{"id":"https://openalex.org/W2213398780","doi":"https://doi.org/10.1145/2824252","title":"A Radix-Independent Error Analysis of the Cornea-Harrison-Tang Method","display_name":"A Radix-Independent Error Analysis of the Cornea-Harrison-Tang Method","publication_year":2016,"publication_date":"2016-05-10","ids":{"openalex":"https://openalex.org/W2213398780","doi":"https://doi.org/10.1145/2824252","mag":"2213398780"},"language":"en","primary_location":{"id":"doi:10.1145/2824252","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2824252","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/hal-01050021","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110628690","display_name":"Claude-Pierre 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"]},{"id":"https://openalex.org/I113428412","display_name":"\u00c9cole Normale Sup\u00e9rieure de Lyon","ror":"https://ror.org/04zmssz18","country_code":"FR","type":"education","lineage":["https://openalex.org/I113428412","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Claude-Pierre Jeannerod","raw_affiliation_strings":["Inria, LIP (CNRS, ENSL, Inria, UCBL), Universit\u00e9 de Lyon, Lyon, France"],"affiliations":[{"raw_affiliation_string":"Inria, LIP (CNRS, ENSL, Inria, UCBL), Universit\u00e9 de Lyon, Lyon, France","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I1326498283","https://openalex.org/I1294671590","https://openalex.org/I113428412"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5110628690"],"corresponding_institution_ids":["https://openalex.org/I100532134","https://openalex.org/I113428412","https://openalex.org/I1294671590","https://openalex.org/I1326498283"],"apc_list":null,"apc_paid":null,"fwci":1.3939,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.82023406,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"42","issue":"3","first_page":"1","last_page":"20"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":1.0,"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":1.0,"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":0.9965999722480774,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9897000193595886,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.9360713958740234},{"id":"https://openalex.org/keywords/round-off-error","display_name":"Round-off error","score":0.7930073738098145},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.642781138420105},{"id":"https://openalex.org/keywords/floating-point","display_name":"Floating point","score":0.6184681057929993},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5628045201301575},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5195479989051819},{"id":"https://openalex.org/keywords/radix","display_name":"Radix (gastropod)","score":0.5022549629211426},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.48283228278160095},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.46681949496269226},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4231388568878174},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4152378439903259},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3320671319961548},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2696937918663025},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1327664852142334}],"concepts":[{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.9360713958740234},{"id":"https://openalex.org/C61005703","wikidata":"https://www.wikidata.org/wiki/Q2145211","display_name":"Round-off error","level":2,"score":0.7930073738098145},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.642781138420105},{"id":"https://openalex.org/C84211073","wikidata":"https://www.wikidata.org/wiki/Q117879","display_name":"Floating point","level":2,"score":0.6184681057929993},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5628045201301575},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5195479989051819},{"id":"https://openalex.org/C2779091547","wikidata":"https://www.wikidata.org/wiki/Q287565","display_name":"Radix (gastropod)","level":2,"score":0.5022549629211426},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.48283228278160095},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.46681949496269226},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4231388568878174},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4152378439903259},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3320671319961548},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2696937918663025},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1327664852142334},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/2824252","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2824252","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01050021v2","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01050021","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"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":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ACM Transactions on Mathematical Software, 2016, &#x27E8;10.1145/2824252&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01050021v2","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01050021","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"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":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ACM Transactions on Mathematical Software, 2016, &#x27E8;10.1145/2824252&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3497078602","display_name":null,"funder_award_id":"ANR-13-INSE-0007 (MetaLibm project)","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W581104972","https://openalex.org/W1535645767","https://openalex.org/W1982696069","https://openalex.org/W2002064155","https://openalex.org/W2020804487","https://openalex.org/W2132612109","https://openalex.org/W2207050309","https://openalex.org/W2292537122","https://openalex.org/W2296909587","https://openalex.org/W2752061190"],"related_works":["https://openalex.org/W3039927303","https://openalex.org/W2383134623","https://openalex.org/W1989068301","https://openalex.org/W4388911419","https://openalex.org/W2061091230","https://openalex.org/W4242955624","https://openalex.org/W4231731735","https://openalex.org/W3185976014","https://openalex.org/W2134876043","https://openalex.org/W196954033"],"abstract_inverted_index":{"Assuming":[0],"floating-point":[1,50,180],"arithmetic":[2,51],"with":[3,25],"a":[4,34,182,192],"fused":[5],"multiply-add":[6],"operation":[7],"and":[8,111,139,170,214,219],"rounding":[9,35,151,171],"to":[10,16,48,153,173,191],"nearest,":[11],"the":[12,20,67,105,119,123,136,140,158],"Cornea-Harrison-Tang":[13],"method":[14,72],"aims":[15],"evaluate":[17],"expressions":[18],"of":[19,38,70,121],"form":[21],"ab":[22],"+":[23,76,88,92,199],"cd":[24],"high":[26],"relative":[27,68,193],"accuracy.":[28],"In":[29],"this":[30,39,71,131],"article,":[31],"we":[32,116],"provide":[33],"error":[36,69,194],"analysis":[37],"method,":[40],"which":[41],"unlike":[42],"previous":[43],"studies":[44],"is":[45,73,104,133,148,152,163,168,172],"not":[46,217],"restricted":[47],"binary":[49],"but":[52],"holds":[53],"for":[54,144],"any":[55],"radix":[56,109,137],"\u03b2.":[57],"We":[58],"show":[59,117],"first":[60],"that":[61,118,189],"an":[62],"asymptotically":[63],"optimal":[64],"bound":[65,132,160],"on":[66,224],"2\u03b2":[74],"u":[75,78,83,87,90,95,99,126,162,198,201,205],"2":[77,79,82,84,86,91,127,161,197,202],"/\u03b2":[80],"-":[81],"=":[85,100],"2/\u03b2":[89,200],"O":[93,124],"(":[94,125],"3":[96,206],"),":[97],"where":[98],"1/2\u03b2":[101],"1-":[102],"p":[103,113,225],"unit":[106],"roundoff":[107],"in":[108],"\u03b2":[110,147,167],"precision":[112],".":[114,207],"Then":[115],"possibility":[120],"removing":[122],")":[128],"term":[129],"from":[130],"governed":[134],"by":[135,227],"parity":[138],"tie-breaking":[141],"strategy":[142],"used":[143],"rounding:":[145],"if":[146,166],"odd":[149],"or":[150],"nearest":[154,174],"even":[155,169],",":[156,176,183,185,187],"then":[157,177],"simpler":[159],"obtained,":[164],"while":[165],"away":[175],"there":[178],"exist":[179],"inputs":[181],"b":[184],"c":[186],"d":[188],"lead":[190],"larger":[195],"than":[196],"\u2014":[203],"4":[204],"All":[208],"these":[209],"results":[210],"hold":[211],"provided":[212],"underflows":[213],"overflows":[215],"do":[216],"occur":[218],"under":[220],"some":[221],"mild":[222],"assumptions":[223],"satisfied":[226],"IEEE":[228],"754-2008":[229],"formats.":[230]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
