How do I reproduce CMPLX+ from HP-32S in Free42?

[E Lye]

Question: How do I reproduce CMPLX+ in Free42?

In

Engineering Applications
Step-by-Step Solutions
for Your HP-32S Calculator

Edition 1 June 1988

Page 106

Circle Determined by Three Points

This program calculates the center (x,y)
and radius (r) of the circle
defined by three noncollinear points.

r^2 = (x —x0)^2 + (y - y0)^2

Other than the formula above, there is no other
explanation on the algorithm. No diagram provided.

I am studying this prior to writing my CTIP program
for Free42 (not 42S simply because that does not
have enough memory for 9999 registers).

It looked TOO SIMPLE compared to the other formulas
I found on the internet so what is the HP secret?

My 32S has died. The 32SII that "repaired" this
developed screen cancer..

I tried SST through the program with pencil and
paper and each time (I really tried! Over 7 times at
least and weeks apart and each gave different results.)

OK, let me try writing the program in Free42, turn
on the printer and reverse engineer this sucker.

And then it hit me - where is CMPLX+ ?

There is no free 32S emulator and I certainly do

not have the ROM image.

Please help.

[Thomas Okken]

Check the HP-42S Owner's Manual, Chapter 6: Complex Numbers (pages 90-99).

In case you don't already have it, there is a link to the manual here: https://thomasokken.com/free42/#doc

[E Lye]

https://www.youtube.com/watch?v=Xk4qMHc9_Lw

A function/key can be used in more than one way
much like a car key employed to open a milk tin.

From my examination of its use for the 32S,
CMPLX+ can be a terse way to perform 2 additions
at one invocation BUT it occurs at the end of a
program that involves fragments of a triangle
I cannot identify and right before a polar to
rectangular conversion. A lot of things are
juggled and the picture is confusing.

I have reached the point where I need to plug
in actual numbers to see what is happening but
I get stuck. How can I be sure there is no
further use of the contents of ST Z and ST T
because the stack is raised and another CMPLX+
follows.

The 42S does not support CMPLX+ and
the 32S does not support COMPLEX
(somewhere I was informed that the 32S and 42S
 came out together)
and this algorithm does not use complex numbers.
Perhaps they are using vectors instead?

https://www.youtube.com/watch?v=CG7pEbM9F7g

shows some analytic solutions. None of the
expressions come close to this RPN program.

What does this programmer know that no one
else knows? Aren't you intrigued?

https://www.youtube.com/watch?v=7BIsfVEc-Cw

My previous attempts are on scraps of paper.
They are not worth documenting. I never
expected that this would drag on like this.
In these I get seriously detailed.

BUT it didn't help.

I don't know who the HP author is. A diagram
sure would be helpful.

By now I resort to actually programming into
Free42 and then . . . . Crash into CMPLX+.
I actually crashed into something that does not exist.

If nobody out there can help, I will attempt to
synthesize CMPLX+ .

Page 138 of the HP-32S Owner's Manual
does not explain what the comtents of stack
registers Z and T are after CMPLX+
. . . and I have no 32S nor emulator to
examine this.
 
Hence I am asking for help.

With Free42 I can afford to "waste" steps.

STO "XX"
Rolldown
STO "YY"
Rolldown
STO "ZZ"
Rolldown
STO "TT"
"reconstruct stack"
RCL "YY"
+
RCL "XX"
RCL "ZZ"
+
RCL "TT"
ENTER
Rolldown
Rolldown

I don't know what to plug into LastX.

[Thomas Okken]

I sent a reply as a private message. I don't see it in my GMail Sent folder, though, so I can't tell if it was routed correctly. Let me know if you didn't get it.