libgcc/config/libbid/bid128.c

/* Copyright (C) 2007-2017 Free Software Foundation, Inc.

This file is part of GCC.

GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
version.

GCC is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
for more details.

Under Section 7 of GPL version 3, you are granted additional
permissions described in the GCC Runtime Library Exception, version
3.1, as published by the Free Software Foundation.

You should have received a copy of the GNU General Public License and
a copy of the GCC Runtime Library Exception along with this program;
see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
<http://www.gnu.org/licenses/>.  */

#include "bid_internal.h"

// 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}},