Parallelizing Imperative Functional Programs: the Vectorization Monad

Abstract

Traditionally a vectorizing compiler matches the iterative constructs of a program against a set of predefined templates. If a loop contains no dependency cycles then a map template can be used; other simple dependencies can often be expressed in terms of fold or scan templates. This paper addresses the template matching problem within the context of functional programming. A small collection of program identities are used to specify vectorizable for-loops. By incorporating these program identities within a monad, all well-typed for-loops in which the body of the loop is expressed using the vectorization monad can be vectorized. This technique enables the elimination of template matching from a vectorizing compiler, and the proof of the safety of vectorization can be performed by a type inference mechanism.