summaryrefslogtreecommitdiffstats
path: root/mfbt/double-conversion/strtod.cc
blob: b097afe0eb915c75dfe574f69b28715ae8ba9da3 (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
// Copyright 2010 the V8 project authors. All rights reserved.
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
//     * Redistributions of source code must retain the above copyright
//       notice, this list of conditions and the following disclaimer.
//     * Redistributions in binary form must reproduce the above
//       copyright notice, this list of conditions and the following
//       disclaimer in the documentation and/or other materials provided
//       with the distribution.
//     * Neither the name of Google Inc. nor the names of its
//       contributors may be used to endorse or promote products derived
//       from this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

#include <stdarg.h>
#include <limits.h>

#include "strtod.h"
#include "bignum.h"
#include "cached-powers.h"
#include "ieee.h"

namespace double_conversion {

// 2^53 = 9007199254740992.
// Any integer with at most 15 decimal digits will hence fit into a double
// (which has a 53bit significand) without loss of precision.
static const int kMaxExactDoubleIntegerDecimalDigits = 15;
// 2^64 = 18446744073709551616 > 10^19
static const int kMaxUint64DecimalDigits = 19;

// Max double: 1.7976931348623157 x 10^308
// Min non-zero double: 4.9406564584124654 x 10^-324
// Any x >= 10^309 is interpreted as +infinity.
// Any x <= 10^-324 is interpreted as 0.
// Note that 2.5e-324 (despite being smaller than the min double) will be read
// as non-zero (equal to the min non-zero double).
static const int kMaxDecimalPower = 309;
static const int kMinDecimalPower = -324;

// 2^64 = 18446744073709551616
static const uint64_t kMaxUint64 = UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF);


static const double exact_powers_of_ten[] = {
  1.0,  // 10^0
  10.0,
  100.0,
  1000.0,
  10000.0,
  100000.0,
  1000000.0,
  10000000.0,
  100000000.0,
  1000000000.0,
  10000000000.0,  // 10^10
  100000000000.0,
  1000000000000.0,
  10000000000000.0,
  100000000000000.0,
  1000000000000000.0,
  10000000000000000.0,
  100000000000000000.0,
  1000000000000000000.0,
  10000000000000000000.0,
  100000000000000000000.0,  // 10^20
  1000000000000000000000.0,
  // 10^22 = 0x21e19e0c9bab2400000 = 0x878678326eac9 * 2^22
  10000000000000000000000.0
};
static const int kExactPowersOfTenSize = ARRAY_SIZE(exact_powers_of_ten);

// Maximum number of significant digits in the decimal representation.
// In fact the value is 772 (see conversions.cc), but to give us some margin
// we round up to 780.
static const int kMaxSignificantDecimalDigits = 780;

static Vector<const char> TrimLeadingZeros(Vector<const char> buffer) {
  for (int i = 0; i < buffer.length(); i++) {
    if (buffer[i] != '0') {
      return buffer.SubVector(i, buffer.length());
    }
  }
  return Vector<const char>(buffer.start(), 0);
}


static Vector<const char> TrimTrailingZeros(Vector<const char> buffer) {
  for (int i = buffer.length() - 1; i >= 0; --i) {
    if (buffer[i] != '0') {
      return buffer.SubVector(0, i + 1);
    }
  }
  return Vector<const char>(buffer.start(), 0);
}


static void CutToMaxSignificantDigits(Vector<const char> buffer,
                                       int exponent,
                                       char* significant_buffer,
                                       int* significant_exponent) {
  for (int i = 0; i < kMaxSignificantDecimalDigits - 1; ++i) {
    significant_buffer[i] = buffer[i];
  }
  // The input buffer has been trimmed. Therefore the last digit must be
  // different from '0'.
  ASSERT(buffer[buffer.length() - 1] != '0');
  // Set the last digit to be non-zero. This is sufficient to guarantee
  // correct rounding.
  significant_buffer[kMaxSignificantDecimalDigits - 1] = '1';
  *significant_exponent =
      exponent + (buffer.length() - kMaxSignificantDecimalDigits);
}


