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 >> >> >> >> >> > > > > --