A Universal Approximation Method and Optimized Hardware Architectures for Arithmetic Functions Based on Stochastic Computing

Stochastic computing (SC) has been applied on the implementations of complex arithmetic functions. Complicated polynomial-based approximations lead to large hardware complexity of previous SC circuits for arithmetic functions. In this paper, a novel piecewise approximation method based on Taylor ser...

Full description

Saved in:

Bibliographic Details
Published in:	IEEE access Vol. 8; p. 1
Main Authors:	Qin, Zidi, Qiu, Yuou, Zheng, Muhan, Dong, Hongxi, Lu, Zhonghai, Wang, Zhongfeng, Pan, Hongbing
Format:	Journal Article
Language:	English
Published:	Piscataway IEEE 01.01.2020 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Approximation Approximation methods Arithmetic arithmetic functions Circuits Complexity Complexity theory Computation Computer architecture Critical path Functions (mathematics) Hardware Indexes Logic gates Mathematical analysis Mathematical functions Optimization Polynomials Series expansion Stochastic computing Taylor series VLSI architecture
ISSN:	2169-3536, 2169-3536
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Abstract	Stochastic computing (SC) has been applied on the implementations of complex arithmetic functions. Complicated polynomial-based approximations lead to large hardware complexity of previous SC circuits for arithmetic functions. In this paper, a novel piecewise approximation method based on Taylor series expansion is proposed for complex arithmetic functions. Efficient implementations based on unipolar stochastic logic are presented for the monotonic functions. Furthermore, detailed optimization schemes are provided for the non-monotonic functions. Using NAND and AND gates as main computing elements, the optimized hardware architectures have extremely low complexity. The experimental results show that a broad range of arithmetic functions can be implemented with the proposed SC circuits, and the mean absolute errors can achieve the order of 1 × 10-3. Compared with the state-of-the-art works, the approximation precision for some typical functions can be increased by more than 8× with our method. In addition, the proposed circuits outperform the previous methods in hardware complexity and critical path significantly.
AbstractList	Stochastic computing (SC) has been applied on the implementations of complex arithmetic functions. Complicated polynomial-based approximations lead to large hardware complexity of previous SC circuits for arithmetic functions. In this paper, a novel piecewise approximation method based on Taylor series expansion is proposed for complex arithmetic functions. Efficient implementations based on unipolar stochastic logic are presented for the monotonic functions. Furthermore, detailed optimization schemes are provided for the non-monotonic functions. Using NAND and AND gates as main computing elements, the optimized hardware architectures have extremely low complexity. The experimental results show that a broad range of arithmetic functions can be implemented with the proposed SC circuits, and the mean absolute errors can achieve the order of 1 × 10-3. Compared with the state-of-the-art works, the approximation precision for some typical functions can be increased by more than 8× with our method. In addition, the proposed circuits outperform the previous methods in hardware complexity and critical path significantly. Stochastic computing (SC) has been applied on the implementations of complex arithmetic functions. Complicated polynomial-based approximations lead to large hardware complexity of previous SC circuits for arithmetic functions. In this paper, a novel piecewise approximation method based on Taylor series expansion is proposed for complex arithmetic functions. Efficient implementations based on unipolar stochastic logic are presented for the monotonic functions. Furthermore, detailed optimization schemes are provided for the non-monotonic functions. Using NAND and AND gates as main computing elements, the optimized hardware architectures have extremely low complexity. The experimental results show that a broad range of arithmetic functions can be implemented with the proposed SC circuits, and the mean absolute errors can achieve the order of 1 x 10(-3). Compared with the state-of-the-art works, the approximation precision for some typical functions can be increased by more than 8x with our method. In addition, the proposed circuits outperform the previous methods in hardware complexity and critical path significantly.
