summaryrefslogtreecommitdiff
path: root/absl/strings/numbers.cc
blob: 48dca919c02abe57019a24787a943a1090aa8aab (plain)
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
// Copyright 2017 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
//
//      http://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.

// This file contains std::string processing functions related to
// numeric values.

#include "absl/strings/numbers.h"

#include <algorithm>
#include <cassert>
#include <cfloat>          // for DBL_DIG and FLT_DIG
#include <cmath>           // for HUGE_VAL
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <iterator>
#include <limits>
#include <memory>
#include <utility>

#include "absl/base/internal/raw_logging.h"
#include "absl/strings/ascii.h"
#include "absl/strings/charconv.h"
#include "absl/strings/internal/bits.h"
#include "absl/strings/internal/memutil.h"
#include "absl/strings/str_cat.h"

namespace absl {
inline namespace lts_2018_06_20 {

bool SimpleAtof(absl::string_view str, float* value) {
  *value = 0.0;
  str = StripAsciiWhitespace(str);
  if (!str.empty() && str[0] == '+') {
    str.remove_prefix(1);
  }
  auto result = absl::from_chars(str.data(), str.data() + str.size(), *value);
  if (result.ec == std::errc::invalid_argument) {
    return false;
  }
  if (result.ptr != str.data() + str.size()) {
    // not all non-whitespace characters consumed
    return false;
  }
  // from_chars() with DR 3801's current wording will return max() on
  // overflow.  SimpleAtof returns infinity instead.
  if (result.ec == std::errc::result_out_of_range) {
    if (*value > 1.0) {
      *value = std::numeric_limits<float>::infinity();
    } else if (*value < -1.0) {
      *value = -std::numeric_limits<float>::infinity();
    }
  }
  return true;
}

bool SimpleAtod(absl::string_view str, double* value) {
  *value = 0.0;
  str = StripAsciiWhitespace(str);
  if (!str.empty() && str[0] == '+') {
    str.remove_prefix(1);
  }
  auto result = absl::from_chars(str.data(), str.data() + str.size(), *value);
  if (result.ec == std::errc::invalid_argument) {
    return false;
  }
  if (result.ptr != str.data() + str.size()) {
    // not all non-whitespace characters consumed
    return false;
  }
  // from_chars() with DR 3801's current wording will return max() on
  // overflow.  SimpleAtod returns infinity instead.
  if (result.ec == std::errc::result_out_of_range) {
    if (*value > 1.0) {
      *value = std::numeric_limits<double>::infinity();
    } else if (*value < -1.0) {
      *value = -std::numeric_limits<double>::infinity();
    }
  }
  return true;
}

namespace {

// TODO(rogeeff): replace with the real released thing once we figure out what
// it is.
inline bool CaseEqual(absl::string_view piece1, absl::string_view piece2) {
  return (piece1.size() == piece2.size() &&
          0 == strings_internal::memcasecmp(piece1.data(), piece2.data(),
                                            piece1.size()));
}

