Re: A022921-code

["Ruud H.G. van Tol" <rvtol@isolution.nl>]

On 2022-12-28 19:53, Ruud H.G. van Tol wrote:
> On 2022-12-28 17:51, Karim Belabas wrote:
> > * Ruud H.G. van Tol [2022-12-28 16:28]:
> > > [ logint(3^(n+1),2) - logint(3^n,2) |n<-[0..98]]
> > >
> > > is half as fast as
> > >
> > > my(n0=logint(3^0,2)); [ -n0 + n0=logint(3^(n+1),2) |n<-[0..98]]
> > >
> > > but IMO looks ugly.
> > >
> > > Is there a both "nice" and fast way to do similar?
> > Not sure about "nice"; but faster, definitely:
> >
> > ? N = 30000;
> > ? w0 = [logint(3^(n+1),2) - logint(3^n,2) | n<-[0..N]];
> > time = 767 ms.
> >
> > ? my(n0=logint(3^0,2)); w1 = [-n0 + n0=logint(3^(n+1),2) |n<-[0..N]];
> > time = 355 ms.
> >
> > ? my(v = [logint(x,2) | x <-powers(3, N+1)]); w = vector(#v-1, i, 
> > v[i+1]-v[i]);
> > time = 20 ms.
> >
> > ? [w == w0, w == w1]
> > %4 = [1, 1]
>
> Pretty "nice" to me.
>
>
> I'm testing on an M1-Max, and could *not* run your fastest alternative 
> under 120ms.
>
>
> But then I slightly changed it to
>
> my(v = [logint(x,2) | x <-powers(3, N+1, 1)]); w = vector(#v-1, i, 
> v[i+1]-v[i])
>
> (so added the explicit '1' with powers)
>
> and then it would run at least twice as fast, and would (sometimes) 
> finish in 29ms.
> How weird is that? (No need to answer!)
>
>
> $ gp --version 2>&1 |sed 's/^ *//'
> GP/PARI CALCULATOR Version 2.15.1 (released)
> arm64 running darwin (aarch64/GMP-6.2.1 kernel) 64-bit version
> compiled: Nov  5 2022, Apple clang version 14.0.0 (clang-1400.0.29.202)
> threading engine: pthread
> (readline v8.2 disabled, extended help enabled)

All split up:

? N= 30000;

? p3=powers(3,N+1);
cpu time = 102 ms, real time = 111 ms.

? p3=powers(3,N+1,1);
cpu time = 31 ms, real time = 43 ms.

? v = [logint(x,2) | x<-p3];
cpu time = 10 ms, real time = 10 ms.

? vector(#v-1, i, v[i+1]-v[i]);
cpu time = 17 ms, real time = 18 ms.

-- Ruud