aboutsummaryrefslogtreecommitdiffstats
path: root/contrib/restricted/abseil-cpp-tstring/y_absl/strings/charconv.cc
blob: fdfbd475e7bf5f884b603468183d0d75d0346714 (plain) (blame)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
// Copyright 2018 The Abseil Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//      https://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

#include "y_absl/strings/charconv.h"

#include <algorithm>
#include <cassert>
#include <cstddef>
#include <cstdint>
#include <limits>
#include <system_error>  // NOLINT(build/c++11)

#include "y_absl/base/casts.h"
#include "y_absl/base/config.h"
#include "y_absl/base/nullability.h"
#include "y_absl/numeric/bits.h"
#include "y_absl/numeric/int128.h"
#include "y_absl/strings/internal/charconv_bigint.h"
#include "y_absl/strings/internal/charconv_parse.h"

// The macro Y_ABSL_BIT_PACK_FLOATS is defined on x86-64, where IEEE floating
// point numbers have the same endianness in memory as a bitfield struct
// containing the corresponding parts.
//
// When set, we replace calls to ldexp() with manual bit packing, which is
// faster and is unaffected by floating point environment.
#ifdef Y_ABSL_BIT_PACK_FLOATS
#error Y_ABSL_BIT_PACK_FLOATS cannot be directly set
#elif defined(__x86_64__) || defined(_M_X64)
#define Y_ABSL_BIT_PACK_FLOATS 1
#endif

// A note about subnormals:
//
// The code below talks about "normals" and "subnormals".  A normal IEEE float
// has a fixed-width mantissa and power of two exponent.  For example, a normal
// `double` has a 53-bit mantissa.  Because the high bit is always 1, it is not
// stored in the representation.  The implicit bit buys an extra bit of
// resolution in the datatype.
//
// The downside of this scheme is that there is a large gap between DBL_MIN and
// zero.  (Large, at least, relative to the different between DBL_MIN and the
// next representable number).  This gap is softened by the "subnormal" numbers,
// which have the same power-of-two exponent as DBL_MIN, but no implicit 53rd
// bit.  An all-bits-zero exponent in the encoding represents subnormals.  (Zero
// is represented as a subnormal with an all-bits-zero mantissa.)
//
// The code below, in calculations, represents the mantissa as a uint64_t.  The
// end result normally has the 53rd bit set.  It represents subnormals by using
// narrower mantissas.

namespace y_absl {
Y_ABSL_NAMESPACE_BEGIN
namespace {

template <typename FloatType>
struct FloatTraits;

template <>
struct FloatTraits<double> {
  using mantissa_t = uint64_t;

  // The number of bits in the given float type.
  static constexpr int kTargetBits = 64;

  // The number of exponent bits in the given float type.
  static constexpr int kTargetExponentBits = 11;

  // The number of mantissa bits in the given float type.  This includes the
  // implied high bit.
  static constexpr int kTargetMantissaBits = 53;

  // The largest supported IEEE exponent, in our integral mantissa
  // representation.
  //
  // If `m` is the largest possible int kTargetMantissaBits bits wide, then
  // m * 2**kMaxExponent is exactly equal to DBL_MAX.
  static constexpr int kMaxExponent = 971;

  // The smallest supported IEEE normal exponent, in our integral mantissa
  // representation.
  //
  // If `m` is the smallest possible int kTargetMantissaBits bits wide, then
  // m * 2**kMinNormalExponent is exactly equal to DBL_MIN.
  static constexpr int kMinNormalExponent = -1074;

  // The IEEE exponent bias.  It equals ((1 << (kTargetExponentBits - 1)) - 1).
  static constexpr int kExponentBias = 1023;

  // The Eisel-Lemire "Shifting to 54/25 Bits" adjustment.  It equals (63 - 1 -
  // kTargetMantissaBits).
  static constexpr int kEiselLemireShift = 9;

  // The Eisel-Lemire high64_mask.  It equals ((1 << kEiselLemireShift) - 1).
  static constexpr uint64_t kEiselLemireMask = uint64_t{0x1FF};

  // The smallest negative integer N (smallest negative means furthest from
  // zero) such that parsing 9999999999999999999eN, with 19 nines, is still
  // positive. Parsing a smaller (more negative) N will produce zero.
  //
  // Adjusting the decimal point and exponent, without adjusting the value,
  // 9999999999999999999eN equals 9.999999999999999999eM where M = N + 18.
  //
  // 9999999999999999999, with 19 nines but no decimal point, is the largest
  // "repeated nines" integer that fits in a uint64_t.
  static constexpr int kEiselLemireMinInclusiveExp10 = -324 - 18;

  // The smallest positive integer N such that parsing 1eN produces infinity.
  // Parsing a smaller N will produce something finite.
  static constexpr int kEiselLemireMaxExclusiveExp10 = 309;

  static double MakeNan(y_absl::Nonnull<const char*> tagp) {
#if Y_ABSL_HAVE_BUILTIN(__builtin_nan)
    // Use __builtin_nan() if available since it has a fix for
    // https://bugs.llvm.org/show_bug.cgi?id=37778
    // std::nan may use the glibc implementation.
    return __builtin_nan(tagp);
#else
    // Support nan no matter which namespace it's in.  Some platforms
    // incorrectly don't put it in namespace std.
    using namespace std;  // NOLINT
    return nan(tagp);
#endif
  }

  // Builds a nonzero floating point number out of the provided parts.
  //
  // This is intended to do the same operation as ldexp(mantissa, exponent),
  // but using purely integer math, to avoid -ffastmath and floating
  // point environment issues.  Using type punning is also faster. We fall back
  // to ldexp on a per-platform basis for portability.
  //
  // `exponent` must be between kMinNormalExponent and kMaxExponent.
  //
  // `mantissa` must either be exactly kTargetMantissaBits wide, in which case
  // a normal value is made, or it must be less narrow than that, in which case
  // `exponent` must be exactly kMinNormalExponent, and a subnormal value is
  // made.
  static double Make(mantissa_t mantissa, int exponent, bool sign) {
#ifndef Y_ABSL_BIT_PACK_FLOATS
    // Support ldexp no matter which namespace it's in.  Some platforms
    // incorrectly don't put it in namespace std.
    using namespace std;  // NOLINT
    return sign ? -ldexp(mantissa, exponent) : ldexp(mantissa, exponent);
#else
    constexpr uint64_t kMantissaMask =
        (uint64_t{1} << (kTargetMantissaBits - 1)) - 1;
    uint64_t dbl = static_cast<uint64_t>(sign) << 63;
    if (mantissa > kMantissaMask) {
      // Normal value.
      // Adjust by 1023 for the exponent representation bias, and an additional
      // 52 due to the implied decimal point in the IEEE mantissa
      // representation.
      dbl += static_cast<uint64_t>(exponent + 1023 + kTargetMantissaBits - 1)
             << 52;
      mantissa &= kMantissaMask;
    } else {
      // subnormal value
      assert(exponent == kMinNormalExponent);
    }
    dbl += mantissa;
    return y_absl::bit_cast<double>(dbl);
#endif  // Y_ABSL_BIT_PACK_FLOATS
  }
};

// Specialization of floating point traits for the `float` type.  See the
// FloatTraits<double> specialization above for meaning of each of the following
// members and methods.
template <>
struct FloatTraits<float> {
  using mantissa_t = uint32_t;

  static constexpr int kTargetBits = 32;
  static constexpr int kTargetExponentBits = 8;
  static constexpr int kTargetMantissaBits = 24;
  static constexpr int kMaxExponent = 104;
  static constexpr int kMinNormalExponent = -149;
  static constexpr int kExponentBias = 127;
  static constexpr int kEiselLemireShift = 38;
  static constexpr uint64_t kEiselLemireMask = uint64_t{0x3FFFFFFFFF};
  static constexpr int kEiselLemireMinInclusiveExp10 = -46 - 18;
  static constexpr int kEiselLemireMaxExclusiveExp10 = 39;

  static float MakeNan(y_absl::Nonnull<const char*> tagp) {
#if Y_ABSL_HAVE_BUILTIN(__builtin_nanf)
    // Use __builtin_nanf() if available since it has a fix for
    // https://bugs.llvm.org/show_bug.cgi?id=37778
    // std::nanf may use the glibc implementation.
    return __builtin_nanf(tagp);
#else
    // Support nanf no matter which namespace it's in.  Some platforms
    // incorrectly don't put it in namespace std.
    using namespace std;  // NOLINT
    return std::nanf(tagp);
#endif
  }

  static float Make(mantissa_t mantissa, int exponent, bool sign) {
#ifndef Y_ABSL_BIT_PACK_FLOATS
    // Support ldexpf no matter which namespace it's in.  Some platforms
    // incorrectly don't put it in namespace std.
    using namespace std;  // NOLINT
    return sign ? -ldexpf(mantissa, exponent) : ldexpf(mantissa, exponent);
#else
    constexpr uint32_t kMantissaMask =
        (uint32_t{1} << (kTargetMantissaBits - 1)) - 1;
    uint32_t flt = static_cast<uint32_t>(sign) << 31;
    if (mantissa > kMantissaMask) {
      // Normal value.
      // Adjust by 127 for the exponent representation bias, and an additional
      // 23 due to the implied decimal point in the IEEE mantissa
      // representation.
      flt += static_cast<uint32_t>(exponent + 127 + kTargetMantissaBits - 1)
             << 23;
      mantissa &= kMantissaMask;
    } else {
      // subnormal value
      assert(exponent == kMinNormalExponent);
    }
    flt += mantissa;
    return y_absl::bit_cast<float>(flt);
#endif  // Y_ABSL_BIT_PACK_FLOATS
  }
};

// Decimal-to-binary conversions require coercing powers of 10 into a mantissa
// and a power of 2.  The two helper functions Power10Mantissa(n) and
// Power10Exponent(n) perform this task.  Together, these represent a hand-
// rolled floating point value which is equal to or just less than 10**n.
//
// The return values satisfy two range guarantees:
//
//   Power10Mantissa(n) * 2**Power10Exponent(n) <= 10**n
//     < (Power10Mantissa(n) + 1) * 2**Power10Exponent(n)
//
//   2**63 <= Power10Mantissa(n) < 2**64.
//
// See the "Table of powers of 10" comment below for a "1e60" example.
//
// Lookups into the power-of-10 table must first check the Power10Overflow() and
// Power10Underflow() functions, to avoid out-of-bounds table access.
//
// Indexes into these tables are biased by -kPower10TableMinInclusive. Valid
// indexes range from kPower10TableMinInclusive to kPower10TableMaxExclusive.
extern const uint64_t kPower10MantissaHighTable[];  // High 64 of 128 bits.
extern const uint64_t kPower10MantissaLowTable[];   // Low  64 of 128 bits.

