ASA: <u>A</u> ccelerating <u>S</u> parse <u>A</u> ccumulation in Column-wise SpGEMM

Sparse linear algebra is an important kernel in many different applications. Among various sparse general matrix-matrix multiplication (SpGEMM) algorithms, Gustavson’s column-wise SpGEMM has good locality when reading input matrix and can be easily parallelized by distributing the computation of columns output to processors. However, accumulation (SPA) step SpGEMM, which merges partial sums from each multiplications row indices, still a performance bottleneck. The state-of-the-art software implementation uses hash table for sum search SPA, makes SPA largest contributor execution time SpGEMM. There are three reasons that cause become bottleneck: (1) probing requires data-dependent branches difficult branch predictor predict correctly; (2) dependent on results probing, it hide latency; (3) collision time-consuming optimizations reduce these collisions require accurate estimation number non-zeros column matrix. This work proposes ASA architecture accelerate SPA. overcomes challenges executing accumulate with single instruction through ISA extension eliminate using dedicated on-chip cache perform pipelined fashion, relying parallel capability set-associative latency, (4) delaying merging overflowed entries. As result, achieves average 2.25× 5.05× speedup as compared Markov clustering application its kernel, respectively. hashing accelerator design, 1.95× kernel.