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/* Copyright (C) 2007, 2009  Free Software Foundation, Inc.
 
This file is part of GCC.
 
GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
version.
 
GCC is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
for more details.
 
Under Section 7 of GPL version 3, you are granted additional
permissions described in the GCC Runtime Library Exception, version
3.1, as published by the Free Software Foundation.
 
You should have received a copy of the GNU General Public License and
a copy of the GCC Runtime Library Exception along with this program;
see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
<http://www.gnu.org/licenses/>.  */
 
#include "bid_internal.h"
 
UINT64 round_const_table[][19] = {
  {	// RN
   0ull,	// 0 extra digits
   5ull,	// 1 extra digits
   50ull,	// 2 extra digits
   500ull,	// 3 extra digits
   5000ull,	// 4 extra digits
   50000ull,	// 5 extra digits
   500000ull,	// 6 extra digits
   5000000ull,	// 7 extra digits
   50000000ull,	// 8 extra digits
   500000000ull,	// 9 extra digits
   5000000000ull,	// 10 extra digits
   50000000000ull,	// 11 extra digits
   500000000000ull,	// 12 extra digits
   5000000000000ull,	// 13 extra digits
   50000000000000ull,	// 14 extra digits
   500000000000000ull,	// 15 extra digits
   5000000000000000ull,	// 16 extra digits
   50000000000000000ull,	// 17 extra digits
   500000000000000000ull	// 18 extra digits
   }
  ,
  {	// RD
   0ull,	// 0 extra digits
   0ull,	// 1 extra digits
   0ull,	// 2 extra digits
   00ull,	// 3 extra digits
   000ull,	// 4 extra digits
   0000ull,	// 5 extra digits
   00000ull,	// 6 extra digits
   000000ull,	// 7 extra digits
   0000000ull,	// 8 extra digits
   00000000ull,	// 9 extra digits
   000000000ull,	// 10 extra digits
   0000000000ull,	// 11 extra digits
   00000000000ull,	// 12 extra digits
   000000000000ull,	// 13 extra digits
   0000000000000ull,	// 14 extra digits
   00000000000000ull,	// 15 extra digits
   000000000000000ull,	// 16 extra digits
   0000000000000000ull,	// 17 extra digits
   00000000000000000ull	// 18 extra digits
   }
  ,
  {	// round to Inf
   0ull,	// 0 extra digits
   9ull,	// 1 extra digits
   99ull,	// 2 extra digits
   999ull,	// 3 extra digits
   9999ull,	// 4 extra digits
   99999ull,	// 5 extra digits
   999999ull,	// 6 extra digits
   9999999ull,	// 7 extra digits
   99999999ull,	// 8 extra digits
   999999999ull,	// 9 extra digits
   9999999999ull,	// 10 extra digits
   99999999999ull,	// 11 extra digits
   999999999999ull,	// 12 extra digits
   9999999999999ull,	// 13 extra digits
   99999999999999ull,	// 14 extra digits
   999999999999999ull,	// 15 extra digits
   9999999999999999ull,	// 16 extra digits
   99999999999999999ull,	// 17 extra digits
   999999999999999999ull	// 18 extra digits
   }
  ,
  {	// RZ
   0ull,	// 0 extra digits
   0ull,	// 1 extra digits
   0ull,	// 2 extra digits
   00ull,	// 3 extra digits
   000ull,	// 4 extra digits
   0000ull,	// 5 extra digits
   00000ull,	// 6 extra digits
   000000ull,	// 7 extra digits
   0000000ull,	// 8 extra digits
   00000000ull,	// 9 extra digits
   000000000ull,	// 10 extra digits
   0000000000ull,	// 11 extra digits
   00000000000ull,	// 12 extra digits
   000000000000ull,	// 13 extra digits
   0000000000000ull,	// 14 extra digits
   00000000000000ull,	// 15 extra digits
   000000000000000ull,	// 16 extra digits
   0000000000000000ull,	// 17 extra digits
   00000000000000000ull	// 18 extra digits
   }
  ,
  {	// round ties away from 0
   0ull,	// 0 extra digits
   5ull,	// 1 extra digits
   50ull,	// 2 extra digits
   500ull,	// 3 extra digits
   5000ull,	// 4 extra digits
   50000ull,	// 5 extra digits
   500000ull,	// 6 extra digits
   5000000ull,	// 7 extra digits
   50000000ull,	// 8 extra digits
   500000000ull,	// 9 extra digits
   5000000000ull,	// 10 extra digits
   50000000000ull,	// 11 extra digits
   500000000000ull,	// 12 extra digits
   5000000000000ull,	// 13 extra digits
   50000000000000ull,	// 14 extra digits
   500000000000000ull,	// 15 extra digits
   5000000000000000ull,	// 16 extra digits
   50000000000000000ull,	// 17 extra digits
   500000000000000000ull	// 18 extra digits
   }
  ,
};
 
