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<li class="toctree-l2 current"><a class="current reference internal" href="#">Matrix Multiplication</a><ul>
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<div class="sphx-glr-example-title section" id="matrix-multiplication">
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<span id="sphx-glr-getting-started-tutorials-03-matrix-multiplication-py"></span><h1>Matrix Multiplication<a class="headerlink" href="#matrix-multiplication" title="Permalink to this headline">¶</a></h1>
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<p>In this tutorial, you will write a 25-lines high-performance FP16 matrix multiplication
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kernel that achieves performance on par with cuBLAS.
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You will specifically learn about:</p>
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<ul class="simple">
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<li><p>Block-level matrix multiplications</p></li>
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<li><p>Multi-dimensional pointer arithmetic</p></li>
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<li><p>Program re-ordering for improved L2 cache hit rate</p></li>
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<li><p>Automatic performance tuning</p></li>
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</ul>
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<div class="section" id="motivations">
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<h2>Motivations<a class="headerlink" href="#motivations" title="Permalink to this headline">¶</a></h2>
|
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<p>Matrix multiplications are a key building block of most modern high-performance computing systems.
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They are notoriously hard to optimize, hence their implementation is generally done by
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hardware vendors themselves as part of so-called “kernel libraries” (e.g., cuBLAS).
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Unfortunately, these libraries are often proprietary and cannot be easily customized
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to accomodate the needs of modern deep learning workloads (e.g., fused activation functions).
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In this tutorial, you will learn how to implement efficient matrix multiplications by
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yourself with Triton, in a way that is easy to customize and extend.</p>
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<p>Roughly speaking, the kernel that we will write will implement the following blocked
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algorithm to multiply a (MxK) by a (KxN) matrix:</p>
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<blockquote>
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<div><div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># do in parallel</span>
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<span class="k">for</span> <span class="n">m</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">M</span><span class="p">,</span> <span class="n">BLOCK_SIZE_M</span><span class="p">):</span>
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<span class="c1"># do in parallel</span>
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<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">0</span><span class="p">,</span> <span class="n">N</span><span class="p">,</span> <span class="n">BLOCK_SIZE_N</span><span class="p">):</span>
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<span class="n">acc</span> <span class="o">=</span> <span class="n">zeros</span><span class="p">((</span><span class="n">BLOCK_SIZE_M</span><span class="p">,</span> <span class="n">BLOCK_SIZE_N</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">float32</span><span class="p">)</span>
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<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">0</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">BLOCK_SIZE_K</span><span class="p">):</span>
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<span class="n">a</span> <span class="o">=</span> <span class="n">A</span><span class="p">[</span><span class="n">m</span> <span class="p">:</span> <span class="n">m</span><span class="o">+</span><span class="n">BLOCK_SIZE_M</span><span class="p">,</span> <span class="n">k</span> <span class="p">:</span> <span class="n">k</span><span class="o">+</span><span class="n">BLOCK_SIZE_K</span><span class="p">]</span>
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||
<span class="n">b</span> <span class="o">=</span> <span class="n">B</span><span class="p">[</span><span class="n">k</span> <span class="p">:</span> <span class="n">k</span><span class="o">+</span><span class="n">BLOCK_SIZE_K</span><span class="p">,</span> <span class="n">n</span> <span class="p">:</span> <span class="n">n</span><span class="o">+</span><span class="n">BLOCK_SIZE_N</span><span class="p">]</span>
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||
<span class="n">acc</span> <span class="o">+=</span> <span class="n">dot</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
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||
<span class="n">C</span><span class="p">[</span><span class="n">m</span> <span class="p">:</span> <span class="n">m</span><span class="o">+</span><span class="n">BLOCK_SIZE_M</span><span class="p">,</span> <span class="n">n</span> <span class="p">:</span> <span class="n">n</span><span class="o">+</span><span class="n">BLOCK_SIZE_N</span><span class="p">]</span> <span class="o">=</span> <span class="n">acc</span><span class="p">;</span>
|
||
</pre></div>
|
||
</div>
|
||
</div></blockquote>
|
||
<p>where each iteration of the doubly-nested for-loop corresponds to a Triton program instance.</p>
|
||
</div>
|
||
<div class="section" id="compute-kernel">
|
||
<h2>Compute Kernel<a class="headerlink" href="#compute-kernel" title="Permalink to this headline">¶</a></h2>
|
||
<p>The above algorithm is, actually, fairly straightforward to implement in Triton.
|
||
The main difficulty comes from the computation of the memory locations at which blocks
|
||
of <code class="code docutils literal notranslate"><span class="pre">A</span></code> and <code class="code docutils literal notranslate"><span class="pre">B</span></code> must be read in the inner loop. For that, we need
|
||
multi-dimensional pointer arithmetics.</p>
|
||
<div class="section" id="pointer-arithmetics">
|
||
<h3>Pointer Arithmetics<a class="headerlink" href="#pointer-arithmetics" title="Permalink to this headline">¶</a></h3>
|
||
<p>For a row-major 2D tensor <code class="code docutils literal notranslate"><span class="pre">X</span></code>, the memory location of <code class="code docutils literal notranslate"><span class="pre">X[i,</span> <span class="pre">j]</span></code> is given b
|
||
y <code class="code docutils literal notranslate"><span class="pre">&X[i,</span> <span class="pre">j]</span> <span class="pre">=</span> <span class="pre">X</span> <span class="pre">+</span> <span class="pre">i*stride_x_0</span> <span class="pre">+</span> <span class="pre">j*stride_x_1</span></code>.
