summaryrefslogtreecommitdiff
path: root/absl/strings/internal/str_format/float_conversion.cc
blob: 2b1fd8cb420bb2b073ea9a8fdfb04c5fb54fbfa1 (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
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
// Copyright 2020 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 "absl/strings/internal/str_format/float_conversion.h"

#include <string.h>

#include <algorithm>
#include <cassert>
#include <cmath>
#include <limits>
#include <string>

#include "absl/base/attributes.h"
#include "absl/base/config.h"
#include "absl/base/optimization.h"
#include "absl/functional/function_ref.h"
#include "absl/meta/type_traits.h"
#include "absl/numeric/bits.h"
#include "absl/numeric/int128.h"
#include "absl/strings/numbers.h"
#include "absl/types/optional.h"
#include "absl/types/span.h"

namespace absl {
ABSL_NAMESPACE_BEGIN
namespace str_format_internal {

namespace {

// The code below wants to avoid heap allocations.
// To do so it needs to allocate memory on the stack.
// `StackArray` will allocate memory on the stack in the form of a uint32_t
// array and call the provided callback with said memory.
// It will allocate memory in increments of 512 bytes. We could allocate the
// largest needed unconditionally, but that is more than we need in most of
// cases. This way we use less stack in the common cases.
class StackArray {
  using Func = absl::FunctionRef<void(absl::Span<uint32_t>)>;
  static constexpr size_t kStep = 512 / sizeof(uint32_t);
  // 5 steps is 2560 bytes, which is enough to hold a long double with the
  // largest/smallest exponents.
  // The operations below will static_assert their particular maximum.
  static constexpr size_t kNumSteps = 5;

  // We do not want this function to be inlined.
  // Otherwise the caller will allocate the stack space unnecessarily for all
  // the variants even though it only calls one.
  template <size_t steps>
  ABSL_ATTRIBUTE_NOINLINE static void RunWithCapacityImpl(Func f) {
    uint32_t values[steps * kStep]{};
    f(absl::MakeSpan(values));
  }

 public:
  static constexpr size_t kMaxCapacity = kStep * kNumSteps;

  static void RunWithCapacity(size_t capacity, Func f) {
    assert(capacity <= kMaxCapacity);
    const size_t step = (capacity + kStep - 1) / kStep;
    assert(step <= kNumSteps);
    switch (step) {
      case 1:
        return RunWithCapacityImpl<1>(f);
      case 2:
        return RunWithCapacityImpl<2>(f);
      case 3:
        return RunWithCapacityImpl<3>(f);
      case 4:
        return RunWithCapacityImpl<4>(f);
      case 5:
        return RunWithCapacityImpl<5>(f);
    }

    assert(false && "Invalid capacity");
  }
};

// Calculates `10 * (*v) + carry` and stores the result in `*v` and returns
// the carry.
template <typename Int>
inline Int MultiplyBy10WithCarry(Int *v, Int carry) {
  using BiggerInt = absl::conditional_t<sizeof(Int) == 4, uint64_t, uint128>;
  BiggerInt tmp = 10 * static_cast<BiggerInt>(*v) + carry;
  *v = static_cast<Int>(tmp);
  return static_cast<Int>(tmp >> (sizeof(Int) * 8));
}

// Calculates `(2^64 * carry + *v) / 10`.
// Stores the quotient in `*v` and returns the remainder.
// Requires: `0 <= carry <= 9`
inline uint64_t DivideBy10WithCarry(uint64_t *v, uint64_t carry) {
  constexpr uint64_t divisor = 10;
  // 2^64 / divisor = chunk_quotient + chunk_remainder / divisor
  constexpr uint64_t chunk_quotient = (uint64_t{1} << 63) / (divisor / 2);
  constexpr uint64_t chunk_remainder = uint64_t{} - chunk_quotient * divisor;

  const uint64_t mod = *v % divisor;
  const uint64_t next_carry = chunk_remainder * carry + mod;
  *v = *v / divisor + carry * chunk_quotient + next_carry / divisor;
  return next_carry % divisor;
}

constexpr bool IsDoubleDouble() {
  // This is the `double-double` representation of `long double`.
  // We do not handle it natively. Fallback to snprintf.
  return std::numeric_limits<long double>::digits ==
         2 * std::numeric_limits<double>::digits;
}

using MaxFloatType =
    typename std::conditional<IsDoubleDouble(), double, long double>::type;

// Generates the decimal representation for an integer of the form `v * 2^exp`,
// where `v` and `exp` are both positive integers.
// It generates the digits from the left (ie the most significant digit first)
// to allow for direct printing into the sink.
//
// Requires `0 <= exp` and `exp <= numeric_limits<MaxFloatType>::max_exponent`.
class BinaryToDecimal {
  static constexpr int ChunksNeeded(int exp) {
    // We will left shift a uint128 by `exp` bits, so we need `128+exp` total
    // bits. Round up to 32.
    // See constructor for details about adding `10%` to the value.
    return (128 + exp + 31) / 32 * 11 / 10;
  }

 public:
  // Run the conversion for `v * 2^exp` and call `f(binary_to_decimal)`.
  // This function will allocate enough stack space to perform the conversion.
  static void RunConversion(uint128 v, int exp,
                            absl::FunctionRef<void(BinaryToDecimal)> f) {
    assert(exp > 0);
    assert(exp <= std::numeric_limits<MaxFloatType>::max_exponent);
    static_assert(
        static_cast<int>(StackArray::kMaxCapacity) >=
            ChunksNeeded(std::numeric_limits<MaxFloatType>::max_exponent),
        "");

    StackArray::RunWithCapacity(
        ChunksNeeded(exp),
        [=](absl::Span<uint32_t> input) { f(BinaryToDecimal(input, v, exp)); });
  }

  int TotalDigits() const {
    return static_cast<int>((decimal_end_ - decimal_start_) * kDigitsPerChunk +
                            CurrentDigits().size());
  }

  // See the current block of digits.
  absl::string_view CurrentDigits() const {
    return absl::string_view(digits_ + kDigitsPerChunk - size_, size_);
  }

