359 _FP_FRAC_LOW_##wc (X) >>= (_FP_WORKBITS); \ 360 } \ 361 FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \ 362 } \ 363 } \ 364 break; \ 365 \ 366 case FP_CLS_ZERO: \ 367 X##_e = 0; \ 368 _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \ 369 break; \ 370 \ 371 case FP_CLS_INF: \ 372 X##_e = _FP_EXPMAX_##fs; \ 373 _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \ 374 break; \ 375 \ 376 case FP_CLS_NAN: \ 377 X##_e = _FP_EXPMAX_##fs; \ 378 if (!_FP_KEEPNANFRACP) \ 379 { \ 380 _FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \ 381 X##_s = _FP_NANSIGN_##fs; \ 382 } \ 383 else \ 384 _FP_SETQNAN (fs, wc, X); \ 385 break; \ 386 } \ 387 } \ 388 while (0) 389 390 /* This one accepts raw argument and not cooked, returns 391 1 if X is a signaling NaN. */ 392 #define _FP_ISSIGNAN(fs, wc, X) \ 393 ({ \ 394 int _FP_ISSIGNAN_ret = 0; \ 395 if (X##_e == _FP_EXPMAX_##fs) \ 396 { \ 397 if (!_FP_FRAC_ZEROP_##wc (X) \ 398 && _FP_FRAC_SNANP (fs, X)) \ 399 _FP_ISSIGNAN_ret = 1; \ 400 } \ 401 _FP_ISSIGNAN_ret; \ 402 }) 403 404 405 406 407 408 /* Addition on semi-raw values. */ 409 #define _FP_ADD_INTERNAL(fs, wc, R, X, Y, OP) \ 410 do \ 411 { \ 412 _FP_CHECK_FLUSH_ZERO (fs, wc, X); \ 413 _FP_CHECK_FLUSH_ZERO (fs, wc, Y); \ 414 if (X##_s == Y##_s) \ 415 { \ 416 /* Addition. */ \ 417 R##_s = X##_s; \ 418 int _FP_ADD_INTERNAL_ediff = X##_e - Y##_e; \ 419 if (_FP_ADD_INTERNAL_ediff > 0) \ 420 { \ 421 R##_e = X##_e; \ 422 if (Y##_e == 0) \ 423 { \ 424 /* Y is zero or denormalized. */ \ 425 if (_FP_FRAC_ZEROP_##wc (Y)) \ 426 { \ 427 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \ 428 _FP_FRAC_COPY_##wc (R, X); \ 429 goto add_done; \ 430 } \ 431 else \ 432 { \ 433 FP_SET_EXCEPTION (FP_EX_DENORM); \ 434 _FP_ADD_INTERNAL_ediff--; \ 435 if (_FP_ADD_INTERNAL_ediff == 0) \ 436 { \ 437 _FP_FRAC_ADD_##wc (R, X, Y); \ 438 goto add3; \ 439 } \ 440 if (X##_e == _FP_EXPMAX_##fs) \ 441 { \ 442 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \ 443 _FP_FRAC_COPY_##wc (R, X); \ 444 goto add_done; \ 445 } \ 446 goto add1; \ 447 } \ 448 } \ 449 else if (X##_e == _FP_EXPMAX_##fs) \ 450 { \ 451 /* X is NaN or Inf, Y is normal. */ \ 452 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \ 453 _FP_FRAC_COPY_##wc (R, X); \ 454 goto add_done; \ 455 } \ 456 \ 457 /* Insert implicit MSB of Y. */ \ 458 _FP_FRAC_HIGH_##fs (Y) |= _FP_IMPLBIT_SH_##fs; \ 459 \ 460 add1: \ 461 /* Shift the mantissa of Y to the right \ 462 _FP_ADD_INTERNAL_EDIFF steps; remember to account \ 463 later for the implicit MSB of X. */ \ 464 if (_FP_ADD_INTERNAL_ediff <= _FP_WFRACBITS_##fs) \ 465 _FP_FRAC_SRS_##wc (Y, _FP_ADD_INTERNAL_ediff, \ 466 _FP_WFRACBITS_##fs); \ 467 else if (!_FP_FRAC_ZEROP_##wc (Y)) \ 468 _FP_FRAC_SET_##wc (Y, _FP_MINFRAC_##wc); \ 469 _FP_FRAC_ADD_##wc (R, X, Y); \ 470 } \ 471 else if (_FP_ADD_INTERNAL_ediff < 0) \ 472 { \ 473 _FP_ADD_INTERNAL_ediff = -_FP_ADD_INTERNAL_ediff; \ 474 R##_e = Y##_e; \ 475 if (X##_e == 0) \ 476 { \ 477 /* X is zero or denormalized. */ \ 478 if (_FP_FRAC_ZEROP_##wc (X)) \ 479 { \ 480 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \ 481 _FP_FRAC_COPY_##wc (R, Y); \ 482 goto add_done; \ 483 } \ 484 else \ 485 { \ 486 FP_SET_EXCEPTION (FP_EX_DENORM); \ 487 _FP_ADD_INTERNAL_ediff--; \ 488 if (_FP_ADD_INTERNAL_ediff == 0) \ 489 { \ 490 _FP_FRAC_ADD_##wc (R, Y, X); \ 491 goto add3; \ 492 } \ 493 if (Y##_e == _FP_EXPMAX_##fs) \ 494 { \ 495 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \ 496 _FP_FRAC_COPY_##wc (R, Y); \ 497 goto add_done; \ 498 } \ 499 goto add2; \ 500 } \ 501 } \ 502 else if (Y##_e == _FP_EXPMAX_##fs) \ 503 { \ 504 /* Y is NaN or Inf, X is normal. */ \ 505 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \ 506 _FP_FRAC_COPY_##wc (R, Y); \ 507 goto add_done; \ 508 } \ 509 \ 510 /* Insert implicit MSB of X. */ \ 511 _FP_FRAC_HIGH_##fs (X) |= _FP_IMPLBIT_SH_##fs; \ 512 \ 513 add2: \ 514 /* Shift the mantissa of X to the right \ 515 _FP_ADD_INTERNAL_EDIFF steps; remember to account \ 516 later for the implicit MSB of Y. */ \ 517 if (_FP_ADD_INTERNAL_ediff <= _FP_WFRACBITS_##fs) \ 518 _FP_FRAC_SRS_##wc (X, _FP_ADD_INTERNAL_ediff, \ 519 _FP_WFRACBITS_##fs); \ 520 else if (!_FP_FRAC_ZEROP_##wc (X)) \ 521 _FP_FRAC_SET_##wc (X, _FP_MINFRAC_##wc); \ 522 _FP_FRAC_ADD_##wc (R, Y, X); \ 523 } \ 524 else \ 525 { \ 526 /* _FP_ADD_INTERNAL_ediff == 0. */ \ 527 if (!_FP_EXP_NORMAL (fs, wc, X)) \ 528 { \ 529 if (X##_e == 0) \ 530 { \ 531 /* X and Y are zero or denormalized. */ \ 532 R##_e = 0; \ 533 if (_FP_FRAC_ZEROP_##wc (X)) \ 534 { \ 535 if (!_FP_FRAC_ZEROP_##wc (Y)) \ 536 FP_SET_EXCEPTION (FP_EX_DENORM); \ 537 _FP_FRAC_COPY_##wc (R, Y); \ 538 goto add_done; \ 539 } \ 540 else if (_FP_FRAC_ZEROP_##wc (Y)) \ 541 { \ 542 FP_SET_EXCEPTION (FP_EX_DENORM); \ 543 _FP_FRAC_COPY_##wc (R, X); \ 544 goto add_done; \ 545 } \ 546 else \ 547 { \ 548 FP_SET_EXCEPTION (FP_EX_DENORM); \ 549 _FP_FRAC_ADD_##wc (R, X, Y); \ 550 if (_FP_FRAC_HIGH_##fs (R) & _FP_IMPLBIT_SH_##fs) \ 551 { \ 552 /* Normalized result. */ \ 553 _FP_FRAC_HIGH_##fs (R) \ 554 &= ~(_FP_W_TYPE) _FP_IMPLBIT_SH_##fs; \ 555 R##_e = 1; \ 556 } \ 557 goto add_done; \ 558 } \ 559 } \ 560 else \ 561 { \ 562 /* X and Y are NaN or Inf. */ \ 563 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \ 564 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \ 565 R##_e = _FP_EXPMAX_##fs; \ 566 if (_FP_FRAC_ZEROP_##wc (X)) \ 567 _FP_FRAC_COPY_##wc (R, Y); \ 568 else if (_FP_FRAC_ZEROP_##wc (Y)) \ 569 _FP_FRAC_COPY_##wc (R, X); \ 570 else \ 571 _FP_CHOOSENAN_SEMIRAW (fs, wc, R, X, Y, OP); \ 572 goto add_done; \ 573 } \ 574 } \ 575 /* The exponents of X and Y, both normal, are equal. The \ 576 implicit MSBs will always add to increase the \ 577 exponent. */ \ 578 _FP_FRAC_ADD_##wc (R, X, Y); \ 579 R##_e = X##_e + 1; \ 580 _FP_FRAC_SRS_##wc (R, 1, _FP_WFRACBITS_##fs); \ 581 if (R##_e == _FP_EXPMAX_##fs) \ 582 /* Overflow to infinity (depending on rounding mode). */ \ 583 _FP_OVERFLOW_SEMIRAW (fs, wc, R); \ 584 goto add_done; \ 585 } \ 586 add3: \ 587 if (_FP_FRAC_HIGH_##fs (R) & _FP_IMPLBIT_SH_##fs) \ 588 { \ 589 /* Overflow. */ \ 590 _FP_FRAC_HIGH_##fs (R) &= ~(_FP_W_TYPE) _FP_IMPLBIT_SH_##fs; \ 591 R##_e++; \ 592 _FP_FRAC_SRS_##wc (R, 1, _FP_WFRACBITS_##fs); \ 593 if (R##_e == _FP_EXPMAX_##fs) \ 594 /* Overflow to infinity (depending on rounding mode). */ \ 595 _FP_OVERFLOW_SEMIRAW (fs, wc, R); \ 596 } \ 597 add_done: ; \ 598 } \ 599 else \ 600 { \ 601 /* Subtraction. */ \ 602 int _FP_ADD_INTERNAL_ediff = X##_e - Y##_e; \ 603 if (_FP_ADD_INTERNAL_ediff > 0) \ 604 { \ 605 R##_e = X##_e; \ 606 R##_s = X##_s; \ 607 if (Y##_e == 0) \ 608 { \ 609 /* Y is zero or denormalized. */ \ 610 if (_FP_FRAC_ZEROP_##wc (Y)) \ 611 { \ 612 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \ 613 _FP_FRAC_COPY_##wc (R, X); \ 614 goto sub_done; \ 615 } \ 616 else \ 617 { \ 618 FP_SET_EXCEPTION (FP_EX_DENORM); \ 619 _FP_ADD_INTERNAL_ediff--; \ 620 if (_FP_ADD_INTERNAL_ediff == 0) \ 621 { \ 622 _FP_FRAC_SUB_##wc (R, X, Y); \ 623 goto sub3; \ 624 } \ 625 if (X##_e == _FP_EXPMAX_##fs) \ 626 { \ 627 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \ 628 _FP_FRAC_COPY_##wc (R, X); \ 629 goto sub_done; \ 630 } \ 631 goto sub1; \ 632 } \ 633 } \ 634 else if (X##_e == _FP_EXPMAX_##fs) \ 635 { \ 636 /* X is NaN or Inf, Y is normal. */ \ 637 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \ 638 _FP_FRAC_COPY_##wc (R, X); \ 639 goto sub_done; \ 640 } \ 641 \ 642 /* Insert implicit MSB of Y. */ \ 643 _FP_FRAC_HIGH_##fs (Y) |= _FP_IMPLBIT_SH_##fs; \ 644 \ 645 sub1: \ 646 /* Shift the mantissa of Y to the right \ 647 _FP_ADD_INTERNAL_EDIFF steps; remember to account \ 648 later for the implicit MSB of X. */ \ 649 if (_FP_ADD_INTERNAL_ediff <= _FP_WFRACBITS_##fs) \ 650 _FP_FRAC_SRS_##wc (Y, _FP_ADD_INTERNAL_ediff, \ 651 _FP_WFRACBITS_##fs); \ 652 else if (!_FP_FRAC_ZEROP_##wc (Y)) \ 653 _FP_FRAC_SET_##wc (Y, _FP_MINFRAC_##wc); \ 654 _FP_FRAC_SUB_##wc (R, X, Y); \ 655 } \ 656 else if (_FP_ADD_INTERNAL_ediff < 0) \ 657 { \ 658 _FP_ADD_INTERNAL_ediff = -_FP_ADD_INTERNAL_ediff; \ 659 R##_e = Y##_e; \ 660 R##_s = Y##_s; \ 661 if (X##_e == 0) \ 662 { \ 663 /* X is zero or denormalized. */ \ 664 if (_FP_FRAC_ZEROP_##wc (X)) \ 665 { \ 666 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \ 667 _FP_FRAC_COPY_##wc (R, Y); \ 668 goto sub_done; \ 669 } \ 670 else \ 671 { \ 672 FP_SET_EXCEPTION (FP_EX_DENORM); \ 673 _FP_ADD_INTERNAL_ediff--; \ 674 if (_FP_ADD_INTERNAL_ediff == 0) \ 675 { \ 676 _FP_FRAC_SUB_##wc (R, Y, X); \ 677 goto sub3; \ 678 } \ 679 if (Y##_e == _FP_EXPMAX_##fs) \ 680 { \ 681 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \ 682 _FP_FRAC_COPY_##wc (R, Y); \ 683 goto sub_done; \ 684 } \ 685 goto sub2; \ 686 } \ 687 } \ 688 else if (Y##_e == _FP_EXPMAX_##fs) \ 689 { \ 690 /* Y is NaN or Inf, X is normal. */ \ 691 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \ 692 _FP_FRAC_COPY_##wc (R, Y); \ 693 goto sub_done; \ 694 } \ 695 \ 696 /* Insert implicit MSB of X. */ \ 697 _FP_FRAC_HIGH_##fs (X) |= _FP_IMPLBIT_SH_##fs; \ 698 \ 699 sub2: \ 700 /* Shift the mantissa of X to the right \ 701 _FP_ADD_INTERNAL_EDIFF steps; remember to account \ 702 later for the implicit MSB of Y. */ \ 703 if (_FP_ADD_INTERNAL_ediff <= _FP_WFRACBITS_##fs) \ 704 _FP_FRAC_SRS_##wc (X, _FP_ADD_INTERNAL_ediff, \ 705 _FP_WFRACBITS_##fs); \ 706 else if (!_FP_FRAC_ZEROP_##wc (X)) \ 707 _FP_FRAC_SET_##wc (X, _FP_MINFRAC_##wc); \ 708 _FP_FRAC_SUB_##wc (R, Y, X); \ 709 } \ 710 else \ 711 { \ 712 /* ediff == 0. */ \ 713 if (!_FP_EXP_NORMAL (fs, wc, X)) \ 714 { \ 715 if (X##_e == 0) \ 716 { \ 717 /* X and Y are zero or denormalized. */ \ 718 R##_e = 0; \ 719 if (_FP_FRAC_ZEROP_##wc (X)) \ 720 { \ 721 _FP_FRAC_COPY_##wc (R, Y); \ 722 if (_FP_FRAC_ZEROP_##wc (Y)) \ 723 R##_s = (FP_ROUNDMODE == FP_RND_MINF); \ 724 else \ 725 { \ 726 FP_SET_EXCEPTION (FP_EX_DENORM); \ 727 R##_s = Y##_s; \ 728 } \ 729 goto sub_done; \ 730 } \ 731 else if (_FP_FRAC_ZEROP_##wc (Y)) \ 732 { \ 733 FP_SET_EXCEPTION (FP_EX_DENORM); \ 734 _FP_FRAC_COPY_##wc (R, X); \ 735 R##_s = X##_s; \ 736 goto sub_done; \ 737 } \ 738 else \ 739 { \ 740 FP_SET_EXCEPTION (FP_EX_DENORM); \ 741 _FP_FRAC_SUB_##wc (R, X, Y); \ 742 R##_s = X##_s; \ 743 if (_FP_FRAC_HIGH_##fs (R) & _FP_IMPLBIT_SH_##fs) \ 744 { \ 745 /* |X| < |Y|, negate result. */ \ 746 _FP_FRAC_SUB_##wc (R, Y, X); \ 747 R##_s = Y##_s; \ 748 } \ 749 else if (_FP_FRAC_ZEROP_##wc (R)) \ 750 R##_s = (FP_ROUNDMODE == FP_RND_MINF); \ 751 goto sub_done; \ 752 } \ 753 } \ 754 else \ 755 { \ 756 /* X and Y are NaN or Inf, of opposite signs. */ \ 757 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \ 758 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \ 759 R##_e = _FP_EXPMAX_##fs; \ 760 if (_FP_FRAC_ZEROP_##wc (X)) \ 761 { \ 762 if (_FP_FRAC_ZEROP_##wc (Y)) \ 763 { \ 764 /* Inf - Inf. */ \ 765 R##_s = _FP_NANSIGN_##fs; \ 766 _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \ 767 _FP_FRAC_SLL_##wc (R, _FP_WORKBITS); \ 