//http://www.timestocome.com

//linda cobb

//winter 98-99

//bisection method for finding the roots of an equation



//**** caution

//algorithm fails if more than one root and brackets are 

//symmetric.. 



//added in hack to correct this error corrected algorithm 

//finds real roots if they exist.  even if there are two

//roots  bracketed area



//no longer fails on functions such as 2x^2 +3x +1 btwn +-9







#include <stdio.h>

#include <math.h>





extern double function(double x);



double bisection(double x1, double x2, double error)

{



  printf("\n l %lf, r %lf", x1, x2);getchar();

  printf("\n f(l) %lf, f(r) %lf", function(x1), function(x2));

  

  

  if(sqrt(function(x1)*function(x1)) <= error){

      return(x1);      

  }

  

  if(function(x1)*function((x1+x2)/2.0) < 0){   //root bracketed here

      bisection(x1, ((x1+x2)/2.0), error);

      

  }else{ 

    

        if(sqrt((x1-x2)*(x1-x2)) <= error/10.0){    //prevents core dumps when stack full

          printf("stuck in corner");

          bisection(-x2, x1/2.0, error);

         }

         else{

      bisection(((x2+x1)/2.0), x2, error);

              }

  

   }

   

}