{
my @values;
my $prev_first;
my $prev_last;

sub cache {
    my ($data, $first, $last) = @_;

    unless ($prev_first and $prev_last) {
        @values = grep defined, @{$data}{$first .. $last};
    } else {
        for ($prev_first .. $first-1) {
            shift @values if defined $data->{$_};
        }

        for ($prev_last+1 .. $last) {
            push @values, $data->{$_} if defined $data->{$_};
        }
    }

    $prev_first = $first;
    $prev_last  = $last;

    sum(@values) / @values;
}
}