Finding Fibonacci With Mathematical Formula in C

Introduction

Finding Fibonacci sequence can be done by a simple logic:

int fibonaci(int n){

    int i,next,a=0,b=1;
    for(i=0;i<n;++i){
   
        if(i<=1){
            next = i;
        }else{
           
            next = a + b;
            a = b;
            b= next;
        }
       
        printf("%d ",next);
    }
}

But here's a math formula. It can solve the case too.

The formula : Fn = (x₁ⁿ – x₂ⁿ) / root(5) (Fn is rounded down)
where X₁ and X₂ are the roots of x² - x - 1=0 equation
to find X₁ and X₂ , we can use the following formula:

So that X₁,X₂ =>

int fibonaci(int n){
   
    int i;float tmp;
   
    //x2 - x - 1 =0
    float x1 = ( 1 + sqrt(5) ) / 2;
    float x2 = (1 - sqrt(5) ) / 2;  
   
    for(i=0;i<n;i++){
               
        tmp = (pow(x1,i) - pow(x2,i)) / sqrt(5);
        printf("%d ",(int)floor(tmp)); //rounding down     
    }
   
    printf("\n");
}

Output: 0 1 1 2......so on

Of course, we don't need to use the math formula in programming, this is just an example.