Optimizing Iterative-based Dividers for an Efficient Natural Logarithm Operator Design

Abstract

This work proposes to optimize iterative-based dividers for a natural logarithm operator design. The logarithm operator approximates the function at the base e. Such an operator is implemented using Taylor Series approximation. In this approximation, the division is a costly operation. In this work, we explore two iterative-based divider circuits for logarithm operator. We also offer an algorithm responsible for allowing input values different from the ones in the convergence region of the Taylor Series, with a reduced number of iterations. Through co-simulation using both the Matlab <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">®</sup> and ModelSim <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">®</sup> softwares, it was possible to determine the approximation quality of the implemented circuits, with a curve response very close to the Matlab one. Moreover, the Goldschmidt divider presents a slightly fewer relative error, mainly for higher input values comparing with Newton-Raphson. Synthesis results show that although the logarithm circuit with Newton-Raphson divider has marginally more area, it is more power-efficient than the one using Goldschmidt divider.