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Eliminate [parallel.alg.{overloads,defns}]
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‎algorithms.html

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<cxx-clause id="parallel.alg">
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<h1>Parallel algorithms</h1>
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<cxx-section id="parallel.alg.general.wavefront">
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<h1>Wavefront Application</h1>
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<p>
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For the purposes of this section, an <i>evaluation</i> is a value computation or side effect of
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an expression, or an execution of a statement. Initialization of a temporary object is considered a
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subexpression of the expression that necessitates the temporary object.
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</p>
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<p>
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An evaluation A <i>contains</i> an evaluation B if:
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<ul>
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<li>A and B are not potentially concurrent ([intro.races]); and</li>
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<li>the start of A is the start of B or the start of A is sequenced before the start of B; and</li>
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<li>the completion of B is the completion of A or the completion of B is sequenced before the completion of A.</li>
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</ul>
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<cxx-note>This includes evaluations occurring in function invocations.</cxx-note>
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</p>
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<p>
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An evaluation A is <i>ordered before</i> an evaluation B if A is deterministically
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sequenced before B. <cxx-note>If A is indeterminately sequenced with respect to B
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or A and B are unsequenced, then A is not ordered before B and B is not ordered
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before A. The ordered before relationship is transitive.</cxx-note>
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</p>
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<cxx-section id="parallel.alg.wavefront">
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<h1>Wavefront Application</h1>
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<p>
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For the purposes of this section, an <i>evaluation</i> is a value computation or side effect of
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an expression, or an execution of a statement. Initialization of a temporary object is considered a
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subexpression of the expression that necessitates the temporary object.
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</p>
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<p>
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For an evaluation A ordered before an evaluation B, both contained in the same
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invocation of an element access function, A is a <i>vertical antecedent</i> of B if:
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<p>
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An evaluation A <i>contains</i> an evaluation B if:
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<ul>
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<li>there exists an evaluation S such that:
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<ul>
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<li>S contains A, and</li>
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<li>S contains all evaluations C (if any) such that A is ordered before C and C is ordered before B,</li>
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<li>but S does not contain B, and</li>
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</ul>
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</li>
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<li>
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control reached B from A without executing any of the following:
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<ul>
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<li>a <code>goto</code> statement or <code>asm</code> declaration that jumps to a statement outside of S, or</li>
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<li>a <code>switch</code> statement executed within S that transfers control into a substatement of a nested selection or iteration statement, or</li>
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<li>a <code>throw</code> <cxx-note>even if caught</cxx-note>, or</li>
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<li>a <code>longjmp</code>.
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</ul>
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</li>
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</ul>
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<ul>
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<li>A and B are not potentially concurrent ([intro.races]); and</li>
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<li>the start of A is the start of B or the start of A is sequenced before the start of B; and</li>
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<li>the completion of B is the completion of A or the completion of B is sequenced before the completion of A.</li>
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</ul>
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<cxx-note>
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Vertical antecedent is an irreflexive, antisymmetric, nontransitive relationship between two evaluations.
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Informally, A is a vertical antecedent of B if A is sequenced immediately before B or A is nested zero or
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more levels within a statement S that immediately precedes B.
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</cxx-note>
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</p>
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<cxx-note>This includes evaluations occurring in function invocations.</cxx-note>
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</p>
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<p>
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In the following, <i>X<sub>i</sub></i> and <i>X<sub>j</sub></i> refer to evaluations of the <i>same</i> expression
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or statement contained in the application of an element access function corresponding to the i<sup>th</sup> and
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j<sup>th</sup> elements of the input sequence. <cxx-note>There might be several evaluations <i>X<sub>k</sub></i>,
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<i>Y<sub>k</sub></i>, etc. of a single expression or statement in application <i>k</i>, for example, if the
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expression or statement appears in a loop within the element access function.</cxx-note>
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</p>
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<p>
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An evaluation A is <i>ordered before</i> an evaluation B if A is deterministically
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sequenced before B. <cxx-note>If A is indeterminately sequenced with respect to B
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or A and B are unsequenced, then A is not ordered before B and B is not ordered
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before A. The ordered before relationship is transitive.</cxx-note>
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</p>
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<p>
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<i>Horizontally matched</i> is an equivalence relationship between two evaluations of the same expression. An
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evaluation B<sub>i</sub> is <i>horizontally matched</i> with an evaluation B<sub>j</sub> if:
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<p>
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For an evaluation A ordered before an evaluation B, both contained in the same
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invocation of an element access function, A is a <i>vertical antecedent</i> of B if:
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<ul>
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<li>there exists an evaluation S such that:
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<ul>
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<li>both are the first evaluations in their respective applications of the element access function, or</li>
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<li>there exist horizontally matched evaluations A<sub>i</sub> and A<sub>j</sub> that are vertical antecedents of evaluations B<sub>i</sub> and B<sub>j</sub>, respectively.
