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  <title>P3179R0: C++ parallel range algorithms</title>
<style data-fill-with="stylesheet">/******************************************************************************
 *                   Style sheet for the W3C specifications                   *
 *
 * Special classes handled by this style sheet include:
 *
 * Indices
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 *     + <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)
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 *     -> ins/del.c### for candidate and proposed changes (amendments)
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 *   - .marker for source-inserted example/figure/issue numbers (<span class='marker'>Issue 4</span>)
 *   - ::before styled for CSS-generated issue/example/figure numbers:
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/******************************************************************************/
/*                         Front Matter & Navigation                          */
/******************************************************************************/

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

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


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

/** Terminology Markup ********************************************************/
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/** Change Marking ************************************************************/

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

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

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

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	details.note[open] > summary {
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/** Assertion Box *************************************************************/
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		background: #EEE;
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/** Advisement Box ************************************************************/
	/*  for attention-grabbing normative statements */

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		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 d5d58a306, updated Fri Jan 26 16:12:28 2024 -0800" name="generator">
  <link href="https://wg21.link/P3179R0" rel="canonical">
  <link href="https://isocpp.org/favicon.ico" rel="icon">
  <meta content="c51f32b729f1e12188f4715abf9c42e0dd366535" name="revision">
<style>/* Boilerplate: style-autolinks */
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  <div class="head">
   <p data-fill-with="logo"></p>
   <h1 class="p-name no-ref" id="title">P3179R0<br>C++ parallel range algorithms</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="2024-03-14">2024-03-14</time></span></h2>
   <div data-fill-with="spec-metadata">
    <dl>
     <dt>This version:
     <dd><a class="u-url" href="https://wg21.link/P3179R0">https://wg21.link/P3179R0</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>SG9, SG1
     <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 proposes adding parallel algorithms that work together with the C++ Ranges library.</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_summary"><span class="secno">2.1</span> <span class="content">Design summary</span></a>
      <li><a href="#coexistence_with_schedulers"><span class="secno">2.2</span> <span class="content">Coexistence with schedulers</span></a>
      <li><a href="#easy_to_switch"><span class="secno">2.3</span> <span class="content">Switch to parallel range algorithms with minimal changes</span></a>
      <li><a href="#return_type"><span class="secno">2.4</span> <span class="content">Algorithm return types</span></a>
      <li><a href="#non_adl_discoverable"><span class="secno">2.5</span> <span class="content">Non ADL-discoverable functions</span></a>
      <li><a href="#random_access_requirement"><span class="secno">2.6</span> <span class="content">Requiring <code class="highlight"><c- n>random_access_iterator</c-></code> or <code class="highlight"><c- n>random_access_range</c-></code> for parallel policies</span></a>
      <li><a href="#const_callable_parameter"><span class="secno">2.7</span> <span class="content"><code class="highlight"><c- k>const</c-></code>-callable parameter</span></a>
      <li><a href="#not_customization_point"><span class="secno">2.8</span> <span class="content">Parallel range algorithms are not customization points</span></a>
      <li><a href="#not_constexpr"><span class="secno">2.9</span> <span class="content">Parallel range algorithms are not <code class="highlight"><c- k>constexpr</c-></code></span></a>
     </ol>
    <li>
     <a href="#more_example"><span class="secno">3</span> <span class="content">More examples</span></a>
     <ol class="toc">
      <li><a href="#less_parallel_call"><span class="secno">3.1</span> <span class="content">Less parallel algorithm calls and better expressiveness</span></a>
     </ol>
    <li>
     <a href="#proposed_api"><span class="secno">4</span> <span class="content">Proposed API</span></a>
     <ol class="toc">
      <li><a href="#possible_impl"><span class="secno">4.1</span> <span class="content">Possible implementation of a parallel range algorithm</span></a>
     </ol>
    <li>
     <a href="#further_work"><span class="secno">5</span> <span class="content">Further exploration</span></a>
     <ol class="toc">
      <li><a href="#thread_safe_views"><span class="secno">5.1</span> <span class="content">Thread-safe views examination</span></a>
      <li><a href="#serial_range_based_absence"><span class="secno">5.2</span> <span class="content">Absence of some serial range-based algorithms</span></a>
