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  <title>p1192R1: Experience report - integrating Executors with Parallel Algorithms</title>
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/******************************************************************************/
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/******************************************************************************/

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/******************************************************************************/

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/******************************************************************************/
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/******************************************************************************/
/*                                    Tables                                  */
/******************************************************************************/

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/** Data tables (and properly marked-up index tables) *************************/
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		 Use class="complex data" for particularly complicated tables --
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		 Use class="long" on table cells with paragraph-like contents
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 <body class="h-entry">
  <div class="head">
   <p data-fill-with="logo"></p>
   <h1 class="p-name no-ref" id="title">p1192R1<br>Experience report - integrating Executors with Parallel Algorithms</h1>
   <h2 class="no-num no-toc no-ref heading settled" id="subtitle"><span class="content">Published Proposal, <time class="dt-updated" datetime="2018-11-05">5 November 2018</time></span></h2>
   <div data-fill-with="spec-metadata">
    <dl>
     <dt>Author:
     <dd>
      <dd class="editor p-author h-card vcard"><a class="p-name fn u-email email" href="mailto:trodgers@redhat.com">Thomas Rodgers</a> (<span class="p-org org">RedHat</span>)
     <dt>Audience:
     <dd>SG1, LEWG
     <dt>Project:
     <dd>ISO JTC1/SC22/WG21: Programming Language C++
    </dl>
   </div>
   <div data-fill-with="warning"></div>
   <hr title="Separator for header">
  </div>
  <div class="p-summary" data-fill-with="abstract">
   <h2 class="no-num no-toc no-ref heading settled" id="abstract"><span class="content">Abstract</span></h2>
   <p>This paper explores integrating Executors with an implementation of the standard parallel algorithms</p>
  </div>
  <nav data-fill-with="table-of-contents" id="toc">
   <h2 class="no-num no-toc no-ref" id="contents">Table of Contents</h2>
   <ol class="toc" role="directory">
    <li><a href="#bg"><span class="secno">1</span> <span class="content">Background</span></a>
    <li><a href="#on"><span class="secno">2</span> <span class="content">Plumbing .on()</span></a>
    <li>
     <a href="#be"><span class="secno">3</span> <span class="content">Digging into the parallel backend</span></a>
     <ol class="toc">
      <li><a href="#cancel_execution"><span class="secno">3.1</span> <span class="content">cancel_execution</span></a>
      <li><a href="#parallel_for"><span class="secno">3.2</span> <span class="content">parallel_for</span></a>
      <li><a href="#parallel_reduce"><span class="secno">3.3</span> <span class="content">parallel_reduce</span></a>
      <li><a href="#parallel_transform_reduce"><span class="secno">3.4</span> <span class="content">parallel_transform_reduce</span></a>
      <li><a href="#parallel_strict_scan"><span class="secno">3.5</span> <span class="content">parallel_strict_scan</span></a>
      <li><a href="#parallel_transform_scan"><span class="secno">3.6</span> <span class="content">parallel_transform_scan</span></a>
      <li><a href="#parallel_stable_sort"><span class="secno">3.7</span> <span class="content">parallel_stable_sort</span></a>
      <li><a href="#parallel_merge"><span class="secno">3.8</span> <span class="content">parallel_merge</span></a>
      <li><a href="#parallel_partial_sort"><span class="secno">3.9</span> <span class="content">parallel_partial_sort</span></a>
     </ol>
    <li><a href="#summary"><span class="secno">4</span> <span class="content">Summary</span></a>
    <li>
     <a href="#references"><span class="secno"></span> <span class="content">References</span></a>
     <ol class="toc">
      <li><a href="#informative"><span class="secno"></span> <span class="content">Informative References</span></a>
     </ol>
   </ol>
  </nav>
  <main>
   <h2 class="heading settled" data-level="1" id="bg"><span class="secno">1. </span><span class="content">Background</span><a class="self-link" href="#bg"></a></h2>
   <p>This paper explores adapting an existing implementation <a data-link-type="biblio" href="#biblio-pstl">[pstl]</a> of C++17 parallel algorithms to use the
executors proposals as outlined in <a data-link-type="biblio" href="#biblio-p0443">[p0443]</a> and <a data-link-type="biblio" href="#biblio-p1019">[p1019]</a>.</p>
   <h2 class="heading settled" data-level="2" id="on"><span class="secno">2. </span><span class="content">Plumbing .on()</span><a class="self-link" href="#on"></a></h2>
    <a data-link-type="biblio" href="#biblio-p1019">[p1019]</a> extends the existing parallel execution policies to take a .on() method which allows an executor to
be passed into a standard algorithm taking an exeuction policy. The .on() method rebinds the execution policy
to the supplied Executor, e.g. 
<pre class="highlight"><span class="k">template</span><span class="o">&lt;</span><span class="k">typename</span> <span class="n">_ExecutionRequirement</span><span class="p">,</span> <span class="k">typename</span> <span class="n">_Executor</span><span class="o">></span>
<span class="k">class</span> <span class="nc">__basic_executor_policy_t</span> <span class="o">:</span> <span class="n">__policy_t</span><span class="o">&lt;</span><span class="n">_ExecutionRequirement</span><span class="o">></span>
<span class="p">{</span>
    <span class="n">_Executor</span> <span class="n">_M_executor</span><span class="p">;</span>

    <span class="k">template</span><span class="o">&lt;</span><span class="k">typename</span> <span class="n">_tp</span><span class="o">></span>
    <span class="k">friend</span> <span class="k">auto</span> <span class="n">__make_execution_policy</span><span class="p">(</span><span class="n">_tp</span> <span class="n">__ex</span><span class="p">)</span> <span class="o">-></span> <span class="n">__basic_executor_policy_t</span><span class="o">&lt;</span><span class="n">_ExecutionRequirement</span><span class="p">,</span> <span class="n">_tp</span><span class="o">></span>
    <span class="p">{</span> <span class="k">return</span> <span class="n">__basic_executor_policy_t</span><span class="o">&lt;</span><span class="n">_ExecutionRequirement</span><span class="p">,</span> <span class="n">_tp</span><span class="o">></span><span class="p">{</span> <span class="n">std</span><span class="o">::</span><span class="n">move</span><span class="p">(</span><span class="n">__ex</span><span class="p">)</span> <span class="p">};</span> <span class="p">}</span>

<span class="k">public</span><span class="o">:</span>
    <span class="n">_Executor</span> <span class="n">executor</span><span class="p">()</span> <span class="k">const</span>
    <span class="p">{</span> <span class="k">return</span> <span class="n">_M_executor</span><span class="p">;</span> <span class="p">}</span>
<span class="p">};</span>

