Re: Comparison of MMA on Various Machines

*Subject*: [mg2738] Re: Comparison of MMA on Various Machines*From*: braunsha at EMBL-Heidelberg.DE (Gerhard Braunshausen)*Date*: Mon, 11 Dec 1995 22:03:26 -0500*Approved*: usenet@wri.com*Distribution*: local*Newsgroups*: wri.mathgroup*Organization*: Wolfram Research, Inc.

thank you all for the many contributions to the above topic To summarise what has been suggested: the timely performance of mathematica 1) depends primarily on the integer speed of the processor (killough at wagner.convex.com ) 2) scales linearly with the clock-rate of the processor (ianc at wri.com ) 3) depends on required packages having been preloaded or not (bruck at mtha.usc.edu) 4) depends on the quality of the compilers used (bouldin at enh.nist.gov) Now I have performed the following benchmark tests on our machine: Sparcstation 10, having two 40Mhz SuperSparc processors with 1Mb cache each 96Mb physical RAM , operating Solaris 2.4 After executing 2+2 to load and initialise the kernel: Timing[3^10000;] 1.st run 2.nd run Factor * 9500/132Mhz/128MB 0.117 sec 0.117 sec 10 .017 sec ----------------- Timing[10000!;] 20.85 sec 0. sec (!!) ~8 or .001 2.783 sec ----------------- hil = Table[1/(i+j-1), {i,30}, {j,30}]; Timing[Det[hil]] 7.0 sec 7.0 sec 5-6 1.3 sec ----------------- Timing[ListPlot[Table[Prime[i],{i,10000}],PlotJoined->True]] 5.53 sec 5.32 sec ~3 1.817 sec ----------------- Timing[N[Pi,3500]] 0.283 sec 0. sec (!!) 1 or .001 .283 sec ----------------- First[Timing[Eigenvalues[Table[Random[],{200},{200}]]]] 13.72 sec 13.27 sec ~3 4.68 sec ----------------- Timing[Factor[x^92259-1];] 3.02 sec 3.02 sec ~3 .97 sec ----------------- Timing[Integrate[1/(1-x^3),x]] 0.82 sec 0.12 sec ~1 or ~2 .733 or .05 sec NOTE: the PowerMac 9500 values were taken from bruck at mtha.usc.edu Expectation: The clockrate suggests a factor 3 slower Sparc timing CONCLUSION: the Eigenvalue, Factor and ListPlot examples perform as expected, although factoring a polynomial and plotting a list does not have any connection to floating point operation. On the other hand, calculating Pi to 3500 digit precision, does have a bearing to floating point speed. The result is thus surprising. A Factor 1 the first time round, and then the SuperSparc is about 1000 times faster during the second run. Why is that? Calculating the Determinant is 5-6 times slower on Sparc; whereas one could expect only a factor 3. The Integer Speeds relevant to calculating a factorial and an integer power yields factors 8 - 10; However, Sparcs were supposed to have better integer performance. So this too is a puzzling result. Puzzling is also, that in the second run, the factorial is performed nearly instantaneously. THUS: there is no clear trend discernible to me, which would indicate that the integer or floating point speed of the processors and/or the clockrates are to be held responsible for the differences. To really know, what we are comparing here, one would need to know the detailed algorithms actually being performed by mathematica for each of the examples. regards --gerhard