HP-35’s x^y Why?

[robve]

(11-03-2021 02:37 AM)robve Wrote:  I strongly suspect that a dedicated key for the y'th root of x (or the x'th root of y with Sharp) surely indicates that negative x with odd y'th roots are supported, e.g. (-27)^1/3 returns -3. This requires some careful implementation logic to determine that x is a perfect reciprocal (e.g. 0.142857142 is really close enough to 1/7, or is it?). I noticed that older and simpler scientific calculators don't support negative x, e.g. Ti-25 and Sharp EL-5100. I don't own a sufficiently large collection of calculators to test this hypothesis, so correct me if I'm wrong.

Let's try this out. While 1/7 equals \( 0.\overline{142857} \), entering 10 digits .1428571429 on a 10 digit calculator should fail, because internally 12 digits are significant with the last 2 rounded off and internally 1/7 has 12 digits (or more depending on the calculator):

Sharp EL-5200:
(-128)^(1/7)=-2 is OK
(-128)^A=-2 with variable A=1/7 is OK
(-128)^(.1428571429) ERROR (as can be expected)

Sharp PC-1474 and PC-E500 and most other Sharp PC:
(-128)^(1/7)=-2 is OK
(-128)^A with variable A=1/7 ERROR because simple variables hold 10 digits in Sharp S-BASIC
(-128)^(.1428571429) ERROR (as can be expected)

HP-35s:
ALG mode: (-128)^INV(7) ERROR
RPN mode: 7 1/x 128 (-) y^x ERROR

Ti 36X:
(-128)^(1/7)=-2 is OK
(-128)^(.1428571429) ERROR (as can be expected)

Sharp EL-506A:
(-128)^(1/7)=-2 is OK
(-128)^(.1428571429) ERROR (as can be expected)

Philips SBC 158
(-128)^(1/7) ERROR also 7-th root of -128 fails
(-128)^(.1428571429) ERROR (as can be expected)

Ti-25
(-128)^(1/7) ERROR
(-128)^(.1428571429) ERROR (as can be expected)

All of these calculators have an n-th root key except the Ti-25. I consider the Philips scientific calculator a nice metallic machine from the early 80s, but not a serious calculator. It also has a quirk: digits are not shifted to the left when entered, the first digits simply stay on the left.

But why, oh why HP-35s did you fail?

- Rob