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<div class="title">C4: Create a Parallel Reduction Graph </div> </div>
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<div class="contents">
<div class="textblock"><p>Parallel tasks normally produce some quantity that needs to be combined or <em>reduced</em> through particular operations, for instance, sum. In this chapter, we are going to demonstrate how to use Cpp-Taskflow to parallelize a reduction workload.</p>
<h1><a class="anchor" id="ReduceARangeOfItemsToASingleResult"></a>
Reduce a Range of Items to a Single Result</h1>
<p><a class="el" href="classtf_1_1FlowBuilder.html#a06b06b57f8ec8bb060951fc71dd375fb" title="construct a task dependency graph of parallel reduction ">tf::Taskflow::reduce(I beg, I end, T& result, B&& bop)</a> is the most common reduction method to create a task dependency graph that reduces a range of items to a single result through a binary operator.</p>
<div class="fragment"><div class="line"> 1: <a class="code" href="classtf_1_1Taskflow.html">tf::Taskflow</a> taskflow;</div><div class="line"> 2:</div><div class="line"> 3: <a class="codeRef" doxygen="/home/twhuang/PhD/Code/cpp-taskflow/doxygen/cppreference-doxygen-web.tag.xml:http://en.cppreference.com/w/" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector<int></a> items {1, 2, 3, 4, 5, 6, 7, 8};</div><div class="line"> 4: <span class="keywordtype">int</span> sum {0};</div><div class="line"> 5:</div><div class="line"> 6: <span class="keyword">auto</span> [S, T] = taskflow.<a class="code" href="classtf_1_1FlowBuilder.html#a06b06b57f8ec8bb060951fc71dd375fb">reduce</a>(items.begin(), items.end(), sum, [] (<span class="keywordtype">int</span> a, <span class="keywordtype">int</span> b) {</div><div class="line"> 7: <span class="keywordflow">return</span> a + b;</div><div class="line"> 8: });</div><div class="line"> 9:</div><div class="line">10: S.<a class="code" href="classtf_1_1Task.html#a08ada0425b490997b6ff7f310107e5e3">name</a>(<span class="stringliteral">"S"</span>);</div><div class="line">11: T.<a class="code" href="classtf_1_1Task.html#a08ada0425b490997b6ff7f310107e5e3">name</a>(<span class="stringliteral">"T"</span>);</div><div class="line">12:</div><div class="line">13: <a class="code" href="classtf_1_1Executor.html">tf::Executor</a>().<a class="code" href="classtf_1_1Executor.html#a81f35d5b0a20ac0646447eb80d97c0aa">run</a>(taskflow).get();</div><div class="line">14:</div><div class="line">15: <a class="codeRef" doxygen="/home/twhuang/PhD/Code/cpp-taskflow/doxygen/cppreference-doxygen-web.tag.xml:http://en.cppreference.com/w/" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"sum = "</span> << sum << <a class="codeRef" doxygen="/home/twhuang/PhD/Code/cpp-taskflow/doxygen/cppreference-doxygen-web.tag.xml:http://en.cppreference.com/w/" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>; <span class="comment">// 36</span></div></div><!-- fragment --><p>Debrief:</p>
<ul>
<li>Line 1 creates a taskflow object </li>
<li>Line 3 creates a vector of integers </li>
<li>Line 4 declares an integer variable <code>sum</code> and initializes it to zero </li>
<li>Line 6-8 constructs a reduction graph that sums up all integer itmes and stores the final result in <code>sum</code> </li>
<li>Line 10-11 names the two synchronization points </li>
<li>Line 13 dispatches the graph for execution </li>
<li>Line 15 prints out the final reduction value</li>
</ul>
<p>The task dependency graph of this example is shown below:</p>
<div class="image">
<img src="reduce1.png" alt="reduce1.png" width="60%"/>
</div>
<p><a class="el" href="classtf_1_1Taskflow.html" title="the class to create a task dependency graph ">Taskflow</a> partitions and distributes the workload evenly across all workers for all reduction methods. In this example, each internal node sums up two integers and the target node <code>T</code> combine all results returned by the internal nodes to a single value.</p>
