libgcc/config/libbid/decimal_data.c

   1 /* Copyright (C) 2007  Free Software Foundation, Inc.
   2
   3 This file is part of GCC.
   4
   5 GCC is free software; you can redistribute it and/or modify it under
   6 the terms of the GNU General Public License as published by the Free
   7 Software Foundation; either version 2, or (at your option) any later
   8 version.
   9
  10 In addition to the permissions in the GNU General Public License, the
  11 Free Software Foundation gives you unlimited permission to link the
  12 compiled version of this file into combinations with other programs,
  13 and to distribute those combinations without any restriction coming
  14 from the use of this file.  (The General Public License restrictions
  15 do apply in other respects; for example, they cover modification of
  16 the file, and distribution when not linked into a combine
  17 executable.)
  18
  19 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
  20 WARRANTY; without even the implied warranty of MERCHANTABILITY or
  21 FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  22 for more details.
  23
  24 You should have received a copy of the GNU General Public License
  25 along with GCC; see the file COPYING.  If not, write to the Free
  26 Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
  27 02110-1301, USA.  */
  28
  29 #include "bid_internal.h"
  30
  31 UINT64 __bid_round_const_table[][19] = {
  32   {     // RN
  33    0ull,        // 0 extra digits
  34    5ull,        // 1 extra digits
  35    50ull,       // 2 extra digits
  36    500ull,      // 3 extra digits
  37    5000ull,     // 4 extra digits
  38    50000ull,    // 5 extra digits
  39    500000ull,   // 6 extra digits
  40    5000000ull,  // 7 extra digits
  41    50000000ull, // 8 extra digits
  42    500000000ull,        // 9 extra digits
  43    5000000000ull,       // 10 extra digits
  44    50000000000ull,      // 11 extra digits
  45    500000000000ull,     // 12 extra digits
  46    5000000000000ull,    // 13 extra digits
  47    50000000000000ull,   // 14 extra digits
  48    500000000000000ull,  // 15 extra digits
  49    5000000000000000ull, // 16 extra digits
  50    50000000000000000ull,        // 17 extra digits
  51    500000000000000000ull        // 18 extra digits
  52    }
  53   ,
  54   {     // RD
  55    0ull,        // 0 extra digits
  56    0ull,        // 1 extra digits
  57    0ull,        // 2 extra digits
  58    00ull,       // 3 extra digits
  59    000ull,      // 4 extra digits
  60    0000ull,     // 5 extra digits
  61    00000ull,    // 6 extra digits
  62    000000ull,   // 7 extra digits
  63    0000000ull,  // 8 extra digits
  64    00000000ull, // 9 extra digits
  65    000000000ull,        // 10 extra digits
  66    0000000000ull,       // 11 extra digits
  67    00000000000ull,      // 12 extra digits
  68    000000000000ull,     // 13 extra digits
  69    0000000000000ull,    // 14 extra digits
  70    00000000000000ull,   // 15 extra digits
  71    000000000000000ull,  // 16 extra digits
  72    0000000000000000ull, // 17 extra digits
  73    00000000000000000ull // 18 extra digits
  74    }
  75   ,
  76   {     // round to Inf
  77    0ull,        // 0 extra digits
  78    9ull,        // 1 extra digits
  79    99ull,       // 2 extra digits
  80    999ull,      // 3 extra digits
  81    9999ull,     // 4 extra digits
  82    99999ull,    // 5 extra digits
  83    999999ull,   // 6 extra digits
  84    9999999ull,  // 7 extra digits
  85    99999999ull, // 8 extra digits
  86    999999999ull,        // 9 extra digits
  87    9999999999ull,       // 10 extra digits
  88    99999999999ull,      // 11 extra digits
  89    999999999999ull,     // 12 extra digits
  90    9999999999999ull,    // 13 extra digits
  91    99999999999999ull,   // 14 extra digits
  92    999999999999999ull,  // 15 extra digits
  93    9999999999999999ull, // 16 extra digits
  94    99999999999999999ull,        // 17 extra digits
  95    999999999999999999ull        // 18 extra digits
  96    }
  97   ,
  98   {     // RZ
  99    0ull,        // 0 extra digits
 100    0ull,        // 1 extra digits
 101    0ull,        // 2 extra digits
 102    00ull,       // 3 extra digits
 103    000ull,      // 4 extra digits
 104    0000ull,     // 5 extra digits
 105    00000ull,    // 6 extra digits
 106    000000ull,   // 7 extra digits
 107    0000000ull,  // 8 extra digits
 108    00000000ull, // 9 extra digits
 109    000000000ull,        // 10 extra digits
 110    0000000000ull,       // 11 extra digits
 111    00000000000ull,      // 12 extra digits
 112    000000000000ull,     // 13 extra digits
 113    0000000000000ull,    // 14 extra digits
 114    00000000000000ull,   // 15 extra digits
 115    000000000000000ull,  // 16 extra digits
 116    0000000000000000ull, // 17 extra digits
 117    00000000000000000ull // 18 extra digits
 118    }
 119   ,
 120   {     // round ties away from 0
 121    0ull,        // 0 extra digits
 122    5ull,        // 1 extra digits
