I wonder input scaling, input offset etc

I found the following code in the gazebo_mavlink_interface.cpp file:

input_reference_[i] = (actuator_controls[input_index_[i]] + input_offset_[i]) * input_scaling_[i] + zero_position_armed_[i];

However, when I printed the input_reference_ values, they seemed to be within the range [0, 1]. But the code above appears to be scaling the magnitude of these values.

What I am curious about is: where do the input_reference_ values get normalized to be within the [0, 1] range? Where does this normalization happen, what do these values represent, and what are their units?

Maybe it helps if you know the other side of this:

And:

Thank you, @JulianOes.
I had some things to take care of, so I checked your reply a bit late. Thank you for teaching me exactly what I was looking for.

I have a few more questions I would like to ask.
I am trying to implement the fault-tolerant control technique, specifically reallocation, using the Gazebo environment. As far as I know, PX4 currently does not support reallocation.
In that case, which files would I need to modify to implement reallocation?
In other words, I would like to know which file contains the allocation matrix.

If PX4 does already support reallocation, could you let me know where that is handled?

Once again, thank you for your response.