  In a previous work, we developed the idea to solve Kepler's equation with a
CORDIC-like algorithm, which does not require any division, but still
multiplications in each iteration. Here we overcome this major shortcoming and
solve Kepler's equation using only bitshifts, additions, and one initial
multiplication. We prescale the initial vector with the eccentricity and the
scale correction factor. The rotation direction is decided without correction
for the changing scale. We find that double CORDIC iterations are
self-correcting and compensate possible wrong rotations in subsequent
iterations. The algorithm needs 75\% more iterations and delivers the eccentric
anomaly and its sine and cosine terms times the eccentricity. The algorithm can
be adopted for the hyperbolic case, too. The new shift-and-add algorithm brings
Kepler's equation close to hardware and allows to solve it with cheap and
simple hardware components.
