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Best Pol/Rect and Complex Number Decomp for 35S
01-26-2019, 12:43 AM
Post: #1
Best Pol/Rect and Complex Number Decomp for 35S
I would like to know what program(s) are best for Complex Number and Polar/Rectangular and related forms decomposition for the 35S.

Thank you.
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01-26-2019, 02:21 AM
Post: #2
RE: Best Pol/Rect and Complex Number Decomp for 35S
(01-26-2019 12:43 AM)Matt Agajanian Wrote:  I would like to know what program(s) are best for Complex Number and Polar/Rectangular and related forms decomposition for the 35S.

Thank you.

Nice ->R and ->P programs from Pauli here:

http://www.hpmuseum.org/cgi-sys/cgiwrap/...i?read=983

--Bob Prosperi
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01-26-2019, 03:29 AM
Post: #3
RE: Best Pol/Rect and Complex Number Decomp for 35S
Thanks! Even though I picked this up several years ago, nice to know its stood the test of time to remain an excellent option.
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01-26-2019, 03:37 AM (This post was last modified: 01-26-2019 03:38 AM by Matt Agajanian.)
Post: #4
RE: Best Pol/Rect and Complex Number Decomp for 35S
(01-26-2019 02:21 AM)rprosperi Wrote:  
(01-26-2019 12:43 AM)Matt Agajanian Wrote:  I would like to know what program(s) are best for Complex Number and Polar/Rectangular and related forms decomposition for the 35S.

Thank you.

Nice ->R and ->P programs from Pauli here:

http://www.hpmuseum.org/cgi-sys/cgiwrap/...i?read=983

Please refresh my memory and clarify what should be on the stack before I run each routine.

Thanks

Thanks
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01-26-2019, 10:40 AM (This post was last modified: 01-26-2019 10:43 AM by ijabbott.)
Post: #5
RE: Best Pol/Rect and Complex Number Decomp for 35S
(01-26-2019 03:37 AM)Matt Agajanian Wrote:  
(01-26-2019 02:21 AM)rprosperi Wrote:  Nice ->R and ->P programs from Pauli here:

http://www.hpmuseum.org/cgi-sys/cgiwrap/...i?read=983

Please refresh my memory and clarify what should be on the stack before I run each routine.

Thanks

Thanks

Looking at the code, program P expects Y=y, X=x, and returns Y=θ, X=r. Vice versa for program R.

— Ian Abbott
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01-26-2019, 01:04 PM
Post: #6
RE: Best Pol/Rect and Complex Number Decomp for 35S
(01-26-2019 10:40 AM)ijabbott Wrote:  Looking at the code, program P expects Y=y, X=x, and returns Y=θ, X=r. Vice versa for program R.

Yes, and if you look closely you'll see these routines preserve the stack (incl LastX) and flags, so they act like built-in functions. Nice!

--Bob Prosperi
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01-26-2019, 04:23 PM (This post was last modified: 01-26-2019 04:47 PM by Dieter.)
Post: #7
RE: Best Pol/Rect and Complex Number Decomp for 35S
(01-26-2019 01:04 PM)rprosperi Wrote:  ...if you look closely you'll see these routines preserve the stack (incl LastX) and flags...

Yes for the stack and flags, but No regarding LastX. Which is not preserved – on exit it contains a complex number or a vector, respectively.

But it can be done. The following modified versions also preserve LastX:

Code:
P001  LBL P
P002  FS? 10
P003  GTO P011
P004: ABS
P005  X<>Y
P006  R↓
P007  R↓
P008  eqn ARG(LASTx+i*REGZ)
P009  eqn ABS(LASTx+i*REGT)
P010  RTN
P011: CF 10
P012  XEQ P004
P013  SF 10
P014  RTN

R001  LBL R
R002  FS? 10
R003  GTO R011
R004: ABS
R005  X<>Y
R006  R↓
R007  R↓
R008  eqn LASTx*SIN(REGZ)
R009  eqn LASTx*COS(REGT)
R010  RTN
R011: CF 10
R012  XEQ R004
R013  SF 10
R014  RTN

The R routine is even one step shorter. ;-)

Equations in programs really are a nice feature of the 35s. They simply return the result in X and push the stack by one level, while no other stack registers – including LastX – are affected. So these programs simply move the original X to LastX (by means of the ABS command in line 004) before they finally return the two results in Y and X.

For those who are not that familiar with the 35s equation mode: REGZ and REGT are entered by pressing the [R↓] key and then selecting the respective register X, Y, Z or T from the menu.

Stack diagram for →P:
Code:
T:  t        t
Z:  z        z
Y:  y   =>   θ
X:  x        r

L:  ?        x

Stack diagram for →R:
Code:
T:  t        t
Z:  z        z
Y:  θ   =>   y
X:  r        x

L:  ?        r

Finally, if the state of flag 10 does not have to be preserved the code can be even shorter. In this case remove line 011...014 and replace line 002...003 with "CF 10".

