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+/* Copyright (C) 2007-2014 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];
+
+}
generated by cgit v1.2.3 (git 2.25.1) at 2024-04-16 17:30:26 +0000