[enriquto]

Well, "common sense" is not the same for everybody then. For a mathematician, the rules 1/0 = INF, 1/(-0) = -INF are perfectly straightforward and common sense (if you think about the limits).

Regarding sqrt(-0)=-0, I concede it looks a bit strange. Yet, as explained in the famous Kahan article "much ado about nothing's sign bit", it turns out to be natural when you work with complex numbers.

As for the nondeterminacy, I suppose you are talking about transcendental functions? The basic arithmetic should be bitwise reproductible.