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  <title>P2500R2: C++ parallel algorithms and P2300</title>
<style data-fill-with="stylesheet">/******************************************************************************
 *                   Style sheet for the W3C specifications                   *
 *
 * Special classes handled by this style sheet include:
 *
 * Indices
 *   - .toc for the Table of Contents (<ol class="toc">)
 *     + <span class="secno"> for the section numbers
 *   - #toc for the Table of Contents (<nav id="toc">)
 *   - ul.index for Indices (<a href="#ref">term</a><span>, in § N.M</span>)
 *   - table.index for Index Tables (e.g. for properties or elements)
 *
 * Structural Markup
 *   - table.data for general data tables
 *     -> use 'scope' attribute, <colgroup>, <thead>, and <tbody> for best results !
 *     -> use <table class='complex data'> for extra-complex tables
 *     -> use <td class='long'> for paragraph-length cell content
 *     -> use <td class='pre'> when manual line breaks/indentation would help readability
 *   - dl.switch for switch statements
 *   - ol.algorithm for algorithms (helps to visualize nesting)
 *   - .figure and .caption (HTML4) and figure and figcaption (HTML5)
 *     -> .sidefigure for right-floated figures
 *   - ins/del
 *     -> ins/del.c### for candidate and proposed changes (amendments)
 *
 * Code
 *   - pre and code
 *
 * Special Sections
 *   - .note       for informative notes             (div, p, span, aside, details)
 *   - .example    for informative examples          (div, p, pre, span)
 *   - .issue      for issues                        (div, p, span)
 *   - .advisement for loud normative statements     (div, p, strong)
 *   - .annoying-warning for spec obsoletion notices (div, aside, details)
 *   - .correction for "candidate corrections"       (div, aside, details, section)
 *   - .addition   for "candidate additions"         (div, aside, details, section)
 *   - .correction.proposed for "proposed corrections" (div, aside, details, section)
 *   - .addition.proposed   for "proposed additions"   (div, aside, details, section)
 *
 * Definition Boxes
 *   - pre.def   for WebIDL definitions
 *   - table.def for tables that define other entities (e.g. CSS properties)
 *   - dl.def    for definition lists that define other entitles (e.g. HTML elements)
 *
 * Numbering
 *   - .secno for section numbers in .toc and headings (<span class='secno'>3.2</span>)
 *   - .marker for source-inserted example/figure/issue numbers (<span class='marker'>Issue 4</span>)
 *   - ::before styled for CSS-generated issue/example/figure numbers:
 *     -> Documents wishing to use this only need to add
 *        figcaption::before,
 *        .caption::before { content: "Figure "  counter(figure) " ";  }
 *        .example::before { content: "Example " counter(example) " "; }
 *        .issue::before   { content: "Issue "   counter(issue) " ";   }
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 * Header Stuff (ignore, just don't conflict with these classes)
 *   - .head for the header
 *   - .copyright for the copyright
 *
 * Outdated warning for old specs
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 *     on its container, depending on the effect desired.
 *     Note that this styling basically doesn't help at all when printing,
 *     since A4 paper isn't much wider than the max-width here.
 *     It's better to design things to fit into a narrower measure if possible.
 *
 *   - js-added ToC jump links (see fixup.js)
 *
 ******************************************************************************/

/* color variables included separately for reliability */

/******************************************************************************/
/*                                    Body                                    */
/******************************************************************************/

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/******************************************************************************/
/*                         Front Matter & Navigation                          */
/******************************************************************************/

/** Header ********************************************************************/

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/** W3C Logo ******************************************************************/

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	/* see also additional rules in Link Styling section */

/** Copyright *****************************************************************/

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/** Back to Top / ToC Toggle **************************************************/

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/** ToC Sidebar ***************************************************************/

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		/* See also Overflow section at the bottom */

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/******************************************************************************/
/*                                Sectioning                                  */
/******************************************************************************/

/** Headings ******************************************************************/

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		page-break-inside: avoid;
		font: 100% sans-serif;   /* Reset all font styling to clear out UA styles */
		font-family: inherit;	/* Inherit the font family. */
		line-height: 1.2;		/* Keep wrapped headings compact */
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	h1, h2, h3 {
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	h3 { font-size: 120%; }
	h4 { font-weight: bold; }
	h5 { font-style: italic; }
	h6 { font-variant: small-caps; }
	dt { font-weight: bold; }

/** Subheadings ***************************************************************/

	h1 + h2,
	#profile-and-date {
		/* #profile-and-date is a subtitle in an H2 under the H1 */
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	h2 + h3,
	h3 + h4,
	h4 + h5,
	h5 + h6 {
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/** Section divider ***********************************************************/

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	:not(.head) > hr::before {
		content: "\2727\2003\2003\2727\2003\2003\2727";
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/******************************************************************************/
/*                            Paragraphs and Lists                            */
/******************************************************************************/

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	dl dd {
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	.head dd + dd { /* compact for header */
		margin-top: -.5em;
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	/* Style for algorithms */
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	}

	/* Put nice boxes around each algorithm. */
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	 padding: .5em;
	 border: thin solid #ddd;
	 border: thin solid var(--algo-border);
	 border-radius: .5em;
	 margin: .5em calc(-0.5em - 1px);
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	[data-algorithm]:not(.heading) > :last-child {
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	/* Style for switch/case <dl>s */
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	margin-left: 0;
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	dl.switch > dd > ol.algorithm,
	dl.switch > dd > .algorithm > ol {
	margin-left: -2em;
	}
	dl.switch {
	padding-left: 2em;
	}
	dl.switch > dt {
	text-indent: -1.5em;
	margin-top: 1em;
	}
	dl.switch > dt + dt {
	margin-top: 0;
	}
	dl.switch > dt::before {
	content: '\21AA';
	padding: 0 0.5em 0 0;
	display: inline-block;
	width: 1em;
	text-align: right;
	line-height: 0.5em;
	}

/** Terminology Markup ********************************************************/


/******************************************************************************/
/*                                 Inline Markup                              */
/******************************************************************************/

/** Terminology Markup ********************************************************/
	dfn   { /* Defining instance */
		font-weight: bolder;
	}
	a > i { /* Instance of term */
		font-style: normal;
	}
	dt dfn code, code.idl {
		font-size: inherit;
	}
	dfn var {
		font-style: normal;
	}

/** Change Marking ************************************************************/

	del {
		color: #aa0000;
		color: var(--del-text);
		background: transparent;
		background: var(--del-bg);
		text-decoration: line-through;
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	ins {
		color: #006100;
		color: var(--ins-text);
		background: transparent;
		background: var(--ins-bg);
		text-decoration: underline;
	}

	/* for amendments (candidate/proposed changes) */

	.amendment ins, .correction ins, .addition ins,
	ins[class^=c] {
		text-decoration-style: dotted;
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	.amendment del, .correction del, .addition del,
	del[class^=c] {
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	.amendment.proposed ins, .correction.proposed ins, .addition.proposed ins,
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	.amendment.proposed del, .correction.proposed del, .addition.proposed del,
	del[class^=c].proposed {
		text-decoration-style: double;
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/** Miscellaneous improvements to inline formatting ***************************/

	sup {
		vertical-align: super;
		font-size: 80%
	}

/******************************************************************************/
/*                                    Code                                    */
/******************************************************************************/

/** General monospace/pre rules ***********************************************/

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		font-size: .9em;
		hyphens: none;
		text-transform: none;
		text-align: left;
		text-align: start;
		font-variant: normal;
		orphans: 3;
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		font-size: 100%;
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	pre {
		margin-top: 1em;
		margin-bottom: 1em;
		overflow: auto;
	}

/** Inline Code fragments *****************************************************/

	/* Do something nice. */

/******************************************************************************/
/*                                    Links                                   */
/******************************************************************************/

/** General Hyperlinks ********************************************************/

	/* We hyperlink a lot, so make it less intrusive */
	a[href] {
		color: #034575;
		color: var(--a-normal-text);
		text-decoration: underline #707070;
		text-decoration: underline var(--a-normal-underline);
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	a:visited {
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	/* Indicate interaction with the link */
	a[href]:focus,
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	a[href]:active {
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	/* Backout above styling for W3C logo */
	.head .logo,
	.head .logo a {
		border: none;
		text-decoration: none;
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/******************************************************************************/
/*                                    Images                                  */
/******************************************************************************/

	img {
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	}

	img, svg {
		/* Intentionally not color-scheme aware. */
		background: white;
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	/* For autogen numbers, add
	  .caption::before, figcaption::before { content: "Figure " counter(figure) ". "; }
	*/

	figure, .figure, .sidefigure {
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		margin: 2.5em 0;
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	.figure img,	.sidefigure img,	figure img,
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		margin: auto;
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	.figure pre, .sidefigure pre, figure pre {
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	.figure table, figure table {
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			float: right;
			width: 50%;
			margin: 0 0 0.5em 0.5em;
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	.caption, figcaption, caption {
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		font-size: 90%;
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	.caption::before, figcaption::before, figcaption > .marker {
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	.caption, figcaption {
		counter-increment: figure;
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	/* DL list is indented 2em, but figure inside it is not */
	dd > .figure, dd > figure { margin-left: -2em; }

/******************************************************************************/
/*                             Colored Boxes                                  */
/******************************************************************************/

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		margin: 1em auto;
		padding: .5em;
		border: .5em;
		border-left-style: solid;
		page-break-inside: avoid;
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	span.issue, span.note {
		padding: .1em .5em .15em;
		border-right-style: solid;
	}

	blockquote > :first-child,
	.note  > p:first-child,
	.issue > p:first-child,
	.amendment > p:first-child,
	.correction > p:first-child,
	.addition > p:first-child {
		margin-top: 0;
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	blockquote > :last-child,
	.note  > p:last-child,
	.issue > p:last-child,
	.amendment > p:last-child,
	.correction > p:last-child,
	.addition > p:last-child {
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	.example::before, .example > .marker,
	.note::before, .note > .marker,
	details.note > summary > .marker,
	.amendment::before, .amendment > .marker,
	details.amendment > summary > .marker,
	.addition::before, .addition > .marker,
	addition.amendment > summary > .marker,
	.correction::before, .correction > .marker,
	correction.amendment > summary > .marker
	{
		text-transform: uppercase;
		padding-right: 1em;
	}

	.example::before, .example > .marker {
		display: block;
		padding-right: 0em;
	}

/** Blockquotes ***************************************************************/

	blockquote {
		border-color: silver;
		border-color: var(--blockquote-border);
		background: transparent;
		background: var(--blockquote-bg);
		color: currentcolor;
		color: var(--blockquote-text);
	}

/** Open issue ****************************************************************/

	.issue {
		border-color: #e05252;
		border-color: var(--issue-border);
		background: #fbe9e9;
		background: var(--issue-bg);
		color: black;
		color: var(--issue-text);
		counter-increment: issue;
		overflow: auto;
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	.issue::before, .issue > .marker {
		color: #831616;
		color: var(--issueheading-text);
	}
	/* Add .issue::before { content: "Issue " counter(issue) " "; } for autogen numbers,
	  or use class="marker" to mark up the issue number in source. */

/** Example *******************************************************************/

	.example {
		border-color: #e0cb52;
		border-color: var(--example-border);
		background: #fcfaee;
		background: var(--example-bg);
		color: black;
		color: var(--example-text);
		counter-increment: example;
		overflow: auto;
		clear: both;
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	.example::before, .example > .marker {
		color: #574b0f;
		color: var(--exampleheading-text);
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	/* Add .example::before { content: "Example " counter(example) " "; } for autogen numbers,
	  or use class="marker" to mark up the example number in source. */

/** Non-normative Note ********************************************************/

	.note {
		border-color: #52e052;
		border-color: var(--note-border);
		background: #e9fbe9;
		background: var(--note-bg);
		color: black;
		color: var(--note-text);
		overflow: auto;
	}

	.note::before, .note > .marker,
	details.note > summary {
		color: hsl(120, 70%, 30%);
		color: var(--noteheading-text);
	}
	/* Add .note::before { content: "Note "; } for autogen label,
	  or use class="marker" to mark up the label in source. */

	details.note[open] > summary {
		border-bottom: 1px silver solid;
		border-bottom: 1px var(--notesummary-underline) solid;
	}

/** Assertion Box *************************************************************/
	/*  for assertions in algorithms */

