On the parallel execution time of tiled loops

作     者：Högstedt, K Carter, L Ferrante, J 

作者机构：AT&T Labs Res Florham Pk NJ 07932 USA Univ Calif San Diego Dept Comp Sci & Engn La Jolla CA 92093 USA 

出 版 物：《IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS》 (IEEE Trans Parallel Distrib Syst)

年 卷 期：2003年第14卷第3期

页      面：307-321页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：US National Science Foundation  (CCR-9504150  CCR-9808946) 

主　　题：tiling blocking compiler optimization parallel compilers 

摘      要：Many computationally-intensive programs, such as those for differential equations, spatial interpolation, and dynamic programming, spend a large portion of their execution time in multiply-nested loops that have a regular stencil of data dependences. Tiling is a well-known compiler optimization that improves performance on such loops, particularly for computers with a multileveled hierarchy of parallelism and memory. Most previous work on tiling is limited in at least one of the following ways: they only handle nested loops of depth two, orthogonal tiling, or rectangular tiles. In our work, we tile loop nests of arbitrary depth using polyhedral tiles. We derive a prediction formula for the execution time of such tiled loops, which can be used by a compiler to automatically determine the tiling parameters that minimizes the execution time. We also explain the notion of rise, a measure of the relationship between the shape of the tiles and the shape of the iteration space generated by the loop nest. The rise is a powerful tool in predicting the execution time of a tiled loop. It allows us to reason about how the tiling affects the length of the longest path of dependent tiles, which is a measure of the execution time of a tiling. We use a model of the tiled iteration space that allows us to determine the length of the longest path of dependent tiles using linear programming. Using the rise, we derive a simple formula for the length of the longest path of dependent tiles in rectilinear iteration spaces, a subclass of the convex iteration spaces, and show how to choose the optimal tile shape.