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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 nontrivial zero > 1/2 + i*14.13... using PARIgp. > > This time, I used PARIgp'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 nontrivial 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 toplevel: 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 toplevel: 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 doublechecking my EulerMaclaurin 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.



