Source/wtf/dtoa/bignum.cc

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This source file includes following definitions.
exponent_
BitSize
AssignUInt16
AssignUInt64
AssignBignum
ReadUInt64
AssignDecimalString
HexCharValue
AssignHexString
AddUInt64
AddBignum
SubtractBignum
ShiftLeft
MultiplyByUInt32
MultiplyByUInt64
MultiplyByPowerOfTen
Square
AssignPowerUInt16
DivideModuloIntBignum
SizeInHexChars
HexCharOfValue
ToHexString
BigitAt
Compare
PlusCompare
Clamp
IsClamped
Zero
Align
BigitsShiftLeft
SubtractTimes
// 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 "config.h"

#include "bignum.h"
#include "utils.h"

namespace WTF {

namespace double_conversion {

    Bignum::Bignum()
    : bigits_(bigits_buffer_, kBigitCapacity), used_digits_(0), exponent_(0) {
        for (int i = 0; i < kBigitCapacity; ++i) {
            bigits_[i] = 0;
        }
    }


    template<typename S>
    static int BitSize(S value) {
        return 8 * sizeof(value);
    }

    // Guaranteed to lie in one Bigit.
    void Bignum::AssignUInt16(uint16_t value) {
        ASSERT(kBigitSize >= BitSize(value));
        Zero();
        if (value == 0) return;

        EnsureCapacity(1);
        bigits_[0] = value;
        used_digits_ = 1;
    }


    void Bignum::AssignUInt64(uint64_t value) {
        const int kUInt64Size = 64;

        Zero();
        if (value == 0) return;

        int needed_bigits = kUInt64Size / kBigitSize + 1;
        EnsureCapacity(needed_bigits);
        for (int i = 0; i < needed_bigits; ++i) {
            bigits_[i] = (uint32_t)value & kBigitMask;
            value = value >> kBigitSize;
        }
        used_digits_ = needed_bigits;
        Clamp();
    }


    void Bignum::AssignBignum(const Bignum& other) {
        exponent_ = other.exponent_;
        for (int i = 0; i < other.used_digits_; ++i) {
            bigits_[i] = other.bigits_[i];
        }
        // Clear the excess digits (if there were any).
        for (int i = other.used_digits_; i < used_digits_; ++i) {
            bigits_[i] = 0;
        }
        used_digits_ = other.used_digits_;
    }


    static uint64_t ReadUInt64(Vector<const char> buffer,
                               int from,
                               int digits_to_read) {
        uint64_t result = 0;
        for (int i = from; i < from + digits_to_read; ++i) {
            int digit = buffer[i] - '0';
            ASSERT(0 <= digit && digit <= 9);
            result = result * 10 + digit;
        }
        return result;
    }


    void Bignum::AssignDecimalString(Vector<const char> value) {
        // 2^64 = 18446744073709551616 > 10^19
        const int kMaxUint64DecimalDigits = 19;
        Zero();
        int length = value.length();
        int pos = 0;
        // Let's just say that each digit needs 4 bits.
        while (length >= kMaxUint64DecimalDigits) {
            uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits);
            pos += kMaxUint64DecimalDigits;
            length -= kMaxUint64DecimalDigits;
            MultiplyByPowerOfTen(kMaxUint64DecimalDigits);
            AddUInt64(digits);
        }
        uint64_t digits = ReadUInt64(value, pos, length);
        MultiplyByPowerOfTen(length);
        AddUInt64(digits);
        Clamp();
    }


    static int HexCharValue(char c) {
        if ('0' <= c && c <= '9') return c - '0';
        if ('a' <= c && c <= 'f') return 10 + c - 'a';
        if ('A' <= c && c <= 'F') return 10 + c - 'A';
        UNREACHABLE();
        return 0;  // To make compiler happy.
    }


    void Bignum::AssignHexString(Vector<const char> value) {
        Zero();
        int length = value.length();

        int needed_bigits = length * 4 / kBigitSize + 1;
        EnsureCapacity(needed_bigits);
        int string_index = length - 1;
        for (int i = 0; i < needed_bigits - 1; ++i) {
            // These bigits are guaranteed to be "full".
            Chunk current_bigit = 0;
            for (int j = 0; j < kBigitSize / 4; j++) {
                current_bigit += HexCharValue(value[string_index--]) << (j * 4);
            }
            bigits_[i] = current_bigit;
        }
        used_digits_ = needed_bigits - 1;

