Google Git
Sign in
gnu / gcc / 4a0fed0c0c7241562eaa5f1a4c916b689429ad86 / . / libgcc / config / libbid / bid128.c
blob: 4c3d2a4f2bb05593c878e1fd4a9b81f397a72206 [file] [log] [blame]
/* Copyright (C) 2007-2021 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"
// the first entry of nr_digits[i - 1] (where 1 <= i <= 113), indicates
// the number of decimal digits needed to represent a binary number with i bits;
// however, if a binary number of i bits may require either k or k + 1 decimal
// digits, then the first entry of nr_digits[i - 1] is 0; in this case if the
// number is less than the value represented by the second and third entries
// concatenated, then the number of decimal digits k is the fourth entry, else
// the number of decimal digits is the fourth entry plus 1
DEC_DIGITS nr_digits[] = { // only the first entry is used if it is not 0
{1, 0x0000000000000000ULL, 0x000000000000000aULL, 1}
, // 1-bit n < 10^1
{1, 0x0000000000000000ULL, 0x000000000000000aULL, 1}
, // 2-bit n < 10^1
{1, 0x0000000000000000ULL, 0x000000000000000aULL, 1}
, // 3-bit n < 10^1
{0, 0x0000000000000000ULL, 0x000000000000000aULL, 1}
, // 4-bit n ? 10^1
{2, 0x0000000000000000ULL, 0x0000000000000064ULL, 2}
, // 5-bit n < 10^2
{2, 0x0000000000000000ULL, 0x0000000000000064ULL, 2}
, // 6-bit n < 10^2
{0, 0x0000000000000000ULL, 0x0000000000000064ULL, 2}
, // 7-bit n ? 10^2
{3, 0x0000000000000000ULL, 0x00000000000003e8ULL, 3}
, // 8-bit n < 10^3
{3, 0x0000000000000000ULL, 0x00000000000003e8ULL, 3}
, // 9-bit n < 10^3
{0, 0x0000000000000000ULL, 0x00000000000003e8ULL, 3}
, // 10-bit n ? 10^3
{4, 0x0000000000000000ULL, 0x0000000000002710ULL, 4}
, // 11-bit n < 10^4
{4, 0x0000000000000000ULL, 0x0000000000002710ULL, 4}
, // 12-bit n < 10^4
{4, 0x0000000000000000ULL, 0x0000000000002710ULL, 4}
, // 13-bit n < 10^4
{0, 0x0000000000000000ULL, 0x0000000000002710ULL, 4}
, // 14-bit n ? 10^4
{5, 0x0000000000000000ULL, 0x00000000000186a0ULL, 5}
, // 15-bit n < 10^5
{5, 0x0000000000000000ULL, 0x00000000000186a0ULL, 5}
, // 16-bit n < 10^5
{0, 0x0000000000000000ULL, 0x00000000000186a0ULL, 5}
, // 17-bit n ? 10^5
{6, 0x0000000000000000ULL, 0x00000000000f4240ULL, 6}
, // 18-bit n < 10^6
{6, 0x0000000000000000ULL, 0x00000000000f4240ULL, 6}
, // 19-bit n < 10^6
{0, 0x0000000000000000ULL, 0x00000000000f4240ULL, 6}
, // 20-bit n ? 10^6
{7, 0x0000000000000000ULL, 0x0000000000989680ULL, 7}
, // 21-bit n < 10^7
{7, 0x0000000000000000ULL, 0x0000000000989680ULL, 7}
, // 22-bit n < 10^7
{7, 0x0000000000000000ULL, 0x0000000000989680ULL, 7}
, // 23-bit n < 10^7
{0, 0x0000000000000000ULL, 0x0000000000989680ULL, 7}
, // 24-bit n ? 10^7
{8, 0x0000000000000000ULL, 0x0000000005f5e100ULL, 8}
, // 25-bit n < 10^8
{8, 0x0000000000000000ULL, 0x0000000005f5e100ULL, 8}
, // 26-bit n < 10^8
{0, 0x0000000000000000ULL, 0x0000000005f5e100ULL, 8}
, // 27-bit n ? 10^8
{9, 0x0000000000000000ULL, 0x000000003b9aca00ULL, 9}
, // 28-bit n < 10^9
{9, 0x0000000000000000ULL, 0x000000003b9aca00ULL, 9}
, // 29-bit n < 10^9
{0, 0x0000000000000000ULL, 0x000000003b9aca00ULL, 9}
, // 30-bit n ? 10^9
{10, 0x0000000000000000ULL, 0x00000002540be400ULL, 10}
, // 31-bit n < 10^10
{10, 0x0000000000000000ULL, 0x00000002540be400ULL, 10}
, // 32-bit n < 10^10
{10, 0x0000000000000000ULL, 0x00000002540be400ULL, 10}
, // 33-bit n < 10^10
{0, 0x0000000000000000ULL, 0x00000002540be400ULL, 10}
, // 34-bit n ? 10^10
{11, 0x0000000000000000ULL, 0x000000174876e800ULL, 11}
, // 35-bit n < 10^11
{11, 0x0000000000000000ULL, 0x000000174876e800ULL, 11}
, // 36-bit n < 10^11
{0, 0x0000000000000000ULL, 0x000000174876e800ULL, 11}
, // 37-bit n ? 10^11
{12, 0x0000000000000000ULL, 0x000000e8d4a51000ULL, 12}
, // 38-bit n < 10^12
{12, 0x0000000000000000ULL, 0x000000e8d4a51000ULL, 12}
, // 39-bit n < 10^12
{0, 0x0000000000000000ULL, 0x000000e8d4a51000ULL, 12}
, // 40-bit n ? 10^12
{13, 0x0000000000000000ULL, 0x000009184e72a000ULL, 13}
, // 41-bit n < 10^13
{13, 0x0000000000000000ULL, 0x000009184e72a000ULL, 13}
, // 42-bit n < 10^13
{13, 0x0000000000000000ULL, 0x000009184e72a000ULL, 13}
, // 43-bit n < 10^13
{0, 0x0000000000000000ULL, 0x000009184e72a000ULL, 13}
, // 44-bit n ? 10^13
{14, 0x0000000000000000ULL, 0x00005af3107a4000ULL, 14}
, // 45-bit n < 10^14
{14, 0x0000000000000000ULL, 0x00005af3107a4000ULL, 14}
, // 46-bit n < 10^14
{0, 0x0000000000000000ULL, 0x00005af3107a4000ULL, 14}
, // 47-bit n ? 10^14
{15, 0x0000000000000000ULL, 0x00038d7ea4c68000ULL, 15}
, // 48-bit n < 10^15
{15, 0x0000000000000000ULL, 0x00038d7ea4c68000ULL, 15}
, // 49-bit n < 10^15
{0, 0x0000000000000000ULL, 0x00038d7ea4c68000ULL, 15}
, // 50-bit n ? 10^15
{16, 0x0000000000000000ULL, 0x002386f26fc10000ULL, 16}
, // 51-bit n < 10^16
{16, 0x0000000000000000ULL, 0x002386f26fc10000ULL, 16}
, // 52-bit n < 10^16
{16, 0x0000000000000000ULL, 0x002386f26fc10000ULL, 16}
, // 53-bit n < 10^16
{0, 0x0000000000000000ULL, 0x002386f26fc10000ULL, 16}
, // 54-bit n ? 10^16
{17, 0x0000000000000000ULL, 0x016345785d8a0000ULL, 17}
, // 55-bit n < 10^17
{17, 0x0000000000000000ULL, 0x016345785d8a0000ULL, 17}
, // 56-bit n < 10^17
{0, 0x0000000000000000ULL, 0x016345785d8a0000ULL, 17}
, // 57-bit n ? 10^17
{18, 0x0000000000000000ULL, 0x0de0b6b3a7640000ULL, 18}
, // 58-bit n < 10^18
{18, 0x0000000000000000ULL, 0x0de0b6b3a7640000ULL, 18}
, // 59-bit n < 10^18
{0, 0x0000000000000000ULL, 0x0de0b6b3a7640000ULL, 18}
, // 60-bit n ? 10^18
{19, 0x0000000000000000ULL, 0x8ac7230489e80000ULL, 19}
, // 61-bit n < 10^19
{19, 0x0000000000000000ULL, 0x8ac7230489e80000ULL, 19}
, // 62-bit n < 10^19
{19, 0x0000000000000000ULL, 0x8ac7230489e80000ULL, 19}
, // 63-bit n < 10^19
{0, 0x0000000000000000ULL, 0x8ac7230489e80000ULL, 19}
, // 64-bit n ? 10^19
{20, 0x0000000000000005ULL, 0x6bc75e2d63100000ULL, 20}
, // 65-bit n < 10^20
{20, 0x0000000000000005ULL, 0x6bc75e2d63100000ULL, 20}
, // 66-bit n < 10^20
{0, 0x0000000000000005ULL, 0x6bc75e2d63100000ULL, 20}
, // 67-bit n ? 10^20
{21, 0x0000000000000036ULL, 0x35c9adc5dea00000ULL, 21}
, // 68-bit n < 10^21
{21, 0x0000000000000036ULL, 0x35c9adc5dea00000ULL, 21}
, // 69-bit n < 10^21
{0, 0x0000000000000036ULL, 0x35c9adc5dea00000ULL, 21}
, // 70-bit n ? 10^21
{22, 0x000000000000021eULL, 0x19e0c9bab2400000ULL, 22}
, // 71-bit n < 10^22
{22, 0x000000000000021eULL, 0x19e0c9bab2400000ULL, 22}
, // 72-bit n < 10^22
{22, 0x000000000000021eULL, 0x19e0c9bab2400000ULL, 22}
, // 73-bit n < 10^22
{0, 0x000000000000021eULL, 0x19e0c9bab2400000ULL, 22}
, // 74-bit n ? 10^22
{23, 0x000000000000152dULL, 0x02c7e14af6800000ULL, 23}
, // 75-bit n < 10^23
{23, 0x000000000000152dULL, 0x02c7e14af6800000ULL, 23}
, // 76-bit n < 10^23
{0, 0x000000000000152dULL, 0x02c7e14af6800000ULL, 23}
, // 77-bit n ? 10^23
{24, 0x000000000000d3c2ULL, 0x1bcecceda1000000ULL, 24}
, // 78-bit n < 10^24
{24, 0x000000000000d3c2ULL, 0x1bcecceda1000000ULL, 24}
, // 79-bit n < 10^24
{0, 0x000000000000d3c2ULL, 0x1bcecceda1000000ULL, 24}
, // 80-bit n ? 10^24
{25, 0x0000000000084595ULL, 0x161401484a000000ULL, 25}
, // 81-bit n < 10^25
{25, 0x0000000000084595ULL, 0x161401484a000000ULL, 25}
, // 82-bit n < 10^25
{25, 0x0000000000084595ULL, 0x161401484a000000ULL, 25}
, // 83-bit n < 10^25
{0, 0x0000000000084595ULL, 0x161401484a000000ULL, 25}
, // 84-bit n ? 10^25
{26, 0x000000000052b7d2ULL, 0xdcc80cd2e4000000ULL, 26}
, // 85-bit n < 10^26
{26, 0x000000000052b7d2ULL, 0xdcc80cd2e4000000ULL, 26}
, // 86-bit n < 10^26
{0, 0x000000000052b7d2ULL, 0xdcc80cd2e4000000ULL, 26}
, // 87-bit n ? 10^26
{27, 0x00000000033b2e3cULL, 0x9fd0803ce8000000ULL, 27}
, // 88-bit n < 10^27
{27, 0x00000000033b2e3cULL, 0x9fd0803ce8000000ULL, 27}
, // 89-bit n < 10^27
{0, 0x00000000033b2e3cULL, 0x9fd0803ce8000000ULL, 27}
, // 90-bit n ? 10^27
{28, 0x00000000204fce5eULL, 0x3e25026110000000ULL, 28}
, // 91-bit n < 10^28
{28, 0x00000000204fce5eULL, 0x3e25026110000000ULL, 28}
, // 92-bit n < 10^28
{28, 0x00000000204fce5eULL, 0x3e25026110000000ULL, 28}
, // 93-bit n < 10^28
{0, 0x00000000204fce5eULL, 0x3e25026110000000ULL, 28}
, // 94-bit n ? 10^28
{29, 0x00000001431e0faeULL, 0x6d7217caa0000000ULL, 29}
, // 95-bit n < 10^29
{29, 0x00000001431e0faeULL, 0x6d7217caa0000000ULL, 29}
, // 96-bit n < 10^29
{0, 0x00000001431e0faeULL, 0x6d7217caa0000000ULL, 29}
, // 97-bit n ? 10^29
{30, 0x0000000c9f2c9cd0ULL, 0x4674edea40000000ULL, 30}
, // 98-bit n < 10^30
{30, 0x0000000c9f2c9cd0ULL, 0x4674edea40000000ULL, 30}
, // 99-bit n < 10^30
{0, 0x0000000c9f2c9cd0ULL, 0x4674edea40000000ULL, 30}
, // 100-bit n ? 10^30
{31, 0x0000007e37be2022ULL, 0xc0914b2680000000ULL, 31}
, // 101-bit n < 10^31
{31, 0x0000007e37be2022ULL, 0xc0914b2680000000ULL, 31}
, // 102-bit n < 10^31
{0, 0x0000007e37be2022ULL, 0xc0914b2680000000ULL, 31}
, // 103-bit n ? 10^31
{32, 0x000004ee2d6d415bULL, 0x85acef8100000000ULL, 32}
, // 104-bit n < 10^32
{32, 0x000004ee2d6d415bULL, 0x85acef8100000000ULL, 32}
, // 105-bit n < 10^32
{32, 0x000004ee2d6d415bULL, 0x85acef8100000000ULL, 32}
, // 106-bit n < 10^32
{0, 0x000004ee2d6d415bULL, 0x85acef8100000000ULL, 32}
, // 107-bit n ? 10^32
{33, 0x0000314dc6448d93ULL, 0x38c15b0a00000000ULL, 33}
, // 108-bit n < 10^33
{33, 0x0000314dc6448d93ULL, 0x38c15b0a00000000ULL, 33}
, // 109-bit n < 10^33
{0, 0x0000314dc6448d93ULL, 0x38c15b0a00000000ULL, 33}
, // 100-bit n ? 10^33
{34, 0x0001ed09bead87c0ULL, 0x378d8e6400000000ULL, 34}
, // 111-bit n < 10^34
{34, 0x0001ed09bead87c0ULL, 0x378d8e6400000000ULL, 34}
, // 112-bit n < 10^34
{0, 0x0001ed09bead87c0ULL, 0x378d8e6400000000ULL, 34} // 113-bit n ? 10^34
//{ 35, 0x0013426172c74d82ULL, 0x2b878fe800000000ULL, 35 } // 114-bit n < 10^35
};
// midpoint64[i - 1] = 1/2 * 10^i = 5 * 10^(i-1), 1 <= i <= 19
UINT64 midpoint64[] = {
0x0000000000000005ULL, // 1/2 * 10^1 = 5 * 10^0
0x0000000000000032ULL, // 1/2 * 10^2 = 5 * 10^1
0x00000000000001f4ULL, // 1/2 * 10^3 = 5 * 10^2
0x0000000000001388ULL, // 1/2 * 10^4 = 5 * 10^3
0x000000000000c350ULL, // 1/2 * 10^5 = 5 * 10^4
0x000000000007a120ULL, // 1/2 * 10^6 = 5 * 10^5
0x00000000004c4b40ULL, // 1/2 * 10^7 = 5 * 10^6
0x0000000002faf080ULL, // 1/2 * 10^8 = 5 * 10^7
0x000000001dcd6500ULL, // 1/2 * 10^9 = 5 * 10^8
0x000000012a05f200ULL, // 1/2 * 10^10 = 5 * 10^9
0x0000000ba43b7400ULL, // 1/2 * 10^11 = 5 * 10^10
0x000000746a528800ULL, // 1/2 * 10^12 = 5 * 10^11
0x0000048c27395000ULL, // 1/2 * 10^13 = 5 * 10^12
0x00002d79883d2000ULL, // 1/2 * 10^14 = 5 * 10^13
0x0001c6bf52634000ULL, // 1/2 * 10^15 = 5 * 10^14
0x0011c37937e08000ULL, // 1/2 * 10^16 = 5 * 10^15
0x00b1a2bc2ec50000ULL, // 1/2 * 10^17 = 5 * 10^16
0x06f05b59d3b20000ULL, // 1/2 * 10^18 = 5 * 10^17
0x4563918244f40000ULL // 1/2 * 10^19 = 5 * 10^18
};
// midpoint128[i - 20] = 1/2 * 10^i = 5 * 10^(i-1), 20 <= i <= 38
UINT128 midpoint128[] = { // the 64-bit word order is L, H
{{0xb5e3af16b1880000ULL, 0x0000000000000002ULL}
}
, // 1/2 * 10^20 = 5 * 10^19
{{0x1ae4d6e2ef500000ULL, 0x000000000000001bULL}
}
, // 1/2 * 10^21 = 5 * 10^20
{{0x0cf064dd59200000ULL, 0x000000000000010fULL}
}
, // 1/2 * 10^22 = 5 * 10^21
{{0x8163f0a57b400000ULL, 0x0000000000000a96ULL}
}
, // 1/2 * 10^23 = 5 * 10^22
{{0x0de76676d0800000ULL, 0x00000000000069e1ULL}
}
, // 1/2 * 10^24 = 5 * 10^23
{{0x8b0a00a425000000ULL, 0x00000000000422caULL}
}
, // 1/2 * 10^25 = 5 * 10^24
{{0x6e64066972000000ULL, 0x0000000000295be9ULL}
}
, // 1/2 * 10^26 = 5 * 10^25
{{0x4fe8401e74000000ULL, 0x00000000019d971eULL}
}
, // 1/2 * 10^27 = 5 * 10^26
{{0x1f12813088000000ULL, 0x000000001027e72fULL}
}
, // 1/2 * 10^28 = 5 * 10^27
{{0x36b90be550000000ULL, 0x00000000a18f07d7ULL}
}
, // 1/2 * 10^29 = 5 * 10^28
{{0x233a76f520000000ULL, 0x000000064f964e68ULL}
}
, // 1/2 * 10^30 = 5 * 10^29
{{0x6048a59340000000ULL, 0x0000003f1bdf1011ULL}
}
, // 1/2 * 10^31 = 5 * 10^30
{{0xc2d677c080000000ULL, 0x0000027716b6a0adULL}
}
, // 1/2 * 10^32 = 5 * 10^31
{{0x9c60ad8500000000ULL, 0x000018a6e32246c9ULL}
}
, // 1/2 * 10^33 = 5 * 10^32
{{0x1bc6c73200000000ULL, 0x0000f684df56c3e0ULL}
}
, // 1/2 * 10^34 = 5 * 10^33
{{0x15c3c7f400000000ULL, 0x0009a130b963a6c1ULL}
}
, // 1/2 * 10^35 = 5 * 10^34
{{0xd9a5cf8800000000ULL, 0x00604be73de4838aULL}
}
, // 1/2 * 10^36 = 5 * 10^35
{{0x807a1b5000000000ULL, 0x03c2f7086aed236cULL}
}
, // 1/2 * 10^37 = 5 * 10^36
{{0x04c5112000000000ULL, 0x259da6542d43623dULL}
} // 1/2 * 10^38 = 5 * 10^37
};
// midpoint192[i - 39] = 1/2 * 10^i = 5 * 10^(i-1), 39 <= i <= 58
UINT192 midpoint192[] = { // the 64-bit word order is L, M, H
{{0x2fb2ab4000000000ULL, 0x78287f49c4a1d662ULL, 0x0000000000000001ULL}
}
,
// 1/2 * 10^39 = 5 * 10^38
{{0xdcfab08000000000ULL, 0xb194f8e1ae525fd5ULL, 0x000000000000000eULL}
}
,
// 1/2 * 10^40 = 5 * 10^39
{{0xa1cae50000000000ULL, 0xefd1b8d0cf37be5aULL, 0x0000000000000092ULL}
}
,
// 1/2 * 10^41 = 5 * 10^40
{{0x51ecf20000000000ULL, 0x5e313828182d6f8aULL, 0x00000000000005bdULL}
}
,
// 1/2 * 10^42 = 5 * 10^41
{{0x3341740000000000ULL, 0xadec3190f1c65b67ULL, 0x0000000000003965ULL}
}
,
// 1/2 * 10^43 = 5 * 10^42
{{0x008e880000000000ULL, 0xcb39efa971bf9208ULL, 0x0000000000023df8ULL}
}
,
// 1/2 * 10^44 = 5 * 10^43
{{0x0591500000000000ULL, 0xf0435c9e717bb450ULL, 0x0000000000166bb7ULL}
}
,
// 1/2 * 10^45 = 5 * 10^44
{{0x37ad200000000000ULL, 0x62a19e306ed50b20ULL, 0x0000000000e0352fULL}
}
,
// 1/2 * 10^46 = 5 * 10^45
{{0x2cc3400000000000ULL, 0xda502de454526f42ULL, 0x0000000008c213d9ULL}
}
,
// 1/2 * 10^47 = 5 * 10^46
{{0xbfa0800000000000ULL, 0x8721caeb4b385895ULL, 0x000000005794c682ULL}
}
,
// 1/2 * 10^48 = 5 * 10^47
{{0x7c45000000000000ULL, 0x4751ed30f03375d9ULL, 0x000000036bcfc119ULL}
}
,
// 1/2 * 10^49 = 5 * 10^48
{{0xdab2000000000000ULL, 0xc93343e962029a7eULL, 0x00000022361d8afcULL}
}
,
// 1/2 * 10^50 = 5 * 10^49
{{0x8af4000000000000ULL, 0xdc00a71dd41a08f4ULL, 0x000001561d276ddfULL}
}
,
// 1/2 * 10^51 = 5 * 10^50
{{0x6d88000000000000ULL, 0x9806872a4904598dULL, 0x00000d5d238a4abeULL}
}
,
// 1/2 * 10^52 = 5 * 10^51
{{0x4750000000000000ULL, 0xf04147a6da2b7f86ULL, 0x000085a36366eb71ULL}
}
,
// 1/2 * 10^53 = 5 * 10^52
{{0xc920000000000000ULL, 0x628ccc8485b2fb3eULL, 0x00053861e2053273ULL}
}
,
// 1/2 * 10^54 = 5 * 10^53
{{0xdb40000000000000ULL, 0xd97ffd2d38fdd073ULL, 0x003433d2d433f881ULL}
}
,
// 1/2 * 10^55 = 5 * 10^54
{{0x9080000000000000ULL, 0x7effe3c439ea2486ULL, 0x020a063c4a07b512ULL}
}
,
// 1/2 * 10^56 = 5 * 10^55
{{0xa500000000000000ULL, 0xf5fee5aa43256d41ULL, 0x14643e5ae44d12b8ULL}
}
,
// 1/2 * 10^57 = 5 * 10^56
{{0x7200000000000000ULL, 0x9bf4f8a69f764490ULL, 0xcbea6f8ceb02bb39ULL}
}
// 1/2 * 10^58 = 5 * 10^57
};
// midpoint256[i - 59] = 1/2 * 10^i = 5 * 10^(i-1), 59 <= i <= 68
UINT256 midpoint256[] = { // the 64-bit word order is LL, LH, HL, HH
{{0x7400000000000000ULL, 0x1791b6823a9eada4ULL,
0xf7285b812e1b5040ULL, 0x0000000000000007ULL}
}
, // 1/2 * 10^59 = 5 * 10^58
{{0x8800000000000000ULL, 0xebb121164a32c86cULL,
0xa793930bcd112280ULL, 0x000000000000004fULL}
}
, // 1/2 * 10^60 = 5 * 10^59
{{0x5000000000000000ULL, 0x34eb4adee5fbd43dULL,
0x8bc3be7602ab5909ULL, 0x000000000000031cULL}
}
, // 1/2 * 10^61 = 5 * 10^60
{{0x2000000000000000ULL, 0x1130ecb4fbd64a65ULL,
0x75a5709c1ab17a5cULL, 0x0000000000001f1dULL}
}
, // 1/2 * 10^62 = 5 * 10^61
{{0x4000000000000000ULL, 0xabe93f11d65ee7f3ULL,
0x987666190aeec798ULL, 0x0000000000013726ULL}
}
, // 1/2 * 10^63 = 5 * 10^62
{{0x8000000000000000ULL, 0xb71c76b25fb50f80ULL,
0xf49ffcfa6d53cbf6ULL, 0x00000000000c2781ULL}
}
, // 1/2 * 10^64 = 5 * 10^63
{{0x0000000000000000ULL, 0x271ca2f7bd129b05ULL,
0x8e3fe1c84545f7a3ULL, 0x0000000000798b13ULL}
}
, // 1/2 * 10^65 = 5 * 10^64
{{0x0000000000000000ULL, 0x871e5dad62ba0e32ULL,
0x8e7ed1d2b4bbac5fULL, 0x0000000004bf6ec3ULL}
}
, // 1/2 * 10^66 = 5 * 10^65
{{0x0000000000000000ULL, 0x472fa8c5db448df4ULL,
0x90f4323b0f54bbbbULL, 0x000000002f7a53a3ULL}
}
, // 1/2 * 10^67 = 5 * 10^66
{{0x0000000000000000ULL, 0xc7dc97ba90ad8b88ULL,
0xa989f64e994f5550ULL, 0x00000001dac74463ULL}
}
, // 1/2 * 10^68 = 5 * 10^67
{{0x0000000000000000ULL, 0xce9ded49a6c77350ULL,
0x9f639f11fd195527ULL, 0x000000128bc8abe4ULL}
}
, // 1/2 * 10^69 = 5 * 10^68
{{0x0000000000000000ULL, 0x122b44e083ca8120ULL,
0x39e436b3e2fd538eULL, 0x000000b975d6b6eeULL}
}
, // 1/2 * 10^70 = 5 * 10^69
{{0x0000000000000000ULL, 0xb5b0b0c525e90b40ULL,
0x42ea2306dde5438cULL, 0x0000073e9a63254eULL}
}
, // 1/2 * 10^71 = 5 * 10^70
{{0x0000000000000000ULL, 0x18e6e7b37b1a7080ULL,
0x9d255e44aaf4a37fULL, 0x0000487207df750eULL}
}
, // 1/2 * 10^72 = 5 * 10^71
{{0x0000000000000000ULL, 0xf9050d02cf086500ULL,
0x2375aeaead8e62f6ULL, 0x0002d4744eba9292ULL}
}
, // 1/2 * 10^73 = 5 * 10^72
{{0x0000000000000000ULL, 0xba32821c1653f200ULL,
0x6298d2d2c78fdda5ULL, 0x001c4c8b1349b9b5ULL}
}
, // 1/2 * 10^74 = 5 * 10^73
{{0x0000000000000000ULL, 0x45f91518df477400ULL,
0xd9f83c3bcb9ea879ULL, 0x011afd6ec0e14115ULL}
}
, // 1/2 * 10^75 = 5 * 10^74
{{0x0000000000000000ULL, 0xbbbad2f8b8ca8800ULL,
0x83b25a55f43294bcULL, 0x0b0de65388cc8adaULL}
}
, // 1/2 * 10^76 = 5 * 10^75
{{0x0000000000000000ULL, 0x554c3db737e95000ULL,
0x24f7875b89f9cf5fULL, 0x6e8aff4357fd6c89ULL}
} // 1/2 * 10^77 = 5 * 10^76
};
// ten2k64[i] = 10^i, 0 <= i <= 19
UINT64 ten2k64[] = {
0x0000000000000001ULL, // 10^0
0x000000000000000aULL, // 10^1
0x0000000000000064ULL, // 10^2
0x00000000000003e8ULL, // 10^3
0x0000000000002710ULL, // 10^4
0x00000000000186a0ULL, // 10^5
0x00000000000f4240ULL, // 10^6
0x0000000000989680ULL, // 10^7
0x0000000005f5e100ULL, // 10^8
0x000000003b9aca00ULL, // 10^9
0x00000002540be400ULL, // 10^10
0x000000174876e800ULL, // 10^11
0x000000e8d4a51000ULL, // 10^12
0x000009184e72a000ULL, // 10^13
0x00005af3107a4000ULL, // 10^14
