| // Copyright 2012 the V8 project authors. All rights reserved. |
| // Use of this source code is governed by a BSD-style license that can be |
| // found in the LICENSE file. |
| |
| #include "src/strtod.h" |
| |
| #include <stdarg.h> |
| #include <cmath> |
| |
| #include "src/bignum.h" |
| #include "src/cached-powers.h" |
| #include "src/double.h" |
| #include "src/globals.h" |
| #include "src/utils.h" |
| |
| namespace v8 { |
| namespace internal { |
| |
| // 2^53 = 9007199254740992. |
| // Any integer with at most 15 decimal digits will hence fit into a double |
| // (which has a 53bit significand) without loss of precision. |
| static const int kMaxExactDoubleIntegerDecimalDigits = 15; |
| // 2^64 = 18446744073709551616 > 10^19 |
| static const int kMaxUint64DecimalDigits = 19; |
| |
| // Max double: 1.7976931348623157 x 10^308 |
| // Min non-zero double: 4.9406564584124654 x 10^-324 |
| // Any x >= 10^309 is interpreted as +infinity. |
| // Any x <= 10^-324 is interpreted as 0. |
| // Note that 2.5e-324 (despite being smaller than the min double) will be read |
| // as non-zero (equal to the min non-zero double). |
| static const int kMaxDecimalPower = 309; |
| static const int kMinDecimalPower = -324; |
| |
| // 2^64 = 18446744073709551616 |
| static const uint64_t kMaxUint64 = V8_2PART_UINT64_C(0xFFFFFFFF, FFFFFFFF); |
| |
| // clang-format off |
| static const double exact_powers_of_ten[] = { |
| 1.0, // 10^0 |
| 10.0, |
| 100.0, |
| 1000.0, |
| 10000.0, |
| 100000.0, |
| 1000000.0, |
| 10000000.0, |
| 100000000.0, |
| 1000000000.0, |
| 10000000000.0, // 10^10 |
| 100000000000.0, |
| 1000000000000.0, |
| 10000000000000.0, |
| 100000000000000.0, |
| 1000000000000000.0, |
| 10000000000000000.0, |
| 100000000000000000.0, |
| 1000000000000000000.0, |
| 10000000000000000000.0, |
| 100000000000000000000.0, // 10^20 |
| 1000000000000000000000.0, |
| // 10^22 = 0x21E19E0C9BAB2400000 = 0x878678326EAC9 * 2^22 |
| 10000000000000000000000.0 |
| }; |
| // clang-format on |
| static const int kExactPowersOfTenSize = arraysize(exact_powers_of_ten); |
| |
| // Maximum number of significant digits in the decimal representation. |
| // In fact the value is 772 (see conversions.cc), but to give us some margin |
| // we round up to 780. |
| static const int kMaxSignificantDecimalDigits = 780; |
| |
| static Vector<const char> TrimLeadingZeros(Vector<const char> buffer) { |
| for (int i = 0; i < buffer.length(); i++) { |
| if (buffer[i] != '0') { |
| return buffer.SubVector(i, buffer.length()); |
| } |
| } |
| return Vector<const char>(buffer.start(), 0); |
| } |
| |
| |
| static Vector<const char> TrimTrailingZeros(Vector<const char> buffer) { |
| for (int i = buffer.length() - 1; i >= 0; --i) { |
| if (buffer[i] != '0') { |
| return buffer.SubVector(0, i + 1); |
| } |
| } |
| return Vector<const char>(buffer.start(), 0); |
| } |
| |
| |
| static void TrimToMaxSignificantDigits(Vector<const char> buffer, |
| int exponent, |
| char* significant_buffer, |
| int* significant_exponent) { |
| for (int i = 0; i < kMaxSignificantDecimalDigits - 1; ++i) { |
| significant_buffer[i] = buffer[i]; |
| } |
| // The input buffer has been trimmed. Therefore the last digit must be |
| // different from '0'. |
| DCHECK_NE(buffer[buffer.length() - 1], '0'); |
| // Set the last digit to be non-zero. This is sufficient to guarantee |
| // correct rounding. |
| significant_buffer[kMaxSignificantDecimalDigits - 1] = '1'; |
| *significant_exponent = |
| exponent + (buffer.length() - kMaxSignificantDecimalDigits); |
| } |
| |
| |
| // Reads digits from the buffer and converts them to a uint64. |
| // Reads in as many digits as fit into a uint64. |
| // When the string starts with "1844674407370955161" no further digit is read. |
| // Since 2^64 = 18446744073709551616 it would still be possible read another |
| // digit if it was less or equal than 6, but this would complicate the code. |
| static uint64_t ReadUint64(Vector<const char> buffer, |
| int* number_of_read_digits) { |
| uint64_t result = 0; |
| int i = 0; |