Author	Wang, Zhongfeng Zheng, Muhan Dong, Hongxi Lu, Zhonghai Pan, Hongbing Qin, Zidi Qiu, Yuou
Author_xml	– sequence: 1 givenname: Zidi surname: Qin fullname: Qin, Zidi organization: School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China. (e-mail: qinzidi@smail.nju.edu.cn) – sequence: 2 givenname: Yuou surname: Qiu fullname: Qiu, Yuou organization: School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China – sequence: 3 givenname: Muhan surname: Zheng fullname: Zheng, Muhan organization: School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China – sequence: 4 givenname: Hongxi surname: Dong fullname: Dong, Hongxi organization: School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China – sequence: 5 givenname: Zhonghai surname: Lu fullname: Lu, Zhonghai organization: School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm 10044, Sweden – sequence: 6 givenname: Zhongfeng surname: Wang fullname: Wang, Zhongfeng organization: School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China – sequence: 7 givenname: Hongbing surname: Pan fullname: Pan, Hongbing organization: School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China
BackLink	https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-272786$$DView record from Swedish Publication Index (Kungliga Tekniska Högskolan)
BookMark	eNp9kU9v1DAQxSNUJErpJ-glEucsjv_E62MILa3UqoelXC3HnjReduNgOy0gPnydTUHAAV9sjd_7aWbe6-xocANk2VmJVmWJxLu6ac43mxVGGK2w4GsixIvsGJeVKAgj1dEf71fZaQhblM46lRg_zn7W-d1gH8AHtcvrcfTum92raN2Q30DsncnVYPLbMdq9_QEmv1TePCoPee11byPoOHkIeed8qtjY7yFanV9Mg54ZIX-vQnIl2iY63asw_zZuP07RDvdvsped2gU4fb5PsruL80_NZXF9-_Gqqa8LTWkVi7ZUylBDEdek4lhrEBQpbVSrkaFAaWdIW9GSa445aZXSCBhhvEUdMthgcpJdLVzj1FaOPk3ov0unrDwUnL-XyqfOdiCxYC0wZBgkImadaFsOBGOOWVsZPrOKhRUeYZzav2gf7Of6QPsSe5ksfF0l_dtFn1b7dYIQ5dZNfkjjSkwZ5RVDa55UYlFp70Lw0Elt4yGG6JXdyRLJOWu5ZC3nrOVz1slL_vH-6un_rrPFZQHgt0MgTASn5Akj-7m-
CODEN	IAECCG
CitedBy_id	crossref_primary_10_3390_technologies10020039 crossref_primary_10_3390_e25121592 crossref_primary_10_1109_TVLSI_2020_3004602 crossref_primary_10_1109_ACCESS_2021_3059482 crossref_primary_10_1109_TC_2021_3085120 crossref_primary_10_1109_TCSI_2021_3133931 crossref_primary_10_1109_TIA_2020_3041808
Cites_doi	10.1109/ICCD.2014.6974706 10.1145/2429384.2429483 10.1109/ASPDAC.2016.7428020 10.1109/TETC.2016.2598726 10.1109/TCSII.2017.2756862 10.1145/2465787.2465794 10.1109/TETC.2016.2618750 10.1109/ICEAC.2012.6471024 10.1109/DSD.2017.29 10.1145/1391469.1391636 10.1109/TCAD.2018.2852752 10.1109/IJCNN.2017.7965993 10.1109/ACCESS.2019.2921104 10.1145/2744769.2747932 10.1109/TC.2010.202 10.1109/MCSoC2018.2018.00045 10.1109/12.954505 10.1109/ACCESS.2016.2523063 10.1145/2463209.2488901 10.1109/ASAP.2019.00018 10.1109/ICCD.2012.6378656 10.1109/TVLSI.2017.2654298
ContentType	Journal Article
Copyright	Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2020
Copyright_xml	– notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2020
DBID	97E ESBDL RIA RIE AAYXX CITATION 7SC 7SP 7SR 8BQ 8FD JG9 JQ2 L7M L~C L~D ADTPV AFDQA AOWAS D8T D8V ZZAVC DOA
DOI	10.1109/ACCESS.2020.2978399
