#include <stdio.h>
#include <math.h>

#define x0 2

#define v0 1

#define t0 0
#define tf 1000

#define w02 3

#define dt 1e-2
#define N ((tf-t0)/dt)

double phi(double x)
{
	return -w02*x;
}

double E(double x, double v)
{
	return v*v/w02 + x*x;
}

int main(void)
{
	double x = x0, xn,
	       t = t0, tn,
	       v = v0, vn;

	FILE *h = fopen("./diferencial.dat","w+");

	double E0 = E(x,v);

	for (int i = 0; i < N; ++i)
	{
		xn = x + vn*dt + 0.5*phi(x)*dt*dt;
		vn = v + 0.5*(phi(xn)+phi(x))*dt;
		tn = t + dt;

		fprintf(h, "%d %f %f %f\n", i, t, x, E(x,v)/E0-1);

		x = xn;
		v = vn;
		t = tn;
	}

	fclose(h);
	return 0;
}