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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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</a>
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概率概念
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分布
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</span>
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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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计算语言学
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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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</span>
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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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|
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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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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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</span>
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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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图神经网络
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免费性能的终结
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#cpu" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
现代CPU如何执行指令
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#simd" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
SIMD：单指令多数据
|
||
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label="SIMD：单指令多数据">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_3" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
向量寄存器
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_4" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
屋顶线模型
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_5" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
延迟与吞吐量
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_6" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
芯片架构全景
|
||
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label="芯片架构全景">
|
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<ul class="md-nav__list">
|
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|
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<li class="md-nav__item">
|
||
<a href="#x86intel-amd" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
x86（Intel, AMD）
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
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|
||
<li class="md-nav__item">
|
||
<a href="#arm" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
ARM
|
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|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
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|
||
<li class="md-nav__item">
|
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<a href="#apple-siliconm1m2m3m4" class="md-nav__link">
|
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<span class="md-ellipsis">
|
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|
||
Apple Silicon（M1/M2/M3/M4）
|
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|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#risc-v" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
RISC-V
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
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|
||
<li class="md-nav__item">
|
||
<a href="#gpunvidiaamdintel" class="md-nav__link">
|
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<span class="md-ellipsis">
|
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|
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GPU（NVIDIA、AMD、Intel）
|
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|
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</span>
|
||
</a>
|
||
|
||
</li>
|
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|
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<li class="md-nav__item">
|
||
<a href="#tpugoogle" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
TPU（Google）
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_7" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
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|
||
热与功耗约束
|
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|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
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|
||
<li class="md-nav__item">
|
||
<a href="#c" class="md-nav__link">
|
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<span class="md-ellipsis">
|
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|
||
实践：在C++中测量性能
|
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|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
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|
||
<li class="md-nav__item">
|
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<a href="#colab" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
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|
||
编程任务（使用CoLab或笔记本）
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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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="../02.%20ARM%20and%20NEON/" class="md-nav__link">
|
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|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
ARM 与 NEON
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../03.%20x86%20and%20AVX/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
x86 与 AVX
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
<li class="md-nav__item">
|
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<a href="../04.%20GPU%20architecture%20and%20CUDA/" class="md-nav__link">
|
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|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
GPU 架构与 CUDA
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
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<a href="../05.%20triton%2C%20TPUs%20and%20pallax/" class="md-nav__link">
|
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|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
Triton、TPU 与 Pallas
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
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<a href="../06.%20RISC-V%20and%20embedded%20systems/" class="md-nav__link">
|