DatabaseName	IEEE Xplore (IEEE) IEEE Xplore Open Access Journals IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Xplore CrossRef Computer and Information Systems Abstracts Electronics & Communications Abstracts Engineered Materials Abstracts METADEX Technology Research Database Materials Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional SwePub SWEPUB Kungliga Tekniska Högskolan full text SwePub Articles SWEPUB Freely available online SWEPUB Kungliga Tekniska Högskolan SwePub Articles full text DOAJ Directory of Open Access Journals
DatabaseTitle	CrossRef Materials Research Database Engineered Materials Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Electronics & Communications Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Advanced Technologies Database with Aerospace METADEX Computer and Information Systems Abstracts Professional
DatabaseTitleList	Materials Research Database
Database_xml	– sequence: 1 dbid: DOA name: DOAJ Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website – sequence: 2 dbid: RIE name: IEEE url: https://ieeexplore.ieee.org/ sourceTypes: Publisher
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering
EISSN	2169-3536
EndPage	1
ExternalDocumentID	oai_doaj_org_article_295be50d5eb6425f9bb7e322725b6d72 oai_DiVA_org_kth_272786 10_1109_ACCESS_2020_2978399 9023974
Genre	orig-research
GrantInformation_xml	– fundername: National Natural Science Foundation of China; National Nature Science Foundation of China grantid: No. 41412020201; No. 61376075 funderid: 10.13039/501100001809
GroupedDBID	0R~ 5VS 6IK 97E AAJGR ABAZT ABVLG ACGFS ADBBV ALMA_UNASSIGNED_HOLDINGS BCNDV BEFXN BFFAM BGNUA BKEBE BPEOZ EBS ESBDL GROUPED_DOAJ IPLJI JAVBF KQ8 M43 M~E O9- OCL OK1 RIA RIE RNS 4.4 AAYXX AGSQL CITATION EJD 7SC 7SP 7SR 8BQ 8FD JG9 JQ2 L7M L~C L~D ADTPV AFDQA AOWAS D8T D8V ZZAVC
ID	FETCH-LOGICAL-c446t-b1aad4d407c3672cce940acdabc0d4e44fd3b6417c7273baac0e5357b0f0d2d23
IEDL.DBID	RIE
ISICitedReferencesCount	9
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000524575400018&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	2169-3536
IngestDate	Fri Oct 03 12:44:06 EDT 2025 Tue Nov 04 16:57:45 EST 2025 Mon Jun 30 05:01:02 EDT 2025 Sat Nov 29 02:42:03 EST 2025 Tue Nov 18 21:00:23 EST 2025 Wed Aug 27 02:35:41 EDT 2025
IsDoiOpenAccess	true
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Language	English
License	https://creativecommons.org/licenses/by/4.0/legalcode
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c446t-b1aad4d407c3672cce940acdabc0d4e44fd3b6417c7273baac0e5357b0f0d2d23
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ORCID	0000-0003-1778-0640
OpenAccessLink	https://ieeexplore.ieee.org/document/9023974
PQID	2454765087
PQPubID	4845423
PageCount	1
ParticipantIDs	proquest_journals_2454765087 crossref_citationtrail_10_1109_ACCESS_2020_2978399 ieee_primary_9023974 doaj_primary_oai_doaj_org_article_295be50d5eb6425f9bb7e322725b6d72 swepub_primary_oai_DiVA_org_kth_272786 crossref_primary_10_1109_ACCESS_2020_2978399
PublicationCentury	2000
PublicationDate	2020-01-01
PublicationDateYYYYMMDD	2020-01-01
PublicationDate_xml	– month: 01 year: 2020 text: 2020-01-01 day: 01
PublicationDecade	2020
PublicationPlace	Piscataway
PublicationPlace_xml	– name: Piscataway
PublicationTitle	IEEE access
PublicationTitleAbbrev	Access
PublicationYear	2020
