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POV's mod(-3, 10) returns -3. I don't have a problem with the
documentation: mod() works as described, returning ((A/B)-int(A/B))*B where
int(A) is not further from 0 than A on a number line.
However I do think that POV's mod() should behave like Perl's, and with
common (I thought) practice, where mod(A,B) lies in the range [0,B) for all
positive B.
Compare the gradient pattern: it used to be mirrored about 0, but post-3.5,
it is a continuous saw-tooth. This new behaviour is what I expect from
mod().
Behaviour for B<0 seems to be debated but for the far more common case of
B>0, I believe mod(A,B) should be >= 0 for all A.
I'm sure the mathematicians in the audience will have their own references,
but here is another: http://en.wikipedia.org/wiki/Modulo_arithmetic
Anybody agree? Anybody care?
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Ard wrote:
> POV's mod(-3, 10) returns -3. I don't have a problem with the
> documentation: mod() works as described, returning ((A/B)-int(A/B))*B where
> int(A) is not further from 0 than A on a number line.
>
> However I do think that POV's mod() should behave like Perl's, and with
> common (I thought) practice, where mod(A,B) lies in the range [0,B) for all
> positive B.
In modulo arithmetic, numbers outside of the 0 to n-1 range simply
aren't in the field.
It would be more precise to call it a remainder function.
Regards,
John
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Ard wrote:
> POV's mod(-3, 10) returns -3. I don't have a problem with the
> documentation: mod() works as described, returning ((A/B)-int(A/B))*B where
> int(A) is not further from 0 than A on a number line.
>
> However I do think that POV's mod() should behave like Perl's, and with
> common (I thought) practice, where mod(A,B) lies in the range [0,B) for all
> positive B.
>
> Compare the gradient pattern: it used to be mirrored about 0, but post-3.5,
> it is a continuous saw-tooth. This new behaviour is what I expect from
> mod().
>
> Behaviour for B<0 seems to be debated but for the far more common case of
> B>0, I believe mod(A,B) should be >= 0 for all A.
>
> I'm sure the mathematicians in the audience will have their own references,
> but here is another: http://en.wikipedia.org/wiki/Modulo_arithmetic
>
> Anybody agree? Anybody care?
POV-Ray follows what the ISO standards for C and C++ use as mod.
Thorsten
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"Ard" <ard### [at] waikato acnz> wrote:
> Anybody agree? Anybody care?
As someone who uses congruences modulo a positive integer quite a bit, I
also am used to thinking of mod(a,b) as returning the "principal value" of
the congruence class (i.e. the number 0 <= r < b), but the fixes are pretty
easy, albiet frustrating when you forget the POVRay definition. And since
I don't use C, C++ or Perl, I can't comment on what's "better," or "more
common" from a programming point of view, though Thorsten's usually pretty
definitive on those questions.
Dave Matthews
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