11th November 2021:
PostgreSQL 14.1, 13.5, 12.9, 11.14, 10.19, and 9.6.24 Released!

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CREATE AGGREGATEname( BASETYPE =input_data_type, SFUNC =sfunc, STYPE =state_type[ , FINALFUNC =ffunc] [ , INITCOND =initial_condition] )

`name`-
The name of an aggregate function to create.

`input_data_type`-
The input data type on which this aggregate function operates. This can be specified as ANY for an aggregate that does not examine its input values (an example is

`count(*)`). `sfunc`-
The name of the state transition function to be called for each input data value. This is normally a function of two arguments, the first being of type

`state_type`and the second of type`input_data_type`. Alternatively, for an aggregate that does not examine its input values, the function takes just one argument of type`state_type`. In either case the function must return a value of type`state_type`. This function takes the current state value and the current input data item, and returns the next state value. `state_type`-
The data type for the aggregate's state value.

`ffunc`-
The name of the final function called to compute the aggregate's result after all input data has been traversed. The function must take a single argument of type

`state_type`. The output data type of the aggregate is defined as the return type of this function. If`ffunc`is not specified, then the ending state value is used as the aggregate's result, and the output type is`state_type`. `initial_condition`-
The initial setting for the state value. This must be a literal constant in the form accepted for the data type

`state_type`. If not specified, the state value starts out NULL.

**CREATE AGGREGATE** allows a user or
programmer to extend Postgres
functionality by defining new aggregate functions. Some aggregate
functions for base types such as `min(integer)` and `avg(double
precision)` are already provided in the base distribution. If
one defines new types or needs an aggregate function not already
provided, then **CREATE AGGREGATE** can be
used to provide the desired features.

An aggregate function is identified by its name and input data type. Two aggregates can have the same name if they operate on different input types. To avoid confusion, do not make an ordinary function of the same name and input data type as an aggregate.

An aggregate function is made from one or two ordinary
functions: a state transition function `sfunc`, and an optional final calculation
function `ffunc`. These are used as
follows:

sfunc( internal-state, next-data-item ) ---> next-internal-stateffunc( internal-state ) ---> aggregate-value

Postgres creates a temporary
variable of data type `stype` to
hold the current internal state of the aggregate. At each input
data item, the state transition function is invoked to calculate
a new internal state value. After all the data has been
processed, the final function is invoked once to calculate the
aggregate's output value. If there is no final function then the
ending state value is returned as-is.

An aggregate function may provide an initial condition, that
is, an initial value for the internal state value. This is
specified and stored in the database as a field of type
`text`, 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.

If the state transition function is declared "strict" in
pg_proc, then it cannot be called with NULL inputs. With such a
transition function, aggregate execution behaves as follows. 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 the first non-NULL input value replaces the state
value, and the transition function is invoked beginning with the
second non-NULL input value. This is handy for implementing
aggregates like `max`. Note that this
behavior is only available when `state_type` is the same as `input_data_type`. When these types are
different, you must supply a non-NULL initial condition or use a
non-strict transition function.

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

If the final function is declared "strict", then it will not
be called when the ending state value is NULL; instead a NULL
result will be output automatically. (Of course this is just the
normal behavior of strict functions.) In any case the final
function has the option of returning NULL. For example, the final
function for `avg` returns NULL when it
sees there were zero input tuples.

Refer to the chapter on aggregate functions in the *PostgreSQL Programmer's Guide* for complete
examples of usage.