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<div class="section" id="exercises-for-tensorir">
<h1><span class="section-number">2.5. </span>Exercises for TensorIR<a class="headerlink" href="#exercises-for-tensorir" title="Permalink to this heading">¶</a></h1>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">IPython</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">tvm</span>
<span class="kn">from</span> <span class="nn">tvm.ir.module</span> <span class="kn">import</span> <span class="n">IRModule</span>
<span class="kn">from</span> <span class="nn">tvm.script</span> <span class="kn">import</span> <span class="n">tir</span> <span class="k">as</span> <span class="n">T</span>
</pre></div>
</div>
<div class="section" id="section-1-how-to-write-tensorir">
<h2><span class="section-number">2.5.1. </span>Section 1: How to Write TensorIR<a class="headerlink" href="#section-1-how-to-write-tensorir" title="Permalink to this heading">¶</a></h2>
<p>In this section, let’s try to write TensorIR manually according to
high-level instructions (e.g., Numpy or Torch). First, we give an
example of element-wise add function, to show what should we do to write
a TensorIR function.</p>
<div class="section" id="example-element-wise-add">
<h3><span class="section-number">2.5.1.1. </span>Example: Element-wise Add<a class="headerlink" href="#example-element-wise-add" title="Permalink to this heading">¶</a></h3>
<p>First, let’s try to use Numpy to write an element-wise add function.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># init data</span>
<span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">16</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
<span class="n">b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># numpy version</span>
<span class="n">c_np</span> <span class="o">=</span> <span class="n">a</span> <span class="o">+</span> <span class="n">b</span>
<span class="n">c_np</span>
</pre></div>
</div>
<div class="output highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">array</span><span class="p">([[</span><span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">],</span>
<span class="p">[</span><span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">],</span>
<span class="p">[</span><span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">],</span>
<span class="p">[</span><span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">]])</span>
</pre></div>
</div>
<p>Before we directly write TensorIR, we should first translate high-level
computation abstraction (e.g., <code class="docutils literal notranslate"><span class="pre">ndarray</span> <span class="pre">+</span> <span class="pre">ndarray</span></code>) to low-level
python implementation (standard for loops with element access and
operation)</p>
<p>Notably, the initial value of the output array (or buffer) is not always
<code class="docutils literal notranslate"><span class="pre">0</span></code>. We need to write or initialize it in our implementation, which is
important for reduction operator (e.g. matmul and conv)</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># low-level numpy version</span>
<span class="k">def</span> <span class="nf">lnumpy_add</span><span class="p">(</span><span class="n">a</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">b</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">c</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">):</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">4</span><span class="p">):</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">4</span><span class="p">):</span>
<span class="n">c</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">+</span> <span class="n">b</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span>
<span class="n">c_lnumpy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">((</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int64</span><span class="p">)</span>
<span class="n">lnumpy_add</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c_lnumpy</span><span class="p">)</span>
<span class="n">c_lnumpy</span>
</pre></div>
</div>
<div class="output highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">array</span><span class="p">([[</span><span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">],</span>
<span class="p">[</span><span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">],</span>
<span class="p">[</span><span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">],</span>
<span class="p">[</span><span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">]])</span>
</pre></div>
</div>
<p>Now, let’s take a further step: translate low-level NumPy implementation
into TensorIR. And compare the result with it comes from NumPy.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># TensorIR version</span>
<span class="nd">@tvm</span><span class="o">.</span><span class="n">script</span><span class="o">.</span><span class="n">ir_module</span>
<span class="k">class</span> <span class="nc">MyAdd</span><span class="p">:</span>
<span class="nd">@T</span><span class="o">.</span><span class="n">prim_func</span>
<span class="k">def</span> <span class="nf">add</span><span class="p">(</span><span class="n">A</span><span class="p">:</span> <span class="n">T</span><span class="o">.</span><span class="n">Buffer</span><span class="p">((</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="s2">"int64"</span><span class="p">),</span>
<span class="n">B</span><span class="p">:</span> <span class="n">T</span><span class="o">.</span><span class="n">Buffer</span><span class="p">((</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="s2">"int64"</span><span class="p">),</span>
<span class="n">C</span><span class="p">:</span> <span class="n">T</span><span class="o">.</span><span class="n">Buffer</span><span class="p">((</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="s2">"int64"</span><span class="p">)):</span>
<span class="n">T</span><span class="o">.</span><span class="n">func_attr</span><span class="p">({</span><span class="s2">"global_symbol"</span><span class="p">:</span> <span class="s2">"add"</span><span class="p">})</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="ow">in</span> <span class="n">T</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">):</span>
<span class="k">with</span> <span class="n">T</span><span class="o">.</span><span class="n">block</span><span class="p">(</span><span class="s2">"C"</span><span class="p">):</span>
<span class="n">vi</span> <span class="o">=</span> <span class="n">T</span><span class="o">.</span><span class="n">axis</span><span class="o">.</span><span class="n">spatial</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="n">i</span><span class="p">)</span>
<span class="n">vj</span> <span class="o">=</span> <span class="n">T</span><span class="o">.</span><span class="n">axis</span><span class="o">.</span><span class="n">spatial</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="n">j</span><span class="p">)</span>
<span class="n">C</span><span class="p">[</span><span class="n">vi</span><span class="p">,</span> <span class="n">vj</span><span class="p">]</span> <span class="o">=</span> <span class="n">A</span><span class="p">[</span><span class="n">vi</span><span class="p">,</span> <span class="n">vj</span><span class="p">]</span> <span class="o">+</span> <span class="n">B</span><span class="p">[</span><span class="n">vi</span><span class="p">,</span> <span class="n">vj</span><span class="p">]</span>
