<!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>P2509R0: A proposal for a type trait to detect value-preserving conversions</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;
		}
		#toc .content:hover,
		#toc .content:focus {
			background: rgba(75%, 75%, 75%, .25);
			background: var(--a-hover-bg);
			border-bottom: 3px solid #054572;
			border-bottom: 3px solid var(--toclink-underline);
			margin-bottom: -3px;
		}
		#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 type="text/css">
    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 cace53f8c, updated Tue Dec 7 12:12:54 2021 -0800" name="generator">
  <link href="https://isocpp.org/favicon.ico" rel="icon">
<style>
ins  {background-color: #CCFFCC; text-decoration: underline;}
del  {background-color: #FFCACA; text-decoration: line-through;}
</style>
<style>/* style-autolinks */

.css.css, .property.property, .descriptor.descriptor {
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 <body class="h-entry">
  <div class="head">
   <p data-fill-with="logo"></p>
   <h1 class="p-name no-ref" id="title">P2509R0<br>A proposal for a type trait to detect value-preserving conversions</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="2021-12-15">2021-12-15</time></span></h2>
   <div data-fill-with="spec-metadata">
    <dl>
     <dt>Issue Tracking:
     <dd><a href="#issues-index">Inline In Spec</a>
     <dt class="editor">Author:
     <dd class="editor p-author h-card vcard"><a class="p-name fn u-email email" href="mailto:giuseppe.dangelo@kdab.com">Giuseppe D'Angelo</a>
     <dt>Audience:
     <dd>SG6, LEWG
     <dt>Project:
     <dd>ISO/IEC JTC1/SC22/WG21 14882: Programming Language — C++
    </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>We propose to add a type trait to detect conversions between

    arithmetic-like types that always preserve the numeric value of the
    source object.</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="#changelog"><span class="secno">1</span> <span class="content">Changelog</span></a>
    <li><a href="#motivation"><span class="secno">2</span> <span class="content">Motivation and Scope</span></a>
    <li><a href="#impact"><span class="secno">3</span> <span class="content">Impact On The Standard</span></a>
    <li>
     <a href="#designdecisions"><span class="secno">4</span> <span class="content">Design Decisions</span></a>
     <ol class="toc">
      <li><a href="#what-defines-a-value-preserving-conversion"><span class="secno">4.1</span> <span class="content">What defines a "value-preserving conversion"?</span></a>
      <li><a href="#what-about-unbounded-types"><span class="secno">4.2</span> <span class="content">What about unbounded types?</span></a>
      <li><a href="#should-the-type-trait-be-specializable-for-user-defined-datatypes"><span class="secno">4.3</span> <span class="content">Should the type trait be specializable for user-defined datatypes?</span></a>
      <li><a href="#narrowing"><span class="secno">4.4</span> <span class="content">Is the proposed trait different from simply detecting narrowing conversions?</span></a>
      <li><a href="#when-should-users-detect-narrowing-conversions-vs-value-preserving-conversions"><span class="secno">4.5</span> <span class="content">When should users detect narrowing conversions vs. value-preserving conversions?</span></a>
      <li><a href="#bikeshedding-naming"><span class="secno">4.6</span> <span class="content">Bikeshedding: naming</span></a>
     </ol>
    <li><a href="#implementationexperience"><span class="secno">5</span> <span class="content">Implementation experience</span></a>
    <li>
     <a href="#technicalspecifications"><span class="secno">6</span> <span class="content">Technical Specifications</span></a>
     <ol class="toc">
      <li><a href="#feature-testing-macro"><span class="secno">6.1</span> <span class="content">Feature testing macro</span></a>
      <li><a href="#proposedwording"><span class="secno">6.2</span> <span class="content">Proposed wording</span></a>
     </ol>
    <li><a href="#acknowledgements"><span class="secno">7</span> <span class="content">Acknowledgements</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>
    <li><a href="#issues-index"><span class="secno"></span> <span class="content">Issues Index</span></a>
   </ol>
  </nav>
  <main>
   <h2 class="heading settled" data-level="1" id="changelog"><span class="secno">1. </span><span class="content">Changelog</span><a class="self-link" href="#changelog"></a></h2>
   <ul>
    <li data-md>
     <p>R0</p>
     <ul>
      <li data-md>
       <p>First submission.</p>
     </ul>
   </ul>
   <h2 class="heading settled" data-level="2" id="motivation"><span class="secno">2. </span><span class="content">Motivation and Scope</span><a class="self-link" href="#motivation"></a></h2>
   <p>Consider a datatype built on top of an arithmetic type:</p>
<pre class="highlight"><c- k>template</c-> <c- o>&lt;</c-><c- k>class</c-> <c- nc>Rep</c-><c- o>></c-> <c- c1>// an arithmetic-like type</c->
<c- k>class</c-> <c- nc>Quantity</c->
<c- p>{</c->
    <c- n>Rep</c-> <c- n>value</c-><c- p>;</c->

    <c- o>~~~</c->
<c- p>};</c->
</pre>
   Examples of such a datatype include the class templates <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>complex</c-></code>, <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>chrono</c-><c- o>::</c-><c- n>duration</c-></code>, <a data-link-type="biblio" href="#biblio-qangle">[QAngle]</a> (proposed for inclusion in Qt),
and so on. 