  // Advance the current view of digits.
  // Returns `false` when no more digits are available.
  bool AdvanceDigits() {
    if (decimal_start_ >= decimal_end_) return false;

    uint32_t w = data_[decimal_start_++];
    for (size_ = 0; size_ < kDigitsPerChunk; w /= 10) {
      digits_[kDigitsPerChunk - ++size_] = w % 10 + '0';
    }
    return true;
  }

 private:
  BinaryToDecimal(absl::Span<uint32_t> data, uint128 v, int exp) : data_(data) {
    // We need to print the digits directly into the sink object without
    // buffering them all first. To do this we need two things:
    // - to know the total number of digits to do padding when necessary
    // - to generate the decimal digits from the left.
    //
    // In order to do this, we do a two pass conversion.
    // On the first pass we convert the binary representation of the value into
    // a decimal representation in which each uint32_t chunk holds up to 9
    // decimal digits.  In the second pass we take each decimal-holding-uint32_t
    // value and generate the ascii decimal digits into `digits_`.
    //
    // The binary and decimal representations actually share the same memory
    // region. As we go converting the chunks from binary to decimal we free
    // them up and reuse them for the decimal representation. One caveat is that
    // the decimal representation is around 7% less efficient in space than the
    // binary one. We allocate an extra 10% memory to account for this. See
    // ChunksNeeded for this calculation.
    int chunk_index = exp / 32;
    decimal_start_ = decimal_end_ = ChunksNeeded(exp);
    const int offset = exp % 32;
    // Left shift v by exp bits.
    data_[chunk_index] = static_cast<uint32_t>(v << offset);
    for (v >>= (32 - offset); v; v >>= 32)
      data_[++chunk_index] = static_cast<uint32_t>(v);

    while (chunk_index >= 0) {
      // While we have more than one chunk available, go in steps of 1e9.
      // `data_[chunk_index]` holds the highest non-zero binary chunk, so keep
      // the variable updated.
      uint32_t carry = 0;
      for (int i = chunk_index; i >= 0; --i) {
        uint64_t tmp = uint64_t{data_[i]} + (uint64_t{carry} << 32);
        data_[i] = static_cast<uint32_t>(tmp / uint64_t{1000000000});
        carry = static_cast<uint32_t>(tmp % uint64_t{1000000000});
      }

      // If the highest chunk is now empty, remove it from view.
      if (data_[chunk_index] == 0) --chunk_index;

      --decimal_start_;
      assert(decimal_start_ != chunk_index);
      data_[decimal_start_] = carry;
    }

    // Fill the first set of digits. The first chunk might not be complete, so
    // handle differently.
    for (uint32_t first = data_[decimal_start_++]; first != 0; first /= 10) {
      digits_[kDigitsPerChunk - ++size_] = first % 10 + '0';
    }
  }

 private:
  static constexpr int kDigitsPerChunk = 9;

  int decimal_start_;
  int decimal_end_;

  char digits_[kDigitsPerChunk];
  int size_ = 0;

  absl::Span<uint32_t> data_;
};

// Converts a value of the form `x * 2^-exp` into a sequence of decimal digits.
// Requires `-exp < 0` and
// `-exp >= limits<MaxFloatType>::min_exponent - limits<MaxFloatType>::digits`.
class FractionalDigitGenerator {
 public:
  // Run the conversion for `v * 2^exp` and call `f(generator)`.
  // This function will allocate enough stack space to perform the conversion.
  static void RunConversion(
      uint128 v, int exp, absl::FunctionRef<void(FractionalDigitGenerator)> f) {
    using Limits = std::numeric_limits<MaxFloatType>;
    assert(-exp < 0);
    assert(-exp >= Limits::min_exponent - 128);
    static_assert(StackArray::kMaxCapacity >=
                      (Limits::digits + 128 - Limits::min_exponent + 31) / 32,
                  "");
    StackArray::RunWithCapacity((Limits::digits + exp + 31) / 32,
                                [=](absl::Span<uint32_t> input) {
                                  f(FractionalDigitGenerator(input, v, exp));
                                });
  }

  // Returns true if there are any more non-zero digits left.
  bool HasMoreDigits() const { return next_digit_ != 0 || chunk_index_ >= 0; }

  // Returns true if the remainder digits are greater than 5000...
  bool IsGreaterThanHalf() const {
    return next_digit_ > 5 || (next_digit_ == 5 && chunk_index_ >= 0);
  }
  // Returns true if the remainder digits are exactly 5000...
  bool IsExactlyHalf() const { return next_digit_ == 5 && chunk_index_ < 0; }

  struct Digits {
    int digit_before_nine;
    int num_nines;
  };

  // Get the next set of digits.
  // They are composed by a non-9 digit followed by a runs of zero or more 9s.
  Digits GetDigits() {
    Digits digits{next_digit_, 0};

    next_digit_ = GetOneDigit();
    while (next_digit_ == 9) {
      ++digits.num_nines;
      next_digit_ = GetOneDigit();
    }

    return digits;
  }

 private:
  // Return the next digit.
  int GetOneDigit() {
    if (chunk_index_ < 0) return 0;

    uint32_t carry = 0;
    for (int i = chunk_index_; i >= 0; --i) {
      carry = MultiplyBy10WithCarry(&data_[i], carry);
    }
    // If the lowest chunk is now empty, remove it from view.
    if (data_[chunk_index_] == 0) --chunk_index_;
    return carry;
  }

  FractionalDigitGenerator(absl::Span<uint32_t> data, uint128 v, int exp)
      : chunk_index_(exp / 32), data_(data) {
    const int offset = exp % 32;
    // Right shift `v` by `exp` bits.
    data_[chunk_index_] = static_cast<uint32_t>(v << (32 - offset));
    v >>= offset;
    // Make sure we don't overflow the data. We already calculated that
    // non-zero bits fit, so we might not have space for leading zero bits.
    for (int pos = chunk_index_; v; v >>= 32)
      data_[--pos] = static_cast<uint32_t>(v);

    // Fill next_digit_, as GetDigits expects it to be populated always.
    next_digit_ = GetOneDigit();
  }

  int next_digit_;
  int chunk_index_;
  absl::Span<uint32_t> data_;
};

// Count the number of leading zero bits.
int LeadingZeros(uint64_t v) { return countl_zero(v); }
int LeadingZeros(uint128 v) {
  auto high = static_cast<uint64_t>(v >> 64);
  auto low = static_cast<uint64_t>(v);
  return high != 0 ? countl_zero(high) : 64 + countl_zero(low);
}

// Round up the text digits starting at `p`.
// The buffer must have an extra digit that is known to not need rounding.
// This is done below by having an extra '0' digit on the left.
void RoundUp(char *p) {
  while (*p == '9' || *p == '.') {
    if (*p == '9') *p = '0';
    --p;
  }
  ++*p;
}

// Check the previous digit and round up or down to follow the round-to-even
// policy.
void RoundToEven(char *p) {
  if (*p == '.') --p;
  if (*p % 2 == 1) RoundUp(p);
}

