A Unified Framework for Systematic Loop Transformations

Abstract

and statement reordering. This framework also includes more general classes of loop transforma-This paper presents a formal mathematical tions which can extract more parallelism from a framework which unifies the existing loop trans-class of programs than the existing techniques. formations. This framework also includes more The particular class of programs are those that general classes of loop transformations, which consist of perfectly nested loops possibly with can extract more parallelism from a class of pro-conditional statements where the guards as well grams than the existing techniques. We classify as the array index expression are affine expresschedules into three classes: uniform, subdomain-sions of the loop indices. variant, and statement-variant. Viewing from In the next section, we describe the notations the degree of parallelism to be gained by loop and terminologies used in the paper. We then transformation, the schedules can also be classi-present a formal mathematical framework which fled as single-sequential level, multiple-sequential unifies the existing loop transformation techlevel, and mixed schedules. We also illustrate the niques, and sets the stage for discussing the more usefulness of the more general loop transforma-general classes of loop transformers in Section 3. tion with an example program. A loop transformer is a function that relates a given loop nest with its transformed version, and 1 the mehd7,1011,1,5, eral classes of schedules. The problem formula-0 in Proceedings of the Third ACM SIGPLAN Sympo-tions for obtaining these schedules are based on-oles sium on PPOPP, April 1991.

Optimizing the linear fascicle evaluation algorithm for many-core systems

“…Code optimization and transformation frameworks have been studied well in the literature for improving data locality and parallelism for regular or a ne array references (Carr et al 1994;Cierniak and Li 1995;Feautrier 1992;Kandemir et al 1998;Kelly and Pugh 1995;Kodukula and Pingali 1996;Li and Pingali 1994;Lu 1991;Pugh 1991;Sarkar and ekkath 1992;ies et al 2001;Wolf et al 1996). Among many frameworks, the polyhedral framework is popular for optimization of a ne loop nests (Bondhugula et al 2008;Cohen et al 2005;Feautrier 1991;Verdoolaege 2010).…”