0x00038d7ea4c68000ULL, // 10^15
0x002386f26fc10000ULL, // 10^16
0x016345785d8a0000ULL, // 10^17
0x0de0b6b3a7640000ULL, // 10^18
0x8ac7230489e80000ULL // 10^19 (20 digits)
};
// ten2k128[i - 20] = 10^i, 20 <= i <= 38
UINT128 ten2k128[] = { // the 64-bit word order is L, H
{{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 (39 digits)
};
// might split into ten2k192[] and ten2k256[]
// ten2k256[i - 39] = 10^i, 39 <= i <= 68
UINT256 ten2k256[] = { // the 64-bit word order is LL, LH, HL, HH
{{0x5f65568000000000ULL, 0xf050fe938943acc4ULL,
0x0000000000000002ULL, 0x0000000000000000ULL}
}
, // 10^39
{{0xb9f5610000000000ULL, 0x6329f1c35ca4bfabULL,
0x000000000000001dULL, 0x0000000000000000ULL}
}
, // 10^40
{{0x4395ca0000000000ULL, 0xdfa371a19e6f7cb5ULL,
0x0000000000000125ULL, 0x0000000000000000ULL}
}
, // 10^41
{{0xa3d9e40000000000ULL, 0xbc627050305adf14ULL,
0x0000000000000b7aULL, 0x0000000000000000ULL}
}
, // 10^42
{{0x6682e80000000000ULL, 0x5bd86321e38cb6ceULL,
0x00000000000072cbULL, 0x0000000000000000ULL}
}
, // 10^43
{{0x011d100000000000ULL, 0x9673df52e37f2410ULL,
0x0000000000047bf1ULL, 0x0000000000000000ULL}
}
, // 10^44
{{0x0b22a00000000000ULL, 0xe086b93ce2f768a0ULL,
0x00000000002cd76fULL, 0x0000000000000000ULL}
}
, // 10^45
{{0x6f5a400000000000ULL, 0xc5433c60ddaa1640ULL,
0x0000000001c06a5eULL, 0x0000000000000000ULL}
}
, // 10^46
{{0x5986800000000000ULL, 0xb4a05bc8a8a4de84ULL,
0x00000000118427b3ULL, 0x0000000000000000ULL}
}
, // 10^47
{{0x7f41000000000000ULL, 0x0e4395d69670b12bULL,
0x00000000af298d05ULL, 0x0000000000000000ULL}
}
, // 10^48
{{0xf88a000000000000ULL, 0x8ea3da61e066ebb2ULL,
0x00000006d79f8232ULL, 0x0000000000000000ULL}
}
, // 10^49
{{0xb564000000000000ULL, 0x926687d2c40534fdULL,
0x000000446c3b15f9ULL, 0x0000000000000000ULL}
}
, // 10^50
{{0x15e8000000000000ULL, 0xb8014e3ba83411e9ULL,
0x000002ac3a4edbbfULL, 0x0000000000000000ULL}
}
, // 10^51
{{0xdb10000000000000ULL, 0x300d0e549208b31aULL,
0x00001aba4714957dULL, 0x0000000000000000ULL}
}
, // 10^52
{{0x8ea0000000000000ULL, 0xe0828f4db456ff0cULL,
0x00010b46c6cdd6e3ULL, 0x0000000000000000ULL}
}
, // 10^53
{{0x9240000000000000ULL, 0xc51999090b65f67dULL,
0x000a70c3c40a64e6ULL, 0x0000000000000000ULL}
}
, // 10^54
{{0xb680000000000000ULL, 0xb2fffa5a71fba0e7ULL,
0x006867a5a867f103ULL, 0x0000000000000000ULL}
}
, // 10^55
{{0x2100000000000000ULL, 0xfdffc78873d4490dULL,
0x04140c78940f6a24ULL, 0x0000000000000000ULL}
}
, // 10^56
{{0x4a00000000000000ULL, 0xebfdcb54864ada83ULL,
0x28c87cb5c89a2571ULL, 0x0000000000000000ULL}
}
, // 10^57 (58 digits)
{{0xe400000000000000ULL, 0x37e9f14d3eec8920ULL,
0x97d4df19d6057673ULL, 0x0000000000000001ULL}
}
, // 10^58
{{0xe800000000000000ULL, 0x2f236d04753d5b48ULL,
0xee50b7025c36a080ULL, 0x000000000000000fULL}
}
, // 10^59
{{0x1000000000000000ULL, 0xd762422c946590d9ULL,
0x4f2726179a224501ULL, 0x000000000000009fULL}
}
, // 10^60
{{0xa000000000000000ULL, 0x69d695bdcbf7a87aULL,
0x17877cec0556b212ULL, 0x0000000000000639ULL}
}
, // 10^61
{{0x4000000000000000ULL, 0x2261d969f7ac94caULL,
0xeb4ae1383562f4b8ULL, 0x0000000000003e3aULL}
}
, // 10^62
{{0x8000000000000000ULL, 0x57d27e23acbdcfe6ULL,
0x30eccc3215dd8f31ULL, 0x0000000000026e4dULL}
}
, // 10^63
{{0x0000000000000000ULL, 0x6e38ed64bf6a1f01ULL,
0xe93ff9f4daa797edULL, 0x0000000000184f03ULL}
}
, // 10^64
{{0x0000000000000000ULL, 0x4e3945ef7a25360aULL,
0x1c7fc3908a8bef46ULL, 0x0000000000f31627ULL}
}
, // 10^65
{{0x0000000000000000ULL, 0x0e3cbb5ac5741c64ULL,
0x1cfda3a5697758bfULL, 0x00000000097edd87ULL}
}
, // 10^66
{{0x0000000000000000ULL, 0x8e5f518bb6891be8ULL,
0x21e864761ea97776ULL, 0x000000005ef4a747ULL}
}
, // 10^67
{{0x0000000000000000ULL, 0x8fb92f75215b1710ULL,
0x5313ec9d329eaaa1ULL, 0x00000003b58e88c7ULL}
}
, // 10^68
{{0x0000000000000000ULL, 0x9d3bda934d8ee6a0ULL,
0x3ec73e23fa32aa4fULL, 0x00000025179157c9ULL}
}
, // 10^69
{{0x0000000000000000ULL, 0x245689c107950240ULL,
0x73c86d67c5faa71cULL, 0x00000172ebad6ddcULL}
}
, // 10^70
{{0x0000000000000000ULL, 0x6b61618a4bd21680ULL,
0x85d4460dbbca8719ULL, 0x00000e7d34c64a9cULL}
}
, // 10^71
{{0x0000000000000000ULL, 0x31cdcf66f634e100ULL,
0x3a4abc8955e946feULL, 0x000090e40fbeea1dULL}
}
, // 10^72
{{0x0000000000000000ULL, 0xf20a1a059e10ca00ULL,
0x46eb5d5d5b1cc5edULL, 0x0005a8e89d752524ULL}
}
, // 10^73
{{0x0000000000000000ULL, 0x746504382ca7e400ULL,
0xc531a5a58f1fbb4bULL, 0x003899162693736aULL}
}
, // 10^74
{{0x0000000000000000ULL, 0x8bf22a31be8ee800ULL,
0xb3f07877973d50f2ULL, 0x0235fadd81c2822bULL}
}
, // 10^75
{{0x0000000000000000ULL, 0x7775a5f171951000ULL,
0x0764b4abe8652979ULL, 0x161bcca7119915b5ULL}
}
, // 10^76
{{0x0000000000000000ULL, 0xaa987b6e6fd2a000ULL,
0x49ef0eb713f39ebeULL, 0xdd15fe86affad912ULL}
} // 10^77
};
// ten2mk128[k - 1] = 10^(-k) * 2^exp (k), where 1 <= k <= 34 and
// exp (k) = shiftright128[k - 1] + 128
UINT128 ten2mk128[] = {
{{0x999999999999999aULL, 0x1999999999999999ULL}
}
, // 10^(-1) * 2^128
{{0x28f5c28f5c28f5c3ULL, 0x028f5c28f5c28f5cULL}
}
, // 10^(-2) * 2^128
{{0x9db22d0e56041894ULL, 0x004189374bc6a7efULL}
}
, // 10^(-3) * 2^128
{{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
};
// shiftright128[] contains the right shift count to obtain C2* from the top
// 128 bits of the 128x128-bit product C2 * Kx
int shiftright128[] = {
0, // 128 - 128
0, // 128 - 128
0, // 128 - 128
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
};
// maskhigh128[] contains the mask to apply to the top 128 bits of the
// 128x128-bit product in order to obtain the high bits of f2*
// the 64-bit word order is L, H
UINT64 maskhigh128[] = {
0x0000000000000000ULL, // 0 = 128 - 128 bits
0x0000000000000000ULL, // 0 = 128 - 128 bits
0x0000000000000000ULL, // 0 = 128 - 128 bits
0x0000000000000007ULL, // 3 = 131 - 128 bits
0x000000000000003fULL, // 6 = 134 - 128 bits
0x00000000000001ffULL, // 9 = 137 - 128 bits
0x0000000000001fffULL, // 13 = 141 - 128 bits
0x000000000000ffffULL, // 16 = 144 - 128 bits
0x000000000007ffffULL, // 19 = 147 - 128 bits
0x00000000007fffffULL, // 23 = 151 - 128 bits
0x0000000003ffffffULL, // 26 = 154 - 128 bits
0x000000001fffffffULL, // 29 = 157 - 128 bits
0x00000001ffffffffULL, // 33 = 161 - 128 bits
0x0000000fffffffffULL, // 36 = 164 - 128 bits
0x0000007fffffffffULL, // 39 = 167 - 128 bits
0x000007ffffffffffULL, // 43 = 171 - 128 bits
0x00003fffffffffffULL, // 46 = 174 - 128 bits
0x0001ffffffffffffULL, // 49 = 177 - 128 bits
0x001fffffffffffffULL, // 53 = 181 - 128 bits
0x00ffffffffffffffULL, // 56 = 184 - 128 bits
0x07ffffffffffffffULL, // 59 = 187 - 128 bits
0x7fffffffffffffffULL, // 63 = 191 - 128 bits
0x0000000000000003ULL, // 2 = 194 - 192 bits
0x000000000000001fULL, // 5 = 197 - 192 bits
0x00000000000001ffULL, // 9 = 201 - 192 bits
0x0000000000000fffULL, // 12 = 204 - 192 bits
0x0000000000007fffULL, // 15 = 207 - 192 bits
0x000000000007ffffULL, // 21 = 211 - 192 bits
0x00000000003fffffULL, // 22 = 214 - 192 bits
0x0000000001ffffffULL, // 25 = 217 - 192 bits
0x000000000fffffffULL, // 28 = 220 - 192 bits
0x00000000ffffffffULL, // 32 = 224 - 192 bits
0x00000007ffffffffULL, // 35 = 227 - 192 bits
0x0000003fffffffffULL // 38 = 230 - 192 bits
};
// onehalf128[] contains the high bits of 1/2 positioned correctly for
// comparison with the high bits of f2*
// the 64-bit word order is L, H
UINT64 onehalf128[] = {
0x0000000000000000ULL, // 0 bits
0x0000000000000000ULL, // 0 bits
0x0000000000000000ULL, // 0 bits
0x0000000000000004ULL, // 3 bits
0x0000000000000020ULL, // 6 bits
0x0000000000000100ULL, // 9 bits
0x0000000000001000ULL, // 13 bits
0x0000000000008000ULL, // 16 bits
0x0000000000040000ULL, // 19 bits
0x0000000000400000ULL, // 23 bits
0x0000000002000000ULL, // 26 bits
0x0000000010000000ULL, // 29 bits
0x0000000100000000ULL, // 33 bits
0x0000000800000000ULL, // 36 bits
0x0000004000000000ULL, // 39 bits
0x0000040000000000ULL, // 43 bits
0x0000200000000000ULL, // 46 bits
0x0001000000000000ULL, // 49 bits
0x0010000000000000ULL, // 53 bits
0x0080000000000000ULL, // 56 bits
0x0400000000000000ULL, // 59 bits
0x4000000000000000ULL, // 63 bits
0x0000000000000002ULL, // 66 bits
0x0000000000000010ULL, // 69 bits
0x0000000000000100ULL, // 73 bits
0x0000000000000800ULL, // 76 bits
0x0000000000004000ULL, // 79 bits
0x0000000000040000ULL, // 83 bits
0x0000000000200000ULL, // 86 bits
0x0000000001000000ULL, // 89 bits
0x0000000008000000ULL, // 92 bits
0x0000000080000000ULL, // 96 bits
0x0000000400000000ULL, // 99 bits
0x0000002000000000ULL // 102 bits
};
UINT64 ten2mk64[] = {
0x199999999999999aULL, // 10^(-1) * 2^ 64
0x028f5c28f5c28f5dULL, // 10^(-2) * 2^ 64
0x004189374bc6a7f0ULL, // 10^(-3) * 2^ 64
0x00346dc5d638865aULL, // 10^(-4) * 2^ 67
0x0029f16b11c6d1e2ULL, // 10^(-5) * 2^ 70
0x00218def416bdb1bULL, // 10^(-6) * 2^ 73
0x0035afe535795e91ULL, // 10^(-7) * 2^ 77
0x002af31dc4611874ULL, // 10^(-8) * 2^ 80
0x00225c17d04dad2aULL, // 10^(-9) * 2^ 83
0x0036f9bfb3af7b76ULL, // 10^(-10) * 2^ 87
0x002bfaffc2f2c92bULL, // 10^(-11) * 2^ 90
0x00232f33025bd423ULL, // 10^(-12) * 2^ 93
0x00384b84d092ed04ULL, // 10^(-13) * 2^ 97
0x002d09370d425737ULL, // 10^(-14) * 2^100
0x0024075f3dceac2cULL, // 10^(-15) * 2^103
0x0039a5652fb11379ULL, // 10^(-16) * 2^107
};
// ten2mk128trunc[] contains T*, the top Ex >= 128 bits of 10^(-k),
// for 1 <= k <= 34
// the 64-bit word order is L, H
UINT128 ten2mk128trunc[] = {
{{0x9999999999999999ULL, 0x1999999999999999ULL}}, // 10^(-1) * 2^128
{{0x28f5c28f5c28f5c2ULL, 0x028f5c28f5c28f5cULL}}, // 10^(-2) * 2^128
{{0x9db22d0e56041893ULL, 0x004189374bc6a7efULL}}, // 10^(-3) * 2^128
{{0x4af4f0d844d013a9ULL, 0x00346dc5d6388659ULL}}, // 10^(-4) * 2^131
{{0x08c3f3e0370cdc87ULL, 0x0029f16b11c6d1e1ULL}}, // 10^(-5) * 2^134
{{0x6d698fe69270b06cULL, 0x00218def416bdb1aULL}}, // 10^(-6) * 2^137
{{0xaf0f4ca41d811a46ULL, 0x0035afe535795e90ULL}}, // 10^(-7) * 2^141
{{0xbf3f70834acdae9fULL, 0x002af31dc4611873ULL}}, // 10^(-8) * 2^144
{{0x65cc5a02a23e254cULL, 0x00225c17d04dad29ULL}}, // 10^(-9) * 2^147
{{0x6fad5cd10396a213ULL, 0x0036f9bfb3af7b75ULL}}, // 10^(-10) * 2^151
{{0xbfbde3da69454e75ULL, 0x002bfaffc2f2c92aULL}}, // 10^(-11) * 2^154
{{0x32fe4fe1edd10b91ULL, 0x00232f33025bd422ULL}}, // 10^(-12) * 2^157
{{0x84ca19697c81ac1bULL, 0x00384b84d092ed03ULL}}, // 10^(-13) * 2^161
{{0x03d4e1213067bce3ULL, 0x002d09370d425736ULL}}, // 10^(-14) * 2^164
{{0x3643e74dc052fd82ULL, 0x0024075f3dceac2bULL}}, // 10^(-15) * 2^167
{{0x56d30baf9a1e626aULL, 0x0039a5652fb11378ULL}}, // 10^(-16) * 2^171
{{0x12426fbfae7eb521ULL, 0x002e1dea8c8da92dULL}}, // 10^(-17) * 2^174
{{0x41cebfcc8b9890e7ULL, 0x0024e4bba3a48757ULL}}, // 10^(-18) * 2^177
{{0x694acc7a78f41b0cULL, 0x003b07929f6da558ULL}}, // 10^(-19) * 2^181
{{0xbaa23d2ec729af3dULL, 0x002f394219248446ULL}}, // 10^(-20) * 2^184
{{0xfbb4fdbf05baf297ULL, 0x0025c768141d369eULL}}, // 10^(-21) * 2^187
{{0x2c54c931a2c4b758ULL, 0x003c7240202ebdcbULL}}, // 10^(-22) * 2^191
{{0x89dd6dc14f03c5e0ULL, 0x00305b66802564a2ULL}}, // 10^(-23) * 2^194
{{0xd4b1249aa59c9e4dULL, 0x0026af8533511d4eULL}}, // 10^(-24) * 2^197
{{0x544ea0f76f60fd48ULL, 0x003de5a1ebb4fbb1ULL}}, // 10^(-25) * 2^201
{{0x76a54d92bf80caa0ULL, 0x00318481895d9627ULL}}, // 10^(-26) * 2^204
{{0x921dd7a89933d54dULL, 0x00279d346de4781fULL}}, // 10^(-27) * 2^207
{{0x8362f2a75b862214ULL, 0x003f61ed7ca0c032ULL}}, // 10^(-28) * 2^211
{{0xcf825bb91604e810ULL, 0x0032b4bdfd4d668eULL}}, // 10^(-29) * 2^214
{{0x0c684960de6a5340ULL, 0x00289097fdd7853fULL}}, // 10^(-30) * 2^217
{{0x3d203ab3e521dc33ULL, 0x002073accb12d0ffULL}}, // 10^(-31) * 2^220
{{0x2e99f7863b696052ULL, 0x0033ec47ab514e65ULL}}, // 10^(-32) * 2^224
{{0x587b2c6b62bab375ULL, 0x002989d2ef743eb7ULL}}, // 10^(-33) * 2^227
{{0xad2f56bc4efbc2c4ULL, 0x00213b0f25f69892ULL}}, // 10^(-34) * 2^230
};
// ten2mk128M[k - 1] = 10^(-k) * 2^exp (k), where 1 <= k <= 4 and
// exp (k) = shiftright128[k - 1] + 128
// the 64-bit word order is L, H
UINT128 ten2mk128M[] = {
{{0xcccccccccccccccdULL, 0xccccccccccccccccULL}}, // 10^(-1) * 2^131
{{0x3d70a3d70a3d70a4ULL, 0xa3d70a3d70a3d70aULL}}, // 10^(-2) * 2^134
{{0x645a1cac083126eaULL, 0x83126e978d4fdf3bULL}}, // 10^(-3) * 2^137
{{0xd3c36113404ea4a9ULL, 0xd1b71758e219652bULL}} // 10^(-4) * 2^141
};
// ten2mk128truncM[] contains T*, the top Ex >= 128 bits of 10^(-k),
// for 1 <= k <= 4; the top bits which are 0 are not represented
// the 64-bit word order is L, H
UINT128 ten2mk128truncM[] = {
{{0xccccccccccccccccULL, 0xccccccccccccccccULL}}, // 10^(-1) * 2^131
{{0x3d70a3d70a3d70a3ULL, 0xa3d70a3d70a3d70aULL}}, // 10^(-2) * 2^134
{{0x645a1cac083126e9ULL, 0x83126e978d4fdf3bULL}}, // 10^(-3) * 2^137
{{0xd3c36113404ea4a8ULL, 0xd1b71758e219652bULL}} // 10^(-4) * 2^141
};
// shiftright128M[] contains the right shift count to obtain C2* from the top
// 128 bits of the 128x128-bit product C2 * Kx
int shiftright128M[] = {
3, // 131 - 128
6, // 134 - 128
9, // 137 - 128
13 // 141 - 128
};
// maskhigh128M[] contains the mask to apply to the top 128 bits of the
// 128x128-bit product in order to obtain the high bits of f*
// the high 64 bits of the mask are 0, so only the low 64 bits are represented
UINT64 maskhigh128M[] = {
0x0000000000000007ULL, // 3 = 131 - 128 bits
0x000000000000003fULL, // 6 = 134 - 128 bits
0x00000000000001ffULL, // 9 = 137 - 128 bits
0x0000000000001fffULL // 13 = 141 - 128 bits
};
// onehalf128M[] contains 1/2 positioned correctly for
// comparison with the high bits of f*
// the high 64 bits are 0, so only the low 64 bits are represented
UINT64 onehalf128M[] = {
0x0000000000000004ULL, // 3 bits
0x0000000000000020ULL, // 6 bits
0x0000000000000100ULL, // 9 bits
0x0000000000001000ULL // 13 bits
};
// ten2mk192M[k - 1] = 10^(-k-4) * 2^exp (k), where 1 <= k <= 19 and
// exp (k) = shiftright128[k - 1] + 128
// the 64-bit word order is L, M, H
UINT192 ten2mk192M[] = {
{{0xcddd6e04c0592104ULL, 0x0fcf80dc33721d53ULL,
0xa7c5ac471b478423ULL}},
// 10^(-5) * 2^208
{{0xd7e45803cd141a6aULL, 0xa63f9a49c2c1b10fULL,
0x8637bd05af6c69b5ULL}},
// 10^(-6) * 2^211
{{0x8ca08cd2e1b9c3dcULL, 0x3d32907604691b4cULL,
0xd6bf94d5e57a42bcULL}},
// 10^(-7) * 2^215
{{0x3d4d3d758161697dULL, 0xfdc20d2b36ba7c3dULL,
0xabcc77118461cefcULL}},
// 10^(-8) * 2^218
{{0xfdd7645e011abacaULL, 0x31680a88f8953030ULL,
0x89705f4136b4a597ULL}},
// 10^(-9) * 2^221
{{0x2fbf06fcce912addULL, 0xb573440e5a884d1bULL,
0xdbe6fecebdedd5beULL}},
// 10^(-10) * 2^225
{{0xf2ff38ca3eda88b1ULL, 0xf78f69a51539d748ULL,
0xafebff0bcb24aafeULL}},
// 10^(-11) * 2^228
{{0xf598fa3b657ba08eULL, 0xf93f87b7442e45d3ULL,
0x8cbccc096f5088cbULL}},
// 10^(-12) * 2^231
{{0x88f4c3923bf900e3ULL, 0x2865a5f206b06fb9ULL,
0xe12e13424bb40e13ULL}},
// 10^(-13) * 2^235
{{0x6d909c74fcc733e9ULL, 0x538484c19ef38c94ULL,
0xb424dc35095cd80fULL}},
// 10^(-14) * 2^238
{{0x57a6e390ca38f654ULL, 0x0f9d37014bf60a10ULL,
0x901d7cf73ab0acd9ULL}},
// 10^(-15) * 2^241
{{0xbf716c1add27f086ULL, 0x4c2ebe687989a9b3ULL,
0xe69594bec44de15bULL}},
// 10^(-16) * 2^245
{{0xff8df0157db98d38ULL, 0x09befeb9fad487c2ULL,
0xb877aa3236a4b449ULL}},
// 10^(-17) * 2^248
{{0x32d7f344649470faULL, 0x3aff322e62439fcfULL,
0x9392ee8e921d5d07ULL}},
// 10^(-18) * 2^251
{{0x1e2652070753e7f5ULL, 0x2b31e9e3d06c32e5ULL,
0xec1e4a7db69561a5ULL}},
// 10^(-19) * 2^255
{{0x181ea8059f76532bULL, 0x88f4bb1ca6bcf584ULL,
0xbce5086492111aeaULL}},
// 10^(-20) * 2^258
{{0x467eecd14c5ea8efULL, 0xd3f6fc16ebca5e03ULL,
0x971da05074da7beeULL}},
// 10^(-21) * 2^261
{{0x70cb148213caa7e5ULL, 0x5324c68b12dd6338ULL,
0xf1c90080baf72cb1ULL}},
// 10^(-22) * 2^265
{{0x8d6f439b43088651ULL, 0x75b7053c0f178293ULL, 0xc16d9a0095928a27ULL}}
// 10^(-23) * 2^268
};
// ten2mk192truncM[] contains T*, the top Ex >= 192 bits of 10^(-k),
// for 5 <= k <= 23; the top bits which are 0 are not represented
// the 64-bit word order is L, M, H
UINT192 ten2mk192truncM[] = {
{{0xcddd6e04c0592103ULL, 0x0fcf80dc33721d53ULL,
0xa7c5ac471b478423ULL}},
// 10^(-5) * 2^208
{{0xd7e45803cd141a69ULL, 0xa63f9a49c2c1b10fULL,
0x8637bd05af6c69b5ULL}},
// 10^(-6) * 2^211
{{0x8ca08cd2e1b9c3dbULL, 0x3d32907604691b4cULL,
0xd6bf94d5e57a42bcULL}},
// 10^(-7) * 2^215
{{0x3d4d3d758161697cULL, 0xfdc20d2b36ba7c3dULL,
0xabcc77118461cefcULL}},
// 10^(-8) * 2^218
{{0xfdd7645e011abac9ULL, 0x31680a88f8953030ULL,
0x89705f4136b4a597ULL}},
// 10^(-9) * 2^221
{{0x2fbf06fcce912adcULL, 0xb573440e5a884d1bULL,
0xdbe6fecebdedd5beULL}},
// 10^(-10) * 2^225
{{0xf2ff38ca3eda88b0ULL, 0xf78f69a51539d748ULL,
0xafebff0bcb24aafeULL}},
// 10^(-11) * 2^228
{{0xf598fa3b657ba08dULL, 0xf93f87b7442e45d3ULL,
0x8cbccc096f5088cbULL}},
// 10^(-12) * 2^231
{{0x88f4c3923bf900e2ULL, 0x2865a5f206b06fb9ULL,
0xe12e13424bb40e13ULL}},
// 10^(-13) * 2^235
{{0x6d909c74fcc733e8ULL, 0x538484c19ef38c94ULL,
0xb424dc35095cd80fULL}},
// 10^(-14) * 2^238
{{0x57a6e390ca38f653ULL, 0x0f9d37014bf60a10ULL,
0x901d7cf73ab0acd9ULL}},
// 10^(-15) * 2^241
{{0xbf716c1add27f085ULL, 0x4c2ebe687989a9b3ULL,
0xe69594bec44de15bULL}},
// 10^(-16) * 2^245
{{0xff8df0157db98d37ULL, 0x09befeb9fad487c2ULL,
0xb877aa3236a4b449ULL}},
// 10^(-17) * 2^248
{{0x32d7f344649470f9ULL, 0x3aff322e62439fcfULL,
0x9392ee8e921d5d07ULL}},
// 10^(-18) * 2^251
{{0x1e2652070753e7f4ULL, 0x2b31e9e3d06c32e5ULL,
0xec1e4a7db69561a5ULL}},
// 10^(-19) * 2^255
{{0x181ea8059f76532aULL, 0x88f4bb1ca6bcf584ULL,
0xbce5086492111aeaULL}},
// 10^(-20) * 2^258
{{0x467eecd14c5ea8eeULL, 0xd3f6fc16ebca5e03ULL,
0x971da05074da7beeULL}},
// 10^(-21) * 2^261
{{0x70cb148213caa7e4ULL, 0x5324c68b12dd6338ULL,
0xf1c90080baf72cb1ULL}},
// 10^(-22) * 2^265
{{0x8d6f439b43088650ULL, 0x75b7053c0f178293ULL, 0xc16d9a0095928a27ULL}}
