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  <title>P2876R1: Proposal to extend &lt;code>std::simd&lt;/code> with more constructors and accessors</title>
<style data-fill-with="stylesheet">/******************************************************************************
 *                   Style sheet for the W3C specifications                   *
 *
 * Special classes handled by this style sheet include:
 *
 * Indices
 *   - .toc for the Table of Contents (<ol class="toc">)
 *     + <span class="secno"> for the section numbers
 *   - #toc for the Table of Contents (<nav id="toc">)
 *   - ul.index for Indices (<a href="#ref">term</a><span>, in § N.M</span>)
 *   - table.index for Index Tables (e.g. for properties or elements)
 *
 * Structural Markup
 *   - table.data for general data tables
 *     -> use 'scope' attribute, <colgroup>, <thead>, and <tbody> for best results !
 *     -> use <table class='complex data'> for extra-complex tables
 *     -> use <td class='long'> for paragraph-length cell content
 *     -> use <td class='pre'> when manual line breaks/indentation would help readability
 *   - dl.switch for switch statements
 *   - ol.algorithm for algorithms (helps to visualize nesting)
 *   - .figure and .caption (HTML4) and figure and figcaption (HTML5)
 *     -> .sidefigure for right-floated figures
 *   - ins/del
 *     -> ins/del.c### for candidate and proposed changes (amendments)
 *
 * Code
 *   - pre and code
 *
 * Special Sections
 *   - .note       for informative notes             (div, p, span, aside, details)
 *   - .example    for informative examples          (div, p, pre, span)
 *   - .issue      for issues                        (div, p, span)
 *   - .advisement for loud normative statements     (div, p, strong)
 *   - .annoying-warning for spec obsoletion notices (div, aside, details)
 *   - .correction for "candidate corrections"       (div, aside, details, section)
 *   - .addition   for "candidate additions"         (div, aside, details, section)
 *   - .correction.proposed for "proposed corrections" (div, aside, details, section)
 *   - .addition.proposed   for "proposed additions"   (div, aside, details, section)
 *
 * Definition Boxes
 *   - pre.def   for WebIDL definitions
 *   - table.def for tables that define other entities (e.g. CSS properties)
 *   - dl.def    for definition lists that define other entitles (e.g. HTML elements)
 *
 * Numbering
 *   - .secno for section numbers in .toc and headings (<span class='secno'>3.2</span>)
 *   - .marker for source-inserted example/figure/issue numbers (<span class='marker'>Issue 4</span>)
 *   - ::before styled for CSS-generated issue/example/figure numbers:
 *     -> Documents wishing to use this only need to add
 *        figcaption::before,
 *        .caption::before { content: "Figure "  counter(figure) " ";  }
 *        .example::before { content: "Example " counter(example) " "; }
 *        .issue::before   { content: "Issue "   counter(issue) " ";   }
 *
 * Header Stuff (ignore, just don't conflict with these classes)
 *   - .head for the header
 *   - .copyright for the copyright
 *
 * Outdated warning for old specs
 *
 * Miscellaneous
 *   - .overlarge for things that should be as wide as possible, even if
 *     that overflows the body text area. This can be used on an item or
 *     on its container, depending on the effect desired.
 *     Note that this styling basically doesn't help at all when printing,
 *     since A4 paper isn't much wider than the max-width here.
 *     It's better to design things to fit into a narrower measure if possible.
 *
 *   - js-added ToC jump links (see fixup.js)
 *
 ******************************************************************************/

/* color variables included separately for reliability */

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

	html {
	}

	body {
		counter-reset: example figure issue;

		/* Layout */
		max-width: 50em;			  /* limit line length to 50em for readability   */
		margin: 0 auto;				/* center text within page                    */
		padding: 1.6em 1.5em 2em 50px; /* assume 16px font size for downlevel clients */
		padding: 1.6em 1.5em 2em calc(26px + 1.5em); /* leave space for status flag    */

		/* Typography */
		line-height: 1.5;
		font-family: sans-serif;
		widows: 2;
		orphans: 2;
		word-wrap: break-word;
		overflow-wrap: break-word;
		hyphens: auto;

		color: black;
		color: var(--text);
		background: white top left fixed no-repeat;
		background: var(--bg) top left fixed no-repeat;
		background-size: 25px auto;
	}


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

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

	div.head { margin-bottom: 1em; }
	div.head hr { border-style: solid; }

	div.head h1 {
		font-weight: bold;
		margin: 0 0 .1em;
		font-size: 220%;
	}

	div.head h2 { margin-bottom: 1.5em;}

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

	.head .logo {
		float: right;
		margin: 0.4rem 0 0.2rem .4rem;
	}

	.head img[src*="logos/W3C"] {
		display: block;
		border: solid #1a5e9a;
		border: solid var(--logo-bg);
		border-width: .65rem .7rem .6rem;
		border-radius: .4rem;
		background: #1a5e9a;
		background: var(--logo-bg);
		color: white;
		color: var(--logo-text);
		font-weight: bold;
	}

	.head a:hover > img[src*="logos/W3C"],
	.head a:focus > img[src*="logos/W3C"] {
		opacity: .8;
	}

	.head a:active > img[src*="logos/W3C"] {
		background: #c00;
		background: var(--logo-active-bg);
		border-color: #c00;
		border-color: var(--logo-active-bg);
	}

