[galib] Floats vs Doubles and GALib

[Peter Jay Salzman]

Hi Sri,

Thanks for the kudos!   :)

It was actually 2 *minutes*, which is a long time in casual numerical
computing use.   ;)

>From what I understand, a Windows machine won't see this additional time.
In fact, double may be slower on Windows since those 64 bit calculations
won't be performed on that platform.  It also suggests that Linux has a
slight speed disadvantage in computation with floats, but the results
would be more accurate.  But I'm really not an expert in this.  It's just
what I gather from that link which said that all fp calcs on Linux and MacOS
are always done internally to 64 bits.

It also might depend on how the app runs, too.  I think that the wide
precision internal calculation only applies to register to register
operations.  If results are put back into main memory, you're still moving
an extra 4 bytes with a double.  I wish I knew more about this stuff...

When I return to work on Monday, I plan on redoing the benchmark on a
Windows machine.

Pete



On Fri 23 Nov 07, 10:59 PM, Sri <kskk02 at gmail.com> said:
> Cool analysis !!! Is that 2 mins or 2 sec's extra ? No idea why they used 
> float's. Double's is what i always use considering memory limitations isnt 
> really a big issue anyway.
>
> sri
>
> ----- Original Message ----- From: "Peter Jay Salzman" <p at dirac.org>
> To: "GALib Mailing List" <galib at MIT.EDU>
> Sent: Friday, November 23, 2007 7:11 PM
> Subject: [galib] Floats vs Doubles and GALib
>
>
> Hi All,
>
> This afternoon I made a 2nd copy of GALib and modified it so that it uses
> doubles instead of floats.  I ran some tests to see whether the difference
> was noticeable.  It was, by quite a bit.
>
> My objective function and initializer:
>
>
>   TYPE objective( GAGenome &g )
>   {
>      GARealGenome& genome = ( GARealGenome& )g;
>
>      TYPE x = genome.gene(0);
>      TYPE y = genome.gene(1);
>      TYPE z = genome.gene(2);
>
>      return exp( -pow(x - 1.0, 2) - pow(y - 2.0, 2) - pow(z - 3.0, 2) );
>   }
>
>   TYPE IC[] = { 0.0, 0.0, 0.0 };
>
>   void initializer( GAGenome &g )
>   {
>      GARealGenome& genome = ( GARealGenome& )g;
>      for( int i = 0; i < 3; ++i )
>         genome.gene(i, IC[i]);
>   }
>
>
> I used a GARealGenome with alleles:
>
>   GARealAlleleSetArray alleles;
>   alleles.add( 0.0, 1.1, GAAllele::INCLUSIVE, GAAllele::INCLUSIVE);
>   alleles.add(-2.0, 4.5, GAAllele::EXCLUSIVE, GAAllele::INCLUSIVE);
>   alleles.add(-4.0, 4.0, GAAllele::EXCLUSIVE, GAAllele::INCLUSIVE);
>   GARealGenome genome(alleles, objective);
>   genome.initializer(initializer);
>
> and a GASteadyState GA.
>
>
>
> The basic results (relative error) are here.  The numbers represent the
> average relative error in the result at a given population size.  The
> average was taken over 3 trials, and by relative error I mean (true -
> numerical)/ true * 100 expressed as a percentage.
>
>   popSize      double      float
>    1500         1.14        2.41
>    5000          .45       1.39
>   10000          .02         .73
>
> In the last 2 trials at N=10000, the "double GA" managed to get the exact
> answer to 7 digits.
>
> In the last 2 trials, I recalled reading that double arithmetic can be
> faster than float arithmetic in C/C++ due to unintentional widening and
> subsequent narrowing of the datatype that can slow down the processor on
> Linux and MacOS [1].  So I timed the last two trials, and here are the times
> for execution (wall clock, unloaded) for the last 2 trials at a population
> of N=10000 in seconds:
>
>   double     float
>   17.1921    19.0479
>   17.6359    19.0986
>
> Two minutes is quite a lot when you're sitting in front of a computer
> waiting for a result.
>
> So I wanted to ask: why does GALib use floats and not doubles?
>
> I created a detailed Excel file that shows results, calculations, and
> timings for the various trials.  If anyone wants to see it, let me know.
>
> I probably can't release the "double GALib" code since this is a project for
> work, even though I spent my day off doing it (I had to modify it further to
> make GALib compile as a DLL under MS Windows (which I use at work).
> However, I don't think anyone would mind if I gave out the program I wrote
> to do the benchmarks.
>
> Thanks,
> Pete
>
> ps- If someone could answer my question about unconstrained genes, I'd
> greatly appreciate it!
>
>
> [1] Linux always performs register to register calculations in double
> precision, while Windows does not.
>
>   http://www.intel.com/support/performancetools/fortran/sb/cs-007783.htm
>
> -- 
> GPG Fingerprint: B9F1 6CF3 47C4 7CD8 D33E  70A9 A3B9 1945 67EA 951D
> Last night I dreamt of 09-f9-11-02-9d-74-e3-5b-d8-41-56-c5-63-56-88-c0
>
> "A mathematician is a machine for converting coffee    p at dirac.org
> into theorems."     -- Paul Erdös                     http://www.dirac.org
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-- 
GPG Fingerprint: B9F1 6CF3 47C4 7CD8 D33E  70A9 A3B9 1945 67EA 951D
Last night I dreamt of 09-f9-11-02-9d-74-e3-5b-d8-41-56-c5-63-56-88-c0

"A mathematician is a machine for converting coffee    p at dirac.org
 into theorems."     -- Paul Erdös                     http://www.dirac.org