Restoring authorship annotation for Anton Samokhvalov <pg83@yandex.ru>. Commit 1 of 2.

1 files changed, 762 insertions, 762 deletions

diff --git a/contrib/libs/double-conversion/bignum.cc b/contrib/libs/double-conversion/bignum.cc
index d077eef3f5..490071facd 100644
--- a/contrib/libs/double-conversion/bignum.cc
+++ b/contrib/libs/double-conversion/bignum.cc
@@ -1,767 +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 "bignum.h"
-#include "utils.h"
-
-namespace double_conversion {
-
-Bignum::Bignum()
+// 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 "bignum.h" 
+#include "utils.h" 
+ 
+namespace double_conversion { 
+ 
+Bignum::Bignum() 
     : bigits_buffer_(), 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) {
-  (void) value;  // Mark variable as used.
-  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();
-  unsigned 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';
-  ASSERT('A' <= c && c <= 'F');
-  return 10 + c - 'A';
-}
-
-
-void Bignum::AssignHexString(Vector<const char> value) {
-  Zero();
-  int length = value.length();
-
-  int needed_bigits = length * 4 / kBigitSize + 1;
-  EnsureCapacity(needed_bigits);
-  int string_index = length - 1;
-  for (int i = 0; i < needed_bigits - 1; ++i) {
-    // These bigits are guaranteed to be "full".
-    Chunk current_bigit = 0;
-    for (int j = 0; j < kBigitSize / 4; j++) {
-      current_bigit += HexCharValue(value[string_index--]) << (j * 4);
-    }
-    bigits_[i] = current_bigit;
-  }
-  used_digits_ = needed_bigits - 1;
-
-  Chunk most_significant_bigit = 0;  // Could be = 0;
-  for (int j = 0; j <= string_index; ++j) {
-    most_significant_bigit <<= 4;
-    most_significant_bigit += HexCharValue(value[j]);
-  }
-  if (most_significant_bigit != 0) {
-    bigits_[used_digits_] = most_significant_bigit;
-    used_digits_++;
-  }
-  Clamp();
-}
-
-
-void Bignum::AddUInt64(uint64_t operand) {
-  if (operand == 0) return;
-  Bignum other;
-  other.AssignUInt64(operand);
-  AddBignum(other);
-}
-
-
-void Bignum::AddBignum(const Bignum& other) {
-  ASSERT(IsClamped());
-  ASSERT(other.IsClamped());
-
-  // If this has a greater exponent than other append zero-bigits to this.
-  // After this call exponent_ <= other.exponent_.
-  Align(other);
-
-  // There are two possibilities:
-  //   aaaaaaaaaaa 0000  (where the 0s represent a's exponent)
-  //     bbbbb 00000000
-  //   ----------------
-  //   ccccccccccc 0000
-  // or
-  //    aaaaaaaaaa 0000
-  //  bbbbbbbbb 0000000
-  //  -----------------
-  //  cccccccccccc 0000
-  // In both cases we might need a carry bigit.
-
-  EnsureCapacity(1 + Max(BigitLength(), other.BigitLength()) - exponent_);
-  Chunk carry = 0;
-  int bigit_pos = other.exponent_ - exponent_;
-  ASSERT(bigit_pos >= 0);
-  for (int i = 0; i < other.used_digits_; ++i) {
-    Chunk sum = bigits_[bigit_pos] + other.bigits_[i] + carry;
-    bigits_[bigit_pos] = sum & kBigitMask;
-    carry = sum >> kBigitSize;
-    bigit_pos++;
-  }
-
-  while (carry != 0) {
-    Chunk sum = bigits_[bigit_pos] + carry;
-    bigits_[bigit_pos] = sum & kBigitMask;
-    carry = sum >> kBigitSize;
-    bigit_pos++;
-  }
-  used_digits_ = Max(bigit_pos, used_digits_);
-  ASSERT(IsClamped());
-}
-
-
-void Bignum::SubtractBignum(const Bignum& other) {
-  ASSERT(IsClamped());
-  ASSERT(other.IsClamped());
-  // We require this to be bigger than other.
-  ASSERT(LessEqual(other, *this));
-
-  Align(other);
-
-  int offset = other.exponent_ - exponent_;
-  Chunk borrow = 0;
-  int i;
-  for (i = 0; i < other.used_digits_; ++i) {
-    ASSERT((borrow == 0) || (borrow == 1));
-    Chunk difference = bigits_[i + offset] - other.bigits_[i] - borrow;
-    bigits_[i + offset] = difference & kBigitMask;
-    borrow = difference >> (kChunkSize - 1);
-  }
-  while (borrow != 0) {
-    Chunk difference = bigits_[i + offset] - borrow;
-    bigits_[i + offset] = difference & kBigitMask;
-    borrow = difference >> (kChunkSize - 1);
-    ++i;
-  }
-  Clamp();
-}
-
-
-void Bignum::ShiftLeft(int shift_amount) {
-  if (used_digits_ == 0) return;
-  exponent_ += shift_amount / kBigitSize;
-  int local_shift = shift_amount % kBigitSize;
-  EnsureCapacity(used_digits_ + 1);
-  BigitsShiftLeft(local_shift);
-}
-
-
-void Bignum::MultiplyByUInt32(uint32_t factor) {
-  if (factor == 1) return;
-  if (factor == 0) {
-    Zero();
-    return;
-  }
-  if (used_digits_ == 0) return;
-
-  // The product of a bigit with the factor is of size kBigitSize + 32.
-  // Assert that this number + 1 (for the carry) fits into double chunk.
