It's too much furniture to do that properly. You may want to overflow an integer. Granted, rings of cardinality 2^64 are unusual at best but I've used 8 & 16 bit size rings forever.
I call this "proposing a strawman solution". I don't know why it works, but it frequently does. I think that doing a long search for The Perfect Solution is akin to premature optimization. Changing focus for a while seems to help.