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<title>Cookbook &raquo; Asynchronous Tasking with Dependencies | Taskflow QuickStart</title>
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<span class="m-breadcrumb"><a href="Cookbook.html">Cookbook</a> &raquo;</span>
Asynchronous Tasking with Dependencies
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<h3>Contents</h3>
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<li><a href="#CreateADynamicTaskGraph">Create a Dynamic Task Graph</a></li>
<li><a href="#SpecifyARagneOfDependentAsyncTasks">Specify a Range of Dependent Async Tasks</a></li>
<li><a href="#UnderstandTheLifeTimeOfADependentAsyncTask">Understand the Lifetime of a Dependent Async Task</a></li>
<li><a href="#CreateADynamicTaskGraphByMultipleThreads">Create a Dynamic Task Graph by Multiple Threads</a></li>
<li><a href="#QueryTheComppletionStatusOfDependentAsyncTasks">Query the Completion Status of Dependent Async Tasks</a></li>
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<p>This chapters discusses how to create a task graph dynamically using asynchronous tasks, which is extremely beneficial for workloads that want to (1) explore task graph parallelism out of dynamic control flow or (2) overlap task graph creation time with individual task execution time. We recommend that you first read <a href="AsyncTasking.html" class="m-doc">Asynchronous Tasking</a> before digesting this chapter.</p><section id="CreateADynamicTaskGraph"><h2><a href="#CreateADynamicTaskGraph">Create a Dynamic Task Graph</a></h2><p>When the construct-and-run model of a task graph is not possible in your application, you can use <a href="classtf_1_1Executor.html#aee02b63d3a91ad5ca5a1c0e71f3e128f" class="m-doc">tf::<wbr />Executor::<wbr />dependent_async</a> and <a href="classtf_1_1Executor.html#a0e2d792f28136b8227b413d0c27d5c7f" class="m-doc">tf::<wbr />Executor::<wbr />silent_dependent_async</a> to create a task graph dynamically. This type of parallelism is also known as <em>on-the-fly</em> task graph parallelism, which offers great flexibility for expressing dynamic task graph parallelism. The example below dynamically creates a task graph of four dependent async tasks, <code>A</code>, <code>B</code>, <code>C</code>, and <code>D</code>, where <code>A</code> runs before <code>B</code> and <code>C</code> and <code>D</code> runs after <code>B</code> and <code>C:</code></p><div class="m-graph"><svg style="width: 24.200rem; height: 9.800rem;" viewBox="0.00 0.00 242.00 98.00">
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</div><pre class="m-code"><span class="n">tf</span><span class="o">::</span><span class="n">Executor</span><span class="w"> </span><span class="n">executor</span><span class="p">;</span>
<span class="n">tf</span><span class="o">::</span><span class="n">AsyncTask</span><span class="w"> </span><span class="n">A</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">executor</span><span class="p">.</span><span class="n">silent_dependent_async</span><span class="p">([](){</span><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;A</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">);</span><span class="w"> </span><span class="p">});</span>
<span class="n">tf</span><span class="o">::</span><span class="n">AsyncTask</span><span class="w"> </span><span class="n">B</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">executor</span><span class="p">.</span><span class="n">silent_dependent_async</span><span class="p">([](){</span><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;B</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">);</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="n">A</span><span class="p">);</span>
<span class="n">tf</span><span class="o">::</span><span class="n">AsyncTask</span><span class="w"> </span><span class="n">C</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">executor</span><span class="p">.</span><span class="n">silent_dependent_async</span><span class="p">([](){</span><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;C</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">);</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="n">A</span><span class="p">);</span>
<span class="k">auto</span><span class="w"> </span><span class="p">[</span><span class="n">D</span><span class="p">,</span><span class="w"> </span><span class="n">fuD</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">executor</span><span class="p">.</span><span class="n">dependent_async</span><span class="p">([](){</span><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;D</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">);</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">C</span><span class="p">);</span>