// The smallest (inclusive) allowed value for use with the Power10Mantissa()
// and Power10Exponent() functions below.  (If a smaller exponent is needed in
// calculations, the end result is guaranteed to underflow.)
constexpr int kPower10TableMinInclusive = -342;

// The largest (exclusive) allowed value for use with the Power10Mantissa() and
// Power10Exponent() functions below.  (If a larger-or-equal exponent is needed
// in calculations, the end result is guaranteed to overflow.)
constexpr int kPower10TableMaxExclusive = 309;

uint64_t Power10Mantissa(int n) {
  return kPower10MantissaHighTable[n - kPower10TableMinInclusive];
}

int Power10Exponent(int n) {
  // The 217706 etc magic numbers encode the results as a formula instead of a
  // table. Their equivalence (over the kPower10TableMinInclusive ..
  // kPower10TableMaxExclusive range) is confirmed by
  // https://github.com/google/wuffs/blob/315b2e52625ebd7b02d8fac13e3cd85ea374fb80/script/print-mpb-powers-of-10.go
  return (217706 * n >> 16) - 63;
}

// Returns true if n is large enough that 10**n always results in an IEEE
// overflow.
bool Power10Overflow(int n) { return n >= kPower10TableMaxExclusive; }

// Returns true if n is small enough that 10**n times a ParsedFloat mantissa
// always results in an IEEE underflow.
bool Power10Underflow(int n) { return n < kPower10TableMinInclusive; }

// Returns true if Power10Mantissa(n) * 2**Power10Exponent(n) is exactly equal
// to 10**n numerically.  Put another way, this returns true if there is no
// truncation error in Power10Mantissa(n).
bool Power10Exact(int n) { return n >= 0 && n <= 27; }

// Sentinel exponent values for representing numbers too large or too close to
// zero to represent in a double.
constexpr int kOverflow = 99999;
constexpr int kUnderflow = -99999;

// Struct representing the calculated conversion result of a positive (nonzero)
// floating point number.
//
// The calculated number is mantissa * 2**exponent (mantissa is treated as an
// integer.)  `mantissa` is chosen to be the correct width for the IEEE float
// representation being calculated.  (`mantissa` will always have the same bit
// width for normal values, and narrower bit widths for subnormals.)
//
// If the result of conversion was an underflow or overflow, exponent is set
// to kUnderflow or kOverflow.
struct CalculatedFloat {
  uint64_t mantissa = 0;
  int exponent = 0;
};

// Returns the bit width of the given uint128.  (Equivalently, returns 128
// minus the number of leading zero bits.)
int BitWidth(uint128 value) {
  if (Uint128High64(value) == 0) {
    // This static_cast is only needed when using a std::bit_width()
    // implementation that does not have the fix for LWG 3656 applied.
    return static_cast<int>(bit_width(Uint128Low64(value)));
  }
  return 128 - countl_zero(Uint128High64(value));
}

// Calculates how far to the right a mantissa needs to be shifted to create a
// properly adjusted mantissa for an IEEE floating point number.
//
// `mantissa_width` is the bit width of the mantissa to be shifted, and
// `binary_exponent` is the exponent of the number before the shift.
//
// This accounts for subnormal values, and will return a larger-than-normal
// shift if binary_exponent would otherwise be too low.
template <typename FloatType>
int NormalizedShiftSize(int mantissa_width, int binary_exponent) {
  const int normal_shift =
      mantissa_width - FloatTraits<FloatType>::kTargetMantissaBits;
  const int minimum_shift =
      FloatTraits<FloatType>::kMinNormalExponent - binary_exponent;
  return std::max(normal_shift, minimum_shift);
}

// Right shifts a uint128 so that it has the requested bit width.  (The
// resulting value will have 128 - bit_width leading zeroes.)  The initial
// `value` must be wider than the requested bit width.
//
// Returns the number of bits shifted.
int TruncateToBitWidth(int bit_width, y_absl::Nonnull<uint128*> value) {
  const int current_bit_width = BitWidth(*value);
  const int shift = current_bit_width - bit_width;
  *value >>= shift;
  return shift;
}

// Checks if the given ParsedFloat represents one of the edge cases that are
// not dependent on number base: zero, infinity, or NaN.  If so, sets *value
// the appropriate double, and returns true.
template <typename FloatType>
bool HandleEdgeCase(const strings_internal::ParsedFloat& input, bool negative,
                    y_absl::Nonnull<FloatType*> value) {
  if (input.type == strings_internal::FloatType::kNan) {
    // A bug in both clang < 7 and gcc would cause the compiler to optimize
    // away the buffer we are building below.  Declaring the buffer volatile
    // avoids the issue, and has no measurable performance impact in
    // microbenchmarks.
    //
    // https://bugs.llvm.org/show_bug.cgi?id=37778
    // https://gcc.gnu.org/bugzilla/show_bug.cgi?id=86113
    constexpr ptrdiff_t kNanBufferSize = 128;
#if (defined(__GNUC__) && !defined(__clang__)) || \
    (defined(__clang__) && __clang_major__ < 7)
    volatile char n_char_sequence[kNanBufferSize];
#else
    char n_char_sequence[kNanBufferSize];
#endif
    if (input.subrange_begin == nullptr) {
      n_char_sequence[0] = '\0';
    } else {
      ptrdiff_t nan_size = input.subrange_end - input.subrange_begin;
      nan_size = std::min(nan_size, kNanBufferSize - 1);
      std::copy_n(input.subrange_begin, nan_size, n_char_sequence);
      n_char_sequence[nan_size] = '\0';
    }
    char* nan_argument = const_cast<char*>(n_char_sequence);
    *value = negative ? -FloatTraits<FloatType>::MakeNan(nan_argument)
                      : FloatTraits<FloatType>::MakeNan(nan_argument);
    return true;
  }
  if (input.type == strings_internal::FloatType::kInfinity) {
    *value = negative ? -std::numeric_limits<FloatType>::infinity()
                      : std::numeric_limits<FloatType>::infinity();
    return true;
  }
  if (input.mantissa == 0) {
    *value = negative ? -0.0 : 0.0;
    return true;
  }
  return false;
}

// Given a CalculatedFloat result of a from_chars conversion, generate the
// correct output values.
//
// CalculatedFloat can represent an underflow or overflow, in which case the
// error code in *result is set.  Otherwise, the calculated floating point
// number is stored in *value.
template <typename FloatType>
void EncodeResult(const CalculatedFloat& calculated, bool negative,
                  y_absl::Nonnull<y_absl::from_chars_result*> result,
                  y_absl::Nonnull<FloatType*> value) {
  if (calculated.exponent == kOverflow) {
    result->ec = std::errc::result_out_of_range;
    *value = negative ? -std::numeric_limits<FloatType>::max()
                      : std::numeric_limits<FloatType>::max();
    return;
  } else if (calculated.mantissa == 0 || calculated.exponent == kUnderflow) {
    result->ec = std::errc::result_out_of_range;
    *value = negative ? -0.0 : 0.0;
    return;
  }
  *value = FloatTraits<FloatType>::Make(
      static_cast<typename FloatTraits<FloatType>::mantissa_t>(
          calculated.mantissa),
      calculated.exponent, negative);
}

// Returns the given uint128 shifted to the right by `shift` bits, and rounds
// the remaining bits using round_to_nearest logic.  The value is returned as a
// uint64_t, since this is the type used by this library for storing calculated
// floating point mantissas.
//
// It is expected that the width of the input value shifted by `shift` will
// be the correct bit-width for the target mantissa, which is strictly narrower
// than a uint64_t.
//
// If `input_exact` is false, then a nonzero error epsilon is assumed.  For
// rounding purposes, the true value being rounded is strictly greater than the
// input value.  The error may represent a single lost carry bit.
//
// When input_exact, shifted bits of the form 1000000... represent a tie, which
// is broken by rounding to even -- the rounding direction is chosen so the low
// bit of the returned value is 0.
//
// When !input_exact, shifted bits of the form 10000000... represent a value
// strictly greater than one half (due to the error epsilon), and so ties are
// always broken by rounding up.
//
// When !input_exact, shifted bits of the form 01111111... are uncertain;
// the true value may or may not be greater than 10000000..., due to the
// possible lost carry bit.  The correct rounding direction is unknown.  In this
// case, the result is rounded down, and `output_exact` is set to false.
//
// Zero and negative values of `shift` are accepted, in which case the word is
// shifted left, as necessary.
uint64_t ShiftRightAndRound(uint128 value, int shift, bool input_exact,
                            y_absl::Nonnull<bool*> output_exact) {
  if (shift <= 0) {
    *output_exact = input_exact;
    return static_cast<uint64_t>(value << -shift);
  }
  if (shift >= 128) {
    // Exponent is so small that we are shifting away all significant bits.
    // Answer will not be representable, even as a subnormal, so return a zero
    // mantissa (which represents underflow).
    *output_exact = true;
    return 0;
  }

  *output_exact = true;
  const uint128 shift_mask = (uint128(1) << shift) - 1;
  const uint128 halfway_point = uint128(1) << (shift - 1);

  const uint128 shifted_bits = value & shift_mask;
  value >>= shift;
  if (shifted_bits > halfway_point) {
    // Shifted bits greater than 10000... require rounding up.
    return static_cast<uint64_t>(value + 1);
  }
  if (shifted_bits == halfway_point) {
    // In exact mode, shifted bits of 10000... mean we're exactly halfway
    // between two numbers, and we must round to even.  So only round up if
    // the low bit of `value` is set.
    //
    // In inexact mode, the nonzero error means the actual value is greater
    // than the halfway point and we must always round up.
    if ((value & 1) == 1 || !input_exact) {
      ++value;
    }
    return static_cast<uint64_t>(value);
  }
  if (!input_exact && shifted_bits == halfway_point - 1) {
    // Rounding direction is unclear, due to error.
    *output_exact = false;
  }
  // Otherwise, round down.
  return static_cast<uint64_t>(value);
}

// Checks if a floating point guess needs to be rounded up, using high precision
// math.
//
// `guess_mantissa` and `guess_exponent` represent a candidate guess for the
// number represented by `parsed_decimal`.
//
// The exact number represented by `parsed_decimal` must lie between the two
// numbers:
//   A = `guess_mantissa * 2**guess_exponent`
//   B = `(guess_mantissa + 1) * 2**guess_exponent`
//
// This function returns false if `A` is the better guess, and true if `B` is
// the better guess, with rounding ties broken by rounding to even.
bool MustRoundUp(uint64_t guess_mantissa, int guess_exponent,
                 const strings_internal::ParsedFloat& parsed_decimal) {
  // 768 is the number of digits needed in the worst case.  We could determine a
  // better limit dynamically based on the value of parsed_decimal.exponent.
  // This would optimize pathological input cases only.  (Sane inputs won't have
  // hundreds of digits of mantissa.)
  y_absl::strings_internal::BigUnsigned<84> exact_mantissa;
  int exact_exponent = exact_mantissa.ReadFloatMantissa(parsed_decimal, 768);

  // Adjust the `guess` arguments to be halfway between A and B.
  guess_mantissa = guess_mantissa * 2 + 1;
  guess_exponent -= 1;

  // In our comparison:
  // lhs = exact = exact_mantissa * 10**exact_exponent
  //             = exact_mantissa * 5**exact_exponent * 2**exact_exponent
  // rhs = guess = guess_mantissa * 2**guess_exponent
  //
  // Because we are doing integer math, we can't directly deal with negative
  // exponents.  We instead move these to the other side of the inequality.
  y_absl::strings_internal::BigUnsigned<84>& lhs = exact_mantissa;
  int comparison;
  if (exact_exponent >= 0) {
    lhs.MultiplyByFiveToTheNth(exact_exponent);
    y_absl::strings_internal::BigUnsigned<84> rhs(guess_mantissa);
    // There are powers of 2 on both sides of the inequality; reduce this to
    // a single bit-shift.
    if (exact_exponent > guess_exponent) {
      lhs.ShiftLeft(exact_exponent - guess_exponent);
    } else {
      rhs.ShiftLeft(guess_exponent - exact_exponent);
    }
    comparison = Compare(lhs, rhs);
  } else {
    // Move the power of 5 to the other side of the equation, giving us:
    // lhs = exact_mantissa * 2**exact_exponent
    // rhs = guess_mantissa * 5**(-exact_exponent) * 2**guess_exponent
    y_absl::strings_internal::BigUnsigned<84> rhs =
        y_absl::strings_internal::BigUnsigned<84>::FiveToTheNth(-exact_exponent);
    rhs.MultiplyBy(guess_mantissa);
    if (exact_exponent > guess_exponent) {
      lhs.ShiftLeft(exact_exponent - guess_exponent);
    } else {
      rhs.ShiftLeft(guess_exponent - exact_exponent);
    }
    comparison = Compare(lhs, rhs);
  }
  if (comparison < 0) {
    return false;
  } else if (comparison > 0) {
    return true;
  } else {
    // When lhs == rhs, the decimal input is exactly between A and B.
    // Round towards even -- round up only if the low bit of the initial
    // `guess_mantissa` was a 1.  We shifted guess_mantissa left 1 bit at
    // the beginning of this function, so test the 2nd bit here.
    return (guess_mantissa & 2) == 2;
  }
}

