Bill Page wrote:
>
> On 13 September 2016 at 17:10, Waldek Hebisch <[email protected]>
> wrote:
> > Bill Page wrote:
> >> ...
> >> Are 0$DFLOAT and 1$DFLOAT really only approximate in FriCAS?
> >> In general I thought the most consistent approach to floats was to
> >> treat all (representable) floating point numbers as exact but to admit
> >> that floating point operations are often necessarily approximate.
> >
> > If a function gets 0 as an argument, then there is good chance to
> > this 0 is mathematically correct. But when mathematically you
> > should get 0, rounding error may lead to small nonzero number.
> > Given that x^y is discontinous at (0,0), depending on definition
> > of x^y at (0, 0) is error prone. So it makes sense to "undefine"
> > it and signal error.
> >
>
> Presumably this argument should apply to any situation where the
> result of a calculation is discontinuous, right? But for example what
> about the case of a logical condition like
>
> x < 0$DFLOAT
>
> Would you argue that this also should be undefined?
There is question of pragmatics. '<' has many valid uses.
'=' is more problematic, but still too useful to ban.
However, I see no natural uses which depend on 0^0 giving
1. More precisely, the natural cases are when it is
known that exponent is exact. But in such case representing
it as floating point number is not so natural.
And since you have '<' and '=' you can roll your own
definition -- without '<' and '=' that would be impossible.
--
Waldek Hebisch
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