<span class="c1">// 2.5, Parallel execution policy</span>
<span class="c1"></span><span class="k">template</span><span class="o">&lt;</span><span class="k">typename</span> <span class="n">_ExecutionRequirement</span><span class="p">,</span> <span class="k">typename</span> <span class="n">_Executor</span><span class="o">></span>
<span class="k">class</span> <span class="nc">__parallel_policy_t</span>
<span class="p">{</span>
    <span class="n">_Executor</span> <span class="n">_M_executor</span><span class="p">;</span>

<span class="k">public</span><span class="o">:</span>
    <span class="k">static</span> <span class="k">constexpr</span> <span class="n">_ExecutionRequirement</span> <span class="n">execution_requirement</span><span class="p">{};</span>

    <span class="k">static</span> <span class="k">constexpr</span> <span class="k">auto</span> <span class="nf">__allow_unsequenced</span><span class="p">()</span> <span class="p">{</span> <span class="k">return</span> <span class="n">execution_requirement</span><span class="p">.</span><span class="n">__allow_parallel</span><span class="p">();</span> <span class="p">}</span>
    <span class="k">static</span> <span class="k">constexpr</span> <span class="k">auto</span> <span class="nf">__allow_vector</span><span class="p">()</span> <span class="p">{</span> <span class="k">return</span> <span class="n">execution_requirement</span><span class="p">.</span><span class="n">__allow_vector</span><span class="p">();</span> <span class="p">}</span>
    <span class="k">static</span> <span class="k">constexpr</span> <span class="k">auto</span> <span class="nf">__allow_parallel</span><span class="p">()</span> <span class="p">{</span> <span class="k">return</span> <span class="n">execution_requirement</span><span class="p">.</span><span class="n">__allow_parallel</span><span class="p">();</span> <span class="p">}</span>

    <span class="n">__parallel_policy_t</span><span class="p">()</span> <span class="o">=</span> <span class="k">default</span><span class="p">;</span>

    <span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">_Tp</span><span class="o">></span>
    <span class="k">auto</span> <span class="n">on</span><span class="p">(</span><span class="n">_Tp</span> <span class="n">__ex</span><span class="p">)</span> <span class="k">const</span> <span class="o">-></span>
        <span class="n">__basic_executor_policy_t</span><span class="o">&lt;</span><span class="n">_ExecutionRequirement</span><span class="p">,</span> <span class="n">_Tp</span><span class="o">></span>
    <span class="p">{</span> <span class="k">return</span> <span class="n">__make_execution_policy</span><span class="p">(</span><span class="n">std</span><span class="o">::</span><span class="n">move</span><span class="p">(</span><span class="n">__ex</span><span class="p">));</span> <span class="p">}</span>

    <span class="n">_Executor</span> <span class="n">executor</span><span class="p">()</span> <span class="k">const</span>
    <span class="p">{</span> <span class="k">return</span> <span class="n">_M_executor</span><span class="p">;</span> <span class="p">}</span>
<span class="p">};</span>

<span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">_Executor</span><span class="o">></span>
<span class="k">using</span> <span class="n">parallel_policy_t</span> <span class="o">=</span> <span class="n">__parallel_policy_t</span><span class="o">&lt;</span><span class="n">bulk_guarantee_t</span><span class="o">::</span><span class="n">parallel_t</span><span class="p">,</span> <span class="n">_Executor</span><span class="o">></span><span class="p">;</span>

<span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">_Executor</span><span class="o">></span>
<span class="k">using</span> <span class="n">parallel_unsequenced_policy_t</span> <span class="o">=</span> <span class="n">__parallel_policy_t</span><span class="o">&lt;</span><span class="n">bulk_guarantee_t</span><span class="o">::</span><span class="n">parallel_unsequenced_t</span><span class="p">,</span> <span class="n">_Executor</span><span class="o">></span><span class="p">;</span>
</pre>
   <p>Intel’s existing implementation relies on Intel’s Thread Building Blocks <a data-link-type="biblio" href="#biblio-tbb">[tbb]</a> library to implement
parallel execution. The implementation, however, envisions that this is a pluggable compile time option
currently only for implementing std::execution::parallel_policy and std::execution::parallel_unsequenced_policy.</p>
   <p>The implementation expects any replacement parallel backend to provide the following functions -</p>
<pre class="highlight"><span class="kt">void</span> <span class="nf">cancel_execution</span><span class="p">();</span>

<span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">Index</span><span class="p">,</span> <span class="k">class</span> <span class="nc">Fp</span><span class="o">></span>
<span class="kt">void</span> <span class="n">parallel_for</span><span class="p">(</span> <span class="n">Index</span> <span class="n">first</span><span class="p">,</span> <span class="n">Index</span> <span class="n">last</span><span class="p">,</span> <span class="n">Fp</span> <span class="n">f</span> <span class="p">);</span>

<span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">Value</span><span class="p">,</span> <span class="k">class</span> <span class="nc">Index</span><span class="p">,</span> <span class="k">class</span> <span class="nc">RealBody</span><span class="p">,</span> <span class="k">class</span> <span class="nc">Reduction</span><span class="o">></span>
<span class="n">Value</span> <span class="n">parallel_reduce</span><span class="p">(</span> <span class="n">Index</span> <span class="n">first</span><span class="p">,</span> <span class="n">Index</span> <span class="n">last</span><span class="p">,</span> <span class="k">const</span> <span class="n">Value</span><span class="o">&amp;</span> <span class="n">identity</span><span class="p">,</span>
                       <span class="k">const</span> <span class="n">RealBody</span><span class="o">&amp;</span> <span class="n">realbody</span><span class="p">,</span> <span class="k">const</span> <span class="n">Reduction</span><span class="o">&amp;</span> <span class="n">reduction</span> <span class="p">);</span>

<span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">Index</span><span class="p">,</span> <span class="k">class</span> <span class="nc">Up</span><span class="p">,</span> <span class="k">class</span> <span class="nc">Tp</span><span class="p">,</span> <span class="k">class</span> <span class="nc">Cp</span><span class="p">,</span> <span class="k">class</span> <span class="nc">Rp</span><span class="o">></span>
<span class="n">Tp</span> <span class="n">parallel_transform_reduce</span><span class="p">(</span> <span class="n">Index</span> <span class="n">first</span><span class="p">,</span> <span class="n">Index</span> <span class="n">last</span><span class="p">,</span>
                              <span class="n">Up</span> <span class="n">u</span><span class="p">,</span> <span class="n">Tp</span> <span class="n">init</span><span class="p">,</span> <span class="n">Cp</span> <span class="n">combine</span><span class="p">,</span> <span class="n">Rp</span> <span class="n">brickreduce</span> <span class="p">);</span>

