ROM and recursion free high accuracy approximation of base-2 logarithm using MacLaurin series

• Published in: Electronics letters Vol. 54; no. 10; pp. 622 - 624
• Main Authors: Khan, A, Kareem, P, Kyung, C.M
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 17.05.2018
• Subjects: approximation theory; average error; base‐2 logarithm; Circuits and systems; computational complexity; low error approximations; MacLaurin series; method maximum error; recursion free high accuracy approximation; low error approximations; approximation theory; MacLaurin series; method maximum error; average error; recursion free high accuracy approximation; base-2 logarithm; computational complexity
• ISSN: 0013-5194; 1350-911X; 1350-911X
• DOI: 10.1049/el.2018.0052

An accurate approximation of base-2 logarithm (log2) in hardware can be used to simplify many complex calculations such as power and division. There are several existing low error approximations of log2, but those approaches are either slow or require a lot of memory. In this letter, the authors propose a new shift and add-based approximation of log2 using Maclaurin series. Experimental results show that with the proposed method maximum error is as less as 0.0102 and average error is reduced to 0.0050. Being independent of a number of bits this approximation can be used for any range of numbers. Results of hardware implementation show that area, power, and frequency of the proposed method are comparable with the existing methods.