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#include <cmath>

#include "bignum-dtoa.h"

#include "bignum.h"

#include "ieee.h"

namespace double_conversion {

static int NormalizedExponent(uint64_t significand, int exponent) {

  DOUBLE_CONVERSION_ASSERT(significand != 0);

  while ((significand & Double::kHiddenBit) == 0) {

    significand = significand << 1;

    exponent = exponent - 1;

  }

  return exponent;

}

// Forward declarations:

// Returns an estimation of k such that 10^(k-1) <= v < 10^k.

static int EstimatePower(int exponent);

// Computes v / 10^estimated_power exactly, as a ratio of two bignums, numerator

// and denominator.

static void InitialScaledStartValues(uint64_t significand,

                                     int exponent,

                                     bool lower_boundary_is_closer,

                                     int estimated_power,

                                     bool need_boundary_deltas,

                                     Bignum* numerator,

                                     Bignum* denominator,

                                     Bignum* delta_minus,

                                     Bignum* delta_plus);

// Multiplies numerator/denominator so that its values lies in the range 1-10.

// Returns decimal_point s.t.

//  v = numerator'/denominator' * 10^(decimal_point-1)

//     where numerator' and denominator' are the values of numerator and

//     denominator after the call to this function.

static void FixupMultiply10(int estimated_power, bool is_even,

                            int* decimal_point,

                            Bignum* numerator, Bignum* denominator,

                            Bignum* delta_minus, Bignum* delta_plus);

// Generates digits from the left to the right and stops when the generated

// digits yield the shortest decimal representation of v.

static void GenerateShortestDigits(Bignum* numerator, Bignum* denominator,

                                   Bignum* delta_minus, Bignum* delta_plus,

                                   bool is_even,

                                   Vector<char> buffer, int* length);

// Generates 'requested_digits' after the decimal point.

static void BignumToFixed(int requested_digits, int* decimal_point,

                          Bignum* numerator, Bignum* denominator,

                          Vector<char> buffer, int* length);

// Generates 'count' digits of numerator/denominator.

// Once 'count' digits have been produced rounds the result depending on the

// remainder (remainders of exactly .5 round upwards). Might update the

// decimal_point when rounding up (for example for 0.9999).

static void GenerateCountedDigits(int count, int* decimal_point,

                                  Bignum* numerator, Bignum* denominator,

                                  Vector<char> buffer, int* length);

void BignumDtoa(double v, BignumDtoaMode mode, int requested_digits,

                Vector<char> buffer, int* length, int* decimal_point) {

  DOUBLE_CONVERSION_ASSERT(v > 0);

  DOUBLE_CONVERSION_ASSERT(!Double(v).IsSpecial());

  uint64_t significand;

  int exponent;

  bool lower_boundary_is_closer;

  if (mode == BIGNUM_DTOA_SHORTEST_SINGLE) {

    float f = static_cast<float>(v);

    DOUBLE_CONVERSION_ASSERT(f == v);

    significand = Single(f).Significand();

    exponent = Single(f).Exponent();

    lower_boundary_is_closer = Single(f).LowerBoundaryIsCloser();

  } else {

    significand = Double(v).Significand();

    exponent = Double(v).Exponent();

    lower_boundary_is_closer = Double(v).LowerBoundaryIsCloser();

  }

  bool need_boundary_deltas =

      (mode == BIGNUM_DTOA_SHORTEST || mode == BIGNUM_DTOA_SHORTEST_SINGLE);

  bool is_even = (significand & 1) == 0;

  int normalized_exponent = NormalizedExponent(significand, exponent);

  // estimated_power might be too low by 1.

  int estimated_power = EstimatePower(normalized_exponent);

  // Shortcut for Fixed.

  // The requested digits correspond to the digits after the point. If the

  // number is much too small, then there is no need in trying to get any

  // digits.

  if (mode == BIGNUM_DTOA_FIXED && -estimated_power - 1 > requested_digits) {

    buffer[0] = '\0';

    *length = 0;

    // Set decimal-point to -requested_digits. This is what Gay does.

    // Note that it should not have any effect anyways since the string is

    // empty.

    *decimal_point = -requested_digits;

    return;

  }

  Bignum numerator;

  Bignum denominator;

  Bignum delta_minus;

  Bignum delta_plus;

  // Make sure the bignum can grow large enough. The smallest double equals

  // 4e-324. In this case the denominator needs fewer than 324*4 binary digits.

