Polynomial Invariant Generation for Floating-Point Programs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917455467642880 |
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| author | Cai, Xuran Chen, Liqian Fu, Hongfei |
| author_facet | Cai, Xuran Chen, Liqian Fu, Hongfei |
| contents | In numeric-intensive computations, it is well known that the execution of floating-point programs is imprecise as floating-point arithmetic incurs round-off errors. Although round-off errors are small for a single floating-point operation, the aggregation of such errors may be dramatic and cause catastrophic program failures. Therefore, to ensure the correctness of floating-point programs, round-off error needs to be carefully taken into account. In this work, we consider polynomial invariant generation for floating-point programs, aiming at generating tight invariants under the perturbation of round-off errors. Our contribution is a novel framework for applying polynomial constraint solving to address the invariant generation problem, which is also the first polynomial constraint solving based approach that handles floating-point errors to our best knowledge.
In our framework, we propose a novel combination of round-off error analysis and polynomial constraint solving, aiming to circumvent the cost of handling a large number of error variables in the floating-point model. Experimental results over a variety of challenging benchmarks show that our framework outperforms SOTA approaches in both time efficiency and the precision of generated invariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15017 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Polynomial Invariant Generation for Floating-Point Programs Cai, Xuran Chen, Liqian Fu, Hongfei Programming Languages In numeric-intensive computations, it is well known that the execution of floating-point programs is imprecise as floating-point arithmetic incurs round-off errors. Although round-off errors are small for a single floating-point operation, the aggregation of such errors may be dramatic and cause catastrophic program failures. Therefore, to ensure the correctness of floating-point programs, round-off error needs to be carefully taken into account. In this work, we consider polynomial invariant generation for floating-point programs, aiming at generating tight invariants under the perturbation of round-off errors. Our contribution is a novel framework for applying polynomial constraint solving to address the invariant generation problem, which is also the first polynomial constraint solving based approach that handles floating-point errors to our best knowledge. In our framework, we propose a novel combination of round-off error analysis and polynomial constraint solving, aiming to circumvent the cost of handling a large number of error variables in the floating-point model. Experimental results over a variety of challenging benchmarks show that our framework outperforms SOTA approaches in both time efficiency and the precision of generated invariants. |
| title | Polynomial Invariant Generation for Floating-Point Programs |
| topic | Programming Languages |
| url | https://arxiv.org/abs/2507.15017 |