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 <sect1 id="xaggr">
  <title>User-Defined Aggregates</title>

  <indexterm zone="xaggr">
   <primary>aggregate functions</primary>
   <secondary>extending</secondary>
  </indexterm>

  <para>
   Aggregate functions  in <productname>PostgreSQL</productname> 
   are expressed as <firstterm>state values</firstterm>
   and <firstterm>state transition functions</firstterm>.
   That is,  an  aggregate  can  be
   defined  in terms of state that is modified whenever an
   input item is processed.  To define a new aggregate
   function, one selects a data type for the state value,
   an initial value for the state, and a state transition
   function.  The state transition function is just an
   ordinary function that could also be used outside the
   context of the aggregate.  A <firstterm>final function</firstterm>
   can also be specified, in case the desired result of the aggregate
   is different from the data that needs to be kept in the running
   state value.
  </para>

  <para>
   Thus, in addition to the argument and result data types seen by a user
   of the aggregate, there is an internal state-value data type that
   may be different from both the argument and result types.
  </para>

  <para>
   If we define an aggregate that does not use a final function,
   we have an aggregate that computes a running function of
   the column values from each row.  <function>sum</>  is  an
   example  of  this  kind  of aggregate.  <function>sum</> starts at
   zero and always adds the current  row's  value  to
   its  running  total.  For example, if we want to make a <function>sum</>
   aggregate to work on a data type for complex numbers,
   we only need the addition function for that data type.
   The aggregate definition would be:
   
<screen>
CREATE AGGREGATE complex_sum (
    sfunc = complex_add,
    basetype = complex,
    stype = complex,
    initcond = '(0,0)'
);

SELECT complex_sum(a) FROM test_complex;

 complex_sum
-------------
 (34,53.9)
</screen>

   (In practice, we'd just name the aggregate <function>sum</function> and rely on
   <productname>PostgreSQL</productname> to figure out which kind
   of sum to apply to a column of type <type>complex</type>.)
  </para>

  <para>
   The above definition of <function>sum</function> will return zero (the initial
   state condition) if there are no nonnull input values.
   Perhaps we want to return null in that case instead --- the SQL standard
   expects <function>sum</function> to behave that way.  We can do this simply by
   omitting the <literal>initcond</literal> phrase, so that the initial state
   condition is null.  Ordinarily this would mean that the <literal>sfunc</literal>
   would need to check for a null state-condition input, but for
   <function>sum</function> and some other simple aggregates like <function>max</> and <function>min</>,
   it would be sufficient to insert the first nonnull input value into
   the state variable and then start applying the transition function
   at the second nonnull input value.  <productname>PostgreSQL</productname>
   will do that automatically if the initial condition is null and
   the transition function is marked <quote>strict</> (i.e., not to be called
   for null inputs).
  </para>
  
  <para>
   Another bit of default behavior for a <quote>strict</> transition function
   is that the previous state value is retained unchanged whenever a
   null input value is encountered.  Thus, null values are ignored.  If you
   need some other behavior for null inputs, just do not define your transition
   function as strict, and code it to test for null inputs and do
   whatever is needed.
  </para>
  
  <para>
   <function>avg</> (average) is a more complex example of an aggregate.  It requires
   two pieces of running state: the sum of the inputs and the count
   of the number of inputs.  The final result is obtained by dividing
   these quantities.  Average is typically implemented by using a
   two-element array as the state value.  For example,
   the built-in implementation of <function>avg(float8)</function>
   looks like:

<programlisting>
CREATE AGGREGATE avg (
    sfunc = float8_accum,
    basetype = float8,
    stype = float8[],
    finalfunc = float8_avg,
    initcond = '{0,0}'
);
</programlisting>
  </para>

  <para>
   For further details see the description of the <command>CREATE
   AGGREGATE</command> command in <xref linkend="reference">.
  </para>
 </sect1>

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