Characterization of data movement requirements for sparse matrix computations on GPUs

Tight data movement lower bounds are known for dense matrix-vector multiplication and dense matrix-matrix multiplication and practical implementations exist on GPUs that achieve performance quite close to the roofline bounds based on operational intensity. For large dense matrices, matrix-vector multiplication is bandwidth-limited and its performance is significantly lower than matrix-matrix multiplication. However, in contrast, the performance of sparse matrix-matrix multiplication (SpGEMM) is generally much lower than that of sparse matrix-vector multiplication (SpMV). In this paper, we use a combination of lower-bounds and upper-bounds analysis of data movement requirements, as well as hardware counter based measurements to gain insights into the performance limitations of existing implementations for SpGEMM on GPUs. The analysis motivates the development of an adaptive work distribution strategy among threads and results in performance enhancement for SpGEMM code on GPUs.