MCS 572 Cray T3E Group Project Suggestions

Fall 1997

Two(2) copies of the report are due Friday 05 December 1997 in class (one graded copy will be returned and the other will be used for the progress report and next class proposal to PSC). Students will make short presentations of group project results in class, starting on Wednesday 03 December 1997.

CAUTION: Projects should have sufficient work to effective utilize the T3E, but should not be so time consuming as to severely affect the performance of other users. Write a group (1 < group < 2) with good load balancing among the group members) report that is a short paper (8 or 15 or so pages plus appendices) as if for publication, i.e., with

1. abstract (short description of problem and results)
2. executive summary (give an itemized brief summary of your paper)
3. introduction (motivate your problem for the class, citing prior work)
4. problem or method
5. results and discussion (should include theoretical explanations of interesting results and graphs; explain results whether good or bad)
6. conclusions (brief)
7. acknowledgements (give thanks to others that helped you and to the Pittsburgh Supercomputer Center of use of the Cray C90 (if you use it) and T3E)
8. references (list articles, books and other documents that you used as sources)
9. appendices: compiler informational code listing (*.lst file in f90 or *.V file if you use the cc compiler), supporting timings.

WARNING: If you use test or sample floating point arrays in your project, make sure they are genuine and random floating point, i.e., do not use trivial integers or numbers with patterns. Consult the class local user's guide for how to run a scalar job to use as a reference measurement. See the Class Cray Local Guide. You are expected to use MPI for parallel programming on the T3E (See the MPI-Laplace example Class Sample Laplace-MPI Fortran Code or Class Sample Laplace-MPI C Code discussed throughly in class and the Class MPI Help pages). Use the MPI_Wtime wall timer for measuring performance times, unless you can find a better timer. Also, if your project is similar to the one you did on the Convex Exemplar SPP1200, then you must give an extensive comparison to your SPP1200 project, so that the work is comparable to what you would do for new project topic.

The Project Suggestions

1. Own Project. A Cray T3E project or your own design, such as optimization of some method connected with your thesis research area, graphical visualization, another course, or some interesting science-engineering area.
2. Statistics Project. Generate suitable sets of random numbers (make sure they are floating point), each with a different sample size N. The function `ranf' is a very good random number generator (RNG), but check it out yourself. Another RNG is `rand'. See the Cray Local Guide or T3E man pages. Describe how you tested the randomness of your data, e.g., test for a uniform random distribution. For each set, compute basic statistics, like mean, variance and Chi-Square test in as efficient vector manner as possible (i.e., make use of the extended Fortran90 intrinsic sum function `sum' on the Cray. Plot T versus N and T versus p. Estimate or compute and plot the Amdahl vector fraction as a function of N. Compare speedups and efficiencies relative to N. Is the Amdahl law operative as the problem size N becomes large? Develop your own performance model that is appropriate for the behavior of the timing data with number of processors p, sample size N and Chi-Square bin size Nb. Does your performance model account for deviations in Amdahl's law?
3. Row versus Column Oriented LU Decomposition Loops. Determine regions of array size where there are efficiency advantages on the Cray using column referencing as opposed to row referencing in reordering LU decomposition multiple loops. Is the simple Fortran column environment argument valid, and if not why not? How strong is the dependence on loop iteration size N? What about rectangular (non-square and very thin) matrices. Make sure your floating point arrays are genuine. (See Dongarra, Gustavson and Karp, SIAM Review, Vol. 26, 1984, pp. 91-122; for the CRAY-1).
4. Validity of Hanson's "Avoid These Things". Investigate a number of Professor Hanson's Rules of Thumb about "Avoiding Certain Optimization Hindering Constructs". Find out the validity on loops (if loops were involved) with sufficient work (ie., bigger than the toy class examples). Find regions of work size, if any, where each rule works. For example: What is the quantitative difference in overhead between common and subroutine argument passing? How much does inlining subroutines and functions save? statement.
5. Iteration Methods. Make a comparison of the performance of Jacobi and Gauss-Seidel methods for Elliptic Partial Differential equations. Gauss-Seidel is better for serial computers, but what about parallel and vector computers? (See Ortega, Intro. Parallel and Vector Solution of Linear Systems, 1988 and related papers.) See Class Sample Laplace-MPI Fortran Code or Class Sample Laplace-MPI C Code that were being revised from PSC.
6. Test whether higher or lower levels of optimization give higher performance. For instance, does the command `f90 -O[n] ... [pgm].f' lead to faster executables for some values of Option Level `[n]' for matrix multiplication or some other application.
7. Compare Performance of MPI Functions/Subroutines. For instance, compare the Collective Communication routine MPI_Bcast with the Blocking Point to Point Communication routine MPI_Send along with MPI_Recv, and with the Nonblocking Point to Point Communication routine MPI_Isend along with MPI_Irecv. Use MPI_Wtime to measure performance times. (Note shmem is the T3E native message passing library. See `man shmem'.)
8. C90 and T3E Performance Comparison. Take some application and make a comparison between optimized performance on the PVP C90 and the MPP T3E.