Translation of serial recursive codes to parallel SIMD codes

Parallelizing compilers are an important way for making parallel systems easy to use and more acceptable to the mainstream of computing. Several approaches to parallelization have been taken, such as loop parallelization and dependence-graph based parallelization. This paper will undertake another approach: the exploitation of recursion in serial recursive coders to translate the latter to parallel nonrecursive SIMD codes. The principal idea is to perform first a formal data-dependence data-flow analysis on both the input partitioning process and the subsolution-merge process to determine the computation and communication of each partition and each merge, then develop a system of equations whereby we derive the sequences of computation instructions and communication instructions along with their processors-enabling/disabling masks for the SIMD target code. We develop the approach, give a code translation algorithm, and apply it to a sample of common recursive algorithms to illustrate its power. The approach is very effective and efficient, especially for recursive algorithms that are balanced and whose input can be padded to an appropriate size without affecting the desired output. For some recursive algorithms that do not fit this category, it will be argued that a top-down MIMD execution of these algorithms is preferable to SIMD execution. Finally, we note that our approach is generalizable to interleaved recursion.