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// Copyright (C) 2011 Milo Yip
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
// THE SOFTWARE.
#ifndef RAPIDJSON_STRTOD_
#define RAPIDJSON_STRTOD_
#include "../rapidjson.h"
#include "ieee754.h"
#include "biginteger.h"
#include "pow10.h"
namespace rapidjson {
namespace internal {
inline double StrtodFastPath(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 NormalPrecision(double d, int p) {
if (p < -308) {
// Prevent expSum < -308, making Pow10(p) = 0
d = StrtodFastPath(d, -308);
d = StrtodFastPath(d, p + 308);
}
else
d = StrtodFastPath(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, bool* adjustToNegative) {
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);
*adjustToNegative = dS.Difference(bS, &delta);
int cmp = delta.Compare(hS);
// If delta is within 1/2 ULP, check for special case when significand is power of two.
// In this case, need to compare with 1/2h in the lower bound.
if (cmp < 0 && *adjustToNegative && // within and dS < bS
db.IsNormal() && (bInt & (bInt - 1)) == 0 && // Power of 2
db.Uint64Value() != RAPIDJSON_UINT64_C2(0x00100000, 0x00000000)) // minimum normal number must not do this
{
delta <<= 1;
return delta.Compare(hS);
}
return cmp;
}
inline double FullPrecision(double d, int p, const char* decimals, size_t length, size_t decimalPosition, int exp) {
RAPIDJSON_ASSERT(d >= 0.0);
RAPIDJSON_ASSERT(length >= 1);
// 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) {
if (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
return StrtodFastPath(d, p);
// Use slow-path with BigInteger comparison
// 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 (length > kMaxDecimalDigit) {
exp += (int(length) - kMaxDecimalDigit);
length = kMaxDecimalDigit;
}
// If too small, underflow to zero
if (int(length) + exp < -324)
return 0.0;
const BigInteger dInt(decimals, length);
const int dExp = (int)decimalPosition - (int)length + exp;
Double approx = NormalPrecision(d, p);
for (int i = 0; i < 10; i++) {
bool adjustToNegative;
int cmp = CheckWithinHalfULP(approx.Value(), dInt, dExp, &adjustToNegative);
if (cmp < 0)
return approx.Value(); // within half ULP
else if (cmp == 0) {
// Round towards even
if (approx.Significand() & 1)
return adjustToNegative ? approx.PreviousPositiveDouble() : approx.NextPositiveDouble();
else
return approx.Value();
}
else // adjustment
approx = adjustToNegative ? approx.PreviousPositiveDouble() : approx.NextPositiveDouble();
}
// This should not happen, but in case there is really a bug, break the infinite-loop
return approx.Value();
}
} // namespace internal
} // namespace rapidjson
#endif // RAPIDJSON_STRTOD_
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