// Constructs a CalculatedFloat from a given mantissa and exponent, but
// with the following normalizations applied:
//
// If rounding has caused mantissa to increase just past the allowed bit
// width, shift and adjust exponent.
//
// If exponent is too high, sets kOverflow.
//
// If mantissa is zero (representing a non-zero value not representable, even
// as a subnormal), sets kUnderflow.
template <typename FloatType>
CalculatedFloat CalculatedFloatFromRawValues(uint64_t mantissa, int exponent) {
  CalculatedFloat result;
  if (mantissa == uint64_t{1} << FloatTraits<FloatType>::kTargetMantissaBits) {
    mantissa >>= 1;
    exponent += 1;
  }
  if (exponent > FloatTraits<FloatType>::kMaxExponent) {
    result.exponent = kOverflow;
  } else if (mantissa == 0) {
    result.exponent = kUnderflow;
  } else {
    result.exponent = exponent;
    result.mantissa = mantissa;
  }
  return result;
}

template <typename FloatType>
CalculatedFloat CalculateFromParsedHexadecimal(
    const strings_internal::ParsedFloat& parsed_hex) {
  uint64_t mantissa = parsed_hex.mantissa;
  int exponent = parsed_hex.exponent;
  // This static_cast is only needed when using a std::bit_width()
  // implementation that does not have the fix for LWG 3656 applied.
  int mantissa_width = static_cast<int>(bit_width(mantissa));
  const int shift = NormalizedShiftSize<FloatType>(mantissa_width, exponent);
  bool result_exact;
  exponent += shift;
  mantissa = ShiftRightAndRound(mantissa, shift,
                                /* input exact= */ true, &result_exact);
  // ParseFloat handles rounding in the hexadecimal case, so we don't have to
  // check `result_exact` here.
  return CalculatedFloatFromRawValues<FloatType>(mantissa, exponent);
}

template <typename FloatType>
CalculatedFloat CalculateFromParsedDecimal(
    const strings_internal::ParsedFloat& parsed_decimal) {
  CalculatedFloat result;

  // Large or small enough decimal exponents will always result in overflow
  // or underflow.
  if (Power10Underflow(parsed_decimal.exponent)) {
    result.exponent = kUnderflow;
    return result;
  } else if (Power10Overflow(parsed_decimal.exponent)) {
    result.exponent = kOverflow;
    return result;
  }

  // Otherwise convert our power of 10 into a power of 2 times an integer
  // mantissa, and multiply this by our parsed decimal mantissa.
  uint128 wide_binary_mantissa = parsed_decimal.mantissa;
  wide_binary_mantissa *= Power10Mantissa(parsed_decimal.exponent);
  int binary_exponent = Power10Exponent(parsed_decimal.exponent);

  // Discard bits that are inaccurate due to truncation error.  The magic
  // `mantissa_width` constants below are justified in
  // https://abseil.io/about/design/charconv. They represent the number of bits
  // in `wide_binary_mantissa` that are guaranteed to be unaffected by error
  // propagation.
  bool mantissa_exact;
  int mantissa_width;
  if (parsed_decimal.subrange_begin) {
    // Truncated mantissa
    mantissa_width = 58;
    mantissa_exact = false;
    binary_exponent +=
        TruncateToBitWidth(mantissa_width, &wide_binary_mantissa);
  } else if (!Power10Exact(parsed_decimal.exponent)) {
    // Exact mantissa, truncated power of ten
    mantissa_width = 63;
    mantissa_exact = false;
    binary_exponent +=
        TruncateToBitWidth(mantissa_width, &wide_binary_mantissa);
  } else {
    // Product is exact
    mantissa_width = BitWidth(wide_binary_mantissa);
    mantissa_exact = true;
  }

  // Shift into an FloatType-sized mantissa, and round to nearest.
  const int shift =
      NormalizedShiftSize<FloatType>(mantissa_width, binary_exponent);
  bool result_exact;
  binary_exponent += shift;
  uint64_t binary_mantissa = ShiftRightAndRound(wide_binary_mantissa, shift,
                                                mantissa_exact, &result_exact);
  if (!result_exact) {
    // We could not determine the rounding direction using int128 math.  Use
    // full resolution math instead.
    if (MustRoundUp(binary_mantissa, binary_exponent, parsed_decimal)) {
      binary_mantissa += 1;
    }
  }

  return CalculatedFloatFromRawValues<FloatType>(binary_mantissa,
                                                 binary_exponent);
}

// As discussed in https://nigeltao.github.io/blog/2020/eisel-lemire.html the
// primary goal of the Eisel-Lemire algorithm is speed, for 99+% of the cases,
// not 100% coverage. As long as Eisel-Lemire doesn’t claim false positives,
// the combined approach (falling back to an alternative implementation when
// this function returns false) is both fast and correct.
template <typename FloatType>
bool EiselLemire(const strings_internal::ParsedFloat& input, bool negative,
                 y_absl::Nonnull<FloatType*> value,
                 y_absl::Nonnull<std::errc*> ec) {
  uint64_t man = input.mantissa;
  int exp10 = input.exponent;
  if (exp10 < FloatTraits<FloatType>::kEiselLemireMinInclusiveExp10) {
    *value = negative ? -0.0 : 0.0;
    *ec = std::errc::result_out_of_range;
    return true;
  } else if (exp10 >= FloatTraits<FloatType>::kEiselLemireMaxExclusiveExp10) {
    // Return max (a finite value) consistent with from_chars and DR 3081. For
    // SimpleAtod and SimpleAtof, post-processing will return infinity.
    *value = negative ? -std::numeric_limits<FloatType>::max()
                      : std::numeric_limits<FloatType>::max();
    *ec = std::errc::result_out_of_range;
    return true;
  }

  // Assert kPower10TableMinInclusive <= exp10 < kPower10TableMaxExclusive.
  // Equivalently, !Power10Underflow(exp10) and !Power10Overflow(exp10).
  static_assert(
      FloatTraits<FloatType>::kEiselLemireMinInclusiveExp10 >=
          kPower10TableMinInclusive,
      "(exp10-kPower10TableMinInclusive) in kPower10MantissaHighTable bounds");
  static_assert(
      FloatTraits<FloatType>::kEiselLemireMaxExclusiveExp10 <=
          kPower10TableMaxExclusive,
      "(exp10-kPower10TableMinInclusive) in kPower10MantissaHighTable bounds");

  // The terse (+) comments in this function body refer to sections of the
  // https://nigeltao.github.io/blog/2020/eisel-lemire.html blog post.
  //
  // That blog post discusses double precision (11 exponent bits with a -1023
  // bias, 52 mantissa bits), but the same approach applies to single precision
  // (8 exponent bits with a -127 bias, 23 mantissa bits). Either way, the
  // computation here happens with 64-bit values (e.g. man) or 128-bit values
  // (e.g. x) before finally converting to 64- or 32-bit floating point.
  //
  // See also "Number Parsing at a Gigabyte per Second, Software: Practice and
  // Experience 51 (8), 2021" (https://arxiv.org/abs/2101.11408) for detail.

  // (+) Normalization.
  int clz = countl_zero(man);
  man <<= static_cast<unsigned int>(clz);
  // The 217706 etc magic numbers are from the Power10Exponent function.
  uint64_t ret_exp2 =
      static_cast<uint64_t>((217706 * exp10 >> 16) + 64 +
                            FloatTraits<FloatType>::kExponentBias - clz);

  // (+) Multiplication.
  uint128 x = static_cast<uint128>(man) *
              static_cast<uint128>(
                  kPower10MantissaHighTable[exp10 - kPower10TableMinInclusive]);

  // (+) Wider Approximation.
  static constexpr uint64_t high64_mask =
      FloatTraits<FloatType>::kEiselLemireMask;
  if (((Uint128High64(x) & high64_mask) == high64_mask) &&
      (man > (std::numeric_limits<uint64_t>::max() - Uint128Low64(x)))) {
    uint128 y =
        static_cast<uint128>(man) *
        static_cast<uint128>(
            kPower10MantissaLowTable[exp10 - kPower10TableMinInclusive]);
    x += Uint128High64(y);
    // For example, parsing "4503599627370497.5" will take the if-true
    // branch here (for double precision), since:
    //  - x   = 0x8000000000000BFF_FFFFFFFFFFFFFFFF
    //  - y   = 0x8000000000000BFF_7FFFFFFFFFFFF400
    //  - man = 0xA000000000000F00
    // Likewise, when parsing "0.0625" for single precision:
    //  - x   = 0x7FFFFFFFFFFFFFFF_FFFFFFFFFFFFFFFF
    //  - y   = 0x813FFFFFFFFFFFFF_8A00000000000000
    //  - man = 0x9C40000000000000
    if (((Uint128High64(x) & high64_mask) == high64_mask) &&
        ((Uint128Low64(x) + 1) == 0) &&
        (man > (std::numeric_limits<uint64_t>::max() - Uint128Low64(y)))) {
      return false;
    }
  }

  // (+) Shifting to 54 Bits (or for single precision, to 25 bits).
  uint64_t msb = Uint128High64(x) >> 63;
  uint64_t ret_man =
      Uint128High64(x) >> (msb + FloatTraits<FloatType>::kEiselLemireShift);
  ret_exp2 -= 1 ^ msb;

  // (+) Half-way Ambiguity.
  //
  // For example, parsing "1e+23" will take the if-true branch here (for double
  // precision), since:
  //  - x       = 0x54B40B1F852BDA00_0000000000000000
  //  - ret_man = 0x002A5A058FC295ED
  // Likewise, when parsing "20040229.0" for single precision:
  //  - x       = 0x4C72894000000000_0000000000000000
  //  - ret_man = 0x000000000131CA25
  if ((Uint128Low64(x) == 0) && ((Uint128High64(x) & high64_mask) == 0) &&
      ((ret_man & 3) == 1)) {
    return false;
  }

  // (+) From 54 to 53 Bits (or for single precision, from 25 to 24 bits).
  ret_man += ret_man & 1;  // Line From54a.
  ret_man >>= 1;           // Line From54b.
  // Incrementing ret_man (at line From54a) may have overflowed 54 bits (53
  // bits after the right shift by 1 at line From54b), so adjust for that.
  //
  // For example, parsing "9223372036854775807" will take the if-true branch
  // here (for double precision), since:
  //  - ret_man = 0x0020000000000000 = (1 << 53)
  // Likewise, when parsing "2147483647.0" for single precision:
  //  - ret_man = 0x0000000001000000 = (1 << 24)
  if ((ret_man >> FloatTraits<FloatType>::kTargetMantissaBits) > 0) {
    ret_exp2 += 1;
    // Conceptually, we need a "ret_man >>= 1" in this if-block to balance
    // incrementing ret_exp2 in the line immediately above. However, we only
    // get here when line From54a overflowed (after adding a 1), so ret_man
    // here is (1 << 53). Its low 53 bits are therefore all zeroes. The only
    // remaining use of ret_man is to mask it with ((1 << 52) - 1), so only its
    // low 52 bits matter. A "ret_man >>= 1" would have no effect in practice.
    //
    // We omit the "ret_man >>= 1", even if it is cheap (and this if-branch is
    // rarely taken) and technically 'more correct', so that mutation tests
    // that would otherwise modify or omit that "ret_man >>= 1" don't complain
    // that such code mutations have no observable effect.
  }