<span class="n">rt_lib</span> <span class="o">=</span> <span class="n">tvm</span><span class="o">.</span><span class="n">build</span><span class="p">(</span><span class="n">MyAdd</span><span class="p">,</span> <span class="n">target</span><span class="o">=</span><span class="s2">"llvm"</span><span class="p">)</span>
<span class="n">a_tvm</span> <span class="o">=</span> <span class="n">tvm</span><span class="o">.</span><span class="n">nd</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="n">b_tvm</span> <span class="o">=</span> <span class="n">tvm</span><span class="o">.</span><span class="n">nd</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
<span class="n">c_tvm</span> <span class="o">=</span> <span class="n">tvm</span><span class="o">.</span><span class="n">nd</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">((</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int64</span><span class="p">))</span>
<span class="n">rt_lib</span><span class="p">[</span><span class="s2">"add"</span><span class="p">](</span><span class="n">a_tvm</span><span class="p">,</span> <span class="n">b_tvm</span><span class="p">,</span> <span class="n">c_tvm</span><span class="p">)</span>
<span class="n">np</span><span class="o">.</span><span class="n">testing</span><span class="o">.</span><span class="n">assert_allclose</span><span class="p">(</span><span class="n">c_tvm</span><span class="o">.</span><span class="n">numpy</span><span class="p">(),</span> <span class="n">c_np</span><span class="p">,</span> <span class="n">rtol</span><span class="o">=</span><span class="mf">1e-5</span><span class="p">)</span>
</pre></div>
</div>
<p>Here, we have finished the TensorIR function. Please take your time to
finish the following exercises</p>
</div>
<div class="section" id="exercise-1-broadcast-add">
<h3><span class="section-number">2.5.1.2. </span>Exercise 1: Broadcast Add<a class="headerlink" href="#exercise-1-broadcast-add" title="Permalink to this heading">¶</a></h3>
<p>Please write a TensorIR function that adds two arrays with broadcasting.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># init data</span>
<span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">16</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
<span class="n">b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># numpy version</span>
<span class="n">c_np</span> <span class="o">=</span> <span class="n">a</span> <span class="o">+</span> <span class="n">b</span>
<span class="n">c_np</span>
</pre></div>
</div>
<div class="output highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">array</span><span class="p">([[</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">],</span>
<span class="p">[</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">8</span><span class="p">],</span>
<span class="p">[</span><span class="mi">12</span><span class="p">,</span> <span class="mi">12</span><span class="p">,</span> <span class="mi">12</span><span class="p">,</span> <span class="mi">12</span><span class="p">],</span>
<span class="p">[</span><span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">16</span><span class="p">]])</span>
</pre></div>
</div>
<p>Please complete the following Module <code class="docutils literal notranslate"><span class="pre">MyAdd</span></code> and run the code to check
your implementation.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nd">@tvm</span><span class="o">.</span><span class="n">script</span><span class="o">.</span><span class="n">ir_module</span>
<span class="k">class</span> <span class="nc">MyAdd</span><span class="p">:</span>
<span class="nd">@T</span><span class="o">.</span><span class="n">prim_func</span>
<span class="k">def</span> <span class="nf">add</span><span class="p">():</span>
<span class="n">T</span><span class="o">.</span><span class="n">func_attr</span><span class="p">({</span><span class="s2">"global_symbol"</span><span class="p">:</span> <span class="s2">"add"</span><span class="p">,</span> <span class="s2">"tir.noalias"</span><span class="p">:</span> <span class="kc">True</span><span class="p">})</span>
<span class="c1"># TODO</span>
<span class="o">...</span>
<span class="n">rt_lib</span> <span class="o">=</span> <span class="n">tvm</span><span class="o">.</span><span class="n">build</span><span class="p">(</span><span class="n">MyAdd</span><span class="p">,</span> <span class="n">target</span><span class="o">=</span><span class="s2">"llvm"</span><span class="p">)</span>
<span class="n">a_tvm</span> <span class="o">=</span> <span class="n">tvm</span><span class="o">.</span><span class="n">nd</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="n">b_tvm</span> <span class="o">=</span> <span class="n">tvm</span><span class="o">.</span><span class="n">nd</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
<span class="n">c_tvm</span> <span class="o">=</span> <span class="n">tvm</span><span class="o">.</span><span class="n">nd</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">((</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int64</span><span class="p">))</span>
<span class="n">rt_lib</span><span class="p">[</span><span class="s2">"add"</span><span class="p">](</span><span class="n">a_tvm</span><span class="p">,</span> <span class="n">b_tvm</span><span class="p">,</span> <span class="n">c_tvm</span><span class="p">)</span>
<span class="n">np</span><span class="o">.</span><span class="n">testing</span><span class="o">.</span><span class="n">assert_allclose</span><span class="p">(</span><span class="n">c_tvm</span><span class="o">.</span><span class="n">numpy</span><span class="p">(),</span> <span class="n">c_np</span><span class="p">,</span> <span class="n">rtol</span><span class="o">=</span><span class="mf">1e-5</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="section" id="exercise-2-2d-convolution">
<h3><span class="section-number">2.5.1.3. </span>Exercise 2: 2D Convolution<a class="headerlink" href="#exercise-2-2d-convolution" title="Permalink to this heading">¶</a></h3>
<p>Then, let’s try to do something challenging: 2D convolution, which is a
common operation in image processing.</p>
<p>Here is the mathematical definition of convolution with NCHW layout:</p>
<div class="math notranslate nohighlight" id="equation-chapter-tensor-program-tensorir-exercises-0">
<span class="eqno">(2.5.1)<a class="headerlink" href="#equation-chapter-tensor-program-tensorir-exercises-0" title="Permalink to this equation">¶</a></span>\[Conv[b, k, i, j] =
\sum_{di, dj, q} A[b, q, strides * i + di, strides * j + dj] * W[k, q, di, dj]\]</div>
<p>, where, <code class="docutils literal notranslate"><span class="pre">A</span></code> is the input tensor, <code class="docutils literal notranslate"><span class="pre">W</span></code> is the weight tensor, <code class="docutils literal notranslate"><span class="pre">b</span></code> is
the batch index, <code class="docutils literal notranslate"><span class="pre">k</span></code> is the out channels, <code class="docutils literal notranslate"><span class="pre">i</span></code> and <code class="docutils literal notranslate"><span class="pre">j</span></code> are indices
