# The task graph: data, dependencies, synchronization

Questions

• How can you express dependencies between SYCL parallel kernels?

Objectives

• Learn how the runtime can handle data movements for us.

• Learn how to work with events to fine-tune dependencies in the task graph.

• Learn about work-group- and work-item-level synchronization.

It should be clear by now that the essential role of the runtime in SYCL applications is to schedule work submitted to the queues in our program as actions and execute all enqueued work in an asynchronous fashion. How is this achieved? In episode Queues, command groups, and kernels, we briefly mentioned the task graph is the underlying abstraction for this purpose in the SYCL execution model. A task graph is composed of nodes and edges, it has a start-to-finish direction, and no self-loops: it is a directed acyclic graph (DAG). Each node is an action to be performed on a device, such as a parallel_for. Each edge connecting two nodes is a dependency between the two, such as the data for task B produced by task A.

It is not usually necessary to directly define the task graph for your application.

• If you use buffers and accessors, the runtime can correctly generate the task graph based on their use in kernel code.

• Similarly when you use USM with implicit data movement.

• For USM with explicit data movements, you are taking up scheduling power. *

However, interacting with the task graph might be necessary to get performance. In this episode, we will explain how to do so.

## In-order and out-of-order queues

The following figure shows some plausible task graphs in an application, i.e. chains of dependencies between tasks.

Examples of a linear chain (left) and Y-pattern (right) of dependencies. The Y-pattern might occur, for example, in the AXPY routine: tasks A and B fill the operand vectors, thus are able to run independently, and task C performs the summation. Task D might be a subsequent reduction. We can always “linearize” a Y-pattern, for example, by using a in-order queue. Figure adapted from [RAB+21].

The first interaction with the task graph happens already at queue construction. The SYCL standard defines two queue flavors: in-order and out-of-order.

Out-of-order queues

This is the default for queue objects and leaves all decisions on task ordering to the runtime, unless we intervene. The runtime will decide ordering based on the data dependencies declared in our code. This can be influenced with various mechanisms which we will discuss shortly.

In-order queues

Each action is assumed to be dependent on the action immediately preceding it in the queue. In-order queues are quite simple to reason about, but they will constrain the runtime too much. Tasks will be serialized in a linear chain, even though they do not read/write to the same data. For this reason, in-order semantics is not the default, but must be set explicitly at construction:

queue ioQ{property::queue::in_order()};


## How to specify dependencies

A command group handler can contain three things only: host code, exactly one action, and specifications of action dependencies. There are three available methods to express the latter:

1. When using in-order queues, each action is implicitly dependent on the action immediately preceding it. Successive tasks must complete strictly in the order in which they were submitted to the queue. This is the simplest way to express a linear chain on dependencies. In-order queues can be excessively constraining. For example, independent computations cannot be overlapped.

2. Through accessors on buffers. In episode Data management with buffers and accessors, we saw that accessors are constructed with a mode and a target. This metadata is enough for the runtime to infer dependencies between different kernels accessing the same buffers.

3. The event-based approach is the most flexible. Methods on the handler class or on the queue class are asynchronous and return immediately objects of the event class. We can pass an event (or a vector of events) to the depends_on method on the handler class or to parallel_for invocations on the queue class.

Expressing the Y-pattern

Methods on queue or handler objects are asynchronous but return event objects immediately. With events, we have granular control over dependencies, since they can be passed as arguments to parallel_for and single_task invocations and also to the depends_on method of the handler class.

  auto a = malloc_shared<double>(N, Q);
auto b = malloc_shared<double>(N, Q);

auto e1 = Q.parallel_for(range { N }, [=](id<1> id) {
a[id[0]] = 1;
});

auto e2 = Q.parallel_for(range { N }, [=](id<1> id) {
b[id[0]] = 2;
});

auto e3 = Q.parallel_for(range { N }, { e1, e2 }, [=](id<1> id) {
a[id[0]] += b[id[0]];
});

for (int i = 1; i < N; i++)
data1[0] += data1[i];

data1[0] /= 3;
});


## Synchronization with the host

We have seen how to handle dependencies between tasks to be run on devices, let’s talk about what happens on the host. Once our device computations are done, we’d obviously like to get the results back on the host. In CUDA/HIP this usually takes the form of device-to-host copies. These represent implicit synchronization points between host and device: we wait until all kernels have completed and then perform the copy. In SYCL, we have few options:

1. We can use the wait method on the queue object. Even though this has been used extensively in our example, it is also the coarsest synchronization level and might not be a good idea in larger-scale applications. We might submit many actions to a queue and using wait will block execution until each and every one of them has completed, which is clearly not always ideal.

2. For finer control, you can synchronize on events: either a single one or a list.

// waiting on a single event

auto e1 = Q.parallel_for(...);
e1.wait();

// waiting on multiple events
auto e2 = Q.parallel_for(...);
event::wait({e2, e3});

3. Use of objects of host_accessor type sits at an even finer level. They define a new dependency between a task in the graph and the host, such that execution cannot proceed past their construction until the data they access is available on the host. More concisely, construction of an host_accessor is blocking.

