The torus: an exercise in constructing a processing surface

Abstract

A "Processing Surface" is defined as a large, dense, and regular arrangement of processor and storage modules on a two-dimensional surface, e.g. a VLSI chip. A general method is described for distributing parallel recursive computations over such a surface. Scope rules enforcing the "locality" of variables and procedure parameters are introduced in the programming language. These rules and a particular interconnection of the modules on the surface make it possible to transmit parameter and variable values between modules without using extraneous communication actions. The choice of the Processing Surface topology for binary recursive computations is discussed and a torus-like topology is chosen.