  // ret_exp2 is a uint64_t. Zero or underflow means that we're in subnormal
  // space. max_exp2 (0x7FF for double precision, 0xFF for single precision) or
  // above means that we're in Inf/NaN space.
  //
  // The if block is equivalent to (but has fewer branches than):
  //   if ((ret_exp2 <= 0) || (ret_exp2 >= max_exp2)) { etc }
  //
  // For example, parsing "4.9406564584124654e-324" will take the if-true
  // branch here, since ret_exp2 = -51.
  static constexpr uint64_t max_exp2 =
      (1 << FloatTraits<FloatType>::kTargetExponentBits) - 1;
  if ((ret_exp2 - 1) >= (max_exp2 - 1)) {
    return false;
  }

#ifndef Y_ABSL_BIT_PACK_FLOATS
  if (FloatTraits<FloatType>::kTargetBits == 64) {
    *value = FloatTraits<FloatType>::Make(
        (ret_man & 0x000FFFFFFFFFFFFFu) | 0x0010000000000000u,
        static_cast<int>(ret_exp2) - 1023 - 52, negative);
    return true;
  } else if (FloatTraits<FloatType>::kTargetBits == 32) {
    *value = FloatTraits<FloatType>::Make(
        (static_cast<uint32_t>(ret_man) & 0x007FFFFFu) | 0x00800000u,
        static_cast<int>(ret_exp2) - 127 - 23, negative);
    return true;
  }
#else
  if (FloatTraits<FloatType>::kTargetBits == 64) {
    uint64_t ret_bits = (ret_exp2 << 52) | (ret_man & 0x000FFFFFFFFFFFFFu);
    if (negative) {
      ret_bits |= 0x8000000000000000u;
    }
    *value = y_absl::bit_cast<double>(ret_bits);
    return true;
  } else if (FloatTraits<FloatType>::kTargetBits == 32) {
    uint32_t ret_bits = (static_cast<uint32_t>(ret_exp2) << 23) |
                        (static_cast<uint32_t>(ret_man) & 0x007FFFFFu);
    if (negative) {
      ret_bits |= 0x80000000u;
    }
    *value = y_absl::bit_cast<float>(ret_bits);
    return true;
  }
#endif  // Y_ABSL_BIT_PACK_FLOATS
  return false;
}

template <typename FloatType>
from_chars_result FromCharsImpl(y_absl::Nonnull<const char*> first,
                                y_absl::Nonnull<const char*> last,
                                FloatType& value, chars_format fmt_flags) {
  from_chars_result result;
  result.ptr = first;  // overwritten on successful parse
  result.ec = std::errc();

  bool negative = false;
  if (first != last && *first == '-') {
    ++first;
    negative = true;
  }
  // If the `hex` flag is *not* set, then we will accept a 0x prefix and try
  // to parse a hexadecimal float.
  if ((fmt_flags & chars_format::hex) == chars_format{} && last - first >= 2 &&
      *first == '0' && (first[1] == 'x' || first[1] == 'X')) {
    const char* hex_first = first + 2;
    strings_internal::ParsedFloat hex_parse =
        strings_internal::ParseFloat<16>(hex_first, last, fmt_flags);
    if (hex_parse.end == nullptr ||
        hex_parse.type != strings_internal::FloatType::kNumber) {
      // Either we failed to parse a hex float after the "0x", or we read
      // "0xinf" or "0xnan" which we don't want to match.
      //
      // However, a string that begins with "0x" also begins with "0", which
      // is normally a valid match for the number zero.  So we want these
      // strings to match zero unless fmt_flags is `scientific`.  (This flag
      // means an exponent is required, which the string "0" does not have.)
      if (fmt_flags == chars_format::scientific) {
        result.ec = std::errc::invalid_argument;
      } else {
        result.ptr = first + 1;
        value = negative ? -0.0 : 0.0;
      }
      return result;
    }
    // We matched a value.
    result.ptr = hex_parse.end;
    if (HandleEdgeCase(hex_parse, negative, &value)) {
      return result;
    }
    CalculatedFloat calculated =
        CalculateFromParsedHexadecimal<FloatType>(hex_parse);
    EncodeResult(calculated, negative, &result, &value);
    return result;
  }
  // Otherwise, we choose the number base based on the flags.
  if ((fmt_flags & chars_format::hex) == chars_format::hex) {
    strings_internal::ParsedFloat hex_parse =
        strings_internal::ParseFloat<16>(first, last, fmt_flags);
    if (hex_parse.end == nullptr) {
      result.ec = std::errc::invalid_argument;
      return result;
    }
    result.ptr = hex_parse.end;
    if (HandleEdgeCase(hex_parse, negative, &value)) {
      return result;
    }
    CalculatedFloat calculated =
        CalculateFromParsedHexadecimal<FloatType>(hex_parse);
    EncodeResult(calculated, negative, &result, &value);
    return result;
  } else {
    strings_internal::ParsedFloat decimal_parse =
        strings_internal::ParseFloat<10>(first, last, fmt_flags);
    if (decimal_parse.end == nullptr) {
      result.ec = std::errc::invalid_argument;
      return result;
    }
    result.ptr = decimal_parse.end;
    if (HandleEdgeCase(decimal_parse, negative, &value)) {
      return result;
    }
    // A nullptr subrange_begin means that the decimal_parse.mantissa is exact
    // (not truncated), a precondition of the Eisel-Lemire algorithm.
    if ((decimal_parse.subrange_begin == nullptr) &&
        EiselLemire<FloatType>(decimal_parse, negative, &value, &result.ec)) {
      return result;
    }
    CalculatedFloat calculated =
        CalculateFromParsedDecimal<FloatType>(decimal_parse);
    EncodeResult(calculated, negative, &result, &value);
    return result;
  }
}
}  // namespace

from_chars_result from_chars(y_absl::Nonnull<const char*> first,
                             y_absl::Nonnull<const char*> last, double& value,
                             chars_format fmt) {
  return FromCharsImpl(first, last, value, fmt);
}

from_chars_result from_chars(y_absl::Nonnull<const char*> first,
                             y_absl::Nonnull<const char*> last, float& value,
                             chars_format fmt) {
  return FromCharsImpl(first, last, value, fmt);
}

namespace {

// Table of powers of 10, from kPower10TableMinInclusive to
// kPower10TableMaxExclusive.
//
// kPower10MantissaHighTable[i - kPower10TableMinInclusive] stores the 64-bit
// mantissa. The high bit is always on.
//
// kPower10MantissaLowTable extends that 64-bit mantissa to 128 bits.
//
// Power10Exponent(i) calculates the power-of-two exponent.
//
// For a number i, this gives the unique mantissaHigh and exponent such that
// (mantissaHigh * 2**exponent) <= 10**i < ((mantissaHigh + 1) * 2**exponent).
//
// For example, Python can confirm that the exact hexadecimal value of 1e60 is:
//    >>> a = 1000000000000000000000000000000000000000000000000000000000000
//    >>> hex(a)
//    '0x9f4f2726179a224501d762422c946590d91000000000000000'
// Adding underscores at every 8th hex digit shows 50 hex digits:
//    '0x9f4f2726_179a2245_01d76242_2c946590_d9100000_00000000_00'.
// In this case, the high bit of the first hex digit, 9, is coincidentally set,
// so we do not have to do further shifting to deduce the 128-bit mantissa:
//   - kPower10MantissaHighTable[60 - kP10TMI] = 0x9f4f2726179a2245U
//   - kPower10MantissaLowTable[ 60 - kP10TMI] = 0x01d762422c946590U
// where kP10TMI is kPower10TableMinInclusive. The low 18 of those 50 hex
// digits are truncated.
//
// 50 hex digits (with the high bit set) is 200 bits and mantissaHigh holds 64
// bits, so Power10Exponent(60) = 200 - 64 = 136. Again, Python can confirm:
//    >>> b = 0x9f4f2726179a2245
//    >>> ((b+0)<<136) <= a
//    True
//    >>> ((b+1)<<136) <= a
//    False
//
// The tables were generated by
// https://github.com/google/wuffs/blob/315b2e52625ebd7b02d8fac13e3cd85ea374fb80/script/print-mpb-powers-of-10.go
// after re-formatting its output into two arrays of N uint64_t values (instead
// of an N element array of uint64_t pairs).

