: rank(rank), size(size), root(root),

branching_factor_(branching_factor > 1? branching_factor

/* default */: default_branching_factor),

level_(0)

{

// The position in the tree, once we've adjusted for non-zero

// roots.

int n = (rank + size - root) % size;

int sum = 0;

int term = 1;

/* The level is the smallest value of k such that

while (sum <= n) {

++level_;

term *= branching_factor_;

sum += term;

}

{

int sum = 0;

int term = 1;

while (n--) {

sum += term;

term *= branching_factor_;

}

return sum;

{

if (rank == root) return rank;

int n = rank + size - 1 - root;

return ((n % size / branching_factor_) + root) % size ;

{

// Zero-based index of this node

int n = (rank + size - root) % size;

// Compute the index of the child (in a zero-based tree)

int child_index = level_index(level_ + 1)

+ branching_factor_ * (n - level_index(level_));

if (child_index >= size) return root;

else return (child_index + root) % size;