I came up with a cute algorithm for arbitrary division with repeated shifts when working on one of my earlier projects, which was an emulator for a trinary comp

I came up with a cute algorithm for arbitrary division with repeated shifts when working on one of my earlier projects, which was an emulator for a trinary computer (where obviously dividing by 3 was a thing of import). A recursive expression is derived like this 1 1 b-a --- - --- = ---- a b a b 1 1 (b-a) 1 --- = --- + ----- --- a b b a If you select 1/b to be nearby a power of your base, this recursive relationship can be expanded until you get adequate precision. e.g. to express 1/7 in terms of divisions by 8 (i.e. binary shifts by 3) 1 1 1 - = - ( 1 + ---) 7 8 7 1 1 1 1 - = - + --- (1 + ---) 7 8 64 7 1 1 1 1 1 - = - + --- + --- ( 1 + --- ) 7 8 64 512 7 So you get v/7 = v>>3 + v>>6 + v>>9 + v>>12 + ... (mind the carry). You sometimes end up needing to do some multiplication too but usually b can be chosen to make the problem a series of trivial operations. Good expression to be able to derive in case you need to rebuild humanity from a box of nand gates. Thanks for coming to my TED talk.