Line data Source code
1 : // Copyright 2012 the V8 project authors. All rights reserved.
2 : // Use of this source code is governed by a BSD-style license that can be
3 : // found in the LICENSE file.
4 :
5 : #include "src/strtod.h"
6 :
7 : #include <stdarg.h>
8 : #include <cmath>
9 :
10 : #include "src/bignum.h"
11 : #include "src/cached-powers.h"
12 : #include "src/double.h"
13 : #include "src/globals.h"
14 : #include "src/utils.h"
15 :
16 : namespace v8 {
17 : namespace internal {
18 :
19 : // 2^53 = 9007199254740992.
20 : // Any integer with at most 15 decimal digits will hence fit into a double
21 : // (which has a 53bit significand) without loss of precision.
22 : static const int kMaxExactDoubleIntegerDecimalDigits = 15;
23 : // 2^64 = 18446744073709551616 > 10^19
24 : static const int kMaxUint64DecimalDigits = 19;
25 :
26 : // Max double: 1.7976931348623157 x 10^308
27 : // Min non-zero double: 4.9406564584124654 x 10^-324
28 : // Any x >= 10^309 is interpreted as +infinity.
29 : // Any x <= 10^-324 is interpreted as 0.
30 : // Note that 2.5e-324 (despite being smaller than the min double) will be read
31 : // as non-zero (equal to the min non-zero double).
32 : static const int kMaxDecimalPower = 309;
33 : static const int kMinDecimalPower = -324;
34 :
35 : // 2^64 = 18446744073709551616
36 : static const uint64_t kMaxUint64 = V8_2PART_UINT64_C(0xFFFFFFFF, FFFFFFFF);
37 :
38 : // clang-format off
39 : static const double exact_powers_of_ten[] = {
40 : 1.0, // 10^0
41 : 10.0,
42 : 100.0,
43 : 1000.0,
44 : 10000.0,
45 : 100000.0,
46 : 1000000.0,
47 : 10000000.0,
48 : 100000000.0,
49 : 1000000000.0,
50 : 10000000000.0, // 10^10
51 : 100000000000.0,
52 : 1000000000000.0,
53 : 10000000000000.0,
54 : 100000000000000.0,
55 : 1000000000000000.0,
56 : 10000000000000000.0,
57 : 100000000000000000.0,
58 : 1000000000000000000.0,
59 : 10000000000000000000.0,
60 : 100000000000000000000.0, // 10^20
61 : 1000000000000000000000.0,
62 : // 10^22 = 0x21E19E0C9BAB2400000 = 0x878678326EAC9 * 2^22
63 : 10000000000000000000000.0
64 : };
65 : // clang-format on
66 : static const int kExactPowersOfTenSize = arraysize(exact_powers_of_ten);
67 :
68 : // Maximum number of significant digits in the decimal representation.
69 : // In fact the value is 772 (see conversions.cc), but to give us some margin
70 : // we round up to 780.
71 : static const int kMaxSignificantDecimalDigits = 780;
72 :
73 : static Vector<const char> TrimLeadingZeros(Vector<const char> buffer) {
74 6746841 : for (int i = 0; i < buffer.length(); i++) {
75 13490680 : if (buffer[i] != '0') {
76 6744138 : return buffer.SubVector(i, buffer.length());
77 : }
78 : }
79 : return Vector<const char>(buffer.start(), 0);
80 : }
81 :
82 :
83 : static Vector<const char> TrimTrailingZeros(Vector<const char> buffer) {
84 6915825 : for (int i = buffer.length() - 1; i >= 0; --i) {
85 13831056 : if (buffer[i] != '0') {
86 6744140 : return buffer.SubVector(0, i + 1);
87 : }
88 : }
89 : return Vector<const char>(buffer.start(), 0);
90 : }
91 :
92 :
93 : static void TrimToMaxSignificantDigits(Vector<const char> buffer,
94 : int exponent,
95 : char* significant_buffer,
96 : int* significant_exponent) {
97 155900 : for (int i = 0; i < kMaxSignificantDecimalDigits - 1; ++i) {
98 155800 : significant_buffer[i] = buffer[i];
99 : }
100 : // The input buffer has been trimmed. Therefore the last digit must be
101 : // different from '0'.
