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| 1 // Copyright 2010 the V8 project authors. All rights reserved. | |
| 2 // Redistribution and use in source and binary forms, with or without | |
| 3 // modification, are permitted provided that the following conditions are | |
| 4 // met: | |
| 5 // | |
| 6 // * Redistributions of source code must retain the above copyright | |
| 7 // notice, this list of conditions and the following disclaimer. | |
| 8 // * Redistributions in binary form must reproduce the above | |
| 9 // copyright notice, this list of conditions and the following | |
| 10 // disclaimer in the documentation and/or other materials provided | |
| 11 // with the distribution. | |
| 12 // * Neither the name of Google Inc. nor the names of its | |
| 13 // contributors may be used to endorse or promote products derived | |
| 14 // from this software without specific prior written permission. | |
| 15 // | |
| 16 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS | |
| 17 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT | |
| 18 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR | |
| 19 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT | |
| 20 // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, | |
| 21 // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT | |
| 22 // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, | |
| 23 // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY | |
| 24 // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT | |
| 25 // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE | |
| 26 // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. | |
| 27 | |
| 28 #include "config.h" | |
| 29 | |
| 30 #include <stdarg.h> | |
| 31 #include <limits.h> | |
| 32 | |
| 33 #include "strtod.h" | |
| 34 #include "bignum.h" | |
| 35 #include "cached-powers.h" | |
| 36 #include "double.h" | |
| 37 | |
| 38 namespace WTF { | |
| 39 | |
| 40 namespace double_conversion { | |
| 41 | |
| 42 // 2^53 = 9007199254740992. | |
| 43 // Any integer with at most 15 decimal digits will hence fit into a double | |
| 44 // (which has a 53bit significand) without loss of precision. | |
| 45 static const int kMaxExactDoubleIntegerDecimalDigits = 15; | |
| 46 // 2^64 = 18446744073709551616 > 10^19 | |
| 47 static const int kMaxUint64DecimalDigits = 19; | |
| 48 | |
| 49 // Max double: 1.7976931348623157 x 10^308 | |
| 50 // Min non-zero double: 4.9406564584124654 x 10^-324 | |
| 51 // Any x >= 10^309 is interpreted as +infinity. | |
| 52 // Any x <= 10^-324 is interpreted as 0. | |
| 53 // Note that 2.5e-324 (despite being smaller than the min double) will be re
ad | |
| 54 // as non-zero (equal to the min non-zero double). | |
| 55 static const int kMaxDecimalPower = 309; | |
| 56 static const int kMinDecimalPower = -324; | |
| 57 | |
| 58 // 2^64 = 18446744073709551616 | |
| 59 static const uint64_t kMaxUint64 = UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF); | |
| 60 | |
| 61 | |
| 62 static const double exact_powers_of_ten[] = { | |
| 63 1.0, // 10^0 | |
| 64 10.0, | |
| 65 100.0, | |
| 66 1000.0, | |
| 67 10000.0, | |
| 68 100000.0, | |
| 69 1000000.0, | |
| 70 10000000.0, | |
| 71 100000000.0, | |
| 72 1000000000.0, | |
| 73 10000000000.0, // 10^10 | |
| 74 100000000000.0, | |
| 75 1000000000000.0, | |
| 76 10000000000000.0, | |
