// CS4414.  Example 2. "Loss of significance"

#include <iostream>
using namespace std;
#include <stdio.h>
#include <math.h> 

#define PRECISION float  // Set precision level   


PRECISION f (PRECISION  x ) {

	return (PRECISION) sqrt(x*x + 1.0) - 1.0; // function of interest
}  

PRECISION better_form_of_f (PRECISION  x ) {

        return  x*x/( (PRECISION) sqrt(x*x + 1.0) + 1.0); // same thing. better form 
}




main() { 



	PRECISION x = 1.0; 

	double Error = 100.0; 


// Output results:

cout << endl; cout << endl;

cout << "----Example ----Loss of significance in subtraction---------" << endl; 


cout << endl;


cout <<  "x"  << "                " << "f(x) = sqrt(x^2 + 1) -1" << "         "
 << "Same f(x) in different form" << endl; 

cout << endl; 

 

	for (int i=0; i >= -20; i-- ) {


		x = pow(10.0, (PRECISION)(i) ); 

		

		Error = 100.0*fabs( ( f(x) -  better_form_of_f(x) )/ better_form_of_f(x) ); 


		printf("%3.2e %s %10.8e %s %10.8e \n", x, "          ", f(x), "              ", better_form_of_f(x) ) ;  

	} 
	
	cout << endl; 


}