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|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
RISC-V 与嵌入式系统
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
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<a href="../07.%20vulkan%20compute%20and%20cross-platform%20GPU/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
Vulkan Compute 与跨平台 GPU
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_18" >
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<label class="md-nav__link" for="__nav_18" id="__nav_18_label" tabindex="0">
|
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|
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|
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|
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<span class="md-ellipsis">
|
||
|
||
|
||
AI 推理
|
||
|
||
|
||
|
||
</span>
|
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|
||
|
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|
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<span class="md-nav__icon md-icon"></span>
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</label>
|
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|
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
|
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<label class="md-nav__title" for="__nav_18">
|
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<span class="md-nav__icon md-icon"></span>
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AI 推理
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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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<li class="md-nav__item">
|
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<a href="../../chapter%2017%3A%20AI%20inference/01.%20quantisation/" class="md-nav__link">
|
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|
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|
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|
||
<span class="md-ellipsis">
|
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|
||
|
||
量化
|
||
|
||
|
||
|
||
</span>
|
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|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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|
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|
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|
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|
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|
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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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<a href="../../chapter%2017%3A%20AI%20inference/02.%20efficient%20architectures/" class="md-nav__link">
|
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|
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|
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|
||
<span class="md-ellipsis">
|
||
|
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|
||
高效架构
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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|
||
|
||
|
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|
||
|
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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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<a href="../../chapter%2017%3A%20AI%20inference/03.%20serving%20and%20batching/" class="md-nav__link">
|
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|
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|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
服务与批处理
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
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|
||
<li class="md-nav__item">
|
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<a href="../../chapter%2017%3A%20AI%20inference/04.%20edge%20inference/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
边缘推理
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2017%3A%20AI%20inference/05.%20scaling%20and%20deployment/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
扩缩与部署
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
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|
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|
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|
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|
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|
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<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_19" >
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|
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<label class="md-nav__link" for="__nav_19" id="__nav_19_label" tabindex="0">
|
||
|
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|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
ML 系统设计
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
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</label>
|
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|
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_19">
|
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<span class="md-nav__icon md-icon"></span>
|
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|
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|
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ML 系统设计
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
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|
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|
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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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<a href="../../chapter%2018%3A%20ML%20systems%20design/01.%20systems%20design%20fundamentals/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
系统设计基础
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
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|
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|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2018%3A%20ML%20systems%20design/02.%20cloud%20computing/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
云计算
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2018%3A%20ML%20systems%20design/03.%20large%20scale%20infrastructure/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
大规模基础设施
