A language - oriented approach to the design ofsystolic chips

The Alpha language results from research on automatic synthesis of systolic algorithms. It is based on the recurrence equation formalism introduced by Karp, Miller and Winograd in 1967. The basic objects of Alpha are variables indexed on integral points of a convex set. It is a functional/equational language, whose deenition is particularly well-suited to expressing regular algorithms, as well as transformations of these algorithms from their initial mathematical speciication to an implementation on a synchronous parallel architecture. In particular, Alpha makes it easy to deene, prove and implement basic transformations such as Leiserson and Saxe's retiming, space-time reindexing, localization, and partitioning. We describe Alpha, its use for expressing and derivating systolic arrays, and the development environment Alpha du Centaur for this language.