In article <3901AA4C.28062CFA@peak.edu.ee> , Margus Ramst 
<mar### [at] peakeduee>  wrote:

> Yes, those conditions should be equivalent.

The are equivalent mathematically, but not in terms of floating-point
arithmetic.

> It seems to be a precision-related issue, since the correct result is achieved
> by adding some very small value to D in the condition (X <= D). Also, when the
> loop is shorter, e.g. D=1, the result is correct for X = X + 0.1
> The second version works because for some reason the condition (X = D)
> evaluates correctly. However, the conditions like (X != D) (X <= D) etc do
> not. I tested this under official 3.1g (Windows & Linux) and Megapov 0.4g
> (Windows) and due to the inconsistency regarding conditional operators, it
> looks like a bug to me. Comments?

Technically it is not a bug but a limit in floating-point precision.  The
reason why the first one works is rather simple:  POV-Ray already contains a
workaround for "is equal" comparisons as well as "is not equal" ones, but
not for smaller/greater (or equal) than ones.  In reality POV-Ray fixes the
problem for the equal and not equal cases with this method:

condition:   f1 = f2
POV-Ray:     if (fabs(f1 - f2) > EPSILON) then false else true

condition:   f1 != f2
POV-Ray:     if (fabs(f1 - f2) > EPSILON) then true else false

The other comparison operators do not take EPSILON into account.  So
practically POV-Ray should contain a workaround for these cases as well.
However, you can also do something like  #while (X <= D+0.0001)  and it will
work.
Further, the documentation should make clear that floating-point math is
_not_ precise. Especially in long operations the error will build up: There
are some more exact specs for this, but you can safely assume about one
digit per operation. Thus, the example above will accumulate a reasonable
error after its twenty iterations.


     Thorsten


____________________________________________________
Thorsten Froehlich
e-mail: mac### [at] povrayorg

I am a member of the POV-Ray Team.
Visit POV-Ray on the web: http://mac.povray.org

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