Even faster quadratic formula for the HP-41C

Even faster quadratic formula for the HP-41C - Printable Version

+- HP Forums (https://www.hpmuseum.org/forum)
+-- Forum: HP Calculators (and very old HP Computers) (/forum-3.html)
+--- Forum: General Forum (/forum-4.html)
+--- Thread: Even faster quadratic formula for the HP-41C (/thread-1531.html)

Even faster quadratic formula for the HP-41C - Gerson W. Barbosa - 06-04-2014 04:25 AM

This is yet another attempt at finding a shorter (but not necessary faster) quadratic formula program for the HP-41C, while preserving the stack register T (Thanks to Jeff Kearns - if it were not because of his interest, I wouldn't have taken a second look at this old thread)

Code:

01 LBL 'Q

02 X<> Z 

03 CHS

04 ST/ Z

05 ST+ X

06 /

07 STO Z

08 X^2

09 +

10 SQRT

11 RCL Y

12 ST+ Z

13 +

14 ST- Y

15 END

x₂ is computed using this well-known property:

\[x_{1}+x_{2}=-\frac{b}{a}\]

Real roots only, but since the stack register T is preserved it will solve the first example for the HP-42S program here.

I'd rather present it here first, before submitting it to the HP-41C Software Library, as any issue I might have overlooked would surely be pointed out soon. Thanks!

Gerson.

PS.: The title should read ...faster quadratic formula program... - as the formula is essentially the same, but I cannot edit it.

RE: Even faster quadratic formula program for the HP-41C - Thomas Klemm - 06-04-2014 05:32 AM

Code:

00 { 22 Byte-Prgm }

01 LBL "Q"

02 X<> ST Z 

03 STO/ ST Z

04 STO+ ST X

05 /

06 ENTER

07 X^2

08 RCL- ST Z

09 SQRT

10 -

11 +/-

12 STO/ ST Y

13 END

x₂ is computed using this well-known property:

\[x_{1}\cdot x_{2}=\frac{c}{a}\]

Cheers
Thomas

RE: Even faster quadratic formula for the HP-41C - Gerson W. Barbosa - 06-04-2014 05:59 AM

(06-04-2014 05:32 AM)Thomas Klemm Wrote:

Code:

00 { 22 Byte-Prgm } 01 LBL "Q" 02 X<> ST Z 03 STO/ ST Z 04 STO+ ST X 05 / 06 ENTER 07 X^2 08 RCL- ST Z 09 SQRT 10 - 11 +/- 12 STO/ ST Y 13 END

x₂ is computed using this well-known property:

\[x_{1}\cdot x_{2}=\frac{c}{a}\]

Cheers
Thomas

Thomas,

I fear there might be trouble when c = 0. Also, the HP-41 lacks recall arithmetic.
Anyway, records exist to be broken. I won't be surprised if you or someone else comes up with a shorter (or a lower byte-count) HP-41 or 42S program.

Cheers,

Gerson.

P.S.: On the HP-42S, replace line 10 with

10 +

P.P.S.: This won't solve the case when both b and c are zero, however.

RE: Even faster quadratic formula program for the HP-41C - Thomas Klemm - 06-04-2014 07:11 AM

(06-04-2014 05:59 AM)Gerson W. Barbosa Wrote: I fear there might be trouble with c = 0.

I know. But then who is going to use this program to solve \(ax^2+bx=0\)?

Quote:Also, the HP-41 lacks recall arithmetic.

I tend to forget this.

Quote:P.S.: On the HP-42S, replace line 10 with
10 +
This won't solve the case when both b and c are zero, however.

Should this solve the problem with the division by zero?
In case of \(c=0\) this depends on the sign of \(b\).
So it doesn't really matter whether we use + or -.
I prefer to have \(x_1\) in register X.

