blob: bbe42258a7a6e6bf04c14113c25c759b9df55e76 [file] [log] [blame]
/* Copyright (C) 2007-2017 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/>. */
#include "bid_internal.h"
UINT64 round_const_table[][19] = {
{ // RN
0ull, // 0 extra digits
5ull, // 1 extra digits
50ull, // 2 extra digits
500ull, // 3 extra digits
5000ull, // 4 extra digits
50000ull, // 5 extra digits
500000ull, // 6 extra digits
5000000ull, // 7 extra digits
50000000ull, // 8 extra digits
500000000ull, // 9 extra digits
5000000000ull, // 10 extra digits
50000000000ull, // 11 extra digits
500000000000ull, // 12 extra digits
5000000000000ull, // 13 extra digits
50000000000000ull, // 14 extra digits
500000000000000ull, // 15 extra digits
5000000000000000ull, // 16 extra digits
50000000000000000ull, // 17 extra digits
500000000000000000ull // 18 extra digits
}
,
{ // RD
0ull, // 0 extra digits
0ull, // 1 extra digits
0ull, // 2 extra digits
00ull, // 3 extra digits
000ull, // 4 extra digits
0000ull, // 5 extra digits
00000ull, // 6 extra digits
000000ull, // 7 extra digits
0000000ull, // 8 extra digits
00000000ull, // 9 extra digits
000000000ull, // 10 extra digits
0000000000ull, // 11 extra digits
00000000000ull, // 12 extra digits
000000000000ull, // 13 extra digits
0000000000000ull, // 14 extra digits
00000000000000ull, // 15 extra digits
000000000000000ull, // 16 extra digits
0000000000000000ull, // 17 extra digits
00000000000000000ull // 18 extra digits
}
,
{ // round to Inf
0ull, // 0 extra digits
9ull, // 1 extra digits
99ull, // 2 extra digits
999ull, // 3 extra digits
9999ull, // 4 extra digits
99999ull, // 5 extra digits
999999ull, // 6 extra digits
9999999ull, // 7 extra digits
99999999ull, // 8 extra digits
999999999ull, // 9 extra digits
9999999999ull, // 10 extra digits
99999999999ull, // 11 extra digits
999999999999ull, // 12 extra digits
9999999999999ull, // 13 extra digits
99999999999999ull, // 14 extra digits
999999999999999ull, // 15 extra digits
9999999999999999ull, // 16 extra digits
99999999999999999ull, // 17 extra digits
999999999999999999ull // 18 extra digits
}
,
{ // RZ
0ull, // 0 extra digits
0ull, // 1 extra digits
0ull, // 2 extra digits
00ull, // 3 extra digits
000ull, // 4 extra digits
0000ull, // 5 extra digits
00000ull, // 6 extra digits
000000ull, // 7 extra digits
0000000ull, // 8 extra digits
00000000ull, // 9 extra digits
000000000ull, // 10 extra digits
0000000000ull, // 11 extra digits
00000000000ull, // 12 extra digits
000000000000ull, // 13 extra digits
0000000000000ull, // 14 extra digits
00000000000000ull, // 15 extra digits
000000000000000ull, // 16 extra digits
0000000000000000ull, // 17 extra digits
00000000000000000ull // 18 extra digits
}
,
{ // round ties away from 0
0ull, // 0 extra digits
5ull, // 1 extra digits
50ull, // 2 extra digits
500ull, // 3 extra digits
5000ull, // 4 extra digits
50000ull, // 5 extra digits
500000ull, // 6 extra digits
5000000ull, // 7 extra digits
50000000ull, // 8 extra digits
500000000ull, // 9 extra digits
5000000000ull, // 10 extra digits
50000000000ull, // 11 extra digits
500000000000ull, // 12 extra digits
5000000000000ull, // 13 extra digits
50000000000000ull, // 14 extra digits
500000000000000ull, // 15 extra digits
5000000000000000ull, // 16 extra digits
50000000000000000ull, // 17 extra digits
500000000000000000ull // 18 extra digits
}
,
};
UINT128 round_const_table_128[][36] = {
{ //RN
{{0ull, 0ull}
}
, // 0 extra digits
{{5ull, 0ull}
}
, // 1 extra digits
{{50ull, 0ull}
}
, // 2 extra digits
{{500ull, 0ull}
}
, // 3 extra digits
{{5000ull, 0ull}
}
, // 4 extra digits
{{50000ull, 0ull}
}
, // 5 extra digits
{{500000ull, 0ull}
}
, // 6 extra digits
{{5000000ull, 0ull}
}
, // 7 extra digits
