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+---
+author: fredrik robertsen
+date: 2025-10-07
+title: exercise 4
+---
+
+## theory
+
+### a) `gather` vs. `allgather`
+
+both are collective operations that attempt to "gather" or unify some
+calculation result. the difference lies in that `gather` sends the combined
+result of all processes' calculations to a single root process, while
+`allgather` redistributes it across all other processes again.
+
+since `allgather` has to do significantly more I/O in the form of communicating
+between processes, it can take more time and thus be slower than a simple
+`gather`.
+
+### d) corner communication in task 6
+
+to communicate the rows and columns, we just have to do simple index magic to
+send all the correct cells to the correct neighbors. this is very tedious.
+
+corners are spicy. you have to correctly pass your corner onto the neighbor who
+is ready to receive your corner, and you have to receive a corner from another
+neighbor who is sending you their corner. all in all, it's actually just as
+complicated as communicating rows and columns; you just need to get some indices
+right and make sure you send the data to the right place.
+
+also, avoid a deadlock by using the correct tags in a `sendrecv`.
+
+### c) periodic vs. non-periodic
+
+periodicity refers to whether or not a cartesian grid wraps around, i.e. if the
+edges of the grid can communicate directly with the processes on their opposite
+side. periodic grids enables wrapping, while non-periodics don't.
+
+this allows for quicker communication between processes that are maximally
+far away from each other.
+
+in this example, the cartesian is not periodic, since we do not need to send any
+data between the edges.
+
+### d) mpi i/o race conditions
+
+with mpi i/o you use collective operations to write the calculated data to the
+filesystem. we can find an offset that let's us write the data into the same
+file in a disjoint region concurrently, avoiding race conditions.