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 <head>
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  <title>P1467R4: Extended floating-point types and standard names</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: medium;
	}
	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,
	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;
		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;
		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-top: 0.1rem;
		/* Larger, more consistently-sized click target */
		display: block;
		/* Reverse color scheme */
		color: black;
		border-color: #3980B5;
		border-bottom-width: 3px !important;
		margin-bottom: 0px !important;
	}
	.toc a:visited {
		border-color: #054572;
	}
	.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;
		line-height: 1.1rem; /* consistent spacing */
	}

	/* 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 .secno { font-size: 85%; }
	.toc > li li li li li { font-size:   85%;    }
	.toc > li li li li li .secno { font-size: 100%; }

	/* @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 {
			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; }
		}
	/* } */

	@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 {
			background: rgba(75%, 75%, 75%, .25);
			border-bottom: 3px solid #054572;
			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 span {
			white-space: nowrap;
			color: transparent; }
		ul.index li a:hover + span,
		ul.index li a:focus + span {
			color: #707070;
		}
	}

/** 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]) {
		background: #f7f8f9;
	}

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

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

	@media print {
		/* Pages have their own margins. */
		html {
			margin: 0;
		}
		/* Serif for print. */
		body {
			font-family: serif;
		}
	}
	@page {
		margin: 1.5cm 1.1cm;
	}

/******************************************************************************/
/*                                    Legacy                                  */
/******************************************************************************/

	/* This rule is inherited from past style sheets. No idea what it's for. */
	.hide { display: none }



/******************************************************************************/
/*                             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 table positioning:
		   "content column" is 50ems wide at max; less on smaller screens.
		   Extra space (after ToC + content) is empty on the right.

		   1. When table < content column, centers table in column.
		   2. When content < table < available, left-aligns.
		   3. When table > 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 40de15f9, updated Thu Jun 11 17:47:04 2020 -0700" name="generator">
  <link href="https://wg21.link/p1467r4" rel="canonical">
  <link href="https://isocpp.org/favicon.ico" rel="icon">
<style>
.ins, ins, ins *, span.ins, span.ins * {
  background-color: rgb(200, 250, 200);
  color: rgb(0, 136, 0);
  text-decoration: underline;
}
.del, del, del *, span.del, span.del * {
  background-color: rgb(250, 200, 200);
  color: rgb(255, 0, 0);
  text-decoration: line-through;
  text-decoration-color: rgb(255, 0, 0);
}
ul {
  list-style-type: "- ";
}
blockquote {
  counter-reset: paragraph;
}
div.numbered, div.newnumbered {
  margin-left: 2em;
  margin-top: 1em;
  margin-bottom: 1em;
}
div.numbered:before, div.newnumbered:before {
  position: absolute;
  margin-left: -2em;
  display-style: block;
}
div.numbered:before {
  content: counter(paragraph);
  counter-increment: paragraph;
}
div.newnumbered:before {
  content: "�";
}
div.numbered ul, div.newnumbered ul {
  counter-reset: list_item;
}
div.numbered li, div.newnumbered li {
  margin-left: 3em;
}
div.numbered li:before, div.newnumbered li:before {
  position: absolute;
  margin-left: -4.8em;
  display-style: block;
}
div.numbered li:before {
  content: "(" counter(paragraph) "." counter(list_item) ")";
  counter-increment: list_item;
}
div.newnumbered li:before {
  content: "(�." counter(list_item) ")";
  counter-increment: list_item;
}
</style>
<style>/* style-autolinks */

.css.css, .property.property, .descriptor.descriptor {
    color: #005a9c;
    font-size: inherit;
    font-family: inherit;
}
.css::before, .property::before, .descriptor::before {
    content: "‘";
}
.css::after, .property::after, .descriptor::after {
    content: "’";
}
.property, .descriptor {
    /* Don't wrap property and descriptor names */
    white-space: nowrap;
}
.type { /* CSS value <type> */
    font-style: italic;
}
pre .property::before, pre .property::after {
    content: "";
}
[data-link-type="property"]::before,
[data-link-type="propdesc"]::before,
[data-link-type="descriptor"]::before,
[data-link-type="value"]::before,
[data-link-type="function"]::before,
[data-link-type="at-rule"]::before,
[data-link-type="selector"]::before,
[data-link-type="maybe"]::before {
    content: "‘";
}
[data-link-type="property"]::after,
[data-link-type="propdesc"]::after,
[data-link-type="descriptor"]::after,
[data-link-type="value"]::after,
[data-link-type="function"]::after,
[data-link-type="at-rule"]::after,
[data-link-type="selector"]::after,
[data-link-type="maybe"]::after {
    content: "’";
}