        Chunk most_significant_bigit = 0;  // Could be = 0;
        for (int j = 0; j <= string_index; ++j) {
            most_significant_bigit <<= 4;
            most_significant_bigit += HexCharValue(value[j]);
        }
        if (most_significant_bigit != 0) {
            bigits_[used_digits_] = most_significant_bigit;
            used_digits_++;
        }
        Clamp();
    }


    void Bignum::AddUInt64(uint64_t operand) {
        if (operand == 0) return;
        Bignum other;
        other.AssignUInt64(operand);
        AddBignum(other);
    }


    void Bignum::AddBignum(const Bignum& other) {
        ASSERT(IsClamped());
        ASSERT(other.IsClamped());

        // If this has a greater exponent than other append zero-bigits to this.
        // After this call exponent_ <= other.exponent_.
        Align(other);

        // There are two possibilities:
        //   aaaaaaaaaaa 0000  (where the 0s represent a's exponent)
        //     bbbbb 00000000
        //   ----------------
        //   ccccccccccc 0000
        // or
        //    aaaaaaaaaa 0000
        //  bbbbbbbbb 0000000
        //  -----------------
        //  cccccccccccc 0000
        // In both cases we might need a carry bigit.

        EnsureCapacity(1 + Max(BigitLength(), other.BigitLength()) - exponent_);
        Chunk carry = 0;
        int bigit_pos = other.exponent_ - exponent_;
        ASSERT(bigit_pos >= 0);
        for (int i = 0; i < other.used_digits_; ++i) {
            Chunk sum = bigits_[bigit_pos] + other.bigits_[i] + carry;
            bigits_[bigit_pos] = sum & kBigitMask;
            carry = sum >> kBigitSize;
            bigit_pos++;
        }

        while (carry != 0) {
            Chunk sum = bigits_[bigit_pos] + carry;
            bigits_[bigit_pos] = sum & kBigitMask;
            carry = sum >> kBigitSize;
            bigit_pos++;
        }
        used_digits_ = Max(bigit_pos, used_digits_);
        ASSERT(IsClamped());
    }


    void Bignum::SubtractBignum(const Bignum& other) {
        ASSERT(IsClamped());
        ASSERT(other.IsClamped());
        // We require this to be bigger than other.
        ASSERT(LessEqual(other, *this));

        Align(other);

        int offset = other.exponent_ - exponent_;
        Chunk borrow = 0;
        int i;
        for (i = 0; i < other.used_digits_; ++i) {
            ASSERT((borrow == 0) || (borrow == 1));
            Chunk difference = bigits_[i + offset] - other.bigits_[i] - borrow;
            bigits_[i + offset] = difference & kBigitMask;
            borrow = difference >> (kChunkSize - 1);
        }
        while (borrow != 0) {
            Chunk difference = bigits_[i + offset] - borrow;
            bigits_[i + offset] = difference & kBigitMask;
            borrow = difference >> (kChunkSize - 1);
            ++i;
        }
        Clamp();
    }


    void Bignum::ShiftLeft(int shift_amount) {
        if (used_digits_ == 0) return;
        exponent_ += shift_amount / kBigitSize;
        int local_shift = shift_amount % kBigitSize;
        EnsureCapacity(used_digits_ + 1);
        BigitsShiftLeft(local_shift);
    }


    void Bignum::MultiplyByUInt32(uint32_t factor) {
        if (factor == 1) return;
        if (factor == 0) {
            Zero();
            return;
        }
        if (used_digits_ == 0) return;

