Baby Steps

A blog about programming, and tiny ways to improve it.

Parallel Pipelines for JS

I’ve been thinking about an alternative way to factor the PJS API. Until now, we’ve had these methods like mapPar(), filterPar() and so forth. They work mostly like their sequential namesakes but execute in parallel. This API has the advantage of being easy to explain and relatively clear, but it’s also not especially flexible nor elegant.

Lately, I’ve been prototyping an alternate design that I call parallel pipelines (that’s just a working title; I expect the name to change). Compared to the older approach, parallel pipelines are a more expressive API that doesn’t clutter up the array prototypes. The design draws on precedent from a lot of other languages, such as Clojure, Ruby, and Scala, which all offer similar capabilities. I’ve prototyped the API on a branch of SpiderMonkey, though the code doesn’t yet run in parallel (it is structured in such a way as to make parallel execution relatively straightforward, though).

CAVEAT: To be clear, this design is just one that’s in my head. I still have to convince everyone else it’s a good idea. :) Oh, and one other caveat: most all the names in here are just temporary, I’m sure they’ll wind up changing. Along with probably everything else.

Pipelines in a nutshell

The API begins with a single method called parallel() attached to Array.prototype and typed object arrays. When you invoke parallel(), no actual computation occurs yet. Instead, the result is a parallel pipeline that, when executed, will iterate over the elements of the array.

You can then call methods like map and filter on this pipeline. None of these transformers takes any immediate action; instead they just return a new parallel pipeline that will, when executed, perform the appropriate map or filter.

So, for example, you might write some code like:

var pipeline = [1, 2, 3, 4, 5].parallel().map(x => x * 3).filter(x % 2);

This yields a pipeline that, when executed, will multiply each element of the array by 3 and then select the results that are even.

Once you’ve finished building up your pipeline, you execute it by using one of two methods, toArray() or reduce(). toArray() will execute the pipeline and return a new array with the results. reduce() will exeute the pipeline but instead of returning an array it reduces the elements returns a single scalar result.

Execution works the same way as PJS today: that is, we will attempt to execute in parallel. If your code mutates global state, or uses other features of JS that are not safe for parallel execution, then you will wind up with a sequential fallback semantics.

So for example, I might write:

var pipeline = [1, 2, 3, 4, 5, 6].parallel().map(x => x * 3).filter(x % 2);

// Returns [3, 9, 15]
var results = pipeline.toArray();

// Returns 27 (i.e., 3+9+15)
var reduction = pipeline.reduce((x, y) => x + y);

Pipelines and typed objects

The pipeline API is integrated with typed objects. Each pipeline stage generates values of a specific type; when you toArray() the result, you get back a typed object array based around this type.

Producing typed object arrays doesn’t incur any limitations vs using a normal JS array, because the element type can always just be any. Moreover, in those cases where you are able to produce a more specialized type, such as int32, you will get big savings in memory usage since typed object arrays enable a very compact representation.

Ranges

In the previous example, I showed how to create a pipeline given an array as the starting point. Sometimes you want to create parallel operations that don’t have any array but simply iterate over a range of integers. One obvious case is when you are producing a fresh array from scratch.

To support this, we will add a new “parallel” module with a variety of functions for producing pipelines from scratch. One such function is range(min, max), which just produces a range of integers starting with min and stepping up to max. So if we wanted to compute the first N fibonnaci numbers in parallel, we could write:

var fibs = parallel.range(0, N).map(fibonacci).toArray();

In fact, using range(), we can implement the parallel() method for normal JS arrays:

Array.prototype.parallel = function() {
    return parallel.range(0, this.length).map(i => this[i]);
}

Shapes and n-dimensional pipelines

Arrays are great, but it frequently happens that we want to work with multiple dimensions. For this reasons, parallel pipelines are not limited to iterating over a single dimensional space. They are can also iterate over multiple dimensions simultaneously.

We call the full iteration space a shape. Shapes are a list, where the length of the shape corresponds to the number of dimensions. So a 1-dimensional iteration, such as that produced by range(), has a shape like [N]. But a 2-d iteration might have the shape [W, H] (where W and H might be the width and height of an image). Similarly, iterating over some 3-D space would have a shape [X, Y, Z].

