Algorithms for parallel addition and parallel polynomial evaluation

Abstract

This paper presents two related algorithms for implementing parallel n-bit binary addition and evaluating n-th degree polynomials, respectively. The approach taken makes use of an iterative construction, the computation tree. The algorithms are particularly effective for moderate values of n and are in accord with well-known asymptotic bounds. In the case of n-bit addition, the implementations constitute look-ahead tree circuits of r-input standard logic elements. Extensions to modular tree structures for lookahead adders are also considered. In the case of parallel polynomial evaluation, the operations of ordinary addition and multiplication are assumed with the capability to employ r arguments simultaneously.