This paper studies the relationship between storage requirements and performance.Storage-related dependences inhibit optimizations for locality and parallelism.

This paper introduces three new compiler transformations for representing and transforming sparse matrix computations and their data representations. In cooperation with run-time inspection, our compiler derives transformed matrix representations and associated transformed code to implement a variety of representations targeting different architecture platforms. This systematic approach to combining code and data transformations on sparse computations, which extends a polyhedral transformation and code generation framework, permits the compiler to compose these transformations with other transformations to generate code that is on average within 5% and often exceeds manually-tuned, highperformance sparse matrix libraries CUSP and OSKI. Additionally, the compiler-generated inspector codes are on average 1.5× faster than OSKI and perform comparably to CUSP, respectively.

In modern computers, a program’s data locality can affect performance significantly. This paper details full sparse tiling, a run-time reordering transformation that improves the data locality for stationary iterative methods such as Gauss–Seidel operating on sparse matrices. In scientific applications such as finite element analysis, these iterative methods dominate the execution time. Full sparse tiling chooses a permutation of the rows and columns of the sparse matrix, and then an order of execution that achieves better data locality. We prove that full sparsetiled Gauss–Seidel generates a solution that is bitwise identical to traditional Gauss–Seidel on the permuted matrix. We also present measurements of the performance improvements and the overheads of full sparse tiling and of cache blocking for irregular grids, a related technique developed by Douglas et al.

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