An efficient and accurate logarithmic multiplier based on operand decomposition

Abstract

Logarithmic Number Systems (LNS) offer a viable alternative in terms of area, delay and power to binary number systems for multiplication and division operations in signalprocessing. The Mitchell Algorithm (MA) proposed in [9], is a simple and low cost approach commonly used for logarithmic multiplication. However, the method involves high error due to piecewise straight line approximation of the logarithm curve. Several methods have been proposed in the literature for improving the accuracy of Mitchell's Algorithm. In this paper, we propose a new method for improving the accuracy of MA using Operand Decomposition (OD). The OD process decreases the number of bits with the value of '1' in the multiplicands and reduces the amount of approximation. The proposed method decreases the error percentage of the Mitchell Algorithm by 44.7% on the average. Since the proposed method does not require any correction term it can be used in combination with other methods for improving the accuracy of the MA based multiplier. Experimental results are presented for random input data, signal and image processing applications, which clearly indicate that the proposed method significantly outperforms previous methods proposed in the literature.

A Fast Hardware Approach for Approximate, Efficient Logarithm and Antilogarithm Computations

“…Compared to these methods, our approach is applicable for applications that require a much higher accuracy. [14] gives an approach for logarithmic multiplication, but they provide results based on random input vectors and compute the average error. We find the worst case error over all possible inputs.…”

“…The Mitchell approximation to find the binary antilogarithm of a number, is given by the expression (13) The error due to this expression is given by (14) We sample the error curve at as many points as required, and store these values in the first entry of a LUT. If are any two adjacent values stored in the memory, we store in the second entry of the LUT.…”

“…The antilogarithm is also computed the same way. It is approximated as (16) The coefficients in this case are found by fitting a polynomial to different segments of the curve given in (14). The improvement in errors is shown in Table IV.…”

Reduced-error constant correction truncated multiplier

“…Software compensation of truncation errors was used in this scheme. Other hybrid strategies [6,7] have also been proposed in the literature.…”

Design and Implementation of an Arithmetic Processor Unit Based on the Logarithmic Number System

“…Debido a que el LNS basa su funcionamiento en las propiedades de las funciones logaritmo y antilogaritmo, este sistema numérico permite realizar operaciones de multiplicación, división y raíz cuadrada haciendo uso de sumas, restas y desplazamientos lógicos en el formato de punto fijo, reduciendo de esta forma la complejidad de la arquitectura hardware de dichas operaciones [2], [3].…”