Exploiting Mixed-Precision Redundancy for Soft-Error Detection in LU Decomposition

Exploiting Mixed-Precision Redundancy for Soft-Error Detection in LU Decomposition | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Exploiting Mixed-Precision Redundancy for Soft-Error Detection in LU Decomposition Nima Sahraneshinsamani, Sandra Catalán, José R. Herrero This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7871757/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract The pursuit of performance through mixed-precision arithmetic has inadvertently created an opportunity for fault tolerance. Building on our Mixed-Precision Panel Factorization (\mpf) algorithm that computes LU decomposition panels in both \FPsixteen{} and \FPsixtyfour{} for speed, we demonstrate that this inherent redundancy enables robust soft-error detection at near-zero additional cost. We introduce a Hybrid detector combining ratio-based outlier analysis with relative-error thresholding. Experimental evaluation shows that Relative achieves high sensitivity with low false positive rate and CrossCheck achieves high sensitivity with near-zero false positive rate, while our Hybrid detector maintains near-zero false positives with moderate sensitivity and complementary coverage for challenging significand bit faults. With the exception of the Ratio detector on U-factor sign-bit upsets, all detectors reliably identify exponent and sign-bit errors. The approach requires minimal additional storage per panel and linear computational cost, making it immediately deployable in production HPC environments where both performance and reliability are critical. algorithmic fault tolerance floating-point arithmetic high-performance computing LU decomposition mixed-precision arithmetic numerical stability pivoting resilience soft-error detection Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 08 Jan, 2026 Reviews received at journal 01 Jan, 2026 Reviews received at journal 09 Dec, 2025 Reviewers agreed at journal 04 Dec, 2025 Reviewers agreed at journal 04 Dec, 2025 Reviewers invited by journal 03 Nov, 2025 Editor assigned by journal 29 Oct, 2025 Submission checks completed at journal 23 Oct, 2025 First submitted to journal 15 Oct, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7871757","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":541910111,"identity":"4234ad77-16ba-4bcb-b01d-687a2d5a2b18","order_by":0,"name":"Nima Sahraneshinsamani","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAr0lEQVRIiWNgGAWjYFACHjApx8BwsIE0Lcaka0kkWj2DfPvZYx9+7qhL33DwcAPDhz9EaDE4k5c8s/fM4dwNBw42MM5sI0YLQ44xA2/bAbAWZl5inCff/8aY8W9bXboBSMsfYhzGcCPHmJm3jTkBrIWBjRiH3XhjzCzbdthwJlDLwV5i/CLfn2PM+LatTp7vxvGHD34Q5TA4kDjAcIAkDQwM/A0kahgFo2AUjIIRAwBYmDzqdjCb5QAAAABJRU5ErkJggg==","orcid":"","institution":"Jaume I University","correspondingAuthor":true,"prefix":"","firstName":"Nima","middleName":"","lastName":"Sahraneshinsamani","suffix":""},{"id":541910112,"identity":"591bbcef-2283-44a7-8c2d-fbfb88277370","order_by":1,"name":"Sandra Catalán","email":"","orcid":"","institution":"Jaume I University","correspondingAuthor":false,"prefix":"","firstName":"Sandra","middleName":"","lastName":"Catalán","suffix":""},{"id":541910113,"identity":"bfc3a61a-a68f-464c-a578-dfc8fd7f28f9","order_by":2,"name":"José R. 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Building on our Mixed-Precision Panel Factorization (\\mpf) algorithm that computes LU decomposition panels in both \\FPsixteen{} and \\FPsixtyfour{} for speed, we demonstrate that this inherent redundancy enables robust soft-error detection at near-zero additional cost. We introduce a \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eHybrid\u003c/span\u003e detector combining ratio-based outlier analysis with relative-error thresholding. Experimental evaluation shows that \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eRelative\u003c/span\u003e achieves high sensitivity with low false positive rate and \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eCrossCheck\u003c/span\u003e achieves high sensitivity with near-zero false positive rate, while our \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eHybrid\u003c/span\u003e detector maintains near-zero false positives with moderate sensitivity and complementary coverage for challenging significand bit faults. With the exception of the \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eRatio\u003c/span\u003e detector on U-factor sign-bit upsets, all detectors reliably identify exponent and sign-bit errors. 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