// Simple integral decimal digit printing for values that fit in 64-bits.
// Returns the pointer to the last written digit.
char *PrintIntegralDigitsFromRightFast(uint64_t v, char *p) {
  do {
    *--p = DivideBy10WithCarry(&v, 0) + '0';
  } while (v != 0);
  return p;
}

// Simple integral decimal digit printing for values that fit in 128-bits.
// Returns the pointer to the last written digit.
char *PrintIntegralDigitsFromRightFast(uint128 v, char *p) {
  auto high = static_cast<uint64_t>(v >> 64);
  auto low = static_cast<uint64_t>(v);

  while (high != 0) {
    uint64_t carry = DivideBy10WithCarry(&high, 0);
    carry = DivideBy10WithCarry(&low, carry);
    *--p = carry + '0';
  }
  return PrintIntegralDigitsFromRightFast(low, p);
}

// Simple fractional decimal digit printing for values that fir in 64-bits after
// shifting.
// Performs rounding if necessary to fit within `precision`.
// Returns the pointer to one after the last character written.
char *PrintFractionalDigitsFast(uint64_t v, char *start, int exp,
                                int precision) {
  char *p = start;
  v <<= (64 - exp);
  while (precision > 0) {
    if (!v) return p;
    *p++ = MultiplyBy10WithCarry(&v, uint64_t{0}) + '0';
    --precision;
  }

  // We need to round.
  if (v < 0x8000000000000000) {
    // We round down, so nothing to do.
  } else if (v > 0x8000000000000000) {
    // We round up.
    RoundUp(p - 1);
  } else {
    RoundToEven(p - 1);
  }

  assert(precision == 0);
  // Precision can only be zero here.
  return p;
}

// Simple fractional decimal digit printing for values that fir in 128-bits
// after shifting.
// Performs rounding if necessary to fit within `precision`.
// Returns the pointer to one after the last character written.
char *PrintFractionalDigitsFast(uint128 v, char *start, int exp,
                                int precision) {
  char *p = start;
  v <<= (128 - exp);
  auto high = static_cast<uint64_t>(v >> 64);
  auto low = static_cast<uint64_t>(v);

  // While we have digits to print and `low` is not empty, do the long
  // multiplication.
  while (precision > 0 && low != 0) {
    uint64_t carry = MultiplyBy10WithCarry(&low, uint64_t{0});
    carry = MultiplyBy10WithCarry(&high, carry);

    *p++ = carry + '0';
    --precision;
  }

  // Now `low` is empty, so use a faster approach for the rest of the digits.
  // This block is pretty much the same as the main loop for the 64-bit case
  // above.
  while (precision > 0) {
    if (!high) return p;
    *p++ = MultiplyBy10WithCarry(&high, uint64_t{0}) + '0';
    --precision;
  }

  // We need to round.
  if (high < 0x8000000000000000) {
    // We round down, so nothing to do.
  } else if (high > 0x8000000000000000 || low != 0) {
    // We round up.
    RoundUp(p - 1);
  } else {
    RoundToEven(p - 1);
  }

  assert(precision == 0);
  // Precision can only be zero here.
  return p;
}

struct FormatState {
  char sign_char;
  int precision;
  const FormatConversionSpecImpl &conv;
  FormatSinkImpl *sink;

  // In `alt` mode (flag #) we keep the `.` even if there are no fractional
  // digits. In non-alt mode, we strip it.
  bool ShouldPrintDot() const { return precision != 0 || conv.has_alt_flag(); }
};

struct Padding {
  int left_spaces;
  int zeros;
  int right_spaces;
};

Padding ExtraWidthToPadding(size_t total_size, const FormatState &state) {
  if (state.conv.width() < 0 ||
      static_cast<size_t>(state.conv.width()) <= total_size) {
    return {0, 0, 0};
  }
  int missing_chars = state.conv.width() - total_size;
  if (state.conv.has_left_flag()) {
    return {0, 0, missing_chars};
  } else if (state.conv.has_zero_flag()) {
    return {0, missing_chars, 0};
  } else {
    return {missing_chars, 0, 0};
  }
}

void FinalPrint(const FormatState &state, absl::string_view data,
                int padding_offset, int trailing_zeros,
                absl::string_view data_postfix) {
  if (state.conv.width() < 0) {
    // No width specified. Fast-path.
    if (state.sign_char != '\0') state.sink->Append(1, state.sign_char);
    state.sink->Append(data);
    state.sink->Append(trailing_zeros, '0');
    state.sink->Append(data_postfix);
    return;
  }

  auto padding = ExtraWidthToPadding((state.sign_char != '\0' ? 1 : 0) +
                                         data.size() + data_postfix.size() +
                                         static_cast<size_t>(trailing_zeros),
                                     state);

  state.sink->Append(padding.left_spaces, ' ');
  if (state.sign_char != '\0') state.sink->Append(1, state.sign_char);
  // Padding in general needs to be inserted somewhere in the middle of `data`.
  state.sink->Append(data.substr(0, padding_offset));
  state.sink->Append(padding.zeros, '0');
  state.sink->Append(data.substr(padding_offset));
  state.sink->Append(trailing_zeros, '0');
  state.sink->Append(data_postfix);
  state.sink->Append(padding.right_spaces, ' ');
}

// Fastpath %f formatter for when the shifted value fits in a simple integral
// type.
// Prints `v*2^exp` with the options from `state`.
template <typename Int>
void FormatFFast(Int v, int exp, const FormatState &state) {
  constexpr int input_bits = sizeof(Int) * 8;

  static constexpr size_t integral_size =
      /* in case we need to round up an extra digit */ 1 +
      /* decimal digits for uint128 */ 40 + 1;
  char buffer[integral_size + /* . */ 1 + /* max digits uint128 */ 128];
  buffer[integral_size] = '.';
  char *const integral_digits_end = buffer + integral_size;
  char *integral_digits_start;
  char *const fractional_digits_start = buffer + integral_size + 1;
  char *fractional_digits_end = fractional_digits_start;

  if (exp >= 0) {
    const int total_bits = input_bits - LeadingZeros(v) + exp;
    integral_digits_start =
        total_bits <= 64
            ? PrintIntegralDigitsFromRightFast(static_cast<uint64_t>(v) << exp,
                                               integral_digits_end)
            : PrintIntegralDigitsFromRightFast(static_cast<uint128>(v) << exp,
                                               integral_digits_end);
  } else {
    exp = -exp;

    integral_digits_start = PrintIntegralDigitsFromRightFast(
        exp < input_bits ? v >> exp : 0, integral_digits_end);
    // PrintFractionalDigits may pull a carried 1 all the way up through the
    // integral portion.
    integral_digits_start[-1] = '0';

    fractional_digits_end =
        exp <= 64 ? PrintFractionalDigitsFast(v, fractional_digits_start, exp,
                                              state.precision)
                  : PrintFractionalDigitsFast(static_cast<uint128>(v),
                                              fractional_digits_start, exp,
                                              state.precision);
    // There was a carry, so include the first digit too.
    if (integral_digits_start[-1] != '0') --integral_digits_start;
  }

  size_t size = fractional_digits_end - integral_digits_start;

