Precision Tail-off?

[Chris Angelico]

On Sat, 18 Feb 2023 at 12:41, Greg Ewing via Python-list
<python-list at python.org> wrote:
>
> On 18/02/23 7:42 am, Richard Damon wrote:
> > On 2/17/23 5:27 AM, Stephen Tucker wrote:
> >> None of the digits in RootNZZZ's string should be different from the
> >> corresponding digits in RootN.
> >
> > Only if the storage format was DECIMAL.
>
> Note that using decimal wouldn't eliminate this particular problem,
> since 1/3 isn't exactly representable in decimal either.
>
> To avoid it you would need to use an algorithm that computes nth
> roots directly rather than raising to the power 1/n.
>

It's somewhat curious that we don't really have that. We have many
other inverse operations - addition and subtraction (not just "negate
and add"), multiplication and division, log and exp - but we have
exponentiation without an arbitrary-root operation. For square roots,
that's not a problem, since we can precisely express the concept
"raise to the 0.5th power", but for anything else, we have to raise to
a fractional power that might be imprecise.

But maybe, in practice, this isn't even a problem?

ChrisA