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| 1 // Copyright 2012 the V8 project authors. All rights reserved. | 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 | 2 // Use of this source code is governed by a BSD-style license that can be |
| 3 // found in the LICENSE file. | 3 // found in the LICENSE file. |
| 4 | 4 |
| 5 #include <stdarg.h> | 5 #include <stdarg.h> |
| 6 #include <cmath> | 6 #include <cmath> |
| 7 | 7 |
| 8 #include "src/v8.h" | 8 #include "src/v8.h" |
| 9 | 9 |
| 10 #include "src/bignum.h" | 10 #include "src/bignum.h" |
| (...skipping 81 matching lines...) Expand 10 before | Expand all | Expand 10 after Loading... |
| 92 | 92 |
| 93 static void TrimToMaxSignificantDigits(Vector<const char> buffer, | 93 static void TrimToMaxSignificantDigits(Vector<const char> buffer, |
| 94 int exponent, | 94 int exponent, |
| 95 char* significant_buffer, | 95 char* significant_buffer, |
| 96 int* significant_exponent) { | 96 int* significant_exponent) { |
| 97 for (int i = 0; i < kMaxSignificantDecimalDigits - 1; ++i) { | 97 for (int i = 0; i < kMaxSignificantDecimalDigits - 1; ++i) { |
| 98 significant_buffer[i] = buffer[i]; | 98 significant_buffer[i] = buffer[i]; |
| 99 } | 99 } |
| 100 // The input buffer has been trimmed. Therefore the last digit must be | 100 // The input buffer has been trimmed. Therefore the last digit must be |
| 101 // different from '0'. | 101 // different from '0'. |
| 102 ASSERT(buffer[buffer.length() - 1] != '0'); | 102 DCHECK(buffer[buffer.length() - 1] != '0'); |
| 103 // Set the last digit to be non-zero. This is sufficient to guarantee | 103 // Set the last digit to be non-zero. This is sufficient to guarantee |
| 104 // correct rounding. | 104 // correct rounding. |
| 105 significant_buffer[kMaxSignificantDecimalDigits - 1] = '1'; | 105 significant_buffer[kMaxSignificantDecimalDigits - 1] = '1'; |
| 106 *significant_exponent = | 106 *significant_exponent = |
| 107 exponent + (buffer.length() - kMaxSignificantDecimalDigits); | 107 exponent + (buffer.length() - kMaxSignificantDecimalDigits); |
| 108 } | 108 } |
| 109 | 109 |
| 110 | 110 |
| 111 // Reads digits from the buffer and converts them to a uint64. | 111 // Reads digits from the buffer and converts them to a uint64. |
| 112 // Reads in as many digits as fit into 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. | 113 // When the string starts with "1844674407370955161" no further digit is read. |
| 114 // Since 2^64 = 18446744073709551616 it would still be possible read another | 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. | 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, | 116 static uint64_t ReadUint64(Vector<const char> buffer, |
| 117 int* number_of_read_digits) { | 117 int* number_of_read_digits) { |
| 118 uint64_t result = 0; | 118 uint64_t result = 0; |
| 119 int i = 0; | 119 int i = 0; |
| 120 while (i < buffer.length() && result <= (kMaxUint64 / 10 - 1)) { | 120 while (i < buffer.length() && result <= (kMaxUint64 / 10 - 1)) { |
| 121 int digit = buffer[i++] - '0'; | 121 int digit = buffer[i++] - '0'; |
| 122 ASSERT(0 <= digit && digit <= 9); | 122 DCHECK(0 <= digit && digit <= 9); |
| 123 result = 10 * result + digit; | 123 result = 10 * result + digit; |
| 124 } | 124 } |
| 125 *number_of_read_digits = i; | 125 *number_of_read_digits = i; |
| 126 return result; | 126 return result; |
| 127 } | 127 } |
| 128 | 128 |
| 129 | 129 |
| 130 // Reads a DiyFp from the buffer. | 130 // Reads a DiyFp from the buffer. |
