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统计学
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抽样
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推断
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概率论
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计数
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概率概念
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分布
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</a>
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贝叶斯
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</span>
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</a>
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信息论
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</span>
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机器学习
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</span>
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<span class="md-nav__icon md-icon"></span>
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机器学习
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经典机器学习
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梯度机器学习
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</span>
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</a>
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深度学习
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</span>
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</a>
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强化学习
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</span>
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</a>
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分布式深度学习
|
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</span>
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|
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|
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|
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</a>
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计算语言学
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<span class="md-nav__icon md-icon"></span>
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语言学基础
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</a>
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嵌入与序列模型
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</a>
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Transformer 与语言模型
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</span>
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|
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</a>
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<span class="md-ellipsis">
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高级文本生成
|
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|
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|
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</span>
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|
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|
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|
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</a>
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计算机视觉
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图像基础
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</span>
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</a>
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目标检测与分割
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多模态学习
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多模态学习
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多模态表征
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</a>
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统一多模态架构
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</span>
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自主系统
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感知
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视觉-语言-动作模型
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自动驾驶
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</a>
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太空与极端机器人
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</span>
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|
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图神经网络
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<li class="md-nav__item">
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<a href="#numpy" class="md-nav__link">
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|
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NumPy
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|
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|
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|
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|
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<li class="md-nav__item">
|
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|
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PyTorch
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|
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JAX
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|
||
|
||
</li>
|
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|
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|
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|
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|
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面向Python工程师的C++快速入门
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</span>
|
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|
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类型和变量
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<a href="#_3" class="md-nav__link">
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内存：栈与堆
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<li class="md-nav__item">
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<a href="#_4" class="md-nav__link">
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模板（泛型）
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<li class="md-nav__item">
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<a href="#_5" class="md-nav__link">
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标准库精华
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|
||
</li>
|
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<a href="#c" class="md-nav__link">
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|
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何时编写自定义C++核函数
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pybind11（通用目的）
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PyTorch C++扩展
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JAX自定义调用
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大局观
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硬件基础
|
||
|
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|
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|
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</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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<li class="md-nav__item">
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<a href="../02.%20ARM%20and%20NEON/" class="md-nav__link">
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<span class="md-ellipsis">
|
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|
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|
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ARM 与 NEON
|
||
|
||
|
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|
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</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
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<span class="md-ellipsis">
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x86 与 AVX
|
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|
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|
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|
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</span>
|
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|
||
|
||
|
||
</a>
|
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</li>
|
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|
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<li class="md-nav__item">
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<span class="md-ellipsis">
|
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GPU 架构与 CUDA
|
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|
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|
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|
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</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
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|
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<span class="md-ellipsis">
|
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|
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|
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Triton、TPU 与 Pallas
|
||
|
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|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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<a href="../06.%20RISC-V%20and%20embedded%20systems/" class="md-nav__link">
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<span class="md-ellipsis">
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RISC-V 与嵌入式系统
|
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|
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|
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|
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</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
||
|
