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

1 files changed, 404 insertions, 404 deletions

diff --git a/contrib/libs/double-conversion/fixed-dtoa.cc b/contrib/libs/double-conversion/fixed-dtoa.cc
index 0f989bceaf..eb5b27d777 100644
--- a/contrib/libs/double-conversion/fixed-dtoa.cc
+++ b/contrib/libs/double-conversion/fixed-dtoa.cc
@@ -1,405 +1,405 @@
-// 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.
-
+// 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 <cmath>
-
-#include "fixed-dtoa.h"
-#include "ieee.h"
-
-namespace double_conversion {
-
-// Represents a 128bit type. This class should be replaced by a native type on
-// platforms that support 128bit integers.
-class UInt128 {
- public:
-  UInt128() : high_bits_(0), low_bits_(0) { }
-  UInt128(uint64_t high, uint64_t low) : high_bits_(high), low_bits_(low) { }
-
-  void Multiply(uint32_t multiplicand) {
-    uint64_t accumulator;
-
-    accumulator = (low_bits_ & kMask32) * multiplicand;
-    uint32_t part = static_cast<uint32_t>(accumulator & kMask32);
-    accumulator >>= 32;
-    accumulator = accumulator + (low_bits_ >> 32) * multiplicand;
-    low_bits_ = (accumulator << 32) + part;
-    accumulator >>= 32;
-    accumulator = accumulator + (high_bits_ & kMask32) * multiplicand;
-    part = static_cast<uint32_t>(accumulator & kMask32);
-    accumulator >>= 32;
-    accumulator = accumulator + (high_bits_ >> 32) * multiplicand;
-    high_bits_ = (accumulator << 32) + part;
-    ASSERT((accumulator >> 32) == 0);
-  }
-
-  void Shift(int shift_amount) {
-    ASSERT(-64 <= shift_amount && shift_amount <= 64);
-    if (shift_amount == 0) {
-      return;
-    } else if (shift_amount == -64) {
-      high_bits_ = low_bits_;
-      low_bits_ = 0;
-    } else if (shift_amount == 64) {
-      low_bits_ = high_bits_;
-      high_bits_ = 0;
-    } else if (shift_amount <= 0) {
-      high_bits_ <<= -shift_amount;
-      high_bits_ += low_bits_ >> (64 + shift_amount);
-      low_bits_ <<= -shift_amount;
-    } else {
-      low_bits_ >>= shift_amount;
-      low_bits_ += high_bits_ << (64 - shift_amount);
-      high_bits_ >>= shift_amount;
-    }
-  }
-
-  // Modifies *this to *this MOD (2^power).
-  // Returns *this DIV (2^power).
-  int DivModPowerOf2(int power) {
-    if (power >= 64) {
-      int result = static_cast<int>(high_bits_ >> (power - 64));
-      high_bits_ -= static_cast<uint64_t>(result) << (power - 64);
-      return result;
-    } else {
-      uint64_t part_low = low_bits_ >> power;
-      uint64_t part_high = high_bits_ << (64 - power);
-      int result = static_cast<int>(part_low + part_high);
-      high_bits_ = 0;
-      low_bits_ -= part_low << power;
-      return result;
-    }
-  }
-
-  bool IsZero() const {
-    return high_bits_ == 0 && low_bits_ == 0;
-  }
-
-  int BitAt(int position) const {
-    if (position >= 64) {
-      return static_cast<int>(high_bits_ >> (position - 64)) & 1;
-    } else {
-      return static_cast<int>(low_bits_ >> position) & 1;
-    }
-  }
-
- private:
-  static const uint64_t kMask32 = 0xFFFFFFFF;
-  // Value == (high_bits_ << 64) + low_bits_
-  uint64_t high_bits_;
-  uint64_t low_bits_;
-};
-
-
-static const int kDoubleSignificandSize = 53;  // Includes the hidden bit.
