Re: Motion: Number format (Motion 33?)
Vincent, P1788
On 12 Apr 2012, at 01:44, Vincent Lefevre wrote:
> Motion
> ======
>
> An argument or a result of some operations covered by the standard
> can be a number. A number is defined at Level 1 as being any member
> of the set Rbar = R U { -oo, +oo } of extended reals. This motion
> defines the corresponding notion at Level 2, called "number format"
> and denoted here F. For an inf-sup interval type, the bounds are
> the members of a number format F. An implementation must support
> at least one number format F...
Thank you for this. I think if it passes it will clarify discussion of Level 2 matters very much. At first reading I see nothing in the content that I disagree with but can I suggest some amendments to wording?
(1) Cite the (sub)clause in IEEE 754 of each reference you make, e.g. change
> which rounding function (among the two possible rounding-direction
> attributes) is used must be defined by the implementation.
to
> which rounding function (among the two possible rounding-direction
> attributes, IEEE 754 §4.3.1) is used must be defined by the implementation.
My Mac keyboard has the symbol "§" (Section). If this isn't readable by everyone, I suggest to use TeX's "\S".
(2) Start paragraphs of the rationale by "On A1." instead of "A1.", and so on, to make clear you are referring back to clauses of the motion.
(3) Make clear, by changing the indentation or inserting a bar "---------", where text is comment to introduce the next clause rather than part of the previous clause, e.g.
> The notion of number format F compatible with an interval type T can
> be defined, if need be...
which looks like part of B4 but actually introduces C1.
(4a) IMO the idea (was it Dmitry's?) of a "number format F compatible with an interval type T" is very sensible. I feel it should be definitely specified by the motion rather than left as "...if need be".
(4b) But the present phrasing around clause C1 doesn't make sense. We wouldn't vote for C1 as written, we would vote for something like
> C1. A number format F is said to be compatible with an interval
> type T if:
> For each non-empty interval I of type T (Level 2), there exists
> a finite number x of F such that x \in I.
>
> For some specific operations involving T-intervals and F-numbers
> (to be decided by later motions), F shall be compatible with T
> (but shouldn't if this isn't really necessary).
Requiring each type to have a compatible format would clarify the cost of defining some exotic types. For instance, if T is the asymmetric triplex interval representation <m,r1,r2> = [m+r1, m+r2] you've used for a recent example, where r1 and r2 can be of the same sign, no "ordinary" FP format F can be compatible. One would have to use double-double or similar.
John Pryce