乐胖代购免代理版

{"id":"https://openalex.org/W2009804058","doi":"https://doi.org/10.1109/arith.2013.8","title":"On the Componentwise Accuracy of Complex Floating-Point Division with an FMA","display_name":"On the Componentwise Accuracy of Complex Floating-Point Division with an FMA","publication_year":2013,"publication_date":"2013-04-01","ids":{"openalex":"https://openalex.org/W2009804058","doi":"https://doi.org/10.1109/arith.2013.8","mag":"2009804058"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/arith.2013.8","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"proceedings-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://ens-lyon.hal.science/ensl-00734339/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110012763","display_name":"C-P Jeannerod","orcid":null},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"C-P Jeannerod","raw_affiliation_strings":["Lab. LIP, Univ. de Lyon, Lyon, France"],"affiliations":[{"raw_affiliation_string":"Lab. LIP, Univ. de Lyon, Lyon, France","institution_ids":["https://openalex.org/I100532134"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102976183","display_name":"Nicolas Louvet","orcid":"https://orcid.org/0000-0002-5861-0819"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"N. Louvet","raw_affiliation_strings":["Lab. LIP, Univ. de Lyon, Lyon, France"],"affiliations":[{"raw_affiliation_string":"Lab. LIP, Univ. de Lyon, Lyon, France","institution_ids":["https://openalex.org/I100532134"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046395330","display_name":"Jean\u2010Michel Muller","orcid":"https://orcid.org/0000-0003-3588-0047"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"J-M Muller","raw_affiliation_strings":["Lab. LIP, Univ. de Lyon, Lyon, France"],"affiliations":[{"raw_affiliation_string":"Lab. LIP, Univ. de Lyon, Lyon, France","institution_ids":["https://openalex.org/I100532134"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.485,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":4,"citation_normalized_percentile":{"value":0.384992,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":78,"max":80},"biblio":{"volume":null,"issue":null,"first_page":"83","last_page":"90"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9999,"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"}},"topics":[{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9999,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9905,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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":0.9866,"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/arithmetic-underflow","display_name":"Arithmetic underflow","score":0.85290045},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.5056269},{"id":"https://openalex.org/keywords/division-algorithm","display_name":"Division algorithm","score":0.4865302},{"id":"https://openalex.org/keywords/fraction","display_name":"Fraction (chemistry)","score":0.41868067}],"concepts":[{"id":"https://openalex.org/C3265923","wikidata":"https://www.wikidata.org/wiki/Q669129","display_name":"Arithmetic underflow","level":2,"score":0.85290045},{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.7248003},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.63943774},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.59931314},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.56845486},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.52078766},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.519562},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.5056269},{"id":"https://openalex.org/C190715199","wikidata":"https://www.wikidata.org/wiki/Q3526714","display_name":"Division algorithm","level":3,"score":0.4865302},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.46185577},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4232052},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.41868067},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.37799686},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/arith.2013.8","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://hal-ens-lyon.archives-ouvertes.fr/ensl-00734339","pdf_url":"https://ens-lyon.hal.science/ensl-00734339/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://hal-ens-lyon.archives-ouvertes.fr/ensl-00734339v2/document","pdf_url":"https://hal-ens-lyon.archives-ouvertes.fr/ensl-00734339v2/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://ens-lyon.hal.science/ensl-00734339v2/file/Jeannerod_Louvet_Muller_final.pdf","pdf_url":"https://ens-lyon.hal.science/ensl-00734339v2/file/Jeannerod_Louvet_Muller_final.pdf","source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://hal-ens-lyon.archives-ouvertes.fr/ensl-00734339v2/file/Jeannerod_Louvet_Muller_final.pdf","pdf_url":"https://hal-ens-lyon.archives-ouvertes.fr/ensl-00734339v2/file/Jeannerod_Louvet_Muller_final.pdf","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://ens-lyon.hal.science/ensl-00734339v2/document","pdf_url":"https://ens-lyon.hal.science/ensl-00734339v2/document","source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.392.6607","pdf_url":"http://hal.inria.fr/docs/00/78/57/86/PDF/Jeannerod_Louvet_Muller_final.pdf","source":{"id":"https://openalex.org/S4306400349","display_name":"CiteSeer