// Writes a two-character representation of 'i' to 'buf'. 'i' must be in the
// range 0 <= i < 100, and buf must have space for two characters. Example:
//   char buf[2];
//   PutTwoDigits(42, buf);
//   // buf[0] == '4'
//   // buf[1] == '2'
inline void PutTwoDigits(size_t i, char* buf) {
  static const char two_ASCII_digits[100][2] = {
    {'0', '0'}, {'0', '1'}, {'0', '2'}, {'0', '3'}, {'0', '4'},
    {'0', '5'}, {'0', '6'}, {'0', '7'}, {'0', '8'}, {'0', '9'},
    {'1', '0'}, {'1', '1'}, {'1', '2'}, {'1', '3'}, {'1', '4'},
    {'1', '5'}, {'1', '6'}, {'1', '7'}, {'1', '8'}, {'1', '9'},
    {'2', '0'}, {'2', '1'}, {'2', '2'}, {'2', '3'}, {'2', '4'},
    {'2', '5'}, {'2', '6'}, {'2', '7'}, {'2', '8'}, {'2', '9'},
    {'3', '0'}, {'3', '1'}, {'3', '2'}, {'3', '3'}, {'3', '4'},
    {'3', '5'}, {'3', '6'}, {'3', '7'}, {'3', '8'}, {'3', '9'},
    {'4', '0'}, {'4', '1'}, {'4', '2'}, {'4', '3'}, {'4', '4'},
    {'4', '5'}, {'4', '6'}, {'4', '7'}, {'4', '8'}, {'4', '9'},
    {'5', '0'}, {'5', '1'}, {'5', '2'}, {'5', '3'}, {'5', '4'},
    {'5', '5'}, {'5', '6'}, {'5', '7'}, {'5', '8'}, {'5', '9'},
    {'6', '0'}, {'6', '1'}, {'6', '2'}, {'6', '3'}, {'6', '4'},
    {'6', '5'}, {'6', '6'}, {'6', '7'}, {'6', '8'}, {'6', '9'},
    {'7', '0'}, {'7', '1'}, {'7', '2'}, {'7', '3'}, {'7', '4'},
    {'7', '5'}, {'7', '6'}, {'7', '7'}, {'7', '8'}, {'7', '9'},
    {'8', '0'}, {'8', '1'}, {'8', '2'}, {'8', '3'}, {'8', '4'},
    {'8', '5'}, {'8', '6'}, {'8', '7'}, {'8', '8'}, {'8', '9'},
    {'9', '0'}, {'9', '1'}, {'9', '2'}, {'9', '3'}, {'9', '4'},
    {'9', '5'}, {'9', '6'}, {'9', '7'}, {'9', '8'}, {'9', '9'}
  };
  assert(i < 100);
  memcpy(buf, two_ASCII_digits[i], 2);
}

}  // namespace

bool SimpleAtob(absl::string_view str, bool* value) {
  ABSL_RAW_CHECK(value != nullptr, "Output pointer must not be nullptr.");
  if (CaseEqual(str, "true") || CaseEqual(str, "t") ||
      CaseEqual(str, "yes") || CaseEqual(str, "y") ||
      CaseEqual(str, "1")) {
    *value = true;
    return true;
  }
  if (CaseEqual(str, "false") || CaseEqual(str, "f") ||
      CaseEqual(str, "no") || CaseEqual(str, "n") ||
      CaseEqual(str, "0")) {
    *value = false;
    return true;
  }
  return false;
}

// ----------------------------------------------------------------------
// FastIntToBuffer() overloads
//
// Like the Fast*ToBuffer() functions above, these are intended for speed.
// Unlike the Fast*ToBuffer() functions, however, these functions write
// their output to the beginning of the buffer.  The caller is responsible
// for ensuring that the buffer has enough space to hold the output.
//
// Returns a pointer to the end of the std::string (i.e. the null character
// terminating the std::string).
// ----------------------------------------------------------------------

namespace {

// Used to optimize printing a decimal number's final digit.
const char one_ASCII_final_digits[10][2] {
  {'0', 0}, {'1', 0}, {'2', 0}, {'3', 0}, {'4', 0},
  {'5', 0}, {'6', 0}, {'7', 0}, {'8', 0}, {'9', 0},
};

}  // namespace

char* numbers_internal::FastIntToBuffer(uint32_t i, char* buffer) {
  uint32_t digits;
  // The idea of this implementation is to trim the number of divides to as few
  // as possible, and also reducing memory stores and branches, by going in
  // steps of two digits at a time rather than one whenever possible.
  // The huge-number case is first, in the hopes that the compiler will output
  // that case in one branch-free block of code, and only output conditional
  // branches into it from below.
  if (i >= 1000000000) {     // >= 1,000,000,000
    digits = i / 100000000;  //      100,000,000
    i -= digits * 100000000;
    PutTwoDigits(digits, buffer);
    buffer += 2;
  lt100_000_000:
    digits = i / 1000000;  // 1,000,000
    i -= digits * 1000000;
    PutTwoDigits(digits, buffer);
    buffer += 2;
  lt1_000_000:
    digits = i / 10000;  // 10,000
    i -= digits * 10000;
    PutTwoDigits(digits, buffer);
    buffer += 2;
  lt10_000:
    digits = i / 100;
    i -= digits * 100;
    PutTwoDigits(digits, buffer);
    buffer += 2;
 lt100:
    digits = i;
    PutTwoDigits(digits, buffer);
    buffer += 2;
    *buffer = 0;
    return buffer;
  }

