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Hello List,
yesterday I installed the 3.1e version of PovRay on my Windows NT4 sp3
computer and discovered a bug in the mathematics part of PovRay:
the mod(A,B) function is meant to provide the modulus of A divided by B.
Per definition the modulus is a NON-NEGATIVE INTEGER value. However if
you ask PovRay to perform modulus calculations with A being negative you
get a negative result:
PovRay definition
mod(0,5) 0 0 OK
mod(1,5) 1 1 OK
mod(2,5) 2 2 OK
mod(3,5) 3 3 OK
mod(4,5) 4 4 OK
mod(5,5) 0 0 OK
mod(6,5) 1 1 OK
mod(7,5) 2 2 OK
BUT
mod(0,5) 0 0 OK
mod(-1,5) -1 4 WRONG
mod(-2,5) -2 3 WRONG
mod(-3,5) -3 2 WRONG
mod(-4,5) -4 1 WRONG
mod(-5,5) 0 0 WRONG
mod(-6,5) -1 4 WRONG
mod(-7,5) -2 3 WRONG
as I noticed this bug was already present in v3.0 of PovRay for win32
and thus I'm wondering if it's a bug or a feature. At least it should be
noted in the documentation that PovRay does not use the standard
definition of the modulus calculation.
Uwe.
-------------------------------------------------
Uwe Zimmermann uwe### [at] geocities com
Dipl. Phys. uwe### [at] elekthse
Department of Electronics
Solid State Electronics
Royal Institute of Technology
Electrum 229
S-16440 Kista-Stockholm
Sweden
http://www.ele.kth.se/FTE/personal/pers_uwe.html
------------------------------------------------
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Uwe Zimmermann wrote:
> the mod(A,B) function is meant to provide the modulus of A divided by B.
> Per definition the modulus is a NON-NEGATIVE INTEGER value. However if
> you ask PovRay to perform modulus calculations with A being negative you
> get a negative result:
...
> as I noticed this bug was already present in v3.0 of PovRay for win32
> and thus I'm wondering if it's a bug or a feature. At least it should be
> noted in the documentation that PovRay does not use the standard
> definition of the modulus calculation.
I think you are wrong. As from my crypography course I know a definition
for modulus, which also allows negative return values. The modulus function
of POV just behaves as I know it from the cryptography course. So I think
the POV modulus function is correct.
By the way if you want always positive modulus values than simply calculate
mod(A,B) if A is positive and
B+mod(A,B) if A is negative
This should give you the definition you know for the moduls function.
Yours Axel
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In article <376F47F5.89E8568D@ele.kth.se> , Uwe Zimmermann <uwe### [at] elekthse>
wrote:
> Hello List,
>
> yesterday I installed the 3.1e version of PovRay on my Windows NT4 sp3
> computer and discovered a bug in the mathematics part of PovRay:
>
> the mod(A,B) function is meant to provide the modulus of A divided by B.
> Per definition the modulus is a NON-NEGATIVE INTEGER value. However if
> you ask PovRay to perform modulus calculations with A being negative you
> get a negative result:
>
> PovRay definition
>
> mod(0,5) 0 0 OK
> mod(1,5) 1 1 OK
> mod(2,5) 2 2 OK
> mod(3,5) 3 3 OK
> mod(4,5) 4 4 OK
> mod(5,5) 0 0 OK
> mod(6,5) 1 1 OK
> mod(7,5) 2 2 OK
>
> BUT
>
> mod(0,5) 0 0 OK
> mod(-1,5) -1 4 WRONG
> mod(-2,5) -2 3 WRONG
> mod(-3,5) -3 2 WRONG
> mod(-4,5) -4 1 WRONG
> mod(-5,5) 0 0 WRONG
> mod(-6,5) -1 4 WRONG
> mod(-7,5) -2 3 WRONG
>
> as I noticed this bug was already present in v3.0 of PovRay for win32
> and thus I'm wondering if it's a bug or a feature. At least it should be
> noted in the documentation that PovRay does not use the standard
> definition of the modulus calculation.
You are right that the C library fmod function (which the POV-Ray mod
function is based on) does not return the mathmatically defined values of a
modulus operation. This is simply the way this POV-Ray function is defined
(because of the internal representation of floating point numbers).
Thorsten
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Axel Baune schrieb:
> I think you are wrong. As from my crypography course I know a definition
> for modulus, which also allows negative return values. The modulus function
In math, they usually call this "remainder", defined like
rem(a,b)=a-b*trunc(a/b).
The modulus is defined as Uwe wrote, i.e.
mod(a,b)=a-b*floor(a/b)
Compilers etc. just say
practicalmod(a,b)=a-b*int(a/b)
where int() is required to act like floor() on positive
arguments and left to the implementor for negative ones.
Ususally it behaves like trunc(), since this is what chips
do.
Ralf
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Uwe Zimmermann <uwe### [at] elekthse> wrote:
: PovRay definition
: mod(-5,5) 0 0 WRONG
Both povray and definition are wrong?-)
--
main(i,_){for(_?--i,main(i+2,"FhhQHFIJD|FQTITFN]zRFHhhTBFHhhTBFysdB"[i]
):5;i&&_>1;printf("%s",_-70?_&1?"[]":" ":(_=0,"\n")),_/=2);} /*- Warp -*/
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Nieminen Mika wrote:
>
> : PovRay definition
>
> : mod(-5,5) 0 0 WRONG
>
> Both povray and definition are wrong?-)
Sorry - Cut and Paste Error 101 ;-))
Uwe.
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