Great read although I'm not sure I understand the assembly part :/
i = 0x5f3759df - ( i >> 1 ); // what the fuck?
People have tried to investigate the origin of this baffling hack and mostly failed. See, e.g., http://www.beyond3d.com/content/articles/8/ .The strangest one I've seen is the fast sqrt() function in SGI OpenGL source code: there's a magic step where a right bit shift is applied to a 32bit IEEE float.
(oops.. just clicked your link, looks like we're related)