The mention of division has triggered a memory. I think I actually saw a library like that once. It was in C, not assembly, and was almost certainly for one specific architecture (probably Intel), but other than that, there was a lot of low-level stuff that claimed to make division faster for all CPU-native data types.

It was above my skill level to just pick up and use, let alone read and understand, but I can tell you that it at least looked legit, and the author seemed earnest in their description, so something like your hypothetical is very much out there.