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For the amount of data sent and received per process is For the routing phase is empty so the optimal rounds suffice. For some allgather rounds are necessary, namely one for each reduction round in which At most, the number of rounds doubles. 40 R. L. Träff Fig. 2. The butterfly reduction algorithm. Fig. 3. Intermediate results after each protocol step when the threshold in round 3. 3 is reached The Improvements: Odd Number of Processes We now present our improvements to the butterfly scheme when is not a powerof-two.

Kraeva, and Y. Zou. MPICHECK: a tool for checking fortran 90 MPI programs. Concurrency and Computation: Practice and Experience, 15(2):93–100, 2003. M. Snir, S. Otto, S. Huss-Lederman, D. Walker, and J. Dongarra. MPI – The Complete Reference, volume 1, The MPI Core. MIT Press, second edition, 1998. J. L. Träff. SMP-aware message passing programming. In Eigth International Workshop on High-level Parallel Programming Models and Supportive Environments (HIPS03), International Parallel and Distributed Processing Symposium (IPDPS 2003), pages 56–65, 2003.

M. Snir, S. Otto, S. Huss-Lederman, D. Walker, and J. Dongarra. MPI – The Complete Reference, volume 1, The MPI Core. MIT Press, second edition, 1998. J. L. Träff. SMP-aware message passing programming. In Eigth International Workshop on High-level Parallel Programming Models and Supportive Environments (HIPS03), International Parallel and Distributed Processing Symposium (IPDPS 2003), pages 56–65, 2003. J. L. Träff, H. Ritzdorf, and R. Hempel. The implementation of MPI-2 one-sided communication for the NEC SX-5.

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