Changes

[[File:njsimasroot.png|500px ]]

The first step was using modulus to set the odd value in the leaf pair equal to the greater value:

modIndex =((ti + q) + (ti + 1) % 2)

The next step was making the thread index progression correspond to the root progression.

To do this, I add one, divide by two, and subtract one, and then add the modulus, as in step one, to account for the lesser of the leaf pair.

Progression = (((ti + 1) / 2) – 1) + ((ti + q) + (ti + 1) % 2)

Finally, I add this progression to the previous leaf total, and subtract the result from the new array index from stage 1:

root = modIndex – (leafTotal + progression)

Since this was all to be done by a single thread, in a single step, I condensed the formula into one line.

((ti + q) + ((ti + 1) % 2)) - (((((ti + 1) / 2) - 1) + ((ti + 1) % 2)) + (t / 2) + 1);