  // In `alt` mode (flag #) we keep the `.` even if there are no fractional
  // digits. In non-alt mode, we strip it.
  if (!state.ShouldPrintDot()) --size;
  FinalPrint(state, absl::string_view(integral_digits_start, size),
             /*padding_offset=*/0,
             static_cast<int>(state.precision - (fractional_digits_end -
                                                 fractional_digits_start)),
             /*data_postfix=*/"");
}

// Slow %f formatter for when the shifted value does not fit in a uint128, and
// `exp > 0`.
// Prints `v*2^exp` with the options from `state`.
// This one is guaranteed to not have fractional digits, so we don't have to
// worry about anything after the `.`.
void FormatFPositiveExpSlow(uint128 v, int exp, const FormatState &state) {
  BinaryToDecimal::RunConversion(v, exp, [&](BinaryToDecimal btd) {
    const size_t total_digits =
        btd.TotalDigits() +
        (state.ShouldPrintDot() ? static_cast<size_t>(state.precision) + 1 : 0);

    const auto padding = ExtraWidthToPadding(
        total_digits + (state.sign_char != '\0' ? 1 : 0), state);

    state.sink->Append(padding.left_spaces, ' ');
    if (state.sign_char != '\0') state.sink->Append(1, state.sign_char);
    state.sink->Append(padding.zeros, '0');

    do {
      state.sink->Append(btd.CurrentDigits());
    } while (btd.AdvanceDigits());

    if (state.ShouldPrintDot()) state.sink->Append(1, '.');
    state.sink->Append(state.precision, '0');
    state.sink->Append(padding.right_spaces, ' ');
  });
}

// Slow %f formatter for when the shifted value does not fit in a uint128, and
// `exp < 0`.
// Prints `v*2^exp` with the options from `state`.
// This one is guaranteed to be < 1.0, so we don't have to worry about integral
// digits.
void FormatFNegativeExpSlow(uint128 v, int exp, const FormatState &state) {
  const size_t total_digits =
      /* 0 */ 1 +
      (state.ShouldPrintDot() ? static_cast<size_t>(state.precision) + 1 : 0);
  auto padding =
      ExtraWidthToPadding(total_digits + (state.sign_char ? 1 : 0), state);
  padding.zeros += 1;
  state.sink->Append(padding.left_spaces, ' ');
  if (state.sign_char != '\0') state.sink->Append(1, state.sign_char);
  state.sink->Append(padding.zeros, '0');

  if (state.ShouldPrintDot()) state.sink->Append(1, '.');

  // Print digits
  int digits_to_go = state.precision;

  FractionalDigitGenerator::RunConversion(
      v, exp, [&](FractionalDigitGenerator digit_gen) {
        // There are no digits to print here.
        if (state.precision == 0) return;

        // We go one digit at a time, while keeping track of runs of nines.
        // The runs of nines are used to perform rounding when necessary.

        while (digits_to_go > 0 && digit_gen.HasMoreDigits()) {
          auto digits = digit_gen.GetDigits();

          // Now we have a digit and a run of nines.
          // See if we can print them all.
          if (digits.num_nines + 1 < digits_to_go) {
            // We don't have to round yet, so print them.
            state.sink->Append(1, digits.digit_before_nine + '0');
            state.sink->Append(digits.num_nines, '9');
            digits_to_go -= digits.num_nines + 1;

          } else {
            // We can't print all the nines, see where we have to truncate.

            bool round_up = false;
            if (digits.num_nines + 1 > digits_to_go) {
              // We round up at a nine. No need to print them.
              round_up = true;
            } else {
              // We can fit all the nines, but truncate just after it.
              if (digit_gen.IsGreaterThanHalf()) {
                round_up = true;
              } else if (digit_gen.IsExactlyHalf()) {
                // Round to even
                round_up =
                    digits.num_nines != 0 || digits.digit_before_nine % 2 == 1;
              }
            }

            if (round_up) {
              state.sink->Append(1, digits.digit_before_nine + '1');
              --digits_to_go;
              // The rest will be zeros.
            } else {
              state.sink->Append(1, digits.digit_before_nine + '0');
              state.sink->Append(digits_to_go - 1, '9');
              digits_to_go = 0;
            }
            return;
          }
        }
      });

  state.sink->Append(digits_to_go, '0');
  state.sink->Append(padding.right_spaces, ' ');
}

template <typename Int>
void FormatF(Int mantissa, int exp, const FormatState &state) {
  if (exp >= 0) {
    const int total_bits = sizeof(Int) * 8 - LeadingZeros(mantissa) + exp;

    // Fallback to the slow stack-based approach if we can't do it in a 64 or
    // 128 bit state.
    if (ABSL_PREDICT_FALSE(total_bits > 128)) {
      return FormatFPositiveExpSlow(mantissa, exp, state);
    }
  } else {
    // Fallback to the slow stack-based approach if we can't do it in a 64 or
    // 128 bit state.
    if (ABSL_PREDICT_FALSE(exp < -128)) {
      return FormatFNegativeExpSlow(mantissa, -exp, state);
    }
  }
  return FormatFFast(mantissa, exp, state);
}

// Grab the group of four bits (nibble) from `n`. E.g., nibble 1 corresponds to
// bits 4-7.
template <typename Int>
uint8_t GetNibble(Int n, int nibble_index) {
  constexpr Int mask_low_nibble = Int{0xf};
  int shift = nibble_index * 4;
  n &= mask_low_nibble << shift;
  return static_cast<uint8_t>((n >> shift) & 0xf);
}

// Add one to the given nibble, applying carry to higher nibbles. Returns true
// if overflow, false otherwise.
template <typename Int>
bool IncrementNibble(int nibble_index, Int *n) {
  constexpr int kShift = sizeof(Int) * 8 - 1;
  constexpr int kNumNibbles = sizeof(Int) * 8 / 4;
  Int before = *n >> kShift;
  // Here we essentially want to take the number 1 and move it into the requsted
  // nibble, then add it to *n to effectively increment the nibble. However,
  // ASan will complain if we try to shift the 1 beyond the limits of the Int,
  // i.e., if the nibble_index is out of range. So therefore we check for this
  // and if we are out of range we just add 0 which leaves *n unchanged, which
  // seems like the reasonable thing to do in that case.
  *n += ((nibble_index >= kNumNibbles) ? 0 : (Int{1} << (nibble_index * 4)));
  Int after = *n >> kShift;
  return (before && !after) || (nibble_index >= kNumNibbles);
}

