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+// 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 <math.h>
+
+#include "fixed-dtoa.h"
+#include "ieee.h"
+
+namespace double_conversion {
+
+// Represents a 128bit type. This class should be replaced by a native type on
+// platforms that support 128bit integers.
+class UInt128 {
+ public:
+ UInt128() : high_bits_(0), low_bits_(0) { }
+ UInt128(uint64_t high, uint64_t low) : high_bits_(high), low_bits_(low) { }
+
+ void Multiply(uint32_t multiplicand) {
+ uint64_t accumulator;
+
+ accumulator = (low_bits_ & kMask32) * multiplicand;
+ uint32_t part = static_cast<uint32_t>(accumulator & kMask32);
+ accumulator >>= 32;
+ accumulator = accumulator + (low_bits_ >> 32) * multiplicand;
+ low_bits_ = (accumulator << 32) + part;
+ accumulator >>= 32;
+ accumulator = accumulator + (high_bits_ & kMask32) * multiplicand;
+ part = static_cast<uint32_t>(accumulator & kMask32);
+ accumulator >>= 32;
+ accumulator = accumulator + (high_bits_ >> 32) * multiplicand;
+ high_bits_ = (accumulator << 32) + part;
+ ASSERT((accumulator >> 32) == 0);
+ }
+
+ void Shift(int shift_amount) {
+ ASSERT(-64 <= shift_amount && shift_amount <= 64);
+ if (shift_amount == 0) {
+ return;
+ } else if (shift_amount == -64) {
+ high_bits_ = low_bits_;
+ low_bits_ = 0;
+ } else if (shift_amount == 64) {
+ low_bits_ = high_bits_;
+ high_bits_ = 0;
+ } else if (shift_amount <= 0) {
+ high_bits_ <<= -shift_amount;
+ high_bits_ += low_bits_ >> (64 + shift_amount);
+ low_bits_ <<= -shift_amount;
+ } else {
+ low_bits_ >>= shift_amount;
+ low_bits_ += high_bits_ << (64 - shift_amount);
+ high_bits_ >>= shift_amount;
+ }
+ }
+
+ // Modifies *this to *this MOD (2^power).
+ // Returns *this DIV (2^power).
+ int DivModPowerOf2(int power) {
+ if (power >= 64) {
+ int result = static_cast<int>(high_bits_ >> (power - 64));
+ high_bits_ -= static_cast<uint64_t>(result) << (power - 64);
+ return result;
+ } else {
+ uint64_t part_low = low_bits_ >> power;
+ uint64_t part_high = high_bits_ << (64 - power);
+ int result = static_cast<int>(part_low + part_high);
+ high_bits_ = 0;
+ low_bits_ -= part_low << power;
+ return result;
+ }
+ }
+
+ bool IsZero() const {
+ return high_bits_ == 0 && low_bits_ == 0;
+ }
+
+ int BitAt(int position) {
+ if (position >= 64) {
+ return static_cast<int>(high_bits_ >> (position - 64)) & 1;
+ } else {
+ return static_cast<int>(low_bits_ >> position) & 1;
+ }
+ }
+
+ private:
+ static const uint64_t kMask32 = 0xFFFFFFFF;
+ // Value == (high_bits_ << 64) + low_bits_
+ uint64_t high_bits_;
+ uint64_t low_bits_;
+};
+
+
+static const int kDoubleSignificandSize = 53; // Includes the hidden bit.
+
+
+static void FillDigits32FixedLength(uint32_t number, int requested_length,
+ Vector<char> buffer, int* length) {
+ for (int i = requested_length - 1; i >= 0; --i) {
+ buffer[(*length) + i] = '0' + number % 10;
+ number /= 10;
+ }
+ *length += requested_length;
+}
+
+
+static void FillDigits32(uint32_t number, Vector<char> buffer, int* length) {
+ int number_length = 0;
+ // We fill the digits in reverse order and exchange them afterwards.
+ while (number != 0) {
+ int digit = number % 10;
+ number /= 10;
+ buffer[(*length) + number_length] = '0' + digit;
+ number_length++;
+ }
+ // Exchange the digits.
+ int i = *length;
+ int j = *length + number_length - 1;
+ while (i < j) {
+ char tmp = buffer[i];
+ buffer[i] = buffer[j];
+ buffer[j] = tmp;
+ i++;
+ j--;
+ }
+ *length += number_length;
+}
+
+
+static void FillDigits64FixedLength(uint64_t number, int requested_length,
+ Vector<char> buffer, int* length) {
+ const uint32_t kTen7 = 10000000;
+ // For efficiency cut the number into 3 uint32_t parts, and print those.
+ uint32_t part2 = static_cast<uint32_t>(number % kTen7);
+ number /= kTen7;
+ uint32_t part1 = static_cast<uint32_t>(number % kTen7);
+ uint32_t part0 = static_cast<uint32_t>(number / kTen7);
+
+ FillDigits32FixedLength(part0, 3, buffer, length);
+ FillDigits32FixedLength(part1, 7, buffer, length);
+ FillDigits32FixedLength(part2, 7, buffer, length);
+}
+
+
+static void FillDigits64(uint64_t number, Vector<char> buffer, int* length) {
+ const uint32_t kTen7 = 10000000;
+ // For efficiency cut the number into 3 uint32_t parts, and print those.