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<li>S contains A, and</li>
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<li>S contains all evaluations C (if any) such that A is ordered before C and C is ordered before B,</li>
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<li>but S does not contain B, and</li>
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</ul>
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<cxx-note>
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<i>Horizontally matched</i> establishes a theoretical <i>lock-step</i> relationship between evaluations in different applications of an element access function.
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</cxx-note>
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</p>
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<p>
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Let <i>f</i> be a function called for each argument list in a sequence of argument lists.
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<i>Wavefront application</i> of <i>f</i> requires that evaluation A<sub>i</sub> be sequenced
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before evaluation B<sub>i</sub> if i &lt; j and and:
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</li>
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<li>
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control reached B from A without executing any of the following:
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<ul>
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<li>A<sub>i</sub> is sequenced before some evaluation B<sub>i</sub> and B<sub>i</sub> is horizontally matched with B<sub>j</sub>, or</li>
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<li>A<sub>i</sub> is horizontally matched with some evaluation A<sub>j</sub> and A<sub>j</sub> is sequenced before B<sub>j<sub>.</li>
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<li>a <code>goto</code> statement or <code>asm</code> declaration that jumps to a statement outside of S, or</li>
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<li>a <code>switch</code> statement executed within S that transfers control into a substatement of a nested selection or iteration statement, or</li>
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<li>a <code>throw</code> <cxx-note>even if caught</cxx-note>, or</li>
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<li>a <code>longjmp</code>.
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</ul>
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</li>
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</ul>
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<cxx-note>
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<i>Wavefront application</i> guarantees that parallel applications i and j execute such that progress on application j never gets <i>ahead</i> of application i.
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</cxx-note>
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<cxx-note>
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The relationships between A<sub>i</sub> and B<sub>i</sub> and between A<sub>j</sub> and B<sub>j</sub> are <i>sequenced before</i>, not <i>vertical antecedent</i>.
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</cxx-note>
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</p>
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</cxx-section>
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<cxx-section id="parallel.alg.overloads">
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<h1><del><code>ExecutionPolicy</code> algorithm overloads</del></h1>
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<del>
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<p>
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The Parallel Algorithms Library provides overloads for each of the algorithms named in
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Table 1, corresponding to the algorithms with the same name in the C++ Standard Algorithms Library.
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For each algorithm in <cxx-ref to="tab.parallel.algorithms"></cxx-ref>, if there are overloads for
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corresponding algorithms with the same name
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in the C++ Standard Algorithms Library,
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the overloads shall have an additional template type parameter named
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<code>ExecutionPolicy</code>, which shall be the first template parameter.
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In addition, each such overload shall have the new function parameter as the
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first function parameter of type <code>ExecutionPolicy&amp;&amp;</code>.
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</p>
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</del>
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<del>
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<p>
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Unless otherwise specified, the semantics of <code>ExecutionPolicy</code> algorithm overloads
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are identical to their overloads without.
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</p>
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</del>
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<del>
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<p>
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Parallel algorithms shall not participate in overload resolution unless
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<code>is_execution_policy&lt;decay_t&lt;ExecutionPolicy&gt;&gt;::value</code> is <code>true</code>.
