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Automated code generation and performance enhancements for sparse tensor algebra have become essential in many real-world applications, such as quantum computing, physical simulations, computational chemistry, and machine learning. General sparse tensor algebra compilers are not always versatile enough to generate asymptotically optimal code for sparse tensor contractions. This paper shows how to generate asymptotically better schedules for complex sparse tensor expressions using kernel fission and fusion. We present generalized loop restructuring transformations to reduce asymptotic time complexity and memory footprint. Furthermore, we present an auto-scheduler that uses a partially ordered set (poset)-based cost model that uses both time and auxiliary memory complexities to prune the search space of schedules. In addition, we highlight the use of Satisfiability Module Theory (SMT) solvers in sparse auto-schedulers to approximate the Pareto frontier of better schedules to the smallest number of possible schedules, with user-defined constraints available at compile-time. Finally, we show that our auto-scheduler can select better-performing schedules and generate code for them. Our results show that the auto-scheduler provided schedules achieve orders-of-magnitude speedup compared to the code generated by the Tensor Algebra Compiler (TACO) for several computations on different real-world tensors.

 

Many applications are designed to perform traversals ontree-likedata structures. Fusing and parallelizing these traversals enhance the performance of applications. Fusing multiple traversals improves the locality of the application. The runtime of an application can be significantly reduced by extracting parallelism and utilizing multi-threading. Prior frameworks have tried to fuse and parallelize tree traversals using coarse-grained approaches, leading to missed fine-grained opportunities for improving performance. Other frameworks have successfully supported fine-grained fusion on heterogeneous tree types but fall short regarding parallelization. We introduce a new frameworkOrchardbuilt on top ofGrafter.Orchard’s novelty lies in allowing the programmer to transform tree traversal applications by automatically applyingfine-grainedfusion and extractingheterogeneousparallelism.Orchardallows the programmer to write general tree traversal applications in a simple and elegant embedded Domain-Specific Language (eDSL). We show that the combination of fine-grained fusion and heterogeneous parallelism performs better than each alone when the conditions are met.

 

While programmers know that memory representation of data structures can have significant effects on performance, compiler support to optimize the layout of those structures is an under-explored field. Prior work has optimized the layout of individual, non-recursive structures without considering how collections of those objects in linked or recursive data structures are laid out. This work introduces Marmoset, a compiler that optimizes the layouts of algebraic datatypes, with a special focus on producing highly optimized, packed data layouts where recursive structures can be traversed with minimal pointer chasing. Marmoset performs an analysis of how a recursive ADT is used across functions to choose a global layout that promotes simple, strided access for that ADT in memory. It does so by building and solving a constraint system to minimize an abstract cost model, yielding a predicted efficient layout for the ADT. Marmoset then builds on top of Gibbon, a prior compiler for packed, mostly-serial representations, to synthesize optimized ADTs. We show experimentally that Marmoset is able to choose optimal layouts across a series of microbenchmarks and case studies, outperforming both Gibbon’s baseline approach, as well as MLton, a Standard ML compiler that uses traditional pointer-heavy representations.