Cordic is an extremely fast and efficient algorithm for implementing trigonometric functions. The most common implementations you can find refer to sin/cos functions but it can be used for their hyperbolic counterparts. Once you have an implementation for sinh/cosh is easy to get tanh. Have a look here...

Each step in the CORDIC algorithm add a scaling of cos(arctan(2^-i)) (or 1/sqrt(1+2^-2i)), so for a 4 steps CORDIC, the total scaling is: cos(arctan(2^-0))*cos(arctan(2^-1))*cos(arctan(2^-2))*cos(arctan(2^-3)) = 0.60883 If you add more iterations, it gets to 0.607252935 and some. As to what to do with that factor, it's up to you and...

The scale factor for the rotation mode of the circular variant of CORDIC can easily be established from first principles. The idea behind CORDIC is to take a point on the unit circle and rotate it, in steps, through the angle u whose sine and cosine we want to determine....