// declare buffer
buffer<double> A{range{256}};

// fill with ones
Q.submit([&](handler &cgh){
accessor aA{A, cgh};
cgh.parallel_for(range{N}, [=](id<1> id){
aA[id] = 1.0;
});
});

// enqueue more work

// host accessor for buffer A
// the constructor will *block* until data is available on host
host_accessor h_a{A};


Note that the same data accessed by an host accessor cannot be “touched” on the device as long as the host_accessor object exists. We can achieve the same behavior just with buffers. We have seen that buffer destructors are also blocking: when a buffer goes out of scope, it will implicitly wait for all actions that use it to complete. If the buffer was initialized with a host pointer, then the runtime will schedule a copy back to the host:

std::vector a(256, 0.0);

{ // open scope
// buffer to a
buffer<double> buf_a(a.data(), range{256});

// use buffer in work submitted to the queue
Q.submit([&](handler &cgh){
auto acc_a = accessor(buf_a, cgh);

cgh.parallel_for(...);
});
} // close scope: buffer destructor will wait and host data will be updated


## Kernel-level communication

### Work-group local memory

ND-range parallel kernels gives us access to kernel-level communication patterns between work-items. Recall that when using ND-ranges, we partition the execution space of a data-parallel kernel into global and local ranges. Each local range is a work-group within the ND-range and it’s in turn partitioned into work-items, the actual units of work in a kernel. Work-items in a work-group have access to work-group local memory which we can use to coordinate efficient execution of the kernel. We work with local memory by using the local_accessor type:

Schematic view of a 3-dimensional nd_range object constructed from global $$8\times 8 \times 8$$ and local $$4\times 4 \times 4$$ ranges, respectively. The different colors represent the work-groups in the ND-range, each made of 64 work-items. Work-items with the same color can cooperate to each other during kernel execution: they have access to work-group local memory and can use it to communicate with each other. Communication between work-items in differently colored work-groups will most likely result in a deadlock.

It is essential to keep in mind these facts about work-group local memory:

1. It is only accessible once a work-group start execution. In practice, this means that local_accessor constructors require a handler object.

2. It is not initialized when a work-group starts execution.

3. It does not persist once the work-group finishes.

Furthermore, it is our responsibility as programmers to synchronize between accesses within the same work-group. We use the barrier method on objects of item type to synchronize work-items. The concept of a barrier might be familiar from MPI programming: when work-items encounter it, they can only move past it at the same time. Work-items that execute faster will wait for those that lag behind. We should use barriers whenever work-items read from/write to local memory that was previously written to/read from by another work-item. This ensures, for example, that results of an operation are actually available before we use them and also that the work-group local memory is consistent for all work-items once we move past the barrier.

Tiled MatMul

We can further optimize the ND-range implementation of matrix multiplication by using tiling. The basic idea is to exploit the fact that each row of the left operand $$\mathbf{A}$$ is reused multiple times to compute elements in the result. If we can structure the local iteration range to work over tiles (subsections) of it, we can achieve better locality.

Each work-item will compute an element in the result matrix $$\mathbf{C}$$ by loading a tile (subsection) of a row of $$\mathbf{A}$$ into work-group local memory and multiplying it with an appropriately sized portion of columns of $$\mathbf{B}$$. The result matrix is held in global memory and addressed through the global range of the ND-range object. Local memory accesses should be faster and each tile is reused multiple times.

Schematics of a tiled implementation of matrix multiplication: $$C_{ij} = \sum_{k}A_{ik}B_{kj}$$. The computation is split into work-groups, each with own local memory. We first load a tile (cyan) of the left operand matrix $$\mathbf{A}$$ into local memory. The tile will be reused multiple times by each work-item to compute the result (green), held in global memory. The right operand matrix $$\mathbf{B}$$ is also accessed from global memory. Figure adapted from [RAB+21].

Don’t do this at home, use optimized BLAS!

You can find a scaffold for the code in the content/code/day-2/04_tiled-matmul/tiled-matmul.cpp file, alongside the CMake script to build the executable. You will have to complete the source code to compile and run correctly: follow the hints in the source file. A working solution is in the solution subfolder.

1. We create a queue and map it to the GPU.

2. We declare the operands as std::vector<double>. Generalize the example in the previous exercise to allow multiplication of non-square matrices. The right-hand side operands are filled with random numbers.

3. We define buffers to the operands and result in our matrix multiplication.

4. We submit work to the queue through a command group handler.

5. We set up accessors for the matrix buffers. We can use access targets and properties to guide the runtime in the creation of the task graph.

6. We also have to set up a local accessor to our tiles. Note that the tile is a 1-dimensional range.

7. Within the handler, we launch a parallel_for with an appropriately sized nd_range execution range. The tile will be our local range and it is 1-dimensional.

8. Obtain indices in the global and local ranges:

• The “global” indices are used to address rows of the left operand, columns of the right operand, and the element in the result matrix..

• The “local” indices are used to address the tile, i.e. the local memory buffer.

9. Define the matrix multiplication kernel function, where we have:

• A tile-strided loop to load data for $$\mathbf{A}$$ from global to local memory.

• A loop over work-items in the tile to compute their product with $$\mathbf{B}$$.

Remember that we need to ensure that the local memory is consistent across work-items after every load and/or store operation!

10. Retrieve the result using a host_accessor.

11. Check that your results are correct.

Keypoints

• The SYCL task graph is built by the runtime and governs execution of our program on heterogeneous hardware.

• Data dependencies are the main ingredients in the task graph construction.

• We can influence the task graph explicitly through events.

• In a data-parallel kernel, work-items within a work-group can cooperate and we can leverage this to our advantage.

Footnotes

*

And with great power, comes great responsibility.

One could also set the host pointer after buffer construction using the set_final_data method.

This is true also for hierarchical parallel kernels.