[Oberon] Modulus on negative number
Peter Matthias
PeterMatthias at web.de
Sat May 13 10:12:37 CEST 2017
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
>
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> Aubrey McIntosh, Ph.D.
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