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2018%3A%20ML%20systems%20design/04.%20ML%20systems%20design/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
ML 系统设计
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2018%3A%20ML%20systems%20design/05.%20ML%20design%20examples/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
ML 设计案例
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
<li class="md-nav__item md-nav__item--nested">
|
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<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_20" >
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<label class="md-nav__link" for="__nav_20" id="__nav_20_label" tabindex="0">
|
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|
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|
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|
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<span class="md-ellipsis">
|
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|
||
|
||
应用 AI
|
||
|
||
|
||
|
||
</span>
|
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|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
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</label>
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|
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_20_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_20">
|
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<span class="md-nav__icon md-icon"></span>
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|
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|
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应用 AI
|
||
|
||
|
||
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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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|
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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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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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<span class="md-ellipsis">
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药物发现
|
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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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智能体系统
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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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<span class="md-ellipsis">
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|
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医疗健康
|
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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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前沿 AI
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量子机器学习
|
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神经形态计算
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太空数据中心
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去中心化 AI
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</span>
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</a>
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脑机接口
|
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</span>
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|
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<a href="#_2" class="md-nav__link">
|
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<span class="md-ellipsis">
|
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|
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免费性能的终结
|
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</span>
|
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</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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现代CPU如何执行指令
|
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</a>
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|
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SIMD：单指令多数据
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<a href="#_3" class="md-nav__link">
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<span class="md-ellipsis">
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向量寄存器
|
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<span class="md-ellipsis">
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屋顶线模型
|
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</span>
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</a>
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</li>
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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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延迟与吞吐量
|
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</a>
|
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</li>
|
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|
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<a href="#_6" class="md-nav__link">
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<span class="md-ellipsis">
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芯片架构全景
|
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|
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</span>
|
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</a>
|
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x86（Intel, AMD）
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</a>
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|
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<li class="md-nav__item">
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<a href="#arm" class="md-nav__link">
|
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<span class="md-ellipsis">
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ARM
|
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</li>
|
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<li class="md-nav__item">
|
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<a href="#apple-siliconm1m2m3m4" class="md-nav__link">
|
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<span class="md-ellipsis">
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Apple Silicon（M1/M2/M3/M4）
|
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</span>
|
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</a>
|
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</li>
|
