ceph/src/rapidjson/include/rapidjson/internal/strtod.h

   1 // Tencent is pleased to support the open source community by making RapidJSON available.
   2 //
   3 // Copyright (C) 2015 THL A29 Limited, a Tencent company, and Milo Yip. All rights reserved.
   4 //
   5 // Licensed under the MIT License (the "License"); you may not use this file except
   6 // in compliance with the License. You may obtain a copy of the License at
   7 //
   8 // http://opensource.org/licenses/MIT
   9 //
  10 // Unless required by applicable law or agreed to in writing, software distributed
  11 // under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR
  12 // CONDITIONS OF ANY KIND, either express or implied. See the License for the
  13 // specific language governing permissions and limitations under the License.
  14
  15 #ifndef RAPIDJSON_STRTOD_
  16 #define RAPIDJSON_STRTOD_
  17
  18 #include "ieee754.h"
  19 #include "biginteger.h"
  20 #include "diyfp.h"
  21 #include "pow10.h"
  22
  23 RAPIDJSON_NAMESPACE_BEGIN
  24 namespace internal {
  25
  26 inline double FastPath(double significand, int exp) {
  27     if (exp < -308)
  28         return 0.0;
  29     else if (exp >= 0)
  30         return significand * internal::Pow10(exp);
  31     else
  32         return significand / internal::Pow10(-exp);
  33 }
  34
  35 inline double StrtodNormalPrecision(double d, int p) {
  36     if (p < -308) {
  37         // Prevent expSum < -308, making Pow10(p) = 0
  38         d = FastPath(d, -308);
  39         d = FastPath(d, p + 308);
  40     }
  41     else
  42         d = FastPath(d, p);
  43     return d;
  44 }
  45
  46 template <typename T>
  47 inline T Min3(T a, T b, T c) {
  48     T m = a;
  49     if (m > b) m = b;
  50     if (m > c) m = c;
  51     return m;
  52 }
  53
  54 inline int CheckWithinHalfULP(double b, const BigInteger& d, int dExp) {
  55     const Double db(b);
  56     const uint64_t bInt = db.IntegerSignificand();
  57     const int bExp = db.IntegerExponent();
  58     const int hExp = bExp - 1;
  59
  60     int dS_Exp2 = 0, dS_Exp5 = 0, bS_Exp2 = 0, bS_Exp5 = 0, hS_Exp2 = 0, hS_Exp5 = 0;
  61
  62     // Adjust for decimal exponent
  63     if (dExp >= 0) {
  64         dS_Exp2 += dExp;
  65         dS_Exp5 += dExp;
  66     }
  67     else {
  68         bS_Exp2 -= dExp;
  69         bS_Exp5 -= dExp;
  70         hS_Exp2 -= dExp;
  71         hS_Exp5 -= dExp;
  72     }
  73
  74     // Adjust for binary exponent
  75     if (bExp >= 0)
  76         bS_Exp2 += bExp;
  77     else {
  78         dS_Exp2 -= bExp;
  79         hS_Exp2 -= bExp;
  80     }
  81
  82     // Adjust for half ulp exponent
  83     if (hExp >= 0)
  84         hS_Exp2 += hExp;
  85     else {
  86         dS_Exp2 -= hExp;
  87         bS_Exp2 -= hExp;
  88     }
  89
  90     // Remove common power of two factor from all three scaled values
  91     int common_Exp2 = Min3(dS_Exp2, bS_Exp2, hS_Exp2);
  92     dS_Exp2 -= common_Exp2;
  93     bS_Exp2 -= common_Exp2;
  94     hS_Exp2 -= common_Exp2;
  95
  96     BigInteger dS = d;
  97     dS.MultiplyPow5(static_cast<unsigned>(dS_Exp5)) <<= static_cast<unsigned>(dS_Exp2);
  98
  99     BigInteger bS(bInt);
 100     bS.MultiplyPow5(static_cast<unsigned>(bS_Exp5)) <<= static_cast<unsigned>(bS_Exp2);
 101
 102     BigInteger hS(1);
