mirror of
https://github.com/ClickHouse/ClickHouse.git
synced 2024-12-01 20:12:02 +00:00
405 lines
15 KiB
C++
405 lines
15 KiB
C++
// 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] = static_cast<char>('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,
|
|
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);
|
|
ASSERT(digit <= 9);
|
|
buffer[*length] = static_cast<char>('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);
|
|
ASSERT(digit <= 9);
|
|
buffer[*length] = static_cast<char>('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, 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
|