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  <title>p0476r2: Bit-casting object representations</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
 *
 * 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)
 *   - .assertion  for assertions                    (div, p, span)
 *   - .advisement for loud normative statements     (div, p, strong)
 *   - .annoying-warning for spec obsoletion notices (div, aside, details)
 *
 * 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
 *
 * 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)
 *
 ******************************************************************************/

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

	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;

		/* Colors */
		color: black;
		background: white 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-width: .65rem .7rem .6rem;
		border-radius: .4rem;
		background: #1a5e9a;
		color: white;
		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;
		border-color: #c00;
	}

	/* 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: 2;
			bottom: 0; left: 0;
			margin: 0;
			min-width: 1.33em;
			border-top-right-radius: 2rem;
			box-shadow: 0 0 2px;
			font-size: 1.5em;
			color: black;
		}
		#toc-nav > a {
			display: block;
			white-space: nowrap;

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

			background: white;
			box-shadow: 0 0 2px;
			border: none;
			border-top-right-radius: 1.33em;
			background: white;
		}
		#toc-nav > #toc-jump {
			padding-bottom: 2em;
			margin-bottom: -1.9em;
		}

		#toc-nav > a:hover,
		#toc-nav > a:focus {
			background: #f8f8f8;
		}
		#toc-nav > a:not(:hover):not(:focus) {
			color: #707070;
		}

		/* 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-toggle-inline {
			vertical-align: 0.05em;
			font-size: 80%;
			color: gray;
			color: hsla(203,20%,40%,.7);
			border-style: none;
			background: transparent;
			position: relative;
		}
		#toc-toggle-inline:hover:not(:active),
		#toc-toggle-inline:focus:not(:active) {
			text-shadow: 1px 1px silver;
			top: -1px;
			left: -1px;
		}

		#toc-nav :active {
			color: #C00;
		}
	}

/** 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);
			background: inherit;
			background-color: #f7f8f9;
			z-index: 1;
			box-shadow: -.1em 0 .25em rgba(0,0,0,.1) 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);
		}
		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);
			background: inherit;
			background-color: #f7f8f9;
			z-index: 1;
			box-shadow: -.1em 0 .25em rgba(0,0,0,.1) 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);
		}

		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;
		background: transparent;
	}

	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,
	#subtitle {
		/* #subtitle 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) > hr {
		font-size: 1.5em;
		text-align: center;
		margin: 1em auto;
		height: auto;
		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;
	}

	/* Put nice boxes around each algorithm. */
	[data-algorithm]:not(.heading) {
	  padding: .5em;
	  border: thin solid #ddd; 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: normal;
	}
	dfn var {
		font-style: normal;
	}

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

	del { color: red;  text-decoration: line-through; }
	ins { color: #080; text-decoration: underline;    }

/** 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;
		page-break-inside: avoid;
		hyphens: none;
		text-transform: none;
	}
	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;
		text-decoration: none;
		border-bottom: 1px solid #707070;
		/* Need a bit of extending for it to look okay */
		padding: 0 1px 0;
		margin: 0 -1px 0;
	}
	a:visited {
		border-bottom-color: #BBB;
	}

	/* Use distinguishing colors when user is interacting with the link */
	a[href]:focus,
	a[href]:hover {
		background: #f8f8f8;
		background: rgba(75%, 75%, 75%, .25);
		border-bottom-width: 3px;
		margin-bottom: -2px;
	}
	a[href]:active {
		color: #C00;
		border-color: #C00;
	}

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

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

	img {
		border-style: none;
	}

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

	.issue,
	.note,
	.example,
	.advisement,
	.assertion,
	blockquote {
		margin: 1em auto;
	}
	.note  > p:first-child,
	.issue > p:first-child,
	blockquote > :first-child {
		margin-top: 0;
	}
	blockquote > :last-child {
		margin-bottom: 0;
	}

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

	blockquote {
		border-color: silver;
	}

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

	.issue {
		border-color: #E05252;
		background: #FBE9E9;
		counter-increment: issue;
		overflow: auto;
	}
	.issue::before, .issue > .marker {
		text-transform: uppercase;
		color: #AE1E1E;
		padding-right: 1em;
		text-transform: uppercase;
	}
	/* 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;
		background: #FCFAEE;
		counter-increment: example;
		overflow: auto;
		clear: both;
	}
	.example::before, .example > .marker {
		text-transform: uppercase;
		color: #827017;
		min-width: 7.5em;
		display: block;
	}
	/* 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;
		background: #E9FBE9;
		overflow: auto;
	}

