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27
28#include <climits>
29#include <cstdarg>
30
31#include <double-conversion/bignum.h>
32#include <double-conversion/cached-powers.h>
33#include <double-conversion/ieee.h>
34#include <double-conversion/strtod.h>
35
36namespace double_conversion {
37
38// 2^53 = 9007199254740992.
39// Any integer with at most 15 decimal digits will hence fit into a double
40// (which has a 53bit significand) without loss of precision.
41static const int kMaxExactDoubleIntegerDecimalDigits = 15;
42// 2^64 = 18446744073709551616 > 10^19
43static const int kMaxUint64DecimalDigits = 19;
44
45// Max double: 1.7976931348623157 x 10^308
46// Min non-zero double: 4.9406564584124654 x 10^-324
47// Any x >= 10^309 is interpreted as +infinity.
48// Any x <= 10^-324 is interpreted as 0.
49// Note that 2.5e-324 (despite being smaller than the min double) will be read
50// as non-zero (equal to the min non-zero double).
51static const int kMaxDecimalPower = 309;
52static const int kMinDecimalPower = -324;
53
54// 2^64 = 18446744073709551616
55static const uint64_t kMaxUint64 = UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF);
56
57
58static const double exact_powers_of_ten[] = {
59 1.0, // 10^0
60 10.0,
61 100.0,
62 1000.0,
63 10000.0,
64 100000.0,
65 1000000.0,
66 10000000.0,
67 100000000.0,
68 1000000000.0,
69 10000000000.0, // 10^10
70 100000000000.0,
71 1000000000000.0,
72 10000000000000.0,
73 100000000000000.0,
74 1000000000000000.0,
75 10000000000000000.0,
76 100000000000000000.0,
77 1000000000000000000.0,
78 10000000000000000000.0,
79 100000000000000000000.0, // 10^20
80 1000000000000000000000.0,
81 // 10^22 = 0x21e19e0c9bab2400000 = 0x878678326eac9 * 2^22
82 10000000000000000000000.0
83};
84static const int kExactPowersOfTenSize = ARRAY_SIZE(exact_powers_of_ten);
85
86// Maximum number of significant digits in the decimal representation.
87// In fact the value is 772 (see conversions.cc), but to give us some margin
88// we round up to 780.
89static const int kMaxSignificantDecimalDigits = 780;
90
91static Vector<const char> TrimLeadingZeros(Vector<const char> buffer) {
92 for (int i = 0; i < buffer.length(); i++) {
93 if (buffer[i] != '0') {
94 return buffer.SubVector(from: i, to: buffer.length());
95 }
96 }
97 return Vector<const char>(buffer.start(), 0);
98}
99
100
101static Vector<const char> TrimTrailingZeros(Vector<const char> buffer) {
102 for (int i = buffer.length() - 1; i >= 0; --i) {
103 if (buffer[i] != '0') {
104 return buffer.SubVector(from: 0, to: i + 1);
105 }
106 }
107 return Vector<const char>(buffer.start(), 0);
108}
109
110
111static void CutToMaxSignificantDigits(Vector<const char> buffer,
112 int exponent,
113 char* significant_buffer,
114 int* significant_exponent) {
115 for (int i = 0; i < kMaxSignificantDecimalDigits - 1; ++i) {
116 significant_buffer[i] = buffer[i];
117 }
118 // The input buffer has been trimmed. Therefore the last digit must be
119 // different from '0'.
120 ASSERT(buffer[buffer.length() - 1] != '0');
121 // Set the last digit to be non-zero. This is sufficient to guarantee
122 // correct rounding.
123 significant_buffer[kMaxSignificantDecimalDigits - 1] = '1';
124 *significant_exponent =
125 exponent + (buffer.length() - kMaxSignificantDecimalDigits);
126}
127
128
129// Trims the buffer and cuts it to at most kMaxSignificantDecimalDigits.
130// If possible the input-buffer is reused, but if the buffer needs to be
131// modified (due to cutting), then the input needs to be copied into the
132// buffer_copy_space.