 123    50ull,       // 2 extra digits
 124    500ull,      // 3 extra digits
 125    5000ull,     // 4 extra digits
 126    50000ull,    // 5 extra digits
 127    500000ull,   // 6 extra digits
 128    5000000ull,  // 7 extra digits
 129    50000000ull, // 8 extra digits
 130    500000000ull,        // 9 extra digits
 131    5000000000ull,       // 10 extra digits
 132    50000000000ull,      // 11 extra digits
 133    500000000000ull,     // 12 extra digits
 134    5000000000000ull,    // 13 extra digits
 135    50000000000000ull,   // 14 extra digits
 136    500000000000000ull,  // 15 extra digits
 137    5000000000000000ull, // 16 extra digits
 138    50000000000000000ull,        // 17 extra digits
 139    500000000000000000ull        // 18 extra digits
 140    }
 141   ,
 142 };
 143
 144 UINT128 __bid_round_const_table_128[][36] = {
 145   {     //RN
 146    {{0ull, 0ull}}
 147    ,    // 0 extra digits
 148    {{5ull, 0ull}}
 149    ,    // 1 extra digits
 150    {{50ull, 0ull}}
 151    ,    // 2 extra digits
 152    {{500ull, 0ull}}
 153    ,    // 3 extra digits
 154    {{5000ull, 0ull}}
 155    ,    // 4 extra digits
 156    {{50000ull, 0ull}}
 157    ,    // 5 extra digits
 158    {{500000ull, 0ull}}
 159    ,    // 6 extra digits
 160    {{5000000ull, 0ull}}
 161    ,    // 7 extra digits
 162    {{50000000ull, 0ull}}
 163    ,    // 8 extra digits
 164    {{500000000ull, 0ull}}
 165    ,    // 9 extra digits
 166    {{5000000000ull, 0ull}}
 167    ,    // 10 extra digits
 168    {{50000000000ull, 0ull}}
 169    ,    // 11 extra digits
 170    {{500000000000ull, 0ull}}
 171    ,    // 12 extra digits
 172    {{5000000000000ull, 0ull}}
 173    ,    // 13 extra digits
 174    {{50000000000000ull, 0ull}}
 175    ,    // 14 extra digits
 176    {{500000000000000ull, 0ull}}
 177    ,    // 15 extra digits
 178    {{5000000000000000ull, 0ull}}
 179    ,    // 16 extra digits
 180    {{50000000000000000ull, 0ull}}
 181    ,    // 17 extra digits
 182    {{500000000000000000ull, 0ull}}
 183    ,    // 18 extra digits
 184    {{5000000000000000000ull, 0ull}}
 185    ,    // 19 extra digits
 186    {{0xb5e3af16b1880000ull, 2ull}}
 187    ,    //20
 188    {{0x1ae4d6e2ef500000ull, 27ull}}
 189    ,    //21
 190    {{0xcf064dd59200000ull, 271ull}}
 191    ,    //22
 192    {{0x8163f0a57b400000ull, 2710ull}}
 193    ,    //23
 194    {{0xde76676d0800000ull, 27105ull}}
 195    ,    //24
 196    {{0x8b0a00a425000000ull, 0x422caull}}
 197    ,    //25
 198    {{0x6e64066972000000ull, 0x295be9ull}}
 199    ,    //26
 200    {{0x4fe8401e74000000ull, 0x19d971eull}}
 201    ,    //27
 202    {{0x1f12813088000000ull, 0x1027e72full}}
 203    ,    //28
 204    {{0x36b90be550000000ull, 0xa18f07d7ull}}
 205    ,    //29
 206    {{0x233a76f520000000ull, 0x64f964e68ull}}
 207    ,    //30
 208    {{0x6048a59340000000ull, 0x3f1bdf1011ull}}
 209    ,    //31
 210    {{0xc2d677c080000000ull, 0x27716b6a0adull}}
 211    ,    //32
 212    {{0x9c60ad8500000000ull, 0x18a6e32246c9ull}}
 213    ,    //33
 214    {{0x1bc6c73200000000ull, 0xf684df56c3e0ull}}
 215    ,    //34
 216    {{0x15c3c7f400000000ull, 0x9a130b963a6c1ull}}
 217    ,    //35
 218    }
 219   ,
 220   {     //RD
 221    {{0ull, 0ull}}
 222    ,    // 0 extra digits
 223    {{0ull, 0ull}}
 224    ,    // 1 extra digits
 225    {{0ull, 0ull}}
 226    ,    // 2 extra digits
 227    {{00ull, 0ull}}
 228    ,    // 3 extra digits
 229    {{000ull, 0ull}}
 230    ,    // 4 extra digits
 231    {{0000ull, 0ull}}
 232    ,    // 5 extra digits
 233    {{00000ull, 0ull}}
 234    ,    // 6 extra digits
 235    {{000000ull, 0ull}}
 236    ,    // 7 extra digits
 237    {{0000000ull, 0ull}}
 238    ,    // 8 extra digits
 239    {{00000000ull, 0ull}}
 240    ,    // 9 extra digits
 241    {{000000000ull, 0ull}}
 242    ,    // 10 extra digits
 243    {{0000000000ull, 0ull}}
 244    ,    // 11 extra digits
 245    {{00000000000ull, 0ull}}
 246    ,    // 12 extra digits
 247    {{000000000000ull, 0ull}}
 248    ,    // 13 extra digits
 249    {{0000000000000ull, 0ull}}
 250    ,    // 14 extra digits
 251    {{00000000000000ull, 0ull}}
 252    ,    // 15 extra digits
 253    {{000000000000000ull, 0ull}}
 254    ,    // 16 extra digits
 255    {{0000000000000000ull, 0ull}}
 256    ,    // 17 extra digits
 257    {{00000000000000000ull, 0ull}}
 258    ,    // 18 extra digits
 259    {{000000000000000000ull, 0ull}}
 260    ,    // 19 extra digits
 261    {{0ull, 0ull}}
 262    ,    //20
 263    {{0ull, 0ull}}
 264    ,    //21
 265    {{0ull, 0ull}}
 266    ,    //22
 267    {{0ull, 0ull}}
 268    ,    //23
 269    {{0ull, 0ull}}
 270    ,    //24
 271    {{0ull, 0ull}}
 272    ,    //25
 273    {{0ull, 0ull}}
 274    ,    //26
 275    {{0ull, 0ull}}
 276    ,    //27
 277    {{0ull, 0ull}}
 278    ,    //28
 279    {{0ull, 0ull}}
 280    ,    //29
 281    {{0ull, 0ull}}
 282    ,    //30
 283    {{0ull, 0ull}}
 284    ,    //31
 285    {{0ull, 0ull}}
 286    ,    //32
 287    {{0ull, 0ull}}
 288    ,    //33
 289    {{0ull, 0ull}}
 290    ,    //34
