Efficient floating-point square root and reciprocal square root algorithms
Authors:
- Leonid Moroz,
- Volodymyr Samotyy,
- Mariusz Węgrzyn,
- Ulyana Dzelendzyak
Abstract
Several algorithms for calculating square roots and inverse square roots are developed. These are oriented on normalized numbers with a floating point for single and double accuracy. The fast inverse square root (FISR) method, on the basis of which the new algorithms have been created, is described. This method demonstrates high efficiency for two iterations with single accuracy and three iterations with double accuracy. The Householder iteration method, which has second order convergence, is used. The optimal parameters of the iterative process are calculated by balancing the values of the positive and negative errors. In comparison with known algorithms, the proposed algorithms reduce the error during the first iteration. For single accuracy, 23.67 correct bits are obtained during the second iteration and for double accuracy 52.00 correct bits are obtained during the third iteration. The same results are obtained during the square root calculation. For single accuracy, 23.43 correct bitsare obtained during the second iteration and for double accuracy 52.00 correct bits are obtained during the third iteration. An algorithm has been developed that performs one multiplication operation less without losing accuracy. This increases the speed of computing the reciprocal of the square root by 12%.
- Record ID
- CUTd3ac6ace803540cfa422e188c1419443
- Publication categories
- ; ;
- Author
- Pages
- 552-559
- Other elements of collation
- tab.; wykr.; Bibliografia (na s.) - 558-559; Bibliografia (liczba pozycji) - 18; Oznaczenie streszczenia - Abstr.
- Substantive notes
- Data wyd. wg cop.
- Book
- IDAACS'2021 : proceedings of the 11th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS), September 22-25, 2021, Cracow, Poland : virtual conference. Vol. 1, Proceedings of the IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems, 2021, [Piscataway], Institute of Electrical and Electronics Engineers, IEEE, ISBN 978-1-6654-2605-3 (electronic)
- Keywords in English
- floating-point, square root, reciprocal square root, Newton-Raphson, Householder
- DOI
- DOI:10.1109/IDAACS53288.2021.9660872 Opening in a new tab
- URL
- https://ieeexplore.ieee.org/document/9660872 Opening in a new tab
- Language
- eng (en) English
- Score (nominal)
- 20
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUTd3ac6ace803540cfa422e188c1419443/
- URN
urn:pkr-prod:CUTd3ac6ace803540cfa422e188c1419443
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.