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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,

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 // (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 <stdarg.h>

 #include <limits.h>

 #include "strtod.h"

 #include "bignum.h"

 #include "cached-powers.h"

 #include "ieee.h"

 namespace double_conversion {

 // 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;

 // 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 = UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF);

 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 = ARRAY_SIZE(exact_powers_of_ten);

 // 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 Vector<const char> TrimTrailingZeros(Vector<const char> buffer) {

   for (int i = buffer.length() - 1; i >= 0; --i) {

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

       return buffer.SubVector(0, i + 1);

     }

   }

   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'.

   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) {

     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';

     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)

   // 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.

   // Note that the ARM simulator is compiled for 32bits. It therefore exhibits

   // the same problem.

   return false;

 #endif

   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));

       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));

       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));

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

       *result *= exact_powers_of_ten[remaining_digits];

       *result *= exact_powers_of_ten[exponent - remaining_digits];

       return true;

     }

   }

   return false;

 }

 // Returns 10^exponent as an exact DiyFp.

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

 static DiyFp AdjustmentPowerOfTen(int exponent) {

   ASSERT(0 < exponent);

   ASSERT(exponent < PowersOfTenCache::kDecimalExponentDistance);

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

   // distance.

   ASSERT(PowersOfTenCache::kDecimalExponentDistance == 8);

   switch (exponent) {

     case 1: return DiyFp(UINT64_2PART_C(0xa0000000, 00000000), -60);

     case 2: return DiyFp(UINT64_2PART_C(0xc8000000, 00000000), -57);

     case 3: return DiyFp(UINT64_2PART_C(0xfa000000, 00000000), -54);

     case 4: return DiyFp(UINT64_2PART_C(0x9c400000, 00000000), -50);

     case 5: return DiyFp(UINT64_2PART_C(0xc3500000, 00000000), -47);

     case 6: return DiyFp(UINT64_2PART_C(0xf4240000, 00000000), -44);

     case 7: return DiyFp(UINT64_2PART_C(0x98968000, 00000000), -40);

     default:

       UNREACHABLE();

       return DiyFp(0, 0);

   }

 }

 // 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;

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

   int old_e = input.e();

   input.Normalize();

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

   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.

       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.

   ASSERT(DiyFp::kSignificandSize == 64);

   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) {

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

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

   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...

   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;

 }

 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);

   exponent = updated_exponent;

   double guess;

   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();

   }

 }

 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;

   double double_guess;

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

   float float_guess = static_cast<float>(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 neigbors 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 = static_cast<float>(double_previous);

 #if defined(DEBUG)

   float f2 = float_guess;

 #endif

   float f3 = static_cast<float>(double_next);

   float f4;

   if (is_correct) {

     f4 = f3;

   } else {

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

     f4 = static_cast<float>(double_next2);

   }

   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;

   }

   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 canditates (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