Enabling mixed-precision in spectral element codes

Mixed-precision computing has the potential to significantly reduce the cost of exascale computations, but determining when and how to implement it in programs can be challenging. In this article, we propose a methodology for enabling mixed-precision with the help of computer arithmetic tools, roofline model, and computer arithmetic techniques. As case studies, we consider Nekbone, a mini-application for the Computational Fluid Dynamics (CFD) solver Nek5000, and a modern Neko CFD application. With the help of the Verificarlo tool and computer arithmetic techniques, we introduce a strategy to address stagnation issues in the preconditioned Conjugate Gradient method in Nekbone and apply these insights to implement a mixed-precision version of Neko. We evaluate the derived mixed-precision versions of these codes by combining metrics in three dimensions: accuracy, time-to-solution, and energy-to-solution. Notably, mixed-precision in Nekbone reduces time-to-solution by roughly 1.62x and energy-to-solution by 2.43x on MareNostrum 5, while in the real-world Neko application, the gain is up to 1.3x in both time and energy, with the accuracy that matches double-precision results.