Homework 5, due 10/13

Calculate Pi with MPI

Within your group, pick a classmate to be the “driver” and do all the actual typing of the code. The driver should share their screen. The other group members will be “navigators,” guiding the overall direction of the code toward the ultimate goal. Feel free to switch roles as frequently as needed. Feel free to discuss the programming problem with your other group mates, too. At the conclusion, you may submit identical code and write-ups as your group mates, specifying your group number.

The value of pi can be computed as follows. Consider a circle of radius r inscribed in a square of side length r. Randomly generate points in the square. Determine the number of points in the square that are also in the circle. If f=nc/ns is the number of points in the circle divided by the number of points in the square then pi can be approximated as pi ~ 4f. Note that the more points generated, the better the approximation.

Exercise

  1. Look at the C or Fortran program ser_pi_calc. Extend this program using collective MPI routines to compute pi in parallel using the method described above. Feel free to use C++, if you prefer, of course.
  2. For the first iteration, perform the same number of “rounds” on each MPI rank. Measure the total runtime using MPI_WTIME(). Vary the number of ranks used from 1 to 4. How does the total runtime change?
  3. Now, divide the number of “rounds” up amongst the number of ranks using the appropriate MPI routines to decide how to distribute the work. Again, run the program on 1 to 4 ranks. How does the runtime vary now?
  4. Now let’s change the number of “darts” and ranks. Use your MPI program to compute pi using total numbers of “darts” of 1E3, 1E6, and 1E9. For each dart count perform a strong scaling study on HPCC with processor counts of 1, 2, 4, 8, 16, 32, and 64. For this, use non-interactive jobs and modify the jobsubmit.sb script as necessary. Make a plot of your scaling results and turn it in along with your code. Give a brief explanation of your results and plot.

What to turn-in

To your git repo, in the hw5 directory, commit your final, working code for the above exercises, plot of your scaling study, and written responses. Your final write-up and code are due in one week, on 10/2.