const uint64_t kPower10MantissaHighTable[] = {
    0xeef453d6923bd65aU, 0x9558b4661b6565f8U, 0xbaaee17fa23ebf76U,
    0xe95a99df8ace6f53U, 0x91d8a02bb6c10594U, 0xb64ec836a47146f9U,
    0xe3e27a444d8d98b7U, 0x8e6d8c6ab0787f72U, 0xb208ef855c969f4fU,
    0xde8b2b66b3bc4723U, 0x8b16fb203055ac76U, 0xaddcb9e83c6b1793U,
    0xd953e8624b85dd78U, 0x87d4713d6f33aa6bU, 0xa9c98d8ccb009506U,
    0xd43bf0effdc0ba48U, 0x84a57695fe98746dU, 0xa5ced43b7e3e9188U,
    0xcf42894a5dce35eaU, 0x818995ce7aa0e1b2U, 0xa1ebfb4219491a1fU,
    0xca66fa129f9b60a6U, 0xfd00b897478238d0U, 0x9e20735e8cb16382U,
    0xc5a890362fddbc62U, 0xf712b443bbd52b7bU, 0x9a6bb0aa55653b2dU,
    0xc1069cd4eabe89f8U, 0xf148440a256e2c76U, 0x96cd2a865764dbcaU,
    0xbc807527ed3e12bcU, 0xeba09271e88d976bU, 0x93445b8731587ea3U,
    0xb8157268fdae9e4cU, 0xe61acf033d1a45dfU, 0x8fd0c16206306babU,
    0xb3c4f1ba87bc8696U, 0xe0b62e2929aba83cU, 0x8c71dcd9ba0b4925U,
    0xaf8e5410288e1b6fU, 0xdb71e91432b1a24aU, 0x892731ac9faf056eU,
    0xab70fe17c79ac6caU, 0xd64d3d9db981787dU, 0x85f0468293f0eb4eU,
    0xa76c582338ed2621U, 0xd1476e2c07286faaU, 0x82cca4db847945caU,
    0xa37fce126597973cU, 0xcc5fc196fefd7d0cU, 0xff77b1fcbebcdc4fU,
    0x9faacf3df73609b1U, 0xc795830d75038c1dU, 0xf97ae3d0d2446f25U,
    0x9becce62836ac577U, 0xc2e801fb244576d5U, 0xf3a20279ed56d48aU,
    0x9845418c345644d6U, 0xbe5691ef416bd60cU, 0xedec366b11c6cb8fU,
    0x94b3a202eb1c3f39U, 0xb9e08a83a5e34f07U, 0xe858ad248f5c22c9U,
    0x91376c36d99995beU, 0xb58547448ffffb2dU, 0xe2e69915b3fff9f9U,
    0x8dd01fad907ffc3bU, 0xb1442798f49ffb4aU, 0xdd95317f31c7fa1dU,
    0x8a7d3eef7f1cfc52U, 0xad1c8eab5ee43b66U, 0xd863b256369d4a40U,
    0x873e4f75e2224e68U, 0xa90de3535aaae202U, 0xd3515c2831559a83U,
    0x8412d9991ed58091U, 0xa5178fff668ae0b6U, 0xce5d73ff402d98e3U,
    0x80fa687f881c7f8eU, 0xa139029f6a239f72U, 0xc987434744ac874eU,
    0xfbe9141915d7a922U, 0x9d71ac8fada6c9b5U, 0xc4ce17b399107c22U,
    0xf6019da07f549b2bU, 0x99c102844f94e0fbU, 0xc0314325637a1939U,
    0xf03d93eebc589f88U, 0x96267c7535b763b5U, 0xbbb01b9283253ca2U,
    0xea9c227723ee8bcbU, 0x92a1958a7675175fU, 0xb749faed14125d36U,
    0xe51c79a85916f484U, 0x8f31cc0937ae58d2U, 0xb2fe3f0b8599ef07U,
    0xdfbdcece67006ac9U, 0x8bd6a141006042bdU, 0xaecc49914078536dU,
    0xda7f5bf590966848U, 0x888f99797a5e012dU, 0xaab37fd7d8f58178U,
    0xd5605fcdcf32e1d6U, 0x855c3be0a17fcd26U, 0xa6b34ad8c9dfc06fU,
    0xd0601d8efc57b08bU, 0x823c12795db6ce57U, 0xa2cb1717b52481edU,
    0xcb7ddcdda26da268U, 0xfe5d54150b090b02U, 0x9efa548d26e5a6e1U,
    0xc6b8e9b0709f109aU, 0xf867241c8cc6d4c0U, 0x9b407691d7fc44f8U,
    0xc21094364dfb5636U, 0xf294b943e17a2bc4U, 0x979cf3ca6cec5b5aU,
    0xbd8430bd08277231U, 0xece53cec4a314ebdU, 0x940f4613ae5ed136U,
    0xb913179899f68584U, 0xe757dd7ec07426e5U, 0x9096ea6f3848984fU,
    0xb4bca50b065abe63U, 0xe1ebce4dc7f16dfbU, 0x8d3360f09cf6e4bdU,
    0xb080392cc4349decU, 0xdca04777f541c567U, 0x89e42caaf9491b60U,
    0xac5d37d5b79b6239U, 0xd77485cb25823ac7U, 0x86a8d39ef77164bcU,
    0xa8530886b54dbdebU, 0xd267caa862a12d66U, 0x8380dea93da4bc60U,
    0xa46116538d0deb78U, 0xcd795be870516656U, 0x806bd9714632dff6U,
    0xa086cfcd97bf97f3U, 0xc8a883c0fdaf7df0U, 0xfad2a4b13d1b5d6cU,
    0x9cc3a6eec6311a63U, 0xc3f490aa77bd60fcU, 0xf4f1b4d515acb93bU,
    0x991711052d8bf3c5U, 0xbf5cd54678eef0b6U, 0xef340a98172aace4U,
    0x9580869f0e7aac0eU, 0xbae0a846d2195712U, 0xe998d258869facd7U,
    0x91ff83775423cc06U, 0xb67f6455292cbf08U, 0xe41f3d6a7377eecaU,
    0x8e938662882af53eU, 0xb23867fb2a35b28dU, 0xdec681f9f4c31f31U,
    0x8b3c113c38f9f37eU, 0xae0b158b4738705eU, 0xd98ddaee19068c76U,
    0x87f8a8d4cfa417c9U, 0xa9f6d30a038d1dbcU, 0xd47487cc8470652bU,
    0x84c8d4dfd2c63f3bU, 0xa5fb0a17c777cf09U, 0xcf79cc9db955c2ccU,
    0x81ac1fe293d599bfU, 0xa21727db38cb002fU, 0xca9cf1d206fdc03bU,
    0xfd442e4688bd304aU, 0x9e4a9cec15763e2eU, 0xc5dd44271ad3cdbaU,
    0xf7549530e188c128U, 0x9a94dd3e8cf578b9U, 0xc13a148e3032d6e7U,
    0xf18899b1bc3f8ca1U, 0x96f5600f15a7b7e5U, 0xbcb2b812db11a5deU,
    0xebdf661791d60f56U, 0x936b9fcebb25c995U, 0xb84687c269ef3bfbU,
    0xe65829b3046b0afaU, 0x8ff71a0fe2c2e6dcU, 0xb3f4e093db73a093U,
    0xe0f218b8d25088b8U, 0x8c974f7383725573U, 0xafbd2350644eeacfU,
    0xdbac6c247d62a583U, 0x894bc396ce5da772U, 0xab9eb47c81f5114fU,
    0xd686619ba27255a2U, 0x8613fd0145877585U, 0xa798fc4196e952e7U,
    0xd17f3b51fca3a7a0U, 0x82ef85133de648c4U, 0xa3ab66580d5fdaf5U,
    0xcc963fee10b7d1b3U, 0xffbbcfe994e5c61fU, 0x9fd561f1fd0f9bd3U,
    0xc7caba6e7c5382c8U, 0xf9bd690a1b68637bU, 0x9c1661a651213e2dU,
    0xc31bfa0fe5698db8U, 0xf3e2f893dec3f126U, 0x986ddb5c6b3a76b7U,
    0xbe89523386091465U, 0xee2ba6c0678b597fU, 0x94db483840b717efU,
    0xba121a4650e4ddebU, 0xe896a0d7e51e1566U, 0x915e2486ef32cd60U,
    0xb5b5ada8aaff80b8U, 0xe3231912d5bf60e6U, 0x8df5efabc5979c8fU,
    0xb1736b96b6fd83b3U, 0xddd0467c64bce4a0U, 0x8aa22c0dbef60ee4U,
    0xad4ab7112eb3929dU, 0xd89d64d57a607744U, 0x87625f056c7c4a8bU,
    0xa93af6c6c79b5d2dU, 0xd389b47879823479U, 0x843610cb4bf160cbU,
    0xa54394fe1eedb8feU, 0xce947a3da6a9273eU, 0x811ccc668829b887U,
    0xa163ff802a3426a8U, 0xc9bcff6034c13052U, 0xfc2c3f3841f17c67U,
    0x9d9ba7832936edc0U, 0xc5029163f384a931U, 0xf64335bcf065d37dU,
    0x99ea0196163fa42eU, 0xc06481fb9bcf8d39U, 0xf07da27a82c37088U,
    0x964e858c91ba2655U, 0xbbe226efb628afeaU, 0xeadab0aba3b2dbe5U,
    0x92c8ae6b464fc96fU, 0xb77ada0617e3bbcbU, 0xe55990879ddcaabdU,
    0x8f57fa54c2a9eab6U, 0xb32df8e9f3546564U, 0xdff9772470297ebdU,
    0x8bfbea76c619ef36U, 0xaefae51477a06b03U, 0xdab99e59958885c4U,
    0x88b402f7fd75539bU, 0xaae103b5fcd2a881U, 0xd59944a37c0752a2U,
    0x857fcae62d8493a5U, 0xa6dfbd9fb8e5b88eU, 0xd097ad07a71f26b2U,
    0x825ecc24c873782fU, 0xa2f67f2dfa90563bU, 0xcbb41ef979346bcaU,
    0xfea126b7d78186bcU, 0x9f24b832e6b0f436U, 0xc6ede63fa05d3143U,
    0xf8a95fcf88747d94U, 0x9b69dbe1b548ce7cU, 0xc24452da229b021bU,
    0xf2d56790ab41c2a2U, 0x97c560ba6b0919a5U, 0xbdb6b8e905cb600fU,
    0xed246723473e3813U, 0x9436c0760c86e30bU, 0xb94470938fa89bceU,
    0xe7958cb87392c2c2U, 0x90bd77f3483bb9b9U, 0xb4ecd5f01a4aa828U,
    0xe2280b6c20dd5232U, 0x8d590723948a535fU, 0xb0af48ec79ace837U,
    0xdcdb1b2798182244U, 0x8a08f0f8bf0f156bU, 0xac8b2d36eed2dac5U,
    0xd7adf884aa879177U, 0x86ccbb52ea94baeaU, 0xa87fea27a539e9a5U,
    0xd29fe4b18e88640eU, 0x83a3eeeef9153e89U, 0xa48ceaaab75a8e2bU,
    0xcdb02555653131b6U, 0x808e17555f3ebf11U, 0xa0b19d2ab70e6ed6U,
    0xc8de047564d20a8bU, 0xfb158592be068d2eU, 0x9ced737bb6c4183dU,
    0xc428d05aa4751e4cU, 0xf53304714d9265dfU, 0x993fe2c6d07b7fabU,
    0xbf8fdb78849a5f96U, 0xef73d256a5c0f77cU, 0x95a8637627989aadU,
    0xbb127c53b17ec159U, 0xe9d71b689dde71afU, 0x9226712162ab070dU,
    0xb6b00d69bb55c8d1U, 0xe45c10c42a2b3b05U, 0x8eb98a7a9a5b04e3U,
    0xb267ed1940f1c61cU, 0xdf01e85f912e37a3U, 0x8b61313bbabce2c6U,
    0xae397d8aa96c1b77U, 0xd9c7dced53c72255U, 0x881cea14545c7575U,
    0xaa242499697392d2U, 0xd4ad2dbfc3d07787U, 0x84ec3c97da624ab4U,
    0xa6274bbdd0fadd61U, 0xcfb11ead453994baU, 0x81ceb32c4b43fcf4U,
    0xa2425ff75e14fc31U, 0xcad2f7f5359a3b3eU, 0xfd87b5f28300ca0dU,
    0x9e74d1b791e07e48U, 0xc612062576589ddaU, 0xf79687aed3eec551U,
    0x9abe14cd44753b52U, 0xc16d9a0095928a27U, 0xf1c90080baf72cb1U,
    0x971da05074da7beeU, 0xbce5086492111aeaU, 0xec1e4a7db69561a5U,