   <p>It’s reasonable to expect that different specializations of this
datatype may convert to each other: a user may want to convert a <code class="highlight"><c- n>Quantity</c-><c- o>&lt;</c-><c- b>int</c-><c- o>></c-></code> to, say, a <code class="highlight"><c- n>Quantity</c-><c- o>&lt;</c-><c- b>long</c-><c- o>></c-></code>.</p>
   <p>This is typically realized via a <em>converting constructor</em>:</p>
<pre class="highlight"><c- k>template</c-> <c- o>&lt;</c-><c- k>class</c-> <c- nc>Rep</c-><c- o>></c->
<c- k>class</c-> <c- nc>Quantity</c->
<c- p>{</c->
    <c- n>Rep</c-> <c- n>value</c-><c- p>;</c->

<c- k>public</c-><c- o>:</c->
    <c- k>template</c-> <c- o>&lt;</c-><c- k>class</c-> <c- nc>Rep2</c-><c- o>></c->
    <c- d>/* explicit/requires (some expression depending on Rep and Rep2) */</c->
    <c- n>Quantity</c-><c- p>(</c-><c- k>const</c-> <c- n>Quantity</c-><c- o>&lt;</c-><c- n>Rep2</c-><c- o>>&amp;</c-> <c- n>other</c-><c- p>);</c->

    <c- o>~~~</c->
<c- p>};</c->
</pre>
   <p>Such a converting constructor is usually somehow "constrained" in order
to prevent information loss and/or undefined behavior from occurring,
as shown in the snippet above. Examples include:</p>
   <ol>
    <li data-md>
     <p>the converting constructor from <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>complex</c-><c- o>&lt;</c-><c- n>From</c-><c- o>></c-></code> to <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>complex</c-><c- o>&lt;</c-><c- n>To</c-><c- o>></c-></code> is <code class="highlight"><c- k>explicit</c-></code> if and only if the conversion from <code class="highlight"><c- n>From</c-></code> to <code class="highlight"><c- n>To</c-></code> is a narrowing conversion ([dcl.init.list],
[complex.special]). Although the Standard does not use the "narrowing
conversion" wording (instead, it fully specifies each and every
specialization, marking the converting constructors <code class="highlight"><c- k>explicit</c-></code> as
appropriate in each specialization), and <a data-link-type="biblio" href="#biblio-p1467r7">[P1467R7]</a> changes the
related wording, the semantics are indeed matching the ones of
detecting a narrowing conversion (see also <a data-link-type="biblio" href="#biblio-p0870r4">[P0870R4]</a>'s motivating
examples);</p>
    <li data-md>
     <p>similarly, the converting constructor from <code class="highlight"><c- n>QAngle</c-><c- o>&lt;</c-><c- n>From</c-><c- o>></c-></code> to <code class="highlight"><c- n>QAngle</c-><c- o>&lt;</c-><c- n>To</c-><c- o>></c-></code> is <code class="highlight"><c- k>explicit</c-></code> if and only if <code class="highlight"><c- n>To</c-></code> cannot exactly represent
any possible value of <code class="highlight"><c- n>From</c-></code>. For instance, this implies that <code class="highlight"><c- n>QAngle</c-><c- o>&lt;</c-><c- b>int</c-><c- o>></c-></code> to <code class="highlight"><c- n>QAngle</c-><c- o>&lt;</c-><c- b>double</c-><c- o>></c-></code> is implicit on x86-64 using the
Itanium ABI (as any 32 bit <code class="highlight"><c- b>int</c-></code> can be precisely converted to a <code class="highlight"><c- n>binary64</c-></code> <code class="highlight"><c- b>double</c-></code>);</p>
    <li data-md>
     <p><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>chrono</c-><c- o>::</c-><c- n>duration</c-></code> uses some ad-hoc detections to exclude
its converting constructor from overload resolution
([time.duration.cons]). These include handling of the tick period,
as well as the ad-hoc trait <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>chrono</c-><c- o>::</c-><c- n>treat_</c->­<c- n>as_</c->­<c- n>floating_</c->­<c- n>point</c-></code>.</p>
   </ol>
   <p>Each approach has its own advantages and disadvantages.</p>
   <ol>
    <li data-md>
     <p>"Constraining" on narrowing conversions allows one to simply side-step
the problem of defining the semantics involved -- one can simply refer
to the core language definition of narrowing. On the other hand, this
may yield counter-intuitive results. For instance a
conversion between <code class="highlight"><c- b>int</c-></code> and <code class="highlight"><c- b>long</c-> <c- b>double</c-></code> is always considered narrowing,
even if it would precisely preserve the source values, and therefore
make <code class="highlight"><c- n>Quantity</c-><c- o>&lt;</c-><c- b>int</c-><c- o>></c-></code> not implictly convert to <code class="highlight"><c- n>Quantity</c-><c- o>&lt;</c-><c- b>long</c-> <c- b>double</c-><c- o>></c-></code>.