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

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

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

body {
    counter-reset: example figure issue;
}
.issue {
    counter-increment: issue;
}
.issue:not(.no-marker)::before {
    content: "Issue " counter(issue);
}

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

figcaption {
    counter-increment: figure;
}
figcaption:not(.no-marker)::before {
    content: "Figure " counter(figure) " ";
}</style>
<style>/* style-hidedel */

            #hidedel:checked ~ del, #hidedel:checked ~ * del { display:none; }
            #hidedel ~ #hidedel-label::before, #hidedel ~ * #hidedel-label::before { content: "☐ "; }
            #hidedel:checked ~ #hidedel-label::before, #hidedel:checked ~ * #hidedel-label::before { content: "☑ "; }
        </style>
<style>/* style-md-lists */

/* This is a weird hack for me not yet following the commonmark spec
   regarding paragraph and lists. */
[data-md] > :first-child {
    margin-top: 0;
}
[data-md] > :last-child {
    margin-bottom: 0;
}</style>
<style>/* style-selflinks */

.heading, .issue, .note, .example, li, dt {
    position: relative;
}
a.self-link {
    position: absolute;
    top: 0;
    left: calc(-1 * (3.5rem - 26px));
    width: calc(3.5rem - 26px);
    height: 2em;
    text-align: center;
    border: none;
    transition: opacity .2s;
    opacity: .5;
}
a.self-link:hover {
    opacity: 1;
}
.heading > a.self-link {
    font-size: 83%;
}
li > a.self-link {
    left: calc(-1 * (3.5rem - 26px) - 2em);
}
dfn > a.self-link {
    top: auto;
    left: auto;
    opacity: 0;
    width: 1.5em;
    height: 1.5em;
    background: gray;
    color: white;
    font-style: normal;
    transition: opacity .2s, background-color .2s, color .2s;
}
dfn:hover > a.self-link {
    opacity: 1;
}
dfn > a.self-link:hover {
    color: black;
}

