1 /* 2 * Ported from a work by Andreas Grabher for Previous, NeXT Computer Emulator, 3 * derived from NetBSD M68040 FPSP functions, 4 * derived from release 2a of the SoftFloat IEC/IEEE Floating-point Arithmetic 5 * Package. Those parts of the code (and some later contributions) are 6 * provided under that license, as detailed below. 7 * It has subsequently been modified by contributors to the QEMU Project, 8 * so some portions are provided under: 9 * the SoftFloat-2a license 10 * the BSD license 11 * GPL-v2-or-later 12 * 13 * Any future contributions to this file will be taken to be licensed under 14 * the Softfloat-2a license unless specifically indicated otherwise. 15 */ 16 17 /* Portions of this work are licensed under the terms of the GNU GPL, 18 * version 2 or later. See the COPYING file in the top-level directory. 19 */ 20 21 #include "qemu/osdep.h" 22 #include "softfloat.h" 23 #include "fpu/softfloat-macros.h" 24 #include "softfloat_fpsp_tables.h" 25 26 static floatx80 propagateFloatx80NaNOneArg(floatx80 a, float_status *status) 27 { 28 if (floatx80_is_signaling_nan(a, status)) { 29 float_raise(float_flag_invalid, status); 30 } 31 32 if (status->default_nan_mode) { 33 return floatx80_default_nan(status); 34 } 35 36 return floatx80_maybe_silence_nan(a, status); 37 } 38 39 /*---------------------------------------------------------------------------- 40 | Returns the modulo remainder of the extended double-precision floating-point 41 | value `a' with respect to the corresponding value `b'. 42 *----------------------------------------------------------------------------*/ 43 44 floatx80 floatx80_mod(floatx80 a, floatx80 b, float_status *status) 45 { 46 flag aSign, zSign; 47 int32_t aExp, bExp, expDiff; 48 uint64_t aSig0, aSig1, bSig; 49 uint64_t qTemp, term0, term1; 50 51 aSig0 = extractFloatx80Frac(a); 52 aExp = extractFloatx80Exp(a); 53 aSign = extractFloatx80Sign(a); 54 bSig = extractFloatx80Frac(b); 55 bExp = extractFloatx80Exp(b); 56 57 if (aExp == 0x7FFF) { 58 if ((uint64_t) (aSig0 << 1) 59 || ((bExp == 0x7FFF) && (uint64_t) (bSig << 1))) { 60 return propagateFloatx80NaN(a, b, status); 61 } 62 goto invalid; 63 } 64 if (bExp == 0x7FFF) { 65 if ((uint64_t) (bSig << 1)) { 66 return propagateFloatx80NaN(a, b, status); 67 } 68 return a; 69 } 70 if (bExp == 0) { 71 if (bSig == 0) { 72 invalid: 73 float_raise(float_flag_invalid, status); 74 return floatx80_default_nan(status); 75 } 76 normalizeFloatx80Subnormal(bSig, &bExp, &bSig); 77 } 78 if (aExp == 0) { 79 if ((uint64_t) (aSig0 << 1) == 0) { 80 return a; 81 } 82 normalizeFloatx80Subnormal(aSig0, &aExp, &aSig0); 83 } 84 bSig |= LIT64(0x8000000000000000); 85 zSign = aSign; 86 expDiff = aExp - bExp; 87 aSig1 = 0; 88 if (expDiff < 0) { 89 return a; 90 } 91 qTemp = (bSig <= aSig0); 92 if (qTemp) { 93 aSig0 -= bSig; 94 } 95 expDiff -= 64; 96 while (0 < expDiff) { 97 qTemp = estimateDiv128To64(aSig0, aSig1, bSig); 98 qTemp = (2 < qTemp) ? qTemp - 2 : 0; 99 mul64To128(bSig, qTemp, &term0, &term1); 100 sub128(aSig0, aSig1, term0, term1, &aSig0, &aSig1); 101 shortShift128Left(aSig0, aSig1, 62, &aSig0, &aSig1); 102 } 103 expDiff += 64; 104 if (0 < expDiff) { 105 qTemp = estimateDiv128To64(aSig0, aSig1, bSig); 106 qTemp = (2 < qTemp) ? qTemp - 2 : 0; 107 qTemp >>= 64 - expDiff; 108 mul64To128(bSig, qTemp << (64 - expDiff), &term0, &term1); 109 sub128(aSig0, aSig1, term0, term1, &aSig0, &aSig1); 110 shortShift128Left(0, bSig, 64 - expDiff, &term0, &term1); 111 while (le128(term0, term1, aSig0, aSig1)) { 112 ++qTemp; 113 sub128(aSig0, aSig1, term0, term1, &aSig0, &aSig1); 114 } 115 } 116 return 117 normalizeRoundAndPackFloatx80( 118 80, zSign, bExp + expDiff, aSig0, aSig1, status); 119 } 120 121 /*---------------------------------------------------------------------------- 122 | Returns the mantissa of the extended double-precision floating-point 123 | value `a'. 124 *----------------------------------------------------------------------------*/ 125 126 floatx80 floatx80_getman(floatx80 a, float_status *status) 127 { 128 flag aSign; 129 int32_t aExp; 130 uint64_t aSig; 131 132 aSig = extractFloatx80Frac(a); 133 aExp = extractFloatx80Exp(a); 134 aSign = extractFloatx80Sign(a); 135 136 if (aExp == 0x7FFF) { 137 if ((uint64_t) (aSig << 1)) { 138 return propagateFloatx80NaNOneArg(a , status); 139 } 140 float_raise(float_flag_invalid , status); 141 return floatx80_default_nan(status); 142 } 143 144 if (aExp == 0) { 145 if (aSig == 0) { 146 return packFloatx80(aSign, 0, 0); 147 } 148 normalizeFloatx80Subnormal(aSig, &aExp, &aSig); 149 } 150 151 return roundAndPackFloatx80(status->floatx80_rounding_precision, aSign, 152 0x3FFF, aSig, 0, status); 153 } 154 155 /*---------------------------------------------------------------------------- 156 | Returns the exponent of the extended double-precision floating-point 157 | value `a' as an extended double-precision value. 