Mercurial > hg > CbC > CbC_gcc
diff libgcc/config/libbid/bid_round.c @ 0:a06113de4d67
first commit
| author | kent <kent@cr.ie.u-ryukyu.ac.jp> |
|---|---|
| date | Fri, 17 Jul 2009 14:47:48 +0900 |
| parents | |
| children | 04ced10e8804 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/libgcc/config/libbid/bid_round.c Fri Jul 17 14:47:48 2009 +0900 @@ -0,0 +1,1049 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC 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 General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +<http://www.gnu.org/licenses/>. */ + +/***************************************************************************** + * + * BID64 encoding: + * **************************************** + * 63 62 53 52 0 + * |---|------------------|--------------| + * | S | Biased Exp (E) | Coeff (c) | + * |---|------------------|--------------| + * + * bias = 398 + * number = (-1)^s * 10^(E-398) * c + * coefficient range - 0 to (2^53)-1 + * COEFF_MAX = 2^53-1 = 9007199254740991 + * + ***************************************************************************** + * + * BID128 encoding: + * 1-bit sign + * 14-bit biased exponent in [0x21, 0x3020] = [33, 12320] + * unbiased exponent in [-6176, 6111]; exponent bias = 6176 + * 113-bit unsigned binary integer coefficient (49-bit high + 64-bit low) + * Note: 10^34-1 ~ 2^112.945555... < 2^113 => coefficient fits in 113 bits + * + * Note: assume invalid encodings are not passed to this function + * + * Round a number C with q decimal digits, represented as a binary integer + * to q - x digits. Six different routines are provided for different values + * of q. The maximum value of q used in the library is q = 3 * P - 1 where + * P = 16 or P = 34 (so q <= 111 decimal digits). + * The partitioning is based on the following, where Kx is the scaled + * integer representing the value of 10^(-x) rounded up to a number of bits + * sufficient to ensure correct rounding: + * + * -------------------------------------------------------------------------- + * q x max. value of a max number min. number + * of bits in C of bits in Kx + * -------------------------------------------------------------------------- + * + * GROUP 1: 64 bits + * round64_2_18 () + * + * 2 [1,1] 10^1 - 1 < 2^3.33 4 4 + * ... ... ... ... ... + * 18 [1,17] 10^18 - 1 < 2^59.80 60 61 + * + * GROUP 2: 128 bits + * round128_19_38 () + * + * 19 [1,18] 10^19 - 1 < 2^63.11 64 65 + * 20 [1,19] 10^20 - 1 < 2^66.44 67 68 + * ... ... ... ... ... + * 38 [1,37] 10^38 - 1 < 2^126.24 127 128 + * + * GROUP 3: 192 bits + * round192_39_57 () + * + * 39 [1,38] 10^39 - 1 < 2^129.56 130 131 + * ... ... ... ... ... + * 57 [1,56] 10^57 - 1 < 2^189.35 190 191 + * + * GROUP 4: 256 bits + * round256_58_76 () + * + * 58 [1,57] 10^58 - 1 < 2^192.68 193 194 + * ... ... ... ... ... + * 76 [1,75] 10^76 - 1 < 2^252.47 253 254 + * + * GROUP 5: 320 bits + * round320_77_96 () + * + * 77 [1,76] 10^77 - 1 < 2^255.79 256 257 + * 78 [1,77] 10^78 - 1 < 2^259.12 260 261 + * ... ... ... ... ... + * 96 [1,95] 10^96 - 1 < 2^318.91 319 320 + * + * GROUP 6: 384 bits + * round384_97_115 () + * + * 97 [1,96] 10^97 - 1 < 2^322.23 323 324 + * ... ... ... ... ... + * 115 [1,114] 10^115 - 1 < 2^382.03 383 384 + * + ****************************************************************************/ + +#include "bid_internal.h" + +void +round64_2_18 (int q, + int x, + UINT64 C, + UINT64 * ptr_Cstar, + int *incr_exp, + int *ptr_is_midpoint_lt_even, + int *ptr_is_midpoint_gt_even, + int *ptr_is_inexact_lt_midpoint, + int *ptr_is_inexact_gt_midpoint) { + + UINT128 P128; + UINT128 fstar; + UINT64 Cstar; + UINT64 tmp64; + int shift; + int ind; + + // Note: + // In round128_2_18() positive numbers with 2 <= q <= 18 will be + // rounded to nearest only for 1 <= x <= 3: + // x = 1 or x = 2 when q = 17 + // x = 2 or x = 3 when q = 18 + // However, for generality and possible uses outside the frame of IEEE 754R + // this implementation works for 1 <= x <= q - 1 + + // assume *ptr_is_midpoint_lt_even, *ptr_is_midpoint_gt_even, + // *ptr_is_inexact_lt_midpoint, and *ptr_is_inexact_gt_midpoint are + // initialized to 0 by the caller + + // round a number C with q decimal digits, 2 <= q <= 18 + // to q - x digits, 1 <= x <= 17 + // C = C + 1/2 * 10^x where the result C fits in 64 bits + // (because the