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Retrospective on an implementation of the Poseidon hash function in Futhark

Posted on September 27, 2020 by Troels Henriksen

Futhark is not a very widely used language, and since the compiler contains no telemetry, my main source of information about usage is when users ask for help or report bugs. From these interactions, it appears that most Futhark users are individual programmers, often scientists or hobbyists, who implement algorithms that have not previously had high-performance implementations. Usually, the users of the programs are the same as their programmers. This is no great surprise - one of the most important strengths of Futhark is that algorithmic experimentation is much easier than in low-level languages like CUDA, while still running much faster than high-level languages such as Haskell. It seems to be a good balance. In this post, I will discuss the experience of using Futhark for something quite different: namely implementing a previously defined algorithm, one with quite straightforward parallelism, and integrating the Futhark code in a nontrivial Rust context.

In January, porcuquine from the Filecoin project wrote me and asked for advice on a potential use of Futhark: implementing the Poseidon hash function, where the most intensive computation involves operations on elements of finite fields, which requires large integers. They already had an implementation in OpenCL, including hand-written GPU assembly. I like to think I was honest in my response, where I explained that while Futhark is probably suitable, its strengths are mainly useful for programs with complex parallel structure, and that its performance probably cannot match hand-written primitives. Fortunately, this was not enough to scare off porcuquine, and over the next several months, he managed to find a great deal of limitations and bugs in the compiler, which I mostly promptly fixed. I think my bug-fixing ethos is quite guilt-driven, as I implicitly suggest that people should use Futhark (because I put it out there and talk about it), and then I feel guilty when they run into problems due to my errors. None of the problems were conceptually deep or concerned the language itself, but rather were all implementation restrictions that just had not been apparent before. Porcuquine’s implementation (hereafter referenced as neptune-triton) simply touched the compiler in ways it had never been touched before. The rest of this post is a summary of the most interesting fixes and improvements that were made as a result of this process. Ultimately, while only time will tell whether Futhark has been useful to Filecoin, I can say that Filecoin has definitely been useful to Futhark.

New primitives

The first challenge, and the one that was easiest to resolve, was adding language primitives for fused multiply-add. Porcuquine did this himself, and the new primitives were made available in version 0.15.1. With the OpenCL and CUDA backends, these primitives map directly to the corresponding operations exposed by the GPU APIs. On the other backends, and in the interpreter, they are simply implemented as well as possible.

After this, things became more difficult.

Static arrays

The core of the Poseidon hash function is computation on elements of finite fields - basically integers (far) more bits than directly supported by the machine. For finite fields, the number of digits (or “limbs”) needed for each field element will be known at compile-time, in contrast to common bignums, which can grow to any size and generally may need allocation at inopportune times, which makes them a poor fit for GPUs.

However, while the number of digits in each field may be finite, we may still need different fields with different sizes, so to avoid duplicating code, we should write a generic implementation that can be instantiated with the desired size. Futhark’s ML-style module system is an excellent fit here. But an important question must still be answered: how do we represent the elements of the field? The obvious choice is an array of 64-bit digits, but for this application, this causes trouble, as the arrays would be quite small (the main field definition uses just four digits). This is by itself not a problem, but the futhark compiler generally assumes that arrays will be large, heap-allocated, and worth parallelising. Thus, small array constant-size arrays is usually a code smell, as it can cause significant and unnecessary overhead. It would be much better to represent these field elements as essentially tuples, and sequentialise operations on them. I have written previously about why Futhark does not automatically do this, and the solution is the same as usual: Parameterise over the representation of field elements, and use the vector library for efficient small arrays. Poseidon did need the library to gain some new facilities, notably foldl and foldr functions to implement carry-based addition. These functions result in quite beautiful and quite efficient fully unrolled code. The nice thing here was that this improvement concerned only library code, not the compiler. It’s nice that Futhark has become robust and expressive enough that not every problem has to be fixed with compiler hacking.

Costly constants

While neptune-triton is in some ways quite simple, as the parallelism is mostly in the form of maps, it did push the language hard in one spot that had not seen much prior pressure. That area was something as superficially trivial as named constants. That is, top-level definitions that are not functions. I wrote about the issue when we fixed it, so I will not repeat myself here, but I am still a little embarrassed that the compiler had room to improve its compile time (for some programs) by almost two orders of magnitude.