  // The maximum double is 1.7976931348623157e308 which needs fewer than

  // 308*4 binary digits.

  DOUBLE_CONVERSION_ASSERT(Bignum::kMaxSignificantBits >= 324*4);

  InitialScaledStartValues(significand, exponent, lower_boundary_is_closer,

                           estimated_power, need_boundary_deltas,

                           &numerator, &denominator,

                           &delta_minus, &delta_plus);

  // We now have v = (numerator / denominator) * 10^estimated_power.

  FixupMultiply10(estimated_power, is_even, decimal_point,

                  &numerator, &denominator,

                  &delta_minus, &delta_plus);

  // We now have v = (numerator / denominator) * 10^(decimal_point-1), and

  //  1 <= (numerator + delta_plus) / denominator < 10

  switch (mode) {

    case BIGNUM_DTOA_SHORTEST:

    case BIGNUM_DTOA_SHORTEST_SINGLE:

      GenerateShortestDigits(&numerator, &denominator,

                             &delta_minus, &delta_plus,

                             is_even, buffer, length);

      break;

    case BIGNUM_DTOA_FIXED:

      BignumToFixed(requested_digits, decimal_point,

                    &numerator, &denominator,

                    buffer, length);

      break;

    case BIGNUM_DTOA_PRECISION:

      GenerateCountedDigits(requested_digits, decimal_point,

                            &numerator, &denominator,

                            buffer, length);

      break;

    default:

      DOUBLE_CONVERSION_UNREACHABLE();

  }

  buffer[*length] = '\0';

}

// The procedure starts generating digits from the left to the right and stops

// when the generated digits yield the shortest decimal representation of v. A

// decimal representation of v is a number lying closer to v than to any other

// double, so it converts to v when read.

//

// This is true if d, the decimal representation, is between m- and m+, the

// upper and lower boundaries. d must be strictly between them if !is_even.

//           m- := (numerator - delta_minus) / denominator

//           m+ := (numerator + delta_plus) / denominator

//

// Precondition: 0 <= (numerator+delta_plus) / denominator < 10.

//   If 1 <= (numerator+delta_plus) / denominator < 10 then no leading 0 digit

//   will be produced. This should be the standard precondition.

static void GenerateShortestDigits(Bignum* numerator, Bignum* denominator,

                                   Bignum* delta_minus, Bignum* delta_plus,

                                   bool is_even,

                                   Vector<char> buffer, int* length) {

  // Small optimization: if delta_minus and delta_plus are the same just reuse

  // one of the two bignums.

  if (Bignum::Equal(*delta_minus, *delta_plus)) {

    delta_plus = delta_minus;

  }

  *length = 0;

  for (;;) {

    uint16_t digit;

    digit = numerator->DivideModuloIntBignum(*denominator);

    DOUBLE_CONVERSION_ASSERT(digit <= 9);  // digit is a uint16_t and therefore always positive.

    // digit = numerator / denominator (integer division).

    // numerator = numerator % denominator.

    buffer[(*length)++] = static_cast<char>(digit + '0');

    // Can we stop already?

    // If the remainder of the division is less than the distance to the lower

    // boundary we can stop. In this case we simply round down (discarding the

    // remainder).

    // Similarly we test if we can round up (using the upper boundary).

    bool in_delta_room_minus;

    bool in_delta_room_plus;

    if (is_even) {

      in_delta_room_minus = Bignum::LessEqual(*numerator, *delta_minus);

    } else {

      in_delta_room_minus = Bignum::Less(*numerator, *delta_minus);

    }

    if (is_even) {

      in_delta_room_plus =

          Bignum::PlusCompare(*numerator, *delta_plus, *denominator) >= 0;

    } else {

      in_delta_room_plus =

          Bignum::PlusCompare(*numerator, *delta_plus, *denominator) > 0;

    }

    if (!in_delta_room_minus && !in_delta_room_plus) {

      // Prepare for next iteration.

      numerator->Times10();

      delta_minus->Times10();

      // We optimized delta_plus to be equal to delta_minus (if they share the

      // same value). So don't multiply delta_plus if they point to the same

      // object.

      if (delta_minus != delta_plus) {

        delta_plus->Times10();

      }

    } else if (in_delta_room_minus && in_delta_room_plus) {

      // Let's see if 2*numerator < denominator.