133static void TrimAndCut(Vector<const char> buffer, int exponent,
134 char* buffer_copy_space, int space_size,
135 Vector<const char>* trimmed, int* updated_exponent) {
136 Vector<const char> left_trimmed = TrimLeadingZeros(buffer);
137 Vector<const char> right_trimmed = TrimTrailingZeros(buffer: left_trimmed);
138 exponent += left_trimmed.length() - right_trimmed.length();
139 if (right_trimmed.length() > kMaxSignificantDecimalDigits) {
140 (void) space_size; // Mark variable as used.
141 ASSERT(space_size >= kMaxSignificantDecimalDigits);
142 CutToMaxSignificantDigits(buffer: right_trimmed, exponent,
143 significant_buffer: buffer_copy_space, significant_exponent: updated_exponent);
144 *trimmed = Vector<const char>(buffer_copy_space,
145 kMaxSignificantDecimalDigits);
146 } else {
147 *trimmed = right_trimmed;
148 *updated_exponent = exponent;
149 }
150}
151
152
153// Reads digits from the buffer and converts them to a uint64.
154// Reads in as many digits as fit into a uint64.
155// When the string starts with "1844674407370955161" no further digit is read.
156// Since 2^64 = 18446744073709551616 it would still be possible read another
157// digit if it was less or equal than 6, but this would complicate the code.
158static uint64_t ReadUint64(Vector<const char> buffer,
159 int* number_of_read_digits) {
160 uint64_t result = 0;
161 int i = 0;
162 while (i < buffer.length() && result <= (kMaxUint64 / 10 - 1)) {
163 int digit = buffer[i++] - '0';
164 ASSERT(0 <= digit && digit <= 9);
165 result = 10 * result + digit;
166 }
167 *number_of_read_digits = i;
168 return result;
169}
170
171
172// Reads a DiyFp from the buffer.
173// The returned DiyFp is not necessarily normalized.
174// If remaining_decimals is zero then the returned DiyFp is accurate.
175// Otherwise it has been rounded and has error of at most 1/2 ulp.
176static void ReadDiyFp(Vector<const char> buffer,
177 DiyFp* result,
178 int* remaining_decimals) {
179 int read_digits;
180 uint64_t significand = ReadUint64(buffer, number_of_read_digits: &read_digits);
181 if (buffer.length() == read_digits) {
182 *result = DiyFp(significand, 0);
183 *remaining_decimals = 0;
184 } else {
185 // Round the significand.
186 if (buffer[read_digits] >= '5') {
187 significand++;
188 }
189 // Compute the binary exponent.
190 int exponent = 0;
191 *result = DiyFp(significand, exponent);
192 *remaining_decimals = buffer.length() - read_digits;
193 }
194}
195
196
197static bool DoubleStrtod(Vector<const char> trimmed,
198 int exponent,
199 double* result) {
200#if !defined(DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS)
201 // NB: Qt uses -Werror=unused-parameter which results in compiler error here
202 // in this branch. Using "(void)x" idiom to prevent the error.
203 (void)trimmed;
204 (void)exponent;
205 (void)result;
206
207 // On x86 the floating-point stack can be 64 or 80 bits wide. If it is
208 // 80 bits wide (as is the case on Linux) then double-rounding occurs and the
209 // result is not accurate.
210 // We know that Windows32 uses 64 bits and is therefore accurate.
211 // Note that the ARM simulator is compiled for 32bits. It therefore exhibits
212 // the same problem.
213 return false;
214#else
215 if (trimmed.length() <= kMaxExactDoubleIntegerDecimalDigits) {
216 int read_digits;
217 // The trimmed input fits into a double.
218 // If the 10^exponent (resp. 10^-exponent) fits into a double too then we
219 // can compute the result-double simply by multiplying (resp. dividing) the
220 // two numbers.
221 // This is possible because IEEE guarantees that floating-point operations
222 // return the best possible approximation.
223 if (exponent < 0 && -exponent < kExactPowersOfTenSize) {
224 // 10^-exponent fits into a double.
