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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.
 //
 // 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 "ieee754.h"
 #include "biginteger.h"
 #include "diyfp.h"
 #include "pow10.h"
 #include <climits>
 #include <limits>
  
 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
 template <typename Ch>
 inline bool StrtodDiyFp(const Ch* 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] >= Ch('5')))
             break;
         significand = significand * 10u + static_cast<unsigned>(decimals[i] - Ch('0'));
     }
  
     if(i < dLen && decimals[i] >= Ch('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);
 }
  
 template <typename Ch>
 inline double StrtodBigInteger(double approx, const Ch* 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();
 }
  
 template <typename Ch>
 inline double StrtodFullPrecision(
     double d, int p, const Ch* 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_