UINT128 round_const_table_128[][36] = {
  {	//RN
   {{0ull, 0ull}
    }
   ,	// 0 extra digits
   {{5ull, 0ull}
    }
   ,	// 1 extra digits
   {{50ull, 0ull}
    }
   ,	// 2 extra digits
   {{500ull, 0ull}
    }
   ,	// 3 extra digits
   {{5000ull, 0ull}
    }
   ,	// 4 extra digits
   {{50000ull, 0ull}
    }
   ,	// 5 extra digits
   {{500000ull, 0ull}
    }
   ,	// 6 extra digits
   {{5000000ull, 0ull}
    }
   ,	// 7 extra digits
   {{50000000ull, 0ull}
    }
   ,	// 8 extra digits
   {{500000000ull, 0ull}
    }
   ,	// 9 extra digits
   {{5000000000ull, 0ull}
    }
   ,	// 10 extra digits
   {{50000000000ull, 0ull}
    }
   ,	// 11 extra digits
   {{500000000000ull, 0ull}
    }
   ,	// 12 extra digits
   {{5000000000000ull, 0ull}
    }
   ,	// 13 extra digits
   {{50000000000000ull, 0ull}
    }
   ,	// 14 extra digits
   {{500000000000000ull, 0ull}
    }
   ,	// 15 extra digits
   {{5000000000000000ull, 0ull}
    }
   ,	// 16 extra digits
   {{50000000000000000ull, 0ull}
    }
   ,	// 17 extra digits
   {{500000000000000000ull, 0ull}
    }
   ,	// 18 extra digits
   {{5000000000000000000ull, 0ull}
    }
   ,	// 19 extra digits
   {{0xb5e3af16b1880000ull, 2ull}
    }
   ,	//20
   {{0x1ae4d6e2ef500000ull, 27ull}
    }
   ,	//21
   {{0xcf064dd59200000ull, 271ull}
    }
   ,	//22
   {{0x8163f0a57b400000ull, 2710ull}
    }
   ,	//23
   {{0xde76676d0800000ull, 27105ull}
    }
   ,	//24
   {{0x8b0a00a425000000ull, 0x422caull}
    }
   ,	//25
   {{0x6e64066972000000ull, 0x295be9ull}
    }
   ,	//26
   {{0x4fe8401e74000000ull, 0x19d971eull}
    }
   ,	//27
   {{0x1f12813088000000ull, 0x1027e72full}
    }
   ,	//28
   {{0x36b90be550000000ull, 0xa18f07d7ull}
    }
   ,	//29
   {{0x233a76f520000000ull, 0x64f964e68ull}
    }
   ,	//30
   {{0x6048a59340000000ull, 0x3f1bdf1011ull}
    }
   ,	//31
   {{0xc2d677c080000000ull, 0x27716b6a0adull}
    }
   ,	//32
   {{0x9c60ad8500000000ull, 0x18a6e32246c9ull}
    }
   ,	//33
   {{0x1bc6c73200000000ull, 0xf684df56c3e0ull}
    }
   ,	//34
   {{0x15c3c7f400000000ull, 0x9a130b963a6c1ull}
    }
   ,	//35
   }
  ,
  {	//RD
   {{0ull, 0ull}
    }
   ,	// 0 extra digits
   {{0ull, 0ull}
    }
   ,	// 1 extra digits
   {{0ull, 0ull}
    }
   ,	// 2 extra digits
   {{00ull, 0ull}
    }
   ,	// 3 extra digits
   {{000ull, 0ull}
    }
   ,	// 4 extra digits
   {{0000ull, 0ull}
    }
   ,	// 5 extra digits
   {{00000ull, 0ull}
    }
   ,	// 6 extra digits
   {{000000ull, 0ull}
    }
   ,	// 7 extra digits
   {{0000000ull, 0ull}
    }
   ,	// 8 extra digits
   {{00000000ull, 0ull}
    }
   ,	// 9 extra digits
   {{000000000ull, 0ull}
    }
   ,	// 10 extra digits
   {{0000000000ull, 0ull}
    }
   ,	// 11 extra digits
   {{00000000000ull, 0ull}
    }
   ,	// 12 extra digits
   {{000000000000ull, 0ull}
    }
   ,	// 13 extra digits
   {{0000000000000ull, 0ull}
    }
   ,	// 14 extra digits
   {{00000000000000ull, 0ull}
    }
   ,	// 15 extra digits
   {{000000000000000ull, 0ull}
    }
   ,	// 16 extra digits
   {{0000000000000000ull, 0ull}
    }
   ,	// 17 extra digits
   {{00000000000000000ull, 0ull}
    }
   ,	// 18 extra digits
   {{000000000000000000ull, 0ull}
    }
   ,	// 19 extra digits
   {{0ull, 0ull}
    }
   ,	//20
   {{0ull, 0ull}
    }
   ,	//21
   {{0ull, 0ull}
    }
   ,	//22
   {{0ull, 0ull}
    }
   ,	//23
   {{0ull, 0ull}
    }
   ,	//24
   {{0ull, 0ull}
    }
   ,	//25
   {{0ull, 0ull}
    }
   ,	//26
   {{0ull, 0ull}
    }
   ,	//27
   {{0ull, 0ull}
    }
   ,	//28
   {{0ull, 0ull}
    }
   ,	//29
   {{0ull, 0ull}
    }
   ,	//30
   {{0ull, 0ull}
    }
   ,	//31
   {{0ull, 0ull}
    }
   ,	//32
   {{0ull, 0ull}
    }
   ,	//33
   {{0ull, 0ull}
    }
   ,	//34
   {{0ull, 0ull}
    }
   ,	//35
   }
  ,
  {	//RU
   {{0ull, 0ull}
    }
   ,	// 0 extra digits
   {{9ull, 0ull}
    }
   ,	// 1 extra digits
   {{99ull, 0ull}
    }
   ,	// 2 extra digits
   {{999ull, 0ull}
    }
   ,	// 3 extra digits
   {{9999ull, 0ull}
    }
   ,	// 4 extra digits
   {{99999ull, 0ull}
    }
   ,	// 5 extra digits
   {{999999ull, 0ull}
    }
   ,	// 6 extra digits
   {{9999999ull, 0ull}
    }
   ,	// 7 extra digits
   {{99999999ull, 0ull}
    }
   ,	// 8 extra digits
   {{999999999ull, 0ull}
    }
   ,	// 9 extra digits
   {{9999999999ull, 0ull}
    }
   ,	// 10 extra digits
   {{99999999999ull, 0ull}
    }
   ,	// 11 extra digits
   {{999999999999ull, 0ull}
    }
   ,	// 12 extra digits
   {{9999999999999ull, 0ull}
    }
   ,	// 13 extra digits
   {{99999999999999ull, 0ull}
    }
   ,	// 14 extra digits
   {{999999999999999ull, 0ull}
    }
   ,	// 15 extra digits
   {{9999999999999999ull, 0ull}
    }
   ,	// 16 extra digits
   {{99999999999999999ull, 0ull}
    }
   ,	// 17 extra digits
   {{999999999999999999ull, 0ull}
