michael@0: // Copyright 2010 the V8 project authors. All rights reserved.
michael@0: // Redistribution and use in source and binary forms, with or without
michael@0: // modification, are permitted provided that the following conditions are
michael@0: // met:
michael@0: //
michael@0: //     * Redistributions of source code must retain the above copyright
michael@0: //       notice, this list of conditions and the following disclaimer.
michael@0: //     * Redistributions in binary form must reproduce the above
michael@0: //       copyright notice, this list of conditions and the following
michael@0: //       disclaimer in the documentation and/or other materials provided
michael@0: //       with the distribution.
michael@0: //     * Neither the name of Google Inc. nor the names of its
michael@0: //       contributors may be used to endorse or promote products derived
michael@0: //       from this software without specific prior written permission.
michael@0: //
michael@0: // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
michael@0: // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
michael@0: // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
michael@0: // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
michael@0: // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
michael@0: // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
michael@0: // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
michael@0: // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
michael@0: // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
michael@0: // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
michael@0: // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
michael@0: 
michael@0: #include <stdarg.h>
michael@0: #include <limits.h>
michael@0: 
michael@0: #include "strtod.h"
michael@0: #include "bignum.h"
michael@0: #include "cached-powers.h"
michael@0: #include "ieee.h"
michael@0: 
michael@0: namespace double_conversion {
michael@0: 
michael@0: // 2^53 = 9007199254740992.
michael@0: // Any integer with at most 15 decimal digits will hence fit into a double
michael@0: // (which has a 53bit significand) without loss of precision.
michael@0: static const int kMaxExactDoubleIntegerDecimalDigits = 15;
michael@0: // 2^64 = 18446744073709551616 > 10^19
michael@0: static const int kMaxUint64DecimalDigits = 19;
michael@0: 
michael@0: // Max double: 1.7976931348623157 x 10^308
michael@0: // Min non-zero double: 4.9406564584124654 x 10^-324
michael@0: // Any x >= 10^309 is interpreted as +infinity.
michael@0: // Any x <= 10^-324 is interpreted as 0.
michael@0: // Note that 2.5e-324 (despite being smaller than the min double) will be read
michael@0: // as non-zero (equal to the min non-zero double).
michael@0: static const int kMaxDecimalPower = 309;
michael@0: static const int kMinDecimalPower = -324;
michael@0: 
michael@0: // 2^64 = 18446744073709551616
michael@0: static const uint64_t kMaxUint64 = UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF);
michael@0: 
michael@0: 
michael@0: static const double exact_powers_of_ten[] = {
michael@0:   1.0,  // 10^0
michael@0:   10.0,
michael@0:   100.0,
michael@0:   1000.0,
michael@0:   10000.0,
michael@0:   100000.0,
michael@0:   1000000.0,
michael@0:   10000000.0,
michael@0:   100000000.0,
michael@0:   1000000000.0,
michael@0:   10000000000.0,  // 10^10
michael@0:   100000000000.0,
michael@0:   1000000000000.0,
michael@0:   10000000000000.0,
michael@0:   100000000000000.0,
michael@0:   1000000000000000.0,
michael@0:   10000000000000000.0,
michael@0:   100000000000000000.0,
michael@0:   1000000000000000000.0,
michael@0:   10000000000000000000.0,
michael@0:   100000000000000000000.0,  // 10^20
michael@0:   1000000000000000000000.0,
michael@0:   // 10^22 = 0x21e19e0c9bab2400000 = 0x878678326eac9 * 2^22
michael@0:   10000000000000000000000.0
michael@0: };
michael@0: static const int kExactPowersOfTenSize = ARRAY_SIZE(exact_powers_of_ten);
michael@0: 
michael@0: // Maximum number of significant digits in the decimal representation.
michael@0: // In fact the value is 772 (see conversions.cc), but to give us some margin
michael@0: // we round up to 780.
