class psc_f
{
public:
psc_f(double alpha) : alpha{ alpha } {}
double operator() (double x) const
{
return sin(alpha * x) + cos(x);
}
private:
double alpha;
};
template <typename F, typename T>
class derivative
{
public:
derivative(const F& f, const T& h) : f{ f }, h{ h } {}
T operator()(const T& x) const
{
return (f(x + h) - f(x)) / h;
}
private:
const F& f;
T h;
};
template <unsigned N, typename F, typename T>
class nth_derivative
{
using prev_derivative = nth_derivative <N - 1, F, T>;
public:
nth_derivative(const F& f, const T& h) : h{ h }, fp{ f, h }
{}
T operator()(const T& x) const
{
return N & 1 ? (fp(x + h) - fp(x)) / h
: (fp(x) - fp(x - h)) / h;
}
private:
T h;
prev_derivative fp;
};
template <typename F, typename T>
class nth_derivative<1, F, T>
: public derivative<F, T>
{
using derivative<F, T >::derivative;
};
int main()
{
nth_derivative<22, psc_f, double> d22_psc_o{ psc_f(1.0),0.00001 };
cout << "22nd der. of sin(x) + cos(x) at 0 is " << d22_psc_o(0.0)
<< '\n';
}
