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MathGroup Archive 1995

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Re: Scientific Web - Speedcomparison Mathematica 2

  • To: mathgroup at smc.vnet.net
  • Subject: [mg2616] Re: Scientific Web - Speedcomparison Mathematica 2
  • From: bruck at mtha.usc.edu (Ronald Bruck)
  • Date: Thu, 30 Nov 1995 20:58:06 -0500

In article <49dr6v$aou at dragonfly.wri.com> Stefan Steinhaus <stst at informatik.uni-frankfurt.de> writes:
>>                  Comparison of Mathematica on Various Machines
>> 
>> -------------------------------------------------------------------------------
>> 
>> Author : Stefan Steinhaus (UNI Frankfurt)
>> E-Mail : stst at informatik.uni-frankfurt.de
>> 
>> -------------------------------------------------------------------------------
>> This is the latest version of Mathematica timing tests; (further results are
>> welcome: stst at informatik.uni-frankfurt.de).

[results deleted]

Dunno why every line in this article was double-quoted.  But I'm glad to see
another suite of timing tests.  This one is very heavily weighted toward
Pentia and 486 systems, with a lowly Power Mac 6100/60 as the best Apple
representative, so I'll drop in my timings on a Power Mac 9500/132.

Power Macintosh 9500/132 with 128MB RAM, VM on
ATI graphics board with 4MB VRAM set to 256 colors, 1152x870 screen
Minimal extensions

Tested 27.11.95 by Ronald Bruck, Department of Mathematics, University of 
Southern California.

One correction had to be made to the source code: test 8 has an extra 
right-square- bracket.  This was deleted and the test was re-run without 
restarting the session.  (Presumably no action had been taken, because the 
syntax was rejected.)

In addition, test 9 is broken across two lines, leading to a complaint by 
Mathematica that it is treating the newline as multiplication.  This is not 
an error--it SHOULD be multiplication--but it is not good Mathematica 
programming form, and may affect timings, depending on user preferences for 
display of error messages. 

Note that in the Integrate[1/(1-x^3),x]  speed is VERY heavily dependent on 
whether the integration package has been loaded.  This points up the 
difficulty of constructing timing tests.  Ideally, all tests should be run 
from a FRESHLY STARTED copy of Mathematica, in which one command has been 
executed (to be sure the kernel has loaded)--I usually execute 2+2 to be 
sure.  If the tests are run after some of the commands, e.g. 
ParametricPlot3D, have already been run, it will significantly alter the 
timing tests, so SOME STANDARDS MUST BE SET.  I would suggest to the authors
of this test, and to Karl Unterkofler, the author of another set of tests,
that they create notebooks which (a) make sure the kernel is loaded and
initialized before the tests are run, and (b) make sure the appropriate
packages are pre-loaded; THEN the notebook should automatically run and
record the timing results.


Here are the results:

After starting the session, and executing 2+2 (to be sure the kernel is 
loaded and initialized):


Timing[3^10000;]

0.017 sec

-----------------
Timing[10000!;]

2.783 sec

-----------------
hil = Table[1/(i+j-1), {i,30}, {j,30}];
Timing[Det[hil]]

1.3 sec

-----------------
Timing[ListPlot[Table[Prime[i],{i,10000}],PlotJoined->True]]

1.817 sec

-----------------
Timing[N[Pi,3500]]

0.283 sec

-----------------
First[Timing[Eigenvalues[Table[Random[],{200},{200}]]]]

4.683 sec

-----------------
Timing[Factor[x^92259-1];]

0.967 sec

-----------------
Timing[Integrate[1/(1-x^3),x]]     (* <--- Note correction!! *)

0.733 sec  when Integrate package is not preloaded
0.05  sec  when Integrate package is preloaded

(This took two different timing runs.)

-----------------
Timing[ParametricPlot3D[{r Cos[Cos[r]]Cos[psi], r Cos[Cos[r]]Sin[psi],r
Sin[Cos[r]]},{r,0.001,9Pi/2+0.001}, {psi,0,3Pi/2},PlotPoints->{72,24}]]

3.917 sec  (including warning message display)

-----------------
bx = 6 Cos[u] (1 + Sin[u]);by = 16 Sin[u];rad = 4 (1 - Cos[u] / 2);
X = If[Pi < u <= 2 Pi, bx + rad Cos[v + Pi], bx + rad Cos[u] Cos[v]];
Y = If[Pi < u <= 2 Pi, by,by + rad Sin[u] Cos[v]];
Z = rad Sin[v];
Timing[ParametricPlot3D[{X, Y, Z},{u, 0, 2 Pi}, {v, 0, 2 Pi},PlotPoints ->
{48,12},Axes -> False,Boxed -> False,ViewPoint-> {1.4, -2.6, -1.7}];]

3.367 sec


These results put the 9500 at the top of the rankings, but the stiffest
competition was only a 90 MHZ Pentium.  I'd like to see how some of the
workstations perform on this benchmarks, especially the Alphas, and how
the new P6 200MHZ (or DUAL P6 200MHZ) systems do.

--Ron Bruck








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