+ uint32_t part2 = static_cast<uint32_t>(number % kTen7);
+ number /= kTen7;
+ uint32_t part1 = static_cast<uint32_t>(number % kTen7);
+ uint32_t part0 = static_cast<uint32_t>(number / kTen7);
+
+ if (part0 != 0) {
+ FillDigits32(part0, buffer, length);
+ FillDigits32FixedLength(part1, 7, buffer, length);
+ FillDigits32FixedLength(part2, 7, buffer, length);
+ } else if (part1 != 0) {
+ FillDigits32(part1, buffer, length);
+ FillDigits32FixedLength(part2, 7, buffer, length);
+ } else {
+ FillDigits32(part2, buffer, length);
+ }
+}
+
+
+static void RoundUp(Vector<char> buffer, int* length, int* decimal_point) {
+ // An empty buffer represents 0.
+ if (*length == 0) {
+ buffer[0] = '1';
+ *decimal_point = 1;
+ *length = 1;
+ return;
+ }
+ // Round the last digit until we either have a digit that was not '9' or until
+ // we reached the first digit.
+ buffer[(*length) - 1]++;
+ for (int i = (*length) - 1; i > 0; --i) {
+ if (buffer[i] != '0' + 10) {
+ return;
+ }
+ buffer[i] = '0';
+ buffer[i - 1]++;
+ }
+ // If the first digit is now '0' + 10, we would need to set it to '0' and add
+ // a '1' in front. However we reach the first digit only if all following
+ // digits had been '9' before rounding up. Now all trailing digits are '0' and
+ // we simply switch the first digit to '1' and update the decimal-point
+ // (indicating that the point is now one digit to the right).
+ if (buffer[0] == '0' + 10) {
+ buffer[0] = '1';
+ (*decimal_point)++;
+ }
+}
+
+
+// The given fractionals number represents a fixed-point number with binary
+// point at bit (-exponent).
+// Preconditions:
+// -128 <= exponent <= 0.
+// 0 <= fractionals * 2^exponent < 1
+// The buffer holds the result.
+// The function will round its result. During the rounding-process digits not
+// generated by this function might be updated, and the decimal-point variable
+// might be updated. If this function generates the digits 99 and the buffer
+// already contained "199" (thus yielding a buffer of "19999") then a
+// rounding-up will change the contents of the buffer to "20000".
+static void FillFractionals(uint64_t fractionals, int exponent,
+ int fractional_count, Vector<char> buffer,
+ int* length, int* decimal_point) {
+ ASSERT(-128 <= exponent && exponent <= 0);
+ // 'fractionals' is a fixed-point number, with binary point at bit
+ // (-exponent). Inside the function the non-converted remainder of fractionals
+ // is a fixed-point number, with binary point at bit 'point'.
+ if (-exponent <= 64) {
+ // One 64 bit number is sufficient.
+ ASSERT(fractionals >> 56 == 0);
+ int point = -exponent;
+ for (int i = 0; i < fractional_count; ++i) {
+ if (fractionals == 0) break;
+ // Instead of multiplying by 10 we multiply by 5 and adjust the point
+ // location. This way the fractionals variable will not overflow.
+ // Invariant at the beginning of the loop: fractionals < 2^point.
+ // Initially we have: point <= 64 and fractionals < 2^56
+ // After each iteration the point is decremented by one.
+ // Note that 5^3 = 125 < 128 = 2^7.
+ // Therefore three iterations of this loop will not overflow fractionals
+ // (even without the subtraction at the end of the loop body). At this
+ // time point will satisfy point <= 61 and therefore fractionals < 2^point
+ // and any further multiplication of fractionals by 5 will not overflow.
+ fractionals *= 5;
+ point--;
+ int digit = static_cast<int>(fractionals >> point);
+ buffer[*length] = '0' + digit;
+ (*length)++;
+ fractionals -= static_cast<uint64_t>(digit) << point;
+ }
+ // If the first bit after the point is set we have to round up.
+ if (((fractionals >> (point - 1)) & 1) == 1) {
+ RoundUp(buffer, length, decimal_point);
+ }
+ } else { // We need 128 bits.
+ ASSERT(64 < -exponent && -exponent <= 128);
+ UInt128 fractionals128 = UInt128(fractionals, 0);
+ fractionals128.Shift(-exponent - 64);
+ int point = 128;
+ for (int i = 0; i < fractional_count; ++i) {
+ if (fractionals128.IsZero()) break;
+ // As before: instead of multiplying by 10 we multiply by 5 and adjust the
+ // point location.
+ // This multiplication will not overflow for the same reasons as before.
+ fractionals128.Multiply(5);
+ point--;
+ int digit = fractionals128.DivModPowerOf2(point);
+ buffer[*length] = '0' + digit;
+ (*length)++;
+ }
+ if (fractionals128.BitAt(point - 1) == 1) {
+ RoundUp(buffer, length, decimal_point);
+ }
+ }
+}
+
+
+// Removes leading and trailing zeros.
