Mixed-precision numerics in scientific applications: survey and perspectives

The explosive demand for artificial intelligence (AI) workloads has led to a significant increase in silicon area dedicated to lower-precision computations on recent high-performance computing hardware designs. However, mixed-precision capabilities, which can achieve performance improvements of 8x compared to double-precision in extreme compute-intensive workloads, remain largely untapped in most scientific applications. A growing number of efforts have shown that mixed-precision algorithmic innovations can deliver superior performance without sacrificing accuracy. These developments should prompt computational scientists to seriously consider whether their scientific modeling and simulation applications could benefit from the acceleration offered by new hardware and mixed-precision algorithms. In this article, we review the literature on relevant applications, existing mixed-precision algorithms, theories, and the available software infrastructure. We then offer our perspective and recommendations on the potential of mixed-precision algorithms to enhance the performance of scientific simulation applications. Broadly, we find that mixed-precision methods can have a large impact on computational science in terms of time-to-solution and energy consumption. This is true not only for a few arithmetic-dominated applications but also, to a more moderate extent, to the many memory bandwidth-bound applications. In many cases, though, the choice of algorithms and regions of applicability will be domain-specific, and thus require input from domain experts. It is helpful to identify cross-cutting computational motifs and their mixed-precision algorithms in this regard. Finally, there are new algorithms being developed to utilize AI hardware and and AI methods to accelerate first-principles computational science, and these should be closely watched as hardware platforms evolve.