Module melior::dialect::ods::sparse_tensor

source ·
Expand description

sparse_tensor dialect.

The SparseTensor dialect supports all the attributes, types, operations, and passes that are required to make sparse tensor types first class citizens within the MLIR compiler infrastructure. The dialect forms a bridge between high-level operations on sparse tensors types and lower-level operations on the actual sparse storage schemes consisting of positions, coordinates, and values. Lower-level support may consist of fully generated code or may be provided by means of a small sparse runtime support library.

The concept of treating sparsity as a property, not a tedious implementation detail, by letting a sparsifier generate sparse code automatically was pioneered for linear algebra by [Bik96] in MT1 (see https://www.aartbik.com/sparse.php) and formalized to tensor algebra by [Kjolstad17,Kjolstad20] in the Sparse Tensor Algebra Compiler (TACO) project (see http://tensor-compiler.org). Please note that we started to prefer the term “sparsifier” over the also commonly used “sparse compiler” terminology to refer to such a pass to make it clear that the sparsifier pass is not a separate compiler, but should be an integral part of any compiler pipeline that is built with the MLIR compiler infrastructure

The MLIR implementation [Biketal22] closely follows the “sparse iteration theory” that forms the foundation of TACO. A rewriting rule is applied to each tensor expression in the Linalg dialect (MLIR’s tensor index notation) where the sparsity of tensors is indicated using the per-level level-types (e.g., dense, compressed, singleton) together with a specification of the order on the levels (see [Chou18] for an in-depth discussions and possible extensions to these level-types). Subsequently, a topologically sorted iteration graph, reflecting the required order on coordinates with respect to the levels of each tensor, is constructed to ensure that all tensors are visited in natural level-coordinate order. Next, iteration lattices are constructed for the tensor expression for every index in topological order. Each iteration lattice point consists of a conjunction of tensor coordinates together with a tensor (sub)expression that needs to be evaluated for that conjunction. Within the lattice, iteration points are ordered according to the way coordinates are exhausted. As such these iteration lattices drive actual sparse code generation, which consists of a relatively straightforward one-to-one mapping from iteration lattices to combinations of for-loops, while-loops, and if-statements. Sparse tensor outputs that materialize uninitialized are handled with direct insertions if all parallel loops are outermost or insertions that indirectly go through a 1-dimensional access pattern expansion (a.k.a. workspace) where feasible [Gustavson72,Bik96,Kjolstad19].

  • [Bik96] Aart J.C. Bik. Compiler Support for Sparse Matrix Computations. PhD thesis, Leiden University, May 1996.
  • [Biketal22] Aart J.C. Bik, Penporn Koanantakool, Tatiana Shpeisman, Nicolas Vasilache, Bixia Zheng, and Fredrik Kjolstad. Compiler Support for Sparse Tensor Computations in MLIR. ACM Transactions on Architecture and Code Optimization, June, 2022. See: https://dl.acm.org/doi/10.1145/3544559
  • [Chou18] Stephen Chou, Fredrik Berg Kjolstad, and Saman Amarasinghe. Format Abstraction for Sparse Tensor Algebra Compilers. Proceedings of the ACM on Programming Languages, October 2018.
  • [Chou20] Stephen Chou, Fredrik Berg Kjolstad, and Saman Amarasinghe. Automatic Generation of Efficient Sparse Tensor Format Conversion Routines. Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation, June, 2020.
  • [Gustavson72] Fred G. Gustavson. Some basic techniques for solving sparse systems of linear equations. In Sparse Matrices and Their Applications, pages 41–52. Plenum Press, New York, 1972.
  • [Kjolstad17] Fredrik Berg Kjolstad, Shoaib Ashraf Kamil, Stephen Chou, David Lugato, and Saman Amarasinghe. The Tensor Algebra Compiler. Proceedings of the ACM on Programming Languages, October 2017.
  • [Kjolstad19] Fredrik Berg Kjolstad, Peter Ahrens, Shoaib Ashraf Kamil, and Saman Amarasinghe. Tensor Algebra Compilation with Workspaces, Proceedings of the IEEE/ACM International Symposium on Code Generation and Optimization, 2019.
  • [Kjolstad20] Fredrik Berg Kjolstad. Sparse Tensor Algebra Compilation. PhD thesis, MIT, February, 2020.

Structs§

Functions§