view release on metacpan or  search on metacpan

Vector.pod  view on Meta::CPAN

C<$set3-E<gt>Union($set1,$set2);>

This method calculates the union of "C<$set1>" and "C<$set2>" and stores
the result in "C<$set3>".

This is usually written as "C<$set3 = $set1 u $set2>" in set theory
(where "u" is the "cup" operator).

(On systems where the "cup" character is unavailable this operator
is often denoted by a plus sign "+".)

In-place calculation is also possible, i.e., "C<$set3>" may be identical
with "C<$set1>" or "C<$set2>" or both.

=item *

C<$vec3-E<gt>And($vec1,$vec2);>

C<$set3-E<gt>Intersection($set1,$set2);>

This method calculates the intersection of "C<$set1>" and "C<$set2>" and
stores the result in "C<$set3>".

This is usually written as "C<$set3 = $set1 n $set2>" in set theory
(where "n" is the "cap" operator).

(On systems where the "cap" character is unavailable this operator
is often denoted by an asterisk "*".)

In-place calculation is also possible, i.e., "C<$set3>" may be identical
with "C<$set1>" or "C<$set2>" or both.

=item *

C<$vec3-E<gt>AndNot($vec1,$vec2);>

C<$set3-E<gt>Difference($set1,$set2);>

This method calculates the difference of "C<$set1>" less "C<$set2>" and
stores the result in "C<$set3>".

This is usually written as "C<$set3 = $set1 \ $set2>" in set theory
(where "\" is the "less" operator).

In-place calculation is also possible, i.e., "C<$set3>" may be identical
with "C<$set1>" or "C<$set2>" or both.

=item *

C<$vec3-E<gt>Xor($vec1,$vec2);>

C<$set3-E<gt>ExclusiveOr($set1,$set2);>

This method calculates the symmetric difference of "C<$set1>" and "C<$set2>"
and stores the result in "C<$set3>".

This can be written as "C<$set3 = ($set1 u $set2) \ ($set1 n $set2)>" in set
theory (the union of the two sets less their intersection).

When sets are implemented as bit vectors then the above formula is
equivalent to the exclusive-or between corresponding bits of the two
bit vectors (hence the name of this method).

Note that this method is also much more efficient than evaluating the
above formula explicitly since it uses a built-in machine language
instruction internally.

In-place calculation is also possible, i.e., "C<$set3>" may be identical
with "C<$set1>" or "C<$set2>" or both.

=item *

C<$vec2-E<gt>Not($vec1);>

C<$set2-E<gt>Complement($set1);>

This method calculates the complement of "C<$set1>" and stores the result
in "C<$set2>".

In "big integer" arithmetic, this is equivalent to calculating the one's
complement of the number stored in the bit vector "C<$set1>" in binary
representation.

In-place calculation is also possible, i.e., "C<$set2>" may be identical
with "C<$set1>".

=item *

C<if ($set1-E<gt>subset($set2))>

Returns "true" ("C<1>") if "C<$set1>" is a subset of "C<$set2>"
(i.e., completely contained in "C<$set2>") and "false" ("C<0>")
otherwise.

This means that any bit which is set ("C<1>") in "C<$set1>" must
also be set in "C<$set2>", but "C<$set2>" may contain set bits
which are not set in "C<$set1>", in order for the condition
of subset relationship to be true between these two sets.

Note that by definition, if two sets are identical, they are
also subsets (and also supersets) of each other.

=item *

C<$norm = $set-E<gt>Norm();>

Returns the norm (number of bits which are set) of the given vector.

This is equivalent to the number of elements contained in the given
set.

Uses a byte lookup table for calculating the number of set bits
per byte, and thus needs a time for evaluation (and a number of
loops) linearly proportional to the length of the given bit vector
(in bytes).

This should be the fastest algorithm on average.

=item *

C<$norm = $set-E<gt>Norm2();>

Returns the norm (number of bits which are set) of the given vector.

This is equivalent to the number of elements contained in the given