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  <title>P3179R2: C++ parallel range algorithms</title>
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 *                   Style sheet for the W3C specifications                   *
 *
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/******************************************************************************/
/*                                 Inline Markup                              */
/******************************************************************************/

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

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/** Assertion Box *************************************************************/
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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>
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      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 }
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    blockquote c-[b] { color: inherit; } /* Keyword.Type */
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    blockquote c-[cs] { color: inherit; } /* Comment.Special */
    blockquote c-[kc] { color: inherit; } /* Keyword.Constant */
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    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/P3179R2" rel="canonical">
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  <div class="head">
   <p data-fill-with="logo"></p>
   <h1 class="p-name no-ref" id="title">P3179R2<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="2024-06-25">2024-06-25</time></span></h2>
   <div data-fill-with="spec-metadata">
    <dl>
     <dt>This version:
     <dd><a class="u-url" href="https://wg21.link/P3179R2">https://wg21.link/P3179R2</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>)
     <dd class="editor p-author h-card vcard"><a class="p-name fn u-email email" href="mailto:brycelelbach@gmail.com">Bryce Adelstein Lelbach (he/him/his)</a> (<span class="p-org org">Nvidia</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>
       <ol class="toc">
        <li><a href="#design_diff_to_cpp20_ranges"><span class="secno">2.1.1</span> <span class="content">Differences to serial range algorithms</span></a>
        <li><a href="#design_diff_to_cpp17_par"><span class="secno">2.1.2</span> <span class="content">Differences to C++17 parallel algorithms</span></a>
        <li><a href="#design_other_aspects"><span class="secno">2.1.3</span> <span class="content">Other design aspects</span></a>
       </ol>
      <li><a href="#coexistence_with_schedulers"><span class="secno">2.2</span> <span class="content">Coexistence with schedulers</span></a>
      <li><a href="#return_type"><span class="secno">2.3</span> <span class="content">Algorithm return types</span></a>
      <li><a href="#non_adl_discoverable"><span class="secno">2.4</span> <span class="content">Non ADL-discoverable functions</span></a>
      <li><a href="#random_access_requirement"><span class="secno">2.5</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></span></a>
      <li><a href="#range_as_output"><span class="secno">2.6</span> <span class="content">Taking <code class="highlight"><c- n>range</c-></code> as an output</span></a>
      <li><a href="#require_bounded_ranges"><span class="secno">2.7</span> <span class="content">Requiring ranges to be bounded</span></a>
      <li><a href="#callable_parameters"><span class="secno">2.8</span> <span class="content">Requirements for callable parameters</span></a>
      <li><a href="#not_customization_point"><span class="secno">2.9</span> <span class="content">Parallel range algorithms are not customization points</span></a>
      <li><a href="#constexpr_support"><span class="secno">2.10</span> <span class="content"><code class="highlight"><c- k>constexpr</c-></code> parallel range algorithms</span></a>
     </ol>
    <li>
     <a href="#more_examples"><span class="secno">3</span> <span class="content">More examples</span></a>
     <ol class="toc">
      <li><a href="#easy_to_switch"><span class="secno">3.1</span> <span class="content">Change existing code to use parallel range algorithms</span></a>
      <li><a href="#less_parallel_call"><span class="secno">3.2</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="#serial_range_based_absence"><span class="secno">5</span> <span class="content">Absence of some serial range-based algorithms</span></a>
    <li>
     <a href="#further_work"><span class="secno">6</span> <span class="content">Further exploration</span></a>
     <ol class="toc">
      <li><a href="#thread_safe_views"><span class="secno">6.1</span> <span class="content">Thread-safe views examination</span></a>
     </ol>
    <li>
     <a href="#revision_history"><span class="secno">7</span> <span class="content">Revision history</span></a>
     <ol class="toc">
      <li><a href="#r1_r2"><span class="secno">7.1</span> <span class="content">R1 => R2</span></a>
      <li><a href="#r0_r1"><span class="secno">7.2</span> <span class="content">R0 => R1</span></a>
     </ol>
    <li>
     <a href="#polls"><span class="secno">8</span> <span class="content">Polls</span></a>
     <ol class="toc">
      <li><a href="#sg9_tokyo_2024"><span class="secno">8.1</span> <span class="content">SG9, Tokyo 2024</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>Users are already using ranges and range adaptors by passing range iterators to the existing non-range parallel
algorithms. <a data-link-type="biblio" href="#biblio-p2408r5" title="Ranges iterators as inputs to non-Ranges algorithms">[P2408R5]</a> was adopted to enable this. This pattern is often featured when teaching C++ parallel algorithms
and appears in many codebases.</p>
   <p><code class="highlight"><c- n>iota</c-></code> and <code class="highlight"><c- n>cartesian_product</c-></code> are especially common, as many compute workloads want to iterate over indices, not
objects, and many work with multidimensional data. <code class="highlight"><c- n>transform</c-></code> is also common, as it enables fusion of element-wise
operations into a single parallel algorithm call, which can avoid the need for temporary storage and is more
performant than two separate calls.</p>
   <p>However, passing range iterators to non-range algorithms is unwieldy and verbose. It is surprising to
users that they cannot simply pass the ranges to the parallel algorithms as they would for serial algorithms.</p>
   <table>
    <tbody>
     <tr>
      <th colspan="2">Scalar-Vector Multiply 
     <tr>
      <th>Before 
      <th>After 
     <tr>
      <td>
<pre class="highlight"><code><c- n>std</c-><c- o>::</c-><c- n>span</c-><double> <c- n>data</c-> <c- o>=</c-> …<c- p>;</c->