{{50000000ull, 0ull}
}
, // 8 extra digits
{{500000000ull, 0ull}
}
, // 9 extra digits
{{5000000000ull, 0ull}
}
, // 10 extra digits
{{50000000000ull, 0ull}
}
, // 11 extra digits
{{500000000000ull, 0ull}
}
, // 12 extra digits
{{5000000000000ull, 0ull}
}
, // 13 extra digits
{{50000000000000ull, 0ull}
}
, // 14 extra digits
{{500000000000000ull, 0ull}
}
, // 15 extra digits
{{5000000000000000ull, 0ull}
}
, // 16 extra digits
{{50000000000000000ull, 0ull}
}
, // 17 extra digits
{{500000000000000000ull, 0ull}
}
, // 18 extra digits
{{5000000000000000000ull, 0ull}
}
, // 19 extra digits
{{0xb5e3af16b1880000ull, 2ull}
}
, //20
{{0x1ae4d6e2ef500000ull, 27ull}
}
, //21
{{0xcf064dd59200000ull, 271ull}
}
, //22
{{0x8163f0a57b400000ull, 2710ull}
}
, //23
{{0xde76676d0800000ull, 27105ull}
}
, //24
{{0x8b0a00a425000000ull, 0x422caull}
}
, //25
{{0x6e64066972000000ull, 0x295be9ull}
}
, //26
{{0x4fe8401e74000000ull, 0x19d971eull}
}
, //27
{{0x1f12813088000000ull, 0x1027e72full}
}
, //28
{{0x36b90be550000000ull, 0xa18f07d7ull}
}
, //29
{{0x233a76f520000000ull, 0x64f964e68ull}
}
, //30
{{0x6048a59340000000ull, 0x3f1bdf1011ull}
}
, //31
{{0xc2d677c080000000ull, 0x27716b6a0adull}
}
, //32
{{0x9c60ad8500000000ull, 0x18a6e32246c9ull}
}
, //33
{{0x1bc6c73200000000ull, 0xf684df56c3e0ull}
}
, //34
{{0x15c3c7f400000000ull, 0x9a130b963a6c1ull}
}
, //35
}
,
{ //RD
{{0ull, 0ull}
}
, // 0 extra digits
{{0ull, 0ull}
}
, // 1 extra digits
{{0ull, 0ull}
}
, // 2 extra digits
{{00ull, 0ull}
}
, // 3 extra digits
{{000ull, 0ull}
}
, // 4 extra digits
{{0000ull, 0ull}
}
, // 5 extra digits
{{00000ull, 0ull}
}
, // 6 extra digits
{{000000ull, 0ull}
}
, // 7 extra digits
{{0000000ull, 0ull}
}
, // 8 extra digits
{{00000000ull, 0ull}
}
, // 9 extra digits
{{000000000ull, 0ull}
}
, // 10 extra digits
{{0000000000ull, 0ull}
}
, // 11 extra digits
{{00000000000ull, 0ull}
}
, // 12 extra digits
{{000000000000ull, 0ull}
}
, // 13 extra digits
{{0000000000000ull, 0ull}
}
, // 14 extra digits
{{00000000000000ull, 0ull}
}
, // 15 extra digits
{{000000000000000ull, 0ull}
}
, // 16 extra digits
{{0000000000000000ull, 0ull}
}
, // 17 extra digits
{{00000000000000000ull, 0ull}
}
, // 18 extra digits
{{000000000000000000ull, 0ull}
}
, // 19 extra digits
{{0ull, 0ull}
}
, //20
{{0ull, 0ull}
}
, //21
{{0ull, 0ull}
}
, //22
{{0ull, 0ull}
}
, //23
{{0ull, 0ull}
}
, //24
{{0ull, 0ull}
}
, //25
{{0ull, 0ull}
}
, //26
{{0ull, 0ull}
}
, //27
{{0ull, 0ull}
}
, //28
{{0ull, 0ull}
}
, //29
{{0ull, 0ull}
}
, //30
{{0ull, 0ull}
}
, //31
{{0ull, 0ull}
}
, //32
{{0ull, 0ull}
}
, //33
{{0ull, 0ull}
}
, //34
{{0ull, 0ull}
}
, //35
}
,
{ //RU
{{0ull, 0ull}
}
, // 0 extra digits
{{9ull, 0ull}
}
, // 1 extra digits
{{99ull, 0ull}
}
, // 2 extra digits
{{999ull, 0ull}
}
, // 3 extra digits
{{9999ull, 0ull}
}
, // 4 extra digits
{{99999ull, 0ull}
}
, // 5 extra digits
{{999999ull, 0ull}
}
, // 6 extra digits
{{9999999ull, 0ull}
}
, // 7 extra digits
{{99999999ull, 0ull}
}
, // 8 extra digits
{{999999999ull, 0ull}
}
, // 9 extra digits
{{9999999999ull, 0ull}
}
, // 10 extra digits
{{99999999999ull, 0ull}
}
, // 11 extra digits
{{999999999999ull, 0ull}
}
, // 12 extra digits
{{9999999999999ull, 0ull}
}
, // 13 extra digits
{{99999999999999ull, 0ull}
}
, // 14 extra digits
{{999999999999999ull, 0ull}
}
, // 15 extra digits
{{9999999999999999ull, 0ull}
}
, // 16 extra digits
{{99999999999999999ull, 0ull}
}
, // 17 extra digits
{{999999999999999999ull, 0ull}
}
, // 18 extra digits
{{9999999999999999999ull, 0ull}
}
, // 19 extra digits
{{0x6BC75E2D630FFFFFull, 0x5ull}
}
, //20
{{0x35C9ADC5DE9FFFFFull, 0x36ull}
}
, //21
{{0x19E0C9BAB23FFFFFull, 0x21eull}
}
, //22
{{0x2C7E14AF67FFFFFull, 0x152dull}
}
, //23
