In this day and age where a megabyte of memory isn’t a big deal, it is hard to recall when you had to conserve every byte of memory. If you are a student of such things, you might enjoy an annotated view of the Apollo 11 DSKY sine and cosine routines. Want to guess how many lines of code that takes? Try 35 for both.
Figuring out how it works takes a little knowledge of how the DSKY works and the number formats involved. Luckily, the site has a feature where you can click on the instructions and see comments and questions from other reviewers.
According to commenter [Luís Batalha], the code uses a polynomial approximation, but not part of the Taylor series as you might expect. Apparently, the polynomial used had less error over the expected range of inputs than a similar number of Taylor terms. He even includes some graphs comparing different methods of computing the functions.
When we land on the moon again, soon, it will be amazing and awe-inspiring. Now think of doing it in a world where the best computer on the planet couldn’t keep up with the PC you have in your garage gathering rust. Even then, the DSKY wasn’t even that computer. It ran with a 12 microsecond clock speed and had a whopping 72 kB of memory — most of it not writable.