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

.highlight:not(.idl) { background: hsl(24, 20%, 95%); }
code.highlight { padding: .1em; border-radius: .3em; }
pre.highlight, pre > code.highlight { display: block; padding: 1em; margin: .5em 0; overflow: auto; border-radius: 0; }
c-[a] { color: #990055 } /* Keyword.Declaration */
c-[b] { color: #990055 } /* Keyword.Type */
c-[c] { color: #708090 } /* Comment */
c-[d] { color: #708090 } /* Comment.Multiline */
c-[e] { color: #0077aa } /* Name.Attribute */
c-[f] { color: #669900 } /* Name.Tag */
c-[g] { color: #222222 } /* Name.Variable */
c-[k] { color: #990055 } /* Keyword */
c-[l] { color: #000000 } /* Literal */
c-[m] { color: #000000 } /* Literal.Number */
c-[n] { color: #0077aa } /* Name */
c-[o] { color: #999999 } /* Operator */
c-[p] { color: #999999 } /* Punctuation */
c-[s] { color: #a67f59 } /* Literal.String */
c-[t] { color: #a67f59 } /* Literal.String.Single */
c-[u] { color: #a67f59 } /* Literal.String.Double */
c-[cp] { color: #708090 } /* Comment.Preproc */
c-[c1] { color: #708090 } /* Comment.Single */
c-[cs] { color: #708090 } /* Comment.Special */
c-[kc] { color: #990055 } /* Keyword.Constant */
c-[kn] { color: #990055 } /* Keyword.Namespace */
c-[kp] { color: #990055 } /* Keyword.Pseudo */
c-[kr] { color: #990055 } /* Keyword.Reserved */
c-[ld] { color: #000000 } /* Literal.Date */
c-[nc] { color: #0077aa } /* Name.Class */
c-[no] { color: #0077aa } /* Name.Constant */
c-[nd] { color: #0077aa } /* Name.Decorator */
c-[ni] { color: #0077aa } /* Name.Entity */
c-[ne] { color: #0077aa } /* Name.Exception */
c-[nf] { color: #0077aa } /* Name.Function */
c-[nl] { color: #0077aa } /* Name.Label */
c-[nn] { color: #0077aa } /* Name.Namespace */
c-[py] { color: #0077aa } /* Name.Property */
c-[ow] { color: #999999 } /* Operator.Word */
c-[mb] { color: #000000 } /* Literal.Number.Bin */
c-[mf] { color: #000000 } /* Literal.Number.Float */
c-[mh] { color: #000000 } /* Literal.Number.Hex */
c-[mi] { color: #000000 } /* Literal.Number.Integer */
c-[mo] { color: #000000 } /* Literal.Number.Oct */
c-[sb] { color: #a67f59 } /* Literal.String.Backtick */
c-[sc] { color: #a67f59 } /* Literal.String.Char */
c-[sd] { color: #a67f59 } /* Literal.String.Doc */
c-[se] { color: #a67f59 } /* Literal.String.Escape */
c-[sh] { color: #a67f59 } /* Literal.String.Heredoc */
c-[si] { color: #a67f59 } /* Literal.String.Interpol */
c-[sx] { color: #a67f59 } /* Literal.String.Other */
c-[sr] { color: #a67f59 } /* Literal.String.Regex */
c-[ss] { color: #a67f59 } /* Literal.String.Symbol */
c-[vc] { color: #0077aa } /* Name.Variable.Class */
c-[vg] { color: #0077aa } /* Name.Variable.Global */
c-[vi] { color: #0077aa } /* Name.Variable.Instance */
c-[il] { color: #000000 } /* Literal.Number.Integer.Long */
</style>
 <body class="h-entry">
  <input id="hidedel" style="display:none" type="checkbox">
  <div class="head">
   <p data-fill-with="logo"></p>
   <h1 class="p-name no-ref" id="title">P1467R4<br>Extended floating-point types and standard names</h1>
   <h2 class="no-num no-toc no-ref heading settled" id="subtitle"><span class="content">Published Proposal, <time class="dt-updated" datetime="2020-06-12">2020-06-12</time></span></h2>
   <div data-fill-with="spec-metadata">
    <dl>
     <dt>This version:
     <dd><a class="u-url" href="https://wg21.link/p1467r4">https://wg21.link/p1467r4</a>
     <dt>Issue Tracking:
     <dd><a href="#issues-index">Inline In Spec</a>
     <dt>Authors:
     <dd>
      <dd class="editor p-author h-card vcard"><a class="p-name fn u-email email" href="mailto:dolsen@nvidia.com">David Olsen</a> (<span class="p-org org">NVIDIA</span>)
     <dd>
      <dd class="editor p-author h-card vcard"><a class="p-name fn u-email email" href="mailto:griwes@griwes.info">Michał Dominiak</a> (<span class="p-org org">NVIDIA</span>)
     <dt>Audience:
     <dd>EWG, LEWG
     <dt>Toggle Diffs:
     <dd>
      <label for="hidedel" id="hidedel-label">Hide deleted text</label>
     <dt>Project:
     <dd>ISO/IEC JTC1/SC22/WG21 14882: Programming Language — C++
    </dl>
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  <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="#abstract"><span class="secno">1</span> <span class="content">Abstract</span></a>
    <li>
     <a href="#revisions"><span class="secno">2</span> <span class="content">Revision history</span></a>
     <ol class="toc">
      <li><a href="#r1"><span class="secno">2.1</span> <span class="content">R0 -> R1 (pre-Cologne)</span></a>
      <li><a href="#r2"><span class="secno">2.2</span> <span class="content">R1 -> R2 (pre-Belfast)</span></a>
      <li><a href="#r3"><span class="secno">2.3</span> <span class="content">R2 -> R3 (pre-Prage)</span></a>
      <li><a href="#r4"><span class="secno">2.4</span> <span class="content">R3 -> R4 (Summer 2020)</span></a>
     </ol>
    <li><a href="#motivation"><span class="secno">3</span> <span class="content">Motivation</span></a>
    <li><a href="#c-compat"><span class="secno">4</span> <span class="content">C Compatibility</span></a>
