/*
 * Calculate Fibonacci numbers using analytic expression
 *
 *    F[n] = 1./sqrt(5.) * ( ((1. + sqrt(5.))/2)^n - ((1. - sqrt(5.))/2)^n ) 
 *
 * To compile: 
 *
 *      make fib2
 *
 *    or
 *
 *      gcc -O0 fib2.c -o fib2
 *
 *    or
 *
 *      clang -O0 fib2.c -o fib2
 */

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

double fibonacci(int);
 
int main(void)
{
    int n = 1474;
    double ff;
    ff = fibonacci(n);
    printf("%d   %g\n", n, ff);
    return 0;
} 

double fibonacci(int n)
{
    double x = sqrt(5.);
    return 1./x*(pow((1.+ x)/2, n) - pow((1. - x)/2, n)); 
}