// 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

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// 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

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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

#include <climits>

#include <cstdarg>

#include "bignum.h"

#include "cached-powers.h"

#include "ieee.h"

#include "strtod.h"

namespace double_conversion {

#if defined(DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS)

// 2^53 = 9007199254740992.

// Any integer with at most 15 decimal digits will hence fit into a double

// (which has a 53bit significand) without loss of precision.

static const int kMaxExactDoubleIntegerDecimalDigits = 15;

#endif // #if defined(DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS)

// 2^64 = 18446744073709551616 > 10^19

static const int kMaxUint64DecimalDigits = 19;

// Max double: 1.7976931348623157 x 10^308

// Min non-zero double: 4.9406564584124654 x 10^-324

// Any x >= 10^309 is interpreted as +infinity.

// Any x <= 10^-324 is interpreted as 0.

// Note that 2.5e-324 (despite being smaller than the min double) will be read

// as non-zero (equal to the min non-zero double).

static const int kMaxDecimalPower = 309;

static const int kMinDecimalPower = -324;

// 2^64 = 18446744073709551616

static const uint64_t kMaxUint64 = DOUBLE_CONVERSION_UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF);

#if defined(DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS)

static const double exact_powers_of_ten[] = {

  1.0,  // 10^0

  10.0,

  100.0,

  1000.0,

  10000.0,

  100000.0,

  1000000.0,

  10000000.0,

  100000000.0,

  1000000000.0,

  10000000000.0,  // 10^10

  100000000000.0,

  1000000000000.0,

  10000000000000.0,

  100000000000000.0,

  1000000000000000.0,

  10000000000000000.0,

  100000000000000000.0,

  1000000000000000000.0,

  10000000000000000000.0,

  100000000000000000000.0,  // 10^20

  1000000000000000000000.0,

  // 10^22 = 0x21e19e0c9bab2400000 = 0x878678326eac9 * 2^22

  10000000000000000000000.0

};

static const int kExactPowersOfTenSize = DOUBLE_CONVERSION_ARRAY_SIZE(exact_powers_of_ten);

#endif // #if defined(DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS)

// Maximum number of significant digits in the decimal representation.

// In fact the value is 772 (see conversions.cc), but to give us some margin

// we round up to 780.

static const int kMaxSignificantDecimalDigits = 780;

static Vector<const char> TrimLeadingZeros(Vector<const char> buffer) {

  for (int i = 0; i < buffer.length(); i++) {

    if (buffer[i] != '0') {

      return buffer.SubVector(i, buffer.length());

    }

  }

  return Vector<const char>(buffer.start(), 0);

}

static void CutToMaxSignificantDigits(Vector<const char> buffer,

                                       int exponent,

                                       char* significant_buffer,

                                       int* significant_exponent) {

  for (int i = 0; i < kMaxSignificantDecimalDigits - 1; ++i) {

    significant_buffer[i] = buffer[i];

  }

  // The input buffer has been trimmed. Therefore the last digit must be

  // different from '0'.

  DOUBLE_CONVERSION_ASSERT(buffer[buffer.length() - 1] != '0');

  // Set the last digit to be non-zero. This is sufficient to guarantee

  // correct rounding.

  significant_buffer[kMaxSignificantDecimalDigits - 1] = '1';

  *significant_exponent =

      exponent + (buffer.length() - kMaxSignificantDecimalDigits);

}

// Trims the buffer and cuts it to at most kMaxSignificantDecimalDigits.

// If possible the input-buffer is reused, but if the buffer needs to be

// modified (due to cutting), then the input needs to be copied into the

// buffer_copy_space.

static void TrimAndCut(Vector<const char> buffer, int exponent,

                       char* buffer_copy_space, int space_size,

                       Vector<const char>* trimmed, int* updated_exponent) {

  Vector<const char> left_trimmed = TrimLeadingZeros(buffer);

  Vector<const char> right_trimmed = TrimTrailingZeros(left_trimmed);

  exponent += left_trimmed.length() - right_trimmed.length();

  if (right_trimmed.length() > kMaxSignificantDecimalDigits) {

    (void) space_size;  // Mark variable as used.

