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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 | /**************************************************************** The author of this software is David M. Gay. Copyright (C) 1998-2001 by Lucent Technologies All Rights Reserved Permission to use, copy, modify, and distribute this software and its documentation for any purpose and without fee is hereby granted, provided that the above copyright notice appear in all copies and that both that the copyright notice and this permission notice and warranty disclaimer appear in supporting documentation, and that the name of Lucent or any of its entities not be used in advertising or publicity pertaining to distribution of the software without specific, written prior permission. LUCENT DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL LUCENT OR ANY OF ITS ENTITIES BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. ****************************************************************/ /* Please send bug reports to David M. Gay (dmg at acm dot org, * with " at " changed at "@" and " dot " changed to "."). */ #include "xlocale_private.h" #include "gdtoaimp.h" #ifndef NO_FENV_H #include <fenv.h> #endif #ifdef USE_LOCALE #include "locale.h" #endif #ifdef IEEE_Arith #ifndef NO_IEEE_Scale #define Avoid_Underflow #undef tinytens /* The factor of 2^106 in tinytens[4] helps us avoid setting the underflow */ /* flag unnecessarily. It leads to a song and dance at the end of strtod. */ static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 9007199254740992.*9007199254740992.e-256 }; #endif #endif #ifdef Honor_FLT_ROUNDS #undef Check_FLT_ROUNDS #define Check_FLT_ROUNDS #else #define Rounding Flt_Rounds #endif double strtod_l #ifdef KR_headers (s00, se, loc) CONST char *s00; char **se; locale_t loc; #else (CONST char *s00, char **se, locale_t loc) #endif { #ifdef Avoid_Underflow int scale; #endif int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, decpt, dsign, e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign; CONST char *s, *s0, *s1; char *strunc = NULL; double aadj; Long L; U adj, aadj1, rv, rv0; ULong y, z; Bigint *bb, *bb1, *bd, *bd0, *bs, *delta; #ifdef SET_INEXACT int inexact, oldinexact; #endif #ifdef USE_LOCALE /*{{*/ NORMALIZE_LOCALE(loc); #ifdef NO_LOCALE_CACHE char *decimalpoint = localeconv_l(loc)->decimal_point; int dplen = strlen(decimalpoint); #else char *decimalpoint; static char *decimalpoint_cache; static int dplen; if (!(s0 = decimalpoint_cache)) { s0 = localeconv_l(loc)->decimal_point; if ((decimalpoint_cache = (char*)MALLOC(strlen(s0) + 1))) { strcpy(decimalpoint_cache, s0); s0 = decimalpoint_cache; } dplen = strlen(s0); } decimalpoint = (char*)s0; #endif /*NO_LOCALE_CACHE*/ #else /*USE_LOCALE}{*/ #define dplen 1 #endif /*USE_LOCALE}}*/ #ifdef Honor_FLT_ROUNDS /*{*/ int Rounding; #ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */ Rounding = Flt_Rounds; #else /*}{*/ Rounding = 1; switch(fegetround()) { case FE_TOWARDZERO: Rounding = 0; break; case FE_UPWARD: Rounding = 2; break; case FE_DOWNWARD: Rounding = 3; } #endif /*}}*/ #endif /*}*/ sign = nz0 = nz = decpt = 0; dval(&rv) = 0.; for(s = s00;;s++) switch(*s) { case '-': sign = 1; /* no break */ case '+': if (*++s) goto break2; /* no