Software basics for computational mathematics

Cody, W. J.

doi:10.1145/1057533.1057535

Cited by 1 publication

(1 citation statement)

References 26 publications

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“…Algorithms for computing logarithms are widely available in the research literature [4][5][6][7][8] and are actively being investigated 9,10 . The most popular algorithms for computing logarithms can be classified into several categories:…”

Section: Introductionmentioning

confidence: 99%

Innovative, simple and efficient algorithms for logarithms with adjustable accuracy

Gepner,

Moroz,

Samotyy

et al. 2023

Preprint

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The computation of logarithmic functions is essential for many computational applications in science and engineering. Various computational techniques have been developed to approximate these functions. In this article, we present a simple and efficient algorithm for calculating the logarithmic function using IEEE 754 standard arithmetic types that minimises the number of arithmetic operations compared to previous implementations. Our starting point is Mitchell’s linear approximation, which reduces the computation of the logarithm to just the addition of the exponent and the significand. We developed a parameterised framework for choosing the number of segments in a piecewise polynomial approximation scheme in combination with polynomial degree and bit manipulation techniques, which allows a tradeoff between the accuracy and efficiency. We measured a speedup by a factor of 3--20 with respect to the C/C++ library software implementation while keeping the absolute error at a low level. This article presents and discusses our proposed implementation, compares it to other logarithm realisations and tests these realisations on various platforms.

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