|
||
Therefore, blocks of pointers for <code class="code docutils literal notranslate"><span class="pre">A[m</span> <span class="pre">:</span> <span class="pre">m+BLOCK_SIZE_M,</span> <span class="pre">k:k+BLOCK_SIZE_K]</span></code> and
|
||
<code class="code docutils literal notranslate"><span class="pre">B[k</span> <span class="pre">:</span> <span class="pre">k+BLOCK_SIZE_K,</span> <span class="pre">n</span> <span class="pre">:</span> <span class="pre">n+BLOCK_SIZE_N]</span></code> can be defined in pseudo-code as:</p>
|
||
<blockquote>
|
||
<div><div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="o">&</span><span class="n">A</span><span class="p">[</span><span class="n">m</span> <span class="p">:</span> <span class="n">m</span><span class="o">+</span><span class="n">BLOCK_SIZE_M</span><span class="p">,</span> <span class="n">k</span><span class="p">:</span><span class="n">k</span><span class="o">+</span><span class="n">BLOCK_SIZE_K</span><span class="p">]</span> <span class="o">=</span> <span class="n">A</span> <span class="o">+</span> <span class="p">(</span><span class="n">m</span> <span class="p">:</span> <span class="n">m</span><span class="o">+</span><span class="n">BLOCK_SIZE_M</span><span class="p">)[:,</span> <span class="kc">None</span><span class="p">]</span><span class="o">*</span><span class="n">A</span><span class="o">.</span><span class="n">stride</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span> <span class="o">+</span> <span class="p">(</span><span class="n">k</span> <span class="p">:</span> <span class="n">k</span><span class="o">+</span><span class="n">BLOCK_SIZE_K</span><span class="p">)[</span><span class="kc">None</span><span class="p">,</span> <span class="p">:]</span><span class="o">*</span><span class="n">A</span><span class="o">.</span><span class="n">stride</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
|
||
<span class="o">&</span><span class="n">B</span><span class="p">[</span><span class="n">k</span> <span class="p">:</span> <span class="n">k</span><span class="o">+</span><span class="n">BLOCK_SIZE_K</span><span class="p">,</span> <span class="n">n</span><span class="p">:</span><span class="n">n</span><span class="o">+</span><span class="n">BLOCK_SIZE_N</span><span class="p">]</span> <span class="o">=</span> <span class="n">B</span> <span class="o">+</span> <span class="p">(</span><span class="n">k</span> <span class="p">:</span> <span class="n">k</span><span class="o">+</span><span class="n">BLOCK_SIZE_K</span><span class="p">)[:,</span> <span class="kc">None</span><span class="p">]</span><span class="o">*</span><span class="n">B</span><span class="o">.</span><span class="n">stride</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span> <span class="o">+</span> <span class="p">(</span><span class="n">n</span> <span class="p">:</span> <span class="n">n</span><span class="o">+</span><span class="n">BLOCK_SIZE_N</span><span class="p">)[</span><span class="kc">None</span><span class="p">,</span> <span class="p">:]</span><span class="o">*</span><span class="n">B</span><span class="o">.</span><span class="n">stride</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
|
||
</pre></div>
|
||
</div>
|
||
</div></blockquote>
|
||
<p>Which means that pointers for blocks of A and B can be initialized (i.e., <code class="code docutils literal notranslate"><span class="pre">k=0</span></code>) in Triton as:</p>
|
||
<blockquote>
|
||
<div><div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">pid_m</span> <span class="o">=</span> <span class="n">triton</span><span class="o">.</span><span class="n">program_id</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||
<span class="n">pid_n</span> <span class="o">=</span> <span class="n">triton</span><span class="o">.</span><span class="n">program_id</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
|
||
<span class="n">rm</span> <span class="o">=</span> <span class="n">pid_m</span> <span class="o">*</span> <span class="n">BLOCK_SIZE_M</span> <span class="o">+</span> <span class="n">triton</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">BLOCK_SIZE_M</span><span class="p">)</span>
|
||
<span class="n">rn</span> <span class="o">=</span> <span class="n">pid_n</span> <span class="o">*</span> <span class="n">BLOCK_SIZE_N</span> <span class="o">+</span> <span class="n">triton</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">BLOCK_SIZE_N</span><span class="p">)</span>
|
||
<span class="n">rk</span> <span class="o">=</span> <span class="n">triton</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">BLOCK_SIZE_K</span><span class="p">)</span>
|
||
<span class="o">//</span> <span class="n">pointer</span> <span class="k">for</span> <span class="n">A</span> <span class="n">operand</span>
|
||
<span class="n">pa</span> <span class="o">=</span> <span class="n">A</span> <span class="o">+</span> <span class="p">(</span><span class="n">rm</span><span class="p">[:,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">*</span> <span class="n">stride_a_0</span> <span class="o">+</span> <span class="n">rk</span><span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="n">stride_a_1</span><span class="p">);</span>
|
||
<span class="o">//</span> <span class="n">pointer</span> <span class="k">for</span> <span class="n">B</span> <span class="n">operand</span>
|
||
<span class="n">pb</span> <span class="o">=</span> <span class="n">B</span> <span class="o">+</span> <span class="p">(</span><span class="n">rk</span><span class="p">[:,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">*</span> <span class="n">stride_b_0</span> <span class="o">+</span> <span class="n">rn</span><span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="n">stride_b_1</span><span class="p">);</span>
|
||
</pre></div>
|
||
</div>
|
||
</div></blockquote>
|
||
<p>And then updated in the inner loop as follows:</p>
|
||
<blockquote>
|
||
<div><div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">pa</span> <span class="o">+=</span> <span class="n">BLOCK_SIZE_K</span> <span class="o">*</span> <span class="n">stride_a_1</span><span class="p">;</span>
|
||
<span class="n">pb</span> <span class="o">+=</span> <span class="n">BLOCK_SIZE_K</span> <span class="o">*</span> <span class="n">stride_b_0</span><span class="p">;</span>
|
||
</pre></div>
|
||
</div>
|
||
</div></blockquote>
|
||
</div>
|
||
<div class="section" id="l2-cache-optimizations">
|
||
<h3>L2 Cache Optimizations<a class="headerlink" href="#l2-cache-optimizations" title="Permalink to this headline">¶</a></h3>
|
||
<p>As mentioned above, each program instance computes a <code class="code docutils literal notranslate"><span class="pre">[BLOCK_SIZE_M,</span> <span class="pre">BLOCK_SIZE_N]</span></code>
|
||
block of <code class="code docutils literal notranslate"><span class="pre">C</span></code>.
|
||
It is important to remember that the order in which these blocks are computed does
|
||
matter, since it affects the L2 cache hit rate of our program. and unfortunately, a
|
||
a simple row-major ordering</p>
|
||
<blockquote>
|
||
<div><div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">pid</span> <span class="o">=</span> <span class="n">triton</span><span class="o">.</span><span class="n">program_id</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
|
||
<span class="n">grid_m</span> <span class="o">=</span> <span class="p">(</span><span class="n">M</span> <span class="o">+</span> <span class="n">BLOCK_SIZE_M</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">//</span> <span class="n">BLOCK_SIZE_M</span><span class="p">;</span>
|
||
<span class="n">grid_n</span> <span class="o">=</span> <span class="p">(</span><span class="n">N</span> <span class="o">+</span> <span class="n">BLOCK_SIZE_N</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">//</span> <span class="n">BLOCK_SIZE_N</span><span class="p">;</span>
|
||
<span class="n">pid_m</span> <span class="o">=</span> <span class="n">pid</span> <span class="o">/</span> <span class="n">grid_n</span><span class="p">;</span>
|
||
<span class="n">pid_n</span> <span class="o">=</span> <span class="n">pid</span> <span class="o">%</span> <span class="n">grid_n</span><span class="p">;</span>
|
||
</pre></div>
|
||
</div>
|
||
</div></blockquote>
|
||
<p>is just not going to cut it.</p>
|
||
<p>One possible solution is to launch blocks in an order that promotes data reuse.
