<!doctype html><html lang="en">
 <head>
  <meta content="text/html; charset=utf-8" http-equiv="Content-Type">
  <meta content="width=device-width, initial-scale=1, shrink-to-fit=no" name="viewport">
  <title>P3445R0: Add utilities for easier type/bit casting in std::simd</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;
    }
    th, td {
      border-left: none;
      border-right: none;
      padding: 0px 10px;
    }
    th {
      text-align: center;
    }

    del { background: #fcc; color: #000; text-decoration: line-through; }
    ins { background: #cfc; color: #000; }
    blockquote .highlight:not(.idl) { background: initial; margin: initial; padding: 0.5em }
    blockquote ul { background: inherit; }
    blockquote code.highlight:not(.idl) { padding: initial; }
    blockquote c-[a] { color: inherit; } /* Keyword.Declaration */
    blockquote c-[b] { color: inherit; } /* Keyword.Type */
    blockquote c-[c] { color: inherit; } /* Comment */
    blockquote c-[d] { color: inherit; } /* Comment.Multiline */
    blockquote c-[e] { color: inherit; } /* Name.Attribute */
    blockquote c-[f] { color: inherit; } /* Name.Tag */
    blockquote c-[g] { color: inherit; } /* Name.Variable */
    blockquote c-[k] { color: inherit; } /* Keyword */
    blockquote c-[l] { color: inherit; } /* Literal */
    blockquote c-[m] { color: inherit; } /* Literal.Number */
    blockquote c-[n] { color: inherit; } /* Name */
    blockquote c-[o] { color: inherit; } /* Operator */
    blockquote c-[p] { color: inherit; } /* Punctuation */
    blockquote c-[s] { color: inherit; } /* Literal.String */
    blockquote c-[t] { color: inherit; } /* Literal.String.Single */
    blockquote c-[u] { color: inherit; } /* Literal.String.Double */
    blockquote c-[cp] { color: inherit; } /* Comment.Preproc */
    blockquote c-[c1] { color: inherit; } /* Comment.Single */
    blockquote c-[cs] { color: inherit; } /* Comment.Special */
    blockquote c-[kc] { color: inherit; } /* Keyword.Constant */
    blockquote c-[kn] { color: inherit; } /* Keyword.Namespace */
    blockquote c-[kp] { color: inherit; } /* Keyword.Pseudo */
    blockquote c-[kr] { color: inherit; } /* Keyword.Reserved */
    blockquote c-[ld] { color: inherit; } /* Literal.Date */
    blockquote c-[nc] { color: inherit; } /* Name.Class */
    blockquote c-[no] { color: inherit; } /* Name.Constant */
    blockquote c-[nd] { color: inherit; } /* Name.Decorator */
    blockquote c-[ni] { color: inherit; } /* Name.Entity */
    blockquote c-[ne] { color: inherit; } /* Name.Exception */
    blockquote c-[nf] { color: inherit; } /* Name.Function */
    blockquote c-[nl] { color: inherit; } /* Name.Label */
    blockquote c-[nn] { color: inherit; } /* Name.Namespace */
    blockquote c-[py] { color: inherit; } /* Name.Property */
    blockquote c-[ow] { color: inherit; } /* Operator.Word */
    blockquote c-[mb] { color: inherit; } /* Literal.Number.Bin */
    blockquote c-[mf] { color: inherit; } /* Literal.Number.Float */
    blockquote c-[mh] { color: inherit; } /* Literal.Number.Hex */
    blockquote c-[mi] { color: inherit; } /* Literal.Number.Integer */
    blockquote c-[mo] { color: inherit; } /* Literal.Number.Oct */
    blockquote c-[sb] { color: inherit; } /* Literal.String.Backtick */
    blockquote c-[sc] { color: inherit; } /* Literal.String.Char */
    blockquote c-[sd] { color: inherit; } /* Literal.String.Doc */
    blockquote c-[se] { color: inherit; } /* Literal.String.Escape */
    blockquote c-[sh] { color: inherit; } /* Literal.String.Heredoc */
    blockquote c-[si] { color: inherit; } /* Literal.String.Interpol */
    blockquote c-[sx] { color: inherit; } /* Literal.String.Other */
    blockquote c-[sr] { color: inherit; } /* Literal.String.Regex */
    blockquote c-[ss] { color: inherit; } /* Literal.String.Symbol */
    blockquote c-[vc] { color: inherit; } /* Name.Variable.Class */
    blockquote c-[vg] { color: inherit; } /* Name.Variable.Global */
    blockquote c-[vi] { color: inherit; } /* Name.Variable.Instance */
    blockquote c-[il] { color: inherit; } /* Literal.Number.Integer.Long */
  </style>
  <meta content="Bikeshed version 74068a90b, updated Wed Mar 22 17:34:51 2023 -0700" name="generator">
  <link href="http://wg21.link/P3440R5" rel="canonical">
  <link href="https://isocpp.org/favicon.ico" rel="icon">
  <meta content="aaaa543789f94e6fdd5ac5b6c298f5b6c92bc727" name="document-revision">
<style>
.ins, ins, ins * {
    background-color: rgb(200, 250, 200);
    color: rgb(0, 136, 0);
    text-decoration: none;
}
.span, span, span * {
    white-space: pre
}
</style>
<style>/* style-autolinks */
.css.css, .property.property, .descriptor.descriptor {
    color: var(--a-normal-text);
    font-size: inherit;
    font-family: inherit;
}
.css::before, .property::before, .descriptor::before {
    content: "‘";
}
.css::after, .property::after, .descriptor::after {
    content: "’";
}
.property, .descriptor {
    /* Don't wrap property and descriptor names */
    white-space: nowrap;
}
.type { /* CSS value <type> */
    font-style: italic;
}
pre .property::before, pre .property::after {
    content: "";
}
[data-link-type="property"]::before,
[data-link-type="propdesc"]::before,
[data-link-type="descriptor"]::before,
[data-link-type="value"]::before,
[data-link-type="function"]::before,
[data-link-type="at-rule"]::before,
[data-link-type="selector"]::before,
[data-link-type="maybe"]::before {
    content: "‘";
}
[data-link-type="property"]::after,
[data-link-type="propdesc"]::after,
[data-link-type="descriptor"]::after,
[data-link-type="value"]::after,
[data-link-type="function"]::after,
[data-link-type="at-rule"]::after,
[data-link-type="selector"]::after,
[data-link-type="maybe"]::after {
    content: "’";
}

[data-link-type].production::before,
[data-link-type].production::after,
.prod [data-link-type]::before,
.prod [data-link-type]::after {
    content: "";
}