      <li><a href="#parallel_range_algorithms_output"><span class="secno">5.3</span> <span class="content">Output for parallel range algorithms</span></a>
     </ol>
    <li>
     <a href="#references"><span class="secno"></span> <span class="content">References</span></a>
     <ol class="toc">
      <li><a href="#informative"><span class="secno"></span> <span class="content">Informative References</span></a>
     </ol>
   </ol>
  </nav>
  <main>
   <h2 class="heading settled" data-level="1" id="motivation"><span class="secno">1. </span><span class="content">Motivation</span><a class="self-link" href="#motivation"></a></h2>
   <p>Standard parallel algorithms with execution policies which set semantic requirements to user-provided callable objects
were a good start for supporting parallelism in the C++ standard.</p>
   <p>The C++ Ranges library - ranges, views, etc. - is a powerful facility to produce lazily evaluated pipelines
that can be processed by range-based algorithms. Together they provide a productive and expressive API
with the room for extra optimizations.</p>
   <p>Combining these two powerful features by adding support for execution policies to the range-based algorithms opens
an opportunity to fuse several computations into one parallel algorithm call, thus reducing the overhead on parallelism.
That is especially valuable for heterogeneous implementations of parallel algorithms, for which the range-based API helps
reducing the number of kernels submitted to an accelerator.</p>
   <p>Earlier, <a data-link-type="biblio" href="#biblio-p2500r2" title="C++ parallel algorithms and P2300">[P2500R2]</a> proposed to add the range-based C++ parallel algorithms together with its primary goal of extending
algorithms with schedulers. We have decided to split those parts to separate papers, which could progress independently.</p>
   <p>This paper is targeted to C++26.</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>
   <p>This proposal addresses absence of execution policy support for C++ range-based algorithms. In the nutshell,
the proposal extends C++ range algorithms with overloads taking any standard C++ execution policy as a function
parameter. These overloads are further referred to as <em>parallel range algorithms</em>.</p>
   <h3 class="heading settled" data-level="2.1" id="design_summary"><span class="secno">2.1. </span><span class="content">Design summary</span><a class="self-link" href="#design_summary"></a></h3>
   <ul>
    <li data-md>
     <p>The parallel range algorithms should be close to C++17 classic ones to use the code with minimal required changes.</p>
    <li data-md>
     <p>The parallel range algorithms should return the same type as the corresponding serial range algorithms.</p>
    <li data-md>
     <p>The proposed algorithms should be special non-ADL discoverable functions, same as serial range algorithms.</p>
    <li data-md>
     <p>The required range and iterator categories should at least be random access for all but <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>execution</c-><c- o>::</c-><c- n>seq</c-></code> execution
policies.</p>
    <li data-md>
     <p>The proposed API should require any callable object passed to an algorithm to have <code class="highlight"><c- k>const</c-></code>-qualified <code class="highlight"><c- k>operator</c-><c- p>()</c-></code>.</p>
    <li data-md>
     <p>The proposed API is not a customization point.</p>
    <li data-md>
     <p>The proposed API is not <code class="highlight"><c- k>constexpr</c-></code>.</p>
   </ul>
   <h3 class="heading settled" data-level="2.2" id="coexistence_with_schedulers"><span class="secno">2.2. </span><span class="content">Coexistence with schedulers</span><a class="self-link" href="#coexistence_with_schedulers"></a></h3>
   <p>We believe that adding parallel range algorithms does not have the risk of conflict with anticipated scheduler-based
algorithms, because an execution policy does not satisfy the requirements for a policy-aware scheduler (<a data-link-type="biblio" href="#biblio-p2500r2" title="C++ parallel algorithms and P2300">[P2500R2]</a>),
a sender (<a data-link-type="biblio" href="#biblio-p3300r0" title="C++ Asynchronous Parallel Algorithms">[P3300R0]</a>), or really anything else from <a data-link-type="biblio" href="#biblio-p2300r7" title="`std::execution`">[P2300R7]</a> that can be used to specify such algorithms.</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>
   <h3 class="heading settled" data-level="2.3" id="easy_to_switch"><span class="secno">2.3. </span><span class="content">Switch to parallel range algorithms with minimal changes</span><a class="self-link" href="#easy_to_switch"></a></h3>
   <p>One of the goals is to require a minimal amount of changes when switching from the existing API to parallel range algorithms.</p>
   <p>The C++17 parallel <code class="highlight"><c- n>for_each</c-></code> call:</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>execution</c-><c- o>::</c-><c- n>par</c-><c- p>,</c-> <c- n>v</c-><c- p>.</c-><c- n>begin</c-><c- p>(),</c-> <c- n>v</c-><c- p>.</c-><c- n>end</c-><c- p>(),</c-> <c- p>[](</c-><c- k>auto</c-><c- o>&amp;</c-> <c- n>x</c-><c- p>)</c-> <c- p>{</c-> <c- o>++</c-><c- n>x</c-><c- p>;</c-> <c- p>});</c->
</pre>
   <p>can be changed to one of the following:</p>
<pre class="language-cpp highlight"><c- c1>// Using an iterator and a sentinel</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>std</c-><c- o>::</c-><c- n>execution</c-><c- o>::</c-><c- n>par</c-><c- p>,</c-> <c- n>v</c-><c- p>.</c-><c- n>begin</c-><c- p>(),</c-> <c- n>v</c-><c- p>.</c-><c- n>end</c-><c- p>(),</c-> <c- p>[](</c-><c- k>auto</c-><c- o>&amp;</c-> <c- n>x</c-><c- p>)</c-> <c- p>{</c-> <c- o>++</c-><c- n>x</c-><c- p>;</c-> <c- p>});</c->