    <li>
     <a href="#core"><span class="secno">5</span> <span class="content">Core language changes</span></a>
     <ol class="toc">
      <li><a href="#core-no-change"><span class="secno">5.1</span> <span class="content">Things that aren’t changing</span></a>
      <li>
       <a href="#extended"><span class="secno">5.2</span> <span class="content">Extended floating-point types</span></a>
       <ol class="toc">
        <li><a href="#extended-reason"><span class="secno">5.2.1</span> <span class="content">Reasoning</span></a>
        <li><a href="#extended-wording"><span class="secno">5.2.2</span> <span class="content">Wording</span></a>
       </ol>
      <li>
       <a href="#rank"><span class="secno">5.3</span> <span class="content">Conversion rank</span></a>
       <ol class="toc">
        <li><a href="#rank-reason"><span class="secno">5.3.1</span> <span class="content">Reasoning</span></a>
        <li><a href="#rank-wording"><span class="secno">5.3.2</span> <span class="content">Wording</span></a>
       </ol>
      <li>
       <a href="#promotion"><span class="secno">5.4</span> <span class="content">Promotion</span></a>
       <ol class="toc">
        <li><a href="#promotion-reason"><span class="secno">5.4.1</span> <span class="content">Reasoning</span></a>
        <li><a href="#promotion-wording"><span class="secno">5.4.2</span> <span class="content">Wording</span></a>
       </ol>
      <li>
       <a href="#implicit"><span class="secno">5.5</span> <span class="content">Implicit conversions</span></a>
       <ol class="toc">
        <li><a href="#implicit-reason"><span class="secno">5.5.1</span> <span class="content">Reasoning</span></a>
        <li><a href="#implicit-wording"><span class="secno">5.5.2</span> <span class="content">Wording</span></a>
       </ol>
      <li>
       <a href="#arithmetic"><span class="secno">5.6</span> <span class="content">Usual arithmetic conversions</span></a>
       <ol class="toc">
        <li><a href="#arithmetic-example"><span class="secno">5.6.1</span> <span class="content">Example</span></a>
        <li><a href="#arithmetic-wording"><span class="secno">5.6.2</span> <span class="content">Wording</span></a>
       </ol>
      <li>
       <a href="#narrow"><span class="secno">5.7</span> <span class="content">Narrowing conversions</span></a>
       <ol class="toc">
        <li><a href="#narrow-reason"><span class="secno">5.7.1</span> <span class="content">Same representation</span></a>
        <li><a href="#narrow-constant"><span class="secno">5.7.2</span> <span class="content">Constant values</span></a>
        <li><a href="#narrow-wording"><span class="secno">5.7.3</span> <span class="content">Wording</span></a>
       </ol>
      <li>
       <a href="#overload"><span class="secno">5.8</span> <span class="content">Overload resolution</span></a>
       <ol class="toc">
        <li><a href="#overload-reason"><span class="secno">5.8.1</span> <span class="content">Reasoning</span></a>
        <li><a href="#overload-wording"><span class="secno">5.8.2</span> <span class="content">Wording</span></a>
        <li>
         <a href="#overload-alternate"><span class="secno">5.8.3</span> <span class="content">Alternate proposals</span></a>
         <ol class="toc">
          <li><a href="#overload-same-rep"><span class="secno">5.8.3.1</span> <span class="content">Prefer same representation</span></a>
          <li><a href="#overload-no-change"><span class="secno">5.8.3.2</span> <span class="content">No change</span></a>
         </ol>
       </ol>
      <li><a href="#pointer"><span class="secno">5.9</span> <span class="content">Pointer conversions</span></a>
      <li><a href="#core-test-macro"><span class="secno">5.10</span> <span class="content">Feature test macro</span></a>
     </ol>
    <li>
     <a href="#library"><span class="secno">6</span> <span class="content">Library changes</span></a>
     <ol class="toc">
      <li>
       <a href="#new-names"><span class="secno">6.1</span> <span class="content">Possible new names</span></a>
       <ol class="toc">
        <li><a href="#new-names-standard"><span class="secno">6.1.1</span> <span class="content">Standard/extended floating-point traits</span></a>
        <li><a href="#new-names-conv"><span class="secno">6.1.2</span> <span class="content">Conversion rank trait</span></a>
       </ol>
      <li>
       <a href="#charconv"><span class="secno">6.2</span> <span class="content"><code class="highlight"><c- o>&lt;</c-><c- n>charconv</c-><c- o>></c-></code></span></a>
       <ol class="toc">
        <li><a href="#charconv-wording"><span class="secno">6.2.1</span> <span class="content">Wording</span></a>
       </ol>
      <li>
       <a href="#format"><span class="secno">6.3</span> <span class="content"><code class="highlight"><c- o>&lt;</c-><c- n>format</c-><c- o>></c-></code></span></a>
       <ol class="toc">
        <li><a href="#format-wording"><span class="secno">6.3.1</span> <span class="content">Wording</span></a>
       </ol>
      <li>