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

	details.note > summary {
		display: block;
		color: hsl(120, 70%, 30%);
	}
	details.note[open] > summary {
		border-bottom: 1px silver solid;
	}

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

	.assertion {
		border-color: #AAA;
		background: #EEE;
	}

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

	.advisement {
		border-color: orange;
		border-style: none solid;
		background: #FFEECC;
	}
	strong.advisement {
		display: block;
		text-align: center;
	}
	.advisement > .marker {
		color: #B35F00;
	}

/** 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: #fdd;
		color: red;
		font-weight: bold;
		padding: .75em 1em;
		border: thick red;
		border-style: solid;
		border-radius: 1em;
	}
	.annoying-warning :last-child {
		margin-bottom: 0;
	}

@media not print {
	details.annoying-warning[open] {
		position: fixed;
		left: 1em;
		right: 1em;
		bottom: 1em;
		z-index: 1000;
	}
}

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

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

	.def {
		padding: .5em 1em;
		background: #DEF;
		margin: 1.2em 0;
		border-left: 0.5em solid #8CCBF2;
	}

/******************************************************************************/
/*                                    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;
	}

	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-top-style: solid;
	}

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

	table.data  thead,
	table.index thead,
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  <div class="head">
   <p data-fill-with="logo"></p>
   <h1 class="p-name no-ref" id="title">p0476r2<br>Bit-casting object representations</h1>
   <h2 class="no-num no-toc no-ref heading settled" id="subtitle"><span class="content">Published Proposal, <time class="dt-updated" datetime="2017-11-10">10 November 2017</time></span></h2>
   <div data-fill-with="spec-metadata">
    <dl>
     <dt>This version:
     <dd><a class="u-url" href="http://wg21.link/P0476r2">http://wg21.link/P0476r2</a>
     <dt>Author:
     <dd>
      <dd class="editor p-author h-card vcard"><a class="p-name fn u-email email" href="mailto:jfbastien@apple.com">JF Bastien</a> (<span class="p-org org">Apple</span>)
     <dt>Audience:
     <dd>LWG
     <dt>Project:
     <dd><span>ISO JTC1/SC22/WG21: Programming Language C++</span>
     <dt>Source:
     <dd><span><a href="https://github.com/jfbastien/papers/blob/master/source/P0476r2.bs">github.com/jfbastien/papers/blob/master/source/P0476r2.bs</a></span>
     <dt>Implementation:
     <dd><span><a href="https://github.com/jfbastien/bit_cast/">github.com/jfbastien/bit_cast/</a></span>
    </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>Obtaining equivalent object representations The Right Way™.</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="#bg"><span class="secno">1</span> <span class="content">Background</span></a>
    <li>
     <a href="#word"><span class="secno">2</span> <span class="content">Proposed Wording</span></a>
     <ol class="toc">
      <li><a href="#bit"><span class="secno">2.1</span> <span class="content">29.� Bit manipulation library [<strong>bit</strong>]</span></a>
      <li><a href="#bitgen"><span class="secno">2.2</span> <span class="content">29.�.1 General [<strong>bit.general</strong>]</span></a>
      <li><a href="#bitsyn"><span class="secno">2.3</span> <span class="content">29.�.2 Header <code class="highlight"><span class="o">&lt;</span><span class="n">bit</span><span class="o">></span></code> synopsis [<strong>bit.syn</strong>]</span></a>
      <li><a href="#bitcast"><span class="secno">2.4</span> <span class="content">29.�.3 Function template <code class="highlight"><span class="n">bit_cast</span></code> [<strong>bit.cast</strong>]</span></a>
      <li><a href="#test"><span class="secno">2.5</span> <span class="content">Feature testing</span></a>
     </ol>
    <li><a href="#appendix"><span class="secno">3</span> <span class="content">Appendix</span></a>
    <li>
     <a href="#rev"><span class="secno">4</span> <span class="content">Revision History</span></a>
     <ol class="toc">
      <li><a href="#r1r2"><span class="secno">4.1</span> <span class="content">r1 ➡ r2</span></a>
      <li><a href="#r0r1"><span class="secno">4.2</span> <span class="content">r0 ➡ r1</span></a>
     </ol>
    <li><a href="#ack"><span class="secno">5</span> <span class="content">Acknowledgement</span></a>