      // If yes, then the next digit would be < 5 and we can round down.

      int compare = Bignum::PlusCompare(*numerator, *numerator, *denominator);

      if (compare < 0) {

        // Remaining digits are less than .5. -> Round down (== do nothing).

      } else if (compare > 0) {

        // Remaining digits are more than .5 of denominator. -> Round up.

        // Note that the last digit could not be a '9' as otherwise the whole

        // loop would have stopped earlier.

        // We still have an assert here in case the preconditions were not

        // satisfied.

        DOUBLE_CONVERSION_ASSERT(buffer[(*length) - 1] != '9');

        buffer[(*length) - 1]++;

      } else {

        // Halfway case.

        // TODO(floitsch): need a way to solve half-way cases.

        //   For now let's round towards even (since this is what Gay seems to

        //   do).

        if ((buffer[(*length) - 1] - '0') % 2 == 0) {

          // Round down => Do nothing.

        } else {

          DOUBLE_CONVERSION_ASSERT(buffer[(*length) - 1] != '9');

          buffer[(*length) - 1]++;

        }

      }

      return;

    } else if (in_delta_room_minus) {

      // Round down (== do nothing).

      return;

    } else {  // in_delta_room_plus

      // Round up.

      // Note again that the last digit could not be '9' since this would have

      // stopped the loop earlier.

      // We still have an DOUBLE_CONVERSION_ASSERT here, in case the preconditions were not

      // satisfied.

      DOUBLE_CONVERSION_ASSERT(buffer[(*length) -1] != '9');

      buffer[(*length) - 1]++;

      return;

    }

  }

}

// Let v = numerator / denominator < 10.

// Then we generate 'count' digits of d = x.xxxxx... (without the decimal point)

// from left to right. Once 'count' digits have been produced we decide whether

// to round up or down. Remainders of exactly .5 round upwards. Numbers such

// as 9.999999 propagate a carry all the way, and change the

// exponent (decimal_point), when rounding upwards.

static void GenerateCountedDigits(int count, int* decimal_point,

                                  Bignum* numerator, Bignum* denominator,

                                  Vector<char> buffer, int* length) {

  DOUBLE_CONVERSION_ASSERT(count >= 0);

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

    uint16_t digit;

    digit = numerator->DivideModuloIntBignum(*denominator);

    DOUBLE_CONVERSION_ASSERT(digit <= 9);  // digit is a uint16_t and therefore always positive.

    // digit = numerator / denominator (integer division).

    // numerator = numerator % denominator.

    buffer[i] = static_cast<char>(digit + '0');

    // Prepare for next iteration.

    numerator->Times10();

  }

  // Generate the last digit.

  uint16_t digit;

  digit = numerator->DivideModuloIntBignum(*denominator);

  if (Bignum::PlusCompare(*numerator, *numerator, *denominator) >= 0) {

    digit++;

  }

  DOUBLE_CONVERSION_ASSERT(digit <= 10);

  buffer[count - 1] = static_cast<char>(digit + '0');

  // Correct bad digits (in case we had a sequence of '9's). Propagate the

  // carry until we hat a non-'9' or til we reach the first digit.

  for (int i = count - 1; i > 0; --i) {

    if (buffer[i] != '0' + 10) break;

    buffer[i] = '0';

    buffer[i - 1]++;

  }

  if (buffer[0] == '0' + 10) {

    // Propagate a carry past the top place.

    buffer[0] = '1';

    (*decimal_point)++;

  }

  *length = count;

}

// Generates 'requested_digits' after the decimal point. It might omit

// trailing '0's. If the input number is too small then no digits at all are

// generated (ex.: 2 fixed digits for 0.00001).

//

// Input verifies:  1 <= (numerator + delta) / denominator < 10.

static void BignumToFixed(int requested_digits, int* decimal_point,

                          Bignum* numerator, Bignum* denominator,

                          Vector<char> buffer, int* length) {

  // Note that we have to look at more than just the requested_digits, since

  // a number could be rounded up. Example: v=0.5 with requested_digits=0.

  // Even though the power of v equals 0 we can't just stop here.

  if (-(*decimal_point) > requested_digits) {

    // The number is definitively too small.

    // Ex: 0.001 with requested_digits == 1.

    // Set decimal-point to -requested_digits. This is what Gay does.