102 : DCHECK_NE(buffer[buffer.length() - 1], '0');
103 : // Set the last digit to be non-zero. This is sufficient to guarantee
104 : // correct rounding.
105 100 : significant_buffer[kMaxSignificantDecimalDigits - 1] = '1';
106 : *significant_exponent =
107 100 : exponent + (buffer.length() - kMaxSignificantDecimalDigits);
108 : }
109 :
110 :
111 : // Reads digits from the buffer and converts them to a uint64.
112 : // Reads in as many digits as fit into a uint64.
113 : // When the string starts with "1844674407370955161" no further digit is read.
114 : // Since 2^64 = 18446744073709551616 it would still be possible read another
115 : // digit if it was less or equal than 6, but this would complicate the code.
116 : static uint64_t ReadUint64(Vector<const char> buffer,
117 : int* number_of_read_digits) {
118 : uint64_t result = 0;
119 : int i = 0;
120 17064473 : while (i < buffer.length() && result <= (kMaxUint64 / 10 - 1)) {
121 20641256 : int digit = buffer[i++] - '0';
122 : DCHECK(0 <= digit && digit <= 9);
123 10320628 : result = 10 * result + digit;
124 : }
125 : *number_of_read_digits = i;
126 : return result;
127 : }
128 :
129 :
130 : // Reads a DiyFp from the buffer.
131 : // The returned DiyFp is not necessarily normalized.
132 : // If remaining_decimals is zero then the returned DiyFp is accurate.
133 : // Otherwise it has been rounded and has error of at most 1/2 ulp.
134 45562 : static void ReadDiyFp(Vector<const char> buffer,
135 : DiyFp* result,
136 : int* remaining_decimals) {
137 : int read_digits;
138 : uint64_t significand = ReadUint64(buffer, &read_digits);
139 45562 : if (buffer.length() == read_digits) {
140 40011 : *result = DiyFp(significand, 0);
141 40011 : *remaining_decimals = 0;
142 : } else {
143 : // Round the significand.
144 11102 : if (buffer[read_digits] >= '5') {
145 2051 : significand++;
146 : }
147 : // Compute the binary exponent.
148 : int exponent = 0;
149 5551 : *result = DiyFp(significand, exponent);
150 5551 : *remaining_decimals = buffer.length() - read_digits;
151 : }
152 45562 : }
153 :
154 :
155 6743845 : static bool DoubleStrtod(Vector<const char> trimmed,
156 : int exponent,
157 : double* result) {
158 : #if (V8_TARGET_ARCH_IA32 || defined(USE_SIMULATOR)) && !defined(_MSC_VER)
159 : // On x86 the floating-point stack can be 64 or 80 bits wide. If it is
160 : // 80 bits wide (as is the case on Linux) then double-rounding occurs and the
161 : // result is not accurate.
162 : // We know that Windows32 with MSVC, unlike with MinGW32, uses 64 bits and is
163 : // therefore accurate.
164 : // Note that the ARM and MIPS simulators are compiled for 32bits. They
165 : // therefore exhibit the same problem.
166 : USE(exact_powers_of_ten);
167 : USE(kMaxExactDoubleIntegerDecimalDigits);
168 : USE(kExactPowersOfTenSize);
169 : return false;
170 : #else
171 6743845 : if (trimmed.length() <= kMaxExactDoubleIntegerDecimalDigits) {
172 : int read_digits;
173 : // The trimmed input fits into a double.
174 : // If the 10^exponent (resp. 10^-exponent) fits into a double too then we
175 : // can compute the result-double simply by multiplying (resp. dividing) the
176 : // two numbers.
177 : // This is possible because IEEE guarantees that floating-point operations
178 : // return the best possible approximation.
179 6701049 : if (exponent < 0 && -exponent < kExactPowersOfTenSize) {
180 : // 10^-exponent fits into a double.
181 5607857 : *result = static_cast<double>(ReadUint64(trimmed, &read_digits));
182 : DCHECK(read_digits == trimmed.length());
183 5607857 : *result /= exact_powers_of_ten[-exponent];
184 5607857 : return true;
185 : }
186 1093192 : if (0 <= exponent && exponent < kExactPowersOfTenSize) {
187 : // 10^exponent fits into a double.