| 131 // The returned DiyFp is not necessarily normalized. | 131 // The returned DiyFp is not necessarily normalized. |
| 132 // If remaining_decimals is zero then the returned DiyFp is accurate. | 132 // If remaining_decimals is zero then the returned DiyFp is accurate. |
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| 170 int read_digits; | 170 int read_digits; |
| 171 // The trimmed input fits into a double. | 171 // The trimmed input fits into a double. |
| 172 // If the 10^exponent (resp. 10^-exponent) fits into a double too then we | 172 // If the 10^exponent (resp. 10^-exponent) fits into a double too then we |
| 173 // can compute the result-double simply by multiplying (resp. dividing) the | 173 // can compute the result-double simply by multiplying (resp. dividing) the |
| 174 // two numbers. | 174 // two numbers. |
| 175 // This is possible because IEEE guarantees that floating-point operations | 175 // This is possible because IEEE guarantees that floating-point operations |
| 176 // return the best possible approximation. | 176 // return the best possible approximation. |
| 177 if (exponent < 0 && -exponent < kExactPowersOfTenSize) { | 177 if (exponent < 0 && -exponent < kExactPowersOfTenSize) { |
| 178 // 10^-exponent fits into a double. | 178 // 10^-exponent fits into a double. |
| 179 *result = static_cast<double>(ReadUint64(trimmed, &read_digits)); | 179 *result = static_cast<double>(ReadUint64(trimmed, &read_digits)); |
| 180 ASSERT(read_digits == trimmed.length()); | 180 DCHECK(read_digits == trimmed.length()); |
| 181 *result /= exact_powers_of_ten[-exponent]; | 181 *result /= exact_powers_of_ten[-exponent]; |
| 182 return true; | 182 return true; |
| 183 } | 183 } |
| 184 if (0 <= exponent && exponent < kExactPowersOfTenSize) { | 184 if (0 <= exponent && exponent < kExactPowersOfTenSize) { |
| 185 // 10^exponent fits into a double. | 185 // 10^exponent fits into a double. |
| 186 *result = static_cast<double>(ReadUint64(trimmed, &read_digits)); | 186 *result = static_cast<double>(ReadUint64(trimmed, &read_digits)); |
| 187 ASSERT(read_digits == trimmed.length()); | 187 DCHECK(read_digits == trimmed.length()); |
| 188 *result *= exact_powers_of_ten[exponent]; | 188 *result *= exact_powers_of_ten[exponent]; |
| 189 return true; | 189 return true; |
| 190 } | 190 } |
| 191 int remaining_digits = | 191 int remaining_digits = |
| 192 kMaxExactDoubleIntegerDecimalDigits - trimmed.length(); | 192 kMaxExactDoubleIntegerDecimalDigits - trimmed.length(); |
| 193 if ((0 <= exponent) && | 193 if ((0 <= exponent) && |
| 194 (exponent - remaining_digits < kExactPowersOfTenSize)) { | 194 (exponent - remaining_digits < kExactPowersOfTenSize)) { |
| 195 // The trimmed string was short and we can multiply it with | 195 // The trimmed string was short and we can multiply it with |
| 196 // 10^remaining_digits. As a result the remaining exponent now fits | 196 // 10^remaining_digits. As a result the remaining exponent now fits |
| 197 // into a double too. | 197 // into a double too. |
| 198 *result = static_cast<double>(ReadUint64(trimmed, &read_digits)); | 198 *result = static_cast<double>(ReadUint64(trimmed, &read_digits)); |
| 199 ASSERT(read_digits == trimmed.length()); | 199 DCHECK(read_digits == trimmed.length()); |
| 200 *result *= exact_powers_of_ten[remaining_digits]; | 200 *result *= exact_powers_of_ten[remaining_digits]; |
| 201 *result *= exact_powers_of_ten[exponent - remaining_digits]; | 201 *result *= exact_powers_of_ten[exponent - remaining_digits]; |
| 202 return true; | 202 return true; |
| 203 } | 203 } |
