On Tue, May 5, 2009 at 11:43 AM, VictorMiller <victorsmil...@gmail.com> wrote: > > 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:
Wow, I didn't know Dell was selling computers back in 1986. :-) [just kiddin'] > > 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 Wow, nice! Give my your C code!! > > > 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 > > > -- William Stein Associate Professor of Mathematics University of Washington http://wstein.org --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
