High-performance conjugate gradient performance improvement on the K computer

Abstract

The high-performance conjugate gradient (HPCG) is new benchmark software for supercomputers that provides a more realistic performance metric than existing benchmarks, such as the LINPACK benchmark. The HPCG measures the speed of solving symmetric sparse linear system equations using the conjugate gradient method preconditioned by a multigrid symmetric Gauss–Seidel smoother. The combination of a sparse linear system and a preconditioned conjugate gradient method is widely used in many scientific and engineering computer applications. This study introduces a tuning method for the K computer. According to weak-scaling measurements on the K computer, it has good parallel scalability. Therefore, our tuning strategy focuses on single CPU performance rather than parallel performance. Single CPU performance strongly depends on memory throughput and multicore utilization. Therefore, we attempt to improve memory/cache access performance and multithreading efficiency. As a result, a HPCG score obtained with the K computer achieved second place at SC’14.