    // Note that it should not have any effect anyways since the string is

    // empty.

    *decimal_point = -requested_digits;

    *length = 0;

    return;

  } else if (-(*decimal_point) == requested_digits) {

    // We only need to verify if the number rounds down or up.

    // Ex: 0.04 and 0.06 with requested_digits == 1.

    DOUBLE_CONVERSION_ASSERT(*decimal_point == -requested_digits);

    // Initially the fraction lies in range (1, 10]. Multiply the denominator

    // by 10 so that we can compare more easily.

    denominator->Times10();

    if (Bignum::PlusCompare(*numerator, *numerator, *denominator) >= 0) {

      // If the fraction is >= 0.5 then we have to include the rounded

      // digit.

      buffer[0] = '1';

      *length = 1;

      (*decimal_point)++;

    } else {

      // Note that we caught most of similar cases earlier.

      *length = 0;

    }

    return;

  } else {

    // The requested digits correspond to the digits after the point.

    // The variable 'needed_digits' includes the digits before the point.

    int needed_digits = (*decimal_point) + requested_digits;

    GenerateCountedDigits(needed_digits, decimal_point,

                          numerator, denominator,

                          buffer, length);

  }

}

// Returns an estimation of k such that 10^(k-1) <= v < 10^k where

// v = f * 2^exponent and 2^52 <= f < 2^53.

// v is hence a normalized double with the given exponent. The output is an

// approximation for the exponent of the decimal approximation .digits * 10^k.

//

// The result might undershoot by 1 in which case 10^k <= v < 10^k+1.

// Note: this property holds for v's upper boundary m+ too.

//    10^k <= m+ < 10^k+1.

//   (see explanation below).

//

// Examples:

//  EstimatePower(0)   => 16

//  EstimatePower(-52) => 0

//

// Note: e >= 0 => EstimatedPower(e) > 0. No similar claim can be made for e<0.

static int EstimatePower(int exponent) {

  // This function estimates log10 of v where v = f*2^e (with e == exponent).

  // Note that 10^floor(log10(v)) <= v, but v <= 10^ceil(log10(v)).

  // Note that f is bounded by its container size. Let p = 53 (the double's

  // significand size). Then 2^(p-1) <= f < 2^p.

  //

  // Given that log10(v) == log2(v)/log2(10) and e+(len(f)-1) is quite close

  // to log2(v) the function is simplified to (e+(len(f)-1)/log2(10)).

  // The computed number undershoots by less than 0.631 (when we compute log3

  // and not log10).

  //

  // Optimization: since we only need an approximated result this computation

  // can be performed on 64 bit integers. On x86/x64 architecture the speedup is

  // not really measurable, though.

  //

  // Since we want to avoid overshooting we decrement by 1e10 so that

  // floating-point imprecisions don't affect us.

  //

  // Explanation for v's boundary m+: the computation takes advantage of

  // the fact that 2^(p-1) <= f < 2^p. Boundaries still satisfy this requirement

  // (even for denormals where the delta can be much more important).

  const double k1Log10 = 0.30102999566398114;  // 1/lg(10)

  // For doubles len(f) == 53 (don't forget the hidden bit).

  const int kSignificandSize = Double::kSignificandSize;

  double estimate = ceil((exponent + kSignificandSize - 1) * k1Log10 - 1e-10);

  return static_cast<int>(estimate);

}

// See comments for InitialScaledStartValues.

static void InitialScaledStartValuesPositiveExponent(

    uint64_t significand, int exponent,

    int estimated_power, bool need_boundary_deltas,

    Bignum* numerator, Bignum* denominator,

    Bignum* delta_minus, Bignum* delta_plus) {

  // A positive exponent implies a positive power.

  DOUBLE_CONVERSION_ASSERT(estimated_power >= 0);

  // Since the estimated_power is positive we simply multiply the denominator

  // by 10^estimated_power.