break */ case 0: goto ret0; case '\t': case '\n': case '\v': case '\f': case '\r': case ' ': continue; default: goto break2; } break2: if (*s == '0') { #ifndef NO_HEX_FP /*{*/ { static CONST FPI fpi = { 53, 1-1023-53+1, 2046-1023-53+1, 1, SI }; Long exp; ULong bits[2]; switch(s[1]) { case 'x': case 'X': { #ifdef Honor_FLT_ROUNDS FPI fpi1 = fpi; fpi1.rounding = Rounding; #else #define fpi1 fpi #endif switch((i = gethex(&s, &fpi1, &exp, &bb, sign, loc)) & STRTOG_Retmask) { case STRTOG_NoNumber: s = s00; sign = 0; case STRTOG_Zero: break; default: if (bb) { copybits(bits, fpi.nbits, bb); Bfree(bb); } ULtod(((U*)&rv)->L, bits, exp, i); }} goto ret; } } #endif /*}*/ nz0 = 1; while(*++s == '0') ; if (!*s) goto ret; } s0 = s; y = z = 0; for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++) if (nd < 9) y = 10*y + c - '0'; else if (nd < 16) z = 10*z + c - '0'; nd0 = nd; #ifdef USE_LOCALE if (c == *decimalpoint) { for(i = 1; decimalpoint[i]; ++i) if (s[i] != decimalpoint[i]) goto dig_done; s += i; c = *s; #else if (c == '.') { c = *++s; #endif decpt = 1; if (!nd) { for(; c == '0'; c = *++s) nz++; if (c > '0' && c <= '9') { s0 = s; nf += nz; nz = 0; goto have_dig; } goto dig_done; } for(; c >= '0' && c <= '9'; c = *++s) { have_dig: nz++; if (c -= '0') { nf += nz; for(i = 1; i < nz; i++) if (nd++ < 9) y *= 10; else if (nd <= DBL_DIG + 1) z *= 10; if (nd++ < 9) y = 10*y + c; else if (nd <= DBL_DIG + 1) z = 10*z + c; nz = 0; } } }/*}*/ dig_done: e = 0; if (c == 'e' || c == 'E') { if (!nd && !nz && !nz0) { goto ret0; } s00 = s; esign = 0; switch(c = *++s) { case '-': esign = 1; case '+': c = *++s; } if (c >= '0' && c <= '9') { while(c == '0') c = *++s; if (c > '0' && c <= '9') { L = c - '0'; s1 = s; while((c = *++s) >= '0' && c <= '9') L = 10*L + c - '0'; if (s - s1 > 8 || L > 19999) /* Avoid confusion from exponents * so large that e might overflow. */ e = 19999; /* safe for 16 bit ints */ else e = (int)L; if (esign) e = -e; } else e = 0; } else s = s00; } if (!nd) { if (!nz && !nz0) { #ifdef INFNAN_CHECK /* Check for Nan and Infinity */ ULong bits[2]; static CONST FPI fpinan = /* only 52 explicit bits */ { 52, 1-1023-53+1, 2046-1023-53+1, 1, SI }; if (!decpt) switch(c) { case 'i': case 'I': if (match(&s,"nf")) { --s; if (!match(&s,"inity")) ++s; word0(&rv) = 0x7ff00000; word1(&rv) = 0; goto ret; } break; case 'n': case 'N': if (match(&s, "an")) { #ifndef No_Hex_NaN if (*s == '(' /*)*/ && hexnan(&s, &fpinan, bits) == STRTOG_NaNbits) { word0(&rv) = 0x7ff00000 | bits[1]; word1(&rv) = bits[0]; } else { #endif word0(&rv) = NAN_WORD0; word1(&rv) = NAN_WORD1; #ifndef No_Hex_NaN } #endif goto ret; } } #endif /* INFNAN_CHECK */ ret0: s = s00; sign = 0; } goto ret; } #define FPIEMIN (1-1023-53+1) // fpi.emin #define FPINBITS 52 // fpi.nbits TRUNCATE_DIGITS(s0, strunc, nd, nd0, nf, FPINBITS, FPIEMIN, dplen); e1 = e -= nf; /* Now we have nd0 digits, starting at s0, followed by a * decimal point, followed by nd-nd0 digits. The number we're * after is the integer represented by those digits times * 10**e */ if (!nd0) nd0 = nd; k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1; dval(&rv) = y; if (k > 9) { #ifdef SET_INEXACT if (k > DBL_DIG) oldinexact = get_inexact(); #endif dval(&rv) = tens[k - 9] * dval(&rv) + z; } bd0 = 