Optimizing Sparse Matrix Computations for Register Reuse in SPARSITY

Abstract. Sparse matrix-vector multiplication is an important computational kernel that tends to perform poorly on modern processors, largely because of its high ratio of memory operations to arithmetic operations. Optimizing this algorithm is difficult, both because of the complexity of memory systems and because the performance is highly dependent on the nonzero structure of the matrix. The Sparsity system is designed to address these problem by allowing users to automatically build sparse matrix kernels that are tuned to their matrices and machines. The most difficult aspect of optimizing these algorithms is selecting among a large set of possible transformations and choosing parameters, such as block size. In this paper we discuss the optimization of two operations: a sparse matrix times a dense vector and a sparse matrix times a set of dense vectors. Our experience indicates that for matrices arising in scientific simulations, register level optimizations are critical, and we foc...

• Type: Conference
• Year: 2001
• Where: ICCS
• Authors: Eun-Jin Im, Katherine A. Yelick
• Keywords: Applied Computing, ICCS 2001, Sparse Matrix, Sparse Matrix Times, Sparse Matrix-vector Multiplication