math.h

/*  This file is part of the Vc library. {{{
Copyright © 2013-2015 Matthias Kretz <kretz@kde.org>

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#ifndef VC_COMMON_MATH_H_
#define VC_COMMON_MATH_H_

#define Vc_COMMON_MATH_H_INTERNAL 1

#include "trigonometric.h"

#include "const.h"
#include "macros.h"

namespace Vc_VERSIONED_NAMESPACE
{
#ifdef Vc_IMPL_SSE
// for SSE, AVX, and AVX2
#include "logarithm.h"
#include "exponential.h"
#ifdef Vc_IMPL_AVX
inline AVX::double_v exp(AVX::double_v _x)
{
    AVX::Vector<double> x = _x;
    typedef AVX::Vector<double> V;
        typedef V::Mask M;
    typedef AVX::Const<double> C;

        const M overflow  = x > Vc::Detail::doubleConstant< 1, 0x0006232bdd7abcd2ull, 9>(); // max log
        const M underflow = x < Vc::Detail::doubleConstant<-1, 0x0006232bdd7abcd2ull, 9>(); // min log

        V px = floor(C::log2_e() * x + 0.5);
        __m128i tmp = _mm256_cvttpd_epi32(px.data());
    const SimdArray<int, V::Size> n = SSE::int_v{tmp};
        x -= px * C::ln2_large(); //Vc::Detail::doubleConstant<1, 0x00062e4000000000ull, -1>();  // ln2
        x -= px * C::ln2_small(); //Vc::Detail::doubleConstant<1, 0x0007f7d1cf79abcaull, -20>(); // ln2

        const double P[] = {
            Vc::Detail::doubleConstant<1, 0x000089cdd5e44be8ull, -13>(),
            Vc::Detail::doubleConstant<1, 0x000f06d10cca2c7eull,  -6>(),
            Vc::Detail::doubleConstant<1, 0x0000000000000000ull,   0>()
        };
        const double Q[] = {
            Vc::Detail::doubleConstant<1, 0x00092eb6bc365fa0ull, -19>(),
            Vc::Detail::doubleConstant<1, 0x0004ae39b508b6c0ull,  -9>(),
            Vc::Detail::doubleConstant<1, 0x000d17099887e074ull,  -3>(),
            Vc::Detail::doubleConstant<1, 0x0000000000000000ull,   1>()
        };
        const V x2 = x * x;
        px = x * ((P[0] * x2 + P[1]) * x2 + P[2]);
        x =  px / ((((Q[0] * x2 + Q[1]) * x2 + Q[2]) * x2 + Q[3]) - px);
        x = V::One() + 2.0 * x;

        x = ldexp(x, n); // == x * 2ⁿ

        x(overflow) = std::numeric_limits<double>::infinity();
        x.setZero(underflow);

        return x;
    }
#endif  // Vc_IMPL_AVX

inline SSE::double_v exp(SSE::double_v::AsArg _x) {
    SSE::Vector<double> x = _x;
    typedef SSE::Vector<double> V;
        typedef V::Mask M;
    typedef SSE::Const<double> C;

        const M overflow  = x > Vc::Detail::doubleConstant< 1, 0x0006232bdd7abcd2ull, 9>(); // max log
        const M underflow = x < Vc::Detail::doubleConstant<-1, 0x0006232bdd7abcd2ull, 9>(); // min log

        V px = floor(C::log2_e() * x + 0.5);
    SimdArray<int, V::Size> n;
        _mm_storel_epi64(reinterpret_cast<__m128i *>(&n), _mm_cvttpd_epi32(px.data()));
        x -= px * C::ln2_large(); //Vc::Detail::doubleConstant<1, 0x00062e4000000000ull, -1>();  // ln2
        x -= px * C::ln2_small(); //Vc::Detail::doubleConstant<1, 0x0007f7d1cf79abcaull, -20>(); // ln2

        const double P[] = {
            Vc::Detail::doubleConstant<1, 0x000089cdd5e44be8ull, -13>(),
            Vc::Detail::doubleConstant<1, 0x000f06d10cca2c7eull,  -6>(),
            Vc::Detail::doubleConstant<1, 0x0000000000000000ull,   0>()
        };
        const double Q[] = {
            Vc::Detail::doubleConstant<1, 0x00092eb6bc365fa0ull, -19>(),
            Vc::Detail::doubleConstant<1, 0x0004ae39b508b6c0ull,  -9>(),
            Vc::Detail::doubleConstant<1, 0x000d17099887e074ull,  -3>(),
            Vc::Detail::doubleConstant<1, 0x0000000000000000ull,   1>()
        };
        const V x2 = x * x;
        px = x * ((P[0] * x2 + P[1]) * x2 + P[2]);
        x =  px / ((((Q[0] * x2 + Q[1]) * x2 + Q[2]) * x2 + Q[3]) - px);
        x = V::One() + 2.0 * x;

        x = ldexp(x, n); // == x * 2ⁿ

        x(overflow) = std::numeric_limits<double>::infinity();
        x.setZero(underflow);

        return x;
    }

#endif
}  // namespace Vc

#undef Vc_COMMON_MATH_H_INTERNAL

#endif // VC_COMMON_MATH_H_