{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,19]],"date-time":"2025-03-19T14:05:30Z","timestamp":1742393130480},"reference-count":0,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Parallel Process. Lett."],"published-print":{"date-parts":[[1994,9]]},"abstract":"<jats:p> For multi-dimensional (M-D) signal and data processing systems, transformation of algorithmic specifications is a major instrument both in code optimization and code generation for parallelizing compilers and in control flow optimization as a preprocessor for architecture synthesis. State-of-the-art transformation techniques are limited to affine index expressions. This is however not sufficient for many important applications in image, speech and numerical processing. In this paper, a novel transformation method is introduced, oriented to the subclass of algorithm specifications that contains modulo expressions of affine functions to index M-D signals. The method employs extensively the concept of Hermite normal form. The transformation method can be carried out in polynomial time, applying only integer arithmetic. <\/jats:p>","DOI":"10.1142\/s0129626494000260","type":"journal-article","created":{"date-parts":[[2004,11,18]],"date-time":"2004-11-18T21:21:13Z","timestamp":1100812873000},"page":"271-280","source":"Crossref","is-referenced-by-count":6,"title":["TRANSFORMATION OF NESTED LOOPS WITH MODULO INDEXING TO AFFINE RECURRENCES"],"prefix":"10.1142","volume":"04","author":[{"given":"FLORIN","family":"BALASA","sequence":"first","affiliation":[{"name":"IMEC, Kapeldreef 75, B-3001 Leuven, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"FRANK H.M.","family":"FRANSSEN","sequence":"additional","affiliation":[{"name":"IMEC, Kapeldreef 75, B-3001 Leuven, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"FRANCKY V.M.","family":"CATTHOOR","sequence":"additional","affiliation":[{"name":"IMEC, Kapeldreef 75, B-3001 Leuven, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"HUGO J. DE","family":"MAN","sequence":"additional","affiliation":[{"name":"IMEC, Kapeldreef 75, B-3001 Leuven, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"container-title":["Parallel Processing Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129626494000260","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T12:17:47Z","timestamp":1565093867000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129626494000260"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,9]]},"references-count":0,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[1994,9]]}},"alternative-id":["10.1142\/S0129626494000260"],"URL":"https:\/\/doi.org\/10.1142\/s0129626494000260","relation":{},"ISSN":["0129-6264","1793-642X"],"issn-type":[{"value":"0129-6264","type":"print"},{"value":"1793-642X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,9]]}}}