[data-link-type=element],
[data-link-type=element-attr] {
    font-family: Menlo, Consolas, "DejaVu Sans Mono", monospace;
    font-size: .9em;
}
[data-link-type=element]::before { content: "<" }
[data-link-type=element]::after  { content: ">" }

[data-link-type=biblio] {
    white-space: pre;
}
</style>
<style>/* style-colors */

/* Any --*-text not paired with a --*-bg is assumed to have a transparent bg */
:root {
    color-scheme: light dark;

    --text: black;
    --bg: white;

    --unofficial-watermark: url(https://www.w3.org/StyleSheets/TR/2016/logos/UD-watermark);

    --logo-bg: #1a5e9a;
    --logo-active-bg: #c00;
    --logo-text: white;

    --tocnav-normal-text: #707070;
    --tocnav-normal-bg: var(--bg);
    --tocnav-hover-text: var(--tocnav-normal-text);
    --tocnav-hover-bg: #f8f8f8;
    --tocnav-active-text: #c00;
    --tocnav-active-bg: var(--tocnav-normal-bg);

    --tocsidebar-text: var(--text);
    --tocsidebar-bg: #f7f8f9;
    --tocsidebar-shadow: rgba(0,0,0,.1);
    --tocsidebar-heading-text: hsla(203,20%,40%,.7);

    --toclink-text: var(--text);
    --toclink-underline: #3980b5;
    --toclink-visited-text: var(--toclink-text);
    --toclink-visited-underline: #054572;

    --heading-text: #005a9c;

    --hr-text: var(--text);

    --algo-border: #def;

    --del-text: red;
    --del-bg: transparent;
    --ins-text: #080;
    --ins-bg: transparent;

    --a-normal-text: #034575;
    --a-normal-underline: #bbb;
    --a-visited-text: var(--a-normal-text);
    --a-visited-underline: #707070;
    --a-hover-bg: rgba(75%, 75%, 75%, .25);
    --a-active-text: #c00;
    --a-active-underline: #c00;

    --blockquote-border: silver;
    --blockquote-bg: transparent;
    --blockquote-text: currentcolor;

    --issue-border: #e05252;
    --issue-bg: #fbe9e9;
    --issue-text: var(--text);
    --issueheading-text: #831616;

    --example-border: #e0cb52;
    --example-bg: #fcfaee;
    --example-text: var(--text);
    --exampleheading-text: #574b0f;

    --note-border: #52e052;
    --note-bg: #e9fbe9;
    --note-text: var(--text);
    --noteheading-text: hsl(120, 70%, 30%);
    --notesummary-underline: silver;

    --assertion-border: #aaa;
    --assertion-bg: #eee;
    --assertion-text: black;

    --advisement-border: orange;
    --advisement-bg: #fec;
    --advisement-text: var(--text);
    --advisementheading-text: #b35f00;

    --warning-border: red;
    --warning-bg: hsla(40,100%,50%,0.95);
    --warning-text: var(--text);

    --amendment-border: #330099;
    --amendment-bg: #F5F0FF;
    --amendment-text: var(--text);
    --amendmentheading-text: #220066;

    --def-border: #8ccbf2;
    --def-bg: #def;
    --def-text: var(--text);
    --defrow-border: #bbd7e9;

    --datacell-border: silver;

    --indexinfo-text: #707070;

    --indextable-hover-text: black;
    --indextable-hover-bg: #f7f8f9;

    --outdatedspec-bg: rgba(0, 0, 0, .5);
    --outdatedspec-text: black;
    --outdated-bg: maroon;
    --outdated-text: white;
    --outdated-shadow: red;

    --editedrec-bg: darkorange;
}
</style>
<style>/* style-counters */
body {
    counter-reset: example figure issue;
}
.issue {
    counter-increment: issue;
}
.issue:not(.no-marker)::before {
    content: "Issue " counter(issue);
}

.example {
    counter-increment: example;
}
.example:not(.no-marker)::before {
    content: "Example " counter(example);
}
.invalid.example:not(.no-marker)::before,
.illegal.example:not(.no-marker)::before {
    content: "Invalid Example" counter(example);
}

figcaption {
    counter-increment: figure;
}
figcaption:not(.no-marker)::before {
    content: "Figure " counter(figure) " ";
}
</style>
<style>/* style-issues */
a[href].issue-return {
    float: right;
    float: inline-end;
    color: var(--issueheading-text);
    font-weight: bold;
    text-decoration: none;
}
</style>
<style>/* style-md-lists */
/* This is a weird hack for me not yet following the commonmark spec
   regarding paragraph and lists. */
[data-md] > :first-child {
    margin-top: 0;
}
[data-md] > :last-child {
    margin-bottom: 0;
}
</style>
<style>/* style-selflinks */

:root {
    --selflink-text: white;
    --selflink-bg: gray;
    --selflink-hover-text: black;
}
.heading, .issue, .note, .example, li, dt {
    position: relative;
}
a.self-link {
    position: absolute;
    top: 0;
    left: calc(-1 * (3.5rem - 26px));
    width: calc(3.5rem - 26px);
    height: 2em;
    text-align: center;
    border: none;
    transition: opacity .2s;
    opacity: .5;
}
a.self-link:hover {
    opacity: 1;
}
.heading > a.self-link {
    font-size: 83%;
}
.example > a.self-link,
.note > a.self-link,
.issue > a.self-link {
    /* These blocks are overflow:auto, so positioning outside
       doesn't work. */
    left: auto;
    right: 0;
}
li > a.self-link {
    left: calc(-1 * (3.5rem - 26px) - 2em);
}
dfn > a.self-link {
    top: auto;
    left: auto;
    opacity: 0;
    width: 1.5em;
    height: 1.5em;
    background: var(--selflink-bg);
    color: var(--selflink-text);
    font-style: normal;
    transition: opacity .2s, background-color .2s, color .2s;
}
dfn:hover > a.self-link {
    opacity: 1;
}
dfn > a.self-link:hover {
    color: var(--selflink-hover-text);
}

a.self-link::before            { content: "¶"; }
.heading > a.self-link::before { content: "§"; }
dfn > a.self-link::before      { content: "#"; }
</style>
<style>/* style-syntax-highlighting */

code.highlight { padding: .1em; border-radius: .3em; }
pre.highlight, pre > code.highlight { display: block; padding: 1em; margin: .5em 0; overflow: auto; border-radius: 0; }

