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# Hermann-SW/proth.gp

Last active March 20, 2024 22:10
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determine count of Proth primes until environment n
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 \\ detemine count of Proth primes until environment n \\ environment l (loops) allows to tune work distribution \\ \\ based on Karim's isProth2(): \\ https://pari.math.u-bordeaux.fr/archives/pari-users-2403/msg00064.html \\ and Bill's parallel implementation: \\ https://pari.math.u-bordeaux.fr/archives/pari-users-2403/msg00067.html \\ isProth2(p) = !(p >> (valuation(p-1,2)<<1)); export(isProth2); nbt=default(nbthreads); doit(n,l)={ my(c=0,B=n\nbt\if(l,l,1)); parfor(ii=0, (n+B-1)\B, my(cc=0,i=ii*B+1); forprime(p=i, min(i+B-1,n), if(isProth2(p),cc++));cc, C, c+=C ); c }; n=eval(getenv("n")); gettime(); t0=getwalltime(); r=doit(n,eval(getenv("l"))); wt=getwalltime()-t0; tt=gettime(); print(nbt); printf("%s × %.3f = %s",strtime(wt),tt/wt/1.0,strtime(tt)); print(r); t0=getwalltime(); c=0;forprime(p=3,n,if(isProth2(p),c++)); wts=getwalltime()-t0; printf("%s (%.3f×)",strtime(wts),wts/wt/1.0); print(c);

### Hermann-SW commented Mar 20, 2024

Bill's original work partitioning corresponds to l=1:

``````hermann@7950x:~\$ n=4636016641 gp -q < proth.gp
32
3,888 ms × 28.742 = 1min, 51,748 ms
10000
47,880 ms (12.315×)
10000
hermann@7950x:~\$
``````

better factor 30.404× of overall time divided by walltime for l=2:

``````hermann@7950x:~\$ n=4636016641 l=2 gp -q < proth.gp
32
3,700 ms × 30.404 = 1min, 52,495 ms
10000
47,095 ms (12.728×)
10000
hermann@7950x:~\$
``````

l=4 slightly better 31.190×:

``````hermann@7950x:~\$ n=4636016641 l=4 gp -q < proth.gp
32
3,662 ms × 31.190 = 1min, 54,217 ms
10000
47,929 ms (13.088×)
10000
hermann@7950x:~\$
``````

even better 31.422× for l=8:

``````hermann@7950x:~\$ n=4636016641 l=8 gp -q < proth.gp
32
3,642 ms × 31.422 = 1min, 54,439 ms
10000
47,621 ms (13.076×)
10000
hermann@7950x:~\$
``````

Factor of parallel walltime by sequential time gets better, from 12.315× up to 13.076×.
Amdahl's law is limiting speedup.

### Hermann-SW commented Mar 20, 2024

For 2.5× n even closer to factor 32×, but the other factor 13.046× seems to be maxed out:

``````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:~\$
``````