<c- b>double</c-> <c- n>C</c-> <c- o>=</c-> …<c- p>;</c->

<c- k>auto</c-> <c- n>indices</c-> <c- o>=</c-> <c- n>std</c-><c- o>::</c-><c- n>views</c-><c- o>::</c-><c- n>iota</c-><c- p>(</c-><c- mi>1</c-><c- p>,</c-> <c- n>data</c-><c- p>.</c-><c- n>size</c-><c- p>());</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_unseq</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>indices</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>indices</c-><c- p>),</c->
  <c- p>[</c-><c- o>=</c-><c- p>]</c-> <c- p>(</c-><c- k>auto</c-> <c- n>i</c-><c- p>)</c-> <c- p>{</c-> <c- n>data</c-><c- p>[</c-><c- n>i</c-><c- p>]</c-> <c- o>*=</c-> <c- n>C</c-><c- p>;</c-> <c- p>});</c->
</double></code></pre>
      <td>
<pre class="highlight"><code><c- n>std</c-><c- o>::</c-><c- n>span</c-><double> <c- n>data</c-> <c- o>=</c-> …<c- p>;</c->
<c- b>double</c-> <c- n>C</c-> <c- o>=</c-> …<c- p>;</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_unseq</c-><c- p>,</c->
  <c- n>std</c-><c- o>::</c-><c- n>views</c-><c- o>::</c-><c- n>iota</c-><c- p>(</c-><c- mi>1</c-><c- p>,</c-> <c- n>data</c-><c- p>.</c-><c- n>size</c-><c- p>()),</c->
  <c- p>[</c-><c- o>=</c-><c- p>]</c-> <c- p>(</c-><c- k>auto</c-> <c- n>i</c-><c- p>)</c-> <c- p>{</c-> <c- n>data</c-><c- p>[</c-><c- n>i</c-><c- p>]</c-> <c- o>*=</c-> <c- n>C</c-><c- p>;</c-> <c- p>});</c->
</double></code></pre>
   </table>
   <table>
    <tbody>
     <tr>
      <th colspan="2">Matrix Transpose 
     <tr>
      <th>Before 
      <th>After 
     <tr>
      <td>
<pre class="highlight"><code><c- n>std</c-><c- o>::</c-><c- n>mdspan</c-> <c- n>A</c-><c- p>{</c-><c- n>input</c-><c- p>,</c->  <c- n>N</c-><c- p>,</c-> <c- n>M</c-><c- p>};</c->
<c- n>std</c-><c- o>::</c-><c- n>mdspan</c-> <c- n>B</c-><c- p>{</c-><c- n>output</c-><c- p>,</c-> <c- n>M</c-><c- p>,</c-> <c- n>N</c-><c- p>};</c->

<c- k>auto</c-> <c- n>indices</c-> <c- o>=</c-> <c- n>std</c-><c- o>::</c-><c- n>views</c-><c- o>::</c-><c- n>cartesian_product</c-><c- p>(</c->
  <c- n>std</c-><c- o>::</c-><c- n>views</c-><c- o>::</c-><c- n>iota</c-><c- p>(</c-><c- mi>0</c-><c- p>,</c-> <c- n>A</c-><c- p>.</c-><c- n>extent</c-><c- p>(</c-><c- mi>0</c-><c- p>)),</c->
  <c- n>std</c-><c- o>::</c-><c- n>views</c-><c- o>::</c-><c- n>iota</c-><c- p>(</c-><c- mi>0</c-><c- p>,</c-> <c- n>A</c-><c- p>.</c-><c- n>extent</c-><c- p>(</c-><c- mi>1</c-><c- p>)));</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_unseq</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>indices</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>indices</c-><c- p>),</c->
  <c- p>[</c-><c- o>=</c-><c- p>]</c-> <c- p>(</c-><c- k>auto</c-> <c- n>idx</c-><c- p>)</c-> <c- p>{</c->
    <c- k>auto</c-> <c- p>[</c-><c- n>i</c-><c- p>,</c-> <c- n>j</c-><c- p>]</c-> <c- o>=</c-> <c- n>idx</c-><c- p>;</c->
    <c- n>B</c-><c- p>[</c-><c- n>j</c-><c- p>,</c-> <c- n>i</c-><c- p>]</c-> <c- o>=</c-> <c- n>A</c-><c- p>[</c-><c- n>i</c-><c- p>,</c-> <c- n>j</c-><c- p>];</c->
  <c- p>});</c->
</code></pre>
      <td>
<pre class="highlight"><code><c- n>std</c-><c- o>::</c-><c- n>mdspan</c-> <c- n>A</c-><c- p>{</c-><c- n>input</c-><c- p>,</c->  <c- n>N</c-><c- p>,</c-> <c- n>M</c-><c- p>};</c->
<c- n>std</c-><c- o>::</c-><c- n>mdspan</c-> <c- n>B</c-><c- p>{</c-><c- n>output</c-><c- p>,</c-> <c- n>M</c-><c- p>,</c-> <c- n>N</c-><c- p>};</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_unseq</c-><c- p>,</c->
  <c- n>std</c-><c- o>::</c-><c- n>views</c-><c- o>::</c-><c- n>cartesian_product</c-><c- p>(</c->
    <c- n>std</c-><c- o>::</c-><c- n>views</c-><c- o>::</c-><c- n>iota</c-><c- p>(</c-><c- mi>0</c-><c- p>,</c-> <c- n>A</c-><c- p>.</c-><c- n>extent</c-><c- p>(</c-><c- mi>0</c-><c- p>)),</c->
    <c- n>std</c-><c- o>::</c-><c- n>views</c-><c- o>::</c-><c- n>iota</c-><c- p>(</c-><c- mi>0</c-><c- p>,</c-> <c- n>A</c-><c- p>.</c-><c- n>extent</c-><c- p>(</c-><c- mi>1</c-><c- p>))),</c->
  <c- p>[</c-><c- o>=</c-><c- p>]</c-> <c- p>(</c-><c- k>auto</c-> <c- n>idx</c-><c- p>)</c-> <c- p>{</c->
    <c- k>auto</c-> <c- p>[</c-><c- n>i</c-><c- p>,</c-> <c- n>j</c-><c- p>]</c-> <c- o>=</c-> <c- n>idx</c-><c- p>;</c->
    <c- n>B</c-><c- p>[</c-><c- n>j</c-><c- p>,</c-> <c- n>i</c-><c- p>]</c-> <c- o>=</c-> <c- n>A</c-><c- p>[</c-><c- n>i</c-><c- p>,</c-> <c- n>j</c-><c- p>];</c->
  <c- p>});</c->
</code></pre>
   </table>
   <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>
   <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 paper proposes 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>
   <p>The proposal is targeted to C++26.</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>
   <h4 class="heading settled" data-level="2.1.1" id="design_diff_to_cpp20_ranges"><span class="secno">2.1.1. </span><span class="content">Differences to serial range algorithms</span><a class="self-link" href="#design_diff_to_cpp20_ranges"></a></h4>
   <p>Comparing to the C++20 serial range algorithms, we propose the following modifications:</p>
   <ul>
    <li data-md>
     <p>The execution policy parameter is added.</p>
    <li data-md>
     <p><code class="highlight"><c- n>for_each</c-></code> and <code class="highlight"><c- n>for_each_n</c-></code> return only an iterator but not the function.</p>
    <li data-md>
     <p>Parallel range algorithms take <code class="highlight"><c- n>range</c-></code>, not an iterator, as an output for the overloads with ranges, and additionally take
an output sentinel for the "iterator and sentinel" overloads. (<a href="#range_as_output">§ 2.6 Taking range as an output</a>)</p>
    <li data-md>
     <p>Until better parallelism-friendly abstractions are proposed, parallel algorithms require <code class="highlight"><c- n>random_access_</c-><c- p>{</c-><c- n>iterator</c-><c- p>,</c-><c- n>range</c-><c- p>}</c-></code>. (<a href="#random_access_requirement">§ 2.5 Requiring random_access_iterator or random_access_range</a>)</p>
    <li data-md>
     <p>At least one of the input sequences as well as the output sequence must be bounded. (<a href="#require_bounded_ranges">§ 2.7 Requiring ranges to be bounded</a>)</p>
   </ul>
   <h4 class="heading settled" data-level="2.1.2" id="design_diff_to_cpp17_par"><span class="secno">2.1.2. </span><span class="content">Differences to C++17 parallel algorithms</span><a class="self-link" href="#design_diff_to_cpp17_par"></a></h4>
   <p>In addition to data sequences being passed as either ranges or "iterator and sentinel" pairs, the following differences
to the C++17 parallel algorithms are proposed:</p>
   <ul>
    <li data-md>
     <p><code class="highlight"><c- n>for_each</c-></code> returns an iterator, not <code class="highlight"><c- b>void</c-></code>.</p>
    <li data-md>
