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Re: Comparison of Mathematica on Various Computers

• To: mathgroup at smc.vnet.net
• Subject: [mg64355] Re: Comparison of Mathematica on Various Computers
• From: Ronald Bruck <bruck at math.usc.edu>
• Date: Mon, 13 Feb 2006 03:15:20 -0500 (EST)
• References: <200602090745.CAA19418@smc.vnet.net> <200602100713.CAA15024@smc.vnet.net> <dsk8m8$i9l$1@smc.vnet.net> <dsmueo$da0$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

In article <dsmueo$da0$1 at smc.vnet.net>, albert <awnl at arcor.de> wrote:

> Renan wrote:
> 
> > On 2/10/06, fizzy <fizzycist at knology.net> wrote:
> >> Can someone explain why AMD does so well on this test and Pentium does so
> >> poorly by comparison??
> >> I am planning to buy a new  computer and these tests seem to indicate
> >> that a Mathematica user should buy an AMD machine.
> > 
> > I'd guess that an Athlon 64 CPU is faster than a Pentium 4
> > (32-bit).(most AMD CPU's that I see in the benchmark are 64-bit)
> 
> hm, I hoped for good answers to that, but my guess is also that it is the
> 64-bit vs. 32-bit which explain the difference to a big extent. Obviously
> it will be less often necessary to use software arbitrary precision
> arithmetic and when you have to it should be a big advantage to be able to
> work with words of double size.
> 
> Maybe it would be worth to check whether there are "unfair" tests within the
> benchmark like numerics with a precision which can be done in hardware on a
> 64-bit processor but needs to be done in software on a 32-bit processor?
> This is just another case where just a single number is not enough to
> decide whether one or the other computer is faster for what you want to do
> with it. So you should probably look into the results for specific parts of
> the benchmark if that's possible...
> 
> > Does Mathematica support special instructions like SSE?
> 
> no idea...

I'm pretty sure the answer is "yes".  It's my understanding that
Mathematica now uses the Gnu Multi-Precision Library, which is
certainly optimized for P4 and (mostly) for AMD64 (but not for
PowerPC).  GMP certainly uses SSE.

There is plenty of documentation on the GMP website,
<http://swox.se/gmp>, as to why 64-bit is so much faster than 32-bit. 
(Four times faster, at the same clock speeds, in multiplying
high-precision floating-point numbers).  See, for example,

  <http://www.swox.se/gmp/32vs64.html>

IIRC there's also (floating around SOMEWHERE as a link on this website,
but I can't find it right now) a comparison of instruction timings
between AMD and P4.  Finally, if you use AMD64 you should try the
64-bit patches at

  <http://www.lix.polytechnique.fr/Labo/Pierrick.Gaudry/mpn_AMD64/>

(YMMV--I had some trouble getting them to work).  I don't know how to
integrate these into Mathematica, either.  (Just use the updated
libraries in /usr/local, or wherever your GMP installation is?)

Finally, the GMP benchmarks are at

     <http://www.swox.com/gmp/gmpbench.html>

comparing processor-by-processor.

I, for one, would certainly appreciate comments by WRI technical
experts on these issues.

--Ron Bruck

• Follow-Ups:
  • Re: Re: Comparison of Mathematica on Various Computers
    • From: János <janos.lobb@yale.edu>

• References:
  • Comparison of Mathematica on Various Computers
    • From: karl unterkofler <karl.unterkofler@fhv.at>
  • Re: Comparison of Mathematica on Various Computers
    • From: "fizzy" <fizzycist@knology.net>