{{0x1BCECCEDA0FFFFFFull, 0xd3c2ull}
}
, //24
{{0x1614014849FFFFFFull, 0x84595ull}
}
, //25
{{0xDCC80CD2E3FFFFFFull, 0x52b7d2ull}
}
, //26
{{0x9FD0803CE7FFFFFFull, 0x33B2E3Cull}
}
, //27
{{0x3E2502610FFFFFFFull, 0x204FCE5Eull}
}
, //28
{{0x6D7217CA9FFFFFFFull, 0x1431E0FAEull}
}
, //29
{{0x4674EDEA3FFFFFFFull, 0xC9F2C9CD0ull}
}
, //30
{{0xC0914B267FFFFFFFull, 0x7E37BE2022ull}
}
, //31
{{0x85ACEF80FFFFFFFFull, 0x4EE2D6D415Bull}
}
, //32
{{0x38c15b09ffffffffull, 0x314dc6448d93ull}
}
, //33
{{0x378d8e63ffffffffull, 0x1ed09bead87c0ull}
}
, //34
{{0x2b878fe7ffffffffull, 0x13426172c74d82ull}
}
, //35
}
,
{ //RZ
{{0ull, 0ull}
}
, // 0 extra digits
{{0ull, 0ull}
}
, // 1 extra digits
{{0ull, 0ull}
}
, // 2 extra digits
{{00ull, 0ull}
}
, // 3 extra digits
{{000ull, 0ull}
}
, // 4 extra digits
{{0000ull, 0ull}
}
, // 5 extra digits
{{00000ull, 0ull}
}
, // 6 extra digits
{{000000ull, 0ull}
}
, // 7 extra digits
{{0000000ull, 0ull}
}
, // 8 extra digits
{{00000000ull, 0ull}
}
, // 9 extra digits
{{000000000ull, 0ull}
}
, // 10 extra digits
{{0000000000ull, 0ull}
}
, // 11 extra digits
{{00000000000ull, 0ull}
}
, // 12 extra digits
{{000000000000ull, 0ull}
}
, // 13 extra digits
{{0000000000000ull, 0ull}
}
, // 14 extra digits
{{00000000000000ull, 0ull}
}
, // 15 extra digits
{{000000000000000ull, 0ull}
}
, // 16 extra digits
{{0000000000000000ull, 0ull}
}
, // 17 extra digits
{{00000000000000000ull, 0ull}
}
, // 18 extra digits
{{000000000000000000ull, 0ull}
}
, // 19 extra digits
{{0ull, 0ull}
}
, //20
{{0ull, 0ull}
}
, //21
{{0ull, 0ull}
}
, //22
{{0ull, 0ull}
}
, //23
{{0ull, 0ull}
}
, //24
{{0ull, 0ull}
}
, //25
{{0ull, 0ull}
}
, //26
{{0ull, 0ull}
}
, //27
{{0ull, 0ull}
}
, //28
{{0ull, 0ull}
}
, //29
{{0ull, 0ull}
}
, //30
{{0ull, 0ull}
}
, //31
{{0ull, 0ull}
}
, //32
{{0ull, 0ull}
}
, //33
{{0ull, 0ull}
}
, //34
{{0ull, 0ull}
}
, //35
}
,
{ //RN, ties away
{{0ull, 0ull}
}
, // 0 extra digits
{{5ull, 0ull}
}
, // 1 extra digits
{{50ull, 0ull}
}
, // 2 extra digits
{{500ull, 0ull}
}
, // 3 extra digits
{{5000ull, 0ull}
}
, // 4 extra digits
{{50000ull, 0ull}
}
, // 5 extra digits
{{500000ull, 0ull}
}
, // 6 extra digits
{{5000000ull, 0ull}
}
, // 7 extra digits
{{50000000ull, 0ull}
}
, // 8 extra digits
{{500000000ull, 0ull}
}
, // 9 extra digits
{{5000000000ull, 0ull}
}
, // 10 extra digits
{{50000000000ull, 0ull}
}
, // 11 extra digits
{{500000000000ull, 0ull}
}
, // 12 extra digits
{{5000000000000ull, 0ull}
}
, // 13 extra digits
{{50000000000000ull, 0ull}
}
, // 14 extra digits
{{500000000000000ull, 0ull}
}
, // 15 extra digits
{{5000000000000000ull, 0ull}
}
, // 16 extra digits
{{50000000000000000ull, 0ull}
}
, // 17 extra digits
{{500000000000000000ull, 0ull}
}
, // 18 extra digits
{{5000000000000000000ull, 0ull}
}
, // 19 extra digits
{{0xb5e3af16b1880000ull, 2ull}
}
, //20
{{0x1ae4d6e2ef500000ull, 27ull}
}
, //21
{{0xcf064dd59200000ull, 271ull}
}
, //22
{{0x8163f0a57b400000ull, 2710ull}
}
, //23
{{0xde76676d0800000ull, 27105ull}
}
, //24
{{0x8b0a00a425000000ull, 0x422caull}
}
, //25
{{0x6e64066972000000ull, 0x295be9ull}
}
, //26
{{0x4fe8401e74000000ull, 0x19d971eull}
}
, //27
{{0x1f12813088000000ull, 0x1027e72full}
}
, //28
{{0x36b90be550000000ull, 0xa18f07d7ull}
}
, //29
{{0x233a76f520000000ull, 0x64f964e68ull}
}
, //30
{{0x6048a59340000000ull, 0x3f1bdf1011ull}
}
, //31
{{0xc2d677c080000000ull, 0x27716b6a0adull}
}
, //32
{{0x9c60ad8500000000ull, 0x18a6e32246c9ull}
}
, //33
{{0x1bc6c73200000000ull, 0xf684df56c3e0ull}
}
, //34
{{0x15c3c7f400000000ull, 0x9a130b963a6c1ull}
}
, //35
}
};
UINT128 reciprocals10_128[] = {
{{0ull, 0ull}
}
, // 0 extra digits
{{0x3333333333333334ull, 0x3333333333333333ull}
}
, // 1 extra digit
{{0x51eb851eb851eb86ull, 0x051eb851eb851eb8ull}