// 10^(-23) * 2^268
};
// shiftright192M[] contains the right shift count to obtain C2* from the top
// 192 bits of the 192x192-bit product C2 * Kx if 0 <= ind <= 14 where ind is
// the index in the table, or from the top 128 bits if 15 <= ind <= 18
int shiftright192M[] = {
16, // 208 - 192
19, // 211 - 192
23, // 215 - 192
26, // 218 - 192
29, // 221 - 192
33, // 225 - 192
36, // 228 - 192
39, // 231 - 192
43, // 235 - 192
46, // 238 - 192
49, // 241 - 192
53, // 245 - 192
56, // 248 - 192
59, // 251 - 192
63, // 255 - 192
2, // 258 - 256
5, // 261 - 256
9, // 265 - 256
12 // 268 - 256
};
// maskhigh192M[] contains the mask to apply to the top 192 bits of the
// 192x192-bit product in order to obtain the high bits of f*
// if 0 <= ind <= 14 where ind is the index in the table, then the high 128 bits
// of the 384-bit mask are 0; if 15 <= ind <= 18 then the high 64 bits are 0
UINT64 maskhigh192M[] = {
0x000000000000ffffULL, // 16 = 208 - 192 bits
0x000000000007ffffULL, // 19 = 211 - 192 bits
0x00000000007fffffULL, // 23 = 215 - 192 bits
0x0000000003ffffffULL, // 26 = 218 - 192 bits
0x000000001fffffffULL, // 29 = 221 - 192 bits
0x00000001ffffffffULL, // 33 = 225 - 192 bits
0x0000000fffffffffULL, // 36 = 228 - 192 bits
0x0000007fffffffffULL, // 39 = 231 - 192 bits
0x000007ffffffffffULL, // 43 = 235 - 192 bits
0x00003fffffffffffULL, // 46 = 238 - 192 bits
0x0001ffffffffffffULL, // 49 = 241 - 192 bits
0x001fffffffffffffULL, // 53 = 245 - 192 bits
0x00ffffffffffffffULL, // 56 = 248 - 192 bits
0x07ffffffffffffffULL, // 59 = 251 - 192 bits
0x7fffffffffffffffULL, // 63 = 255 - 192 bits
0x0000000000000003ULL, // 2 = 258 - 256 bits
0x000000000000001fULL, // 5 = 261 - 256 bits
0x00000000000001ffULL, // 9 = 265 - 256 bits
0x0000000000000fffULL // 12 = 268 - 256 bits
};
// onehalf192M[] contains 1/2 positioned correctly for
// comparison with the high bits of f*
// if 0 <= ind <= 14 where ind is the index in the table, then the high 128 bits
// of the 384-bit mask are 0; if 15 <= ind <= 18 then the high 648 bits are 0
UINT64 onehalf192M[] = {
0x0000000000008000ULL, // 16 = 208 - 192 bits
0x0000000000040000ULL, // 19 = 211 - 192 bits
0x0000000000400000ULL, // 23 = 215 - 192 bits
0x0000000002000000ULL, // 26 = 218 - 192 bits
0x0000000010000000ULL, // 29 = 221 - 192 bits
0x0000000100000000ULL, // 33 = 225 - 192 bits
0x0000000800000000ULL, // 36 = 228 - 192 bits
0x0000004000000000ULL, // 39 = 231 - 192 bits
0x0000040000000000ULL, // 43 = 235 - 192 bits
0x0000200000000000ULL, // 46 = 238 - 192 bits
0x0001000000000000ULL, // 49 = 241 - 192 bits
0x0010000000000000ULL, // 53 = 245 - 192 bits
0x0080000000000000ULL, // 56 = 248 - 192 bits
0x0400000000000000ULL, // 59 = 251 - 192 bits
0x4000000000000000ULL, // 63 = 255 - 192 bits
0x0000000000000002ULL, // 2 = 258 - 256 bits
0x0000000000000010ULL, // 5 = 261 - 256 bits
0x0000000000000100ULL, // 9 = 265 - 256 bits
0x0000000000000800ULL // 12 = 268 - 256 bits
};
// ten2mk256M[k - 1] = 10^(-k-23) * 2^exp (k), where 1 <= k <= 11 and
// exp (k) = shiftright128[k - 1] + 128
UINT256 ten2mk256M[] = { // the 64-bit word order is LL, LH, HL, HH
{{0xf23472530ce6e3edULL, 0xd78c3615cf3a050cULL,
0xc4926a9672793542ULL, 0x9abe14cd44753b52ULL}}, // 10^(-24) * 2^335
{{0xe9ed83b814a49fe1ULL, 0x8c1389bc7ec33b47ULL,
0x3a83ddbd83f52204ULL, 0xf79687aed3eec551ULL}}, // 10^(-25) * 2^339
{{0x87f1362cdd507fe7ULL, 0x3cdc6e306568fc39ULL,
0x95364afe032a819dULL, 0xc612062576589ddaULL}}, // 10^(-26) * 2^342
{{0x9ff42b5717739986ULL, 0xca49f1c05120c9c7ULL,
0x775ea264cf55347dULL, 0x9e74d1b791e07e48ULL}}, // 10^(-27) * 2^345
{{0xccb9def1bf1f5c09ULL, 0x76dcb60081ce0fa5ULL,
0x8bca9d6e188853fcULL, 0xfd87b5f28300ca0dULL}}, // 10^(-28) * 2^349
{{0xa3c7e58e327f7cd4ULL, 0x5f16f80067d80c84ULL,
0x096ee45813a04330ULL, 0xcad2f7f5359a3b3eULL}}, // 10^(-29) * 2^352
{{0xb6398471c1ff9710ULL, 0x18df2ccd1fe00a03ULL,
0xa1258379a94d028dULL, 0xa2425ff75e14fc31ULL}}, // 10^(-30) * 2^355
{{0xf82e038e34cc78daULL, 0x4718f0a419800802ULL,
0x80eacf948770ced7ULL, 0x81ceb32c4b43fcf4ULL}}, // 10^(-31) * 2^358
{{0x59e338e387ad8e29ULL, 0x0b5b1aa028ccd99eULL,
0x67de18eda5814af2ULL, 0xcfb11ead453994baULL}}, // 10^(-32) * 2^362
{{0x47e8fa4f9fbe0b54ULL, 0x6f7c154ced70ae18ULL,
0xecb1ad8aeacdd58eULL, 0xa6274bbdd0fadd61ULL}}, // 10^(-33) * 2^365
{{0xd320c83fb2fe6f76ULL, 0xbf967770bdf3be79ULL,
0xbd5af13bef0b113eULL, 0x84ec3c97da624ab4ULL}} // 10^(-34) * 2^368
};
// ten2mk256truncM[] contains T*, the top Ex >= 256 bits of 10^(-k),
// for 24 <= k <= 34; the top bits which are 0 are not represented
UINT256 ten2mk256truncM[] = { // the 64-bit word order is LL, LH, HL, HH
{{0xf23472530ce6e3ecULL, 0xd78c3615cf3a050cULL,
0xc4926a9672793542ULL, 0x9abe14cd44753b52ULL}}, // 10^(-24) * 2^335
{{0xe9ed83b814a49fe0ULL, 0x8c1389bc7ec33b47ULL,
0x3a83ddbd83f52204ULL, 0xf79687aed3eec551ULL}}, // 10^(-25) * 2^339
{{0x87f1362cdd507fe6ULL, 0x3cdc6e306568fc39ULL,
0x95364afe032a819dULL, 0xc612062576589ddaULL}}, // 10^(-26) * 2^342
{{0x775ea264cf55347cULL, 0x9ff42b5717739986ULL,
0xca49f1c05120c9c7ULL, 0x9e74d1b791e07e48ULL}}, // 10^(-27) * 2^345
{{0xccb9def1bf1f5c08ULL, 0x76dcb60081ce0fa5ULL,
0x8bca9d6e188853fcULL, 0xfd87b5f28300ca0dULL}}, // 10^(-28) * 2^349
{{0xa3c7e58e327f7cd3ULL, 0x5f16f80067d80c84ULL,
0x096ee45813a04330ULL, 0xcad2f7f5359a3b3eULL}}, // 10^(-29) * 2^352
{{0xb6398471c1ff970fULL, 0x18df2ccd1fe00a03ULL,
0xa1258379a94d028dULL, 0xa2425ff75e14fc31ULL}}, // 10^(-30) * 2^355
{{0xf82e038e34cc78d9ULL, 0x4718f0a419800802ULL,
0x80eacf948770ced7ULL, 0x81ceb32c4b43fcf4ULL}}, // 10^(-31) * 2^358
{{0x59e338e387ad8e28ULL, 0x0b5b1aa028ccd99eULL,
0x67de18eda5814af2ULL, 0xcfb11ead453994baULL}}, // 10^(-32) * 2^362
{{0x47e8fa4f9fbe0b53ULL, 0x6f7c154ced70ae18ULL,
0xecb1ad8aeacdd58eULL, 0xa6274bbdd0fadd61ULL}}, // 10^(-33) * 2^365
{{0xd320c83fb2fe6f75ULL, 0xbf967770bdf3be79ULL,
0xbd5af13bef0b113eULL, 0x84ec3c97da624ab4ULL}} // 10^(-34) * 2^368
};
// shiftright256M[] contains the right shift count to obtain C2* from the top
// 192 bits of the 256x256-bit product C2 * Kx
int shiftright256M[] = {
15, // 335 - 320
19, // 339 - 320
22, // 342 - 320
25, // 345 - 320
29, // 349 - 320
32, // 352 - 320 // careful of 32-bit machines!
35, // 355 - 320
38, // 358 - 320
42, // 362 - 320
45, // 365 - 320
48 // 368 - 320
};
// maskhigh256M[] contains the mask to apply to the top 192 bits of the
// 256x256-bit product in order to obtain the high bits of f*
UINT64 maskhigh256M[] = {
0x0000000000007fffULL, // 15 = 335 - 320 bits
0x000000000007ffffULL, // 19 = 339 - 320 bits
0x00000000003fffffULL, // 22 = 342 - 320 bits
0x0000000001ffffffULL, // 25 = 345 - 320 bits
0x000000001fffffffULL, // 29 = 349 - 320 bits
0x00000000ffffffffULL, // 32 = 352 - 320 bits
0x00000007ffffffffULL, // 35 = 355 - 320 bits
0x0000003fffffffffULL, // 38 = 358 - 320 bits
0x000003ffffffffffULL, // 42 = 362 - 320 bits
0x00001fffffffffffULL, // 45 = 365 - 320 bits
0x0000ffffffffffffULL // 48 = 368 - 320 bits
};
// onehalf256M[] contains 1/2 positioned correctly for comparison with the
// high bits of f*; the high 128 bits of the 512-bit mask are 0
UINT64 onehalf256M[] = {
0x0000000000004000ULL, // 15 = 335 - 320 bits
0x0000000000040000ULL, // 19 = 339 - 320 bits
0x0000000000200000ULL, // 22 = 342 - 320 bits
0x0000000001000000ULL, // 25 = 345 - 320 bits
0x0000000010000000ULL, // 29 = 349 - 320 bits
0x0000000080000000ULL, // 32 = 352 - 320 bits
0x0000000400000000ULL, // 35 = 355 - 320 bits
0x0000002000000000ULL, // 38 = 358 - 320 bits
0x0000020000000000ULL, // 42 = 362 - 320 bits
0x0000100000000000ULL, // 45 = 365 - 320 bits
0x0000800000000000ULL // 48 = 368 - 320 bits
};
// char_table2[] is used to convert n to string, where 10 <= n <= 99
unsigned char char_table2[180] = {
'1', '0',
'1', '1',
'1', '2',
'1', '3',
'1', '4',
'1', '5',
'1', '6',
'1', '7',
'1', '8',
'1', '9',
'2', '0',
'2', '1',
'2', '2',
'2', '3',
'2', '4',
'2', '5',
'2', '6',
'2', '7',
'2', '8',
'2', '9',
'3', '0',
'3', '1',
'3', '2',
'3', '3',
'3', '4',
'3', '5',
'3', '6',
'3', '7',
'3', '8',
'3', '9',
'4', '0',
'4', '1',
'4', '2',
'4', '3',
'4', '4',
'4', '5',
'4', '6',
'4', '7',
'4', '8',
'4', '9',
'5', '0',
'5', '1',
'5', '2',
'5', '3',
'5', '4',
'5', '5',
'5', '6',
'5', '7',
'5', '8',
'5', '9',
'6', '0',
'6', '1',
'6', '2',
'6', '3',
'6', '4',
'6', '5',
'6', '6',
'6', '7',
'6', '8',
'6', '9',
'7', '0',
'7', '1',
'7', '2',
'7', '3',
'7', '4',
'7', '5',
'7', '6',
'7', '7',
'7', '8',
'7', '9',
'8', '0',
'8', '1',
'8', '2',
'8', '3',
'8', '4',
'8', '5',
'8', '6',
'8', '7',
'8', '8',
'8', '9',
'9', '0',
'9', '1',
'9', '2',
'9', '3',
'9', '4',
'9', '5',
'9', '6',
'9', '7',
'9', '8',
'9', '9'
};
// char_table3[] is used to convert n to string, where 000 <= n <= 999
unsigned char char_table3[3000] = {
'0', '0', '0',
'0', '0', '1',
'0', '0', '2',
'0', '0', '3',
'0', '0', '4',
'0', '0', '5',
'0', '0', '6',
'0', '0', '7',
'0', '0', '8',
'0', '0', '9',
'0', '1', '0',
'0', '1', '1',
'0', '1', '2',
'0', '1', '3',
'0', '1', '4',
'0', '1', '5',
'0', '1', '6',
'0', '1', '7',
'0', '1', '8',
'0', '1', '9',
'0', '2', '0',
'0', '2', '1',
'0', '2', '2',
'0', '2', '3',
'0', '2', '4',
'0', '2', '5',
'0', '2', '6',
'0', '2', '7',
'0', '2', '8',
'0', '2', '9',
'0', '3', '0',
'0', '3', '1',
'0', '3', '2',
'0', '3', '3',
'0', '3', '4',
'0', '3', '5',
'0', '3', '6',
'0', '3', '7',
'0', '3', '8',
'0', '3', '9',
'0', '4', '0',
'0', '4', '1',
'0', '4', '2',
'0', '4', '3',
'0', '4', '4',
'0', '4', '5',
'0', '4', '6',
'0', '4', '7',
'0', '4', '8',
'0', '4', '9',
'0', '5', '0',
'0', '5', '1',
'0', '5', '2',
'0', '5', '3',
'0', '5', '4',
'0', '5', '5',
'0', '5', '6',
'0', '5', '7',
'0', '5', '8',
'0', '5', '9',
'0', '6', '0',
'0', '6', '1',
'0', '6', '2',
'0', '6', '3',
'0', '6', '4',
'0', '6', '5',
'0', '6', '6',
'0', '6', '7',
'0', '6', '8',
'0', '6', '9',
'0', '7', '0',
'0', '7', '1',
'0', '7', '2',
'0', '7', '3',
'0', '7', '4',
'0', '7', '5',
'0', '7', '6',
'0', '7', '7',
'0', '7', '8',
'0', '7', '9',
'0', '8', '0',
'0', '8', '1',
'0', '8', '2',
'0', '8', '3',
'0', '8', '4',
'0', '8', '5',
'0', '8', '6',
'0', '8', '7',
'0', '8', '8',
'0', '8', '9',
'0', '9', '0',
'0', '9', '1',
'0', '9', '2',
'0', '9', '3',
'0', '9', '4',
'0', '9', '5',
'0', '9', '6',
'0', '9', '7',
'0', '9', '8',
'0', '9', '9',
'1', '0', '0',
'1', '0', '1',
'1', '0', '2',
'1', '0', '3',
'1', '0', '4',
'1', '0', '5',
'1', '0', '6',
'1', '0', '7',
'1', '0', '8',
'1', '0', '9',
'1', '1', '0',
'1', '1', '1',
'1', '1', '2',
'1', '1', '3',
'1', '1', '4',
'1', '1', '5',
'1', '1', '6',
'1', '1', '7',
'1', '1', '8',
'1', '1', '9',
'1', '2', '0',
'1', '2', '1',
'1', '2', '2',
'1', '2', '3',
'1', '2', '4',
'1', '2', '5',
'1', '2', '6',
'1', '2', '7',
'1', '2', '8',
'1', '2', '9',
'1', '3', '0',
'1', '3', '1',
'1', '3', '2',
'1', '3', '3',
'1', '3', '4',
'1', '3', '5',
'1', '3', '6',
'1', '3', '7',
'1', '3', '8',
'1', '3', '9',
'1', '4', '0',
'1', '4', '1',
'1', '4', '2',
'1', '4', '3',
'1', '4', '4',
'1', '4', '5',
'1', '4', '6',
'1', '4', '7',
'1', '4', '8',
'1', '4', '9',
'1', '5', '0',
'1', '5', '1',
'1', '5', '2',
'1', '5', '3',
'1', '5', '4',
'1', '5', '5',
'1', '5', '6',
'1', '5', '7',
'1', '5', '8',
'1', '5', '9',
'1', '6', '0',
'1', '6', '1',
'1', '6', '2',
'1', '6', '3',
'1', '6', '4',
'1', '6', '5',
'1', '6', '6',
'1', '6', '7',
'1', '6', '8',
'1', '6', '9',
'1', '7', '0',
'1', '7', '1',
'1', '7', '2',
'1', '7', '3',
'1', '7', '4',
'1', '7', '5',
'1', '7', '6',
'1', '7', '7',
'1', '7', '8',
'1', '7', '9',
'1', '8', '0',
'1', '8', '1',
'1', '8', '2',
'1', '8', '3',
'1', '8', '4',
'1', '8', '5',
'1', '8', '6',
'1', '8', '7',
'1', '8', '8',
'1', '8', '9',
'1', '9', '0',
'1', '9', '1',
'1', '9', '2',
'1', '9', '3',
'1', '9', '4',
'1', '9', '5',
'1', '9', '6',
'1', '9', '7',
'1', '9', '8',
'1', '9', '9',
'2', '0', '0',
'2', '0', '1',
'2', '0', '2',
'2', '0', '3',
'2', '0', '4',
'2', '0', '5',
'2', '0', '6',
'2', '0', '7',
'2', '0', '8',
'2', '0', '9',
'2', '1', '0',
'2', '1', '1',
'2', '1', '2',
'2', '1', '3',
'2', '1', '4',
'2', '1', '5',
'2', '1', '6',
'2', '1', '7',
'2', '1', '8',
'2', '1', '9',
'2', '2', '0',
'2', '2', '1',
'2', '2', '2',
'2', '2', '3',
'2', '2', '4',
'2', '2', '5',
'2', '2', '6',
'2', '2', '7',
'2', '2', '8',
'2', '2', '9',
'2', '3', '0',
'2', '3', '1',
'2', '3', '2',
'2', '3', '3',
'2', '3', '4',
'2', '3', '5',
'2', '3', '6',
'2', '3', '7',
'2', '3', '8',
'2', '3', '9',
'2', '4', '0',
'2', '4', '1',
'2', '4', '2',
'2', '4', '3',
'2', '4', '4',
'2', '4', '5',
'2', '4', '6',
'2', '4', '7',
'2', '4', '8',
'2', '4', '9',
'2', '5', '0',
'2', '5', '1',
'2', '5', '2',
'2', '5', '3',
'2', '5', '4',
'2', '5', '5',
'2', '5', '6',
'2', '5', '7',
'2', '5', '8',
'2', '5', '9',
'2', '6', '0',
'2', '6', '1',
'2', '6', '2',
'2', '6', '3',
'2', '6', '4',
'2', '6', '5',
'2', '6', '6',
'2', '6', '7',
'2', '6', '8',
'2', '6', '9',
'2', '7', '0',
'2', '7', '1',
'2', '7', '2',
'2', '7', '3',
'2', '7', '4',
'2', '7', '5',
'2', '7', '6',
'2', '7', '7',
'2', '7', '8',
'2', '7', '9',
'2', '8', '0',
'2', '8', '1',
'2', '8', '2',
'2', '8', '3',
'2', '8', '4',
'2', '8', '5',
'2', '8', '6',
'2', '8', '7',
'2', '8', '8',
'2', '8', '9',
'2', '9', '0',
'2', '9', '1',
'2', '9', '2',
'2', '9', '3',
'2', '9', '4',
'2', '9', '5',
'2', '9', '6',
'2', '9', '7',
'2', '9', '8',
'2', '9', '9',
'3', '0', '0',
'3', '0', '1',
'3', '0', '2',
'3', '0', '3',
'3', '0', '4',
'3', '0', '5',
'3', '0', '6',
'3', '0', '7',
'3', '0', '8',
'3', '0', '9',
'3', '1', '0',
'3', '1', '1',
'3', '1', '2',
'3', '1', '3',
'3', '1', '4',
'3', '1', '5',
'3', '1', '6',
'3', '1', '7',
'3', '1', '8',
'3', '1', '9',
'3', '2', '0',
'3', '2', '1',
'3', '2', '2',
'3', '2', '3',
'3', '2', '4',
'3', '2', '5',
'3', '2', '6',
'3', '2', '7',
'3', '2', '8',
'3', '2', '9',
'3', '3', '0',
'3', '3', '1',
'3', '3', '2',
'3', '3', '3',
'3', '3', '4',
'3', '3', '5',
'3', '3', '6',
'3', '3', '7',
'3', '3', '8',
'3', '3', '9',
'3', '4', '0',
'3', '4', '1',
'3', '4', '2',
'3', '4', '3',
'3', '4', '4',
'3', '4', '5',
'3', '4', '6',
'3', '4', '7',
'3', '4', '8',
'3', '4', '9',
'3', '5', '0',
'3', '5', '1',
'3', '5', '2',
'3', '5', '3',
'3', '5', '4',
'3', '5', '5',
'3', '5', '6',
'3', '5', '7',
'3', '5', '8',
'3', '5', '9',
'3', '6', '0',
'3', '6', '1',
'3', '6', '2',
'3', '6', '3',
'3', '6', '4',
'3', '6', '5',
'3', '6', '6',
'3', '6', '7',
'3', '6', '8',
'3', '6', '9',
'3', '7', '0',
'3', '7', '1',
'3', '7', '2',
'3', '7', '3',
'3', '7', '4',
'3', '7', '5',
'3', '7', '6',
'3', '7', '7',
'3', '7', '8',
'3', '7', '9',
'3', '8', '0',
'3', '8', '1',
'3', '8', '2',
'3', '8', '3',
'3', '8', '4',
'3', '8', '5',
'3', '8', '6',
'3', '8', '7',
'3', '8', '8',
'3', '8', '9',
'3', '9', '0',
'3', '9', '1',
'3', '9', '2',
'3', '9', '3',
'3', '9', '4',
'3', '9', '5',
'3', '9', '6',
'3', '9', '7',
'3', '9', '8',
'3', '9', '9',
'4', '0', '0',
'4', '0', '1',
'4', '0', '2',
'4', '0', '3',
'4', '0', '4',
'4', '0', '5',
'4', '0', '6',
'4', '0', '7',
'4', '0', '8',
'4', '0', '9',
'4', '1', '0',
'4', '1', '1',
'4', '1', '2',
'4', '1', '3',
'4', '1', '4',
'4', '1', '5',
'4', '1', '6',
'4', '1', '7',
'4', '1', '8',
'4', '1', '9',
'4', '2', '0',
'4', '2', '1',
'4', '2', '2',
'4', '2', '3',
'4', '2', '4',
'4', '2', '5',
'4', '2', '6',
'4', '2', '7',
'4', '2', '8',
'4', '2', '9',
'4', '3', '0',
'4', '3', '1',
'4', '3', '2',
'4', '3', '3',
'4', '3', '4',
'4', '3', '5',
'4', '3', '6',
'4', '3', '7',
'4', '3', '8',
'4', '3', '9',
'4', '4', '0',
'4', '4', '1',
'4', '4', '2',
'4', '4', '3',
'4', '4', '4',
'4', '4', '5',
'4', '4', '6',
'4', '4', '7',
'4', '4', '8',
'4', '4', '9',
'4', '5', '0',
'4', '5', '1',
'4', '5', '2',
'4', '5', '3',
'4', '5', '4',
'4', '5', '5',
'4', '5', '6',
'4', '5', '7',
'4', '5', '8',
'4', '5', '9',
'4', '6', '0',
'4', '6', '1',
'4', '6', '2',
'4', '6', '3',
'4', '6', '4',
'4', '6', '5',
'4', '6', '6',
'4', '6', '7',
'4', '6', '8',
'4', '6', '9',
'4', '7', '0',
'4', '7', '1',
'4', '7', '2',
'4', '7', '3',
'4', '7', '4',
'4', '7', '5',
'4', '7', '6',
'4', '7', '7',
'4', '7', '8',
'4', '7', '9',
'4', '8', '0',
'4', '8', '1',
'4', '8', '2',
'4', '8', '3',
'4', '8', '4',
'4', '8', '5',
'4', '8', '6',
'4', '8', '7',
'4', '8', '8',
'4', '8', '9',
'4', '9', '0',
'4', '9', '1',
'4', '9', '2',
'4', '9', '3',
'4', '9', '4',
'4', '9', '5',
'4', '9', '6',
'4', '9', '7',
'4', '9', '8',
'4', '9', '9',
'5', '0', '0',
'5', '0', '1',
'5', '0', '2',
'5', '0', '3',
'5', '0', '4',
'5', '0', '5',
'5', '0', '6',
'5', '0', '7',
'5', '0', '8',
'5', '0', '9',
'5', '1', '0',
'5', '1', '1',
'5', '1', '2',
'5', '1', '3',
'5', '1', '4',
'5', '1', '5',
'5', '1', '6',
'5', '1', '7',
'5', '1', '8',
'5', '1', '9',
'5', '2', '0',
'5', '2', '1',
'5', '2', '2',
'5', '2', '3',
'5', '2', '4',
'5', '2', '5',
'5', '2', '6',
'5', '2', '7',
'5', '2', '8',
'5', '2', '9',
'5', '3', '0',
'5', '3', '1',
'5', '3', '2',
'5', '3', '3',
'5', '3', '4',
'5', '3', '5',
'5', '3', '6',
'5', '3', '7',
'5', '3', '8',
'5', '3', '9',
'5', '4', '0',
'5', '4', '1',
'5', '4', '2',
'5', '4', '3',
'5', '4', '4',
'5', '4', '5',
'5', '4', '6',
'5', '4', '7',
'5', '4', '8',
'5', '4', '9',
'5', '5', '0',
'5', '5', '1',
'5', '5', '2',
'5', '5', '3',
'5', '5', '4',
'5', '5', '5',
'5', '5', '6',
'5', '5', '7',
'5', '5', '8',
'5', '5', '9',
'5', '6', '0',
'5', '6', '1',
'5', '6', '2',
'5', '6', '3',
'5', '6', '4',
'5', '6', '5',
'5', '6', '6',
'5', '6', '7',
'5', '6', '8',
'5', '6', '9',
'5', '7', '0',
'5', '7', '1',
'5', '7', '2',
'5', '7', '3',
'5', '7', '4',
'5', '7', '5',