    DOUBLE_CONVERSION_ASSERT(space_size >= kMaxSignificantDecimalDigits);

    CutToMaxSignificantDigits(right_trimmed, exponent,

                              buffer_copy_space, updated_exponent);

    *trimmed = Vector<const char>(buffer_copy_space,

                                 kMaxSignificantDecimalDigits);

  } else {

    *trimmed = right_trimmed;

    *updated_exponent = exponent;

  }

}

// Reads digits from the buffer and converts them to a uint64.

// Reads in as many digits as fit into a uint64.

// When the string starts with "1844674407370955161" no further digit is read.

// Since 2^64 = 18446744073709551616 it would still be possible read another

// digit if it was less or equal than 6, but this would complicate the code.

static uint64_t ReadUint64(Vector<const char> buffer,

                           int* number_of_read_digits) {

  uint64_t result = 0;

  int i = 0;

  while (i < buffer.length() && result <= (kMaxUint64 / 10 - 1)) {

    int digit = buffer[i++] - '0';

    DOUBLE_CONVERSION_ASSERT(0 <= digit && digit <= 9);

    result = 10 * result + digit;

  }

  *number_of_read_digits = i;

  return result;

}

// Reads a DiyFp from the buffer.

// The returned DiyFp is not necessarily normalized.

// If remaining_decimals is zero then the returned DiyFp is accurate.

// Otherwise it has been rounded and has error of at most 1/2 ulp.

static void ReadDiyFp(Vector<const char> buffer,

                      DiyFp* result,

                      int* remaining_decimals) {

  int read_digits;

  uint64_t significand = ReadUint64(buffer, &read_digits);

  if (buffer.length() == read_digits) {

    *result = DiyFp(significand, 0);

    *remaining_decimals = 0;

  } else {

    // Round the significand.

    if (buffer[read_digits] >= '5') {

      significand++;

    }

    // Compute the binary exponent.

    int exponent = 0;

    *result = DiyFp(significand, exponent);

    *remaining_decimals = buffer.length() - read_digits;

  }

}

static bool DoubleStrtod(Vector<const char> trimmed,

                         int exponent,

                         double* result) {

#if !defined(DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS)

  // Avoid "unused parameter" warnings

  (void) trimmed;

  (void) exponent;

  (void) result;

  // On x86 the floating-point stack can be 64 or 80 bits wide. If it is

  // 80 bits wide (as is the case on Linux) then double-rounding occurs and the

  // result is not accurate.

  // We know that Windows32 uses 64 bits and is therefore accurate.

  return false;

#else

  if (trimmed.length() <= kMaxExactDoubleIntegerDecimalDigits) {

    int read_digits;

    // The trimmed input fits into a double.

    // If the 10^exponent (resp. 10^-exponent) fits into a double too then we

    // can compute the result-double simply by multiplying (resp. dividing) the

    // two numbers.

    // This is possible because IEEE guarantees that floating-point operations

    // return the best possible approximation.

    if (exponent < 0 && -exponent < kExactPowersOfTenSize) {

      // 10^-exponent fits into a double.

      *result = static_cast<double>(ReadUint64(trimmed, &read_digits));

      DOUBLE_CONVERSION_ASSERT(read_digits == trimmed.length());

      *result /= exact_powers_of_ten[-exponent];

      return true;

    }

    if (0 <= exponent && exponent < kExactPowersOfTenSize) {

      // 10^exponent fits into a double.

      *result = static_cast<double>(ReadUint64(trimmed, &read_digits));

      DOUBLE_CONVERSION_ASSERT(read_digits == trimmed.length());

      *result *= exact_powers_of_ten[exponent];

      return true;

    }

    int remaining_digits =

        kMaxExactDoubleIntegerDecimalDigits - trimmed.length();

    if ((0 <= exponent) &&

        (exponent - remaining_digits < kExactPowersOfTenSize)) {

      // The trimmed string was short and we can multiply it with

      // 10^remaining_digits. As a result the remaining exponent now fits

      // into a double too.

