As a comparison I just ran my old C program (implementing the algorithm in my paper with Lagarias and Odlyzko) on my workstation which is a fast Dell '86 box (sorry I don't have more details) running Red Hat:
time ./findn 249999999999999 n=249_999_999_999_999 pi(249_999_999_999_999)=7_783_516_108_362 real 0m18.826s user 0m18.628s sys 0m0.028s On May 5, 4:18 am, mabshoff <mabsh...@googlemail.com> wrote: > On May 5, 12:44 am, "Dr. David Kirkby" <david.kir...@onetel.net> > wrote: > > > mabshoff wrote: > > <SNIP> > > Hi Dave, > > > > We are talking about two different limits here. > > > No, we were not - just a confusing way I wrote it. A memory alloction > > issue is completely different to limiting an algorithm due to concerns > > about it. > > Well, I certainly am. To recap: > > (a) prime_pi() used to use to be trivially implemented as len > (prime_range()) > (b) len(prime_range()) sucks memory and performance wise, i.e. eats > in excess of 124GB for input n=2^35 and plainly segfaults for n=2^50. > (c) we have known failures of the new prime_pi() for some inputs, > i.e. n=2^47 > > So what I am doing is: > > (a) cap the new prime_pi() to 2^40 since that is the upper bound we > can verify via doctests in reasonable time. Given the wide testing I > have done this seems to work. > (c) cap prime_range() to a reasonable value and/or rewrite it sanely > - this has not happened yet. > > > As a matter of interested, what does Sage give for > > primepi(249999999999999)? Is it the same as Mathematica (7783516108362)? > > Sage.math, i.e. 64 bit, gives me: > > sage: time prime_pi(249999999999999) > CPU times: user 1241.60 s, sys: 1.07 s, total: 1242.67 s > Wall time: 1243.69 s > 7783516108362 > > Since this is 20 minutes CPU time on a fast box we cannot make this a > doctest, even a long one. I guess we need to implement a better > algorithm :p > > > It would be interesting if it gave the same result as Mathematica on any > > of the computers. > > > In[95]:= PrimePi[249999999999999] > > Out[95]= 7783516108362 > > > Dave > > Cheers, > > Michael --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