// Trims the buffer and cuts it to at most kMaxSignificantDecimalDigits.
// If possible the input-buffer is reused, but if the buffer needs to be
// modified (due to cutting), then the input needs to be copied into the
// buffer_copy_space.
static void TrimAndCut(Vector<const char> buffer, int exponent,
                       char* buffer_copy_space, int space_size,
                       Vector<const char>* trimmed, int* updated_exponent) {
  Vector<const char> left_trimmed = TrimLeadingZeros(buffer);
  Vector<const char> right_trimmed = TrimTrailingZeros(left_trimmed);
  exponent += left_trimmed.length() - right_trimmed.length();
  if (right_trimmed.length() > kMaxSignificantDecimalDigits) {
    ASSERT(space_size >= kMaxSignificantDecimalDigits);
    CutToMaxSignificantDigits(right_trimmed, exponent,
                              buffer_copy_space, updated_exponent);
    *trimmed = Vector<const char>(buffer_copy_space,
                                 kMaxSignificantDecimalDigits);
  } else {
    *trimmed = right_trimmed;
    *updated_exponent = exponent;
  }
}


// Reads digits from the buffer and converts them to a uint64.
// Reads in as many digits as fit into a uint64.
// When the string starts with "1844674407370955161" no further digit is read.
// Since 2^64 = 18446744073709551616 it would still be possible read another
// digit if it was less or equal than 6, but this would complicate the code.
static uint64_t ReadUint64(Vector<const char> buffer,
                           int* number_of_read_digits) {
  uint64_t result = 0;
  int i = 0;
  while (i < buffer.length() && result <= (kMaxUint64 / 10 - 1)) {
    int digit = buffer[i++] - '0';
    ASSERT(0 <= digit && digit <= 9);
    result = 10 * result + digit;
  }
  *number_of_read_digits = i;
  return result;
}


// Reads a DiyFp from the buffer.
// The returned DiyFp is not necessarily normalized.
// If remaining_decimals is zero then the returned DiyFp is accurate.
// Otherwise it has been rounded and has error of at most 1/2 ulp.
static void ReadDiyFp(Vector<const char> buffer,
                      DiyFp* result,
                      int* remaining_decimals) {
  int read_digits;
  uint64_t significand = ReadUint64(buffer, &read_digits);
  if (buffer.length() == read_digits) {
    *result = DiyFp(significand, 0);
    *remaining_decimals = 0;
  } else {
    // Round the significand.
    if (buffer[read_digits] >= '5') {
      significand++;
    }
    // Compute the binary exponent.
    int exponent = 0;
    *result = DiyFp(significand, exponent);
    *remaining_decimals = buffer.length() - read_digits;
  }
}


static bool DoubleStrtod(Vector<const char> trimmed,
                         int exponent,
                         double* result) {
#if !defined(DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS)
  // On x86 the floating-point stack can be 64 or 80 bits wide. If it is
  // 80 bits wide (as is the case on Linux) then double-rounding occurs and the
  // result is not accurate.
  // We know that Windows32 uses 64 bits and is therefore accurate.
  // Note that the ARM simulator is compiled for 32bits. It therefore exhibits
  // the same problem.
  return false;
#endif
  if (trimmed.length() <= kMaxExactDoubleIntegerDecimalDigits) {
    int read_digits;
    // The trimmed input fits into a double.
    // If the 10^exponent (resp. 10^-exponent) fits into a double too then we
    // can compute the result-double simply by multiplying (resp. dividing) the
    // two numbers.
    // This is possible because IEEE guarantees that floating-point operations
    // return the best possible approximation.
    if (exponent < 0 && -exponent < kExactPowersOfTenSize) {
      // 10^-exponent fits into a double.
      *result = static_cast<double>(ReadUint64(trimmed, &read_digits));
      ASSERT(read_digits == trimmed.length());
      *result /= exact_powers_of_ten[-exponent];
      return true;
    }
    if (0 <= exponent && exponent < kExactPowersOfTenSize) {
      // 10^exponent fits into a double.
      *result = static_cast<double>(ReadUint64(trimmed, &read_digits));
      ASSERT(read_digits == trimmed.length());
      *result *= exact_powers_of_ten[exponent];
      return true;
    }
    int remaining_digits =
        kMaxExactDoubleIntegerDecimalDigits - trimmed.length();
    if ((0 <= exponent) &&
        (exponent - remaining_digits < kExactPowersOfTenSize)) {
      // The trimmed string was short and we can multiply it with
      // 10^remaining_digits. As a result the remaining exponent now fits
      // into a double too.
      *result = static_cast<double>(ReadUint64(trimmed, &read_digits));
      ASSERT(read_digits == trimmed.length());
      *result *= exact_powers_of_ten[remaining_digits];
      *result *= exact_powers_of_ten[exponent - remaining_digits];
      return true;
    }
  }
  return false;
}


