about summary refs log blame commit diff
path: root/absl/strings/internal/str_format/float_conversion.cc
blob: a761a5a5f9cee95125eb0c6013bb4abf131ea8c2 (plain) (tree)
1
2
3
4
5
6
7
8
9
10
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


                                                              
 


                    
                 

                 
                                 
                             






                                         
 
                
                    



                               































































































































































































































































































































































































































                                                                                



                                                                          



















                                                                        

                                                                           







































































                                                                               


                                                                                























                                                                               


                                                                              























































































                                                                               




                                       
                                                                            






                                                        
                                                                               



                                             
                                                               



                                   
                           



                                                            
                                                  



















































                                                                        

                                                                  
                            
                                            
                      


                                                                               
                             


                                                                               




                                                                               
                                                     














































                                                                              







                                                                              



                         





                                                                               









                                                                 

                                                                         




























































































































































                                                                                
                                       









                                                                           


                                                             





                                                                                
                             
                                 
                                    





                                 
                                                    





                                  
                                                                     






                                        
                                        
                    
                                        















                                                              
                                                  
 

                                             


                                                     





























                                                                                
       






                                                     


                                                                               





                                                    


                              

                                                                               





               
                                                                          
                                             






                                                                   


                                    
                                                                    



                                             
                                                                     




                                             
                  
                    
#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/internal/bits.h"
#include "absl/base/optimization.h"
#include "absl/functional/function_ref.h"
#include "absl/meta/type_traits.h"
#include "absl/numeric/int128.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;
}

// 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<long double>::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<long double>::max_exponent);
    static_assert(
        StackArray::kMaxCapacity >=
            ChunksNeeded(std::numeric_limits<long double>::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 size_t 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<long double>::min_exponent - limits<long double>::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) {
    assert(-exp < 0);
    assert(-exp >= std::numeric_limits<long double>::min_exponent - 128);
    static_assert(
        StackArray::kMaxCapacity >=
            (128 - std::numeric_limits<long double>::min_exponent + 31) / 32,
        "");
    StackArray::RunWithCapacity((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 base_internal::CountLeadingZeros64(v); }
int LeadingZeros(uint128 v) {
  auto high = static_cast<uint64_t>(v >> 64);
  auto low = static_cast<uint64_t>(v);
  return high != 0 ? base_internal::CountLeadingZeros64(high)
                   : 64 + base_internal::CountLeadingZeros64(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 || 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(absl::string_view data, int trailing_zeros,
                const FormatState &state) {
  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');
    return;
  }

  auto padding =
      ExtraWidthToPadding((state.sign_char != '\0' ? 1 : 0) + data.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);
  state.sink->Append(padding.zeros, '0');
  state.sink->Append(data);
  state.sink->Append(trailing_zeros, '0');
  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(absl::string_view(integral_digits_start, size),
             static_cast<int>(state.precision - (fractional_digits_end -
                                                 fractional_digits_start)),
             state);
}

// 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);
}

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

  return FloatToSink(v, conv, sink);
}

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