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 // 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 <math.h>

 #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) {

     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] = '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, int requested_length,

                                     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);

       buffer[*length] = '0' + digit;

       (*length)++;

       fractionals -= static_cast<uint64_t>(digit) << point;

     }

     // If the first bit after the point is set we have to round up.

     if (((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);

       buffer[*length] = '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, divisor_power, 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