A Modification of the Fast Inverse Square Root Algorithm

被引：6

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：

COMPUTATION | 2019年 / 7卷 / 03期

关键词：

floating-point arithmetic; inverse square root; magic constant; Newton-Raphson method; DIVISION; UNIT;

D O I：

10.3390/computation7030041

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：14

共 50 条

[1] Fast Differentiable Matrix Square Root and Inverse Square Root
Song, Yue
Sebe, Nicu
Wang, Wei
[J]. arXiv, 2022,
[2] Fast Differentiable Matrix Square Root and Inverse Square Root
Song, Yue
Sebe, Nicu
Wang, Wei
[J]. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 2023, 45 (06) : 7367 - 7380
[3] Hardware architecture design and mapping of 'Fast Inverse Square Root' algorithm
Zafar, Saad
Adapa, Raviteja
[J]. 2014 INTERNATIONAL CONFERENCE ON ADVANCES IN ELECTRICAL ENGINEERING (ICAEE), 2014,
[4] A Fast FPGA Based Architecture for Computation of Square Root and Inverse Square Root
Hasnat, Abul
Bhattacharyya, Tanima
Dey, Atanu
Halder, Santanu
Bhattacharjee, Debotosh
[J]. PROCEEDINGS OF 2ND INTERNATIONAL CONFERENCE ON 2017 DEVICES FOR INTEGRATED CIRCUIT (DEVIC), 2017, : 383 - 387
[5] Fast enclosure for a matrix inverse square root
Miyajima, Shinya
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 467 : 116 - 135
[6] FAST ALGORITHM COMPUTES SQUARE ROOT
KOMUSIN, B
[J]. EDN, 1987, 32 (24) : 250 - 252
[7] Square Root and Inverse Square Root Computation Using a Fast FPGA Based Architecture
Hasnat, Abul
Dey, Atanu
Halder, Santanu
Bhattacharjee, Debotosh
[J]. JOURNAL OF ACTIVE AND PASSIVE ELECTRONIC DEVICES, 2018, 13 (2-3): : 135 - 147
[8] SQUARE-ROOT ALGORITHM IS FAST AND SIMPLE
GRAPPEL, RD
[J]. EDN, 1986, 31 (08) : 246 - &
[9] SQUARE-ROOT ALGORITHM IS FAST AND SIMPLE
GRAPPEL, RD
[J]. EDN, 1988, 33 (15A) : 144 - &
[10] Modified Fast Inverse Square Root and Square Root Approximation Algorithms: The Method of Switching Magic Constants
Moroz, Leonid V.
Samotyy, Volodymyr V.
Horyachyy, Oleh Y.
[J]. COMPUTATION, 2021, 9 (02) : 1 - 23

← 1 2 3 4 5 →