 291    {{0ull, 0ull}}
 292    ,    //35
 293    }
 294   ,
 295   {     //RU
 296    {{0ull, 0ull}}
 297    ,    // 0 extra digits
 298    {{9ull, 0ull}}
 299    ,    // 1 extra digits
 300    {{99ull, 0ull}}
 301    ,    // 2 extra digits
 302    {{999ull, 0ull}}
 303    ,    // 3 extra digits
 304    {{9999ull, 0ull}}
 305    ,    // 4 extra digits
 306    {{99999ull, 0ull}}
 307    ,    // 5 extra digits
 308    {{999999ull, 0ull}}
 309    ,    // 6 extra digits
 310    {{9999999ull, 0ull}}
 311    ,    // 7 extra digits
 312    {{99999999ull, 0ull}}
 313    ,    // 8 extra digits
 314    {{999999999ull, 0ull}}
 315    ,    // 9 extra digits
 316    {{9999999999ull, 0ull}}
 317    ,    // 10 extra digits
 318    {{99999999999ull, 0ull}}
 319    ,    // 11 extra digits
 320    {{999999999999ull, 0ull}}
 321    ,    // 12 extra digits
 322    {{9999999999999ull, 0ull}}
 323    ,    // 13 extra digits
 324    {{99999999999999ull, 0ull}}
 325    ,    // 14 extra digits
 326    {{999999999999999ull, 0ull}}
 327    ,    // 15 extra digits
 328    {{9999999999999999ull, 0ull}}
 329    ,    // 16 extra digits
 330    {{99999999999999999ull, 0ull}}
 331    ,    // 17 extra digits
 332    {{999999999999999999ull, 0ull}}
 333    ,    // 18 extra digits
 334    {{9999999999999999999ull, 0ull}}
 335    ,    // 19 extra digits
 336    {{0x6BC75E2D630FFFFFull, 0x5ull}}
 337    ,    //20
 338    {{0x35C9ADC5DE9FFFFFull, 0x36ull}}
 339    ,    //21
 340    {{0x19E0C9BAB23FFFFFull, 0x21eull}}
 341    ,    //22
 342    {{0x2C7E14AF67FFFFFull, 0x152dull}}
 343    ,    //23
 344    {{0x1BCECCEDA0FFFFFFull, 0xd3c2ull}}
 345    ,    //24
 346    {{0x1614014849FFFFFFull, 0x84595ull}}
 347    ,    //25
 348    {{0xDCC80CD2E3FFFFFFull, 0x52b7d2ull}}
 349    ,    //26
 350    {{0x9FD0803CE7FFFFFFull, 0x33B2E3Cull}}
 351    ,    //27
 352    {{0x3E2502610FFFFFFFull, 0x204FCE5Eull}}
 353    ,    //28
 354    {{0x6D7217CA9FFFFFFFull, 0x1431E0FAEull}}
 355    ,    //29
 356    {{0x4674EDEA3FFFFFFFull, 0xC9F2C9CD0ull}}
 357    ,    //30
 358    {{0xC0914B267FFFFFFFull, 0x7E37BE2022ull}}
 359    ,    //31
 360    {{0x85ACEF80FFFFFFFFull, 0x4EE2D6D415Bull}}
 361    ,    //32
 362    {{0x38c15b09ffffffffull, 0x314dc6448d93ull}}
 363    ,    //33
 364    {{0x378d8e63ffffffffull, 0x1ed09bead87c0ull}}
 365    ,    //34
 366    {{0x2b878fe7ffffffffull, 0x13426172c74d82ull}}
 367    ,    //35
 368    }
 369   ,
 370   {     //RZ
 371    {{0ull, 0ull}}
 372    ,    // 0 extra digits
 373    {{0ull, 0ull}}
 374    ,    // 1 extra digits
 375    {{0ull, 0ull}}
 376    ,    // 2 extra digits
 377    {{00ull, 0ull}}
 378    ,    // 3 extra digits
 379    {{000ull, 0ull}}
 380    ,    // 4 extra digits
 381    {{0000ull, 0ull}}
 382    ,    // 5 extra digits
 383    {{00000ull, 0ull}}
 384    ,    // 6 extra digits
 385    {{000000ull, 0ull}}
 386    ,    // 7 extra digits
 387    {{0000000ull, 0ull}}
 388    ,    // 8 extra digits
 389    {{00000000ull, 0ull}}
 390    ,    // 9 extra digits
 391    {{000000000ull, 0ull}}
 392    ,    // 10 extra digits
 393    {{0000000000ull, 0ull}}
 394    ,    // 11 extra digits
 395    {{00000000000ull, 0ull}}
 396    ,    // 12 extra digits
 397    {{000000000000ull, 0ull}}
 398    ,    // 13 extra digits
 399    {{0000000000000ull, 0ull}}
 400    ,    // 14 extra digits
 401    {{00000000000000ull, 0ull}}
 402    ,    // 15 extra digits
 403    {{000000000000000ull, 0ull}}
 404    ,    // 16 extra digits
 405    {{0000000000000000ull, 0ull}}
 406    ,    // 17 extra digits
 407    {{00000000000000000ull, 0ull}}
 408    ,    // 18 extra digits
 409    {{000000000000000000ull, 0ull}}
 410    ,    // 19 extra digits
 411    {{0ull, 0ull}}
 412    ,    //20
 413    {{0ull, 0ull}}
 414    ,    //21
 415    {{0ull, 0ull}}
 416    ,    //22
 417    {{0ull, 0ull}}
 418    ,    //23
 419    {{0ull, 0ull}}
 420    ,    //24
 421    {{0ull, 0ull}}
 422    ,    //25
 423    {{0ull, 0ull}}
 424    ,    //26
 425    {{0ull, 0ull}}
 426    ,    //27
 427    {{0ull, 0ull}}
 428    ,    //28
 429    {{0ull, 0ull}}
 430    ,    //29
 431    {{0ull, 0ull}}
 432    ,    //30
 433    {{0ull, 0ull}}
 434    ,    //31
 435    {{0ull, 0ull}}
 436    ,    //32
 437    {{0ull, 0ull}}
 438    ,    //33
 439    {{0ull, 0ull}}
 440    ,    //34
 441    {{0ull, 0ull}}
 442    ,    //35
 443    }
 444   ,
 445   {     //RN, ties away
 446    {{0ull, 0ull}}
 447    ,    // 0 extra digits
 448    {{5ull, 0ull}}
 449    ,    // 1 extra digits
 450    {{50ull, 0ull}}
 451    ,    // 2 extra digits
 452    {{500ull, 0ull}}
 453    ,    // 3 extra digits
 454    {{5000ull, 0ull}}
 455    ,    // 4 extra digits
 456    {{50000ull, 0ull}}
 457    ,    // 5 extra digits
 458    {{500000ull, 0ull}}
 459    ,    // 6 extra digits
 460    {{5000000ull, 0ull}}
 461    ,    // 7 extra digits
 462    {{50000000ull, 0ull}}
 463    ,    // 8 extra digits
 464    {{500000000ull, 0ull}}
 465    ,    // 9 extra digits
 466    {{5000000000ull, 0ull}}
 467    ,    // 10 extra digits
 468    {{50000000000ull, 0ull}}
