Abstract
We propose a new benchmark for high-performance (HP) computers. Similar to High Performance Conjugate Gradient (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 architectures 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 transfer, which alone could improve solver performance. Considering these trends, an HP benchmark that allows the use of different precisions for solving important scientific problems will be valuable for many different disciplines, and we also hope to promote the design of future HP 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 performance of the reference mixed (double and single) precision Geometric Multi-Grid solvers on current top-ranked architectures. We also discuss challenges of designing such a benchmark, along with our preliminary numerical results using 16-bit numerical values (half and bfloat precisions) for solving a sparse linear system of equations.
| Original language | English |
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| Title of host publication | Proceedings of PMBS 2022 |
| Subtitle of host publication | Performance Modeling, Benchmarking and Simulation of High Performance Computer Systems, Held in conjunction with SC 2022: The International Conference for High Performance Computing, Networking, Storage and Analysis |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 112-122 |
| Number of pages | 11 |
| ISBN (Electronic) | 9781665451857 |
| DOIs | |
| State | Published - 2022 |
| Externally published | Yes |
| Event | 13th IEEE/ACM International Workshop on Performance Modeling, Benchmarking and Simulation of High Performance Computer Systems, PMBS 2022 - Dallas, United States Duration: Nov 13 2022 → Nov 18 2022 |
Publication series
| Name | Proceedings of PMBS 2022: Performance Modeling, Benchmarking and Simulation of High Performance Computer Systems, Held in conjunction with SC 2022: The International Conference for High Performance Computing, Networking, Storage and Analysis |
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Conference
| Conference | 13th IEEE/ACM International Workshop on Performance Modeling, Benchmarking and Simulation of High Performance Computer Systems, PMBS 2022 |
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| Country/Territory | United States |
| City | Dallas |
| Period | 11/13/22 → 11/18/22 |
Funding
In response to these growing interests, there are several efforts to investigate multi-precision algorithms on emerging computers [5]. This includes the xSDK multi-precision project funded by the ECP [1]. Since a significant portion of scientific simulation time may be spent solving sparse linear systems of equations, xSDK’s effort includes development of multi-precision algorithms for solving such linear systems, numerical and performance studies of the resulting multi-precision solvers, and deployment of resulting mixed-precision software.