{"id":"https://openalex.org/W2255550028","doi":"https://doi.org/10.6092/issn.1972-5787/4359","title":"Innocuous Double Rounding of Basic Arithmetic Operations","display_name":"Innocuous Double Rounding of Basic Arithmetic Operations","publication_year":2014,"publication_date":"2014-06-27","ids":{"openalex":"https://openalex.org/W2255550028","doi":"https://doi.org/10.6092/issn.1972-5787/4359","mag":"2255550028"},"language":"en","primary_location":{"id":"pmh:oai:HAL:hal-01091186v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01091186","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":"http://jfr.unibo.it","raw_type":"info:eu-repo/semantics/article"},"type":"article","indexed_in":["datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-01091186","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101715842","display_name":"Pierre Le Roux","orcid":"https://orcid.org/0000-0002-0512-0437"},"institutions":[{"id":"https://openalex.org/I2803085393","display_name":"American Society of Association Executives","ror":"https://ror.org/02xwzkh23","country_code":"US","type":"other","lineage":["https://openalex.org/I2803085393"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Roux, Pierre","raw_affiliation_strings":["ISAE, ONERA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ISAE, ONERA","institution_ids":["https://openalex.org/I2803085393"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101715842"],"corresponding_institution_ids":["https://openalex.org/I2803085393"],"apc_list":null,"apc_paid":null,"fwci":0.3574,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.66583122,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9771000146865845,"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/T10363","display_name":"Low-power high-performance VLSI design","score":0.9769999980926514,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.9539502859115601},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.8635975122451782},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48775607347488403},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43003609776496887},{"id":"https://openalex.org/keywords/operating-system","display_name":"Operating system","score":0.09351861476898193}],"concepts":[{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.9539502859115601},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.8635975122451782},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48775607347488403},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43003609776496887},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.09351861476898193}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:HAL:hal-01091186v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01091186","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":"http://jfr.unibo.it","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:748fef18ca2444d08db615872c085d56","is_oa":true,"landing_page_url":"https://doaj.org/article/748fef18ca2444d08db615872c085d56","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Formalized Reasoning, Vol 7, Iss 1, Pp 131-142 (2014)","raw_type":"article"},{"id":"doi:10.6092/issn.1972-5787/4359","is_oa":true,"landing_page_url":"https://doi.org/10.6092/issn.1972-5787/4359","pdf_url":null,"source":{"id":"https://openalex.org/S7407050985","display_name":"Universit\u00e0 degli Studi di Bologna","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"article-journal"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01091186v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01091186","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":"http://jfr.unibo.it","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W1968552504","https://openalex.org/W2034572143","https://openalex.org/W2130920933"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W4220780102","https://openalex.org/W1502401885","https://openalex.org/W2410881844","https://openalex.org/W3196334750","https://openalex.org/W2004257129","https://openalex.org/W2116281088","https://openalex.org/W2016668641","https://openalex.org/W2255550028","https://openalex.org/W191585069"],"abstract_inverted_index":{"Double":[0,41],"rounding":[1,36,42,87],"occurs":[2],"when":[3,34,47],"a":[4,18],"floating-point":[5,73,82],"value":[6],"is":[7,88,107],"first":[8],"rounded":[9,16],"to":[10,17,37,77,130],"an":[11,54],"intermediate":[12,113],"precision":[13,106],"before":[14],"being":[15],"final":[19,39,105],"precision.":[20,40],"The":[21],"result":[22,32],"of":[23,121],"two":[24],"such":[25,65],"consecutive":[26],"roundings":[27],"can":[28],"differ":[29],"from":[30],"the":[31,38,49,61,69,78,81,91,104,112,118],"obtained":[33],"directly":[35],"practically":[43],"happens,":[44],"for":[45,90],"instance,":[46],"implementing":[48],"IEEE754":[50],"binary32":[51],"format":[52],"with":[53],"arithmetic":[55,83,93],"unit":[56],"performing":[57],"operations":[58,94],"only":[59],"in":[60,68,80],"larger":[62,110],"binary64":[63],"format,":[64],"as":[66,101,103],"done":[67],"PowerPC":[70],"or":[71],"x87":[72],"units.":[74],"It":[75],"belongs":[76],"folklore":[79],"community":[84],"that":[85],"double":[86],"innocuous":[89],"basic":[92],"(addition,":[95],"division,":[96],"multiplication,":[97],"and":[98,127],"square":[99],"root)":[100],"soon":[102],"about":[108],"twice":[109],"than":[111,133],"one.":[114],"This":[115],"paper":[116],"adresses":[117],"formal":[119],"proof":[120],"this":[122],"fact":[123],"considering":[124],"underflow":[125],"cases":[126],"its":[128],"extension":[129],"radices":[131],"other":[132],"two.":[134]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}
