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To do this, I would need to be able to access the root node of a given leaf in a parallel way. The determinant factor would have to be the thread index. Achieving this was a bit of a math problem.
The fact is, this problem could have been solved very simply using if statements. This would have, however, increase thread divergence and therefore slowed down the kernel. In this way, the fact that I solved this problem mathematically could be viewed as an optimization in itself, by reducing thread divergence.