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 // Copyright 2010 the V8 project authors. All rights reserved.

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 // 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.

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 #include "bignum.h"

 #include "utils.h"

 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] = 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_] = 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] = tmp & kBigitMask;

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

         (product_high << (32 - kBigitSize));

   }

   while (carry != 0) {

     EnsureCapacity(used_digits_ + 1);

     bigits_[used_digits_] = 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 `this` divided by other

     // is 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] - (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);

   }

   Clamp();

 }

 }  // namespace double_conversion