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An MPIRequest is a message sent from a rank greater than zero to the coordinator (rank zero), informing the coordinator of an operation that the rank wants to do and the tensor that it wants to apply the operation to.
The request rank is necessary to create a consistent ordering of results, for example in the allgather where the order of outputs should be sorted by rank.
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An MPIResponse is a message sent from the coordinator (rank zero) to a rank greater than zero, informing the rank of an operation should be performed now. If the operation requested would result in an error (for example, due to a type or shape mismatch), then the MPIResponse can contain an error and an error message instead. Finally, an MPIResponse can be a DONE message (if there are no more tensors to reduce on this tick of the background loop) or SHUTDOWN if all MPI processes should shut down.
Empty if the type is DONE or SHUTDOWN.
Empty unless response_type is ERROR.
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