225 *result = static_cast<double>(ReadUint64(buffer: trimmed, number_of_read_digits: &read_digits));
226 ASSERT(read_digits == trimmed.length());
227 *result /= exact_powers_of_ten[-exponent];
228 return true;
229 }
230 if (0 <= exponent && exponent < kExactPowersOfTenSize) {
231 // 10^exponent fits into a double.
232 *result = static_cast<double>(ReadUint64(buffer: trimmed, number_of_read_digits: &read_digits));
233 ASSERT(read_digits == trimmed.length());
234 *result *= exact_powers_of_ten[exponent];
235 return true;
236 }
237 int remaining_digits =
238 kMaxExactDoubleIntegerDecimalDigits - trimmed.length();
239 if ((0 <= exponent) &&
240 (exponent - remaining_digits < kExactPowersOfTenSize)) {
241 // The trimmed string was short and we can multiply it with
242 // 10^remaining_digits. As a result the remaining exponent now fits
243 // into a double too.
244 *result = static_cast<double>(ReadUint64(buffer: trimmed, number_of_read_digits: &read_digits));
245 ASSERT(read_digits == trimmed.length());
246 *result *= exact_powers_of_ten[remaining_digits];
247 *result *= exact_powers_of_ten[exponent - remaining_digits];
248 return true;
249 }
250 }
251 return false;
252#endif
253}
254
255
256// Returns 10^exponent as an exact DiyFp.
257// The given exponent must be in the range [1; kDecimalExponentDistance[.
258static DiyFp AdjustmentPowerOfTen(int exponent) {
259 ASSERT(0 < exponent);
260 ASSERT(exponent < PowersOfTenCache::kDecimalExponentDistance);
261 // Simply hardcode the remaining powers for the given decimal exponent
262 // distance.
263 ASSERT(PowersOfTenCache::kDecimalExponentDistance == 8);
264 switch (exponent) {
265 case 1: return DiyFp(UINT64_2PART_C(0xa0000000, 00000000), -60);
266 case 2: return DiyFp(UINT64_2PART_C(0xc8000000, 00000000), -57);
267 case 3: return DiyFp(UINT64_2PART_C(0xfa000000, 00000000), -54);
268 case 4: return DiyFp(UINT64_2PART_C(0x9c400000, 00000000), -50);
269 case 5: return DiyFp(UINT64_2PART_C(0xc3500000, 00000000), -47);
270 case 6: return DiyFp(UINT64_2PART_C(0xf4240000, 00000000), -44);
271 case 7: return DiyFp(UINT64_2PART_C(0x98968000, 00000000), -40);
272 default:
273 UNREACHABLE();
274 }
275}
276
277
278// If the function returns true then the result is the correct double.
279// Otherwise it is either the correct double or the double that is just below
280// the correct double.
281static bool DiyFpStrtod(Vector<const char> buffer,
282 int exponent,
283 double* result) {
284 DiyFp input;
285 int remaining_decimals;
286 ReadDiyFp(buffer, result: &input, remaining_decimals: &remaining_decimals);
287 // Since we may have dropped some digits the input is not accurate.
288 // If remaining_decimals is different than 0 than the error is at most
289 // .5 ulp (unit in the last place).
290 // We don't want to deal with fractions and therefore keep a common
291 // denominator.
292 const int kDenominatorLog = 3;
293 const int kDenominator = 1 << kDenominatorLog;
294 // Move the remaining decimals into the exponent.
