> floats can be NaN and integers should be low(int) if they are invalid (low(int) is a pointless value anyway as it has no positive equivalent).

I have long thought that we need a NaI (not an integer) value for our signed ints. Ideally, the CPU would have overflow-aware instructions similar to floats that return this value on overflow and cost the same as wrapping addition/multiplication/etc.

From an implementation point of view, it would be similar to NaN; a designated sentinel value that all the arithmetic operations are made aware of and have special rules around producing and consuming.