158 *----------------------------------------------------------------------------*/ 159 160 floatx80 floatx80_getexp(floatx80 a, float_status *status) 161 { 162 flag aSign; 163 int32_t aExp; 164 uint64_t aSig; 165 166 aSig = extractFloatx80Frac(a); 167 aExp = extractFloatx80Exp(a); 168 aSign = extractFloatx80Sign(a); 169 170 if (aExp == 0x7FFF) { 171 if ((uint64_t) (aSig << 1)) { 172 return propagateFloatx80NaNOneArg(a , status); 173 } 174 float_raise(float_flag_invalid , status); 175 return floatx80_default_nan(status); 176 } 177 178 if (aExp == 0) { 179 if (aSig == 0) { 180 return packFloatx80(aSign, 0, 0); 181 } 182 normalizeFloatx80Subnormal(aSig, &aExp, &aSig); 183 } 184 185 return int32_to_floatx80(aExp - 0x3FFF, status); 186 } 187 188 /*---------------------------------------------------------------------------- 189 | Scales extended double-precision floating-point value in operand `a' by 190 | value `b'. The function truncates the value in the second operand 'b' to 191 | an integral value and adds that value to the exponent of the operand 'a'. 192 | The operation performed according to the IEC/IEEE Standard for Binary 193 | Floating-Point Arithmetic. 194 *----------------------------------------------------------------------------*/ 195 196 floatx80 floatx80_scale(floatx80 a, floatx80 b, float_status *status) 197 { 198 flag aSign, bSign; 199 int32_t aExp, bExp, shiftCount; 200 uint64_t aSig, bSig; 201 202 aSig = extractFloatx80Frac(a); 203 aExp = extractFloatx80Exp(a); 204 aSign = extractFloatx80Sign(a); 205 bSig = extractFloatx80Frac(b); 206 bExp = extractFloatx80Exp(b); 207 bSign = extractFloatx80Sign(b); 208 209 if (bExp == 0x7FFF) { 210 if ((uint64_t) (bSig << 1) || 211 ((aExp == 0x7FFF) && (uint64_t) (aSig << 1))) { 212 return propagateFloatx80NaN(a, b, status); 213 } 214 float_raise(float_flag_invalid , status); 215 return floatx80_default_nan(status); 216 } 217 if (aExp == 0x7FFF) { 218 if ((uint64_t) (aSig << 1)) { 219 return propagateFloatx80NaN(a, b, status); 220 } 221 return packFloatx80(aSign, floatx80_infinity.high, 222 floatx80_infinity.low); 223 } 224 if (aExp == 0) { 225 if (aSig == 0) { 226 return packFloatx80(aSign, 0, 0); 227 } 228 if (bExp < 0x3FFF) { 229 return a; 230 } 231 normalizeFloatx80Subnormal(aSig, &aExp, &aSig); 232 } 233 234 if (bExp < 0x3FFF) { 235 return a; 236 } 237 238 if (0x400F < bExp) { 239 aExp = bSign ? -0x6001 : 0xE000; 240 return roundAndPackFloatx80(status->floatx80_rounding_precision, 241 aSign, aExp, aSig, 0, status); 242 } 243 244 shiftCount = 0x403E - bExp; 245 bSig >>= shiftCount; 246 aExp = bSign ? (aExp - bSig) : (aExp + bSig); 247 248 return roundAndPackFloatx80(status->floatx80_rounding_precision, 249 aSign, aExp, aSig, 0, status); 250 } 251 252 floatx80 floatx80_move(floatx80 a, float_status *status) 253 { 254 flag aSign; 255 int32_t aExp; 256 uint64_t aSig; 257 258 aSig = extractFloatx80Frac(a); 259 aExp = extractFloatx80Exp(a); 260 aSign = extractFloatx80Sign(a); 261 262 if (aExp == 0x7FFF) { 263 if ((uint64_t)(aSig << 1)) { 264 return propagateFloatx80NaNOneArg(a, status); 265 } 266 return a; 267 } 268 if (aExp == 0) { 269 if (aSig == 0) { 270 return a; 271 } 272 normalizeRoundAndPackFloatx80(status->floatx80_rounding_precision, 273 aSign, aExp, aSig, 0, status); 274 } 275 return roundAndPackFloatx80(status->floatx80_rounding_precision, aSign, 276 aExp, aSig, 0, status); 277 } 278 279 /*---------------------------------------------------------------------------- 280 | Algorithms for transcendental functions supported by MC68881 and MC68882 281 | mathematical coprocessors. The functions are derived from FPSP library. 282 *----------------------------------------------------------------------------*/ 283 284 #define one_exp 0x3FFF 285 #define one_sig LIT64(0x8000000000000000) 286 287 /*---------------------------------------------------------------------------- 288 | Function for compactifying extended double-precision floating point values. 289 *----------------------------------------------------------------------------*/ 290 291 static int32_t floatx80_make_compact(int32_t aExp, uint64_t aSig) 292 { 293 return (aExp << 16) | (aSig >> 48); 294 } 295 296 /*---------------------------------------------------------------------------- 297 | Log base e of x plus 1 298 *----------------------------------------------------------------------------*/ 299 300 floatx80 floatx80_lognp1(floatx80 a, float_status *status) 301 { 302 flag aSign; 303 int32_t aExp; 304 uint64_t aSig, fSig; 305 306 int8_t user_rnd_mode, user_rnd_prec; 307 308 int32_t compact, j, k; 309 floatx80 fp0, fp1, fp2, fp3, f, logof2, klog2, saveu; 310 311 aSig = extractFloatx80Frac(a); 312 aExp = extractFloatx80Exp(a); 313 aSign = extractFloatx80Sign(a); 314 315 if (aExp == 0x7FFF) { 316 if ((uint64_t) (aSig << 1)) { 317 propagateFloatx80NaNOneArg(a, status); 318 } 319 if (aSign) { 320 float_raise(float_flag_invalid, status); 321 return floatx80_default_nan(status); 322 } 323 return packFloatx80(0, floatx80_infinity.high, floatx80_infinity.low); 324 } 325 326 if (aExp == 0 && aSig == 0) { 327 return packFloatx80(aSign, 0, 0); 328 } 329 330 if (aSign && aExp >= one_exp) { 331 if (aExp == one_exp && aSig == one_sig) { 332 float_raise(float_flag_divbyzero, status); 333 packFloatx80(aSign, floatx80_infinity.high, floatx80_infinity.low); 334 } 335 float_raise(float_flag_invalid, status); 