# [Oberon] Modulus on negative number

Aubrey McIntosh aubrey.mcintosh at utexas.edu
Fri May 12 22:43:27 CEST 2017

```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>
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
>>> 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 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
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