	.assertion {
		border-color: #AAA;
		border-color: var(--assertion-border);
		background: #EEE;
		background: var(--assertion-bg);
		color: black;
		color: var(--assertion-text);
	}

/** Advisement Box ************************************************************/
	/*  for attention-grabbing normative statements */

	.advisement {
		border-color: orange;
		border-color: var(--advisement-border);
		border-style: none solid;
		background: #fec;
		background: var(--advisement-bg);
		color: black;
		color: var(--advisement-text);
	}
	strong.advisement {
		display: block;
		text-align: center;
	}
	.advisement::before, .advisement > .marker {
		color: #b35f00;
		color: var(--advisementheading-text);
	}

/** Amendment Box *************************************************************/

	.amendment, .correction, .addition {
		border-color: #330099;
		border-color: var(--amendment-border);
		background: #F5F0FF;
		background: var(--amendment-bg);
		color: black;
		color: var(--amendment-text);
	}
	.amendment.proposed, .correction.proposed, .addition.proposed {
		border-style: solid;
		border-block-width: 0.25em;
	}
	.amendment::before, .amendment > .marker,
	details.amendment > summary::before, details.amendment > summary > .marker,
	.correction::before, .correction > .marker,
	details.correction > summary::before, details.correction > summary > .marker,
	.addition::before, .addition > .marker,
	details.addition > summary::before, details.addition > summary > .marker {
		color: #220066;
		color: var(--amendmentheading-text);
	}
	.amendment.proposed::before, .amendment.proposed > .marker,
	details.amendment.proposed > summary::before, details.amendment.proposed > summary > .marker,
	.correction.proposed::before, .correction.proposed > .marker,
	details.correction.proposed > summary::before, details.correction.proposed > summary > .marker,
	.addition.proposed::before, .addition.proposed > .marker,
	details.addition.proposed > summary::before, details.addition.proposed > summary > .marker {
		font-weight: bold;
	}

/** Spec Obsoletion Notice ****************************************************/
	/* obnoxious obsoletion notice for older/abandoned specs. */

	details {
		display: block;
	}
	summary {
		font-weight: bolder;
	}

	.annoying-warning:not(details),
	details.annoying-warning:not([open]) > summary,
	details.annoying-warning[open] {
		background: hsla(40,100%,50%,0.95);
		background: var(--warning-bg);
		color: black;
		color: var(--warning-text);
		padding: .75em 1em;
		border: red;
		border: var(--warning-border);
		border-style: solid none;
		box-shadow: 0 2px 8px black;
		text-align: center;
	}
	.annoying-warning :last-child {
		margin-bottom: 0;
	}

@media not print {
	details.annoying-warning[open] {
		position: fixed;
		left: 0;
		right: 0;
		bottom: 2em;
		z-index: 1000;
	}
}

	details.annoying-warning:not([open]) > summary {
		text-align: center;
	}

/** Entity Definition Boxes ***************************************************/

	.def {
		padding: .5em 1em;
		background: #def;
		background: var(--def-bg);
		margin: 1.2em 0;
		border-left: 0.5em solid #8ccbf2;
		border-left: 0.5em solid var(--def-border);
		color: black;
		color: var(--def-text);
	}

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

	th, td {
		text-align: left;
		text-align: start;
	}

/** Property/Descriptor Definition Tables *************************************/

	table.def {
		/* inherits .def box styling, see above */
		width: 100%;
		border-spacing: 0;
	}

	table.def td,
	table.def th {
		padding: 0.5em;
		vertical-align: baseline;
		border-bottom: 1px solid #bbd7e9;
		border-bottom: 1px solid var(--defrow-border);
	}

	table.def > tbody > tr:last-child th,
	table.def > tbody > tr:last-child td {
		border-bottom: 0;
	}

	table.def th {
		font-style: italic;
		font-weight: normal;
		padding-left: 1em;
		width: 3em;
	}

	/* For when values are extra-complex and need formatting for readability */
	table td.pre {
		white-space: pre-wrap;
	}

	/* A footnote at the bottom of a def table */
	table.def td.footnote {
		padding-top: 0.6em;
	}
	table.def td.footnote::before {
		content: " ";
		display: block;
		height: 0.6em;
		width: 4em;
		border-top: thin solid;
	}

/** Data tables (and properly marked-up index tables) *************************/
	/*
		<table class="data"> highlights structural relationships in a table
		when correct markup is used (e.g. thead/tbody, th vs. td, scope attribute)

		Use class="complex data" for particularly complicated tables --
		(This will draw more lines: busier, but clearer.)

		Use class="long" on table cells with paragraph-like contents
		(This will adjust text alignment accordingly.)
		Alternately use class="longlastcol" on tables, to have the last column assume "long".
	*/

	table {
		word-wrap: normal;
		overflow-wrap: normal;
		hyphens: manual;
	}

	table.data,
	table.index {
		margin: 1em auto;
		border-collapse: collapse;
		border: hidden;
		width: 100%;
	}
	table.data caption,
	table.index caption {
		max-width: 50em;
		margin: 0 auto 1em;
	}

	table.data td,  table.data th,
	table.index td, table.index th {
		padding: 0.5em 1em;
		border-width: 1px;
		border-color: silver;
		border-color: var(--datacell-border);
		border-top-style: solid;
	}

	table.data thead td:empty {
		padding: 0;
		border: 0;
	}

	table.data  thead,
	table.index thead,
	table.data  tbody,
	table.index tbody {
		border-bottom: 2px solid;
	}

	table.data colgroup,
	table.index colgroup {
		border-left: 2px solid;
	}

	table.data  tbody th:first-child,
	table.index tbody th:first-child  {
		border-right: 2px solid;
		border-top: 1px solid silver;
		border-top: 1px solid var(--datacell-border);
		padding-right: 1em;
	}

	table.data th[colspan],
	table.data td[colspan] {
		text-align: center;
	}

	table.complex.data th,
	table.complex.data td {
		border: 1px solid silver;
		border: 1px solid var(--datacell-border);
		text-align: center;
	}

	table.data.longlastcol td:last-child,
	table.data td.long {
		vertical-align: baseline;
		text-align: left;
	}

	table.data img {
		vertical-align: middle;
	}


/*
Alternate table alignment rules

	table.data,
	table.index {
		text-align: center;
	}

	table.data  thead th[scope="row"],
	table.index thead th[scope="row"] {
		text-align: right;
	}

	table.data  tbody th:first-child,
	table.index tbody th:first-child  {
		text-align: right;
	}

Possible extra rowspan handling

	table.data  tbody th[rowspan]:not([rowspan='1']),
	table.index tbody th[rowspan]:not([rowspan='1']),
	table.data  tbody td[rowspan]:not([rowspan='1']),
	table.index tbody td[rowspan]:not([rowspan='1']) {
		border-left: 1px solid silver;
	}

	table.data  tbody th[rowspan]:first-child,
	table.index tbody th[rowspan]:first-child,
	table.data  tbody td[rowspan]:first-child,
	table.index tbody td[rowspan]:first-child{
		border-left: 0;
		border-right: 1px solid silver;
	}
*/

/******************************************************************************/
/*                                  Indices                                   */
/******************************************************************************/


/** Table of Contents *********************************************************/

	.toc a {
		/* More spacing; use padding to make it part of the click target. */
		padding: 0.1rem 1px 0;
		/* Larger, more consistently-sized click target */
		display: block;
		/* Switch to using border-bottom for underlines */
		text-decoration: none;
		border-bottom: 1px solid;
		/* Reverse color scheme */
		color: black;
		color: var(--toclink-text);
		border-color: #3980b5;
		border-color: var(--toclink-underline);
	}
	.toc a:visited {
		color: black;
		color: var(--toclink-visited-text);
		border-color: #054572;
		border-color: var(--toclink-visited-underline);
	}
	.toc a:focus,
	.toc a:hover {
		background: rgba(75%, 75%, 75%, .25);
		background: var(--a-hover-bg);
		border-bottom-width: 3px;
		margin-bottom: -2px;
	}
	.toc a:not(:focus):not(:hover) {
		/* Allow colors to cascade through from link styling */
		border-bottom-color: transparent;
	}

	.toc, .toc ol, .toc ul, .toc li {
		list-style: none; /* Numbers must be inlined into source */
		/* because generated content isn't search/selectable and markers can't do multilevel yet */
		margin:  0;
		padding: 0;
	}
	.toc {
		line-height: 1.1em;
	}

	/* ToC not indented until third level, but font style & margins show hierarchy */
	.toc > li			{ font-weight: bold;   }
	.toc > li li		 { font-weight: normal; }
	.toc > li li li	  { font-size:   95%;	}
	.toc > li li li li	{ font-size:   90%;	}
	.toc > li li li li li { font-size:   85%;	}

	/* @supports not (display:grid) { */
		.toc > li			{ margin: 1.5rem 0;	}
		.toc > li li		 { margin: 0.3rem 0;	}
		.toc > li li li	  { margin-left: 2rem;   }

		/* Section numbers in a column of their own */
		.toc .secno {
			float: left;
			width: 4rem;
			white-space: nowrap;
		}
		.toc > li li li li .secno { font-size: 85%; }
		.toc > li li li li li .secno { font-size: 100%; }

		.toc li {
			clear: both;
		}

		:not(li) > .toc			 { margin-left:  5rem; }
		.toc .secno				 { margin-left: -5rem; }
		.toc > li li li .secno	  { margin-left: -7rem; }
		.toc > li li li li .secno	{ margin-left: -9rem; }
		.toc > li li li li li .secno { margin-left: -11rem; }

		/* Tighten up indentation in narrow ToCs */
		@media (max-width: 30em) {
			:not(li) > .toc			 { margin-left:  4rem; }
			.toc .secno				 { margin-left: -4rem; }
			.toc > li li li			 { margin-left:  1rem; }
			.toc > li li li .secno	  { margin-left: -5rem; }
			.toc > li li li li .secno	{ margin-left: -6rem; }
			.toc > li li li li li .secno { margin-left: -7rem; }
		}
		/* Loosen it on wide screens */
		@media screen and (min-width: 78em) {
			body:not(.toc-inline) :not(li) > .toc			 { margin-left:  4rem; }
			body:not(.toc-inline) .toc .secno				 { margin-left: -4rem; }
			body:not(.toc-inline) .toc > li li li			 { margin-left:  1rem; }
			body:not(.toc-inline) .toc > li li li .secno	  { margin-left: -5rem; }
			body:not(.toc-inline) .toc > li li li li .secno	{ margin-left: -6rem; }
			body:not(.toc-inline) .toc > li li li li li .secno { margin-left: -7rem; }
	}
	/* } */

	@supports (display:grid) and (display:contents) {
		/* Use #toc over .toc to override non-@supports rules. */
		#toc {
			display: grid;
			align-content: start;
			grid-template-columns: auto 1fr;
			grid-column-gap: 1rem;
			column-gap: 1rem;
			grid-row-gap: .6rem;
			row-gap: .6rem;
		}
		#toc h2 {
			grid-column: 1 / -1;
			margin-bottom: 0;
		}
		#toc ol,
		#toc li,
		#toc a {
			display: contents;
			/* Switch <a> to subgrid when supported */
		}
		#toc span {
			margin: 0;
		}
		#toc > .toc > li > a > span {
			/* The spans of the top-level list,
			  comprising the first items of each top-level section. */
			margin-top: 1.1rem;
		}
		#toc#toc .secno { /* Ugh, need more specificity to override base.css */
			grid-column: 1;
			width: auto;
			margin-left: 0;
		}
		#toc .content {
			grid-column: 2;
			width: auto;
			margin-right: 1rem;
			border-bottom: 3px solid transparent;
			margin-bottom: -3px;
		}
		#toc .content:hover,
		#toc .content:focus {
			background: rgba(75%, 75%, 75%, .25);
			background: var(--a-hover-bg);
			border-bottom-color: #054572;
			border-bottom-color: var(--toclink-underline);
		}
		#toc li li li .content {
			margin-left: 1rem;
		}
		#toc li li li li .content {
			margin-left: 2rem;
		}
	}


