swSpAMM: optimizing large-scale sparse approximate matrix multiplication on Sunway Taihulight

Although matrix multiplication plays an essential role in a wide range of applications, previous works only focus on optimizing dense or sparse matrix multiplications. The Sparse Approximate Matrix Multiply (SpAMM) is an algorithm to accelerate the multiplication of decay matrices, the sparsity of which is between dense and sparse matrices. In addition, large-scale decay matrix multiplication is performed in scientific applications to solve cutting-edge problems. To optimize large-scale decay matrix multiplication using SpAMM on supercomputers such as Sunway Taihulight, we present swSpAMM, an optimized SpAMM algorithm by adapting the computation characteristics to the architecture features of Sunway Taihulight. Specifically, we propose both intra-node and inter-node optimizations to accelerate swSpAMM for large-scale execution. For intra-node optimizations, we explore algorithm parallelization and block-major data layout that are tailored to better utilize the architecture advantage of Sunway processor. For inter-node optimizations, we propose a matrix organization strategy for better distributing sub-matrices across nodes and a dynamic scheduling strategy for improving load balance across nodes. We compare swSpAMM with the existing GEMM library on a single node as well as large-scale matrix multiplication methods on multiple nodes. The experiment results show that swSpAMM achieves a speedup up to 14.5× and 2.2× when compared to xMath library on a single node and 2D GEMM method on multiple nodes, respectively.