<h1><a class="anchor" id="TransformAndReduce"></a>
Transform and Reduce</h1>
<p>It is common to transform each item into a new data type and then perform reduction on the transformed sequences. <a class="el" href="classtf_1_1Taskflow.html" title="the class to create a task dependency graph ">Taskflow</a> provides a method, <a class="el" href="classtf_1_1FlowBuilder.html#a08d669f2286cb90fd5ba7dade1e93fef" title="constructs a task dependency graph of parallel transformation and reduction ">tf::Taskflow::transform_reduce(I beg, I end, T& result, B&& bop, U&& uop)</a>, that fuses these two operators together to save memory reads and writes. The example below takes a string and transforms each digit to an integer number, and then applies reduction to sum up all integer numbers.</p>
<div class="fragment"><div class="line"> 1: <a class="codeRef" doxygen="/home/twhuang/PhD/Code/cpp-taskflow/doxygen/cppreference-doxygen-web.tag.xml:http://en.cppreference.com/w/" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> str = <span class="stringliteral">"12345678"</span>;</div><div class="line"> 2: <span class="keywordtype">int</span> sum {0};</div><div class="line"> 3:</div><div class="line"> 4: <span class="keyword">auto</span> [S, T] = taskflow.<a class="code" href="classtf_1_1FlowBuilder.html#a08d669f2286cb90fd5ba7dade1e93fef">transform_reduce</a>(str.begin(), str.end(), sum,</div><div class="line"> 5: [] (<span class="keywordtype">int</span> a, <span class="keywordtype">int</span> b) {</div><div class="line"> 6: <span class="keywordflow">return</span> a + b;</div><div class="line"> 7: }, </div><div class="line"> 8: [] (<span class="keywordtype">char</span> c) -> <span class="keywordtype">int</span> {</div><div class="line"> 9: <span class="keywordflow">return</span> c - <span class="charliteral">'0'</span>;</div><div class="line">10: } </div><div class="line">11: ); </div><div class="line">12:</div><div class="line">13: <span class="comment">// sum will be 36 after execution</span></div></div><!-- fragment --><p>Debrief:</p>
<ul>
<li>Line 1 creates a string of eight digits </li>
<li>Line 2 declares an integer variables and initializes it to zero </li>
<li>Line 4-11 constructs a reduction graph that converts each character of the string into an integer and computes the sum of all integers</li>
</ul>
<p><a class="el" href="classtf_1_1Taskflow.html" title="the class to create a task dependency graph ">Taskflow</a> has another overload <a class="el" href="classtf_1_1FlowBuilder.html#a9b81ad3b206a63adff8b8bc423f8c425" title="constructs a task dependency graph of parallel transformation and reduction ">tf::Taskflow::transform_reduce(I beg, I end, T& result, B&& bop1, P&& bop2, U&& uop)</a> that takes an additional binary operator <code>bop2</code> to combine the result of <code>uop</code> and the dereferencing of an input iterator to a data type that is acceptable as input to <code>bop1</code>. This is useful when extra computation is required during the reduction process.</p>
<div class="fragment"><div class="line"> 1: <a class="codeRef" doxygen="/home/twhuang/PhD/Code/cpp-taskflow/doxygen/cppreference-doxygen-web.tag.xml:http://en.cppreference.com/w/" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> str = <span class="stringliteral">"12345678"</span>;</div><div class="line"> 2:</div><div class="line"> 3: <span class="keywordtype">double</span> sum {0};</div><div class="line"> 4:</div><div class="line"> 5: <span class="keyword">auto</span> [S, T] = taskflow.