<span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">Index</span><span class="p">,</span> <span class="k">class</span> <span class="nc">Up</span><span class="p">,</span> <span class="k">class</span> <span class="nc">Tp</span><span class="p">,</span> <span class="k">class</span> <span class="nc">Cp</span><span class="p">,</span> <span class="k">class</span> <span class="nc">Rp</span><span class="p">,</span> <span class="k">class</span> <span class="nc">Sp</span><span class="o">></span>
<span class="n">Tp</span> <span class="n">parallel_transform_scan</span><span class="p">(</span> <span class="n">Index</span> <span class="n">n</span><span class="p">,</span> <span class="n">Up</span> <span class="n">u</span><span class="p">,</span> <span class="n">Tp</span> <span class="n">init</span><span class="p">,</span> <span class="n">Cp</span> <span class="n">combine</span><span class="p">,</span>
                            <span class="n">Rp</span> <span class="n">brickreduce</span><span class="p">,</span> <span class="n">Sp</span> <span class="n">scan</span> <span class="p">);</span>

<span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">Index</span><span class="p">,</span> <span class="k">class</span> <span class="nc">Tp</span><span class="p">,</span> <span class="k">class</span> <span class="nc">Rp</span><span class="p">,</span> <span class="k">class</span> <span class="nc">Cp</span><span class="p">,</span> <span class="k">class</span> <span class="nc">Sp</span><span class="p">,</span> <span class="k">class</span> <span class="nc">Ap</span><span class="o">></span>
<span class="kt">void</span> <span class="n">parallel_strict_scan</span><span class="p">(</span> <span class="n">Index</span> <span class="n">n</span><span class="p">,</span> <span class="n">Tp</span> <span class="n">initial</span><span class="p">,</span> <span class="n">Rp</span> <span class="n">reduce</span><span class="p">,</span> <span class="n">Cp</span> <span class="n">combine</span><span class="p">,</span>
                           <span class="n">Sp</span> <span class="n">scan</span><span class="p">,</span> <span class="n">Ap</span> <span class="n">apex</span> <span class="p">);</span>

<span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">RandomAccessIterator</span><span class="p">,</span> <span class="k">class</span> <span class="nc">Compare</span><span class="p">,</span> <span class="k">class</span> <span class="nc">LeafSort</span><span class="o">></span>
<span class="kt">void</span> <span class="n">parallel_stable_sort</span><span class="p">(</span> <span class="n">RandomAccessIterator</span> <span class="n">xs</span><span class="p">,</span> <span class="n">RandomAccessIterator</span> <span class="n">xe</span><span class="p">,</span>
                           <span class="n">Compare</span> <span class="n">comp</span><span class="p">,</span> <span class="n">LeafSort</span> <span class="n">leafsort</span> <span class="p">);</span>

<span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">RandomAccessIterator1</span><span class="p">,</span> <span class="k">class</span> <span class="nc">RandomAccessIterator2</span><span class="p">,</span>
         <span class="k">class</span> <span class="nc">RandomAccessIterator3</span><span class="p">,</span>
         <span class="k">class</span> <span class="nc">Compare</span><span class="p">,</span> <span class="k">class</span> <span class="nc">LeafMerge</span><span class="o">></span>
<span class="kt">void</span> <span class="n">parallel_merge</span><span class="p">(</span> <span class="n">RandomAccessIterator1</span> <span class="n">xs</span><span class="p">,</span> <span class="n">RandomAccessIterator1</span> <span class="n">xe</span><span class="p">,</span>
                     <span class="n">RandomAccessIterator2</span> <span class="n">ys</span><span class="p">,</span> <span class="n">RandomAccessIterator2</span> <span class="n">ye</span><span class="p">,</span>
                     <span class="n">RandomAccessIterator3</span> <span class="n">zs</span><span class="p">,</span>
                     <span class="n">Compare</span> <span class="n">comp</span><span class="p">,</span> <span class="n">LeafMerge</span> <span class="n">leafmerge</span> <span class="p">);</span>

<span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">RandomAccessIterator</span><span class="p">,</span> <span class="k">class</span> <span class="nc">Compare</span><span class="o">></span>
<span class="kt">void</span> <span class="n">parallel_partial_sort</span><span class="p">(</span> <span class="n">RandomAccessIterator</span> <span class="n">xs</span><span class="p">,</span> <span class="n">RandomAccessIterator</span> <span class="n">xm</span><span class="p">,</span>
                            <span class="n">RandomAccessIterator</span> <span class="n">xe</span><span class="p">,</span> <span class="n">Compare</span> <span class="n">comp</span> <span class="p">);</span>
</pre>
   <p>None of these functions take an execution policy, and thus no way to communicate the executor
supplied to .on(). There needs to be a way to carry the execution policy from the user visible library
API to the backend. The obvious change to call signatures is to accept the execution policy as the first
parameter is explored in this paper, eg.</p>
<pre class="highlight"><span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">ExecutionPolicy</span><span class="p">,</span> <span class="k">class</span> <span class="nc">Index</span><span class="p">,</span> <span class="k">class</span> <span class="nc">Up</span><span class="p">,</span> <span class="k">class</span> <span class="nc">Tp</span><span class="p">,</span> <span class="k">class</span> <span class="nc">Cp</span><span class="p">,</span> <span class="k">class</span> <span class="nc">Rp</span><span class="o">></span>
<span class="n">Tp</span> <span class="n">parallel_transform_reduce</span><span class="p">(</span> <span class="n">ExecutionPolicy</span><span class="o">&amp;&amp;</span> <span class="n">exec</span><span class="p">,</span>
                              <span class="n">Index</span> <span class="n">first</span><span class="p">,</span> <span class="n">Index</span> <span class="n">last</span><span class="p">,</span>
                              <span class="n">Up</span> <span class="n">u</span><span class="p">,</span> <span class="n">Tp</span> <span class="n">init</span><span class="p">,</span> <span class="n">Cp</span> <span class="n">combine</span><span class="p">,</span> <span class="n">Rp</span> <span class="n">brickreduce</span> <span class="p">);</span>
</pre>
   <p>Obviously the implementation layer above the backend needs to be modified to pass through the execution policy
to the backend as well -</p>
<pre class="highlight"><span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">_ExecutionPolicy</span><span class="p">,</span> <span class="k">class</span> <span class="nc">_ForwardIterator</span><span class="p">,</span> <span class="k">class</span> <span class="nc">_Function</span><span class="o">></span>
<span class="n">__pstl</span><span class="o">::</span><span class="n">internal</span><span class="o">::</span><span class="n">enable_if_execution_policy</span><span class="o">&lt;</span><span class="n">_ExecutionPolicy</span><span class="p">,</span> <span class="kt">void</span><span class="o">></span>
<span class="n">for_each</span><span class="p">(</span><span class="n">_ExecutionPolicy</span><span class="o">&amp;&amp;</span> <span class="n">__exec</span><span class="p">,</span> <span class="n">_ForwardIterator</span> <span class="n">__first</span><span class="p">,</span> <span class="n">_ForwardIterator</span> <span class="n">__last</span><span class="p">,</span> <span class="n">_Function</span> <span class="n">__f</span><span class="p">)</span> <span class="p">{</span>
    <span class="k">using</span> <span class="k">namespace</span> <span class="n">__pstl</span><span class="p">;</span>
    <span class="n">internal</span><span class="o">::</span><span class="n">pattern_walk1</span><span class="p">(</span><span class="n">std</span><span class="o">::</span><span class="n">forward</span><span class="o">&lt;</span><span class="n">_ExecutionPolicy</span><span class="o">></span><span class="p">(</span><span class="n">__exec</span><span class="p">),</span>
                            <span class="n">__first</span><span class="p">,</span> <span class="n">__last</span><span class="p">,</span> <span class="n">__f</span><span class="p">,</span>
                            <span class="n">internal</span><span class="o">::</span><span class="n">is_vectorization_preferred</span><span class="o">&lt;</span><span class="n">_ExecutionPolicy</span><span class="p">,</span><span class="n">_ForwardIterator</span><span class="o">></span><span class="p">(</span><span class="n">__exec</span><span class="p">),</span>
                            <span class="n">internal</span><span class="o">::</span><span class="n">is_parallelization_preferred</span><span class="o">&lt;</span><span class="n">_ExecutionPolicy</span><span class="p">,</span><span class="n">_ForwardIterator</span><span class="o">></span><span class="p">(</span><span class="n">__exec</span><span class="p">));</span>
<span class="p">}</span>

