Adaptive sparse matrix-matrix multiplication on the GPU

Abstract

In the ongoing efforts targeting the vectorization of linear algebra primitives, sparse matrix-matrix multiplication (SpGEMM) has received considerably less attention than sparse Matrix-Vector multiplication (SpMV). While both are equally important, this disparity can be attributed mainly to the additional formidable challenges raised by SpGEMM. In this paper, we present a dynamic approach for addressing SpGEMM on the GPU. Our approach works directly on the standard compressed sparse rows (CSR) data format. In comparison to previous SpGEMM implementations, our approach guarantees a homogeneous, load-balanced access pattern to the first input matrix and improves memory access to the second input matrix. It adaptively re-purposes GPU threads during execution and maximizes the time efficient on-chip scratchpad memory can be used. Adhering to a completely deterministic scheduling pattern guarantees bit-stable results during repetitive execution, a property missing from other approaches. Evaluation on an extensive sparse matrix benchmark suggests our approach being the fastest SpGEMM implementation for highly sparse matrices (80% of the set). When bit-stable results are sought, our approach is the fastest across the entire test set.