       <a href="#cmath"><span class="secno">6.4</span> <span class="content"><code class="highlight"><c- o>&lt;</c-><c- n>cmath</c-><c- o>></c-></code></span></a>
       <ol class="toc">
        <li><a href="#cmath-wording"><span class="secno">6.4.1</span> <span class="content">Wording</span></a>
       </ol>
      <li>
       <a href="#complex"><span class="secno">6.5</span> <span class="content"><code class="highlight"><c- o>&lt;</c-><c- n>complex</c-><c- o>></c-></code></span></a>
       <ol class="toc">
        <li><a href="#complex-wording"><span class="secno">6.5.1</span> <span class="content">Wording</span></a>
       </ol>
      <li>
       <a href="#atomic"><span class="secno">6.6</span> <span class="content"><code class="highlight"><c- o>&lt;</c-><c- n>atomic</c-><c- o>></c-></code></span></a>
       <ol class="toc">
        <li><a href="#atomic-wording"><span class="secno">6.6.1</span> <span class="content">Wording</span></a>
       </ol>
      <li><a href="#lib-test-macro"><span class="secno">6.7</span> <span class="content">Feature test macro</span></a>
     </ol>
    <li>
     <a href="#alias"><span class="secno">7</span> <span class="content">Type aliases</span></a>
     <ol class="toc">
      <li><a href="#alias-header"><span class="secno">7.1</span> <span class="content">Header name</span></a>
      <li><a href="#alias-formats"><span class="secno">7.2</span> <span class="content">Supported formats</span></a>
      <li><a href="#alias-alias"><span class="secno">7.3</span> <span class="content">Aliasing standard types</span></a>
      <li><a href="#layout-vs-behavior"><span class="secno">7.4</span> <span class="content">Layout vs. behavior</span></a>
      <li><a href="#test-macros"><span class="secno">7.5</span> <span class="content">Feature test macros</span></a>
      <li>
       <a href="#names"><span class="secno">7.6</span> <span class="content">Names</span></a>
       <ol class="toc">
        <li><a href="#floatX_t"><span class="secno">7.6.1</span> <span class="content"><code class="highlight"><c- n>floatX_t</c-></code></span></a>
        <li><a href="#fp_namespace"><span class="secno">7.6.2</span> <span class="content"><code class="highlight"><c- n>fp</c-><c- o>::</c-><c- n>binaryX_t</c-></code></span></a>
        <li><a href="#fp_binaryX_t"><span class="secno">7.6.3</span> <span class="content"><code class="highlight"><c- n>fp_binaryX_t</c-></code></span></a>
       </ol>
      <li><a href="#literals"><span class="secno">7.7</span> <span class="content">Literal suffixes</span></a>
     </ol>
    <li>
     <a href="#references"><span class="secno"></span> <span class="content">References</span></a>
     <ol class="toc">
      <li><a href="#informative"><span class="secno"></span> <span class="content">Informative References</span></a>
     </ol>
    <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="abstract"><span class="secno">1. </span><span class="content">Abstract</span><a class="self-link" href="#abstract"></a></h2>
   <p>Allow implementations to define <em>extended floating-point types</em> in addition to the three standard floating-point types.  Define rules for how the extended floating-point types interact with each other and with other types without changing the behavior of the existing standard floating-point types.  Specify the rules for type conversions, arithmetic conversions, promotions, narrowing conversions, and overload resolution in a way that strikes a balance between behaving like existing types and encouraging safe code.  Specify the necessary library support, mostly additional overloads for functions that take floating-point arguments, for the extended floating-point types.</p>
   <p>Define an optional set of <code class="highlight"><c- o>&lt;</c-><c- n>cstdint</c-><c- o>></c-></code>-style type aliases for floating-point types matching specific, well-known floating-point layouts.</p>
   <h2 class="heading settled" data-level="2" id="revisions"><span class="secno">2. </span><span class="content">Revision history</span><a class="self-link" href="#revisions"></a></h2>
   <h3 class="heading settled" data-level="2.1" id="r1"><span class="secno">2.1. </span><span class="content">R0 -> R1 (pre-Cologne)</span><a class="self-link" href="#r1"></a></h3>
   <p>Applied guidance from <a href="http://wiki.edg.com/bin/view/Wg21kona2019/SG6MinutesP1468">SG6</a> in Kona 2019:</p>
   <ol>
    <li data-md>
     <p>Make the floating-point conversion rank not ordered between types with overlapping (but not subsetted) ranges of finite values.  This makes the ranking a partial order.</p>
    <li data-md>
     <p>Narrowing conversions are now based on floating-point conversion rank instead of ranges of finite values, which preservesthe current narrowing conversions relations between standard floating-point types; it also interacts favorably with the rank being a partial ordering.</p>
    <li data-md>
     <p>Operations that deal with floating-point types whose conversion ranks are unordered are now ill-formed.</p>
    <li data-md>
     <p>The relevant parts of the guidance have been applied to the library wording section as well.</p>