|
||
This can be done by ‘super-grouping’ blocks in groups of <code class="code docutils literal notranslate"><span class="pre">GROUP_M</span></code> rows before
|
||
switching to the next column:</p>
|
||
<blockquote>
|
||
<div><div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">pid</span> <span class="o">=</span> <span class="n">triton</span><span class="o">.</span><span class="n">program_id</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
|
||
<span class="n">width</span> <span class="o">=</span> <span class="n">GROUP_M</span> <span class="o">*</span> <span class="n">grid_n</span><span class="p">;</span>
|
||
<span class="n">group_id</span> <span class="o">=</span> <span class="n">pid</span> <span class="o">//</span> <span class="n">width</span><span class="p">;</span>
|
||
<span class="c1"># we need to handle the case where M % (GROUP_M*BLOCK_SIZE_M) != 0</span>
|
||
<span class="n">group_size</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">grid_m</span> <span class="o">-</span> <span class="n">group_id</span> <span class="o">*</span> <span class="n">GROUP_M</span><span class="p">,</span> <span class="n">GROUP_M</span><span class="p">);</span>
|
||
<span class="n">pid_m</span> <span class="o">=</span> <span class="n">group_id</span> <span class="o">*</span> <span class="n">GROUP_M</span> <span class="o">+</span> <span class="p">(</span><span class="n">pid</span> <span class="o">%</span> <span class="n">group_size</span><span class="p">);</span>
|
||
<span class="n">pid_n</span> <span class="o">=</span> <span class="p">(</span><span class="n">pid</span> <span class="o">%</span> <span class="n">width</span><span class="p">)</span> <span class="o">//</span> <span class="p">(</span><span class="n">group_size</span><span class="p">);</span>
|
||
</pre></div>
|
||
</div>
|
||
</div></blockquote>
|
||
<p>For example, in the following matmul where each matrix is 9 blocks by 9 blocks,
|
||
we can see that if we compute the output in row-major ordering, we need to load 90
|
||
blocks into SRAM to compute the first 9 output blocks, but if we do it in grouped
|
||
ordering, we only need to load 54 blocks.</p>
|
||
<blockquote>
|
||
<div><img alt="../../_images/grouped_vs_row_major_ordering.png" src="../../_images/grouped_vs_row_major_ordering.png" />
|
||
</div></blockquote>
|
||
<p>In practice, this can improve the performance of our matrix multiplication kernel by
|
||
more than 10% on some hardware architecture (e.g., 220 to 245 TFLOPS on A100).</p>
|
||
</div>
|
||
</div>
|
||
<div class="section" id="final-result">
|
||
<h2>Final Result<a class="headerlink" href="#final-result" title="Permalink to this headline">¶</a></h2>
|
||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">torch</span>
|
||
<span class="kn">import</span> <span class="nn">triton</span>
|
||
<span class="kn">import</span> <span class="nn">triton.language</span> <span class="k">as</span> <span class="nn">tl</span>
|
||
|
||
<span class="c1"># %</span>
|
||
<span class="c1"># :code:`triton.jit`'ed functions can be auto-tuned by using the `triton.autotune`</span>
|
||
<span class="c1"># decorator, which consumes:</span>
|
||
<span class="c1"># - A list of :code:`triton.Config` objects that define different configurations of</span>
|
||
<span class="c1"># meta-parameters (e.g., BLOCK_SIZE_M) and compilation options (e.g., num_warps) to try</span>
|
||
<span class="c1"># - An autotuning *key* whose change in values will trigger evaluation of all the</span>
|
||
<span class="c1"># provided configs</span>
|
||
|
||
<span class="nd">@triton</span><span class="o">.</span><span class="n">autotune</span><span class="p">(</span>
|
||
<span class="n">configs</span><span class="o">=</span><span class="p">[</span>
|
||
<span class="n">triton</span><span class="o">.</span><span class="n">Config</span><span class="p">({</span><span class="s1">'BLOCK_SIZE_M'</span><span class="p">:</span> <span class="mi">128</span><span class="p">,</span> <span class="s1">'BLOCK_SIZE_N'</span><span class="p">:</span> <span class="mi">256</span><span class="p">,</span> <span class="s1">'BLOCK_SIZE_K'</span><span class="p">:</span> <span class="mi">32</span><span class="p">,</span> <span class="s1">'GROUP_SIZE_M'</span><span class="p">:</span> <span class="mi">8</span><span class="p">},</span> <span class="n">num_stages</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">num_warps</span><span class="o">=</span><span class="mi">8</span><span class="p">),</span>
|
||
<span class="n">triton</span><span class="o">.</span><span class="n">Config</span><span class="p">({</span><span class="s1">'BLOCK_SIZE_M'</span><span class="p">:</span> <span class="mi">256</span><span class="p">,</span> <span class="s1">'BLOCK_SIZE_N'</span><span class="p">:</span> <span class="mi">128</span><span class="p">,</span> <span class="s1">'BLOCK_SIZE_K'</span><span class="p">:</span> <span class="mi">32</span><span class="p">,</span> <span class="s1">'GROUP_SIZE_M'</span><span class="p">:</span> <span class="mi">8</span><span class="p">},</span> <span class="n">num_stages</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">num_warps</span><span class="o">=</span><span class="mi">8</span><span class="p">),</span>
|
||
<span class="n">triton</span><span class="o">.</span><span class="n">Config</span><span class="p">({</span><span class="s1">'BLOCK_SIZE_M'</span><span class="p">:</span> <span class="mi">256</span><span class="p">,</span> <span class="s1">'BLOCK_SIZE_N'</span><span class="p">:</span> <span class="mi">64</span><span class="p">,</span> <span class="s1">'BLOCK_SIZE_K'</span><span class="p">:</span> <span class="mi">32</span><span class="p">,</span> <span class="s1">'GROUP_SIZE_M'</span><span class="p">:</span> <span class="mi">8</span><span class="p">},</span> <span class="n">num_stages</span><span class="o">=</span><span class="mi">4</span><span class="p">,</span> <span class="n">num_warps</span><span class="o">=</span><span class="mi">4</span><span class="p">),</span>
|
||
<span class="n">triton</span><span class="o">.</span><span class="n">Config</span><span class="p">({</span><span class="s1">'BLOCK_SIZE_M'</span><span class="p">:</span> <span class="mi">64</span> <span class="p">,</span> <span class="s1">'BLOCK_SIZE_N'</span><span class="p">:</span> <span class="mi">256</span><span class="p">,</span> <span class="s1">'BLOCK_SIZE_K'</span><span class="p">:</span> <span class="mi">32</span><span class="p">,</span> <span class="s1">'GROUP_SIZE_M'</span><span class="p">:</span> <span class="mi">8</span><span class="p">},</span> <span class="n">num_stages</span><span class="o">=</span><span class="mi">4</span><span class="p">,</span> <span class="n">num_warps</span><span class="o">=</span><span class="mi">4</span><span class="p">),</span>
|
||
<span class="n">triton</span><span class="o">.</span><span class="n">Config</span><span class="p">({</span><span class="s1">'BLOCK_SIZE_M'</span><span class="p">:</span> <span class="mi">128</span><span class="p">,</span> <span class="s1">'BLOCK_SIZE_N'</span><span class="p">:</span> <span class="mi">128</span><span class="p">,</span> <span class="s1">'BLOCK_SIZE_K'</span><span class="p">:</span> <span class="mi">32</span><span class="p">,</span> <span class="s1">'GROUP_SIZE_M'</span><span class="p">:</span> <span class="mi">8</span><span class="p">},</span> <span class="n">num_stages</span><span class="o">=</span><span class="mi">4</span><span class="p">,</span> <span class="n">num_warps</span><span class="o">=</span><span class="mi">4</span><span class="p">),</span>