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<a href="../07.%20vulkan%20compute%20and%20cross-platform%20GPU/" class="md-nav__link">
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<span class="md-ellipsis">
|
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||
Vulkan Compute 与跨平台 GPU
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
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</a>
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||
|
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<span class="md-ellipsis">
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|
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AI 推理
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|
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AI 推理
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<span class="md-ellipsis">
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量化
|
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|
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|
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|
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</span>
|
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|
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|
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|
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</a>
|
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</li>
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|
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<span class="md-ellipsis">
|
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|
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高效架构
|
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|
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|
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|
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</span>
|
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|
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|
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|
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</a>
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</li>
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<span class="md-ellipsis">
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服务与批处理
|
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|
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|
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|
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</span>
|
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|
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|
||
|
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</a>
|
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</li>
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<a href="../../chapter%2017%3A%20AI%20inference/04.%20edge%20inference/" class="md-nav__link">
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|
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<span class="md-ellipsis">
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|
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|
||
边缘推理
|
||
|
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|
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|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
||
|
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<li class="md-nav__item">
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<a href="../../chapter%2017%3A%20AI%20inference/05.%20scaling%20and%20deployment/" class="md-nav__link">
|
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|
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|
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|
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<span class="md-ellipsis">
|
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|
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|
||
扩缩与部署
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
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</a>
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|
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</ul>
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</nav>
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||
|
||
|
||
|
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<li class="md-nav__item md-nav__item--nested">
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<span class="md-ellipsis">
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|
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|
||
ML 系统设计
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|
||
|
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|
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</span>
|
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|
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|
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|
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<span class="md-nav__icon md-icon"></span>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
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<span class="md-nav__icon md-icon"></span>
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ML 系统设计
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|
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|
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</label>
|
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<ul class="md-nav__list" data-md-scrollfix>
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|
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|
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<span class="md-ellipsis">
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|
||
系统设计基础
|
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|
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|
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|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
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|
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|
||
云计算
|
||
|
||
|
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|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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|
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|
||
|
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<span class="md-ellipsis">
|
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|
||
|
||
大规模基础设施
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
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|
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|
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<span class="md-ellipsis">
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|
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ML 系统设计
|
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|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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|
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<span class="md-ellipsis">
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|
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ML 设计案例
|
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|
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|
||
|
||
</span>
|
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|
||
|
||
|
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</a>
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应用 AI
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</span>
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<span class="md-nav__icon md-icon"></span>
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<span class="md-nav__icon md-icon"></span>
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应用 AI
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<a href="../../chapter%2019%3A%20applied%20AI/01.%20AI%20for%20finance/" class="md-nav__link">
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<span class="md-ellipsis">
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AI 金融
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|
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|
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</span>
|
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|
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|
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|
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</a>
|
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</li>
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<li class="md-nav__item">
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<span class="md-ellipsis">
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蛋白质设计
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</span>
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|
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|
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|
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</a>
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药物发现
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</span>
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|
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</a>
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智能体系统
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</span>
|
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|
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|
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|
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</a>
|
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<span class="md-ellipsis">
