05-31-2016, 04:54 PM
Arithmetic-Geometric Mean
HP-15C
HP-67
Examples:
1) AGM(3,4)
3 ENTER 4 f A -> 3.482027677 (6)
2) AGM(12345,6789)
12345 ENTER 6789 f A -> 9359.761031 (2)
3) √(2* π*√(2* π)/AGM(1,√(2))) = Γ(1/4)
2 π * √x g LASTx * 2 √x 1 f A / √x --> 3.625609909 (8)
4 1/x 1 - f x! --> 3.625609908
Notes:
1) Examples above on the HP-15C, first version program;
2) The second HP-15C program version uses the numbered register 0, but preserves its original content;
3) All versions preserve the original stack-register X;
4) The programs are based on an HP-41C program by Jean-Marc Baillard:
Optimization suggestions welcome.
Gerson.
HP-15C
Code:
001- f LBL A 42 21 11
002- ENTER 36
003- f LBL 0 42 21 0
004- R↓ 33
005- STO I 44 25
006- X≷Y 34
007- + 40
008- g LSTx 43 36
009- RCL× I 45 20 25
010- √x 11
011- X≷Y 34
012- 2 2
013- ÷ 10
014- X≷Y 34
015- RCL I 45 25
016- g TEST 6 43 30 6
017- GTO 0 22 0
018- g R↑ 43 33
019- X≷Y 34
020- g RTN 43 32
Code:
001- f LBL A 42 21 11
002- g R↑ 43 33
003- f LBL 0 42 21 00
004- R↓ 33
005- ENTER 36
006- f X≷ 0 42 4 0
007- R↓ 33
008- X≷Y 34
009- + 40
010- . 48
011- 5 5
012- X≷Y 34
013- × 20
014- g LSTx 43 36
015- RCL- 0 45 30 0
016- RCL× 0 45 20 0
017- √x 11
018- g R↑ 43 33
019- f X≷ 0 42 4 0
020- g TEST 6 43 30 6
021- GTO 0 22 0
022- g R↑ 43 33
023- X≷Y 34
024- g RTN 43 32
HP-67
Code:
001 *LBLA 31 25 11
002 ENT↑ 41
003 *LBL0 31 25 00
004 R↓ 35 53
005 STOI 35 33
006 X≷Y 35 52
007 + 61
008 LSTX 35 82
009 RCLI 35 34
010 × 71
011 √X 31 54
012 X≷Y 35 52
013 2 02
014 ÷ 81
015 X≷Y 35 52
016 RCLI 35 34
017 X≠Y? 32 61
018 GTO0 22 00
019 R↑ 35 54
020 X≷Y 35 52
021 RTN 35 22
Examples:
1) AGM(3,4)
3 ENTER 4 f A -> 3.482027677 (6)
2) AGM(12345,6789)
12345 ENTER 6789 f A -> 9359.761031 (2)
3) √(2* π*√(2* π)/AGM(1,√(2))) = Γ(1/4)
2 π * √x g LASTx * 2 √x 1 f A / √x --> 3.625609909 (8)
4 1/x 1 - f x! --> 3.625609908
Notes:
1) Examples above on the HP-15C, first version program;
2) The second HP-15C program version uses the numbered register 0, but preserves its original content;
3) All versions preserve the original stack-register X;
4) The programs are based on an HP-41C program by Jean-Marc Baillard:
Code:
01 LBL "AGM"
02 ENTER^
03 LBL 01
04 CLX
05 RCL Z
06 RCL Y
07 +
08 2
09 /
10 RCL Y
11 SQRT
12 R^
13 SQRT
14 *
15 R^
16 X#Y?
17 GTO 01
18 END
Optimization suggestions welcome.
Gerson.