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Unified Computer Arithmetic for Handheld GPUs
Published in Krzysztof Iniewski, Circuits at the Nanoscale, 2018
Byeong-Gyu Nam, Hyejung Kim, Hoi-Jun Yoo
The logarithm to arbitrary constant base can be computed by multiplying a constant with the binary logarithm, according to the equation () logbx=k×log2xwhere k=1/log2b
Orthogonal arrays in statistics and computer science
Published in Jürgen Bierbrauer, Introduction to Coding Theory, 2016
Recall that log is the binary logarithm. pc(X) is the probability that, upon two independent draws from X, the same element is drawn. This is obviously related to the defining property of an ∊-U hash family (see Definition 6.3 and the interpretation following it). The Jensen inequality (Theorem 8.7) shows that the Rényi entropy R(X) is upper bounded by the Shannon entropy H(X).
Unsupervised image thresholding: hardware architecture and its usage for FPGA-SoC platform
Published in International Journal of Electronics, 2019
Jai Gopal Pandey, Abhijit Karmakar
The above computation method works for the integer number. The same circuit can also be deployed for obtaining the binary logarithm fractional numbers. For this, the shifting method is used (Kim et al., 2006). Let us consider m represents a fractional binary number for which the binary logarithm computation is required. The number m is left-shifted by n bits and it becomes . By this method, we compute the binary logarithm for m and from the output the term n gets subtracted, i.e. . In the above realization of the threshold computation circuit, there is no need to perform the antilogarithm operation. This is due to the fact that only in expression (17), there is only need for finding out for which grey-level value expression (17) reaches its maximal value. The circuit required to compute the maximum value (MAX) is realized using a 16-bit comparator, where it gets input from the logarithmic BCV unit. As expressed in (17), an optimum threshold value is obtained when the term attains its maximum value.