{"id":"https://openalex.org/W3098574009","doi":"https://doi.org/10.1137/15m1021908","title":"Fast and Accurate Evaluation of Wigner 3$j$, 6$j$, and 9$j$ Symbols Using Prime Factorization and Multiword Integer Arithmetic","display_name":"Fast and Accurate Evaluation of Wigner 3$j$, 6$j$, and 9$j$ Symbols Using Prime Factorization and Multiword Integer Arithmetic","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W3098574009","doi":"https://doi.org/10.1137/15m1021908","mag":"3098574009"},"language":"en","primary_location":{"id":"doi:10.1137/15m1021908","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1021908","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1504.08329","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"H. T. Johansson","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"H. T. Johansson","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"C. Forss\u00e9n","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"C. Forss\u00e9n","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":14.4965,"has_fulltext":false,"cited_by_count":73,"citation_normalized_percentile":{"value":0.98800743,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"38","issue":"1","first_page":"A376","last_page":"A384"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.21719999611377716,"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":0.21719999611377716,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.16380000114440918,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.10029999911785126,"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/rounding","display_name":"Rounding","score":0.7145000100135803},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.666700005531311},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6263999938964844},{"id":"https://openalex.org/keywords/prime-factor","display_name":"Prime factor","score":0.6187999844551086},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5026000142097473},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.4657000005245209},{"id":"https://openalex.org/keywords/prime-number","display_name":"Prime number","score":0.4602000117301941},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4311999976634979}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7343000173568726},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.7145000100135803},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.666700005531311},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6263999938964844},{"id":"https://openalex.org/C30860621","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime factor","level":3,"score":0.6187999844551086},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5026000142097473},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.4657000005245209},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.4602000117301941},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4311999976634979},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42480000853538513},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4221000075340271},{"id":"https://openalex.org/C83581934","wikidata":"https://www.wikidata.org/wiki/Q527381","display_name":"Arbitrary-precision arithmetic","level":2,"score":0.3968000113964081},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38429999351501465},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.3499999940395355},{"id":"https://openalex.org/C173808221","wikidata":"https://www.wikidata.org/wiki/Q50705","display_name":"Square number","level":2,"score":0.3328000009059906},{"id":"https://openalex.org/C119677069","wikidata":"https://www.wikidata.org/wiki/Q4846249","display_name":"Integer factorization","level":4,"score":0.3075000047683716},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.30230000615119934},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.29339998960494995},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2833999991416931},{"id":"https://openalex.org/C3017489831","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Running time","level":2,"score":0.2786000072956085},{"id":"https://openalex.org/C61005703","wikidata":"https://www.wikidata.org/wiki/Q2145211","display_name":"Round-off error","level":2,"score":0.2703000009059906},{"id":"https://openalex.org/C23230895","wikidata":"https://www.wikidata.org/wiki/Q104752","display_name":"Coprime integers","level":2,"score":0.2687000036239624},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.26660001277923584}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/15m1021908","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1021908","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1504.08329","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1504.08329","pdf_url":"https://arxiv.org/pdf/1504.08329","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:research.chalmers.se:233850","is_oa":false,"landing_page_url":"https://research.chalmers.se/en/publication/233850","pdf_url":null,"source":{"id":"https://openalex.org/S4306402469","display_name":"Chalmers Research (Chalmers University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66862912","host_organization_name":"Chalmers University of Technology","host_organization_lineage":["https://openalex.org/I66862912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1504.08329","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1504.08329","pdf_url":"https://arxiv.org/pdf/1504.08329","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5437768239","display_name":null,"funder_award_id":"IG2012-5158","funder_id":"https://openalex.org/F4320320939","funder_display_name":"Swedish Foundation for International Cooperation in Research and Higher Education"},{"id":"https://openalex.org/G675320460","display_name":null,"funder_award_id":"DE-AC05-00OR22725","funder_id":"https://openalex.org/F4320338287","funder_display_name":"Oak Ridge National Laboratory"},{"id":"https://openalex.org/G8837978433","display_name":null,"funder_award_id":"240603","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"id":"https://openalex.org/F4320320939","display_name":"Swedish Foundation for International Cooperation in Research and Higher Education","ror":"https://ror.org/0561xc723"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"},{"id":"https://openalex.org/F4320338287","display_name":"Oak Ridge National Laboratory","ror":"https://ror.org/01qz5mb56"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1977116050","https://openalex.org/W1994029108","https://openalex.org/W2001630977","https://openalex.org/W2010654974","https://openalex.org/W2018281894","https://openalex.org/W2034182457","https://openalex.org/W2061222860","https://openalex.org/W2087868883","https://openalex.org/W2088055284","https://openalex.org/W4249983369"],"related_works":[],"abstract_inverted_index":{"We":[0,52],"present":[1],"an":[2],"efficient":[3],"implementation":[4],"for":[5,67],"the":[6,24,61,80,87,95,116,128],"evaluation":[7],"of":[8,27,39,41,63,70,83,115,130],"Wigner":[9],"$3j$,":[10],"$6j$,":[11],"and":[12,36,133],"$9j$":[13],"symbols.":[14],"These":[15],"represent":[16],"numerical":[17,54],"transformation":[18],"coefficients":[19],"that":[20],"are":[21],"used":[22],"in":[23,86,94,107],"quantum":[25],"theory":[26],"angular":[28],"momentum.":[29],"They":[30],"can":[31,45],"be":[32,46],"expressed":[33],"as":[34,79],"sums":[35],"square":[37],"roots":[38],"ratios":[40],"integers.":[42],"The":[43],"integers":[44,105],"very":[47],"large":[48,103],"due":[49,57],"to":[50,58,101],"factorials.":[51],"avoid":[53],"precision":[55],"loss":[56],"cancellation":[59],"through":[60],"use":[62],"multiword":[64,104],"integer":[65],"arithmetic":[66],"exact":[68],"accumulation":[69],"all":[71],"sums.":[72],"A":[73],"fixed":[74],"relative":[75],"accuracy":[76],"is":[77,106],"maintained":[78],"limited":[81],"number":[82],"floating-point":[84],"operations":[85],"final":[88],"step":[89],"incur":[90],"rounding":[91],"errors":[92],"only":[93],"least":[96],"significant":[97],"bits.":[98],"Time":[99],"spent":[100],"evaluate":[102],"turn":[108],"reduced":[109],"by":[110],"using":[111],"explicit":[112],"prime":[113],"factorization":[114],"ingoing":[117],"factorials,":[118],"thereby":[119],"improving":[120],"execution":[121],"speed.":[122],"Comparison":[123],"with":[124],"existing":[125],"routines":[126],"shows":[127],"efficiency":[129],"our":[131],"approach,":[132],"we":[134],"therefore":[135],"provide":[136],"a":[137],"computer":[138],"code":[139],"based":[140],"on":[141],"this":[142],"work.":[143]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":12},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3}],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2020-11-23T00:00:00"}