michael@0: static const int kMaxSignificantDecimalDigits = 780;
michael@0: 
michael@0: static Vector<const char> TrimLeadingZeros(Vector<const char> buffer) {
michael@0:   for (int i = 0; i < buffer.length(); i++) {
michael@0:     if (buffer[i] != '0') {
michael@0:       return buffer.SubVector(i, buffer.length());
michael@0:     }
michael@0:   }
michael@0:   return Vector<const char>(buffer.start(), 0);
michael@0: }
michael@0: 
michael@0: 
michael@0: static Vector<const char> TrimTrailingZeros(Vector<const char> buffer) {
michael@0:   for (int i = buffer.length() - 1; i >= 0; --i) {
michael@0:     if (buffer[i] != '0') {
michael@0:       return buffer.SubVector(0, i + 1);
michael@0:     }
michael@0:   }
michael@0:   return Vector<const char>(buffer.start(), 0);
michael@0: }
michael@0: 
michael@0: 
michael@0: static void CutToMaxSignificantDigits(Vector<const char> buffer,
michael@0:                                        int exponent,
michael@0:                                        char* significant_buffer,
michael@0:                                        int* significant_exponent) {
michael@0:   for (int i = 0; i < kMaxSignificantDecimalDigits - 1; ++i) {
michael@0:     significant_buffer[i] = buffer[i];
michael@0:   }
michael@0:   // The input buffer has been trimmed. Therefore the last digit must be
michael@0:   // different from '0'.
michael@0:   ASSERT(buffer[buffer.length() - 1] != '0');
michael@0:   // Set the last digit to be non-zero. This is sufficient to guarantee
michael@0:   // correct rounding.
michael@0:   significant_buffer[kMaxSignificantDecimalDigits - 1] = '1';
michael@0:   *significant_exponent =
michael@0:       exponent + (buffer.length() - kMaxSignificantDecimalDigits);
michael@0: }
michael@0: 
michael@0: 
michael@0: // Trims the buffer and cuts it to at most kMaxSignificantDecimalDigits.
michael@0: // If possible the input-buffer is reused, but if the buffer needs to be
michael@0: // modified (due to cutting), then the input needs to be copied into the
michael@0: // buffer_copy_space.
michael@0: static void TrimAndCut(Vector<const char> buffer, int exponent,
michael@0:                        char* buffer_copy_space, int space_size,
michael@0:                        Vector<const char>* trimmed, int* updated_exponent) {
michael@0:   Vector<const char> left_trimmed = TrimLeadingZeros(buffer);
michael@0:   Vector<const char> right_trimmed = TrimTrailingZeros(left_trimmed);
michael@0:   exponent += left_trimmed.length() - right_trimmed.length();
michael@0:   if (right_trimmed.length() > kMaxSignificantDecimalDigits) {
michael@0:     ASSERT(space_size >= kMaxSignificantDecimalDigits);
michael@0:     CutToMaxSignificantDigits(right_trimmed, exponent,
michael@0:                               buffer_copy_space, updated_exponent);
michael@0:     *trimmed = Vector<const char>(buffer_copy_space,
michael@0:                                  kMaxSignificantDecimalDigits);
michael@0:   } else {
michael@0:     *trimmed = right_trimmed;
michael@0:     *updated_exponent = exponent;
michael@0:   }
michael@0: }
michael@0: 
michael@0: 
michael@0: // Reads digits from the buffer and converts them to a uint64.
michael@0: // Reads in as many digits as fit into a uint64.
michael@0: // When the string starts with "1844674407370955161" no further digit is read.
michael@0: // Since 2^64 = 18446744073709551616 it would still be possible read another
michael@0: // digit if it was less or equal than 6, but this would complicate the code.
michael@0: static uint64_t ReadUint64(Vector<const char> buffer,
michael@0:                            int* number_of_read_digits) {
michael@0:   uint64_t result = 0;
michael@0:   int i = 0;
michael@0:   while (i < buffer.length() && result <= (kMaxUint64 / 10 - 1)) {
michael@0:     int digit = buffer[i++] - '0';
michael@0:     ASSERT(0 <= digit && digit <= 9);
michael@0:     result = 10 * result + digit;
michael@0:   }
michael@0:   *number_of_read_digits = i;
michael@0:   return result;
michael@0: }
michael@0: 
michael@0: 
michael@0: // Reads a DiyFp from the buffer.
