| Index: third_party/WebKit/Source/wtf/dtoa/strtod.cc
|
| diff --git a/third_party/WebKit/Source/wtf/dtoa/strtod.cc b/third_party/WebKit/Source/wtf/dtoa/strtod.cc
|
| index 998a0c4e912bcb9ab9bce844343c445685271378..0de14e94fc07ecd00eb1d5d27fd141dd4ba25d8b 100644
|
| --- a/third_party/WebKit/Source/wtf/dtoa/strtod.cc
|
| +++ b/third_party/WebKit/Source/wtf/dtoa/strtod.cc
|
| @@ -27,419 +27,403 @@
|
|
|
| #include "strtod.h"
|
|
|
| +#include <limits.h>
|
| +#include <stdarg.h>
|
| #include "bignum.h"
|
| #include "cached-powers.h"
|
| #include "double.h"
|
| -#include <stdarg.h>
|
| -#include <limits.h>
|
|
|
| namespace WTF {
|
|
|
| namespace double_conversion {
|
|
|
| - // 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 = UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF);
|
| -
|
| -
|
| - 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
|
| - };
|
| - static const int kExactPowersOfTenSize = ARRAY_SIZE(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);
|
| +// 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 = UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF);
|
| +
|
| +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};
|
| +static const int kExactPowersOfTenSize = ARRAY_SIZE(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());
|
| }
|
| -
|
| -
|
| - 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'.
|
| - ASSERT(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);
|
| + }
|
| + 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);
|
| }
|
| -
|
| - // 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';
|
| - ASSERT(0 <= digit && digit <= 9);
|
| - result = 10 * result + digit;
|
| - }
|
| - *number_of_read_digits = i;
|
| - return result;
|
| + }
|
| + 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'.
|
| + ASSERT(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';
|
| + ASSERT(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++;
|
| }
|
| -
|
| -
|
| - // 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) {
|
| + // 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 !defined(DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS)
|
| - // 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 uses 64 bits and is therefore accurate.
|
| - // Note that the ARM simulator is compiled for 32bits. It therefore exhibits
|
| - // the same problem.
|
| - return false;
|
| + // 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 uses 64 bits and is therefore accurate.
|
| + // Note that the ARM simulator is compiled for 32bits. It therefore exhibits
|
| + // the same problem.
|
| + return false;
|
| #endif
|
| - 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));
|
| - ASSERT(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));
|
| - ASSERT(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));
|
| - ASSERT(read_digits == trimmed.length());
|
| - *result *= exact_powers_of_ten[remaining_digits];
|
| - *result *= exact_powers_of_ten[exponent - remaining_digits];
|
| - return true;
|
| - }
|
| - }
|
| - return false;
|
| + 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));
|
| + ASSERT(read_digits == trimmed.length());
|
| + *result /= exact_powers_of_ten[-exponent];
|
| + return true;
|
| }
|
| -
|
| -
|
| - // Returns 10^exponent as an exact DiyFp.
|
| - // The given exponent must be in the range [1; kDecimalExponentDistance[.
|
| - static DiyFp AdjustmentPowerOfTen(int exponent) {
|
| - ASSERT(0 < exponent);
|
| - ASSERT(exponent < PowersOfTenCache::kDecimalExponentDistance);
|
| - // Simply hardcode the remaining powers for the given decimal exponent
|
| - // distance.
|
| - ASSERT(PowersOfTenCache::kDecimalExponentDistance == 8);
|
| - switch (exponent) {
|
| - case 1: return DiyFp(UINT64_2PART_C(0xa0000000, 00000000), -60);
|
| - case 2: return DiyFp(UINT64_2PART_C(0xc8000000, 00000000), -57);
|
| - case 3: return DiyFp(UINT64_2PART_C(0xfa000000, 00000000), -54);
|
| - case 4: return DiyFp(UINT64_2PART_C(0x9c400000, 00000000), -50);
|
| - case 5: return DiyFp(UINT64_2PART_C(0xc3500000, 00000000), -47);
|
| - case 6: return DiyFp(UINT64_2PART_C(0xf4240000, 00000000), -44);
|
| - case 7: return DiyFp(UINT64_2PART_C(0x98968000, 00000000), -40);
|
| - default:
|
| - UNREACHABLE();
|
| - return DiyFp(0, 0);
|
| - }
|
| - }
|
| -
|
| -
|
| - // 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();
|
| -
|
| - ASSERT(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.
