#include <stdio.h>
#include <math.h>
/* #define NDEBUG 1 */
#include <assert.h>

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

double displacement; 

double f (double x){
  return (x * x - displacement);
}

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

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

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);
}  


double my_sqrt(double x){
  double res;
  assert(x >= 0);
  displacement = x; 
  res = findRootBetween(0,x);
  assert(isSmallNumber(res*res - x));
  return res;
}

int main(void) {

  printf("my_sqrt(15.0): %lf\n", my_sqrt(15.0));
  printf("my_sqrt(20.0): %lf\n", my_sqrt(20.0));
  printf("my_sqrt(2.0): %lf\n", my_sqrt(2.0));
  printf("my_sqrt(16.0): %lf\n", my_sqrt(16.0));
  
  return 0;
}