| 204 } | 204 } |
| 205 return false; | 205 return false; |
| 206 } | 206 } |
| 207 | 207 |
| 208 | 208 |
| 209 // Returns 10^exponent as an exact DiyFp. | 209 // Returns 10^exponent as an exact DiyFp. |
| 210 // The given exponent must be in the range [1; kDecimalExponentDistance[. | 210 // The given exponent must be in the range [1; kDecimalExponentDistance[. |
| 211 static DiyFp AdjustmentPowerOfTen(int exponent) { | 211 static DiyFp AdjustmentPowerOfTen(int exponent) { |
| 212 ASSERT(0 < exponent); | 212 DCHECK(0 < exponent); |
| 213 ASSERT(exponent < PowersOfTenCache::kDecimalExponentDistance); | 213 DCHECK(exponent < PowersOfTenCache::kDecimalExponentDistance); |
| 214 // Simply hardcode the remaining powers for the given decimal exponent | 214 // Simply hardcode the remaining powers for the given decimal exponent |
| 215 // distance. | 215 // distance. |
| 216 ASSERT(PowersOfTenCache::kDecimalExponentDistance == 8); | 216 DCHECK(PowersOfTenCache::kDecimalExponentDistance == 8); |
| 217 switch (exponent) { | 217 switch (exponent) { |
| 218 case 1: return DiyFp(V8_2PART_UINT64_C(0xa0000000, 00000000), -60); | 218 case 1: return DiyFp(V8_2PART_UINT64_C(0xa0000000, 00000000), -60); |
| 219 case 2: return DiyFp(V8_2PART_UINT64_C(0xc8000000, 00000000), -57); | 219 case 2: return DiyFp(V8_2PART_UINT64_C(0xc8000000, 00000000), -57); |
| 220 case 3: return DiyFp(V8_2PART_UINT64_C(0xfa000000, 00000000), -54); | 220 case 3: return DiyFp(V8_2PART_UINT64_C(0xfa000000, 00000000), -54); |
| 221 case 4: return DiyFp(V8_2PART_UINT64_C(0x9c400000, 00000000), -50); | 221 case 4: return DiyFp(V8_2PART_UINT64_C(0x9c400000, 00000000), -50); |
| 222 case 5: return DiyFp(V8_2PART_UINT64_C(0xc3500000, 00000000), -47); | 222 case 5: return DiyFp(V8_2PART_UINT64_C(0xc3500000, 00000000), -47); |
| 223 case 6: return DiyFp(V8_2PART_UINT64_C(0xf4240000, 00000000), -44); | 223 case 6: return DiyFp(V8_2PART_UINT64_C(0xf4240000, 00000000), -44); |
| 224 case 7: return DiyFp(V8_2PART_UINT64_C(0x98968000, 00000000), -40); | 224 case 7: return DiyFp(V8_2PART_UINT64_C(0x98968000, 00000000), -40); |
| 225 default: | 225 default: |
| 226 UNREACHABLE(); | 226 UNREACHABLE(); |
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| 246 const int kDenominatorLog = 3; | 246 const int kDenominatorLog = 3; |
| 247 const int kDenominator = 1 << kDenominatorLog; | 247 const int kDenominator = 1 << kDenominatorLog; |
| 248 // Move the remaining decimals into the exponent. | 248 // Move the remaining decimals into the exponent. |
| 249 exponent += remaining_decimals; | 249 exponent += remaining_decimals; |
| 250 int64_t error = (remaining_decimals == 0 ? 0 : kDenominator / 2); | 250 int64_t error = (remaining_decimals == 0 ? 0 : kDenominator / 2); |
| 251 | 251 |
| 252 int old_e = input.e(); | 252 int old_e = input.e(); |
| 253 input.Normalize(); | 253 input.Normalize(); |
| 254 error <<= old_e - input.e(); | 254 error <<= old_e - input.e(); |
| 255 | 255 |
| 256 ASSERT(exponent <= PowersOfTenCache::kMaxDecimalExponent); | 256 DCHECK(exponent <= PowersOfTenCache::kMaxDecimalExponent); |
| 257 if (exponent < PowersOfTenCache::kMinDecimalExponent) { | 257 if (exponent < PowersOfTenCache::kMinDecimalExponent) { |
| 258 *result = 0.0; | 258 *result = 0.0; |
| 259 return true; | 259 return true; |
| 260 } | 260 } |
| 261 DiyFp cached_power; | 261 DiyFp cached_power; |
| 262 int cached_decimal_exponent; | 262 int cached_decimal_exponent; |
| 263 PowersOfTenCache::GetCachedPowerForDecimalExponent(exponent, | 263 PowersOfTenCache::GetCachedPowerForDecimalExponent(exponent, |
