PowerMac Comparison

• To: MATHGROUP at yoda.physics.unc.edu
• Subject: PowerMac Comparison
• From: Richard Mercer <richard at rmercer.wright.edu>
• Date: Tue, 14 Jun 1994 12:34:40 -0700

```MathGroupers,

Here is a contribution to the various requests for comparing the PowerMac to
Motorola-based Mathematica platforms. I apologize for the lack of Intel-based
and Unix workstation computers; perhaps others who have more convenient access
to them can fill us in. I tested a PowerMac 7100AV, a color NeXTstation, a
Centris 650, and a Mac IIcx with 50mhz Daystar acceleration (w/fpu).

I selected five computations making a variety of demands on Mathematica. I have
done this primarily to satisfy my own curiosity (having already purchased a
PowerMac); unfortunately two of the computations are not generally
reproduceable. There are certainly many aspects of Mathematica not tested for
here, but I doubt that any results dramatically different will be discovered.

Timings were generated by Mathematica using the Preferences:Action checkbox
"Display clock timing for each evaluation". The accuracy of these was checked
by stopwatch as well. On the NeXT the timings were done by stopwatch alone as
the timings given by Mathematica were inaccurate. Computations 1-3 were run
several times and the best result taken. Computations 4 and 5 were run once.

Mathematica version 2.2.2 was used on the PowerMac and the Mac IIcx; the other
two used version 2.2.

Computation #1: Arithmetic - polynomial
f[x_]:= 4x-4x^2;
Nest[f,0.6,5000]

Results #1:
PowerMac 7100 601/66mhz: 5.87 seconds          1.00
NeXT 68040/25mhz: 14.84 seconds                2.53
Mac Centris 650 68040/25mhz: 18.02 seconds     3.07
Mac IIcx 68030/50mhz: 38.33 seconds            6.53

Computation #2: Arithmetic - transcendental
f[x_]:= BesselJ[0,x];
Nest[f,0.6,2500]
Results #2:
PowerMac 7100 601/66mhz: 11.28 seconds         1.00
NeXT 68040/25mhz: 25.79 seconds                2.29
Mac Centris 650 68040/25mhz: 46.88 seconds     4.16
Mac IIcx 68030/50mhz: 81.12 seconds            7.19

Computation #3: Graphics - 3D
Plot3D[Sin[x y],{x,-2,2},{y,-2,2},PlotPoints->30];
Results #3:
PowerMac 7100 601/66mhz: 6.70 seconds          1.00
NeXT 68040/25mhz: 14.84 seconds                2.21
Mac Centris 650 68040/25mhz: 11.12 seconds     1.66
Mac IIcx 50mhz: 15.32 seconds                  2.29

<<calcE.m  (a package slightly over 200K in size)
Results #4:
PowerMac 7100 601/66mhz: 14.42 seconds         1.00
NeXT 68040/25mhz: 66.85 seconds                4.64
Mac Centris 650 68040/25mhz: 49.13 seconds     3.41
Mac IIcx 50mhz: 78.85 seconds                  5.47

Computation #5: Complex 2-D Graphics and Logic
Plot[4x^2+9y^2=36,{-3,3},{-2,2},Frame,
Grid[{0.25,0.25},Fill[4x^2+9y^2=36]]
];
Results #5:
PowerMac 7100 601/66mhz: 19.88 seconds         1.00
NeXT 68040/25mhz: 36.12 seconds                1.82
Mac Centris 650 68040/25mhz: 58.18 seconds     2.93
Mac IIcx 50mhz: 103.47 seconds                 5.20

Analysis: Results for the various Quadra models can likely be projected from
the Centris data. It seems clear that the PowerMac will be generally 2-4 times
faster than a Quadra at most tasks. Surprisingly the greatest speed improvement
is in the loading of packages, for which not disk speed but rather kernel
processing speed is the bottleneck.
Computation #3 is almost entirely based on Postscript rendering speed as the
values needed for plotting are computed almost instantly. Based on the
relatively poor performance here, it seems that Postscript rendering is not
entirely in native mode, or at least is not fully optimized. (If it were
entirely emulated, there would probably be no improvement at all.) The poor
result of the NeXT here is likely based on a larger number of pixels to be
rendered to generate a graphic of standard size.
Claims have been published that Mathematica is
"up to 10 times faster on a PowerMac than on any 680x0-based machine and
renders graphics up to five times faster." (MacWeek, 5.30.94) One wonders what
680x0 machine they were thinking of. Actually it is 15-20 times faster than a
stock Mac IIcx, and probably 50 times faster than the original 8mhz 68000 Mac!
Hopefully the results above will give you a better picture.
Note: Beware of comparisons based on the Mathematica "Timing" command, which
clock cpu time only and not actual elapsed time.

Semi-Disclaimer: I have no direct connection with either Apple Computer or
Wolfram Researcher (aside from being recognized by the latter as a "Mathematica
Developer"). However I am a long-time user of products from both and am
interested in seeing both be successful.

If you are curious about calcE, demonstration files are available on
MathSource, items 0204-691 (for Mathematica v2.0) and 0206-435 (for Mathematica
v2.1 and higher). The full documentation is available as item 0206-750.
Or you can email me for further information.

*********************************************************************
Richard Mercer                             513-873-2191 office
Department of Mathematics and Statistics   513-873-2785 message
Wright State University                    513-873-3301 fax
Dayton, OH 45435                           NeXTmail welcome!
richard at rmercer.wright.edu        or       rmercer at desire.wright.edu
*********************************************************************

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