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

2025-08-13

AI Summary

Hardware heterogeneity and underutilized performance potential of low-precision computation in exascale supercomputers hinder efficient acceleration of structured linear algebra. Method: This paper proposes an FFT-accelerated mixed-precision GPU algorithm tailored for block-triangular Toeplitz matrices. It introduces a dynamic mixed-precision framework, leveraging Pareto frontier analysis to achieve optimal accuracy–performance trade-offs. Via Hipify-based source-level porting, deep ROCm ecosystem optimization, and rocBLAS integration, the work achieves the first seamless migration and extension of CUDA-only FFT algorithms to AMD GPUs (MI250X/MI300X/MI355X). Contributions/Results: (1) High-performance, cross-architecture (especially AMD) mixed-precision portability; (2) Strong scaling across 2048 GPUs on the OLCF Frontier supercomputer; (3) Zero-code-modification deployment, significantly enhancing computational efficiency and applicability across diverse HPC platforms.

Technology Category

• Machine Learning: Hardware-aware ML
• Search and Optimization: Mixed Discrete/Continuous Search
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Enabling mixed-precision algorithms for HPC workflows
• Achieving performance portability across diverse GPU architectures
• Optimizing FFT-based matrix-vector products for block-triangular Toeplitz matrices

Innovation

• Hipify for GPU performance portability
• Dynamic mixed-precision framework optimization
• rocBLAS integration for AMD GPU acceleration