arXiv subjects

Tobias Grosser

Publications and source records attributed to Tobias Grosser.

At least 19 recordsLinked to original sources

arXiv2026

A Dynamic Intermediate Representation for Hybrid Quantum-Classical Programs

Quantum compilers typically follow the circuit model, representing programs as fixed sequences of gates. This static view breaks down in hybrid quantum-classical applications, where gate choices depend on runtime data or measurement results. We introduce a new Intermediate Representation (IR) that elevates gates to first-class values, enabling their dynamic creation, composition, and control. This unified representation allows classical computation to steer quantum behaviour, capturing phenomena including stochastic gate selection, adaptive error correction, and measurement-driven computation within a single framework. Case studies in noise modelling, randomised compilation, error correction, and measurement-based quantum computing show that our IR expresses these programs compactly and supports optimisations that were not possible in the circuit model. Evaluation on a benchmark suite of hybrid quantum-classical programs indicates that our IR represents programs compactly and facilitates compiler analysis and transformation.

cs.PL↗

arXiv2026

E-Graphs as a Persistent Compiler Abstraction

Recent algorithmic advances have made equality saturation an appealing technique for program optimization, avoiding the phase-ordering problem by separating the discovery of equivalent expressions from optimal expression selection. Existing work leveraging equality saturation in compilers uses either external equality saturation libraries or custom implementations that are coupled to the specific application. These approaches are inherently limited, as the first discards semantic equivalences when translating back from the external library, while the second restricts equality saturation to a single level of abstraction. We propose an alternative approach that represents an e-graph natively in code, facilitating the application of constructive compiler passes that maintain the e-graph state throughout the compilation flow. We present Tamagoyaki, an implementation of this approach in MLIR and demonstrate its versatility through partial re-implementations of two equality saturation applications. Our software case study improves performance by 1.18$\times$ on average, whilst our hardware case study reduces circuit delay by up to 11% over standard equality saturation. Building on reusable compiler infrastructure, our work expands the scope of equality saturation, making it persistent across and interleavable with other analyses and transformations.

cs.PL↗

arXiv2026

An MLIR Lowering Pipeline for Stencils at Wafer-Scale

The Cerebras Wafer-Scale Engine (WSE) delivers performance at an unprecedented scale of over 900,000 compute units, all connected via a single-wafer on-chip interconnect. Initially designed for AI, the WSE architecture is also well-suited for High Performance Computing (HPC). However, its distributed asynchronous programming model diverges significantly from the simple sequential or bulk-synchronous programs that one would typically derive for a given mathematical program description. Targeting the WSE requires a bespoke re-implementation when porting existing code. The absence of WSE support in compilers such as MLIR, meant that there was little hope for automating this process. Stencils are ubiquitous in HPC, and in this paper we explore the hypothesis that domain specific information about stencils can be leveraged by the compiler to automatically target the WSE without requiring application-level code changes. We present a compiler pipeline that transforms stencil-based kernels into highly optimized CSL code for the WSE, bridging the semantic gap between the mathematical representation of the problem and the WSE's asynchronous execution model. Based upon five benchmarks across three HPC programming technologies, running on both the Cerebras WSE2 and WSE3, our approach delivers comparable, if not slightly better, performance than manually optimized code. Furthermore, without requiring any application level code changes, performance on the WSE3 is around 14 times faster than 128 Nvidia A100 GPUs and 20 times faster than 128 nodes of a CPU-based Cray-EX supercomputer when using our approach.

cs.DC↗

arXiv2025

The Configuration Wall: Characterization and Elimination of Accelerator Configuration Overhead

