(35s 42s/DM42 50G) Quadratic formula

[mchris]

Probably someone has done it before, but...
Inspired by a HP41C program I found for the quadratic formula that uses only the 4 level stack, no INPUTs, no extra registers, I thought maybe I could do something similar with the HP35s, despite that it doesn't have the register arithmetic with the stack registers. The program uses the equivalent formula -(b/2a)±SQRT((b/2a)^2-(c/a)). The fact there is only 2 terms makes it easier. I don't think it could be done with the (-b±SQRT(b^2-4ac))/2a formula. We press a ENTER b ENTER c XEQ Q and the 2 solutions, real or complex returned in X and Y registers. No INPUTs, no extra registers, just the stack, in just 29 steps.

Code:

Q001        LBL Q
Q002        EQN REGZ
Q003        /
Q004        RDN
Q005        X<>Y
Q006        /
Q007        2
Q008        /
Q009        +/-
Q010        ENTER
Q011        X^2
Q012        RUP
Q013        -
Q014        X>=0?
Q015        GTO Q021
Q016        +/-
Q017        SQRT
Q018        i
Q019        *
Q020        GTO Q022
Q021        SQRT
Q022        ENTER
Q023        ENTER
Q024        EQN REGT
Q025        +
Q026        RDN
Q027        -
Q028        RUP
Q029        RTN

[PedroLeiva]

I tried this examples from HP 25 Application Program Manual:

ax2 + bx + c = 0

Examples
1 . X2 + X - 6 = 0
2. 3 X2 + 2x -1 = 0
3. 2X2 - 3x + 5 = 0

Solution
1. D = 6.25
Xl = -3.00
X2 = 2.00
2. D = 0.44
Xl = -1.00
X2 = 0.33
3. D = -1.94
Xl , X2 = 0.75 ± 1.39 i

For the first case with your program: x1= -3, x2= 3; the rest INVALID DATA
The program looks nice, but some corrections have to be made. Pedro

[mchris]

I tried the examples you mentioned and I get the correct answers. Did you key the program correctly?

[PedroLeiva]

(05-25-2020 03:52 PM)mchris Wrote:  I tried the examples you mentioned and I get the correct answers. Did you key the program correctly?

Yes I did. Only one doubt, in steps 04 and 26, RDN code I got it by pressing blue shift (right arrow) and key coordinate 1,4 (first colum, forth row) -> E, wich shows in blue RND intaed of RDN. Maybe I am confused. Please confirm. Another option is to send an emulator file. Pedro

[pinkman]

(05-25-2020 03:52 PM)mchris Wrote:  I tried the examples you mentioned and I get the correct answers. Did you key the program correctly?

Same for me, it works fine.

[pinkman]

(05-25-2020 04:19 PM)PedroLeiva Wrote:  

(05-25-2020 03:52 PM)mchris Wrote:  I tried the examples you mentioned and I get the correct answers. Did you key the program correctly?

Yes I did. Only one doubt, in steps 04 and 26, RDN code I got it by pressing blue shift (right arrow) and key coordinate 1,4 (first colum, forth row) -> E, wich shows in blue RND intaed of RDN. Maybe I am confused. Please confirm. Pedro

RDN stands for Register Down: R↓
RUP stands for Register Up: R↑

[PedroLeiva]

(05-25-2020 04:25 PM)pinkman Wrote:  

(05-25-2020 04:19 PM)PedroLeiva Wrote:  Yes I did. Only one doubt, in steps 04 and 26, RDN code I got it by pressing blue shift (right arrow) and key coordinate 1,4 (first colum, forth row) -> E, wich shows in blue RND intaed of RDN. Maybe I am confused. Please confirm. Pedro

RDN stands for Register Down: R↓
RUP stands for Register Up: R↑

Great, TYVM. It Works perfect now. Pedro

[mchris]

The same logic can be ported to 42s/DM42 and 50g.
42s/DM42

Code:

01▸LBL "QE"
02 RCL ST Z
03 +/-
04 STO÷ ST Z
05 ÷
06 X<>Y
07 2
08 ÷
09 STO ST Z
10 STO ST T
11 X↑2
12 +
13 SQRT
14 STO- ST Z
15 +
16 END

50g

Code:

« 3 PICK / 3 ROLLD SWAP / 2 / NEG DUP SQ ROT – √ DUP2 + EVAL 3 ROLLD – EVAL »

[Joe Horn]

This is "cheating" but the 50g can do it in two steps:

<< →V3 PROOT >>

BYTES: 18 #75EEh

[John Keith]

(05-04-2023 09:02 PM)mchris Wrote:  50g

Code:

« 3 PICK / 3 ROLLD SWAP / 2 / NEG DUP SQ ROT – √ DUP2 + EVAL 3 ROLLD – EVAL »

On the HP 49 and HP 50, 3 PICK can be replaced by PICK3, and 3 ROLLD can be replaced by UNROT. Each of those changes saves 2.5 bytes and a small amount of time.

Also, on the 28 and 48, ROT ROT is faster than 3 ROLLD. This only matters inside a loop but it may be useful to know.

[mchris]

Thanks, I'm beginner RPL user.