<c- c1>// Switching to use a range</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>std</c-><c- o>::</c-><c- n>execution</c-><c- o>::</c-><c- n>par</c-><c- p>,</c-> <c- n>v</c-><c- p>,</c-> <c- p>[](</c-><c- k>auto</c-><c- o>&amp;</c-> <c- n>x</c-><c- p>)</c-> <c- p>{</c-> <c- o>++</c-><c- n>x</c-><c- p>;</c-> <c- p>});</c->
</pre>
   <p>If serial range algorithms are used in the code, switching to parallel version would look like in the example below.</p>
   <p>The C++20 range-based <code class="highlight"><c- n>for_each</c-></code> call:</p>
<pre class="language-cpp highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>for_each</c-><c- p>(</c-><c- n>v</c-><c- p>,</c-> <c- p>[](</c-><c- k>auto</c-><c- o>&amp;</c-> <c- n>x</c-><c- p>)</c-> <c- p>{</c-> <c- o>++</c-><c- n>x</c-><c- p>;</c-> <c- p>});</c->
</pre>
   <p>becomes:</p>
<pre class="language-cpp highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>for_each</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>v</c-><c- p>,</c-> <c- p>[](</c-><c- k>auto</c-><c- o>&amp;</c-> <c- n>x</c-><c- p>)</c-> <c- p>{</c-> <c- o>++</c-><c- n>x</c-><c- p>;</c-> <c- p>});</c->
</pre>
   <p>As you can see the changes are pretty simple:</p>
   <ul>
    <li data-md>
     <p>In the first case only the namespace is changed, and users might also change <code class="highlight"><c- n>v</c-><c- p>.</c-><c- n>begin</c-><c- p>(),</c-> <c- n>v</c-><c- p>.</c-><c- n>end</c-><c- p>()</c-></code> to just <code class="highlight"><c- n>v</c-></code>.</p>
    <li data-md>
     <p>In the second case an execution policy is added as the first function argument. The same is true for
the <em>Iterator</em> + <em>Sentinel</em> overload</p>
   </ul>
   <h3 class="heading settled" data-level="2.4" id="return_type"><span class="secno">2.4. </span><span class="content">Algorithm return types</span><a class="self-link" href="#return_type"></a></h3>
   <p>We explored possible algorithm return types and came to conclusion that returning the same type as serial range
algorithms is the preferred option to make the changes for enabling parallelism minimal.</p>
   <p>We can consider the same example as in the previous paragraph.</p>
<pre class="language-cpp highlight"><c- c1>// for_each_result&lt;I, Fun> may be used instead of auto</c->
<c- k>auto</c-> <c- n>res</c-> <c- o>=</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>v</c-><c- p>,</c-> <c- p>[](</c-><c- k>auto</c-><c- o>&amp;</c-> <c- n>x</c-><c- p>)</c-> <c- p>{</c-> <c- o>++</c-><c- n>x</c-><c- p>;</c-> <c- p>});</c->
</pre>
   <p>becomes:</p>
<pre class="language-cpp highlight"><c- c1>// for_each_result&lt;I, Fun> may be used instead of auto</c->
<c- k>auto</c-> <c- n>res</c-> <c- o>=</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>std</c-><c- o>::</c-><c- n>execution</c-><c- o>::</c-><c- n>par</c-><c- p>,</c-> <c- n>v</c-><c- p>,</c-> <c- p>[](</c-><c- k>auto</c-><c- o>&amp;</c-> <c- n>x</c-><c- p>)</c-> <c- p>{</c-> <c- o>++</c-><c- n>x</c-><c- p>;</c-> <c- p>});</c->
</pre>
   <h3 class="heading settled" data-level="2.5" id="non_adl_discoverable"><span class="secno">2.5. </span><span class="content">Non ADL-discoverable functions</span><a class="self-link" href="#non_adl_discoverable"></a></h3>
   <p>We believe the proposed functions should be non-ADL discoverable same as serial range algorithms. Whether
a serial version is implemented with the special compiler support or as a global callable object, adding overloads
for the parallel version should not be a problem. Please see <a href="#possible_impl">§ 4.1 Possible implementation of a parallel range algorithm</a> for more information.</p>
   <h3 class="heading settled" data-level="2.6" id="random_access_requirement"><span class="secno">2.6. </span><span class="content">Requiring <code class="highlight"><c- n>random_access_iterator</c-></code> or <code class="highlight"><c- n>random_access_range</c-></code> for parallel policies</span><a class="self-link" href="#random_access_requirement"></a></h3>
   <p>C++17 parallel algorithms require <em>LegacyForwardIterator</em> for input data sequences. Although it might be useful for <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>execution</c-><c- o>::</c-><c- n>seq</c-></code> policy, it does not make a lot of sense for an actual parallel implementation. We are not aware
of an existing implementation supporting forward iterators well for any of <code class="highlight"><c- n>unseq</c-></code>, <code class="highlight"><c- n>par</c-></code> or <code class="highlight"><c- n>par_unseq</c-></code> policies.
oneAPI Data Parallel C++ library (oneDPL) supports forward iterators only for a very few algorithms, only for <code class="highlight"><c- n>par</c-></code> and only in the implementation based on oneTBB.</p>
   <p>We think that requiring <code class="highlight"><c- n>random_access_iterator</c-></code> or <code class="highlight"><c- n>random_access_range</c-></code> for <code class="highlight"><c- n>unseq</c-></code>, <code class="highlight"><c- n>par</c-></code>, and <code class="highlight"><c- n>par_unseq</c-></code> policies will make the user experience better because it sets the right expectations from the very beginning.
The <code class="highlight"><c- n>seq</c-></code> policy would still require <code class="highlight"><c- n>forward_iterator</c-></code> or <code class="highlight"><c- n>forward_range</c-></code>.</p>
   <h3 class="heading settled" data-level="2.7" id="const_callable_parameter"><span class="secno">2.7. </span><span class="content"><code class="highlight"><c- k>const</c-></code>-callable parameter</span><a class="self-link" href="#const_callable_parameter"></a></h3>
   <p>We believe that parallel range algorithms should require function objects for predicates, comparators, functions expected
by <code class="highlight"><c- n>for_each</c-></code>, etc. to be <code class="highlight"><c- k>const</c-></code>-callable . It seems important to add that requirement for the extra safety
it gives when parallelism is introduced to existing serial code, providing compile-time diagnostics for mutable
function objects which might be unsafe for parallel execution.</p>
   <p>The following example works fine for serial code. While it compiles for parallel code, users should not assume that the
semantics remains intact. Since the parallel version of <code class="highlight"><c- n>for_each</c-></code> requires function object to be copyable, it
is not guaranteed that all <code class="highlight"><c- n>for_each</c-></code> iterations are processed by the same function object. Practically speaking, users
cannot rely on accumulating any state modifications in a parallel <code class="highlight"><c- n>for_each</c-></code> call.</p>
<pre class="language-cpp highlight"><c- k>struct</c-> <c- nc>callable</c->
<c- p>{</c->
    <c- b>void</c-> <c- nf>operator</c-><c- p>()(</c-><c- b>int</c-><c- o>&amp;</c-> <c- n>x</c-><c- p>)</c->
    <c- p>{</c->
        <c- o>++</c-><c- n>x</c-><c- p>;</c->
        <c- o>++</c-><c- n>i</c-><c- p>;</c-> <c- c1>// race here for parallel code</c->
    <c- p>}</c->
    <c- b>int</c-> <c- nf>get_i</c-><c- p>()</c-> <c- k>const</c-> <c- p>{</c->
        <c- k>return</c-> <c- n>i</c-><c- p>;</c->
    <c- p>}</c->
<c- k>private</c-><c- o>:</c->
    <c- b>int</c-> <c- n>i</c-> <c- o>=</c-> <c- mi>0</c-><c- p>;</c->
<c- p>};</c->

