Arithmetic-Geometric Mean (HP-15C, HP-67)
05-31-2016, 04:54 PM
Post: #1
 Gerson W. Barbosa Senior Member Posts: 1,238 Joined: Dec 2013
Arithmetic-Geometric Mean (HP-15C, HP-67)
Arithmetic-Geometric Mean

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.
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