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Re: Where's the Speed?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg19852] Re: [mg19764] Where's the Speed?
*From*: wexler at neptune.phys.ufl.edu (Carlos Wexler)
*Date*: Sun, 19 Sep 1999 01:20:36 -0400
*Organization*: University of Florida, Gainesville
*References*: <7rshul$3i3@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Repeating the same calculations in a "SunOS einstein 5.6 Generic_105181-13
sun4u sparc SUNW,Ultra-4" w/ M3 gives 6.43 s and 4.23 s respectively...
Not much gain from loosing the aritrary precision...
Carlos
In article <7rshul$3i3 at smc.vnet.net>,
Richard Bills <Richard_Bills at email.msn.com> wrote:
[...]
>Compiling also bypasses arbitrary precision math, which can be 25 times
>slower than machine precision math in Mathematica. For example, compare the
>computation times of these (on an ancient computer):
>
>b1 = Table[i^10 + 7, {i, 100000}]; // Timing (* arbitrary precision math
>*)
>{98.59 Second, Null}
>
>b1[[100000]]
>100000000000000000000000000000000000000000000000007
>
>b2 = Table[N[i]^10. + 7.0, {i, 100000}]; // Timing (* machine precision
>math *)
>{3.19 Second, Null}
>
>b2[[100000]]
>1.*10^60
>
>The C code shown below (Borland Builder 3.0) performs the same computation
>in 0.7 seconds ( 7 seconds for 10^6 values), and is therefore about 5 times
>faster than machine precision code in Mathematica. However, this C code
>does not give the correct result that Mathematica gives.
>
>_________________________________________________________________________
>#pragma hdrstop
>#include <condefs.h>
>#include <time.h>
>#include <stdio.h>
>#include <dos.h>
>#include <math.h>
>
>
>
>
>//--------------------------------------------------------------------------
>-
>#pragma argsused
>int main(int argc, char **argv)
>{
> time_t tstart,tend;
>
> tstart=time(NULL);
>
> double *data = new double[1000000];
>
> for(int i=1; i<=1000000; i++)
> {
> data[i-1]=pow(i,10)+7;
> }
>
> tend=time(NULL);
>
> printf("computation time: %d\n", tend-tstart);
> printf("end result: %f\n",data[1000000-1]);
>
> int tin;
> scanf("%d", &tin);
>
>
>
>
> return 0;
>}
>
>____________________________________________________________________
>
>If the computation is replaced with the expression ((i*2.3467) + 7.)/3., the
>C version is only 4 times faster than Mathematica, which is not bad, all
>things considered.
>
>I think it would be helpful if WRI published a book or technical notes on
>computational optimization in Mathematica. They are in the best position to
>do so.
>
>Hope that helps.
>
>
>Sincerely,
>
>Richard E. Bills
>Tucson, AZ, USA
>
>
>
>
>-----Original Message-----
>From: Kevin J. McCann <kevin.mccann at jhuapl.edu>
To: mathgroup at smc.vnet.net
>Subject: [mg19852] [mg19764] Where's the Speed?
>
>
>>I have read and heard a lot of hype about Mathematica 4.0
>>
>>"featuring a
>> New Generation of
>> Fast Numerics"
>>
>>e.g. on www.wri.com .
>>
>>However, in the real world it is hard to find anything to get excited
>about.
>>I have had several disappointing results from 4.0, here are the latest:
>>
>>On a P450/NT I ran a very simple Crank-Nicholson integration of a
>>one-dimensional quantum free-particle wave-packet with x-dimensioned to
>1001
>>points and time to 401 points - no error checks or adaptive stepsize, just
>>plug-and-chug. Runtime under 4.0 was 501 seconds, 3.0 was 480 seconds, but
>>who's quibbling; however, in FORTRAN this ran in 8 seconds. I don't even
>>consider this to be "fast numerics", but 501 seconds sure isn't. I would
>>like to know where all this speed is so I can use some of it, or am I
>>missing something?
>>
>>When I ran the FORTRAN code and then read it into Mathematica, it still was
>faster
>>than the Mathematica code alone, although the ReadList I used on the ASCII
>>file did take some time. When I upped the dimensions to 2001 x 1001, the
>>FORTRAN ran in about 40 s - most of this is for the output; however, when I
>>tried to read it in to Mathematica, it took forever, and on the subsequent
>plot it
>>bombed the Kernel. I then made the mistake of saving the NB which managed
>>to acquire an error so that I can't open it anymore - 6 Mb of useless NB!
>>
>>
>>
>>--
>>
>>Kevin J. McCann
>>Johns Hopkins University APL
>>
>>
>>
>>
>>
>
>
>
>
--
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