336 return floatx80_default_nan(status); 337 } 338 339 if (aExp < 0x3f99 || (aExp == 0x3f99 && aSig == one_sig)) { 340 /* <= min threshold */ 341 float_raise(float_flag_inexact, status); 342 return floatx80_move(a, status); 343 } 344 345 user_rnd_mode = status->float_rounding_mode; 346 user_rnd_prec = status->floatx80_rounding_precision; 347 status->float_rounding_mode = float_round_nearest_even; 348 status->floatx80_rounding_precision = 80; 349 350 compact = floatx80_make_compact(aExp, aSig); 351 352 fp0 = a; /* Z */ 353 fp1 = a; 354 355 fp0 = floatx80_add(fp0, float32_to_floatx80(make_float32(0x3F800000), 356 status), status); /* X = (1+Z) */ 357 358 aExp = extractFloatx80Exp(fp0); 359 aSig = extractFloatx80Frac(fp0); 360 361 compact = floatx80_make_compact(aExp, aSig); 362 363 if (compact < 0x3FFE8000 || compact > 0x3FFFC000) { 364 /* |X| < 1/2 or |X| > 3/2 */ 365 k = aExp - 0x3FFF; 366 fp1 = int32_to_floatx80(k, status); 367 368 fSig = (aSig & LIT64(0xFE00000000000000)) | LIT64(0x0100000000000000); 369 j = (fSig >> 56) & 0x7E; /* DISPLACEMENT FOR 1/F */ 370 371 f = packFloatx80(0, 0x3FFF, fSig); /* F */ 372 fp0 = packFloatx80(0, 0x3FFF, aSig); /* Y */ 373 374 fp0 = floatx80_sub(fp0, f, status); /* Y-F */ 375 376 lp1cont1: 377 /* LP1CONT1 */ 378 fp0 = floatx80_mul(fp0, log_tbl[j], status); /* FP0 IS U = (Y-F)/F */ 379 logof2 = packFloatx80(0, 0x3FFE, LIT64(0xB17217F7D1CF79AC)); 380 klog2 = floatx80_mul(fp1, logof2, status); /* FP1 IS K*LOG2 */ 381 fp2 = floatx80_mul(fp0, fp0, status); /* FP2 IS V=U*U */ 382 383 fp3 = fp2; 384 fp1 = fp2; 385 386 fp1 = floatx80_mul(fp1, float64_to_floatx80( 387 make_float64(0x3FC2499AB5E4040B), status), 388 status); /* V*A6 */ 389 fp2 = floatx80_mul(fp2, float64_to_floatx80( 390 make_float64(0xBFC555B5848CB7DB), status), 391 status); /* V*A5 */ 392 fp1 = floatx80_add(fp1, float64_to_floatx80( 393 make_float64(0x3FC99999987D8730), status), 394 status); /* A4+V*A6 */ 395 fp2 = floatx80_add(fp2, float64_to_floatx80( 396 make_float64(0xBFCFFFFFFF6F7E97), status), 397 status); /* A3+V*A5 */ 398 fp1 = floatx80_mul(fp1, fp3, status); /* V*(A4+V*A6) */ 399 fp2 = floatx80_mul(fp2, fp3, status); /* V*(A3+V*A5) */ 400 fp1 = floatx80_add(fp1, float64_to_floatx80( 401 make_float64(0x3FD55555555555A4), status), 402 status); /* A2+V*(A4+V*A6) */ 403 fp2 = floatx80_add(fp2, float64_to_floatx80( 404 make_float64(0xBFE0000000000008), status), 405 status); /* A1+V*(A3+V*A5) */ 406 fp1 = floatx80_mul(fp1, fp3, status); /* V*(A2+V*(A4+V*A6)) */ 407 fp2 = floatx80_mul(fp2, fp3, status); /* V*(A1+V*(A3+V*A5)) */ 408 fp1 = floatx80_mul(fp1, fp0, status); /* U*V*(A2+V*(A4+V*A6)) */ 409 fp0 = floatx80_add(fp0, fp2, status); /* U+V*(A1+V*(A3+V*A5)) */ 410 411 fp1 = floatx80_add(fp1, log_tbl[j + 1], 412 status); /* LOG(F)+U*V*(A2+V*(A4+V*A6)) */ 413 fp0 = floatx80_add(fp0, fp1, status); /* FP0 IS LOG(F) + LOG(1+U) */ 414 415 status->float_rounding_mode = user_rnd_mode; 416 status->floatx80_rounding_precision = user_rnd_prec; 417 418 a = floatx80_add(fp0, klog2, status); 419 420 float_raise(float_flag_inexact, status); 421 422 return a; 423 } else if (compact < 0x3FFEF07D || compact > 0x3FFF8841) { 424 /* |X| < 1/16 or |X| > -1/16 */ 425 /* LP1CARE */ 426 fSig = (aSig & LIT64(0xFE00000000000000)) | LIT64(0x0100000000000000); 427 f = packFloatx80(0, 0x3FFF, fSig); /* F */ 428 j = (fSig >> 56) & 0x7E; /* DISPLACEMENT FOR 1/F */ 429 430 if (compact >= 0x3FFF8000) { /* 1+Z >= 1 */ 431 /* KISZERO */ 432 fp0 = floatx80_sub(float32_to_floatx80(make_float32(0x3F800000), 433 status), f, status); /* 1-F */ 434 fp0 = floatx80_add(fp0, fp1, status); /* FP0 IS Y-F = (1-F)+Z */ 435 fp1 = packFloatx80(0, 0, 0); /* K = 0 */ 436 } else { 437 /* KISNEG */ 438 fp0 = floatx80_sub(float32_to_floatx80(make_float32(0x40000000), 439 status), f, status); /* 2-F */ 440 fp1 = floatx80_add(fp1, fp1, status); /* 2Z */ 441 fp0 = floatx80_add(fp0, fp1, status); /* FP0 IS Y-F = (2-F)+2Z */ 442 fp1 = packFloatx80(1, one_exp, one_sig); /* K = -1 */ 443 } 444 goto lp1cont1; 445 } else { 446 /* LP1ONE16 */ 447 fp1 = floatx80_add(fp1, fp1, status); /* FP1 IS 2Z */ 448 fp0 = floatx80_add(fp0, float32_to_floatx80(make_float32(0x3F800000), 449 status), status); /* FP0 IS 1+X */ 450 451 /* LP1CONT2 */ 452 fp1 = floatx80_div(fp1, fp0, status); /* U */ 453 saveu = fp1; 454 fp0 = floatx80_mul(fp1, fp1, status); /* FP0 IS V = U*U */ 455 fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS W = V*V */ 456 457 fp3 = float64_to_floatx80(make_float64(0x3F175496ADD7DAD6), 458 status); /* B5 */ 459 fp2 = float64_to_floatx80(make_float64(0x3F3C71C2FE80C7E0), 460 status); /* B4 */ 461 fp3 = floatx80_mul(fp3, fp1, status); /* W*B5 */ 462 fp2 = floatx80_mul(fp2, fp1, status); /* W*B4 */ 463 fp3 = floatx80_add(fp3, float64_to_floatx80( 464 make_float64(0x3F624924928BCCFF), status), 465 status); /* B3+W*B5 */ 466 fp2 = floatx80_add(fp2, float64_to_floatx80( 467 make_float64(0x3F899999999995EC), status), 468 status); /* B2+W*B4 */ 469 fp1 = floatx80_mul(fp1, fp3, status); /* W*(B3+W*B5) */ 470 fp2 = floatx80_mul(fp2, fp0, status); /* V*(B2+W*B4) */ 471 fp1 = floatx80_add(fp1, float64_to_floatx80( 