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<div class="section" id="Vector-Addition">
<h1>Vector Addition<a class="headerlink" href="#Vector-Addition" title="Permalink to this headline"></a></h1>
<p>In this tutorial, we will see how to construct a simple, high-performance vector addition using Triton. You will learn: * The basic syntax of the Triton programming language * The best practices for creating PyTorch custom operators using the <code class="docutils literal notranslate"><span class="pre">triton.kernel</span></code> Python API * The best practices for validating and benchmarking custom ops against native reference implementations</p>
<div class="section" id="Writing-the-Compute-Kernel">
<h2>Writing the Compute Kernel<a class="headerlink" href="#Writing-the-Compute-Kernel" title="Permalink to this headline"></a></h2>
<p>Each compute kernel is declared using the <code class="docutils literal notranslate"><span class="pre">__global__</span></code> attribute, and executed many times in parallel on different chunks of data (See the <a class="reference external" href="https://en.wikipedia.org/wiki/SPMD">Single Program, Multiple Data</a> programming model for more details).</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n">__global__</span> <span class="kt">void</span> <span class="n">add</span><span class="p">(</span><span class="kt">float</span><span class="o">*</span> <span class="n">z</span><span class="p">,</span> <span class="kt">float</span><span class="o">*</span> <span class="n">x</span><span class="p">,</span> <span class="kt">float</span><span class="o">*</span> <span class="n">y</span><span class="p">,</span> <span class="kt">int</span> <span class="n">N</span><span class="p">){</span>
<span class="c1">// The `get_program_id(i)` returns the i-th coordinate</span>
<span class="c1">// of the program in the overaching SPMD context</span>
<span class="c1">// (a.k.a launch grid). This is what allows us to process</span>
<span class="c1">// different chunks of data in parallel.</span>
<span class="c1">// For those similar with CUDA, `get_program_id({0,1,2})`</span>
<span class="c1">// is similar to blockIdx.{x,y,z}</span>
<span class="kt">int</span> <span class="n">pid</span> <span class="o">=</span> <span class="n">get_program_id</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
<span class="c1">// In Triton, arrays are first-class citizen. In other words,</span>
<span class="c1">// they are primitives data-types and are -- contrary to C and</span>
<span class="c1">// CUDA -- not implemented as pointers to contiguous chunks of</span>
<span class="c1">// memory.</span>
<span class="c1">// In the few lines below, we create an array of `BLOCK` pointers</span>
<span class="c1">// whose memory values are, e.g.:</span>
<span class="c1">// [z + pid*BLOCK + 0, z + pid*BLOCK + 1, ..., z + pid*BLOCK + BLOCK - 1]</span>
<span class="c1">// Note: here BLOCK is expected to be a pre-processor macro defined at compile-time</span>
<span class="kt">int</span> <span class="n">offset</span><span class="p">[</span><span class="n">BLOCK</span><span class="p">]</span> <span class="o">=</span> <span class="n">pid</span> <span class="o">*</span> <span class="n">BLOCK</span> <span class="o">+</span> <span class="mi">0</span> <span class="p">...</span> <span class="n">BLOCK</span><span class="p">;</span>
<span class="kt">float</span><span class="o">*</span> <span class="n">pz</span> <span class="p">[</span><span class="n">BLOCK</span><span class="p">]</span> <span class="o">=</span> <span class="n">z</span> <span class="o">+</span> <span class="n">offset</span><span class="p">;</span>
<span class="kt">float</span><span class="o">*</span> <span class="n">px</span> <span class="p">[</span><span class="n">BLOCK</span><span class="p">]</span> <span class="o">=</span> <span class="n">x</span> <span class="o">+</span> <span class="n">offset</span><span class="p">;</span>
<span class="kt">float</span><span class="o">*</span> <span class="n">py</span> <span class="p">[</span><span class="n">BLOCK</span><span class="p">]</span> <span class="o">=</span> <span class="n">y</span> <span class="o">+</span> <span class="n">offset</span><span class="p">;</span>
<span class="c1">// Simple element-wise control-flow for load/store operations can</span>
<span class="c1">// be achieved using the the ternary operator `cond ? val_true : val_false`</span>
<span class="c1">// or the conditional dereferencing operator `*?(cond)ptr</span>
<span class="c1">// Here, we make sure that we do not access memory out-of-bounds when we</span>
<span class="c1">// write-back `z`</span>
<span class="kt">bool</span> <span class="n">check</span><span class="p">[</span><span class="n">BLOCK</span><span class="p">]</span> <span class="o">=</span> <span class="n">offset</span> <span class="o">&lt;</span> <span class="n">N</span><span class="p">;</span>
<span class="o">*?</span><span class="p">(</span><span class="n">check</span><span class="p">)</span><span class="n">pz</span> <span class="o">=</span> <span class="o">*?</span><span class="p">(</span><span class="n">check</span><span class="p">)</span><span class="n">px</span> <span class="o">+</span> <span class="o">*?</span><span class="p">(</span><span class="n">check</span><span class="p">)</span><span class="n">py</span><span class="p">;</span>
