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Hierarchical search algorithm for error detection in floating-point arithmetic expressions

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Abstract

Scientific and engineering applications rely on floating-point arithmetic to approximate real numbers. Due to the inherent rounding errors in floating-point numbers, error propagation during calculations can accumulate and lead to serious errors that may compromise the safety and reliability of the program. In theory, the most accurate method of error detection is to exhaustively search all possible floating-point inputs, but this is not feasible in practice due to the huge search space involved. Effectively and efficiently detecting maximum floating-point errors has been a challenge. To address this challenge, we design and implement an error detection tool for floating-point arithmetic expressions called HSED. It leverages modified mantissas under double precision floating-point types to simulate hierarchical searches from either half or single precision to double precision. Experimental results show that for 32 single-parameter arithmetic expressions in the FPBench benchmark test set, the error detection effects and performance of HSED are significantly better than the state-of-the-art error detection tools Herbie, S3FP and ATOMU. HSED outperforms Herbie, Herbie+, S3FP and ATOMU in 24, 19, 27 and 25 cases, respectively. The average time taken by Herbie, Herbie+, and S3FP is 1.82, 11.20, and 129.15 times longer than HSED, respectively.

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Data availability

The datasets used for the experiments are benchmark datasets. The experimental data can be reproduced in the github open source address.

Code availability

The github open source address will be included here when the paper is accepted.

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Funding

Supported by the Open Project Program of the State Key Laboratory of Mathematical Engineering and Advanced Computing. Fund No. 2023B02.

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Author notes

  1. Zuoyan Zhang and Jinchen Xu these authors contributed equally to this work.

Authors and Affiliations

  1. Information Engineering University, No. 62 Science Anenue, High-Tech Zone, Zhengzhou, 450001, Henan, China

    Zuoyan Zhang, Jinchen Xu, Jiangwei Hao, Yang Qu, Haotian He & Bei Zhou

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  1. Zuoyan Zhang
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  2. Jinchen Xu
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  3. Jiangwei Hao
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  4. Yang Qu
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  6. Bei Zhou
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Contributions

ZZ and JX were responsible for the methodology, implementation and writing; YQ and HH were responsible for some of the experiments; JH was involved in the review and supervision; and BZ was involved in the editing, review and supervision.

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Correspondence to Bei Zhou.

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Zhang, Z., Xu, J., Hao, J. et al. Hierarchical search algorithm for error detection in floating-point arithmetic expressions. J Supercomput 80, 1183–1205 (2024). https://doi.org/10.1007/s11227-023-05523-6

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