Dieter
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01-26-2019, 07:02 PM
Post: #8
RE: Best Pol/Rect and Complex Number Decomp for 35S
Excellent, Dieter, as always!
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01-26-2019, 07:17 PM
Post: #9
RE: Best Pol/Rect and Complex Number Decomp for 35S
(01-26-2019 07:02 PM)Gene Wrote:  Excellent, Dieter, as always!

And cool too! Thanks.
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01-26-2019, 08:49 PM (This post was last modified: 01-26-2019 09:16 PM by Dieter.)
Post: #10
RE: Best Pol/Rect and Complex Number Decomp for 35S
(01-26-2019 12:43 AM)Matt Agajanian Wrote:  I would like to know what program(s) are best for Complex Number and Polar/Rectangular and related forms decomposition for the 35S.

Here is my attempt at a complex decomposition routine:

Code:
C001  LBL C
C002  FS? 10
C003  GTO C014
C004  ABS
C005  x≠0?
C006  GTO C009
C007  ENTER
C008  RTN
C009: eqn SGN(SIN(ARG(LASTx)))*ABS(LASTx-SQ(REGX)/LASTx)/2
C010  X<>Y
C011  R↓
C012  eqn SGN(COS(ARG(LASTx)))*ABS(LASTx+SQ(REGT)/LASTx)/2
C013  RTN
C014: CF 10
C015  XEQ C004
C016  SF 10
C017  RTN

Stack diagram:
Code:
T:  t        z
Z:  z        y
Y:  y   =>   im
X:  re+i·im  re

L:  ?        re+i·im

The code has not seen much testing, so please try it, see what you get and report any errors and problems here.
Edit: added a few steps to make the routine also work for 0+0i.

Dieter
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01-27-2019, 03:47 AM
Post: #11
RE: Best Pol/Rect and Complex Number Decomp for 35S
(01-26-2019 04:23 PM)Dieter Wrote:  
(01-26-2019 01:04 PM)rprosperi Wrote:  ...if you look closely you'll see these routines preserve the stack (incl LastX) and flags...

Yes for the stack and flags, but No regarding LastX. Which is not preserved – on exit it contains a complex number or a vector, respectively.

Well, that should teach me! I read a post claiming all was preserved and while I bothered to check the flags (by reading code) and the stack contents (by testing), and all was confirmed, I did not check the LastX and extrapolated it too was safe. Never, ever assume...

Thanks for this alternate version Dieter. For the 2nd time in a week, after not touching it for a couple years, I've decided to enter programs in my 35S. If I learned about how useful and well-behaved equations are on the 35S when I got mine in 2007, I've totally forgotten it, so Pauli and your programs are good examples of how this feature can be used to build well-behaved functions pretty easily.

--Bob Prosperi
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01-27-2019, 08:26 AM (This post was last modified: 01-27-2019 08:29 AM by Gerald H.)
Post: #12
RE: Best Pol/Rect and Complex Number Decomp for 35S
For complex decomposition, returns real part to stack level X & imaginary to variable I:

Code:
1    LBL A
2    STO I
3    R↓
4    ABS(I)*COS(ARG(I))+0*(ABS(I)*SIN(ARG(I))►I)
5    RTN
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01-27-2019, 09:14 AM (This post was last modified: 01-27-2019 03:05 PM by Dieter.)
Post: #13
RE: Best Pol/Rect and Complex Number Decomp for 35S
(01-27-2019 08:26 AM)Gerald H Wrote:  
Code:
4    ABS(I)*COS(ARG(I))+0*(ABS(I)*SIN(ARG(I))►I)

That's a nice approach, with a much less complicated formula than the one I used. Combining it with my original solution the result would look like this:

Code:
C001  LBL C
C002  FS? 10
C003  GTO C010
C004: ARG
C005  eqn ABS(LASTX)*SIN(REGX)
C006  X<>Y
C007  R↓
C008  eqn ABS(LASTX)*COS(REGT)
C009  RTN
C010: CF 10
C011  XEQ C004
C012  SF 10
C013  RTN

Maybe this version is a bit more prone to roundoff errors so that the last digit may be slightly off here and there:

 1i1  =>  0,99999999998, 0,999999999997
-4i3  => -3,99999999999, 3,00000000001
 0i3  =>  1,4689...E-11, 3

The last example assumes radians mode.

OK, this may happen anytime as all we got are 12 digits instead of 15 the 35s uses internally. But on average the more complicated formulas in post #10 seem to exibit less of such problems. In all three cases it returns accurate results. Maybe because sine and cosine of the angle are avoided (only their sign is considered).

Dieter
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