      *result = static_cast<double>(ReadUint64(trimmed, &read_digits));

      DOUBLE_CONVERSION_ASSERT(read_digits == trimmed.length());

      *result *= exact_powers_of_ten[remaining_digits];

      *result *= exact_powers_of_ten[exponent - remaining_digits];

      return true;

    }

  }

  return false;

#endif

}

// Returns 10^exponent as an exact DiyFp.

// The given exponent must be in the range [1; kDecimalExponentDistance[.

static DiyFp AdjustmentPowerOfTen(int exponent) {

  DOUBLE_CONVERSION_ASSERT(0 < exponent);

  DOUBLE_CONVERSION_ASSERT(exponent < PowersOfTenCache::kDecimalExponentDistance);

  // Simply hardcode the remaining powers for the given decimal exponent

  // distance.

  DOUBLE_CONVERSION_ASSERT(PowersOfTenCache::kDecimalExponentDistance == 8);

  switch (exponent) {

    case 1: return DiyFp(DOUBLE_CONVERSION_UINT64_2PART_C(0xa0000000, 00000000), -60);

    case 2: return DiyFp(DOUBLE_CONVERSION_UINT64_2PART_C(0xc8000000, 00000000), -57);

    case 3: return DiyFp(DOUBLE_CONVERSION_UINT64_2PART_C(0xfa000000, 00000000), -54);

    case 4: return DiyFp(DOUBLE_CONVERSION_UINT64_2PART_C(0x9c400000, 00000000), -50);

    case 5: return DiyFp(DOUBLE_CONVERSION_UINT64_2PART_C(0xc3500000, 00000000), -47);

    case 6: return DiyFp(DOUBLE_CONVERSION_UINT64_2PART_C(0xf4240000, 00000000), -44);

    case 7: return DiyFp(DOUBLE_CONVERSION_UINT64_2PART_C(0x98968000, 00000000), -40);

    default:

      DOUBLE_CONVERSION_UNREACHABLE();

  }

}

// If the function returns true then the result is the correct double.

// Otherwise it is either the correct double or the double that is just below

// the correct double.

static bool DiyFpStrtod(Vector<const char> buffer,

                        int exponent,

                        double* result) {

  DiyFp input;

  int remaining_decimals;

  ReadDiyFp(buffer, &input, &remaining_decimals);

  // Since we may have dropped some digits the input is not accurate.

  // If remaining_decimals is different than 0 than the error is at most

  // .5 ulp (unit in the last place).

  // We don't want to deal with fractions and therefore keep a common

  // denominator.

  const int kDenominatorLog = 3;

  const int kDenominator = 1 << kDenominatorLog;

  // Move the remaining decimals into the exponent.

  exponent += remaining_decimals;

  uint64_t error = (remaining_decimals == 0 ? 0 : kDenominator / 2);

  int old_e = input.e();

  input.Normalize();

  error <<= old_e - input.e();

  DOUBLE_CONVERSION_ASSERT(exponent <= PowersOfTenCache::kMaxDecimalExponent);

  if (exponent < PowersOfTenCache::kMinDecimalExponent) {

    *result = 0.0;

    return true;

  }

  DiyFp cached_power;

  int cached_decimal_exponent;

  PowersOfTenCache::GetCachedPowerForDecimalExponent(exponent,

                                                     &cached_power,

                                                     &cached_decimal_exponent);

  if (cached_decimal_exponent != exponent) {

    int adjustment_exponent = exponent - cached_decimal_exponent;

    DiyFp adjustment_power = AdjustmentPowerOfTen(adjustment_exponent);

    input.Multiply(adjustment_power);

    if (kMaxUint64DecimalDigits - buffer.length() >= adjustment_exponent) {

      // The product of input with the adjustment power fits into a 64 bit

      // integer.