<a class="code" href="classtf_1_1FlowBuilder.html#a08d669f2286cb90fd5ba7dade1e93fef">transform_reduce</a>(str.begin(), str.end(), sum,</div><div class="line"> 6: [] (<span class="keywordtype">double</span> a, <span class="keywordtype">double</span> b) {</div><div class="line"> 7: <span class="keywordflow">return</span> a + b;</div><div class="line"> 8: }, </div><div class="line"> 9: [] (<span class="keywordtype">double</span> a, <span class="keywordtype">char</span> c) -> <span class="keywordtype">double</span> {</div><div class="line">10: <span class="keywordflow">return</span> a + (c - <span class="charliteral">'0'</span>);</div><div class="line">11: }, </div><div class="line">12: [] (<span class="keywordtype">char</span> c) -> <span class="keywordtype">double</span> {</div><div class="line">13: <span class="keywordflow">return</span> <span class="keyword">static_cast<</span><span class="keywordtype">double</span><span class="keyword">></span>(c - <span class="charliteral">'0'</span>);</div><div class="line">14: } </div><div class="line">15: ); </div><div class="line">16:</div><div class="line">17: <span class="comment">// sum will be 36 after execution</span></div></div><!-- fragment --><p>Debrief:</p>
<ul>
<li>Line 1 creates a string of eight digits </li>
<li>Line 3 declares an integer variable and initializes it to zero </li>
<li>Line 5 constructs a reduction graph that represents the reduction workload </li>
<li>Line 6-8 takes a binary operator to combine two transformed data </li>
<li>Line 9-11 takes a binary operator to combine one raw data together with a transformed data </li>
<li>Line 12-14 takes a unary operator to transform one raw data to the reduced data type</li>
</ul>
<p>The difference between the two overloads appears in the second binary operator. Instead of converting every item to the reduced data type, this binary operator provides a more fine-grained control over reduction.</p>
<h1><a class="anchor" id="Chapter4Example1"></a>
Example 1: Find the Min/Max Element</h1>
<p>One common workload of using reduce is to find the minimum or the maximum element in a range of items. This example demonstrates how to use the method <a class="el" href="classtf_1_1FlowBuilder.html#a06b06b57f8ec8bb060951fc71dd375fb" title="construct a task dependency graph of parallel reduction ">tf::Taskflow::reduce</a> to find the minimum element in a data set.</p>
<div class="fragment"><div class="line"> 1: #include <taskflow/taskflow.hpp></div><div class="line"> 2:</div><div class="line"> 3: <span class="keywordtype">int</span> main() {</div><div class="line"> 4:</div><div class="line"> 5: <a class="code" href="classtf_1_1Taskflow.html">tf::Taskflow</a> taskflow;</div><div class="line"> 6:</div><div class="line"> 7: <a class="codeRef" doxygen="/home/twhuang/PhD/Code/cpp-taskflow/doxygen/cppreference-doxygen-web.tag.xml:http://en.cppreference.com/w/" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector<int></a> items {4, 2, 1, 3, 7, 8, 6, 5};</div><div class="line"> 8: <span class="keywordtype">int</span> <a class="codeRef" doxygen="/home/twhuang/PhD/Code/cpp-taskflow/doxygen/cppreference-doxygen-web.tag.xml:http://en.cppreference.com/w/" href="http://en.cppreference.com/w/cpp/algorithm/min.html">min</a> = <a class="codeRef" doxygen="/home/twhuang/PhD/Code/cpp-taskflow/doxygen/cppreference-doxygen-web.tag.xml:http://en.cppreference.com/w/" href="http://en.cppreference.com/w/cpp/types/numeric_limits/max.html">std::numeric_limits<int>::max</a>();</div><div class="line"> 9:</div><div class="line">10: taskflow.<a class="code" href="classtf_1_1FlowBuilder.html#a06b06b57f8ec8bb060951fc71dd375fb">reduce</a>(items.begin(), items.end(), min, [] (<span class="keywordtype">int</span> a, <span class="keywordtype">int</span> b) {</div><div class="line">11: <span class="keywordflow">return</span> <a class="codeRef" doxygen="/home/twhuang/PhD/Code/cpp-taskflow/doxygen/cppreference-doxygen-web.tag.xml:http://en.cppreference.com/w/" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(a, b);</div><div class="line">12: });</div><div class="line">13:</div><div class="line">14: <a class="code" href="classtf_1_1Executor.html">tf::Executor</a>().