for image hight and width, <code class="docutils literal notranslate"><span class="pre">di</span></code> and <code class="docutils literal notranslate"><span class="pre">dj</span></code> are the indices of the
weight, <code class="docutils literal notranslate"><span class="pre">q</span></code> is the input channel, and <code class="docutils literal notranslate"><span class="pre">strides</span></code> is the stride of the
filter window.</p>
<p>In the exercise, we pick a small and simple case with
<code class="docutils literal notranslate"><span class="pre">stride=1,</span> <span class="pre">padding=0</span></code>.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">N</span><span class="p">,</span> <span class="n">CI</span><span class="p">,</span> <span class="n">H</span><span class="p">,</span> <span class="n">W</span><span class="p">,</span> <span class="n">CO</span><span class="p">,</span> <span class="n">K</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span>
<span class="n">OUT_H</span><span class="p">,</span> <span class="n">OUT_W</span> <span class="o">=</span> <span class="n">H</span> <span class="o">-</span> <span class="n">K</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">W</span> <span class="o">-</span> <span class="n">K</span> <span class="o">+</span> <span class="mi">1</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">N</span><span class="o">*</span><span class="n">CI</span><span class="o">*</span><span class="n">H</span><span class="o">*</span><span class="n">W</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">CI</span><span class="p">,</span> <span class="n">H</span><span class="p">,</span> <span class="n">W</span><span class="p">)</span>
<span class="n">weight</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">CO</span><span class="o">*</span><span class="n">CI</span><span class="o">*</span><span class="n">K</span><span class="o">*</span><span class="n">K</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">CO</span><span class="p">,</span> <span class="n">CI</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">K</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># torch version</span>
<span class="kn">import</span> <span class="nn">torch</span>
<span class="n">data_torch</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="n">weight_torch</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">(</span><span class="n">weight</span><span class="p">)</span>
<span class="n">conv_torch</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">functional</span><span class="o">.</span><span class="n">conv2d</span><span class="p">(</span><span class="n">data_torch</span><span class="p">,</span> <span class="n">weight_torch</span><span class="p">)</span>
<span class="n">conv_torch</span> <span class="o">=</span> <span class="n">conv_torch</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">int64</span><span class="p">)</span>
<span class="n">conv_torch</span>
</pre></div>
</div>
<div class="output highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">array</span><span class="p">([[[[</span> <span class="mi">474</span><span class="p">,</span> <span class="mi">510</span><span class="p">,</span> <span class="mi">546</span><span class="p">,</span> <span class="mi">582</span><span class="p">,</span> <span class="mi">618</span><span class="p">,</span> <span class="mi">654</span><span class="p">],</span>
<span class="p">[</span> <span class="mi">762</span><span class="p">,</span> <span class="mi">798</span><span class="p">,</span> <span class="mi">834</span><span class="p">,</span> <span class="mi">870</span><span class="p">,</span> <span class="mi">906</span><span class="p">,</span> <span class="mi">942</span><span class="p">],</span>
<span class="p">[</span><span class="mi">1050</span><span class="p">,</span> <span class="mi">1086</span><span class="p">,</span> <span class="mi">1122</span><span class="p">,</span> <span class="mi">1158</span><span class="p">,</span> <span class="mi">1194</span><span class="p">,</span> <span class="mi">1230</span><span class="p">],</span>
<span class="p">[</span><span class="mi">1338</span><span class="p">,</span> <span class="mi">1374</span><span class="p">,</span> <span class="mi">1410</span><span class="p">,</span> <span class="mi">1446</span><span class="p">,</span> <span class="mi">1482</span><span class="p">,</span> <span class="mi">1518</span><span class="p">],</span>
<span class="p">[</span><span class="mi">1626</span><span class="p">,</span> <span class="mi">1662</span><span class="p">,</span> <span class="mi">1698</span><span class="p">,</span> <span class="mi">1734</span><span class="p">,</span> <span class="mi">1770</span><span class="p">,</span> <span class="mi">1806</span><span class="p">],</span>
<span class="p">[</span><span class="mi">1914</span><span class="p">,</span> <span class="mi">1950</span><span class="p">,</span> <span class="mi">1986</span><span class="p">,</span> <span class="mi">2022</span><span class="p">,</span> <span class="mi">2058</span><span class="p">,</span> <span class="mi">2094</span><span class="p">]],</span>
<span class="p">[[</span><span class="mi">1203</span><span class="p">,</span> <span class="mi">1320</span><span class="p">,</span> <span class="mi">1437</span><span class="p">,</span> <span class="mi">1554</span><span class="p">,</span> <span class="mi">1671</span><span class="p">,</span> <span class="mi">1788</span><span class="p">],</span>
<span class="p">[</span><span class="mi">2139</span><span class="p">,</span> <span class="mi">2256</span><span class="p">,</span> <span class="mi">2373</span><span class="p">,</span> <span class="mi">2490</span><span class="p">,</span> <span class="mi">2607</span><span class="p">,</span> <span class="mi">2724</span><span class="p">],</span>
<span class="p">[</span><span class="mi">3075</span><span class="p">,</span> <span class="mi">3192</span><span class="p">,</span> <span class="mi">3309</span><span class="p">,</span> <span class="mi">3426</span><span class="p">,</span> <span class="mi">3543</span><span class="p">,</span> <span class="mi">3660</span><span class="p">],</span>
<span class="p">[</span><span class="mi">4011</span><span class="p">,</span> <span class="mi">4128</span><span class="p">,</span> <span class="mi">4245</span><span class="p">,</span> <span class="mi">4362</span><span class="p">,</span> <span class="mi">4479</span><span class="p">,</span> <span class="mi">4596</span><span class="p">],</span>
<span class="p">[</span><span class="mi">4947</span><span class="p">,</span> <span class="mi">5064</span><span class="p">,</span> <span class="mi">5181</span><span class="p">,</span> <span class="mi">5298</span><span class="p">,</span> <span class="mi">5415</span><span class="p">,</span> <span class="mi">5532</span><span class="p">],</span>
<span class="p">[</span><span class="mi">5883</span><span class="p">,</span> <span class="mi">6000</span><span class="p">,</span> <span class="mi">6117</span><span class="p">,</span> <span class="mi">6234</span><span class="p">,</span> <span class="mi">6351</span><span class="p">,</span> <span class="mi">6468</span><span class="p">]]]])</span>
</pre></div>
</div>
<p>Please complete the following Module <code class="docutils literal notranslate"><span class="pre">MyConv</span></code> and run the code to
check your implementation.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nd">@tvm</span><span class="o">.</span><span class="n">script</span><span class="o">.</span><span class="n">ir_module</span>