    }
   ,	// 18 extra digits
   {{9999999999999999999ull, 0ull}
    }
   ,	// 19 extra digits
   {{0x6BC75E2D630FFFFFull, 0x5ull}
    }
   ,	//20
   {{0x35C9ADC5DE9FFFFFull, 0x36ull}
    }
   ,	//21
   {{0x19E0C9BAB23FFFFFull, 0x21eull}
    }
   ,	//22
   {{0x2C7E14AF67FFFFFull, 0x152dull}
    }
   ,	//23
   {{0x1BCECCEDA0FFFFFFull, 0xd3c2ull}
    }
   ,	//24
   {{0x1614014849FFFFFFull, 0x84595ull}
    }
   ,	//25
   {{0xDCC80CD2E3FFFFFFull, 0x52b7d2ull}
    }
   ,	//26
   {{0x9FD0803CE7FFFFFFull, 0x33B2E3Cull}
    }
   ,	//27
   {{0x3E2502610FFFFFFFull, 0x204FCE5Eull}
    }
   ,	//28
   {{0x6D7217CA9FFFFFFFull, 0x1431E0FAEull}
    }
   ,	//29
   {{0x4674EDEA3FFFFFFFull, 0xC9F2C9CD0ull}
    }
   ,	//30
   {{0xC0914B267FFFFFFFull, 0x7E37BE2022ull}
    }
   ,	//31
   {{0x85ACEF80FFFFFFFFull, 0x4EE2D6D415Bull}
    }
   ,	//32
   {{0x38c15b09ffffffffull, 0x314dc6448d93ull}
    }
   ,	//33
   {{0x378d8e63ffffffffull, 0x1ed09bead87c0ull}
    }
   ,	//34
   {{0x2b878fe7ffffffffull, 0x13426172c74d82ull}
    }
   ,	//35
   }
  ,
  {	//RZ
   {{0ull, 0ull}
    }
   ,	// 0 extra digits
   {{0ull, 0ull}
    }
   ,	// 1 extra digits
   {{0ull, 0ull}
    }
   ,	// 2 extra digits
   {{00ull, 0ull}
    }
   ,	// 3 extra digits
   {{000ull, 0ull}
    }
   ,	// 4 extra digits
   {{0000ull, 0ull}
    }
   ,	// 5 extra digits
   {{00000ull, 0ull}
    }
   ,	// 6 extra digits
   {{000000ull, 0ull}
    }
   ,	// 7 extra digits
   {{0000000ull, 0ull}
    }
   ,	// 8 extra digits
   {{00000000ull, 0ull}
    }
   ,	// 9 extra digits
   {{000000000ull, 0ull}
    }
   ,	// 10 extra digits
   {{0000000000ull, 0ull}
    }
   ,	// 11 extra digits
   {{00000000000ull, 0ull}
    }
   ,	// 12 extra digits
   {{000000000000ull, 0ull}
    }
   ,	// 13 extra digits
   {{0000000000000ull, 0ull}
    }
   ,	// 14 extra digits
   {{00000000000000ull, 0ull}
    }
   ,	// 15 extra digits
   {{000000000000000ull, 0ull}
    }
   ,	// 16 extra digits
   {{0000000000000000ull, 0ull}
    }
   ,	// 17 extra digits
   {{00000000000000000ull, 0ull}
    }
   ,	// 18 extra digits
   {{000000000000000000ull, 0ull}
    }
   ,	// 19 extra digits
   {{0ull, 0ull}
    }
   ,	//20
   {{0ull, 0ull}
    }
   ,	//21
   {{0ull, 0ull}
    }
   ,	//22
   {{0ull, 0ull}
    }
   ,	//23
   {{0ull, 0ull}
    }
   ,	//24
   {{0ull, 0ull}
    }
   ,	//25
   {{0ull, 0ull}
    }
   ,	//26
   {{0ull, 0ull}
    }
   ,	//27
   {{0ull, 0ull}
    }
   ,	//28
   {{0ull, 0ull}
    }
   ,	//29
   {{0ull, 0ull}
    }
   ,	//30
   {{0ull, 0ull}
    }
   ,	//31
   {{0ull, 0ull}
    }
   ,	//32
   {{0ull, 0ull}
    }
   ,	//33
   {{0ull, 0ull}
    }
   ,	//34
   {{0ull, 0ull}
    }
   ,	//35
   }
  ,
  {	//RN, ties away
   {{0ull, 0ull}
    }
   ,	// 0 extra digits
   {{5ull, 0ull}
    }
   ,	// 1 extra digits
   {{50ull, 0ull}
    }
   ,	// 2 extra digits
   {{500ull, 0ull}
    }
   ,	// 3 extra digits
   {{5000ull, 0ull}
    }
   ,	// 4 extra digits
   {{50000ull, 0ull}
    }
   ,	// 5 extra digits
   {{500000ull, 0ull}
    }
   ,	// 6 extra digits
   {{5000000ull, 0ull}
    }
   ,	// 7 extra digits
   {{50000000ull, 0ull}
    }
   ,	// 8 extra digits
   {{500000000ull, 0ull}
    }
   ,	// 9 extra digits
   {{5000000000ull, 0ull}
    }
   ,	// 10 extra digits
   {{50000000000ull, 0ull}
    }
   ,	// 11 extra digits
   {{500000000000ull, 0ull}
    }
   ,	// 12 extra digits
   {{5000000000000ull, 0ull}
    }
   ,	// 13 extra digits
   {{50000000000000ull, 0ull}
    }
   ,	// 14 extra digits
   {{500000000000000ull, 0ull}
    }
   ,	// 15 extra digits
   {{5000000000000000ull, 0ull}
    }
   ,	// 16 extra digits
   {{50000000000000000ull, 0ull}
    }
   ,	// 17 extra digits
   {{500000000000000000ull, 0ull}
    }
   ,	// 18 extra digits
   {{5000000000000000000ull, 0ull}
    }
   ,	// 19 extra digits
   {{0xb5e3af16b1880000ull, 2ull}
    }
   ,	//20
   {{0x1ae4d6e2ef500000ull, 27ull}
    }
   ,	//21
   {{0xcf064dd59200000ull, 271ull}
    }
   ,	//22
   {{0x8163f0a57b400000ull, 2710ull}
    }
   ,	//23
   {{0xde76676d0800000ull, 27105ull}
    }
   ,	//24
   {{0x8b0a00a425000000ull, 0x422caull}
    }
   ,	//25
   {{0x6e64066972000000ull, 0x295be9ull}
    }
   ,	//26
   {{0x4fe8401e74000000ull, 0x19d971eull}
    }
   ,	//27
   {{0x1f12813088000000ull, 0x1027e72full}
    }
   ,	//28
   {{0x36b90be550000000ull, 0xa18f07d7ull}
    }
   ,	//29
   {{0x233a76f520000000ull, 0x64f964e68ull}
    }
   ,	//30
   {{0x6048a59340000000ull, 0x3f1bdf1011ull}
    }
   ,	//31
   {{0xc2d677c080000000ull, 0x27716b6a0adull}
    }
   ,	//32
   {{0x9c60ad8500000000ull, 0x18a6e32246c9ull}
    }
   ,	//33
   {{0x1bc6c73200000000ull, 0xf684df56c3e0ull}
    }
   ,	//34
   {{0x15c3c7f400000000ull, 0x9a130b963a6c1ull}
    }
   ,	//35
   }
};
 
