strtod.h

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// Tencent is pleased to support the open source community by making RapidJSON
// available.
//
// Copyright (C) 2015 THL A29 Limited, a Tencent company, and Milo Yip. All
// rights reserved.
//
// Licensed under the MIT License (the "License"); you may not use this file
// except in compliance with the License. You may obtain a copy of the License
// at
//
// http://opensource.org/licenses/MIT
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
// WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
// License for the specific language governing permissions and limitations under
// the License.

#ifndef RAPIDJSON_STRTOD_
#define RAPIDJSON_STRTOD_

#include <climits>
#include <limits>
#include "biginteger.h"
#include "diyfp.h"
#include "ieee754.h"
#include "pow10.h"

RAPIDJSON_NAMESPACE_BEGIN
namespace internal {

inline double FastPath(double significand, int exp) {
  if (exp < -308)
    return 0.0;
  else if (exp >= 0)
    return significand * internal::Pow10(exp);
  else
    return significand / internal::Pow10(-exp);
}

inline double StrtodNormalPrecision(double d, int p) {
  if (p < -308) {
    // Prevent expSum < -308, making Pow10(p) = 0
    d = FastPath(d, -308);
    d = FastPath(d, p + 308);
  } else
    d = FastPath(d, p);
  return d;
}

template <typename T>
inline T Min3(T a, T b, T c) {
  T m = a;
  if (m > b) m = b;
  if (m > c) m = c;
  return m;
}

inline int CheckWithinHalfULP(double b, const BigInteger &d, int dExp) {
  const Double db(b);
  const uint64_t bInt = db.IntegerSignificand();
  const int bExp = db.IntegerExponent();
  const int hExp = bExp - 1;

  int dS_Exp2 = 0, dS_Exp5 = 0, bS_Exp2 = 0, bS_Exp5 = 0, hS_Exp2 = 0,
      hS_Exp5 = 0;

  // Adjust for decimal exponent
  if (dExp >= 0) {
    dS_Exp2 += dExp;
    dS_Exp5 += dExp;
  } else {
    bS_Exp2 -= dExp;
    bS_Exp5 -= dExp;
    hS_Exp2 -= dExp;
    hS_Exp5 -= dExp;
  }

  // Adjust for binary exponent
  if (bExp >= 0)
    bS_Exp2 += bExp;
  else {
    dS_Exp2 -= bExp;
    hS_Exp2 -= bExp;
  }

  // Adjust for half ulp exponent
  if (hExp >= 0)
    hS_Exp2 += hExp;
  else {
    dS_Exp2 -= hExp;
    bS_Exp2 -= hExp;
  }

  // Remove common power of two factor from all three scaled values
  int common_Exp2 = Min3(dS_Exp2, bS_Exp2, hS_Exp2);
  dS_Exp2 -= common_Exp2;
  bS_Exp2 -= common_Exp2;
  hS_Exp2 -= common_Exp2;

  BigInteger dS = d;
  dS.MultiplyPow5(static_cast<unsigned>(dS_Exp5)) <<=
      static_cast<unsigned>(dS_Exp2);

  BigInteger bS(bInt);
  bS.MultiplyPow5(static_cast<unsigned>(bS_Exp5)) <<=
      static_cast<unsigned>(bS_Exp2);

  BigInteger hS(1);
  hS.MultiplyPow5(static_cast<unsigned>(hS_Exp5)) <<=
      static_cast<unsigned>(hS_Exp2);

  BigInteger delta(0);
  dS.Difference(bS, &delta);

  return delta.Compare(hS);
}

inline bool StrtodFast(double d, int p, double *result) {
  // Use fast path for string-to-double conversion if possible
  // see
  // http://www.exploringbinary.com/fast-path-decimal-to-floating-point-conversion/
  if (p > 22 && p < 22 + 16) {
    // Fast Path Cases In Disguise
    d *= internal::Pow10(p - 22);
    p = 22;
  }

  if (p >= -22 && p <= 22 && d <= 9007199254740991.0) {  // 2^53 - 1
    *result = FastPath(d, p);
    return true;
  } else
    return false;
}

// Compute an approximation and see if it is within 1/2 ULP
inline bool StrtodDiyFp(const char *decimals, int dLen, int dExp,
                        double *result) {
  uint64_t significand = 0;
  int i = 0;  // 2^64 - 1 = 18446744073709551615, 1844674407370955161 =
              // 0x1999999999999999
  for (; i < dLen; i++) {
    if (significand > RAPIDJSON_UINT64_C2(0x19999999, 0x99999999) ||
        (significand == RAPIDJSON_UINT64_C2(0x19999999, 0x99999999) &&
         decimals[i] > '5'))
      break;
    significand = significand * 10u + static_cast<unsigned>(decimals[i] - '0');
  }

  if (i < dLen && decimals[i] >= '5')  // Rounding
    significand++;

  int remaining = dLen - i;
  const int kUlpShift = 3;
  const int kUlp = 1 << kUlpShift;
  int64_t error = (remaining == 0) ? 0 : kUlp / 2;