// Return a mask with 1's in the given nibble and all lower nibbles.
template <typename Int>
Int MaskUpToNibbleInclusive(int nibble_index) {
  constexpr int kNumNibbles = sizeof(Int) * 8 / 4;
  static const Int ones = ~Int{0};
  return ones >> std::max(0, 4 * (kNumNibbles - nibble_index - 1));
}

// Return a mask with 1's below the given nibble.
template <typename Int>
Int MaskUpToNibbleExclusive(int nibble_index) {
  return nibble_index <= 0 ? 0 : MaskUpToNibbleInclusive<Int>(nibble_index - 1);
}

template <typename Int>
Int MoveToNibble(uint8_t nibble, int nibble_index) {
  return Int{nibble} << (4 * nibble_index);
}

// Given mantissa size, find optimal # of mantissa bits to put in initial digit.
//
// In the hex representation we keep a single hex digit to the left of the dot.
// However, the question as to how many bits of the mantissa should be put into
// that hex digit in theory is arbitrary, but in practice it is optimal to
// choose based on the size of the mantissa. E.g., for a `double`, there are 53
// mantissa bits, so that means that we should put 1 bit to the left of the dot,
// thereby leaving 52 bits to the right, which is evenly divisible by four and
// thus all fractional digits represent actual precision. For a `long double`,
// on the other hand, there are 64 bits of mantissa, thus we can use all four
// bits for the initial hex digit and still have a number left over (60) that is
// a multiple of four. Once again, the goal is to have all fractional digits
// represent real precision.
template <typename Float>
constexpr int HexFloatLeadingDigitSizeInBits() {
  return std::numeric_limits<Float>::digits % 4 > 0
             ? std::numeric_limits<Float>::digits % 4
             : 4;
}

// This function captures the rounding behavior of glibc for hex float
// representations. E.g. when rounding 0x1.ab800000 to a precision of .2
// ("%.2a") glibc will round up because it rounds toward the even number (since
// 0xb is an odd number, it will round up to 0xc). However, when rounding at a
// point that is not followed by 800000..., it disregards the parity and rounds
// up if > 8 and rounds down if < 8.
template <typename Int>
bool HexFloatNeedsRoundUp(Int mantissa, int final_nibble_displayed,
                          uint8_t leading) {
  // If the last nibble (hex digit) to be displayed is the lowest on in the
  // mantissa then that means that we don't have any further nibbles to inform
  // rounding, so don't round.
  if (final_nibble_displayed <= 0) {
    return false;
  }
  int rounding_nibble_idx = final_nibble_displayed - 1;
  constexpr int kTotalNibbles = sizeof(Int) * 8 / 4;
  assert(final_nibble_displayed <= kTotalNibbles);
  Int mantissa_up_to_rounding_nibble_inclusive =
      mantissa & MaskUpToNibbleInclusive<Int>(rounding_nibble_idx);
  Int eight = MoveToNibble<Int>(8, rounding_nibble_idx);
  if (mantissa_up_to_rounding_nibble_inclusive != eight) {
    return mantissa_up_to_rounding_nibble_inclusive > eight;
  }
  // Nibble in question == 8.
  uint8_t round_if_odd = (final_nibble_displayed == kTotalNibbles)
                             ? leading
                             : GetNibble(mantissa, final_nibble_displayed);
  return round_if_odd % 2 == 1;
}

// Stores values associated with a Float type needed by the FormatA
// implementation in order to avoid templatizing that function by the Float
// type.
struct HexFloatTypeParams {
  template <typename Float>
  explicit HexFloatTypeParams(Float)
      : min_exponent(std::numeric_limits<Float>::min_exponent - 1),
        leading_digit_size_bits(HexFloatLeadingDigitSizeInBits<Float>()) {
    assert(leading_digit_size_bits >= 1 && leading_digit_size_bits <= 4);
  }

  int min_exponent;
  int leading_digit_size_bits;
};

// Hex Float Rounding. First check if we need to round; if so, then we do that
// by manipulating (incrementing) the mantissa, that way we can later print the
// mantissa digits by iterating through them in the same way regardless of
// whether a rounding happened.
template <typename Int>
void FormatARound(bool precision_specified, const FormatState &state,
                  uint8_t *leading, Int *mantissa, int *exp) {
  constexpr int kTotalNibbles = sizeof(Int) * 8 / 4;
  // Index of the last nibble that we could display given precision.
  int final_nibble_displayed =
      precision_specified ? std::max(0, (kTotalNibbles - state.precision)) : 0;
  if (HexFloatNeedsRoundUp(*mantissa, final_nibble_displayed, *leading)) {
    // Need to round up.
    bool overflow = IncrementNibble(final_nibble_displayed, mantissa);
    *leading += (overflow ? 1 : 0);
    if (ABSL_PREDICT_FALSE(*leading > 15)) {
      // We have overflowed the leading digit. This would mean that we would
      // need two hex digits to the left of the dot, which is not allowed. So
      // adjust the mantissa and exponent so that the result is always 1.0eXXX.
      *leading = 1;
      *mantissa = 0;
      *exp += 4;
    }
  }
  // Now that we have handled a possible round-up we can go ahead and zero out
  // all the nibbles of the mantissa that we won't need.
  if (precision_specified) {
    *mantissa &= ~MaskUpToNibbleExclusive<Int>(final_nibble_displayed);
  }
}

template <typename Int>
void FormatANormalize(const HexFloatTypeParams float_traits, uint8_t *leading,
                      Int *mantissa, int *exp) {
  constexpr int kIntBits = sizeof(Int) * 8;
  static const Int kHighIntBit = Int{1} << (kIntBits - 1);
  const int kLeadDigitBitsCount = float_traits.leading_digit_size_bits;
  // Normalize mantissa so that highest bit set is in MSB position, unless we
  // get interrupted by the exponent threshold.
  while (*mantissa && !(*mantissa & kHighIntBit)) {
    if (ABSL_PREDICT_FALSE(*exp - 1 < float_traits.min_exponent)) {
      *mantissa >>= (float_traits.min_exponent - *exp);
      *exp = float_traits.min_exponent;
      return;
    }
    *mantissa <<= 1;
    --*exp;
  }
  // Extract bits for leading digit then shift them away leaving the
  // fractional part.
  *leading =
      static_cast<uint8_t>(*mantissa >> (kIntBits - kLeadDigitBitsCount));
  *exp -= (*mantissa != 0) ? kLeadDigitBitsCount : *exp;
  *mantissa <<= kLeadDigitBitsCount;
}

template <typename Int>
void FormatA(const HexFloatTypeParams float_traits, Int mantissa, int exp,
             bool uppercase, const FormatState &state) {
  // Int properties.
  constexpr int kIntBits = sizeof(Int) * 8;
  constexpr int kTotalNibbles = sizeof(Int) * 8 / 4;
  // Did the user specify a precision explicitly?
  const bool precision_specified = state.conv.precision() >= 0;

