Deterministic or not?

2 January 2013

One of the interesting questions with respect to Parallel JS is what the semantics ought to be if you attempt a parallel operation with a kernel function that has side-effects. There are basically three reasonable options:

  1. Deterministic results where possible: The function behaves “as if” it executed sequentially, executing the kernel from 0 to n, just like
  2. Error: An exception is thrown.
  3. Non-determinstic results: The function behaves “as if” it executed sequentially, but the items were mapped in an unspecified order.

The branch currently implements option 3: I believe it is the most consistent and will yield the best performance. However, reasonable people can differ on this point, so I want to make my case.

Why not ensure deterministic results?

At first glance, at least, it seems like having deterministic results would be the most convenient option. After all, could then be used as a drop-in equivalent to However, there are two reasons that I am concerned about this option:

  1. Deterministic results are not possible for all operations.
  2. Deterministic ordering can hamper efficient parallel execution.

Deterministic results are not possible for all operations.

If you examine the specification for ParallelArray.reduce(), you will see that it permits reduce() to reduce the items in the array in any order:

This means that the result of reduce() is only deterministic if the kernel function is associative and commutative. Without this requirement, implementations would be severely limited in how they could perform parallel reduction, and in some cases parallel execution would be too expensive to be worthwhile (interestingly, the sequential fallback would be more expensive too, because the best sequential ordering for reduction is not parallelizable at all).

For this reason, I am wary of telling users that ParallelArray methods have equivalent semantics to Array methods. This is only partially true and it can never be fully true. In general, I think users will want the best parallel performance they can get, and they will accept whatever restrictions are required to get it.

Deterministic ordering can hamper efficient parallel execution.

We just saw that, in the case of reduce(), any deterministic ordering either prevents efficient parallel execution or it prevents efficient sequential execution. To a lesser degree, the same is true of map(). Unlike reduce(), though, the problems with map() are somewhat subtle.

You may recall that when we perform parallel execution, there is always the possibility of bailout. A bailout can occur because we detect that a write would cause a visible side-effect, but it can also occur for arbitrary, internal reasons. Bailouts often occur because there is some portion of the code that has not yet been executed in the warmup runs, and hence the type information that we gathered was inaccurate.

The question is, when a bailout occurs, what do we do with the results that were successfully computed by the previous parallel iterations? It would be very nice if we were able to make use of those results. If we do guarantee deterministic results, however, this is somewhat tricky.

Imagine for a moment there are just two threads processing a 1000-element array. In our current system, each worker will be responsible for mapping half of the array. So imagine that the first worker has processed indices 0 to 22 when it encounters a bailout due to insufficient type information. To gather type information, we need to execute iteration 23 sequentially in the interpreter. In fact, while we’re in the interpreter, it’s probably best if we do a chunk of iterations—say, 23 to 32 or so, just to gather up more data. Meanwhile, let’s say that the second worker has processed entries 500 to 600 before it notices that the first worker bailed out and follows suit.

Unfortunately, if we are guaranteeting deterministic results, it is very difficult for us to make use of the results for entries 500 to 600 that were already computed. It’s possible, after all, that when we re-run iterations 23 to 32 in the interpreter, they will modify shared state, and that could affect the computations that already occurred. In effect, all parallel iterations are inherently speculative.

As annoying as it is to have to throw away indices 500 to 600, it is equally annoying if the bailout should occur in the second worker (say, while processing index 601). In that case, we have a problem: we’d like to run index 601 in the interpreter, but it’s possible that this too will cause side-effects. That means that we must ensure that all indices prior to 601 are fully processed (which, at the time of bailout, they are not). Given enough bookkeeping, we can manage this too: we could perhaps re-spawn parallel workers to process from 23 to 600, for example, and then re-spawn to process from 600 to 1000.

What if we don’t guarantee deterministic ordering?

If, however, we choose not to guarantee deterministic results, these problems become much simpler. When a bailout occurs, we can simply have each worker execute sequentially from wherever it left off. So to continue with our example, worker 0 would run from indices 23 to 30 or so, and perhaps worker 1 would run from 601 to 632. This way they can both gather a bit more data. Then we resume parallel execution.

This is in fact more-or-less exactly what our current code does. Each worker tracks its current position. Whenever the kernel function is invoked, it processes the next data it has to proccess, and it updates its current position as it goes. If a bailout occurs, then the current position is not updated, so when the kernel function is invoked next (which will be from the interpreter), it will pick up where it left off and process for a while. I can dive into the intimate details of this in a separate post.

What about reporting an error?

Prohibiting impure operations altogether does enable the same optimizations as nondeterministic ordering, but (as I argued in a previous post) it does so by imposing a significant and unnecessary implementation and performance burden on the sequential fallback code. So I am not a fan of this approach.

The take-away

My feeling is this. Deterministic ordering sounds like it makes things easier for the end-user, but the story is actually more complex, as only some operations are deterministic. Moreover it imposes performance burdens on the implementation, so even the “good guys” who stick to pure operations will pay the price, at least until optimizations become more highly tuned to cover all kinds of corner cases.

In general, I think people will turn to ParallelArray when they have pure operations to perform: for pure operations, deterministic ordering simply imposes a performance burden. If you have an impure operation for which ordering is significant, it seems to me you would be better off just using normal arrays or coding the operation in a sequential fashion.

Clearly this is an area where reasonable people can differ, though, and I would not be surprised if we ultimately decide to guarantee determinism where possible (i.e., map() and filter()).