On Tue, May 6, 2008 at 11:55 AM, David Harvey <[EMAIL PROTECTED]> wrote: > > > On May 6, 2008, at 2:19 PM, Mike Hansen wrote: > > >> Probably not so cool, since it would be like 50 machines vs one > >> machine. > > > > Sure, but the Mathematica blog post is scalablity: "In Mathematica, a > > core principle is that everything should be scalable. So in my job of > > creating algorithms for Mathematica I have to make sure that > > everything I produce is scalable." > > But Pari's algorithm is already parallelisable (just farm off a bunch > of euler factors to each thread).
Yep. I was about to point out that I was joking in my remark about parallelizing your code. I certainly agree with the above suggested way to parallelize computing zeta. > > The only advantage my algorithm has in "scalability" is that each > thread needs only O(1) memory, instead of O(n log n) which would be > required for Pari's algorithm. So if memory were tight, but you had > lots of processors, and your n was really big, then perhaps this > algorithm would win. But when I think about the actual numbers > involved, the economics just don't work out. Even 80 processors is a > pathetically small number, given a 50x serial slowdown in the > algorithm. You would need thousands of cpus to even consider this > approach. And even then, it would only be worthwhile if each cpu had > very limited memory. Hmm... That's exactly the configuration of a lot of interesting supercomputers these days. See http://domino.research.ibm.com/comm/research_projects.nsf/pages/bluegene.index.html They have these single-cabinet tiny memory 1024 processor machines... -- 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 [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