0; if (nd <= DBL_DIG #ifndef RND_PRODQUOT #ifndef Honor_FLT_ROUNDS && Flt_Rounds == 1 #endif #endif ) { if (!e) goto ret; if (e > 0) { if (e <= Ten_pmax) { #ifdef VAX goto vax_ovfl_check; #else #ifdef Honor_FLT_ROUNDS /* round correctly FLT_ROUNDS = 2 or 3 */ if (sign) { dval(&rv) = -dval(&rv); sign = 0; } #endif /* rv = */ rounded_product(dval(&rv), tens[e]); goto ret; #endif } i = DBL_DIG - nd; if (e <= Ten_pmax + i) { /* A fancier test would sometimes let us do * this for larger i values. */ #ifdef Honor_FLT_ROUNDS /* round correctly FLT_ROUNDS = 2 or 3 */ if (sign) { dval(&rv) = -dval(&rv); sign = 0; } #endif e -= i; dval(&rv) *= tens[i]; #ifdef VAX /* VAX exponent range is so narrow we must * worry about overflow here... */ vax_ovfl_check: word0(&rv) -= P*Exp_msk1; /* rv = */ rounded_product(dval(&rv), tens[e]); if ((word0(&rv) & Exp_mask) > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) goto ovfl; word0(&rv) += P*Exp_msk1; #else /* rv = */ rounded_product(dval(&rv), tens[e]); #endif goto ret; } } #ifndef Inaccurate_Divide else if (e >= -Ten_pmax) { #ifdef Honor_FLT_ROUNDS /* round correctly FLT_ROUNDS = 2 or 3 */ if (sign) { dval(&rv) = -dval(&rv); sign = 0; } #endif /* rv = */ rounded_quotient(dval(&rv), tens[-e]); goto ret; } #endif } e1 += nd - k; #ifdef IEEE_Arith #ifdef SET_INEXACT inexact = 1; if (k <= DBL_DIG) oldinexact = get_inexact(); #endif #ifdef Avoid_Underflow scale = 0; #endif #ifdef Honor_FLT_ROUNDS if (Rounding >= 2) { if (sign) Rounding = Rounding == 2 ? 0 : 2; else if (Rounding != 2) Rounding = 0; } #endif #endif /*IEEE_Arith*/ /* Get starting approximation = rv * 10**e1 */ if (e1 > 0) { if ( (i = e1 & 15) !=0) dval(&rv) *= tens[i]; if (e1 &= ~15) { if (e1 > DBL_MAX_10_EXP) { ovfl: #ifndef NO_ERRNO errno = ERANGE; #endif /* Can't trust HUGE_VAL */ #ifdef IEEE_Arith #ifdef Honor_FLT_ROUNDS switch(Rounding) { case 0: /* toward 0 */ case 3: /* toward -infinity */ word0(&rv) = Big0; word1(&rv) = Big1; break; default: word0(&rv) = Exp_mask; word1(&rv) = 0; } #else /*Honor_FLT_ROUNDS*/ word0(&rv) = Exp_mask; word1(&rv) = 0; #endif /*Honor_FLT_ROUNDS*/ #ifdef SET_INEXACT /* set overflow bit */ dval(&rv0) = 1e300; dval(&rv0) *= dval(&rv0); #endif #else /*IEEE_Arith*/ word0(&rv) = Big0; word1(&rv) = Big1; #endif /*IEEE_Arith*/ if (bd0) goto retfree; goto ret; } e1 >>= 4; for(j = 0; e1 > 1; j++, e1 >>= 1) if (e1 & 1) dval(&rv) *= bigtens[j]; /* The last multiplication could overflow. */ word0(&rv) -= P*Exp_msk1; dval(&rv) *= bigtens[j]; if ((z = word0(&rv) & Exp_mask) > Exp_msk1*(DBL_MAX_EXP+Bias-P)) goto ovfl; if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) { /* set to largest number */ /* (Can't trust DBL_MAX) */ word0(&rv) = Big0; word1(&rv) = Big1; } else word0(&rv) += P*Exp_msk1; } } else if (e1 < 0) { e1 = -e1; if ( (i = e1 & 15) !=0) dval(&rv) /= tens[i]; if (e1 >>= 4) { if (e1 >= 1 << n_bigtens) goto undfl; #ifdef Avoid_Underflow if (e1 & Scale_Bit) scale = 2*P; for(j = 0; e1 > 0; j++, e1 >>= 1) if (e1 & 1) dval(&rv) *= tinytens[j]; if (scale && (j = 2*P + 1 - ((word0(&rv) & Exp_mask) >> Exp_shift)) > 0) { /* scaled rv is denormal; zap j low bits */ if (j >= 32) { word1(&rv) = 0; if (j >= 53) word0(&rv) = (P+2)*Exp_msk1; else word0(&rv) &= 0xffffffff << (j-32); } else word1(&rv) &= 0xffffffff << j; } #else for(j = 0; e1 > 1; j++, e1 >>= 1) if (e1 & 1) dval(&rv) *= tinytens[j]; /* The last multiplication could underflow. */ dval(&rv0) = dval(&rv); dval(&rv) *= tinytens[j]; if (!dval(&rv)) { dval(&rv) = 2.