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

  <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; 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;

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 server process crashes, 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 commuted 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>
     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 may 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 may 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 had better be
     equality for some data type.
    </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
     equality.
    </para>

    <para>
     To be marked <literal>HASHES</literal>, the join operator must appear
     in a hash index operator class.  This is not enforced when you create
     the operator, since of course the referencing operator class couldn't
     exist yet.  But attempts to use the operator in hash joins will fail
     at runtime if no such operator class exists.  The system needs the
     operator class to find the datatype-specific hash function for the
     operator's input datatype.  Of course, you must also supply a suitable
     hash function before you can create the operator class.
    </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 may be
     uninteresting pad bits, you can't 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>

    <note>
    <para>
     The function underlying a hashjoinable 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 hashjoinable 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 non-NULL inputs.  If this rule is
     not followed, hash-optimization of <literal>IN</> operations may
     generate wrong results.  (Specifically, <literal>IN</> might return
     FALSE where the correct answer per spec 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</> (<literal>SORT1</>, <literal>SORT2</>, <literal>LTCMP</>, <literal>GTCMP</>)</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 unlike hash join, where the left and right
     data types had better be the same (or at least bitwise equivalent),
     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>
     Execution of a merge join requires that the system be able to identify
     four operators related to the merge-join equality operator: less-than
     comparison for the left operand data type, less-than comparison for the
     right operand data type, less-than comparison between the two data types, and
     greater-than comparison between the two data types.  (These are actually
     four distinct operators if the merge-joinable operator has two different
     operand data types; but when the operand types are the same the three
     less-than operators are all the same operator.)
     It is possible to
     specify these operators individually by name, as the <literal>SORT1</>,
     <literal>SORT2</>, <literal>LTCMP</>, and <literal>GTCMP</> options
     respectively.  The system will fill in the default names
     <literal>&lt;</>, <literal>&lt;</>, <literal>&lt;</>, <literal>&gt;</>
     respectively if any of these are omitted when <literal>MERGES</> is
     specified.  Also, <literal>MERGES</> will be assumed to be implied if any
     of these four operator options appear, so it is possible to specify
     just some of them and let the system fill in the rest.
    </para>

    <para>
     The operand data types of the four comparison operators can be deduced
     from the operand types of the merge-joinable operator, so just as with
     <literal>COMMUTATOR</>, only the operator names need be given in these
     clauses.  Unless you are using peculiar choices of operator names,
     it's sufficient to write <literal>MERGES</> and let the system fill in
     the details.
     (As with <literal>COMMUTATOR</> and <literal>NEGATOR</>, the system is
     able to make dummy
     operator entries if you happen to define the equality operator before
     the other ones.)
    </para>

    <para>
     There are additional restrictions on operators that you mark
     merge-joinable.  These restrictions are not currently checked by
     <command>CREATE OPERATOR</command>, but errors may occur when
     the operator is used if any are not true:

     <itemizedlist>
      <listitem>
       <para>
	A merge-joinable equality operator must have a merge-joinable
        commutator (itself if the two operand data types are the same, or a related
        equality operator if they are different).
       </para>
      </listitem>

      <listitem>
       <para>
        If there is a merge-joinable operator relating any two data types
	A and B, and another merge-joinable operator relating B to any
	third data type C, then A and C must also have a merge-joinable
	operator; in other words, having a merge-joinable operator must
	be transitive.
       </para>
      </listitem>

      <listitem>
       <para>
        Bizarre results will ensue at runtime if the four comparison
	operators you name do not sort the data values compatibly.
       </para>
      </listitem>
     </itemizedlist>
    </para>

    <note>
    <para>
     The function underlying a mergejoinable 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>

    <note>
    <para>
     <literal>GROUP BY</> and <literal>DISTINCT</> operations require each
     datatype being grouped or compared to have a mergejoinable
     equality operator named <literal>=</>.  The equality operator and its
     associated <literal>SORT1</> operator are used to implement these
     operations.  Also, the associated <literal>SORT1</> operator is the
     default ordering operator for <literal>ORDER BY</>.
    </para>
    </note>

    <note>
    <para>
     In <ProductName>PostgreSQL</ProductName> versions before 7.3,
     the <literal>MERGES</> shorthand was not available: to make a
     merge-joinable operator one had to write both <literal>SORT1</> and
     <literal>SORT2</> explicitly.  Also, the <literal>LTCMP</> and
     <literal>GTCMP</>
     options did not exist; the names of those operators were hardwired as
     <literal>&lt;</> and <literal>&gt;</> respectively.
    </para>
    </note>
   </sect2>
  </sect1>

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