// Returns 10^exponent as an exact DiyFp.
// The given exponent must be in the range [1; kDecimalExponentDistance[.
static DiyFp AdjustmentPowerOfTen(int exponent) {
  ASSERT(0 < exponent);
  ASSERT(exponent < PowersOfTenCache::kDecimalExponentDistance);
  // Simply hardcode the remaining powers for the given decimal exponent
  // distance.
  ASSERT(PowersOfTenCache::kDecimalExponentDistance == 8);
  switch (exponent) {
    case 1: return DiyFp(UINT64_2PART_C(0xa0000000, 00000000), -60);
    case 2: return DiyFp(UINT64_2PART_C(0xc8000000, 00000000), -57);
    case 3: return DiyFp(UINT64_2PART_C(0xfa000000, 00000000), -54);
    case 4: return DiyFp(UINT64_2PART_C(0x9c400000, 00000000), -50);
    case 5: return DiyFp(UINT64_2PART_C(0xc3500000, 00000000), -47);
    case 6: return DiyFp(UINT64_2PART_C(0xf4240000, 00000000), -44);
    case 7: return DiyFp(UINT64_2PART_C(0x98968000, 00000000), -40);
    default:
      UNREACHABLE();
      return DiyFp(0, 0);
  }
}


// If the function returns true then the result is the correct double.
// Otherwise it is either the correct double or the double that is just below
// the correct double.
static bool DiyFpStrtod(Vector<const char> buffer,
                        int exponent,
                        double* result) {
  DiyFp input;
  int remaining_decimals;
  ReadDiyFp(buffer, &input, &remaining_decimals);
  // Since we may have dropped some digits the input is not accurate.
  // If remaining_decimals is different than 0 than the error is at most
  // .5 ulp (unit in the last place).
  // We don't want to deal with fractions and therefore keep a common
  // denominator.
  const int kDenominatorLog = 3;
  const int kDenominator = 1 << kDenominatorLog;
  // Move the remaining decimals into the exponent.
  exponent += remaining_decimals;
  int error = (remaining_decimals == 0 ? 0 : kDenominator / 2);

  int old_e = input.e();
  input.Normalize();
  error <<= old_e - input.e();

  ASSERT(exponent <= PowersOfTenCache::kMaxDecimalExponent);
  if (exponent < PowersOfTenCache::kMinDecimalExponent) {
    *result = 0.0;
    return true;
  }
  DiyFp cached_power;
  int cached_decimal_exponent;
  PowersOfTenCache::GetCachedPowerForDecimalExponent(exponent,
                                                     &cached_power,
                                                     &cached_decimal_exponent);

  if (cached_decimal_exponent != exponent) {
    int adjustment_exponent = exponent - cached_decimal_exponent;
    DiyFp adjustment_power = AdjustmentPowerOfTen(adjustment_exponent);
    input.Multiply(adjustment_power);
    if (kMaxUint64DecimalDigits - buffer.length() >= adjustment_exponent) {
      // The product of input with the adjustment power fits into a 64 bit
      // integer.
      ASSERT(DiyFp::kSignificandSize == 64);
    } else {
      // The adjustment power is exact. There is hence only an error of 0.5.
      error += kDenominator / 2;
    }
  }

  input.Multiply(cached_power);
  // The error introduced by a multiplication of a*b equals
  //   error_a + error_b + error_a*error_b/2^64 + 0.5
  // Substituting a with 'input' and b with 'cached_power' we have
  //   error_b = 0.5  (all cached powers have an error of less than 0.5 ulp),
  //   error_ab = 0 or 1 / kDenominator > error_a*error_b/ 2^64
  int error_b = kDenominator / 2;
  int error_ab = (error == 0 ? 0 : 1);  // We round up to 1.
  int fixed_error = kDenominator / 2;
  error += error_b + error_ab + fixed_error;

  old_e = input.e();
  input.Normalize();
  error <<= old_e - input.e();

