<div dir="ltr">Wojciech,<div>read the book, chapter 16<br><div>----------------------------------------------</div><div><div>16.3. Floating-point arithmetic</div><div>The RISC uses the IEEE Standard for representing REAL (floating-point) numbers with 32 bits.</div><div>The word is divided into 3 fields: s for the sign, e for the exponent, and m for the mantissa. The</div><div>value is</div><div> x = (-1)s × 2e-127 × 1.m with 1.0 ≤ m < 2.0 (normalized form)</div><div>Numbers are represented in sign-magnitude form. This implies that for sign inversion only the sign</div><div>bit must be inverted, and exponent and mantissa remain unchanged.</div><div>Zero is a special case represented by 32 0-bits, and therefore has to be treated separately.</div><div>Furthermore, e = 255 denotes "not a number". It is generated in the case of arithmetic overflow.</div></div><div>-------------------------------------</div></div><div>Traditionally oberon raised a trap on div by 0. </div><div>See also the Trap routine in System.Mod.</div><div>I have not checked yet how the O07 sources / compiler handle all this. I will keep my eyes open while I am building this quick and dirty Scheme / XML to Risc compiler.</div><div><br></div><div>Cheers,</div><div>J.</div><div><br></div><div><br></div></div><div class="gmail_extra"><br><div class="gmail_quote">On Wed, May 17, 2017 at 2:11 AM, Skulski, Wojciech <span dir="ltr"><<a href="mailto:skulski@pas.rochester.edu" target="_blank">skulski@pas.rochester.edu</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><span class="">> x DIV 0 is undefined.<br>
<br>
</span>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.<br>
<br>
The following two questions are somewhat related to this discussion.<br>
<br>
1. Does Oberon support NaN? If not then maybe it should?<br>
<br>
2. Could the "undefined" become "defined as NaN" in all numerical cases which are now undefined?<br>
<br>
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.<br>
<br>
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.<br>
<br>
Any thoughts?<br>
<br>
Wojtek<br>
______________________________<wbr>__________<br>
From: Oberon [<a href="mailto:oberon-bounces@lists.inf.ethz.ch">oberon-bounces@lists.inf.<wbr>ethz.ch</a>] on behalf of Jörg [<a href="mailto:joerg.straube@iaeth.ch">joerg.straube@iaeth.ch</a>]<br>
Sent: Tuesday, May 16, 2017 2:33 AM<br>
<span class="">To: ETH Oberon and related systems<br>
Subject: Re: [Oberon] Modulus on negative number<br>
<br>
</span><div><div class="h5">0 MOD x is 0 for all x except 0. In Oberon only defined for positive x<br>
<br>
x DIV 0 is undefined. If you read the hitchhiker's guide to the galaxy the answer is 42 :-)<br>
<br>
br<br>
Jörg<br>
<br>
> Am 15.05.2017 um 20:45 schrieb Tomas Kral <<a href="mailto:thomas.kral@email.cz">thomas.kral@email.cz</a>>:<br>
><br>
> Hi,<br>
><br>
> EDIT - the reason I ask, is that until now I thought that a remainder<br>
> is a computing synonym for the modulus.<br>
><br>
> Also, I remember that one of the early<br>
> Intel processors had problems with zero division, but some<br>
> maths people argued that it was alright as zero division depends on the<br>
> rate of convergence.<br>
><br>
> But Maths was never my cup of tea.<br>
><br>