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医疗健康
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</span>
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前沿 AI
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</span>
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<span class="md-nav__icon md-icon"></span>
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前沿 AI
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量子机器学习
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</span>
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</a>
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<span class="md-ellipsis">
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神经形态计算
|
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|
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</span>
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|
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|
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</a>
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<span class="md-ellipsis">
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太空数据中心
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|
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</span>
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</a>
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去中心化 AI
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</span>
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</a>
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<span class="md-ellipsis">
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脑机接口
|
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|
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|
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</span>
|
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|
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|
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</a>
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<div class="md-sidebar__scrollwrap">
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<div class="md-sidebar__inner">
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目录
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为什么Python前端搭配C++后端
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</span>
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</a>
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<a href="#ml" class="md-nav__link">
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<span class="md-ellipsis">
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ML框架的结构
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NumPy
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PyTorch
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JAX
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面向Python工程师的C++快速入门
|
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<a href="#_1" class="md-nav__link">
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<span class="md-ellipsis">
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类型和变量
|
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</a>
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|
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|
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<li class="md-nav__item">
|
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<a href="#_2" class="md-nav__link">
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函数
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|
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|
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<li class="md-nav__item">
|
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<a href="#_3" class="md-nav__link">
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<span class="md-ellipsis">
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内存：栈与堆
|
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|
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</span>
|
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</a>
|
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|
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</li>
|
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|
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<li class="md-nav__item">
|
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<a href="#_4" class="md-nav__link">
|
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<span class="md-ellipsis">
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模板（泛型）
|
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</a>
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|
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</li>
|
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|
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<li class="md-nav__item">
|
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<a href="#_5" class="md-nav__link">
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<span class="md-ellipsis">
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标准库精华
|
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|
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|
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</ul>
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|
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<a href="#c" class="md-nav__link">
|
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<span class="md-ellipsis">
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|
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何时编写自定义C++核函数
|
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如何将C++绑定到Python
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pybind11（通用目的）
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|
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|
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PyTorch C++扩展
|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="#jax_1" class="md-nav__link">
|
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<span class="md-ellipsis">
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|
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JAX自定义调用
|
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|
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</a>
|
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|
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|
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|
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</ul>
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|
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<li class="md-nav__item">
|
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<a href="#_6" class="md-nav__link">
|
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<span class="md-ellipsis">
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|
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大局观
|
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|
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</span>
|
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</a>
|
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|
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</li>
|
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|
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<li class="md-nav__item">
|
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<a href="#gclang" class="md-nav__link">
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<span class="md-ellipsis">
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|
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编程任务（用g++或clang++编译）
|
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|
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</span>
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</a>
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|
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|
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|
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</ul>
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</div>
|
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</div>
|
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|
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<div class="md-content" data-md-component="content">
|
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|
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<article class="md-content__inner md-typeset">
|
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|
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|
||
|
||
|
||
|
||
|
||
|
||
|
||
<h1 id="cml">为什么是C++以及ML框架如何工作<a class="headerlink" href="#cml" title="Permanent link">¶</a></h1>
|
||
<p><em>本书中每一次 <code>jnp.matmul</code>、每一次 <code>torch.nn.Linear</code>、每一次 <code>np.dot</code> 调用，底层都在执行C++和CUDA代码。本文档揭开帷幕：为何ML框架采用这种架构，面向Python工程师的C++快速入门，何时编写自定义C++核函数，以及如何将其绑定到Python——这是连接你所写代码与所运行硬件之间的桥梁。</em></p>
|
||
<ul>
|
||
<li>
|
||
<p>你花了15章写Python。你导入了JAX，调用了<code>jax.grad</code>，运行了训练循环，构建了模型。一切感觉都像是Python。但事实是：<strong>几乎没有实际计算发生在Python中。</strong></p>
|
||
</li>
|
||
<li>
|
||
<p>当你在PyTorch中写 <code>output = model(input)</code> 或在JAX中写 <code>output = jnp.matmul(W, x)</code> 时，Python几乎什么都不做。它构建一个计算的描述（一个操作图），然后将其交给执行真正工作的C++/CUDA后端。Python是方向盘；C++是引擎。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="pythonc">为什么Python前端搭配C++后端<a class="headerlink" href="#pythonc" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>这种双语言架构的存在是因为Python和C++擅长截然不同的事情：</li>
|
||
</ul>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th></th>
|
||
<th>Python</th>
|
||
<th>C++</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr>
|
||