 469    ,    // 11 extra digits
 470    {{500000000000ull, 0ull}}
 471    ,    // 12 extra digits
 472    {{5000000000000ull, 0ull}}
 473    ,    // 13 extra digits
 474    {{50000000000000ull, 0ull}}
 475    ,    // 14 extra digits
 476    {{500000000000000ull, 0ull}}
 477    ,    // 15 extra digits
 478    {{5000000000000000ull, 0ull}}
 479    ,    // 16 extra digits
 480    {{50000000000000000ull, 0ull}}
 481    ,    // 17 extra digits
 482    {{500000000000000000ull, 0ull}}
 483    ,    // 18 extra digits
 484    {{5000000000000000000ull, 0ull}}
 485    ,    // 19 extra digits
 486    {{0xb5e3af16b1880000ull, 2ull}}
 487    ,    //20
 488    {{0x1ae4d6e2ef500000ull, 27ull}}
 489    ,    //21
 490    {{0xcf064dd59200000ull, 271ull}}
 491    ,    //22
 492    {{0x8163f0a57b400000ull, 2710ull}}
 493    ,    //23
 494    {{0xde76676d0800000ull, 27105ull}}
 495    ,    //24
 496    {{0x8b0a00a425000000ull, 0x422caull}}
 497    ,    //25
 498    {{0x6e64066972000000ull, 0x295be9ull}}
 499    ,    //26
 500    {{0x4fe8401e74000000ull, 0x19d971eull}}
 501    ,    //27
 502    {{0x1f12813088000000ull, 0x1027e72full}}
 503    ,    //28
 504    {{0x36b90be550000000ull, 0xa18f07d7ull}}
 505    ,    //29
 506    {{0x233a76f520000000ull, 0x64f964e68ull}}
 507    ,    //30
 508    {{0x6048a59340000000ull, 0x3f1bdf1011ull}}
 509    ,    //31
 510    {{0xc2d677c080000000ull, 0x27716b6a0adull}}
 511    ,    //32
 512    {{0x9c60ad8500000000ull, 0x18a6e32246c9ull}}
 513    ,    //33
 514    {{0x1bc6c73200000000ull, 0xf684df56c3e0ull}}
 515    ,    //34
 516    {{0x15c3c7f400000000ull, 0x9a130b963a6c1ull}}
 517    ,    //35
 518    }
 519 };
 520
 521
 522 UINT128 __bid_reciprocals10_128[] = {
 523   {{0ull, 0ull}}
 524   ,     // 0 extra digits
 525   {{0x3333333333333334ull, 0x3333333333333333ull}}
 526   ,     // 1 extra digit
 527   {{0x51eb851eb851eb86ull, 0x051eb851eb851eb8ull}}
 528   ,     // 2 extra digits
 529   {{0x3b645a1cac083127ull, 0x0083126e978d4fdfull}}
 530   ,     // 3 extra digits
 531   {{0x4af4f0d844d013aaULL, 0x00346dc5d6388659ULL}}
 532   ,     //  10^(-4) * 2^131
 533   {{0x08c3f3e0370cdc88ULL, 0x0029f16b11c6d1e1ULL}}
 534   ,     //  10^(-5) * 2^134
 535   {{0x6d698fe69270b06dULL, 0x00218def416bdb1aULL}}
 536   ,     //  10^(-6) * 2^137
 537   {{0xaf0f4ca41d811a47ULL, 0x0035afe535795e90ULL}}
 538   ,     //  10^(-7) * 2^141
 539   {{0xbf3f70834acdaea0ULL, 0x002af31dc4611873ULL}}
 540   ,     //  10^(-8) * 2^144
 541   {{0x65cc5a02a23e254dULL, 0x00225c17d04dad29ULL}}
 542   ,     //  10^(-9) * 2^147
 543   {{0x6fad5cd10396a214ULL, 0x0036f9bfb3af7b75ULL}}
 544   ,     // 10^(-10) * 2^151
 545   {{0xbfbde3da69454e76ULL, 0x002bfaffc2f2c92aULL}}
 546   ,     // 10^(-11) * 2^154
 547   {{0x32fe4fe1edd10b92ULL, 0x00232f33025bd422ULL}}
 548   ,     // 10^(-12) * 2^157
 549   {{0x84ca19697c81ac1cULL, 0x00384b84d092ed03ULL}}
 550   ,     // 10^(-13) * 2^161
 551   {{0x03d4e1213067bce4ULL, 0x002d09370d425736ULL}}
 552   ,     // 10^(-14) * 2^164
 553   {{0x3643e74dc052fd83ULL, 0x0024075f3dceac2bULL}}
 554   ,     // 10^(-15) * 2^167
 555   {{0x56d30baf9a1e626bULL, 0x0039a5652fb11378ULL}}
 556   ,     // 10^(-16) * 2^171
 557   {{0x12426fbfae7eb522ULL, 0x002e1dea8c8da92dULL}}
 558   ,     // 10^(-17) * 2^174
 559   {{0x41cebfcc8b9890e8ULL, 0x0024e4bba3a48757ULL}}
 560   ,     // 10^(-18) * 2^177
 561   {{0x694acc7a78f41b0dULL, 0x003b07929f6da558ULL}}
 562   ,     // 10^(-19) * 2^181
 563   {{0xbaa23d2ec729af3eULL, 0x002f394219248446ULL}}
 564   ,     // 10^(-20) * 2^184
 565   {{0xfbb4fdbf05baf298ULL, 0x0025c768141d369eULL}}
 566   ,     // 10^(-21) * 2^187
 567   {{0x2c54c931a2c4b759ULL, 0x003c7240202ebdcbULL}}
 568   ,     // 10^(-22) * 2^191
 569   {{0x89dd6dc14f03c5e1ULL, 0x00305b66802564a2ULL}}
 570   ,     // 10^(-23) * 2^194
 571   {{0xd4b1249aa59c9e4eULL, 0x0026af8533511d4eULL}}
 572   ,     // 10^(-24) * 2^197
 573   {{0x544ea0f76f60fd49ULL, 0x003de5a1ebb4fbb1ULL}}
 574   ,     // 10^(-25) * 2^201
 575   {{0x76a54d92bf80caa1ULL, 0x00318481895d9627ULL}}
 576   ,     // 10^(-26) * 2^204
 577   {{0x921dd7a89933d54eULL, 0x00279d346de4781fULL}}
 578   ,     // 10^(-27) * 2^207
 579   {{0x8362f2a75b862215ULL, 0x003f61ed7ca0c032ULL}}
 580   ,     // 10^(-28) * 2^211
 581   {{0xcf825bb91604e811ULL, 0x0032b4bdfd4d668eULL}}
 582   ,     // 10^(-29) * 2^214
 583   {{0x0c684960de6a5341ULL, 0x00289097fdd7853fULL}}
 584   ,     // 10^(-30) * 2^217
 585   {{0x3d203ab3e521dc34ULL, 0x002073accb12d0ffULL}}
 586   ,     // 10^(-31) * 2^220
 587   {{0x2e99f7863b696053ULL, 0x0033ec47ab514e65ULL}}
 588   ,     // 10^(-32) * 2^224
 589   {{0x587b2c6b62bab376ULL, 0x002989d2ef743eb7ULL}}
 590   ,     // 10^(-33) * 2^227
 591   {{0xad2f56bc4efbc2c5ULL, 0x00213b0f25f69892ULL}}
 592   ,     // 10^(-34) * 2^230
 593   {{0x0f2abc9d8c9689d1ull, 0x01a95a5b7f87a0efull}}
 594   ,     // 35 extra digits
 595 };
 596
 597
 598 int __bid_recip_scale[] = {
 599   129 - 128,    // 1
 600   129 - 128,    // 1/10
 601   129 - 128,    // 1/10^2
 602   129 - 128,    // 1/10^3
 603   3,    // 131 - 128