 103     hS.MultiplyPow5(static_cast<unsigned>(hS_Exp5)) <<= static_cast<unsigned>(hS_Exp2);
 104
 105     BigInteger delta(0);
 106     dS.Difference(bS, &delta);
 107
 108     return delta.Compare(hS);
 109 }
 110
 111 inline bool StrtodFast(double d, int p, double* result) {
 112     // Use fast path for string-to-double conversion if possible
 113     // see http://www.exploringbinary.com/fast-path-decimal-to-floating-point-conversion/
 114     if (p > 22  && p < 22 + 16) {
 115         // Fast Path Cases In Disguise
 116         d *= internal::Pow10(p - 22);
 117         p = 22;
 118     }
 119
 120     if (p >= -22 && p <= 22 && d <= 9007199254740991.0) { // 2^53 - 1
 121         *result = FastPath(d, p);
 122         return true;
 123     }
 124     else
 125         return false;
 126 }
 127
 128 // Compute an approximation and see if it is within 1/2 ULP
 129 inline bool StrtodDiyFp(const char* decimals, size_t length, size_t decimalPosition, int exp, double* result) {
 130     uint64_t significand = 0;
 131     size_t i = 0;   // 2^64 - 1 = 18446744073709551615, 1844674407370955161 = 0x1999999999999999
 132     for (; i < length; i++) {
 133         if (significand  >  RAPIDJSON_UINT64_C2(0x19999999, 0x99999999) ||
 134             (significand == RAPIDJSON_UINT64_C2(0x19999999, 0x99999999) && decimals[i] > '5'))
 135             break;
 136         significand = significand * 10u + static_cast<unsigned>(decimals[i] - '0');
 137     }
 138
 139     if (i < length && decimals[i] >= '5') // Rounding
 140         significand++;
 141
 142     size_t remaining = length - i;
 143     const unsigned kUlpShift = 3;
 144     const unsigned kUlp = 1 << kUlpShift;
 145     int64_t error = (remaining == 0) ? 0 : kUlp / 2;
 146
 147     DiyFp v(significand, 0);
 148     v = v.Normalize();
 149     error <<= -v.e;
 150
 151     const int dExp = static_cast<int>(decimalPosition) - static_cast<int>(i) + exp;
 152
 153     int actualExp;
 154     DiyFp cachedPower = GetCachedPower10(dExp, &actualExp);
 155     if (actualExp != dExp) {
 156         static const DiyFp kPow10[] = {
 157             DiyFp(RAPIDJSON_UINT64_C2(0xa0000000, 00000000), -60),  // 10^1
 158             DiyFp(RAPIDJSON_UINT64_C2(0xc8000000, 00000000), -57),  // 10^2
 159             DiyFp(RAPIDJSON_UINT64_C2(0xfa000000, 00000000), -54),  // 10^3
 160             DiyFp(RAPIDJSON_UINT64_C2(0x9c400000, 00000000), -50),  // 10^4
 161             DiyFp(RAPIDJSON_UINT64_C2(0xc3500000, 00000000), -47),  // 10^5
 162             DiyFp(RAPIDJSON_UINT64_C2(0xf4240000, 00000000), -44),  // 10^6
 163             DiyFp(RAPIDJSON_UINT64_C2(0x98968000, 00000000), -40)   // 10^7
 164         };
 165         int  adjustment = dExp - actualExp - 1;
 166         RAPIDJSON_ASSERT(adjustment >= 0 && adjustment < 7);
 167         v = v * kPow10[adjustment];
 168         if (length + static_cast<unsigned>(adjustment)> 19u) // has more digits than decimal digits in 64-bit
 169             error += kUlp / 2;
 170     }
 171
 172     v = v * cachedPower;
 173
 174     error += kUlp + (error == 0 ? 0 : 1);
 175
 176     const int oldExp = v.e;
 177     v = v.Normalize();
 178     error <<= oldExp - v.e;
 179
 180     const unsigned effectiveSignificandSize = Double::EffectiveSignificandSize(64 + v.e);
