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| References | (1 earlier) <m3241t$ihv$1@dont-email.me> <mailman.15379.1414830070.18130.python-list@python.org> <m325dt$lsl$1@dont-email.me> <mailman.15380.1414830791.18130.python-list@python.org> <m3265d$o6q$1@dont-email.me> |
|---|---|
| Date | 2014-11-01 19:45 +1100 |
| Subject | Re: Challenge: optimizing isqrt |
| From | Chris Angelico <rosuav@gmail.com> |
| Newsgroups | comp.lang.python |
| Message-ID | <mailman.15381.1414831554.18130.python-list@python.org> (permalink) |
On Sat, Nov 1, 2014 at 7:38 PM, Christian Gollwitzer <auriocus@gmx.de> wrote: > Am 01.11.14 09:33, schrieb Chris Angelico: >> >> On Sat, Nov 1, 2014 at 7:25 PM, Christian Gollwitzer <auriocus@gmx.de> >> wrote: >>>> >>>> Part of the point of that algorithm is that it never uses FP, and is >>>> therefore not limited by FP restrictions. >>> >>> >>> >>> which are??? >> >> >> Most notably, the inability to represent every integer beyond 2**53, >> and the inability to represent any integer beyond 2**1024. This >> algorithm should work fine with any positive integer. >> > OK so you did not bother to look at my proposed alternative implementation. > If I understood Steven correctly, he wanted to speed up the original isqrt > algorithm by using FP when this is possible. I have shown how to do it for > n<2**1022 (maybe 2**1024, I'm to lean to check it). I admit that there is > some microoptimizatio left, e.g. the first division is done twice, the > comparison should be bits>1022, not n>2*1022 etc. I did look at it. Trouble is, I don't know floating point's details well enough to prove that there are no *other* limitations. FWIW, I've proven the algorithm as far as 2**38. That's still a long way short of 2**53, though, and getting as far as 2**39 would, with my brute-force checker, require between 2.5 and 5 hours. I've made some improvements over the original, but it's still slow. ChrisA
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Challenge: optimizing isqrt Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-11-01 12:29 +1100
Re: Challenge: optimizing isqrt Chris Angelico <rosuav@gmail.com> - 2014-11-01 13:12 +1100
Re: Challenge: optimizing isqrt Christian Gollwitzer <auriocus@gmx.de> - 2014-11-01 09:02 +0100
Re: Challenge: optimizing isqrt Christian Gollwitzer <auriocus@gmx.de> - 2014-11-01 09:09 +0100
Re: Challenge: optimizing isqrt Chris Angelico <rosuav@gmail.com> - 2014-11-01 19:13 +1100
Re: Challenge: optimizing isqrt Christian Gollwitzer <auriocus@gmx.de> - 2014-11-01 09:25 +0100
Re: Challenge: optimizing isqrt Chris Angelico <rosuav@gmail.com> - 2014-11-01 19:33 +1100
Re: Challenge: optimizing isqrt Christian Gollwitzer <auriocus@gmx.de> - 2014-11-01 09:38 +0100
Re: Challenge: optimizing isqrt Chris Angelico <rosuav@gmail.com> - 2014-11-01 19:45 +1100
Re: Challenge: optimizing isqrt Akira Li <4kir4.1i@gmail.com> - 2014-11-01 12:12 +0300
Re: Challenge: optimizing isqrt Serhiy Storchaka <storchaka@gmail.com> - 2014-11-20 20:00 +0200
Re: Challenge: optimizing isqrt Stephen Tucker <stephen_tucker@sil.org> - 2014-11-21 08:15 +0000
Re: Challenge: optimizing isqrt Dave Angel <davea@davea.name> - 2014-11-23 10:43 -0500
Re: Challenge: optimizing isqrt Serhiy Storchaka <storchaka@gmail.com> - 2014-11-25 21:31 +0200
Re: Challenge: optimizing isqrt Dave Angel <davea@davea.name> - 2014-11-25 19:46 -0500
Re: Challenge: optimizing isqrt Stephen Tucker <stephen_tucker@sil.org> - 2014-11-26 07:57 +0000
Re: Challenge: optimizing isqrt Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-11-26 21:25 +1100
Re: Challenge: optimizing isqrt Serhiy Storchaka <storchaka@gmail.com> - 2014-11-26 18:24 +0200
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