188 1089842 : *result = static_cast<double>(ReadUint64(trimmed, &read_digits));
189 : DCHECK(read_digits == trimmed.length());
190 1089842 : *result *= exact_powers_of_ten[exponent];
191 1089842 : return true;
192 : }
193 : int remaining_digits =
194 3350 : kMaxExactDoubleIntegerDecimalDigits - trimmed.length();
195 5967 : if ((0 <= exponent) &&
196 2617 : (exponent - remaining_digits < kExactPowersOfTenSize)) {
197 : // The trimmed string was short and we can multiply it with
198 : // 10^remaining_digits. As a result the remaining exponent now fits
199 : // into a double too.
200 584 : *result = static_cast<double>(ReadUint64(trimmed, &read_digits));
201 : DCHECK(read_digits == trimmed.length());
202 584 : *result *= exact_powers_of_ten[remaining_digits];
203 584 : *result *= exact_powers_of_ten[exponent - remaining_digits];
204 584 : return true;
205 : }
206 : }
207 : return false;
208 : #endif
209 : }
210 :
211 :
212 : // Returns 10^exponent as an exact DiyFp.
213 : // The given exponent must be in the range [1; kDecimalExponentDistance[.
214 44155 : static DiyFp AdjustmentPowerOfTen(int exponent) {
215 : DCHECK_LT(0, exponent);
216 : DCHECK_LT(exponent, PowersOfTenCache::kDecimalExponentDistance);
217 : // Simply hardcode the remaining powers for the given decimal exponent
218 : // distance.
219 : DCHECK_EQ(PowersOfTenCache::kDecimalExponentDistance, 8);
220 44155 : switch (exponent) {
221 : case 1:
222 7084 : return DiyFp(V8_2PART_UINT64_C(0xA0000000, 00000000), -60);
223 : case 2:
224 996 : return DiyFp(V8_2PART_UINT64_C(0xC8000000, 00000000), -57);
225 : case 3:
226 1802 : return DiyFp(V8_2PART_UINT64_C(0xFA000000, 00000000), -54);
227 : case 4:
228 7124 : return DiyFp(V8_2PART_UINT64_C(0x9C400000, 00000000), -50);
229 : case 5:
230 18338 : return DiyFp(V8_2PART_UINT64_C(0xC3500000, 00000000), -47);
231 : case 6:
232 7353 : return DiyFp(V8_2PART_UINT64_C(0xF4240000, 00000000), -44);
233 : case 7:
234 1458 : return DiyFp(V8_2PART_UINT64_C(0x98968000, 00000000), -40);
235 : default:
236 0 : UNREACHABLE();
237 : }
238 : }
239 :
240 :
241 : // If the function returns true then the result is the correct double.
242 : // Otherwise it is either the correct double or the double that is just below
243 : // the correct double.
244 45563 : static bool DiyFpStrtod(Vector<const char> buffer,
245 : int exponent,
246 : double* result) {
247 : DiyFp input;
248 : int remaining_decimals;
249 45563 : ReadDiyFp(buffer, &input, &remaining_decimals);
250 : // Since we may have dropped some digits the input is not accurate.
251 : // If remaining_decimals is different than 0 than the error is at most
252 : // .5 ulp (unit in the last place).
253 : // We don't want to deal with fractions and therefore keep a common
254 : // denominator.
255 : const int kDenominatorLog = 3;
256 : const int kDenominator = 1 << kDenominatorLog;
257 : // Move the remaining decimals into the exponent.