<span class="p">}</span>
</pre></div>
</div>
<p>The existence of arrays as a primitive data-type for Triton comes with a number of advantages that are highlighted in the <a class="reference external" href="http://www.eecs.harvard.edu/~htk/publication/2019-mapl-tillet-kung-cox.pdf">MAPL’2019 Triton paper</a>.</p>
</div>
<div class="section" id="Writing-the-Torch-bindings">
<h2>Writing the Torch bindings<a class="headerlink" href="#Writing-the-Torch-bindings" title="Permalink to this headline"></a></h2>
<p>The only thing that matters when it comes to Triton and Torch is the <code class="docutils literal notranslate"><span class="pre">triton.kernel</span></code> class. This allows you to transform the above C-like function into a callable python object that can be used to modify <code class="docutils literal notranslate"><span class="pre">torch.tensor</span></code> objects.</p>
<p>To create a <code class="docutils literal notranslate"><span class="pre">triton.kernel</span></code>, you only need three things: * <code class="docutils literal notranslate"><span class="pre">source:</span> <span class="pre">string</span></code>: the source-code of the kernel you want to create * <code class="docutils literal notranslate"><span class="pre">device:</span> <span class="pre">torch.device</span></code>: the device you want to compile this code for * <code class="docutils literal notranslate"><span class="pre">defines:</span> <span class="pre">dict</span></code>: the set of macros that you want the pre-processor to <code class="docutils literal notranslate"><span class="pre">#define</span></code> for you</p>
<p>Note: The constructor of <code class="docutils literal notranslate"><span class="pre">triton.kernel</span></code> does some just-in-time compilation, so expect some overhead there. For this reason, I personally like to initialize kernels lazily in a cache (see <code class="docutils literal notranslate"><span class="pre">_kernels</span></code> variable below). This also makes it possible to choose the compilation device dynamically based on the type of the operator’s inputs.</p>
<div class="nbinput nblast docutils container">
<div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[10]:
</pre></div>
</div>
<div class="input_area highlight-ipython3 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="c1"># source-code for Triton compute kernel</span>
<span class="c1"># here we just copy-paste the above code without the extensive comments.</span>
<span class="c1"># you may prefer to store it in a .c file and load it from there instead.</span>
<span class="n">_src</span> <span class="o">=</span> <span class="s2">&quot;&quot;&quot;</span>
<span class="s2">__global__ void add(float* z, float* x, float* y, int N){</span>
<span class="s2"> // program id</span>
<span class="s2"> int pid = get_program_id(0);</span>
<span class="s2"> // create arrays of pointers</span>
<span class="s2"> int offset[BLOCK] = pid * BLOCK + 0 ... BLOCK;</span>
<span class="s2"> float* pz[BLOCK] = z + offset;</span>
<span class="s2"> float* px[BLOCK] = x + offset;</span>
<span class="s2"> float* py[BLOCK] = y + offset;</span>
<span class="s2"> // bounds checking</span>
<span class="s2"> bool check[BLOCK] = offset &lt; N;</span>
<span class="s2"> // write-back</span>
<span class="s2"> *?(check)pz = *?(check)px + *?(check)py;</span>
<span class="s2">}</span>
<span class="s2"> &quot;&quot;&quot;</span>
<span class="c1"># This function returns a callable `triton.kernel` object</span>
<span class="c1"># created from the above source code.</span>
<span class="c1"># For portability, we maintain a cache of kernels for different `torch.device`</span>
<span class="c1"># We compile the kernel with -DBLOCK=1024</span>
<span class="n">_kernels</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
<span class="k">def</span> <span class="nf">make_add_kernel</span><span class="p">(</span><span class="n">device</span><span class="p">):</span>
<span class="k">if</span> <span class="n">device</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">_kernels</span><span class="p">:</span>
<span class="n">defines</span> <span class="o">=</span> <span class="p">{</span><span class="s1">&#39;BLOCK&#39;</span><span class="p">:</span> <span class="mi">1024</span><span class="p">}</span>
<span class="n">_kernels</span><span class="p">[</span><span class="n">device</span><span class="p">]</span> <span class="o">=</span> <span class="n">triton</span><span class="o">.</span><span class="n">kernel</span><span class="p">(</span><span class="n">_src</span><span class="p">,</span> <span class="n">device</span><span class="o">=</span><span class="n">device</span><span class="p">,</span> <span class="n">defines</span><span class="o">=</span><span class="n">defines</span><span class="p">)</span>
<span class="k">return</span> <span class="n">_kernels</span><span class="p">[</span><span class="n">device</span><span class="p">]</span>