<span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">_ExecutionPolicy</span><span class="p">,</span> <span class="k">class</span> <span class="nc">_ForwardIterator</span><span class="p">,</span> <span class="k">class</span> <span class="nc">_Function</span><span class="p">,</span> <span class="k">class</span> <span class="nc">_IsVector</span><span class="o">></span>
<span class="kt">void</span> <span class="n">pattern_walk1</span><span class="p">(</span> <span class="n">_ExecutionPolicy</span><span class="o">&amp;&amp;</span><span class="p">,</span> <span class="n">_ForwardIterator</span> <span class="n">__first</span><span class="p">,</span> <span class="n">_ForwardIterator</span> <span class="n">__last</span><span class="p">,</span> <span class="n">_Function</span> <span class="n">__f</span><span class="p">,</span> <span class="n">_IsVector</span> <span class="n">__is_vector</span><span class="p">,</span>
                    <span class="cm">/*parallel=*/</span><span class="n">std</span><span class="o">::</span><span class="n">false_type</span> <span class="p">)</span> <span class="k">noexcept</span> <span class="p">{</span>
    <span class="n">internal</span><span class="o">::</span><span class="n">brick_walk1</span><span class="p">(</span> <span class="n">__first</span><span class="p">,</span> <span class="n">__last</span><span class="p">,</span> <span class="n">__f</span><span class="p">,</span> <span class="n">__is_vector</span> <span class="p">);</span>
<span class="p">}</span>

