PostgreSQL 9.3.2 Documentation
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# 35.10. User-defined Aggregates

Aggregate functions in PostgreSQL are expressed in terms of state values and state transition functions. That is, an aggregate operates using a state value that is updated as each successive input row 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 final function 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.

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 might be different from both the argument and result types.

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. `sum` is an example of this kind of aggregate. `sum` starts at zero and always adds the current row's value to its running total. For example, if we want to make a `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:

    CREATE AGGREGATE sum (complex)
    (
        sfunc = complex_add,
        stype = complex,
        initcond = '(0,0)'
    );

    SELECT sum(a) FROM test_complex;

       sum
    -----------
     (34,53.9)

(Notice that we are relying on function overloading: there is more than one aggregate named `sum`, but PostgreSQL can figure out which kind of sum applies to a column of type `complex`.)

The above definition of `sum` 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 `sum` to behave that way. We can do this simply by omitting the `initcond` phrase, so that the initial state condition is null. Ordinarily this would mean that the `sfunc` would need to check for a null state-condition input. But for `sum` and some other simple aggregates like `max` and `min`, it is 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. PostgreSQL will do that automatically if the initial condition is null and the transition function is marked "strict" (i.e., not to be called for null inputs).

Another bit of default behavior for a "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, do not declare your transition function as strict; instead code it to test for null inputs and do whatever is needed.

`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 an array as the state value. For example, the built-in implementation of `avg(float8)` looks like:

    CREATE AGGREGATE avg (float8)
    (
        sfunc = float8_accum,
        stype = float8[],
        finalfunc = float8_avg,
        initcond = '{0,0,0}'
    );

(`float8_accum` requires a three-element array, not just two elements, because it accumulates the sum of squares as well as the sum and count of the inputs. This is so that it can be used for some other aggregates besides `avg`.)

Aggregate functions can use polymorphic state transition functions or final functions, so that the same functions can be used to implement multiple aggregates. See Section 35.2.5 for an explanation of polymorphic functions. Going a step further, the aggregate function itself can be specified with polymorphic input type(s) and state type, allowing a single aggregate definition to serve for multiple input data types. Here is an example of a polymorphic aggregate:

    CREATE AGGREGATE array_accum (anyelement)
    (
        sfunc = array_append,
        stype = anyarray,
        initcond = '{}'
    );

Here, the actual state type for any aggregate call is the array type having the actual input type as elements. The behavior of the aggregate is to concatenate all the inputs into an array of that type. (Note: the built-in aggregate `array_agg` provides similar functionality, with better performance than this definition would have.)

Here's the output using two different actual data types as arguments:

    SELECT attrelid::regclass, array_accum(attname)
        FROM pg_attribute
        WHERE attnum > 0 AND attrelid = 'pg_tablespace'::regclass
        GROUP BY attrelid;

       attrelid    |              array_accum
    ---------------+---------------------------------------
     pg_tablespace | {spcname,spcowner,spcacl,spcoptions}
    (1 row)

    SELECT attrelid::regclass, array_accum(atttypid::regtype)
        FROM pg_attribute
        WHERE attnum > 0 AND attrelid = 'pg_tablespace'::regclass
        GROUP BY attrelid;

       attrelid    |        array_accum
    ---------------+---------------------------
     pg_tablespace | {name,oid,aclitem[],text[]}
    (1 row)

A function written in C can detect that it is being called as an aggregate transition or final function by calling `AggCheckCallContext`, for example:

    if (AggCheckCallContext(fcinfo, NULL))

One reason for checking this is that when it is true for a transition function, the first input must be a temporary transition value and can therefore safely be modified in-place rather than allocating a new copy. See `int8inc()` for an example. (This is the only case where it is safe for a function to modify a pass-by-reference input. In particular, aggregate final functions should not modify their inputs in any case, because in some cases they will be re-executed on the same final transition value.)

For further details see the CREATE AGGREGATE command.

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