[Oberon] Modulus on negative number
Skulski, Wojciech
skulski at pas.rochester.edu
Wed May 17 02:11:17 CEST 2017
> x DIV 0 is undefined.
I thought than every programming language will rise a trap on division by 0, either integer or floating point. I would be surprised if Oberon did not.
The following two questions are somewhat related to this discussion.
1. Does Oberon support NaN? If not then maybe it should?
2. Could the "undefined" become "defined as NaN" in all numerical cases which are now undefined?
Rationale: The presently "undefined" wasnot implemented for efficiency reasons. (Correct me if this statement is wrong.) If the result is truly undefined and left to the implementation, then wrong results can be quietly produced and passed to further processing. On the other hand, if the "undefined" becomes a NaN, then NaNs can be handled by the application code.
Example: I know of at least one system (IGOR from Wavemetrics) where I can initialize the arrays with NaNs and then selectively fill them with good data. Whatever is not filled will stay NaN and then it is omitted from plotting. IGOR interprets NaNs as "do not care". It is a very effective solution in practice.
Any thoughts?
Wojtek
________________________________________
From: Oberon [oberon-bounces at lists.inf.ethz.ch] on behalf of Jörg [joerg.straube at iaeth.ch]
Sent: Tuesday, May 16, 2017 2:33 AM
To: ETH Oberon and related systems
Subject: Re: [Oberon] Modulus on negative number
0 MOD x is 0 for all x except 0. In Oberon only defined for positive x
x DIV 0 is undefined. If you read the hitchhiker's guide to the galaxy the answer is 42 :-)
br
Jörg
> Am 15.05.2017 um 20:45 schrieb Tomas Kral <thomas.kral at email.cz>:
>
> Hi,
>
> EDIT - the reason I ask, is that until now I thought that a remainder
> is a computing synonym for the modulus.
>
> Also, I remember that one of the early
> Intel processors had problems with zero division, but some
> maths people argued that it was alright as zero division depends on the
> rate of convergence.
>
> But Maths was never my cup of tea.
>
> At last I took some interest in this MOD'ulus discussion. I wonder how
> it is (un)defined in Math / Oberon
>
> x DIV 0
> 0 MOD x
>
> Tomas
>
> On Mon, 15 May 2017 09:57:08 +0200
> Jörg <joerg.straube at iaeth.ch> wrote:
>
>> It is. MOD is defined as C x C -> C
>> Jörg
>>
>>> Am 14.05.2017 um 20:17 schrieb Aubrey McIntosh
>>> <aubrey.mcintosh at utexas.edu>:
>>>
>>> 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:
>>>>>
>>>>> 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!
>>>>> https://urldefense.proofpoint.com/v2/url?u=http-3A__stackoverflow.com_a_4403556&d=DwIGaQ&c=kbmfwr1Yojg42sGEpaQh5ofMHBeTl9EI2eaqQZhHbOU&r=uUiA_zLpwaGJIlq-_BM9w1wVOuyqPwHi3XzJRa-ybV0&m=ps5mHvQsNtHNKZSV9DHVBm8g9m0ba-VkduQrd87yJ_s&s=X-h4LxwGezYLCFsYvDAYoiGUS5kUt32UCwcp6a3YmWs&e=
>>>>> <https://urldefense.proofpoint.com/v2/url?u=http-3A__stackoverflow.com_a_4403556&d=DwIGaQ&c=kbmfwr1Yojg42sGEpaQh5ofMHBeTl9EI2eaqQZhHbOU&r=uUiA_zLpwaGJIlq-_BM9w1wVOuyqPwHi3XzJRa-ybV0&m=ps5mHvQsNtHNKZSV9DHVBm8g9m0ba-VkduQrd87yJ_s&s=X-h4LxwGezYLCFsYvDAYoiGUS5kUt32UCwcp6a3YmWs&e= >
