Re: Forth PARANOIA

BruceMcF wrote:
On May 24, 9:52 pm, "Ed" <nos...@xxxxxxxxxxx> wrote:
Marcel Hendrix wrote:
...
I also fixed a second bug ( 0^0 should be 1 ).

The ability to turn nothing into something is surely the province of
the Gods and delusional engineers. For mere mortals, the most we
could hope for is:

0 ^ anyvalue = 0

However even this is more convention than legal math (i.e. what to
do in an impossible situation without aborting).

Yes, but anyvalue ^ 0 = 1

Since

(anyvalue)^8 = (anyvalue)^(8+0) = (anyvalue^8)x(anyvalue^0)

so (anyvalue^0) must be a multiplicative identity, which for every
number other than exactly 0 can only be 1.

Another reason that 0^0 is taken to be 1 that is especially relevant
to floating point is that (0+delta)^0=1 for all delta, including delta
arbitrarily small. Therefore there is an infinite number of real
numbers all represented by fp 0.0 for which (0.0)^0 is, in fact,
exactly 1. Since from delta approaching zero from both the negative
and positive side, (0+delta)^0 is exactly 1, equating 0^0 to zero
introduces a needless discontinuity.

I'm not a mathematician so I leave it to the experts to prove or
disprove. If mathematics determines a computation to be illegal
then it is an error and 'discontinuous' no matter what.

In that case, I'd prefer a 0 result which can signal 'error' and is
testable, rather than a 1 which could result from a valid computation.

As regards zero and its powers, here's a reference:
http://mathforum.org/library/drmath/view/55764.html



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