use strict;
use warnings;
use Benchmark qw(cmpthese timethese);
################################################################################
my $results = timethese($ARGV[0]//-5, {
	'no_integer_module  ' =>\&no_integer,
	'with_integer_module' =>\&with_integer,
    });
cmpthese( $results );
################################################################################
sub no_integer{
  my $n=1002;

  my $len = 1 + 10 * $n / 3;

  my $pi;
  my @a= (2) x $len;
  my $nines = 0;

  my $predigit = 0;

  for (my $j =1; $j < $n + 1; ++$j){
    my $q = 0;
    for my $i (reverse 0..$len - 1) {
        my $x = 10 * $a[$i] + $q * ($i + 1);
        my $divisor = 2 * $i + 1;
        $a[$i] = $x % $divisor;
        $q = $x / $divisor;
    }
    $a[0]=$q%10;
    $q=$q/10;
    if (9 == $q){ ++$nines;   }
    elsif(10 == $q){
          $pi.=$predigit + 1;
          for (my $k = 0; $k < $nines; $k++){$pi.=0} # print 0
          $predigit = $nines = 0;
    }
    else{
         $pi.= $predigit;
         $predigit = $q;
         if(0 != $nines){
              for (my $k = 0; $k < $nines; $k++) {
                  $pi.=9;
              }
              $nines = 0;
        }
    }
  }
}
################################################################################
sub with_integer{
  use integer;
  my $n=1002;

  my $len = 1 + 10 * $n / 3;

  my $pi;
  my @a= (2) x $len;
  my $nines = 0;

  my $predigit = 0;

  for (my $j =1; $j < $n + 1; ++$j){
    my $q = 0;
    for my $i (reverse 0..$len - 1) {
        my $x = 10 * $a[$i] + $q * ($i + 1);
        my $divisor = 2 * $i + 1;
        $a[$i] = $x % $divisor;
        $q = $x / $divisor;
    }
    $a[0]=$q%10;
    $q=$q/10;
    if (9 == $q){ ++$nines;   }
    elsif(10 == $q){
          $pi.=$predigit + 1;
          for (my $k = 0; $k < $nines; $k++){$pi.=0} # print 0
          $predigit = $nines = 0;
    }
    else{
         $pi.= $predigit;
         $predigit = $q;
         if(0 != $nines){
              for (my $k = 0; $k < $nines; $k++) {
                  $pi.=9;
              }
              $nines = 0;
        }
    }
  }
}

##</code><code>##

Benchmark: running no_integer_module  , with_integer_module for at least 20 CPU seconds...

no_integer_module  : 21 wallclock secs (20.64 usr +  0.00 sys = 20.64 CPU) @  0.92/s (n=19)
with_integer_module: 21 wallclock secs (20.50 usr +  0.00 sys = 20.50 CPU) @  1.37/s (n=28)

                    s/iter no_integer_module   with_integer_module
no_integer_module     1.09                  --                -33%
with_integer_module  0.732                 48%                  --