Question❓

I am a bit stuck with the internals of the interaction between the time step loop and the controller. Here are some questions:

1. What exactly are q and qold? I could not find the mentioned work by Cechino. I probably also misread the latter variable as $q_{old}$, but it does not store some q. Instead it seems to store some time step length

   OrdinaryDiffEq.jl/lib/OrdinaryDiffEqCore/src/integrators/controllers.jl

   Line 74 in 4abda1b

   integrator.qold = DiffEqBase.value(integrator.dt) / q

2. What is the purpose of spliting the accept logic into two functions stepsize_controller! and step_accept_controller!?
3. On the docs page for the controller (https://docs.sciml.ai/DiffEqDocs/stable/extras/timestepping/), should the first equation just be a err^{scaled} or is there really some index involved that I missed?
4. Is accept_step_controller considered internal API? If not, should it be included in the docs page?