Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s)

[Gerson W. Barbosa]

(01-18-2020 10:25 AM)grsbanks Wrote:  Could you enclose your listings in "code" tags? It makes the whole post shorter and tidier.

As you please, but you’ll have to scroll down to see the new HP-42S/Free42 version is now 36 steps long, LBL and END included :-)

Code:


00 { 73-Byte Prgm }
01▸LBL "EL"
02 RCL- ST Y
03 X<>Y
04 RCL+ ST L
05 STO 01
06 ÷
07 X↑2
08 ENTER
09 ENTER
10 ENTER
11 7
12 ×
13 544
14 -
15 ×
16 3328
17 +
18 ×
19 4096
20 -
21 STO÷ 01
22 R↓
23 -93
24 ×
25 224
26 +
27 ×
28 2304
29 +
30 ×
31 4096
32 -
33 RCL× 01
34 PI
35 ×
36 END

The corresponding wp34s version is 41 steps longs – too many constants, remove a few and it will be perfect! :-)
Perhaps someone has a trick to save a step or two...

wp34s version:

Code:



001:LBL A
002:⇆ XYYY
003:STO+ Y
004:©-
005:RCL/ I
006:x²
007:FILL
008:# 007
009:×
010:# 032
011:STO J
012:# 017
013:×
014:-  
015:×  
016:# 104
017:RCL× J
018:+
019:×
020:# 128
021:RCL× J
022:-
023:STO/ I
024:R↓
025:# 007
026:RCL× J
027:# 093
028:RCL× Z
029:-
030:×
031:# 072
032:RCL× J
033:+
034:×
035:# 128
036:RCL× J
037:-
038:RCL× I
039:# π 
040:×
041:END

p ≈ π(a + b){h²[h²(-93h² + 224) + 2304] - 4096}/{h²[h²(7h² - 544) + 3328] - 4096}

where

h = [(a - b)/(a + b)]

Thanks for your suggestion. This indeed looks cleaner now.

Edited after saving one step in the wp34s program.

PS:

1) The wp34s program can fit in 40 steps, including LBL and END;

2) The following is even more accurate, giving an error of only 116.385 km for our usual example – that’s about the distance from Milan to Parma.

p ≈ π(a + b){h²[h²(-381h² + 548) + 8448] - 13312}/{h²[h²(34h² - 2188) + 11776] - 13312}

Same number of steps on Free42/HP-42S, taking up a few more bytes.

Code:



00 { 79-Byte Prgm }
01▸LBL "EL"
02 RCL- ST Y
03 X<>Y
04 RCL+ ST L
05 STO 01
06 ÷
07 X↑2
08 ENTER
09 ENTER
10 ENTER
11 34
12 ×
13 2188
14 -
15 ×
16 11776
17 +
18 ×
19 13312
20 -
21 STO÷ 01
22 R↓
23 -381
24 ×
25 548
26 +
27 ×
28 8448
29 +
30 ×
31 13312
32 -
33 RCL× 01
34 PI
35 ×
36 END