|
| - ASSERT(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.
|
| - ASSERT(DiyFp::kSignificandSize == 64);
|
| - ASSERT(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;
|
| - }
|
| + if (0 <= exponent && exponent < kExactPowersOfTenSize) {
|
| + // 10^exponent fits into a double.
|
| + *result = static_cast<double>(ReadUint64(trimmed, &read_digits));
|
| + ASSERT(read_digits == trimmed.length());
|
| + *result *= exact_powers_of_ten[exponent];
|
| + 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 == Double::Infinity()) {
|
| - return guess;
|
| - }
|
| -
|
| - DiyFp upper_boundary = Double(guess).UpperBoundary();
|
| -
|
| - ASSERT(buffer.length() + exponent <= kMaxDecimalPower + 1);
|
| - ASSERT(buffer.length() + exponent > kMinDecimalPower);
|
| - ASSERT(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...
|
| - ASSERT(((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();
|
| - }
|
| + 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));
|
| + ASSERT(read_digits == trimmed.length());
|
| + *result *= exact_powers_of_ten[remaining_digits];
|
| + *result *= exact_powers_of_ten[exponent - remaining_digits];
|
| + return true;
|
| }
|
| -
|
| -
|
| - 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 Double::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);
|
| + }
|
| + return false;
|
| +}
|
| +
|
| +// Returns 10^exponent as an exact DiyFp.
|
| +// The given exponent must be in the range [1; kDecimalExponentDistance[.
|
| +static DiyFp AdjustmentPowerOfTen(int exponent) {
|
| + ASSERT(0 < exponent);
|
| + ASSERT(exponent < PowersOfTenCache::kDecimalExponentDistance);
|
| + // Simply hardcode the remaining powers for the given decimal exponent
|
| + // distance.
|
| + ASSERT(PowersOfTenCache::kDecimalExponentDistance == 8);
|
| + switch (exponent) {
|
| + case 1:
|
| + return DiyFp(UINT64_2PART_C(0xa0000000, 00000000), -60);
|
| + case 2:
|
| + return DiyFp(UINT64_2PART_C(0xc8000000, 00000000), -57);
|
| + case 3:
|
| + return DiyFp(UINT64_2PART_C(0xfa000000, 00000000), -54);
|
| + case 4:
|
| + return DiyFp(UINT64_2PART_C(0x9c400000, 00000000), -50);
|
| + case 5:
|
| + return DiyFp(UINT64_2PART_C(0xc3500000, 00000000), -47);
|
| + case 6:
|
| + return DiyFp(UINT64_2PART_C(0xf4240000, 00000000), -44);
|
| + case 7:
|
| + return DiyFp(UINT64_2PART_C(0x98968000, 00000000), -40);
|
| + default:
|
| + UNREACHABLE();
|
| + return DiyFp(0, 0);
|
| + }
|
| +}
|
| +
|
| +// 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();
|
| +
|
| + ASSERT(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.
|
| + ASSERT(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.
|
| + ASSERT(DiyFp::kSignificandSize == 64);
|
| + ASSERT(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 == Double::Infinity()) {
|
| + return guess;
|
| + }
|
| +
|
| + DiyFp upper_boundary = Double(guess).UpperBoundary();
|
| +
|
| + ASSERT(buffer.length() + exponent <= kMaxDecimalPower + 1);
|
| + ASSERT(buffer.length() + exponent > kMinDecimalPower);
|
| + ASSERT(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...
|
| + ASSERT(((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 Double::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 double_conversion
|
|
|
| -} // namespace WTF
|
| +} // namespace WTF
|
|
|