(42S) Quadratic formula - stack only

[anderson]

A few years after I graduated I put my Hp 42S in a drawer. It slowly drained it's batteries. All the programs I spent so much time writing were gone and it just laid the for about 15 years. But, recently I screwed myself on some important thing using a windows calculator. So I invested some cash in a pack of LR44 batteries and in a few minutes I was back in a RPN world. A few hours later I started rewriting my library. Here is current iteration of my quadratic formula quadratic equation solver. I know this was done many times but as it is now, I find it simple and useful. Main goals were:
- do not use registers
- try to use only only stack
- after presenting results in readable form preserve both solution in Y and X register.

So here it is:

Code:



The program calculates both solutions to quadratic equation using quadratic formula.

Equation: ax^2 + bx + c = 0
Formula:  x1,2 = (-b+-SQRT(b^2-4ac))/2a 

INPUT
Program expects input parameters (quadratic equations coefficients) on stack:

T    ?    - not important, it will be overwritten
Z    a
Y    b
X    c

OUTPUT
Output is on the stack
T    2a                    Left over from calculation
Z    SQRT(Discriminant)    I did not manage to leave Discriminant on the stack and calculate using only stack.
Y    x1                    First root
X    x2                    Second root.

Optionaly; Discriminant can be stored in a variable, and put on stack after calculation.

NOTES
The program uses only stack and ALPHA register.


LBL 00            Error handling routine
"Coefficient "    Inform a user about an error.
|-"a is 0"
AVIEW
CLX                Because of OCD, restore coefficients on the stack as they were entered
RDOWN            [0, a, b, c]
STOP            At this point user can examine existing coefficients, enter new ones and reexecute program, either with R/S or XEQ.

LBL    "QUADFML"    This is the entry point into the program execution. Stack should be populated with [?,a,b,c].
RCL ST Z        [a,b,c,a]
X=0?    
GTO 00    
*                [a, a, b, ac]
4                stack [a,b,ac,4]
*                [a, a, b, 4ac]
RCL ST Y        [a, b, 4ac, b]
X^2                [a, b, 4ac, b^2]
x<>Y            [a, b, b^2, 4ac]
-                [a, a, b, b^2-4ac] v nadaljevanju uporabim    D = b^2-4ac    SD=SQRT(D)
"Discriminant:LF"    --LF denotes LineFeed symbol. Optional: ommit if you do not need to display discriminant.
PROMPT
STO "QUADDISC"    [a,a,b,D]    -- this step is optional see below
SQRT            [a,a,b,SD] we must calculate SQRT(D) now, because there is not enough place on stack to hold 2a, D, SQRT(D), x1,....
2                [a,b,SD,2]
RCL* ST T        [a,b,SD,2a] a is not needed anymore
x<> ST Z        [a,2a,SD,b]
+/-                [a,2a,SD.-b]
ENTER            [2a,SD,-b,-b]
RCL- ST Z        [2a,SD,-b,-b-SD]
RCL/ ST T        [2a,SD,-b,x1]    x1=(-b-SD)/2a
x<>y            [2a,SD,x1,-b]
RCL+ ST Z        [2a,SD,x1,-b+SD]
RCL/ ST T        [2a,SD,x1,x2]     x2=(-b+SD)/2a, stack now contains SQRT(D) and both solutions. I have not found a way to preserve discriminant using only stack.
-- optional formated output
"x1="
ARCL ST Y
|-"x2="            |- = concat symbol = [shift] [ALPHA] [ENTER]
ARCL ST X
AVIEW

In the past I did write some programs to so symbolic algebra and equation solving, symbolic integration, simplification and factorization of algebraic expression… all the sweeties that 42S lacked right from the box. I just have to find all my paper notes somewhere in the drawers.

[rprosperi]

(04-01-2018 09:22 PM)anderson Wrote:  In the past I did write some programs to so symbolic algebra and equation solving, symbolic integration, simplification and factorization of algebraic expression… all the sweeties that 42S lacked right from the box. I just have to find all my paper notes somewhere in the drawers.

First, welcome to the forum.

Second, thanks for sharing this 42S program. The 42S is quite a hot topic at the moment, as SwissMicros has recently introduced a modern version called the DM42, based on Thomas Okken's excellent Free42 Simulator, with a huge LCD, easy connection to the PC, improved Alpha keyboard and many other improvements. Look around the forum and you'll see lots of discussion and excitement about the DM42.

Also, we look forward to seeing some of the programs you mention; those are topics not typically covered so they should lead to a lot of discussion.