/** Index *********************************************************************/

	/* Index Lists: Layout */
	ul.index	  { margin-left: 0; columns: 15em; text-indent: 1em hanging; }
	ul.index li	{ margin-left: 0; list-style: none; break-inside: avoid; }
	ul.index li li { margin-left: 1em; }
	ul.index dl	{ margin-top: 0; }
	ul.index dt	{ margin: .2em 0 .2em 20px;}
	ul.index dd	{ margin: .2em 0 .2em 40px;}
	/* Index Lists: Typography */
	ul.index ul,
	ul.index dl { font-size: smaller; }
	@media not print {
		ul.index li a + span {
			white-space: nowrap;
			color: transparent; }
		ul.index li a:hover + span,
		ul.index li a:focus + span {
			color: #707070;
			color: var(--indexinfo-text);
		}
	}

/** Index Tables *****************************************************/
	/* See also the data table styling section, which this effectively subclasses */

	table.index {
		font-size: small;
		border-collapse: collapse;
		border-spacing: 0;
		text-align: left;
		margin: 1em 0;
	}

	table.index td,
	table.index th {
		padding: 0.4em;
	}

	table.index tr:hover td:not([rowspan]),
	table.index tr:hover th:not([rowspan]) {
		color: black;
		color: var(--indextable-hover-text);
		background: #f7f8f9;
		background: var(--indextable-hover-bg);
	}

	/* The link in the first column in the property table (formerly a TD) */
	table.index th:first-child a {
		font-weight: bold;
	}

/** Outdated warning **********************************************************/

.outdated-spec {
	color: black;
	color: var(--outdatedspec-text);
	background-color: rgba(0,0,0,0.5);
	background-color: var(--outdatedspec-bg);
}

.outdated-warning {
	position: fixed;
	bottom: 50%;
	left: 0;
	right: 0;
	margin: 0 auto;
	width: 50%;
	background: maroon;
	background: var(--outdated-bg);
	color: white;
	color: var(--outdated-text);
	border-radius: 1em;
	box-shadow: 0 0 1em red;
	box-shadow: 0 0 1em var(--outdated-shadow);
	padding: 2em;
	text-align: center;
	z-index: 2;
}

.outdated-warning a {
	color: currentcolor;
	background: transparent;
}

.edited-rec-warning {
	background: darkorange;
	background: var(--editedrec-bg);
	box-shadow: 0 0 1em;
}

.outdated-warning button {
	color: var(--outdated-text);
	border-radius: 1em;
	box-shadow: 0 0 1em red;
	box-shadow: 0 0 1em var(--outdated-shadow);
	padding: 2em;
	text-align: center;
	z-index: 2;
}

.outdated-warning a {
	color: currentcolor;
	background: transparent;
}

.edited-rec-warning {
	background: darkorange;
	background: var(--editedrec-bg);
	box-shadow: 0 0 1em;
}

.outdated-warning button {
	position: absolute;
	top: 0;
	right:0;
	margin: 0;
	border: 0;
	padding: 0.25em 0.5em;
	background: transparent;
	color: white;
	color: var(--outdated-text);
	font:1em sans-serif;
	text-align:center;
}

.outdated-warning span {
	display: block;
}

.outdated-collapsed {
	bottom: 0;
	border-radius: 0;
	width: 100%;
	padding: 0;
}

/******************************************************************************/
/*                                    Print                                   */
/******************************************************************************/

	@media print {
		/* Pages have their own margins. */
		html {
			margin: 0;
		}
		/* Serif for print. */
		body {
			font-family: serif;
		}

		.outdated-warning {
			position: absolute;
			border-style: solid;
			border-color: red;
		}

		.outdated-warning input {
			display: none;
		}
	}
	@page {
		margin: 1.5cm 1.1cm;
	}



/******************************************************************************/
/*                             Overflow Control                               */
/******************************************************************************/

	.figure .caption, .sidefigure .caption, figcaption {
		/* in case figure is overlarge, limit caption to 50em */
		max-width: 50rem;
		margin-left: auto;
		margin-right: auto;
	}
	.overlarge {
		/* Magic to create good item positioning:
		  "content column" is 50ems wide at max; less on smaller screens.
		  Extra space (after ToC + content) is empty on the right.

		  1. When item < content column, centers item in column.
		  2. When content < item < available, left-aligns.
		  3. When item > available, fills available + scroll bar.
		*/
		display: grid;
		grid-template-columns: minmax(0, 50em);
	}
	.overlarge > table {
		/* limit preferred width of table */
		max-width: 50em;
		margin-left: auto;
		margin-right: auto;
	}

	@media (min-width: 55em) {
		.overlarge {
			margin-right: calc(13px + 26.5rem - 50vw);
			max-width: none;
		}
	}
	@media screen and (min-width: 78em) {
		body:not(.toc-inline) .overlarge {
			/* 30.5em body padding 50em content area */
			margin-right: calc(40em - 50vw) !important;
		}
	}
	@media screen and (min-width: 90em) {
		body:not(.toc-inline) .overlarge {
			/* 4em html margin 30.5em body padding 50em content area */
			margin-right: calc(84.5em - 100vw) !important;
		}
	}

	@media not print {
		.overlarge {
			overflow-x: auto;
			/* See Lea Verou's explanation background-attachment:
			* http://lea.verou.me/2012/04/background-attachment-local/
			*
			background: top left  / 4em 100% linear-gradient(to right,  #ffffff, rgba(255, 255, 255, 0)) local,
						top right / 4em 100% linear-gradient(to left, #ffffff, rgba(255, 255, 255, 0)) local,
						top left  / 1em 100% linear-gradient(to right,  #c3c3c5, rgba(195, 195, 197, 0)) scroll,
						top right / 1em 100% linear-gradient(to left, #c3c3c5, rgba(195, 195, 197, 0)) scroll,
						white;
			background-repeat: no-repeat;
			*/
		}
	}
</style>
<style>
    table, th, td {
      border: 1px solid black;
      border-collapse: collapse;
      vertical-align: top;
    }
    th, td {
      border-left: none;
      border-right: none;
      padding: 0px 10px;
    }
    th {
      text-align: center;
    }