-
-
-static void FillDigits32FixedLength(uint32_t number, int requested_length,
-                                    Vector<char> buffer, int* length) {
-  for (int i = requested_length - 1; i >= 0; --i) {
-    buffer[(*length) + i] = '0' + number % 10;
-    number /= 10;
-  }
-  *length += requested_length;
-}
-
-
-static void FillDigits32(uint32_t number, Vector<char> buffer, int* length) {
-  int number_length = 0;
-  // We fill the digits in reverse order and exchange them afterwards.
-  while (number != 0) {
-    int digit = number % 10;
-    number /= 10;
-    buffer[(*length) + number_length] = static_cast<char>('0' + digit);
-    number_length++;
-  }
-  // Exchange the digits.
-  int i = *length;
-  int j = *length + number_length - 1;
-  while (i < j) {
-    char tmp = buffer[i];
-    buffer[i] = buffer[j];
-    buffer[j] = tmp;
-    i++;
-    j--;
-  }
-  *length += number_length;
-}
-
-
-static void FillDigits64FixedLength(uint64_t number,
-                                    Vector<char> buffer, int* length) {
-  const uint32_t kTen7 = 10000000;
-  // For efficiency cut the number into 3 uint32_t parts, and print those.
-  uint32_t part2 = static_cast<uint32_t>(number % kTen7);
-  number /= kTen7;
-  uint32_t part1 = static_cast<uint32_t>(number % kTen7);
-  uint32_t part0 = static_cast<uint32_t>(number / kTen7);
-
-  FillDigits32FixedLength(part0, 3, buffer, length);
-  FillDigits32FixedLength(part1, 7, buffer, length);
-  FillDigits32FixedLength(part2, 7, buffer, length);
-}
-
-
-static void FillDigits64(uint64_t number, Vector<char> buffer, int* length) {
-  const uint32_t kTen7 = 10000000;
-  // For efficiency cut the number into 3 uint32_t parts, and print those.
-  uint32_t part2 = static_cast<uint32_t>(number % kTen7);
-  number /= kTen7;
-  uint32_t part1 = static_cast<uint32_t>(number % kTen7);
-  uint32_t part0 = static_cast<uint32_t>(number / kTen7);
-
-  if (part0 != 0) {
-    FillDigits32(part0, buffer, length);
-    FillDigits32FixedLength(part1, 7, buffer, length);
-    FillDigits32FixedLength(part2, 7, buffer, length);
-  } else if (part1 != 0) {
-    FillDigits32(part1, buffer, length);
-    FillDigits32FixedLength(part2, 7, buffer, length);
-  } else {
-    FillDigits32(part2, buffer, length);
-  }
-}
-
-
-static void RoundUp(Vector<char> buffer, int* length, int* decimal_point) {
-  // An empty buffer represents 0.
-  if (*length == 0) {
-    buffer[0] = '1';
-    *decimal_point = 1;
-    *length = 1;
-    return;
-  }
-  // Round the last digit until we either have a digit that was not '9' or until
-  // we reached the first digit.
-  buffer[(*length) - 1]++;
-  for (int i = (*length) - 1; i > 0; --i) {
-    if (buffer[i] != '0' + 10) {
-      return;
-    }
-    buffer[i] = '0';
-    buffer[i - 1]++;
-  }
-  // If the first digit is now '0' + 10, we would need to set it to '0' and add
-  // a '1' in front. However we reach the first digit only if all following
-  // digits had been '9' before rounding up. Now all trailing digits are '0' and
-  // we simply switch the first digit to '1' and update the decimal-point
-  // (indicating that the point is now one digit to the right).
-  if (buffer[0] == '0' + 10) {
-    buffer[0] = '1';
-    (*decimal_point)++;
-  }
-}
-
-
-// The given fractionals number represents a fixed-point number with binary
-// point at bit (-exponent).
-// Preconditions:
-//   -128 <= exponent <= 0.
-//   0 <= fractionals * 2^exponent < 1
-//   The buffer holds the result.
-// The function will round its result. During the rounding-process digits not
-// generated by this function might be updated, and the decimal-point variable
-// might be updated. If this function generates the digits 99 and the buffer
-// already contained "199" (thus yielding a buffer of "19999") then a
-// rounding-up will change the contents of the buffer to "20000".
