strtod.h Source File

strtod.h Source File#

Composable Kernel: strtod.h Source File
// 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
template <typename Ch>
inline bool StrtodDiyFp(const Ch* 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] >= Ch('5')))
            break;
        significand = significand * 10u + static_cast<unsigned>(decimals[i] - Ch('0'));
    }
 
    if(i < dLen && decimals[i] >= Ch('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);
}
 
template <typename Ch>
inline double StrtodBigInteger(double approx, const Ch* 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();
}
 
template <typename Ch>
inline double StrtodFullPrecision(
    double d, int p, const Ch* 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_