Fast inverse square root

Curiously enough, today, such a hack is completely pointless (at least on x86): the <i>rsqrtps</i> instruction can do 4 of these in just 3 clock cycles, with higher accuracy to boot.<p>Most modern instruction sets with remotely decent floating point support have a similar instruction, in large part <i>because</i> of the prevalence of hacks like this in the past.

I remember when this was being discussed over at gamedev.net, where Chris Lomont came up with his version. The wikipedia article explains it much clearer though :-P<p>The history of this particular hack can be found over at Beyond3D:<p>Part 1: <a href="http://www.beyond3d.com/content/articles/8/" rel="nofollow">http://www.beyond3d.com/content/articles/8/</a><p>Part 2: <a href="http://www.beyond3d.com/content/articles/15/" rel="nofollow">http://www.beyond3d.com/content/articles/15/</a><p>They trace it all the way back to Greg Walsh, who apparently came up with the hack while working on the Titan graphics computer at Ardent Computer in the late 80's, who got the idea while working with Cleve Moler, the author of matlab.

I hope someday to actually understand this. It seems to come up once a year or so, and each time I understand a bit more... so hopefully in a few years...

I think the best paper that explains the magic number (0x5f3759df) is <a href="http://www.lomont.org/Math/Papers/2003/InvSqrt.pdf" rel="nofollow">http://www.lomont.org/Math/Papers/2003/InvSqrt.pdf</a><p>Lomont traces the history of the algorithm and the possible way that the magic number was derived - including more magic numbers (0x5f375a86)

"isn't that just x*x?"