[Oberon] Modulus on negative number

[Peter Matthias]

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.
> 1502 Devon Circle
> Austin TX 78723
> (512) 348-7401
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>
>
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