{"id":"https://openalex.org/W2007736689","doi":"https://doi.org/10.1137/0220048","title":"Fast Parallel Arithmetic via Modular Representation","display_name":"Fast Parallel Arithmetic via Modular Representation","publication_year":1991,"publication_date":"1991-08-01","ids":{"openalex":"https://openalex.org/W2007736689","doi":"https://doi.org/10.1137/0220048","mag":"2007736689"},"language":"en","primary_location":{"id":"doi:10.1137/0220048","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0220048","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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/A5090365916","display_name":"George I. Davida","orcid":null},"institutions":[{"id":"https://openalex.org/I43579087","display_name":"University of Wisconsin\u2013Milwaukee","ror":"https://ror.org/031q21x57","country_code":"US","type":"education","lineage":["https://openalex.org/I43579087"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"George I. Davida","raw_affiliation_strings":["Univ. of Wisconsin Milwaukee"],"affiliations":[{"raw_affiliation_string":"Univ. of Wisconsin Milwaukee","institution_ids":["https://openalex.org/I43579087"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082128133","display_name":"Bruce Litow","orcid":null},"institutions":[{"id":"https://openalex.org/I43579087","display_name":"University of Wisconsin\u2013Milwaukee","ror":"https://ror.org/031q21x57","country_code":"US","type":"education","lineage":["https://openalex.org/I43579087"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bruce Litow","raw_affiliation_strings":["Univ. of Wisconsin Milwaukee"],"affiliations":[{"raw_affiliation_string":"Univ. of Wisconsin Milwaukee","institution_ids":["https://openalex.org/I43579087"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5090365916"],"corresponding_institution_ids":["https://openalex.org/I43579087"],"apc_list":null,"apc_paid":null,"fwci":3.6758,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.93084608,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"20","issue":"4","first_page":"756","last_page":"765"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9994999766349792,"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/T10363","display_name":"Low-power high-performance VLSI design","score":0.9994000196456909,"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/T11130","display_name":"Coding theory and cryptography","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/modular-design","display_name":"Modular design","score":0.765544056892395},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.6868422031402588},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6457172632217407},{"id":"https://openalex.org/keywords/modular-arithmetic","display_name":"Modular arithmetic","score":0.6251051425933838},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5367653965950012},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.52796471118927},{"id":"https://openalex.org/keywords/division","display_name":"Division (mathematics)","score":0.4607042372226715},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40207982063293457},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3566116392612457},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32907646894454956},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.32575029134750366}],"concepts":[{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.765544056892395},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6868422031402588},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6457172632217407},{"id":"https://openalex.org/C32049820","wikidata":"https://www.wikidata.org/wiki/Q319400","display_name":"Modular arithmetic","level":3,"score":0.6251051425933838},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5367653965950012},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.52796471118927},{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.4607042372226715},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40207982063293457},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3566116392612457},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32907646894454956},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.32575029134750366},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0220048","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0220048","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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":9,"referenced_works":["https://openalex.org/W1964539827","https://openalex.org/W2003519998","https://openalex.org/W2017205387","https://openalex.org/W2027501230","https://openalex.org/W2088141885","https://openalex.org/W2126466445","https://openalex.org/W2752061190","https://openalex.org/W4206794571","https://openalex.org/W4239679971"],"related_works":["https://openalex.org/W2506252583","https://openalex.org/W2036954759","https://openalex.org/W4238090084","https://openalex.org/W3086669545","https://openalex.org/W2255754718","https://openalex.org/W377643703","https://openalex.org/W590541131","https://openalex.org/W4206809139","https://openalex.org/W4294326371","https://openalex.org/W4246298538"],"abstract_inverted_index":{"An":[0],"almost":[1],"uniform":[2,57],"$NC^1":[3,58],"$":[4,59],"circuit":[5,13,21,60],"family":[6],"for":[7,28,41,65],"integer":[8],"division":[9],"is":[10,15,23,39],"presented.":[11],"The":[12,20],"size":[14,64],"$O(n^6":[16],"/":[17],"\\log":[18],"(n))$.":[19],"design":[22],"based":[24],"on":[25],"modular":[26,51,70],"representation":[27],"integers":[29,68],"below":[30],"$2^n":[31],"$.":[32],"In":[33],"particular,":[34],"a":[35,47,56],"very":[36],"efficient":[37],"technique":[38],"introduced":[40],"computing":[42],"\u201c$a":[43],"<":[44],"b$?\u201d":[45],"when":[46],"and":[48],"b":[49],"in":[50,69],"representation.":[52,71],"This":[53],"leads":[54],"to":[55],"of":[61,67],"$O(n^2":[62],")$":[63],"comparison":[66]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
