A Modification of the Fast Inverse Square Root Algorithm

We present a new algorithm for the approximate evaluation of the inverse square root for single-precision floating-point numbers. This is a modification of the famous fast inverse square root code. We use the same “magic constant” to compute the seed solution, but then, we apply Newton–Raphson corre...

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Vydáno v:Computation Ročník 7; číslo 3; s. 41
Hlavní autoři: Walczyk, Cezary J., Moroz, Leonid V., Cieśliński, Jan L.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Basel MDPI AG 01.09.2019
Témata:
Accuracy
Algorithms
Approximation
Floating point arithmetic
inverse square root
magic constant
Newton–Raphson method
ISSN:2079-3197, 2079-3197
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Shrnutí:We present a new algorithm for the approximate evaluation of the inverse square root for single-precision floating-point numbers. This is a modification of the famous fast inverse square root code. We use the same “magic constant” to compute the seed solution, but then, we apply Newton–Raphson corrections with modified coefficients. As compared to the original fast inverse square root code, the new algorithm is two-times more accurate in the case of one Newton–Raphson correction and almost seven-times more accurate in the case of two corrections. We discuss relative errors within our analytical approach and perform numerical tests of our algorithm for all numbers of the type float.
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ISSN:2079-3197
2079-3197
DOI:10.3390/computation7030041