C program. I need help finishing the logic for finding partners.

The user will pass two command line arguments, the number of threads to create $($m$)$ and n$,$ the number they wish to compute the quadruple roots from $1$ to n of$.$ m and n will always be a power of $2.$ The threads will access a shared global array where the partial sum of the quadruple root will be stored. To find these partial sums, each thread will have a partner on the opposite half of the array. So for example if the user chooses to create $8$ threads, thread $0$ will be partnered with thread $4,$ thread $1$ with thread $5,$ thread $2$ with thread $6,$ and thread $3$ with thread $7.$ The partial sum is the sum of the partners, and is then stored in the upper parter and pthread$\_$join$()$ is called. Now that the threads are halved, new partners must be made. Now $6$ will be partnered with $4$ and $7$ with $5.$ This partnering, summing, storing, and reducing will continue until there is only one thread left.

I am struggling to find an algorithm to correctly find the partner index. I really only need the upper half of the array to be consistent as that's who will call pthread$\_$join$().$ We cannot use math library functions like log$()$ or pow$(),$ we must use bit$-$shift operations and XOR to determine parterns. We were told a partner could be found by taking itpartners's ID XORed with $2^($r$-$i$)$ where r $=$ log$($m$)$ and i is the iteration, but I have not found that to be consistent. Please help!