[std-interval] discontinuity flag

Prof.Dr.J.Wolff von Gudenberg wolff at informatik.uni-wuerzburg.de
Thu Oct 5 14:41:01 PDT 2006

Dear Intervalers,
a short notice to clarify defintion and use  of the discontinuity flag

>>> 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
Our proposal is a flag as u user defined boolean variable, so not a 
global (hardware) flag.
standard functions come with 2 interfaces, one completely ignoring the 
flag and one that sets it in case of discontinuity or being undefined

John's description of context
4. Hence the typical pattern of use is
- The DESOLVE manual tells the Engineer how to implement APPFCN, including
   to do so without clearing the DISCONT flag.

At run time
- Trusted Code DESOLVE clears the DISCONT flag.
- DESOLVE calls Untrusted Code APPFCN.
- On return DESOLVE inspects the flag. If it remains un-set, and APPFCN is
   written correctly, the Brouwer conditions have been rigorously verified.
clearly describes the scenario
and the engineer has to rewrite his source code anyhow if it is applied 
in the context of a new (interval) solver

Another point: We are afraid of delegating some of the behavior 
(semantics) to the compiler. Experience with compilers has shown that 
they usually do not understand the proper handling of arithmetic flags 
or settings, see the switching of the rounding mode, e.g.

Prof. Dr. Juergen Wolff v. Gudenberg <wolff at informatik.uni-wuerzburg.de>
      o    Lehrstuhl fuer Informatik II
     / \   Universitaet Wuerzburg             Phone: +49 (0)931-888-6602
InfoII o  Am Hubland                         Fax:   +49 (0)931-888-6603
   / \     D-97074 Wuerzburg
  o   o    http://www2.informatik.uni-wuerzburg.de/staff/wvg/

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