        // The product of a bigit with the factor is of size kBigitSize + 32.
        // Assert that this number + 1 (for the carry) fits into double chunk.
        ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1);
        DoubleChunk carry = 0;
        for (int i = 0; i < used_digits_; ++i) {
            DoubleChunk product = static_cast<DoubleChunk>(factor) * bigits_[i] + carry;
            bigits_[i] = static_cast<Chunk>(product & kBigitMask);
            carry = (product >> kBigitSize);
        }
        while (carry != 0) {
            EnsureCapacity(used_digits_ + 1);
            bigits_[used_digits_] = (uint32_t)carry & kBigitMask;
            used_digits_++;
            carry >>= kBigitSize;
        }
    }


    void Bignum::MultiplyByUInt64(uint64_t factor) {
        if (factor == 1) return;
        if (factor == 0) {
            Zero();
            return;
        }
        ASSERT(kBigitSize < 32);
        uint64_t carry = 0;
        uint64_t low = factor & 0xFFFFFFFF;
        uint64_t high = factor >> 32;
        for (int i = 0; i < used_digits_; ++i) {
            uint64_t product_low = low * bigits_[i];
            uint64_t product_high = high * bigits_[i];
            uint64_t tmp = (carry & kBigitMask) + product_low;
            bigits_[i] = (uint32_t)tmp & kBigitMask;
            carry = (carry >> kBigitSize) + (tmp >> kBigitSize) +
            (product_high << (32 - kBigitSize));
        }
        while (carry != 0) {
            EnsureCapacity(used_digits_ + 1);
            bigits_[used_digits_] = (uint32_t)carry & kBigitMask;
            used_digits_++;
            carry >>= kBigitSize;
        }
    }


    void Bignum::MultiplyByPowerOfTen(int exponent) {
        const uint64_t kFive27 = UINT64_2PART_C(0x6765c793, fa10079d);
        const uint16_t kFive1 = 5;
        const uint16_t kFive2 = kFive1 * 5;
        const uint16_t kFive3 = kFive2 * 5;
        const uint16_t kFive4 = kFive3 * 5;
        const uint16_t kFive5 = kFive4 * 5;
        const uint16_t kFive6 = kFive5 * 5;
        const uint32_t kFive7 = kFive6 * 5;
        const uint32_t kFive8 = kFive7 * 5;
        const uint32_t kFive9 = kFive8 * 5;
        const uint32_t kFive10 = kFive9 * 5;
        const uint32_t kFive11 = kFive10 * 5;
        const uint32_t kFive12 = kFive11 * 5;
        const uint32_t kFive13 = kFive12 * 5;
        const uint32_t kFive1_to_12[] =
        { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6,
            kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 };

        ASSERT(exponent >= 0);
        if (exponent == 0) return;
        if (used_digits_ == 0) return;

        // We shift by exponent at the end just before returning.
        int remaining_exponent = exponent;
        while (remaining_exponent >= 27) {
            MultiplyByUInt64(kFive27);
            remaining_exponent -= 27;
        }
        while (remaining_exponent >= 13) {
            MultiplyByUInt32(kFive13);
            remaining_exponent -= 13;
        }
        if (remaining_exponent > 0) {
            MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]);
        }
        ShiftLeft(exponent);
    }


    void Bignum::Square() {
        ASSERT(IsClamped());
        int product_length = 2 * used_digits_;
        EnsureCapacity(product_length);

