{"paper":{"title":"Improvements on the accelerated integer GCD algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.NT"],"primary_cat":"cs.DC","authors_text":"Christian Lavault (LIPN), Sidi Mohamed Sedjelmaci (LIPN)","submitted_at":"2014-02-10T20:43:46Z","abstract_excerpt":"The present paper analyses and presents several improvements to the algorithm for finding the $(a,b)$-pairs of integers used in the $k$-ary reduction of the right-shift $k$-ary integer GCD algorithm. While the worst-case complexity of Weber's \"Accelerated integer GCD algorithm\" is $\\cO\\l(\\log_\\phi(k)^2\\r)$, we show that the worst-case number of iterations of the while loop is exactly $\\tfrac 12 \\l\\lfloor \\log_{\\phi}(k)\\r\\rfloor$, where $\\phi := \\tfrac 12 \\l(1+\\sqrt{5}\\r)$.\\par We suggest improvements on the average complexity of the latter algorithm and also present two new faster residual alg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2266","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}