.highlight:not(.idl) { background: rgba(0, 0, 0, .03); }
c-[a] { color: #990055 } /* Keyword.Declaration */
c-[b] { color: #990055 } /* Keyword.Type */
c-[c] { color: #708090 } /* Comment */
c-[d] { color: #708090 } /* Comment.Multiline */
c-[e] { color: #0077aa } /* Name.Attribute */
c-[f] { color: #669900 } /* Name.Tag */
c-[g] { color: #222222 } /* Name.Variable */
c-[k] { color: #990055 } /* Keyword */
c-[l] { color: #000000 } /* Literal */
c-[m] { color: #000000 } /* Literal.Number */
c-[n] { color: #0077aa } /* Name */
c-[o] { color: #999999 } /* Operator */
c-[p] { color: #999999 } /* Punctuation */
c-[s] { color: #a67f59 } /* Literal.String */
c-[t] { color: #a67f59 } /* Literal.String.Single */
c-[u] { color: #a67f59 } /* Literal.String.Double */
c-[cp] { color: #708090 } /* Comment.Preproc */
c-[c1] { color: #708090 } /* Comment.Single */
c-[cs] { color: #708090 } /* Comment.Special */
c-[kc] { color: #990055 } /* Keyword.Constant */
c-[kn] { color: #990055 } /* Keyword.Namespace */
c-[kp] { color: #990055 } /* Keyword.Pseudo */
c-[kr] { color: #990055 } /* Keyword.Reserved */
c-[ld] { color: #000000 } /* Literal.Date */
c-[nc] { color: #0077aa } /* Name.Class */
c-[no] { color: #0077aa } /* Name.Constant */
c-[nd] { color: #0077aa } /* Name.Decorator */
c-[ni] { color: #0077aa } /* Name.Entity */
c-[ne] { color: #0077aa } /* Name.Exception */
c-[nf] { color: #0077aa } /* Name.Function */
c-[nl] { color: #0077aa } /* Name.Label */
c-[nn] { color: #0077aa } /* Name.Namespace */
c-[py] { color: #0077aa } /* Name.Property */
c-[ow] { color: #999999 } /* Operator.Word */
c-[mb] { color: #000000 } /* Literal.Number.Bin */
c-[mf] { color: #000000 } /* Literal.Number.Float */
c-[mh] { color: #000000 } /* Literal.Number.Hex */
c-[mi] { color: #000000 } /* Literal.Number.Integer */
c-[mo] { color: #000000 } /* Literal.Number.Oct */
c-[sb] { color: #a67f59 } /* Literal.String.Backtick */
c-[sc] { color: #a67f59 } /* Literal.String.Char */
c-[sd] { color: #a67f59 } /* Literal.String.Doc */
c-[se] { color: #a67f59 } /* Literal.String.Escape */
c-[sh] { color: #a67f59 } /* Literal.String.Heredoc */
c-[si] { color: #a67f59 } /* Literal.String.Interpol */
c-[sx] { color: #a67f59 } /* Literal.String.Other */
c-[sr] { color: #a67f59 } /* Literal.String.Regex */
c-[ss] { color: #a67f59 } /* Literal.String.Symbol */
c-[vc] { color: #0077aa } /* Name.Variable.Class */
c-[vg] { color: #0077aa } /* Name.Variable.Global */
c-[vi] { color: #0077aa } /* Name.Variable.Instance */
c-[il] { color: #000000 } /* Literal.Number.Integer.Long */
</style>
<style>/* style-darkmode */

@media (prefers-color-scheme: dark) {
    :root {
        --text: #ddd;
        --bg: black;

        --unofficial-watermark: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' width='400' height='400'%3E%3Cg fill='%23100808' transform='translate(200 200) rotate(-45) translate(-200 -200)' stroke='%23100808' stroke-width='3'%3E%3Ctext x='50%25' y='220' style='font: bold 70px sans-serif; text-anchor: middle; letter-spacing: 6px;'%3EUNOFFICIAL%3C/text%3E%3Ctext x='50%25' y='305' style='font: bold 70px sans-serif; text-anchor: middle; letter-spacing: 6px;'%3EDRAFT%3C/text%3E%3C/g%3E%3C/svg%3E");

        --logo-bg: #1a5e9a;
        --logo-active-bg: #c00;
        --logo-text: white;

        --tocnav-normal-text: #999;
        --tocnav-normal-bg: var(--bg);
        --tocnav-hover-text: var(--tocnav-normal-text);
        --tocnav-hover-bg: #080808;
        --tocnav-active-text: #f44;
        --tocnav-active-bg: var(--tocnav-normal-bg);

        --tocsidebar-text: var(--text);
        --tocsidebar-bg: #080808;
        --tocsidebar-shadow: rgba(255,255,255,.1);
        --tocsidebar-heading-text: hsla(203,20%,40%,.7);

        --toclink-text: var(--text);
        --toclink-underline: #6af;
        --toclink-visited-text: var(--toclink-text);
        --toclink-visited-underline: #054572;

        --heading-text: #8af;

        --hr-text: var(--text);

        --algo-border: #456;

        --del-text: #f44;
        --del-bg: transparent;
        --ins-text: #4a4;
        --ins-bg: transparent;

        --a-normal-text: #6af;
        --a-normal-underline: #555;
        --a-visited-text: var(--a-normal-text);
        --a-visited-underline: var(--a-normal-underline);
        --a-hover-bg: rgba(25%, 25%, 25%, .2);
        --a-active-text: #f44;
        --a-active-underline: var(--a-active-text);

        --borderedblock-bg: rgba(255, 255, 255, .05);

        --blockquote-border: silver;
        --blockquote-bg: var(--borderedblock-bg);
        --blockquote-text: currentcolor;

        --issue-border: #e05252;
        --issue-bg: var(--borderedblock-bg);
        --issue-text: var(--text);
        --issueheading-text: hsl(0deg, 70%, 70%);

        --example-border: hsl(50deg, 90%, 60%);
        --example-bg: var(--borderedblock-bg);
        --example-text: var(--text);
        --exampleheading-text: hsl(50deg, 70%, 70%);

        --note-border: hsl(120deg, 100%, 35%);
        --note-bg: var(--borderedblock-bg);
        --note-text: var(--text);
        --noteheading-text: hsl(120, 70%, 70%);
        --notesummary-underline: silver;

        --assertion-border: #444;
        --assertion-bg: var(--borderedblock-bg);
        --assertion-text: var(--text);

        --advisement-border: orange;
        --advisement-bg: #222218;
        --advisement-text: var(--text);
        --advisementheading-text: #f84;

        --warning-border: red;
        --warning-bg: hsla(40,100%,20%,0.95);
        --warning-text: var(--text);

        --amendment-border: #330099;
        --amendment-bg: #080010;
        --amendment-text: var(--text);
        --amendmentheading-text: #cc00ff;