+// If leading zeros are removed then the decimal point position is adjusted.
+static void TrimZeros(Vector<char> buffer, int* length, int* decimal_point) {
+ while (*length > 0 && buffer[(*length) - 1] == '0') {
+ (*length)--;
+ }
+ int first_non_zero = 0;
+ while (first_non_zero < *length && buffer[first_non_zero] == '0') {
+ first_non_zero++;
+ }
+ if (first_non_zero != 0) {
+ for (int i = first_non_zero; i < *length; ++i) {
+ buffer[i - first_non_zero] = buffer[i];
+ }
+ *length -= first_non_zero;
+ *decimal_point -= first_non_zero;
+ }
+}
+
+
+bool FastFixedDtoa(double v,
+ int fractional_count,
+ Vector<char> buffer,
+ int* length,
+ int* decimal_point) {
+ const uint32_t kMaxUInt32 = 0xFFFFFFFF;
+ uint64_t significand = Double(v).Significand();
+ int exponent = Double(v).Exponent();
+ // v = significand * 2^exponent (with significand a 53bit integer).
+ // If the exponent is larger than 20 (i.e. we may have a 73bit number) then we
+ // don't know how to compute the representation. 2^73 ~= 9.5*10^21.
+ // If necessary this limit could probably be increased, but we don't need
+ // more.
+ if (exponent > 20) return false;
+ if (fractional_count > 20) return false;
+ *length = 0;
+ // At most kDoubleSignificandSize bits of the significand are non-zero.
+ // Given a 64 bit integer we have 11 0s followed by 53 potentially non-zero
+ // bits: 0..11*..0xxx..53*..xx
+ if (exponent + kDoubleSignificandSize > 64) {
+ // The exponent must be > 11.
+ //
+ // We know that v = significand * 2^exponent.
+ // And the exponent > 11.
+ // We simplify the task by dividing v by 10^17.
+ // The quotient delivers the first digits, and the remainder fits into a 64
+ // bit number.
+ // Dividing by 10^17 is equivalent to dividing by 5^17*2^17.
+ const uint64_t kFive17 = UINT64_2PART_C(0xB1, A2BC2EC5); // 5^17
+ uint64_t divisor = kFive17;
+ int divisor_power = 17;
+ uint64_t dividend = significand;
+ uint32_t quotient;
+ uint64_t remainder;
+ // Let v = f * 2^e with f == significand and e == exponent.
+ // Then need q (quotient) and r (remainder) as follows:
+ // v = q * 10^17 + r
+ // f * 2^e = q * 10^17 + r
+ // f * 2^e = q * 5^17 * 2^17 + r
+ // If e > 17 then
+ // f * 2^(e-17) = q * 5^17 + r/2^17
+ // else
+ // f = q * 5^17 * 2^(17-e) + r/2^e
+ if (exponent > divisor_power) {
+ // We only allow exponents of up to 20 and therefore (17 - e) <= 3
+ dividend <<= exponent - divisor_power;
+ quotient = static_cast<uint32_t>(dividend / divisor);
+ remainder = (dividend % divisor) << divisor_power;
+ } else {
+ divisor <<= divisor_power - exponent;
+ quotient = static_cast<uint32_t>(dividend / divisor);
+ remainder = (dividend % divisor) << exponent;
+ }
+ FillDigits32(quotient, buffer, length);
+ FillDigits64FixedLength(remainder, divisor_power, buffer, length);
+ *decimal_point = *length;
+ } else if (exponent >= 0) {
+ // 0 <= exponent <= 11
+ significand <<= exponent;
+ FillDigits64(significand, buffer, length);
+ *decimal_point = *length;
+ } else if (exponent > -kDoubleSignificandSize) {
+ // We have to cut the number.
+ uint64_t integrals = significand >> -exponent;
+ uint64_t fractionals = significand - (integrals << -exponent);
+ if (integrals > kMaxUInt32) {
+ FillDigits64(integrals, buffer, length);
+ } else {
+ FillDigits32(static_cast<uint32_t>(integrals), buffer, length);
+ }
+ *decimal_point = *length;
+ FillFractionals(fractionals, exponent, fractional_count,
+ buffer, length, decimal_point);
+ } else if (exponent < -128) {
+ // This configuration (with at most 20 digits) means that all digits must be
+ // 0.
+ ASSERT(fractional_count <= 20);
+ buffer[0] = '\0';
+ *length = 0;
+ *decimal_point = -fractional_count;
+ } else {
+ *decimal_point = 0;
+ FillFractionals(significand, exponent, fractional_count,
+ buffer, length, decimal_point);
+ }
+ TrimZeros(buffer, length, decimal_point);
+ buffer[*length] = '\0';
+ if ((*length) == 0) {
+ // The string is empty and the decimal_point thus has no importance. Mimick
+ // Gay's dtoa and and set it to -fractional_count.
+ *decimal_point = -fractional_count;
+ }
+ return true;
+}
+
+} // namespace double_conversion
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