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 <sect1 id="xoper">
  <title>User-Defined Operators</title>

  <indexterm zone="xoper">
   <primary>operator</primary>
   <secondary>user-defined</secondary>
  </indexterm>

  <para>
   Every operator is <quote>syntactic sugar</quote> for a call to an
   underlying function that does the real work; so you must
   first create the underlying function before you can create
   the operator.  However, an operator is <emphasis>not merely</emphasis>
   syntactic sugar, because it carries additional information
   that helps the query planner optimize queries that use the
   operator.  The next section will be devoted to explaining
   that additional information.
  </para>

  <para>
   <productname>PostgreSQL</productname> supports left unary, right
   unary, and binary operators.  Operators can be
   overloaded;<indexterm><primary>overloading</primary><secondary>operators</secondary></indexterm>
   that is, the same operator name can be used for different operators
   that have different numbers and types of operands.  When a query is
   executed, the system determines the operator to call from the
   number and types of the provided operands.
  </para>

  <para>
   Here is an example of creating an operator for adding two complex
   numbers.  We assume we've already created the definition of type
   <type>complex</type> (see <xref linkend="xtypes">).  First we need a
   function that does the work, then we can define the operator:

<programlisting>
CREATE FUNCTION complex_add(complex, complex)
    RETURNS complex
    AS '<replaceable>filename</replaceable>', 'complex_add'
    LANGUAGE C IMMUTABLE STRICT;

CREATE OPERATOR + (
    leftarg = complex,
    rightarg = complex,
    procedure = complex_add,
    commutator = +
);
</programlisting>
  </para>

  <para>
   Now we could execute a query like this:
     
<screen>
SELECT (a + b) AS c FROM test_complex;

        c
-----------------
 (5.2,6.05)
 (133.42,144.95)
</screen>
  </para>

  <para>
   We've shown how to create a binary operator here.  To create unary
   operators, just omit one of <literal>leftarg</> (for left unary) or
   <literal>rightarg</> (for right unary).  The <literal>procedure</>
   clause and the argument clauses are the only required items in
   <command>CREATE OPERATOR</command>.  The <literal>commutator</>
   clause shown in the example is an optional hint to the query
   optimizer.  Further details about <literal>commutator</> and other
   optimizer hints appear in the next section.
  </para>
 </sect1>

  <sect1 id="xoper-optimization">
   <title>Operator Optimization Information</title>

   <para>
    A <productname>PostgreSQL</productname> operator definition can include
    several optional clauses that tell the system useful things about how
    the operator behaves.  These clauses should be provided whenever
    appropriate, because they can make for considerable speedups in execution
    of queries that use the operator.  But if you provide them, you must be
    sure that they are right!  Incorrect use of an optimization clause can
    result in slow queries, subtly wrong output, or other Bad Things.
    You can always leave out an optimization clause if you are not sure
    about it; the only consequence is that queries might run slower than
    they need to.
   </para>

   <para>
    Additional optimization clauses might be added in future versions of
    <productname>PostgreSQL</productname>.  The ones described here are all
    the ones that release &version; understands.
   </para>

   <sect2>
    <title><literal>COMMUTATOR</></title>

    <para>
     The <literal>COMMUTATOR</> clause, if provided, names an operator that is the
     commutator of the operator being defined.  We say that operator A is the
     commutator of operator B if (x A y) equals (y B x) for all possible input
     values x, y.  Notice that B is also the commutator of A.  For example,
     operators <literal>&lt;</> and <literal>&gt;</> for a particular data type are usually each others'
     commutators, and operator <literal>+</> is usually commutative with itself.
     But operator <literal>-</> is usually not commutative with anything.
    </para>

    <para>
     The left operand type of a commutable operator is the same as the
     right operand type of its commutator, and vice versa.  So the name of
     the commutator operator is all that <productname>PostgreSQL</productname>
     needs to be given to look up the commutator, and that's all that needs to
     be provided in the <literal>COMMUTATOR</> clause.
    </para>

    <para>
     It's critical to provide commutator information for operators that
     will be used in indexes and join clauses, because this allows the
     query optimizer to <quote>flip around</> such a clause to the forms
     needed for different plan types.  For example, consider a query with
     a WHERE clause like <literal>tab1.x = tab2.y</>, where <literal>tab1.x</>
     and <literal>tab2.y</> are of a user-defined type, and suppose that
     <literal>tab2.y</> is indexed.  The optimizer cannot generate an
     index scan unless it can determine how to flip the clause around to
     <literal>tab2.y = tab1.x</>, because the index-scan machinery expects
     to see the indexed column on the left of the operator it is given.
     <productname>PostgreSQL</productname> will <emphasis>not</> simply
     assume that this is a valid transformation &mdash; the creator of the
     <literal>=</> operator must specify that it is valid, by marking the
     operator with commutator information.
    </para>