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

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

	p.copyright,
	p.copyright small { font-size: small; }

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

	@media print {
		#toc-nav {
			display: none;
		}
	}
	@media not print {
		#toc-nav {
			position: fixed;
			z-index: 3;
			bottom: 0; left: 0;
			margin: 0;
			min-width: 1.33em;
			border-top-right-radius: 2rem;
			box-shadow: 0 0 2px;
			font-size: 1.5em;
		}
		#toc-nav > a {
			display: block;
			white-space: nowrap;

			height: 1.33em;
			padding: .1em 0.3em;
			margin: 0;

			box-shadow: 0 0 2px;
			border: none;
			border-top-right-radius: 1.33em;

			color: #707070;
			color: var(--tocnav-normal-text);
			background: white;
			background: var(--tocnav-normal-bg);
		}
		#toc-nav > a:hover,
		#toc-nav > a:focus {
			color: black;
			color: var(--tocnav-hover-text);
			background: #f8f8f8;
			background: var(--tocnav-hover-bg);
		}
		#toc-nav > a:active {
			color: #c00;
			color: var(--tocnav-active-text);
			background: white;
			background: var(--tocnav-active-bg);
		}

		#toc-nav > #toc-jump {
			padding-bottom: 2em;
			margin-bottom: -1.9em;
		}

		/* statusbar gets in the way on keyboard focus; remove once browsers fix */
		#toc-nav > a[href="#toc"]:not(:hover):focus:last-child {
			padding-bottom: 1.5rem;
		}

		#toc-nav:not(:hover) > a:not(:focus) > span + span {
			/* Ideally this uses :focus-within on #toc-nav */
			display: none;
		}
		#toc-nav > a > span + span {
			padding-right: 0.2em;
		}
	}

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

	/* Floating sidebar */
	@media screen {
		body.toc-sidebar #toc {
			position: fixed;
			top: 0; bottom: 0;
			left: 0;
			width: 23.5em;
			max-width: 80%;
			max-width: calc(100% - 2em - 26px);
			overflow: auto;
			padding: 0 1em;
			padding-left: 42px;
			padding-left: calc(1em + 26px);
			color: black;
			color: var(--tocsidebar-text);
			background: inherit;
			background-color: #f7f8f9;
			background-color: var(--tocsidebar-bg);
			z-index: 1;
			box-shadow: -.1em 0 .25em rgba(0,0,0,.1) inset;
			box-shadow: -.1em 0 .25em var(--tocsidebar-shadow) inset;
		}
		body.toc-sidebar #toc h2 {
			margin-top: .8rem;
			font-variant: small-caps;
			font-variant: all-small-caps;
			text-transform: lowercase;
			font-weight: bold;
			color: gray;
			color: hsla(203,20%,40%,.7);
			color: var(--tocsidebar-heading-text);
		}
		body.toc-sidebar #toc-jump:not(:focus) {
			width: 0;
			height: 0;
			padding: 0;
			position: absolute;
			overflow: hidden;
		}
	}
	/* Hide main scroller when only the ToC is visible anyway */
	@media screen and (max-width: 28em) {
		body.toc-sidebar {
			overflow: hidden;
		}
	}

	/* Sidebar with its own space */
	@media screen and (min-width: 78em) {
		body:not(.toc-inline) #toc {
			position: fixed;
			top: 0; bottom: 0;
			left: 0;
			width: 23.5em;
			overflow: auto;
			padding: 0 1em;
			padding-left: 42px;
			padding-left: calc(1em + 26px);
			color: black;
			color: var(--tocsidebar-text);
			background: inherit;
			background-color: #f7f8f9;
			background-color: var(--tocsidebar-bg);
			z-index: 1;
			box-shadow: -.1em 0 .25em rgba(0,0,0,.1) inset;
			box-shadow: -.1em 0 .25em var(--tocsidebar-shadow) inset;
		}
		body:not(.toc-inline) #toc h2 {
			margin-top: .8rem;
			font-variant: small-caps;
			font-variant: all-small-caps;
			text-transform: lowercase;
			font-weight: bold;
			color: gray;
			color: hsla(203,20%,40%,.7);
			color: var(--tocsidebar-heading-text);
		}

		body:not(.toc-inline) {
			padding-left: 29em;
		}
		/* See also Overflow section at the bottom */

		body:not(.toc-inline) #toc-jump:not(:focus) {
			width: 0;
			height: 0;
			padding: 0;
			position: absolute;
			overflow: hidden;
		}
	}
	@media screen and (min-width: 90em) {
		body:not(.toc-inline) {
			margin: 0 4em;
		}
	}

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

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

	h1, h2, h3, h4, h5, h6, dt {
		page-break-after: avoid;
		page-break-inside: avoid;
		font: 100% sans-serif;   /* Reset all font styling to clear out UA styles */
		font-family: inherit;	/* Inherit the font family. */
		line-height: 1.2;		/* Keep wrapped headings compact */
		hyphens: manual;		/* Hyphenated headings look weird */
	}

	h2, h3, h4, h5, h6 {
		margin-top: 3rem;
	}

	h1, h2, h3 {
		color: #005A9C;
		color: var(--heading-text);
	}

	h1 { font-size: 170%; }
	h2 { font-size: 140%; }
	h3 { font-size: 120%; }
	h4 { font-weight: bold; }
	h5 { font-style: italic; }
	h6 { font-variant: small-caps; }
	dt { font-weight: bold; }

