Yes I can:

gp -f
          GP/PARI CALCULATOR Version 2.6.2 (development 15281-15d6bae)
          amd64 running linux (x86-64/GMP-5.0.1 kernel) 64-bit version
    compiled: Nov  4 2013, gcc version 4.8.1 (Ubuntu 4.8.1-2ubuntu1~12.04) 
                           threading engine: pthread
                 (readline v6.0 enabled, extended help enabled)

                     Copyright (C) 2000-2013 The PARI Group

PARI/GP is free software, covered by the GNU General Public License, and comes 
WITHOUT ANY WARRANTY WHATSOEVER.

Type ? for help, \q to quit.
Type ?12 for how to get moral (and possibly technical) support.

parisize = 8000000, primelimit = 500000
?  f()=sumnum(n=1,1,-log(cos(1/n)));
? \p 100
   realprecision = 115 significant digits (100 digits displayed)
? f()
%2 = 0.94536905472633293526609521540827019761 + 0.E-32*I
? \p 308
   realprecision = 308 significant digits
? f()
%3 = 0.94536905472633293526609521540827019712 + 0.E-32*I

Charles Greathouse
Analyst/Programmer
Case Western Reserve University


On Mon, Nov 4, 2013 at 2:53 AM, Karim Belabas <Karim.Belabas@math.u-bordeaux1.fr> wrote:
* Charles Greathouse [2013-11-04 07:33]:
> Package: pari
> Version: 2.6.2 (development 15281-15d6bae)
>
> I noticed that when I run sumnum I don't get more precise output after 38
> digits. The calculations take longer, but no more digits are returned. I
> expected to see output precision increase (even if not as high as input
> precision due to cancellation) but I don't see any increase at all.
>
> > f()=sumnum(n=1,1,-log(cos(1/n)));
> > #
> > \p 38
> > f()
> time = 113 ms.
> %2 = 0.94536905472633293526609521540827019799 + 0.E-33*I
> > \p 308
>    realprecision = 308 significant digits
> > f()
> time = 3,417 ms.
> %3 = 0.94536905472633293526609521540827019712 + 0.E-32*I

Hi Charles,

can you reproduce that in a clean sessions (gp -f), I can't:

?  f()=sumnum(n=1,1,-log(cos(1/n)));
? f()
%2 = 0.94536905472633293526609521540827019799 + 0.E-17*I
? \p100
   realprecision = 115 significant digits (100 digits displayed)
? f()
%3 = 0.9453690547263329352660952154082701981169960920660979883727147177759417063171903868942921481386240934 + 0.E-17*I

Cheers,

    K.B.
--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite Bordeaux 1          Fax: (+33) (0)5 40 00 69 50
351, cours de la Liberation    http://www.math.u-bordeaux1.fr/~kbelabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux1.fr/  [PARI/GP]
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