(41C) and (42S) Arithmetic-Geometric Mean

[Werner]

In a lengthy thread about bore hole volumes not so long ago, I came up with the following, thanks to Albert Chan and Gerson W. Barbosa (stack-only, 41/42 compatible and reg Z preserved):

Code:

00 { 27-Byte Prgm } @   X       Y       Z       T
01▸LBL 02
02 X<>Y
03 X<> ST T
04 2
05 ÷
06▸LBL "AGM" @          a       b       z
07 STO ST T @           a       b       z       a
08 X<>Y
09 STO+ ST T @          b       a       z       2AM
10 STO× ST Y
11 X<>Y
12 SQRT @               GM      b       z       2AM
13 X≠Y?
14 GTO 02
15 R↓
16 END

I you want to show "AGM=.." at the end, for Free42 and DM42 there's a way that does not use the Alpha register: just add

LSTO "AGM"
VIEW "AGM"

at the end.

Cheers, Werner