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

	h1 + h2,
	#profile-and-date {
		/* #profile-and-date is a subtitle in an H2 under the H1 */
		margin-top: 0;
	}
	h2 + h3,
	h3 + h4,
	h4 + h5,
	h5 + h6 {
		margin-top: 1.2em; /* = 1 x line-height */
	}

/** Section divider ***********************************************************/

	:not(.head) > :not(.head) + hr {
		font-size: 1.5em;
		text-align: center;
		margin: 1em auto;
		height: auto;
		color: black;
		color: var(--hr-text);
		border: transparent solid 0;
		background: transparent;
	}
	:not(.head) > hr::before {
		content: "\2727\2003\2003\2727\2003\2003\2727";
	}

/******************************************************************************/
/*                            Paragraphs and Lists                            */
/******************************************************************************/

	p {
		margin: 1em 0;
	}

	dd > p:first-child,
	li > p:first-child {
		margin-top: 0;
	}

	ul, ol {
		margin-left: 0;
		padding-left: 2em;
	}

	li {
		margin: 0.25em 0 0.5em;
		padding: 0;
	}

	dl dd {
		margin: 0 0 .5em 2em;
	}

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

	/* Style for algorithms */
	ol.algorithm ol:not(.algorithm),
	.algorithm > ol ol:not(.algorithm) {
	border-left: 0.5em solid #DEF;
	border-left: 0.5em solid var(--algo-border);
	}

	/* Put nice boxes around each algorithm. */
	[data-algorithm]:not(.heading) {
	 padding: .5em;
	 border: thin solid #ddd;
	 border: thin solid var(--algo-border);
	 border-radius: .5em;
	 margin: .5em calc(-0.5em - 1px);
	}
	[data-algorithm]:not(.heading) > :first-child {
	 margin-top: 0;
	}
	[data-algorithm]:not(.heading) > :last-child {
	 margin-bottom: 0;
	}

	/* Style for switch/case <dl>s */
	dl.switch > dd > ol.only,
	dl.switch > dd > .only > ol {
	margin-left: 0;
	}
	dl.switch > dd > ol.algorithm,
	dl.switch > dd > .algorithm > ol {
	margin-left: -2em;
	}
	dl.switch {
	padding-left: 2em;
	}
	dl.switch > dt {
	text-indent: -1.5em;
	margin-top: 1em;
	}
	dl.switch > dt + dt {
	margin-top: 0;
	}
	dl.switch > dt::before {
	content: '\21AA';
	padding: 0 0.5em 0 0;
	display: inline-block;
	width: 1em;
	text-align: right;
	line-height: 0.5em;
	}

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


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

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

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

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

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

	.amendment ins, .correction ins, .addition ins,
	ins[class^=c] {
		text-decoration-style: dotted;
	}
	.amendment del, .correction del, .addition del,
	del[class^=c] {
		text-decoration-style: dotted;
	}
	.amendment.proposed ins, .correction.proposed ins, .addition.proposed ins,
	ins[class^=c].proposed {
		text-decoration-style: double;
	}
	.amendment.proposed del, .correction.proposed del, .addition.proposed del,
	del[class^=c].proposed {
		text-decoration-style: double;
	}

/** Miscellaneous improvements to inline formatting ***************************/

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

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

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

	pre, code, samp {
		font-family: Menlo, Consolas, "DejaVu Sans Mono", Monaco, monospace;
		font-size: .9em;
		hyphens: none;
		text-transform: none;
		text-align: left;
		text-align: start;
		font-variant: normal;
		orphans: 3;
		widows: 3;
		page-break-before: avoid;
	}
	pre code,
	code code {
		font-size: 100%;
	}

	pre {
		margin-top: 1em;
		margin-bottom: 1em;
		overflow: auto;
	}

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

	/* Do something nice. */

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

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

	/* We hyperlink a lot, so make it less intrusive */
	a[href] {
		color: #034575;
		color: var(--a-normal-text);
		text-decoration: underline #707070;
		text-decoration: underline var(--a-normal-underline);
		text-decoration-skip-ink: none;
	}
	a:visited {
		color: #034575;
		color: var(--a-visited-text);
		text-decoration-color: #bbb;
		text-decoration-color: var(--a-visited-underline);
	}

	/* Indicate interaction with the link */
	a[href]:focus,
	a[href]:hover {
		text-decoration-thickness: 2px;
	}
	a[href]:active {
		color: #c00;
		color: var(--a-active-text);
		text-decoration-color: #c00;
		text-decoration-color: var(--a-active-underline);
	}

	/* Backout above styling for W3C logo */
	.head .logo,
	.head .logo a {
		border: none;
		text-decoration: none;
		background: transparent;
	}