X (The Pennsylvania State University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130769515","host_organization_name":"Pennsylvania State University","host_organization_lineage":["https://openalex.org/I130769515"],"host_organization_lineage_names":["Pennsylvania State University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://hal-ens-lyon.archives-ouvertes.fr/ensl-00734339","pdf_url":"https://ens-lyon.hal.science/ensl-00734339/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":13,"referenced_works":["https://openalex.org/W1535645767","https://openalex.org/W1555915743","https://openalex.org/W1590147927","https://openalex.org/W1963994066","https://openalex.org/W1969155620","https://openalex.org/W1982696069","https://openalex.org/W2002064155","https://openalex.org/W2019612162","https://openalex.org/W2020804487","https://openalex.org/W2090843623","https://openalex.org/W245914994","https://openalex.org/W2725179571","https://openalex.org/W605824955"],"related_works":["https://openalex.org/W4310051342","https://openalex.org/W3118522067","https://openalex.org/W2388178587","https://openalex.org/W2162724120","https://openalex.org/W2094996819","https://openalex.org/W2087502554","https://openalex.org/W1977244761","https://openalex.org/W1618607655","https://openalex.org/W1601585824","https://openalex.org/W13027601"],"abstract_inverted_index":{"This":[0],"paper":[1],"deals":[2],"with":[3,146,156,187,225],"the":[4,36,50,73,89,115,138,147,189,201,216,230],"accuracy":[5,34,109],"of":[6,49,75,79,111,117,140,142,149,197,203],"complex":[7,76],"division":[8,165],"in":[9,35,72],"radix-two":[10],"floating-point":[11],"arithmetic.":[12],"Assuming":[13],"that":[14,23,84,93,210,229,244],"a":[15,107,171,226],"fused":[16],"multiply-add":[17],"(FMA)":[18],"instruction":[19],"is":[20,170,179,214,248],"available":[21],"and":[22,86,130,243],"no":[24],"underflow/overflow":[25],"occurs,":[26],"we":[27,160,193,223],"study":[28],"how":[29],"to":[30,44,58,62,144,237],"ensure":[31],"high":[32],"relative":[33,131,177],"component":[37,175],"wise":[38,176],"sense.":[39],"Since":[40],"this":[41,157,204,245],"essentially":[42,215],"reduces":[43],"evaluating":[45],"accurately":[46],"three":[47,60],"expressions":[48,81],"form":[51],"ac+bd,":[52],"an":[53],"obvious":[54],"approach":[55],"would":[56],"be":[57,97,234],"perform":[59],"calls":[61],"Kahan's":[63,150,154],"compensated":[64],"algorithm":[65,155,169,205,228],"for":[66,114,137,199],"2":[67,69],"by":[68],"determinants.":[70],"However,":[71],"context":[74],"division,":[77],"two":[78,118,163],"those":[80],"are":[82,221],"such":[83,112],"ac":[85],"bd":[87],"have":[88],"same":[90],"sign,":[91],"suggesting":[92],"cheaper":[94],"schemes":[95,113],"should":[96],"used":[98],"here":[99],"(since":[100],"cancellation":[101],"cannot":[102],"occur).":[103],"We":[104],"first":[105,168],"give":[106],"detailed":[108],"analysis":[110],"sum":[116],"nonnegative":[119],"products,":[120],"providing":[121],"not":[122],"only":[123],"sharp":[124],"bounds":[125],"on":[126],"both":[127],"their":[128],"absolute":[129],"errors,":[132],"but":[133],"also":[134,194],"sufficient":[135],"conditions":[136],"output":[139,148],"one":[141],"them":[143],"coincide":[145],"algorithm.":[151],"By":[152],"combining":[153],"particular":[158],"scheme,":[159],"then":[161],"deduce":[162],"new":[164],"algorithms.":[166],"Our":[167],"straight-line":[172],"program":[173],"whose":[174],"error":[178,202],"always":[180],"at":[181],"most":[182],"5u+13u":[183],"2":[186,241],"u":[188],"unit":[190],"round":[191],"off,":[192],"provide":[195],"examples":[196],"inputs":[198],"which":[200],"approaches":[206],"5u,":[207],"thus":[208],"showing":[209],"our":[211],"upper":[212],"bound":[213,231,247],"best":[217],"possible.":[218],"When":[219],"tests":[220],"allowed":[222],"show":[224],"second":[227],"above":[232],"can":[233],"further":[235],"reduced":[236],"4.5u+9u":[238],",":[242],"improved":[246],"reasonably":[249],"sharp.":[250]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2009804058","counts_by_year":[{"year":2018,"cited_by_count":2},{"year":2015,"cited_by_count":2}],"updated_date":"2024-12-07T19:46:27.712589","created_date":"2016-06-24"}