c++ comparison of two double values not working properly

Look at this code:

#include 
#include 
using namespace std;
class Sphere
{

    double r;
public:
    double V() const { return (4/3) * 3.14 * pow(r,3); }
    bool equal(const Sphere& s) const
    {
        cout  << V() << " == " << s.V() << " : " << ( V() == s.V() );
        return ( V() == s.V() );

    }


    explicit Sphere(double rr = 1): r(rr){}

};
main()
{
    Sphere s(3);
    s.equal(s);
}

The output is 84.78 == 84.78 : 0 which means the same method doesn't return the same value every time, even though all parameters are static?

But if I write 3.0 instead of 3.14 in the V() method definition, like this:

double V() const { return (4/3) * 3.0 * pow(r,3); }

Then, the output is: 84.78 == 84.78 : 1

What is going on here? I need this method, for my program, which will compare volumes of two objects, but it is impossible? I banged my head for so long to figure out what is the cause of the problem and luckily I found it, but now I don't understand why?? Does it have something to do with the compiler (GCC) or am I missing something important here?

Answer

Comparing floating point values using the == operator is very error prone; two values that should be equal may not be due to arithmetic rounding errors. The common way to compare these is to use an epsilon:

bool double_equals(double a, double b, double epsilon = 0.001)
{
    return std::abs(a - b) < epsilon;
}