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GRID-Machine-0.127
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/ GRID::Machine::perlparintro

NAME

GRID::Machine::perlparintro - A brief and basic introduction to Parallel Distributed Computing in Perl

SYNOPSIS

$ time gridpipes.pl 1 1000000000
Process 0: machine = beowulf partial = 3.141593 pi = 3.141593
Pi = 3.141593. N = 1000000000 Time = 27.058693

real    0m28.917s
user    0m0.584s
sys     0m0.192s

pp2@nereida:~/LGRID_Machine/examples$ time gridpipes.pl 2 1000000000
Process 0: machine = beowulf partial = 1.570796 pi = 1.570796
Process 1: machine = orion partial = 1.570796 pi = 3.141592
Pi = 3.141592. N = 1000000000 Time = 15.094719

real    0m17.684s
user    0m0.904s
sys     0m0.260s


pp2@nereida:~/LGRID_Machine/examples$ time gridpipes.pl 3 1000000000
Process 0: machine = beowulf partial = 1.047198 pi = 1.047198
Process 1: machine = orion partial = 1.047198 pi = 2.094396
Process 2: machine = nereida partial = 1.047198 pi = 3.141594
Pi = 3.141594. N = 1000000000 Time = 10.971036

real    0m13.700s
user    0m0.952s
sys     0m0.240s

SUMMARY

The total computational power of institutions as a whole has dramatically rised in the last decades, but due to distributed ownership and administration restrictions, individuals are not able to capitalize such computing power. Many machines sit idle for very long periods of time while their owners are busy doing other things. Many of them run some sort of UNIX, have Perl installed and provide SSH access.

If such is your scenario you can use GRID::Machine to have perl interpreters running in those nodes and make them collaborate to give you more computational power and more fun. All this without having to ask administrators or having to install any additional software.

This tutorial introduces the basics of parallel computing by means of a simple program that distributes the evaluation of some mathematical expression between several machines. The computational results show that - when the problem is large enough - a substantial improving is gained in performance: The execution times is reduced to the half by using two machines.

REQUIREMENTS

To experiment with the examples in this tutorial you will need at least two Unix machines with Perl and SSH. 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 "FUZZY" PARALLEL CLUSTER

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:

  • Generate a public key use the ssh-keygen utility. For example:

    local.machine$ ssh-keygen -t rsa -N ''

    The option -t selects the type of key you want to generate. There are three types of keys: rsa1, rsa and dsa. The -N option is followed by the passphrase. The -N '' setting indicates that no pasphrase will be used. This is useful when used with key restrictions or when dealing with cron jobs, batch commands and automatic processing which is the context in which this module was designed. If still you don't like to have a private key without passphrase, provide a passphrase and use ssh-agent to avoid the inconvenience of typing the passphrase each time. ssh-agent is a program you run once per login sesion and load your keys into. From that moment on, any ssh client will contact ssh-agent and no more passphrase typing will be needed.

    By default, your identification will be saved in a file /home/user/.ssh/id_rsa. Your public key will be saved in /home/user/.ssh/id_rsa.pub.

  • Once you have generated a key pair, you must install the public key on the remote machine. To do it, append the public component of the key in

    /home/user/.ssh/id_rsa.pub

    to file

    /home/user/.ssh/authorized_keys

    on the remote machine. If the ssh-copy-id script is available, you can do it using:

    local.machine$ ssh-copy-id -i ~/.ssh/id_rsa.pub user@remote.machine

    Alternatively you can write the following command:

    $ ssh remote.machine "umask 077; cat >> .ssh/authorized_keys" < /home/user/.ssh/id_rsa.pub

    The umask command is needed since the SSH server will refuse to read a /home/user/.ssh/authorized_keys files which have loose permissions.

  • Edit your local configuration file /home/user/.ssh/config (see man ssh_config in UNIX) and create a new section for GRID::Machine connections to that host. Here follows an example:

    ...

# A new section inside the config file: 
# it will be used when writing a command like: 
#                     $ ssh gridyum 

Host gridyum

# My username in the remote machine
user my_login_in_the_remote_machine

# The actual name of the machine: by default the one provided in the
# command line
Hostname real.machine.name

# The port to use: by default 22
Port 2048

# The identitiy pair to use. By default ~/.ssh/id_rsa and ~/.ssh/id_dsa
IdentityFile /home/user/.ssh/yumid

# Useful to detect a broken network
BatchMode yes

# Useful when the home directory is shared across machines,
# to avoid warnings about changed host keys when connecting
# to local host
NoHostAuthenticationForLocalhost yes


# Another section ...
Host another.remote.machine an.alias.for.this.machine
user mylogin_there

...