|
||
<span class="n">triton</span><span class="o">.</span><span class="n">Config</span><span class="p">({</span><span class="s1">'BLOCK_SIZE_M'</span><span class="p">:</span> <span class="mi">128</span><span class="p">,</span> <span class="s1">'BLOCK_SIZE_N'</span><span class="p">:</span> <span class="mi">64</span> <span class="p">,</span> <span class="s1">'BLOCK_SIZE_K'</span><span class="p">:</span> <span class="mi">32</span><span class="p">,</span> <span class="s1">'GROUP_SIZE_M'</span><span class="p">:</span> <span class="mi">8</span><span class="p">},</span> <span class="n">num_stages</span><span class="o">=</span><span class="mi">4</span><span class="p">,</span> <span class="n">num_warps</span><span class="o">=</span><span class="mi">4</span><span class="p">),</span>
|
||
<span class="n">triton</span><span class="o">.</span><span class="n">Config</span><span class="p">({</span><span class="s1">'BLOCK_SIZE_M'</span><span class="p">:</span> <span class="mi">64</span> <span class="p">,</span> <span class="s1">'BLOCK_SIZE_N'</span><span class="p">:</span> <span class="mi">128</span><span class="p">,</span> <span class="s1">'BLOCK_SIZE_K'</span><span class="p">:</span> <span class="mi">32</span><span class="p">,</span> <span class="s1">'GROUP_SIZE_M'</span><span class="p">:</span> <span class="mi">8</span><span class="p">},</span> <span class="n">num_stages</span><span class="o">=</span><span class="mi">4</span><span class="p">,</span> <span class="n">num_warps</span><span class="o">=</span><span class="mi">4</span><span class="p">),</span>
|
||
<span class="n">triton</span><span class="o">.</span><span class="n">Config</span><span class="p">({</span><span class="s1">'BLOCK_SIZE_M'</span><span class="p">:</span> <span class="mi">128</span><span class="p">,</span> <span class="s1">'BLOCK_SIZE_N'</span><span class="p">:</span> <span class="mi">32</span> <span class="p">,</span> <span class="s1">'BLOCK_SIZE_K'</span><span class="p">:</span> <span class="mi">32</span><span class="p">,</span> <span class="s1">'GROUP_SIZE_M'</span><span class="p">:</span> <span class="mi">8</span><span class="p">},</span> <span class="n">num_stages</span><span class="o">=</span><span class="mi">4</span><span class="p">,</span> <span class="n">num_warps</span><span class="o">=</span><span class="mi">4</span><span class="p">),</span>
|
||
<span class="n">triton</span><span class="o">.</span><span class="n">Config</span><span class="p">({</span><span class="s1">'BLOCK_SIZE_M'</span><span class="p">:</span> <span class="mi">64</span> <span class="p">,</span> <span class="s1">'BLOCK_SIZE_N'</span><span class="p">:</span> <span class="mi">32</span> <span class="p">,</span> <span class="s1">'BLOCK_SIZE_K'</span><span class="p">:</span> <span class="mi">32</span><span class="p">,</span> <span class="s1">'GROUP_SIZE_M'</span><span class="p">:</span> <span class="mi">8</span><span class="p">},</span> <span class="n">num_stages</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">num_warps</span><span class="o">=</span><span class="mi">2</span><span class="p">),</span>
|
||
<span class="n">triton</span><span class="o">.</span><span class="n">Config</span><span class="p">({</span><span class="s1">'BLOCK_SIZE_M'</span><span class="p">:</span> <span class="mi">32</span> <span class="p">,</span> <span class="s1">'BLOCK_SIZE_N'</span><span class="p">:</span> <span class="mi">64</span> <span class="p">,</span> <span class="s1">'BLOCK_SIZE_K'</span><span class="p">:</span> <span class="mi">32</span><span class="p">,</span> <span class="s1">'GROUP_SIZE_M'</span><span class="p">:</span> <span class="mi">8</span><span class="p">},</span> <span class="n">num_stages</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">num_warps</span><span class="o">=</span><span class="mi">2</span><span class="p">),</span>
|
||
<span class="p">],</span>
|
||
<span class="n">key</span><span class="o">=</span><span class="p">[</span><span class="s1">'M'</span><span class="p">,</span> <span class="s1">'N'</span><span class="p">,</span> <span class="s1">'K'</span><span class="p">],</span>
|
||
<span class="p">)</span>
|
||
<span class="c1"># %</span>
|
||
<span class="c1"># We can now define our kernel as normal, using all the techniques presented above</span>
|
||
<span class="nd">@triton</span><span class="o">.</span><span class="n">jit</span>
|
||
<span class="k">def</span> <span class="nf">matmul_kernel</span><span class="p">(</span>
|
||
<span class="c1"># Pointers to matrices</span>
|
||
<span class="n">a_ptr</span><span class="p">,</span>
|
||
<span class="n">b_ptr</span><span class="p">,</span>
|
||
<span class="n">c_ptr</span><span class="p">,</span>
|
||
<span class="c1"># Matrix dimensions</span>
|
||
<span class="n">M</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="c1"># The stride variables represent how much to increase the ptr by when moving by 1</span>
|
||
<span class="c1"># element in a particular dimension. E.g. stride_am is how much to increase a_ptr</span>
|
||
<span class="c1"># by to get the element one row down (A has M rows)</span>
|
||
<span class="n">stride_am</span><span class="p">,</span>
|
||
<span class="n">stride_ak</span><span class="p">,</span>
|
||
<span class="n">stride_bk</span><span class="p">,</span>
|
||
<span class="n">stride_bn</span><span class="p">,</span>
|
||
<span class="n">stride_cm</span><span class="p">,</span>
|
||
<span class="n">stride_cn</span><span class="p">,</span>
|
||
<span class="o">**</span><span class="n">meta</span><span class="p">,</span>
|
||
<span class="p">):</span>
|
||
<span class="sd">"""Kernel for computing the matmul AB = C</span>
|
||
|
||
<span class="sd"> A has shape (M, K), B has shape (K, N) and C has shape (M, N)</span>
|
||
<span class="sd"> """</span>
|
||
<span class="c1"># extract meta-parameters</span>
|
||
<span class="n">BLOCK_SIZE_M</span> <span class="o">=</span> <span class="n">meta</span><span class="p">[</span><span class="s1">'BLOCK_SIZE_M'</span><span class="p">]</span>
|
||
<span class="n">BLOCK_SIZE_N</span> <span class="o">=</span> <span class="n">meta</span><span class="p">[</span><span class="s1">'BLOCK_SIZE_N'</span><span class="p">]</span>
|
||
<span class="n">BLOCK_SIZE_K</span> <span class="o">=</span> <span class="n">meta</span><span class="p">[</span><span class="s1">'BLOCK_SIZE_K'</span><span class="p">]</span>
|
||
<span class="n">GROUP_SIZE_M</span> <span class="o">=</span> <span class="mi">8</span>
|
||
<span class="n">pid</span> <span class="o">=</span> <span class="n">tl</span><span class="o">.</span><span class="n">program_id</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
|
||
|
||
<span class="c1"># the number of blocks is the ceil(M / BLOCK_SIZE_M) since we need an extra block</span>
|
||
<span class="c1"># Note that this will lead to some quantization in performance where time-taken jumps</span>
|
||
<span class="c1"># when you need to add a new block</span>
|
||
