C Program to find out root using Bisection

Given a function f(x) which is continuous in the interval [a, b] and satisfying the property hat f(a)*f(b) < 0, there exists a root of the function f(x) in the interval [a, b]. The bisection algorithm works as follows where t: and 8 are small values specified by the user.

• Compute the midpoint, c, of the interval [a, b] as c= (a+b )/2.

• Compute f(c). If f(c) < t:, stop and print c as the required root.

• If f(a)*f(c) < 0, replace the search interval with [a, c]. The root will be found in this smaller Intervals Else, replace the search interval with [b, c].

• If the size of the search interval< 8, then stop and print c as root.

#include <stdlib.h> 
 #include <math.h> 
 #include <stdio.h> 
 /* function prototypes */ 
 int bisection(double(*func)(double), 
 double xa, double xb, double *xroot, 
 double eps, double delta, int maxiter); 
 double foobar(double x); 
 double myfunc(double x); 
 double foobar(double x) 
 { 
    return (exp(x)-2.0); 
 } 
    double myfunc(double x) 
    { 
      return x*x - 3.0; 
    } 
     int bisection(double(*yfunc)(double), 
      double xa, double xb, double *xroot, 
       double eps, double delta, int maxiter) 
      { 
                  double xmid,fmid,fa,fb; 
                  int iter; 
                  fa= yfunc(xa); 
                  fb = yfunc(xb); 
               /*check whether the required precondition for bisection is satisfied*/ 
               if(fa*fb > 0.0) 
               { 
                    printf("ERROR: f'a=fb> 0.0, Bisection wi 11 not work!"); 
                    exit(EXIT_FAILURE); 
               } 
        /* check if xa or xb is a root */ 
              if(fabs(fa)<eps) 
              { 
                  *xroot = xa; 
                  return 2; 
              } 
                         else if (fabs(fb)<eps) 
                         { 
                            *xroot = xa; 
                            return 2; 
                         } 
               /* else begin bisection search for a root in the interval [xa,xb]*/ 
        for(iter=0;iter<maxiter;iter++) 
        { 
                xmid = (xa+xb)/2.0; 
                fmid = yfunc(xmid); 
                *xroot = xmid; 
                 if(fabs(fmid)<eps) 
                { 
                  return 1; /*absolute convergence achieved*/ 
                } 
                         if(fabs(xa-xb)<delta) 
                         { 
                             return 2;/* relative convergence achieved */ 
                             /*shrink the search interval*/ 
                         } 
                if(fb*fmid<0.0) 
                  { 
                    xa = xmid; 
                    fa=fmid; 
                  } 
                           else 
                            { 
                             xb = xmid; 
                             fb=fmid; 
              } 
      } 
                   /*failed to find root within maxiter iterations*/ 
  return 0; 
 } 
       int main() 
       { 
                 double xroot; 
                 int flag; 
                 clrscr(); 
                 flag=bisection(foobar,0.0,4.0,&xroot,1.e-16,1.e-6,500); 
                 printf("root =%lg, foobar(root)=%lg\n",xroot,foobar(xroot)); 
                 printf("return value is %d\n\n",flag); 
                 flag=bisection(sin,1.0,4.0,&xroot,1.e-16,1.e-6,500); 
                 printf("root =%lg, sin(root)=%lg\n",xroot,sin(xroot)); 
                 printf("return value is %d\n\n",flag); 
                 flag=bisection(myfunc,1.0,4.0,&xroot,1.e-16,1.e-16,500); 
                 printf("root =%lg, myfunc(root)=%lg\n" ,xroot,myfunc(xroot)); 
                 printf("return value is %d\n\n",flag); 
                 getch(); 
               return 0; 
       }