Magical Square Root Implementation In Quake III by Carmack

[valarauca1]

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]

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]

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

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

[rys]

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

[theophrastus]

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."

[krisdol]

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".

[rcfox]

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.

[deletes]

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

[boroadlkjq]

Are there other weird number hacks like this one?

[matwood]

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;
    }