rapidjson/internal/strtod.h

0001 // Tencent is pleased to support the open source community by making RapidJSON available.
0002 //
0003 // Copyright (C) 2015 THL A29 Limited, a Tencent company, and Milo Yip.
0004 //
0005 // Licensed under the MIT License (the "License"); you may not use this file except
0006 // in compliance with the License. You may obtain a copy of the License at
0007 //
0008 // http://opensource.org/licenses/MIT
0009 //
0010 // Unless required by applicable law or agreed to in writing, software distributed
0011 // under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR
0012 // CONDITIONS OF ANY KIND, either express or implied. See the License for the
0013 // specific language governing permissions and limitations under the License.
0014
0015 #ifndef RAPIDJSON_STRTOD_
0016 #define RAPIDJSON_STRTOD_
0017
0018 #include "ieee754.h"
0019 #include "biginteger.h"
0020 #include "diyfp.h"
0021 #include "pow10.h"
0022 #include <climits>
0023 #include <limits>
0024
0025 RAPIDJSON_NAMESPACE_BEGIN
0026 namespace internal {
0027
0028 inline double FastPath(double significand, int exp) {
0029     if (exp < -308)
0030         return 0.0;
0031     else if (exp >= 0)
0032         return significand * internal::Pow10(exp);
0033     else
0034         return significand / internal::Pow10(-exp);
0035 }
0036
0037 inline double StrtodNormalPrecision(double d, int p) {
0038     if (p < -308) {
0039         // Prevent expSum < -308, making Pow10(p) = 0
0040         d = FastPath(d, -308);
0041         d = FastPath(d, p + 308);
0042     }
0043     else
0044         d = FastPath(d, p);
0045     return d;
0046 }
0047
0048 template <typename T>
0049 inline T Min3(T a, T b, T c) {
0050     T m = a;
0051     if (m > b) m = b;
0052     if (m > c) m = c;
0053     return m;
0054 }
0055
0056 inline int CheckWithinHalfULP(double b, const BigInteger& d, int dExp) {
0057     const Double db(b);
0058     const uint64_t bInt = db.IntegerSignificand();
0059     const int bExp = db.IntegerExponent();
0060     const int hExp = bExp - 1;
0061
0062     int dS_Exp2 = 0, dS_Exp5 = 0, bS_Exp2 = 0, bS_Exp5 = 0, hS_Exp2 = 0, hS_Exp5 = 0;
0063
0064     // Adjust for decimal exponent
0065     if (dExp >= 0) {
0066         dS_Exp2 += dExp;
0067         dS_Exp5 += dExp;
0068     }
0069     else {
0070         bS_Exp2 -= dExp;
0071         bS_Exp5 -= dExp;
0072         hS_Exp2 -= dExp;
0073         hS_Exp5 -= dExp;
0074     }
0075
0076     // Adjust for binary exponent
0077     if (bExp >= 0)
0078         bS_Exp2 += bExp;
0079     else {
0080         dS_Exp2 -= bExp;
0081         hS_Exp2 -= bExp;
0082     }
0083
0084     // Adjust for half ulp exponent
0085     if (hExp >= 0)
0086         hS_Exp2 += hExp;
0087     else {
0088         dS_Exp2 -= hExp;
0089         bS_Exp2 -= hExp;
0090     }
0091
0092     // Remove common power of two factor from all three scaled values
0093     int common_Exp2 = Min3(dS_Exp2, bS_Exp2, hS_Exp2);
0094     dS_Exp2 -= common_Exp2;
0095     bS_Exp2 -= common_Exp2;
0096     hS_Exp2 -= common_Exp2;
0097
0098     BigInteger dS = d;
0099     dS.MultiplyPow5(static_cast<unsigned>(dS_Exp5)) <<= static_cast<unsigned>(dS_Exp2);
0100
0101     BigInteger bS(bInt);
0102     bS.MultiplyPow5(static_cast<unsigned>(bS_Exp5)) <<= static_cast<unsigned>(bS_Exp2);
0103
0104     BigInteger hS(1);
0105     hS.MultiplyPow5(static_cast<unsigned>(hS_Exp5)) <<= static_cast<unsigned>(hS_Exp2);
0106
0107     BigInteger delta(0);
0108     dS.Difference(bS, &delta);
