strtod.h

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// 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 "../rapidjson.h"
#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(dS_Exp5) <<= dS_Exp2;

 BigInteger bS(bInt);
 bS.MultiplyPow5(bS_Exp5) <<= bS_Exp2;

 BigInteger hS(1);
 hS.MultiplyPow5(hS_Exp5) <<= 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 * 10 + (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;
 int error = (remaining == 0) ? 0 : kUlp / 2;

 DiyFp v(significand, 0);
 v = v.Normalize();
 error <<= -v.e;

 const int dExp = (int)decimalPosition - (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 + 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 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 + 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 + error) {
 rounded.f++;
 if (rounded.f & (DiyFp::kDpHiddenBit << 1)) { // rounding overflows mantissa (issue #340)
 rounded.f >>= 1;
 rounded.e++;
 }
 }

 *result = rounded.ToDouble();

 return halfWay - error >= precisionBits || precisionBits >= halfWay + 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 = (int)decimalPosition - (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 ((int)length > kMaxDecimalDigit) {
 int delta = (int(length) - kMaxDecimalDigit);
 exp += delta;
 decimalPosition -= 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_