Incorrect Circular motion : What your controller do ?

Well I have this is general question about how the controller will behave when an incorrect circular interpolation is present in the NC.

Lets say from the starting point to the end point, the arc center set make it impossible from a mathematical point of view to follow a constant radius.
What will the machine do ?
I know that the controller will most probably throw an error, but in the other hand there is a tolerance on the mathematical definition of the G02/G3 move right?

So within this tolerance what the movement will be?
Will it try to recompute the arc center? Can it move with radius variation? Can it move toward a point that is not exactly the one set in G02/03 XY ?
Let me know what you think or maybe what you have observed.

This is pure curiosity by the way.

Mach3 has about a 1/2" of allowable tolerance, which you can use to actually cut spirals with G2/G3 moves.
Other controllers will just throw an error and not run at all.