     <p>Algorithms require <code class="highlight"><c- n>random_access_</c-><c- p>{</c-><c- n>iterator</c-><c- p>,</c-><c- n>range</c-><c- p>}</c-></code>, and not <em>LegacyForwardIterator</em>.</p>
    <li data-md>
     <p>At least one of the input sequences as well as the output sequence must be bounded.</p>
   </ul>
   <h4 class="heading settled" data-level="2.1.3" id="design_other_aspects"><span class="secno">2.1.3. </span><span class="content">Other design aspects</span><a class="self-link" href="#design_other_aspects"></a></h4>
   <ul>
    <li data-md>
     <p>Except as mentioned above, the parallel range algorithms should return the same type as the corresponding serial range algorithms. (<a href="#return_type">§ 2.3 Algorithm return types</a>)</p>
    <li data-md>
     <p>The proposed algorithms should follow the design of serial range algorithms with regard to name lookup. (<a href="#non_adl_discoverable">§ 2.4 Non ADL-discoverable functions</a>)</p>
    <li data-md>
     <p>The proposed algorithms should require callable object passed to an algorithm to be <code class="highlight"><c- n>regular_invocable</c-></code> where possible. (<a href="#callable_parameters">§ 2.8 Requirements for callable parameters</a>)</p>
    <li data-md>
     <p>The proposed APIs are not customization points. (<a href="#not_customization_point">§ 2.9 Parallel range algorithms are not customization points</a>)</p>
    <li data-md>
     <p>The proposed algorithms should follow the design of C++17 parallel algorithms with regard to <code class="highlight"><c- k>constexpr</c-></code> support. (<a href="#constexpr_support">§ 2.10 constexpr parallel range algorithms</a>)</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-p2300r9" title="`std::execution`">[P2300R9]</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="return_type"><span class="secno">2.3. </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>
<pre class="language-cpp highlight"><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>sort</c-><c- p>(</c-><c- n>v</c-><c- p>);</c->
</pre>
   <p>becomes:</p>
<pre class="language-cpp highlight"><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>sort</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->
</pre>
   <p>However, <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>ranges</c-><c- o>::</c-><c- n>for_each_n</c-></code> require special consideration because previous
design decisions suggest that there should be a difference between serial and parallel versions.</p>
   <p>The following table summarizes return value types for the existing variants of these two algorithms:</p>
   <table>
    <tbody>
     <tr>
      <th>API
      <th>Return type
     <tr>
      <td><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>for_each</c-></code>
      <td><code class="highlight"><c- n>Function</c-></code>
     <tr>
      <td>Parallel <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>for_each</c-></code>
      <td><code class="highlight"><c- b>void</c-></code>
     <tr>
      <td><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>for_each_n</c-></code>
      <td><code class="highlight"><c- n>Iterator</c-></code>
     <tr>
      <td>Parallel <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>for_each_n</c-></code>
      <td><code class="highlight"><c- n>Iterator</c-></code>
     <tr>
      <td><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>for_each</c-></code>
      <td><code class="highlight"><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>Range</c-><c- o>></c-><c- p>,</c-> <c- n>Function</c-><c- o>></c-></code>
     <tr>
      <td><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>for_each</c-></code>, <code class="highlight"><c- n>I</c-></code> + <code class="highlight"><c- n>S</c-></code> overload
      <td><code class="highlight"><c- n>for_each_result</c-><c- o>&lt;</c-><c- n>Iterator</c-><c- p>,</c-> <c- n>Function</c-><c- o>></c-></code>
     <tr>
      <td><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>for_each_n</c-></code>
      <td><code class="highlight"><c- n>for_each_n_result</c-><c- o>&lt;</c-><c- n>Iterator</c-><c- p>,</c-> <c- n>Function</c-><c- o>></c-></code>
   </table>
   <p>While the serial <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>for_each</c-></code> returns the obtained function object with all modifications it might have accumulated,
the return type for the parallel <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>for_each</c-></code> is <code class="highlight"><c- b>void</c-></code> because, as stated in the standard, "parallelization often
does not permit efficient state accumulation". For efficient parallelism an implementation can make multiple copies of
the function object, which for that purpose is allowed to be copyable and not just movable like for the serial <code class="highlight"><c- n>for_each</c-></code>.
That implies that users cannot rely on any state accumulation within that function object, so it does not make sense
(and might be even dangerous) to return it.</p>
   <p>In <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-></code>, the return type of <code class="highlight"><c- n>for_each</c-></code> and <code class="highlight"><c- n>for_each_n</c-></code> is unified to return both an iterator and the function
object.</p>
   <p>Based on the analysis above and <a href="#sg9_tokyo_2024">the feedback from SG9</a> we think that the most reasonable return type
for parallel variants of <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>ranges</c-><c- o>::</c-><c- n>for_each_n</c-></code> should be:</p>
   <table>
    <tbody>
     <tr>
      <th>API
      <th>Return type
     <tr>
      <td>Parallel <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>for_each</c-></code>
      <td><code class="highlight"><c- n>ranges</c-><c- o>::</c-><c- n>borrowed_iterator_t</c-><c- o>&lt;</c-><c- n>Range</c-><c- o>></c-></code>
     <tr>
      <td>Parallel <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>for_each</c-></code>, <code class="highlight"><c- n>I</c-></code> + <code class="highlight"><c- n>S</c-></code> overload
      <td><code class="highlight"><c- n>Iterator</c-></code>
     <tr>
      <td>Parallel <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>for_each_n</c-></code>
      <td><code class="highlight"><c- n>Iterator</c-></code>
   </table>
   <h3 class="heading settled" data-level="2.4" id="non_adl_discoverable"><span class="secno">2.4. </span><span class="content">Non ADL-discoverable functions</span><a class="self-link" href="#non_adl_discoverable"></a></h3>
   <p>We believe the proposed functionality should have the same behavior as serial range algorithms regarding the name lookup.