This could be surprising for users.</p>
    <li data-md>
     <p>"Constraining" on whether the conversion would precisely preserve
any possible source value may give more expected results, in line
with the idea that implicit conversions never lose information. On the
other hand, this would risk limiting the portability of the one’s
source code, by introducing source incompatibilities when porting the
code to a new platform. For instance, this could mean that <code class="highlight"><c- n>Quantity</c-><c- o>&lt;</c-><c- b>long</c-> <c- b>double</c-><c- o>></c-></code> would be implictly convertible to <code class="highlight"><c- n>Quantity</c-><c- o>&lt;</c-><c- b>double</c-><c- o>></c-></code> on x86-64 when using the MSVC ABI (where both <code class="highlight"><c- b>long</c-> <c- b>double</c-></code> and <code class="highlight"><c- b>double</c-></code> actually use <code class="highlight"><c- n>binary64</c-></code>, and therefore can
represent the very same values), but not on the Itanium ABI (where <code class="highlight"><c- b>long</c-> <c- b>double</c-></code> instead uses the x86 80-bit extended precision format).</p>
    <li data-md>
     <p>An ad-hoc approach allows for maximum flexibility in terms of semantics,
but it may also be surprising or frustrating to use correctly.
For instance, a user defining a custom floating-point type (e.g. <code class="highlight"><c- n>float16</c-></code>)
may forget to also specialize <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>chrono</c-><c- o>::</c-><c- n>treat_</c->­<c- n>as_</c->­<c- n>floating_</c->­<c- n>point</c-></code>, therefore
causing confusion when using something like <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>chrono</c-><c- o>::</c-><c- n>duration</c-><c- o>&lt;</c-><c- n>float16</c-><c- o>></c-></code>:</p>
<pre class="highlight"><c- k>using</c-> <c- k>namespace</c-> <c- n>std</c-><c- o>::</c-><c- n>chrono</c-><c- p>;</c->
<c- n>duration</c-><c- o>&lt;</c-><c- b>double</c-><c- o>></c->  <c- n>dd</c-><c- p>;</c->
<c- n>duration</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c->   <c- n>df</c->   <c- o>=</c-> <c- n>dd</c-><c- p>;</c->  <c- c1>// OK even if narrowing</c->
<c- n>duration</c-><c- o>&lt;</c-><c- n>float16</c-><c- o>></c-> <c- n>df16</c-> <c- o>=</c-> <c- n>dd</c-><c- p>;</c->  <c- c1>// ERROR unless treat_­as_­floating_­point has been specialized</c->
</pre>
   </ol>
   <p>The Standard Library does not provide any facilities for helping in the
implemention of cases 1 and 2. (Case 3 is by definition ad-hoc and
therefore one cannot provide generic facilities for it.)</p>
   <p>Case 1 is supposed to be tackled by <a data-link-type="biblio" href="#biblio-p0870r4">[P0870R4]</a>, which aims at introducing
a type trait to detect narrowing conversions.</p>
   <p>We are therefore left with case 2, which is the subject of the present
proposal. Here we propose to add a type trait to detect whether a
conversion exists between two types and that conversion always
preserves values exactly.</p>
   <h2 class="heading settled" data-level="3" id="impact"><span class="secno">3. </span><span class="content">Impact On The Standard</span><a class="self-link" href="#impact"></a></h2>
   <p>This proposal is a pure library extension. It proposes changes to
the <code class="highlight"><c- o>&lt;</c-><c- n>type_traits</c-><c- o>></c-></code> header.</p>
   <p>This proposal does not depend on any other library extensions.</p>
   <p>This proposal does not require any changes in the core language.</p>
   <p><a data-link-type="biblio" href="#biblio-p0870r4">[P0870R4]</a> ("A proposal for a type trait to detect narrowing
conversions") is very related to this proposal. During a mailing list
review of <a data-link-type="biblio" href="#biblio-p0870r4">[P0870R4]</a> by SG6, it has been brought forward that users of
that trait might find some behaviors counter-intuitive. The trait
described by the present proposal complements <a data-link-type="biblio" href="#biblio-p0870r4">[P0870R4]</a>'s.</p>
   <p>This proposal is related to <a data-link-type="biblio" href="#biblio-p1467r7">[P1467R7]</a> ("Extended floating-point types
and standard names"), in at least two important aspects. First, the
trait that we are proposing is going to defined in a way that correctly
interoperates with the proposed extended floating-point types. Second, <a data-link-type="biblio" href="#biblio-p1467r7">[P1467R7]</a> introduces a <em>conversion rank</em> of floating-point types.
