/* 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. 
    @param[in] x The input to the function f. */ 
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.
    @param[in] x The first double the sign of which is to be compared with y.
    @param[in] y The second double the sign of which is to be compared with x. 
    @return A boolean represented as an int in C (false = zero, true = non zero). */
int sameSign(double x, double y){
  return (x > 0 && y > 0) || (x < 0 && y < 0);
}

/** Return the mid point in between x and y.
    @param[in] x The first double.
    @param[in] y The second double.  */ 
double middleOf(double x, double y){
  return x + (y - x)/2;
}

/** Is x considered to be very close to 0.0.
    @param[in] x The input to be evaluated.
    @return A boolean represented as an int in C (false = zero, true = non zero). */
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.
   @param[in] l The lower limit of the interval in which to search for a root.
   @param[in] u The upper limit of the interval in which to search for a root.
   @return The x-value r for which f(x) is close to zero.
   @pre 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; 

    do{
      printf("%s","Find a ROOT between which numbers: ");
      numbers = scanf("%lf%lf", &x, &y);

      if (numbers == 2 && !sameSign(f(x),f(y))){
          double solution = findRootBetween(x,y);
          printf("\nThere is a root in %lf\n", solution);
        }
      else if (numbers == 2 && sameSign(f(x),f(y)))
          printf("\nf must have different signs in %lf and %lf\n",
                  x, y);
      else if (numbers != 2)
          printf("\nBye\n\n");
    }
    while (numbers == 2);

    return 0;
}