CS378: High-Performance Parallel Computing

Assignment 1: Optimize matrix-matrix multiplication

• Files
• Instructions:
  • Download and run the basic code:
    1. Log on to an Intel Pentium (R) III based machine.
    2. Create a subdirectory for all of your assignments.
    3. Download the files assign1.tar.gz and ATLAS.tar.gz
    4. Uncompress and untar the two files assign1.tar.gz and ATLAS.tar.gz:
       • gunzip *.gz
       • tar -xf assign1_tar
       • tar -xf ATLAS_tar
       Subdirectory ATLAS will now contain a set of Basic Linear Algebra Subprograms (BLAS) for the Pentium III. Subdirectory assign1 will now contain a number of files xsassociated with matrix-matrix multiplication.
    5. cd assign1
    6. Modify file Makefile to set the path to where the ATLAS directory is (first line of file).
    7. Type "make". This will create a file test_gemm.x
    8. Type "./test_gemm.x". This will execute a driver routine for timing the matrix-matrix multiply.
    9. Enter the number of repeats. The time for the matrix-matrix multiply will be the shortest time measured over the entered number of repeats.
    10. Enter the range of problems to be timed. "50 500 50" will time all matrix problems 50x50 to 500x500 in steps of 50.
    11. Enter "-1" to quit the execution.
    12. Start up a MATLAB sessions by typing "matlab" (if matlab is installed).
    13. Cut and paste the output from test_gemm.x into MATLAB to create a graph.
  • Optimize the matrix-matrix multiplication in my_gemm.c . This is the routine that is reported as "ME" in the graph. Some possible optimizations:
    • Rewrite in terms of dot-products and use the CBLAS (C interface to the Basic Linear Algebra Subprograms) routine cblas_ddot.
    • Rewrite in terms of "axpy" operations and use the CBLAS (C interface to the Basic Linear Algebra Subprograms) routine cblas_daxpy.
    • Rewrite in terms of matrix-vector multiplication and use the CBLAS routine cblas_dgemv.
    • No, you are not allowed to simply make it a call to the CBLAS routine cblas_dgemm, which implements the matrix-matrix multiply.
  • You may wish to read
    • PHiPAC: Automatically tuned BLAS
      on how to write high performance C code. Note: I will hand this out on friday 1/18
    • ATLAS Similar system as PHiPAC using similar techniques.
    • John Gunnels, Greg Henry, and Robert van de Geijn, " High-Performance Matrix Multiplication Algorithms for Architectures with Hierarchical Memories " FLAME Working Note #4, The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-2001-22. June 2001.