  // ========== Normalize/Denormalize ==========
  exp += kIntBits;  // make all digits fractional digits.
  // This holds the (up to four) bits of leading digit, i.e., the '1' in the
  // number 0x1.e6fp+2. It's always > 0 unless number is zero or denormal.
  uint8_t leading = 0;
  FormatANormalize(float_traits, &leading, &mantissa, &exp);

  // =============== Rounding ==================
  // Check if we need to round; if so, then we do that by manipulating
  // (incrementing) the mantissa before beginning to print characters.
  FormatARound(precision_specified, state, &leading, &mantissa, &exp);

  // ============= Format Result ===============
  // This buffer holds the "0x1.ab1de3" portion of "0x1.ab1de3pe+2". Compute the
  // size with long double which is the largest of the floats.
  constexpr size_t kBufSizeForHexFloatRepr =
      2                                                // 0x
      + std::numeric_limits<MaxFloatType>::digits / 4  // number of hex digits
      + 1                                              // round up
      + 1;                                             // "." (dot)
  char digits_buffer[kBufSizeForHexFloatRepr];
  char *digits_iter = digits_buffer;
  const char *const digits =
      static_cast<const char *>("0123456789ABCDEF0123456789abcdef") +
      (uppercase ? 0 : 16);

  // =============== Hex Prefix ================
  *digits_iter++ = '0';
  *digits_iter++ = uppercase ? 'X' : 'x';

  // ========== Non-Fractional Digit ===========
  *digits_iter++ = digits[leading];

  // ================== Dot ====================
  // There are three reasons we might need a dot. Keep in mind that, at this
  // point, the mantissa holds only the fractional part.
  if ((precision_specified && state.precision > 0) ||
      (!precision_specified && mantissa > 0) || state.conv.has_alt_flag()) {
    *digits_iter++ = '.';
  }

  // ============ Fractional Digits ============
  int digits_emitted = 0;
  while (mantissa > 0) {
    *digits_iter++ = digits[GetNibble(mantissa, kTotalNibbles - 1)];
    mantissa <<= 4;
    ++digits_emitted;
  }
  int trailing_zeros =
      precision_specified ? state.precision - digits_emitted : 0;
  assert(trailing_zeros >= 0);
  auto digits_result = string_view(digits_buffer, digits_iter - digits_buffer);

  // =============== Exponent ==================
  constexpr size_t kBufSizeForExpDecRepr =
      numbers_internal::kFastToBufferSize  // requred for FastIntToBuffer
      + 1                                  // 'p' or 'P'
      + 1;                                 // '+' or '-'
  char exp_buffer[kBufSizeForExpDecRepr];
  exp_buffer[0] = uppercase ? 'P' : 'p';
  exp_buffer[1] = exp >= 0 ? '+' : '-';
  numbers_internal::FastIntToBuffer(exp < 0 ? -exp : exp, exp_buffer + 2);

  // ============ Assemble Result ==============
  FinalPrint(state,           //
             digits_result,   // 0xN.NNN...
             2,               // offset in `data` to start padding if needed.
             trailing_zeros,  // num remaining mantissa padding zeros
             exp_buffer);     // exponent
}

char *CopyStringTo(absl::string_view v, char *out) {
  std::memcpy(out, v.data(), v.size());
  return out + v.size();
}

template <typename Float>
bool FallbackToSnprintf(const Float v, const FormatConversionSpecImpl &conv,
                        FormatSinkImpl *sink) {
  int w = conv.width() >= 0 ? conv.width() : 0;
  int p = conv.precision() >= 0 ? conv.precision() : -1;
  char fmt[32];
  {
    char *fp = fmt;
    *fp++ = '%';
    fp = CopyStringTo(FormatConversionSpecImplFriend::FlagsToString(conv), fp);
    fp = CopyStringTo("*.*", fp);
    if (std::is_same<long double, Float>()) {
      *fp++ = 'L';
    }
    *fp++ = FormatConversionCharToChar(conv.conversion_char());
    *fp = 0;
    assert(fp < fmt + sizeof(fmt));
  }
  std::string space(512, '\0');
  absl::string_view result;
  while (true) {
    int n = snprintf(&space[0], space.size(), fmt, w, p, v);
    if (n < 0) return false;
    if (static_cast<size_t>(n) < space.size()) {
      result = absl::string_view(space.data(), n);
      break;
    }
    space.resize(n + 1);
  }
  sink->Append(result);
  return true;
}

// 128-bits in decimal: ceil(128*log(2)/log(10))
//   or std::numeric_limits<__uint128_t>::digits10
constexpr int kMaxFixedPrecision = 39;

constexpr int kBufferLength = /*sign*/ 1 +
                              /*integer*/ kMaxFixedPrecision +
                              /*point*/ 1 +
                              /*fraction*/ kMaxFixedPrecision +
                              /*exponent e+123*/ 5;

struct Buffer {
  void push_front(char c) {
    assert(begin > data);
    *--begin = c;
  }
  void push_back(char c) {
    assert(end < data + sizeof(data));
    *end++ = c;
  }
  void pop_back() {
    assert(begin < end);
    --end;
  }

  char &back() {
    assert(begin < end);
    return end[-1];
  }

  char last_digit() const { return end[-1] == '.' ? end[-2] : end[-1]; }

  int size() const { return static_cast<int>(end - begin); }

  char data[kBufferLength];
  char *begin;
  char *end;
};

enum class FormatStyle { Fixed, Precision };

// If the value is Inf or Nan, print it and return true.
// Otherwise, return false.
template <typename Float>
bool ConvertNonNumericFloats(char sign_char, Float v,
                             const FormatConversionSpecImpl &conv,
                             FormatSinkImpl *sink) {
  char text[4], *ptr = text;
  if (sign_char != '\0') *ptr++ = sign_char;
  if (std::isnan(v)) {
    ptr = std::copy_n(
        FormatConversionCharIsUpper(conv.conversion_char()) ? "NAN" : "nan", 3,
        ptr);
  } else if (std::isinf(v)) {
    ptr = std::copy_n(
        FormatConversionCharIsUpper(conv.conversion_char()) ? "INF" : "inf", 3,
        ptr);
  } else {
    return false;
  }

  return sink->PutPaddedString(string_view(text, ptr - text), conv.width(), -1,
                               conv.has_left_flag());
}

