5874 lines
200 KiB
HTML
5874 lines
200 KiB
HTML
|
||
<!doctype html>
|
||
<html lang="zh" class="no-js">
|
||
<head>
|
||
|
||
<meta charset="utf-8">
|
||
<meta name="viewport" content="width=device-width,initial-scale=1">
|
||
|
||
<meta name="description" content="一本开源的直觉优先教科书，从零开始覆盖数学、计算机科学和人工智能（中文翻译版）。">
|
||
|
||
|
||
<meta name="author" content="Henry Ndubuaku (flykhan 译)">
|
||
|
||
|
||
<link rel="canonical" href="https://flykhan.github.io/maths-cs-ai-compendium-zh/chapter%2016%3A%20SIMD%20and%20GPU%20programming/03.%20x86%20and%20AVX/">
|
||
|
||
|
||
<link rel="prev" href="../02.%20ARM%20and%20NEON/">
|
||
|
||
|
||
<link rel="next" href="../04.%20GPU%20architecture%20and%20CUDA/">
|
||
|
||
|
||
|
||
|
||
|
||
<link rel="icon" href="../../assets/images/favicon.png">
|
||
<meta name="generator" content="mkdocs-1.6.1, mkdocs-material-9.7.6">
|
||
|
||
|
||
|
||
<title>x86 与 AVX - 数学、计算机科学与 AI 百科全书</title>
|
||
|
||
|
||
|
||
<link rel="stylesheet" href="../../assets/stylesheets/main.484c7ddc.min.css">
|
||
|
||
|
||
<link rel="stylesheet" href="../../assets/stylesheets/palette.ab4e12ef.min.css">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
|
||
<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Roboto:300,300i,400,400i,700,700i%7CRoboto+Mono:400,400i,700,700i&display=fallback">
|
||
<style>:root{--md-text-font:"Roboto";--md-code-font:"Roboto Mono"}</style>
|
||
|
||
|
||
|
||
<script>__md_scope=new URL("../..",location),__md_hash=e=>[...e].reduce(((e,_)=>(e<<5)-e+_.charCodeAt(0)),0),__md_get=(e,_=localStorage,t=__md_scope)=>JSON.parse(_.getItem(t.pathname+"."+e)),__md_set=(e,_,t=localStorage,a=__md_scope)=>{try{t.setItem(a.pathname+"."+e,JSON.stringify(_))}catch(e){}}</script>
|
||
|
||
|
||
|
||
|
||
|
||
</head>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<body dir="ltr" data-md-color-scheme="default" data-md-color-primary="slate" data-md-color-accent="indigo">
|
||
|
||
|
||
<input class="md-toggle" data-md-toggle="drawer" type="checkbox" id="__drawer" autocomplete="off">
|
||
<input class="md-toggle" data-md-toggle="search" type="checkbox" id="__search" autocomplete="off">
|
||
<label class="md-overlay" for="__drawer"></label>
|
||
<div data-md-component="skip">
|
||
|
||
|
||
<a href="#x86avx" class="md-skip">
|
||
跳转至
|
||
</a>
|
||
|
||
</div>
|
||
<div data-md-component="announce">
|
||
|
||
</div>
|
||
|
||
|
||
|
||
|
||
<header class="md-header" data-md-component="header">
|
||
<nav class="md-header__inner md-grid" aria-label="页眉">
|
||
<a href="../.." title="数学、计算机科学与 AI 百科全书" class="md-header__button md-logo" aria-label="数学、计算机科学与 AI 百科全书" data-md-component="logo">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 8a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3 3 3 0 0 0 3 3m0 3.54C9.64 9.35 6.5 8 3 8v11c3.5 0 6.64 1.35 9 3.54 2.36-2.19 5.5-3.54 9-3.54V8c-3.5 0-6.64 1.35-9 3.54"/></svg>
|
||
|
||
</a>
|
||
<label class="md-header__button md-icon" for="__drawer">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 6h18v2H3zm0 5h18v2H3zm0 5h18v2H3z"/></svg>
|
||
</label>
|
||
<div class="md-header__title" data-md-component="header-title">
|
||
<div class="md-header__ellipsis">
|
||
<div class="md-header__topic">
|
||
<span class="md-ellipsis">
|
||
数学、计算机科学与 AI 百科全书
|
||
</span>
|
||
</div>
|
||
<div class="md-header__topic" data-md-component="header-topic">
|
||
<span class="md-ellipsis">
|
||
|
||
x86 与 AVX
|
||
|
||
</span>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
|
||
<form class="md-header__option" data-md-component="palette">
|
||
|
||
|
||
|
||
|
||
<input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="slate" data-md-color-accent="indigo" aria-label="切换到深色模式" type="radio" name="__palette" id="__palette_0">
|
||
|
||
<label class="md-header__button md-icon" title="切换到深色模式" for="__palette_1" hidden>
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 8a4 4 0 0 0-4 4 4 4 0 0 0 4 4 4 4 0 0 0 4-4 4 4 0 0 0-4-4m0 10a6 6 0 0 1-6-6 6 6 0 0 1 6-6 6 6 0 0 1 6 6 6 6 0 0 1-6 6m8-9.31V4h-4.69L12 .69 8.69 4H4v4.69L.69 12 4 15.31V20h4.69L12 23.31 15.31 20H20v-4.69L23.31 12z"/></svg>
|
||
</label>
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="slate" data-md-color-accent="indigo" aria-label="切换到浅色模式" type="radio" name="__palette" id="__palette_1">
|
||
|
||
<label class="md-header__button md-icon" title="切换到浅色模式" for="__palette_0" hidden>
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 18c-.89 0-1.74-.2-2.5-.55C11.56 16.5 13 14.42 13 12s-1.44-4.5-3.5-5.45C10.26 6.2 11.11 6 12 6a6 6 0 0 1 6 6 6 6 0 0 1-6 6m8-9.31V4h-4.69L12 .69 8.69 4H4v4.69L.69 12 4 15.31V20h4.69L12 23.31 15.31 20H20v-4.69L23.31 12z"/></svg>
|
||
</label>
|
||
|
||
|
||
</form>
|
||
|
||
|
||
|
||
<script>var palette=__md_get("__palette");if(palette&&palette.color){if("(prefers-color-scheme)"===palette.color.media){var media=matchMedia("(prefers-color-scheme: light)"),input=document.querySelector(media.matches?"[data-md-color-media='(prefers-color-scheme: light)']":"[data-md-color-media='(prefers-color-scheme: dark)']");palette.color.media=input.getAttribute("data-md-color-media"),palette.color.scheme=input.getAttribute("data-md-color-scheme"),palette.color.primary=input.getAttribute("data-md-color-primary"),palette.color.accent=input.getAttribute("data-md-color-accent")}for(var[key,value]of Object.entries(palette.color))document.body.setAttribute("data-md-color-"+key,value)}</script>
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-header__button md-icon" for="__search">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
|
||
</label>
|
||
<div class="md-search" data-md-component="search" role="dialog">
|
||
<label class="md-search__overlay" for="__search"></label>
|
||
<div class="md-search__inner" role="search">
|
||
<form class="md-search__form" name="search">
|
||
<input type="text" class="md-search__input" name="query" aria-label="搜索" placeholder="搜索" autocapitalize="off" autocorrect="off" autocomplete="off" spellcheck="false" data-md-component="search-query" required>
|
||
<label class="md-search__icon md-icon" for="__search">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11z"/></svg>
|
||
</label>
|
||
<nav class="md-search__options" aria-label="查找">
|
||
|
||
<button type="reset" class="md-search__icon md-icon" title="清空当前内容" aria-label="清空当前内容" tabindex="-1">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 6.41 17.59 5 12 10.59 6.41 5 5 6.41 10.59 12 5 17.59 6.41 19 12 13.41 17.59 19 19 17.59 13.41 12z"/></svg>
|
||
</button>
|
||
</nav>
|
||
|
||
<div class="md-search__suggest" data-md-component="search-suggest"></div>
|
||
|
||
</form>
|
||
<div class="md-search__output">
|
||
<div class="md-search__scrollwrap" tabindex="0" data-md-scrollfix>
|
||
<div class="md-search-result" data-md-component="search-result">
|
||
<div class="md-search-result__meta">
|
||
正在初始化搜索引擎
|
||
</div>
|
||
<ol class="md-search-result__list" role="presentation"></ol>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
|
||
|
||
<div class="md-header__source">
|
||
<a href="https://github.com/flykhan/maths-cs-ai-compendium-zh" title="前往仓库" class="md-source" data-md-component="source">
|
||
<div class="md-source__icon md-icon">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path d="M439.6 236.1 244 40.5c-5.4-5.5-12.8-8.5-20.4-8.5s-15 3-20.4 8.4L162.5 81l51.5 51.5c27.1-9.1 52.7 16.8 43.4 43.7l49.7 49.7c34.2-11.8 61.2 31 35.5 56.7-26.5 26.5-70.2-2.9-56-37.3L240.3 199v121.9c25.3 12.5 22.3 41.8 9.1 55-6.4 6.4-15.2 10.1-24.3 10.1s-17.8-3.6-24.3-10.1c-17.6-17.6-11.1-46.9 11.2-56v-123c-20.8-8.5-24.6-30.7-18.6-45L142.6 101 8.5 235.1C3 240.6 0 247.9 0 255.5s3 15 8.5 20.4l195.6 195.7c5.4 5.4 12.7 8.4 20.4 8.4s15-3 20.4-8.4l194.7-194.7c5.4-5.4 8.4-12.8 8.4-20.4s-3-15-8.4-20.4"/></svg>
|
||
</div>
|
||
<div class="md-source__repository">
|
||
flykhan/maths-cs-ai-compendium-zh
|
||
</div>
|
||
</a>
|
||
</div>
|
||
|
||
</nav>
|
||
|
||
</header>
|
||
|
||
<div class="md-container" data-md-component="container">
|
||
|
||
|
||
|
||
|
||
|
||
<nav class="md-tabs" aria-label="标签" data-md-component="tabs">
|
||
<div class="md-grid">
|
||
<ul class="md-tabs__list">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../.." class="md-tabs__link">
|
||
|
||
|
||
|
||
|
||
|
||
首页
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2001%3A%20vectors/01.%20vector%20spaces/" class="md-tabs__link">
|
||
|
||
|
||
|
||
向量
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2002%3A%20matrices/01.%20matrix%20properties/" class="md-tabs__link">
|
||
|
||
|
||
|
||
矩阵
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2003%3A%20calculus/01.%20differential%20calculus/" class="md-tabs__link">
|
||
|
||
|
||
|
||
微积分
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2004%3A%20statistics/01.%20fundamentals/" class="md-tabs__link">
|
||
|
||
|
||
|
||
统计学
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2005%3A%20probability/01.%20counting/" class="md-tabs__link">
|
||
|
||
|
||
|
||
概率论
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2006%3A%20machine%20learning/01.%20classical%20machine%20learning/" class="md-tabs__link">
|
||
|
||
|
||
|
||
机器学习
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2007%3A%20computational%20linguistics/01.%20linguistic%20foundations/" class="md-tabs__link">
|
||
|
||
|
||
|
||
计算语言学
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2008%3A%20computer%20vision/01.%20image%20fundamentals/" class="md-tabs__link">
|
||
|
||
|
||
|
||
计算机视觉
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2009%3A%20audio%20and%20speech/01.%20digital%20signal%20processing/" class="md-tabs__link">
|
||
|
||
|
||
|
||
音频与语音
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2010%3A%20multimodal%20learning/01.%20multimodal%20representations/" class="md-tabs__link">
|
||
|
||
|
||
|
||
多模态学习
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2011%3A%20autonomous%20systems/01.%20perception/" class="md-tabs__link">
|
||
|
||
|
||
|
||
自主系统
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2012%3A%20graph%20neural%20networks/01.%20geometric%20deep%20learning/" class="md-tabs__link">
|
||
|
||
|
||
|
||
图神经网络
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2013%3A%20computing%20and%20OS/01.%20discrete%20maths/" class="md-tabs__link">
|
||
|
||
|
||
|
||
计算机与操作系统
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2014%3A%20data%20structures%20and%20algorithms/00.%20foundations/" class="md-tabs__link">
|
||
|
||
|
||
|
||
数据结构与算法
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2015%3A%20production%20software%20engineering/01.%20linux%20and%20CMD/" class="md-tabs__link">
|
||
|
||
|
||
|
||
生产级软件工程
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item md-tabs__item--active">
|
||
<a href="../00.%20why%20C%2B%2B%20and%20how%20ML%20frameworks%20work/" class="md-tabs__link">
|
||
|
||
|
||
|
||
SIMD 与 GPU 编程
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2017%3A%20AI%20inference/01.%20quantisation/" class="md-tabs__link">
|
||
|
||
|
||
|
||
AI 推理
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2018%3A%20ML%20systems%20design/01.%20systems%20design%20fundamentals/" class="md-tabs__link">
|
||
|
||
|
||
|
||
ML 系统设计
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2019%3A%20applied%20AI/01.%20AI%20for%20finance/" class="md-tabs__link">
|
||
|
||
|
||
|
||
应用 AI
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-tabs__item">
|
||
<a href="../../chapter%2020%3A%20bleeding%20edge%20AI/01.%20quantum%20machine%20learning/" class="md-tabs__link">
|
||
|
||
|
||
|
||
前沿 AI
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</div>
|
||
</nav>
|
||
|
||
|
||
|
||
<main class="md-main" data-md-component="main">
|
||
<div class="md-main__inner md-grid">
|
||
|
||
|
||
|
||
<div class="md-sidebar md-sidebar--primary" data-md-component="sidebar" data-md-type="navigation" >
|
||
<div class="md-sidebar__scrollwrap">
|
||
<div class="md-sidebar__inner">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<nav class="md-nav md-nav--primary md-nav--lifted" aria-label="导航栏" data-md-level="0">
|
||
<label class="md-nav__title" for="__drawer">
|
||
<a href="../.." title="数学、计算机科学与 AI 百科全书" class="md-nav__button md-logo" aria-label="数学、计算机科学与 AI 百科全书" data-md-component="logo">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 8a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3 3 3 0 0 0 3 3m0 3.54C9.64 9.35 6.5 8 3 8v11c3.5 0 6.64 1.35 9 3.54 2.36-2.19 5.5-3.54 9-3.54V8c-3.5 0-6.64 1.35-9 3.54"/></svg>
|
||
|
||
</a>
|
||
数学、计算机科学与 AI 百科全书
|
||
</label>
|
||
|
||
<div class="md-nav__source">
|
||
<a href="https://github.com/flykhan/maths-cs-ai-compendium-zh" title="前往仓库" class="md-source" data-md-component="source">
|
||
<div class="md-source__icon md-icon">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path d="M439.6 236.1 244 40.5c-5.4-5.5-12.8-8.5-20.4-8.5s-15 3-20.4 8.4L162.5 81l51.5 51.5c27.1-9.1 52.7 16.8 43.4 43.7l49.7 49.7c34.2-11.8 61.2 31 35.5 56.7-26.5 26.5-70.2-2.9-56-37.3L240.3 199v121.9c25.3 12.5 22.3 41.8 9.1 55-6.4 6.4-15.2 10.1-24.3 10.1s-17.8-3.6-24.3-10.1c-17.6-17.6-11.1-46.9 11.2-56v-123c-20.8-8.5-24.6-30.7-18.6-45L142.6 101 8.5 235.1C3 240.6 0 247.9 0 255.5s3 15 8.5 20.4l195.6 195.7c5.4 5.4 12.7 8.4 20.4 8.4s15-3 20.4-8.4l194.7-194.7c5.4-5.4 8.4-12.8 8.4-20.4s-3-15-8.4-20.4"/></svg>
|
||
</div>
|
||
<div class="md-source__repository">
|
||
flykhan/maths-cs-ai-compendium-zh
|
||
</div>
|
||
</a>
|
||
</div>
|
||
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../.." class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
首页
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_2" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_2" id="__nav_2_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
向量
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_2">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
向量
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2001%3A%20vectors/01.%20vector%20spaces/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
向量空间
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2001%3A%20vectors/02.%20vector%20properties/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
向量性质
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2001%3A%20vectors/03.%20norms%20and%20metrics/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
范数与度量
