/**
    @file Fibonacci_fast.c
    @author: Krishna Vedala
    @date 2 October, 2019
    @brief Compute \f$m^{mth}\f$ Fibonacci number using the formulae:
    \f{eqnarray*}{
        F_{2n-1} &=& F_n^2 + F_{n-1}^2 \\ 
        F_{2n}   &=& F_n\left(2F_{n-1} + F_n\right)
   \f}
*/

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

/**
    Returns the \f$n^{th}\f$ and \f$n+1^{th}\f$ Fibonacci number.
    The return variables are C & D respectively.
 */
void fib(unsigned long n, unsigned long *C, unsigned long *D) 
{ 
    //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;
} 
  
int main(int argc, char *argv[])
{
	unsigned long number, result;
    
    setlocale(LC_NUMERIC, "");  // format the printf output

	//Asks for the number/position of term in Fibonnacci sequence
    if (argc == 2)
        number = atoi(argv[1]);
    else {
        printf("Enter the value of n(n starts from 0 ): ");
        scanf("%lu", &number);
    }
    
    fib(number, &result, NULL);
    
	printf("The nth term is : %'lu \n", result);
	
	return 0;
}