You rule Tilly!

I had to point out the mod operator in this function:

sub gcd {
    my ($n, $m) = @_;
    while ($m) {
      my $k = $n % $m;
      ($n, $m) = ($m, $k);
    }
    return $n;
}

. . . particularly the use of the mod operator. I remember reading Robert Sedgewick's Mastering Algorithms in C++ and really getting a kick out of the first example - Euclide's greatest common denominator formula.

At first, Sedgewick implemented it with the division operator:

my $k = $n / $m;

Then he explained that replacing the / operator with the % operator results in about 75% less iterations through the while loop. Incredible.

Jeff