   </ol>
   <p>Afterwards, applied suggestions from <a href="http://wiki.edg.com/bin/view/Wg21kona2019/P1467">EWGI</a> in Kona 2019 (this modifies some of the points above):</p>
   <ol>
    <li data-md>
     <p>Apply the suggestion to make types where one has a wider range of finite values, but a lower precision than the other, unordered in their conversion rank, and therefore make operations that mix them ill-formed. The motivating example was IEEE-754 <code class="highlight"><c- n>binary16</c-></code> and <code class="highlight"><c- n>bfloat16</c-></code>; see <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p1467r1.html#rank">Floating-point conversion rank</a> for more details. This change also caused this paper to drop the term "range of finite values", since the modified semantics are better expressed in terms of sets of values of the types.</p>
    <li data-md>
     <p>Add a change to narrowing conversions, to only allow exact conversions to happen.</p>
    <li data-md>
     <p>Explicitly list parts of the language that are not changed by this paper; provide a more detailed analysis of the standard library impact.</p>
   </ol>
   <h3 class="heading settled" data-level="2.2" id="r2"><span class="secno">2.2. </span><span class="content">R1 -> R2 (pre-Belfast)</span><a class="self-link" href="#r2"></a></h3>
   <p>Changes based on feedback in Cologne from <a href="http://wiki.edg.com/bin/view/Wg21cologne2019/SG6P1468">SG6</a>, <a href="http://wiki.edg.com/bin/view/Wg21cologne2019/P1467">LEWGI</a>, and <a href="http://wiki.edg.com/bin/view/Wg21cologne2019/P1468">EWGI</a>.  Further changes came from further development of the paper by the authors, especially <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p1467r2.html#overload">overload resolution</a>.</p>
   <ul>
    <li data-md>
     <p>Revised floating-point <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p1467r2.html#promotion">promotion</a> rules.  Removed all promotions other than <code class="highlight"><c- b>float</c-></code> to <code class="highlight"><c- b>double</c-></code>.  Added wording for promoting values passed to varargs functions.</p>
    <li data-md>
     <p>Added the section on <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p1467r2.html#implicit">implicit conversions</a>.</p>
    <li data-md>
     <p>Added the section on <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p1467r2.html#overload">overload resolution</a>.</p>
    <li data-md>
     <p>Added the section about <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p1467r2.html#core-test-macro">feature test macros</a>.</p>
    <li data-md>
     <p>Added the sections about the possibility of new <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p1467r2.html#new-names">library traits</a>.</p>
    <li data-md>
     <p>Changed the wording for the <code class="highlight"><c- n>abs</c-></code> function in the <code class="highlight"><c- o>&lt;</c-><c- n>cmath</c-><c- o>></c-></code> section.</p>
    <li data-md>
     <p>Added constraints to the I/O streams overloads for <code class="highlight"><c- n>complex</c-></code> to only support standard floating-point types.</p>
    <li data-md>
     <p>Added the section about possible changes to <code class="highlight"><c- o>&lt;</c-><c- n>atomic</c-><c- o>></c-></code>.</p>
   </ul>
   <h3 class="heading settled" data-level="2.3" id="r3"><span class="secno">2.3. </span><span class="content">R2 -> R3 (pre-Prage)</span><a class="self-link" href="#r3"></a></h3>
   <p>Changes based on feedback in Belfast from <a href="http://wiki.edg.com/bin/view/Wg21belfast/P1467-EWG">EWG</a>.</p>
   <ul>
    <li data-md>
     <p>Change the <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2020/p1467r3.html#overload">overload resolution</a> rules, removing the rule that prefers one standard conversion over another based on conversion rank.  Replace it with a rule that prefers one standard conversion over another only when the two types have the same representation.</p>
    <li data-md>
     <p>As a result of the overload resolution change, change floating-point <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2020/p1467r3.html#promotion">promotion</a> so that any type smaller than <code class="highlight"><c- b>double</c-></code> promotes to <code class="highlight"><c- b>double</c-></code>.</p>
    <li data-md>
     <p>Allow implicit conversions between pointer types that point to floating-point types with the same representation.</p>
   </ul>
   <h3 class="heading settled" data-level="2.4" id="r4"><span class="secno">2.4. </span><span class="content">R3 -> R4 (Summer 2020)</span><a class="self-link" href="#r4"></a></h3>
   <p>Merge <a href="http://wg21.link/p1468r3">P1468</a> into P1467.  The two papers were separate proposals when first written.  But over time they have become intertwined, with design decisions in one paper affecting the feasibility of the other.  So the two papers are being merged into a single proposal in P1467R4.</p>