<span class="n">n_blocks_m</span> <span class="o">=</span> <span class="p">(</span><span class="n">M</span> <span class="o">+</span> <span class="n">BLOCK_SIZE_M</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">//</span> <span class="n">BLOCK_SIZE_M</span>
|
||
<span class="n">n_blocks_n</span> <span class="o">=</span> <span class="p">(</span><span class="n">N</span> <span class="o">+</span> <span class="n">BLOCK_SIZE_N</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">//</span> <span class="n">BLOCK_SIZE_N</span>
|
||
|
||
<span class="c1"># Map PIDs to the block they should compute. This is done in a grouped ordering</span>
|
||
<span class="c1"># to promote L2 cache reuse.</span>
|
||
<span class="n">n_output_blocks_in_group</span> <span class="o">=</span> <span class="n">GROUP_SIZE_M</span> <span class="o">*</span> <span class="n">n_blocks_n</span>
|
||
<span class="n">group_id</span> <span class="o">=</span> <span class="n">pid</span> <span class="o">//</span> <span class="n">n_output_blocks_in_group</span>
|
||
<span class="n">first_m_block_in_group</span> <span class="o">=</span> <span class="n">group_id</span> <span class="o">*</span> <span class="n">GROUP_SIZE_M</span>
|
||
|
||
<span class="c1"># If the number of blocks is not divisible by the group size, the last group is smaller</span>
|
||
<span class="n">group_size_m</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">n_blocks_m</span> <span class="o">-</span> <span class="n">first_m_block_in_group</span><span class="p">,</span> <span class="n">GROUP_SIZE_M</span><span class="p">)</span>
|
||
|
||
<span class="c1"># Within a group, we compute in col-major ordering, block_m and block_n are the</span>
|
||
<span class="c1"># output row and col that this program is computing in terms of blocks</span>
|
||
<span class="n">block_m</span> <span class="o">=</span> <span class="n">first_m_block_in_group</span> <span class="o">+</span> <span class="p">(</span><span class="n">pid</span> <span class="o">%</span> <span class="n">group_size_m</span><span class="p">)</span>
|
||
<span class="n">block_n</span> <span class="o">=</span> <span class="p">(</span><span class="n">pid</span> <span class="o">%</span> <span class="n">n_output_blocks_in_group</span><span class="p">)</span> <span class="o">//</span> <span class="n">group_size_m</span>
|
||
|
||
<span class="c1"># Convert from block indices back to element indices</span>
|
||
<span class="n">m_start</span> <span class="o">=</span> <span class="n">block_m</span> <span class="o">*</span> <span class="n">BLOCK_SIZE_M</span>
|
||
<span class="n">n_start</span> <span class="o">=</span> <span class="n">block_n</span> <span class="o">*</span> <span class="n">BLOCK_SIZE_N</span>
|
||
|
||
<span class="c1"># Expand out to all the offsets for each of the elements in this block.</span>
|
||
<span class="n">m_offsets_a</span> <span class="o">=</span> <span class="p">(</span><span class="n">m_start</span> <span class="o">+</span> <span class="n">tl</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">BLOCK_SIZE_M</span><span class="p">))[:,</span> <span class="kc">None</span><span class="p">]</span>
|
||
<span class="n">n_offsets_b</span> <span class="o">=</span> <span class="p">(</span><span class="n">n_start</span> <span class="o">+</span> <span class="n">tl</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">BLOCK_SIZE_N</span><span class="p">))[</span><span class="kc">None</span><span class="p">,</span> <span class="p">:]</span>
|
||
<span class="n">k_offsets</span> <span class="o">=</span> <span class="n">tl</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">BLOCK_SIZE_K</span><span class="p">)</span>
|
||
|
||
<span class="c1"># Get the pointers for the first block of each. We will advance this pointer</span>
|
||
<span class="c1"># as we move in the K direction and accumulate.</span>
|
||
<span class="c1"># a_ptrs should contain BLOCK_SIZE_M * BLOCK_SIZE_K pointers</span>
|
||
<span class="n">a_ptrs</span> <span class="o">=</span> <span class="n">a_ptr</span> <span class="o">+</span> <span class="p">(</span><span class="n">stride_am</span> <span class="o">*</span> <span class="n">m_offsets_a</span> <span class="o">+</span> <span class="n">stride_ak</span> <span class="o">*</span> <span class="n">k_offsets</span><span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="p">:])</span>
|
||
<span class="c1"># b_ptrs should contain BLOCK_SIZE_K * BLOCK_SIZE_N pointers</span>
|
||
<span class="n">b_ptrs</span> <span class="o">=</span> <span class="n">b_ptr</span> <span class="o">+</span> <span class="p">(</span><span class="n">stride_bk</span> <span class="o">*</span> <span class="n">k_offsets</span><span class="p">[:,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">+</span> <span class="n">stride_bn</span> <span class="o">*</span> <span class="n">n_offsets_b</span><span class="p">)</span>
|
||
<span class="c1"># We accumulate internally in fp32, but the output is written out in the dtype</span>
|
||
<span class="c1"># of the tensor when it is stored</span>
|
||
<span class="n">accumulator</span> <span class="o">=</span> <span class="n">tl</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">BLOCK_SIZE_M</span><span class="p">,</span> <span class="n">BLOCK_SIZE_N</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tl</span><span class="o">.</span><span class="n">float32</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">0</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">BLOCK_SIZE_K</span><span class="p">):</span>
|
||
<span class="c1"># Note that for simplicity, we don't apply a mask here. This means that if K is</span>
|
||
<span class="c1"># not a multiple of BLOCK_SIZE_K, this will access out-of-bounds memory and</span>
|
||
<span class="c1"># accumulate it incorrectly.</span>
|
||
<span class="n">a</span> <span class="o">=</span> <span class="n">tl</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="n">a_ptrs</span><span class="p">)</span>
|
||
<span class="n">b</span> <span class="o">=</span> <span class="n">tl</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="n">b_ptrs</span><span class="p">)</span>
|
||
<span class="c1"># We accumulate along the K dimension</span>
|
||
<span class="n">accumulator</span> <span class="o">+=</span> <span class="n">tl</span><span class="o">.</span><span class="n">dot</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="c1"># Advance the ptrs to the next K block</span>
|
||
<span class="n">a_ptrs</span> <span class="o">+=</span> <span class="n">BLOCK_SIZE_K</span> <span class="o">*</span> <span class="n">stride_ak</span>
|
||
<span class="n">b_ptrs</span> <span class="o">+=</span> <span class="n">BLOCK_SIZE_K</span> <span class="o">*</span> <span class="n">stride_bk</span>
|
||
<span class="c1"># triton can accept arbitrary activation function via metaparameters!</span>
|
||
<span class="k">if</span> <span class="n">meta</span><span class="p">[</span><span class="s1">'ACTIVATION'</span><span class="p">]:</span>
|
||
<span class="n">accumulator</span> <span class="o">=</span> <span class="n">meta</span><span class="p">[</span><span class="s1">'ACTIVATION'</span><span class="p">](</span><span class="n">accumulator</span><span class="p">)</span>
|
||
|
||
<span class="n">m_offsets_c</span> <span class="o">=</span> <span class="p">(</span><span class="n">m_start</span> <span class="o">+</span> <span class="n">tl</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">BLOCK_SIZE_M</span><span class="p">))[:,</span> <span class="kc">None</span><span class="p">]</span>