        // Comba multiplication: compute each column separately.
        // Example: r = a2a1a0 * b2b1b0.
        //    r =  1    * a0b0 +
        //        10    * (a1b0 + a0b1) +
        //        100   * (a2b0 + a1b1 + a0b2) +
        //        1000  * (a2b1 + a1b2) +
        //        10000 * a2b2
        //
        // In the worst case we have to accumulate nb-digits products of digit*digit.
        //
        // Assert that the additional number of bits in a DoubleChunk are enough to
        // sum up used_digits of Bigit*Bigit.
        if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) {
            UNIMPLEMENTED();
        }
        DoubleChunk accumulator = 0;
        // First shift the digits so we don't overwrite them.
        int copy_offset = used_digits_;
        for (int i = 0; i < used_digits_; ++i) {
            bigits_[copy_offset + i] = bigits_[i];
        }
        // We have two loops to avoid some 'if's in the loop.
        for (int i = 0; i < used_digits_; ++i) {
            // Process temporary digit i with power i.
            // The sum of the two indices must be equal to i.
            int bigit_index1 = i;
            int bigit_index2 = 0;
            // Sum all of the sub-products.
            while (bigit_index1 >= 0) {
                Chunk chunk1 = bigits_[copy_offset + bigit_index1];
                Chunk chunk2 = bigits_[copy_offset + bigit_index2];
                accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
                bigit_index1--;
                bigit_index2++;
            }
            bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
            accumulator >>= kBigitSize;
        }
        for (int i = used_digits_; i < product_length; ++i) {
            int bigit_index1 = used_digits_ - 1;
            int bigit_index2 = i - bigit_index1;
            // Invariant: sum of both indices is again equal to i.
            // Inner loop runs 0 times on last iteration, emptying accumulator.
            while (bigit_index2 < used_digits_) {
                Chunk chunk1 = bigits_[copy_offset + bigit_index1];
                Chunk chunk2 = bigits_[copy_offset + bigit_index2];
                accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
                bigit_index1--;
                bigit_index2++;
            }
            // The overwritten bigits_[i] will never be read in further loop iterations,
            // because bigit_index1 and bigit_index2 are always greater
            // than i - used_digits_.
            bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
            accumulator >>= kBigitSize;
        }
        // Since the result was guaranteed to lie inside the number the
        // accumulator must be 0 now.
        ASSERT(accumulator == 0);

        // Don't forget to update the used_digits and the exponent.
        used_digits_ = product_length;
        exponent_ *= 2;
        Clamp();
    }


    void Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) {
        ASSERT(base != 0);
        ASSERT(power_exponent >= 0);
        if (power_exponent == 0) {
            AssignUInt16(1);
            return;
        }
        Zero();
        int shifts = 0;
        // We expect base to be in range 2-32, and most often to be 10.
        // It does not make much sense to implement different algorithms for counting
        // the bits.
        while ((base & 1) == 0) {
            base >>= 1;
            shifts++;
        }
        int bit_size = 0;
        int tmp_base = base;
        while (tmp_base != 0) {
            tmp_base >>= 1;
            bit_size++;
        }
        int final_size = bit_size * power_exponent;
        // 1 extra bigit for the shifting, and one for rounded final_size.
        EnsureCapacity(final_size / kBigitSize + 2);

        // Left to Right exponentiation.
        int mask = 1;
        while (power_exponent >= mask) mask <<= 1;

        // The mask is now pointing to the bit above the most significant 1-bit of
        // power_exponent.
        // Get rid of first 1-bit;
        mask >>= 2;
        uint64_t this_value = base;

        bool delayed_multipliciation = false;
        const uint64_t max_32bits = 0xFFFFFFFF;
        while (mask != 0 && this_value <= max_32bits) {
            this_value = this_value * this_value;
            // Verify that there is enough space in this_value to perform the
            // multiplication.  The first bit_size bits must be 0.
            if ((power_exponent & mask) != 0) {
                uint64_t base_bits_mask =
                ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1);
                bool high_bits_zero = (this_value & base_bits_mask) == 0;
                if (high_bits_zero) {
                    this_value *= base;
                } else {
                    delayed_multipliciation = true;
                }
            }
            mask >>= 1;
        }
        AssignUInt64(this_value);
        if (delayed_multipliciation) {
            MultiplyByUInt32(base);
        }

        // Now do the same thing as a bignum.
        while (mask != 0) {
            Square();
            if ((power_exponent & mask) != 0) {
                MultiplyByUInt32(base);
            }
            mask >>= 1;
        }

        // And finally add the saved shifts.
        ShiftLeft(shifts * power_exponent);
    }


    // Precondition: this/other < 16bit.
    uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) {
        ASSERT(IsClamped());
        ASSERT(other.IsClamped());
        ASSERT(other.used_digits_ > 0);

        // Easy case: if we have less digits than the divisor than the result is 0.
        // Note: this handles the case where this == 0, too.
        if (BigitLength() < other.BigitLength()) {
            return 0;
        }

        Align(other);

        uint16_t result = 0;

