// 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

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//       copyright notice, this list of conditions and the following

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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

#include <algorithm>

#include <cstring>

#include "bignum.h"

#include "utils.h"

namespace double_conversion {

Bignum::Chunk& Bignum::RawBigit(const int index) {

  DOUBLE_CONVERSION_ASSERT(static_cast<unsigned>(index) < kBigitCapacity);

  return bigits_buffer_[index];

}

const Bignum::Chunk& Bignum::RawBigit(const int index) const {

  DOUBLE_CONVERSION_ASSERT(static_cast<unsigned>(index) < kBigitCapacity);

  return bigits_buffer_[index];

}

template<typename S>

static int BitSize(const S value) {

  (void) value;  // Mark variable as used.

  return 8 * sizeof(value);

}

// Guaranteed to lie in one Bigit.

void Bignum::AssignUInt16(const uint16_t value) {

  DOUBLE_CONVERSION_ASSERT(kBigitSize >= BitSize(value));

  Zero();

  if (value > 0) {

    RawBigit(0) = value;

    used_bigits_ = 1;

  }

}

void Bignum::AssignUInt64(uint64_t value) {

  Zero();

  for(int i = 0; value > 0; ++i) {

    RawBigit(i) = value & kBigitMask;

    value >>= kBigitSize;

    ++used_bigits_;

  }

}

void Bignum::AssignBignum(const Bignum& other) {

  exponent_ = other.exponent_;

  for (int i = 0; i < other.used_bigits_; ++i) {

    RawBigit(i) = other.RawBigit(i);

  }

  used_bigits_ = other.used_bigits_;

}

static uint64_t ReadUInt64(const Vector<const char> buffer,

                           const int from,

                           const int digits_to_read) {

  uint64_t result = 0;

  for (int i = from; i < from + digits_to_read; ++i) {

    const int digit = buffer[i] - '0';

    DOUBLE_CONVERSION_ASSERT(0 <= digit && digit <= 9);

    result = result * 10 + digit;

  }

  return result;

}

void Bignum::AssignDecimalString(const Vector<const char> value) {

  // 2^64 = 18446744073709551616 > 10^19

  static const int kMaxUint64DecimalDigits = 19;

  Zero();

  int length = value.length();

  unsigned pos = 0;

  // Let's just say that each digit needs 4 bits.

  while (length >= kMaxUint64DecimalDigits) {

    const uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits);

    pos += kMaxUint64DecimalDigits;

    length -= kMaxUint64DecimalDigits;

    MultiplyByPowerOfTen(kMaxUint64DecimalDigits);

    AddUInt64(digits);

  }

  const uint64_t digits = ReadUInt64(value, pos, length);

  MultiplyByPowerOfTen(length);

  AddUInt64(digits);

  Clamp();

}

static uint64_t HexCharValue(const int c) {

  if ('0' <= c && c <= '9') {

    return c - '0';

  }

  if ('a' <= c && c <= 'f') {

    return 10 + c - 'a';

  }

  DOUBLE_CONVERSION_ASSERT('A' <= c && c <= 'F');

  return 10 + c - 'A';

}

// Unlike AssignDecimalString(), this function is "only" used

// for unit-tests and therefore not performance critical.

void Bignum::AssignHexString(Vector<const char> value) {

  Zero();

  // Required capacity could be reduced by ignoring leading zeros.

  EnsureCapacity(((value.length() * 4) + kBigitSize - 1) / kBigitSize);

  DOUBLE_CONVERSION_ASSERT(sizeof(uint64_t) * 8 >= kBigitSize + 4);  // TODO: static_assert

  // Accumulates converted hex digits until at least kBigitSize bits.

