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Dominique Lohez wrote:
Nate Hayes a écrit :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 decorationsI agree the program must never lie, and I don't see that it does.Ye, It does not le However one may fell frustrated if the continuous function p(x) can never seen as continuous by the program except when only a single piece of the definition scheme is used.
True. However, I note that *none* of the proposed decoration schemes so far solve this problem.
The question is could we intentionally use a definition scheme in order to recover the continuity Possibly at the cost of a widening of the interval component of the result. And then how can we ask How can we insure the continuity statement of the new scheme?
It is a very good question worthy of consideration. I've thought about it for a long time myself, but have never found a satisfactory answer. The main problem seems to be is it requires global information that could only be provided by a computer algebra system (CAS). This seems to be outside the scope of IEEE 1788. Even if it weren't, there are limits even to what kind of assistance a CAS can provide, and I'm skeptical a truly general-purose solution that is guaranteed to work for all cases could be found. However, it doesn't mean I wouldn't be happy to find a solution, if such a solution truly exists. I guess I'm just saying I don't see what such a solution could possibly be. Do you have some ideas? Nate
DominiqueThe 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. NateDominique-- 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-- Dr Dominique LOHEZ ISEN 41, Bd Vauban F59046 LILLE France Phone : +33 (0)3 20 30 40 71 Email: Dominique.Lohez@xxxxxxx