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<h1 id="armneon">ARM与NEON<a class="headerlink" href="#armneon" title="Permanent link">&para;</a></h1>
<p><em>ARM处理器驱动着每一部智能手机、大多数平板电脑、Apple的笔记本电脑以及日益增长的数据中心服务器份额。本文涵盖ARM架构、使用C++内联函数的NEON SIMD编程、用于可伸缩向量处理的SVE/SVE2、Apple Silicon特性以及实际向量化核函数示例</em></p>
<ul>
<li>
<p>如果你拥有iPhone、MacBook或使用AWS Graviton实例，你正在运行ARM。ARM的功耗效率使其在移动和嵌入式领域占据主导地位，并在服务器和ML推理方面日益具有竞争力。理解ARM SIMD让你能够编写在大多数人实际使用的硬件上快速运行的代码。</p>
</li>
<li>
<p>有关生产中ARM SIMD核函数的实际例子，请参见<strong>Cactus</strong>——面向移动设备和可穿戴设备的低延迟AI引擎：<a href="https://github.com/cactus-compute/cactus">github.com/cactus-compute/cactus</a>。Cactus实现了自定义ARM NEON和NPU加速的注意机制、KV缓存量化和分块预填充核函数，在ARM CPU上实现了最快的推理，且RAM比其它引擎低10倍。其三层架构（引擎→图→核函数）是本文中SIMD概念如何用于构建生产级ML基础设施的具体实例。</p>
</li>
</ul>
<h2 id="arm">ARM架构基础<a class="headerlink" href="#arm" title="Permanent link">&para;</a></h2>
<ul>
<li>
<p>ARM是一种<strong>RISC</strong>（精简指令集计算机）架构（第13章）。关键特征：</p>
<ul>
<li>
<p><strong>加载-存储架构</strong>：算术指令只操作寄存器，从不直接操作内存。要对内存中的两个数相加，你必须：(1) 将它们加载到寄存器，(2) 将寄存器相加，(3) 将结果存回内存。这比x86更简单（x86可以在一条指令中加一个寄存器和一个内存位置），但使得流水线更清晰。</p>
</li>
<li>
<p><strong>定长指令</strong>：每个ARMv8（AArch64）指令恰好32位。这使得解码快速且可预测（不像x86的可变长指令，长度可以是1-15字节）。</p>
</li>
<li>
<p><strong>32个通用寄存器</strong>（x0-x30，每个64位）加上栈指针（sp）和零寄存器（xzr）。相比之下x86有16个通用寄存器。更多寄存器 = 更少内存访问 = 更快代码。</p>
</li>
<li>
<p><strong>32个SIMD/浮点寄存器</strong>（v0-v31，每个128位）用于NEON和浮点操作。</p>
</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="c1">// ARM汇编（仅感受风格——你将使用内联函数，而非汇编）</span>
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="c1">// 两寄存器相加</span>
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="n">add</span><span class="w"> </span><span class="n">x0</span><span class="p">,</span><span class="w"> </span><span class="n">x1</span><span class="p">,</span><span class="w"> </span><span class="n">x2</span><span class="w"> </span><span class="c1">// x0 = x1 + x2</span>
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="c1">// 从内存加载</span>
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="n">ldr</span><span class="w"> </span><span class="n">x0</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="n">x1</span><span class="p">]</span><span class="w"> </span><span class="c1">// x0 = *x1（从x1中的地址加载64位）</span>
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="c1">// NEON：加四个浮点数</span>
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="n">fadd</span><span class="w"> </span><span class="n">v0</span><span class="mf">.4</span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">v1</span><span class="mf">.4</span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">v2</span><span class="mf">.4</span><span class="n">s</span><span class="w"> </span><span class="c1">// v0 = v1 + v2（四个32位浮点数）</span>
</code></pre></div>
<ul>
<li>你不会写汇编。你将使用<strong>内联函数</strong>：与特定指令一对一映射的C/C++函数。编译器处理寄存器分配、调度和其他底层细节。</li>
</ul>
<h2 id="neon128simd">NEON：128位SIMD<a class="headerlink" href="#neon128simd" title="Permanent link">&para;</a></h2>
<ul>
<li><strong>NEON</strong>是ARM的SIMD扩展。每个NEON寄存器宽128位，可容纳：</li>
</ul>
<table>
<thead>
<tr>
<th>数据类型</th>
<th>每寄存器元素数</th>
<th>表示法</th>
</tr>
</thead>
<tbody>
<tr>
<td>float32</td>
<td>4</td>
<td><code>float32x4_t</code></td>
</tr>
<tr>
<td>float16</td>
<td>8</td>
<td><code>float16x8_t</code></td>
</tr>
<tr>
<td>int32</td>
<td>4</td>
<td><code>int32x4_t</code></td>
</tr>
<tr>
<td>int16</td>
<td>8</td>
<td><code>int16x8_t</code></td>
</tr>
<tr>
<td>int8</td>
<td>16</td>
<td><code>int8x16_t</code></td>
</tr>
</tbody>
</table>
<ul>
<li>128位比x86的AVX（256位）或AVX-512（512位）窄。但ARM以出色的功耗效率和广泛的可用性弥补了这一点。</li>
</ul>
<h3 id="neon">NEON内联函数：基础<a class="headerlink" href="#neon" title="Permanent link">&para;</a></h3>
<ul>
<li>NEON内联函数遵循命名约定：<code>v[操作][限定符]_[类型]</code></li>
</ul>
<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf">&lt;arm_neon.h&gt;</span>
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a>
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="c1">// 从内存加载4个浮点数到NEON寄存器</span>
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="n">float32x4_t</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">vld1q_f32</span><span class="p">(</span><span class="n">ptr</span><span class="p">);</span><span class="w"> </span><span class="c1">// vld1q = vector load 1, q = 128位（四字）</span>
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a>
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="c1">// 从NEON寄存器存储4个浮点数到内存</span>
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="n">vst1q_f32</span><span class="p">(</span><span class="n">out_ptr</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">// vst1q = vector store 1, q = 128位</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">// 算术运算</span>
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="n">float32x4_t</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">vaddq_f32</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 = a + b（4个浮点数）</span>
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="n">float32x4_t</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">vmulq_f32</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 = a * b（4个浮点数）</span>
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="n">float32x4_t</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">vfmaq_f32</span><span class="p">(</span><span class="n">c</span><span class="p">,</span><span class="w"> </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 = c + a * b（融合乘加，4个浮点数）</span>
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a>
<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="c1">// 比较（返回掩码：若真则全1，若假则全0）</span>
<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="n">uint32x4_t</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">vcgtq_f32</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">// mask[i] = (a[i] &gt; b[i]) ? 0xFFFFFFFF : 0</span>
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a>
<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="c1">// 基于掩码选择元素（类似numpy.where）</span>
<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="n">float32x4_t</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">vbslq_f32</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="n">b</span><span class="p">);</span><span class="w"> </span><span class="c1">// result[i] = mask[i] ? a[i] : b[i]</span>
<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a>
<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="c1">// 归约：将所有4个元素求和为标量</span>
<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="kt">float</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vaddvq_f32</span><span class="p">(</span><span class="n">a</span><span class="p">);</span><span class="w"> </span><span class="c1">// total = a[0] + a[1] + a[2] + a[3]</span>
</code></pre></div>
<ul>