 181     unsigned precisionSize = 64 - effectiveSignificandSize;
 182     if (precisionSize + kUlpShift >= 64) {
 183         unsigned scaleExp = (precisionSize + kUlpShift) - 63;
 184         v.f >>= scaleExp;
 185         v.e += scaleExp;
 186         error = (error >> scaleExp) + 1 + static_cast<int>(kUlp);
 187         precisionSize -= scaleExp;
 188     }
 189
 190     DiyFp rounded(v.f >> precisionSize, v.e + static_cast<int>(precisionSize));
 191     const uint64_t precisionBits = (v.f & ((uint64_t(1) << precisionSize) - 1)) * kUlp;
 192     const uint64_t halfWay = (uint64_t(1) << (precisionSize - 1)) * kUlp;
 193     if (precisionBits >= halfWay + static_cast<unsigned>(error)) {
 194         rounded.f++;
 195         if (rounded.f & (DiyFp::kDpHiddenBit << 1)) { // rounding overflows mantissa (issue #340)
 196             rounded.f >>= 1;
 197             rounded.e++;
 198         }
 199     }
 200
 201     *result = rounded.ToDouble();
 202
 203     return halfWay - static_cast<unsigned>(error) >= precisionBits || precisionBits >= halfWay + static_cast<unsigned>(error);
 204 }
 205
 206 inline double StrtodBigInteger(double approx, const char* decimals, size_t length, size_t decimalPosition, int exp) {
 207     const BigInteger dInt(decimals, length);
 208     const int dExp = static_cast<int>(decimalPosition) - static_cast<int>(length) + exp;
 209     Double a(approx);
 210     int cmp = CheckWithinHalfULP(a.Value(), dInt, dExp);
 211     if (cmp < 0)
 212         return a.Value();  // within half ULP
 213     else if (cmp == 0) {
 214         // Round towards even
 215         if (a.Significand() & 1)
 216             return a.NextPositiveDouble();
 217         else
 218             return a.Value();
 219     }
 220     else // adjustment
 221         return a.NextPositiveDouble();
 222 }
 223
 224 inline double StrtodFullPrecision(double d, int p, const char* decimals, size_t length, size_t decimalPosition, int exp) {
 225     RAPIDJSON_ASSERT(d >= 0.0);
 226     RAPIDJSON_ASSERT(length >= 1);
 227
 228     double result;
 229     if (StrtodFast(d, p, &result))
 230         return result;
 231
 232     // Trim leading zeros
 233     while (*decimals == '0' && length > 1) {
 234         length--;
 235         decimals++;
 236         decimalPosition--;
 237     }
 238
 239     // Trim trailing zeros
 240     while (decimals[length - 1] == '0' && length > 1) {
 241         length--;
 242         decimalPosition--;
 243         exp++;
 244     }
 245
 246     // Trim right-most digits
 247     const int kMaxDecimalDigit = 780;
 248     if (static_cast<int>(length) > kMaxDecimalDigit) {
 249         int delta = (static_cast<int>(length) - kMaxDecimalDigit);
 250         exp += delta;
 251         decimalPosition -= static_cast<unsigned>(delta);
 252         length = kMaxDecimalDigit;
 253     }
 254
 255     // If too small, underflow to zero
 256     if (int(length) + exp < -324)
 257         return 0.0;
 258
 259     if (StrtodDiyFp(decimals, length, decimalPosition, exp, &result))
 260         return result;
 261
 262     // Use approximation from StrtodDiyFp and make adjustment with BigInteger comparison
 263     return StrtodBigInteger(result, decimals, length, decimalPosition, exp);
 264 }
 265
 266 } // namespace internal
 267 RAPIDJSON_NAMESPACE_END
 268
 269 #endif // RAPIDJSON_STRTOD_