{"id":"https://openalex.org/W2003885518","doi":"https://doi.org/10.1142/s0129626494000260","title":"TRANSFORMATION OF NESTED LOOPS WITH MODULO INDEXING TO AFFINE RECURRENCES","display_name":"TRANSFORMATION OF NESTED LOOPS WITH MODULO INDEXING TO AFFINE RECURRENCES","publication_year":1994,"publication_date":"1994-09-01","ids":{"openalex":"https://openalex.org/W2003885518","doi":"https://doi.org/10.1142/s0129626494000260","mag":"2003885518"},"language":"en","primary_location":{"id":"doi:10.1142/s0129626494000260","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129626494000260","pdf_url":null,"source":{"id":"https://openalex.org/S18360026","display_name":"Parallel Processing Letters","issn_l":"0129-6264","issn":["0129-6264","1793-642X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Parallel Processing Letters","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/A5026837255","display_name":"Florin Balasa","orcid":null},"institutions":[{"id":"https://openalex.org/I4210114974","display_name":"IMEC","ror":"https://ror.org/02kcbn207","country_code":"BE","type":"nonprofit","lineage":["https://openalex.org/I4210114974"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"FLORIN BALASA","raw_affiliation_strings":["IMEC, Kapeldreef 75, B-3001 Leuven, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMEC, Kapeldreef 75, B-3001 Leuven, Belgium","institution_ids":["https://openalex.org/I4210114974"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082700569","display_name":"F. Franssen","orcid":null},"institutions":[{"id":"https://openalex.org/I4210114974","display_name":"IMEC","ror":"https://ror.org/02kcbn207","country_code":"BE","type":"nonprofit","lineage":["https://openalex.org/I4210114974"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"FRANK H.M. FRANSSEN","raw_affiliation_strings":["IMEC, Kapeldreef 75, B-3001 Leuven, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMEC, Kapeldreef 75, B-3001 Leuven, Belgium","institution_ids":["https://openalex.org/I4210114974"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033235745","display_name":"Francky Catthoor","orcid":"https://orcid.org/0000-0002-3599-8515"},"institutions":[{"id":"https://openalex.org/I4210114974","display_name":"IMEC","ror":"https://ror.org/02kcbn207","country_code":"BE","type":"nonprofit","lineage":["https://openalex.org/I4210114974"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"FRANCKY V.M. CATTHOOR","raw_affiliation_strings":["IMEC, Kapeldreef 75, B-3001 Leuven, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMEC, Kapeldreef 75, B-3001 Leuven, Belgium","institution_ids":["https://openalex.org/I4210114974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005662218","display_name":"H.J. De Man","orcid":null},"institutions":[{"id":"https://openalex.org/I4210114974","display_name":"IMEC","ror":"https://ror.org/02kcbn207","country_code":"BE","type":"nonprofit","lineage":["https://openalex.org/I4210114974"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"HUGO J. DE MAN","raw_affiliation_strings":["IMEC, Kapeldreef 75, B-3001 Leuven, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMEC, Kapeldreef 75, B-3001 Leuven, Belgium","institution_ids":["https://openalex.org/I4210114974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3935,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.80448023,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"04","issue":"03","first_page":"271","last_page":"280"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9983000159263611,"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":0.9983000159263611,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9972000122070312,"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"}},{"id":"https://openalex.org/T10904","display_name":"Embedded Systems Design Techniques","score":0.9891999959945679,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/affine-transformation","display_name":"Affine transformation","score":0.7342624664306641},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.684404730796814},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.683127224445343},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6634854078292847},{"id":"https://openalex.org/keywords/nested-loop-join","display_name":"Nested loop join","score":0.5993127226829529},{"id":"https://openalex.org/keywords/preprocessor","display_name":"Preprocessor","score":0.5127740502357483},{"id":"https://openalex.org/keywords/code-generation","display_name":"Code generation","score":0.4836253225803375},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4808705449104309},{"id":"https://openalex.org/keywords/compiler","display_name":"Compiler","score":0.47521549463272095},{"id":"https://openalex.org/keywords/register-allocation","display_name":"Register