[nycticorax]

This is only somewhat related, but: Has there ever been a language that adopted IEEE-754-like semantics for integer types? (Yes, I know this would be slow without hardware support.) By this I mean adding valid values for (signed) ints to represent positive infinity, negative infinity, and not-a-number; then use these values as the results of overflow, underflow, and division by zero in the natural way. It just seems like if these sort of values are useful in floating-point arithmetic, they might well be useful for integer arithmetic as well, for many of the same reasons.

[AlotOfReading]

If you rename +/- Inf, that's what saturating arithmetic is. Very likely your language and hardware already supports it.

NaN is almost always a mistake, and adding it breaks the law of identity. You don't want it.

[nycticorax]

OK, I did not know about [saturation arithmetic](https://en.wikipedia.org/wiki/Saturation_arithmetic). Cool!

But I can't agree with the claim that "nan is almost always a mistake". Certainly if you're doing floating-point computation on large arrays, the last thing you want is e.g. for an error to be thrown in a elementwise division just because two corresponding elements both happen to be zero.

It's true that nan!=nan is one of the more 'controversial' parts of the standard, that possibly would have been decided the other way in a perfect world. But it was also a reasonable pragmatic decision at the time the standard was developed. See here: https://stackoverflow.com/a/1573715/1013442