Merge branch 'master' of https://github.com/pauldb89/cdec

1 files changed, 558 insertions, 0 deletions

diff --git a/klm/util/double-conversion/strtod.cc b/klm/util/double-conversion/strtod.cc
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+++ b/klm/util/double-conversion/strtod.cc
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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,
+// 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[] = {
+  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);
+#ifndef NDEBUG
+  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);
+  }
+#ifndef NDEBUG
+  ASSERT(f1 <= f2 && f2 <= f3 && f3 <= f4);
+#endif
+
+  // 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