        --def-border: #8ccbf2;
        --def-bg: #080818;
        --def-text: var(--text);
        --defrow-border: #136;

        --datacell-border: silver;

        --indexinfo-text: #aaa;

        --indextable-hover-text: var(--text);
        --indextable-hover-bg: #181818;

        --outdatedspec-bg: rgba(255, 255, 255, .5);
        --outdatedspec-text: black;
        --outdated-bg: maroon;
        --outdated-text: white;
        --outdated-shadow: red;

        --editedrec-bg: darkorange;
    }
    /* In case a transparent-bg image doesn't expect to be on a dark bg,
       which is quite common in practice... */
    img { background: white; }
}

@media (prefers-color-scheme: dark) {
    :root {
        --selflink-text: black;
        --selflink-bg: silver;
        --selflink-hover-text: white;
    }
}

@media (prefers-color-scheme: dark) {
    .highlight:not(.idl) { background: rgba(255, 255, 255, .05); }

    c-[a] { color: #d33682 } /* Keyword.Declaration */
    c-[b] { color: #d33682 } /* Keyword.Type */
    c-[c] { color: #2aa198 } /* Comment */
    c-[d] { color: #2aa198 } /* Comment.Multiline */
    c-[e] { color: #268bd2 } /* Name.Attribute */
    c-[f] { color: #b58900 } /* Name.Tag */
    c-[g] { color: #cb4b16 } /* Name.Variable */
    c-[k] { color: #d33682 } /* Keyword */
    c-[l] { color: #657b83 } /* Literal */
    c-[m] { color: #657b83 } /* Literal.Number */
    c-[n] { color: #268bd2 } /* Name */
    c-[o] { color: #657b83 } /* Operator */
    c-[p] { color: #657b83 } /* Punctuation */
    c-[s] { color: #6c71c4 } /* Literal.String */
    c-[t] { color: #6c71c4 } /* Literal.String.Single */
    c-[u] { color: #6c71c4 } /* Literal.String.Double */
    c-[ch] { color: #2aa198 } /* Comment.Hashbang */
    c-[cp] { color: #2aa198 } /* Comment.Preproc */
    c-[cpf] { color: #2aa198 } /* Comment.PreprocFile */
    c-[c1] { color: #2aa198 } /* Comment.Single */
    c-[cs] { color: #2aa198 } /* Comment.Special */
    c-[kc] { color: #d33682 } /* Keyword.Constant */
    c-[kn] { color: #d33682 } /* Keyword.Namespace */
    c-[kp] { color: #d33682 } /* Keyword.Pseudo */
    c-[kr] { color: #d33682 } /* Keyword.Reserved */
    c-[ld] { color: #657b83 } /* Literal.Date */
    c-[nc] { color: #268bd2 } /* Name.Class */
    c-[no] { color: #268bd2 } /* Name.Constant */
    c-[nd] { color: #268bd2 } /* Name.Decorator */
    c-[ni] { color: #268bd2 } /* Name.Entity */
    c-[ne] { color: #268bd2 } /* Name.Exception */
    c-[nf] { color: #268bd2 } /* Name.Function */
    c-[nl] { color: #268bd2 } /* Name.Label */
    c-[nn] { color: #268bd2 } /* Name.Namespace */
    c-[py] { color: #268bd2 } /* Name.Property */
    c-[ow] { color: #657b83 } /* Operator.Word */
    c-[mb] { color: #657b83 } /* Literal.Number.Bin */
    c-[mf] { color: #657b83 } /* Literal.Number.Float */
    c-[mh] { color: #657b83 } /* Literal.Number.Hex */
    c-[mi] { color: #657b83 } /* Literal.Number.Integer */
    c-[mo] { color: #657b83 } /* Literal.Number.Oct */
    c-[sa] { color: #6c71c4 } /* Literal.String.Affix */
    c-[sb] { color: #6c71c4 } /* Literal.String.Backtick */
    c-[sc] { color: #6c71c4 } /* Literal.String.Char */
    c-[dl] { color: #6c71c4 } /* Literal.String.Delimiter */
    c-[sd] { color: #6c71c4 } /* Literal.String.Doc */
    c-[se] { color: #6c71c4 } /* Literal.String.Escape */
    c-[sh] { color: #6c71c4 } /* Literal.String.Heredoc */
    c-[si] { color: #6c71c4 } /* Literal.String.Interpol */
    c-[sx] { color: #6c71c4 } /* Literal.String.Other */
    c-[sr] { color: #6c71c4 } /* Literal.String.Regex */
    c-[ss] { color: #6c71c4 } /* Literal.String.Symbol */
    c-[fm] { color: #268bd2 } /* Name.Function.Magic */
    c-[vc] { color: #cb4b16 } /* Name.Variable.Class */
    c-[vg] { color: #cb4b16 } /* Name.Variable.Global */
    c-[vi] { color: #cb4b16 } /* Name.Variable.Instance */
    c-[vm] { color: #cb4b16 } /* Name.Variable.Magic */
    c-[il] { color: #657b83 } /* Literal.Number.Integer.Long */
}
</style>
 <body class="h-entry">
  <div class="head">
   <p data-fill-with="logo"></p>
   <h1 class="p-name no-ref" id="title">P3445R0<br>Add utilities for easier type/bit casting in std::simd</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="2024-10-16">2024-10-16</time></span></h2>
   <div data-fill-with="spec-metadata">
    <dl>
     <dt>This version:
     <dd><a class="u-url" href="http://wg21.link/P3440R5">http://wg21.link/P3440R5</a>
     <dt class="editor">Author:
     <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>)
     <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>Two types of casting are very commonly found in code which uses <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code>: type-casts which change the element type while keeping the same number of elements, and bit-casts which can change both the type and the number of elements while keeping the underlying bit representation the same. Both of these are verbose when used and would benefit from alternative forms which make them more concise and more useable.</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>
     <ol class="toc">
      <li><a href="#type_casting_motivation"><span class="secno">1.1</span> <span class="content">Type casting</span></a>
      <li><a href="#bit_cast_motivation"><span class="secno">1.2</span> <span class="content">Bit-casting</span></a>
     </ol>
    <li><a href="#impl_experience"><span class="secno">2</span> <span class="content">Implementation experience</span></a>
    <li>
     <a href="#wording"><span class="secno">3</span> <span class="content">Wording</span></a>
     <ol class="toc">
      <li><a href="#wording_simd_synopsis"><span class="secno">3.1</span> <span class="content">Add [<strong>simd.casts</strong>] to the synopsis</span></a>
      <li><a href="#wording_simd_casts"><span class="secno">3.2</span> <span class="content">Add new simd cast section [<strong>simd.casts</strong>]</span></a>
     </ol>
   </ol>
  </nav>
  <main>
   <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>There are two types of casting in <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> - type-casting and bit-casting -
which would benefit from alternative forms which make them simpler to use, more
readable, and provide some extra utility which is otherwise unavailable.</p>
   <h3 class="heading settled" data-level="1.1" id="type_casting_motivation"><span class="secno">1.1. </span><span class="content">Type casting</span><a class="self-link" href="#type_casting_motivation"></a></h3>
   <p>Type casting in <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> occurs when the programmer wants to change the type
(and therefore value) of the elements of a <code class="highlight"><c- n>basic_simd</c-></code> without changing the
number of elements. The constructors in <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> allow this to be expressed
by a direct call to a constructor, or through a static_cast, but the type
definition of the destination must be setup in advance (e.g., using <code class="highlight"><c- n>rebind_simd_t</c-></code>). This can lead to code which is verbose, which in turn makes it
difficult the code difficult to read and understand quickly. We suggest that a
short-hand called <code class="highlight"><c- n>simd_cast</c-></code> is provided to make it easy to create the new type
and perform the element-by-element cast. The following code shows two ways to write a function using existing facilities:</p>
<pre class="language-cpp highlight"><c- k>template</c-><c- o>&lt;</c-><c- k>typename</c-> <c- nc>T</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>ABI</c-><c- o>></c->
<c- k>auto</c-> <c- n>incrementAsFloat1</c-><c- p>(</c-><c- k>const</c-> <c- n>basic_simd</c-><c- o>&lt;</c-><c- n>T</c-><c- p>,</c-> <c- n>ABI</c-><c- o>>&amp;</c-> <c- n>x</c-><c- p>)</c->
<c- p>{</c->
    <c- c1>// Use constructor.</c->
    <c- k>return</c-> <c- n>rebind_simd_t</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- n>basic_simd</c-><c- o>&lt;</c-><c- n>T</c-><c- p>,</c-> <c- n>ABI</c-><c- o>>></c-><c- p>(</c-><c- n>x</c-><c- p>)</c-> <c- o>+</c-> <c- mf>1.0f</c-><c- p>;</c->
<c- p>}</c->