|
||
<span class="n">n_offsets_c</span> <span class="o">=</span> <span class="p">(</span><span class="n">n_start</span> <span class="o">+</span> <span class="n">tl</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">BLOCK_SIZE_N</span><span class="p">))[</span><span class="kc">None</span><span class="p">,</span> <span class="p">:]</span>
|
||
<span class="n">c_ptrs</span> <span class="o">=</span> <span class="n">c_ptr</span> <span class="o">+</span> <span class="n">stride_cm</span> <span class="o">*</span> <span class="n">m_offsets_c</span> <span class="o">+</span> <span class="n">stride_cn</span> <span class="o">*</span> <span class="n">n_offsets_c</span>
|
||
<span class="n">mask</span> <span class="o">=</span> <span class="p">(</span><span class="n">m_offsets_c</span> <span class="o"><</span> <span class="n">M</span><span class="p">)</span> <span class="o">&</span> <span class="p">(</span><span class="n">n_offsets_c</span> <span class="o"><</span> <span class="n">N</span><span class="p">)</span>
|
||
<span class="n">tl</span><span class="o">.</span><span class="n">store</span><span class="p">(</span><span class="n">c_ptrs</span><span class="p">,</span> <span class="n">accumulator</span><span class="p">,</span> <span class="n">mask</span><span class="o">=</span><span class="n">mask</span><span class="p">)</span>
|
||
|
||
|
||
<span class="c1"># we can fuse `leaky_relu` by providing it as an `ACTIVATION` meta-parameter in `_matmul`</span>
|
||
<span class="nd">@triton</span><span class="o">.</span><span class="n">jit</span>
|
||
<span class="k">def</span> <span class="nf">leaky_relu</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
|
||
<span class="k">return</span> <span class="n">tl</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">x</span> <span class="o">>=</span> <span class="mi">0</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="mf">0.01</span> <span class="o">*</span> <span class="n">x</span><span class="p">)</span>
|
||
</pre></div>
|
||
</div>
|
||
<p>We can now create a convenience wrapper function that only takes two input tensors
|
||
and (1) checks any shape constraint; (2) allocates the output; (3) launches the above kernel</p>
|
||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">matmul</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">activation</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||
<span class="c1"># checks constraints</span>
|
||
<span class="k">assert</span> <span class="n">a</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">==</span> <span class="n">b</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="s2">"incompatible dimensions"</span>
|
||
<span class="k">assert</span> <span class="n">a</span><span class="o">.</span><span class="n">is_contiguous</span><span class="p">(),</span> <span class="s2">"matrix A must be contiguous"</span>
|
||
<span class="k">assert</span> <span class="n">b</span><span class="o">.</span><span class="n">is_contiguous</span><span class="p">(),</span> <span class="s2">"matrix B must be contiguous"</span>
|
||
<span class="n">M</span><span class="p">,</span> <span class="n">K</span> <span class="o">=</span> <span class="n">a</span><span class="o">.</span><span class="n">shape</span>
|
||
<span class="n">K</span><span class="p">,</span> <span class="n">N</span> <span class="o">=</span> <span class="n">b</span><span class="o">.</span><span class="n">shape</span>
|
||
<span class="k">assert</span> <span class="p">(</span>
|
||
<span class="n">K</span> <span class="o">%</span> <span class="mi">32</span> <span class="o">==</span> <span class="mi">0</span>
|
||
<span class="p">),</span> <span class="s2">"We don't check memory-out-of-bounds with K so K must be divisible by BLOCK_SIZE_K"</span>
|
||
<span class="c1"># allocates output</span>
|
||
<span class="n">c</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">empty</span><span class="p">((</span><span class="n">M</span><span class="p">,</span> <span class="n">N</span><span class="p">),</span> <span class="n">device</span><span class="o">=</span><span class="n">a</span><span class="o">.</span><span class="n">device</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">a</span><span class="o">.</span><span class="n">dtype</span><span class="p">)</span>
|
||
<span class="c1"># 1D launch kernel where each block gets its own program.</span>
|
||
<span class="n">grid</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">META</span><span class="p">:</span> <span class="p">(</span>
|
||
<span class="n">triton</span><span class="o">.</span><span class="n">cdiv</span><span class="p">(</span><span class="n">M</span><span class="p">,</span> <span class="n">META</span><span class="p">[</span><span class="s1">'BLOCK_SIZE_M'</span><span class="p">])</span> <span class="o">*</span> <span class="n">triton</span><span class="o">.</span><span class="n">cdiv</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">META</span><span class="p">[</span><span class="s1">'BLOCK_SIZE_N'</span><span class="p">]),</span>
|
||
<span class="p">)</span>
|
||
<span class="n">matmul_kernel</span><span class="p">[</span><span class="n">grid</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</span><span class="p">,</span>
|
||
<span class="n">M</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">a</span><span class="o">.</span><span class="n">stride</span><span class="p">(</span><span class="mi">0</span><span class="p">),</span>
|
||
<span class="n">a</span><span class="o">.</span><span class="n">stride</span><span class="p">(</span><span class="mi">1</span><span class="p">),</span>
|
||
<span class="n">b</span><span class="o">.</span><span class="n">stride</span><span class="p">(</span><span class="mi">0</span><span class="p">),</span>
|
||
<span class="n">b</span><span class="o">.</span><span class="n">stride</span><span class="p">(</span><span class="mi">1</span><span class="p">),</span>
|
||
<span class="n">c</span><span class="o">.</span><span class="n">stride</span><span class="p">(</span><span class="mi">0</span><span class="p">),</span>
|
||
<span class="n">c</span><span class="o">.</span><span class="n">stride</span><span class="p">(</span><span class="mi">1</span><span class="p">),</span>
|
||
<span class="n">ACTIVATION</span><span class="o">=</span><span class="n">activation</span><span class="p">,</span>
|
||
<span class="p">)</span>
|
||
<span class="k">return</span> <span class="n">c</span>
|
||
</pre></div>
|
||
</div>
|
||
</div>
|
||
<div class="section" id="unit-test">
|
||
<h2>Unit Test<a class="headerlink" href="#unit-test" title="Permalink to this headline">¶</a></h2>
|
||
<p>We can test our custom matrix multiplication operation against a native torch implementation (i.e., cuBLAS)</p>
|
||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">torch</span><span class="o">.</span><span class="n">manual_seed</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||
<span class="n">a</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">((</span><span class="mi">512</span><span class="p">,</span> <span class="mi">512</span><span class="p">),</span> <span class="n">device</span><span class="o">=</span><span class="s1">'cuda'</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">float16</span><span class="p">)</span>
