High-Performance GMRES Multi-Precision Benchmark: Design, Performance, and Challenges

We propose a new benchmark for high-performance (HP) computers that uses a variation of the Generalized Minimum RESidual method (GMRES). Similar to High Performance Conjugate Gradients (HPCG), the new benchmark is designed to rank computers based on how fast they can solve a sparse linear system of equations, exhibiting computational and communication requirements typical in many scientific applications. The main novelty of the new benchmark is that it is now based on Generalized Minimum Residual method (GMRES) (combined with Geometric Multi-Grid preconditioner and Gauss-Seidel smoother) and provides the flexibility to utilize lower precision arithmetic. This is motivated by new hardware platforms that deliver lower-precision arithmetic at higher performance. There are other machines that do not follow this trend. However, using a lower-precision arithmetic reduces the required amount of data volume, which could alone improve solver performance. Considering these trends, an HPC benchmark that allows the use of different precisions for solving important scientific problems will be valuable for many different disciplines. We also hope to promote the design of future HPC computers that can utilize mixed-precision arithmetic for achieving high application performance. We present our initial design of the new benchmark, its reference implementation, and the baseline performance of the mixed (double and single) precision Geometric Multi-Grid solvers on the current top-ranked architectures. We also discuss the challenges of designing such a benchmark, along with preliminary numerical results using 16-bit numerical values, both half and bfloat precisions, for solving a sparse linear system of equations.