<c- n>callable</c-> <c- n>c</c-><c- p>;</c->

<c- c1>// serial for_each call</c->
<c- k>auto</c-> <c- n>fun</c-> <c- o>=</c-> <c- n>std</c-><c- o>::</c-><c- n>for_each</c-><c- p>(</c-><c- n>v</c-><c- p>.</c-><c- n>begin</c-><c- p>(),</c-> <c- n>v</c-><c- p>.</c-><c- n>end</c-><c- p>(),</c-> <c- n>c</c-><c- p>);</c->

<c- c1>// parallel for_each call</c->
<c- c1>// The callable object cannot be read because parallel for_each version purposefully returns void</c->
<c- n>std</c-><c- o>::</c-><c- n>for_each</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>v</c-><c- p>.</c-><c- n>begin</c-><c- p>(),</c-> <c- n>v</c-><c- p>.</c-><c- n>end</c-><c- p>(),</c-> <c- n>c</c-><c- p>);</c->

<c- c1>// for_each serial range version call</c->
<c- k>auto</c-> <c- p>[</c-><c- n>_</c-><c- p>,</c-> <c- n>fun</c-><c- p>]</c-> <c- o>=</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>v</c-><c- p>.</c-><c- n>begin</c-><c- p>(),</c-> <c- n>v</c-><c- p>.</c-><c- n>end</c-><c- p>(),</c-> <c- n>c</c-><c- p>);</c->
</pre>
   <p>As we stated above we would like to preserve the return types of serial range algorithms, therefore the parallel <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>for_each</c-></code> still returns a copy of the callable object. However, we propose it to fail to compile if
the <code class="highlight"><c- k>operator</c-><c- p>()</c-></code> of the callable is not marked as <code class="highlight"><c- k>const</c-></code>:</p>
<pre class="language-cpp highlight"><c- c1>// callable is used from the previous code snippet</c->
<c- c1>// Fails to compile with our proposal because callable::operator() is not const-qualified</c->
<c- n>callable</c-> <c- n>c</c-><c- p>;</c->
<c- k>auto</c-> <c- p>[</c-><c- n>_</c-><c- p>,</c-> <c- n>fun</c-><c- p>]</c-> <c- o>=</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>std</c-><c- o>::</c-><c- n>execution</c-><c- o>::</c-><c- n>par</c-><c- p>,</c-> <c- n>v</c-><c- p>.</c-><c- n>begin</c-><c- p>(),</c-> <c- n>v</c-><c- p>.</c-><c- n>end</c-><c- p>(),</c-> <c- n>c</c-><c- p>);</c->
</pre>
   <p>Of course, that requirement is easy to overcome by wrapping the callable object. In that case, it is user’s responsibility
to make sure that the code is free from data races. Please see the example below:</p>
<pre class="language-cpp highlight"><c- c1>// callable is used from the previous code snippet</c->
<c- c1>// Wrapping a callable objection with std::reference_wrapper compiles, but might result in data races</c->
<c- n>callable</c-> <c- n>c</c-><c- p>;</c->
<c- k>auto</c-> <c- p>[</c-><c- n>_</c-><c- p>,</c-> <c- n>fun</c-><c- p>]</c-> <c- o>=</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>std</c-><c- o>::</c-><c- n>execution</c-><c- o>::</c-><c- n>par</c-><c- p>,</c-> <c- n>v</c-><c- p>.</c-><c- n>begin</c-><c- p>(),</c-> <c- n>v</c-><c- p>.</c-><c- n>end</c-><c- p>(),</c-> <c- n>std</c-><c- o>::</c-><c- n>ref</c-><c- p>(</c-><c- n>c</c-><c- p>));</c->
</pre>
   <h3 class="heading settled" data-level="2.8" id="not_customization_point"><span class="secno">2.8. </span><span class="content">Parallel range algorithms are not customization points</span><a class="self-link" href="#not_customization_point"></a></h3>
   <p>We do not propose the parallel range algorithms to be customization points because it’s unclear which parameter
to customize for. One could argue that customizations may exist for execution policies, but we expect custom execution
policies to become unnecessary once the C++ algorithms will work with schedulers/senders/receivers.</p>
   <h3 class="heading settled" data-level="2.9" id="not_constexpr"><span class="secno">2.9. </span><span class="content">Parallel range algorithms are not <code class="highlight"><c- k>constexpr</c-></code></span><a class="self-link" href="#not_constexpr"></a></h3>
   <p>We do not propose the new parallel algorithms to be <code class="highlight"><c- k>constexpr</c-></code>. We are aware of <a data-link-type="biblio" href="#biblio-p2902r0" title="constexpr &apos;Parallel&apos; Algorithms">[P2902R0]</a> and might align with it
in the future, however we don’t think that making parallel algorithms <code class="highlight"><c- k>constexpr</c-></code> should be a primary design goal.</p>
   <h2 class="heading settled" data-level="3" id="more_example"><span class="secno">3. </span><span class="content">More examples</span><a class="self-link" href="#more_example"></a></h2>
