Performance Evaluation of Accurate Matrix-Matrix Multiplication on GPU Using Sparse Matrix Multiplications

Basic Linear Algebra Subprograms (BLAS) is a frequently used numerical library for linear algebra computations. However, it places little emphasis on computational accuracy, especially with respect to the accuracy assurance of the results. Consequently, a high-precision matrix-matrix multiplications algorithm that assures the precision by double precision operation is proposed. In this study, we proposed to calculate sub-matrix computations generated by accurate matrix-matrix multiplication on GPU. We contribute the following two points: (1) We evaluate the performance of sparse matrix - dense matrix multiplication (SpMM) using sparse matrix - vector multiplications on GPU with the property of allowing dense matrices to be transformed into sparse matrices during the accurate matrix - matrix multiplication algorithm; (2) We evaluate above SpMM using sparse matrix - sparse matrix multiplications (SpMxSpM) on GPU. Results on the Reedbush-H supercomputer system at The University of Tokyo indicate that (1) The implementation of SpMM in the CRS format achieves a 3.24-times speedup on GPU compared with a CPU and (2) The implementation of SpMxSpM achieves a 8.44-times speedup compared with SpMM.