| while (i < buffer.length() && result <= (kMaxUint64 / 10 - 1)) { |
| int digit = buffer[i++] - '0'; |
| DCHECK(0 <= digit && digit <= 9); |
| result = 10 * result + digit; |
| } |
| *number_of_read_digits = i; |
| return result; |
| } |
| |
| |
| // Reads a DiyFp from the buffer. |
| // The returned DiyFp is not necessarily normalized. |
| // If remaining_decimals is zero then the returned DiyFp is accurate. |
| // Otherwise it has been rounded and has error of at most 1/2 ulp. |
| static void ReadDiyFp(Vector<const char> buffer, |
| DiyFp* result, |
| int* remaining_decimals) { |
| int read_digits; |
| uint64_t significand = ReadUint64(buffer, &read_digits); |
| if (buffer.length() == read_digits) { |
| *result = DiyFp(significand, 0); |
| *remaining_decimals = 0; |
| } else { |
| // Round the significand. |
| if (buffer[read_digits] >= '5') { |
| significand++; |
| } |
| // Compute the binary exponent. |
| int exponent = 0; |
| *result = DiyFp(significand, exponent); |
| *remaining_decimals = buffer.length() - read_digits; |
| } |
| } |
| |
| |
| static bool DoubleStrtod(Vector<const char> trimmed, |
| int exponent, |
| double* result) { |
| #if (V8_TARGET_ARCH_IA32 || defined(USE_SIMULATOR)) && !defined(_MSC_VER) |
| // On x86 the floating-point stack can be 64 or 80 bits wide. If it is |
| // 80 bits wide (as is the case on Linux) then double-rounding occurs and the |
| // result is not accurate. |
| // We know that Windows32 with MSVC, unlike with MinGW32, uses 64 bits and is |
| // therefore accurate. |
| // Note that the ARM and MIPS simulators are compiled for 32bits. They |
| // therefore exhibit the same problem. |
| USE(exact_powers_of_ten); |
| USE(kMaxExactDoubleIntegerDecimalDigits); |
| USE(kExactPowersOfTenSize); |
| return false; |
| #else |
| if (trimmed.length() <= kMaxExactDoubleIntegerDecimalDigits) { |
| int read_digits; |
| // The trimmed input fits into a double. |
| // If the 10^exponent (resp. 10^-exponent) fits into a double too then we |
| // can compute the result-double simply by multiplying (resp. dividing) the |
| // two numbers. |
| // This is possible because IEEE guarantees that floating-point operations |
| // return the best possible approximation. |
| if (exponent < 0 && -exponent < kExactPowersOfTenSize) { |
| // 10^-exponent fits into a double. |
| *result = static_cast<double>(ReadUint64(trimmed, &read_digits)); |
| DCHECK(read_digits == trimmed.length()); |
| *result /= exact_powers_of_ten[-exponent]; |
| return true; |
| } |
| if (0 <= exponent && exponent < kExactPowersOfTenSize) { |
| // 10^exponent fits into a double. |
| *result = static_cast<double>(ReadUint64(trimmed, &read_digits)); |
| DCHECK(read_digits == trimmed.length()); |
| *result *= exact_powers_of_ten[exponent]; |
| return true; |
| } |
| int remaining_digits = |
| kMaxExactDoubleIntegerDecimalDigits - trimmed.length(); |
| if ((0 <= exponent) && |
| (exponent - remaining_digits < kExactPowersOfTenSize)) { |
| // The trimmed string was short and we can multiply it with |
| // 10^remaining_digits. As a result the remaining exponent now fits |
| // into a double too. |
| *result = static_cast<double>(ReadUint64(trimmed, &read_digits)); |
| DCHECK(read_digits == trimmed.length()); |
| *result *= exact_powers_of_ten[remaining_digits]; |
| *result *= exact_powers_of_ten[exponent - remaining_digits]; |
| return true; |
| } |
| } |
| return false; |
| #endif |
| } |
| |
| |
| // Returns 10^exponent as an exact DiyFp. |
| // The given exponent must be in the range [1; kDecimalExponentDistance[. |
| static DiyFp AdjustmentPowerOfTen(int exponent) { |
| DCHECK_LT(0, exponent); |
| DCHECK_LT(exponent, PowersOfTenCache::kDecimalExponentDistance); |
| // Simply hardcode the remaining powers for the given decimal exponent |
| // distance. |
| DCHECK_EQ(PowersOfTenCache::kDecimalExponentDistance, 8); |
| switch (exponent) { |
| case 1: |
| return DiyFp(V8_2PART_UINT64_C(0xA0000000, 00000000), -60); |
| case 2: |
| return DiyFp(V8_2PART_UINT64_C(0xC8000000, 00000000), -57); |
| case 3: |
