# [Oberon] Modulus on negative number

Aubrey McIntosh aubrey.mcintosh at utexas.edu
Sun May 14 20:17:22 CEST 2017

```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:
>>
>>
>>     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?
>>
>>
>>         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
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