largest value is 999999999999999999 + 50000000000000000 = + // 0x0e92596fd628ffff, which fits in 60 bits) + ind = x - 1; // 0 <= ind <= 16 + C = C + midpoint64[ind]; + // kx ~= 10^(-x), kx = Kx64[ind] * 2^(-Ex), 0 <= ind <= 16 + // P128 = (C + 1/2 * 10^x) * kx * 2^Ex = (C + 1/2 * 10^x) * Kx + // the approximation kx of 10^(-x) was rounded up to 64 bits + __mul_64x64_to_128MACH (P128, C, Kx64[ind]); + // calculate C* = floor (P128) and f* + // Cstar = P128 >> Ex + // fstar = low Ex bits of P128 + shift = Ex64m64[ind]; // in [3, 56] + Cstar = P128.w[1] >> shift; + fstar.w[1] = P128.w[1] & mask64[ind]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mxtrunc64[ind], e.g. + // if x=1, T*=ten2mxtrunc64[0]=0xcccccccccccccccc + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has q - x decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has q - x decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has q - x decimal digits, + // correct by Property 1) + // in the caling function n = C* * 10^(e+x) + + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (fstar.w[1] > half64[ind] || + (fstar.w[1] == half64[ind] && fstar.w[0])) { + // f* > 1/2 and the result may be exact + // Calculate f* - 1/2 + tmp64 = fstar.w[1] - half64[ind]; + if (tmp64 || fstar.w[0] > ten2mxtrunc64[ind]) { // f* - 1/2 > 10^(-x) + *ptr_is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + *ptr_is_inexact_gt_midpoint = 1; + } + // check for midpoints (could do this before determining inexactness) + if (fstar.w[1] == 0 && fstar.w[0] <= ten2mxtrunc64[ind]) { + // the result is a midpoint + if (Cstar & 0x01) { // Cstar is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result may be 0 + Cstar--; // Cstar is now even + *ptr_is_midpoint_gt_even = 1; + *ptr_is_inexact_lt_midpoint = 0; + *ptr_is_inexact_gt_midpoint = 0; + } else { // else MP in [ODD, EVEN] + *ptr_is_midpoint_lt_even = 1; + *ptr_is_inexact_lt_midpoint = 0; + *ptr_is_inexact_gt_midpoint = 0; + } + } + // check for rounding overflow, which occurs if Cstar = 10^(q-x) + ind = q - x; // 1 <= ind <= q - 1 + if (Cstar == ten2k64[ind]) { // if Cstar = 10^(q-x) + Cstar = ten2k64[ind - 1]; // Cstar = 10^(q-x-1) + *incr_exp = 1; + } else { // 10^33 <= Cstar <= 10^34 - 1 + *incr_exp = 0; + } + *ptr_Cstar = Cstar; +} + + +void +round128_19_38 (int q, + int x, + UINT128 C, + UINT128 * ptr_Cstar, + int *incr_exp, + int *ptr_is_midpoint_lt_even, + int *ptr_is_midpoint_gt_even, + int *ptr_is_inexact_lt_midpoint, + int *ptr_is_inexact_gt_midpoint) { + + UINT256 P256; + UINT256 fstar; + UINT128 Cstar; + UINT64 tmp64; + int shift; + int ind; + + // Note: + // In round128_19_38() positive numbers with 19 <= q <= 38 will be + // rounded to nearest only for 1 <= x <= 23: + // x = 3 or x = 4 when q = 19 + // x = 4 or x = 5 when q = 20 + // ... + // x = 18 or x = 19 when q = 34 + // x = 1 or x = 2 or x = 19 or x = 20 when q = 35 + // x = 2 or x = 3 or x = 20 or x = 21 when q = 36 + // x = 3 or x = 4 or x = 21 or x = 22 when q = 37 + // x = 4 or x = 5 or x = 22 or x = 23 when q = 38 + // However, for generality and possible uses outside the frame of IEEE 754R + // this implementation works for 1 <= x <= q - 1 + + // assume *ptr_is_midpoint_lt_even, *ptr_is_midpoint_gt_even, + // *ptr_is_inexact_lt_midpoint, and *ptr_is_inexact_gt_midpoint are + // initialized to 0 by the caller + + // round a number C with q decimal digits, 19 <= q <= 38 + // to q - x digits, 1 <= x <= 37 + // C = C + 1/2 * 10^x where the result C fits in 128 bits + // (because the largest value is 99999999999999999999999999999999999999 + + // 5000000000000000000000000000000000000 = + // 0x4efe43b0c573e7e68a043d8fffffffff, which fits is 127 bits) + + ind = x - 1; // 0 <= ind <= 36 + if (ind <= 18) { // if 0 <= ind <= 18 + tmp64 = C.w[0]; + C.w[0] = C.w[0] + midpoint64[ind]; + if (C.w[0] < tmp64) + C.w[1]++; + } else { // if 19 <= ind <= 37 + tmp64 = C.w[0]; + C.w[0] = C.w[0] + midpoint128[ind - 19].w[0]; + if (C.w[0] < tmp64) { + C.w[1]++; + } + C.w[1] = C.w[1] + midpoint128[ind - 19].w[1]; + } + // kx ~= 10^(-x), kx = Kx128[ind] * 2^(-Ex), 0 <= ind <= 36 + // P256 = (C + 1/2 * 10^x) * kx * 2^Ex = (C + 1/2 * 10^x) * Kx + // the approximation kx of 10^(-x) was rounded up to 128 bits + __mul_128x128_to_256 (P256, C, Kx128[ind]); + // calculate C* = floor (P256) and