The problem was in the context of looking up min_by_key with the key being a floating-point number, so I think the only NaN-check necessary should be for that key. I did not intend to imply that it should be done for all calculations, only those that need totally-ordered floats. (Or if you are really sure NaN will never happen, you leave out the check altogether, and claim total ordering anyway.)
I guess that is a particularly bad use case of specialization, which itself is proposed as an RFC [1] and approved for implementation. It would look pretty similar to, say, C++'s `vector<T>` and `vector<bool>` split, because it does something more than what it should do. Probably the better solution is to merge PartialOrd and Ord, as the benefit from having two traits has been always unclear (I personally have no strong opinion against or for that though).
