Re: Draft decoration system for discussion
Michell
Am 04.12.2012 05:34, schrieb Michel Hack:
Page 33, 8.8.3, Unbounded dac intervals.
Consider the function 1/(1000 - log(x)) for positive x. This
is undefined for a very large x (outside 754 binary64 range),
In level 1 the function is bounded
so in level 2, although overflow happend
IMHO wie can now decide whther oo means an overflow or the true infinity
The decorated function evaluation
x =[1,oo]_dac // the dac decoration indicates the interval as the set
x>= 1
log x =[0,oo]_dac // all x >=0
1000 - log x = [-oo,1000]_dac //
1/(1000 - log x) = [-oo,oo]_trv// division by 0
in contrast to [1,oo]_trv // this interval contains a true sinfgularity
so at Level 2 it would be bounded.
not realy
However, if an interval
input is [1,+oo;dac], the dac must not be allowed to propagate
because that input range does contain the large pole.
I'm not saying the document is wrong; I just feel a bit uneasy...
with this comment you probably feel more uneasy
Jürgen
Page 33, 8.8.4, propagation order (just above the Notes).
It might be nice to describe the two sides of trv as "good" and "bad".
Page 34, last para of 8.8.5: "may provide versions ... add a decoration"
Does this partially address Nate's concern? Would it be worthwhile
to standardize (and expect implementations to use different names)
SOME useful decorated Hull and Intersection operations -- granted
that the default, unadorned operations would be bare-only?
Page 35, 8.8.7, 1st sentence: what does "defined in $6.3" refer to?
Page 35, 8.8.7, amended newDec function, typo: instaed
Page 35, 8.8.7, Note. "com describes a Level 2 property".
The notions seems perfectly well-defined at Level 1, where it simply
excludes empty and unbounded inputs; in all other cases it is, at
Level 1, equivalent to dac. The real benefit does indeed show up at
Level 2, due to the guarantees on intermediate results mentioned at
the end of the next paragraph (bottom of page 35).
Page 36, 8.8.8, Compressed decorated intervals.
As formulated by means of a decoration threshold this too makes sense
as a Level 1 concept, though the practical consequences show primarily
at Level 3. The level 1 domain is the union of the set of non-empty
bare intervals and a discrete set of decorations, in a cross product
with a constant threshold (i.e. it is a family of domains parameterized
by the threshold).
Page 36, 8.8.8, normalInterval() function (just past middle of page):
This description is totally garbled.
Michel.
---Sent: 2012-12-04 05:47:11 UTC
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