Yq. Yang et al., MINIMAL DATA DEPENDENCE ABSTRACTIONS FOR LOOP TRANSFORMATIONS - EXTENDED VERSION, International journal of parallel programming, 23(4), 1995, pp. 359-388
Citations number
33
Categorie Soggetti
Computer Sciences","Computer Science Theory & Methods
Many abstractions of program dependences have already been proposed, s
uch as the Dependence Distance, the Dependence Direction Vector, the D
ependence Level or the Dependence Cone. These different abstractions h
ave different precisions. The minimal abstraction associated to a tran
sformation is the abstraction that contains the minimal amount of info
rmation necessary to decide when such a transformation is legal. Minim
al abstractions for loop reordering and unimodular transformations are
presented. As an example, the dependence cone, which approximates dep
endences by a convex cone of the dependence distance vectors, is the m
inimal abstraction for unimodular transformations. It also contains en
ough information for legally applying all loop reordering transformati
ons and finding the same set of valid mono- and multi-dimensional line
ar schedules as the dependence distance set.