> At last I took some interest in this MOD'ulus discussion. I wonder how<br>
> it is (un)defined in Math / Oberon<br>
><br>
> x DIV 0<br>
> 0 MOD x<br>
><br>
> Tomas<br>
><br>
> On Mon, 15 May 2017 09:57:08 +0200<br>
> Jörg <<a href="mailto:joerg.straube@iaeth.ch">joerg.straube@iaeth.ch</a>> wrote:<br>
><br>
>> It is. MOD is defined as C x C -> C<br>
>> Jörg<br>
>><br>
>>> Am 14.05.2017 um 20:17 schrieb Aubrey McIntosh<br>
>>> <<a href="mailto:aubrey.mcintosh@utexas.edu">aubrey.mcintosh@utexas.edu</a>>:<br>
>>><br>
>>> I have not checked my number theory book lately, but I don't think<br>
>>> (i.e., don't remember) that it is defined mathematically for<br>
>>> negative divisors either.<br>
>>><br>
>>>> On Sat, May 13, 2017 at 3:12 AM, Peter Matthias<br>
>>>> <<a href="mailto:PeterMatthias@web.de">PeterMatthias@web.de</a>> wrote: Agreed. However, -1 MOD -12 or 1 MOD<br>
>>>> -12 is not defined in Oberon.<br>
>>>><br>
>>>><br>
>>>>> Am 12.05.2017 um 22:43 schrieb Aubrey McIntosh:<br>
>>>>> for -1 MOD 12, the mathematically correct answers which are<br>
>>>>> consistent with the language report, are<br>
>>>>> q=-1, r=11.<br>
>>>>><br>
>>>>> This definition works very well, for example, to implement wrap<br>
>>>>> around strip chart displays.<br>
>>>>><br>
>>>>><br>
>>>>> On Fri, May 12, 2017 at 2:28 PM, Peter Matthias<br>
>>>>> <<a href="mailto:PeterMatthias@web.de">PeterMatthias@web.de</a> <mailto:<a href="mailto:PeterMatthias@web.de">PeterMatthias@web.de</a>>> wrote:<br>
>>>>><br>
>>>>> Warming up the thread to give supposedly correct answer:<br>
>>>>><br>
>>>>> Am 16.02.2017 um 00:00 schrieb Peter Matthias:<br>
>>>>><br>
>>>>><br>
>>>>><br>
>>>>> Am 15.02.2017 um 04:21 schrieb Srinivas Nayak:<br>
>>>>><br>
>>>>> Dear All,<br>
>>>>><br>
>>>>> Recently I come across modulus on a negative number.<br>
>>>>> Will it produce a negative number or positive?<br>
>>>>> Someone says both are correct!<br>
</div></div>>>>>> <a href="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=" rel="noreferrer" target="_blank">https://urldefense.proofpoint.<wbr>com/v2/url?u=http-3A__<wbr>stackoverflow.com_a_4403556&d=<wbr>DwIGaQ&c=<wbr>kbmfwr1Yojg42sGEpaQh5ofMHBeTl9<wbr>EI2eaqQZhHbOU&r=uUiA_<wbr>zLpwaGJIlq-_<wbr>BM9w1wVOuyqPwHi3XzJRa-ybV0&m=<wbr>ps5mHvQsNtHNKZSV9DHVBm8g9m0ba-<wbr>VkduQrd87yJ_s&s=X-<wbr>h4LxwGezYLCFsYvDAYoiGUS5kUt32U<wbr>Cwcp6a3YmWs&e=</a><br>
>>>>> <<a href="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=" rel="noreferrer" target="_blank">https://urldefense.<wbr>proofpoint.com/v2/url?u=http-<wbr>3A__stackoverflow.com_a_<wbr>4403556&d=DwIGaQ&c=<wbr>kbmfwr1Yojg42sGEpaQh5ofMHBeTl9<wbr>EI2eaqQZhHbOU&r=uUiA_<wbr>zLpwaGJIlq-_<wbr>BM9w1wVOuyqPwHi3XzJRa-ybV0&m=<wbr>ps5mHvQsNtHNKZSV9DHVBm8g9m0ba-<wbr>VkduQrd87yJ_s&s=X-<wbr>h4LxwGezYLCFsYvDAYoiGUS5kUt32U<wbr>Cwcp6a3YmWs&e=</a> ><br>
<div><div class="h5">>>>>> Which one is mathematically correct?<br>
>>>>> Surprisingly different languages calculate it<br>
>>>>> differently even! What is Oberon's way?<br>
>>>>><br>
>>>>><br>
>>>>> The theory was already answered. In practice, all compiler<br>
>>>>> implementations I used (native X86, Shark, MIPS), give<br>
>>>>> wrong result when<br>
>>>>> both, divident and divisor are negative. I fixed it just<br>
>>>>> yesterday for<br>
