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doc/src/sgml/ref/create_aggregate.sgml
PostgreSQL documentation
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<refentry id="SQL-CREATEAGGREGATE">
 <indexterm zone="sql-createaggregate">
  <primary>CREATE AGGREGATE</primary>
 </indexterm>

 <refmeta>
  <refentrytitle>CREATE AGGREGATE</refentrytitle>
  <manvolnum>7</manvolnum>
  <refmiscinfo>SQL - Language Statements</refmiscinfo>
 </refmeta>

 <refnamediv>
  <refname>CREATE AGGREGATE</refname>
  <refpurpose>define a new aggregate function</refpurpose>
 </refnamediv>

 <refsynopsisdiv>
<synopsis>
CREATE AGGREGATE <replaceable class="parameter">name</replaceable> ( [ <replaceable class="parameter">argmode</replaceable> ] [ <replaceable class="parameter">argname</replaceable> ] <replaceable class="parameter">arg_data_type</replaceable> [ , ... ] ) (
    SFUNC = <replaceable class="PARAMETER">sfunc</replaceable>,
    STYPE = <replaceable class="PARAMETER">state_data_type</replaceable>
    [ , SSPACE = <replaceable class="PARAMETER">state_data_size</replaceable> ]
    [ , FINALFUNC = <replaceable class="PARAMETER">ffunc</replaceable> ]
    [ , FINALFUNC_EXTRA ]
    [ , COMBINEFUNC = <replaceable class="PARAMETER">combinefunc</replaceable> ]
    [ , SERIALFUNC = <replaceable class="PARAMETER">serialfunc</replaceable> ]
    [ , DESERIALFUNC = <replaceable class="PARAMETER">deserialfunc</replaceable> ]
    [ , SERIALTYPE = <replaceable class="PARAMETER">serialtype</replaceable> ]
    [ , INITCOND = <replaceable class="PARAMETER">initial_condition</replaceable> ]
    [ , MSFUNC = <replaceable class="PARAMETER">msfunc</replaceable> ]
    [ , MINVFUNC = <replaceable class="PARAMETER">minvfunc</replaceable> ]
    [ , MSTYPE = <replaceable class="PARAMETER">mstate_data_type</replaceable> ]
    [ , MSSPACE = <replaceable class="PARAMETER">mstate_data_size</replaceable> ]
    [ , MFINALFUNC = <replaceable class="PARAMETER">mffunc</replaceable> ]
    [ , MFINALFUNC_EXTRA ]
    [ , MINITCOND = <replaceable class="PARAMETER">minitial_condition</replaceable> ]
    [ , SORTOP = <replaceable class="PARAMETER">sort_operator</replaceable> ]
)

CREATE AGGREGATE <replaceable class="parameter">name</replaceable> ( [ [ <replaceable class="parameter">argmode</replaceable> ] [ <replaceable class="parameter">argname</replaceable> ] <replaceable class="parameter">arg_data_type</replaceable> [ , ... ] ]
                        ORDER BY [ <replaceable class="parameter">argmode</replaceable> ] [ <replaceable class="parameter">argname</replaceable> ] <replaceable class="parameter">arg_data_type</replaceable> [ , ... ] ) (
    SFUNC = <replaceable class="PARAMETER">sfunc</replaceable>,
    STYPE = <replaceable class="PARAMETER">state_data_type</replaceable>
    [ , SSPACE = <replaceable class="PARAMETER">state_data_size</replaceable> ]
    [ , FINALFUNC = <replaceable class="PARAMETER">ffunc</replaceable> ]
    [ , FINALFUNC_EXTRA ]
    [ , COMBINEFUNC = <replaceable class="PARAMETER">combinefunc</replaceable> ]
    [ , SERIALFUNC = <replaceable class="PARAMETER">serialfunc</replaceable> ]
    [ , DESERIALFUNC = <replaceable class="PARAMETER">deserialfunc</replaceable> ]
    [ , SERIALTYPE = <replaceable class="PARAMETER">serialtype</replaceable> ]
    [ , INITCOND = <replaceable class="PARAMETER">initial_condition</replaceable> ]
    [ , HYPOTHETICAL ]
)

