Using Static Analysis to Derive Imperative Code from ALPHA

In this article, we demonstrate a translation methodology which transforms a high level algorithmic speciication written in the Alpha language to an imperative data parallel language. Alpha is a functional language which was designed to facilitate the kinds of static analyses needed for doing regular array synthesis. We show that the same methods which are used for solving regular array synthesis problems can be applied to the compilation of Alpha as a functional language. We informally introduce the Alpha language with the aid of examples and explain how it is adapted to doing static analysis and transformation. We rst show how an Alpha program can be naively implemented by viewing it as a set of monolithic arrays and their lling functions, implemented using applicative caching. We then show how static analysis can be used to improve the eeciency of this naive implementation by orders of magnitude. We present a compilation method which makes incremental transformations on the abstract syntax tree of an Alpha program in order to make performance improvements and optimize it for a given architecture. The compilation steps described include scheduling, alignment, partitioning, allocation, loop nest generation, and code generation and they are illustrated with a running example. We discuss some of the static analysis issues which come up at each of these steps and brieey describe what static analysis tools are used. L'application de l'analyse statique a la derivation de code d'un programme fonctionnel R esum e : Ce papier pr esente une m ethodologie de transformation d'une sp eciication algorithmique de haut niveau cod ee en Alpha en un langage imp eratif a parall elisme de donn ees. Alpha est un langage fonctionnel d edi e aux types d'analyse statique requis pour la synth ese de r eseaux r eguliers. Nous montrons que les m ethodes de r esolution des probl emes li es a la synth ese de r eseaux r eguliers peuvent ^ etre appliqu ees a la compilation de Alpha en tant que langage fonctionnel. Pour cela, apr es avoir introduit de mani ere informelle le langage Alpha, son adaptation a l'analyse statique et aux transformations de programmes est explicit ee. Ensuite, nous pr esentons une impl ementation na ve d'un programme Alpha sous forme d'un ensemble de tableaux monolithiques dont les fonctions de remplissage font appel a la technique de cache applicative. Gr^ ace a l'analyse statique, l'eecacit e de cette premi …