FAQ 4.53 How do I manipulate arrays of bits?

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4.53: How do I manipulate arrays of bits?

    Use "pack()" and "unpack()", or else "vec()" and the bitwise operations.

    For example, you don't have to store individual bits in an array (which
    would mean that you're wasting a lot of space). To convert an array of
    bits to a string, use "vec()" to set the right bits. This sets $vec to
    have bit N set only if $ints[N] was set:

            @ints = (...); # array of bits, e.g. ( 1, 0, 0, 1, 1, 0 ... )
            $vec = '';
            foreach( 0 .. $#ints ) {
                    vec($vec,$_,1) = 1 if $ints[$_];

    The string $vec only takes up as many bits as it needs. For instance, if
    you had 16 entries in @ints, $vec only needs two bytes to store them
    (not counting the scalar variable overhead).

    Here's how, given a vector in $vec, you can get those bits into your
    @ints array:

            sub bitvec_to_list {
                    my $vec = shift;
                    my @ints;
                    # Find null-byte density then select best algorithm
                    if ($vec =~ tr/// / length $vec > 0.95) {
                            use integer;
                            my $i;

                            # This method is faster with mostly null-bytes
                            while($vec =~ /[^]/g ) {
                                    $i = -9 + 8 * pos $vec;
                                    push @ints, $i if vec($vec, ++$i, 1);
                                    push @ints, $i if vec($vec, ++$i, 1);
                                    push @ints, $i if vec($vec, ++$i, 1);
                                    push @ints, $i if vec($vec, ++$i, 1);
                                    push @ints, $i if vec($vec, ++$i, 1);
                                    push @ints, $i if vec($vec, ++$i, 1);
                                    push @ints, $i if vec($vec, ++$i, 1);
                                    push @ints, $i if vec($vec, ++$i, 1);
                    else {
                            # This method is a fast general algorithm
                            use integer;
                            my $bits = unpack "b*", $vec;
                            push @ints, 0 if $bits =~ s/^(\d)// && $1;
                            push @ints, pos $bits while($bits =~ /1/g);

                    return \@ints;

    This method gets faster the more sparse the bit vector is. (Courtesy of
    Tim Bunce and Winfried Koenig.)

    You can make the while loop a lot shorter with this suggestion from
    Benjamin Goldberg:

            while($vec =~ /[^]+/g ) {
                    push @ints, grep vec($vec, $_, 1), $-[0] * 8 .. $+[0] * 8;

    Or use the CPAN module "Bit::Vector":

            $vector = Bit::Vector->new($num_of_bits);
            @ints = $vector->Index_List_Read();

    "Bit::Vector" provides efficient methods for bit vector, sets of small
    integers and "big int" math.

    Here's a more extensive illustration using vec():

            # vec demo
            $vector = "\xff\x0f\xef\xfe";
            print "Ilya's string \xff\x0f\xef\xfe represents the number ",
            unpack("N", $vector), "\n";
            $is_set = vec($vector, 23, 1);
            print "Its 23rd bit is ", $is_set ? "set" : "clear", ".\n";




            sub set_vec {
                    my ($offset, $width, $value) = @_;
                    my $vector = '';
                    vec($vector, $offset, $width) = $value;
                    print "offset=$offset width=$width value=$value\n";

            sub pvec {
                    my $vector = shift;
                    my $bits = unpack("b*", $vector);
                    my $i = 0;
                    my $BASE = 8;

                    print "vector length in bytes: ", length($vector), "\n";
                    @bytes = unpack("A8" x length($vector), $bits);
                    print "bits are: @bytes\n\n";


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