<span class="k">class</span> <span class="nc">MyConv</span><span class="p">:</span>
<span class="nd">@T</span><span class="o">.</span><span class="n">prim_func</span>
<span class="k">def</span> <span class="nf">conv</span><span class="p">():</span>
<span class="n">T</span><span class="o">.</span><span class="n">func_attr</span><span class="p">({</span><span class="s2">"global_symbol"</span><span class="p">:</span> <span class="s2">"conv"</span><span class="p">,</span> <span class="s2">"tir.noalias"</span><span class="p">:</span> <span class="kc">True</span><span class="p">})</span>
<span class="c1"># TODO</span>
<span class="o">...</span>
<span class="n">rt_lib</span> <span class="o">=</span> <span class="n">tvm</span><span class="o">.</span><span class="n">build</span><span class="p">(</span><span class="n">MyConv</span><span class="p">,</span> <span class="n">target</span><span class="o">=</span><span class="s2">"llvm"</span><span class="p">)</span>
<span class="n">data_tvm</span> <span class="o">=</span> <span class="n">tvm</span><span class="o">.</span><span class="n">nd</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="n">weight_tvm</span> <span class="o">=</span> <span class="n">tvm</span><span class="o">.</span><span class="n">nd</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">weight</span><span class="p">)</span>
<span class="n">conv_tvm</span> <span class="o">=</span> <span class="n">tvm</span><span class="o">.</span><span class="n">nd</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">((</span><span class="n">N</span><span class="p">,</span> <span class="n">CO</span><span class="p">,</span> <span class="n">OUT_H</span><span class="p">,</span> <span class="n">OUT_W</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int64</span><span class="p">))</span>
<span class="n">rt_lib</span><span class="p">[</span><span class="s2">"conv"</span><span class="p">](</span><span class="n">data_tvm</span><span class="p">,</span> <span class="n">weight_tvm</span><span class="p">,</span> <span class="n">conv_tvm</span><span class="p">)</span>
<span class="n">np</span><span class="o">.</span><span class="n">testing</span><span class="o">.</span><span class="n">assert_allclose</span><span class="p">(</span><span class="n">conv_tvm</span><span class="o">.</span><span class="n">numpy</span><span class="p">(),</span> <span class="n">conv_torch</span><span class="p">,</span> <span class="n">rtol</span><span class="o">=</span><span class="mf">1e-5</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<div class="section" id="section-2-how-to-transform-tensorir">
<h2><span class="section-number">2.5.2. </span>Section 2: How to Transform TensorIR<a class="headerlink" href="#section-2-how-to-transform-tensorir" title="Permalink to this heading">¶</a></h2>
<p>In the lecture, we learned that TensorIR is not only a programming
language but also an abstraction for program transformation. In this
section, let’s try to transform the program. We take <code class="docutils literal notranslate"><span class="pre">bmm_relu</span></code>
(<code class="docutils literal notranslate"><span class="pre">batched_matmul_relu</span></code>) in our studies, which is a variant of
operations that common appear in models such as transformers.</p>
<div class="section" id="parallel-vectorize-and-unroll">
<h3><span class="section-number">2.5.2.1. </span>Parallel, Vectorize and Unroll<a class="headerlink" href="#parallel-vectorize-and-unroll" title="Permalink to this heading">¶</a></h3>
<p>First, we introduce some new primitives, <code class="docutils literal notranslate"><span class="pre">parallel</span></code>, <code class="docutils literal notranslate"><span class="pre">vectorize</span></code> and
<code class="docutils literal notranslate"><span class="pre">unroll</span></code>. These three primitives operate on loops to indicate how this
loop executes. Here is the example:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nd">@tvm</span><span class="o">.</span><span class="n">script</span><span class="o">.</span><span class="n">ir_module</span>
<span class="k">class</span> <span class="nc">MyAdd</span><span class="p">:</span>
<span class="nd">@T</span><span class="o">.</span><span class="n">prim_func</span>
<span class="k">def</span> <span class="nf">add</span><span class="p">(</span><span class="n">A</span><span class="p">:</span> <span class="n">T</span><span class="o">.</span><span class="n">Buffer</span><span class="p">((</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="s2">"int64"</span><span class="p">),</span>
<span class="n">B</span><span class="p">:</span> <span class="n">T</span><span class="o">.</span><span class="n">Buffer</span><span class="p">((</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="s2">"int64"</span><span class="p">),</span>
<span class="n">C</span><span class="p">:</span> <span class="n">T</span><span class="o">.</span><span class="n">Buffer</span><span class="p">((</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="s2">"int64"</span><span class="p">)):</span>
<span class="n">T</span><span class="o">.</span><span class="n">func_attr</span><span class="p">({</span><span class="s2">"global_symbol"</span><span class="p">:</span> <span class="s2">"add"</span><span class="p">})</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="ow">in</span> <span class="n">T</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">):</span>
<span class="k">with</span> <span class="n">T</span><span class="o">.</span><span class="n">block</span><span class="p">(</span><span class="s2">"C"</span><span class="p">):</span>
<span class="n">vi</span> <span class="o">=</span> <span class="n">T</span><span class="o">.</span><span class="n">axis</span><span class="o">.</span><span class="n">spatial</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="n">i</span><span class="p">)</span>
<span class="n">vj</span> <span class="o">=</span> <span class="n">T</span><span class="o">.</span><span class="n">axis</span><span class="o">.</span><span class="n">spatial</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="n">j</span><span class="p">)</span>
<span class="n">C</span><span class="p">[</span><span class="n">vi</span><span class="p">,</span> <span class="n">vj</span><span class="p">]</span> <span class="o">=</span> <span class="n">A</span><span class="p">[</span><span class="n">vi</span><span class="p">,</span> <span class="n">vj</span><span class="p">]</span> <span class="o">+</span> <span class="n">B</span><span class="p">[</span><span class="n">vi</span><span class="p">,</span> <span class="n">vj</span><span class="p">]</span>
<span class="n">sch</span> <span class="o">=</span> <span class="n">tvm</span><span class="o">.</span><span class="n">tir</span><span class="o">.</span><span class="n">Schedule</span><span class="p">(</span><span class="n">MyAdd</span><span class="p">)</span>
<span class="n">block</span> <span class="o">=</span> <span class="n">sch</span><span class="o">.</span><span class="n">get_block</span><span class="p">(</span><span class="s2">"C"</span><span class="p">,</span> <span class="n">func_name</span><span class="o">=</span><span class="s2">"add"</span><span class="p">)</span>