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</p>
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</del>
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<del>
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<table is="cxx-table" id="tab.parallel.algorithms" class="list">
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<caption><del>Table of parallel algorithms</del></caption>
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<tr>
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<td><code>adjacent_difference</code></td>
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<td><code>adjacent_find</code></td>
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<td><code>all_of</code></td>
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<td><code>any_of</code></td>
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</tr>
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<tr>
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<td><code>copy</code></td>
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<td><code>copy_if</code></td>
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<td><code>copy_n</code></td>
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<td><code>count</code></td>
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</tr>
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<tr>
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<td><code>count_if</code></td>
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<td><code>equal</code></td>
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<td><code>exclusive_scan</code></td>
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<td><code>fill</code></td>
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</tr>
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<tr>
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<td><code>fill_n</code></td>
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<td><code>find</code></td>
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<td><code>find_end</code></td>
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<td><code>find_first_of</code></td>
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</tr>
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<tr>
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<td><code>find_if</code></td>
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<td><code>find_if_not</code></td>
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<td><code>for_each</code></td>
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<td><code>for_each_n</code></td>
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</tr>
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<tr>
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<td><code>generate</code></td>
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<td><code>generate_n</code></td>
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<td><code>includes</code></td>
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<td><code>inclusive_scan</code></td>
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</tr>
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<tr>
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<td><code>inner_product</code></td>
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<td><code>inplace_merge</code></td>
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<td><code>is_heap</code></td>
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<td><code>is_heap_until</code></td>
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</tr>
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<tr>
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<td><code>is_partitioned</code></td>
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<td><code>is_sorted</code></td>
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<td><code>is_sorted_until</code></td>
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<td><code>lexicographical_compare</code></td>
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</tr>
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<tr>
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<td><code>max_element</code></td>
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<td><code>merge</code></td>
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<td><code>min_element</code></td>
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<td><code>minmax_element</code></td>
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</tr>
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<tr>
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<td><code>mismatch</code></td>
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<td><code>move</code></td>
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<td><code>none_of</code></td>
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<td><code>nth_element</code></td>
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</tr>
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<tr>
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<td><code>partial_sort</code></td>
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<td><code>partial_sort_copy</code></td>
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<td><code>partition</code></td>
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<td><code>partition_copy</code></td>
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</tr>
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<tr>
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<td><code>reduce</code></td>
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<td><code>remove</code></td>
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<td><code>remove_copy</code></td>
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<td><code>remove_copy_if</code></td>
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</tr>
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<tr>
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<td><code>remove_if</code></td>
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<td><code>replace</code></td>
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<td><code>replace_copy</code></td>
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<td><code>replace_copy_if</code></td>
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</tr>
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<tr>
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<td><code>replace_if</code></td>
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<td><code>reverse</code></td>
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<td><code>reverse_copy</code></td>
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<td><code>rotate</code></td>
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</tr>
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<tr>
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<td><code>rotate_copy</code></td>
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<td><code>search</code></td>
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<td><code>search_n</code></td>
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<td><code>set_difference</code></td>
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</tr>
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<tr>
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<td><code>set_intersection</code></td>
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<td><code>set_symmetric_difference</code></td>
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<td><code>set_union</code></td>
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<td><code>sort</code></td>
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</tr>
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<tr>
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<td><code>stable_partition</code></td>
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<td><code>stable_sort</code></td>
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<td><code>swap_ranges</code></td>
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<td><code>transform</code></td>
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</tr>
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<tr>
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<td><code>transform_exclusive_scan</code></td>
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<td><code>transform_inclusive_scan</code></td>
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<td><code>transform_reduce</code></td>
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<td><code>uninitialized_copy</code></td>
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</tr>
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<tr>
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<td><code>uninitialized_copy_n</code></td>
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<td><code>uninitialized_fill</code></td>
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<td><code>uninitialized_fill_n</code></td>
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<td><code>unique</code></td>
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</tr>
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<tr>
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<td><code>unique_copy</code></td>
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<td></td>
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<td></td>
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<td></td>
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</tr>
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</table>
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</del>
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<del>
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<cxx-note>
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Not all algorithms in the Standard Library have counterparts in <cxx-ref to="tab.parallel.algorithms"></cxx-ref>.
