text: ﻿// -*- tab-width: 2; indent-tabs-mode: nil; coding: utf-8-with-signature -*-
  // 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 "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
  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_
  