<td>开发速度</td>
|
||
<td>快（动态类型、REPL、无需编译）</td>
|
||
<td>慢（静态类型、头文件、编译时间长）</td>
|
||
</tr>
|
||
<tr>
|
||
<td>执行速度</td>
|
||
<td>比C慢约100倍（解释型、GIL）</td>
|
||
<td>接近硬件速度（编译型、无开销）</td>
|
||
</tr>
|
||
<tr>
|
||
<td>内存控制</td>
|
||
<td>自动（GC），无法控制布局</td>
|
||
<td>手动，精确控制每一个字节</td>
|
||
</tr>
|
||
<tr>
|
||
<td>硬件访问</td>
|
||
<td>无（无SIMD、无GPU、无自定义内存）</td>
|
||
<td>全面（内联函数、CUDA、内联汇编）</td>
|
||
</tr>
|
||
<tr>
|
||
<td>生态系统</td>
|
||
<td>ML丰富（笔记本、可视化、数据）</td>
|
||
<td>系统丰富（操作系统、驱动、引擎）</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<ul>
|
||
<li>
|
||
<p>核心见解：<strong>每种语言发挥其优势</strong>。Python处理人力生产力重要的事务（实验设计、超参数调优、数据探索）。C++处理机器性能重要的事务（矩阵乘法、卷积、注意力核函数）。</p>
|
||
</li>
|
||
<li>
|
||
<p>一次矩阵乘法 <code>jnp.matmul(A, B)</code>，其中 <span class="arithmatex">\(A\)</span> 为 <span class="arithmatex">\(4096 \times 4096\)</span>，执行约1370亿次浮点运算。在纯Python（嵌套循环）中需要约30分钟。在使用AVX-512 SIMD和多线程优化后的C++中，只需约10毫秒。差距达<strong>180,000倍</strong>。再多的Python技巧也无法弥合这一鸿沟。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="ml">ML框架的结构<a class="headerlink" href="#ml" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>每个主流ML框架都遵循相同的架构：</li>
|
||
</ul>
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a>用户代码（Python）
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> ↓
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>Python API层（torch.nn、jax.numpy、numpy）
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> ↓
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>调度/JIT编译器（torch.compile、XLA、NumPy调度）
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> ↓
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>C++核函数库（ATen/PyTorch、XLA、BLAS/LAPACK）
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> ↓
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>硬件特定后端（CUDA、cuDNN、MKL、oneDNN、Metal）
|
||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a> ↓
|
||
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>硬件（CPU SIMD单元、GPU核心、TPU MXU）
|
||
</code></pre></div>
|
||
<h3 id="numpy">NumPy<a class="headerlink" href="#numpy" title="Permanent link">¶</a></h3>
|
||
<ul>
|
||
<li>
|
||
<p>NumPy的核心用C编写。当你调用 <code>np.dot(A, B)</code> 时，Python调用一个C函数，该函数调用BLAS（基本线性代数子程序），通常是Intel MKL或OpenBLAS。BLAS是手工优化的C和Fortran代码，使用SIMD指令、缓存感知的内存访问模式和多线程。数十年优化致力于让矩阵乘法更快。</p>
|
||
</li>
|
||
<li>
|
||
<p>NumPy仅支持CPU，不使用GPU。但在CPU上，它极其快速，因为它委托给可用的最佳BLAS实现。</p>
|
||
</li>
|
||
</ul>
|
||
<h3 id="pytorch">PyTorch<a class="headerlink" href="#pytorch" title="Permanent link">¶</a></h3>
|
||
<ul>
|
||
<li>
|
||
<p>PyTorch的计算引擎是<strong>ATen</strong>（张量库），用C++编写。ATen实现了约2000个张量操作（add、matmul、conv2d、softmax...），每个都有CPU和CUDA后端。</p>
|
||
</li>
|
||
<li>
|
||
<p>当你调用 <code>torch.matmul(A, B)</code> 时：</p>
|
||
<ol>
|
||
<li>Python调度到ATen的C++函数。</li>
|
||
<li>ATen检查设备（CPU或CUDA）和数据类型。</li>
|
||
<li>在CPU上：调用MKL/OpenBLAS。在GPU上：调用cuBLAS（NVIDIA的GPU优化BLAS）。</li>
|
||
<li>结果包装在Python张量对象中并返回。</li>
|
||
</ol>
|
||
</li>
|
||
<li>
|
||
<p><strong>torch.compile</strong>（PyTorch 2.0+）更进一步：它追踪你的Python代码，构建计算图，并使用<strong>Triton</strong>（GPU）或<strong>C++/OpenMP</strong>（CPU）编译。编译后的代码融合操作，消除Python开销，可以比即时模式快2-5倍。</p>
|
||
</li>
|
||
</ul>
|
||
<h3 id="jax">JAX<a class="headerlink" href="#jax" title="Permanent link">¶</a></h3>
|
||
<ul>
|
||
<li>
|
||
<p>JAX将Python函数编译为<strong>XLA</strong>（加速线性代数），Google的ML编译器。当你 <code>jax.jit</code> 一个函数时：</p>
|
||
<ol>
|
||
<li>JAX追踪函数，将操作捕获为XLA计算图（HLO——高级操作）。</li>
|
||
<li>XLA优化图：融合操作，消除冗余计算，优化内存布局。</li>
|
||
<li>XLA编译为目标后端：CPU（通过LLVM）、GPU（通过CUDA/PTX）或TPU（通过TPU特定指令）。</li>
|
||
<li>编译后的代码直接在硬件上运行，零Python参与。</li>
|
||
</ol>
|
||
</li>
|
||
<li>
|
||
<p>这就是为什么 <code>jax.jit</code> 如此重要：没有它，每个操作都是独立的Python→C++往返。有了它，整个函数是一个单一的编译核函数。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="pythonc_1">面向Python工程师的C++快速入门<a class="headerlink" href="#pythonc_1" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>你不需要成为C++专家。你需要理解足够的知识来阅读核函数代码、编写简单的扩展以及理解性能讨论。以下是精华内容。</li>
|
||
</ul>
|
||
<h3 id="_1">类型和变量<a class="headerlink" href="#_1" title="Permanent link">¶</a></h3>
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="c1">// C++需要显式类型（不像Python）</span>
|
||
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 32位整数</span>
|
||
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="kt">float</span><span class="w"> </span><span class="n">loss</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0.5f</span><span class="p">;</span><span class="w"> </span><span class="c1">// 32位浮点数</span>
|
||
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="kt">double</span><span class="w"> </span><span class="n">lr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3e-4</span><span class="p">;</span><span class="w"> </span><span class="c1">// 64位浮点数</span>
|
||
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="kt">bool</span><span class="w"> </span><span class="n">training</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">true</span><span class="p">;</span><span class="w"> </span><span class="c1">// 布尔值</span>
|
||
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a>
|
||
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="c1">// 数组（固定大小，栈分配）</span>
|
||
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="kt">float</span><span class="w"> </span><span class="n">weights</span><span class="p">[</span><span class="mi">1024</span><span class="p">];</span><span class="w"> </span><span class="c1">// 1024个浮点数，内存中连续</span>
|
||
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a>
|
||
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="c1">// 指针：保存内存地址的变量</span>
|
||
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="kt">float</span><span class="o">*</span><span class="w"> </span><span class="n">ptr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">weights</span><span class="p">;</span><span class="w"> </span><span class="c1">// ptr指向weights的第一个元素</span>
|
||
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="kt">float</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ptr</span><span class="p">[</span><span class="mi">42</span><span class="p">];</span><span class="w"> </span><span class="c1">// 通过指针运算访问元素42</span>
|
||
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="c1">// ptr[42] 等价于 *(ptr + 42)</span>
|
||
</code></pre></div>
|
||
<ul>
|
||
<li><strong>指针</strong>是与Python最大的概念差异。在Python中，一切都是引用，你从不需要思考内存地址。在C++中，指针让你直接访问内存——强大但危险（悬空指针、缓冲区溢出）。</li>
|
||
</ul>
|
||
<h3 id="_2">函数<a class="headerlink" href="#_2" title="Permanent link">¶</a></h3>
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="c1">// 函数声明：返回类型 名字(参数类型 参数名)</span>
|
||
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">float</span><span class="w"> </span><span class="nf">relu</span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">x</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mf">0.0f</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">x</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="mf">0.0f</span><span class="p">;</span>
|
||
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a>
|
||
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="c1">// 传引用（避免拷贝大对象）</span>
|
||
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="kt">void</span><span class="w"> </span><span class="nf">scale_vector</span><span class="p">(</span><span class="n">std</span><span class="o">::</span><span class="n">vector</span><span class="o"><</span><span class="kt">float</span><span class="o">>&</span><span class="w"> </span><span class="n">vec</span><span class="p">,</span><span class="w"> </span><span class="kt">float</span><span class="w"> </span><span class="n">factor</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">size_t</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">vec</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w"> </span><span class="n">vec</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="n">factor</span><span class="p">;</span>
|
||
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="p">}</span>
|
||
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a>
|
||
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="c1">// const引用：只读，无拷贝</span>
|
||
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="kt">float</span><span class="w"> </span><span class="nf">sum</span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">vector</span><span class="o"><</span><span class="kt">float</span><span class="o">>&</span><span class="w"> </span><span class="n">vec</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w"> </span><span class="kt">float</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0.0f</span><span class="p">;</span>
|
||
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">x</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">vec</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 基于范围的for循环（类似Python的for x in vec）</span>
|
||
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span>
|
||
<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">total</span><span class="p">;</span>
|
||
<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
<h3 id="_3">内存：栈与堆<a class="headerlink" href="#_3" title="Permanent link">¶</a></h3>
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="c1">// 栈分配：快速，自动生命周期（函数返回时释放）</span>
|
||
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">float</span><span class="w"> </span><span class="n">buffer</span><span class="p">[</span><span class="mi">256</span><span class="p">];</span><span class="w"> </span><span class="c1">// 栈上的256个浮点数</span>
|
||
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a>
|
||
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="c1">// 堆分配：手动，在函数外仍然存活</span>
|
||