<c- k>template</c-><c- o>&lt;</c-><c- k>typename</c-> <c- nc>T</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>ABI</c-><c- o>></c->
<c- k>auto</c-> <c- n>incrementAsFloat</c-><c- p>(</c-><c- k>const</c-> <c- n>basic_simd</c-><c- o>&lt;</c-><c- n>T</c-><c- p>,</c-> <c- n>ABI</c-><c- o>>&amp;</c-> <c- n>x</c-><c- p>)</c->
<c- p>{</c->
    <c- c1>// Use static_cast</c->
    <c- k>using</c-> <c- n>OUT</c-> <c- o>=</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- n>basic_simd</c-><c- o>&lt;</c-><c- n>T</c-><c- p>,</c-> <c- n>ABI</c-><c- o>>::</c-><c- n>size</c-><c- o>></c-><c- p>;</c->
    <c- k>return</c-> <c- k>static_cast</c-><c- o>&lt;</c-><c- n>OUT</c-><c- o>></c-><c- p>(</c-><c- n>x</c-><c- p>)</c-> <c- o>+</c-> <c- mf>1.0f</c-><c- p>;</c->
<c- p>}</c-></pre>
   <p>Note that there are other ways to write these, perhaps using extra aliases or
intermediate temporary variables to improve readability. However, it is much cleaner to be able to write them like this instead:</p>
<pre class="language-cpp highlight"><c- k>template</c-><c- o>&lt;</c-><c- k>typename</c-> <c- nc>T</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>ABI</c-><c- o>></c->
<c- k>auto</c-> <c- n>incrementAsFloat</c-><c- p>(</c-><c- k>const</c-> <c- n>basic_simd</c-><c- o>&lt;</c-><c- n>T</c-><c- p>,</c-> <c- n>ABI</c-><c- o>>&amp;</c-> <c- n>x</c-><c- p>)</c->
<c- p>{</c->
    <c- k>return</c-> <c- n>simd_cast</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c-><c- p>(</c-><c- n>x</c-><c- p>)</c-> <c- o>+</c-> <c- mf>1.0f</c-><c- p>;</c->
<c- p>}</c-></pre>
   <p>The <code class="highlight"><c- n>simd_cast</c-></code> variant is much more readable and it captures the intent of the
programmer very concisely.</p>
   <p>Of course there are times when the type-conversion may also require a change in
ABI (e.g., to create a new element type with an alternative target type) in
which <code class="highlight"><c- n>simd_cast</c-></code> wouldn’t suffice, but for the majority of the code we have
encountered the simpler <code class="highlight"><c- n>simd_cast</c-></code> captures the programmer’s requirements.</p>
   <p>Another good reason to use <code class="highlight"><c- n>simd_cast</c-></code> is that it enables simd-generic code to
be written. It is desirable to be able to write a generic algorithm once,
initially using scalar types to get the code working, and then later
substituting with a <code class="highlight"><c- n>simd</c-></code> type. In such code we want a uniform way to cast from
the implementation value type to a new type without having to reflect upon
whether the type is simd or scalar. A variant of <code class="highlight"><c- n>simd_cast</c-></code> can be provided
which works on scalar types or simd types. For example, the following code could
work with either in that case:</p>
<pre class="language-cpp highlight"><c- c1>// simd-generic function</c->
<c- k>auto</c-> <c- n>incrementAsFloat</c-><c- p>(</c-><c- k>auto</c-> <c- n>x</c-><c- p>)</c-> <c- p>{</c->
    <c- k>return</c-> <c- n>simd_cast</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c-><c- p>(</c-><c- n>x</c-><c- p>)</c-> <c- o>+</c-> <c- mf>1.0f</c-><c- p>;</c->
<c- p>}</c->

<c- c1>// Call with scalar:</c->
<c- k>auto</c-> <c- n>w1</c-> <c- o>=</c-> <c- n>incrementAsFloat</c-><c- p>(</c-><c- mf>23.f</c-><c- p>);</c->