 
UINT128 reciprocals10_128[] = {
  {{0ull, 0ull}
   }
  ,	// 0 extra digits
  {{0x3333333333333334ull, 0x3333333333333333ull}
   }
  ,	// 1 extra digit
  {{0x51eb851eb851eb86ull, 0x051eb851eb851eb8ull}
   }
  ,	// 2 extra digits
  {{0x3b645a1cac083127ull, 0x0083126e978d4fdfull}
   }
  ,	// 3 extra digits
  {{0x4af4f0d844d013aaULL, 0x00346dc5d6388659ULL}
   }
  ,	//  10^(-4) * 2^131
  {{0x08c3f3e0370cdc88ULL, 0x0029f16b11c6d1e1ULL}
   }
  ,	//  10^(-5) * 2^134
  {{0x6d698fe69270b06dULL, 0x00218def416bdb1aULL}
   }
  ,	//  10^(-6) * 2^137
  {{0xaf0f4ca41d811a47ULL, 0x0035afe535795e90ULL}
   }
  ,	//  10^(-7) * 2^141
  {{0xbf3f70834acdaea0ULL, 0x002af31dc4611873ULL}
   }
  ,	//  10^(-8) * 2^144
  {{0x65cc5a02a23e254dULL, 0x00225c17d04dad29ULL}
   }
  ,	//  10^(-9) * 2^147
  {{0x6fad5cd10396a214ULL, 0x0036f9bfb3af7b75ULL}
   }
  ,	// 10^(-10) * 2^151
  {{0xbfbde3da69454e76ULL, 0x002bfaffc2f2c92aULL}
   }
  ,	// 10^(-11) * 2^154
  {{0x32fe4fe1edd10b92ULL, 0x00232f33025bd422ULL}
   }
  ,	// 10^(-12) * 2^157
  {{0x84ca19697c81ac1cULL, 0x00384b84d092ed03ULL}
   }
  ,	// 10^(-13) * 2^161
  {{0x03d4e1213067bce4ULL, 0x002d09370d425736ULL}
   }
  ,	// 10^(-14) * 2^164
  {{0x3643e74dc052fd83ULL, 0x0024075f3dceac2bULL}
   }
  ,	// 10^(-15) * 2^167
  {{0x56d30baf9a1e626bULL, 0x0039a5652fb11378ULL}
   }
  ,	// 10^(-16) * 2^171
  {{0x12426fbfae7eb522ULL, 0x002e1dea8c8da92dULL}
   }
  ,	// 10^(-17) * 2^174
  {{0x41cebfcc8b9890e8ULL, 0x0024e4bba3a48757ULL}
   }
  ,	// 10^(-18) * 2^177
  {{0x694acc7a78f41b0dULL, 0x003b07929f6da558ULL}
   }
  ,	// 10^(-19) * 2^181
  {{0xbaa23d2ec729af3eULL, 0x002f394219248446ULL}
   }
  ,	// 10^(-20) * 2^184
  {{0xfbb4fdbf05baf298ULL, 0x0025c768141d369eULL}
   }
  ,	// 10^(-21) * 2^187
  {{0x2c54c931a2c4b759ULL, 0x003c7240202ebdcbULL}
   }
  ,	// 10^(-22) * 2^191
  {{0x89dd6dc14f03c5e1ULL, 0x00305b66802564a2ULL}
   }
  ,	// 10^(-23) * 2^194
  {{0xd4b1249aa59c9e4eULL, 0x0026af8533511d4eULL}
   }
  ,	// 10^(-24) * 2^197
  {{0x544ea0f76f60fd49ULL, 0x003de5a1ebb4fbb1ULL}
   }
  ,	// 10^(-25) * 2^201
  {{0x76a54d92bf80caa1ULL, 0x00318481895d9627ULL}
   }
  ,	// 10^(-26) * 2^204
  {{0x921dd7a89933d54eULL, 0x00279d346de4781fULL}
   }
  ,	// 10^(-27) * 2^207
  {{0x8362f2a75b862215ULL, 0x003f61ed7ca0c032ULL}
   }
  ,	// 10^(-28) * 2^211
  {{0xcf825bb91604e811ULL, 0x0032b4bdfd4d668eULL}
   }
  ,	// 10^(-29) * 2^214
  {{0x0c684960de6a5341ULL, 0x00289097fdd7853fULL}
   }
  ,	// 10^(-30) * 2^217
  {{0x3d203ab3e521dc34ULL, 0x002073accb12d0ffULL}
   }
  ,	// 10^(-31) * 2^220
  {{0x2e99f7863b696053ULL, 0x0033ec47ab514e65ULL}
   }
  ,	// 10^(-32) * 2^224
  {{0x587b2c6b62bab376ULL, 0x002989d2ef743eb7ULL}
   }
  ,	// 10^(-33) * 2^227
  {{0xad2f56bc4efbc2c5ULL, 0x00213b0f25f69892ULL}
   }
  ,	// 10^(-34) * 2^230
  {{0x0f2abc9d8c9689d1ull, 0x01a95a5b7f87a0efull}
   }
  ,	// 35 extra digits
};
 