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2001%3A%20vectors/04.%20products/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
向量积
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2001%3A%20vectors/05.%20basis%20and%20duality/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
基与对偶性
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_3" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_3" id="__nav_3_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
矩阵
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_3">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
矩阵
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2002%3A%20matrices/01.%20matrix%20properties/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
矩阵性质
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2002%3A%20matrices/02.%20matrix%20types/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
矩阵类型
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2002%3A%20matrices/03.%20operations/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
矩阵运算
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2002%3A%20matrices/04.%20linear%20transformations/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
线性变换
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2002%3A%20matrices/05.%20decompositions/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
矩阵分解
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_4" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_4" id="__nav_4_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
微积分
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_4">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
微积分
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2003%3A%20calculus/01.%20differential%20calculus/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
微分
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2003%3A%20calculus/02.%20integral%20calculus/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
积分
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2003%3A%20calculus/03.%20multivariate%20calculus/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
多元微积分
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2003%3A%20calculus/04.%20function%20approximation/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
函数逼近
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2003%3A%20calculus/05.%20optimisation/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
优化
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_5" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_5" id="__nav_5_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
统计学
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_5">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
统计学
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2004%3A%20statistics/01.%20fundamentals/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
基础
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2004%3A%20statistics/02.%20measures/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
统计量
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2004%3A%20statistics/03.%20sampling/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
抽样
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2004%3A%20statistics/04.%20hypothesis%20testing/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
假设检验
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2004%3A%20statistics/05.%20inference/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
推断
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_6" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_6" id="__nav_6_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
概率论
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_6">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
概率论
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2005%3A%20probability/01.%20counting/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
计数
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2005%3A%20probability/02.%20probability%20concepts/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
概率概念
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2005%3A%20probability/03.%20distributions/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
分布
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2005%3A%20probability/04.%20bayesian/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
贝叶斯
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2005%3A%20probability/05.%20information%20theory/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
信息论
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_7" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_7" id="__nav_7_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
机器学习
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_7">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
机器学习
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2006%3A%20machine%20learning/01.%20classical%20machine%20learning/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
经典机器学习
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2006%3A%20machine%20learning/02.%20gradient%20machine%20learning/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
梯度机器学习
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2006%3A%20machine%20learning/03.%20deep%20learning/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
深度学习
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2006%3A%20machine%20learning/04.%20reinforcement%20learning/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
强化学习
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2006%3A%20machine%20learning/05.%20distributed%20deep%20learning/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
分布式深度学习
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_8" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_8" id="__nav_8_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
计算语言学
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_8">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
计算语言学
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2007%3A%20computational%20linguistics/01.%20linguistic%20foundations/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
语言学基础
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2007%3A%20computational%20linguistics/02.%20text%20processing%20and%20classic%20NLP/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
文本处理与经典 NLP
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2007%3A%20computational%20linguistics/03.%20embeddings%20and%20sequence%20models/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
嵌入与序列模型
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2007%3A%20computational%20linguistics/04.%20transformers%20and%20language%20models/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
Transformer 与语言模型
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2007%3A%20computational%20linguistics/05.%20advanced%20text%20generation/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
高级文本生成
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_9" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_9" id="__nav_9_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
计算机视觉
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_9">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
计算机视觉
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2008%3A%20computer%20vision/01.%20image%20fundamentals/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
图像基础
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2008%3A%20computer%20vision/02.%20convolutional%20networks/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
卷积网络
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2008%3A%20computer%20vision/03.%20object%20detection%20and%20segmentation/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
目标检测与分割
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2008%3A%20computer%20vision/04.%20vision%20transformers%20and%20generation/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
ViT 与生成模型
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2008%3A%20computer%20vision/05.%20video%20and%203D%20vision/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
视频与 3D 视觉
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_10" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_10" id="__nav_10_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
音频与语音
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_10">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
音频与语音
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2009%3A%20audio%20and%20speech/01.%20digital%20signal%20processing/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
数字信号处理
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2009%3A%20audio%20and%20speech/02.%20automatic%20speech%20recognition/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
自动语音识别
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2009%3A%20audio%20and%20speech/03.%20text%20to%20speech%20and%20voice/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
语音合成
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2009%3A%20audio%20and%20speech/04.%20speaker%20and%20audio%20analysis/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
说话人与音频分析
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2009%3A%20audio%20and%20speech/05.%20source%20separation%20and%20noise/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
源分离与降噪
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_11" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_11" id="__nav_11_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
多模态学习
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_11">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
多模态学习
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2010%3A%20multimodal%20learning/01.%20multimodal%20representations/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
多模态表征
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2010%3A%20multimodal%20learning/02.%20vision%20language%20models/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
视觉语言模型
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2010%3A%20multimodal%20learning/03.%20image%20and%20video%20tokenisation/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
图像与视频 Token 化
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2010%3A%20multimodal%20learning/04.%20cross-modal%20generation/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
跨模态生成
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2010%3A%20multimodal%20learning/05.%20unified%20multimodal%20architectures/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
统一多模态架构
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_12" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_12" id="__nav_12_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
自主系统
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_12">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
自主系统
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2011%3A%20autonomous%20systems/01.%20perception/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
感知
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2011%3A%20autonomous%20systems/02.%20robot%20learning/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
机器人学习
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2011%3A%20autonomous%20systems/03.%20vision-language-action%20models/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
视觉-语言-动作模型
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2011%3A%20autonomous%20systems/04.%20self-driving/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
自动驾驶
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2011%3A%20autonomous%20systems/05.%20space%20and%20extreme%20robotics/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
太空与极端机器人
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_13" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_13" id="__nav_13_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
图神经网络
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_13">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
图神经网络
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2012%3A%20graph%20neural%20networks/01.%20geometric%20deep%20learning/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
几何深度学习
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2012%3A%20graph%20neural%20networks/02.%20graph%20theory/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
图论
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2012%3A%20graph%20neural%20networks/03.%20graph%20neural%20networks/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
图神经网络
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2012%3A%20graph%20neural%20networks/04.%20graph%20attention%20networks/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
图注意力网络
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2012%3A%20graph%20neural%20networks/05.%203d%20graph%20networks/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
3D 图网络
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_14" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_14" id="__nav_14_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
计算机与操作系统
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_14">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
计算机与操作系统
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2013%3A%20computing%20and%20OS/01.%20discrete%20maths/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
离散数学
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2013%3A%20computing%20and%20OS/02.%20computer%20architecture/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
计算机体系结构
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2013%3A%20computing%20and%20OS/03.%20operating%20systems/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
操作系统
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2013%3A%20computing%20and%20OS/04.%20concurrency%20and%20parallelism/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
并发与并行
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2013%3A%20computing%20and%20OS/05.%20programming%20languages/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
编程语言
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_15" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_15" id="__nav_15_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
