strtod.cc revision 3fb3ca8c7ca439d408449a395897395c0faae8d1
1// Copyright 2011 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 <stdarg.h> 29#include <math.h> 30 31#include "platform.h" 32#include "utils.h" 33#include "strtod.h" 34#include "bignum.h" 35#include "cached-powers.h" 36#include "double.h" 37 38namespace v8 { 39namespace internal { 40 41// 2^53 = 9007199254740992. 42// Any integer with at most 15 decimal digits will hence fit into a double 43// (which has a 53bit significand) without loss of precision. 44static const int kMaxExactDoubleIntegerDecimalDigits = 15; 45// 2^64 = 18446744073709551616 > 10^19 46static const int kMaxUint64DecimalDigits = 19; 47 48// Max double: 1.7976931348623157 x 10^308 49// Min non-zero double: 4.9406564584124654 x 10^-324 50// Any x >= 10^309 is interpreted as +infinity. 51// Any x <= 10^-324 is interpreted as 0. 52// Note that 2.5e-324 (despite being smaller than the min double) will be read 53// as non-zero (equal to the min non-zero double). 54static const int kMaxDecimalPower = 309; 55static const int kMinDecimalPower = -324; 56 57// 2^64 = 18446744073709551616 58static const uint64_t kMaxUint64 = V8_2PART_UINT64_C(0xFFFFFFFF, FFFFFFFF); 59 60 61static const double exact_powers_of_ten[] = { 62 1.0, // 10^0 63 10.0, 64 100.0, 65 1000.0, 66 10000.0, 67 100000.0, 68 1000000.0, 69 10000000.0, 70 100000000.0, 71 1000000000.0, 72 10000000000.0, // 10^10 73 100000000000.0, 74 1000000000000.0, 75 10000000000000.0, 76 100000000000000.0, 77 1000000000000000.0, 78 10000000000000000.0, 79 100000000000000000.0, 80 1000000000000000000.0, 81 10000000000000000000.0, 82 100000000000000000000.0, // 10^20 83 1000000000000000000000.0, 84 // 10^22 = 0x21e19e0c9bab2400000 = 0x878678326eac9 * 2^22 85 10000000000000000000000.0 86}; 87static const int kExactPowersOfTenSize = ARRAY_SIZE(exact_powers_of_ten); 88 89// Maximum number of significant digits in the decimal representation. 90// In fact the value is 772 (see conversions.cc), but to give us some margin 91// we round up to 780. 92static const int kMaxSignificantDecimalDigits = 780; 93 94static Vector<const char> TrimLeadingZeros(Vector<const char> buffer) { 95 for (int i = 0; i < buffer.length(); i++) { 96 if (buffer[i] != '0') { 97 return buffer.SubVector(i, buffer.length()); 98 } 99 } 100 return Vector<const char>(buffer.start(), 0); 101} 102 103 104static Vector<const char> TrimTrailingZeros(Vector<const char> buffer) { 105 for (int i = buffer.length() - 1; i >= 0; --i) { 106 if (buffer[i] != '0') { 107 return buffer.SubVector(0, i + 1); 108 } 109 } 110 return Vector<const char>(buffer.start(), 0); 111} 112 113 114static void TrimToMaxSignificantDigits(Vector<const char> buffer, 115 int exponent, 116 char* significant_buffer, 117 int* significant_exponent) { 118 for (int i = 0; i < kMaxSignificantDecimalDigits - 1; ++i) { 119 significant_buffer[i] = buffer[i]; 120 } 121 // The input buffer has been trimmed. Therefore the last digit must be 122 // different from '0'. 123 ASSERT(buffer[buffer.length() - 1] != '0'); 124 // Set the last digit to be non-zero. This is sufficient to guarantee 125 // correct rounding. 126 significant_buffer[kMaxSignificantDecimalDigits - 1] = '1'; 127 *significant_exponent = 128 exponent + (buffer.length() - kMaxSignificantDecimalDigits); 129} 130 131// Reads digits from the buffer and converts them to a uint64. 132// Reads in as many digits as fit into a uint64. 133// When the string starts with "1844674407370955161" no further digit is read. 134// Since 2^64 = 18446744073709551616 it would still be possible read another 135// digit if it was less or equal than 6, but this would complicate the code. 136static uint64_t ReadUint64(Vector<const char> buffer, 137 int* number_of_read_digits) { 138 uint64_t result = 0; 139 int i = 0; 140 while (i < buffer.length() && result <= (kMaxUint64 / 10 - 1)) { 141 int digit = buffer[i++] - '0'; 142 ASSERT(0 <= digit && digit <= 9); 143 result = 10 * result + digit; 144 } 145 *number_of_read_digits = i; 146 return result; 147} 148 149 150// Reads a DiyFp from the buffer. 