  if (i < 100) {
    digits = i;
    if (i >= 10) goto lt100;
    memcpy(buffer, one_ASCII_final_digits[i], 2);
    return buffer + 1;
  }
  if (i < 10000) {  //    10,000
    if (i >= 1000) goto lt10_000;
    digits = i / 100;
    i -= digits * 100;
    *buffer++ = '0' + digits;
    goto lt100;
  }
  if (i < 1000000) {  //    1,000,000
    if (i >= 100000) goto lt1_000_000;
    digits = i / 10000;  //    10,000
    i -= digits * 10000;
    *buffer++ = '0' + digits;
    goto lt10_000;
  }
  if (i < 100000000) {  //    100,000,000
    if (i >= 10000000) goto lt100_000_000;
    digits = i / 1000000;  //   1,000,000
    i -= digits * 1000000;
    *buffer++ = '0' + digits;
    goto lt1_000_000;
  }
  // we already know that i < 1,000,000,000
  digits = i / 100000000;  //   100,000,000
  i -= digits * 100000000;
  *buffer++ = '0' + digits;
  goto lt100_000_000;
}

char* numbers_internal::FastIntToBuffer(int32_t i, char* buffer) {
  uint32_t u = i;
  if (i < 0) {
    *buffer++ = '-';
    // We need to do the negation in modular (i.e., "unsigned")
    // arithmetic; MSVC++ apprently warns for plain "-u", so
    // we write the equivalent expression "0 - u" instead.
    u = 0 - u;
  }
  return numbers_internal::FastIntToBuffer(u, buffer);
}

char* numbers_internal::FastIntToBuffer(uint64_t i, char* buffer) {
  uint32_t u32 = static_cast<uint32_t>(i);
  if (u32 == i) return numbers_internal::FastIntToBuffer(u32, buffer);

  // Here we know i has at least 10 decimal digits.
  uint64_t top_1to11 = i / 1000000000;
  u32 = static_cast<uint32_t>(i - top_1to11 * 1000000000);
  uint32_t top_1to11_32 = static_cast<uint32_t>(top_1to11);

  if (top_1to11_32 == top_1to11) {
    buffer = numbers_internal::FastIntToBuffer(top_1to11_32, buffer);
  } else {
    // top_1to11 has more than 32 bits too; print it in two steps.
    uint32_t top_8to9 = static_cast<uint32_t>(top_1to11 / 100);
    uint32_t mid_2 = static_cast<uint32_t>(top_1to11 - top_8to9 * 100);
    buffer = numbers_internal::FastIntToBuffer(top_8to9, buffer);
    PutTwoDigits(mid_2, buffer);
    buffer += 2;
  }

  // We have only 9 digits now, again the maximum uint32_t can handle fully.
  uint32_t digits = u32 / 10000000;  // 10,000,000
  u32 -= digits * 10000000;
  PutTwoDigits(digits, buffer);
  buffer += 2;
  digits = u32 / 100000;  // 100,000
  u32 -= digits * 100000;
  PutTwoDigits(digits, buffer);
  buffer += 2;
  digits = u32 / 1000;  // 1,000
  u32 -= digits * 1000;
  PutTwoDigits(digits, buffer);
  buffer += 2;
  digits = u32 / 10;
  u32 -= digits * 10;
  PutTwoDigits(digits, buffer);
  buffer += 2;
  memcpy(buffer, one_ASCII_final_digits[u32], 2);
  return buffer + 1;
}

char* numbers_internal::FastIntToBuffer(int64_t i, char* buffer) {
  uint64_t u = i;
  if (i < 0) {
    *buffer++ = '-';
    u = 0 - u;
  }
  return numbers_internal::FastIntToBuffer(u, buffer);
}

// Given a 128-bit number expressed as a pair of uint64_t, high half first,
// return that number multiplied by the given 32-bit value.  If the result is
// too large to fit in a 128-bit number, divide it by 2 until it fits.
static std::pair<uint64_t, uint64_t> Mul32(std::pair<uint64_t, uint64_t> num,
                                           uint32_t mul) {
  uint64_t bits0_31 = num.second & 0xFFFFFFFF;
  uint64_t bits32_63 = num.second >> 32;
  uint64_t bits64_95 = num.first & 0xFFFFFFFF;
  uint64_t bits96_127 = num.first >> 32;

