Greetings.

I have something which you might find mildly interesting. (Please don't attempt the following unless you have some serious CPU power available, and several hundred MB of hard drive space free.)

  darcs get http://www.orphi.me.uk/darcs/Chaos
  cd Chaos
  ghc -O2 --make System1
  ./System1

On my super-hyper-monster machine, the program takes an entire 15 minutes to run to completion. When it's done, you should have 500 images sitting in front of you. (They're in PPM format - hence the several hundred MB of disk space!) The images are the frames that make up an animation; if you can find a way to "play" this animation, you'll be treated to a truely psychedelic light show! (If not then you'll just have to admire them one at a time. The first few dozen frames are quite boring by the way...)

If you want to, you can change the image size. For example, "./System1 800" will render at 800x800 pixels instead of the default 200x200. (Be prepaired for big slowdowns!)

What is it?

Well, it's a physical simulation of a "chaos pendulum". That is, a magnetic pendulum suspended over a set of magnets. The pendulum would just swing back and forth, but the magnets perturb its path in complex and unpredictable ways.

However, rather than simulate just 1 pendulum, the program simulates 40,000 of them, all at once! For each pixel, a pendulum is initialised with a velocity of zero and an initial position corresponding to the pixel coordinates. As the pendulums swing, each pixel is coloured according to the proximity of the corresponding pendulum to the tree magnets.

Help requested...

Can anybody tell me how to make the program go faster?

I already replaced all the lists with IOUArrays, which resulted in big, big speedups (and a large decrease in memory usage). But I don't know how to make it go any faster. I find it worrying that the process of converting pendulum positions to colours appears to take significantly longer than the much more complex task of performing the numerical integration to discover the new pendulum positions. Indeed, using GHC's profiling tools indicates that the most time is spent executing the function "quant8". This function is defined as:

  quant8 :: Double -> Word8
  quant8 = floor . (0xFF *)

I can't begin to imagine how this can be the most compute-intensive part of the program when I've got all sorts of heavy metal maths going on with the numerical integration and so forth...! Anyway, if anybody can tell me how to make it run faster, I'd be most appriciative!

Also, is there an easy way to make the program use both of the CPUs in my PC? (Given that the program maps two functions over two big IOUArrays...)

Finally, if anybody has any random comments about the [lack of] qualify in my source code, feel free...