 
int recip_scale[] = {
  129 - 128,	// 1
  129 - 128,	// 1/10
  129 - 128,	// 1/10^2
  129 - 128,	// 1/10^3
  3,	// 131 - 128
  6,	// 134 - 128
  9,	// 137 - 128
  13,	// 141 - 128
  16,	// 144 - 128
  19,	// 147 - 128
  23,	// 151 - 128
  26,	// 154 - 128
  29,	// 157 - 128
  33,	// 161 - 128
  36,	// 164 - 128
  39,	// 167 - 128
  43,	// 171 - 128
  46,	// 174 - 128
  49,	// 177 - 128
  53,	// 181 - 128
  56,	// 184 - 128
  59,	// 187 - 128
  63,	// 191 - 128
 
  66,	// 194 - 128
  69,	// 197 - 128
  73,	// 201 - 128
  76,	// 204 - 128
  79,	// 207 - 128
  83,	// 211 - 128
  86,	// 214 - 128
  89,	// 217 - 128
  92,	// 220 - 128
  96,	// 224 - 128
  99,	// 227 - 128
  102,	// 230 - 128
  109,	// 237 - 128, 1/10^35
};
 
 
// tables used in computation
int estimate_decimal_digits[129] = {
  1,	//2^0 =1     < 10^0
  1,	//2^1 =2     < 10^1
  1,	//2^2 =4     < 10^1
  1,	//2^3 =8     < 10^1
  2,	//2^4 =16    < 10^2
  2,	//2^5 =32    < 10^2
  2,	//2^6 =64    < 10^2
  3,	//2^7 =128   < 10^3
  3,	//2^8 =256   < 10^3
  3,	//2^9 =512   < 10^3
  4,	//2^10=1024  < 10^4
  4,	//2^11=2048  < 10^4
  4,	//2^12=4096  < 10^4
  4,	//2^13=8192  < 10^4
  5,	//2^14=16384 < 10^5
  5,	//2^15=32768 < 10^5
 
  5,	//2^16=65536     < 10^5
  6,	//2^17=131072    < 10^6
  6,	//2^18=262144    < 10^6
  6,	//2^19=524288    < 10^6
  7,	//2^20=1048576   < 10^7
  7,	//2^21=2097152   < 10^7
  7,	//2^22=4194304   < 10^7
  7,	//2^23=8388608   < 10^7
  8,	//2^24=16777216  < 10^8
  8,	//2^25=33554432  < 10^8
  8,	//2^26=67108864  < 10^8
  9,	//2^27=134217728 < 10^9
  9,	//2^28=268435456 < 10^9
  9,	//2^29=536870912 < 10^9
  10,	//2^30=1073741824< 10^10
  10,	//2^31=2147483648< 10^10
 
  10,	//2^32=4294967296     < 10^10
  10,	//2^33=8589934592     < 10^10
  11,	//2^34=17179869184    < 10^11
  11,	//2^35=34359738368    < 10^11
  11,	//2^36=68719476736    < 10^11
  12,	//2^37=137438953472   < 10^12
  12,	//2^38=274877906944   < 10^12
  12,	//2^39=549755813888   < 10^12
  13,	//2^40=1099511627776  < 10^13
  13,	//2^41=2199023255552  < 10^13
  13,	//2^42=4398046511104  < 10^13
  13,	//2^43=8796093022208  < 10^13
  14,	//2^44=17592186044416 < 10^14
  14,	//2^45=35184372088832 < 10^14
  14,	//2^46=70368744177664 < 10^14
  15,	//2^47=140737488355328< 10^15
 
  15,	//2^48=281474976710656    < 10^15
  15,	//2^49=562949953421312    < 10^15
  16,	//2^50=1125899906842624   < 10^16
  16,	//2^51=2251799813685248   < 10^16
  16,	//2^52=4503599627370496   < 10^16
  16,	//2^53=9007199254740992   < 10^16
  17,	//2^54=18014398509481984  < 10^17
  17,	//2^55=36028797018963968  < 10^17
  17,	//2^56=72057594037927936  < 10^17
  18,	//2^57=144115188075855872 < 10^18
  18,	//2^58=288230376151711744 < 10^18
  18,	//2^59=576460752303423488 < 10^18
  19,	//2^60=1152921504606846976< 10^19
  19,	//2^61=2305843009213693952< 10^19
  19,	//2^62=4611686018427387904< 10^19
  19,	//2^63=9223372036854775808< 10^19
 
  20,	//2^64=18446744073709551616
  20,	//2^65=36893488147419103232
  20,	//2^66=73786976294838206464
  21,	//2^67=147573952589676412928
  21,	//2^68=295147905179352825856
  21,	//2^69=590295810358705651712
  22,	//2^70=1180591620717411303424
  22,	//2^71=2361183241434822606848
  22,	//2^72=4722366482869645213696
  22,	//2^73=9444732965739290427392
  23,	//2^74=18889465931478580854784
  23,	//2^75=37778931862957161709568
  23,	//2^76=75557863725914323419136
  24,	//2^77=151115727451828646838272
  24,	//2^78=302231454903657293676544
  24,	//2^79=604462909807314587353088
 
  25,	//2^80=1208925819614629174706176
  25,	//2^81=2417851639229258349412352
  25,	//2^82=4835703278458516698824704
  25,	//2^83=9671406556917033397649408
  26,	//2^84=19342813113834066795298816
  26,	//2^85=38685626227668133590597632
  26,	//2^86=77371252455336267181195264
  27,	//2^87=154742504910672534362390528
  27,	//2^88=309485009821345068724781056
  27,	//2^89=618970019642690137449562112
  28,	//2^90=1237940039285380274899124224
  28,	//2^91=2475880078570760549798248448
  28,	//2^92=4951760157141521099596496896
  28,	//2^93=9903520314283042199192993792
  29,	//2^94=19807040628566084398385987584
  29,	//2^95=39614081257132168796771975168
  29,	//2^96=79228162514264337593543950336
 
  30,	//2^97=158456325028528675187087900672
  30,	//2^98=316912650057057350374175801344
  30,	//2^99=633825300114114700748351602688
  31,	//2^100=1267650600228229401496703205376
  31,	//2^101=2535301200456458802993406410752
  31,	//2^102=5070602400912917605986812821504
  32,	//2^103=10141204801825835211973625643008
  32,	//2^104=20282409603651670423947251286016
  32,	//2^105=40564819207303340847894502572032
  32,	//2^106=81129638414606681695789005144064
  33,	//2^107=162259276829213363391578010288128
  33,	// 2^108
  33,	// 2^109
  34,	// 2^110
  34,	// 2^111
  34,	// 2^112
  35,	// 2^113
  35,	// 2^114
  35,	// 2^115
  35,	// 2^116
  36,	// 2^117
  36,	// 2^118
  36,	// 2^119
  37,	// 2^120
  37,	// 2^121
  37,	// 2^122
  38,	// 2^123
  38,	// 2^124
  38,	// 2^125
  38,	// 2^126
  39,	// 2^127
  39	// 2^128
};
 
