Matrix Transpose, Block, and Vector Case

Tuning Strategy

For details about the SIMD instruction set, see SIMD Instruction Set.

When cache line alignment addresses are ensured, transpose matrix B and select an appropriate block size to use vectorized instructions for optimization.

Procedure

1. Run the intrinsics_transpose_B_matmult case.

   1	./matmul 8192 5

   Command output:

   1 2 3

   Size is 8192, Matrix multiplication method is: 5, Check correctness is: 0 Initialization time = 2.787161s Matrix multiplication time = 2.600979s

   When the matrix determinant is 8192, the parallel computing takes approximately 2.6s.

2. Create a roofline analysis task for intrinsics_transpose_B_matmult.

   Analyze the roofline task using the command line tool.

   1	devkit tuner roofline -o intrinsics_transpose_B_matmult_8192 -m region ./matmul 8192 5

   Command output:

   1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

   Note: 1. Roofline task is currently only supported on the 920 platform. 2. The application must be a binary file in ELF format, and read permissions are required to detect the format of the application. 3. Roofline task collection needs to ensure the application has finished running. 4. The estimated time of roofline collection is about 3 * application estimated time. 5. Roofline analysis is available only on physical machines. 6. You can learn about the roofline profiling method by looking at document /usr/local/devkit/tuner/docs/ROOFLINE_KNOW_HOW.MD RFCOLLECT: Start collection for ./matmul RFCOLLECT: Launch application to collect performance metrics of ./matmul Size is 8192, Matrix multiplication method is: 5, Check correctness is: 0 Initialization time = 2.751606s ROOFLINE_EVENTS are initialized. Matrix multiplication time = 2.741322s RFCOLLECT: Launch application to do binary instrumentation of ./matmul Size is 8192, Matrix multiplication method is: 5, Check correctness is: 0 Initialization time = 8.353003s Matrix multiplication time = 2.519457s RFCOLLECT: Launch benchmarks for measuring roofs RFCOLLECT: Processing all collected data RFCOLLECT: Result is captured at /matrix_multiplication/rfcollect-20240506-201408.json RFCOLLECT: Run "rfreport /matrix_multiplication/rfcollect-20240506-201408.json" to get report. Get roofline report ... The roofline json report: /matrix_multiplication/intrinsics_transpose_B_matmult_8192.json The roofline html report: /matrix_multiplication/intrinsics_transpose_B_matmult_8192.html

3. View the intrinsics_transpose_B_matmult_8192.html report.
   Figure 4 intrinsics_transpose_B_matmult_8192.html
   

   In this case, Parallel Threads of roofs is 128, Elapsed Time is 2.652 seconds, GFLOP Count is 1717.987, and Performance is 647.781 GFLOPS.

Tuning Result

After intrinsics vectorized instructions are used, the computation process changes greatly. The computation amount increases by 47.1% (from 1168.231 GFLOP to 1717.987 GFLOP). The vectorized instructions greatly improve the end-to-end performance. For details, see the following table.