What is the best way to attach static methods to classes rather than to instances of a class?

Question

If I have a method for calculating the greatest common divisor of two integers as:

public static int GCD(int a, int b)
{
    return b == 0 ? a : GCD(b, a % b);
}

What would be the best way to attach that to the System.Math class?

Here are the three ways I have come up with:

public static int GCD(this int a, int b)
{
    return b == 0 ? a : b.GCD(a % b);
}

// Lame...

var gcd = a.GCD(b);

and:

public static class RationalMath
{
    public static int GCD(int a, int b)
    {
        return b == 0 ? a : GCD(b, a % b);
    }
}

// Lame...

var gcd = RationalMath.GCD(a, b);

and:

public static int GCD(this Type math, int a, int b)
{
    return b == 0 ? a : typeof(Math).GCD(b, a % b);
}

// Neat?

var gcd = typeof(Math).GCD(a, b);

The desired syntax is Math.GCD since that is the standard for all mathematical functions.

Any suggestions? What should I do to get the desired syntax?

Answer 1

You cannot. Extension methods are just syntactic sugar for calling a static function and passing an instance of a particular type. Given that, they operate only on instances, as they must be defined by passing a this parameter of the type you want to attach to.

Answer 2

I would prefer the one with RationalMath. You really don't need extension methods here, because their aim is to mimic instance methods of objects of you can't modify. But here one should use plain old static method.