<span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">_ExecutionPolicy</span><span class="p">,</span> <span class="k">class</span> <span class="nc">_ForwardIterator</span><span class="p">,</span> <span class="k">class</span> <span class="nc">_Function</span><span class="p">,</span> <span class="k">class</span> <span class="nc">_IsVector</span><span class="o">></span>
<span class="kt">void</span> <span class="n">pattern_walk1</span><span class="p">(</span> <span class="n">_ExecutionPolicy</span><span class="o">&amp;&amp;</span> <span class="n">__exec</span><span class="p">,</span> <span class="n">_ForwardIterator</span> <span class="n">__first</span><span class="p">,</span> <span class="n">_ForwardIterator</span> <span class="n">__last</span><span class="p">,</span> <span class="n">_Function</span> <span class="n">__f</span><span class="p">,</span> <span class="n">_IsVector</span> <span class="n">__is_vector</span><span class="p">,</span>
                    <span class="cm">/*parallel=*/</span><span class="n">std</span><span class="o">::</span><span class="n">true_type</span> <span class="p">)</span> <span class="p">{</span>
    <span class="n">internal</span><span class="o">::</span><span class="n">except_handler</span><span class="p">([</span><span class="o">=</span><span class="p">]()</span> <span class="p">{</span>
        <span class="n">par_backend</span><span class="o">::</span><span class="n">parallel_for</span><span class="p">(</span> <span class="n">std</span><span class="o">::</span><span class="n">forward</span><span class="o">&lt;</span><span class="n">_ExecutionPolicy</span><span class="o">></span><span class="p">(</span><span class="n">__exec</span><span class="p">),</span>
                                   <span class="n">__first</span><span class="p">,</span> <span class="n">__last</span><span class="p">,</span>
                                   <span class="p">[</span><span class="n">__f</span><span class="p">,</span><span class="n">__is_vector</span><span class="p">](</span><span class="n">_ForwardIterator</span> <span class="n">__i</span><span class="p">,</span> <span class="n">_ForwardIterator</span> <span class="n">__j</span><span class="p">)</span> <span class="p">{</span>
                                       <span class="n">internal</span><span class="o">::</span><span class="n">brick_walk1</span><span class="p">(</span> <span class="n">__i</span><span class="p">,</span> <span class="n">__j</span><span class="p">,</span> <span class="n">__f</span><span class="p">,</span> <span class="n">__is_vector</span> <span class="p">);</span>
                                   <span class="p">});</span>
        <span class="p">});</span>
<span class="p">}</span>
</pre>
   <p>Intel’s implementation never conceived of execution policies being used for anything other than tag dispatch types, which
given the library’s design approach, makes this change a fairly sprawling one to apply. The p1019 approach otherwise fits
well within the existing implementation.</p>
   <h2 class="heading settled" data-level="3" id="be"><span class="secno">3. </span><span class="content">Digging into the parallel backend</span><a class="self-link" href="#be"></a></h2>
    As noted in the preceding section, the <a data-link-type="biblio" href="#biblio-pstl">[pstl]</a> parallel code requires any replacement backend to provide the following capabilities - 
   <h3 class="heading settled" data-level="3.1" id="cancel_execution"><span class="secno">3.1. </span><span class="content">cancel_execution</span><a class="self-link" href="#cancel_execution"></a></h3>
    Is used to eagerly cancel execution, used by algorithms like find_if. The implementation is fairly straight forward - 
<pre class="highlight"><span class="c1">// Wrapper for tbb::task</span>
<span class="c1"></span><span class="kr">inline</span> <span class="kt">void</span> <span class="nf">cancel_execution</span><span class="p">()</span> <span class="p">{</span>
    <span class="n">tbb</span><span class="o">::</span><span class="n">task</span><span class="o">::</span><span class="n">self</span><span class="p">().</span><span class="n">group</span><span class="p">()</span><span class="o">-></span><span class="n">cancel_group_execution</span><span class="p">();</span>
<span class="p">}</span>
</pre>
   <p>Every other backend entry point establishes an isolated task group using the following pattern -</p>
<pre class="highlight"><span class="n">tbb</span><span class="o">::</span><span class="n">this_task_arena</span><span class="o">::</span><span class="n">isolate</span><span class="p">([</span><span class="o">=</span><span class="p">]()</span> <span class="p">{</span>
    <span class="c1">// interesting bits go here...</span>
<span class="c1"></span><span class="p">});</span>
</pre>
   <p>Currently task cancellation is <em>not</em> covered in either <a data-link-type="biblio" href="#biblio-p0443">[p0443]</a> or <a data-link-type="biblio" href="#biblio-p1019">[p1019]</a>. It is also not strictly required of any backend to support
task cancellation. In that case, those algorithms like find_if that might benefit from early termination would just potentially do more work.</p>
   <h3 class="heading settled" data-level="3.2" id="parallel_for"><span class="secno">3.2. </span><span class="content">parallel_for</span><a class="self-link" href="#parallel_for"></a></h3>
    Delegates directly to the tbb supplied implementation - 
<pre class="highlight"><span class="c1">//! Evaluation of brick f[i,j) for each subrange [i,j) of [first,last)</span>
<span class="c1">// wrapper over tbb::parallel_for</span>
<span class="c1"></span><span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">_Index</span><span class="p">,</span> <span class="k">class</span> <span class="nc">_Fp</span><span class="o">></span>
<span class="kt">void</span> <span class="n">parallel_for</span><span class="p">(</span><span class="n">_Index</span> <span class="n">__first</span><span class="p">,</span> <span class="n">_Index</span> <span class="n">__last</span><span class="p">,</span> <span class="n">_Fp</span> <span class="n">__f</span><span class="p">)</span> <span class="p">{</span>
    <span class="n">tbb</span><span class="o">::</span><span class="n">this_task_arena</span><span class="o">::</span><span class="n">isolate</span><span class="p">([</span><span class="o">=</span><span class="p">]()</span> <span class="p">{</span>
