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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.
References
-
-
1)
-
5. Juang, T.-B., Meher, P.K., Jan, K.-S.: ‘High-performance logarithmic converters using novel two-region bit-level manipulation schemes’. IEEE 2011 Int. Symp. on VLSI Design, Automation and Test (VLSI-DAT), Hsinchu, Taiwan, April 2011, pp. 1–4.
-
2)
-
2. SanGregory, S.L., Brothers, C., Gallagher, D., et al: ‘A fast, low-power logarithm approximation with CMOS VLSI implementation’. IEEE 42nd Midwest Symp. on Circuits and Systems, Las Cruces, NM, USA, August 1999, , pp. 388–391.
-
3)
-
4. Juang, T.-B., Chen, S.-H., Cheng, H.-J.: ‘A lower error and rom-free logarithmic converter for digital signal processing applications’, Trans. Circuits Syst. II, Express Briefs, 2009, 56, (12), pp. 931–935 (doi: 10.1109/TCSII.2009.2035270).
-
4)
-
6. Kareem, P., Naqvi, S.R., Kyung, C.-M.: ‘A low error add and shift-based efficient implementation of base-2 logarithm’. IEEE 2017 Int. Conf. on Electrical Engineering (ICEE), Lahore, Pakistan, March 2017, pp. 1–6.
-
5)
-
3. Abed, K.H., Siferd, R.E.: ‘CMOS VLSI implementation of a low-power logarithmic converter’, Trans. Comput., 2003, 52, (11), pp. 1421–1433 (doi: 10.1109/TC.2003.1244940).
-
6)
-
1. Mitchell, J.N.: ‘Computer multiplication and division using binary logarithms’, IRE Trans. Electron. Comput., 1962, EC-11, (4), pp. 512–517 (doi: 10.1109/TEC.1962.5219391).
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ROM and recursion free high accuracy approximation of base-2 logarithm using MacLaurin series