Mixed-Precision Sparse Approximate Inverse Preconditioning Algorithm on GPU

In this study, in order to further improve the construction efficiency of sparse approximate inverse (SPAI) preconditioners, we attempt to explore the construction method of SPAI preconditioners in mixed-precision mode from the perspective of single and double precision mixing, and thus propose two mixed-precision SPAI preconditioning algorithms on GPU, abbreviated as MP-SSPAI and MP-HeuriSPAI, respectively. In MP-SSPAI, with original static SPAI preconditioning algorithm as the research object, we mainly consider the following factors to construct its preconditioner in mixed-precision mode: 1) use single precision as much as possible to improve computational efficiency of the preconditioner while ensuring its validity; 2) store certain components in single precision after they have been determined to require single-precision computation to improve read efficiency; and 3) maintain the high-precision output of the preconditioner to ensure that it is computed with high precision when applied to the iterative algorithm. In MP-HeuriSPAI, a mixed-precision heuristic dynamic SPAI preconditioning algorithm on GPU is presented based on the above factors, using HeuriSPAI as the object of study. The experimental results demonstrate the effectiveness and high performance of the proposed MP-SSPAI and MP-HeuriSPAI by comparing them with their respective double-precision versions, single-precision versions, and extended versions.