<a class="code" href="classtf_1_1Executor.html#a81f35d5b0a20ac0646447eb80d97c0aa">run</a>(taskflow).get();</div><div class="line">15:</div><div class="line">16: <a class="codeRef" doxygen="/home/twhuang/PhD/Code/cpp-taskflow/doxygen/cppreference-doxygen-web.tag.xml:http://en.cppreference.com/w/" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << min << std::endl; <span class="comment">// 1</span></div><div class="line">17:</div><div class="line">18: <span class="keywordflow">return</span> 0;</div><div class="line">19: }</div></div><!-- fragment --><p>Similarly, the example below finds the maximum element in a data set.</p>
<div class="fragment"><div class="line"> 1: #include <taskflow/taskflow.hpp></div><div class="line"> 2:</div><div class="line"> 3: <span class="keywordtype">int</span> main() {</div><div class="line"> 4:</div><div class="line"> 5: <a class="code" href="classtf_1_1Taskflow.html">tf::Taskflow</a> taskflow;</div><div class="line"> 6:</div><div class="line"> 7: <a class="codeRef" doxygen="/home/twhuang/PhD/Code/cpp-taskflow/doxygen/cppreference-doxygen-web.tag.xml:http://en.cppreference.com/w/" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector<int></a> items {4, 2, 1, 3, 7, 8, 6, 5};</div><div class="line"> 8: <span class="keywordtype">int</span> <a class="codeRef" doxygen="/home/twhuang/PhD/Code/cpp-taskflow/doxygen/cppreference-doxygen-web.tag.xml:http://en.cppreference.com/w/" href="http://en.cppreference.com/w/cpp/algorithm/max.html">max</a> = <a class="codeRef" doxygen="/home/twhuang/PhD/Code/cpp-taskflow/doxygen/cppreference-doxygen-web.tag.xml:http://en.cppreference.com/w/" href="http://en.cppreference.com/w/cpp/types/numeric_limits/min.html">std::numeric_limits<int>::min</a>();</div><div class="line"> 9:</div><div class="line">10: taskflow.<a class="code" href="classtf_1_1FlowBuilder.html#a06b06b57f8ec8bb060951fc71dd375fb">reduce</a>(items.begin(), items.end(), max, [] (<span class="keywordtype">int</span> a, <span class="keywordtype">int</span> b) {</div><div class="line">11: <span class="keywordflow">return</span> <a class="codeRef" doxygen="/home/twhuang/PhD/Code/cpp-taskflow/doxygen/cppreference-doxygen-web.tag.xml:http://en.cppreference.com/w/" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(a, b);</div><div class="line">12: });</div><div class="line">13:</div><div class="line">14: <a class="code" href="classtf_1_1Executor.html">tf::Executor</a>().<a class="code" href="classtf_1_1Executor.html#a81f35d5b0a20ac0646447eb80d97c0aa">run</a>(taskflow).get();</div><div class="line">15:</div><div class="line">16: <a class="codeRef" doxygen="/home/twhuang/PhD/Code/cpp-taskflow/doxygen/cppreference-doxygen-web.tag.xml:http://en.cppreference.com/w/" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << max << std::endl; <span class="comment">// 8</span></div><div class="line">17:</div><div class="line">18: <span class="keywordflow">return</span> 0;</div><div class="line">19: }</div></div><!-- fragment --><h1><a class="anchor" id="Chapter4Example2"></a>
Example 2: Pipeline a Reduction Graph</h1>
<p>The <a class="el" href="classtf_1_1FlowBuilder.html#a06b06b57f8ec8bb060951fc71dd375fb" title="construct a task dependency graph of parallel reduction ">tf::Taskflow::reduce</a> method returns a task pair as two synchronization points of the reduction graph which can be used to pipeline with other tasks. The example below demonstrates how to pipeline a reduction graph with other tasks.</p>
