Initial import

third_party/double-conversion/bignum.cc

@@ -0,0 +1,775 @@
+// 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 "libc/macros.h"
+#include "third_party/double-conversion/bignum.h"
+#include "third_party/double-conversion/utils.h"
+
+asm(".ident\t\"\\n\\n\
+double-conversion (BSD-3)\\n\
+Copyright 2010 the V8 project authors\"");
+asm(".include \"libc/disclaimer.inc\"");
+
+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;  // Accumulates converted hex digits until at least
+  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) {
+    RawBigit(used_bigits_++) = tmp;
+  }
+  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 + 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_ = 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_ += (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_ = 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 >= 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 = MIN(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_ += zero_bigits;
+    exponent_ -= 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