  // Works with non-factor-of-four kBigitSizes.

  uint64_t tmp = 0;

  for (int cnt = 0; !value.is_empty(); value.pop_back()) {

    tmp |= (HexCharValue(value.last()) << cnt);

    if ((cnt += 4) >= kBigitSize) {

      RawBigit(used_bigits_++) = (tmp & kBigitMask);

      cnt -= kBigitSize;

      tmp >>= kBigitSize;

    }

  }

  if (tmp > 0) {

    DOUBLE_CONVERSION_ASSERT(tmp <= kBigitMask);

    RawBigit(used_bigits_++) = static_cast<Bignum::Chunk>(tmp & kBigitMask);

  }

  Clamp();

}

void Bignum::AddUInt64(const uint64_t operand) {

  if (operand == 0) {

    return;

  }

  Bignum other;

  other.AssignUInt64(operand);

  AddBignum(other);

}

void Bignum::AddBignum(const Bignum& other) {

  DOUBLE_CONVERSION_ASSERT(IsClamped());

  DOUBLE_CONVERSION_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 + (std::max)(BigitLength(), other.BigitLength()) - exponent_);

  Chunk carry = 0;

  int bigit_pos = other.exponent_ - exponent_;

  DOUBLE_CONVERSION_ASSERT(bigit_pos >= 0);

  for (int i = used_bigits_; i < bigit_pos; ++i) {

    RawBigit(i) = 0;

  }

  for (int i = 0; i < other.used_bigits_; ++i) {

    const Chunk my = (bigit_pos < used_bigits_) ? RawBigit(bigit_pos) : 0;

    const Chunk sum = my + other.RawBigit(i) + carry;

    RawBigit(bigit_pos) = sum & kBigitMask;

    carry = sum >> kBigitSize;

    ++bigit_pos;

  }

  while (carry != 0) {

    const Chunk my = (bigit_pos < used_bigits_) ? RawBigit(bigit_pos) : 0;

    const Chunk sum = my + carry;

    RawBigit(bigit_pos) = sum & kBigitMask;

    carry = sum >> kBigitSize;

    ++bigit_pos;

  }

  used_bigits_ = static_cast<int16_t>(std::max(bigit_pos, static_cast<int>(used_bigits_)));

  DOUBLE_CONVERSION_ASSERT(IsClamped());

}

void Bignum::SubtractBignum(const Bignum& other) {

  DOUBLE_CONVERSION_ASSERT(IsClamped());

  DOUBLE_CONVERSION_ASSERT(other.IsClamped());

  // We require this to be bigger than other.

  DOUBLE_CONVERSION_ASSERT(LessEqual(other, *this));

  Align(other);

  const int offset = other.exponent_ - exponent_;

  Chunk borrow = 0;

  int i;

  for (i = 0; i < other.used_bigits_; ++i) {

    DOUBLE_CONVERSION_ASSERT((borrow == 0) || (borrow == 1));

    const Chunk difference = RawBigit(i + offset) - other.RawBigit(i) - borrow;

    RawBigit(i + offset) = difference & kBigitMask;

    borrow = difference >> (kChunkSize - 1);

  }

  while (borrow != 0) {

    const Chunk difference = RawBigit(i + offset) - borrow;

    RawBigit(i + offset) = difference & kBigitMask;

    borrow = difference >> (kChunkSize - 1);

    ++i;

  }

  Clamp();

}

void Bignum::ShiftLeft(const int shift_amount) {

  if (used_bigits_ == 0) {

    return;

  }

  exponent_ += static_cast<int16_t>(shift_amount / kBigitSize);

  const int local_shift = shift_amount % kBigitSize;

  EnsureCapacity(used_bigits_ + 1);

  BigitsShiftLeft(local_shift);

}

void Bignum::MultiplyByUInt32(const uint32_t factor) {

  if (factor == 1) {

    return;

  }

  if (factor == 0) {

    Zero();

    return;

  }

  if (used_bigits_ == 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.