f* + // Cstar = P256 >> Ex + // fstar = low Ex bits of P256 + shift = Ex128m128[ind]; // in [2, 63] but have to consider two cases + if (ind <= 18) { // if 0 <= ind <= 18 + Cstar.w[0] = (P256.w[2] >> shift) | (P256.w[3] << (64 - shift)); + Cstar.w[1] = (P256.w[3] >> shift); + fstar.w[0] = P256.w[0]; + fstar.w[1] = P256.w[1]; + fstar.w[2] = P256.w[2] & mask128[ind]; + fstar.w[3] = 0x0ULL; + } else { // if 19 <= ind <= 37 + Cstar.w[0] = P256.w[3] >> shift; + Cstar.w[1] = 0x0ULL; + fstar.w[0] = P256.w[0]; + fstar.w[1] = P256.w[1]; + fstar.w[2] = P256.w[2]; + fstar.w[3] = P256.w[3] & mask128[ind]; + } + // the top Ex bits of 10^(-x) are T* = ten2mxtrunc64[ind], e.g. + // if x=1, T*=ten2mxtrunc128[0]=0xcccccccccccccccccccccccccccccccc + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has q - x decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has q - x decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has q - x decimal digits, + // correct by Property 1) + // in the caling function n = C* * 10^(e+x) + + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind <= 18) { // if 0 <= ind <= 18 + if (fstar.w[2] > half128[ind] || + (fstar.w[2] == half128[ind] && (fstar.w[1] || fstar.w[0]))) { + // f* > 1/2 and the result may be exact + // Calculate f* - 1/2 + tmp64 = fstar.w[2] - half128[ind]; + if (tmp64 || fstar.w[1] > ten2mxtrunc128[ind].w[1] || (fstar.w[1] == ten2mxtrunc128[ind].w[1] && fstar.w[0] > ten2mxtrunc128[ind].w[0])) { // f* - 1/2 > 10^(-x) + *ptr_is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + *ptr_is_inexact_gt_midpoint = 1; + } + } else { // if 19 <= ind <= 37 + if (fstar.w[3] > half128[ind] || (fstar.w[3] == half128[ind] && + (fstar.w[2] || fstar.w[1] + || fstar.w[0]))) { + // f* > 1/2 and the result may be exact + // Calculate f* - 1/2 + tmp64 = fstar.w[3] - half128[ind]; + if (tmp64 || fstar.w[2] || fstar.w[1] > ten2mxtrunc128[ind].w[1] || (fstar.w[1] == ten2mxtrunc128[ind].w[1] && fstar.w[0] > ten2mxtrunc128[ind].w[0])) { // f* - 1/2 > 10^(-x) + *ptr_is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + *ptr_is_inexact_gt_midpoint = 1; + } + } + // check for midpoints (could do this before determining inexactness) + if (fstar.w[3] == 0 && fstar.w[2] == 0 && + (fstar.w[1] < ten2mxtrunc128[ind].w[1] || + (fstar.w[1] == ten2mxtrunc128[ind].w[1] && + fstar.w[0] <= ten2mxtrunc128[ind].w[0]))) { + // the result is a midpoint + if (Cstar.w[0] & 0x01) { // Cstar is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result may be 0 + Cstar.w[0]--; // Cstar is now even + if (Cstar.w[0] == 0xffffffffffffffffULL) { + Cstar.w[1]--; + } + *ptr_is_midpoint_gt_even = 1; + *ptr_is_inexact_lt_midpoint = 0; + *ptr_is_inexact_gt_midpoint = 0; + } else { // else MP in [ODD, EVEN] + *ptr_is_midpoint_lt_even = 1; + *ptr_is_inexact_lt_midpoint = 0; + *ptr_is_inexact_gt_midpoint = 0; + } + } + // check for rounding overflow, which occurs if Cstar = 10^(q-x) + ind = q - x; // 1 <= ind <= q - 1 + if (ind <= 19) { + if (Cstar.w[1] == 0x0ULL && Cstar.w[0] == ten2k64[ind]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k64[ind - 1]; // Cstar = 10^(q-x-1) + *incr_exp = 1; + } else { + *incr_exp = 0; + } + } else if (ind == 20) { + // if ind = 20 + if (Cstar.w[1] == ten2k128[0].w[1] + && Cstar.w[0] == ten2k128[0].w[0]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k64[19]; // Cstar = 10^(q-x-1) + Cstar.w[1] = 0x0ULL; + *incr_exp = 1; + } else { + *incr_exp = 0; + } + } else { // if 21 <= ind <= 37 + if (Cstar.w[1] == ten2k128[ind - 20].w[1] && + Cstar.w[0] == ten2k128[ind - 20].w[0]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k128[ind - 21].w[0]; // Cstar = 10^(q-x-1) + Cstar.w[1] = ten2k128[ind - 21].w[1]; + *incr_exp = 1; + } else { + *incr_exp = 0; + } + } + ptr_Cstar->w[1] = Cstar.w[1]; + ptr_Cstar->w[0] = Cstar.w[0]; +} + + +void +round192_39_57 (int q, + int x, + UINT192 C, + UINT192 * ptr_Cstar, + int *incr_exp, + int *ptr_is_midpoint_lt_even, + int *ptr_is_midpoint_gt_even, + int *ptr_is_inexact_lt_midpoint, + int *ptr_is_inexact_gt_midpoint) { + + UINT384 P384; + UINT384 fstar; + UINT192 Cstar; + UINT64 tmp64; + int shift; + int ind; + + // Note: + // In round192_39_57() positive numbers with 39 <= q <= 57 will be + // rounded to nearest only for 5 <= x <= 42: + // x = 23 or x = 24 or x = 5 or x = 6 when q = 39 + // x = 24 or x = 25 or x = 6 or x = 7 when q = 40 + // ... + // x = 41 or x = 42 or x = 23 or x = 24 when q = 57 + // However, for generality and possible uses outside the frame of IEEE 754R + // this implementation works for 1 <= x <= q - 1 + + // assume *ptr_is_midpoint_lt_even, *ptr_is_midpoint_gt_even, + // *ptr_is_inexact_lt_midpoint, and *ptr_is_inexact_gt_midpoint are + // initialized to 0 by the caller + + // round a number C with q decimal digits, 39 <= q <= 57 + // to q - x digits, 1 <= x <= 56 + // C = C + 1/2 * 10^x where the result C fits in 192 bits + // (because the largest value is + // 999999999999999999999999999999999999999999999999999999999 + + // 50000000000000000000000000000000000000000000000000000000 = + // 0x2ad282f212a1da846afdaf18c034ff09da7fffffffffffff, which fits in 190 bits) + ind = x - 1; // 0 <= ind <= 55 + if (ind <= 18) { // if 0 <= ind <= 18 + tmp64 = C.w[0]; + C.w[0] = C.w[0] + midpoint64[ind]; + if (C.w[0] < tmp64) { + C.w[1]++; + if (C.w[1] == 0x0) { + C.w[2]++; + } + } + } else if (ind <= 37) { // if 19 <= ind <= 37 + tmp64 = C.w[0]; + C.w[0] = C.w[0] + midpoint128[ind - 19].w[0]; + if (C.w[0] < tmp64) { + C.w[1]++; + if (C.w[1] == 0x0) { + C.w[2]++; + } + } + tmp64 = C.w[1]; + C.w[1] = C.w[1] + midpoint128[ind - 19].w[1]; + if (C.w[1] < tmp64) { + C.w[2]++; + } + } else { // if 38 <= ind <= 57 (actually ind <= 55) + tmp64 = C.w[0]; + C.w[0] = C.w[0] + midpoint192[ind - 38].w[0]; + if (C.w[0] < tmp64) { + C.w[1]++; + if (C.w[1] == 0x0ull) { + C.w[2]++; + } + } + tmp64 = C.w[1]; + C.w[1] = C.w[1] + midpoint192[ind - 38].w[1]; + if (C.w[1] < tmp64) { + C.w[2]++; + } + C.w[2] = C.w[2] + midpoint192[ind - 38].w[2]; + } + // kx ~= 10^(-x), kx = Kx192[ind] * 2^(-Ex), 0 <= ind <= 55 + // P384 = (C + 1/2 * 10^x) * kx * 2^Ex = (C + 1/2 * 10^x) * Kx + // the approximation kx of 10^(-x) was rounded up to 192 bits + __mul_192x192_to_384 (P384, C, Kx192[ind]); + // calculate C* = floor (P384) and f* + // Cstar = P384 >> Ex + // fstar = low Ex bits of P384 + shift = Ex192m192[ind]; // in [1, 63] but have to consider three cases + if (ind <= 18) { // if 0 <= ind <= 18 + Cstar.w[2] = (P384.w[5] >> shift); + Cstar.w[1] = (P384.w[5] << (64 - shift)) | (P384.w[4] >> shift); + Cstar.w[0] = (P384.w[4] << (64 - shift)) | (P384.w[3] >> shift); + fstar.w[5] = 0x0ULL; + fstar.w[4] = 0x0ULL; + fstar.w[3] = P384.w[3] & mask192[ind]; + fstar.w[2] = P384.w[2]; + fstar.w[1] = P384.w[1]; + fstar.w[0] = P384.w[0]; + } else if (ind <= 37) { // if 19 <= ind <= 37 + Cstar.w[2] = 0x0ULL; + Cstar.w[1] = P384.w[5] >> shift; + Cstar.w[0] = (P384.w[5] << (64 - shift)) | (P384.w[4] >> shift); + fstar.w[5] = 0x0ULL; + fstar.w[4] = P384.w[4] & mask192[ind]; + fstar.w[3] = P384.w[3]; + fstar.w[2] = P384.w[2]; + fstar.w[1] = P384.w[1]; + fstar.w[0] = P384.w[0]; + } else { // if 38 <= ind <= 57 + Cstar.w[2] = 0x0ULL; + Cstar.w[1] = 0x0ULL; + Cstar.w[0] = P384.w[5] >> shift; + fstar.w[5] = P384.w[5] & mask192[ind]; + fstar.w[4] = P384.w[4]; + fstar.w[3] = P384.w[3]; + fstar.w[2] = P384.w[2]; + fstar.w[1] = P384.w[1]; + fstar.w[0] = P384.w[0]; + } + + // the top Ex bits of 10^(-x) are T* = ten2mxtrunc192[ind], e.g. if x=1, + // T*=ten2mxtrunc192[0]=0xcccccccccccccccccccccccccccccccccccccccccccccccc + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has q - x decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has q - x decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has q - x decimal digits, + // correct by Property 1) + // in the caling function n = C* * 10^(e+x) + + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind <= 18) { // if 0 <= ind <= 18 + if (fstar.w[3] > half192[ind] || (fstar.w[3] == half192[ind] && + (fstar.w[2] || fstar.w[1] + || fstar.w[0]))) { + // f* > 1/2 and the result may be exact + // Calculate f* - 1/2 + tmp64 = fstar.w[3] - half192[ind]; + if (tmp64 || fstar.w[2] > ten2mxtrunc192[ind].w[2] || (fstar.w[2] == ten2mxtrunc192[ind].w[2] && fstar.w[1] > ten2mxtrunc192[ind].w[1]) || (fstar.w[2] == ten2mxtrunc192[ind].w[2] && fstar.w[1] == ten2mxtrunc192[ind].w[1] && fstar.w[0] > ten2mxtrunc192[ind].w[0])) { // f* - 1/2 > 10^(-x) + *ptr_is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + *ptr_is_inexact_gt_midpoint = 1; + } + } else if (ind <= 37) { // if 19 <= ind <= 37 + if (fstar.w[4] > half192[ind] || (fstar.w[4] == half192[ind] && + (fstar.w[3] || fstar.w[2] + || fstar.w[1] || fstar.w[0]))) { + // f* > 1/2 and the result may be exact + // Calculate f* - 1/2 + tmp64 = fstar.w[4] - half192[ind]; + if (tmp64 || fstar.w[3] || fstar.w[2] > ten2mxtrunc192[ind].w[2] || (fstar.w[2] == ten2mxtrunc192[ind].w[2] && fstar.w[1] > ten2mxtrunc192[ind].w[1]) || (fstar.w[2] == ten2mxtrunc192[ind].w[2] && fstar.w[1] == ten2mxtrunc192[ind].w[1] && fstar.w[0] > ten2mxtrunc192[ind].w[0])) { // f* - 1/2 > 10^(-x) + *ptr_is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + *ptr_is_inexact_gt_midpoint = 1; + } + } else { // if 38 <= ind <= 55 + if (fstar.w[5] > half192[ind] || (fstar.w[5] == half192[ind] && + (fstar.w[4] || fstar.w[3] + || fstar.w[2] || fstar.w[1] + || fstar.w[0]))) { + // f* > 1/2 and the result may be exact + // Calculate f* - 1/2 + tmp64 = fstar.w[5] - half192[ind]; + if (tmp64 || fstar.w[4] || fstar.w[3] || fstar.w[2] > ten2mxtrunc192[ind].w[2] || (fstar.w[2] == ten2mxtrunc192[ind].w[2] && fstar.w[1] > ten2mxtrunc192[ind].w[1]) || (fstar.w[2] == ten2mxtrunc192[ind].w[2] && fstar.w[1] == ten2mxtrunc192[ind].w[1] && fstar.w[0] > ten2mxtrunc192[ind].w[0])) { // f* - 1/2 > 10^(-x) + *ptr_is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + *ptr_is_inexact_gt_midpoint = 1; + } + } + // check for midpoints (could do this before determining inexactness) + if (fstar.w[5] == 0 && fstar.w[4] == 0 && fstar.w[3] == 0 && + (fstar.w[2] < ten2mxtrunc192[ind].w[2] || + (fstar.w[2] == ten2mxtrunc192[ind].w[2] && + fstar.w[1] < ten2mxtrunc192[ind].w[1]) || + (fstar.w[2] == ten2mxtrunc192[ind].w[2] && + fstar.w[1] == ten2mxtrunc192[ind].w[1] && + fstar.w[0] <= ten2mxtrunc192[ind].w[0]))) { + // the result is a midpoint + if (Cstar.w[0] & 0x01) { // Cstar is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result may be 0 + Cstar.w[0]--; // Cstar is now even + if (Cstar.w[0] == 0xffffffffffffffffULL) { + Cstar.w[1]--; + if (Cstar.w[1] == 0xffffffffffffffffULL) { + Cstar.w[2]--; + } + } + *ptr_is_midpoint_gt_even = 1; + *ptr_is_inexact_lt_midpoint = 0; + *ptr_is_inexact_gt_midpoint = 0; + } else { // else MP in [ODD, EVEN] + *ptr_is_midpoint_lt_even = 1; + *ptr_is_inexact_lt_midpoint = 0; + *ptr_is_inexact_gt_midpoint = 0; + } + } + // check for rounding overflow, which occurs if Cstar = 10^(q-x) + ind = q - x; // 1 <= ind <= q - 1 + if (ind <= 19) { + if (Cstar.w[2] == 0x0ULL && Cstar.w[1] == 0x0ULL && + Cstar.w[0] == ten2k64[ind]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k64[ind - 1]; // Cstar = 10^(q-x-1) + *incr_exp = 1; + } else { + *incr_exp = 0; + } + } else if (ind == 20) { + // if ind = 20 + if (Cstar.w[2] == 0x0ULL && Cstar.w[1] == ten2k128[0].w[1] && + Cstar.w[0] == ten2k128[0].w[0]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k64[19]; // Cstar = 10^(q-x-1) + Cstar.w[1] = 0x0ULL; + *incr_exp = 1; + } else { + *incr_exp = 0; + } + } else if (ind <= 38) { // if 21 <= ind <= 38 + if (Cstar.w[2] == 0x0ULL && Cstar.w[1] == ten2k128[ind - 20].w[1] && + Cstar.w[0] == ten2k128[ind - 20].w[0]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k128[ind - 21].w[0]; // Cstar = 10^(q-x-1) + Cstar.w[1] = ten2k128[ind - 21].w[1]; + *incr_exp = 1; + } else { + *incr_exp = 0; + } + } else if (ind == 39) { + if (Cstar.w[2] == ten2k256[0].w[2] && Cstar.w[1] == ten2k256[0].w[1] + && Cstar.w[0] == ten2k256[0].w[0]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k128[18].w[0]; // Cstar = 10^(q-x-1) + Cstar.w[1] = ten2k128[18].w[1]; + Cstar.w[2] = 0x0ULL; + *incr_exp = 1; + } else { + *incr_exp = 0; + } + } else { // if 40 <= ind <= 56 + if (Cstar.w[2] == ten2k256[ind - 39].w[2] && + Cstar.w[1] == ten2k256[ind - 39].w[1] && + Cstar.w[0] == ten2k256[ind - 39].w[0]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k256[ind - 40].w[0]; // Cstar = 10^(q-x-1) + Cstar.w[1] = ten2k256[ind - 40].w[1]; + Cstar.w[2] = ten2k256[ind - 40].w[2]; + *incr_exp = 1; + } else { + *incr_exp = 0; + } + } + ptr_Cstar->w[2] = Cstar.w[2]; + ptr_Cstar->w[1] = Cstar.w[1]; + ptr_Cstar->w[0] = Cstar.w[0]; +} + + +void +round256_58_76 (int q, + int x, + UINT256 C, + UINT256 * ptr_Cstar, + int *incr_exp, + int *ptr_is_midpoint_lt_even, + int *ptr_is_midpoint_gt_even, + int *ptr_is_inexact_lt_midpoint, + int *ptr_is_inexact_gt_midpoint) { + + UINT512 P512; + UINT512 fstar; + UINT256 