Optimal Tiling
نویسندگان
چکیده
Iteration space tiling is a common strategy used by parallelizing compilers to reduce communication overhead. We address the problem of determining the optimal tile size (which minimizes the total execution time of the program), for a particular program schema. We use a realistic model of the architecture which accounts for coprocessors that permit overlapping of communication and computation, context switching times, etc. Determining the optimal tile size is shown to reduce to a non-linear optimization problem. We solve this analytically, yielding a closed form solution that involves only parameters of the architecture and program that are easily determined at compile time. It can thus be used by a compiler before code generation. Although we solve the problem for a particular schema of programs, our results can be generalized to uniform dependence loops and also to certain classes of loop programs with dynamic dependence vectors. Pavage Optimal R esum e : Le partitionnement en tuiles de l'espace d'it erations est une strat egie souvent utilis ee par les compilateurs parall eliseurs pour r eduire le co^ ut des communications. Nous consid erons la d etermination de la taille optimale de la tuile dans un cas particulier. Nous utilisons un mod ele r ealiste d'architecture qui prend en compte les coprocesseurs de communication, le recouvrement calculs/communications etc. La d etermination de la taille optimale de la tuile se ram ene alors a un probl eme d'optimisation non-lin eaire ayant comme fonction objectif le temps total d'ex ecution du programme. Pour ce probl eme nous obtenons une solution analytique qui n'implique que des param etres de l'architecture et du programme facilement d etermin es a la compilation. Ceci permet l'utilisation de cette solution analytique avant la g en eration du code. Bien que nous consid erons un sch ema particulier de programme, nos r esultats peuvent ^ etre facilement g en eralis es au cas des boucles de d ependances uniformes et pour une classe de boucles ayant des vecteurs de d ependences dynamiques.
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تاریخ انتشار 1994