  // The picture so far: each of these 64-bit values has only the lower 32 bits
  // filled in.
  // bits96_127:          [ 00000000 xxxxxxxx ]
  // bits64_95:                    [ 00000000 xxxxxxxx ]
  // bits32_63:                             [ 00000000 xxxxxxxx ]
  // bits0_31:                                       [ 00000000 xxxxxxxx ]

  bits0_31 *= mul;
  bits32_63 *= mul;
  bits64_95 *= mul;
  bits96_127 *= mul;

  // Now the top halves may also have value, though all 64 of their bits will
  // never be set at the same time, since they are a result of a 32x32 bit
  // multiply.  This makes the carry calculation slightly easier.
  // bits96_127:          [ mmmmmmmm | mmmmmmmm ]
  // bits64_95:                    [ | mmmmmmmm mmmmmmmm | ]
  // bits32_63:                      |        [ mmmmmmmm | mmmmmmmm ]
  // bits0_31:                       |                 [ | mmmmmmmm mmmmmmmm ]
  // eventually:        [ bits128_up | ...bits64_127.... | ..bits0_63... ]

  uint64_t bits0_63 = bits0_31 + (bits32_63 << 32);
  uint64_t bits64_127 = bits64_95 + (bits96_127 << 32) + (bits32_63 >> 32) +
                        (bits0_63 < bits0_31);
  uint64_t bits128_up = (bits96_127 >> 32) + (bits64_127 < bits64_95);
  if (bits128_up == 0) return {bits64_127, bits0_63};

  int shift = 64 - strings_internal::CountLeadingZeros64(bits128_up);
  uint64_t lo = (bits0_63 >> shift) + (bits64_127 << (64 - shift));
  uint64_t hi = (bits64_127 >> shift) + (bits128_up << (64 - shift));
  return {hi, lo};
}

// Compute num * 5 ^ expfive, and return the first 128 bits of the result,
// where the first bit is always a one.  So PowFive(1, 0) starts 0b100000,
// PowFive(1, 1) starts 0b101000, PowFive(1, 2) starts 0b110010, etc.
static std::pair<uint64_t, uint64_t> PowFive(uint64_t num, int expfive) {
  std::pair<uint64_t, uint64_t> result = {num, 0};
  while (expfive >= 13) {
    // 5^13 is the highest power of five that will fit in a 32-bit integer.
    result = Mul32(result, 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5);
    expfive -= 13;
  }
  constexpr int powers_of_five[13] = {
      1,
      5,
      5 * 5,
      5 * 5 * 5,
      5 * 5 * 5 * 5,
      5 * 5 * 5 * 5 * 5,
      5 * 5 * 5 * 5 * 5 * 5,
      5 * 5 * 5 * 5 * 5 * 5 * 5,
      5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
      5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
      5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
      5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
      5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5};
  result = Mul32(result, powers_of_five[expfive & 15]);
  int shift = strings_internal::CountLeadingZeros64(result.first);
  if (shift != 0) {
    result.first = (result.first << shift) + (result.second >> (64 - shift));
    result.second = (result.second << shift);
  }
  return result;
}

struct ExpDigits {
  int32_t exponent;
  char digits[6];
};

