Fast Calculation of Cube and Inverse Cube Roots Using a Magic Constant and Its Implementation on Microcontrollers

Leonid Moroz, Volodymyr Samotyy, Cezary J. Walczyk and Jan L. Cieśliński
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Leonid Moroz: Department of Information Technologies Security, Institute of Computer Technologies, Automation, and Metrology, Lviv Polytechnic National University, 79013 Lviv, Ukraine
Volodymyr Samotyy: Department of Automatic Control and Information Technology, Faculty of Electrical and Computer Engineering, Cracow University of Technology, 31155 Cracow, Poland
Cezary J. Walczyk: Department of Mathematical Methods in Physics, Faculty of Physics, University of Bialystok, 15245 Bialystok, Poland
Jan L. Cieśliński: Department of Mathematical Methods in Physics, Faculty of Physics, University of Bialystok, 15245 Bialystok, Poland

Energies, 2021, vol. 14, issue 4, 1-13

Abstract: We develop a bit manipulation technique for single precision floating point numbers which leads to new algorithms for fast computation of the cube root and inverse cube root. It uses the modified iterative Newton–Raphson method (the first order of convergence) and Householder method (the second order of convergence) to increase the accuracy of the results. The proposed algorithms demonstrate high efficiency and reduce error several times in the first iteration in comparison with known algorithms. After two iterations 22.84 correct bits were obtained for single precision. Experimental tests showed that our novel algorithm is faster and more accurate than library functions for microcontrollers.

Keywords: floating point; cube root; inverse cube root; Newton–Raphson; Householder (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2021
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