 
UINT128 power10_table_128[] = {
  {{0x0000000000000001ull, 0x0000000000000000ull}},	// 10^0
  {{0x000000000000000aull, 0x0000000000000000ull}},	// 10^1
  {{0x0000000000000064ull, 0x0000000000000000ull}},	// 10^2
  {{0x00000000000003e8ull, 0x0000000000000000ull}},	// 10^3
  {{0x0000000000002710ull, 0x0000000000000000ull}},	// 10^4
  {{0x00000000000186a0ull, 0x0000000000000000ull}},	// 10^5
  {{0x00000000000f4240ull, 0x0000000000000000ull}},	// 10^6
  {{0x0000000000989680ull, 0x0000000000000000ull}},	// 10^7
  {{0x0000000005f5e100ull, 0x0000000000000000ull}},	// 10^8
  {{0x000000003b9aca00ull, 0x0000000000000000ull}},	// 10^9
  {{0x00000002540be400ull, 0x0000000000000000ull}},	// 10^10
  {{0x000000174876e800ull, 0x0000000000000000ull}},	// 10^11
  {{0x000000e8d4a51000ull, 0x0000000000000000ull}},	// 10^12
  {{0x000009184e72a000ull, 0x0000000000000000ull}},	// 10^13
  {{0x00005af3107a4000ull, 0x0000000000000000ull}},	// 10^14
  {{0x00038d7ea4c68000ull, 0x0000000000000000ull}},	// 10^15
  {{0x002386f26fc10000ull, 0x0000000000000000ull}},	// 10^16
  {{0x016345785d8a0000ull, 0x0000000000000000ull}},	// 10^17
  {{0x0de0b6b3a7640000ull, 0x0000000000000000ull}},	// 10^18
  {{0x8ac7230489e80000ull, 0x0000000000000000ull}},	// 10^19
  {{0x6bc75e2d63100000ull, 0x0000000000000005ull}},	// 10^20
  {{0x35c9adc5dea00000ull, 0x0000000000000036ull}},	// 10^21
  {{0x19e0c9bab2400000ull, 0x000000000000021eull}},	// 10^22
  {{0x02c7e14af6800000ull, 0x000000000000152dull}},	// 10^23
  {{0x1bcecceda1000000ull, 0x000000000000d3c2ull}},	// 10^24
  {{0x161401484a000000ull, 0x0000000000084595ull}},	// 10^25
  {{0xdcc80cd2e4000000ull, 0x000000000052b7d2ull}},	// 10^26
  {{0x9fd0803ce8000000ull, 0x00000000033b2e3cull}},	// 10^27
  {{0x3e25026110000000ull, 0x00000000204fce5eull}},	// 10^28
  {{0x6d7217caa0000000ull, 0x00000001431e0faeull}},	// 10^29
  {{0x4674edea40000000ull, 0x0000000c9f2c9cd0ull}},	// 10^30
  {{0xc0914b2680000000ull, 0x0000007e37be2022ull}},	// 10^31
  {{0x85acef8100000000ull, 0x000004ee2d6d415bull}},	// 10^32
  {{0x38c15b0a00000000ull, 0x0000314dc6448d93ull}},	// 10^33
  {{0x378d8e6400000000ull, 0x0001ed09bead87c0ull}},	// 10^34
  {{0x2b878fe800000000ull, 0x0013426172c74d82ull}},	// 10^35
  {{0xb34b9f1000000000ull, 0x00c097ce7bc90715ull}},	// 10^36
  {{0x00f436a000000000ull, 0x0785ee10d5da46d9ull}},	// 10^37
  {{0x098a224000000000ull, 0x4b3b4ca85a86c47aull}},	// 10^38
};
 
 
int estimate_bin_expon[] = {
  0,	// 10^0
  3,	// 10^1
  6,	// 10^2
  9,	// 10^3
  13,	// 10^4
  16,	// 10^5
  19,	// 10^6
  23,	// 10^7
  26,	// 10^8
  29,	// 10^9
  33,	// 10^10
  36,	// 10^11
  39,	// 10^12
  43,	// 10^13
  46,	// 10^14
  49,	// 10^15
  53	// 10^16
};
 
 
UINT64 power10_index_binexp[] = {
  0x000000000000000aull,
  0x000000000000000aull,
  0x000000000000000aull,
  0x000000000000000aull,
  0x0000000000000064ull,
  0x0000000000000064ull,
  0x0000000000000064ull,
  0x00000000000003e8ull,
  0x00000000000003e8ull,
  0x00000000000003e8ull,
  0x0000000000002710ull,
  0x0000000000002710ull,
  0x0000000000002710ull,
  0x0000000000002710ull,
  0x00000000000186a0ull,
  0x00000000000186a0ull,
  0x00000000000186a0ull,
  0x00000000000f4240ull,
  0x00000000000f4240ull,
  0x00000000000f4240ull,
  0x0000000000989680ull,
  0x0000000000989680ull,
  0x0000000000989680ull,
  0x0000000000989680ull,
  0x0000000005f5e100ull,
  0x0000000005f5e100ull,
  0x0000000005f5e100ull,
  0x000000003b9aca00ull,
  0x000000003b9aca00ull,
  0x000000003b9aca00ull,
  0x00000002540be400ull,
  0x00000002540be400ull,
  0x00000002540be400ull,
  0x00000002540be400ull,
  0x000000174876e800ull,
  0x000000174876e800ull,
  0x000000174876e800ull,
  0x000000e8d4a51000ull,
  0x000000e8d4a51000ull,
  0x000000e8d4a51000ull,
  0x000009184e72a000ull,
  0x000009184e72a000ull,
  0x000009184e72a000ull,
  0x000009184e72a000ull,
  0x00005af3107a4000ull,
  0x00005af3107a4000ull,
  0x00005af3107a4000ull,
  0x00038d7ea4c68000ull,
  0x00038d7ea4c68000ull,
  0x00038d7ea4c68000ull,
  0x002386f26fc10000ull,
  0x002386f26fc10000ull,
  0x002386f26fc10000ull,
  0x002386f26fc10000ull,
  0x016345785d8a0000ull,
  0x016345785d8a0000ull,
  0x016345785d8a0000ull,
  0x0de0b6b3a7640000ull,
  0x0de0b6b3a7640000ull,
  0x0de0b6b3a7640000ull,
  0x8ac7230489e80000ull,
  0x8ac7230489e80000ull,
  0x8ac7230489e80000ull,
  0x8ac7230489e80000ull
};
 