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<li class="md-nav__item">
|
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<a href="#risc-v" class="md-nav__link">
|
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<span class="md-ellipsis">
|
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|
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RISC-V
|
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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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<a href="#gpunvidiaamdintel" class="md-nav__link">
|
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<span class="md-ellipsis">
|
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GPU（NVIDIA、AMD、Intel）
|
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</a>
|
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|
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<li class="md-nav__item">
|
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<a href="#tpugoogle" class="md-nav__link">
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<span class="md-ellipsis">
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TPU（Google）
|
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|
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</span>
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</a>
|
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</li>
|
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</ul>
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<a href="#_7" class="md-nav__link">
|
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<span class="md-ellipsis">
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|
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热与功耗约束
|
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|
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</span>
|
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</a>
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</li>
|
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<li class="md-nav__item">
|
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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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实践：在C++中测量性能
|
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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="#colab" class="md-nav__link">
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<span class="md-ellipsis">
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编程任务（使用CoLab或笔记本）
|
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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="_1">硬件基础<a class="headerlink" href="#_1" title="Permanent link">¶</a></h1>
|
||
<p><em>在编写SIMD或GPU代码之前，你需要了解所编程的硬件。本文涵盖为什么并行性取代了时钟速度、现代CPU如何执行指令、什么是SIMD、用于推理性能的屋顶线模型，以及芯片架构的全景</em></p>
|
||
<ul>
|
||
<li>几十年来，软件免费变快：购买一个时钟频率更高的新CPU，你的程序无需修改一行代码就能运行得更快。这个时代大约在2005年结束。理解它为何结束以及什么替代了它，对任何想编写快速代码的人都至关重要。</li>
|
||
</ul>
|
||
<h2 id="_2">免费性能的终结<a class="headerlink" href="#_2" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>
|
||
<p><strong>摩尔定律</strong>（1965年）观察到芯片上的晶体管数量大约每两年翻一番。这一规律维持了60年。更多晶体管意味着更小的晶体管，进而意味着更高的时钟频率，从而意味着更快的程序。</p>
|
||
</li>
|
||
<li>
|
||
<p>但在2005年左右，时钟频率在大约4 GHz处撞上了墙壁。问题是<strong>功耗</strong>。芯片消耗的功率大约为：</p>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[P \propto C \cdot V^2 \cdot f\]</div>
|
||
<ul>
|
||
<li>
|
||
<p>其中 <span class="arithmatex">\(C\)</span> 是电容（与晶体管数量成正比），<span class="arithmatex">\(V\)</span> 是电压，<span class="arithmatex">\(f\)</span> 是时钟频率。要提高频率，必须提高电压（以使晶体管更快地切换）。但功耗与 <span class="arithmatex">\(V^2 \cdot f\)</span> 成比例，所以频率的小幅增加会导致功耗（和热量）的大幅增加。在4 GHz时，芯片已经达到100+瓦。达到8 GHz需要不切实际的冷却方案。</p>
|
||
</li>
|
||
<li>
|
||
<p>解决方案：不让单个核心更快，而是在同一芯片上放置<strong>多个核心</strong>。一个4核芯片在3 GHz下使用与单个核心在4.5 GHz下相似的功耗，但可以做4倍的并行工作。这就是为什么每个现代CPU都有多个核心，以及为什么并行性（SIMD、多线程、GPU计算）是获得更高性能的唯一途径。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>对ML的影响</strong>：一个在单核上需要10分钟的训练步骤，无法通过购买更快的CPU来加速。只能通过使用更多核心（数据并行性，第6章）、更宽的SIMD单元（本章）或GPU（数千个核心）来加速。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="cpu">现代CPU如何执行指令<a class="headerlink" href="#cpu" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>
|
||
<p>现代CPU核心远比第13章中简单的取指-译码-执行模型复杂。它使用几种技巧来每周期执行更多指令：</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>超标量执行</strong>：CPU有多个执行单元（ALU、FPU、加载/存储单元），可以同时执行多个独立的指令。如果指令不相互依赖，现代核心每周期可能执行4-6条指令。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>乱序执行（OoO）</strong>：CPU不按程序顺序执行指令。它向前看指令流，找到输入已准备好的指令，并立即执行，不论其位置。这隐藏了延迟：当一条指令等待来自内存的数据时（100+周期），CPU执行其他已准备好的指令。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>分支预测</strong>：条件分支（<code>if</code>语句、循环条件）造成不确定性：CPU在条件被评估之前不知道走哪条路径。为了避免停顿，CPU<strong>预测</strong>结果并沿预测路径投机执行。如果预测正确（使用现代预测器超过95%），则没有时间损失。如果错误，投机工作被丢弃，执行正确路径（约15周期惩罚）。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>投机执行</strong>：分支预测的延伸。CPU执行<em>可能</em>不需要的指令，赌它们会被需要。这填充了流水线并保持执行单元忙碌。</p>
|
||
</li>
|
||
<li>
|
||
<p>所有这些都是自动的——CPU无需任何程序员干预即可完成。但它们只帮助<strong>指令级并行性（ILP）</strong>：单条流内相互独立的指令。对于<strong>数据级并行性</strong>（对许多数据元素执行相同操作），我们需要SIMD。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="simd">SIMD：单指令多数据<a class="headerlink" href="#simd" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>
|
||
<p><strong>SIMD</strong>是将一条指令同时应用于多个数据元素的思想。不是将两个数相加，而是在一条指令中将两个4（或8、或16）元素向量相加。</p>
|
||
</li>
|
||
<li>
|
||
<p>无SIMD（标量）：</p>
|
||
</li>
|
||
</ul>
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1">// 逐元素相加两数组：4条加法指令</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><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="mi">4</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-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="w"> </span><span class="n">c</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">a</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">b</span><span class="p">[</span><span class="n">i</span><span class="p">];</span><span class="w"> </span><span class="c1">// 每次迭代一次加法</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
<ul>
|
||
<li>有SIMD（向量化）：</li>
|
||
</ul>
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="c1">// 两数组相加：1条SIMD指令完成所有4次加法</span>
|
||
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><immintrin.h></span><span class="c1"> // x86 SIMD内联函数</span>
|
||
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a>
|
||
