Re: Decorations and Motion 22
Arnold, Nate
I like your proposed 5-value decoration scheme (extract from Arnold's 10th Oct email quoted below). A couple of queries.
A. I had forgotten that, when promoting a bare to a decorated interval in the context of, say,
(bare xx) op (decorated yy), returning (decorated zz)
it is good sense to allot the most *pessimistic* decoration consistent with the available information, not the most optimistic.
On 26 Oct 2010, at 16:55, Arnold Neumaier wrote:
> In the 5-value decoration scheme I had suggested, this would mean
> that a bare interval is promoted to a decorated interval with decoration 4 if it is Empty, and decoration 2 otherwise.
Why decoration 2, "possibly everywhere defined"? Consider the function g(x) defined by the expression sqrt(2*x-x). Evaluating its interval version on [-3,-1] we get
sqrt([-6,-2]-[-3,-1]) = sqrt([-5,1]) = [0,1]
though g is nowhere defined on [-3,-1].
Thus the nonempty interval [0,1] could have arisen from evaluating a function that is nowhere defined on its input box. I deduce from this that correct pessimistic promotion of a nonempty interval gives it decoration 3, not 2.
B. Can you explain, with examples, what "bounded" in the description of dec=0 refers to please?
- The output interval zz?
- The input box for a possible function that produced zz?
- The exact range of that possible function over its input box?
Making a more general point, I feel it would be VERY useful for someone to draft USER DOCUMENTATION for the exception handling. It would explain, say, for an intelligent scientific-computing undergraduate, what these features can achieve; give examples including code; give examples that show pitfalls and why the design is chosen as it is. If we can describe it simply, it improves our confidence that we have a viable and useful design.
Anyone willing to have their arm twisted? Or to twist someone's arm? Ideally this valuable work should be shared by more than one person.
John Pryce
On 10 Oct 2010, at 12:15, Arnold Neumaier wrote:
> proposed wording for a possible motion:
>
> ========================================================================
> It is proposed that precisely the following five decorations shall be available:
>
> dec = 0: safe = everywhere defined, continuous, and bounded)
> dec = 1: everywhere defined
> dec = 2: possibly everywhere defined
> dec = 3: nowhere defined
> dec = 4: not valid
>
> In all interval exchange formats, a decoration is encoded by an
> unsigned integer dec taking one of the values 0, 1, 2, 3, or 4.
> The encoding in a datatype is left to the implementor.
>
>
> The following unary predicates shall be provided for bare decorations
> and for decorated intervals of any supported idatatype:
>
> isValid dec<4
> possiblyNonempty dec<3
> everywhereDefined dec<2
> isSafe dec<1
>
> notValid dec>3
> isEmpty dec>2
> possiblyUndefined dec>1
> notSafe dec>0
> ======================================================================