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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 | /* Software floating-point emulation. Basic two-word fraction declaration and manipulation. Copyright (C) 1997,1998,1999 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Richard Henderson (rth@cygnus.com), Jakub Jelinek (jj@ultra.linux.cz), David S. Miller (davem@redhat.com) and Peter Maydell (pmaydell@chiark.greenend.org.uk). 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. */ #define _FP_FRAC_DECL_2(X) _FP_W_TYPE X##_f0, X##_f1 #define _FP_FRAC_COPY_2(D,S) (D##_f0 = S##_f0, D##_f1 = S##_f1) #define _FP_FRAC_SET_2(X,I) __FP_FRAC_SET_2(X, I) #define _FP_FRAC_HIGH_2(X) (X##_f1) #define _FP_FRAC_LOW_2(X) (X##_f0) #define _FP_FRAC_WORD_2(X,w) (X##_f##w) #define _FP_FRAC_SLL_2(X,N) \ do { \ if ((N) < _FP_W_TYPE_SIZE) \ { \ if (__builtin_constant_p(N) && (N) == 1) \ { \ X##_f1 = X##_f1 + X##_f1 + (((_FP_WS_TYPE)(X##_f0)) < 0); \ X##_f0 += X##_f0; \ } \ else \ { \ X##_f1 = X##_f1 << (N) | X##_f0 >> (_FP_W_TYPE_SIZE - (N)); \ X##_f0 <<= (N); \ } \ } \ else \ { \ X##_f1 = X##_f0 << ((N) - _FP_W_TYPE_SIZE); \ X##_f0 = 0; \ } \ } while (0) #define _FP_FRAC_SRL_2(X,N) \ do { \ if ((N) < _FP_W_TYPE_SIZE) \ { \ X##_f0 = X##_f0 >> (N) | X##_f1 << (_FP_W_TYPE_SIZE - (N)); \ X##_f1 >>= (N); \ } \ else \ { \ X##_f0 = X##_f1 >> ((N) - _FP_W_TYPE_SIZE); \ X##_f1 = 0; \ } \ } while (0) /* Right shift with sticky-lsb. */ #define _FP_FRAC_SRS_2(X,N,sz) \ do { \ if ((N) < _FP_W_TYPE_SIZE) \ { \ X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N) | \ (__builtin_constant_p(N) && (N) == 1 \ ? X##_f0 & 1 \ : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0)); \ X##_f1 >>= (N); \ } \ else \ { \ X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE) | \ (((X##_f1 << (sz - (N))) | X##_f0) != 0)); \ X##_f1 = 0; \ } \ } while (0) #define _FP_FRAC_ADDI_2(X,I) \ __FP_FRAC_ADDI_2(X##_f1, X##_f0, I) #define _FP_FRAC_ADD_2(R,X,Y) \ __FP_FRAC_ADD_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0) #define _FP_FRAC_SUB_2(R,X,Y) \ __FP_FRAC_SUB_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0) #define _FP_FRAC_DEC_2(X,Y) \ __FP_FRAC_DEC_2(X##_f1, X##_f0, Y##_f1, Y##_f0) #define _FP_FRAC_CLZ_2(R,X) \ do { \ if (X##_f1) \ __FP_CLZ(R,X##_f1); \ else \ { \ __FP_CLZ(R,X##_f0); \ R += _FP_W_TYPE_SIZE; \ } \ } while(0) /* Predicates */ #define _FP_FRAC_NEGP_2(X) ((_FP_WS_TYPE)X##_f1 < 0) #define _FP_FRAC_ZEROP_2(X) ((X##_f1 | X##_f0) == 0) #define _FP_FRAC_OVERP_2(fs,X) (_FP_FRAC_HIGH_##fs(X) & _FP_OVERFLOW_##fs) #define _FP_FRAC_EQ_2(X, Y) (X##_f1 == Y##_f1 && X##_f0 == Y##_f0) #define _FP_FRAC_GT_2(X, Y) \ (X##_f1 > Y##_f1 || X##_f1 == Y##_f1 && X##_f0 > Y##_f0) #define _FP_FRAC_GE_2(X, Y) \ (X##_f1 > Y##_f1 || X##_f1 == Y##_f1 && X##_f0 >= Y##_f0) #define _FP_ZEROFRAC_2 0, 0 #define _FP_MINFRAC_2 0, 1 #define _FP_MAXFRAC_2 (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0) /* * Internals */ #define __FP_FRAC_SET_2(X,I1,I0) (X##_f0 = I0, X##_f1 = I1) #define __FP_CLZ_2(R, xh, xl) \ do { \ if (xh) \ __FP_CLZ(R,xh); \ else \ { \ __FP_CLZ(R,xl); \ R += _FP_W_TYPE_SIZE; \ } \ } while(0) #if 0 #ifndef __FP_FRAC_ADDI_2 #define __FP_FRAC_ADDI_2(xh, xl, i) \ (xh += ((xl += i) < i)) #endif #ifndef __FP_FRAC_ADD_2 #define __FP_FRAC_ADD_2(rh, rl, xh, xl, yh, yl) \ (rh = xh + yh + ((rl = xl + yl) < xl)) #endif #ifndef __FP_FRAC_SUB_2 #define __FP_FRAC_SUB_2(rh, rl, xh, xl, yh, yl) \ (rh = xh - yh - ((rl = xl - yl) > xl)) #endif #ifndef __FP_FRAC_DEC_2 #define __FP_FRAC_DEC_2(xh, xl, yh, yl) \ do { \ UWtype _t = xl; \ xh -= yh + ((xl -= yl) > _t); \ } while (0) #endif #else #undef __FP_FRAC_ADDI_2 #define __FP_FRAC_ADDI_2(xh, xl, i) add_ssaaaa(xh, xl, xh, xl, 0, i) #undef __FP_FRAC_ADD_2 #define __FP_FRAC_ADD_2 add_ssaaaa #undef __FP_FRAC_SUB_2 #define __FP_FRAC_SUB_2 sub_ddmmss #undef __FP_FRAC_DEC_2 #define __FP_FRAC_DEC_2(xh, xl, yh, yl) sub_ddmmss(xh, xl, xh, xl, yh, yl) #endif /* * Unpack the raw bits of a native fp value. Do not classify or * normalize the data. */ #define _FP_UNPACK_RAW_2(fs, X, val) \ do { \ union _FP_UNION_##fs _flo; _flo.flt = (val); \ \ X##_f0 = _flo.bits.frac0; \ X##_f1 = _flo.bits.frac1; \ X##_e = _flo.bits.exp; \ X##_s = _flo.bits.sign; \ } while (0) #define _FP_UNPACK_RAW_2_P(fs, X, val) \ do { \ union _FP_UNION_##fs *_flo = \ (union _FP_UNION_##fs *)(val); \ \ X##_f0 = _flo->bits.frac0; \ X##_f1 = _flo->bits.frac1; \ X##_e = _flo->bits.exp; \ X##_s = _flo->bits.sign; \ } while (0) /* * Repack the raw bits of a native fp value. */ #define _FP_PACK_RAW_2(fs, val, X) \ do { \ union _FP_UNION_##fs _flo; \ \ _flo.bits.frac0 = X##_f0; \ _flo.bits.frac1 = X##_f1; \ _flo.bits.exp = X##_e; \ _flo.bits.sign = X##_s; \ \ (val) = _flo.flt; \ } while (0) #define _FP_PACK_RAW_2_P(fs, val, X) \ do { \ union _FP_UNION_##fs *_flo = \ (union _FP_UNION_##fs *)(val); \ \ _flo->bits.frac0 = X##_f0; \ _flo->bits.frac1 = X##_f1; \ _flo->bits.exp = X##_e; \ _flo->bits.sign = X##_s; \ } while (0) /* * Multiplication algorithms: */ /* Given a 1W * 1W => 2W primitive, do the extended multiplication. */ #define _FP_MUL_MEAT_2_wide(wfracbits, R, X, Y, doit) \ do { \ _FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \ \ doit(_FP_FRAC_WORD_4(_z,1), _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0); \ doit(_b_f1, _b_f0, X##_f0, Y##_f1); \ doit(_c_f1, _c_f0, X##_f1, Y##_f0); \ doit(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2), X##_f1, Y##_f1); \ \ __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ _FP_FRAC_WORD_4(_z,1), 0, _b_f1, _b_f0, \ _FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ _FP_FRAC_WORD_4(_z,1)); \ __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ _FP_FRAC_WORD_4(_z,1), 0, _c_f1, _c_f0, \ _FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ _FP_FRAC_WORD_4(_z,1)); \ \ /* Normalize since we know where the msb of the multiplicands \ were (bit B), we know that the msb of the of the product is \ at either 2B or 2B-1. */ \ _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits); \ R##_f0 = _FP_FRAC_WORD_4(_z,0); \ R##_f1 = _FP_FRAC_WORD_4(_z,1); \ } while (0) /* Given a 1W * 1W => 2W primitive, do the extended multiplication. Do only 3 multiplications instead of four. This one is for machines where multiplication is much more expensive than subtraction. */ #define _FP_MUL_MEAT_2_wide_3mul(wfracbits, R, X, Y, doit) \ do { \ _FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \ _FP_W_TYPE _d; \ int _c1, _c2; \ \ _b_f0 = X##_f0 + X##_f1; \ _c1 = _b_f0 < X##_f0; \ _b_f1 = Y##_f0 + Y##_f1; \ _c2 = _b_f1 < Y##_f0; \ doit(_d, _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0); \ doit(_FP_FRAC_WORD_4(_z,2), _FP_FRAC_WORD_4(_z,1), _b_f0, _b_f1); \ doit(_c_f1, _c_f0, X##_f1, Y##_f1); \ \ _b_f0 &= -_c2; \ _b_f1 &= -_c1; \ __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ _FP_FRAC_WORD_4(_z,1), (_c1 & _c2), 0, _d, \ 0, _FP_FRAC_WORD_4(_z,2), _FP_FRAC_WORD_4(_z,1)); \ __FP_FRAC_ADDI_2(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ _b_f0); \ __FP_FRAC_ADDI_2(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ _b_f1); \ __FP_FRAC_DEC_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ _FP_FRAC_WORD_4(_z,1), \ 0, _d, _FP_FRAC_WORD_4(_z,0)); \ __FP_FRAC_DEC_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ _FP_FRAC_WORD_4(_z,1), 0, _c_f1, _c_f0); \ __FP_FRAC_ADD_2(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2), \ _c_f1, _c_f0, \ _FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2)); \ \ /* Normalize since we know where the msb of the multiplicands \ were (bit B), we know that the msb of the of the product is \ at either 2B or 2B-1. */ \ _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits); \ R##_f0 = _FP_FRAC_WORD_4(_z,0); \ R##_f1 = _FP_FRAC_WORD_4(_z,1); \ } while (0) #define _FP_MUL_MEAT_2_gmp(wfracbits, R, X, Y) \ do { \ _FP_FRAC_DECL_4(_z); \ _FP_W_TYPE _x[2], _y[2]; \ _x[0] = X##_f0; _x[1] = X##_f1; \ _y[0] = Y##_f0; _y[1] = Y##_f1; \ \ mpn_mul_n(_z_f, _x, _y, 2); \ \ /* Normalize since we know where the msb of the multiplicands \ were (bit B), we know that the msb of the of the product is \ at either 2B or 2B-1. */ \ _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits); \ R##_f0 = _z_f[0]; \ R##_f1 = _z_f[1]; \ } while (0) /* Do at most 120x120=240 bits multiplication using double floating point multiplication. This is useful if floating point multiplication has much bigger throughput than integer multiply. It is supposed to work for _FP_W_TYPE_SIZE 64 and wfracbits between 106 and 120 only. Caller guarantees that X and Y has (1LLL << (wfracbits - 1)) set. SETFETZ is a macro which will disable all FPU exceptions and set rounding towards zero, RESETFE should optionally reset it back. */ #define _FP_MUL_MEAT_2_120_240_double(wfracbits, R, X, Y, setfetz, resetfe) \ do { \ static const double _const[] = { \ /* 2^-24 */ 5.9604644775390625e-08, \ /* 2^-48 */ 3.5527136788005009e-15, \ /* 2^-72 */ 2.1175823681357508e-22, \ /* 2^-96 */ 1.2621774483536189e-29, \ /* 2^28 */ 2.68435456e+08, \ /* 2^4 */ 1.600000e+01, \ /* 2^-20 */ 9.5367431640625e-07, \ /* 2^-44 */ 5.6843418860808015e-14, \ /* 2^-68 */ 3.3881317890172014e-21, \ /* 2^-92 */ 2.0194839173657902e-28, \ /* 2^-116 */ 1.2037062152420224e-35}; \ double _a240, _b240, _c240, _d240, _e240, _f240, \ _g240, _h240, _i240, _j240, _k240; \ union { double d; UDItype i; } _l240, _m240, _n240, _o240, \ _p240, _q240, _r240, _s240; \ UDItype _t240, _u240, _v240, _w240, _x240, _y240 = 0; \ \ if (wfracbits < 106 || wfracbits > 120) \ abort(); \ \ setfetz; \ \ _e240 = (double)(long)(X##_f0 & 0xffffff); \ _j240 = (double)(long)(Y##_f0 & 0xffffff); \ _d240 = (double)(long)((X##_f0 >> 24) & 0xffffff); \ _i240 = (double)(long)((Y##_f0 >> 24) & 0xffffff); \ _c240 = (double)(long)(((X##_f1 << 16) & 0xffffff) | (X##_f0 >> 48)); \ _h240 = (double)(long)(((Y##_f1 << 16) & 0xffffff) | (Y##_f0 >> 48)); \ _b240 = (double)(long)((X##_f1 >> 8) & 0xffffff); \ _g240 = (double)(long)((Y##_f1 >> 8) & 0xffffff); \ _a240 = (double)(long)(X##_f1 >> 32); \ _f240 = (double)(long)(Y##_f1 >> 32); \ _e240 *= _const[3]; \ _j240 *= _const[3]; \ _d240 *= _const[2]; \ _i240 *= _const[2]; \ _c240 *= _const[1]; \ _h240 *= _const[1]; \ _b240 *= _const[0]; \ _g240 *= _const[0]; \ _s240.d = _e240*_j240;\ _r240.d = _d240*_j240 + _e240*_i240;\ _q240.d = _c240*_j240 + _d240*_i240 + _e240*_h240;\ _p240.d = _b240*_j240 + _c240*_i240 + _d240*_h240 + _e240*_g240;\ _o240.d = _a240*_j240 + _b240*_i240 + _c240*_h240 + _d240*_g240 + _e240*_f240;\ _n240.d = _a240*_i240 + _b240*_h240 + _c240*_g240 + _d240*_f240; \ _m240.d = _a240*_h240 + _b240*_g240 + _c240*_f240; \ _l240.d = _a240*_g240 + _b240*_f240; \ _k240 = _a240*_f240; \ _r240.d += _s240.d; \ _q240.d += _r240.d; \ _p240.d += _q240.d; \ _o240.d += _p240.d; \ _n240.d += _o240.d; \ _m240.d += _n240.d; \ _l240.d += _m240.d; \ _k240 += _l240.d; \ _s240.d -= ((_const[10]+_s240.d)-_const[10]); \ _r240.d -= ((_const[9]+_r240.d)-_const[9]); \ _q240.d -= ((_const[8]+_q240.d)-_const[8]); \ _p240.d -= ((_const[7]+_p240.d)-_const[7]); \ _o240.d += _const[7]; \ _n240.d += _const[6]; \ _m240.d += _const[5]; \ _l240.d += _const[4]; \ if (_s240.d != 0.0) _y240 = 1; \ if (_r240.d != 0.0) _y240 = 1; \ if (_q240.d != 0.0) _y240 = 1; \ if (_p240.d != 0.0) _y240 = 1; \ _t240 = (DItype)_k240; \ _u240 = _l240.i; \ _v240 = _m240.i; \ _w240 = _n240.i; \ _x240 = _o240.i; \ R##_f1 = (_t240 << (128 - (wfracbits - 1))) \ | ((_u240 & 0xffffff) >> ((wfracbits - 1) - 104)); \ R##_f0 = ((_u240 & 0xffffff) << (168 - (wfracbits - 1))) \ | ((_v240 & 0xffffff) << (144 - (wfracbits - 1))) \ | ((_w240 & 0xffffff) << (120 - (wfracbits - 1))) \ | ((_x240 & 0xffffff) >> ((wfracbits - 1) - 96)) \ | _y240; \ resetfe; \ } while (0) /* * Division algorithms: */ #define _FP_DIV_MEAT_2_udiv(fs, R, X, Y) \ do { \ _FP_W_TYPE _n_f2, _n_f1, _n_f0, _r_f1, _r_f0, _m_f1, _m_f0; \ if (_FP_FRAC_GT_2(X, Y)) \ { \ _n_f2 = X##_f1 >> 1; \ _n_f1 = X##_f1 << (_FP_W_TYPE_SIZE - 1) | X##_f0 >> 1; \ _n_f0 = X##_f0 << (_FP_W_TYPE_SIZE - 1); \ } \ else \ { \ R##_e--; \ _n_f2 = X##_f1; \ _n_f1 = X##_f0; \ _n_f0 = 0; \ } \ \ /* Normalize, i.e. make the most significant bit of the \ denominator set. */ \ _FP_FRAC_SLL_2(Y, _FP_WFRACXBITS_##fs); \ \ udiv_qrnnd(R##_f1, _r_f1, _n_f2, _n_f1, Y##_f1); \ umul_ppmm(_m_f1, _m_f0, R##_f1, Y##_f0); \ _r_f0 = _n_f0; \ if (_FP_FRAC_GT_2(_m, _r)) \ { \ R##_f1--; \ _FP_FRAC_ADD_2(_r, Y, _r); \ if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \ { \ R##_f1--; \ _FP_FRAC_ADD_2(_r, Y, _r); \ } \ } \ _FP_FRAC_DEC_2(_r, _m); \ \ if (_r_f1 == Y##_f1) \ { \ /* This is a special case, not an optimization \ (_r/Y##_f1 would not fit into UWtype). \ As _r is guaranteed to be < Y, R##_f0 can be either \ (UWtype)-1 or (UWtype)-2. But as we