{"paper":{"title":"Polynomial Invariant Generation for Floating-Point Programs","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"A framework combines round-off error analysis with polynomial constraint solving to generate tight invariants for floating-point programs.","cross_cats":[],"primary_cat":"cs.PL","authors_text":"Hongfei Fu, Liqian Chen, Xuran Cai","submitted_at":"2025-07-20T16:02:17Z","abstract_excerpt":"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 o"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The combination of round-off error analysis and polynomial constraint solving can circumvent the cost of handling a large number of error variables in the floating-point model without losing tightness of the generated invariants.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A framework merges round-off error analysis and polynomial constraint solving to generate tight invariants for floating-point programs and outperforms prior methods on benchmarks.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A framework combines round-off error analysis with polynomial constraint solving to generate tight invariants for floating-point programs.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b9734d1c8a4e7da24f1622d9c0d46f13e7635a935ea83e3db15ca953f7ec1793"},"source":{"id":"2507.15017","kind":"arxiv","version":4},"verdict":{"id":"9dd8106b-2d89-4d9a-982e-b3a5be7055c3","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T03:56:52.405740Z","strongest_claim":"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.","one_line_summary":"A framework merges round-off error analysis and polynomial constraint solving to generate tight invariants for floating-point programs and outperforms prior methods on benchmarks.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The combination of round-off error analysis and polynomial constraint solving can circumvent the cost of handling a large number of error variables in the floating-point model without losing tightness of the generated invariants.","pith_extraction_headline":"A framework combines round-off error analysis with polynomial constraint solving to generate tight invariants for floating-point programs."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.15017/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}