Re: Discussion paper: what are the level 2 datums?
Dan, P1788
Thanks for the comments on this paper.
On 5 Oct 2010, at 19:41, Dan Zuras Intervals wrote:
> ... While most of what you say about the meaning of 754
> Table 3.1 is correct, I have difficulty with the term
> 'tagged'. The phrase "for a particular format" is not
> so much to tag a floating-point value as to define
> which finite subset of the Reals lives at level 2 &,
> therefore, which set of representations need to live
> at level 3 to accomodate them. That is, there is a
> different Table 3.1 for each floating-point datatype.
>
> As far as 754 is concerned, the Binary32 value 2.0 is
> the same as the Binary64 value 2.0 as well as the
> Decimal128 value 2.0
I think you are 100% agreeing with what I MEAN, even if I'm not saying it as clearly as I would like.
> (although this last is further
> 'tagged', if you will, with a particular element chosen
> from the cohort of values that are all equal to 2).
NO! The first Note in 1.1 explicitly says this is not the case. There, there is a "cohort" of values -0 and +0 equal to 0. But the interval [0,2] is NOT tagged by the particular one chosen.
> ... The issue of whether two values chosen from two different
> datatypes may be compared or not is a language issue.
Precisely. WITHIN 754, they can't, not between different radices. 754§5.11 para 1:
"it shall be possible to compare one floating-point datum to another in that format (see 5.6.1). Additionally, floating-point data represented in different formats shall be comparable as long as the operands’ formats have the same radix."
> ... (We toyed with the idea of providing inter-radix comparisons
> just for this purpose but ultimately rejected the idea as
> both too hard to do & too silly. :-)
Precisely.
> ... Still, issues of radix aside, a level 2 value is a level
> 2 value. That is, it is an element of the Reals. If two
> such values exist in two different level 2 sets, they are
> still considered equal without any consideration of the
> type they came from.
Yes. IN CONTEXT. You are still 100% agreeing with me but failing to see it!
> Similarly, I think it should be true that the interval
> [0,2] or [-0,2] or [+0,2] all be considered equal no
> matter which level 2 set they are chosen from.
YES, when asking what the mathematical value of sin([0,2]) should be.
NO, when discussing to what pairs of values a "compareEqual" predicate may be applied.
John