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1 // © 2018 and later: Unicode, Inc. and others.
2 // License & terms of use: http://www.unicode.org/copyright.html
3 //
4 // From the double-conversion library. Original license:
5 //
6 // Copyright 2010 the V8 project authors. All rights reserved.
7 // Redistribution and use in source and binary forms, with or without
8 // modification, are permitted provided that the following conditions are
9 // met:
10 //
11 // * Redistributions of source code must retain the above copyright
12 // notice, this list of conditions and the following disclaimer.
13 // * Redistributions in binary form must reproduce the above
14 // copyright notice, this list of conditions and the following
15 // disclaimer in the documentation and/or other materials provided
16 // with the distribution.
17 // * Neither the name of Google Inc. nor the names of its
18 // contributors may be used to endorse or promote products derived
19 // from this software without specific prior written permission.
20 //
21 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
22 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
23 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
24 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
25 // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
26 // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
27 // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
28 // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
29 // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
30 // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
31 // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
32
33 // ICU PATCH: ifdef around UCONFIG_NO_FORMATTING
34 #include "unicode/utypes.h"
35 #if !UCONFIG_NO_FORMATTING
36
37 #include <climits>
38 #include <cstdarg>
39
40 // ICU PATCH: Customize header file paths for ICU.
41
42 #include "double-conversion-bignum.h"
43 #include "double-conversion-cached-powers.h"
44 #include "double-conversion-ieee.h"
45 #include "double-conversion-strtod.h"
46
47 // ICU PATCH: Wrap in ICU namespace
48 U_NAMESPACE_BEGIN
49
50 namespace double_conversion {
51
52 // 2^53 = 9007199254740992.
53 // Any integer with at most 15 decimal digits will hence fit into a double
54 // (which has a 53bit significand) without loss of precision.
55 static const int kMaxExactDoubleIntegerDecimalDigits = 15;
56 // 2^64 = 18446744073709551616 > 10^19
57 static const int kMaxUint64DecimalDigits = 19;
58
59 // Max double: 1.7976931348623157 x 10^308
60 // Min non-zero double: 4.9406564584124654 x 10^-324
61 // Any x >= 10^309 is interpreted as +infinity.
62 // Any x <= 10^-324 is interpreted as 0.
63 // Note that 2.5e-324 (despite being smaller than the min double) will be read
64 // as non-zero (equal to the min non-zero double).
65 static const int kMaxDecimalPower = 309;
66 static const int kMinDecimalPower = -324;
67
68 // 2^64 = 18446744073709551616
69 static const uint64_t kMaxUint64 = DOUBLE_CONVERSION_UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF);
70
71
72 static const double exact_powers_of_ten[] = {
73 1.0, // 10^0
74 10.0,
75 100.0,
76 1000.0,
77 10000.0,
78 100000.0,
79 1000000.0,
80 10000000.0,
81 100000000.0,
82 1000000000.0,
83 10000000000.0, // 10^10
84 100000000000.0,
85 1000000000000.0,
86 10000000000000.0,
87 100000000000000.0,
88 1000000000000000.0,
89 10000000000000000.0,
90 100000000000000000.0,
91 1000000000000000000.0,
92 10000000000000000000.0,
93 100000000000000000000.0, // 10^20
94 1000000000000000000000.0,
95 // 10^22 = 0x21e19e0c9bab2400000 = 0x878678326eac9 * 2^22
96 10000000000000000000000.0
97 };
98 static const int kExactPowersOfTenSize = DOUBLE_CONVERSION_ARRAY_SIZE(exact_powers_of_ten);
99
100 // Maximum number of significant digits in the decimal representation.
101 // In fact the value is 772 (see conversions.cc), but to give us some margin
102 // we round up to 780.
103 static const int kMaxSignificantDecimalDigits = 780;
104
105 static Vector<const char> TrimLeadingZeros(Vector<const char> buffer) {
106 for (int i = 0; i < buffer.length(); i++) {
107 if (buffer[i] != '0') {
108 return buffer.SubVector(i, buffer.length());
109 }
110 }
111 return Vector<const char>(buffer.start(), 0);
112 }
113
114
115 static Vector<const char> TrimTrailingZeros(Vector<const char> buffer) {
116 for (int i = buffer.length() - 1; i >= 0; --i) {
117 if (buffer[i] != '0') {
118 return buffer.SubVector(0, i + 1);
119 }
120 }
121 return Vector<const char>(buffer.start(), 0);
122 }
123
124
125 static void CutToMaxSignificantDigits(Vector<const char> buffer,
126 int exponent,
127 char* significant_buffer,
128 int* significant_exponent) {
129 for (int i = 0; i < kMaxSignificantDecimalDigits - 1; ++i) {
130 significant_buffer[i] = buffer[i];
131 }
132 // The input buffer has been trimmed. Therefore the last digit must be
133 // different from '0'.