0109
0110     return delta.Compare(hS);
0111 }
0112
0113 inline bool StrtodFast(double d, int p, double* result) {
0114     // Use fast path for string-to-double conversion if possible
0115     // see http://www.exploringbinary.com/fast-path-decimal-to-floating-point-conversion/
0116     if (p > 22  && p < 22 + 16) {
0117         // Fast Path Cases In Disguise
0118         d *= internal::Pow10(p - 22);
0119         p = 22;
0120     }
0121
0122     if (p >= -22 && p <= 22 && d <= 9007199254740991.0) { // 2^53 - 1
0123         *result = FastPath(d, p);
0124         return true;
0125     }
0126     else
0127         return false;
0128 }
0129
0130 // Compute an approximation and see if it is within 1/2 ULP
0131 template<typename Ch>
0132 inline bool StrtodDiyFp(const Ch* decimals, int dLen, int dExp, double* result) {
0133     uint64_t significand = 0;
0134     int i = 0;   // 2^64 - 1 = 18446744073709551615, 1844674407370955161 = 0x1999999999999999
0135     for (; i < dLen; i++) {
0136         if (significand  >  RAPIDJSON_UINT64_C2(0x19999999, 0x99999999) ||
0137             (significand == RAPIDJSON_UINT64_C2(0x19999999, 0x99999999) && decimals[i] > Ch('5')))
0138             break;
0139         significand = significand * 10u + static_cast<unsigned>(decimals[i] - Ch('0'));
0140     }
0141
0142     if (i < dLen && decimals[i] >= Ch('5')) // Rounding
0143         significand++;
0144
0145     int remaining = dLen - i;
0146     const int kUlpShift = 3;
0147     const int kUlp = 1 << kUlpShift;
0148     int64_t error = (remaining == 0) ? 0 : kUlp / 2;
0149
0150     DiyFp v(significand, 0);
0151     v = v.Normalize();
0152     error <<= -v.e;
0153
0154     dExp += remaining;
0155
0156     int actualExp;
0157     DiyFp cachedPower = GetCachedPower10(dExp, &actualExp);
0158     if (actualExp != dExp) {
0159         static const DiyFp kPow10[] = {
0160             DiyFp(RAPIDJSON_UINT64_C2(0xa0000000, 0x00000000), -60),  // 10^1
0161             DiyFp(RAPIDJSON_UINT64_C2(0xc8000000, 0x00000000), -57),  // 10^2
0162             DiyFp(RAPIDJSON_UINT64_C2(0xfa000000, 0x00000000), -54),  // 10^3
0163             DiyFp(RAPIDJSON_UINT64_C2(0x9c400000, 0x00000000), -50),  // 10^4
0164             DiyFp(RAPIDJSON_UINT64_C2(0xc3500000, 0x00000000), -47),  // 10^5
0165             DiyFp(RAPIDJSON_UINT64_C2(0xf4240000, 0x00000000), -44),  // 10^6
0166             DiyFp(RAPIDJSON_UINT64_C2(0x98968000, 0x00000000), -40)   // 10^7
0167         };
0168         int adjustment = dExp - actualExp;
0169         RAPIDJSON_ASSERT(adjustment >= 1 && adjustment < 8);
0170         v = v * kPow10[adjustment - 1];
0171         if (dLen + adjustment > 19) // has more digits than decimal digits in 64-bit
0172             error += kUlp / 2;
0173     }
0174
0175     v = v * cachedPower;
0176
0177     error += kUlp + (error == 0 ? 0 : 1);
0178
0179     const int oldExp = v.e;
0180     v = v.Normalize();
0181     error <<= oldExp - v.e;
0182
0183     const int effectiveSignificandSize = Double::EffectiveSignificandSize(64 + v.e);
0184     int precisionSize = 64 - effectiveSignificandSize;
0185     if (precisionSize + kUlpShift >= 64) {
0186         int scaleExp = (precisionSize + kUlpShift) - 63;
0187         v.f >>= scaleExp;
0188         v.e += scaleExp;
0189         error = (error >> scaleExp) + 1 + kUlp;
0190         precisionSize -= scaleExp;
0191     }
0192
0193     DiyFp rounded(v.f >> precisionSize, v.e + precisionSize);
