A Fixed-Point Natural Logarithm Approximation Hardware Design Using Taylor Series

Abstract

The logarithm function is employed in several areas of knowledge because its curve approximates various physical and chemical phenomena. In this work, we propose an operator which can approximate the logarithm function at the base e. Such an operator is implemented using Taylor Series approximation with five terms. We also offer an algorithm responsible for allowing input values different from the ones that are included in the convergence region of the Taylor Series. Through co-simulations 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> simulators, it was possible to determine that the approximation error remains less than 0.6% for the entire input range. The input range used in this paper is in integer format with a one-byte length, and the system output has 19 bits with 4.15 form.