Publisher	IEEE The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher_xml	– name: IEEE – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
References	ref12 ref23 ref15 ref14 ref20 ref11 ref22 ref10 ref21 ref2 ref1 ref16 ref19 ref18 alaghi (ref13) 2014 ref8 ref7 ref9 ref4 ref3 ref6 ref5 weikang qian (ref17) 2008
References_xml	– ident: ref12 doi: 10.1109/ICCD.2014.6974706 – ident: ref15 doi: 10.1145/2429384.2429483 – ident: ref23 doi: 10.1109/ASPDAC.2016.7428020 – start-page: 1 year: 2014 ident: ref13 article-title: Fast and accurate computation using stochastic circuits publication-title: Proc Des Autom Test Eur (DATE) Conf – ident: ref1 doi: 10.1109/TETC.2016.2598726 – ident: ref21 doi: 10.1109/TCSII.2017.2756862 – ident: ref14 doi: 10.1145/2465787.2465794 – ident: ref19 doi: 10.1109/TETC.2016.2618750 – ident: ref2 doi: 10.1109/ICEAC.2012.6471024 – ident: ref22 doi: 10.1109/DSD.2017.29 – start-page: 648 year: 2008 ident: ref17 article-title: the synthesis of robust polynomial arithmetic with stochastic logic publication-title: 2008 45th ACM/IEEE Design Automation Conference DAC doi: 10.1145/1391469.1391636 – ident: ref8 doi: 10.1109/TCAD.2018.2852752 – ident: ref5 doi: 10.1109/IJCNN.2017.7965993 – ident: ref7 doi: 10.1109/ACCESS.2019.2921104 – ident: ref3 doi: 10.1145/2744769.2747932 – ident: ref18 doi: 10.1109/TC.2010.202 – ident: ref4 doi: 10.1109/MCSoC2018.2018.00045 – ident: ref11 doi: 10.1109/12.954505 – ident: ref10 doi: 10.1109/ACCESS.2016.2523063 – ident: ref9 doi: 10.1145/2463209.2488901 – ident: ref20 doi: 10.1109/ASAP.2019.00018 – ident: ref16 doi: 10.1109/ICCD.2012.6378656 – ident: ref6 doi: 10.1109/TVLSI.2017.2654298
SSID	ssj0000816957
Score	2.2153432
Snippet	Stochastic computing (SC) has been applied on the implementations of complex arithmetic functions. Complicated polynomial-based approximations lead to large...
SourceID	doaj swepub proquest crossref ieee
SourceType	Open Website Open Access Repository Aggregation Database Enrichment Source Index Database Publisher
StartPage	1
SubjectTerms	Approximation Approximation methods Arithmetic arithmetic functions Circuits Complexity Complexity theory Computation Computer architecture Critical path Functions (mathematics) Hardware Indexes Logic gates Mathematical analysis Mathematical functions Optimization Polynomials Series expansion Stochastic computing Taylor series VLSI architecture
SummonAdditionalLinks	– databaseName: DOAJ Directory of Open Access Journals dbid: DOA link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1Lb9QwELZQxQEOCCiIlIJ8QJwIdZw4Xh_ThRUHKEg81JvlV7QRdFvtpgVV_fHM2O6SXuDC1bI9tr-xPePHN4S8qCrb9AEnkm_7sml5KK2XouR9i1QuolcuIv1eHh3Njo_Vp0moL3wTluiB08AdcCVsEMyLYMFUhrLWygBaKLmwrZdx9WVSTZypuAbPqlYJmWmGKqYOuvkcegQOIWevOZ53RLbXP1tRZOzPIVZuWptTBtG46yzuk3vZXKRdauYDciusHpK7ExLBXXLV0fy6AjMiRfivIf1HpB9ieGhqVp5-hKXhZLgMnuJd_U-zDrSb3CFsKBivkDKMyxP81kgXsN9FlaSHsM95CrV9Hk_d0iCvM02xIED8I_J18fbL_F2ZYyqUDhy_sbSVMb7x4Ma5upXcuaAaZpw31jHfhKbpfQ0DXUmHho01xrEgaiEt65nnntePyc7qdBWeECoka1UPKNQezL5KGUBGyMbaOiDLVygIvx5e7TLhOMa9-KGj48GUTphoxERnTAryalvoLPFt_D37IeK2zYpk2TEBVEhnFdL_UqGC7CLq20oUfviVTUH2r7VA54m90RwJ0NCqlQV5mTTjhvA3w7cuCv8-LjVIkLN273-08Sm5g_1Ohz_7ZGdcn4dn5La7GIfN-nlU_t8aJAez priority: 102 providerName: Directory of Open Access Journals