151// The returned DiyFp is not necessarily normalized. 152// If remaining_decimals is zero then the returned DiyFp is accurate. 153// Otherwise it has been rounded and has error of at most 1/2 ulp. 154static void ReadDiyFp(Vector<const char> buffer, 155 DiyFp* result, 156 int* remaining_decimals) { 157 int read_digits; 158 uint64_t significand = ReadUint64(buffer, &read_digits); 159 if (buffer.length() == read_digits) { 160 *result = DiyFp(significand, 0); 161 *remaining_decimals = 0; 162 } else { 163 // Round the significand. 164 if (buffer[read_digits] >= '5') { 165 significand++; 166 } 167 // Compute the binary exponent. 168 int exponent = 0; 169 *result = DiyFp(significand, exponent); 170 *remaining_decimals = buffer.length() - read_digits; 171 } 172} 173 174 175static bool DoubleStrtod(Vector<const char> trimmed, 176 int exponent, 177 double* result) { 178#if (defined(V8_TARGET_ARCH_IA32) || defined(USE_SIMULATOR)) && !defined(WIN32) 179 // On x86 the floating-point stack can be 64 or 80 bits wide. If it is 180 // 80 bits wide (as is the case on Linux) then double-rounding occurs and the 181 // result is not accurate. 182 // We know that Windows32 uses 64 bits and is therefore accurate. 183 // Note that the ARM simulator is compiled for 32bits. It therefore exhibits 184 // the same problem. 185 return false; 186#endif 187 if (trimmed.length() <= kMaxExactDoubleIntegerDecimalDigits) { 188 int read_digits; 189 // The trimmed input fits into a double. 190 // If the 10^exponent (resp. 10^-exponent) fits into a double too then we 191 // can compute the result-double simply by multiplying (resp. dividing) the 192 // two numbers. 193 // This is possible because IEEE guarantees that floating-point operations 194 // return the best possible approximation. 195 if (exponent < 0 && -exponent < kExactPowersOfTenSize) { 196 // 10^-exponent fits into a double. 197 *result = static_cast<double>(ReadUint64(trimmed, &read_digits)); 198 ASSERT(read_digits == trimmed.length()); 199 *result /= exact_powers_of_ten[-exponent]; 200 return true; 201 } 202 if (0 <= exponent && exponent < kExactPowersOfTenSize) { 203 // 10^exponent fits into a double. 204 *result = static_cast<double>(ReadUint64(trimmed, &read_digits)); 205 ASSERT(read_digits == trimmed.length()); 206 *result *= exact_powers_of_ten[exponent]; 207 return true; 208 } 209 int remaining_digits = 210 kMaxExactDoubleIntegerDecimalDigits - trimmed.length(); 211 if ((0 <= exponent) && 212 (exponent - remaining_digits < kExactPowersOfTenSize)) { 213 // The trimmed string was short and we can multiply it with 214 // 10^remaining_digits. As a result the remaining exponent now fits 215 // into a double too. 216 *result = static_cast<double>(ReadUint64(trimmed, &read_digits)); 217 ASSERT(read_digits == trimmed.length()); 218 *result *= exact_powers_of_ten[remaining_digits]; 219 *result *= exact_powers_of_ten[exponent - remaining_digits]; 220 return true; 221 } 222 } 223 return false; 224} 225 226 227// Returns 10^exponent as an exact DiyFp. 228// The given exponent must be in the range [1; kDecimalExponentDistance[. 229static DiyFp AdjustmentPowerOfTen(int exponent) { 230 ASSERT(0 < exponent); 231 ASSERT(exponent < PowersOfTenCache::kDecimalExponentDistance); 232 // Simply hardcode the remaining powers for the given decimal exponent 233 // distance. 234 ASSERT(PowersOfTenCache::kDecimalExponentDistance == 8); 235 switch (exponent) { 236 case 1: return DiyFp(V8_2PART_UINT64_C(0xa0000000, 00000000), -60); 237 case 2: return DiyFp(V8_2PART_UINT64_C(0xc8000000, 00000000), -57); 238 case 3: return DiyFp(V8_2PART_UINT64_C(0xfa000000, 00000000), -54); 239 case 4: return DiyFp(V8_2PART_UINT64_C(0x9c400000, 00000000), -50); 240 case 5: return DiyFp(V8_2PART_UINT64_C(0xc3500000, 00000000), -47); 241 case 6: return DiyFp(V8_2PART_UINT64_C(0xf4240000, 00000000), -44); 242 case 7: return DiyFp(V8_2PART_UINT64_C(0x98968000, 00000000), -40); 243 default: 244 UNREACHABLE(); 245 return DiyFp(0, 0); 246 } 247} 248 249 250// If the function returns true then the result is the correct double. 