DIV: An Index & Value compression method for SpMV on large matrices

Abstract

SpMV on large matrices is a heavily memory-bound kernel, a characteristic attributed to its extremely low computational intensity. To address this, research has mainly focused on compressing the matrix indices. Nevertheless, the values of a matrix usually occupy up to two thirds of the total size. Research on value compression, on the other hand, has been limited to specific matrix types. In this paper, we propose DIV, a combined index and value lossless compression scheme, based on variations of delta and run-length encoding, that achieves substantially improved SpMV performance for large matrices, i.e., those that exceed the CPU cache. We evaluate its performance against other state-of-the-art matrix formats, on an Intel Xeon and an AMD EPYC platform. Our format achieves and geometric mean speedup respectively versus the Intel MKL library. We finally demonstrate the applicability of DIV on a Biconjugate Gradient Stabilized solver, where we also achieve significant speedups.