-static void FillFractionals(uint64_t fractionals, int exponent,
-                            int fractional_count, Vector<char> buffer,
-                            int* length, int* decimal_point) {
-  ASSERT(-128 <= exponent && exponent <= 0);
-  // 'fractionals' is a fixed-point number, with binary point at bit
-  // (-exponent). Inside the function the non-converted remainder of fractionals
-  // is a fixed-point number, with binary point at bit 'point'.
-  if (-exponent <= 64) {
-    // One 64 bit number is sufficient.
-    ASSERT(fractionals >> 56 == 0);
-    int point = -exponent;
-    for (int i = 0; i < fractional_count; ++i) {
-      if (fractionals == 0) break;
-      // Instead of multiplying by 10 we multiply by 5 and adjust the point
-      // location. This way the fractionals variable will not overflow.
-      // Invariant at the beginning of the loop: fractionals < 2^point.
-      // Initially we have: point <= 64 and fractionals < 2^56
-      // After each iteration the point is decremented by one.
-      // Note that 5^3 = 125 < 128 = 2^7.
-      // Therefore three iterations of this loop will not overflow fractionals
-      // (even without the subtraction at the end of the loop body). At this
-      // time point will satisfy point <= 61 and therefore fractionals < 2^point
-      // and any further multiplication of fractionals by 5 will not overflow.
-      fractionals *= 5;
-      point--;
-      int digit = static_cast<int>(fractionals >> point);
-      ASSERT(digit <= 9);
-      buffer[*length] = static_cast<char>('0' + digit);
-      (*length)++;
-      fractionals -= static_cast<uint64_t>(digit) << point;
-    }
-    // If the first bit after the point is set we have to round up.
-    ASSERT(fractionals == 0 || point - 1 >= 0);
-    if ((fractionals != 0) && ((fractionals >> (point - 1)) & 1) == 1) {
-      RoundUp(buffer, length, decimal_point);
-    }
-  } else {  // We need 128 bits.
-    ASSERT(64 < -exponent && -exponent <= 128);
-    UInt128 fractionals128 = UInt128(fractionals, 0);
-    fractionals128.Shift(-exponent - 64);
-    int point = 128;
-    for (int i = 0; i < fractional_count; ++i) {
-      if (fractionals128.IsZero()) break;
-      // As before: instead of multiplying by 10 we multiply by 5 and adjust the
-      // point location.
-      // This multiplication will not overflow for the same reasons as before.
-      fractionals128.Multiply(5);
-      point--;
-      int digit = fractionals128.DivModPowerOf2(point);
-      ASSERT(digit <= 9);
-      buffer[*length] = static_cast<char>('0' + digit);
-      (*length)++;
-    }
-    if (fractionals128.BitAt(point - 1) == 1) {
-      RoundUp(buffer, length, decimal_point);
-    }
-  }
-}
-
-
-// Removes leading and trailing zeros.
-// If leading zeros are removed then the decimal point position is adjusted.
-static void TrimZeros(Vector<char> buffer, int* length, int* decimal_point) {
-  while (*length > 0 && buffer[(*length) - 1] == '0') {
-    (*length)--;
-  }
-  int first_non_zero = 0;
-  while (first_non_zero < *length && buffer[first_non_zero] == '0') {
-    first_non_zero++;
-  }
-  if (first_non_zero != 0) {
-    for (int i = first_non_zero; i < *length; ++i) {
-      buffer[i - first_non_zero] = buffer[i];
-    }
-    *length -= first_non_zero;
-    *decimal_point -= first_non_zero;
-  }
-}
-
-
-bool FastFixedDtoa(double v,
-                   int fractional_count,
-                   Vector<char> buffer,
-                   int* length,
-                   int* decimal_point) {
-  const uint32_t kMaxUInt32 = 0xFFFFFFFF;
-  uint64_t significand = Double(v).Significand();
-  int exponent = Double(v).Exponent();
-  // v = significand * 2^exponent (with significand a 53bit integer).
-  // If the exponent is larger than 20 (i.e. we may have a 73bit number) then we
-  // don't know how to compute the representation. 2^73 ~= 9.5*10^21.
