{"id":"https://openalex.org/W2901155929","doi":"https://doi.org/10.1109/tc.2018.2882537","title":"Improved Affine Arithmetic-Based Precision Analysis for Polynomial Function Evaluation","display_name":"Improved Affine Arithmetic-Based Precision Analysis for Polynomial Function Evaluation","publication_year":2018,"publication_date":"2018-11-21","ids":{"openalex":"https://openalex.org/W2901155929","doi":"https://doi.org/10.1109/tc.2018.2882537","mag":"2901155929"},"language":"en","primary_location":{"id":"doi:10.1109/tc.2018.2882537","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.2018.2882537","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","0016-9340","1557-9956","2326-3814"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computers","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086930942","display_name":"Rima Bellal","orcid":"https://orcid.org/0000-0002-7317-4808"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rima Bellal","raw_affiliation_strings":["Division de Micro\u00e9lectronique et Nanotechnologie, CDTA, Algiers, Algeria"],"raw_orcid":"https://orcid.org/0000-0002-7317-4808","affiliations":[{"raw_affiliation_string":"Division de Micro\u00e9lectronique et Nanotechnologie, CDTA, Algiers, Algeria","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044010884","display_name":"El\u2010Sedik Lamini","orcid":"https://orcid.org/0000-0001-6786-1110"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"El-sedik Lamini","raw_affiliation_strings":["Division de Micro\u00e9lectronique et Nanotechnologie, CDTA, Algiers, Algeria"],"raw_orcid":"https://orcid.org/0000-0001-6786-1110","affiliations":[{"raw_affiliation_string":"Division de Micro\u00e9lectronique et Nanotechnologie, CDTA, Algiers, Algeria","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054807235","display_name":"Hac\u00e8ne Belbachir","orcid":"https://orcid.org/0000-0001-8540-3033"},"institutions":[{"id":"https://openalex.org/I157169809","display_name":"University of Sciences and Technology Houari Boumediene","ror":"https://ror.org/02kb89c09","country_code":"DZ","type":"education","lineage":["https://openalex.org/I157169809"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Hacene Belbachir","raw_affiliation_strings":["Faculty of Mathematics RECITS Laboratory, USTHB, Bab Ezzouar, Algiers, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics RECITS Laboratory, USTHB, Bab Ezzouar, Algiers, Algeria","institution_ids":["https://openalex.org/I157169809"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071357775","display_name":"Samir Tagzout","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Samir Tagzout","raw_affiliation_strings":["Groupe Brandt, P\u00f4le Industrie, CEVITAL, Garidi II, Kouba, Algeirs, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Groupe Brandt, P\u00f4le Industrie, CEVITAL, Garidi II, Kouba, Algeirs, Algeria","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039079296","display_name":"Adel Belouchrani","orcid":"https://orcid.org/0000-0002-4579-7346"},"institutions":[{"id":"https://openalex.org/I2802493600","display_name":"Polytechnic School of Algiers","ror":"https://ror.org/05t0zwy08","country_code":"DZ","type":"education","lineage":["https://openalex.org/I2802493600"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Adel Belouchrani","raw_affiliation_strings":["LDCCP Lab. Ecole Nationale Polytechnique BP, El Harrach, Algiers, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LDCCP Lab. Ecole Nationale Polytechnique BP, El Harrach, Algiers, Algeria","institution_ids":["https://openalex.org/I2802493600"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8241,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.76647849,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"68","issue":"5","first_page":"702","last_page":"712"},"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/T10363","display_name":"Low-power high-performance VLSI design","score":0.9993000030517578,"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"}},{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.996399998664856,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/affine-arithmetic","display_name":"Affine arithmetic","score":0.7939014434814453},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.7238309383392334},{"id":"https://openalex.org/keywords/saturation-arithmetic","display_name":"Saturation arithmetic","score":0.658706545829773},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.6171147227287292},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5962189435958862},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5358949899673462},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5126394629478455},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.507401168346405},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49216121435165405},{"id":"https://openalex.org/keywords/quantization","display_name":"Quantization (signal processing)","score":0.4917471706867218},{"id":"https://openalex.org/keywords/word-length","display_name":"Word length","score":0.4766940772533417},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46793267130851746},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44399380683898926},{"id":"https://openalex.org/keywords/arbitrary-precision-arithmetic","display_name":"Arbitrary-precision