Bignum implementation of Strtod.

This removes the dependency on Gay's strtod.

Review URL: http://codereview.chromium.org/4060001

git-svn-id: http://v8.googlecode.com/svn/branches/bleeding_edge@5778 ce2b1a6d-e550-0410-aec6-3dcde31c8c00

diff --git a/src/SConscript b/src/SConscript
index 596caf7f04931d0460fe57bf83f95d9ce604f4ff..030c64369bfda85f05f22010598b07479a746aac 100755 (executable)
--- a/src/SConscript
+++ b/src/SConscript
@@ -40,6 +40,7 @@ SOURCES = {
     api.cc
     assembler.cc
     ast.cc
+    bignum.cc
     bootstrapper.cc
     builtins.cc
     cached-powers.cc

diff --git a/src/bignum.cc b/src/bignum.cc
new file mode 100644 (file)
index 0000000..dd1537a
--- /dev/null
+++ b/src/bignum.cc
@@ -0,0 +1,767 @@
+// 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 "v8.h"
+
+#include "bignum.h"
+#include "utils.h"
+
+namespace v8 {
+namespace internal {
+
+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 = V8_2PART_UINT64_C(0x6765c793, fa10079d);
+  const uint16_t kFive1 = 5;
+  const uint16_t kFive2 = kFive1 * 5;
+  const uint16_t kFive3 = kFive2 * 5;
+  const uint16_t kFive4 = kFive3 * 5;
+  const uint16_t kFive5 = kFive4 * 5;
+  const uint16_t kFive6 = kFive5 * 5;
+  const uint32_t kFive7 = kFive6 * 5;
+  const uint32_t kFive8 = kFive7 * 5;
+  const uint32_t kFive9 = kFive8 * 5;
+  const uint32_t kFive10 = kFive9 * 5;
+  const uint32_t kFive11 = kFive10 * 5;
+  const uint32_t kFive12 = kFive11 * 5;
+  const uint32_t kFive13 = kFive12 * 5;
+  const uint32_t kFive1_to_12[] =
+      { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6,
+        kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 };
+
+  ASSERT(exponent >= 0);
+  if (exponent == 0) return;
+  if (used_digits_ == 0) return;
+
+  // We shift by exponent at the end just before returning.
+  int remaining_exponent = exponent;
+  while (remaining_exponent >= 27) {
+    MultiplyByUInt64(kFive27);
+    remaining_exponent -= 27;
+  }
+  while (remaining_exponent >= 13) {
+    MultiplyByUInt32(kFive13);
+    remaining_exponent -= 13;
+  }
+  if (remaining_exponent > 0) {
+    MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]);
+  }
+  ShiftLeft(exponent);
+}
+
+
+void Bignum::Square() {
+  ASSERT(IsClamped());
+  int product_length = 2 * used_digits_;
+  EnsureCapacity(product_length);
+
+  // Comba multiplication: compute each column separately.
+  // Example: r = a2a1a0 * b2b1b0.
+  //    r =  1    * a0b0 +
+  //        10    * (a1b0 + a0b1) +
+  //        100   * (a2b0 + a1b1 + a0b2) +
+  //        1000  * (a2b1 + a1b2) +
+  //        10000 * a2b2
+  //
+  // In the worst case we have to accumulate nb-digits products of digit*digit.
+  //
+  // Assert that the additional number of bits in a DoubleChunk are enough to
+  // sum up used_digits of Bigit*Bigit.
+  if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) {
+    UNIMPLEMENTED();
+  }
+  DoubleChunk accumulator = 0;
+  // First shift the digits so we don't overwrite them.
+  int copy_offset = used_digits_;
+  for (int i = 0; i < used_digits_; ++i) {
+    bigits_[copy_offset + i] = bigits_[i];
+  }
+  // We have two loops to avoid some 'if's in the loop.
+  for (int i = 0; i < used_digits_; ++i) {
+    // Process temporary digit i with power i.
+    // The sum of the two indices must be equal to i.
+    int bigit_index1 = i;
+    int bigit_index2 = 0;
+    // Sum all of the sub-products.
+    while (bigit_index1 >= 0) {
+      Chunk chunk1 = bigits_[copy_offset + bigit_index1];
+      Chunk chunk2 = bigits_[copy_offset + bigit_index2];
+      accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
+      bigit_index1--;
+      bigit_index2++;
+    }
+    bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
+    accumulator >>= kBigitSize;
+  }
+  for (int i = used_digits_; i < product_length; ++i) {
+    int bigit_index1 = used_digits_ - 1;
+    int bigit_index2 = i - bigit_index1;
+    // Invariant: sum of both indices is again equal to i.
+    // Inner loop runs 0 times on last iteration, emptying accumulator.
+    while (bigit_index2 < used_digits_) {
+      Chunk chunk1 = bigits_[copy_offset + bigit_index1];
+      Chunk chunk2 = bigits_[copy_offset + bigit_index2];
+      accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
+      bigit_index1--;
+      bigit_index2++;
+    }
+    // The overwritten bigits_[i] will never be read in further loop iterations,
+    // because bigit_index1 and bigit_index2 are always greater
+    // than i - used_digits_.
+    bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
+    accumulator >>= kBigitSize;
+  }
+  // Since the result was guaranteed to lie inside the number the
+  // accumulator must be 0 now.
+  ASSERT(accumulator == 0);
+
+  // Don't forget to update the used_digits and the exponent.
+  used_digits_ = product_length;
+  exponent_ *= 2;
+  Clamp();
+}
+
+
+void Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) {
+  ASSERT(base != 0);
+  ASSERT(power_exponent >= 0);
+  if (power_exponent == 0) {
+    AssignUInt16(1);
+    return;
+  }
+  Zero();
+  int shifts = 0;
+  // We expect base to be in range 2-32, and most often to be 10.
+  // It does not make much sense to implement different algorithms for counting
+  // the bits.
+  while ((base & 1) == 0) {
+    base >>= 1;
+    shifts++;
+  }
+  int bit_size = 0;
+  int tmp_base = base;
+  while (tmp_base != 0) {
+    tmp_base >>= 1;
+    bit_size++;
+  }
+  int final_size = bit_size * power_exponent;
+  // 1 extra bigit for the shifting, and one for rounded final_size.
+  EnsureCapacity(final_size / kBigitSize + 2);
+
+  // Left to Right exponentiation.
+  int mask = 1;
+  while (power_exponent >= mask) mask <<= 1;
+
+  // The mask is now pointing to the bit above the most significant 1-bit of
+  // power_exponent.
+  // Get rid of first 1-bit;
+  mask >>= 2;
+  uint64_t this_value = base;
+
+  bool delayed_multipliciation = false;
+  const uint64_t max_32bits = 0xFFFFFFFF;
+  while (mask != 0 && this_value <= max_32bits) {
+    this_value = this_value * this_value;
+    // Verify that there is enough space in this_value to perform the
+    // multiplication.  The first bit_size bits must be 0.
+    if ((power_exponent & mask) != 0) {
+      uint64_t base_bits_mask =
+          ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1);
+      bool high_bits_zero = (this_value & base_bits_mask) == 0;
+      if (high_bits_zero) {
+        this_value *= base;
+      } else {
+        delayed_multipliciation = true;
+      }
+    }
+    mask >>= 1;
+  }
+  AssignUInt64(this_value);
+  if (delayed_multipliciation) {
+    MultiplyByUInt32(base);
+  }
+
+  // Now do the same thing as a bignum.
+  while (mask != 0) {
+    Square();
+    if ((power_exponent & mask) != 0) {
+      MultiplyByUInt32(base);
+    }
+    mask >>= 1;
+  }
+
+  // And finally add the saved shifts.
+  ShiftLeft(shifts * power_exponent);
+}
+
+
+// Precondition: this/other < 16bit.
+uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) {
+  ASSERT(IsClamped());
+  ASSERT(other.IsClamped());
+  ASSERT(other.used_digits_ > 0);
+
+  // Easy case: if we have less digits than the divisor than the result is 0.
+  // Note: this handles the case where this == 0, too.
+  if (BigitLength() < other.BigitLength()) {
+    return 0;
+  }
+
+  Align(other);
+
+  uint16_t result = 0;
+
+  // Start by removing multiples of 'other' until both numbers have the same
+  // number of digits.
+  while (BigitLength() > other.BigitLength()) {
+    // This naive approach is extremely inefficient if the this divided other
+    // might be big. This function is implemented for doubleToString where
+    // the result should be small (less than 10).
+    ASSERT(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16));
+    // Remove the multiples of the first digit.
+    // Example this = 23 and other equals 9. -> Remove 2 multiples.
+    result += bigits_[used_digits_ - 1];
+    SubtractTimes(other, bigits_[used_digits_ - 1]);
+  }
+
+  ASSERT(BigitLength() == other.BigitLength());
+
+  // Both bignums are at the same length now.
+  // Since other has more than 0 digits we know that the access to
+  // bigits_[used_digits_ - 1] is safe.
+  Chunk this_bigit = bigits_[used_digits_ - 1];
+  Chunk other_bigit = other.bigits_[other.used_digits_ - 1];
+
+  if (other.used_digits_ == 1) {
+    // Shortcut for easy (and common) case.
+    int quotient = this_bigit / other_bigit;
+    bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient;
+    result += quotient;
+    Clamp();
+    return result;
+  }
+
+  int division_estimate = this_bigit / (other_bigit + 1);
+  result += division_estimate;
+  SubtractTimes(other, division_estimate);
+
+  if (other_bigit * (division_estimate + 1) > this_bigit) {
+    // No need to even try to subtract. Even if other's remaining digits were 0
+    // another subtraction would be too much.
+    return result;
+  }
+
+  while (LessEqual(other, *this)) {
+    SubtractBignum(other);
+    result++;
+  }
+  return result;
+}
+
+
+template<typename S>
+static int SizeInHexChars(S number) {
+  ASSERT(number > 0);
+  int result = 0;
+  while (number != 0) {
+    number >>= 4;
+    result++;
+  }
+  return result;
+}
+
+
+static char HexCharOfValue(int value) {
+  ASSERT(0 <= value && value <= 16);
+  if (value < 10) return value + '0';
+  return value - 10 + 'A';
+}
+
+
+bool Bignum::ToHexString(char* buffer, int buffer_size) const {
+  ASSERT(IsClamped());
+  // Each bigit must be printable as separate hex-character.
+  ASSERT(kBigitSize % 4 == 0);
+  const int kHexCharsPerBigit = kBigitSize / 4;
+
+  if (used_digits_ == 0) {
+    if (buffer_size < 2) return false;
+    buffer[0] = '0';
+    buffer[1] = '\0';
+    return true;
+  }
+  // We add 1 for the terminating '\0' character.
+  int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit +
+      SizeInHexChars(bigits_[used_digits_ - 1]) + 1;
+  if (needed_chars > buffer_size) return false;
+  int string_index = needed_chars - 1;
+  buffer[string_index--] = '\0';
+  for (int i = 0; i < exponent_; ++i) {
+    for (int j = 0; j < kHexCharsPerBigit; ++j) {
+      buffer[string_index--] = '0';
+    }
+  }
+  for (int i = 0; i < used_digits_ - 1; ++i) {
+    Chunk current_bigit = bigits_[i];
+    for (int j = 0; j < kHexCharsPerBigit; ++j) {
+      buffer[string_index--] = HexCharOfValue(current_bigit & 0xF);
+      current_bigit >>= 4;
+    }
+  }
+  // And finally the last bigit.
+  Chunk most_significant_bigit = bigits_[used_digits_ - 1];
+  while (most_significant_bigit != 0) {
+    buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF);
+    most_significant_bigit >>= 4;
+  }
+  return true;
+}
+
+
+Bignum::Chunk Bignum::BigitAt(int index) const {
+  if (index >= BigitLength()) return 0;
+  if (index < exponent_) return 0;
+  return bigits_[index - exponent_];
+}
+
+
+int Bignum::Compare(const Bignum& a, const Bignum& b) {
+  ASSERT(a.IsClamped());
+  ASSERT(b.IsClamped());
+  int bigit_length_a = a.BigitLength();
+  int bigit_length_b = b.BigitLength();
+  if (bigit_length_a < bigit_length_b) return -1;
+  if (bigit_length_a > bigit_length_b) return +1;
+  for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i) {
+    Chunk bigit_a = a.BigitAt(i);
+    Chunk bigit_b = b.BigitAt(i);
+    if (bigit_a < bigit_b) return -1;
+    if (bigit_a > bigit_b) return +1;
+    // Otherwise they are equal up to this digit. Try the next digit.
+  }
+  return 0;
+}
+
+
+int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) {
+  ASSERT(a.IsClamped());
+  ASSERT(b.IsClamped());
+  ASSERT(c.IsClamped());
+  if (a.BigitLength() < b.BigitLength()) {
+    return PlusCompare(b, a, c);
+  }
+  if (a.BigitLength() + 1 < c.BigitLength()) return -1;
+  if (a.BigitLength() > c.BigitLength()) return +1;
+  // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than
+  // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one
+  // of 'a'.
+  if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) {
+    return -1;
+  }
+
+  Chunk borrow = 0;
+  // Starting at min_exponent all digits are == 0. So no need to compare them.
+  int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_);
+  for (int i = c.BigitLength() - 1; i >= min_exponent; --i) {
+    Chunk chunk_a = a.BigitAt(i);
+    Chunk chunk_b = b.BigitAt(i);
+    Chunk chunk_c = c.BigitAt(i);
+    Chunk sum = chunk_a + chunk_b;
+    if (sum > chunk_c + borrow) {
+      return +1;
+    } else {
+      borrow = chunk_c + borrow - sum;
+      if (borrow > 1) return -1;
+      borrow <<= kBigitSize;
+    }
+  }
+  if (borrow == 0) return 0;
+  return -1;
+}
+
+
+void Bignum::Clamp() {
+  while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) {
+    used_digits_--;
+  }
+  if (used_digits_ == 0) {
+    // Zero.
+    exponent_ = 0;
+  }
+}
+
+
+bool Bignum::IsClamped() const {
+  return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0;
+}
+
+
+void Bignum::Zero() {
+  for (int i = 0; i < used_digits_; ++i) {
+    bigits_[i] = 0;
+  }
+  used_digits_ = 0;
+  exponent_ = 0;
+}
+
+
+void Bignum::Align(const Bignum& other) {
+  if (exponent_ > other.exponent_) {
+    // If "X" represents a "hidden" digit (by the exponent) then we are in the
+    // following case (a == this, b == other):
+    // a:  aaaaaaXXXX   or a:   aaaaaXXX
+    // b:     bbbbbbX      b: bbbbbbbbXX
+    // We replace some of the hidden digits (X) of a with 0 digits.
+    // a:  aaaaaa000X   or a:   aaaaa0XX
+    int zero_digits = exponent_ - other.exponent_;
+    EnsureCapacity(used_digits_ + zero_digits);
+    for (int i = used_digits_ - 1; i >= 0; --i) {
+      bigits_[i + zero_digits] = bigits_[i];
+    }
+    for (int i = 0; i < zero_digits; ++i) {
+      bigits_[i] = 0;
+    }
+    used_digits_ += zero_digits;
+    exponent_ -= zero_digits;
+    ASSERT(used_digits_ >= 0);
+    ASSERT(exponent_ >= 0);
+  }
+}
+
+
+void Bignum::BigitsShiftLeft(int shift_amount) {
+  ASSERT(shift_amount < kBigitSize);
+  ASSERT(shift_amount >= 0);
+  Chunk carry = 0;
+  for (int i = 0; i < used_digits_; ++i) {
+    Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount);
+    bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask;
+    carry = new_carry;
+  }
+  if (carry != 0) {
+    bigits_[used_digits_] = carry;
+    used_digits_++;
+  }
+}
+
+
+void Bignum::SubtractTimes(const Bignum& other, int factor) {
+  ASSERT(exponent_ <= other.exponent_);
+  if (factor < 3) {
+    for (int i = 0; i < factor; ++i) {
+      SubtractBignum(other);
+    }
+    return;
+  }
+  Chunk borrow = 0;
+  int exponent_diff = other.exponent_ - exponent_;
+  for (int i = 0; i < other.used_digits_; ++i) {
+    DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigits_[i];
+    DoubleChunk remove = borrow + product;
+    Chunk difference = bigits_[i + exponent_diff] - (remove & kBigitMask);
+    bigits_[i + exponent_diff] = difference & kBigitMask;
+    borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) +
+                                (remove >> kBigitSize));
+  }
+  for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) {
+    if (borrow == 0) return;
+    Chunk difference = bigits_[i] - borrow;
+    bigits_[i] = difference & kBigitMask;
+    borrow = difference >> (kChunkSize - 1);
+    ++i;
+  }
+  Clamp();
+}
+
+
+} }  // namespace v8::internal