Neptune-triton is not a very large program by most standards, but the Futhark compiler uses a compilation strategy that makes sure every program gets a chance to make it big! Specifically, Futhark aggressively inlines almost every function at every point it is used. This is not because function calls are expensive (they are not), but because inlining is perhaps the most fundamental enabler of other optimisations. You cannot do loop fusion if the two loops are separated by a function call! Normal compilers spend a lot of time and effort on developing heuristics for which functions to inline, in order to balance code growth and optimisation opportunities, but in Futhark we take the easy way out. This works surprisingly well in practice, because Futhark programs tend to be small, and in particular functions that are called in many places tend to be small. Unfortunately, neptune-triton is not like most Futhark programs.

Fundamentally, neptune-triton is about performing operations on the elements of finite fields. Unsurprisingly, this means that for example the addition function is frequently called from many different locations. Due to the use of static vectors, each of these calls result in an inlined unrolled loop. This makes the generated code quite large. And there is not even much profit to be had: inlining those arithmetic code sequences does not expose any opportunities for optimisation. While neptune-triton’s heavy pressure on the inliner did motivate some compiler improvements that ultimately benefited all programs (mainly parallelisation and interleaving of simplification with inlining), the right solution is clearly to improve our heuristics for inlining. Via manual use of the #[noinline] attribute, I have verified that this could substantially cut compile times.

In theory, large generated GPU kernels could also have a negative performance impact at run-time. In practice, it appears that GPUs are not particularly sensitive to program size - or at least, the kernels will have to be much larger than even what Futhark generates. However, large GPU kernels do still take a while to load, as this requires a form of JIT compilation, which in practice manifests as long program startup times. OpenCL (and CUDA) does allow one to extract the final machine-specific compiled GPU kernel, which can be used to speed up subsequent loads substantially, but Futhark does not make this usage very convenient. This is definitely something we should look at making more accessible.

Also, some low-quality OpenCL implementations (particularly the one Apple uses in macOS) can crash on large programs, further motivating the generation of smaller programs.


Futhark was never intended for writing full applications. Rather, it was always intended that Futhark programs would be invoked by programs written in other languages through a low-level C API. While we did design and implement that API and used it for toy purposes, neptune-triton was the first time it was really put through its paces. Fortunately, it held up well! The choice to design a very low-level API, while verbose, meant that we had little implicit or automatic behaviour that could cause subtle integration issues. Indeed, the main thing neptune-triton accomplished was to encourage us to actually write down full and accurate documentation for the API, which had until then been documented via scattered examples and blog posts.

One interesting aspect of neptune-triton is that it is intended to be made available as a Rust library. To bridge the gap from Rust to the C code generated by Futhark, neptune-triton makes use of genfut, a Rust-Futhark bridge developed by Valdemar Erk. This did require some improvements to genfut, but I was not directly involved, and they did not require any compiler modifications - a nice affirmation of the usability of our C API.

Security audit

After neptune-triton became (supposedly!) correct and (demonstrably!) fast, I was asked whether I would be interested in doing a paid security audit of the implementation. I was initially hesitant, as security audits are best done by third parties with no prior interest or involvement. But I was convinced to agree after it was clarified that the audit concerned not the Futhark compiler itself, nor the cryptographic primitives in neptune-triton, but rather whether neptune-triton itself made correct use of Futhark and its API. That sounded interesting, in particular because it would be an opportunity to think systematically about what it means to use Futhark correctly, and to document it for future use. The final report is publicly available and I believe it is a good starting point for auditing other Futhark programs.

One of the most challenging aspects of writing the report was judging the risk of compiler bugs. Any nontrivial compiler is going to have miscompilation bugs (with rare exceptions), and as Futhark is a pretty complicated compiler with relatively few users, the risk is significant. However, I managed to identify two compensating factors:

Finally, as Futhark is an actually pure language (with no escape hatches like Haskell), any malfunction in a Futhark program is realistically going to be limited to corrupting memory or computing incorrect results - it will not mistakenly delete files from the disk or anything of the sort.

In summary

Optimising compilers are big bags of tricks and heuristics. When mature, it looks like they take a holistic view of compilation, but really the bag has just become so full that it is hard to understand what is happening anymore. This works because most programs are actually quite similar with respect to their optimisation needs. Futhark is not yet this mature, so sometimes we get a program, like neptune-triton, that jut happens to hit multiple weak points at once. But now those points have been fixed, and while it was fun and interesting, I hope it will be a while before we encounter a program of this kind again.