A unified iteration space transformation framework for sparse and dense tensor algebra
Name
1237564498-MIT.pdf
Size
2.42 MB
Format
Adobe PDF
Checksum (MD5)
2340264cd86bd5de4250c27cd2a739bf
Author(s)
Senanayake, Ryan Michael.
Advisor(s)
Saman Amarasinghe.
Date Issued
2020
Publisher
Massachusetts Institute of Technology
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.
Description
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).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
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.
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