   <h3 class="heading settled" data-level="3.1" id="less_parallel_call"><span class="secno">3.1. </span><span class="content">Less parallel algorithm calls and better expressiveness</span><a class="self-link" href="#less_parallel_call"></a></h3>
   <p>Let’s consider the following example:</p>
<pre class="language-cpp highlight"><c- n>reverse</c-><c- p>(</c-><c- n>policy</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>transform</c-><c- p>(</c-><c- n>policy</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>begin</c-><c- p>(</c-><c- n>result</c-><c- p>),</c-> <c- p>[](</c-><c- k>auto</c-> <c- n>i</c-><c- p>){</c-> <c- k>return</c-> <c- n>i</c-> <c- o>*</c-> <c- n>i</c-><c- p>;</c-> <c- p>});</c->
<c- k>auto</c-> <c- n>res</c-> <c- o>=</c-> <c- n>any_of</c-><c- p>(</c-><c- n>policy</c-><c- p>,</c-> <c- n>begin</c-><c- p>(</c-><c- n>result</c-><c- p>),</c-> <c- n>end</c-><c- p>(</c-><c- n>result</c-><c- p>),</c-> <c- n>pred</c-><c- p>);</c->
</pre>
   <p>It has three stages and eventually tries to answer the question if the input sequence contains an element after reversing
and transforming it. The interesting considerations are:</p>
   <ul>
    <li data-md>
     <p>Since the example has three parallel stages, it adds extra overhead for parallel computation per algorithm.</p>
    <li data-md>
     <p>The first two stages will complete for all elements before the <code class="highlight"><c- n>any_of</c-></code> stage is started, though it is not required for
correctness. If reverse and transformation would be done on the fly, a good implementation of <code class="highlight"><c- n>any_of</c-></code> might have
skipped the remaining work when <code class="highlight"><c- n>pred</c-></code> returns <code class="highlight">true</code>, thus providing more performance.</p>
   </ul>
   <p>Let’s make it better:</p>
<pre class="language-cpp highlight"><c- c1>// With fancy iterators</c->
<c- k>auto</c-> <c- n>res</c-> <c- o>=</c-> <c- n>any_of</c-><c- p>(</c-><c- n>policy</c-><c- p>,</c->
                  <c- n>make_transform_iterator</c-><c- p>(</c-><c- n>make_reverse_iterator</c-><c- p>(</c-><c- n>end</c-><c- p>(</c-><c- n>data</c-><c- p>)),</c->
                                          <c- p>[](</c-><c- k>auto</c-> <c- n>i</c-><c- p>){</c-> <c- k>return</c-> <c- n>i</c-> <c- o>*</c-> <c- n>i</c-><c- p>;</c-> <c- p>}),</c->
                  <c- n>make_transform_iterator</c-><c- p>(</c-><c- n>make_reverse_iterator</c-><c- p>(</c-><c- n>begin</c-><c- p>(</c-><c- n>data</c-><c- p>)),</c->
                                          <c- p>[](</c-><c- k>auto</c-> <c- n>i</c-><c- p>){</c-> <c- k>return</c-> <c- n>i</c-> <c- o>*</c-> <c- n>i</c-><c- p>;</c-> <c- p>}),</c->
                  <c- n>pred</c-><c- p>);</c->
</pre>
   <p>Now there is only one parallel algorithm call, and <code class="highlight"><c- n>any_of</c-></code> can skip unneeded work. However, this
variation also has interesting considerations:</p>
   <ul>
    <li data-md>
     <p>First, it doesn’t compile. We use <code class="highlight"><c- n>transform</c-> <c- n>iterator</c-></code> to pass the transformation function,
but the two <code class="highlight"><c- n>make_transform_iterator</c-></code> expressions use two different lambdas, and
the iterator type for <code class="highlight"><c- n>any_of</c-></code> cannot be deduced because the types of <code class="highlight"><c- n>transform_iterator</c-></code> do not match.
One of the options to make it compile is to store a lambda in a variable.</p>
    <li data-md>
     <p>Second, it requires using a non-standard iterator.</p>
    <li data-md>
     <p>Third, the expressiveness of the code is not good: it is hard to read while easy to make a mistake
like the one described in the first bullet.</p>
   </ul>
   <p>Let’s improve the example further with the proposed API:</p>
<pre class="language-cpp highlight"><c- c1>// With ranges</c->
<c- k>auto</c-> <c- n>res</c-> <c- o>=</c-> <c- n>any_of</c-><c- p>(</c-><c- n>policy</c-><c- p>,</c-> <c- n>data</c-> <c- o>|</c-> <c- n>views</c-><c- o>::</c-><c- n>reverse</c-> <c- o>|</c-> <c- n>views</c-><c- o>::</c-><c- n>transform</c-><c- p>([](</c-><c- k>auto</c-> <c- n>i</c-><c- p>){</c-> <c- k>return</c-> <c- n>i</c-> <c- o>*</c-> <c- n>i</c-><c- p>;</c-> <c- p>}),</c->
                  <c- n>pred</c-><c- p>);</c->
</pre>