diff --git a/src/bignum.h b/src/bignum.h
new file mode 100644 (file)
index 0000000..1d2bff6
--- /dev/null
+++ b/src/bignum.h
@@ -0,0 +1,140 @@
+// 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.
+
+#ifndef V8_BIGNUM_H_
+#define V8_BIGNUM_H_
+
+namespace v8 {
+namespace internal {
+
+class Bignum {
+ public:
+  // 3584 = 128 * 28. We can represent 2^3584 > 10^1000 accurately.
+  // This bignum can encode much bigger numbers, since it contains an
+  // exponent.
+  static const int kMaxSignificantBits = 3584;
+
+  Bignum();
+  void AssignUInt16(uint16_t value);
+  void AssignUInt64(uint64_t value);
+  void AssignBignum(const Bignum& other);
+
+  void AssignDecimalString(Vector<const char> value);
+  void AssignHexString(Vector<const char> value);
+
+  void AssignPowerUInt16(uint16_t base, int exponent);
+
+  void AddUInt16(uint16_t operand);
+  void AddUInt64(uint64_t operand);
+  void AddBignum(const Bignum& other);
+  // Precondition: this >= other.
+  void SubtractBignum(const Bignum& other);
+
+  void Square();
+  void ShiftLeft(int shift_amount);
+  void MultiplyByUInt32(uint32_t factor);
+  void MultiplyByUInt64(uint64_t factor);
+  void MultiplyByPowerOfTen(int exponent);
+  void Times10() { return MultiplyByUInt32(10); }
+  // Pseudocode:
+  //  int result = this / other;
+  //  this = this % other;
+  // In the worst case this function is in O(this/other).
+  uint16_t DivideModuloIntBignum(const Bignum& other);
+
+  bool ToHexString(char* buffer, int buffer_size) const;
+
+  static int Compare(const Bignum& a, const Bignum& b);
+  static bool Equal(const Bignum& a, const Bignum& b) {
+    return Compare(a, b) == 0;
+  }
+  static bool LessEqual(const Bignum& a, const Bignum& b) {
+    return Compare(a, b) <= 0;
+  }
+  static bool Less(const Bignum& a, const Bignum& b) {
+    return Compare(a, b) < 0;
+  }
+  // Returns Compare(a + b, c);
+  static int PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c);
+  // Returns a + b == c
+  static bool PlusEqual(const Bignum& a, const Bignum& b, const Bignum& c) {
+    return PlusCompare(a, b, c) == 0;
+  }
+  // Returns a + b <= c
+  static bool PlusLessEqual(const Bignum& a, const Bignum& b, const Bignum& c) {
+    return PlusCompare(a, b, c) <= 0;
+  }
+  // Returns a + b < c
+  static bool PlusLess(const Bignum& a, const Bignum& b, const Bignum& c) {
+    return PlusCompare(a, b, c) < 0;
+  }
+ private:
+  typedef uint32_t Chunk;
+  typedef uint64_t DoubleChunk;
+
+  static const int kChunkSize = sizeof(Chunk) * 8;
+  static const int kDoubleChunkSize = sizeof(DoubleChunk) * 8;
+  // With bigit size of 28 we loose some bits, but a double still fits easily
+  // into two chunks, and more importantly we can use the Comba multiplication.
+  static const int kBigitSize = 28;
+  static const Chunk kBigitMask = (1 << kBigitSize) - 1;
+  // Every instance allocates kBigitLength chunks on the stack. Bignums cannot
+  // grow. There are no checks if the stack-allocated space is sufficient.
+  static const int kBigitCapacity = kMaxSignificantBits / kBigitSize;
+
+  void EnsureCapacity(int size) {
+    if (size > kBigitCapacity) {
+      UNREACHABLE();
+    }
+  }
+  void Align(const Bignum& other);
+  void Clamp();
+  bool IsClamped() const;
+  void Zero();
+  // Requires this to have enough capacity (no tests done).
+  // Updates used_digits_ if necessary.
+  // by must be < kBigitSize.
+  void BigitsShiftLeft(int shift_amount);
+  // BigitLength includes the "hidden" digits encoded in the exponent.
+  int BigitLength() const { return used_digits_ + exponent_; }
+  Chunk BigitAt(int index) const;
+  void SubtractTimes(const Bignum& other, int factor);
+
+  Chunk bigits_buffer_[kBigitCapacity];
+  // A vector backed by bigits_buffer_. This way accesses to the array are
+  // checked for out-of-bounds errors.
+  Vector<Chunk> bigits_;
+  int used_digits_;
+  // The Bignum's value equals value(bigits_) * 2^(exponent_ * kBigitSize).
+  int exponent_;
+
+  DISALLOW_COPY_AND_ASSIGN(Bignum);
+};
+
+} }  // namespace v8::internal
+
+#endif  // V8_BIGNUM_H_

diff --git a/src/double.h b/src/double.h
index e805173e07e799249484df8f187c1c3ac61c05e5..9db8ea7c48b0339b5dab21a1a69cf991612b9efb 100644 (file)
--- a/src/double.h
+++ b/src/double.h
@@ -82,6 +82,11 @@ class Double {
     return d64_;
   }
 
+  double NextDouble() const {
+    if (d64_ == kInfinity) return kInfinity;
+    return Double(d64_ + 1).value();
+  }
+
   int Exponent() const {
     if (IsDenormal()) return kDenormalExponent;
 
@@ -120,19 +125,20 @@ class Double {
         ((d64 & kSignificandMask) != 0);
   }
 
-
   bool IsInfinite() const {
     uint64_t d64 = AsUint64();
     return ((d64 & kExponentMask) == kExponentMask) &&
         ((d64 & kSignificandMask) == 0);
   }
 
-
   int Sign() const {
     uint64_t d64 = AsUint64();
     return (d64 & kSignMask) == 0? 1: -1;
   }
 
+  DiyFp UpperBoundary() const {
+    return DiyFp(Significand() * 2 + 1, Exponent() - 1);
+  }
 
   // Returns the two boundaries of this.
   // The bigger boundary (m_plus) is normalized. The lower boundary has the same

diff --git a/src/strtod.cc b/src/strtod.cc
index 0ed1b0d914791280dea19a54837ebc6673f164ec..0523d885f97cfddd98f6f00f8583e7230128149a 100644 (file)
--- a/src/strtod.cc
+++ b/src/strtod.cc
@@ -31,6 +31,7 @@
 #include "v8.h"
 
 #include "strtod.h"
+#include "bignum.h"
 #include "cached-powers.h"
 #include "double.h"
 
@@ -83,44 +84,12 @@ static const double exact_powers_of_ten[] = {
   // 10^22 = 0x21e19e0c9bab2400000 = 0x878678326eac9 * 2^22
   10000000000000000000000.0
 };
-
 static const int kExactPowersOfTenSize = ARRAY_SIZE(exact_powers_of_ten);
 
