{"id":"https://openalex.org/W2974644665","doi":"https://doi.org/10.1109/tcsi.2019.2939563","title":"A Universal Method of Linear Approximation With Controllable Error for the Efficient Implementation of Transcendental Functions","display_name":"A Universal Method of Linear Approximation With Controllable Error for the Efficient Implementation of Transcendental Functions","publication_year":2019,"publication_date":"2019-09-19","ids":{"openalex":"https://openalex.org/W2974644665","doi":"https://doi.org/10.1109/tcsi.2019.2939563","mag":"2974644665"},"language":"en","primary_location":{"id":"doi:10.1109/tcsi.2019.2939563","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2019.2939563","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"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 Circuits and Systems I: Regular Papers","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/A5042919154","display_name":"Huaqing Sun","orcid":"https://orcid.org/0000-0002-7669-4606"},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huaqing Sun","raw_affiliation_strings":["School of Electronic Science and Engineering, Nanjing University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-7669-4606","affiliations":[{"raw_affiliation_string":"School of Electronic Science and Engineering, Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063032740","display_name":"Yuanyong Luo","orcid":"https://orcid.org/0000-0002-4450-066X"},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuanyong Luo","raw_affiliation_strings":["School of Electronic Science and Engineering, Nanjing University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-4450-066X","affiliations":[{"raw_affiliation_string":"School of Electronic Science and Engineering, Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084305618","display_name":"Yajun Ha","orcid":"https://orcid.org/0000-0003-4244-5916"},"institutions":[{"id":"https://openalex.org/I30809798","display_name":"ShanghaiTech University","ror":"https://ror.org/030bhh786","country_code":"CN","type":"education","lineage":["https://openalex.org/I30809798"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yajun Ha","raw_affiliation_strings":["School of Information Science and Technology, ShanghaiTech University, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0003-4244-5916","affiliations":[{"raw_affiliation_string":"School of Information Science and Technology, ShanghaiTech University, Shanghai, China","institution_ids":["https://openalex.org/I30809798"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055917015","display_name":"Yinghuan Shi","orcid":"https://orcid.org/0000-0003-4534-7318"},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yinghuan Shi","raw_affiliation_strings":["Department of Computer Science and Technology, Nanjing University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0003-4534-7318","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Technology, Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I36399199"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074250521","display_name":"Yang Gao","orcid":"https://orcid.org/0000-0002-2488-1813"},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yang Gao","raw_affiliation_strings":["Department of Computer Science and Technology, Nanjing University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-2488-1813","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Technology, Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I36399199"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034410301","display_name":"Qinghong Shen","orcid":"https://orcid.org/0000-0003-3104-8659"},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qinghong Shen","raw_affiliation_strings":["School of Electronic Science and Engineering, Nanjing University, Nanjing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electronic Science and Engineering, Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027952470","display_name":"Hongbing Pan","orcid":"https://orcid.org/0000-0002-7181-8278"},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongbing Pan","raw_affiliation_strings":["School of Electronic Science and Engineering, Nanjing University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-7181-8278","affiliations":[{"raw_affiliation_string":"School of Electronic Science and Engineering, Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.9075,"has_fulltext":false,"cited_by_count":63,"citation_normalized_percentile":{"value":0.94209302,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"67","issue":"1","first_page":"177","last_page":"188"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9995999932289124,"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":0.9995999932289124,"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/T10320","display_name":"Neural Networks and Applications","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.9876000285148621,"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/approximation-error","display_name":"Approximation error","score":0.703274667263031},{"id":"https://openalex.org/keywords/sigmoid-function","display_name":"Sigmoid function","score":0.6674792170524597},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function approximation","score":0.5963844656944275},{"id":"https://openalex.org/keywords/hyperbolic-function","display_name":"Hyperbolic function","score":0.5732629299163818},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5505363345146179},{"id":"https://openalex.org/keywords/transcendental-function","display_name":"Transcendental function","score":0.5389995574951172},{"id":"https://openalex.org/keywords/inverse-trigonometric-functions","display_name":"Inverse trigonometric functions","score":0.49772003293037415},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.486975759267807},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.4841468930244446},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4770059883594513},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.458418071269989},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.45638397336006165},{"id":"https://openalex.org/keywords/transcendental-equation","display_name":"Transcendental equation","score":0.4244592785835266},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4190446734428406},{"id":"https://openalex.org/keywords/overhead","display_name":"Overhead (engineering)","score":0.4162343740463257},{"id":"https://openalex.org/keywords/linear-approximation","display_name":"Linear