path: root/contrib/libs/double-conversion/strtod.cc

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#include <climits>
#include <cstdarg>
 
#include "bignum.h" 
#include "cached-powers.h" 
#include "ieee.h" 
#include "strtod.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) { 
    (void) space_size;  // Mark variable as used. 
    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; 
#else
  if (trimmed.length() <= kMaxExactDoubleIntegerDecimalDigits) { 
    int read_digits; 
    // The trimmed input fits into a double. 
    // If the 10^exponent (resp. 10^-exponent) fits into a double too then we 
    // can compute the result-double simply by multiplying (resp. dividing) the 
    // two numbers. 
    // This is possible because IEEE guarantees that floating-point operations 
    // return the best possible approximation. 
    if (exponent < 0 && -exponent < kExactPowersOfTenSize) { 
      // 10^-exponent fits into a double. 
      *result = static_cast<double>(ReadUint64(trimmed, &read_digits)); 
      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; 
#endif
} 
 
 
// 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(); 
  } 
} 
 
 
// If the function returns true then the result is the correct double. 
// Otherwise it is either the correct double or the double that is just below 
// the correct double. 
static bool DiyFpStrtod(Vector<const char> buffer, 
                        int exponent, 
                        double* result) { 
  DiyFp input; 
  int remaining_decimals; 
  ReadDiyFp(buffer, &input, &remaining_decimals); 
  // Since we may have dropped some digits the input is not accurate. 
  // If remaining_decimals is different than 0 than the error is at most 
  // .5 ulp (unit in the last place). 
  // We don't want to deal with fractions and therefore keep a common 
  // denominator. 
  const int kDenominatorLog = 3; 
  const int kDenominator = 1 << kDenominatorLog; 
  // Move the remaining decimals into the exponent. 
  exponent += remaining_decimals; 
  uint64_t error = (remaining_decimals == 0 ? 0 : kDenominator / 2); 
 
  int old_e = input.e(); 
  input.Normalize(); 
  error <<= old_e - input.e(); 
 
  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(); 
  } 
} 
 
static float SanitizedDoubletof(double d) {
  ASSERT(d >= 0.0);
  // ASAN has a sanitize check that disallows casting doubles to floats if
  // they are too big.
  // https://clang.llvm.org/docs/UndefinedBehaviorSanitizer.html#available-checks
  // The behavior should be covered by IEEE 754, but some projects use this
  // flag, so work around it.
  float max_finite = 3.4028234663852885981170418348451692544e+38;
  // The half-way point between the max-finite and infinity value.
  // Since infinity has an even significand everything equal or greater than
  // this value should become infinity.
  double half_max_finite_infinity =
      3.40282356779733661637539395458142568448e+38;
  if (d >= max_finite) {
    if (d >= half_max_finite_infinity) {
      return Single::Infinity();
    } else {
      return max_finite;
    }
  } else {
    return static_cast<float>(d);
  }
}

float Strtof(Vector<const char> buffer, int exponent) { 
  char copy_buffer[kMaxSignificantDecimalDigits]; 
  Vector<const char> trimmed; 
  int updated_exponent; 
  TrimAndCut(buffer, exponent, copy_buffer, kMaxSignificantDecimalDigits, 
             &trimmed, &updated_exponent); 
  exponent = updated_exponent; 
 
  double double_guess; 
  bool is_correct = ComputeGuess(trimmed, exponent, &double_guess); 
 
  float float_guess = SanitizedDoubletof(double_guess);
  if (float_guess == double_guess) { 
    // This shortcut triggers for integer values. 
    return float_guess; 
  } 
 
  // We must catch double-rounding. Say the double has been rounded up, and is 
  // now a boundary of a float, and rounds up again. This is why we have to 
  // look at previous too. 
  // Example (in decimal numbers): 
  //    input: 12349 
  //    high-precision (4 digits): 1235 
  //    low-precision (3 digits): 
  //       when read from input: 123 
  //       when rounded from high precision: 124. 
  // To do this we simply look at the 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 = SanitizedDoubletof(double_previous);
  float f2 = float_guess; 
  float f3 = SanitizedDoubletof(double_next);
  float f4; 
  if (is_correct) { 
    f4 = f3; 
  } else { 
    double double_next2 = Double(double_next).NextDouble(); 
    f4 = SanitizedDoubletof(double_next2);
  } 
  (void) f2;  // Mark variable as used. 
  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 candidates (in the same way that
  // double_guess was the lower candidate for a double-precision guess). 
  float guess = f1; 
  float next = f4; 
  DiyFp upper_boundary; 
  if (guess == 0.0f) { 
    float min_float = 1e-45f; 
    upper_boundary = Double(static_cast<double>(min_float) / 2).AsDiyFp(); 
  } else { 
    upper_boundary = Single(guess).UpperBoundary(); 
  } 
  int comparison = CompareBufferWithDiyFp(trimmed, exponent, upper_boundary); 
  if (comparison < 0) { 
    return guess; 
  } else if (comparison > 0) { 
    return next; 
  } else if ((Single(guess).Significand() & 1) == 0) { 
    // Round towards even. 
    return guess; 
  } else { 
    return next; 
  } 
} 
 
}  // namespace double_conversion