768 FP_SET_EXCEPTION (FP_EX_INVALID \ 769 | FP_EX_INVALID_ISI); \ 770 } \ 771 else \ 772 { \ 773 /* Inf - NaN. */ \ 774 R##_s = Y##_s; \ 775 _FP_FRAC_COPY_##wc (R, Y); \ 776 } \ 777 } \ 778 else \ 779 { \ 780 if (_FP_FRAC_ZEROP_##wc (Y)) \ 781 { \ 782 /* NaN - Inf. */ \ 783 R##_s = X##_s; \ 784 _FP_FRAC_COPY_##wc (R, X); \ 785 } \ 786 else \ 787 { \ 788 /* NaN - NaN. */ \ 789 _FP_CHOOSENAN_SEMIRAW (fs, wc, R, X, Y, OP); \ 790 } \ 791 } \ 792 goto sub_done; \ 793 } \ 794 } \ 795 /* The exponents of X and Y, both normal, are equal. The \ 796 implicit MSBs cancel. */ \ 797 R##_e = X##_e; \ 798 _FP_FRAC_SUB_##wc (R, X, Y); \ 799 R##_s = X##_s; \ 800 if (_FP_FRAC_HIGH_##fs (R) & _FP_IMPLBIT_SH_##fs) \ 801 { \ 802 /* |X| < |Y|, negate result. */ \ 803 _FP_FRAC_SUB_##wc (R, Y, X); \ 804 R##_s = Y##_s; \ 805 } \ 806 else if (_FP_FRAC_ZEROP_##wc (R)) \ 807 { \ 808 R##_e = 0; \ 809 R##_s = (FP_ROUNDMODE == FP_RND_MINF); \ 810 goto sub_done; \ 811 } \ 812 goto norm; \ 813 } \ 814 sub3: \ 815 if (_FP_FRAC_HIGH_##fs (R) & _FP_IMPLBIT_SH_##fs) \ 816 { \ 817 int _FP_ADD_INTERNAL_diff; \ 818 /* Carry into most significant bit of larger one of X and Y, \ 819 canceling it; renormalize. */ \ 820 _FP_FRAC_HIGH_##fs (R) &= _FP_IMPLBIT_SH_##fs - 1; \ 821 norm: \ 822 _FP_FRAC_CLZ_##wc (_FP_ADD_INTERNAL_diff, R); \ 823 _FP_ADD_INTERNAL_diff -= _FP_WFRACXBITS_##fs; \ 824 _FP_FRAC_SLL_##wc (R, _FP_ADD_INTERNAL_diff); \ 825 if (R##_e <= _FP_ADD_INTERNAL_diff) \ 826 { \ 827 /* R is denormalized. */ \ 828 _FP_ADD_INTERNAL_diff \ 829 = _FP_ADD_INTERNAL_diff - R##_e + 1; \ 830 _FP_FRAC_SRS_##wc (R, _FP_ADD_INTERNAL_diff, \ 831 _FP_WFRACBITS_##fs); \ 832 R##_e = 0; \ 833 } \ 834 else \ 835 { \ 836 R##_e -= _FP_ADD_INTERNAL_diff; \ 837 _FP_FRAC_HIGH_##fs (R) &= ~(_FP_W_TYPE) _FP_IMPLBIT_SH_##fs; \ 838 } \ 839 } \ 840 sub_done: ; \ 841 } \ 842 } \ 843 while (0) 844 845 #define _FP_ADD(fs, wc, R, X, Y) _FP_ADD_INTERNAL (fs, wc, R, X, Y, '+') 846 #define _FP_SUB(fs, wc, R, X, Y) \ 847 do \ 848 { \ 849 if (!(Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))) \ 850 Y##_s ^= 1; \ 851 _FP_ADD_INTERNAL (fs, wc, R, X, Y, '-'); \ 852 } \ 853 while (0) 854 855 856 /* Main negation routine. The input value is raw. */ 857 858 #define _FP_NEG(fs, wc, R, X) \ 859 do \ 860 { \ 861 _FP_FRAC_COPY_##wc (R, X); \ 862 R##_e = X##_e; \ 863 R##_s = 1 ^ X##_s; \ 864 } \ 865 while (0) 866 867 868 /* Main multiplication routine. The input values should be cooked. */ 869 870 #define _FP_MUL(fs, wc, R, X, Y) \ 871 do \ 872 { \ 873 R##_s = X##_s ^ Y##_s; \ 874 R##_e = X##_e + Y##_e + 1; \ 875 switch (_FP_CLS_COMBINE (X##_c, Y##_c)) \ 876 { \ 877 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NORMAL): \ 878 R##_c = FP_CLS_NORMAL; \ 879 \ 880 _FP_MUL_MEAT_##fs (R, X, Y); \ 881 \ 882 if (_FP_FRAC_OVERP_##wc (fs, R)) \ 883 _FP_FRAC_SRS_##wc (R, 1, _FP_WFRACBITS_##fs); \ 884 else \ 885 R##_e--; \ 886 break; \ 887 \ 888 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \ 889 _FP_CHOOSENAN (fs, wc, R, X, Y, '*'); \ 890 break; \ 891 \ 892 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NORMAL): \ 893 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_INF): \ 894 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_ZERO): \ 895 R##_s = X##_s; \ 896 \ 897 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \ 898 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \ 899 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \ 900 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \ 901 _FP_FRAC_COPY_##wc (R, X); \ 902 R##_c = X##_c; \ 903 break; \ 904 \ 905 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NAN): \ 906 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NAN): \ 907 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NAN): \ 908 R##_s = Y##_s; \ 909 \ 910 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_INF): \ 911 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_ZERO): \ 912 _FP_FRAC_COPY_##wc (R, Y); \ 913 R##_c = Y##_c; \ 914 break; \ 915 \ 916 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \ 917 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \ 918 R##_s = _FP_NANSIGN_##fs; \ 919 R##_c = FP_CLS_NAN; \ 920 _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \ 921 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_IMZ); \ 922 break; \ 923 \ 924 default: \ 925 abort (); \ 926 } \ 927 } \ 928 while (0) 929 930 931 /* Fused multiply-add. The input values should be cooked. */ 932 933 #define _FP_FMA(fs, wc, dwc, R, X, Y, Z) \ 934 do \ 935 { \ 936 FP_DECL_##fs (_FP_FMA_T); \ 937 _FP_FMA_T##_s = X##_s ^ Y##_s; \ 938 _FP_FMA_T##_e = X##_e + Y##_e + 1; \ 939 switch (_FP_CLS_COMBINE (X##_c, Y##_c)) \ 940 { \ 941 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NORMAL): \ 942 switch (Z##_c) \ 943 { \ 944 case FP_CLS_INF: \ 945 case FP_CLS_NAN: \ 946 R##_s = Z##_s; \ 947 _FP_FRAC_COPY_##wc (R, Z); \ 948 R##_c = Z##_c; \ 949 break; \ 950 \ 951 case FP_CLS_ZERO: \ 952 R##_c = FP_CLS_NORMAL; \ 953 R##_s = _FP_FMA_T##_s; \ 954 R##_e = _FP_FMA_T##_e; \ 955 \ 956 _FP_MUL_MEAT_##fs (R, X, Y); \ 957 \ 958 if (_FP_FRAC_OVERP_##wc (fs, R)) \ 959 _FP_FRAC_SRS_##wc (R, 1, _FP_WFRACBITS_##fs); \ 960 else \ 961 R##_e--; \ 962 break; \ 963 \ 964 case FP_CLS_NORMAL:; \ 965 _FP_FRAC_DECL_##dwc (_FP_FMA_TD); \ 966 _FP_FRAC_DECL_##dwc (_FP_FMA_ZD); \ 967 _FP_FRAC_DECL_##dwc (_FP_FMA_RD); \ 968 _FP_MUL_MEAT_DW_##fs (_FP_FMA_TD, X, Y); \ 969 R##_e = _FP_FMA_T##_e; \ 970 int _FP_FMA_tsh \ 971 = _FP_FRAC_HIGHBIT_DW_##dwc (fs, _FP_FMA_TD) == 0; \ 972 _FP_FMA_T##_e -= _FP_FMA_tsh; \ 973 int _FP_FMA_ediff = _FP_FMA_T##_e - Z##_e; \ 974 if (_FP_FMA_ediff >= 0) \ 975 { \ 976 int _FP_FMA_shift \ 977 = _FP_WFRACBITS_##fs - _FP_FMA_tsh - _FP_FMA_ediff; \ 978 if (_FP_FMA_shift <= -_FP_WFRACBITS_##fs) \ 979 _FP_FRAC_SET_##dwc (_FP_FMA_ZD, _FP_MINFRAC_##dwc); \ 980 else \ 981 { \ 982 _FP_FRAC_COPY_##dwc##_##wc (_FP_FMA_ZD, Z); \ 983 if (_FP_FMA_shift < 0) \ 984 _FP_FRAC_SRS_##dwc (_FP_FMA_ZD, -_FP_FMA_shift, \ 985 _FP_WFRACBITS_DW_##fs); \ 986 else if (_FP_FMA_shift > 0) \ 987 _FP_FRAC_SLL_##dwc (_FP_FMA_ZD, _FP_FMA_shift); \ 988 } \ 989 R##_s = _FP_FMA_T##_s; \ 990 if (_FP_FMA_T##_s == Z##_s) \ 991 _FP_FRAC_ADD_##dwc (_FP_FMA_RD, _FP_FMA_TD, \ 992 _FP_FMA_ZD); \ 993 else \ 994 { \ 995 _FP_FRAC_SUB_##dwc (_FP_FMA_RD, _FP_FMA_TD, \ 996 _FP_FMA_ZD); \ 997 if (_FP_FRAC_NEGP_##dwc (_FP_FMA_RD)) \ 998 { \ 999 R##_s = Z##_s; \ 1000 _FP_FRAC_SUB_##dwc (_FP_FMA_RD, _FP_FMA_ZD, \ 1001 _FP_FMA_TD); \ 1002 } \ 1003 } \ 1004 } \ 1005 else \ 1006 { \ 1007 R##_e = Z##_e; \ 1008 R##_s = Z##_s; \ 1009 _FP_FRAC_COPY_##dwc##_##wc (_FP_FMA_ZD, Z); \ 1010 _FP_FRAC_SLL_##dwc (_FP_FMA_ZD, _FP_WFRACBITS_##fs); \ 1011 int _FP_FMA_shift = -_FP_FMA_ediff - _FP_FMA_tsh; \ 1012 if (_FP_FMA_shift >= _FP_WFRACBITS_DW_##fs) \ 1013 _FP_FRAC_SET_##dwc (_FP_FMA_TD, _FP_MINFRAC_##dwc); \ 1014 else if (_FP_FMA_shift > 0) \ 1015 _FP_FRAC_SRS_##dwc (_FP_FMA_TD, _FP_FMA_shift, \ 1016 _FP_WFRACBITS_DW_##fs); \ 1017 if (Z##_s == _FP_FMA_T##_s) \ 1018 _FP_FRAC_ADD_##dwc (_FP_FMA_RD, _FP_FMA_ZD, \ 1019 _FP_FMA_TD); \ 1020 else \ 1021 _FP_FRAC_SUB_##dwc (_FP_FMA_RD, _FP_FMA_ZD, \ 1022 _FP_FMA_TD); \ 1023 } \ 1024 if (_FP_FRAC_ZEROP_##dwc (_FP_FMA_RD)) \ 1025 { \ 1026 if (_FP_FMA_T##_s == Z##_s) \ 1027 R##_s = Z##_s; \ 1028 else \ 1029 R##_s = (FP_ROUNDMODE == FP_RND_MINF); \ 1030 _FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \ 1031 R##_c = FP_CLS_ZERO; \ 1032 } \ 1033 else \ 1034 { \ 1035 int _FP_FMA_rlz; \ 1036 _FP_FRAC_CLZ_##dwc (_FP_FMA_rlz, _FP_FMA_RD); \ 1037 _FP_FMA_rlz -= _FP_WFRACXBITS_DW_##fs; \ 1038 R##_e -= _FP_FMA_rlz; \ 1039 int _FP_FMA_shift = _FP_WFRACBITS_##fs - _FP_FMA_rlz; \ 1040 if (_FP_FMA_shift > 0) \ 1041 _FP_FRAC_SRS_##dwc (_FP_FMA_RD, _FP_FMA_shift, \ 1042 _FP_WFRACBITS_DW_##fs); \ 1043 else if (_FP_FMA_shift < 0) \ 1044 _FP_FRAC_SLL_##dwc (_FP_FMA_RD, -_FP_FMA_shift); \ 1045 _FP_FRAC_COPY_##wc##_##dwc (R, _FP_FMA_RD); \ 1046 R##_c = FP_CLS_NORMAL; \ 1047 } \ 1048 break; \ 1049 } \ 1050 goto done_fma; \ 1051 \ 1052 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \ 1053 _FP_CHOOSENAN (fs, wc, _FP_FMA_T, X, Y, '*'); \ 1054 break; \ 1055 \ 1056 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NORMAL): \ 1057 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_INF): \ 1058 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_ZERO): \ 1059 _FP_FMA_T##_s = X##_s; \ 1060 \ 1061 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \ 1062 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \ 1063 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \ 1064 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \ 1065 _FP_FRAC_COPY_##wc (_FP_FMA_T, X); \ 1066 _FP_FMA_T##_c = X##_c; \ 1067 break; \ 1068 \ 1069 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NAN): \ 1070 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NAN): \ 1071 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NAN): \ 1072 _FP_FMA_T##_s = Y##_s; \ 1073 \ 1074 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_INF): \ 1075 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_ZERO): \ 1076 _FP_FRAC_COPY_##wc (_FP_FMA_T, Y); \ 1077 _FP_FMA_T##_c = Y##_c; \ 1078 break; \ 1079 \ 1080 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \ 1081 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \ 1082 _FP_FMA_T##_s = _FP_NANSIGN_##fs; \ 1083 _FP_FMA_T##_c = FP_CLS_NAN; \ 1084 _FP_FRAC_SET_##wc (_FP_FMA_T, _FP_NANFRAC_##fs); \ 1085 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_IMZ_FMA); \ 1086 break; \ 1087 \ 1088 default: \ 1089 abort (); \ 1090 } \ 1091 \ 1092 /* T = X * Y is zero, infinity or NaN. */ \ 1093 switch (_FP_CLS_COMBINE (_FP_FMA_T##_c, Z##_c)) \ 1094 { \ 1095 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \ 1096 _FP_CHOOSENAN (fs, wc, R, _FP_FMA_T, Z, '+'); \ 1097 break; \ 1098 \ 1099 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NORMAL): \ 1100 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_INF): \ 1101 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_ZERO): \ 1102 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \ 1103 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \ 1104 R##_s = _FP_FMA_T##_s; \ 1105 _FP_FRAC_COPY_##wc (R, _FP_FMA_T); \ 1106 R##_c = _FP_FMA_T##_c; \ 1107 break; \ 1108 \ 1109 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NAN): \ 1110 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NAN): \ 1111 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \ 1112 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \ 1113 R##_s = Z##_s; \ 1114 _FP_FRAC_COPY_##wc (R, Z); \ 1115 R##_c = Z##_c; \ 1116 break; \ 1117 \ 1118 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \ 1119 if (_FP_FMA_T##_s == Z##_s) \ 1120 { \ 1121 R##_s = Z##_s; \ 1122 _FP_FRAC_COPY_##wc (R, Z); \ 1123 R##_c = Z##_c; \ 1124 } \ 1125 else \ 1126 { \ 1127 R##_s = _FP_NANSIGN_##fs; \ 1128 R##_c = FP_CLS_NAN; \ 1129 _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \ 1130 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_ISI); \ 1131 } \ 1132 break; \ 1133 \ 1134 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \ 1135 if (_FP_FMA_T##_s == Z##_s) \ 1136 R##_s = Z##_s; \ 1137 else \ 1138 R##_s = (FP_ROUNDMODE == FP_RND_MINF); \ 1139 _FP_FRAC_COPY_##wc (R, Z); \ 1140 R##_c = Z##_c; \ 1141 break; \ 1142 \ 1143 default: \ 1144 abort (); \ 1145 } \ 1146 done_fma: ; \ 1147 } \ 1148 while (0) 1149 1150 1151 /* Main division routine. The input values should be cooked. */ 1152 1153 #define _FP_DIV(fs, wc, R, X, Y) \ 1154 do \ 1155 { \ 1156 R##_s = X##_s ^ Y##_s; \ 1157 R##_e = X##_e - Y##_e; \ 1158 switch (_FP_CLS_COMBINE (X##_c, Y##_c)) \ 1159 { \ 1160 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NORMAL): \ 1161 R##_c = FP_CLS_NORMAL; \ 1162 \ 1163 _FP_DIV_MEAT_##fs (R, X, Y); \ 1164 break; \ 1165 \ 1166 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \ 1167 _FP_CHOOSENAN (fs, wc, R, X, Y, '/'); \ 1168 break; \ 1169 \ 1170 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NORMAL): \ 1171 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_INF): \ 1172 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_ZERO): \ 1173 R##_s = X##_s; \ 1174 _FP_FRAC_COPY_##wc (R, X); \ 1175 R##_c = X##_c; \ 1176 break; \ 1177 \ 1178 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NAN): \ 1179 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NAN): \ 1180 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NAN): \ 1181 R##_s = Y##_s; \ 1182 _FP_FRAC_COPY_##wc (R, Y); \ 1183 R##_c = Y##_c; \ 1184 break; \ 1185 \ 1186 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_INF): \ 1187 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \ 1188 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \ 1189 R##_c = FP_CLS_ZERO; \ 1190 break; \ 1191 \ 1192 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_ZERO): \ 1193 FP_SET_EXCEPTION (FP_EX_DIVZERO); \ 1194 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \ 1195 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \ 1196 R##_c = FP_CLS_INF; \ 1197 break; \ 1198 \ 1199 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \ 1200 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \ 1201 R##_s = _FP_NANSIGN_##fs; \ 1202 R##_c = FP_CLS_NAN; \ 1203 _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \ 1204 FP_SET_EXCEPTION (FP_EX_INVALID \ 1205 | (X##_c == FP_CLS_INF \ 1206 ? FP_EX_INVALID_IDI \ 1207 : FP_EX_INVALID_ZDZ)); \ 1208 break; \ 1209 \ 1210 default: \ 1211 abort (); \ 1212 } \ 1213 } \ 1214 while (0) 1215 1216 1217 /* Helper for comparisons. EX is 0 not to raise exceptions, 1 to 1218 raise exceptions for signaling NaN operands, 2 to raise exceptions 1219 for all NaN operands. Conditionals are organized to allow the 1220 compiler to optimize away code based on the value of EX. */ 1221 1222 #define _FP_CMP_CHECK_NAN(fs, wc, X, Y, ex) \ 1223 do \ 1224 { \ 1225 /* The arguments are unordered, which may or may not result in \ 1226 an exception. */ \ 1227 if (ex) \ 1228 { \ 1229 /* At least some cases of unordered arguments result in \ 1230 exceptions; check whether this is one. */ \ 1231 if (FP_EX_INVALID_SNAN || FP_EX_INVALID_VC) \ 1232 { \ 1233 /* Check separately for each case of "invalid" \ 1234 exceptions. */ \ 1235 if ((ex) == 2) \ 1236 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_VC); \ 1237 if (_FP_ISSIGNAN (fs, wc, X) \ 1238 || _FP_ISSIGNAN (fs, wc, Y)) \ 1239 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_SNAN); \ 1240 } \ 1241 /* Otherwise, we only need to check whether to raise an \ 1242 exception, not which case or cases it is. */ \ 1243 else if ((ex) == 2 \ 1244 || _FP_ISSIGNAN (fs, wc, X) \ 1245 || _FP_ISSIGNAN (fs, wc, Y)) \ 1246 FP_SET_EXCEPTION (FP_EX_INVALID); \ 1247 } \ 1248 } \ 1249 while (0) 1250 1251 /* Main differential comparison routine. The inputs should be raw not 1252 cooked. The return is -1, 0, 1 for normal values, UN 1253 otherwise. */ 1254 1255 #define _FP_CMP(fs, wc, ret, X, Y, un, ex) \ 1256 do \ 1257 { \ 1258 /* NANs are unordered. */ \ 1259 if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \ 1260 || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))) \ 1261 { \ 1262 (ret) = (un); \ 1263 _FP_CMP_CHECK_NAN (fs, wc, X, Y, (ex)); \ 1264 } \ 1265 else \ 1266 { \ 1267 int _FP_CMP_is_zero_x; \ 1268 int _FP_CMP_is_zero_y; \ 1269 \ 1270 _FP_CHECK_FLUSH_ZERO (fs, wc, X); \ 1271 _FP_CHECK_FLUSH_ZERO (fs, wc, Y); \ 1272 \ 1273 _FP_CMP_is_zero_x \ 1274 = (!X##_e && _FP_FRAC_ZEROP_##wc (X)) ? 1 : 0; \ 1275 _FP_CMP_is_zero_y \ 1276 = (!Y##_e && _FP_FRAC_ZEROP_##wc (Y)) ? 1 : 0; \ 1277 \ 1278 if (_FP_CMP_is_zero_x && _FP_CMP_is_zero_y) \ 1279 (ret) = 0; \ 1280 else if (_FP_CMP_is_zero_x) \ 1281 (ret) = Y##_s ? 1 : -1; \ 1282 else if (_FP_CMP_is_zero_y) \ 1283 (ret) = X##_s ? -1 : 1; \ 1284 else if (X##_s != Y##_s) \ 1285 (ret) = X##_s ? -1 : 1; \ 1286 else if (X##_e > Y##_e) \ 1287 (ret) = X##_s ? -1 : 1; \ 1288 else if (X##_e < Y##_e) \ 1289 (ret) = X##_s ? 1 : -1; \ 1290 else if (_FP_FRAC_GT_##wc (X, Y)) \ 1291 (ret) = X##_s ? -1 : 1; \ 1292 else if (_FP_FRAC_GT_##wc (Y, X)) \ 1293 (ret) = X##_s ? 1 : -1; \ 1294 else \ 1295 (ret) = 0; \ 1296 } \ 1297 } \ 1298 while (0) 1299 1300 1301 /* Simplification for strict equality. */ 1302 1303 #define _FP_CMP_EQ(fs, wc, ret, X, Y, ex) \ 1304 do \ 1305 { \ 1306 /* NANs are unordered. */ \ 1307 if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \ 1308 || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))) \ 1309 { \ 1310 (ret) = 1; \ 1311 _FP_CMP_CHECK_NAN (fs, wc, X, Y, (ex)); \ 1312 } \ 1313 else \ 1314 { \ 1315 _FP_CHECK_FLUSH_ZERO (fs, wc, X); \ 1316 _FP_CHECK_FLUSH_ZERO (fs, wc, Y); \ 1317 \ 1318 (ret) = !