Cstar; + UINT64 tmp64; + int shift; + int ind; + + // Note: + // In round256_58_76() positive numbers with 58 <= q <= 76 will be + // rounded to nearest only for 24 <= x <= 61: + // x = 42 or x = 43 or x = 24 or x = 25 when q = 58 + // x = 43 or x = 44 or x = 25 or x = 26 when q = 59 + // ... + // x = 60 or x = 61 or x = 42 or x = 43 when q = 76 + // However, for generality and possible uses outside the frame of IEEE 754R + // this implementation works for 1 <= x <= q - 1 + + // assume *ptr_is_midpoint_lt_even, *ptr_is_midpoint_gt_even, + // *ptr_is_inexact_lt_midpoint, and *ptr_is_inexact_gt_midpoint are + // initialized to 0 by the caller + + // round a number C with q decimal digits, 58 <= q <= 76 + // to q - x digits, 1 <= x <= 75 + // C = C + 1/2 * 10^x where the result C fits in 256 bits + // (because the largest value is 9999999999999999999999999999999999999999 + // 999999999999999999999999999999999999 + 500000000000000000000000000 + // 000000000000000000000000000000000000000000000000 = + // 0x1736ca15d27a56cae15cf0e7b403d1f2bd6ebb0a50dc83ffffffffffffffffff, + // which fits in 253 bits) + ind = x - 1; // 0 <= ind <= 74 + if (ind <= 18) { // if 0 <= ind <= 18 + tmp64 = C.w[0]; + C.w[0] = C.w[0] + midpoint64[ind]; + if (C.w[0] < tmp64) { + C.w[1]++; + if (C.w[1] == 0x0) { + C.w[2]++; + if (C.w[2] == 0x0) { + C.w[3]++; + } + } + } + } else if (ind <= 37) { // if 19 <= ind <= 37 + tmp64 = C.w[0]; + C.w[0] = C.w[0] + midpoint128[ind - 19].w[0]; + if (C.w[0] < tmp64) { + C.w[1]++; + if (C.w[1] == 0x0) { + C.w[2]++; + if (C.w[2] == 0x0) { + C.w[3]++; + } + } + } + tmp64 = C.w[1]; + C.w[1] = C.w[1] + midpoint128[ind - 19].w[1]; + if (C.w[1] < tmp64) { + C.w[2]++; + if (C.w[2] == 0x0) { + C.w[3]++; + } + } + } else if (ind <= 57) { // if 38 <= ind <= 57 + tmp64 = C.w[0]; + C.w[0] = C.w[0] + midpoint192[ind - 38].w[0]; + if (C.w[0] < tmp64) { + C.w[1]++; + if (C.w[1] == 0x0ull) { + C.w[2]++; + if (C.w[2] == 0x0) { + C.w[3]++; + } + } + } + tmp64 = C.w[1]; + C.w[1] = C.w[1] + midpoint192[ind - 38].w[1]; + if (C.w[1] < tmp64) { + C.w[2]++; + if (C.w[2] == 0x0) { + C.w[3]++; + } + } + tmp64 = C.w[2]; + C.w[2] = C.w[2] + midpoint192[ind - 38].w[2]; + if (C.w[2] < tmp64) { + C.w[3]++; + } + } else { // if 58 <= ind <= 76 (actually 58 <= ind <= 74) + tmp64 = C.w[0]; + C.w[0] = C.w[0] + midpoint256[ind - 58].w[0]; + if (C.w[0] < tmp64) { + C.w[1]++; + if (C.w[1] == 0x0ull) { + C.w[2]++; + if (C.w[2] == 0x0) { + C.w[3]++; + } + } + } + tmp64 = C.w[1]; + C.w[1] = C.w[1] + midpoint256[ind - 58].w[1]; + if (C.w[1] < tmp64) { + C.w[2]++; + if (C.w[2] == 0x0) { + C.w[3]++; + } + } + tmp64 = C.w[2]; + C.w[2] = C.w[2] + midpoint256[ind - 58].w[2]; + if (C.w[2] < tmp64) { + C.w[3]++; + } + C.w[3] = C.w[3] + midpoint256[ind - 58].w[3]; + } + // kx ~= 10^(-x), kx = Kx256[ind] * 2^(-Ex), 0 <= ind <= 74 + // P512 = (C + 1/2 * 10^x) * kx * 2^Ex = (C + 1/2 * 10^x) * Kx + // the approximation kx of 10^(-x) was rounded up to 192 bits + __mul_256x256_to_512 (P512, C, Kx256[ind]); + // calculate C* = floor (P512) and f* + // Cstar = P512 >> Ex + // fstar = low Ex bits of P512 + shift = Ex256m256[ind]; // in [0, 63] but have to consider four cases + if (ind <= 18) { // if 0 <= ind <= 18 + Cstar.w[3] = (P512.w[7] >> shift); + Cstar.w[2] = (P512.w[7] << (64 - shift)) | (P512.w[6] >> shift); + Cstar.w[1] = (P512.w[6] << (64 - shift)) | (P512.w[5] >> shift); + Cstar.w[0] = (P512.w[5] << (64 - shift)) | (P512.w[4] >> shift); + fstar.w[7] = 0x0ULL; + fstar.w[6] = 0x0ULL; + fstar.w[5] = 0x0ULL; + fstar.w[4] = P512.w[4] & mask256[ind]; + fstar.w[3] = P512.w[3]; + fstar.w[2] = P512.w[2]; + fstar.w[1] = P512.w[1]; + fstar.w[0] = P512.w[0]; + } else if (ind <= 37) { // if 19 <= ind <= 37 + Cstar.w[3] = 0x0ULL; + Cstar.w[2] = P512.w[7] >> shift; + Cstar.w[1] = (P512.w[7] << (64 - shift)) | (P512.w[6] >> shift); + Cstar.w[0] = (P512.w[6] << (64 - shift)) | (P512.w[5] >> shift); + fstar.w[7] = 0x0ULL; + fstar.w[6] = 0x0ULL; + fstar.w[5] = P512.w[5] & mask256[ind]; + fstar.w[4] = P512.w[4]; + fstar.w[3] = P512.w[3]; + fstar.w[2] = P512.w[2]; + fstar.w[1] = P512.w[1]; + fstar.w[0] = P512.w[0]; + } else if (ind <= 56) { // if 38 <= ind <= 56 + Cstar.w[3] = 0x0ULL; + Cstar.w[2] = 0x0ULL; + Cstar.w[1] = P512.w[7] >> shift; + Cstar.w[0] = (P512.w[7] << (64 - shift)) | (P512.w[6] >> shift); + fstar.w[7] = 