<phrase>or the old syntax</phrase>

CREATE AGGREGATE <replaceable class="PARAMETER">name</replaceable> (
    BASETYPE = <replaceable class="PARAMETER">base_type</replaceable>,
    SFUNC = <replaceable class="PARAMETER">sfunc</replaceable>,
    STYPE = <replaceable class="PARAMETER">state_data_type</replaceable>
    [ , SSPACE = <replaceable class="PARAMETER">state_data_size</replaceable> ]
    [ , FINALFUNC = <replaceable class="PARAMETER">ffunc</replaceable> ]
    [ , FINALFUNC_EXTRA ]
    [ , COMBINEFUNC = <replaceable class="PARAMETER">combinefunc</replaceable> ]
    [ , SERIALFUNC = <replaceable class="PARAMETER">serialfunc</replaceable> ]
    [ , DESERIALFUNC = <replaceable class="PARAMETER">deserialfunc</replaceable> ]
    [ , SERIALTYPE = <replaceable class="PARAMETER">serialtype</replaceable> ]
    [ , INITCOND = <replaceable class="PARAMETER">initial_condition</replaceable> ]
    [ , MSFUNC = <replaceable class="PARAMETER">msfunc</replaceable> ]
    [ , MINVFUNC = <replaceable class="PARAMETER">minvfunc</replaceable> ]
    [ , MSTYPE = <replaceable class="PARAMETER">mstate_data_type</replaceable> ]
    [ , MSSPACE = <replaceable class="PARAMETER">mstate_data_size</replaceable> ]
    [ , MFINALFUNC = <replaceable class="PARAMETER">mffunc</replaceable> ]
    [ , MFINALFUNC_EXTRA ]
    [ , MINITCOND = <replaceable class="PARAMETER">minitial_condition</replaceable> ]
    [ , SORTOP = <replaceable class="PARAMETER">sort_operator</replaceable> ]
)
</synopsis>
 </refsynopsisdiv>

 <refsect1>
  <title>Description</title>

  <para>
   <command>CREATE AGGREGATE</command> defines a new aggregate
   function. Some basic and commonly-used aggregate functions are
   included with the distribution; they are documented in <xref
   linkend="functions-aggregate">. If one defines new types or needs
   an aggregate function not already provided, then <command>CREATE
   AGGREGATE</command> can be used to provide the desired features.
  </para>

  <para>
   If a schema name is given (for example, <literal>CREATE AGGREGATE
   myschema.myagg ...</>) then the aggregate function is created in the
   specified schema.  Otherwise it is created in the current schema.
  </para>

  <para>
   An aggregate function is identified by its name and input data type(s).
   Two aggregates in the same schema can have the same name if they operate on
   different input types.  The
   name and input data type(s) of an aggregate must also be distinct from
   the name and input data type(s) of every ordinary function in the same
   schema.
   This behavior is identical to overloading of ordinary function names
   (see <xref linkend="sql-createfunction">).
  </para>

  <para>
   A simple aggregate function is made from one or two ordinary
   functions:
   a state transition function
   <replaceable class="PARAMETER">sfunc</replaceable>,
   and an optional final calculation function
   <replaceable class="PARAMETER">ffunc</replaceable>.
   These are used as follows:
<programlisting>
<replaceable class="PARAMETER">sfunc</replaceable>( internal-state, next-data-values ) ---> next-internal-state
<replaceable class="PARAMETER">ffunc</replaceable>( internal-state ) ---> aggregate-value
</programlisting>
  </para>

  <para>
   <productname>PostgreSQL</productname> creates a temporary variable
   of data type <replaceable class="PARAMETER">stype</replaceable>
   to hold the current internal state of the aggregate.  At each input row,
   the aggregate argument value(s) are calculated and
   the state transition function is invoked with the current state value
   and the new argument value(s) to calculate a new
   internal state value.  After all the rows have been processed,
   the final function is invoked once to calculate the aggregate's return
   value.  If there is no final function then the ending state value
   is returned as-is.
  </para>

  <para>
   An aggregate function can provide an initial condition,
   that is, an initial value for the internal state value.
   This is specified and stored in the database as a value of type
   <type>text</type>, but it must be a valid external representation
   of a constant of the state value data type.  If it is not supplied
   then the state value starts out null.
  </para>