-  ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1);
-  DoubleChunk carry = 0;
-  for (int i = 0; i < used_digits_; ++i) {
-    DoubleChunk product = static_cast<DoubleChunk>(factor) * bigits_[i] + carry;
-    bigits_[i] = static_cast<Chunk>(product & kBigitMask);
-    carry = (product >> kBigitSize);
-  }
-  while (carry != 0) {
-    EnsureCapacity(used_digits_ + 1);
-    bigits_[used_digits_] = carry & kBigitMask;
-    used_digits_++;
-    carry >>= kBigitSize;
-  }
-}
-
-
-void Bignum::MultiplyByUInt64(uint64_t factor) {
-  if (factor == 1) return;
-  if (factor == 0) {
-    Zero();
-    return;
-  }
-  ASSERT(kBigitSize < 32);
-  uint64_t carry = 0;
-  uint64_t low = factor & 0xFFFFFFFF;
-  uint64_t high = factor >> 32;
-  for (int i = 0; i < used_digits_; ++i) {
-    uint64_t product_low = low * bigits_[i];
-    uint64_t product_high = high * bigits_[i];
-    uint64_t tmp = (carry & kBigitMask) + product_low;
-    bigits_[i] = tmp & kBigitMask;
-    carry = (carry >> kBigitSize) + (tmp >> kBigitSize) +
-        (product_high << (32 - kBigitSize));
-  }
-  while (carry != 0) {
-    EnsureCapacity(used_digits_ + 1);
-    bigits_[used_digits_] = carry & kBigitMask;
-    used_digits_++;
-    carry >>= kBigitSize;
-  }
-}
-
-
-void Bignum::MultiplyByPowerOfTen(int exponent) {
-  const uint64_t kFive27 = UINT64_2PART_C(0x6765c793, fa10079d);
-  const uint16_t kFive1 = 5;
-  const uint16_t kFive2 = kFive1 * 5;
-  const uint16_t kFive3 = kFive2 * 5;
-  const uint16_t kFive4 = kFive3 * 5;
-  const uint16_t kFive5 = kFive4 * 5;
-  const uint16_t kFive6 = kFive5 * 5;
-  const uint32_t kFive7 = kFive6 * 5;
-  const uint32_t kFive8 = kFive7 * 5;
-  const uint32_t kFive9 = kFive8 * 5;
-  const uint32_t kFive10 = kFive9 * 5;
-  const uint32_t kFive11 = kFive10 * 5;
-  const uint32_t kFive12 = kFive11 * 5;
-  const uint32_t kFive13 = kFive12 * 5;
-  const uint32_t kFive1_to_12[] =
-      { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6,
-        kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 };
-
-  ASSERT(exponent >= 0);
-  if (exponent == 0) return;
-  if (used_digits_ == 0) return;
-
-  // We shift by exponent at the end just before returning.
-  int remaining_exponent = exponent;
-  while (remaining_exponent >= 27) {
-    MultiplyByUInt64(kFive27);
-    remaining_exponent -= 27;
-  }
-  while (remaining_exponent >= 13) {
-    MultiplyByUInt32(kFive13);
-    remaining_exponent -= 13;
-  }
-  if (remaining_exponent > 0) {
-    MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]);
-  }
-  ShiftLeft(exponent);
-}
-
-
-void Bignum::Square() {
-  ASSERT(IsClamped());
-  int product_length = 2 * used_digits_;
-  EnsureCapacity(product_length);
-
-  // Comba multiplication: compute each column separately.
-  // Example: r = a2a1a0 * b2b1b0.
-  //    r =  1    * a0b0 +
-  //        10    * (a1b0 + a0b1) +
-  //        100   * (a2b0 + a1b1 + a0b2) +
-  //        1000  * (a2b1 + a1b2) +
-  //        10000 * a2b2
-  //
-  // In the worst case we have to accumulate nb-digits products of digit*digit.
-  //
-  // Assert that the additional number of bits in a DoubleChunk are enough to
-  // sum up used_digits of Bigit*Bigit.
-  if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) {
-    UNIMPLEMENTED();
-  }
-  DoubleChunk accumulator = 0;
-  // First shift the digits so we don't overwrite them.
-  int copy_offset = used_digits_;
-  for (int i = 0; i < used_digits_; ++i) {
-    bigits_[copy_offset + i] = bigits_[i];
-  }
-  // We have two loops to avoid some 'if's in the loop.
-  for (int i = 0; i < used_digits_; ++i) {
-    // Process temporary digit i with power i.
-    // The sum of the two indices must be equal to i.
-    int bigit_index1 = i;
-    int bigit_index2 = 0;
-    // Sum all of the sub-products.
-    while (bigit_index1 >= 0) {
-      Chunk chunk1 = bigits_[copy_offset + bigit_index1];
-      Chunk chunk2 = bigits_[copy_offset + bigit_index2];
-      accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
-      bigit_index1--;
-      bigit_index2++;
-    }
-    bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
-    accumulator >>= kBigitSize;
-  }
-  for (int i = used_digits_; i < product_length; ++i) {
-    int bigit_index1 = used_digits_ - 1;
-    int bigit_index2 = i - bigit_index1;
-    // Invariant: sum of both indices is again equal to i.
-    // Inner loop runs 0 times on last iteration, emptying accumulator.
-    while (bigit_index2 < used_digits_) {
-      Chunk chunk1 = bigits_[copy_offset + bigit_index1];
-      Chunk chunk2 = bigits_[copy_offset + bigit_index2];
-      accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
-      bigit_index1--;
-      bigit_index2++;
-    }
-    // The overwritten bigits_[i] will never be read in further loop iterations,
-    // because bigit_index1 and bigit_index2 are always greater
-    // than i - used_digits_.
-    bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
-    accumulator >>= kBigitSize;
-  }
-  // Since the result was guaranteed to lie inside the number the
-  // accumulator must be 0 now.
