Rather than "wrong", I would describe those implementations as "not fully general". They work perfectly when `n < some large number` as opposed to `n < some lar

Rather than "wrong", I would describe those implementations as "not fully general". They work perfectly when `n < some large number` as opposed to `n < some large number * 2`. The latter is the best you can do with the function signature, but that is somewhat arbitrary. You could easily choose a 64 bit index and exceed all practical needs.