Posted on January 13, 2019 by Troels Henriksen

When designing a programming language, you sometimes encounter design questions that have little impact, and whose implementation either way is straightforward, but which force you to think about the core philosophy of the language. This post is about one such issue as encountered in Futhark.

I shall start with an example. By now, we have a decent amount of experience with having other people, mostly students, write Futhark code. One common technique we have observed is to use small constant-sized arrays as a data structure. This may be a habit that comes from NumPy or other array languages, where this seems to be a popular style. For example, we might represent a point in three-dimensional space as a three-element array:

type vec3 = [3]f32

A function for computing the dot product of two such vectors can then be defined as:

let dot (a: vec3) (b: vec3) = reduce (+) 0 (map2 (*) a b)

This runs correctly, but the programmer may be dismayed at the run-time performance. The reason is that the Futhark compiler treats arrays uniformly: they are located on the heap (possibly the GPU if using an appropriate compiler), and collective operations like map2 and reduce are executed on the GPU. The base overhead of launching a GPU operation seems to be at least 10μs, which is vastly slower than multiplying and summing six floats on the CPU. Essentially, the compiler treats all arrays as potentially large and worth processing in parallel, which makes working on small arrays carry a disproportionate overhead.

In this particular case, the compiler does statically know the size of the array, although it might not in general. Why, then, does the compiler not simply compile operations on this small array in a more efficient manner? Mostly because it is not clear what the threshold should be for considering an array “small”. There is certainly no need for computing the dot product of a three-element vector in parallel, but what about 100 elements? Or 1000? What if the vector is already resident in GPU memory because it is the result of a preceding operation? No matter which cutoff point we pick, there will be some hidden threshold, invisible to the programmer, that may have a dramatic impact on application performance. There will always be some application for which the threshold is too large or too small.

We really have three options open to use:

Treat all arrays uniformly as potentially large. Treat arrays below some threshold as “small” and compile them differently. Combine options (1) and (2) but generating multiple versions of the code, then dynamically pick the best one based on the array sizes encountered. This involves performing semi-automated calibration to fit the cut-over threshold to the specific hardware and code in question.

All of these carry disadvantages. (1) works poorly for small arrays, and (2) is unpredictable and does not handle arrays with a statically-unknown size, but which happen to be small at run-time. Having program performance depend to such a degree on whether the compiler can statically deduce the size of an array, and compare it to some built-in threshold, sounds like a frustrating programming experience. Further, it becomes hard to explain to Futhark programmers how they should write their code to get the performance they seek, since the compiler will be making its own guesses about what to do.

Option (3) could in principle work, but it assumes a sufficiently smart compiler; always a dicey proposition. In practice, it would require lengthy post-compilation calibration, similar to profile-guided optimisation, before the programmer would get a valid impression of the run-time performance of their code. While such a complex approach is sometimes necessary (and we have a paper coming up about doing just that in a different setting!), it really seems overkill for this simple problem.

While the Futhark compiler is undoubtedly a complex beast, we wish to minimise how much of its internal structure and assumptions programmers are expected to learn (Futhark is for the desert!). Our choice is thus to go with option (1), primarily because it has simple rules for programmers to follow. Returning to the original example, it should instead be written this way:

type vec3 = {x: f32, y: f32, z: f32} let dot (a: vec3) (b: vec3) = a.x*b.x + a.y*b.y + a.z*b.z

This will behave predictably, since scalar components of records and tuples are typically stored in registers (if they fit).

However, this approach does have the major drawback that it is specialised to three-dimensional vectors, while the original implementation could be straightforwardly extended to handle arbitrary dimensions. While it is no great problem to duplicate something as simple as this dot product, it would be very annoying to repeat all of our code to handle both array- and record/tuple representations.

Fortunately, Futhark’s higher-order module system allows us to write generic code that is parameterised over some data representation. The module system has been discussed in a previous post, but here is a quick example of how a generic dot product can be written with the aid of the modules from the vector package:

module mk_dotprod(V: vector) = { let dotprod (a: V.vector f32) (b: V.vector f32) = V.reduce (+) 0 (V.map (\(x, y) -> x+y) (V.zip a b)) }

While we are using terms like map and reduce as in our original formulation, their implementation depends on how the module parameter V is instantiated. For example, we can instantiate it with a module where the V.vector type is represented as a three-element tuple, and V.reduce / V.map are unrolled sequential loops:

module vector_2 = cat_vector vector_1 vector_1 module vector_3 = cat_vector vector_2 vector_1 module dotprod_3 = mk_dotprod vector_3

Now we can say dotprod_3.dotprod to access a function that is identical (after some straightforward compiler simplifications) to the specialised dotprod we wrote for three-element records.

Similarly, we can instantiate mk_dotprod with a module that represents vectors as arrays, and provides parallel implementations of V.reduce / V.map :

module dotprod_any = mk_dotprod any_vector

Of course, the vector package already provides a parametric module, vspace (docs), that contains common operations like dot product.

In conclusion: the Futhark compiler performs a great deal of compiler magic to generate high-performance code. This is not really avoidable. However, we need to pick our battles and decide where it does major restructuring of the code, and where it compiles in a predictable manner. Our currently philosophy is to let the compiler aggressively rearrange the structure of any parallelism present, but compile “scalar code” in a predictable manner. Also, if you tell it that something is parallel (by using an actual parallel map ), then the compiler will take it seriously.

The real takeaway here is that we need to be clear in our documentation and educational resources that where possible, you should prefer tuples and records over tiny arrays.