  DiyFp v(significand, 0);
  v = v.Normalize();
  error <<= -v.e;

  dExp += remaining;

  int actualExp;
  DiyFp cachedPower = GetCachedPower10(dExp, &actualExp);
  if (actualExp != dExp) {
    static const DiyFp kPow10[] = {
        DiyFp(RAPIDJSON_UINT64_C2(0xa0000000, 0x00000000), -60),  // 10^1
        DiyFp(RAPIDJSON_UINT64_C2(0xc8000000, 0x00000000), -57),  // 10^2
        DiyFp(RAPIDJSON_UINT64_C2(0xfa000000, 0x00000000), -54),  // 10^3
        DiyFp(RAPIDJSON_UINT64_C2(0x9c400000, 0x00000000), -50),  // 10^4
        DiyFp(RAPIDJSON_UINT64_C2(0xc3500000, 0x00000000), -47),  // 10^5
        DiyFp(RAPIDJSON_UINT64_C2(0xf4240000, 0x00000000), -44),  // 10^6
        DiyFp(RAPIDJSON_UINT64_C2(0x98968000, 0x00000000), -40)   // 10^7
    };
    int adjustment = dExp - actualExp;
    RAPIDJSON_ASSERT(adjustment >= 1 && adjustment < 8);
    v = v * kPow10[adjustment - 1];
    if (dLen + adjustment >
        19)  // has more digits than decimal digits in 64-bit
      error += kUlp / 2;
  }

  v = v * cachedPower;

  error += kUlp + (error == 0 ? 0 : 1);

  const int oldExp = v.e;
  v = v.Normalize();
  error <<= oldExp - v.e;

  const int effectiveSignificandSize =
      Double::EffectiveSignificandSize(64 + v.e);
  int precisionSize = 64 - effectiveSignificandSize;
  if (precisionSize + kUlpShift >= 64) {
    int scaleExp = (precisionSize + kUlpShift) - 63;
    v.f >>= scaleExp;
    v.e += scaleExp;
    error = (error >> scaleExp) + 1 + kUlp;
    precisionSize -= scaleExp;
  }

  DiyFp rounded(v.f >> precisionSize, v.e + precisionSize);
  const uint64_t precisionBits =
      (v.f & ((uint64_t(1) << precisionSize) - 1)) * kUlp;
  const uint64_t halfWay = (uint64_t(1) << (precisionSize - 1)) * kUlp;
  if (precisionBits >= halfWay + static_cast<unsigned>(error)) {
    rounded.f++;
    if (rounded.f & (DiyFp::kDpHiddenBit
                     << 1)) {  // rounding overflows mantissa (issue #340)
      rounded.f >>= 1;
      rounded.e++;
    }
  }

  *result = rounded.ToDouble();

  return halfWay - static_cast<unsigned>(error) >= precisionBits ||
         precisionBits >= halfWay + static_cast<unsigned>(error);
}

inline double StrtodBigInteger(double approx, const char *decimals, int dLen,
                               int dExp) {
  RAPIDJSON_ASSERT(dLen >= 0);
  const BigInteger dInt(decimals, static_cast<unsigned>(dLen));
  Double a(approx);
  int cmp = CheckWithinHalfULP(a.Value(), dInt, dExp);
  if (cmp < 0)
    return a.Value();  // within half ULP
  else if (cmp == 0) {
    // Round towards even
    if (a.Significand() & 1)
      return a.NextPositiveDouble();
    else
      return a.Value();
  } else  // adjustment
    return a.NextPositiveDouble();
}

inline double StrtodFullPrecision(double d, int p, const char *decimals,
                                  size_t length, size_t decimalPosition,
                                  int exp) {
  RAPIDJSON_ASSERT(d >= 0.0);
  RAPIDJSON_ASSERT(length >= 1);

  double result = 0.0;
  if (StrtodFast(d, p, &result)) return result;

  RAPIDJSON_ASSERT(length <= INT_MAX);
  int dLen = static_cast<int>(length);

  RAPIDJSON_ASSERT(length >= decimalPosition);
  RAPIDJSON_ASSERT(length - decimalPosition <= INT_MAX);
  int dExpAdjust = static_cast<int>(length - decimalPosition);

  RAPIDJSON_ASSERT(exp >= INT_MIN + dExpAdjust);
  int dExp = exp - dExpAdjust;

  // Make sure length+dExp does not overflow
  RAPIDJSON_ASSERT(dExp <= INT_MAX - dLen);

  // Trim leading zeros
  while (dLen > 0 && *decimals == '0') {
    dLen--;
    decimals++;
  }

  // Trim trailing zeros
  while (dLen > 0 && decimals[dLen - 1] == '0') {
    dLen--;
    dExp++;
  }

  if (dLen == 0) {  // Buffer only contains zeros.
    return 0.0;
  }

  // Trim right-most digits
  const int kMaxDecimalDigit = 767 + 1;
  if (dLen > kMaxDecimalDigit) {
    dExp += dLen - kMaxDecimalDigit;
    dLen = kMaxDecimalDigit;
  }

  // If too small, underflow to zero.
  // Any x <= 10^-324 is interpreted as zero.
  if (dLen + dExp <= -324) return 0.0;

  // If too large, overflow to infinity.
  // Any x >= 10^309 is interpreted as +infinity.
  if (dLen + dExp > 309) return std::numeric_limits<double>::infinity();

  if (StrtodDiyFp(decimals, dLen, dExp, &result)) return result;

  // Use approximation from StrtodDiyFp and make adjustment with BigInteger
  // comparison
  return StrtodBigInteger(result, decimals, dLen, dExp);
}

}  // namespace internal
RAPIDJSON_NAMESPACE_END

#endif  // RAPIDJSON_STRTOD_