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double-conversion-bignum.cpp (25387B)

---

// © 2018 and later: Unicode, Inc. and others.
// License & terms of use: http://www.unicode.org/copyright.html
//
// From the double-conversion library. Original license:
//
// Copyright 2010 the V8 project authors. All rights reserved.
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// modification, are permitted provided that the following conditions are
// met:
//
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// ICU PATCH: ifdef around UCONFIG_NO_FORMATTING
#include "unicode/utypes.h"
#if !UCONFIG_NO_FORMATTING

#include <algorithm>
#include <cstring>

// ICU PATCH: Customize header file paths for ICU.

#include "double-conversion-bignum.h"
#include "double-conversion-utils.h"

// ICU PATCH: Wrap in ICU namespace
U_NAMESPACE_BEGIN

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

// ICU PATCH: Close ICU namespace
U_NAMESPACE_END
#endif // ICU PATCH: close #if !UCONFIG_NO_FORMATTING