Perimeter of the Ellipse (HP-15C)

[Albert Chan]

Here is Ellipse perimeter, AGM based version, without recursion.

10 DEF FNP(A,B) @ S=A*A+B*B @ T=1
20 REPEAT @ G=B @ K=(A-B)/2 @ B=SQRT(A*B) @ A=A-K @ T=T+T @ S=S-T*K*K @ UNTIL G=B
30 FNP = S/B*PI @ END DEF

> FNP(20,1)
80.3885123826


Comment: we can test convergence of S instead. This may reduce loop count by 1.

20 REPEAT @ K=(A-B)/2 @ B=SQRT(A*B) @ A=A-K @ T=T+T @ K=T*K*K @ S=S-K @ UNTIL S=S+K