| 77 100000000000000.0, | |
| 78 1000000000000000.0, | |
| 79 10000000000000000.0, | |
| 80 100000000000000000.0, | |
| 81 1000000000000000000.0, | |
| 82 10000000000000000000.0, | |
| 83 100000000000000000000.0, // 10^20 | |
| 84 1000000000000000000000.0, | |
| 85 // 10^22 = 0x21e19e0c9bab2400000 = 0x878678326eac9 * 2^22 | |
| 86 10000000000000000000000.0 | |
| 87 }; | |
| 88 static const int kExactPowersOfTenSize = ARRAY_SIZE(exact_powers_of_ten); | |
| 89 | |
| 90 // Maximum number of significant digits in the decimal representation. | |
| 91 // In fact the value is 772 (see conversions.cc), but to give us some margin | |
| 92 // we round up to 780. | |
| 93 static const int kMaxSignificantDecimalDigits = 780; | |
| 94 | |
| 95 static Vector<const char> TrimLeadingZeros(Vector<const char> buffer) { | |
| 96 for (int i = 0; i < buffer.length(); i++) { | |
| 97 if (buffer[i] != '0') { | |
| 98 return buffer.SubVector(i, buffer.length()); | |
| 99 } | |
| 100 } | |
| 101 return Vector<const char>(buffer.start(), 0); | |
| 102 } | |
| 103 | |
| 104 | |
| 105 static Vector<const char> TrimTrailingZeros(Vector<const char> buffer) { | |
| 106 for (int i = buffer.length() - 1; i >= 0; --i) { | |
| 107 if (buffer[i] != '0') { | |
| 108 return buffer.SubVector(0, i + 1); | |
| 109 } | |
| 110 } | |
| 111 return Vector<const char>(buffer.start(), 0); | |
| 112 } | |
| 113 | |
| 114 | |
| 115 static void TrimToMaxSignificantDigits(Vector<const char> buffer, | |
| 116 int exponent, | |
| 117 char* significant_buffer, | |
| 118 int* significant_exponent) { | |
| 119 for (int i = 0; i < kMaxSignificantDecimalDigits - 1; ++i) { | |
| 120 significant_buffer[i] = buffer[i]; | |
| 121 } | |
| 122 // The input buffer has been trimmed. Therefore the last digit must be | |
| 123 // different from '0'. | |
| 124 ASSERT(buffer[buffer.length() - 1] != '0'); | |
| 125 // Set the last digit to be non-zero. This is sufficient to guarantee | |
| 126 // correct rounding. | |
| 127 significant_buffer[kMaxSignificantDecimalDigits - 1] = '1'; | |
| 128 *significant_exponent = | |
| 129 exponent + (buffer.length() - kMaxSignificantDecimalDigits); | |
| 130 } | |
| 131 | |
| 132 // Reads digits from the buffer and converts them to a uint64. | |
| 133 // Reads in as many digits as fit into a uint64. | |
| 134 // When the string starts with "1844674407370955161" no further digit is rea
d. | |
| 135 // Since 2^64 = 18446744073709551616 it would still be possible read another | |
| 136 // digit if it was less or equal than 6, but this would complicate the code. | |
| 137 static uint64_t ReadUint64(Vector<const char> buffer, | |
| 138 int* number_of_read_digits) { | |
| 139 uint64_t result = 0; | |
| 140 int i = 0; | |
| 141 while (i < buffer.length() && result <= (kMaxUint64 / 10 - 1)) { | |
| 142 int digit = buffer[i++] - '0'; | |
| 143 ASSERT(0 <= digit && digit <= 9); | |
| 144 result = 10 * result + digit; | |
| 145 } | |
| 146 *number_of_read_digits = i; | |
| 147 return result; | |
| 148 } | |
| 149 | |
| 150 | |
| 151 // Reads a DiyFp from the buffer. | |
| 152 // The returned DiyFp is not necessarily normalized. | |
| 153 // If remaining_decimals is zero then the returned DiyFp is accurate. | |
| 154 // Otherwise it has been rounded and has error of at most 1/2 ulp. | |
| 155 static void ReadDiyFp(Vector<const char> buffer, | |
