Numeric Function Generators Using Piecewise Arithmetic Expressions

Abstract

Abstract-This paper proposes new architectures for numeric function generators (NFGs) using piecewise arithmetic expressions. The proposed architectures are programmable, and they realize a wide range of numeric functions. To design an NFG for a given function, we partition the domain of the function into uniform segments, and transform a subfunction in each segment into an arithmetic spectrum. From this arithmetic spectrum, we derive an arithmetic expression, and realize the arithmetic expression with hardware. Since the arithmetic spectrum has many zero coefficients and repeated coefficients, by storing only distinct nonzero coefficients in a