/******************************************************************************/
/*                                    Images                                  */
/******************************************************************************/

	img {
		border-style: none;
	}

	img, svg {
		/* Intentionally not color-scheme aware. */
		background: white;
	}

	/* For autogen numbers, add
	  .caption::before, figcaption::before { content: "Figure " counter(figure) ". "; }
	*/

	figure, .figure, .sidefigure {
		page-break-inside: avoid;
		text-align: center;
		margin: 2.5em 0;
	}
	.figure img,	.sidefigure img,	figure img,
	.figure object, .sidefigure object, figure object {
		max-width: 100%;
		margin: auto;
		height: auto;
	}
	.figure pre, .sidefigure pre, figure pre {
		text-align: left;
		display: table;
		margin: 1em auto;
	}
	.figure table, figure table {
		margin: auto;
	}
	@media screen and (min-width: 20em) {
		.sidefigure {
			float: right;
			width: 50%;
			margin: 0 0 0.5em 0.5em;
		}
	}
	.caption, figcaption, caption {
		font-style: italic;
		font-size: 90%;
	}
	.caption::before, figcaption::before, figcaption > .marker {
		font-weight: bold;
	}
	.caption, figcaption {
		counter-increment: figure;
	}

	/* DL list is indented 2em, but figure inside it is not */
	dd > .figure, dd > figure { margin-left: -2em; }

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

	.issue, .note, .example, .assertion, .advisement, blockquote,
	.amendment, .correction, .addition {
		margin: 1em auto;
		padding: .5em;
		border: .5em;
		border-left-style: solid;
		page-break-inside: avoid;
	}
	span.issue, span.note {
		padding: .1em .5em .15em;
		border-right-style: solid;
	}

	blockquote > :first-child,
	.note  > p:first-child,
	.issue > p:first-child,
	.amendment > p:first-child,
	.correction > p:first-child,
	.addition > p:first-child {
		margin-top: 0;
	}
	blockquote > :last-child,
	.note  > p:last-child,
	.issue > p:last-child,
	.amendment > p:last-child,
	.correction > p:last-child,
	.addition > p:last-child {
		margin-bottom: 0;
	}


	.issue::before, .issue > .marker,
	.example::before, .example > .marker,
	.note::before, .note > .marker,
	details.note > summary > .marker,
	.amendment::before, .amendment > .marker,
	details.amendment > summary > .marker,
	.addition::before, .addition > .marker,
	addition.amendment > summary > .marker,
	.correction::before, .correction > .marker,
	correction.amendment > summary > .marker
	{
		text-transform: uppercase;
		padding-right: 1em;
	}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


/*
Alternate table alignment rules

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

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

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

Possible extra rowspan handling

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

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

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


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

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

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

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

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

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

		.toc li {
			clear: both;
		}

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

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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