数据结构与算法
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_15">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
数据结构与算法
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2014%3A%20data%20structures%20and%20algorithms/00.%20foundations/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
基础
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2014%3A%20data%20structures%20and%20algorithms/01.%20arrays%20and%20hashing/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
数组与哈希
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2014%3A%20data%20structures%20and%20algorithms/02.%20linked%20lists%2C%20stacks%2C%20and%20queues/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
链表、栈与队列
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2014%3A%20data%20structures%20and%20algorithms/03.%20trees/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
树
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2014%3A%20data%20structures%20and%20algorithms/04.%20graphs/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
图
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2014%3A%20data%20structures%20and%20algorithms/05.%20sorting%20and%20search/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
排序与搜索
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_16" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_16" id="__nav_16_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
生产级软件工程
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_16">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
生产级软件工程
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2015%3A%20production%20software%20engineering/01.%20linux%20and%20CMD/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
Linux 与命令行
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2015%3A%20production%20software%20engineering/02.%20git%20and%20repository%20management/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
Git 与仓库管理
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2015%3A%20production%20software%20engineering/03.%20codebase%20design/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
代码设计
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2015%3A%20production%20software%20engineering/04.%20testing%20and%20quality%20assurance/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
测试与质量保障
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2015%3A%20production%20software%20engineering/05.%20deployment%20and%20devops/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
部署与 DevOps
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--active md-nav__item--section md-nav__item--nested">
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" checked>
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_17" id="__nav_17_label" tabindex="">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
SIMD 与 GPU 编程
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="true">
|
||
<label class="md-nav__title" for="__nav_17">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
SIMD 与 GPU 编程
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../00.%20why%20C%2B%2B%20and%20how%20ML%20frameworks%20work/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
为什么是 C++ 及 ML 框架原理
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../01.%20hardware%20fundamentals/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
硬件基础
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../02.%20ARM%20and%20NEON/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
ARM 与 NEON
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--active">
|
||
|
||
<input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__link md-nav__link--active" for="__toc">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
x86 与 AVX
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<a href="./" class="md-nav__link md-nav__link--active">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
x86 与 AVX
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
|
||
|
||
|
||
<nav class="md-nav md-nav--secondary" aria-label="目录">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__title" for="__toc">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
目录
|
||
</label>
|
||
<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#x86-simd" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
x86 SIMD演进
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#avx2" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
AVX2编程
|
||
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label="AVX2编程">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_1" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
内联函数命名约定
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_2" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
加载和存储数据
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_3" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
算术运算
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#avx2_1" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
实践示例：AVX2点积
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#avx2-softmax" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
实践示例：AVX2 Softmax（简化版）
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#avx-512" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
AVX-512
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#intel-amx" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
Intel AMX：矩阵乘法硬件
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_4" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
内存对齐
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_5" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
性能陷阱
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_6" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
性能分析
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#x86intelamdgclang" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
编程任务（在x86——Intel/AMD上用g++或clang++编译）
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../04.%20GPU%20architecture%20and%20CUDA/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
GPU 架构与 CUDA
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../05.%20triton%2C%20TPUs%20and%20pallax/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
Triton、TPU 与 Pallas
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../06.%20RISC-V%20and%20embedded%20systems/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
RISC-V 与嵌入式系统
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<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>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_18" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_18" id="__nav_18_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
AI 推理
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_18">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
AI 推理
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2017%3A%20AI%20inference/01.%20quantisation/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
量化
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2017%3A%20AI%20inference/02.%20efficient%20architectures/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
高效架构
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2017%3A%20AI%20inference/03.%20serving%20and%20batching/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
服务与批处理
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<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">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_19" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_19" id="__nav_19_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
ML 系统设计
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_19">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
ML 系统设计
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<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>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<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>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_20" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_20" id="__nav_20_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
应用 AI
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_20_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_20">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
应用 AI
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2019%3A%20applied%20AI/01.%20AI%20for%20finance/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
AI 金融
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2019%3A%20applied%20AI/02.%20protein%20design/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
蛋白质设计
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2019%3A%20applied%20AI/03.%20drug%20discovery/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
药物发现
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2019%3A%20applied%20AI/04.%20agentic%20systems/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
智能体系统
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2019%3A%20applied%20AI/05.%20healthcare/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
医疗健康
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_21" >
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_21" id="__nav_21_label" tabindex="0">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
前沿 AI
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_21_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_21">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
前沿 AI
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2020%3A%20bleeding%20edge%20AI/01.%20quantum%20machine%20learning/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
量子机器学习
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2020%3A%20bleeding%20edge%20AI/02.%20neuromorphic%20computing/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
神经形态计算
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2020%3A%20bleeding%20edge%20AI/03.%20datacentres%20in%20space/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
太空数据中心
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2020%3A%20bleeding%20edge%20AI/04.%20decentralised%20AI/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
去中心化 AI
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter%2020%3A%20bleeding%20edge%20AI/05.%20brain%20machine%20interfaces/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
脑机接口
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
|
||
|
||
<div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
|
||
<div class="md-sidebar__scrollwrap">
|
||
<div class="md-sidebar__inner">
|
||
|
||
|
||
<nav class="md-nav md-nav--secondary" aria-label="目录">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__title" for="__toc">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
目录
|
||
</label>
|
||
<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#x86-simd" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
x86 SIMD演进
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#avx2" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
AVX2编程
|
||
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label="AVX2编程">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_1" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
内联函数命名约定
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_2" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
加载和存储数据
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_3" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
算术运算
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#avx2_1" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
实践示例：AVX2点积
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#avx2-softmax" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
实践示例：AVX2 Softmax（简化版）
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#avx-512" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
AVX-512
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#intel-amx" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
Intel AMX：矩阵乘法硬件
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_4" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
内存对齐
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_5" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
性能陷阱
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_6" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
性能分析
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#x86intelamdgclang" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
编程任务（在x86——Intel/AMD上用g++或clang++编译）
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
|
||
</nav>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
|
||
|
||
<div class="md-content" data-md-component="content">
|
||
|
||
<article class="md-content__inner md-typeset">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<h1 id="x86avx">x86与AVX<a class="headerlink" href="#x86avx" title="Permanent link">¶</a></h1>
|
||
<p><em>x86处理器来自Intel和AMD，主导着大多数ML训练所在的数据中心服务器。本文涵盖x86 SIMD的演进、AVX/AVX2内联函数编程、AVX-512、用于矩阵操作的Intel AMX、内存对齐、性能陷阱以及性能分析——在全球最常见的服务器CPU上榨取最大性能的工具。</em></p>
|
||
<ul>
|
||
<li>如果你的训练在云虚拟机（AWS、GCP、Azure）上运行，它几乎肯定运行在x86上。即使是GPU密集训练也有CPU瓶颈：数据加载、预处理、梯度聚合和检查点保存都在CPU上运行。使用x86 SIMD优化这些环节可以有意义地减少端到端训练时间。</li>
|
||
</ul>
|
||
<h2 id="x86-simd">x86 SIMD演进<a class="headerlink" href="#x86-simd" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>x86 SIMD经历了越来越宽的向量寄存器：</li>
|
||
</ul>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>代次</th>
|
||
<th>年份</th>
|
||
<th>寄存器宽度</th>
|
||
<th>寄存器数量</th>
|
||
<th>关键特性</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr>
|
||
<td>MMX</td>
|
||
<td>1997</td>
|
||
<td>64位</td>
|
||
<td>8（mm0-7）</td>
|
||
<td>仅整数，与FPU共享</td>
|
||
</tr>
|
||
<tr>
|
||
<td>SSE</td>
|
||
<td>1999</td>
|
||
<td>128位</td>
|
||
<td>8（xmm0-7）</td>
|
||
<td>4个浮点数，专用寄存器</td>
|
||
</tr>
|
||
<tr>
|
||
<td>SSE2</td>
|
||
<td>2001</td>
|
||
<td>128位</td>
|
||
<td>8/16</td>
|
||
<td>2个双精度浮点数，整数操作</td>
|
||
</tr>
|
||
<tr>
|
||
<td>AVX</td>
|
||
<td>2011</td>
|
||
<td>256位</td>
|
||
<td>16（ymm0-15）</td>
|
||
<td>8个浮点数，三操作数指令</td>
|
||
</tr>
|
||
<tr>
|
||
<td>AVX2</td>
|
||
<td>2013</td>
|
||
<td>256位</td>
|
||
<td>16</td>
|
||
<td>整数256位，FMA，收集</td>
|
||
</tr>
|
||
<tr>
|
||
<td>AVX-512</td>
|
||
<td>2017</td>
|
||
<td>512位</td>
|
||
<td>32（zmm0-31）</td>
|
||
<td>16个浮点数，掩码寄存器，分散</td>
|
||
</tr>
|
||
<tr>
|
||
<td>AMX</td>
|
||
<td>2023</td>
|
||
<td>瓦片寄存器</td>
|
||