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Vertical antecedent is an irreflexive, antisymmetric, nontransitive relationship between two evaluations.
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Informally, A is a vertical antecedent of B if A is sequenced immediately before B or A is nested zero or
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more levels within a statement S that immediately precedes B.
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</cxx-note>
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</del>
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</cxx-section>
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</cxx-section>
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</p>
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<cxx-section id="parallel.alg.defns">
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<h1><del>Definitions</del></h1>
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<p>
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In the following, <i>X<sub>i</sub></i> and <i>X<sub>j</sub></i> refer to evaluations of the <i>same</i> expression
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or statement contained in the application of an element access function corresponding to the i<sup>th</sup> and
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j<sup>th</sup> elements of the input sequence. <cxx-note>There might be several evaluations <i>X<sub>k</sub></i>,
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<i>Y<sub>k</sub></i>, etc. of a single expression or statement in application <i>k</i>, for example, if the
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expression or statement appears in a loop within the element access function.</cxx-note>
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</p>
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<del>
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<p>
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Define <code><em>GENERALIZED_SUM</em>(op, a1, ..., aN)</code> as follows:
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<i>Horizontally matched</i> is an equivalence relationship between two evaluations of the same expression. An
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evaluation B<sub>i</sub> is <i>horizontally matched</i> with an evaluation B<sub>j</sub> if:
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<ul>
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<li><code>a1</code> when <code>N</code> is <code>1</code></li>
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<li>
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<code>op(<em>GENERALIZED_SUM</em>(op, b1, ..., bK)</code>, <code><em>GENERALIZED_SUM</em>(op, bM, ..., bN))</code> where
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<ul>
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<li><code>b1, ..., bN</code> may be any permutation of <code>a1, ..., aN</code> and</li>
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<li><code>1 &lt; K+1 = M &le; N</code>.</li>
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</ul>
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</li>
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<li>both are the first evaluations in their respective applications of the element access function, or</li>
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<li>there exist horizontally matched evaluations A<sub>i</sub> and A<sub>j</sub> that are vertical antecedents of evaluations B<sub>i</sub> and B<sub>j</sub>, respectively.
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</ul>
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<cxx-note>
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<i>Horizontally matched</i> establishes a theoretical <i>lock-step</i> relationship between evaluations in different applications of an element access function.
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</cxx-note>
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</p>
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</del>
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<del>
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<p>
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Define <code><em>GENERALIZED_NONCOMMUTATIVE_SUM</em>(op, a1, ..., aN)</code> as follows:
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Let <i>f</i> be a function called for each argument list in a sequence of argument lists.
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<i>Wavefront application</i> of <i>f</i> requires that evaluation A<sub>i</sub> be sequenced
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before evaluation B<sub>i</sub> if i &lt; j and and:
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<ul>
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<li><code>a1</code> when <code>N</code> is <code>1</code></li>
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<li>
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<code>op(<em>GENERALIZED_NONCOMMUTATIVE_SUM</em>(op, a1, ..., aK), <em>GENERALIZED_NONCOMMUTATIVE_SUM</em>(op, aM, </code><br>
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<code>..., aN)</code> where <code>1 &lt; K+1 = M &le; N</code>.
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</li>
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<li>A<sub>i</sub> is sequenced before some evaluation B<sub>i</sub> and B<sub>i</sub> is horizontally matched with B<sub>j</sub>, or</li>
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<li>A<sub>i</sub> is horizontally matched with some evaluation A<sub>j</sub> and A<sub>j</sub> is sequenced before B<sub>j<sub>.</li>
30491
</ul>
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<cxx-note>
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<i>Wavefront application</i> guarantees that parallel applications i and j execute such that progress on application j never gets <i>ahead</i> of application i.
95+
</cxx-note>
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<cxx-note>
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The relationships between A<sub>i</sub> and B<sub>i</sub> and between A<sub>j</sub> and B<sub>j</sub> are <i>sequenced before</i>, not <i>vertical antecedent</i>.
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</cxx-note>
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</p>
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</del>
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</cxx-section>
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<cxx-section id="parallel.alg.ops">

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