   <p>The example above lacks the drawbacks described for the previous variations:</p>
   <ul>
    <li data-md>
     <p>There is only one algorithm call;</p>
    <li data-md>
     <p>The implementation might skip unnecessary work;</p>
    <li data-md>
     <p>There is no room for the lambda type mistake;</p>
    <li data-md>
     <p>The readability is much better compared to the second variation and not worse than in the first one.</p>
   </ul>
   <h2 class="heading settled" data-level="4" id="proposed_api"><span class="secno">4. </span><span class="content">Proposed API</span><a class="self-link" href="#proposed_api"></a></h2>
   <p class="note" role="note"><span class="marker">Note:</span> <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>for_each</c-></code> is used as a reference point. When the design is ratified, it will be spread across
other algorithms.</p>
<pre class="language-cpp highlight"><c- c1>// Policy-based API</c->
<c- k>template</c-> <c- o>&lt;</c-><c- k>class</c-> <c- nc>ExecutionPolicy</c-><c- p>,</c-> <c- n>policy</c-><c- o>-</c-><c- n>dependent</c-><c- o>-</c-><c- n>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- 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>ExecutionPolicy</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- k>class</c-> <c- nc>ExecutionPolicy</c-><c- p>,</c-> <c- n>policy</c-><c- o>-</c-><c- n>dependent</c-><c- o>-</c-><c- n>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- n>ranges</c-><c- o>::</c-><c- n>for_each_result</c-><c- o>&lt;</c-><c- n>ranges</c-><c- o>::</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>ExecutionPolicy</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->
</pre>
   <p><code class="highlight"><c- n>policy</c-><c- o>-</c-><c- n>dependent</c-><c- o>-</c-><c- n>iterator</c-></code> and <code class="highlight"><c- n>policy</c-><c- o>-</c-><c- n>dependent</c-><c- o>-</c-><c- n>range</c-></code> are exposition only concepts defined as:</p>
   <ul>
    <li data-md>
     <p>If <code class="highlight"><c- n>ExecutionPolicy</c-></code> type is <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>execution</c-><c- o>:</c-><c- n>sequenced_policy</c-></code> then <code class="highlight"><c- n>policy</c-><c- o>-</c-><c- n>dependent</c-><c- o>-</c-><c- n>iterator</c-></code> is the <code class="highlight"><c- n>forward_iterator</c-></code> concept and <code class="highlight"><c- n>policy</c-><c- o>-</c-><c- n>dependent</c-><c- o>-</c-><c- n>range</c-></code> is the <code class="highlight"><c- n>forward_range</c-></code> concept.</p>
    <li data-md>
     <p>Otherwise, <code class="highlight"><c- n>policy</c-><c- o>-</c-><c- n>dependent</c-><c- o>-</c-><c- n>iterator</c-></code> is the <code class="highlight"><c- n>random_access_iterator</c-></code> concept and <code class="highlight"><c- n>policy</c-><c- o>-</c-><c- n>dependent</c-><c- o>-</c-><c- n>range</c-></code> is
the <code class="highlight"><c- n>random_access_range</c-></code> concept.</p>
   </ul>
   <h3 class="heading settled" data-level="4.1" id="possible_impl"><span class="secno">4.1. </span><span class="content">Possible implementation of a parallel range algorithm</span><a class="self-link" href="#possible_impl"></a></h3>
<pre class="language-cpp highlight"><c- c1>// A possible implementation of std::ranges::for_each</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- c1>// The dedicated overload for sequenced_policy. Requires forward_iterator</c->
    <c- k>template</c-><c- o>&lt;</c-><c- n>forward_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- 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- k>operator</c-><c- p>()(</c-><c- k>const</c-> <c- n>std</c-><c- o>::</c-><c- n>execution</c-><c- o>::</c-><c- n>sequenced_policy</c-><c- o>&amp;</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>for</c-> <c- p>(;</c-> <c- n>first</c-> <c- o>!=</c-> <c- n>last</c-><c- p>;</c-> <c- o>++</c-><c- n>first</c-><c- p>)</c->
        <c- p>{</c->
            <c- n>std</c-><c- o>::</c-><c- n>invoke</c-><c- p>(</c-><c- n>f</c-><c- p>,</c-> <c- n>std</c-><c- o>::</c-><c- n>invoke</c-><c- p>(</c-><c- n>proj</c-><c- p>,</c-> <c- o>*</c-><c- n>first</c-><c- p>));</c->
        <c- p>}</c->
        <c- k>return</c-> <c- p>{</c-><c- n>std</c-><c- o>::</c-><c- n>move</c-><c- p>(</c-><c- n>first</c-><c- p>),</c-> <c- n>std</c-><c- o>::</c-><c- n>move</c-><c- p>(</c-><c- n>f</c-><c- p>)};</c->
    <c- p>}</c->

