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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.
//
// 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
inline bool StrtodDiyFp(const char* 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] > '5'))
break;
significand = significand * 10u + static_cast<unsigned>(decimals[i] - '0');
}
if (i < dLen && decimals[i] >= '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);
}
inline double StrtodBigInteger(double approx, const char* 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();
}
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 = 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_