-
-extern "C" double gay_strtod(const char* s00, const char** se);
-
-static double old_strtod(Vector<const char> buffer, int exponent) {
-  // gay_strtod is broken on Linux,x86. For numbers with few decimal digits
-  // the computation is done using floating-point operations which (on Linux)
-  // are prone to double-rounding errors.
-  // By adding several zeroes to the buffer gay_strtod falls back to a slower
-  // (but correct) algorithm.
-  const int kInsertedZeroesCount = 20;
-  char gay_buffer[1024];
-  Vector<char> gay_buffer_vector(gay_buffer, sizeof(gay_buffer));
-  int pos = 0;
-  for (int i = 0; i < buffer.length(); ++i) {
-    gay_buffer_vector[pos++] = buffer[i];
-  }
-  for (int i = 0; i < kInsertedZeroesCount; ++i) {
-    gay_buffer_vector[pos++] = '0';
-  }
-  exponent -= kInsertedZeroesCount;
-  gay_buffer_vector[pos++] = 'e';
-  if (exponent < 0) {
-    gay_buffer_vector[pos++] = '-';
-    exponent = -exponent;
-  }
-  const int kNumberOfExponentDigits = 5;
-  for (int i = kNumberOfExponentDigits - 1; i >= 0; i--) {
-    gay_buffer_vector[pos + i] = exponent % 10 + '0';
-    exponent /= 10;
-  }
-  pos += kNumberOfExponentDigits;
-  gay_buffer_vector[pos] = '\0';
-  return gay_strtod(gay_buffer, NULL);
-}
-
+// Maximum number of significant digits in the decimal representation.
+// In fact the value is 772 (see conversions.cc), but to give us some margin
+// we round up to 780.
+static const int kMaxSignificantDecimalDigits = 780;
 
 static Vector<const char> TrimLeadingZeros(Vector<const char> buffer) {
   for (int i = 0; i < buffer.length(); i++) {
@@ -142,6 +111,23 @@ static Vector<const char> TrimTrailingZeros(Vector<const char> buffer) {
 }
 
 
+static void TrimToMaxSignificantDigits(Vector<const char> buffer,
+                                       int exponent,
+                                       char* significant_buffer,
+                                       int* significant_exponent) {
+  for (int i = 0; i < kMaxSignificantDecimalDigits - 1; ++i) {
+    significant_buffer[i] = buffer[i];
+  }
+  // The input buffer has been trimmed. Therefore the last digit must be
+  // different from '0'.
+  ASSERT(buffer[buffer.length() - 1] != '0');
+  // Set the last digit to be non-zero. This is sufficient to guarantee
+  // correct rounding.
+  significant_buffer[kMaxSignificantDecimalDigits - 1] = '1';
+  *significant_exponent =
+      exponent + (buffer.length() - kMaxSignificantDecimalDigits);
+}
+
 // Reads digits from the buffer and converts them to a uint64.
 // Reads in as many digits as fit into a uint64.
 // When the string starts with "1844674407370955161" no further digit is read.
@@ -374,20 +360,81 @@ static bool DiyFpStrtod(Vector<const char> buffer,
 }
 
 
+// Returns the correct double for the buffer*10^exponent.
+// The variable guess should be a close guess that is either the correct double
+// or its lower neighbor (the nearest double less than the correct one).
+// Preconditions:
+//   buffer.length() + exponent <= kMaxDecimalPower + 1
+//   buffer.length() + exponent > kMinDecimalPower
+//   buffer.length() <= kMaxDecimalSignificantDigits
+static double BignumStrtod(Vector<const char> buffer,
+                           int exponent,
+                           double guess) {
+  if (guess == V8_INFINITY) {
+    return guess;
+  }
+
+  DiyFp upper_boundary = Double(guess).UpperBoundary();
+
+  ASSERT(buffer.length() + exponent <= kMaxDecimalPower + 1);
+  ASSERT(buffer.length() + exponent > kMinDecimalPower);
+  ASSERT(buffer.length() <= kMaxSignificantDecimalDigits);
+  // Make sure that the Bignum will be able to hold all our numbers.
+  // Our Bignum implementation has a separate field for exponents. Shifts will
+  // consume at most one bigit (< 64 bits).
+  // ln(10) == 3.3219...
+  ASSERT(((kMaxDecimalPower + 1) * 333 / 100) < Bignum::kMaxSignificantBits);
+  Bignum input;
+  Bignum boundary;
+  input.AssignDecimalString(buffer);
+  boundary.AssignUInt64(upper_boundary.f());
+  if (exponent >= 0) {
+    input.MultiplyByPowerOfTen(exponent);
+  } else {
+    boundary.MultiplyByPowerOfTen(-exponent);
+  }
+  if (upper_boundary.e() > 0) {
+    boundary.ShiftLeft(upper_boundary.e());
+  } else {
+    input.ShiftLeft(-upper_boundary.e());
+  }
+  int comparison = Bignum::Compare(input, boundary);
+  if (comparison < 0) {
+    return guess;
+  } else if (comparison > 0) {
+    return Double(guess).NextDouble();
+  } else if ((Double(guess).Significand() & 1) == 0) {
+    // Round towards even.
+    return guess;
+  } else {
+    return Double(guess).NextDouble();
+  }
+}
+
+
 double Strtod(Vector<const char> buffer, int exponent) {
   Vector<const char> left_trimmed = TrimLeadingZeros(buffer);
   Vector<const char> trimmed = TrimTrailingZeros(left_trimmed);
   exponent += left_trimmed.length() - trimmed.length();
   if (trimmed.length() == 0) return 0.0;
+  if (trimmed.length() > kMaxSignificantDecimalDigits) {
+    char significant_buffer[kMaxSignificantDecimalDigits];
+    int significant_exponent;
+    TrimToMaxSignificantDigits(trimmed, exponent,
+                               significant_buffer, &significant_exponent);
+    trimmed =
+        Vector<const char>(significant_buffer, kMaxSignificantDecimalDigits);
+    exponent = significant_exponent;
+  }
   if (exponent + trimmed.length() - 1 >= kMaxDecimalPower) return V8_INFINITY;
   if (exponent + trimmed.length() <= kMinDecimalPower) return 0.0;
 
-  double result;
-  if (DoubleStrtod(trimmed, exponent, &result) ||
-      DiyFpStrtod(trimmed, exponent, &result)) {
-    return result;
+  double guess;
+  if (DoubleStrtod(trimmed, exponent, &guess) ||
+      DiyFpStrtod(trimmed, exponent, &guess)) {
+    return guess;
   }
-  return old_strtod(trimmed, exponent);
+  return BignumStrtod(trimmed, exponent, guess);
 }
 
 } }  // namespace v8::internal

diff --git a/test/cctest/SConscript b/test/cctest/SConscript
index 006653c2e8e4156536155a3f0a5b1b103b38209f..620cd825cca98a867f5e344ee5eb7ef226c5f708 100644 (file)
--- a/test/cctest/SConscript
+++ b/test/cctest/SConscript
@@ -41,6 +41,7 @@ SOURCES = {
     'test-alloc.cc',
     'test-api.cc',
     'test-ast.cc',
+    'test-bignum.cc',
     'test-circular-queue.cc',
     'test-compiler.cc',
     'test-conversions.cc',