<span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="n">sch</span><span class="o">.</span><span class="n">get_loops</span><span class="p">(</span><span class="n">block</span><span class="p">)</span>
<span class="n">i0</span><span class="p">,</span> <span class="n">i1</span> <span class="o">=</span> <span class="n">sch</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">factors</span><span class="o">=</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
<span class="n">sch</span><span class="o">.</span><span class="n">parallel</span><span class="p">(</span><span class="n">i0</span><span class="p">)</span>
<span class="n">sch</span><span class="o">.</span><span class="n">unroll</span><span class="p">(</span><span class="n">i1</span><span class="p">)</span>
<span class="n">sch</span><span class="o">.</span><span class="n">vectorize</span><span class="p">(</span><span class="n">j</span><span class="p">)</span>
<span class="n">IPython</span><span class="o">.</span><span class="n">display</span><span class="o">.</span><span class="n">Code</span><span class="p">(</span><span class="n">sch</span><span class="o">.</span><span class="n">mod</span><span class="o">.</span><span class="n">script</span><span class="p">(),</span> <span class="n">language</span><span class="o">=</span><span class="s2">"python"</span><span class="p">)</span>
</pre></div>
</div>
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.output_html .il { color: #666666 } /* Literal.Number.Integer.Long */</style><div class="highlight"><pre><span></span><span class="c1"># from tvm.script import ir as I</span>
<span class="c1"># from tvm.script import tir as T</span>
<span class="nd">@I</span><span class="o">.</span><span class="n">ir_module</span>
<span class="k">class</span> <span class="nc">Module</span><span class="p">:</span>
<span class="nd">@T</span><span class="o">.</span><span class="n">prim_func</span>
<span class="k">def</span> <span class="nf">add</span><span class="p">(</span><span class="n">A</span><span class="p">:</span> <span class="n">T</span><span class="o">.</span><span class="n">Buffer</span><span class="p">((</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="s2">"int64"</span><span class="p">),</span> <span class="n">B</span><span class="p">:</span> <span class="n">T</span><span class="o">.</span><span class="n">Buffer</span><span class="p">((</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="s2">"int64"</span><span class="p">),</span> <span class="n">C</span><span class="p">:</span> <span class="n">T</span><span class="o">.</span><span class="n">Buffer</span><span class="p">((</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="s2">"int64"</span><span class="p">)):</span>
<span class="c1"># with T.block("root"):</span>
<span class="k">for</span> <span class="n">i_0</span> <span class="ow">in</span> <span class="n">T</span><span class="o">.</span><span class="n">parallel</span><span class="p">(</span><span class="mi">2</span><span class="p">):</span>
<span class="k">for</span> <span class="n">i_1</span> <span class="ow">in</span> <span class="n">T</span><span class="o">.</span><span class="n">unroll</span><span class="p">(</span><span class="mi">2</span><span class="p">):</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="n">T</span><span class="o">.</span><span class="n">vectorized</span><span class="p">(</span><span class="mi">4</span><span class="p">):</span>
<span class="k">with</span> <span class="n">T</span><span class="o">.</span><span class="n">block</span><span class="p">(</span><span class="s2">"C"</span><span class="p">):</span>
<span class="n">vi</span> <span class="o">=</span> <span class="n">T</span><span class="o">.</span><span class="n">axis</span><span class="o">.</span><span class="n">spatial</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="n">i_0</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">i_1</span><span class="p">)</span>
<span class="n">vj</span> <span class="o">=</span> <span class="n">T</span><span class="o">.</span><span class="n">axis</span><span class="o">.</span><span class="n">spatial</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="n">j</span><span class="p">)</span>
<span class="n">T</span><span class="o">.</span><span class="n">reads</span><span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="n">vi</span><span class="p">,</span> <span class="n">vj</span><span class="p">],</span> <span class="n">B</span><span class="p">[</span><span class="n">vi</span><span class="p">,</span> <span class="n">vj</span><span class="p">])</span>
<span class="n">T</span><span class="o">.</span><span class="n">writes</span><span class="p">(</span><span class="n">C</span><span class="p">[</span><span class="n">vi</span><span class="p">,</span> <span class="n">vj</span><span class="p">])</span>
<span class="n">C</span><span class="p">[</span><span class="n">vi</span><span class="p">,</span> <span class="n">vj</span><span class="p">]</span> <span class="o">=</span> <span class="n">A</span><span class="p">[</span><span class="n">vi</span><span class="p">,</span> <span class="n">vj</span><span class="p">]</span> <span class="o">+</span> <span class="n">B</span><span class="p">[</span><span class="n">vi</span><span class="p">,</span> <span class="n">vj</span><span class="p">]</span>
</pre></div></div>
<div class="section" id="exercise-3-transform-a-batch-matmul-program">
<h3><span class="section-number">2.5.2.2. </span>Exercise 3: Transform a batch matmul program<a class="headerlink" href="#exercise-3-transform-a-batch-matmul-program" title="Permalink to this heading">¶</a></h3>
<p>Now, let’s go back to the <code class="docutils literal notranslate"><span class="pre">bmm_relu</span></code> exercise. First, Let’s see the
definition of <code class="docutils literal notranslate"><span class="pre">bmm</span></code>:</p>
<ul class="simple">
<li><p><span class="math notranslate nohighlight">\(Y_{n, i, j} = \sum_k A_{n, i, k} \times B_{n, k, j}\)</span></p></li>
<li><p><span class="math notranslate nohighlight">\(C_{n, i, j} = \mathbb{relu}(Y_{n,i,j}) = \mathbb{max}(Y_{n, i, j}, 0)\)</span></p></li>
</ul>
<p>It’s your time to write the TensorIR for <code class="docutils literal notranslate"><span class="pre">bmm_relu</span></code>. We provide the
lnumpy func as hint:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">lnumpy_mm_relu_v2</span><span class="p">(</span><span class="n">A</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">B</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">C</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">):</span>
<span class="n">Y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">((</span><span class="mi">16</span><span class="p">,</span> <span class="mi">128</span><span class="p">,</span> <span class="mi">128</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="s2">"float32"</span><span class="p">)</span>
<span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">16</span><span class="p">):</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">128</span><span class="p">):</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">128</span><span class="p">):</span>
<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">128</span><span class="p">):</span>