134 DOUBLE_CONVERSION_ASSERT(buffer[buffer.length() - 1] != '0');
135 // Set the last digit to be non-zero. This is sufficient to guarantee
136 // correct rounding.
137 significant_buffer[kMaxSignificantDecimalDigits - 1] = '1';
138 *significant_exponent =
139 exponent + (buffer.length() - kMaxSignificantDecimalDigits);
140 }
141
142
143 // Trims the buffer and cuts it to at most kMaxSignificantDecimalDigits.
144 // If possible the input-buffer is reused, but if the buffer needs to be
145 // modified (due to cutting), then the input needs to be copied into the
146 // buffer_copy_space.
147 static void TrimAndCut(Vector<const char> buffer, int exponent,
148 char* buffer_copy_space, int space_size,
149 Vector<const char>* trimmed, int* updated_exponent) {
150 Vector<const char> left_trimmed = TrimLeadingZeros(buffer);
151 Vector<const char> right_trimmed = TrimTrailingZeros(left_trimmed);
152 exponent += left_trimmed.length() - right_trimmed.length();
153 if (right_trimmed.length() > kMaxSignificantDecimalDigits) {
154 (void) space_size; // Mark variable as used.
155 DOUBLE_CONVERSION_ASSERT(space_size >= kMaxSignificantDecimalDigits);
156 CutToMaxSignificantDigits(right_trimmed, exponent,
157 buffer_copy_space, updated_exponent);
158 *trimmed = Vector<const char>(buffer_copy_space,
159 kMaxSignificantDecimalDigits);
160 } else {
161 *trimmed = right_trimmed;
162 *updated_exponent = exponent;
163 }
164 }
165
166
167 // Reads digits from the buffer and converts them to a uint64.
168 // Reads in as many digits as fit into a uint64.
169 // When the string starts with "1844674407370955161" no further digit is read.
170 // Since 2^64 = 18446744073709551616 it would still be possible read another
171 // digit if it was less or equal than 6, but this would complicate the code.
172 static uint64_t ReadUint64(Vector<const char> buffer,
173 int* number_of_read_digits) {
174 uint64_t result = 0;
175 int i = 0;
176 while (i < buffer.length() && result <= (kMaxUint64 / 10 - 1)) {
177 int digit = buffer[i++] - '0';
178 DOUBLE_CONVERSION_ASSERT(0 <= digit && digit <= 9);
179 result = 10 * result + digit;
180 }
181 *number_of_read_digits = i;
182 return result;
183 }
184
185
186 // Reads a DiyFp from the buffer.
187 // The returned DiyFp is not necessarily normalized.
188 // If remaining_decimals is zero then the returned DiyFp is accurate.
189 // Otherwise it has been rounded and has error of at most 1/2 ulp.
190 static void ReadDiyFp(Vector<const char> buffer,
191 DiyFp* result,
192 int* remaining_decimals) {
193 int read_digits;
194 uint64_t significand = ReadUint64(buffer, &read_digits);
195 if (buffer.length() == read_digits) {
196 *result = DiyFp(significand, 0);
197 *remaining_decimals = 0;
198 } else {
199 // Round the significand.
200 if (buffer[read_digits] >= '5') {
201 significand++;
202 }
203 // Compute the binary exponent.
204 int exponent = 0;
205 *result = DiyFp(significand, exponent);
206 *remaining_decimals = buffer.length() - read_digits;
207 }
208 }
209
210
211 static bool DoubleStrtod(Vector<const char> trimmed,
212 int exponent,
213 double* result) {
214 #if !defined(DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS)
215 // On x86 the floating-point stack can be 64 or 80 bits wide. If it is
216 // 80 bits wide (as is the case on Linux) then double-rounding occurs and the
217 // result is not accurate.
218 // We know that Windows32 uses 64 bits and is therefore accurate.
219 // Note that the ARM simulator is compiled for 32bits. It therefore exhibits
220 // the same problem.
221 return false;
222 #else
223 if (trimmed.length() <= kMaxExactDoubleIntegerDecimalDigits) {
224 int read_digits;
225 // The trimmed input fits into a double.