    <c- c1>// The overload for unsequenced and parallel policies. Requires random_access_iterator</c->
    <c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>ExecutionPolicy</c-><c- p>,</c-> <c- n>random_access_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>requires</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- 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- k>operator</c-><c- p>()(</c-><c- n>ExecutionPolicy</c-><c- o>&amp;&amp;</c-> <c- n>exec</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- c1>// properly handle execution policy; for the reference, a serial</c->
        <c- c1>// implementation is provided</c->
        <c- k>for</c-> <c- p>(;</c-> <c- n>first</c-> <c- o>!=</c-> <c- n>last</c-><c- p>;</c-> <c- o>++</c-><c- n>first</c-><c- p>)</c->
        <c- p>{</c->
            <c- n>std</c-><c- o>::</c-><c- n>invoke</c-><c- p>(</c-><c- n>f</c-><c- p>,</c-> <c- n>std</c-><c- o>::</c-><c- n>invoke</c-><c- p>(</c-><c- n>proj</c-><c- p>,</c-> <c- o>*</c-><c- n>first</c-><c- p>));</c->
        <c- p>}</c->
        <c- k>return</c-> <c- p>{</c-><c- n>std</c-><c- o>::</c-><c- n>move</c-><c- p>(</c-><c- n>first</c-><c- p>),</c-> <c- n>std</c-><c- o>::</c-><c- n>move</c-><c- p>(</c-><c- n>f</c-><c- p>)};</c->
    <c- p>}</c->