    0x9392ee8e921d5d07U, 0xb877aa3236a4b449U, 0xe69594bec44de15bU,
    0x901d7cf73ab0acd9U, 0xb424dc35095cd80fU, 0xe12e13424bb40e13U,
    0x8cbccc096f5088cbU, 0xafebff0bcb24aafeU, 0xdbe6fecebdedd5beU,
    0x89705f4136b4a597U, 0xabcc77118461cefcU, 0xd6bf94d5e57a42bcU,
    0x8637bd05af6c69b5U, 0xa7c5ac471b478423U, 0xd1b71758e219652bU,
    0x83126e978d4fdf3bU, 0xa3d70a3d70a3d70aU, 0xccccccccccccccccU,
    0x8000000000000000U, 0xa000000000000000U, 0xc800000000000000U,
    0xfa00000000000000U, 0x9c40000000000000U, 0xc350000000000000U,
    0xf424000000000000U, 0x9896800000000000U, 0xbebc200000000000U,
    0xee6b280000000000U, 0x9502f90000000000U, 0xba43b74000000000U,
    0xe8d4a51000000000U, 0x9184e72a00000000U, 0xb5e620f480000000U,
    0xe35fa931a0000000U, 0x8e1bc9bf04000000U, 0xb1a2bc2ec5000000U,
    0xde0b6b3a76400000U, 0x8ac7230489e80000U, 0xad78ebc5ac620000U,
    0xd8d726b7177a8000U, 0x878678326eac9000U, 0xa968163f0a57b400U,
    0xd3c21bcecceda100U, 0x84595161401484a0U, 0xa56fa5b99019a5c8U,
    0xcecb8f27f4200f3aU, 0x813f3978f8940984U, 0xa18f07d736b90be5U,
    0xc9f2c9cd04674edeU, 0xfc6f7c4045812296U, 0x9dc5ada82b70b59dU,
    0xc5371912364ce305U, 0xf684df56c3e01bc6U, 0x9a130b963a6c115cU,
    0xc097ce7bc90715b3U, 0xf0bdc21abb48db20U, 0x96769950b50d88f4U,
    0xbc143fa4e250eb31U, 0xeb194f8e1ae525fdU, 0x92efd1b8d0cf37beU,
    0xb7abc627050305adU, 0xe596b7b0c643c719U, 0x8f7e32ce7bea5c6fU,
    0xb35dbf821ae4f38bU, 0xe0352f62a19e306eU, 0x8c213d9da502de45U,
    0xaf298d050e4395d6U, 0xdaf3f04651d47b4cU, 0x88d8762bf324cd0fU,
    0xab0e93b6efee0053U, 0xd5d238a4abe98068U, 0x85a36366eb71f041U,
    0xa70c3c40a64e6c51U, 0xd0cf4b50cfe20765U, 0x82818f1281ed449fU,
    0xa321f2d7226895c7U, 0xcbea6f8ceb02bb39U, 0xfee50b7025c36a08U,
    0x9f4f2726179a2245U, 0xc722f0ef9d80aad6U, 0xf8ebad2b84e0d58bU,
    0x9b934c3b330c8577U, 0xc2781f49ffcfa6d5U, 0xf316271c7fc3908aU,
    0x97edd871cfda3a56U, 0xbde94e8e43d0c8ecU, 0xed63a231d4c4fb27U,
    0x945e455f24fb1cf8U, 0xb975d6b6ee39e436U, 0xe7d34c64a9c85d44U,
    0x90e40fbeea1d3a4aU, 0xb51d13aea4a488ddU, 0xe264589a4dcdab14U,
    0x8d7eb76070a08aecU, 0xb0de65388cc8ada8U, 0xdd15fe86affad912U,
    0x8a2dbf142dfcc7abU, 0xacb92ed9397bf996U, 0xd7e77a8f87daf7fbU,
    0x86f0ac99b4e8dafdU, 0xa8acd7c0222311bcU, 0xd2d80db02aabd62bU,
    0x83c7088e1aab65dbU, 0xa4b8cab1a1563f52U, 0xcde6fd5e09abcf26U,
    0x80b05e5ac60b6178U, 0xa0dc75f1778e39d6U, 0xc913936dd571c84cU,
    0xfb5878494ace3a5fU, 0x9d174b2dcec0e47bU, 0xc45d1df942711d9aU,
    0xf5746577930d6500U, 0x9968bf6abbe85f20U, 0xbfc2ef456ae276e8U,
    0xefb3ab16c59b14a2U, 0x95d04aee3b80ece5U, 0xbb445da9ca61281fU,
    0xea1575143cf97226U, 0x924d692ca61be758U, 0xb6e0c377cfa2e12eU,
    0xe498f455c38b997aU, 0x8edf98b59a373fecU, 0xb2977ee300c50fe7U,
    0xdf3d5e9bc0f653e1U, 0x8b865b215899f46cU, 0xae67f1e9aec07187U,
    0xda01ee641a708de9U, 0x884134fe908658b2U, 0xaa51823e34a7eedeU,
    0xd4e5e2cdc1d1ea96U, 0x850fadc09923329eU, 0xa6539930bf6bff45U,
    0xcfe87f7cef46ff16U, 0x81f14fae158c5f6eU, 0xa26da3999aef7749U,
    0xcb090c8001ab551cU, 0xfdcb4fa002162a63U, 0x9e9f11c4014dda7eU,
    0xc646d63501a1511dU, 0xf7d88bc24209a565U, 0x9ae757596946075fU,
    0xc1a12d2fc3978937U, 0xf209787bb47d6b84U, 0x9745eb4d50ce6332U,
    0xbd176620a501fbffU, 0xec5d3fa8ce427affU, 0x93ba47c980e98cdfU,
    0xb8a8d9bbe123f017U, 0xe6d3102ad96cec1dU, 0x9043ea1ac7e41392U,
    0xb454e4a179dd1877U, 0xe16a1dc9d8545e94U, 0x8ce2529e2734bb1dU,
    0xb01ae745b101e9e4U, 0xdc21a1171d42645dU, 0x899504ae72497ebaU,
    0xabfa45da0edbde69U, 0xd6f8d7509292d603U, 0x865b86925b9bc5c2U,
    0xa7f26836f282b732U, 0xd1ef0244af2364ffU, 0x8335616aed761f1fU,
    0xa402b9c5a8d3a6e7U, 0xcd036837130890a1U, 0x802221226be55a64U,
    0xa02aa96b06deb0fdU, 0xc83553c5c8965d3dU, 0xfa42a8b73abbf48cU,
    0x9c69a97284b578d7U, 0xc38413cf25e2d70dU, 0xf46518c2ef5b8cd1U,
    0x98bf2f79d5993802U, 0xbeeefb584aff8603U, 0xeeaaba2e5dbf6784U,
    0x952ab45cfa97a0b2U, 0xba756174393d88dfU, 0xe912b9d1478ceb17U,
    0x91abb422ccb812eeU, 0xb616a12b7fe617aaU, 0xe39c49765fdf9d94U,
    0x8e41ade9fbebc27dU, 0xb1d219647ae6b31cU, 0xde469fbd99a05fe3U,
    0x8aec23d680043beeU, 0xada72ccc20054ae9U, 0xd910f7ff28069da4U,
    0x87aa9aff79042286U, 0xa99541bf57452b28U, 0xd3fa922f2d1675f2U,
    0x847c9b5d7c2e09b7U, 0xa59bc234db398c25U, 0xcf02b2c21207ef2eU,
    0x8161afb94b44f57dU, 0xa1ba1ba79e1632dcU, 0xca28a291859bbf93U,
    0xfcb2cb35e702af78U, 0x9defbf01b061adabU, 0xc56baec21c7a1916U,
    0xf6c69a72a3989f5bU, 0x9a3c2087a63f6399U, 0xc0cb28a98fcf3c7fU,
    0xf0fdf2d3f3c30b9fU, 0x969eb7c47859e743U, 0xbc4665b596706114U,
    0xeb57ff22fc0c7959U, 0x9316ff75dd87cbd8U, 0xb7dcbf5354e9beceU,
    0xe5d3ef282a242e81U, 0x8fa475791a569d10U, 0xb38d92d760ec4455U,
    0xe070f78d3927556aU, 0x8c469ab843b89562U, 0xaf58416654a6babbU,
    0xdb2e51bfe9d0696aU, 0x88fcf317f22241e2U, 0xab3c2fddeeaad25aU,
    0xd60b3bd56a5586f1U, 0x85c7056562757456U, 0xa738c6bebb12d16cU,
    0xd106f86e69d785c7U, 0x82a45b450226b39cU, 0xa34d721642b06084U,
    0xcc20ce9bd35c78a5U, 0xff290242c83396ceU, 0x9f79a169bd203e41U,
    0xc75809c42c684dd1U, 0xf92e0c3537826145U, 0x9bbcc7a142b17ccbU,
    0xc2abf989935ddbfeU, 0xf356f7ebf83552feU, 0x98165af37b2153deU,
    0xbe1bf1b059e9a8d6U, 0xeda2ee1c7064130cU, 0x9485d4d1c63e8be7U,
    0xb9a74a0637ce2ee1U, 0xe8111c87c5c1ba99U, 0x910ab1d4db9914a0U,
    0xb54d5e4a127f59c8U, 0xe2a0b5dc971f303aU, 0x8da471a9de737e24U,
    0xb10d8e1456105dadU, 0xdd50f1996b947518U, 0x8a5296ffe33cc92fU,
    0xace73cbfdc0bfb7bU, 0xd8210befd30efa5aU, 0x8714a775e3e95c78U,
    0xa8d9d1535ce3b396U, 0xd31045a8341ca07cU, 0x83ea2b892091e44dU,
    0xa4e4b66b68b65d60U, 0xce1de40642e3f4b9U, 0x80d2ae83e9ce78f3U,
    0xa1075a24e4421730U, 0xc94930ae1d529cfcU, 0xfb9b7cd9a4a7443cU,
    0x9d412e0806e88aa5U, 0xc491798a08a2ad4eU, 0xf5b5d7ec8acb58a2U,
    0x9991a6f3d6bf1765U, 0xbff610b0cc6edd3fU, 0xeff394dcff8a948eU,
    0x95f83d0a1fb69cd9U, 0xbb764c4ca7a4440fU, 0xea53df5fd18d5513U,
    0x92746b9be2f8552cU, 0xb7118682dbb66a77U, 0xe4d5e82392a40515U,
    0x8f05b1163ba6832dU, 0xb2c71d5bca9023f8U, 0xdf78e4b2bd342cf6U,
    0x8bab8eefb6409c1aU, 0xae9672aba3d0c320U, 0xda3c0f568cc4f3e8U,
    0x8865899617fb1871U, 0xaa7eebfb9df9de8dU, 0xd51ea6fa85785631U,
    0x8533285c936b35deU, 0xa67ff273b8460356U, 0xd01fef10a657842cU,
    0x8213f56a67f6b29bU, 0xa298f2c501f45f42U, 0xcb3f2f7642717713U,
    0xfe0efb53d30dd4d7U, 0x9ec95d1463e8a506U, 0xc67bb4597ce2ce48U,
    0xf81aa16fdc1b81daU, 0x9b10a4e5e9913128U, 0xc1d4ce1f63f57d72U,
    0xf24a01a73cf2dccfU, 0x976e41088617ca01U, 0xbd49d14aa79dbc82U,
    0xec9c459d51852ba2U, 0x93e1ab8252f33b45U, 0xb8da1662e7b00a17U,
    0xe7109bfba19c0c9dU, 0x906a617d450187e2U, 0xb484f9dc9641e9daU,
    0xe1a63853bbd26451U, 0x8d07e33455637eb2U, 0xb049dc016abc5e5fU,
    0xdc5c5301c56b75f7U, 0x89b9b3e11b6329baU, 0xac2820d9623bf429U,
    0xd732290fbacaf133U, 0x867f59a9d4bed6c0U, 0xa81f301449ee8c70U,
    0xd226fc195c6a2f8cU, 0x83585d8fd9c25db7U, 0xa42e74f3d032f525U,
    0xcd3a1230c43fb26fU, 0x80444b5e7aa7cf85U, 0xa0555e361951c366U,
    0xc86ab5c39fa63440U, 0xfa856334878fc150U, 0x9c935e00d4b9d8d2U,
    0xc3b8358109e84f07U, 0xf4a642e14c6262c8U, 0x98e7e9cccfbd7dbdU,
    0xbf21e44003acdd2cU, 0xeeea5d5004981478U, 0x95527a5202df0ccbU,
    0xbaa718e68396cffdU, 0xe950df20247c83fdU, 0x91d28b7416cdd27eU,
    0xb6472e511c81471dU, 0xe3d8f9e563a198e5U, 0x8e679c2f5e44ff8fU,
};