| 264 &cached_power, | 264 &cached_power, |
| 265 &cached_decimal_exponent); | 265 &cached_decimal_exponent); |
| 266 | 266 |
| 267 if (cached_decimal_exponent != exponent) { | 267 if (cached_decimal_exponent != exponent) { |
| 268 int adjustment_exponent = exponent - cached_decimal_exponent; | 268 int adjustment_exponent = exponent - cached_decimal_exponent; |
| 269 DiyFp adjustment_power = AdjustmentPowerOfTen(adjustment_exponent); | 269 DiyFp adjustment_power = AdjustmentPowerOfTen(adjustment_exponent); |
| 270 input.Multiply(adjustment_power); | 270 input.Multiply(adjustment_power); |
| 271 if (kMaxUint64DecimalDigits - buffer.length() >= adjustment_exponent) { | 271 if (kMaxUint64DecimalDigits - buffer.length() >= adjustment_exponent) { |
| 272 // The product of input with the adjustment power fits into a 64 bit | 272 // The product of input with the adjustment power fits into a 64 bit |
| 273 // integer. | 273 // integer. |
| 274 ASSERT(DiyFp::kSignificandSize == 64); | 274 DCHECK(DiyFp::kSignificandSize == 64); |
| 275 } else { | 275 } else { |
| 276 // The adjustment power is exact. There is hence only an error of 0.5. | 276 // The adjustment power is exact. There is hence only an error of 0.5. |
| 277 error += kDenominator / 2; | 277 error += kDenominator / 2; |
| 278 } | 278 } |
| 279 } | 279 } |
| 280 | 280 |
| 281 input.Multiply(cached_power); | 281 input.Multiply(cached_power); |
| 282 // The error introduced by a multiplication of a*b equals | 282 // The error introduced by a multiplication of a*b equals |
| 283 // error_a + error_b + error_a*error_b/2^64 + 0.5 | 283 // error_a + error_b + error_a*error_b/2^64 + 0.5 |
| 284 // Substituting a with 'input' and b with 'cached_power' we have | 284 // Substituting a with 'input' and b with 'cached_power' we have |
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| 306 int shift_amount = (precision_digits_count + kDenominatorLog) - | 306 int shift_amount = (precision_digits_count + kDenominatorLog) - |
| 307 DiyFp::kSignificandSize + 1; | 307 DiyFp::kSignificandSize + 1; |
| 308 input.set_f(input.f() >> shift_amount); | 308 input.set_f(input.f() >> shift_amount); |
| 309 input.set_e(input.e() + shift_amount); | 309 input.set_e(input.e() + shift_amount); |
| 310 // We add 1 for the lost precision of error, and kDenominator for | 310 // We add 1 for the lost precision of error, and kDenominator for |
| 311 // the lost precision of input.f(). | 311 // the lost precision of input.f(). |
| 312 error = (error >> shift_amount) + 1 + kDenominator; | 312 error = (error >> shift_amount) + 1 + kDenominator; |
| 313 precision_digits_count -= shift_amount; | 313 precision_digits_count -= shift_amount; |
| 314 } | 314 } |
| 315 // We use uint64_ts now. This only works if the DiyFp uses uint64_ts too. | 315 // We use uint64_ts now. This only works if the DiyFp uses uint64_ts too. |
| 316 ASSERT(DiyFp::kSignificandSize == 64); | 316 DCHECK(DiyFp::kSignificandSize == 64); |
| 317 ASSERT(precision_digits_count < 64); | 317 DCHECK(precision_digits_count < 64); |
| 318 uint64_t one64 = 1; | 318 uint64_t one64 = 1; |
| 319 uint64_t precision_bits_mask = (one64 << precision_digits_count) - 1; | 319 uint64_t precision_bits_mask = (one64 << precision_digits_count) - 1; |
| 320 uint64_t precision_bits = input.f() & precision_bits_mask; | 320 uint64_t precision_bits = input.f() & precision_bits_mask; |
| 321 uint64_t half_way = one64 << (precision_digits_count - 1); | 321 uint64_t half_way = one64 << (precision_digits_count - 1); |