Contemporary compute platforms increasingly offload compute kernels from CPU to integrated hardware accelerators to reach maximum performance per Watt. Unfortunately, the time the CPU spends on setup control and synchronization has increased with growing accelerator complexity. For systems with complex accelerators, this means that performance can be configuration-bound. Faster accelerators are more severely impacted by this overlooked performance drop, which we call the configuration wall. Prior work evidences this wall and proposes ad-hoc solutions to reduce configuration overhead. However, these solutions are not universally applicable, nor do they offer comprehensive insights into the underlying causes of performance degradation. In this work, we first introduce a widely-applicable variant of the well-known roofline model to quantify when system performance is configuration-bound. To move systems out of the performance-bound region, we subsequently propose a domain-specific compiler abstraction and associated optimization passes. We implement the abstraction and passes in the MLIR compiler framework to run optimized binaries on open-source architectures to prove its effectiveness and generality. Experiments demonstrate a geomean performance boost of 2x on the open-source OpenGeMM system, by eliminating redundant configuration cycles and by automatically hiding the remaining configuration cycles. Our work provides key insights in how accelerator performance is affected by setup mechanisms, thereby facilitating automatic code generation for circumventing the configuration wall.

cs.PF↗

arXiv2025

eqsat: An Equality Saturation Dialect for Non-destructive Rewriting

With recent algorithmic improvements and easy-to-use libraries, equality saturation is being picked up for hardware design, program synthesis, theorem proving, program optimization, and more. Existing work on using equality saturation for program optimization makes use of external equality saturation libraries such as egg, typically generating a single optimized expression. In the context of a compiler, such an approach uses equality saturation to replace a small number of passes. In this work, we propose an alternative approach that represents equality saturation natively in the compiler's intermediate representation, facilitating the application of constructive compiler passes that maintain the e-graph state throughout the compilation flow. We take LLVM's MLIR framework and propose a new MLIR dialect named eqsat that represents e-graphs in MLIR code. This not only provides opportunities to rethink e-matching and extraction techniques by orchestrating existing MLIR passes, such as common subexpression elimination, but also avoids translation overhead between the chosen e-graph library and MLIR. Our eqsat intermediate representation (IR) allows programmers to apply equality saturation on arbitrary domain-specific IRs using the same flow as other compiler transformations in MLIR.

cs.PL↗

arXiv2025

A shared compilation stack for distributed-memory parallelism in stencil DSLs

Domain Specific Languages (DSLs) increase programmer productivity and provide high performance. Their targeted abstractions allow scientists to express problems at a high level, providing rich details that optimizing compilers can exploit to target current- and next-generation supercomputers. The convenience and performance of DSLs come with significant development and maintenance costs. The siloed design of DSL compilers and the resulting inability to benefit from shared infrastructure cause uncertainties around longevity and the adoption of DSLs at scale. By tailoring the broadly-adopted MLIR compiler framework to HPC, we bring the same synergies that the machine learning community already exploits across their DSLs (e.g. Tensorflow, PyTorch) to the finite-difference stencil HPC community. We introduce new HPC-specific abstractions for message passing targeting distributed stencil computations. We demonstrate the sharing of common components across three distinct HPC stencil-DSL compilers: Devito, PSyclone, and the Open Earth Compiler, showing that our framework generates high-performance executables based upon a shared compiler ecosystem.

cs.DC↗

arXiv2025

A Multi-level Compiler Backend for Accelerated Micro-kernels Targeting RISC-V ISA Extensions

High-performance micro-kernels must fully exploit today's diverse and specialized hardware to deliver peak performance to DNNs. While higher-level optimizations for DNNs are offered by numerous compilers (e.g., MLIR, TVM, OpenXLA), performance-critical micro-kernels are left to specialized code generators or handwritten assembly. Even though widely-adopted compilers (e.g., LLVM, GCC) offer tuned backends, their CPU-focused input abstraction, unstructured IR, and general-purpose best-effort design inhibit tailored code generation for innovative hardware. We think it is time to widen the classical hourglass backend and embrace progressive lowering across a diverse set of structured abstractions to bring domain-specific code generation to compiler backends. We demonstrate this concept by implementing a custom backend for a RISC-V-based accelerator with hardware loops and streaming registers, leveraging knowledge about the hardware at levels of abstraction that match its custom ISA. We use incremental register allocation over structured IRs, while dropping classical spilling heuristics, and show up to 90% FPU utilization across key DNN kernels. By breaking the backend hourglass model, we reopen the path from domain-specific abstractions to specialized hardware.

