{"id":"https://openalex.org/W2057897685","doi":"https://doi.org/10.1145/159737.159749","title":"On the lattice structure of the add-with-carry and subtract-with-borrow random number generators","display_name":"On the lattice structure of the add-with-carry and subtract-with-borrow random number generators","publication_year":1993,"publication_date":"1993-10-01","ids":{"openalex":"https://openalex.org/W2057897685","doi":"https://doi.org/10.1145/159737.159749","mag":"2057897685"},"language":"en","primary_location":{"id":"doi:10.1145/159737.159749","is_oa":false,"landing_page_url":"https://doi.org/10.1145/159737.159749","pdf_url":null,"source":{"id":"https://openalex.org/S38703467","display_name":"ACM Transactions on Modeling and Computer Simulation","issn_l":"1049-3301","issn":["1049-3301","1558-1195"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-b","cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Modeling and Computer Simulation","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/A5066752048","display_name":"Shu Tezuka","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210145865","display_name":"IBM Research - Tokyo","ror":"https://ror.org/04915qk43","country_code":"JP","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210114115","https://openalex.org/I4210145865"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Shu Tezuka","raw_affiliation_strings":["IBM Research Tokyo Research Lab, Tokyo, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM Research Tokyo Research Lab, Tokyo, Japan","institution_ids":["https://openalex.org/I4210145865"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091510633","display_name":"Pierre L\u2019Ecuyer","orcid":"https://orcid.org/0000-0002-3184-0796","observed_orcids":["https://orcid.org/0000-0002-3184-0796"]},"institutions":[{"id":"https://openalex.org/I70931966","display_name":"Universit\u00e9 de Montr\u00e9al","ror":"https://ror.org/0161xgx34","country_code":"CA","type":"education","lineage":["https://openalex.org/I70931966"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Pierre L'Ecuyer","raw_affiliation_strings":["Univ. de Montre\u00b4al, Montreal, P.Q., Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. de Montre\u00b4al, Montreal, P.Q., Canada","institution_ids":["https://openalex.org/I70931966"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013194127","display_name":"Raymond Couture","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I43406934","display_name":"Universit\u00e9 Laval","ror":"https://ror.org/04sjchr03","country_code":"CA","type":"education","lineage":["https://openalex.org/I43406934"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Raymond Couture","raw_affiliation_strings":["Univ. Laval, Ste.-Foy, P.Q., Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. Laval, Ste.-Foy, P.Q., Canada","institution_ids":["https://openalex.org/I43406934"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.6103,"has_fulltext":false,"cited_by_count":52,"citation_normalized_percentile":{"value":0.93922018,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":96},"biblio":{"volume":"3","issue":"4","first_page":"315","last_page":"331"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11195","display_name":"Simulation Techniques and Applications","score":0.0010000000474974513,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T13806","display_name":"Mathematical and Computational Methods","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lattice-structures","display_name":"lattice structures","score":0.7250000238418579},{"id":"https://openalex.org/keywords/linear-congruential-generator","display_name":"linear congruential generator","score":0.9269999861717224},{"id":"https://openalex.org/keywords/spectral-test","display_name":"spectral test","score":0.5789999961853027},{"id":"https://openalex.org/keywords/pseudorandom-number-generators","display_name":"pseudorandom number generators","score":0.7440000176429749},{"id":"https://openalex.org/keywords/long-period","display_name":"long period","score":0.382999986410141}],"concepts":[{"id":"https://openalex.org/C140642157","wikidata":"https://www.wikidata.org/wiki/Q1623338","display_name":"Pseudorandom number generator","level":2,"score":0.8540469408035278},{"id":"https://openalex.org/C201866948","wikidata":"https://www.wikidata.org/wiki/Q228206","display_name":"Random number generation","level":2,"score":0.7662880420684814},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7303811311721802},{"id":"https://openalex.org/C141890704","wikidata":"https://www.wikidata.org/wiki/Q1190228","display_name":"Linear congruential generator","level":3,"score":0.5907377004623413},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5511122941970825},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5177677869796753},{"id":"https://openalex.org/C2776299755","wikidata":"https://www.wikidata.org/wiki/Q432449","display_name":"Carry (investment)","level":2,"score":0.41107994318008423},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2682267129421234},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.10521841049194336},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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:10.1145/159737.159749","is_oa":false,"landing_page_url":"https://doi.org/10.1145/159737.159749","pdf_url":null,"source":{"id":"https://openalex.org/S38703467","display_name":"ACM Transactions on Modeling and Computer Simulation","issn_l":"1049-3301","issn":["1049-3301","1558-1195"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-b","cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Modeling and Computer Simulation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1569612250","https://openalex.org/W1992242854","https://openalex.org/W2007153925","https://openalex.org/W2030269782","https://openalex.org/W2035093001","https://openalex.org/W2035743124","https://openalex.org/W2043419861","https://openalex.org/W2074107405","https://openalex.org/W2114833710","https://openalex.org/W2144056562","https://openalex.org/W2752853835"],"related_works":["https://openalex.org/W2011090873","https://openalex.org/W2101130532","https://openalex.org/W4205806207","https://openalex.org/W2054944103","https://openalex.org/W4237723644","https://openalex.org/W2772380824","https://openalex.org/W2161451071","https://openalex.org/W3112950156","https://openalex.org/W44435986","https://openalex.org/W1988459222"],"abstract_inverted_index":{"Marsaglia":[0],"and":[1,14,91,111],"Zaman":[2],"recently":[3],"proposed":[4],"new":[5],"classes":[6],"of":[7,20,59,72],"random":[8],"number":[9,26],"generators,":[10,86],"called":[11],"add-with-carry":[12],"(AWC)":[13],"subtract-with-borrow":[15],"(SWB),":[16],"which":[17],"are":[18,37],"capable":[19],"quickly":[21],"generating":[22],"very":[23,29,45],"long-period":[24],"(pseudo)-random":[25],"sequences":[27,36,43],"using":[28],"little":[30],"memory.":[31],"We":[32,94],"show":[33,96],"that":[34,120],"these":[35],"essentially":[38],"equivalent":[39],"to":[40,103],"linear":[41,63,84],"congruential":[42,64,85],"with":[44],"large":[46,62],"prime":[47],"moduli.":[48],"So,":[49],"the":[50,69,79,89,98,109,118],"AWC/SWB":[51,121],"generators":[52,74,122],"can":[53,75,100],"be":[54,76,101],"viewed":[55],"as":[56,82],"efficient":[57,105],"ways":[58],"implementing":[60],"such":[61,73],"generators.":[65],"As":[66],"a":[67],"consequence,":[68],"theoretical":[70],"properties":[71],"studied":[77],"in":[78,128],"same":[80],"way":[81],"for":[83,108],"namely,":[87],"via":[88],"spectral":[90],"lattice":[92,126],"tests.":[93],"also":[95],"how":[97],"equivalence":[99],"exploited":[102],"implement":[104],"jumping-ahead":[106],"facilities":[107],"AWC":[110],"SWB":[112],"sequences.":[113],"Our":[114],"numerical":[115],"examples":[116],"illustrate":[117],"fact":[119],"have":[123],"extremely":[124],"bad":[125],"structure":[127],"high":[129],"dimensions.":[130]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-09-26T08:19:03.415552","created_date":"2025-10-10T00:00:00"}
