The value of -0 as distinguished from +0 has a few uses. The most obvious one is preserving sign in the case of overflow. A less obvious use case is handling br

The value of -0 as distinguished from +0 has a few uses. The most obvious one is preserving sign in the case of overflow. A less obvious use case is handling branch cuts. There are uses in a few more cases: I've heard it's occasionally useful in things like coordinate systems, since something like "0°5'3" W" can be stored as (-0.0, 5, 3) after explosion and still display correctly. It's definitely niche, but it does have its uses. Returning a distinct value that retains the fact that it overflowed is quite useful--if you get that result out of the computation, you know you overflowed the computation rather than silently getting a meaningless result. Note in particular that infinities end up being sticky values: once a value goes infinite, it tends to stay infinity, which isn't true for largest finite values. Distinguishing between various kinds of "invalid" values turns out to be moderately useful in practice--I've used infinities a couple of times in my own code. NaNs are useful in representing a different kind of error than overflowed computation. Now there is a lot of room to criticize IEEE 754 here: "x != x" was quite frankly a mistake (basically the primary reason for it was the creators wanted to make testing for NaN easier than calling isnan(x)...). sNaNs are of course an abomination that just makes things worse. Multiple NaN payloads were originally intended (in part) to let developers debug the sources of NaNs, but this requires support that never really materialized. However, NaN payloads did find new use in making NaN-boxing a useful technique, and dedicating an entire exponent to special values simplifies several numerical analysis lemmas.