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// Copyright 2010 the V8 project authors. All rights reserved.
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above
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// copyright notice, this list of conditions and the following
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// disclaimer in the documentation and/or other materials provided
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// with the distribution.
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// * Neither the name of Google Inc. nor the names of its
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// contributors may be used to endorse or promote products derived
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// from this software without specific prior written permission.
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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#include "fixed-dtoa.h"
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namespace double_conversion {
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// Represents a 128bit type. This class should be replaced by a native type on
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// platforms that support 128bit integers.
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UInt128() : high_bits_(0), low_bits_(0) { }
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UInt128(uint64_t high, uint64_t low) : high_bits_(high), low_bits_(low) { }
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void Multiply(uint32_t multiplicand) {
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accumulator = (low_bits_ & kMask32) * multiplicand;
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uint32_t part = static_cast<uint32_t>(accumulator & kMask32);
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accumulator = accumulator + (low_bits_ >> 32) * multiplicand;
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low_bits_ = (accumulator << 32) + part;
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accumulator = accumulator + (high_bits_ & kMask32) * multiplicand;
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part = static_cast<uint32_t>(accumulator & kMask32);
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accumulator = accumulator + (high_bits_ >> 32) * multiplicand;
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high_bits_ = (accumulator << 32) + part;
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ASSERT((accumulator >> 32) == 0);
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void Shift(int shift_amount) {
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ASSERT(-64 <= shift_amount && shift_amount <= 64);
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if (shift_amount == 0) {
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} else if (shift_amount == -64) {
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high_bits_ = low_bits_;
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} else if (shift_amount == 64) {
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low_bits_ = high_bits_;
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} else if (shift_amount <= 0) {
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high_bits_ <<= -shift_amount;
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high_bits_ += low_bits_ >> (64 + shift_amount);
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low_bits_ <<= -shift_amount;
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low_bits_ >>= shift_amount;
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low_bits_ += high_bits_ << (64 - shift_amount);
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high_bits_ >>= shift_amount;
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// Modifies *this to *this MOD (2^power).
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// Returns *this DIV (2^power).
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int DivModPowerOf2(int power) {
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int result = static_cast<int>(high_bits_ >> (power - 64));
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high_bits_ -= static_cast<uint64_t>(result) << (power - 64);
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uint64_t part_low = low_bits_ >> power;
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uint64_t part_high = high_bits_ << (64 - power);
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int result = static_cast<int>(part_low + part_high);
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low_bits_ -= part_low << power;
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return high_bits_ == 0 && low_bits_ == 0;
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int BitAt(int position) {
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if (position >= 64) {
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return static_cast<int>(high_bits_ >> (position - 64)) & 1;
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return static_cast<int>(low_bits_ >> position) & 1;
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static const uint64_t kMask32 = 0xFFFFFFFF;
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// Value == (high_bits_ << 64) + low_bits_
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static const int kDoubleSignificandSize = 53; // Includes the hidden bit.
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static void FillDigits32FixedLength(uint32_t number, int requested_length,
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Vector<char> buffer, int* length) {
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for (int i = requested_length - 1; i >= 0; --i) {
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buffer[(*length) + i] = '0' + number % 10;
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*length += requested_length;
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static void FillDigits32(uint32_t number, Vector<char> buffer, int* length) {
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int number_length = 0;
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// We fill the digits in reverse order and exchange them afterwards.
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while (number != 0) {
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int digit = number % 10;
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buffer[(*length) + number_length] = '0' + digit;
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// Exchange the digits.
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int j = *length + number_length - 1;
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char tmp = buffer[i];
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buffer[i] = buffer[j];
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*length += number_length;
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static void FillDigits64FixedLength(uint64_t number, int requested_length,
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Vector<char> buffer, int* length) {
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const uint32_t kTen7 = 10000000;
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// For efficiency cut the number into 3 uint32_t parts, and print those.
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uint32_t part2 = static_cast<uint32_t>(number % kTen7);
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uint32_t part1 = static_cast<uint32_t>(number % kTen7);
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uint32_t part0 = static_cast<uint32_t>(number / kTen7);
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FillDigits32FixedLength(part0, 3, buffer, length);
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FillDigits32FixedLength(part1, 7, buffer, length);
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FillDigits32FixedLength(part2, 7, buffer, length);
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static void FillDigits64(uint64_t number, Vector<char> buffer, int* length) {
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const uint32_t kTen7 = 10000000;
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// For efficiency cut the number into 3 uint32_t parts, and print those.