    del { background: #fcc; color: #000; text-decoration: line-through; }
    ins { background: #cfc; color: #000; }
    blockquote .highlight:not(.idl) { background: initial; margin: initial; padding: 0.5em }
    blockquote ul { background: inherit; }
    blockquote code.highlight:not(.idl) { padding: initial; }
    blockquote c-[a] { color: inherit; } /* Keyword.Declaration */
    blockquote c-[b] { color: inherit; } /* Keyword.Type */
    blockquote c-[c] { color: inherit; } /* Comment */
    blockquote c-[d] { color: inherit; } /* Comment.Multiline */
    blockquote c-[e] { color: inherit; } /* Name.Attribute */
    blockquote c-[f] { color: inherit; } /* Name.Tag */
    blockquote c-[g] { color: inherit; } /* Name.Variable */
    blockquote c-[k] { color: inherit; } /* Keyword */
    blockquote c-[l] { color: inherit; } /* Literal */
    blockquote c-[m] { color: inherit; } /* Literal.Number */
    blockquote c-[n] { color: inherit; } /* Name */
    blockquote c-[o] { color: inherit; } /* Operator */
    blockquote c-[p] { color: inherit; } /* Punctuation */
    blockquote c-[s] { color: inherit; } /* Literal.String */
    blockquote c-[t] { color: inherit; } /* Literal.String.Single */
    blockquote c-[u] { color: inherit; } /* Literal.String.Double */
    blockquote c-[cp] { color: inherit; } /* Comment.Preproc */
    blockquote c-[c1] { color: inherit; } /* Comment.Single */
    blockquote c-[cs] { color: inherit; } /* Comment.Special */
    blockquote c-[kc] { color: inherit; } /* Keyword.Constant */
    blockquote c-[kn] { color: inherit; } /* Keyword.Namespace */
    blockquote c-[kp] { color: inherit; } /* Keyword.Pseudo */
    blockquote c-[kr] { color: inherit; } /* Keyword.Reserved */
    blockquote c-[ld] { color: inherit; } /* Literal.Date */
    blockquote c-[nc] { color: inherit; } /* Name.Class */
    blockquote c-[no] { color: inherit; } /* Name.Constant */
    blockquote c-[nd] { color: inherit; } /* Name.Decorator */
    blockquote c-[ni] { color: inherit; } /* Name.Entity */
    blockquote c-[ne] { color: inherit; } /* Name.Exception */
    blockquote c-[nf] { color: inherit; } /* Name.Function */
    blockquote c-[nl] { color: inherit; } /* Name.Label */
    blockquote c-[nn] { color: inherit; } /* Name.Namespace */
    blockquote c-[py] { color: inherit; } /* Name.Property */
    blockquote c-[ow] { color: inherit; } /* Operator.Word */
    blockquote c-[mb] { color: inherit; } /* Literal.Number.Bin */
    blockquote c-[mf] { color: inherit; } /* Literal.Number.Float */
    blockquote c-[mh] { color: inherit; } /* Literal.Number.Hex */
    blockquote c-[mi] { color: inherit; } /* Literal.Number.Integer */
    blockquote c-[mo] { color: inherit; } /* Literal.Number.Oct */
    blockquote c-[sb] { color: inherit; } /* Literal.String.Backtick */
    blockquote c-[sc] { color: inherit; } /* Literal.String.Char */
    blockquote c-[sd] { color: inherit; } /* Literal.String.Doc */
    blockquote c-[se] { color: inherit; } /* Literal.String.Escape */
    blockquote c-[sh] { color: inherit; } /* Literal.String.Heredoc */
    blockquote c-[si] { color: inherit; } /* Literal.String.Interpol */
    blockquote c-[sx] { color: inherit; } /* Literal.String.Other */
    blockquote c-[sr] { color: inherit; } /* Literal.String.Regex */
    blockquote c-[ss] { color: inherit; } /* Literal.String.Symbol */
    blockquote c-[vc] { color: inherit; } /* Name.Variable.Class */
    blockquote c-[vg] { color: inherit; } /* Name.Variable.Global */
    blockquote c-[vi] { color: inherit; } /* Name.Variable.Instance */
    blockquote c-[il] { color: inherit; } /* Literal.Number.Integer.Long */
  </style>
  <meta content="Bikeshed version d29f71adb, updated Wed Jul 19 11:08:56 2023 -0700" name="generator">
  <link href="https://wg21.link/P2500R2" rel="canonical">
  <link href="https://isocpp.org/favicon.ico" rel="icon">
  <meta content="a0befbbf44a57a906ce300dfab1a47ee10b7b925" name="document-revision">
<style>/* Boilerplate: style-autolinks */
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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">P2500R2<br>C++ parallel algorithms and P2300</h1>
   <h2 class="no-num no-toc no-ref heading settled" id="profile-and-date"><span class="content">Published Proposal, <time class="dt-updated" datetime="2023-10-15">2023-10-15</time></span></h2>
   <div data-fill-with="spec-metadata">
    <dl>
     <dt>This version:
     <dd><a class="u-url" href="https://wg21.link/P2500R2">https://wg21.link/P2500R2</a>
     <dt class="editor">Authors:
     <dd class="editor p-author h-card vcard"><a class="p-name fn u-email email" href="mailto:ruslan.arutyunyan@intel.com">Ruslan Arutyunyan</a> (<span class="p-org org">Intel</span>)
     <dd class="editor p-author h-card vcard"><a class="p-name fn u-email email" href="mailto:alexey.kukanov@intel.com">Alexey Kukanov</a> (<span class="p-org org">Intel</span>)
     <dt>Audience:
     <dd>SG1, LEWG
     <dt>Project:
     <dd>ISO/IEC 14882 Programming Languages — C++, ISO/IEC JTC1/SC22/WG21
    </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 provides the facilities to integrate <a data-link-type="biblio" href="#biblio-p2300r7" title="`std::execution`">[P2300R7]</a> with C++ 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="#motivation"><span class="secno">1</span> <span class="content">Motivation</span></a>
    <li>
     <a href="#design_overview"><span class="secno">2</span> <span class="content">Design overview</span></a>
     <ol class="toc">
      <li><a href="#design_goals"><span class="secno">2.1</span> <span class="content">Design goals</span></a>
      <li>
       <a href="#combine_scheduler_with_policy"><span class="secno">2.2</span> <span class="content">Combining a scheduler with a policy</span></a>
       <ol class="toc">
        <li><a href="#sched_for_parallel_algorithms"><span class="secno">2.2.1</span> <span class="content">Why <code class="highlight"><c- n>scheduler</c-></code></span></a>
        <li><a href="#alternative_parallel_algorithms"><span class="secno">2.2.2</span> <span class="content">Alternative API</span></a>
        <li><a href="#extensibility_considerations"><span class="secno">2.2.3</span> <span class="content">Extensibility considerations</span></a>
       </ol>
      <li><a href="#customizable_functions"><span class="secno">2.3</span> <span class="content">Parallel algorithms are customizable functions</span></a>
      <li>
       <a href="#cover_classic_and_range"><span class="secno">2.4</span> <span class="content">Covering both "classic" and range algorithms</span></a>
       <ol class="toc">
        <li><a href="#serial_range_based_absence"><span class="secno">2.4.1</span> <span class="content">Absence of serial range-based algorithms</span></a>
       </ol>
      <li><a href="#policies_for_ranges"><span class="secno">2.5</span> <span class="content">Standard execution policies for range algorithms</span></a>
     </ol>
    <li><a href="#proposed_api"><span class="secno">3</span> <span class="content">Proposed API</span></a>
    <li>
     <a href="#api_overview"><span class="secno">4</span> <span class="content">API Overview</span></a>
     <ol class="toc">
      <li>
       <a href="#parallel_algorithm_impl"><span class="secno">4.1</span> <span class="content">Possible implementations of a parallel algorithm</span></a>
       <ol class="toc">
        <li><a href="#alg_customize_tag_invoke"><span class="secno">4.1.1</span> <span class="content">Customizable with <code class="highlight"><c- n>tag_invoke</c-></code></span></a>
        <li><a href="#alg_customize_language"><span class="secno">4.1.2</span> <span class="content">Customizable with language support</span></a>
       </ol>
      <li><a href="#execute_on_cpo"><span class="secno">4.2</span> <span class="content"><code class="highlight"><c- n>execute_on</c-></code></span></a>
      <li><a href="#policy_aware_scheduler"><span class="secno">4.3</span> <span class="content"><code class="highlight"><c- n>policy_aware_scheduler</c-></code></span></a>
      <li><a href="#exec_concept"><span class="secno">4.4</span> <span class="content"><code class="highlight"><c- n>execution_policy</c-></code> concept</span></a>
     </ol>
    <li><a href="#further_work"><span class="secno">5</span> <span class="content">Further exploration</span></a>
    <li>
     <a href="#revision_history#"><span class="secno">6</span> <span class="content">Revision History</span></a>
     <ol class="toc">
      <li><a href="#r1_r2"><span class="secno">6.1</span> <span class="content">R1 => R2</span></a>
      <li><a href="#r0_r1"><span class="secno">6.2</span> <span class="content">R0 => R1</span></a>
     </ol>
    <li><a href="#acknowledgements"><span class="secno">7</span> <span class="content">Acknowledgements</span></a>
    <li>
     <a href="#references"><span class="secno"></span> <span class="content">References</span></a>
     <ol class="toc">
      <li><a href="#normative"><span class="secno"></span> <span class="content">Normative References</span></a>
      <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="motivation"><span class="secno">1. </span><span class="content">Motivation</span><a class="self-link" href="#motivation"></a></h2>
   <p>C++ parallel algorithms, together with executions policies, were a good start for supporting parallelism in the C++ standard.
The C++ standard execution policies represent "how" a particular algorithm should be executed; in other words,
they set semantic requirements to user callable objects passed to parallel algorithms.
However, there is no explicit way to specify what hardware an algorithm should be executed on.</p>
   <p>In the absence of a better facility in the C++ standard library, custom execution policies combine semantics
of both "how" and "where" the code should be executed as well a semantic restrictions on the user supplied callable.
Examples can be seen in <a href="https://nvidia.github.io/thrust/api/groups/group__execution__policies.html">Thrust</a> and <a href="https://oneapi-src.github.io/oneDPL/parallel_api/execution_policies.html">oneDPL</a> libraries.</p>
   <p><a data-link-type="biblio" href="#biblio-p2300r7" title="`std::execution`">[P2300R7]</a> introduces the <code class="highlight"><c- n>scheduler</c-></code> concept that represents an execution context.
Compared to execution policies, <code class="highlight"><c- n>scheduler</c-></code> is a more flexible abstraction for answering "where" the code
should be executed, because a <code class="highlight"><c- n>scheduler</c-></code> could be tightly connected to the platform it sends work to.</p>
   <p>As <a data-link-type="biblio" href="#biblio-p2300r7" title="`std::execution`">[P2300R7]</a> progresses towards likely standardization for C++26, we should answer the question how other parts
of the C++ standard library would interoperate with schedulers, senders and/or receivers.</p>
   <p><a data-link-type="biblio" href="#biblio-p2214r2" title="A Plan for C++23 Ranges">[P2214R2]</a> outlined a plan to extend the Ranges library in C++23. This plan puts adding parallel overloads
for range algorithms into "Tier 2", motivating that, among other factors, by the need to carefully consider
how these algorithm overloads work when <a data-link-type="biblio" href="#biblio-p2300r7" title="`std::execution`">[P2300R7]</a> lands in the standard. To the best of our knowledge,
nobody has yet approached this question.</p>
   <p>This paper is targeted to C++26 and proposes a way for standard C++ algorithms to utilize <a data-link-type="biblio" href="#biblio-p2300r7" title="`std::execution`">[P2300R7]</a> facilities.</p>
   <h2 class="heading settled" data-level="2" id="design_overview"><span class="secno">2. </span><span class="content">Design overview</span><a class="self-link" href="#design_overview"></a></h2>
   <h3 class="heading settled" data-level="2.1" id="design_goals"><span class="secno">2.1. </span><span class="content">Design goals</span><a class="self-link" href="#design_goals"></a></h3>
   <p>A key question that should be addressed is how the API of C++ algorithms, including parallel and range based algorithms,
should be extended or modified to express the notion that a certain algorithm should run in a certain execution context.
We strive for minimal, incremental API changes that preserve the overall usage experience as well as the core semantics
of algorithms and execution policies. For example, the execution of algorithms should remain synchronous,
i.e. complete all the work upon return.</p>
   <p>However, given a wide variety of possible standard and 3rd-party execution contexts, it would be naive to expect
all of them being capable of executing any C++ code. In particular, an execution context might not support
certain execution policy semantics. The design should therefore allow execution semantics to be adjusted when possible,
for example by using <code class="highlight"><c- n>par</c-></code> instead of <code class="highlight"><c- n>par_unseq</c-></code> but not vice versa.</p>
   <p>Another important design goal is to allow implementers of a particular execution context to customize the implementation
of standard algorithms for that context. We consider this a requirement so as to provide the best possible implementation
for a given platform. At the same time, an algorithm should also have a default implementation, presumably expressed
via other algorithms or basis routines (see <a href="#further_work">§ 5 Further exploration</a>), allowing customization of only what is necessary
to achieve optimal performance for a given execution context.</p>
   <h3 class="heading settled" data-level="2.2" id="combine_scheduler_with_policy"><span class="secno">2.2. </span><span class="content">Combining a scheduler with a policy</span><a class="self-link" href="#combine_scheduler_with_policy"></a></h3>
   <p>To achieve the first goal, we propose extending the current approach of C++ parallel algorithms to allow
a <em>policy-aware scheduler</em> that combines a policy and a representation of an execution context, in addition to
the existing standard execution policies. This follows the existing practice of using a single argument to specify
both "where" and "how" to execute an algorithm. It forces binding a policy with a context prior to the algorithm
invocation, allowing for better handling of possible mismatches between the two in case the execution context cannot
properly support the semantics of the policy, as well as for reuse of the resulting policy-aware scheduler instance.</p>
   <p>An example declaration of <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>for_each</c-></code> for the outlined approach would be:</p>
<pre class="language-cpp highlight"><c- k>template</c-> <c- o>&lt;</c-><c- n>policy_aware_scheduler</c-> <c- n>Scheduler</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>ForwardIterator</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>Function</c-><c- o>></c->
<c- b>void</c-> <c- n>for_each</c-><c- p>(</c-><c- n>Scheduler</c-><c- o>&amp;&amp;</c-> <c- n>sched</c-><c- p>,</c-> <c- n>ForwardIterator</c-> <c- n>first</c-><c- p>,</c-> <c- n>ForwardIterator</c-> <c- n>last</c-><c- p>,</c-> <c- n>Function</c-> <c- n>f</c-><c- p>);</c->
</pre>
   <p>A <code class="highlight"><c- n>policy_aware_scheduler</c-></code> is obtained with the <code class="highlight"><c- n>execute_on</c-></code> function applied to a desired scheduler
and a desired execution policy. Eventually, invoking a parallel algorithm to execute by a scheduler
looks like:</p>
<pre class="language-cpp highlight"><c- n>std</c-><c- o>::</c-><c- n>for_each</c-><c- p>(</c-><c- n>std</c-><c- o>::</c-><c- n>execute_on</c-><c- p>(</c-><c- n>scheduler</c-><c- p>,</c-> <c- n>std</c-><c- o>::</c-><c- n>execution</c-><c- o>::</c-><c- n>par</c-><c- p>),</c-> <c- n>begin</c-><c- p>(</c-><c- n>data</c-><c- p>),</c-> <c- n>end</c-><c- p>(</c-><c- n>data</c-><c- p>),</c-> <c- n>callable</c-><c- p>);</c->
</pre>
   <p>See <a href="#policy_aware_scheduler">§ 4.3 policy_aware_scheduler</a> and <a href="#execute_on_cpo">§ 4.2 execute_on</a> sections for more details.</p>
   <h4 class="heading settled" data-level="2.2.1" id="sched_for_parallel_algorithms"><span class="secno">2.2.1. </span><span class="content">Why <code class="highlight"><c- n>scheduler</c-></code></span><a class="self-link" href="#sched_for_parallel_algorithms"></a></h4>
   <p>The proposed API is blocking by design and behaves similarly to C++17 parallel algorithms. That means, when an
algorithm returns the execution is complete. The algorithm can internally utilize a complex dependency graph
of sub-computations, and a <code class="highlight"><c- n>scheduler</c-></code> allows to obtain as many senders as needed to implement such a graph.</p>
   <p>If we imagine that the algorithm takes a <code class="highlight"><c- n>sender</c-></code>, it is unclear what to do then because that <code class="highlight"><c- n>sender</c-></code> could represent
an arbitrary dependency chain built by the user, and all possible strategies of handling it we could imagine seem bad:</p>
   <ul>
    <li data-md>
     <p>We could ignore the <code class="highlight"><c- n>sender</c-></code> and just obtain the <code class="highlight"><c- n>scheduler</c-></code> from it, but that is likely not what users would expect.</p>
    <li data-md>
     <p>We could run <code class="highlight"><c- n>sync_wait</c-></code> on <code class="highlight"><c- n>sender</c-></code> and then run the dependency graph that is built by the algorithm implementation,
but in this case we lose the value <code class="highlight"><c- n>sync_wait</c-></code> might return.</p>
    <li data-md>
     <p>We could build the <code class="highlight"><c- n>sender</c-></code> into the algorithm implementation chain, but it is still unclear what to do with the possible
return value of the <code class="highlight"><c- n>sender</c-></code>. For example, it might return <code class="highlight"><c- b>int</c-></code> while the algorithm semantically returns an iterator.</p>
   </ul>
   <p>Furthermore, from the perspective of customization we are interested in an execution context that is exactly represented by
a <code class="highlight"><c- n>scheduler</c-></code>.</p>
   <p>We believe the design does not prohibit adding other constrained functions that accepts and returns senders,
should that be of interest; for example:</p>
<pre class="language-cpp highlight"><c- k>template</c-> <c- o>&lt;</c-><c- n>sender</c-> <c- n>Sender</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>ForwardIterator</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>Function</c-><c- o>></c->
<c- n>sender</c-> <c- k>auto</c-> <c- n>for_each</c-><c- p>(</c-><c- n>Sender</c-> <c- n>s</c-><c- p>,</c-> <c- n>ForwardIterator</c-> <c- n>first</c-><c- p>,</c-> <c- n>ForwardIterator</c-> <c- n>last</c-><c- p>,</c-> <c- n>Function</c-> <c- n>f</c-><c- p>);</c->
</pre>
   <p>Such <a href="https://wg21.link/p2300r7#sender-algorithm">sender algorithms</a> would not have the problems outlined in the analysis above,
because of no requirement to execute immediately. The dependency graph of the computation would continue
the graph to which <code class="highlight"><c- n>s</c-></code> belongs, and the returned sender would signal completion of the algorithm to any
receiver bound to it. In this paper, however, we do not plan to further explore this direction.</p>
   <h4 class="heading settled" data-level="2.2.2" id="alternative_parallel_algorithms"><span class="secno">2.2.2. </span><span class="content">Alternative API</span><a class="self-link" href="#alternative_parallel_algorithms"></a></h4>
   <p>An alternative API might instead take both <code class="highlight"><c- n>scheduler</c-></code> and <code class="highlight"><c- n>execution_policy</c-></code> as function parameters.</p>
<pre class="language-cpp highlight"><c- k>template</c-> <c- o>&lt;</c-><c- n>scheduler</c-> <c- n>Scheduler</c-><c- p>,</c-> <c- n>execution_policy</c-> <c- n>Policy</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>ForwardIterator</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>Function</c-><c- o>></c->
<c- b>void</c-> <c- n>for_each</c-><c- p>(</c-><c- n>Scheduler</c-><c- o>&amp;&amp;</c-> <c- n>sched</c-><c- p>,</c-> <c- n>Policy</c-><c- o>&amp;&amp;</c-> <c- n>p</c-><c- p>,</c-> <c- n>ForwardIterator</c-> <c- n>first</c-><c- p>,</c-> <c- n>ForwardIterator</c-> <c- n>last</c-><c- p>,</c-> <c- n>Function</c-> <c- n>f</c-><c- p>);</c->
</pre>
   <p>However, in our opinion it complicates the signature for no good reason. The algorithm implementation would still first need
to check if the scheduler can work with the execution policy, just on a later stage comparing to the preferred approach.
Such a check would have to be redirected to the scheduler and/or the policy itself, and so would anyway require either
something like <a href="#execute_on_cpo">§ 4.2 execute_on</a> or a member function defined by schedulers or by execution policies.</p>
   <h4 class="heading settled" data-level="2.2.3" id="extensibility_considerations"><span class="secno">2.2.3. </span><span class="content">Extensibility considerations</span><a class="self-link" href="#extensibility_considerations"></a></h4>
   <p>In the discussion of the <a data-link-type="biblio" href="#biblio-p2500r1" title="C++ parallel algorithms and P2300">[P2500R1]</a>, a question about extensibility of the proposed approach was asked.
In case of a need to further parameterize execution of an algorithm, for example by a memory allocation
mechanism, a data partitioning strategy, a NUMA domain, etc., how would this be done?</p>
   <p>In our opinion, these and other execution parameters conceptually map to either "how" or "where" the execution
is performed - and therefore, could likely be added as configuration options for either the policy or the scheduler.
For example, the best way to allocate temporary data storage needed for execution of an algorithm usually depends
on which device or platform the execution should happen, and therefore should be associated with the scheduler.
Data partitioning strategies, on the other hand, associate more closely with execution policies, even though
best performing strategies might vary for different platforms and devices. In any case, configuring schedulers
and policies seems sufficient as the extensibility approach.</p>
   <p>That said, we are open to hear about potential configuration parameters that do not match well to a policy
nor to a scheduler, and change the <code class="highlight"><c- n>policy_aware_scheduler</c-></code> concept to something more generic.</p>
   <h3 class="heading settled" data-level="2.3" id="customizable_functions"><span class="secno">2.3. </span><span class="content">Parallel algorithms are customizable functions</span><a class="self-link" href="#customizable_functions"></a></h3>
   <p>In line with the second design goal, we use the notion of <em>customizable functions</em> for parallel algorithms.
It is essentially the same notion as proposed in <a href="https://wg21.link/p2547r1#terminology">Language support for customisable functions § terminology</a>, but without specific details.
Similar to the algorithm function templates in <code class="highlight"><c- k>namespace</c-> <c- nn>std</c-><c- o>::</c-><c- nn>ranges</c-></code>, these cannot be found by argument-dependent lookup.
In addition, these functions can be customized for a particular policy-aware scheduler. 
The implementation should invoke such a customization, if exists, otherwise execute a default generic implementation.
That allows customizing every particular algorithm by <code class="highlight"><c- n>scheduler</c-></code> vendors, if necessary.</p>
   <p>This paper does not explore the exact customization mechanism that might eventually be used, but it should be consistent
across all algorithms which may be customized by an execution context. The practical alternatives to consider are <a href="https://wg21.link/p2300r7#spec-func.tag_invoke">`std::execution` § spec-func.tag_invoke</a> and <a data-link-type="biblio" href="#biblio-p2547r1" title="Language support for customisable functions">[P2547R1]</a>.
Ideally we prefer to define the parallel algorithms in a way that does not depend on a particular customization mechanism,
however that might not be practical due to the syntactic differences in how customizations are declared.</p>
   <h3 class="heading settled" data-level="2.4" id="cover_classic_and_range"><span class="secno">2.4. </span><span class="content">Covering both "classic" and range algorithms</span><a class="self-link" href="#cover_classic_and_range"></a></h3>
   <p><a data-link-type="biblio" href="#biblio-p2500r0" title="C++17 parallel algorithms and P2300">[P2500R0]</a> suggested to only extend the "classic" C++17 parallel algorithms with a policy-aware scheduler,
without touching the C++20 constrained algorithms over ranges. Besides being limited in scope, that also has several drawbacks:</p>
   <ul>
    <li data-md>
     <p>Keeping the existing algorithm names (<code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>for_each</c-></code> etc.) and yet allowing their customization requires us to:</p>
     <ul>
      <li data-md>
       <p>Either redefine the names as customization point objects or as function objects supporting the <code class="highlight"><c- n>tag_invoke</c-></code> mechanism.
That would likely be considered as an ABI breaking change.</p>
      <li data-md>
       <p>Or add function overloads constrained with <code class="highlight"><c- n>policy_aware_scheduler</c-></code>, and require that they call new, specially defined
customization point objects, like <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>for_each_cpo</c-></code>. Making this for every algorithm would double the number of entities.</p>
     </ul>
    <li data-md>
     <p>The API with iterator pairs is more restrictive than with the iterator-and-sentinel pairs.
One can pass two iterators as the arguments to range-based algorithms that take iterator and sentinel, while it is not possible
to pass a sentinel instead of the second iterator to a "classic" algorithm.</p>
   </ul>
   <p>In the current revision, we instead propose to define customizable algorithms with scheduling support in <code class="highlight"><c- k>namespace</c-> <c- nn>std</c-><c- o>::</c-><c- nn>ranges</c-></code> Implementation-wise, that most likely means extending the existing function object types with new constrained overloads
of <code class="highlight"><c- k>operator</c-><c- p>()</c-></code>, which we think should not create any breaking changes. The algorithm functions in <code class="highlight"><c- k>namespace</c-> <c- nn>std</c-></code> can then be supplemented with new overloads for <code class="highlight"><c- n>policy_aware_scheduler</c-></code> that are required to call respective algorithms
from <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-></code>. This approach eliminates the drawbacks described above and also addresses the desire to support
the execution semantics for the range-based algorithms. The consequence is that algorithms in <code class="highlight"><c- n>std</c-></code> can be customized only via range-based algorithms. We think it is a reasonable tradeoff comparing to dozens of artificial
customization points or potential ABI breaks.</p>
   <h4 class="heading settled" data-level="2.4.1" id="serial_range_based_absence"><span class="secno">2.4.1. </span><span class="content">Absence of serial range-based algorithms</span><a class="self-link" href="#serial_range_based_absence"></a></h4>
   <p>We understand that some range-based algorithms do not exist even as serial ones today.
For example <code class="highlight"><c- o>&lt;</c-><c- n>numeric</c-><c- o>></c-></code> does not have respective algorithms in <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-></code>. It is supposed to
be addressed either by this or by a complementary paper.</p>
   <h3 class="heading settled" data-level="2.5" id="policies_for_ranges"><span class="secno">2.5. </span><span class="content">Standard execution policies for range algorithms</span><a class="self-link" href="#policies_for_ranges"></a></h3>
   <p>Since this proposal addresses the problem of extending range algorithms to work with schedulers, we think it makes sense
to address the lack of execution policy overloads for range algorithms as well. Such overloads can be safely added without
any risk of conflict with the scheduler support, as an execution policy does not satisfy the requirements for a policy-aware
scheduler, and vice versa.</p>
   <p>At this point we do not, however, discuss how the appearance of schedulers may or should impact the execution rules for parallel
algorithms specified in <a href="https://eel.is/c++draft/algorithms.parallel.exec">[algorithms.parallel.exec]</a>, and just assume
that the same rules apply to the range algorithms with execution policies.</p>
   <h2 class="heading settled" data-level="3" id="proposed_api"><span class="secno">3. </span><span class="content">Proposed API</span><a class="self-link" href="#proposed_api"></a></h2>
   <p>Note that <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>for_each</c-></code> and <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>for_each</c-></code> are used as references. When the design is ratified, it will be applied
to all parallel algorithms.</p>
   <p>All the examples are also based on the <code class="highlight"><c- n>for_each</c-></code> algorithms.</p>
   <h2 class="heading settled" data-level="4" id="api_overview"><span class="secno">4. </span><span class="content">API Overview</span><a class="self-link" href="#api_overview"></a></h2>
<pre class="language-cpp highlight"><c- c1>// Execution policy concept</c->
<c- k>template</c-> <c- o>&lt;</c-><c- k>typename</c-> <c- nc>ExecutionPolicy</c-><c- o>></c->
<c- k>concept</c-> <c- nc>execution_policy</c-> <c- o>=</c-> <c- n>std</c-><c- o>::</c-><c- n>is_execution_policy_v</c-><c- o>&lt;</c-><c- n>std</c-><c- o>::</c-><c- n>remove_cvref_t</c-><c- o>&lt;</c-><c- n>ExecutionPolicy</c-><c- o>>></c-><c- p>;</c->

