Finally, a Polymorphic Linear Algebra Language

Many different data analytics tasks boil down to linear algebra primitives. In practice, for each different type of workload, data scientists use a particular specialised library. In this paper, we present Pilatus, a polymorphic iterative linear algebra language, applicable to various types of data analytics workloads. The design of this domain-specific language (DSL) is inspired by both mathematics and programming languages: its basic constructs are borrowed from abstract algebra, whereas the key technology behind its polymorphic design uses the tagless final approach (a.k.a. polymorphic embedding/object algebras). This design enables us to change the behaviour of arithmetic operations to express matrix algebra, graph algorithms, logical probabilistic programs, and differentiable programs. Crucially, the polymorphic design of Pilatus allows us to use multistage programming and rewrite-based optimisation to recover the performance of specialised code, supporting fixed sized matrices, algebraic optimisations, and fusion.

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Lionel Emile Vincent Parreaux, Amir Shaikhha
2019
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https://infoscience.epfl.ch/record/266001?ln=en

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StagedSAC: a case study in performance-oriented DSL development

Hassan Chafi, Martin Odersky, Tiark Rompf, Vlad Ureche

Domain-specific languages (DSLs) can bridge the gap between high-level programming and efficient execution. However, implementing compiler tool-chains for performance oriented DSLs requires significant effort. Recent research has produced methodologies and frameworks that promise to reduce this development effort by enabling quick transition from library-only, purely embedded DSLs to optimizing compilation. In this case study we report on our experience implementing a compiler for StagedSAC. StagedSAC is a DSL for arithmetic processing with multidimensional arrays modeled after the stand-alone language SAC (Single Assignment C). The main language feature of both SAC and StagedSAC is a loop construction that enables high-level and concise implementations of array algorithms. At the same time, the functional semantics of the two languages allow for advanced compiler optimizations and parallel code generation. We describe how we were able to quickly evolve from a pure library DSL to a performance-oriented compiler with a good speedup and only minor syntax changes using the technique of Lightweight Modular Staging. We also describe the optimizations we perform to obtain fast code and how we plan to generate parallel code with minimal effort using the Delite framework.

ACM2011

Spiral in Scala: Towards the Systematic Construction of Generators for Performance Libraries

Martin Odersky, Tiark Rompf, Alen Stojanov

Program generators for high performance libraries are an appealing solution to the recurring problem of porting and optimizing code with every new processor generation, but only few such generators exist to date. This is due to not only the difficulty of the design, but also of the actual implementation, which often results in an ad-hoc collection of standalone programs and scripts that are hard to extend, maintain, or reuse. In this paper we ask whether and which programming language concepts and features are needed to enable a more systematic construction of such generators. The systematic approach we advocate extrapolates from existing generators: a) describing the problem and algorithmic knowledge using one, or several, domain-specific languages (DSLs), b) expressing optimizations and choices as rewrite rules on DSL programs, c) designing data structures that can be configured to control the type of code that is generated and the data representation used, and d) using autotuning to select the best-performing alternative. As a case study, we implement a small, but representative subset of Spiral in Scala using the Lightweight Modular Staging (LMS) framework. The first main contribution of this paper is the realization of c) using type classes to abstract over staging decisions, i.e. which pieces of a computation are performed immediately and for which pieces code is generated. Specifically, we abstract over different complex data representations jointly with different code representations including generating loops versus unrolled code with scalar replacement-a crucial and usually tedious performance transformation. The second main contribution is to provide full support for a) and d) within the LMS framework: we extend LMS to support translation between different DSLs and autotuning through search.

Assoc Computing Machinery2014

Domain-specific language

A domain-specific language (DSL) is a computer language specialized to a particular application domain. This is in contrast to a general-purpose language (GPL), which is broadly applicable across dom

Abstract algebra

In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattic

Programming language

A programming language is a system of notation for writing computer programs. Most programming languages are text-based formal languages, but they may also be graphical. They are a kind of computer