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

double exact(double t) { return sin(t); }

double dy(double t, double y) { return cos(t); }

double rk4_step(double y, double t, double h) {
    double k1 = h * dy(t, y);
    double k2 = h * dy(t + 0.5 * h, y + 0.5 * k1);
    double k3 = h * dy(t + 0.5 * h, y + 0.5 * k2);
    double k4 = h * dy(t + h, y + k3);
    return  y + (k1 + k4)/ 6.0 + (k2+k3) / 3.0;
}

double loop (int steps, double h, int n, double y, double t) {
    if (n < steps)
        return loop(steps, h, n+1, rk4_step(y,t,h), t+h);
    else return y;
}

int main() {
    double h = 0.1;
    double y = loop(102, h, 1, 1.0, 0.0);
    double err = fabs(y - exact(102 * h));
    int large = 10000000;
    double y2 = loop(large, h, 1, 1.0, 0.0);
    printf("%d\n",
           (fabs(y2 - (exact(large * h))) < 2. * err));
    return 0;
}