 
int short_recip_scale[] = {
  1,
  65 - 64,
  69 - 64,
  71 - 64,
  75 - 64,
  78 - 64,
  81 - 64,
  85 - 64,
  88 - 64,
  91 - 64,
  95 - 64,
  98 - 64,
  101 - 64,
  105 - 64,
  108 - 64,
  111 - 64,
  115 - 64,	//114 - 64
  118 - 64
};
 
 
UINT64 reciprocals10_64[] = {
  1ull,	// dummy value for 0 extra digits
  0x3333333333333334ull,	// 1 extra digit
  0x51eb851eb851eb86ull,
  0x20c49ba5e353f7cfull,
  0x346dc5d63886594bull,
  0x29f16b11c6d1e109ull,
  0x218def416bdb1a6eull,
  0x35afe535795e90b0ull,
  0x2af31dc4611873c0ull,
  0x225c17d04dad2966ull,
  0x36f9bfb3af7b7570ull,
  0x2bfaffc2f2c92ac0ull,
  0x232f33025bd42233ull,
  0x384b84d092ed0385ull,
  0x2d09370d42573604ull,
  0x24075f3dceac2b37ull,
  0x39a5652fb1137857ull,
  0x2e1dea8c8da92d13ull
};
 
 
 
UINT128 power10_index_binexp_128[] = {
  {{0x000000000000000aull, 0x0000000000000000ull}},
  {{0x000000000000000aull, 0x0000000000000000ull}},
  {{0x000000000000000aull, 0x0000000000000000ull}},
  {{0x000000000000000aull, 0x0000000000000000ull}},
  {{0x0000000000000064ull, 0x0000000000000000ull}},
  {{0x0000000000000064ull, 0x0000000000000000ull}},
  {{0x0000000000000064ull, 0x0000000000000000ull}},
  {{0x00000000000003e8ull, 0x0000000000000000ull}},
  {{0x00000000000003e8ull, 0x0000000000000000ull}},
  {{0x00000000000003e8ull, 0x0000000000000000ull}},
  {{0x0000000000002710ull, 0x0000000000000000ull}},
  {{0x0000000000002710ull, 0x0000000000000000ull}},
  {{0x0000000000002710ull, 0x0000000000000000ull}},
  {{0x0000000000002710ull, 0x0000000000000000ull}},
  {{0x00000000000186a0ull, 0x0000000000000000ull}},
  {{0x00000000000186a0ull, 0x0000000000000000ull}},
  {{0x00000000000186a0ull, 0x0000000000000000ull}},
  {{0x00000000000f4240ull, 0x0000000000000000ull}},
  {{0x00000000000f4240ull, 0x0000000000000000ull}},
  {{0x00000000000f4240ull, 0x0000000000000000ull}},
  {{0x0000000000989680ull, 0x0000000000000000ull}},
  {{0x0000000000989680ull, 0x0000000000000000ull}},
  {{0x0000000000989680ull, 0x0000000000000000ull}},
  {{0x0000000000989680ull, 0x0000000000000000ull}},
  {{0x0000000005f5e100ull, 0x0000000000000000ull}},
  {{0x0000000005f5e100ull, 0x0000000000000000ull}},
  {{0x0000000005f5e100ull, 0x0000000000000000ull}},
  {{0x000000003b9aca00ull, 0x0000000000000000ull}},
  {{0x000000003b9aca00ull, 0x0000000000000000ull}},
  {{0x000000003b9aca00ull, 0x0000000000000000ull}},
  {{0x00000002540be400ull, 0x0000000000000000ull}},
  {{0x00000002540be400ull, 0x0000000000000000ull}},
  {{0x00000002540be400ull, 0x0000000000000000ull}},
  {{0x00000002540be400ull, 0x0000000000000000ull}},
  {{0x000000174876e800ull, 0x0000000000000000ull}},
  {{0x000000174876e800ull, 0x0000000000000000ull}},
  {{0x000000174876e800ull, 0x0000000000000000ull}},
  {{0x000000e8d4a51000ull, 0x0000000000000000ull}},
  {{0x000000e8d4a51000ull, 0x0000000000000000ull}},
  {{0x000000e8d4a51000ull, 0x0000000000000000ull}},
  {{0x000009184e72a000ull, 0x0000000000000000ull}},
  {{0x000009184e72a000ull, 0x0000000000000000ull}},
  {{0x000009184e72a000ull, 0x0000000000000000ull}},
  {{0x000009184e72a000ull, 0x0000000000000000ull}},
  {{0x00005af3107a4000ull, 0x0000000000000000ull}},
  {{0x00005af3107a4000ull, 0x0000000000000000ull}},
  {{0x00005af3107a4000ull, 0x0000000000000000ull}},
  {{0x00038d7ea4c68000ull, 0x0000000000000000ull}},
  {{0x00038d7ea4c68000ull, 0x0000000000000000ull}},
  {{0x00038d7ea4c68000ull, 0x0000000000000000ull}},
  {{0x002386f26fc10000ull, 0x0000000000000000ull}},
  {{0x002386f26fc10000ull, 0x0000000000000000ull}},
  {{0x002386f26fc10000ull, 0x0000000000000000ull}},
  {{0x002386f26fc10000ull, 0x0000000000000000ull}},
  {{0x016345785d8a0000ull, 0x0000000000000000ull}},
  {{0x016345785d8a0000ull, 0x0000000000000000ull}},
  {{0x016345785d8a0000ull, 0x0000000000000000ull}},
  {{0x0de0b6b3a7640000ull, 0x0000000000000000ull}},
  {{0x0de0b6b3a7640000ull, 0x0000000000000000ull}},
  {{0x0de0b6b3a7640000ull, 0x0000000000000000ull}},