0194     const uint64_t precisionBits = (v.f & ((uint64_t(1) << precisionSize) - 1)) * kUlp;
0195     const uint64_t halfWay = (uint64_t(1) << (precisionSize - 1)) * kUlp;
0196     if (precisionBits >= halfWay + static_cast<unsigned>(error)) {
0197         rounded.f++;
0198         if (rounded.f & (DiyFp::kDpHiddenBit << 1)) { // rounding overflows mantissa (issue #340)
0199             rounded.f >>= 1;
0200             rounded.e++;
0201         }
0202     }
0203
0204     *result = rounded.ToDouble();
0205
0206     return halfWay - static_cast<unsigned>(error) >= precisionBits || precisionBits >= halfWay + static_cast<unsigned>(error);
0207 }
0208
0209 template<typename Ch>
0210 inline double StrtodBigInteger(double approx, const Ch* decimals, int dLen, int dExp) {
0211     RAPIDJSON_ASSERT(dLen >= 0);
0212     const BigInteger dInt(decimals, static_cast<unsigned>(dLen));
0213     Double a(approx);
0214     int cmp = CheckWithinHalfULP(a.Value(), dInt, dExp);
0215     if (cmp < 0)
0216         return a.Value();  // within half ULP
0217     else if (cmp == 0) {
0218         // Round towards even
0219         if (a.Significand() & 1)
0220             return a.NextPositiveDouble();
0221         else
0222             return a.Value();
0223     }
0224     else // adjustment
0225         return a.NextPositiveDouble();
0226 }
0227
0228 template<typename Ch>
0229 inline double StrtodFullPrecision(double d, int p, const Ch* decimals, size_t length, size_t decimalPosition, int exp) {
0230     RAPIDJSON_ASSERT(d >= 0.0);
0231     RAPIDJSON_ASSERT(length >= 1);
0232
0233     double result = 0.0;
0234     if (StrtodFast(d, p, &result))
0235         return result;
0236
0237     RAPIDJSON_ASSERT(length <= INT_MAX);
0238     int dLen = static_cast<int>(length);
0239
0240     RAPIDJSON_ASSERT(length >= decimalPosition);
0241     RAPIDJSON_ASSERT(length - decimalPosition <= INT_MAX);
0242     int dExpAdjust = static_cast<int>(length - decimalPosition);
0243
0244     RAPIDJSON_ASSERT(exp >= INT_MIN + dExpAdjust);
0245     int dExp = exp - dExpAdjust;
0246
0247     // Make sure length+dExp does not overflow
0248     RAPIDJSON_ASSERT(dExp <= INT_MAX - dLen);
0249
0250     // Trim leading zeros
0251     while (dLen > 0 && *decimals == '0') {
0252         dLen--;
0253         decimals++;
0254     }
0255
0256     // Trim trailing zeros
0257     while (dLen > 0 && decimals[dLen - 1] == '0') {
0258         dLen--;
0259         dExp++;
0260     }
0261
0262     if (dLen == 0) { // Buffer only contains zeros.
0263         return 0.0;
0264     }
0265
0266     // Trim right-most digits
0267     const int kMaxDecimalDigit = 767 + 1;
0268     if (dLen > kMaxDecimalDigit) {
0269         dExp += dLen - kMaxDecimalDigit;
0270         dLen = kMaxDecimalDigit;
0271     }
0272
0273     // If too small, underflow to zero.
0274     // Any x <= 10^-324 is interpreted as zero.
0275     if (dLen + dExp <= -324)
0276         return 0.0;
0277
0278     // If too large, overflow to infinity.
0279     // Any x >= 10^309 is interpreted as +infinity.
0280     if (dLen + dExp > 309)
0281         return std::numeric_limits<double>::infinity();
0282
0283     if (StrtodDiyFp(decimals, dLen, dExp, &result))
0284         return result;
0285
0286     // Use approximation from StrtodDiyFp and make adjustment with BigInteger comparison
0287     return StrtodBigInteger(result, decimals, dLen, dExp);
0288 }
0289
0290 } // namespace internal
0291 RAPIDJSON_NAMESPACE_END
0292
0293 #endif // RAPIDJSON_STRTOD_