<td>8个瓦片</td>
|
||
<td>矩阵乘法（BF16，INT8）</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<ul>
|
||
<li>
|
||
<p>每一代都将向量化代码的吞吐量翻倍。用SSE内联函数编写的代码可以在2001年以来制造的每一个x86 CPU上运行。AVX2需要2013年以后的CPU。AVX-512需要Intel Xeon和一些消费级芯片。AMX是最新的（Sapphire Rapids及以后）。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>向后兼容性</strong>：x86 SSE寄存器（xmm）是AVX寄存器（ymm）的低128位，后者是AVX-512寄存器（zmm）的低256位。旧的SSE代码无需修改即可在新的CPU上运行。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="avx2">AVX2编程<a class="headerlink" href="#avx2" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>AVX2操作256位寄存器（YMM），同时处理8个浮点数或4个双精度浮点数。它是可移植高性能代码的甜点区域：在几乎所有现代x86 CPU（2013+）上可用。</li>
|
||
</ul>
|
||
<h3 id="_1">内联函数命名约定<a class="headerlink" href="#_1" title="Permanent link">¶</a></h3>
|
||
<ul>
|
||
<li>
|
||
<p>所有x86内联函数遵循模式：<code>_mm[宽度]_[操作]_[类型]</code></p>
|
||
<ul>
|
||
<li><code>_mm</code> = MMX/SSE（128位），<code>_mm256</code> = AVX（256位），<code>_mm512</code> = AVX-512（512位）</li>
|
||
<li>操作：<code>add</code>、<code>mul</code>、<code>fmadd</code>、<code>load</code>、<code>store</code>、<code>set</code> 等</li>
|
||
<li>类型：<code>ps</code> = 打包单精度（float32），<code>pd</code> = 打包双精度（float64），<code>epi32</code> = 打包int32，<code>si256</code> = 256位整数</li>
|
||
</ul>
|
||
</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="cp">#include</span><span class="w"> </span><span class="cpf"><immintrin.h></span><span class="c1"> // 所有x86 SIMD内联函数</span>
|
||
<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><span class="c1">// 数据类型</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="n">__m256</span><span class="w"> </span><span class="n">a</span><span class="p">;</span><span class="w"> </span><span class="c1">// 256位寄存器，保存8个float32</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="n">__m256d</span><span class="w"> </span><span class="n">b</span><span class="p">;</span><span class="w"> </span><span class="c1">// 256位寄存器，保存4个float64</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="n">__m256i</span><span class="w"> </span><span class="n">c</span><span class="p">;</span><span class="w"> </span><span class="c1">// 256位寄存器，保存整数（8x32、16x16或32x8）</span>
|
||
</code></pre></div>
|
||
<h3 id="_2">加载和存储数据<a class="headerlink" href="#_2" 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">// 从内存加载8个浮点数</span>
|
||
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="n">__m256</span><span class="w"> </span><span class="n">v</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_loadu_ps</span><span class="p">(</span><span class="n">ptr</span><span class="p">);</span><span class="w"> </span><span class="c1">// 非对齐加载（适用于任何地址）</span>
|
||
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="n">__m256</span><span class="w"> </span><span class="n">v</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_load_ps</span><span class="p">(</span><span class="n">ptr</span><span class="p">);</span><span class="w"> </span><span class="c1">// 对齐加载（ptr必须32字节对齐，更快）</span>
|
||
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a>
|
||
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="c1">// 存储8个浮点数到内存</span>
|
||
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="n">_mm256_storeu_ps</span><span class="p">(</span><span class="n">out_ptr</span><span class="p">,</span><span class="w"> </span><span class="n">v</span><span class="p">);</span><span class="w"> </span><span class="c1">// 非对齐存储</span>
|
||
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="n">_mm256_store_ps</span><span class="p">(</span><span class="n">out_ptr</span><span class="p">,</span><span class="w"> </span><span class="n">v</span><span class="p">);</span><span class="w"> </span><span class="c1">// 对齐存储</span>
|
||
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a>
|
||
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="c1">// 将单个值广播到所有8个通道</span>
|
||
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="n">__m256</span><span class="w"> </span><span class="n">ones</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_set1_ps</span><span class="p">(</span><span class="mf">1.0f</span><span class="p">);</span><span class="w"> </span><span class="c1">// [1, 1, 1, 1, 1, 1, 1, 1]</span>
|
||
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a>
|
||
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="c1">// 设置各个值（很少需要）</span>
|
||
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="n">__m256</span><span class="w"> </span><span class="n">v</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_set_ps</span><span class="p">(</span><span class="mi">7</span><span class="p">,</span><span class="mi">6</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 注意：逆序！</span>
|
||
<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a>
|
||
<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="c1">// 零寄存器</span>
|
||
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="n">__m256</span><span class="w"> </span><span class="n">z</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_setzero_ps</span><span class="p">();</span>
|
||
</code></pre></div>
|
||
<h3 id="_3">算术运算<a class="headerlink" href="#_3" 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="n">__m256</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_add_ps</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">);</span><span class="w"> </span><span class="c1">// c[i] = a[i] + b[i]</span>
|
||
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="n">__m256</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_mul_ps</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">);</span><span class="w"> </span><span class="c1">// d[i] = a[i] * b[i]</span>
|
||
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="n">__m256</span><span class="w"> </span><span class="n">e</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_sub_ps</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">);</span><span class="w"> </span><span class="c1">// e[i] = a[i] - b[i]</span>
|
||
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="n">__m256</span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_div_ps</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">);</span><span class="w"> </span><span class="c1">// f[i] = a[i] / b[i]（比乘法慢）</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">// 融合乘加：r = a * b + c（一条指令，一次舍入）</span>
|
||
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="n">__m256</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_fmadd_ps</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span><span class="w"> </span><span class="c1">// ML最重要的指令</span>
|
||
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a>
|
||
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="c1">// 最小值和最大值</span>
|
||
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="n">__m256</span><span class="w"> </span><span class="n">mn</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_min_ps</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">);</span><span class="w"> </span><span class="c1">// min(a[i], b[i]) — 用于裁剪</span>
|
||
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="n">__m256</span><span class="w"> </span><span class="n">mx</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_max_ps</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">);</span><span class="w"> </span><span class="c1">// max(a[i], b[i]) — 用于ReLU</span>
|
||
</code></pre></div>
|
||
<h3 id="avx2_1">实践示例：AVX2点积<a class="headerlink" href="#avx2_1" 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="cp">#include</span><span class="w"> </span><span class="cpf"><immintrin.h></span>
|
||
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
|
||
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="kt">float</span><span class="w"> </span><span class="nf">dot_avx2</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">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-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="n">__m256</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">_mm256_setzero_ps</span><span class="p">();</span><span class="w"> </span><span class="c1">// 8个累加器初始化为0</span>
|
||
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a>
|
||
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </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>
|
||
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </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">8</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="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">8</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="n">__m256</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">_mm256_loadu_ps</span><span class="p">(</span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="n">__m256</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">_mm256_loadu_ps</span><span class="p">(</span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></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">_mm256_fmadd_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="n">sum</span><span class="p">);</span><span class="w"> </span><span class="c1">// sum += va * vb</span>
|
||
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a>
|
||
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w"> </span><span class="c1">// 水平归约：将sum的8个元素相加</span>
|
||
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="c1">// 步骤1：将上128位加到下128位</span>
|
||
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="kr">__m128</span><span class="w"> </span><span class="n">hi</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_extractf128_ps</span><span class="p">(</span><span class="n">sum</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w"> </span><span class="kr">__m128</span><span class="w"> </span><span class="n">lo</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_castps256_ps128</span><span class="p">(</span><span class="n">sum</span><span class="p">);</span>
|
||
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w"> </span><span class="kr">__m128</span><span class="w"> </span><span class="n">sum128</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">hi</span><span class="p">,</span><span class="w"> </span><span class="n">lo</span><span class="p">);</span><span class="w"> </span><span class="c1">// 4个部分和</span>
|
||
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a>
|
||
<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w"> </span><span class="c1">// 步骤2：在128位寄存器内水平相加</span>
|
||
<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w"> </span><span class="n">sum128</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm_hadd_ps</span><span class="p">(</span><span class="n">sum128</span><span class="p">,</span><span class="w"> </span><span class="n">sum128</span><span class="p">);</span><span class="w"> </span><span class="c1">// [a+b, c+d, a+b, c+d]</span>
|
||
<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w"> </span><span class="n">sum128</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm_hadd_ps</span><span class="p">(</span><span class="n">sum128</span><span class="p">,</span><span class="w"> </span><span class="n">sum128</span><span class="p">);</span><span class="w"> </span><span class="c1">// [a+b+c+d, ...]</span>
|
||
<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a>
|
||
<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="w"> </span><span class="kt">float</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">_mm_cvtss_f32</span><span class="p">(</span><span class="n">sum128</span><span class="p">);</span><span class="w"> </span><span class="c1">// 提取标量</span>
|
||
<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a>
|
||
<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="w"> </span><span class="c1">// 标量清理</span>
|
||
<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="w"> </span><span class="k">for</span><span class="w"> </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-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a><span class="w"> </span><span class="n">result</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-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a>
|
||
<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></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-3-31" name="__codelineno-3-31" href="#__codelineno-3-31"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
<ul>
|
||
<li>
|
||
<p><strong>为什么水平归约如此丑陋</strong>：SIMD是为垂直操作设计的（通道0与通道0，通道1与通道1）。水平操作（跨通道求和）与硬件对抗。这就是点积在末尾有尴尬归约代码的原因。向量化循环是简洁的；归约是样板代码。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>性能</strong>：与NEON版本（文件02）相比，AVX2每次迭代处理8个浮点数，而NEON处理4个。对于长向量，这比NEON快2倍（忽略内存带宽限制）。</p>
|
||
</li>
|
||
</ul>
|
||
<h3 id="avx2-softmax">实践示例：AVX2 Softmax（简化版）<a class="headerlink" href="#avx2-softmax" title="Permanent link">¶</a></h3>
|
||
<ul>
|
||
<li>Softmax需要：找到最大值，减去它，求指数，求和，除法。以下是最值查找步骤：</li>
|
||
</ul>
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="kt">float</span><span class="w"> </span><span class="nf">vector_max_avx2</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">data</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-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="w"> </span><span class="n">__m256</span><span class="w"> </span><span class="n">max_vec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_set1_ps</span><span class="p">(</span><span class="o">-</span><span class="n">INFINITY</span><span class="p">);</span>
|
||
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a>
|
||
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w"> </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>
|
||
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </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">8</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="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">8</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w"> </span><span class="n">__m256</span><span class="w"> </span><span class="n">v</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_loadu_ps</span><span class="p">(</span><span class="n">data</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w"> </span><span class="n">max_vec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_max_ps</span><span class="p">(</span><span class="n">max_vec</span><span class="p">,</span><span class="w"> </span><span class="n">v</span><span class="p">);</span>
