// 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_