<span class="k">if</span> <span class="n">k</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">Y</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">Y</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">Y</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">+</span> <span class="n">A</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">k</span><span class="p">]</span> <span class="o">*</span> <span class="n">B</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span>
<span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">16</span><span class="p">):</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">128</span><span class="p">):</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">128</span><span class="p">):</span>
<span class="n">C</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">Y</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">],</span> <span class="mi">0</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nd">@tvm</span><span class="o">.</span><span class="n">script</span><span class="o">.</span><span class="n">ir_module</span>
<span class="k">class</span> <span class="nc">MyBmmRelu</span><span class="p">:</span>
<span class="nd">@T</span><span class="o">.</span><span class="n">prim_func</span>
<span class="k">def</span> <span class="nf">bmm_relu</span><span class="p">():</span>
<span class="n">T</span><span class="o">.</span><span class="n">func_attr</span><span class="p">({</span><span class="s2">"global_symbol"</span><span class="p">:</span> <span class="s2">"bmm_relu"</span><span class="p">,</span> <span class="s2">"tir.noalias"</span><span class="p">:</span> <span class="kc">True</span><span class="p">})</span>
<span class="c1"># TODO</span>
<span class="o">...</span>
<span class="n">sch</span> <span class="o">=</span> <span class="n">tvm</span><span class="o">.</span><span class="n">tir</span><span class="o">.</span><span class="n">Schedule</span><span class="p">(</span><span class="n">MyBmmRelu</span><span class="p">)</span>
<span class="n">IPython</span><span class="o">.</span><span class="n">display</span><span class="o">.</span><span class="n">Code</span><span class="p">(</span><span class="n">sch</span><span class="o">.</span><span class="n">mod</span><span class="o">.</span><span class="n">script</span><span class="p">(),</span> <span class="n">language</span><span class="o">=</span><span class="s2">"python"</span><span class="p">)</span>
<span class="c1"># Also please validate your result</span>
</pre></div>
</div>
<p>In this exercise, let’s focus on transform the original program to a
specific target. Note that the target program may not be the best one
due to different hardware. But this exercise aims to let students
understand how to transform the program to a wanted one. Here is the
target program:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nd">@tvm</span><span class="o">.</span><span class="n">script</span><span class="o">.</span><span class="n">ir_module</span>
<span class="k">class</span> <span class="nc">TargetModule</span><span class="p">:</span>
<span class="nd">@T</span><span class="o">.</span><span class="n">prim_func</span>
<span class="k">def</span> <span class="nf">bmm_relu</span><span class="p">(</span><span class="n">A</span><span class="p">:</span> <span class="n">T</span><span class="o">.</span><span class="n">Buffer</span><span class="p">((</span><span class="mi">16</span><span class="p">,</span> <span class="mi">128</span><span class="p">,</span> <span class="mi">128</span><span class="p">),</span> <span class="s2">"float32"</span><span class="p">),</span> <span class="n">B</span><span class="p">:</span> <span class="n">T</span><span class="o">.</span><span class="n">Buffer</span><span class="p">((</span><span class="mi">16</span><span class="p">,</span> <span class="mi">128</span><span class="p">,</span> <span class="mi">128</span><span class="p">),</span> <span class="s2">"float32"</span><span class="p">),</span> <span class="n">C</span><span class="p">:</span> <span class="n">T</span><span class="o">.</span><span class="n">Buffer</span><span class="p">((</span><span class="mi">16</span><span class="p">,</span> <span class="mi">128</span><span class="p">,</span> <span class="mi">128</span><span class="p">),</span> <span class="s2">"float32"</span><span class="p">))</span> <span class="o">-></span> <span class="kc">None</span><span class="p">:</span>
<span class="n">T</span><span class="o">.</span><span class="n">func_attr</span><span class="p">({</span><span class="s2">"global_symbol"</span><span class="p">:</span> <span class="s2">"bmm_relu"</span><span class="p">,</span> <span class="s2">"tir.noalias"</span><span class="p">:</span> <span class="kc">True</span><span class="p">})</span>
<span class="n">Y</span> <span class="o">=</span> <span class="n">T</span><span class="o">.</span><span class="n">alloc_buffer</span><span class="p">([</span><span class="mi">16</span><span class="p">,</span> <span class="mi">128</span><span class="p">,</span> <span class="mi">128</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="s2">"float32"</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i0</span> <span class="ow">in</span> <span class="n">T</span><span class="o">.</span><span class="n">parallel</span><span class="p">(</span><span class="mi">16</span><span class="p">):</span>
<span class="k">for</span> <span class="n">i1</span><span class="p">,</span> <span class="n">i2_0</span> <span class="ow">in</span> <span class="n">T</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="mi">128</span><span class="p">,</span> <span class="mi">16</span><span class="p">):</span>
<span class="k">for</span> <span class="n">ax0_init</span> <span class="ow">in</span> <span class="n">T</span><span class="o">.</span><span class="n">vectorized</span><span class="p">(</span><span class="mi">8</span><span class="p">):</span>
<span class="k">with</span> <span class="n">T</span><span class="o">.</span><span class="n">block</span><span class="p">(</span><span class="s2">"Y_init"</span><span class="p">):</span>
<span class="n">n</span><span class="p">,</span> <span class="n">i</span> <span class="o">=</span> <span class="n">T</span><span class="o">.</span><span class="n">axis</span><span class="o">.</span><span class="n">remap</span><span class="p">(</span><span class="s2">"SS"</span><span class="p">,</span> <span class="p">[</span><span class="n">i0</span><span class="p">,</span> <span class="n">i1</span><span class="p">])</span>
<span class="n">j</span> <span class="o">=</span> <span class="n">T</span><span class="o">.</span><span class="n">axis</span><span class="o">.</span><span class="n">spatial</span><span class="p">(</span><span class="mi">128</span><span class="p">,</span> <span class="n">i2_0</span> <span class="o">*</span> <span class="mi">8</span> <span class="o">+</span> <span class="n">ax0_init</span><span class="p">)</span>
<span class="n">Y</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">T</span><span class="o">.</span><span class="n">float32</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="k">for</span> <span class="n">ax1_0</span> <span class="ow">in</span> <span class="n">T</span><span class="o">.</span><span class="n">serial</span><span class="p">(</span><span class="mi">32</span><span class="p">):</span>
<span class="k">for</span> <span class="n">ax1_1</span> <span class="ow">in</span> <span class="n">T</span><span class="o">.</span><span class="n">unroll</span><span class="p">(</span><span class="mi">4</span><span class="p">):</span>