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="kt">float</span><span class="o">*</span><span class="w"> </span><span class="n">data</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">float</span><span class="p">[</span><span class="n">n</span><span class="p">];</span><span class="w"> </span><span class="c1">// 在堆上分配n个浮点数</span>
|
||
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="c1">// ... 使用data ...</span>
|
||
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="k">delete</span><span class="p">[]</span><span class="w"> </span><span class="n">data</span><span class="p">;</span><span class="w"> </span><span class="c1">// 必须手动释放（没有垃圾回收器）</span>
|
||
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a>
|
||
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="c1">// 现代C++：智能指针（自动清理，类似Python引用）</span>
|
||
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><memory></span>
|
||
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="k">auto</span><span class="w"> </span><span class="n">data</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">make_unique</span><span class="o"><</span><span class="kt">float</span><span class="p">[]</span><span class="o">></span><span class="p">(</span><span class="n">n</span><span class="p">);</span><span class="w"> </span><span class="c1">// 离开作用域时自动释放</span>
|
||
</code></pre></div>
|
||
<ul>
|
||
<li><strong>关键规则</strong>：栈快速但有限（通常1-8 MB）。大数组（张量、特征图）必须放在堆上。在Python中，一切都在堆上，GC处理清理。在C++中，你自行管理（或使用智能指针）。</li>
|
||
</ul>
|
||
<h3 id="_4">模板（泛型）<a class="headerlink" href="#_4" title="Permanent link">¶</a></h3>
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="c1">// 适用于任何数值类型的函数</span>
|
||
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="k">template</span><span class="w"> </span><span class="o"><</span><span class="k">typename</span><span class="w"> </span><span class="nc">T</span><span class="o">></span>
|
||
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="n">T</span><span class="w"> </span><span class="n">add</span><span class="p">(</span><span class="n">T</span><span class="w"> </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">T</span><span class="w"> </span><span class="n">b</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
|
||
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a>
|
||
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="n">add</span><span class="o"><</span><span class="kt">float</span><span class="o">></span><span class="p">(</span><span class="mf">1.5f</span><span class="p">,</span><span class="w"> </span><span class="mf">2.5f</span><span class="p">);</span><span class="w"> </span><span class="c1">// 返回 4.0f</span>
|
||
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="n">add</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">);</span><span class="w"> </span><span class="c1">// 返回 7</span>
|
||
</code></pre></div>
|
||
<ul>
|
||
<li>模板是C++库（如ATen）编写适用于float16、float32、float64等的代码而不重复实现的方式。</li>
|
||
</ul>
|
||
<h3 id="_5">标准库精华<a class="headerlink" href="#_5" title="Permanent link">¶</a></h3>
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><vector></span><span class="c1"> // 动态数组（类似Python list）</span>
|
||
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><string></span><span class="c1"> // 字符串类型</span>
|
||
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><unordered_map></span><span class="c1"> // 哈希映射（类似Python dict）</span>
|
||
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><algorithm></span><span class="c1"> // sort、find、transform等</span>
|
||
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><cmath></span><span class="c1"> // 数学函数</span>
|
||
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a>
|
||
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="n">std</span><span class="o">::</span><span class="n">vector</span><span class="o"><</span><span class="kt">float</span><span class="o">></span><span class="w"> </span><span class="n">vec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mf">1.0f</span><span class="p">,</span><span class="w"> </span><span class="mf">2.0f</span><span class="p">,</span><span class="w"> </span><span class="mf">3.0f</span><span class="p">};</span>
|
||
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="n">vec</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mf">4.0f</span><span class="p">);</span><span class="w"> </span><span class="c1">// 追加</span>
|
||
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="kt">float</span><span class="w"> </span><span class="n">first</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vec</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span><span class="w"> </span><span class="c1">// 索引</span>
|
||
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="kt">size_t</span><span class="w"> </span><span class="n">len</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vec</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="c1">// 长度</span>
|
||
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a>
|
||
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="n">std</span><span class="o">::</span><span class="n">unordered_map</span><span class="o"><</span><span class="n">std</span><span class="o">::</span><span class="n">string</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">counts</span><span class="p">;</span>
|
||
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="n">counts</span><span class="p">[</span><span class="s">"hello"</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">5</span><span class="p">;</span><span class="w"> </span><span class="c1">// 插入</span>
|
||
<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">counts</span><span class="p">.</span><span class="n">count</span><span class="p">(</span><span class="s">"hello"</span><span class="p">))</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="c1">// 检查存在性</span>
|
||
</code></pre></div>
|
||
<h2 id="c">何时编写自定义C++核函数<a class="headerlink" href="#c" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>
|
||
<p>大多数ML工程师从不需要写C++。框架的内置操作覆盖了99%的用例。仅在以下情况考虑自定义C++：</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>框架中不存在你的操作</strong>：新颖的激活函数、自定义注意力模式、无法表示为现有操作组合的特殊损失函数。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>融合操作以提高性能</strong>：你的模型执行 <code>relu(layernorm(matmul(x, W) + b))</code>。每个操作启动一个独立的核函数，读写内存，并同步。一个融合核函数在一次遍历中完成所有工作，避免内存往返。这可快2-5倍。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>减少内存使用</strong>：自定义核函数可以在不存储所有中间激活的情况下计算梯度（核函数级别的梯度检查点）。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>针对新型硬件</strong>：新的加速器（如Cerebras、Groq）可能没有框架支持。你需要直接编写核函数。</p>
|
||
</li>
|
||
<li>
|
||
<p>对于情况1-2，<strong>Triton</strong>（第16章文件05）通常足够且比直接编写CUDA C更简单。只有在Triton无法表达你的需求时才下降到CUDA C。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="cpython">如何将C++绑定到Python<a class="headerlink" href="#cpython" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>编写C++只是工作的一半。你还需要从Python调用它。</li>
|
||
</ul>
|
||
<h3 id="pybind11">pybind11（通用目的）<a class="headerlink" href="#pybind11" title="Permanent link">¶</a></h3>
|
||
<ul>
|
||
<li>pybind11用最少的样板代码为C++函数创建Python绑定：</li>
|
||
</ul>
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="c1">// my_ops.cpp</span>
|
||
<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><pybind11/pybind11.h></span>
|
||
<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><pybind11/numpy.h></span>
|
||
<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="k">namespace</span><span class="w"> </span><span class="nn">py</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nn">pybind11</span><span class="p">;</span>
|
||
<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a>
|
||
<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="c1">// 一个简单的自定义操作</span>
|
||
<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="n">py</span><span class="o">::</span><span class="n">array_t</span><span class="o"><</span><span class="kt">float</span><span class="o">></span><span class="w"> </span><span class="n">custom_relu</span><span class="p">(</span><span class="n">py</span><span class="o">::</span><span class="n">array_t</span><span class="o"><</span><span class="kt">float</span><span class="o">></span><span class="w"> </span><span class="n">input</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="n">buf</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">input</span><span class="p">.</span><span class="n">request</span><span class="p">();</span>
|
||
<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w"> </span><span class="kt">float</span><span class="o">*</span><span class="w"> </span><span class="n">ptr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">static_cast</span><span class="o"><</span><span class="kt">float</span><span class="o">*></span><span class="p">(</span><span class="n">buf</span><span class="p">.</span><span class="n">ptr</span><span class="p">);</span>
|
||
<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w"> </span><span class="kt">size_t</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buf</span><span class="p">.</span><span class="n">size</span><span class="p">;</span>
|
||
<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a>
|
||
<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="n">result</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">py</span><span class="o">::</span><span class="n">array_t</span><span class="o"><</span><span class="kt">float</span><span class="o">></span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
|
||
<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w"> </span><span class="kt">float</span><span class="o">*</span><span class="w"> </span><span class="n">out</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">static_cast</span><span class="o"><</span><span class="kt">float</span><span class="o">*></span><span class="p">(</span><span class="n">result</span><span class="p">.</span><span class="n">request</span><span class="p">().</span><span class="n">ptr</span><span class="p">);</span>
