More MPI

• Collective Communications
  • Back to pi.
  • We could do

    if (id != 0) {
       MPI_Send(& pi, 1, MPI_DOUBLE, 0,0 MPI_COMM_WORLD);
    } else {
       double tmp;
       for(int i=1; i < world_rank; ++i) {
          MPI_RECV(& tmp; 1, MPI_DOUBLE, i,0, MPI_COMM_WORLD);
       }
       pi += tmp;
    } 

  • Or some version, I didn't compile it.
  • But this would not be the smartest move.
• Consider a binary tree of the processes
  • 2n+1 and 2n+2 could send to process n
  • There is a little logic,

  • if (2*id+2 < world_size) {
        MPI_RECV(tmp1,,2*id+2, ) ;
        MPI_RECV(tmp2,,2*id+1, ) ;
        snd = tmp1+tmp2+myvalue;
    else if (2*id+1 < world_size) {
        MPI_RECV(tmp1,,2*id+1, ) ;
        snd = tmp1+myvalue;
    }  else {
        snd = myvalue
    }
    
    if (id != 0) {
        MPI_Send(snd, ... (id-1)/2);
    } 

  • Again, I didn't test this, but it is within $\epsilon$;
• MPI provides this in collective communications
  • int MPI_Bcast(void *buffer, int count, MPI_Datatype datatype, int root, MPI_Comm comm)
  • Sends a message to all nodes from the root.
  • This can use an efficient broadcast based on the topology
  • Ie it can be optimized locally.
  • All nodes in the communication will have the value stored in the root node.
• int MPI_Reduce(const void *sendbuf, void *recvbuf, int count, MPI_Datatype datatype, MPI_Op op, int root, MPI_Comm comm)
  • Will collect up the tree
  • Using the collective operation
  • The result will be stored in the root.
  • See pi.cpp
• There is an equivalent int MPI_Scatter(const void *sendbuf, int sendcount, MPI_Datatype sendtype, void *recvbuf, int recvcount, MPI_Datatype recvtype, int root, MPI_Comm comm)
• There is also MPI_ALL_REDUCE which ends with the sum in all nodes.
• int MPI_Gather(const void *sendbuf, int sendcount, MPI_Datatype sendtype, void *recvbuf, int recvcount, MPI_Datatype recvtype, int root, MPI_Comm comm) and ALL_GATHER , along with SCATTER
  • Work on an array of values.
  • My data is at point myid in the final array.