In fixed-point arithmetic, polynomials are implemented over specific bit-vector sizes. A bit-vector of size m represents integer values from 0 to 2m--1 (or integers reduced modulo 2m). This implies that finite word-length (m) bit-vector arithmetic manifests itself as algebra over finite integer rings of residue classes Z2m . Contemporary algebra-based synthesis techniques model polynomial computations over unique factorization domains (UFDs) such as fields, Euclidean and integral domains. However, the finite ring Z2m , which is a nonunique factorization domain (nonUFD), does not fall in this category, rendering contemporary approaches inapplicable.4.1 Problem Modeling and General Approach Due to a large number of ADD, mult operations in these designs, designers often employ ingenious ... In many cases, the design choice is that of a single, uniform system word-length for the computations . ... Such arithmetic with composite moduli can be modeled as polynomial functions over / : Z2Ali x Z2TM2 x ac ac ac x Z2Ald a ar Z2m. Here, (ni, n2, ac ac ac n^)anbsp;...
|Title||:||High-level Synthesis of Polynomial Datapaths Using Finite Integer Algebras|
|Publisher||:||ProQuest - 2008|