Re: Four vs. five decorations
Dominique Lohez wrote:
Your example works very nicely at level 1 and lower level because the
vale are small integers and rational numbers with denominator which
are power of 2 .
Replace 2 by 3 and a lot of problems arises: You have to use partial
interval overlapping other the piecewise defined function may be
undefined.
Suppose that you work with the Dan Zuras' potential well functions with a
> 0
potential (x) = sqrt(x² -a) if |x| >= sqrt(a)
-sqrt(a-x^2 ) if |x | <= sqrt(a)
To keep the function defined in the interval of use the function have to
be modified in contradictory in the various intervals
The approximate function of the initially continuous function may become
not continuous.
The problem is really difficult.
Ah, yes. I completely agree.
(and thank you very much for the clarification, BTW)
If for example we have the interval extension
P(X) = U(X) \union V(X)
with
U(X) = sqrt((|X| \intersect [roundDown(sqrt(a)),+Inf])^2-a)
V(X) = -sqrt(a-(|X| \intersect [0,roundUp(a)]))
Then we may get a U(X) or V(X) decorated conservatively... possibly even
"undefined" if the rounding errors are too big.
Even a cautious programmer may fail.
Thus the program must never lie
It must never believe the programmer implicit extra-assertions and check
from known data and decorations
I agree the program must never lie, and I don't see that it does.
The known data and decorations are only as valid as the program and provided
input data. There is old saying in computer science: "garbage in, garbage
out".
It think it will not be possible to make a standard that compensates for
bugs in poorly written programs. Even with the aid of very powerful computer
algebra systems, this probably will not always be possible.
The liability of such failures should fall on the shoulders of the
programmers and not be traced back to known failures in the IEEE 1788
decoration system, i.e., as long as the stated conditions hold, it should be
provable the source of failure is not the IEEE 1788 standard.
This does mean P1788 should be careful to specify exactly the conditions
under which the standard applies.
Nate
Dominique
--
Dr Dominique LOHEZ
ISEN
41, Bd Vauban
F59046 LILLE
France
Phone : +33 (0)3 20 30 40 71
Email: Dominique.Lohez@xxxxxxx
--
Dr Dominique LOHEZ
ISEN
41, Bd Vauban
F59046 LILLE
France
Phone : +33 (0)3 20 30 40 71
Email: Dominique.Lohez@xxxxxxx