| 156 DiyFp* result, | |
| 157 int* remaining_decimals) { | |
| 158 int read_digits; | |
| 159 uint64_t significand = ReadUint64(buffer, &read_digits); | |
| 160 if (buffer.length() == read_digits) { | |
| 161 *result = DiyFp(significand, 0); | |
| 162 *remaining_decimals = 0; | |
| 163 } else { | |
| 164 // Round the significand. | |
| 165 if (buffer[read_digits] >= '5') { | |
| 166 significand++; | |
| 167 } | |
| 168 // Compute the binary exponent. | |
| 169 int exponent = 0; | |
| 170 *result = DiyFp(significand, exponent); | |
| 171 *remaining_decimals = buffer.length() - read_digits; | |
| 172 } | |
| 173 } | |
| 174 | |
| 175 | |
| 176 static bool DoubleStrtod(Vector<const char> trimmed, | |
| 177 int exponent, | |
| 178 double* result) { | |
| 179 #if !defined(DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS) | |
| 180 // On x86 the floating-point stack can be 64 or 80 bits wide. If it is | |
| 181 // 80 bits wide (as is the case on Linux) then double-rounding occurs an
d the | |
| 182 // result is not accurate. | |
| 183 // We know that Windows32 uses 64 bits and is therefore accurate. | |
| 184 // Note that the ARM simulator is compiled for 32bits. It therefore exhi
bits | |
| 185 // the same problem. | |
| 186 return false; | |
| 187 #endif | |
| 188 if (trimmed.length() <= kMaxExactDoubleIntegerDecimalDigits) { | |
| 189 int read_digits; | |
| 190 // The trimmed input fits into a double. | |
| 191 // If the 10^exponent (resp. 10^-exponent) fits into a double too th
en we | |
| 192 // can compute the result-double simply by multiplying (resp. dividi
ng) the | |
| 193 // two numbers. | |
| 194 // This is possible because IEEE guarantees that floating-point oper
ations | |
| 195 // return the best possible approximation. | |
| 196 if (exponent < 0 && -exponent < kExactPowersOfTenSize) { | |
| 197 // 10^-exponent fits into a double. | |
| 198 *result = static_cast<double>(ReadUint64(trimmed, &read_digits))
; | |
| 199 ASSERT(read_digits == trimmed.length()); | |
| 200 *result /= exact_powers_of_ten[-exponent]; | |
| 201 return true; | |
| 202 } | |
| 203 if (0 <= exponent && exponent < kExactPowersOfTenSize) { | |
| 204 // 10^exponent fits into a double. | |
| 205 *result = static_cast<double>(ReadUint64(trimmed, &read_digits))
; | |
| 206 ASSERT(read_digits == trimmed.length()); | |
| 207 *result *= exact_powers_of_ten[exponent]; | |
| 208 return true; | |
| 209 } | |
| 210 int remaining_digits = | |
| 211 kMaxExactDoubleIntegerDecimalDigits - trimmed.length(); | |
| 212 if ((0 <= exponent) && | |
| 213 (exponent - remaining_digits < kExactPowersOfTenSize)) { | |
| 214 // The trimmed string was short and we can multiply it with | |
| 215 // 10^remaining_digits. As a result the remaining exponent now f
its | |
| 216 // into a double too. | |
| 217 *result = static_cast<double>(ReadUint64(trimmed, &read_digits))
; | |
| 218 ASSERT(read_digits == trimmed.length()); | |
| 219 *result *= exact_powers_of_ten[remaining_digits]; | |
| 220 *result *= exact_powers_of_ten[exponent - remaining_digits]; | |
| 221 return true; | |
| 222 } | |
| 223 } | |
| 224 return false; | |
| 225 } | |
| 226 | |
| 227 | |
| 228 // Returns 10^exponent as an exact DiyFp. | |
| 229 // The given exponent must be in the range [1; kDecimalExponentDistance[. | |
| 230 static DiyFp AdjustmentPowerOfTen(int exponent) { | |