This is done in order to properly extend the definition of usual
arithmetic conversions to the extended floating-point types. Our
proposal is however <em>not</em> going to make use of this ranking, for the
simple reason that the ranking does not necessarily take into account
the set of representable values of each floating-point type. For
instance, <code class="highlight"><c- b>long</c-> <c- b>double</c-></code> is considered to unconditionally have higher
ranking than <code class="highlight"><c- b>double</c-></code>, even on architectures where the two types have
an identical representation. This aspect, as well as the impact of <a data-link-type="biblio" href="#biblio-p1467r7">[P1467R7]</a> on the definition of narrowing conversions, is discussed in
the <a href="#narrowing">§ 4.4 Is the proposed trait different from simply detecting narrowing conversions?</a> paragraph.</p>
   <p><a data-link-type="biblio" href="#biblio-p1619r1">[P1619R1]</a> and <a data-link-type="biblio" href="#biblio-p1998r1">[P1998R1]</a> introduce functions (called respectively <code class="highlight"><c- n>can_convert</c-></code> and <code class="highlight"><c- n>is_value_lossless_convertable</c-></code>) that check whether a
given value of an integer type can be represented by another integer
type. This is in line with the spirit of detecting value-preserving
conversions, namely, preventing loss of information and/or preventing
undefined behavior. While this proposal works on types, the functions
examine specific values; we therefore think that the proposals are
somehow orthogonal to the current proposal.</p>
   <p>Finally, <a data-link-type="biblio" href="#biblio-p1841r1">[P1841R1]</a> ("Individually Specializable Numeric Traits") is
proposing to add individual traits for numeric types, complementing
and/or replacing the information that is currently found in the <code class="highlight"><c- n>numeric_limits</c-></code> class template. We do not see this as a problem, as
the functionality that we need in order to implement the trait we are
proposing is found, with identical meaning, both in <code class="highlight"><c- n>numeric_limits</c-></code> and in <a data-link-type="biblio" href="#biblio-p1841r1">[P1841R1]</a>'s proposed traits. However, this "double definition"
could impact the desired wording. Here, we seek SG6 and LEWG guidance.</p>
   <h2 class="heading settled" data-level="4" id="designdecisions"><span class="secno">4. </span><span class="content">Design Decisions</span><a class="self-link" href="#designdecisions"></a></h2>
   <h3 class="heading settled" data-level="4.1" id="what-defines-a-value-preserving-conversion"><span class="secno">4.1. </span><span class="content">What defines a "value-preserving conversion"?</span><a class="self-link" href="#what-defines-a-value-preserving-conversion"></a></h3>
   <p>Answering this question accurately is essential in order to have
a proper definition for the type trait that we are proposing.</p>
   <p>Given a conversion from type <code class="highlight"><c- n>From</c-></code> to a type <code class="highlight"><c- n>To</c-></code>, the semantic
operation that we want to model is that the value represented by the <code class="highlight"><c- n>From</c-></code> object preserves its numeric value after the conversion.</p>
   <p>Giving an operational definition is challenging, due to how C++
implicit conversions operate.</p>
   <p>Note that merely requiring that a "round-trip" conversion from <code class="highlight"><c- n>From</c-></code>,
to <code class="highlight"><c- n>To</c-></code>, and back to <code class="highlight"><c- n>From</c-></code> to yield back the original value is a
necessary but not sufficient condition. (For instance, <code class="highlight"><c- b>int</c-></code> to <code class="highlight"><c- b>unsigned</c-> <c- b>int</c-></code> is not a value-preserving conversion, despite the fact
that all such round-trip conversions would keep the original values.)
