/
ieee.h
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/
ieee.h
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#ifndef FASTEXP_IEEE_H
#define FASTEXP_IEEE_H
namespace fastexp
{
template<typename Real, size_t degree, size_t i = 0> struct PolynomialFit;
template<typename Real> struct Info;
template<typename Real, size_t degree>
struct IEEE {
static Real evaluate(Real x) {
using unsigned_t = typename Info<Real>::unsigned_t;
constexpr unsigned_t shift = static_cast<unsigned_t>(1) << Info<Real>::shift;
x *= Info<Real>::log2e;
Real xi = floor(x);
Real xf = x - xi;
Real k = PolynomialFit<Real, degree, 0>::evaluate(xf) + 1.0;
unsigned_t e = reinterpret_cast<const unsigned_t &>(k);
e += shift * static_cast<unsigned_t>(xi);
return reinterpret_cast<Real &>(e);
}
};
////////////////////////////////////////////////////////////////////////////////
// Polynomial coefficients for error function fit.
////////////////////////////////////////////////////////////////////////////////
template<> struct Info<float> {
using unsigned_t = uint32_t;
static constexpr uint32_t shift = 23;
static constexpr float log2e = 1.442695040;
};
template<> struct Info<double> {
using unsigned_t = uint64_t;
static constexpr uint64_t shift = 52;
static constexpr double log2e = 1.442695040;
};
template<typename Real, size_t degree>
struct Data;
template<typename Real>
struct Data<Real, 1> {
static constexpr Real coefficients[2] = {-0.05288671,
0.99232129};
};
template<typename Real> constexpr Real Data<Real, 1>::coefficients[2];
template<typename Real>
struct Data<Real, 2> {
static constexpr Real coefficients[3] = {0.00365539,
0.64960693,
0.34271434};
};
template<typename Real> constexpr Real Data<Real, 2>::coefficients[3];
template<typename Real>
struct Data<Real, 3> {
static constexpr Real coefficients[4] = {-1.77187919e-04,
6.96787180e-01,
2.24169036e-01,
7.90302044e-02};
};
template<typename Real> constexpr Real Data<Real, 3>::coefficients[4];
template<typename Real>
struct Data<Real, 4> {
static constexpr Real coefficients[5] = { 6.58721338e-06,
6.92937406e-01,
2.41696769e-01,
5.16742848e-02,
1.36779598e-02};
};
template<typename Real> constexpr Real Data<Real, 4>::coefficients[5];
template<typename Real>
struct Data<Real, 5> {
static constexpr Real coefficients[6] = {6.58721338e-06,
6.92937406e-01,
2.41696769e-01,
5.16742848e-02,
1.36779598e-02};
};
template<typename Real> constexpr Real Data<Real, 5>::coefficients[6];
template<typename Real>
struct Data<Real, 6> {
static constexpr Real coefficients[7] = {-1.97880719e-07,
6.93156327e-01,
2.40133447e-01,
5.58740717e-02,
8.94160147e-03,
1.89454334e-03};
};
template<typename Real> constexpr Real Data<Real, 6>::coefficients[7];
template<typename Real>
struct Data<Real, 7> {
static constexpr Real coefficients[8] = {4.97074799e-09,
6.93146861e-01,
2.40230956e-01,
5.54792541e-02,
9.68583180e-03,
1.23835751e-03,
2.18728611e-04};
};
template<typename Real> constexpr Real Data<Real, 7>::coefficients[8];
template<typename Real>
struct Data<Real, 8> {
static constexpr Real coefficients[9] = {-1.06974751e-10,
6.93147190e-01,
2.40226337e-01,
5.55053726e-02,
9.61338873e-03,
1.34310382e-03,
1.42959529e-04,
2.16483090e-05};
};
template<typename Real> constexpr Real Data<Real, 8>::coefficients[9];
template<typename Real>
struct Data<Real, 9> {
static constexpr Real coefficients[10] = {2.00811867e-12,
6.93147180e-01,
2.40226512e-01,
5.55040573e-02,
9.61838113e-03,
1.33265219e-03,
1.55193275e-04,
1.41484217e-05,
1.87497191e-06};
};
template<typename Real> Real constexpr Data<Real, 9>::coefficients[10];
template<typename Real, size_t degree, size_t i>
struct PolynomialFit {
inline static Real evaluate(Real x) {
Real p = PolynomialFit<Real, degree, i + 1>::evaluate(x) * x;
p += Data<Real, degree>::coefficients[i];
return p;
}
};
template<typename Real, size_t degree>
struct PolynomialFit<Real, degree, degree> {
inline static Real evaluate(Real x) {
return Data<Real, degree>::coefficients[degree];
}
};
template<typename Real>
struct PolynomialFit<Real, 0, 0> {
inline static Real evaluate(Real x) {
return x;
}
};
} // fastexp
#endif // FASTEXP_IEEE_H