    <li>
     <a href="#references"><span class="secno"></span> <span class="content">References</span></a>
     <ol class="toc">
      <li><a href="#informative"><span class="secno"></span> <span class="content">Informative References</span></a>
     </ol>
   </ol>
  </nav>
  <main>
   <p>This paper is a revision of <a data-link-type="biblio" href="#biblio-p0476r1">[P0476r1]</a>, addressing LEWG comments from the 2017
Toronto meeting as well as comments from LEWG and LWG from the 2017 Albuquerque
meeting. See <a href="#rev">§4 Revision History</a> for details.</p>
   <h2 class="heading settled" data-level="1" id="bg"><span class="secno">1. </span><span class="content">Background</span><a class="self-link" href="#bg"></a></h2>
   <p>Low-level code often seeks to interpret objects of one type as another: keep the
same bits, but obtain an object of a different type. Doing so correctly is
error-prone: using <code class="highlight"><span class="k">reinterpret_cast</span></code> or <code class="highlight"><span class="k">union</span></code> runs afoul of type-aliasing
rules yet these are the intuitive solutions developers mistakenly turn to.</p>
   <p>Attuned developers use <code class="highlight"><span class="n">aligned_storage</span></code> with <code class="highlight"><span class="n">memcpy</span></code>, avoiding alignment
pitfalls and allowing them to bit-cast non-default-constructible types.</p>
   <p>This proposal uses appropriate concepts to prevent misuse. As the sample
implementation demonstrates we could as well use <code class="highlight"><span class="k">static_assert</span></code> or template
SFINAE, but the timing of this library feature will likely coincide with
concept’s standardization.</p>
   <p>Furthermore, it is currently impossible to implement a <code class="highlight"><span class="k">constexpr</span></code> bit-cast
function, as <code class="highlight"><span class="n">memcpy</span></code> itself isn’t <code class="highlight"><span class="k">constexpr</span></code>. Marking the proposed function as <code class="highlight"><span class="k">constexpr</span></code> doesn’t require or prevent <code class="highlight"><span class="n">memcpy</span></code> from becoming <code class="highlight"><span class="k">constexpr</span></code>, but
requires compiler support. This leaves implementations free to use their own
internal solution (e.g. LLVM has <a href="http://llvm.org/docs/LangRef.html#bitcast-to-instruction">a <code class="highlight"><span class="n">bitcast</span></code> opcode</a>).</p>
   <p>We should standardize this oft-used idiom, and avoid the pitfalls once and for
all.</p>
   <h2 class="heading settled" data-level="2" id="word"><span class="secno">2. </span><span class="content">Proposed Wording</span><a class="self-link" href="#word"></a></h2>
   <p>Below, substitute the <code class="highlight">�</code> character with a number or name the editor finds
appropriate for the sub-section.</p>
   <p>In 20.5.1.2 [<strong>headers</strong>] add the header <code class="highlight"><span class="o">&lt;</span><span class="n">bit</span><span class="o">></span></code> to:</p>
   <ul>
    <li data-md="">
     <p>Table 16 — C++ library headers</p>
    <li data-md="">
     <p>Table 19 — C++ headers for freestanding implementations</p>
   </ul>
   <p>In the numerics section, add the following:</p>
   <ins>
    <h3 class="heading settled" data-level="2.1" id="bit"><span class="secno">2.1. </span><span class="content">29.� Bit manipulation library [<strong>bit</strong>]</span><a class="self-link" href="#bit"></a></h3>
    <h3 class="heading settled" data-level="2.2" id="bitgen"><span class="secno">2.2. </span><span class="content">29.�.1 General [<strong>bit.general</strong>]</span><a class="self-link" href="#bitgen"></a></h3>
    <p>The header <code class="highlight"><span class="o">&lt;</span><span class="n">bit</span><span class="o">></span></code> provides components to access, manipulate and process both
individual bits and bit sequences.</p>
    <h3 class="heading settled" data-level="2.3" id="bitsyn"><span class="secno">2.3. </span><span class="content">29.�.2 Header <code class="highlight"><span class="o">&lt;</span><span class="n">bit</span><span class="o">></span></code> synopsis [<strong>bit.syn</strong>]</span><a class="self-link" href="#bitsyn"></a></h3>
<pre class="highlight"><span class="k">namespace</span> <span class="n">std</span> <span class="p">{</span>
  