-  // If necessary this limit could probably be increased, but we don't need
-  // more.
-  if (exponent > 20) return false;
-  if (fractional_count > 20) return false;
-  *length = 0;
-  // At most kDoubleSignificandSize bits of the significand are non-zero.
-  // Given a 64 bit integer we have 11 0s followed by 53 potentially non-zero
-  // bits:  0..11*..0xxx..53*..xx
-  if (exponent + kDoubleSignificandSize > 64) {
-    // The exponent must be > 11.
-    //
-    // We know that v = significand * 2^exponent.
-    // And the exponent > 11.
-    // We simplify the task by dividing v by 10^17.
-    // The quotient delivers the first digits, and the remainder fits into a 64
-    // bit number.
-    // Dividing by 10^17 is equivalent to dividing by 5^17*2^17.
-    const uint64_t kFive17 = UINT64_2PART_C(0xB1, A2BC2EC5);  // 5^17
-    uint64_t divisor = kFive17;
-    int divisor_power = 17;
-    uint64_t dividend = significand;
-    uint32_t quotient;
-    uint64_t remainder;
-    // Let v = f * 2^e with f == significand and e == exponent.
-    // Then need q (quotient) and r (remainder) as follows:
-    //   v            = q * 10^17       + r
-    //   f * 2^e      = q * 10^17       + r
-    //   f * 2^e      = q * 5^17 * 2^17 + r
-    // If e > 17 then
-    //   f * 2^(e-17) = q * 5^17        + r/2^17
-    // else
-    //   f  = q * 5^17 * 2^(17-e) + r/2^e
-    if (exponent > divisor_power) {
-      // We only allow exponents of up to 20 and therefore (17 - e) <= 3
-      dividend <<= exponent - divisor_power;
-      quotient = static_cast<uint32_t>(dividend / divisor);
-      remainder = (dividend % divisor) << divisor_power;
-    } else {
-      divisor <<= divisor_power - exponent;
-      quotient = static_cast<uint32_t>(dividend / divisor);
-      remainder = (dividend % divisor) << exponent;
-    }
-    FillDigits32(quotient, buffer, length);
-    FillDigits64FixedLength(remainder, buffer, length);
-    *decimal_point = *length;
-  } else if (exponent >= 0) {
-    // 0 <= exponent <= 11
-    significand <<= exponent;
-    FillDigits64(significand, buffer, length);
-    *decimal_point = *length;
-  } else if (exponent > -kDoubleSignificandSize) {
-    // We have to cut the number.
-    uint64_t integrals = significand >> -exponent;
-    uint64_t fractionals = significand - (integrals << -exponent);
-    if (integrals > kMaxUInt32) {
-      FillDigits64(integrals, buffer, length);
-    } else {
-      FillDigits32(static_cast<uint32_t>(integrals), buffer, length);
-    }
-    *decimal_point = *length;
-    FillFractionals(fractionals, exponent, fractional_count,
-                    buffer, length, decimal_point);
-  } else if (exponent < -128) {
-    // This configuration (with at most 20 digits) means that all digits must be
-    // 0.
-    ASSERT(fractional_count <= 20);
-    buffer[0] = '\0';
-    *length = 0;
-    *decimal_point = -fractional_count;
-  } else {
-    *decimal_point = 0;
-    FillFractionals(significand, exponent, fractional_count,
-                    buffer, length, decimal_point);
-  }
-  TrimZeros(buffer, length, decimal_point);
-  buffer[*length] = '\0';
-  if ((*length) == 0) {
-    // The string is empty and the decimal_point thus has no importance. Mimick
-    // Gay's dtoa and and set it to -fractional_count.
-    *decimal_point = -fractional_count;
-  }
-  return true;
-}
-
-}  // namespace double_conversion
+ 
+#include "fixed-dtoa.h" 
+#include "ieee.h" 
+ 
+namespace double_conversion { 
+ 
+// Represents a 128bit type. This class should be replaced by a native type on 
+// platforms that support 128bit integers. 
