That's why you always normalize the quaternion first, and the article seems to require the normalized form:

Q.54 How do I convert a quaternion to a rotation matrix?

Assuming that a quaternion has been created in the form:

Q = |X Y Z W|

At least, I would read |X Y Z W| as meaning normalized(X Y Z W)

I don't see this notation explicitly defined when they describe quaternion normalization (Q.52) though, so I agree this leaves much out. It's more a cheat sheet than learning material.

> You need to replace sqrt(1 - a*a) assumptions with actual components, and use atan2 instead of acos

I'm kind of rusty with this, but I think the reason we don't do that is that it's cheaper to normalize then convert rather than use the non-normalized conversion formula. Correct me if I'm wrong.