{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T14:54:32Z","timestamp":1773932072674,"version":"3.50.1"},"reference-count":171,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"1","license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"name":"European Union Horizon 2020","award":["779391"],"award-info":[{"award-number":["779391"]}]},{"name":"Fundacao para a Ciencia e a Tecnologia","award":["UIDB\/50021\/2020"],"award-info":[{"award-number":["UIDB\/50021\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Circuits Syst. Mag."],"published-print":{"date-parts":[[2021]]},"DOI":"10.1109\/mcas.2020.3027425","type":"journal-article","created":{"date-parts":[[2021,2,13]],"date-time":"2021-02-13T02:47:31Z","timestamp":1613184451000},"page":"6-40","source":"Crossref","is-referenced-by-count":43,"title":["Nonconventional Computer Arithmetic Circuits, Systems and Applications"],"prefix":"10.1109","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8066-221X","authenticated-orcid":false,"given":"Leonel","family":"Sousa","sequence":"first","affiliation":[{"name":"Superior Tecnico, Universidade de Lisboa, Lisbon, 1000-029, Portugal"}]}],"member":"263","reference":[{"key":"ref170","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1987-0866109-5"},{"key":"ref171","doi-asserted-by":"publisher","DOI":"10.1109\/CESYS.2018.8723960"},{"key":"ref168","year":"0","journal-title":"Quantum inspire (QI)"},{"key":"ref169","year":"0","journal-title":"Scalable quantum systems"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1109\/ARITH.1997.614901"},{"key":"ref38","author":"mohan","year":"2017","journal-title":"Arithmetic Circuits for DSP Applications"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-0041-0"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1109\/TEC.1959.5219515"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1142\/ACSET"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1109\/CircuitsAndSystems.2013.6671617"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1109\/MC.1984.1659138"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-49742-6"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1109\/MCAS.2015.2484118"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-49742-6_1"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1109\/ARITH.2001.930125"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1002\/0471221120"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1109\/VLSI-SoC.2015.7314386"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1109\/FPT.2003.1275734"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2015.2409059"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2010.51"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1109\/4.90098"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.3850\/9783981537079_0174"},{"key":"ref101","doi-asserted-by":"publisher","DOI":"10.1109\/TCT.1971.1083337"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2007.70791"},{"key":"ref100","year":"2019","journal-title":"Ferroelectric transistor technologies"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1109\/DSD.2003.1231957"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1145\/2234336.2234343"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1109\/ICROIT.2014.6798385"},{"key":"ref154","doi-asserted-by":"publisher","DOI":"10.1109\/5992.909000"},{"key":"ref153","doi-asserted-by":"publisher","DOI":"10.1109\/SFCS.1994.365700"},{"key":"ref156","doi-asserted-by":"publisher","DOI":"10.1109\/SFCS.1994.365701"},{"key":"ref155","author":"kaye","year":"2007","journal-title":"An Introduction to Quantum Computing"},{"key":"ref150","first-page":"465","author":"gentry","year":"2012","journal-title":"Fully Homomorphic Encryption with Polylog Overhead"},{"key":"ref152","author":"jordan","year":"2011","journal-title":"Quantum Algorithm Zoo"},{"key":"ref151","doi-asserted-by":"publisher","DOI":"10.1016\/j.future.2019.01.046"},{"key":"ref146","first-page":"13","article-title":"On Lov&#x00E1;sz&#x2019; lattice reduction and the nearest lattice point problem (shortened version)","author":"babai","year":"0","journal-title":"Proc 2nd Symp Theoretical Aspects of Computer