<span class="k">for</span> <span class="n">ax0</span> <span class="ow">in</span> <span class="n">T</span><span class="o">.</span><span class="n">serial</span><span class="p">(</span><span class="mi">8</span><span class="p">):</span>
<span class="k">with</span> <span class="n">T</span><span class="o">.</span><span class="n">block</span><span class="p">(</span><span class="s2">"Y_update"</span><span class="p">):</span>
<span class="n">n</span><span class="p">,</span> <span class="n">i</span> <span class="o">=</span> <span class="n">T</span><span class="o">.</span><span class="n">axis</span><span class="o">.</span><span class="n">remap</span><span class="p">(</span><span class="s2">"SS"</span><span class="p">,</span> <span class="p">[</span><span class="n">i0</span><span class="p">,</span> <span class="n">i1</span><span class="p">])</span>
<span class="n">j</span> <span class="o">=</span> <span class="n">T</span><span class="o">.</span><span class="n">axis</span><span class="o">.</span><span class="n">spatial</span><span class="p">(</span><span class="mi">128</span><span class="p">,</span> <span class="n">i2_0</span> <span class="o">*</span> <span class="mi">8</span> <span class="o">+</span> <span class="n">ax0</span><span class="p">)</span>
<span class="n">k</span> <span class="o">=</span> <span class="n">T</span><span class="o">.</span><span class="n">axis</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="mi">128</span><span class="p">,</span> <span class="n">ax1_0</span> <span class="o">*</span> <span class="mi">4</span> <span class="o">+</span> <span class="n">ax1_1</span><span class="p">)</span>
<span class="n">Y</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">Y</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">+</span> <span class="n">A</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">k</span><span class="p">]</span> <span class="o">*</span> <span class="n">B</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span>
<span class="k">for</span> <span class="n">i2_1</span> <span class="ow">in</span> <span class="n">T</span><span class="o">.</span><span class="n">vectorized</span><span class="p">(</span><span class="mi">8</span><span class="p">):</span>
<span class="k">with</span> <span class="n">T</span><span class="o">.</span><span class="n">block</span><span class="p">(</span><span class="s2">"C"</span><span class="p">):</span>
<span class="n">n</span><span class="p">,</span> <span class="n">i</span> <span class="o">=</span> <span class="n">T</span><span class="o">.</span><span class="n">axis</span><span class="o">.</span><span class="n">remap</span><span class="p">(</span><span class="s2">"SS"</span><span class="p">,</span> <span class="p">[</span><span class="n">i0</span><span class="p">,</span> <span class="n">i1</span><span class="p">])</span>
<span class="n">j</span> <span class="o">=</span> <span class="n">T</span><span class="o">.</span><span class="n">axis</span><span class="o">.</span><span class="n">spatial</span><span class="p">(</span><span class="mi">128</span><span class="p">,</span> <span class="n">i2_0</span> <span class="o">*</span> <span class="mi">8</span> <span class="o">+</span> <span class="n">i2_1</span><span class="p">)</span>
<span class="n">C</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">T</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">Y</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">],</span> <span class="n">T</span><span class="o">.</span><span class="n">float32</span><span class="p">(</span><span class="mi">0</span><span class="p">))</span>
</pre></div>
</div>
<p>Your task is to transform the original program to the target program.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">sch</span> <span class="o">=</span> <span class="n">tvm</span><span class="o">.</span><span class="n">tir</span><span class="o">.</span><span class="n">Schedule</span><span class="p">(</span><span class="n">MyBmmRelu</span><span class="p">)</span>
<span class="c1"># TODO: transformations</span>
<span class="c1"># Hints: you can use</span>
<span class="c1"># `IPython.display.Code(sch.mod.script(), language="python")`</span>
<span class="c1"># or `print(sch.mod.script())`</span>
<span class="c1"># to show the current program at any time during the transformation.</span>
<span class="c1"># Step 1. Get blocks</span>
<span class="n">Y</span> <span class="o">=</span> <span class="n">sch</span><span class="o">.</span><span class="n">get_block</span><span class="p">(</span><span class="s2">"Y"</span><span class="p">,</span> <span class="n">func_name</span><span class="o">=</span><span class="s2">"bmm_relu"</span><span class="p">)</span>
<span class="o">...</span>
<span class="c1"># Step 2. Get loops</span>
<span class="n">b</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">,</span> <span class="n">k</span> <span class="o">=</span> <span class="n">sch</span><span class="o">.</span><span class="n">get_loops</span><span class="p">(</span><span class="n">Y</span><span class="p">)</span>
<span class="o">...</span>
<span class="c1"># Step 3. Organize the loops</span>
<span class="n">k0</span><span class="p">,</span> <span class="n">k1</span> <span class="o">=</span> <span class="n">sch</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="n">k</span><span class="p">,</span> <span class="o">...</span><span class="p">)</span>
<span class="n">sch</span><span class="o">.</span><span class="n">reorder</span><span class="p">(</span><span class="o">...</span><span class="p">)</span>
<span class="n">sch</span><span class="o">.</span><span class="n">compute_at</span><span class="o">/</span><span class="n">reverse_compute_at</span><span class="p">(</span><span class="o">...</span><span class="p">)</span>
<span class="o">...</span>
<span class="c1"># Step 4. decompose reduction</span>
<span class="n">Y_init</span> <span class="o">=</span> <span class="n">sch</span><span class="o">.</span><span class="n">decompose_reduction</span><span class="p">(</span><span class="n">Y</span><span class="p">,</span> <span class="o">...</span><span class="p">)</span>
<span class="o">...</span>
<span class="c1"># Step 5. vectorize / parallel / unroll</span>
<span class="n">sch</span><span class="o">.</span><span class="n">vectorize</span><span class="p">(</span><span class="o">...</span><span class="p">)</span>
<span class="n">sch</span><span class="o">.</span><span class="n">parallel</span><span class="p">(</span><span class="o">...</span><span class="p">)</span>
<span class="n">sch</span><span class="o">.</span><span class="n">unroll</span><span class="p">(</span><span class="o">...</span><span class="p">)</span>
<span class="o">...</span>
<span class="n">IPython</span><span class="o">.</span><span class="n">display</span><span class="o">.</span><span class="n">Code</span><span class="p">(</span><span class="n">sch</span><span class="o">.</span><span class="n">mod</span><span class="o">.</span><span class="n">script</span><span class="p">(),</span> <span class="n">language</span><span class="o">=</span><span class="s2">"python"</span><span class="p">)</span>
</pre></div>
</div>
<p><strong>OPTIONAL</strong> If we want to make sure the transformed program is exactly
the same as the given target, we can use <code class="docutils literal notranslate"><span class="pre">assert_structural_equal</span></code>.
