Eduardo Segredo González > GRID-Cluster > GRID::Cluster::Tutorial

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NAME ^

GRID::Cluster::Tutorial - An introduction to parallel computing using components

SYNOPSIS ^

  $ time ./pi_grid.pl -co MachineConfig.pm -N 1000000000 -np 1
  Calculating Pi with 1000000000 iterations and 1 processes
  Elapsed Time: 56.591251 seconds
  Pi Value: 3.141593

  real    0m58.374s
  user    0m0.520s
  sys     0m0.048s

  $ time ./pi_grid.pl -co MachineConfig.pm -N 1000000000 -np 2
  Calculating Pi with 1000000000 iterations and 2 processes
  Elapsed Time: 28.459958 seconds
  Pi Value: 3.141592

  real    0m30.610s
  user    0m0.524s
  sys     0m0.056s

  $ time ./pi_grid.pl -co MachineConfig.pm -N 1000000000 -np 3
  Calculating Pi with 1000000000 iterations and 3 processes
  Elapsed Time: 20.956588 seconds
  Pi Value: 3.141594

  real    0m22.549s
  user    0m0.296s
  sys     0m0.068s

  $ time ./pi_grid.pl -co MachineConfig.pm -N 1000000000 -np 6
  Calculating Pi with 1000000000 iterations and 6 processes
  Elapsed Time: 15.694753 seconds
  Pi Value: 3.141594

  real    0m17.285s
  user    0m0.304s
  sys     0m0.104s

  $ time ./pi_grid.pl -co MachineConfig.pm -N 1000000000 -np 12
  Calculating Pi with 1000000000 iterations and 12 processes
  Elapsed Time: 13.246352 seconds
  Pi Value: 3.141588

  real    0m14.798s
  user    0m0.328s
  sys     0m0.116s

  $ time ./pi_grid.pl -co MachineConfig.pm -N 1000000000 -np 15
  Calculating Pi with 1000000000 iterations and 15 processes
  Elapsed Time: 12.924256 seconds
  Pi Value: 3.1416

  real    0m14.500s
  user    0m0.372s
  sys     0m0.108s

SUMMARY ^

Programming is difficult. Parallel programming is harder. As a rule of thumb, 20% of the code is responsible for 80% of the computing time. As anyone working in High Performance Computing knows, optimizing the computing time and optimizing programmer's time are contradictory goals. Therefore, the Pareto Principle applies when considering the total benefits of optimizing: We must find a compromise between the efforts and costs of the High Performance Computing component (HPC) versus the High Performance Programming component (HPP). Another spoke in the Parallel Computing wheel is the need of staff for the set-up, administration and maintenance of the available computer networks. These requirements make difficult the exploitation of distributed systems, specially when several organizations are engaged.

This work explores the convenience of using dynamic languages (like Ruby, Perl or Python) as coordination languages for components written using different HPC tools. The very high programming level provided by these languages make feasible a 'zero administration' setup of a cluster while the use of HPC languages contributes to preserve highest levels of performance. Results show that the overwhelming gain in programmer's time does not implies any loss of performance.

REQUIREMENTS ^

To experiment with the examples in this tutorial you will need at least two Unix machines with SSH, Perl and an installation of the module GRID::Machine from Casiano Rodriguez. If you are not familiar with Perl or Linux this module probably isn't for you. If you are not familiar with SSH, see

BUILDING A PARALLEL VIRTUAL MACHINE ^

SSH includes the ability to authenticate users using public keys. Instead of authenticating the user with a password, the SSH server on the remote machine will verify a challenge signed by the user's private key against its copy of the user's public key. To achieve this automatic ssh-authentication you have to:

A PARALLEL ALGORITHM ^

The selected case of study for this tutorial is the computation of the number Pi using numerical integration. This is not, in fact, a good way to compute Pi, but makes a good example of how to exploit several machines to fulfill a coordination task.

To obtain the value of the number Pi, the area under the curve 4/(1+x*x) in the interval [0,1] must be computed. To obtain an approximated value of the number Pi, this interval can be divided into N sub-intervals of size 1/N. Adding up the areas of the small rectangles with base 1/N and height the value of the curve 4/(1+x*x) in the middle of the interval, an approximation is obtained. Since the goal is to optimize the execution time, the sum of the areas will be distributed among the processors. Every different process located on remote machines will have assigned a logical identifier numbered from 0 to np-1 (being np the total number of processes) and each machine will sum up the areas of roughly N/np intervals.

To achieve a higher performance the code executed by every process has been written in C language:

  1  #include <stdio.h>
  2  #include <stdlib.h>
  3
  4  main(int argc, char **argv) {
  5    int id, N, np, i;
  6    double sum, left;
  7
  8    if (argc != 4) {
  9      printf("Usage:\n%s id N np\n",argv[0]);
 10      exit(1);
 11    }
 12
 13    id = atoi(argv[1]);
 14    N  = atoi(argv[2]);
 15    np = atoi(argv[3]);
 16
 17    for(i = id, sum = 0; i < N; i += np) {
 18      double x = (i + 0.5) / N;
 19      sum += 4 / (1 + x * x);
 20    }
 21
 22    sum /= N;
 23    printf("%lf\n", sum);
 24    exit(0);
 25  }

The program receives three arguments: The first one, id identifies the process with a logical number, the second one, N, is the total number of intervals, the third np is the number of processes being used. Notice the for loop at line 17: Process id sums up the areas corresponding to intervals id, id+np, id+2*np, etc. The program concludes writing to the standard output the partial sum.