        <span class="n">tbb</span><span class="o">::</span><span class="n">parallel_for</span><span class="p">(</span><span class="n">tbb</span><span class="o">::</span><span class="n">blocked_range</span><span class="o">&lt;</span><span class="n">_Index</span><span class="o">></span><span class="p">(</span><span class="n">__first</span><span class="p">,</span> <span class="n">__last</span><span class="p">),</span> <span class="n">parallel_for_body</span><span class="o">&lt;</span><span class="n">_Index</span><span class="p">,</span> <span class="n">_Fp</span><span class="o">></span><span class="p">(</span><span class="n">__f</span><span class="p">));</span>
    <span class="p">});</span>
<span class="p">}</span>
</pre>
   <p>As with TBB, <a data-link-type="biblio" href="#biblio-p0443">[p0443]</a> has direct support for parallel_for in the form of Bulk one-way execution with blocking semantics
required() on .execute(). Mapping the executor modified pstl backend parallel_for to the appropriate execute() call is a
simple exercise (TODO provide example).</p>
   <p>It is out of scope for executors to provide more sophisticated control structures, so all remaining backend APIs must
supply control structures which may be written in terms of <a data-link-type="biblio" href="#biblio-p0443">[p0443]</a>.</p>
   <h3 class="heading settled" data-level="3.3" id="parallel_reduce"><span class="secno">3.3. </span><span class="content">parallel_reduce</span><a class="self-link" href="#parallel_reduce"></a></h3>
    Delegates directly to the tbb supplied implementation - 
<pre class="highlight"><span class="c1">//! Evaluation of brick f[i,j) for each subrange [i,j) of [first,last)</span>
<span class="c1">// wrapper over tbb::parallel_reduce</span>
<span class="c1"></span><span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">_Value</span><span class="p">,</span> <span class="k">class</span> <span class="nc">_Index</span><span class="p">,</span> <span class="k">typename</span> <span class="n">_RealBody</span><span class="p">,</span> <span class="k">typename</span> <span class="n">_Reduction</span><span class="o">></span>
<span class="n">_Value</span> <span class="n">parallel_reduce</span><span class="p">(</span><span class="n">_Index</span> <span class="n">__first</span><span class="p">,</span> <span class="n">_Index</span> <span class="n">__last</span><span class="p">,</span> <span class="k">const</span> <span class="n">_Value</span><span class="o">&amp;</span> <span class="n">__identity</span><span class="p">,</span> <span class="k">const</span> <span class="n">_RealBody</span><span class="o">&amp;</span> <span class="n">__real_body</span><span class="p">,</span>
                       <span class="k">const</span> <span class="n">_Reduction</span><span class="o">&amp;</span> <span class="n">__reduction</span><span class="p">)</span> <span class="p">{</span>
    <span class="k">return</span> <span class="n">tbb</span><span class="o">::</span><span class="n">this_task_arena</span><span class="o">::</span><span class="n">isolate</span><span class="p">([</span><span class="n">__first</span><span class="p">,</span> <span class="n">__last</span><span class="p">,</span> <span class="o">&amp;</span><span class="n">__identity</span><span class="p">,</span> <span class="o">&amp;</span><span class="n">__real_body</span><span class="p">,</span> <span class="o">&amp;</span><span class="n">__reduction</span><span class="p">]()</span> <span class="o">-></span> <span class="n">_Value</span> <span class="p">{</span>
        <span class="k">return</span> <span class="n">tbb</span><span class="o">::</span><span class="n">parallel_reduce</span><span class="p">(</span><span class="n">tbb</span><span class="o">::</span><span class="n">blocked_range</span><span class="o">&lt;</span><span class="n">_Index</span><span class="o">></span><span class="p">(</span><span class="n">__first</span><span class="p">,</span> <span class="n">__last</span><span class="p">),</span> <span class="n">__identity</span><span class="p">,</span>
            <span class="p">[</span><span class="n">__real_body</span><span class="p">](</span><span class="k">const</span> <span class="n">tbb</span><span class="o">::</span><span class="n">blocked_range</span><span class="o">&lt;</span><span class="n">_Index</span><span class="o">>&amp;</span> <span class="n">__r</span><span class="p">,</span> <span class="k">const</span> <span class="n">_Value</span><span class="o">&amp;</span> <span class="n">__value</span><span class="p">)</span><span class="o">-></span> <span class="n">_Value</span> <span class="p">{</span>
            <span class="k">return</span> <span class="n">__real_body</span><span class="p">(</span><span class="n">__r</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="n">__r</span><span class="p">.</span><span class="n">end</span><span class="p">(),</span> <span class="n">__value</span><span class="p">);</span>
        <span class="p">},</span>
        <span class="n">__reduction</span><span class="p">);</span>
    <span class="p">});</span>
<span class="p">}</span>
</pre>
   <p>A review of the Intel TBB implementation of parallel_reduce suggests that this functionality can be implemented
in terms of <a data-link-type="biblio" href="#biblio-p0443">[p0443]</a>'s relationship_t::fork_t and relationship_t::continuation_t properties.</p>
   <h3 class="heading settled" data-level="3.4" id="parallel_transform_reduce"><span class="secno">3.4. </span><span class="content">parallel_transform_reduce</span><a class="self-link" href="#parallel_transform_reduce"></a></h3>
    Is written in terms of parallel_reduce - 
<pre class="highlight"><span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">_Index</span><span class="p">,</span> <span class="k">class</span> <span class="nc">_Up</span><span class="p">,</span> <span class="k">class</span> <span class="nc">_Tp</span><span class="p">,</span> <span class="k">class</span> <span class="nc">_Cp</span><span class="p">,</span> <span class="k">class</span> <span class="nc">_Rp</span><span class="o">></span>