<c- c1>// Policy aware scheduler</c->
<c- k>template</c-> <c- o>&lt;</c-><c- k>typename</c-> <c- nc>S</c-><c- o>></c->
<c- k>concept</c-> <c- nc>policy_aware_scheduler</c-> <c- o>=</c-> <c- n>scheduler</c-><c- o>&lt;</c-><c- n>S</c-><c- o>></c-> <c- o>&amp;&amp;</c-> <c- k>requires</c-> <c- p>(</c-><c- n>S</c-> <c- n>s</c-><c- p>)</c->
<c- p>{</c->
    <c- k>typename</c-> <c- nc>S</c-><c- o>::</c-><c- n>base_scheduler_type</c-><c- p>;</c->
    <c- k>typename</c-> <c- nc>S</c-><c- o>::</c-><c- n>policy_type</c-><c- p>;</c->
    <c- p>{</c-> <c- n>s</c-><c- p>.</c-><c- n>get_policy</c-><c- p>()</c-> <c- p>}</c-> <c- o>-></c-> <c- n>execution_policy</c-><c- p>;</c->
<c- p>};</c->

<c- c1>// execute_on customization point</c->
<c- kr>inline</c-> <c- k>namespace</c-> <c- d>/* unspecified */</c->
<c- p>{</c->
<c- kr>inline</c-> <c- k>constexpr</c-> <c- d>/* unspecified */</c-> <c- n>execute_on</c-> <c- o>=</c-> <c- d>/* unspecified */</c-><c- p>;</c->
<c- p>}</c->

<c- c1>// std::ranges::for_each as an parallel algorithm example. Others can be done similarly</c->

