{"paper":{"title":"A New Modular Division Algorithm and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DC","authors_text":"Christian Lavault (LIPN), Sidi Mohamed Sedjelmaci (LIPN)","submitted_at":"2013-12-09T20:34:42Z","abstract_excerpt":"The present paper proposes a new parallel algorithm for the modular division $u/v\\bmod \\beta^s$, where $u,\\; v,\\; \\beta$ and $s$ are positive integers $(\\beta\\ge 2)$. The algorithm combines the classical add-and-shift multiplication scheme with a new propagation carry technique. This \"Pen and Paper Inverse\" ({\\em PPI}) algorithm, is better suited for systolic parallelization in a \"least-significant digit first\" pipelined manner. Although it is equivalent to Jebelean's modular division algorithm~\\cite{jeb2} in terms of performance (time complexity, work, efficiency), the linear parallelization "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2570","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"}