<span class="n">fuD</span><span class="p">.</span><span class="n">get</span><span class="p">();</span><span class="w"> </span><span class="c1">// wait for D to finish, which in turn means A, B, C have finished</span></pre><p>Both <a href="classtf_1_1Executor.html#aee02b63d3a91ad5ca5a1c0e71f3e128f" class="m-doc">tf::<wbr />Executor::<wbr />dependent_async</a> and <a href="classtf_1_1Executor.html#a0e2d792f28136b8227b413d0c27d5c7f" class="m-doc">tf::<wbr />Executor::<wbr />silent_dependent_async</a> create a task of type <a href="classtf_1_1AsyncTask.html" class="m-doc">tf::<wbr />AsyncTask</a> to run the given function asynchronously. Additionally, <a href="classtf_1_1Executor.html#aee02b63d3a91ad5ca5a1c0e71f3e128f" class="m-doc">tf::<wbr />Executor::<wbr />dependent_async</a> returns a <a href="https://en.cppreference.com/w/cpp/thread/future">std::<wbr />future</a> that eventually holds the result of the execution. When returning from both calls, the executor has scheduled a worker to run the task whenever its dependencies are met. That is, task execution happens <em>simultaneously</em> with the creation of the task graph, which is different from constructing a Taskflow and running it from an executor, illustrated in the figure below:</p><img class="m-image" src="dependent_async_execution_diagram.png" alt="Image" /><p>Since this model only allows relating a dependency from the current task to a previously created task, you need a correct topological order of graph expression. In our example, there are only two possible topological orderings, either <code>ABCD</code> or <code>ACBD</code>. The code below shows another feasible order of expressing this dynamic task graph parallelism:</p><pre class="m-code"><span class="n">tf</span><span class="o">::</span><span class="n">Executor</span><span class="w"> </span><span class="n">executor</span><span class="p">;</span>
<span class="n">tf</span><span class="o">::</span><span class="n">AsyncTask</span><span class="w"> </span><span class="n">A</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">executor</span><span class="p">.</span><span class="n">silent_dependent_async</span><span class="p">([](){</span><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;A</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">);</span><span class="w"> </span><span class="p">});</span>
<span class="n">tf</span><span class="o">::</span><span class="n">AsyncTask</span><span class="w"> </span><span class="n">C</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">executor</span><span class="p">.</span><span class="n">silent_dependent_async</span><span class="p">([](){</span><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;C</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">);</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="n">A</span><span class="p">);</span>
<span class="n">tf</span><span class="o">::</span><span class="n">AsyncTask</span><span class="w"> </span><span class="n">B</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">executor</span><span class="p">.</span><span class="n">silent_dependent_async</span><span class="p">([](){</span><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;B</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">);</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="n">A</span><span class="p">);</span>
<span class="k">auto</span><span class="w"> </span><span class="p">[</span><span class="n">D</span><span class="p">,</span><span class="w"> </span><span class="n">fuD</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">executor</span><span class="p">.</span><span class="n">dependent_async</span><span class="p">([](){</span><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;D</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">);</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">C</span><span class="p">);</span>
<span class="n">fuD</span><span class="p">.</span><span class="n">get</span><span class="p">();</span><span class="w"> </span><span class="c1">// wait for D to finish, which in turn means A, B, C have finished</span></pre><p>In addition to using <a href="https://en.cppreference.com/w/cpp/thread/future">std::<wbr />future</a> to synchronize the execution, you can use <a href="classtf_1_1Executor.html#ab9aa252f70e9a40020a1e5a89d485b85" class="m-doc">tf::<wbr />Executor::<wbr />wait_for_all</a> to wait for all scheduled tasks to finish:</p><pre class="m-code"><span class="n">tf</span><span class="o">::</span><span class="n">Executor</span><span class="w"> </span><span class="n">executor</span><span class="p">;</span>
<span class="n">tf</span><span class="o">::</span><span class="n">AsyncTask</span><span class="w"> </span><span class="n">A</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">executor</span><span class="p">.</span><span class="n">silent_dependent_async</span><span class="p">([](){</span><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;A</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">);</span><span class="w"> </span><span class="p">});</span>
<span class="n">tf</span><span class="o">::</span><span class="n">AsyncTask</span><span class="w"> </span><span class="n">B</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">executor</span><span class="p">.</span><span class="n">silent_dependent_async</span><span class="p">([](){</span><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;B</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">);</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="n">A</span><span class="p">);</span>