<div class="fragment"><div class="line"> 1: #include <taskflow/taskflow.hpp></div><div class="line"> 2:</div><div class="line"> 3: <span class="keywordtype">int</span> main() {</div><div class="line"> 4:</div><div class="line"> 5: <a class="code" href="classtf_1_1Taskflow.html">tf::Taskflow</a> taskflow;</div><div class="line"> 6:</div><div class="line"> 7: <a class="codeRef" doxygen="/home/twhuang/PhD/Code/cpp-taskflow/doxygen/cppreference-doxygen-web.tag.xml:http://en.cppreference.com/w/" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector<int></a> items{1024};</div><div class="line"> 8: <span class="keywordtype">int</span> min = <a class="codeRef" doxygen="/home/twhuang/PhD/Code/cpp-taskflow/doxygen/cppreference-doxygen-web.tag.xml:http://en.cppreference.com/w/" href="http://en.cppreference.com/w/cpp/types/numeric_limits/max.html">std::numeric_limits<int>::max</a>();</div><div class="line"> 9:</div><div class="line">10: <a class="code" href="classtf_1_1Task.html">tf::Task</a> T1 = taskflow.<a class="code" href="classtf_1_1FlowBuilder.html#a4d52a7fe2814b264846a2085e931652c">emplace</a>([&] () { <span class="comment">// modifier task</span></div><div class="line">11: <span class="keywordflow">for</span>(<span class="keyword">auto</span>& item : items) {</div><div class="line">12: item = ::rand();</div><div class="line">13: }</div><div class="line">14: });</div><div class="line">15:</div><div class="line">16: <span class="keyword">auto</span> [S, T] = taskflow.<a class="code" href="classtf_1_1FlowBuilder.html#a06b06b57f8ec8bb060951fc71dd375fb">reduce</a>(items.begin(), items.end(), min, [] (<span class="keywordtype">int</span> a, <span class="keywordtype">int</span> b) {</div><div class="line">17: <span class="keywordflow">return</span> <a class="codeRef" doxygen="/home/twhuang/PhD/Code/cpp-taskflow/doxygen/cppreference-doxygen-web.tag.xml:http://en.cppreference.com/w/" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(a, b);</div><div class="line">18: });</div><div class="line">19:</div><div class="line">20: <a class="code" href="classtf_1_1Task.html">tf::Task</a> T2 = taskflow.<a class="code" href="classtf_1_1FlowBuilder.html#a4d52a7fe2814b264846a2085e931652c">emplace</a>([&] () { <span class="comment">// printer task</span></div><div class="line">21: <a class="codeRef" doxygen="/home/twhuang/PhD/Code/cpp-taskflow/doxygen/cppreference-doxygen-web.tag.xml:http://en.cppreference.com/w/" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"min is "</span> << min << std::endl;</div><div class="line">22: });</div><div class="line">23:</div><div class="line">24: T1.<a class="code" href="classtf_1_1Task.html#a8c78c453295a553c1c016e4062da8588">precede</a>(S); <span class="comment">// modifier task precedes the reducer</span></div><div class="line">25: T.<a class="code" href="classtf_1_1Task.html#a8c78c453295a553c1c016e4062da8588">precede</a>(T2); <span class="comment">// reducer precedes the printer task</span></div><div class="line">26:</div><div class="line">27: <a class="code" href="classtf_1_1Executor.html">tf::Executor</a>().<a class="code" href="classtf_1_1Executor.html#a81f35d5b0a20ac0646447eb80d97c0aa">run</a>(taskflow);</div><div class="line">28:</div><div class="line">29: <span class="keywordflow">return</span> 0;</div><div class="line">30: }</div></div><!-- fragment --><p>Debrief: </p><ul>
<li>Line 5 creates a taskflow object with four worker threads </li>
<li>Line 7 creates a vector of 1024 uninitialized integers </li>
<li>Line 8 creates an integer value and initializes it to the maximum representable value of <code>int</code> </li>
<li>Line 10-14 creates a modifier task that initializes the vector to random integer values </li>
<li>Line 16-18 creates a reduction graph to find the minimum element in the vector </li>
<li>Line 20-22 creates a task that prints the minimum value found after the reduction finishes </li>
<li>Line 24-25 adds two dependency links to implement our control flow </li>
<li>Line 27 dispatches the task dependency graph to threads and waits until the execution completes</li>
</ul>