}
, // 2 extra digits
{{0x3b645a1cac083127ull, 0x0083126e978d4fdfull}
}
, // 3 extra digits
{{0x4af4f0d844d013aaULL, 0x00346dc5d6388659ULL}
}
, // 10^(-4) * 2^131
{{0x08c3f3e0370cdc88ULL, 0x0029f16b11c6d1e1ULL}
}
, // 10^(-5) * 2^134
{{0x6d698fe69270b06dULL, 0x00218def416bdb1aULL}
}
, // 10^(-6) * 2^137
{{0xaf0f4ca41d811a47ULL, 0x0035afe535795e90ULL}
}
, // 10^(-7) * 2^141
{{0xbf3f70834acdaea0ULL, 0x002af31dc4611873ULL}
}
, // 10^(-8) * 2^144
{{0x65cc5a02a23e254dULL, 0x00225c17d04dad29ULL}
}
, // 10^(-9) * 2^147
{{0x6fad5cd10396a214ULL, 0x0036f9bfb3af7b75ULL}
}
, // 10^(-10) * 2^151
{{0xbfbde3da69454e76ULL, 0x002bfaffc2f2c92aULL}
}
, // 10^(-11) * 2^154
{{0x32fe4fe1edd10b92ULL, 0x00232f33025bd422ULL}
}
, // 10^(-12) * 2^157
{{0x84ca19697c81ac1cULL, 0x00384b84d092ed03ULL}
}
, // 10^(-13) * 2^161
{{0x03d4e1213067bce4ULL, 0x002d09370d425736ULL}
}
, // 10^(-14) * 2^164
{{0x3643e74dc052fd83ULL, 0x0024075f3dceac2bULL}
}
, // 10^(-15) * 2^167
{{0x56d30baf9a1e626bULL, 0x0039a5652fb11378ULL}
}
, // 10^(-16) * 2^171
{{0x12426fbfae7eb522ULL, 0x002e1dea8c8da92dULL}
}
, // 10^(-17) * 2^174
{{0x41cebfcc8b9890e8ULL, 0x0024e4bba3a48757ULL}
}
, // 10^(-18) * 2^177
{{0x694acc7a78f41b0dULL, 0x003b07929f6da558ULL}
}
, // 10^(-19) * 2^181
{{0xbaa23d2ec729af3eULL, 0x002f394219248446ULL}
}
, // 10^(-20) * 2^184
{{0xfbb4fdbf05baf298ULL, 0x0025c768141d369eULL}
}
, // 10^(-21) * 2^187
{{0x2c54c931a2c4b759ULL, 0x003c7240202ebdcbULL}
}
, // 10^(-22) * 2^191
{{0x89dd6dc14f03c5e1ULL, 0x00305b66802564a2ULL}
}
, // 10^(-23) * 2^194
{{0xd4b1249aa59c9e4eULL, 0x0026af8533511d4eULL}
}
, // 10^(-24) * 2^197
{{0x544ea0f76f60fd49ULL, 0x003de5a1ebb4fbb1ULL}
}
, // 10^(-25) * 2^201
{{0x76a54d92bf80caa1ULL, 0x00318481895d9627ULL}
}
, // 10^(-26) * 2^204
{{0x921dd7a89933d54eULL, 0x00279d346de4781fULL}
}
, // 10^(-27) * 2^207
{{0x8362f2a75b862215ULL, 0x003f61ed7ca0c032ULL}
}
, // 10^(-28) * 2^211
{{0xcf825bb91604e811ULL, 0x0032b4bdfd4d668eULL}
}
, // 10^(-29) * 2^214
{{0x0c684960de6a5341ULL, 0x00289097fdd7853fULL}
}
, // 10^(-30) * 2^217
{{0x3d203ab3e521dc34ULL, 0x002073accb12d0ffULL}
}
, // 10^(-31) * 2^220
{{0x2e99f7863b696053ULL, 0x0033ec47ab514e65ULL}
}
, // 10^(-32) * 2^224
{{0x587b2c6b62bab376ULL, 0x002989d2ef743eb7ULL}
}
, // 10^(-33) * 2^227
{{0xad2f56bc4efbc2c5ULL, 0x00213b0f25f69892ULL}
}
, // 10^(-34) * 2^230
{{0x0f2abc9d8c9689d1ull, 0x01a95a5b7f87a0efull}
}
, // 35 extra digits
};
int recip_scale[] = {
129 - 128, // 1
129 - 128, // 1/10
129 - 128, // 1/10^2
129 - 128, // 1/10^3
3, // 131 - 128
6, // 134 - 128
9, // 137 - 128
13, // 141 - 128
16, // 144 - 128
19, // 147 - 128
23, // 151 - 128
26, // 154 - 128
29, // 157 - 128
33, // 161 - 128
36, // 164 - 128
39, // 167 - 128
43, // 171 - 128
46, // 174 - 128
49, // 177 - 128
53, // 181 - 128
56, // 184 - 128
59, // 187 - 128
63, // 191 - 128
66, // 194 - 128
69, // 197 - 128
73, // 201 - 128
76, // 204 - 128
79, // 207 - 128
83, // 211 - 128
86, // 214 - 128
89, // 217 - 128
92, // 220 - 128
96, // 224 - 128
99, // 227 - 128
102, // 230 - 128
109, // 237 - 128, 1/10^35
};
// tables used in computation
int estimate_decimal_digits[129] = {
1, //2^0 =1 < 10^0
1, //2^1 =2 < 10^1
1, //2^2 =4 < 10^1
1, //2^3 =8 < 10^1
2, //2^4 =16 < 10^2
2, //2^5 =32 < 10^2
2, //2^6 =64 < 10^2
3, //2^7 =128 < 10^3
3, //2^8 =256 < 10^3
3, //2^9 =512 < 10^3
4, //2^10=1024 < 10^4
4, //2^11=2048 < 10^4
4, //2^12=4096 < 10^4
4, //2^13=8192 < 10^4
5, //2^14=16384 < 10^5
5, //2^15=32768 < 10^5
5, //2^16=65536 < 10^5
6, //2^17=131072 < 10^6
6, //2^18=262144 < 10^6
6, //2^19=524288 < 10^6
7, //2^20=1048576 < 10^7
7, //2^21=2097152 < 10^7
7, //2^22=4194304 < 10^7
7, //2^23=8388608 < 10^7
8, //2^24=16777216 < 10^8
8, //2^25=33554432 < 10^8
