fibonacci_fast.c File Reference

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

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

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Functions
void	fib (unsigned long n, unsigned long *C, unsigned long *D)
	Get the \(n^{th}\) and \(n+1^{th}\) Fibonacci number using recursive half-interval decimation.
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
	)

Get the \(n^{th}\) and \(n+1^{th}\) Fibonacci number using recursive half-interval decimation.

Parameters

[in]	n	index of Fibonacci number to get
[out]	C	left half interval value - end result here. Cannot be NULL
[out]	D	right half interval can be discarded at end and can be NULL

{
    // 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;
}

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main()

int main	(	int	argc,
		char *	argv[]
	)

main function

{
    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;
}

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