On Tue, Sep 20, 2011 at 11:47 PM, Richard O'Keefe
On 21/09/2011, at 2:18 PM, Casey McCann wrote:
I still don't see why it makes sense to add separate IEEE comparisons instead of just adding a standard partial order class, though.
In any mathematical partial order, we expect x `le` x to be a law. But in IEEE arithmetic, if x is a NaN, x `le` x is false. I don't see how to reconcile these.
Ah, true. There is an obvious way to reconcile this that almost suffices, and is what I'd had in mind--simply declare that, just as positive and negative zero are distinct values but identified with each other by the ordering, let NaN be "disidentified" with itself. Essentially this treats NaN as representing an unbounded collection of distinct, but indistinguishable and incomparable, values, where you never end up getting the same one twice. This interpretation is self-consistent so long as the expressions being compared are distinct to begin with, but now that you point it out explicitly I realize it not only can't be justified when comparing syntactically identical terms, but that given equivalent expressions it would imply that a pure function gives different results each time, which is not in any way a satisfactory result of something that's trying to *improve* the semantics involved! So that's a bust. Bother. Specialized comparisons providing IEEE semantics seems the best option after all, then. I'd still like to see a standard partial order type class, but apparently it wouldn't help in this case. - C.