// Round up the last digit of the value.
// It will carry over and potentially overflow. 'exp' will be adjusted in that
// case.
template <FormatStyle mode>
void RoundUp(Buffer *buffer, int *exp) {
  char *p = &buffer->back();
  while (p >= buffer->begin && (*p == '9' || *p == '.')) {
    if (*p == '9') *p = '0';
    --p;
  }

  if (p < buffer->begin) {
    *p = '1';
    buffer->begin = p;
    if (mode == FormatStyle::Precision) {
      std::swap(p[1], p[2]);  // move the .
      ++*exp;
      buffer->pop_back();
    }
  } else {
    ++*p;
  }
}

void PrintExponent(int exp, char e, Buffer *out) {
  out->push_back(e);
  if (exp < 0) {
    out->push_back('-');
    exp = -exp;
  } else {
    out->push_back('+');
  }
  // Exponent digits.
  if (exp > 99) {
    out->push_back(exp / 100 + '0');
    out->push_back(exp / 10 % 10 + '0');
    out->push_back(exp % 10 + '0');
  } else {
    out->push_back(exp / 10 + '0');
    out->push_back(exp % 10 + '0');
  }
}

template <typename Float, typename Int>
constexpr bool CanFitMantissa() {
  return
#if defined(__clang__) && !defined(__SSE3__)
      // Workaround for clang bug: https://bugs.llvm.org/show_bug.cgi?id=38289
      // Casting from long double to uint64_t is miscompiled and drops bits.
      (!std::is_same<Float, long double>::value ||
       !std::is_same<Int, uint64_t>::value) &&
#endif
      std::numeric_limits<Float>::digits <= std::numeric_limits<Int>::digits;
}

template <typename Float>
struct Decomposed {
  using MantissaType =
      absl::conditional_t<std::is_same<long double, Float>::value, uint128,
                          uint64_t>;
  static_assert(std::numeric_limits<Float>::digits <= sizeof(MantissaType) * 8,
                "");
  MantissaType mantissa;
  int exponent;
};

// Decompose the double into an integer mantissa and an exponent.
template <typename Float>
Decomposed<Float> Decompose(Float v) {
  int exp;
  Float m = std::frexp(v, &exp);
  m = std::ldexp(m, std::numeric_limits<Float>::digits);
  exp -= std::numeric_limits<Float>::digits;

  return {static_cast<typename Decomposed<Float>::MantissaType>(m), exp};
}

// Print 'digits' as decimal.
// In Fixed mode, we add a '.' at the end.
// In Precision mode, we add a '.' after the first digit.
template <FormatStyle mode, typename Int>
int PrintIntegralDigits(Int digits, Buffer *out) {
  int printed = 0;
  if (digits) {
    for (; digits; digits /= 10) out->push_front(digits % 10 + '0');
    printed = out->size();
    if (mode == FormatStyle::Precision) {
      out->push_front(*out->begin);
      out->begin[1] = '.';
    } else {
      out->push_back('.');
    }
  } else if (mode == FormatStyle::Fixed) {
    out->push_front('0');
    out->push_back('.');
    printed = 1;
  }
  return printed;
}

// Back out 'extra_digits' digits and round up if necessary.
bool RemoveExtraPrecision(int extra_digits, bool has_leftover_value,
                          Buffer *out, int *exp_out) {
  if (extra_digits <= 0) return false;

  // Back out the extra digits
  out->end -= extra_digits;

  bool needs_to_round_up = [&] {
    // We look at the digit just past the end.
    // There must be 'extra_digits' extra valid digits after end.
    if (*out->end > '5') return true;
    if (*out->end < '5') return false;
    if (has_leftover_value || std::any_of(out->end + 1, out->end + extra_digits,
                                          [](char c) { return c != '0'; }))
      return true;

    // Ends in ...50*, round to even.
    return out->last_digit() % 2 == 1;
  }();

  if (needs_to_round_up) {
    RoundUp<FormatStyle::Precision>(out, exp_out);
  }
  return true;
}

// Print the value into the buffer.
// This will not include the exponent, which will be returned in 'exp_out' for
// Precision mode.
template <typename Int, typename Float, FormatStyle mode>
bool FloatToBufferImpl(Int int_mantissa, int exp, int precision, Buffer *out,
                       int *exp_out) {
  assert((CanFitMantissa<Float, Int>()));

  const int int_bits = std::numeric_limits<Int>::digits;

  // In precision mode, we start printing one char to the right because it will
  // also include the '.'
  // In fixed mode we put the dot afterwards on the right.
  out->begin = out->end =
      out->data + 1 + kMaxFixedPrecision + (mode == FormatStyle::Precision);

  if (exp >= 0) {
    if (std::numeric_limits<Float>::digits + exp > int_bits) {
      // The value will overflow the Int
      return false;
    }
    int digits_printed = PrintIntegralDigits<mode>(int_mantissa << exp, out);
    int digits_to_zero_pad = precision;
    if (mode == FormatStyle::Precision) {
      *exp_out = digits_printed - 1;
      digits_to_zero_pad -= digits_printed - 1;
      if (RemoveExtraPrecision(-digits_to_zero_pad, false, out, exp_out)) {
        return true;
      }
    }
    for (; digits_to_zero_pad-- > 0;) out->push_back('0');
    return true;
  }

  exp = -exp;
  // We need at least 4 empty bits for the next decimal digit.
  // We will multiply by 10.
  if (exp > int_bits - 4) return false;

  const Int mask = (Int{1} << exp) - 1;

  // Print the integral part first.
  int digits_printed = PrintIntegralDigits<mode>(int_mantissa >> exp, out);
  int_mantissa &= mask;

  int fractional_count = precision;
  if (mode == FormatStyle::Precision) {
    if (digits_printed == 0) {
      // Find the first non-zero digit, when in Precision mode.
      *exp_out = 0;
      if (int_mantissa) {
        while (int_mantissa <= mask) {
          int_mantissa *= 10;
          --*exp_out;
        }
      }
      out->push_front(static_cast<char>(int_mantissa >> exp) + '0');
      out->push_back('.');
      int_mantissa &= mask;
    } else {
      // We already have a digit, and a '.'
      *exp_out = digits_printed - 1;
      fractional_count -= *exp_out;
      if (RemoveExtraPrecision(-fractional_count, int_mantissa != 0, out,
                               exp_out)) {
        // If we had enough digits, return right away.
        // The code below will try to round again otherwise.
        return true;
      }
    }
  }

  auto get_next_digit = [&] {
    int_mantissa *= 10;
    int digit = static_cast<int>(int_mantissa >> exp);
    int_mantissa &= mask;
    return digit;
  };

