Perimeter of the Ellipse (HP-15C)

[C.Ret]

Code:

001- ►LBL E
002-    x=y ?  GTO 8                                ; Test for circle
004-    STO 0  x<>y  STO+0  -  CHS  STO 1  STO/0    ; Initiate  R0:y=(a+b)/(a-b)  and R1:(a-b)
011-    RCL/1  2  x²  LSTx  GSB 0  3  1/x  +        ; Initiate  c_0_=4/(2*y- 1)+1/3 
019-    11  GSB.2  GSB 3  GSB 3  GSB 1  GSB 1       ; Iterate   c_i+1_=n/(d*y-c_i_)
026-    RCL+0  RCL*1  GTO 9                         ; Compute   (a-b)*(y+c)

Code:

029-     ►LBL.2    12  GTO 0                        ; ── ─── ─── d=12 ─┐    
033-     ►LBL 1     1  GTO 4                        ; ── n=1 ─┐        │
036-     ►LBL 3     3                               ; ── n=3 ─┤        │
038-     ►LBL 4     4                               ;         └─ d=4 ──┤
040-     ►LBL 0        RCL 0  *  R^  -  /  RTN      ;                  └─ c=n/(d*y-c) ───

Code:

047-  ►LBL 8     2  *                               ; Compute   P(a,a)=2πa
050-  ►LBL 9     PI  *                              ; Compute   P(a,b)~π(a-b)(y+1/(4y-1/(4y-3/(4y-3/(4y-11/(12y-(4/(2*Y-1)+1/3))))))) 
053- RTN