/*
 * Fibonacci numbers: F[n] = F[n-1] + F[n-2], F[0] = 0, F[1] = 1
 * 
 * Analytic expression: F[n] = (phi^n - psi^n)/(phi - psi), 
 *                      phi = (1 + sqrt(5))/2, psi = 1 - phi
 */

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

int main() {
    long i = 1L, j = 0L, k;        /* k <--> F[n], i <--> F[n-1], j <--> F[n-2] */
    int n;
    double phi, psi, phi_p, psi_p, d, f;

    phi = 0.5*(1 + sqrt(5.));
    psi = 1. - phi;
    d = 1./(phi - psi);            /* 1./sqrt(5.) */

    printf("%2d     %15ld      %42.16f\n", 0, j, 0.);
    printf("%2d     %15ld      %42.16f\n", 1, i, 1.);

    phi_p = phi;
    psi_p = psi;

    for (n = 2; n < 70; n++){
        k = i + j;
        phi_p *= phi;
        psi_p *= psi;
        f = d*(phi_p - psi_p);     /* F[n] */

        printf("%2d     %15ld      %42.16f\n", n, k, f);
        j = i;
        i = k;
    }

    return(0);
}