-  ASSERT(accumulator == 0);
-
-  // Don't forget to update the used_digits and the exponent.
-  used_digits_ = product_length;
-  exponent_ *= 2;
-  Clamp();
-}
-
-
-void Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) {
-  ASSERT(base != 0);
-  ASSERT(power_exponent >= 0);
-  if (power_exponent == 0) {
-    AssignUInt16(1);
-    return;
-  }
-  Zero();
-  int shifts = 0;
-  // We expect base to be in range 2-32, and most often to be 10.
-  // It does not make much sense to implement different algorithms for counting
-  // the bits.
-  while ((base & 1) == 0) {
-    base >>= 1;
-    shifts++;
-  }
-  int bit_size = 0;
-  int tmp_base = base;
-  while (tmp_base != 0) {
-    tmp_base >>= 1;
-    bit_size++;
-  }
-  int final_size = bit_size * power_exponent;
-  // 1 extra bigit for the shifting, and one for rounded final_size.
-  EnsureCapacity(final_size / kBigitSize + 2);
-
-  // Left to Right exponentiation.
-  int mask = 1;
-  while (power_exponent >= mask) mask <<= 1;
-
-  // The mask is now pointing to the bit above the most significant 1-bit of
-  // power_exponent.
-  // Get rid of first 1-bit;
-  mask >>= 2;
-  uint64_t this_value = base;
-
+  for (int i = 0; i < kBigitCapacity; ++i) { 
+    bigits_[i] = 0; 
+  } 
+} 
+ 
+ 
+template<typename S> 
+static int BitSize(S value) { 
+  (void) value;  // Mark variable as used. 
+  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(); 
+  unsigned 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'; 
+  ASSERT('A' <= c && c <= 'F'); 
+  return 10 + c - 'A'; 
+} 
+ 
+ 
+void Bignum::AssignHexString(Vector<const char> value) { 
+  Zero(); 
+  int length = value.length(); 
+ 
+  int needed_bigits = length * 4 / kBigitSize + 1; 
+  EnsureCapacity(needed_bigits); 
+  int string_index = length - 1; 
+  for (int i = 0; i < needed_bigits - 1; ++i) { 
+    // These bigits are guaranteed to be "full". 
+    Chunk current_bigit = 0; 
+    for (int j = 0; j < kBigitSize / 4; j++) { 
+      current_bigit += HexCharValue(value[string_index--]) << (j * 4); 
+    } 
+    bigits_[i] = current_bigit; 
+  } 
+  used_digits_ = needed_bigits - 1; 
+ 
+  Chunk most_significant_bigit = 0;  // Could be = 0; 
+  for (int j = 0; j <= string_index; ++j) { 
+    most_significant_bigit <<= 4; 
+    most_significant_bigit += HexCharValue(value[j]); 
+  } 
+  if (most_significant_bigit != 0) { 
+    bigits_[used_digits_] = most_significant_bigit; 
+    used_digits_++; 
+  } 
+  Clamp(); 
+} 
+ 
+ 
+void Bignum::AddUInt64(uint64_t operand) { 
+  if (operand == 0) return; 
+  Bignum other; 
+  other.AssignUInt64(operand); 
+  AddBignum(other); 
+} 
+ 
+ 
+void Bignum::AddBignum(const Bignum& other) { 
+  ASSERT(IsClamped()); 
+  ASSERT(other.IsClamped()); 
+ 
+  // If this has a greater exponent than other append zero-bigits to this. 
+  // After this call exponent_ <= other.exponent_. 
+  Align(other); 
+ 
+  // There are two possibilities: 
+  //   aaaaaaaaaaa 0000  (where the 0s represent a's exponent) 
+  //     bbbbb 00000000 
+  //   ---------------- 
+  //   ccccccccccc 0000 
+  // or 
+  //    aaaaaaaaaa 0000 
+  //  bbbbbbbbb 0000000 
+  //  ----------------- 
+  //  cccccccccccc 0000 
+  // In both cases we might need a carry bigit. 
+ 
+  EnsureCapacity(1 + Max(BigitLength(), other.BigitLength()) - exponent_); 
+  Chunk carry = 0; 
+  int bigit_pos = other.exponent_ - exponent_; 
+  ASSERT(bigit_pos >= 0); 
+  for (int i = 0; i < other.used_digits_; ++i) { 
+    Chunk sum = bigits_[bigit_pos] + other.bigits_[i] + carry; 
+    bigits_[bigit_pos] = sum & kBigitMask; 
+    carry = sum >> kBigitSize; 
+    bigit_pos++; 
+  } 
+ 
+  while (carry != 0) { 
+    Chunk sum = bigits_[bigit_pos] + carry; 
+    bigits_[bigit_pos] = sum & kBigitMask; 
+    carry = sum >> kBigitSize; 
+    bigit_pos++; 
+  } 
+  used_digits_ = Max(bigit_pos, used_digits_); 
+  ASSERT(IsClamped()); 
+} 
+ 
+ 
+void Bignum::SubtractBignum(const Bignum& other) { 
+  ASSERT(IsClamped()); 
+  ASSERT(other.IsClamped()); 
+  // We require this to be bigger than other. 