    <c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>ExecutionPolicy</c-><c- p>,</c-> <c- n>forward_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- n>ranges</c-><c- o>::</c-><c- n>for_each_result</c-><c- o>&lt;</c-><c- n>ranges</c-><c- o>::</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>ExecutionPolicy</c-><c- o>&amp;&amp;</c-> <c- n>exec</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>std</c-><c- o>::</c-><c- n>forward</c-><c- o>&lt;</c-><c- n>ExecutionPolicy</c-><c- o>></c-><c- p>(</c-><c- n>exec</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>
   <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>
   <h3 class="heading settled" data-level="5.1" id="thread_safe_views"><span class="secno">5.1. </span><span class="content">Thread-safe views examination</span><a class="self-link" href="#thread_safe_views"></a></h3>
   <p>We need to understand better whether using some <code class="highlight"><c- n>views</c-></code> with parallel algorithms might result in data races.
At first glance, requiring iterators and ranges to provide random access should be sufficient to prevent
such issues, but we want to be sure.</p>
   <h3 class="heading settled" data-level="5.2" id="serial_range_based_absence"><span class="secno">5.2. </span><span class="content">Absence of some serial range-based algorithms</span><a class="self-link" href="#serial_range_based_absence"></a></h3>
   <p>We understand that some useful algorithms, for example, most of generalized numeric operations <a href="https://eel.is/c++draft/numeric.ops">[numeric.ops]</a> do not yet exist in <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-></code> even in a serial version. It is supposed to be addressed either by this or by a complementary paper.</p>
   <h3 class="heading settled" data-level="5.3" id="parallel_range_algorithms_output"><span class="secno">5.3. </span><span class="content">Output for parallel range algorithms</span><a class="self-link" href="#parallel_range_algorithms_output"></a></h3>
   <p>Serial range algorithms take only <code class="highlight"><c- n>output_iterator</c-></code> as the result. In other words, there is no overload (for example, for <code class="highlight"><c- n>copy_if</c-></code> algorithm) that takes both input and output as <code class="highlight"><c- n>range</c-></code>. We would like to explore whether it’s worth
adding such an overload for parallel range algorithms because it might be more useful to have both input and output as
ranges, for safety and performance reasons.</p>
   <p><code class="highlight"><c- n>copy_if</c-></code> is a good example also because it doesn’t require both input and output sequence to have the same size. But for
parallelization purpose it is useful to know the size of passed sequences in advance. If the output for <code class="highlight"><c- n>copy_if</c-></code> is an
iterator, not a range we don’t know the output sequence size and we cannot rely on the input sequence size.</p>
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  <h2 class="no-num no-ref heading settled" id="references"><span class="content">References</span><a class="self-link" href="#references"></a></h2>
  <h3 class="no-num no-ref heading settled" id="informative"><span class="content">Informative References</span><a class="self-link" href="#informative"></a></h3>
  <dl>
   <dt id="biblio-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-p2500r2">[P2500R2]
   <dd>Ruslan Arutyunyan, Alexey Kukanov. <a href="https://wg21.link/p2500r2"><cite>C++ parallel algorithms and P2300</cite></a>. 15 October 2023. URL: <a href="https://wg21.link/p2500r2">https://wg21.link/p2500r2</a>
   <dt id="biblio-p2902r0">[P2902R0]
   <dd>Oliver Rosten. <a href="https://wg21.link/p2902r0"><cite>constexpr 'Parallel' Algorithms</cite></a>. 17 June 2023. URL: <a href="https://wg21.link/p2902r0">https://wg21.link/p2902r0</a>
   <dt id="biblio-p3300r0">[P3300R0]
   <dd>Bryce Adelstein Lelbach. <a href="https://wg21.link/p3300r0"><cite>C++ Asynchronous Parallel Algorithms</cite></a>. URL: <a href="https://wg21.link/p3300r0">https://wg21.link/p3300r0</a>
  </dl>