Improving the Accuracy of the Fast Inverse Square Root by Modifying Newton–Raphson Corrections

Direct computation of functions using low-complexity algorithms can be applied both for hardware constraints and in systems where storage capacity is a challenge for processing a large volume of data. We present improved algorithms for fast calculation of the inverse square root function for single-...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Vol. 23; no. 1; p. 86
Main Authors: Walczyk, Cezary J., Moroz, Leonid V., Cieśliński, Jan L.
Format: Journal Article
Language:English
Published: Switzerland MDPI AG 09.01.2021
MDPI
Subjects:
Accuracy
Algorithms
Approximation
approximation of functions
Computer graphics
Field programmable gate arrays
Floating point arithmetic
inverse square root
Libraries
magic constant
Mathematical analysis
Mathematical functions
Newton-Raphson method
Storage capacity
magic constant
floating-point arithmetic
approximation of functions
inverse square root
Newton–Raphson method
ISSN:1099-4300, 1099-4300
Online Access:Get full text
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Summary:Direct computation of functions using low-complexity algorithms can be applied both for hardware constraints and in systems where storage capacity is a challenge for processing a large volume of data. We present improved algorithms for fast calculation of the inverse square root function for single-precision and double-precision floating-point numbers. Higher precision is also discussed. Our approach consists in minimizing maximal errors by finding optimal magic constants and modifying the Newton–Raphson coefficients. The obtained algorithms are much more accurate than the original fast inverse square root algorithm and have similar very low computational costs.
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ISSN:1099-4300
1099-4300
DOI:10.3390/e23010086