Similarly, requiring that the original value and the value after the
conversion compare equal (incl. taking NaN into account) is necessary
but not sufficient.</p>
   <p>Instead, one can give a semantic definition: a conversion is
value-preserving if and only if any possible value of type <code class="highlight"><c- n>From</c-></code>, when
converted to type <code class="highlight"><c- n>To</c-></code>, is exactly represented by the result of the
conversion. This includes numeric values, but also special values (NaN,
infinities, signed zeroes, ...) in case of floating-point types. The
wording "exactly represented" is already used by core language when
dealing with conversions (cf. [conv.double], [conv.fpint]), so we don’t
have to define it ourselves.</p>
   <p>The above semantics can be expressed in generic code by using the
facilities provided by <code class="highlight"><c- n>numeric_limits</c-></code>.</p>
   <p>(For instance, an unsigned integer type <code class="highlight"><c- n>I1</c-></code> has a value-preserving
conversion towards a signed integer type <code class="highlight"><c- n>I2</c-></code> if and only if <code class="highlight"><c- n>numeric_limits</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>>::</c-><c- n>radix</c-></code> raised to the power of <code class="highlight"><c- n>numeric_limits</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>>::</c-><c- n>digits</c-></code> is less than or equal to <code class="highlight"><c- n>numeric_limits</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>>::</c-><c- n>radix</c-></code> raised to the power of <code class="highlight"><c- n>numeric_limits</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>>::</c-><c- n>digits</c-></code>. On the
other hand, there is no value-preserving conversion from <code class="highlight"><c- n>I2</c-></code> to <code class="highlight"><c- n>I1</c-></code>.)</p>
   <p>This can be generalized to all the other conversions between arithmetic
types, by using their signedness (<code class="highlight"><c- n>is_signed</c-></code>), the <code class="highlight"><c- n>radix</c-></code>, the number
of digits (<code class="highlight"><c- n>digits</c-></code>), and for floating-point numbers (<code class="highlight"><c- n>is_integral</c-></code> is <code class="highlight">false</code>) the <code class="highlight"><c- n>max_exponent</c-></code> (or equivalently the minimum and maximum
finite values representable, by using <code class="highlight"><c- n>min</c-><c- p>()</c-></code> and <code class="highlight"><c- n>max</c-><c- p>()</c-></code> respectively).</p>
   <h3 class="heading settled" data-level="4.2" id="what-about-unbounded-types"><span class="secno">4.2. </span><span class="content">What about unbounded types?</span><a class="self-link" href="#what-about-unbounded-types"></a></h3>
   <p><code class="highlight"><c- n>numeric_limits</c-></code> allows to identify types that may represent a
non-finite set of values via the <code class="highlight"><c- n>is_bounded</c-></code> static data member.
While all foundamental types are bounded, a user may define unbounded
arithmetic types (for instance, an arbitrary precision type).</p>
   <p>The issue with such types is that we cannot entirely reason about them
in terms of <code class="highlight"><c- n>numeric_limits</c-></code> data members / member functions: many of
them are not meaningful for unbounded types.</p>
   <p>We can universally claim that the following conversions are not value-preserving:</p>
   <ul>
    <li data-md>
     <p>from an unbounded type to a bounded type;</p>
    <li data-md>
     <p>from a signed integer type to an unsigned integer type (bounded or not);</p>
    <li data-md>
     <p>from a floating-point type to an integer type (bounded or not);</p>
    <li data-md>
     <p>from a floating-point type that can represent special values (infinities, NaN, etc.) to a floating-point type (bounded or not) that cannot represent those values.</p>
   </ul>
   <p>We cannot however reason about are the conversions:</p>
   <ul>
    <li data-md>
     <p>from an unsigned integer type towards an unbounded signed integer type;</p>
    <li data-md>
     <p>from an arbitrary type towards an unbounded floating-point type,</p>
   </ul>
   <p>because there is no way (in general) to know what is the set of
representable values of an unbounded type. For instance, an
implementation of a unbounded type may use a "default" precision but
still let users tune it at runtime, globally and/or on a per-object
basis. A conversion towards an object of "default" precision may cause
information loss; while tuning the precision and then doing the
conversion would not. Since this property is not a static property of
the <code class="highlight"><c- n>To</c-></code> type, we cannot statically reason about it.</p>
   <p>We are therefore going to make a judgement call for these last two
cases: if it exists an implicit conversion between a type <code class="highlight"><c- n>From</c-></code> and
an unbonded type <code class="highlight"><c- n>To</c-></code>, and we cannot otherwise establish that the
