Guide:TAUChapel

Chapel

MonteCarlo example

To test out some Chapel's language features let us program a MonteCarlo simulation to calculate PI. We can calculate PI by assessing how many points with coordinates x,y fit in the unit circle, ie x^2+y^2<=1.

Basic

Here is the basic routine that computes PI:

proc compute_pi(p_x: [] real(64), p_y: [] real(64)) : real {

 var c : sync int;
 c = 0;
 forall i in 1..n {
   if (x ** 2 + y ** 2 <= 1) then
       c += 1;
 }
 return c * 4.0 / n;

}

Notice that the forall here will compute each iteration in parallel, hence the need to define variable c as a sync variable. Performance here is limited by the need to synchronize access to c. Take a look of this profile:

70% percent of the time is spent in synchronization. Let's see if we can do better.

Procedure promotion

One feature of Chapel is procedure promotion, this is where calling a procedure that takes scalar arguments with an array, will have be as if each element of the array is passed to the procedure in parallel:

proc compute_pi(p_x: [] real(64), p_y: [] real(64)) : real {

 var c : sync int;
 forall i in in_circle(p_x, p_y) {
   c += i;
 }
 return c * 4.0 / n;

}
proc in_circle(x: real(64), y: real(64)): bool
{
  return (x ** 2 + y ** 2) <= 1;
}

Reduction

Furthermore with reorganization will allow us to take advantage of Chapel's built in reduction:

proc compute_pi(p_x: [] real(64), p_y: [] real(64)) : real {

 var c : int;
 c= +reduce in_circle(p_x, p_y);
 return c * 4.0 / n;

}

This also improves performance:

Multiple Locales

Let's look at how the array of x and y values are allocated:

var p_x: [1..n] real(64);
var p_y: [1..n] real(64);

However Chapel provides a way to distribute these array across multiple locales:

const space = {1..n};
var Dom: domain(1) dmapped Block(boundingBox=space) = space;

var p_x: [Dom] real(64);
var p_y: [Dom] real(64);

This Block mapping will allocate the elements block-wise among the locales. Furthermore the reduction used earlier will continue to work.