What happens when kernel code is interrupted?

If the interrupt handler and other kernel code need access to the same data, you need to protect against that, which is usually done by a spinlock great care must be taken, you don't want to introduce a deadlock ,and you must ensure such a spinlock is not held for too long. For spinlocks used in a hardware interrupt handler you have to disable interrupts on that processor whilst holding the lock - which in linux is done with the function spin_lock_irqsave().

The kernel code which was interrupted by this interrupt in the first place gets interrupted.

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