<c- c1>// Call with simd:</c->
<c- k>auto</c-> <c- n>w2</c-> <c- o>=</c-> <c- n>incrementAsFloat</c-><c- p>(</c-><c- n>simd</c-><c- o>&lt;</c-><c- b>int</c-><c- o>></c-><c- p>(</c-><c- n>ptr</c-><c- p>));</c-></pre>
   <p>Finally, it is worth noting that while it would be straight-forward for
programmers to define <code class="highlight"><c- n>simd_cast</c-></code> or an equivalent themselves, it is such a
common utility that it is better for it to be defined just once in <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> itself.</p>
   <h3 class="heading settled" data-level="1.2" id="bit_cast_motivation"><span class="secno">1.2. </span><span class="content">Bit-casting</span><a class="self-link" href="#bit_cast_motivation"></a></h3>
   <p>The second type of casting operation is bit-casting, where the underlying bit
pattern is interpreted as though it were a different <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> value. In such
a conversion not only can the element type change, but the number of elements
could also change. For example, a <code class="highlight"><c- n>simd</c-><c- o>&lt;</c-><c- b>uint16_t</c-><c- p>,</c-> <c- mi>8</c-><c- o>></c-></code> could be bit-cast into <code class="highlight"><c- n>simd</c-><c- o>&lt;</c-><c- b>uint8_t</c-><c- p>,</c-> <c- mi>16</c-><c- o>></c-></code> to access the individual bytes of the original.</p>
   <p>The existing <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>bit_cast</c-></code> function already allows a value of a <code class="highlight"><c- n>basic_simd</c-></code> type to
be bit-cast into a different <code class="highlight"><c- n>basic_simd</c-></code> type:</p>
<pre class="language-cpp highlight"><c- c1>// Do something to a complex simd value ([[R2663R5]]).</c->
<c- k>template</c-><c- o>&lt;</c-><c- k>typename</c-> <c- nc>T</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>ABI</c-><c- o>></c->
<c- k>auto</c-> <c- n>fn</c-><c- p>(</c-><c- k>const</c-> <c- n>basic_simd</c-><c- o>&lt;</c-><c- n>std</c-><c- o>::</c-><c- n>complex</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-><c- p>,</c-> <c- n>ABI</c-><c- o>>&amp;</c-> <c- n>x</c-><c- p>)</c->
<c- p>{</c->
  <c- c1>// Setup a type to represent the raw floating point elements in the</c->
  <c- c1>// complex simd types. This doubles the number of elements in the simd.</c->
  <c- k>constexpr</c-> <c- b>int</c-> <c- n>numNativeCmplxElements</c-> <c- o>=</c-> <c- n>simd</c-><c- o>&lt;</c-><c- n>std</c-><c- o>::</c-><c- n>complex</c-><c- o>&lt;</c-><c- b>float</c-><c- o>>>::</c-><c- n>size</c-><c- p>;</c->
  <c- k>using</c-> <c- n>AsFloat</c-> <c- o>=</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- n>numNativeCmplxElements</c-> <c- o>*</c-> <c- mi>2</c-><c- o>></c-><c- p>;</c->

  <c- c1>// Do the bit-cast conversion to obtain the raw float elements.</c->
  <c- k>auto</c-> <c- n>asT</c-> <c- o>=</c-> <c- n>std</c-><c- o>::</c-><c- n>bit_cast</c-><c- o>&lt;</c-><c- n>AsFloat</c-><c- o>></c-><c- p>(</c-><c- n>x</c-><c- p>);</c->
  <c- k>auto</c-> <c- n>result</c-> <c- o>=</c-> <c- p>...;</c-> <c- c1>// e.g., call an Intel intrinsic like _mm512_fmsubadd_ps</c->

  <c- c1>// Convert back to its original complex form.</c->
  <c- k>return</c-> <c- n>std</c-><c- o>::</c-><c- n>bit_cast</c-><c- o>&lt;</c-><c- n>basic_simd</c-><c- o>&lt;</c-><c- n>std</c-><c- o>::</c-><c- n>complex</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-><c- p>,</c-> <c- n>ABI</c-><c- o>>></c-><c- p>(</c-><c- n>result</c-><c- p>);</c->
<c- p>}</c-></pre>
   <p>This example shows the verbose mechanics of making that conversion. The correct
type needs to be created by calculating the appropriate number of new elements
for the bit-cast element type, and then creating a suitable type using those
elements, before <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>bit_cast</c-></code> can be called. It would be more convenient to
be able to specify the new element type as part of a new <code class="highlight"><c- n>simd_bit_cast</c-></code> function:</p>
<pre class="highlight"><c- k>template</c-><c- o>&lt;</c-><c- k>typename</c-> <c- nc>T</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>ABI</c-><c- o>></c->
<c- k>auto</c-> <c- n>fn</c-><c- p>(</c-><c- k>const</c-> <c- n>basic_simd</c-><c- o>&lt;</c-><c- n>std</c-><c- o>::</c-><c- n>complex</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-><c- p>,</c-> <c- n>ABI</c-><c- o>>&amp;</c-> <c- n>x</c-><c- p>)</c->
<c- p>{</c->
  <c- k>auto</c-> <c- n>asT</c-> <c- o>=</c-> <c- n>simd_bit_cast</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-><c- p>(</c-><c- n>x</c-><c- p>);</c->
  <c- k>auto</c-> <c- n>result</c-> <c- o>=</c-> <c- p>...;</c-> <c- c1>// e.g., call an Intel intrinsic like _mm512_fmsubadd_ps</c->

  <c- k>return</c-> <c- n>simd_bit_cast</c-><c- o>&lt;</c-><c- n>std</c-><c- o>::</c-><c- n>complex</c-><c- o>&lt;</c-><c- n>T</c-><c- o>>></c-><c- p>(</c-><c- n>result</c-><c- p>);</c->
<c- p>}</c-></pre>
   <p>The <code class="highlight"><c- n>simd_bit_cast</c-></code> can also be overloaded for scalar types to allow
simd-generic programming. It will be equivalent to a <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>bit_cast</c-></code> in those
circumstances.</p>
   <p>Like <code class="highlight"><c- n>simd_cast</c-></code>, the <code class="highlight"><c- n>simd_bit_cast</c-></code> is easily defined by the programmer if
they want it, but it is such a useful function that it
should be defined once in <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> for all programmers to use.</p>
   <p>Note that no functions will be provided to bit-cast <code class="highlight"><c- n>simd_mask</c-></code> types because
the underlying implementation of a mask can vary by target.</p>
   <h2 class="heading settled" data-level="2" id="impl_experience"><span class="secno">2. </span><span class="content">Implementation experience</span><a class="self-link" href="#impl_experience"></a></h2>
   <p>In Intel’s implementation of <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> the <code class="highlight"><c- n>simd_bit_cast</c-></code> function was added
very early on because it is so widely used.</p>
   <p>The implementation of Intel’s <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> itself uses <code class="highlight"><c- n>simd_bit_cast</c-></code> to make it
easier to interface to compiler intrinsics. Intrinsics often require particular
data types to be used to achieve certain effects, and the bit-cast allows the
underlying bits to be quickly and easily reinterpreted.</p>
   <p>Intel uses <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> in a number of internal software projects, and some of
those (particularly wireless or packet-processing) need to be able to
easily reinterpret the underlying bits in different ways.</p>
   <h2 class="heading settled" data-level="3" id="wording"><span class="secno">3. </span><span class="content">Wording</span><a class="self-link" href="#wording"></a></h2>
   <h3 class="heading settled" data-level="3.1" id="wording_simd_synopsis"><span class="secno">3.1. </span><span class="content">Add [<strong>simd.casts</strong>] to the synopsis</span><a class="self-link" href="#wording_simd_synopsis"></a></h3>
   <p>Add the following to the [<strong>simd.syn</strong>] section:</p>
   <ins>
    <blockquote>
<pre class="highlight"><c- c1>// [simd.copy], basic_simd cast functions</c->

