Code Generation for General Loops Using Methods from Computational Geometry

This paper deals with general nested loops and proposes a novel dynamic scheduling technique. General loops contain complex loop bodies (consisting of arbitrary program statements, such as assignments, conditions and repetitions) that exhibit uniform loop-carried dependencies. Therefore it is now possible to achieve efficient parallelization for a vast class of loops, mostly found in DSP, PDEs, signal and video coding. At the core of this technique lies a simple and efficient dynamic rule (SDS Successive Dynamic Scheduling) for determining the next ready-to-beexecuted iteration at runtime. The central idea is to schedule the iterations on-the-fly by using SDS, along the optimal hyperplane (determined using the QuickHull algorithm). Furthermore, a tool (CRONUS/1) that implements this theory and automatically produces the SPMD parallel code for message passing architectures is presented. As a testing case study, the FSBM motion estimation algorithm (used in video coding standards, e.g., MPEG-2, H.261) was used. The tool was also tested on a suite of randomly generated loops. The experimental results validate the presented theory and corroborate the efficiency of the generated parallel code.