Fast inverse square root (English Wikipedia)

Moroz et al. 2018. Moroz, Leonid V.; Walczyk, Cezary J.; Hrynchyshyn, Andriy; Holimath, Vijay; Cieslinski, Jan L. (January 2018). "Fast calculation of inverse square root with the use of magic constant analytical approach". Applied Mathematics and Computation. 316 (C). Elsevier Science Inc.: 245–255. arXiv:1603.04483. doi:10.1016/j.amc.2017.08.025. S2CID 7494112.

beyond3d.com

Sommefeldt, Rys (2006-12-19). "Origin of Quake3's Fast InvSqrt() - Part Two". Beyond3D. Retrieved 2008-04-19.
Sommefeldt, Rys (2006-11-29). "Origin of Quake3's Fast InvSqrt()". Beyond3D. Retrieved 2009-02-12.

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Ruskin, Elan (2009-10-16). "Timing square root". Some Assembly Required. Archived from the original on 2021-02-08. Retrieved 2015-05-07.

csdn.net

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"Discussion on CSDN". Archived from the original on 2015-07-02.

daxia.com

McEniry 2007, p. 2, 16. McEniry, Charles (August 2007). "The Mathematics Behind the Fast Inverse Square Root Function Code" (PDF). Archived from the original (PDF) on 2015-05-11.
McEniry 2007, p. 3. McEniry, Charles (August 2007). "The Mathematics Behind the Fast Inverse Square Root Function Code" (PDF). Archived from the original (PDF) on 2015-05-11.
McEniry 2007, p. 6. McEniry, Charles (August 2007). "The Mathematics Behind the Fast Inverse Square Root Function Code" (PDF). Archived from the original (PDF) on 2015-05-11.

doi.org

Blinn 1997, pp. 80–84. Blinn, Jim (July 1997). "Floating Point Tricks". IEEE Computer Graphics & Applications. 17 (4): 80. doi:10.1109/38.595279.
Zafar, Saad; Adapa, Raviteja (January 2014). "Hardware architecture design and mapping of 'Fast Inverse Square Root' algorithm". 2014 International Conference on Advances in Electrical Engineering (ICAEE). pp. 1–4. doi:10.1109/ICAEE.2014.6838433. ISBN 978-1-4799-3543-7. S2CID 2005623.
Middendorf 2007, pp. 155–164. Middendorf, Lars; Mühlbauer, Felix; Umlauf, George; Bodba, Christophe (June 1, 2007). "Embedded Vertex Shader in FPGA" (PDF). In Rettberg, Achin (ed.). Embedded System Design: Topics, Techniques and Trends. IFIP TC10 Working Conference:International Embedded Systems Symposium (IESS). et al. Irvine, California: Springer. doi:10.1007/978-0-387-72258-0_14. ISBN 978-0-387-72257-3. Archived (PDF) from the original on 2019-05-01.
Goldberg 1991, p. 7. Goldberg, David (1991). "What every computer scientist should know about floating-point arithmetic". ACM Computing Surveys. 23 (1): 5–48. doi:10.1145/103162.103163. S2CID 222008826.
Goldberg 1991, pp. 15–20. Goldberg, David (1991). "What every computer scientist should know about floating-point arithmetic". ACM Computing Surveys. 23 (1): 5–48. doi:10.1145/103162.103163. S2CID 222008826.
Goldberg 1991, p. 16. Goldberg, David (1991). "What every computer scientist should know about floating-point arithmetic". ACM Computing Surveys. 23 (1): 5–48. doi:10.1145/103162.103163. S2CID 222008826.
Moroz et al. 2018. Moroz, Leonid V.; Walczyk, Cezary J.; Hrynchyshyn, Andriy; Holimath, Vijay; Cieslinski, Jan L. (January 2018). "Fast calculation of inverse square root with the use of magic constant analytical approach". Applied Mathematics and Computation. 316 (C). Elsevier Science Inc.: 245–255. arXiv:1603.04483. doi:10.1016/j.amc.2017.08.025. S2CID 7494112.
Muller, Jean-Michel (December 2020). "Elementary Functions and Approximate Computing". Proceedings of the IEEE. 108 (12): 2146. doi:10.1109/JPROC.2020.2991885. ISSN 0018-9219. S2CID 219047769.

github.com

feilipu. "z88dk is a collection of software development tools that targets the 8080 and z80 computers". GitHub.

gutenberg.org

Hardy 1908, p. 323. Hardy, Godfrey (1908). A Course of Pure Mathematics. Cambridge, UK: Cambridge University Press. ISBN 0-521-72055-9.

ieee.org

ieeexplore.ieee.org

Zafar, Saad; Adapa, Raviteja (January 2014). "Hardware architecture design and mapping of 'Fast Inverse Square Root' algorithm". 2014 International Conference on Advances in Electrical Engineering (ICAEE). pp. 1–4. doi:10.1109/ICAEE.2014.6838433. ISBN 978-1-4799-3543-7. S2CID 2005623.
Muller, Jean-Michel (December 2020). "Elementary Functions and Approximate Computing". Proceedings of the IEEE. 108 (12): 2146. doi:10.1109/JPROC.2020.2991885. ISSN 0018-9219. S2CID 219047769.

inbetweennames.net

Peelar, Shane (1 June 2021). "Fast reciprocal square root... in 1997?!".

