矩阵转置&block&vector示例

调优思路

关于SIMD指令集详情请参见SIMD指令集。

图1 SIMD指令集

图2 矩阵转置&block&vector代码 1

图3 矩阵转置&block&vector代码 2

在保证cacheline对齐寻址的情况下，对矩阵B进行转置，并选择合适block size进行向量化指令优化。

操作步骤

1. 运行intrinsics_transpose_B_matmult示例。

   ./matmul 8192 5

   返回信息如下：

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

   矩阵行列大小为8192情况下，并行计算耗时2.6秒左右。

2. 创建intrinsics_transpose_B_matmult的Roofline任务。

   使用命令行工具进行roofline任务分析。

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

   返回信息如下：

   Note:
     1. Roofline task is currently only supported on the 920 platform.
     2. The application must be a binary file in ELF format.
     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. 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. 查看intrinsics_transpose_B_matmult_8192报告。
   图4 intrinsics_transpose_B_matmult_8192报告
   

   此时获取的roofs的并行度为128，获取到Elapsed Time 2.664s，GFLOP Count 1717.987，Performance 647.781 GFLOPS。

优化效果

使用intrinsics向量化指令后，计算方式发生很大的变化，计算量有47.1%的增加（从1168.231GFLOP到1717.987GFLOP），同时向量化指令也有更大的性能提升，因此端到端性能有了大幅提升，详见下表。

图5 对比分析