//This program illustrates why you should not compare floating point numbers for equality
//It also how how to do so safely

#include <iostream>
#include <cmath>
#include <iomanip>
using namespace std;

int main()
{
    float k = 0;
    cout << setprecision(8);
//Notice that k never hits 1000.0  exactly!
//If you change the test to ask for equality, you will get an endless loop!
    while (k <= 1000.0)
    {
        k+=0.01;
//display the last few iterations
        if (k > 999.9)
        {
            cout << fixed  <"Last few iterations\n";
            cout  << "k is "  << k << "\t";
        }
    }
//Now let's test if three floating point sides of a triangle form a right triangle
    double a = 3.00000000001, b = 4.0000000002, c;
    c = sqrt(a*a + b*b);
//compute the hypotenuse and test  for equality according to the Pythagorean theorem
   cout << "\n\nTesting for strict equality\n";
   if (a*a + b*b == c*c)
    {
        cout << "Sides a = "  << a << " b = " << b << " and c = " << c <<
                "\nform a right triangle\n";
    }
    else
    {
        cout << "Sides a = "  << a << " b = " << b << " and c = " << c <<
                "\ndo not form a right triangle\n";
    }
//Now test within a tolerance level of equality
     cout << "\n\nTesting for equality using a tolerance\n";
     if (abs(a*a + b*b - c*c) <= 1E-8 )
         cout << "Sides a = "  << a << " b = " << b << " and c = " << c <<
                "\nform a right triangle\n";
    else
         cout << "ides a = "  << a << " b = " << b << " and c = " << c <<
                "\ndo not form a right triangle\n";
    return 0;
}