<c- c1>// Policy-based API</c->
<c- k>template</c-><c- o>&lt;</c-><c- n>execution_policy</c-> <c- n>Policy</c-><c- p>,</c-> <c- n>input_iterator</c-> <c- n>I</c-><c- p>,</c-> <c- n>sentinel_for</c-><c- o>&lt;</c-><c- n>I</c-><c- o>></c-> <c- n>S</c-><c- p>,</c-> <c- k>class</c-> <c- nc>Proj</c-> <c- o>=</c-> <c- n>identity</c-><c- p>,</c->
         <c- n>indirectly_unary_invocable</c-><c- o>&lt;</c-><c- n>projected</c-><c- o>&lt;</c-><c- n>I</c-><c- p>,</c-> <c- n>Proj</c-><c- o>>></c-> <c- n>Fun</c-><c- o>></c->
  <c- k>constexpr</c-> <c- n>ranges</c-><c- o>::</c-><c- n>for_each_result</c-><c- o>&lt;</c-><c- n>I</c-><c- p>,</c-> <c- n>Fun</c-><c- o>></c->
    <c- n>ranges</c-><c- o>::</c-><c- n>for_each</c-><c- p>(</c-><c- n>Policy</c-><c- o>&amp;&amp;</c-> <c- n>policy</c-><c- p>,</c-> <c- n>I</c-> <c- n>first</c-><c- p>,</c-> <c- n>S</c-> <c- n>last</c-><c- p>,</c-> <c- n>Fun</c-> <c- n>f</c-><c- p>,</c-> <c- n>Proj</c-> <c- n>proj</c-> <c- o>=</c-> <c- p>{});</c->
<c- k>template</c-><c- o>&lt;</c-><c- n>execution_policy</c-> <c- n>Policy</c-><c- p>,</c-> <c- n>input_range</c-> <c- n>R</c-><c- p>,</c-> <c- k>class</c-> <c- nc>Proj</c-> <c- o>=</c-> <c- n>identity</c-><c- p>,</c->
         <c- n>indirectly_unary_invocable</c-><c- o>&lt;</c-><c- n>projected</c-><c- o>&lt;</c-><c- n>iterator_t</c-><c- o>&lt;</c-><c- n>R</c-><c- o>></c-><c- p>,</c-> <c- n>Proj</c-><c- o>>></c-> <c- n>Fun</c-><c- o>></c->
  <c- k>constexpr</c-> <c- n>ranges</c-><c- o>::</c-><c- n>for_each_result</c-><c- o>&lt;</c-><c- n>borrowed_iterator_t</c-><c- o>&lt;</c-><c- n>R</c-><c- o>></c-><c- p>,</c-> <c- n>Fun</c-><c- o>></c->
    <c- n>ranges</c-><c- o>::</c-><c- n>for_each</c-><c- p>(</c-><c- n>Policy</c-><c- o>&amp;&amp;</c-> <c- n>policy</c-><c- p>,</c-> <c- n>R</c-><c- o>&amp;&amp;</c-> <c- n>r</c-><c- p>,</c-> <c- n>Fun</c-> <c- n>f</c-><c- p>,</c-> <c- n>Proj</c-> <c- n>proj</c-> <c- o>=</c-> <c- p>{});</c->

<c- c1>// Scheduler-based API</c->
<c- k>template</c-><c- o>&lt;</c-><c- n>policy_aware_scheduler</c-> <c- n>Scheduler</c-><c- p>,</c-> <c- n>input_iterator</c-> <c- n>I</c-><c- p>,</c-> <c- n>sentinel_for</c-><c- o>&lt;</c-><c- n>I</c-><c- o>></c-> <c- n>S</c-><c- p>,</c->
         <c- k>class</c-> <c- nc>Proj</c-> <c- o>=</c-> <c- n>identity</c-><c- p>,</c-> <c- n>indirectly_unary_invocable</c-><c- o>&lt;</c-><c- n>projected</c-><c- o>&lt;</c-><c- n>I</c-><c- p>,</c-> <c- n>Proj</c-><c- o>>></c-> <c- n>Fun</c-><c- o>></c->
  <c- k>constexpr</c-> <c- n>ranges</c-><c- o>::</c-><c- n>for_each_result</c-><c- o>&lt;</c-><c- n>I</c-><c- p>,</c-> <c- n>Fun</c-><c- o>></c->
    <c- n>ranges</c-><c- o>::</c-><c- n>for_each</c-><c- p>(</c-><c- n>Scheduler</c-> <c- n>sched</c-><c- p>,</c-> <c- n>I</c-> <c- n>first</c-><c- p>,</c-> <c- n>S</c-> <c- n>last</c-><c- p>,</c-> <c- n>Fun</c-> <c- n>f</c-><c- p>,</c-> <c- n>Proj</c-> <c- n>proj</c-> <c- o>=</c-> <c- p>{})</c-> <c- d>/*customizable*/</c-><c- p>;</c->
<c- k>template</c-><c- o>&lt;</c-><c- n>policy_aware_scheduler</c-> <c- n>Scheduler</c-><c- p>,</c-> <c- n>input_range</c-> <c- n>R</c-><c- p>,</c-> <c- k>class</c-> <c- nc>Proj</c-> <c- o>=</c-> <c- n>identity</c-><c- p>,</c->
         <c- n>indirectly_unary_invocable</c-><c- o>&lt;</c-><c- n>projected</c-><c- o>&lt;</c-><c- n>iterator_t</c-><c- o>&lt;</c-><c- n>R</c-><c- o>></c-><c- p>,</c-> <c- n>Proj</c-><c- o>>></c-> <c- n>Fun</c-><c- o>></c->
  <c- k>constexpr</c-> <c- n>ranges</c-><c- o>::</c-><c- n>for_each_result</c-><c- o>&lt;</c-><c- n>borrowed_iterator_t</c-><c- o>&lt;</c-><c- n>R</c-><c- o>></c-><c- p>,</c-> <c- n>Fun</c-><c- o>></c->
    <c- n>ranges</c-><c- o>::</c-><c- n>for_each</c-><c- p>(</c-><c- n>Scheduler</c-> <c- n>sched</c-><c- p>,</c-> <c- n>R</c-><c- o>&amp;&amp;</c-> <c- n>r</c-><c- p>,</c-> <c- n>Fun</c-> <c- n>f</c-><c- p>,</c-> <c- n>Proj</c-> <c- n>proj</c-> <c- o>=</c-> <c- p>{})</c-> <c- d>/*customizable*/</c-><c- p>;</c->

<c- c1>// "Classic" parallel algorithms with scheduler</c->
<c- k>template</c-> <c- o>&lt;</c-><c- n>policy_aware_scheduler</c-> <c- n>Scheduler</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>ForwardIterator</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>Function</c-><c- o>></c->
  <c- b>void</c->
    <c- n>for_each</c-><c- p>(</c-><c- n>Scheduler</c-><c- o>&amp;&amp;</c-> <c- n>sched</c-><c- p>,</c-> <c- n>ForwardIterator</c-> <c- n>first</c-><c- p>,</c-> <c- n>ForwardIterator</c-> <c- n>last</c-><c- p>,</c-> <c- n>Function</c-> <c- n>f</c-><c- p>);</c->
</pre>
   <h3 class="heading settled" data-level="4.1" id="parallel_algorithm_impl"><span class="secno">4.1. </span><span class="content">Possible implementations of a parallel algorithm</span><a class="self-link" href="#parallel_algorithm_impl"></a></h3>
   <p>Depending on the particular customization mechanism we eventually select, a parallel algorithm can be implemented
in one of the following ways.</p>
   <p>The current design proposes that all APIs are customizable via one customization point, which is the overload
that takes <code class="highlight"><c- n>I</c-></code> and <code class="highlight"><c- n>S</c-></code> (iterator and sentinel), and all other overloads are redirected to that customization point.
We expect that implementers prefer customizing necessary algorithms just once with all associated overloads
automatically covered. It is unclear at this point if there should be the flexibility of customizing every particular
overload individually but we are open to exploring with interested parties where they think this might be useful.</p>
   <h4 class="heading settled" data-level="4.1.1" id="alg_customize_tag_invoke"><span class="secno">4.1.1. </span><span class="content">Customizable with <code class="highlight"><c- n>tag_invoke</c-></code></span><a class="self-link" href="#alg_customize_tag_invoke"></a></h4>
<pre class="language-cpp highlight"><c- c1>// std::ranges::for_each possible implementation</c->
<c- k>namespace</c-> <c- nn>ranges</c->
<c- p>{</c->
<c- k>namespace</c-> <c- nn>__detail</c->
<c- p>{</c->
<c- k>struct</c-> <c- nc>__for_each_fn</c->
<c- p>{</c->
    <c- c1>// ...</c->
    <c- c1>// Existing serial overloads</c->
    <c- c1>// ...</c->

    <c- k>template</c-><c- o>&lt;</c-><c- n>policy_aware_scheduler</c-> <c- n>Scheduler</c-><c- p>,</c-> <c- n>input_iterator</c-> <c- n>I</c-><c- p>,</c-> <c- n>sentinel_for</c-><c- o>&lt;</c-><c- n>I</c-><c- o>></c-> <c- n>S</c-><c- p>,</c->
             <c- k>class</c-> <c- nc>Proj</c-> <c- o>=</c-> <c- n>identity</c-><c- p>,</c-> <c- n>indirectly_unary_invocable</c-><c- o>&lt;</c-><c- n>projected</c-><c- o>&lt;</c-><c- n>I</c-><c- p>,</c-> <c- n>Proj</c-><c- o>>></c-> <c- n>Fun</c-><c- o>></c->
    <c- k>constexpr</c-> <c- n>for_each_result</c-><c- o>&lt;</c-><c- n>I</c-><c- p>,</c-> <c- n>Fun</c-><c- o>></c->
    <c- k>operator</c-><c- p>()(</c-><c- n>Scheduler</c-> <c- n>sched</c-><c- p>,</c-> <c- n>I</c-> <c- n>first</c-><c- p>,</c-> <c- n>S</c-> <c- n>last</c-><c- p>,</c-> <c- n>Fun</c-> <c- n>f</c-><c- p>,</c-> <c- n>Proj</c-> <c- n>proj</c-> <c- o>=</c-> <c- p>{})</c-> <c- k>const</c->
    <c- p>{</c->
        <c- k>if</c-> <c- k>constexpr</c-> <c- p>(</c-><c- n>std</c-><c- o>::</c-><c- n>tag_invocable</c-><c- o>&lt;</c-><c- n>__for_each_fn</c-><c- p>,</c-> <c- n>Scheduler</c-><c- p>,</c-> <c- n>I</c-><c- p>,</c-> <c- n>S</c-><c- p>,</c-> <c- n>Fun</c-><c- p>,</c-> <c- n>Proj</c-><c- p>)</c->
        <c- p>{</c->
            <c- n>std</c-><c- o>::</c-><c- n>tag_invoke</c-><c- p>(</c-><c- o>*</c-><c- k>this</c-><c- p>,</c-> <c- n>sched</c-><c- p>,</c-> <c- n>first</c-><c- p>,</c-> <c- n>last</c-><c- p>,</c-> <c- n>f</c-><c- p>,</c-> <c- n>proj</c-><c- p>);</c->
        <c- p>}</c->
        <c- k>else</c->
        <c- p>{</c->
            <c- c1>// default implementation</c->
        <c- p>}</c->
    <c- p>}</c->

