/* Copyright (C) 2007  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 2, or (at your option) any later
version.

In addition to the permissions in the GNU General Public License, the
Free Software Foundation gives you unlimited permission to link the
compiled version of this file into combinations with other programs,
and to distribute those combinations without any restriction coming
from the use of this file.  (The General Public License restrictions
do apply in other respects; for example, they cover modification of
the file, and distribution when not linked into a combine
executable.)

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.

You should have received a copy of the GNU General Public License
along with GCC; see the file COPYING.  If not, write to the Free
Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301, USA.  */

#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
};