// SplitToSix converts value, a positive double-precision floating-point number,
// into a base-10 exponent and 6 ASCII digits, where the first digit is never
// zero.  For example, SplitToSix(1) returns an exponent of zero and a digits
// array of {'1', '0', '0', '0', '0', '0'}.  If value is exactly halfway between
// two possible representations, e.g. value = 100000.5, then "round to even" is
// performed.
static ExpDigits SplitToSix(const double value) {
  ExpDigits exp_dig;
  int exp = 5;
  double d = value;
  // First step: calculate a close approximation of the output, where the
  // value d will be between 100,000 and 999,999, representing the digits
  // in the output ASCII array, and exp is the base-10 exponent.  It would be
  // faster to use a table here, and to look up the base-2 exponent of value,
  // however value is an IEEE-754 64-bit number, so the table would have 2,000
  // entries, which is not cache-friendly.
  if (d >= 999999.5) {
    if (d >= 1e+261) exp += 256, d *= 1e-256;
    if (d >= 1e+133) exp += 128, d *= 1e-128;
    if (d >= 1e+69) exp += 64, d *= 1e-64;
    if (d >= 1e+37) exp += 32, d *= 1e-32;
    if (d >= 1e+21) exp += 16, d *= 1e-16;
    if (d >= 1e+13) exp += 8, d *= 1e-8;
    if (d >= 1e+9) exp += 4, d *= 1e-4;
    if (d >= 1e+7) exp += 2, d *= 1e-2;
    if (d >= 1e+6) exp += 1, d *= 1e-1;
  } else {
    if (d < 1e-250) exp -= 256, d *= 1e256;
    if (d < 1e-122) exp -= 128, d *= 1e128;
    if (d < 1e-58) exp -= 64, d *= 1e64;
    if (d < 1e-26) exp -= 32, d *= 1e32;
    if (d < 1e-10) exp -= 16, d *= 1e16;
    if (d < 1e-2) exp -= 8, d *= 1e8;
    if (d < 1e+2) exp -= 4, d *= 1e4;
    if (d < 1e+4) exp -= 2, d *= 1e2;
    if (d < 1e+5) exp -= 1, d *= 1e1;
  }
  // At this point, d is in the range [99999.5..999999.5) and exp is in the
  // range [-324..308]. Since we need to round d up, we want to add a half
  // and truncate.
  // However, the technique above may have lost some precision, due to its
  // repeated multiplication by constants that each may be off by half a bit
  // of precision.  This only matters if we're close to the edge though.
  // Since we'd like to know if the fractional part of d is close to a half,
  // we multiply it by 65536 and see if the fractional part is close to 32768.
  // (The number doesn't have to be a power of two,but powers of two are faster)
  uint64_t d64k = d * 65536;
  int dddddd;  // A 6-digit decimal integer.
  if ((d64k % 65536) == 32767 || (d64k % 65536) == 32768) {
    // OK, it's fairly likely that precision was lost above, which is
    // not a surprise given only 52 mantissa bits are available.  Therefore
    // redo the calculation using 128-bit numbers.  (64 bits are not enough).

    // Start out with digits rounded down; maybe add one below.
    dddddd = static_cast<int>(d64k / 65536);

    // mantissa is a 64-bit integer representing M.mmm... * 2^63.  The actual
    // value we're representing, of course, is M.mmm... * 2^exp2.
    int exp2;
    double m = std::frexp(value, &exp2);
    uint64_t mantissa = m * (32768.0 * 65536.0 * 65536.0 * 65536.0);
    // std::frexp returns an m value in the range [0.5, 1.0), however we
    // can't multiply it by 2^64 and convert to an integer because some FPUs
    // throw an exception when converting an number higher than 2^63 into an
    // integer - even an unsigned 64-bit integer!  Fortunately it doesn't matter
    // since m only has 52 significant bits anyway.
    mantissa <<= 1;
    exp2 -= 64;  // not needed, but nice for debugging

    // OK, we are here to compare:
    //     (dddddd + 0.5) * 10^(exp-5)  vs.  mantissa * 2^exp2
    // so we can round up dddddd if appropriate.  Those values span the full
    // range of 600 orders of magnitude of IEE 64-bit floating-point.
    // Fortunately, we already know they are very close, so we don't need to
    // track the base-2 exponent of both sides.  This greatly simplifies the
    // the math since the 2^exp2 calculation is unnecessary and the power-of-10
    // calculation can become a power-of-5 instead.

    std::pair<uint64_t, uint64_t> edge, val;
    if (exp >= 6) {
      // Compare (dddddd + 0.5) * 5 ^ (exp - 5) to mantissa
      // Since we're tossing powers of two, 2 * dddddd + 1 is the
      // same as dddddd + 0.5
      edge = PowFive(2 * dddddd + 1, exp - 5);

      val.first = mantissa;
      val.second = 0;
    } else {
      // We can't compare (dddddd + 0.5) * 5 ^ (exp - 5) to mantissa as we did
      // above because (exp - 5) is negative.  So we compare (dddddd + 0.5) to
      // mantissa * 5 ^ (5 - exp)
      edge = PowFive(2 * dddddd + 1, 0);

      val = PowFive(mantissa, 5 - exp);
    }
    // printf("exp=%d %016lx %016lx vs %016lx %016lx\n", exp, val.first,
    //        val.second, edge.first, edge.second);
    if (val > edge) {
      dddddd++;
    } else if (val == edge) {
      dddddd += (dddddd & 1);
    }
  } else {
    // Here, we are not close to the edge.
    dddddd = static_cast<int>((d64k + 32768) / 65536);
  }
  if (dddddd == 1000000) {
    dddddd = 100000;
    exp += 1;
  }
  exp_dig.exponent = exp;

  int two_digits = dddddd / 10000;
  dddddd -= two_digits * 10000;
  PutTwoDigits(two_digits, &exp_dig.digits[0]);

  two_digits = dddddd / 100;
  dddddd -= two_digits * 100;
  PutTwoDigits(two_digits, &exp_dig.digits[2]);