226 // If the 10^exponent (resp. 10^-exponent) fits into a double too then we
227 // can compute the result-double simply by multiplying (resp. dividing) the
228 // two numbers.
229 // This is possible because IEEE guarantees that floating-point operations
230 // return the best possible approximation.
231 if (exponent < 0 && -exponent < kExactPowersOfTenSize) {
232 // 10^-exponent fits into a double.
233 *result = static_cast<double>(ReadUint64(trimmed, &read_digits));
234 DOUBLE_CONVERSION_ASSERT(read_digits == trimmed.length());
235 *result /= exact_powers_of_ten[-exponent];
236 return true;
237 }
238 if (0 <= exponent && exponent < kExactPowersOfTenSize) {
239 // 10^exponent fits into a double.
240 *result = static_cast<double>(ReadUint64(trimmed, &read_digits));
241 DOUBLE_CONVERSION_ASSERT(read_digits == trimmed.length());
242 *result *= exact_powers_of_ten[exponent];
243 return true;
244 }
245 int remaining_digits =
246 kMaxExactDoubleIntegerDecimalDigits - trimmed.length();
247 if ((0 <= exponent) &&
248 (exponent - remaining_digits < kExactPowersOfTenSize)) {
249 // The trimmed string was short and we can multiply it with
250 // 10^remaining_digits. As a result the remaining exponent now fits
251 // into a double too.
252 *result = static_cast<double>(ReadUint64(trimmed, &read_digits));
253 DOUBLE_CONVERSION_ASSERT(read_digits == trimmed.length());
254 *result *= exact_powers_of_ten[remaining_digits];
255 *result *= exact_powers_of_ten[exponent - remaining_digits];
256 return true;
257 }
258 }
259 return false;
260 #endif
261 }
262
263
264 // Returns 10^exponent as an exact DiyFp.
265 // The given exponent must be in the range [1; kDecimalExponentDistance[.
266 static DiyFp AdjustmentPowerOfTen(int exponent) {
267 DOUBLE_CONVERSION_ASSERT(0 < exponent);
268 DOUBLE_CONVERSION_ASSERT(exponent < PowersOfTenCache::kDecimalExponentDistance);
269 // Simply hardcode the remaining powers for the given decimal exponent
270 // distance.
271 DOUBLE_CONVERSION_ASSERT(PowersOfTenCache::kDecimalExponentDistance == 8);
272 switch (exponent) {
273 case 1: return DiyFp(DOUBLE_CONVERSION_UINT64_2PART_C(0xa0000000, 00000000), -60);
274 case 2: return DiyFp(DOUBLE_CONVERSION_UINT64_2PART_C(0xc8000000, 00000000), -57);
275 case 3: return DiyFp(DOUBLE_CONVERSION_UINT64_2PART_C(0xfa000000, 00000000), -54);
276 case 4: return DiyFp(DOUBLE_CONVERSION_UINT64_2PART_C(0x9c400000, 00000000), -50);
277 case 5: return DiyFp(DOUBLE_CONVERSION_UINT64_2PART_C(0xc3500000, 00000000), -47);
278 case 6: return DiyFp(DOUBLE_CONVERSION_UINT64_2PART_C(0xf4240000, 00000000), -44);
279 case 7: return DiyFp(DOUBLE_CONVERSION_UINT64_2PART_C(0x98968000, 00000000), -40);
280 default:
281 DOUBLE_CONVERSION_UNREACHABLE();
282 }
283 }
284
285
286 // If the function returns true then the result is the correct double.
287 // Otherwise it is either the correct double or the double that is just below
288 // the correct double.
289 static bool DiyFpStrtod(Vector<const char> buffer,
290 int exponent,
291 double* result) {
292 DiyFp input;
293 int remaining_decimals;
294 ReadDiyFp(buffer, &input, &remaining_decimals);
295 // Since we may have dropped some digits the input is not accurate.
296 // If remaining_decimals is different than 0 than the error is at most
297 // .5 ulp (unit in the last place).
298 // We don't want to deal with fractions and therefore keep a common
299 // denominator.
300 const int kDenominatorLog = 3;
301 const int kDenominator = 1 << kDenominatorLog;
302 // Move the remaining decimals into the exponent.