  // Print fractional_count more digits, if available.
  for (; fractional_count > 0; --fractional_count) {
    out->push_back(get_next_digit() + '0');
  }

  int next_digit = get_next_digit();
  if (next_digit > 5 ||
      (next_digit == 5 && (int_mantissa || out->last_digit() % 2 == 1))) {
    RoundUp<mode>(out, exp_out);
  }

  return true;
}

template <FormatStyle mode, typename Float>
bool FloatToBuffer(Decomposed<Float> decomposed, int precision, Buffer *out,
                   int *exp) {
  if (precision > kMaxFixedPrecision) return false;

  // Try with uint64_t.
  if (CanFitMantissa<Float, std::uint64_t>() &&
      FloatToBufferImpl<std::uint64_t, Float, mode>(
          static_cast<std::uint64_t>(decomposed.mantissa),
          static_cast<std::uint64_t>(decomposed.exponent), precision, out, exp))
    return true;

#if defined(ABSL_HAVE_INTRINSIC_INT128)
  // If that is not enough, try with __uint128_t.
  return CanFitMantissa<Float, __uint128_t>() &&
         FloatToBufferImpl<__uint128_t, Float, mode>(
             static_cast<__uint128_t>(decomposed.mantissa),
             static_cast<__uint128_t>(decomposed.exponent), precision, out,
             exp);
#endif
  return false;
}

void WriteBufferToSink(char sign_char, absl::string_view str,
                       const FormatConversionSpecImpl &conv,
                       FormatSinkImpl *sink) {
  int left_spaces = 0, zeros = 0, right_spaces = 0;
  int missing_chars =
      conv.width() >= 0 ? std::max(conv.width() - static_cast<int>(str.size()) -
                                       static_cast<int>(sign_char != 0),
                                   0)
                        : 0;
  if (conv.has_left_flag()) {
    right_spaces = missing_chars;
  } else if (conv.has_zero_flag()) {
    zeros = missing_chars;
  } else {
    left_spaces = missing_chars;
  }

  sink->Append(left_spaces, ' ');
  if (sign_char != '\0') sink->Append(1, sign_char);
  sink->Append(zeros, '0');
  sink->Append(str);
  sink->Append(right_spaces, ' ');
}

template <typename Float>
bool FloatToSink(const Float v, const FormatConversionSpecImpl &conv,
                 FormatSinkImpl *sink) {
  // Print the sign or the sign column.
  Float abs_v = v;
  char sign_char = 0;
  if (std::signbit(abs_v)) {
    sign_char = '-';
    abs_v = -abs_v;
  } else if (conv.has_show_pos_flag()) {
    sign_char = '+';
  } else if (conv.has_sign_col_flag()) {
    sign_char = ' ';
  }

  // Print nan/inf.
  if (ConvertNonNumericFloats(sign_char, abs_v, conv, sink)) {
    return true;
  }

  int precision = conv.precision() < 0 ? 6 : conv.precision();

  int exp = 0;

  auto decomposed = Decompose(abs_v);

  Buffer buffer;

  FormatConversionChar c = conv.conversion_char();

  if (c == FormatConversionCharInternal::f ||
      c == FormatConversionCharInternal::F) {
    FormatF(decomposed.mantissa, decomposed.exponent,
            {sign_char, precision, conv, sink});
    return true;
  } else if (c == FormatConversionCharInternal::e ||
             c == FormatConversionCharInternal::E) {
    if (!FloatToBuffer<FormatStyle::Precision>(decomposed, precision, &buffer,
                                               &exp)) {
      return FallbackToSnprintf(v, conv, sink);
    }
    if (!conv.has_alt_flag() && buffer.back() == '.') buffer.pop_back();
    PrintExponent(
        exp, FormatConversionCharIsUpper(conv.conversion_char()) ? 'E' : 'e',
        &buffer);
  } else if (c == FormatConversionCharInternal::g ||
             c == FormatConversionCharInternal::G) {
    precision = std::max(0, precision - 1);
    if (!FloatToBuffer<FormatStyle::Precision>(decomposed, precision, &buffer,
                                               &exp)) {
      return FallbackToSnprintf(v, conv, sink);
    }
    if (precision + 1 > exp && exp >= -4) {
      if (exp < 0) {
        // Have 1.23456, needs 0.00123456
        // Move the first digit
        buffer.begin[1] = *buffer.begin;
        // Add some zeros
        for (; exp < -1; ++exp) *buffer.begin-- = '0';
        *buffer.begin-- = '.';
        *buffer.begin = '0';
      } else if (exp > 0) {
        // Have 1.23456, needs 1234.56
        // Move the '.' exp positions to the right.
        std::rotate(buffer.begin + 1, buffer.begin + 2, buffer.begin + exp + 2);
      }
      exp = 0;
    }
    if (!conv.has_alt_flag()) {
      while (buffer.back() == '0') buffer.pop_back();
      if (buffer.back() == '.') buffer.pop_back();
    }
    if (exp) {
      PrintExponent(
          exp, FormatConversionCharIsUpper(conv.conversion_char()) ? 'E' : 'e',
          &buffer);
    }
  } else if (c == FormatConversionCharInternal::a ||
             c == FormatConversionCharInternal::A) {
    bool uppercase = (c == FormatConversionCharInternal::A);
    FormatA(HexFloatTypeParams(Float{}), decomposed.mantissa,
            decomposed.exponent, uppercase, {sign_char, precision, conv, sink});
    return true;
  } else {
    return false;
  }

  WriteBufferToSink(sign_char,
                    absl::string_view(buffer.begin, buffer.end - buffer.begin),
                    conv, sink);

  return true;
}

}  // namespace

bool ConvertFloatImpl(long double v, const FormatConversionSpecImpl &conv,
                      FormatSinkImpl *sink) {
  if (IsDoubleDouble()) {
    return FallbackToSnprintf(v, conv, sink);
  }

  return FloatToSink(v, conv, sink);
}

bool ConvertFloatImpl(float v, const FormatConversionSpecImpl &conv,
                      FormatSinkImpl *sink) {
  return FloatToSink(static_cast<double>(v), conv, sink);
}

bool ConvertFloatImpl(double v, const FormatConversionSpecImpl &conv,
                      FormatSinkImpl *sink) {
  return FloatToSink(v, conv, sink);
}

}  // namespace str_format_internal
ABSL_NAMESPACE_END
}  // namespace absl