HP-35’s x^y Why?

[Albert Chan]

(11-03-2021 07:47 AM)J-F Garnier Wrote:  An additional benefit of the nth-root is a marginally improved accuracy.
Example on Saturn-based HP machines:
125^(1/3) = 4.9999...
but XROOT(125,3)=5 exactly.

Does HP71B has XROOT (or equivalent ?)
I am curious of how to efficiently implement this ...

(11-03-2021 01:44 PM)robve Wrote:  Implementation logic of ^ dictates to check that 1/(1/x) = x or close enough with respect to macheps.
If 1/(1/x) ~= x integer then (-y)^(1/x) = -(y^(1/x)).

Implementation logic is whatever the designer think it should behave.

Example, HP71B does not check reciprocal = "close enough" integer.
Negative number raised to non-integer exponent is a automatic fail.

>1/(1/3)
3
>(-8)^(1/3)
ERR:Neg^Non-int

(11-03-2021 02:38 PM)robve Wrote:  This cheap Casio gets it right:

Casio fx-115ES plus
(-128)^(1/7)=-2 OK
(-128)^(.1428571429) ERROR (as can be expected)

It can also be fooled to get it wrong

(-128)^(1÷6.999) = 2.00019808 ???