Parallel destructive updating in strict functional languages

Abstract

In our recent paper, we gave an efficient interprocedural update analysis algorithm for strict functional languages with flat arrays and sequential evaluation. In this paper, we show that the same algorithm extends to a parallel functional language with additional constructs for partitioning and combining arrays. Even with parallel evaluation, the complexity of the analysis remains polynomial. The analysis has been implemented and the results show that several numerical algorithms such as direct and iterative methods for solving linear equations, LU, Cholesky, and QR factorizations, multigrid methods for solving partial differential equations, and non-numeric algorithms such as sorting can be implemented functionally with all updates made destructive. We describe a new array construct to specify a collection of updates on an array and show that problems like histogram, inverse permutation, and polynomial multiplication have efficient parallel functional solutions. Monolithic array operators can be considered as a special case of this new construct.