矩阵转置&block示例

调优思路

1. 在对B矩阵进行转置保证cache line对齐寻址的情况下，迭代小区域的block减少cache miss。
2. block的size调整需要根据实际cache size大小和具体环境配置综合考虑。

图1 矩阵转置示意

图2 矩阵转置&block代码

操作步骤

1. 运行矩阵行列大小为8192的block_transpose_B_matmult示例。

   ./matmul 8192 4

   返回信息如下：

   Size is 8192, Matrix multiplication method is: 4, Check correctness is: 0
   Initialization time = 2.787273s
   Matrix multiplication time = 3.711554s

   矩阵行列大小为8192情况下，并行计算耗时3.7秒左右。

2. 创建矩阵行列大小为8192的block_transpose_B_matmult示例的Roofline任务。

   devkit tuner roofline -o block_transpose_B_matmult_8192 -m region ./matmul 8192 4

   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: 4, Check correctness is: 0
   Initialization time = 2.794598s
   ROOFLINE_EVENTS are initialized.
   Matrix multiplication time = 3.743286s
   RFCOLLECT: Launch application to do binary instrumentation of ./matmul
   Size is 8192, Matrix multiplication method is: 4, Check correctness is: 0
   Initialization time = 8.353251s
   Matrix multiplication time = 3.849523s
   RFCOLLECT: Launch benchmarks for measuring roofs
   RFCOLLECT: Processing all collected data
   RFCOLLECT: Result is captured at /matrix_multiplication/rfcollect-20240506-195201.json
   RFCOLLECT: Run "rfreport /matrix_multiplication/rfcollect-20240506-195201.json" to get report.
   
   Get roofline report ...
   The roofline json report: /matrix_multiplication/block_transpose_B_matmult_8192.json
   The roofline html report: /matrix_multiplication/block_transpose_B_matmult_8192.html

3. 查看block_transpose_B_matmult_8192_html报告。
   图3 block_transpose_B_matmult_8192_html报告
   

   此时获取的roofs的并行度为128，获取到Elapsed Time 3.646s, GFLOP Count 1168.231，Performance 320.399 GFLOPS。

优化效果

使用内部block块循环增加了6.25%的额外计算（从1099.512 GFLOP到1168.231 GFLOP）， 但整体性能有191.9%提升，因此端到端性能有大幅提升，详见下表。

1. 图3 block_transpose_B_matmult_8192_html报告中的L1、L2、L3和DDR均处于Compute and Memory Bound区域。
2. 当前内存瓶颈在L1和L2，主要在L2。
3. 缓存局部效应：Cache line utilization相比于矩阵转置型示例变好，计算密度（FLOP/Byte）：L1 ≈ L2 < L3 < DDR。

图4 对比分析