On Tue, 2007-07-31 at 22:16 -0700, Justin C. Walker wrote: > > On Jul 31, 2007, at 18:36 , William Stein wrote: > > > > > Hi, > > > > Just to extend this thread some more, a few remarks. > > While we're extending this, here's my $0.02 canadian (:-})
[...] > Checking partition count computation: > > On a Core 2 Duo 2.33 Mhz, computing the number of partitions of 10^9: > Mathematica 5.2 (PartitionsP[10^9]: 95.5115 s > Sage 2.7.2.1 (number_of_partitions(10^9): 125.2 s > Jon Bober's code (i386: 'jb 1000000000'): 160 s > > I wonder why our Core 2 Duo timings are so different? > That is puzzling. Are you sure that you have the latest version of the code? The source file should have 'Version .3' at the top. You can get the latest version, or at least that latest version minus some memory leak fixes, via hg_sage.pull(), or from http://www.math.lsa.umich.edu/~bober/partitions_c.cc The last version I posted to the list was significantly slower than what I have now (especially since I think I accidently had significant improvements commented out in the last code I posted to the list.) > All of the executables are "i386" binaries (32-bit x86). > > One oddity: Jon Bober's code produced a value ending in > '30457526857797923685688339', while Mathematica and SAGE produced one > ending in '30457526831036667979062760', so they differ. > I am fairly confident that the answer ends in '339', since I have seen it so many times while testing my code. In fact, this is what is in the graphic on page 5 (page 27 of the pdf) of the Mathematica book. Wikipedia doesn't 'know' any congruences that p(10^9) should satisfy, so I can't use that to check the value. I'll try to figure out what the right answer should be. If your willing, try computing p(10^9 + 139) with all three. The answer should be divisible by 5, 7, and 11. (We should have been using this as a test case all along.) Incidentally, I while I was writing this email, some tests I was running just finished. The latest version of my code and the current version of sage both give the answer ending in '339'. If Mathematica and SAGE (ie PARI?) both give the same wrong answer, then there might be something fishy going on. > Justin > > -- > Justin C. Walker, Curmudgeon at Large > Institute for the Absorption of Federal Funds > ----------- > If it weren't for carbon-14, I wouldn't date at all. > ----------- > > > > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