Title	A Universal Approximation Method and Optimized Hardware Architectures for Arithmetic Functions Based on Stochastic Computing
URI	https://ieeexplore.ieee.org/document/9023974 https://www.proquest.com/docview/2454765087 https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-272786 https://doaj.org/article/295be50d5eb6425f9bb7e322725b6d72
Volume	8
WOSCitedRecordID	wos000524575400018&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVAON databaseName: DOAJ Directory of Open Access Journals customDbUrl: eissn: 2169-3536 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000816957 issn: 2169-3536 databaseCode: DOA dateStart: 20130101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals – providerCode: PRVHPJ databaseName: ROAD: Directory of Open Access Scholarly Resources customDbUrl: eissn: 2169-3536 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000816957 issn: 2169-3536 databaseCode: M~E dateStart: 20130101 isFulltext: true titleUrlDefault: https://road.issn.org providerName: ISSN International Centre
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1Lb9QwELbaigMceBVESql8QJya1nHsuD6mS1ccaEHiod4iv6KNSnfRbloQQvx2Zhw3bCWExCWKIscPfWN7Zuz5hpCXRWFFG3Ai-arNRcVDbr2SOW8rpHKRrXYR6bfq7Ozo_Fy_3yD7YyxMCCFePgsH-BrP8v3CXaGr7FBjJKYSm2RTqWqI1Rr9KZhAQkuViIUKpg_ryQTGACYgZwccPRyR3_XP5hM5-lNSldv65TpnaNxnpg_-r4cPyf2kT9J6EIBHZCPMH5N7ayyD2-RnTdP1CyyIHOLfuyFgkZ7G_NHUzD19B2vHZfcjeIqH-d_MMtB67ZBhRUG7hS9dP7vEuEc6hQ0xyiw9ho3QU6jtQ79wM4PEz3RIFgHNPyGfpicfJ2_ylHQhd2AZ9rktjPHCg53nykpx54IWzDhvrGNeBCFaX9pKFMqh5mONcSzIUirLWua55-VTsjVfzMMzQqVilW6lrUoPemGhjbVKKmFtGZAGLGSE36DRuMRIjokxvjTRMmG6GSBsEMImQZiR_fGnrwMhx7-LHyPMY1Fk044fALYmTU4oK22QzMsAI-Mgn9DRACud4tB5r3hGthHqsZKEckZ2b4SmSTN_1XBkSEO1V2Xk1SBItxp_3X2uY-MX_ayBFtRRtfP36p-TuziSwd-zS7b65VV4Qe64675bLfei8wCep79O9uJM-A181Acz
linkProvider	IEEE
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1Lb9QwELZKQQIOvFpEoIAPiFPTOo4dN8d0YVXEdkGioN6s-BFtBN1Fuykg1B_fGccNWwkhcYssx2PrG3vGj_mGkFdZZkTjcSK5oklFwX1qnJIpbwqkcpFNaQPSEzWdHpyelh83yO4QC-O9D4_P_B5-hrt8t7DneFS2X2IkphI3yE3MnBWjtYYTFUwhUUoVqYUyVu5XoxGMAjaBnO1xPOMIDK9_zE9g6Y9pVa57mOusocHSjO__Xx8fkHvRo6RVrwIPyYafPyJ313gGt8hFReMDDKyILOK_2j5kkR6HDNK0njv6AVaPs_a3dxSv83_WS0-rtWuGFQX_FkrabnaGkY90DCYxaC09BFPoKLT2qVvYWY3Uz7RPFwHit8nn8duT0VEa0y6kFvaGXWqyunbCwU7P5oXi1vpSsNq62ljmhBeicbkpRKYs-j6mri3zMpfKsIY57nj-mGzOF3P_hFCpWFE20hS5A88wK2tjlFTCmNwjEZhPCL9CQ9vISY6pMb7psDdhpe4h1AihjhAmZHf46XtPyfHv6ocI81AV-bRDAcCm4_SEutJ4yZz0MDIOGgod9bDWKQ6dd4onZAuhHhqJKCdk50ppdJz7K82RIw0dX5WQ170iXRP-pv1SBeFfu5kGCeqgePr35l-S20cnxxM9eTd9_4zcwVH1pz87ZLNbnvvn5Jb90bWr5YswEy4B57EIVg
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+Universal+Approximation+Method+and+Optimized+Hardware+Architectures+for+Arithmetic+Functions+Based+on+Stochastic+Computing&rft.jtitle=IEEE+access&rft.au=Qin%2C+Zidi&rft.au=Qiu%2C+Yuou&rft.au=Zheng%2C+Muhan&rft.au=Dong%2C+Hongxi&rft.date=2020-01-01&rft.issn=2169-3536&rft.eissn=2169-3536&rft.volume=8&rft.spage=46229&rft.epage=46241&rft_id=info:doi/10.1109%2FACCESS.2020.2978399&rft.externalDBID=n%2Fa&rft.externalDocID=10_1109_ACCESS_2020_2978399
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2169-3536&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2169-3536&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2169-3536&client=summon