{"id":"https://openalex.org/W7163691437","doi":"https://doi.org/10.48550/arxiv.2606.06386","title":"On GPU Implementation for Multi-Precision Integer Division","display_name":"On GPU Implementation for Multi-Precision Integer Division","publication_year":2026,"publication_date":"2026-06-04","ids":{"openalex":"https://openalex.org/W7163691437","doi":"https://doi.org/10.48550/arxiv.2606.06386"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.06386","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.06386","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.06386","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137934763","display_name":"Martin B. Marchioro","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marchioro, Martin B.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137980813","display_name":"Aske N. Raahauge","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Raahauge, Aske N.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137940294","display_name":"Marc I. L\u00f8venskjold","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"L\u00f8venskjold, Marc I.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137968883","display_name":"Cosmin E. Oancea","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Oancea, Cosmin E.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5137659926","display_name":"Stephen M. Watt","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Watt, Stephen M.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.7703999876976013,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.7703999876976013,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.18799999356269836,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.030799999833106995,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.7685999870300293},{"id":"https://openalex.org/keywords/division","display_name":"Division (mathematics)","score":0.6326000094413757},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4763999879360199},{"id":"https://openalex.org/keywords/division-algorithm","display_name":"Division algorithm","score":0.47099998593330383},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4277999997138977},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.3702999949455261},{"id":"https://openalex.org/keywords/multiple","display_name":"Multiple","score":0.33149999380111694}],"concepts":[{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.7685999870300293},{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.6326000094413757},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5491999983787537},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5109999775886536},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4763999879360199},{"id":"https://openalex.org/C190715199","wikidata":"https://www.wikidata.org/wiki/Q3526714","display_name":"Division algorithm","level":3,"score":0.47099998593330383},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4277999997138977},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3862000107765198},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.3702999949455261},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.364300012588501},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.33799999952316284},{"id":"https://openalex.org/C164680029","wikidata":"https://www.wikidata.org/wiki/Q1055293","display_name":"Multiple","level":2,"score":0.33149999380111694},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3294999897480011},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.30889999866485596},{"id":"https://openalex.org/C141603448","wikidata":"https://www.wikidata.org/wiki/Q134830","display_name":"Prefix","level":2,"score":0.3018999993801117},{"id":"https://openalex.org/C83581934","wikidata":"https://www.wikidata.org/wiki/Q527381","display_name":"Arbitrary-precision arithmetic","level":2,"score":0.30079999566078186},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2953000068664551},{"id":"https://openalex.org/C144559511","wikidata":"https://www.wikidata.org/wiki/Q2986279","display_name":"Principal (computer security)","level":2,"score":0.28870001435279846},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.2669999897480011},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2526000142097473},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.25200000405311584},{"id":"https://openalex.org/C84211073","wikidata":"https://www.wikidata.org/wiki/Q117879","display_name":"Floating point","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.06386","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.06386","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.06386","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.06386","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"the":[3,25,33,94,97],"issues":[4],"arising":[5],"in":[6,32,71],"implementing":[7],"a":[8,20,68],"fast":[9],"integer":[10,34,50],"division":[11],"algorithm":[12,18],"on":[13,24,38,76,82],"general":[14],"purpose":[15],"GPUs.":[16],"The":[17,41],"uses":[19],"Newton":[21],"iteration":[22],"based":[23],"shifted":[26],"inverse":[27],"operation,":[28],"keeping":[29],"all":[30],"arithmetic":[31],"domain":[35],"and":[36,79,85],"relying":[37],"data-parallel":[39],"operators.":[40],"principal":[42],"contribution":[43],"is":[44],"an":[45,87],"efficient":[46],"GPU/CUDA":[47],"implementation":[48],"for":[49,96],"precisions":[51],"from":[52],"$2^{15}$":[53],"to":[54,93],"$2^{18}$":[55],"--":[56],"sizes":[57],"not":[58],"supported":[59],"by":[60],"\\cgbn{}":[61],"division.":[62],"We":[63],"propose":[64],"algorithmic":[65],"refinements,":[66],"define":[67],"cost":[69],"model":[70,95],"terms":[72],"of":[73],"multiplications,":[74],"build":[75],"prefix":[77],"sums":[78],"previous":[80],"work":[81],"multi-precision":[83],"multiplication,":[84],"present":[86],"evaluation":[88],"showing":[89],"near-optimal":[90],"performance":[91],"relative":[92],"target":[98],"precision.":[99]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-06T00:00:00"}