>>>>> all non x86 versions.<br>
>>>>><br>
>>>>><br>
>>>>> I should have read the language report before making such<br>
>>>>> claims.<br>
>>>>><br>
>>>>> Oberon Report says:<br>
>>>>><br>
>>>>> "The operators DIV and MOD apply to integer operands only.<br>
>>>>> They are related by the following formulas defined for any<br>
>>>>> dividend x and positive divisors y:<br>
>>>>> x = (x DIV y) * y + (x MOD y)<br>
>>>>> 0 ≤ (x MOD y) < y"<br>
>>>>><br>
>>>>> Oberon07-Report says:<br>
>>>>><br>
>>>>> "The operators DIV and MOD apply to integer operands only.<br>
>>>>> Let q = x DIV y, and r = x MOD y.<br>
>>>>> Then quotient q and remainder r are defined by the equation<br>
>>>>> x = q*y + r 0 <= r < y"<br>
>>>>><br>
>>>>> Last statement obviously cannot be met if y is negative.<br>
>>>>><br>
>>>>> So in short: Don't use DIV/MOD for negative divisors as the<br>
>>>>> result is not defined.<br>
>>>>><br>
>>>>>> From the implemtation point of view this perfectly makes<br>
>>>>>> sense as<br>
>>>>> negative divisors are seldom used and correction for DIV of<br>
>>>>> the usually stupid hardware implementation only takes 3 additional<br>
>>>>> instructions compared to at least 6 for a complete definition.<br>
>>>>> Simple SHIFT/AND instructions for power of 2 divisors easily<br>
>>>>> outwight these 3 additional instructions.<br>
>>>>><br>
>>>>><br>
>>>>> Peter<br>
>>>>><br>
>>>>> --<br>
>>>>> <a href="mailto:Oberon@lists.inf.ethz.ch">Oberon@lists.inf.ethz.ch</a> <mailto:<a href="mailto:Oberon@lists.inf.ethz.ch">Oberon@lists.inf.ethz.<wbr>ch</a>><br>
>>>>> mailing list for ETH Oberon and related systems<br>
</div></div>>>>>> <a href="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=" rel="noreferrer" target="_blank">https://urldefense.proofpoint.<wbr>com/v2/url?u=https-3A__lists.<wbr>inf.ethz.ch_mailman_listinfo_<wbr>oberon&d=DwIGaQ&c=<wbr>kbmfwr1Yojg42sGEpaQh5ofMHBeTl9<wbr>EI2eaqQZhHbOU&r=uUiA_<wbr>zLpwaGJIlq-_<wbr>BM9w1wVOuyqPwHi3XzJRa-ybV0&m=<wbr>ps5mHvQsNtHNKZSV9DHVBm8g9m0ba-<wbr>VkduQrd87yJ_s&s=<wbr>esLBXjxJsUPeCtzIcBqI4xjbU1MDc9<wbr>qNKXrXL9_h5XM&e=</a><br>
>>>>> <<a href="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=" rel="noreferrer" target="_blank">https://urldefense.<wbr>proofpoint.com/v2/url?u=https-<wbr>3A__lists.inf.ethz.ch_mailman_<wbr>listinfo_oberon&d=DwIGaQ&c=<wbr>kbmfwr1Yojg42sGEpaQh5ofMHBeTl9<wbr>EI2eaqQZhHbOU&r=uUiA_<wbr>zLpwaGJIlq-_<wbr>BM9w1wVOuyqPwHi3XzJRa-ybV0&m=<wbr>ps5mHvQsNtHNKZSV9DHVBm8g9m0ba-<wbr>VkduQrd87yJ_s&s=<wbr>esLBXjxJsUPeCtzIcBqI4xjbU1MDc9<wbr>qNKXrXL9_h5XM&e=</a> ><br>
<span class="">>>>>><br>
>>>>><br>
>>>>><br>
>>>>><br>
>>>>> --<br>
>>>>> Aubrey McIntosh, Ph.D.<br>
>>>>> 1502 Devon Circle<br>
>>>>> Austin TX 78723<br>
>>>>> <a href="tel:%28512%29%20348-7401" value="+15123487401">(512) 348-7401</a><br>
>>>>><br>
>>>>><br>
>>>>><br>
>>>>> --<br>
>>>>> <a href="mailto:Oberon@lists.inf.ethz.ch">Oberon@lists.inf.ethz.ch</a> mailing list for ETH Oberon and related<br>
</span>>>>>> systems <a href="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=" rel="noreferrer" target="_blank">https://urldefense.proofpoint.<wbr>com/v2/url?u=https-3A__lists.<wbr>inf.ethz.ch_mailman_listinfo_<wbr>oberon&d=DwIGaQ&c=<wbr>kbmfwr1Yojg42sGEpaQh5ofMHBeTl9<wbr>EI2eaqQZhHbOU&r=uUiA_<wbr>zLpwaGJIlq-_<wbr>BM9w1wVOuyqPwHi3XzJRa-ybV0&m=<wbr>ps5mHvQsNtHNKZSV9DHVBm8g9m0ba-<wbr>VkduQrd87yJ_s&s=<wbr>esLBXjxJsUPeCtzIcBqI4xjbU1MDc9<wbr>qNKXrXL9_h5XM&e=</a><br>
