Chain-based Scheduling: Part I { Loop Transformations and Code Generation Chain-based Scheduling: Part I { Loop Transformations and Code Generation

Chain-based scheduling 1] is an eecient partitioning and scheduling scheme for nested loops on distributed-memory multicomputers. The idea is to take advantage of the regular data dependence structure of a nested loop to overlap and pipeline the communication and computation. Most partitioning and scheduling algorithms proposed for nested loops on multicomputers 1,2,3] are graph algorithms on the iteration space of the nested loop. The graph algorithms for partitioning and scheduling are too expensive (at least O(N), where N is the total number of iterations) to be implemented in parallelizing compilers. Graph algorithms also need large data structures to store the result of the partitioning and scheduling. In this paper, we propose compiler loop transformations and the code generation to generate chain-based parallel codes for nested loops on multi-computers. The cost of the loop transformations is O(nd), where n is the number of nesting loops and d is the number of data dependences. Both n and d are very small in real programs. The loop transformations and code generation for chain-based partitioning and scheduling enable paralleliz-ing compilers to generate parallel codes which contain all partitioning and scheduling information that the parallel processors need at run time.