(X##_e == Y##_e \ 1319 && _FP_FRAC_EQ_##wc (X, Y) \ 1320 && (X##_s == Y##_s \ 1321 || (!X##_e && _FP_FRAC_ZEROP_##wc (X)))); \ 1322 } \ 1323 } \ 1324 while (0) 1325 1326 /* Version to test unordered. */ 1327 1328 #define _FP_CMP_UNORD(fs, wc, ret, X, Y, ex) \ 1329 do \ 1330 { \ 1331 (ret) = ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \ 1332 || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))); \ 1333 if (ret) \ 1334 _FP_CMP_CHECK_NAN (fs, wc, X, Y, (ex)); \ 1335 } \ 1336 while (0) 1337 1338 /* Main square root routine. The input value should be cooked. */ 1339 1340 #define _FP_SQRT(fs, wc, R, X) \ 1341 do \ 1342 { \ 1343 _FP_FRAC_DECL_##wc (_FP_SQRT_T); \ 1344 _FP_FRAC_DECL_##wc (_FP_SQRT_S); \ 1345 _FP_W_TYPE _FP_SQRT_q; \ 1346 switch (X##_c) \ 1347 { \ 1348 case FP_CLS_NAN: \ 1349 _FP_FRAC_COPY_##wc (R, X); \ 1350 R##_s = X##_s; \ 1351 R##_c = FP_CLS_NAN; \ 1352 break; \ 1353 case FP_CLS_INF: \ 1354 if (X##_s) \ 1355 { \ 1356 R##_s = _FP_NANSIGN_##fs; \ 1357 R##_c = FP_CLS_NAN; /* NAN */ \ 1358 _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \ 1359 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_SQRT); \ 1360 } \ 1361 else \ 1362 { \ 1363 R##_s = 0; \ 1364 R##_c = FP_CLS_INF; /* sqrt(+inf) = +inf */ \ 1365 } \ 1366 break; \ 1367 case FP_CLS_ZERO: \ 1368 R##_s = X##_s; \ 1369 R##_c = FP_CLS_ZERO; /* sqrt(+-0) = +-0 */ \ 1370 break; \ 1371 case FP_CLS_NORMAL: \ 1372 R##_s = 0; \ 1373 if (X##_s) \ 1374 { \ 1375 R##_c = FP_CLS_NAN; /* NAN */ \ 1376 R##_s = _FP_NANSIGN_##fs; \ 1377 _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \ 1378 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_SQRT); \ 1379 break; \ 1380 } \ 1381 R##_c = FP_CLS_NORMAL; \ 1382 if (X##_e & 1) \ 1383 _FP_FRAC_SLL_##wc (X, 1); \ 1384 R##_e = X##_e >> 1; \ 1385 _FP_FRAC_SET_##wc (_FP_SQRT_S, _FP_ZEROFRAC_##wc); \ 1386 _FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \ 1387 _FP_SQRT_q = _FP_OVERFLOW_##fs >> 1; \ 1388 _FP_SQRT_MEAT_##wc (R, _FP_SQRT_S, _FP_SQRT_T, X, \ 1389 _FP_SQRT_q); \ 1390 } \ 1391 } \ 1392 while (0) 1393 1394 /* Convert from FP to integer. Input is raw. */ 1395 1396 /* RSIGNED can have following values: 1397 0: the number is required to be 0..(2^rsize)-1, if not, NV is set plus 1398 the result is either 0 or (2^rsize)-1 depending on the sign in such 1399 case. 1400 1: the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not, 1401 NV is set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1 1402 depending on the sign in such case. 1403 2: the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not, 1404 NV is set plus the result is reduced modulo 2^rsize. 1405 -1: the number is required to be -(2^(rsize-1))..(2^rsize)-1, if not, NV is 1406 set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1 1407 depending on the sign in such case. */ 1408 #define _FP_TO_INT(fs, wc, r, X, rsize, rsigned) \ 1409 do \ 1410 { \ 1411 if (X##_e < _FP_EXPBIAS_##fs) \ 1412 { \ 1413 (r) = 0; \ 1414 if (X##_e == 0) \ 1415 { \ 1416 if (!_FP_FRAC_ZEROP_##wc (X)) \ 1417 { \ 1418 if (!FP_DENORM_ZERO) \ 1419 FP_SET_EXCEPTION (FP_EX_INEXACT); \ 1420 FP_SET_EXCEPTION (FP_EX_DENORM); \ 1421 } \ 1422 } \ 1423 else \ 1424 FP_SET_EXCEPTION (FP_EX_INEXACT); \ 1425 } \ 1426 else if ((rsigned) == 2 \ 1427 && (X##_e \ 1428 >= ((_FP_EXPMAX_##fs \ 1429 < _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs + (rsize) - 1) \ 1430 ? _FP_EXPMAX_##fs \ 1431 : _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs + (rsize) - 1))) \ 1432 { \ 1433 /* Overflow resulting in 0. */ \ 1434 (r) = 0; \ 1435 FP_SET_EXCEPTION (FP_EX_INVALID \ 1436 | FP_EX_INVALID_CVI \ 1437 | ((FP_EX_INVALID_SNAN \ 1438 && _FP_ISSIGNAN (fs, wc, X)) \ 1439 ? FP_EX_INVALID_SNAN \ 1440 : 0)); \ 1441 } \ 1442 else if ((rsigned) != 2 \ 1443 && (X##_e >= (_FP_EXPMAX_##fs < _FP_EXPBIAS_##fs + (rsize) \ 1444 ? _FP_EXPMAX_##fs \ 1445 : (_FP_EXPBIAS_##fs + (rsize) \ 1446 - ((rsigned) > 0 || X##_s))) \ 1447 || (!(rsigned) && X##_s))) \ 1448 { \ 1449 /* Overflow or converting to the most negative integer. */ \ 1450 if (rsigned) \ 1451 { \ 1452 (r) = 1; \ 1453 (r) <<= (rsize) - 1; \ 1454 (r) -= 1 - X##_s; \ 1455 } \ 1456 else \ 1457 { \ 1458 (r) = 0; \ 1459 if (!X##_s) \ 1460 (r) = ~(r); \ 1461 } \ 1462 \ 1463 if (_FP_EXPBIAS_##fs + (rsize) - 1 < _FP_EXPMAX_##fs \ 1464 && (rsigned) \ 1465 && X##_s \ 1466 && X##_e == _FP_EXPBIAS_##fs + (rsize) - 1) \ 1467 { \ 1468 /* Possibly converting to most negative integer; check the \ 1469 mantissa. */ \ 1470 int _FP_TO_INT_inexact = 0; \ 1471 (void) ((_FP_FRACBITS_##fs > (rsize)) \ 1472 ? ({ \ 1473 _FP_FRAC_SRST_##wc (X, _FP_TO_INT_inexact, \ 1474 _FP_FRACBITS_##fs - (rsize), \ 1475 _FP_FRACBITS_##fs); \ 1476 0; \ 1477 }) \ 1478 : 0); \ 1479 if (!