/* This is a C program to find the root of the 
non-linear equation f(x)=0 using the Bisection 
algorithm, given an initial interval x1<= x <= x2. */    

#include<stdio.h>
#include<math.h>
double f(double); 

int main (void)
{
	double x1,x2,x3,f1,f2,f3;   
        int ib,n;
	double epsilon,error;
        printf("Enter the lower and upper bounds of the interval:\n");
        scanf("%lf%lf",&x1,&x2);
        printf("Specify convergence criterion as a fraction of initial "
               "interval\n");
        scanf("%lf",&epsilon);
        f1 = f(x1);
        f2 = f(x2); 

/* Check Interval */ 
        while(f1*f2>0) {
        	printf("f1*f2>0, try another interval\n");
                printf("Enter the lower and upper bounds of the interval:\n");
        	scanf("%lf%lf",&x1,&x2); 
                f1 = f(x1); 
       	 	f2 = f(x2);}   

	x3 = (x2+x1)/2.0;
        f3 = f(x3);
	error = fabs(x2-x1);
	n = log(error/x3/epsilon)/log(2.0);
	if(fabs(x3)<epsilon)     /* divide by zero situation */
	        n = log(error/epsilon/epsilon)/log(2.0);
 /* Start bisections */ 
        for(ib=0;ib<=n;++ib) {
                if (f3*f1>0.0) {x1=x3;f1=f3;}
                else {x2=x3;f2=f3;} 
	 	x3 = (x1+x2)/2.0;
                f3 = f(x3);
		error = fabs(x2-x1);
	}  
        printf("Iteration converged. Root is %e\n",x3);
        printf("The function value at root is %e\n",f3);
	printf("The convergence error is %e\n",error);

	return(0);
}