Optimization techniques for sparse matrix-vector multiplication on GPUs

Sparse linear algebra is fundamental to numerous areas of applied mathematics, science and engineering. In this paper, we propose an efficient data structure named AdELL+ for optimizing the SpMV kernel on GPUs, focusing on performance bottlenecks of sparse computation. The foundation of our work is an ELL-based adaptive format which copes with matrix irregularity using balanced warps composed using a parametrized warp-balancing heuristic. We also address the intrinsic bandwidth-limited nature of SpMV with warp granularity, blocking, delta compression and nonzero unrolling, targeting both memory footprint and memory hierarchy efficiency. Finally, we introduce a novel online auto-tuning approach that uses a quality metric to predict efficient block factors and that hides preprocessing overhead with useful SpMV computation. Our experimental results show that AdELL+ achieves comparable or better performance over other state-of-the-art SpMV sparse formats proposed in academia (BCCOO) and industry (CSR+ and CSR-Adaptive). Moreover, our auto-tuning approach makes AdELL+ viable for real world applications. (C) 2016 Elsevier Inc. All rights reserved.