251// Otherwise it is either the correct double or the double that is just below 252// the correct double. 253static bool DiyFpStrtod(Vector<const char> buffer, 254 int exponent, 255 double* result) { 256 DiyFp input; 257 int remaining_decimals; 258 ReadDiyFp(buffer, &input, &remaining_decimals); 259 // Since we may have dropped some digits the input is not accurate. 260 // If remaining_decimals is different than 0 than the error is at most 261 // .5 ulp (unit in the last place). 262 // We don't want to deal with fractions and therefore keep a common 263 // denominator. 264 const int kDenominatorLog = 3; 265 const int kDenominator = 1 << kDenominatorLog; 266 // Move the remaining decimals into the exponent. 267 exponent += remaining_decimals; 268 int error = (remaining_decimals == 0 ? 0 : kDenominator / 2); 269 270 int old_e = input.e(); 271 input.Normalize(); 272 error <<= old_e - input.e(); 273 274 ASSERT(exponent <= PowersOfTenCache::kMaxDecimalExponent); 275 if (exponent < PowersOfTenCache::kMinDecimalExponent) { 276 *result = 0.0; 277 return true; 278 } 279 DiyFp cached_power; 280 int cached_decimal_exponent; 281 PowersOfTenCache::GetCachedPowerForDecimalExponent(exponent, 282 &cached_power, 283 &cached_decimal_exponent); 284 285 if (cached_decimal_exponent != exponent) { 286 int adjustment_exponent = exponent - cached_decimal_exponent; 287 DiyFp adjustment_power = AdjustmentPowerOfTen(adjustment_exponent); 288 input.Multiply(adjustment_power); 289 if (kMaxUint64DecimalDigits - buffer.length() >= adjustment_exponent) { 290 // The product of input with the adjustment power fits into a 64 bit 291 // integer. 292 ASSERT(DiyFp::kSignificandSize == 64); 293 } else { 294 // The adjustment power is exact. There is hence only an error of 0.5. 295 error += kDenominator / 2; 296 } 297 } 298 299 input.Multiply(cached_power); 300 // The error introduced by a multiplication of a*b equals 301 // error_a + error_b + error_a*error_b/2^64 + 0.5 302 // Substituting a with 'input' and b with 'cached_power' we have 303 // error_b = 0.5 (all cached powers have an error of less than 0.5 ulp), 304 // error_ab = 0 or 1 / kDenominator > error_a*error_b/ 2^64 305 int error_b = kDenominator / 2; 306 int error_ab = (error == 0 ? 0 : 1); // We round up to 1. 307 int fixed_error = kDenominator / 2; 308 error += error_b + error_ab + fixed_error; 309 310 old_e = input.e(); 311 input.Normalize(); 312 error <<= old_e - input.e(); 313 314 // See if the double's significand changes if we add/subtract the error. 315 int order_of_magnitude = DiyFp::kSignificandSize + input.e(); 316 int effective_significand_size = 317 Double::SignificandSizeForOrderOfMagnitude(order_of_magnitude); 318 int precision_digits_count = 319 DiyFp::kSignificandSize - effective_significand_size; 320 if (precision_digits_count + kDenominatorLog >= DiyFp::kSignificandSize) { 321 // This can only happen for very small denormals. In this case the 322 // half-way multiplied by the denominator exceeds the range of an uint64. 323 // Simply shift everything to the right. 324 int shift_amount = (precision_digits_count + kDenominatorLog) - 325 DiyFp::kSignificandSize + 1; 326 input.set_f(input.f() >> shift_amount); 327 input.set_e(input.e() + shift_amount); 328 // We add 1 for the lost precision of error, and kDenominator for 329 // the lost precision of input.f(). 