Science"},{"key":"ref147","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2020.2983020"},{"key":"ref148","doi-asserted-by":"publisher","DOI":"10.1145\/1536414.1536440"},{"key":"ref149","author":"smart","year":"2011","journal-title":"Fully Homomorphic SIMD Operations"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1109\/ICCD.2014.6974707"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1109\/FPL.2015.7293962"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-03730-7"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.1145\/2465787.2465794"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1145\/1465482.1465505"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1109\/HPCA.2018.00065"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1145\/3177837"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1109\/ACSSC.2001.987765"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2008.126"},{"key":"ref167","doi-asserted-by":"publisher","DOI":"10.1109\/DSD.2003.1231911"},{"key":"ref166","author":"bajard","year":"2016","journal-title":"A Full RNS Variant of FV Like Somewhat Homomorphic Encryption Schemes"},{"key":"ref165","author":"mathworld","year":"0","journal-title":"Modular inverse"},{"key":"ref164","doi-asserted-by":"publisher","DOI":"10.1109\/ARITH.1993.378115"},{"key":"ref163","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(96)00058-3"},{"key":"ref162","doi-asserted-by":"publisher","DOI":"10.1145\/2400682.2400692"},{"key":"ref161","doi-asserted-by":"publisher","DOI":"10.1109\/ICRC.2016.7738716"},{"key":"ref160","author":"asfaw","year":"2020","journal-title":"Learn quantum computation using qiskit"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2015.2435773"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2017.2690420"},{"key":"ref6","year":"2019","journal-title":"7nm Technology"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/TED.2012.2198481"},{"key":"ref159","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1998.0164"},{"key":"ref8","author":"lapedus","year":"2018","journal-title":"Big trouble at 3nm"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2017.2669108"},{"key":"ref7","year":"2003","journal-title":"International Technology Roadmap for Semiconductors Emerging research devices"},{"key":"ref157","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1998.0163"},{"key":"ref158","author":"nielsen","year":"2011","journal-title":"Quantum Computation and Quantum Information"},{"key":"ref9","year":"2015","journal-title":"International Technology Roadmap of Semiconductors 2 0 Beyond CMOS"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1109\/TVLSI.2019.2919609"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1109\/TVLSI.2016.2577609"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1109\/ISPACS.2014.7024441"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1109\/SCET.2012.6342081"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1109\/TVLSI.2016.2516522"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1109\/ARITH.2007.16"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2004.2"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2015.2401026"},{"key":"ref127","article-title":"Rethinking floating point for deep learning","author":"johnson","year":"2018"},{"key":"ref126","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1109\/TVLSI.2014.2308014","article-title":"Fast sign detection algorithm for the RNS moduli set {2n+1 - 1, 2n &#x2013; 1, 2n}","volume":"23","author":"xu","year":"2015","journal-title":"IEEE Trans Very Large Scale Integr (VLSI) Syst"},{"key":"ref125","doi-asserted-by":"publisher","DOI":"10.1109\/TVLSI.2015.2484618"},{"key":"ref124","doi-asserted-by":"publisher","DOI":"10.1109\/JSSC.2016.2616357"},{"key":"ref73","doi-asserted-by":"publisher","DOI":"10.1109\/JETCAS.2019.2935464"},{"key":"ref72","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2018.2871163"},{"key":"ref129","first-page":"71","article-title":"Beating floating point at its own game: Posit arithmetic","volume":"4","author":"gustafson","year":"2017","journal-title":"International Journal on Supercomputing Frontiers and