diff --git a/test/cctest/test-bignum.cc b/test/cctest/test-bignum.cc
new file mode 100644 (file)
index 0000000..9aa5ef3
--- /dev/null
+++ b/test/cctest/test-bignum.cc
@@ -0,0 +1,1502 @@
+// 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 <stdlib.h>
+
+#include "v8.h"
+
+#include "platform.h"
+#include "cctest.h"
+#include "bignum.h"
+
+using namespace v8::internal;
+
+
+static const int kBufferSize = 1024;
+
+static void AssignHexString(Bignum* bignum, const char* str) {
+  bignum->AssignHexString(Vector<const char>(str, StrLength(str)));
+}
+
+
+static void AssignDecimalString(Bignum* bignum, const char* str) {
+  bignum->AssignDecimalString(Vector<const char>(str, StrLength(str)));
+}
+
+
+TEST(Assign) {
+  char buffer[kBufferSize];
+  Bignum bignum;
+  Bignum bignum2;
+  bignum.AssignUInt16(0);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("0", buffer);
+  bignum.AssignUInt16(0xA);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("A", buffer);
+  bignum.AssignUInt16(0x20);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("20", buffer);
+
+
+  bignum.AssignUInt64(0);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("0", buffer);
+  bignum.AssignUInt64(0xA);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("A", buffer);
+  bignum.AssignUInt64(0x20);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("20", buffer);
+  bignum.AssignUInt64(0x100);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("100", buffer);
+
+  // The first real test, since this will not fit into one bigit.
+  bignum.AssignUInt64(0x12345678);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("12345678", buffer);
+
+  uint64_t big = V8_2PART_UINT64_C(0xFFFFFFFF, FFFFFFFF);
+  bignum.AssignUInt64(big);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("FFFFFFFFFFFFFFFF", buffer);
+
+  big = V8_2PART_UINT64_C(0x12345678, 9ABCDEF0);
+  bignum.AssignUInt64(big);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("123456789ABCDEF0", buffer);
+
+  bignum2.AssignBignum(bignum);
+  CHECK(bignum2.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("123456789ABCDEF0", buffer);
+
+  AssignDecimalString(&bignum, "0");
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("0", buffer);
+
+  AssignDecimalString(&bignum, "1");
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1", buffer);
+
+  AssignDecimalString(&bignum, "1234567890");
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("499602D2", buffer);
+
+  AssignHexString(&bignum, "0");
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("0", buffer);
+
+  AssignHexString(&bignum, "123456789ABCDEF0");
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("123456789ABCDEF0", buffer);
+}
+
+
+TEST(ShiftLeft) {
+  char buffer[kBufferSize];
+  Bignum bignum;
+  AssignHexString(&bignum, "0");
+  bignum.ShiftLeft(100);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("0", buffer);
+
+  AssignHexString(&bignum, "1");
+  bignum.ShiftLeft(1);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("2", buffer);
+
+  AssignHexString(&bignum, "1");
+  bignum.ShiftLeft(4);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("10", buffer);
+
+  AssignHexString(&bignum, "1");
+  bignum.ShiftLeft(32);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("100000000", buffer);
+
+  AssignHexString(&bignum, "1");
+  bignum.ShiftLeft(64);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("10000000000000000", buffer);
+
+  AssignHexString(&bignum, "123456789ABCDEF");
+  bignum.ShiftLeft(64);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("123456789ABCDEF0000000000000000", buffer);
+  bignum.ShiftLeft(1);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("2468ACF13579BDE0000000000000000", buffer);
+}
+
+
+TEST(AddUInt64) {
+  char buffer[kBufferSize];
+  Bignum bignum;
+  AssignHexString(&bignum, "0");
+  bignum.AddUInt64(0xA);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("A", buffer);
+
+  AssignHexString(&bignum, "1");
+  bignum.AddUInt64(0xA);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("B", buffer);
+
+  AssignHexString(&bignum, "1");
+  bignum.AddUInt64(0x100);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("101", buffer);
+
+  AssignHexString(&bignum, "1");
+  bignum.AddUInt64(0xFFFF);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("10000", buffer);
+
+  AssignHexString(&bignum, "FFFFFFF");
+  bignum.AddUInt64(0x1);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("10000000", buffer);
+
+  AssignHexString(&bignum, "10000000000000000000000000000000000000000000");
+  bignum.AddUInt64(0xFFFF);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1000000000000000000000000000000000000000FFFF", buffer);
+
+  AssignHexString(&bignum, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF");
+  bignum.AddUInt64(0x1);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("100000000000000000000000000000000000000000000", buffer);
+
+  bignum.AssignUInt16(0x1);
+  bignum.ShiftLeft(100);
+  bignum.AddUInt64(1);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("10000000000000000000000001", buffer);
+
+  bignum.AssignUInt16(0x1);
+  bignum.ShiftLeft(100);
+  bignum.AddUInt64(0xFFFF);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1000000000000000000000FFFF", buffer);
+
+  AssignHexString(&bignum, "0");
+  bignum.AddUInt64(V8_2PART_UINT64_C(0xA, 00000000));
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("A00000000", buffer);
+
+  AssignHexString(&bignum, "1");
+  bignum.AddUInt64(V8_2PART_UINT64_C(0xA, 00000000));
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("A00000001", buffer);
+
+  AssignHexString(&bignum, "1");
+  bignum.AddUInt64(V8_2PART_UINT64_C(0x100, 00000000));
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("10000000001", buffer);
+
+  AssignHexString(&bignum, "1");
+  bignum.AddUInt64(V8_2PART_UINT64_C(0xFFFF, 00000000));
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("FFFF00000001", buffer);
+
+  AssignHexString(&bignum, "FFFFFFF");
+  bignum.AddUInt64(V8_2PART_UINT64_C(0x1, 00000000));
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("10FFFFFFF", buffer);
+
+  AssignHexString(&bignum, "10000000000000000000000000000000000000000000");
+  bignum.AddUInt64(V8_2PART_UINT64_C(0xFFFF, 00000000));
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("10000000000000000000000000000000FFFF00000000", buffer);
+
+  AssignHexString(&bignum, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF");
+  bignum.AddUInt64(V8_2PART_UINT64_C(0x1, 00000000));
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1000000000000000000000000000000000000FFFFFFFF", buffer);
+
+  bignum.AssignUInt16(0x1);
+  bignum.ShiftLeft(100);
+  bignum.AddUInt64(V8_2PART_UINT64_C(0x1, 00000000));
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("10000000000000000100000000", buffer);
+
+  bignum.AssignUInt16(0x1);
+  bignum.ShiftLeft(100);
+  bignum.AddUInt64(V8_2PART_UINT64_C(0xFFFF, 00000000));
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("10000000000000FFFF00000000", buffer);
+}
+
+
+TEST(AddBignum) {
+  char buffer[kBufferSize];
+  Bignum bignum;
+  Bignum other;
+
+  AssignHexString(&other, "1");
+  AssignHexString(&bignum, "0");
+  bignum.AddBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1", buffer);
+
+  AssignHexString(&bignum, "1");
+  bignum.AddBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("2", buffer);
+
+  AssignHexString(&bignum, "FFFFFFF");
+  bignum.AddBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("10000000", buffer);
+
+  AssignHexString(&bignum, "FFFFFFFFFFFFFF");
+  bignum.AddBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("100000000000000", buffer);
+
+  AssignHexString(&bignum, "10000000000000000000000000000000000000000000");
+  bignum.AddBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("10000000000000000000000000000000000000000001", buffer);
+
+  AssignHexString(&other, "1000000000000");
+
+  AssignHexString(&bignum, "1");
+  bignum.AddBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1000000000001", buffer);
+
+  AssignHexString(&bignum, "FFFFFFF");
+  bignum.AddBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("100000FFFFFFF", buffer);
+
+  AssignHexString(&bignum, "10000000000000000000000000000000000000000000");
+  bignum.AddBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("10000000000000000000000000000001000000000000", buffer);
+
+  AssignHexString(&bignum, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF");
+  bignum.AddBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1000000000000000000000000000000FFFFFFFFFFFF", buffer);
+
+  bignum.AssignUInt16(0x1);
+  bignum.ShiftLeft(100);
+  bignum.AddBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("10000000000001000000000000", buffer);
+
+  other.ShiftLeft(64);
+  // other == "10000000000000000000000000000"
+
+  bignum.AssignUInt16(0x1);
+  bignum.AddBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("10000000000000000000000000001", buffer);
+
+  AssignHexString(&bignum, "FFFFFFF");
+  bignum.AddBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1000000000000000000000FFFFFFF", buffer);
+
+  AssignHexString(&bignum, "10000000000000000000000000000000000000000000");
+  bignum.AddBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("10000000000000010000000000000000000000000000", buffer);
+
+  AssignHexString(&bignum, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF");
+  bignum.AddBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("100000000000000FFFFFFFFFFFFFFFFFFFFFFFFFFFF", buffer);
+
+  bignum.AssignUInt16(0x1);
+  bignum.ShiftLeft(100);
+  bignum.AddBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("10010000000000000000000000000", buffer);
+}
+
+
+TEST(SubtractBignum) {
+  char buffer[kBufferSize];
+  Bignum bignum;
+  Bignum other;
+
+  AssignHexString(&bignum, "1");
+  AssignHexString(&other, "0");
+  bignum.SubtractBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1", buffer);
+
+  AssignHexString(&bignum, "2");
+  AssignHexString(&other, "0");
+  bignum.SubtractBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("2", buffer);
+
+  AssignHexString(&bignum, "10000000");
+  AssignHexString(&other, "1");
+  bignum.SubtractBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("FFFFFFF", buffer);
+
+  AssignHexString(&bignum, "100000000000000");
+  AssignHexString(&other, "1");
+  bignum.SubtractBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("FFFFFFFFFFFFFF", buffer);
+
+  AssignHexString(&bignum, "10000000000000000000000000000000000000000001");
+  AssignHexString(&other, "1");
+  bignum.SubtractBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("10000000000000000000000000000000000000000000", buffer);
+
+  AssignHexString(&bignum, "1000000000001");
+  AssignHexString(&other, "1000000000000");
+  bignum.SubtractBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1", buffer);
+
+  AssignHexString(&bignum, "100000FFFFFFF");
+  AssignHexString(&other, "1000000000000");
+  bignum.SubtractBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("FFFFFFF", buffer);
+
+  AssignHexString(&bignum, "10000000000000000000000000000001000000000000");
+  AssignHexString(&other, "1000000000000");
+  bignum.SubtractBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("10000000000000000000000000000000000000000000", buffer);
+
+  AssignHexString(&bignum, "1000000000000000000000000000000FFFFFFFFFFFF");
+  AssignHexString(&other, "1000000000000");
+  bignum.SubtractBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", buffer);
+
+  bignum.AssignUInt16(0x1);
+  bignum.ShiftLeft(100);
+  // "10 0000 0000 0000 0000 0000 0000"
+  AssignHexString(&other, "1000000000000");
+  bignum.SubtractBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("FFFFFFFFFFFFF000000000000", buffer);
+
+  AssignHexString(&other, "1000000000000");
+  other.ShiftLeft(48);
+  // other == "1000000000000000000000000"
+
+  bignum.AssignUInt16(0x1);
+  bignum.ShiftLeft(100);
+  // bignum == "10000000000000000000000000"
+  bignum.SubtractBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("F000000000000000000000000", buffer);
+
+  other.AssignUInt16(0x1);
+  other.ShiftLeft(35);
+  // other == "800000000"
+  AssignHexString(&bignum, "FFFFFFF");
+  bignum.ShiftLeft(60);
+  // bignum = FFFFFFF000000000000000
+  bignum.SubtractBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("FFFFFFEFFFFFF800000000", buffer);
+
+  AssignHexString(&bignum, "10000000000000000000000000000000000000000000");
