Agreed.

> Using `mid = (low + high) / 2` has an overflow bug if you're not using infinite precision, but there are several other potential problems even in the simplest algorithm.

Well, if you are doing binary search on eg items you actually hold in memory (or even disk) storage somewhere, like items in a sorted array (or git commits), then these days with 64 bit integers the overflow isn't a problem: there's just not enough storage to get anywhere close to overflow territory.

A back of the envelope calculation estimates that we as humanity have produced enough memory and disk storage in total that we'd need around 75 bits to address each byte independently. But for a single calculation on a single computer 63 bits are probably enough for the foreseeable future. (I didn't go all the way to 64 bits, because you need a bit of headroom, so you don't run into the overflow issues.)