|
||
<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a>
|
||
<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">size_t</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w"> </span><span class="n">out</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ptr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">ptr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">result</span><span class="p">;</span>
|
||
<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="p">}</span>
|
||
<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a>
|
||
<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="n">PYBIND11_MODULE</span><span class="p">(</span><span class="n">my_ops</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="w"> </span><span class="n">m</span><span class="p">.</span><span class="n">def</span><span class="p">(</span><span class="s">"custom_relu"</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">custom_relu</span><span class="p">,</span><span class="w"> </span><span class="s">"自定义ReLU操作"</span><span class="p">);</span>
|
||
<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="c1"># 编译</span>
|
||
<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>pip<span class="w"> </span>install<span class="w"> </span>pybind11
|
||
<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a>c++<span class="w"> </span>-O3<span class="w"> </span>-shared<span class="w"> </span>-std<span class="o">=</span>c++17<span class="w"> </span>-fPIC<span class="w"> </span><span class="k">$(</span>python3<span class="w"> </span>-m<span class="w"> </span>pybind11<span class="w"> </span>--includes<span class="k">)</span><span class="w"> </span>my_ops.cpp<span class="w"> </span>-o<span class="w"> </span>my_ops<span class="k">$(</span>python3-config<span class="w"> </span>--extension-suffix<span class="k">)</span>
|
||
</code></pre></div>
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="c1"># 从Python使用</span>
|
||
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kn">import</span><span class="w"> </span><span class="nn">my_ops</span>
|
||
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
|
||
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a>
|
||
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="o">-</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="o">-</span><span class="mf">3.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
|
||
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="n">y</span> <span class="o">=</span> <span class="n">my_ops</span><span class="o">.</span><span class="n">custom_relu</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
||
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="nb">print</span><span class="p">(</span><span class="n">y</span><span class="p">)</span> <span class="c1"># [0. 2. 0. 4.]</span>
|
||
</code></pre></div>
|
||
<h3 id="pytorch-c">PyTorch C++扩展<a class="headerlink" href="#pytorch-c" title="Permanent link">¶</a></h3>
|
||
<ul>
|
||
<li>PyTorch提供了一种简化的方式来添加自定义操作：</li>
|
||
</ul>
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="c1">// custom_op.cpp</span>
|
||
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><torch/extension.h></span>
|
||
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a>
|
||
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="n">torch</span><span class="o">::</span><span class="n">Tensor</span><span class="w"> </span><span class="nf">custom_gelu</span><span class="p">(</span><span class="n">torch</span><span class="o">::</span><span class="n">Tensor</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">x</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">0.5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="mf">1.0</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">torch</span><span class="o">::</span><span class="n">erf</span><span class="p">(</span><span class="n">x</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">sqrt</span><span class="p">(</span><span class="mf">2.0</span><span class="p">)));</span>
|
||
<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="p">}</span>
|
||
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a>
|
||
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="n">PYBIND11_MODULE</span><span class="p">(</span><span class="n">TORCH_EXTENSION_NAME</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w"> </span><span class="n">m</span><span class="p">.</span><span class="n">def</span><span class="p">(</span><span class="s">"custom_gelu"</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">custom_gelu</span><span class="p">,</span><span class="w"> </span><span class="s">"自定义GELU激活函数"</span><span class="p">);</span>
|
||
<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1"># 动态加载和编译</span>
|
||
<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kn">from</span><span class="w"> </span><span class="nn">torch.utils.cpp_extension</span><span class="w"> </span><span class="kn">import</span> <span class="n">load</span>
|
||
<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a>
|
||
<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="n">custom_ops</span> <span class="o">=</span> <span class="n">load</span><span class="p">(</span>
|
||
<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a> <span class="n">name</span><span class="o">=</span><span class="s2">"custom_ops"</span><span class="p">,</span>
|
||
<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a> <span class="n">sources</span><span class="o">=</span><span class="p">[</span><span class="s2">"custom_op.cpp"</span><span class="p">],</span>
|
||
<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a> <span class="n">extra_cflags</span><span class="o">=</span><span class="p">[</span><span class="s2">"-O3"</span><span class="p">],</span>
|
||
<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="p">)</span>
|
||
<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a>
|
||
<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="n">x</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">1000</span><span class="p">)</span>
|
||
<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="n">y</span> <span class="o">=</span> <span class="n">custom_ops</span><span class="o">.</span><span class="n">custom_gelu</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
||
</code></pre></div>
|
||
<ul>
|
||
<li><code>torch.utils.cpp_extension.load</code> 编译C++代码，创建共享库，并将其作为Python模块加载，全在一个调用中完成。这是在PyTorch中实验自定义C++操作的最简单方式。</li>
|
||
</ul>
|
||
<h3 id="jax_1">JAX自定义调用<a class="headerlink" href="#jax_1" title="Permanent link">¶</a></h3>
|
||
<ul>
|
||
<li>
|
||
<p>JAX使用XLA自定义调用。过程更为复杂（你需要向XLA注册一个C函数），但概念相同：编写C/C++，绑定，从Python调用。</p>
|
||
</li>
|
||
<li>
|
||
<p>对于大多数JAX用户，<strong>Pallas</strong>（在文件05中介绍）是更好的选择：它让你用类似Python的语法编写GPU核函数，由XLA编译，无需离开JAX生态系统。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="_6">大局观<a class="headerlink" href="#_6" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>
|
||
<p>本文解释了Python和硬件之间的层次。本章剩余文件将深入探讨：</p>
|
||
<ul>
|
||
<li><strong>文件01</strong>：硬件本身（CPU架构、GPU架构、内存系统）</li>
|
||
<li><strong>文件02-03</strong>：CPU上的SIMD编程（ARM NEON、x86 AVX）——编写使用CPU向量单元的C++代码</li>
|
||
<li><strong>文件04</strong>：使用CUDA的GPU编程——编写在数千个GPU核心上运行的C++代码</li>
|
||
<li><strong>文件05</strong>：Triton、Pallas和更高级的GPU编程——编写编译为GPU核函数的Python代码</li>
|
||
</ul>
|
||
</li>
|
||
<li>
|
||
<p>这种递进反映了抽象阶梯：C++内联函数（最低层、最多控制）→ CUDA（GPU专用）→ Triton/Pallas（Python风格、编译型）→ JAX/PyTorch（最高层、自动）。每一层以控制权换取便利性。理解较低层使你成为较高层的更好使用者。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="gclang">编程任务（用g++或clang++编译）<a class="headerlink" href="#gclang" title="Permanent link">¶</a></h2>
|
||
<ol>
|
||
<li>
|
||
<p>编写你的第一个C++程序。分配一个数组，填充数据，计算总和，并测量时间。这介绍了编译、数组、指针和计时。
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="c1">// task1_basics.cpp</span>
|
||
<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="c1">// 编译：g++ -O3 -o task1 task1_basics.cpp</span>
|
||
<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="c1">// 运行：./task1</span>
|
||
<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a>
|
||
<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><iostream></span>
|
||
<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><chrono></span>
|
||
<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><vector></span>
|
||
<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a>
|
||
<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="kt">int</span><span class="w"> </span><span class="nf">main</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">N</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">10'000'000</span><span class="p">;</span><span class="w"> </span><span class="c1">// C++允许'作为数字分隔符</span>
|
||
<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">vector</span><span class="o"><</span><span class="kt">float</span><span class="o">></span><span class="w"> </span><span class="n">data</span><span class="p">(</span><span class="n">N</span><span class="p">);</span>
|
||
<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a>
|
||
<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w"> </span><span class="c1">// 填充数组</span>
|
||
<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">N</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w"> </span><span class="n">data</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">static_cast</span><span class="o"><</span><span class="kt">float</span><span class="o">></span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">0.001f</span><span class="p">;</span>
|
||
<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a>
|
||
<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w"> </span><span class="c1">// 计算总和</span>