.outdated-warning span {
	display: block;
}

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

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

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

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

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



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

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

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

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

	@media not print {
		.overlarge {
			overflow-x: auto;
			/* See Lea Verou's explanation background-attachment:
			* http://lea.verou.me/2012/04/background-attachment-local/
			*
			background: top left  / 4em 100% linear-gradient(to right,  #ffffff, rgba(255, 255, 255, 0)) local,
						top right / 4em 100% linear-gradient(to left, #ffffff, rgba(255, 255, 255, 0)) local,
						top left  / 1em 100% linear-gradient(to right,  #c3c3c5, rgba(195, 195, 197, 0)) scroll,
						top right / 1em 100% linear-gradient(to left, #c3c3c5, rgba(195, 195, 197, 0)) scroll,
						white;
			background-repeat: no-repeat;
			*/
		}
	}
</style>
<style>
    table, th, td {
      border: 1px solid black;
      border-collapse: collapse;
      vertical-align: top;
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    th, td {
      border-left: none;
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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 }
    blockquote ul { background: inherit; }
    blockquote code.highlight:not(.idl) { padding: initial; }
    blockquote c-[a] { color: inherit; } /* Keyword.Declaration */
    blockquote c-[b] { color: inherit; } /* Keyword.Type */
    blockquote c-[c] { color: inherit; } /* Comment */
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    blockquote c-[c1] { color: inherit; } /* Comment.Single */
    blockquote c-[cs] { color: inherit; } /* Comment.Special */
    blockquote c-[kc] { color: inherit; } /* Keyword.Constant */
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    blockquote c-[ni] { color: inherit; } /* Name.Entity */
    blockquote c-[ne] { color: inherit; } /* Name.Exception */
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    blockquote c-[mi] { color: inherit; } /* Literal.Number.Integer */
    blockquote c-[mo] { color: inherit; } /* Literal.Number.Oct */
    blockquote c-[sb] { color: inherit; } /* Literal.String.Backtick */
    blockquote c-[sc] { color: inherit; } /* Literal.String.Char */
    blockquote c-[sd] { color: inherit; } /* Literal.String.Doc */
    blockquote c-[se] { color: inherit; } /* Literal.String.Escape */
    blockquote c-[sh] { color: inherit; } /* Literal.String.Heredoc */
    blockquote c-[si] { color: inherit; } /* Literal.String.Interpol */
    blockquote c-[sx] { color: inherit; } /* Literal.String.Other */
    blockquote c-[sr] { color: inherit; } /* Literal.String.Regex */
    blockquote c-[ss] { color: inherit; } /* Literal.String.Symbol */
    blockquote c-[vc] { color: inherit; } /* Name.Variable.Class */
    blockquote c-[vg] { color: inherit; } /* Name.Variable.Global */
    blockquote c-[vi] { color: inherit; } /* Name.Variable.Instance */
    blockquote c-[il] { color: inherit; } /* Literal.Number.Integer.Long */
  </style>
  <meta content="Bikeshed version 74068a90b, updated Wed Mar 22 17:34:51 2023 -0700" name="generator">
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   <p data-fill-with="logo"></p>
   <h1 class="p-name no-ref" id="title">P2876R1<br>Proposal to extend <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> with more constructors and accessors</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="2024-05-22">2024-05-22</time></span></h2>
   <div data-fill-with="spec-metadata">
    <dl>
     <dt>This version:
     <dd><a class="u-url" href="https://isocpp.org/files/papers/P2876R1.html">https://isocpp.org/files/papers/P2876R1.html</a>
     <dt class="editor">Authors:
     <dd class="editor p-author h-card vcard"><a class="p-name fn u-email email" href="mailto:daniel.towner@intel.com">Daniel Towner</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:m.kretz@gsi.de">Matthias Kretz</a> (<span class="p-org org">GSI</span>)
     <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>)
     <dt>Audience:
     <dd>LEWG
     <dt>Project:
     <dd>ISO/IEC 14882 Programming Languages — C++, ISO/IEC JTC1/SC22/WG21
    </dl>
   </div>
   <div data-fill-with="warning"></div>
   <hr title="Separator for header">
  </div>
  <div class="p-summary" data-fill-with="abstract">
   <h2 class="no-num no-toc no-ref heading settled" id="abstract"><span class="content">Abstract</span></h2>
   <p>Proposal to provide additional constructors and accessors for <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code></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="#intro"><span class="secno">1</span> <span class="content">Motivation</span></a>
    <li>
     <a href="#bitset"><span class="secno">2</span> <span class="content">Bitset</span></a>
     <ol class="toc">
      <li><a href="#bitset_impl"><span class="secno">2.1</span> <span class="content">Implementation experience</span></a>
     </ol>
    <li>
     <a href="#integral_mask_ctor"><span class="secno">3</span> <span class="content">Conversion to and from integral value bit representations</span></a>
     <ol class="toc">
      <li><a href="#compact_ctor"><span class="secno">3.1</span> <span class="content">Building a mask from a compact bit representation</span></a>
      <li><a href="#compact_accessor"><span class="secno">3.2</span> <span class="content">Compact bit accessor</span></a>
      <li><a href="#integral_impl"><span class="secno">3.3</span> <span class="content">Implementation experience</span></a>
     </ol>
    <li>
     <a href="#initialization_list"><span class="secno">4</span> <span class="content">Initialising from a list</span></a>
     <ol class="toc">
      <li><a href="#variadic_ctor"><span class="secno">4.1</span> <span class="content">Variadic constructor</span></a>
      <li><a href="#initialisation_list_constructor"><span class="secno">4.2</span> <span class="content">Initialisation-list constructor</span></a>
     </ol>
    <li><a href="#wording"><span class="secno">5</span> <span class="content">Wording</span></a>
    <li><a href="#revisions"><span class="secno">6</span> <span class="content">Revision History</span></a>
    <li>
     <a href="#references"><span class="secno"></span> <span class="content">References</span></a>
     <ol class="toc">
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   <h2 class="heading settled" data-level="1" id="intro"><span class="secno">1. </span><span class="content">Motivation</span><a class="self-link" href="#intro"></a></h2>
   <p>The <a data-link-type="biblio" href="#biblio-p1928r3" title="Merge data-parallel types from the Parallelism TS 2">[P1928R3]</a> proposal outlines a number of constructors and accessors which
can be used to move data in and out of a <code class="highlight"><c- n>simd</c-></code> object. However, there are a number
of other data types in the standard C++ libraries which provide a form of
data-parallel value storage, such as <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>bitset</c-></code> and types which implement
the <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>contiguous_range</c-></code> concept such as <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>span</c-></code>. It is desirable
to be able to easily convert those to and from <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> values too. In this