+  ASSERT(LessEqual(other, *this)); 
+ 
+  Align(other); 
+ 
+  int offset = other.exponent_ - exponent_; 
+  Chunk borrow = 0; 
+  int i; 
+  for (i = 0; i < other.used_digits_; ++i) { 
+    ASSERT((borrow == 0) || (borrow == 1)); 
+    Chunk difference = bigits_[i + offset] - other.bigits_[i] - borrow; 
+    bigits_[i + offset] = difference & kBigitMask; 
+    borrow = difference >> (kChunkSize - 1); 
+  } 
+  while (borrow != 0) { 
+    Chunk difference = bigits_[i + offset] - borrow; 
+    bigits_[i + offset] = difference & kBigitMask; 
+    borrow = difference >> (kChunkSize - 1); 
+    ++i; 
+  } 
+  Clamp(); 
+} 
+ 
+ 
+void Bignum::ShiftLeft(int shift_amount) { 
+  if (used_digits_ == 0) return; 
+  exponent_ += shift_amount / kBigitSize; 
+  int local_shift = shift_amount % kBigitSize; 
+  EnsureCapacity(used_digits_ + 1); 
+  BigitsShiftLeft(local_shift); 
+} 
+ 
+ 
+void Bignum::MultiplyByUInt32(uint32_t factor) { 
+  if (factor == 1) return; 
+  if (factor == 0) { 
+    Zero(); 
+    return; 
+  } 
+  if (used_digits_ == 0) return; 
+ 
+  // The product of a bigit with the factor is of size kBigitSize + 32. 
+  // Assert that this number + 1 (for the carry) fits into double chunk. 
+  ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1); 
+  DoubleChunk carry = 0; 
+  for (int i = 0; i < used_digits_; ++i) { 
+    DoubleChunk product = static_cast<DoubleChunk>(factor) * bigits_[i] + carry; 
+    bigits_[i] = static_cast<Chunk>(product & kBigitMask); 
+    carry = (product >> kBigitSize); 
+  } 
+  while (carry != 0) { 
+    EnsureCapacity(used_digits_ + 1); 
+    bigits_[used_digits_] = carry & kBigitMask; 
+    used_digits_++; 
+    carry >>= kBigitSize; 
+  } 
+} 
+ 
+ 
+void Bignum::MultiplyByUInt64(uint64_t factor) { 
+  if (factor == 1) return; 
+  if (factor == 0) { 
+    Zero(); 
+    return; 
+  } 
+  ASSERT(kBigitSize < 32); 
+  uint64_t carry = 0; 
+  uint64_t low = factor & 0xFFFFFFFF; 
+  uint64_t high = factor >> 32; 
+  for (int i = 0; i < used_digits_; ++i) { 
+    uint64_t product_low = low * bigits_[i]; 
+    uint64_t product_high = high * bigits_[i]; 
+    uint64_t tmp = (carry & kBigitMask) + product_low; 
+    bigits_[i] = tmp & kBigitMask; 
+    carry = (carry >> kBigitSize) + (tmp >> kBigitSize) + 
+        (product_high << (32 - kBigitSize)); 
+  } 
+  while (carry != 0) { 
+    EnsureCapacity(used_digits_ + 1); 
+    bigits_[used_digits_] = carry & kBigitMask; 
+    used_digits_++; 
+    carry >>= kBigitSize; 
+  } 
+} 
+ 
+ 
+void Bignum::MultiplyByPowerOfTen(int exponent) { 
+  const uint64_t kFive27 = UINT64_2PART_C(0x6765c793, fa10079d); 
+  const uint16_t kFive1 = 5; 
+  const uint16_t kFive2 = kFive1 * 5; 
+  const uint16_t kFive3 = kFive2 * 5; 
+  const uint16_t kFive4 = kFive3 * 5; 
+  const uint16_t kFive5 = kFive4 * 5; 
+  const uint16_t kFive6 = kFive5 * 5; 
+  const uint32_t kFive7 = kFive6 * 5; 
+  const uint32_t kFive8 = kFive7 * 5; 
+  const uint32_t kFive9 = kFive8 * 5; 
+  const uint32_t kFive10 = kFive9 * 5; 
+  const uint32_t kFive11 = kFive10 * 5; 
+  const uint32_t kFive12 = kFive11 * 5; 
+  const uint32_t kFive13 = kFive12 * 5; 
+  const uint32_t kFive1_to_12[] = 
+      { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6, 
+        kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 }; 
+ 
+  ASSERT(exponent >= 0); 
+  if (exponent == 0) return; 
+  if (used_digits_ == 0) return; 
+ 
+  // We shift by exponent at the end just before returning. 
+  int remaining_exponent = exponent; 
+  while (remaining_exponent >= 27) { 
+    MultiplyByUInt64(kFive27); 
+    remaining_exponent -= 27; 
+  } 
+  while (remaining_exponent >= 13) { 
+    MultiplyByUInt32(kFive13); 
+    remaining_exponent -= 13; 
+  } 
+  if (remaining_exponent > 0) { 
+    MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]); 
+  } 
+  ShiftLeft(exponent); 
+} 
+ 
+ 
+void Bignum::Square() { 
+  ASSERT(IsClamped()); 
+  int product_length = 2 * used_digits_; 
+  EnsureCapacity(product_length); 
+ 
+  // Comba multiplication: compute each column separately. 
+  // Example: r = a2a1a0 * b2b1b0. 
+  //    r =  1    * a0b0 + 
+  //        10    * (a1b0 + a0b1) + 
+  //        100   * (a2b0 + a1b1 + a0b2) + 
+  //        1000  * (a2b1 + a1b2) + 
+  //        10000 * a2b2 
+  // 
+  // In the worst case we have to accumulate nb-digits products of digit*digit. 
+  // 
+  // Assert that the additional number of bits in a DoubleChunk are enough to 
+  // sum up used_digits of Bigit*Bigit. 
+  if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) { 
+    UNIMPLEMENTED(); 
+  } 
+  DoubleChunk accumulator = 0; 
+  // First shift the digits so we don't overwrite them. 
+  int copy_offset = used_digits_; 
+  for (int i = 0; i < used_digits_; ++i) { 
+    bigits_[copy_offset + i] = bigits_[i]; 
+  } 
+  // We have two loops to avoid some 'if's in the loop. 
