Precision Tail-off?

[Peter J. Holzer]

On 2023-02-18 03:52:51 +0000, Oscar Benjamin wrote:
> On Sat, 18 Feb 2023 at 01:47, Chris Angelico <rosuav at gmail.com> wrote:
> > On Sat, 18 Feb 2023 at 12:41, Greg Ewing via Python-list
> > > 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.
> 
> Various libraries can do this. Both SymPy and NumPy have cbrt for cube roots:

Yes, but that's a special case. Chris was talking about arbitrary
(integer) roots. My calculator has a button labelled [x√y], but my
processor doesn't have an equivalent operation. Come to think of it, it
doesn't even have a a y**x operation - just some simpler operations
which can be used to implement it. GCC doesn't inline pow(y, x) on
x86/64 - it just calls the library function.

        hp

-- 
   _  | Peter J. Holzer    | Story must make more sense than reality.
|_|_) |                    |
| |   | hjp at hjp.at         |    -- Charles Stross, "Creative writing
__/   | http://www.hjp.at/ |       challenge!"
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