approximation","score":0.4156329333782196},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38371211290359497},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3778316378593445},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3762320578098297},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.3553345799446106},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1768103539943695},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.17591670155525208},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08004039525985718}],"concepts":[{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.703274667263031},{"id":"https://openalex.org/C81388566","wikidata":"https://www.wikidata.org/wiki/Q526668","display_name":"Sigmoid function","level":3,"score":0.6674792170524597},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.5963844656944275},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.5732629299163818},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5505363345146179},{"id":"https://openalex.org/C43321923","wikidata":"https://www.wikidata.org/wiki/Q864333","display_name":"Transcendental function","level":2,"score":0.5389995574951172},{"id":"https://openalex.org/C68827188","wikidata":"https://www.wikidata.org/wiki/Q674533","display_name":"Inverse trigonometric functions","level":2,"score":0.49772003293037415},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.486975759267807},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.4841468930244446},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4770059883594513},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.458418071269989},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.45638397336006165},{"id":"https://openalex.org/C139609574","wikidata":"https://www.wikidata.org/wiki/Q2273509","display_name":"Transcendental equation","level":3,"score":0.4244592785835266},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4190446734428406},{"id":"https://openalex.org/C2779960059","wikidata":"https://www.wikidata.org/wiki/Q7113681","display_name":"Overhead (engineering)","level":2,"score":0.4162343740463257},{"id":"https://openalex.org/C160824197","wikidata":"https://www.wikidata.org/wiki/Q2071054","display_name":"Linear approximation","level":3,"score":0.4156329333782196},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38371211290359497},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3778316378593445},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3762320578098297},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3553345799446106},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1768103539943695},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.17591670155525208},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08004039525985718},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcsi.2019.2939563","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2019.2939563","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"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 Circuits and Systems I: Regular Papers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3583143112","display_name":null,"funder_award_id":"61376075","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7289005036","display_name":null,"funder_award_id":"41412020201","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1972425002","https://openalex.org/W1973695593","https://openalex.org/W1978262091","https://openalex.org/W2023745373","https://openalex.org/W2045146697","https://openalex.org/W2071654592","https://openalex.org/W2082863931","https://openalex.org/W2105084502","https://openalex.org/W2110953186","https://openalex.org/W2111013824","https://openalex.org/W2113542749","https://openalex.org/W2122685238","https://openalex.org/W2123360365","https://openalex.org/W2136996778","https://openalex.org/W2138399676","https://openalex.org/W2149699057","https://openalex.org/W2151577341","https://openalex.org/W2167425979","https://openalex.org/W2168590567","https://openalex.org/W2169621283","https://openalex.org/W2309272862","https://openalex.org/W2329484403","https://openalex.org/W2539422612","https://openalex.org/W2591659919","https://openalex.org/W2730834423","https://openalex.org/W2901837052","https://openalex.org/W2945886900"],"related_works":["https://openalex.org/W2018801570","https://openalex.org/W2132448502","https://openalex.org/W2605253858","https://openalex.org/W2093884883","https://openalex.org/W2947634856","https://openalex.org/W2888929985","https://openalex.org/W3014029144","https://openalex.org/W2096111257","https://openalex.org/W2892326952","https://openalex.org/W4390893163"],"abstract_inverted_index":{"Transcendental":[0],"functions":[1,11,27,44,93,134],"are":[2],"commonly":[3],"used":[4,152],"in":[5,72,153,180],"many":[6,29],"fields":[7],"such":[8],"as":[9],"nonlinear":[10],"of":[12,20,25,107,112,142],"artificial":[13],"neural":[14],"networks":[15],"(ANNs).":[16],"Due":[17],"to":[18,67,102],"nonlinearity":[19],"these":[21],"functions,":[22,156],"hardware":[23,126],"implementation":[24],"the":[26,35,69,73,99,104,110,143,158,168,190],"faces":[28],"challenges.":[30],"Some":[31],"methods":[32,49,151],"cannot":[33,41],"control":[34],"approximation":[36,63,84,169],"accuracy":[37,170],"beforehand,":[38],"or":[39],"they":[40],"approximate":[42,52,131],"target":[43,144],"accurately":[45],"and":[46,123,135,162,176,187,196],"efficiently.":[47],"Other":[48],"can":[50,130],"only":[51],"a":[53,79,113],"particular":[54],"function":[55],"without":[56],"generality.":[57],"A":[58],"universal":[59],"piecewise":[60,81],"linear":[61,82],"(PWL)":[62,83],"method":[64,85,97,166,183],"is":[65,94,184],"proposed":[66],"solve":[68],"problems":[70],"existing":[71],"above":[74],"methods.":[75],"In":[76],"this":[77],"paper,":[78],"general":[80],"with":[86,149],"controllable":[87,114],"maximum":[88,115],"absolute":[89,116],"error":[90],"for":[91],"transcend-ental":[92],"proposed.":[95],"The":[96],"has":[98],"self-adaptive":[100],"capability":[101],"choose":[103],"smallest":[105],"number":[106],"segments":[108,122],"under":[109],"constraint":[111],"error.":[117],"Therefore,":[118],"it":[119,129,188],"requires":[120],"fewer":[121],"incurs":[124],"less":[125],"overhead.":[127],"Moreover,":[128],"any":[132,140],"transcendental":[133,155],"does":[136],"not":[137],"rely":[138],"on":[139],"properties":[141],"function.":[145],"Comparing":[146],"our":[147,165,182],"work":[148],"other":[150],"three":[154],"including":[157],"sigmoid,":[159],"hyperbolic":[160],"tangent,":[161],"logarithmic":[163],"function,":[164],"improves":[167],"by":[171,193],"4.5":[172],"times,":[173,175,178],"2.1":[174],"1.3":[177],"respectively;":[179],"addition,":[181],"more":[185],"efficient":[186],"reduces":[189],"circuit":[191],"area":[192],"49.9%,":[194],"22.4%,":[195],"28.5%,":[197],"respectively.":[198]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}