303 exponent += remaining_decimals;
304 uint64_t error = (remaining_decimals == 0 ? 0 : kDenominator / 2);
305
306 int old_e = input.e();
307 input.Normalize();
308 error <<= old_e - input.e();
309
310 DOUBLE_CONVERSION_ASSERT(exponent <= PowersOfTenCache::kMaxDecimalExponent);
311 if (exponent < PowersOfTenCache::kMinDecimalExponent) {
312 *result = 0.0;
313 return true;
314 }
315 DiyFp cached_power;
316 int cached_decimal_exponent;
317 PowersOfTenCache::GetCachedPowerForDecimalExponent(exponent,
318 &cached_power,
319 &cached_decimal_exponent);
320
321 if (cached_decimal_exponent != exponent) {
322 int adjustment_exponent = exponent - cached_decimal_exponent;
323 DiyFp adjustment_power = AdjustmentPowerOfTen(adjustment_exponent);
324 input.Multiply(adjustment_power);
325 if (kMaxUint64DecimalDigits - buffer.length() >= adjustment_exponent) {
326 // The product of input with the adjustment power fits into a 64 bit
327 // integer.
328 DOUBLE_CONVERSION_ASSERT(DiyFp::kSignificandSize == 64);
329 } else {
330 // The adjustment power is exact. There is hence only an error of 0.5.
331 error += kDenominator / 2;
332 }
333 }
334
335 input.Multiply(cached_power);
336 // The error introduced by a multiplication of a*b equals
337 // error_a + error_b + error_a*error_b/2^64 + 0.5
338 // Substituting a with 'input' and b with 'cached_power' we have
339 // error_b = 0.5 (all cached powers have an error of less than 0.5 ulp),
340 // error_ab = 0 or 1 / kDenominator > error_a*error_b/ 2^64
341 int error_b = kDenominator / 2;
342 int error_ab = (error == 0 ? 0 : 1); // We round up to 1.
343 int fixed_error = kDenominator / 2;
344 error += error_b + error_ab + fixed_error;
345
346 old_e = input.e();
347 input.Normalize();
348 error <<= old_e - input.e();
349
350 // See if the double's significand changes if we add/subtract the error.
351 int order_of_magnitude = DiyFp::kSignificandSize + input.e();
352 int effective_significand_size =
353 Double::SignificandSizeForOrderOfMagnitude(order_of_magnitude);
354 int precision_digits_count =
355 DiyFp::kSignificandSize - effective_significand_size;
356 if (precision_digits_count + kDenominatorLog >= DiyFp::kSignificandSize) {
357 // This can only happen for very small denormals. In this case the
358 // half-way multiplied by the denominator exceeds the range of an uint64.
359 // Simply shift everything to the right.
360 int shift_amount = (precision_digits_count + kDenominatorLog) -
361 DiyFp::kSignificandSize + 1;
362 input.set_f(input.f() >> shift_amount);
363 input.set_e(input.e() + shift_amount);
364 // We add 1 for the lost precision of error, and kDenominator for
365 // the lost precision of input.f().
366 error = (error >> shift_amount) + 1 + kDenominator;
367 precision_digits_count -= shift_amount;
368 }
369 // We use uint64_ts now. This only works if the DiyFp uses uint64_ts too.
370 DOUBLE_CONVERSION_ASSERT(DiyFp::kSignificandSize == 64);
371 DOUBLE_CONVERSION_ASSERT(precision_digits_count < 64);
372 uint64_t one64 = 1;
373 uint64_t precision_bits_mask = (one64 << precision_digits_count) - 1;
374 uint64_t precision_bits = input.f() & precision_bits_mask;
375 uint64_t half_way = one64 << (precision_digits_count - 1);
376 precision_bits *= kDenominator;
377 half_way *= kDenominator;
378 DiyFp rounded_input(input.f() >> precision_digits_count,
379 input.e() + precision_digits_count);
380 if (precision_bits >= half_way + error) {
381 rounded_input.set_f(rounded_input.f() + 1);
382 }
383 // If the last_bits are too close to the half-way case than we are too
384 // inaccurate and round down. In this case we return false so that we can
385 // fall back to a more precise algorithm.
386
387 *result = Double(rounded_input).value();
388 if (half_way - error < precision_bits && precision_bits < half_way + error) {
389 // Too imprecise. The caller will have to fall back to a slower version.
390 // However the returned number is guaranteed to be either the correct
391 // double, or the next-lower double.
392 return false;
393 } else {
394 return true;
395 }
396 }
397
398
399 // Returns
400 // - -1 if buffer*10^exponent < diy_fp.
401 // - 0 if buffer*10^exponent == diy_fp.
402 // - +1 if buffer*10^exponent > diy_fp.
