The Tor Browser: mfbt/double-conversion/strtod.cc@6474c204b198 (annotated)

mfbt/double-conversion/strtod.cc@6474c204b198 (annotated)

mfbt/double-conversion/strtod.cc

Wed, 31 Dec 2014 06:09:35 +0100

author: Michael Schloh von Bennewitz <michael@schloh.com>
date: Wed, 31 Dec 2014 06:09:35 +0100
changeset 0: 6474c204b198
permissions: -rw-r--r--

Cloned upstream origin tor-browser at tor-browser-31.3.0esr-4.5-1-build1
revision ID fc1c9ff7c1b2defdbc039f12214767608f46423f for hacking purpose.

 // 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,
 // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 // (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[] = {
 .0,  // 10^0
 .0,
 .0,
 .0,
 .0,
 .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

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mfbt/double-conversion/strtod.cc@6474c204b198 (annotated)

mfbt/double-conversion/strtod.cc