in rapidjson/internal/strtod.h [129:204]
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);
}