| 231 ASSERT(0 < exponent); | |
| 232 ASSERT(exponent < PowersOfTenCache::kDecimalExponentDistance); | |
| 233 // Simply hardcode the remaining powers for the given decimal exponent | |
| 234 // distance. | |
| 235 ASSERT(PowersOfTenCache::kDecimalExponentDistance == 8); | |
| 236 switch (exponent) { | |
| 237 case 1: return DiyFp(UINT64_2PART_C(0xa0000000, 00000000), -60); | |
| 238 case 2: return DiyFp(UINT64_2PART_C(0xc8000000, 00000000), -57); | |
| 239 case 3: return DiyFp(UINT64_2PART_C(0xfa000000, 00000000), -54); | |
| 240 case 4: return DiyFp(UINT64_2PART_C(0x9c400000, 00000000), -50); | |
| 241 case 5: return DiyFp(UINT64_2PART_C(0xc3500000, 00000000), -47); | |
| 242 case 6: return DiyFp(UINT64_2PART_C(0xf4240000, 00000000), -44); | |
| 243 case 7: return DiyFp(UINT64_2PART_C(0x98968000, 00000000), -40); | |
| 244 default: | |
| 245 UNREACHABLE(); | |
| 246 return DiyFp(0, 0); | |
| 247 } | |
| 248 } | |
| 249 | |
| 250 | |
| 251 // If the function returns true then the result is the correct double. | |
| 252 // Otherwise it is either the correct double or the double that is just belo
w | |
| 253 // the correct double. | |
| 254 static bool DiyFpStrtod(Vector<const char> buffer, | |
| 255 int exponent, | |
| 256 double* result) { | |
| 257 DiyFp input; | |
| 258 int remaining_decimals; | |
| 259 ReadDiyFp(buffer, &input, &remaining_decimals); | |
| 260 // Since we may have dropped some digits the input is not accurate. | |
| 261 // If remaining_decimals is different than 0 than the error is at most | |
| 262 // .5 ulp (unit in the last place). | |
| 263 // We don't want to deal with fractions and therefore keep a common | |
| 264 // denominator. | |
| 265 const int kDenominatorLog = 3; | |
| 266 const int kDenominator = 1 << kDenominatorLog; | |
| 267 // Move the remaining decimals into the exponent. | |
| 268 exponent += remaining_decimals; | |
| 269 int error = (remaining_decimals == 0 ? 0 : kDenominator / 2); | |
| 270 | |
| 271 int old_e = input.e(); | |
| 272 input.Normalize(); | |
| 273 error <<= old_e - input.e(); | |
| 274 | |
| 275 ASSERT(exponent <= PowersOfTenCache::kMaxDecimalExponent); | |
| 276 if (exponent < PowersOfTenCache::kMinDecimalExponent) { | |
| 277 *result = 0.0; | |
| 278 return true; | |
| 279 } | |
| 280 DiyFp cached_power; | |
| 281 int cached_decimal_exponent; | |
| 282 PowersOfTenCache::GetCachedPowerForDecimalExponent(exponent, | |
| 283 &cached_power, | |
| 284 &cached_decimal_expon
ent); | |
| 285 | |
| 286 if (cached_decimal_exponent != exponent) { | |
| 287 int adjustment_exponent = exponent - cached_decimal_exponent; | |
| 288 DiyFp adjustment_power = AdjustmentPowerOfTen(adjustment_exponent); | |
| 289 input.Multiply(adjustment_power); | |
| 290 if (kMaxUint64DecimalDigits - buffer.length() >= adjustment_exponent
) { | |
| 291 // The product of input with the adjustment power fits into a 64
bit | |
| 292 // integer. | |
| 293 ASSERT(DiyFp::kSignificandSize == 64); | |
| 294 } else { | |
| 295 // The adjustment power is exact. There is hence only an error o
f 0.5. | |
| 296 error += kDenominator / 2; | |
| 297 } | |
| 298 } | |
| 299 | |
| 300 input.Multiply(cached_power); | |
| 301 // The error introduced by a multiplication of a*b equals | |
| 302 // error_a + error_b + error_a*error_b/2^64 + 0.5 | |
| 303 // Substituting a with 'input' and b with 'cached_power' we have | |
