A Framework for Generating Distributed-Memory Parallel Programs for Block Recursive Algorithms

A framework for synthesizing communication-efficient distributed-memory parallel programs for block recursive algorithms such as the fast Fourier transform (FFT) and Strassen's matrix multiplication is presented. This framework is based on an algebraic representation of the algorithms, which involves the tensor (Kronecker) product and other matrix operations. This representation is useful in analyzing the communication implications of computation partitioning and data distributions. The programs are synthesized under two different target program models. These two models are based on different ways of managing the distribution of data for optimizing communication. The first model uses point-to-point interprocessor communication primitives, whereas the second model uses data redistribution primitives involving collective all-to-many communication. These two program models are shown to be suitable for different ranges of problem size. The methodology is illustrated by synthesizing communication-efficient programs for the FFT. This framework has been incorporated into the EXTENT system for automatic generation of parallel/vector programs for block recursive algorithms.