Sympiler: Transforming Sparse Matrix Codes by Decoupling Symbolic Analysis

Abstract

Sympiler is a domain-specific code generator that optimizes sparse matrix computations by decoupling the symbolic analysis phase from the numerical manipulation stage in sparse codes. The computation patterns in sparse numerical methods are guided by the input sparsity structure and the sparse algorithm itself. In many real-world simulations, the sparsity pattern changes little or not at all. Sympiler takes advantage of these properties to symbolically analyze sparse codes at compile time and to apply inspector-guided transformations that enable applying low-level transformations to sparse codes. As a result, the Sympiler-generated code outperforms highly-optimized matrix factorization codes from commonly-used specialized libraries, obtaining average speedups over Eigen and CHOLMOD of $3.8 \times$ and $1.5 \times$ respectively. CCS Concepts • Software and its engineering $\rightarrow$ Source code generation; • Computing methodologies $\rightarrow$ Parallel programming languages;