Piecewise Arithmetic Expressions of Numeric Functions and Their Application to Design of Numeric Function Generators

Piecewise arithmetic expressions of numeric functions and their applicatio to design of numeric function generators

A fast segmentation algorithm for piecewise polynomial numeric function generators

We give an efficient algorithm for partitioning the domain of a numeric function f into segments. The function f is realized as a polynomial in each segment, and a lookup table stores the coefficients of the polynomial. Such an algorithm is an essential part of the design of lookup table methods [5,8,9,12,14,15] for realizing numeric functions, such as sin(πx), ln(x), and √ −ln(x). Our algorith...

Numeric Function Generators

We show the architecture and design of a numeric function generator that realizes, at high speed, arithmetic functions, like log x, sin x, 1 x , etc.. This approach is general; different circuits are not needed for different functions. Further, composite functions, like log (sin ( 1 x )) can be realized as easily as individual functions. A tutorial description of the method is presented, follow...

Numeric Function Generators Using Decision Diagrams for Discrete Functions

This paper introduces design methods for numeric function generators (NFGs) using decision diagrams. NFGs are hardware accelerators to compute values of numeric functions such as trigonometric, logarithmic, square root, and reciprocal functions. Most existing design methods for NFGs are intended only for a specific class of numeric functions. However, by using decision diagrams for discrete fun...

A Systematic Design Method for Two-Variable Numeric Function Generators Using Multiple-Valued Decision Diagrams

This paper proposes a high-speed architecture to realize two-variable numeric functions. It represents the given function as an edgevalued multiple-valued decision diagram (EVMDD), and shows a systematic design method based on the EVMDD. To achieve a design, we characterize a numeric function f by the values of l and p for which f is an l-restricted Mp-monotone increasing function. Here, l is a...