Algorithm transformations for computational and data broadcast

Abstract

Problems that must be resolved for the constraints imposed by VLSI technology are computational and data broadcast. Algorithms must be transformed into a form that uses data propagation instead of data broadcast. The techniques introduced here are classified as the transformation of iterative algorithms to a recurrence form, the transformation of recurrence form to a single assignment form, the transformation of the recurrences in iterative algorithms and fulfilling the index forms of the algorithms. Systems of affine recurrence equations are analyzed here and computational and data broadcast are defined in context of the definition of data dependence and affine recurrence equations. A method for data broadcast elimination is introduced in [1, 2] and expands the system of affine recurrence equations into new recurrence equations, that define data propagation and eliminates the data dependencies where computational or data broadcast occurs. Some improvements of these techniques are presented to make the applic ion of the broadcast elimination method easier and more straight forward. A system of affine recurrence equations with broadcast property is always obtained by applying these procedures. The method of broadcast elimination successfully transforms this system of affine recurrence equations into a system of uniform recurrence equations which can be used for parallel implementation on VLSI processor arrays.