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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Leonid Moroz & Volodymyr Samotyy & Cezary J. Walczyk & Jan L. Cieśliński, 2021. "Fast Calculation of Cube and Inverse Cube Roots Using a Magic Constant and Its Implementation on Microcontrollers," Energies, MDPI, vol. 14(4), pages 1-13, February.
    • Handle: RePEc:gam:jeners:v:14:y:2021:i:4:p:1058-:d:501066
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    References listed on IDEAS

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    1. Moroz, Leonid V. & Walczyk, Cezary J. & Hrynchyshyn, Andriy & Holimath, Vijay & Cieśliński, Jan L., 2018. "Fast calculation of inverse square root with the use of magic constant – analytical approach," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 245-255.
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