Automatic Exploration of Reduced Floating-Point Representations in Iterative Methods

Abstract

With the ever-increasing need for computation of scientific applications, new application domains, and major energy constraints, the landscape of floating-point computation is changing. New floating-point representation formats are emerging and there is a need for tools to simulate their impact in legacy codes. In this paper, we propose an automatic tool to evaluate the effect of adapting the floating point precision for each operation over time, which is particularly useful in iterative schemes. We present a backend to emulate any IEEE-754 floating-point operation in lower precision. We tested the numerical errors resilience of our solutions thanks to Monte Carlo Arithmetic and demonstrated the effectiveness of this methodology on YALES2, a large Combustion-CFD HPC code, by achieving 28% to 67% reduction in communication volume by lowering precision.