+  for (int i = 0; i < used_digits_; ++i) { 
+    // Process temporary digit i with power i. 
+    // The sum of the two indices must be equal to i. 
+    int bigit_index1 = i; 
+    int bigit_index2 = 0; 
+    // Sum all of the sub-products. 
+    while (bigit_index1 >= 0) { 
+      Chunk chunk1 = bigits_[copy_offset + bigit_index1]; 
+      Chunk chunk2 = bigits_[copy_offset + bigit_index2]; 
+      accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; 
+      bigit_index1--; 
+      bigit_index2++; 
+    } 
+    bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask; 
+    accumulator >>= kBigitSize; 
+  } 
+  for (int i = used_digits_; i < product_length; ++i) { 
+    int bigit_index1 = used_digits_ - 1; 
+    int bigit_index2 = i - bigit_index1; 
+    // Invariant: sum of both indices is again equal to i. 
+    // Inner loop runs 0 times on last iteration, emptying accumulator. 
+    while (bigit_index2 < used_digits_) { 
+      Chunk chunk1 = bigits_[copy_offset + bigit_index1]; 
+      Chunk chunk2 = bigits_[copy_offset + bigit_index2]; 
+      accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; 
+      bigit_index1--; 
+      bigit_index2++; 
+    } 
+    // The overwritten bigits_[i] will never be read in further loop iterations, 
+    // because bigit_index1 and bigit_index2 are always greater 
+    // than i - used_digits_. 
+    bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask; 
+    accumulator >>= kBigitSize; 
+  } 
+  // Since the result was guaranteed to lie inside the number the 
+  // accumulator must be 0 now. 
+  ASSERT(accumulator == 0); 
+ 
+  // Don't forget to update the used_digits and the exponent. 
+  used_digits_ = product_length; 
+  exponent_ *= 2; 
+  Clamp(); 
+} 
+ 
+ 
+void Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) { 
+  ASSERT(base != 0); 
+  ASSERT(power_exponent >= 0); 
+  if (power_exponent == 0) { 
+    AssignUInt16(1); 
+    return; 
+  } 
+  Zero(); 
+  int shifts = 0; 
+  // We expect base to be in range 2-32, and most often to be 10. 
+  // It does not make much sense to implement different algorithms for counting 
+  // the bits. 
+  while ((base & 1) == 0) { 
+    base >>= 1; 
+    shifts++; 
+  } 
+  int bit_size = 0; 
+  int tmp_base = base; 
+  while (tmp_base != 0) { 
+    tmp_base >>= 1; 
+    bit_size++; 
+  } 
+  int final_size = bit_size * power_exponent; 
+  // 1 extra bigit for the shifting, and one for rounded final_size. 
+  EnsureCapacity(final_size / kBigitSize + 2); 
+ 
+  // Left to Right exponentiation. 
+  int mask = 1; 
+  while (power_exponent >= mask) mask <<= 1; 
+ 
+  // The mask is now pointing to the bit above the most significant 1-bit of 
+  // power_exponent. 
+  // Get rid of first 1-bit; 
+  mask >>= 2; 
+  uint64_t this_value = base; 
+ 
   bool delayed_multiplication = false;
-  const uint64_t max_32bits = 0xFFFFFFFF;
-  while (mask != 0 && this_value <= max_32bits) {
-    this_value = this_value * this_value;
-    // Verify that there is enough space in this_value to perform the
-    // multiplication.  The first bit_size bits must be 0.
-    if ((power_exponent & mask) != 0) {
+  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) { 
       ASSERT(bit_size > 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 {
+      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_multiplication = true;
-      }
-    }
-    mask >>= 1;
-  }
-  AssignUInt64(this_value);
+      } 
+    } 
+    mask >>= 1; 
+  } 
+  AssignUInt64(this_value); 
   if (delayed_multiplication) {
-    MultiplyByUInt32(base);
-  }
-
-  // Now do the same thing as a bignum.
-  while (mask != 0) {
-    Square();
-    if ((power_exponent & mask) != 0) {
-      MultiplyByUInt32(base);
-    }
-    mask >>= 1;
-  }
-
-  // And finally add the saved shifts.
-  ShiftLeft(shifts * power_exponent);
-}
-
-
-// Precondition: this/other < 16bit.
-uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) {
-  ASSERT(IsClamped());
-  ASSERT(other.IsClamped());
-  ASSERT(other.used_digits_ > 0);
-
-  // Easy case: if we have less digits than the divisor than the result is 0.
-  // Note: this handles the case where this == 0, too.
-  if (BigitLength() < other.BigitLength()) {
-    return 0;
-  }
-
-  Align(other);
-
-  uint16_t result = 0;
-
-  // Start by removing multiples of 'other' until both numbers have the same
-  // number of digits.
-  while (BigitLength() > other.BigitLength()) {
-    // This naive approach is extremely inefficient if `this` divided by other
-    // is big. This function is implemented for doubleToString where
-    // the result should be small (less than 10).
-    ASSERT(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16));
-    ASSERT(bigits_[used_digits_ - 1] < 0x10000);
-    // Remove the multiples of the first digit.
-    // Example this = 23 and other equals 9. -> Remove 2 multiples.
-    result += static_cast<uint16_t>(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;
-    ASSERT(quotient < 0x10000);
-    result += static_cast<uint16_t>(quotient);
-    Clamp();
-    return result;
-  }
-
-  int division_estimate = this_bigit / (other_bigit + 1);
-  ASSERT(division_estimate < 0x10000);
-  result += static_cast<uint16_t>(division_estimate);
-  SubtractTimes(other, division_estimate);
-
-  if (other_bigit * (division_estimate + 1) > this_bigit) {
-    // No need to even try to subtract. Even if other's remaining digits were 0
-    // another subtraction would be too much.
