# factorial($n) computes the factorial of $n,
#   using an iterative algorithm.
sub factorial {
    my ($n) = shift;
    my ($result, $i) = (1, 2);
    for ( ; $i <= $n; $i++) {
        $result *= $i;
    }
    return $result;
}

# factorial_recursive($n) computes the factorial of $n,
#   using a recursive algorithm.
sub factorial_recursive {
    my ($n) = shift;
    return $n if $n <= 2;
    return $n * factorial_recursive($n - 1);
}

sub factorial_approx {
    return sqrt (1.5707963267949 * $_[0]) *
        (($_[0] / 2.71828182845905) ** $_[0]);
}