<span class="n">_Tp</span> <span class="n">parallel_transform_reduce</span><span class="p">(</span> <span class="n">_Index</span> <span class="n">__first</span><span class="p">,</span> <span class="n">_Index</span> <span class="n">__last</span><span class="p">,</span> <span class="n">_Up</span> <span class="n">__u</span><span class="p">,</span> <span class="n">_Tp</span> <span class="n">__init</span><span class="p">,</span> <span class="n">_Cp</span> <span class="n">__combine</span><span class="p">,</span> <span class="n">_Rp</span> <span class="n">__brick_reduce</span><span class="p">)</span> <span class="p">{</span>
    <span class="n">par_trans_red_body</span><span class="o">&lt;</span><span class="n">_Index</span><span class="p">,</span> <span class="n">_Up</span><span class="p">,</span> <span class="n">_Tp</span><span class="p">,</span> <span class="n">_Cp</span><span class="p">,</span> <span class="n">_Rp</span><span class="o">></span> <span class="n">__body</span><span class="p">(</span><span class="n">__u</span><span class="p">,</span> <span class="n">__init</span><span class="p">,</span> <span class="n">__combine</span><span class="p">,</span> <span class="n">__brick_reduce</span><span class="p">);</span>
    <span class="c1">// The grain size of 3 is used in order to provide mininum 2 elements for each body</span>
<span class="c1"></span>    <span class="n">tbb</span><span class="o">::</span><span class="n">this_task_arena</span><span class="o">::</span><span class="n">isolate</span><span class="p">([</span><span class="n">__first</span><span class="p">,</span> <span class="n">__last</span><span class="p">,</span> <span class="o">&amp;</span><span class="n">__body</span><span class="p">]()</span> <span class="p">{</span>
        <span class="n">tbb</span><span class="o">::</span><span class="n">parallel_reduce</span><span class="p">(</span><span class="n">tbb</span><span class="o">::</span><span class="n">blocked_range</span><span class="o">&lt;</span><span class="n">_Index</span><span class="o">></span><span class="p">(</span><span class="n">__first</span><span class="p">,</span> <span class="n">__last</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="n">__body</span><span class="p">);</span>
    <span class="p">});</span>
    <span class="k">return</span> <span class="n">__body</span><span class="p">.</span><span class="n">sum</span><span class="p">();</span>
<span class="p">}</span>
</pre>
   <p>As, such, it is not really a basis operation for the parallel backend. It is however, likely a customization point for
an implementation supplied backend.</p>
   <h3 class="heading settled" data-level="3.5" id="parallel_strict_scan"><span class="secno">3.5. </span><span class="content">parallel_strict_scan</span><a class="self-link" href="#parallel_strict_scan"></a></h3>
    The <a data-link-type="biblio" href="#biblio-pstl">[pstl]</a> parallel backend provides a full implementation, adapted from <a data-link-type="biblio" href="#biblio-cilk">[cilk]</a> which makes the following demands of the <a data-link-type="biblio" href="#biblio-tbb">[tbb]</a> backend - 
<pre class="highlight"><span class="n">tbb</span><span class="o">::</span><span class="n">parallel_invoke</span><span class="p">(</span>
        <span class="p">[</span><span class="o">=</span><span class="p">]</span> <span class="p">{</span><span class="n">par_backend</span><span class="o">::</span><span class="n">upsweep</span><span class="p">(</span><span class="n">__i</span><span class="p">,</span> <span class="n">__k</span><span class="p">,</span> <span class="n">__tilesize</span><span class="p">,</span> <span class="n">__r</span><span class="p">,</span> <span class="n">__tilesize</span><span class="p">,</span> <span class="n">__reduce</span><span class="p">,</span> <span class="n">__combine</span><span class="p">);</span> <span class="p">},</span>
        <span class="p">[</span><span class="o">=</span><span class="p">]</span> <span class="p">{</span><span class="n">par_backend</span><span class="o">::</span><span class="n">upsweep</span><span class="p">(</span><span class="n">__i</span> <span class="o">+</span> <span class="n">__k</span><span class="p">,</span> <span class="n">__m</span> <span class="o">-</span> <span class="n">__k</span><span class="p">,</span> <span class="n">__tilesize</span><span class="p">,</span> <span class="n">__r</span> <span class="o">+</span> <span class="n">__k</span><span class="p">,</span> <span class="n">__lastsize</span><span class="p">,</span> <span class="n">__reduce</span><span class="p">,</span> <span class="n">__combine</span><span class="p">);</span> <span class="p">}</span>
<span class="p">);</span>
</pre>
   <p>parallel_invoke here simply spawning a tree of tasks and waiting for the sub-tree’s completion. This is a generic control
structure which can be implemented in terms of <a data-link-type="biblio" href="#biblio-p0443">[p0443]</a> one way execution with barrier synchronization.</p>
   <h3 class="heading settled" data-level="3.6" id="parallel_transform_scan"><span class="secno">3.6. </span><span class="content">parallel_transform_scan</span><a class="self-link" href="#parallel_transform_scan"></a></h3>
    Is implemented in terms of <a data-link-type="biblio" href="#biblio-tbb">[tbb]</a>'s parallel_scan - 
<pre class="highlight"><span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">_Index</span><span class="p">,</span> <span class="k">class</span> <span class="nc">_Up</span><span class="p">,</span> <span class="k">class</span> <span class="nc">_Tp</span><span class="p">,</span> <span class="k">class</span> <span class="nc">_Cp</span><span class="p">,</span> <span class="k">class</span> <span class="nc">_Rp</span><span class="p">,</span> <span class="k">class</span> <span class="nc">_Sp</span><span class="o">></span>
<span class="n">_Tp</span> <span class="n">parallel_transform_scan</span><span class="p">(</span><span class="n">_Index</span> <span class="n">__n</span><span class="p">,</span> <span class="n">_Up</span> <span class="n">__u</span><span class="p">,</span> <span class="n">_Tp</span> <span class="n">__init</span><span class="p">,</span> <span class="n">_Cp</span> <span class="n">__combine</span><span class="p">,</span> <span class="n">_Rp</span> <span class="n">__brick_reduce</span><span class="p">,</span> <span class="n">_Sp</span> <span class="n">__scan</span><span class="p">)</span> <span class="p">{</span>
    <span class="k">if</span> <span class="p">(</span><span class="n">__n</span> <span class="o">&lt;=</span> <span class="mi">0</span><span class="p">)</span>
        <span class="k">return</span> <span class="n">__init</span><span class="p">;</span>

