blame: source/code/Libs/include/cereal/external/rapidjson/internal/strtod.h

// 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 CEREAL_RAPIDJSON_STRTOD_

#define CEREAL_RAPIDJSON_STRTOD_

#include "ieee754.h"

#include "biginteger.h"

#include "diyfp.h"

#include "pow10.h"

CEREAL_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, 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  >  CEREAL_RAPIDJSON_UINT64_C2(0x19999999, 0x99999999) ||

            (significand == CEREAL_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(CEREAL_RAPIDJSON_UINT64_C2(0xa0000000, 00000000), -60),  // 10^1

            DiyFp(CEREAL_RAPIDJSON_UINT64_C2(0xc8000000, 00000000), -57),  // 10^2

            DiyFp(CEREAL_RAPIDJSON_UINT64_C2(0xfa000000, 00000000), -54),  // 10^3

            DiyFp(CEREAL_RAPIDJSON_UINT64_C2(0x9c400000, 00000000), -50),  // 10^4

            DiyFp(CEREAL_RAPIDJSON_UINT64_C2(0xc3500000, 00000000), -47),  // 10^5

            DiyFp(CEREAL_RAPIDJSON_UINT64_C2(0xf4240000, 00000000), -44),  // 10^6

            DiyFp(CEREAL_RAPIDJSON_UINT64_C2(0x98968000, 00000000), -40)   // 10^7

        };

        int  adjustment = dExp - actualExp - 1;

        CEREAL_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);

}

inline double StrtodBigInteger(double approx, const char* decimals, size_t length, size_t decimalPosition, int exp) {

    const BigInteger dInt(decimals, length);

    const int dExp = static_cast<int>(decimalPosition) - static_cast<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) {

    CEREAL_RAPIDJSON_ASSERT(d >= 0.0);

    CEREAL_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 (static_cast<int>(length) > kMaxDecimalDigit) {

        int delta = (static_cast<int>(length) - kMaxDecimalDigit);

        exp += delta;

        decimalPosition -= static_cast<unsigned>(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

CEREAL_RAPIDJSON_NAMESPACE_END

#endif // CEREAL_RAPIDJSON_STRTOD_