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uint32_t part2 = static_cast<uint32_t>(number % kTen7);
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uint32_t part1 = static_cast<uint32_t>(number % kTen7);
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uint32_t part0 = static_cast<uint32_t>(number / kTen7);
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FillDigits32(part0, buffer, length);
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FillDigits32FixedLength(part1, 7, buffer, length);
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FillDigits32FixedLength(part2, 7, buffer, length);
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} else if (part1 != 0) {
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FillDigits32(part1, buffer, length);
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FillDigits32FixedLength(part2, 7, buffer, length);
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FillDigits32(part2, buffer, length);
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static void RoundUp(Vector<char> buffer, int* length, int* decimal_point) {
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// An empty buffer represents 0.
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// Round the last digit until we either have a digit that was not '9' or until
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// we reached the first digit.
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buffer[(*length) - 1]++;
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for (int i = (*length) - 1; i > 0; --i) {
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if (buffer[i] != '0' + 10) {
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// If the first digit is now '0' + 10, we would need to set it to '0' and add
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// a '1' in front. However we reach the first digit only if all following
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// digits had been '9' before rounding up. Now all trailing digits are '0' and
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// we simply switch the first digit to '1' and update the decimal-point
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// (indicating that the point is now one digit to the right).
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if (buffer[0] == '0' + 10) {
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// The given fractionals number represents a fixed-point number with binary
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// point at bit (-exponent).
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// -128 <= exponent <= 0.
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// 0 <= fractionals * 2^exponent < 1
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// The buffer holds the result.
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// The function will round its result. During the rounding-process digits not
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// generated by this function might be updated, and the decimal-point variable
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// might be updated. If this function generates the digits 99 and the buffer
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// already contained "199" (thus yielding a buffer of "19999") then a
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// rounding-up will change the contents of the buffer to "20000".
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static void FillFractionals(uint64_t fractionals, int exponent,
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int fractional_count, Vector<char> buffer,
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int* length, int* decimal_point) {
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ASSERT(-128 <= exponent && exponent <= 0);
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// 'fractionals' is a fixed-point number, with binary point at bit
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// (-exponent). Inside the function the non-converted remainder of fractionals
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// is a fixed-point number, with binary point at bit 'point'.
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if (-exponent <= 64) {
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// One 64 bit number is sufficient.
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ASSERT(fractionals >> 56 == 0);
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int point = -exponent;
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for (int i = 0; i < fractional_count; ++i) {
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if (fractionals == 0) break;
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// Instead of multiplying by 10 we multiply by 5 and adjust the point
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// location. This way the fractionals variable will not overflow.
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// Invariant at the beginning of the loop: fractionals < 2^point.
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// Initially we have: point <= 64 and fractionals < 2^56
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// After each iteration the point is decremented by one.
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// Note that 5^3 = 125 < 128 = 2^7.
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// Therefore three iterations of this loop will not overflow fractionals
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// (even without the subtraction at the end of the loop body). At this
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// time point will satisfy point <= 61 and therefore fractionals < 2^point
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// and any further multiplication of fractionals by 5 will not overflow.
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int digit = static_cast<int>(fractionals >> point);
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buffer[*length] = '0' + digit;
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fractionals -= static_cast<uint64_t>(digit) << point;
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// If the first bit after the point is set we have to round up.
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if (((fractionals >> (point - 1)) & 1) == 1) {
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RoundUp(buffer, length, decimal_point);
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} else { // We need 128 bits.
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ASSERT(64 < -exponent && -exponent <= 128);
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UInt128 fractionals128 = UInt128(fractionals, 0);
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fractionals128.Shift(-exponent - 64);
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for (int i = 0; i < fractional_count; ++i) {
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if (fractionals128.IsZero()) break;
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// As before: instead of multiplying by 10 we multiply by 5 and adjust the
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// This multiplication will not overflow for the same reasons as before.
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fractionals128.Multiply(5);
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int digit = fractionals128.DivModPowerOf2(point);
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buffer[*length] = '0' + digit;
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if (fractionals128.BitAt(point - 1) == 1) {
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RoundUp(buffer, length, decimal_point);
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// Removes leading and trailing zeros.