For now, the new overloads are supposed to be special functions that are not discoverable by ADL (the status quo of the
standard for serial range algorithms).</p>
   <p><a data-link-type="biblio" href="#biblio-p3136r0" title="Retiring niebloids">[P3136R0]</a> suggests to respecify range algorithms to be actual function objects. If adopted, that proposal will
apply to all algorithms in the <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-></code> namespace, thus automatically covering the parallel algorithms we propose.</p>
   <p>Either way, adding parallel versions of the range algorithms 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="2.5" id="random_access_requirement"><span class="secno">2.5. </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></span><a class="self-link" href="#random_access_requirement"></a></h3>
   <p>C++17 parallel algorithms minimally require <em>LegacyForwardIterator</em> for data sequences, but in our opinion, it is not quite
suitable for an efficient parallel implementation. Therefore for parallel range algorithms we propose to require
random access ranges and iterators.</p>
   <p>Though the feedback we received in Tokyo requested to support forward ranges, we would like this question to be discussed
in more detail. Using parallel algorithms with forward ranges will in most cases give little to no benefit,
and may even reduce performance due to extra overheads. We believe that forward ranges and iterators are bad abstractions
for parallel data processing, and allowing those could result in wrong expectations and unsatisfactory user experience
with parallel algorithms.</p>
   <p>Many parallel programming models that are well known and widely used in the industry, including OpenMP, OpenCL, CUDA,
SYCL, oneTBB, define iteration or data spaces for their parallel constructs in ways that allow creating sufficient
parallel work quickly and efficiently. A key property for this is the ability to split the work into smaller chunks.
These programming models allow to control the amount of work per chunk and sometimes the ways chunks are created
and/or scheduled. All these also support iteration spaces up to at least 3 dimensions.</p>
   <p>Except for <code class="highlight"><c- n>tbb</c-><c- o>::</c-><c- n>parallel_for_each</c-></code> in oneTBB which can work with forward iterators, these parallel programming models
require random access iterators or some equivalent, such as numeric indexes or pointers. This is natural,
as referring to an arbitrary point in the iteration space at constant time is the main and by far simplest way
to create parallel work. Forward iterators, on the other hand, are notoriously bad for splitting a sequence
that can only be done in linear time. Moreover, if the output of an algorithm should preserve the order of its input,
which is typical for the C++ algorithms, it requires additional synchronization or/and additional space with forward
iterators and comes almost for granted with random access ones.</p>
   <p>These very programming models are often used as backends to implement the C++ standard parallelism. Not surprisingly,
most implementations fall back to serial processing if data sequences have no random access. Of the GNU libstdc++,
LLVM libc++, and MSVC’s standard library, only the latter attempts to process forward iterator based sequences in parallel,
for which it first needs to serially iterate over a whole sequence once or even twice.
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>Returning to the SG1/SG9 feedback, there seemingly are two main reasons why others do not want to restrict
parallel algorithms by only random access ranges:</p>
   <ul>
    <li data-md>
     <p>That would prevent some useful views, such as <code class="highlight"><c- n>filter_view</c-></code>, from being used with parallel range algorithms.</p>
    <li data-md>
     <p>That would be inconsistent with the C++17 parallel algorithms.</p>
   </ul>
   <p>Given the other aspects of the proposed design, we believe some degree of inconsistency with C++17 parallel algorithms
is inevitable and should not become a gating factor for important design decisions.</p>
   <p>The question of supporting the standard views that do not provide random access is very important. We think though
that it should better be addressed through proper abstractions and new concepts defining iteration spaces, including
multidimensional ones, suitable for parallel algorithms. We intend to work on developing these (likely in another paper),
however it requires time and effort to make it right, and we think trying to squeeze that into C++26 adds significant risks.
For now, random access ranges with known bounds (see <a href="#require_bounded_ranges">§ 2.7 Requiring ranges to be bounded</a>) is probably the best approximation
that exists in the standard. Starting from that and gradually enabling other types of iteration spaces
in a source-compatible manner seems to us better than blanket allowance of any <code class="highlight"><c- n>forward_range</c-></code>.</p>
   <h3 class="heading settled" data-level="2.6" id="range_as_output"><span class="secno">2.6. </span><span class="content">Taking <code class="highlight"><c- n>range</c-></code> as an output</span><a class="self-link" href="#range_as_output"></a></h3>
   <p>We would like to propose a range as the output for the overloads that take ranges for input. Similarly, we propose
a sentinel for output where input is passed as "iterator and sentinel". See <a href="#proposed_api">§ 4 Proposed API</a> for the examples.</p>
   <p>The reasons for that are:</p>
   <ul>
    <li data-md>
     <p>It creates a safer API where all the data sequences have known limits.</p>
    <li data-md>
     <p>Not for all algorithms the output size is defined by the input size. An example is <code class="highlight"><c- n>copy_if</c-></code> (and similar algorithms with <em>filtering</em> semantics), where the output sequence is allowed to be shorter than the input one.
Knowing the expected size of the output may open opportunities for more efficient parallel implementations.</p>
    <li data-md>
     <p>Passing a range for output makes code a bit simpler in the cases typical for parallel execution.</p>
   </ul>
   <p>It is worth noting that to various degrees these reasons are also applicable to serial algorithms.</p>
   <p>There are already range algorithms  - <code class="highlight"><c- n>fill</c-></code>, <code class="highlight"><c- n>generate</c-></code>, and <code class="highlight"><c- n>iota</c-></code> - that take a range or an "iterator and sentinel" pair
for their output. Their specifics is absence of input sequences, so the output sequence needs a boundary.
Nevertheless, these are precedents of specifying output as a range, and extending it from algorithms with zero input sequences
to those with one or more seems appropriate.</p>
   <p>We think that in practice parallel algorithms mainly write the output data into a container or storage
with preallocated space, for efficiency reasons. So, typically parallel algorithms receive <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>begin</c-><c- p>(</c-><c- n>v</c-><c- p>)</c-></code> or <code class="highlight"><c- n>v</c-><c- p>.</c-><c- n>begin</c-><c- p>()</c-></code> or <code class="highlight"><c- n>v</c-><c- p>.</c-><c- n>data</c-><c- p>()</c-></code> for output, where <code class="highlight"><c- n>v</c-></code> is an instance of <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>vector</c-></code> or <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>array</c-></code>.