  PutTwoDigits(dddddd, &exp_dig.digits[4]);
  return exp_dig;
}

// Helper function for fast formatting of floating-point.
// The result is the same as "%g", a.k.a. "%.6g".
size_t numbers_internal::SixDigitsToBuffer(double d, char* const buffer) {
  static_assert(std::numeric_limits<float>::is_iec559,
                "IEEE-754/IEC-559 support only");

  char* out = buffer;  // we write data to out, incrementing as we go, but
                       // FloatToBuffer always returns the address of the buffer
                       // passed in.

  if (std::isnan(d)) {
    strcpy(out, "nan");  // NOLINT(runtime/printf)
    return 3;
  }
  if (d == 0) {  // +0 and -0 are handled here
    if (std::signbit(d)) *out++ = '-';
    *out++ = '0';
    *out = 0;
    return out - buffer;
  }
  if (d < 0) {
    *out++ = '-';
    d = -d;
  }
  if (std::isinf(d)) {
    strcpy(out, "inf");  // NOLINT(runtime/printf)
    return out + 3 - buffer;
  }

  auto exp_dig = SplitToSix(d);
  int exp = exp_dig.exponent;
  const char* digits = exp_dig.digits;
  out[0] = '0';
  out[1] = '.';
  switch (exp) {
    case 5:
      memcpy(out, &digits[0], 6), out += 6;
      *out = 0;
      return out - buffer;
    case 4:
      memcpy(out, &digits[0], 5), out += 5;
      if (digits[5] != '0') {
        *out++ = '.';
        *out++ = digits[5];
      }
      *out = 0;
      return out - buffer;
    case 3:
      memcpy(out, &digits[0], 4), out += 4;
      if ((digits[5] | digits[4]) != '0') {
        *out++ = '.';
        *out++ = digits[4];
        if (digits[5] != '0') *out++ = digits[5];
      }
      *out = 0;
      return out - buffer;
    case 2:
      memcpy(out, &digits[0], 3), out += 3;
      *out++ = '.';
      memcpy(out, &digits[3], 3);
      out += 3;
      while (out[-1] == '0') --out;
      if (out[-1] == '.') --out;
      *out = 0;
      return out - buffer;
    case 1:
      memcpy(out, &digits[0], 2), out += 2;
      *out++ = '.';
      memcpy(out, &digits[2], 4);
      out += 4;
      while (out[-1] == '0') --out;
      if (out[-1] == '.') --out;
      *out = 0;
      return out - buffer;
    case 0:
      memcpy(out, &digits[0], 1), out += 1;
      *out++ = '.';
      memcpy(out, &digits[1], 5);
      out += 5;
      while (out[-1] == '0') --out;
      if (out[-1] == '.') --out;
      *out = 0;
      return out - buffer;
    case -4:
      out[2] = '0';
      ++out;
      ABSL_FALLTHROUGH_INTENDED;
    case -3:
      out[2] = '0';
      ++out;
      ABSL_FALLTHROUGH_INTENDED;
    case -2:
      out[2] = '0';
      ++out;
      ABSL_FALLTHROUGH_INTENDED;
    case -1:
      out += 2;
      memcpy(out, &digits[0], 6);
      out += 6;
      while (out[-1] == '0') --out;
      *out = 0;
      return out - buffer;
  }
  assert(exp < -4 || exp >= 6);
  out[0] = digits[0];
  assert(out[1] == '.');
  out += 2;
  memcpy(out, &digits[1], 5), out += 5;
  while (out[-1] == '0') --out;
  if (out[-1] == '.') --out;
  *out++ = 'e';
  if (exp > 0) {
    *out++ = '+';
  } else {
    *out++ = '-';
    exp = -exp;
  }
  if (exp > 99) {
    int dig1 = exp / 100;
    exp -= dig1 * 100;
    *out++ = '0' + dig1;
  }
  PutTwoDigits(exp, out);
  out += 2;
  *out = 0;
  return out - buffer;
}