_FP_FRAC_ZEROP_##wc (X)) \ 1480 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \ 1481 else if (_FP_TO_INT_inexact) \ 1482 FP_SET_EXCEPTION (FP_EX_INEXACT); \ 1483 } \ 1484 else \ 1485 FP_SET_EXCEPTION (FP_EX_INVALID \ 1486 | FP_EX_INVALID_CVI \ 1487 | ((FP_EX_INVALID_SNAN \ 1488 && _FP_ISSIGNAN (fs, wc, X)) \ 1489 ? FP_EX_INVALID_SNAN \ 1490 : 0)); \ 1491 } \ 1492 else \ 1493 { \ 1494 int _FP_TO_INT_inexact = 0; \ 1495 _FP_FRAC_HIGH_RAW_##fs (X) |= _FP_IMPLBIT_##fs; \ 1496 if (X##_e >= _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs - 1) \ 1497 { \ 1498 _FP_FRAC_ASSEMBLE_##wc ((r), X, (rsize)); \ 1499 (r) <<= X##_e - _FP_EXPBIAS_##fs - _FP_FRACBITS_##fs + 1; \ 1500 } \ 1501 else \ 1502 { \ 1503 _FP_FRAC_SRST_##wc (X, _FP_TO_INT_inexact, \ 1504 (_FP_FRACBITS_##fs + _FP_EXPBIAS_##fs - 1 \ 1505 - X##_e), \ 1506 _FP_FRACBITS_##fs); \ 1507 _FP_FRAC_ASSEMBLE_##wc ((r), X, (rsize)); \ 1508 } \ 1509 if ((rsigned) && X##_s) \ 1510 (r) = -(r); \ 1511 if ((rsigned) == 2 && X##_e >= _FP_EXPBIAS_##fs + (rsize) - 1) \ 1512 { \ 1513 /* Overflow or converting to the most negative integer. */ \ 1514 if (X##_e > _FP_EXPBIAS_##fs + (rsize) - 1 \ 1515 || !X##_s \ 1516 || (r) != (((typeof (r)) 1) << ((rsize) - 1))) \ 1517 { \ 1518 _FP_TO_INT_inexact = 0; \ 1519 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \ 1520 } \ 1521 } \ 1522 if (_FP_TO_INT_inexact) \ 1523 FP_SET_EXCEPTION (FP_EX_INEXACT); \ 1524 } \ 1525 } \ 1526 while (0) 1527 1528 /* Convert integer to fp. Output is raw. RTYPE is unsigned even if 1529 input is signed. */ 1530 #define _FP_FROM_INT(fs, wc, X, r, rsize, rtype) \ 1531 do \ 1532 { \ 1533 if (r) \ 1534 { \ 1535 rtype _FP_FROM_INT_ur; \ 1536 \ 1537 if ((X##_s = ((r) < 0))) \ 1538 (r) = -(rtype) (r); \ 1539 \ 1540 _FP_FROM_INT_ur = (rtype) (r); \ 1541 (void) (((rsize) <= _FP_W_TYPE_SIZE) \ 1542 ? ({ \ 1543 int _FP_FROM_INT_lz; \ 1544 __FP_CLZ (_FP_FROM_INT_lz, \ 1545 (_FP_W_TYPE) _FP_FROM_INT_ur); \ 1546 X##_e = (_FP_EXPBIAS_##fs + _FP_W_TYPE_SIZE - 1 \ 1547 - _FP_FROM_INT_lz); \ 1548 }) \ 1549 : (((rsize) <= 2 * _FP_W_TYPE_SIZE) \ 1550 ? ({ \ 1551 int _FP_FROM_INT_lz; \ 1552 __FP_CLZ_2 (_FP_FROM_INT_lz, \ 1553 (_FP_W_TYPE) (_FP_FROM_INT_ur \ 1554 >> _FP_W_TYPE_SIZE), \ 1555 (_FP_W_TYPE) _FP_FROM_INT_ur); \ 1556 X##_e = (_FP_EXPBIAS_##fs + 2 * _FP_W_TYPE_SIZE - 1 \ 1557 - _FP_FROM_INT_lz); \ 1558 }) \ 1559 : (abort (), 0))); \ 1560 \ 1561 if ((rsize) - 1 + _FP_EXPBIAS_##fs >= _FP_EXPMAX_##fs \ 1562 && X##_e >= _FP_EXPMAX_##fs) \ 1563 { \ 1564 /* Exponent too big; overflow to infinity. (May also \ 1565 happen after rounding below.) */ \ 1566 _FP_OVERFLOW_SEMIRAW (fs, wc, X); \ 1567 goto pack_semiraw; \ 1568 } \ 1569 \ 1570 if ((rsize) <= _FP_FRACBITS_##fs \ 1571 || X##_e < _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs) \ 1572 { \ 1573 /* Exactly representable; shift left. */ \ 1574 _FP_FRAC_DISASSEMBLE_##wc (X, _FP_FROM_INT_ur, (rsize)); \ 1575 if (_FP_EXPBIAS_##fs + _FP_FRACBITS_##fs - 1 - X##_e > 0) \ 1576 _FP_FRAC_SLL_##wc (X, (_FP_EXPBIAS_##fs \ 1577 + _FP_FRACBITS_##fs - 1 - X##_e)); \ 1578 } \ 1579 else \ 1580 { \ 1581 /* More bits in integer than in floating type; need to \ 1582 round. */ \ 1583 if (_FP_EXPBIAS_##fs + _FP_WFRACBITS_##fs - 1 < X##_e) \ 1584 _FP_FROM_INT_ur \ 1585 = ((_FP_FROM_INT_ur >> (X##_e - _FP_EXPBIAS_##fs \ 1586 - _FP_WFRACBITS_##fs + 1)) \ 1587 | ((_FP_FROM_INT_ur \ 1588 << ((rsize) - (X##_e - _FP_EXPBIAS_##fs \ 1589 - _FP_WFRACBITS_##fs + 1))) \ 1590 != 0)); \ 1591 _FP_FRAC_DISASSEMBLE_##wc (X, _FP_FROM_INT_ur, (rsize)); \ 1592 if ((_FP_EXPBIAS_##fs + _FP_WFRACBITS_##fs - 1 - X##_e) > 0) \ 1593 _FP_FRAC_SLL_##wc (X, (_FP_EXPBIAS_##fs \ 1594 + _FP_WFRACBITS_##fs - 1 - X##_e)); \ 1595 _FP_FRAC_HIGH_##fs (X) &= ~(_FP_W_TYPE) _FP_IMPLBIT_SH_##fs; \ 1596 pack_semiraw: \ 1597 _FP_PACK_SEMIRAW (fs, wc, X); \ 1598 } \ 1599 } \ 1600 else \ 1601 { \ 1602 X##_s = 0; \ 1603 X##_e = 0; \ 1604 _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \ 1605 } \ 1606 } \ 1607 while (0) 1608 1609 1610 /* Extend from a narrower floating-point format to a wider one. Input 1611 and output are raw. */ 1612 #define FP_EXTEND(dfs, sfs, dwc, swc, D, S) \ 1613 do \ 1614 { \ 1615 if (_FP_FRACBITS_##dfs < _FP_FRACBITS_##sfs \ 1616 || (_FP_EXPMAX_##dfs - _FP_EXPBIAS_##dfs \ 1617 < _FP_EXPMAX_##sfs - _FP_EXPBIAS_##sfs) \ 1618 || (_FP_EXPBIAS_##dfs < _FP_EXPBIAS_##sfs + _FP_FRACBITS_##sfs - 1 \ 1619 && _FP_EXPBIAS_##dfs != _FP_EXPBIAS_##sfs)) \ 1620 abort (); \ 1621 D##_s = S##_s; \ 1622 _FP_FRAC_COPY_##dwc##_##swc (D, S); \ 1623 if (_FP_EXP_NORMAL (sfs, swc, S)) \ 1624 { \ 1625 D##_e = S##_e + _FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs; \ 1626 _FP_FRAC_SLL_##dwc (D, (_FP_FRACBITS_##dfs - _FP_FRACBITS_##sfs)); \ 1627 } \ 1628 else \ 1629 { \ 1630 if (S##_e == 0) \ 1631 { \ 1632 _FP_CHECK_FLUSH_ZERO (sfs, swc, S); \ 1633 if (_FP_FRAC_ZEROP_##swc (S)) \ 1634 D##_e = 0; \ 1635 else if (_FP_EXPBIAS_##dfs \ 1636 < _FP_EXPBIAS_##sfs + _FP_FRACBITS_##sfs - 1) \ 1637 { \ 1638 FP_SET_EXCEPTION (FP_EX_DENORM); \ 1639 _FP_FRAC_SLL_##dwc (D, (_FP_FRACBITS_##dfs \ 1640 - _FP_FRACBITS_##sfs)); \ 1641 D##_e = 0; \ 1642 if (FP_TRAPPING_EXCEPTIONS & FP_EX_UNDERFLOW) \ 1643 FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \ 1644 } \ 1645 else \ 1646 { \ 1647 int FP_EXTEND_lz; \ 1648 FP_SET_EXCEPTION (FP_EX_DENORM); \ 1649 _FP_FRAC_CLZ_##swc (FP_EXTEND_lz, S); \ 1650 _FP_FRAC_SLL_##dwc (D, \ 1651 FP_EXTEND_lz + _FP_FRACBITS_##dfs \ 1652 - _FP_FRACTBITS_##sfs); \ 1653 D##_e = (_FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs + 1 \ 1654 + _FP_FRACXBITS_##sfs - FP_EXTEND_lz); \ 1655 } \ 1656 } \ 1657 else \ 1658 { \ 1659 D##_e = _FP_EXPMAX_##dfs; \ 1660 if (!