Allowing <code class="highlight"><c- n>v</c-></code> to be passed directly for output in the same way as for input results in a slightly simpler code.</p>
   <p>Also, using classes such as <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>back_insert_iterator</c-></code> or <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ostream_iterator</c-></code>, which do not have a range underneath,
is already not possible with C++17 parallel algorithms that require at least forward iterators.
Migrating such code to use algorithms with execution policies will require modifications in any case.</p>
   <p>All in all, we think for parallel algorithms taking ranges and sentinels for output makes more sense than only taking an iterator.</p>
   <p>The main concern we have heard about this approach is the mismatch between serial and parallel variations.
That is, if serial range algorithms only take iterators for output and parallel range algorithms only take ranges,
switching between those will always require code changes. That can be resolved by:</p>
   <ul>
    <li data-md>
     <p>(A) adding <em>output-as-range</em> to serial range algorithms,</p>
    <li data-md>
     <p>(B) adding <em>output-as-iterator</em> to parallel range algorithms</p>
   </ul>
   <p>or both.</p>
   <p>The option (A) gives some of the described benefits to serial range algorithms as well; one could argue that it
would be a useful addition on its own.
The option (B) does not seem to have benefits besides the aligned semantics, while it has the downside of not enforcing
the requirements we propose in <a href="#require_bounded_ranges">§ 2.7 Requiring ranges to be bounded</a>.</p>
   <p>With either (A) or (B), the output parameter for range algorithm overloads could be both a range and an iterator.
In the formal wording, this could be represented either as two separate overloads with different requirements
on that parameter, or with an exposition-only <em>range-or-iterator</em> concept that combines the requirements
by logical disjunction, as its name suggest. We did not explore which makes more sense; at glance, there seems
to be little practical difference for library implementors.</p>
   <p>For "iterator and sentinel" overloads we prefer to always require a sentinel for output, despite the mismatch with
the corresponding serial overloads.</p>
   <h3 class="heading settled" data-level="2.7" id="require_bounded_ranges"><span class="secno">2.7. </span><span class="content">Requiring ranges to be bounded</span><a class="self-link" href="#require_bounded_ranges"></a></h3>
   <p>One of the requirements we want to put on the parallel range algorithms is to disallow unbounded input and output.
The reasons for that are:</p>
   <ul>
    <li data-md>
     <p>First, for efficient parallel implementation we need to know the iteration space bounds. Otherwise, it’s hard to
apply the "divide and conquer" strategy for creating work for multiple execution threads.</p>
    <li data-md>
     <p>Second, while serial range algorithms allow passing an "infinite" range like <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>views</c-><c- o>::</c-><c- n>iota</c-><c- p>(</c-><c- mi>0</c-><c- p>)</c-></code>,
it may result in an endless loop. It’s hard to imagine usefulness of that in the case of parallel execution.
Requiring data sequences to be bounded potentially prevents errors at run-time.</p>
   </ul>
   <p>We have evaluated a few options to specify such a requirement, and for now decided to use the <code class="highlight"><c- n>sized_sentinel_for</c-></code> concept.
It is sufficient for the purpose and at the same does not require anything that a random access range would not already provide.
For comparison, the <code class="highlight"><c- n>sized_range</c-></code> concept adds a requirement of <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>size</c-><c- p>(</c-><c- n>r</c-><c- p>)</c-></code> to be well-formed for a range <code class="highlight"><c- n>r</c-></code>.</p>
   <p>In the case of two or more input ranges or sequences, it is sufficient for just one to be bounded.
The other input ranges are then assumed to have at least as many elements as the bounded one.
This enables unbounded ranges such as <code class="highlight"><c- n>views</c-><c- o>::</c-><c- n>repeat</c-></code> in certain useful patterns, for example:</p>
<pre class="language-cpp highlight"><c- b>void</c-> <c- nf>normalize_parallel</c-><c- p>(</c-><c- n>range</c-> <c- k>auto</c-><c- o>&amp;&amp;</c-> <c- n>v</c-><c- p>)</c-> <c- p>{</c->
  <c- k>auto</c-> <c- n>mx</c-> <c- o>=</c-> <c- n>reduce</c-><c- p>(</c-><c- n>execution</c-><c- o>::</c-><c- n>par</c-><c- p>,</c-> <c- n>v</c-><c- p>,</c-> <c- n>ranges</c-><c- o>::</c-><c- n>max</c-><c- p>{});</c->
  <c- n>transform</c-><c- p>(</c-><c- n>execution</c-><c- o>::</c-><c- n>par</c-><c- p>,</c-> <c- n>v</c-><c- p>,</c-> <c- n>views</c-><c- o>::</c-><c- n>repeat</c-><c- p>(</c-><c- n>mx</c-><c- p>),</c-> <c- n>v</c-><c- p>,</c-> <c- n>divides</c-><c- p>);</c->
<c- p>}</c->
</pre>
   <p>At the same time, for an output range (that we propose in <a href="#range_as_output">§ 2.6 Taking range as an output</a>) our preference is to have a boundary
independently on the input range(s). The main motivation is to follow established practices of secure coding, which
recommend or even require to always specify the size of the output in order to prevent out-of-range data modifications.
We think this will not impose any practical limitation on which ranges can be used for the output of a parallel algorithm,
as we could not find or invent an example of a random-access writable range which would also be unbounded.</p>
   <p>If several provided ranges or sequences are bounded, an algorithm should stop as soon as the end is reached for the shortest one.
There are already precedents in the standard that an algorithm takes two sequences with potentially different input sizes
and chooses the smaller size as the number of iterations it is going to make, such as <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>transform</c-></code> and <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>mismatch</c-></code>. For the record, <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>transform</c-></code> (including the overload with execution policy) doesn’t support
different input sizes, while <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>mismatch</c-></code> does.</p>
   <h3 class="heading settled" data-level="2.8" id="callable_parameters"><span class="secno">2.8. </span><span class="content">Requirements for callable parameters</span><a class="self-link" href="#callable_parameters"></a></h3>
   <p>In <a data-link-type="biblio" href="#biblio-p3179r0" title="C++ parallel range algorithms">[P3179R0]</a> we proposed that parallel range algorithms should require function objects for predicates, comparators, etc.
to have <code class="highlight"><c- k>const</c-></code>-qualified <code class="highlight"><c- k>operator</c-><c- p>()</c-></code>, with the intent to provide compile-time diagnostics for mutable	function objects
which might be unsafe for parallel execution. We have got contradictory feedback from SG1 and SG9 on that topic:
SG1 preferred to keep the behavior consistent with C++17 parallel algorithms, while SG9 supported our design intent.</p>
   <p>We did extra investigation and decided that requiring <code class="highlight"><c- k>const</c-></code>-qualified operator at compile-time is not strictly necessary
because:</p>
   <ul>
    <li data-md>
     <p>The vast majority of the serial range algorithms requires function objects to be <code class="highlight"><c- n>regular_invocable</c-></code> (or its derivatives),
which already has the semantical requirement of not modifying either the function object or its arguments.
