Code generation methods for tiling transformations

Goumas, G; Athanasaki, M; Koziris, N

dc.contributor.author	Goumas, G	en
dc.contributor.author	Athanasaki, M	en
dc.contributor.author	Koziris, N	en
dc.date.accessioned	2014-03-01T01:17:37Z
dc.date.available	2014-03-01T01:17:37Z
dc.date.issued	2002	en
dc.identifier.issn	1016-2364	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/14592
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-0036756475&partnerID=40&md5=dc7e1f78f361359ec9bc89df7d1f1a49	en
dc.relation.uri	http://www.dsclab.ece.ntua.gr/~nkoziris/papers/jise2002.pdf	en
dc.relation.uri	http://www.cslab.ece.ntua.gr/~goumas/downloads/jise2002.pdf	en
dc.relation.uri	http://www.informatik.uni-trier.de/~ley/db/journals/jise/jise18.html#GoumasAK02	en
dc.relation.uri	http://www.iis.sinica.edu.tw/page/jise/2002/200209_02.html	en
dc.relation.uri	http://www.cslab.ntua.gr/~nkoziris/papers/jise2002.pdf	en
dc.subject	Code generation	en
dc.subject	Fourier-Motzkin elimination	en
dc.subject	Loop tiling	en
dc.subject	Non-unimodular transformations	en
dc.subject	Supernodes	en
dc.subject.classification	Computer Science, Information Systems	en
dc.subject.other	Codes (symbols)	en
dc.subject.other	Data storage equipment	en
dc.subject.other	Iterative methods	en
dc.subject.other	Mathematical transformations	en
dc.subject.other	Matrix algebra	en
dc.subject.other	Pipeline processing systems	en
dc.subject.other	Automatic code generation	en
dc.subject.other	Code generation methods	en
dc.subject.other	Fourier-Motzkin eliminations	en
dc.subject.other	Multilevel memory hierarchies	en
dc.subject.other	Supernode transformations	en
dc.subject.other	Tiling transformations	en
dc.subject.other	Parallel processing systems	en
dc.title	Code generation methods for tiling transformations	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	2002	en
heal.abstract	Tiling or supernode transformation has been widely used to improve locality in multi-level memory hierarchies, as well as to efficiently execute loops on parallel architectures. However, automatic code generation for tiled loops can be a very complex compiler work due to non-rectangular tile shapes and arbitrary iteration space bounds. In this paper, we first survey code generation methods for nested loops which are transformed using non-unimodular transformations. All methods are based on Fourier-Motzkin (FM) elimination. Next, we consider and enhance previous work on rewriting tiled loops by considering parallelepiped tiles and arbitrary iteration space shapes. In order to generate tiled code, all methods first enumerate the tiles containing points within the iteration space, and second, sweep the points within each tile. For the first, we extend previous work in order to access all tile origins correctly, while for the latter, we propose the transformation of the initial parallelepiped tile iteration space into a rectangular one, so as to generate code efficiently with the aid of a non-unimodular transformation matrix and its Hermite Normal Form (HNF). The resulting systems of inequalities are much simpler than those in bibliography; thus their solutions are determined more efficiently using the FM elimination. Experimental results which compare all presented approaches, show that the proposed method for generating tiled code is significantly faster, and thus rewriting any n-D tiled loop in a much more efficient and direct way.	en
heal.publisher	INST INFORMATION SCIENCE	en
heal.journalName	Journal of Information Science and Engineering	en
dc.identifier.isi	ISI:000179232200003	en
dc.identifier.volume	18	en
dc.identifier.issue	5	en
dc.identifier.spage	667	en
dc.identifier.epage	691	en