'5', '7', '6',
'5', '7', '7',
'5', '7', '8',
'5', '7', '9',
'5', '8', '0',
'5', '8', '1',
'5', '8', '2',
'5', '8', '3',
'5', '8', '4',
'5', '8', '5',
'5', '8', '6',
'5', '8', '7',
'5', '8', '8',
'5', '8', '9',
'5', '9', '0',
'5', '9', '1',
'5', '9', '2',
'5', '9', '3',
'5', '9', '4',
'5', '9', '5',
'5', '9', '6',
'5', '9', '7',
'5', '9', '8',
'5', '9', '9',
'6', '0', '0',
'6', '0', '1',
'6', '0', '2',
'6', '0', '3',
'6', '0', '4',
'6', '0', '5',
'6', '0', '6',
'6', '0', '7',
'6', '0', '8',
'6', '0', '9',
'6', '1', '0',
'6', '1', '1',
'6', '1', '2',
'6', '1', '3',
'6', '1', '4',
'6', '1', '5',
'6', '1', '6',
'6', '1', '7',
'6', '1', '8',
'6', '1', '9',
'6', '2', '0',
'6', '2', '1',
'6', '2', '2',
'6', '2', '3',
'6', '2', '4',
'6', '2', '5',
'6', '2', '6',
'6', '2', '7',
'6', '2', '8',
'6', '2', '9',
'6', '3', '0',
'6', '3', '1',
'6', '3', '2',
'6', '3', '3',
'6', '3', '4',
'6', '3', '5',
'6', '3', '6',
'6', '3', '7',
'6', '3', '8',
'6', '3', '9',
'6', '4', '0',
'6', '4', '1',
'6', '4', '2',
'6', '4', '3',
'6', '4', '4',
'6', '4', '5',
'6', '4', '6',
'6', '4', '7',
'6', '4', '8',
'6', '4', '9',
'6', '5', '0',
'6', '5', '1',
'6', '5', '2',
'6', '5', '3',
'6', '5', '4',
'6', '5', '5',
'6', '5', '6',
'6', '5', '7',
'6', '5', '8',
'6', '5', '9',
'6', '6', '0',
'6', '6', '1',
'6', '6', '2',
'6', '6', '3',
'6', '6', '4',
'6', '6', '5',
'6', '6', '6',
'6', '6', '7',
'6', '6', '8',
'6', '6', '9',
'6', '7', '0',
'6', '7', '1',
'6', '7', '2',
'6', '7', '3',
'6', '7', '4',
'6', '7', '5',
'6', '7', '6',
'6', '7', '7',
'6', '7', '8',
'6', '7', '9',
'6', '8', '0',
'6', '8', '1',
'6', '8', '2',
'6', '8', '3',
'6', '8', '4',
'6', '8', '5',
'6', '8', '6',
'6', '8', '7',
'6', '8', '8',
'6', '8', '9',
'6', '9', '0',
'6', '9', '1',
'6', '9', '2',
'6', '9', '3',
'6', '9', '4',
'6', '9', '5',
'6', '9', '6',
'6', '9', '7',
'6', '9', '8',
'6', '9', '9',
'7', '0', '0',
'7', '0', '1',
'7', '0', '2',
'7', '0', '3',
'7', '0', '4',
'7', '0', '5',
'7', '0', '6',
'7', '0', '7',
'7', '0', '8',
'7', '0', '9',
'7', '1', '0',
'7', '1', '1',
'7', '1', '2',
'7', '1', '3',
'7', '1', '4',
'7', '1', '5',
'7', '1', '6',
'7', '1', '7',
'7', '1', '8',
'7', '1', '9',
'7', '2', '0',
'7', '2', '1',
'7', '2', '2',
'7', '2', '3',
'7', '2', '4',
'7', '2', '5',
'7', '2', '6',
'7', '2', '7',
'7', '2', '8',
'7', '2', '9',
'7', '3', '0',
'7', '3', '1',
'7', '3', '2',
'7', '3', '3',
'7', '3', '4',
'7', '3', '5',
'7', '3', '6',
'7', '3', '7',
'7', '3', '8',
'7', '3', '9',
'7', '4', '0',
'7', '4', '1',
'7', '4', '2',
'7', '4', '3',
'7', '4', '4',
'7', '4', '5',
'7', '4', '6',
'7', '4', '7',
'7', '4', '8',
'7', '4', '9',
'7', '5', '0',
'7', '5', '1',
'7', '5', '2',
'7', '5', '3',
'7', '5', '4',
'7', '5', '5',
'7', '5', '6',
'7', '5', '7',
'7', '5', '8',
'7', '5', '9',
'7', '6', '0',
'7', '6', '1',
'7', '6', '2',
'7', '6', '3',
'7', '6', '4',
'7', '6', '5',
'7', '6', '6',
'7', '6', '7',
'7', '6', '8',
'7', '6', '9',
'7', '7', '0',
'7', '7', '1',
'7', '7', '2',
'7', '7', '3',
'7', '7', '4',
'7', '7', '5',
'7', '7', '6',
'7', '7', '7',
'7', '7', '8',
'7', '7', '9',
'7', '8', '0',
'7', '8', '1',
'7', '8', '2',
'7', '8', '3',
'7', '8', '4',
'7', '8', '5',
'7', '8', '6',
'7', '8', '7',
'7', '8', '8',
'7', '8', '9',
'7', '9', '0',
'7', '9', '1',
'7', '9', '2',
'7', '9', '3',
'7', '9', '4',
'7', '9', '5',
'7', '9', '6',
'7', '9', '7',
'7', '9', '8',
'7', '9', '9',
'8', '0', '0',
'8', '0', '1',
'8', '0', '2',
'8', '0', '3',
'8', '0', '4',
'8', '0', '5',
'8', '0', '6',
'8', '0', '7',
'8', '0', '8',
'8', '0', '9',
'8', '1', '0',
'8', '1', '1',
'8', '1', '2',
'8', '1', '3',
'8', '1', '4',
'8', '1', '5',
'8', '1', '6',
'8', '1', '7',
'8', '1', '8',
'8', '1', '9',
'8', '2', '0',
'8', '2', '1',
'8', '2', '2',
'8', '2', '3',
'8', '2', '4',
'8', '2', '5',
'8', '2', '6',
'8', '2', '7',
'8', '2', '8',
'8', '2', '9',
'8', '3', '0',
'8', '3', '1',
'8', '3', '2',
'8', '3', '3',
'8', '3', '4',
'8', '3', '5',
'8', '3', '6',
'8', '3', '7',
'8', '3', '8',
'8', '3', '9',
'8', '4', '0',
'8', '4', '1',
'8', '4', '2',
'8', '4', '3',
'8', '4', '4',
'8', '4', '5',
'8', '4', '6',
'8', '4', '7',
'8', '4', '8',
'8', '4', '9',
'8', '5', '0',
'8', '5', '1',
'8', '5', '2',
'8', '5', '3',
'8', '5', '4',
'8', '5', '5',
'8', '5', '6',
'8', '5', '7',
'8', '5', '8',
'8', '5', '9',
'8', '6', '0',
'8', '6', '1',
'8', '6', '2',
'8', '6', '3',
'8', '6', '4',
'8', '6', '5',
'8', '6', '6',
'8', '6', '7',
'8', '6', '8',
'8', '6', '9',
'8', '7', '0',
'8', '7', '1',
'8', '7', '2',
'8', '7', '3',
'8', '7', '4',
'8', '7', '5',
'8', '7', '6',
'8', '7', '7',
'8', '7', '8',
'8', '7', '9',
'8', '8', '0',
'8', '8', '1',
'8', '8', '2',
'8', '8', '3',
'8', '8', '4',
'8', '8', '5',
'8', '8', '6',
'8', '8', '7',
'8', '8', '8',
'8', '8', '9',
'8', '9', '0',
'8', '9', '1',
'8', '9', '2',
'8', '9', '3',
'8', '9', '4',
'8', '9', '5',
'8', '9', '6',
'8', '9', '7',
'8', '9', '8',
'8', '9', '9',
'9', '0', '0',
'9', '0', '1',
'9', '0', '2',
'9', '0', '3',
'9', '0', '4',
'9', '0', '5',
'9', '0', '6',
'9', '0', '7',
'9', '0', '8',
'9', '0', '9',
'9', '1', '0',
'9', '1', '1',
'9', '1', '2',
'9', '1', '3',
'9', '1', '4',
'9', '1', '5',
'9', '1', '6',
'9', '1', '7',
'9', '1', '8',
'9', '1', '9',
'9', '2', '0',
'9', '2', '1',
'9', '2', '2',
'9', '2', '3',
'9', '2', '4',
'9', '2', '5',
'9', '2', '6',
'9', '2', '7',
'9', '2', '8',
'9', '2', '9',
'9', '3', '0',
'9', '3', '1',
'9', '3', '2',
'9', '3', '3',
'9', '3', '4',
'9', '3', '5',
'9', '3', '6',
'9', '3', '7',
'9', '3', '8',
'9', '3', '9',
'9', '4', '0',
'9', '4', '1',
'9', '4', '2',
'9', '4', '3',
'9', '4', '4',
'9', '4', '5',
'9', '4', '6',
'9', '4', '7',
'9', '4', '8',
'9', '4', '9',
'9', '5', '0',
'9', '5', '1',
'9', '5', '2',
'9', '5', '3',
'9', '5', '4',
'9', '5', '5',
'9', '5', '6',
'9', '5', '7',
'9', '5', '8',
'9', '5', '9',
'9', '6', '0',
'9', '6', '1',
'9', '6', '2',
'9', '6', '3',
'9', '6', '4',
'9', '6', '5',
'9', '6', '6',
'9', '6', '7',
'9', '6', '8',
'9', '6', '9',
'9', '7', '0',
'9', '7', '1',
'9', '7', '2',
'9', '7', '3',
'9', '7', '4',
'9', '7', '5',
'9', '7', '6',
'9', '7', '7',
'9', '7', '8',
'9', '7', '9',
'9', '8', '0',
'9', '8', '1',
'9', '8', '2',
'9', '8', '3',
'9', '8', '4',
'9', '8', '5',
'9', '8', '6',
'9', '8', '7',
'9', '8', '8',
'9', '8', '9',
'9', '9', '0',
'9', '9', '1',
'9', '9', '2',
'9', '9', '3',
'9', '9', '4',
'9', '9', '5',
'9', '9', '6',
'9', '9', '7',
'9', '9', '8',
'9', '9', '9'
};
// ten2m3k64[], shift_ten2m3k64[] used for conversion from BID128 to string
UINT64 ten2m3k64[] = {
0x4189374bc6a7ef9eull, // 4189374bc6a7ef9e * 2^-72 = (10^-3)RP,63
0x10c6f7a0b5ed8d37ull, // 10c6f7a0b5ed8d37 * 2^-80 = (10^-6)RP,61
0x44b82fa09b5a52ccull, // 44b82fa09b5a52cc * 2^-92 = (10^-9)RP,63
0x119799812dea111aull, // 119799812dea111a * 2^-100 = (10^-12)RP,61
0x480ebe7b9d58566dull // 480ebe7b9d58566d * 2^-112 = (10^-15)RP,63
};
unsigned int shift_ten2m3k64[] = {
8, // 72 - 64
16, // 80 - 64
28, // 92 - 64
36, // 100 - 64
48 // 112 - 64
};
UINT128 ten2m3k128[] = {
{{0xb22d0e5604189375ull, 0x4189374bc6a7ef9dull}},
// 4189374bc6a7ef9d b22d0e5604189375 * 2^-136 = (10^-3)RP,127
{{0xb4c7f34938583622ull, 0x10c6f7a0b5ed8d36ull}},
// 10c6f7a0b5ed8d36 b4c7f34938583622 * 2^-144 = (10^-6)RP,125
{{0x98b405447c4a9819ull, 0x44b82fa09b5a52cbull}},
// 44b82fa09b5a52cb 98b405447c4a9819 * 2^-156 = (10^-9)RP,127
{{0x7f27f0f6e885c8bbull, 0x119799812dea1119ull}},
// 119799812dea1119 7f27f0f6e885c8bb * 2^-164 = (10^-12)RP,125
{{0x87ce9b80a5fb0509ull, 0x480ebe7b9d58566cull}},
// 480ebe7b9d58566c 87ce9b80a5fb0509 * 2^-176 = (10^-15)RP,127
{{0xe75fe645cc4873faull, 0x12725dd1d243aba0ull}},
// 12725dd1d243aba0 e75fe645cc4873fa * 2^-184 = (10^-18)RP,125
{{0x69fb7e0b75e52f02ull, 0x4b8ed0283a6d3df7ull}},
// 4b8ed0283a6d3df7 69fb7e0b75e52f02 * 2^-196 = (10^-21)RP,127
{{0x58924d52ce4f26a9ull, 0x1357c299a88ea76aull}},
// 1357c299a88ea76a 58924d52ce4f26a9 * 2^-204 = (10^-24)RP,125
{{0x3baf513267aa9a3full, 0x4f3a68dbc8f03f24ull}},
// 4f3a68dbc8f03f24 3baf513267aa9a3f * 2^-216 = (10^-27)RP,127
{{0x3424b06f3529a052ull, 0x14484bfeebc29f86ull}},
// 14484bfeebc29f86 3424b06f3529a052 * 2^-224 = (10^-30)RP,125
{{0xf658d6c57566eac8ull, 0x5313a5dee87d6eb0ull}}
// 5313a5dee87d6eb0 f658d6c57566eac8 * 2^-236 = (10^-33)RP,127
};
unsigned int shift_ten2m3k128[] = {
8, // 136 - 128
16, // 144 - 128
28, // 156 - 128
36, // 164 - 128
48, // 176 - 128
56, // 184 - 128
4, // 196 - 192
12, // 204 - 192
24, // 216 - 192
32, // 224 - 192
44 // 236 - 192
};
/***************************************************************************
*************** TABLES FOR GENERAL ROUNDING FUNCTIONS *********************
***************************************************************************/
// Note: not all entries in these tables will be used with IEEE 754R decimal
// floating-point arithmetic
// a) In round128_2_18() numbers with 2 <= q <= 18 will be rounded only
// for 1 <= x <= 3:
// x = 1 or x = 2 when q = 17
// x = 2 or x = 3 when q = 18
// b) In round128_19_38() numbers with 19 <= q <= 38 will be rounded 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
// c) ...
// However, for generality and possible uses outside the frame of IEEE 754R
// this implementation includes table values for all x in [1, q - 1]
// Note: 64-bit tables generated with ten2mx64.ma; output in ten2mx64.out
// Kx from 10^(-x) ~= Kx * 2^(-Ex); Kx rounded up to 64 bits, 1 <= x <= 17
UINT64 Kx64[] = {
0xcccccccccccccccdULL, // 10^-1 ~= cccccccccccccccd * 2^-67
0xa3d70a3d70a3d70bULL, // 10^-2 ~= a3d70a3d70a3d70b * 2^-70
0x83126e978d4fdf3cULL, // 10^-3 ~= 83126e978d4fdf3c * 2^-73
0xd1b71758e219652cULL, // 10^-4 ~= d1b71758e219652c * 2^-77
0xa7c5ac471b478424ULL, // 10^-5 ~= a7c5ac471b478424 * 2^-80
0x8637bd05af6c69b6ULL, // 10^-6 ~= 8637bd05af6c69b6 * 2^-83
0xd6bf94d5e57a42bdULL, // 10^-7 ~= d6bf94d5e57a42bd * 2^-87
0xabcc77118461cefdULL, // 10^-8 ~= abcc77118461cefd * 2^-90
0x89705f4136b4a598ULL, // 10^-9 ~= 89705f4136b4a598 * 2^-93
0xdbe6fecebdedd5bfULL, // 10^-10 ~= dbe6fecebdedd5bf * 2^-97
0xafebff0bcb24aaffULL, // 10^-11 ~= afebff0bcb24aaff * 2^-100
0x8cbccc096f5088ccULL, // 10^-12 ~= 8cbccc096f5088cc * 2^-103
0xe12e13424bb40e14ULL, // 10^-13 ~= e12e13424bb40e14 * 2^-107
0xb424dc35095cd810ULL, // 10^-14 ~= b424dc35095cd810 * 2^-110
0x901d7cf73ab0acdaULL, // 10^-15 ~= 901d7cf73ab0acda * 2^-113
0xe69594bec44de15cULL, // 10^-16 ~= e69594bec44de15c * 2^-117
0xb877aa3236a4b44aULL // 10^-17 ~= b877aa3236a4b44a * 2^-120
};
// Ex-64 from 10^(-x) ~= Kx * 2^(-Ex); Kx rounded up to 64 bits, 1 <= x <= 17
unsigned int Ex64m64[] = {
3, // 67 - 64, Ex = 67
6, // 70 - 64, Ex = 70
9, // 73 - 64, Ex = 73
13, // 77 - 64, Ex = 77
16, // 80 - 64, Ex = 80
19, // 83 - 64, Ex = 83
23, // 87 - 64, Ex = 87
26, // 90 - 64, Ex = 90
29, // 93 - 64, Ex = 93
33, // 97 - 64, Ex = 97
36, // 100 - 64, Ex = 100
39, // 103 - 64, Ex = 103
43, // 107 - 64, Ex = 107
46, // 110 - 64, Ex = 110
49, // 113 - 64, Ex = 113
53, // 117 - 64, Ex = 117
56 // 120 - 64, Ex = 120
};
// Values of 1/2 in the right position to be compared with the fraction from
// C * kx, 1 <= x <= 17; the fraction consists of the low Ex bits in C * kx
// (these values are aligned with the high 64 bits of the fraction)
UINT64 half64[] = {
0x0000000000000004ULL, // half / 2^64 = 4
0x0000000000000020ULL, // half / 2^64 = 20
0x0000000000000100ULL, // half / 2^64 = 100
0x0000000000001000ULL, // half / 2^64 = 1000
0x0000000000008000ULL, // half / 2^64 = 8000
0x0000000000040000ULL, // half / 2^64 = 40000
0x0000000000400000ULL, // half / 2^64 = 400000
0x0000000002000000ULL, // half / 2^64 = 2000000
0x0000000010000000ULL, // half / 2^64 = 10000000
0x0000000100000000ULL, // half / 2^64 = 100000000
0x0000000800000000ULL, // half / 2^64 = 800000000
0x0000004000000000ULL, // half / 2^64 = 4000000000
0x0000040000000000ULL, // half / 2^64 = 40000000000
0x0000200000000000ULL, // half / 2^64 = 200000000000
0x0001000000000000ULL, // half / 2^64 = 1000000000000
0x0010000000000000ULL, // half / 2^64 = 10000000000000
0x0080000000000000ULL // half / 2^64 = 80000000000000
};
// Values of mask in the right position to obtain the high Ex - 64 bits
// of the fraction from C * kx, 1 <= x <= 17; the fraction consists of
// the low Ex bits in C * kx
UINT64 mask64[] = {
0x0000000000000007ULL, // mask / 2^64
0x000000000000003fULL, // mask / 2^64
0x00000000000001ffULL, // mask / 2^64
0x0000000000001fffULL, // mask / 2^64
0x000000000000ffffULL, // mask / 2^64
0x000000000007ffffULL, // mask / 2^64
0x00000000007fffffULL, // mask / 2^64
0x0000000003ffffffULL, // mask / 2^64
0x000000001fffffffULL, // mask / 2^64
0x00000001ffffffffULL, // mask / 2^64
0x0000000fffffffffULL, // mask / 2^64
0x0000007fffffffffULL, // mask / 2^64
0x000007ffffffffffULL, // mask / 2^64
0x00003fffffffffffULL, // mask / 2^64
0x0001ffffffffffffULL, // mask / 2^64
0x001fffffffffffffULL, // mask / 2^64
0x00ffffffffffffffULL // mask / 2^64
};
// Values of 10^(-x) trancated to Ex bits beyond the binary point, and
// in the right position to be compared with the fraction from C * kx,
// 1 <= x <= 17; the fraction consists of the low Ex bits in C * kx
// (these values are aligned with the low 64 bits of the fraction)
UINT64 ten2mxtrunc64[] = {
0xccccccccccccccccULL, // (ten2mx >> 64) = cccccccccccccccc
0xa3d70a3d70a3d70aULL, // (ten2mx >> 64) = a3d70a3d70a3d70a
0x83126e978d4fdf3bULL, // (ten2mx >> 64) = 83126e978d4fdf3b
0xd1b71758e219652bULL, // (ten2mx >> 64) = d1b71758e219652b
0xa7c5ac471b478423ULL, // (ten2mx >> 64) = a7c5ac471b478423
0x8637bd05af6c69b5ULL, // (ten2mx >> 64) = 8637bd05af6c69b5
0xd6bf94d5e57a42bcULL, // (ten2mx >> 64) = d6bf94d5e57a42bc
0xabcc77118461cefcULL, // (ten2mx >> 64) = abcc77118461cefc
0x89705f4136b4a597ULL, // (ten2mx >> 64) = 89705f4136b4a597
0xdbe6fecebdedd5beULL, // (ten2mx >> 64) = dbe6fecebdedd5be
0xafebff0bcb24aafeULL, // (ten2mx >> 64) = afebff0bcb24aafe
0x8cbccc096f5088cbULL, // (ten2mx >> 64) = 8cbccc096f5088cb
0xe12e13424bb40e13ULL, // (ten2mx >> 64) = e12e13424bb40e13
0xb424dc35095cd80fULL, // (ten2mx >> 64) = b424dc35095cd80f
0x901d7cf73ab0acd9ULL, // (ten2mx >> 64) = 901d7cf73ab0acd9
0xe69594bec44de15bULL, // (ten2mx >> 64) = e69594bec44de15b
0xb877aa3236a4b449ULL // (ten2mx >> 64) = b877aa3236a4b449
};
// Note: 128-bit tables generated with ten2mx128.ma; output in ten2mx128.out
// The order of the 64-bit components is L, H
// Kx from 10^(-x) ~= Kx * 2^(-Ex); Kx rounded up to 128 bits, 1 <= x <= 37
UINT128 Kx128[] = {
{{0xcccccccccccccccdULL, 0xccccccccccccccccULL}},
// 10^-1 ~= cccccccccccccccccccccccccccccccd * 2^-131
{{0x3d70a3d70a3d70a4ULL, 0xa3d70a3d70a3d70aULL}},
// 10^-2 ~= a3d70a3d70a3d70a3d70a3d70a3d70a4 * 2^-134
{{0x645a1cac083126eaULL, 0x83126e978d4fdf3bULL}},
// 10^-3 ~= 83126e978d4fdf3b645a1cac083126ea * 2^-137
{{0xd3c36113404ea4a9ULL, 0xd1b71758e219652bULL}},
// 10^-4 ~= d1b71758e219652bd3c36113404ea4a9 * 2^-141
{{0x0fcf80dc33721d54ULL, 0xa7c5ac471b478423ULL}},
// 10^-5 ~= a7c5ac471b4784230fcf80dc33721d54 * 2^-144
{{0xa63f9a49c2c1b110ULL, 0x8637bd05af6c69b5ULL}},
// 10^-6 ~= 8637bd05af6c69b5a63f9a49c2c1b110 * 2^-147
{{0x3d32907604691b4dULL, 0xd6bf94d5e57a42bcULL}},
// 10^-7 ~= d6bf94d5e57a42bc3d32907604691b4d * 2^-151
{{0xfdc20d2b36ba7c3eULL, 0xabcc77118461cefcULL}},
// 10^-8 ~= abcc77118461cefcfdc20d2b36ba7c3e * 2^-154
{{0x31680a88f8953031ULL, 0x89705f4136b4a597ULL}},
// 10^-9 ~= 89705f4136b4a59731680a88f8953031 * 2^-157
{{0xb573440e5a884d1cULL, 0xdbe6fecebdedd5beULL}},
// 10^-10 ~= dbe6fecebdedd5beb573440e5a884d1c * 2^-161
{{0xf78f69a51539d749ULL, 0xafebff0bcb24aafeULL}},
// 10^-11 ~= afebff0bcb24aafef78f69a51539d749 * 2^-164
{{0xf93f87b7442e45d4ULL, 0x8cbccc096f5088cbULL}},
// 10^-12 ~= 8cbccc096f5088cbf93f87b7442e45d4 * 2^-167
{{0x2865a5f206b06fbaULL, 0xe12e13424bb40e13ULL}},
// 10^-13 ~= e12e13424bb40e132865a5f206b06fba * 2^-171
{{0x538484c19ef38c95ULL, 0xb424dc35095cd80fULL}},
// 10^-14 ~= b424dc35095cd80f538484c19ef38c95 * 2^-174
{{0x0f9d37014bf60a11ULL, 0x901d7cf73ab0acd9ULL}},
// 10^-15 ~= 901d7cf73ab0acd90f9d37014bf60a11 * 2^-177
{{0x4c2ebe687989a9b4ULL, 0xe69594bec44de15bULL}},
// 10^-16 ~= e69594bec44de15b4c2ebe687989a9b4 * 2^-181
{{0x09befeb9fad487c3ULL, 0xb877aa3236a4b449ULL}},
// 10^-17 ~= b877aa3236a4b44909befeb9fad487c3 * 2^-184
{{0x3aff322e62439fd0ULL, 0x9392ee8e921d5d07ULL}},
// 10^-18 ~= 9392ee8e921d5d073aff322e62439fd0 * 2^-187
{{0x2b31e9e3d06c32e6ULL, 0xec1e4a7db69561a5ULL}},
// 10^-19 ~= ec1e4a7db69561a52b31e9e3d06c32e6 * 2^-191
{{0x88f4bb1ca6bcf585ULL, 0xbce5086492111aeaULL}},
// 10^-20 ~= bce5086492111aea88f4bb1ca6bcf585 * 2^-194
{{0xd3f6fc16ebca5e04ULL, 0x971da05074da7beeULL}},
// 10^-21 ~= 971da05074da7beed3f6fc16ebca5e04 * 2^-197
{{0x5324c68b12dd6339ULL, 0xf1c90080baf72cb1ULL}},
// 10^-22 ~= f1c90080baf72cb15324c68b12dd6339 * 2^-201
{{0x75b7053c0f178294ULL, 0xc16d9a0095928a27ULL}},
// 10^-23 ~= c16d9a0095928a2775b7053c0f178294 * 2^-204
{{0xc4926a9672793543ULL, 0x9abe14cd44753b52ULL}},
// 10^-24 ~= 9abe14cd44753b52c4926a9672793543 * 2^-207
{{0x3a83ddbd83f52205ULL, 0xf79687aed3eec551ULL}},
// 10^-25 ~= f79687aed3eec5513a83ddbd83f52205 * 2^-211
{{0x95364afe032a819eULL, 0xc612062576589ddaULL}},
// 10^-26 ~= c612062576589dda95364afe032a819e * 2^-214
{{0x775ea264cf55347eULL, 0x9e74d1b791e07e48ULL}},
// 10^-27 ~= 9e74d1b791e07e48775ea264cf55347e * 2^-217
{{0x8bca9d6e188853fdULL, 0xfd87b5f28300ca0dULL}},
// 10^-28 ~= fd87b5f28300ca0d8bca9d6e188853fd * 2^-221
{{0x096ee45813a04331ULL, 0xcad2f7f5359a3b3eULL}},
// 10^-29 ~= cad2f7f5359a3b3e096ee45813a04331 * 2^-224
