EXC/ x<>Rn for stack efficiency

[Thomas Klemm]

This looks like an XY problem to me.
Here is a program to calculate the great circle distance between two points A and B on a sphere.
Since no registers are used, the initial question X is not relevant.
All you ever wanted is a solution for Y.

Program

This program works for most HP calculators:

HP-25

Code:

01: 21       : x<->y
02: 22       : Rv
03: 41       : -
04: 14 05    : f COS
05: 21       : x<->y
06: 01       : 1
07: 14 09    : f ->R
08: 21       : x<->y
09: 22       : Rv
10: 61       : *
11: 21       : x<->y
12: 01       : 1
13: 14 09    : f ->R
14: 21       : x<->y
15: 22       : Rv
16: 61       : *
17: 22       : Rv
18: 61       : *
19: 21       : x<->y
20: 22       : Rv
21: 51       : +
22: 15 05    : g COS-1

HP-15C

Code:

   001 {          34 } x↔y
   002 {          33 } R⬇
   003 {          30 } −
   004 {          24 } COS
   005 {          34 } x↔y
   006 {           1 } 1
   007 {       42  1 } f → R
   008 {          34 } x↔y
   009 {          33 } R⬇
   010 {          20 } ×
   011 {          34 } x↔y
   012 {           1 } 1
   013 {       42  1 } f → R
   014 {          34 } x↔y
   015 {          33 } R⬇
   016 {          20 } ×
   017 {          33 } R⬇
   018 {          20 } ×
   019 {          34 } x↔y
   020 {          33 } R⬇
   021 {          40 } +
   022 {       43 24 } g COS⁻¹

HP-42S

Code:

00 { 24-Byte Prgm }
01 X<>Y
02 R↓
03 -
04 COS
05 X<>Y
06 1
07 →REC
08 X<>Y
09 R↓
10 ×
11 X<>Y
12 1
13 →REC
14 X<>Y
15 R↓
16 ×
17 R↓
18 ×
19 X<>Y
20 R↓
21 +
22 ACOS
23 END

Example

This is the example provided for the SR-56:

Point A: \(33^\circ 54.5'\) N, \(94^\circ 56.2'\) W
Point B: \(33^\circ 59.6'\) S, \(151^\circ 25.6'\) E

DEG

33.5430 →HR
33.908333

94.5612 →HR
94.936667

-33.5936 →HR
-33.993333

-151.2536 →HR
-151.426667

R/S
125.999888

If we want to get the result in nautical miles we can multiply the result by 60:

60
×

7559.993276

Or then we could convert degrees to radians and multiply the result by earth's radius.

Formula

(06-15-2017 10:29 AM)Paul Dale Wrote:  It ought to be possible to calculate the distance using the modified Vincenty formula on the 25:

These programs use the same formula as the original program for the SR-56:

\(
\Delta \sigma =\arccos \left ( \sin \phi _{1}\sin \phi _{2}+\cos \phi _{1}\cos \phi _{2}\cos(\Delta \lambda ) \right )
\)

Conversion

(06-15-2017 09:01 AM)Dieter Wrote:  This will for instance show that the complete routine in the first steps (which is called several times as SBR 00) is obsolete since it does a simple d.ms to decimal degrees conversion (e.g. it turns 42°50' into 42,8333°). The 25 and 33 have a dedicated function for this.

Well, not exactly.
Therefore we have to convert e.g. \(94^\circ {56.2}'\) to \(94^\circ {56}' {12}''\) in our heads.

References

• SR-56 Application Library
  

The original link to this document appears to be broken.

(06-15-2017 09:01 AM)Dieter Wrote:  But I am sure that HP25 great circle programs already exist. ;-)

• HP-25 Applications Programs
• HP-19C/29C Solutions: Navigation
• HP-65 Navigation Pac 1
• HP-67/HP-97 Navigation Pac I
  

Cf. Programs/Library1/HP25-AP24.25:

Code:

01: 24 00    : RCL 0
02: 14 04    : f SIN
03: 24 01    : RCL 1
04: 14 04    : f SIN
05: 61       : *
06: 24 00    : RCL 0
07: 14 05    : f COS
08: 24 01    : RCL 1
09: 14 05    : f COS
10: 61       : *
11: 24 02    : RCL 2
12: 14 05    : f COS
13: 61       : *
14: 51       : +
15: 23 03    : STO 3
16: 15 05    : g COS-1
17: 23 04    : STO 4
18: 06       : 6
19: 00       : 0
20: 61       : *
21: 74       : R/S
22: 24 01    : RCL 1
23: 14 04    : f SIN
24: 24 00    : RCL 0
25: 14 04    : f SIN
26: 24 03    : RCL 3
27: 61       : *
28: 41       : -
29: 24 00    : RCL 0
30: 14 05    : f COS
31: 71       : /
32: 24 04    : RCL 4
33: 14 04    : f SIN
34: 71       : /
35: 15 05    : g COS-1
36: 24 02    : RCL 2
37: 14 04    : f SIN
38: 15 41    : g x<0
39: 13 47    : GTO 47
40: 22       : Rv
41: 03       : 3
42: 06       : 6
43: 00       : 0
44: 21       : x<->y
45: 41       : -
46: 13 00    : GTO 00
47: 22       : Rv
48: 13 00    : GTO 00
49: 13 00    : GTO 00