pub fn non_leaf_nodes_left(data_index: u128) -> u128 {
    // This formula is derived as follows:
    // To get the heights of peaks before this data index was inserted, bit-decompose
    // the number of leaves before it was inserted.
    // Number of leaves in tree of height h = 2^h
    // Number of nodes in tree of height h = 2^(h + 1) - 1
    // Number of non-leaves is `#(nodes) - #(leaves)`.
    let mut ret = 0;
    for h in 0..u128::BITS {
        if (1 << h) & data_index != 0 {
            ret += (1 << h) - 1;
        }
    }

    ret
}