paper we shall examine the benefits of providing constructors for building <code class="highlight"><c- n>simd</c-></code> or <code class="highlight"><c- n>simd_mask</c-></code> values from other types, and for adding accessors
which allow them to be converted back into other types from their equivalent
SIMD values. Some of these proposals were briefly outlined in <a data-link-type="biblio" href="#biblio-p2638r0" title="Intel&apos;s response to P1915R0 for std::simd parallelism in TS 2">[P2638R0]</a>, and
some proposals are new.</p>
   <h2 class="heading settled" data-level="2" id="bitset"><span class="secno">2. </span><span class="content">Bitset</span><a class="self-link" href="#bitset"></a></h2>
   <p><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>bitset</c-></code> has many characteristics in common with a <code class="highlight"><c- n>simd_mask</c-></code> value and it is useful to be able to use a <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>bitset</c-></code> value as a mask and
vice versa. There is no easy way for a programmer to concisely and efficiently
achieve these interchange conversions so we propose that a constructor and an
accessor are provided in <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code>. Firstly, a constructor can be provided
for a <code class="highlight"><c- n>simd_mask</c-></code>:</p>
<pre class="language-cpp highlight"><c- k>constexpr</c-> <c- n>simd_mask</c-><c- p>(</c-><c- k>const</c-> <c- n>std</c-><c- o>::</c-><c- n>bitset</c-><c- o>&lt;</c-><c- n>size</c-><c- o>>&amp;</c-> <c- n>b</c-><c- p>);</c-></pre>
   <p>This constructor allows a bitset with the same number of elements as a SIMD value to be used to build a <code class="highlight"><c- n>simd_mask</c-></code> for that value. Each element in the constructor mask has the same boolean value as the
respective element from the incoming bitset. It is not marked as explicit, so a bitset
can be conveniently used anywhere that a simd_mask could be.</p>
   <p>A <code class="highlight"><c- n>simd_mask</c-></code> can be converted into an equivalent <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>bitset</c-></code> using a conversion operator:</p>
<pre class="language-cpp highlight"><c- k>constexpr</c-> <c- n>simd_mask</c-><c- o>::</c-><c- k>operator</c-> <c- n>std</c-><c- o>::</c-><c- n>bitset</c-><c- o>&lt;</c-><c- n>size</c-><c- o>></c-><c- p>()</c-> <c- k>const</c-><c- p>;</c-></pre>
   <p>or alternatively though a named method which makes it explicitly clear that the conversion is happening:</p>
<pre class="language-cpp highlight"><c- k>constexpr</c-> <c- n>std</c-><c- o>::</c-><c- n>bitset</c-><c- o>&lt;</c-><c- n>size</c-><c- o>></c-> <c- n>simd_mask</c-><c- o>::</c-><c- n>to_bitset</c-><c- p>()</c-> <c- k>const</c-><c- p>;</c-></pre>
   <p>The output bitset value will have the same size as the simd_mask, and every
element in the bitset will have the same value as its respective simd_mask
element.</p>
   <h3 class="heading settled" data-level="2.1" id="bitset_impl"><span class="secno">2.1. </span><span class="content">Implementation experience</span><a class="self-link" href="#bitset_impl"></a></h3>
   <p>When working with ABIs which already have compact bit representations (e.g.,
AVX512 predicate registers) then converting to and from bitset is efficient.
Conversion to and from wide element representations of masks (e.g., SSE or AVX),
is more expensive but the <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> library
implementation is able to exploit the internal implementation details to make it
more efficient than anything that the user could do using the public <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> API.</p>
   <h2 class="heading settled" data-level="3" id="integral_mask_ctor"><span class="secno">3. </span><span class="content">Conversion to and from integral value bit representations</span><a class="self-link" href="#integral_mask_ctor"></a></h2>
   <p>There are several ways that <code class="highlight"><c- n>simd_mask</c-></code>-like values could be stored, ranging from
wide-element values (e.g., SSE, AVX), compact mask (e.g., ARM or AVX-512
predicates), bitsets, or byte-valued memory regions (e.g., <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd_mask</c-><c- o>::</c-><c- n>copy_to</c-></code>). The <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> API already has the ability
to convert wide elements to and from simd_masks using, for example, the <code class="highlight"><c- k>operator</c-><c- o>+</c-></code>. However, it can be useful to be able to convert to and from
compact masks represented using raw bits stored in an integral value (something
which <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>bitset</c-></code> also supports explicitly). In this section we propose
ways of constructing and accessing packed bits stored in integral values.</p>
   <h3 class="heading settled" data-level="3.1" id="compact_ctor"><span class="secno">3.1. </span><span class="content">Building a mask from a compact bit representation</span><a class="self-link" href="#compact_ctor"></a></h3>
   <p>When working with SIMD values of fixed sizes (rather than native types whose
size can vary by target) it can be useful to express a mask pattern directly.
For example, suppose a programmer requires a custom bit pattern, such as <code class="highlight"><c- mb>0b10101101011010010101</c-></code>. There is currently no easy or direct way to encode
that pattern into a simd_mask value. For example, <code class="highlight"><c- n>simd_mask</c-></code> has
constructors which take a generator or a byte-valued memory region as input, but neither of
these lend themselves to concisely encoding an arbitrary bit pattern.</p>
   <p>We propose that the following constructor could be provided:</p>
<pre class="language-cpp highlight"><c- k>constexpr</c-> <c- n>simd_mask</c-><c- p>(</c-><c- k>auto</c-> <c- n>std</c-><c- o>::</c-><c- n>unsigned_integral</c-> <c- n>bits</c-><c- p>)</c-> <c- k>noexcept</c-><c- p>;</c-></pre>
   <p>The simd_mask is constructed such that the first (rightmost, least significant)
M bit positions are set to the corresponding bit values of <code class="highlight"><c- n>bits</c-></code>, where
M is the smaller of N and the number of bits in the value representation of <code class="highlight"><c- n>pattern</c-></code>. If M is less than the size of the mask then the remaining bit
positions are initialized to zeroes.</p>
   <p>The issue with using a <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>unsigned_integral</c-></code> as the container for the
input is that it might contain too many bits for a small mask, or too few bits
for a big mask. Without a way of representing an arbitrary number of bits in
an integral value (e.g., C23’s bit-precise <code class="highlight"><c- n>_BitInt</c-></code>) we are limited to only
allowing up to 64-bits to be inserted into a simd_mask, analagous to the same
limits as a <code class="highlight"><c- nl>std</c-><c- p>:</c-><c- n>bitset</c-></code>.</p>
   <h3 class="heading settled" data-level="3.2" id="compact_accessor"><span class="secno">3.2. </span><span class="content">Compact bit accessor</span><a class="self-link" href="#compact_accessor"></a></h3>
   <p>There is currently no easy way for mask bits to be extracted from a <code class="highlight"><c- n>simd_mask</c-></code> in a compact form. Neither of the existing methods to extract is
efficient when used for this. For example, a mask’s values can becauseextracted
a an array of bytes:</p>
<pre class="language-cpp highlight"><c- k>auto</c-> <c- n>simd_mask</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c-> <c- n>mask</c-> <c- o>=</c-> <c- p>...;</c->