Observe that, since infinite precision numbers are not being used, errors introduced by rounding and truncation imply that increasing N would not lead to a more precise evaluation of the number Pi.

COORDINATING A PARALLEL VIRTUAL MACHINE ^

To coordinate the component program aforementioned, a driver has been written. This driver uses GRID::Cluster and runs a number of copies of the former C program in a set of available machines, adding up partial results as soon as they are available:

  1 #!/usr/bin/perl
  2 use warnings;
  3 use strict;
  4 use GRID::Cluster;
  5 use Time::HiRes qw(time gettimeofday tv_interval);
  6 use Getopt::Long;
  7 use List::Util qw(sum);
  8 use Pod::Usage;

First lines load the modules:

Next lines present the initialization process, where the command line parameters introduced by the user are obtained:

 10 my $config = 'MachineConfig.pm';
 11 my $np = 1;
 12 my $N = 100;
 13 my $clean = 0;
 14
 15 GetOptions(
 16   'config=s' => \$config, # Module containing the definition of %machine and %map_id_machine
 17   'np=i'     => \$np,
 18   'N=i'      => \$N,
 19   'clean'    => \$clean,
 20   'help'     => sub { pod2usage( -exitval => 0, -verbose => 2,) },
 21 ) or pod2usage(-msg => "Bad usage\n", -exitval => 1, -verbose => 1,);
 22
 23 my ($debug,  $max_num_np) = do $config;
 24
 25 my @machine = sort { $max_num_np->{$b} <=> $max_num_np->{$a} } keys  %$max_num_np;

At lines 15-21, the function GetOptions obtains the command line parameters introduced by the user and checks if the program usage is correct. One of the command line parameters is the name of a file which contains the configuration of the virtual parallel machine. The syntax of a configuration file is as follows:

  my %debug = (
    host1 => 0,
    host2 => 0,
    host3 => 0,
    host4 => 0,
    ...
    IP address/name => 0 | 1,
  );

  my %max_num_proc = (
    host1 => 1,
    host2 => 2,
    host3 => 1,
    host4 => 3,
    ...
    IP address/name => N,
  );

  return (\%debug, \%max_num_proc);

The variable %debug allows to activate the GRID::Cluster debug mode in every machine of the virtual parallel machine. On the other hand, the variable %max_num_proc stores the maximum number of processes that can be instantiated in every machine of the virtual parallel machine. These two variables are initialized at line 23.

The variable @machine stores the IP addresses/names of the machines where a user has SSH access. These machines will constitute the virtual parallel machine. At line 25 the machines are sorted taking into account the maximum number of processes supported by each one.

 27 my $c = GRID::Cluster->new(host_names => \@machine, debug => $debug, max_num_np => $max_num_np)
 28    || die "No machines has been initialized in the cluster";
 29
 30 $np ||= $c->get_num_machines();
 31
 32 $c->copyandmake(
 33       dir => 'pi',
 34       makeargs => 'pi',
 35       files => [ qw{pi.c Makefile} ],
 36       cleanfiles => $clean,
 37       cleandirs => $clean, # remove the whole directory at the end
 38       keepdir => 1,
 39     );
 40
 41 $c->chdir("pi/") || die "Can't change to pi/\n";

At line 27 a new GRID::Cluster object is instantiated, using the method new. The number of processes is obtained from an argument specified in the command line by the user, or by the use of the method get_num_machines at line 30. The call to copyandmake at lines 32-39 copies (using scp) the files pi.c and Makefile to a directory named pi on the remote machine. The directory pi will be created if it does not exists. After the file transfer, the command specified by the option make will be executed with the arguments specified in the option makeargs. If the make option isn't specified but there is a file named Makefile between the transferred files, the make program will be executed. Set the make option to number 0 or the string '' to avoid the execution of any command after the transfer. The transferred files will be removed when the connection finishes if the option cleanfiles is set. More radical, the option cleandirs will remove the created directory and all the files below it. Observe that the directory and the files will be kept if they were not created by this connection. The call to copyandmake by default sets dir as the current directory in the remote machine. Set the option keepdir to one to avoid this. The method chdir (line 41) of a GRID::Cluster object changes the working directory of every remote machine associated to the virtual parallel machine.

 43 my @commands = map {  "./pi $_ $N $np |" } 0..$np-1;
 44
 45 my $t0 = [gettimeofday];
 46
 47 my $pi = sum @{$c->qx(@commands)};
 48
 49 my $elapsed = tv_interval($t0);
 50
 51 print "Calculating Pi with $N iterations and $np processes\n";
 52 print "Elapsed Time: $elapsed seconds\n";
 53 print "Pi Value: $pi\n";

Last step consists in creating the commands that are going to be executed in different machines (line 43) by the use of the method qx of a GRID::Cluster object. This method allows the execution of different tasks or processes following an approximation based on farms, this is, initially, a maximum number of processes are run, and when one of them finishes its execution, a new process is run, if there are more pending processes to be executed. This feature allows a good load balancing among different machines.