        // Start by removing multiples of 'other' until both numbers have the same
        // number of digits.
        while (BigitLength() > other.BigitLength()) {
            // This naive approach is extremely inefficient if the this divided other
            // might be big. This function is implemented for doubleToString where
            // the result should be small (less than 10).
            ASSERT(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16));
            // Remove the multiples of the first digit.
            // Example this = 23 and other equals 9. -> Remove 2 multiples.
            result += bigits_[used_digits_ - 1];
            SubtractTimes(other, bigits_[used_digits_ - 1]);
        }

        ASSERT(BigitLength() == other.BigitLength());

        // Both bignums are at the same length now.
        // Since other has more than 0 digits we know that the access to
        // bigits_[used_digits_ - 1] is safe.
        Chunk this_bigit = bigits_[used_digits_ - 1];
        Chunk other_bigit = other.bigits_[other.used_digits_ - 1];

        if (other.used_digits_ == 1) {
            // Shortcut for easy (and common) case.
            int quotient = this_bigit / other_bigit;
            bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient;
            result += quotient;
            Clamp();
            return result;
        }

        int division_estimate = this_bigit / (other_bigit + 1);
        result += division_estimate;
        SubtractTimes(other, division_estimate);

        if (other_bigit * (division_estimate + 1) > this_bigit) {
            // No need to even try to subtract. Even if other's remaining digits were 0
            // another subtraction would be too much.
            return result;
        }

        while (LessEqual(other, *this)) {
            SubtractBignum(other);
            result++;
        }
        return result;
    }


    template<typename S>
    static int SizeInHexChars(S number) {
        ASSERT(number > 0);
        int result = 0;
        while (number != 0) {
            number >>= 4;
            result++;
        }
        return result;
    }


    static char HexCharOfValue(int value) {
        ASSERT(0 <= value && value <= 16);
        if (value < 10) return value + '0';
        return value - 10 + 'A';
    }


    bool Bignum::ToHexString(char* buffer, int buffer_size) const {
        ASSERT(IsClamped());
        // Each bigit must be printable as separate hex-character.
        ASSERT(kBigitSize % 4 == 0);
        const int kHexCharsPerBigit = kBigitSize / 4;

        if (used_digits_ == 0) {
            if (buffer_size < 2) return false;
            buffer[0] = '0';
            buffer[1] = '\0';
            return true;
        }
        // We add 1 for the terminating '\0' character.
        int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit +
        SizeInHexChars(bigits_[used_digits_ - 1]) + 1;
        if (needed_chars > buffer_size) return false;
        int string_index = needed_chars - 1;
        buffer[string_index--] = '\0';
        for (int i = 0; i < exponent_; ++i) {
            for (int j = 0; j < kHexCharsPerBigit; ++j) {
                buffer[string_index--] = '0';
            }
        }
        for (int i = 0; i < used_digits_ - 1; ++i) {
            Chunk current_bigit = bigits_[i];
            for (int j = 0; j < kHexCharsPerBigit; ++j) {
                buffer[string_index--] = HexCharOfValue(current_bigit & 0xF);
                current_bigit >>= 4;
            }
        }
        // And finally the last bigit.
        Chunk most_significant_bigit = bigits_[used_digits_ - 1];
        while (most_significant_bigit != 0) {
            buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF);
            most_significant_bigit >>= 4;
        }
        return true;
    }


    Bignum::Chunk Bignum::BigitAt(int index) const {
        if (index >= BigitLength()) return 0;
        if (index < exponent_) return 0;
        return bigits_[index - exponent_];
    }


    int Bignum::Compare(const Bignum& a, const Bignum& b) {
        ASSERT(a.IsClamped());
        ASSERT(b.IsClamped());
        int bigit_length_a = a.BigitLength();
        int bigit_length_b = b.BigitLength();
        if (bigit_length_a < bigit_length_b) return -1;
        if (bigit_length_a > bigit_length_b) return +1;
        for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i) {
            Chunk bigit_a = a.BigitAt(i);
            Chunk bigit_b = b.BigitAt(i);
            if (bigit_a < bigit_b) return -1;
            if (bigit_a > bigit_b) return +1;
            // Otherwise they are equal up to this digit. Try the next digit.
        }
        return 0;
    }


    int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) {
        ASSERT(a.IsClamped());
        ASSERT(b.IsClamped());
        ASSERT(c.IsClamped());
        if (a.BigitLength() < b.BigitLength()) {
            return PlusCompare(b, a, c);
        }
        if (a.BigitLength() + 1 < c.BigitLength()) return -1;
        if (a.BigitLength() > c.BigitLength()) return +1;
        // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than
        // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one
        // of 'a'.
        if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) {
            return -1;
        }

