/* mpfr_get_decimal64 -- convert a multiple precision floating-point number to a IEEE 754r decimal64 float See http://gcc.gnu.org/ml/gcc/2006-06/msg00691.html, http://gcc.gnu.org/onlinedocs/gcc/Decimal-Float.html, and TR 24732 . Copyright 2006-2015 Free Software Foundation, Inc. Contributed by the AriC and Caramel projects, INRIA. This file is part of the GNU MPFR Library. The GNU MPFR Library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version. The GNU MPFR 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 Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */ #include /* for strtol */ #include "mpfr-impl.h" #define ISDIGIT(c) ('0' <= c && c <= '9') #ifdef MPFR_WANT_DECIMAL_FLOATS #ifndef DEC64_MAX # define DEC64_MAX 9.999999999999999E384dd #endif #ifdef DPD_FORMAT static int T[1000] = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 10, 11, 42, 43, 74, 75, 106, 107, 78, 79, 26, 27, 58, 59, 90, 91, 122, 123, 94, 95, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 138, 139, 170, 171, 202, 203, 234, 235, 206, 207, 154, 155, 186, 187, 218, 219, 250, 251, 222, 223, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 266, 267, 298, 299, 330, 331, 362, 363, 334, 335, 282, 283, 314, 315, 346, 347, 378, 379, 350, 351, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 394, 395, 426, 427, 458, 459, 490, 491, 462, 463, 410, 411, 442, 443, 474, 475, 506, 507, 478, 479, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 592, 593, 594, 595, 596, 597, 598, 599, 600, 601, 608, 609, 610, 611, 612, 613, 614, 615, 616, 617, 624, 625, 626, 627, 628, 629, 630, 631, 632, 633, 522, 523, 554, 555, 586, 587, 618, 619, 590, 591, 538, 539, 570, 571, 602, 603, 634, 635, 606, 607, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 656, 657, 658, 659, 660, 661, 662, 663, 664, 665, 672, 673, 674, 675, 676, 677, 678, 679, 680, 681, 688, 689, 690, 691, 692, 693, 694, 695, 696, 697, 704, 705, 706, 707, 708, 709, 710, 711, 712, 713, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 736, 737, 738, 739, 740, 741, 742, 743, 744, 745, 752, 753, 754, 755, 756, 757, 758, 759, 760, 761, 650, 651, 682, 683, 714, 715, 746, 747, 718, 719, 666, 667, 698, 699, 730, 731, 762, 763, 734, 735, 768, 769, 770, 771, 772, 773, 774, 775, 776, 777, 784, 785, 786, 787, 788, 789, 790, 791, 792, 793, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 816, 817, 818, 819, 820, 821, 822, 823, 824, 825, 832, 833, 834, 835, 836, 837, 838, 839, 840, 841, 848, 849, 850, 851, 852, 853, 854, 855, 856, 857, 864, 865, 866, 867, 868, 869, 870, 871, 872, 873, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 778, 779, 810, 811, 842, 843, 874, 875, 846, 847, 794, 795, 826, 827, 858, 859, 890, 891, 862, 863, 896, 897, 898, 899, 900, 901, 902, 903, 904, 905, 912, 913, 914, 915, 916, 917, 918, 919, 920, 921, 928, 929, 930, 931, 932, 933, 934, 935, 936, 937, 944, 945, 946, 947, 948, 949, 950, 951, 952, 953, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 976, 977, 978, 979, 980, 981, 982, 983, 984, 985, 992, 993, 994, 995, 996, 997, 998, 999, 1000, 1001, 1008, 1009, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 906, 907, 938, 939, 970, 971, 1002, 1003, 974, 975, 922, 923, 954, 955, 986, 987, 1018, 1019, 990, 991, 12, 13, 268, 269, 524, 525, 780, 781, 46, 47, 28, 29, 284, 285, 540, 541, 796, 797, 62, 63, 44, 45, 300, 301, 556, 557, 812, 813, 302, 303, 60, 61, 316, 317, 572, 573, 828, 829, 318, 319, 76, 77, 332, 333, 588, 589, 844, 845, 558, 559, 92, 93, 348, 349, 604, 605, 860, 861, 574, 575, 108, 109, 364, 365, 620, 621, 876, 877, 814, 815, 124, 125, 380, 381, 636, 637, 892, 893, 830, 831, 14, 15, 270, 271, 526, 527, 782, 783, 110, 111, 30, 31, 286, 287, 542, 543, 798, 799, 126, 127, 140, 141, 396, 397, 652, 653, 908, 909, 174, 175, 156, 157, 412, 413, 668, 669, 924, 925, 190, 191, 172, 173, 428, 429, 684, 685, 940, 