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Diffstat (limited to 'NorthstarDLL/include/rapidjson/internal/strtod.h')
| -rw-r--r-- | NorthstarDLL/include/rapidjson/internal/strtod.h | 269 |
1 files changed, 269 insertions, 0 deletions
diff --git a/NorthstarDLL/include/rapidjson/internal/strtod.h b/NorthstarDLL/include/rapidjson/internal/strtod.h new file mode 100644 index 00000000..289c413b --- /dev/null +++ b/NorthstarDLL/include/rapidjson/internal/strtod.h @@ -0,0 +1,269 @@ +// 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" + +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, size_t length, size_t decimalPosition, int exp, double* result) { + uint64_t significand = 0; + size_t i = 0; // 2^64 - 1 = 18446744073709551615, 1844674407370955161 = 0x1999999999999999 + for (; i < length; 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 < length && decimals[i] >= '5') // Rounding + significand++; + + size_t remaining = length - i; + const unsigned kUlpShift = 3; + const unsigned kUlp = 1 << kUlpShift; + int64_t error = (remaining == 0) ? 0 : kUlp / 2; + + DiyFp v(significand, 0); + v = v.Normalize(); + error <<= -v.e; + + const int dExp = static_cast<int>(decimalPosition) - static_cast<int>(i) + exp; + + int actualExp; + DiyFp cachedPower = GetCachedPower10(dExp, &actualExp); + if (actualExp != dExp) { + static const DiyFp kPow10[] = { + DiyFp(RAPIDJSON_UINT64_C2(0xa0000000, 00000000), -60), // 10^1 + DiyFp(RAPIDJSON_UINT64_C2(0xc8000000, 00000000), -57), // 10^2 + DiyFp(RAPIDJSON_UINT64_C2(0xfa000000, 00000000), -54), // 10^3 + DiyFp(RAPIDJSON_UINT64_C2(0x9c400000, 00000000), -50), // 10^4 + DiyFp(RAPIDJSON_UINT64_C2(0xc3500000, 00000000), -47), // 10^5 + DiyFp(RAPIDJSON_UINT64_C2(0xf4240000, 00000000), -44), // 10^6 + DiyFp(RAPIDJSON_UINT64_C2(0x98968000, 00000000), -40) // 10^7 + }; + int adjustment = dExp - actualExp - 1; + RAPIDJSON_ASSERT(adjustment >= 0 && adjustment < 7); + v = v * kPow10[adjustment]; + if (length + static_cast<unsigned>(adjustment)> 19u) // 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 unsigned effectiveSignificandSize = Double::EffectiveSignificandSize(64 + v.e); + unsigned precisionSize = 64 - effectiveSignificandSize; + if (precisionSize + kUlpShift >= 64) { + unsigned scaleExp = (precisionSize + kUlpShift) - 63; + v.f >>= scaleExp; + v.e += scaleExp; + error = (error >> scaleExp) + 1 + static_cast<int>(kUlp); + precisionSize -= scaleExp; + } + + DiyFp rounded(v.f >> precisionSize, v.e + static_cast<int>(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, size_t length, size_t decimalPosition, int exp) { + const BigInteger dInt(decimals, length); + const int dExp = static_cast<int>(decimalPosition) - static_cast<int>(length) + exp; + 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; + if (StrtodFast(d, p, &result)) + return result; + + // Trim leading zeros + while (*decimals == '0' && length > 1) { + length--; + decimals++; + decimalPosition--; + } + + // Trim trailing zeros + while (decimals[length - 1] == '0' && length > 1) { + length--; + decimalPosition--; + exp++; + } + + // Trim right-most digits + const int kMaxDecimalDigit = 780; + if (static_cast<int>(length) > kMaxDecimalDigit) { + int delta = (static_cast<int>(length) - kMaxDecimalDigit); + exp += delta; + decimalPosition -= static_cast<unsigned>(delta); + length = kMaxDecimalDigit; + } + + // If too small, underflow to zero + if (int(length) + exp < -324) + return 0.0; + + if (StrtodDiyFp(decimals, length, decimalPosition, exp, &result)) + return result; + + // Use approximation from StrtodDiyFp and make adjustment with BigInteger comparison + return StrtodBigInteger(result, decimals, length, decimalPosition, exp); +} + +} // namespace internal +RAPIDJSON_NAMESPACE_END + +#endif // RAPIDJSON_STRTOD_ |