矩阵转置型示例

查看矩阵行列大小为8192的指标

1. 并行示例并行数已经调整到128，实际计算时间很短，2048 size不足以展示其功能，为了便于分析有效性，以8192 size运行相关任务。
2. 以最基础的并行计算（method 1）做为基准case， 在此基础上进行method 2，4，5，6的相关case进行任务分析（由于method 3与method 2类似，不额外进行采集）。
3. 请根据实际服务器中物理核数选择合适的矩阵size开展任务，可以由小到大的调整，最终确定合适的值。

1. 运行矩阵行列大小为8192的parallel_matmult示例。

   1	./matmul 8192 1

   返回信息如下：

   1 2 3

   Size is 8192, Matrix multiplication method is: 1, Check correctness is: 0 Initialization time = 2.751910s Matrix multiplication time = 521.832686s

   矩阵行列大小为8192情况下，并行计算耗时607秒左右。

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

   1	devkit tuner roofline -o parallel_matmult_8192 -m region ./matmul 8192 1

   返回信息如下：

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

   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: 1, Check correctness is: 0 Initialization time = 2.793709s ROOFLINE_EVENTS are initialized. Matrix multiplication time = 516.902512s RFCOLLECT: Launch application to do binary instrumentation of ./matmul Size is 8192, Matrix multiplication method is: 1, Check correctness is: 0 Initialization time = 8.352283s Matrix multiplication time = 496.935396s RFCOLLECT: Launch benchmarks for measuring roofs RFCOLLECT: Processing all collected data RFCOLLECT: Result is captured at /matrix_multiplication/rfcollect-20240506-160802.json RFCOLLECT: Run "rfreport /matrix_multiplication/rfcollect-20240506-160802.json" to get report. Get roofline report ... The roofline json report: /matrix_multiplication/parallel_matmult_8192.json The roofline html report: /matrix_multiplication/parallel_matmult_8192.html

3. 查看parallel_matmult_8192_html报告。
   图1 parallel_matmult_8192_html报告
   

   此时获取的roofs的并行度为128，获取到Elapsed Time 516.824s，GFLOP Count 1099.512，Performance 2.127 GFLOPS。

   

   后续示例将以parallel_matmult_8192_html报告结果作为基准进行比较。

调优思路

1. 图1中所有的点均处于Memory bound区域。
2. 当前内存瓶颈在DDR和L3，主要是DDR。
3. 缓存局部效应：L1的计算密度（FLOP/BYTE）最大，即L1上命中的数据最少。
   图2 数据的不同寻址Size
   
   图3 数据的不同寻址方式
   
   • Sequential load：逐步读取数组的每个元素，即full cache line utilization为100%（good）。
   • Stride load：从缓存行读取数组的每第4个元素，即cache line utilization为25% （worse），该情况下导致L2 Bytes大于L1 Bytes，因此L2 Flop/Byte小于L1 Flop/Byte。
   • Random load：随机访问情况下，缓存访问没有局部性，cache line utilization较随机且必定很差（bad）。

从上述分析可以知道，当前的程序的瓶颈点在于内存，在于L1 cache利用率不足。

操作步骤

通过对矩阵B进行转置，保证cache line对齐寻址，实现Sequential load模式，提高cache命中率，优化并行示例中的性能瓶颈。

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

   1	./matmul 8192 2

   返回信息如下：

   1 2 3

   Size is 8192, Matrix multiplication method is: 2, Check correctness is: 0 Initialization time = 2.752044s Matrix multiplication time = 12.562781s

   矩阵行列大小为8192情况下，并行计算耗时12.5秒左右。

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

   1	devkit tuner roofline -m region -o transpose_B_matmult_8192 ./matmul 8192 2

   返回信息如下：

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

   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: 2, Check correctness is: 0 Initialization time = 2.793919s ROOFLINE_EVENTS are initialized. Matrix multiplication time = 10.419904s RFCOLLECT: Launch application to do binary instrumentation of ./matmul Size is 8192, Matrix multiplication method is: 2, Check correctness is: 0 Initialization time = 8.543225s Matrix multiplication time = 11.596018s RFCOLLECT: Launch benchmarks for measuring roofs RFCOLLECT: Processing all collected data RFCOLLECT: Result is captured at /matrix_multiplication/rfcollect-20240506-160802.json RFCOLLECT: Run "rfreport /matrix_multiplication/rfcollect-20240506-160802.json" to get report. Get roofline report ... The roofline json report: /matrix_multiplication/transpose_B_matmult_8192.json The roofline html report: /matrix_multiplication/transpose_B_matmult_8192.html

3. 查看transpose_B_matmult_8192_html报告。
   图6 transpose_B_matmult_8192_html报告
   

   此时获取的roofs的并行度为128，获取到Elapsed Time 10.017s，GFLOP Count 1099.512，Performance 109.763 GFLOPS。

优化效果

1. L1处于Memory Bound区域，L2、L3和DDR处于Compute and Memory Bound区域。
2. 当前内存瓶颈主要在L1和L3，较好的利用了高速cache介质。
3. 缓存局部效应Cache line utilization相比与之前变好，计算密度（Flop/Byte）：L1 < L2 < L3 < DDR。