  <para>
   If the state transition function is declared <quote>strict</quote>,
   then it cannot be called with null inputs.  With such a transition
   function, aggregate execution behaves as follows.  Rows with any null input
   values are ignored (the function is not called and the previous state value
   is retained).  If the initial state value is null, then at the first row
   with all-nonnull input values, the first argument value replaces the state
   value, and the transition function is invoked at each subsequent row with
   all-nonnull input values.
   This is handy for implementing aggregates like <function>max</function>.
   Note that this behavior is only available when
   <replaceable class="PARAMETER">state_data_type</replaceable>
   is the same as the first
   <replaceable class="PARAMETER">arg_data_type</replaceable>.
   When these types are different, you must supply a nonnull initial
   condition or use a nonstrict transition function.
  </para>

  <para>
   If the state transition function is not strict, then it will be called
   unconditionally at each input row, and must deal with null inputs
   and null state values for itself.  This allows the aggregate
   author to have full control over the aggregate's handling of null values.
  </para>

  <para>
   If the final function is declared <quote>strict</quote>, then it will not
   be called when the ending state value is null; instead a null result
   will be returned automatically.  (Of course this is just the normal
   behavior of strict functions.)  In any case the final function has
   the option of returning a null value.  For example, the final function for
   <function>avg</function> returns null when it sees there were zero
   input rows.
  </para>

  <para>
   Sometimes it is useful to declare the final function as taking not just
   the state value, but extra parameters corresponding to the aggregate's
   input values.  The main reason for doing this is if the final function
   is polymorphic and the state value's data type would be inadequate to
   pin down the result type.  These extra parameters are always passed as
   NULL (and so the final function must not be strict when
   the <literal>FINALFUNC_EXTRA</> option is used), but nonetheless they
   are valid parameters.  The final function could for example make use
   of <function>get_fn_expr_argtype</> to identify the actual argument type
   in the current call.
  </para>

  <para>
   An aggregate can optionally support <firstterm>moving-aggregate mode</>,
   as described in <xref linkend="xaggr-moving-aggregates">.  This requires
   specifying the <literal>MSFUNC</>, <literal>MINVFUNC</>,
   and <literal>MSTYPE</> parameters, and optionally
   the <literal>MSPACE</>, <literal>MFINALFUNC</>, <literal>MFINALFUNC_EXTRA</>,
   and <literal>MINITCOND</> parameters.  Except for <literal>MINVFUNC</>,
   these parameters work like the corresponding simple-aggregate parameters
   without <literal>M</>; they define a separate implementation of the
   aggregate that includes an inverse transition function.
  </para>

  <para>
   The syntax with <literal>ORDER BY</literal> in the parameter list creates
   a special type of aggregate called an <firstterm>ordered-set
   aggregate</firstterm>; or if <literal>HYPOTHETICAL</> is specified, then
   a <firstterm>hypothetical-set aggregate</firstterm> is created.  These
   aggregates operate over groups of sorted values in order-dependent ways,
   so that specification of an input sort order is an essential part of a
   call.  Also, they can have <firstterm>direct</> arguments, which are
   arguments that are evaluated only once per aggregation rather than once
   per input row.  Hypothetical-set aggregates are a subclass of ordered-set
   aggregates in which some of the direct arguments are required to match,
   in number and data types, the aggregated argument columns.  This allows
   the values of those direct arguments to be added to the collection of
   aggregate-input rows as an additional <quote>hypothetical</> row.
  </para>

  <para>
   Aggregates that behave like <function>MIN</> or <function>MAX</> can
   sometimes be optimized by looking into an index instead of scanning every
   input row.  If this aggregate can be so optimized, indicate it by
   specifying a <firstterm>sort operator</>.  The basic requirement is that
   the aggregate must yield the first element in the sort ordering induced by
   the operator; in other words:
<programlisting>
SELECT agg(col) FROM tab;
</programlisting>
   must be equivalent to:
<programlisting>
SELECT col FROM tab ORDER BY col USING sortop LIMIT 1;
</programlisting>
   Further assumptions are that the aggregate ignores null inputs, and that
   it delivers a null result if and only if there were no non-null inputs.
   Ordinarily, a data type's <literal>&lt;</> operator is the proper sort
   operator for <function>MIN</>, and <literal>&gt;</> is the proper sort
   operator for <function>MAX</>.  Note that the optimization will never
   actually take effect unless the specified operator is the <quote>less
   than</quote> or <quote>greater than</quote> strategy member of a B-tree
   index operator class.
  </para>