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// If leading zeros are removed then the decimal point position is adjusted.
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static void TrimZeros(Vector<char> buffer, int* length, int* decimal_point) {
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while (*length > 0 && buffer[(*length) - 1] == '0') {
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int first_non_zero = 0;
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while (first_non_zero < *length && buffer[first_non_zero] == '0') {
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if (first_non_zero != 0) {
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for (int i = first_non_zero; i < *length; ++i) {
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buffer[i - first_non_zero] = buffer[i];
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*length -= first_non_zero;
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*decimal_point -= first_non_zero;
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bool FastFixedDtoa(double v,
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int fractional_count,
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int* decimal_point) {
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const uint32_t kMaxUInt32 = 0xFFFFFFFF;
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uint64_t significand = Double(v).Significand();
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int exponent = Double(v).Exponent();
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// v = significand * 2^exponent (with significand a 53bit integer).
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// If the exponent is larger than 20 (i.e. we may have a 73bit number) then we
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// don't know how to compute the representation. 2^73 ~= 9.5*10^21.
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// If necessary this limit could probably be increased, but we don't need
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if (exponent > 20) return false;
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if (fractional_count > 20) return false;
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// At most kDoubleSignificandSize bits of the significand are non-zero.
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// Given a 64 bit integer we have 11 0s followed by 53 potentially non-zero
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// bits: 0..11*..0xxx..53*..xx
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if (exponent + kDoubleSignificandSize > 64) {
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// The exponent must be > 11.
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// We know that v = significand * 2^exponent.
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// And the exponent > 11.
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// We simplify the task by dividing v by 10^17.
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// The quotient delivers the first digits, and the remainder fits into a 64
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// Dividing by 10^17 is equivalent to dividing by 5^17*2^17.
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const uint64_t kFive17 = UINT64_2PART_C(0xB1, A2BC2EC5); // 5^17
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uint64_t divisor = kFive17;
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int divisor_power = 17;
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uint64_t dividend = significand;
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// Let v = f * 2^e with f == significand and e == exponent.
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// Then need q (quotient) and r (remainder) as follows:
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// f * 2^e = q * 10^17 + r
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// f * 2^e = q * 5^17 * 2^17 + r
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// f * 2^(e-17) = q * 5^17 + r/2^17
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// f = q * 5^17 * 2^(17-e) + r/2^e
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if (exponent > divisor_power) {
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// We only allow exponents of up to 20 and therefore (17 - e) <= 3
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dividend <<= exponent - divisor_power;
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quotient = static_cast<uint32_t>(dividend / divisor);
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remainder = (dividend % divisor) << divisor_power;
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divisor <<= divisor_power - exponent;
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quotient = static_cast<uint32_t>(dividend / divisor);
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remainder = (dividend % divisor) << exponent;
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FillDigits32(quotient, buffer, length);
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FillDigits64FixedLength(remainder, divisor_power, buffer, length);
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*decimal_point = *length;
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} else if (exponent >= 0) {
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// 0 <= exponent <= 11
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significand <<= exponent;
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FillDigits64(significand, buffer, length);
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*decimal_point = *length;
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} else if (exponent > -kDoubleSignificandSize) {
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// We have to cut the number.
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uint64_t integrals = significand >> -exponent;
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uint64_t fractionals = significand - (integrals << -exponent);
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if (integrals > kMaxUInt32) {
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FillDigits64(integrals, buffer, length);
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FillDigits32(static_cast<uint32_t>(integrals), buffer, length);
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*decimal_point = *length;
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FillFractionals(fractionals, exponent, fractional_count,
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buffer, length, decimal_point);
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} else if (exponent < -128) {
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// This configuration (with at most 20 digits) means that all digits must be
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ASSERT(fractional_count <= 20);
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*decimal_point = -fractional_count;
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FillFractionals(significand, exponent, fractional_count,
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buffer, length, decimal_point);
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TrimZeros(buffer, length, decimal_point);
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buffer[*length] = '\0';
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if ((*length) == 0) {
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// The string is empty and the decimal_point thus has no importance. Mimick
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// Gay's dtoa and and set it to -fractional_count.
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*decimal_point = -fractional_count;
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} // namespace double_conversion
added
removed
mozilla/mfbt/double-conversion/fixed-dtoa.cc