   <p>Changes based on feedback in Prague from EWG, where the discussion was all about what the goals of the proposal should be.  The group settled on a set of design decisions (see the <a href="https://github.com/cplusplus/papers/issues/227#issuecomment-584655443">poll results</a>) that strike a balance between the existing behavior of arithmetic types and a "safe by default" strategy.</p>
   <p>Changes between <a href="http://wg21.link/p1467r3">P1467R3</a> and P1647R4:</p>
   <ul>
    <li data-md>
     <p>Add section <a href="#c-compat">§ 4 C Compatibility</a></p>
    <li data-md>
     <p>Revert the rules for floating-point <a href="#promotion">§ 5.4 Promotion</a> back to what they were in <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p1467r2.html#promotion">P1647R2</a>, which is essentially unchanged from the current C++ standard.  This was necessitated by changes to the overload resolution rules.</p>
    <li data-md>
     <p>Resolve the open issue of <a href="#implicit">§ 5.5 Implicit conversions</a>.  In R3, it was undecided if potentially lossy conversions should be implicit.  EWG in Prague was strongly in favor of requiring lossy conversions to be explicit.  The section on implicit conversions now reflects that guidance.</p>
    <li data-md>
     <p>Revert the rules for <a href="#overload">§ 5.8 Overload resolution</a> back to what they were in <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p1467r2.html#overload">P1647R2</a>, with a small fix to the proposed wording changes.  Two alternate ideas for overload resolution are now listed.</p>
    <li data-md>
     <p>Withdraw the proposed change for <a href="#pointer">§ 5.9 Pointer conversions</a>.</p>
   </ul>
   <p>Changes to the content of <a href="http://wg21.link/p1468r3">P1468R3</a> as it was merged into P1647R4:</p>
   <ul>
    <li data-md>
     <p>Changed the proposed <a href="#literals">§ 7.7 Literal suffixes</a> to match what will be available in C2x.</p>
   </ul>
   <h2 class="heading settled" data-level="3" id="motivation"><span class="secno">3. </span><span class="content">Motivation</span><a class="self-link" href="#motivation"></a></h2>
   <p>16-bit floating-point support is becoming more widely available in both hardware (ARM CPUs and NVIDIA GPUs) and software (OpenGL, CUDA, and LLVM IR).  Programmers wanting to take advantage of 16-bit floating-point support have been stymied by the lack of built-in compiler support for the type.  A common workaround is to define a class type with all of the conversion operators and overloaded arithmetic operators to make it behave as much as possible like a built-in type.  But that approach is cumbersome and incomplete, requiring inline assembly or other compiler-specific magic to generate efficient code.</p>
   <p>The problem of efficiently using newer floating-point types that haven’t traditionally been supported can’t be solved through user-defined libraries.  A possible solution of an implementation changing <code class="highlight"><c- b>float</c-></code> to be a 16-bit type would be unpopular because users want support for newer floating-point types in addition to the standard types, and because users have come to expect <code class="highlight"><c- b>float</c-></code> and <code class="highlight"><c- b>double</c-></code> to be 32- and 64-bit types and have lots of existing code written with that assumption.</p>
   <p>This problem is worth solving, and there is no viable solution under the current standard.  So changing the core language in an extensible and backward-compatible way is appropriate.  Providing a standard way for implementations to support 16-bit floating-point types will result in better code, more portable code, and wider use of those types.</p>
   <p>While deciding what names to give to the 16-bit floating-point types, it was decided that C++ would benefit from having standard names for other larger floating-point types that are commonly used.  Having names for specific floating-point formats allows users to more clearly specify their intent.  If a user writes code that is designed for an IEEE 64-bit binary floating-point type, the code is more clear if it uses a name that is guaranteed to be IEEE 64-bit, and the failure mode is more immediate (a compilation error) if the code is ported to a system where an IEEE 64-bit type is not available.  This part of the proposal is a revival, with modifications, of <a data-link-type="biblio" href="#biblio-n1703">[N1703]</a>, which in 2013 proposed adding typedefs for fixed-layout floating-point types to both C and C++, but was not adopted by either language.</p>
   <p>The motivation for the current approach of extended floating-point types comes from discussion of the previous paper <a data-link-type="biblio" href="#biblio-p0192">[P0192]</a>.  That proposal’s single new standard type of <code class="highlight"><c- b>short</c-> <c- b>float</c-></code> was considered insufficient, preventing the use of both IEEE-754 16-bit and <code class="highlight"><c- n>bfloat16</c-></code> in the same application.  When that proposal was rejected in November 2018, the current, more expansive, proposal was developed.  It is not feasible to predict which floating-point types, or even how many different types, will be used in the future, so this proposal allows for as many types as the implementation sees fit.</p>
