root/src/fixed-dtoa.cc
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DEFINITIONS
This source file includes following definitions.
- low_bits_
- low_bits_
- Multiply
- Shift
- DivModPowerOf2
- IsZero
- BitAt
- FillDigits32FixedLength
- FillDigits32
- FillDigits64FixedLength
- FillDigits64
- RoundUp
- FillFractionals
- TrimZeros
- FastFixedDtoa
// Copyright 2011 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 "../include/v8stdint.h"
#include "checks.h"
#include "utils.h"
#include "double.h"
#include "fixed-dtoa.h"
namespace v8 {
namespace internal {
// 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 = V8_2PART_UINT64_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 v8::internal