    This way you don't have to specify your login name on the remote machine even if it differs from your login name in the local machine, you don't have to specify the port if it isn't 22, etc. This is the recommended way to work with GRID::Machine. Avoid cluttering the constructor new.

  • Once the public key is installed on the server you should be able to authenticate using your private key

    $ ssh remote.machine
Linux remote.machine 2.6.15-1-686-smp #2 SMP Mon Mar 6 15:34:50 UTC 2006 i686
Last login: Sat Jul  7 13:34:00 2007 from local.machine
user@remote.machine:~$

    You can also automatically execute commands in the remote server:

    local.machine$ ssh remote.machine uname -a
Linux remote.machine 2.6.15-1-686-smp #2 SMP Mon Mar 6 15:34:50 UTC 2006 i686 GNU/Linux

  • Once you have installed GRID::Machine you can check that perl can be executed in that machine using this one-liner:

    $ perl -e 'use GRID::Machine qw(is_operative); print is_operative("ssh", "beowulf")."\n"'
1

A PARALLEL ALGORITHM

In this manual we have used several times as an example the computation of an approach to number Pi (3.14159...) using numerical integration. To understand it, take into account that the area under the curve 1/(1+x**2) between 0 and 1 is Pi/4 = (3.1415...)/4 as it shows the following debugger session:

pp2@nereida:~/public_html/cgi-bin$ perl -wde 0
main::(-e:1):   0
  DB<1>  use Math::Integral::Romberg 'integral'
  DB<2> p integral(sub { my $x = shift; 4/(1+$x*$x) }, 0, 1);
3.14159265358972

The module Math::Integral::Romberg provides the function integral that allow us to compute the area of a given function in some interval. In fact - if you remember your high school days - it is easy to see the reason: the integral of 4/(1+$x*$x) is 4*arctg($x) and so its area between 0 and 1 is given by:

4*(arctg(1) - arctg(0)) = 4 * arctg(1) = 4 * Pi / 4 = Pi

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 task.

To compute the area under 4/(1+$x*$x) we have divided up the interval [0,1] into sub-intervals of size 1/N and add 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. The following debugger session illustrates the idea:

pp2@nereida:~$ perl -wde 0
main::(-e:1):   0
DB<1> use List::Util qw(sum)
DB<2> $N = 6
DB<3> @divisions = map { $_/$N } 0..($N-1)
DB<4> sub f { my $x = shift; 4/(1+$x*$x) }
DB<5> @halves = map { $_+0.5/$N } @divisions
DB<6> $area = sum(map { f($_)/$N } @halves)
DB<7> p $area
3.14390742722244

To optimize the execution time we distribute the sum in line 6 $area = sum(map { f($_)/$N } @halves) among several processes. The processes are numbered from 0 to np-1. Each process sums up the areas of roughly N/np intervals. We can spedup the computation if each process is allocated to a different processor (or core).

To achieve a higher performance the code to execute on each machine is written in C:

~/src/perl/grid-machine/examples$ cat -n pi.c
   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    id = atoi(argv[1]);
  13    N = atoi(argv[2]);
  14    np = atoi(argv[3]);
  15    for(i=id, sum = 0; i<N; i+=np) {
  16      double x = (i + 0.5)/N;
  17      sum += 4 / (1 + x*x);
  18    }
  19    sum /= N;
  20    printf("%lf\n", sum);
  21    exit(0);
  22  }

The program receives (lines 8-14) three arguments: The first one, id, identifies the machine with a logical number, the second one, N, is the total number of intervals, the third np is the number of machines being used. Notice the for loop at line 15: Processor id sums up the areas corresponding to intervals id, id+np, id+2*np, etc. The program concludes writing to STDOUT the partial sum.

Observe that, since we aren't using infinite precision numbers errors introduced by rounding and truncation imply that increasing N would not lead to a more precise evaluation of Pi.

To get the executable we have a simple Makefile:

pp2@nereida:~/LGRID_Machine/examples$ cat -n Makefile
   1  pi:
   2          cc pi.c -o pi

PARALLEL COMPUTING MADE EASY: USING GRID::Machine::Group

The GRID::Machine::Group module provides Parallel Remote Procedure Calls (RPC) to a cluster of machines via a SSH connection. The result of a remote call is a GRID::Machine::Group::Result object.

