Novel seed generation and quadrature-based square rooting algorithms
Abstract The square root operation is indispensable in a myriad of computational science and engineering applications. Various computational techniques have been devised to approximate its value. In particular, convergence methods employed in this regard are highly affected by the initial approximat...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Nature Portfolio
2022-11-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-022-25039-y |
| _version_ | 1811207571486277632 |
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| author | Amal Altamimi Belgacem Ben Youssef |
| author_facet | Amal Altamimi Belgacem Ben Youssef |
| author_sort | Amal Altamimi |
| collection | DOAJ |
| description | Abstract The square root operation is indispensable in a myriad of computational science and engineering applications. Various computational techniques have been devised to approximate its value. In particular, convergence methods employed in this regard are highly affected by the initial approximation of the seed value. Research shows that the provision of an initial approximation with higher accuracy yields fewer additional iterations to calculate the square root. In this article, we propose two novel algorithms. The first one presents a seed generation technique that depends on bit manipulation and whose output is to be used as an initial value in the calculation of square roots. The second one describes a quadrature-based square rooting method that utilizes a rectangle as the plane figure for squaring. We provide error estimation of the former using the vertical parabola equation and employ a suitable lookup table, for the latter, to store needed cosine values. The seed generation approach produces a significant reduction in the number of iterations of up to 84.42% for selected convergence methods. The main advantages of our proposed square rooting algorithm lie in its high accuracy and in its requirement of just a single iteration. Our proposed algorithm also provides for lower computational latency, measured in the number of clock cycles, compared to Newton–Raphson’s and Bakhshali’s square rooting methods. |
| first_indexed | 2024-04-12T04:06:34Z |
| format | Article |
| id | doaj.art-a8fc87d7bb29427899698d24ee6d556f |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-04-12T04:06:34Z |
| publishDate | 2022-11-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-a8fc87d7bb29427899698d24ee6d556f2022-12-22T03:48:36ZengNature PortfolioScientific Reports2045-23222022-11-0112111910.1038/s41598-022-25039-yNovel seed generation and quadrature-based square rooting algorithmsAmal Altamimi0Belgacem Ben Youssef1Department of Computer Engineering, College of Computer & Information Sciences, King Saud UniversityDepartment of Computer Engineering, College of Computer & Information Sciences, King Saud UniversityAbstract The square root operation is indispensable in a myriad of computational science and engineering applications. Various computational techniques have been devised to approximate its value. In particular, convergence methods employed in this regard are highly affected by the initial approximation of the seed value. Research shows that the provision of an initial approximation with higher accuracy yields fewer additional iterations to calculate the square root. In this article, we propose two novel algorithms. The first one presents a seed generation technique that depends on bit manipulation and whose output is to be used as an initial value in the calculation of square roots. The second one describes a quadrature-based square rooting method that utilizes a rectangle as the plane figure for squaring. We provide error estimation of the former using the vertical parabola equation and employ a suitable lookup table, for the latter, to store needed cosine values. The seed generation approach produces a significant reduction in the number of iterations of up to 84.42% for selected convergence methods. The main advantages of our proposed square rooting algorithm lie in its high accuracy and in its requirement of just a single iteration. Our proposed algorithm also provides for lower computational latency, measured in the number of clock cycles, compared to Newton–Raphson’s and Bakhshali’s square rooting methods.https://doi.org/10.1038/s41598-022-25039-y |
| spellingShingle | Amal Altamimi Belgacem Ben Youssef Novel seed generation and quadrature-based square rooting algorithms Scientific Reports |
| title | Novel seed generation and quadrature-based square rooting algorithms |
| title_full | Novel seed generation and quadrature-based square rooting algorithms |
| title_fullStr | Novel seed generation and quadrature-based square rooting algorithms |
| title_full_unstemmed | Novel seed generation and quadrature-based square rooting algorithms |
| title_short | Novel seed generation and quadrature-based square rooting algorithms |
| title_sort | novel seed generation and quadrature based square rooting algorithms |
| url | https://doi.org/10.1038/s41598-022-25039-y |
| work_keys_str_mv | AT amalaltamimi novelseedgenerationandquadraturebasedsquarerootingalgorithms AT belgacembenyoussef novelseedgenerationandquadraturebasedsquarerootingalgorithms |