8, //2^26=67108864 < 10^8
9, //2^27=134217728 < 10^9
9, //2^28=268435456 < 10^9
9, //2^29=536870912 < 10^9
10, //2^30=1073741824< 10^10
10, //2^31=2147483648< 10^10
10, //2^32=4294967296 < 10^10
10, //2^33=8589934592 < 10^10
11, //2^34=17179869184 < 10^11
11, //2^35=34359738368 < 10^11
11, //2^36=68719476736 < 10^11
12, //2^37=137438953472 < 10^12
12, //2^38=274877906944 < 10^12
12, //2^39=549755813888 < 10^12
13, //2^40=1099511627776 < 10^13
13, //2^41=2199023255552 < 10^13
13, //2^42=4398046511104 < 10^13
13, //2^43=8796093022208 < 10^13
14, //2^44=17592186044416 < 10^14
14, //2^45=35184372088832 < 10^14
14, //2^46=70368744177664 < 10^14
15, //2^47=140737488355328< 10^15
15, //2^48=281474976710656 < 10^15
15, //2^49=562949953421312 < 10^15
16, //2^50=1125899906842624 < 10^16
16, //2^51=2251799813685248 < 10^16
16, //2^52=4503599627370496 < 10^16
16, //2^53=9007199254740992 < 10^16
17, //2^54=18014398509481984 < 10^17
17, //2^55=36028797018963968 < 10^17
17, //2^56=72057594037927936 < 10^17
18, //2^57=144115188075855872 < 10^18
18, //2^58=288230376151711744 < 10^18
18, //2^59=576460752303423488 < 10^18
19, //2^60=1152921504606846976< 10^19
19, //2^61=2305843009213693952< 10^19
19, //2^62=4611686018427387904< 10^19
19, //2^63=9223372036854775808< 10^19
20, //2^64=18446744073709551616
20, //2^65=36893488147419103232
20, //2^66=73786976294838206464
21, //2^67=147573952589676412928
21, //2^68=295147905179352825856
21, //2^69=590295810358705651712
22, //2^70=1180591620717411303424
22, //2^71=2361183241434822606848
22, //2^72=4722366482869645213696
22, //2^73=9444732965739290427392
23, //2^74=18889465931478580854784
23, //2^75=37778931862957161709568
23, //2^76=75557863725914323419136
24, //2^77=151115727451828646838272
24, //2^78=302231454903657293676544
24, //2^79=604462909807314587353088
25, //2^80=1208925819614629174706176
25, //2^81=2417851639229258349412352
25, //2^82=4835703278458516698824704
25, //2^83=9671406556917033397649408
26, //2^84=19342813113834066795298816
26, //2^85=38685626227668133590597632
26, //2^86=77371252455336267181195264
27, //2^87=154742504910672534362390528
27, //2^88=309485009821345068724781056
27, //2^89=618970019642690137449562112
28, //2^90=1237940039285380274899124224
28, //2^91=2475880078570760549798248448
28, //2^92=4951760157141521099596496896
28, //2^93=9903520314283042199192993792
29, //2^94=19807040628566084398385987584
29, //2^95=39614081257132168796771975168
29, //2^96=79228162514264337593543950336
30, //2^97=158456325028528675187087900672
30, //2^98=316912650057057350374175801344
30, //2^99=633825300114114700748351602688
31, //2^100=1267650600228229401496703205376
31, //2^101=2535301200456458802993406410752
31, //2^102=5070602400912917605986812821504
32, //2^103=10141204801825835211973625643008
32, //2^104=20282409603651670423947251286016
32, //2^105=40564819207303340847894502572032
32, //2^106=81129638414606681695789005144064
33, //2^107=162259276829213363391578010288128
33, // 2^108
33, // 2^109
34, // 2^110
34, // 2^111
34, // 2^112
35, // 2^113
35, // 2^114
35, // 2^115
35, // 2^116
36, // 2^117
36, // 2^118
36, // 2^119
37, // 2^120
37, // 2^121
37, // 2^122
38, // 2^123
38, // 2^124
38, // 2^125
38, // 2^126
39, // 2^127
39 // 2^128
};
UINT128 power10_table_128[] = {
{{0x0000000000000001ull, 0x0000000000000000ull}}, // 10^0
{{0x000000000000000aull, 0x0000000000000000ull}}, // 10^1
{{0x0000000000000064ull, 0x0000000000000000ull}}, // 10^2
{{0x00000000000003e8ull, 0x0000000000000000ull}}, // 10^3
{{0x0000000000002710ull, 0x0000000000000000ull}}, // 10^4
{{0x00000000000186a0ull, 0x0000000000000000ull}}, // 10^5
{{0x00000000000f4240ull, 0x0000000000000000ull}}, // 10^6
{{0x0000000000989680ull, 0x0000000000000000ull}}, // 10^7