const uint64_t kPower10MantissaLowTable[] = {
    0x113faa2906a13b3fU, 0x4ac7ca59a424c507U, 0x5d79bcf00d2df649U,
    0xf4d82c2c107973dcU, 0x79071b9b8a4be869U, 0x9748e2826cdee284U,
    0xfd1b1b2308169b25U, 0xfe30f0f5e50e20f7U, 0xbdbd2d335e51a935U,
    0xad2c788035e61382U, 0x4c3bcb5021afcc31U, 0xdf4abe242a1bbf3dU,
    0xd71d6dad34a2af0dU, 0x8672648c40e5ad68U, 0x680efdaf511f18c2U,
    0x0212bd1b2566def2U, 0x014bb630f7604b57U, 0x419ea3bd35385e2dU,
    0x52064cac828675b9U, 0x7343efebd1940993U, 0x1014ebe6c5f90bf8U,
    0xd41a26e077774ef6U, 0x8920b098955522b4U, 0x55b46e5f5d5535b0U,
    0xeb2189f734aa831dU, 0xa5e9ec7501d523e4U, 0x47b233c92125366eU,
    0x999ec0bb696e840aU, 0xc00670ea43ca250dU, 0x380406926a5e5728U,
    0xc605083704f5ecf2U, 0xf7864a44c633682eU, 0x7ab3ee6afbe0211dU,
    0x5960ea05bad82964U, 0x6fb92487298e33bdU, 0xa5d3b6d479f8e056U,
    0x8f48a4899877186cU, 0x331acdabfe94de87U, 0x9ff0c08b7f1d0b14U,
    0x07ecf0ae5ee44dd9U, 0xc9e82cd9f69d6150U, 0xbe311c083a225cd2U,
    0x6dbd630a48aaf406U, 0x092cbbccdad5b108U, 0x25bbf56008c58ea5U,
    0xaf2af2b80af6f24eU, 0x1af5af660db4aee1U, 0x50d98d9fc890ed4dU,
    0xe50ff107bab528a0U, 0x1e53ed49a96272c8U, 0x25e8e89c13bb0f7aU,
    0x77b191618c54e9acU, 0xd59df5b9ef6a2417U, 0x4b0573286b44ad1dU,
    0x4ee367f9430aec32U, 0x229c41f793cda73fU, 0x6b43527578c1110fU,
    0x830a13896b78aaa9U, 0x23cc986bc656d553U, 0x2cbfbe86b7ec8aa8U,
    0x7bf7d71432f3d6a9U, 0xdaf5ccd93fb0cc53U, 0xd1b3400f8f9cff68U,
    0x23100809b9c21fa1U, 0xabd40a0c2832a78aU, 0x16c90c8f323f516cU,
    0xae3da7d97f6792e3U, 0x99cd11cfdf41779cU, 0x40405643d711d583U,
    0x482835ea666b2572U, 0xda3243650005eecfU, 0x90bed43e40076a82U,
    0x5a7744a6e804a291U, 0x711515d0a205cb36U, 0x0d5a5b44ca873e03U,
    0xe858790afe9486c2U, 0x626e974dbe39a872U, 0xfb0a3d212dc8128fU,
    0x7ce66634bc9d0b99U, 0x1c1fffc1ebc44e80U, 0xa327ffb266b56220U,
    0x4bf1ff9f0062baa8U, 0x6f773fc3603db4a9U, 0xcb550fb4384d21d3U,
    0x7e2a53a146606a48U, 0x2eda7444cbfc426dU, 0xfa911155fefb5308U,
    0x793555ab7eba27caU, 0x4bc1558b2f3458deU, 0x9eb1aaedfb016f16U,
    0x465e15a979c1cadcU, 0x0bfacd89ec191ec9U, 0xcef980ec671f667bU,
    0x82b7e12780e7401aU, 0xd1b2ecb8b0908810U, 0x861fa7e6dcb4aa15U,
    0x67a791e093e1d49aU, 0xe0c8bb2c5c6d24e0U, 0x58fae9f773886e18U,
    0xaf39a475506a899eU, 0x6d8406c952429603U, 0xc8e5087ba6d33b83U,
    0xfb1e4a9a90880a64U, 0x5cf2eea09a55067fU, 0xf42faa48c0ea481eU,
    0xf13b94daf124da26U, 0x76c53d08d6b70858U, 0x54768c4b0c64ca6eU,
    0xa9942f5dcf7dfd09U, 0xd3f93b35435d7c4cU, 0xc47bc5014a1a6dafU,
    0x359ab6419ca1091bU, 0xc30163d203c94b62U, 0x79e0de63425dcf1dU,
    0x985915fc12f542e4U, 0x3e6f5b7b17b2939dU, 0xa705992ceecf9c42U,
    0x50c6ff782a838353U, 0xa4f8bf5635246428U, 0x871b7795e136be99U,
    0x28e2557b59846e3fU, 0x331aeada2fe589cfU, 0x3ff0d2c85def7621U,
    0x0fed077a756b53a9U, 0xd3e8495912c62894U, 0x64712dd7abbbd95cU,
    0xbd8d794d96aacfb3U, 0xecf0d7a0fc5583a0U, 0xf41686c49db57244U,
    0x311c2875c522ced5U, 0x7d633293366b828bU, 0xae5dff9c02033197U,
    0xd9f57f830283fdfcU, 0xd072df63c324fd7bU, 0x4247cb9e59f71e6dU,
    0x52d9be85f074e608U, 0x67902e276c921f8bU, 0x00ba1cd8a3db53b6U,
    0x80e8a40eccd228a4U, 0x6122cd128006b2cdU, 0x796b805720085f81U,
    0xcbe3303674053bb0U, 0xbedbfc4411068a9cU, 0xee92fb5515482d44U,
    0x751bdd152d4d1c4aU, 0xd262d45a78a0635dU, 0x86fb897116c87c34U,
    0xd45d35e6ae3d4da0U, 0x8974836059cca109U, 0x2bd1a438703fc94bU,
    0x7b6306a34627ddcfU, 0x1a3bc84c17b1d542U, 0x20caba5f1d9e4a93U,
    0x547eb47b7282ee9cU, 0xe99e619a4f23aa43U, 0x6405fa00e2ec94d4U,
    0xde83bc408dd3dd04U, 0x9624ab50b148d445U, 0x3badd624dd9b0957U,
    0xe54ca5d70a80e5d6U, 0x5e9fcf4ccd211f4cU, 0x7647c3200069671fU,
    0x29ecd9f40041e073U, 0xf468107100525890U, 0x7182148d4066eeb4U,
    0xc6f14cd848405530U, 0xb8ada00e5a506a7cU, 0xa6d90811f0e4851cU,
    0x908f4a166d1da663U, 0x9a598e4e043287feU, 0x40eff1e1853f29fdU,
    0xd12bee59e68ef47cU, 0x82bb74f8301958ceU, 0xe36a52363c1faf01U,
    0xdc44e6c3cb279ac1U, 0x29ab103a5ef8c0b9U, 0x7415d448f6b6f0e7U,
    0x111b495b3464ad21U, 0xcab10dd900beec34U, 0x3d5d514f40eea742U,
    0x0cb4a5a3112a5112U, 0x47f0e785eaba72abU, 0x59ed216765690f56U,
    0x306869c13ec3532cU, 0x1e414218c73a13fbU, 0xe5d1929ef90898faU,
    0xdf45f746b74abf39U, 0x6b8bba8c328eb783U, 0x066ea92f3f326564U,
    0xc80a537b0efefebdU, 0xbd06742ce95f5f36U, 0x2c48113823b73704U,
    0xf75a15862ca504c5U, 0x9a984d73dbe722fbU, 0xc13e60d0d2e0ebbaU,
    0x318df905079926a8U, 0xfdf17746497f7052U, 0xfeb6ea8bedefa633U,
    0xfe64a52ee96b8fc0U, 0x3dfdce7aa3c673b0U, 0x06bea10ca65c084eU,
    0x486e494fcff30a62U, 0x5a89dba3c3efccfaU, 0xf89629465a75e01cU,
    0xf6bbb397f1135823U, 0x746aa07ded582e2cU, 0xa8c2a44eb4571cdcU,
    0x92f34d62616ce413U, 0x77b020baf9c81d17U, 0x0ace1474dc1d122eU,
    0x0d819992132456baU, 0x10e1fff697ed6c69U, 0xca8d3ffa1ef463c1U,
    0xbd308ff8a6b17cb2U, 0xac7cb3f6d05ddbdeU, 0x6bcdf07a423aa96bU,
    0x86c16c98d2c953c6U, 0xe871c7bf077ba8b7U, 0x11471cd764ad4972U,
    0xd598e40d3dd89bcfU, 0x4aff1d108d4ec2c3U, 0xcedf722a585139baU,
    0xc2974eb4ee658828U, 0x733d226229feea32U, 0x0806357d5a3f525fU,
    0xca07c2dcb0cf26f7U, 0xfc89b393dd02f0b5U, 0xbbac2078d443ace2U,
    0xd54b944b84aa4c0dU, 0x0a9e795e65d4df11U, 0x4d4617b5ff4a16d5U,
    0x504bced1bf8e4e45U, 0xe45ec2862f71e1d6U, 0x5d767327bb4e5a4cU,
    0x3a6a07f8d510f86fU, 0x890489f70a55368bU, 0x2b45ac74ccea842eU,
    0x3b0b8bc90012929dU, 0x09ce6ebb40173744U, 0xcc420a6a101d0515U,
    0x9fa946824a12232dU, 0x47939822dc96abf9U, 0x59787e2b93bc56f7U,
    0x57eb4edb3c55b65aU, 0xede622920b6b23f1U, 0xe95fab368e45ecedU,
    0x11dbcb0218ebb414U, 0xd652bdc29f26a119U, 0x4be76d3346f0495fU,
    0x6f70a4400c562ddbU, 0xcb4ccd500f6bb952U, 0x7e2000a41346a7a7U,
    0x8ed400668c0c28c8U, 0x728900802f0f32faU, 0x4f2b40a03ad2ffb9U,
    0xe2f610c84987bfa8U, 0x0dd9ca7d2df4d7c9U, 0x91503d1c79720dbbU,
    0x75a44c6397ce912aU, 0xc986afbe3ee11abaU, 0xfbe85badce996168U,
    0xfae27299423fb9c3U, 0xdccd879fc967d41aU, 0x5400e987bbc1c920U,
    0x290123e9aab23b68U, 0xf9a0b6720aaf6521U, 0xf808e40e8d5b3e69U,
    0xb60b1d1230b20e04U, 0xb1c6f22b5e6f48c2U, 0x1e38aeb6360b1af3U,
    0x25c6da63c38de1b0U, 0x579c487e5a38ad0eU, 0x2d835a9df0c6d851U,
    0xf8e431456cf88e65U, 0x1b8e9ecb641b58ffU, 0xe272467e3d222f3fU,
    0x5b0ed81dcc6abb0fU, 0x98e947129fc2b4e9U, 0x3f2398d747b36224U,
    0x8eec7f0d19a03aadU, 0x1953cf68300424acU, 0x5fa8c3423c052dd7U,
    0x3792f412cb06794dU, 0xe2bbd88bbee40bd0U, 0x5b6aceaeae9d0ec4U,
    0xf245825a5a445275U, 0xeed6e2f0f0d56712U, 0x55464dd69685606bU,
    0xaa97e14c3c26b886U, 0xd53dd99f4b3066a8U, 0xe546a8038efe4029U,
    0xde98520472bdd033U, 0x963e66858f6d4440U, 0xdde7001379a44aa8U,
    0x5560c018580d5d52U, 0xaab8f01e6e10b4a6U, 0xcab3961304ca70e8U,
    0x3d607b97c5fd0d22U, 0x8cb89a7db77c506aU, 0x77f3608e92adb242U,
    0x55f038b237591ed3U, 0x6b6c46dec52f6688U, 0x2323ac4b3b3da015U,
    0xabec975e0a0d081aU, 0x96e7bd358c904a21U, 0x7e50d64177da2e54U,
    0xdde50bd1d5d0b9e9U, 0x955e4ec64b44e864U, 0xbd5af13bef0b113eU,
    0xecb1ad8aeacdd58eU, 0x67de18eda5814af2U, 0x80eacf948770ced7U,
    0xa1258379a94d028dU, 0x096ee45813a04330U, 0x8bca9d6e188853fcU,
    0x775ea264cf55347dU, 0x95364afe032a819dU, 0x3a83ddbd83f52204U,
    0xc4926a9672793542U, 0x75b7053c0f178293U, 0x5324c68b12dd6338U,
    0xd3f6fc16ebca5e03U, 0x88f4bb1ca6bcf584U, 0x2b31e9e3d06c32e5U,
    0x3aff322e62439fcfU, 0x09befeb9fad487c2U, 0x4c2ebe687989a9b3U,