|
||
<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">chrono</span><span class="o">::</span><span class="n">high_resolution_clock</span><span class="o">::</span><span class="n">now</span><span class="p">();</span>
|
||
<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w"> </span><span class="kt">float</span><span class="w"> </span><span class="n">sum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0.0f</span><span class="p">;</span>
|
||
<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">N</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="w"> </span><span class="n">sum</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">data</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
|
||
<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="n">end</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">chrono</span><span class="o">::</span><span class="n">high_resolution_clock</span><span class="o">::</span><span class="n">now</span><span class="p">();</span>
|
||
<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">elapsed</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">chrono</span><span class="o">::</span><span class="n">duration</span><span class="o"><</span><span class="kt">double</span><span class="p">,</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">milli</span><span class="o">></span><span class="p">(</span><span class="n">end</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">start</span><span class="p">).</span><span class="n">count</span><span class="p">();</span>
|
||
<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a>
|
||
<a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">cout</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"总和: "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">sum</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">endl</span><span class="p">;</span>
|
||
<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">cout</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"时间: "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">elapsed</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">" ms"</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">endl</span><span class="p">;</span>
|
||
<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">cout</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"元素数: "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">N</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">endl</span><span class="p">;</span>
|
||
<a id="__codelineno-11-30" name="__codelineno-11-30" href="#__codelineno-11-30"></a><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">cout</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"吞吐量: "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="p">(</span><span class="n">N</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">float</span><span class="p">))</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">elapsed</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">1e6</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">" GB/s"</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">endl</span><span class="p">;</span>
|
||
<a id="__codelineno-11-31" name="__codelineno-11-31" href="#__codelineno-11-31"></a>
|
||
<a id="__codelineno-11-32" name="__codelineno-11-32" href="#__codelineno-11-32"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-11-33" name="__codelineno-11-33" href="#__codelineno-11-33"></a><span class="p">}</span>
|
||
</code></pre></div></p>
|
||
</li>
|
||
<li>
|
||
<p>编写一个C++函数在数组上计算ReLU，然后使用pybind11构建Python绑定。从Python调用它并与NumPy比较速度。
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">// task2_relu.cpp</span>
|
||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="c1">// 编译：c++ -O3 -shared -std=c++17 -fPIC $(python3 -m pybind11 --includes) \</span>
|
||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="c1">// task2_relu.cpp -o my_relu$(python3-config --extension-suffix)</span>
|
||
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
|
||
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><pybind11/pybind11.h></span>
|
||
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><pybind11/numpy.h></span>
|
||
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="k">namespace</span><span class="w"> </span><span class="nn">py</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nn">pybind11</span><span class="p">;</span>
|
||
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a>
|
||
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="n">py</span><span class="o">::</span><span class="n">array_t</span><span class="o"><</span><span class="kt">float</span><span class="o">></span><span class="w"> </span><span class="n">cpp_relu</span><span class="p">(</span><span class="n">py</span><span class="o">::</span><span class="n">array_t</span><span class="o"><</span><span class="kt">float</span><span class="o">></span><span class="w"> </span><span class="n">input</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="n">buf</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">input</span><span class="p">.</span><span class="n">request</span><span class="p">();</span>
|
||
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="kt">float</span><span class="o">*</span><span class="w"> </span><span class="n">ptr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">static_cast</span><span class="o"><</span><span class="kt">float</span><span class="o">*></span><span class="p">(</span><span class="n">buf</span><span class="p">.</span><span class="n">ptr</span><span class="p">);</span>
|
||
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buf</span><span class="p">.</span><span class="n">size</span><span class="p">;</span>
|
||
<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a>
|
||
<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="n">result</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">py</span><span class="o">::</span><span class="n">array_t</span><span class="o"><</span><span class="kt">float</span><span class="o">></span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
|
||
<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w"> </span><span class="kt">float</span><span class="o">*</span><span class="w"> </span><span class="n">out</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">static_cast</span><span class="o"><</span><span class="kt">float</span><span class="o">*></span><span class="p">(</span><span class="n">result</span><span class="p">.</span><span class="n">request</span><span class="p">().</span><span class="n">ptr</span><span class="p">);</span>
|
||
<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a>
|
||
<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w"> </span><span class="n">out</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ptr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mf">0.0f</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">ptr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="mf">0.0f</span><span class="p">;</span>
|
||
<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">result</span><span class="p">;</span>
|
||
<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="p">}</span>
|
||
<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a>
|
||
<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="n">PYBIND11_MODULE</span><span class="p">(</span><span class="n">my_relu</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a><span class="w"> </span><span class="n">m</span><span class="p">.</span><span class="n">def</span><span class="p">(</span><span class="s">"relu"</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">cpp_relu</span><span class="p">,</span><span class="w"> </span><span class="s">"C++ ReLU"</span><span class="p">);</span>
|
||
<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="c1"># test_relu.py — 在编译上述C++模块后运行</span>
|
||
<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
|
||
<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="kn">import</span><span class="w"> </span><span class="nn">time</span>
|
||
<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="kn">import</span><span class="w"> </span><span class="nn">my_relu</span> <span class="c1"># 编译后的C++模块</span>
|
||
<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>
|
||
<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">10_000_000</span><span class="p">)</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
|
||
<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>
|
||
<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="c1"># C++ ReLU</span>
|
||
<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="n">start</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
|
||
<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a><span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">100</span><span class="p">):</span>
|
||
<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a> <span class="n">y_cpp</span> <span class="o">=</span> <span class="n">my_relu</span><span class="o">.</span><span class="n">relu</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
||
<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a><span class="n">cpp_time</span> <span class="o">=</span> <span class="p">(</span><span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">start</span><span class="p">)</span> <span class="o">/</span> <span class="mi">100</span>
|
||
<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a>
|
||
<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a><span class="c1"># NumPy ReLU</span>
|
||
<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a><span class="n">start</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
|
||
