Various changes to primality testing #2063
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fingolfin
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Also remove unused (and unusable, due to hardcoding a broken link) IsBPSWPseudoPrime_VerifyCorrectness
This reflects the current state of the art, see <http://www.trnicely.net/misc/bpsw.html>
While in theory, there might be fewer divisions to compute (as a commented
in the removed code suggests), the magnitude of the involved operands also
plays a role for efficiency; in a (single) GcdInt operation, the arguments
quickly get smaller, so most divisions end up being performed on immediate
integers.
Some quick experiments comparing the two approaches confirm this, massively:
gap> Number([0..2^16],n->ForAny(Primes{[27..168]},p->0=(2^255+n) mod p));; time;
5623
vs.
gap> Number([0..2^16], n-> 1<>GcdInt(2^255 + n,
> 841284107844892882230924743483896036230303226400884429367479745\
> 182396425076313801080105888842525657179186823477095844441732607\
> 309415612117497325122570590402649274666448191740488756513678929\
> 402959775310209214502833707784648441319210161128261125112776114\
> 119620471154579797706399078932717575475133487349361392344929340\
> 84356041841547537781640044258066541550710400764797315999285813));; time;
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What specifically do you wish me to do here? |
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@Stefan-Kohl I thought you might be familiar with the primality testing code, and thus could possible review the changes in this commit. (UPDATE: err, I meant "PR", not "commit") |
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I think Jack Schmidt has written most of the primality testing code. I have so far taken only a quick glance at that code, not more. And already that has been years ago. If you would like to have an expert opinion, I'd suggest you to ask Jack. -- Although I haven't heard from him since a while now, he is still among the members of the GAP Support Group as listed here: http://www.gap-system.org/Contacts/People/supportgroup.html |
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@fingolfin we need to add this to release notes for GAP 4.10 at https://github.com/gap-system/gap/wiki/Release-notes-for-GAP-4.10. The current PR title is too generic - perhaps you could suggest a more specific title or edit that wiki page and put a more specific description there? |
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