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We propose the Sparse Abstract Machine (SAM), an abstract machine model for targeting sparse tensor algebra to reconfigurable and fixed-function spatial dataflow accelerators. SAM defines a streaming dataflow abstraction with sparse primitives that encompass a large space of scheduled tensor algebra expressions. SAM dataflow graphs naturally separate tensor formats from algorithms and are expressive enough to incorporate arbitrary iteration orderings and many hardware-specific op timizations. We also present Custard, a compiler from a high-level language to SAM that demonstrates SAM's usefulness as an intermediate representation. We automatica lly bind from SAM to a streaming dataflow simulator. We evaluate the generality and extensibility of SAM, explore the performance space of sparse tensor algebra optim izations using SAM, and show SAM's ability to represent dataflow hardware.
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Indexed Streams: A Formal Intermediate Representation for Fused Contraction Programs
We introduce indexed streams, a formal operational model and intermediate representation that describes the fused execution of a contraction language that encompasses both sparse tensor algebra and relational algebra. We prove that the indexed stream model is correct with respect to a functional semantics. We also develop a compiler for contraction expressions that uses indexed streams as an intermediate representation. The compiler is only 540 lines of code, but we show that its performance can match both the TACO compiler for sparse tensor algebra and the SQLite and DuckDB query processing libraries for relational algebra.
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- PAR ID:
- 10466652
- Publisher / Repository:
- ACM
- Date Published:
- Journal Name:
- Proceedings of the ACM on Programming Languages
- Volume:
- 7
- Issue:
- PLDI
- ISSN:
- 2475-1421
- Page Range / eLocation ID:
- 1169 to 1193
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1145/3591268