      DOUBLE_CONVERSION_ASSERT(DiyFp::kSignificandSize == 64);

    } else {

      // The adjustment power is exact. There is hence only an error of 0.5.

      error += kDenominator / 2;

    }

  }

  input.Multiply(cached_power);

  // The error introduced by a multiplication of a*b equals

  //   error_a + error_b + error_a*error_b/2^64 + 0.5

  // Substituting a with 'input' and b with 'cached_power' we have

  //   error_b = 0.5  (all cached powers have an error of less than 0.5 ulp),

  //   error_ab = 0 or 1 / kDenominator > error_a*error_b/ 2^64

  int error_b = kDenominator / 2;

  int error_ab = (error == 0 ? 0 : 1);  // We round up to 1.

  int fixed_error = kDenominator / 2;

  error += error_b + error_ab + fixed_error;

  old_e = input.e();

  input.Normalize();

  error <<= old_e - input.e();

  // See if the double's significand changes if we add/subtract the error.

  int order_of_magnitude = DiyFp::kSignificandSize + input.e();

  int effective_significand_size =

      Double::SignificandSizeForOrderOfMagnitude(order_of_magnitude);

  int precision_digits_count =

      DiyFp::kSignificandSize - effective_significand_size;

  if (precision_digits_count + kDenominatorLog >= DiyFp::kSignificandSize) {

    // This can only happen for very small denormals. In this case the

    // half-way multiplied by the denominator exceeds the range of an uint64.

    // Simply shift everything to the right.

    int shift_amount = (precision_digits_count + kDenominatorLog) -

        DiyFp::kSignificandSize + 1;

    input.set_f(input.f() >> shift_amount);

    input.set_e(input.e() + shift_amount);

    // We add 1 for the lost precision of error, and kDenominator for

    // the lost precision of input.f().

    error = (error >> shift_amount) + 1 + kDenominator;

    precision_digits_count -= shift_amount;

  }

  // We use uint64_ts now. This only works if the DiyFp uses uint64_ts too.

  DOUBLE_CONVERSION_ASSERT(DiyFp::kSignificandSize == 64);

  DOUBLE_CONVERSION_ASSERT(precision_digits_count < 64);

  uint64_t one64 = 1;

  uint64_t precision_bits_mask = (one64 << precision_digits_count) - 1;

  uint64_t precision_bits = input.f() & precision_bits_mask;

  uint64_t half_way = one64 << (precision_digits_count - 1);

  precision_bits *= kDenominator;

  half_way *= kDenominator;

  DiyFp rounded_input(input.f() >> precision_digits_count,

                      input.e() + precision_digits_count);

  if (precision_bits >= half_way + error) {

    rounded_input.set_f(rounded_input.f() + 1);

  }

  // If the last_bits are too close to the half-way case than we are too

  // inaccurate and round down. In this case we return false so that we can

  // fall back to a more precise algorithm.

  *result = Double(rounded_input).value();

  if (half_way - error < precision_bits && precision_bits < half_way + error) {

    // Too imprecise. The caller will have to fall back to a slower version.

    // However the returned number is guaranteed to be either the correct

    // double, or the next-lower double.

    return false;

  } else {

    return true;

  }

}

// Returns

//   - -1 if buffer*10^exponent < diy_fp.

//   -  0 if buffer*10^exponent == diy_fp.

//   - +1 if buffer*10^exponent > diy_fp.

// Preconditions:

//   buffer.length() + exponent <= kMaxDecimalPower + 1

//   buffer.length() + exponent > kMinDecimalPower

//   buffer.length() <= kMaxDecimalSignificantDigits

static int CompareBufferWithDiyFp(Vector<const char> buffer,

                                  int exponent,

                                  DiyFp diy_fp) {

  DOUBLE_CONVERSION_ASSERT(buffer.length() + exponent <= kMaxDecimalPower + 1);

  DOUBLE_CONVERSION_ASSERT(buffer.length() + exponent > kMinDecimalPower);

  DOUBLE_CONVERSION_ASSERT(buffer.length() <= kMaxSignificantDecimalDigits);

  // Make sure that the Bignum will be able to hold all our numbers.

