Floating-Point Inverse Square Root Algorithm Based on Taylor-Series Expansion

This brief describes a segmented structure to deal with inverse square root in floating-point digital calculation arithmetic, based on Taylor-Series expansion; it uses only the small number of their expansion terms to achieve a fast evaluation of these functions in high precision. Taylor-series expa...

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Bibliographic Details
Published inIEEE transactions on circuits and systems. II, Express briefs Vol. 68; no. 7; pp. 2640 - 2644
Main Authors Wei, Jianglin, Kuwana, Anna, Kobayashi, Haruo, Kubo, Kazuyoshi, Tanaka, Yuuki
Format Journal Article
LanguageEnglish
Published New York IEEE 01.07.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
algorithm
Algorithms
Approximation algorithms
Convergence
division
Floating point arithmetic
Floating-point
Hardware
inverse squares root
Mathematical analysis
Numerical simulation
Series (mathematics)
Series expansion
Signal processing algorithms
Table lookup
Taylor series
Taylor-series expansion
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Summary:This brief describes a segmented structure to deal with inverse square root in floating-point digital calculation arithmetic, based on Taylor-Series expansion; it uses only the small number of their expansion terms to achieve a fast evaluation of these functions in high precision. Taylor-series expansions of the inverse square root are examined for several center points with their convergence ranges, and the inverse square root calculation algorithm trade-offs among accuracy, numbers of multiplications/additions/subtractions and LUT sizes are shown; the designer can choose the optimal algorithm for his digital inverse square root calculation, and build its conceptual dedicated hardware architecture design with the contents described here.
ISSN:1549-7747
1558-3791
DOI:10.1109/TCSII.2021.3062358