| 322 precision_bits *= kDenominator; | 322 precision_bits *= kDenominator; |
| 323 half_way *= kDenominator; | 323 half_way *= kDenominator; |
| 324 DiyFp rounded_input(input.f() >> precision_digits_count, | 324 DiyFp rounded_input(input.f() >> precision_digits_count, |
| 325 input.e() + precision_digits_count); | 325 input.e() + precision_digits_count); |
| 326 if (precision_bits >= half_way + error) { | 326 if (precision_bits >= half_way + error) { |
| 327 rounded_input.set_f(rounded_input.f() + 1); | 327 rounded_input.set_f(rounded_input.f() + 1); |
| (...skipping 23 matching lines...) Expand all Loading... |
| 351 // buffer.length() <= kMaxDecimalSignificantDigits | 351 // buffer.length() <= kMaxDecimalSignificantDigits |
| 352 static double BignumStrtod(Vector<const char> buffer, | 352 static double BignumStrtod(Vector<const char> buffer, |
| 353 int exponent, | 353 int exponent, |
| 354 double guess) { | 354 double guess) { |
| 355 if (guess == V8_INFINITY) { | 355 if (guess == V8_INFINITY) { |
| 356 return guess; | 356 return guess; |
| 357 } | 357 } |
| 358 | 358 |
| 359 DiyFp upper_boundary = Double(guess).UpperBoundary(); | 359 DiyFp upper_boundary = Double(guess).UpperBoundary(); |
| 360 | 360 |
| 361 ASSERT(buffer.length() + exponent <= kMaxDecimalPower + 1); | 361 DCHECK(buffer.length() + exponent <= kMaxDecimalPower + 1); |
| 362 ASSERT(buffer.length() + exponent > kMinDecimalPower); | 362 DCHECK(buffer.length() + exponent > kMinDecimalPower); |
| 363 ASSERT(buffer.length() <= kMaxSignificantDecimalDigits); | 363 DCHECK(buffer.length() <= kMaxSignificantDecimalDigits); |
| 364 // Make sure that the Bignum will be able to hold all our numbers. | 364 // Make sure that the Bignum will be able to hold all our numbers. |
| 365 // Our Bignum implementation has a separate field for exponents. Shifts will | 365 // Our Bignum implementation has a separate field for exponents. Shifts will |
| 366 // consume at most one bigit (< 64 bits). | 366 // consume at most one bigit (< 64 bits). |
| 367 // ln(10) == 3.3219... | 367 // ln(10) == 3.3219... |
| 368 ASSERT(((kMaxDecimalPower + 1) * 333 / 100) < Bignum::kMaxSignificantBits); | 368 DCHECK(((kMaxDecimalPower + 1) * 333 / 100) < Bignum::kMaxSignificantBits); |
| 369 Bignum input; | 369 Bignum input; |
| 370 Bignum boundary; | 370 Bignum boundary; |
| 371 input.AssignDecimalString(buffer); | 371 input.AssignDecimalString(buffer); |
| 372 boundary.AssignUInt64(upper_boundary.f()); | 372 boundary.AssignUInt64(upper_boundary.f()); |
| 373 if (exponent >= 0) { | 373 if (exponent >= 0) { |
| 374 input.MultiplyByPowerOfTen(exponent); | 374 input.MultiplyByPowerOfTen(exponent); |
| 375 } else { | 375 } else { |
| 376 boundary.MultiplyByPowerOfTen(-exponent); | 376 boundary.MultiplyByPowerOfTen(-exponent); |
| 377 } | 377 } |
| 378 if (upper_boundary.e() > 0) { | 378 if (upper_boundary.e() > 0) { |
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| 413 | 413 |
| 414 double guess; | 414 double guess; |
| 415 if (DoubleStrtod(trimmed, exponent, &guess) || | 415 if (DoubleStrtod(trimmed, exponent, &guess) || |
| 416 DiyFpStrtod(trimmed, exponent, &guess)) { | 416 DiyFpStrtod(trimmed, exponent, &guess)) { |
| 417 return guess; | 417 return guess; |
| 418 } | 418 } |
| 419 return BignumStrtod(trimmed, exponent, guess); | 419 return BignumStrtod(trimmed, exponent, guess); |
| 420 } | 420 } |
| 421 | 421 |
| 422 } } // namespace v8::internal | 422 } } // namespace v8::internal |
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