<c- b>bool</c-> <c- n>maskAsBytes</c-><c- p>[</c-><c- mi>1024</c-><c- p>];</c->
<c- n>mask</c-><c- p>.</c-><c- n>copy_to</c-><c- p>(</c-><c- n>maskAsBytes</c-><c- p>);</c-></pre>
   <p>This copies each mask element to a byte in the supplied output iterator, but
there is no easy way to go from that form to a compact bit representation.</p>
   <p>The other way to extract the contents of a simd_mask is to convert it into a
SIMD value representation. In the following example the mask contents are
converted to elements which are either 0.0f or 1.0f according to their respective mask
bit:</p>
<pre class="language-cpp highlight"><c- k>auto</c-> <c- n>simd_mask</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c-> <c- n>mask</c-> <c- o>=</c-> <c- p>...;</c->

<c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c-> <c- n>output</c-> <c- o>=</c-> <c- o>+</c-><c- n>mask</c-><c- p>;</c-></pre>
   <p>But this doesn’t allow easy conversion to a copmact set of bits either.</p>
   <p>To make it possible to extract compacted bits as an unsigned integral value we
propose to borrow an idea from <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>bitst</c-></code>and provide:</p>
<pre class="language-cpp highlight"><c- k>constexpr</c-> <c- n>std</c-><c- o>::</c-><c- b>uint64_t</c-> <c- nf>simd_mask::to_ullong</c-><c- p>()</c-> <c- k>const</c-> <c- k>noexcept</c-><c- p>;</c-></pre>
   <p>This will copy up to 64 mask elements to an output value, storing each mask
element in a single bit. Unfortunately this potentially loses bits, since <code class="highlight"><c- n>to_ullong</c-></code> will only emit those bits which can be contained in a 64-bit
representation. As with the unsigned_integral constructor this could be solved
if the C23 bit-precise <code class="highlight"><c- n>_BitInt</c-></code> type was available in C++.</p>
   <h3 class="heading settled" data-level="3.3" id="integral_impl"><span class="secno">3.3. </span><span class="content">Implementation experience</span><a class="self-link" href="#integral_impl"></a></h3>
   <p>In some problem domains, such as telecommunications, compact representations of
bits as integers are very common and it is very important to be able to
efficiently convert to and from this format. Providing an API to make it easy to
convert masks to and from this representation proved invaluable in writing
concise meaningful code in this problem domain.</p>
   <p>On a machine with compact mask representation (e.g., we tested on AVX-512) the
masks are already stored in compact form, so converting to and from an integer
representation was trivial.</p>
   <p>On a machine with wide mask representation (e.g., SSE, AVX, AVX2) it is not easy or
efficient to use compact representation if only the standard <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> API
can be used (e.g., converting to a byte memory and then from that to individual
bits). Efficient conversion is only possible if target-specific instructions are
used, and the programmer writes non-portable code to use them. For these targets
then, it was better that a uniform API into a compact format was provided and
handled efficiently by <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> itself.</p>
   <p>Constructing and accessing bits through the bitset pathway (e.g., <code class="highlight"><c- n>mask</c-><c- p>.</c-><c- n>to_bitset</c-><c- p>().</c-><c- n>to_ullong</c-><c- p>()</c-></code>) proved also to be inefficient under some
conditions. Even on targets which already had compact mask representation, the
extra step in storing data temporarily in a bitset added to the overhead of the
conversion. The extra step was difficult to remove because data would be moved
in/out of a bitmask in 64-bit blocks, and in/out of a simd_mask in blocks whose
sizes were governed by the operation in progress. This mismatch in sizes made it
difficult to smooth out the data flow across the conversion. Further work will
be done to determine if better code generation is possible.</p>
   <h2 class="heading settled" data-level="4" id="initialization_list"><span class="secno">4. </span><span class="content">Initialising from a list</span><a class="self-link" href="#initialization_list"></a></h2>
   <p>Inevitably the programmer will want to be able to construct SIMD values with
lists of known constants, such as for a lookup table. A reasonable way to achieve
this would be to an initialisation list style syntax, as follows:</p>
<pre class="language-cpp highlight"><c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- mi>4</c-><c- o>></c-> <c- n>myLut</c-> <c- o>=</c-> <c- p>{</c-><c- mf>2.f</c-><c- p>,</c-> <c- mf>9.f</c-><c- p>,</c-> <c- mf>23.f</c-><c- p>,</c-> <c- mf>45.f</c-><c- p>};</c-></pre>
   <p>In this case the number of values in the initialiser list exactly matches the
number of elements in the <code class="highlight"><c- n>simd</c-></code> value. We recommend that an exact match should
be enforced to avoid accidental mismatches. For example:</p>
<pre class="highlight"><c- n>simd</c-><c- o>&lt;</c-><c- b>int32_t</c-><c- o>></c-> <c- n>table</c-> <c- o>=</c-> <c- p>{</c-><c- mi>1</c-><c- p>,</c-> <c- mi>2</c-><c- p>,</c-> <c- mi>3</c-><c- p>,</c-> <c- mi>4</c-><c- p>,</c-> <c- mi>5</c-><c- p>,</c-> <c- mi>6</c-><c- p>,</c-> <c- mi>7</c-><c- p>,</c-> <c- mi>8</c-><c- p>};</c-></pre>
