fixed-dtoa.cc   [plain text]

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#include "config.h"

#include <math.h>

#include "UnusedParam.h"
#include "fixed-dtoa.h"
#include "double.h"

namespace WTF {

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) {
        UNUSED_PARAM(requested_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

} // namespace WTF