I am trying to find a mathematical function that would provide certain weighting to the values of my algorithm. Namely, having two values, x,y, I would like to provide a function that would favour big differences between x and y. Ideally, it would return 1, if x = -inf and y = +inf (or vice versa) and 0, if they are equal. On top of that, I would like it to be non-linear in growth.
I hope the above makes sense. Thank you very much in advance for your comments and answers.