  <span class="c1">// 29.�.3 bit_cast
</span>  <span class="k">template</span><span class="o">&lt;</span><span class="k">typename</span> <span class="n">To</span><span class="p">,</span> <span class="k">typename</span> <span class="n">From</span><span class="o">></span>
  <span class="k">constexpr</span> <span class="n">To</span> <span class="n">bit_cast</span><span class="p">(</span><span class="k">const</span> <span class="n">From</span><span class="o">&amp;</span> <span class="n">from</span><span class="p">)</span> <span class="k">noexcept</span><span class="p">;</span>
  
<span class="p">}</span>
</pre>
    <h3 class="heading settled" data-level="2.4" id="bitcast"><span class="secno">2.4. </span><span class="content">29.�.3 Function template <code class="highlight"><span class="n">bit_cast</span></code> [<strong>bit.cast</strong>]</span><a class="self-link" href="#bitcast"></a></h3>
<pre class="highlight"><span class="k">template</span><span class="o">&lt;</span><span class="k">typename</span> <span class="n">To</span><span class="p">,</span> <span class="k">typename</span> <span class="n">From</span><span class="o">></span>
<span class="k">constexpr</span> <span class="n">To</span> <span class="n">bit_cast</span><span class="p">(</span><span class="k">const</span> <span class="n">From</span><span class="o">&amp;</span> <span class="n">from</span><span class="p">)</span> <span class="k">noexcept</span><span class="p">;</span>
</pre>
    <ol>
     <li>
      <em>Remarks</em>: 
      <p>This function shall not participate in overload resolution unless:</p>
      <ul>
       <li><code class="highlight"><span class="k">sizeof</span><span class="p">(</span><span class="n">To</span><span class="p">)</span> <span class="o">=</span><span class="o">=</span> <span class="k">sizeof</span><span class="p">(</span><span class="n">From</span><span class="p">)</span></code> is <code class="highlight">true</code>;
       <li><code class="highlight"><span class="n">is_trivially_copyable_v</span><span class="o">&lt;</span><span class="n">To</span><span class="o">></span></code> is <code class="highlight">true</code>; and
       <li><code class="highlight"><span class="n">is_trivially_copyable_v</span><span class="o">&lt;</span><span class="n">From</span><span class="o">></span></code> is <code class="highlight">true</code>.
      </ul>
      <p>This function shall be <code class="highlight"><span class="k">constexpr</span></code> if and only if <code class="highlight"><span class="n">To</span></code>, <code class="highlight"><span class="n">From</span></code>, and the types
  of all subobjects of <code class="highlight"><span class="n">To</span></code> and <code class="highlight"><span class="n">From</span></code> are types <code class="highlight"><span class="n">T</span></code> such that:</p>
      <ul>
       <li><code class="highlight"><span class="n">is_union_v</span><span class="o">&lt;</span><span class="n">T</span><span class="o">></span></code> is <code class="highlight">false</code>;
       <li><code class="highlight"><span class="n">is_pointer_v</span><span class="o">&lt;</span><span class="n">T</span><span class="o">></span></code> is <code class="highlight">false</code>;
       <li><code class="highlight"><span class="n">is_member_pointer_v</span><span class="o">&lt;</span><span class="n">T</span><span class="o">></span></code> is <code class="highlight">false</code>;
       <li><code class="highlight"><span class="n">is_volatile_v</span><span class="o">&lt;</span><span class="n">T</span><span class="o">></span></code> is <code class="highlight">false</code>; and
       <li><code class="highlight"><span class="n">T</span></code> has no non-static data members of reference type.
      </ul>
     <li>
      <em>Returns</em>: 
      <p>An object of type <code class="highlight"><span class="n">To</span></code>. Each bit of the value representation of the result
    is equal to the corresponding bit in the object representation of <code class="highlight"><span class="n">from</span></code>. Padding bits of the <code class="highlight"><span class="n">To</span></code> object are unspecified. If there is no
    value of type <code class="highlight"><span class="n">To</span></code> corresponding to the value representation produced, the
    behavior is undefined. If there are multiple such values, which value is
    produced is unspecified.</p>
    </ol>
   </ins>
