The Static Parallelization of Loops and Recursions

We demonstrate approaches to the static parallelization of loops and recursions on the example of the polynomial product. Phrased as a loop nest, the polynomial product can be parallelized automatically by applying a space-time mapping technique based on linear algebra and linear programming. One can choose a parallel program that is optimal with respect to some objective function like the number of execution steps, processors, channels, etc. However,at best,linear execution time complexity can be atained. Through phrasing the polynomial product as a divide-and-conquer recursion, one can obtain a parallel program with sublinear execution time. In this case, the target program is not derived by an automatic search but given as a program skeleton, which can be deduced by a sequence of equational program transformations. We discuss the use of such skeletons, compare and assess the models in which loops and divide-and-conquer resursions are parallelized and comment on the performance properties of the resulting parallel implementations.