Efficient search for inputs causing high floating-point errors

Author:

Chiang Wei-Fan1,Gopalakrishnan Ganesh1,Rakamaric Zvonimir1,Solovyev Alexey1

Affiliation:

1. University of Utah, Salt Lake City, UT, USA

Abstract

Tools for floating-point error estimation are fundamental to program understanding and optimization. In this paper, we focus on tools for determining the input settings to a floating point routine that maximizes its result error. Such tools can help support activities such as precision allocation, performance optimization, and auto-tuning. We benchmark current abstraction-based precision analysis methods, and show that they often do not work at scale, or generate highly pessimistic error estimates, often caused by non-linear operators or complex input constraints that define the set of legal inputs. We show that while concrete-testing-based error estimation methods based on maintaining shadow values at higher precision can search out higher error-inducing inputs, suit able heuristic search guidance is key to finding higher errors. We develop a heuristic search algorithm called Binary Guided Random Testing (BGRT). In 45 of the 48 total benchmarks, including many real-world routines, BGRT returns higher guaranteed errors. We also evaluate BGRT against two other heuristic search methods called ILS and PSO, obtaining better results.

Publisher

Association for Computing Machinery (ACM)

Subject

Computer Graphics and Computer-Aided Design,Software

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1. Floating-Point TVPI Abstract Domain;Proceedings of the ACM on Programming Languages;2024-06-20

2. Input Range Generation for Compiler-Induced Numerical Inconsistencies;Proceedings of the 38th ACM International Conference on Supercomputing;2024-05-30

3. Odyssey: An Interactive Workbench for Expert-Driven Floating-Point Expression Rewriting;Proceedings of the 36th Annual ACM Symposium on User Interface Software and Technology;2023-10-29

4. Hierarchical search algorithm for error detection in floating-point arithmetic expressions;The Journal of Supercomputing;2023-07-10

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