A Loop-aware Autotuner for High-Precision Floating-point Applications

Many scientific applications (e.g., molecular dynamics, climate modeling and astrophysical simulations) rely on floating-point arithmetic. Due to its approximate nature, the use of floating-point arithmetic can lead to inaccuracy and reproducibility issues, which can be particularly significant for long running applications. Indeed, previous work has shown that 64-bit IEEE floating-point arithmetic can be insufficient for many algorithms and applications, such as ill-conditioned linear systems, large summations, long-time or large-scale physical simulations, and experimental mathematics applications. To overcome these issues, existing work has proposed high-precision floating-point libraries (e.g., the GNU multiple precision arithmetic library), but these libraries come at the cost of significant execution time. In this work, we propose an auto-tuner for applications requiring high-precision floating-point arithmetic to deliver a prescribed level of accuracy. Our auto-tuner uses compiler analysis to discriminate operations and variables that require high-precision from those that can be handled using standard IEEE 64-bit floating-point arithmetic, and it generates a mixed precision program that trades off performance and accuracy by selectively using different precisions for different variables and operations. In particular, our auto-tuner leverages loop and data dependences analysis to quickly identify precision-sensitive variables and operations and provide results that are robust to different input datasets. We test our auto-tuner on a mix of applications with different computational patterns.