Overloading non-std operators

[Stewbond]

The comparison operator (==) is pretty useless when comparing doubles due to floating point errors.

I can use a function:

bool almost_equal(double a, double b)
{
    return std::abs(a-b) <=   std::numeric_limits<double>::epsilon() 
                            * std::max(std::abs(a), std::abs(b)) 
                            * 3.; // 3 ULPs gives us a good "almost equal"
}

but operator ~= seems like it would be intuitive too for an "Almost equal" comparator.
bool operator ~= (double a, double b) { /* ... */ }

Of course this doesn't compile (at least in VS2010). Is it possible to overload non-standard operators like this or is this a limitation of the C++ language?

If not, is it possible to re-define the bool operator== (double a, double b) operator?

[hamsterman]

It is not possible to overload non standard operators and it is not possible to overload an operator with primitive types on both sides.

[Stewbond]

Too bad. I'll stick with conventional functions.