<span class="n">tf</span><span class="o">::</span><span class="n">AsyncTask</span><span class="w"> </span><span class="n">C</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">executor</span><span class="p">.</span><span class="n">silent_dependent_async</span><span class="p">([](){</span><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;C</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">);</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="n">A</span><span class="p">);</span>
<span class="n">tf</span><span class="o">::</span><span class="n">AsyncTask</span><span class="w"> </span><span class="n">D</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">executor</span><span class="p">.</span><span class="n">silent_dependent_async</span><span class="p">([](){</span><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;D</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">);</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">C</span><span class="p">);</span>
<span class="n">executor</span><span class="p">.</span><span class="n">wait_for_all</span><span class="p">();</span></pre></section><section id="SpecifyARagneOfDependentAsyncTasks"><h2><a href="#SpecifyARagneOfDependentAsyncTasks">Specify a Range of Dependent Async Tasks</a></h2><p>Both <a href="classtf_1_1Executor.html#aee02b63d3a91ad5ca5a1c0e71f3e128f" class="m-doc">tf::<wbr />Executor::<wbr />dependent_async(F&amp;&amp; func, Tasks&amp;&amp;... tasks)</a> and <a href="classtf_1_1Executor.html#a0e2d792f28136b8227b413d0c27d5c7f" class="m-doc">tf::<wbr />Executor::<wbr />silent_dependent_async(F&amp;&amp; func, Tasks&amp;&amp;... tasks)</a> accept an arbitrary number of tasks in the dependency list. If the number of dependent tasks is unknown at programming time, such as those relying on runtime variables, you can use the following two overloads to specify dependent tasks in an iterable range <code>[first, last)</code>:</p><ul><li><a href="classtf_1_1Executor.html#a01e51e564f5def845506bcf6b4bb1664" class="m-doc">tf::<wbr />Executor::<wbr />dependent_async(F&amp;&amp; func, I first, I last)</a></li><li><a href="classtf_1_1Executor.html#aa9b08e47e68ae1e568f18aa7104cb9b1" class="m-doc">tf::<wbr />Executor::<wbr />silent_dependent_async(F&amp;&amp; func, I first, I last)</a></li></ul><p>The code below creates an asynchronous task that depends on <code>N</code> previously created asynchronous tasks stored in a vector, where <code>N</code> is a runtime variable:</p><pre class="m-code"><span class="n">tf</span><span class="o">::</span><span class="n">Executor</span><span class="w"> </span><span class="n">executor</span><span class="p">;</span>
<span class="n">std</span><span class="o">::</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">tf</span><span class="o">::</span><span class="n">AsyncTask</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dependents</span><span class="p">;</span>
<span class="k">for</span><span class="p">(</span><span class="kt">size_t</span><span class="w"> </span><span class="n">i</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">&lt;</span><span class="n">N</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// N is a runtime variable</span>
<span class="w"> </span><span class="n">dependents</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">executor</span><span class="p">.</span><span class="n">silent_dependent_async</span><span class="p">([](){}));</span>
<span class="p">}</span>
<span class="n">executor</span><span class="p">.</span><span class="n">silent_dependent_async</span><span class="p">([](){},</span><span class="w"> </span><span class="n">dependents</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">dependents</span><span class="p">.</span><span class="n">end</span><span class="p">());</span>
<span class="n">executor</span><span class="p">.</span><span class="n">wait_for_all</span><span class="p">();</span></pre></section><section id="UnderstandTheLifeTimeOfADependentAsyncTask"><h2><a href="#UnderstandTheLifeTimeOfADependentAsyncTask">Understand the Lifetime of a Dependent Async Task</a></h2><p>A <a href="classtf_1_1AsyncTask.html" class="m-doc">tf::<wbr />AsyncTask</a> is a lightweight handle that retains <em>shared</em> ownership of a dependent async task created by an executor. This shared ownership ensures that the async task remains alive when adding it to the dependency list of another async task, thus avoiding the classical <a href="https://en.wikipedia.org/wiki/ABA_problem">ABA problem</a>.</p><pre class="m-code"><span class="c1">// main thread retains shared ownership of async task A</span>
<span class="n">tf</span><span class="o">::</span><span class="n">AsyncTask</span><span class="w"> </span><span class="n">A</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">executor</span><span class="p">.</span><span class="n">silent_dependent_async</span><span class="p">([](){});</span>
<span class="c1">// task A remains alive (i.e., at least one ref count by the main thread) </span>
