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We have published a number of research papers on Futhark, and hopefully more will follow in the future. They are presented below in reverse chronological order.

Papers on language design and implementation

Compiling Generalized Histograms for GPU

Presented at SC '20 (pdf)

An explanation of the implementation strategy behind Futhark's reduce_by_index construct. The paper mostly focuses on the low-level performance analysis needed to make this construct run fast, but is also some discussion of the language integration, and some of the compiler optimisations. We have made the research artifact available, which also contains a CUDA library implementation of the ideas.

Bounds Checking on GPU

Presented at HLPP '20 (pdf)

Few GPU-targeting languages perform bounds checking, because it is surprisingly tricky to do well on a GPU. For years, Futhark would also refuse to compile code that required bounds checks (or similar safety checks) in parallel code, with the programmer having to resort do disabling bounds checks. However, eventually we found a simple and efficient way to implement bounds checking, which we describe in this paper.

Compositional Deep Learning in Futhark

Presented at FHPNC '19 (pdf, bib)

This paper presents a library for implementing neural networks in Futhark. The library functions are generically typed and the composition structure allows for networks to be trained (using back-propagation) and for trained networks to be used for predicting new results (using forward-propagation). Individual layers in a network can take different forms ranging over dense sigmoid layers to convolutional layers. We demonstrate that Futhark's elimination of higher-order functions and modules leads to efficient generated code, with comparison to TensorFlow.

The code is available and the paper itself is a distillation of Duc Minh Tran's bachelor's thesis.

Data-Parallel Flattening by Expansion

Presented at ARRAY '19 (pdf, bib)

One of Futhark's main difficulties is its restriction to regular parallelism. This paper presents a programming technique for expressing certain kinds of irregular data-parallel problems in a regular manner.

Incremental Flattening for Nested Data Parallelism

Presented at PPOPP '19 (pdf, bib)

This paper expands on the compilation scheme presented in our PLDI 2017 paper, to employ a multi-versioned approach, in which the parallelism in the program is mapped to multiple independent (but semantically equivalent) code versions, and the best one picked at run-time based on the concrete input data observed. The title is an homage to the paper Data-Only Flattening for Nested Data Parallelism, which also seeks to improve on the inefficiency of full flattening. See also the blog post on the paper.

Research artifact available here.

High-Performance Defunctionalisation in Futhark

Presented at TFP '18 (pdf, bib)

Futhark initially did not support higher-order functions, because the usual compilation strategy creates a great degree of indirection, which can inhibit optimisation and efficient compilation. In this paper, we present a de functionalisation transformation that relies on type-based restrictions on the use of expressions of functional type, such that we can completely eliminate higher-order functions in all cases, without introducing any branching. We prove the correctness of the transformation and discuss its implementation in Futhark, a data-parallel functional language that generates GPU code. The use of these restricted higher-order functions has no impact on run-time performance, and we argue that we gain many of the benefits of general higher-order functions, without in most practical cases being hindered by the restrictions. An extended treatment can be found in Anders Kiel Hovgaard's master's thesis, available here.

Static Interpretation of Higher-Order Modules in Futhark

Presented at ICFP '18 (pdf, bib)

This paper discusses the higher-order ML-style module system available in Futhark. Most of the discussion is a theoretical treatment, including a formally-verified implementation in Coq. The implementation in the Futhark compiler does not use this verified implementation for a variety of reasons, but it does almost exactly follow the semantic object definitions given in the paper.

Modular Acceleration: Tricky Cases of Functional High-Performance Computing

Presented at FHPC '18 (pdf, bib)

This case study examines the data-parallel functional implementation of three algorithms: generation of quasi-random Sobol numbers, breadth-first search, and calibration of Heston market parameters via a least-squares procedure. We show that while all these problems permit elegant functional implementations, good performance depends on subtle issues that must be confronted in both the implementations of the algorithms themselves, as well as the compiler that is responsible for ultimately generating high-performance code. In particular, we demonstrate a modular technique for generating quasi-random Sobol numbers in an efficient manner, study the efficient implementation of an irregular graph algorithm without sacrificing parallelism, and argue for the utility of nested regular data parallelism in the context of nonlinear parameter calibration.

