#include <stdio.h>
#include <stdlib.h>
#include <math.h>
 
double pol1 (double x){
  /* (x - 5.0) * (x - 3.0) * (x + 7.0) */
  return (x*x*x - x*x - 41.0 * x + 105.0);
}

double pol2 (double x){
  return (x*x - 2.0);
}


int sameSign(double x, double y){
  return (x > 0 && y > 0) || (x < 0 && y < 0);
}

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

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

/* Precondition: The sign of f(l) and f(u) are different */
double findRootBetween(double (*f)(double), 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);
}  

int main (void){
  double x, y;
  int numbers; 
  int function_selection;
  double (*fn)(double);  //fn is a pointer to a function:   double -> double
  int done = 0;

  do{
    /* Select function: */
    printf("Select function:\n");
    printf("1: x*x*x - x*x - 41.0 * x + 105.0\n");
    printf("2: x*x - 2.0\n");
    printf("3: sin\n");
    printf("4: EXIT\n");
    scanf("%d", &function_selection);
    switch(function_selection){
      case 1:
        fn = pol1; break;
      case 2:
        fn = pol2; break;
      case 3:
        fn = sin; break;
      default:
        done = 1;
    }

    /* Find a root in selected function: */
    if (!done){
      printf("%s","Find a ROOT between which numbers: ");
      numbers = scanf("%lf%lf", &x, &y);

      if (numbers == 2 && !sameSign(fn(x),fn(y))){
         double solution = findRootBetween( fn , x ,y);
         printf("\nThere is a root in %lf\n\n", solution);
      }
      else if (numbers == 2 && sameSign(fn(x),fn(y)))
         printf("\nf must have different signs in %lf and %lf\n\n",
                x, y);
      else if (numbers != 2)
         done = 1;
    }
  }
  while (!done);
  return 0;
}