While not enforced at compile-time, it seems good enough for our purpose because it demands having the same function
object state between invocations (independently of <code class="highlight"><c- k>const</c-></code> qualifier), and it is consistent with serial range algorithms.</p>
    <li data-md>
     <p>Remaining algorithms should be considered individually. For example, <code class="highlight"><c- n>for_each</c-></code> using a mutable <code class="highlight"><c- k>operator</c-><c- p>()</c-></code> is of less
concern if the algorithm does not return the function object (see more detailed analysis below).
For <code class="highlight"><c- n>generate</c-></code>, a non-mutable callable appears to be of very limited use: in order to produce multiple values while not
taking any arguments, a generator should typically maintain and update some state.</p>
   </ul>
   <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>// a data race if the callable is executed concurrently</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>We allow the same callable to be used in the proposed <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>for_each</c-></code>.</p>
<pre class="language-cpp highlight"><c- c1>// callable is used from the previous code snippet</c->
<c- n>callable</c-> <c- n>c</c-><c- p>;</c->
<c- c1>// The returned iterator is ignored</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>Again, even though <code class="highlight"><c- n>c</c-></code> accumulates state modifications, one cannot rely on that because an algorithm implementation
is allowed to make as many copies of <code class="highlight"><c- n>c</c-></code> as it wants. Of course, this can be overcome by using <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>reference_wrapper</c-></code> but that might lead to data races.</p>
<pre class="language-cpp highlight"><c- c1>// callable is used from the previous code snippet</c->
<c- c1>// Wrapping a callable object with std::reference_wrapper compiles, but might result in data races</c->
<c- n>callable</c-> <c- n>c</c-><c- p>;</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>
   <p>Our conclusion is that it’s user responsibility to provide such a callable that avoids data races, same as for C++17 parallel
algorithms.</p>
   <h3 class="heading settled" data-level="2.9" id="not_customization_point"><span class="secno">2.9. </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="2.10" id="constexpr_support"><span class="secno">2.10. </span><span class="content"><code class="highlight"><c- k>constexpr</c-></code> parallel range algorithms</span><a class="self-link" href="#constexpr_support"></a></h3>
   <p><a data-link-type="biblio" href="#biblio-p2902r0" title="constexpr &apos;Parallel&apos; Algorithms">[P2902R0]</a> suggests allowing algorithms with execution policies to be used in constant expressions.
We do not consider that as a primary design goal for our work, however we will happily align with that proposal
in the future once it progresses towards adoption into the working draft.</p>
   <h2 class="heading settled" data-level="3" id="more_examples"><span class="secno">3. </span><span class="content">More examples</span><a class="self-link" href="#more_examples"></a></h2>
   <h3 class="heading settled" data-level="3.1" id="easy_to_switch"><span class="secno">3.1. </span><span class="content">Change existing code to use parallel range algorithms</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. However, that simplicity should not create hidden issues negatively impacting the overall user experience.
We believe that the proposal provides a good balance in that regard.</p>
   <p>As an example, let’s look at using <code class="highlight"><c- n>for_each</c-></code> to apply a lambda function to all elements of a <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>vector</c-> <c- n>v</c-></code>.</p>
   <p>For the serial 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>switching to the parallel version will look like:</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>In this simple case, the only change is an execution policy added as the first function argument. It will also hold for
the "iterator and sentinel" overload of <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>for_each</c-></code>.</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 iterator and 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>// Using vector as 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>So, here only changing the namespace is necessary, though 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>
   <p>However, for other algorithms more changes might be necessary.</p>
   <h3 class="heading settled" data-level="3.2" id="less_parallel_call"><span class="secno">3.2. </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> and <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>transform</c-></code> are used as reference points.
When the design is ratified, it will be spread across other algorithms.</p>
<pre class="language-cpp highlight"><c- c1>// for_each</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>sized_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>I</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>random_access_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>requires</c-> <c- n>sized_sentinel_for</c-><c- o>&lt;</c-><c- n>ranges</c-><c- o>::</c-><c- n>sentinel_t</c-><c- o>&lt;</c-><c- n>R</c-><c- o>></c-><c- p>,</c-> <c- n>ranges</c-><c- o>::</c-><c- n>iterator_t</c-><c- o>&lt;</c-><c- n>R</c-><c- o>>></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- 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->

<c- c1>// binary transform with an output range and an output sentinel</c->
<c- k>template</c-><c- o>&lt;</c-> <c- k>typename</c-> <c- nc>ExecutionPolicy</c-><c- p>,</c->
          <c- n>random_access_iterator</c-> <c- n>I1</c-><c- p>,</c-> <c- n>sentinel_for</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>></c-> <c- n>S1</c-><c- p>,</c->
          <c- n>random_access_iterator</c-> <c- n>I2</c-><c- p>,</c-> <c- n>sentinel_for</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>></c-> <c- n>S2</c-><c- p>,</c->
          <c- n>random_access_iterator</c-> <c- n>O</c-><c- p>,</c-> <c- n>sized_sentinel_for</c-><c- o>&lt;</c-><c- n>O</c-><c- o>></c-> <c- n>SO</c-><c- p>,</c->
          <c- n>copy_constructible</c-> <c- n>F</c-><c- p>,</c->