 604   6,    // 134 - 128
 605   9,    // 137 - 128
 606   13,   // 141 - 128
 607   16,   // 144 - 128
 608   19,   // 147 - 128
 609   23,   // 151 - 128
 610   26,   // 154 - 128
 611   29,   // 157 - 128
 612   33,   // 161 - 128
 613   36,   // 164 - 128
 614   39,   // 167 - 128
 615   43,   // 171 - 128
 616   46,   // 174 - 128
 617   49,   // 177 - 128
 618   53,   // 181 - 128
 619   56,   // 184 - 128
 620   59,   // 187 - 128
 621   63,   // 191 - 128
 622
 623   66,   // 194 - 128
 624   69,   // 197 - 128
 625   73,   // 201 - 128
 626   76,   // 204 - 128
 627   79,   // 207 - 128
 628   83,   // 211 - 128
 629   86,   // 214 - 128
 630   89,   // 217 - 128
 631   92,   // 220 - 128
 632   96,   // 224 - 128
 633   99,   // 227 - 128
 634   102,  // 230 - 128
 635   109,  // 237 - 128, 1/10^35
 636 };
 637
 638
 639 // tables used in computation
 640 int __bid_estimate_decimal_digits[129] = {
 641   1,    //2^0 =1     < 10^0
 642   1,    //2^1 =2     < 10^1
 643   1,    //2^2 =4     < 10^1
 644   1,    //2^3 =8     < 10^1
 645   2,    //2^4 =16    < 10^2
 646   2,    //2^5 =32    < 10^2
 647   2,    //2^6 =64    < 10^2
 648   3,    //2^7 =128   < 10^3
 649   3,    //2^8 =256   < 10^3
 650   3,    //2^9 =512   < 10^3
 651   4,    //2^10=1024  < 10^4
 652   4,    //2^11=2048  < 10^4
 653   4,    //2^12=4096  < 10^4
 654   4,    //2^13=8192  < 10^4
 655   5,    //2^14=16384 < 10^5
 656   5,    //2^15=32768 < 10^5
 657
 658   5,    //2^16=65536     < 10^5
 659   6,    //2^17=131072    < 10^6
 660   6,    //2^18=262144    < 10^6
 661   6,    //2^19=524288    < 10^6
 662   7,    //2^20=1048576   < 10^7
 663   7,    //2^21=2097152   < 10^7
 664   7,    //2^22=4194304   < 10^7
 665   7,    //2^23=8388608   < 10^7
 666   8,    //2^24=16777216  < 10^8
 667   8,    //2^25=33554432  < 10^8
 668   8,    //2^26=67108864  < 10^8
 669   9,    //2^27=134217728 < 10^9
 670   9,    //2^28=268435456 < 10^9
 671   9,    //2^29=536870912 < 10^9
 672   10,   //2^30=1073741824< 10^10
 673   10,   //2^31=2147483648< 10^10
 674
 675   10,   //2^32=4294967296     < 10^10
 676   10,   //2^33=8589934592     < 10^10
 677   11,   //2^34=17179869184    < 10^11
 678   11,   //2^35=34359738368    < 10^11
 679   11,   //2^36=68719476736    < 10^11
 680   12,   //2^37=137438953472   < 10^12
 681   12,   //2^38=274877906944   < 10^12
 682   12,   //2^39=549755813888   < 10^12
 683   13,   //2^40=1099511627776  < 10^13
 684   13,   //2^41=2199023255552  < 10^13
 685   13,   //2^42=4398046511104  < 10^13
 686   13,   //2^43=8796093022208  < 10^13
 687   14,   //2^44=17592186044416 < 10^14
 688   14,   //2^45=35184372088832 < 10^14
 689   14,   //2^46=70368744177664 < 10^14
 690   15,   //2^47=140737488355328< 10^15
 691
 692   15,   //2^48=281474976710656    < 10^15
 693   15,   //2^49=562949953421312    < 10^15
 694   16,   //2^50=1125899906842624   < 10^16
 695   16,   //2^51=2251799813685248   < 10^16
 696   16,   //2^52=4503599627370496   < 10^16
 697   16,   //2^53=9007199254740992   < 10^16
 698   17,   //2^54=18014398509481984  < 10^17
 699   17,   //2^55=36028797018963968  < 10^17
 700   17,   //2^56=72057594037927936  < 10^17
 701   18,   //2^57=144115188075855872 < 10^18
 702   18,   //2^58=288230376151711744 < 10^18
 703   18,   //2^59=576460752303423488 < 10^18
 704   19,   //2^60=1152921504606846976< 10^19
 705   19,   //2^61=2305843009213693952< 10^19
 706   19,   //2^62=4611686018427387904< 10^19
 707   19,   //2^63=9223372036854775808< 10^19
 708
 709   20,   //2^64=18446744073709551616
 710   20,   //2^65=36893488147419103232
 711   20,   //2^66=73786976294838206464
 712   21,   //2^67=147573952589676412928
 713   21,   //2^68=295147905179352825856
 714   21,   //2^69=590295810358705651712
 715   22,   //2^70=1180591620717411303424
 716   22,   //2^71=2361183241434822606848
 717   22,   //2^72=4722366482869645213696
 718   22,   //2^73=9444732965739290427392
 719   23,   //2^74=18889465931478580854784
 720   23,   //2^75=37778931862957161709568
 721   23,   //2^76=75557863725914323419136
 722   24,   //2^77=151115727451828646838272
 723   24,   //2^78=302231454903657293676544
 724   24,   //2^79=604462909807314587353088
 725
 726   25,   //2^80=1208925819614629174706176
 727   25,   //2^81=2417851639229258349412352
 728   25,   //2^82=4835703278458516698824704
 729   25,   //2^83=9671406556917033397649408
 730   26,   //2^84=19342813113834066795298816
 731   26,   //2^85=38685626227668133590597632
 732   26,   //2^86=77371252455336267181195264
 733   27,   //2^87=154742504910672534362390528
 734   27,   //2^88=309485009821345068724781056
 735   27,   //2^89=618970019642690137449562112
 736   28,   //2^90=1237940039285380274899124224
 737   28,   //2^91=2475880078570760549798248448
 738   28,   //2^92=4951760157141521099596496896
 739   28,   //2^93=9903520314283042199192993792
 740   29,   //2^94=19807040628566084398385987584
 741   29,   //2^95=39614081257132168796771975168
 742   29,   //2^96=79228162514264337593543950336
 743
 744   30,   //2^97=158456325028528675187087900672