michael@0: // The returned DiyFp is not necessarily normalized.
michael@0: // If remaining_decimals is zero then the returned DiyFp is accurate.
michael@0: // Otherwise it has been rounded and has error of at most 1/2 ulp.
michael@0: static void ReadDiyFp(Vector<const char> buffer,
michael@0:                       DiyFp* result,
michael@0:                       int* remaining_decimals) {
michael@0:   int read_digits;
michael@0:   uint64_t significand = ReadUint64(buffer, &read_digits);
michael@0:   if (buffer.length() == read_digits) {
michael@0:     *result = DiyFp(significand, 0);
michael@0:     *remaining_decimals = 0;
michael@0:   } else {
michael@0:     // Round the significand.
michael@0:     if (buffer[read_digits] >= '5') {
michael@0:       significand++;
michael@0:     }
michael@0:     // Compute the binary exponent.
michael@0:     int exponent = 0;
michael@0:     *result = DiyFp(significand, exponent);
michael@0:     *remaining_decimals = buffer.length() - read_digits;
michael@0:   }
michael@0: }
michael@0: 
michael@0: 
michael@0: static bool DoubleStrtod(Vector<const char> trimmed,
michael@0:                          int exponent,
michael@0:                          double* result) {
michael@0: #if !defined(DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS)
michael@0:   // On x86 the floating-point stack can be 64 or 80 bits wide. If it is
michael@0:   // 80 bits wide (as is the case on Linux) then double-rounding occurs and the
michael@0:   // result is not accurate.
michael@0:   // We know that Windows32 uses 64 bits and is therefore accurate.
michael@0:   // Note that the ARM simulator is compiled for 32bits. It therefore exhibits
michael@0:   // the same problem.
michael@0:   return false;
michael@0: #endif
michael@0:   if (trimmed.length() <= kMaxExactDoubleIntegerDecimalDigits) {
michael@0:     int read_digits;
michael@0:     // The trimmed input fits into a double.
michael@0:     // If the 10^exponent (resp. 10^-exponent) fits into a double too then we
michael@0:     // can compute the result-double simply by multiplying (resp. dividing) the
michael@0:     // two numbers.
michael@0:     // This is possible because IEEE guarantees that floating-point operations
michael@0:     // return the best possible approximation.
michael@0:     if (exponent < 0 && -exponent < kExactPowersOfTenSize) {
michael@0:       // 10^-exponent fits into a double.
michael@0:       *result = static_cast<double>(ReadUint64(trimmed, &read_digits));
michael@0:       ASSERT(read_digits == trimmed.length());
michael@0:       *result /= exact_powers_of_ten[-exponent];
michael@0:       return true;
michael@0:     }
michael@0:     if (0 <= exponent && exponent < kExactPowersOfTenSize) {
michael@0:       // 10^exponent fits into a double.
michael@0:       *result = static_cast<double>(ReadUint64(trimmed, &read_digits));
michael@0:       ASSERT(read_digits == trimmed.length());
michael@0:       *result *= exact_powers_of_ten[exponent];
michael@0:       return true;
michael@0:     }
michael@0:     int remaining_digits =
michael@0:         kMaxExactDoubleIntegerDecimalDigits - trimmed.length();
michael@0:     if ((0 <= exponent) &&
michael@0:         (exponent - remaining_digits < kExactPowersOfTenSize)) {
michael@0:       // The trimmed string was short and we can multiply it with
michael@0:       // 10^remaining_digits. As a result the remaining exponent now fits
michael@0:       // into a double too.
michael@0:       *result = static_cast<double>(ReadUint64(trimmed, &read_digits));
michael@0:       ASSERT(read_digits == trimmed.length());
michael@0:       *result *= exact_powers_of_ten[remaining_digits];
michael@0:       *result *= exact_powers_of_ten[exponent - remaining_digits];
michael@0:       return true;
michael@0:     }
michael@0:   }
michael@0:   return false;
michael@0: }
michael@0: 
michael@0: 
michael@0: // Returns 10^exponent as an exact DiyFp.
