This paper shows how to compile sparse array programming languages. A sparse array programming language is an array programming language that supports element-wise application, reduction, and broadcasting of arbitrary functions over dense and sparse arrays with any fill value. Such a language has great expressive power and can express sparse and dense linear and tensor algebra, functions over images, exclusion and inclusion filters, and even graph algorithms. Our compiler strategy generalizes prior work in the literature on sparse tensor algebra compilation to support any function applied to sparse arrays, instead of only addition and multiplication. To achieve this, we generalize the notion of sparse iteration spaces beyond intersections and unions. These iteration spaces are automatically derived by considering how algebraic properties annotated onto functions interact with the fill values of the arrays. We then show how to compile these iteration spaces to efficient code. When compared with two widely-used Python sparse array packages, our evaluation shows that we generate built-in sparse array library features with a performance of 1.4× to 53.7× when measured against PyData/Sparse for user-defined functions and between 0.98× and 5.53× when measured against SciPy/Sparse for sparse array slicing. Our technique outperforms PyData/Sparse by 6.58× to 70.3×, and (where applicable) performs between 0.96× and 28.9× that of a dense NumPy implementation, on end-to-end sparse array applications. We also implement graph linear algebra kernels in our system with a performance of between 0.56× and 3.50× compared to that of the hand-optimized SuiteSparse:GraphBLAS library.

Nested parallelism has proved to be a popular approach for programming the rapidly expanding range of multicore computers. It allows programmers to express parallelism at a high level and relies on a run-time system and a scheduler to deliver efficiency and scalability. As a result, many programming languages and extensions that support nested parallelism have been developed, including in C/C++, Java, Haskell, and ML. Yet, writing efficient and scalable nested parallel programs remains challenging, primarily due to difficult concurrency bugs arising from destructive updates or effects. For decades, researchers have argued that functional programming can simplify writing parallel programs by allowing more control over effects but functional programs continue to underperform in comparison to parallel programs written in lower-level languages. The fundamental difficulty with functional languages is that they have high demand for memory, and this demand only grows with parallelism. In this paper, we identify a memory property, called disentanglement, of nested-parallel programs, and propose memory management techniques for improved efficiency and scalability. Disentanglement allows for (destructive) effects as long as concurrently executing threads do not gain knowledge of the memory objects allocated by each other. We formally define disentanglement by considering an ML-like higher-order language with mutable references and presenting a dynamic semantics for it that enables reasoning about computation graphs of nested parallel programs. Based on this graph semantics, we formalize a classic correctness propertyÐ determinacy race freedomÐand prove that it implies disentanglement. This establishes that disentanglement applies to a relatively broad class of parallel programs. We then propose memory management techniques for nested-parallel programs that take advantage of disentanglement for improved efficiency and scalability. We show that these techniques are practical by extending the MLton compiler for Standard ML to support this form of nested parallelism. Our empirical evaluation shows that our techniques are efficient and scale well. CCS Concepts: • Software and its engineering → Garbage collection; Parallel programming languages; Functional languages; • Theory of computation → Parallel algorithms.

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