Design and Implementation of the Futhark Programming Language

Troels Henriksens PhD thesis (revised), defended in November of 2017 (pdf, bib)

This PhD thesis describes the overall background and motivation behind the development of Futhark, as well as a collection of some of the core implementation techniques (size-dependent typing, fusion, moderate flattening, tiling). The treatment is high level, and the technicalities of the concrete compiler implementation is not discussed in great detail. The first part of the thesis describes the overall philosophy behind the design and implementation of Futhark, and is fairly readable. The latter part of the thesis, which discusses concrete program transformations, is a more difficult read, and probably only of interest to academics. The empirical evaluation chapter is a good description of what Futhark does well, and what it does not so well (at least as of the time the thesis was written).

Strategies for Regular Segmented Reductions on GPU

Presented at FHPC '17 (pdf, bib)

A description of an implementation technique for regular segmented reductions on GPU. The technique is based on having three different strategies for dealing with different problem classes. This is the technique currently used by the Futhark compiler, but it is presented in a general setting, and could be used by other libraries and languages that make use of regular segmented reductions.

Futhark: Purely Functional GPU-Programming with Nested Parallelism and In-Place Array Updates

Presented at PLDI '17 (pdf, bib)

A general and self-contained description of the main points of the design and implementation of Futhark, including pieces of fusion, a formalisation of the uniqueness typing rules, and our mechanism for kernel extraction. The latter is the main novelty, as it allows the Futhark compiler to exploit regular nested parallelism in a more efficient (albeit also more restricted) manner than full flattening, while still being more powerful than approaches that support only flat parallelism. The accompanying benchmark suite is freely accessible.

APL on GPUs - A TAIL from the Past, Scribbled in Futhark

Presented at FHPC '16 (pdf, bib)

A paper describing an APL compiler (apltail) that operates by translating APL into a typed array intermediate language (TAIL), and from there into Futhark. While the Futhark details are light, the paper demonstrates a simple use of Futhark as a target language for a compiler. We succeed in achieving decent speedup on several (small) APL programs. The accompanying benchmark suite may be worth a look.

Design and GPGPU Performance of Futhark’s Redomap Construct

Presented at ARRAY '16 (pdf, bib)

A detailed presentation of one of Futhark's internal language constructs - redomap - which is used to represent various forms of map-reduce-fusion. We present some microbenchmarks implemented in both Thrust and Futhark and discuss their relative performance.

Size Slicing - A Hybrid Approach to Size Inference in Futhark

Presented at FHPC '14 (pdf, bib)

Futhark supports automatic size inference of arrays, and this paper describes our approach, which is based on slicing. The descriptions are still up-to-date, although the Futhark source language has since grown support for user-defined size annotations, which can sometimes enable the compiler to make better assumptions about the shapes of arrays.

Bounds Checking: An Instance of Hybrid Analysis

Presented at ARRAY '14 (pdf, bib)

We implemented a novel form of bounds checking by extracting predicate functions from programs with array indexing. These predicates functioned as sufficient conditions for all bounds checks in the original program: if the extracted predicates evaluated to true, then every array index was guaranteed to be in bounds. The idea is that this produces an efficient alternative to precise bounds checking even for very complicated accesses (such as indirect indexing). The idea works, but was hard to implement and maintain and thus distracted us from our core work, so it is no longer used in the Futhark compiler. Instead, we provide an unsafe keyword that one can use to remove bounds checks that would otherwise hinder parallelisation. In the future, we might return to this work.

A T2 Graph-Reduction Approach To Fusion

Presented at FHPC '13 (pdf, bib)

A presentation of the core of the producer-consumer fusion algorithm in the Futhark compiler (although the language was called L0 at the time). The description of the fundamental algorithm is still correct, although it does not cover some of the newer language additions, nor does it describe horisontal fusion.

Application Papers

These papers are not about Futhark as a language or compiler, but use it to build or show something.

Selected Student Projects