michael@0: // The given exponent must be in the range [1; kDecimalExponentDistance[.
michael@0: static DiyFp AdjustmentPowerOfTen(int exponent) {
michael@0:   ASSERT(0 < exponent);
michael@0:   ASSERT(exponent < PowersOfTenCache::kDecimalExponentDistance);
michael@0:   // Simply hardcode the remaining powers for the given decimal exponent
michael@0:   // distance.
michael@0:   ASSERT(PowersOfTenCache::kDecimalExponentDistance == 8);
michael@0:   switch (exponent) {
michael@0:     case 1: return DiyFp(UINT64_2PART_C(0xa0000000, 00000000), -60);
michael@0:     case 2: return DiyFp(UINT64_2PART_C(0xc8000000, 00000000), -57);
michael@0:     case 3: return DiyFp(UINT64_2PART_C(0xfa000000, 00000000), -54);
michael@0:     case 4: return DiyFp(UINT64_2PART_C(0x9c400000, 00000000), -50);
michael@0:     case 5: return DiyFp(UINT64_2PART_C(0xc3500000, 00000000), -47);
michael@0:     case 6: return DiyFp(UINT64_2PART_C(0xf4240000, 00000000), -44);
michael@0:     case 7: return DiyFp(UINT64_2PART_C(0x98968000, 00000000), -40);
michael@0:     default:
michael@0:       UNREACHABLE();
michael@0:       return DiyFp(0, 0);
michael@0:   }
michael@0: }
michael@0: 
michael@0: 
michael@0: // If the function returns true then the result is the correct double.
michael@0: // Otherwise it is either the correct double or the double that is just below
michael@0: // the correct double.
michael@0: static bool DiyFpStrtod(Vector<const char> buffer,
michael@0:                         int exponent,
michael@0:                         double* result) {
michael@0:   DiyFp input;
michael@0:   int remaining_decimals;
michael@0:   ReadDiyFp(buffer, &input, &remaining_decimals);
michael@0:   // Since we may have dropped some digits the input is not accurate.
michael@0:   // If remaining_decimals is different than 0 than the error is at most
michael@0:   // .5 ulp (unit in the last place).
michael@0:   // We don't want to deal with fractions and therefore keep a common
michael@0:   // denominator.
michael@0:   const int kDenominatorLog = 3;
michael@0:   const int kDenominator = 1 << kDenominatorLog;
michael@0:   // Move the remaining decimals into the exponent.
michael@0:   exponent += remaining_decimals;
michael@0:   int error = (remaining_decimals == 0 ? 0 : kDenominator / 2);
michael@0: 
michael@0:   int old_e = input.e();
michael@0:   input.Normalize();
michael@0:   error <<= old_e - input.e();
michael@0: 
michael@0:   ASSERT(exponent <= PowersOfTenCache::kMaxDecimalExponent);
michael@0:   if (exponent < PowersOfTenCache::kMinDecimalExponent) {
michael@0:     *result = 0.0;
michael@0:     return true;
michael@0:   }
michael@0:   DiyFp cached_power;
michael@0:   int cached_decimal_exponent;
michael@0:   PowersOfTenCache::GetCachedPowerForDecimalExponent(exponent,
michael@0:                                                      &cached_power,
michael@0:                                                      &cached_decimal_exponent);
michael@0: 
michael@0:   if (cached_decimal_exponent != exponent) {
michael@0:     int adjustment_exponent = exponent - cached_decimal_exponent;
michael@0:     DiyFp adjustment_power = AdjustmentPowerOfTen(adjustment_exponent);
michael@0:     input.Multiply(adjustment_power);
michael@0:     if (kMaxUint64DecimalDigits - buffer.length() >= adjustment_exponent) {
michael@0:       // The product of input with the adjustment power fits into a 64 bit
michael@0:       // integer.
michael@0:       ASSERT(DiyFp::kSignificandSize == 64);
michael@0:     } else {
michael@0:       // The adjustment power is exact. There is hence only an error of 0.5.
