{"paper":{"title":"FLoPS: Semantics, Operations, and Properties of P3109 Floating-Point Representations in Lean","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A Lean formal model of the P3109 low-precision floating-point standard verifies that FastTwoSum computes exact overflow errors under saturation for any rounding mode while ExtractScalar properties fail at one-bit precision.","cross_cats":[],"primary_cat":"cs.MS","authors_text":"Jay P Lim, Santosh Nagarakatte, Sehyeok Park, Tung-Che Chang","submitted_at":"2026-02-17T19:30:24Z","abstract_excerpt":"The upcoming IEEE-P3109 standard for low-precision floating-point arithmetic can become the foundation of future machine learning hardware and software. Unlike IEEE-754, P3109 introduces a parametric framework defined by bitwidth, precision, signedness, and domain. This flexibility results in a vast combinatorial space of formats -- some with as little as one bit of precision -- alongside novel features such as stochastic rounding and saturation arithmetic. These deviations create a unique verification gap that this paper intends to address. This paper presents FLoPS, Formalization in Lean of "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We reveal that FastTwoSum exhibits a novel property of computing exact 'overflow error' under saturation using any rounding mode, whereas previously established properties of the ExtractScalar algorithm fail for formats with one bit of precision.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The Lean encoding faithfully captures the informal semantics and edge cases of the P3109 draft standard, including all interactions between saturation, stochastic rounding, and subnormal handling.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A Lean formalization of P3109 that verifies FastTwoSum computes exact overflow error under saturation for any rounding mode and shows ExtractScalar properties fail at one-bit precision.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A Lean formal model of the P3109 low-precision floating-point standard verifies that FastTwoSum computes exact overflow errors under saturation for any rounding mode while ExtractScalar properties fail at one-bit precision.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"21f50d9059fcc52e5e29077f324919dc1bcdd017fcf0c2636a6aa0adbed8c933"},"source":{"id":"2602.15965","kind":"arxiv","version":3},"verdict":{"id":"8ca17efa-f71d-4cf8-8c2e-cf0b92810f8e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T21:51:25.474877Z","strongest_claim":"We reveal that FastTwoSum exhibits a novel property of computing exact 'overflow error' under saturation using any rounding mode, whereas previously established properties of the ExtractScalar algorithm fail for formats with one bit of precision.","one_line_summary":"A Lean formalization of P3109 that verifies FastTwoSum computes exact overflow error under saturation for any rounding mode and shows ExtractScalar properties fail at one-bit precision.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The Lean encoding faithfully captures the informal semantics and edge cases of the P3109 draft standard, including all interactions between saturation, stochastic rounding, and subnormal handling.","pith_extraction_headline":"A Lean formal model of the P3109 low-precision floating-point standard verifies that FastTwoSum computes exact overflow errors under saturation for any rounding mode while ExtractScalar properties fail at one-bit precision."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.15965/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":2,"snapshot_sha256":"c4934009e8c776bafd50b63e19756020b5533130b0ee4d4ad51bd5d74784ccd3"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}