Re: Motion 31: V04.2: case, reverse case, reverse fma
> My inclination is to say "it shall return hull(Case(c,g,h))",
> which is how I'll write the Level 2 text unless someone objects.
I don't object. I am just writing the checker of P1788 implementations.
So I asked this question to be sure that the checker must report an error
if an implementation returns
case([1,1],Empty,[2,2]) = Empty .
> I propose to omit those. For fma, my (top of the head) belief is
> that constraint propagation algorithms rarely need to worry
> about saving one rounding, which is what it seems
> a reverse fma would give compared with splitting it into a reverse * and reverse +.
> For case (or Case) I haven't studied its reverse form at all, and would be glad if someone does.
Ok, the checker will not be able to check reversed interval versions of ternary operations.
Thank you for the clarification.
-Dima
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От: j.d.pryce@xxxxxxxxxxxx
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Отправленные: Суббота, 11 Февраль 2012 г 14:07:10 GMT +03:00 Москва, Санкт-Петербург, Волгоград
Тема: Re: Motion 31: V04.2: case, reverse case, reverse fma
Dmitry
On 10 Feb 2012, at 05:58, Dmitry Nadezhin wrote:
> So we have the natural interval extension "case(c,g,h)"
> and the "simple" interval extension "Case(c,g,h)".
> What will be the Level2 conformance requirements for this function ?
> Will implementation that returns "hull(case(c,g,h))" conform ?
> Or shall it return "hull(Case(c,g,h))" ?
> Or implementation may choose any of the above ?
My inclination is to say "it shall return hull(Case(c,g,h))", which is how I'll write the Level 2 text unless someone objects.
> The other question is about reverse-mode elementary functions.
> The text says about reverse-mode unary and binary functions.
> Now we have two required ternary functions: "fma(x,y,z)" and "case(c,g,h)".
> Will standard mention reverse interval extensions of them ?
> If yes, will the "case" have the natural reverse interval extension
> or some "simple" reverse interval extension ?
I propose to omit those. For fma, my (top of the head) belief is that constraint propagation algorithms rarely need to worry about saving one rounding, which is what it seems a reverse fma would give compared with splitting it into a reverse * and reverse +. For case (or Case) I haven't studied its reverse form at all, and would be glad if someone does.
I may be quite wrong.
John
> ----- Исходное сообщение -----
> От: j.d.pryce@xxxxxxxxxxxx
> Кому: stds-1788@xxxxxxxxxxxxxxxxx
> Отправленные: Среда, 8 Февраль 2012 г 15:39:07 GMT +03:00 Москва, Санкт-Петербург, Волгоград
> Тема: Re: Motion 31: V04.2 Revision of proposed Level 1 text
>
> Dmitry, P1788
>
> Thanks for these comments, sorry for the delay responding.
>
> On 25 Jan 2012, at 19:07, Dmitry Nadezhin wrote:
>> Here are some small comments:
>>
>> 1) case(c,g,h)
>> The point function is defined as
>> (1) case(c,g,h) = if (c < 0) g else h
>> It's natural interval extension is
>> (2) case(C,G,H) = Empty, if (C isEmpty) or (G isEmpty) or (H isEmpty)
>> G, if (C.sup < 0) and not (H isEmpty)
>> H, if (C.inf >= 0) and not (G isEmpty)
>> hull(G U H), if (C.inf < 0) and (C.sup >= 0) and not (G isEmpty) and (not H isEmpty)
>> The document says that natural interval extension is
>> (3) case(C,G,H) = Empty, if (C is Empty)
>> G, if (C.sup < 0)
>> H, if (C.inf >= 0)
>> hull(G U H), if (C.inf < 0) and (C.sup >= 0)
>> This is not true. (3) is not natural interval extension, (3) is wider interval extension.
> Yes, I see you are correct. Careless of me and others not to notice this.
>
>> Nevertheless, I like more the definition (3).
>> If the implementation is forced to compute case according to the tightest definition (2),
>> it has to always compute both G and H subexpressions.
>> The definition (3) allows to skip computation of G and H in some cases.
>>
>> My opinion is to keep definition (3) of case(C,G,H),
>> but call (3) "recommended interval extension" instead of "natural interval extension".
> My first impression is to like this idea. But not "recommended", which has its own meaning in clause 5. Try "simple" or "preferred" or ...?