Re: Powers too slow?

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Thu, Dec 14, 2023 at 08:12:22PM -0800, Ilya Zakharevich wrote:
> On Thu, Dec 14, 2023 at 06:40:37PM -0800, Ilya Zakharevich wrote:
> > It seems that some powers take 2x the time they should take:
> > 
> >   (18:31) gp > localprec(1111111); 1111111^(31/10);
> >   time = 453 ms.
> >   (18:31) gp > localprec(1111111); 1111111.^(1/10)*1111111^3;
> >   time = 234 ms.
> 
> Oups, this mixes integers and floating point bases!  However, with pure
> integer bases this only becomes slightly more pronounced.

? localprec(1111111); (1111111^(31/10))
  *** _^_: Warning: increasing stack size to 16000000.
time = 197 ms.
%5 = 5518843593084694525.5922480458188863341
? localprec(1111111); (1111111^(1/10))^31
  *** _^_: Warning: increasing stack size to 16000000.
time = 202 ms.
%6 = 5518843593084694525.5922480458188863341
? localprec(1111111); (1111111^(1/10))*(1111111^3)
  *** _^_: Warning: increasing stack size to 16000000.
time = 122 ms.
%7 = 5518843593084694525.5922480458188863341

So maybe we could change powfrac to use %6 instead of %7,
assuming the base is much smaller than the precision,
because otherwise this is slower:

? A=(10^1111111-1)/9;
time = 17 ms.
? localprec(11); A^(31/10)
%10 = 1.3862712636533488637941870000827053413E3444441
  ***   last result computed in 0 ms.
? localprec(11); A^(1/10)*A^3
time = 50 ms.
%11 = 1.3862712636533488638E3444441

Cheers,
Bill.