## C, , fibonacci_fast.c

/**
@file
@author [Krishna Vedala](https://github.com/kvedala)
@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 <locale.h>
#include <stdio.h>
#include <stdlib.h>

/**
* Get the \f$n^{th}\f$ and \f$n+1^{th}\f$ Fibonacci number using recursive
* half-interval decimation.
* \param [in] n index of Fibonacci number to get
* \param [out] C left half interval value - end result here. Cannot be NULL
* \param [out] D right half interval can be discarded at end and can be NULL
*/
void fib(unsigned long n, unsigned long *C, unsigned long *D)
{
// Out of Range checking
// commented out since n is unsigned integer
// if (n < 0)
// {
//     printf("\nNo Such term !\n");
//     exit(0);
// }

unsigned long a, b, c, d;

if (n == 0)
{
C[0] = 0;
if (D) /* if D is not NULL */
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) /* if D is not NULL */
D[0] = a + b;
return;
}

/**
* main function
*/
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;
}