+  bignum.SubtractBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF800000000", buffer);
+
+  AssignHexString(&bignum, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF");
+  bignum.SubtractBignum(other);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFF", buffer);
+}
+
+
+TEST(MultiplyUInt32) {
+  char buffer[kBufferSize];
+  Bignum bignum;
+
+  AssignHexString(&bignum, "0");
+  bignum.MultiplyByUInt32(0x25);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("0", buffer);
+
+  AssignHexString(&bignum, "2");
+  bignum.MultiplyByUInt32(0x5);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("A", buffer);
+
+  AssignHexString(&bignum, "10000000");
+  bignum.MultiplyByUInt32(0x9);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("90000000", buffer);
+
+  AssignHexString(&bignum, "100000000000000");
+  bignum.MultiplyByUInt32(0xFFFF);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("FFFF00000000000000", buffer);
+
+  AssignHexString(&bignum, "100000000000000");
+  bignum.MultiplyByUInt32(0xFFFFFFFF);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("FFFFFFFF00000000000000", buffer);
+
+  AssignHexString(&bignum, "1234567ABCD");
+  bignum.MultiplyByUInt32(0xFFF);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("12333335552433", buffer);
+
+  AssignHexString(&bignum, "1234567ABCD");
+  bignum.MultiplyByUInt32(0xFFFFFFF);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("12345679998A985433", buffer);
+
+  AssignHexString(&bignum, "FFFFFFFFFFFFFFFF");
+  bignum.MultiplyByUInt32(0x2);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1FFFFFFFFFFFFFFFE", buffer);
+
+  AssignHexString(&bignum, "FFFFFFFFFFFFFFFF");
+  bignum.MultiplyByUInt32(0x4);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("3FFFFFFFFFFFFFFFC", buffer);
+
+  AssignHexString(&bignum, "FFFFFFFFFFFFFFFF");
+  bignum.MultiplyByUInt32(0xF);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("EFFFFFFFFFFFFFFF1", buffer);
+
+  AssignHexString(&bignum, "FFFFFFFFFFFFFFFF");
+  bignum.MultiplyByUInt32(0xFFFFFF);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("FFFFFEFFFFFFFFFF000001", buffer);
+
+  bignum.AssignUInt16(0x1);
+  bignum.ShiftLeft(100);
+  // "10 0000 0000 0000 0000 0000 0000"
+  bignum.MultiplyByUInt32(2);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("20000000000000000000000000", buffer);
+
+  bignum.AssignUInt16(0x1);
+  bignum.ShiftLeft(100);
+  // "10 0000 0000 0000 0000 0000 0000"
+  bignum.MultiplyByUInt32(0xF);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("F0000000000000000000000000", buffer);
+
+  bignum.AssignUInt16(0xFFFF);
+  bignum.ShiftLeft(100);
+  // "FFFF0 0000 0000 0000 0000 0000 0000"
+  bignum.MultiplyByUInt32(0xFFFF);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("FFFE00010000000000000000000000000", buffer);
+
+  bignum.AssignUInt16(0xFFFF);
+  bignum.ShiftLeft(100);
+  // "FFFF0 0000 0000 0000 0000 0000 0000"
+  bignum.MultiplyByUInt32(0xFFFFFFFF);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("FFFEFFFF00010000000000000000000000000", buffer);
+
+  bignum.AssignUInt16(0xFFFF);
+  bignum.ShiftLeft(100);
+  // "FFFF0 0000 0000 0000 0000 0000 0000"
+  bignum.MultiplyByUInt32(0xFFFFFFFF);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("FFFEFFFF00010000000000000000000000000", buffer);
+
+  AssignDecimalString(&bignum, "15611230384529777");
+  bignum.MultiplyByUInt32(10000000);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("210EDD6D4CDD2580EE80", buffer);
+}
+
+
+TEST(MultiplyUInt64) {
+  char buffer[kBufferSize];
+  Bignum bignum;
+
+  AssignHexString(&bignum, "0");
+  bignum.MultiplyByUInt64(0x25);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("0", buffer);
+
+  AssignHexString(&bignum, "2");
+  bignum.MultiplyByUInt64(0x5);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("A", buffer);
+
+  AssignHexString(&bignum, "10000000");
+  bignum.MultiplyByUInt64(0x9);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("90000000", buffer);
+
+  AssignHexString(&bignum, "100000000000000");
+  bignum.MultiplyByUInt64(0xFFFF);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("FFFF00000000000000", buffer);
+
+  AssignHexString(&bignum, "100000000000000");
+  bignum.MultiplyByUInt64(V8_2PART_UINT64_C(0xFFFFFFFF, FFFFFFFF));
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("FFFFFFFFFFFFFFFF00000000000000", buffer);
+
+  AssignHexString(&bignum, "1234567ABCD");
+  bignum.MultiplyByUInt64(0xFFF);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("12333335552433", buffer);
+
+  AssignHexString(&bignum, "1234567ABCD");
+  bignum.MultiplyByUInt64(V8_2PART_UINT64_C(0xFF, FFFFFFFF));
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1234567ABCBDCBA985433", buffer);
+
+  AssignHexString(&bignum, "FFFFFFFFFFFFFFFF");
+  bignum.MultiplyByUInt64(0x2);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1FFFFFFFFFFFFFFFE", buffer);
+
+  AssignHexString(&bignum, "FFFFFFFFFFFFFFFF");
+  bignum.MultiplyByUInt64(0x4);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("3FFFFFFFFFFFFFFFC", buffer);
+
+  AssignHexString(&bignum, "FFFFFFFFFFFFFFFF");
+  bignum.MultiplyByUInt64(0xF);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("EFFFFFFFFFFFFFFF1", buffer);
+
+  AssignHexString(&bignum, "FFFFFFFFFFFFFFFF");
+  bignum.MultiplyByUInt64(V8_2PART_UINT64_C(0xFFFFFFFF, FFFFFFFF));
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("FFFFFFFFFFFFFFFE0000000000000001", buffer);
+
+  bignum.AssignUInt16(0x1);
+  bignum.ShiftLeft(100);
+  // "10 0000 0000 0000 0000 0000 0000"
+  bignum.MultiplyByUInt64(2);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("20000000000000000000000000", buffer);
+
+  bignum.AssignUInt16(0x1);
+  bignum.ShiftLeft(100);
+  // "10 0000 0000 0000 0000 0000 0000"
+  bignum.MultiplyByUInt64(0xF);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("F0000000000000000000000000", buffer);
+
+  bignum.AssignUInt16(0xFFFF);
+  bignum.ShiftLeft(100);
+  // "FFFF0 0000 0000 0000 0000 0000 0000"
+  bignum.MultiplyByUInt64(0xFFFF);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("FFFE00010000000000000000000000000", buffer);
+
+  bignum.AssignUInt16(0xFFFF);
+  bignum.ShiftLeft(100);
+  // "FFFF0 0000 0000 0000 0000 0000 0000"
+  bignum.MultiplyByUInt64(0xFFFFFFFF);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("FFFEFFFF00010000000000000000000000000", buffer);
+
+  bignum.AssignUInt16(0xFFFF);
+  bignum.ShiftLeft(100);
+  // "FFFF0 0000 0000 0000 0000 0000 0000"
+  bignum.MultiplyByUInt64(V8_2PART_UINT64_C(0xFFFFFFFF, FFFFFFFF));
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("FFFEFFFFFFFFFFFF00010000000000000000000000000", buffer);
+
+  AssignDecimalString(&bignum, "15611230384529777");
+  bignum.MultiplyByUInt64(V8_2PART_UINT64_C(0x8ac72304, 89e80000));
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1E10EE4B11D15A7F3DE7F3C7680000", buffer);
+}
+
+
+TEST(MultiplyPowerOfTen) {
+  char buffer[kBufferSize];
+  Bignum bignum;
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(1);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("3034", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(2);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1E208", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(3);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("12D450", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(4);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("BC4B20", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(5);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("75AEF40", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(6);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("498D5880", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(7);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("2DF857500", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(8);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1CBB369200", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(9);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("11F5021B400", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(10);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("B3921510800", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(11);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("703B4D2A5000", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(12);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("4625103A72000", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(13);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("2BD72A24874000", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(14);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1B667A56D488000", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(15);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("11200C7644D50000", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(16);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("AB407C9EB0520000", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(17);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("6B084DE32E3340000", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(18);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("42E530ADFCE0080000", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(19);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("29CF3E6CBE0C0500000", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(20);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1A218703F6C783200000", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(21);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1054F4627A3CB1F400000", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(22);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("A3518BD8C65EF38800000", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(23);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("6612F7677BFB5835000000", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(24);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("3FCBDAA0AD7D17212000000", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(25);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("27DF68A46C6E2E74B4000000", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(26);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("18EBA166C3C4DD08F08000000", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(27);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("F9344E03A5B0A259650000000", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(28);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("9BC0B0C2478E6577DF20000000", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(29);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("61586E796CB8FF6AEB740000000", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(30);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("3CD7450BE3F39FA2D32880000000", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(31);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("26068B276E7843C5C3F9500000000", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(50);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("149D1B4CFED03B23AB5F4E1196EF45C08000000000000", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(100);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("5827249F27165024FBC47DFCA9359BF316332D1B91ACEECF471FBAB06D9B2"
+           "0000000000000000000000000", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(200);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("64C1F5C06C3816AFBF8DAFD5A3D756365BB0FD020E6F084E759C1F7C99E4F"
+           "55B9ACC667CEC477EB958C2AEEB3C6C19BA35A1AD30B35C51EB72040920000"
+           "0000000000000000000000000000000000000000000000", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(500);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("96741A625EB5D7C91039FEB5C5ACD6D9831EDA5B083D800E6019442C8C8223"
+           "3EAFB3501FE2058062221E15121334928880827DEE1EC337A8B26489F3A40A"
+           "CB440A2423734472D10BFCE886F41B3AF9F9503013D86D088929CA86EEB4D8"
+           "B9C831D0BD53327B994A0326227CFD0ECBF2EB48B02387AAE2D4CCCDF1F1A1"
+           "B8CC4F1FA2C56AD40D0E4DAA9C28CDBF0A549098EA13200000000000000000"
+           "00000000000000000000000000000000000000000000000000000000000000"
+           "0000000000000000000000000000000000000000000000", buffer);
+
+  AssignDecimalString(&bignum, "1234");