michael@0:       error += kDenominator / 2;
michael@0:     }
michael@0:   }
michael@0: 
michael@0:   input.Multiply(cached_power);
michael@0:   // The error introduced by a multiplication of a*b equals
michael@0:   //   error_a + error_b + error_a*error_b/2^64 + 0.5
michael@0:   // Substituting a with 'input' and b with 'cached_power' we have
michael@0:   //   error_b = 0.5  (all cached powers have an error of less than 0.5 ulp),
michael@0:   //   error_ab = 0 or 1 / kDenominator > error_a*error_b/ 2^64
michael@0:   int error_b = kDenominator / 2;
michael@0:   int error_ab = (error == 0 ? 0 : 1);  // We round up to 1.
michael@0:   int fixed_error = kDenominator / 2;
michael@0:   error += error_b + error_ab + fixed_error;
michael@0: 
michael@0:   old_e = input.e();
michael@0:   input.Normalize();
michael@0:   error <<= old_e - input.e();
michael@0: 
michael@0:   // See if the double's significand changes if we add/subtract the error.
michael@0:   int order_of_magnitude = DiyFp::kSignificandSize + input.e();
michael@0:   int effective_significand_size =
michael@0:       Double::SignificandSizeForOrderOfMagnitude(order_of_magnitude);
michael@0:   int precision_digits_count =
michael@0:       DiyFp::kSignificandSize - effective_significand_size;
michael@0:   if (precision_digits_count + kDenominatorLog >= DiyFp::kSignificandSize) {
michael@0:     // This can only happen for very small denormals. In this case the
michael@0:     // half-way multiplied by the denominator exceeds the range of an uint64.
michael@0:     // Simply shift everything to the right.
michael@0:     int shift_amount = (precision_digits_count + kDenominatorLog) -
michael@0:         DiyFp::kSignificandSize + 1;
michael@0:     input.set_f(input.f() >> shift_amount);
michael@0:     input.set_e(input.e() + shift_amount);
michael@0:     // We add 1 for the lost precision of error, and kDenominator for
michael@0:     // the lost precision of input.f().
michael@0:     error = (error >> shift_amount) + 1 + kDenominator;
michael@0:     precision_digits_count -= shift_amount;
michael@0:   }
michael@0:   // We use uint64_ts now. This only works if the DiyFp uses uint64_ts too.
michael@0:   ASSERT(DiyFp::kSignificandSize == 64);
michael@0:   ASSERT(precision_digits_count < 64);
michael@0:   uint64_t one64 = 1;
michael@0:   uint64_t precision_bits_mask = (one64 << precision_digits_count) - 1;
michael@0:   uint64_t precision_bits = input.f() & precision_bits_mask;
michael@0:   uint64_t half_way = one64 << (precision_digits_count - 1);
michael@0:   precision_bits *= kDenominator;
michael@0:   half_way *= kDenominator;
michael@0:   DiyFp rounded_input(input.f() >> precision_digits_count,
michael@0:                       input.e() + precision_digits_count);
michael@0:   if (precision_bits >= half_way + error) {
michael@0:     rounded_input.set_f(rounded_input.f() + 1);
michael@0:   }
michael@0:   // If the last_bits are too close to the half-way case than we are too
michael@0:   // inaccurate and round down. In this case we return false so that we can
michael@0:   // fall back to a more precise algorithm.
michael@0: 
michael@0:   *result = Double(rounded_input).value();
michael@0:   if (half_way - error < precision_bits && precision_bits < half_way + error) {
michael@0:     // Too imprecise. The caller will have to fall back to a slower version.
michael@0:     // However the returned number is guaranteed to be either the correct
michael@0:     // double, or the next-lower double.
michael@0:     return false;
michael@0:   } else {
michael@0:     return true;
michael@0:   }
michael@0: }
michael@0: 
michael@0: 
michael@0: // Returns
michael@0: //   - -1 if buffer*10^exponent < diy_fp.
michael@0: //   -  0 if buffer*10^exponent == diy_fp.
michael@0: //   - +1 if buffer*10^exponent > diy_fp.
