{"id":"https://openalex.org/W2012015111","doi":"https://doi.org/10.1109/asap.2013.6567564","title":"The Denormal Logarithmic Number System","display_name":"The Denormal Logarithmic Number System","publication_year":2013,"publication_date":"2013-06-01","ids":{"openalex":"https://openalex.org/W2012015111","doi":"https://doi.org/10.1109/asap.2013.6567564","mag":"2012015111"},"language":"en","primary_location":{"id":"doi:10.1109/asap.2013.6567564","is_oa":false,"landing_page_url":"https://doi.org/10.1109/asap.2013.6567564","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 IEEE 24th International Conference on Application-Specific Systems, Architectures and Processors","raw_type":"proceedings-article"},"type":"preprint","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/A5016062910","display_name":"Mark G. Arnold","orcid":"https://orcid.org/0000-0001-5175-2374"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mark G. Arnold","raw_affiliation_strings":["XLNS Research, PO Box 605 Laramie WY 82070 USA"],"affiliations":[{"raw_affiliation_string":"XLNS Research, PO Box 605 Laramie WY 82070 USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040945336","display_name":"Caroline Collange","orcid":null},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Caroline Collange","raw_affiliation_strings":["INRIA, Centre de recherche Rennes - Bretagne Atlantique, Rennes, France"],"affiliations":[{"raw_affiliation_string":"INRIA, Centre de recherche Rennes - Bretagne Atlantique, Rennes, France","institution_ids":["https://openalex.org/I1326498283"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5016062910"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.65678055,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.73173811,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"8","issue":null,"first_page":"117","last_page":"124"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9969000220298767,"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":0.9968000054359436,"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/arithmetic-underflow","display_name":"Arithmetic underflow","score":0.9934309720993042},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6628768444061279},{"id":"https://openalex.org/keywords/floating-point","display_name":"Floating point","score":0.6079700589179993},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.5284711718559265},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5117125511169434},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5030319094657898},{"id":"https://openalex.org/keywords/computer-hardware","display_name":"Computer hardware","score":0.502582311630249},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.45025765895843506},{"id":"https://openalex.org/keywords/fixed-point-arithmetic","display_name":"Fixed-point arithmetic","score":0.4471144378185272},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.4385733902454376},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4107380509376526},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.3665560781955719},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2276022732257843},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.13273879885673523}],"concepts":[{"id":"https://openalex.org/C3265923","wikidata":"https://www.wikidata.org/wiki/Q669129","display_name":"Arithmetic underflow","level":2,"score":0.9934309720993042},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6628768444061279},{"id":"https://openalex.org/C84211073","wikidata":"https://www.wikidata.org/wiki/Q117879","display_name":"Floating point","level":2,"score":0.6079700589179993},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.5284711718559265},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5117125511169434},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5030319094657898},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.502582311630249},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.45025765895843506},{"id":"https://openalex.org/C163973906","wikidata":"https://www.wikidata.org/wiki/Q649900","display_name":"Fixed-point arithmetic","level":3,"score":0.4471144378185272},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.4385733902454376},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4107380509376526},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.3665560781955719},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2276022732257843},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.13273879885673523},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/asap.2013.6567564","is_oa":false,"landing_page_url":"https://doi.org/10.1109/asap.2013.6567564","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 