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gcc/libgcc/config/libbid/bid_round.c
Jakub Jelinek 8d9254fc8a Update copyright years. 
From-SVN: r279813
2020-01-01 12:51:42 +01:00

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/* Copyright (C) 2007-2020 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];
}
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