cs.PL↗

arXiv2024

Compressing Structured Tensor Algebra

Tensor algebra is a crucial component for data-intensive workloads such as machine learning and scientific computing. As the complexity of data grows, scientists often encounter a dilemma between the highly specialized dense tensor algebra and efficient structure-aware algorithms provided by sparse tensor algebra. In this paper, we introduce DASTAC, a framework to propagate the tensors's captured high-level structure down to low-level code generation by incorporating techniques such as automatic data layout compression, polyhedral analysis, and affine code generation. Our methodology reduces memory footprint by automatically detecting the best data layout, heavily benefits from polyhedral optimizations, leverages further optimizations, and enables parallelization through MLIR. Through extensive experimentation, we show that DASTAC achieves 1 to 2 orders of magnitude speedup over TACO, a state-of-the-art sparse tensor compiler, and StructTensor, a state-of-the-art structured tensor algebra compiler, with a significantly lower memory footprint.

cs.PL↗

arXiv2024

Strided Difference Bound Matrices

A wide range of symbolic analysis and optimization problems can be formalized using polyhedra. Sub-classes of polyhedra, also known as sub-polyhedral domains, are sought for their lower space and time complexity. We introduce the Strided Difference Bound Matrix (SDBM) domain, which represents a sweet spot in the context of optimizing compilers. Its expressiveness and efficient algorithms are particularly well suited to the construction of machine learning compilers. We present decision algorithms, abstract domain operators and computational complexity proofs for SDBM. We also conduct an empirical study with the MLIR compiler framework to validate the domain's practical applicability. We characterize a sub-class of SDBMs that frequently occurs in practice, and demonstrate even faster algorithms on this sub-class.

cs.SC↗

arXiv2024

Verifying Peephole Rewriting In SSA Compiler IRs

There is an increasing need for domain-specific reasoning in modern compilers. This has fueled the use of tailored intermediate representations (IRs) based on static single assignment (SSA), like in the MLIR compiler framework. Interactive theorem provers (ITPs) provide strong guarantees for the end-to-end verification of compilers (e.g., CompCert). However, modern compilers and their IRs evolve at a rate that makes proof engineering alongside them prohibitively expensive. Nevertheless, well-scoped push-button automated verification tools such as the Alive peephole verifier for LLVM-IR gained recognition in domains where SMT solvers offer efficient (semi) decision procedures. In this paper, we aim to combine the convenience of automation with the versatility of ITPs for verifying peephole rewrites across domain-specific IRs. We formalize a core calculus for SSA-based IRs that is generic over the IR and covers so-called regions (nested scoping used by many domain-specific IRs in the MLIR ecosystem). Our mechanization in the Lean proof assistant provides a user-friendly frontend for translating MLIR syntax into our calculus. We provide scaffolding for defining and verifying peephole rewrites, offering tactics to eliminate the abstraction overhead of our SSA calculus. We prove correctness theorems about peephole rewriting, as well as two classical program transformations. To evaluate our framework, we consider three use cases from the MLIR ecosystem that cover different levels of abstractions: (1) bitvector rewrites from LLVM, (2) structured control flow, and (3) fully homomorphic encryption. We envision that our mechanization provides a foundation for formally verified rewrites on new domain-specific IRs.