        Chunk borrow = 0;
        // Starting at min_exponent all digits are == 0. So no need to compare them.
        int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_);
        for (int i = c.BigitLength() - 1; i >= min_exponent; --i) {
            Chunk chunk_a = a.BigitAt(i);
            Chunk chunk_b = b.BigitAt(i);
            Chunk chunk_c = c.BigitAt(i);
            Chunk sum = chunk_a + chunk_b;
            if (sum > chunk_c + borrow) {
                return +1;
            } else {
                borrow = chunk_c + borrow - sum;
                if (borrow > 1) return -1;
                borrow <<= kBigitSize;
            }
        }
        if (borrow == 0) return 0;
        return -1;
    }


    void Bignum::Clamp() {
        while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) {
            used_digits_--;
        }
        if (used_digits_ == 0) {
            // Zero.
            exponent_ = 0;
        }
    }


    bool Bignum::IsClamped() const {
        return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0;
    }


    void Bignum::Zero() {
        for (int i = 0; i < used_digits_; ++i) {
            bigits_[i] = 0;
        }
        used_digits_ = 0;
        exponent_ = 0;
    }


    void Bignum::Align(const Bignum& other) {
        if (exponent_ > other.exponent_) {
            // If "X" represents a "hidden" digit (by the exponent) then we are in the
            // following case (a == this, b == other):
            // a:  aaaaaaXXXX   or a:   aaaaaXXX
            // b:     bbbbbbX      b: bbbbbbbbXX
            // We replace some of the hidden digits (X) of a with 0 digits.
            // a:  aaaaaa000X   or a:   aaaaa0XX
            int zero_digits = exponent_ - other.exponent_;
            EnsureCapacity(used_digits_ + zero_digits);
            for (int i = used_digits_ - 1; i >= 0; --i) {
                bigits_[i + zero_digits] = bigits_[i];
            }
            for (int i = 0; i < zero_digits; ++i) {
                bigits_[i] = 0;
            }
            used_digits_ += zero_digits;
            exponent_ -= zero_digits;
            ASSERT(used_digits_ >= 0);
            ASSERT(exponent_ >= 0);
        }
    }


    void Bignum::BigitsShiftLeft(int shift_amount) {
        ASSERT(shift_amount < kBigitSize);
        ASSERT(shift_amount >= 0);
        Chunk carry = 0;
        for (int i = 0; i < used_digits_; ++i) {
            Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount);
            bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask;
            carry = new_carry;
        }
        if (carry != 0) {
            bigits_[used_digits_] = carry;
            used_digits_++;
        }
    }


    void Bignum::SubtractTimes(const Bignum& other, int factor) {
        ASSERT(exponent_ <= other.exponent_);
        if (factor < 3) {
            for (int i = 0; i < factor; ++i) {
                SubtractBignum(other);
            }
            return;
        }
        Chunk borrow = 0;
        int exponent_diff = other.exponent_ - exponent_;
        for (int i = 0; i < other.used_digits_; ++i) {
            DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigits_[i];
            DoubleChunk remove = borrow + product;
            Chunk difference = bigits_[i + exponent_diff] - ((uint32_t)remove & kBigitMask);
            bigits_[i + exponent_diff] = difference & kBigitMask;
            borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) +
                                        (remove >> kBigitSize));
        }
        for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) {
            if (borrow == 0) return;
            Chunk difference = bigits_[i] - borrow;
            bigits_[i] = difference & kBigitMask;
            borrow = difference >> (kChunkSize - 1);
            ++i;
        }
        Clamp();
    }


}  // namespace double_conversion

} // namespace WTF
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root/Source/wtf/dtoa/bignum.cc

DEFINITIONS
