Hmm, rolling averages. You can convert that from N**2 to linear, if you can assume you're moving through the numbers in sequence. Also, converting your hash to an array would be better.
Try something like this:
#!/usr/bin/perl
use strict;
use warnings;
## setup
my ($gap, $elements, $first, $i) = (10000, 20000, 10000, 0);
my @data = map { rand } (1 .. $elements);
## compute initial sum
my $sum = 0;
$sum += $_ for @data[0 .. $gap];
## go through @data serially computing averages
while (1) {
printf("average of %d to %d: %d",
$i + $first, $i + $first + $gap, $sum / $gap);
$sum -= $data[$i]; # subtract old 1st element
last if ++$i + $gap > $elements; # stop when done
$sum += $data[$i + $gap]; # add new last element
}
HTH
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