Prefix sums

Overview

Prefix sums is a very simple, basic parallel algorithm commonly used as the building block of many applications. Also known as a scan, each process will sumate their value with every preceding processes' value. For instance, p=0 returns its value, p=1 returns p=1 + p=0 values, p=2 returns p=2 + p=1 + p=0 values. The MPI reduce command often implements the communication via the logarithmic structure shown below.

Source Code

#include <maths>
#include <io>
#include <string>

var processes:=10;

function void main(var argc:Int,var argv:array[String]) {
   var a:Int :: allocated[multiple[]];
   var p;
   par p from 0 to processes - 1 {
      var mine:Int;	// Force to be an integer as randomnumber function defaults to double
      mine:= randomnumber(0,toint(argv[1]));
      var i;
      for i from 0 to processes - 1 {
         var myvalue:=mine;
         if (i < p) myvalue:=0;
         (a :: reduce[i, "sum"]):=myvalue;
      };		
      print(itostring(p)+" "+itostring(mine)+" = "+itostring(a)+"\n");
   };
};

This code requires at least Mesham version 1.0

Notes

The user can provide, via command line options, the range of the random number to find. The (relative) complexity of the prefix sums is taken away by using the reduce primitive communication type.

Download

Download the entire prefix sums source code here