Cheers
Thomas

RE: Even faster quadratic formula for the HP-41C - Paul Dale - 06-04-2014 07:33 AM

The same program for a 34S is very very tiny Smile

- Pauli

RE: Even faster quadratic formula for the HP-41C - walter b - 06-04-2014 08:52 AM

(06-04-2014 07:33 AM)Paul Dale Wrote: The same program for a 34S is very very tiny

You can say that Smile

d:-)

RE: Even faster quadratic formula for the HP-41C - Ángel Martin - 06-04-2014 10:14 AM

(06-04-2014 07:33 AM)Paul Dale Wrote: The same program for a 34S is very very tiny

Not tinier than "QROOT" in the SandMath ;-)

RE: Even faster quadratic formula for the HP-41C - Paul Dale - 06-04-2014 10:22 AM

(06-04-2014 10:14 AM)Ángel Martin Wrote: Not tinier than "QROOT" in the SandMath ;-)

Same number of steps Smile

- Pauli

RE: Even faster quadratic formula for the HP-41C - rprosperi - 06-04-2014 01:07 PM

(06-04-2014 07:11 AM)Thomas Klemm Wrote:
(06-04-2014 05:59 AM)Gerson W. Barbosa Wrote: Also, the HP-41 lacks recall arithmetic.
I tend to forget this.

I re-learn this every time I come back to using my 41. Which I suppose means I never really learn it all...

Very nice Gerson. Short AND sweet.

RE: Even faster quadratic formula for the HP-41C - Gerson W. Barbosa - 06-08-2014 02:55 AM

(06-04-2014 07:33 AM)Paul Dale Wrote: The same program for a 34S is very very tiny

It won't solve this one, however, unlike the HP-42S programs (mine and Thomas's). But what would CSLVQ (SSIZE8 mode only) be useful for anyway?

Gerson.

RE: Even faster quadratic formula for the HP-41C - Gerson W. Barbosa - 06-08-2014 03:00 AM

(06-04-2014 08:52 AM)walter b Wrote:
(06-04-2014 07:33 AM)Paul Dale Wrote: The same program for a 34S is very very tiny

You can say that

d:-)

In another post, about two years ago, I said "nothing beats SLVQ on the WP 34S, however". Definite a killjoy, but very useful :-) (I remember having used SLVQ in a program once).

Gerson.

RE: Even faster quadratic formula for the HP-41C - Gerson W. Barbosa - 06-08-2014 03:41 AM

(06-04-2014 01:07 PM)rprosperi Wrote: Very nice Gerson. Short AND sweet.

Thanks, Bob!

For the sake of documentation I should have mentioned that I have used the quadratic formula in this form, valid when a = -1:

\[x_{1}= \frac{b}{2}+\sqrt{\left ( \frac{b}{2} \right )^{2}+c}\]

Please see Allen's post in this thread from 2007.

Regards,

Gerson.

RE: Even faster quadratic formula for the HP-41C - Ángel Martin - 06-08-2014 09:26 AM

(06-08-2014 02:55 AM)Gerson W. Barbosa Wrote: It won't solve this one, however, unlike the HP-42S programs (mine and Thomas's). But what would CSLVQ (SSIZE8 mode only) be useful for anyway?

ZQRT in the 41Z module does too ;-)

RE: Even faster quadratic formula for the HP-41C - Gerson W. Barbosa - 06-08-2014 06:25 PM

(06-08-2014 09:26 AM)Ángel Martin Wrote:
(06-08-2014 02:55 AM)Gerson W. Barbosa Wrote: It won't solve this one, however, unlike the HP-42S programs (mine and Thomas's). But what would CSLVQ (SSIZE8 mode only) be useful for anyway?

ZQRT in the 41Z module does too ;-)

...with no native complex number support, you might have said! Sorry for my ignorance!

Gerson.

RE: Even faster quadratic formula for the HP-41C - Ángel Martin - 06-09-2014 02:24 PM

Yes, quadratic and cubic equations with complex coefficients and obviously results. Interestingly, I took the opportunity to review the code in the 41Z - finding a typo (a.k.a. bug) on the Spherical Hankel functions (not in the Bessel functions, those were ok). It appears that, like rust, bugs never sleep!