    <para>
     When you are defining a self-commutative operator, you just do it.
     When you are defining a pair of commutative operators, things are
     a little trickier: how can the first one to be defined refer to the
     other one, which you haven't defined yet?  There are two solutions
     to this problem:

     <itemizedlist>
      <listitem>
       <para>
        One way is to omit the <literal>COMMUTATOR</> clause in the first operator that
        you define, and then provide one in the second operator's definition.
        Since <productname>PostgreSQL</productname> knows that commutative
        operators come in pairs, when it sees the second definition it will
        automatically go back and fill in the missing <literal>COMMUTATOR</> clause in
        the first definition.
       </para>
      </listitem>

      <listitem>
       <para>
        The other, more straightforward way is just to include <literal>COMMUTATOR</> clauses
        in both definitions.  When <productname>PostgreSQL</productname> processes
        the first definition and realizes that <literal>COMMUTATOR</> refers to a nonexistent
        operator, the system will make a dummy entry for that operator in the
        system catalog.  This dummy entry will have valid data only
        for the operator name, left and right operand types, and result type,
        since that's all that <productname>PostgreSQL</productname> can deduce
        at this point.  The first operator's catalog entry will link to this
        dummy entry.  Later, when you define the second operator, the system
        updates the dummy entry with the additional information from the second
        definition.  If you try to use the dummy operator before it's been filled
        in, you'll just get an error message.
       </para>
      </listitem>
     </itemizedlist>
    </para>
   </sect2>

   <sect2>
    <title><literal>NEGATOR</></title>

    <para>
     The <literal>NEGATOR</> clause, if provided, names an operator that is the
     negator of the operator being defined.  We say that operator A
     is the negator of operator B if both return Boolean results and
     (x A y) equals NOT (x B y) for all possible inputs x, y.
     Notice that B is also the negator of A.
     For example, <literal>&lt;</> and <literal>&gt;=</> are a negator pair for most data types.
     An operator can never validly be its own negator.
    </para>

   <para>
    Unlike commutators, a pair of unary operators could validly be marked
    as each others' negators; that would mean (A x) equals NOT (B x)
    for all x, or the equivalent for right unary operators.
   </para>

   <para>
    An operator's negator must have the same left and/or right operand types
    as the operator to be defined, so just as with <literal>COMMUTATOR</>, only the operator
    name need be given in the <literal>NEGATOR</> clause.
   </para>

   <para>
    Providing a negator is very helpful to the query optimizer since
    it allows expressions like <literal>NOT (x = y)</> to be simplified into
    <literal>x &lt;&gt; y</>.  This comes up more often than you might think, because
    <literal>NOT</> operations can be inserted as a consequence of other rearrangements.
   </para>

   <para>
    Pairs of negator operators can be defined using the same methods
    explained above for commutator pairs.
   </para>

  </sect2>

  <sect2>
   <title><literal>RESTRICT</></title>

   <para>
    The <literal>RESTRICT</> clause, if provided, names a restriction selectivity
    estimation function for the operator.  (Note that this is a function
    name, not an operator name.)  <literal>RESTRICT</> clauses only make sense for
    binary operators that return <type>boolean</>.  The idea behind a restriction
    selectivity estimator is to guess what fraction of the rows in a
    table will satisfy a <literal>WHERE</literal>-clause condition of the form:
<programlisting>
column OP constant
</programlisting>
    for the current operator and a particular constant value.
    This assists the optimizer by
    giving it some idea of how many rows will be eliminated by <literal>WHERE</>
    clauses that have this form.  (What happens if the constant is on
    the left, you might be wondering?  Well, that's one of the things that
    <literal>COMMUTATOR</> is for...)
   </para>