<span class="c1"># This is a standard torch custom autograd Function</span>
<span class="c1"># The only difference is that we can now use the above kernel</span>
<span class="c1"># in the `forward` and `backward` functions.`</span>
<span class="k">class</span> <span class="nc">_add</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">autograd</span><span class="o">.</span><span class="n">Function</span><span class="p">):</span>
<span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="n">ctx</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
<span class="c1"># constraints of the op</span>
<span class="k">assert</span> <span class="n">x</span><span class="o">.</span><span class="n">dtype</span> <span class="o">==</span> <span class="n">torch</span><span class="o">.</span><span class="n">float32</span>
<span class="c1"># *allocate output*</span>
<span class="n">z</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">empty_like</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="c1"># *create launch grid*:</span>
<span class="c1"># this is a function which takes compilation parameters `opt`</span>
<span class="c1"># as input and returns a tuple of int (i.e., launch grid) for the kernel.</span>
<span class="c1"># triton.cdiv is a shortcut for ceil division:</span>
<span class="c1"># triton.cdiv(a, b) = (a + b - 1) // b</span>
<span class="n">N</span> <span class="o">=</span> <span class="n">z</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="n">grid</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">opt</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">N</span><span class="p">,</span> <span class="n">opt</span><span class="o">.</span><span class="n">BLOCK</span><span class="p">),</span> <span class="p">)</span>
<span class="c1"># *launch kernel*:</span>
<span class="c1"># pointer to the data of torch tensors can be retrieved with</span>
<span class="c1"># the `.data_ptr()` method</span>
<span class="n">kernel</span> <span class="o">=</span> <span class="n">make_add_kernel</span><span class="p">(</span><span class="n">z</span><span class="o">.</span><span class="n">device</span><span class="p">)</span>
<span class="n">kernel</span><span class="p">(</span><span class="n">z</span><span class="o">.</span><span class="n">data_ptr</span><span class="p">(),</span> <span class="n">x</span><span class="o">.</span><span class="n">data_ptr</span><span class="p">(),</span> <span class="n">y</span><span class="o">.</span><span class="n">data_ptr</span><span class="p">(),</span> <span class="n">N</span><span class="p">,</span> <span class="n">grid</span> <span class="o">=</span> <span class="n">grid</span><span class="p">)</span>
<span class="k">return</span> <span class="n">z</span>
<span class="c1"># Just like we standard PyTorch ops</span>
<span class="c1"># We use the `.apply` method to create a</span>
<span class="c1"># callable object for our function</span>
<span class="n">add</span> <span class="o">=</span> <span class="n">_add</span><span class="o">.</span><span class="n">apply</span>
</pre></div>
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</div>
<p>At this point <code class="docutils literal notranslate"><span class="pre">add(x,</span> <span class="pre">y)</span></code> is equivalent to <code class="docutils literal notranslate"><span class="pre">x</span> <span class="pre">+</span> <span class="pre">y</span></code> for contiguous tensors. Now let’s test and benchmark it!</p>
</div>
<div class="section" id="Writing-a-Unit-Test">
<h2>Writing a Unit Test<a class="headerlink" href="#Writing-a-Unit-Test" title="Permalink to this headline"></a></h2>
<div class="nbinput docutils container">
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<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">x</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">98432</span><span class="p">,</span> <span class="n">device</span><span class="o">=</span><span class="s1">&#39;cuda&#39;</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">98432</span><span class="p">,</span> <span class="n">device</span><span class="o">=</span><span class="s1">&#39;cuda&#39;</span><span class="p">)</span>
<span class="n">za</span> <span class="o">=</span> <span class="n">x</span> <span class="o">+</span> <span class="n">y</span>
<span class="n">zb</span> <span class="o">=</span> <span class="n">add</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">za</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">zb</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;The maximum difference between torch and triton is &#39;</span>
<span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">torch</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">za</span> <span class="o">-</span> <span class="n">zb</span><span class="p">))</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">)</span>
</pre></div>
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tensor([1.3713, 1.3076, 0.4940, ..., 0.6682, 1.1984, 1.2696], device=&#39;cuda:0&#39;)
tensor([1.3713, 1.3076, 0.4940, ..., 0.6682, 1.1984, 1.2696], device=&#39;cuda:0&#39;)
The maximum difference between torch and triton is 0.0
</pre></div></div>
