Awesome writeup, thanks!

Came across something similar a couple of days ago while browsing the source code of Marathon (one of the early games of Jason Jones and Bungie, later of Halo fame). At the time, Bungie were the Mac equivalent of id software, and Jason Jones the equivalent of John Carmack.

http://marathon.svn.sourceforge.net/viewvc/marathon/branches... (look for isqrt())

There's a great explanation in the comments.

This code was most likely written by Jason, probably around '93-'94.