/*  A program that finds a root in a continuous function f by use of the
 *  bisection method.
 *  Programmer: Kurt Normark, Aalborg University, normark@cs.aau.dk.
 *  Version 0.9, September 15, 2010.
 */

#include <stdio.h>
#include <math.h>

/*  The function in which we search for a root */ 
double f (double x){
  /* (x - 5.0) * (x - 3.0) * (x + 7.0) */
  return (x*x*x - x*x - 41.0 * x + 105.0);
}

/*  Return whether x and y have the same sign */
int sameSign(double x, double y){
  return (x > 0 && y > 0) || (x < 0 && y < 0);
}

/*  Return the mid point in between x and y */ 
double middleOf(double x, double y){
  return x + (y - x)/2;
}

/*  Is x considered to be very close to 0.0 */
int isSmallNumber(double x){
  return (fabs(x) < 0.0000001);
}   

/*  Search for a root of the continuous function f between the parameters l and u.
    A root is a double r for which f(r) is very close to 0.0.
    As a precondition it is assumed that the sign of f(l) and f(u) are different. */
double findRootBetween(double l, double u){
 while (!isSmallNumber(f(middleOf(l,u)))){ 
   if(sameSign(f(middleOf(l,u)), f(u)))
     u = middleOf(l,u);
   else 
     l = middleOf(l,u);
 }
 return middleOf(l,u);
}  

/*  A sample interactive driver of the root searching for f. */ 
int main (void){
    double x, y;
    int numbers; 

    // Repeat until scanf does not read two doubles:
    do{

      // Prompt user for input:
      printf("%s","Find a ROOT between which numbers: ");
      numbers = scanf("%lf%lf", &x, &y);

      // Distinguish between 3 cases:
      if (numbers == 2 && !sameSign(f(x),f(y))){      // The expected case
          double solution = findRootBetween(x,y);
          printf("\nThere is a root in %lf\n", solution);
        }

      else if (numbers == 2 && sameSign(f(x),f(y)))   // Same sign case
          printf("\nf must have different signs in %lf and %lf\n",
                  x, y);

      else if (numbers != 2)                          // Exit case
          printf("\nBye\n\n");
    }
    while (numbers == 2);

    return 0;
}