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="kr">__m128</span><span class="w"> </span><span class="n">va</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm_load_ps</span><span class="p">(</span><span class="n">a</span><span class="p">);</span><span class="w"> </span><span class="c1">// 加载4个浮点数到128位寄存器</span>
|
||
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="kr">__m128</span><span class="w"> </span><span class="n">vb</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm_load_ps</span><span class="p">(</span><span class="n">b</span><span class="p">);</span><span class="w"> </span><span class="c1">// 加载4个浮点数到另一个寄存器</span>
|
||
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="kr">__m128</span><span class="w"> </span><span class="n">vc</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm_add_ps</span><span class="p">(</span><span class="n">va</span><span class="p">,</span><span class="w"> </span><span class="n">vb</span><span class="p">);</span><span class="w"> </span><span class="c1">// 同时相加所有4对</span>
|
||
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="n">_mm_store_ps</span><span class="p">(</span><span class="n">c</span><span class="p">,</span><span class="w"> </span><span class="n">vc</span><span class="p">);</span><span class="w"> </span><span class="c1">// 存储4个结果</span>
|
||
</code></pre></div>
|
||
<ul>
|
||
<li>SIMD版本用1/4的指令完成相同工作。这是理论上的4倍加速，通过每条指令处理4个浮点数而非1个实现。</li>
|
||
</ul>
|
||
<h3 id="_3">向量寄存器<a class="headerlink" href="#_3" title="Permanent link">¶</a></h3>
|
||
<ul>
|
||
<li>SIMD指令操作<strong>向量寄存器</strong>：保存多个数据元素的宽寄存器。</li>
|
||
</ul>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>寄存器宽度</th>
|
||
<th>浮点数（32位）</th>
|
||
<th>双精度浮点数（64位）</th>
|
||
<th>名称</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr>
|
||
<td>128位</td>
|
||
<td>4</td>
|
||
<td>2</td>
|
||
<td>SSE（x86）、NEON（ARM）</td>
|
||
</tr>
|
||
<tr>
|
||
<td>256位</td>
|
||
<td>8</td>
|
||
<td>4</td>
|
||
<td>AVX/AVX2（x86）</td>
|
||
</tr>
|
||
<tr>
|
||
<td>512位</td>
|
||
<td>16</td>
|
||
<td>8</td>
|
||
<td>AVX-512（x86）</td>
|
||
</tr>
|
||
<tr>
|
||
<td>可变（128-2048）</td>
|
||
<td>可变</td>
|
||
<td>可变</td>
|
||
<td>SVE/SVE2（ARM）</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<ul>
|
||
<li>
|
||
<p>更宽的寄存器 = 更多并行性。一条512位AVX-512指令一次处理16个浮点数，是标量代码理论上的16倍加速。实际上，由于内存带宽限制（计算速度可能超过向CPU输送数据的速度），加速比更低。</p>
|
||
</li>
|
||
<li>
|
||
<p>对于ML：float32值的矩阵乘法从SIMD中获益巨大。内循环（两个向量的点积）直接映射到SIMD乘加指令。这就是为什么BLAS库（NumPy和PyTorch调用的）用SIMD进行了如此深度优化。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="_4">屋顶线模型<a class="headerlink" href="#_4" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>
|
||
<p>你如何知道你的代码是否快速？<strong>屋顶线模型</strong>提供了一个框架，根据两个硬件限制来描述性能：</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>峰值计算能力</strong>（FLOPS）：每秒最大浮点运算次数。对于一个4 GHz CPU，配备256位AVX（每条指令8个浮点数）和2个FMA单元：<span class="arithmatex">\(4 \times 10^9 \times 8 \times 2 = 64\)</span> GFLOPS。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>峰值内存带宽</strong>（字节/秒）：数据从内存到CPU的最大传输速度。现代CPU可能有50 GB/s的内存带宽。</p>
|
||
</li>
|
||
<li>
|
||
<p>代码的<strong>算术强度</strong>是计算与内存访问的比率：</p>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[\text{算术强度} = \frac{\text{FLOPS}}{\text{传输的字节数}}\]</div>
|
||
<ul>
|
||
<li>
|
||
<p>如果算术强度低（每加载字节的操作数少），你的代码是<strong>内存受限的</strong>：大部分时间花在等待数据上。让计算更快（更宽的SIMD、更高的时钟）不会有帮助。</p>
|
||
</li>
|
||
<li>
|
||
<p>如果算术强度高（每字节多次操作），你的代码是<strong>计算受限的</strong>：大部分时间花在计算上。更快的内存不会有帮助。</p>
|
||
</li>
|
||
<li>
|
||
<p>屋顶线：</p>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[\text{可达FLOPS} = \min\left(\text{峰值FLOPS}, \; \text{带宽} \times \text{算术强度}\right)\]</div>
|
||
<ul>
|
||
<li>
|
||
<p><strong>矩阵乘法</strong>具有高算术强度：<span class="arithmatex">\(O(n^3)\)</span> 次操作作用于 <span class="arithmatex">\(O(n^2)\)</span> 数据，因此强度 <span class="arithmatex">\(\approx O(n)\)</span>。对于大矩阵，它是计算受限的。这就是为什么GPU（高计算能力）主导矩阵密集型的ML工作负载。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>逐元素操作</strong>（ReLU、加法、乘法）具有低算术强度：每加载一个元素1次操作。这些是内存受限的。让GPU更快没有帮助；你需要更快的内存（或者将这些操作与计算密集型操作融合，以避免独立的内存往返）。</p>
|
||
</li>
|
||
<li>
|
||
<p>屋顶线模型解释了为什么<strong>核函数融合</strong>如此重要：将matmul与偏置加法和ReLU组合成一个核函数，避免了将中间结果写入内存并重新读取，将三个内存受限操作转化为一个计算受限操作。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="_5">延迟与吞吐量<a class="headerlink" href="#_5" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>
|
||
<p><strong>延迟</strong>是完成一个操作所需的时间。<strong>吞吐量</strong>是单位时间内完成的操作数量。</p>
|
||
</li>
|
||
<li>
|
||
<p>打个比方：公交车延迟高（每站都停），但吞吐量高（一次搭载50人）。出租车延迟低（直达你的目的地），但吞吐量低（搭载1-4人）。</p>
|
||
</li>
|
||
<li>
|
||
<p>GPU是公交车：每次操作延迟高（每条指令需要许多周期完成），但吞吐量巨大（数千个核心同时处理）。CPU是出租车：延迟低（乱序执行、分支预测、深层缓存最小化延迟），但吞吐量有限（4-64个核心）。</p>
|
||
</li>
|
||
<li>
|
||
<p>这就是为什么GPU更适合ML训练（吞吐量重要：处理数百万个样本）而CPU更适合操作系统任务（延迟重要：立即响应按键）。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>流水线</strong>将延迟转化为吞吐量。如果一条指令需要5个周期，但流水线每周期开始一条新指令，则吞吐量是每条指令1周期（即使每条指令需要5个周期完成）。这和第13章的CPU流水线是同一原理，但它适用于每个层面：SIMD单元、内存控制器和GPU核心都是流水线化的。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="_6">芯片架构全景<a class="headerlink" href="#_6" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>你编写代码的硬件决定了哪些SIMD指令可用：</li>
|
||
</ul>
|
||
<h3 id="x86intel-amd">x86（Intel, AMD）<a class="headerlink" href="#x86intel-amd" title="Permanent link">¶</a></h3>
|
||
<ul>
|
||
<li>
|
||
<p>主导台式机、笔记本电脑和数据中心CPU。SIMD：SSE（128位）、AVX/AVX2（256位）、AVX-512（512位）。Intel AMX提供专用的矩阵乘法单元用于AI工作负载。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>优势</strong>：最高单核性能、最宽SIMD、成熟的软件生态系统（MKL、oneDNN）。</p>
|
||
</li>
|
||
<li><strong>弱点</strong>：高功耗、复杂指令集、昂贵。</li>
|
||
</ul>
|
||
<h3 id="arm">ARM<a class="headerlink" href="#arm" title="Permanent link">¶</a></h3>
|
||
<ul>
|
||
<li>
|
||
<p>主导移动设备（每一部智能手机），在服务器（AWS Graviton、Ampere Altra）和笔记本电脑（Apple M系列）中增长。SIMD：NEON（128位）、SVE/SVE2（可伸缩，128-2048位）。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>优势</strong>：出色的功耗效率（每瓦性能）、自定义核心（Apple M4在单核性能上媲美Intel，功耗仅为其一小部分）。</p>
|
||
</li>
|
||
<li><strong>弱点</strong>：较窄的SIMD（NEON仅为128位，虽SVE可更宽）、用于HPC的软件生态系统较小。</li>
|
||
</ul>
|
||
<h3 id="apple-siliconm1m2m3m4">Apple Silicon（M1/M2/M3/M4）<a class="headerlink" href="#apple-siliconm1m2m3m4" title="Permanent link">¶</a></h3>
|
||
<ul>
|
||
<li>
|
||
<p>基于ARM并带有自定义扩展。包含<strong>AMX</strong>（Apple矩阵扩展）——未公开的矩阵乘法单元，Accelerate框架将其用于BLAS操作。统一内存架构：CPU和GPU共享同一物理内存，消除了CPU↔GPU拷贝的瓶颈。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>对于ML</strong>：Apple的神经网络引擎（16核，专用ML加速器）和统一内存使M系列芯片在本地ML推理和小规模训练方面出奇地强大。不过没有CUDA：你必须使用Metal（Apple的GPU API）或MLX（Apple的ML框架）。</p>
|
||
</li>
|
||
</ul>
|
||
<h3 id="risc-v">RISC-V<a class="headerlink" href="#risc-v" title="Permanent link">¶</a></h3>