{{0x0000000005f5e100ull, 0x0000000000000000ull}}, // 10^8
{{0x000000003b9aca00ull, 0x0000000000000000ull}}, // 10^9
{{0x00000002540be400ull, 0x0000000000000000ull}}, // 10^10
{{0x000000174876e800ull, 0x0000000000000000ull}}, // 10^11
{{0x000000e8d4a51000ull, 0x0000000000000000ull}}, // 10^12
{{0x000009184e72a000ull, 0x0000000000000000ull}}, // 10^13
{{0x00005af3107a4000ull, 0x0000000000000000ull}}, // 10^14
{{0x00038d7ea4c68000ull, 0x0000000000000000ull}}, // 10^15
{{0x002386f26fc10000ull, 0x0000000000000000ull}}, // 10^16
{{0x016345785d8a0000ull, 0x0000000000000000ull}}, // 10^17
{{0x0de0b6b3a7640000ull, 0x0000000000000000ull}}, // 10^18
{{0x8ac7230489e80000ull, 0x0000000000000000ull}}, // 10^19
{{0x6bc75e2d63100000ull, 0x0000000000000005ull}}, // 10^20
{{0x35c9adc5dea00000ull, 0x0000000000000036ull}}, // 10^21
{{0x19e0c9bab2400000ull, 0x000000000000021eull}}, // 10^22
{{0x02c7e14af6800000ull, 0x000000000000152dull}}, // 10^23
{{0x1bcecceda1000000ull, 0x000000000000d3c2ull}}, // 10^24
{{0x161401484a000000ull, 0x0000000000084595ull}}, // 10^25
{{0xdcc80cd2e4000000ull, 0x000000000052b7d2ull}}, // 10^26
{{0x9fd0803ce8000000ull, 0x00000000033b2e3cull}}, // 10^27
{{0x3e25026110000000ull, 0x00000000204fce5eull}}, // 10^28
{{0x6d7217caa0000000ull, 0x00000001431e0faeull}}, // 10^29
{{0x4674edea40000000ull, 0x0000000c9f2c9cd0ull}}, // 10^30
{{0xc0914b2680000000ull, 0x0000007e37be2022ull}}, // 10^31
{{0x85acef8100000000ull, 0x000004ee2d6d415bull}}, // 10^32
{{0x38c15b0a00000000ull, 0x0000314dc6448d93ull}}, // 10^33
{{0x378d8e6400000000ull, 0x0001ed09bead87c0ull}}, // 10^34
{{0x2b878fe800000000ull, 0x0013426172c74d82ull}}, // 10^35
{{0xb34b9f1000000000ull, 0x00c097ce7bc90715ull}}, // 10^36
{{0x00f436a000000000ull, 0x0785ee10d5da46d9ull}}, // 10^37
{{0x098a224000000000ull, 0x4b3b4ca85a86c47aull}}, // 10^38
};
int estimate_bin_expon[] = {
0, // 10^0
3, // 10^1
6, // 10^2
9, // 10^3
13, // 10^4
16, // 10^5
19, // 10^6
23, // 10^7
26, // 10^8
29, // 10^9
33, // 10^10
36, // 10^11
39, // 10^12
43, // 10^13
46, // 10^14
49, // 10^15
53 // 10^16
};
UINT64 power10_index_binexp[] = {
0x000000000000000aull,
0x000000000000000aull,
0x000000000000000aull,
0x000000000000000aull,
0x0000000000000064ull,
0x0000000000000064ull,
0x0000000000000064ull,
0x00000000000003e8ull,
0x00000000000003e8ull,
0x00000000000003e8ull,
0x0000000000002710ull,
0x0000000000002710ull,
0x0000000000002710ull,
0x0000000000002710ull,
0x00000000000186a0ull,
0x00000000000186a0ull,
0x00000000000186a0ull,
0x00000000000f4240ull,
0x00000000000f4240ull,
0x00000000000f4240ull,
0x0000000000989680ull,
0x0000000000989680ull,
0x0000000000989680ull,
0x0000000000989680ull,
0x0000000005f5e100ull,
0x0000000005f5e100ull,
0x0000000005f5e100ull,
0x000000003b9aca00ull,
0x000000003b9aca00ull,
0x000000003b9aca00ull,
0x00000002540be400ull,
0x00000002540be400ull,
0x00000002540be400ull,
0x00000002540be400ull,
0x000000174876e800ull,
0x000000174876e800ull,
0x000000174876e800ull,
0x000000e8d4a51000ull,
0x000000e8d4a51000ull,
0x000000e8d4a51000ull,
0x000009184e72a000ull,
0x000009184e72a000ull,
0x000009184e72a000ull,
0x000009184e72a000ull,
0x00005af3107a4000ull,
0x00005af3107a4000ull,
0x00005af3107a4000ull,
0x00038d7ea4c68000ull,
0x00038d7ea4c68000ull,
0x00038d7ea4c68000ull,
0x002386f26fc10000ull,
0x002386f26fc10000ull,
0x002386f26fc10000ull,
0x002386f26fc10000ull,
0x016345785d8a0000ull,
0x016345785d8a0000ull,
0x016345785d8a0000ull,
0x0de0b6b3a7640000ull,
0x0de0b6b3a7640000ull,
0x0de0b6b3a7640000ull,
0x8ac7230489e80000ull,
0x8ac7230489e80000ull,
0x8ac7230489e80000ull,
0x8ac7230489e80000ull
};
int short_recip_scale[] = {
1,
65 - 64,
69 - 64,
71 - 64,
75 - 64,
78 - 64,
81 - 64,
85 - 64,
88 - 64,
91 - 64,
