Polynomial methods for allocating complex components

Methods for performing component matching by expressing an arithmetic specification and a bit-level description of an implementation as word-level polynomials have been demonstrated for combinational circuits. This representation allows the functionality of a specification and existing implementation to be compared. We present extensions to this basic method that allow polynomial models to be constructed for circuits that employ sequential elements as well as feedback. Furthermore, we derive a means of approximating the functionality of nonpolynomial functions and determining a bound on the error of this approximation. These methods are used to synthesize an infinite impulse response filter from a library of potential implementations.