  // numerator = v.

  numerator->AssignUInt64(significand);

  numerator->ShiftLeft(exponent);

  // denominator = 10^estimated_power.

  denominator->AssignPowerUInt16(10, estimated_power);

  if (need_boundary_deltas) {

    // Introduce a common denominator so that the deltas to the boundaries are

    // integers.

    denominator->ShiftLeft(1);

    numerator->ShiftLeft(1);

    // Let v = f * 2^e, then m+ - v = 1/2 * 2^e; With the common

    // denominator (of 2) delta_plus equals 2^e.

    delta_plus->AssignUInt16(1);

    delta_plus->ShiftLeft(exponent);

    // Same for delta_minus. The adjustments if f == 2^p-1 are done later.

    delta_minus->AssignUInt16(1);

    delta_minus->ShiftLeft(exponent);

  }

}

// See comments for InitialScaledStartValues

static void InitialScaledStartValuesNegativeExponentPositivePower(

    uint64_t significand, int exponent,

    int estimated_power, bool need_boundary_deltas,

    Bignum* numerator, Bignum* denominator,

    Bignum* delta_minus, Bignum* delta_plus) {

  // v = f * 2^e with e < 0, and with estimated_power >= 0.

  // This means that e is close to 0 (have a look at how estimated_power is

  // computed).

  // numerator = significand

  //  since v = significand * 2^exponent this is equivalent to

  //  numerator = v * / 2^-exponent

  numerator->AssignUInt64(significand);

  // denominator = 10^estimated_power * 2^-exponent (with exponent < 0)

  denominator->AssignPowerUInt16(10, estimated_power);

  denominator->ShiftLeft(-exponent);

  if (need_boundary_deltas) {

    // Introduce a common denominator so that the deltas to the boundaries are

    // integers.

    denominator->ShiftLeft(1);

    numerator->ShiftLeft(1);

    // Let v = f * 2^e, then m+ - v = 1/2 * 2^e; With the common

    // denominator (of 2) delta_plus equals 2^e.

    // Given that the denominator already includes v's exponent the distance

    // to the boundaries is simply 1.

    delta_plus->AssignUInt16(1);

    // Same for delta_minus. The adjustments if f == 2^p-1 are done later.

    delta_minus->AssignUInt16(1);

  }

}

// See comments for InitialScaledStartValues

static void InitialScaledStartValuesNegativeExponentNegativePower(

    uint64_t significand, int exponent,

    int estimated_power, bool need_boundary_deltas,

    Bignum* numerator, Bignum* denominator,

    Bignum* delta_minus, Bignum* delta_plus) {

  // Instead of multiplying the denominator with 10^estimated_power we

  // multiply all values (numerator and deltas) by 10^-estimated_power.

  // Use numerator as temporary container for power_ten.

  Bignum* power_ten = numerator;

  power_ten->AssignPowerUInt16(10, -estimated_power);

  if (need_boundary_deltas) {

    // Since power_ten == numerator we must make a copy of 10^estimated_power

    // before we complete the computation of the numerator.

    // delta_plus = delta_minus = 10^estimated_power

    delta_plus->AssignBignum(*power_ten);

    delta_minus->AssignBignum(*power_ten);

  }

  // numerator = significand * 2 * 10^-estimated_power

  //  since v = significand * 2^exponent this is equivalent to

  // numerator = v * 10^-estimated_power * 2 * 2^-exponent.

  // Remember: numerator has been abused as power_ten. So no need to assign it

  //  to itself.

  DOUBLE_CONVERSION_ASSERT(numerator == power_ten);

  numerator->MultiplyByUInt64(significand);

  // denominator = 2 * 2^-exponent with exponent < 0.

  denominator->AssignUInt16(1);

  denominator->ShiftLeft(-exponent);

  if (need_boundary_deltas) {

    // Introduce a common denominator so that the deltas to the boundaries are

    // integers.

    numerator->ShiftLeft(1);

    denominator->ShiftLeft(1);

    // With this shift the boundaries have their correct value, since

    // delta_plus = 10^-estimated_power, and

    // delta_minus = 10^-estimated_power.

    // These assignments have been done earlier.

    // The adjustments if f == 2^p-1 (lower boundary is closer) are done later.

  }

}

// Let v = significand * 2^exponent.

// Computes v / 10^estimated_power exactly, as a ratio of two bignums, numerator

// and denominator. The functions GenerateShortestDigits and

// GenerateCountedDigits will then convert this ratio to its decimal

// representation d, with the required accuracy.

// Then d * 10^estimated_power is the representation of v.

// (Note: the fraction and the estimated_power might get adjusted before

// generating the decimal representation.)

//

// The initial start values consist of:

//  - a scaled numerator: s.t. numerator/denominator == v / 10^estimated_power.

//  - a scaled (common) denominator.