0x0ULL; + fstar.w[6] = P512.w[6] & mask256[ind]; + fstar.w[5] = P512.w[5]; + fstar.w[4] = P512.w[4]; + fstar.w[3] = P512.w[3]; + fstar.w[2] = P512.w[2]; + fstar.w[1] = P512.w[1]; + fstar.w[0] = P512.w[0]; + } else if (ind == 57) { + Cstar.w[3] = 0x0ULL; + Cstar.w[2] = 0x0ULL; + Cstar.w[1] = 0x0ULL; + Cstar.w[0] = P512.w[7]; + fstar.w[7] = 0x0ULL; + fstar.w[6] = P512.w[6]; + fstar.w[5] = P512.w[5]; + fstar.w[4] = P512.w[4]; + fstar.w[3] = P512.w[3]; + fstar.w[2] = P512.w[2]; + fstar.w[1] = P512.w[1]; + fstar.w[0] = P512.w[0]; + } else { // if 58 <= ind <= 74 + Cstar.w[3] = 0x0ULL; + Cstar.w[2] = 0x0ULL; + Cstar.w[1] = 0x0ULL; + Cstar.w[0] = P512.w[7] >> shift; + fstar.w[7] = P512.w[7] & mask256[ind]; + fstar.w[6] = P512.w[6]; + fstar.w[5] = P512.w[5]; + fstar.w[4] = P512.w[4]; + fstar.w[3] = P512.w[3]; + fstar.w[2] = P512.w[2]; + fstar.w[1] = P512.w[1]; + fstar.w[0] = P512.w[0]; + } + + // the top Ex bits of 10^(-x) are T* = ten2mxtrunc256[ind], e.g. if x=1, + // T*=ten2mxtrunc256[0]= + // 0xcccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has q - x decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has q - x decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has q - x decimal digits, + // correct by Property 1) + // in the caling function n = C* * 10^(e+x) + + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind <= 18) { // if 0 <= ind <= 18 + if (fstar.w[4] > half256[ind] || (fstar.w[4] == half256[ind] && + (fstar.w[3] || fstar.w[2] + || fstar.w[1] || fstar.w[0]))) { + // f* > 1/2 and the result may be exact + // Calculate f* - 1/2 + tmp64 = fstar.w[4] - half256[ind]; + if (tmp64 || fstar.w[3] > ten2mxtrunc256[ind].w[2] || (fstar.w[3] == ten2mxtrunc256[ind].w[3] && fstar.w[2] > ten2mxtrunc256[ind].w[2]) || (fstar.w[3] == ten2mxtrunc256[ind].w[3] && fstar.w[2] == ten2mxtrunc256[ind].w[2] && fstar.w[1] > ten2mxtrunc256[ind].w[1]) || (fstar.w[3] == ten2mxtrunc256[ind].w[3] && fstar.w[2] == ten2mxtrunc256[ind].w[2] && fstar.w[1] == ten2mxtrunc256[ind].w[1] && fstar.w[0] > ten2mxtrunc256[ind].w[0])) { // f* - 1/2 > 10^(-x) + *ptr_is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + *ptr_is_inexact_gt_midpoint = 1; + } + } else if (ind <= 37) { // if 19 <= ind <= 37 + if (fstar.w[5] > half256[ind] || (fstar.w[5] == half256[ind] && + (fstar.w[4] || fstar.w[3] + || fstar.w[2] || fstar.w[1] + || fstar.w[0]))) { + // f* > 1/2 and the result may be exact + // Calculate f* - 1/2 + tmp64 = fstar.w[5] - half256[ind]; + if (tmp64 || fstar.w[4] || fstar.w[3] > ten2mxtrunc256[ind].w[3] || (fstar.w[3] == ten2mxtrunc256[ind].w[3] && fstar.w[2] > ten2mxtrunc256[ind].w[2]) || (fstar.w[3] == ten2mxtrunc256[ind].w[3] && fstar.w[2] == ten2mxtrunc256[ind].w[2] && fstar.w[1] > ten2mxtrunc256[ind].w[1]) || (fstar.w[3] == ten2mxtrunc256[ind].w[3] && fstar.w[2] == ten2mxtrunc256[ind].w[2] && fstar.w[1] == ten2mxtrunc256[ind].w[1] && fstar.w[0] > ten2mxtrunc256[ind].w[0])) { // f* - 1/2 > 10^(-x) + *ptr_is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + *ptr_is_inexact_gt_midpoint = 1; + } + } else if (ind <= 57) { // if 38 <= ind <= 57 + if (fstar.w[6] > half256[ind] || (fstar.w[6] == half256[ind] && + (fstar.w[5] || fstar.w[4] + || fstar.w[3] || fstar.w[2] + || fstar.w[1] || fstar.w[0]))) { + // f* > 1/2 and the result may be exact + // Calculate f* - 1/2 + tmp64 = fstar.w[6] - half256[ind]; + if (tmp64 || fstar.w[5] || fstar.w[4] || fstar.w[3] > ten2mxtrunc256[ind].w[3] || (fstar.w[3] == ten2mxtrunc256[ind].w[3] && fstar.w[2] > ten2mxtrunc256[ind].w[2]) || (fstar.w[3] == ten2mxtrunc256[ind].w[3] && fstar.w[2] == ten2mxtrunc256[ind].w[2] && fstar.w[1] > ten2mxtrunc256[ind].w[1]) || (fstar.w[3] == ten2mxtrunc256[ind].w[3] && fstar.w[2] == ten2mxtrunc256[ind].w[2] && fstar.w[1] == ten2mxtrunc256[ind].w[1] && fstar.w[0] > ten2mxtrunc256[ind].w[0])) { // f* - 1/2 > 10^(-x) + *ptr_is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + *ptr_is_inexact_gt_midpoint = 1; + } + } else { // if 58 <= ind <= 74 + if (fstar.w[7] > half256[ind] || (fstar.w[7] == half256[ind] && + (fstar.w[6] || fstar.w[5] + || fstar.w[4] || fstar.w[3] + || fstar.w[2] || fstar.w[1] + || fstar.w[0]))) { + // f* > 1/2 and the result may be exact + // Calculate f* - 1/2 + tmp64 = fstar.w[7] - half256[ind]; + if (tmp64 || fstar.w[6] || fstar.w[5] || fstar.w[4] || fstar.w[3] > ten2mxtrunc256[ind].w[3] || (fstar.w[3] == ten2mxtrunc256[ind].w[3] && fstar.w[2] > ten2mxtrunc256[ind].w[2]) || (fstar.w[3] == ten2mxtrunc256[ind].w[3] && fstar.w[2] == ten2mxtrunc256[ind].w[2] && fstar.w[1] > ten2mxtrunc256[ind].w[1]) || (fstar.w[3] == ten2mxtrunc256[ind].w[3] && fstar.w[2] == ten2mxtrunc256[ind].w[2] && fstar.w[1] == ten2mxtrunc256[ind].w[1] && fstar.w[0] > ten2mxtrunc256[ind].w[0])) { // f* - 1/2 > 10^(-x) + *ptr_is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + *ptr_is_inexact_gt_midpoint = 1; + } + } + // check for midpoints (could do this before determining inexactness) + if (fstar.w[7] == 0 && fstar.w[6] == 0 && + fstar.w[5] == 0 && fstar.w[4] == 0 && + (fstar.w[3] < ten2mxtrunc256[ind].w[3] || + (fstar.w[3] == ten2mxtrunc256[ind].w[3] && + fstar.w[2] < ten2mxtrunc256[ind].w[2]) || + (fstar.w[3] == ten2mxtrunc256[ind].w[3] && + fstar.w[2] == ten2mxtrunc256[ind].w[2] && + fstar.w[1] < ten2mxtrunc256[ind].w[1]) || + (fstar.w[3] == ten2mxtrunc256[ind].w[3] && + fstar.w[2] == ten2mxtrunc256[ind].w[2] && + fstar.w[1] == ten2mxtrunc256[ind].w[1] && + fstar.w[0] <= ten2mxtrunc256[ind].w[0]))) { + // the result is a midpoint + if (Cstar.w[0] & 0x01) { // Cstar is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result may be 0 + Cstar.w[0]--; // Cstar is now even + if (Cstar.w[0] == 0xffffffffffffffffULL) { + Cstar.w[1]--; + if (Cstar.w[1] == 0xffffffffffffffffULL) { + Cstar.w[2]--; + if (Cstar.w[2] == 0xffffffffffffffffULL) { + Cstar.w[3]--; + } + } + } + *ptr_is_midpoint_gt_even = 1; + *ptr_is_inexact_lt_midpoint = 0; + *ptr_is_inexact_gt_midpoint = 0; + } else { // else MP in [ODD, EVEN] + *ptr_is_midpoint_lt_even = 1; + *ptr_is_inexact_lt_midpoint = 0; + *ptr_is_inexact_gt_midpoint = 0; + } + } + // check for rounding overflow, which occurs if Cstar = 10^(q-x) + ind = q - x; // 1 <= ind <= q - 1 + if (ind <= 19) { + if (Cstar.w[3] == 0x0ULL && Cstar.w[2] == 0x0ULL && + Cstar.w[1] == 0x0ULL && Cstar.w[0] == ten2k64[ind]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k64[ind - 1]; // Cstar = 10^(q-x-1) + *incr_exp = 1; + } else { + *incr_exp = 0; + } + } else if (ind == 20) { + // if ind = 20 + if (Cstar.w[3] == 0x0ULL && Cstar.w[2] == 0x0ULL && + Cstar.w[1] == ten2k128[0].w[1] + && Cstar.w[0] == ten2k128[0].w[0]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k64[19]; // Cstar = 10^(q-x-1) + Cstar.w[1] = 0x0ULL; + *incr_exp = 1; + } else { + *incr_exp = 0; + } + } else if (ind <= 38) { // if 21 <= ind <= 38 + if (Cstar.w[3] == 0x0ULL && Cstar.w[2] == 0x0ULL && + Cstar.w[1] == ten2k128[ind - 20].w[1] && + Cstar.w[0] == ten2k128[ind - 20].w[0]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k128[ind - 21].w[0]; // Cstar = 10^(q-x-1) + Cstar.w[1] = ten2k128[ind - 21].w[1]; + *incr_exp = 1; + } else { + *incr_exp = 0; + } + } else if (ind == 39) { + if (Cstar.w[3] == 0x0ULL && Cstar.w[2] == ten2k256[0].w[2] && + Cstar.w[1] == ten2k256[0].w[1] + && Cstar.w[0] == ten2k256[0].w[0]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k128[18].w[0]; // Cstar = 10^(q-x-1) + Cstar.w[1] = ten2k128[18].w[1]; + Cstar.w[2] = 0x0ULL; + *incr_exp = 1; + } else { + *incr_exp = 0; + } + } else if (ind <= 57) { // if 40 <= ind <= 57 + if (Cstar.w[3] == 0x0ULL && Cstar.w[2] == ten2k256[ind - 39].w[2] && + Cstar.w[1] == ten2k256[ind - 39].w[1] && + Cstar.w[0] == ten2k256[ind - 39].w[0]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k256[ind - 40].w[0]; // Cstar = 10^(q-x-1) + Cstar.w[1] = ten2k256[ind - 40].w[1]; + Cstar.w[2] = ten2k256[ind - 40].w[2]; + *incr_exp = 1; + } else { + *incr_exp = 0; + } + // else if (ind == 58) is not needed becauae we do not have ten2k192[] yet + } else { // if 58 <= ind <= 77 (actually 58 <= ind <= 74) + if (Cstar.w[3] == ten2k256[ind - 39].w[3] && + Cstar.w[2] == ten2k256[ind - 39].w[2] && + Cstar.w[1] == ten2k256[ind - 39].w[1] && + Cstar.w[0] == ten2k256[ind - 39].w[0]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k256[ind - 40].w[0]; // Cstar = 10^(q-x-1) + Cstar.w[1] = ten2k256[ind - 40].w[1]; + Cstar.w[2] = ten2k256[ind - 40].w[2]; + Cstar.w[3] = ten2k256[ind - 40].w[3]; + *incr_exp = 1; + } else { + *incr_exp = 0; + } + } + ptr_Cstar->w[3] = Cstar.w[3]; + ptr_Cstar->w[2] = Cstar.w[2]; + ptr_Cstar->w[1] = Cstar.w[1]; + ptr_Cstar->w[0] = Cstar.w[0]; + +}