{"id":"https://openalex.org/W2162655755","doi":"https://doi.org/10.1051/ita:2007002","title":"Correct rounding of algebraic functions","display_name":"Correct rounding of algebraic functions","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2162655755","doi":"https://doi.org/10.1051/ita:2007002","mag":"2162655755"},"language":"en","primary_location":{"id":"doi:10.1051/ita:2007002","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ita:2007002","pdf_url":null,"source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Theoretical Informatics and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://ens-lyon.hal.science/ensl-00143230","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058275399","display_name":"Nicolas Brisebarre","orcid":"https://orcid.org/0000-0002-4220-2132"},"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/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"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"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Nicolas Brisebarre","raw_affiliation_strings":["Laboratoire LIP (CNRS/ENS Lyon/INRIA/Univ. Lyon 1), Projet Ar\u00e9naire, 46 all\u00e9e d'Italie, 69364 Lyon Cedex 07, France; Nicolas.Brisebarre@ens-lyon.fr; Jean-Michel.Muller@ens-lyon.fr","Laboratoire LaMUSE, Universit\u00e9 J. Monnet (Saint-\u00c9tienne), 23, rue du Dr P. Michelon, 42023 Saint-\u00c9tienne Cedex 02, France","Laboratoire LIP (CNRS/ENS Lyon/INRIA/Univ. Lyon 1), Projet Ar\u00e9naire, 46 all\u00e9e d'Italie, 69364 Lyon Cedex 07, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire LIP (CNRS/ENS Lyon/INRIA/Univ. Lyon 1), Projet Ar\u00e9naire, 46 all\u00e9e d'Italie, 69364 Lyon Cedex 07, France; Nicolas.Brisebarre@ens-lyon.fr; Jean-Michel.Muller@ens-lyon.fr","institution_ids":["https://openalex.org/I113428412","https://openalex.org/I100532134","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Laboratoire LaMUSE, Universit\u00e9 J. Monnet (Saint-\u00c9tienne), 23, rue du Dr P. Michelon, 42023 Saint-\u00c9tienne Cedex 02, France","institution_ids":[]},{"raw_affiliation_string":"Laboratoire LIP (CNRS/ENS Lyon/INRIA/Univ. Lyon 1), Projet Ar\u00e9naire, 46 all\u00e9e d'Italie, 69364 Lyon Cedex 07, France","institution_ids":["https://openalex.org/I113428412","https://openalex.org/I1326498283","https://openalex.org/I100532134","https://openalex.org/I1294671590"]}]},{"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/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"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/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jean-Michel Muller","raw_affiliation_strings":["Laboratoire LIP (CNRS/ENS Lyon/INRIA/Univ. Lyon 1), Projet Ar\u00e9naire, 46 all\u00e9e d'Italie, 69364 Lyon Cedex 07, France; Nicolas.Brisebarre@ens-lyon.fr; Jean-Michel.Muller@ens-lyon.fr","Laboratoire LIP (CNRS/ENS Lyon/INRIA/Univ. Lyon 1), Projet Ar\u00e9naire, 46 all\u00e9e d'Italie, 69364 Lyon Cedex 07, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire LIP (CNRS/ENS Lyon/INRIA/Univ. Lyon 1), Projet Ar\u00e9naire, 46 all\u00e9e d'Italie, 69364 Lyon Cedex 07, France; Nicolas.Brisebarre@ens-lyon.fr; Jean-Michel.Muller@ens-lyon.fr","institution_ids":["https://openalex.org/I113428412","https://openalex.org/I100532134","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Laboratoire LIP (CNRS/ENS Lyon/INRIA/Univ. Lyon 1), Projet Ar\u00e9naire, 46 all\u00e9e d'Italie, 69364 Lyon Cedex 07, France","institution_ids":["https://openalex.org/I113428412","https://openalex.org/I1326498283","https://openalex.org/I100532134","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5058275399"],"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":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.17191448,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"41","issue":"1","first_page":"71","last_page":"83"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.998199999332428,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.998199999332428,"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":0.9973999857902527,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9936000108718872,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.9002494812011719},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.7650572657585144},{"id":"https://openalex.org/keywords/diophantine-approximation","display_name":"Diophantine approximation","score":0.6105890870094299},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5423787832260132},{"id":"https://openalex.org/keywords/algebraic-operation","display_name":"Algebraic