Mixed-Precision Performance Portability of FFT-Based GPU-Accelerated Algorithms for Block-Triangular Toeplitz Matrices

Abstract: The hardware diversity displayed in leadership-class computing facilities, alongside the immense performance boosts exhibited by today's GPUs when computing in lower precision, provide a strong incentive for scientific HPC workflows to adopt mixed-precision algorithms and performance portability models. We present an on-the-fly framework using Hipify for performance portability and apply it to FFTMatvec-an HPC application that computes matrix-vector products with block-triangular Toeplitz matrices. Our approach enables FFTMatvec, initially a CUDA-only application, to run seamlessly on AMD GPUs with excellent observed performance. Performance optimizations for AMD GPUs are integrated directly into the open-source rocBLAS library, keeping the application code unchanged. We then present a dynamic mixed-precision framework for FFTMatvec; a Pareto front analysis determines the optimal mixed-precision configuration for a desired error tolerance. Results are shown for AMD Instinct MI250X, MI300X, and the newly launched MI355X GPUs. The performance-portable, mixed-precision FFTMatvec is scaled to 2,048 GPUs on the OLCF Frontier supercomputer.