Maximally and arbitrarily fast implementation of linear and feedback linear computations

Abstract

By establishing a relationship between the basic properties of linear computations and eight optimizing transformations (distributivity, associativity, commutativity, inverse and zero element law, common subexpression replication and elimination, constant propagation), a computer-aided design platform is developed to optimally speed-up an arbitrary instance from this large class of computations with respect to those transformations. Furthermore, arbitrarily fast implementation of an arbitrary linear computation is obtained by adding loop unrolling to the transformations set. During this process, a novel Horner pipelining scheme is used so that the area-time (AT) product is maintained constant, regardless of achieved speed-up. We also present a generalization of the new approach so that an important subclass of nonlinear computations, named feedback linear computations, is efficiently, maximally, and arbitrarily sped-up.