Re: Motion 52: final "Expressions" text for vote
Vincent
Am 22.11.2013 13:19, schrieb Vincent Lefevre:
On 2013-11-21 18:35:10 -0800, Dmitry Nadezhin wrote:
Vincent,
In general, this should remain true for NaI. IMHO, the cases for
which this is not true should be listed.
In current draft, this is not true.
inf([NaI]) = NaN
inf(intervalPart([NaI])) = inf([Empty]) = +inf
convexHull([0,1]_com,[NaI])=[NaI]
convexHull(intervalPart([0,1]_com,intervalPart([NaI]))=convexHull([0,1],[Empty])=[0,1]
What do you mean by "this should remain true" ?
Well, for an arithmetic operation f, this seems to be true: in §8.2,
"Such an operation phi, with interval inputs x_1, ..., x_k carrying
decorations dx_1, ..., dx_k, shall compute the same interval output
y as the corresponding bare interval extension of phi---hence
dependent on the x_i but not on the dx_i.",
and in §11.6 (set-based only),
"By the definition of a bare interval extension, the interval part w
depends only on the input intervals v;".
I have some questions:
I propose some answers:
1. Is the above sentence of §8.2 an error or does the standard
require this to be still true for NaI? In any flavor?
NaI propagates in all operations, but NaI is NotanInterval
2. Does the standard require that if there's a NaI in any input,
then the result of f be NaI (for *any* flavor)?
for setbased yes
3. In the set-based flavor, according to the propagation order, if
there's a NaI in input (thus will decoration ill), then the result
shall have the decoration ill. Does the standard require that such
an interval be Empty?
the decoration ill is only used by NaI. intervalPart(naI) is undefined
and causes an exception
§11.4 doesn't seem to forbid NonEmpty_ill: it doesn't mention ill
at all and says "No other combinations are essentially forbidden."
but perhaps the ill case has been forgotten.
IMO ill is not a decoration, it only goes with NaI
4. In the set-based flavor (and other flavors supporting Empty?),
in the bare version, if there is an Empty in input (thus the box
is empty), shall the result be Empty?
yes
(I wonder whether such a requirement can block some optimizations,
e.g. in a filter where the main goal is to be as fast as possible,
though not always getting accurate results.)
Then, is there any contradiction between the answers to the above
items?
Jürgen
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