Isn't it possible that all of the integers that have been or will ever be encountered, anywhere, any time, in human history, number less than 2^182? In which case you could argue that integer multiplication is O(1) via LUT :)

Everything is a lookup table in non-standard arithmetic but that's not useful for someone writing the code b/c they don't have access to non-standard integers & have to write an algorithm to reconstruct it.