| return DiyFp(V8_2PART_UINT64_C(0xFA000000, 00000000), -54); |
| case 4: |
| return DiyFp(V8_2PART_UINT64_C(0x9C400000, 00000000), -50); |
| case 5: |
| return DiyFp(V8_2PART_UINT64_C(0xC3500000, 00000000), -47); |
| case 6: |
| return DiyFp(V8_2PART_UINT64_C(0xF4240000, 00000000), -44); |
| case 7: |
| return DiyFp(V8_2PART_UINT64_C(0x98968000, 00000000), -40); |
| default: |
| UNREACHABLE(); |
| } |
| } |
| |
| |
| // If the function returns true then the result is the correct double. |
| // Otherwise it is either the correct double or the double that is just below |
| // the correct double. |
| static bool DiyFpStrtod(Vector<const char> buffer, |
| int exponent, |
| double* result) { |
| DiyFp input; |
| int remaining_decimals; |
| ReadDiyFp(buffer, &input, &remaining_decimals); |
| // Since we may have dropped some digits the input is not accurate. |
| // If remaining_decimals is different than 0 than the error is at most |
| // .5 ulp (unit in the last place). |
| // We don't want to deal with fractions and therefore keep a common |
| // denominator. |
| const int kDenominatorLog = 3; |
| const int kDenominator = 1 << kDenominatorLog; |
| // Move the remaining decimals into the exponent. |
| exponent += remaining_decimals; |
| int64_t error = (remaining_decimals == 0 ? 0 : kDenominator / 2); |
| |
| int old_e = input.e(); |
| input.Normalize(); |
| error <<= old_e - input.e(); |
| |
| DCHECK_LE(exponent, PowersOfTenCache::kMaxDecimalExponent); |
| if (exponent < PowersOfTenCache::kMinDecimalExponent) { |
| *result = 0.0; |
| return true; |
| } |
| DiyFp cached_power; |
| int cached_decimal_exponent; |
| PowersOfTenCache::GetCachedPowerForDecimalExponent(exponent, |
| &cached_power, |
| &cached_decimal_exponent); |
| |
| if (cached_decimal_exponent != exponent) { |
| int adjustment_exponent = exponent - cached_decimal_exponent; |
| DiyFp adjustment_power = AdjustmentPowerOfTen(adjustment_exponent); |
| input.Multiply(adjustment_power); |
| if (kMaxUint64DecimalDigits - buffer.length() >= adjustment_exponent) { |
| // The product of input with the adjustment power fits into a 64 bit |
| // integer. |
| DCHECK_EQ(DiyFp::kSignificandSize, 64); |
| } else { |
| // The adjustment power is exact. There is hence only an error of 0.5. |
| error += kDenominator / 2; |
| } |
| } |
| |
| input.Multiply(cached_power); |
| // The error introduced by a multiplication of a*b equals |
| // error_a + error_b + error_a*error_b/2^64 + 0.5 |
| // Substituting a with 'input' and b with 'cached_power' we have |
| // error_b = 0.5 (all cached powers have an error of less than 0.5 ulp), |
| // error_ab = 0 or 1 / kDenominator > error_a*error_b/ 2^64 |
| int error_b = kDenominator / 2; |
| int error_ab = (error == 0 ? 0 : 1); // We round up to 1. |
| int fixed_error = kDenominator / 2; |
| error += error_b + error_ab + fixed_error; |
| |
| old_e = input.e(); |
| input.Normalize(); |
| error <<= old_e - input.e(); |
| |
| // See if the double's significand changes if we add/subtract the error. |
| int order_of_magnitude = DiyFp::kSignificandSize + input.e(); |
| int effective_significand_size = |
| Double::SignificandSizeForOrderOfMagnitude(order_of_magnitude); |
| int precision_digits_count = |
| DiyFp::kSignificandSize - effective_significand_size; |
| if (precision_digits_count + kDenominatorLog >= DiyFp::kSignificandSize) { |
| // This can only happen for very small denormals. In this case the |
| // half-way multiplied by the denominator exceeds the range of an uint64. |
| // Simply shift everything to the right. |
| int shift_amount = (precision_digits_count + kDenominatorLog) - |
| DiyFp::kSignificandSize + 1; |
| input.set_f(input.f() >> shift_amount); |
| input.set_e(input.e() + shift_amount); |
| // We add 1 for the lost precision of error, and kDenominator for |
| // the lost precision of input.f(). |
| error = (error >> shift_amount) + 1 + kDenominator; |
| precision_digits_count -= shift_amount; |
| } |
| // We use uint64_ts now. This only works if the DiyFp uses uint64_ts too. |
| DCHECK_EQ(DiyFp::kSignificandSize, 64); |