lomont.org

Lomont 2003, p. 1-2. Lomont, Chris (February 2003). "Fast Inverse Square Root" (PDF). Retrieved 2009-02-13.
Lomont 2003, p. 1. Lomont, Chris (February 2003). "Fast Inverse Square Root" (PDF). Retrieved 2009-02-13.
Lomont 2003. Lomont, Chris (February 2003). "Fast Inverse Square Root" (PDF). Retrieved 2009-02-13.
Lomont 2003, p. 3. Lomont, Chris (February 2003). "Fast Inverse Square Root" (PDF). Retrieved 2009-02-13.
Lomont 2003, p. 10. Lomont, Chris (February 2003). "Fast Inverse Square Root" (PDF). Retrieved 2009-02-13.
Lomont 2003, pp. 10–11. Lomont, Chris (February 2003). "Fast Inverse Square Root" (PDF). Retrieved 2009-02-13.

mathworks.com

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Moler, Cleve (19 June 2012). "Symplectic Spacewar". MATLAB Central - Cleve's Corner. MATLAB. Retrieved 2014-07-21.

mrob.com

Munafo, Robert. "Notable Properties of Specific Numbers". mrob.com. Archived from the original on 16 November 2018.

mrober.io

Matthew Robertson (2012-04-24). "A Brief History of InvSqrt" (PDF). UNBSJ.

netlib.org

"sqrt implementation in fdlibm - See W. Kahan and K.C. Ng's discussion in comments in lower half of this code".

semanticscholar.org

api.semanticscholar.org

Zafar, Saad; Adapa, Raviteja (January 2014). "Hardware architecture design and mapping of 'Fast Inverse Square Root' algorithm". 2014 International Conference on Advances in Electrical Engineering (ICAEE). pp. 1–4. doi:10.1109/ICAEE.2014.6838433. ISBN 978-1-4799-3543-7. S2CID 2005623.
Goldberg 1991, p. 7. Goldberg, David (1991). "What every computer scientist should know about floating-point arithmetic". ACM Computing Surveys. 23 (1): 5–48. doi:10.1145/103162.103163. S2CID 222008826.
Goldberg 1991, pp. 15–20. Goldberg, David (1991). "What every computer scientist should know about floating-point arithmetic". ACM Computing Surveys. 23 (1): 5–48. doi:10.1145/103162.103163. S2CID 222008826.
Goldberg 1991, p. 16. Goldberg, David (1991). "What every computer scientist should know about floating-point arithmetic". ACM Computing Surveys. 23 (1): 5–48. doi:10.1145/103162.103163. S2CID 222008826.
Moroz et al. 2018. Moroz, Leonid V.; Walczyk, Cezary J.; Hrynchyshyn, Andriy; Holimath, Vijay; Cieslinski, Jan L. (January 2018). "Fast calculation of inverse square root with the use of magic constant analytical approach". Applied Mathematics and Computation. 316 (C). Elsevier Science Inc.: 245–255. arXiv:1603.04483. doi:10.1016/j.amc.2017.08.025. S2CID 7494112.
Muller, Jean-Michel (December 2020). "Elementary Functions and Approximate Computing". Proceedings of the IEEE. 108 (12): 2146. doi:10.1109/JPROC.2020.2991885. ISSN 0018-9219. S2CID 219047769.

springer.com

link.springer.com

Middendorf 2007, pp. 155–164. Middendorf, Lars; Mühlbauer, Felix; Umlauf, George; Bodba, Christophe (June 1, 2007). "Embedded Vertex Shader in FPGA" (PDF). In Rettberg, Achin (ed.). Embedded System Design: Topics, Techniques and Trends. IFIP TC10 Working Conference:International Embedded Systems Symposium (IESS). et al. Irvine, California: Springer. doi:10.1007/978-0-387-72258-0_14. ISBN 978-0-387-72257-3. Archived (PDF) from the original on 2019-05-01.

web.archive.org

Ruskin, Elan (2009-10-16). "Timing square root". Some Assembly Required. Archived from the original on 2021-02-08. Retrieved 2015-05-07.
Munafo, Robert. "Notable Properties of Specific Numbers". mrob.com. Archived from the original on 16 November 2018.
"Discussion on CSDN". Archived from the original on 2015-07-02.
Middendorf 2007, pp. 155–164. Middendorf, Lars; Mühlbauer, Felix; Umlauf, George; Bodba, Christophe (June 1, 2007). "Embedded Vertex Shader in FPGA" (PDF). In Rettberg, Achin (ed.). Embedded System Design: Topics, Techniques and Trends. IFIP TC10 Working Conference:International Embedded Systems Symposium (IESS). et al. Irvine, California: Springer. doi:10.1007/978-0-387-72258-0_14. ISBN 978-0-387-72257-3. Archived (PDF) from the original on 2019-05-01.
"quake3-1.32b/code/game/q_math.c". Quake III Arena. id Software. Archived from the original on 2017-07-29. Retrieved 2017-01-21.{{cite web}}: CS1 maint: bot: original URL status unknown (link)
McEniry 2007, p. 2, 16. McEniry, Charles (August 2007). "The Mathematics Behind the Fast Inverse Square Root Function Code" (PDF). Archived from the original (PDF) on 2015-05-11.
McEniry 2007, p. 3. McEniry, Charles (August 2007). "The Mathematics Behind the Fast Inverse Square Root Function Code" (PDF). Archived from the original (PDF) on 2015-05-11.
McEniry 2007, p. 6. McEniry, Charles (August 2007). "The Mathematics Behind the Fast Inverse Square Root Function Code" (PDF). Archived from the original (PDF) on 2015-05-11.
Kadlec, Jan (2010). "Řrřlog::Improving the fast inverse square root" (personal blog). Archived from the original on 2018-07-09. Retrieved 2020-12-14.{{cite web}}: CS1 maint: bot: original URL status unknown (link)

worldcat.org

Muller, Jean-Michel (December 2020). "Elementary Functions and Approximate Computing". Proceedings of the IEEE. 108 (12): 2146. doi:10.1109/JPROC.2020.2991885. ISSN 0018-9219. S2CID 219047769.