  <para>
   To be able to create an aggregate function, you must
   have <literal>USAGE</literal> privilege on the argument types, the state
   type(s), and the return type, as well as <literal>EXECUTE</literal>
   privilege on the transition and final functions.
  </para>
 </refsect1>

 <refsect1>
  <title>Parameters</title>

  <variablelist>
   <varlistentry>
    <term><replaceable class="PARAMETER">name</replaceable></term>
    <listitem>
     <para>
      The name (optionally schema-qualified) of the aggregate function
      to create.
     </para>
    </listitem>
   </varlistentry>

   <varlistentry>
    <term><replaceable class="parameter">argmode</replaceable></term>

    <listitem>
     <para>
      The mode of an argument: <literal>IN</> or <literal>VARIADIC</>.
      (Aggregate functions do not support <literal>OUT</> arguments.)
      If omitted, the default is <literal>IN</>.  Only the last argument
      can be marked <literal>VARIADIC</>.
     </para>
    </listitem>
   </varlistentry>

   <varlistentry>
    <term><replaceable class="parameter">argname</replaceable></term>

    <listitem>
     <para>
      The name of an argument.  This is currently only useful for
      documentation purposes.  If omitted, the argument has no name.
     </para>
    </listitem>
   </varlistentry>

   <varlistentry>
    <term><replaceable class="PARAMETER">arg_data_type</replaceable></term>
    <listitem>
     <para>
      An input data type on which this aggregate function operates.
      To create a zero-argument aggregate function, write <literal>*</>
      in place of the list of argument specifications.  (An example of such an
      aggregate is <function>count(*)</function>.)
     </para>
    </listitem>
   </varlistentry>

   <varlistentry>
    <term><replaceable class="PARAMETER">base_type</replaceable></term>
    <listitem>
     <para>
      In the old syntax for <command>CREATE AGGREGATE</>, the input data type
      is specified by a <literal>basetype</> parameter rather than being
      written next to the aggregate name.  Note that this syntax allows
      only one input parameter.  To define a zero-argument aggregate function
      with this syntax, specify the <literal>basetype</> as
      <literal>"ANY"</> (not <literal>*</>).
      Ordered-set aggregates cannot be defined with the old syntax.
     </para>
    </listitem>
   </varlistentry>

   <varlistentry>
    <term><replaceable class="PARAMETER">sfunc</replaceable></term>
    <listitem>
     <para>
      The name of the state transition function to be called for each
      input row.  For a normal <replaceable class="PARAMETER">N</>-argument
      aggregate function, the <replaceable class="PARAMETER">sfunc</>
      must take <replaceable class="PARAMETER">N</>+1 arguments,
      the first being of type <replaceable
      class="PARAMETER">state_data_type</replaceable> and the rest
      matching the declared input data type(s) of the aggregate.
      The function must return a value of type <replaceable
      class="PARAMETER">state_data_type</replaceable>.  This function
      takes the current state value and the current input data value(s),
      and returns the next state value.
     </para>

     <para>
      For ordered-set (including hypothetical-set) aggregates, the state
      transition function receives only the current state value and the
      aggregated arguments, not the direct arguments.  Otherwise it is the
      same.
     </para>
    </listitem>
   </varlistentry>

   <varlistentry>
    <term><replaceable class="PARAMETER">state_data_type</replaceable></term>
    <listitem>
     <para>
      The data type for the aggregate's state value.
     </para>
    </listitem>
   </varlistentry>

   <varlistentry>
    <term><replaceable class="PARAMETER">state_data_size</replaceable></term>
    <listitem>
     <para>
      The approximate average size (in bytes) of the aggregate's state value.
      If this parameter is omitted or is zero, a default estimate is used
      based on the <replaceable>state_data_type</>.
      The planner uses this value to estimate the memory required for a
      grouped aggregate query.  The planner will consider using hash
      aggregation for such a query only if the hash table is estimated to fit
      in <xref linkend="guc-work-mem">; therefore, large values of this
      parameter discourage use of hash aggregation.
     </para>
    </listitem>
   </varlistentry>