+class UInt128 { 
+ public: 
+  UInt128() : high_bits_(0), low_bits_(0) { } 
+  UInt128(uint64_t high, uint64_t low) : high_bits_(high), low_bits_(low) { } 
+ 
+  void Multiply(uint32_t multiplicand) { 
+    uint64_t accumulator; 
+ 
+    accumulator = (low_bits_ & kMask32) * multiplicand; 
+    uint32_t part = static_cast<uint32_t>(accumulator & kMask32); 
+    accumulator >>= 32; 
+    accumulator = accumulator + (low_bits_ >> 32) * multiplicand; 
+    low_bits_ = (accumulator << 32) + part; 
+    accumulator >>= 32; 
+    accumulator = accumulator + (high_bits_ & kMask32) * multiplicand; 
+    part = static_cast<uint32_t>(accumulator & kMask32); 
+    accumulator >>= 32; 
+    accumulator = accumulator + (high_bits_ >> 32) * multiplicand; 
+    high_bits_ = (accumulator << 32) + part; 
+    ASSERT((accumulator >> 32) == 0); 
+  } 
+ 
+  void Shift(int shift_amount) { 
+    ASSERT(-64 <= shift_amount && shift_amount <= 64); 
+    if (shift_amount == 0) { 
+      return; 
+    } else if (shift_amount == -64) { 
+      high_bits_ = low_bits_; 
+      low_bits_ = 0; 
+    } else if (shift_amount == 64) { 
+      low_bits_ = high_bits_; 
+      high_bits_ = 0; 
+    } else if (shift_amount <= 0) { 
+      high_bits_ <<= -shift_amount; 
+      high_bits_ += low_bits_ >> (64 + shift_amount); 
+      low_bits_ <<= -shift_amount; 
+    } else { 
+      low_bits_ >>= shift_amount; 
+      low_bits_ += high_bits_ << (64 - shift_amount); 
+      high_bits_ >>= shift_amount; 
+    } 
+  } 
+ 
+  // Modifies *this to *this MOD (2^power). 
+  // Returns *this DIV (2^power). 
+  int DivModPowerOf2(int power) { 
+    if (power >= 64) { 
+      int result = static_cast<int>(high_bits_ >> (power - 64)); 
+      high_bits_ -= static_cast<uint64_t>(result) << (power - 64); 
+      return result; 
+    } else { 
+      uint64_t part_low = low_bits_ >> power; 
+      uint64_t part_high = high_bits_ << (64 - power); 
+      int result = static_cast<int>(part_low + part_high); 
+      high_bits_ = 0; 
+      low_bits_ -= part_low << power; 
+      return result; 
+    } 
+  } 
+ 
+  bool IsZero() const { 
+    return high_bits_ == 0 && low_bits_ == 0; 
+  } 
+ 
+  int BitAt(int position) const { 
+    if (position >= 64) { 
+      return static_cast<int>(high_bits_ >> (position - 64)) & 1; 
+    } else { 
+      return static_cast<int>(low_bits_ >> position) & 1; 
+    } 
+  } 
+ 
+ private: 
+  static const uint64_t kMask32 = 0xFFFFFFFF; 
+  // Value == (high_bits_ << 64) + low_bits_ 
+  uint64_t high_bits_; 
+  uint64_t low_bits_; 
+}; 
+ 
+ 
+static const int kDoubleSignificandSize = 53;  // Includes the hidden bit. 
+ 
+ 
+static void FillDigits32FixedLength(uint32_t number, int requested_length, 
+                                    Vector<char> buffer, int* length) { 
+  for (int i = requested_length - 1; i >= 0; --i) { 
+    buffer[(*length) + i] = '0' + number % 10; 
+    number /= 10; 
+  } 
+  *length += requested_length; 
+} 
+ 
+ 
+static void FillDigits32(uint32_t number, Vector<char> buffer, int* length) { 
+  int number_length = 0; 
+  // We fill the digits in reverse order and exchange them afterwards. 
+  while (number != 0) { 
+    int digit = number % 10; 
+    number /= 10; 
+    buffer[(*length) + number_length] = static_cast<char>('0' + digit); 
+    number_length++; 
+  } 
+  // Exchange the digits. 
