HP-35’s x^y Why?

[robve]

(11-03-2021 07:45 AM)Albert Chan Wrote:  You are assuming the reason it fail is INV(INV(7)) does not revert back to 7 ?
My guess is it never even check that.

Negative number raised to non-integer exponent is a automatic fail.

Try (-128)^INV(3) instead, since INV(INV(3)) = 3 (binary or decimal, any precision)

Yes. 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)).

Yes. Obviously, for negative x and non-integer y.

Sort of. However, assuming y is limited to "easy" integer reciprocals only, then this is still an epic fail.

Another fail:

Casio fx-7000G:
(-128)^(1/7) ERROR
(-128)^(.1428571429) ERROR (as can be expected)

Of course, the Casio allows an explicit nth root operation and so does the HP 35s:
7 n-root (-128)=-2 OK

I'm not impressed by this Casio either.

The lazy way to implement n-th root is to check if x is integer and calculate x n-root -y with -(x n-root y) = -(y^(1/x) = -EXP(LOG(y)/x).

The correct way for a calculator's implementation logic is to consider the fact that x n-root y = y^(1/x) = signum(y) |y|^(1/x) if x is integer. By using this identity and root-power symmetry we can also avoid taking the LOG of a negative number.

- Rob