<li><strong><code>vfmaq_f32</code></strong>（融合乘加）是ML最重要的SIMD指令。它用一次舍入步骤计算 <span class="arithmatex">\(c = c + a \times b\)</span>（比分开乘然后加更精确）。点积、矩阵乘法和卷积都由FMA构建。</li>
</ul>
<h3 id="_1">实践示例：向量化点积<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h3>
<ul>
<li>点积是矩阵乘法的内循环。让我们先用标量C++编写，然后用NEON向量化。</li>
</ul>
<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf">&lt;arm_neon.h&gt;</span>
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a>
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="c1">// 标量点积</span>
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></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-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></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-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></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">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></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">a</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">b</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">sum</span><span class="p">;</span>
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="p">}</span>
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a>
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="c1">// NEON向量化点积</span>
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="kt">float</span><span class="w"> </span><span class="nf">dot_neon</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-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w"> </span><span class="n">float32x4_t</span><span class="w"> </span><span class="n">sum_vec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vdupq_n_f32</span><span class="p">(</span><span class="mf">0.0f</span><span class="p">);</span><span class="w"> </span><span class="c1">// 初始化4个累加器为0</span>
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a>
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w"> </span><span class="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-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></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">4</span><span class="w"> </span><span class="o">&lt;=</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">4</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w"> </span><span class="n">float32x4_t</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">vld1q_f32</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><span class="w"> </span><span class="c1">// 从a加载4个元素</span>
<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w"> </span><span class="n">float32x4_t</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">vld1q_f32</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><span class="w"> </span><span class="c1">// 从b加载4个元素</span>
<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w"> </span><span class="n">sum_vec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vfmaq_f32</span><span class="p">(</span><span class="n">sum_vec</span><span class="p">,</span><span class="w"> </span><span class="n">va</span><span class="p">,</span><span class="w"> </span><span class="n">vb</span><span class="p">);</span><span class="w"> </span><span class="c1">// sum_vec += va * vb</span>
<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a>
<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w"> </span><span class="c1">// 将4个累加器归约为单一标量</span>
<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></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="n">vaddvq_f32</span><span class="p">(</span><span class="n">sum_vec</span><span class="p">);</span>
<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a>
<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w"> </span><span class="c1">// 处理剩余元素（如果n不是4的倍数）</span>
<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></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">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></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">a</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">b</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a>
<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></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-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="p">}</span>
</code></pre></div>
<ul>
<li>
<p><strong>关键C++概念</strong>：</p>
<ul>
<li><code>const float*</code>：指向只读浮点数据的指针。<code>const</code> 承诺我们不会通过此指针修改数据。</li>
<li><code>a + i</code>：指针运算。<code>a + i</code> 指向数组的第 <span class="arithmatex">\(i\)</span> 个元素（等同于 <code>&amp;a[i]</code>）。</li>
<li>末尾的"清理循环"处理 <span class="arithmatex">\(n\)</span> 不是4的倍数的情况。这是SIMD代码中的通用模式：用向量化块处理主体部分，然后用标量代码处理余数。</li>
</ul>
</li>
<li>
<p><strong>为什么 <code>sum_vec</code> 中使用4个累加器</strong>：我们使用4个独立的累加器（每个SIMD通道一个），而不是单个标量累加器。这避免了数据依赖：每次迭代的FMA依赖于 <code>sum_vec</code>，但有了4个独立通道，CPU可以对FMAs进行流水线处理。最后，我们将4个部分和归约为一个。</p>
</li>
</ul>
<h3 id="relu">实践示例：向量化ReLU<a class="headerlink" href="#relu" title="Permanent link">&para;</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">&lt;arm_neon.h&gt;</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">void</span><span class="w"> </span><span class="nf">relu_neon</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">input</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">output</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">float32x4_t</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">vdupq_n_f32</span><span class="p">(</span><span class="mf">0.0f</span><span class="p">);</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">4</span><span class="w"> </span><span class="o">&lt;=</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">4</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">float32x4_t</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">vld1q_f32</span><span class="p">(</span><span class="n">input</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">float32x4_t</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">vmaxq_f32</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><span class="w"> </span><span class="c1">// max(x, 0) = ReLU</span>
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w"> </span><span class="n">vst1q_f32</span><span class="p">(</span><span class="n">output</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">result</span><span class="p">);</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">// 标量清理</span>
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></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">&lt;</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-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="n">output</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">input</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">input</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="p">}</span>