-    return result;
-  }
-
-  while (LessEqual(other, *this)) {
-    SubtractBignum(other);
-    result++;
-  }
-  return result;
-}
-
-
-template<typename S>
-static int SizeInHexChars(S number) {
-  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 static_cast<char>(value + '0');
-  return static_cast<char>(value - 10 + 'A');
-}
-
-
-bool Bignum::ToHexString(char* buffer, int buffer_size) const {
-  ASSERT(IsClamped());
-  // Each bigit must be printable as separate hex-character.
-  ASSERT(kBigitSize % 4 == 0);
-  const int kHexCharsPerBigit = kBigitSize / 4;
-
-  if (used_digits_ == 0) {
-    if (buffer_size < 2) return false;
-    buffer[0] = '0';
-    buffer[1] = '\0';
-    return true;
-  }
-  // We add 1 for the terminating '\0' character.
-  int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit +
-      SizeInHexChars(bigits_[used_digits_ - 1]) + 1;
-  if (needed_chars > buffer_size) return false;
-  int string_index = needed_chars - 1;
-  buffer[string_index--] = '\0';
-  for (int i = 0; i < exponent_; ++i) {
-    for (int j = 0; j < kHexCharsPerBigit; ++j) {
-      buffer[string_index--] = '0';
-    }
-  }
-  for (int i = 0; i < used_digits_ - 1; ++i) {
-    Chunk current_bigit = bigits_[i];
-    for (int j = 0; j < kHexCharsPerBigit; ++j) {
-      buffer[string_index--] = HexCharOfValue(current_bigit & 0xF);
-      current_bigit >>= 4;
-    }
-  }
-  // And finally the last bigit.
-  Chunk most_significant_bigit = bigits_[used_digits_ - 1];
-  while (most_significant_bigit != 0) {
-    buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF);
-    most_significant_bigit >>= 4;
-  }
-  return true;
-}
-
-
-Bignum::Chunk Bignum::BigitAt(int index) const {
-  if (index >= BigitLength()) return 0;
-  if (index < exponent_) return 0;
-  return bigits_[index - exponent_];
-}
-
-
-int Bignum::Compare(const Bignum& a, const Bignum& b) {
-  ASSERT(a.IsClamped());
-  ASSERT(b.IsClamped());
-  int bigit_length_a = a.BigitLength();
-  int bigit_length_b = b.BigitLength();
-  if (bigit_length_a < bigit_length_b) return -1;
-  if (bigit_length_a > bigit_length_b) return +1;
-  for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i) {
-    Chunk bigit_a = a.BigitAt(i);
-    Chunk bigit_b = b.BigitAt(i);
-    if (bigit_a < bigit_b) return -1;
-    if (bigit_a > bigit_b) return +1;
-    // Otherwise they are equal up to this digit. Try the next digit.
-  }
-  return 0;
-}
-
-
-int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) {
-  ASSERT(a.IsClamped());
-  ASSERT(b.IsClamped());
-  ASSERT(c.IsClamped());
-  if (a.BigitLength() < b.BigitLength()) {
-    return PlusCompare(b, a, c);
-  }
-  if (a.BigitLength() + 1 < c.BigitLength()) return -1;
-  if (a.BigitLength() > c.BigitLength()) return +1;
-  // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than
-  // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one
-  // of 'a'.
-  if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) {
-    return -1;
-  }
-
-  Chunk borrow = 0;
-  // Starting at min_exponent all digits are == 0. So no need to compare them.
-  int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_);
-  for (int i = c.BigitLength() - 1; i >= min_exponent; --i) {
-    Chunk chunk_a = a.BigitAt(i);
-    Chunk chunk_b = b.BigitAt(i);
-    Chunk chunk_c = c.BigitAt(i);
-    Chunk sum = chunk_a + chunk_b;
-    if (sum > chunk_c + borrow) {
-      return +1;
-    } else {
-      borrow = chunk_c + borrow - sum;
-      if (borrow > 1) return -1;
-      borrow <<= kBigitSize;
-    }
-  }
-  if (borrow == 0) return 0;
-  return -1;
-}
-
-
-void Bignum::Clamp() {
-  while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) {
-    used_digits_--;
-  }
-  if (used_digits_ == 0) {
-    // Zero.
-    exponent_ = 0;
-  }
-}
-
-
-bool Bignum::IsClamped() const {
-  return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0;
-}
-
-
-void Bignum::Zero() {
-  for (int i = 0; i < used_digits_; ++i) {
-    bigits_[i] = 0;
-  }
-  used_digits_ = 0;
-  exponent_ = 0;
-}
-
-
-void Bignum::Align(const Bignum& other) {
-  if (exponent_ > other.exponent_) {
-    // If "X" represents a "hidden" digit (by the exponent) then we are in the
-    // following case (a == this, b == other):
-    // a:  aaaaaaXXXX   or a:   aaaaaXXX
-    // b:     bbbbbbX      b: bbbbbbbbXX
-    // We replace some of the hidden digits (X) of a with 0 digits.
