Exploring and Exploiting Runtime Reconfigurable Floating Point Precision in Scientific Computing: a Case Study for Solving PDEs

TL;DR

This paper introduces a runtime reconfigurable floating-point multiplier (R2F2) that dynamically adjusts precision during scientific computations, significantly reducing errors and resource usage while maintaining accuracy in PDE solutions.

Contribution

The paper presents a novel R2F2 architecture enabling dynamic precision adjustment in floating-point multipliers for scientific computing, improving efficiency and numerical stability.

Findings

16-bit R2F2 reduces error rates by 70.2% compared to half-precision.

R2F2 achieves same results as 32-bit precision using 16 or fewer bits.

Standard half precision fails in some scientific simulations.

Abstract

Scientific computing applications, such as computational fluid dynamics and climate modeling, typically rely on 64-bit double-precision floating-point operations, which are extremely costly in terms of computation, memory, and energy. While the machine learning community has successfully utilized low-precision computations, scientific computing remains cautious due to concerns about numerical stability. To tackle this long-standing challenge, we propose a novel approach to dynamically adjust the floating-point data precision at runtime, maintaining computational fidelity using lower bit widths. We first conduct a thorough analysis of data range distributions during scientific simulations to identify opportunities and challenges for dynamic precision adjustment. We then propose a runtime reconfigurable, flexible floating-point multiplier (R2F2), which automatically and dynamically adjusts multiplication precision based on the current operands, ensuring accurate results with lower bit widths. Our evaluation shows that 16-bit R2F2 significantly reduces error rates by 70.2\% compared to standard half-precision, with resource overhead ranging from a 5% reduction to a 7% increase and no latency overhead. In two representative scientific computing applications, R2F2, using 16 or fewer bits, can achieve the same simulation results as 32-bit precision, while standard half precision will fail. This study pioneers runtime reconfigurable arithmetic, demonstrating great potential to enhance scientific computing efficiency. Code available at https://github.com/sharc-lab/R2F2.