Re: Bare decorations (was ...level 2 datums)
Baker Kearfott wrote:
Nate, John, Vladik, Arnold, et al,
Having "swapped out" my attention to the list for a couple of days, I am
somewhat bewildered by this line. In particular, where is it leading?
Unfortunately, I do worry this discussion is taking us backwards, not
forwards. Hence my (possibly futile) efforts to turn it around.
Is it getting us any closer to standard wording upon which we can agree?
My understanding was that the original intent of the levels in P-754 was
as a device to aid in developing the standard and coming to a consensus,
not as a set of dictates from a higher power to be upheld at all costs
and to engender controversy.
I apologise if people see this as being unproductive. However, I think
straying off-course in regards to this topic (exception handling) is not
justified and will cost P1788 lots of additional (unnecessary) time and
effort. This is why for this particular issue I defend the status-quo.
For me, the controversey is not what are the various levels, or even what
are the names of things at the various levels. The rub is mainly what Arnold
recently explained, i.e.:
Arnold Neumaier wrote:
One of the decorated intervals, namely (Empty,invalid), serves as
the NaI that John Pryce is asking for in his draft of a position paper.
But he wants to give it an additional separate existence, which is
both unneccesary and against the spirit of the whole decoration concept
as argued in the rationale for Motion 8 (which you'd read again to have
the context).
This also includes John's proposal to abolish bare decorations, which, in my
view, are the most useful part of the existing exception-handling model.
This is why I see John's position paper is an effort to "start over from
scratch" with a new exception-handling system, one that in my view raises
doubts and new complications.
This is why I'm concerned.
If I really saw it was just an issue of terminology, I wouldn't care so
much.
Nate Hayes
Furthermore, I also am a bit confused by what
exactly the levels are, if they they are taken to be as defined on page 10
of the draft standard. In particular, already at level 2, we are talking
of "machine intervals."
I'm hoping we can quickly get beyond the sticking points here and resolve
what I
feel are true issues (e.g. do we specify mid / rad operations, exactly
how do the decorations behave and what decorations do we have).
Sincerely,
Baker
On 10/25/2010 4:31 AM, John Pryce wrote:
Nate
On 25 Oct 2010, at 06:09, Nate Hayes wrote:
It is possible to discuss Level 2 in the abstract, but there is NO way
to
define a specific Level 2 floating-point or interval datatype without
describing it by some sort of formula, which usually amounts to a
representation.
I'm sorry, John, but this is not true.
It is done all the time. A good reference is Bertrand Meyer's book on
object-oriented design where he describes an abstract datatype (ADT)
purely
in mathematical terms by:
-- its types (i.e., its mathematical sets)
-- its functions
-- its axioms
-- its preconditions (if any)
I have read books on OO design; indeed I consulted one of Grady Booch's
while composing that last email. Maybe what's at issue is what my words
"amounts to a representation" mean. So I ask you
How can one specify the set F of level 2 datums of IEEE 754's
"binary32" datatype in a representation-free way?
The specification must enable one to answer the question "how many such
datums are there?", i.e. to find the cardinality of F explicitly -- a
boring but valid level 2 question.
John
--
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R. Baker Kearfott, rbk@xxxxxxxxxxxxx (337) 482-5346 (fax)
(337) 482-5270 (work) (337) 993-1827 (home)
URL: http://interval.louisiana.edu/kearfott.html
Department of Mathematics, University of Louisiana at Lafayette
(Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
Box 4-1010, Lafayette, LA 70504-1010, USA
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