Mixed-Precision Computing for Scientific Discovery: Formats, Co-Design, and Responsible Approximation

2026-09-29

AI Summary

This project addresses the energy efficiency constraints and precision challenges introduced by heterogeneous accelerators in scientific computing. With "energy consumption per trusted solution" as its core objective, it establishes a mixed-precision computing framework. This work innovatively proposes a "reckless yet responsible" computing paradigm that integrates novel number formats, floating-point emulation, hardware-software co-design, and multi-level resource management to effectively balance aggressive low-precision arithmetic with system-level detection and verification. Furthermore, the project systematically reviews the technological landscape and development trajectories of this field, distills a list of open problems, and provides comprehensive design guidelines. Ultimately, it offers both a theoretical foundation and practical reference for next-generation energy-efficient scientific computing.

Abstract

Reduced and mixed precision have moved from a niche optimization to a central design axis in scientific computing and engineering, driven by energy constraints, heterogeneous accelerators, and the convergence of simulation and machine learning. This paper organizes the landscape around seven coupled themes---number formats, floating-point emulation, emerging architectures, hardware/software co-design, relation to other approximations, software design, and precision as a multilevel resource ---and, for each theme, synthesizes the state of the art, future directions, and open questions. We emphasize \emph{energy per trusted solution} as the core objective, and we frame \say{recklessly responsible} computing as a pragmatic doctrine: exploit low precision aggressively, but with systematic detection, escalation, and certification pathways.

Problem

• mixed-precision computing
• scientific computing
• energy efficiency
• responsible approximation
• hardware-software co-design

Innovation

• Mixed-Precision Computing
• Hardware-Software Co-design
• Energy Efficiency
• Responsible Approximation
• Number Formats