[ratmice]

Without the low int the even/odd theorem falls apart for wrap around I've definitely seen algorithms that rely upon that.

I would agree, whether error values are in or out of band is pretty context dependent such as whether you answered a homework question wrong, or your dog ate it. One is not a condition that can be graded.

[Mond_]

Meh, you also see algorithms that have subtle bugs because the author assumed that for every integer x, -x has the same absolute value and opposite sign.

I view both of these as not great. If you strictly want to rely on wraparound behavior, ideally you specify exactly how you're planning to wrap around in the code.

[umanwizard]

What is the "even/odd theorem" ?

[ratmice]

that all integers are either even or odd, and that for an even integer that integer + 1 and - 1 are odd and vice versa for odd numbers. That the negative numbers have an additional digit from the positive numbers ensures that low(integer) and high(integer) have different parity. So when you wrap around with overflow or underflow you continue to transition from an even to odd, or odd to even.