   <varlistentry>
    <term><replaceable class="PARAMETER">ffunc</replaceable></term>
    <listitem>
     <para>
      The name of the final function called to compute the aggregate's
      result after all input rows have been traversed.
      For a normal aggregate, this function
      must take a single argument of type <replaceable
      class="PARAMETER">state_data_type</replaceable>.  The return
      data type of the aggregate is defined as the return type of this
      function.  If <replaceable class="PARAMETER">ffunc</replaceable>
      is not specified, then the ending state value is used as the
      aggregate's result, and the return type is <replaceable
      class="PARAMETER">state_data_type</replaceable>.
     </para>

     <para>
      For ordered-set (including hypothetical-set) aggregates, the
      final function receives not only the final state value,
      but also the values of all the direct arguments.
     </para>

     <para>
      If <literal>FINALFUNC_EXTRA</> is specified, then in addition to the
      final state value and any direct arguments, the final function
      receives extra NULL values corresponding to the aggregate's regular
      (aggregated) arguments.  This is mainly useful to allow correct
      resolution of the aggregate result type when a polymorphic aggregate
      is being defined.
     </para>
    </listitem>
   </varlistentry>

   <varlistentry>
    <term><replaceable class="PARAMETER">combinefunc</replaceable></term>
    <listitem>
     <para>
      The <replaceable class="PARAMETER">combinefunc</replaceable> may
      optionally be specified in order to allow the aggregate function to
      support partial aggregation. This is a prerequisite to allow the
      aggregate to participate in certain optimizations such as parallel
      aggregation.
     </para>

     <para>
      This function can be thought of as an <replaceable class="PARAMETER">
      sfunc</replaceable>, where instead of acting upon individual input rows
      and adding these to the aggregate state, it adds other aggregate states
      to the aggregate state.
     </para>

     <para>
      The <replaceable class="PARAMETER">combinefunc</replaceable> must accept
      two arguments of <replaceable class="PARAMETER">state_data_type
      </replaceable> and return <replaceable class="PARAMETER">state_data_type
      </replaceable>. Optionally this function may be <quote>strict</quote>. In
      this case the function will not be called when either of the input states
      are null.
     </para>
 
     <para>
      For aggregate functions with an <literal>INTERNAL</literal>
      <replaceable class="PARAMETER">state_data_type</replaceable> the
      <replaceable class="PARAMETER">combinefunc</replaceable> must not be
      <quote>strict</quote>. In this scenario the
      <replaceable class="PARAMETER">combinefunc</replaceable> must take charge
      and ensure that the null states are handled correctly and that the state
      being returned is a pointer to memory which belongs in the aggregate
      memory context.
     </para>
    </listitem>
   </varlistentry>

   <varlistentry>
    <term><replaceable class="PARAMETER">serialfunc</replaceable></term>
    <listitem>
     <para>
      In order to allow aggregate functions with an <literal>INTERNAL</>
      <replaceable class="PARAMETER">state_data_type</replaceable> to
      participate in parallel aggregation, the aggregate must have a valid
      <replaceable class="PARAMETER">serialfunc</replaceable>, which must
      serialize the aggregate state into <replaceable class="PARAMETER">
      serialtype</replaceable>. This function must take a single argument of
      <replaceable class="PARAMETER">state_data_type</replaceable> and return
      <replaceable class="PARAMETER">serialtype</replaceable>. A
      corresponding <replaceable class="PARAMETER">deserialfunc</replaceable>
      is also required.
     </para>
    </listitem>
   </varlistentry>

   <varlistentry>
    <term><replaceable class="PARAMETER">deserialfunc</replaceable></term>
    <listitem>
     <para>
      Deserializes a previously serialized aggregate state back into
      <replaceable class="PARAMETER">state_data_type</replaceable>. This
      function must take a single argument of <replaceable class="PARAMETER">
      serialtype</replaceable> and return <replaceable class="PARAMETER">
      state_data_type</replaceable>.
     </para>
    </listitem>
   </varlistentry>