At line 47, the method qx returns a list with the partial sums calculated by every process executed in the virtual parallel machine, and by the use of the function sum, a sum of all these results is performed, obtaining the value of the number Pi.

COMPUTATIONAL RESULTS ^

The execution of the C program on each of the three involved machines is presented in following lines. The number of intervals N has been fixed to 1,000,000,000.

  $ time ./pi 0 1000000000 1
  3.141593
  real    0m56.959s
  user    0m56.492s
  sys     0m0.004s

  $ time ./pi 0 1000000000 1
  3.141593
  real    0m30.862s
  user    0m30.850s
  sys     0m0.012s

  $ time ./pi 0 1000000000 1
  3.141593
  real    0m29.026s
  user    0m28.654s
  sys     0m0.049s

These results indicate that the first machine is slower than the other two.

Now let us run the driver using only the fastest machine and one process. The time spent is comparable to the pure C time, and that is great because the overhead introduced by the coordination tasks is not as large:

  $ time ./pi_grid.pl -co MachineConfig.pm -N 1000000000 -np 1
  Calculating Pi with 1000000000 iterations and 1 processes
  Elapsed Time: 30.919523 seconds
  Pi Value: 3.141593

  real    0m32.690s
  user    0m0.516s
  sys     0m0.060s

Now we are going to execute the driver using two different machines, each one with only one process:

  $ time ./pi_grid.pl -co MachineConfig.pm -N 1000000000 -np 2
  Calculating Pi with 1000000000 iterations and 2 processes
  Elapsed Time: 28.459958 seconds
  Pi Value: 3.141592

  real    0m30.610s
  user    0m0.524s
  sys     0m0.056s

We can see that the sequential pure C version took 56 seconds in the slowest machine. By using two machines, each one with one process, the time has been reduced to 23 seconds. This a factor of 56/31 = 1.80 times faster. This factor is even better if I don't consider the set-up time: 56/29 = 1.93. The total time decreases if three machines are used, every one with only one process:

  $ time ./pi_grid.pl -co MachineConfig.pm -N 1000000000 -np 3
  Calculating Pi with 1000000000 iterations and 3 processes
  Elapsed Time: 20.956588 seconds
  Pi Value: 3.141594

  real    0m22.549s
  user    0m0.296s
  sys     0m0.068s

which gives a speed factor of 56/23 = 2.43 or not considering the set-up time 56/21 = 2.66.

If you increase the number of processes, the use of the method qx allows to obtain better results, due to the load balancing produced by the use of a mechanism based on a farm. The results increasing the number of processes (but only using three machines, every one with a process in every moment) are in the following lines:

  $ time ./pi_grid.pl -co MachineConfig.pm -N 1000000000 -np 6
  Calculating Pi with 1000000000 iterations and 6 processes
  Elapsed Time: 15.694753 seconds
  Pi Value: 3.141594

  real    0m17.285s
  user    0m0.304s
  sys     0m0.104s

  $ time ./pi_grid.pl -co MachineConfig.pm -N 1000000000 -np 12
  Calculating Pi with 1000000000 iterations and 12 processes
  Elapsed Time: 13.246352 seconds
  Pi Value: 3.141588

  real    0m14.798s
  user    0m0.328s
  sys     0m0.116s

  $ time ./pi_grid.pl -co MachineConfig.pm -N 1000000000 -np 15
  Calculating Pi with 1000000000 iterations and 15 processes
  Elapsed Time: 12.924256 seconds
  Pi Value: 3.1416

  real    0m14.500s
  user    0m0.372s
  sys     0m0.108s

Using 3 processes with 3 machines (every one with only one process), the fastest machines have to wait for the slowest one to finish the execution. Using 6, 12 and 15 processes, the time is decreased. Because of the heterogeneity of the different machines, while the slowest machine is executing a process, the fastest one has executed several processes. More processes are executed in less time by the fastest machine (load balancing) and the consequence is a decrease in the total execution time.

SEE ALSO ^

AUTHORS ^

Eduardo Segredo Gonzalez <esegredo@ull.es> and Casiano Rodriguez Leon <casiano@ull.es>

AKNOWLEDGEMENTS ^

This work has been supported by the EC (FEDER) and the Spanish Ministry of Science and Innovation inside the 'Plan Nacional de I+D+i' with the contract number TIN2008-06491-C04-02.

Also, it has been supported by the Canary Government project number PI2007/015.

The work of Eduardo Segredo was funded by grant FPU-AP2009-0457.

COPYRIGHT AND LICENSE ^

Copyright (C) 2010 by Casiano Rodriguez Leon and Eduardo Segredo Gonzalez. All rights reserved.

This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself, either Perl version 5.12.2 or, at your option, any later version of Perl 5 you may have available.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

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