 745   30,   //2^98=316912650057057350374175801344
 746   30,   //2^99=633825300114114700748351602688
 747   31,   //2^100=1267650600228229401496703205376
 748   31,   //2^101=2535301200456458802993406410752
 749   31,   //2^102=5070602400912917605986812821504
 750   32,   //2^103=10141204801825835211973625643008
 751   32,   //2^104=20282409603651670423947251286016
 752   32,   //2^105=40564819207303340847894502572032
 753   32,   //2^106=81129638414606681695789005144064
 754   33,   //2^107=162259276829213363391578010288128
 755   33,   // 2^108
 756   33,   // 2^109
 757   34,   // 2^110
 758   34,   // 2^111
 759   34,   // 2^112
 760   35,   // 2^113
 761   35,   // 2^114
 762   35,   // 2^115
 763   35,   // 2^116
 764   36,   // 2^117
 765   36,   // 2^118
 766   36,   // 2^119
 767   37,   // 2^120
 768   37,   // 2^121
 769   37,   // 2^122
 770   38,   // 2^123
 771   38,   // 2^124
 772   38,   // 2^125
 773   38,   // 2^126
 774   39,   // 2^127
 775   39    // 2^128
 776 };
 777
 778
 779 UINT128 __bid_power10_table_128[] = {
 780   {{0x0000000000000001ull, 0x0000000000000000ull}},     // 10^0
 781   {{0x000000000000000aull, 0x0000000000000000ull}},     // 10^1
 782   {{0x0000000000000064ull, 0x0000000000000000ull}},     // 10^2
 783   {{0x00000000000003e8ull, 0x0000000000000000ull}},     // 10^3
 784   {{0x0000000000002710ull, 0x0000000000000000ull}},     // 10^4
 785   {{0x00000000000186a0ull, 0x0000000000000000ull}},     // 10^5
 786   {{0x00000000000f4240ull, 0x0000000000000000ull}},     // 10^6
 787   {{0x0000000000989680ull, 0x0000000000000000ull}},     // 10^7
 788   {{0x0000000005f5e100ull, 0x0000000000000000ull}},     // 10^8
 789   {{0x000000003b9aca00ull, 0x0000000000000000ull}},     // 10^9
 790   {{0x00000002540be400ull, 0x0000000000000000ull}},     // 10^10
 791   {{0x000000174876e800ull, 0x0000000000000000ull}},     // 10^11
 792   {{0x000000e8d4a51000ull, 0x0000000000000000ull}},     // 10^12
 793   {{0x000009184e72a000ull, 0x0000000000000000ull}},     // 10^13
 794   {{0x00005af3107a4000ull, 0x0000000000000000ull}},     // 10^14
 795   {{0x00038d7ea4c68000ull, 0x0000000000000000ull}},     // 10^15
 796   {{0x002386f26fc10000ull, 0x0000000000000000ull}},     // 10^16
 797   {{0x016345785d8a0000ull, 0x0000000000000000ull}},     // 10^17
 798   {{0x0de0b6b3a7640000ull, 0x0000000000000000ull}},     // 10^18
 799   {{0x8ac7230489e80000ull, 0x0000000000000000ull}},     // 10^19
 800   {{0x6bc75e2d63100000ull, 0x0000000000000005ull}},     // 10^20
 801   {{0x35c9adc5dea00000ull, 0x0000000000000036ull}},     // 10^21
 802   {{0x19e0c9bab2400000ull, 0x000000000000021eull}},     // 10^22
 803   {{0x02c7e14af6800000ull, 0x000000000000152dull}},     // 10^23
 804   {{0x1bcecceda1000000ull, 0x000000000000d3c2ull}},     // 10^24
 805   {{0x161401484a000000ull, 0x0000000000084595ull}},     // 10^25
 806   {{0xdcc80cd2e4000000ull, 0x000000000052b7d2ull}},     // 10^26
 807   {{0x9fd0803ce8000000ull, 0x00000000033b2e3cull}},     // 10^27
 808   {{0x3e25026110000000ull, 0x00000000204fce5eull}},     // 10^28
 809   {{0x6d7217caa0000000ull, 0x00000001431e0faeull}},     // 10^29
 810   {{0x4674edea40000000ull, 0x0000000c9f2c9cd0ull}},     // 10^30
 811   {{0xc0914b2680000000ull, 0x0000007e37be2022ull}},     // 10^31
 812   {{0x85acef8100000000ull, 0x000004ee2d6d415bull}},     // 10^32
 813   {{0x38c15b0a00000000ull, 0x0000314dc6448d93ull}},     // 10^33
 814   {{0x378d8e6400000000ull, 0x0001ed09bead87c0ull}},     // 10^34
 815   {{0x2b878fe800000000ull, 0x0013426172c74d82ull}},     // 10^35
 816   {{0xb34b9f1000000000ull, 0x00c097ce7bc90715ull}},     // 10^36
 817   {{0x00f436a000000000ull, 0x0785ee10d5da46d9ull}},     // 10^37
 818   {{0x098a224000000000ull, 0x4b3b4ca85a86c47aull}},     // 10^38
 819 };
 820
 821
 822 int __bid_estimate_bin_expon[] = {
 823   0,    // 10^0
 824   3,    // 10^1
 825   6,    // 10^2
 826   9,    // 10^3
 827   13,   // 10^4
 828   16,   // 10^5
 829   19,   // 10^6
 830   23,   // 10^7
 831   26,   // 10^8
 832   29,   // 10^9
 833   33,   // 10^10
 834   36,   // 10^11
 835   39,   // 10^12
 836   43,   // 10^13
 837   46,   // 10^14
 838   49,   // 10^15
 839   53    // 10^16
 840 };
 841
 842
 843 UINT64 __bid_power10_index_binexp[] = {
 844   0x000000000000000aull,
 845   0x000000000000000aull,
 846   0x000000000000000aull,
 847   0x000000000000000aull,
 848   0x0000000000000064ull,
 849   0x0000000000000064ull,
 850   0x0000000000000064ull,
 851   0x00000000000003e8ull,
 852   0x00000000000003e8ull,
 853   0x00000000000003e8ull,
 854   0x0000000000002710ull,
 855   0x0000000000002710ull,
 856   0x0000000000002710ull,
 857   0x0000000000002710ull,
 858   0x00000000000186a0ull,
 859   0x00000000000186a0ull,
 860   0x00000000000186a0ull,
 861   0x00000000000f4240ull,
 862   0x00000000000f4240ull,
 863   0x00000000000f4240ull,
 864   0x0000000000989680ull,
 865   0x0000000000989680ull,
 866   0x0000000000989680ull,
 867   0x0000000000989680ull,
 868   0x0000000005f5e100ull,
 869   0x0000000005f5e100ull,
 870   0x0000000005f5e100ull,
