Algebraic Recurrence Transformations For Massive Parallelism

Abstract

Recursions generally present a bottleneck for the mapping of algorithms onto massively parallel architectures. A great deal of work has been done showing how to break this bottleneck using look-ahead computation. By applying results of P. Kogge and H. Stone (IEEE Trans. Comput., vol. C-22, pp. 786-793, 1973) it was shown that few basic algebraic axioms are sufficient for speeding up recursions by look-ahead techniques. This allows one to generalize architectures derived for special cases. Furthermore, it was shown that the look-ahead computation technique, known to date only for recursions with up to two operations, can be generalized to recursions with n operations. This allows the design of massively parallel architectures for more complex recursions. General algebraic examinations of expressions as described here can be applied to feedforward expressions, as well. >