-    // a:  aaaaaa000X   or a:   aaaaa0XX
-    int zero_digits = exponent_ - other.exponent_;
-    EnsureCapacity(used_digits_ + zero_digits);
-    for (int i = used_digits_ - 1; i >= 0; --i) {
-      bigits_[i + zero_digits] = bigits_[i];
-    }
-    for (int i = 0; i < zero_digits; ++i) {
-      bigits_[i] = 0;
-    }
-    used_digits_ += zero_digits;
-    exponent_ -= zero_digits;
-    ASSERT(used_digits_ >= 0);
-    ASSERT(exponent_ >= 0);
-  }
-}
-
-
-void Bignum::BigitsShiftLeft(int shift_amount) {
-  ASSERT(shift_amount < kBigitSize);
-  ASSERT(shift_amount >= 0);
-  Chunk carry = 0;
-  for (int i = 0; i < used_digits_; ++i) {
-    Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount);
-    bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask;
-    carry = new_carry;
-  }
-  if (carry != 0) {
-    bigits_[used_digits_] = carry;
-    used_digits_++;
-  }
-}
-
-
-void Bignum::SubtractTimes(const Bignum& other, int factor) {
-  ASSERT(exponent_ <= other.exponent_);
-  if (factor < 3) {
-    for (int i = 0; i < factor; ++i) {
-      SubtractBignum(other);
-    }
-    return;
-  }
-  Chunk borrow = 0;
-  int exponent_diff = other.exponent_ - exponent_;
-  for (int i = 0; i < other.used_digits_; ++i) {
-    DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigits_[i];
-    DoubleChunk remove = borrow + product;
-    Chunk difference = bigits_[i + exponent_diff] - (remove & kBigitMask);
-    bigits_[i + exponent_diff] = difference & kBigitMask;
-    borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) +
-                                (remove >> kBigitSize));
-  }
-  for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) {
-    if (borrow == 0) return;
-    Chunk difference = bigits_[i] - borrow;
-    bigits_[i] = difference & kBigitMask;
-    borrow = difference >> (kChunkSize - 1);
-  }
-  Clamp();
-}
-
-
-}  // namespace double_conversion
+    MultiplyByUInt32(base); 
+  } 
+ 
+  // Now do the same thing as a bignum. 
+  while (mask != 0) { 
+    Square(); 
+    if ((power_exponent & mask) != 0) { 
+      MultiplyByUInt32(base); 
+    } 
+    mask >>= 1; 
+  } 
+ 
+  // And finally add the saved shifts. 
+  ShiftLeft(shifts * power_exponent); 
+} 
+ 
+ 
+// Precondition: this/other < 16bit. 
+uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) { 
+  ASSERT(IsClamped()); 
+  ASSERT(other.IsClamped()); 
+  ASSERT(other.used_digits_ > 0); 
+ 
+  // Easy case: if we have less digits than the divisor than the result is 0. 
+  // Note: this handles the case where this == 0, too. 
+  if (BigitLength() < other.BigitLength()) { 
+    return 0; 
+  } 
+ 
+  Align(other); 
+ 
+  uint16_t result = 0; 
+ 
+  // Start by removing multiples of 'other' until both numbers have the same 
+  // number of digits. 
+  while (BigitLength() > other.BigitLength()) { 
+    // This naive approach is extremely inefficient if `this` divided by other 
+    // is big. This function is implemented for doubleToString where 
+    // the result should be small (less than 10). 
+    ASSERT(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16)); 
+    ASSERT(bigits_[used_digits_ - 1] < 0x10000); 
+    // Remove the multiples of the first digit. 
+    // Example this = 23 and other equals 9. -> Remove 2 multiples. 
+    result += static_cast<uint16_t>(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; 
+    ASSERT(quotient < 0x10000); 
+    result += static_cast<uint16_t>(quotient); 
+    Clamp(); 
+    return result; 
+  } 
+ 
+  int division_estimate = this_bigit / (other_bigit + 1); 
+  ASSERT(division_estimate < 0x10000); 
+  result += static_cast<uint16_t>(division_estimate); 
+  SubtractTimes(other, division_estimate); 
+ 
+  if (other_bigit * (division_estimate + 1) > this_bigit) { 
+    // No need to even try to subtract. Even if other's remaining digits were 0 
+    // another subtraction would be too much. 
+    return result; 
+  } 
+ 
+  while (LessEqual(other, *this)) { 
+    SubtractBignum(other); 
+    result++; 
+  } 
+  return result; 
+} 
+ 
+ 
+template<typename S> 
+static int SizeInHexChars(S number) { 
+  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 static_cast<char>(value + '0'); 
+  return static_cast<char>(value - 10 + 'A'); 
+} 
+ 
+ 
+bool Bignum::ToHexString(char* buffer, int buffer_size) const { 
+  ASSERT(IsClamped()); 
+  // Each bigit must be printable as separate hex-character. 
+  ASSERT(kBigitSize % 4 == 0); 
+  const int kHexCharsPerBigit = kBigitSize / 4; 
+ 
+  if (used_digits_ == 0) { 
+    if (buffer_size < 2) return false; 
+    buffer[0] = '0'; 
+    buffer[1] = '\0'; 
+    return true; 
+  } 
+  // We add 1 for the terminating '\0' character. 
+  int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit + 
+      SizeInHexChars(bigits_[used_digits_ - 1]) + 1; 
+  if (needed_chars > buffer_size) return false; 
+  int string_index = needed_chars - 1; 
+  buffer[string_index--] = '\0'; 
+  for (int i = 0; i < exponent_; ++i) { 
+    for (int j = 0; j < kHexCharsPerBigit; ++j) { 
+      buffer[string_index--] = '0'; 
+    } 
+  } 
+  for (int i = 0; i < used_digits_ - 1; ++i) { 
+    Chunk current_bigit = bigits_[i]; 
+    for (int j = 0; j < kHexCharsPerBigit; ++j) { 
+      buffer[string_index--] = HexCharOfValue(current_bigit & 0xF); 
+      current_bigit >>= 4; 
+    } 
+  } 
+  // And finally the last bigit. 
