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author | Matt A. Tobin <mattatobin@localhost.localdomain> | 2018-02-02 04:16:08 -0500 |
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committer | Matt A. Tobin <mattatobin@localhost.localdomain> | 2018-02-02 04:16:08 -0500 |
commit | 5f8de423f190bbb79a62f804151bc24824fa32d8 (patch) | |
tree | 10027f336435511475e392454359edea8e25895d /mfbt/double-conversion/fixed-dtoa.cc | |
parent | 49ee0794b5d912db1f95dce6eb52d781dc210db5 (diff) | |
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Add m-esr52 at 52.6.0
Diffstat (limited to 'mfbt/double-conversion/fixed-dtoa.cc')
-rw-r--r-- | mfbt/double-conversion/fixed-dtoa.cc | 402 |
1 files changed, 402 insertions, 0 deletions
diff --git a/mfbt/double-conversion/fixed-dtoa.cc b/mfbt/double-conversion/fixed-dtoa.cc new file mode 100644 index 000000000..d56b1449b --- /dev/null +++ b/mfbt/double-conversion/fixed-dtoa.cc @@ -0,0 +1,402 @@ +// 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 |