+  bignum.MultiplyByPowerOfTen(1000);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1258040F99B1CD1CC9819C676D413EA50E4A6A8F114BB0C65418C62D399B81"
+           "6361466CA8E095193E1EE97173553597C96673AF67FAFE27A66E7EF2E5EF2E"
+           "E3F5F5070CC17FE83BA53D40A66A666A02F9E00B0E11328D2224B8694C7372"
+           "F3D536A0AD1985911BD361496F268E8B23112500EAF9B88A9BC67B2AB04D38"
+           "7FEFACD00F5AF4F764F9ABC3ABCDE54612DE38CD90CB6647CA389EA0E86B16"
+           "BF7A1F34086E05ADBE00BD1673BE00FAC4B34AF1091E8AD50BA675E0381440"
+           "EA8E9D93E75D816BAB37C9844B1441C38FC65CF30ABB71B36433AF26DD97BD"
+           "ABBA96C03B4919B8F3515B92826B85462833380DC193D79F69D20DD6038C99"
+           "6114EF6C446F0BA28CC772ACBA58B81C04F8FFDE7B18C4E5A3ABC51E637FDF"
+           "6E37FDFF04C940919390F4FF92000000000000000000000000000000000000"
+           "00000000000000000000000000000000000000000000000000000000000000"
+           "00000000000000000000000000000000000000000000000000000000000000"
+           "00000000000000000000000000000000000000000000000000000000000000"
+           "0000000000000000000000000000", buffer);
+
+  Bignum bignum2;
+  AssignHexString(&bignum2, "3DA774C07FB5DF54284D09C675A492165B830D5DAAEB2A7501"
+                            "DA17CF9DFA1CA2282269F92A25A97314296B717E3DCBB9FE17"
+                            "41A842FE2913F540F40796F2381155763502C58B15AF7A7F88"
+                            "6F744C9164FF409A28F7FA0C41F89ED79C1BE9F322C8578B97"
+                            "841F1CBAA17D901BE1230E3C00E1C643AF32638B5674E01FEA"
+                            "96FC90864E621B856A9E1CE56E6EB545B9C2F8F0CC10DDA88D"
+                            "CC6D282605F8DB67044F2DFD3695E7BA63877AE16701536AE6"
+                            "567C794D0BFE338DFBB42D92D4215AF3BB22BF0A8B283FDDC2"
+                            "C667A10958EA6D2");
+  CHECK(bignum2.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("3DA774C07FB5DF54284D09C675A492165B830D5DAAEB2A7501"
+           "DA17CF9DFA1CA2282269F92A25A97314296B717E3DCBB9FE17"
+           "41A842FE2913F540F40796F2381155763502C58B15AF7A7F88"
+           "6F744C9164FF409A28F7FA0C41F89ED79C1BE9F322C8578B97"
+           "841F1CBAA17D901BE1230E3C00E1C643AF32638B5674E01FEA"
+           "96FC90864E621B856A9E1CE56E6EB545B9C2F8F0CC10DDA88D"
+           "CC6D282605F8DB67044F2DFD3695E7BA63877AE16701536AE6"
+           "567C794D0BFE338DFBB42D92D4215AF3BB22BF0A8B283FDDC2"
+           "C667A10958EA6D2", buffer);
+
+  bignum.AssignBignum(bignum2);
+  bignum.MultiplyByPowerOfTen(1);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("2688A8F84FD1AB949930261C0986DB4DF931E85A8AD2FA8921284EE1C2BC51"
+           "E55915823BBA5789E7EC99E326EEE69F543ECE890929DED9AC79489884BE57"
+           "630AD569E121BB76ED8DAC8FB545A8AFDADF1F8860599AFC47A93B6346C191"
+           "7237F5BD36B73EB29371F4A4EE7A116CB5E8E5808D1BEA4D7F7E3716090C13"
+           "F29E5DDA53F0FD513362A2D20F6505314B9419DB967F8A8A89589FC43917C3"
+           "BB892062B17CBE421DB0D47E34ACCCE060D422CFF60DCBD0277EE038BD509C"
+           "7BC494D8D854F5B76696F927EA99BC00C4A5D7928434", buffer);
+
+  bignum.AssignBignum(bignum2);
+  bignum.MultiplyByPowerOfTen(2);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1815699B31E30B3CDFBE17D185F44910BBBF313896C3DC95B4B9314D19B5B32"
+           "F57AD71655476B630F3E02DF855502394A74115A5BA2B480BCBCD5F52F6F69D"
+           "E6C5622CB5152A54788BD9D14B896DE8CB73B53C3800DDACC9C51E0C38FAE76"
+           "2F9964232872F9C2738E7150C4AE3F1B18F70583172706FAEE26DC5A78C77A2"
+           "FAA874769E52C01DA5C3499F233ECF3C90293E0FB69695D763DAA3AEDA5535B"
+           "43DAEEDF6E9528E84CEE0EC000C3C8495C1F9C89F6218AF4C23765261CD5ADD"
+           "0787351992A01E5BB8F2A015807AE7A6BB92A08", buffer);
+
+  bignum.AssignBignum(bignum2);
+  bignum.MultiplyByPowerOfTen(5);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("5E13A4863ADEE3E5C9FE8D0A73423D695D62D8450CED15A8C9F368952C6DC3"
+           "F0EE7D82F3D1EFB7AF38A3B3920D410AFCAD563C8F5F39116E141A3C5C14B3"
+           "58CD73077EA35AAD59F6E24AD98F10D5555ABBFBF33AC361EAF429FD5FBE94"
+           "17DA9EF2F2956011F9F93646AA38048A681D984ED88127073443247CCC167C"
+           "B354A32206EF5A733E73CF82D795A1AD598493211A6D613C39515E0E0F6304"
+           "DCD9C810F3518C7F6A7CB6C81E99E02FCC65E8FDB7B7AE97306CC16A8631CE"
+           "0A2AEF6568276BE4C176964A73C153FDE018E34CB4C2F40", buffer);
+
+  bignum.AssignBignum(bignum2);
+  bignum.MultiplyByPowerOfTen(10);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("8F8CB8EB51945A7E815809F6121EF2F4E61EF3405CD9432CAD2709749EEAFD"
+           "1B81E843F14A3667A7BDCCC9E0BB795F63CDFDB62844AC7438976C885A0116"
+           "29607DA54F9C023CC366570B7637ED0F855D931752038A614922D0923E382C"
+           "B8E5F6C975672DB76E0DE471937BB9EDB11E28874F1C122D5E1EF38CECE9D0"
+           "0723056BCBD4F964192B76830634B1D322B7EB0062F3267E84F5C824343A77"
+           "4B7DCEE6DD464F01EBDC8C671BB18BB4EF4300A42474A6C77243F2A12B03BF"
+           "0443C38A1C0D2701EDB393135AE0DEC94211F9D4EB51F990800", buffer);
+
+  bignum.AssignBignum(bignum2);
+  bignum.MultiplyByPowerOfTen(50);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("107A8BE345E24407372FC1DE442CBA696BC23C4FFD5B4BDFD9E5C39559815"
+           "86628CF8472D2D589F2FC2BAD6E0816EC72CBF85CCA663D8A1EC6C51076D8"
+           "2D247E6C26811B7EC4D4300FB1F91028DCB7B2C4E7A60C151161AA7E65E79"
+           "B40917B12B2B5FBE7745984D4E8EFA31F9AE6062427B068B144A9CB155873"
+           "E7C0C9F0115E5AC72DC5A73C4796DB970BF9205AB8C77A6996EB1B417F9D1"
+           "6232431E6313C392203601B9C22CC10DDA88DCC6D282605F8DB67044F2DFD"
+           "3695E7BA63877AE16701536AE6567C794D0BFE338DFBB42D924CF964BD2C0"
+           "F586E03A2FCD35A408000000000000", buffer);
+
+  bignum.AssignBignum(bignum2);
+  bignum.MultiplyByPowerOfTen(100);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("46784A90ACD0ED3E7759CC585FB32D36EB6034A6F78D92604E3BAA5ED3D8B"
+           "6E60E854439BE448897FB4B7EA5A3D873AA0FCB3CFFD80D0530880E45F511"
+           "722A50CE7E058B5A6F5464DB7500E34984EE3202A9441F44FA1554C0CEA96"
+           "B438A36F25E7C9D56D71AE2CD313EC37534DA299AC0854FC48591A7CF3171"
+           "31265AA4AE62DE32344CE7BEEEF894AE686A2DAAFE5D6D9A10971FFD9C064"
+           "5079B209E1048F58B5192D41D84336AC4C8C489EEF00939CFC9D55C122036"
+           "01B9C22CC10DDA88DCC6D282605F8DB67044F2DFD3695E7BA3F67B96D3A32"
+           "E11FB5561B68744C4035B0800DC166D49D98E3FD1D5BB2000000000000000"
+           "0000000000", buffer);
+
+  bignum.AssignBignum(bignum2);
+  bignum.MultiplyByPowerOfTen(200);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("508BD351221DF139D72D88CDC0416845A53EE2D0E6B98352509A9AC312F8C"
+           "6CB1A144889416201E0B6CE66EA3EBE259B5FD79ECFC1FD77963CE516CC7E"
+           "2FE73D4B5B710C19F6BCB092C7A2FD76286543B8DBD2C596DFF2C896720BA"
+           "DFF7BC9C366ACEA3A880AEC287C5E6207DF2739B5326FC19D773BD830B109"
+           "ED36C7086544BF8FDB9D4B73719C2B5BC2F571A5937EC46876CD428281F6B"
+           "F287E1E07F25C1B1D46BC37324FF657A8B2E0071DB83B86123CA34004F406"
+           "001082D7945E90C6E8C9A9FEC2B44BE0DDA46E9F52B152E4D1336D2FCFBC9"
+           "96E30CA0082256737365158FE36482AA7EB9DAF2AB128F10E7551A3CD5BE6"
+           "0A922F3A7D5EED38B634A7EC95BCF7021BA6820A292000000000000000000"
+           "00000000000000000000000000000000", buffer);
+
+  bignum.AssignBignum(bignum2);
+  bignum.MultiplyByPowerOfTen(500);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("7845F900E475B5086885BAAAE67C8E85185ACFE4633727F82A4B06B5582AC"
+           "BE933C53357DA0C98C20C5AC900C4D76A97247DF52B79F48F9E35840FB715"
+           "D392CE303E22622B0CF82D9471B398457DD3196F639CEE8BBD2C146873841"
+           "F0699E6C41F04FC7A54B48CEB995BEB6F50FE81DE9D87A8D7F849CC523553"
+           "7B7BBBC1C7CAAFF6E9650BE03B308C6D31012AEF9580F70D3EE2083ADE126"
+           "8940FA7D6308E239775DFD2F8C97FF7EBD525DAFA6512216F7047A62A93DC"
+           "38A0165BDC67E250DCC96A0181DE935A70B38704DC71819F02FC5261FF7E1"
+           "E5F11907678B0A3E519FF4C10A867B0C26CE02BE6960BA8621A87303C101C"
+           "3F88798BB9F7739655946F8B5744E6B1EAF10B0C5621330F0079209033C69"
+           "20DE2E2C8D324F0624463735D482BF291926C22A910F5B80FA25170B6B57D"
+           "8D5928C7BCA3FE87461275F69BD5A1B83181DAAF43E05FC3C72C4E93111B6"
+           "6205EBF49B28FEDFB7E7526CBDA658A332000000000000000000000000000"
+           "0000000000000000000000000000000000000000000000000000000000000"
+           "0000000000000000000000000000000000000", buffer);
+}
+
+
+TEST(DivideModuloIntBignum) {
+  char buffer[kBufferSize];
+  Bignum bignum;
+  Bignum other;
+  Bignum third;
+
+  bignum.AssignUInt16(10);
+  other.AssignUInt16(2);
+  CHECK_EQ(5, bignum.DivideModuloIntBignum(other));
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("0", buffer);
+
+  bignum.AssignUInt16(10);
+  bignum.ShiftLeft(500);
+  other.AssignUInt16(2);
+  other.ShiftLeft(500);
+  CHECK_EQ(5, bignum.DivideModuloIntBignum(other));
+  CHECK_EQ("0", buffer);
+
+  bignum.AssignUInt16(11);
+  other.AssignUInt16(2);
+  CHECK_EQ(5, bignum.DivideModuloIntBignum(other));
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1", buffer);
+
+  bignum.AssignUInt16(10);
+  bignum.ShiftLeft(500);
+  other.AssignUInt16(1);
+  bignum.AddBignum(other);
+  other.AssignUInt16(2);
+  other.ShiftLeft(500);
+  CHECK_EQ(5, bignum.DivideModuloIntBignum(other));
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1", buffer);
+
+  bignum.AssignUInt16(10);
+  bignum.ShiftLeft(500);
+  other.AssignBignum(bignum);
+  bignum.MultiplyByUInt32(0x1234);
+  third.AssignUInt16(0xFFF);
+  bignum.AddBignum(third);
+  CHECK_EQ(0x1234, bignum.DivideModuloIntBignum(other));
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("FFF", buffer);
+
+  bignum.AssignUInt16(10);
+  AssignHexString(&other, "1234567890");
+  CHECK_EQ(0, bignum.DivideModuloIntBignum(other));
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("A", buffer);
+
+  AssignHexString(&bignum, "12345678");
+  AssignHexString(&other, "3789012");
+  CHECK_EQ(5, bignum.DivideModuloIntBignum(other));
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("D9861E", buffer);
+
+  AssignHexString(&bignum, "70000001");
+  AssignHexString(&other, "1FFFFFFF");
+  CHECK_EQ(3, bignum.DivideModuloIntBignum(other));
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("10000004", buffer);
+
+  AssignHexString(&bignum, "28000000");
+  AssignHexString(&other, "12A05F20");
+  CHECK_EQ(2, bignum.DivideModuloIntBignum(other));
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("2BF41C0", buffer);
+
+  bignum.AssignUInt16(10);
+  bignum.ShiftLeft(500);
+  other.AssignBignum(bignum);
+  bignum.MultiplyByUInt32(0x1234);
+  third.AssignUInt16(0xFFF);
+  other.SubtractBignum(third);
+  CHECK_EQ(0x1234, bignum.DivideModuloIntBignum(other));
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1232DCC", buffer);
+  CHECK_EQ(0, bignum.DivideModuloIntBignum(other));
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1232DCC", buffer);
+}
+
+
+TEST(Compare) {
+  Bignum bignum1;
+  Bignum bignum2;
+  bignum1.AssignUInt16(1);
+  bignum2.AssignUInt16(1);
+  CHECK_EQ(0, Bignum::Compare(bignum1, bignum2));
+  CHECK(Bignum::Equal(bignum1, bignum2));
+  CHECK(Bignum::LessEqual(bignum1, bignum2));
+  CHECK(!Bignum::Less(bignum1, bignum2));
+
+  bignum1.AssignUInt16(0);
+  bignum2.AssignUInt16(1);
+  CHECK_EQ(-1, Bignum::Compare(bignum1, bignum2));
+  CHECK_EQ(+1, Bignum::Compare(bignum2, bignum1));
+  CHECK(!Bignum::Equal(bignum1, bignum2));
+  CHECK(!Bignum::Equal(bignum2, bignum1));
+  CHECK(Bignum::LessEqual(bignum1, bignum2));
+  CHECK(!Bignum::LessEqual(bignum2, bignum1));
+  CHECK(Bignum::Less(bignum1, bignum2));
+  CHECK(!Bignum::Less(bignum2, bignum1));
+
+  AssignHexString(&bignum1, "1234567890ABCDEF12345");
+  AssignHexString(&bignum2, "1234567890ABCDEF12345");
+  CHECK_EQ(0, Bignum::Compare(bignum1, bignum2));
+
+  AssignHexString(&bignum1, "1234567890ABCDEF12345");
+  AssignHexString(&bignum2, "1234567890ABCDEF12346");
+  CHECK_EQ(-1, Bignum::Compare(bignum1, bignum2));
+  CHECK_EQ(+1, Bignum::Compare(bignum2, bignum1));
+
+  AssignHexString(&bignum1, "1234567890ABCDEF12345");
+  bignum1.ShiftLeft(500);
+  AssignHexString(&bignum2, "1234567890ABCDEF12345");
+  bignum2.ShiftLeft(500);
+  CHECK_EQ(0, Bignum::Compare(bignum1, bignum2));
+
+  AssignHexString(&bignum1, "1234567890ABCDEF12345");
+  bignum1.ShiftLeft(500);
+  AssignHexString(&bignum2, "1234567890ABCDEF12346");
+  bignum2.ShiftLeft(500);