| 304 // error_b = 0.5 (all cached powers have an error of less than 0.5 ul
p), | |
| 305 // error_ab = 0 or 1 / kDenominator > error_a*error_b/ 2^64 | |
| 306 int error_b = kDenominator / 2; | |
| 307 int error_ab = (error == 0 ? 0 : 1); // We round up to 1. | |
| 308 int fixed_error = kDenominator / 2; | |
| 309 error += error_b + error_ab + fixed_error; | |
| 310 | |
| 311 old_e = input.e(); | |
| 312 input.Normalize(); | |
| 313 error <<= old_e - input.e(); | |
| 314 | |
| 315 // See if the double's significand changes if we add/subtract the error. | |
| 316 int order_of_magnitude = DiyFp::kSignificandSize + input.e(); | |
| 317 int effective_significand_size = | |
| 318 Double::SignificandSizeForOrderOfMagnitude(order_of_magnitude); | |
| 319 int precision_digits_count = | |
| 320 DiyFp::kSignificandSize - effective_significand_size; | |
| 321 if (precision_digits_count + kDenominatorLog >= DiyFp::kSignificandSize)
{ | |
| 322 // This can only happen for very small denormals. In this case the | |
| 323 // half-way multiplied by the denominator exceeds the range of an ui
nt64. | |
| 324 // Simply shift everything to the right. | |
| 325 int shift_amount = (precision_digits_count + kDenominatorLog) - | |
| 326 DiyFp::kSignificandSize + 1; | |
| 327 input.set_f(input.f() >> shift_amount); | |
| 328 input.set_e(input.e() + shift_amount); | |
| 329 // We add 1 for the lost precision of error, and kDenominator for | |
| 330 // the lost precision of input.f(). | |
| 331 error = (error >> shift_amount) + 1 + kDenominator; | |
| 332 precision_digits_count -= shift_amount; | |
| 333 } | |
| 334 // We use uint64_ts now. This only works if the DiyFp uses uint64_ts too
. | |
| 335 ASSERT(DiyFp::kSignificandSize == 64); | |
| 336 ASSERT(precision_digits_count < 64); | |
| 337 uint64_t one64 = 1; | |
| 338 uint64_t precision_bits_mask = (one64 << precision_digits_count) - 1; | |
| 339 uint64_t precision_bits = input.f() & precision_bits_mask; | |
| 340 uint64_t half_way = one64 << (precision_digits_count - 1); | |
| 341 precision_bits *= kDenominator; | |
| 342 half_way *= kDenominator; | |
| 343 DiyFp rounded_input(input.f() >> precision_digits_count, | |
| 344 input.e() + precision_digits_count); | |
| 345 if (precision_bits >= half_way + error) { | |
| 346 rounded_input.set_f(rounded_input.f() + 1); | |
| 347 } | |
| 348 // If the last_bits are too close to the half-way case than we are too | |
| 349 // inaccurate and round down. In this case we return false so that we ca
n | |
| 350 // fall back to a more precise algorithm. | |
| 351 | |
| 352 *result = Double(rounded_input).value(); | |
| 353 if (half_way - error < precision_bits && precision_bits < half_way + err
or) { | |
| 354 // Too imprecise. The caller will have to fall back to a slower vers
ion. | |
| 355 // However the returned number is guaranteed to be either the correc
t | |
| 356 // double, or the next-lower double. | |
| 357 return false; | |
| 358 } else { | |
| 359 return true; | |
| 360 } | |
| 361 } | |
| 362 | |
| 363 | |
| 364 // Returns the correct double for the buffer*10^exponent. | |
| 365 // The variable guess should be a close guess that is either the correct dou
ble | |
| 366 // or its lower neighbor (the nearest double less than the correct one). | |
| 367 // Preconditions: | |
| 368 // buffer.length() + exponent <= kMaxDecimalPower + 1 | |