403 // Preconditions:
404 // buffer.length() + exponent <= kMaxDecimalPower + 1
405 // buffer.length() + exponent > kMinDecimalPower
406 // buffer.length() <= kMaxDecimalSignificantDigits
407 static int CompareBufferWithDiyFp(Vector<const char> buffer,
408 int exponent,
409 DiyFp diy_fp) {
410 DOUBLE_CONVERSION_ASSERT(buffer.length() + exponent <= kMaxDecimalPower + 1);
411 DOUBLE_CONVERSION_ASSERT(buffer.length() + exponent > kMinDecimalPower);
412 DOUBLE_CONVERSION_ASSERT(buffer.length() <= kMaxSignificantDecimalDigits);
413 // Make sure that the Bignum will be able to hold all our numbers.
414 // Our Bignum implementation has a separate field for exponents. Shifts will
415 // consume at most one bigit (< 64 bits).
416 // ln(10) == 3.3219...
417 DOUBLE_CONVERSION_ASSERT(((kMaxDecimalPower + 1) * 333 / 100) < Bignum::kMaxSignificantBits);
418 Bignum buffer_bignum;
419 Bignum diy_fp_bignum;
420 buffer_bignum.AssignDecimalString(buffer);
421 diy_fp_bignum.AssignUInt64(diy_fp.f());
422 if (exponent >= 0) {
423 buffer_bignum.MultiplyByPowerOfTen(exponent);
424 } else {
425 diy_fp_bignum.MultiplyByPowerOfTen(-exponent);
426 }
427 if (diy_fp.e() > 0) {
428 diy_fp_bignum.ShiftLeft(diy_fp.e());
429 } else {
430 buffer_bignum.ShiftLeft(-diy_fp.e());
431 }
432 return Bignum::Compare(buffer_bignum, diy_fp_bignum);
433 }
434
435
436 // Returns true if the guess is the correct double.
437 // Returns false, when guess is either correct or the next-lower double.
438 static bool ComputeGuess(Vector<const char> trimmed, int exponent,
439 double* guess) {
440 if (trimmed.length() == 0) {
441 *guess = 0.0;
442 return true;
443 }
444 if (exponent + trimmed.length() - 1 >= kMaxDecimalPower) {
445 *guess = Double::Infinity();
446 return true;
447 }
448 if (exponent + trimmed.length() <= kMinDecimalPower) {
449 *guess = 0.0;
450 return true;
451 }
452
453 if (DoubleStrtod(trimmed, exponent, guess) ||
454 DiyFpStrtod(trimmed, exponent, guess)) {
455 return true;
456 }
457 if (*guess == Double::Infinity()) {
458 return true;
459 }
460 return false;
461 }
462
463 #if U_DEBUG // needed for ICU only in debug mode
464 static bool IsDigit(const char d) {
465 return ('0' <= d) && (d <= '9');
466 }
467
468 static bool IsNonZeroDigit(const char d) {
469 return ('1' <= d) && (d <= '9');
470 }
471
472 static bool AssertTrimmedDigits(const Vector<const char>& buffer) {
473 for(int i = 0; i < buffer.length(); ++i) {
474 if(!IsDigit(buffer[i])) {
475 return false;
476 }
477 }
478 return (buffer.length() == 0) || (IsNonZeroDigit(buffer[0]) && IsNonZeroDigit(buffer[buffer.length()-1]));
479 }
480 #endif // needed for ICU only in debug mode
481
482 double StrtodTrimmed(Vector<const char> trimmed, int exponent) {
483 DOUBLE_CONVERSION_ASSERT(trimmed.length() <= kMaxSignificantDecimalDigits);
484 DOUBLE_CONVERSION_ASSERT(AssertTrimmedDigits(trimmed));
485 double guess;
486 const bool is_correct = ComputeGuess(trimmed, exponent, &guess);
487 if (is_correct) {
488 return guess;
489 }
490 DiyFp upper_boundary = Double(guess).UpperBoundary();
491 int comparison = CompareBufferWithDiyFp(trimmed, exponent, upper_boundary);
492 if (comparison < 0) {
493 return guess;
494 } else if (comparison > 0) {
495 return Double(guess).NextDouble();
496 } else if ((Double(guess).Significand() & 1) == 0) {
497 // Round towards even.