+  int i = *length; 
+  int j = *length + number_length - 1; 
+  while (i < j) { 
+    char tmp = buffer[i]; 
+    buffer[i] = buffer[j]; 
+    buffer[j] = tmp; 
+    i++; 
+    j--; 
+  } 
+  *length += number_length; 
+} 
+ 
+ 
+static void FillDigits64FixedLength(uint64_t number, 
+                                    Vector<char> buffer, int* length) { 
+  const uint32_t kTen7 = 10000000; 
+  // For efficiency cut the number into 3 uint32_t parts, and print those. 
+  uint32_t part2 = static_cast<uint32_t>(number % kTen7); 
+  number /= kTen7; 
+  uint32_t part1 = static_cast<uint32_t>(number % kTen7); 
+  uint32_t part0 = static_cast<uint32_t>(number / kTen7); 
+ 
+  FillDigits32FixedLength(part0, 3, buffer, length); 
+  FillDigits32FixedLength(part1, 7, buffer, length); 
+  FillDigits32FixedLength(part2, 7, buffer, length); 
+} 
+ 
+ 
+static void FillDigits64(uint64_t number, Vector<char> buffer, int* length) { 
+  const uint32_t kTen7 = 10000000; 
+  // For efficiency cut the number into 3 uint32_t parts, and print those. 
+  uint32_t part2 = static_cast<uint32_t>(number % kTen7); 
+  number /= kTen7; 
+  uint32_t part1 = static_cast<uint32_t>(number % kTen7); 
+  uint32_t part0 = static_cast<uint32_t>(number / kTen7); 
+ 
+  if (part0 != 0) { 
+    FillDigits32(part0, buffer, length); 
+    FillDigits32FixedLength(part1, 7, buffer, length); 
+    FillDigits32FixedLength(part2, 7, buffer, length); 
+  } else if (part1 != 0) { 
+    FillDigits32(part1, buffer, length); 
+    FillDigits32FixedLength(part2, 7, buffer, length); 
+  } else { 
+    FillDigits32(part2, buffer, length); 
+  } 
+} 
+ 
+ 
+static void RoundUp(Vector<char> buffer, int* length, int* decimal_point) { 
+  // An empty buffer represents 0. 
+  if (*length == 0) { 
+    buffer[0] = '1'; 
+    *decimal_point = 1; 
+    *length = 1; 
+    return; 
+  } 
+  // Round the last digit until we either have a digit that was not '9' or until 
+  // we reached the first digit. 
+  buffer[(*length) - 1]++; 
+  for (int i = (*length) - 1; i > 0; --i) { 
+    if (buffer[i] != '0' + 10) { 
+      return; 
+    } 
+    buffer[i] = '0'; 
+    buffer[i - 1]++; 
+  } 
+  // If the first digit is now '0' + 10, we would need to set it to '0' and add 
+  // a '1' in front. However we reach the first digit only if all following 
+  // digits had been '9' before rounding up. Now all trailing digits are '0' and 
+  // we simply switch the first digit to '1' and update the decimal-point 
+  // (indicating that the point is now one digit to the right). 
+  if (buffer[0] == '0' + 10) { 
+    buffer[0] = '1'; 
+    (*decimal_point)++; 
+  } 
+} 
+ 
+ 
+// The given fractionals number represents a fixed-point number with binary 
+// point at bit (-exponent). 
+// Preconditions: 
+//   -128 <= exponent <= 0. 
+//   0 <= fractionals * 2^exponent < 1 
+//   The buffer holds the result. 
+// The function will round its result. During the rounding-process digits not 
+// generated by this function might be updated, and the decimal-point variable 
+// might be updated. If this function generates the digits 99 and the buffer 
+// already contained "199" (thus yielding a buffer of "19999") then a 
+// rounding-up will change the contents of the buffer to "20000". 