To iterate over a parallel shape, you can use the parallel.shape() function. For example, the following command iterates over a 5x5 space, and produces a two-dimensional typed object array of integers:

var matrix = parallel.shape([5, 5])
                     .map(([x, y]) => x + y)
                     .toArray();

You can see that shape() produces a vector [x, y] specifying the current coordinates of each element in the space. In this case, we map that result and add x and y, which means that the end result will be:

0 1 2 3 4
1 2 3 4 5
2 3 4 5 6
3 4 5 6 7
4 5 6 7 8

Another way to get N-dimensional iteration is to start with an N-dimensional typed object array. The parallel() method on typed object arrays takes an optional depth argument specifying how many of the outer dimensions you want to iterate over in parallel; this argument defaults to 1. This means we could further transform our matrix as shown here:

var matrix2 = matrix.parallel(2).map(i => i + 1).toArray();

The end result would be to add one to each cell in the matrix:

1 2 3 4 5
2 3 4 5 6
3 4 5 6 7
4 5 6 7 8
5 6 7 8 9

Deferred pipelines

All the pipelines I showed so far were essentially “single shot”. They began with a fixed array and applied various operations to it and then created a result. But sometimes you would like to specify a pipeline and then apply it to multiple different arrays. To support this, you can create a “detached” pipeline. For example, the following code would create a pipeline for incrementing each element by one:

var pipeline = parallel.detached().map(i => i + 1);

Before you actually execute a detached pipeline, you must attach it to a specific input. The result is a new, attached pipeline which can then be converted to an array or reduced. Of course, you can attach the pipeline many times:

// yields [2, 3, 4]
pipeline.attach([1, 2, 3]).toArray();

// yields 12
pipeline.attach([2, 3, 4]).reduce((a,b) => a+b).reduce();

Put it all together

Here is relatively complete, if informal, description of the pipeline methods I’ve thought about thus far.

Creating pipelines

The fundamental ways to create a pipeline are the methods range(), shape(), and detached(), all available from a parallel module. In addition, Array.prototype and the prototype for typed object arrays both feature a parallel() method that creates a pipeline as we showed before.

Transforming pipelines

Each of the methods described here are available on all pipelines. Each produces a new pipeline.

The most common methods for transforming a pipeline will probably be map and mapTo:

  1. pipeline.map(func) – invokes func on each element, preserving the same output type as pipeline.
  2. pipeline.mapTo(type, [func]) – invokes func on each element, converting the result to have the type type. In fact, func is optional if you just want to convert between types.

map and mapTo are somewhat special in that they work equally well over any number of dimensions. The rest of the available methods always operate only over the outermost dimension of the pipeline. They also create a single dimensional output. Because this is a blog post and not a spec, I won’t bother writing out the descriptions in detail:

  1. pipeline.flatMap(func) – like map, but flatten one layer of arrays
  2. pipeline.filter(func) – drop elements for which func returns false
  3. pipeline.scan(func) – prefix sum
  4. pipeline.scatter(...) – move elements from one index to another

Finally, there is the attach() method, which is only applicable to detached pipelines. It produces a new pipeline that is attached to a specific input. If the pipeline is already attached, an exception results.

Executing pipelines

There are two fundamental ways to execute a pipeline:

  1. pipeline.toArray() – executes the pipeline and collects the result into a new typed object array. The dimensions and type of this array are determined by the pipeline.
  2. pipeline.reduce(func, [initial]) – executes the pipeline and reduces the results using func, possibly with an initial value. Returns the result of this reduction.

Open questions

Should pipelines provide the index to the callback? I decided to strive for simplicity and just say that pipeline transformers like map always pass a single value to their callback. I imagine we could add an enumerate transformer if indices are desired. But then again, this pollutes the value being produced with indices that just have to be stripped away. So maybe it’s better to just pass the index as a second argment that the user can use or ignore as they choose. I imagine that the index will be an integer for a 1D pipeline, and an array for a multidimensional pipeline.

Should pipelines be iterable? It has been suggested that pipelines be iterable. I guess that this would be equivalent to collecting the pipeline into an array and then iterating over that. (Since, unless you are doing a map operation, the only real purpose for iteration is to produce side-effects.) This would be say enough to add, I just was worried that it might be misleading to see code like this:

for (var e of array.parallel().map(...)) {
    /* Maybe it looks like this for loop body
       executes in parallel? (Which it doesn't.) */
}

Updates

  • Renamed collect() to toArray(), which seems clearer.

Comments