Datadeps (Data Dependencies)

For many programs, the restriction that tasks cannot write to their arguments feels overly restrictive and makes certain kinds of programs (such as in-place linear algebra) hard to express efficiently in Dagger. Thankfully, there is a solution: spawn_datadeps. This function constructs a "datadeps region", within which tasks are allowed to write to their arguments, with parallelism controlled via dependencies specified via argument annotations. Let's look at a simple example to make things concrete:

A = rand(1000)
B = rand(1000)
C = zeros(1000)
add!(X, Y) = X .+= Y
Dagger.spawn_datadeps() do
    Dagger.@spawn add!(InOut(B), In(A))
    Dagger.@spawn copyto!(Out(C), In(B))

In this example, we have two Dagger tasks being launched, one adding A into B, and the other copying B into C. The add! task is specifying that A is being only read from (In for "input"), and that B is being read from and written to (Out for "output", InOut for "input and output"). The copyto task, similarly, is specifying that B is being read from, and C is only being written to.

Without spawn_datadeps and In, Out, and InOut, the result of these tasks would be undefined; the two tasks could execute in parallel, or the copyto! could occur before the add!, resulting in all kinds of mayhem. However, spawn_datadeps changes things: because we have told Dagger how our tasks access their arguments, Dagger knows to control the parallelism and ordering, and ensure that add! executes and finishes before copyto! begins, ensuring that copyto! "sees" the changes to B before executing.

There is another important aspect of spawn_datadeps that makes the above code work: if all of the Dagger.@spawn macros are removed, along with the dependency specifiers, the program would still produce the same results, without using Dagger. In other words, the parallel (Dagger) version of the program produces identical results to the serial (non-Dagger) version of the program. This is similar to using Dagger with purely functional tasks and without spawn_datadeps - removing Dagger.@spawn will still result in a correct (sequential and possibly slower) version of the program. Basically, spawn_datadeps will ensure that Dagger respects the ordering and dependencies of a program, while still providing parallelism, where possible.

But where is the parallelism? The above example doesn't actually have any parallelism to exploit! Let's take a look at another example to see the datadeps model truly shine:

# Tree reduction of multiple arrays into the first array
function tree_reduce!(op::Base.Callable, As::Vector{<:Array})
    Dagger.spawn_datadeps() do
        to_reduce = Vector[]
        push!(to_reduce, As)
        while !isempty(to_reduce)
            As = pop!(to_reduce)
            n = length(As)
            if n == 2
                Dagger.@spawn Base.mapreducedim!(identity, op, InOut(As[1]), In(As[2]))
            elseif n > 2
                push!(to_reduce, [As[1], As[div(n,2)+1]])
                push!(to_reduce, As[1:div(n,2)])
                push!(to_reduce, As[div(n,2)+1:end])
    return As[1]

As = [rand(1000) for _ in 1:1000]
Bs = copy.(As)
tree_reduce!(+, As)
@assert isapprox(As[1], reduce((x,y)->x .+ y, Bs))

In the above implementation of tree_reduce! (which is designed to perform an elementwise reduction across a vector of arrays), we have a tree reduction operation where pairs of arrays are reduced, starting with neighboring pairs, and then reducing pairs of reduction results, etc. until the final result is in As[1]. We can see that the application of Dagger to this algorithm is simple - only the single Base.mapreducedim! call is passed to Dagger - yet due to the data dependencies and the algorithm's structure, there should be plenty of parallelism to be exploited across each of the parallel reductions at each "level" of the reduction tree. Specifically, any two Dagger.@spawn calls which access completely different pairs of arrays can execute in parallel, while any call which has an In on an array will wait for any previous call which has an InOut on that same array.

Additionally, we can notice a powerful feature of this model - if the Dagger.@spawn macro is removed, the code still remains correct, but simply runs sequentially. This means that the structure of the program doesn't have to change in order to use Dagger for parallelization, which can make applying Dagger to existing algorithms quite effortless.