    <c- k>template</c-><c- o>&lt;</c-><c- n>policy_aware_scheduler</c-> <c- n>Scheduler</c-><c- p>,</c-> <c- n>input_range</c-> <c- n>R</c-><c- p>,</c-> <c- k>class</c-> <c- nc>Proj</c-> <c- o>=</c-> <c- n>identity</c-><c- p>,</c->
             <c- n>indirectly_unary_invocable</c-><c- o>&lt;</c-><c- n>projected</c-><c- o>&lt;</c-><c- n>iterator_t</c-><c- o>&lt;</c-><c- n>R</c-><c- o>></c-><c- p>,</c-> <c- n>Proj</c-><c- o>>></c-> <c- n>Fun</c-><c- o>></c->
    <c- k>constexpr</c-> <c- n>for_each_result</c-><c- o>&lt;</c-><c- n>borrowed_iterator_t</c-><c- o>&lt;</c-><c- n>R</c-><c- o>></c-><c- p>,</c-> <c- n>Fun</c-><c- o>></c->
    <c- k>operator</c-><c- p>()(</c-><c- n>Scheduler</c-> <c- n>sched</c-><c- p>,</c-> <c- n>R</c-><c- o>&amp;&amp;</c-> <c- n>r</c-><c- p>,</c-> <c- n>Fun</c-> <c- n>f</c-><c- p>,</c-> <c- n>Proj</c-> <c- n>proj</c-> <c- o>=</c-> <c- p>{})</c-> <c- k>const</c->
    <c- p>{</c->
        <c- k>return</c-> <c- p>(</c-><c- o>*</c-><c- k>this</c-><c- p>)(</c-><c- n>sched</c-><c- p>,</c-> <c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>begin</c-><c- p>(</c-><c- n>r</c-><c- p>),</c-> <c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>end</c-><c- p>(</c-><c- n>r</c-><c- p>),</c-> <c- n>f</c-><c- p>,</c-> <c- n>proj</c-><c- p>);</c->
    <c- p>}</c->
<c- p>};</c-> <c- c1>// struct for_each</c->
<c- p>}</c-> <c- c1>// namespace __detail</c->
<c- kr>inline</c-> <c- k>namespace</c-> <c- nn>__for_each_fn_namespace</c->
<c- p>{</c->
<c- kr>inline</c-> <c- k>constexpr</c-> <c- n>__detail</c-><c- o>::</c-><c- n>__for_each_fn</c-> <c- n>for_each</c-><c- p>;</c->
<c- p>}</c-> <c- c1>// __for_each_fn_namespace</c->
<c- p>}</c-> <c- c1>// namespace ranges</c->
</pre>
   <p>A customization for that approach might look like:</p>
<pre class="language-cpp highlight"><c- k>namespace</c-> <c- nn>cuda</c->
<c- p>{</c->
<c- k>struct</c-> <c- nc>scheduler</c->
<c- p>{</c->
    <c- k>template</c-><c- o>&lt;</c-><c- n>std</c-><c- o>::</c-><c- n>input_iterator</c-> <c- n>I</c-><c- p>,</c-> <c- n>std</c-><c- o>::</c-><c- n>sentinel_for</c-><c- o>&lt;</c-><c- n>I</c-><c- o>></c-> <c- n>S</c-><c- p>,</c->
            <c- k>class</c-> <c- nc>Proj</c-> <c- o>=</c-> <c- n>std</c-><c- o>::</c-><c- n>identity</c-><c- p>,</c-> <c- n>std</c-><c- o>::</c-><c- n>indirectly_unary_invocable</c-><c- o>&lt;</c-><c- n>std</c-><c- o>::</c-><c- n>projected</c-><c- o>&lt;</c-><c- n>I</c-><c- p>,</c-> <c- n>Proj</c-><c- o>>></c-> <c- n>Fun</c-><c- o>></c->
    <c- k>friend</c-> <c- k>constexpr</c-> <c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>for_each_result</c-><c- o>&lt;</c-><c- n>I</c-><c- p>,</c-> <c- n>Fun</c-><c- o>></c->
    <c- n>tag_invoke</c-><c- p>(</c-><c- n>std</c-><c- o>::</c-><c- n>tag_t</c-><c- o>&lt;</c-><c- n>ranges</c-><c- o>::</c-><c- n>for_each</c-><c- o>></c-><c- p>,</c-> <c- n>scheduler</c-><c- p>,</c-> <c- n>I</c-> <c- n>first</c-><c- p>,</c-> <c- n>S</c-> <c- n>last</c-><c- p>,</c-> <c- n>Fun</c-> <c- n>f</c-><c- p>,</c-> <c- n>Proj</c-> <c- n>proj</c-> <c- o>=</c-> <c- p>{})</c->
    <c- p>{</c->
        <c- c1>// CUDA efficient implementation</c->
        <c- k>return</c-> <c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>for_each_result</c-><c- p>{</c-><c- n>last</c-><c- p>,</c-> <c- n>f</c-><c- p>};</c->
    <c- p>}</c->
<c- p>};</c->
<c- p>}</c->
</pre>
   <h4 class="heading settled" data-level="4.1.2" id="alg_customize_language"><span class="secno">4.1.2. </span><span class="content">Customizable with language support</span><a class="self-link" href="#alg_customize_language"></a></h4>
   <p>Here we assume that all <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>for_each</c-></code> overloads, including ones that do not take a policy or a scheduler,
are defined as <code class="highlight"><c- n>customizable</c-></code> or <code class="highlight"><c- k>final</c-></code> functions (in the sense of <a data-link-type="biblio" href="#biblio-p2547r1" title="Language support for customisable functions">[P2547R1]</a>). We have not explored if it is
practical to change the existing implementations of range algorithms in such a way.</p>
<pre class="language-cpp highlight"><c- c1>// std::ranges::for_each possible implementation</c->
<c- k>namespace</c-> <c- nn>ranges</c->
<c- p>{</c->
    <c- c1>// ...</c->
    <c- c1>// Existing serial overloads</c->
    <c- c1>// ...</c->

    <c- k>template</c-><c- o>&lt;</c-><c- n>policy_aware_scheduler</c-> <c- n>Scheduler</c-><c- p>,</c-> <c- n>input_iterator</c-> <c- n>I</c-><c- p>,</c-> <c- n>sentinel_for</c-><c- o>&lt;</c-><c- n>I</c-><c- o>></c-> <c- n>S</c-><c- p>,</c->
             <c- k>class</c-> <c- nc>Proj</c-> <c- o>=</c-> <c- n>identity</c-><c- p>,</c-> <c- n>indirectly_unary_invocable</c-><c- o>&lt;</c-><c- n>projected</c-><c- o>&lt;</c-><c- n>I</c-><c- p>,</c-> <c- n>Proj</c-><c- o>>></c-> <c- n>Fun</c-><c- o>></c->
    <c- k>constexpr</c-> <c- n>for_each_result</c-><c- o>&lt;</c-><c- n>I</c-><c- p>,</c-> <c- n>Fun</c-><c- o>></c->
    <c- n>for_each</c-><c- p>(</c-><c- n>Scheduler</c-> <c- n>sched</c-><c- p>,</c-> <c- n>I</c-> <c- n>first</c-><c- p>,</c-> <c- n>S</c-> <c- n>last</c-><c- p>,</c-> <c- n>Fun</c-> <c- n>f</c-><c- p>,</c-> <c- n>Proj</c-> <c- n>proj</c-> <c- o>=</c-> <c- p>{})</c-> <c- n>customizable</c-><c- p>;</c->

    <c- k>template</c-><c- o>&lt;</c-><c- n>policy_aware_scheduler</c-> <c- n>Scheduler</c-><c- p>,</c-> <c- n>input_iterator</c-> <c- n>I</c-><c- p>,</c-> <c- n>sentinel_for</c-><c- o>&lt;</c-><c- n>I</c-><c- o>></c-> <c- n>S</c-><c- p>,</c->
             <c- k>class</c-> <c- nc>Proj</c-> <c- o>=</c-> <c- n>identity</c-><c- p>,</c-> <c- n>indirectly_unary_invocable</c-><c- o>&lt;</c-><c- n>projected</c-><c- o>&lt;</c-><c- n>I</c-><c- p>,</c-> <c- n>Proj</c-><c- o>>></c-> <c- n>Fun</c-><c- o>></c->
    <c- k>constexpr</c-> <c- n>for_each_result</c-><c- o>&lt;</c-><c- n>I</c-><c- p>,</c-> <c- n>Fun</c-><c- o>></c->
    <c- n>for_each</c-><c- p>(</c-><c- n>Scheduler</c-><c- o>&amp;&amp;</c-> <c- n>sched</c-><c- p>,</c-> <c- n>I</c-> <c- n>first</c-><c- p>,</c-> <c- n>S</c-> <c- n>last</c-><c- p>,</c-> <c- n>Fun</c-> <c- n>f</c-><c- p>,</c-> <c- n>Proj</c-> <c- n>proj</c-> <c- o>=</c-> <c- p>{})</c-> <c- k>default</c->
    <c- p>{</c->
        <c- c1>// default implementation</c->
    <c- p>}</c->

    <c- k>template</c-><c- o>&lt;</c-><c- n>policy_aware_scheduler</c-> <c- n>Scheduler</c-><c- p>,</c-> <c- n>input_range</c-> <c- n>R</c-><c- p>,</c-> <c- k>class</c-> <c- nc>Proj</c-> <c- o>=</c-> <c- n>identity</c-><c- p>,</c->
             <c- n>indirectly_unary_invocable</c-><c- o>&lt;</c-><c- n>projected</c-><c- o>&lt;</c-><c- n>iterator_t</c-><c- o>&lt;</c-><c- n>R</c-><c- o>></c-><c- p>,</c-> <c- n>Proj</c-><c- o>>></c-> <c- n>Fun</c-><c- o>></c->
    <c- k>constexpr</c-> <c- n>for_each_result</c-><c- o>&lt;</c-><c- n>borrowed_iterator_t</c-><c- o>&lt;</c-><c- n>R</c-><c- o>></c-><c- p>,</c-> <c- n>Fun</c-><c- o>></c->
    <c- n>for_each</c-><c- p>(</c-><c- n>Scheduler</c-> <c- n>sched</c-><c- p>,</c-> <c- n>R</c-><c- o>&amp;&amp;</c-> <c- n>r</c-><c- p>,</c-> <c- n>Fun</c-> <c- n>f</c-><c- p>,</c-> <c- n>Proj</c-> <c- n>proj</c-> <c- o>=</c-> <c- p>{})</c->
    <c- p>{</c->
        <c- k>return</c-> <c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>for_each</c-><c- p>(</c-><c- n>sched</c-><c- p>,</c-> <c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>begin</c-><c- p>(</c-><c- n>r</c-><c- p>),</c-> <c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>end</c-><c- p>(</c-><c- n>r</c-><c- p>),</c-> <c- n>f</c-><c- p>,</c-> <c- n>proj</c-><c- p>);</c->
    <c- p>}</c->
<c- p>}</c->
</pre>
   <h3 class="heading settled" data-level="4.2" id="execute_on_cpo"><span class="secno">4.2. </span><span class="content"><code class="highlight"><c- n>execute_on</c-></code></span><a class="self-link" href="#execute_on_cpo"></a></h3>
   <p><code class="highlight"><c- n>execute_on</c-></code> is the customization point that serves the purpose of tying a <code class="highlight"><c- n>scheduler</c-></code> and an <code class="highlight"><c- n>execution_policy</c-></code>.</p>
   <p>A possible implementation is:</p>
<pre class="language-cpp highlight"><c- k>namespace</c-> <c- nn>__detail</c->
<c- p>{</c->
<c- k>class</c-> <c- nc>__policy_aware_scheduler_adaptor</c-><c- p>;</c-> <c- c1>// exposition-only</c->

<c- k>struct</c-> <c- nc>__execute_on_fn</c-> <c- p>{</c->
    <c- k>template</c-> <c- o>&lt;</c-><c- k>typename</c-> <c- nc>Scheduler</c-><c- p>,</c-> <c- n>execution_policy</c-> <c- n>Policy</c-><c- o>></c->
    <c- k>auto</c-> <c- k>operator</c-><c- p>()(</c-><c- n>Scheduler</c-> <c- n>sched</c-><c- p>,</c-> <c- n>Policy</c-> <c- n>policy</c-><c- p>)</c-> <c- k>const</c->
    <c- p>{</c->
        <c- k>if</c-> <c- k>constexpr</c-> <c- p>(</c-><c- n>std</c-><c- o>::</c-><c- n>tag_invocable</c-><c- o>&lt;</c-><c- n>__execute_on_fn</c-><c- p>,</c-> <c- n>Scheduler</c-><c- p>,</c-> <c- n>Policy</c-><c- o>></c-><c- p>)</c->
        <c- p>{</c->
            <c- k>return</c-> <c- n>std</c-><c- o>::</c-><c- n>tag_invoke</c-><c- p>(</c-><c- o>*</c-><c- k>this</c-><c- p>,</c-> <c- n>sched</c-><c- p>,</c-> <c- n>policy</c-><c- p>);</c->
        <c- p>}</c->
        <c- k>else</c-> 
        <c- p>{</c->
            <c- k>return</c-> <c- n>__policy_aware_scheduler_adaptor</c-><c- p>(</c-><c- n>sched</c-><c- p>,</c-> <c- n>std</c-><c- o>::</c-><c- n>execution</c-><c- o>::</c-><c- n>seq</c-><c- p>);</c-> 
        <c- p>}</c->
    <c- p>}</c->
<c- p>};</c-> <c- c1>// __execute_on_fn</c->
<c- p>}</c-> <c- c1>// namespace __detail</c->

