Title :
Optimization of Imprecise Circuits Represented by Taylor Series and Real-Valued Polynomials
Author :
Pang, Yu ; Radecka, Kartazyna ; Zilic, Zeljko
Author_Institution :
Dept. of Electr. & Comput. Eng., McGill Univ., Montreal, QC, Canada
Abstract :
Arithmetic circuits in general do not match specifications exactly, leading to different implementations within allowed imprecision. We present a technique to search for the least expensive fixed-point implementations for a given error bound. The method is practical in real applications and overcomes traditional precision analysis pessimism, as it allows simultaneous selection of multiple word lengths and even some function approximation, primarily based on Taylor series. Starting from real-valued representation, such as Taylor series, we rely on arithmetic transform to explore maximum imprecision by a branch-and-bound search algorithm to investigate imprecision. We also adopt a new tight-bound interval scheme, and derive a precision optimization algorithm that explores multiple precision parameters to get an implementation with smallest area cost.
Keywords :
fixed point arithmetic; polynomials; series (mathematics); tree searching; Taylor series; arithmetic circuits; arithmetic transform; branch-and-bound search; error bound; fixed-point implementation; imprecise circuits; precision analysis; precision optimization; real-valued polynomials; tight-bound interval scheme; Boolean functions; Circuits; Computer errors; Cost function; Data structures; Fixed-point arithmetic; Function approximation; Polynomials; Process design; Taylor series; Arithmetic imprecision; Taylor series; arithmetic transform; fixed-point arithmetic; optimization; polynomials;
Journal_Title :
Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on
DOI :
10.1109/TCAD.2010.2049154