Exploring and Exploiting Runtime Reconfigurable Floating Point Precision in Scientific Computing: a Case Study for Solving PDEs
<|reference_start|>Exploring and Exploiting Runtime Reconfigurable Floating Point Precision in Scientific Computing: a Case Study for Solving PDEs: 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.<|reference_end|>
@article{hao2024exploring,
    title={Exploring and Exploiting Runtime Reconfigurable Floating Point Precision
  in Scientific Computing: a Case Study for Solving PDEs},
    author={Cong "Callie" Hao},
    journal={arXiv preprint arXiv:2409.15073},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.15073},
    primaryClass={cs.AR}
}