<p>In the reduction graph, each worker thread applies the give reduce operator to a partition of 1024/4 = 512 items. The final minimum value is stored in the variable <code>min</code>. Since the variable <code>min</code> participates in the reduction process, it is users' responsibility to initialize it to a proper value.</p>
<h1><a class="anchor" id="Chapter4Example3"></a>
Example 3: Find the Minimum L1-norm</h1>
<p>The example below applies the method <a class="el" href="classtf_1_1FlowBuilder.html#a08d669f2286cb90fd5ba7dade1e93fef" title="constructs a task dependency graph of parallel transformation and reduction ">tf::Taskflow::transform_reduce</a> to find the minimum L1-norm out of a point set.</p>
<div class="fragment"><div class="line"> 1: #include <taskflow/taskflow.hpp></div><div class="line"> 2: </div><div class="line"> 3: <span class="keyword">struct </span>Point {</div><div class="line"> 4: <span class="keywordtype">int</span> x1 {::rand() % 10 - 5}; <span class="comment">// random value</span></div><div class="line"> 5: <span class="keywordtype">int</span> x2 {::rand() % 10 - 5}; <span class="comment">// random value</span></div><div class="line"> 6: };</div><div class="line"> 7: </div><div class="line"> 8: <span class="keywordtype">int</span> main() {</div><div class="line"> 9: </div><div class="line">10: <a class="code" href="classtf_1_1Taskflow.html">tf::Taskflow</a> taskflow;</div><div class="line">11: </div><div class="line">12: <a class="codeRef" doxygen="/home/twhuang/PhD/Code/cpp-taskflow/doxygen/cppreference-doxygen-web.tag.xml:http://en.cppreference.com/w/" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector<Point></a> points {1024};</div><div class="line">13: <span class="keywordtype">int</span> min = <a class="codeRef" doxygen="/home/twhuang/PhD/Code/cpp-taskflow/doxygen/cppreference-doxygen-web.tag.xml:http://en.cppreference.com/w/" href="http://en.cppreference.com/w/cpp/types/numeric_limits/max.html">std::numeric_limits<int>::max</a>();</div><div class="line">14: </div><div class="line">15: taskflow.<a class="code" href="classtf_1_1FlowBuilder.html#a08d669f2286cb90fd5ba7dade1e93fef">transform_reduce</a>(points.begin(), points.end(), min,</div><div class="line">16: [] (<span class="keywordtype">int</span> a, <span class="keywordtype">int</span> b) {</div><div class="line">17: <span class="keywordflow">return</span> <a class="codeRef" doxygen="/home/twhuang/PhD/Code/cpp-taskflow/doxygen/cppreference-doxygen-web.tag.xml:http://en.cppreference.com/w/" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(a, b);</div><div class="line">18: },</div><div class="line">19: [] (<span class="keyword">const</span> Point& point) -> <span class="keywordtype">int</span> { <span class="comment">// Find the L1-norm of the point</span></div><div class="line">20: <span class="keywordflow">return</span> std::abs(point.x1) + std::abs(point.x2);</div><div class="line">21: }</div><div class="line">22: );</div><div class="line">23: </div><div class="line">24: <a class="code" href="classtf_1_1Executor.html">tf::Executor</a>().<a class="code" href="classtf_1_1Executor.html#a81f35d5b0a20ac0646447eb80d97c0aa">run</a>(taskflow).get();</div><div class="line">25: </div><div class="line">26: <span class="keywordflow">return</span> 0;</div><div class="line">27: }</div></div><!-- fragment --><p>Debrief: </p><ul>
<li>Line 3-6 declares a point struct at 2D plane </li>
<li>Line 10 creates a taskflow object with four worker threads </li>
<li>Line 12 creates a vector of 1024 randomly initialized points </li>
<li>Line 13 creates an integer value and initializes it to the maximum representable value of <code>int</code> </li>
<li>Line 15-22 applies transform-reduce operation to find the point with the minimum L1 distance </li>
<li>Line 24 dispatches the task dependency graph to threads and waits until the execution completes </li>
</ul>
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