+static void FillFractionals(uint64_t fractionals, int exponent, 
+                            int fractional_count, Vector<char> buffer, 
+                            int* length, int* decimal_point) { 
+  ASSERT(-128 <= exponent && exponent <= 0); 
+  // 'fractionals' is a fixed-point number, with binary point at bit 
+  // (-exponent). Inside the function the non-converted remainder of fractionals 
+  // is a fixed-point number, with binary point at bit 'point'. 
+  if (-exponent <= 64) { 
+    // One 64 bit number is sufficient. 
+    ASSERT(fractionals >> 56 == 0); 
+    int point = -exponent; 
+    for (int i = 0; i < fractional_count; ++i) { 
+      if (fractionals == 0) break; 
+      // Instead of multiplying by 10 we multiply by 5 and adjust the point 
+      // location. This way the fractionals variable will not overflow. 
+      // Invariant at the beginning of the loop: fractionals < 2^point. 
+      // Initially we have: point <= 64 and fractionals < 2^56 
+      // After each iteration the point is decremented by one. 
+      // Note that 5^3 = 125 < 128 = 2^7. 
+      // Therefore three iterations of this loop will not overflow fractionals 
+      // (even without the subtraction at the end of the loop body). At this 
+      // time point will satisfy point <= 61 and therefore fractionals < 2^point 
+      // and any further multiplication of fractionals by 5 will not overflow. 
+      fractionals *= 5; 
+      point--; 
+      int digit = static_cast<int>(fractionals >> point); 
+      ASSERT(digit <= 9); 
+      buffer[*length] = static_cast<char>('0' + digit); 
+      (*length)++; 
+      fractionals -= static_cast<uint64_t>(digit) << point; 
+    } 
+    // If the first bit after the point is set we have to round up. 
+    ASSERT(fractionals == 0 || point - 1 >= 0); 
+    if ((fractionals != 0) && ((fractionals >> (point - 1)) & 1) == 1) { 
+      RoundUp(buffer, length, decimal_point); 
+    } 
+  } else {  // We need 128 bits. 
+    ASSERT(64 < -exponent && -exponent <= 128); 
+    UInt128 fractionals128 = UInt128(fractionals, 0); 
+    fractionals128.Shift(-exponent - 64); 
+    int point = 128; 
+    for (int i = 0; i < fractional_count; ++i) { 
+      if (fractionals128.IsZero()) break; 
+      // As before: instead of multiplying by 10 we multiply by 5 and adjust the 
+      // point location. 
+      // This multiplication will not overflow for the same reasons as before. 
+      fractionals128.Multiply(5); 
+      point--; 
+      int digit = fractionals128.DivModPowerOf2(point); 
+      ASSERT(digit <= 9); 
+      buffer[*length] = static_cast<char>('0' + digit); 
+      (*length)++; 
+    } 
+    if (fractionals128.BitAt(point - 1) == 1) { 
+      RoundUp(buffer, length, decimal_point); 
+    } 
+  } 
+} 
+ 
+ 
+// Removes leading and trailing zeros. 
+// If leading zeros are removed then the decimal point position is adjusted. 
+static void TrimZeros(Vector<char> buffer, int* length, int* decimal_point) { 
+  while (*length > 0 && buffer[(*length) - 1] == '0') { 
+    (*length)--; 
+  } 
+  int first_non_zero = 0; 
+  while (first_non_zero < *length && buffer[first_non_zero] == '0') { 
+    first_non_zero++; 
+  } 
+  if (first_non_zero != 0) { 
+    for (int i = first_non_zero; i < *length; ++i) { 
+      buffer[i - first_non_zero] = buffer[i]; 
+    } 
+    *length -= first_non_zero; 
+    *decimal_point -= first_non_zero; 
+  } 
+} 
+ 
+ 
+bool FastFixedDtoa(double v, 
+                   int fractional_count, 
+                   Vector<char> buffer, 
+                   int* length, 
+                   int* decimal_point) { 
+  const uint32_t kMaxUInt32 = 0xFFFFFFFF; 
+  uint64_t significand = Double(v).Significand(); 
+  int exponent = Double(v).Exponent(); 
+  // v = significand * 2^exponent (with significand a 53bit integer). 
