Insights from Optimizing HPL Performance on Exascale Systems: A Comparative Analysis of Panel Factorization

High performance LINPACK (HPL) remains the primary benchmark for evaluating supercomputing performance. It includes many parts with substantial internal complexity, and its performance is affected by a large number of parameters that interact in ways that are difficult to predict on large-scale heterogeneous supercomputer systems. We present a comprehensive performance analysis of HPL on Frontier, the world's first exascale supercomputer, which achieved HPL performance of 1.35 exaflops. Through empirical parameter tuning, detailed modeling, and comparative evaluation, we uncover critical performance insights, share lessons learned, and outline best practices for effective parameter tuning on exascale systems. We introduce and evaluate two novel PDFACT strategies: a dedicated-thread (DT) variant and a GPU-based variant (GPUPDFACT) implementation using HIP cooperative groups, demonstrating that GPU-based factorization outperforms conventional CPU-based PDFACT on Frontier's architecture. Our findings establish key performance factors for HPL on exascale systems and offer valuable guidance for future high-performance computing and benchmarking efforts.