fibonacci_formula.c File Reference

Finding Fibonacci number of any n number using [Binet's closed form formula](https://en.wikipedia.org/wiki/Fibonacci_number#Binet's_formula) compute \(f_{nth}\) Fibonacci number using the binet's formula: Fn = 1√5 * (1+√5 / 2)^n+1 − 1√5 * (1−√5 / 2)^n+1. More...

#include <math.h>
#include <stdio.h>
#include <assert.h>

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Functions
int	fib (unsigned int n)
	for pow and sqrt for printf for assert
static void	test ()
	Self-test implementations.
int	main ()
	Main function.

Detailed Description

Finding Fibonacci number of any n number using [Binet's closed form formula](https://en.wikipedia.org/wiki/Fibonacci_number#Binet's_formula) compute \(f_{nth}\) Fibonacci number using the binet's formula: Fn = 1√5 * (1+√5 / 2)^n+1 − 1√5 * (1−√5 / 2)^n+1.

Author

GrandSir

Function Documentation

fib()

int fib

(

unsigned int

n

)

for pow and sqrt for printf for assert

Parameters

n	index of number in Fibonacci sequence

Returns

nth value of fibonacci sequence for all n >= 0

                        {
    float seq = (1 / sqrt(5) * pow(((1 + sqrt(5)) / 2), n + 1)) - (1 / sqrt(5) * pow(((1 - sqrt(5)) / 2), n + 1));
 
    // removing unnecessary fractional part by implicitly converting float to int
    return seq;
}

main()

int main

(

void

)

Main function.

Returns

0 on exit

           {
    test();  // run self-test implementations
 
    for(int i = 0; i <= 10; i++){
        printf("%d. fibonacci number is: %d\n", i, fib(i));
    }
    return 0;
}

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test()

static void test ( void  )

static

Self-test implementations.

Returns

void

                    {
    /* this ensures that the first 10 number of fibonacci sequence
     * (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89)
     * matches with algorithm
    */
    assert(fib(0) == 1);
    assert(fib(1) == 1);
    assert(fib(2) == 2);
    assert(fib(3) == 3);
    assert(fib(4) == 5);
    assert(fib(5) == 8);
    assert(fib(6) == 13);
    assert(fib(7) == 21);
    assert(fib(8) == 34);
    assert(fib(9) == 55);
    assert(fib(10) == 89);
    
    printf("All tests have successfully passed!\n");
}

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