michael@0: // Preconditions:
michael@0: //   buffer.length() + exponent <= kMaxDecimalPower + 1
michael@0: //   buffer.length() + exponent > kMinDecimalPower
michael@0: //   buffer.length() <= kMaxDecimalSignificantDigits
michael@0: static int CompareBufferWithDiyFp(Vector<const char> buffer,
michael@0:                                   int exponent,
michael@0:                                   DiyFp diy_fp) {
michael@0:   ASSERT(buffer.length() + exponent <= kMaxDecimalPower + 1);
michael@0:   ASSERT(buffer.length() + exponent > kMinDecimalPower);
michael@0:   ASSERT(buffer.length() <= kMaxSignificantDecimalDigits);
michael@0:   // Make sure that the Bignum will be able to hold all our numbers.
michael@0:   // Our Bignum implementation has a separate field for exponents. Shifts will
michael@0:   // consume at most one bigit (< 64 bits).
michael@0:   // ln(10) == 3.3219...
michael@0:   ASSERT(((kMaxDecimalPower + 1) * 333 / 100) < Bignum::kMaxSignificantBits);
michael@0:   Bignum buffer_bignum;
michael@0:   Bignum diy_fp_bignum;
michael@0:   buffer_bignum.AssignDecimalString(buffer);
michael@0:   diy_fp_bignum.AssignUInt64(diy_fp.f());
michael@0:   if (exponent >= 0) {
michael@0:     buffer_bignum.MultiplyByPowerOfTen(exponent);
michael@0:   } else {
michael@0:     diy_fp_bignum.MultiplyByPowerOfTen(-exponent);
michael@0:   }
michael@0:   if (diy_fp.e() > 0) {
michael@0:     diy_fp_bignum.ShiftLeft(diy_fp.e());
michael@0:   } else {
michael@0:     buffer_bignum.ShiftLeft(-diy_fp.e());
michael@0:   }
michael@0:   return Bignum::Compare(buffer_bignum, diy_fp_bignum);
michael@0: }
michael@0: 
michael@0: 
michael@0: // Returns true if the guess is the correct double.
michael@0: // Returns false, when guess is either correct or the next-lower double.
michael@0: static bool ComputeGuess(Vector<const char> trimmed, int exponent,
michael@0:                          double* guess) {
michael@0:   if (trimmed.length() == 0) {
michael@0:     *guess = 0.0;
michael@0:     return true;
michael@0:   }
michael@0:   if (exponent + trimmed.length() - 1 >= kMaxDecimalPower) {
michael@0:     *guess = Double::Infinity();
michael@0:     return true;
michael@0:   }
michael@0:   if (exponent + trimmed.length() <= kMinDecimalPower) {
michael@0:     *guess = 0.0;
michael@0:     return true;
michael@0:   }
michael@0: 
michael@0:   if (DoubleStrtod(trimmed, exponent, guess) ||
michael@0:       DiyFpStrtod(trimmed, exponent, guess)) {
michael@0:     return true;
michael@0:   }
michael@0:   if (*guess == Double::Infinity()) {
michael@0:     return true;
michael@0:   }
michael@0:   return false;
michael@0: }
michael@0: 
michael@0: double Strtod(Vector<const char> buffer, int exponent) {
michael@0:   char copy_buffer[kMaxSignificantDecimalDigits];
michael@0:   Vector<const char> trimmed;
michael@0:   int updated_exponent;
michael@0:   TrimAndCut(buffer, exponent, copy_buffer, kMaxSignificantDecimalDigits,
michael@0:              &trimmed, &updated_exponent);
michael@0:   exponent = updated_exponent;
michael@0: 
michael@0:   double guess;
michael@0:   bool is_correct = ComputeGuess(trimmed, exponent, &guess);
michael@0:   if (is_correct) return guess;
michael@0: 
michael@0:   DiyFp upper_boundary = Double(guess).UpperBoundary();
michael@0:   int comparison = CompareBufferWithDiyFp(trimmed, exponent, upper_boundary);
michael@0:   if (comparison < 0) {
michael@0:     return guess;
michael@0:   } else if (comparison > 0) {
michael@0:     return Double(guess).NextDouble();
michael@0:   } else if ((Double(guess).Significand() & 1) == 0) {
michael@0:     // Round towards even.
