my $dist = ($start - $end + 1) % $max_length;

##</code><code>##

    my $dist = dist($start, $end);

sub dist {
    my $start = shift // die;
    my $end   = shift // die;

    if ( $end >= $start ) {    # simple range
        return $end - $start + 1;
    }

    # warpped range
    return $max_length - $start + 1 + $end;
}