{{0xa1258379a94d028eULL, 0xa2425ff75e14fc31ULL}},
// 10^-30 ~= a2425ff75e14fc31a1258379a94d028e * 2^-227
{{0x80eacf948770ced8ULL, 0x81ceb32c4b43fcf4ULL}},
// 10^-31 ~= 81ceb32c4b43fcf480eacf948770ced8 * 2^-230
{{0x67de18eda5814af3ULL, 0xcfb11ead453994baULL}},
// 10^-32 ~= cfb11ead453994ba67de18eda5814af3 * 2^-234
{{0xecb1ad8aeacdd58fULL, 0xa6274bbdd0fadd61ULL}},
// 10^-33 ~= a6274bbdd0fadd61ecb1ad8aeacdd58f * 2^-237
{{0xbd5af13bef0b113fULL, 0x84ec3c97da624ab4ULL}},
// 10^-34 ~= 84ec3c97da624ab4bd5af13bef0b113f * 2^-240
{{0x955e4ec64b44e865ULL, 0xd4ad2dbfc3d07787ULL}},
// 10^-35 ~= d4ad2dbfc3d07787955e4ec64b44e865 * 2^-244
{{0xdde50bd1d5d0b9eaULL, 0xaa242499697392d2ULL}},
// 10^-36 ~= aa242499697392d2dde50bd1d5d0b9ea * 2^-247
{{0x7e50d64177da2e55ULL, 0x881cea14545c7575ULL}}
// 10^-37 ~= 881cea14545c75757e50d64177da2e55 * 2^-250
};
// Ex-128 from 10^(-x) ~= Kx*2^(-Ex); Kx rounded up to 128 bits, 1 <= x <= 37
unsigned int Ex128m128[] = {
3, // 131 - 128, Ex = 131
6, // 134 - 128, Ex = 134
9, // 137 - 128, Ex = 137
13, // 141 - 128, Ex = 141
16, // 144 - 128, Ex = 144
19, // 147 - 128, Ex = 147
23, // 151 - 128, Ex = 151
26, // 154 - 128, Ex = 154
29, // 157 - 128, Ex = 157
33, // 161 - 128, Ex = 161
36, // 164 - 128, Ex = 164
39, // 167 - 128, Ex = 167
43, // 171 - 128, Ex = 171
46, // 174 - 128, Ex = 174
49, // 177 - 128, Ex = 177
53, // 181 - 128, Ex = 181
56, // 184 - 128, Ex = 184
59, // 187 - 128, Ex = 187
63, // 191 - 128, Ex = 191
2, // 194 - 192, Ex = 194
5, // 197 - 192, Ex = 197
9, // 201 - 192, Ex = 201
12, // 204 - 192, Ex = 204
15, // 207 - 192, Ex = 207
19, // 211 - 192, Ex = 211
22, // 214 - 192, Ex = 214
25, // 217 - 192, Ex = 217
29, // 221 - 192, Ex = 221
32, // 224 - 192, Ex = 224
35, // 227 - 192, Ex = 227
38, // 230 - 192, Ex = 230
42, // 234 - 192, Ex = 234
45, // 237 - 192, Ex = 237
48, // 240 - 192, Ex = 240
52, // 244 - 192, Ex = 244
55, // 247 - 192, Ex = 247
58 // 250 - 192, Ex = 250
};
// Values of 1/2 in the right position to be compared with the fraction from
// C * kx, 1 <= x <= 37; the fraction consists of the low Ex bits in C * kx
// (these values are aligned with the high 128 bits of the fraction)
UINT64 half128[] = {
0x0000000000000004ULL, // half / 2^128 = 4
0x0000000000000020ULL, // half / 2^128 = 20
0x0000000000000100ULL, // half / 2^128 = 100
0x0000000000001000ULL, // half / 2^128 = 1000
0x0000000000008000ULL, // half / 2^128 = 8000
0x0000000000040000ULL, // half / 2^128 = 40000
0x0000000000400000ULL, // half / 2^128 = 400000
0x0000000002000000ULL, // half / 2^128 = 2000000
0x0000000010000000ULL, // half / 2^128 = 10000000
0x0000000100000000ULL, // half / 2^128 = 100000000
0x0000000800000000ULL, // half / 2^128 = 800000000
0x0000004000000000ULL, // half / 2^128 = 4000000000
0x0000040000000000ULL, // half / 2^128 = 40000000000
0x0000200000000000ULL, // half / 2^128 = 200000000000
0x0001000000000000ULL, // half / 2^128 = 1000000000000
0x0010000000000000ULL, // half / 2^128 = 10000000000000
0x0080000000000000ULL, // half / 2^128 = 80000000000000
0x0400000000000000ULL, // half / 2^128 = 400000000000000
0x4000000000000000ULL, // half / 2^128 = 4000000000000000
0x0000000000000002ULL, // half / 2^192 = 2
0x0000000000000010ULL, // half / 2^192 = 10
0x0000000000000100ULL, // half / 2^192 = 100
0x0000000000000800ULL, // half / 2^192 = 800
0x0000000000004000ULL, // half / 2^192 = 4000
0x0000000000040000ULL, // half / 2^192 = 40000
0x0000000000200000ULL, // half / 2^192 = 200000
0x0000000001000000ULL, // half / 2^192 = 1000000
0x0000000010000000ULL, // half / 2^192 = 10000000
0x0000000080000000ULL, // half / 2^192 = 80000000
0x0000000400000000ULL, // half / 2^192 = 400000000
0x0000002000000000ULL, // half / 2^192 = 2000000000
0x0000020000000000ULL, // half / 2^192 = 20000000000
0x0000100000000000ULL, // half / 2^192 = 100000000000
0x0000800000000000ULL, // half / 2^192 = 800000000000
0x0008000000000000ULL, // half / 2^192 = 8000000000000
0x0040000000000000ULL, // half / 2^192 = 40000000000000
0x0200000000000000ULL // half / 2^192 = 200000000000000
};
// Values of mask in the right position to obtain the high Ex - 128 or Ex - 192
// bits of the fraction from C * kx, 1 <= x <= 37; the fraction consists of
// the low Ex bits in C * kx
UINT64 mask128[] = {
0x0000000000000007ULL, // mask / 2^128
0x000000000000003fULL, // mask / 2^128
0x00000000000001ffULL, // mask / 2^128
0x0000000000001fffULL, // mask / 2^128
0x000000000000ffffULL, // mask / 2^128
0x000000000007ffffULL, // mask / 2^128
0x00000000007fffffULL, // mask / 2^128
0x0000000003ffffffULL, // mask / 2^128
0x000000001fffffffULL, // mask / 2^128
0x00000001ffffffffULL, // mask / 2^128
0x0000000fffffffffULL, // mask / 2^128
0x0000007fffffffffULL, // mask / 2^128
0x000007ffffffffffULL, // mask / 2^128
0x00003fffffffffffULL, // mask / 2^128
0x0001ffffffffffffULL, // mask / 2^128
0x001fffffffffffffULL, // mask / 2^128
0x00ffffffffffffffULL, // mask / 2^128
0x07ffffffffffffffULL, // mask / 2^128
0x7fffffffffffffffULL, // mask / 2^128
0x0000000000000003ULL, // mask / 2^192
0x000000000000001fULL, // mask / 2^192
0x00000000000001ffULL, // mask / 2^192
0x0000000000000fffULL, // mask / 2^192
0x0000000000007fffULL, // mask / 2^192
0x000000000007ffffULL, // mask / 2^192
0x00000000003fffffULL, // mask / 2^192
0x0000000001ffffffULL, // mask / 2^192
0x000000001fffffffULL, // mask / 2^192
0x00000000ffffffffULL, // mask / 2^192
0x00000007ffffffffULL, // mask / 2^192
0x0000003fffffffffULL, // mask / 2^192
0x000003ffffffffffULL, // mask / 2^192
0x00001fffffffffffULL, // mask / 2^192
0x0000ffffffffffffULL, // mask / 2^192
0x000fffffffffffffULL, // mask / 2^192
0x007fffffffffffffULL, // mask / 2^192
0x03ffffffffffffffULL // mask / 2^192
};
// Values of 10^(-x) trancated to Ex bits beyond the binary point, and
// in the right position to be compared with the fraction from C * kx,
// 1 <= x <= 37; the fraction consists of the low Ex bits in C * kx
// (these values are aligned with the low 128 bits of the fraction)
UINT128 ten2mxtrunc128[] = {
{{0xccccccccccccccccULL, 0xccccccccccccccccULL}},
// (ten2mx >> 128) = cccccccccccccccccccccccccccccccc
{{0x3d70a3d70a3d70a3ULL, 0xa3d70a3d70a3d70aULL}},
// (ten2mx >> 128) = a3d70a3d70a3d70a3d70a3d70a3d70a3
{{0x645a1cac083126e9ULL, 0x83126e978d4fdf3bULL}},
// (ten2mx >> 128) = 83126e978d4fdf3b645a1cac083126e9
{{0xd3c36113404ea4a8ULL, 0xd1b71758e219652bULL}},
// (ten2mx >> 128) = d1b71758e219652bd3c36113404ea4a8
{{0x0fcf80dc33721d53ULL, 0xa7c5ac471b478423ULL}},
// (ten2mx >> 128) = a7c5ac471b4784230fcf80dc33721d53
{{0xa63f9a49c2c1b10fULL, 0x8637bd05af6c69b5ULL}},
// (ten2mx >> 128) = 8637bd05af6c69b5a63f9a49c2c1b10f
{{0x3d32907604691b4cULL, 0xd6bf94d5e57a42bcULL}},
// (ten2mx >> 128) = d6bf94d5e57a42bc3d32907604691b4c
{{0xfdc20d2b36ba7c3dULL, 0xabcc77118461cefcULL}},
// (ten2mx >> 128) = abcc77118461cefcfdc20d2b36ba7c3d
{{0x31680a88f8953030ULL, 0x89705f4136b4a597ULL}},
// (ten2mx >> 128) = 89705f4136b4a59731680a88f8953030
{{0xb573440e5a884d1bULL, 0xdbe6fecebdedd5beULL}},
// (ten2mx >> 128) = dbe6fecebdedd5beb573440e5a884d1b
{{0xf78f69a51539d748ULL, 0xafebff0bcb24aafeULL}},
// (ten2mx >> 128) = afebff0bcb24aafef78f69a51539d748
{{0xf93f87b7442e45d3ULL, 0x8cbccc096f5088cbULL}},
// (ten2mx >> 128) = 8cbccc096f5088cbf93f87b7442e45d3
{{0x2865a5f206b06fb9ULL, 0xe12e13424bb40e13ULL}},
// (ten2mx >> 128) = e12e13424bb40e132865a5f206b06fb9
{{0x538484c19ef38c94ULL, 0xb424dc35095cd80fULL}},
// (ten2mx >> 128) = b424dc35095cd80f538484c19ef38c94
{{0x0f9d37014bf60a10ULL, 0x901d7cf73ab0acd9ULL}},
// (ten2mx >> 128) = 901d7cf73ab0acd90f9d37014bf60a10
{{0x4c2ebe687989a9b3ULL, 0xe69594bec44de15bULL}},
// (ten2mx >> 128) = e69594bec44de15b4c2ebe687989a9b3
{{0x09befeb9fad487c2ULL, 0xb877aa3236a4b449ULL}},
// (ten2mx >> 128) = b877aa3236a4b44909befeb9fad487c2
{{0x3aff322e62439fcfULL, 0x9392ee8e921d5d07ULL}},
// (ten2mx >> 128) = 9392ee8e921d5d073aff322e62439fcf
{{0x2b31e9e3d06c32e5ULL, 0xec1e4a7db69561a5ULL}},
// (ten2mx >> 128) = ec1e4a7db69561a52b31e9e3d06c32e5
{{0x88f4bb1ca6bcf584ULL, 0xbce5086492111aeaULL}},
// (ten2mx >> 128) = bce5086492111aea88f4bb1ca6bcf584
{{0xd3f6fc16ebca5e03ULL, 0x971da05074da7beeULL}},
// (ten2mx >> 128) = 971da05074da7beed3f6fc16ebca5e03
{{0x5324c68b12dd6338ULL, 0xf1c90080baf72cb1ULL}},
// (ten2mx >> 128) = f1c90080baf72cb15324c68b12dd6338
{{0x75b7053c0f178293ULL, 0xc16d9a0095928a27ULL}},
// (ten2mx >> 128) = c16d9a0095928a2775b7053c0f178293
{{0xc4926a9672793542ULL, 0x9abe14cd44753b52ULL}},
// (ten2mx >> 128) = 9abe14cd44753b52c4926a9672793542
{{0x3a83ddbd83f52204ULL, 0xf79687aed3eec551ULL}},
// (ten2mx >> 128) = f79687aed3eec5513a83ddbd83f52204
{{0x95364afe032a819dULL, 0xc612062576589ddaULL}},
// (ten2mx >> 128) = c612062576589dda95364afe032a819d
{{0x775ea264cf55347dULL, 0x9e74d1b791e07e48ULL}},
// (ten2mx >> 128) = 9e74d1b791e07e48775ea264cf55347d
{{0x8bca9d6e188853fcULL, 0xfd87b5f28300ca0dULL}},
// (ten2mx >> 128) = fd87b5f28300ca0d8bca9d6e188853fc
{{0x096ee45813a04330ULL, 0xcad2f7f5359a3b3eULL}},
// (ten2mx >> 128) = cad2f7f5359a3b3e096ee45813a04330
{{0xa1258379a94d028dULL, 0xa2425ff75e14fc31ULL}},
// (ten2mx >> 128) = a2425ff75e14fc31a1258379a94d028d
{{0x80eacf948770ced7ULL, 0x81ceb32c4b43fcf4ULL}},
// (ten2mx >> 128) = 81ceb32c4b43fcf480eacf948770ced7
{{0x67de18eda5814af2ULL, 0xcfb11ead453994baULL}},
// (ten2mx >> 128) = cfb11ead453994ba67de18eda5814af2
{{0xecb1ad8aeacdd58eULL, 0xa6274bbdd0fadd61ULL}},
// (ten2mx >> 128) = a6274bbdd0fadd61ecb1ad8aeacdd58e
{{0xbd5af13bef0b113eULL, 0x84ec3c97da624ab4ULL}},
// (ten2mx >> 128) = 84ec3c97da624ab4bd5af13bef0b113e
{{0x955e4ec64b44e864ULL, 0xd4ad2dbfc3d07787ULL}},
// (ten2mx >> 128) = d4ad2dbfc3d07787955e4ec64b44e864
{{0xdde50bd1d5d0b9e9ULL, 0xaa242499697392d2ULL}},
// (ten2mx >> 128) = aa242499697392d2dde50bd1d5d0b9e9
{{0x7e50d64177da2e54ULL, 0x881cea14545c7575ULL}}
// (ten2mx >> 128) = 881cea14545c75757e50d64177da2e54
};
UINT192 Kx192[] = {
{{0xcccccccccccccccdULL, 0xccccccccccccccccULL,
0xccccccccccccccccULL}},
// 10^-1 ~= cccccccccccccccccccccccccccccccccccccccccccccccd * 2^-195
{{0xd70a3d70a3d70a3eULL, 0x3d70a3d70a3d70a3ULL,
0xa3d70a3d70a3d70aULL}},
// 10^-2 ~= a3d70a3d70a3d70a3d70a3d70a3d70a3d70a3d70a3d70a3e * 2^-198
{{0x78d4fdf3b645a1cbULL, 0x645a1cac083126e9ULL,
0x83126e978d4fdf3bULL}},
// 10^-3 ~= 83126e978d4fdf3b645a1cac083126e978d4fdf3b645a1cb * 2^-201
{{0xc154c985f06f6945ULL, 0xd3c36113404ea4a8ULL,
0xd1b71758e219652bULL}},
// 10^-4 ~= d1b71758e219652bd3c36113404ea4a8c154c985f06f6945 * 2^-205
{{0xcddd6e04c0592104ULL, 0x0fcf80dc33721d53ULL,
0xa7c5ac471b478423ULL}},
// 10^-5 ~= a7c5ac471b4784230fcf80dc33721d53cddd6e04c0592104 * 2^-208
{{0xd7e45803cd141a6aULL, 0xa63f9a49c2c1b10fULL,
0x8637bd05af6c69b5ULL}},
// 10^-6 ~= 8637bd05af6c69b5a63f9a49c2c1b10fd7e45803cd141a6a * 2^-211
{{0x8ca08cd2e1b9c3dcULL, 0x3d32907604691b4cULL,
0xd6bf94d5e57a42bcULL}},
// 10^-7 ~= d6bf94d5e57a42bc3d32907604691b4c8ca08cd2e1b9c3dc * 2^-215
{{0x3d4d3d758161697dULL, 0xfdc20d2b36ba7c3dULL,
0xabcc77118461cefcULL}},
// 10^-8 ~= abcc77118461cefcfdc20d2b36ba7c3d3d4d3d758161697d * 2^-218
{{0xfdd7645e011abacaULL, 0x31680a88f8953030ULL,
0x89705f4136b4a597ULL}},
// 10^-9 ~= 89705f4136b4a59731680a88f8953030fdd7645e011abaca * 2^-221
{{0x2fbf06fcce912addULL, 0xb573440e5a884d1bULL,
0xdbe6fecebdedd5beULL}},
// 10^-10 ~= dbe6fecebdedd5beb573440e5a884d1b2fbf06fcce912add * 2^-225
{{0xf2ff38ca3eda88b1ULL, 0xf78f69a51539d748ULL,
0xafebff0bcb24aafeULL}},
// 10^-11 ~= afebff0bcb24aafef78f69a51539d748f2ff38ca3eda88b1 * 2^-228
{{0xf598fa3b657ba08eULL, 0xf93f87b7442e45d3ULL,
0x8cbccc096f5088cbULL}},
// 10^-12 ~= 8cbccc096f5088cbf93f87b7442e45d3f598fa3b657ba08e * 2^-231
{{0x88f4c3923bf900e3ULL, 0x2865a5f206b06fb9ULL,
0xe12e13424bb40e13ULL}},
// 10^-13 ~= e12e13424bb40e132865a5f206b06fb988f4c3923bf900e3 * 2^-235
{{0x6d909c74fcc733e9ULL, 0x538484c19ef38c94ULL,
0xb424dc35095cd80fULL}},
// 10^-14 ~= b424dc35095cd80f538484c19ef38c946d909c74fcc733e9 * 2^-238
{{0x57a6e390ca38f654ULL, 0x0f9d37014bf60a10ULL,
0x901d7cf73ab0acd9ULL}},
// 10^-15 ~= 901d7cf73ab0acd90f9d37014bf60a1057a6e390ca38f654 * 2^-241
{{0xbf716c1add27f086ULL, 0x4c2ebe687989a9b3ULL,
0xe69594bec44de15bULL}},
// 10^-16 ~= e69594bec44de15b4c2ebe687989a9b3bf716c1add27f086 * 2^-245
{{0xff8df0157db98d38ULL, 0x09befeb9fad487c2ULL,
0xb877aa3236a4b449ULL}},
// 10^-17 ~= b877aa3236a4b44909befeb9fad487c2ff8df0157db98d38 * 2^-248
{{0x32d7f344649470faULL, 0x3aff322e62439fcfULL,
0x9392ee8e921d5d07ULL}},
// 10^-18 ~= 9392ee8e921d5d073aff322e62439fcf32d7f344649470fa * 2^-251
{{0x1e2652070753e7f5ULL, 0x2b31e9e3d06c32e5ULL,
0xec1e4a7db69561a5ULL}},
// 10^-19 ~= ec1e4a7db69561a52b31e9e3d06c32e51e2652070753e7f5 * 2^-255
{{0x181ea8059f76532bULL, 0x88f4bb1ca6bcf584ULL,
0xbce5086492111aeaULL}},
// 10^-20 ~= bce5086492111aea88f4bb1ca6bcf584181ea8059f76532b * 2^-258
{{0x467eecd14c5ea8efULL, 0xd3f6fc16ebca5e03ULL,
0x971da05074da7beeULL}},
// 10^-21 ~= 971da05074da7beed3f6fc16ebca5e03467eecd14c5ea8ef * 2^-261
{{0x70cb148213caa7e5ULL, 0x5324c68b12dd6338ULL,
0xf1c90080baf72cb1ULL}},
// 10^-22 ~= f1c90080baf72cb15324c68b12dd633870cb148213caa7e5 * 2^-265
{{0x8d6f439b43088651ULL, 0x75b7053c0f178293ULL,
0xc16d9a0095928a27ULL}},
// 10^-23 ~= c16d9a0095928a2775b7053c0f1782938d6f439b43088651 * 2^-268
{{0xd78c3615cf3a050dULL, 0xc4926a9672793542ULL,
0x9abe14cd44753b52ULL}},
// 10^-24 ~= 9abe14cd44753b52c4926a9672793542d78c3615cf3a050d * 2^-271
{{0x8c1389bc7ec33b48ULL, 0x3a83ddbd83f52204ULL,
0xf79687aed3eec551ULL}},
// 10^-25 ~= f79687aed3eec5513a83ddbd83f522048c1389bc7ec33b48 * 2^-275
{{0x3cdc6e306568fc3aULL, 0x95364afe032a819dULL,
0xc612062576589ddaULL}},
// 10^-26 ~= c612062576589dda95364afe032a819d3cdc6e306568fc3a * 2^-278
{{0xca49f1c05120c9c8ULL, 0x775ea264cf55347dULL,
0x9e74d1b791e07e48ULL}},
// 10^-27 ~= 9e74d1b791e07e48775ea264cf55347dca49f1c05120c9c8 * 2^-281
{{0x76dcb60081ce0fa6ULL, 0x8bca9d6e188853fcULL,
0xfd87b5f28300ca0dULL}},
// 10^-28 ~= fd87b5f28300ca0d8bca9d6e188853fc76dcb60081ce0fa6 * 2^-285
{{0x5f16f80067d80c85ULL, 0x096ee45813a04330ULL,
0xcad2f7f5359a3b3eULL}},
// 10^-29 ~= cad2f7f5359a3b3e096ee45813a043305f16f80067d80c85 * 2^-288
{{0x18df2ccd1fe00a04ULL, 0xa1258379a94d028dULL,
0xa2425ff75e14fc31ULL}},
// 10^-30 ~= a2425ff75e14fc31a1258379a94d028d18df2ccd1fe00a04 * 2^-291
{{0x4718f0a419800803ULL, 0x80eacf948770ced7ULL,
0x81ceb32c4b43fcf4ULL}},
// 10^-31 ~= 81ceb32c4b43fcf480eacf948770ced74718f0a419800803 * 2^-294
{{0x0b5b1aa028ccd99fULL, 0x67de18eda5814af2ULL,
0xcfb11ead453994baULL}},
// 10^-32 ~= cfb11ead453994ba67de18eda5814af20b5b1aa028ccd99f * 2^-298
{{0x6f7c154ced70ae19ULL, 0xecb1ad8aeacdd58eULL,
0xa6274bbdd0fadd61ULL}},
// 10^-33 ~= a6274bbdd0fadd61ecb1ad8aeacdd58e6f7c154ced70ae19 * 2^-301
{{0xbf967770bdf3be7aULL, 0xbd5af13bef0b113eULL,
0x84ec3c97da624ab4ULL}},
// 10^-34 ~= 84ec3c97da624ab4bd5af13bef0b113ebf967770bdf3be7a * 2^-304
{{0x65bd8be79652ca5dULL, 0x955e4ec64b44e864ULL,
0xd4ad2dbfc3d07787ULL}},
// 10^-35 ~= d4ad2dbfc3d07787955e4ec64b44e86465bd8be79652ca5d * 2^-308
{{0xeafe098611dbd517ULL, 0xdde50bd1d5d0b9e9ULL,
0xaa242499697392d2ULL}},
// 10^-36 ~= aa242499697392d2dde50bd1d5d0b9e9eafe098611dbd517 * 2^-311
{{0xbbfe6e04db164413ULL, 0x7e50d64177da2e54ULL,
0x881cea14545c7575ULL}},
// 10^-37 ~= 881cea14545c75757e50d64177da2e54bbfe6e04db164413 * 2^-314
{{0x2cca49a15e8a0684ULL, 0x96e7bd358c904a21ULL,
0xd9c7dced53c72255ULL}},
// 10^-38 ~= d9c7dced53c7225596e7bd358c904a212cca49a15e8a0684 * 2^-318
{{0x8a3b6e1ab2080537ULL, 0xabec975e0a0d081aULL,
0xae397d8aa96c1b77ULL}},
// 10^-39 ~= ae397d8aa96c1b77abec975e0a0d081a8a3b6e1ab2080537 * 2^-321
{{0x3b62be7bc1a0042cULL, 0x2323ac4b3b3da015ULL,
0x8b61313bbabce2c6ULL}},
// 10^-40 ~= 8b61313bbabce2c62323ac4b3b3da0153b62be7bc1a0042c * 2^-324
{{0x5f0463f935ccd379ULL, 0x6b6c46dec52f6688ULL,
0xdf01e85f912e37a3ULL}},
// 10^-41 ~= df01e85f912e37a36b6c46dec52f66885f0463f935ccd379 * 2^-328
{{0x7f36b660f7d70f94ULL, 0x55f038b237591ed3ULL,
0xb267ed1940f1c61cULL}},
// 10^-42 ~= b267ed1940f1c61c55f038b237591ed37f36b660f7d70f94 * 2^-331
{{0xcc2bc51a5fdf3faaULL, 0x77f3608e92adb242ULL,
0x8eb98a7a9a5b04e3ULL}},
// 10^-43 ~= 8eb98a7a9a5b04e377f3608e92adb242cc2bc51a5fdf3faa * 2^-334
{{0xe046082a32fecc42ULL, 0x8cb89a7db77c506aULL,
0xe45c10c42a2b3b05ULL}},
// 10^-44 ~= e45c10c42a2b3b058cb89a7db77c506ae046082a32fecc42 * 2^-338
{{0x4d04d354f598a368ULL, 0x3d607b97c5fd0d22ULL,
0xb6b00d69bb55c8d1ULL}},
// 10^-45 ~= b6b00d69bb55c8d13d607b97c5fd0d224d04d354f598a368 * 2^-341
{{0x3d9d75dd9146e920ULL, 0xcab3961304ca70e8ULL,
0x9226712162ab070dULL}},
// 10^-46 ~= 9226712162ab070dcab3961304ca70e83d9d75dd9146e920 * 2^-344
{{0xc8fbefc8e8717500ULL, 0xaab8f01e6e10b4a6ULL,
0xe9d71b689dde71afULL}},
// 10^-47 ~= e9d71b689dde71afaab8f01e6e10b4a6c8fbefc8e8717500 * 2^-348
{{0x3a63263a538df734ULL, 0x5560c018580d5d52ULL,
0xbb127c53b17ec159ULL}},
// 10^-48 ~= bb127c53b17ec1595560c018580d5d523a63263a538df734 * 2^-351
{{0x2eb5b82ea93e5f5dULL, 0xdde7001379a44aa8ULL,
0x95a8637627989aadULL}},
// 10^-49 ~= 95a8637627989aaddde7001379a44aa82eb5b82ea93e5f5d * 2^-354
{{0x4abc59e441fd6561ULL, 0x963e66858f6d4440ULL,
0xef73d256a5c0f77cULL}},
// 10^-50 ~= ef73d256a5c0f77c963e66858f6d44404abc59e441fd6561 * 2^-358
{{0x6efd14b69b311de7ULL, 0xde98520472bdd033ULL,
0xbf8fdb78849a5f96ULL}},
// 10^-51 ~= bf8fdb78849a5f96de98520472bdd0336efd14b69b311de7 * 2^-361
{{0x259743c548f417ecULL, 0xe546a8038efe4029ULL,
0x993fe2c6d07b7fabULL}},
// 10^-52 ~= 993fe2c6d07b7fabe546a8038efe4029259743c548f417ec * 2^-364