295 exponent += remaining_decimals;
296 uint64_t error = (remaining_decimals == 0 ? 0 : kDenominator / 2);
297
298 int old_e = input.e();
299 input.Normalize();
300 error <<= old_e - input.e();
301
302 ASSERT(exponent <= PowersOfTenCache::kMaxDecimalExponent);
303 if (exponent < PowersOfTenCache::kMinDecimalExponent) {
304 *result = 0.0;
305 return true;
306 }
307 DiyFp cached_power;
308 int cached_decimal_exponent;
309 PowersOfTenCache::GetCachedPowerForDecimalExponent(requested_exponent: exponent,
310 power: &cached_power,
311 found_exponent: &cached_decimal_exponent);
312
313 if (cached_decimal_exponent != exponent) {
314 int adjustment_exponent = exponent - cached_decimal_exponent;
315 DiyFp adjustment_power = AdjustmentPowerOfTen(exponent: adjustment_exponent);
316 input.Multiply(other: adjustment_power);
317 if (kMaxUint64DecimalDigits - buffer.length() >= adjustment_exponent) {
318 // The product of input with the adjustment power fits into a 64 bit
319 // integer.
320 ASSERT(DiyFp::kSignificandSize == 64);
321 } else {
322 // The adjustment power is exact. There is hence only an error of 0.5.
323 error += kDenominator / 2;
324 }
325 }
326
327 input.Multiply(other: cached_power);
328 // The error introduced by a multiplication of a*b equals
329 // error_a + error_b + error_a*error_b/2^64 + 0.5
330 // Substituting a with 'input' and b with 'cached_power' we have
331 // error_b = 0.5 (all cached powers have an error of less than 0.5 ulp),
332 // error_ab = 0 or 1 / kDenominator > error_a*error_b/ 2^64
333 int error_b = kDenominator / 2;
334 int error_ab = (error == 0 ? 0 : 1); // We round up to 1.
335 int fixed_error = kDenominator / 2;
336 error += error_b + error_ab + fixed_error;
337
338 old_e = input.e();
339 input.Normalize();
340 error <<= old_e - input.e();
341
342 // See if the double's significand changes if we add/subtract the error.
343 int order_of_magnitude = DiyFp::kSignificandSize + input.e();
344 int effective_significand_size =
345 Double::SignificandSizeForOrderOfMagnitude(order: order_of_magnitude);
346 int precision_digits_count =
347 DiyFp::kSignificandSize - effective_significand_size;
348 if (precision_digits_count + kDenominatorLog >= DiyFp::kSignificandSize) {
349 // This can only happen for very small denormals. In this case the
350 // half-way multiplied by the denominator exceeds the range of an uint64.
351 // Simply shift everything to the right.
352 int shift_amount = (precision_digits_count + kDenominatorLog) -
353 DiyFp::kSignificandSize + 1;
354 input.set_f(input.f() >> shift_amount);
355 input.set_e(input.e() + shift_amount);
356 // We add 1 for the lost precision of error, and kDenominator for
357 // the lost precision of input.f().
358 error = (error >> shift_amount) + 1 + kDenominator;
359 precision_digits_count -= shift_amount;
360 }
361 // We use uint64_ts now. This only works if the DiyFp uses uint64_ts too.
362 ASSERT(DiyFp::kSignificandSize == 64);
363 ASSERT(precision_digits_count < 64);
364 uint64_t one64 = 1;
365 uint64_t precision_bits_mask = (one64 << precision_digits_count) - 1;
366 uint64_t precision_bits = input.f() & precision_bits_mask;
367 uint64_t half_way = one64 << (precision_digits_count - 1);
368 precision_bits *= kDenominator;
369 half_way *= kDenominator;
370 DiyFp rounded_input(input.f() >> precision_digits_count,
371 input.e() + precision_digits_count);
372 if (precision_bits >= half_way + error) {
373 rounded_input.set_f(rounded_input.f() + 1);
374 }
375 // If the last_bits are too close to the half-way case than we are too
376 // inaccurate and round down. In this case we return false so that we can
377 // fall back to a more precise algorithm.
378
379 *result = Double(rounded_input).value();
380 if (half_way - error < precision_bits && precision_bits < half_way + error) {
381 // Too imprecise. The caller will have to fall back to a slower version.
382 // However the returned number is guaranteed to be either the correct
383 // double, or the next-lower double.
384 return false;
385 } else {
386 return true;
387 }
388}
389
390
391// Returns
392// - -1 if buffer*10^exponent < diy_fp.
393// - 0 if buffer*10^exponent == diy_fp.