|
||
<ul>
|
||
<li>
|
||
<p>开源ISA。无许可费用（不像ARM）。在嵌入式系统、物联网和研究领域增长。SIMD："V"（向量）扩展提供类似于ARM SVE的可伸缩向量处理。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>对于ML</strong>：在ML工作负载上尚不能与x86/ARM竞争，但值得关注。几个AI加速器初创公司使用RISC-V核心。</p>
|
||
</li>
|
||
</ul>
|
||
<h3 id="gpunvidiaamdintel">GPU（NVIDIA、AMD、Intel）<a class="headerlink" href="#gpunvidiaamdintel" title="Permanent link">¶</a></h3>
|
||
<ul>
|
||
<li>在文件04-05中深入介绍。数千个为吞吐量优化的简单核心。NVIDIA以CUDA主导ML；AMD以ROCm竞争；Intel以Arc GPU和Gaudi加速器进入市场。</li>
|
||
</ul>
|
||
<h3 id="tpugoogle">TPU（Google）<a class="headerlink" href="#tpugoogle" title="Permanent link">¶</a></h3>
|
||
<ul>
|
||
<li>专门为ML设计的自定义ASIC。为矩阵乘法优化的脉动阵列。在文件05中介绍。</li>
|
||
</ul>
|
||
<h2 id="_7">热与功耗约束<a class="headerlink" href="#_7" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>
|
||
<p>性能最终受限于功耗和散热：</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>TDP</strong>（热设计功耗）：芯片可以持续消耗的最大功率。笔记本电脑CPU可能有15W TDP；服务器CPU 250W；数据中心GPU 700W（NVIDIA B200）。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>暗硅</strong>：在任何给定时刻，为了保持在热预算内，必须关闭芯片的相当大一部分晶体管。理论上芯片可以同时使用所有晶体管，但会熔化。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>功耗效率</strong>（FLOPS/瓦）日益成为重要指标，而非原始FLOPS。这就是为什么：</p>
|
||
<ul>
|
||
<li>ARM正在接管数据中心（相比x86更好的FLOPS/瓦）。</li>
|
||
<li>TPU尽管峰值FLOPS较低，但仍与GPU竞争（对于ML工作负载，FLOPS/瓦好得多）。</li>
|
||
<li>量化（INT8、FP8）不仅关乎内存：它也降低了每次操作的功耗。</li>
|
||
</ul>
|
||
</li>
|
||
<li>
|
||
<p>对于大规模ML：训练前沿LLM数月消耗兆瓦级功率。电费可能超过硬件成本。功耗效率直接影响AI研究的经济性。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="c">实践：在C++中测量性能<a class="headerlink" href="#c" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>要推理性能，你需要测量它。以下是一个最小的C++基准测试设置：</li>
|
||
</ul>
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><iostream></span>
|
||
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><chrono></span>
|
||
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><vector></span>
|
||
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a>
|
||
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="c1">// 标量加法</span>
|
||
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">add_scalar</span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="kt">float</span><span class="o">*</span><span class="w"> </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">float</span><span class="o">*</span><span class="w"> </span><span class="n">b</span><span class="p">,</span><span class="w"> </span><span class="kt">float</span><span class="o">*</span><span class="w"> </span><span class="n">c</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></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-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w"> </span><span class="n">c</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">a</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">b</span><span class="p">[</span><span class="n">i</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="p">}</span>
|
||
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="p">}</span>
|
||
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a>
|
||
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></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-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></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">1</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="mi">24</span><span class="p">;</span><span class="w"> </span><span class="c1">// 约1600万个元素</span>
|
||
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></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">a</span><span class="p">(</span><span class="n">N</span><span class="p">,</span><span class="w"> </span><span class="mf">1.0f</span><span class="p">),</span><span class="w"> </span><span class="n">b</span><span class="p">(</span><span class="n">N</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="n">c</span><span class="p">(</span><span class="n">N</span><span class="p">);</span>
|
||
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a>
|
||
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w"> </span><span class="c1">// 预热（填充缓存，触发频率缩放）</span>
|
||
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w"> </span><span class="n">add_scalar</span><span class="p">(</span><span class="n">a</span><span class="p">.</span><span class="n">data</span><span class="p">(),</span><span class="w"> </span><span class="n">b</span><span class="p">.</span><span class="n">data</span><span class="p">(),</span><span class="w"> </span><span class="n">c</span><span class="p">.</span><span class="n">data</span><span class="p">(),</span><span class="w"> </span><span class="n">N</span><span class="p">);</span>
|
||
<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a>
|
||
<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w"> </span><span class="c1">// 基准测试</span>
|
||
<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></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-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a>
|
||
<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></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">trial</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">trial</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">100</span><span class="p">;</span><span class="w"> </span><span class="n">trial</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w"> </span><span class="n">add_scalar</span><span class="p">(</span><span class="n">a</span><span class="p">.</span><span class="n">data</span><span class="p">(),</span><span class="w"> </span><span class="n">b</span><span class="p">.</span><span class="n">data</span><span class="p">(),</span><span class="w"> </span><span class="n">c</span><span class="p">.</span><span class="n">data</span><span class="p">(),</span><span class="w"> </span><span class="n">N</span><span class="p">);</span>
|
||
<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a>
|
||
<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></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-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></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="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-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a>
|
||