cs.PL↗

arXiv2024

Sidekick compilation with xDSL

Traditionally, compiler researchers either conduct experiments within an existing production compiler or develop their own prototype compiler; both options come with trade-offs. On one hand, prototyping in a production compiler can be cumbersome, as they are often optimized for program compilation speed at the expense of software simplicity and development speed. On the other hand, the transition from a prototype compiler to production requires significant engineering work. To bridge this gap, we introduce the concept of sidekick compiler frameworks, an approach that uses multiple frameworks that interoperate with each other by leveraging textual interchange formats and declarative descriptions of abstractions. Each such compiler framework is specialized for specific use cases, such as performance or prototyping. Abstractions are by design shared across frameworks, simplifying the transition from prototyping to production. We demonstrate this idea with xDSL, a sidekick for MLIR focused on prototyping and teaching. xDSL interoperates with MLIR through a shared textual IR and the exchange of IRs through an IR Definition Language. The benefits of sidekick compiler frameworks are evaluated by showing on three use cases how xDSL impacts their development: teaching, DSL compilation, and rewrite system prototyping. We also investigate the trade-offs that xDSL offers, and demonstrate how we simplify the transition between frameworks using the IRDL dialect. With sidekick compilation, we envision a future in which engineers minimize the cost of development by choosing a framework built for their immediate needs, and later transitioning to production with minimal overhead.

cs.PL↗

arXiv2023

mlirSynth: Automatic, Retargetable Program Raising in Multi-Level IR using Program Synthesis

MLIR is an emerging compiler infrastructure for modern hardware, but existing programs cannot take advantage of MLIR's high-performance compilation if they are described in lower-level general purpose languages. Consequently, to avoid programs needing to be rewritten manually, this has led to efforts to automatically raise lower-level to higher-level dialects in MLIR. However, current methods rely on manually-defined raising rules, which limit their applicability and make them challenging to maintain as MLIR dialects evolve. We present mlirSynth -- a novel approach which translates programs from lower-level MLIR dialects to high-level ones without manually defined rules. Instead, it uses available dialect definitions to construct a program space and searches it effectively using type constraints and equivalences. We demonstrate its effectiveness \revi{by raising C programs} to two distinct high-level MLIR dialects, which enables us to use existing high-level dialect specific compilation flows. On Polybench, we show a greater coverage than previous approaches, resulting in geomean speedups of 2.5x (Intel) and 3.4x (AMD) over state-of-the-art compilation flows for the C programming language. mlirSynth also enables retargetability to domain-specific accelerators, resulting in a geomean speedup of 21.6x on a TPU.

cs.PL↗

arXiv2023

Fortran performance optimisation and auto-parallelisation by leveraging MLIR-based domain specific abstractions in Flang

MLIR has become popular since it was open sourced in 2019. A sub-project of LLVM, the flexibility provided by MLIR to represent Intermediate Representations (IR) as dialects at different abstraction levels, to mix these, and to leverage transformations between dialects provides opportunities for automated program optimisation and parallelisation. In addition to general purpose compilers built upon MLIR, domain specific abstractions have also been developed. In this paper we explore complimenting the Flang MLIR general purpose compiler by combining with the domain specific Open Earth Compiler's MLIR stencil dialect. Developing transformations to discover and extracts stencils from Fortran, this specialisation delivers between a 2 and 10 times performance improvement for our benchmarks on a Cray supercomputer compared to using Flang alone. Furthermore, by leveraging existing MLIR transformations we develop an auto-parallelisation approach targeting multi-threaded and distributed memory parallelism, and optimised execution on GPUs, without any modifications to the serial Fortran source code.

cs.DC↗

arXiv2023

Stencil-HMLS: A multi-layered approach to the automatic optimisation of stencil codes on FPGA

The challenges associated with effectively programming FPGAs have been a major blocker in popularising reconfigurable architectures for HPC workloads. However new compiler technologies, such as MLIR, are providing new capabilities which potentially deliver the ability to extract domain specific information and drive automatic structuring of codes for FPGAs. In this paper we explore domain specific optimisations for stencils, a fundamental access pattern in scientific computing, to obtain high performance on FPGAs via automated code structuring. We propose Stencil-HMLS, a multi-layered approach to automatic optimisation of stencil codes and introduce the HLS dialect, which brings FPGA programming into the MLIR ecosystem. Using the PSyclone Fortran DSL, we demonstrate an improvement of 14-100$\times$ with respect to the next best performant state-of-the-art tool. Furthermore, our approach is 14 to 92 times more energy efficient than the next most energy efficient approach.

