# weight_to_dist: takes a hash mapping key to weight and returns
    # a hash mapping key to probability
    sub weight_to_dist {
        my %weights = @_;
        my %dist    = ();
        my $total   = 0;
        my ($key, $weight);
        local $_;

        foreach (values %weights) {
            $total += $_;
        }
        while ( ($key, $weight) = each %weights ) {
            $dist{$key} = $weight/$total;
        }

        return %dist;
    }

    # weighted_rand: takes a hash mapping key to probability, and
    # returns the corresponding element
    sub weighted_rand {
        my %dist = @_;
        my ($key, $weight);

        while (1) {                     # to avoid floating point inaccuracies
            my $rand = rand;
            while ( ($key, $weight) = each %dist ) {
                return $key if ($rand -= $weight) < 0;
            }
        }
    }