| 369 // buffer.length() + exponent > kMinDecimalPower | |
| 370 // buffer.length() <= kMaxDecimalSignificantDigits | |
| 371 static double BignumStrtod(Vector<const char> buffer, | |
| 372 int exponent, | |
| 373 double guess) { | |
| 374 if (guess == Double::Infinity()) { | |
| 375 return guess; | |
| 376 } | |
| 377 | |
| 378 DiyFp upper_boundary = Double(guess).UpperBoundary(); | |
| 379 | |
| 380 ASSERT(buffer.length() + exponent <= kMaxDecimalPower + 1); | |
| 381 ASSERT(buffer.length() + exponent > kMinDecimalPower); | |
| 382 ASSERT(buffer.length() <= kMaxSignificantDecimalDigits); | |
| 383 // Make sure that the Bignum will be able to hold all our numbers. | |
| 384 // Our Bignum implementation has a separate field for exponents. Shifts
will | |
| 385 // consume at most one bigit (< 64 bits). | |
| 386 // ln(10) == 3.3219... | |
| 387 ASSERT(((kMaxDecimalPower + 1) * 333 / 100) < Bignum::kMaxSignificantBit
s); | |
| 388 Bignum input; | |
| 389 Bignum boundary; | |
| 390 input.AssignDecimalString(buffer); | |
| 391 boundary.AssignUInt64(upper_boundary.f()); | |
| 392 if (exponent >= 0) { | |
| 393 input.MultiplyByPowerOfTen(exponent); | |
| 394 } else { | |
| 395 boundary.MultiplyByPowerOfTen(-exponent); | |
| 396 } | |
| 397 if (upper_boundary.e() > 0) { | |
| 398 boundary.ShiftLeft(upper_boundary.e()); | |
| 399 } else { | |
| 400 input.ShiftLeft(-upper_boundary.e()); | |
| 401 } | |
| 402 int comparison = Bignum::Compare(input, boundary); | |
| 403 if (comparison < 0) { | |
| 404 return guess; | |
| 405 } else if (comparison > 0) { | |
| 406 return Double(guess).NextDouble(); | |
| 407 } else if ((Double(guess).Significand() & 1) == 0) { | |
| 408 // Round towards even. | |
| 409 return guess; | |
| 410 } else { | |
| 411 return Double(guess).NextDouble(); | |
| 412 } | |
| 413 } | |
| 414 | |
| 415 | |
| 416 double Strtod(Vector<const char> buffer, int exponent) { | |
| 417 Vector<const char> left_trimmed = TrimLeadingZeros(buffer); | |
| 418 Vector<const char> trimmed = TrimTrailingZeros(left_trimmed); | |
| 419 exponent += left_trimmed.length() - trimmed.length(); | |
| 420 if (trimmed.length() == 0) return 0.0; | |
| 421 if (trimmed.length() > kMaxSignificantDecimalDigits) { | |
| 422 char significant_buffer[kMaxSignificantDecimalDigits]; | |
| 423 int significant_exponent; | |
| 424 TrimToMaxSignificantDigits(trimmed, exponent, | |
| 425 significant_buffer, &significant_exponent
); | |
| 426 return Strtod(Vector<const char>(significant_buffer, | |
| 427 kMaxSignificantDecimalDigits), | |
| 428 significant_exponent); | |
| 429 } | |
| 430 if (exponent + trimmed.length() - 1 >= kMaxDecimalPower) { | |
| 431 return Double::Infinity(); | |
| 432 } | |
| 433 if (exponent + trimmed.length() <= kMinDecimalPower) { | |
| 434 return 0.0; | |
| 435 } | |
| 436 | |
| 437 double guess; | |
| 438 if (DoubleStrtod(trimmed, exponent, &guess) || | |
| 439 DiyFpStrtod(trimmed, exponent, &guess)) { | |
| 440 return guess; | |
| 441 } | |
| 442 return BignumStrtod(trimmed, exponent, guess); | |
| 443 } | |
| 444 | |
| 445 } // namespace double_conversion | |
| 446 | |
| 447 } // namespace WTF | |
| OLD | NEW |
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Chromium Code Reviews
Issue 14238015:
Move Source/WTF/wtf to Source/wtf (Closed)
Base URL: svn://svn.chromium.org/blink/trunk