complex bakeoffs and error bounds

[David G. Hough at validgh]

Parts of the recent discussions about complex extensions to C have 
incorporated notions like "you can't tell if an infinity is a genuine infinity
or an overflow" and "you can't tell if a zero is a genuine zero or an
underflow" and indeed you can't - a number is just a number and may not be
the number you want, and if you don't have any kind of error bound then
you don't know whether your result means anything or not, whether it's
-0, +inf, or 3.    Some people draw the conclusion from this that 
computers shouldn't produced signed zeros or infinities which might well
be misinterpreted, but they might as well go on to the obvious conclusion
that no computation should proceed beyond the first rounding error, for
computations that do may sometimes produce results that are subject to
misinterpretation if no estimate of their uncertainty is also provided.

Interval arithmetic is one approach to dealing with uncertainty.

But I think the main point is not that 3 can be misinterpreted, but that it
can be meaningful when properly supported.   Same for -0 and +inf - even in
complex arithmetic there are occasions when the sign bit has a meaningful
interpretation, and to discard or obscure
those sign bits because they are sometimes meaningless is not helpful.

Then the proper question is "what system of dealing with sign bits in most
often meaningful in problems in which one might conceivably look at the
sign bits?"