  DOUBLE_CONVERSION_ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1);

  DoubleChunk carry = 0;

  for (int i = 0; i < used_bigits_; ++i) {

    const DoubleChunk product = static_cast<DoubleChunk>(factor) * RawBigit(i) + carry;

    RawBigit(i) = static_cast<Chunk>(product & kBigitMask);

    carry = (product >> kBigitSize);

  }

  while (carry != 0) {

    EnsureCapacity(used_bigits_ + 1);

    RawBigit(used_bigits_) = carry & kBigitMask;

    used_bigits_++;

    carry >>= kBigitSize;

  }

}

void Bignum::MultiplyByUInt64(const uint64_t factor) {

  if (factor == 1) {

    return;

  }

  if (factor == 0) {

    Zero();

    return;

  }

  if (used_bigits_ == 0) {

    return;

  }

  DOUBLE_CONVERSION_ASSERT(kBigitSize < 32);

  uint64_t carry = 0;

  const uint64_t low = factor & 0xFFFFFFFF;

  const uint64_t high = factor >> 32;

  for (int i = 0; i < used_bigits_; ++i) {

    const uint64_t product_low = low * RawBigit(i);

    const uint64_t product_high = high * RawBigit(i);

    const uint64_t tmp = (carry & kBigitMask) + product_low;

    RawBigit(i) = tmp & kBigitMask;

    carry = (carry >> kBigitSize) + (tmp >> kBigitSize) +

        (product_high << (32 - kBigitSize));

  }

  while (carry != 0) {

    EnsureCapacity(used_bigits_ + 1);

    RawBigit(used_bigits_) = carry & kBigitMask;

    used_bigits_++;

    carry >>= kBigitSize;

  }

}

void Bignum::MultiplyByPowerOfTen(const int exponent) {

  static const uint64_t kFive27 = DOUBLE_CONVERSION_UINT64_2PART_C(0x6765c793, fa10079d);

  static const uint16_t kFive1 = 5;

  static const uint16_t kFive2 = kFive1 * 5;

  static const uint16_t kFive3 = kFive2 * 5;

  static const uint16_t kFive4 = kFive3 * 5;

  static const uint16_t kFive5 = kFive4 * 5;

  static const uint16_t kFive6 = kFive5 * 5;

  static const uint32_t kFive7 = kFive6 * 5;

  static const uint32_t kFive8 = kFive7 * 5;

  static const uint32_t kFive9 = kFive8 * 5;

  static const uint32_t kFive10 = kFive9 * 5;

  static const uint32_t kFive11 = kFive10 * 5;

  static const uint32_t kFive12 = kFive11 * 5;

  static const uint32_t kFive13 = kFive12 * 5;

  static const uint32_t kFive1_to_12[] =

      { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6,

        kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 };

  DOUBLE_CONVERSION_ASSERT(exponent >= 0);

  if (exponent == 0) {

    return;

  }

  if (used_bigits_ == 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() {

  DOUBLE_CONVERSION_ASSERT(IsClamped());

  const int product_length = 2 * used_bigits_;

  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_bigits_) {

    DOUBLE_CONVERSION_UNIMPLEMENTED();

  }

  DoubleChunk accumulator = 0;

  // First shift the digits so we don't overwrite them.

  const int copy_offset = used_bigits_;

  for (int i = 0; i < used_bigits_; ++i) {

    RawBigit(copy_offset + i) = RawBigit(i);

  }

  // We have two loops to avoid some 'if's in the loop.

  for (int i = 0; i < used_bigits_; ++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) {

      const Chunk chunk1 = RawBigit(copy_offset + bigit_index1);

      const Chunk chunk2 = RawBigit(copy_offset + bigit_index2);

      accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;

      bigit_index1--;

      bigit_index2++;

    }

    RawBigit(i) = static_cast<Chunk>(accumulator) & kBigitMask;

    accumulator >>= kBigitSize;

  }

  for (int i = used_bigits_; i < product_length; ++i) {

    int bigit_index1 = used_bigits_ - 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_bigits_) {

      const Chunk chunk1 = RawBigit(copy_offset + bigit_index1);

      const Chunk chunk2 = RawBigit(copy_offset + bigit_index2);

      accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;

      bigit_index1--;

      bigit_index2++;

    }

    // The overwritten RawBigit(i) will never be read in further loop iterations,

    // because bigit_index1 and bigit_index2 are always greater

    // than i - used_bigits_.

    RawBigit(i) = static_cast<Chunk>(accumulator) & kBigitMask;

    accumulator >>= kBigitSize;

  }

  // Since the result was guaranteed to lie inside the number the

  // accumulator must be 0 now.

