#include <stdio.h>
#include <stdlib.h>
#include <math.h>
 
double f (double x){
  /* (x - 5.0) * (x - 3.0) * (x + 7.0) */
  return (x*x*x - x*x - 41.0 * x + 105.0);
}

int sameSign(double x, double y){
  return x * y >= 0.0;
}

double middleOf(double x, double y){
  return x + (y - x)/2;
}

int isSmallNumber(double x){
  return (fabs(x) < 0.0000001);
}   

double findRootBetween(double l, double u){
  if (isSmallNumber(f(middleOf(l,u))))
     return middleOf(l,u);
  else if (sameSign(f(middleOf(l,u)), f(u)))
     return findRootBetween(l, middleOf(l,u));
  else if (!sameSign(f(middleOf(l,u)), f(u)))
     return findRootBetween(middleOf(l,u),u);
  else exit(-1);
}  

int main (void){
    double x, y;
    int numbers; 

    printf("RECURSIVE ROOT FINDING\n\n");

    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;
}