{"id":"https://openalex.org/W2160017500","doi":"https://doi.org/10.1109/tc.1973.5009113","title":"On the Precision Attainable with Various Floating-Point Number Systems","display_name":"On the Precision Attainable with Various Floating-Point Number Systems","publication_year":1973,"publication_date":"1973-06-01","ids":{"openalex":"https://openalex.org/W2160017500","doi":"https://doi.org/10.1109/tc.1973.5009113","mag":"2160017500"},"language":"en","primary_location":{"id":"doi:10.1109/tc.1973.5009113","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.1973.5009113","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/A5078366249","display_name":"Richard P. Brent","orcid":"https://orcid.org/0000-0002-8495-7437"},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]},{"id":"https://openalex.org/I4210114115","display_name":"IBM Research - Thomas J. Watson Research Center","ror":"https://ror.org/0265w5591","country_code":"US","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210114115"]}],"countries":["AU","US"],"is_corresponding":true,"raw_author_name":"Richard P. Brent","raw_affiliation_strings":["Computer Centre, Australian National University, Canberra, ACT, Australia","Mathematical Sciences Department, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Centre, Australian National University, Canberra, ACT, Australia","institution_ids":["https://openalex.org/I118347636"]},{"raw_affiliation_string":"Mathematical Sciences Department, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, USA","institution_ids":["https://openalex.org/I4210114115"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5078366249"],"corresponding_institution_ids":["https://openalex.org/I118347636","https://openalex.org/I4210114115"],"apc_list":null,"apc_paid":null,"fwci":2.6612,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.91973071,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"C-22","issue":"6","first_page":"601","last_page":"607"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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":0.9922999739646912,"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/floating-point","display_name":"Floating point","score":0.8309729099273682},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6270149350166321},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.6188036203384399},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5902829170227051},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5619654655456543},{"id":"https://openalex.org/keywords/round-off-error","display_name":"Round-off error","score":0.5577352046966553},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5502885580062866},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.47274458408355713},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.46952787041664124},{"id":"https://openalex.org/keywords/fraction","display_name":"Fraction (chemistry)","score":0.44609925150871277},{"id":"https://openalex.org/keywords/real-number","display_name":"Real number","score":0.44513002038002014},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4293120801448822},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.42571526765823364},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37612462043762207},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.31218937039375305},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0989525318145752}],"concepts":[{"id":"https://openalex.org/C84211073","wikidata":"https://www.wikidata.org/wiki/Q117879","display_name":"Floating point","level":2,"score":0.8309729099273682},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6270149350166321},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.6188036203384399},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5902829170227051},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5619654655456543},{"id":"https://openalex.org/C61005703","wikidata":"https://www.wikidata.org/wiki/Q2145211","display_name":"Round-off error","level":2,"score":0.5577352046966553},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5502885580062866},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.47274458408355713},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46952787041664124},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.44609925150871277},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.44513002038002014},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4293120801448822},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.42571526765823364},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37612462043762207},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31218937039375305},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0989525318145752},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tc.1973.5009113","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.1973.5009113","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W141418607","https://openalex.org/W1496427046","https://openalex.org/W1533113230","https://openalex.org/W1964699416","https://openalex.org/W1966287322","https://openalex.org/W1969568570","https://openalex.org/W1971912261","https://openalex.org/W1974247102","https://openalex.org/W1981359206","https://openalex.org/W2001780669","https://openalex.org/W2013737143","https://openalex.org/W2022765508","https://openalex.org/W2036645931","https://openalex.org/W2037324677","https://openalex.org/W2051150863","https://openalex.org/W2059147138","https://openalex.org/W2070025169","https://openalex.org/W2075584602","https://openalex.org/W2077221255","https://openalex.org/W2084562780","https://openalex.org/W2091336566","https://openalex.org/W2095035380","https://openalex.org/W2096103974","https://openalex.org/W2104466937","https://openalex.org/W2132592167","https://openalex.org/W2157266542","https://openalex.org/W2313752832","https://openalex.org/W2751862591","https://openalex.org/W2752061190","https://openalex.org/W2752853835","https://openalex.org/W4230818032","https://openalex.org/W4301627828"],"related_works":["https://openalex.org/W3039927303","https://openalex.org/W2075472361","https://openalex.org/W2110769336","https://openalex.org/W2383134623","https://openalex.org/W90649232","https://openalex.org/W1989068301","https://openalex.org/W2032140442","https://openalex.org/W2326884861","https://openalex.org/W110295737","https://openalex.org/W2728270059"],"abstract_inverted_index":{"For":[0],"scientific":[1],"computations":[2,97],"on":[3,63,69],"a":[4,16,115,124],"digital":[5],"computer":[6],"the":[7,25,36,41,56,64,70,73,77,110,127,132,148,163,166],"set":[8,18],"of":[9,20,32,51,66,72,94,102,114,165],"real":[10],"numbers":[11,144],"is":[12,62,119,129,140,162],"usually":[13],"approximated":[14],"by":[15],"finite":[17],"F":[19,33],"``floating-point''":[21],"numbers.":[22],"We":[23],"compare":[24,48],"numerical":[26],"accuracy":[27],"possible":[28],"with":[29],"different":[30,49],"choices":[31,50],"having":[34],"approximately":[35],"same":[37,42],"range":[38],"and":[39,82,91,126],"requiring":[40],"word":[43],"length.":[44],"In":[45],"particular,":[46],"we":[47],"base":[52,138,156,160],"(or":[53,158],"radix)":[54],"in":[55],"usual":[57,167],"floating-point":[58,96],"systems.":[59,168],"The":[60],"emphasis":[61],"choice":[65],"F,":[67],"not":[68,120],"details":[71],"number":[74,118],"representation":[75],"or":[76],"arithmetic,":[78],"but":[79],"both":[80],"rounded":[81],"truncated":[83],"arithmetic":[84],"are":[85,89,107,145],"considered.":[86],"Theoretical":[87],"results":[88],"given,":[90],"some":[92],"simulations":[93],"typical":[95],"(forming":[98],"sums,":[99],"solving":[100],"systems":[101],"linear":[103],"equations,":[104],"finding":[105],"eigenvalues)":[106],"described.":[108],"If":[109,142],"leading":[111],"fraction":[112],"bit":[113,150],"normalized":[116],"base-2":[117],"stored":[121,153],"explicitly":[122],"(saving":[123],"bit),":[125],"criterion":[128],"to":[130],"minimize":[131],"mean":[133],"square":[134],"roundoff":[135],"error,":[136],"then":[137,155],"2":[139],"best.":[141],"unnormalized":[143],"allowed,":[146],"so":[147],"first":[149],"must":[151],"be":[152],"explicitly,":[154],"4":[157],"sometimes":[159],"8)":[161],"best":[164]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}