_FP_FRAC_ZEROP_##swc (S)) \ 1661 { \ 1662 if (_FP_FRAC_SNANP (sfs, S)) \ 1663 FP_SET_EXCEPTION (FP_EX_INVALID \ 1664 | FP_EX_INVALID_SNAN); \ 1665 _FP_FRAC_SLL_##dwc (D, (_FP_FRACBITS_##dfs \ 1666 - _FP_FRACBITS_##sfs)); \ 1667 _FP_SETQNAN (dfs, dwc, D); \ 1668 } \ 1669 } \ 1670 } \ 1671 } \ 1672 while (0) 1673 1674 /* Truncate from a wider floating-point format to a narrower one. 1675 Input and output are semi-raw. */ 1676 #define FP_TRUNC(dfs, sfs, dwc, swc, D, S) \ 1677 do \ 1678 { \ 1679 if (_FP_FRACBITS_##sfs < _FP_FRACBITS_##dfs \ 1680 || (_FP_EXPBIAS_##sfs < _FP_EXPBIAS_##dfs + _FP_FRACBITS_##dfs - 1 \ 1681 && _FP_EXPBIAS_##sfs != _FP_EXPBIAS_##dfs)) \ 1682 abort (); \ 1683 D##_s = S##_s; \ 1684 if (_FP_EXP_NORMAL (sfs, swc, S)) \ 1685 { \ 1686 D##_e = S##_e + _FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs; \ 1687 if (D##_e >= _FP_EXPMAX_##dfs) \ 1688 _FP_OVERFLOW_SEMIRAW (dfs, dwc, D); \ 1689 else \ 1690 { \ 1691 if (D##_e <= 0) \ 1692 { \ 1693 if (D##_e < 1 - _FP_FRACBITS_##dfs) \ 1694 { \ 1695 _FP_FRAC_SET_##swc (S, _FP_ZEROFRAC_##swc); \ 1696 _FP_FRAC_LOW_##swc (S) |= 1; \ 1697 } \ 1698 else \ 1699 { \ 1700 _FP_FRAC_HIGH_##sfs (S) |= _FP_IMPLBIT_SH_##sfs; \ 1701 _FP_FRAC_SRS_##swc (S, (_FP_WFRACBITS_##sfs \ 1702 - _FP_WFRACBITS_##dfs \ 1703 + 1 - D##_e), \ 1704 _FP_WFRACBITS_##sfs); \ 1705 } \ 1706 D##_e = 0; \ 1707 } \ 1708 else \ 1709 _FP_FRAC_SRS_##swc (S, (_FP_WFRACBITS_##sfs \ 1710 - _FP_WFRACBITS_##dfs), \ 1711 _FP_WFRACBITS_##sfs); \ 1712 _FP_FRAC_COPY_##dwc##_##swc (D, S); \ 1713 } \ 1714 } \ 1715 else \ 1716 { \ 1717 if (S##_e == 0) \ 1718 { \ 1719 _FP_CHECK_FLUSH_ZERO (sfs, swc, S); \ 1720 D##_e = 0; \ 1721 if (_FP_FRAC_ZEROP_##swc (S)) \ 1722 _FP_FRAC_SET_##dwc (D, _FP_ZEROFRAC_##dwc); \ 1723 else \ 1724 { \ 1725 FP_SET_EXCEPTION (FP_EX_DENORM); \ 1726 if (_FP_EXPBIAS_##sfs \ 1727 < _FP_EXPBIAS_##dfs + _FP_FRACBITS_##dfs - 1) \ 1728 { \ 1729 _FP_FRAC_SRS_##swc (S, (_FP_WFRACBITS_##sfs \ 1730 - _FP_WFRACBITS_##dfs), \ 1731 _FP_WFRACBITS_##sfs); \ 1732 _FP_FRAC_COPY_##dwc##_##swc (D, S); \ 1733 } \ 1734 else \ 1735 { \ 1736 _FP_FRAC_SET_##dwc (D, _FP_ZEROFRAC_##dwc); \ 1737 _FP_FRAC_LOW_##dwc (D) |= 1; \ 1738 } \ 1739 } \ 1740 } \ 1741 else \ 1742 { \ 1743 D##_e = _FP_EXPMAX_##dfs; \ 1744 if (_FP_FRAC_ZEROP_##swc (S)) \ 1745 _FP_FRAC_SET_##dwc (D, _FP_ZEROFRAC_##dwc); \ 1746 else \ 1747 { \ 1748 _FP_CHECK_SIGNAN_SEMIRAW (sfs, swc, S); \ 1749 _FP_FRAC_SRL_##swc (S, (_FP_WFRACBITS_##sfs \ 1750 - _FP_WFRACBITS_##dfs)); \ 1751 _FP_FRAC_COPY_##dwc##_##swc (D, S); \ 1752 /* Semi-raw NaN must have all workbits cleared. */ \ 1753 _FP_FRAC_LOW_##dwc (D) \ 1754 &= ~(_FP_W_TYPE) ((1 << _FP_WORKBITS) - 1); \ 1755 _FP_SETQNAN_SEMIRAW (dfs, dwc, D); \ 1756 } \ 1757 } \ 1758 } \ 1759 } \ 1760 while (0) 1761 1762 /* Helper primitives. */ 1763 1764 /* Count leading zeros in a word. */ 1765 1766 #ifndef __FP_CLZ 1767 /* GCC 3.4 and later provide the builtins for us. */ 1768 # define __FP_CLZ(r, x) \ 1769 do \ 1770 { \ 1771 if (sizeof (_FP_W_TYPE) == sizeof (unsigned int)) \ 1772 (r) = __builtin_clz (x); \ 1773 else if (sizeof (_FP_W_TYPE) == sizeof (unsigned long)) \ 1774 (r) = __builtin_clzl (x); \ 1775 else if (sizeof (_FP_W_TYPE) == sizeof (unsigned long long)) \ 1776 (r) = __builtin_clzll (x); \ 1777 else \ 1778 abort (); \ 1779 } \ 1780 while (0) 1781 #endif /* ndef __FP_CLZ */ 1782 1783 #define _FP_DIV_HELP_imm(q, r, n, d) \ 1784 do \ 1785 { \ 1786 (q) = (n) / (d), (r) = (n) % (d); \ 1787 } \ 1788 while (0) 1789 1790 1791 /* A restoring bit-by-bit division primitive. */ 1792 1793 #define _FP_DIV_MEAT_N_loop(fs, wc, R, X, Y) \ 1794 do \ 1795 { \ 1796 int _FP_DIV_MEAT_N_loop_count = _FP_WFRACBITS_##fs; \ 1797 _FP_FRAC_DECL_##wc (_FP_DIV_MEAT_N_loop_u); \ 1798 _FP_FRAC_DECL_##wc (_FP_DIV_MEAT_N_loop_v); \ 1799 _FP_FRAC_COPY_##wc (_FP_DIV_MEAT_N_loop_u, X); \ 1800 _FP_FRAC_COPY_##wc (_FP_DIV_MEAT_N_loop_v, Y); \ 1801 _FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \ 1802 /* Normalize _FP_DIV_MEAT_N_LOOP_U and _FP_DIV_MEAT_N_LOOP_V. */ \ 1803 _FP_FRAC_SLL_##wc (_FP_DIV_MEAT_N_loop_u, _FP_WFRACXBITS_##fs); \ 1804 _FP_FRAC_SLL_##wc (_FP_DIV_MEAT_N_loop_v, _FP_WFRACXBITS_##fs); \ 1805 /* First round. Since the operands are normalized, either the \ 1806 first or second bit will be set in the fraction. Produce a \ 1807 normalized result by checking which and adjusting the loop \ 1808 count and exponent accordingly. */ \ 1809 if (_FP_FRAC_GE_1 (_FP_DIV_MEAT_N_loop_u, _FP_DIV_MEAT_N_loop_v)) \ 1810 { \ 1811 _FP_FRAC_SUB_##wc (_FP_DIV_MEAT_N_loop_u, \ 1812 _FP_DIV_MEAT_N_loop_u, \ 1813 _FP_DIV_MEAT_N_loop_v); \ 1814 _FP_FRAC_LOW_##wc (R) |= 1; \ 1815 _FP_DIV_MEAT_N_loop_count--; \ 1816 } \ 1817 else \ 1818 R##_e--; \ 1819 /* Subsequent rounds. */ \ 1820 do \ 1821 { \ 1822 int _FP_DIV_MEAT_N_loop_msb \ 1823 = (_FP_WS_TYPE) _FP_FRAC_HIGH_##wc (_FP_DIV_MEAT_N_loop_u) < 0; \ 1824 _FP_FRAC_SLL_##wc (_FP_DIV_MEAT_N_loop_u, 1); \ 1825 _FP_FRAC_SLL_##wc (R, 1); \ 1826 if (_FP_DIV_MEAT_N_loop_msb \ 1827 || _FP_FRAC_GE_1 (_FP_DIV_MEAT_N_loop_u, \ 1828 _FP_DIV_MEAT_N_loop_v)) \ 1829 { \ 1830 _FP_FRAC_SUB_##wc (_FP_DIV_MEAT_N_loop_u, \ 1831 _FP_DIV_MEAT_N_loop_u, \ 1832 _FP_DIV_MEAT_N_loop_v); \ 1833 _FP_FRAC_LOW_##wc (R) |= 1; \ 1834 } \ 1835 } \ 1836 while (--_FP_DIV_MEAT_N_loop_count > 0); \ 1837 /* If there's anything left in _FP_DIV_MEAT_N_LOOP_U, the result \ 1838 is inexact. */ \ 1839 _FP_FRAC_LOW_##wc (R) \ 1840 |= !_FP_FRAC_ZEROP_##wc (_FP_DIV_MEAT_N_loop_u); \ 1841 } \ 1842 while (0) 1843 1844 #define _FP_DIV_MEAT_1_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 1, R, X, Y) 1845 #define _FP_DIV_MEAT_2_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 2, R, X, Y) 1846 #define _FP_DIV_MEAT_4_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 4, R, X, Y) 1847