[Oberon] Modulus on negative number
Tomas Kral
thomas.kral at email.cz
Mon May 15 11:28:17 CEST 2017
Hi,
At last I took some interest in this MOD'ulo discussion. I wonder how
it is (un)defined in Math / Oberon
x DIV 0
0 MOD x
Tomas
On Mon, 15 May 2017 09:57:08 +0200
Jörg <joerg.straube at iaeth.ch> wrote:
> It is. MOD is defined as C x C -> C
> Jörg
>
> > Am 14.05.2017 um 20:17 schrieb Aubrey McIntosh
> > <aubrey.mcintosh at utexas.edu>:
> >
> > I have not checked my number theory book lately, but I don't think
> > (i.e., don't remember) that it is defined mathematically for
> > negative divisors either.
> >
> >> On Sat, May 13, 2017 at 3:12 AM, Peter Matthias
> >> <PeterMatthias at web.de> wrote: Agreed. However, -1 MOD -12 or 1 MOD
> >> -12 is not defined in Oberon.
> >>
> >>
> >>> Am 12.05.2017 um 22:43 schrieb Aubrey McIntosh:
> >>> for -1 MOD 12, the mathematically correct answers which are
> >>> consistent with the language report, are
> >>> q=-1, r=11.
> >>>
> >>> This definition works very well, for example, to implement wrap
> >>> around strip chart displays.
> >>>
> >>>
> >>> On Fri, May 12, 2017 at 2:28 PM, Peter Matthias
> >>> <PeterMatthias at web.de <mailto:PeterMatthias at web.de>> wrote:
> >>>
> >>> Warming up the thread to give supposedly correct answer:
> >>>
> >>> Am 16.02.2017 um 00:00 schrieb Peter Matthias:
> >>>
> >>>
> >>>
> >>> Am 15.02.2017 um 04:21 schrieb Srinivas Nayak:
> >>>
> >>> Dear All,
> >>>
> >>> Recently I come across modulus on a negative number.
> >>> Will it produce a negative number or positive?
> >>> Someone says both are correct!
> >>> http://stackoverflow.com/a/4403556
> >>> <http://stackoverflow.com/a/4403556>
> >>> Which one is mathematically correct?
> >>> Surprisingly different languages calculate it
> >>> differently even! What is Oberon's way?
> >>>
> >>>
> >>> The theory was already answered. In practice, all compiler
> >>> implementations I used (native X86, Shark, MIPS), give
> >>> wrong result when
> >>> both, divident and divisor are negative. I fixed it just
> >>> yesterday for
> >>> all non x86 versions.
> >>>
> >>>
> >>> I should have read the language report before making such
> >>> claims.
> >>>
> >>> Oberon Report says:
> >>>
> >>> "The operators DIV and MOD apply to integer operands only.
> >>> They are related by the following formulas defined for any
> >>> dividend x and positive divisors y:
> >>> x = (x DIV y) * y + (x MOD y)
> >>> 0 ≤ (x MOD y) < y"
> >>>
> >>> Oberon07-Report says:
> >>>
> >>> "The operators DIV and MOD apply to integer operands only.
> >>> Let q = x DIV y, and r = x MOD y.
> >>> Then quotient q and remainder r are defined by the equation
> >>> x = q*y + r 0 <= r < y"
> >>>
> >>> Last statement obviously cannot be met if y is negative.
> >>>
> >>> So in short: Don't use DIV/MOD for negative divisors as the
> >>> result is not defined.
> >>>
> >>> >From the implemtation point of view this perfectly makes
> >>> >sense as
> >>> negative divisors are seldom used and correction for DIV of
> >>> the usually stupid hardware implementation only takes 3 additional
> >>> instructions compared to at least 6 for a complete definition.
> >>> Simple SHIFT/AND instructions for power of 2 divisors easily
> >>> outwight these 3 additional instructions.
> >>>
> >>>
> >>> Peter
> >>>
> >>> --
> >>> Oberon at lists.inf.ethz.ch <mailto:Oberon at lists.inf.ethz.ch>
> >>> mailing list for ETH Oberon and related systems
> >>> https://lists.inf.ethz.ch/mailman/listinfo/oberon
> >>> <https://lists.inf.ethz.ch/mailman/listinfo/oberon>
> >>>
> >>>
> >>>
> >>>
> >>> --
> >>> Aubrey McIntosh, Ph.D.
> >>> 1502 Devon Circle
> >>> Austin TX 78723
> >>> (512) 348-7401
> >>>
> >>>
> >>>
> >>> --
> >>> Oberon at lists.inf.ethz.ch mailing list for ETH Oberon and related
> >>> systems https://lists.inf.ethz.ch/mailman/listinfo/oberon
> >>>
> >> --
> >> Oberon at lists.inf.ethz.ch mailing list for ETH Oberon and related
> >> systems https://lists.inf.ethz.ch/mailman/listinfo/oberon
> >
> >
> >
> > --
> > Aubrey McIntosh, Ph.D.
> > 1502 Devon Circle
> > Austin TX 78723
> > (512) 348-7401
> >
> > --
> > Oberon at lists.inf.ethz.ch mailing list for ETH Oberon and related
> > systems https://lists.inf.ethz.ch/mailman/listinfo/oberon
--
Tomas Kral <thomas.kral at email.cz>
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