Threaded accurate matrix-matrix multiplications with sparse matrix-vector 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. Although some algorithms for ensuring the computational accuracy of BLAS operations have been studied, there is a need for performance evaluation in advanced computer architectures. In this study, we parallelize high-precision matrix-matrix multiplication using thread-level parallelism. In addition, we conduct a performance evaluation from the viewpoints of execution speed and accuracy. We implement a method to convert dense matrices into sparse matrices by exploiting the nature of the target algorithm and adapting sparse-vector multiplication. Results obtained using the FX100 supercomputer system at Nagoya University indicate that (1) implementation with the ELL format achieves 1.43x speedup and (2) a maximum of 38x speedup compared to conventional implementation for dense matrix operations with dgemm.