</code></pre></div>
<ul>
<li><code>vmaxq_f32</code> 计算两个向量的逐元素最大值。由于一个向量全为零，这恰好就是ReLU。无需分支，无需比较——仅一条指令。</li>
</ul>
<h2 id="i8mm">I8MM：整数矩阵乘法<a class="headerlink" href="#i8mm" title="Permanent link">&para;</a></h2>
<ul>
<li>
<p><strong>I8MM</strong>（Int8矩阵乘法）是ARMv8.6扩展，增加了用于INT8矩阵乘法（INT32累加）的专用指令——这正是量化ML推理所需要的。</p>
</li>
<li>
<p>关键指令是 <strong><code>SMMLA</code></strong>（有符号矩阵乘加）：它接受两个8×2块的INT8值，并将结果累加到2×2块的INT32中：</p>
</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="cp">#include</span><span class="w"> </span><span class="cpf">&lt;arm_neon.h&gt;</span>
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="c1">// I8MM：将两个8元素INT8向量相乘，累加到4个INT32结果中</span>
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="c1">// 这从2x8 × 8x2输入块计算输出矩阵的一个2x2瓦片</span>
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="kt">void</span><span class="w"> </span><span class="nf">matmul_i8mm_tile</span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="kt">int8_t</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">int8_t</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">int32_t</span><span class="o">*</span><span class="w"> </span><span class="n">C</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="c1">// 从A加载8字节（2行各4元素，打包）</span>
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w"> </span><span class="n">int8x16_t</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">vld1q_s8</span><span class="p">(</span><span class="n">A</span><span class="p">);</span><span class="w"> </span><span class="c1">// 16字节 = 2行 × 8元素</span>
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="n">int8x16_t</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">vld1q_s8</span><span class="p">(</span><span class="n">B</span><span class="p">);</span><span class="w"> </span><span class="c1">// 16字节 = 2行 × 8元素</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">// 加载现有累加器（2x2 = 4个int32值）</span>
<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w"> </span><span class="n">int32x4_t</span><span class="w"> </span><span class="n">acc</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vld1q_s32</span><span class="p">(</span><span class="n">C</span><span class="p">);</span>
<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a>
<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w"> </span><span class="c1">// I8MM指令：acc += A_tile × B_tile^T</span>
<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w"> </span><span class="c1">// 从2×8 × 8×2输入计算2×2输出</span>
<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w"> </span><span class="n">acc</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vmmlaq_s32</span><span class="p">(</span><span class="n">acc</span><span class="p">,</span><span class="w"> </span><span class="n">va</span><span class="p">,</span><span class="w"> </span><span class="n">vb</span><span class="p">);</span><span class="w"> </span><span class="c1">// I8MM指令</span>
<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a>
<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w"> </span><span class="n">vst1q_s32</span><span class="p">(</span><span class="n">C</span><span class="p">,</span><span class="w"> </span><span class="n">acc</span><span class="p">);</span>
<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="p">}</span>
</code></pre></div>
<ul>
<li>
<p><strong>为什么I8MM重要</strong>：没有I8MM时，NEON上的INT8矩阵乘法需要加宽乘法（<code>vmull</code>）后跟成对加法——每个输出元素需要多条指令。有了I8MM，硬件在一条指令中完成8元素点积（2×8 × 8×2 = 2×2）。对于INT8推理工作负载，这比纯NEON快4-8倍。</p>
</li>
<li>
<p><strong>可用性</strong>：Apple M1+（所有Apple Silicon）、ARM Cortex-A510/A710/X2+（ARMv9）、AWS Graviton3+。用 <code>#ifdef __ARM_FEATURE_MATMUL_INT8</code> 检查。</p>
</li>
<li>
<p>对于ML推理：在ARM服务器（Graviton）或Apple Silicon上运行的INT8量化模型（第18章）从I8MM中获益巨大。ONNX Runtime和llama.cpp等框架在运行时检测I8MM并自动使用优化核函数。</p>
</li>
</ul>
<h2 id="smesme2">SME和SME2：可伸缩矩阵扩展<a class="headerlink" href="#smesme2" title="Permanent link">&para;</a></h2>
<ul>
<li>
<p><strong>SME</strong>（可伸缩矩阵扩展）是ARM对Intel AMX和NVIDIA张量核心的回应：用于矩阵操作的专用硬件。SME2（ARMv9.2）进一步扩展了它。</p>
</li>
<li>
<p>SME引入了<strong>ZA瓦片寄存器</strong>：存储在硬件中的2D矩阵，最大可达SVL×SVL字节（其中SVL是流向量长度，通常每维128-512位）。与NEON（1D向量）甚至SVE（1D可伸缩向量）不同，SME原生操作<strong>2D瓦片</strong>。</p>
</li>
<li>
<p>编程模型有两种模式：</p>
<ul>
<li><strong>普通模式</strong>：标准ARM执行（NEON、SVE正常工作）。</li>
<li><strong>流SVE模式</strong>：通过 <code>smstart</code> 进入，启用SME指令。SVE指令在此模式下也可工作，但可能使用不同的寄存器宽度。</li>
</ul>
</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="cp">#include</span><span class="w"> </span><span class="cpf">&lt;arm_sme.h&gt;</span>
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="c1">// SME2：矩阵乘法的外积累加</span>
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="c1">// 将A_col × B_row 累加到ZA瓦片寄存器中</span>
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="kt">void</span><span class="w"> </span><span class="nf">sme2_matmul_outer</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_col</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_row</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">K</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w"> </span><span class="c1">// 进入流模式</span>
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w"> </span><span class="c1">// smstart; // （通过编译器内联或内联汇编完成）</span>
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a>
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w"> </span><span class="c1">// 清零ZA瓦片累加器</span>
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w"> </span><span class="n">svzero_za</span><span class="p">();</span>
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a>
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="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">k</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">k</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">K</span><span class="p">;</span><span class="w"> </span><span class="n">k</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w"> </span><span class="c1">// 将A的一列和B的一行加载到SVE寄存器中</span>
<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w"> </span><span class="n">svfloat32_t</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">svld1_f32</span><span class="p">(</span><span class="n">svptrue_b32</span><span class="p">(),</span><span class="w"> </span><span class="o">&amp;</span><span class="n">A_col</span><span class="p">[</span><span class="n">k</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">SVL</span><span class="p">]);</span>
<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w"> </span><span class="n">svfloat32_t</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">svld1_f32</span><span class="p">(</span><span class="n">svptrue_b32</span><span class="p">(),</span><span class="w"> </span><span class="o">&amp;</span><span class="n">B_row</span><span class="p">[</span><span class="n">k</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">SVL</span><span class="p">]);</span>