   <p>On an Intel SSE target the default <code class="highlight"><c- n>simd</c-></code> will have 4 values, so the table is
truncated. On an Intel AVX-512 target the <code class="highlight"><c- n>simd</c-></code> will have 16 values, so some
values will be left value initialised (or undefined). Only on an Intel AVX
target will the <code class="highlight"><c- n>simd</c-></code> contain exactly the right number of values. This change
in behaviour by a change in target is unlikely to be what the user requires or
expects. If the user created a table with a set number of values, then the
destination <code class="highlight"><c- n>simd</c-></code> should match in size. This differs to the initialisation of
an array, for example, where setting too few elements will result in other
elements being value-initialised.</p>
   <p>To permit an initialisation list syntax for <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> it is necessary to
create a constructor which allows this style. There are two possible ways to
achieve this: with a variadic constructor, and with an explicit initialisation
list overload. We look at both of these in turn, and then discuss some of their
trade-offs.</p>
   <h3 class="heading settled" data-level="4.1" id="variadic_ctor"><span class="secno">4.1. </span><span class="content">Variadic constructor</span><a class="self-link" href="#variadic_ctor"></a></h3>
   <p>A variadic constructor takes a variadic number of arguments and puts each
argument into the respective SIMD value element position. Our initial idea for
the constructor is to define it as follows:</p>
<pre class="language-cpp highlight"><c- k>template</c-><c- o>&lt;</c-><c- k>typename</c-> <c- nc>U0</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>U1</c-><c- p>,</c-> <c- k>typename</c-><c- p>...</c-> <c- n>Us</c-><c- o>></c->
<c- k>constexpr</c-> <c- n>simd</c-><c- o>::</c-><c- n>simd</c-><c- p>(</c-><c- n>U0</c-> <c- n>u0</c-><c- p>,</c-> <c- n>U1</c-> <c- n>u1</c-><c- p>,</c-> <c- n>Us</c-><c- p>...</c-> <c- n>us</c-><c- p>)</c->
<c- k>requires</c-><c- p>(</c-><c- k>sizeof</c-><c- p>...(</c-><c- n>Us</c-><c- p>)</c-> <c- o>==</c-> <c- p>(</c-><c- n>size</c-> <c- o>-</c-> <c- mi>2</c-><c- p>));</c-></pre>
   <p>This constructor requires one element to be given for every possible element of
the <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> being constructed. Note that two initial arguments are provided,
followed by a variadic pack. We believe that having a variadic pack which is
easily differentiated to the other common constructor - the broadcast - will
reduce compilation times. This constructor is only considered when there are at
least two arguments, rather than if it took a single pack which would then need
to be considered for every call to a constructor.</p>
   <h3 class="heading settled" data-level="4.2" id="initialisation_list_constructor"><span class="secno">4.2. </span><span class="content">Initialisation-list constructor</span><a class="self-link" href="#initialisation_list_constructor"></a></h3>
   <p>An initializer-list constructor would be specified like this:</p>
<pre class="language-cpp highlight"><c- k>constexpr</c-> <c- n>simd</c-><c- p>(</c-><c- n>std</c-><c- o>::</c-><c- n>initializer_list</c-><c- o>&lt;</c-><c- n>value_type</c-><c- o>></c-> <c- n>list</c-><c- p>);</c-></pre>
   <p>While this does work in principal, the difficulty with it is that it does not
allow the size of the source list to be known at compile-time, making it
impossible to check that the input source list matches the <code class="highlight"><c- n>simd</c-></code>’s size. That
can only be done by a run-time check, which adds extra overhead.</p>
   <h2 class="heading settled" data-level="5" id="wording"><span class="secno">5. </span><span class="content">Wording</span><a class="self-link" href="#wording"></a></h2>
   <p>TBD</p>
   <h2 class="heading settled" data-level="6" id="revisions"><span class="secno">6. </span><span class="content">Revision History</span><a class="self-link" href="#revisions"></a></h2>
   <p>R0 => R1</p>
   <ul>
    <li data-md>
     <p>Moved range constructor into its own paper <span>[P3299R0]</span></p>
    <li data-md>
     <p>Updated discussion of initialiser-list-like constructor.</p>
   </ul>
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  <h2 class="no-num no-ref heading settled" id="references"><span class="content">References</span><a class="self-link" href="#references"></a></h2>
  <h3 class="no-num no-ref heading settled" id="informative"><span class="content">Informative References</span><a class="self-link" href="#informative"></a></h3>
  <dl>
   <dt id="biblio-p1928r3">[P1928R3]
   <dd>Matthias Kretz. <a href="https://wg21.link/p1928r3"><cite>Merge data-parallel types from the Parallelism TS 2</cite></a>. 3 February 2023. URL: <a href="https://wg21.link/p1928r3">https://wg21.link/p1928r3</a>
   <dt id="biblio-p2638r0">[P2638R0]
   <dd>Daniel Towner. <a href="https://wg21.link/p2638r0"><cite>Intel's response to P1915R0 for std::simd parallelism in TS 2</cite></a>. 22 September 2022. URL: <a href="https://wg21.link/p2638r0">https://wg21.link/p2638r0</a>
  </dl>