  // Our Bignum implementation has a separate field for exponents. Shifts will

  // consume at most one bigit (< 64 bits).

  // ln(10) == 3.3219...

  DOUBLE_CONVERSION_ASSERT(((kMaxDecimalPower + 1) * 333 / 100) < Bignum::kMaxSignificantBits);

  Bignum buffer_bignum;

  Bignum diy_fp_bignum;

  buffer_bignum.AssignDecimalString(buffer);

  diy_fp_bignum.AssignUInt64(diy_fp.f());

  if (exponent >= 0) {

    buffer_bignum.MultiplyByPowerOfTen(exponent);

  } else {

    diy_fp_bignum.MultiplyByPowerOfTen(-exponent);

  }

  if (diy_fp.e() > 0) {

    diy_fp_bignum.ShiftLeft(diy_fp.e());

  } else {

    buffer_bignum.ShiftLeft(-diy_fp.e());

  }

  return Bignum::Compare(buffer_bignum, diy_fp_bignum);

}

// Returns true if the guess is the correct double.

// Returns false, when guess is either correct or the next-lower double.

static bool ComputeGuess(Vector<const char> trimmed, int exponent,

                         double* guess) {

  if (trimmed.length() == 0) {

    *guess = 0.0;

    return true;

  }

  if (exponent + trimmed.length() - 1 >= kMaxDecimalPower) {

    *guess = Double::Infinity();

    return true;

  }

  if (exponent + trimmed.length() <= kMinDecimalPower) {

    *guess = 0.0;

    return true;

  }

  if (DoubleStrtod(trimmed, exponent, guess) ||

      DiyFpStrtod(trimmed, exponent, guess)) {

    return true;

  }

  if (*guess == Double::Infinity()) {

    return true;

  }

  return false;

}

static bool IsDigit(const char d) {

  return ('0' <= d) && (d <= '9');

}

static bool IsNonZeroDigit(const char d) {

  return ('1' <= d) && (d <= '9');

}

#ifdef __has_cpp_attribute

#if __has_cpp_attribute(maybe_unused)

[[maybe_unused]]

#endif

#endif

static bool AssertTrimmedDigits(const Vector<const char>& buffer) {

  for(int i = 0; i < buffer.length(); ++i) {

    if(!IsDigit(buffer[i])) {

      return false;

    }

  }

  return (buffer.length() == 0) || (IsNonZeroDigit(buffer[0]) && IsNonZeroDigit(buffer[buffer.length()-1]));

}

double StrtodTrimmed(Vector<const char> trimmed, int exponent) {

  DOUBLE_CONVERSION_ASSERT(trimmed.length() <= kMaxSignificantDecimalDigits);

  DOUBLE_CONVERSION_ASSERT(AssertTrimmedDigits(trimmed));

  double guess;

  const bool is_correct = ComputeGuess(trimmed, exponent, &guess);

  if (is_correct) {

    return guess;

  }

  DiyFp upper_boundary = Double(guess).UpperBoundary();

  int comparison = CompareBufferWithDiyFp(trimmed, exponent, upper_boundary);

  if (comparison < 0) {

    return guess;

  } else if (comparison > 0) {

    return Double(guess).NextDouble();

  } else if ((Double(guess).Significand() & 1) == 0) {

    // Round towards even.

    return guess;

  } else {

    return Double(guess).NextDouble();

  }

}

double Strtod(Vector<const char> buffer, int exponent) {

  char copy_buffer[kMaxSignificantDecimalDigits];

  Vector<const char> trimmed;

  int updated_exponent;

  TrimAndCut(buffer, exponent, copy_buffer, kMaxSignificantDecimalDigits,

             &trimmed, &updated_exponent);

  return StrtodTrimmed(trimmed, updated_exponent);

}

static float SanitizedDoubletof(double d) {

  DOUBLE_CONVERSION_ASSERT(d >= 0.0);

  // ASAN has a sanitize check that disallows casting doubles to floats if

  // they are too big.

