bisection root-finding method
#include<stdio.h>
#include<math.h>
/* SIGN function definition as a macro */
#define sign(x) (x > 0) ? 1 : ((x < 0) ? -1 : 0)
/* functions prototype */
float f (float x);
int f_disp (int i, float a, float b, float c);
int main(void){
float a = -2; /* left point */
float b = 5; /* right point */
float TOL = 1E-2; /* tolerance */
float NMAX = 1000; /* maximum number of iterations */
float c = 0; /* estimated root */
int i = 0; /* index */
c = (a + b)/2; /* calculate the midpoint */
/* Display the table header and initial data */
printf("i\ta\t\tb\t\tc\t\tf(a)\t\tf(b)\t\tf(c)\n");
f_disp(i, a, b, c);
/* Evaluate loop until the result is less than the tolerance
* maximum number of iterations is not yet reached*/
if (f(c) == 0){
/* If the first midpoint gives f(c) = 0, c is the root */
printf("Root is: %f \n", c);}
else{
while ((fabs(f(c)) > TOL) && (i<=NMAX)){
if (sign(f(c)) == sign(f(a))){
/* f(c) has same sign as f(a) */
a = c;}
else{
/* f(c) has same sign as f(b) */
b = c;}
c = (a+b)/2; /* midpoint update */
f_disp(i+1, a, b, c); /* display current data */
i++; /* index increment */}}
/* Display results */
printf("\nRoot is c=%.7f found after %d iterations\n", c, i);
printf("The value of the function f(c) is: %.10f\n", f(c));
return 0;}
/* function definition */
float f (float x){
float y;
y = 10 - x*x;
return y;}
/* display function definition */
int f_disp (int i, float a, float b, float c){
printf("%d\t%.7f\t%.7f\t%.7f\t", i, a, b, c);
printf("%.7f\t%.7f\t%.7f\n", f(a), f(b), f(c));
return 0;}