Innovations"},{"key":"ref71","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2015.2462721"},{"key":"ref128","author":"kulisch","year":"2012","journal-title":"Computer Arithmetic and Validity"},{"key":"ref70","doi-asserted-by":"publisher","DOI":"10.1007\/s12559-009-9009-8"},{"key":"ref76","doi-asserted-by":"publisher","DOI":"10.1145\/2897937.2898057"},{"key":"ref130","doi-asserted-by":"publisher","DOI":"10.1109\/ICCD.2017.24"},{"key":"ref77","doi-asserted-by":"publisher","DOI":"10.1145\/3061639.3062307"},{"key":"ref74","doi-asserted-by":"publisher","DOI":"10.1145\/2893356"},{"key":"ref75","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2020.3006451"},{"key":"ref133","doi-asserted-by":"publisher","DOI":"10.1145\/3037697.3037746"},{"key":"ref134","doi-asserted-by":"publisher","DOI":"10.1109\/TVLSI.2017.2654298"},{"key":"ref131","doi-asserted-by":"publisher","DOI":"10.1109\/TMSCS.2016.2601326"},{"key":"ref78","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2018.2889732"},{"key":"ref132","doi-asserted-by":"publisher","DOI":"10.1109\/ICCD.2011.6081391"},{"key":"ref79","doi-asserted-by":"publisher","DOI":"10.1145\/3307650.3322270"},{"key":"ref136","doi-asserted-by":"publisher","DOI":"10.1145\/3061639.3062290"},{"key":"ref135","doi-asserted-by":"publisher","DOI":"10.23919\/DATE.2017.7926951"},{"key":"ref138","doi-asserted-by":"publisher","DOI":"10.1145\/359340.359342"},{"key":"ref137","doi-asserted-by":"publisher","DOI":"10.1145\/3316781.3317911"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1145\/1391469.1391636"},{"key":"ref139","doi-asserted-by":"publisher","DOI":"10.2307\/2007970"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1109\/12.954505"},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2019.2949779"},{"key":"ref63","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2012.231"},{"key":"ref64","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.2018.2858338"},{"key":"ref140","doi-asserted-by":"publisher","DOI":"10.1109\/ARITH.2001.930104"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2010.202"},{"key":"ref141","doi-asserted-by":"publisher","DOI":"10.1109\/ASAP.2010.5541000"},{"key":"ref66","article-title":"Position paper, revisiting stochastic computation: Approximate estimation of machine learning kernels","author":"gupta","year":"0","journal-title":"Proc Position Paper Workshop Approximate Comput Across Syst Stack (WACAS)"},{"key":"ref142","doi-asserted-by":"publisher","DOI":"10.1109\/MCAS.2016.2614714"},{"key":"ref67","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.2017.2778107"},{"key":"ref143","doi-asserted-by":"publisher","DOI":"10.1109\/ASPDAC.2013.6509667"},{"key":"ref68","doi-asserted-by":"publisher","DOI":"10.1145\/2627369.2627645"},{"key":"ref144","doi-asserted-by":"publisher","DOI":"10.1109\/SFCS.1994.365700"},{"key":"ref2","article-title":"How much data is generated every minute?","year":"2018","journal-title":"Socialmediatoday"},{"key":"ref69","year":"2020","journal-title":"The human memory Brain neurons & synapses"},{"key":"ref145","first-page":"25","year":"2016","journal-title":"NIST"},{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1002\/bltj.20117"},{"key":"ref109","doi-asserted-by":"publisher","DOI":"10.1142\/S0129054104002546"},{"key":"ref95","doi-asserted-by":"publisher","DOI":"10.1109\/JPHOT.2017.2766087"},{"key":"ref108","doi-asserted-by":"publisher","DOI":"10.1126\/science.273.5272.220"},{"key":"ref94","doi-asserted-by":"publisher","DOI":"10.1109\/ICRC.2019.8914700"},{"key":"ref107","doi-asserted-by":"publisher","DOI":"10.23919\/DATE48585.2020.9116555"},{"key":"ref93","doi-asserted-by":"publisher","DOI":"10.1364\/OL.43.002026"},{"key":"ref106","doi-asserted-by":"publisher","DOI":"10.1109\/ISSCC.2018.8310399"},{"key":"ref92","doi-asserted-by":"publisher","DOI":"10.1063\/1.5080753"},{"key":"ref105","doi-asserted-by":"publisher","DOI":"10.1109\/NANO.2017.8117440"},{"key":"ref91","doi-asserted-by":"publisher","DOI":"10.1088\/0953-2048\/26\/3\/035010"},{"key":"ref104","doi-asserted-by":"publisher","DOI":"10.2172\/1424888"},{"key":"ref90","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-019-46595-w"},{"key":"ref103","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-020-1942-4"},{"key":"ref102","doi-asserted-by":"publisher","DOI":"10.1109\/ASAP.2019.00-10"},{"key":"ref111","doi-asserted-by":"publisher","DOI":"10.1109\/TNB.2017.2726682"},{"key":"ref112","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-019-13310-2"},{"key":"ref110","author":"ignatova","year":"2008","journal-title":"DNA