Aggregate functions in Postgres are expressed as state values and state transition functions. 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 datatype 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.
Actually, in order to make it easier to construct useful aggregates from existing functions, an aggregate can have one or two separate state values, one or two transition functions to update those state values, and a final function that computes the actual aggregate result from the ending state values.
Thus there can be as many as four datatypes involved: the type of the input data items, the type of the aggregate's result, and the types of the two state values. Only the input and result datatypes are seen by a user of the aggregate.
Some state transition functions need to look at each successive input to compute the next state value, while others ignore the specific input value and simply update their internal state. (The most useful example of the second kind is a running count of the number of input items.) The Postgres aggregate machinery defines sfunc1 for an aggregate as a function that is passed both the old state value and the current input value, while sfunc2 is a function that is passed only the old state value.
If we define an aggregate that uses only sfunc1, we have an aggregate that computes a running function of the attribute values from each instance. "Sum" is an example of this kind of aggregate. "Sum" starts at zero and always adds the current instance's value to its running total. For example, if we want to make a Sum aggregate to work on a datatype for complex numbers, we only need the addition function for that datatype. The aggregate definition is:
CREATE AGGREGATE complex_sum (
sfunc1 = complex_add,
basetype = complex,
stype1 = complex,
initcond1 = '(0,0)'
);
SELECT complex_sum(a) FROM test_complex;
+------------+
|complex_sum |
+------------+
|(34,53.9) |
+------------+
(In practice, we'd just name the aggregate "sum", and rely on
Postgres to figure out which kind
of sum to apply to a complex column.)
If we define only sfunc2, we are specifying an aggregate that computes a running function that is independent of the attribute values from each instance. "Count" is the most common example of this kind of aggregate. "Count" starts at zero and adds one to its running total for each instance, ignoring the instance value. Here, we use the built-in int4inc routine to do the work for us. This routine increments (adds one to) its argument.
CREATE AGGREGATE my_count (
sfunc2 = int4inc, -- add one
basetype = int4,
stype2 = int4,
initcond2 = '0'
);
SELECT my_count(*) as emp_count from EMP;
+----------+
|emp_count |
+----------+
|5 |
+----------+
"Average" is an example of an aggregate that requires both a function to compute the running sum and a function to compute the running count. When all of the instances have been processed, the final answer for the aggregate is the running sum divided by the running count. We use the int4pl and int4inc routines we used before as well as the Postgres integer division routine, int4div, to compute the division of the sum by the count.
CREATE AGGREGATE my_average (
sfunc1 = int4pl, -- sum
basetype = int4,
stype1 = int4,
sfunc2 = int4inc, -- count
stype2 = int4,
finalfunc = int4div, -- division
initcond1 = '0',
initcond2 = '0'
);
SELECT my_average(salary) as emp_average FROM EMP;
+------------+
|emp_average |
+------------+
|1640 |
+------------+
For further details see CREATE AGGREGATE in The PostgreSQL User's Guide.