This manual is for an old version of Hazelcast Jet, use the latest stable version.

The single most important kind of processing Jet does is aggregation. In general it is a transformation of a set of input values into a single output value. The function that does this transformation is called the "aggregate function". A basic example is `sum` applied to a set of integer numbers, but the result can also be a complex value, for example a list of all the input items.

Jet's library contains a range of predefined aggregate functions, but it also exposes an abstraction, called `AggregateOperation`, that allows you to plug in your own. Since Jet does the aggregation in a parallelized and distributed way, you can't simply supply a piece of Java code that does it; we need you to break it down into several smaller pieces that fit into Jet's processing engine.

The ability to compute the aggregate function in parallel comes at a cost: Jet must be able to give a slice of the total data set to each processing unit and then combine the partial results from all the units. The combining step is crucial: it will only make sense if we're combining the partial results of a commutative associative function (CA for short). On the example of `sum` this is trivial: we know from elementary school that `+` is a CA operation. If you have a stream of numbers: `{17, 37, 5, 11, 42}`, you can sum up `{17, 5}` separately from `{42, 11, 37}` and then combine the partial sums (also note the reordering of the elements).

If you need something more complex, like `average`, it doesn't by itself have this property; however if you add one more ingredient, the `finish` function, you can express it easily. Jet allows you to first compute some CA function, whose partial results can be combined, and then at the very end apply the `finish` function on the fully combined result. To compute the `average`, your CA function will output the pair `(sum, count)`. Two such pairs are trivial to combine by summing each component. The `finish` function will be `sum / count`.

In addition to the mathematical side, there is also the practical one: you have to provide Jet with a specific mutable object, called the `accumulator`, which will keep the "running score" of the operation in progress. For the `average` example, it would be something like

``````public class AvgAccumulator {
private long sum;
private long count;

public void accumulate(long value) {
sum += value;
count++;
}

public void combine(AvgAccumulator that) {
this.sum += that.sum;
this.count += that.sum;
}

public double finish() {
return (double) sum / count;
}
}
``````

This object will also have to be serializable, and preferrably with Hazelcast's serialization instead of Java's because in a group-by operation there's one accumulator per each key and all of them have to be sent across the network to be combined and finished.

Instead of requiring you to write a complete class from scratch, Jet separates the concern of holding the accumulated state from that of the computation performed on it. This means that you just need one accumulator class per the kind of structure that holds the accumulated data, as opposed to one per each aggregate operation. Jet's library offers in the `com.hazelcast.jet.accumulator` package several such classes, one of them being `LongLongAccumulator`, which is a match for our `average` function. You'll just have to supply the logic on top of it.

Specifically, you have to provide a set of five functions (we call them "primitives"):

• `create` a new accumulator object.
• `accumulate` the data of an item by mutating the accumulator's state.
• `combine` the contents of the right-hand accumulator into the left-hand one.
• `deduct` the contents of the right-hand accumulator from the left-hand one (undo the effects of `combine`).
• `finish` accumulation by transforming the accumulator object into the final result.

So far we mentioned all of these except for `deduct`. This one is optional and Jet can manage without it, but if you are computing a sliding window over an infinite stream, this primitive can give a significant performance boost because it allows Jet to reuse the results of the previous calculations.

If you happen to have a deeper familiarity with JDK's java.util.stream API, you'll find `AggregateOperation` quite similar to `Collector`, which is also a holder of several functional primitives. Jet's definitions are slightly different, though, and there's also the additional `deduct` primitive.

Let's see how this works with our `average` function. Using `LongLongAccumulator` we can express our `accumulate` primitive as

``````(acc, n) -> {
acc.setValue1(acc.getValue1() + n);
acc.setValue2(acc.getValue2() + 1);
}
``````

The `finish` primitive will be

``````acc -> (double) acc.getValue1() / acc.getValue2()
``````

Now we have to define the other three primitives to match our main logic. For `create` we just refer to the constructor: `LongLongAccumulator::new`. The `combine` primitive expects you to update the left-hand accumulator with the contents of the right-hand one, so:

``````(left, right) -> {
left.setValue1(left.getValue1() + right.getValue1());
left.setValue2(left.getValue2() + right.getValue2());
}
``````

Deducting must undo the effect of a previous `combine`:

``````(left, right) -> {
left.setValue1(left.getValue1() - right.getValue1());
left.setValue2(left.getValue2() - right.getValue2());
}
``````

All put together, we can define our counting operation as follows:

``````AggregateOperation1<Long, LongLongAccumulator, Double> aggrOp = AggregateOperation
.withCreate(LongLongAccumulator::new)
.andAccumulate((acc, n) -> {
acc.setValue1(acc.getValue1() + n);
acc.setValue2(acc.getValue2() + 1);
})
.andCombine((left, right) -> {
left.setValue1(left.getValue1() + right.getValue1());
left.setValue2(left.getValue2() + right.getValue2());
})
.andDeduct((left, right) -> {
left.setValue1(left.getValue1() - right.getValue1());
left.setValue2(left.getValue2() - right.getValue2());
})
.andFinish(acc -> (double) acc.getValue1() / acc.getValue2());
``````

Let's stop for a second to look at the type we got: `AggregateOperation1<Long, LongLongAccumulator, Double>`. Its type parameters are:

1. `Long`: the type of the input item
2. `LongLongAccumulator`: the type of the accumulator
3. `Double`: the type of the result

Specifically note the `1` at the end of the type's name: it signifies that it's the specialization of the general `AggregateOperation` to exactly one input stream. In Hazelcast Jet you can also perform a co-grouping operation, aggregating several input streams together. Since the number of input types is variable, the general `AggregateOperation` type cannot statically capture them and we need separate subtypes. We decided to statically support up to three input types; if you need more, you'll have to resort to the less typesafe, general `AggregateOperation`.

Let us now study a use case that calls for co-grouping. We are interested in the behavior of users in an online shop application and want to gather the following statistics for each user:

1. total load time of the visited product pages
2. quantity of items added to the shopping cart
3. amount paid for bought items

This data is dispersed among separate datasets: `PageVisit`, `AddToCart` and `Payment`. Note that in each case we're dealing with a simple `sum` applied to a field in the input item. We can perform a co-group transform with the following aggregate operation:

``````AggregateOperation3<PageVisit, AddToCart, Payment, LongAccumulator[], long[]> aggrOp =
AggregateOperation
.withCreate(() -> Stream.generate(LongAccumulator::new)
.limit(3)
.toArray(LongAccumulator[]::new))
Note how we got an `AggregateOperation3` and how it captured each input type. When we use it as an argument to a co-group transform, the compiler will ensure that the `ComputeStage`s we attach it to have the correct type and are in the correct order.
On the other hand, if you use the co-group builder object, you'll construct the aggregate operation by calling `andAccumulate(tag, accFn)` with all the tags you got from the co-group builder, and the static type will be just `AggregateOperation`. The compiler won't be able to match up the inputs to their treatment in the aggregate operation.