[Shootout-list] Mandelbrot Set for CMUCL and SBCL 2nd try

[Will M. Farr]

Hello all,

Not that I'm an expert numerical analyst, but it seems to me that most 
scientists would definitely accept small floating point differences, 
particularly in a computation which is known to be unstable.  For 
example, when computing trajectories of particles in a "dynamically 
rich" system (i.e. a chaotic one), nobody cares about the exact points 
on the trajectory; they compute statistical properties of the 
trajectories---maybe the heat, or the velocity dispersion or something 
similar---instead.  I suppose that, ideally, the correct computation 
here could be to determine the fractal dimension of the produced 
mandelbrot set, and see that it agreed across implementations (I'm not 
suggesting that you do that, just that this is the sort of quantity 
that a mathematician would compare across algorithms or programs).

Will


On 29 Mar 2005, at 11:46 AM, Greg Buchholz wrote:

> --- Pascal Obry <pascal@obry.net> wrote:
>>
>> Greg,
>>
>>>     Try chaning line 35 from...
>>> (when (not (dotimes (n 50)
>>> ...to...
>>> (when (not (dotimes (n 51)
>>
>> I tried something like that for the Ada bench. It turns out that
>> swaping some
>> lines to do the computation and test in the very same way as C did fix
>> the
>> problem. Yet I think this is not a good solution.
>
>    With some very well reasoned argument, you might be able to convince
> me that we shouldn't require our floating point benchmarks to be
> implemented the same.  But not wanting to correct a fence post error is
> not one of those arguments.  And I think any die-hard numerical guy 
> would
> scoff at a language which wouldn't allow him to implement his algorithm
> correctly.  The root problem is that fixed precision floating point 
> math
> is neither distributive nor associative, so you can't order your
> calculations willy-nilly and expect the same answer.  So the question 
> is,
> should the shootout require absolute exactness, or should we allow a
> little bit of roundoff error caused by the common misconception that 
> our
> floating point hardware is infinitely precise?  It's an interesting
> question that the shootout needs to decide.
>
> Faithfully,
>
> Greg Buchholz
>
>
> P.S.  A well reasoned argument might consist of stating that the
> mandelbrot set isn't well-conditioned or numerically stable.  But that
> doesn't address the question about the other floating point benchmarks.
> Also note that there are currently 20 programs which are able to 
> produce
> the exact result on the mandelbrot test.
>
>
>
>
> 		
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