#include <iostream>
#include <cmath>

using namespace std;

int main(int argc, char *argv[])
{
	long int max_num_term, i;
	double x, true_exp, approx_exp, new_approx_exp;
	double current_term, new_term;

	// set x and true value
	x = 1.5;
	true_exp = exp(x);

	// set max number of terms
	max_num_term = 6;

	// Calculation exp(x) = sum_{i=0} x^i/i!
	approx_exp = 1.0;
	current_term = 1.0;
	for(i = 1; i <= max_num_term; i++)
	{
		current_term *= x / (double)i;
		new_approx_exp = approx_exp + current_term;
		// don't add useless terms
		if(new_approx_exp == approx_exp)
		{
			cerr << "STOP!: i = " << i << endl;
			break;
		}
		approx_exp = new_approx_exp;
	}

	// print a result
	cout << "Approximation of exp(" << x << ") = " << approx_exp << endl;
	cout << "True value    of exp(" << x << ") = " << true_exp << endl;

	return 0;
}