<span class="c1">// when being added to the dependency list of async task B</span>
<span class="n">tf</span><span class="o">::</span><span class="n">AsyncTask</span><span class="w"> </span><span class="n">B</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">executor</span><span class="p">.</span><span class="n">silent_dependent_async</span><span class="p">([](){},</span><span class="w"> </span><span class="n">A</span><span class="p">);</span></pre><p>Currently, <a href="classtf_1_1AsyncTask.html" class="m-doc">tf::<wbr />AsyncTask</a> is implemented based on the logic of C++ smart pointer <a href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html" class="m-doc-external">std::<wbr />shared_ptr</a> and is considered cheap to copy or move as long as only a handful of objects own it. When a worker completes an async task, it will remove the task from the executor, decrementing the number of shared owners by one. If that counter reaches zero, the task is destroyed.</p></section><section id="CreateADynamicTaskGraphByMultipleThreads"><h2><a href="#CreateADynamicTaskGraphByMultipleThreads">Create a Dynamic Task Graph by Multiple Threads</a></h2><p>You can use multiple threads to create a dynamic task graph as long as the order of simultaneously creating tasks is topologically correct. The example below uses creates a dynamic task graph using three threads (including the main thread), where task <code>A</code> runs before task <code>B</code> and task <code>C:</code></p><pre class="m-code"><span class="n">tf</span><span class="o">::</span><span class="n">Executor</span><span class="w"> </span><span class="n">executor</span><span class="p">;</span>
<span class="c1">// main thread creates a dependent async task A</span>
<span class="n">tf</span><span class="o">::</span><span class="n">AsyncTask</span><span class="w"> </span><span class="n">A</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">executor</span><span class="p">.</span><span class="n">silent_dependent_async</span><span class="p">([](){});</span>
<span class="c1">// spawn a new thread to create an async task B that runs after A</span>
<span class="n">std</span><span class="o">::</span><span class="kr">thread</span><span class="w"> </span><span class="nf">t1</span><span class="p">([</span><span class="o">&amp;</span><span class="p">](){</span>
<span class="w"> </span><span class="n">tf</span><span class="o">::</span><span class="n">AsyncTask</span><span class="w"> </span><span class="n">B</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">executor</span><span class="p">.</span><span class="n">silent_dependent_async</span><span class="p">([](){},</span><span class="w"> </span><span class="n">A</span><span class="p">);</span>
<span class="p">});</span>
<span class="c1">// spawn a new thread to create an async task C that runs after A</span>
<span class="n">std</span><span class="o">::</span><span class="kr">thread</span><span class="w"> </span><span class="nf">t2</span><span class="p">([</span><span class="o">&amp;</span><span class="p">](){</span>
<span class="w"> </span><span class="n">tf</span><span class="o">::</span><span class="n">AsyncTask</span><span class="w"> </span><span class="n">C</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">executor</span><span class="p">.</span><span class="n">silent_dependent_async</span><span class="p">([](){},</span><span class="w"> </span><span class="n">A</span><span class="p">);</span>
<span class="p">});</span>
<span class="n">executor</span><span class="p">.</span><span class="n">wait_for_all</span><span class="p">();</span>
<span class="n">t1</span><span class="p">.</span><span class="n">join</span><span class="p">();</span>
<span class="n">t2</span><span class="p">.</span><span class="n">join</span><span class="p">();</span></pre><p>Regardless of <code>t1</code> runs before or after <code>t2</code>, the resulting topological order is always correct with the graph definition, either <code>ABC</code> or <code>ACB</code>.</p></section><section id="QueryTheComppletionStatusOfDependentAsyncTasks"><h2><a href="#QueryTheComppletionStatusOfDependentAsyncTasks">Query the Completion Status of Dependent Async Tasks</a></h2><p>When you create a dependent async task, you can query its completion status by <a href="classtf_1_1AsyncTask.html#aefeefa30d7cafdfbb7dc8def542e8e51" class="m-doc">tf::<wbr />AsyncTask::<wbr />is_done</a>, which returns <code>true</code> upon completion or <code>false</code> otherwise. A completed dependent async task indicates that a worker has executed its associated callable.</p><pre class="m-code"><span class="c1">// create a dependent async task that returns 100</span>
<span class="k">auto</span><span class="w"> </span><span class="p">[</span><span class="n">task</span><span class="p">,</span><span class="w"> </span><span class="n">fu</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">executor</span><span class="p">.</span><span class="n">dependent_async</span><span class="p">([](){</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">100</span><span class="p">;</span><span class="w"> </span><span class="p">});</span>