+  CHECK_EQ(-1, Bignum::Compare(bignum1, bignum2));
+  CHECK_EQ(+1, Bignum::Compare(bignum2, bignum1));
+
+  bignum1.AssignUInt16(1);
+  bignum1.ShiftLeft(64);
+  AssignHexString(&bignum2, "10000000000000000");
+  CHECK_EQ(0, Bignum::Compare(bignum1, bignum2));
+  CHECK_EQ(0, Bignum::Compare(bignum2, bignum1));
+
+  bignum1.AssignUInt16(1);
+  bignum1.ShiftLeft(64);
+  AssignHexString(&bignum2, "10000000000000001");
+  CHECK_EQ(-1, Bignum::Compare(bignum1, bignum2));
+  CHECK_EQ(+1, Bignum::Compare(bignum2, bignum1));
+
+  bignum1.AssignUInt16(1);
+  bignum1.ShiftLeft(96);
+  AssignHexString(&bignum2, "10000000000000001");
+  bignum2.ShiftLeft(32);
+  CHECK_EQ(-1, Bignum::Compare(bignum1, bignum2));
+  CHECK_EQ(+1, Bignum::Compare(bignum2, bignum1));
+
+  AssignHexString(&bignum1, "FFFFFFFFFFFFFFFF");
+  bignum2.AssignUInt16(1);
+  bignum2.ShiftLeft(64);
+  CHECK_EQ(-1, Bignum::Compare(bignum1, bignum2));
+  CHECK_EQ(+1, Bignum::Compare(bignum2, bignum1));
+
+  AssignHexString(&bignum1, "FFFFFFFFFFFFFFFF");
+  bignum1.ShiftLeft(32);
+  bignum2.AssignUInt16(1);
+  bignum2.ShiftLeft(96);
+  CHECK_EQ(-1, Bignum::Compare(bignum1, bignum2));
+  CHECK_EQ(+1, Bignum::Compare(bignum2, bignum1));
+
+  AssignHexString(&bignum1, "FFFFFFFFFFFFFFFF");
+  bignum1.ShiftLeft(32);
+  bignum2.AssignUInt16(1);
+  bignum2.ShiftLeft(95);
+  CHECK_EQ(+1, Bignum::Compare(bignum1, bignum2));
+  CHECK_EQ(-1, Bignum::Compare(bignum2, bignum1));
+
+  AssignHexString(&bignum1, "FFFFFFFFFFFFFFFF");
+  bignum1.ShiftLeft(32);
+  bignum2.AssignUInt16(1);
+  bignum2.ShiftLeft(100);
+  CHECK_EQ(-1, Bignum::Compare(bignum1, bignum2));
+  CHECK_EQ(+1, Bignum::Compare(bignum2, bignum1));
+
+  AssignHexString(&bignum1, "100000000000000");
+  bignum2.AssignUInt16(1);
+  bignum2.ShiftLeft(14*4);
+  CHECK_EQ(0, Bignum::Compare(bignum1, bignum2));
+  CHECK_EQ(0, Bignum::Compare(bignum2, bignum1));
+
+  AssignHexString(&bignum1, "100000000000001");
+  bignum2.AssignUInt16(1);
+  bignum2.ShiftLeft(14*4);
+  CHECK_EQ(+1, Bignum::Compare(bignum1, bignum2));
+  CHECK_EQ(-1, Bignum::Compare(bignum2, bignum1));
+
+  AssignHexString(&bignum1, "200000000000000");
+  bignum2.AssignUInt16(3);
+  bignum2.ShiftLeft(14*4);
+  CHECK_EQ(-1, Bignum::Compare(bignum1, bignum2));
+  CHECK_EQ(+1, Bignum::Compare(bignum2, bignum1));
+}
+
+
+TEST(PlusCompare) {
+  Bignum a;
+  Bignum b;
+  Bignum c;
+  a.AssignUInt16(1);
+  b.AssignUInt16(0);
+  c.AssignUInt16(1);
+  CHECK_EQ(0, Bignum::PlusCompare(a, b, c));
+  CHECK(Bignum::PlusEqual(a, b, c));
+  CHECK(Bignum::PlusLessEqual(a, b, c));
+  CHECK(!Bignum::PlusLess(a, b, c));
+
+  a.AssignUInt16(0);
+  b.AssignUInt16(0);
+  c.AssignUInt16(1);
+  CHECK_EQ(-1, Bignum::PlusCompare(a, b, c));
+  CHECK_EQ(+1, Bignum::PlusCompare(c, b, a));
+  CHECK(!Bignum::PlusEqual(a, b, c));
+  CHECK(!Bignum::PlusEqual(c, b, a));
+  CHECK(Bignum::PlusLessEqual(a, b, c));
+  CHECK(!Bignum::PlusLessEqual(c, b, a));
+  CHECK(Bignum::PlusLess(a, b, c));
+  CHECK(!Bignum::PlusLess(c, b, a));
+
+  AssignHexString(&a, "1234567890ABCDEF12345");
+  b.AssignUInt16(1);
+  AssignHexString(&c, "1234567890ABCDEF12345");
+  CHECK_EQ(+1, Bignum::PlusCompare(a, b, c));
+
+  AssignHexString(&a, "1234567890ABCDEF12344");
+  b.AssignUInt16(1);
+  AssignHexString(&c, "1234567890ABCDEF12345");
+  CHECK_EQ(0, Bignum::PlusCompare(a, b, c));
+
+  AssignHexString(&a, "1234567890");
+  a.ShiftLeft(11*4);
+  AssignHexString(&b, "ABCDEF12345");
+  AssignHexString(&c, "1234567890ABCDEF12345");
+  CHECK_EQ(0, Bignum::PlusCompare(a, b, c));
+
+  AssignHexString(&a, "1234567890");
+  a.ShiftLeft(11*4);
+  AssignHexString(&b, "ABCDEF12344");
+  AssignHexString(&c, "1234567890ABCDEF12345");
+  CHECK_EQ(-1, Bignum::PlusCompare(a, b, c));
+
+  AssignHexString(&a, "1234567890");
+  a.ShiftLeft(11*4);
+  AssignHexString(&b, "ABCDEF12346");
+  AssignHexString(&c, "1234567890ABCDEF12345");
+  CHECK_EQ(1, Bignum::PlusCompare(a, b, c));
+
+  AssignHexString(&a, "1234567891");
+  a.ShiftLeft(11*4);
+  AssignHexString(&b, "ABCDEF12345");
+  AssignHexString(&c, "1234567890ABCDEF12345");
+  CHECK_EQ(1, Bignum::PlusCompare(a, b, c));
+
+  AssignHexString(&a, "1234567889");
+  a.ShiftLeft(11*4);
+  AssignHexString(&b, "ABCDEF12345");
+  AssignHexString(&c, "1234567890ABCDEF12345");
+  CHECK_EQ(-1, Bignum::PlusCompare(a, b, c));
+
+  AssignHexString(&a, "1234567890");
+  a.ShiftLeft(11*4 + 32);
+  AssignHexString(&b, "ABCDEF12345");
+  b.ShiftLeft(32);
+  AssignHexString(&c, "1234567890ABCDEF12345");
+  c.ShiftLeft(32);
+  CHECK_EQ(0, Bignum::PlusCompare(a, b, c));
+
+  AssignHexString(&a, "1234567890");
+  a.ShiftLeft(11*4 + 32);
+  AssignHexString(&b, "ABCDEF12344");
+  b.ShiftLeft(32);
+  AssignHexString(&c, "1234567890ABCDEF12345");
+  c.ShiftLeft(32);
+  CHECK_EQ(-1, Bignum::PlusCompare(a, b, c));
+
+  AssignHexString(&a, "1234567890");
+  a.ShiftLeft(11*4 + 32);
+  AssignHexString(&b, "ABCDEF12346");
+  b.ShiftLeft(32);
+  AssignHexString(&c, "1234567890ABCDEF12345");
+  c.ShiftLeft(32);
+  CHECK_EQ(1, Bignum::PlusCompare(a, b, c));
+
+  AssignHexString(&a, "1234567891");
+  a.ShiftLeft(11*4 + 32);
+  AssignHexString(&b, "ABCDEF12345");
+  b.ShiftLeft(32);
+  AssignHexString(&c, "1234567890ABCDEF12345");
+  c.ShiftLeft(32);
+  CHECK_EQ(1, Bignum::PlusCompare(a, b, c));
+
+  AssignHexString(&a, "1234567889");
+  a.ShiftLeft(11*4 + 32);
+  AssignHexString(&b, "ABCDEF12345");
+  b.ShiftLeft(32);
+  AssignHexString(&c, "1234567890ABCDEF12345");
+  c.ShiftLeft(32);
+  CHECK_EQ(-1, Bignum::PlusCompare(a, b, c));
+
+  AssignHexString(&a, "1234567890");
+  a.ShiftLeft(11*4 + 32);
+  AssignHexString(&b, "ABCDEF12345");
+  b.ShiftLeft(32);
+  AssignHexString(&c, "1234567890ABCDEF1234500000000");
+  CHECK_EQ(0, Bignum::PlusCompare(a, b, c));
+
+  AssignHexString(&a, "1234567890");
+  a.ShiftLeft(11*4 + 32);
+  AssignHexString(&b, "ABCDEF12344");
+  b.ShiftLeft(32);
+  AssignHexString(&c, "1234567890ABCDEF1234500000000");
+  CHECK_EQ(-1, Bignum::PlusCompare(a, b, c));
+
+  AssignHexString(&a, "1234567890");
+  a.ShiftLeft(11*4 + 32);
+  AssignHexString(&b, "ABCDEF12346");
+  b.ShiftLeft(32);
+  AssignHexString(&c, "1234567890ABCDEF1234500000000");
+  CHECK_EQ(1, Bignum::PlusCompare(a, b, c));
+
+  AssignHexString(&a, "1234567891");
+  a.ShiftLeft(11*4 + 32);
+  AssignHexString(&b, "ABCDEF12345");
+  b.ShiftLeft(32);
+  AssignHexString(&c, "1234567890ABCDEF1234500000000");
+  CHECK_EQ(1, Bignum::PlusCompare(a, b, c));
+
+  AssignHexString(&a, "1234567889");
+  a.ShiftLeft(11*4 + 32);
+  AssignHexString(&b, "ABCDEF12345");
+  b.ShiftLeft(32);
+  AssignHexString(&c, "1234567890ABCDEF1234500000000");
+  CHECK_EQ(-1, Bignum::PlusCompare(a, b, c));
+
+  AssignHexString(&a, "1234567890");
+  a.ShiftLeft(11*4 + 32);
+  AssignHexString(&b, "ABCDEF12345");
+  AssignHexString(&c, "123456789000000000ABCDEF12345");
+  CHECK_EQ(0, Bignum::PlusCompare(a, b, c));
+
+  AssignHexString(&a, "1234567890");
+  a.ShiftLeft(11*4 + 32);
+  AssignHexString(&b, "ABCDEF12346");
+  AssignHexString(&c, "123456789000000000ABCDEF12345");
+  CHECK_EQ(1, Bignum::PlusCompare(a, b, c));
+
+  AssignHexString(&a, "1234567890");
+  a.ShiftLeft(11*4 + 32);
+  AssignHexString(&b, "ABCDEF12344");
+  AssignHexString(&c, "123456789000000000ABCDEF12345");
+  CHECK_EQ(-1, Bignum::PlusCompare(a, b, c));
+
+  AssignHexString(&a, "1234567890");
+  a.ShiftLeft(11*4 + 32);
+  AssignHexString(&b, "ABCDEF12345");
+  b.ShiftLeft(16);
+  AssignHexString(&c, "12345678900000ABCDEF123450000");
+  CHECK_EQ(0, Bignum::PlusCompare(a, b, c));
+
+  AssignHexString(&a, "1234567890");
+  a.ShiftLeft(11*4 + 32);
+  AssignHexString(&b, "ABCDEF12344");
+  b.ShiftLeft(16);
+  AssignHexString(&c, "12345678900000ABCDEF123450000");
+  CHECK_EQ(-1, Bignum::PlusCompare(a, b, c));
+
+  AssignHexString(&a, "1234567890");
+  a.ShiftLeft(11*4 + 32);
+  AssignHexString(&b, "ABCDEF12345");
+  b.ShiftLeft(16);
+  AssignHexString(&c, "12345678900000ABCDEF123450001");
+  CHECK_EQ(-1, Bignum::PlusCompare(a, b, c));
+
+  AssignHexString(&a, "1234567890");
+  a.ShiftLeft(11*4 + 32);
+  AssignHexString(&b, "ABCDEF12346");
+  b.ShiftLeft(16);
+  AssignHexString(&c, "12345678900000ABCDEF123450000");
+  CHECK_EQ(+1, Bignum::PlusCompare(a, b, c));
+}
+
+
+TEST(Square) {
+  Bignum bignum;
+  char buffer[kBufferSize];
+
+  bignum.AssignUInt16(1);
+  bignum.Square();
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1", buffer);
+
+  bignum.AssignUInt16(2);
+  bignum.Square();
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("4", buffer);
+
+  bignum.AssignUInt16(10);
+  bignum.Square();
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("64", buffer);
+
+  AssignHexString(&bignum, "FFFFFFF");
+  bignum.Square();
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("FFFFFFE0000001", buffer);
+
+  AssignHexString(&bignum, "FFFFFFFFFFFFFF");
+  bignum.Square();
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("FFFFFFFFFFFFFE00000000000001", buffer);
+}
+
+
+TEST(AssignPowerUInt16) {
+  Bignum bignum;
+  char buffer[kBufferSize];
+
+  bignum.AssignPowerUInt16(1, 0);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1", buffer);
+
+  bignum.AssignPowerUInt16(1, 1);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1", buffer);
+
+  bignum.AssignPowerUInt16(1, 2);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1", buffer);
+
+  bignum.AssignPowerUInt16(2, 0);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1", buffer);
+
+  bignum.AssignPowerUInt16(2, 1);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("2", buffer);
+
+  bignum.AssignPowerUInt16(2, 2);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("4", buffer);
+
+  bignum.AssignPowerUInt16(16, 1);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("10", buffer);
+
+  bignum.AssignPowerUInt16(16, 2);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("100", buffer);
+
+  bignum.AssignPowerUInt16(16, 5);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("100000", buffer);
+
+  bignum.AssignPowerUInt16(16, 8);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("100000000", buffer);
+
+  bignum.AssignPowerUInt16(16, 16);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("10000000000000000", buffer);
+
+  bignum.AssignPowerUInt16(16, 30);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1000000000000000000000000000000", buffer);
+
+  bignum.AssignPowerUInt16(10, 0);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1", buffer);
+
+  bignum.AssignPowerUInt16(10, 1);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("A", buffer);
+
+  bignum.AssignPowerUInt16(10, 2);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("64", buffer);
+
+  bignum.AssignPowerUInt16(10, 5);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("186A0", buffer);
+
+  bignum.AssignPowerUInt16(10, 8);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("5F5E100", buffer);
+
+  bignum.AssignPowerUInt16(10, 16);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("2386F26FC10000", buffer);
+
+  bignum.AssignPowerUInt16(10, 30);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("C9F2C9CD04674EDEA40000000", buffer);
+
+  bignum.AssignPowerUInt16(10, 31);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("7E37BE2022C0914B2680000000", buffer);
+
+  bignum.AssignPowerUInt16(2, 0);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1", buffer);
+
+  bignum.AssignPowerUInt16(2, 100);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("10000000000000000000000000", buffer);
+
+  bignum.AssignPowerUInt16(17, 0);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1", buffer);
+
+  bignum.AssignPowerUInt16(17, 99);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("1942BB9853FAD924A3D4DD92B89B940E0207BEF05DB9C26BC1B757"
+           "80BE0C5A2C2990E02A681224F34ED68558CE4C6E33760931",
+           buffer);
+
+  bignum.AssignPowerUInt16(0xFFFF, 99);
+  CHECK(bignum.ToHexString(buffer, kBufferSize));
+  CHECK_EQ("FF9D12F09B886C54E77E7439C7D2DED2D34F669654C0C2B6B8C288250"
+           "5A2211D0E3DC9A61831349EAE674B11D56E3049D7BD79DAAD6C9FA2BA"
+           "528E3A794299F2EE9146A324DAFE3E88967A0358233B543E233E575B9"
+           "DD4E3AA7942146426C328FF55BFD5C45E0901B1629260AF9AE2F310C5"
+           "50959FAF305C30116D537D80CF6EBDBC15C5694062AF1AC3D956D0A41"
+           "B7E1B79FF11E21D83387A1CE1F5882B31E4B5D8DE415BDBE6854466DF"
+           "343362267A7E8833119D31D02E18DB5B0E8F6A64B0ED0D0062FFFF",
+           buffer);
+}

