{"id":"https://openalex.org/W7135115667","doi":"https://doi.org/10.48550/arxiv.2603.10196","title":"Fully Symbolic Analysis of Loop Locality: Using Imaginary Reuse to Infer Real Performance","display_name":"Fully Symbolic Analysis of Loop Locality: Using Imaginary Reuse to Infer Real Performance","publication_year":2026,"publication_date":"2026-03-10","ids":{"openalex":"https://openalex.org/W7135115667","doi":"https://doi.org/10.48550/arxiv.2603.10196"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.10196","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.10196","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.10196","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5128875134","display_name":"Yifan Zhu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhu, Yifan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026683719","display_name":"Yekai Pan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pan, Yekai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128848975","display_name":"Chen Ding","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ding, Chen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5128814223","display_name":"Yanghui Wu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wu, Yanghui","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9350000023841858,"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"}},"topics":[{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9350000023841858,"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"}},{"id":"https://openalex.org/T10101","display_name":"Cloud Computing and Resource Management","score":0.01140000019222498,"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/T10317","display_name":"Advanced Database Systems and Queries","score":0.010300000198185444,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/locality","display_name":"Locality","score":0.7827000021934509},{"id":"https://openalex.org/keywords/compiler","display_name":"Compiler","score":0.6452999711036682},{"id":"https://openalex.org/keywords/nested-loop-join","display_name":"Nested loop join","score":0.5918999910354614},{"id":"https://openalex.org/keywords/locality-of-reference","display_name":"Locality of reference","score":0.5525000095367432},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.545799970626831},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5095000267028809},{"id":"https://openalex.org/keywords/cache","display_name":"Cache","score":0.4916999936103821},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.45089998841285706},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.4487000107765198}],"concepts":[{"id":"https://openalex.org/C2779808786","wikidata":"https://www.wikidata.org/wiki/Q6664603","display_name":"Locality","level":2,"score":0.7827000021934509},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7767999768257141},{"id":"https://openalex.org/C169590947","wikidata":"https://www.wikidata.org/wiki/Q47506","display_name":"Compiler","level":2,"score":0.6452999711036682},{"id":"https://openalex.org/C1306188","wikidata":"https://www.wikidata.org/wiki/Q4060687","display_name":"Nested loop join","level":2,"score":0.5918999910354614},{"id":"https://openalex.org/C27602214","wikidata":"https://www.wikidata.org/wiki/Q1868547","display_name":"Locality of reference","level":3,"score":0.5525000095367432},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.545799970626831},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5095000267028809},{"id":"https://openalex.org/C115537543","wikidata":"https://www.wikidata.org/wiki/Q165596","display_name":"Cache","level":2,"score":0.4916999936103821},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.4684999883174896},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.45089998841285706},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.4487000107765198},{"id":"https://openalex.org/C65620979","wikidata":"https://www.wikidata.org/wiki/Q7661176","display_name":"Symbolic data analysis","level":2,"score":0.4332999885082245},{"id":"https://openalex.org/C190902152","wikidata":"https://www.wikidata.org/wiki/Q1325106","display_name":"Optimizing compiler","level":3,"score":0.41359999775886536},{"id":"https://openalex.org/C206588197","wikidata":"https://www.wikidata.org/wiki/Q846574","display_name":"Reuse","level":2,"score":0.41040000319480896},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3991999924182892},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.3919000029563904},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3889000117778778},{"id":"https://openalex.org/C184670325","wikidata":"https://www.wikidata.org/wiki/Q512604","display_name":"Loop (graph theory)","level":2,"score":0.3736000061035156},{"id":"https://openalex.org/C79581498","wikidata":"https://www.wikidata.org/wiki/Q1367530","display_name":"Suite","level":2,"score":0.3598000109195709},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.33719998598098755},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.3206000030040741},{"id":"https://openalex.org/C189783530","wikidata":"https://www.wikidata.org/wiki/Q352090","display_name":"CPU cache","level":3,"score":0.2985999882221222},{"id":"https://openalex.org/C106624574","wikidata":"https://www.wikidata.org/wiki/Q5270387","display_name":"Diagrammatic reasoning","level":2,"score":0.2980000078678131},{"id":"https://openalex.org/C82653869","wikidata":"https://www.wikidata.org/wiki/Q6675821","display_name":"Loop fusion","level":3,"score":0.29670000076293945},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.2953000068664551},{"id":"https://openalex.org/C29331672","wikidata":"https://www.wikidata.org/wiki/Q3354468","display_name":"Loop optimization","level":4,"score":0.28200000524520874},{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.27880001068115234},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.25699999928474426}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.10196","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.10196","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.10196","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.10196","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,51,92],"new":[4],"theory":[5,13],"of":[6,54,66],"locality":[7,19,72],"and":[8,17,22,36,39,43,58,86,97],"its":[9],"compiler":[10,24,62],"support.":[11],"The":[12],"is":[14,107],"fully":[15],"symbolic":[16],"derives":[18],"as":[20],"polynomials,":[21],"the":[23,61,71,77,103],"analysis":[25],"supports":[26],"affine":[27],"loop":[28,99],"nests.":[29],"They":[30],"derive":[31,70],"cache-performance":[32],"scaling":[33,47],"in":[34,102],"quadratic":[35],"reciprocal":[37],"expressions":[38],"are":[40],"more":[41],"general":[42],"precise":[44],"than":[45,91],"empirical":[46],"rules.":[48],"Evaluated":[49],"on":[50],"benchmark":[52],"suite":[53],"41":[55,67],"scientific":[56],"kernels":[57],"tensor":[59],"operations,":[60],"requires":[63],"an":[64],"average":[65],"seconds":[68],"to":[69,110],"polynomials.":[73],"After":[74],"derivation,":[75],"predicting":[76],"cache":[78,87],"miss":[79],"count":[80],"for":[81],"any":[82],"given":[83],"input":[84],"size":[85],"configuration":[88],"takes":[89],"less":[90],"millisecond.":[93],"Across":[94],"all":[95],"tests--with":[96],"without":[98],"fusion--the":[100],"accuracy":[101],"data":[104,114],"movement":[105],"prediction":[106],"99.6\\%,":[108],"compared":[109],"simulated":[111],"set-associative":[112],"L1":[113],"cache.":[115]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-03-13T00:00:00"}