know what kind \ of bits it is (sticky, guard, round), we don't care. \ We also don't care what the reminder is, because the \ guard bit will be set anyway. -jj */ \ R##_f0 = -1; \ } \ else \ { \ udiv_qrnnd(R##_f0, _r_f1, _r_f1, _r_f0, Y##_f1); \ umul_ppmm(_m_f1, _m_f0, R##_f0, Y##_f0); \ _r_f0 = 0; \ if (_FP_FRAC_GT_2(_m, _r)) \ { \ R##_f0--; \ _FP_FRAC_ADD_2(_r, Y, _r); \ if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \ { \ R##_f0--; \ _FP_FRAC_ADD_2(_r, Y, _r); \ } \ } \ if (!_FP_FRAC_EQ_2(_r, _m)) \ R##_f0 |= _FP_WORK_STICKY; \ } \ } while (0) #define _FP_DIV_MEAT_2_gmp(fs, R, X, Y) \ do { \ _FP_W_TYPE _x[4], _y[2], _z[4]; \ _y[0] = Y##_f0; _y[1] = Y##_f1; \ _x[0] = _x[3] = 0; \ if (_FP_FRAC_GT_2(X, Y)) \ { \ R##_e++; \ _x[1] = (X##_f0 << (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE) | \ X##_f1 >> (_FP_W_TYPE_SIZE - \ (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE))); \ _x[2] = X##_f1 << (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE); \ } \ else \ { \ _x[1] = (X##_f0 << (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE) | \ X##_f1 >> (_FP_W_TYPE_SIZE - \ (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE))); \ _x[2] = X##_f1 << (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE); \ } \ \ (void) mpn_divrem (_z, 0, _x, 4, _y, 2); \ R##_f1 = _z[1]; \ R##_f0 = _z[0] | ((_x[0] | _x[1]) != 0); \ } while (0) /* * Square root algorithms: * We have just one right now, maybe Newton approximation * should be added for those machines where division is fast. */ #define _FP_SQRT_MEAT_2(R, S, T, X, q) \ do { \ while (q) \ { \ T##_f1 = S##_f1 + q; \ if (T##_f1 <= X##_f1) \ { \ S##_f1 = T##_f1 + q; \ X##_f1 -= T##_f1; \ R##_f1 += q; \ } \ _FP_FRAC_SLL_2(X, 1); \ q >>= 1; \ } \ q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \ while (q != _FP_WORK_ROUND) \ { \ T##_f0 = S##_f0 + q; \ T##_f1 = S##_f1; \ if (T##_f1 < X##_f1 || \ (T##_f1 == X##_f1 && T##_f0 <= X##_f0)) \ { \ S##_f0 = T##_f0 + q; \ S##_f1 += (T##_f0 > S##_f0); \ _FP_FRAC_DEC_2(X, T); \ R##_f0 += q; \ } \ _FP_FRAC_SLL_2(X, 1); \ q >>= 1; \ } \ if (X##_f0 | X##_f1) \ { \ if (S##_f1 < X##_f1 || \ (S##_f1 == X##_f1 && S##_f0 < X##_f0)) \ R##_f0 |= _FP_WORK_ROUND; \ R##_f0 |= _FP_WORK_STICKY; \ } \ } while (0) /* * Assembly/disassembly for converting to/from integral types. * No shifting or overflow handled here. */ #define _FP_FRAC_ASSEMBLE_2(r, X, rsize) \ do { \ if (rsize <= _FP_W_TYPE_SIZE) \ r = X##_f0; \ else \ { \ r = X##_f1; \ r <<= _FP_W_TYPE_SIZE; \ r += X##_f0; \ } \ } while (0) #define _FP_FRAC_DISASSEMBLE_2(X, r, rsize) \ do { \ X##_f0 = r; \ X##_f1 = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE); \ } while (0) /* * Convert FP values between word sizes */ #define _FP_FRAC_CONV_1_2(dfs, sfs, D, S) \ do { \ if (S##_c != FP_CLS_NAN) \ _FP_FRAC_SRS_2(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs), \ _FP_WFRACBITS_##sfs); \ else \ _FP_FRAC_SRL_2(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs)); \ D##_f = S##_f0; \ } while (0) #define _FP_FRAC_CONV_2_1(dfs, sfs, D, S) \ do { \ D##_f0 = S##_f; \ D##_f1 = 0; \ _FP_FRAC_SLL_2(D, (_FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs)); \ } while (0) |