<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">total_bytes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3.0</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="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="mi">100</span><span class="p">;</span><span class="w"> </span><span class="c1">// 读a、读b、写c</span>
|
||
<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">bandwidth</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">total_bytes</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">1e9</span><span class="p">;</span><span class="w"> </span><span class="c1">// GB/s</span>
|
||
<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a>
|
||
<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></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">" s</span><span class="se">\n</span><span class="s">"</span><span class="p">;</span>
|
||
<a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></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">"带宽: "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">bandwidth</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">" GB/s</span><span class="se">\n</span><span class="s">"</span><span class="p">;</span>
|
||
<a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a>
|
||
<a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></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-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="c1"># 启用优化编译</span>
|
||
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>g++<span class="w"> </span>-O3<span class="w"> </span>-march<span class="o">=</span>native<span class="w"> </span>-o<span class="w"> </span>bench<span class="w"> </span>bench.cpp
|
||
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a>./bench
|
||
</code></pre></div>
|
||
<ul>
|
||
<li>
|
||
<p><strong>这段代码中的关键C++概念</strong>：</p>
|
||
<ul>
|
||
<li><code>#include <vector></code>：动态数组（<code>std::vector<float></code>）——类似Python的<code>list</code>但带类型且在内存中连续。</li>
|
||
<li><code>a.data()</code>：返回底层数组的原始指针（<code>float*</code>）——SIMD内联函数需要。</li>
|
||
<li><code>std::chrono</code>：用于基准测试的高分辨率计时器。</li>
|
||
<li><code>-O3</code>：最高编译器优化级别。编译器可能自动向量化你的循环（自动使用SIMD）。<code>-march=native</code> 启用你的CPU支持的所有SIMD指令。</li>
|
||
</ul>
|
||
</li>
|
||
<li>
|
||
<p><strong>为什么需要预热</strong>：首次运行填充缓存并可能触发CPU频率缩放（睿频加速）。后续运行更具代表性。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>为什么测量带宽</strong>：对于内存受限的操作（如逐元素加法），有意义的度量是带宽（GB/s），而不是FLOPS。如果你的测量带宽接近硬件极限（DDR5约50 GB/s），你是内存受限的，SIMD不会有多大帮助（瓶颈是内存，而非计算）。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="colab">编程任务（使用CoLab或笔记本）<a class="headerlink" href="#colab" title="Permanent link">¶</a></h2>
|
||
<ol>
|
||
<li>
|
||
<p>计算常见ML操作的算术强度，并将它们分类为内存受限或计算受限。
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax.numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">jnp</span>
|
||
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
|
||
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="k">def</span><span class="w"> </span><span class="nf">arithmetic_intensity</span><span class="p">(</span><span class="n">flops</span><span class="p">,</span> <span class="n">bytes_transferred</span><span class="p">):</span>
|
||
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a> <span class="k">return</span> <span class="n">flops</span> <span class="o">/</span> <span class="n">bytes_transferred</span>
|
||
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a>
|
||
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="c1"># 逐元素ReLU：每元素1次比较，读取+写入</span>
|
||
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="n">n</span> <span class="o">=</span> <span class="mi">1024</span>
|
||
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="n">relu_flops</span> <span class="o">=</span> <span class="n">n</span> <span class="c1"># 每元素1次操作</span>
|
||
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="n">relu_bytes</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">n</span> <span class="o">*</span> <span class="mi">4</span> <span class="c1"># 读取输入+写入输出（float32）</span>
|
||
<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"ReLU: </span><span class="si">{</span><span class="n">arithmetic_intensity</span><span class="p">(</span><span class="n">relu_flops</span><span class="p">,</span><span class="w"> </span><span class="n">relu_bytes</span><span class="p">)</span><span class="si">:</span><span class="s2">.2f</span><span class="si">}</span><span class="s2"> FLOPS/byte → 内存受限"</span><span class="p">)</span>
|
||
<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a>
|
||
<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="c1"># 矩阵乘法：2*n^3次操作，读取2*n^2 + 写入n^2个浮点数</span>
|
||
<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="n">matmul_flops</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">n</span><span class="o">**</span><span class="mi">3</span>
|
||
<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="n">matmul_bytes</span> <span class="o">=</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">n</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="mi">4</span> <span class="c1"># 读取A + 读取B + 写入C</span>
|
||
<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"矩阵乘法 (</span><span class="si">{</span><span class="n">n</span><span class="si">}</span><span class="s2">×</span><span class="si">{</span><span class="n">n</span><span class="si">}</span><span class="s2">): </span><span class="si">{</span><span class="n">arithmetic_intensity</span><span class="p">(</span><span class="n">matmul_flops</span><span class="p">,</span><span class="w"> </span><span class="n">matmul_bytes</span><span class="p">)</span><span class="si">:</span><span class="s2">.0f</span><span class="si">}</span><span class="s2"> FLOPS/byte → 计算受限"</span><span class="p">)</span>
|
||
<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a>
|
||
<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="c1"># 层归一化：约5n次操作（均值、方差、归一化），读取+写入</span>
|
||
<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="n">ln_flops</span> <span class="o">=</span> <span class="mi">5</span> <span class="o">*</span> <span class="n">n</span>
|
||
<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="n">ln_bytes</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">n</span> <span class="o">*</span> <span class="mi">4</span>
|
||
