LAPSE:2023.29731
Published Article
LAPSE:2023.29731
Fast Calculation of Cube and Inverse Cube Roots Using a Magic Constant and Its Implementation on Microcontrollers
April 13, 2023
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.
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.
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Keywords
cube root, floating point, Householder, inverse cube root, Newton–Raphson
Subject
Suggested Citation
Moroz L, Samotyy V, Walczyk CJ, Cieśliński JL. Fast Calculation of Cube and Inverse Cube Roots Using a Magic Constant and Its Implementation on Microcontrollers. (2023). LAPSE:2023.29731
Author Affiliations
Moroz L: Department of Information Technologies Security, Institute of Computer Technologies, Automation, and Metrology, Lviv Polytechnic National University, 79013 Lviv, Ukraine
Samotyy V: Department of Automatic Control and Information Technology, Faculty of Electrical and Computer Engineering, Cracow University of Technology, 31155 Cracow, Poland [ORCID]
Walczyk CJ: Department of Mathematical Methods in Physics, Faculty of Physics, University of Bialystok, 15245 Bialystok, Poland [ORCID]
Cieśliński JL: Department of Mathematical Methods in Physics, Faculty of Physics, University of Bialystok, 15245 Bialystok, Poland [ORCID]
Samotyy V: Department of Automatic Control and Information Technology, Faculty of Electrical and Computer Engineering, Cracow University of Technology, 31155 Cracow, Poland [ORCID]
Walczyk CJ: Department of Mathematical Methods in Physics, Faculty of Physics, University of Bialystok, 15245 Bialystok, Poland [ORCID]
Cieśliński JL: Department of Mathematical Methods in Physics, Faculty of Physics, University of Bialystok, 15245 Bialystok, Poland [ORCID]
Journal Name
Energies
Volume
14
Issue
4
First Page
1058
Year
2021
Publication Date
2021-02-18
ISSN
1996-1073
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Original Submission
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PII: en14041058, Publication Type: Journal Article
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LAPSE:2023.29731
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https://doi.org/10.3390/en14041058
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Apr 13, 2023
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