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each UE (my_id) is given by the process rank for each UE in the process group associated with the communicator MPI_COMM_WORLD (for information about communicators and other MPI details, see the MPI appendix, Appendix B) We use the number of UEs and the ID to assign loop ranges (i_start and i_end) to each UE Because the number of steps may not be evenly divided by the number of UEs, we have to make sure the last UE runs up to the last step in the calculation After the partial sums have been computed on each UE, we multiply by the step size, step, and then use the MPI_Reduce() routine to combine the partial sums into a global sum (Reduction operations are described in more detail in the Implementation Mechanisms design space) This global value will only be available in the process with my_id == 0, so we direct that process to print the answer In essence, what we have done in the example in Fig 53 is to replicate the key data (in this case, the partial summation value, sum), use the UE's ID to explicitly split up the work into blocks with one block per UE, and then recombine the local results into the final global result The challenge in applying this pattern is to (1) split up the data correctly, (2) correctly recombine the results, and (3) achieve an even distribution of the work The first two steps were trivial in this example The load balance, however, is a bit more difficult Unfortunately, the simple procedure we used in Fig 53 could result in significantly more work for the last UE if the number of UEs does not evenly divide the number of steps For a more even distribution of the work, we need to spread out the extra iterations among multiple UEs We show one way to do this in the program fragment in Fig 54 We compute the number of iterations left over after dividing the number of steps by the number of processors (rem) We will increase the number of iterations computed by the first rem UEs to cover that amount of work The code in Fig 54 accomplishes that task These sorts of index adjustments are the bane of programmers using the SPMD pattern Such code is error prone and the source of hours of frustration as program readers try to understand the reasoning behind this logic.

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