    0x0f9d37014bf60a10U, 0x538484c19ef38c94U, 0x2865a5f206b06fb9U,
    0xf93f87b7442e45d3U, 0xf78f69a51539d748U, 0xb573440e5a884d1bU,
    0x31680a88f8953030U, 0xfdc20d2b36ba7c3dU, 0x3d32907604691b4cU,
    0xa63f9a49c2c1b10fU, 0x0fcf80dc33721d53U, 0xd3c36113404ea4a8U,
    0x645a1cac083126e9U, 0x3d70a3d70a3d70a3U, 0xccccccccccccccccU,
    0x0000000000000000U, 0x0000000000000000U, 0x0000000000000000U,
    0x0000000000000000U, 0x0000000000000000U, 0x0000000000000000U,
    0x0000000000000000U, 0x0000000000000000U, 0x0000000000000000U,
    0x0000000000000000U, 0x0000000000000000U, 0x0000000000000000U,
    0x0000000000000000U, 0x0000000000000000U, 0x0000000000000000U,
    0x0000000000000000U, 0x0000000000000000U, 0x0000000000000000U,
    0x0000000000000000U, 0x0000000000000000U, 0x0000000000000000U,
    0x0000000000000000U, 0x0000000000000000U, 0x0000000000000000U,
    0x0000000000000000U, 0x0000000000000000U, 0x0000000000000000U,
    0x0000000000000000U, 0x4000000000000000U, 0x5000000000000000U,
    0xa400000000000000U, 0x4d00000000000000U, 0xf020000000000000U,
    0x6c28000000000000U, 0xc732000000000000U, 0x3c7f400000000000U,
    0x4b9f100000000000U, 0x1e86d40000000000U, 0x1314448000000000U,
    0x17d955a000000000U, 0x5dcfab0800000000U, 0x5aa1cae500000000U,
    0xf14a3d9e40000000U, 0x6d9ccd05d0000000U, 0xe4820023a2000000U,
    0xdda2802c8a800000U, 0xd50b2037ad200000U, 0x4526f422cc340000U,
    0x9670b12b7f410000U, 0x3c0cdd765f114000U, 0xa5880a69fb6ac800U,
    0x8eea0d047a457a00U, 0x72a4904598d6d880U, 0x47a6da2b7f864750U,
    0x999090b65f67d924U, 0xfff4b4e3f741cf6dU, 0xbff8f10e7a8921a4U,
    0xaff72d52192b6a0dU, 0x9bf4f8a69f764490U, 0x02f236d04753d5b4U,
    0x01d762422c946590U, 0x424d3ad2b7b97ef5U, 0xd2e0898765a7deb2U,
    0x63cc55f49f88eb2fU, 0x3cbf6b71c76b25fbU, 0x8bef464e3945ef7aU,
    0x97758bf0e3cbb5acU, 0x3d52eeed1cbea317U, 0x4ca7aaa863ee4bddU,
    0x8fe8caa93e74ef6aU, 0xb3e2fd538e122b44U, 0x60dbbca87196b616U,
    0xbc8955e946fe31cdU, 0x6babab6398bdbe41U, 0xc696963c7eed2dd1U,
    0xfc1e1de5cf543ca2U, 0x3b25a55f43294bcbU, 0x49ef0eb713f39ebeU,
    0x6e3569326c784337U, 0x49c2c37f07965404U, 0xdc33745ec97be906U,
    0x69a028bb3ded71a3U, 0xc40832ea0d68ce0cU, 0xf50a3fa490c30190U,
    0x792667c6da79e0faU, 0x577001b891185938U, 0xed4c0226b55e6f86U,
    0x544f8158315b05b4U, 0x696361ae3db1c721U, 0x03bc3a19cd1e38e9U,
    0x04ab48a04065c723U, 0x62eb0d64283f9c76U, 0x3ba5d0bd324f8394U,
    0xca8f44ec7ee36479U, 0x7e998b13cf4e1ecbU, 0x9e3fedd8c321a67eU,
    0xc5cfe94ef3ea101eU, 0xbba1f1d158724a12U, 0x2a8a6e45ae8edc97U,
    0xf52d09d71a3293bdU, 0x593c2626705f9c56U, 0x6f8b2fb00c77836cU,
    0x0b6dfb9c0f956447U, 0x4724bd4189bd5eacU, 0x58edec91ec2cb657U,
    0x2f2967b66737e3edU, 0xbd79e0d20082ee74U, 0xecd8590680a3aa11U,
    0xe80e6f4820cc9495U, 0x3109058d147fdcddU, 0xbd4b46f0599fd415U,
    0x6c9e18ac7007c91aU, 0x03e2cf6bc604ddb0U, 0x84db8346b786151cU,
    0xe612641865679a63U, 0x4fcb7e8f3f60c07eU, 0xe3be5e330f38f09dU,
    0x5cadf5bfd3072cc5U, 0x73d9732fc7c8f7f6U, 0x2867e7fddcdd9afaU,
    0xb281e1fd541501b8U, 0x1f225a7ca91a4226U, 0x3375788de9b06958U,
    0x0052d6b1641c83aeU, 0xc0678c5dbd23a49aU, 0xf840b7ba963646e0U,
    0xb650e5a93bc3d898U, 0xa3e51f138ab4cebeU, 0xc66f336c36b10137U,
    0xb80b0047445d4184U, 0xa60dc059157491e5U, 0x87c89837ad68db2fU,
    0x29babe4598c311fbU, 0xf4296dd6fef3d67aU, 0x1899e4a65f58660cU,
    0x5ec05dcff72e7f8fU, 0x76707543f4fa1f73U, 0x6a06494a791c53a8U,
    0x0487db9d17636892U, 0x45a9d2845d3c42b6U, 0x0b8a2392ba45a9b2U,
    0x8e6cac7768d7141eU, 0x3207d795430cd926U, 0x7f44e6bd49e807b8U,
    0x5f16206c9c6209a6U, 0x36dba887c37a8c0fU, 0xc2494954da2c9789U,
    0xf2db9baa10b7bd6cU, 0x6f92829494e5acc7U, 0xcb772339ba1f17f9U,
    0xff2a760414536efbU, 0xfef5138519684abaU, 0x7eb258665fc25d69U,
    0xef2f773ffbd97a61U, 0xaafb550ffacfd8faU, 0x95ba2a53f983cf38U,
    0xdd945a747bf26183U, 0x94f971119aeef9e4U, 0x7a37cd5601aab85dU,
    0xac62e055c10ab33aU, 0x577b986b314d6009U, 0xed5a7e85fda0b80bU,
    0x14588f13be847307U, 0x596eb2d8ae258fc8U, 0x6fca5f8ed9aef3bbU,
    0x25de7bb9480d5854U, 0xaf561aa79a10ae6aU, 0x1b2ba1518094da04U,
    0x90fb44d2f05d0842U, 0x353a1607ac744a53U, 0x42889b8997915ce8U,
    0x69956135febada11U, 0x43fab9837e699095U, 0x94f967e45e03f4bbU,
    0x1d1be0eebac278f5U, 0x6462d92a69731732U, 0x7d7b8f7503cfdcfeU,
    0x5cda735244c3d43eU, 0x3a0888136afa64a7U, 0x088aaa1845b8fdd0U,
    0x8aad549e57273d45U, 0x36ac54e2f678864bU, 0x84576a1bb416a7ddU,
    0x656d44a2a11c51d5U, 0x9f644ae5a4b1b325U, 0x873d5d9f0dde1feeU,
    0xa90cb506d155a7eaU, 0x09a7f12442d588f2U, 0x0c11ed6d538aeb2fU,
    0x8f1668c8a86da5faU, 0xf96e017d694487bcU, 0x37c981dcc395a9acU,
    0x85bbe253f47b1417U, 0x93956d7478ccec8eU, 0x387ac8d1970027b2U,
    0x06997b05fcc0319eU, 0x441fece3bdf81f03U, 0xd527e81cad7626c3U,
    0x8a71e223d8d3b074U, 0xf6872d5667844e49U, 0xb428f8ac016561dbU,
    0xe13336d701beba52U, 0xecc0024661173473U, 0x27f002d7f95d0190U,
    0x31ec038df7b441f4U, 0x7e67047175a15271U, 0x0f0062c6e984d386U,
    0x52c07b78a3e60868U, 0xa7709a56ccdf8a82U, 0x88a66076400bb691U,
    0x6acff893d00ea435U, 0x0583f6b8c4124d43U, 0xc3727a337a8b704aU,
    0x744f18c0592e4c5cU, 0x1162def06f79df73U, 0x8addcb5645ac2ba8U,
    0x6d953e2bd7173692U, 0xc8fa8db6ccdd0437U, 0x1d9c9892400a22a2U,
    0x2503beb6d00cab4bU, 0x2e44ae64840fd61dU, 0x5ceaecfed289e5d2U,
    0x7425a83e872c5f47U, 0xd12f124e28f77719U, 0x82bd6b70d99aaa6fU,
    0x636cc64d1001550bU, 0x3c47f7e05401aa4eU, 0x65acfaec34810a71U,
    0x7f1839a741a14d0dU, 0x1ede48111209a050U, 0x934aed0aab460432U,
    0xf81da84d5617853fU, 0x36251260ab9d668eU, 0xc1d72b7c6b426019U,
    0xb24cf65b8612f81fU, 0xdee033f26797b627U, 0x169840ef017da3b1U,
    0x8e1f289560ee864eU, 0xf1a6f2bab92a27e2U, 0xae10af696774b1dbU,
    0xacca6da1e0a8ef29U, 0x17fd090a58d32af3U, 0xddfc4b4cef07f5b0U,
    0x4abdaf101564f98eU, 0x9d6d1ad41abe37f1U, 0x84c86189216dc5edU,
    0x32fd3cf5b4e49bb4U, 0x3fbc8c33221dc2a1U, 0x0fabaf3feaa5334aU,
    0x29cb4d87f2a7400eU, 0x743e20e9ef511012U, 0x914da9246b255416U,
    0x1ad089b6c2f7548eU, 0xa184ac2473b529b1U, 0xc9e5d72d90a2741eU,
    0x7e2fa67c7a658892U, 0xddbb901b98feeab7U, 0x552a74227f3ea565U,
    0xd53a88958f87275fU, 0x8a892abaf368f137U, 0x2d2b7569b0432d85U,
    0x9c3b29620e29fc73U, 0x8349f3ba91b47b8fU, 0x241c70a936219a73U,
    0xed238cd383aa0110U, 0xf4363804324a40aaU, 0xb143c6053edcd0d5U,
    0xdd94b7868e94050aU, 0xca7cf2b4191c8326U, 0xfd1c2f611f63a3f0U,
    0xbc633b39673c8cecU, 0xd5be0503e085d813U, 0x4b2d8644d8a74e18U,
    0xddf8e7d60ed1219eU, 0xcabb90e5c942b503U, 0x3d6a751f3b936243U,
    0x0cc512670a783ad4U, 0x27fb2b80668b24c5U, 0xb1f9f660802dedf6U,
    0x5e7873f8a0396973U, 0xdb0b487b6423e1e8U, 0x91ce1a9a3d2cda62U,
    0x7641a140cc7810fbU, 0xa9e904c87fcb0a9dU, 0x546345fa9fbdcd44U,
    0xa97c177947ad4095U, 0x49ed8eabcccc485dU, 0x5c68f256bfff5a74U,
    0x73832eec6fff3111U, 0xc831fd53c5ff7eabU, 0xba3e7ca8b77f5e55U,
    0x28ce1bd2e55f35ebU, 0x7980d163cf5b81b3U, 0xd7e105bcc332621fU,
    0x8dd9472bf3fefaa7U, 0xb14f98f6f0feb951U, 0x6ed1bf9a569f33d3U,
    0x0a862f80ec4700c8U, 0xcd27bb612758c0faU, 0x8038d51cb897789cU,
    0xe0470a63e6bd56c3U, 0x1858ccfce06cac74U, 0x0f37801e0c43ebc8U,
    0xd30560258f54e6baU, 0x47c6b82ef32a2069U, 0x4cdc331d57fa5441U,
    0xe0133fe4adf8e952U, 0x58180fddd97723a6U, 0x570f09eaa7ea7648U,
};

}  // namespace
Y_ABSL_NAMESPACE_END
}  // namespace y_absl