   <para>
    Writing new restriction selectivity estimation functions is far beyond
    the scope of this chapter, but fortunately you can usually just use
    one of the system's standard estimators for many of your own operators.
    These are the standard restriction estimators:
    <simplelist>
     <member><function>eqsel</> for <literal>=</></member>
     <member><function>neqsel</> for <literal>&lt;&gt;</></member>
     <member><function>scalarltsel</> for <literal>&lt;</> or <literal>&lt;=</></member>
     <member><function>scalargtsel</> for <literal>&gt;</> or <literal>&gt;=</></member>
   </simplelist>
    It might seem a little odd that these are the categories, but they
    make sense if you think about it.  <literal>=</> will typically accept only
    a small fraction of the rows in a table; <literal>&lt;&gt;</> will typically reject
    only a small fraction.  <literal>&lt;</> will accept a fraction that depends on
    where the given constant falls in the range of values for that table
    column (which, it just so happens, is information collected by
    <command>ANALYZE</command> and made available to the selectivity estimator).
    <literal>&lt;=</> will accept a slightly larger fraction than <literal>&lt;</> for the same
    comparison constant, but they're close enough to not be worth
    distinguishing, especially since we're not likely to do better than a
    rough guess anyhow.  Similar remarks apply to <literal>&gt;</> and <literal>&gt;=</>.
   </para>

   <para>
    You can frequently get away with using either <function>eqsel</function> or <function>neqsel</function> for
    operators that have very high or very low selectivity, even if they
    aren't really equality or inequality.  For example, the
    approximate-equality geometric operators use <function>eqsel</function> on the assumption that
    they'll usually only match a small fraction of the entries in a table.
   </para>

   <para>
    You can use <function>scalarltsel</> and <function>scalargtsel</> for comparisons on data types that
    have some sensible means of being converted into numeric scalars for
    range comparisons.  If possible, add the data type to those understood
    by the function <function>convert_to_scalar()</function> in <filename>src/backend/utils/adt/selfuncs.c</filename>.
    (Eventually, this function should be replaced by per-data-type functions
    identified through a column of the <classname>pg_type</> system catalog; but that hasn't happened
    yet.)  If you do not do this, things will still work, but the optimizer's
    estimates won't be as good as they could be.
   </para>

   <para>
    There are additional selectivity estimation functions designed for geometric
    operators in <filename>src/backend/utils/adt/geo_selfuncs.c</filename>: <function>areasel</function>, <function>positionsel</function>,
    and <function>contsel</function>.  At this writing these are just stubs, but you might want
    to use them (or even better, improve them) anyway.
   </para>
   </sect2>

   <sect2>
    <title><literal>JOIN</></title>

    <para>
     The <literal>JOIN</> clause, if provided, names a join selectivity
     estimation function for the operator.  (Note that this is a function
     name, not an operator name.)  <literal>JOIN</> clauses only make sense for
     binary operators that return <type>boolean</type>.  The idea behind a join
     selectivity estimator is to guess what fraction of the rows in a
     pair of tables will satisfy a <literal>WHERE</>-clause condition of the form:
<programlisting>
table1.column1 OP table2.column2
</programlisting>
     for the current operator.  As with the <literal>RESTRICT</literal> clause, this helps
     the optimizer very substantially by letting it figure out which
     of several possible join sequences is likely to take the least work.
    </para>

    <para>
     As before, this chapter will make no attempt to explain how to write
     a join selectivity estimator function, but will just suggest that
     you use one of the standard estimators if one is applicable:
     <simplelist>
      <member><function>eqjoinsel</> for <literal>=</></member>
      <member><function>neqjoinsel</> for <literal>&lt;&gt;</></member>
      <member><function>scalarltjoinsel</> for <literal>&lt;</> or <literal>&lt;=</></member>
      <member><function>scalargtjoinsel</> for <literal>&gt;</> or <literal>&gt;=</></member>
      <member><function>areajoinsel</> for 2D area-based comparisons</member>
      <member><function>positionjoinsel</> for 2D position-based comparisons</member>
      <member><function>contjoinsel</> for 2D containment-based comparisons</member>
     </simplelist>
    </para>
   </sect2>

   <sect2>
    <title><literal>HASHES</></title>

    <para>
     The <literal>HASHES</literal> clause, if present, tells the system that
     it is permissible to use the hash join method for a join based on this
     operator.  <literal>HASHES</> only makes sense for a binary operator that
     returns <literal>boolean</>, and in practice the operator must represent
     equality for some data type or pair of data types.
    </para>

    <para>
     The assumption underlying hash join is that the join operator can
     only return true for pairs of left and right values that hash to the
     same hash code.  If two values get put in different hash buckets, the
     join will never compare them at all, implicitly assuming that the
     result of the join operator must be false.  So it never makes sense
     to specify <literal>HASHES</literal> for operators that do not represent
     some form of equality.  In most cases it is only practical to support
     hashing for operators that take the same data type on both sides.
     However, sometimes it is possible to design compatible hash functions
     for two or more data types; that is, functions that will generate the
     same hash codes for <quote>equal</> values, even though the values
     have different representations.  For example, it's fairly simple
     to arrange this property when hashing integers of different widths.
    </para>

