2.9.1. Problem

2.9.2. Solution

sub gaussian_rand {
    my ($u1, $u2);  # uniformly distributed random numbers
    my $w;          # variance, then a weight
    my ($g1, $g2);  # gaussian-distributed numbers

    do {
        $u1 = 2 * rand( ) - 1;
        $u2 = 2 * rand( ) - 1;
        $w = $u1*$u1 + $u2*$u2;
    } while ($w >= 1 || $w =  = 0);

    $w = sqrt( (-2 * log($w))  / $w );
    $g2 = $u1 * $w;
    $g1 = $u2 * $w;
    # return both if wanted, else just one
    return wantarray ? ($g1, $g2) : $g1;
}

# 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;
        }
    }
}

2.9.4. See Also