namespace {
// Represents integer values of digits.
// Uses 36 to indicate an invalid character since we support
// bases up to 36.
static const int8_t kAsciiToInt[256] = {
    36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36,  // 16 36s.
    36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36,
    36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 0,  1,  2,  3,  4,  5,
    6,  7,  8,  9,  36, 36, 36, 36, 36, 36, 36, 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,
    36, 36, 36, 36, 36, 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, 36, 36, 36, 36, 36, 36,
    36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36,
    36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36,
    36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36,
    36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36,
    36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36,
    36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36,
    36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36};

// Parse the sign and optional hex or oct prefix in text.
inline bool safe_parse_sign_and_base(absl::string_view* text /*inout*/,
                                     int* base_ptr /*inout*/,
                                     bool* negative_ptr /*output*/) {
  if (text->data() == nullptr) {
    return false;
  }

  const char* start = text->data();
  const char* end = start + text->size();
  int base = *base_ptr;

  // Consume whitespace.
  while (start < end && absl::ascii_isspace(start[0])) {
    ++start;
  }
  while (start < end && absl::ascii_isspace(end[-1])) {
    --end;
  }
  if (start >= end) {
    return false;
  }

  // Consume sign.
  *negative_ptr = (start[0] == '-');
  if (*negative_ptr || start[0] == '+') {
    ++start;
    if (start >= end) {
      return false;
    }
  }

  // Consume base-dependent prefix.
  //  base 0: "0x" -> base 16, "0" -> base 8, default -> base 10
  //  base 16: "0x" -> base 16
  // Also validate the base.
  if (base == 0) {
    if (end - start >= 2 && start[0] == '0' &&
        (start[1] == 'x' || start[1] == 'X')) {
      base = 16;
      start += 2;
      if (start >= end) {
        // "0x" with no digits after is invalid.
        return false;
      }
    } else if (end - start >= 1 && start[0] == '0') {
      base = 8;
      start += 1;
    } else {
      base = 10;
    }
  } else if (base == 16) {
    if (end - start >= 2 && start[0] == '0' &&
        (start[1] == 'x' || start[1] == 'X')) {
      start += 2;
      if (start >= end) {
        // "0x" with no digits after is invalid.
        return false;
      }
    }
  } else if (base >= 2 && base <= 36) {
    // okay
  } else {
    return false;
  }
  *text = absl::string_view(start, end - start);
  *base_ptr = base;
  return true;
}

// Consume digits.
//
// The classic loop:
//
//   for each digit
//     value = value * base + digit
//   value *= sign
//
// The classic loop needs overflow checking.  It also fails on the most
// negative integer, -2147483648 in 32-bit two's complement representation.
//
// My improved loop:
//
//  if (!negative)
//    for each digit
//      value = value * base
//      value = value + digit
//  else
//    for each digit
//      value = value * base
//      value = value - digit
//
// Overflow checking becomes simple.

// Lookup tables per IntType:
// vmax/base and vmin/base are precomputed because division costs at least 8ns.
// TODO(junyer): Doing this per base instead (i.e. an array of structs, not a
// struct of arrays) would probably be better in terms of d-cache for the most
// commonly used bases.
template <typename IntType>
struct LookupTables {
  static const IntType kVmaxOverBase[];
  static const IntType kVminOverBase[];
};

// An array initializer macro for X/base where base in [0, 36].
// However, note that lookups for base in [0, 1] should never happen because
// base has been validated to be in [2, 36] by safe_parse_sign_and_base().
#define X_OVER_BASE_INITIALIZER(X)                                        \
  {                                                                       \
    0, 0, X / 2, X / 3, X / 4, X / 5, X / 6, X / 7, X / 8, X / 9, X / 10, \
        X / 11, X / 12, X / 13, X / 14, X / 15, X / 16, X / 17, X / 18,   \
        X / 19, X / 20, X / 21, X / 22, X / 23, X / 24, X / 25, X / 26,   \
        X / 27, X / 28, X / 29, X / 30, X / 31, X / 32, X / 33, X / 34,   \
        X / 35, X / 36,                                                   \
  }

template <typename IntType>
const IntType LookupTables<IntType>::kVmaxOverBase[] =
    X_OVER_BASE_INITIALIZER(std::numeric_limits<IntType>::max());

template <typename IntType>
const IntType LookupTables<IntType>::kVminOverBase[] =
    X_OVER_BASE_INITIALIZER(std::numeric_limits<IntType>::min());