<c- k>template</c-><c- o>&lt;</c-><c- k>typename</c-> <c- nc>To</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>From</c-><c- o>></c-> <c- k>constexpr</c-> <c- n>To</c-> <c- n>simd_cast</c-><c- p>(</c-><c- k>const</c-> <c- n>From</c-><c- o>&amp;</c-> <c- n>x</c-><c- p>);</c->

<c- k>template</c-><c- o>&lt;</c-><c- k>typename</c-> <c- nc>To</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>From</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>Abi</c-><c- o>></c->
<c- k>constexpr</c-> <c- n>rebind_simd_t</c-><c- o>&lt;</c-><c- n>To</c-><c- p>,</c-> <c- n>basic_simd</c-><c- o>&lt;</c-><c- n>From</c-><c- p>,</c-> <c- n>Abi</c-><c- o>>></c->
<c- n>simd_cast</c-><c- p>(</c-><const abi basic_simdU00026ltU0003BfromU0002C><c- o>&amp;</c-> <c- n>x</c-><c- p>);</c->

<c- k>template</c-><c- o>&lt;</c-><c- k>typename</c-> <c- nc>To</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>From</c-><c- o>></c-> <c- k>constexpr</c-> <c- n>To</c-> <c- n>simd_bit_cast</c-><c- p>(</c-><c- k>const</c-> <c- n>From</c-><c- o>&amp;</c-> <c- n>x</c-><c- p>);</c->

<c- k>template</c-><c- o>&lt;</c-><c- k>typename</c-> <c- nc>To</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>From</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>Abi</c-><c- o>></c->
<c- k>constexpr</c-> <c- n>simd</c-><c- o>&lt;</c-><c- n>To</c-><c- p>,</c-> <c- p>(</c-><c- n>basic_simd</c-><c- o>&lt;</c-><c- n>From</c-><c- p>,</c-> <c- n>Abi</c-><c- o>>::</c-><c- n>size</c-> <c- o>*</c-> <c- k>sizeof</c-><c- p>(</c-><c- n>From</c-><c- p>))</c-> <c- o>/</c-> <c- k>sizeof</c-><c- p>(</c-><c- n>To</c-><c- p>)</c-><c- o>></c->
<c- n>simd_bit_cast</c-><c- p>(</c-><c- k>const</c-> <c- n>basic_simd</c-><c- o>&lt;</c-><c- n>From</c-><c- p>,</c-> <c- n>Abi</c-><c- o>>&amp;</c-> <c- n>x</c-><c- p>);</c-></const></pre>
    </blockquote>
   </ins>
   <h3 class="heading settled" data-level="3.2" id="wording_simd_casts"><span class="secno">3.2. </span><span class="content">Add new simd cast section [<strong>simd.casts</strong>]</span><a class="self-link" href="#wording_simd_casts"></a></h3>
   <ins>
    <blockquote>
     <p><b>� <code class="highlight"><c- n>basic_simd</c-></code> casts [simd.casts]</b></p>
<pre class="highlight"><c- mi>1</c-><c- p>)</c-> <c- k>template</c-><c- o>&lt;</c-><c- k>typename</c-> <c- nc>To</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>From</c-><c- o>></c-> <c- k>constexpr</c-> <c- n>To</c-> <c- n>simd_cast</c-><c- p>(</c-><c- k>const</c-> <c- n>From</c-><c- o>&amp;</c-> <c- n>x</c-><c- p>);</c->

<c- mi>2</c-><c- p>)</c-> <c- k>template</c-><c- o>&lt;</c-><c- k>typename</c-> <c- nc>To</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>From</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>Abi</c-><c- o>></c->
   <c- k>constexpr</c-> <c- n>rebind_simd_t</c-><c- o>&lt;</c-><c- n>To</c-><c- p>,</c-> <c- n>basic_simd</c-><c- o>&lt;</c-><c- n>From</c-><c- p>,</c-> <c- n>Abi</c-><c- o>>></c->
   <c- n>simd_cast</c-><c- p>(</c-><const abi basic_simdU00026ltU0003BfromU0002C><c- o>&amp;</c-> <c- n>x</c-><c- p>);</c-></const></pre>
     <p><i>Returns</i>:</p>
     <ul>
      <li data-md>
       <p>For the first overload, equivalent to returning <code class="highlight"><c- k>static_cast</c-><c- o>&lt;</c-><c- n>To</c-><c- o>></c-><c- p>(</c-><c- n>x</c-><c- p>)</c-></code>.</p>
      <li data-md>
       <p>For the second overload, equivalent to returning <code class="highlight"><c- k>static_cast</c-><c- o>&lt;</c-><c- n>rebind_simd_t</c-><c- o>&lt;</c-><c- n>To</c-><c- p>,</c-> <c- n>basic_simd</c-><c- o>&lt;</c-><c- n>From</c-><c- p>,</c-> <c- n>Abi</c-><c- o>>>></c-><c- p>(</c-><c- n>x</c-><c- p>)</c-></code>.</p>
     </ul>
<pre class="highlight"><c- mi>1</c-><c- p>)</c-> <c- k>template</c-><c- o>&lt;</c-><c- k>typename</c-> <c- nc>To</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>From</c-><c- o>></c-> <c- k>constexpr</c-> <c- n>To</c-> <c- n>simd_bit_cast</c-><c- p>(</c-><c- k>const</c-> <c- n>From</c-><c- o>&amp;</c-> <c- n>x</c-><c- p>);</c->