  // https://clang.llvm.org/docs/UndefinedBehaviorSanitizer.html#available-checks

  // The behavior should be covered by IEEE 754, but some projects use this

  // flag, so work around it.

  float max_finite = 3.4028234663852885981170418348451692544e+38;

  // The half-way point between the max-finite and infinity value.

  // Since infinity has an even significand everything equal or greater than

  // this value should become infinity.

  double half_max_finite_infinity =

      3.40282356779733661637539395458142568448e+38;

  if (d >= max_finite) {

    if (d >= half_max_finite_infinity) {

      return Single::Infinity();

    } else {

      return max_finite;

    }

  } else {

    return static_cast<float>(d);

  }

}

float Strtof(Vector<const char> buffer, int exponent) {

  char copy_buffer[kMaxSignificantDecimalDigits];

  Vector<const char> trimmed;

  int updated_exponent;

  TrimAndCut(buffer, exponent, copy_buffer, kMaxSignificantDecimalDigits,

             &trimmed, &updated_exponent);

  exponent = updated_exponent;

  return StrtofTrimmed(trimmed, exponent);

}

float StrtofTrimmed(Vector<const char> trimmed, int exponent) {

  DOUBLE_CONVERSION_ASSERT(trimmed.length() <= kMaxSignificantDecimalDigits);

  DOUBLE_CONVERSION_ASSERT(AssertTrimmedDigits(trimmed));

  double double_guess;

  bool is_correct = ComputeGuess(trimmed, exponent, &double_guess);

  float float_guess = SanitizedDoubletof(double_guess);

  if (float_guess == double_guess) {

    // This shortcut triggers for integer values.

    return float_guess;

  }

  // We must catch double-rounding. Say the double has been rounded up, and is

  // now a boundary of a float, and rounds up again. This is why we have to

  // look at previous too.

  // Example (in decimal numbers):

  //    input: 12349

  //    high-precision (4 digits): 1235

  //    low-precision (3 digits):

  //       when read from input: 123

  //       when rounded from high precision: 124.

  // To do this we simply look at the neighbors of the correct result and see

  // if they would round to the same float. If the guess is not correct we have

  // to look at four values (since two different doubles could be the correct

  // double).

  double double_next = Double(double_guess).NextDouble();

  double double_previous = Double(double_guess).PreviousDouble();

  float f1 = SanitizedDoubletof(double_previous);

  float f2 = float_guess;

  float f3 = SanitizedDoubletof(double_next);

  float f4;

  if (is_correct) {

    f4 = f3;

  } else {

    double double_next2 = Double(double_next).NextDouble();

    f4 = SanitizedDoubletof(double_next2);

  }

  (void) f2;  // Mark variable as used.

  DOUBLE_CONVERSION_ASSERT(f1 <= f2 && f2 <= f3 && f3 <= f4);

  // If the guess doesn't lie near a single-precision boundary we can simply

  // return its float-value.

  if (f1 == f4) {

    return float_guess;

  }

  DOUBLE_CONVERSION_ASSERT((f1 != f2 && f2 == f3 && f3 == f4) ||

         (f1 == f2 && f2 != f3 && f3 == f4) ||

         (f1 == f2 && f2 == f3 && f3 != f4));

  // guess and next are the two possible candidates (in the same way that

  // double_guess was the lower candidate for a double-precision guess).

  float guess = f1;

  float next = f4;

  DiyFp upper_boundary;

  if (guess == 0.0f) {

    float min_float = 1e-45f;

    upper_boundary = Double(static_cast<double>(min_float) / 2).AsDiyFp();

  } else {

    upper_boundary = Single(guess).UpperBoundary();

  }

  int comparison = CompareBufferWithDiyFp(trimmed, exponent, upper_boundary);

  if (comparison < 0) {

    return guess;

  } else if (comparison > 0) {

    return next;

  } else if ((Single(guess).Significand() & 1) == 0) {

    // Round towards even.

    return guess;

  } else {

    return next;

  }

}

}  // namespace double_conversion