forall-loops: data-parallel loops

The forall-loop is Chapel's central concept for expressing data parallelism. Forall-loops are similar to coforall-loops in that both are parallel variants of Chapel's for-loop. However, where a coforall-loop creates a concurrent task per iteration and a for-loop is executed serially by a single task, a forall-loop may use an arbitrary number of tasks to execute the loop. As a result, it may execute serially using a single task, or it can use any number of tasks up to the number of iterations (or even beyond, though that is unusual).

More specifically, the actual number of tasks used to execute a forall-loop is determined by its iterand expressions. The iterands specify parallel iterators, either directly or via expressions whose types support default parallel iterator methods (ranges, domains, and arrays being key examples). These iterators typically select the number of tasks to use based on dynamic information such as the size of the loop and/or the number of available processors. In addition to specifying the degree of concurrency to use, parallel iterators also determine where their tasks run and how the loop's iterations will be divided between them. These choices are referred to as the scheduling policy for the loop.

In practice, the default parallel iterators for many expressions create a number of tasks proportional to the amount of system parallelism that they are targeting. For example, by default a local forall loop will typically create a number of tasks equal to the number of processor cores available on its compute node. In contrast, a forall loop over a distributed array will typically create a task per core across all of the compute nodes to which the array is distributed.

As with coforall-loops, the original task that encounters a forall-loop will not proceed until the tasks executing the loop's iterations have completed.

Motivation for forall-loops

As a simple motivating example, consider the following serial loop that increments every element in a million-element array A:

const n = 1000000;
var A: [1..n] real;

for a in A do
  a += 1.0;

Since the array is large and the loop's iterations are independent of one other, it would likely be beneficial to accelerate this computation by executing it in parallel. A coforall-loop could be used to express the parallelism:

coforall a in A do
  a += 1.0;

However, a coforall-loop would likely be overkill for this situation since it would create one million tasks, each of which is only responsible for incrementing a single element. For most hardware platforms, this would generate more concurrency than the system could execute in parallel. Moreover, the cost of creating, scheduling, and destroying the tasks would likely overshadow the small amount of computation that each one performs. Better would be to create a smaller number of tasks and assign a number of loop iterations to each, as a means of amortizing the task creation overheads while avoiding overwhelming the target system with too much concurrency.

This is precisely what forall-loops are for. While they result in parallel execution like coforalls, they typically use a number of tasks that is appropriate for the system, dividing the loop's iterations between them. Thus, we could write this parallel loop as:

forall a in A do
  a += 1.0;

In slightly more detail, the number of tasks used to implement a forall-loop is determined by its iterand expression(s), in this case the array A. As declared here, A uses the default implementation (domain map) which causes it to be allocated locally to the compute node on which the active task is running. The default parallel iterator for A creates a number of tasks equal to the number of available processor cores and divides the iterations evenly between them. For example, if this program were running on a quad-core processor, A's parallel iterator would create four tasks and assign each of them 250,000 (a quarter) of the array elements / loop iterations. Note that these policy choices are simply defaults and can be overridden by the programmer using various mechanisms covered in subsequent sections.

Characteristics of Forall-loop Bodies

Because the number of tasks used to execute a forall-loop is not well-defined, such loops must be serializable. This means that the loop's iterations must be written such that they can legally be executed by a single task. At the same time, since the loop's iterations are likely to execute in parallel, there should be no sensitivity to the order in which they will execute—in practice, the iterands may schedule them in whatever order they choose. To that end, by using a forall-loop, the user is asserting that it is safe to run the iterations serially or in parallel, and in any order.

Practically speaking, these characteristics mean that there can be no synchronization dependences between iterations of a forall-loop as there could be in a coforall-loop; doing so could cause deadlock depending on how the iterations are mapped to tasks. In addition, there should typically be no loop-carried dependences across iterations since doing so can lead to race conditions and nondeterministic behavior.

As a simple example of a race condition in a forall loop, consider the following example whose output is nondeterministic in Chapel:

forall i in 2..n-1 do
  A[i] = A[i-1] + A[i+1];

Intuitively, it appears that the user hopes to replace each of the interior elements of A with the sum of its neighbors in parallel. However, whenever multiple tasks are used to implement the loop, there will be a race. Specifically, for a given iteration i, there is no guarantee that the A[i-1] and A[i+1] elements it reads will still contain the original input values of A as opposed to ones that were just computed and written by another task running in parallel. The resulting values of the array elements will therefore depend on the number of tasks running, how the iterations are divided between them, and the specific timing of when each iteration executes relative to its neighbors. In other words, the outcome is highly unpredictable.

In contrast, if the forall-loop were executed by a single task serially and in a specific order, it would be deterministic. However, it would still not implement the presumed computation since some reads of neighboring elements would necessarily refer to values that had already been updated. For example, if the elements were computed in ascending order, each access to A[i-1] would read a value that had just overwritten the intended value in the previous iteration.

The lesson in this example is that when using a forall-loop, the programmer asserts that the loop's iterations can execute safely in parallel and is responsible for the outcome when they cannot. Chapel does not prevent nondeterministic forall loops from being written, it merely implements the parallelism that the programmer specifies.

Here are two variations of the previous loop which are parallel-safe:

forall i in 2..n-1 by 2 do
  A[i] = A[i-1] + A[i+1];

var B: [1..n] real;
forall i in 2..n-1 do
  B[i] = A[i-1] + A[i+1];

In the first loop, the race condition is eliminated since the loop only iterates over every other element of A. This guarantees that the elements of A being written are independent of the ones being read and eliminates the potential for races between tasks. In the second loop, the overlap is eliminated by reading from A and writing into a second array, B. In this way, it again guarantees that no task will read values that are potentially being written by other tasks in parallel.

Starting from our original array A which stored 1.0 in every position, the results of A and B after executing the loops above would be as follows (for n == 8):

A is: 1.0 2.0 1.0 2.0 1.0 2.0 1.0 1.0
B is: 0.0 2.0 4.0 2.0 4.0 2.0 3.0 0.0

Zippered forall loops

Like for- and coforall-loops, forall-loops support zippered iteration. In this case, the first iterand in the zippering (called the leader) controls the loop scheduling policies. All the other iterands (followers) are implemented in a way that guarantees that corresponding iterations will line up in spite of the parallel execution. How such iterators are written will be covered in later sections.