   <varlistentry>
    <term><replaceable class="PARAMETER">serialtype</replaceable></term>
    <listitem>
     <para>
      The data type to into which an <literal>INTERNAL</literal> aggregate
      state should be serialized.
     </para>
    </listitem>
   </varlistentry>

   <varlistentry>
    <term><replaceable class="PARAMETER">initial_condition</replaceable></term>
    <listitem>
     <para>
      The initial setting for the state value.  This must be a string
      constant in the form accepted for the data type <replaceable
      class="PARAMETER">state_data_type</replaceable>.  If not
      specified, the state value starts out null.
     </para>
    </listitem>
   </varlistentry>

   <varlistentry>
    <term><replaceable class="PARAMETER">msfunc</replaceable></term>
    <listitem>
     <para>
      The name of the forward state transition function to be called for each
      input row in moving-aggregate mode.  This is exactly like the regular
      transition function, except that its first argument and result are of
      type <replaceable>mstate_data_type</>, which might be different
      from <replaceable>state_data_type</>.
     </para>
    </listitem>
   </varlistentry>

   <varlistentry>
    <term><replaceable class="PARAMETER">minvfunc</replaceable></term>
    <listitem>
     <para>
      The name of the inverse state transition function to be used in
      moving-aggregate mode.  This function has the same argument and
      result types as <replaceable>msfunc</>, but it is used to remove
      a value from the current aggregate state, rather than add a value to
      it.  The inverse transition function must have the same strictness
      attribute as the forward state transition function.
     </para>
    </listitem>
   </varlistentry>

   <varlistentry>
    <term><replaceable class="PARAMETER">mstate_data_type</replaceable></term>
    <listitem>
     <para>
      The data type for the aggregate's state value, when using
      moving-aggregate mode.
     </para>
    </listitem>
   </varlistentry>

   <varlistentry>
    <term><replaceable class="PARAMETER">mstate_data_size</replaceable></term>
    <listitem>
     <para>
      The approximate average size (in bytes) of the aggregate's state
      value, when using moving-aggregate mode.  This works the same as
      <replaceable>state_data_size</>.
     </para>
    </listitem>
   </varlistentry>

   <varlistentry>
    <term><replaceable class="PARAMETER">mffunc</replaceable></term>
    <listitem>
     <para>
      The name of the final function called to compute the aggregate's
      result after all input rows have been traversed, when using
      moving-aggregate mode.  This works the same as <replaceable>ffunc</>,
      except that its first argument's type
      is <replaceable>mstate_data_type</> and extra dummy arguments are
      specified by writing <literal>MFINALFUNC_EXTRA</>.
      The aggregate result type determined by <replaceable>mffunc</>
      or <replaceable>mstate_data_type</> must match that determined by the
      aggregate's regular implementation.
     </para>
    </listitem>
   </varlistentry>

   <varlistentry>
    <term><replaceable class="PARAMETER">minitial_condition</replaceable></term>
    <listitem>
     <para>
      The initial setting for the state value, when using moving-aggregate
      mode.  This works the same as <replaceable>initial_condition</>.
     </para>
    </listitem>
   </varlistentry>

   <varlistentry>
    <term><replaceable class="PARAMETER">sort_operator</replaceable></term>
    <listitem>
     <para>
      The associated sort operator for a <function>MIN</>- or
      <function>MAX</>-like aggregate.
      This is just an operator name (possibly schema-qualified).
      The operator is assumed to have the same input data types as
      the aggregate (which must be a single-argument normal aggregate).
     </para>
    </listitem>
   </varlistentry>

   <varlistentry>
    <term><literal>HYPOTHETICAL</literal></term>
    <listitem>
     <para>
      For ordered-set aggregates only, this flag specifies that the aggregate
      arguments are to be processed according to the requirements for
      hypothetical-set aggregates: that is, the last few direct arguments must
      match the data types of the aggregated (<literal>WITHIN GROUP</>)
      arguments.  The <literal>HYPOTHETICAL</literal> flag has no effect on
      run-time behavior, only on parse-time resolution of the data types and
      collations of the aggregate's arguments.
     </para>
    </listitem>
   </varlistentry>
  </variablelist>

