1. CS 179: GPU Programming Lab 7 Recitation: The MPI/CUDA Wave Equation Solver

2. MPI/CUDA – Wave Equation  Big idea: Divide our data array between n processes!

3. MPI/CUDA – Wave Equation  Problem if we’re at the boundary of a process! x t t-1 t+1

4. Wave Equation – Simple Solution  After every time-step, each process gives its leftmost and rightmost piece of “current” data to neighbor processes! Proc0 Proc1 Proc2Proc3 Proc4

5. Wave Equation – Simple Solution  Pieces of data to communicate: Proc0 Proc1 Proc2Proc3 Proc4

6. Wave Equation – Simple Solution  Can do this with MPI_Irecv, MPI_Isend, MPI_Wait:  Suppose process has rank r:  If we’re not the rightmost process:  Send data to process r+1  Receive data from process r+1  If we’re not the leftmost process:  Send data to process r-1  Receive data from process r-1  Wait on requests

7. Wave Equation – Simple Solution  Boundary conditions:  Use MPI_Comm_rank and MPI_Comm_size  Rank 0 process will set leftmost condition  Rank (size-1) process will set rightmost condition

8. Simple Solution – Problems  Communication can be expensive!  Expensive to communicate every timestep to send 1 value!  Better solution: Send some m values every m timesteps!

9. Possible Implementation  Initial setup: (Assume 3 processes) Proc0Proc1 Proc2

10. Possible Implementation  Give each array “redundant regions”  (Assume communication interval = 3) Proc0Proc1 Proc2

11. Possible Implementation  Every (3) timesteps, send some of your data to neighbor processes!

12. Possible Implementation  Send “current” data (current at time of communication) Proc0Proc1 Proc2

13. Possible Implementation  Then send “old” data Proc0Proc1 Proc2

14.  Then…  Do our calculation as normal, if we’re not at the ends of our array  Our entire array, including redundancies!

15. What about corruption?  Suppose we’ve just copied our data… (assume a non- boundary process) . = valid  ? = garbage  ~ = doesn’t matter  (Recall that there exist only 3 spaces – gray areas are nonexistent in our current time

16. What about corruption?  Calculate new data…  Value unknown!

17. What about corruption?  Time t+1:  Current -> old, new -> current (and space for old is overwritten by new…)

18. What about corruption?  More garbage data!  “Garbage in, garbage out!”

19. What about corruption?  Time t+2…

20. What about corruption?  Even more garbage!

21. What about corruption?  Time t+3…  Core data region - corruption imminent!?

22. What about corruption?  Saved!  Data exchange occurs after communication interval has passed!

23. “It’s okay to play with garbage… just don’t get sick”

24. Boundary Conditions  Applied only at the leftmost and rightmost process!

25. Boundary corruption?  Examine left-most process:  We never copy to it, so left redundant region is garbage! (B = boundary condition set)

26. Boundary corruption?  Calculation brings garbage into non-redundant region!

27. Boundary corruption?  …but boundary condition is set at every interval!

28. Other details  To run programs with MPI, use the “mpirun” command, e.g. mpirun -np (number of processes) (your program and arguments)  CMS machines: Add this to your.bashrc file: alias mpirun=/cs/courses/cs179/openmpi-1.6.4/bin/mpirun

29. Common bugs (and likely causes)  Lock-up (it seems like nothing’s happening):  Often an MPI issue – locks up on MPI_Wait because some request wasn’t fulfilled  Check that all sends have corresponding receives  Your wave looks weird:  Likely cause 1: Garbage data is being passed between processes  Likely cause 2: Redundant regions aren’t being refreshed and/or are contaminating non-redundant regions

30.  Your wave is flat-zero:  Left boundary condition isn’t being initialized and/or isn’t propagating  Same reasons as previous Common bugs (and likely causes)

31.  General debugging tips:  Run at MPI with process number = 1 or 2  Set kernel to write constant value