258 45562 : exponent += remaining_decimals;
259 45562 : int64_t error = (remaining_decimals == 0 ? 0 : kDenominator / 2);
260 :
261 : int old_e = input.e();
262 : input.Normalize();
263 45562 : error <<= old_e - input.e();
264 :
265 : DCHECK_LE(exponent, PowersOfTenCache::kMaxDecimalExponent);
266 45562 : if (exponent < PowersOfTenCache::kMinDecimalExponent) {
267 0 : *result = 0.0;
268 0 : return true;
269 : }
270 : DiyFp cached_power;
271 : int cached_decimal_exponent;
272 : PowersOfTenCache::GetCachedPowerForDecimalExponent(exponent,
273 : &cached_power,
274 45562 : &cached_decimal_exponent);
275 :
276 45561 : if (cached_decimal_exponent != exponent) {
277 44156 : int adjustment_exponent = exponent - cached_decimal_exponent;
278 44156 : DiyFp adjustment_power = AdjustmentPowerOfTen(adjustment_exponent);
279 44156 : input.Multiply(adjustment_power);
280 44158 : if (kMaxUint64DecimalDigits - buffer.length() >= adjustment_exponent) {
281 : // The product of input with the adjustment power fits into a 64 bit
282 : // integer.
283 : DCHECK_EQ(DiyFp::kSignificandSize, 64);
284 : } else {
285 : // The adjustment power is exact. There is hence only an error of 0.5.
286 34965 : error += kDenominator / 2;
287 : }
288 : }
289 :
290 45563 : input.Multiply(cached_power);
291 : // The error introduced by a multiplication of a*b equals
292 : // error_a + error_b + error_a*error_b/2^64 + 0.5
293 : // Substituting a with 'input' and b with 'cached_power' we have
294 : // error_b = 0.5 (all cached powers have an error of less than 0.5 ulp),
295 : // error_ab = 0 or 1 / kDenominator > error_a*error_b/ 2^64
296 : int error_b = kDenominator / 2;
297 45563 : int error_ab = (error == 0 ? 0 : 1); // We round up to 1.
298 : int fixed_error = kDenominator / 2;
299 45563 : error += error_b + error_ab + fixed_error;
300 :
301 : old_e = input.e();
302 : input.Normalize();
303 45563 : error <<= old_e - input.e();
304 :
305 : // See if the double's significand changes if we add/subtract the error.
306 45563 : int order_of_magnitude = DiyFp::kSignificandSize + input.e();
307 : int effective_significand_size =
308 : Double::SignificandSizeForOrderOfMagnitude(order_of_magnitude);
309 : int precision_digits_count =
310 45563 : DiyFp::kSignificandSize - effective_significand_size;
311 45563 : if (precision_digits_count + kDenominatorLog >= DiyFp::kSignificandSize) {
312 : // This can only happen for very small denormals. In this case the
313 : // half-way multiplied by the denominator exceeds the range of an uint64.
314 : // Simply shift everything to the right.
315 : int shift_amount = (precision_digits_count + kDenominatorLog) -
316 74 : DiyFp::kSignificandSize + 1;
317 74 : input.set_f(input.f() >> shift_amount);
318 74 : input.set_e(input.e() + shift_amount);
319 : // We add 1 for the lost precision of error, and kDenominator for
320 : // the lost precision of input.f().
321 74 : error = (error >> shift_amount) + 1 + kDenominator;
322 : precision_digits_count -= shift_amount;
323 : }
324 : // We use uint64_ts now. This only works if the DiyFp uses uint64_ts too.
325 : DCHECK_EQ(DiyFp::kSignificandSize, 64);
326 : DCHECK_LT(precision_digits_count, 64);
327 : uint64_t one64 = 1;
328 45563 : uint64_t precision_bits_mask = (one64 << precision_digits_count) - 1;
329 45563 : uint64_t precision_bits = input.f() & precision_bits_mask;
330 45563 : uint64_t half_way = one64 << (precision_digits_count - 1);
331 45563 : precision_bits *= kDenominator;
332 45563 : half_way *= kDenominator;
333 : DiyFp rounded_input(input.f() >> precision_digits_count,
334 45563 : input.e() + precision_digits_count);
335 45563 : if (precision_bits >= half_way + error) {
336 22685 : rounded_input.set_f(rounded_input.f() + 1);
337 : }
338 : // If the last_bits are too close to the half-way case than we are too
339 : // inaccurate and round down. In this case we return false so that we can
340 : // fall back to a more precise algorithm.
341 :
342 45563 : *result = Double(rounded_input).value();
343 45563 : if (half_way - error < precision_bits && precision_bits < half_way + error) {
344 : // Too imprecise. The caller will have to fall back to a slower version.
