Re: A Level 2 query
>
> I assume that these kinds of things exist in other interval
> library designs where people have made some effort to
> extract single-use expressions, are willing to consider
> differentiation / max / min extraction, etc. From the
> perspective of the language/compiler-for-intervals
> design, I think the routine
>
> SUB(X)
> SUB=X-X
> RETURN
>
> should return [0,0] for finite intervals. I'm unsure about
> what is best if X is not-an-interval. (etc)
>
> Anyway, my question is still -- if the compiler works hard to come
> up with a tighter enclosure (by doing SUE simplification, polynomial
> root finding, etc) is that going to violate the standard, or is it
> irrelevant to the standard being supra-library, and nothing to
> worry about :)
My feeling is that it will be a long time before compilers would do this,
so I would not consider what they could do.
As a side question/comment.
During my PhD in the late 90s, I was looking for a subroutine that, given
polynomial coefficients that are intervals, produces tight interval containing
the range of this polynomial over some interval. I could not find such,
although there were articles on the topic. I am wondering if such an implementation
exists now.
Ned
>
> RJF
>
>
>
>>
>> If so, then the standard should make it very clear that interval
>> arguments of functions are to be evaluated differently from regular
>> interval variables.
>>
>> Cheers,
>>
>> Bill
>>
>> On 6/20/13 7:27 AM, Richard Fateman wrote:
>>> I am unclear as to whether you are excluding from consideration as
>>> standard-conforming the following compiler
>>> "optimization":
>>>
>>> let y := ...some explicit polynomial P in the interval variable x.
>>>
>>>
>>> The compiler recognizes P as a polynomial, computes (at compile time)
>>> locations and values at
>>> its relative maxima and minima, and at run-time uses this information
>>> to
>>> compute inf(y) and sup(y) on the interval x entirely without
>>> dependency slop.
>>> And perhaps with great speed compared to evaluating P.
>>>
>>> RJF
>>>
>>>
>>> On 6/20/2013 6:05 AM, John Pryce wrote:
>>>> Ian, Jürgen, P1788
>>>>
>>>> What I get from these replies is that the T -> T operation *should*
>>>> be mandatory. Ian's comments are important but they apply to
>>>> expressions. Those are a language issue and we IMO
>>>> (a) *should not* make requirements about expression-evaluation
>>>> (beyond containment);
>>>> (b) *should* make recommendations on the lines Ian proposes.
>>>> Actually, thinking about it, I'm less sure about (a).
>>>>
>>>>
>>> <snip>
>>>
>>
>>