|
||
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a>
|
||
<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w"> </span><span class="c1">// 将8个最大值归约为1个</span>
|
||
<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w"> </span><span class="kr">__m128</span><span class="w"> </span><span class="n">hi</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_extractf128_ps</span><span class="p">(</span><span class="n">max_vec</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||
<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w"> </span><span class="kr">__m128</span><span class="w"> </span><span class="n">lo</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_castps256_ps128</span><span class="p">(</span><span class="n">max_vec</span><span class="p">);</span>
|
||
<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w"> </span><span class="kr">__m128</span><span class="w"> </span><span class="n">max128</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm_max_ps</span><span class="p">(</span><span class="n">hi</span><span class="p">,</span><span class="w"> </span><span class="n">lo</span><span class="p">);</span>
|
||
<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a>
|
||
<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w"> </span><span class="c1">// 通过混洗和取最大值找到单一最大值</span>
|
||
<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w"> </span><span class="n">max128</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm_max_ps</span><span class="p">(</span><span class="n">max128</span><span class="p">,</span><span class="w"> </span><span class="n">_mm_shuffle_ps</span><span class="p">(</span><span class="n">max128</span><span class="p">,</span><span class="w"> </span><span class="n">max128</span><span class="p">,</span><span class="w"> </span><span class="mb">0b01001110</span><span class="p">));</span>
|
||
<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w"> </span><span class="n">max128</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm_max_ps</span><span class="p">(</span><span class="n">max128</span><span class="p">,</span><span class="w"> </span><span class="n">_mm_shuffle_ps</span><span class="p">(</span><span class="n">max128</span><span class="p">,</span><span class="w"> </span><span class="n">max128</span><span class="p">,</span><span class="w"> </span><span class="mb">0b10110001</span><span class="p">));</span>
|
||
<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a>
|
||
<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w"> </span><span class="kt">float</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">_mm_cvtss_f32</span><span class="p">(</span><span class="n">max128</span><span class="p">);</span>
|
||
<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a>
|
||
<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w"> </span><span class="k">for</span><span class="w"> </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-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w"> </span><span class="n">result</span><span class="w"> </span><span class="o">=</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">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="n">result</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-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a>
|
||
<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></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-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
<ul>
|
||
<li><code>_mm_shuffle_ps</code> 指令在寄存器内重排元素。二进制常量 <code>0b01001110</code> 控制哪些元素去哪里。这称为<strong>置换</strong>，它直接连接到置换矩阵（第2章）：打乱SIMD通道是做硬件级别的乘以置换矩阵。</li>
|
||
</ul>
|
||
<h2 id="avx-512">AVX-512<a class="headerlink" href="#avx-512" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>AVX-512再次加倍宽度：512位寄存器（ZMM），同时处理16个浮点数。</li>
|
||
</ul>
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="n">__m512</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">_mm512_loadu_ps</span><span class="p">(</span><span class="n">ptr</span><span class="p">);</span><span class="w"> </span><span class="c1">// 加载16个浮点数</span>
|
||
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="n">__m512</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm512_fmadd_ps</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span><span class="w"> </span><span class="c1">// 16个FMA同时进行</span>
|
||
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><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="n">_mm512_reduce_add_ps</span><span class="p">(</span><span class="n">a</span><span class="p">);</span><span class="w"> </span><span class="c1">// 内置水平求和（无需手动归约！）</span>
|
||
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>
|
||
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="c1">// 掩码操作：操作通道子集</span>
|
||
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="n">__mmask16</span><span class="w"> </span><span class="n">mask</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm512_cmpgt_ps_mask</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">zero</span><span class="p">);</span><span class="w"> </span><span class="c1">// 哪些通道 > 0？</span>
|
||
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="n">__m512</span><span class="w"> </span><span class="n">relu</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm512_maskz_mov_ps</span><span class="p">(</span><span class="n">mask</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">);</span><span class="w"> </span><span class="c1">// 负通道置零 = ReLU</span>
|
||
</code></pre></div>
|
||
<ul>
|
||
<li>
|
||
<p><strong>掩码寄存器</strong>（<code>__mmask16</code>）是AVX-512最强大的功能。每个位控制一个通道是否参与操作。这取代了标量清理循环：最后一次迭代使用掩码，只有有效通道是激活的，处理任何向量长度而无需单独标量循环。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>AVX-512频率降频</strong>：在许多Intel CPU上，使用AVX-512指令会导致CPU暂时降低时钟频率（以保持在热限制内）。这意味着对于短时爆发，AVX-512并不总是比AVX2快——频率惩罚可能抵消更宽向量的优势。对于持续工作负载（如矩阵乘法），AVX-512胜出。对于混合代码（部分SIMD、部分标量），频率转换可能造成损失。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="intel-amx">Intel AMX：矩阵乘法硬件<a class="headerlink" href="#intel-amx" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li><strong>AMX</strong>（高级矩阵扩展）增加了专用矩阵乘法单元。AMX操作的不是SIMD向量，而是<strong>瓦片</strong>：2D数据块（最多16行 × 每行64字节）。</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="cp">#include</span><span class="w"> </span><span class="cpf"><immintrin.h></span>
|
||
<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
|
||
<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="c1">// AMX瓦片乘法：C += A * B（BF16格式）</span>
|
||
<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="c1">// A为16x32 BF16，B为32x16 BF16，C为16x16 FP32</span>
|
||
<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="n">_tile_loadd</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">a_ptr</span><span class="p">,</span><span class="w"> </span><span class="n">stride_a</span><span class="p">);</span><span class="w"> </span><span class="c1">// 从A加载瓦片0</span>
|
||
<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="n">_tile_loadd</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">b_ptr</span><span class="p">,</span><span class="w"> </span><span class="n">stride_b</span><span class="p">);</span><span class="w"> </span><span class="c1">// 从B加载瓦片1</span>
|
||
<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="n">_tile_dpbf16ps</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span><span class="w"> </span><span class="c1">// 瓦片2 += 瓦片0 * 瓦片1（BF16矩阵乘法，FP32累加）</span>
|
||
<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="n">_tile_stored</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="n">c_ptr</span><span class="p">,</span><span class="w"> </span><span class="n">stride_c</span><span class="p">);</span><span class="w"> </span><span class="c1">// 存储瓦片2到C</span>
|
||
</code></pre></div>
|
||
<ul>
|
||
<li>
|
||
<p>AMX在一条指令中执行完整的16×32 × 32×16矩阵乘法。这是数百次FMA操作同时进行，专门为Transformer推理中主导的小矩阵乘法设计（注意力得分计算、MLP层）。</p>
|
||
</li>
|
||
<li>
|
||
<p>AMX支持BF16（bfloat16）和INT8，匹配ML推理中使用的精度。结合用于其他操作的AVX-512，配备AMX的CPU（Intel Sapphire Rapids、Emerald Rapids）可以在Transformer推理中与入门级GPU竞争。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="_4">内存对齐<a class="headerlink" href="#_4" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li><strong>对齐内存访问</strong>是指数据地址是向量寄存器宽度的倍数（SSE为16字节、AVX为32字节、AVX-512为64字节）。对齐访问在某些CPU上更快，并且是 <code>_mm256_load_ps</code>（相对于 <code>_mm256_loadu_ps</code>）的要求。</li>
|
||
</ul>
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="c1">// 分配对齐内存</span>
|
||
<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></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="p">(</span><span class="kt">float</span><span class="o">*</span><span class="p">)</span><span class="n">aligned_alloc</span><span class="p">(</span><span class="mi">32</span><span class="p">,</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="c1">// AVX的32字节对齐</span>
|
||
<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a>
|
||
<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="c1">// C++对齐分配</span>
|
||
<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><new></span>
|
||
<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></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="p">(</span><span class="n">std</span><span class="o">::</span><span class="n">align_val_t</span><span class="p">(</span><span class="mi">32</span><span class="p">))</span><span class="w"> </span><span class="kt">float</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
|
||
<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a>
|
||
<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="c1">// 或者使用编译器属性</span>
|
||
<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="k">alignas</span><span class="p">(</span><span class="mi">32</span><span class="p">)</span><span class="w"> </span><span class="kt">float</span><span class="w"> </span><span class="n">data</span><span class="p">[</span><span class="mi">1024</span><span class="p">];</span>
|
||
</code></pre></div>
|
||
<ul>
|
||
<li><strong>实际上</strong>：在现代CPU（Haswell及以后）上，当数据不跨越缓存行边界时，非对齐加载（<code>loadu</code>）几乎与对齐加载一样快。非对齐访问的性能惩罚已基本消失，但缓存行分割（数据跨越两个64字节缓存行）仍可能使特定加载变慢约2倍。对齐分配完全避免了这种情况。</li>
|
||
</ul>
|
||
<h2 id="_5">性能陷阱<a class="headerlink" href="#_5" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>
|
||
<p><strong>AVX-SSE转换惩罚</strong>：在较旧的Intel CPU（Skylake之前）上，在AVX（256位）和SSE（128位）指令之间切换会造成惩罚（约70周期）。这就是为什么你应该在从使用AVX的函数返回之前使用 <code>_mm256_zeroupper()</code>（或 <code>vzeroupper</code> 指令）清除YMM寄存器的上128位。现代CPU（Skylake+）没有此惩罚。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>寄存器压力</strong>：AVX2有16个YMM寄存器。如果你的核函数使用太多变量，编译器会将寄存器溢出到栈（内存），从而破坏性能。保持内循环简单，活变量少。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>数据依赖</strong>：<code>sum = _mm256_fmadd_ps(a, b, sum)</code> 对 <code>sum</code> 有依赖：每次迭代必须等待前一个FMA完成（约4-5个周期的延迟）。解决方案：使用多个独立累加器并在结束时归约：</p>
|
||
</li>
|
||
</ul>
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="c1">// 单累加器：受FMA延迟限制（4-5个周期）</span>
|
||
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="n">__m256</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">_mm256_setzero_ps</span><span class="p">();</span>
|
||
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(...)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></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">_mm256_fmadd_ps</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">,</span><span class="w"> </span><span class="n">sum</span><span class="p">);</span><span class="w"> </span><span class="c1">// 每个依赖前一个</span>
|
||
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a>
|
||
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="c1">// 四个累加器：4倍吞吐量（隐藏延迟）</span>
|
||
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="n">__m256</span><span class="w"> </span><span class="n">sum0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_setzero_ps</span><span class="p">();</span>
|
||
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="n">__m256</span><span class="w"> </span><span class="n">sum1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_setzero_ps</span><span class="p">();</span>
|
||
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="n">__m256</span><span class="w"> </span><span class="n">sum2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_setzero_ps</span><span class="p">();</span>
|
||
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="n">__m256</span><span class="w"> </span><span class="n">sum3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_setzero_ps</span><span class="p">();</span>
|
||
<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="k">for</span><span class="w"> </span><span class="p">(...)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w"> </span><span class="n">sum0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_fmadd_ps</span><span class="p">(</span><span class="n">a0</span><span class="p">,</span><span class="w"> </span><span class="n">b0</span><span class="p">,</span><span class="w"> </span><span class="n">sum0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 独立</span>
|
||
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w"> </span><span class="n">sum1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_fmadd_ps</span><span class="p">(</span><span class="n">a1</span><span class="p">,</span><span class="w"> </span><span class="n">b1</span><span class="p">,</span><span class="w"> </span><span class="n">sum1</span><span class="p">);</span><span class="w"> </span><span class="c1">// 独立</span>
|
||
<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w"> </span><span class="n">sum2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_fmadd_ps</span><span class="p">(</span><span class="n">a2</span><span class="p">,</span><span class="w"> </span><span class="n">b2</span><span class="p">,</span><span class="w"> </span><span class="n">sum2</span><span class="p">);</span><span class="w"> </span><span class="c1">// 独立</span>
|
||
<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w"> </span><span class="n">sum3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_fmadd_ps</span><span class="p">(</span><span class="n">a3</span><span class="p">,</span><span class="w"> </span><span class="n">b3</span><span class="p">,</span><span class="w"> </span><span class="n">sum3</span><span class="p">);</span><span class="w"> </span><span class="c1">// 独立</span>
