Re: Comparison of MMA on Various Machines

• To: mathgroup at smc.vnet.net
• Subject: [mg2738] Re: Comparison of MMA on Various Machines
• From: Gerhard Braunshausen <braunsha at EMBL-Heidelberg.DE>
• Date: Mon, 11 Dec 1995 22:03:26 -0500

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

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