P1788
Am 07.03.2012 16:00, schrieb Ulrich Kulisch:
Dear
P1788 members:
P1788 considers intervals of \overline{IR}, the set of closed
and connected sets of real numbers. In mathematics the
midpoint of an interval is well defined for elements of the
set IR, the set of nonempty, colsed and bounded real
intervals.
During the last 12 months the question was discussed whether
and how the midpoint should be defined for elements of the set
\overline{IR}\IR. I have great sympathy with Dan's resistance
of returning NaN in these cases. First of all, this answer may
be wrong. Think of an interval of IR where the lower and the
upper bound are greater than Fmax. This interval has a real
number as its midpoint. It is just not compubable within the
given floating-point system. An answer like "not calculable"
or perhaps "indefinite" (a native English speaking colleague
may find a better denotation) seems to me being more
appropriate. Second: Arithmetic of \overline{IR} is strictly
based on mathematical grounds and it is free of exceptions. So
elements of IEEE 754 like NaN which are more of a speculative
nature should not unnecessarily be introduced into P1788.
Now, the question remains, how should the midpoint of elements
of \overline{IR}\IR be defined? I think there is no need at
all defining it within P1788. We also don't give a definition
of the logarithm for negative numbers. If a user has a
reasonable application where he needs a splitting point for an
unbounded interval or the empty set we should let him the
freedom defining it in a way that is appropriate for his
application. We don't need this definition in the standard.
I think that is a good idea and in full accordance with the
definition of the interval functions where 1/[0,0] is not defined.
That is the level 1 view.
at level 2 we have to specify a value for any interval in
\overline{IR} \IR
I support to return NaN. IMO there is no other choice for the
emptyset.
For unbounded intervals returning +oo or -oo could keep some
information about the sign.
But I don't think it is worthwhile the effort.
In this case, as Vincent says, the main purpose is to inform the
attentive user
Juergen
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