On Thursday 22 May 2008, Bill Hart wrote: > Hi Martin, > > This version works great. Here are the times on my unburdened 2.8Ghz > Opteron. First the Magma times, then the times for an older version of > m4ri and now, for the first time ever, the new Magma beating times: > > 10000x10000: 2.940s 3.13s 2.25s > > 16384x16384: 9.250s 12.96s 8.80s > > 20000x20000: 16.57s 22.43s 15.48 > > 32000x32000: 59.1s 90.2s 57.8s
Bill, I suppose that also means that now we actually beat (or are close to beating) Magma on the C2D "for real". My M4RI times are quite similar on the C2D as your times on your Opteron. But my version of Magma (on the C2D) is much worse than your version of Magma (on the Opteron). So it is probably best to assume at least your times for Magma on my machine too. Martin PS: I wonder if this argument makes sense: We have a complexity of n^2.807 and a CPU of say 2.333 Ghz which can operate on 64 bits per clock (128 if we use SSE2). So if we had optimal code (no missed branch predictions, no caching issues, everything optimal) we would expect a running time of n^2.807 / 64 / 2.333 / 10^9 If we plug in 20,000 for n we'd get 7.923 seconds w.o. SSE2 and 3.961 with SSE2. So our implementation (12.2 s) is a factor of ~1.5 or ~3 away from being optimal? Does that sound correct or complete bollocks? -- name: Martin Albrecht _pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99 _www: http://www.informatik.uni-bremen.de/~malb _jab: [EMAIL PROTECTED] --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