  // See if the double's significand changes if we add/subtract the error.
  int order_of_magnitude = DiyFp::kSignificandSize + input.e();
  int effective_significand_size =
      Double::SignificandSizeForOrderOfMagnitude(order_of_magnitude);
  int precision_digits_count =
      DiyFp::kSignificandSize - effective_significand_size;
  if (precision_digits_count + kDenominatorLog >= DiyFp::kSignificandSize) {
    // This can only happen for very small denormals. In this case the
    // half-way multiplied by the denominator exceeds the range of an uint64.
    // Simply shift everything to the right.
    int shift_amount = (precision_digits_count + kDenominatorLog) -
        DiyFp::kSignificandSize + 1;
    input.set_f(input.f() >> shift_amount);
    input.set_e(input.e() + shift_amount);
    // We add 1 for the lost precision of error, and kDenominator for
    // the lost precision of input.f().
    error = (error >> shift_amount) + 1 + kDenominator;
    precision_digits_count -= shift_amount;
  }
  // We use uint64_ts now. This only works if the DiyFp uses uint64_ts too.
  ASSERT(DiyFp::kSignificandSize == 64);
  ASSERT(precision_digits_count < 64);
  uint64_t one64 = 1;
  uint64_t precision_bits_mask = (one64 << precision_digits_count) - 1;
  uint64_t precision_bits = input.f() & precision_bits_mask;
  uint64_t half_way = one64 << (precision_digits_count - 1);
  precision_bits *= kDenominator;
  half_way *= kDenominator;
  DiyFp rounded_input(input.f() >> precision_digits_count,
                      input.e() + precision_digits_count);
  if (precision_bits >= half_way + error) {
    rounded_input.set_f(rounded_input.f() + 1);
  }
  // If the last_bits are too close to the half-way case than we are too
  // inaccurate and round down. In this case we return false so that we can
  // fall back to a more precise algorithm.

  *result = Double(rounded_input).value();
  if (half_way - error < precision_bits && precision_bits < half_way + error) {
    // Too imprecise. The caller will have to fall back to a slower version.
    // However the returned number is guaranteed to be either the correct
    // double, or the next-lower double.
    return false;
  } else {
    return true;
  }
}


// Returns
//   - -1 if buffer*10^exponent < diy_fp.
//   -  0 if buffer*10^exponent == diy_fp.
//   - +1 if buffer*10^exponent > diy_fp.
// Preconditions:
//   buffer.length() + exponent <= kMaxDecimalPower + 1
//   buffer.length() + exponent > kMinDecimalPower
//   buffer.length() <= kMaxDecimalSignificantDigits
static int CompareBufferWithDiyFp(Vector<const char> buffer,
                                  int exponent,
                                  DiyFp diy_fp) {
  ASSERT(buffer.length() + exponent <= kMaxDecimalPower + 1);
  ASSERT(buffer.length() + exponent > kMinDecimalPower);
  ASSERT(buffer.length() <= kMaxSignificantDecimalDigits);
  // Make sure that the Bignum will be able to hold all our numbers.
  // Our Bignum implementation has a separate field for exponents. Shifts will
  // consume at most one bigit (< 64 bits).
  // ln(10) == 3.3219...
  ASSERT(((kMaxDecimalPower + 1) * 333 / 100) < Bignum::kMaxSignificantBits);
  Bignum buffer_bignum;
  Bignum diy_fp_bignum;
  buffer_bignum.AssignDecimalString(buffer);
  diy_fp_bignum.AssignUInt64(diy_fp.f());
  if (exponent >= 0) {
    buffer_bignum.MultiplyByPowerOfTen(exponent);
  } else {
    diy_fp_bignum.MultiplyByPowerOfTen(-exponent);
  }
  if (diy_fp.e() > 0) {
    diy_fp_bignum.ShiftLeft(diy_fp.e());
  } else {
    buffer_bignum.ShiftLeft(-diy_fp.e());
  }
  return Bignum::Compare(buffer_bignum, diy_fp_bignum);
}