330 error = (error >> shift_amount) + 1 + kDenominator; 331 precision_digits_count -= shift_amount; 332 } 333 // We use uint64_ts now. This only works if the DiyFp uses uint64_ts too. 334 ASSERT(DiyFp::kSignificandSize == 64); 335 ASSERT(precision_digits_count < 64); 336 uint64_t one64 = 1; 337 uint64_t precision_bits_mask = (one64 << precision_digits_count) - 1; 338 uint64_t precision_bits = input.f() & precision_bits_mask; 339 uint64_t half_way = one64 << (precision_digits_count - 1); 340 precision_bits *= kDenominator; 341 half_way *= kDenominator; 342 DiyFp rounded_input(input.f() >> precision_digits_count, 343 input.e() + precision_digits_count); 344 if (precision_bits >= half_way + error) { 345 rounded_input.set_f(rounded_input.f() + 1); 346 } 347 // If the last_bits are too close to the half-way case than we are too 348 // inaccurate and round down. In this case we return false so that we can 349 // fall back to a more precise algorithm. 350 351 *result = Double(rounded_input).value(); 352 if (half_way - error < precision_bits && precision_bits < half_way + error) { 353 // Too imprecise. The caller will have to fall back to a slower version. 354 // However the returned number is guaranteed to be either the correct 355 // double, or the next-lower double. 356 return false; 357 } else { 358 return true; 359 } 360} 361 362 363// Returns the correct double for the buffer*10^exponent. 364// The variable guess should be a close guess that is either the correct double 365// or its lower neighbor (the nearest double less than the correct one). 366// Preconditions: 367// buffer.length() + exponent <= kMaxDecimalPower + 1 368// buffer.length() + exponent > kMinDecimalPower 369// buffer.length() <= kMaxDecimalSignificantDigits 370static double BignumStrtod(Vector<const char> buffer, 371 int exponent, 372 double guess) { 373 if (guess == V8_INFINITY) { 374 return guess; 375 } 376 377 DiyFp upper_boundary = Double(guess).UpperBoundary(); 378 379 ASSERT(buffer.length() + exponent <= kMaxDecimalPower + 1); 380 ASSERT(buffer.length() + exponent > kMinDecimalPower); 381 ASSERT(buffer.length() <= kMaxSignificantDecimalDigits); 382 // Make sure that the Bignum will be able to hold all our numbers. 383 // Our Bignum implementation has a separate field for exponents. Shifts will 384 // consume at most one bigit (< 64 bits). 385 // ln(10) == 3.3219... 386 ASSERT(((kMaxDecimalPower + 1) * 333 / 100) < Bignum::kMaxSignificantBits); 387 Bignum input; 388 Bignum boundary; 389 input.AssignDecimalString(buffer); 390 boundary.AssignUInt64(upper_boundary.f()); 391 if (exponent >= 0) { 392 input.MultiplyByPowerOfTen(exponent); 393 } else { 394 boundary.MultiplyByPowerOfTen(-exponent); 395 } 396 if (upper_boundary.e() > 0) { 397 boundary.ShiftLeft(upper_boundary.e()); 398 } else { 399 input.ShiftLeft(-upper_boundary.e()); 400 } 401 int comparison = Bignum::Compare(input, boundary); 402 if (comparison < 0) { 403 return guess; 404 } else if (comparison > 0) { 405 return Double(guess).NextDouble(); 406 } else if ((Double(guess).Significand() & 1) == 0) { 407 // Round towards even. 408 return guess; 409 } else { 410 return Double(guess).NextDouble(); 411 } 412} 413 414 415double Strtod(Vector<const char> buffer, int exponent) { 416 Vector<const char> left_trimmed = TrimLeadingZeros(buffer); 417 Vector<const char> trimmed = TrimTrailingZeros(left_trimmed); 418 exponent += left_trimmed.length() - trimmed.length(); 419 if (trimmed.length() == 0) return 0.0; 420 if (trimmed.length() > kMaxSignificantDecimalDigits) { 421 char significant_buffer[kMaxSignificantDecimalDigits]; 422 int significant_exponent; 423 TrimToMaxSignificantDigits(trimmed, exponent, 424 significant_buffer, &significant_exponent); 425 return Strtod(Vector<const char>(significant_buffer, 426 kMaxSignificantDecimalDigits), 427 significant_exponent); 428 } 429 if (exponent + trimmed.length() - 1 >= kMaxDecimalPower) return V8_INFINITY; 430 if (exponent + trimmed.length() <= kMinDecimalPower) return 0.0; 431 432 double guess; 433 if (DoubleStrtod(trimmed, exponent, &guess) || 434 DiyFpStrtod(trimmed, exponent, &guess)) { 435 return guess; 436 } 437 return BignumStrtod(trimmed, exponent, guess); 438} 439 440} } // namespace v8::internal 441