cs.DC↗

arXiv2022

TensorFlow as a DSL for stencil-based computation on the Cerebras Wafer Scale Engine

The Cerebras Wafer Scale Engine (WSE) is an accelerator that combines hundreds of thousands of AI-cores onto a single chip. Whilst this technology has been designed for machine learning workloads, the significant amount of available raw compute means that it is also a very interesting potential target for accelerating traditional HPC computational codes. Many of these algorithms are stencil-based, where update operations involve contributions from neighbouring elements, and in this paper we explore the suitability of this technology for such codes from the perspective of an early adopter of the technology, compared to CPUs and GPUs. Using TensorFlow as the interface, we explore the performance and demonstrate that, whilst there is still work to be done around exposing the programming interface to users, performance of the WSE is impressive as it out performs four V100 GPUs by two and a half times and two Intel Xeon Platinum CPUs by around 114 times in our experiments. There is significant potential therefore for this technology to play an important role in accelerating HPC codes on future exascale supercomputers.

cs.DC↗

arXiv2022

MOM: Matrix Operations in MLIR

Modern research in code generators for dense linear algebra computations has shown the ability to produce optimized code with a performance which compares and often exceeds the one of state-of-the-art implementations by domain experts. However, the underlying infrastructure is often developed in isolation making the interconnection of logically combinable systems complicated if not impossible. In this paper, we propose to leverage MLIR as a unifying compiler infrastructure for the optimization of dense linear algebra operations. We propose a new MLIR dialect for expressing linear algebraic computations including matrix properties to enable high-level algorithmic transformations. The integration of this new dialect in MLIR enables end-to-end compilation of matrix computations via conversion to existing lower-level dialects already provided by the framework.

cs.PL↗

arXiv2022

Lambda the Ultimate SSA: Optimizing Functional Programs in SSA

Static Single Assignment (SSA) is the workhorse of modern optimizing compilers for imperative programming languages. However, functional languages have been slow to adopt SSA and prefer to use intermediate representations based on minimal lambda calculi due to SSA's inability to express higher order constructs. We exploit a new SSA construct -- regions -- in order to express functional optimizations via classical SSA based reasoning. Region optimization currently relies on ad-hoc analyses and transformations on imperative programs. These ad-hoc transformations are sufficient for imperative languages as regions are used in a limited fashion. In contrast, we use regions pervasively to model sub-expressions in our functional IR. This motivates us to systematize region optimizations. We extend classical SSA reasoning to regions for functional-style analyses and transformations. We implement a new SSA+regions based backend for LEAN4, a theorem prover that implements a purely functional, dependently typed programming language. Our backend is feature-complete and handles all constructs of LEAN4's functional intermediate representation λrc within the SSA framework. We evaluate our proposed region optimizations by optimizing λrc within an SSA+regions based framework implemented in MLIR and demonstrating performance parity with the current LEAN4 backend. We believe our work will pave the way for a unified optimization framework capable of representing, analyzing, and optimizing both functional and imperative languages.

cs.PL↗

arXiv2020

Extracting Clean Performance Models from Tainted Programs

Performance models are well-known instruments to understand the scaling behavior of parallel applications. They express how performance changes as key execution parameters, such as the number of processes or the size of the input problem, vary. Besides reasoning about program behavior, such models can also be automatically derived from performance data. This is called empirical performance modeling. While this sounds simple at the first glance, this approach faces several serious interrelated challenges, including expensive performance measurements, inaccuracies inflicted by noisy benchmark data, and overall complex experiment design, starting with the selection of the right parameters. The more parameters one considers, the more experiments are needed and the stronger the impact of noise. In this paper, we show how taint analysis, a technique borrowed from the domain of computer security, can substantially improve the modeling process, lowering its cost, improving model quality, and help validate performance models and experimental setups.

cs.DC↗