Computing"},{"key":"ref98","doi-asserted-by":"publisher","DOI":"10.1145\/1899390.1899394"},{"key":"ref99","doi-asserted-by":"publisher","DOI":"10.1109\/TED.2019.2897960"},{"key":"ref96","doi-asserted-by":"publisher","DOI":"10.1504\/IJCAT.2015.071421"},{"key":"ref97","doi-asserted-by":"publisher","DOI":"10.1109\/MM.2019.2892165"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1049\/el:19710039"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1109\/T-C.1975.224172"},{"key":"ref12","article-title":"Convolutional neural networks using logarithmic data representation","volume":"abs 1603 1025","author":"miyashita","year":"2016","journal-title":"CoRR"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1109\/12.2148"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2005.54"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/ARITH.1999.762839"},{"key":"ref118","year":"2019","journal-title":"Ibm will soon launch a 53-qubit quantum computer"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1109\/ARITH.1999.762845"},{"key":"ref82","doi-asserted-by":"publisher","DOI":"10.1147\/rd.176.0525"},{"key":"ref117","doi-asserted-by":"publisher","DOI":"10.1238\/Physica.Topical.076a00165"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1109\/12.863041"},{"key":"ref81","doi-asserted-by":"publisher","DOI":"10.1109\/ISCAS.2018.8351702"},{"key":"ref18","first-page":"337","article-title":"Performance-improved computation of very large word-length LNS addition\/subtraction using signed-digit arithmetic","author":"chen","year":"0","journal-title":"Proc IEEE Int Conf Appl -Specific Syst Archit Process (ASAP)"},{"key":"ref84","doi-asserted-by":"publisher","DOI":"10.1016\/j.mejo.2015.03.016"},{"key":"ref119","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.103.150502"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1109\/12.863040"},{"key":"ref83","author":"hinton","year":"1984","journal-title":"Boltzmann Machines Constraint Satisfaction Networks that Learn"},{"key":"ref114","doi-asserted-by":"publisher","DOI":"10.1109\/TNB.2011.2167757"},{"key":"ref113","doi-asserted-by":"publisher","DOI":"10.1109\/TNB.2016.2574359"},{"key":"ref116","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.76.042319"},{"key":"ref80","doi-asserted-by":"publisher","DOI":"10.1016\/j.micpro.2016.09.015"},{"key":"ref115","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.102.040501"},{"key":"ref120","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2018.2842646"},{"key":"ref89","doi-asserted-by":"publisher","DOI":"10.5120\/ijca2017913500"},{"key":"ref121","article-title":"Applying the residue number system to network inference","author":"abdelhamid","year":"2017"},{"key":"ref122","doi-asserted-by":"publisher","DOI":"10.1109\/ICRC.2018.8638592"},{"key":"ref123","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2019.2951083"},{"key":"ref85","doi-asserted-by":"publisher","DOI":"10.1007\/s11227-019-02788-8"},{"key":"ref86","doi-asserted-by":"publisher","DOI":"10.1007\/s11047-016-9553-6"},{"key":"ref87","doi-asserted-by":"publisher","DOI":"10.12693\/APhysPolA.133.329"},{"key":"ref88","doi-asserted-by":"publisher","DOI":"10.1038\/35005001"}],"container-title":["IEEE Circuits and Systems Magazine"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/7384\/9353729\/09353741.pdf?arnumber=9353741","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,10]],"date-time":"2022-05-10T14:52:02Z","timestamp":1652194322000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/9353741\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"references-count":171,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.1109\/mcas.2020.3027425","relation":{},"ISSN":["1531-636X","1558-0830"],"issn-type":[{"value":"1531-636X","type":"print"},{"value":"1558-0830","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021]]}}}