345 : // However the returned number is guaranteed to be either the correct
346 : // double, or the next-lower double.
347 : return false;
348 : } else {
349 45330 : return true;
350 : }
351 : }
352 :
353 :
354 : // Returns the correct double for the buffer*10^exponent.
355 : // The variable guess should be a close guess that is either the correct double
356 : // or its lower neighbor (the nearest double less than the correct one).
357 : // Preconditions:
358 : // buffer.length() + exponent <= kMaxDecimalPower + 1
359 : // buffer.length() + exponent > kMinDecimalPower
360 : // buffer.length() <= kMaxDecimalSignificantDigits
361 233 : static double BignumStrtod(Vector<const char> buffer,
362 : int exponent,
363 : double guess) {
364 233 : if (guess == V8_INFINITY) {
365 : return guess;
366 : }
367 :
368 : DiyFp upper_boundary = Double(guess).UpperBoundary();
369 :
370 : DCHECK(buffer.length() + exponent <= kMaxDecimalPower + 1);
371 : DCHECK_GT(buffer.length() + exponent, kMinDecimalPower);
372 : DCHECK_LE(buffer.length(), kMaxSignificantDecimalDigits);
373 : // Make sure that the Bignum will be able to hold all our numbers.
374 : // Our Bignum implementation has a separate field for exponents. Shifts will
375 : // consume at most one bigit (< 64 bits).
376 : // ln(10) == 3.3219...
377 : DCHECK_LT((kMaxDecimalPower + 1) * 333 / 100, Bignum::kMaxSignificantBits);
378 233 : Bignum input;
379 233 : Bignum boundary;
380 233 : input.AssignDecimalString(buffer);
381 233 : boundary.AssignUInt64(upper_boundary.f());
382 233 : if (exponent >= 0) {
383 91 : input.MultiplyByPowerOfTen(exponent);
384 : } else {
385 142 : boundary.MultiplyByPowerOfTen(-exponent);
386 : }
387 233 : if (upper_boundary.e() > 0) {
388 110 : boundary.ShiftLeft(upper_boundary.e());
389 : } else {
390 123 : input.ShiftLeft(-upper_boundary.e());
391 : }
392 233 : int comparison = Bignum::Compare(input, boundary);
393 233 : if (comparison < 0) {
394 : return guess;
395 173 : } else if (comparison > 0) {
396 81 : return Double(guess).NextDouble();
397 92 : } else if ((Double(guess).Significand() & 1) == 0) {
398 : // Round towards even.
399 : return guess;
400 : } else {
401 45 : return Double(guess).NextDouble();
402 : }
403 : }
404 :
405 :
406 6744437 : double Strtod(Vector<const char> buffer, int exponent) {
407 : Vector<const char> left_trimmed = TrimLeadingZeros(buffer);
408 : Vector<const char> trimmed = TrimTrailingZeros(left_trimmed);
409 6744437 : exponent += left_trimmed.length() - trimmed.length();
410 6744437 : if (trimmed.length() == 0) return 0.0;
411 6744141 : if (trimmed.length() > kMaxSignificantDecimalDigits) {
412 : char significant_buffer[kMaxSignificantDecimalDigits];
413 : int significant_exponent;
414 : TrimToMaxSignificantDigits(trimmed, exponent,
415 : significant_buffer, &significant_exponent);
416 100 : return Strtod(Vector<const char>(significant_buffer,
417 : kMaxSignificantDecimalDigits),
418 100 : significant_exponent);
419 : }
420 6744041 : if (exponent + trimmed.length() - 1 >= kMaxDecimalPower) return V8_INFINITY;
421 6743962 : if (exponent + trimmed.length() <= kMinDecimalPower) return 0.0;
422 :
423 : double guess;
424 6789410 : if (DoubleStrtod(trimmed, exponent, &guess) ||
425 45563 : DiyFpStrtod(trimmed, exponent, &guess)) {
426 6743610 : return guess;
427 : }
428 233 : return BignumStrtod(trimmed, exponent, guess);
429 : }
430 :
431 : } // namespace internal
432 122004 : } // namespace v8
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