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Topic: PARI/gp wins my Riemann zeta speed contest, so far
Replies: 9   Last Post: Feb 15, 2013 10:43 PM

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 David Bernier Posts: 3,662 Registered: 12/13/04
Re: PARI/gp wins my Riemann zeta speed contest, so far
Posted: Feb 7, 2013 1:19 PM

On 01/21/2013 12:23 AM, David Bernier wrote:
> I had done my own Riemann zeta computations with Bernoulli numbers,
> computing in days a few 10,000 (say 55,000) decimals of
> the imaginary part of the first non-trivial zero
> 1/2 + i*14.13... using PARI-gp.
>
> This time, I used PARI-gp's own zeta(.):
>
> ? system(date);zeta(t);system(date)
> Sun Jan 20 03:36:28 EST 2013
> Sun Jan 20 07:10:17 EST 2013
>
>
> // 20,000 decimals precision
> // t is with 1/10^400 of first non-trivial zero.
>
> 3 hours and 34 minutes for 20017 significant digits
> near 1/2 + i*14.134725141734693790457251983562470270784257
>
>
>
> ? \p
> realprecision = 20017 significant digits (20000 digits displayed)
> ? a=zeta(t);

[...]

With realprecision \p set to 40,000 digits, something strange
happened with zeta(.):

? zeta(s)
*** at top-level: zeta(s)
*** ^-------
*** zeta: the PARI stack overflows !
current stack size: 500000000 (476.837 Mbytes)
[hint] you can increase GP stack with allocatemem()

*** Break loop: type 'break' to go back to GP
break> break

? allocatemem(2000000000)
*** Warning: new stack size = 2000000000 (1907.349 Mbytes).
? zeta(s)
^C *** at top-level: zeta(s)
*** ^-------
*** zeta: user interrupt after 38h, 47min, 59,768 ms.

about 39 hours and has not completed. > 500 MB of stack needed.

I was double-checking my Euler-Maclaurin computations.

To be continued ...

David Bernier

--
dracut:/# lvm vgcfgrestore
File descriptor 9 (/.console_lock) leaked on lvm invocation. Parent PID
993: sh
Please specify a *single* volume group to restore.

Date Subject Author
1/21/13 David Bernier
1/21/13 James Waldby
1/21/13 David Bernier
1/21/13 David Bernier
1/21/13 James Waldby
2/3/13 David Bernier
1/21/13 James Waldby
2/7/13 David Bernier
2/15/13 David Bernier
2/15/13 David Bernier