*dval(&rv0); dval(&rv) *= tinytens[j]; #endif if (!dval(&rv)) { undfl: dval(&rv) = 0.; #ifndef NO_ERRNO errno = ERANGE; #endif if (bd0) goto retfree; goto ret; } #ifndef Avoid_Underflow word0(&rv) = Tiny0; word1(&rv) = Tiny1; /* The refinement below will clean * this approximation up. */ } #endif } } /* Now the hard part -- adjusting rv to the correct value.*/ /* Put digits into bd: true value = bd * 10^e */ bd0 = s2b(s0, nd0, nd, y, dplen); for(;;) { bd = Balloc(bd0->k); Bcopy(bd, bd0); bb = d2b(dval(&rv), &bbe, &bbbits); /* rv = bb * 2^bbe */ bs = i2b(1); if (e >= 0) { bb2 = bb5 = 0; bd2 = bd5 = e; } else { bb2 = bb5 = -e; bd2 = bd5 = 0; } if (bbe >= 0) bb2 += bbe; else bd2 -= bbe; bs2 = bb2; #ifdef Honor_FLT_ROUNDS if (Rounding != 1) bs2++; #endif #ifdef Avoid_Underflow j = bbe - scale; i = j + bbbits - 1; /* logb(&rv) */ if (i < Emin) /* denormal */ j += P - Emin; else j = P + 1 - bbbits; #else /*Avoid_Underflow*/ #ifdef Sudden_Underflow #ifdef IBM j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3); #else j = P + 1 - bbbits; #endif #else /*Sudden_Underflow*/ j = bbe; i = j + bbbits - 1; /* logb(&rv) */ if (i < Emin) /* denormal */ j += P - Emin; else j = P + 1 - bbbits; #endif /*Sudden_Underflow*/ #endif /*Avoid_Underflow*/ bb2 += j; bd2 += j; #ifdef Avoid_Underflow bd2 += scale; #endif i = bb2 < bd2 ? bb2 : bd2; if (i > bs2) i = bs2; if (i > 0) { bb2 -= i; bd2 -= i; bs2 -= i; } if (bb5 > 0) { bs = pow5mult(bs, bb5); bb1 = mult(bs, bb); Bfree(bb); bb = bb1; } if (bb2 > 0) bb = lshift(bb, bb2); if (bd5 > 0) bd = pow5mult(bd, bd5); if (bd2 > 0) bd = lshift(bd, bd2); if (bs2 > 0) bs = lshift(bs, bs2); delta = diff(bb, bd); dsign = delta->sign; delta->sign = 0; i = cmp(delta, bs); #ifdef Honor_FLT_ROUNDS if (Rounding != 1) { if (i < 0) { /* Error is less than an ulp */ if (!delta->x[0] && delta->wds <= 1) { /* exact */ #ifdef SET_INEXACT inexact = 0; #endif break; } if (Rounding) { if (dsign) { dval(&adj) = 1.; goto apply_adj; } } else if (!dsign) { dval(&adj) = -1.; if (!word1(&rv) && !(word0(&rv) & Frac_mask)) { y = word0(&rv) & Exp_mask; #ifdef Avoid_Underflow if (!scale || y > 2*P*Exp_msk1) #else if (y) #endif { delta = lshift(delta,Log2P); if (cmp(delta, bs) <= 0) dval(&adj) = -0.5; } } apply_adj: #ifdef Avoid_Underflow if (scale && (y = word0(&rv) & Exp_mask) <= 2*P*Exp_msk1) word0(&adj) += (2*P+1)*Exp_msk1 - y; #else #ifdef Sudden_Underflow if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) { word0(&rv) += P*Exp_msk1; dval(&rv) += adj*ulp(&rv); word0(&rv) -= P*Exp_msk1; } else #endif /*Sudden_Underflow*/ #endif /*Avoid_Underflow*/ dval(&rv) += dval(&adj)*ulp(&rv); } break; } dval(&adj) = ratio(delta, bs); if (dval(&adj) < 1.) dval(&adj) = 1.; if (dval(&adj) <= 0x7ffffffe) { /* dval(&adj) = Rounding ? ceil(&adj) : floor(&adj); */ y = dval(&adj); if (y != dval(&adj)) { if (!