          <c- k>class</c-> <c- nc>Proj1</c-> <c- o>=</c-> <c- n>identity</c-><c- p>,</c-> <c- k>class</c-> <c- nc>Proj2</c-> <c- o>=</c-> <c- n>identity</c-> <c- o>></c->
<c- k>requires</c-> <c- n>indirectly_writable</c-><c- o>&lt;</c-><c- n>O</c-><c- p>,</c->
             <c- n>indirect_result_t</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>projected</c-><c- o>&lt;</c-><c- n>I1</c-><c- p>,</c-> <c- n>Proj1</c-><c- o>></c-><c- p>,</c-> <c- n>projected</c-><c- o>&lt;</c-><c- n>I2</c-><c- p>,</c-> <c- n>Proj2</c-><c- o>>>></c->
         <c- o>&amp;&amp;</c-> <c- p>(</c-><c- n>sized_sentinel_for</c-><c- o>&lt;</c-><c- n>S1</c-><c- p>,</c-> <c- n>I1</c-><c- o>></c-> <c- o>||</c-> <c- n>sized_sentinel_for</c-><c- o>&lt;</c-><c- n>S2</c-><c- p>,</c-> <c- n>I2</c-><c- o>></c-><c- p>)</c->
<c- k>constexpr</c-> <c- n>binary_transform_result</c-><c- o>&lt;</c-><c- n>I1</c-><c- p>,</c-> <c- n>I2</c-><c- p>,</c-> <c- n>O</c-><c- o>></c->
    <c- n>transform</c-><c- p>(</c-> <c- n>ExecutionPolicy</c-><c- o>&amp;&amp;</c-> <c- n>policy</c-><c- p>,</c-> <c- n>I1</c-> <c- n>first1</c-><c- p>,</c-> <c- n>S1</c-> <c- n>last1</c-><c- p>,</c-> <c- n>I2</c-> <c- n>first2</c-><c- p>,</c-> <c- n>S2</c-> <c- n>last2</c-><c- p>,</c-> <c- n>O</c-> <c- n>result</c-><c- p>,</c-> <c- n>SO</c-> <c- n>s</c-><c- p>,</c->
               <c- n>F</c-> <c- n>binary_op</c-><c- p>,</c-> <c- n>Proj1</c-> <c- n>proj1</c-> <c- o>=</c-> <c- p>{},</c-> <c- n>Proj2</c-> <c- n>proj2</c-> <c- o>=</c-> <c- p>{}</c-> <c- p>);</c->

<c- k>template</c-><c- o>&lt;</c-> <c- k>typename</c-> <c- nc>ExecutionPolicy</c-><c- p>,</c->
          <c- n>ranges</c-><c- o>::</c-><c- n>random_access_range</c-> <c- n>R1</c-><c- p>,</c->
          <c- n>ranges</c-><c- o>::</c-><c- n>random_access_range</c-> <c- n>R2</c-><c- p>,</c->
          <c- n>ranges</c-><c- o>::</c-><c- n>random_access_range</c-> <c- n>RR</c-><c- p>,</c->
          <c- n>copy_constructible</c-> <c- n>F</c-><c- p>,</c->
          <c- k>class</c-> <c- nc>Proj1</c-> <c- o>=</c-> <c- n>identity</c-><c- p>,</c-> <c- k>class</c-> <c- nc>Proj2</c-> <c- o>=</c-> <c- n>identity</c-> <c- o>></c->
<c- k>requires</c-> <c- n>indirectly_writable</c-><c- o>&lt;</c-><c- n>ranges</c-><c- o>::</c-><c- n>iterator_t</c-><c- o>&lt;</c-><c- n>RR</c-><c- o>></c-><c- p>,</c->
             <c- n>indirect_result_t</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c->
                 <c- n>projected</c-><c- o>&lt;</c-><c- n>ranges</c-><c- o>::</c-><c- n>iterator_t</c-><c- o>&lt;</c-><c- n>R1</c-><c- o>></c-><c- p>,</c-> <c- n>Proj1</c-><c- o>></c-><c- p>,</c->
                 <c- n>projected</c-><c- o>&lt;</c-><c- n>ranges</c-><c- o>::</c-><c- n>iterator_t</c-><c- o>&lt;</c-><c- n>R2</c-><c- o>></c-><c- p>,</c-> <c- n>Proj2</c-><c- o>>>></c->
         <c- o>&amp;&amp;</c-> <c- p>(</c-><c- n>sized_sentinel_for</c-><c- o>&lt;</c-><c- n>ranges</c-><c- o>::</c-><c- n>sentinel_t</c-><c- o>&lt;</c-><c- n>R1</c-><c- o>></c-><c- p>,</c-> <c- n>ranges</c-><c- o>::</c-><c- n>iterator_t</c-><c- o>&lt;</c-><c- n>R1</c-><c- o>>></c->
             <c- o>||</c-> <c- n>sized_sentinel_for</c-><c- o>&lt;</c-><c- n>ranges</c-><c- o>::</c-><c- n>sentinel_t</c-><c- o>&lt;</c-><c- n>R2</c-><c- o>></c-><c- p>,</c-> <c- n>ranges</c-><c- o>::</c-><c- n>iterator_t</c-><c- o>&lt;</c-><c- n>R2</c-><c- o>>></c-><c- p>)</c->
         <c- o>&amp;&amp;</c-> <c- n>sized_sentinel_for</c-><c- o>&lt;</c-><c- n>ranges</c-><c- o>::</c-><c- n>sentinel_t</c-><c- o>&lt;</c-><c- n>RR</c-><c- o>></c-><c- p>,</c-> <c- n>ranges</c-><c- o>::</c-><c- n>iterator_t</c-><c- o>&lt;</c-><c- n>RR</c-><c- o>>></c->
<c- k>constexpr</c-> <c- n>binary_transform_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>R1</c-><c- o>></c-><c- p>,</c->
                                  <c- n>ranges</c-><c- o>::</c-><c- n>borrowed_iterator_t</c-><c- o>&lt;</c-><c- n>R2</c-><c- o>></c-><c- p>,</c->
                                  <c- n>ranges</c-><c- o>::</c-><c- n>borrowed_iterator_t</c-><c- o>&lt;</c-><c- n>RR</c-><c- o>>></c->
    <c- n>transform</c-><c- p>(</c-> <c- n>ExecutionPolicy</c-><c- o>&amp;&amp;</c-> <c- n>policy</c-><c- p>,</c-> <c- n>R1</c-><c- o>&amp;&amp;</c-> <c- n>r1</c-><c- p>,</c-> <c- n>R2</c-><c- o>&amp;&amp;</c-> <c- n>r2</c-><c- p>,</c-> <c- n>RR</c-><c- o>&amp;&amp;</c-> <c- n>result</c-><c- p>,</c-> <c- n>F</c-> <c- n>binary_op</c-><c- p>,</c->
               <c- n>Proj1</c-> <c- n>proj1</c-> <c- o>=</c-> <c- p>{},</c-> <c- n>Proj2</c-> <c- n>proj2</c-> <c- o>=</c-> <c- p>{}</c-> <c- p>);</c->

</pre>
   <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 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>sized_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>I</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 the execution policy;</c->
        <c- c1>// for the reference, a serial 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- n>first</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>random_access_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>borrowed_iterator_t</c-><c- o>&lt;</c-><c- n>R</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="serial_range_based_absence"><span class="secno">5. </span><span class="content">Absence of some serial range-based algorithms</span><a class="self-link" href="#serial_range_based_absence"></a></h2>
   <p>We understand that some useful algorithms do not yet exist in <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-></code>, for example, most of generalized numeric
operations <a href="https://eel.is/c++draft/numeric.ops">[numeric.ops]</a>. The goal of this paper is however limited to
adding overloads with <code class="highlight"><c- n>ExecutionPolicy</c-></code> to the existing algorithms in <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-></code> namespace. Any follow-up paper that
adds <code class="highlight"><c- o>&lt;</c-><c- n>numeric</c-><c- o>></c-></code> algorithms to <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-></code> should also consider adding dedicated overloads with <code class="highlight"><c- n>ExecutionPolicy</c-></code>.</p>
   <h2 class="heading settled" data-level="6" id="further_work"><span class="secno">6. </span><span class="content">Further exploration</span><a class="self-link" href="#further_work"></a></h2>
   <h3 class="heading settled" data-level="6.1" id="thread_safe_views"><span class="secno">6.1. </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.
