Re: Fw: Overflow and Inf
If I may be permitted to phantasize a bit further, it is actually
conceivable that the decorated-inifinity concept could be adapted
to BFP.
In 2008 we were still unable to define the Q-bit (QNaN vs SNaN)
for BFP -- only to recommend a choice. Eventually we may reach
the point where everybody agrees. (For DFP it was nailed down.)
Suppose we reserve TWO high-order fraction bits instead of one
for the highest-biased-exponent (all ones) case. Then we could
have:
00 Undecorated Infinity; remaining bits assumed zero
01 Signalling NaN (with payload)
10 Decorated Infinity (further decoration details?)
11 Quiet NaN (with payload)
Unfortunately that doesn't work; in fact, no 2-bit method stands
a chance to be compatible: to be useful, Decorated Infinity would
have to be a Signalling NaN on old equipment. But Signalling NaNs
should also be convertible to QNaNs by a simple bit-OR. Would three
bits work?
There is another problem, already discussed in the earlier discussions
of this topic: the inverse of a decorated infinity needs to be a
decorated zero, or (as I called it previously) an inexact signed zero,
i.e. the equivalent of Underflow. This may not be necessary for IA,
but an FP standard needs to think about it -- and it's not pretty.
**********
In conclusion, I think this issue needs to be resolved strictly in
the Interval Arithmetic context. There is no sensible FP equivalent.
We may need FP-primitive assistance along the lines discussed by
Arnold Neumaier and Ian McIntosh -- but we must not try to assign
FloatingPoint semantics to it.
Michel.
---Sent: 2010-09-29 21:14:16 UTC