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Re: Re: Comparison of Mathematica on Various Computers

On Feb 13, 2006, at 3:15 AM, Ronald Bruck wrote:

> 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).


Is there a drop in replacement of a high speed library for PowerPC ?   
I have now a dual core PowerPC G5 chip at 2Ghz and it is benchmarking  
out not even twice as fast as my old 1.2Ghz G4 used to do.  I  
expected much more...

János

> 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

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