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 <chapter id="xaggr">
  <title>Extending <acronym>SQL</acronym>: 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 output 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 input 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 input 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 is:
   
<programlisting>
CREATE AGGREGATE complex_sum (
    sfunc = complex_add,
    basetype = complex,
    stype = complex,
    initcond = '(0,0)'
);
</programlisting>

<screen>
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 non-null 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's sufficient to insert the first non-null input value into
   the state variable and then start applying the transition function
   at the second non-null 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 define your transition
   function as non-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 transition 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>
 </chapter>

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