  DOUBLE_CONVERSION_ASSERT(accumulator == 0);

  // Don't forget to update the used_digits and the exponent.

  used_bigits_ = static_cast<int16_t>(product_length);

  exponent_ *= 2;

  Clamp();

}

void Bignum::AssignPowerUInt16(uint16_t base, const int power_exponent) {

  DOUBLE_CONVERSION_ASSERT(base != 0);

  DOUBLE_CONVERSION_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++;

  }

  const 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_multiplication = 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) {

      DOUBLE_CONVERSION_ASSERT(bit_size > 0);

      const uint64_t base_bits_mask =

        ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1);

      const bool high_bits_zero = (this_value & base_bits_mask) == 0;

      if (high_bits_zero) {

        this_value *= base;

      } else {

        delayed_multiplication = true;

      }

    }

    mask >>= 1;

  }

  AssignUInt64(this_value);

  if (delayed_multiplication) {

    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) {

  DOUBLE_CONVERSION_ASSERT(IsClamped());

  DOUBLE_CONVERSION_ASSERT(other.IsClamped());

  DOUBLE_CONVERSION_ASSERT(other.used_bigits_ > 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 `this` divided by other

    // is big. This function is implemented for doubleToString where

    // the result should be small (less than 10).

    DOUBLE_CONVERSION_ASSERT(other.RawBigit(other.used_bigits_ - 1) >= ((1 << kBigitSize) / 16));

    DOUBLE_CONVERSION_ASSERT(RawBigit(used_bigits_ - 1) < 0x10000);

    // Remove the multiples of the first digit.

    // Example this = 23 and other equals 9. -> Remove 2 multiples.

    result += static_cast<uint16_t>(RawBigit(used_bigits_ - 1));

    SubtractTimes(other, RawBigit(used_bigits_ - 1));

  }

  DOUBLE_CONVERSION_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

  // RawBigit(used_bigits_ - 1) is safe.

  const Chunk this_bigit = RawBigit(used_bigits_ - 1);

  const Chunk other_bigit = other.RawBigit(other.used_bigits_ - 1);

  if (other.used_bigits_ == 1) {

    // Shortcut for easy (and common) case.

    int quotient = this_bigit / other_bigit;

    RawBigit(used_bigits_ - 1) = this_bigit - other_bigit * quotient;

    DOUBLE_CONVERSION_ASSERT(quotient < 0x10000);

    result += static_cast<uint16_t>(quotient);

    Clamp();

    return result;

  }

  const int division_estimate = this_bigit / (other_bigit + 1);

  DOUBLE_CONVERSION_ASSERT(division_estimate < 0x10000);

  result += static_cast<uint16_t>(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) {

  DOUBLE_CONVERSION_ASSERT(number > 0);

  int result = 0;

  while (number != 0) {

    number >>= 4;

    result++;

  }

  return result;

}

static char HexCharOfValue(const int value) {

  DOUBLE_CONVERSION_ASSERT(0 <= value && value <= 16);

  if (value < 10) {

    return static_cast<char>(value + '0');

  }

  return static_cast<char>(value - 10 + 'A');

}

bool Bignum::ToHexString(char* buffer, const int buffer_size) const {

  DOUBLE_CONVERSION_ASSERT(IsClamped());

  // Each bigit must be printable as separate hex-character.

  DOUBLE_CONVERSION_ASSERT(kBigitSize % 4 == 0);

  static const int kHexCharsPerBigit = kBigitSize / 4;

  if (used_bigits_ == 0) {

    if (buffer_size < 2) {

      return false;

    }

    buffer[0] = '0';

    buffer[1] = '\0';

    return true;

  }

  // We add 1 for the terminating '\0' character.

  const int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit +

    SizeInHexChars(RawBigit(used_bigits_ - 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_bigits_ - 1; ++i) {

    Chunk current_bigit = RawBigit(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 = RawBigit(used_bigits_ - 1);

  while (most_significant_bigit != 0) {

    buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF);

    most_significant_bigit >>= 4;

  }

  return true;

}

Bignum::Chunk Bignum::BigitOrZero(const int index) const {

  if (index >= BigitLength()) {

    return 0;