+  Chunk most_significant_bigit = bigits_[used_digits_ - 1]; 
+  while (most_significant_bigit != 0) { 
+    buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF); 
+    most_significant_bigit >>= 4; 
+  } 
+  return true; 
+} 
+ 
+ 
+Bignum::Chunk Bignum::BigitAt(int index) const { 
+  if (index >= BigitLength()) return 0; 
+  if (index < exponent_) return 0; 
+  return bigits_[index - exponent_]; 
+} 
+ 
+ 
+int Bignum::Compare(const Bignum& a, const Bignum& b) { 
+  ASSERT(a.IsClamped()); 
+  ASSERT(b.IsClamped()); 
+  int bigit_length_a = a.BigitLength(); 
+  int bigit_length_b = b.BigitLength(); 
+  if (bigit_length_a < bigit_length_b) return -1; 
+  if (bigit_length_a > bigit_length_b) return +1; 
+  for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i) { 
+    Chunk bigit_a = a.BigitAt(i); 
+    Chunk bigit_b = b.BigitAt(i); 
+    if (bigit_a < bigit_b) return -1; 
+    if (bigit_a > bigit_b) return +1; 
+    // Otherwise they are equal up to this digit. Try the next digit. 
+  } 
+  return 0; 
+} 
+ 
+ 
+int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) { 
+  ASSERT(a.IsClamped()); 
+  ASSERT(b.IsClamped()); 
+  ASSERT(c.IsClamped()); 
+  if (a.BigitLength() < b.BigitLength()) { 
+    return PlusCompare(b, a, c); 
+  } 
+  if (a.BigitLength() + 1 < c.BigitLength()) return -1; 
+  if (a.BigitLength() > c.BigitLength()) return +1; 
+  // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than 
+  // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one 
+  // of 'a'. 
+  if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) { 
+    return -1; 
+  } 
+ 
+  Chunk borrow = 0; 
+  // Starting at min_exponent all digits are == 0. So no need to compare them. 
+  int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_); 
+  for (int i = c.BigitLength() - 1; i >= min_exponent; --i) { 
+    Chunk chunk_a = a.BigitAt(i); 
+    Chunk chunk_b = b.BigitAt(i); 
+    Chunk chunk_c = c.BigitAt(i); 
+    Chunk sum = chunk_a + chunk_b; 
+    if (sum > chunk_c + borrow) { 
+      return +1; 
+    } else { 
+      borrow = chunk_c + borrow - sum; 
+      if (borrow > 1) return -1; 
+      borrow <<= kBigitSize; 
+    } 
+  } 
+  if (borrow == 0) return 0; 
+  return -1; 
+} 
+ 
+ 
+void Bignum::Clamp() { 
+  while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) { 
+    used_digits_--; 
+  } 
+  if (used_digits_ == 0) { 
+    // Zero. 
+    exponent_ = 0; 
+  } 
+} 
+ 
+ 
+bool Bignum::IsClamped() const { 
+  return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0; 
+} 
+ 
+ 
+void Bignum::Zero() { 
+  for (int i = 0; i < used_digits_; ++i) { 
+    bigits_[i] = 0; 
+  } 
+  used_digits_ = 0; 
+  exponent_ = 0; 
+} 
+ 
+ 
+void Bignum::Align(const Bignum& other) { 
+  if (exponent_ > other.exponent_) { 
+    // If "X" represents a "hidden" digit (by the exponent) then we are in the 
+    // following case (a == this, b == other): 
+    // a:  aaaaaaXXXX   or a:   aaaaaXXX 
+    // b:     bbbbbbX      b: bbbbbbbbXX 
+    // We replace some of the hidden digits (X) of a with 0 digits. 
+    // a:  aaaaaa000X   or a:   aaaaa0XX 
+    int zero_digits = exponent_ - other.exponent_; 
+    EnsureCapacity(used_digits_ + zero_digits); 
+    for (int i = used_digits_ - 1; i >= 0; --i) { 
+      bigits_[i + zero_digits] = bigits_[i]; 
+    } 
+    for (int i = 0; i < zero_digits; ++i) { 
+      bigits_[i] = 0; 
+    } 
+    used_digits_ += zero_digits; 
+    exponent_ -= zero_digits; 
+    ASSERT(used_digits_ >= 0); 
+    ASSERT(exponent_ >= 0); 
+  } 
+} 
+ 
+ 
+void Bignum::BigitsShiftLeft(int shift_amount) { 
+  ASSERT(shift_amount < kBigitSize); 
+  ASSERT(shift_amount >= 0); 
+  Chunk carry = 0; 
+  for (int i = 0; i < used_digits_; ++i) { 
+    Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount); 
+    bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask; 
+    carry = new_carry; 
+  } 
+  if (carry != 0) { 
+    bigits_[used_digits_] = carry; 
+    used_digits_++; 
+  } 
+} 
+ 
+ 
+void Bignum::SubtractTimes(const Bignum& other, int factor) { 
+  ASSERT(exponent_ <= other.exponent_); 
+  if (factor < 3) { 
+    for (int i = 0; i < factor; ++i) { 
+      SubtractBignum(other); 
+    } 
+    return; 
+  } 
+  Chunk borrow = 0; 
+  int exponent_diff = other.exponent_ - exponent_; 
+  for (int i = 0; i < other.used_digits_; ++i) { 
+    DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigits_[i]; 
+    DoubleChunk remove = borrow + product; 
+    Chunk difference = bigits_[i + exponent_diff] - (remove & kBigitMask); 
+    bigits_[i + exponent_diff] = difference & kBigitMask; 
+    borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) + 
+                                (remove >> kBigitSize)); 
+  } 
+  for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) { 
+    if (borrow == 0) return; 
+    Chunk difference = bigits_[i] - borrow; 
+    bigits_[i] = difference & kBigitMask; 
+    borrow = difference >> (kChunkSize - 1); 
+  } 
+  Clamp(); 
+} 
+ 
+ 
+}  // namespace double_conversion