((Rounding>>1) ^ dsign)) y++; dval(&adj) = y; } } #ifdef Avoid_Underflow if (scale && (y = word0(&rv) & Exp_mask) <= 2*P*Exp_msk1) word0(&adj) += (2*P+1)*Exp_msk1 - y; #else #ifdef Sudden_Underflow if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) { word0(&rv) += P*Exp_msk1; dval(&adj) *= ulp(&rv); if (dsign) dval(&rv) += adj; else dval(&rv) -= adj; word0(&rv) -= P*Exp_msk1; goto cont; } #endif /*Sudden_Underflow*/ #endif /*Avoid_Underflow*/ dval(&adj) *= ulp(&rv); if (dsign) { if (word0(&rv) == Big0 && word1(&rv) == Big1) goto ovfl; dval(&rv) += dval(&adj); } else dval(&rv) -= dval(&adj); goto cont; } #endif /*Honor_FLT_ROUNDS*/ if (i < 0) { /* Error is less than half an ulp -- check for * special case of mantissa a power of two. */ if (dsign || word1(&rv) || word0(&rv) & Bndry_mask #ifdef IEEE_Arith #ifdef Avoid_Underflow || (word0(&rv) & Exp_mask) <= (2*P+1)*Exp_msk1 #else || (word0(&rv) & Exp_mask) <= Exp_msk1 #endif #endif ) { #ifdef SET_INEXACT if (!delta->x[0] && delta->wds <= 1) inexact = 0; #endif break; } if (!delta->x[0] && delta->wds <= 1) { /* exact result */ #ifdef SET_INEXACT inexact = 0; #endif break; } delta = lshift(delta,Log2P); if (cmp(delta, bs) > 0) goto drop_down; break; } if (i == 0) { /* exactly half-way between */ if (dsign) { if ((word0(&rv) & Bndry_mask1) == Bndry_mask1 && word1(&rv) == ( #ifdef Avoid_Underflow (scale && (y = word0(&rv) & Exp_mask) <= 2*P*Exp_msk1) ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) : #endif 0xffffffff)) { /*boundary case -- increment exponent*/ word0(&rv) = (word0(&rv) & Exp_mask) + Exp_msk1 #ifdef IBM | Exp_msk1 >> 4 #endif ; word1(&rv) = 0; #ifdef Avoid_Underflow dsign = 0; #endif break; } } else if (!(word0(&rv) & Bndry_mask) && !word1(&rv)) { drop_down: /* boundary case -- decrement exponent */ #ifdef Sudden_Underflow /*{{*/ L = word0(&rv) & Exp_mask; #ifdef IBM if (L < Exp_msk1) #else #ifdef Avoid_Underflow if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1)) #else if (L <= Exp_msk1) #endif /*Avoid_Underflow*/ #endif /*IBM*/ goto undfl; L -= Exp_msk1; #else /*Sudden_Underflow}{*/ #ifdef Avoid_Underflow if (scale) { L = word0(&rv) & Exp_mask; if (L <= (2*P+1)*Exp_msk1) { if (L > (P+2)*Exp_msk1) /* round even ==> */ /* accept rv */ break; /* rv = smallest denormal */ goto undfl; } } #endif /*Avoid_Underflow*/ L = (word0(&rv) & Exp_mask) - Exp_msk1; #endif /*Sudden_Underflow}}*/ word0(&rv) = L | Bndry_mask1; word1(&rv) = 0xffffffff; #ifdef IBM goto cont; #else break; #endif } #ifndef ROUND_BIASED if (!(word1(&rv) & LSB)) break; #endif if (dsign) dval(&rv) += ulp(&rv); #ifndef ROUND_BIASED else { dval(&rv) -= ulp(&rv); #ifndef Sudden_Underflow if (!dval(&rv)) goto undfl; #endif } #ifdef Avoid_Underflow dsign = 1 - dsign; #endif #endif break; } if ((aadj = ratio(delta, bs)) <= 2.) { if (dsign) aadj = dval(&aadj1) = 1.; else if (word1(&rv) || word0(&rv) & Bndry_mask) { #ifndef Sudden_Underflow if (word1(&rv) == Tiny1 && !word0(&rv)) goto undfl; #endif aadj = 1.; dval(&aadj1) = -1.; } else { /* special case -- power of FLT_RADIX to be */ /* rounded down... */ if (aadj < 2./FLT_RADIX) aadj = 1./FLT_RADIX; else aadj *= 0.5; dval(&aadj1) = -aadj; } } else { aadj *= 0.5; dval(&aadj1) = dsign ? aadj : -aadj; #ifdef Check_FLT_ROUNDS switch(Rounding) { case 2: /* towards +infinity */ dval(&aadj1) -= 0.5; break; case 0: /* towards 0 */ case 3: /* towards -infinity */ dval(&aadj1) += 0.5; } #else if (Flt_Rounds == 0) dval(&aadj1) += 0.5; #endif /*Check_FLT_ROUNDS*/ } y = word0(&rv) & Exp_mask; /* Check for overflow */ if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) { dval(&rv0) = dval(&rv); word0(&rv) -= P*Exp_msk1; dval(&adj) = dval(&aadj1) * ulp(&rv); dval(&rv) += dval(&adj); if ((word0(&rv) & Exp_mask) >= Exp_msk1*(DBL_MAX_EXP+Bias-P)) { if (word0(&rv0) == Big0 && word1(&rv0) == Big1) goto ovfl; word0(&rv) = Big0; word1(&rv) = Big1; goto cont; } else word0(&rv) += P*Exp_msk1; } else { #ifdef Avoid_Underflow if (scale && y <= 2*P*Exp_msk1) { if (aadj <= 0x7fffffff) { if ((z = aadj) <= 0) z = 1; aadj = z; dval(&aadj1) = dsign ? aadj : -aadj; } word0(&aadj1) += (2*P+1)*Exp_msk1 - y; } dval(&adj) = dval(&aadj1) * ulp(&rv); dval(&rv) += dval(&adj); #else #ifdef Sudden_Underflow if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) { dval(&rv0) = dval(&rv); word0(&rv) += P*Exp_msk1; dval(&adj) = dval(&aadj1) * ulp(&rv); dval(&rv) += adj; #ifdef IBM if ((word0(&rv) & Exp_mask) < P*Exp_msk1) #else if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) #endif { if (word0(&rv0) == Tiny0 && word1(&rv0) == Tiny1) goto undfl; word0(&rv) = Tiny0; word1(&rv) = Tiny1; goto cont; } else word0(&rv) -= P*Exp_msk1; } else { dval(&adj) = dval(&aadj1) * ulp(&rv); dval(&rv) += adj; } #else /*Sudden_Underflow*/ /* Compute dval(&adj) so that the IEEE rounding rules will * correctly round rv + dval(&adj) in some half-way cases. * If rv * ulp(&rv) is denormalized (i.e., * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid * trouble from bits lost to denormalization; * example: 1.2e-307 . */ if (y <= (P-1)*Exp_msk1 && aadj > 1.) { dval(&aadj1) = (double)(int)(aadj + 0.5); if (!dsign) dval(&aadj1) = -dval(&aadj1); } dval(&adj) = dval(&aadj1) * ulp(&rv); dval(&rv) += adj; #endif /*Sudden_Underflow*/ #endif /*Avoid_Underflow*/ } z = word0(&rv) & Exp_mask; #ifndef SET_INEXACT #ifdef Avoid_Underflow if (!scale) #endif if (y == z) { /* Can we stop now? */ L = (Long)aadj; aadj -= L; /* The tolerances below are conservative. */ if (dsign || word1(&rv) || word0(&rv) & Bndry_mask) { if (aadj < .4999999 || aadj > .5000001) break; } else if (aadj < .4999999/FLT_RADIX) break; } #endif cont: Bfree(bb); Bfree(bd); Bfree(bs); Bfree(delta); } #ifdef SET_INEXACT if (inexact) { if (!oldinexact) { word0(&rv0) = Exp_1 + (70 << Exp_shift); word1(&rv0) = 0; dval(&rv0) += 1.; } } else if (!oldinexact) clear_inexact(); #endif #ifdef Avoid_Underflow if (scale) { word0(&rv0) = Exp_1 - 2*P*Exp_msk1; word1(&rv0) = 0; dval(&rv) *= dval(&rv0); #ifndef NO_ERRNO /* try to avoid the bug of testing an 8087 register value */ #if defined(IEEE_Arith) && __DARWIN_UNIX03 if (!(word0(&rv) & Exp_mask)) #else if (word0(&rv) == 0 && word1(&rv) == 0) #endif errno = ERANGE; #endif } #endif /* Avoid_Underflow */ #ifdef SET_INEXACT if (inexact && !(word0(&rv) & Exp_mask)) { /* set underflow bit */ dval(&rv0) = 1e-300; dval(&rv0) *= dval(&rv0); } #endif retfree: Bfree(bb); Bfree(bd); Bfree(bs); Bfree(bd0); Bfree(delta); ret: if (se) *se = (char *)s; if (strunc) #ifdef FREE FREE(strunc); #else free(strunc); #endif return sign ? -dval(&rv) : dval(&rv); } double strtod #ifdef KR_headers (s00, se) CONST char *s00; char **se; #else (CONST char *s00, char **se) #endif { return strtod_l(s00, se, __current_locale()); } |