The call at line 31 returns a new instance of a GRID::Machine::Group object. The object is blessed in a unique class that inherits from GRID::Machine::Group. That is, the new object is a singleton. When later the cluster object GRID::Machine::Group is provided with new methods, those are installed in the singleton class.

$ cat -n pi7.pl
   1  #!/usr/bin/perl -w
   2  use strict;
   3  use GRID::Machine;
   4  use GRID::Machine::Group;
   5  use List::Util qw(sum);
   6  
   7  my @MACHINE_NAMES = split /\s+/, $ENV{MACHINES};
   8  my $code = << 'EOFUNCTION';
   9     double sigma(int id, int N, int np) {
  10       double sum = 0;
  11       int i;
  12       for(i = id; i < N; i += np) {
  13           double x = (i + 0.5) / N;
  14           sum += 4 / (1 + x * x);
  15       }
  16       sum /= N; 
  17       return sum;
  18     }
  19  EOFUNCTION
  20  ;
  21  
  22  my @m = map { 
  23                GRID::Machine->new(
  24                   host => $_, 
  25                   wait => 5, 
  26                   uses => [ qq{Inline  'C' => q{$code}} ],
  27                   survive => 1,
  28                ) 
  29              } @MACHINE_NAMES;
  30  
  31  my $c = GRID::Machine::Group->new(cluster => [ @m ]);
  32  
  33  my ($N, $np, $pi)  = (1000, 4, 0);
  34  
  35  my @args = map {  [$_, $N, $np] } 0..$np-1;
  36  
  37  my @r = $c->eval(q{ sigma(@_) }, args => \@args)->Results;
  38  
  39  print sum(@r)."\n";

The eval method of GRID::Machine::Group (see line 37 in the example below) computes some code on each of the machines belonging to the cluster object.

In this example, Inline::C is used in the remote machines to make the computation more efficient. We assume that Inline::C is already installed in the remote machines.

Performance

The following code is a modification of the canonical example computing pi. Timers have been included (lines 28 and 31) to see the influence of the number of processors:

$ cat -n pi.pl
   1  #!/usr/bin/perl -w
   2  use strict;
   3  use GRID::Machine;
   4  use GRID::Machine::Group;
   5  use List::Util qw(sum);
   6  use Time::HiRes qw(time gettimeofday tv_interval);
   7  
   8  my @MACHINE_NAMES = split /:+/, ($ENV{MACHINES} || '');
   9  @MACHINE_NAMES = ('', '') unless @MACHINE_NAMES;
  10  
  11  my @m = map { GRID::Machine->new(host => $_, wait => 5, survive => 1) } @MACHINE_NAMES;
  12  
  13  my $c = GRID::Machine::Group->new(cluster => [ @m ]);
  14  
  15  $c->sub(suma_areas => q{
  16     my ($id, $N, $np) = @_;
  17       
  18     my $sum = 0;
  19     for (my $i = $id; $i < $N; $i += $np) {
  20         my $x = ($i + 0.5) / $N;
  21         $sum += 4 / (1 + $x * $x);
  22     }
  23     $sum /= $N; 
  24  });
  25  
  26  my ($N, $np, $pi)  = (1e7, 4, 0);
  27  
  28  my @args = map {  [$_, $N, $np] } 0..$np-1;
  29  
  30  my $t0 = [gettimeofday];
  31  $pi = sum($c->suma_areas(args => \@args)->Results);
  32  my $elapsed = tv_interval ($t0);
  33  print "Pi = $pi. N = $N Time = $elapsed\n";

When executed in one machine, it takes 5.387676 seconds:

~/grid-machine$ export MACHINES='local'
~/grid-machine$ perl  examples/pi.pl
Pi = 3.14159265358978. N = 10000000 Time = 5.059222

When executed in a cluster with two nodes we get a speedup of 1.93 = 5.06/2.62:

~/grid-machine$ export MACHINES='local imac'
~/grid-machine$ perl  examples/pi.pl
Pi = 3.14159265358978. N = 10000000 Time = 2.625359

When executed in a machine with two cores, it also has an almost linear speedup:

~/grid-machine$ unset MACHINES
~/grid-machine$ perl  examples/pi.pl
Pi = 3.14159265358978. N = 10000000 Time = 2.685503