  }

  if (index < exponent_) {

    return 0;

  }

  return RawBigit(index - exponent_);

}

int Bignum::Compare(const Bignum& a, const Bignum& b) {

  DOUBLE_CONVERSION_ASSERT(a.IsClamped());

  DOUBLE_CONVERSION_ASSERT(b.IsClamped());

  const int bigit_length_a = a.BigitLength();

  const 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 >= (std::min)(a.exponent_, b.exponent_); --i) {

    const Chunk bigit_a = a.BigitOrZero(i);

    const Chunk bigit_b = b.BigitOrZero(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) {

  DOUBLE_CONVERSION_ASSERT(a.IsClamped());

  DOUBLE_CONVERSION_ASSERT(b.IsClamped());

  DOUBLE_CONVERSION_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.

  const int min_exponent = (std::min)((std::min)(a.exponent_, b.exponent_), c.exponent_);

  for (int i = c.BigitLength() - 1; i >= min_exponent; --i) {

    const Chunk chunk_a = a.BigitOrZero(i);

    const Chunk chunk_b = b.BigitOrZero(i);

    const Chunk chunk_c = c.BigitOrZero(i);

    const 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_bigits_ > 0 && RawBigit(used_bigits_ - 1) == 0) {

    used_bigits_--;

  }

  if (used_bigits_ == 0) {

    // Zero.

    exponent_ = 0;

  }

}

void Bignum::Align(const Bignum& other) {

  if (exponent_ > other.exponent_) {

    // If "X" represents a "hidden" bigit (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

    const int zero_bigits = exponent_ - other.exponent_;

    EnsureCapacity(used_bigits_ + zero_bigits);

    for (int i = used_bigits_ - 1; i >= 0; --i) {

      RawBigit(i + zero_bigits) = RawBigit(i);

    }

    for (int i = 0; i < zero_bigits; ++i) {

      RawBigit(i) = 0;

    }

    used_bigits_ += static_cast<int16_t>(zero_bigits);

    exponent_ -= static_cast<int16_t>(zero_bigits);

    DOUBLE_CONVERSION_ASSERT(used_bigits_ >= 0);

    DOUBLE_CONVERSION_ASSERT(exponent_ >= 0);

  }

}

void Bignum::BigitsShiftLeft(const int shift_amount) {

  DOUBLE_CONVERSION_ASSERT(shift_amount < kBigitSize);

  DOUBLE_CONVERSION_ASSERT(shift_amount >= 0);

  Chunk carry = 0;

  for (int i = 0; i < used_bigits_; ++i) {

    const Chunk new_carry = RawBigit(i) >> (kBigitSize - shift_amount);

    RawBigit(i) = ((RawBigit(i) << shift_amount) + carry) & kBigitMask;

    carry = new_carry;

  }

  if (carry != 0) {

    RawBigit(used_bigits_) = carry;

    used_bigits_++;

  }

}

void Bignum::SubtractTimes(const Bignum& other, const int factor) {

  DOUBLE_CONVERSION_ASSERT(exponent_ <= other.exponent_);

  if (factor < 3) {

    for (int i = 0; i < factor; ++i) {

      SubtractBignum(other);

    }

    return;

  }

  Chunk borrow = 0;

  const int exponent_diff = other.exponent_ - exponent_;

  for (int i = 0; i < other.used_bigits_; ++i) {

    const DoubleChunk product = static_cast<DoubleChunk>(factor) * other.RawBigit(i);

    const DoubleChunk remove = borrow + product;

    const Chunk difference = RawBigit(i + exponent_diff) - (remove & kBigitMask);

    RawBigit(i + exponent_diff) = difference & kBigitMask;

    borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) +

                                (remove >> kBigitSize));

  }

  for (int i = other.used_bigits_ + exponent_diff; i < used_bigits_; ++i) {

    if (borrow == 0) {

      return;

    }

    const Chunk difference = RawBigit(i) - borrow;

    RawBigit(i) = difference & kBigitMask;

    borrow = difference >> (kChunkSize - 1);

  }

  Clamp();

}

}  // namespace double_conversion