diff --git a/test/cctest/test-strtod.cc b/test/cctest/test-strtod.cc
index 56b26ea1eb90f8526431bcfb8cd4ef473dd52695..34c474ff16e51e2a4076fe15a1334df095e3a8b9 100644 (file)
--- a/test/cctest/test-strtod.cc
+++ b/test/cctest/test-strtod.cc
@@ -4,7 +4,10 @@
 
 #include "v8.h"
 
+#include "bignum.h"
 #include "cctest.h"
+#include "diy-fp.h"
+#include "double.h"
 #include "strtod.h"
 
 using namespace v8::internal;
@@ -202,11 +205,14 @@ TEST(Strtod) {
   CHECK_EQ(1.7976931348623158E+308, StrtodChar("17976931348623158", 292));
   CHECK_EQ(V8_INFINITY, StrtodChar("17976931348623159", 292));
 
-  // The following number is the result of 89255.0/1e-22. Both floating-point
+  // The following number is the result of 89255.0/1e22. Both floating-point
   // numbers can be accurately represented with doubles. However on Linux,x86
   // the floating-point stack is set to 80bits and the double-rounding
   // introduces an error.
   CHECK_EQ(89255e-22, StrtodChar("89255", -22));
+
+  // Some random values.
+  CHECK_EQ(358416272e-33, StrtodChar("358416272", -33));
   CHECK_EQ(104110013277974872254e-225,
            StrtodChar("104110013277974872254", -225));
 
@@ -252,4 +258,158 @@ TEST(Strtod) {
            StrtodChar("1234567890123456789052345", 114));
   CHECK_EQ(1234567890123456789052345e115,
            StrtodChar("1234567890123456789052345", 115));
+
+  // Boundary cases.
+  // 0x1FFFFFFFFFFFF * 2^3 = 72057594037927928
+  //                   next: 72057594037927936
+  //               boundary: 72057594037927932
+  CHECK_EQ(72057594037927928.0, StrtodChar("72057594037927928", 0));
+  CHECK_EQ(72057594037927936.0, StrtodChar("72057594037927936", 0));
+  CHECK_EQ(72057594037927936.0, StrtodChar("72057594037927932", 0));
+  CHECK_EQ(72057594037927928.0, StrtodChar("7205759403792793199999", -5));
+  CHECK_EQ(72057594037927936.0, StrtodChar("7205759403792793200001", -5));
+
+  // 0x1FFFFFFFFFFFF * 2^10 = 9223372036854774784
+  //                    next: 9223372036854775808
+  //                boundary: 9223372036854775296
+  CHECK_EQ(9223372036854774784.0, StrtodChar("9223372036854774784", 0));
+  CHECK_EQ(9223372036854775808.0, StrtodChar("9223372036854775808", 0));
+  CHECK_EQ(9223372036854775296.0, StrtodChar("9223372036854775296", 0));
+  CHECK_EQ(9223372036854774784.0, StrtodChar("922337203685477529599999", -5));
+  CHECK_EQ(9223372036854775808.0, StrtodChar("922337203685477529600001", -5));
+
+  // 0x1FFFFFFFFFFFF * 2^50 = 10141204801825834086073718800384
+  //                    next: 10141204801825835211973625643008
+  //                boundary: 10141204801825834649023672221696
+  CHECK_EQ(10141204801825834086073718800384.0,
+           StrtodChar("10141204801825834086073718800384", 0));
+  CHECK_EQ(10141204801825835211973625643008.0,
+           StrtodChar("10141204801825835211973625643008", 0));
+  CHECK_EQ(10141204801825834649023672221696.0,
+           StrtodChar("10141204801825834649023672221696", 0));
+  CHECK_EQ(10141204801825834086073718800384.0,
+           StrtodChar("1014120480182583464902367222169599999", -5));
+  CHECK_EQ(10141204801825835211973625643008.0,
+           StrtodChar("1014120480182583464902367222169600001", -5));
+
+  // 0x1FFFFFFFFFFFF * 2^99 = 5708990770823838890407843763683279797179383808
+  //                    next: 5708990770823839524233143877797980545530986496
+  //                boundary: 5708990770823839207320493820740630171355185152
+  CHECK_EQ(5708990770823838890407843763683279797179383808.0,
+           StrtodChar("5708990770823838890407843763683279797179383808", 0));
+  CHECK_EQ(5708990770823839524233143877797980545530986496.0,
+           StrtodChar("5708990770823839524233143877797980545530986496", 0));
+  CHECK_EQ(5708990770823839207320493820740630171355185152.0,
+           StrtodChar("5708990770823839207320493820740630171355185152", 0));
+  CHECK_EQ(5708990770823838890407843763683279797179383808.0,
+           StrtodChar("5708990770823839207320493820740630171355185151999", -3));
+  CHECK_EQ(5708990770823839524233143877797980545530986496.0,
+           StrtodChar("5708990770823839207320493820740630171355185152001", -3));
+}
+
+
+static int CompareBignumToDiyFp(const Bignum& bignum_digits,
+                                int bignum_exponent,
+                                DiyFp diy_fp) {
+  Bignum bignum;
+  bignum.AssignBignum(bignum_digits);
+  Bignum other;
+  other.AssignUInt64(diy_fp.f());
+  if (bignum_exponent >= 0) {
+    bignum.MultiplyByPowerOfTen(bignum_exponent);
+  } else {
+    other.MultiplyByPowerOfTen(-bignum_exponent);
+  }
+  if (diy_fp.e() >= 0) {
+    other.ShiftLeft(diy_fp.e());
+  } else {
+    bignum.ShiftLeft(-diy_fp.e());
+  }
+  return Bignum::Compare(bignum, other);
+}
+
+
+static bool CheckDouble(Vector<const char> buffer,
+                        int exponent,
+                        double to_check) {
+  DiyFp lower_boundary;
+  DiyFp upper_boundary;
+  Bignum input_digits;
+  input_digits.AssignDecimalString(buffer);
+  if (to_check == 0.0) {
+    const double kMinDouble = 4e-324;
+    // Check that the buffer*10^exponent < (0 + kMinDouble)/2.
+    Double d(kMinDouble);
+    d.NormalizedBoundaries(&lower_boundary, &upper_boundary);
+    return CompareBignumToDiyFp(input_digits, exponent, lower_boundary) <= 0;
+  }
+  if (to_check == V8_INFINITY) {
+    const double kMaxDouble = 1.7976931348623157e308;
+    // Check that the buffer*10^exponent >= boundary between kMaxDouble and inf.
+    Double d(kMaxDouble);
+    d.NormalizedBoundaries(&lower_boundary, &upper_boundary);
+    return CompareBignumToDiyFp(input_digits, exponent, upper_boundary) >= 0;
+  }
+  Double d(to_check);
+  d.NormalizedBoundaries(&lower_boundary, &upper_boundary);
+  if ((d.Significand() & 1) == 0) {
+    return CompareBignumToDiyFp(input_digits, exponent, lower_boundary) >= 0 &&
+        CompareBignumToDiyFp(input_digits, exponent, upper_boundary) <= 0;
+  } else {
+    return CompareBignumToDiyFp(input_digits, exponent, lower_boundary) > 0 &&
+        CompareBignumToDiyFp(input_digits, exponent, upper_boundary) < 0;
+  }
+}
+
+
+// Copied from v8.cc and adapted to make the function deterministic.
+static uint32_t DeterministicRandom() {
+  // Random number generator using George Marsaglia's MWC algorithm.
+  static uint32_t hi = 0;
+  static uint32_t lo = 0;
+
+  // Initialization values don't have any special meaning. (They are the result
+  // of two calls to random().)
+  if (hi == 0) hi = 0xbfe166e7;
+  if (lo == 0) lo = 0x64d1c3c9;
+
+  // Mix the bits.
+  hi = 36969 * (hi & 0xFFFF) + (hi >> 16);
+  lo = 18273 * (lo & 0xFFFF) + (lo >> 16);
+  return (hi << 16) + (lo & 0xFFFF);
+}
+
+
+static const int kBufferSize = 1024;
+static const int kShortStrtodRandomCount = 2;
+static const int kLargeStrtodRandomCount = 2;
+
+TEST(RandomStrtod) {
+  char buffer[kBufferSize];
+  for (int length = 1; length < 15; length++) {
+    for (int i = 0; i < kShortStrtodRandomCount; ++i) {
+      int pos = 0;
+      for (int j = 0; j < length; ++j) {
+        buffer[pos++] = random() % 10 + '0';
+      }
+      int exponent = DeterministicRandom() % (25*2 + 1) - 25 - length;
+      buffer[pos] = '\0';
+      Vector<const char> vector(buffer, pos);
+      double strtod_result = Strtod(vector, exponent);
+      CHECK(CheckDouble(vector, exponent, strtod_result));
+    }
+  }
+  for (int length = 15; length < 800; length += 2) {
+    for (int i = 0; i < kLargeStrtodRandomCount; ++i) {
+      int pos = 0;
+      for (int j = 0; j < length; ++j) {
+        buffer[pos++] = random() % 10 + '0';
+      }
+      int exponent = DeterministicRandom() % (308*2 + 1) - 308 - length;
+      buffer[pos] = '\0';
+      Vector<const char> vector(buffer, pos);
+      double strtod_result = Strtod(vector, exponent);
+      CHECK(CheckDouble(vector, exponent, strtod_result));
+    }
+  }
 }

diff --git a/tools/gyp/v8.gyp b/tools/gyp/v8.gyp
index 3e40fcc67ac37ef50730542ccce2ce08711e348f..bfb89219b558bd3b63185a203282c81c5b9b64e5 100644 (file)
--- a/tools/gyp/v8.gyp
+++ b/tools/gyp/v8.gyp
@@ -280,6 +280,10 @@
         '../../src/ast.cc',
         '../../src/ast-inl.h',
         '../../src/ast.h',
+        '../../src/bignum.cc',
+        '../../src/bignum.h',
+        '../../src/bignum-dtoa.cc',
+        '../../src/bignum-dtoa.h',
         '../../src/bootstrapper.cc',
         '../../src/bootstrapper.h',
         '../../src/builtins.cc',

diff --git a/tools/visual_studio/v8_base.vcproj b/tools/visual_studio/v8_base.vcproj
index bddf38e217dae32cce3224ad6302dd746778d98c..d1ee48d6da7b49404174fe16f3cc95eff5452f90 100644 (file)
--- a/tools/visual_studio/v8_base.vcproj
+++ b/tools/visual_studio/v8_base.vcproj
@@ -144,6 +144,22 @@
                                        />
                                </FileConfiguration>
                        </File>
+               <File
+                               RelativePath="..\..\src\bignum.cc"
+                               >
+                       </File>
+               <File
+                               RelativePath="..\..\src\bignum.h"
+                               >
+                       </File>
+               <File
+                               RelativePath="..\..\src\bignum-dtoa.cc"
+                               >
+                       </File>
+               <File
+                               RelativePath="..\..\src\bignum-dtoa.h"
+                               >
+                       </File>
                <File
                                RelativePath="..\..\src\dtoa.cc"
                                >
@@ -240,6 +256,22 @@
                                RelativePath="..\..\src\ast.h"
                                >
                        </File>
+                       <File
+                               RelativePath="..\..\src\bignum.cc"
+                               >
+                       </File>
+                       <File
+                               RelativePath="..\..\src\bignum.h"
+                               >
+                       </File>
+                       <File
+                               RelativePath="..\..\src\bignum-dtoa.cc"
+                               >
+                       </File>
+                       <File
+                               RelativePath="..\..\src\bignum-dtoa.h"
+                               >
+                       </File>
                        <File
                                RelativePath="..\..\src\bootstrapper.cc"
                                >