>>>>> 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://urldefense.proofpoint.com/v2/url?u=https-3A__lists.inf.ethz.ch_mailman_listinfo_oberon&d=DwIGaQ&c=kbmfwr1Yojg42sGEpaQh5ofMHBeTl9EI2eaqQZhHbOU&r=uUiA_zLpwaGJIlq-_BM9w1wVOuyqPwHi3XzJRa-ybV0&m=ps5mHvQsNtHNKZSV9DHVBm8g9m0ba-VkduQrd87yJ_s&s=esLBXjxJsUPeCtzIcBqI4xjbU1MDc9qNKXrXL9_h5XM&e=
>>>>> <https://urldefense.proofpoint.com/v2/url?u=https-3A__lists.inf.ethz.ch_mailman_listinfo_oberon&d=DwIGaQ&c=kbmfwr1Yojg42sGEpaQh5ofMHBeTl9EI2eaqQZhHbOU&r=uUiA_zLpwaGJIlq-_BM9w1wVOuyqPwHi3XzJRa-ybV0&m=ps5mHvQsNtHNKZSV9DHVBm8g9m0ba-VkduQrd87yJ_s&s=esLBXjxJsUPeCtzIcBqI4xjbU1MDc9qNKXrXL9_h5XM&e= >
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> --
>>>>> 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://urldefense.proofpoint.com/v2/url?u=https-3A__lists.inf.ethz.ch_mailman_listinfo_oberon&d=DwIGaQ&c=kbmfwr1Yojg42sGEpaQh5ofMHBeTl9EI2eaqQZhHbOU&r=uUiA_zLpwaGJIlq-_BM9w1wVOuyqPwHi3XzJRa-ybV0&m=ps5mHvQsNtHNKZSV9DHVBm8g9m0ba-VkduQrd87yJ_s&s=esLBXjxJsUPeCtzIcBqI4xjbU1MDc9qNKXrXL9_h5XM&e=
>>>>>
>>>> --
>>>> Oberon at lists.inf.ethz.ch mailing list for ETH Oberon and related
>>>> systems https://urldefense.proofpoint.com/v2/url?u=https-3A__lists.inf.ethz.ch_mailman_listinfo_oberon&d=DwIGaQ&c=kbmfwr1Yojg42sGEpaQh5ofMHBeTl9EI2eaqQZhHbOU&r=uUiA_zLpwaGJIlq-_BM9w1wVOuyqPwHi3XzJRa-ybV0&m=ps5mHvQsNtHNKZSV9DHVBm8g9m0ba-VkduQrd87yJ_s&s=esLBXjxJsUPeCtzIcBqI4xjbU1MDc9qNKXrXL9_h5XM&e=
>>>
>>>
>>>
>>> --
>>> 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://urldefense.proofpoint.com/v2/url?u=https-3A__lists.inf.ethz.ch_mailman_listinfo_oberon&d=DwIGaQ&c=kbmfwr1Yojg42sGEpaQh5ofMHBeTl9EI2eaqQZhHbOU&r=uUiA_zLpwaGJIlq-_BM9w1wVOuyqPwHi3XzJRa-ybV0&m=ps5mHvQsNtHNKZSV9DHVBm8g9m0ba-VkduQrd87yJ_s&s=esLBXjxJsUPeCtzIcBqI4xjbU1MDc9qNKXrXL9_h5XM&e=
>
>
>
> --
> Tomas Kral <thomas.kral at email.cz>
> --
> Oberon at lists.inf.ethz.ch mailing list for ETH Oberon and related systems
> https://urldefense.proofpoint.com/v2/url?u=https-3A__lists.inf.ethz.ch_mailman_listinfo_oberon&d=DwIGaQ&c=kbmfwr1Yojg42sGEpaQh5ofMHBeTl9EI2eaqQZhHbOU&r=uUiA_zLpwaGJIlq-_BM9w1wVOuyqPwHi3XzJRa-ybV0&m=ps5mHvQsNtHNKZSV9DHVBm8g9m0ba-VkduQrd87yJ_s&s=esLBXjxJsUPeCtzIcBqI4xjbU1MDc9qNKXrXL9_h5XM&e=
>
>
> --
> Tomas Kral <thomas.kral at email.cz>
> --
> Oberon at lists.inf.ethz.ch mailing list for ETH Oberon and related systems
> https://urldefense.proofpoint.com/v2/url?u=https-3A__lists.inf.ethz.ch_mailman_listinfo_oberon&d=DwIGaQ&c=kbmfwr1Yojg42sGEpaQh5ofMHBeTl9EI2eaqQZhHbOU&r=uUiA_zLpwaGJIlq-_BM9w1wVOuyqPwHi3XzJRa-ybV0&m=ps5mHvQsNtHNKZSV9DHVBm8g9m0ba-VkduQrd87yJ_s&s=esLBXjxJsUPeCtzIcBqI4xjbU1MDc9qNKXrXL9_h5XM&e=
--
Oberon at lists.inf.ethz.ch mailing list for ETH Oberon and related systems
https://urldefense.proofpoint.com/v2/url?u=https-3A__lists.inf.ethz.ch_mailman_listinfo_oberon&d=DwIGaQ&c=kbmfwr1Yojg42sGEpaQh5ofMHBeTl9EI2eaqQZhHbOU&r=uUiA_zLpwaGJIlq-_BM9w1wVOuyqPwHi3XzJRa-ybV0&m=ps5mHvQsNtHNKZSV9DHVBm8g9m0ba-VkduQrd87yJ_s&s=esLBXjxJsUPeCtzIcBqI4xjbU1MDc9qNKXrXL9_h5XM&e=
More information about the Oberon
mailing list