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Krishna Vedala 2020-05-25 18:42:52 -04:00
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misc/Fibonacci_fast.c
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@ -1,76 +1,81 @@
/**
@file Fibonacci_fast.c
@author: Krishna Vedala
@file
@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-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>
#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){
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)
if (D)
D[0] = 1;
return;
}
fib(n >> 1, &c, &d); /**< Compute F(n/2) */
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 */
if (n % 2 == 0) /* If n is even */
{
C[0] = a;
if(D)
if (D)
D[0] = b;
return;
}
/**< If n is odd */
C[0] = b;
if(D)
if (D)
D[0] = a + b;
return;
}
}
/**
* main function
*/
int main(int argc, char *argv[])
{
unsigned long number, result;
setlocale(LC_NUMERIC, ""); // format the printf output
unsigned long number, result;
//Asks for the number/position of term in Fibonnacci sequence
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 {
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;
printf("The nth term is : %'lu \n", result);
return 0;
}