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#include <cmath>

#include <double-conversion/fixed-dtoa.h>

#include <double-conversion/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