<span class="c1">// loops until the dependent async task completes</span>
<span class="k">while</span><span class="p">(</span><span class="o">!</span><span class="n">task</span><span class="p">.</span><span class="n">is_done</span><span class="p">());</span>
<span class="n">assert</span><span class="p">(</span><span class="n">fu</span><span class="p">.</span><span class="n">get</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">100</span><span class="p">);</span></pre><p><a href="classtf_1_1AsyncTask.html#aefeefa30d7cafdfbb7dc8def542e8e51" class="m-doc">tf::<wbr />AsyncTask::<wbr />is_done</a> is useful when you need to wait on the result of a dependent async task before moving onto the next program instruction. Often, <a href="classtf_1_1AsyncTask.html" class="m-doc">tf::<wbr />AsyncTask</a> is used together with <a href="classtf_1_1Executor.html#a0fc6eb19f168dc4a9cd0a7c6187c1d2d" class="m-doc">tf::<wbr />Executor::<wbr />corun_until</a> to keep a worker awake in its work-stealing loop to avoid deadlock (see <a href="ExecuteTaskflow.html#ExecuteATaskflowFromAnInternalWorker" class="m-doc">Execute a Taskflow from an Internal Worker</a> for more details). For instance, the code below implements the famous Fibonacci sequence using recursive asynchronous tasking:</p><pre class="m-code"><span class="n">tf</span><span class="o">::</span><span class="n">Executor</span><span class="w"> </span><span class="n">executor</span><span class="p">;</span>
<span class="n">std</span><span class="o">::</span><span class="n">function</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="o">&gt;</span><span class="w"> </span><span class="n">fibonacci</span><span class="p">;</span>
<span class="c1">// calculate the Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89</span>
<span class="n">fibonacci</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="o">&amp;</span><span class="p">](</span><span class="kt">int</span><span class="w"> </span><span class="n">N</span><span class="p">){</span>
<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">N</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">N</span><span class="p">;</span><span class="w"> </span>
<span class="w"> </span><span class="p">}</span>
<span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="p">[</span><span class="n">t1</span><span class="p">,</span><span class="w"> </span><span class="n">fu1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">executor</span><span class="p">.</span><span class="n">dependent_async</span><span class="p">(</span><span class="n">std</span><span class="o">::</span><span class="n">bind</span><span class="p">(</span><span class="n">fibonacci</span><span class="p">,</span><span class="w"> </span><span class="n">N</span><span class="mi">-1</span><span class="p">));</span>
<span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="p">[</span><span class="n">t2</span><span class="p">,</span><span class="w"> </span><span class="n">fu2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">executor</span><span class="p">.</span><span class="n">dependent_async</span><span class="p">(</span><span class="n">std</span><span class="o">::</span><span class="n">bind</span><span class="p">(</span><span class="n">fibonacci</span><span class="p">,</span><span class="w"> </span><span class="n">N</span><span class="mi">-2</span><span class="p">));</span>
<span class="w"> </span><span class="n">executor</span><span class="p">.</span><span class="n">corun_until</span><span class="p">([</span><span class="o">&amp;</span><span class="p">](){</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">t1</span><span class="p">.</span><span class="n">is_done</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">t2</span><span class="p">.</span><span class="n">is_done</span><span class="p">();</span><span class="w"> </span><span class="p">});</span>
<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">fu1</span><span class="p">.</span><span class="n">get</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">fu2</span><span class="p">.</span><span class="n">get</span><span class="p">();</span>
<span class="p">};</span>
<span class="k">auto</span><span class="w"> </span><span class="p">[</span><span class="n">task</span><span class="p">,</span><span class="w"> </span><span class="n">fib11</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">executor</span><span class="p">.</span><span class="n">dependent_async</span><span class="p">(</span><span class="n">std</span><span class="o">::</span><span class="n">bind</span><span class="p">(</span><span class="n">fibonacci</span><span class="p">,</span><span class="w"> </span><span class="mi">11</span><span class="p">));</span>
<span class="n">assert</span><span class="p">(</span><span class="n">fib11</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">89</span><span class="p">);</span><span class="w"> </span><span class="c1">// the 11-th Fibonacci number is 89</span></pre></section>
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