{{0x3c25393ba7ecf313ULL, 0xd53dd99f4b3066a8ULL,
0xf53304714d9265dfULL}},
// 10^-53 ~= f53304714d9265dfd53dd99f4b3066a83c25393ba7ecf313 * 2^-368
{{0x96842dc95323f5a9ULL, 0xaa97e14c3c26b886ULL,
0xc428d05aa4751e4cULL}},
// 10^-54 ~= c428d05aa4751e4caa97e14c3c26b88696842dc95323f5a9 * 2^-371
{{0xab9cf16ddc1cc487ULL, 0x55464dd69685606bULL,
0x9ced737bb6c4183dULL}},
// 10^-55 ~= 9ced737bb6c4183d55464dd69685606bab9cf16ddc1cc487 * 2^-374
{{0xac2e4f162cfad40bULL, 0xeed6e2f0f0d56712ULL, 0xfb158592be068d2eULL}}
// 10^-56 ~= fb158592be068d2eeed6e2f0f0d56712ac2e4f162cfad40b * 2^-378
};
unsigned int Ex192m192[] = {
3, // 195 - 192, Ex = 195
6, // 198 - 192, Ex = 198
9, // 201 - 192, Ex = 201
13, // 205 - 192, Ex = 205
16, // 208 - 192, Ex = 208
19, // 211 - 192, Ex = 211
23, // 215 - 192, Ex = 215
26, // 218 - 192, Ex = 218
29, // 221 - 192, Ex = 221
33, // 225 - 192, Ex = 225
36, // 228 - 192, Ex = 228
39, // 231 - 192, Ex = 231
43, // 235 - 192, Ex = 235
46, // 238 - 192, Ex = 238
49, // 241 - 192, Ex = 241
53, // 245 - 192, Ex = 245
56, // 248 - 192, Ex = 248
59, // 251 - 192, Ex = 251
63, // 255 - 192, Ex = 255
2, // 258 - 256, Ex = 258
5, // 261 - 256, Ex = 261
9, // 265 - 256, Ex = 265
12, // 268 - 256, Ex = 268
15, // 271 - 256, Ex = 271
19, // 275 - 256, Ex = 275
22, // 278 - 256, Ex = 278
25, // 281 - 256, Ex = 281
29, // 285 - 256, Ex = 285
32, // 288 - 256, Ex = 288
35, // 291 - 256, Ex = 291
38, // 294 - 256, Ex = 294
42, // 298 - 256, Ex = 298
45, // 301 - 256, Ex = 301
48, // 304 - 256, Ex = 304
52, // 308 - 256, Ex = 308
55, // 311 - 256, Ex = 311
58, // 314 - 256, Ex = 314
62, // 318 - 256, Ex = 318
1, // 321 - 320, Ex = 321
4, // 324 - 320, Ex = 324
8, // 328 - 320, Ex = 328
11, // 331 - 320, Ex = 331
14, // 334 - 320, Ex = 334
18, // 338 - 320, Ex = 338
21, // 341 - 320, Ex = 341
24, // 344 - 320, Ex = 344
28, // 348 - 320, Ex = 348
31, // 351 - 320, Ex = 351
34, // 354 - 320, Ex = 354
38, // 358 - 320, Ex = 358
41, // 361 - 320, Ex = 361
44, // 364 - 320, Ex = 364
48, // 368 - 320, Ex = 368
51, // 371 - 320, Ex = 371
54, // 374 - 320, Ex = 374
58 // 378 - 320, Ex = 378
};
UINT64 half192[] = {
0x0000000000000004ULL, // half / 2^192 = 4
0x0000000000000020ULL, // half / 2^192 = 20
0x0000000000000100ULL, // half / 2^192 = 100
0x0000000000001000ULL, // half / 2^192 = 1000
0x0000000000008000ULL, // half / 2^192 = 8000
0x0000000000040000ULL, // half / 2^192 = 40000
0x0000000000400000ULL, // half / 2^192 = 400000
0x0000000002000000ULL, // half / 2^192 = 2000000
0x0000000010000000ULL, // half / 2^192 = 10000000
0x0000000100000000ULL, // half / 2^192 = 100000000
0x0000000800000000ULL, // half / 2^192 = 800000000
0x0000004000000000ULL, // half / 2^192 = 4000000000
0x0000040000000000ULL, // half / 2^192 = 40000000000
0x0000200000000000ULL, // half / 2^192 = 200000000000
0x0001000000000000ULL, // half / 2^192 = 1000000000000
0x0010000000000000ULL, // half / 2^192 = 10000000000000
0x0080000000000000ULL, // half / 2^192 = 80000000000000
0x0400000000000000ULL, // half / 2^192 = 400000000000000
0x4000000000000000ULL, // half / 2^192 = 4000000000000000
0x0000000000000002ULL, // half / 2^256 = 2
0x0000000000000010ULL, // half / 2^256 = 10
0x0000000000000100ULL, // half / 2^256 = 100
0x0000000000000800ULL, // half / 2^256 = 800
0x0000000000004000ULL, // half / 2^256 = 4000
0x0000000000040000ULL, // half / 2^256 = 40000
0x0000000000200000ULL, // half / 2^256 = 200000
0x0000000001000000ULL, // half / 2^256 = 1000000
0x0000000010000000ULL, // half / 2^256 = 10000000
0x0000000080000000ULL, // half / 2^256 = 80000000
0x0000000400000000ULL, // half / 2^256 = 400000000
0x0000002000000000ULL, // half / 2^256 = 2000000000
0x0000020000000000ULL, // half / 2^256 = 20000000000
0x0000100000000000ULL, // half / 2^256 = 100000000000
0x0000800000000000ULL, // half / 2^256 = 800000000000
0x0008000000000000ULL, // half / 2^256 = 8000000000000
0x0040000000000000ULL, // half / 2^256 = 40000000000000
0x0200000000000000ULL, // half / 2^256 = 200000000000000
0x2000000000000000ULL, // half / 2^256 = 2000000000000000
0x0000000000000001ULL, // half / 2^320 = 1
0x0000000000000008ULL, // half / 2^320 = 8
0x0000000000000080ULL, // half / 2^320 = 80
0x0000000000000400ULL, // half / 2^320 = 400
0x0000000000002000ULL, // half / 2^320 = 2000
0x0000000000020000ULL, // half / 2^320 = 20000
0x0000000000100000ULL, // half / 2^320 = 100000
0x0000000000800000ULL, // half / 2^320 = 800000
0x0000000008000000ULL, // half / 2^320 = 8000000
0x0000000040000000ULL, // half / 2^320 = 40000000
0x0000000200000000ULL, // half / 2^320 = 200000000
0x0000002000000000ULL, // half / 2^320 = 2000000000
0x0000010000000000ULL, // half / 2^320 = 10000000000
0x0000080000000000ULL, // half / 2^320 = 80000000000
0x0000800000000000ULL, // half / 2^320 = 800000000000
0x0004000000000000ULL, // half / 2^320 = 4000000000000
0x0020000000000000ULL, // half / 2^320 = 20000000000000
0x0200000000000000ULL // half / 2^320 = 200000000000000
};
UINT64 mask192[] = {
0x0000000000000007ULL, // mask / 2^192
0x000000000000003fULL, // mask / 2^192
0x00000000000001ffULL, // mask / 2^192
0x0000000000001fffULL, // mask / 2^192
0x000000000000ffffULL, // mask / 2^192
0x000000000007ffffULL, // mask / 2^192
0x00000000007fffffULL, // mask / 2^192
0x0000000003ffffffULL, // mask / 2^192
0x000000001fffffffULL, // mask / 2^192
0x00000001ffffffffULL, // mask / 2^192
0x0000000fffffffffULL, // mask / 2^192
0x0000007fffffffffULL, // mask / 2^192
0x000007ffffffffffULL, // mask / 2^192
0x00003fffffffffffULL, // mask / 2^192
0x0001ffffffffffffULL, // mask / 2^192
0x001fffffffffffffULL, // mask / 2^192
0x00ffffffffffffffULL, // mask / 2^192
0x07ffffffffffffffULL, // mask / 2^192
0x7fffffffffffffffULL, // mask / 2^192
0x0000000000000003ULL, // mask / 2^256
0x000000000000001fULL, // mask / 2^256
0x00000000000001ffULL, // mask / 2^256
0x0000000000000fffULL, // mask / 2^256
0x0000000000007fffULL, // mask / 2^256
0x000000000007ffffULL, // mask / 2^256
0x00000000003fffffULL, // mask / 2^256
0x0000000001ffffffULL, // mask / 2^256
0x000000001fffffffULL, // mask / 2^256
0x00000000ffffffffULL, // mask / 2^256
0x00000007ffffffffULL, // mask / 2^256
0x0000003fffffffffULL, // mask / 2^256
0x000003ffffffffffULL, // mask / 2^256
0x00001fffffffffffULL, // mask / 2^256
0x0000ffffffffffffULL, // mask / 2^256
0x000fffffffffffffULL, // mask / 2^256
0x007fffffffffffffULL, // mask / 2^256
0x03ffffffffffffffULL, // mask / 2^256
0x3fffffffffffffffULL, // mask / 2^256
0x0000000000000001ULL, // mask / 2^320
0x000000000000000fULL, // mask / 2^320
0x00000000000000ffULL, // mask / 2^320
0x00000000000007ffULL, // mask / 2^320
0x0000000000003fffULL, // mask / 2^320
0x000000000003ffffULL, // mask / 2^320
0x00000000001fffffULL, // mask / 2^320
0x0000000000ffffffULL, // mask / 2^320
0x000000000fffffffULL, // mask / 2^320
0x000000007fffffffULL, // mask / 2^320
0x00000003ffffffffULL, // mask / 2^320
0x0000003fffffffffULL, // mask / 2^320
0x000001ffffffffffULL, // mask / 2^320
0x00000fffffffffffULL, // mask / 2^320
0x0000ffffffffffffULL, // mask / 2^320
0x0007ffffffffffffULL, // mask / 2^320
0x003fffffffffffffULL, // mask / 2^320
0x03ffffffffffffffULL // mask / 2^320
};
UINT192 ten2mxtrunc192[] = {
{{0xccccccccccccccccULL, 0xccccccccccccccccULL,
0xccccccccccccccccULL}},
// (ten2mx >> 192) = cccccccccccccccccccccccccccccccccccccccccccccccc
{{0xd70a3d70a3d70a3dULL, 0x3d70a3d70a3d70a3ULL,
0xa3d70a3d70a3d70aULL}},
// (ten2mx >> 192) = a3d70a3d70a3d70a3d70a3d70a3d70a3d70a3d70a3d70a3d
{{0x78d4fdf3b645a1caULL, 0x645a1cac083126e9ULL,
0x83126e978d4fdf3bULL}},
// (ten2mx >> 192) = 83126e978d4fdf3b645a1cac083126e978d4fdf3b645a1ca
{{0xc154c985f06f6944ULL, 0xd3c36113404ea4a8ULL,
0xd1b71758e219652bULL}},
// (ten2mx >> 192) = d1b71758e219652bd3c36113404ea4a8c154c985f06f6944
{{0xcddd6e04c0592103ULL, 0x0fcf80dc33721d53ULL,
0xa7c5ac471b478423ULL}},
// (ten2mx >> 192) = a7c5ac471b4784230fcf80dc33721d53cddd6e04c0592103
{{0xd7e45803cd141a69ULL, 0xa63f9a49c2c1b10fULL,
0x8637bd05af6c69b5ULL}},
// (ten2mx >> 192) = 8637bd05af6c69b5a63f9a49c2c1b10fd7e45803cd141a69
{{0x8ca08cd2e1b9c3dbULL, 0x3d32907604691b4cULL,
0xd6bf94d5e57a42bcULL}},
// (ten2mx >> 192) = d6bf94d5e57a42bc3d32907604691b4c8ca08cd2e1b9c3db
{{0x3d4d3d758161697cULL, 0xfdc20d2b36ba7c3dULL,
0xabcc77118461cefcULL}},
// (ten2mx >> 192) = abcc77118461cefcfdc20d2b36ba7c3d3d4d3d758161697c
{{0xfdd7645e011abac9ULL, 0x31680a88f8953030ULL,
0x89705f4136b4a597ULL}},
// (ten2mx >> 192) = 89705f4136b4a59731680a88f8953030fdd7645e011abac9
{{0x2fbf06fcce912adcULL, 0xb573440e5a884d1bULL,
0xdbe6fecebdedd5beULL}},
// (ten2mx >> 192) = dbe6fecebdedd5beb573440e5a884d1b2fbf06fcce912adc
{{0xf2ff38ca3eda88b0ULL, 0xf78f69a51539d748ULL,
0xafebff0bcb24aafeULL}},
// (ten2mx >> 192) = afebff0bcb24aafef78f69a51539d748f2ff38ca3eda88b0
{{0xf598fa3b657ba08dULL, 0xf93f87b7442e45d3ULL,
0x8cbccc096f5088cbULL}},
// (ten2mx >> 192) = 8cbccc096f5088cbf93f87b7442e45d3f598fa3b657ba08d
{{0x88f4c3923bf900e2ULL, 0x2865a5f206b06fb9ULL,
0xe12e13424bb40e13ULL}},
// (ten2mx >> 192) = e12e13424bb40e132865a5f206b06fb988f4c3923bf900e2
{{0x6d909c74fcc733e8ULL, 0x538484c19ef38c94ULL,
0xb424dc35095cd80fULL}},
// (ten2mx >> 192) = b424dc35095cd80f538484c19ef38c946d909c74fcc733e8
{{0x57a6e390ca38f653ULL, 0x0f9d37014bf60a10ULL,
0x901d7cf73ab0acd9ULL}},
// (ten2mx >> 192) = 901d7cf73ab0acd90f9d37014bf60a1057a6e390ca38f653
{{0xbf716c1add27f085ULL, 0x4c2ebe687989a9b3ULL,
0xe69594bec44de15bULL}},
// (ten2mx >> 192) = e69594bec44de15b4c2ebe687989a9b3bf716c1add27f085
{{0xff8df0157db98d37ULL, 0x09befeb9fad487c2ULL,
0xb877aa3236a4b449ULL}},
// (ten2mx >> 192) = b877aa3236a4b44909befeb9fad487c2ff8df0157db98d37
{{0x32d7f344649470f9ULL, 0x3aff322e62439fcfULL,
0x9392ee8e921d5d07ULL}},
// (ten2mx >> 192) = 9392ee8e921d5d073aff322e62439fcf32d7f344649470f9
{{0x1e2652070753e7f4ULL, 0x2b31e9e3d06c32e5ULL,
0xec1e4a7db69561a5ULL}},
// (ten2mx >> 192) = ec1e4a7db69561a52b31e9e3d06c32e51e2652070753e7f4
{{0x181ea8059f76532aULL, 0x88f4bb1ca6bcf584ULL,
0xbce5086492111aeaULL}},
// (ten2mx >> 192) = bce5086492111aea88f4bb1ca6bcf584181ea8059f76532a
{{0x467eecd14c5ea8eeULL, 0xd3f6fc16ebca5e03ULL,
0x971da05074da7beeULL}},
// (ten2mx >> 192) = 971da05074da7beed3f6fc16ebca5e03467eecd14c5ea8ee
{{0x70cb148213caa7e4ULL, 0x5324c68b12dd6338ULL,
0xf1c90080baf72cb1ULL}},
// (ten2mx >> 192) = f1c90080baf72cb15324c68b12dd633870cb148213caa7e4
{{0x8d6f439b43088650ULL, 0x75b7053c0f178293ULL,
0xc16d9a0095928a27ULL}},
// (ten2mx >> 192) = c16d9a0095928a2775b7053c0f1782938d6f439b43088650
{{0xd78c3615cf3a050cULL, 0xc4926a9672793542ULL,
0x9abe14cd44753b52ULL}},
// (ten2mx >> 192) = 9abe14cd44753b52c4926a9672793542d78c3615cf3a050c
{{0x8c1389bc7ec33b47ULL, 0x3a83ddbd83f52204ULL,
0xf79687aed3eec551ULL}},
// (ten2mx >> 192) = f79687aed3eec5513a83ddbd83f522048c1389bc7ec33b47
{{0x3cdc6e306568fc39ULL, 0x95364afe032a819dULL,
0xc612062576589ddaULL}},
// (ten2mx >> 192) = c612062576589dda95364afe032a819d3cdc6e306568fc39
{{0xca49f1c05120c9c7ULL, 0x775ea264cf55347dULL,
0x9e74d1b791e07e48ULL}},
// (ten2mx >> 192) = 9e74d1b791e07e48775ea264cf55347dca49f1c05120c9c7
{{0x76dcb60081ce0fa5ULL, 0x8bca9d6e188853fcULL,
0xfd87b5f28300ca0dULL}},
// (ten2mx >> 192) = fd87b5f28300ca0d8bca9d6e188853fc76dcb60081ce0fa5
{{0x5f16f80067d80c84ULL, 0x096ee45813a04330ULL,
0xcad2f7f5359a3b3eULL}},
// (ten2mx >> 192) = cad2f7f5359a3b3e096ee45813a043305f16f80067d80c84
{{0x18df2ccd1fe00a03ULL, 0xa1258379a94d028dULL,
0xa2425ff75e14fc31ULL}},
// (ten2mx >> 192) = a2425ff75e14fc31a1258379a94d028d18df2ccd1fe00a03
{{0x4718f0a419800802ULL, 0x80eacf948770ced7ULL,
0x81ceb32c4b43fcf4ULL}},
// (ten2mx >> 192) = 81ceb32c4b43fcf480eacf948770ced74718f0a419800802
{{0x0b5b1aa028ccd99eULL, 0x67de18eda5814af2ULL,
0xcfb11ead453994baULL}},
// (ten2mx >> 192) = cfb11ead453994ba67de18eda5814af20b5b1aa028ccd99e
{{0x6f7c154ced70ae18ULL, 0xecb1ad8aeacdd58eULL,
0xa6274bbdd0fadd61ULL}},
// (ten2mx >> 192) = a6274bbdd0fadd61ecb1ad8aeacdd58e6f7c154ced70ae18
{{0xbf967770bdf3be79ULL, 0xbd5af13bef0b113eULL,
0x84ec3c97da624ab4ULL}},
// (ten2mx >> 192) = 84ec3c97da624ab4bd5af13bef0b113ebf967770bdf3be79
{{0x65bd8be79652ca5cULL, 0x955e4ec64b44e864ULL,
0xd4ad2dbfc3d07787ULL}},
// (ten2mx >> 192) = d4ad2dbfc3d07787955e4ec64b44e86465bd8be79652ca5c
{{0xeafe098611dbd516ULL, 0xdde50bd1d5d0b9e9ULL,
0xaa242499697392d2ULL}},
// (ten2mx >> 192) = aa242499697392d2dde50bd1d5d0b9e9eafe098611dbd516
{{0xbbfe6e04db164412ULL, 0x7e50d64177da2e54ULL,
0x881cea14545c7575ULL}},
// (ten2mx >> 192) = 881cea14545c75757e50d64177da2e54bbfe6e04db164412
{{0x2cca49a15e8a0683ULL, 0x96e7bd358c904a21ULL,
0xd9c7dced53c72255ULL}},
// (ten2mx >> 192) = d9c7dced53c7225596e7bd358c904a212cca49a15e8a0683
{{0x8a3b6e1ab2080536ULL, 0xabec975e0a0d081aULL,
0xae397d8aa96c1b77ULL}},
// (ten2mx >> 192) = ae397d8aa96c1b77abec975e0a0d081a8a3b6e1ab2080536
{{0x3b62be7bc1a0042bULL, 0x2323ac4b3b3da015ULL,
0x8b61313bbabce2c6ULL}},
// (ten2mx >> 192) = 8b61313bbabce2c62323ac4b3b3da0153b62be7bc1a0042b
{{0x5f0463f935ccd378ULL, 0x6b6c46dec52f6688ULL,
0xdf01e85f912e37a3ULL}},
// (ten2mx >> 192) = df01e85f912e37a36b6c46dec52f66885f0463f935ccd378
{{0x7f36b660f7d70f93ULL, 0x55f038b237591ed3ULL,
0xb267ed1940f1c61cULL}},
// (ten2mx >> 192) = b267ed1940f1c61c55f038b237591ed37f36b660f7d70f93
{{0xcc2bc51a5fdf3fa9ULL, 0x77f3608e92adb242ULL,
0x8eb98a7a9a5b04e3ULL}},
// (ten2mx >> 192) = 8eb98a7a9a5b04e377f3608e92adb242cc2bc51a5fdf3fa9
{{0xe046082a32fecc41ULL, 0x8cb89a7db77c506aULL,
0xe45c10c42a2b3b05ULL}},
// (ten2mx >> 192) = e45c10c42a2b3b058cb89a7db77c506ae046082a32fecc41
{{0x4d04d354f598a367ULL, 0x3d607b97c5fd0d22ULL,
0xb6b00d69bb55c8d1ULL}},
// (ten2mx >> 192) = b6b00d69bb55c8d13d607b97c5fd0d224d04d354f598a367
{{0x3d9d75dd9146e91fULL, 0xcab3961304ca70e8ULL,
0x9226712162ab070dULL}},
// (ten2mx >> 192) = 9226712162ab070dcab3961304ca70e83d9d75dd9146e91f
{{0xc8fbefc8e87174ffULL, 0xaab8f01e6e10b4a6ULL,
0xe9d71b689dde71afULL}},
// (ten2mx >> 192) = e9d71b689dde71afaab8f01e6e10b4a6c8fbefc8e87174ff
{{0x3a63263a538df733ULL, 0x5560c018580d5d52ULL,
0xbb127c53b17ec159ULL}},
// (ten2mx >> 192) = bb127c53b17ec1595560c018580d5d523a63263a538df733
{{0x2eb5b82ea93e5f5cULL, 0xdde7001379a44aa8ULL,
0x95a8637627989aadULL}},
// (ten2mx >> 192) = 95a8637627989aaddde7001379a44aa82eb5b82ea93e5f5c
{{0x4abc59e441fd6560ULL, 0x963e66858f6d4440ULL,
0xef73d256a5c0f77cULL}},
// (ten2mx >> 192) = ef73d256a5c0f77c963e66858f6d44404abc59e441fd6560
{{0x6efd14b69b311de6ULL, 0xde98520472bdd033ULL,
0xbf8fdb78849a5f96ULL}},
// (ten2mx >> 192) = bf8fdb78849a5f96de98520472bdd0336efd14b69b311de6
{{0x259743c548f417ebULL, 0xe546a8038efe4029ULL,
0x993fe2c6d07b7fabULL}},
// (ten2mx >> 192) = 993fe2c6d07b7fabe546a8038efe4029259743c548f417eb
{{0x3c25393ba7ecf312ULL, 0xd53dd99f4b3066a8ULL,
0xf53304714d9265dfULL}},
// (ten2mx >> 192) = f53304714d9265dfd53dd99f4b3066a83c25393ba7ecf312
{{0x96842dc95323f5a8ULL, 0xaa97e14c3c26b886ULL,
0xc428d05aa4751e4cULL}},
// (ten2mx >> 192) = c428d05aa4751e4caa97e14c3c26b88696842dc95323f5a8
{{0xab9cf16ddc1cc486ULL, 0x55464dd69685606bULL,
0x9ced737bb6c4183dULL}},
// (ten2mx >> 192) = 9ced737bb6c4183d55464dd69685606bab9cf16ddc1cc486
{{0xac2e4f162cfad40aULL, 0xeed6e2f0f0d56712ULL, 0xfb158592be068d2eULL}}
// (ten2mx >> 192) = fb158592be068d2eeed6e2f0f0d56712ac2e4f162cfad40a
};
UINT256 Kx256[] = {
{{0xcccccccccccccccdULL, 0xccccccccccccccccULL,
0xccccccccccccccccULL, 0xccccccccccccccccULL}},
// 10^-1 ~= cccccccccccccccc cccccccccccccccc
// cccccccccccccccccccccccccccccccd * 2^-259
{{0x70a3d70a3d70a3d8ULL, 0xd70a3d70a3d70a3dULL,
0x3d70a3d70a3d70a3ULL, 0xa3d70a3d70a3d70aULL}},
// 10^-2 ~= a3d70a3d70a3d70a 3d70a3d70a3d70a3
// d70a3d70a3d70a3d70a3d70a3d70a3d8 * 2^-262
{{0xc083126e978d4fe0ULL, 0x78d4fdf3b645a1caULL,
0x645a1cac083126e9ULL, 0x83126e978d4fdf3bULL}},
// 10^-3 ~= 83126e978d4fdf3b 645a1cac083126e9
// 78d4fdf3b645a1cac083126e978d4fe0 * 2^-265
{{0x67381d7dbf487fccULL, 0xc154c985f06f6944ULL,
0xd3c36113404ea4a8ULL, 0xd1b71758e219652bULL}},
// 10^-4 ~= d1b71758e219652b d3c36113404ea4a8
// c154c985f06f694467381d7dbf487fcc * 2^-269
{{0x85c67dfe32a0663dULL, 0xcddd6e04c0592103ULL,
0x0fcf80dc33721d53ULL, 0xa7c5ac471b478423ULL}},
// 10^-5 ~= a7c5ac471b478423 fcf80dc33721d53
// cddd6e04c059210385c67dfe32a0663d * 2^-272
{{0x37d1fe64f54d1e97ULL, 0xd7e45803cd141a69ULL,
0xa63f9a49c2c1b10fULL, 0x8637bd05af6c69b5ULL}},
// 10^-6 ~= 8637bd05af6c69b5 a63f9a49c2c1b10f
// d7e45803cd141a6937d1fe64f54d1e97 * 2^-275
{{0x8c8330a1887b6425ULL, 0x8ca08cd2e1b9c3dbULL,
0x3d32907604691b4cULL, 0xd6bf94d5e57a42bcULL}},
// 10^-7 ~= d6bf94d5e57a42bc 3d32907604691b4c
// 8ca08cd2e1b9c3db8c8330a1887b6425 * 2^-279
{{0x7068f3b46d2f8351ULL, 0x3d4d3d758161697cULL,
0xfdc20d2b36ba7c3dULL, 0xabcc77118461cefcULL}},
// 10^-8 ~= abcc77118461cefc fdc20d2b36ba7c3d
// 3d4d3d758161697c7068f3b46d2f8351 * 2^-282
{{0xf387295d242602a7ULL, 0xfdd7645e011abac9ULL,
0x31680a88f8953030ULL, 0x89705f4136b4a597ULL}},
// 10^-9 ~= 89705f4136b4a597 31680a88f8953030
// fdd7645e011abac9f387295d242602a7 * 2^-285
{{0xb8d8422ea03cd10bULL, 0x2fbf06fcce912adcULL,
0xb573440e5a884d1bULL, 0xdbe6fecebdedd5beULL}},
// 10^-10 ~= dbe6fecebdedd5be b573440e5a884d1b
// 2fbf06fcce912adcb8d8422ea03cd10b * 2^-289
{{0x93e034f219ca40d6ULL, 0xf2ff38ca3eda88b0ULL,
0xf78f69a51539d748ULL, 0xafebff0bcb24aafeULL}},
// 10^-11 ~= afebff0bcb24aafe f78f69a51539d748
// f2ff38ca3eda88b093e034f219ca40d6 * 2^-292
{{0x4319c3f4e16e9a45ULL, 0xf598fa3b657ba08dULL,
0xf93f87b7442e45d3ULL, 0x8cbccc096f5088cbULL}},
