{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/automatic-verification-of-floating-point","title":"Automatic Verification of Floating-Point Accumulation Networks","arxiv_id":"2505.18791","date":"2025-05-24","proceeding":null,"authors":["David K. Zhang","Alex Aiken"],"abstract":"Floating-point accumulation networks (FPANs) are key building blocks used in many floating-point algorithms, including compensated summation and double-double arithmetic. FPANs are notoriously difficult to analyze, and algorithms using FPANs are often published without rigorous correctness proofs. In fact, on at least one occasion, a published error bound for a widely used FPAN was later found to be incorrect. In this paper, we present an automatic procedure that produces computer-verified proofs of several FPAN correctness properties, including error bounds that are tight to the nearest bit. Our approach is underpinned by a novel floating-point abstraction that models the sign, exponent, and number of leading and trailing zeros and ones in the mantissa of each number flowing through an FPAN. We also present a new FPAN for double-double addition that is faster and more accurate than the previous best known algorithm.","url_abs":"https://arxiv.org/abs/2505.18791v1","url_pdf":"https://arxiv.org/pdf/2505.18791v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"automatic-verification-of-floating-point","repo_url":"https://github.com/dzhang314/fpanverifier","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}