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x root y on hp42s - David Griffith - 04-07-2012

I'm trying to turn the cube root program in the 42s's manual into an "x root y" program, but I'm having trouble understanding how to recall the Y register. Would please paste an nth-root program here?


Re: x root y on hp42s - Alexander Oestert - 04-07-2012

To recall X, Y, Z, T from the stack on th 42s, press

[RCL] and [.] and you will be presented with soft key choices. The same for STO.

Another way to access Y is to do X<>Y




Re: x root y on hp42s - Gerson W. Barbosa - 04-07-2012

The following results match what I get with x|/y on the HP32 SII, except for the error messages. This can be optimized for size, of course.

             00 { 41-Byte Prgm }
01>LBL "XROOT"
02 STO ST Z
03 X<>Y
04 X>=0?
05 GTO 00
06 X<>Y
07 2
08 MOD
09 X=0?
10 DOT
11 Rv
12 X<>Y
13 ENTER
14 FP
15 X!=0?
16 DOT
17 Rv
18 Rv
19>LBL 00
20 SIGN
21 LASTX
22 RCL ST Z
23 1/X
24 Y^X
25 ABS
26 ×
27 .END.

Keystrokes Display

27 +/- ENTER 3 XEQ XROOT -3
32 +/- ENTER 5 XEQ XROOT -2
27 +/- ENTER 3 +/- XEQ XROOT -3.33333333333E-1
32 +/- ENTER 5 +/- XEQ XROOT -4.99999999999E-1
32 ENTER 5 +/- XEQ XROOT 0.5
625 ENTER 4 XEQ XROOT 5
625 ENTER 4 +/- XEQ XROOT 0.2
625 +/- 4 XEQ XROOT Invalid Type
27.5 ENTER 3.5 +/- XEQ XROOT 3.87937790083E-1
27.5 +/- ENTER 3.5 XEQ XROOT Invalid Type
27.5 +/- ENTER 3.5 +/- XEQ XROOT Invalid Type
27.5 ENTER 3.5 XEQ XROOT 2.577732888
5 ENTER 0 XEQ XROOT Divide by 0

P.S.: Real arguments only.

Edited: 8 Apr 2012, 12:00 a.m.


Re: x root y on hp42s - Dieter - 04-08-2012

Hi Gerson,

Quote:
The following results match what I get with x|/y on the HP32 SII ...

27 +/- ENTER 3 XEQ XROOT -3


Fine. And now try the cube root of 729. Does it still match ?-)
Quote:
32 +/- ENTER 5 +/- XEQ XROOT -4.99999999999E-1

My 35s here returns exactly -0,5. What does your 32sII say? I cannot imagine the result is any different.

BTW, it can be shown that evaluating roots this way may exhibit an error up to several units in the last significant digit. That's why I was so eager about CUBERT and XROOT in the 34s. ;-)

Dieter


Re: x root y on hp42s - Paul Dale - 04-08-2012

The 34S will still exhibit the same error in the last place, but due to the increased internal precision, it will likely be hidden resulting in an effective +/- 1 ULP in the result.


- Pauli


Re: x root y on hp42s - Gerson W. Barbosa - 04-08-2012

Hello Dieter,

Quote:
And now try the cube root of 729. Does it still match ?-)

It practically matches: 8.99999999998.

Quote:
Quote:
32 +/- ENTER 5 +/- XEQ XROOT -4.99999999999E-1

My 35s here returns exactly -0,5.

So does my HP-32SII. "Practically" is the word I missed. My fault, sorry!
Quote:
That's why I was so eager about CUBERT and XROOT in the 34s. ;-)

It's a pity the latter is not available from the keyboard. IMHO, it should be a better companion to yx than LOGx, which of course should stay. Where to find room for both on the keyboard? I think ./, is superfluous as RDX. and RDX, are available under MODE. But I am aware time for keyboard layout suggestions is over...

Gerson.


Re: x root y on hp42s - Dieter - 04-08-2012

Yes, that's why there are guard digits. With its 39-digit precision and 16 resp. 32 digit output, I think the 34s may look at all this quite relaxed. ;-)

Dieter


Re: x root y on hp42s - Dieter - 04-08-2012

Gerson,

Quote:
It practically matches: 8.99999999998.

Aaaaaha! ;-)

But it gets even worse. Try the 6th root of 531441. In cases like these the error may be as large at 5 ULP.

Quote:
It's a pity the latter is not available from the keyboard. IMHO, it should be a better companion to y^x than LOGx, which of course should stay. Where to find room for both on the keyboard?

I think XROOT would fit nicely on the (green shifted) sqrt / x^2 key.
Oooops... guess what - that's exactly where it is placed on the 35s. :-)
Quote:
But I am aware time for keyboard layout suggestions is over...

Walter always says that the 34s is a moving target. So nothing is fixed. ;-)

Dieter


Re: x root y on hp42s - Walter B - 04-08-2012

Quote:
I think ./, is superfluous as RDX. and RDX, are available under MODE. But I am aware time for keyboard layout suggestions is over...

Sim, Gerson - you're right with your second sentence. And the label ./, was caused by the fact that at design time our North American friends kept asking for an easy way to change the radix mark whenever they got a comma calculator ;-) And since we meanwhile put an alpha menu on said label, we can't change that easily (BTW I remember we had a discussion about that very label some (many?) months ago, but I don't remember when).


Re: x root y on hp42s - Gerson W. Barbosa - 04-08-2012

Quote:
And the label ./, was caused by the fact that at design time our North American friends kept asking for an easy way to change the radix mark whenever they got a comma calculator ;-)

On the other hand, this also allows for an easy way to accidentally change the radix mark. I missed that discussion, however.


Re: x root y on hp42s - Walter B - 04-08-2012

Quote:


On the other hand, this also allows for an easy way to accidentally change the radix mark. I missed that discussion, however.


You're right again, but you can correct that accident most easily :-)


Re: x root y on hp42s - Paul Dale - 04-08-2012

Double precision carries 34 digits not 32 :-)

- Pauli


Re: x root y on hp42s - Paul Dale - 04-08-2012

Quote:
Walter always says that the 34s is a moving target. So nothing is fixed. ;-)

The keyboard layout is a little less fluid than everything else.


- Pauli


Re: x root y on hp42s - Walter B - 04-08-2012

... for that reason it's called 'double' ;-)


Re: x root y on hp42s - Paul Dale - 04-08-2012

It is called double because it occupies 128 bits of memory whereas single precision occupies 64 bits. There is logic here.

In reality, we're using double and quadruple precision. Single precision being 32 bits which allows seven digits.


The gain in digits is made possible by not doubling the size of the exponent field and not duplicating the sign bit with each doubling in length of the number.


- Pauli