    <span class="n">trans_scan_body</span><span class="o">&lt;</span><span class="n">_Index</span><span class="p">,</span> <span class="n">_Up</span><span class="p">,</span> <span class="n">_Tp</span><span class="p">,</span> <span class="n">_Cp</span><span class="p">,</span> <span class="n">_Rp</span><span class="p">,</span> <span class="n">_Sp</span><span class="o">></span> <span class="n">__body</span><span class="p">(</span><span class="n">__u</span><span class="p">,</span> <span class="n">__init</span><span class="p">,</span> <span class="n">__combine</span><span class="p">,</span> <span class="n">__brick_reduce</span><span class="p">,</span> <span class="n">__scan</span><span class="p">);</span>
    <span class="k">auto</span> <span class="n">__range</span> <span class="o">=</span> <span class="n">tbb</span><span class="o">::</span><span class="n">blocked_range</span><span class="o">&lt;</span><span class="n">_Index</span><span class="o">></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">tbb</span><span class="o">::</span><span class="n">this_task_arena</span><span class="o">::</span><span class="n">isolate</span><span class="p">([</span><span class="n">__range</span><span class="p">,</span> <span class="o">&amp;</span><span class="n">__body</span><span class="p">]()</span> <span class="p">{</span>
        <span class="n">tbb</span><span class="o">::</span><span class="n">parallel_scan</span><span class="p">(</span><span class="n">__range</span><span class="p">,</span> <span class="n">__body</span><span class="p">);</span>
    <span class="p">});</span>
    <span class="k">return</span> <span class="n">__body</span><span class="p">.</span><span class="n">sum</span><span class="p">();</span>
<span class="p">}</span>
</pre>
   <p>It is likely that parallel_transform_scan can be built in terms of the same basis operations as parallel_strict_scan, and thus
is is implementable in terms of <a data-link-type="biblio" href="#biblio-p0443">[p0443]</a>.</p>
   <h3 class="heading settled" data-level="3.7" id="parallel_stable_sort"><span class="secno">3.7. </span><span class="content">parallel_stable_sort</span><a class="self-link" href="#parallel_stable_sort"></a></h3>
    The <a data-link-type="biblio" href="#biblio-pstl">[pstl]</a> parallel backend provides a full implementation of this algorithm, which makes the following demands of the <a data-link-type="biblio" href="#biblio-tbb">[tbb]</a> backend - 
<pre class="highlight"><span class="n">tbb</span><span class="o">::</span><span class="n">task</span><span class="o">*</span> <span class="n">__right</span> <span class="o">=</span> <span class="k">new</span><span class="p">(</span><span class="n">tbb</span><span class="o">::</span><span class="n">task</span><span class="o">::</span><span class="n">allocate_additional_child_of</span><span class="p">(</span><span class="o">*</span><span class="n">parent</span><span class="p">()))</span>
    <span class="n">merge_task</span><span class="p">(</span><span class="n">__xm</span><span class="p">,</span> <span class="n">_M_xe</span><span class="p">,</span> <span class="n">__ym</span><span class="p">,</span> <span class="n">_M_ye</span><span class="p">,</span> <span class="n">__zm</span><span class="p">,</span> <span class="n">_M_comp</span><span class="p">,</span> <span class="n">_M_cleanup</span><span class="p">,</span> <span class="n">_M_leaf_merge</span><span class="p">);</span>
<span class="n">tbb</span><span class="o">::</span><span class="n">task</span><span class="o">::</span><span class="n">spawn</span><span class="p">(</span><span class="o">*</span><span class="n">__right</span><span class="p">);</span>
<span class="n">tbb</span><span class="o">::</span><span class="n">task</span><span class="o">::</span><span class="n">recycle_as_continuation</span><span class="p">();</span>
</pre>
   <p>The task tree dependency tracking in this code would seem to be covered by <a data-link-type="biblio" href="#biblio-p0443">[p0443]</a>'s relationship_t::fork_t and
relationship_t::continuation_t properties.</p>
<pre class="highlight"><span class="k">template</span><span class="o">&lt;</span><span class="k">typename</span> <span class="n">_RandomAccessIterator</span><span class="p">,</span> <span class="k">typename</span> <span class="n">_Compare</span><span class="p">,</span> <span class="k">typename</span> <span class="n">_LeafSort</span><span class="o">></span>
<span class="kt">void</span> <span class="n">parallel_stable_sort</span><span class="p">(</span><span class="n">_RandomAccessIterator</span> <span class="n">__xs</span><span class="p">,</span> <span class="n">_RandomAccessIterator</span> <span class="n">__xe</span><span class="p">,</span> <span class="n">_Compare</span> <span class="n">__comp</span><span class="p">,</span> <span class="n">_LeafSort</span> <span class="n">__leaf_sort</span><span class="p">)</span> <span class="p">{</span>
    <span class="n">tbb</span><span class="o">::</span><span class="n">this_task_arena</span><span class="o">::</span><span class="n">isolate</span><span class="p">([</span><span class="o">=</span><span class="p">]()</span> <span class="p">{</span>
        <span class="c1">//sorting based on task tree and parallel merge</span>
<span class="c1"></span>        <span class="k">typedef</span> <span class="k">typename</span> <span class="n">std</span><span class="o">::</span><span class="n">iterator_traits</span><span class="o">&lt;</span><span class="n">_RandomAccessIterator</span><span class="o">>::</span><span class="n">value_type</span> <span class="n">_ValueType</span><span class="p">;</span>
        <span class="k">if</span> <span class="p">(</span><span class="n">__xe</span> <span class="o">-</span> <span class="n">__xs</span> <span class="o">></span> <span class="n">__PSTL_STABLE_SORT_CUT_OFF</span><span class="p">)</span> <span class="p">{</span>
          <span class="n">par_backend</span><span class="o">::</span><span class="n">buffer</span><span class="o">&lt;</span><span class="n">_ValueType</span><span class="o">></span> <span class="n">__buf</span><span class="p">(</span><span class="n">__xe</span> <span class="o">-</span> <span class="n">__xs</span><span class="p">);</span>
            <span class="k">if</span> <span class="p">(</span><span class="n">__buf</span><span class="p">)</span> <span class="p">{</span>
              <span class="k">typedef</span> <span class="n">stable_sort_task</span><span class="o">&lt;</span><span class="n">_RandomAccessIterator</span><span class="p">,</span> <span class="n">_ValueType</span><span class="o">*</span><span class="p">,</span> <span class="n">_Compare</span><span class="p">,</span> <span class="n">_LeafSort</span><span class="o">></span> <span class="n">_TaskType</span><span class="p">;</span>
              <span class="n">tbb</span><span class="o">::</span><span class="n">task</span><span class="o">::</span><span class="n">spawn_root_and_wait</span><span class="p">(</span><span class="o">*</span><span class="k">new</span><span class="p">(</span><span class="n">tbb</span><span class="o">::</span><span class="n">task</span><span class="o">::</span><span class="n">allocate_root</span><span class="p">())</span> <span class="n">_TaskType</span><span class="p">(</span><span class="n">__xs</span><span class="p">,</span> <span class="n">__xe</span><span class="p">,</span> <span class="p">(</span><span class="n">_ValueType</span><span class="o">*</span><span class="p">)</span><span class="n">__buf</span><span class="p">.</span><span class="n">get</span><span class="p">(),</span> <span class="mi">2</span><span class="p">,</span>
                                                                                         <span class="n">__comp</span><span class="p">,</span> <span class="n">__leaf_sort</span><span class="p">));</span>
                <span class="k">return</span><span class="p">;</span>
            <span class="p">}</span>
        <span class="p">}</span>
        <span class="c1">// Not enough memory available or sort too small - fall back on serial sort</span>
<span class="c1"></span>        <span class="n">__leaf_sort</span><span class="p">(</span><span class="n">__xs</span><span class="p">,</span> <span class="n">__xe</span><span class="p">,</span> <span class="n">__comp</span><span class="p">);</span>
    <span class="p">});</span>
<span class="p">}</span>
</pre>
   <p>This is <a data-link-type="biblio" href="#biblio-p0443">[p0443]</a> .execute() on an executor where the blocking property has been required.</p>
   <h3 class="heading settled" data-level="3.8" id="parallel_merge"><span class="secno">3.8. </span><span class="content">parallel_merge</span><a class="self-link" href="#parallel_merge"></a></h3>
    The <a data-link-type="biblio" href="#biblio-pstl">[pstl]</a> parallel backend provides a full implementation of this algorithm which makes the same requirements, in terms
of basis functions, as parallel_stable_sort. 
   <h3 class="heading settled" data-level="3.9" id="parallel_partial_sort"><span class="secno">3.9. </span><span class="content">parallel_partial_sort</span><a class="self-link" href="#parallel_partial_sort"></a></h3>
    The <a data-link-type="biblio" href="#biblio-pstl">[pstl]</a> parallel backend provides a full implementation of this algorithm which makes the same requirements, in terms
of basis functions, as parallel_stable_sort and parallel_transform_reduce. 
   <h2 class="heading settled" data-level="4" id="summary"><span class="secno">4. </span><span class="content">Summary</span><a class="self-link" href="#summary"></a></h2>
    After reviewing an existing implementation of C++17 algorithms, with an eye to determining whether the executor design as
proposed is sufficient to implement the execution abstractions for that implementation, the author concludes that this
is feasible with a reference implementation in progress. 
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  <h2 class="no-num no-ref heading settled" id="references"><span class="content">References</span><a class="self-link" href="#references"></a></h2>
  <h3 class="no-num no-ref heading settled" id="informative"><span class="content">Informative References</span><a class="self-link" href="#informative"></a></h3>
  <dl>
   <dt id="biblio-cilk">[CILK]
   <dd><a href="https://www.cilkplus.org/">Intel Cilk(TM) Plus</a>. URL: <a href="https://www.cilkplus.org/">https://www.cilkplus.org/</a>
   <dt id="biblio-p0443">[P0443]
   <dd>Jared Hoberock, et. al.. <a href="https://wg21.link/p0443">A Unified Executors Proposal for C++</a>. May 07, 2018. URL: <a href="https://wg21.link/p0443">https://wg21.link/p0443</a>
   <dt id="biblio-p1019">[P1019]
   <dd>Jared Hoberock. <a href="https://wg21.link/p1019">Integrating Executors with Parallel Algorithms</a>. May 07, 2018. URL: <a href="https://wg21.link/p1019">https://wg21.link/p1019</a>
   <dt id="biblio-pstl">[PSTL]
   <dd><a href="https://github.com/intel/parallelstl">Intel Parallel STL implementation</a>. URL: <a href="https://github.com/intel/parallelstl">https://github.com/intel/parallelstl</a>
   <dt id="biblio-tbb">[TBB]
   <dd><a href="https://www.threadingbuildingblocks.org/">Thread Building Blocks (Intel TBB)</a>. URL: <a href="https://www.threadingbuildingblocks.org/">https://www.threadingbuildingblocks.org/</a>
  </dl>