operation","score":0.5235109925270081},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.46616488695144653},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4453323483467102},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4036313593387604},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3585173487663269},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34370648860931396},{"id":"https://openalex.org/keywords/diophantine-equation","display_name":"Diophantine equation","score":0.32730913162231445},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14335033297538757},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.04998531937599182}],"concepts":[{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.9002494812011719},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.7650572657585144},{"id":"https://openalex.org/C102966492","wikidata":"https://www.wikidata.org/wiki/Q1227061","display_name":"Diophantine approximation","level":3,"score":0.6105890870094299},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5423787832260132},{"id":"https://openalex.org/C136003732","wikidata":"https://www.wikidata.org/wiki/Q3854337","display_name":"Algebraic operation","level":3,"score":0.5235109925270081},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.46616488695144653},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4453323483467102},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4036313593387604},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3585173487663269},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34370648860931396},{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.32730913162231445},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14335033297538757},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.04998531937599182},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1051/ita:2007002","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ita:2007002","pdf_url":null,"source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Theoretical Informatics and Applications","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.143.6624","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.143.6624","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://perso.ens-lyon.fr/jean-michel.muller/algtmd.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:ensl-00143230v1","is_oa":true,"landing_page_url":"https://ens-lyon.hal.science/ensl-00143230","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":"RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), 2007, 41 (1), pp.71-83. ⟨10.1051/ita:2007002⟩","raw_type":"Journal articles"},{"id":"pmh:oai:numdam.org:ITA_2007__41_1_71_0","is_oa":false,"landing_page_url":"https://www.numdam.org/articles/10.1051/ita:2007002/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"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"}],"best_oa_location":{"id":"pmh:oai:HAL:ensl-00143230v1","is_oa":true,"landing_page_url":"https://ens-lyon.hal.science/ensl-00143230","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":"RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), 2007, 41 (1), pp.71-83. ⟨10.1051/ita:2007002⟩","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1591257293","https://openalex.org/W1968834151","https://openalex.org/W1982329115","https://openalex.org/W2041998527","https://openalex.org/W2054625478","https://openalex.org/W2063551290","https://openalex.org/W2104895541","https://openalex.org/W2105365571","https://openalex.org/W2109304932","https://openalex.org/W2122306828","https://openalex.org/W2140571294","https://openalex.org/W2149538173","https://openalex.org/W2204310803","https://openalex.org/W2744679739","https://openalex.org/W3038928148","https://openalex.org/W4239953946","https://openalex.org/W4242706295"],"related_works":["https://openalex.org/W2050144047","https://openalex.org/W4298709754","https://openalex.org/W2135580938","https://openalex.org/W2614739812","https://openalex.org/W2372854171","https://openalex.org/W3143745619","https://openalex.org/W196064004","https://openalex.org/W1559473997","https://openalex.org/W4211175933","https://openalex.org/W2392216692"],"abstract_inverted_index":{"We":[0],"explicit":[1],"the":[2,5,26],"link":[3],"between":[4],"computer":[6],"arithmetic":[7],"problem":[8],"of":[9],"providing":[10],"correctly":[11,36],"rounded":[12],"algebraic":[13],"functions":[14],"and":[15],"some":[16],"diophantine":[17],"approximation":[18],"issues.":[19],"This":[20],"allows":[21],"to":[22,35],"get":[23],"bounds":[24],"on":[25],"accuracy":[27],"with":[28],"which":[29],"intermediate":[30],"calculations":[31],"must":[32],"be":[33],"performed":[34],"round":[37],"these":[38],"functions.":[39]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}