conversion is not value-preserving, then we are going to assume that
the conversion <em>is</em> value-preserving (in other words, that the <code class="highlight"><c- n>To</c-></code> type is always going to use enough precision to correctly represent any
possible value of <code class="highlight"><c- n>From</c-></code>).</p>
   <h3 class="heading settled" data-level="4.3" id="should-the-type-trait-be-specializable-for-user-defined-datatypes"><span class="secno">4.3. </span><span class="content">Should the type trait be specializable for user-defined datatypes?</span><a class="self-link" href="#should-the-type-trait-be-specializable-for-user-defined-datatypes"></a></h3>
   <p>For the moment, we are <em>not</em> proposing it. This is consistent with the
other type traits defined in [meta] (cf. [meta.rqmts]/4).</p>
   <p>However, a program may add specializations to <code class="highlight"><c- n>numeric_limits</c-></code> (or
equivalently to <a data-link-type="biblio" href="#biblio-p1841r1">[P1841R1]</a>'s traits) for user-defined datatypes. We
expect the type trait that we are proposing to be indeed defined in
terms of <code class="highlight"><c- n>numeric_limits</c-></code>, and therefore we believe that users can use
that customization point in order to properly define the behavior of
our type trait. For this very reason, we are also <em>not</em> limiting our
type trait to work only with fundamental types.</p>
   <h3 class="heading settled" data-level="4.4" id="narrowing"><span class="secno">4.4. </span><span class="content">Is the proposed trait different from simply detecting narrowing conversions?</span><a class="self-link" href="#narrowing"></a></h3>
   <p>It is, in several ways:</p>
   <ul>
    <li data-md>
     <p>The definition of narrowing conversions between floating-point types
do not take into account the actual values representable by them. For
instance, a conversion from <code class="highlight"><c- b>long</c-> <c- b>double</c-></code> to <code class="highlight"><c- b>double</c-></code> is always
considered narrowing ([dcl.init.list]/7.2) even on architectures where
the two datatypes are backed by the very same representation (for
instance on architectures using IEEE754’s <code class="highlight"><c- n>binary64</c-></code> representation, such
as x86-64 under the MSVC ABI). The trait we are proposing would instead
take into account implementation-specific quantities. <a data-link-type="biblio" href="#biblio-p1467r7">[P1467R7]</a> proposes changes to the definition of narrowing conversions between
floating-point types (by introducing conversion ranks); such changes
are in line with the existing definition, in the sense that they do
not necessarily take into account the actual values representable by
a given type.</p>
    <li data-md>
     <p>Conversions from integer types to floating-point types are always
considered narrowing, even when the destination type can precisely
represent all the values of the source type ([dcl.init.list]/7.3).
This is the case for instance between <code class="highlight"><c- b>int</c-></code> and <code class="highlight"><c- b>double</c-></code> on x86-64
(under all the commonly used ABIs).</p>
    <li data-md>
     <p>Conversions from pointers to <code class="highlight"><c- b>bool</c-></code> are considered to be narrowing
([dcl.init.list]/7.5); however, the trait we are proposing only deals
with arithmetic-like types.</p>
    <li data-md>
     <p>Similarly, we are not dealing with (unscoped) enumeration types,
which are not arithmetic-like types.</p>
   </ul>
   <p>For these reasons we believe the trait we are proposing is actually
complementing <a data-link-type="biblio" href="#biblio-p0870r4">[P0870R4]</a>'s <code class="highlight"><c- n>is_convertible_without_narrowing</c-></code>, thus
giving users the ability of choosing the trait that best serves their
use cases.</p>
   <h3 class="heading settled" data-level="4.5" id="when-should-users-detect-narrowing-conversions-vs-value-preserving-conversions"><span class="secno">4.5. </span><span class="content">When should users detect narrowing conversions vs. value-preserving conversions?</span><a class="self-link" href="#when-should-users-detect-narrowing-conversions-vs-value-preserving-conversions"></a></h3>
   <p>It is hard to give a clear-cut answer to this question. The Standard
Library itself is inconsistent in this regard.</p>
   <p>We believe that each option comes with pros and cons (e.g. flexibility
vs. portability, see <a href="#motivation">§ 2 Motivation and Scope</a>) that each user has to evaluate
for themselves. We believe however that it is important to offer <em>both</em> options so that users <em>can</em> make the choice.</p>
   <h3 class="heading settled" data-level="4.6" id="bikeshedding-naming"><span class="secno">4.6. </span><span class="content">Bikeshedding: naming</span><a class="self-link" href="#bikeshedding-naming"></a></h3>
   <p>Many thanks go to Matthias Kretz, who proposed <code class="highlight"><c- n>is_value_preserving_conversion</c-></code> on SG6’s reflector. We’ve just adapted