<c- kr>inline</c-> <c- k>namespace</c-> <c- nn>__execute_on_fn_namespace</c->
<c- p>{</c->
<c- kr>inline</c-> <c- k>constexpr</c-> <c- n>__detail</c-><c- o>::</c-><c- n>__execute_on_fn</c-> <c- n>execute_on</c-><c- p>;</c->
<c- p>}</c-> <c- c1>// __execute_on_fn_namespace</c->
</pre>
   <p>Unless specially restricted, scheduler types which will be defined in the standard should be capable and therefore
required to support all the standard execution policies. For these schedulers, falling back to sequential execution
for any unknown 3rd party policy may also be desirable.</p>
   <p>Generally, however, it is up to the scheduler to decide whether to provide a fallback for unknown and unsupported policies
or not, and if yes, to define what this fallback is doing. For example, SYCL-based or CUDA-based schedulers cannot
fallback to sequential execution because it is generally impossible. Such a scheduler might represent an accelerator
where sequential execution is not supported. Executing sequentially on a CPU might be incorrect too if the data
is allocated on another device and inaccessible for the CPU.</p>
   <p>Based on the above, we propose that:</p>
   <ul>
    <li data-md>
     <p><code class="highlight"><c- n>execute_on</c-></code> has the default implementation that somehow matches the given scheduler with the <code class="highlight"><c- n>sequenced_policy</c-></code>;</p>
    <li data-md>
     <p>if for the given <code class="highlight"><c- n>scheduler</c-></code> and execution policy the customization of <code class="highlight"><c- n>execute_on</c-></code> fails to compile
or causes a runtime error, it is still a valid implementation.</p>
   </ul>
   <p>A customization might look like:</p>
<pre class="language-cpp highlight"><c- c1>// tag_invoke based customization</c->
<c- k>namespace</c-> <c- nn>sycl</c-> 
<c- p>{</c->
    <c- k>template</c-> <c- o>&lt;</c-><c- k>typename</c-> <c- nc>ExecutionPolicy</c-><c- o>></c->
    <c- k>constexpr</c-> <c- k>auto</c-> <c- n>is_par_unseq_v</c-><c- p>;</c-> <c- c1>// exposition-only</c->

    <c- k>class</c-> <c- nc>__policy_aware_scheduler_adaptor</c-><c- p>;</c-> <c- c1>// exposition-only</c->

    <c- k>struct</c-> <c- nc>scheduler</c-> <c- p>{</c->
        <c- k>template</c-> <c- o>&lt;</c-><c- n>std</c-><c- o>::</c-><c- n>execution_policy</c-> <c- n>Policy</c-><c- o>></c->
        <c- k>friend</c-> <c- k>auto</c-> <c- n>tag_invoke</c-><c- p>(</c-><c- n>std</c-><c- o>::</c-><c- n>tag_t</c-><c- o>&lt;</c-><c- n>std</c-><c- o>::</c-><c- n>execute_on</c-><c- o>></c-><c- p>,</c-> <c- n>scheduler</c-> <c- n>sched</c-><c- p>,</c-> <c- n>Policy</c-> <c- n>policy</c-><c- p>)</c->
        <c- p>{</c->
            <c- k>static_assert</c-><c- p>(</c-><c- n>is_par_unseq_v</c-><c- o>&lt;</c-><c- n>Policy</c-><c- o>></c-><c- p>,</c-> <c- s>"SYCL scheduler currently supports par_unseq policy only"</c-><c- p>);</c->
            <c- k>return</c-> <c- n>__policy_aware_scheduler_adaptor</c-><c- p>{</c-><c- n>sched</c-><c- p>,</c-> <c- n>std</c-><c- o>::</c-><c- n>forward</c-><c- o>&lt;</c-><c- n>Policy</c-><c- o>></c-><c- p>(</c-><c- n>policy</c-><c- p>)};</c->
        <c- p>}</c->
    <c- p>};</c->
<c- p>}</c->
</pre>
   <h3 class="heading settled" data-level="4.3" id="policy_aware_scheduler"><span class="secno">4.3. </span><span class="content"><code class="highlight"><c- n>policy_aware_scheduler</c-></code></span><a class="self-link" href="#policy_aware_scheduler"></a></h3>
   <p><code class="highlight"><c- n>policy_aware_scheduler</c-></code> is a concept that represents an entity that combines <code class="highlight"><c- n>scheduler</c-></code> and <code class="highlight"><c- n>execution_policy</c-></code>. It allows to get both execution policy type and execution policy object
from the <code class="highlight"><c- n>policy_aware_scheduler</c-></code> returned by <code class="highlight"><c- n>execute_on</c-></code> call.</p>
   <p class="note" role="note"><span class="marker">Note:</span> <code class="highlight"><c- n>policy_type</c-></code> and <code class="highlight"><c- n>execution_policy</c-></code> object are not necessarily the same which <code class="highlight"><c- n>execute_on</c-></code> was called with.</p>
<pre class="language-cpp highlight"><c- k>template</c-> <c- o>&lt;</c-><c- k>typename</c-> <c- nc>S</c-><c- o>></c->
<c- k>concept</c-> <c- nc>policy_aware_scheduler</c-> <c- o>=</c-> <c- n>scheduler</c-><c- o>&lt;</c-><c- n>S</c-><c- o>></c-> <c- o>&amp;&amp;</c-> <c- k>requires</c-> <c- p>(</c-><c- n>S</c-> <c- n>s</c-><c- p>)</c-> <c- p>{</c->
    <c- k>typename</c-> <c- nc>S</c-><c- o>::</c-><c- n>base_scheduler_type</c-><c- p>;</c->
    <c- k>typename</c-> <c- nc>S</c-><c- o>::</c-><c- n>policy_type</c-><c- p>;</c->
    <c- p>{</c-> <c- n>s</c-><c- p>.</c-><c- n>get_policy</c-><c- p>()</c-> <c- p>}</c-> <c- o>-></c-> <c- n>execution_policy</c-><c- p>;</c->
<c- p>};</c->
</pre>
   <p>See <a href="#exec_concept">§ 4.4 execution_policy concept</a> for more details about <code class="highlight"><c- n>execution_policy</c-></code> concept.</p>
   <p>Customizations of the parallel algorithms can reuse the existing implementation (e.g., TBB-based, SYCL-based, CUDA-based)
of parallel algorithms with <code class="highlight"><c- n>ExecutionPolicy</c-></code> template parameter for "known" <code class="highlight"><c- n>base_scheduler_type</c-></code> type.</p>
   <h3 class="heading settled" data-level="4.4" id="exec_concept"><span class="secno">4.4. </span><span class="content"><code class="highlight"><c- n>execution_policy</c-></code> concept</span><a class="self-link" href="#exec_concept"></a></h3>
   <p>The execution policy concept is necessary if we want to constrain the return type of the <code class="highlight"><c- n>s</c-><c- p>.</c-><c- n>get_policy</c-><c- p>()</c-></code> method for <code class="highlight"><c- n>policy_aware_scheduler</c-></code>.</p>
   <p>Since the scheduler tells "where" algorithms are executed and policies tell "how" algorithms are executed, we consider
the set of policies currently defined in the <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>execution</c-></code> namespace to be sufficient. So, the concept definition could look like:</p>
<pre class="language-cpp highlight"><c- k>template</c-> <c- o>&lt;</c-><c- k>typename</c-> <c- nc>ExecutionPolicy</c-><c- o>></c->
<c- k>concept</c-> <c- nc>execution_policy</c-> <c- o>=</c-> <c- n>std</c-><c- o>::</c-><c- n>is_execution_policy_v</c-><c- o>&lt;</c-><c- n>std</c-><c- o>::</c-><c- n>remove_cvref_t</c-><c- o>&lt;</c-><c- n>ExecutionPolicy</c-><c- o>>></c-><c- p>;</c->
</pre>
   <p>We are open to make it more generic to allow adding custom policies for a particular scheduler, if somebody sees the value in it.
For that case we either need to allow specializing <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>is_execution_policy</c-></code> or to define another trait.</p>
   <h2 class="heading settled" data-level="5" id="further_work"><span class="secno">5. </span><span class="content">Further exploration</span><a class="self-link" href="#further_work"></a></h2>
   <p>The authors plan to explore how to specify a set of basic functions (a so-called "parallel backend") which
parallel algorithms can be expressed with. It might be proposed in a separate paper based on the analysis.</p>
   <h2 class="heading settled" data-level="6" id="revision_history#"><span class="secno">6. </span><span class="content">Revision History</span><a class="self-link" href="#revision_history%23"></a></h2>
   <h3 class="heading settled" data-level="6.1" id="r1_r2"><span class="secno">6.1. </span><span class="content">R1 => R2</span><a class="self-link" href="#r1_r2"></a></h3>
   <ul>
    <li data-md>
     <p>Changed <code class="highlight"><c- n>execute_on</c-></code> implementation to advice sequential execution</p>
    <li data-md>
     <p>Allowed <code class="highlight"><c- n>execute_on</c-></code> customizations to cause a compile-time or a run-time error</p>
    <li data-md>
     <p>Added customization examples for an algorithm and <code class="highlight"><c- n>execute_on</c-></code></p>
    <li data-md>
     <p>Added a subsection on extensibility of the proposed approach</p>
    <li data-md>
     <p>Added a possible signature of a lazy <code class="highlight"><c- n>for_each</c-></code> algorithm</p>
   </ul>
   <h3 class="heading settled" data-level="6.2" id="r0_r1"><span class="secno">6.2. </span><span class="content">R0 => R1</span><a class="self-link" href="#r0_r1"></a></h3>
   <ul>
    <li data-md>
     <p>Defined the API in terms of "customizable functions" instead of CPO</p>
    <li data-md>
     <p>Set range-based algorithms as the primary customization point for schedulers</p>
    <li data-md>
     <p>Proposed support for standard execution policies to range-based algorithms</p>
    <li data-md>
     <p>Defined scheduler-aware parallel algorithms in <code class="highlight"><c- k>namespace</c-> <c- nn>std</c-></code> via constrained overloads redirecting to the range-based analogues</p>
    <li data-md>
     <p>Clarified behavior of execute_on</p>
   </ul>
   <h2 class="heading settled" data-level="7" id="acknowledgements"><span class="secno">7. </span><span class="content">Acknowledgements</span><a class="self-link" href="#acknowledgements"></a></h2>
   <ul>
    <li data-md>
     <p>Thanks to Thomas Rodgers for reviewing and improving the wording, and for his feedback on execution semantics.</p>
   </ul>
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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="normative"><span class="content">Normative References</span><a class="self-link" href="#normative"></a></h3>
  <dl>
   <dt id="biblio-p2300r7">[P2300R7]
   <dd>Eric Niebler, Michał Dominiak, Georgy Evtushenko, Lewis Baker, Lucian Radu Teodorescu, Lee Howes, Kirk Shoop, Michael Garland, Bryce Adelstein Lelbach. <a href="https://wg21.link/p2300r7"><cite>`std::execution`</cite></a>. 21 April 2023. URL: <a href="https://wg21.link/p2300r7">https://wg21.link/p2300r7</a>
   <dt id="biblio-p2547r1">[P2547R1]
   <dd>Lewis Baker, Corentin Jabot, Gašper Ažman. <a href="https://wg21.link/p2547r1"><cite>Language support for customisable functions</cite></a>. 16 July 2022. URL: <a href="https://wg21.link/p2547r1">https://wg21.link/p2547r1</a>
  </dl>
  <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-p2214r2">[P2214R2]
   <dd>Barry Revzin, Conor Hoekstra, Tim Song. <a href="https://wg21.link/p2214r2"><cite>A Plan for C++23 Ranges</cite></a>. 18 February 2022. URL: <a href="https://wg21.link/p2214r2">https://wg21.link/p2214r2</a>
   <dt id="biblio-p2500r0">[P2500R0]
   <dd>Ruslan Arutyunyan. <a href="https://wg21.link/p2500r0"><cite>C++17 parallel algorithms and P2300</cite></a>. 15 October 2022. URL: <a href="https://wg21.link/p2500r0">https://wg21.link/p2500r0</a>
   <dt id="biblio-p2500r1">[P2500R1]
   <dd>Ruslan Arutyunyan, Alexey Kukanov. <a href="https://wg21.link/p2500r1"><cite>C++ parallel algorithms and P2300</cite></a>. 17 May 2023. URL: <a href="https://wg21.link/p2500r1">https://wg21.link/p2500r1</a>
  </dl>