// 10^-12 ~= 8cbccc096f5088cb f93f87b7442e45d3
// f598fa3b657ba08d4319c3f4e16e9a45 * 2^-295
{{0x04f606549be42a07ULL, 0x88f4c3923bf900e2ULL,
0x2865a5f206b06fb9ULL, 0xe12e13424bb40e13ULL}},
// 10^-13 ~= e12e13424bb40e13 2865a5f206b06fb9
// 88f4c3923bf900e204f606549be42a07 * 2^-299
{{0x03f805107cb68806ULL, 0x6d909c74fcc733e8ULL,
0x538484c19ef38c94ULL, 0xb424dc35095cd80fULL}},
// 10^-14 ~= b424dc35095cd80f 538484c19ef38c94
// 6d909c74fcc733e803f805107cb68806 * 2^-302
{{0x3660040d3092066bULL, 0x57a6e390ca38f653ULL,
0x0f9d37014bf60a10ULL, 0x901d7cf73ab0acd9ULL}},
// 10^-15 ~= 901d7cf73ab0acd9 f9d37014bf60a10
// 57a6e390ca38f6533660040d3092066b * 2^-305
{{0x23ccd3484db670abULL, 0xbf716c1add27f085ULL,
0x4c2ebe687989a9b3ULL, 0xe69594bec44de15bULL}},
// 10^-16 ~= e69594bec44de15b 4c2ebe687989a9b3
// bf716c1add27f08523ccd3484db670ab * 2^-309
{{0x4fd70f6d0af85a23ULL, 0xff8df0157db98d37ULL,
0x09befeb9fad487c2ULL, 0xb877aa3236a4b449ULL}},
// 10^-17 ~= b877aa3236a4b449 9befeb9fad487c2
// ff8df0157db98d374fd70f6d0af85a23 * 2^-312
{{0x0cac0c573bf9e1b6ULL, 0x32d7f344649470f9ULL,
0x3aff322e62439fcfULL, 0x9392ee8e921d5d07ULL}},
// 10^-18 ~= 9392ee8e921d5d07 3aff322e62439fcf
// 32d7f344649470f90cac0c573bf9e1b6 * 2^-315
{{0xe11346f1f98fcf89ULL, 0x1e2652070753e7f4ULL,
0x2b31e9e3d06c32e5ULL, 0xec1e4a7db69561a5ULL}},
// 10^-19 ~= ec1e4a7db69561a5 2b31e9e3d06c32e5
// 1e2652070753e7f4e11346f1f98fcf89 * 2^-319
{{0x4da9058e613fd93aULL, 0x181ea8059f76532aULL,
0x88f4bb1ca6bcf584ULL, 0xbce5086492111aeaULL}},
// 10^-20 ~= bce5086492111aea 88f4bb1ca6bcf584
// 181ea8059f76532a4da9058e613fd93a * 2^-322
{{0xa48737a51a997a95ULL, 0x467eecd14c5ea8eeULL,
0xd3f6fc16ebca5e03ULL, 0x971da05074da7beeULL}},
// 10^-21 ~= 971da05074da7bee d3f6fc16ebca5e03
// 467eecd14c5ea8eea48737a51a997a95 * 2^-325
{{0x3a71f2a1c428c421ULL, 0x70cb148213caa7e4ULL,
0x5324c68b12dd6338ULL, 0xf1c90080baf72cb1ULL}},
// 10^-22 ~= f1c90080baf72cb1 5324c68b12dd6338
// 70cb148213caa7e43a71f2a1c428c421 * 2^-329
{{0x2ec18ee7d0209ce8ULL, 0x8d6f439b43088650ULL,
0x75b7053c0f178293ULL, 0xc16d9a0095928a27ULL}},
// 10^-23 ~= c16d9a0095928a27 75b7053c0f178293
// 8d6f439b430886502ec18ee7d0209ce8 * 2^-332
{{0xf23472530ce6e3edULL, 0xd78c3615cf3a050cULL,
0xc4926a9672793542ULL, 0x9abe14cd44753b52ULL}},
// 10^-24 ~= 9abe14cd44753b52 c4926a9672793542
// d78c3615cf3a050cf23472530ce6e3ed * 2^-335
{{0xe9ed83b814a49fe1ULL, 0x8c1389bc7ec33b47ULL,
0x3a83ddbd83f52204ULL, 0xf79687aed3eec551ULL}},
// 10^-25 ~= f79687aed3eec551 3a83ddbd83f52204
// 8c1389bc7ec33b47e9ed83b814a49fe1 * 2^-339
{{0x87f1362cdd507fe7ULL, 0x3cdc6e306568fc39ULL,
0x95364afe032a819dULL, 0xc612062576589ddaULL}},
// 10^-26 ~= c612062576589dda 95364afe032a819d
// 3cdc6e306568fc3987f1362cdd507fe7 * 2^-342
{{0x9ff42b5717739986ULL, 0xca49f1c05120c9c7ULL,
0x775ea264cf55347dULL, 0x9e74d1b791e07e48ULL}},
// 10^-27 ~= 9e74d1b791e07e48 775ea264cf55347d
// ca49f1c05120c9c79ff42b5717739986 * 2^-345
{{0xccb9def1bf1f5c09ULL, 0x76dcb60081ce0fa5ULL,
0x8bca9d6e188853fcULL, 0xfd87b5f28300ca0dULL}},
// 10^-28 ~= fd87b5f28300ca0d 8bca9d6e188853fc
// 76dcb60081ce0fa5ccb9def1bf1f5c09 * 2^-349
{{0xa3c7e58e327f7cd4ULL, 0x5f16f80067d80c84ULL,
0x096ee45813a04330ULL, 0xcad2f7f5359a3b3eULL}},
// 10^-29 ~= cad2f7f5359a3b3e 96ee45813a04330
// 5f16f80067d80c84a3c7e58e327f7cd4 * 2^-352
{{0xb6398471c1ff9710ULL, 0x18df2ccd1fe00a03ULL,
0xa1258379a94d028dULL, 0xa2425ff75e14fc31ULL}},
// 10^-30 ~= a2425ff75e14fc31 a1258379a94d028d
// 18df2ccd1fe00a03b6398471c1ff9710 * 2^-355
{{0xf82e038e34cc78daULL, 0x4718f0a419800802ULL,
0x80eacf948770ced7ULL, 0x81ceb32c4b43fcf4ULL}},
// 10^-31 ~= 81ceb32c4b43fcf4 80eacf948770ced7
// 4718f0a419800802f82e038e34cc78da * 2^-358
{{0x59e338e387ad8e29ULL, 0x0b5b1aa028ccd99eULL,
0x67de18eda5814af2ULL, 0xcfb11ead453994baULL}},
// 10^-32 ~= cfb11ead453994ba 67de18eda5814af2
// b5b1aa028ccd99e59e338e387ad8e29 * 2^-362
{{0x47e8fa4f9fbe0b54ULL, 0x6f7c154ced70ae18ULL,
0xecb1ad8aeacdd58eULL, 0xa6274bbdd0fadd61ULL}},
// 10^-33 ~= a6274bbdd0fadd61 ecb1ad8aeacdd58e
// 6f7c154ced70ae1847e8fa4f9fbe0b54 * 2^-365
{{0xd320c83fb2fe6f76ULL, 0xbf967770bdf3be79ULL,
0xbd5af13bef0b113eULL, 0x84ec3c97da624ab4ULL}},
// 10^-34 ~= 84ec3c97da624ab4 bd5af13bef0b113e
// bf967770bdf3be79d320c83fb2fe6f76 * 2^-368
{{0x85014065eb30b257ULL, 0x65bd8be79652ca5cULL,
0x955e4ec64b44e864ULL, 0xd4ad2dbfc3d07787ULL}},
// 10^-35 ~= d4ad2dbfc3d07787 955e4ec64b44e864
// 65bd8be79652ca5c85014065eb30b257 * 2^-372
{{0xd0cdcd1e55c08eacULL, 0xeafe098611dbd516ULL,
0xdde50bd1d5d0b9e9ULL, 0xaa242499697392d2ULL}},
// 10^-36 ~= aa242499697392d2 dde50bd1d5d0b9e9
// eafe098611dbd516d0cdcd1e55c08eac * 2^-375
{{0x40a4a418449a0bbdULL, 0xbbfe6e04db164412ULL,
0x7e50d64177da2e54ULL, 0x881cea14545c7575ULL}},
// 10^-37 ~= 881cea14545c7575 7e50d64177da2e54
// bbfe6e04db16441240a4a418449a0bbd * 2^-378
{{0x9aa1068d3a9012c8ULL, 0x2cca49a15e8a0683ULL,
0x96e7bd358c904a21ULL, 0xd9c7dced53c72255ULL}},
// 10^-38 ~= d9c7dced53c72255 96e7bd358c904a21
// 2cca49a15e8a06839aa1068d3a9012c8 * 2^-382
{{0x154d9ed7620cdbd3ULL, 0x8a3b6e1ab2080536ULL,
0xabec975e0a0d081aULL, 0xae397d8aa96c1b77ULL}},
// 10^-39 ~= ae397d8aa96c1b77 abec975e0a0d081a
// 8a3b6e1ab2080536154d9ed7620cdbd3 * 2^-385
{{0x443e18ac4e70afdcULL, 0x3b62be7bc1a0042bULL,
0x2323ac4b3b3da015ULL, 0x8b61313bbabce2c6ULL}},
// 10^-40 ~= 8b61313bbabce2c6 2323ac4b3b3da015
// 3b62be7bc1a0042b443e18ac4e70afdc * 2^-388
{{0x6d30277a171ab2f9ULL, 0x5f0463f935ccd378ULL,
0x6b6c46dec52f6688ULL, 0xdf01e85f912e37a3ULL}},
// 10^-41 ~= df01e85f912e37a3 6b6c46dec52f6688
// 5f0463f935ccd3786d30277a171ab2f9 * 2^-392
{{0x8a8cec61ac155bfbULL, 0x7f36b660f7d70f93ULL,
0x55f038b237591ed3ULL, 0xb267ed1940f1c61cULL}},
// 10^-42 ~= b267ed1940f1c61c 55f038b237591ed3
// 7f36b660f7d70f938a8cec61ac155bfb * 2^-395
{{0x3ba3f04e23444996ULL, 0xcc2bc51a5fdf3fa9ULL,
0x77f3608e92adb242ULL, 0x8eb98a7a9a5b04e3ULL}},
// 10^-43 ~= 8eb98a7a9a5b04e3 77f3608e92adb242
// cc2bc51a5fdf3fa93ba3f04e23444996 * 2^-398
{{0xf9064d49d206dc22ULL, 0xe046082a32fecc41ULL,
0x8cb89a7db77c506aULL, 0xe45c10c42a2b3b05ULL}},
// 10^-44 ~= e45c10c42a2b3b05 8cb89a7db77c506a
// e046082a32fecc41f9064d49d206dc22 * 2^-402
{{0xfa6b7107db38b01bULL, 0x4d04d354f598a367ULL,
0x3d607b97c5fd0d22ULL, 0xb6b00d69bb55c8d1ULL}},
// 10^-45 ~= b6b00d69bb55c8d1 3d607b97c5fd0d22
// 4d04d354f598a367fa6b7107db38b01b * 2^-405
{{0xfb8927397c2d59b0ULL, 0x3d9d75dd9146e91fULL,
0xcab3961304ca70e8ULL, 0x9226712162ab070dULL}},
// 10^-46 ~= 9226712162ab070d cab3961304ca70e8
// 3d9d75dd9146e91ffb8927397c2d59b0 * 2^-408
{{0xf8db71f5937bc2b2ULL, 0xc8fbefc8e87174ffULL,
0xaab8f01e6e10b4a6ULL, 0xe9d71b689dde71afULL}},
// 10^-47 ~= e9d71b689dde71af aab8f01e6e10b4a6
// c8fbefc8e87174fff8db71f5937bc2b2 * 2^-412
{{0x2d7c5b2adc630228ULL, 0x3a63263a538df733ULL,
0x5560c018580d5d52ULL, 0xbb127c53b17ec159ULL}},
// 10^-48 ~= bb127c53b17ec159 5560c018580d5d52
// 3a63263a538df7332d7c5b2adc630228 * 2^-415
{{0x24637c2249e8ce87ULL, 0x2eb5b82ea93e5f5cULL,
0xdde7001379a44aa8ULL, 0x95a8637627989aadULL}},
// 10^-49 ~= 95a8637627989aad dde7001379a44aa8
// 2eb5b82ea93e5f5c24637c2249e8ce87 * 2^-418
{{0x3a38c69d430e173eULL, 0x4abc59e441fd6560ULL,
0x963e66858f6d4440ULL, 0xef73d256a5c0f77cULL}},
// 10^-50 ~= ef73d256a5c0f77c 963e66858f6d4440
// 4abc59e441fd65603a38c69d430e173e * 2^-422
{{0x94fa387dcf3e78feULL, 0x6efd14b69b311de6ULL,
0xde98520472bdd033ULL, 0xbf8fdb78849a5f96ULL}},
// 10^-51 ~= bf8fdb78849a5f96 de98520472bdd033
// 6efd14b69b311de694fa387dcf3e78fe * 2^-425
{{0xaa61c6cb0c31fa65ULL, 0x259743c548f417ebULL,
0xe546a8038efe4029ULL, 0x993fe2c6d07b7fabULL}},
// 10^-52 ~= 993fe2c6d07b7fab e546a8038efe4029
// 259743c548f417ebaa61c6cb0c31fa65 * 2^-428
{{0xaa360ade79e990a2ULL, 0x3c25393ba7ecf312ULL,
0xd53dd99f4b3066a8ULL, 0xf53304714d9265dfULL}},
// 10^-53 ~= f53304714d9265df d53dd99f4b3066a8
// 3c25393ba7ecf312aa360ade79e990a2 * 2^-432
{{0x882b3be52e5473b5ULL, 0x96842dc95323f5a8ULL,
0xaa97e14c3c26b886ULL, 0xc428d05aa4751e4cULL}},
// 10^-54 ~= c428d05aa4751e4c aa97e14c3c26b886
// 96842dc95323f5a8882b3be52e5473b5 * 2^-435
{{0xd355c98425105c91ULL, 0xab9cf16ddc1cc486ULL,
0x55464dd69685606bULL, 0x9ced737bb6c4183dULL}},
// 10^-55 ~= 9ced737bb6c4183d 55464dd69685606b
// ab9cf16ddc1cc486d355c98425105c91 * 2^-438
{{0xebbc75a03b4d60e7ULL, 0xac2e4f162cfad40aULL,
0xeed6e2f0f0d56712ULL, 0xfb158592be068d2eULL}},
// 10^-56 ~= fb158592be068d2e eed6e2f0f0d56712
// ac2e4f162cfad40aebbc75a03b4d60e7 * 2^-442
{{0x8963914cfc3de71fULL, 0x568b727823fbdcd5ULL,
0xf245825a5a445275ULL, 0xc8de047564d20a8bULL}},
// 10^-57 ~= c8de047564d20a8b f245825a5a445275
// 568b727823fbdcd58963914cfc3de71f * 2^-445
{{0xd44fa770c9cb1f4cULL, 0x453c5b934ffcb0aaULL,
0x5b6aceaeae9d0ec4ULL, 0xa0b19d2ab70e6ed6ULL}},
// 10^-58 ~= a0b19d2ab70e6ed6 5b6aceaeae9d0ec4
// 453c5b934ffcb0aad44fa770c9cb1f4c * 2^-448
{{0xdd0c85f3d4a27f70ULL, 0x37637c75d996f3bbULL,
0xe2bbd88bbee40bd0ULL, 0x808e17555f3ebf11ULL}},
// 10^-59 ~= 808e17555f3ebf11 e2bbd88bbee40bd0
// 37637c75d996f3bbdd0c85f3d4a27f70 * 2^-451
{{0x61ada31fba9d98b3ULL, 0x256bfa5628f185f9ULL,
0x3792f412cb06794dULL, 0xcdb02555653131b6ULL}},
// 10^-60 ~= cdb02555653131b6 3792f412cb06794d
// 256bfa5628f185f961ada31fba9d98b3 * 2^-455
{{0xe7be1c196217ad5cULL, 0x51232eab53f46b2dULL,
0x5fa8c3423c052dd7ULL, 0xa48ceaaab75a8e2bULL}},
// 10^-61 ~= a48ceaaab75a8e2b 5fa8c3423c052dd7
// 51232eab53f46b2de7be1c196217ad5c * 2^-458
{{0x52fe7ce11b46244aULL, 0x40e8f222a99055beULL,
0x1953cf68300424acULL, 0x83a3eeeef9153e89ULL}},
// 10^-62 ~= 83a3eeeef9153e89 1953cf68300424ac
// 40e8f222a99055be52fe7ce11b46244a * 2^-461
{{0x51972e34f8703a10ULL, 0x34a7e9d10f4d55fdULL,
0x8eec7f0d19a03aadULL, 0xd29fe4b18e88640eULL}},
// 10^-63 ~= d29fe4b18e88640e 8eec7f0d19a03aad
// 34a7e9d10f4d55fd51972e34f8703a10 * 2^-465
{{0x0e128b5d938cfb40ULL, 0x2a1fee40d90aab31ULL,
0x3f2398d747b36224ULL, 0xa87fea27a539e9a5ULL}},
// 10^-64 ~= a87fea27a539e9a5 3f2398d747b36224
// 2a1fee40d90aab310e128b5d938cfb40 * 2^-468
{{0x3e753c4adc70c900ULL, 0xbb4cbe9a473bbc27ULL,
0x98e947129fc2b4e9ULL, 0x86ccbb52ea94baeaULL}},
// 10^-65 ~= 86ccbb52ea94baea 98e947129fc2b4e9
// bb4cbe9a473bbc273e753c4adc70c900 * 2^-471
{{0x30bb93aafa4e0e66ULL, 0x9214642a0b92c6a5ULL,
0x5b0ed81dcc6abb0fULL, 0xd7adf884aa879177ULL}},
// 10^-66 ~= d7adf884aa879177 5b0ed81dcc6abb0f
// 9214642a0b92c6a530bb93aafa4e0e66 * 2^-475
{{0xc0960fbbfb71a51fULL, 0xa8105021a2dbd21dULL,
0xe272467e3d222f3fULL, 0xac8b2d36eed2dac5ULL}},
// 10^-67 ~= ac8b2d36eed2dac5 e272467e3d222f3f
// a8105021a2dbd21dc0960fbbfb71a51f * 2^-478
{{0x66de72fcc927b74cULL, 0xb9a6a6814f1641b1ULL,
0x1b8e9ecb641b58ffULL, 0x8a08f0f8bf0f156bULL}},
// 10^-68 ~= 8a08f0f8bf0f156b 1b8e9ecb641b58ff
// b9a6a6814f1641b166de72fcc927b74c * 2^-481
{{0xd7ca5194750c5879ULL, 0xf5d770cee4f0691bULL,
0xf8e431456cf88e65ULL, 0xdcdb1b2798182244ULL}},
// 10^-69 ~= dcdb1b2798182244 f8e431456cf88e65
// f5d770cee4f0691bd7ca5194750c5879 * 2^-485
{{0xdfd50e105da379faULL, 0x9179270bea59edafULL,
0x2d835a9df0c6d851ULL, 0xb0af48ec79ace837ULL}},
// 10^-70 ~= b0af48ec79ace837 2d835a9df0c6d851
// 9179270bea59edafdfd50e105da379fa * 2^-488
{{0x19773e737e1c6195ULL, 0x0dfa85a321e18af3ULL,
0x579c487e5a38ad0eULL, 0x8d590723948a535fULL}},
// 10^-71 ~= 8d590723948a535f 579c487e5a38ad0e
// dfa85a321e18af319773e737e1c6195 * 2^-491
{{0xf58b971f302d68efULL, 0x165da29e9c9c1184ULL,
0x25c6da63c38de1b0ULL, 0xe2280b6c20dd5232ULL}},
// 10^-72 ~= e2280b6c20dd5232 25c6da63c38de1b0
// 165da29e9c9c1184f58b971f302d68ef * 2^-495
{{0xc46fac18f3578725ULL, 0x4517b54bb07cdad0ULL,
0x1e38aeb6360b1af3ULL, 0xb4ecd5f01a4aa828ULL}},
// 10^-73 ~= b4ecd5f01a4aa828 1e38aeb6360b1af3
// 4517b54bb07cdad0c46fac18f3578725 * 2^-498
{{0x36bfbce0c2ac6c1eULL, 0x9dac910959fd7bdaULL,
0xb1c6f22b5e6f48c2ULL, 0x90bd77f3483bb9b9ULL}},
// 10^-74 ~= 90bd77f3483bb9b9 b1c6f22b5e6f48c2
// 9dac910959fd7bda36bfbce0c2ac6c1e * 2^-501
{{0x2465fb01377a4696ULL, 0x2f7a81a88ffbf95dULL,
0xb60b1d1230b20e04ULL, 0xe7958cb87392c2c2ULL}}
// 10^-75 ~= e7958cb87392c2c2 b60b1d1230b20e04
// 2f7a81a88ffbf95d2465fb01377a4696 * 2^-505
};
unsigned int Ex256m256[] = {
3, // 259 - 256, Ex = 259
6, // 262 - 256, Ex = 262
9, // 265 - 256, Ex = 265
13, // 269 - 256, Ex = 269
16, // 272 - 256, Ex = 272
19, // 275 - 256, Ex = 275
23, // 279 - 256, Ex = 279
26, // 282 - 256, Ex = 282
29, // 285 - 256, Ex = 285
33, // 289 - 256, Ex = 289
36, // 292 - 256, Ex = 292
39, // 295 - 256, Ex = 295
43, // 299 - 256, Ex = 299
46, // 302 - 256, Ex = 302
49, // 305 - 256, Ex = 305
53, // 309 - 256, Ex = 309
56, // 312 - 256, Ex = 312
59, // 315 - 256, Ex = 315
63, // 319 - 256, Ex = 319
2, // 322 - 320, Ex = 322
5, // 325 - 320, Ex = 325
9, // 329 - 320, Ex = 329
12, // 332 - 320, Ex = 332
15, // 335 - 320, Ex = 335
19, // 339 - 320, Ex = 339
22, // 342 - 320, Ex = 342
25, // 345 - 320, Ex = 345
29, // 349 - 320, Ex = 349
32, // 352 - 320, Ex = 352
35, // 355 - 320, Ex = 355
38, // 358 - 320, Ex = 358
42, // 362 - 320, Ex = 362
45, // 365 - 320, Ex = 365
48, // 368 - 320, Ex = 368
52, // 372 - 320, Ex = 372
55, // 375 - 320, Ex = 375
58, // 378 - 320, Ex = 378
62, // 382 - 320, Ex = 382
1, // 385 - 384, Ex = 385
4, // 388 - 384, Ex = 388
8, // 392 - 384, Ex = 392
11, // 395 - 384, Ex = 395
14, // 398 - 384, Ex = 398
18, // 402 - 384, Ex = 402
21, // 405 - 384, Ex = 405
24, // 408 - 384, Ex = 408
28, // 412 - 384, Ex = 412
31, // 415 - 384, Ex = 415
34, // 418 - 384, Ex = 418
38, // 422 - 384, Ex = 422
41, // 425 - 384, Ex = 425
44, // 428 - 384, Ex = 428
48, // 432 - 384, Ex = 432
51, // 435 - 384, Ex = 435
54, // 438 - 384, Ex = 438
58, // 442 - 384, Ex = 442
61, // 445 - 384, Ex = 445
0, // 448 - 448, Ex = 448
3, // 451 - 448, Ex = 451
7, // 455 - 448, Ex = 455
10, // 458 - 448, Ex = 458
13, // 461 - 448, Ex = 461
17, // 465 - 448, Ex = 465
20, // 468 - 448, Ex = 468
23, // 471 - 448, Ex = 471
27, // 475 - 448, Ex = 475
30, // 478 - 448, Ex = 478
33, // 481 - 448, Ex = 481
37, // 485 - 448, Ex = 485
40, // 488 - 448, Ex = 488
43, // 491 - 448, Ex = 491
47, // 495 - 448, Ex = 495
50, // 498 - 448, Ex = 498
53, // 501 - 448, Ex = 501
57 // 505 - 448, Ex = 505
};
UINT64 half256[] = {
0x0000000000000004ULL, // half / 2^256 = 4
0x0000000000000020ULL, // half / 2^256 = 20
0x0000000000000100ULL, // half / 2^256 = 100
0x0000000000001000ULL, // half / 2^256 = 1000
0x0000000000008000ULL, // half / 2^256 = 8000
0x0000000000040000ULL, // half / 2^256 = 40000
0x0000000000400000ULL, // half / 2^256 = 400000
0x0000000002000000ULL, // half / 2^256 = 2000000
0x0000000010000000ULL, // half / 2^256 = 10000000
0x0000000100000000ULL, // half / 2^256 = 100000000
0x0000000800000000ULL, // half / 2^256 = 800000000
0x0000004000000000ULL, // half / 2^256 = 4000000000
0x0000040000000000ULL, // half / 2^256 = 40000000000
0x0000200000000000ULL, // half / 2^256 = 200000000000
0x0001000000000000ULL, // half / 2^256 = 1000000000000
0x0010000000000000ULL, // half / 2^256 = 10000000000000
0x0080000000000000ULL, // half / 2^256 = 80000000000000
0x0400000000000000ULL, // half / 2^256 = 400000000000000
0x4000000000000000ULL, // half / 2^256 = 4000000000000000
0x0000000000000002ULL, // half / 2^320 = 2
0x0000000000000010ULL, // half / 2^320 = 10
0x0000000000000100ULL, // half / 2^320 = 100
0x0000000000000800ULL, // half / 2^320 = 800
0x0000000000004000ULL, // half / 2^320 = 4000
0x0000000000040000ULL, // half / 2^320 = 40000
0x0000000000200000ULL, // half / 2^320 = 200000
0x0000000001000000ULL, // half / 2^320 = 1000000
0x0000000010000000ULL, // half / 2^320 = 10000000
0x0000000080000000ULL, // half / 2^320 = 80000000
0x0000000400000000ULL, // half / 2^320 = 400000000
0x0000002000000000ULL, // half / 2^320 = 2000000000
0x0000020000000000ULL, // half / 2^320 = 20000000000
0x0000100000000000ULL, // half / 2^320 = 100000000000
0x0000800000000000ULL, // half / 2^320 = 800000000000
0x0008000000000000ULL, // half / 2^320 = 8000000000000
0x0040000000000000ULL, // half / 2^320 = 40000000000000
0x0200000000000000ULL, // half / 2^320 = 200000000000000
0x2000000000000000ULL, // half / 2^320 = 2000000000000000
0x0000000000000001ULL, // half / 2^384 = 1
0x0000000000000008ULL, // half / 2^384 = 8
0x0000000000000080ULL, // half / 2^384 = 80
0x0000000000000400ULL, // half / 2^384 = 400
0x0000000000002000ULL, // half / 2^384 = 2000
0x0000000000020000ULL, // half / 2^384 = 20000
0x0000000000100000ULL, // half / 2^384 = 100000
0x0000000000800000ULL, // half / 2^384 = 800000
0x0000000008000000ULL, // half / 2^384 = 8000000
0x0000000040000000ULL, // half / 2^384 = 40000000
0x0000000200000000ULL, // half / 2^384 = 200000000
0x0000002000000000ULL, // half / 2^384 = 2000000000
0x0000010000000000ULL, // half / 2^384 = 10000000000
0x0000080000000000ULL, // half / 2^384 = 80000000000
0x0000800000000000ULL, // half / 2^384 = 800000000000
0x0004000000000000ULL, // half / 2^384 = 4000000000000
0x0020000000000000ULL, // half / 2^384 = 20000000000000
0x0200000000000000ULL, // half / 2^384 = 200000000000000
0x1000000000000000ULL, // half / 2^384 = 1000000000000000
0x8000000000000000ULL, // half / 2^384 = 8000000000000000
0x0000000000000004ULL, // half / 2^448 = 4
0x0000000000000040ULL, // half / 2^448 = 40
0x0000000000000200ULL, // half / 2^448 = 200
0x0000000000001000ULL, // half / 2^448 = 1000
0x0000000000010000ULL, // half / 2^448 = 10000
0x0000000000080000ULL, // half / 2^448 = 80000
0x0000000000400000ULL, // half / 2^448 = 400000
0x0000000004000000ULL, // half / 2^448 = 4000000
0x0000000020000000ULL, // half / 2^448 = 20000000
0x0000000100000000ULL, // half / 2^448 = 100000000
