Do you have any links that describe the correct implementation? We may need to add a call to Math.Sqrt in the line 230, but definitely not in the place you pointed - as the call to Sqrt may not be necessary in the case when the length is zero.

I use the formula at below link and I think it is correct. I can re-build a same quaternion from axis & angle from original quaternion.

http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToAngle/

In that, they use sqrt(1- w_w), and it is same as sqrt(x_x + y_y + z_z) when the quaternion is normalized. Calling Math.Sqrt at line 230 is ok also.

Thank you for information. This should be fixed now.