941, 430, 431, 188, 189, 444, 445, 700, 701, 956, 957, 446, 447, 204, 205, 460, 461, 716, 717, 972, 973, 686, 687, 220, 221, 476, 477, 732, 733, 988, 989, 702, 703, 236, 237, 492, 493, 748, 749, 1004, 1005, 942, 943, 252, 253, 508, 509, 764, 765, 1020, 1021, 958, 959, 142, 143, 398, 399, 654, 655, 910, 911, 238, 239, 158, 159, 414, 415, 670, 671, 926, 927, 254, 255}; #endif /* construct a decimal64 NaN */ static _Decimal64 get_decimal64_nan (void) { union ieee_double_extract x; union ieee_double_decimal64 y; x.s.exp = 1984; /* G[0]..G[4] = 11111: quiet NaN */ y.d = x.d; return y.d64; } /* construct the decimal64 Inf with given sign */ static _Decimal64 get_decimal64_inf (int negative) { union ieee_double_extract x; union ieee_double_decimal64 y; x.s.sig = (negative) ? 1 : 0; x.s.exp = 1920; /* G[0]..G[4] = 11110: Inf */ y.d = x.d; return y.d64; } /* construct the decimal64 zero with given sign */ static _Decimal64 get_decimal64_zero (int negative) { union ieee_double_decimal64 y; /* zero has the same representation in binary64 and decimal64 */ y.d = negative ? DBL_NEG_ZERO : 0.0; return y.d64; } /* construct the decimal64 smallest non-zero with given sign */ static _Decimal64 get_decimal64_min (int negative) { return negative ? - 1E-398dd : 1E-398dd; } /* construct the decimal64 largest finite number with given sign */ static _Decimal64 get_decimal64_max (int negative) { return negative ? - DEC64_MAX : DEC64_MAX; } /* one-to-one conversion: s is a decimal string representing a number x = m * 10^e which must be exactly representable in the decimal64 format, i.e. (a) the mantissa m has at most 16 decimal digits (b1) -383 <= e <= 384 with m integer multiple of 10^(-15), |m| < 10 (b2) or -398 <= e <= 369 with m integer, |m| < 10^16. Assumes s is neither NaN nor +Inf nor -Inf. */ static _Decimal64 string_to_Decimal64 (char *s) { long int exp = 0; char m[17]; long n = 0; /* mantissa length */ char *endptr[1]; union ieee_double_extract x; union ieee_double_decimal64 y; #ifdef DPD_FORMAT unsigned int G, d1, d2, d3, d4, d5; #endif /* read sign */ if (*s == '-') { x.s.sig = 1; s ++; } else x.s.sig = 0; /* read mantissa */ while (ISDIGIT (*s)) m[n++] = *s++; exp = n; if (*s == '.') { s ++; while (ISDIGIT (*s)) m[n++] = *s++; } /* we have exp digits before decimal point, and a total of n digits */ exp -= n; /* we will consider an integer mantissa */ MPFR_ASSERTN(n <= 16); if (*s == 'E' || *s == 'e') exp += strtol (s + 1, endptr, 10); else *endptr = s; MPFR_ASSERTN(**endptr == '\0'); MPFR_ASSERTN(-398 <= exp && exp <= (long) (385 - n)); while (n < 16) { m[n++] = '0'; exp --; } /* now n=16 and -398 <= exp <= 369 */ m[n] = '\0'; /* compute biased exponent */ exp += 398; MPFR_ASSERTN(exp >= -15); if (exp < 0) { int i; n = -exp; /* check the last n digits of the mantissa are zero */ for (i = 1; i <= n; i++) MPFR_ASSERTN(m[16 - n] == '0'); /* shift the first (16-n) digits to the right */ for (i = 16 - n - 1; i >= 0; i--) m[i + n] = m[i]; /* zero the first n digits */ for (i = 0; i < n; i ++) m[i] = '0'; exp = 0; } /* now convert to DPD or BID */ #ifdef DPD_FORMAT #define CH(d) (d - '0') if (m[0] >= '8') G = (3 << 11) | ((exp & 768) << 1) | ((CH(m[0]) & 1) << 8); else G = ((exp & 768) << 3) | (CH(m[0]) << 8); /* now the most 5 significant bits of G are filled */ G |= exp & 255; d1 = T[100 * CH(m[1]) + 10 * CH(m[2]) + CH(m[3])]; /* 10-bit encoding */ d2 = T[100 * CH(m[4]) + 10 * CH(m[5]) + CH(m[6])]; /* 10-bit encoding */ d3 = T[100 * CH(m[7]) + 10 * CH(m[8]) + CH(m[9])]; /* 10-bit encoding */ d4 = T[100 * CH(m[10]) + 10 * CH(m[11]) + CH(m[12])]; /* 10-bit encoding */ d5 = T[100 * CH(m[13]) + 10 * CH(m[14]) + CH(m[15])]; /* 10-bit encoding */ x.s.exp = G >> 2; x.s.manh = ((G & 3) << 18) | (d1 << 8) | (d2 >> 2); x.s.manl = (d2 & 3) << 30; x.s.manl |= (d3 << 20) | (d4 << 10) | d5; #else /* BID format */ { mp_size_t rn; mp_limb_t rp[2]; int case_i = strcmp (m, "9007199254740992") < 0; for (n = 0; n < 16; n++) m[n] -= '0'; rn = mpn_set_str (rp, (unsigned char *) m, 16, 10); if (rn == 1) rp[1] = 0; #if GMP_NUMB_BITS > 32 rp[1] = rp[1] << (GMP_NUMB_BITS - 32); rp[1] |= rp[0] >> 32; rp[0] &= 4294967295UL; #endif if (case_i) { /* s < 2^53: case i) */ x.s.exp = exp << 1; x.s.manl = rp[0]; /* 32 bits */ x.s.manh = rp[1] & 1048575; /* 20 low bits */ x.s.exp |= rp[1] >> 20; /* 1 bit */ } else /* s >= 2^53: case ii) */ { x.s.exp = 1536 | (exp >> 1); x.s.manl = rp[0]; x.s.manh = (rp[1] ^ 2097152) | ((exp & 1) << 19); } } #endif /* DPD_FORMAT */ y.d = x.d; return y.d64; } _Decimal64 mpfr_get_decimal64 (mpfr_srcptr src, mpfr_rnd_t rnd_mode) { int negative; mpfr_exp_t e; /* the encoding of NaN, Inf, zero is the same under DPD or BID */ if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (src))) { if (MPFR_IS_NAN (src)) return get_decimal64_nan (); negative = MPFR_IS_NEG (src); if (MPFR_IS_INF (src)) return get_decimal64_inf (negative); MPFR_ASSERTD (MPFR_IS_ZERO(src)); return get_decimal64_zero (negative); } e = MPFR_GET_EXP (src); negative = MPFR_IS_NEG (src); if (MPFR_UNLIKELY(rnd_mode == MPFR_RNDA)) rnd_mode = negative ? MPFR_RNDD : MPFR_RNDU; /* the smallest decimal64 number is 10^(-398), with 2^(-1323) < 10^(-398) < 2^(-1322) */ if (MPFR_UNLIKELY (e < -1323)) /* src <= 2^(-1324) < 1/2*10^(-398) */ { if (rnd_mode == MPFR_RNDZ || rnd_mode == MPFR_RNDN || (rnd_mode == MPFR_RNDD && negative == 0) || (rnd_mode == MPFR_RNDU && negative != 0)) return get_decimal64_zero (negative); else /* return the smallest non-zero number */ return get_decimal64_min (negative); } /* the largest decimal64 number is just below 10^(385) < 2^1279 */ else if (MPFR_UNLIKELY (e > 1279)) /* then src >= 2^1279 */ { if (rnd_mode == MPFR_RNDZ || (rnd_mode == MPFR_RNDU && negative != 0) || (rnd_mode == MPFR_RNDD && negative == 0)) return get_decimal64_max (negative); else return get_decimal64_inf (negative); } else { /* we need to store the sign (1), the mantissa (16), and the terminating character, thus we need at least 18 characters in s */ char s[23]; mpfr_get_str (s, &e, 10, 16, src, rnd_mode); /* the smallest normal number is 1.000...000E-383, which corresponds to s=[0.]1000...000 and e=-382 */ if (e < -382) { /* the smallest subnormal number is 0.000...001E-383 = 1E-398, which corresponds to s=[0.]1000...000 and e=-397 */ if (e < -397) { if (rnd_mode == MPFR_RNDN && e == -398) { /* If 0.5E-398 < |src| < 1E-398 (smallest subnormal), src should round to +/- 1E-398 in MPFR_RNDN. */ mpfr_get_str (s, &e, 10, 1, src, MPFR_RNDA); return e == -398 && s[negative] <= '5' ? get_decimal64_zero (negative) : get_decimal64_min (negative); } if (rnd_mode == MPFR_RNDZ || rnd_mode == MPFR_RNDN || (rnd_mode == MPFR_RNDD && negative == 0) || (rnd_mode == MPFR_RNDU && negative != 0)) return get_decimal64_zero (negative); else /* return the smallest non-zero number */ return get_decimal64_min (negative); } else { mpfr_exp_t e2; long digits = 16 - (-382 - e); /* if e = -397 then 16 - (-382 - e) = 1 */ mpfr_get_str (s, &e2, 10, digits, src, rnd_mode); /* Warning: we can have e2 = e + 1 here, when rounding to nearest or away from zero. */ s[negative + digits] = 'E'; sprintf (s + negative + digits + 1, "%ld", (long int)e2 - digits); return string_to_Decimal64 (s); } } /* the largest number is 9.999...999E+384, which corresponds to s=[0.]9999...999 and e=385 */ else if (e > 385) { if (rnd_mode == MPFR_RNDZ || (rnd_mode == MPFR_RNDU && negative != 0) || (rnd_mode == MPFR_RNDD && negative == 0)) return get_decimal64_max (negative); else return get_decimal64_inf (negative); } else /* -382 <= e <= 385 */ { s[16 + negative] = 'E'; sprintf (s + 17 + negative, "%ld", (long int)e - 16); return string_to_Decimal64 (s); } } } #endif /* MPFR_WANT_DECIMAL_FLOATS */