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

被引：8

作者：

Walczyk, Cezary J. ^{[1
]}

Moroz, Leonid V. ^{[2
]}

Cieslinski, Jan L. ^{[1
]}

机构：

[1] Uniwersytet Bialymstoku, Wydzial Fizyki, Ul Ciolkowskiego 1L, PL-15245 Bialystok, Poland

[2] Lviv Polytech Natl Univ, Dept Secur Informat & Technol, St Kn Romana 1-3, UA-79000 Lvov, Ukraine

来源：

ENTROPY | 2021年 / 23卷 / 01期

关键词：

approximation of functions; floating-point arithmetic; Newton– Raphson method; inverse square root; magic constant;

D O I：

10.3390/e23010086

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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.

引用

页码：1 / 21

页数：20

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