394// - +1 if buffer*10^exponent > diy_fp.
395// Preconditions:
396// buffer.length() + exponent <= kMaxDecimalPower + 1
397// buffer.length() + exponent > kMinDecimalPower
398// buffer.length() <= kMaxDecimalSignificantDigits
399static int CompareBufferWithDiyFp(Vector<const char> buffer,
400 int exponent,
401 DiyFp diy_fp) {
402 ASSERT(buffer.length() + exponent <= kMaxDecimalPower + 1);
403 ASSERT(buffer.length() + exponent > kMinDecimalPower);
404 ASSERT(buffer.length() <= kMaxSignificantDecimalDigits);
405 // Make sure that the Bignum will be able to hold all our numbers.
406 // Our Bignum implementation has a separate field for exponents. Shifts will
407 // consume at most one bigit (< 64 bits).
408 // ln(10) == 3.3219...
409 ASSERT(((kMaxDecimalPower + 1) * 333 / 100) < Bignum::kMaxSignificantBits);
410 Bignum buffer_bignum;
411 Bignum diy_fp_bignum;
412 buffer_bignum.AssignDecimalString(value: buffer);
413 diy_fp_bignum.AssignUInt64(value: diy_fp.f());
414 if (exponent >= 0) {
415 buffer_bignum.MultiplyByPowerOfTen(exponent);
416 } else {
417 diy_fp_bignum.MultiplyByPowerOfTen(exponent: -exponent);
418 }
419 if (diy_fp.e() > 0) {
420 diy_fp_bignum.ShiftLeft(shift_amount: diy_fp.e());
421 } else {
422 buffer_bignum.ShiftLeft(shift_amount: -diy_fp.e());
423 }
424 return Bignum::Compare(a: buffer_bignum, b: diy_fp_bignum);
425}
426
427
428// Returns true if the guess is the correct double.
429// Returns false, when guess is either correct or the next-lower double.
430static bool ComputeGuess(Vector<const char> trimmed, int exponent,
431 double* guess) {
432 if (trimmed.length() == 0) {
433 *guess = 0.0;
434 return true;
435 }
436 if (exponent + trimmed.length() - 1 >= kMaxDecimalPower) {
437 *guess = Double::Infinity();
438 return true;
439 }
440 if (exponent + trimmed.length() <= kMinDecimalPower) {
441 *guess = 0.0;
442 return true;
443 }
444
445 if (DoubleStrtod(trimmed, exponent, result: guess) ||
446 DiyFpStrtod(buffer: trimmed, exponent, result: guess)) {
447 return true;
448 }
449 if (*guess == Double::Infinity()) {
450 return true;
451 }
452 return false;
453}
454
455double Strtod(Vector<const char> buffer, int exponent) {
456 char copy_buffer[kMaxSignificantDecimalDigits];
457 Vector<const char> trimmed;
458 int updated_exponent;
459 TrimAndCut(buffer, exponent, buffer_copy_space: copy_buffer, space_size: kMaxSignificantDecimalDigits,
460 trimmed: &trimmed, updated_exponent: &updated_exponent);
461 exponent = updated_exponent;
462
463 double guess;
464 bool is_correct = ComputeGuess(trimmed, exponent, guess: &guess);
465 if (is_correct) return guess;
466
467 DiyFp upper_boundary = Double(guess).UpperBoundary();
468 int comparison = CompareBufferWithDiyFp(buffer: trimmed, exponent, diy_fp: upper_boundary);
469 if (comparison < 0) {
470 return guess;
471 } else if (comparison > 0) {
472 return Double(guess).NextDouble();
473 } else if ((Double(guess).Significand() & 1) == 0) {
474 // Round towards even.
475 return guess;
476 } else {
477 return Double(guess).NextDouble();
478 }
479}
480
481static float SanitizedDoubletof(double d) {
482 ASSERT(d >= 0.0);
483 // ASAN has a sanitize check that disallows casting doubles to floats if
484 // they are too big.