|
||
<span class="n">b</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">((</span><span class="mi">512</span><span class="p">,</span> <span class="mi">512</span><span class="p">),</span> <span class="n">device</span><span class="o">=</span><span class="s1">'cuda'</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">float16</span><span class="p">)</span>
|
||
<span class="n">triton_output</span> <span class="o">=</span> <span class="n">matmul</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">activation</span><span class="o">=</span><span class="kc">None</span><span class="p">)</span>
|
||
<span class="n">torch_output</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">matmul</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="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"triton_output=</span><span class="si">{</span><span class="n">triton_output</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"torch_output=</span><span class="si">{</span><span class="n">torch_output</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
|
||
<span class="k">if</span> <span class="n">triton</span><span class="o">.</span><span class="n">testing</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">triton_output</span><span class="p">,</span> <span class="n">torch_output</span><span class="p">):</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s2">"✅ Triton and Torch match"</span><span class="p">)</span>
|
||
<span class="k">else</span><span class="p">:</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s2">"❌ Triton and Torch differ"</span><span class="p">)</span>
|
||
</pre></div>
|
||
</div>
|
||
<p class="sphx-glr-script-out">Out:</p>
|
||
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>triton_output=tensor([[ 1.1045, -36.9688, 31.4688, ..., -11.3984, 24.4531, -32.3438],
|
||
[ 6.3555, -19.6094, 34.0938, ..., -5.8945, 5.2891, 6.8867],
|
||
[-32.0625, 5.9492, 15.3984, ..., -21.3906, -23.9844, -10.1328],
|
||
...,
|
||
[ -5.7031, 7.4492, 8.2656, ..., -10.6953, -40.0000, 17.7500],
|
||
[ 25.5000, 24.3281, -8.4688, ..., -18.9375, 32.5312, -29.9219],
|
||
[ -5.3477, 4.9844, 11.8906, ..., 5.5898, 6.4023, -17.3125]],
|
||
device='cuda:0', dtype=torch.float16)
|
||
torch_output=tensor([[ 1.1045, -36.9688, 31.4688, ..., -11.3906, 24.4531, -32.3438],
|
||
[ 6.3516, -19.6094, 34.0938, ..., -5.8906, 5.2812, 6.8828],
|
||
[-32.0625, 5.9531, 15.3984, ..., -21.4062, -23.9844, -10.1328],
|
||
...,
|
||
[ -5.7070, 7.4492, 8.2656, ..., -10.6953, -40.0000, 17.7500],
|
||
[ 25.5000, 24.3438, -8.4609, ..., -18.9375, 32.5312, -29.9219],
|
||
[ -5.3477, 4.9805, 11.8828, ..., 5.5859, 6.4023, -17.3125]],
|
||
device='cuda:0', dtype=torch.float16)
|
||
✅ Triton and Torch match
|
||
</pre></div>
|
||
</div>
|
||
</div>
|
||
<div class="section" id="benchmark">
|
||
<h2>Benchmark<a class="headerlink" href="#benchmark" title="Permalink to this headline">¶</a></h2>
|
||
<div class="section" id="square-matrix-performance">
|
||
<h3>Square Matrix Performance<a class="headerlink" href="#square-matrix-performance" title="Permalink to this headline">¶</a></h3>
|
||
<p>We can now compare the performance of our kernel against that of cuBLAS. Here we focus on square matrices, but feel free to arrange this script as you wish to benchmark any other matrix shape.</p>
|
||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nd">@triton</span><span class="o">.</span><span class="n">testing</span><span class="o">.</span><span class="n">perf_report</span><span class="p">(</span>
|
||
<span class="n">triton</span><span class="o">.</span><span class="n">testing</span><span class="o">.</span><span class="n">Benchmark</span><span class="p">(</span>
|
||
<span class="n">x_names</span><span class="o">=</span><span class="p">[</span><span class="s1">'M'</span><span class="p">,</span> <span class="s1">'N'</span><span class="p">,</span> <span class="s1">'K'</span><span class="p">],</span> <span class="c1"># argument names to use as an x-axis for the plot</span>
|
||
<span class="n">x_vals</span><span class="o">=</span><span class="p">[</span>
|
||
<span class="mi">128</span> <span class="o">*</span> <span class="n">i</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">1</span><span class="p">,</span> <span class="mi">33</span><span class="p">)</span>
|
||
<span class="p">],</span> <span class="c1"># different possible values for `x_name`</span>
|
||
<span class="n">line_arg</span><span class="o">=</span><span class="s1">'provider'</span><span class="p">,</span> <span class="c1"># argument name whose value corresponds to a different line in the plot</span>
|
||
<span class="c1"># possible values for `line_arg``</span>
|
||
<span class="n">line_vals</span><span class="o">=</span><span class="p">[</span><span class="s1">'cublas'</span><span class="p">,</span> <span class="s1">'cublas + relu'</span><span class="p">,</span> <span class="s1">'triton'</span><span class="p">,</span> <span class="s1">'triton + relu'</span><span class="p">],</span>
|
||
<span class="c1"># label name for the lines</span>
|
||
<span class="n">line_names</span><span class="o">=</span><span class="p">[</span><span class="s2">"cuBLAS"</span><span class="p">,</span> <span class="s2">"cuBLAS (+ torch.nn.LeakyReLU)"</span><span class="p">,</span> <span class="s2">"Triton"</span><span class="p">,</span> <span class="s2">"Triton (+ LeakyReLU)"</span><span class="p">],</span>
|
||
<span class="c1"># line styles</span>
|
||
<span class="n">styles</span><span class="o">=</span><span class="p">[(</span><span class="s1">'green'</span><span class="p">,</span> <span class="s1">'-'</span><span class="p">),</span> <span class="p">(</span><span class="s1">'green'</span><span class="p">,</span> <span class="s1">'--'</span><span class="p">),</span> <span class="p">(</span><span class="s1">'blue'</span><span class="p">,</span> <span class="s1">'-'</span><span class="p">),</span> <span class="p">(</span><span class="s1">'blue'</span><span class="p">,</span> <span class="s1">'--'</span><span class="p">)],</span>
|
||
<span class="n">ylabel</span><span class="o">=</span><span class="s2">"TFLOPS"</span><span class="p">,</span> <span class="c1"># label name for the y-axis</span>
|
||
<span class="n">plot_name</span><span class="o">=</span><span class="s2">"matmul-performance"</span><span class="p">,</span> <span class="c1"># name for the plot. Used also as a file name for saving the plot.</span>
|
||
<span class="n">args</span><span class="o">=</span><span class="p">{},</span>
|
||
<span class="p">)</span>
|
||
<span class="p">)</span>
|
||
<span class="k">def</span> <span class="nf">benchmark</span><span class="p">(</span><span class="n">M</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">provider</span><span class="p">):</span>
|
||
<span class="n">a</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">((</span><span class="n">M</span><span class="p">,</span> <span class="n">K</span><span class="p">),</span> <span class="n">device</span><span class="o">=</span><span class="s1">'cuda'</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">float16</span><span class="p">)</span>
|
||