While some investigation was done by other authors in <a data-link-type="biblio" href="#biblio-p3159r0" title="C++ Range Adaptors and Parallel Algorithms">[P3159R0]</a>, it’s mostly not about the data races but about
ability to parallelize processing of data represented by various views.</p>
   <p>We need to invest more time to understand the implications of sharing a state between <code class="highlight"><c- n>view</c-></code> and <code class="highlight"><c- n>iterator</c-></code> on the possibility
of data races. One example is <code class="highlight"><c- n>transform_view</c-></code>, where iterators keep pointers to the function object that is stored
in the view itself.</p>
   <p>Here are questions we want to answer (potentially not a complete list):</p>
   <ul>
    <li data-md>
     <p>Do users have enough control to guarantee absence of data races for such views?</p>
    <li data-md>
     <p>Are races not possible because of implementation strategy chosen by standard libraries?</p>
    <li data-md>
     <p>Do we need to add extra requirements towards thread safety to the standard views?</p>
   </ul>
   <h2 class="heading settled" data-level="7" id="revision_history"><span class="secno">7. </span><span class="content">Revision history</span><a class="self-link" href="#revision_history"></a></h2>
   <h3 class="heading settled" data-level="7.1" id="r1_r2"><span class="secno">7.1. </span><span class="content">R1 => R2</span><a class="self-link" href="#r1_r2"></a></h3>
   <ul>
    <li data-md>
     <p>Summarize proposed differences from the serial range algorithms and from the non-range parallel algorithms</p>
    <li data-md>
     <p>Allow all but one input sequences to be unbounded</p>
    <li data-md>
     <p>List existing algorithms that take ranges for output</p>
    <li data-md>
     <p>Update arguments and mitigations for using ranges for output</p>
    <li data-md>
     <p>Add more arguments in support of random access ranges</p>
    <li data-md>
     <p>Fix the signatures of <code class="highlight"><c- n>for_each</c-></code> to match the proposed design</p>
   </ul>
   <h3 class="heading settled" data-level="7.2" id="r0_r1"><span class="secno">7.2. </span><span class="content">R0 => R1</span><a class="self-link" href="#r0_r1"></a></h3>
   <ul>
    <li data-md>
     <p>Address the feedback from SG1 and SG9 review</p>
    <li data-md>
     <p>Add more information about iterator constraints</p>
    <li data-md>
     <p>Propose <code class="highlight"><c- n>range</c-></code> as an output for the algorithms</p>
    <li data-md>
     <p>Require ranges to be bounded</p>
   </ul>
   <h2 class="heading settled" data-level="8" id="polls"><span class="secno">8. </span><span class="content">Polls</span><a class="self-link" href="#polls"></a></h2>
   <h3 class="heading settled" data-level="8.1" id="sg9_tokyo_2024"><span class="secno">8.1. </span><span class="content">SG9, Tokyo 2024</span><a class="self-link" href="#sg9_tokyo_2024"></a></h3>
   <p>Poll 1: <code class="highlight"><c- n>for_each</c-></code> shouldn’t return the callable</p>
   <table>
    <tbody>
     <tr>
      <th>SF
      <th>F
      <th>N
      <th>A
      <th>SA
     <tr>
      <td>2
      <td>4
      <td>2
      <td>0
      <td>0
   </table>
   <p>Poll 2: Parallel <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-></code> algos should return the same type as serial <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-></code> algos</p>
   <table>
    <tbody>
     <tr>
      <td>Unanimous consent.
   </table>
   <p>Poll 3: Parallel ranges algos should require <code class="highlight"><c- n>forward_range</c-></code>, not <code class="highlight"><c- n>random_access_range</c-></code></p>
   <table>
    <tbody>
     <tr>
      <th>SF
      <th>F
      <th>N
      <th>A
      <th>SA
     <tr>
      <td>3
      <td>2
      <td>3
      <td>1
      <td>1
   </table>
   <p>Poll 4: Range-based parallel algos should require const operator()</p>
   <table>
    <tbody>
     <tr>
      <th>SF
      <th>F
      <th>N
      <th>A
      <th>SA
     <tr>
      <td>0
      <td>7
      <td>2
      <td>0
      <td>0
   </table>
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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-p2300r9">[P2300R9]
   <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/p2300r9"><cite>`std::execution`</cite></a>. 2 April 2024. URL: <a href="https://wg21.link/p2300r9">https://wg21.link/p2300r9</a>
   <dt id="biblio-p2408r5">[P2408R5]
   <dd>David Olsen. <a href="https://wg21.link/p2408r5"><cite>Ranges iterators as inputs to non-Ranges algorithms</cite></a>. 22 April 2022. URL: <a href="https://wg21.link/p2408r5">https://wg21.link/p2408r5</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-p3136r0">[P3136R0]
   <dd>Tim Song. <a href="https://wg21.link/p3136r0"><cite>Retiring niebloids</cite></a>. 15 February 2024. URL: <a href="https://wg21.link/p3136r0">https://wg21.link/p3136r0</a>
   <dt id="biblio-p3159r0">[P3159R0]
   <dd>Bryce Adelstein Lelbach. <a href="https://wg21.link/p3159r0"><cite>C++ Range Adaptors and Parallel Algorithms</cite></a>. 18 March 2024. URL: <a href="https://wg21.link/p3159r0">https://wg21.link/p3159r0</a>
   <dt id="biblio-p3179r0">[P3179R0]
   <dd>Ruslan Arutyunyan, Alexey Kukanov. <a href="https://wg21.link/p3179r0"><cite>C++ parallel range algorithms</cite></a>. 15 March 2024. URL: <a href="https://wg21.link/p3179r0">https://wg21.link/p3179r0</a>
   <dt id="biblio-p3300r0">[P3300R0]
   <dd>Bryce Adelstein Lelbach. <a href="https://wg21.link/p3300r0"><cite>C++ Asynchronous Parallel Algorithms</cite></a>. 15 February 2024. URL: <a href="https://wg21.link/p3300r0">https://wg21.link/p3300r0</a>
  </dl>