Comparison of Reproducible Parallel Preconditioned BiCGSTAB Algorithm Based on ExBLAS and ReproBLAS

Abstract

Krylov subspace algorithms are important methods for solving linear systems. In order to solve large-scale linear systems and speed up the solution of linear systems, one has to use parallelism techniques. However, parallelism often enlarge the non-associativity of floating-point operations. This can lead to non-reproducibility of the computations. This paper compares the performance of the parallel preconditioned BiCGSTAB algorithm implemented with two different libraries (ExBLAS and ReproBLAS) that can ensure reproducibility of the computations. To address the effect of the compiler, we explicitly utilize the fma instructions. Finally, numerical experiments show that the BiCGSTAB algorithms based on the two BLAS implementations are reproducible, the BiCGSTAB algorithm based on ExBLAS is more accurate but more time-consuming, and the BiCGSTAB algorithm based on ReproBLAS is relatively less accurate but less expensive.