<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a>
<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w"> </span><span class="c1">// 外积：ZA += a × b^T</span>
<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w"> </span><span class="c1">// 这在一个指令中累加一个SVL×SVL瓦片</span>
<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w"> </span><span class="n">svmopa_za32_f32_m</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">svptrue_b32</span><span class="p">(),</span><span class="w"> </span><span class="n">svptrue_b32</span><span class="p">(),</span><span class="w"> </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">);</span>
<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a>
<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="w"> </span><span class="c1">// 将ZA瓦片存储到内存</span>
<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="w"> </span><span class="c1">// svst1_za(...);</span>
<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a>
<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="w"> </span><span class="c1">// 退出流模式</span>
<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a><span class="w"> </span><span class="c1">// smstop;</span>
<a id="__codelineno-5-27" name="__codelineno-5-27" href="#__codelineno-5-27"></a><span class="p">}</span>
</code></pre></div>
<ul>
<li>
<p><strong>关键概念</strong>：</p>
<ul>
<li><strong><code>svmopa</code></strong>（外积累加）：核心SME指令。它计算两个向量的完整外积并累加到ZA瓦片中。对于SVL=512位（16个浮点数），这是一个16×16外积——一条指令中256次FMA操作。</li>
<li><strong>ZA瓦片</strong>：在流模式中跨指令持久存在。你将多个外积（每个K迭代一个）累加到同一瓦片中，构建完整的矩阵乘法瓦片。</li>
<li><strong>流模式</strong>：SME指令仅在流模式下工作。进入/退出流模式的开销意味着SME最适合持续的矩阵计算，而非短时爆发。</li>
</ul>
</li>
<li>
<p><strong>SME2新增</strong>：多向量操作（同时处理2或4个SVE向量）、额外的瓦片操作以及与普通模式的改进集成。</p>
</li>
<li>
<p><strong>可用性</strong>：ARM Neoverse V2（AWS Graviton4）、一些即将推出的移动芯片。截至2026年尚未出现在Apple Silicon上。SME仍处于早期阶段——大多数ML框架还没有SME优化的核函数。</p>
</li>
<li>
<p><strong>演进脉络</strong>：NEON（128位向量，逐元素）→ I8MM（INT8矩阵瓦片）→ SVE（可伸缩向量）→ SME（可伸缩2D矩阵瓦片）。每一代都更接近硬件原生矩阵操作。</p>
</li>
</ul>
<h2 id="svesve2">SVE和SVE2：可伸缩向量扩展<a class="headerlink" href="#svesve2" title="Permanent link">&para;</a></h2>
<ul>
<li>NEON具有固定的128位宽度。<strong>SVE</strong>（可伸缩向量扩展）引入了<strong>向量长度无关（VLA）编程</strong>：你编写一次代码，它在任何向量宽度（128到2048位）的硬件上运行。硬件在运行时确定宽度。</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">&lt;arm_sve.h&gt;</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="kt">void</span><span class="w"> </span><span class="nf">add_sve</span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="kt">float</span><span class="o">*</span><span class="w"> </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">float</span><span class="o">*</span><span class="w"> </span><span class="n">b</span><span class="p">,</span><span class="w"> </span><span class="kt">float</span><span class="o">*</span><span class="w"> </span><span class="n">c</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></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-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w"> </span><span class="n">svbool_t</span><span class="w"> </span><span class="n">pred</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">svwhilelt_b32</span><span class="p">(</span><span class="n">i</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">// 谓词：哪些通道是激活的</span>
<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a>
<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">svptest_any</span><span class="p">(</span><span class="n">svptrue_b32</span><span class="p">(),</span><span class="w"> </span><span class="n">pred</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w"> </span><span class="n">svfloat32_t</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">svld1</span><span class="p">(</span><span class="n">pred</span><span class="p">,</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">i</span><span class="p">);</span>
<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w"> </span><span class="n">svfloat32_t</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">svld1</span><span class="p">(</span><span class="n">pred</span><span class="p">,</span><span class="w"> </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-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w"> </span><span class="n">svst1</span><span class="p">(</span><span class="n">pred</span><span class="p">,</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">i</span><span class="p">,</span><span class="w"> </span><span class="n">svadd_x</span><span class="p">(</span><span class="n">pred</span><span class="p">,</span><span class="w"> </span><span class="n">va</span><span class="p">,</span><span class="w"> </span><span class="n">vb</span><span class="p">));</span>
<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a>
<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">svcntw</span><span class="p">();</span><span class="w"> </span><span class="c1">// 按硬件向量宽度前进（以32位元素计）</span>
<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w"> </span><span class="n">pred</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">svwhilelt_b32</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="p">}</span>
</code></pre></div>
<ul>
<li>
<p><strong>谓词寄存器</strong>（<code>svbool_t</code>）取代了标量清理循环。每个通道有一个谓词位：激活的通道参与，非激活的被屏蔽。<code>svwhilelt_b32(i, n)</code> 指令创建一个谓词，其中对应 <code>i, i+1, ..., n-1</code> 的通道被激活。这自动处理了尾部。</p>
</li>
<li>
<p><strong><code>svcntw()</code></strong> 在运行时返回每个向量寄存器中32位元素的数量。在具有256位SVE的CPU上，返回8。在512位SVE上，返回16。你的代码自动适应。</p>
</li>
<li>
<p>SVE在ARM Neoverse V1/V2上可用（AWS Graviton3/4，一些服务器芯片）。在Apple Silicon上尚不可用。</p>
</li>
</ul>
<h2 id="apple-silicon">Apple Silicon特性<a class="headerlink" href="#apple-silicon" title="Permanent link">&para;</a></h2>
<ul>
<li>
<p>Apple的M系列芯片（M1、M2、M3、M4）是基于ARM的自定义微架构：</p>
</li>
<li>
<p><strong>性能核心和效率核心</strong>：P核心（Firestorm/Avalanche等）用于重型计算，E核心（Icestorm/Blizzard等）用于后台任务。调度器将线程分配给适当的核心类型。</p>
</li>
<li>
<p><strong>AMX</strong>（Apple矩阵扩展）：专用矩阵乘法单元，独立于NEON。AMX未公开（Apple不发布ISA），但Accelerate框架内部将其用于BLAS操作。当你在Mac上调用 <code>np.dot</code> 时，它通过Accelerate，后者使用AMX。你不能直接对AMX编程（除非逆向工程）。</p>
</li>
<li>
<p><strong>统一内存</strong>：CPU和GPU共享同一物理RAM。在其他系统上，数据必须从CPU内存拷贝到GPU内存（通过PCIe，约32 GB/s）。在Apple Silicon上，无需拷贝——GPU读取CPU写入的同一内存。这消除了ML工作负载的主要瓶颈。</p>
</li>
<li>
<p><strong>神经网络引擎</strong>：一个16核专用ML加速器。INT8推理时达到约30 TOPS（每秒万亿次操作）。Core ML将其用于设备端推理。</p>
</li>
<li>
<p><strong>Apple Silicon上的ML</strong>：使用MLX（Apple的ML框架），它专为统一内存架构设计。PyTorch也有MPS（Metal性能着色器）后端支持，尽管不如CUDA成熟。</p>
</li>
</ul>
<h2 id="_2">自动向量化<a class="headerlink" href="#_2" title="Permanent link">&para;</a></h2>
<ul>
<li>
<p>编写SIMD内联函数很繁琐。<strong>编译器</strong>能自动向量化你的代码吗？</p>
</li>
<li>