<a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a><span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">100</span><span class="p">):</span>
|
||
<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a> <span class="n">y_np</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">maximum</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a><span class="n">np_time</span> <span class="o">=</span> <span class="p">(</span><span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">start</span><span class="p">)</span> <span class="o">/</span> <span class="mi">100</span>
|
||
<a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a>
|
||
<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"C++ ReLU: </span><span class="si">{</span><span class="n">cpp_time</span><span class="o">*</span><span class="mi">1000</span><span class="si">:</span><span class="s2">.2f</span><span class="si">}</span><span class="s2"> ms"</span><span class="p">)</span>
|
||
<a id="__codelineno-13-21" name="__codelineno-13-21" href="#__codelineno-13-21"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"NumPy ReLU: </span><span class="si">{</span><span class="n">np_time</span><span class="o">*</span><span class="mi">1000</span><span class="si">:</span><span class="s2">.2f</span><span class="si">}</span><span class="s2"> ms"</span><span class="p">)</span>
|
||
<a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"匹配: </span><span class="si">{</span><span class="n">np</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">y_cpp</span><span class="p">,</span><span class="w"> </span><span class="n">y_np</span><span class="p">)</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
|
||
</code></pre></div></p>
|
||
</li>
|
||
<li>
|
||
<p>编写一个C++程序，演示为何内存布局很重要。比较行优先与列优先访问模式并测量性能差异。
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="c1">// task3_layout.cpp</span>
|
||
<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="c1">// 编译：g++ -O3 -o task3 task3_layout.cpp</span>
|
||
<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a>
|
||
<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><iostream></span>
|
||
<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><chrono></span>
|
||
<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><vector></span>
|
||
<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>
|
||
<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="kt">int</span><span class="w"> </span><span class="nf">main</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">N</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">4096</span><span class="p">;</span>
|
||
<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">vector</span><span class="o"><</span><span class="kt">float</span><span class="o">></span><span class="w"> </span><span class="n">matrix</span><span class="p">(</span><span class="n">N</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">N</span><span class="p">,</span><span class="w"> </span><span class="mf">1.0f</span><span class="p">);</span>
|
||
<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a>
|
||
<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w"> </span><span class="c1">// 行优先访问：连续内存地址（缓存友好）</span>
|
||
<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">chrono</span><span class="o">::</span><span class="n">high_resolution_clock</span><span class="o">::</span><span class="n">now</span><span class="p">();</span>
|
||
<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w"> </span><span class="kt">float</span><span class="w"> </span><span class="n">sum_row</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0.0f</span><span class="p">;</span>
|
||
<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">N</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">N</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w"> </span><span class="n">sum_row</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">matrix</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">N</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">j</span><span class="p">];</span><span class="w"> </span><span class="c1">// 步长1访问</span>
|
||
<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="n">end</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">chrono</span><span class="o">::</span><span class="n">high_resolution_clock</span><span class="o">::</span><span class="n">now</span><span class="p">();</span>
|
||
<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">row_ms</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">chrono</span><span class="o">::</span><span class="n">duration</span><span class="o"><</span><span class="kt">double</span><span class="p">,</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">milli</span><span class="o">></span><span class="p">(</span><span class="n">end</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">start</span><span class="p">).</span><span class="n">count</span><span class="p">();</span>
|
||
<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a>
|
||
<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a><span class="w"> </span><span class="c1">// 列优先访问：步长N访问（缓存不友好）</span>
|
||
<a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">chrono</span><span class="o">::</span><span class="n">high_resolution_clock</span><span class="o">::</span><span class="n">now</span><span class="p">();</span>
|
||
<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a><span class="w"> </span><span class="kt">float</span><span class="w"> </span><span class="n">sum_col</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0.0f</span><span class="p">;</span>
|
||
<a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">N</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">N</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-14-28" name="__codelineno-14-28" href="#__codelineno-14-28"></a><span class="w"> </span><span class="n">sum_col</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">matrix</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">N</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">j</span><span class="p">];</span><span class="w"> </span><span class="c1">// 步长N访问（缓存缺失！）</span>
|
||
<a id="__codelineno-14-29" name="__codelineno-14-29" href="#__codelineno-14-29"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-14-30" name="__codelineno-14-30" href="#__codelineno-14-30"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-14-31" name="__codelineno-14-31" href="#__codelineno-14-31"></a><span class="w"> </span><span class="n">end</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">chrono</span><span class="o">::</span><span class="n">high_resolution_clock</span><span class="o">::</span><span class="n">now</span><span class="p">();</span>
|
||
<a id="__codelineno-14-32" name="__codelineno-14-32" href="#__codelineno-14-32"></a><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">col_ms</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">chrono</span><span class="o">::</span><span class="n">duration</span><span class="o"><</span><span class="kt">double</span><span class="p">,</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">milli</span><span class="o">></span><span class="p">(</span><span class="n">end</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">start</span><span class="p">).</span><span class="n">count</span><span class="p">();</span>
|
||
<a id="__codelineno-14-33" name="__codelineno-14-33" href="#__codelineno-14-33"></a>
|
||
<a id="__codelineno-14-34" name="__codelineno-14-34" href="#__codelineno-14-34"></a><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">cout</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"行优先（缓存友好）: "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">row_ms</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">" ms"</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">endl</span><span class="p">;</span>
|
||
<a id="__codelineno-14-35" name="__codelineno-14-35" href="#__codelineno-14-35"></a><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">cout</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"列优先（缓存不友好）: "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">col_ms</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">" ms"</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">endl</span><span class="p">;</span>
|
||
<a id="__codelineno-14-36" name="__codelineno-14-36" href="#__codelineno-14-36"></a><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">cout</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"减速比: "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">col_ms</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">row_ms</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"x"</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">endl</span><span class="p">;</span>
|
||
<a id="__codelineno-14-37" name="__codelineno-14-37" href="#__codelineno-14-37"></a><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">cout</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"（两个和: "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">sum_row</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">", "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">sum_col</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"）"</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">endl</span><span class="p">;</span>
|
||
<a id="__codelineno-14-38" name="__codelineno-14-38" href="#__codelineno-14-38"></a>
|
||
<a id="__codelineno-14-39" name="__codelineno-14-39" href="#__codelineno-14-39"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-14-40" name="__codelineno-14-40" href="#__codelineno-14-40"></a><span class="p">}</span>
|
||
</code></pre></div></p>
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