95 - 64,
98 - 64,
101 - 64,
105 - 64,
108 - 64,
111 - 64,
115 - 64, //114 - 64
118 - 64
};
UINT64 reciprocals10_64[] = {
1ull, // dummy value for 0 extra digits
0x3333333333333334ull, // 1 extra digit
0x51eb851eb851eb86ull,
0x20c49ba5e353f7cfull,
0x346dc5d63886594bull,
0x29f16b11c6d1e109ull,
0x218def416bdb1a6eull,
0x35afe535795e90b0ull,
0x2af31dc4611873c0ull,
0x225c17d04dad2966ull,
0x36f9bfb3af7b7570ull,
0x2bfaffc2f2c92ac0ull,
0x232f33025bd42233ull,
0x384b84d092ed0385ull,
0x2d09370d42573604ull,
0x24075f3dceac2b37ull,
0x39a5652fb1137857ull,
0x2e1dea8c8da92d13ull
};
UINT128 power10_index_binexp_128[] = {
{{0x000000000000000aull, 0x0000000000000000ull}},
{{0x000000000000000aull, 0x0000000000000000ull}},
{{0x000000000000000aull, 0x0000000000000000ull}},
{{0x000000000000000aull, 0x0000000000000000ull}},
{{0x0000000000000064ull, 0x0000000000000000ull}},
{{0x0000000000000064ull, 0x0000000000000000ull}},
{{0x0000000000000064ull, 0x0000000000000000ull}},
{{0x00000000000003e8ull, 0x0000000000000000ull}},
{{0x00000000000003e8ull, 0x0000000000000000ull}},
{{0x00000000000003e8ull, 0x0000000000000000ull}},
{{0x0000000000002710ull, 0x0000000000000000ull}},
{{0x0000000000002710ull, 0x0000000000000000ull}},
{{0x0000000000002710ull, 0x0000000000000000ull}},
{{0x0000000000002710ull, 0x0000000000000000ull}},
{{0x00000000000186a0ull, 0x0000000000000000ull}},
{{0x00000000000186a0ull, 0x0000000000000000ull}},
{{0x00000000000186a0ull, 0x0000000000000000ull}},
{{0x00000000000f4240ull, 0x0000000000000000ull}},
{{0x00000000000f4240ull, 0x0000000000000000ull}},
{{0x00000000000f4240ull, 0x0000000000000000ull}},
{{0x0000000000989680ull, 0x0000000000000000ull}},
{{0x0000000000989680ull, 0x0000000000000000ull}},
{{0x0000000000989680ull, 0x0000000000000000ull}},
{{0x0000000000989680ull, 0x0000000000000000ull}},
{{0x0000000005f5e100ull, 0x0000000000000000ull}},
{{0x0000000005f5e100ull, 0x0000000000000000ull}},
{{0x0000000005f5e100ull, 0x0000000000000000ull}},
{{0x000000003b9aca00ull, 0x0000000000000000ull}},
{{0x000000003b9aca00ull, 0x0000000000000000ull}},
{{0x000000003b9aca00ull, 0x0000000000000000ull}},
{{0x00000002540be400ull, 0x0000000000000000ull}},
{{0x00000002540be400ull, 0x0000000000000000ull}},
{{0x00000002540be400ull, 0x0000000000000000ull}},
{{0x00000002540be400ull, 0x0000000000000000ull}},
{{0x000000174876e800ull, 0x0000000000000000ull}},
{{0x000000174876e800ull, 0x0000000000000000ull}},
{{0x000000174876e800ull, 0x0000000000000000ull}},
{{0x000000e8d4a51000ull, 0x0000000000000000ull}},
{{0x000000e8d4a51000ull, 0x0000000000000000ull}},
{{0x000000e8d4a51000ull, 0x0000000000000000ull}},
{{0x000009184e72a000ull, 0x0000000000000000ull}},
{{0x000009184e72a000ull, 0x0000000000000000ull}},
{{0x000009184e72a000ull, 0x0000000000000000ull}},
{{0x000009184e72a000ull, 0x0000000000000000ull}},
{{0x00005af3107a4000ull, 0x0000000000000000ull}},
{{0x00005af3107a4000ull, 0x0000000000000000ull}},
{{0x00005af3107a4000ull, 0x0000000000000000ull}},
{{0x00038d7ea4c68000ull, 0x0000000000000000ull}},
{{0x00038d7ea4c68000ull, 0x0000000000000000ull}},
{{0x00038d7ea4c68000ull, 0x0000000000000000ull}},
{{0x002386f26fc10000ull, 0x0000000000000000ull}},
{{0x002386f26fc10000ull, 0x0000000000000000ull}},
{{0x002386f26fc10000ull, 0x0000000000000000ull}},
{{0x002386f26fc10000ull, 0x0000000000000000ull}},
{{0x016345785d8a0000ull, 0x0000000000000000ull}},
{{0x016345785d8a0000ull, 0x0000000000000000ull}},
{{0x016345785d8a0000ull, 0x0000000000000000ull}},
{{0x0de0b6b3a7640000ull, 0x0000000000000000ull}},
{{0x0de0b6b3a7640000ull, 0x0000000000000000ull}},
{{0x0de0b6b3a7640000ull, 0x0000000000000000ull}},
{{0x8ac7230489e80000ull, 0x0000000000000000ull}},
{{0x8ac7230489e80000ull, 0x0000000000000000ull}},