<p>可以的，但有限制。现代编译器（GCC、Clang）可以自动向量化简单循环：</p>
</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">// 编译器可以自动向量化此代码（使用 -O3 -march=native）</span>
<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">add_auto</span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="kt">float</span><span class="o">*</span><span class="w"> </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">float</span><span class="o">*</span><span class="w"> </span><span class="n">b</span><span class="p">,</span><span class="w"> </span><span class="kt">float</span><span class="o">*</span><span class="w"> </span><span class="n">c</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></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">&lt;</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-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w"> </span><span class="n">c</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="p">}</span>
</code></pre></div>
<ul>
<li><strong>有助于自动向量化的模式</strong>：<ul>
<li>简单的循环，迭代次数已知。</li>
<li>迭代之间无数据依赖（<code>c[i]</code> 不依赖于 <code>c[i-1]</code>）。</li>
<li>连续内存访问（无分散/聚集）。</li>
<li><code>const</code> 和 <code>restrict</code> 指针（告知编译器数组不重叠）。</li>
</ul>
</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">// restrict 告诉编译器：a、b、c 指向不重叠的内存</span>
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">add_restrict</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">__restrict__</span><span class="w"> </span><span class="n">a</span><span class="p">,</span>
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><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">__restrict__</span><span class="w"> </span><span class="n">b</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="kt">float</span><span class="o">*</span><span class="w"> </span><span class="n">__restrict__</span><span class="w"> </span><span class="n">c</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></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">&lt;</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-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w"> </span><span class="n">c</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="p">}</span>
</code></pre></div>
<ul>
<li>
<p>没有 <code>restrict</code>，编译器必须假设 <code>c</code> 可能与 <code>a</code> 或 <code>b</code> 重叠（写入 <code>c[i]</code> 可能改变 <code>a[i+1]</code>），从而阻止向量化。</p>
</li>
<li>
<p><strong>阻止自动向量化的模式</strong>：</p>
<ul>
<li>数据依赖：<code>a[i] = a[i-1] + b[i]</code>（每次迭代依赖前一次）。</li>
<li>复杂控制流：循环内的 <code>if</code> 语句（除非编译器能转换为谓词化）。</li>
<li>循环内的函数调用（除非函数被内联）。</li>
<li>指针别名（数组可能重叠，没有 <code>restrict</code>）。</li>
</ul>
</li>
<li>
<p><strong>检查自动向量化</strong>：使用编译器标志查看哪些被向量化了：</p>
</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"># GCC：显示向量化决策</span>
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>g++<span class="w"> </span>-O3<span class="w"> </span>-march<span class="o">=</span>native<span class="w"> </span>-fopt-info-vec-optimized<span class="w"> </span>code.cpp
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a>
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="c1"># Clang：显示向量化报告</span>
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a>clang++<span class="w"> </span>-O3<span class="w"> </span>-march<span class="o">=</span>native<span class="w"> </span>-Rpass<span class="o">=</span>loop-vectorize<span class="w"> </span>code.cpp
</code></pre></div>
<ul>
<li><strong>何时使用内联函数 vs 自动向量化</strong>：从干净的C++和编译器优化开始。如果编译器向量化了你的循环，很好。如果性能仍不足，检查编译器的向量化报告以理解原因，然后仅为关键内循环编写内联函数。过早使用内联函数会让代码难以阅读而没有确定的收益。</li>
</ul>
<h2 id="armgclangmac-mlinux-aarch64">编程任务（在ARM上用g++或clang++编译——Mac M系列或Linux aarch64）<a class="headerlink" href="#armgclangmac-mlinux-aarch64" title="Permanent link">&para;</a></h2>
<ol>
<li>
<p>编写标量点积和NEON向量化点积。对两者进行基准测试并测量加速比。
<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_neon_dot.cpp</span>
<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="c1">// 编译（Mac/ARM Linux）：clang++ -O3 -o task1 task1_neon_dot.cpp</span>
<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="c1">// 注意：NEON在AArch64上默认启用，无需特殊标志</span>
<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a>
<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">&lt;iostream&gt;</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">&lt;chrono&gt;</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">&lt;vector&gt;</span>
<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf">&lt;arm_neon.h&gt;</span>
<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a>
<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="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-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></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-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></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">&lt;</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-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></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">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-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></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-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="p">}</span>
<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a>
<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="kt">float</span><span class="w"> </span><span class="nf">dot_neon</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-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="w"> </span><span class="n">float32x4_t</span><span class="w"> </span><span class="n">sum_vec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vdupq_n_f32</span><span class="p">(</span><span class="mf">0.0f</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="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-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></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="mi">4</span><span class="w"> </span><span class="o">&lt;=</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">4</span><span class="p">)</span><span class="w"> </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="n">float32x4_t</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">vld1q_f32</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-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w"> </span><span class="n">float32x4_t</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">vld1q_f32</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-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="w"> </span><span class="n">sum_vec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vfmaq_f32</span><span class="p">(</span><span class="n">sum_vec</span><span class="p">,</span><span class="w"> </span><span class="n">va</span><span class="p">,</span><span class="w"> </span><span class="n">vb</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="p">}</span>
