Context switch internals?

At a high level, there are two separate mechanisms to understand. The first is the kernel entry/exit mechanism: this switches a single running thread from running usermode code to running kernel code in the context of that thread, and back again. The second is the context switch mechanism itself, which switches in kernel mode from running in the context of one thread to another.

What you missed during step 2 is that the stack gets switched from a thread's user-level stack (where you pushed args) to a thread's protected-level stack. The current context of the thread interrupted by the syscall is actually saved on this protected stack. Inside the ISR and just before entering the kernel, this protected-stack is again switched to the kernel stack you are talking about.

Once inside the kernel, kernel functions such as scheduler's functions eventually use the kernel-stack. Later on, a thread gets elected by the scheduler and the system returns to the ISR, it switchs back from the kernel stack to the newly elected (or the former if no higher priority thread is active) thread's protected-level stack, wich eventually contains the new thread context. Therefore the context is restored from this stack by code automatically (depending on the underlying architecture).

Finally, a special instruction restores the latest touchy resgisters such as the stack pointer and the instruction pointer. Back in the userland...

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