fibonacci_fast.c File Reference

Compute \(m^{mth}\) Fibonacci number using the formulae: More...

#include <locale.h>
#include <stdio.h>
#include <stdlib.h>

Include dependency graph for fibonacci_fast.c:

Functions
void	fib (unsigned long n, unsigned long *C, unsigned long *D)
	Returns the \(n^{th}\) and \(n+1^{th}\) Fibonacci number. More...
int	main (int argc, char *argv[])
	main function

Detailed Description

Compute \(m^{mth}\) Fibonacci number using the formulae:

Author

Krishna Vedala

Date

2 October, 2019

\begin{eqnarray*} F_{2n-1} &=& F_n^2 + F_{n-1}^2 \\ F_{2n} &=& F_n\left(2F_{n-1} + F_n\right) \end{eqnarray*}

Function Documentation

fib()

void fib	(	unsigned long	n,
		unsigned long *	C,
		unsigned long *	D
	)

Returns the \(n^{th}\) and \(n+1^{th}\) Fibonacci number.

The return variables are C & D respectively.

{
    // Out of Range checking
    if (n < 0)
    {
        printf("\nNo Such term !\n");
        exit(0);
    }
 
    unsigned long a, b, c, d;
 
    if (n == 0)
    {
        C[0] = 0;
        if (D)
            D[0] = 1;
        return;
    }
 
    fib(n >> 1, &c, &d); /* Compute F(n/2) */
 
    a = c * ((d << 1) - c);
    b = c * c + d * d;
    if (n % 2 == 0) /* If n is even */
    {
        C[0] = a;
        if (D)
            D[0] = b;
        return;
    }
 
    /**< If n is odd */
    C[0] = b;
    if (D)
        D[0] = a + b;
    return;
}