485 // https://clang.llvm.org/docs/UndefinedBehaviorSanitizer.html#available-checks
486 // The behavior should be covered by IEEE 754, but some projects use this
487 // flag, so work around it.
488 float max_finite = 3.4028234663852885981170418348451692544e+38;
489 // The half-way point between the max-finite and infinity value.
490 // Since infinity has an even significand everything equal or greater than
491 // this value should become infinity.
492 double half_max_finite_infinity =
493 3.40282356779733661637539395458142568448e+38;
494 if (d >= max_finite) {
495 if (d >= half_max_finite_infinity) {
496 return Single::Infinity();
497 } else {
498 return max_finite;
499 }
500 } else {
501 return static_cast<float>(d);
502 }
503}
504
505float Strtof(Vector<const char> buffer, int exponent) {
506 char copy_buffer[kMaxSignificantDecimalDigits];
507 Vector<const char> trimmed;
508 int updated_exponent;
509 TrimAndCut(buffer, exponent, buffer_copy_space: copy_buffer, space_size: kMaxSignificantDecimalDigits,
510 trimmed: &trimmed, updated_exponent: &updated_exponent);
511 exponent = updated_exponent;
512
513 double double_guess;
514 bool is_correct = ComputeGuess(trimmed, exponent, guess: &double_guess);
515
516 float float_guess = SanitizedDoubletof(d: double_guess);
517 if (float_guess == double_guess) {
518 // This shortcut triggers for integer values.
519 return float_guess;
520 }
521
522 // We must catch double-rounding. Say the double has been rounded up, and is
523 // now a boundary of a float, and rounds up again. This is why we have to
524 // look at previous too.
525 // Example (in decimal numbers):
526 // input: 12349
527 // high-precision (4 digits): 1235
528 // low-precision (3 digits):
529 // when read from input: 123
530 // when rounded from high precision: 124.
531 // To do this we simply look at the neigbors of the correct result and see
532 // if they would round to the same float. If the guess is not correct we have
533 // to look at four values (since two different doubles could be the correct
534 // double).
535
536 double double_next = Double(double_guess).NextDouble();
537 double double_previous = Double(double_guess).PreviousDouble();
538
539 float f1 = SanitizedDoubletof(d: double_previous);
540 float f2 = float_guess;
541 float f3 = SanitizedDoubletof(d: double_next);
542 float f4;
543 if (is_correct) {
544 f4 = f3;
545 } else {
546 double double_next2 = Double(double_next).NextDouble();
547 f4 = SanitizedDoubletof(d: double_next2);
548 }
549 (void) f2; // Mark variable as used.
550 ASSERT(f1 <= f2 && f2 <= f3 && f3 <= f4);
551
552 // If the guess doesn't lie near a single-precision boundary we can simply
553 // return its float-value.
554 if (f1 == f4) {
555 return float_guess;
556 }
557
558 ASSERT((f1 != f2 && f2 == f3 && f3 == f4) ||
559 (f1 == f2 && f2 != f3 && f3 == f4) ||
560 (f1 == f2 && f2 == f3 && f3 != f4));
561
562 // guess and next are the two possible candidates (in the same way that
563 // double_guess was the lower candidate for a double-precision guess).
564 float guess = f1;
565 float next = f4;
566 DiyFp upper_boundary;
567 if (guess == 0.0f) {
568 float min_float = 1e-45f;
569 upper_boundary = Double(static_cast<double>(min_float) / 2).AsDiyFp();
570 } else {
571 upper_boundary = Single(guess).UpperBoundary();
572 }
573 int comparison = CompareBufferWithDiyFp(buffer: trimmed, exponent, diy_fp: upper_boundary);
574 if (comparison < 0) {
575 return guess;
576 } else if (comparison > 0) {
577 return next;
578 } else if ((Single(guess).Significand() & 1) == 0) {
579 // Round towards even.
580 return guess;
581 } else {
582 return next;
583 }
584}
585
586} // namespace double_conversion
587

source code of qtbase/src/3rdparty/double-conversion/strtod.cc