art with code

2008-08-31

prelude.ml: some parallel combinators

Thanks to mfp pasting me Jon Harrop's(?) invoke-function, prelude.ml now has pmap.

How about drawing some fractals with it?

mandelbrot.ml:

open Prelude

let niter = 255
let limit = 4.0

let iter_z cr ci =
let rec aux i zr zi = if i >= niter then 0 else
let nzr = zr *. zr -. zi *. zi +. cr
and nzi = 2.0 *. zr *. zi +. ci in
if nzr *. nzr +. nzi *. nzi > limit then 255-i
else aux (i+1) nzr nzi in
aux 0 0.0 0.0

let draw_row w h y =
sinit (fun x ->
let cr = 2.0 *. float x /. float w -. 1.5 in
let ci = 2.0 *. float y /. float h -. 1.0 in
chr (iter_z cr ci)
) w

let square_fractal process_count d =
let header = sprintf "P5 %i %i 255\n" d d in
header ^ (join "" @@ pmap ~process_count (draw_row d d) (1--d))

let () =
let img = square_fractal (parseInt Sys.argv.(1)) (parseInt Sys.argv.(2)) in
writeFile Sys.argv.(3) img


Compile with ocamlfind opt -package unix,pcre -linkpkg -o mandelbrot prelude.ml mandelbrot.ml

And marvel at the speedup:

$ time ./mandelbrot 1 1000 test.pgm

real 0m1.617s
user 0m1.596s
sys 0m0.024s

$ time ./mandelbrot 2 1000 test2.pgm

real 0m0.843s
user 0m1.536s
sys 0m0.012s

$ diff test.pgm test2.pgm && echo No difference
No difference


[edit]
Stepping up the abstraction ladder: par_sinit does parallel string init (string init = allocate string, fill it by mapping over its indices), so we can write square_fractal in terms of string creation. If you're familiar with GLSL fragment shaders, this should ring some bells.

let draw_fractal ?process_count w h =
par_sinit ?process_count (fun i ->
let y, x = quot_rem i w in
let cr = 2.0 *. float x /. float w -. 1.5 in
let ci = 2.0 *. float y /. float h -. 1. in
chr (iter_z cr ci)
) (w*h)

let square_fractal process_count d =
let header = sprintf "P5 %i %i 255\n" d d in
header ^ (draw_fractal ~process_count d d)


The GLSL version of draw_fractal's kernel would look something like this (dropped niter to 50 to make it run at 50fps instead of 10fps):

#version 120

uniform float w;
uniform float h;

vec4 iter_z(float cr, float ci) {
float nzr, nzi, zr = 0.0, zi = 0.0;
vec4 color = vec4(0.0);
for (int i=0; i<50; i++) {
nzr = zr * zr - zi * zi + cr;
nzi = 2.0 * zr * zi + ci;
if (nzr * nzr + nzi * nzi > 4.0) {
color = vec4(1.0 - (i / 50.0));
break;
}
zr = nzr;
zi = nzi;
}
color.a = 1.0;
return color;
}

void main(void) {
float x = gl_TexCoord[0].s;
float y = gl_TexCoord[0].t;
float cr = 2.0 * x / w - 1.5;
float ci = 2.0 * y / h - 1.0;
gl_FragColor = iter_z(cr, ci);
}

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