 871   0x000000003b9aca00ull,
 872   0x000000003b9aca00ull,
 873   0x000000003b9aca00ull,
 874   0x00000002540be400ull,
 875   0x00000002540be400ull,
 876   0x00000002540be400ull,
 877   0x00000002540be400ull,
 878   0x000000174876e800ull,
 879   0x000000174876e800ull,
 880   0x000000174876e800ull,
 881   0x000000e8d4a51000ull,
 882   0x000000e8d4a51000ull,
 883   0x000000e8d4a51000ull,
 884   0x000009184e72a000ull,
 885   0x000009184e72a000ull,
 886   0x000009184e72a000ull,
 887   0x000009184e72a000ull,
 888   0x00005af3107a4000ull,
 889   0x00005af3107a4000ull,
 890   0x00005af3107a4000ull,
 891   0x00038d7ea4c68000ull,
 892   0x00038d7ea4c68000ull,
 893   0x00038d7ea4c68000ull,
 894   0x002386f26fc10000ull,
 895   0x002386f26fc10000ull,
 896   0x002386f26fc10000ull,
 897   0x002386f26fc10000ull,
 898   0x016345785d8a0000ull,
 899   0x016345785d8a0000ull,
 900   0x016345785d8a0000ull,
 901   0x0de0b6b3a7640000ull,
 902   0x0de0b6b3a7640000ull,
 903   0x0de0b6b3a7640000ull,
 904   0x8ac7230489e80000ull,
 905   0x8ac7230489e80000ull,
 906   0x8ac7230489e80000ull,
 907   0x8ac7230489e80000ull
 908 };
 909
 910
 911 int __bid_short_recip_scale[] = {
 912   1,
 913   65 - 64,
 914   69 - 64,
 915   71 - 64,
 916   75 - 64,
 917   78 - 64,
 918   81 - 64,
 919   85 - 64,
 920   88 - 64,
 921   91 - 64,
 922   95 - 64,
 923   98 - 64,
 924   101 - 64,
 925   105 - 64,
 926   108 - 64,
 927   111 - 64,
 928   115 - 64,     //114 - 64
 929   118 - 64
 930 };
 931
 932
 933 UINT64 __bid_reciprocals10_64[] = {
 934   1ull, // dummy value for 0 extra digits
 935   0x3333333333333334ull,        // 1 extra digit
 936   0x51eb851eb851eb86ull,
 937   0x20c49ba5e353f7cfull,
 938   0x346dc5d63886594bull,
 939   0x29f16b11c6d1e109ull,
 940   0x218def416bdb1a6eull,
 941   0x35afe535795e90b0ull,
 942   0x2af31dc4611873c0ull,
 943   0x225c17d04dad2966ull,
 944   0x36f9bfb3af7b7570ull,
 945   0x2bfaffc2f2c92ac0ull,
 946   0x232f33025bd42233ull,
 947   0x384b84d092ed0385ull,
 948   0x2d09370d42573604ull,
 949   0x24075f3dceac2b37ull,
 950   0x39a5652fb1137857ull,
 951   0x2e1dea8c8da92d13ull
 952 };
 953
 954
 955
 956 UINT128 __bid_power10_index_binexp_128[] = {
 957   {{0x000000000000000aull, 0x0000000000000000ull}},
 958   {{0x000000000000000aull, 0x0000000000000000ull}},
 959   {{0x000000000000000aull, 0x0000000000000000ull}},
 960   {{0x000000000000000aull, 0x0000000000000000ull}},
 961   {{0x0000000000000064ull, 0x0000000000000000ull}},
 962   {{0x0000000000000064ull, 0x0000000000000000ull}},
 963   {{0x0000000000000064ull, 0x0000000000000000ull}},
 964   {{0x00000000000003e8ull, 0x0000000000000000ull}},
 965   {{0x00000000000003e8ull, 0x0000000000000000ull}},
 966   {{0x00000000000003e8ull, 0x0000000000000000ull}},
 967   {{0x0000000000002710ull, 0x0000000000000000ull}},
 968   {{0x0000000000002710ull, 0x0000000000000000ull}},
 969   {{0x0000000000002710ull, 0x0000000000000000ull}},
 970   {{0x0000000000002710ull, 0x0000000000000000ull}},
 971   {{0x00000000000186a0ull, 0x0000000000000000ull}},
 972   {{0x00000000000186a0ull, 0x0000000000000000ull}},
 973   {{0x00000000000186a0ull, 0x0000000000000000ull}},
 974   {{0x00000000000f4240ull, 0x0000000000000000ull}},
 975   {{0x00000000000f4240ull, 0x0000000000000000ull}},
 976   {{0x00000000000f4240ull, 0x0000000000000000ull}},
 977   {{0x0000000000989680ull, 0x0000000000000000ull}},
 978   {{0x0000000000989680ull, 0x0000000000000000ull}},
 979   {{0x0000000000989680ull, 0x0000000000000000ull}},
 980   {{0x0000000000989680ull, 0x0000000000000000ull}},
 981   {{0x0000000005f5e100ull, 0x0000000000000000ull}},
 982   {{0x0000000005f5e100ull, 0x0000000000000000ull}},
 983   {{0x0000000005f5e100ull, 0x0000000000000000ull}},
 984   {{0x000000003b9aca00ull, 0x0000000000000000ull}},
 985   {{0x000000003b9aca00ull, 0x0000000000000000ull}},
 986   {{0x000000003b9aca00ull, 0x0000000000000000ull}},
 987   {{0x00000002540be400ull, 0x0000000000000000ull}},
 988   {{0x00000002540be400ull, 0x0000000000000000ull}},
 989   {{0x00000002540be400ull, 0x0000000000000000ull}},
 990   {{0x00000002540be400ull, 0x0000000000000000ull}},
 991   {{0x000000174876e800ull, 0x0000000000000000ull}},
 992   {{0x000000174876e800ull, 0x0000000000000000ull}},
 993   {{0x000000174876e800ull, 0x0000000000000000ull}},
 994   {{0x000000e8d4a51000ull, 0x0000000000000000ull}},
 995   {{0x000000e8d4a51000ull, 0x0000000000000000ull}},
 996   {{0x000000e8d4a51000ull, 0x0000000000000000ull}},
 997   {{0x000009184e72a000ull, 0x0000000000000000ull}},
 998   {{0x000009184e72a000ull, 0x0000000000000000ull}},
 999   {{0x000009184e72a000ull, 0x0000000000000000ull}},
1000   {{0x000009184e72a000ull, 0x0000000000000000ull}},
1001   {{0x00005af3107a4000ull, 0x0000000000000000ull}},
1002   {{0x00005af3107a4000ull, 0x0000000000000000ull}},
1003   {{0x00005af3107a4000ull, 0x0000000000000000ull}},
1004   {{0x00038d7ea4c68000ull, 0x0000000000000000ull}},
1005   {{0x00038d7ea4c68000ull, 0x0000000000000000ull}},
1006   {{0x00038d7ea4c68000ull, 0x0000000000000000ull}},