<c- mi>2</c-><c- p>)</c-> <c- k>template</c-><c- o>&lt;</c-><c- k>typename</c-> <c- nc>To</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>From</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>Abi</c-><c- o>></c->
   <c- k>constexpr</c-> <c- n>simd</c-><c- o>&lt;</c-><c- n>To</c-><c- p>,</c-> <c- p>(</c-><c- n>basic_simd</c-><c- o>&lt;</c-><c- n>From</c-><c- p>,</c-> <c- n>Abi</c-><c- o>>::</c-><c- n>size</c-> <c- o>*</c-> <c- k>sizeof</c-><c- p>(</c-><c- n>From</c-><c- p>))</c-> <c- o>/</c-> <c- k>sizeof</c-><c- p>(</c-><c- n>To</c-><c- p>)</c-><c- o>></c->
   <c- n>simd_bit_cast</c-><c- p>(</c-><c- k>const</c-> <c- n>basic_simd</c-><c- o>&lt;</c-><c- n>From</c-><c- p>,</c-> <c- n>Abi</c-><c- o>>&amp;</c-> <c- n>x</c-><c- p>);</c-></pre>
     <p><i>Returns</i>:</p>
     <ul>
      <li data-md>
       <p>For the first overload, equivalent to returning <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>bit_cast</c-><c- o>&lt;</c-><c- n>To</c-><c- o>></c-><c- p>(</c-><c- n>x</c-><c- p>)</c-></code>.</p>
      <li data-md>
       <p>For the second overload, equivalent to returning <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>bit_cast</c-><c- o>&lt;</c-><c- n>simd</c-><c- o>&lt;</c-><c- n>To</c-><c- p>,</c-> <c- p>(</c-><c- n>basic_simd</c-><c- o>&lt;</c-><c- n>From</c-><c- p>,</c-> <c- n>Abi</c-><c- o>>::</c-><c- n>size</c-> <c- o>*</c-> <c- k>sizeof</c-><c- p>(</c-><c- n>From</c-><c- p>))</c-> <c- o>/</c-> <c- k>sizeof</c-><c- p>(</c-><c- n>To</c-><c- p>)</c-><c- o>>></c-><c- p>(</c-><c- n>x</c-><c- p>)</c-></code>.</p>
     </ul>
    </blockquote>
   </ins>
  </main>
<script>
(function() {
  "use strict";
  var collapseSidebarText = '<span aria-hidden="true">←</span> '
                          + '<span>Collapse Sidebar</span>';
  var expandSidebarText   = '<span aria-hidden="true">→</span> '
                          + '<span>Pop Out Sidebar</span>';
  var tocJumpText         = '<span aria-hidden="true">↑</span> '
                          + '<span>Jump to Table of Contents</span>';

  var sidebarMedia = window.matchMedia('screen and (min-width: 78em)');
  var autoToggle   = function(e){ toggleSidebar(e.matches) };
  if(sidebarMedia.addListener) {
    sidebarMedia.addListener(autoToggle);
  }

  function toggleSidebar(on) {
    if (on == undefined) {
      on = !document.body.classList.contains('toc-sidebar');
    }

    /* Don’t scroll to compensate for the ToC if we’re above it already. */
    var headY = 0;
    var head = document.querySelector('.head');
    if (head) {
      // terrible approx of "top of ToC"
      headY += head.offsetTop + head.offsetHeight;
    }
    var skipScroll = window.scrollY < headY;

    var toggle = document.getElementById('toc-toggle');
    var tocNav = document.getElementById('toc');
    if (on) {
      var tocHeight = tocNav.offsetHeight;
      document.body.classList.add('toc-sidebar');
      document.body.classList.remove('toc-inline');
      toggle.innerHTML = collapseSidebarText;
      if (!skipScroll) {
        window.scrollBy(0, 0 - tocHeight);
      }
      tocNav.focus();
      sidebarMedia.addListener(autoToggle); // auto-collapse when out of room
    }
    else {
      document.body.classList.add('toc-inline');
      document.body.classList.remove('toc-sidebar');
      toggle.innerHTML = expandSidebarText;
      if (!skipScroll) {
        window.scrollBy(0, tocNav.offsetHeight);
      }
      if (toggle.matches(':hover')) {
        /* Unfocus button when not using keyboard navigation,
           because I don’t know where else to send the focus. */
        toggle.blur();
      }
    }
  }

  function createSidebarToggle() {
    /* Create the sidebar toggle in JS; it shouldn’t exist when JS is off. */
    var toggle = document.createElement('a');
      /* This should probably be a button, but appearance isn’t standards-track.*/
    toggle.id = 'toc-toggle';
    toggle.class = 'toc-toggle';
    toggle.href = '#toc';
    toggle.innerHTML = collapseSidebarText;

    sidebarMedia.addListener(autoToggle);
    var toggler = function(e) {
      e.preventDefault();
      sidebarMedia.removeListener(autoToggle); // persist explicit off states
      toggleSidebar();
      return false;
    }
    toggle.addEventListener('click', toggler, false);


    /* Get <nav id=toc-nav>, or make it if we don’t have one. */
    var tocNav = document.getElementById('toc-nav');
    if (!tocNav) {
      tocNav = document.createElement('p');
      tocNav.id = 'toc-nav';
      /* Prepend for better keyboard navigation */
      document.body.insertBefore(tocNav, document.body.firstChild);
    }
    /* While we’re at it, make sure we have a Jump to Toc link. */
    var tocJump = document.getElementById('toc-jump');
    if (!tocJump) {
      tocJump = document.createElement('a');
      tocJump.id = 'toc-jump';
      tocJump.href = '#toc';
      tocJump.innerHTML = tocJumpText;
      tocNav.appendChild(tocJump);
    }

    tocNav.appendChild(toggle);
  }

  var toc = document.getElementById('toc');
  if (toc) {
    createSidebarToggle();
    toggleSidebar(sidebarMedia.matches);

    /* If the sidebar has been manually opened and is currently overlaying the text
       (window too small for the MQ to add the margin to body),
       then auto-close the sidebar once you click on something in there. */
    toc.addEventListener('click', function(e) {
      if(e.target.tagName.toLowerCase() == "a" && document.body.classList.contains('toc-sidebar') && !sidebarMedia.matches) {
        toggleSidebar(false);
      }
    }, false);
  }
  else {
    console.warn("Can’t find Table of Contents. Please use <nav id='toc'> around the ToC.");
  }

  /* Wrap tables in case they overflow */
  var tables = document.querySelectorAll(':not(.overlarge) > table.data, :not(.overlarge) > table.index');
  var numTables = tables.length;
  for (var i = 0; i < numTables; i++) {
    var table = tables[i];
    var wrapper = document.createElement('div');
    wrapper.className = 'overlarge';
    table.parentNode.insertBefore(wrapper, table);
    wrapper.appendChild(table);
  }

})();
</script>