Perimeter of the Ellipse (HP-15C)

[C.Ret]

Code:

001- ►LBL E
002-     STO 2  x²  x<>y  STO 1  x²  +  STO 3  1  STO 0        ; Initiate  R2:b  R1:a  R3:S◄a²+b²  R0:t
011-     ►LBL 0
012-        RCL 1  ENTER^  RCL*2  √x  x<> 2  -  2  STO*0  /    ; Compute   R2:b◄√ab  R0:t◄t+t     k◄(a-b)/2 
021-        STO-1  x²  RCL*0  STO-3                            ;           R1:a◄a-k            R3:S◄S-t*k²
025-        RCL+3  RCL 3  x<y?  GTO 0                          ; Repeat while  S+t*k² > S                (Test 8) 
029-    RCL/2  PI  *
032- RTN                                                       ; Return    P(a,b)◄S/B*π