498 return guess;
499 } else {
500 return Double(guess).NextDouble();
501 }
502 }
503
504 double Strtod(Vector<const char> buffer, int exponent) {
505 char copy_buffer[kMaxSignificantDecimalDigits];
506 Vector<const char> trimmed;
507 int updated_exponent;
508 TrimAndCut(buffer, exponent, copy_buffer, kMaxSignificantDecimalDigits,
509 &trimmed, &updated_exponent);
510 return StrtodTrimmed(trimmed, updated_exponent);
511 }
512
513 static float SanitizedDoubletof(double d) {
514 DOUBLE_CONVERSION_ASSERT(d >= 0.0);
515 // ASAN has a sanitize check that disallows casting doubles to floats if
516 // they are too big.
517 // https://clang.llvm.org/docs/UndefinedBehaviorSanitizer.html#available-checks
518 // The behavior should be covered by IEEE 754, but some projects use this
519 // flag, so work around it.
520 float max_finite = 3.4028234663852885981170418348451692544e+38;
521 // The half-way point between the max-finite and infinity value.
522 // Since infinity has an even significand everything equal or greater than
523 // this value should become infinity.
524 double half_max_finite_infinity =
525 3.40282356779733661637539395458142568448e+38;
526 if (d >= max_finite) {
527 if (d >= half_max_finite_infinity) {
528 return Single::Infinity();
529 } else {
530 return max_finite;
531 }
532 } else {
533 return static_cast<float>(d);
534 }
535 }
536
537 float Strtof(Vector<const char> buffer, int exponent) {
538 char copy_buffer[kMaxSignificantDecimalDigits];
539 Vector<const char> trimmed;
540 int updated_exponent;
541 TrimAndCut(buffer, exponent, copy_buffer, kMaxSignificantDecimalDigits,
542 &trimmed, &updated_exponent);
543 exponent = updated_exponent;
544
545 double double_guess;
546 bool is_correct = ComputeGuess(trimmed, exponent, &double_guess);
547
548 float float_guess = SanitizedDoubletof(double_guess);
549 if (float_guess == double_guess) {
550 // This shortcut triggers for integer values.
551 return float_guess;
552 }
553
554 // We must catch double-rounding. Say the double has been rounded up, and is
555 // now a boundary of a float, and rounds up again. This is why we have to
556 // look at previous too.
557 // Example (in decimal numbers):
558 // input: 12349
559 // high-precision (4 digits): 1235
560 // low-precision (3 digits):
561 // when read from input: 123
562 // when rounded from high precision: 124.
563 // To do this we simply look at the neigbors of the correct result and see
564 // if they would round to the same float. If the guess is not correct we have
565 // to look at four values (since two different doubles could be the correct
566 // double).
567
568 double double_next = Double(double_guess).NextDouble();
569 double double_previous = Double(double_guess).PreviousDouble();
570
571 float f1 = SanitizedDoubletof(double_previous);
572 float f2 = float_guess;
573 float f3 = SanitizedDoubletof(double_next);
574 float f4;
575 if (is_correct) {
576 f4 = f3;
577 } else {
578 double double_next2 = Double(double_next).NextDouble();
579 f4 = SanitizedDoubletof(double_next2);
580 }
581 (void) f2; // Mark variable as used.
582 DOUBLE_CONVERSION_ASSERT(f1 <= f2 && f2 <= f3 && f3 <= f4);
583
584 // If the guess doesn't lie near a single-precision boundary we can simply
585 // return its float-value.
586 if (f1 == f4) {
587 return float_guess;
588 }
589
590 DOUBLE_CONVERSION_ASSERT((f1 != f2 && f2 == f3 && f3 == f4) ||
591 (f1 == f2 && f2 != f3 && f3 == f4) ||
592 (f1 == f2 && f2 == f3 && f3 != f4));
593
594 // guess and next are the two possible candidates (in the same way that
595 // double_guess was the lower candidate for a double-precision guess).
596 float guess = f1;
597 float next = f4;
598 DiyFp upper_boundary;
599 if (guess == 0.0f) {
600 float min_float = 1e-45f;
601 upper_boundary = Double(static_cast<double>(min_float) / 2).AsDiyFp();
602 } else {
603 upper_boundary = Single(guess).UpperBoundary();
604 }
605 int comparison = CompareBufferWithDiyFp(trimmed, exponent, upper_boundary);
606 if (comparison < 0) {
607 return guess;
608 } else if (comparison > 0) {
609 return next;
610 } else if ((Single(guess).Significand() & 1) == 0) {
611 // Round towards even.
612 return guess;
613 } else {
614 return next;
615 }
616 }
617
618 } // namespace double_conversion
619
620 // ICU PATCH: Close ICU namespace
621 U_NAMESPACE_END
622 #endif // ICU PATCH: close #if !UCONFIG_NO_FORMATTING