  {{0x8ac7230489e80000ull, 0x0000000000000000ull}},
  {{0x8ac7230489e80000ull, 0x0000000000000000ull}},
  {{0x8ac7230489e80000ull, 0x0000000000000000ull}},
  {{0x8ac7230489e80000ull, 0x0000000000000000ull}},
  {{0x6bc75e2d63100000ull, 0x0000000000000005ull}},	// 10^20
  {{0x6bc75e2d63100000ull, 0x0000000000000005ull}},	// 10^20
  {{0x6bc75e2d63100000ull, 0x0000000000000005ull}},	// 10^20
  {{0x35c9adc5dea00000ull, 0x0000000000000036ull}},	// 10^21
  {{0x35c9adc5dea00000ull, 0x0000000000000036ull}},	// 10^21
  {{0x35c9adc5dea00000ull, 0x0000000000000036ull}},	// 10^21
  {{0x19e0c9bab2400000ull, 0x000000000000021eull}},	// 10^22
  {{0x19e0c9bab2400000ull, 0x000000000000021eull}},	// 10^22
  {{0x19e0c9bab2400000ull, 0x000000000000021eull}},	// 10^22
  {{0x19e0c9bab2400000ull, 0x000000000000021eull}},	// 10^22
  {{0x02c7e14af6800000ull, 0x000000000000152dull}},	// 10^23
  {{0x02c7e14af6800000ull, 0x000000000000152dull}},	// 10^23
  {{0x02c7e14af6800000ull, 0x000000000000152dull}},	// 10^23
  {{0x1bcecceda1000000ull, 0x000000000000d3c2ull}},	// 10^24
  {{0x1bcecceda1000000ull, 0x000000000000d3c2ull}},	// 10^24
  {{0x1bcecceda1000000ull, 0x000000000000d3c2ull}},	// 10^24
  {{0x161401484a000000ull, 0x0000000000084595ull}},	// 10^25
  {{0x161401484a000000ull, 0x0000000000084595ull}},	// 10^25
  {{0x161401484a000000ull, 0x0000000000084595ull}},	// 10^25
  {{0x161401484a000000ull, 0x0000000000084595ull}},	// 10^25
  {{0xdcc80cd2e4000000ull, 0x000000000052b7d2ull}},	// 10^26
  {{0xdcc80cd2e4000000ull, 0x000000000052b7d2ull}},	// 10^26
  {{0xdcc80cd2e4000000ull, 0x000000000052b7d2ull}},	// 10^26
  {{0x9fd0803ce8000000ull, 0x00000000033b2e3cull}},	// 10^27
  {{0x9fd0803ce8000000ull, 0x00000000033b2e3cull}},	// 10^27
  {{0x9fd0803ce8000000ull, 0x00000000033b2e3cull}},	// 10^27
  {{0x3e25026110000000ull, 0x00000000204fce5eull}},	// 10^28
  {{0x3e25026110000000ull, 0x00000000204fce5eull}},	// 10^28
  {{0x3e25026110000000ull, 0x00000000204fce5eull}},	// 10^28
  {{0x3e25026110000000ull, 0x00000000204fce5eull}},	// 10^28
  {{0x6d7217caa0000000ull, 0x00000001431e0faeull}},	// 10^29
  {{0x6d7217caa0000000ull, 0x00000001431e0faeull}},	// 10^29
  {{0x6d7217caa0000000ull, 0x00000001431e0faeull}},	// 10^29
  {{0x4674edea40000000ull, 0x0000000c9f2c9cd0ull}},	// 10^30
  {{0x4674edea40000000ull, 0x0000000c9f2c9cd0ull}},	// 10^30
  {{0x4674edea40000000ull, 0x0000000c9f2c9cd0ull}},	// 10^30
  {{0xc0914b2680000000ull, 0x0000007e37be2022ull}},	// 10^31
  {{0xc0914b2680000000ull, 0x0000007e37be2022ull}},	// 10^31
  {{0xc0914b2680000000ull, 0x0000007e37be2022ull}},	// 10^31
  {{0x85acef8100000000ull, 0x000004ee2d6d415bull}},	// 10^32
  {{0x85acef8100000000ull, 0x000004ee2d6d415bull}},	// 10^32
  {{0x85acef8100000000ull, 0x000004ee2d6d415bull}},	// 10^32
  {{0x85acef8100000000ull, 0x000004ee2d6d415bull}},	// 10^32
  {{0x38c15b0a00000000ull, 0x0000314dc6448d93ull}},	// 10^33
  {{0x38c15b0a00000000ull, 0x0000314dc6448d93ull}},	// 10^33
  {{0x38c15b0a00000000ull, 0x0000314dc6448d93ull}},	// 10^33, entry 112
  {{0x378d8e6400000000ull, 0x0001ed09bead87c0ull}},	// 10^34
  {{0x378d8e6400000000ull, 0x0001ed09bead87c0ull}},	// 10^34
  {{0x378d8e6400000000ull, 0x0001ed09bead87c0ull}},	// 10^34
  {{0x2b878fe800000000ull, 0x0013426172c74d82ull}},	// 10^35
  {{0x2b878fe800000000ull, 0x0013426172c74d82ull}},	// 10^35
  {{0x2b878fe800000000ull, 0x0013426172c74d82ull}},	// 10^35
  {{0x2b878fe800000000ull, 0x0013426172c74d82ull}},	// 10^35
  {{0xb34b9f1000000000ull, 0x00c097ce7bc90715ull}},	// 10^36
  {{0x00f436a000000000ull, 0x0785ee10d5da46d9ull}},	// 10^37
  {{0x00f436a000000000ull, 0x0785ee10d5da46d9ull}},	// 10^37
  {{0x00f436a000000000ull, 0x0785ee10d5da46d9ull}},	// 10^37
  {{0x098a224000000000ull, 0x4b3b4ca85a86c47aull}},	// 10^38
  {{0x098a224000000000ull, 0x4b3b4ca85a86c47aull}},	// 10^38
  {{0x098a224000000000ull, 0x4b3b4ca85a86c47aull}},	// 10^38
  {{0x098a224000000000ull, 0x4b3b4ca85a86c47aull}},	// 10^38
};