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x root y on hp42s


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Post: #2
04-07-2012, 04:23 AM
David Griffith Offline
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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?

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Post: #3
04-07-2012, 04:39 AM
Alexander Oestert Offline
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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

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Post: #4
04-07-2012, 11:51 PM
Gerson W. Barbosa Offline
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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.

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Post: #5
04-08-2012, 06:17 AM
Dieter Offline
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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

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Post: #6
04-08-2012, 06:22 AM
Paul Dale Offline
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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

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Post: #7
04-08-2012, 12:06 PM
Dieter Offline
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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

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Post: #8
04-08-2012, 06:14 PM
Paul Dale Offline
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Double precision carries 34 digits not 32 :-)

- Pauli

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Post: #9
04-08-2012, 10:34 PM
Walter B Offline
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... for that reason it's called 'double' ;-)

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Post: #10
04-08-2012, 11:14 PM
Paul Dale Offline
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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

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Post: #11
04-08-2012, 11:37 AM
Gerson W. Barbosa Offline
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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.

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Post: #12
04-08-2012, 12:17 PM
Dieter Offline
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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

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Post: #13
04-08-2012, 06:16 PM
Paul Dale Offline
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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

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Post: #14
04-08-2012, 12:21 PM
Walter B Offline
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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).
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Post: #15
04-08-2012, 12:39 PM
Gerson W. Barbosa Offline
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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.

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Post: #16
04-08-2012, 12:43 PM
Walter B Offline
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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 :-)
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