| DCHECK_LT(precision_digits_count, 64); |
| uint64_t one64 = 1; |
| uint64_t precision_bits_mask = (one64 << precision_digits_count) - 1; |
| uint64_t precision_bits = input.f() & precision_bits_mask; |
| uint64_t half_way = one64 << (precision_digits_count - 1); |
| precision_bits *= kDenominator; |
| half_way *= kDenominator; |
| DiyFp rounded_input(input.f() >> precision_digits_count, |
| input.e() + precision_digits_count); |
| if (precision_bits >= half_way + error) { |
| rounded_input.set_f(rounded_input.f() + 1); |
| } |
| // If the last_bits are too close to the half-way case than we are too |
| // inaccurate and round down. In this case we return false so that we can |
| // fall back to a more precise algorithm. |
| |
| *result = Double(rounded_input).value(); |
| if (half_way - error < precision_bits && precision_bits < half_way + error) { |
| // Too imprecise. The caller will have to fall back to a slower version. |
| // However the returned number is guaranteed to be either the correct |
| // double, or the next-lower double. |
| return false; |
| } else { |
| return true; |
| } |
| } |
| |
| |
| // Returns the correct double for the buffer*10^exponent. |
| // The variable guess should be a close guess that is either the correct double |
| // or its lower neighbor (the nearest double less than the correct one). |
| // Preconditions: |
| // buffer.length() + exponent <= kMaxDecimalPower + 1 |
| // buffer.length() + exponent > kMinDecimalPower |
| // buffer.length() <= kMaxDecimalSignificantDigits |
| static double BignumStrtod(Vector<const char> buffer, |
| int exponent, |
| double guess) { |
| if (guess == V8_INFINITY) { |
| return guess; |
| } |
| |
| DiyFp upper_boundary = Double(guess).UpperBoundary(); |
| |
| DCHECK(buffer.length() + exponent <= kMaxDecimalPower + 1); |
| DCHECK_GT(buffer.length() + exponent, kMinDecimalPower); |
| DCHECK_LE(buffer.length(), kMaxSignificantDecimalDigits); |
| // Make sure that the Bignum will be able to hold all our numbers. |
| // Our Bignum implementation has a separate field for exponents. Shifts will |
| // consume at most one bigit (< 64 bits). |
| // ln(10) == 3.3219... |
| DCHECK_LT((kMaxDecimalPower + 1) * 333 / 100, Bignum::kMaxSignificantBits); |
| Bignum input; |
| Bignum boundary; |
| input.AssignDecimalString(buffer); |
| boundary.AssignUInt64(upper_boundary.f()); |
| if (exponent >= 0) { |
| input.MultiplyByPowerOfTen(exponent); |
| } else { |
| boundary.MultiplyByPowerOfTen(-exponent); |
| } |
| if (upper_boundary.e() > 0) { |
| boundary.ShiftLeft(upper_boundary.e()); |
| } else { |
| input.ShiftLeft(-upper_boundary.e()); |
| } |
| int comparison = Bignum::Compare(input, boundary); |
| if (comparison < 0) { |
| return guess; |
| } else if (comparison > 0) { |
| return Double(guess).NextDouble(); |
| } else if ((Double(guess).Significand() & 1) == 0) { |
| // Round towards even. |
| return guess; |
| } else { |
| return Double(guess).NextDouble(); |
| } |
| } |
| |
| |
| double Strtod(Vector<const char> buffer, int exponent) { |
| Vector<const char> left_trimmed = TrimLeadingZeros(buffer); |
| Vector<const char> trimmed = TrimTrailingZeros(left_trimmed); |
| exponent += left_trimmed.length() - trimmed.length(); |
| if (trimmed.length() == 0) return 0.0; |
| if (trimmed.length() > kMaxSignificantDecimalDigits) { |
| char significant_buffer[kMaxSignificantDecimalDigits]; |
| int significant_exponent; |
| TrimToMaxSignificantDigits(trimmed, exponent, |
| significant_buffer, &significant_exponent); |
| return Strtod(Vector<const char>(significant_buffer, |
| kMaxSignificantDecimalDigits), |
| significant_exponent); |
| } |
| if (exponent + trimmed.length() - 1 >= kMaxDecimalPower) return V8_INFINITY; |
| if (exponent + trimmed.length() <= kMinDecimalPower) return 0.0; |
| |
| double guess; |
| if (DoubleStrtod(trimmed, exponent, &guess) || |
| DiyFpStrtod(trimmed, exponent, &guess)) { |
| return guess; |
| } |
| return BignumStrtod(trimmed, exponent, guess); |
| } |
| |
| } // namespace internal |
| } // namespace v8 |