0x0000001000000000ULL, // half / 2^448 = 1000000000
0x0000008000000000ULL, // half / 2^448 = 8000000000
0x0000040000000000ULL, // half / 2^448 = 40000000000
0x0000400000000000ULL, // half / 2^448 = 400000000000
0x0002000000000000ULL, // half / 2^448 = 2000000000000
0x0010000000000000ULL, // half / 2^448 = 10000000000000
0x0100000000000000ULL // half / 2^448 = 100000000000000
};
UINT64 mask256[] = {
0x0000000000000007ULL, // mask / 2^256
0x000000000000003fULL, // mask / 2^256
0x00000000000001ffULL, // mask / 2^256
0x0000000000001fffULL, // mask / 2^256
0x000000000000ffffULL, // mask / 2^256
0x000000000007ffffULL, // mask / 2^256
0x00000000007fffffULL, // mask / 2^256
0x0000000003ffffffULL, // mask / 2^256
0x000000001fffffffULL, // mask / 2^256
0x00000001ffffffffULL, // mask / 2^256
0x0000000fffffffffULL, // mask / 2^256
0x0000007fffffffffULL, // mask / 2^256
0x000007ffffffffffULL, // mask / 2^256
0x00003fffffffffffULL, // mask / 2^256
0x0001ffffffffffffULL, // mask / 2^256
0x001fffffffffffffULL, // mask / 2^256
0x00ffffffffffffffULL, // mask / 2^256
0x07ffffffffffffffULL, // mask / 2^256
0x7fffffffffffffffULL, // mask / 2^256
0x0000000000000003ULL, // mask / 2^320
0x000000000000001fULL, // mask / 2^320
0x00000000000001ffULL, // mask / 2^320
0x0000000000000fffULL, // mask / 2^320
0x0000000000007fffULL, // mask / 2^320
0x000000000007ffffULL, // mask / 2^320
0x00000000003fffffULL, // mask / 2^320
0x0000000001ffffffULL, // mask / 2^320
0x000000001fffffffULL, // mask / 2^320
0x00000000ffffffffULL, // mask / 2^320
0x00000007ffffffffULL, // mask / 2^320
0x0000003fffffffffULL, // mask / 2^320
0x000003ffffffffffULL, // mask / 2^320
0x00001fffffffffffULL, // mask / 2^320
0x0000ffffffffffffULL, // mask / 2^320
0x000fffffffffffffULL, // mask / 2^320
0x007fffffffffffffULL, // mask / 2^320
0x03ffffffffffffffULL, // mask / 2^320
0x3fffffffffffffffULL, // mask / 2^320
0x0000000000000001ULL, // mask / 2^384
0x000000000000000fULL, // mask / 2^384
0x00000000000000ffULL, // mask / 2^384
0x00000000000007ffULL, // mask / 2^384
0x0000000000003fffULL, // mask / 2^384
0x000000000003ffffULL, // mask / 2^384
0x00000000001fffffULL, // mask / 2^384
0x0000000000ffffffULL, // mask / 2^384
0x000000000fffffffULL, // mask / 2^384
0x000000007fffffffULL, // mask / 2^384
0x00000003ffffffffULL, // mask / 2^384
0x0000003fffffffffULL, // mask / 2^384
0x000001ffffffffffULL, // mask / 2^384
0x00000fffffffffffULL, // mask / 2^384
0x0000ffffffffffffULL, // mask / 2^384
0x0007ffffffffffffULL, // mask / 2^384
0x003fffffffffffffULL, // mask / 2^384
0x03ffffffffffffffULL, // mask / 2^384
0x1fffffffffffffffULL, // mask / 2^384
0xffffffffffffffffULL, // mask / 2^384
0x0000000000000007ULL, // mask / 2^448
0x000000000000007fULL, // mask / 2^448
0x00000000000003ffULL, // mask / 2^448
0x0000000000001fffULL, // mask / 2^448
0x000000000001ffffULL, // mask / 2^448
0x00000000000fffffULL, // mask / 2^448
0x00000000007fffffULL, // mask / 2^448
0x0000000007ffffffULL, // mask / 2^448
0x000000003fffffffULL, // mask / 2^448
0x00000001ffffffffULL, // mask / 2^448
0x0000001fffffffffULL, // mask / 2^448
0x000000ffffffffffULL, // mask / 2^448
0x000007ffffffffffULL, // mask / 2^448
0x00007fffffffffffULL, // mask / 2^448
0x0003ffffffffffffULL, // mask / 2^448
0x001fffffffffffffULL, // mask / 2^448
0x01ffffffffffffffULL // mask / 2^448
};
UINT256 ten2mxtrunc256[] = {
{{0xccccccccccccccccULL, 0xccccccccccccccccULL,
0xccccccccccccccccULL, 0xccccccccccccccccULL}},
// (ten2mx >> 256) = cccccccccccccccc cccccccccccccccc
// cccccccccccccccccccccccccccccccc
{{0x70a3d70a3d70a3d7ULL, 0xd70a3d70a3d70a3dULL,
0x3d70a3d70a3d70a3ULL, 0xa3d70a3d70a3d70aULL}},
// (ten2mx >> 256) = a3d70a3d70a3d70a 3d70a3d70a3d70a3
// d70a3d70a3d70a3d70a3d70a3d70a3d7
{{0xc083126e978d4fdfULL, 0x78d4fdf3b645a1caULL,
0x645a1cac083126e9ULL, 0x83126e978d4fdf3bULL}},
// (ten2mx >> 256) = 83126e978d4fdf3b 645a1cac083126e9
// 78d4fdf3b645a1cac083126e978d4fdf
{{0x67381d7dbf487fcbULL, 0xc154c985f06f6944ULL,
0xd3c36113404ea4a8ULL, 0xd1b71758e219652bULL}},
// (ten2mx >> 256) = d1b71758e219652b d3c36113404ea4a8
// c154c985f06f694467381d7dbf487fcb
{{0x85c67dfe32a0663cULL, 0xcddd6e04c0592103ULL,
0x0fcf80dc33721d53ULL, 0xa7c5ac471b478423ULL}},
// (ten2mx >> 256) = a7c5ac471b478423 fcf80dc33721d53
// cddd6e04c059210385c67dfe32a0663c
{{0x37d1fe64f54d1e96ULL, 0xd7e45803cd141a69ULL,
0xa63f9a49c2c1b10fULL, 0x8637bd05af6c69b5ULL}},
// (ten2mx >> 256) = 8637bd05af6c69b5 a63f9a49c2c1b10f
// d7e45803cd141a6937d1fe64f54d1e96
{{0x8c8330a1887b6424ULL, 0x8ca08cd2e1b9c3dbULL,
0x3d32907604691b4cULL, 0xd6bf94d5e57a42bcULL}},
// (ten2mx >> 256) = d6bf94d5e57a42bc 3d32907604691b4c
// 8ca08cd2e1b9c3db8c8330a1887b6424
{{0x7068f3b46d2f8350ULL, 0x3d4d3d758161697cULL,
0xfdc20d2b36ba7c3dULL, 0xabcc77118461cefcULL}},
// (ten2mx >> 256) = abcc77118461cefc fdc20d2b36ba7c3d
// 3d4d3d758161697c7068f3b46d2f8350
{{0xf387295d242602a6ULL, 0xfdd7645e011abac9ULL,
0x31680a88f8953030ULL, 0x89705f4136b4a597ULL}},
// (ten2mx >> 256) = 89705f4136b4a597 31680a88f8953030
// fdd7645e011abac9f387295d242602a6
{{0xb8d8422ea03cd10aULL, 0x2fbf06fcce912adcULL,
0xb573440e5a884d1bULL, 0xdbe6fecebdedd5beULL}},
// (ten2mx >> 256) = dbe6fecebdedd5be b573440e5a884d1b
// 2fbf06fcce912adcb8d8422ea03cd10a
{{0x93e034f219ca40d5ULL, 0xf2ff38ca3eda88b0ULL,
0xf78f69a51539d748ULL, 0xafebff0bcb24aafeULL}},
// (ten2mx >> 256) = afebff0bcb24aafe f78f69a51539d748
// f2ff38ca3eda88b093e034f219ca40d5
{{0x4319c3f4e16e9a44ULL, 0xf598fa3b657ba08dULL,
0xf93f87b7442e45d3ULL, 0x8cbccc096f5088cbULL}},
// (ten2mx >> 256) = 8cbccc096f5088cb f93f87b7442e45d3
// f598fa3b657ba08d4319c3f4e16e9a44
{{0x04f606549be42a06ULL, 0x88f4c3923bf900e2ULL,
0x2865a5f206b06fb9ULL, 0xe12e13424bb40e13ULL}},
// (ten2mx >> 256) = e12e13424bb40e13 2865a5f206b06fb9
// 88f4c3923bf900e204f606549be42a06
{{0x03f805107cb68805ULL, 0x6d909c74fcc733e8ULL,
0x538484c19ef38c94ULL, 0xb424dc35095cd80fULL}},
// (ten2mx >> 256) = b424dc35095cd80f 538484c19ef38c94
// 6d909c74fcc733e803f805107cb68805
{{0x3660040d3092066aULL, 0x57a6e390ca38f653ULL,
0x0f9d37014bf60a10ULL, 0x901d7cf73ab0acd9ULL}},
// (ten2mx >> 256) = 901d7cf73ab0acd9 f9d37014bf60a10
// 57a6e390ca38f6533660040d3092066a
{{0x23ccd3484db670aaULL, 0xbf716c1add27f085ULL,
0x4c2ebe687989a9b3ULL, 0xe69594bec44de15bULL}},
// (ten2mx >> 256) = e69594bec44de15b 4c2ebe687989a9b3
// bf716c1add27f08523ccd3484db670aa
{{0x4fd70f6d0af85a22ULL, 0xff8df0157db98d37ULL,
0x09befeb9fad487c2ULL, 0xb877aa3236a4b449ULL}},
// (ten2mx >> 256) = b877aa3236a4b449 9befeb9fad487c2
// ff8df0157db98d374fd70f6d0af85a22
{{0x0cac0c573bf9e1b5ULL, 0x32d7f344649470f9ULL,
0x3aff322e62439fcfULL, 0x9392ee8e921d5d07ULL}},
// (ten2mx >> 256) = 9392ee8e921d5d07 3aff322e62439fcf
// 32d7f344649470f90cac0c573bf9e1b5
{{0xe11346f1f98fcf88ULL, 0x1e2652070753e7f4ULL,
0x2b31e9e3d06c32e5ULL, 0xec1e4a7db69561a5ULL}},
// (ten2mx >> 256) = ec1e4a7db69561a5 2b31e9e3d06c32e5
// 1e2652070753e7f4e11346f1f98fcf88
{{0x4da9058e613fd939ULL, 0x181ea8059f76532aULL,
0x88f4bb1ca6bcf584ULL, 0xbce5086492111aeaULL}},
// (ten2mx >> 256) = bce5086492111aea 88f4bb1ca6bcf584
// 181ea8059f76532a4da9058e613fd939
{{0xa48737a51a997a94ULL, 0x467eecd14c5ea8eeULL,
0xd3f6fc16ebca5e03ULL, 0x971da05074da7beeULL}},
// (ten2mx >> 256) = 971da05074da7bee d3f6fc16ebca5e03
// 467eecd14c5ea8eea48737a51a997a94
{{0x3a71f2a1c428c420ULL, 0x70cb148213caa7e4ULL,
0x5324c68b12dd6338ULL, 0xf1c90080baf72cb1ULL}},
// (ten2mx >> 256) = f1c90080baf72cb1 5324c68b12dd6338
// 70cb148213caa7e43a71f2a1c428c420
{{0x2ec18ee7d0209ce7ULL, 0x8d6f439b43088650ULL,
0x75b7053c0f178293ULL, 0xc16d9a0095928a27ULL}},
// (ten2mx >> 256) = c16d9a0095928a27 75b7053c0f178293
// 8d6f439b430886502ec18ee7d0209ce7
{{0xf23472530ce6e3ecULL, 0xd78c3615cf3a050cULL,
0xc4926a9672793542ULL, 0x9abe14cd44753b52ULL}},
// (ten2mx >> 256) = 9abe14cd44753b52 c4926a9672793542
// d78c3615cf3a050cf23472530ce6e3ec
{{0xe9ed83b814a49fe0ULL, 0x8c1389bc7ec33b47ULL,
0x3a83ddbd83f52204ULL, 0xf79687aed3eec551ULL}},
// (ten2mx >> 256) = f79687aed3eec551 3a83ddbd83f52204
// 8c1389bc7ec33b47e9ed83b814a49fe0
{{0x87f1362cdd507fe6ULL, 0x3cdc6e306568fc39ULL,
0x95364afe032a819dULL, 0xc612062576589ddaULL}},
// (ten2mx >> 256) = c612062576589dda 95364afe032a819d
// 3cdc6e306568fc3987f1362cdd507fe6
{{0x9ff42b5717739985ULL, 0xca49f1c05120c9c7ULL,
0x775ea264cf55347dULL, 0x9e74d1b791e07e48ULL}},
// (ten2mx >> 256) = 9e74d1b791e07e48 775ea264cf55347d
// ca49f1c05120c9c79ff42b5717739985
{{0xccb9def1bf1f5c08ULL, 0x76dcb60081ce0fa5ULL,
0x8bca9d6e188853fcULL, 0xfd87b5f28300ca0dULL}},
// (ten2mx >> 256) = fd87b5f28300ca0d 8bca9d6e188853fc
// 76dcb60081ce0fa5ccb9def1bf1f5c08
{{0xa3c7e58e327f7cd3ULL, 0x5f16f80067d80c84ULL,
0x096ee45813a04330ULL, 0xcad2f7f5359a3b3eULL}},
// (ten2mx >> 256) = cad2f7f5359a3b3e 96ee45813a04330
// 5f16f80067d80c84a3c7e58e327f7cd3
{{0xb6398471c1ff970fULL, 0x18df2ccd1fe00a03ULL,
0xa1258379a94d028dULL, 0xa2425ff75e14fc31ULL}},
// (ten2mx >> 256) = a2425ff75e14fc31 a1258379a94d028d
// 18df2ccd1fe00a03b6398471c1ff970f
{{0xf82e038e34cc78d9ULL, 0x4718f0a419800802ULL,
0x80eacf948770ced7ULL, 0x81ceb32c4b43fcf4ULL}},
// (ten2mx >> 256) = 81ceb32c4b43fcf4 80eacf948770ced7
// 4718f0a419800802f82e038e34cc78d9
{{0x59e338e387ad8e28ULL, 0x0b5b1aa028ccd99eULL,
0x67de18eda5814af2ULL, 0xcfb11ead453994baULL}},
// (ten2mx >> 256) = cfb11ead453994ba 67de18eda5814af2
// b5b1aa028ccd99e59e338e387ad8e28
{{0x47e8fa4f9fbe0b53ULL, 0x6f7c154ced70ae18ULL,
0xecb1ad8aeacdd58eULL, 0xa6274bbdd0fadd61ULL}},
// (ten2mx >> 256) = a6274bbdd0fadd61 ecb1ad8aeacdd58e
// 6f7c154ced70ae1847e8fa4f9fbe0b53
{{0xd320c83fb2fe6f75ULL, 0xbf967770bdf3be79ULL,
0xbd5af13bef0b113eULL, 0x84ec3c97da624ab4ULL}},
// (ten2mx >> 256) = 84ec3c97da624ab4 bd5af13bef0b113e
// bf967770bdf3be79d320c83fb2fe6f75
{{0x85014065eb30b256ULL, 0x65bd8be79652ca5cULL,
0x955e4ec64b44e864ULL, 0xd4ad2dbfc3d07787ULL}},
// (ten2mx >> 256) = d4ad2dbfc3d07787 955e4ec64b44e864
// 65bd8be79652ca5c85014065eb30b256
{{0xd0cdcd1e55c08eabULL, 0xeafe098611dbd516ULL,
0xdde50bd1d5d0b9e9ULL, 0xaa242499697392d2ULL}},
// (ten2mx >> 256) = aa242499697392d2 dde50bd1d5d0b9e9
// eafe098611dbd516d0cdcd1e55c08eab
{{0x40a4a418449a0bbcULL, 0xbbfe6e04db164412ULL,
0x7e50d64177da2e54ULL, 0x881cea14545c7575ULL}},
// (ten2mx >> 256) = 881cea14545c7575 7e50d64177da2e54
// bbfe6e04db16441240a4a418449a0bbc
{{0x9aa1068d3a9012c7ULL, 0x2cca49a15e8a0683ULL,
0x96e7bd358c904a21ULL, 0xd9c7dced53c72255ULL}},
// (ten2mx >> 256) = d9c7dced53c72255 96e7bd358c904a21
// 2cca49a15e8a06839aa1068d3a9012c7
{{0x154d9ed7620cdbd2ULL, 0x8a3b6e1ab2080536ULL,
0xabec975e0a0d081aULL, 0xae397d8aa96c1b77ULL}},
// (ten2mx >> 256) = ae397d8aa96c1b77 abec975e0a0d081a
// 8a3b6e1ab2080536154d9ed7620cdbd2
{{0x443e18ac4e70afdbULL, 0x3b62be7bc1a0042bULL,
0x2323ac4b3b3da015ULL, 0x8b61313bbabce2c6ULL}},
// (ten2mx >> 256) = 8b61313bbabce2c6 2323ac4b3b3da015
// 3b62be7bc1a0042b443e18ac4e70afdb
{{0x6d30277a171ab2f8ULL, 0x5f0463f935ccd378ULL,
0x6b6c46dec52f6688ULL, 0xdf01e85f912e37a3ULL}},
// (ten2mx >> 256) = df01e85f912e37a3 6b6c46dec52f6688
// 5f0463f935ccd3786d30277a171ab2f8
{{0x8a8cec61ac155bfaULL, 0x7f36b660f7d70f93ULL,
0x55f038b237591ed3ULL, 0xb267ed1940f1c61cULL}},
// (ten2mx >> 256) = b267ed1940f1c61c 55f038b237591ed3
// 7f36b660f7d70f938a8cec61ac155bfa
{{0x3ba3f04e23444995ULL, 0xcc2bc51a5fdf3fa9ULL,
0x77f3608e92adb242ULL, 0x8eb98a7a9a5b04e3ULL}},
// (ten2mx >> 256) = 8eb98a7a9a5b04e3 77f3608e92adb242
// cc2bc51a5fdf3fa93ba3f04e23444995
{{0xf9064d49d206dc21ULL, 0xe046082a32fecc41ULL,
0x8cb89a7db77c506aULL, 0xe45c10c42a2b3b05ULL}},
// (ten2mx >> 256) = e45c10c42a2b3b05 8cb89a7db77c506a
// e046082a32fecc41f9064d49d206dc21
{{0xfa6b7107db38b01aULL, 0x4d04d354f598a367ULL,
0x3d607b97c5fd0d22ULL, 0xb6b00d69bb55c8d1ULL}},
// (ten2mx >> 256) = b6b00d69bb55c8d1 3d607b97c5fd0d22
// 4d04d354f598a367fa6b7107db38b01a
{{0xfb8927397c2d59afULL, 0x3d9d75dd9146e91fULL,
0xcab3961304ca70e8ULL, 0x9226712162ab070dULL}},
// (ten2mx >> 256) = 9226712162ab070d cab3961304ca70e8
// 3d9d75dd9146e91ffb8927397c2d59af
{{0xf8db71f5937bc2b1ULL, 0xc8fbefc8e87174ffULL,
0xaab8f01e6e10b4a6ULL, 0xe9d71b689dde71afULL}},
// (ten2mx >> 256) = e9d71b689dde71af aab8f01e6e10b4a6
// c8fbefc8e87174fff8db71f5937bc2b1
{{0x2d7c5b2adc630227ULL, 0x3a63263a538df733ULL,
0x5560c018580d5d52ULL, 0xbb127c53b17ec159ULL}},
// (ten2mx >> 256) = bb127c53b17ec159 5560c018580d5d52
// 3a63263a538df7332d7c5b2adc630227
{{0x24637c2249e8ce86ULL, 0x2eb5b82ea93e5f5cULL,
0xdde7001379a44aa8ULL, 0x95a8637627989aadULL}},
// (ten2mx >> 256) = 95a8637627989aad dde7001379a44aa8
// 2eb5b82ea93e5f5c24637c2249e8ce86
{{0x3a38c69d430e173dULL, 0x4abc59e441fd6560ULL,
0x963e66858f6d4440ULL, 0xef73d256a5c0f77cULL}},
// (ten2mx >> 256) = ef73d256a5c0f77c 963e66858f6d4440
// 4abc59e441fd65603a38c69d430e173d
{{0x94fa387dcf3e78fdULL, 0x6efd14b69b311de6ULL,
0xde98520472bdd033ULL, 0xbf8fdb78849a5f96ULL}},
// (ten2mx >> 256) = bf8fdb78849a5f96 de98520472bdd033
// 6efd14b69b311de694fa387dcf3e78fd
{{0xaa61c6cb0c31fa64ULL, 0x259743c548f417ebULL,
0xe546a8038efe4029ULL, 0x993fe2c6d07b7fabULL}},
// (ten2mx >> 256) = 993fe2c6d07b7fab e546a8038efe4029
// 259743c548f417ebaa61c6cb0c31fa64
{{0xaa360ade79e990a1ULL, 0x3c25393ba7ecf312ULL,
0xd53dd99f4b3066a8ULL, 0xf53304714d9265dfULL}},
// (ten2mx >> 256) = f53304714d9265df d53dd99f4b3066a8
// 3c25393ba7ecf312aa360ade79e990a1
{{0x882b3be52e5473b4ULL, 0x96842dc95323f5a8ULL,
0xaa97e14c3c26b886ULL, 0xc428d05aa4751e4cULL}},
// (ten2mx >> 256) = c428d05aa4751e4c aa97e14c3c26b886
// 96842dc95323f5a8882b3be52e5473b4
{{0xd355c98425105c90ULL, 0xab9cf16ddc1cc486ULL,
0x55464dd69685606bULL, 0x9ced737bb6c4183dULL}},
// (ten2mx >> 256) = 9ced737bb6c4183d 55464dd69685606b
// ab9cf16ddc1cc486d355c98425105c90
{{0xebbc75a03b4d60e6ULL, 0xac2e4f162cfad40aULL,
0xeed6e2f0f0d56712ULL, 0xfb158592be068d2eULL}},
// (ten2mx >> 256) = fb158592be068d2e eed6e2f0f0d56712
// ac2e4f162cfad40aebbc75a03b4d60e6
{{0x8963914cfc3de71eULL, 0x568b727823fbdcd5ULL,
0xf245825a5a445275ULL, 0xc8de047564d20a8bULL}},
// (ten2mx >> 256) = c8de047564d20a8b f245825a5a445275
// 568b727823fbdcd58963914cfc3de71e
{{0xd44fa770c9cb1f4bULL, 0x453c5b934ffcb0aaULL,
0x5b6aceaeae9d0ec4ULL, 0xa0b19d2ab70e6ed6ULL}},
// (ten2mx >> 256) = a0b19d2ab70e6ed6 5b6aceaeae9d0ec4
// 453c5b934ffcb0aad44fa770c9cb1f4b
{{0xdd0c85f3d4a27f6fULL, 0x37637c75d996f3bbULL,
0xe2bbd88bbee40bd0ULL, 0x808e17555f3ebf11ULL}},
// (ten2mx >> 256) = 808e17555f3ebf11 e2bbd88bbee40bd0
// 37637c75d996f3bbdd0c85f3d4a27f6f
{{0x61ada31fba9d98b2ULL, 0x256bfa5628f185f9ULL,
0x3792f412cb06794dULL, 0xcdb02555653131b6ULL}},
// (ten2mx >> 256) = cdb02555653131b6 3792f412cb06794d
// 256bfa5628f185f961ada31fba9d98b2
{{0xe7be1c196217ad5bULL, 0x51232eab53f46b2dULL,
0x5fa8c3423c052dd7ULL, 0xa48ceaaab75a8e2bULL}},
// (ten2mx >> 256) = a48ceaaab75a8e2b 5fa8c3423c052dd7
// 51232eab53f46b2de7be1c196217ad5b
{{0x52fe7ce11b462449ULL, 0x40e8f222a99055beULL,
0x1953cf68300424acULL, 0x83a3eeeef9153e89ULL}},
// (ten2mx >> 256) = 83a3eeeef9153e89 1953cf68300424ac
// 40e8f222a99055be52fe7ce11b462449
{{0x51972e34f8703a0fULL, 0x34a7e9d10f4d55fdULL,
0x8eec7f0d19a03aadULL, 0xd29fe4b18e88640eULL}},
// (ten2mx >> 256) = d29fe4b18e88640e 8eec7f0d19a03aad
// 34a7e9d10f4d55fd51972e34f8703a0f
{{0x0e128b5d938cfb3fULL, 0x2a1fee40d90aab31ULL,
0x3f2398d747b36224ULL, 0xa87fea27a539e9a5ULL}},
// (ten2mx >> 256) = a87fea27a539e9a5 3f2398d747b36224
// 2a1fee40d90aab310e128b5d938cfb3f
{{0x3e753c4adc70c8ffULL, 0xbb4cbe9a473bbc27ULL,
0x98e947129fc2b4e9ULL, 0x86ccbb52ea94baeaULL}},
// (ten2mx >> 256) = 86ccbb52ea94baea 98e947129fc2b4e9
// bb4cbe9a473bbc273e753c4adc70c8ff
{{0x30bb93aafa4e0e65ULL, 0x9214642a0b92c6a5ULL,
0x5b0ed81dcc6abb0fULL, 0xd7adf884aa879177ULL}},
// (ten2mx >> 256) = d7adf884aa879177 5b0ed81dcc6abb0f
// 9214642a0b92c6a530bb93aafa4e0e65
{{0xc0960fbbfb71a51eULL, 0xa8105021a2dbd21dULL,
0xe272467e3d222f3fULL, 0xac8b2d36eed2dac5ULL}},
// (ten2mx >> 256) = ac8b2d36eed2dac5 e272467e3d222f3f
// a8105021a2dbd21dc0960fbbfb71a51e
{{0x66de72fcc927b74bULL, 0xb9a6a6814f1641b1ULL,
0x1b8e9ecb641b58ffULL, 0x8a08f0f8bf0f156bULL}},
// (ten2mx >> 256) = 8a08f0f8bf0f156b 1b8e9ecb641b58ff
// b9a6a6814f1641b166de72fcc927b74b
{{0xd7ca5194750c5878ULL, 0xf5d770cee4f0691bULL,
0xf8e431456cf88e65ULL, 0xdcdb1b2798182244ULL}},
// (ten2mx >> 256) = dcdb1b2798182244 f8e431456cf88e65
// f5d770cee4f0691bd7ca5194750c5878
{{0xdfd50e105da379f9ULL, 0x9179270bea59edafULL,
0x2d835a9df0c6d851ULL, 0xb0af48ec79ace837ULL}},
// (ten2mx >> 256) = b0af48ec79ace837 2d835a9df0c6d851
// 9179270bea59edafdfd50e105da379f9
{{0x19773e737e1c6194ULL, 0x0dfa85a321e18af3ULL,
0x579c487e5a38ad0eULL, 0x8d590723948a535fULL}},
// (ten2mx >> 256) = 8d590723948a535f 579c487e5a38ad0e
// dfa85a321e18af319773e737e1c6194
{{0xf58b971f302d68eeULL, 0x165da29e9c9c1184ULL,
0x25c6da63c38de1b0ULL, 0xe2280b6c20dd5232ULL}},
// (ten2mx >> 256) = e2280b6c20dd5232 25c6da63c38de1b0
// 165da29e9c9c1184f58b971f302d68ee
{{0xc46fac18f3578724ULL, 0x4517b54bb07cdad0ULL,
0x1e38aeb6360b1af3ULL, 0xb4ecd5f01a4aa828ULL}},
// (ten2mx >> 256) = b4ecd5f01a4aa828 1e38aeb6360b1af3
// 4517b54bb07cdad0c46fac18f3578724
{{0x36bfbce0c2ac6c1dULL, 0x9dac910959fd7bdaULL,
0xb1c6f22b5e6f48c2ULL, 0x90bd77f3483bb9b9ULL}},
// (ten2mx >> 256) = 90bd77f3483bb9b9 b1c6f22b5e6f48c2
// 9dac910959fd7bda36bfbce0c2ac6c1d
{{0x2465fb01377a4695ULL, 0x2f7a81a88ffbf95dULL,
0xb60b1d1230b20e04ULL, 0xe7958cb87392c2c2ULL}}
// (ten2mx >> 256) = e7958cb87392c2c2 b60b1d1230b20e04
// 2f7a81a88ffbf95d2465fb01377a4695
};