   <h3 class="heading settled" data-level="2.5" id="test"><span class="secno">2.5. </span><span class="content">Feature testing</span><a class="self-link" href="#test"></a></h3>
   <p>The <code class="highlight"><span class="n">__cpp_lib_bit_cast</span></code> feature test macro should be added.</p>
   <h2 class="heading settled" data-level="3" id="appendix"><span class="secno">3. </span><span class="content">Appendix</span><a class="self-link" href="#appendix"></a></h2>
   <p>The Standard’s [<strong>basic.types</strong>] section explicitly blesses <code class="highlight"><span class="n">memcpy</span></code>:</p>
   <blockquote>
    <p>For any trivially copyable type <code class="highlight"><span class="n">T</span></code>, if two pointers to <code class="highlight"><span class="n">T</span></code> point to distinct <code class="highlight"><span class="n">T</span></code> objects <code class="highlight"><span class="n">obj1</span></code> and <code class="highlight"><span class="n">obj2</span></code>, where neither <code class="highlight"><span class="n">obj1</span></code> nor <code class="highlight"><span class="n">obj2</span></code> is a base-class
  subobject, if the <em>underlying bytes</em> (1.7) making up <code class="highlight"><span class="n">obj1</span></code> are copied into <code class="highlight"><span class="n">obj2</span></code>, <code class="highlight"><span class="n">obj2</span></code> shall subsequently hold the same value as <code class="highlight"><span class="n">obj1</span></code>.</p>
    <p>[<em>Example:</em></p>
<pre class="highlight">    <span class="n">T</span><span class="o">*</span> <span class="n">t1p</span><span class="p">;</span>
    <span class="n">T</span><span class="o">*</span> <span class="n">t2p</span><span class="p">;</span>
    <span class="c1">// provided that t2p points to an initialized object ...
</span>    <span class="n">std</span><span class="o">:</span><span class="o">:</span><span class="n">memcpy</span><span class="p">(</span><span class="n">t1p</span><span class="p">,</span> <span class="n">t2p</span><span class="p">,</span> <span class="k">sizeof</span><span class="p">(</span><span class="n">T</span><span class="p">)</span><span class="p">)</span><span class="p">;</span>
    <span class="c1">// at this point, every subobject of trivially copyable type in *t1p contains
</span>    <span class="c1">// the same value as the corresponding subobject in *t2p
</span></pre>
     — <em>end example</em>] 
   </blockquote>
   <p>Whereas section [<strong>class.union</strong>] says:</p>
   <blockquote>
    <p>In a union, at most one of the non-static data members can be
  active at any time, that is, the value of at most one of the
  non-static data members can be stored in a union at any time.</p>
   </blockquote>
   <h2 class="heading settled" data-level="4" id="rev"><span class="secno">4. </span><span class="content">Revision History</span><a class="self-link" href="#rev"></a></h2>
   <h3 class="heading settled" data-level="4.1" id="r1r2"><span class="secno">4.1. </span><span class="content">r1 ➡ r2</span><a class="self-link" href="#r1r2"></a></h3>
   <p>The paper was reviewed by LEWG at the 2017 Toronto meeting and feedback was
provided. In the 2017 Albuquerque meeting LEWG provided feedback regarding usage
of concepts while discussing <a data-link-type="biblio" href="#biblio-p0802r0">[P0802r0]</a>, and EWG reviewed the paper:</p>
   <ul>
    <li data-md="">
     <p>Use "shall not participate in overload resolution" wording instead of a
requires clause.</p>
    <li data-md="">
     <p>The author was asked to explore naming. LEWG took a poll in Albuquerque and
voted to keep <code class="highlight"><span class="n">bit_cast</span></code>.</p>
    <li data-md="">
     <p>There was strong sentiment that this facility should be available in
freestanding implementations. LEWG is changing its guidance regarding
freestanding header granularity, but until guidance is actually changed it
was decided that a currently freestanding header should be used. LEWG took a
poll in Albuquerque, and the new <code class="highlight"><span class="o">&lt;</span><span class="n">bit</span><span class="o">></span></code> header was chosen instead of <code class="highlight"><span class="o">&lt;</span><span class="n">cstddef</span><span class="o">></span></code>.</p>
    <li data-md="">
     <p>Call out that <code class="highlight"><span class="k">constexpr</span></code> requires compiler support.</p>
    <li data-md="">