#undef X_OVER_BASE_INITIALIZER

template <typename IntType>
inline bool safe_parse_positive_int(absl::string_view text, int base,
                                    IntType* value_p) {
  IntType value = 0;
  const IntType vmax = std::numeric_limits<IntType>::max();
  assert(vmax > 0);
  assert(base >= 0);
  assert(vmax >= static_cast<IntType>(base));
  const IntType vmax_over_base = LookupTables<IntType>::kVmaxOverBase[base];
  const char* start = text.data();
  const char* end = start + text.size();
  // loop over digits
  for (; start < end; ++start) {
    unsigned char c = static_cast<unsigned char>(start[0]);
    int digit = kAsciiToInt[c];
    if (digit >= base) {
      *value_p = value;
      return false;
    }
    if (value > vmax_over_base) {
      *value_p = vmax;
      return false;
    }
    value *= base;
    if (value > vmax - digit) {
      *value_p = vmax;
      return false;
    }
    value += digit;
  }
  *value_p = value;
  return true;
}

template <typename IntType>
inline bool safe_parse_negative_int(absl::string_view text, int base,
                                    IntType* value_p) {
  IntType value = 0;
  const IntType vmin = std::numeric_limits<IntType>::min();
  assert(vmin < 0);
  assert(vmin <= 0 - base);
  IntType vmin_over_base = LookupTables<IntType>::kVminOverBase[base];
  // 2003 c++ standard [expr.mul]
  // "... the sign of the remainder is implementation-defined."
  // Although (vmin/base)*base + vmin%base is always vmin.
  // 2011 c++ standard tightens the spec but we cannot rely on it.
  // TODO(junyer): Handle this in the lookup table generation.
  if (vmin % base > 0) {
    vmin_over_base += 1;
  }
  const char* start = text.data();
  const char* end = start + text.size();
  // loop over digits
  for (; start < end; ++start) {
    unsigned char c = static_cast<unsigned char>(start[0]);
    int digit = kAsciiToInt[c];
    if (digit >= base) {
      *value_p = value;
      return false;
    }
    if (value < vmin_over_base) {
      *value_p = vmin;
      return false;
    }
    value *= base;
    if (value < vmin + digit) {
      *value_p = vmin;
      return false;
    }
    value -= digit;
  }
  *value_p = value;
  return true;
}

// Input format based on POSIX.1-2008 strtol
// http://pubs.opengroup.org/onlinepubs/9699919799/functions/strtol.html
template <typename IntType>
inline bool safe_int_internal(absl::string_view text, IntType* value_p,
                              int base) {
  *value_p = 0;
  bool negative;
  if (!safe_parse_sign_and_base(&text, &base, &negative)) {
    return false;
  }
  if (!negative) {
    return safe_parse_positive_int(text, base, value_p);
  } else {
    return safe_parse_negative_int(text, base, value_p);
  }
}

template <typename IntType>
inline bool safe_uint_internal(absl::string_view text, IntType* value_p,
                               int base) {
  *value_p = 0;
  bool negative;
  if (!safe_parse_sign_and_base(&text, &base, &negative) || negative) {
    return false;
  }
  return safe_parse_positive_int(text, base, value_p);
}
}  // anonymous namespace

namespace numbers_internal {
bool safe_strto32_base(absl::string_view text, int32_t* value, int base) {
  return safe_int_internal<int32_t>(text, value, base);
}

bool safe_strto64_base(absl::string_view text, int64_t* value, int base) {
  return safe_int_internal<int64_t>(text, value, base);
}

bool safe_strtou32_base(absl::string_view text, uint32_t* value, int base) {
  return safe_uint_internal<uint32_t>(text, value, base);
}

bool safe_strtou64_base(absl::string_view text, uint64_t* value, int base) {
  return safe_uint_internal<uint64_t>(text, value, base);
}
}  // namespace numbers_internal

}  // inline namespace lts_2018_06_20
}  // namespace absl