allocation","score":0.46629685163497925},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.4425026476383209},{"id":"https://openalex.org/keywords/search-engine-indexing","display_name":"Search engine indexing","score":0.4190193712711334},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.3118512034416199},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3030749559402466},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.18531516194343567},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.11542123556137085},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09682324528694153}],"concepts":[{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.7342624664306641},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.684404730796814},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.683127224445343},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6634854078292847},{"id":"https://openalex.org/C1306188","wikidata":"https://www.wikidata.org/wiki/Q4060687","display_name":"Nested loop join","level":2,"score":0.5993127226829529},{"id":"https://openalex.org/C34736171","wikidata":"https://www.wikidata.org/wiki/Q918333","display_name":"Preprocessor","level":2,"score":0.5127740502357483},{"id":"https://openalex.org/C133162039","wikidata":"https://www.wikidata.org/wiki/Q1061077","display_name":"Code generation","level":3,"score":0.4836253225803375},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4808705449104309},{"id":"https://openalex.org/C169590947","wikidata":"https://www.wikidata.org/wiki/Q47506","display_name":"Compiler","level":2,"score":0.47521549463272095},{"id":"https://openalex.org/C128916667","wikidata":"https://www.wikidata.org/wiki/Q1343660","display_name":"Register allocation","level":3,"score":0.46629685163497925},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.4425026476383209},{"id":"https://openalex.org/C75165309","wikidata":"https://www.wikidata.org/wiki/Q2258979","display_name":"Search engine indexing","level":2,"score":0.4190193712711334},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.3118512034416199},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3030749559402466},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.18531516194343567},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.11542123556137085},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09682324528694153},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0129626494000260","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129626494000260","pdf_url":null,"source":{"id":"https://openalex.org/S18360026","display_name":"Parallel Processing Letters","issn_l":"0129-6264","issn":["0129-6264","1793-642X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Parallel Processing Letters","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.55.740","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.55.740","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.imec.be/pub/vsdm/reports/memory_optimisation/loop_modulo_trafo.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2140712297","https://openalex.org/W2373710463","https://openalex.org/W2251007391","https://openalex.org/W2059179631","https://openalex.org/W4310506209","https://openalex.org/W2369241479","https://openalex.org/W61798728","https://openalex.org/W2047109966","https://openalex.org/W2107896839","https://openalex.org/W4246262935"],"abstract_inverted_index":{"For":[0],"multi-dimensional":[1],"(M-D)":[2],"signal":[3],"and":[4,20,26,58],"data":[5],"processing":[6],"systems,":[7],"transformation":[8,38,66,99],"of":[9,74,81,94],"algorithmic":[10],"specifications":[11,76],"is":[12,47,68],"a":[13,32,64],"major":[14],"instrument":[15],"both":[16],"in":[17,27,55,105],"code":[18,21],"optimization":[19,30],"generation":[22],"for":[23,34,51],"parallelizing":[24],"compilers":[25],"control":[28],"flow":[29],"as":[31],"preprocessor":[33],"architecture":[35],"synthesis.":[36],"State-of-the-art":[37],"techniques":[39],"are":[40],"limited":[41],"to":[42,71,84],"affine":[43,82],"index":[44,85],"expressions.":[45],"This":[46],"however":[48],"not":[49],"sufficient":[50],"many":[52],"important":[53],"applications":[54],"image,":[56],"speech":[57],"numerical":[59],"processing.":[60],"In":[61],"this":[62],"paper,":[63],"novel":[65],"method":[67,89,100],"introduced,":[69],"oriented":[70],"the":[72,92],"subclass":[73],"algorithm":[75],"that":[77],"contains":[78],"modulo":[79],"expressions":[80],"functions":[83],"M-D":[86],"signals.":[87],"The":[88,98],"employs":[90],"extensively":[91],"concept":[93],"Hermite":[95],"normal":[96],"form.":[97],"can":[101],"be":[102],"carried":[103],"out":[104],"polynomial":[106],"time,":[107],"applying":[108],"only":[109],"integer":[110],"arithmetic.":[111]},"counts_by_year":[{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}