Re: How to efficiently count Proth primes with GP parfor?

[hermann@stamm-wilbrandt.de]

Missing gist link:
https://gist.github.com/Hermann-SW/558728c025a1f2d3dace008292bac897

On 2024-03-20 23:20, hermann@stamm-wilbrandt.de wrote:
> On 2024-03-20 15:53, hermann@stamm-wilbrandt.de wrote:
> > ? export(isProth2)
> > ?
> > my(nbt=default(nbthreads));my(c=0,B=4636016641\nbt);parfor(ii=0,(4636016641+B-1)\B,my(cc=0,i=ii*B+1);forprime(p=i,min(i+B-1,4636016641),cc+=isProth2(p));cc,C,c+=C);c
> > cpu time = 2min, 27,991 ms, real time = 5,000 ms.
> > %12 = 10000
> > ?
> >
> >
> > Wow -- 3193% CPU !!!
> While using Karim's isProth2() I improved Bill's parallel work
> distribution scheme.
>
> Instead of blocks of size B=n\nbt now block are of size 
> B=n\nbt\if(l,l,1).
> Since distribution of primes as well as distribution of Proth primes
> is not the same for lower half ad higher half, making each of the 32
> hardware threaas work l smaller but more evenly distributed work
> areas.
>
> All in new proth.gp gist with comments showing increased l effects.
> Overall speedup is limited by Amdahls law.
> I increased from n slghtly more than 4 billiom for first 10,000 Proth
> primes to 100 billion:
>
> hermann@7950x:~$ n=10^11 l=32 gp -q < proth.gp
> 32
> 1min, 10,058 ms × 31.784 = 37min, 6,695 ms
> 39170
> 15min, 13,952 ms (13.046×)
> 39170
> hermann@7950x:~$
>
>
> Very close to factor 32× between gettime() overall time and
> getwalltime() sequential time.
> Not much better factor than 13× between sequential getwalltime() and
> parallel getwalltime().
>
> Regards,
>
> Hermann.