WORKING HARDER: COORDINATING A CLUSTER

The program gridpipes.pl following in the lines below runs $np copies of the former C program in a set @machines of available machines, adding up the partial results as soon as they arrive.

pp2@nereida:~/LGRID_Machine/examples$ cat -n gridpipes.pl
   1  #!/usr/bin/perl
   2  use warnings;
   3  use strict;
   4  use IO::Select;
   5  use GRID::Machine;
   6  use Time::HiRes qw(time gettimeofday tv_interval);

The first lines load the modules:

  • GRID::Machine will be used to open SSH connections with the remote machines and control the execution environment

  • IO::Select will be used to process the results as soon as they start to arrive.

  • Time::HiRes will be used to time the processes so that we can compare times and see if there is any gain in this approach

 8  my @machine = qw{beowulf orion nereida};
 9  my $nummachines = @machine;
10  my %machine; # Hash of GRID::Machine objects
11  #my %debug = (beowulf => 12345, orion => 0, nereida => 0);
12  my %debug = (beowulf => 0, orion => 0, nereida => 0);
13
14  my $np = shift || $nummachines; # number of processes
15  my $lp = $np-1;
16
17  my $N = shift || 100;
18
19  my @pid;  # List of process pids
20  my @proc; # List of handles
21  my %id;   # Gives the ID for a given handle
22
23  my $cleanup = 0;
24
25  my $pi = 0;
26
27  my $readset = IO::Select->new();

Variable @machine stores the IP addresses/names of the machines we have SSH access. These machines will constitute our 'virtual' parallel machine. For each of these machines (see the for loop in lines 30-46) a SSH connection is created (line 31) via GRID::Machine->new. The resulting GRID::Machine objects will be stored inside the hash %machine (line 44).

29  my $i = 0;
30  for (@machine){
31    my $m = GRID::Machine->new(host => $_, debug => $debug{$_}, );
32
33    $m->copyandmake(
34      dir => 'pi',
35      makeargs => 'pi',
36      files => [ qw{pi.c Makefile} ],
37      cleanfiles => $cleanup,
38      cleandirs => $cleanup, # remove the whole directory at the end
39      keepdir => 1
40    ); 
41    $m->chdir("pi/");
42    die "Can't execute 'pi'\n" unless $m->_x("pi")->result;
43
44    $machine{$_} = $m;
45    last unless $i++ < $np;
46  }

The call to copyandmake at line 33 copies (using scp) the files pi.c and Makefile to a directory named pi in the remote machine. The directory pi will be created if it does not exists. After the file transfer the command specified by the copyandmake option

make => 'command'

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 '' if you want 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'nt created by this connection. The call to copyandmake by default sets dir as the current directory in the remote machine. Use the option keepdir => 1 to one to avoid this.

After the involved files are transferred and executables have been built, the program proceeds to open $np processes. The call to open at line 52 executes the pi program in the remote machine $m. In a list context returns a handler - that can be used to read from the process - and the PID of the child process. The new handler $proc[$_] is added to the IO::Select object $readset at line 53. The hash %id stores the relation between handlers and logical process identifiers.

48  my $t0 = [gettimeofday];
49  for (0..$lp) {
50    my $hn = $machine[$_ % $nummachines];
51    my $m = $machine{$hn};
52    ($proc[$_], $pid[$_]) = $m->open("./pi $_ $N $np |");
53    $readset->add($proc[$_]);
54    my $address = 0+$proc[$_];
55    $id{$address} = $_;
56  }

During the last stage the master node simply waits in the IO::Select object listening on each of the channels. As soon as a result is received it is added to the total sum for $pi:

58  my @ready;
59  my $count = 0;
60  do {
61    push @ready, $readset->can_read unless @ready;
62    my $handle = shift @ready;
63
64    my $me = $id{0+$handle};
65
66    my ($partial);
67    my $numBytesRead = sysread($handle,  $partial, 1024);
68    chomp($partial);
69
70    $pi += $partial;
71    print "Process $me: machine = $machine[$me % $nummachines] partial = $partial pi = $pi\n";
72
73    $readset->remove($handle) if eof($handle);
74  } until (++$count == $np);
75
76  my $elapsed = tv_interval ($t0);
77  print "Pi = $pi. N = $N Time = $elapsed\n";