|
||
<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="p">}</span>
|
||
<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="n">sum0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_add_ps</span><span class="p">(</span><span class="n">sum0</span><span class="p">,</span><span class="w"> </span><span class="n">sum1</span><span class="p">);</span>
|
||
<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="n">sum2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_add_ps</span><span class="p">(</span><span class="n">sum2</span><span class="p">,</span><span class="w"> </span><span class="n">sum3</span><span class="p">);</span>
|
||
<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="n">sum0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_add_ps</span><span class="p">(</span><span class="n">sum0</span><span class="p">,</span><span class="w"> </span><span class="n">sum2</span><span class="p">);</span>
|
||
</code></pre></div>
|
||
<ul>
|
||
<li>这是<strong>循环展开</strong>以隐藏延迟。CPU可以背靠背发出FMAs，因为它们写入不同的寄存器。这是数值代码中最有影响力的微优化之一。</li>
|
||
</ul>
|
||
<h2 id="_6">性能分析<a class="headerlink" href="#_6" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li><strong>性能计数器</strong>提供硬件级测量：</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"># Linux perf（需要内核支持）</span>
|
||
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>perf<span class="w"> </span>stat<span class="w"> </span>./my_program<span class="w"> </span><span class="c1"># 基本计数器：周期、指令、IPC</span>
|
||
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a>perf<span class="w"> </span>stat<span class="w"> </span>-e<span class="w"> </span>cache-misses,cache-references<span class="w"> </span>./my_program<span class="w"> </span><span class="c1"># 缓存行为</span>
|
||
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a>perf<span class="w"> </span>record<span class="w"> </span>-g<span class="w"> </span>./my_program<span class="w"> </span><span class="o">&&</span><span class="w"> </span>perf<span class="w"> </span>report<span class="w"> </span><span class="c1"># 调用图分析</span>
|
||
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a>
|
||
<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="c1"># Intel VTune（详细的x86性能分析）</span>
|
||
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a>vtune<span class="w"> </span>-collect<span class="w"> </span>hotspots<span class="w"> </span>--<span class="w"> </span>./my_program
|
||
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a>vtune<span class="w"> </span>-collect<span class="w"> </span>memory-access<span class="w"> </span>--<span class="w"> </span>./my_program<span class="w"> </span><span class="c1"># 内存带宽分析</span>
|
||
</code></pre></div>
|
||
<ul>
|
||
<li><strong>需要关注什么</strong>：<ul>
|
||
<li><strong>IPC</strong>（每周期指令数）：CPU被使用的效率。IPC > 2 良好。IPC < 1 表明内存停顿或分支预测错误。</li>
|
||
<li><strong>缓存缺失率</strong>：高L1/L2缺失率表明数据局部性差。需重构数据访问模式。</li>
|
||
<li><strong>分支预测错误率</strong>：> 5% 表明分支不可预测。如可能，转换为无分支代码（SIMD比较+混合）。</li>
|
||
<li><strong>实际FLOPS vs 屋顶线</strong>：将你的实测FLOPS与屋顶线模型（文件01）比较。如果你低于屋顶线，还有改进空间。</li>
|
||
</ul>
|
||
</li>
|
||
</ul>
|
||
<h2 id="x86intelamdgclang">编程任务（在x86——Intel/AMD上用g++或clang++编译）<a class="headerlink" href="#x86intelamdgclang" title="Permanent link">¶</a></h2>
|
||
<ol>
|
||
<li>
|
||
<p>编写标量点积和AVX2点积。对两者进行基准测试并测量8路SIMD带来的加速比。
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// task1_avx_dot.cpp</span>
|
||
<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="c1">// 编译：g++ -O3 -mavx2 -mfma -o task1 task1_avx_dot.cpp</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="cp">#include</span><span class="w"> </span><span class="cpf"><iostream></span>
|
||
<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><chrono></span>
|
||
<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><vector></span>
|
||
<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><immintrin.h></span>
|
||
<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a>
|
||
<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="kt">float</span><span class="w"> </span><span class="nf">dot_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">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-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></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-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></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="n">sum</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-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">sum</span><span class="p">;</span>
|
||
<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="p">}</span>
|
||
<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a>
|
||
<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="kt">float</span><span class="w"> </span><span class="nf">dot_avx2</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">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-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w"> </span><span class="n">__m256</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">_mm256_setzero_ps</span><span class="p">();</span>
|
||
<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w"> </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>
|
||
<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w"> </span><span class="k">for</span><span class="w"> </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">8</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="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">8</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="w"> </span><span class="n">__m256</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">_mm256_loadu_ps</span><span class="p">(</span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="w"> </span><span class="n">__m256</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">_mm256_loadu_ps</span><span class="p">(</span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></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">_mm256_fmadd_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="n">sum</span><span class="p">);</span>
|
||
<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w"> </span><span class="c1">// 归约：上128加到下128，然后水平相加</span>
|
||
<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="w"> </span><span class="kr">__m128</span><span class="w"> </span><span class="n">hi</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_extractf128_ps</span><span class="p">(</span><span class="n">sum</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||
<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="w"> </span><span class="kr">__m128</span><span class="w"> </span><span class="n">lo</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_castps256_ps128</span><span class="p">(</span><span class="n">sum</span><span class="p">);</span>
|
||
<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="w"> </span><span class="kr">__m128</span><span class="w"> </span><span class="n">r</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">hi</span><span class="p">,</span><span class="w"> </span><span class="n">lo</span><span class="p">);</span>
|
||
<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm_hadd_ps</span><span class="p">(</span><span class="n">r</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">);</span>
|
||
<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm_hadd_ps</span><span class="p">(</span><span class="n">r</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">);</span>
|
||
<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a><span class="w"> </span><span class="kt">float</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">_mm_cvtss_f32</span><span class="p">(</span><span class="n">r</span><span class="p">);</span>
|
||
<a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a><span class="w"> </span><span class="k">for</span><span class="w"> </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="n">result</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-10-31" name="__codelineno-10-31" href="#__codelineno-10-31"></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-10-32" name="__codelineno-10-32" href="#__codelineno-10-32"></a><span class="p">}</span>
|
||
<a id="__codelineno-10-33" name="__codelineno-10-33" href="#__codelineno-10-33"></a>
|
||
<a id="__codelineno-10-34" name="__codelineno-10-34" href="#__codelineno-10-34"></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-10-35" name="__codelineno-10-35" href="#__codelineno-10-35"></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>
|
||
<a id="__codelineno-10-36" name="__codelineno-10-36" href="#__codelineno-10-36"></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>
|
||
<a id="__codelineno-10-37" name="__codelineno-10-37" href="#__codelineno-10-37"></a>
|
||
<a id="__codelineno-10-38" name="__codelineno-10-38" href="#__codelineno-10-38"></a><span class="w"> </span><span class="k">volatile</span><span class="w"> </span><span class="kt">float</span><span class="w"> </span><span class="n">s1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dot_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">N</span><span class="p">);</span>
|
||
<a id="__codelineno-10-39" name="__codelineno-10-39" href="#__codelineno-10-39"></a><span class="w"> </span><span class="k">volatile</span><span class="w"> </span><span class="kt">float</span><span class="w"> </span><span class="n">s2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dot_avx2</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">N</span><span class="p">);</span>
|
||
<a id="__codelineno-10-40" name="__codelineno-10-40" href="#__codelineno-10-40"></a>
|
||
<a id="__codelineno-10-41" name="__codelineno-10-41" href="#__codelineno-10-41"></a><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="n">bench</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="o">&</span><span class="p">](</span><span class="k">auto</span><span class="w"> </span><span class="n">fn</span><span class="p">,</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">char</span><span class="o">*</span><span class="w"> </span><span class="n">name</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-10-42" name="__codelineno-10-42" href="#__codelineno-10-42"></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-10-43" name="__codelineno-10-43" href="#__codelineno-10-43"></a><span class="w"> </span><span class="k">volatile</span><span class="w"> </span><span class="kt">float</span><span class="w"> </span><span class="n">s</span><span class="p">;</span>
|
||
<a id="__codelineno-10-44" name="__codelineno-10-44" href="#__codelineno-10-44"></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">t</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">t</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">t</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="n">s</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fn</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">N</span><span class="p">);</span>
|
||
<a id="__codelineno-10-45" name="__codelineno-10-45" href="#__codelineno-10-45"></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-10-46" name="__codelineno-10-46" href="#__codelineno-10-46"></a><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">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><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">100</span><span class="p">;</span>
|
||
<a id="__codelineno-10-47" name="__codelineno-10-47" href="#__codelineno-10-47"></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="n">name</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">ms</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">" ms（结果: "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">s</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"）</span><span class="se">\n</span><span class="s">"</span><span class="p">;</span>
|
||
<a id="__codelineno-10-48" name="__codelineno-10-48" href="#__codelineno-10-48"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">ms</span><span class="p">;</span>
|
||
<a id="__codelineno-10-49" name="__codelineno-10-49" href="#__codelineno-10-49"></a><span class="w"> </span><span class="p">};</span>
|
||
<a id="__codelineno-10-50" name="__codelineno-10-50" href="#__codelineno-10-50"></a>
|
||
<a id="__codelineno-10-51" name="__codelineno-10-51" href="#__codelineno-10-51"></a><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">t1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bench</span><span class="p">(</span><span class="n">dot_scalar</span><span class="p">,</span><span class="w"> </span><span class="s">"标量"</span><span class="p">);</span>
|
||
<a id="__codelineno-10-52" name="__codelineno-10-52" href="#__codelineno-10-52"></a><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">t2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bench</span><span class="p">(</span><span class="n">dot_avx2</span><span class="p">,</span><span class="w"> </span><span class="s">"AVX2 "</span><span class="p">);</span>
|
||
<a id="__codelineno-10-53" name="__codelineno-10-53" href="#__codelineno-10-53"></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">"加速比: "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">t1</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">t2</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"x</span><span class="se">\n</span><span class="s">"</span><span class="p">;</span>
|
||
<a id="__codelineno-10-54" name="__codelineno-10-54" href="#__codelineno-10-54"></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-10-55" name="__codelineno-10-55" href="#__codelineno-10-55"></a><span class="p">}</span>
|
||
</code></pre></div></p>
|
||
</li>
|
||
<li>
|
||
<p>使用 <code>_mm256_max_ps</code> 实现AVX2 ReLU并与标量循环比较。然后尝试使用多累加器（循环展开）以隐藏FMA延迟。
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="c1">// task2_avx_relu.cpp</span>
|
||
<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="c1">// 编译：g++ -O3 -mavx2 -o task2 task2_avx_relu.cpp</span>
|
||
<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a>
|
||
<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><iostream></span>
|
||