<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></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="n">vaddvq_f32</span><span class="p">(</span><span class="n">sum_vec</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="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">&lt;</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-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></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-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a><span class="p">}</span>
<a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a>
<a id="__codelineno-10-31" name="__codelineno-10-31" href="#__codelineno-10-31"></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-10-32" name="__codelineno-10-32" href="#__codelineno-10-32"></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&#39;000&#39;000</span><span class="p">;</span>
<a id="__codelineno-10-33" name="__codelineno-10-33" href="#__codelineno-10-33"></a><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">float</span><span class="o">&gt;</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-10-34" name="__codelineno-10-34" href="#__codelineno-10-34"></a>
<a id="__codelineno-10-35" name="__codelineno-10-35" href="#__codelineno-10-35"></a><span class="w"> </span><span class="c1">// 预热</span>
<a id="__codelineno-10-36" name="__codelineno-10-36" href="#__codelineno-10-36"></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-10-37" name="__codelineno-10-37" href="#__codelineno-10-37"></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_neon</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-10-38" name="__codelineno-10-38" href="#__codelineno-10-38"></a>
<a id="__codelineno-10-39" name="__codelineno-10-39" href="#__codelineno-10-39"></a><span class="w"> </span><span class="c1">// 标量基准测试</span>
<a id="__codelineno-10-40" name="__codelineno-10-40" href="#__codelineno-10-40"></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-10-41" name="__codelineno-10-41" href="#__codelineno-10-41"></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">&lt;</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-10-42" name="__codelineno-10-42" href="#__codelineno-10-42"></a><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-10-43" name="__codelineno-10-43" href="#__codelineno-10-43"></a><span class="w"> </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">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-10-45" name="__codelineno-10-45" href="#__codelineno-10-45"></a><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">scalar_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">&lt;</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">&gt;</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-10-46" name="__codelineno-10-46" href="#__codelineno-10-46"></a>
<a id="__codelineno-10-47" name="__codelineno-10-47" href="#__codelineno-10-47"></a><span class="w"> </span><span class="c1">// NEON基准测试</span>
<a id="__codelineno-10-48" name="__codelineno-10-48" href="#__codelineno-10-48"></a><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">chrono</span><span class="o">::</span><span class="n">high_resolution_clock</span><span class="o">::</span><span class="n">now</span><span class="p">();</span>
<a id="__codelineno-10-49" name="__codelineno-10-49" href="#__codelineno-10-49"></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">&lt;</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-10-50" name="__codelineno-10-50" href="#__codelineno-10-50"></a><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_neon</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-10-51" name="__codelineno-10-51" href="#__codelineno-10-51"></a><span class="w"> </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="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-10-53" name="__codelineno-10-53" href="#__codelineno-10-53"></a><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">neon_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">&lt;</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">&gt;</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-10-54" name="__codelineno-10-54" href="#__codelineno-10-54"></a>
<a id="__codelineno-10-55" name="__codelineno-10-55" href="#__codelineno-10-55"></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">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;标量: &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">scalar_ms</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot; ms（结果: &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">s1</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;）</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">;</span>
<a id="__codelineno-10-56" name="__codelineno-10-56" href="#__codelineno-10-56"></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">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;NEON: &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">neon_ms</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot; ms（结果: &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">s2</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;）</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">;</span>
<a id="__codelineno-10-57" name="__codelineno-10-57" href="#__codelineno-10-57"></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">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;加速比: &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">scalar_ms</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">neon_ms</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;x</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">;</span>
<a id="__codelineno-10-58" name="__codelineno-10-58" href="#__codelineno-10-58"></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-10-59" name="__codelineno-10-59" href="#__codelineno-10-59"></a><span class="p">}</span>
</code></pre></div></p>
</li>
<li>
<p>实现NEON ReLU和softmax最大值查找。练习使用不同操作的加载→计算→存储模式。
<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_neon_ops.cpp</span>