1007   {{0x002386f26fc10000ull, 0x0000000000000000ull}},
1008   {{0x002386f26fc10000ull, 0x0000000000000000ull}},
1009   {{0x002386f26fc10000ull, 0x0000000000000000ull}},
1010   {{0x002386f26fc10000ull, 0x0000000000000000ull}},
1011   {{0x016345785d8a0000ull, 0x0000000000000000ull}},
1012   {{0x016345785d8a0000ull, 0x0000000000000000ull}},
1013   {{0x016345785d8a0000ull, 0x0000000000000000ull}},
1014   {{0x0de0b6b3a7640000ull, 0x0000000000000000ull}},
1015   {{0x0de0b6b3a7640000ull, 0x0000000000000000ull}},
1016   {{0x0de0b6b3a7640000ull, 0x0000000000000000ull}},
1017   {{0x8ac7230489e80000ull, 0x0000000000000000ull}},
1018   {{0x8ac7230489e80000ull, 0x0000000000000000ull}},
1019   {{0x8ac7230489e80000ull, 0x0000000000000000ull}},
1020   {{0x8ac7230489e80000ull, 0x0000000000000000ull}},
1021   {{0x6bc75e2d63100000ull, 0x0000000000000005ull}},     // 10^20
1022   {{0x6bc75e2d63100000ull, 0x0000000000000005ull}},     // 10^20
1023   {{0x6bc75e2d63100000ull, 0x0000000000000005ull}},     // 10^20
1024   {{0x35c9adc5dea00000ull, 0x0000000000000036ull}},     // 10^21
1025   {{0x35c9adc5dea00000ull, 0x0000000000000036ull}},     // 10^21
1026   {{0x35c9adc5dea00000ull, 0x0000000000000036ull}},     // 10^21
1027   {{0x19e0c9bab2400000ull, 0x000000000000021eull}},     // 10^22
1028   {{0x19e0c9bab2400000ull, 0x000000000000021eull}},     // 10^22
1029   {{0x19e0c9bab2400000ull, 0x000000000000021eull}},     // 10^22
1030   {{0x19e0c9bab2400000ull, 0x000000000000021eull}},     // 10^22
1031   {{0x02c7e14af6800000ull, 0x000000000000152dull}},     // 10^23
1032   {{0x02c7e14af6800000ull, 0x000000000000152dull}},     // 10^23
1033   {{0x02c7e14af6800000ull, 0x000000000000152dull}},     // 10^23
1034   {{0x1bcecceda1000000ull, 0x000000000000d3c2ull}},     // 10^24
1035   {{0x1bcecceda1000000ull, 0x000000000000d3c2ull}},     // 10^24
1036   {{0x1bcecceda1000000ull, 0x000000000000d3c2ull}},     // 10^24
1037   {{0x161401484a000000ull, 0x0000000000084595ull}},     // 10^25
1038   {{0x161401484a000000ull, 0x0000000000084595ull}},     // 10^25
1039   {{0x161401484a000000ull, 0x0000000000084595ull}},     // 10^25
1040   {{0x161401484a000000ull, 0x0000000000084595ull}},     // 10^25
1041   {{0xdcc80cd2e4000000ull, 0x000000000052b7d2ull}},     // 10^26
1042   {{0xdcc80cd2e4000000ull, 0x000000000052b7d2ull}},     // 10^26
1043   {{0xdcc80cd2e4000000ull, 0x000000000052b7d2ull}},     // 10^26
1044   {{0x9fd0803ce8000000ull, 0x00000000033b2e3cull}},     // 10^27
1045   {{0x9fd0803ce8000000ull, 0x00000000033b2e3cull}},     // 10^27
1046   {{0x9fd0803ce8000000ull, 0x00000000033b2e3cull}},     // 10^27
1047   {{0x3e25026110000000ull, 0x00000000204fce5eull}},     // 10^28
1048   {{0x3e25026110000000ull, 0x00000000204fce5eull}},     // 10^28
1049   {{0x3e25026110000000ull, 0x00000000204fce5eull}},     // 10^28
1050   {{0x3e25026110000000ull, 0x00000000204fce5eull}},     // 10^28
1051   {{0x6d7217caa0000000ull, 0x00000001431e0faeull}},     // 10^29
1052   {{0x6d7217caa0000000ull, 0x00000001431e0faeull}},     // 10^29
1053   {{0x6d7217caa0000000ull, 0x00000001431e0faeull}},     // 10^29
1054   {{0x4674edea40000000ull, 0x0000000c9f2c9cd0ull}},     // 10^30
1055   {{0x4674edea40000000ull, 0x0000000c9f2c9cd0ull}},     // 10^30
1056   {{0x4674edea40000000ull, 0x0000000c9f2c9cd0ull}},     // 10^30
1057   {{0xc0914b2680000000ull, 0x0000007e37be2022ull}},     // 10^31
1058   {{0xc0914b2680000000ull, 0x0000007e37be2022ull}},     // 10^31
1059   {{0xc0914b2680000000ull, 0x0000007e37be2022ull}},     // 10^31
1060   {{0x85acef8100000000ull, 0x000004ee2d6d415bull}},     // 10^32
1061   {{0x85acef8100000000ull, 0x000004ee2d6d415bull}},     // 10^32
1062   {{0x85acef8100000000ull, 0x000004ee2d6d415bull}},     // 10^32
1063   {{0x85acef8100000000ull, 0x000004ee2d6d415bull}},     // 10^32
1064   {{0x38c15b0a00000000ull, 0x0000314dc6448d93ull}},     // 10^33
1065   {{0x38c15b0a00000000ull, 0x0000314dc6448d93ull}},     // 10^33
1066   {{0x38c15b0a00000000ull, 0x0000314dc6448d93ull}},     // 10^33, entry 112
1067   {{0x378d8e6400000000ull, 0x0001ed09bead87c0ull}},     // 10^34
1068   {{0x378d8e6400000000ull, 0x0001ed09bead87c0ull}},     // 10^34
1069   {{0x378d8e6400000000ull, 0x0001ed09bead87c0ull}},     // 10^34
1070   {{0x2b878fe800000000ull, 0x0013426172c74d82ull}},     // 10^35
1071   {{0x2b878fe800000000ull, 0x0013426172c74d82ull}},     // 10^35
1072   {{0x2b878fe800000000ull, 0x0013426172c74d82ull}},     // 10^35
1073   {{0x2b878fe800000000ull, 0x0013426172c74d82ull}},     // 10^35
1074   {{0xb34b9f1000000000ull, 0x00c097ce7bc90715ull}},     // 10^36
1075   {{0x00f436a000000000ull, 0x0785ee10d5da46d9ull}},     // 10^37
1076   {{0x00f436a000000000ull, 0x0785ee10d5da46d9ull}},     // 10^37
1077   {{0x00f436a000000000ull, 0x0785ee10d5da46d9ull}},     // 10^37
1078   {{0x098a224000000000ull, 0x4b3b4ca85a86c47aull}},     // 10^38
1079   {{0x098a224000000000ull, 0x4b3b4ca85a86c47aull}},     // 10^38
1080   {{0x098a224000000000ull, 0x4b3b4ca85a86c47aull}},     // 10^38
1081   {{0x098a224000000000ull, 0x4b3b4ca85a86c47aull}},     // 10^38
1082
1083 };