arithmetic","score":0.3642142415046692},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.10449972748756409}],"concepts":[{"id":"https://openalex.org/C167315692","wikidata":"https://www.wikidata.org/wiki/Q3622729","display_name":"Affine arithmetic","level":3,"score":0.7939014434814453},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.7238309383392334},{"id":"https://openalex.org/C182775192","wikidata":"https://www.wikidata.org/wiki/Q913725","display_name":"Saturation arithmetic","level":3,"score":0.658706545829773},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.6171147227287292},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5962189435958862},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5358949899673462},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5126394629478455},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.507401168346405},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49216121435165405},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.4917471706867218},{"id":"https://openalex.org/C3019641298","wikidata":"https://www.wikidata.org/wiki/Q625642","display_name":"Word length","level":2,"score":0.4766940772533417},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46793267130851746},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44399380683898926},{"id":"https://openalex.org/C83581934","wikidata":"https://www.wikidata.org/wiki/Q527381","display_name":"Arbitrary-precision arithmetic","level":2,"score":0.3642142415046692},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.10449972748756409},{"id":"https://openalex.org/C204321447","wikidata":"https://www.wikidata.org/wiki/Q30642","display_name":"Natural language processing","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tc.2018.2882537","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.2018.2882537","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","0016-9340","1557-9956","2326-3814"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W171428496","https://openalex.org/W1540584048","https://openalex.org/W1965612527","https://openalex.org/W1974352941","https://openalex.org/W1977057259","https://openalex.org/W1986396242","https://openalex.org/W1989584178","https://openalex.org/W2002649790","https://openalex.org/W2020013154","https://openalex.org/W2076688134","https://openalex.org/W2078644732","https://openalex.org/W2083553720","https://openalex.org/W2086163366","https://openalex.org/W2088106051","https://openalex.org/W2089607228","https://openalex.org/W2100494504","https://openalex.org/W2108141766","https://openalex.org/W2108505641","https://openalex.org/W2109591842","https://openalex.org/W2118230018","https://openalex.org/W2118482121","https://openalex.org/W2130070037","https://openalex.org/W2130454051","https://openalex.org/W2131433010","https://openalex.org/W2131526547","https://openalex.org/W2134578847","https://openalex.org/W2137478259","https://openalex.org/W2138399676","https://openalex.org/W2139535992","https://openalex.org/W2141555595","https://openalex.org/W2153316377","https://openalex.org/W2164726178","https://openalex.org/W2169867540","https://openalex.org/W2221264131","https://openalex.org/W2227234579","https://openalex.org/W2247373330","https://openalex.org/W2538184078","https://openalex.org/W2570233623","https://openalex.org/W2586558147","https://openalex.org/W2750751278","https://openalex.org/W2794074965","https://openalex.org/W3145313321","https://openalex.org/W6679061569"],"related_works":["https://openalex.org/W1885677000","https://openalex.org/W2568181300","https://openalex.org/W1559551218","https://openalex.org/W1531645310","https://openalex.org/W2073476805","https://openalex.org/W2118036253","https://openalex.org/W1965905913","https://openalex.org/W2087454352","https://openalex.org/W4235638977","https://openalex.org/W2349168892"],"abstract_inverted_index":{"Word-length":[0],"allocation":[1],"is":[2,35,72],"the":[3,60,64,75,84],"most":[4],"important":[5],"design":[6],"phase":[7],"to":[8],"optimize":[9],"hardware":[10],"resources":[11],"while":[12],"guaranteeing":[13],"a":[14,47,67],"determined":[15],"accuracy":[16],"for":[17,29,46],"circuits":[18],"with":[19],"fixed-point":[20],"numbers.":[21],"This":[22],"paper":[23],"presents":[24],"an":[25,42,90],"enhanced":[26],"precision":[27],"analysis":[28],"degree-n":[30,48],"polynomial":[31,49],"Horner's":[32,50],"rule.":[33,51],"It":[34,52],"based":[36],"on":[37],"affine":[38],"arithmetic":[39],"and":[40],"introduces":[41],"error":[43,57,71],"propagating":[44],"formula":[45],"takes":[53],"into":[54],"account":[55],"quantization":[56],"of":[58],"all":[59],"circuit's":[61],"connections":[62],"including":[63],"inputs.":[65],"Furthermore,":[66],"tighter":[68],"upper":[69,86],"bound":[70,87],"defined,":[73],"exploiting":[74],"dependencies":[76],"between":[77],"intermediate":[78],"connections.":[79],"Hardware":[80],"implementations":[81],"show":[82],"that":[83,93],"proposed":[85],"results":[88],"in":[89],"area":[91],"reduction":[92],"reaches":[94],"70":[95],"percent.":[96]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}