+  // If the exponent is larger than 20 (i.e. we may have a 73bit number) then we 
+  // don't know how to compute the representation. 2^73 ~= 9.5*10^21. 
+  // If necessary this limit could probably be increased, but we don't need 
+  // more. 
+  if (exponent > 20) return false; 
+  if (fractional_count > 20) return false; 
+  *length = 0; 
+  // At most kDoubleSignificandSize bits of the significand are non-zero. 
+  // Given a 64 bit integer we have 11 0s followed by 53 potentially non-zero 
+  // bits:  0..11*..0xxx..53*..xx 
+  if (exponent + kDoubleSignificandSize > 64) { 
+    // The exponent must be > 11. 
+    // 
+    // We know that v = significand * 2^exponent. 
+    // And the exponent > 11. 
+    // We simplify the task by dividing v by 10^17. 
+    // The quotient delivers the first digits, and the remainder fits into a 64 
+    // bit number. 
+    // Dividing by 10^17 is equivalent to dividing by 5^17*2^17. 
+    const uint64_t kFive17 = UINT64_2PART_C(0xB1, A2BC2EC5);  // 5^17 
+    uint64_t divisor = kFive17; 
+    int divisor_power = 17; 
+    uint64_t dividend = significand; 
+    uint32_t quotient; 
+    uint64_t remainder; 
+    // Let v = f * 2^e with f == significand and e == exponent. 
+    // Then need q (quotient) and r (remainder) as follows: 
+    //   v            = q * 10^17       + r 
+    //   f * 2^e      = q * 10^17       + r 
+    //   f * 2^e      = q * 5^17 * 2^17 + r 
+    // If e > 17 then 
+    //   f * 2^(e-17) = q * 5^17        + r/2^17 
+    // else 
+    //   f  = q * 5^17 * 2^(17-e) + r/2^e 
+    if (exponent > divisor_power) { 
+      // We only allow exponents of up to 20 and therefore (17 - e) <= 3 
+      dividend <<= exponent - divisor_power; 
+      quotient = static_cast<uint32_t>(dividend / divisor); 
+      remainder = (dividend % divisor) << divisor_power; 
+    } else { 
+      divisor <<= divisor_power - exponent; 
+      quotient = static_cast<uint32_t>(dividend / divisor); 
+      remainder = (dividend % divisor) << exponent; 
+    } 
+    FillDigits32(quotient, buffer, length); 
+    FillDigits64FixedLength(remainder, buffer, length); 
+    *decimal_point = *length; 
+  } else if (exponent >= 0) { 
+    // 0 <= exponent <= 11 
+    significand <<= exponent; 
+    FillDigits64(significand, buffer, length); 
+    *decimal_point = *length; 
+  } else if (exponent > -kDoubleSignificandSize) { 
+    // We have to cut the number. 
+    uint64_t integrals = significand >> -exponent; 
+    uint64_t fractionals = significand - (integrals << -exponent); 
+    if (integrals > kMaxUInt32) { 
+      FillDigits64(integrals, buffer, length); 
+    } else { 
+      FillDigits32(static_cast<uint32_t>(integrals), buffer, length); 
+    } 
+    *decimal_point = *length; 
+    FillFractionals(fractionals, exponent, fractional_count, 
+                    buffer, length, decimal_point); 
+  } else if (exponent < -128) { 
+    // This configuration (with at most 20 digits) means that all digits must be 
+    // 0. 
+    ASSERT(fractional_count <= 20); 
+    buffer[0] = '\0'; 
+    *length = 0; 
+    *decimal_point = -fractional_count; 
+  } else { 
+    *decimal_point = 0; 
+    FillFractionals(significand, exponent, fractional_count, 
+                    buffer, length, decimal_point); 
+  } 
+  TrimZeros(buffer, length, decimal_point); 
+  buffer[*length] = '\0'; 
+  if ((*length) == 0) { 
+    // The string is empty and the decimal_point thus has no importance. Mimick 
+    // Gay's dtoa and and set it to -fractional_count. 
+    *decimal_point = -fractional_count; 
+  } 
+  return true; 
+} 
+ 
+}  // namespace double_conversion