| // Copyright 2011 the V8 project authors. All rights reserved. |
| // Use of this source code is governed by a BSD-style license that can be |
| // found in the LICENSE file. |
| |
| #include <stdint.h> |
| |
| #include <cmath> |
| |
| #include "src/base/logging.h" |
| #include "src/utils.h" |
| |
| #include "src/double.h" |
| #include "src/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; |
| DCHECK_EQ(accumulator >> 32, 0); |
| } |
| |
| void Shift(int shift_amount) { |
| DCHECK(-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 DtoaRoundUp(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) { |
| DCHECK(-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. |
| DCHECK_EQ(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) { |
| DtoaRoundUp(buffer, length, decimal_point); |
| } |
| } else { // We need 128 bits. |
| DCHECK(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) { |
| DtoaRoundUp(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. |
| DCHECK_LE(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 internal |
| } // namespace v8 |