<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"><chrono></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"><vector></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"><immintrin.h></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">void</span><span class="w"> </span><span class="nf">relu_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">in</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">out</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-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></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-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></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">in</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">in</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-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="p">}</span>
|
||
<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a>
|
||
<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="kt">void</span><span class="w"> </span><span class="nf">relu_avx2</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">in</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">out</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-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w"> </span><span class="n">__m256</span><span class="w"> </span><span class="n">zero</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_setzero_ps</span><span class="p">();</span>
|
||
<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w"> </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>
|
||
<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w"> </span><span class="k">for</span><span class="w"> </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">8</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="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">8</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w"> </span><span class="n">__m256</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">_mm256_loadu_ps</span><span class="p">(</span><span class="n">in</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</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="n">_mm256_storeu_ps</span><span class="p">(</span><span class="n">out</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">_mm256_max_ps</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">zero</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="p">}</span>
|
||
<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="w"> </span><span class="k">for</span><span class="w"> </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="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">in</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">in</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-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="p">}</span>
|
||
<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a>
|
||
<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="c1">// 展开：每次迭代处理32个浮点数（4 x 8）</span>
|
||
<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="kt">void</span><span class="w"> </span><span class="nf">relu_avx2_unrolled</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">in</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">out</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-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a><span class="w"> </span><span class="n">__m256</span><span class="w"> </span><span class="n">zero</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_setzero_ps</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="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>
|
||
<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a><span class="w"> </span><span class="k">for</span><span class="w"> </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">32</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="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">32</span><span class="p">)</span><span class="w"> </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">__m256</span><span class="w"> </span><span class="n">x0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_loadu_ps</span><span class="p">(</span><span class="n">in</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-11-31" name="__codelineno-11-31" href="#__codelineno-11-31"></a><span class="w"> </span><span class="n">__m256</span><span class="w"> </span><span class="n">x1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_loadu_ps</span><span class="p">(</span><span class="n">in</span><span class="w"> </span><span class="o">+</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">8</span><span class="p">);</span>
|
||
<a id="__codelineno-11-32" name="__codelineno-11-32" href="#__codelineno-11-32"></a><span class="w"> </span><span class="n">__m256</span><span class="w"> </span><span class="n">x2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_loadu_ps</span><span class="p">(</span><span class="n">in</span><span class="w"> </span><span class="o">+</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">16</span><span class="p">);</span>
|
||
<a id="__codelineno-11-33" name="__codelineno-11-33" href="#__codelineno-11-33"></a><span class="w"> </span><span class="n">__m256</span><span class="w"> </span><span class="n">x3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_mm256_loadu_ps</span><span class="p">(</span><span class="n">in</span><span class="w"> </span><span class="o">+</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">24</span><span class="p">);</span>
|
||
<a id="__codelineno-11-34" name="__codelineno-11-34" href="#__codelineno-11-34"></a><span class="w"> </span><span class="n">_mm256_storeu_ps</span><span class="p">(</span><span class="n">out</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">_mm256_max_ps</span><span class="p">(</span><span class="n">x0</span><span class="p">,</span><span class="w"> </span><span class="n">zero</span><span class="p">));</span>
|
||
<a id="__codelineno-11-35" name="__codelineno-11-35" href="#__codelineno-11-35"></a><span class="w"> </span><span class="n">_mm256_storeu_ps</span><span class="p">(</span><span class="n">out</span><span class="w"> </span><span class="o">+</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">8</span><span class="p">,</span><span class="w"> </span><span class="n">_mm256_max_ps</span><span class="p">(</span><span class="n">x1</span><span class="p">,</span><span class="w"> </span><span class="n">zero</span><span class="p">));</span>
|
||
<a id="__codelineno-11-36" name="__codelineno-11-36" href="#__codelineno-11-36"></a><span class="w"> </span><span class="n">_mm256_storeu_ps</span><span class="p">(</span><span class="n">out</span><span class="w"> </span><span class="o">+</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">16</span><span class="p">,</span><span class="w"> </span><span class="n">_mm256_max_ps</span><span class="p">(</span><span class="n">x2</span><span class="p">,</span><span class="w"> </span><span class="n">zero</span><span class="p">));</span>
|
||
<a id="__codelineno-11-37" name="__codelineno-11-37" href="#__codelineno-11-37"></a><span class="w"> </span><span class="n">_mm256_storeu_ps</span><span class="p">(</span><span class="n">out</span><span class="w"> </span><span class="o">+</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">24</span><span class="p">,</span><span class="w"> </span><span class="n">_mm256_max_ps</span><span class="p">(</span><span class="n">x3</span><span class="p">,</span><span class="w"> </span><span class="n">zero</span><span class="p">));</span>
|
||
<a id="__codelineno-11-38" name="__codelineno-11-38" href="#__codelineno-11-38"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-11-39" name="__codelineno-11-39" href="#__codelineno-11-39"></a><span class="w"> </span><span class="k">for</span><span class="w"> </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">8</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="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">8</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-11-40" name="__codelineno-11-40" href="#__codelineno-11-40"></a><span class="w"> </span><span class="n">_mm256_storeu_ps</span><span class="p">(</span><span class="n">out</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">_mm256_max_ps</span><span class="p">(</span><span class="n">_mm256_loadu_ps</span><span class="p">(</span><span class="n">in</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">zero</span><span class="p">));</span>
|
||
<a id="__codelineno-11-41" name="__codelineno-11-41" href="#__codelineno-11-41"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-11-42" name="__codelineno-11-42" href="#__codelineno-11-42"></a><span class="w"> </span><span class="k">for</span><span class="w"> </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="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">in</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">in</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-11-43" name="__codelineno-11-43" href="#__codelineno-11-43"></a><span class="p">}</span>
|
||
<a id="__codelineno-11-44" name="__codelineno-11-44" href="#__codelineno-11-44"></a>
|
||
<a id="__codelineno-11-45" name="__codelineno-11-45" href="#__codelineno-11-45"></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-11-46" name="__codelineno-11-46" href="#__codelineno-11-46"></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">16'000'000</span><span class="p">;</span>
|
||
<a id="__codelineno-11-47" name="__codelineno-11-47" href="#__codelineno-11-47"></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">in</span><span class="p">(</span><span class="n">N</span><span class="p">),</span><span class="w"> </span><span class="n">out</span><span class="p">(</span><span class="n">N</span><span class="p">);</span>
|
||
<a id="__codelineno-11-48" name="__codelineno-11-48" href="#__codelineno-11-48"></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="n">in</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="p">(</span><span class="kt">float</span><span class="p">)(</span><span class="n">i</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">200</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">100.0f</span><span class="p">;</span>
|
||
<a id="__codelineno-11-49" name="__codelineno-11-49" href="#__codelineno-11-49"></a>
|
||
<a id="__codelineno-11-50" name="__codelineno-11-50" href="#__codelineno-11-50"></a><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="n">bench</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="o">&</span><span class="p">](</span><span class="k">auto</span><span class="w"> </span><span class="n">fn</span><span class="p">,</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">char</span><span class="o">*</span><span class="w"> </span><span class="n">name</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-11-51" name="__codelineno-11-51" href="#__codelineno-11-51"></a><span class="w"> </span><span class="n">fn</span><span class="p">(</span><span class="n">in</span><span class="p">.</span><span class="n">data</span><span class="p">(),</span><span class="w"> </span><span class="n">out</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><span class="w"> </span><span class="c1">// 预热</span>
|
||
<a id="__codelineno-11-52" name="__codelineno-11-52" href="#__codelineno-11-52"></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-11-53" name="__codelineno-11-53" href="#__codelineno-11-53"></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">t</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">t</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">t</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="n">fn</span><span class="p">(</span><span class="n">in</span><span class="p">.</span><span class="n">data</span><span class="p">(),</span><span class="w"> </span><span class="n">out</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-11-54" name="__codelineno-11-54" href="#__codelineno-11-54"></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-11-55" name="__codelineno-11-55" href="#__codelineno-11-55"></a><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">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><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">100</span><span class="p">;</span>
|
||
<a id="__codelineno-11-56" name="__codelineno-11-56" href="#__codelineno-11-56"></a><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">bw</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2.0</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="n">ms</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">1e6</span><span class="p">;</span><span class="w"> </span><span class="c1">// 读取+写入</span>
|
||
<a id="__codelineno-11-57" name="__codelineno-11-57" href="#__codelineno-11-57"></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="n">name</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">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">bw</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-11-58" name="__codelineno-11-58" href="#__codelineno-11-58"></a><span class="w"> </span><span class="p">};</span>
|
||
<a id="__codelineno-11-59" name="__codelineno-11-59" href="#__codelineno-11-59"></a>
|
||
<a id="__codelineno-11-60" name="__codelineno-11-60" href="#__codelineno-11-60"></a><span class="w"> </span><span class="n">bench</span><span class="p">(</span><span class="n">relu_scalar</span><span class="p">,</span><span class="w"> </span><span class="s">"标量 "</span><span class="p">);</span>
|
||
<a id="__codelineno-11-61" name="__codelineno-11-61" href="#__codelineno-11-61"></a><span class="w"> </span><span class="n">bench</span><span class="p">(</span><span class="n">relu_avx2</span><span class="p">,</span><span class="w"> </span><span class="s">"AVX2 "</span><span class="p">);</span>
|
||
<a id="__codelineno-11-62" name="__codelineno-11-62" href="#__codelineno-11-62"></a><span class="w"> </span><span class="n">bench</span><span class="p">(</span><span class="n">relu_avx2_unrolled</span><span class="p">,</span><span class="w"> </span><span class="s">"AVX2展开 "</span><span class="p">);</span>
|
||
<a id="__codelineno-11-63" name="__codelineno-11-63" href="#__codelineno-11-63"></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-11-64" name="__codelineno-11-64" href="#__codelineno-11-64"></a><span class="p">}</span>