<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"LayerNorm: </span><span class="si">{</span><span class="n">arithmetic_intensity</span><span class="p">(</span><span class="n">ln_flops</span><span class="p">,</span><span class="w"> </span><span class="n">ln_bytes</span><span class="p">)</span><span class="si">:</span><span class="s2">.2f</span><span class="si">}</span><span class="s2"> FLOPS/byte → 内存受限"</span><span class="p">)</span>
|
||
<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a>
|
||
<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="c1"># 3x3卷积：2*9*C_in*C_out*H*W，读取卷积核+特征图+写入输出</span>
|
||
<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="n">C_in</span><span class="p">,</span> <span class="n">C_out</span><span class="p">,</span> <span class="n">H</span><span class="p">,</span> <span class="n">W</span> <span class="o">=</span> <span class="mi">64</span><span class="p">,</span> <span class="mi">128</span><span class="p">,</span> <span class="mi">32</span><span class="p">,</span> <span class="mi">32</span>
|
||
<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="n">conv_flops</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="mi">9</span> <span class="o">*</span> <span class="n">C_in</span> <span class="o">*</span> <span class="n">C_out</span> <span class="o">*</span> <span class="n">H</span> <span class="o">*</span> <span class="n">W</span>
|
||
<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="n">conv_bytes</span> <span class="o">=</span> <span class="p">(</span><span class="mi">9</span> <span class="o">*</span> <span class="n">C_in</span> <span class="o">*</span> <span class="n">C_out</span> <span class="o">+</span> <span class="n">C_in</span> <span class="o">*</span> <span class="n">H</span> <span class="o">*</span> <span class="n">W</span> <span class="o">+</span> <span class="n">C_out</span> <span class="o">*</span> <span class="n">H</span> <span class="o">*</span> <span class="n">W</span><span class="p">)</span> <span class="o">*</span> <span class="mi">4</span>
|
||
<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Conv3x3: </span><span class="si">{</span><span class="n">arithmetic_intensity</span><span class="p">(</span><span class="n">conv_flops</span><span class="p">,</span><span class="w"> </span><span class="n">conv_bytes</span><span class="p">)</span><span class="si">:</span><span class="s2">.0f</span><span class="si">}</span><span class="s2"> FLOPS/byte → 计算受限"</span><span class="p">)</span>
|
||
</code></pre></div></p>
|
||
</li>
|
||
<li>
|
||
<p>演示为什么并行性重要。比较顺序执行与并行（NumPy）执行随数据规模增长的表现。
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></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-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kn">import</span><span class="w"> </span><span class="nn">time</span>
|
||
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a>
|
||
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="p">[</span><span class="mi">1000</span><span class="p">,</span> <span class="mi">10000</span><span class="p">,</span> <span class="mi">100000</span><span class="p">,</span> <span class="mi">1000000</span><span class="p">,</span> <span class="mi">10000000</span><span class="p">]:</span>
|
||
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a> <span class="n">a</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="n">n</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-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a> <span class="n">b</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="n">n</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-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a>
|
||
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a> <span class="c1"># "顺序执行"（Python循环）</span>
|
||
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></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-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a> <span class="n">c</span> <span class="o">=</span> <span class="p">[</span><span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="n">b</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">min</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="mi">100000</span><span class="p">))]</span> <span class="c1"># 上限10万以确保合理</span>
|
||
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a> <span class="n">seq_time</span> <span class="o">=</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>
|
||
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a> <span class="k">if</span> <span class="n">n</span> <span class="o">></span> <span class="mi">100000</span><span class="p">:</span>
|
||
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a> <span class="n">seq_time</span> <span class="o">*=</span> <span class="n">n</span> <span class="o">/</span> <span class="mi">100000</span> <span class="c1"># 外推</span>
|
||
<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a>
|
||
<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a> <span class="c1"># "并行"（NumPy，内部使用SIMD+多线程）</span>
|
||
<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></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-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a> <span class="n">c</span> <span class="o">=</span> <span class="n">a</span> <span class="o">*</span> <span class="n">b</span>
|
||
<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a> <span class="n">par_time</span> <span class="o">=</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>
|
||
<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a>
|
||
<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a> <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"n=</span><span class="si">{</span><span class="n">n</span><span class="si">:</span><span class="s2">>10,</span><span class="si">}</span><span class="s2"> 顺序=</span><span class="si">{</span><span class="n">seq_time</span><span class="si">:</span><span class="s2">.4f</span><span class="si">}</span><span class="s2">s 并行=</span><span class="si">{</span><span class="n">par_time</span><span class="si">:</span><span class="s2">.6f</span><span class="si">}</span><span class="s2">s "</span>
|
||
<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a> <span class="sa">f</span><span class="s2">"加速比=</span><span class="si">{</span><span class="n">seq_time</span><span class="o">/</span><span class="n">par_time</span><span class="si">:</span><span class="s2">.0f</span><span class="si">}</span><span class="s2">x"</span><span class="p">)</span>
|
||
</code></pre></div></p>
|
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