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Saman Amarasinghe. Senanayake, Ryan Michael. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science 2021-02-19T20:20:36Z 2021-02-19T20:20:36Z 2020 2020 https://hdl.handle.net/1721.1/129852 1237564498 Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, February, 2020 Cataloged from student-submitted PDF of thesis. Includes bibliographical references (pages 95-99). This work addresses the problem of optimizing mixed sparse and dense tensor algebra in a compiler. I show that standard loop transformations, such as strip-mining, tiling, collapsing, parallelization and vectorization, can be applied to irregular loops over sparse iteration spaces. I also show how these transformations can be applied to the contiguous value arrays of sparse tensor data structures, which I call their position spaces, to unlock load-balanced tiling and parallelism. These concepts have been prototyped in the open-source TACO system, where they are exposed as a scheduling API similar to the Halide domain-specific language for dense computations. Using this scheduling API, I show how to optimize mixed sparse/dense tensor algebra expressions, how to generate load-balanced code by scheduling sparse tensor algebra in position space, and how to generate sparse tensor algebra GPU code. As shown in the evaluation, these transformations allow us to generate code that is competitive with many hand-optimized implementations from the literature. by Ryan Michael Senanayake. M.Eng. M.Eng. Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science 99 pages eng Massachusetts Institute of Technology MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided. http://dspace.mit.edu/handle/1721.1/7582 Electrical Engineering and Computer Science. A unified iteration space transformation framework for sparse and dense tensor algebra Thesis application/pdf 2021-02-19T20:20:06Z Publication Master EECS unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="fac2bf78-0f9b-4b0b-af0b-36782bddb510"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>A unified iteration space transformation framework for sparse and dense tensor algebra</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2020</PublicationDate> <Authors> <Author> <DisplayName>Senanayake, Ryan Michael.</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Electrical Engineering and Computer Science.</Keyword> <Abstract>This work addresses the problem of optimizing mixed sparse and dense tensor algebra in a compiler. I show that standard loop transformations, such as strip-mining, tiling, collapsing, parallelization and vectorization, can be applied to irregular loops over sparse iteration spaces. I also show how these transformations can be applied to the contiguous value arrays of sparse tensor data structures, which I call their position spaces, to unlock load-balanced tiling and parallelism. These concepts have been prototyped in the open-source TACO system, where they are exposed as a scheduling API similar to the Halide domain-specific language for dense computations. Using this scheduling API, I show how to optimize mixed sparse/dense tensor algebra expressions, how to generate load-balanced code by scheduling sparse tensor algebra in position space, and how to generate sparse tensor algebra GPU code. As shown in the evaluation, these transformations allow us to generate code that is competitive with many hand-optimized implementations from the literature.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>