[std-interval] Discontinuity flag

[Prof.Dr.J.Wolff von Gudenberg]

Dear Intervalers,
 during the SCAN 2006 meeting in Duisburg the following points have been 
discussed.

The GAMM activity group for Computer Arithmetic and Scientific Computing 
strongly supports the efforts to standardize
interval arithmetic in C++

The discussion showed that
Standard functions MUST set a flag when the argument interval is not 
completely contained in the domain of the function
Otherwise (i.e without the flag) verification of the result with fixed 
points or other assertions that need continuity is not possible
A whole branch of interval arithmetic will not be supported by the 
standard in that case.

We propose (together with G. Melquiond) That this flag can be managed by 
the user himself.
The elementary functions (at least those with bounded domain) have to 
set this flag in the case
when the argument interval is not completely contained in the domain of 
the function
interval<T> sqrt ( interval<T> x, bool& flag)
will be a proper interface
Such a function is also necessary for the division operator
interval<T> divide ( interval<T> x, interval<T> y, bool& flag)
interval<T> divide ( T x, interval<T>y,  bool& flag)
multiplication and addition are ok.


Walter Kraemer
Juergen Wolff v Gudenberg