# [Oberon] Modulus on negative number

Jörg joerg.straube at iaeth.ch
Sat May 13 11:13:19 CEST 2017

```Hi

Just for completeness, the result should be
1 MOD -12 = -11
-1 MOD -12 = -1

Jörg

> Am 13.05.2017 um 10:12 schrieb Peter Matthias <PeterMatthias at web.de>:
>
> 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

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