// Returns true if the guess is the correct double.
// Returns false, when guess is either correct or the next-lower double.
static bool ComputeGuess(Vector<const char> trimmed, int exponent,
                         double* guess) {
  if (trimmed.length() == 0) {
    *guess = 0.0;
    return true;
  }
  if (exponent + trimmed.length() - 1 >= kMaxDecimalPower) {
    *guess = Double::Infinity();
    return true;
  }
  if (exponent + trimmed.length() <= kMinDecimalPower) {
    *guess = 0.0;
    return true;
  }

  if (DoubleStrtod(trimmed, exponent, guess) ||
      DiyFpStrtod(trimmed, exponent, guess)) {
    return true;
  }
  if (*guess == Double::Infinity()) {
    return true;
  }
  return false;
}

double Strtod(Vector<const char> buffer, int exponent) {
  char copy_buffer[kMaxSignificantDecimalDigits];
  Vector<const char> trimmed;
  int updated_exponent;
  TrimAndCut(buffer, exponent, copy_buffer, kMaxSignificantDecimalDigits,
             &trimmed, &updated_exponent);
  exponent = updated_exponent;

  double guess;
  bool is_correct = ComputeGuess(trimmed, exponent, &guess);
  if (is_correct) return guess;

  DiyFp upper_boundary = Double(guess).UpperBoundary();
  int comparison = CompareBufferWithDiyFp(trimmed, exponent, upper_boundary);
  if (comparison < 0) {
    return guess;
  } else if (comparison > 0) {
    return Double(guess).NextDouble();
  } else if ((Double(guess).Significand() & 1) == 0) {
    // Round towards even.
    return guess;
  } else {
    return Double(guess).NextDouble();
  }
}

float Strtof(Vector<const char> buffer, int exponent) {
  char copy_buffer[kMaxSignificantDecimalDigits];
  Vector<const char> trimmed;
  int updated_exponent;
  TrimAndCut(buffer, exponent, copy_buffer, kMaxSignificantDecimalDigits,
             &trimmed, &updated_exponent);
  exponent = updated_exponent;

  double double_guess;
  bool is_correct = ComputeGuess(trimmed, exponent, &double_guess);

  float float_guess = static_cast<float>(double_guess);
  if (float_guess == double_guess) {
    // This shortcut triggers for integer values.
    return float_guess;
  }

  // We must catch double-rounding. Say the double has been rounded up, and is
  // now a boundary of a float, and rounds up again. This is why we have to
  // look at previous too.
  // Example (in decimal numbers):
  //    input: 12349
  //    high-precision (4 digits): 1235
  //    low-precision (3 digits):
  //       when read from input: 123
  //       when rounded from high precision: 124.
  // To do this we simply look at the neigbors of the correct result and see
  // if they would round to the same float. If the guess is not correct we have
  // to look at four values (since two different doubles could be the correct
  // double).

  double double_next = Double(double_guess).NextDouble();
  double double_previous = Double(double_guess).PreviousDouble();

  float f1 = static_cast<float>(double_previous);
  float f2 = float_guess;
  float f3 = static_cast<float>(double_next);
  float f4;
  if (is_correct) {
    f4 = f3;
  } else {
    double double_next2 = Double(double_next).NextDouble();
    f4 = static_cast<float>(double_next2);
  }
  (void) f2; // Mark variable as used.
  ASSERT(f1 <= f2 && f2 <= f3 && f3 <= f4);

  // If the guess doesn't lie near a single-precision boundary we can simply
  // return its float-value.
  if (f1 == f4) {
    return float_guess;
  }

  ASSERT((f1 != f2 && f2 == f3 && f3 == f4) ||
         (f1 == f2 && f2 != f3 && f3 == f4) ||
         (f1 == f2 && f2 == f3 && f3 != f4));

  // guess and next are the two possible canditates (in the same way that
  // double_guess was the lower candidate for a double-precision guess).
  float guess = f1;
  float next = f4;
  DiyFp upper_boundary;
  if (guess == 0.0f) {
    float min_float = 1e-45f;
    upper_boundary = Double(static_cast<double>(min_float) / 2).AsDiyFp();
  } else {
    upper_boundary = Single(guess).UpperBoundary();
  }
  int comparison = CompareBufferWithDiyFp(trimmed, exponent, upper_boundary);
  if (comparison < 0) {
    return guess;
  } else if (comparison > 0) {
    return next;
  } else if ((Single(guess).Significand() & 1) == 0) {
    // Round towards even.
    return guess;
  } else {
    return next;
  }
}

}  // namespace double_conversion