     <p>Make <code class="highlight"><span class="k">constexpr</span></code> conditional, similar to variant’s [variant.ctor] wording,
based on an EWG straw poll in Albuquerque.</p>
    <li data-md="">
     <p>LWG review made the <code class="highlight"><span class="k">constexpr</span></code> remark recursive, and tuned the return
wording, asking CWG to review the changes.</p>
    <li data-md="">
     <p>LWG review requested that this paper also add the <code class="highlight"><span class="o">&lt;</span><span class="n">bit</span><span class="o">></span></code> header, and let
the editor resolve races if multiple papers add the header concurrently.</p>
    <li data-md="">
     <p>CWG substantially tuned the wording.</p>
   </ul>
   <h3 class="heading settled" data-level="4.2" id="r0r1"><span class="secno">4.2. </span><span class="content">r0 ➡ r1</span><a class="self-link" href="#r0r1"></a></h3>
   <p>The paper was reviewed by LEWG at the 2016 Issaquah meeting:</p>
   <ul>
    <li data-md="">
     <p>Remove the standard layout requirement—trivially copyable suffices for the <code class="highlight"><span class="n">memcpy</span></code> requirement.</p>
    <li data-md="">
     <p>We discussed removing <code class="highlight"><span class="k">constexpr</span></code>, but there was no consent either way. There was some suggestion that it’ll be hard for implementers, but there’s also some desire (by the same implementers) to have those features available in order to support things like <code class="highlight"><span class="k">constexpr</span></code> instances of <code class="highlight"><span class="n">std</span><span class="o">:</span><span class="o">:</span><span class="n">variant</span></code>.</p>
    <li data-md="">
     <p>The pointer-forbidding logic was removed. It was initially there to help developers when a better tool is available, but it’s easily worked around (e.g. with a <code class="highlight"><span class="k">struct</span></code> containing a pointer). Note that this doesn’t prevent <code class="highlight"><span class="k">constexpr</span></code> versions of <code class="highlight"><span class="n">bit_cast</span></code>: the implementation is allowed to error out on <code class="highlight"><span class="n">bit_cast</span></code> of pointer.</p>
    <li data-md="">
     <p>Some discussion about concepts-usage, but it seems like mostly an LWG issue and we’re reasonably sure that concepts will land before this or in a compatible vehicle.</p>
   </ul>
   <p>Straw polls:</p>
   <ul>
    <li data-md="">
     <p>Do we want to see <a data-link-type="biblio" href="#biblio-p0476r0">[P0476r0]</a> again? unanimous consent.</p>
    <li data-md="">
     <p><code class="highlight"><span class="n">bit_cast</span></code> should allow pointer types in <code class="highlight"><span class="n">To</span></code> and <code class="highlight"><span class="n">From</span></code>. <strong>SF F N A SA</strong> 4 5 4 2 1</p>
    <li data-md="">
     <p><code class="highlight"><span class="n">bit_cast</span></code> should be <code class="highlight"><span class="k">constexpr</span></code>? <strong>SF F N A SA</strong> 4 3 7 2 3</p>
   </ul>
   <h2 class="heading settled" data-level="5" id="ack"><span class="secno">5. </span><span class="content">Acknowledgement</span><a class="self-link" href="#ack"></a></h2>
   <p>Thanks to Saam Barati, Jeffrey Yasskin, and Sam Benzaquen for their early review
and suggested improvements.</p>
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  <h2 class="no-num no-ref heading settled" id="references"><span class="content">References</span><a class="self-link" href="#references"></a></h2>
  <h3 class="no-num no-ref heading settled" id="informative"><span class="content">Informative References</span><a class="self-link" href="#informative"></a></h3>
  <dl>
   <dt id="biblio-p0476r0">[P0476r0]
   <dd>JF Bastien. <a href="https://wg21.link/p0476r0">Bit-casting object representations</a>. 16 October 2016. URL: <a href="https://wg21.link/p0476r0">https://wg21.link/p0476r0</a>
   <dt id="biblio-p0476r1">[P0476r1]
   <dd>JF Bastien. <a href="https://wg21.link/p0476r1">Bit-casting object representations</a>. 11 November 2016. URL: <a href="https://wg21.link/p0476r1">https://wg21.link/p0476r1</a>
   <dt id="biblio-p0802r0">[P0802r0]
   <dd>Beman Dawes, Nicolai Josuttis, Walter E. Brown, Bob Steagall. <a href="https://wg21.link/p0802r0">Applying Concepts to the Standard Library</a>. URL: <a href="https://wg21.link/p0802r0">https://wg21.link/p0802r0</a>
  </dl>