The intarray module provides a number of useful functions
  and operators for manipulating null-free arrays of integers.
  There is also support for indexed searches using some of the operators.
 
All of these operations will throw an error if a supplied array contains any NULL elements.
Many of these operations are only sensible for one-dimensional arrays. Although they will accept input arrays of more dimensions, the data is treated as though it were a linear array in storage order.
intarray Functions and Operators
   The functions provided by the intarray module
   are shown in Table F.9, the operators
   in Table F.10.
  
Table F.9. intarray Functions
Table F.10. intarray Operators
   (Before PostgreSQL 8.2, the containment operators @> and
   <@ were respectively called @ and ~.
   These names are still available, but are deprecated and will eventually be
   retired.  Notice that the old names are reversed from the convention
   formerly followed by the core geometric data types!)
  
   The operators &&, @> and
   <@ are equivalent to PostgreSQL's built-in
   operators of the same names, except that they work only on integer arrays
   that do not contain nulls, while the built-in operators work for any array
   type.  This restriction makes them faster than the built-in operators
   in many cases.
  
   The @@ and ~~ operators test whether an array
   satisfies a query, which is expressed as a value of a
   specialized data type query_int.  A query
   consists of integer values that are checked against the elements of
   the array, possibly combined using the operators &
   (AND), | (OR), and ! (NOT).  Parentheses
   can be used as needed.  For example,
   the query 1&(2|3) matches arrays that contain 1
   and also contain either 2 or 3.
  
   intarray provides index support for the
   &&, @>, <@,
   and @@ operators, as well as regular array equality.
  
   Two GiST index operator classes are provided:
   gist__int_ops (used by default) is suitable for
   small- to medium-size data sets, while
   gist__intbig_ops uses a larger signature and is more
   suitable for indexing large data sets (i.e., columns containing
   a large number of distinct array values).
   The implementation uses an RD-tree data structure with
   built-in lossy compression.
  
   There is also a non-default GIN operator class
   gin__int_ops supporting the same operators.
  
The choice between GiST and GIN indexing depends on the relative performance characteristics of GiST and GIN, which are discussed elsewhere.
-- a message can be in one or more “sections”
CREATE TABLE message (mid INT PRIMARY KEY, sections INT[], ...);
-- create specialized index
CREATE INDEX message_rdtree_idx ON message USING GIST (sections gist__int_ops);
-- select messages in section 1 OR 2 - OVERLAP operator
SELECT message.mid FROM message WHERE message.sections && '{1,2}';
-- select messages in sections 1 AND 2 - CONTAINS operator
SELECT message.mid FROM message WHERE message.sections @> '{1,2}';
-- the same, using QUERY operator
SELECT message.mid FROM message WHERE message.sections @@ '1&2'::query_int;
   The source directory contrib/intarray/bench contains a
   benchmark test suite, which can be run against an installed
   PostgreSQL server.  (It also requires DBD::Pg
   to be installed.)  To run:
  
cd .../contrib/intarray/bench createdb TEST psql -c "CREATE EXTENSION intarray" TEST ./create_test.pl | psql TEST ./bench.pl
   The bench.pl script has numerous options, which
   are displayed when it is run without any arguments.
  
   All work was done by Teodor Sigaev (<teodor@sigaev.ru>) and
   Oleg Bartunov (<oleg@sai.msu.su>). See
   http://www.sai.msu.su/~megera/postgres/gist/ for
   additional information. Andrey Oktyabrski did a great work on adding new
   functions and operations.