the name to make it more in line with the other existing traits.</p>
   <h2 class="heading settled" data-level="5" id="implementationexperience"><span class="secno">5. </span><span class="content">Implementation experience</span><a class="self-link" href="#implementationexperience"></a></h2>
   <p>A working prototype of the changes proposed by this paper,
done on top of GCC 11, is available in this <a data-link-type="biblio" href="#biblio-p2509-gcc">GCC branch</a> on
GitHub.</p>
   <h2 class="heading settled" data-level="6" id="technicalspecifications"><span class="secno">6. </span><span class="content">Technical Specifications</span><a class="self-link" href="#technicalspecifications"></a></h2>
   <p>All the proposed changes are relative to <a data-link-type="biblio" href="#biblio-n4892">[N4892]</a>.</p>
   <h3 class="heading settled" data-level="6.1" id="feature-testing-macro"><span class="secno">6.1. </span><span class="content">Feature testing macro</span><a class="self-link" href="#feature-testing-macro"></a></h3>
   <p>Add to the list in [version.syn]:</p>
<pre class="highlight"><ins><c- cp>#define __cpp_­lib_­is_value_preserving_convertible YYYYMML  </c-><c- c1>// also in &lt;type_traits></c->
</ins></pre>
   <p>with the value specified as usual (year and month of adoption).</p>
   <h3 class="heading settled" data-level="6.2" id="proposedwording"><span class="secno">6.2. </span><span class="content">Proposed wording</span><a class="self-link" href="#proposedwording"></a></h3>
   <p>Modify [meta.type.synop] as follows:</p>
<pre class="highlight"><c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>From</c-><c- p>,</c-> <c- k>class</c-> <c- nc>To</c-><c- o>></c-> <c- k>struct</c-> <c- nc>is_nothrow_convertible</c-><c- p>;</c->
<ins><c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>From</c-><c- p>,</c-> <c- k>class</c-> <c- nc>To</c-><c- o>></c-> <c- k>struct</c-> <c- nc>is_value_preserving_convertible</c-><c- p>;</c-></ins>
</pre>
<pre class="highlight"><c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>From</c-><c- p>,</c-> <c- k>class</c-> <c- nc>To</c-><c- o>></c->
  <c- kr>inline</c-> <c- k>constexpr</c-> <c- b>bool</c-> <c- n>is_nothrow_convertible_v</c-> <c- o>=</c-> <c- n>is_</c->­<c- n>nothrow_</c->­<c- n>convertible</c-><c- o>&lt;</c-><c- n>From</c-><c- p>,</c-> <c- n>To</c-><c- o>>::</c-><c- n>value</c-><c- p>;</c->
<ins><c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>From</c-><c- p>,</c-> <c- k>class</c-> <c- nc>To</c-><c- o>></c->
    <c- kr>inline</c-> <c- k>constexpr</c-> <c- b>bool</c-> <c- n>is_value_preserving_convertible_v</c-> <c- o>=</c-> <c- n>is_value_preserving_convertible</c-><c- o>&lt;</c-><c- n>From</c-><c- p>,</c-> <c- n>To</c-><c- o>>::</c-><c- n>value</c-><c- p>;</c-></ins>
</pre>
   <p>Add a new row to the "Type relationship predicates" ([tab:meta.rel]) table:</p>
   <blockquote>
    <p>
     <strong>Template</strong>: 
     <ins><code class="highlight"><c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>From</c-><c- p>,</c-> <c- k>class</c-> <c- nc>To</c-><c- o>></c-> <c- k>struct</c-> <c- nc>is_value_preserving_convertible</c-><c- p>;</c-></code></ins>
    </p>
    <p>
     <strong>Condition</strong>: 
     <ins><em>see below</em></ins>
    </p>
    <p>
     <strong>Comments</strong>: 
     <ins><code class="highlight"><c- n>numeric_limits</c-><c- o>&lt;</c-><c- n>From</c-><c- o>>::</c-><c- n>is_specialized</c-></code> shall be <code class="highlight">true</code>,
and <code class="highlight"><c- n>numeric_limits</c-><c- o>&lt;</c-><c- n>To</c-><c- o>>::</c-><c- n>is_specialized</c-></code> shall be <code class="highlight">true</code>.</ins>
    </p>
   </blockquote>
   <p class="issue" id="issue-4f2c38f5"><a class="self-link" href="#issue-4f2c38f5"></a> what about <a data-link-type="biblio" href="#biblio-p1841r1">[P1841R1]</a>'s traits?</p>
   <p class="issue" id="issue-10275029"><a class="self-link" href="#issue-10275029"></a> is L(E)WG fine at adding a dependency from <code class="highlight"><c- o>&lt;</c-><c- n>type_traits</c-><c- o>></c-></code> to <code class="highlight"><c- o>&lt;</c-><c- n>limits</c-><c- o>></c-></code>?</p>
   <p>Add a new paragraph at the end of [meta.rel]:</p>
   <blockquote>
    <ins> <strong>6</strong> The predicate condition for a template specialization <code class="highlight"><c- n>is_value_preserving_convertible</c-><c- o>&lt;</c-><c- n>From</c-><c- p>,</c-> <c- n>To</c-><c- o>></c-></code> is satisfied if and only if <code class="highlight"><c- n>is_</c->­<c- n>convertible_v</c-><c- o>&lt;</c-><c- n>From</c-><c- p>,</c-> <c- n>To</c-><c- o>></c-></code> is <code class="highlight">true</code>, and each and every possible
value representable by a source object of type <code class="highlight"><c- n>From</c-></code> is exactly
represented by the object obtained after converting the source object
from <code class="highlight"><c- n>From</c-></code> to <code class="highlight"><c- n>To</c-></code> using an implicit conversion ([conv]).