<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="c1">// 编译：clang++ -O3 -o task2 task2_neon_ops.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">&lt;iostream&gt;</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">&lt;vector&gt;</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">&lt;cmath&gt;</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">&lt;arm_neon.h&gt;</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_neon</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="n">float32x4_t</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">vdupq_n_f32</span><span class="p">(</span><span class="mf">0.0f</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="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-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></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">4</span><span class="w"> </span><span class="o">&lt;=</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">4</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w"> </span><span class="n">float32x4_t</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">vld1q_f32</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-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w"> </span><span class="n">vst1q_f32</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">vmaxq_f32</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-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><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="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">&lt;</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">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">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="mi">0</span><span class="p">;</span>
<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="p">}</span>
<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a>
<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="kt">float</span><span class="w"> </span><span class="nf">max_neon</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-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w"> </span><span class="n">float32x4_t</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">vdupq_n_f32</span><span class="p">(</span><span class="o">-</span><span class="n">INFINITY</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="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-11-22" 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="mi">4</span><span class="w"> </span><span class="o">&lt;=</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">4</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="w"> </span><span class="n">max_vec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vmaxq_f32</span><span class="p">(</span><span class="n">max_vec</span><span class="p">,</span><span class="w"> </span><span class="n">vld1q_f32</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-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="w"> </span><span class="kt">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">vmaxvq_f32</span><span class="p">(</span><span class="n">max_vec</span><span class="p">);</span>
<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></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">&lt;</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">result</span><span class="w"> </span><span class="o">&gt;</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-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></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-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="p">}</span>
<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a>
<a id="__codelineno-11-30" name="__codelineno-11-30" href="#__codelineno-11-30"></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-11-31" name="__codelineno-11-31" href="#__codelineno-11-31"></a><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">float</span><span class="o">&gt;</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="mi">-3</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">-1</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">-5</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">7</span><span class="p">,</span><span class="w"> </span><span class="mi">-2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</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">std</span><span class="o">::</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">float</span><span class="o">&gt;</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="n">size</span><span class="p">());</span>
<a id="__codelineno-11-33" name="__codelineno-11-33" href="#__codelineno-11-33"></a>
<a id="__codelineno-11-34" name="__codelineno-11-34" href="#__codelineno-11-34"></a><span class="w"> </span><span class="n">relu_neon</span><span class="p">(</span><span class="n">data</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">data</span><span class="p">.</span><span class="n">size</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">std</span><span class="o">::</span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;ReLU: &quot;</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="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">x</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">out</span><span class="p">)</span><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">&lt;&lt;</span><span class="w"> </span><span class="n">x</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot; &quot;</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">std</span><span class="o">::</span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">;</span>
<a id="__codelineno-11-38" name="__codelineno-11-38" href="#__codelineno-11-38"></a>
<a id="__codelineno-11-39" name="__codelineno-11-39" href="#__codelineno-11-39"></a><span class="w"> </span><span class="kt">float</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">max_neon</span><span class="p">(</span><span class="n">data</span><span class="p">.</span><span class="n">data</span><span class="p">(),</span><span class="w"> </span><span class="n">data</span><span class="p">.</span><span class="n">size</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">std</span><span class="o">::</span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;最大值: &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">mx</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;（期望值: 7）</span><span class="se">\n</span><span class="s">&quot;</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="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-11-42" name="__codelineno-11-42" href="#__codelineno-11-42"></a><span class="p">}</span>
</code></pre></div></p>
</li>
<li>
<p>比较自动向量化代码与手写NEON内联函数。用 <code>-fopt-info-vec</code>（GCC）或 <code>-Rpass=loop-vectorize</code>（Clang）编译以查看编译器的操作。
<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_auto_vs_manual.cpp</span>
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="c1">// 编译：clang++ -O3 -Rpass=loop-vectorize -o task3 task3_auto_vs_manual.cpp</span>
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="c1">// （或）：g++ -O3 -fopt-info-vec-optimized -o task3 task3_auto_vs_manual.cpp</span>
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf">&lt;iostream&gt;</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">&lt;chrono&gt;</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">&lt;vector&gt;</span>
