Need help to derive the Complexity! Please help me regarding this one! What will be the communication and computation complexity of this code??

While (m&gt;0) do
{
   While ((m mod 2)==0) do
       {
          m ← ⌊m/2⌋ 
         //parties communicate m times;
       }
m = m – 1;
}


This code been modified from the book "Fundamental of computer algorithm" by Sahni.So according to that, it seemed computational complexity is O(logm) as m decreases by a factor of at least 2. But can i say communication complexity is O(logm) as well?? Probably not; i'm really confused!!
If $m &gt; 0$ is even then the two parties communicate $m/2$ times at their first round of communication. If $m &gt; 1$ is odd then they communicate $(m-1)/2$ times at their first round of communication. In particular, the communication complexity is not $O(\log m)$, but at least $\Omega(m)$. In fact, it is also $O(m)$, but you'll have to figure out why yourself.