</div>
<p>Seems to work!</p>
</div>
<div class="section" id="Writing-a-Benchmark">
<h2>Writing a Benchmark<a class="headerlink" href="#Writing-a-Benchmark" title="Permalink to this headline"></a></h2>
<p>The performance of our GPU code can be benchmark using the <code class="docutils literal notranslate"><span class="pre">torch.cuda.Event(enable_timing=True)</span></code> wrapper. Below is a simple function that benchmarks <code class="docutils literal notranslate"><span class="pre">rep</span></code> runs of our kernels after <code class="docutils literal notranslate"><span class="pre">warmup</span></code> “cold” runs.</p>
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<span></span><span class="c1"># We now want to benchmark the performance of `add`</span>
<span class="c1"># Against that of PyTorch for increasing vector sizes</span>
<span class="k">def</span> <span class="nf">do_bench</span><span class="p">(</span><span class="n">fn</span><span class="p">,</span> <span class="n">warmup</span> <span class="o">=</span> <span class="mi">10</span><span class="p">,</span> <span class="n">rep</span> <span class="o">=</span> <span class="mi">50</span><span class="p">):</span>
<span class="n">start_event</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">cuda</span><span class="o">.</span><span class="n">Event</span><span class="p">(</span><span class="n">enable_timing</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">end_event</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">cuda</span><span class="o">.</span><span class="n">Event</span><span class="p">(</span><span class="n">enable_timing</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">ret</span> <span class="o">=</span> <span class="n">fn</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="n">warmup</span><span class="p">):</span>
<span class="n">fn</span><span class="p">()</span>
<span class="n">torch</span><span class="o">.</span><span class="n">cuda</span><span class="o">.</span><span class="n">synchronize</span><span class="p">()</span>
<span class="n">start_event</span><span class="o">.</span><span class="n">record</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="n">rep</span><span class="p">):</span>
<span class="n">fn</span><span class="p">()</span>
<span class="n">end_event</span><span class="o">.</span><span class="n">record</span><span class="p">()</span>
<span class="n">torch</span><span class="o">.</span><span class="n">cuda</span><span class="o">.</span><span class="n">synchronize</span><span class="p">()</span>
<span class="n">time_ms</span> <span class="o">=</span> <span class="n">start_event</span><span class="o">.</span><span class="n">elapsed_time</span><span class="p">(</span><span class="n">end_event</span><span class="p">)</span> <span class="o">/</span> <span class="n">rep</span>
<span class="k">return</span> <span class="n">time_ms</span>
</pre></div>
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</div>
<p>We can now benchmark our custom op for vectors of increasing sizes to get a sense of how it does</p>
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<span></span><span class="k">for</span> <span class="n">N</span> <span class="ow">in</span> <span class="p">[</span><span class="mi">2</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">17</span><span class="p">,</span> <span class="mi">26</span><span class="p">,</span> <span class="mi">1</span><span class="p">)]:</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">rand</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">&#39;cuda&#39;</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">rand</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">&#39;cuda&#39;</span><span class="p">)</span>
<span class="n">triton_ms</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">add</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">))</span>
<span class="n">torch_ms</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">x</span> <span class="o">+</span> <span class="n">y</span><span class="p">)</span>
<span class="c1"># print the performance of triton and torch as well as the achieved bandwidth</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">N</span><span class="si">}</span><span class="s1"> </span><span class="si">{</span><span class="n">triton_ms</span><span class="si">:</span><span class="s1">.3f</span><span class="si">}</span><span class="s1"> </span><span class="si">{</span><span class="n">torch_ms</span><span class="si">:</span><span class="s1">.3f</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">)</span>
</pre></div>
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131072 0.020 0.003
262144 0.019 0.004
524288 0.016 0.016
1048576 0.033 0.033
2097152 0.071 0.070
4194304 0.142 0.144
8388608 0.287 0.286
16777216 0.572 0.568
33554432 1.139 1.110
</pre></div></div>
</div>
<p>Our op is on-par with Torch’s vectorized element-wise kernel when the vectors are large enough. One caveat is that the latency of PyTorch is much smaller for small vectors (3us vs 18-20us). This is something we are actively working on to reduce.</p>
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