michael@0:     return guess;
michael@0:   } else {
michael@0:     return Double(guess).NextDouble();
michael@0:   }
michael@0: }
michael@0: 
michael@0: float Strtof(Vector<const char> buffer, int exponent) {
michael@0:   char copy_buffer[kMaxSignificantDecimalDigits];
michael@0:   Vector<const char> trimmed;
michael@0:   int updated_exponent;
michael@0:   TrimAndCut(buffer, exponent, copy_buffer, kMaxSignificantDecimalDigits,
michael@0:              &trimmed, &updated_exponent);
michael@0:   exponent = updated_exponent;
michael@0: 
michael@0:   double double_guess;
michael@0:   bool is_correct = ComputeGuess(trimmed, exponent, &double_guess);
michael@0: 
michael@0:   float float_guess = static_cast<float>(double_guess);
michael@0:   if (float_guess == double_guess) {
michael@0:     // This shortcut triggers for integer values.
michael@0:     return float_guess;
michael@0:   }
michael@0: 
michael@0:   // We must catch double-rounding. Say the double has been rounded up, and is
michael@0:   // now a boundary of a float, and rounds up again. This is why we have to
michael@0:   // look at previous too.
michael@0:   // Example (in decimal numbers):
michael@0:   //    input: 12349
michael@0:   //    high-precision (4 digits): 1235
michael@0:   //    low-precision (3 digits):
michael@0:   //       when read from input: 123
michael@0:   //       when rounded from high precision: 124.
michael@0:   // To do this we simply look at the neigbors of the correct result and see
michael@0:   // if they would round to the same float. If the guess is not correct we have
michael@0:   // to look at four values (since two different doubles could be the correct
michael@0:   // double).
michael@0: 
michael@0:   double double_next = Double(double_guess).NextDouble();
michael@0:   double double_previous = Double(double_guess).PreviousDouble();
michael@0: 
michael@0:   float f1 = static_cast<float>(double_previous);
michael@0: #if defined(DEBUG)
michael@0:   float f2 = float_guess;
michael@0: #endif
michael@0:   float f3 = static_cast<float>(double_next);
michael@0:   float f4;
michael@0:   if (is_correct) {
michael@0:     f4 = f3;
michael@0:   } else {
michael@0:     double double_next2 = Double(double_next).NextDouble();
michael@0:     f4 = static_cast<float>(double_next2);
michael@0:   }
michael@0:   ASSERT(f1 <= f2 && f2 <= f3 && f3 <= f4);
michael@0: 
michael@0:   // If the guess doesn't lie near a single-precision boundary we can simply
michael@0:   // return its float-value.
michael@0:   if (f1 == f4) {
michael@0:     return float_guess;
michael@0:   }
michael@0: 
michael@0:   ASSERT((f1 != f2 && f2 == f3 && f3 == f4) ||
michael@0:          (f1 == f2 && f2 != f3 && f3 == f4) ||
michael@0:          (f1 == f2 && f2 == f3 && f3 != f4));
michael@0: 
michael@0:   // guess and next are the two possible canditates (in the same way that
michael@0:   // double_guess was the lower candidate for a double-precision guess).
michael@0:   float guess = f1;
michael@0:   float next = f4;
michael@0:   DiyFp upper_boundary;
michael@0:   if (guess == 0.0f) {
michael@0:     float min_float = 1e-45f;
michael@0:     upper_boundary = Double(static_cast<double>(min_float) / 2).AsDiyFp();
michael@0:   } else {
michael@0:     upper_boundary = Single(guess).UpperBoundary();
michael@0:   }
michael@0:   int comparison = CompareBufferWithDiyFp(trimmed, exponent, upper_boundary);
michael@0:   if (comparison < 0) {
michael@0:     return guess;
michael@0:   } else if (comparison > 0) {
michael@0:     return next;
michael@0:   } else if ((Single(guess).Significand() & 1) == 0) {
michael@0:     // Round towards even.
michael@0:     return guess;
michael@0:   } else {
michael@0:     return next;
michael@0:   }
michael@0: }
michael@0: 
michael@0: }  // namespace double_conversion