Futhark as target language for an APL compiler

Posted on June 20, 2016 by Troels Henriksen

Futhark is an array programming language - a family of languages with little widespread usage today, unless we count languages such as Matlab, R, or perhaps the Numpy library for Python. Despite their relative obscurity today, array languages are one of the oldest language families around. Ken Iverson started design on his APL programming language in 1957, although it took a few more years before it was fully specified and implemented. The 1979 Turing Award was awarded to Iverson for his work on APL.

APL is most famous for being cryptic and concise, which is partially due to its use of a unique character set. For example, to sum an array A with its transpose and then sum the rows, we would say:


If one looks a little deeper, APL actually has very straightforward syntactic rules and is quite easy to learn. However, this post is not about programming in APL - it is about implementing APL.

APL and related languages are typically implemented with interpreters. This is partially due to APL being dynamically typed, and partially due to array languages able to get decent performance if the interpretative overhead is amortised by an efficient implementation of array primitives. One APL variant, the K programming language, is famous for its performance (and perhaps even more cryptic syntax). However, the interpreter approach does have its limitations. In the above example, both the transposed array ⍉A and the sum A+⍉A will be created in memory, even though they are merely temporary values that end up being consumed by the reduction (the +/ part). In Futhark, we would write it like this:

let main(a: [n][n]i32): []i32 =
  let a_t = transpose(a)
  let a_sum = zipWith(\(r0: []i32, r1: []i32): [n]i32  ->
                        zipWith(+, r0, r1),
                      a, a_t)
  in map(\(r: []i32): i32  ->
           reduce(+, 0, r),

This is significantly more verbose. However, the Futhark compiler employs loop fusion to combine the different operations into a single efficient loop, and is able to turn the entire program into GPU code. Ideally, we want the concision of APL, but with the performance that can be achieved with an optimising compiler.

One APL compiler project is apltail, which is based on translating programs written in (a subset of) APL into a typed array intermediate language (TAIL). TAIL is a fairly conventional statically typed functional language, where the implicit behaviour of APL has been made explicit. From there, it turns out to be a relatively straightforward task to implement a compiler from TAIL to Futhark, which ultimately results in a compilation pipeline from APL to optimised GPU code. We have summarised our work in a paper submitted to FHPC’16 (preprint).

This work is interesting for two reasons: first, it enables a level of high-performance programming in APL that has been hard to achieve before. Second, it serves as a demonstration of Futhark’s suitability as a compiler target (in contrast to human-written code). Such a demonstration requires not only sufficient language expressivity, but also that the code produced by the translation is able to be optimised approximately as well as hand-written code. This is particularly important for array languages, where large-scale structural transformations (like fusion) are of critical importance for performance.

While the user experience is still rather raw, we hope that this work can serve as the first step to using Futhark as a back-end optimiser for various different languages.