PERFORMANCE: COMPUTATIONAL RESULTS

Let us see the time it takes the execution of the pure C program on each of the involved nodes (nereida, beowulf and orion). To have an idea of how things work for a comptuation large enough we set $N to 1 000 000 000 intervals:

pp2@nereida:~/LGRID_Machine/examples$ time ssh nereida 'pi/pi 0 1000000000 1'
3.141593

real    0m32.534s
user    0m0.036s
sys     0m0.008s

pp2@nereida:~/LGRID_Machine/examples$ time ssh beowulf 'pi/pi 0 1000000000 1'
3.141593

real    0m27.020s
user    0m0.036s
sys     0m0.008s

casiano@beowulf:~$ time ssh orion 'pi/pi 0 1000000000 1'
3.141593

real    0m29.120s
user    0m0.028s
sys     0m0.003s

As you can see, there is some heterogeneity here. Machine nereida (my desktop) is slower than the others two. beowulf is the fastest.

Now let us run the parallel perl program in nereida using only the beowulf node. The time spent is roughly comparable to the pure C time. That is nice: The overhead introduced by the coordination tasks is not as large (compare it with the beowulf entry above):

pp2@nereida:~/LGRID_Machine/examples$ time gridpipes.pl 1 1000000000
Process 0: machine = beowulf partial = 3.141593 pi = 3.141593
Pi = 3.141593. N = 1000000000 Time = 27.058693

real    0m28.917s
user    0m0.584s
sys     0m0.192s

Now comes the true test: will it be faster using two nodes? how much?

pp2@nereida:~/LGRID_Machine/examples$ time gridpipes.pl 2 1000000000
Process 0: machine = beowulf partial = 1.570796 pi = 1.570796
Process 1: machine = orion partial = 1.570796 pi = 3.141592
Pi = 3.141592. N = 1000000000 Time = 15.094719

real    0m17.684s
user    0m0.904s
sys     0m0.260s

We can see that the sequential pure C version took 32 seconds in my desktop (nereida). By using two machines I have SSH access I have reduced that time to roughly 18 seconds. This a factor of 32/18 = 1.8 times faster. This factor is even better if I don't consider the set-up time: 32/15 = 2.1. The total time decreases if I use the three machines:

pp2@nereida:~/LGRID_Machine/examples$ time gridpipes.pl 3 1000000000
Process 0: machine = beowulf partial = 1.047198 pi = 1.047198
Process 1: machine = orion partial = 1.047198 pi = 2.094396
Process 2: machine = nereida partial = 1.047198 pi = 3.141594
Pi = 3.141594. N = 1000000000 Time = 10.971036

real    0m13.700s
user    0m0.952s
sys     0m0.240s

which gives a speed factor of 32/13.7 = 2.3 or not considering the set-up time 32/10.9 = 2.9.

What happens if you have multiprocessor machine. The results highly depend on the underlying architecture. My machine nereida is a dual Xeon:

nereida:/tmp/graphviz-2.20.2# cat /proc/cpuinfo
processor       : 0
vendor_id       : GenuineIntel
cpu family      : 15
model           : 2
model name      : Intel(R) Xeon(TM) CPU 2.66GHz
stepping        : 5
cpu MHz         : 2658.041
cache size      : 512 KB
physical id     : 0
.......................................

processor       : 1
vendor_id       : GenuineIntel
cpu family      : 15
model           : 2
model name      : Intel(R) Xeon(TM) CPU 2.66GHz
stepping        : 5
cpu MHz         : 2658.041
cache size      : 512 KB
physical id     : 0
...................................

After changing the Makefile to include the -O3 option and the line defining the set of machines in gridpipes.pl (addresses in the subnetwork 127.0.0 are mapped to localhost):

my @machine = qw{127.0.0.1 127.0.0.2 127.0.0.3 127.0.0.4};

We have the following results:

pp2@nereida:~/LGRID_Machine/examples$ time gridpipes.pl 1 1000000000
Process 0: machine = 127.0.0.1 partial = 3.141593 pi = 3.141593
Pi = 3.141593. N = 1000000000 Time = 32.968117

real    0m33.858s
user    0m0.336s
sys     0m0.128s

pp2@nereida:~/LGRID_Machine/examples$ time gridpipes.pl 2 1000000000
Process 1: machine = 127.0.0.2 partial = 1.570796 pi = 1.570796
Process 0: machine = 127.0.0.1 partial = 1.570796 pi = 3.141592
Pi = 3.141592. N = 1000000000 Time = 16.552487

real    0m18.076s
user    0m0.504s
sys     0m0.188s

Which gives an speed up near 2.