  <para>
   The parameters of <command>CREATE AGGREGATE</command> can be
   written in any order, not just the order illustrated above.
  </para>
 </refsect1>

 <refsect1>
  <title>Notes</title>

   <para>
    In parameters that specify support function names, you can write
    a schema name if needed, for example <literal>SFUNC = public.sum</>.
    Do not write argument types there, however &mdash; the argument types
    of the support functions are determined from other parameters.
   </para>

   <para>
    If an aggregate supports moving-aggregate mode, it will improve
    calculation efficiency when the aggregate is used as a window function
    for a window with moving frame start (that is, a frame start mode other
    than <literal>UNBOUNDED PRECEDING</>).  Conceptually, the forward
    transition function adds input values to the aggregate's state when
    they enter the window frame from the bottom, and the inverse transition
    function removes them again when they leave the frame at the top.  So,
    when values are removed, they are always removed in the same order they
    were added.  Whenever the inverse transition function is invoked, it will
    thus receive the earliest added but not yet removed argument value(s).
    The inverse transition function can assume that at least one row will
    remain in the current state after it removes the oldest row.  (When this
    would not be the case, the window function mechanism simply starts a
    fresh aggregation, rather than using the inverse transition function.)
   </para>

   <para>
    The forward transition function for moving-aggregate mode is not
    allowed to return NULL as the new state value. If the inverse
    transition function returns NULL, this is taken as an indication that
    the inverse function cannot reverse the state calculation for this
    particular input, and so the aggregate calculation will be redone from
    scratch for the current frame starting position.  This convention
    allows moving-aggregate mode to be used in situations where there are
    some infrequent cases that are impractical to reverse out of the
    running state value.
   </para>

   <para>
    If no moving-aggregate implementation is supplied,
    the aggregate can still be used with moving frames,
    but <productname>PostgreSQL</productname> will recompute the whole
    aggregation whenever the start of the frame moves.
    Note that whether or not the aggregate supports moving-aggregate
    mode, <productname>PostgreSQL</productname> can handle a moving frame
    end without recalculation; this is done by continuing to add new values
    to the aggregate's state.  It is assumed that the final function does
    not damage the aggregate's state value, so that the aggregation can be
    continued even after an aggregate result value has been obtained for
    one set of frame boundaries.
   </para>

   <para>
    The syntax for ordered-set aggregates allows <literal>VARIADIC</>
    to be specified for both the last direct parameter and the last
    aggregated (<literal>WITHIN GROUP</>) parameter.  However, the
    current implementation restricts use of <literal>VARIADIC</>
    in two ways.  First, ordered-set aggregates can only use
    <literal>VARIADIC "any"</>, not other variadic array types.
    Second, if the last direct parameter is <literal>VARIADIC "any"</>,
    then there can be only one aggregated parameter and it must also
    be <literal>VARIADIC "any"</>.  (In the representation used in the
    system catalogs, these two parameters are merged into a single
    <literal>VARIADIC "any"</> item, since <structname>pg_proc</> cannot
    represent functions with more than one <literal>VARIADIC</> parameter.)
    If the aggregate is a hypothetical-set aggregate, the direct arguments
    that match the <literal>VARIADIC "any"</> parameter are the hypothetical
    ones; any preceding parameters represent additional direct arguments
    that are not constrained to match the aggregated arguments.
   </para>

   <para>
    Currently, ordered-set aggregates do not need to support
    moving-aggregate mode, since they cannot be used as window functions.
   </para>
 </refsect1>

 <refsect1>
  <title>Examples</title>

  <para>
   See <xref linkend="xaggr">.
  </para>
 </refsect1>

 <refsect1>
  <title>Compatibility</title>

  <para>
   <command>CREATE AGGREGATE</command> is a
   <productname>PostgreSQL</productname> language extension.  The SQL
   standard does not provide for user-defined aggregate functions.
  </para>
 </refsect1>

 <refsect1>
  <title>See Also</title>

  <simplelist type="inline">
   <member><xref linkend="sql-alteraggregate"></member>
   <member><xref linkend="sql-dropaggregate"></member>
  </simplelist>
 </refsect1>
</refentry>