    <para>
     To be marked <literal>HASHES</literal>, the join operator must appear
     in a hash index operator family.  This is not enforced when you create
     the operator, since of course the referencing operator family couldn't
     exist yet.  But attempts to use the operator in hash joins will fail
     at run time if no such operator family exists.  The system needs the
     operator family to find the data-type-specific hash function(s) for the
     operator's input data type(s).  Of course, you must also create suitable
     hash functions before you can create the operator family.
    </para>

    <para>
     Care should be exercised when preparing a hash function, because there
     are machine-dependent ways in which it might fail to do the right thing.
     For example, if your data type is a structure in which there might be
     uninteresting pad bits, you cannot simply pass the whole structure to
     <function>hash_any</>.  (Unless you write your other operators and
     functions to ensure that the unused bits are always zero, which is the
     recommended strategy.)
     Another example is that on machines that meet the <acronym>IEEE</>
     floating-point standard, negative zero and positive zero are different
     values (different bit patterns) but they are defined to compare equal.
     If a float value might contain negative zero then extra steps are needed
     to ensure it generates the same hash value as positive zero.
    </para>

    <para>
     A hash-joinable operator must have a commutator (itself if the two
     operand data types are the same, or a related equality operator
     if they are different) that appears in the same operator family.
     If this is not the case, planner errors might occur when the operator
     is used.  Also, it is a good idea (but not strictly required) for
     a hash operator family that supports multiple data types to provide
     equality operators for every combination of the data types; this
     allows better optimization.
    </para>

    <note>
    <para>
     The function underlying a hash-joinable operator must be marked
     immutable or stable.  If it is volatile, the system will never
     attempt to use the operator for a hash join.
    </para>
    </note>

    <note>
    <para>
     If a hash-joinable operator has an underlying function that is marked
     strict, the
     function must also be complete: that is, it should return true or
     false, never null, for any two nonnull inputs.  If this rule is
     not followed, hash-optimization of <literal>IN</> operations might
     generate wrong results.  (Specifically, <literal>IN</> might return
     false where the correct answer according to the standard would be null;
     or it might yield an error complaining that it wasn't prepared for a
     null result.)
    </para>
    </note>

   </sect2>

   <sect2>
    <title><literal>MERGES</></title>

    <para>
     The <literal>MERGES</literal> clause, if present, tells the system that
     it is permissible to use the merge-join method for a join based on this
     operator.  <literal>MERGES</> only makes sense for a binary operator that
     returns <literal>boolean</>, and in practice the operator must represent
     equality for some data type or pair of data types.
    </para>

    <para>
     Merge join is based on the idea of sorting the left- and right-hand tables
     into order and then scanning them in parallel.  So, both data types must
     be capable of being fully ordered, and the join operator must be one
     that can only succeed for pairs of values that fall at the
     <quote>same place</>
     in the sort order.  In practice this means that the join operator must
     behave like equality.  But it is possible to merge-join two
     distinct data types so long as they are logically compatible.  For
     example, the <type>smallint</type>-versus-<type>integer</type>
     equality operator is merge-joinable.
     We only need sorting operators that will bring both data types into a
     logically compatible sequence.
    </para>

    <para>
     To be marked <literal>MERGES</literal>, the join operator must appear
     as an equality member of a <literal>btree</> index operator family.
     This is not enforced when you create
     the operator, since of course the referencing operator family couldn't
     exist yet.  But the operator will not actually be used for merge joins
     unless a matching operator family can be found.  The
     <literal>MERGES</literal> flag thus acts as a hint to the planner that
     it's worth looking for a matching operator family.
    </para>

    <para>
     A merge-joinable operator must have a commutator (itself if the two
     operand data types are the same, or a related equality operator
     if they are different) that appears in the same operator family.
     If this is not the case, planner errors might occur when the operator
     is used.  Also, it is a good idea (but not strictly required) for
     a <literal>btree</> operator family that supports multiple data types to provide
     equality operators for every combination of the data types; this
     allows better optimization.
    </para>

    <note>
    <para>
     The function underlying a merge-joinable operator must be marked
     immutable or stable.  If it is volatile, the system will never
     attempt to use the operator for a merge join.
    </para>
    </note>
   </sect2>
  </sect1>
