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-// © 2018 and later: Unicode, Inc. and others.
-// License & terms of use: http://www.unicode.org/copyright.html
-//
-// From the double-conversion library. Original license:
-//
-// 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.
-
-// ICU PATCH: ifdef around UCONFIG_NO_FORMATTING
-#include "unicode/utypes.h"
-#if !UCONFIG_NO_FORMATTING
-
-#include <stdarg.h>
-#include <limits.h>
-
-// ICU PATCH: Customize header file paths for ICU.
-// The file fixed-dtoa.h is not needed.
-
-#include "double-conversion-strtod.h"
-#include "double-conversion-bignum.h"
-#include "double-conversion-cached-powers.h"
-#include "double-conversion-ieee.h"
-
-// ICU PATCH: Wrap in ICU namespace
-U_NAMESPACE_BEGIN
-
-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) {
- (void) space_size; // Mark variable as used.
- 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();
- }
-}
-
-
-// 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;
- uint64_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
-// - -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);
- float f2 = float_guess;
- 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);
- }
- (void) f2; // Mark variable as used.
- 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
-
-// ICU PATCH: Close ICU namespace
-U_NAMESPACE_END
-#endif // ICU PATCH: close #if !UCONFIG_NO_FORMATTING