(42s) Hypergeometric function for HP-42s (UPDATED)

[Namir]

Hypergeometric function for HP-42s
=================================

Code calculates values for the hypergeometric function F(alpha, beta, gamma, x). The code uses the gamma function to help calculate the value of the hypergeometric function.

Memory Map
=========

Code:

R00 = x
R01 = alpha
R02 = beta
R03 = gamma_var
R04 = toler
R05 = sum - > fx value
R06 = k (loop control variable).
R11 = gamma(alpha)
R12 = gamma(beta)
R13 = gamma(gamma_var)

HP-42S Listing
=========

NOTE: The following code was updated per suggestions of Velentin Alibillo to shorten the code by a few statements.

Code:

01 LBL "HGFX"
02 A^B^C^
03 PROMPT
04 STO 00
05 RDN
06 STO 03
07 GAMMA
08 STO 13
09 RDN
10 STO 02
11 GAMMA
12 STO 12
13 RDN
14 STO 01
15 GAMMA
16 STO 11
17 TOLER?
18 PROMPT
19 STO 04
20 1
21 STO 06
22 0
23 STO 05
24 LBL 00
25 1
26 STO+ 0
27 RCL 01
28 RCL+ 0
29 GAMMA
30 RCL 11
31 ÷
32 RCL 03
33 RCL+ 0
34 GAMMA
35 RCL 13
36 ÷
37 ÷
38 RCL 02
39 RCL+ 0
40 GAMMA
41 RCL 12
42 ÷
43 ×
44 RCL 05
45 N!
46 ÷
47 RCL 00
48 RCL 05
49 Y^X
50 ×
51 STO+ 0
52 ABS
53 RCL 04
54 X=Y?
55 GTO 00
56 RCL 06
57 RTN

Usage
=====

1) Press [XEQ] HGFX. The program displays the prompt "A^B^C^X?"
2) Enter the value for parameter alpha and press ENTER.
3) Enter the value for parameter beta and press ENTER.
4) Enter the value for parameter gamma and press ENTER.
5) Enter the value for x and press R/S. The program displays the prompt "TOLER?"
6) Enter a small value for the tolerance and press R/S.
7) The program displays the value of the hypergeometric function.

Example
=======

To calculate F(1.5, 1.5, 2.5, 0.3), perform the following steps:

1) Press [XEQ] HGFX. The program displays the prompt "A^B^C^X?"
2) Enter the value 1.5 for parameter alpha and press ENTER.
3) Enter the value 1.5 for parameter beta and press ENTER.
4) Enter the value 2.5 for parameter gamma and press ENTER.
5) Enter the value 0.3 for x and press R/S. The program displays the prompt "TOLER?"
6) Enter a small value 1E-15 for the tolerance and press R/S.
7) The program displays 1.36956073 as the value of the hypergeometric function.

[Valentin Albillo]

.
Hi, Namir,

(10-30-2023 05:29 PM)Namir Wrote:  HP-42S Listing
=========

01 LBL "HGFX"
02 A^B^C^X?
03 PROMPT
04 STO 00
05 RDN
06 STO 03
07 RDN
8 STO 02
9 RDN
10 STO 01
11 TOLER?
12 PROMPT
13 STO 04
14 1
15 STO 06
16 0
17 STO 05
18 RCL 01
19 GAMMA
20 STO 11
21 RCL 02
22 GAMMA
23 STO 12
24 RCL 03
25 GAMMA
26 STO 13
27 LBL 00
28 1
29 STO+ 05
30 RCL 01
31 RCL 05
32 +
33 GAMMA
34 RCL 11
35 ÷
36 RCL 03
37 RCL 05
38 +
39 GAMMA
40 RCL 12
41 ÷
42 ÷
43 RCL 02
44 RCL 05
45 +
46 GAMMA
47 RCL 13
48 ÷
49 ×
50 RCL 05
51 N!
52 ÷
53 RCL 00
54 RCL 05
55 Y^X
56 ×
57 STO+ 06
58 ABS
59 RCL 04
60 X=Y?
61 GTO 00
62 RCL 06
63 RTN

Some hopefully useful comments:

1. Change the Subject of your OP from "Hypergeometric function for HP-42s" to "(42S) Hypergeometric function", to conform to the titling style in this forum.

2. I've seen that this program for the 42S is essentially the same as the one you recently posted to the 41C Library, essentially just replacing the calls to your GAM4 program by the 42S built-in GAMMA function.

However, the 42S also has RCL arithmetic (which the 41C lacks) and it can be put to good use in several places, for instance:


30 RCL 01
31 RCL 05
32 +


can be replaced by:


30 RCL 01
31 RCL+ 05


saving one line (32 + is no longer necessary). You can do this with lines 30-32, 34-35 (RCL÷ 11), 36-38, 40-41, 43-45 and 47-48, saving 6 lines in all.

3. You can also save further lines replacing this code:
...
06 STO 03
07 RDN
08 STO 02
09 RDN
10 STO 01
11 TOLER?
12 PROMPT
13 STO 04
14 1
15 STO 06
16 0
17 STO 05
18 RCL 01
19 GAMMA
20 STO 11
21 RCL 02
22 GAMMA
23 STO 12
24 RCL 03
25 GAMMA
26 STO 13
27 LBL 00


by this code:
...
06 STO 03
07 GAMMA
08 STO 13
09 RDN
10 STO 02
11 GAMMA
12 STO 12
13 RDN
14 STO 01
15 GAMMA
16 STO 11
17 TOLER?
18 PROMPT
19 STO 04
20 1
21 STO 06
22 0
23 STO 05
24 LBL 00
...


saving an additional 3 lines with no change in functionality (just very slightly faster.)

Best regards.
V.

[Werner]

Yes, but RCL+ nn always takes 3 bytes, while RCL nn + only takes 2, for n=00 to 15 included.
Cheers, Werner

[Namir]

Thanks Valentine for your tips and comments. Will update the code!

Namir

[Namir]

HP-42S listing in first posting of this thread has been updated.

Namir