(^ 0.0 0.0) AND (^ 0 0.0)

[Daniel L. Weinreb <dlw at SCRC-TENEX at MIT-MC>]

I want to forward this to the rest of you.  Common Lisp currently says
that zero to the zero is one, although it isn't careful about what data
types it's talking about; I assume that is means floating point.

    Date: Wednesday, 1 December 1982  02:03-EST
    From: Alan Bawden <ALAN at SCRC-TENEX>
    Just for the record let me clarify the issue about 0.0^0.0 .  Consider
    taking the limit of A^X as X approaches 0.0 (from above).  If A is
    different from 0.0 (and 0 as well incidentally), then the limit of this is
    1.0 .  On the other hand, if A=0.0 (or 0) then the limit is 0.0 .  Thus
    there would be a discontinuity of the function 0.0^X (as well as 0^X) at
    the point 0.0 if we were to decide that 0.0^0.0 (and 0^0.0) = 1.0 .
    Discontinuities in floating point functions are bad (as I understand the
    philosophy of floating point) because they mean that a small difference in
    floating point truncation and roundoff can be magnified arbitrarily.