CONCLUSIONS, LIMITATIONS AND FUTURE WORK

This example shows how to take advantage of the computational power of idle stations and the very high level of programming offered by Perl to improve the performance of an application. High Performance Programming (HPP, as provided by Very High Level Languages) and High Performance Computing (HPC) have been always two opposites ends of the spectrum: if you optimize programmer's time (HPP) computing time suffers (HPC) and viceversa. A synergetic combination of HPC and HPP tools can bring the best of both worlds.

This example however is too simplistic and does not address some important limitations that point to what must be done. I look forward for CPAN modules filling these gaps:

  • The former example does not address the load balancing problem. The load balancing problem is the problem to find the optimal work distribution among nodes, network links and any other involved resources, in order to get an optimal resource utilization.

  • Fault tolerance in the workers: What happens if one of the worker machines is shutdown in the middle of a computation? or the connection goes down? What mechanisms are provided?

  • Fault tolerance in the master: What if the master node goes down? Has the computation to restart from scratch?

  • Dynamic Resources: What happens if a new machine that previously was down is now available? Can we add it to our pool of resources?

SEE ALSO

THE FULL CODE

The Driver: File gridpipes.pl

$ cat gridpipes.pl
#!/usr/bin/perl
use warnings;
use strict;
use IO::Select;
use GRID::Machine;
use Time::HiRes qw(time gettimeofday tv_interval);

my @machine = qw{beowulf orion nereida};
my $nummachines = @machine;
my %machine; # Hash of GRID::Machine objects
#my %debug = (beowulf => 12345, orion => 0, nereida => 0);
my %debug = (beowulf => 0, orion => 0, nereida => 0);

my $np = shift || $nummachines; # number of processes
my $lp = $np-1;

my $N = shift || 100;

my @pid;  # List of process pids
my @proc; # List of handles
my %id;   # Gives the ID for a given handle

my $cleanup = 1;

my $pi = 0;

my $readset = IO::Select->new();

my $i = 0;
for (@machine){
  my $m = GRID::Machine->new(host => $_, debug => $debug{$_}, );

  $m->copyandmake(
    dir => 'pi',
    makeargs => 'pi',
    files => [ qw{pi.c Makefile} ],
    cleanfiles => $cleanup,
    cleandirs => $cleanup, # remove the whole directory at the end
    keepdir => 1,
  );

  $m->chdir("pi/");

  die "Can't execute 'pi'\n" unless $m->_x("pi")->result;

  $machine{$_} = $m;
  last unless $i++ < $np;
}

my $t0 = [gettimeofday];
for (0..$lp) {
  my $hn = $machine[$_ % $nummachines];
  my $m = $machine{$hn};
  ($proc[$_], $pid[$_]) = $m->open("./pi $_ $N $np |");
  $readset->add($proc[$_]);
  my $address = 0+$proc[$_];
  $id{$address} = $_;
}

my @ready;
my $count = 0;
do {
  push @ready, $readset->can_read unless @ready;
  my $handle = shift @ready;

  my $me = $id{0+$handle};

  my ($partial);
  my $numBytesRead = sysread($handle,  $partial, 1024);
  chomp($partial);

  $pi += $partial;
  print "Process $me: machine = $machine[$me % $nummachines] partial = $partial pi = $pi\n";

  $readset->remove($handle) if eof($handle);
} until (++$count == $np);

my $elapsed = tv_interval ($t0);
print "Pi = $pi. N = $N Time = $elapsed\n";

The Application. File pi.c

$ cat pi.c
#include <stdio.h>
#include <stdlib.h>

main(int argc, char **argv) {
  int id, N, np, i;
  double sum, left;

  if (argc != 4) {
    printf("Usage:\n%s id N np\n",argv[0]);
    exit(1);
  }
  id = atoi(argv[1]);
  N = atoi(argv[2]);
  np = atoi(argv[3]);
  for(i=id, sum = 0; i<N; i+=np) {
    double x = (i + 0.5)/N;
    sum += 4 / (1 + x*x);
  }
  sum /= N;
  fflush(stdout);
  printf("%lf\n", sum);
}

Makefile

$ cat Makefile
pi:
        cc pi.c -o pi