//  optionally (used by GenerateShortestDigits to decide if it has the shortest

//  decimal converting back to v):

//  - v - m-: the distance to the lower boundary.

//  - m+ - v: the distance to the upper boundary.

//

// v, m+, m-, and therefore v - m- and m+ - v all share the same denominator.

//

// Let ep == estimated_power, then the returned values will satisfy:

//  v / 10^ep = numerator / denominator.

//  v's boundaries m- and m+:

//    m- / 10^ep == v / 10^ep - delta_minus / denominator

//    m+ / 10^ep == v / 10^ep + delta_plus / denominator

//  Or in other words:

//    m- == v - delta_minus * 10^ep / denominator;

//    m+ == v + delta_plus * 10^ep / denominator;

//

// Since 10^(k-1) <= v < 10^k    (with k == estimated_power)

//  or       10^k <= v < 10^(k+1)

//  we then have 0.1 <= numerator/denominator < 1

//           or    1 <= numerator/denominator < 10

//

// It is then easy to kickstart the digit-generation routine.

//

// The boundary-deltas are only filled if the mode equals BIGNUM_DTOA_SHORTEST

// or BIGNUM_DTOA_SHORTEST_SINGLE.

static void InitialScaledStartValues(uint64_t significand,

                                     int exponent,

                                     bool lower_boundary_is_closer,

                                     int estimated_power,

                                     bool need_boundary_deltas,

                                     Bignum* numerator,

                                     Bignum* denominator,

                                     Bignum* delta_minus,

                                     Bignum* delta_plus) {

  if (exponent >= 0) {

    InitialScaledStartValuesPositiveExponent(

        significand, exponent, estimated_power, need_boundary_deltas,

        numerator, denominator, delta_minus, delta_plus);

  } else if (estimated_power >= 0) {

    InitialScaledStartValuesNegativeExponentPositivePower(

        significand, exponent, estimated_power, need_boundary_deltas,

        numerator, denominator, delta_minus, delta_plus);

  } else {

    InitialScaledStartValuesNegativeExponentNegativePower(

        significand, exponent, estimated_power, need_boundary_deltas,

        numerator, denominator, delta_minus, delta_plus);

  }

  if (need_boundary_deltas && lower_boundary_is_closer) {

    // The lower boundary is closer at half the distance of "normal" numbers.

    // Increase the common denominator and adapt all but the delta_minus.

    denominator->ShiftLeft(1);  // *2

    numerator->ShiftLeft(1);    // *2

    delta_plus->ShiftLeft(1);   // *2

  }

}

// This routine multiplies numerator/denominator so that its values lies in the

// range 1-10. That is after a call to this function we have:

//    1 <= (numerator + delta_plus) /denominator < 10.

// Let numerator the input before modification and numerator' the argument

// after modification, then the output-parameter decimal_point is such that

//  numerator / denominator * 10^estimated_power ==

//    numerator' / denominator' * 10^(decimal_point - 1)

// In some cases estimated_power was too low, and this is already the case. We

// then simply adjust the power so that 10^(k-1) <= v < 10^k (with k ==

// estimated_power) but do not touch the numerator or denominator.

// Otherwise the routine multiplies the numerator and the deltas by 10.

static void FixupMultiply10(int estimated_power, bool is_even,

                            int* decimal_point,

                            Bignum* numerator, Bignum* denominator,

                            Bignum* delta_minus, Bignum* delta_plus) {

  bool in_range;

  if (is_even) {

    // For IEEE doubles half-way cases (in decimal system numbers ending with 5)

    // are rounded to the closest floating-point number with even significand.

    in_range = Bignum::PlusCompare(*numerator, *delta_plus, *denominator) >= 0;

  } else {

    in_range = Bignum::PlusCompare(*numerator, *delta_plus, *denominator) > 0;

  }

  if (in_range) {

    // Since numerator + delta_plus >= denominator we already have

    // 1 <= numerator/denominator < 10. Simply update the estimated_power.

    *decimal_point = estimated_power + 1;

  } else {

    *decimal_point = estimated_power;

    numerator->Times10();

    if (Bignum::Equal(*delta_minus, *delta_plus)) {

      delta_minus->Times10();

      delta_plus->AssignBignum(*delta_minus);

    } else {

      delta_minus->Times10();

      delta_plus->Times10();

    }

  }

}

}  // namespace double_conversion