Fast calculation of inverse square root with the use of magic constant – analytical approach

Leonid V. Moroz, Cezary J. Walczyk, Andriy Hrynchyshyn, Vijay Holimath and Jan L. Cieśliński

Applied Mathematics and Computation, 2018, vol. 316, issue C, 245-255

Abstract: We present a mathematical analysis of transformations used in fast calculation of inverse square root for single-precision floating-point numbers. Optimal values of the so called magic constants are derived in a systematic way, minimizing either relative or absolute errors. We show that the value of the magic constant can depend on the number of Newton–Raphson iterations. We present results for one and two iterations.

Keywords: Floating-point arithmetic; Inverse square root; Magic constant; Newton–Raphson method (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:316:y:2018:i:c:p:245-255

DOI: 10.1016/j.amc.2017.08.025

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