#define _USE_MATH_DEFINES
#include <fstream>
#include <iostream>
#include <math.h>
#include <iomanip>
#include <ctype.h>

using namespace std;

template<typename T>
using func = T(*)(T, T);

template <typename T>
T fun(T x) {
	return cos(x / 2.);
}

template <typename T>
T poch(T x) {
	return -0.5 * sin(x / 2.);
}

template <typename T>
T progresywna(T h, T x) {
	return (fun(x + h) - fun(x)) / h;
}

template <typename T>
T wsteczna(T h, T x) {
	return (fun(x) - fun(x - h)) / h;
}

template <typename T>
T centralna(T h, T x) {
	return (fun(x + h) - fun(x - h)) / (2 * h);
}

template <typename T>
T x0_3pkt(T h, T x) {
	return (-1.5*fun(x) + 2 * fun(x + h) - 0.5*fun(x + 2 * h)) / h;
}

template <typename T>
T xn_3pkt(T h, T x) {
	return (0.5*fun(x - 2 * h) - 2 * fun(x - h) + 1.5*fun(x)) / h;
}

template <typename T>
void plot(string name, T x, func<T> f) {
	T h = 0.2;
	ofstream outfile(name);

	for (int i = 0; i < 100; i++) {
		outfile << log10(h) << " " << log10(fabs(poch(x) - f(h, x))) << endl;
		h /= 2.0;
	}

	outfile.close();
}

template <typename T>
void make_plot(T x0, T xn, T xc) {
	string name = typeid(T).name();
	plot(name + "1.txt", x0, progresywna);
	plot(name + "2.txt", x0, x0_3pkt);
	plot(name + "3.txt", xn, wsteczna);
	plot(name + "4.txt", xn, xn_3pkt);
	plot(name + "5.txt", xc, progresywna);
	plot(name + "6.txt", xc, wsteczna);
	plot(name + "7.txt", xc, centralna);
}

int main() {
	make_plot<double>(0, M_PI, M_PI / 2);
	make_plot<float>(0, M_PI, M_PI / 2);
	return 0;
}