Re: The current proposal

[Ralph Baker Kearfott <rbk@xxxxxxxxxxxxx>]

> > Arnold Neumaier schrieb:
> > > Nate Hayes schrieb:
> >
> > > > > > whereas the "ideal" result would be
> > > > > >
> > > > > >    (-Inf,b] + (Inf,Inf) = [0,Inf),
> > > > > >
> > > > > > assuming the "infinity is number" paradigm where the infinity is not
> > > > > > a member of the interval but rather a token for an unbounded real
> > > > > > endpoint.
> > >
> > > 1/[-1,0] + 1e400 should give in exact arithmetic [-inf,1e400],
> > > hence with infinity-as-number [-inf,inf] in verified floating
> > > point arithmetic.
> > >
> > > If you don't allow the operation 1/[-1,0] to give the value
> > > [-inf,0] then the division operation is not appropriate for
> > > applications to global oto=imization.
> > >
> > > But if you assume 1/[-1,0] = [-inf,0], your proposal gives the
> > > severe underestimate [0,inf].
>
> No.
>
> In your example, zero is a member of the denominator, so infinity is a
> member of the result produced by the reciprocal operation. If zero is not
> a member of the denominator, then
>
>    1/[-1,0) + 1e400 = (-Inf,-1] + (Inf,Inf) = [0,Inf).


Or, alternatively:

   1/[-1,0) + 1e400 = (-Inf,-1] + [MAX_FLOAT,Inf) = (-Inf,Inf),

i.e., depending on how the number 1e400 is converted, it may produce the result (-Inf,Inf).

Nate Hayes
Sunfish Studio, LLC