|
||
</code></pre></div></p>
|
||
</li>
|
||
<li>
|
||
<p>测量内存对齐的效果。比较在大数组上的对齐加载与非对齐加载。
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">// task3_alignment.cpp</span>
|
||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="c1">// 编译：g++ -O3 -mavx2 -o task3 task3_alignment.cpp</span>
|
||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a>
|
||
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><iostream></span>
|
||
<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"><chrono></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"><cstdlib></span>
|
||
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf"><immintrin.h></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="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-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></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">16'000'000</span><span class="p">;</span>
|
||
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a>
|
||
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w"> </span><span class="c1">// 对齐分配（AVX2为32字节）</span>
|
||
<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w"> </span><span class="kt">float</span><span class="o">*</span><span class="w"> </span><span class="n">aligned</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">float</span><span class="o">*</span><span class="p">)</span><span class="n">aligned_alloc</span><span class="p">(</span><span class="mi">32</span><span class="p">,</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>
|
||
<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a>
|
||
<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w"> </span><span class="c1">// 非对齐：从对齐边界偏移4字节（1个浮点数）</span>
|
||
<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w"> </span><span class="kt">float</span><span class="o">*</span><span class="w"> </span><span class="n">raw</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">float</span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">((</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="p">)</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>
|
||
<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w"> </span><span class="kt">float</span><span class="o">*</span><span class="w"> </span><span class="n">unaligned</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">raw</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 保证未对齐</span>
|
||
<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a>
|
||
<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></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-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="w"> </span><span class="n">aligned</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">1.0f</span><span class="p">;</span>
|
||
<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w"> </span><span class="n">unaligned</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">1.0f</span><span class="p">;</span>
|
||
<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a>
|
||
<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="n">bench</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="o">&</span><span class="p">](</span><span class="kt">float</span><span class="o">*</span><span class="w"> </span><span class="n">ptr</span><span class="p">,</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="n">use_aligned</span><span class="p">,</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">char</span><span class="o">*</span><span class="w"> </span><span class="n">name</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="w"> </span><span class="n">__m256</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">_mm256_setzero_ps</span><span class="p">();</span>
|
||
<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a><span class="w"> </span><span class="c1">// 预热</span>
|
||
<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></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="mi">8</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="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">8</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></a><span class="w"> </span><span class="n">__m256</span><span class="w"> </span><span class="n">v</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">use_aligned</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">_mm256_load_ps</span><span class="p">(</span><span class="n">ptr</span><span class="w"> </span><span class="o">+</span><span class="w"> </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">_mm256_loadu_ps</span><span class="p">(</span><span class="n">ptr</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></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">_mm256_add_ps</span><span class="p">(</span><span class="n">sum</span><span class="p">,</span><span class="w"> </span><span class="n">v</span><span class="p">);</span>
|
||
<a id="__codelineno-12-30" name="__codelineno-12-30" href="#__codelineno-12-30"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-12-31" name="__codelineno-12-31" href="#__codelineno-12-31"></a>
|
||
<a id="__codelineno-12-32" name="__codelineno-12-32" href="#__codelineno-12-32"></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-12-33" name="__codelineno-12-33" href="#__codelineno-12-33"></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">t</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">t</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">t</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-12-34" name="__codelineno-12-34" href="#__codelineno-12-34"></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">_mm256_setzero_ps</span><span class="p">();</span>
|
||
<a id="__codelineno-12-35" name="__codelineno-12-35" href="#__codelineno-12-35"></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="mi">8</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="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">8</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-12-36" name="__codelineno-12-36" href="#__codelineno-12-36"></a><span class="w"> </span><span class="n">__m256</span><span class="w"> </span><span class="n">v</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">use_aligned</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">_mm256_load_ps</span><span class="p">(</span><span class="n">ptr</span><span class="w"> </span><span class="o">+</span><span class="w"> </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">_mm256_loadu_ps</span><span class="p">(</span><span class="n">ptr</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-12-37" name="__codelineno-12-37" href="#__codelineno-12-37"></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">_mm256_add_ps</span><span class="p">(</span><span class="n">sum</span><span class="p">,</span><span class="w"> </span><span class="n">v</span><span class="p">);</span>
|
||
<a id="__codelineno-12-38" name="__codelineno-12-38" href="#__codelineno-12-38"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-12-39" name="__codelineno-12-39" href="#__codelineno-12-39"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-12-40" name="__codelineno-12-40" href="#__codelineno-12-40"></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-12-41" name="__codelineno-12-41" href="#__codelineno-12-41"></a><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">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><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">100</span><span class="p">;</span>
|
||
<a id="__codelineno-12-42" name="__codelineno-12-42" href="#__codelineno-12-42"></a><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">bw</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">double</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">ms</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">1e6</span><span class="p">;</span>
|
||
<a id="__codelineno-12-43" name="__codelineno-12-43" href="#__codelineno-12-43"></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="n">name</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">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">bw</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-12-44" name="__codelineno-12-44" href="#__codelineno-12-44"></a><span class="w"> </span><span class="p">};</span>
|
||
<a id="__codelineno-12-45" name="__codelineno-12-45" href="#__codelineno-12-45"></a>
|
||
<a id="__codelineno-12-46" name="__codelineno-12-46" href="#__codelineno-12-46"></a><span class="w"> </span><span class="n">bench</span><span class="p">(</span><span class="n">aligned</span><span class="p">,</span><span class="w"> </span><span class="nb">true</span><span class="p">,</span><span class="w"> </span><span class="s">"对齐加载 "</span><span class="p">);</span>
|
||
<a id="__codelineno-12-47" name="__codelineno-12-47" href="#__codelineno-12-47"></a><span class="w"> </span><span class="n">bench</span><span class="p">(</span><span class="n">unaligned</span><span class="p">,</span><span class="w"> </span><span class="nb">false</span><span class="p">,</span><span class="w"> </span><span class="s">"非对齐加载"</span><span class="p">);</span>
|
||
<a id="__codelineno-12-48" name="__codelineno-12-48" href="#__codelineno-12-48"></a>
|
||
<a id="__codelineno-12-49" name="__codelineno-12-49" href="#__codelineno-12-49"></a><span class="w"> </span><span class="n">free</span><span class="p">(</span><span class="n">aligned</span><span class="p">);</span>
|
||
<a id="__codelineno-12-50" name="__codelineno-12-50" href="#__codelineno-12-50"></a><span class="w"> </span><span class="n">free</span><span class="p">(</span><span class="n">raw</span><span class="p">);</span>
|
||
<a id="__codelineno-12-51" name="__codelineno-12-51" href="#__codelineno-12-51"></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-12-52" name="__codelineno-12-52" href="#__codelineno-12-52"></a><span class="p">}</span>
|
||
</code></pre></div></p>
|
||
</li>
|
||
</ol>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
</article>
|
||
</div>
|
||
|
||
|
||
<script>var target=document.getElementById(location.hash.slice(1));target&&target.name&&(target.checked=target.name.startsWith("__tabbed_"))</script>
|
||
</div>
|
||
|
||
<button type="button" class="md-top md-icon" data-md-component="top" hidden>
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 20h-2V8l-5.5 5.5-1.42-1.42L12 4.16l7.92 7.92-1.42 1.42L13 8z"/></svg>
|
||
回到页面顶部
|
||
</button>
|
||
|
||
</main>
|
||
|
||
<footer class="md-footer">
|
||
|
||
|
||
|
||
<nav class="md-footer__inner md-grid" aria-label="页脚" >
|
||
|
||
|
||
<a href="../02.%20ARM%20and%20NEON/" class="md-footer__link md-footer__link--prev" aria-label="上一页: ARM 与 NEON">
|
||
<div class="md-footer__button md-icon">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11z"/></svg>
|
||
</div>
|
||
<div class="md-footer__title">
|
||
<span class="md-footer__direction">
|
||
上一页
|
||
</span>
|
||
<div class="md-ellipsis">
|
||
ARM 与 NEON
|
||
</div>
|
||
</div>
|
||
</a>
|
||
|
||
|
||
|
||
<a href="../04.%20GPU%20architecture%20and%20CUDA/" class="md-footer__link md-footer__link--next" aria-label="下一页: GPU 架构与 CUDA">
|
||
<div class="md-footer__title">
|
||
<span class="md-footer__direction">
|
||
下一页
|
||
</span>
|
||
<div class="md-ellipsis">
|
||
GPU 架构与 CUDA
|
||
</div>
|
||
</div>
|
||
<div class="md-footer__button md-icon">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M4 11v2h12l-5.5 5.5 1.42 1.42L19.84 12l-7.92-7.92L10.5 5.5 16 11z"/></svg>
|
||
</div>
|
||
</a>
|
||
|
||
</nav>
|
||
|
||
|
||
<div class="md-footer-meta md-typeset">
|
||
<div class="md-footer-meta__inner md-grid">
|
||
<div class="md-copyright">
|
||
|
||
|
||
Made with
|
||
<a href="https://squidfunk.github.io/mkdocs-material/" target="_blank" rel="noopener">
|
||
Material for MkDocs
|
||
</a>
|
||
|
||
</div>
|
||
|
||
|
||
<div class="md-social">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<a href="https://github.com/flykhan/maths-cs-ai-compendium-zh" target="_blank" rel="noopener" title="github.com" class="md-social__link">
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path d="M173.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6m-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3m44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9M252.8 8C114.1 8 8 113.3 8 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C436.2 457.8 504 362.9 504 252 504 113.3 391.5 8 252.8 8M105.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1m-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7m32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1m-11.4-14.7c-1.6 1-1.6 3.6 0 5.9s4.3 3.3 5.6 2.3c1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2"/></svg>
|
||
</a>
|
||
|
||
</div>
|
||
|
||
</div>
|
||
</div>
|
||
</footer>
|
||
|
||
</div>
|
||
<div class="md-dialog" data-md-component="dialog">
|
||
<div class="md-dialog__inner md-typeset"></div>
|
||
</div>
|
||
|
||
|
||
|
||
|
||
|
||
<script id="__config" type="application/json">{"annotate": null, "base": "../..", "features": ["navigation.tabs", "navigation.sections", "navigation.expand", "navigation.top", "navigation.footer", "search.suggest", "search.highlight", "content.code.copy", "toc.follow"], "search": "../../assets/javascripts/workers/search.2c215733.min.js", "tags": null, "translations": {"clipboard.copied": "\u5df2\u590d\u5236", "clipboard.copy": "\u590d\u5236", "search.result.more.one": "\u5728\u8be5\u9875\u4e0a\u8fd8\u6709 1 \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.more.other": "\u5728\u8be5\u9875\u4e0a\u8fd8\u6709 # \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.none": "\u6ca1\u6709\u627e\u5230\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.one": "\u627e\u5230 1 \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.other": "# \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.placeholder": "\u952e\u5165\u4ee5\u5f00\u59cb\u641c\u7d22", "search.result.term.missing": "\u7f3a\u5c11", "select.version": "\u9009\u62e9\u5f53\u524d\u7248\u672c"}, "version": null}</script>
|
||
|
||
|
||
<script src="../../assets/javascripts/bundle.79ae519e.min.js"></script>
|
||
|
||
<script src="../../javascripts/mathjax.js"></script>
|
||
|
||
<script src="https://unpkg.com/mathjax@3/es5/tex-mml-chtml.js"></script>
|
||
|
||
|
||
</body>
|
||
</html> |