<span class="">>>>>><br>
>>>> --<br>
>>>> <a href="mailto:Oberon@lists.inf.ethz.ch">Oberon@lists.inf.ethz.ch</a> mailing list for ETH Oberon and related<br>
</span>>>>> systems <a href="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=" rel="noreferrer" target="_blank">https://urldefense.proofpoint.<wbr>com/v2/url?u=https-3A__lists.<wbr>inf.ethz.ch_mailman_listinfo_<wbr>oberon&d=DwIGaQ&c=<wbr>kbmfwr1Yojg42sGEpaQh5ofMHBeTl9<wbr>EI2eaqQZhHbOU&r=uUiA_<wbr>zLpwaGJIlq-_<wbr>BM9w1wVOuyqPwHi3XzJRa-ybV0&m=<wbr>ps5mHvQsNtHNKZSV9DHVBm8g9m0ba-<wbr>VkduQrd87yJ_s&s=<wbr>esLBXjxJsUPeCtzIcBqI4xjbU1MDc9<wbr>qNKXrXL9_h5XM&e=</a><br>
<span class="">>>><br>
>>><br>
>>><br>
>>> --<br>
>>> Aubrey McIntosh, Ph.D.<br>
>>> 1502 Devon Circle<br>
>>> Austin TX 78723<br>
>>> <a href="tel:%28512%29%20348-7401" value="+15123487401">(512) 348-7401</a><br>
>>><br>
>>> --<br>
>>> <a href="mailto:Oberon@lists.inf.ethz.ch">Oberon@lists.inf.ethz.ch</a> mailing list for ETH Oberon and related<br>
</span>>>> systems <a href="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=" rel="noreferrer" target="_blank">https://urldefense.proofpoint.<wbr>com/v2/url?u=https-3A__lists.<wbr>inf.ethz.ch_mailman_listinfo_<wbr>oberon&d=DwIGaQ&c=<wbr>kbmfwr1Yojg42sGEpaQh5ofMHBeTl9<wbr>EI2eaqQZhHbOU&r=uUiA_<wbr>zLpwaGJIlq-_<wbr>BM9w1wVOuyqPwHi3XzJRa-ybV0&m=<wbr>ps5mHvQsNtHNKZSV9DHVBm8g9m0ba-<wbr>VkduQrd87yJ_s&s=<wbr>esLBXjxJsUPeCtzIcBqI4xjbU1MDc9<wbr>qNKXrXL9_h5XM&e=</a><br>
<span class="">><br>
><br>
><br>
> --<br>
> Tomas Kral <<a href="mailto:thomas.kral@email.cz">thomas.kral@email.cz</a>><br>
> --<br>
> <a href="mailto:Oberon@lists.inf.ethz.ch">Oberon@lists.inf.ethz.ch</a> mailing list for ETH Oberon and related systems<br>
</span>> <a href="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=" rel="noreferrer" target="_blank">https://urldefense.proofpoint.<wbr>com/v2/url?u=https-3A__lists.<wbr>inf.ethz.ch_mailman_listinfo_<wbr>oberon&d=DwIGaQ&c=<wbr>kbmfwr1Yojg42sGEpaQh5ofMHBeTl9<wbr>EI2eaqQZhHbOU&r=uUiA_<wbr>zLpwaGJIlq-_<wbr>BM9w1wVOuyqPwHi3XzJRa-ybV0&m=<wbr>ps5mHvQsNtHNKZSV9DHVBm8g9m0ba-<wbr>VkduQrd87yJ_s&s=<wbr>esLBXjxJsUPeCtzIcBqI4xjbU1MDc9<wbr>qNKXrXL9_h5XM&e=</a><br>
<span class="">><br>
><br>
> --<br>
> Tomas Kral <<a href="mailto:thomas.kral@email.cz">thomas.kral@email.cz</a>><br>
> --<br>
> <a href="mailto:Oberon@lists.inf.ethz.ch">Oberon@lists.inf.ethz.ch</a> mailing list for ETH Oberon and related systems<br>
</span>> <a href="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=" rel="noreferrer" target="_blank">https://urldefense.proofpoint.<wbr>com/v2/url?u=https-3A__lists.<wbr>inf.ethz.ch_mailman_listinfo_<wbr>oberon&d=DwIGaQ&c=<wbr>kbmfwr1Yojg42sGEpaQh5ofMHBeTl9<wbr>EI2eaqQZhHbOU&r=uUiA_<wbr>zLpwaGJIlq-_<wbr>BM9w1wVOuyqPwHi3XzJRa-ybV0&m=<wbr>ps5mHvQsNtHNKZSV9DHVBm8g9m0ba-<wbr>VkduQrd87yJ_s&s=<wbr>esLBXjxJsUPeCtzIcBqI4xjbU1MDc9<wbr>qNKXrXL9_h5XM&e=</a><br>
<span class="">--<br>
<a href="mailto:Oberon@lists.inf.ethz.ch">Oberon@lists.inf.ethz.ch</a> mailing list for ETH Oberon and related systems<br>
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