Note that this step is an optional step in this exercise. It’s good
enough if you transformed the program <strong>towards</strong> the target and get
performance improvement.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">tvm</span><span class="o">.</span><span class="n">ir</span><span class="o">.</span><span class="n">assert_structural_equal</span><span class="p">(</span><span class="n">sch</span><span class="o">.</span><span class="n">mod</span><span class="p">,</span> <span class="n">TargetModule</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Pass"</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="section" id="build-and-evaluate">
<h3><span class="section-number">2.5.2.3. </span>Build and Evaluate<a class="headerlink" href="#build-and-evaluate" title="Permalink to this heading">¶</a></h3>
<p>Finally we can evaluate the performance of the transformed program.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">before_rt_lib</span> <span class="o">=</span> <span class="n">tvm</span><span class="o">.</span><span class="n">build</span><span class="p">(</span><span class="n">MyBmmRelu</span><span class="p">,</span> <span class="n">target</span><span class="o">=</span><span class="s2">"llvm"</span><span class="p">)</span>
<span class="n">after_rt_lib</span> <span class="o">=</span> <span class="n">tvm</span><span class="o">.</span><span class="n">build</span><span class="p">(</span><span class="n">sch</span><span class="o">.</span><span class="n">mod</span><span class="p">,</span> <span class="n">target</span><span class="o">=</span><span class="s2">"llvm"</span><span class="p">)</span>
<span class="n">a_tvm</span> <span class="o">=</span> <span class="n">tvm</span><span class="o">.</span><span class="n">nd</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="mi">128</span><span class="p">,</span> <span class="mi">128</span><span class="p">)</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="s2">"float32"</span><span class="p">))</span>
<span class="n">b_tvm</span> <span class="o">=</span> <span class="n">tvm</span><span class="o">.</span><span class="n">nd</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="mi">128</span><span class="p">,</span> <span class="mi">128</span><span class="p">)</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="s2">"float32"</span><span class="p">))</span>
<span class="n">c_tvm</span> <span class="o">=</span> <span class="n">tvm</span><span class="o">.</span><span class="n">nd</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="mi">128</span><span class="p">,</span> <span class="mi">128</span><span class="p">)</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="s2">"float32"</span><span class="p">))</span>
<span class="n">after_rt_lib</span><span class="p">[</span><span class="s2">"bmm_relu"</span><span class="p">](</span><span class="n">a_tvm</span><span class="p">,</span> <span class="n">b_tvm</span><span class="p">,</span> <span class="n">c_tvm</span><span class="p">)</span>
<span class="n">before_timer</span> <span class="o">=</span> <span class="n">before_rt_lib</span><span class="o">.</span><span class="n">time_evaluator</span><span class="p">(</span><span class="s2">"bmm_relu"</span><span class="p">,</span> <span class="n">tvm</span><span class="o">.</span><span class="n">cpu</span><span class="p">())</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Before transformation:"</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">before_timer</span><span class="p">(</span><span class="n">a_tvm</span><span class="p">,</span> <span class="n">b_tvm</span><span class="p">,</span> <span class="n">c_tvm</span><span class="p">))</span>
<span class="n">f_timer</span> <span class="o">=</span> <span class="n">after_rt_lib</span><span class="o">.</span><span class="n">time_evaluator</span><span class="p">(</span><span class="s2">"bmm_relu"</span><span class="p">,</span> <span class="n">tvm</span><span class="o">.</span><span class="n">cpu</span><span class="p">())</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"After transformation:"</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">f_timer</span><span class="p">(</span><span class="n">a_tvm</span><span class="p">,</span> <span class="n">b_tvm</span><span class="p">,</span> <span class="n">c_tvm</span><span class="p">))</span>
</pre></div>
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<ul>
<li><a class="reference internal" href="#">2.5. Exercises for TensorIR</a><ul>
<li><a class="reference internal" href="#section-1-how-to-write-tensorir">2.5.1. Section 1: How to Write TensorIR</a><ul>
<li><a class="reference internal" href="#example-element-wise-add">2.5.1.1. Example: Element-wise Add</a></li>
<li><a class="reference internal" href="#exercise-1-broadcast-add">2.5.1.2. Exercise 1: Broadcast Add</a></li>
<li><a class="reference internal" href="#exercise-2-2d-convolution">2.5.1.3. Exercise 2: 2D Convolution</a></li>
</ul>
</li>
<li><a class="reference internal" href="#section-2-how-to-transform-tensorir">2.5.2. Section 2: How to Transform TensorIR</a><ul>
<li><a class="reference internal" href="#parallel-vectorize-and-unroll">2.5.2.1. Parallel, Vectorize and Unroll</a></li>
<li><a class="reference internal" href="#exercise-3-transform-a-batch-matmul-program">2.5.2.2. Exercise 3: Transform a batch matmul program</a></li>
<li><a class="reference internal" href="#build-and-evaluate">2.5.2.3. Build and Evaluate</a></li>
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