Magical Square Root Implementation In Quake III by Carmack

http://www.codemaestro.com/reviews/9

by geeku • 12 years ago

42 16 12 years ago

valarauca1• 12 years ago

Horrible article.

First the implementation solves for the 'Inverse Square Root', not the square root. [1] Secondly the algorithm's author isn't actually known but the earliest person it can be traced too is Gary Tarolli [1].

[1] https://en.wikipedia.org/wiki/Fast_inverse_square_root

It really bothers me when people write something and their own sources differ from what their writing let alone wikipedia.

ColinWright• 12 years ago

In case this doesn't get many up votes, and not much discussion, it's worth understanding that this story has been submitted and discussed many, many, many times in the past. It's a wonderful hack, using techniques and skills of which the vast majority of programmers these days have no experience.

It's worth reading, learning, and understanding, if only to be grateful that most of your life you'll never have to resort to such tricks. Sadly, that also means you'll never get the chance to experience the sheer joy of creating something like this.

Having said that, this article is actually really, really poor, and most of its value lies in the references provided by people in the comments. Many of the other submissions here on HN are much better.

cwyers• 12 years ago

Here's a much better article on the same topic:

http://www.beyond3d.com/content/articles/8

rys• 12 years ago

Crikey, over 7 years since I did the investigation (basic email, didn't try that hard) for that article. Time flies!

theophrastus• 12 years ago

It ought to be pointed out that this method (and many others even more cunning) are detailed in the delightful tome "Hacker's Delight" (ISBN 978-0-201-91465-8) by Henry S. Warren

on about page 481 or so:

"The Newton step is a standard Newton-Raphson calculation for the reciprocal square root function (see Appendix B). Simply repeating this step reduces the relative error to the range 0 to -0.0000047. The optimal constant for this is 0x5F37599E."

rcfox3• 12 years ago

I wish the myriad articles about this interesting hack would bother to mention that it relies on undefined behaviour. Any time you find yourself doing this:

    *(foo*)

you're probably breaking the strict aliasing rule.

deletes3• 12 years ago

The behavior is defined, if you disable the rule or your compiler doesn't follow it.

rcfox3• 12 years ago

That's the opposite of "defined", in the context of a language discussion.

boroadlkjq• 12 years ago

Are there other weird number hacks like this one?

matwood2• 12 years ago

Look at the hashCode() implementations in http://grepcode.com/file/repository.grepcode.com/java/root/j...

For example:

public static int hashCode(double a[])

{

if (a == null) return 0;

        int result = 1;
        for (double element : a) {
            long bits = Double.doubleToLongBits(element);
            result = 31 * result + (int)(bits ^ (bits >>> 32));
        }
        return result;
    }

snotrockets• 12 years ago

Why is this weird? It's the textbook method for doing hashes.

krisdol• 12 years ago

I don't know why, but I'm supremely bothered by the author getting the name of Carmack's company wrong so many times. It's "Id" (or "id") Software, not "ID" Software. It's not pronounced "eye dee".

Magical Square Root Implementation In Quake III by Carmack

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