Functional–Based Synthesis of a Systolic Array for GCD Computation

Abstract

We synthesise a systolic pass-through array for the computation of the greatest common divisor (GCD) of multiple precision integers. The synthesis method uses the conceptual similarity between the inductive structure of a systolic array (a head processor followed by an identical tail array) and the inductive decomposition of the argument by a functional program. By formal analysis, we identify the structure of the functions which can be realized by pass-through arrays. Then, by equational rewriting, we transform the expression of the list function which must be realized into an expression having the required structure. The resulting expression reveals the scalar function which must be implemented by each individual processor.