1. Parallel Programming and Algorithms – MPI Collective Operations David Monismith CS599 Feb. 10, 2015 Based upon MPI: A Message-Passing Interface Standard 3.0 by the Message Passing Interface Forum, 2012. Available at http://www.mpi-forum.org/docs/mpi-3.0/mpi30-report.pdf

2. Last Time Introduced MPI and Batch Scripts Discussed Blocking Send/Receive Discussed Collective Message Patterns in Theory

3. This Time Time for Worksheet 6 Implementation of Collective Message Patterns.

4. Collective Message Patterns Collective message patterns include patterns such as broadcast, reduce, scatter, and gather. When using a collective function call in MPI, the call must be made in every process in the communicator. For now, we are using MPI_COMM_WORLD as our communicator. Therefore, we will make collective function calls in every process

5. Broadcast Broadcast is a one-to-all function. Recall that in a broadcast, the same data is sent to every process. MPI’s Broadcast operation is implemented via the use of the MPI_Bcast function. Broadcast must be called in every process.

6. MPI_Bcast Function signature: MPI_Bcast(buffer, count, dataType, source, comm) buffer – address of buffer (data to send/recv) count – number of items in the buffer dataType – the MPI type of the data in the buffer source – the rank of the process sending the broadcast comm – the communication (often MPI_COMM_WORLD)

7. Example See bcast.c from the course website This example sends a message from process rank 0 to all other processes.

8. Gather Gather allows for one process to receive individualized messages from all other processes. That is, gather is an all-to-one function. MPI’s Gather Operation is implemented via the MPI_Gather function. This function allows one process to collect equally sized individualized messages from all other processes.

9. MPI_Gather Function signature: MPI_Gather(sendBuffer, sendCount, sendType, recvBuffer, recvCount, recvType, rootProcessId, comm) sendBuffer – the data to be sent to the root process sendCount – the number of data items to be sent sendType – the type of the data items to be sent recvBuffer – the buffer in which the data will be stored in the root process (this may be NULL in non-root processes) recvCount – the number of elements for any single receive (must be non-negative and only significant at root) recvType – the data type of elements that will be received rootProcessId – the rank of the receiving process comm – the communicator (e.g. MPI_COMM_WORLD)

10. Example See gather.c from the examples page on the course website. This example computes the square of N numbers from 0 to N-1 and prints every 100 th square. Squares are divided among M processes such that each process computes M/N squares.

11. Scatter The scatter operation sends individualized messages from a source process to all other processes. Note that the source process itself receives one of these messages. Scatter is implemented in MPI using the MPI_Scatter function.

12. MPI_Scatter The function signature for scatter follows: MPI_Scatter(sendBuffer, sendCount, sendType, recvBuffer, recvCount, recvType, source, comm) sendBuffer – starting address of the data to be sent (the entire array) sendCount – the amount of data to send to each process from the source sendType – the type of the data being sent recvBuffer – starting address of the location where data will be received recvCount – the amount of data to receive recvType – the type of data to receive source – the identifier of the process sending the data comm – the communicator (e.g. MPI_COMM_WORLD)

13. Example See scatter.c on the course examples webpage. This program provides an example of using the scatter function to send equally sized chunks of an array of random integers to all processes. Each process computes and prints the average of its chunk.

14. Reduce A reduce operation allows us to take many individual values and combine them using an associative operator. Such operators include +, *, min, max, and various logical operators like && and ||. We have seen such operations before in shared memory programming via OpenMP. MPI implements reduce using the MPI_Reduce function and allows for many scalar reductions to be performed in one function call.

15. MPI_Reduce The function signature for reduce follows: MPI_Reduce(sendBuffer, recvBuffer, count, dataType, operation, root, comm) sendBuffer – starting address of the data to be sent (the entire array) recvBuffer – starting address of the location where data will be received count – the number of reduce results (i.e. the size of the sendBuffer) dataType – the type of data in the send and receive buffers operation – the reduce operation to perform root – the process id that the reduce results will be sent to comm – the communicator (e.g. MPI_COMM_WORLD)

16. MPI_Reduce Operations MPI_SUM – sum MPI_MIN – minimum MPI_MAX – maximum MPI_PROD – product MPI_LAND – logical and MPI_LOR – logical or MPI_BAND – bitwise and MPI_BOR – bitwise or MPI_LXOR – logical xor MPI_BXOR – bitwise xor

17. Example See reduce.c on the examples page of the course website. This example performs a scalar sum reduction on 1,000,000,000 integers across multiple processes. Also see reduce3D.c, which performs a 3D sum reduction across 1,000,000,000 3D points. Notice that the reduce operation includes the root process as one of the processes that perform computations.

18. Next time MPI_Barrier – barrier operation in MPI Other MPI All-to-all communications