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf">&lt;arm_neon.h&gt;</span>
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a>
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="c1">// 让编译器自动向量化</span>
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="kt">void</span><span class="w"> </span><span class="nf">add_auto</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">__restrict__</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">__restrict__</span><span class="w"> </span><span class="n">b</span><span class="p">,</span>
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w"> </span><span class="kt">float</span><span class="o">*</span><span class="w"> </span><span class="n">__restrict__</span><span class="w"> </span><span class="n">c</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></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">&lt;</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-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w"> </span><span class="n">c</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="p">}</span>
<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a>
<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="c1">// 手写NEON</span>
<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="kt">void</span><span class="w"> </span><span class="nf">add_neon</span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="kt">float</span><span class="o">*</span><span class="w"> </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">float</span><span class="o">*</span><span class="w"> </span><span class="n">b</span><span class="p">,</span><span class="w"> </span><span class="kt">float</span><span class="o">*</span><span class="w"> </span><span class="n">c</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></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-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></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="mi">4</span><span class="w"> </span><span class="o">&lt;=</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">4</span><span class="p">)</span><span class="w"> </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="n">vst1q_f32</span><span class="p">(</span><span class="n">c</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">vaddq_f32</span><span class="p">(</span><span class="n">vld1q_f32</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><span class="w"> </span><span class="n">vld1q_f32</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-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a><span class="w"> </span><span class="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">&lt;</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">c</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="p">}</span>
<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a>
<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></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-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></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&#39;000&#39;000</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">std</span><span class="o">::</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">float</span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">(</span><span class="n">N</span><span class="p">,</span><span class="w"> </span><span class="mf">1.0f</span><span class="p">),</span><span class="w"> </span><span class="n">b</span><span class="p">(</span><span class="n">N</span><span class="p">,</span><span class="w"> </span><span class="mf">2.0f</span><span class="p">),</span><span class="w"> </span><span class="n">c</span><span class="p">(</span><span class="n">N</span><span class="p">);</span>
<a id="__codelineno-12-30" name="__codelineno-12-30" href="#__codelineno-12-30"></a>
<a id="__codelineno-12-31" name="__codelineno-12-31" href="#__codelineno-12-31"></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">&amp;</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-12-32" name="__codelineno-12-32" href="#__codelineno-12-32"></a><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">c</span><span class="p">.</span><span class="n">data</span><span class="p">(),</span><span class="w"> </span><span class="n">N</span><span class="p">);</span><span class="w"> </span><span class="c1">// 预热</span>
<a id="__codelineno-12-33" name="__codelineno-12-33" href="#__codelineno-12-33"></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-12-34" name="__codelineno-12-34" href="#__codelineno-12-34"></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">&lt;</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">a</span><span class="p">.</span><span class="n">data</span><span class="p">(),</span><span class="w"> </span><span class="n">b</span><span class="p">.</span><span class="n">data</span><span class="p">(),</span><span class="w"> </span><span class="n">c</span><span class="p">.</span><span class="n">data</span><span class="p">(),</span><span class="w"> </span><span class="n">N</span><span class="p">);</span>
<a id="__codelineno-12-35" name="__codelineno-12-35" href="#__codelineno-12-35"></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-12-36" name="__codelineno-12-36" href="#__codelineno-12-36"></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">&lt;</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">&gt;</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-12-37" name="__codelineno-12-37" href="#__codelineno-12-37"></a><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">name</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;: &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">ms</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot; ms</span><span class="se">\n</span><span class="s">&quot;</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>
<a id="__codelineno-12-40" name="__codelineno-12-40" href="#__codelineno-12-40"></a><span class="w"> </span><span class="n">bench</span><span class="p">(</span><span class="n">add_auto</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;自动向量化&quot;</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="n">bench</span><span class="p">(</span><span class="n">add_neon</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;手写NEON&quot;</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="c1">// 它们应该非常接近——编译器能很好地自动向量化这个简单循环</span>
<a id="__codelineno-12-43" name="__codelineno-12-43" href="#__codelineno-12-43"></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-12-44" name="__codelineno-12-44" href="#__codelineno-12-44"></a><span class="p">}</span>
</code></pre></div></p>
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