{{0x8ac7230489e80000ull, 0x0000000000000000ull}},
{{0x8ac7230489e80000ull, 0x0000000000000000ull}},
{{0x6bc75e2d63100000ull, 0x0000000000000005ull}}, // 10^20
{{0x6bc75e2d63100000ull, 0x0000000000000005ull}}, // 10^20
{{0x6bc75e2d63100000ull, 0x0000000000000005ull}}, // 10^20
{{0x35c9adc5dea00000ull, 0x0000000000000036ull}}, // 10^21
{{0x35c9adc5dea00000ull, 0x0000000000000036ull}}, // 10^21
{{0x35c9adc5dea00000ull, 0x0000000000000036ull}}, // 10^21
{{0x19e0c9bab2400000ull, 0x000000000000021eull}}, // 10^22
{{0x19e0c9bab2400000ull, 0x000000000000021eull}}, // 10^22
{{0x19e0c9bab2400000ull, 0x000000000000021eull}}, // 10^22
{{0x19e0c9bab2400000ull, 0x000000000000021eull}}, // 10^22
{{0x02c7e14af6800000ull, 0x000000000000152dull}}, // 10^23
{{0x02c7e14af6800000ull, 0x000000000000152dull}}, // 10^23
{{0x02c7e14af6800000ull, 0x000000000000152dull}}, // 10^23
{{0x1bcecceda1000000ull, 0x000000000000d3c2ull}}, // 10^24
{{0x1bcecceda1000000ull, 0x000000000000d3c2ull}}, // 10^24
{{0x1bcecceda1000000ull, 0x000000000000d3c2ull}}, // 10^24
{{0x161401484a000000ull, 0x0000000000084595ull}}, // 10^25
{{0x161401484a000000ull, 0x0000000000084595ull}}, // 10^25
{{0x161401484a000000ull, 0x0000000000084595ull}}, // 10^25
{{0x161401484a000000ull, 0x0000000000084595ull}}, // 10^25
{{0xdcc80cd2e4000000ull, 0x000000000052b7d2ull}}, // 10^26
{{0xdcc80cd2e4000000ull, 0x000000000052b7d2ull}}, // 10^26
{{0xdcc80cd2e4000000ull, 0x000000000052b7d2ull}}, // 10^26
{{0x9fd0803ce8000000ull, 0x00000000033b2e3cull}}, // 10^27
{{0x9fd0803ce8000000ull, 0x00000000033b2e3cull}}, // 10^27
{{0x9fd0803ce8000000ull, 0x00000000033b2e3cull}}, // 10^27
{{0x3e25026110000000ull, 0x00000000204fce5eull}}, // 10^28
{{0x3e25026110000000ull, 0x00000000204fce5eull}}, // 10^28
{{0x3e25026110000000ull, 0x00000000204fce5eull}}, // 10^28
{{0x3e25026110000000ull, 0x00000000204fce5eull}}, // 10^28
{{0x6d7217caa0000000ull, 0x00000001431e0faeull}}, // 10^29
{{0x6d7217caa0000000ull, 0x00000001431e0faeull}}, // 10^29
{{0x6d7217caa0000000ull, 0x00000001431e0faeull}}, // 10^29
{{0x4674edea40000000ull, 0x0000000c9f2c9cd0ull}}, // 10^30
{{0x4674edea40000000ull, 0x0000000c9f2c9cd0ull}}, // 10^30
{{0x4674edea40000000ull, 0x0000000c9f2c9cd0ull}}, // 10^30
{{0xc0914b2680000000ull, 0x0000007e37be2022ull}}, // 10^31
{{0xc0914b2680000000ull, 0x0000007e37be2022ull}}, // 10^31
{{0xc0914b2680000000ull, 0x0000007e37be2022ull}}, // 10^31
{{0x85acef8100000000ull, 0x000004ee2d6d415bull}}, // 10^32
{{0x85acef8100000000ull, 0x000004ee2d6d415bull}}, // 10^32
{{0x85acef8100000000ull, 0x000004ee2d6d415bull}}, // 10^32
{{0x85acef8100000000ull, 0x000004ee2d6d415bull}}, // 10^32
{{0x38c15b0a00000000ull, 0x0000314dc6448d93ull}}, // 10^33
{{0x38c15b0a00000000ull, 0x0000314dc6448d93ull}}, // 10^33
{{0x38c15b0a00000000ull, 0x0000314dc6448d93ull}}, // 10^33, entry 112
{{0x378d8e6400000000ull, 0x0001ed09bead87c0ull}}, // 10^34
{{0x378d8e6400000000ull, 0x0001ed09bead87c0ull}}, // 10^34
{{0x378d8e6400000000ull, 0x0001ed09bead87c0ull}}, // 10^34
{{0x2b878fe800000000ull, 0x0013426172c74d82ull}}, // 10^35
{{0x2b878fe800000000ull, 0x0013426172c74d82ull}}, // 10^35
{{0x2b878fe800000000ull, 0x0013426172c74d82ull}}, // 10^35
{{0x2b878fe800000000ull, 0x0013426172c74d82ull}}, // 10^35
{{0xb34b9f1000000000ull, 0x00c097ce7bc90715ull}}, // 10^36
{{0x00f436a000000000ull, 0x0785ee10d5da46d9ull}}, // 10^37
{{0x00f436a000000000ull, 0x0785ee10d5da46d9ull}}, // 10^37
{{0x00f436a000000000ull, 0x0785ee10d5da46d9ull}}, // 10^37
{{0x098a224000000000ull, 0x4b3b4ca85a86c47aull}}, // 10^38
{{0x098a224000000000ull, 0x4b3b4ca85a86c47aull}}, // 10^38
{{0x098a224000000000ull, 0x4b3b4ca85a86c47aull}}, // 10^38
{{0x098a224000000000ull, 0x4b3b4ca85a86c47aull}}, // 10^38
};