[<em>Note 4</em>: This includes values such as infinity, quiet and signaling
"Not a Number", and so on. -- <em>end note</em>]
[<em>Note 5</em>: If <code class="highlight"><c- n>numeric_limits</c-><c- o>&lt;</c-><c- n>From</c-><c- o>>::</c-><c- n>is_bounded</c-></code> is <code class="highlight">false</code> and <code class="highlight"><c- n>numeric_limits</c-><c- o>&lt;</c-><c- n>To</c-><c- o>>::</c-><c- n>is_bounded</c-></code> is <code class="highlight">true</code>, then the predicate
condition shall not be satisfied. If <code class="highlight"><c- n>numeric_limits</c-><c- o>&lt;</c-><c- n>To</c-><c- o>>::</c-><c- n>is_bounded</c-></code> is <code class="highlight">false</code>, an implementation is allowed to assume that any value
representable by a source object of type <code class="highlight"><c- n>From</c-></code> is exactly represented
by the object obtained after converting the source object from <code class="highlight"><c- n>From</c-></code> to <code class="highlight"><c- n>To</c-></code>, unless it can otherwise detect that this is not the case (for
instance, if <code class="highlight"><c- n>From</c-></code> is a signed integer type and <code class="highlight"><c- n>To</c-></code> is unsigned). —<wbr><em>end note</em> ] </ins>
   </blockquote>
   <h2 class="heading settled" data-level="7" id="acknowledgements"><span class="secno">7. </span><span class="content">Acknowledgements</span><a class="self-link" href="#acknowledgements"></a></h2>
   <p>Thanks to KDAB for supporting this work.</p>
   <p>All remaining errors are ours and ours only.</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-n4892">[N4892]
   <dd>Thomas Köppe. <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2021/n4892.pdf"><cite>Working Draft, Standard for Programming Language C++</cite></a>. URL: <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2021/n4892.pdf">http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2021/n4892.pdf</a>
   <dt id="biblio-p0870r4">[P0870R4]
   <dd>Giuseppe D'Angelo. <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2020/p0870r4.html"><cite>A proposal for a type trait to detect narrowing conversions</cite></a>. URL: <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2020/p0870r4.html">http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2020/p0870r4.html</a>
   <dt id="biblio-p1467r7">[P1467R7]
   <dd>David Olsen; Ilya Burylov; Michał Dominiak. <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2021/p1467r7.html"><cite>Extended floating-point types and standard names</cite></a>. URL: <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2021/p1467r7.html">http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2021/p1467r7.html</a>
   <dt id="biblio-p1619r1">[P1619R1]
   <dd>Lisa Lippincott. <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p1619r1.pdf"><cite>Functions for Testing Boundary Conditions on Integer Operations</cite></a>. URL: <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p1619r1.pdf">http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p1619r1.pdf</a>
   <dt id="biblio-p1841r1">[P1841R1]
   <dd>Walter E. Brown. <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2020/p1841r1.pdf"><cite>Individually Specializable Numeric Traits</cite></a>. URL: <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2020/p1841r1.pdf">http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2020/p1841r1.pdf</a>
   <dt id="biblio-p1998r1">[P1998R1]
   <dd>Ryan McDougall. <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2020/p1998r1.pdf"><cite>Simple Facility for Lossless Integer Conversion</cite></a>. URL: <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2020/p1998r1.pdf">http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2020/p1998r1.pdf</a>
   <dt id="biblio-p2509-gcc">[P2509-GCC]
   <dd>Giuseppe D'Angelo. <a href="https://github.com/dangelog/gcc/tree/std-proposals"><cite>P2509 prototype implementation</cite></a>. URL: <a href="https://github.com/dangelog/gcc/tree/std-proposals">https://github.com/dangelog/gcc/tree/std-proposals</a>
   <dt id="biblio-qangle">[QAngle]
   <dd>Giuseppe D'Angelo. <a href="https://codereview.qt-project.org/c/qt/qtbase/+/191717"><cite>Long live Q(Generic)Angle!</cite></a>. URL: <a href="https://codereview.qt-project.org/c/qt/qtbase/+/191717">https://codereview.qt-project.org/c/qt/qtbase/+/191717</a>
  </dl>
  <h2 class="no-num no-ref heading settled" id="issues-index"><span class="content">Issues Index</span><a class="self-link" href="#issues-index"></a></h2>
  <div style="counter-reset:issue">
   <div class="issue"> what about <a data-link-type="biblio" href="#biblio-p1841r1">[P1841R1]</a>'s traits? <a class="issue-return" href="#issue-4f2c38f5" title="Jump to section">↵</a></div>
   <div class="issue"> is L(E)WG fine at adding a dependency from <code class="highlight"><c- o>&lt;</c-><c- n>type_traits</c-><c- o>></c-></code> to <code class="highlight"><c- o>&lt;</c-><c- n>limits</c-><c- o>></c-></code>? <a class="issue-return" href="#issue-10275029" title="Jump to section">↵</a></div>
  </div>