472 make_float64(0x3FB5555555555555), status), 473 status); /* B1+W*(B3+W*B5) */ 474 475 fp0 = floatx80_mul(fp0, saveu, status); /* FP0 IS U*V */ 476 fp1 = floatx80_add(fp1, fp2, 477 status); /* B1+W*(B3+W*B5) + V*(B2+W*B4) */ 478 fp0 = floatx80_mul(fp0, fp1, 479 status); /* U*V*([B1+W*(B3+W*B5)] + [V*(B2+W*B4)]) */ 480 481 status->float_rounding_mode = user_rnd_mode; 482 status->floatx80_rounding_precision = user_rnd_prec; 483 484 a = floatx80_add(fp0, saveu, status); 485 486 /*if (!floatx80_is_zero(a)) { */ 487 float_raise(float_flag_inexact, status); 488 /*} */ 489 490 return a; 491 } 492 } 493 494 /*---------------------------------------------------------------------------- 495 | Log base e 496 *----------------------------------------------------------------------------*/ 497 498 floatx80 floatx80_logn(floatx80 a, float_status *status) 499 { 500 flag aSign; 501 int32_t aExp; 502 uint64_t aSig, fSig; 503 504 int8_t user_rnd_mode, user_rnd_prec; 505 506 int32_t compact, j, k, adjk; 507 floatx80 fp0, fp1, fp2, fp3, f, logof2, klog2, saveu; 508 509 aSig = extractFloatx80Frac(a); 510 aExp = extractFloatx80Exp(a); 511 aSign = extractFloatx80Sign(a); 512 513 if (aExp == 0x7FFF) { 514 if ((uint64_t) (aSig << 1)) { 515 propagateFloatx80NaNOneArg(a, status); 516 } 517 if (aSign == 0) { 518 return packFloatx80(0, floatx80_infinity.high, 519 floatx80_infinity.low); 520 } 521 } 522 523 adjk = 0; 524 525 if (aExp == 0) { 526 if (aSig == 0) { /* zero */ 527 float_raise(float_flag_divbyzero, status); 528 return packFloatx80(1, floatx80_infinity.high, 529 floatx80_infinity.low); 530 } 531 if ((aSig & one_sig) == 0) { /* denormal */ 532 normalizeFloatx80Subnormal(aSig, &aExp, &aSig); 533 adjk = -100; 534 aExp += 100; 535 a = packFloatx80(aSign, aExp, aSig); 536 } 537 } 538 539 if (aSign) { 540 float_raise(float_flag_invalid, status); 541 return floatx80_default_nan(status); 542 } 543 544 user_rnd_mode = status->float_rounding_mode; 545 user_rnd_prec = status->floatx80_rounding_precision; 546 status->float_rounding_mode = float_round_nearest_even; 547 status->floatx80_rounding_precision = 80; 548 549 compact = floatx80_make_compact(aExp, aSig); 550 551 if (compact < 0x3FFEF07D || compact > 0x3FFF8841) { 552 /* |X| < 15/16 or |X| > 17/16 */ 553 k = aExp - 0x3FFF; 554 k += adjk; 555 fp1 = int32_to_floatx80(k, status); 556 557 fSig = (aSig & LIT64(0xFE00000000000000)) | LIT64(0x0100000000000000); 558 j = (fSig >> 56) & 0x7E; /* DISPLACEMENT FOR 1/F */ 559 560 f = packFloatx80(0, 0x3FFF, fSig); /* F */ 561 fp0 = packFloatx80(0, 0x3FFF, aSig); /* Y */ 562 563 fp0 = floatx80_sub(fp0, f, status); /* Y-F */ 564 565 /* LP1CONT1 */ 566 fp0 = floatx80_mul(fp0, log_tbl[j], status); /* FP0 IS U = (Y-F)/F */ 567 logof2 = packFloatx80(0, 0x3FFE, LIT64(0xB17217F7D1CF79AC)); 568 klog2 = floatx80_mul(fp1, logof2, status); /* FP1 IS K*LOG2 */ 569 fp2 = floatx80_mul(fp0, fp0, status); /* FP2 IS V=U*U */ 570 571 fp3 = fp2; 572 fp1 = fp2; 573 574 fp1 = floatx80_mul(fp1, float64_to_floatx80( 575 make_float64(0x3FC2499AB5E4040B), status), 576 status); /* V*A6 */ 577 fp2 = floatx80_mul(fp2, float64_to_floatx80( 578 make_float64(0xBFC555B5848CB7DB), status), 579 status); /* V*A5 */ 580 fp1 = floatx80_add(fp1, float64_to_floatx80( 581 make_float64(0x3FC99999987D8730), status), 582 status); /* A4+V*A6 */ 583 fp2 = floatx80_add(fp2, float64_to_floatx80( 584 make_float64(0xBFCFFFFFFF6F7E97), status), 585 status); /* A3+V*A5 */ 586 fp1 = floatx80_mul(fp1, fp3, status); /* V*(A4+V*A6) */ 587 fp2 = floatx80_mul(fp2, fp3, status); /* V*(A3+V*A5) */ 588 fp1 = floatx80_add(fp1, float64_to_floatx80( 589 make_float64(0x3FD55555555555A4), status), 590 status); /* A2+V*(A4+V*A6) */ 591 fp2 = floatx80_add(fp2, float64_to_floatx80( 592 make_float64(0xBFE0000000000008), status), 593 status); /* A1+V*(A3+V*A5) */ 594 fp1 = floatx80_mul(fp1, fp3, status); /* V*(A2+V*(A4+V*A6)) */ 595 fp2 = floatx80_mul(fp2, fp3, status); /* V*(A1+V*(A3+V*A5)) */ 596 fp1 = floatx80_mul(fp1, fp0, status); /* U*V*(A2+V*(A4+V*A6)) */ 597 fp0 = floatx80_add(fp0, fp2, status); /* U+V*(A1+V*(A3+V*A5)) */ 598 599 fp1 = floatx80_add(fp1, log_tbl[j + 1], 600 status); /* LOG(F)+U*V*(A2+V*(A4+V*A6)) */ 601 fp0 = floatx80_add(fp0, fp1, status); /* FP0 IS LOG(F) + LOG(1+U) */ 602 603 status->float_rounding_mode = user_rnd_mode; 604 status->floatx80_rounding_precision = user_rnd_prec; 605 606 a = floatx80_add(fp0, klog2, status); 607 608 float_raise(float_flag_inexact, status); 609 610 return a; 611 } else { /* |X-1| >= 1/16 */ 612 fp0 = a; 613 fp1 = a; 614 fp1 = floatx80_sub(fp1, float32_to_floatx80(make_float32(0x3F800000), 615 status), status); /* FP1 IS X-1 */ 616 fp0 = floatx80_add(fp0, float32_to_floatx80(make_float32(0x3F800000), 617 status), status); /* FP0 IS X+1 */ 618 fp1 = floatx80_add(fp1, fp1, status); /* FP1 IS 2(X-1) */ 619 620 /* LP1CONT2 */ 621 fp1 = floatx80_div(fp1, fp0, status); /* U */ 622 saveu = fp1; 623 fp0 = floatx80_mul(fp1, fp1, status); /* FP0 IS V = U*U */ 624 fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS W = V*V */ 625 626 fp3 = float64_to_floatx80(make_float64(0x3F175496ADD7DAD6), 627 status); /* B5 */ 628 fp2 = float64_to_floatx80(make_float64(0x3F3C71C2FE80C7E0), 629 status); /* B4 */ 630 fp3 = floatx80_mul(fp3, fp1, status); /* W*B5 */ 631 fp2 = floatx80_mul(fp2, fp1, status); /* W*B4 */ 632 fp3 = floatx80_add(fp3, float64_to_floatx80( 633 make_float64(0x3F624924928BCCFF), status), 634 status); /* B3+W*B5 */ 635 fp2 = floatx80_add(fp2, float64_to_floatx80( 636 make_float64(0x3F899999999995EC), status), 637 status); /* B2+W*B4 */ 638 fp1 = floatx80_mul(fp1, fp3, status); /* W*(B3+W*B5) */ 639 fp2 = floatx80_mul(fp2, fp0, status); /* V*(B2+W*B4) */ 640 fp1 = floatx80_add(fp1, float64_to_floatx80( 641 make_float64(0x3FB5555555555555), status), 642 status); /* B1+W*(B3+W*B5) */ 643 644 fp0 = floatx80_mul(fp0, saveu, status); /* FP0 IS U*V */ 645 fp1 = floatx80_add(fp1, fp2, status); /* B1+W*(B3+W*B5) + V*(B2+W*B4) */ 646 fp0 = floatx80_mul(fp0, fp1, 647 status); /* U*V*([B1+W*(B3+W*B5)] + [V*(B2+W*B4)]) */ 648 649 status->float_rounding_mode = user_rnd_mode; 650 status->floatx80_rounding_precision = user_rnd_prec; 651 652 a = floatx80_add(fp0, saveu, status); 653 654 /*if (!floatx80_is_zero(a)) { */ 655 float_raise(float_flag_inexact, status); 656 /*} */ 657 658 return a; 659 } 660 } 661 662 /*---------------------------------------------------------------------------- 663 | Log base 10 664 *----------------------------------------------------------------------------*/ 665 666 floatx80 floatx80_log10(floatx80 a, float_status *status) 667 { 668 flag aSign; 669 int32_t aExp; 670 uint64_t aSig; 671 672 int8_t user_rnd_mode, user_rnd_prec; 673 674 floatx80 fp0, fp1; 675 676 aSig = extractFloatx80Frac(a); 677 aExp = extractFloatx80Exp(a); 678 aSign = extractFloatx80Sign(a); 679 680 if (aExp == 0x7FFF) { 681 if ((uint64_t) (aSig << 1)) { 682 propagateFloatx80NaNOneArg(a, status); 683 } 684 if (aSign == 0) { 685 return packFloatx80(0, floatx80_infinity.high, 686 floatx80_infinity.low); 687 } 688 } 689 690 if (aExp == 0 && aSig == 0) { 691 float_raise(float_flag_divbyzero, status); 692 return packFloatx80(1, floatx80_infinity.high, 693 floatx80_infinity.low); 694 } 695 696 if (aSign) { 697 float_raise(float_flag_invalid, status); 698 return floatx80_default_nan(status); 699 } 700 701 user_rnd_mode = status->float_rounding_mode; 702 user_rnd_prec = status->floatx80_rounding_precision; 703 status->float_rounding_mode = float_round_nearest_even; 704 status->floatx80_rounding_precision = 80; 705 706 fp0 = floatx80_logn(a, status); 707 fp1 = packFloatx80(0, 0x3FFD, LIT64(0xDE5BD8A937287195)); /* INV_L10 */ 708 709 status->float_rounding_mode = user_rnd_mode; 710 status->floatx80_rounding_precision = user_rnd_prec; 711 712 a = floatx80_mul(fp0, fp1, status); /* LOGN(X)*INV_L10 */ 713 714 float_raise(float_flag_inexact, status); 715 716 return a; 717 } 718 719 /*---------------------------------------------------------------------------- 720 | Log base 2 721 *----------------------------------------------------------------------------*/ 722 723 floatx80 floatx80_log2(floatx80 a, float_status *status) 724 { 725 flag aSign; 726 int32_t aExp; 727 uint64_t aSig; 728 729 int8_t user_rnd_mode, user_rnd_prec; 730 731 floatx80 fp0, fp1; 732 733 aSig = extractFloatx80Frac(a); 734 aExp = extractFloatx80Exp(a); 735 aSign = extractFloatx80Sign(a); 736 737 if (aExp == 0x7FFF) { 738 if ((uint64_t) (aSig << 1)) { 739 propagateFloatx80NaNOneArg(a, status); 740 } 741 if (aSign == 0) { 742 return packFloatx80(0, floatx80_infinity.high, 743 floatx80_infinity.low); 744 } 745 } 746 747 if (aExp == 0) { 748 if (aSig == 0) { 749 float_raise(float_flag_divbyzero, status); 750 return packFloatx80(1, floatx80_infinity.high, 751 floatx80_infinity.low); 752 } 753 normalizeFloatx80Subnormal(aSig, &aExp, &aSig); 754 } 755 756 if (aSign) { 757 float_raise(float_flag_invalid, status); 758 return floatx80_default_nan(status); 759 } 760 761 user_rnd_mode = status->float_rounding_mode; 762 user_rnd_prec = status->floatx80_rounding_precision; 763 status->float_rounding_mode = float_round_nearest_even; 764 status->floatx80_rounding_precision = 80; 765 766 if (aSig == one_sig) { /* X is 2^k */ 767 status->float_rounding_mode = user_rnd_mode; 768 status->floatx80_rounding_precision = user_rnd_prec; 769 770 a = int32_to_floatx80(aExp - 0x3FFF, status); 771 } else { 772 fp0 = floatx80_logn(a, status); 773 fp1 = packFloatx80(0, 0x3FFF, LIT64(0xB8AA3B295C17F0BC)); /* INV_L2 */ 774 775 status->float_rounding_mode = user_rnd_mode; 776 status->floatx80_rounding_precision = user_rnd_prec; 777 778 a = floatx80_mul(fp0, fp1, status); /* LOGN(X)*INV_L2 */ 779 } 780 781 float_raise(float_flag_inexact, status); 782 783 return a; 784 } 785 786 /*---------------------------------------------------------------------------- 787 | e to x 788 *----------------------------------------------------------------------------*/ 789 790 floatx80 floatx80_etox(floatx80 a, float_status *status) 791 { 792 flag aSign; 793 int32_t aExp; 794 uint64_t aSig; 795 796 int8_t user_rnd_mode, user_rnd_prec; 797 798 int32_t compact, n, j, k, m, m1; 799 floatx80 fp0, fp1, fp2, fp3, l2, scale, adjscale; 800 flag adjflag; 801 802 aSig = extractFloatx80Frac(a); 803 aExp = extractFloatx80Exp(a); 804 aSign = extractFloatx80Sign(a); 805 806 if (aExp == 0x7FFF) { 807 if ((uint64_t) (aSig << 1)) { 808 return propagateFloatx80NaNOneArg(a, status); 809 } 810 if (aSign) { 811 return packFloatx80(0, 0, 0); 812 } 813 return packFloatx80(0, floatx80_infinity.high, 814 floatx80_infinity.low); 815 } 816 817 if (aExp == 0 && aSig == 0) { 818 return packFloatx80(0, one_exp, one_sig); 819 } 820 821 user_rnd_mode = status->float_rounding_mode; 822 user_rnd_prec = status->floatx80_rounding_precision; 823 status->float_rounding_mode = float_round_nearest_even; 824 status->floatx80_rounding_precision = 80; 825 826 adjflag = 0; 827 828 if (aExp >= 0x3FBE) { /* |X| >= 2^(-65) */ 829 compact = floatx80_make_compact(aExp, aSig); 830 831 if (compact < 0x400CB167) { /* |X| < 16380 log2 */ 832 fp0 = a; 833 fp1 = a; 834 fp0 = floatx80_mul(fp0, float32_to_floatx80( 835 make_float32(0x42B8AA3B), status), 836 status); /* 64/log2 * X */ 837 adjflag = 0; 838 n = floatx80_to_int32(fp0, status); /* int(64/log2*X) */ 839 fp0 = int32_to_floatx80(n, status); 840 841 j = n & 0x3F; /* J = N mod 64 */ 842 m = n / 64; /* NOTE: this is really arithmetic right shift by 6 */ 843 if (n < 0 && j) { 844 /* arithmetic right shift is division and 845 * round towards minus infinity 846 */ 847 m--; 848 } 849 m += 0x3FFF; /* biased exponent of 2^(M) */ 850 851 expcont1: 852 fp2 = fp0; /* N */ 853 fp0 = floatx80_mul(fp0, float32_to_floatx80( 854 make_float32(0xBC317218), status), 855 status); /* N * L1, L1 = lead(-log2/64) */ 856 l2 = packFloatx80(0, 0x3FDC, LIT64(0x82E308654361C4C6)); 857 fp2 = floatx80_mul(fp2, l2, status); /* N * L2, L1+L2 = -log2/64 */ 858 fp0 = floatx80_add(fp0, fp1, status); /* X + N*L1 */ 859 fp0 = floatx80_add(fp0, fp2, status); /* R */ 860 861 fp1 = floatx80_mul(fp0, fp0, status); /* S = R*R */ 862 fp2 = float32_to_floatx80(make_float32(0x3AB60B70), 863 status); /* A5 */ 864 fp2 = floatx80_mul(fp2, fp1, status); /* fp2 is S*A5 */ 865 fp3 = floatx80_mul(float32_to_floatx80(make_float32(0x3C088895), 866 status), fp1, 867 status); /* fp3 is S*A4 */ 868 fp2 = floatx80_add(fp2, float64_to_floatx80(make_float64( 869 0x3FA5555555554431), status), 870 status); /* fp2 is A3+S*A5 */ 871 fp3 = floatx80_add(fp3, float64_to_floatx80(make_float64( 872 0x3FC5555555554018), status), 873 status); /* fp3 is A2+S*A4 */ 874 fp2 = floatx80_mul(fp2, fp1, status); /* fp2 is S*(A3+S*A5) */ 875 fp3 = floatx80_mul(fp3, fp1, status); /* fp3 is S*(A2+S*A4) */ 876 fp2 = floatx80_add(fp2, float32_to_floatx80( 877 make_float32(0x3F000000), status), 878 status); /* fp2 is A1+S*(A3+S*A5) */ 879 fp3 = floatx80_mul(fp3, fp0, status); /* fp3 IS R*S*(A2+S*A4) */ 880 fp2 = floatx80_mul(fp2, fp1, 881 status); /* fp2 IS S*(A1+S*(A3+S*A5)) */ 882 fp0 = floatx80_add(fp0, fp3, status); /* fp0 IS R+R*S*(A2+S*A4) */ 883 fp0 = floatx80_add(fp0, fp2, status); /* fp0 IS EXP(R) - 1 */ 884 885 fp1 = exp_tbl[j]; 886 fp0 = floatx80_mul(fp0, fp1, status); /* 2^(J/64)*(Exp(R)-1) */ 887 fp0 = floatx80_add(fp0, float32_to_floatx80(exp_tbl2[j], status), 888 status); /* accurate 2^(J/64) */ 889 fp0 = floatx80_add(fp0, fp1, 890 status); /* 2^(J/64) + 2^(J/64)*(Exp(R)-1) */ 891 892 scale = packFloatx80(0, m, one_sig); 893 if (adjflag) { 894 adjscale = packFloatx80(0, m1, one_sig); 895 fp0 = floatx80_mul(fp0, adjscale, status); 896 } 897 898 status->float_rounding_mode = user_rnd_mode; 899 status->floatx80_rounding_precision = user_rnd_prec; 900 901 a = floatx80_mul(fp0, scale, status); 902 903 float_raise(float_flag_inexact, status); 904 905 return a; 906 } else { /* |X| >= 16380 log2 */ 907 if (compact > 0x400CB27C) { /* |X| >= 16480 log2 */ 908 status->float_rounding_mode = user_rnd_mode; 909 status->floatx80_rounding_precision = user_rnd_prec; 910 if (aSign) { 911 a = roundAndPackFloatx80( 912 status->floatx80_rounding_precision, 913 0, -0x1000, aSig, 0, status); 914 } else { 915 a = roundAndPackFloatx80( 916 status->floatx80_rounding_precision, 917 0, 0x8000, aSig, 0, status); 918 } 919 float_raise(float_flag_inexact, status); 920 921 return a; 922 } else { 923 fp0 = a; 924 fp1 = a; 925 fp0 = floatx80_mul(fp0, float32_to_floatx80( 926 make_float32(0x42B8AA3B), status), 927 status); /* 64/log2 * X */ 928 adjflag = 1; 929 n = floatx80_to_int32(fp0, status); /* int(64/log2*X) */ 930 fp0 = int32_to_floatx80(n, status); 931 932 j = n & 0x3F; /* J = N mod 64 */ 933 /* NOTE: this is really arithmetic right shift by 6 */ 934 k = n / 64; 935 if (n < 0 && j) { 936 /* arithmetic right shift is division and 937 * round towards minus infinity 938 */ 939 k--; 940 } 941 /* NOTE: this is really arithmetic right shift by 1 */ 942 m1 = k / 2; 943 if (k < 0 && (k & 1)) { 944 /* arithmetic right shift is division and 945 * round towards minus infinity 946 */ 947 m1--; 948 } 949 m = k - m1; 950 m1 += 0x3FFF; /* biased exponent of 2^(M1) */ 951 m += 0x3FFF; /* biased exponent of 2^(M) */ 952 953 goto expcont1; 954 } 955 } 956 } else { /* |X| < 2^(-65) */ 957 status->float_rounding_mode = user_rnd_mode; 958 status->floatx80_rounding_precision = user_rnd_prec; 959 960 a = floatx80_add(a, float32_to_floatx80(make_float32(0x3F800000), 961 status), status); /* 1 + X */ 962 963 float_raise(float_flag_inexact, status); 964 965 return a; 966 } 967 } 968 969 /*---------------------------------------------------------------------------- 970 | 2 to x 971 *----------------------------------------------------------------------------*/ 972 973 floatx80 floatx80_twotox(floatx80 a, float_status *status) 974 { 975 flag aSign; 976 int32_t aExp; 977 uint64_t aSig; 978 979 int8_t user_rnd_mode, user_rnd_prec; 980 981 int32_t compact, n, j, l, m, m1; 982 floatx80 fp0, fp1, fp2, fp3, adjfact, fact1, fact2; 983 984 aSig = extractFloatx80Frac(a); 985 aExp = extractFloatx80Exp(a); 986 aSign = extractFloatx80Sign(a); 987 988 if (aExp == 0x7FFF) { 989 if ((uint64_t) (aSig << 1)) { 990 return propagateFloatx80NaNOneArg(a, status); 991 } 992 if (aSign) { 993 return packFloatx80(0, 0, 0); 994 } 995 return packFloatx80(0, floatx80_infinity.high, 996 floatx80_infinity.low); 997 } 998 999 if (aExp == 0 && aSig == 0) { 1000 return packFloatx80(0, one_exp, one_sig); 1001 } 1002 1003 user_rnd_mode = status->float_rounding_mode; 1004 user_rnd_prec = status->floatx80_rounding_precision; 1005 status->float_rounding_mode = float_round_nearest_even; 1006 status->floatx80_rounding_precision = 80; 1007 1008 fp0 = a; 1009 1010 compact = floatx80_make_compact(aExp, aSig); 1011 1012 if (compact < 0x3FB98000 || compact > 0x400D80C0) { 1013 /* |X| > 16480 or |X| < 2^(-70) */ 1014 if (compact > 0x3FFF8000) { /* |X| > 16480 */ 1015 status->float_rounding_mode = user_rnd_mode; 1016 status->floatx80_rounding_precision = user_rnd_prec; 1017 1018 if (aSign) { 1019 return roundAndPackFloatx80(status->floatx80_rounding_precision, 1020 0, -0x1000, aSig, 0, status); 1021 } else { 1022 return roundAndPackFloatx80(status->floatx80_rounding_precision, 1023 0, 0x8000, aSig, 0, status); 1024 } 1025 } else { /* |X| < 2^(-70) */ 1026 status->float_rounding_mode = user_rnd_mode; 1027 status->floatx80_rounding_precision = user_rnd_prec; 1028 1029 a = floatx80_add(fp0, float32_to_floatx80( 1030 make_float32(0x3F800000), status), 1031 status); /* 1 + X */ 1032 1033 float_raise(float_flag_inexact, status); 1034 1035 return a; 1036 } 1037 } else { /* 2^(-70) <= |X| <= 16480 */ 1038 fp1 = fp0; /* X */ 1039 fp1 = floatx80_mul(fp1, float32_to_floatx80( 1040 make_float32(0x42800000), status), 1041 status); /* X * 64 */ 1042 n = floatx80_to_int32(fp1, status); 1043 fp1 = int32_to_floatx80(n, status); 1044 j = n & 0x3F; 1045 l = n / 64; /* NOTE: this is really arithmetic right shift by 6 */ 1046 if (n < 0 && j) { 1047 /* arithmetic right shift is division and 1048 * round towards minus infinity 1049 */ 1050 l--; 1051 } 1052 m = l / 2; /* NOTE: this is really arithmetic right shift by 1 */ 1053 if (l < 0 && (l & 1)) { 1054 /* arithmetic right shift is division and 1055 * round towards minus infinity 1056 */ 1057 m--; 1058 } 1059 m1 = l - m; 1060 m1 += 0x3FFF; /* ADJFACT IS 2^(M') */ 1061 1062 adjfact = packFloatx80(0, m1, one_sig); 1063 fact1 = exp2_tbl[j]; 1064 fact1.high += m; 1065 fact2.high = exp2_tbl2[j] >> 16; 1066 fact2.high += m; 1067 fact2.low = (uint64_t)(exp2_tbl2[j] & 0xFFFF); 1068 fact2.low <<= 48; 1069 1070 fp1 = floatx80_mul(fp1, float32_to_floatx80( 1071 make_float32(0x3C800000), status), 1072 status); /* (1/64)*N */ 1073 fp0 = floatx80_sub(fp0, fp1, status); /* X - (1/64)*INT(64 X) */ 1074 fp2 = packFloatx80(0, 0x3FFE, LIT64(0xB17217F7D1CF79AC)); /* LOG2 */ 1075 fp0 = floatx80_mul(fp0, fp2, status); /* R */ 1076 1077 /* EXPR */ 1078 fp1 = floatx80_mul(fp0, fp0, status); /* S = R*R */ 1079 fp2 = float64_to_floatx80(make_float64(0x3F56C16D6F7BD0B2), 1080 status); /* A5 */ 1081 fp3 = float64_to_floatx80(make_float64(0x3F811112302C712C), 1082 status); /* A4 */ 1083 fp2 = floatx80_mul(fp2, fp1, status); /* S*A5 */ 1084 fp3 = floatx80_mul(fp3, fp1, status); /* S*A4 */ 1085 fp2 = floatx80_add(fp2, float64_to_floatx80( 1086 make_float64(0x3FA5555555554CC1), status), 1087 status); /* A3+S*A5 */ 1088 fp3 = floatx80_add(fp3, float64_to_floatx80( 1089 make_float64(0x3FC5555555554A54), status), 1090 status); /* A2+S*A4 */ 1091 fp2 = floatx80_mul(fp2, fp1, status); /* S*(A3+S*A5) */ 1092 fp3 = floatx80_mul(fp3, fp1, status); /* S*(A2+S*A4) */ 1093 fp2 = floatx80_add(fp2, float64_to_floatx80( 1094 make_float64(0x3FE0000000000000), status), 1095 status); /* A1+S*(A3+S*A5) */ 1096 fp3 = floatx80_mul(fp3, fp0, status); /* R*S*(A2+S*A4) */ 1097 1098 fp2 = floatx80_mul(fp2, fp1, status); /* S*(A1+S*(A3+S*A5)) */ 1099 fp0 = floatx80_add(fp0, fp3, status); /* R+R*S*(A2+S*A4) */ 1100 fp0 = floatx80_add(fp0, fp2, status); /* EXP(R) - 1 */ 1101 1102 fp0 = floatx80_mul(fp0, fact1, status); 1103 fp0 = floatx80_add(fp0, fact2, status); 1104 fp0 = floatx80_add(fp0, fact1, status); 1105 1106 status->float_rounding_mode = user_rnd_mode; 1107 status->floatx80_rounding_precision = user_rnd_prec; 1108 1109 a = floatx80_mul(fp0, adjfact, status); 1110 1111 float_raise(float_flag_inexact, status); 1112 1113 return a; 1114 } 1115 } 1116 1117 /*---------------------------------------------------------------------------- 1118 | 10 to x 1119 *----------------------------------------------------------------------------*/ 1120 1121 floatx80 floatx80_tentox(floatx80 a, float_status *status) 1122 { 1123 flag aSign; 1124 int32_t aExp; 1125 uint64_t aSig; 1126 1127 int8_t user_rnd_mode, user_rnd_prec; 1128 1129 int32_t compact, n, j, l, m, m1; 1130 floatx80 fp0, fp1, fp2, fp3, adjfact, fact1, fact2; 1131 1132 aSig = extractFloatx80Frac(a); 1133 aExp = extractFloatx80Exp(a); 1134 aSign = extractFloatx80Sign(a); 1135 1136 if (aExp == 0x7FFF) { 1137 if ((uint64_t) (aSig << 1)) { 1138 return propagateFloatx80NaNOneArg(a, status); 1139 } 1140 if (aSign) { 1141 return packFloatx80(0, 0, 0); 1142 } 1143 return packFloatx80(0, floatx80_infinity.high, 1144 floatx80_infinity.low); 1145 } 1146 1147 if (aExp == 0 && aSig == 0) { 1148 return packFloatx80(0, one_exp, one_sig); 1149 } 1150 1151 user_rnd_mode = status->float_rounding_mode; 1152 user_rnd_prec = status->floatx80_rounding_precision; 1153 status->float_rounding_mode = float_round_nearest_even; 1154 status->floatx80_rounding_precision = 80; 1155 1156 fp0 = a; 1157 1158 compact = floatx80_make_compact(aExp, aSig); 1159 1160 if (compact < 0x3FB98000 || compact > 0x400B9B07) { 1161 /* |X| > 16480 LOG2/LOG10 or |X| < 2^(-70) */ 1162 if (compact > 0x3FFF8000) { /* |X| > 16480 */ 1163 status->float_rounding_mode = user_rnd_mode; 1164 status->floatx80_rounding_precision = user_rnd_prec; 1165 1166 if (aSign) { 1167 return roundAndPackFloatx80(status->floatx80_rounding_precision, 1168 0, -0x1000, aSig, 0, status); 1169 } else { 1170 return roundAndPackFloatx80(status->floatx80_rounding_precision, 1171 0, 0x8000, aSig, 0, status); 1172 } 1173 } else { /* |X| < 2^(-70) */ 1174 status->float_rounding_mode = user_rnd_mode; 1175 status->floatx80_rounding_precision = user_rnd_prec; 1176 1177 a = floatx80_add(fp0, float32_to_floatx80( 1178 make_float32(0x3F800000), status), 1179 status); /* 1 + X */ 1180 1181 float_raise(float_flag_inexact, status); 1182 1183 return a; 1184 } 1185 } else { /* 2^(-70) <= |X| <= 16480 LOG 2 / LOG 10 */ 1186 fp1 = fp0; /* X */ 1187 fp1 = floatx80_mul(fp1, float64_to_floatx80( 1188 make_float64(0x406A934F0979A371), 1189 status), status); /* X*64*LOG10/LOG2 */ 1190 n = floatx80_to_int32(fp1, status); /* N=INT(X*64*LOG10/LOG2) */ 1191 fp1 = int32_to_floatx80(n, status); 1192 1193 j = n & 0x3F; 1194 l = n / 64; /* NOTE: this is really arithmetic right shift by 6 */ 1195 if (n < 0 && j) { 1196 /* arithmetic right shift is division and 1197 * round towards minus infinity 1198 */ 1199 l--; 1200 } 1201 m = l / 2; /* NOTE: this is really arithmetic right shift by 1 */ 1202 if (l < 0 && (l & 1)) { 1203 /* arithmetic right shift is division and 1204 * round towards minus infinity 1205 */ 1206 m--; 1207 } 1208 m1 = l - m; 1209 m1 += 0x3FFF; /* ADJFACT IS 2^(M') */ 1210 1211 adjfact = packFloatx80(0, m1, one_sig); 1212 fact1 = exp2_tbl[j]; 1213 fact1.high += m; 1214 fact2.high = exp2_tbl2[j] >> 16; 1215 fact2.high += m; 1216 fact2.low = (uint64_t)(exp2_tbl2[j] & 0xFFFF); 1217 fact2.low <<= 48; 1218 1219 fp2 = fp1; /* N */ 1220 fp1 = floatx80_mul(fp1, float64_to_floatx80( 1221 make_float64(0x3F734413509F8000), status), 1222 status); /* N*(LOG2/64LOG10)_LEAD */ 1223 fp3 = packFloatx80(1, 0x3FCD, LIT64(0xC0219DC1DA994FD2)); 1224 fp2 = floatx80_mul(fp2, fp3, status); /* N*(LOG2/64LOG10)_TRAIL */ 1225 fp0 = floatx80_sub(fp0, fp1, status); /* X - N L_LEAD */ 1226 fp0 = floatx80_sub(fp0, fp2, status); /* X - N L_TRAIL */ 1227 fp2 = packFloatx80(0, 0x4000, LIT64(0x935D8DDDAAA8AC17)); /* LOG10 */ 1228 fp0 = floatx80_mul(fp0, fp2, status); /* R */ 1229 1230 /* EXPR */ 1231 fp1 = floatx80_mul(fp0, fp0, status); /* S = R*R */ 1232 fp2 = float64_to_floatx80(make_float64(0x3F56C16D6F7BD0B2), 1233 status); /* A5 */ 1234 fp3 = float64_to_floatx80(make_float64(0x3F811112302C712C), 1235 status); /* A4 */ 1236 fp2 = floatx80_mul(fp2, fp1, status); /* S*A5 */ 1237 fp3 = floatx80_mul(fp3, fp1, status); /* S*A4 */ 1238 fp2 = floatx80_add(fp2, float64_to_floatx80( 1239 make_float64(0x3FA5555555554CC1), status), 1240 status); /* A3+S*A5 */ 1241 fp3 = floatx80_add(fp3, float64_to_floatx80( 1242 make_float64(0x3FC5555555554A54), status), 1243 status); /* A2+S*A4 */ 1244 fp2 = floatx80_mul(fp2, fp1, status); /* S*(A3+S*A5) */ 1245 fp3 = floatx80_mul(fp3, fp1, status); /* S*(A2+S*A4) */ 1246 fp2 = floatx80_add(fp2, float64_to_floatx80( 1247 make_float64(0x3FE0000000000000), status), 1248 status); /* A1+S*(A3+S*A5) */ 1249 fp3 = floatx80_mul(fp3, fp0, status); /* R*S*(A2+S*A4) */ 1250 1251 fp2 = floatx80_mul(fp2, fp1, status); /* S*(A1+S*(A3+S*A5)) */ 1252 fp0 = floatx80_add(fp0, fp3, status); /* R+R*S*(A2+S*A4) */ 1253 fp0 = floatx80_add(fp0, fp2, status); /* EXP(R) - 1 */ 1254 1255 fp0 = floatx80_mul(fp0, fact1, status); 1256 fp0 = floatx80_add(fp0, fact2, status); 1257 fp0 = floatx80_add(fp0, fact1, status); 1258 1259 status->float_rounding_mode = user_rnd_mode; 1260 status->floatx80_rounding_precision = user_rnd_prec; 1261 1262 a = floatx80_mul(fp0, adjfact, status); 1263 1264 float_raise(float_flag_inexact, status); 1265 1266 return a; 1267 } 1268 } 1269