<span class="n">b</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">((</span><span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">),</span> <span class="n">device</span><span class="o">=</span><span class="s1">'cuda'</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">float16</span><span class="p">)</span>
|
||
<span class="k">if</span> <span class="n">provider</span> <span class="o">==</span> <span class="s1">'cublas'</span><span class="p">:</span>
|
||
<span class="n">ms</span><span class="p">,</span> <span class="n">min_ms</span><span class="p">,</span> <span class="n">max_ms</span> <span class="o">=</span> <span class="n">triton</span><span class="o">.</span><span class="n">testing</span><span class="o">.</span><span class="n">do_bench</span><span class="p">(</span><span class="k">lambda</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">matmul</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="k">if</span> <span class="n">provider</span> <span class="o">==</span> <span class="s1">'triton'</span><span class="p">:</span>
|
||
<span class="n">ms</span><span class="p">,</span> <span class="n">min_ms</span><span class="p">,</span> <span class="n">max_ms</span> <span class="o">=</span> <span class="n">triton</span><span class="o">.</span><span class="n">testing</span><span class="o">.</span><span class="n">do_bench</span><span class="p">(</span><span class="k">lambda</span><span class="p">:</span> <span class="n">matmul</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="k">if</span> <span class="n">provider</span> <span class="o">==</span> <span class="s1">'cublas + relu'</span><span class="p">:</span>
|
||
<span class="n">torch_relu</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">ReLU</span><span class="p">(</span><span class="n">inplace</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
|
||
<span class="n">ms</span><span class="p">,</span> <span class="n">min_ms</span><span class="p">,</span> <span class="n">max_ms</span> <span class="o">=</span> <span class="n">triton</span><span class="o">.</span><span class="n">testing</span><span class="o">.</span><span class="n">do_bench</span><span class="p">(</span>
|
||
<span class="k">lambda</span><span class="p">:</span> <span class="n">torch_relu</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">matmul</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="p">)</span>
|
||
<span class="k">if</span> <span class="n">provider</span> <span class="o">==</span> <span class="s1">'triton + relu'</span><span class="p">:</span>
|
||
<span class="n">ms</span><span class="p">,</span> <span class="n">min_ms</span><span class="p">,</span> <span class="n">max_ms</span> <span class="o">=</span> <span class="n">triton</span><span class="o">.</span><span class="n">testing</span><span class="o">.</span><span class="n">do_bench</span><span class="p">(</span>
|
||
<span class="k">lambda</span><span class="p">:</span> <span class="n">matmul</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">activation</span><span class="o">=</span><span class="n">leaky_relu</span><span class="p">)</span>
|
||
<span class="p">)</span>
|
||
<span class="n">perf</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">ms</span><span class="p">:</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">M</span> <span class="o">*</span> <span class="n">N</span> <span class="o">*</span> <span class="n">K</span> <span class="o">*</span> <span class="mf">1e-12</span> <span class="o">/</span> <span class="p">(</span><span class="n">ms</span> <span class="o">*</span> <span class="mf">1e-3</span><span class="p">)</span>
|
||
<span class="k">return</span> <span class="n">perf</span><span class="p">(</span><span class="n">ms</span><span class="p">),</span> <span class="n">perf</span><span class="p">(</span><span class="n">max_ms</span><span class="p">),</span> <span class="n">perf</span><span class="p">(</span><span class="n">min_ms</span><span class="p">)</span>
|
||
|
||
|
||
<span class="n">benchmark</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">show_plots</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">print_data</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
|
||
</pre></div>
|
||
</div>
|
||
<img alt="03 matrix multiplication" class="sphx-glr-single-img" src="../../_images/sphx_glr_03-matrix-multiplication_001.png" />
|
||
<p class="sphx-glr-script-out">Out:</p>
|
||
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>matmul-performance:
|
||
M cuBLAS ... Triton Triton (+ LeakyReLU)
|
||
0 128.0 0.455111 ... 0.512000 0.512000
|
||
1 256.0 2.978909 ... 3.276800 2.978909
|
||
2 384.0 7.372800 ... 8.507077 8.507077
|
||
3 512.0 14.563555 ... 16.384000 15.420235
|
||
4 640.0 22.260869 ... 24.380953 24.380953
|
||
5 768.0 32.768000 ... 34.028308 34.028308
|
||
6 896.0 39.025776 ... 40.140799 39.025776
|
||
7 1024.0 49.932191 ... 53.773130 52.428801
|
||
8 1152.0 45.242181 ... 46.656000 46.656000
|
||
9 1280.0 51.200001 ... 56.888887 56.109587
|
||
10 1408.0 64.138541 ... 64.902096 64.902096
|
||
11 1536.0 80.430545 ... 76.106321 76.106321
|
||
12 1664.0 63.372618 ... 62.061463 62.061463
|
||
13 1792.0 72.983276 ... 69.810085 69.810085
|
||
14 1920.0 69.120002 ... 70.172588 69.120002
|
||
15 2048.0 73.584279 ... 74.898285 73.584279
|
||
16 2176.0 82.813365 ... 78.916269 79.540109
|
||
17 2304.0 68.056616 ... 73.275679 73.275679
|
||
18 2432.0 71.125224 ... 81.197876 81.908060
|
||
19 2560.0 77.649287 ... 76.560748 75.676673
|
||
20 2688.0 84.108772 ... 81.053536 84.108772
|
||
21 2816.0 80.469019 ... 79.298560 78.726003
|
||
22 2944.0 81.832567 ... 79.737653 79.104810
|
||
23 3072.0 82.540970 ... 80.890151 83.146995
|
||
24 3200.0 84.210524 ... 89.260810 87.791493
|
||
25 3328.0 83.130825 ... 86.736504 82.275764
|
||
26 3456.0 78.578525 ... 83.459178 85.767626
|
||
27 3584.0 87.808000 ... 92.410473 95.148565
|
||
28 3712.0 85.601834 ... 85.601834 88.876645
|
||
29 3840.0 84.615146 ... 86.875096 87.148936
|
||
30 3968.0 92.512459 ... 83.807647 83.520835
|
||
31 4096.0 93.596744 ... 90.748973 90.321484
|
||
|
||
[32 rows x 5 columns]
|
||
</pre></div>
|
||
</div>
|
||
<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> ( 2 minutes 16.405 seconds)</p>
|
||
<div class="sphx-glr-footer class sphx-glr-footer-example docutils container" id="sphx-glr-download-getting-started-tutorials-03-matrix-multiplication-py">
|
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<div class="sphx-glr-download sphx-glr-download-python docutils container">
|
||
<p><a class="reference download internal" download="" href="../../_downloads/d5fee5b55a64e47f1b5724ec39adf171/03-matrix-multiplication.py"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Python</span> <span class="pre">source</span> <span class="pre">code:</span> <span class="pre">03-matrix-multiplication.py</span></code></a></p>
|
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|
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<div class="sphx-glr-download sphx-glr-download-jupyter docutils container">
|
||
<p><a class="reference download internal" download="" href="../../_downloads/b51b68bc1c6b1a5e509f67800b6235af/03-matrix-multiplication.ipynb"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Jupyter</span> <span class="pre">notebook:</span> <span class="pre">03-matrix-multiplication.ipynb</span></code></a></p>
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