Fast Square Root Calculation without Division for High Performance Control Systems of Power Electronics

Dianov, Anton; Anuchin, Alecksey; Bodrov, Alexey

doi:10.30941/cestems.2022.00020

Cited by 3 publications

(4 citation statements)

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“…We provide in Table 4 the total number of clock cycles for six square rooting methods in addition to our proposed algorithm. We note that the approximation method by Dianov et al 52 yields the least number of clock cycles with a value of 34 then Goldschmidt with 35 clock cycles followed by the polynomial approximation with 39 clock cycles. Whereas these performance results are obtained with reduced accuracy, the approximation by the aforementioned methods can still be acceptable for square root calculation when the latency is of higher importance.…”

Section: Resultsmentioning

confidence: 77%

“…The performance and accuracy results of the reviewed methods are evaluated and compared to the proposed algorithm. The seed selection for iterative methods is based on the initial estimation reported in the works of Dianov et al 1 , 52 . For Newton–Raphson’s method, the initial value is estimated by finding k , so that .…”

Section: Resultsmentioning

confidence: 99%

“…For any positive integer x up to and assuming a four-decimal-digit accuracy for the square root value, we analyzed the impact of using different seed values on the number of iterations for the Newton–Raphson’s method. Four variations are considered: (a) the seed is initialized with x as a baseline for this comparison; (b) the seed reported by Dianov et al 52 ; (c) the seed is initialized using Blinn’s method; and (d) the seed is obtained using our bit-manipulation approach, . The obtained results are reported in Fig.…”

Section: Resultsmentioning

confidence: 99%

“…A recent square rooting method used for control systems of power electronics was developed by Dianov et al 52 . The method is based on a division-free approximation of the parabola with a hyperbola.…”

Section: Related Workmentioning

confidence: 99%

See 3 more Smart Citations

Novel seed generation and quadrature-based square rooting algorithms

Altamimi

Youssef

2022

Sci Rep

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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.

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Section: Resultsmentioning

confidence: 77%