IEEE 24th International Conference on Application-Specific Systems, Architectures and Processors","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W119852392","https://openalex.org/W1510182197","https://openalex.org/W1998747003","https://openalex.org/W2032892910","https://openalex.org/W2045146697","https://openalex.org/W2072651214","https://openalex.org/W2094274063","https://openalex.org/W2101173251","https://openalex.org/W2107166538","https://openalex.org/W2107624728","https://openalex.org/W2108659637","https://openalex.org/W2112324995","https://openalex.org/W2125440714","https://openalex.org/W2127097384","https://openalex.org/W2138705371","https://openalex.org/W2143812865","https://openalex.org/W2146084561","https://openalex.org/W2147698585","https://openalex.org/W2151511325","https://openalex.org/W2161427592","https://openalex.org/W2162084083","https://openalex.org/W2166215763","https://openalex.org/W2166343987","https://openalex.org/W4246318765","https://openalex.org/W4285719527","https://openalex.org/W6604914175"],"related_works":["https://openalex.org/W1553523118","https://openalex.org/W2182501133","https://openalex.org/W2163593765","https://openalex.org/W2288224894","https://openalex.org/W2738437680","https://openalex.org/W2762011242","https://openalex.org/W2513406307","https://openalex.org/W2186262220","https://openalex.org/W1436021108","https://openalex.org/W2076717173"],"abstract_inverted_index":{"Economical":[0],"hardware":[1],"often":[2,150],"uses":[3,97],"a":[4,110,121,190,202,274],"FiXed-point":[5],"Number":[6,66],"System":[7,67],"(FXNS),":[8],"whose":[9],"constant":[10],"absolute":[11],"precision":[12,22,73],"is":[13,46,120],"acceptable":[14],"for":[15,33,51,87,132,152,273],"many":[16],"signal-processing":[17],"algorithms.":[18],"The":[19,62,130,170],"almost-constant":[20],"relative":[21],"of":[23,44,82,123,126,197,217,246,278],"the":[24,42,52,115,124,136,148,155,175,215,237,241,258],"more":[25,230],"expensive":[26],"Floating-Point":[27],"(FP)":[28],"number":[29,112],"system":[30],"simplifies":[31],"design,":[32],"example,":[34],"by":[35,221],"eliminating":[36],"worries":[37],"about":[38],"FXNS":[39,50,127],"overflow":[40],"because":[41],"range":[43,71,176,186],"FP":[45,57,75,104],"much":[47,77],"larger":[48],"than":[49,231],"same":[53],"wordsize;":[54],"however,":[55],"primitive":[56],"introduces":[58],"another":[59],"problem:":[60],"underflow.":[61],"conventional":[63,264],"Signed":[64],"Logarithmic":[65],"(SLNS)":[68],"offers":[69],"similar":[70,102],"and":[72,85,91,128,147,250,270],"as":[74,266,268],"with":[76,100,235,253],"better":[78],"performance":[79],"(in":[80],"terms":[81],"power,":[83],"speed":[84],"area)":[86],"multiplication,":[88],"division,":[89],"powers":[90],"roots.":[92],"Moderate-precision":[93],"addition":[94,249],"in":[95,140,177],"SLNS":[96,234,248,265],"table":[98],"lookup":[99],"properties":[101,125],"to":[103,162,211,228,261],"(including":[105],"underflow).":[106],"This":[107],"paper":[108],"proposes":[109],"new":[111],"system,":[113],"called":[114],"Denormal":[116],"LNS":[117],"(DLNS),":[118],"which":[119,178],"hybrid":[122],"SLNS.":[129,195],"inspiration":[131],"DLNS":[133,157,223,269],"comes":[134],"from":[135],"denormal":[137],"numbers":[138],"found":[139],"IEEE-754":[141],"(that":[142],"provide":[143],"better,":[144],"gradual":[145,179,184,204],"underflow)":[146],"\u03bc-law":[149],"used":[151],"speech":[153],"encoding;":[154],"novel":[156,242,259],"circuit":[158,243],"here":[159],"allows":[160,173],"arithmetic":[161],"be":[163],"performed":[164],"directly":[165],"on":[166,263],"such":[167],"encoded":[168],"data.":[169],"proposed":[171],"approach":[172],"customizing":[174],"underflow":[180,185,205],"occurs.":[181],"A":[182],"wide":[183],"acts":[187,193],"like":[188,194],"FXNS;":[189],"narrow":[191],"one":[192],"Simulation":[196],"an":[198,232],"FFT":[199],"application":[200,219],"illustrates":[201],"moderate":[203],"decreasing":[206],"bit-switching":[207],"activity":[208,226],"15%":[209],"compared":[210],"underflow-free":[212],"SLNS,":[213],"at":[214],"cost":[216],"increasing":[218],"error":[220],"30%.":[222],"reduces":[224],"switching":[225],"5%":[227],"20%":[229],"abruptly-underflowing":[233],"one-half":[236],"error.":[238],"Synthesis":[239],"shows":[240],"primarily":[244],"consists":[245],"traditional":[247],"subtraction":[251],"tables,":[252],"additional":[254],"datapaths":[255],"that":[256],"allow":[257],"ALU":[260],"act":[262],"well":[267],"mixed":[271],"data,":[272],"worst-case":[275],"area":[276],"overhead":[277],"26%.":[279]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}