A new diagonal blocking format and model of cache behavior for sparse matrices

Algorithms for the sparse matrix-vector multiplication (shortly SpMxV) are important building blocks in solvers of sparse systems of linear equations. Due to matrix sparsity, the memory access patterns are irregular and the utilization of a cache suffers from low spatial and\ud temporal locality. To reduce this effect, the diagonal register blocking format was designed. This paper introduces a new combined format, called\ud CARB, for storing sparse matrices that extends possibilities of the diagonal register blocking format.\ud \ud We have also developed a probabilistic model for estimating the numbers of cache misses during the SpMxV in the CARB format. Using HW cache monitoring tools, we compare the predicted numbers of cache misses with real numbers on Intel x86 architecture with L1 and L2 caches. The average accuracy of our analytical model is around 95% in case of\ud L2 cache and 88% in case of L1 cache