The Tor Browser: comparison mfbt/double-conversion/strtod.cc

--1:000000000000
+:2bd0fd41fbab
+// Copyright 2010 the V8 project authors. All rights reserved.
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+//     * Redistributions of source code must retain the above copyright
+//       notice, this list of conditions and the following disclaimer.
+//     * Redistributions in binary form must reproduce the above
+//       copyright notice, this list of conditions and the following
+//       disclaimer in the documentation and/or other materials provided
+//       with the distribution.
+//     * Neither the name of Google Inc. nor the names of its
+//       contributors may be used to endorse or promote products derived
+//       from this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+#include <stdarg.h>
+#include <limits.h>
+#include "strtod.h"
+#include "bignum.h"
+#include "cached-powers.h"
+#include "ieee.h"
+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);
+}
+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 CutToMaxSignificantDigits(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);
+}
+// Trims the buffer and cuts it to at most kMaxSignificantDecimalDigits.
+// If possible the input-buffer is reused, but if the buffer needs to be
+// modified (due to cutting), then the input needs to be copied into the
+// buffer_copy_space.
+static void TrimAndCut(Vector<const char> buffer, int exponent,
+char* buffer_copy_space, int space_size,
+Vector<const char>* trimmed, int* updated_exponent) {
+Vector<const char> left_trimmed = TrimLeadingZeros(buffer);
+Vector<const char> right_trimmed = TrimTrailingZeros(left_trimmed);
+exponent += left_trimmed.length() - right_trimmed.length();
+if (right_trimmed.length() > kMaxSignificantDecimalDigits) {
+ASSERT(space_size >= kMaxSignificantDecimalDigits);
+CutToMaxSignificantDigits(right_trimmed, exponent,
+buffer_copy_space, updated_exponent);
+*trimmed = Vector<const char>(buffer_copy_space,
+kMaxSignificantDecimalDigits);
+} else {
+*trimmed = right_trimmed;
+*updated_exponent = exponent;
+}
+}
+// 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++;
+}
+// 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;
+#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;
+}
+// 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;
+int 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
+//   - -1 if buffer*10^exponent < diy_fp.
+//   -  0 if buffer*10^exponent == diy_fp.
+//   - +1 if buffer*10^exponent > diy_fp.
+// Preconditions:
+//   buffer.length() + exponent <= kMaxDecimalPower + 1
+//   buffer.length() + exponent > kMinDecimalPower
+//   buffer.length() <= kMaxDecimalSignificantDigits
+static int CompareBufferWithDiyFp(Vector<const char> buffer,
+int exponent,
+DiyFp diy_fp) {
+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 buffer_bignum;
+Bignum diy_fp_bignum;
+buffer_bignum.AssignDecimalString(buffer);
+diy_fp_bignum.AssignUInt64(diy_fp.f());
+if (exponent >= 0) {
+buffer_bignum.MultiplyByPowerOfTen(exponent);
+} else {
+diy_fp_bignum.MultiplyByPowerOfTen(-exponent);
+}
+if (diy_fp.e() > 0) {
+diy_fp_bignum.ShiftLeft(diy_fp.e());
+} else {
+buffer_bignum.ShiftLeft(-diy_fp.e());
+}
+return Bignum::Compare(buffer_bignum, diy_fp_bignum);
+}
+// Returns true if the guess is the correct double.
+// Returns false, when guess is either correct or the next-lower double.
+static bool ComputeGuess(Vector<const char> trimmed, int exponent,
+double* guess) {
+if (trimmed.length() == 0) {
+*guess = 0.0;
+return true;
+}
+if (exponent + trimmed.length() - 1 >= kMaxDecimalPower) {
+*guess = Double::Infinity();
+return true;
+}
+if (exponent + trimmed.length() <= kMinDecimalPower) {
+*guess = 0.0;
+return true;
+}
+if (DoubleStrtod(trimmed, exponent, guess) ||
+DiyFpStrtod(trimmed, exponent, guess)) {
+return true;
+}
+if (*guess == Double::Infinity()) {
+return true;
+}
+return false;
+}
+double Strtod(Vector<const char> buffer, int exponent) {
+char copy_buffer[kMaxSignificantDecimalDigits];
+Vector<const char> trimmed;
+int updated_exponent;
+TrimAndCut(buffer, exponent, copy_buffer, kMaxSignificantDecimalDigits,
+&trimmed, &updated_exponent);
+exponent = updated_exponent;
+double guess;
+bool is_correct = ComputeGuess(trimmed, exponent, &guess);
+if (is_correct) return guess;
+DiyFp upper_boundary = Double(guess).UpperBoundary();
+int comparison = CompareBufferWithDiyFp(trimmed, exponent, upper_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();
+}
+}
+float Strtof(Vector<const char> buffer, int exponent) {
+char copy_buffer[kMaxSignificantDecimalDigits];
+Vector<const char> trimmed;
+int updated_exponent;
+TrimAndCut(buffer, exponent, copy_buffer, kMaxSignificantDecimalDigits,
+&trimmed, &updated_exponent);
+exponent = updated_exponent;
+double double_guess;
+bool is_correct = ComputeGuess(trimmed, exponent, &double_guess);
+float float_guess = static_cast<float>(double_guess);
+if (float_guess == double_guess) {
+// This shortcut triggers for integer values.
+return float_guess;
+}
+// We must catch double-rounding. Say the double has been rounded up, and is
+// now a boundary of a float, and rounds up again. This is why we have to
+// look at previous too.
+// Example (in decimal numbers):
+//    input: 12349
+//    high-precision (4 digits): 1235
+//    low-precision (3 digits):
+//       when read from input: 123
+//       when rounded from high precision: 124.
+// To do this we simply look at the neigbors of the correct result and see
+// if they would round to the same float. If the guess is not correct we have
+// to look at four values (since two different doubles could be the correct
+// double).
+double double_next = Double(double_guess).NextDouble();
+double double_previous = Double(double_guess).PreviousDouble();
+float f1 = static_cast<float>(double_previous);
+#if defined(DEBUG)
+float f2 = float_guess;
+#endif
+float f3 = static_cast<float>(double_next);
+float f4;
+if (is_correct) {
+f4 = f3;
+} else {
+double double_next2 = Double(double_next).NextDouble();
+f4 = static_cast<float>(double_next2);
+}
+ASSERT(f1 <= f2 && f2 <= f3 && f3 <= f4);
+// If the guess doesn't lie near a single-precision boundary we can simply
+// return its float-value.
+if (f1 == f4) {
+return float_guess;
+}
+ASSERT((f1 != f2 && f2 == f3 && f3 == f4) ||
+(f1 == f2 && f2 != f3 && f3 == f4) ||
+(f1 == f2 && f2 == f3 && f3 != f4));
+// guess and next are the two possible canditates (in the same way that
+// double_guess was the lower candidate for a double-precision guess).
+float guess = f1;
+float next = f4;
+DiyFp upper_boundary;
+if (guess == 0.0f) {
+float min_float = 1e-45f;
+upper_boundary = Double(static_cast<double>(min_float) / 2).AsDiyFp();
+} else {
+upper_boundary = Single(guess).UpperBoundary();
+}
+int comparison = CompareBufferWithDiyFp(trimmed, exponent, upper_boundary);
+if (comparison < 0) {
+return guess;
+} else if (comparison > 0) {
+return next;
+} else if ((Single(guess).Significand() & 1) == 0) {
+// Round towards even.
+return guess;
+} else {
+return next;
+}
+}
+}  // namespace double_conversion

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comparison: mfbt/double-conversion/strtod.cc

mfbt/double-conversion/strtod.cc