   <h2 class="heading settled" data-level="4" id="c-compat"><span class="secno">4. </span><span class="content">C Compatibility</span><a class="self-link" href="#c-compat"></a></h2>
   <p>The C standards committee, WG14, is proposing significant extensions to floating-point support in C as a new annex to the C2x standard.  (The latest version is on an internal wiki and is not publicly available.  An earlier version of the proposal is in <a data-link-type="biblio" href="#biblio-n2405">[N2405]</a>.)  The changes being worked on for C are compatible with the changes proposed for C++ in this proposal.  Users will be able to write code that that uses IEEE floating-point types, include 16-bit binary, that compiles and behaves the same in both languages.</p>
   <p>The C proposal adds optional types <code class="highlight"><c- n>_Float</c-><em><c- n>N</c-></em></code>, where <em>N</em> is 16, 32, 64, 128, or greater than 128 and divisible by 32. <code class="highlight"><c- n>_Float</c-><em><c- n>N</c-></em></code> is an IEEE binary floating-point type with the given size.  These types should behave the same as the named aliases proposed <a href="#alias-formats">below</a>.  (Except that C does not define a type for the non-IEEE <code class="highlight"><c- n>bfloat16</c-></code> format.)  The proposed usual arithmetic conversions when mixing different floating-point types are essentially the same in both languages.</p>
   <p>There are two areas of divergence between the C and C++ proposals that are worth mentioning:</p>
   <ol>
    <li data-md>
     <p>Names: The C proposal uses <code class="highlight"><c- n>_Float16</c-></code>, <code class="highlight"><c- n>_Float32</c-></code>, <code class="highlight"><c- n>_Float64</c-></code>, and <code class="highlight"><c- n>_Float128</c-></code> as keywords naming the IEEE types.  This paper proposes type aliases in the <code class="highlight"><c- n>std</c-></code> namespace. (See <a href="#names">§ 7.6 Names</a>)  Since C++ likes to have all its library names in namespace <code class="highlight"><c- n>std</c-></code>, and C does not have namespace <code class="highlight"><c- n>std</c-></code> at all, this area of divergence seems unavoidable.  The C++ implementation could use <code class="highlight"><c- n>_Float16</c-></code>, <code class="highlight"><c- n>_Float32</c-></code>, etc. as the names of the extended floating-point types behind the <code class="highlight"><c- n>std</c-><c- o>::</c-></code> type aliases, allowing the use of the C names in both languages.  But code that wants to work in both C and C++ and wants to maximize portability will need at least one <code class="highlight"><c- cp>#if</c-></code>, such as (with C++ names still subject to change):</p>
<pre class="highlight"><code class="highlight"><c- cp><c- cp>#ifdef __cplusplus</c-></c->
  <c- cp><c- cp>#include</c-></c-> &lt;stdfloat>
  <c- k><c- k>using</c-></c-> <c- n><c- n>my_fp16_t</c-></c-> <c- o><c- o>=</c-></c-> <c- n><c- n>std</c-></c-><c- o><c- o>::</c-></c-><c- n><c- n>float16_t</c-></c-><c- p><c- p>;</c-></c->
<c- cp><c- cp>#else</c-></c->
  <c- k><c- k>typedef</c-></c-> <c- n><c- n>_Float16</c-></c-> <c- n><c- n>my_fp16_t</c-></c-><c- p><c- p>;</c-></c->
<c- cp><c- cp>#endif</c-></c->
</code></pre>
    <li data-md>
     <p>Implicit conversions: In this C++ proposal, narrowing conversions between floating-point types have to be explicit. (See <a href="#implicit">§ 5.5 Implicit conversions</a>)  In the C proposal, conversions between floating-point types can be done implicitly, even when they are narrowing and potentially lossy.  This will result in code using floating-point types that will compile as C but not as C++.  While this divergence is unfortunate, it is acceptable because code using extended floating-point types that compiles successfully in both languages will behave the same in both languages.</p>
   </ol>
   <p>The authors are comfortable with this proposal and the C proposal proceeding in parallel.  The two proposals together move the two languages in compatible directions and do not cause unreasonable divergence.  The authors are monitoring the progress of the C proposal and will raise issues with WG14 or WG21 (or both) if the proposals start to diverge as they evolve.</p>
   <h2 class="heading settled" data-level="5" id="core"><span class="secno">5. </span><span class="content">Core language changes</span><a class="self-link" href="#core"></a></h2>
   <h3 class="heading settled" data-level="5.1" id="core-no-change"><span class="secno">5.1. </span><span class="content">Things that aren’t changing</span><a class="self-link" href="#core-no-change"></a></h3>
   <p>It is currently implementation-defined whether or not the floating-point types support infinity and NaN.  That is not changing.  That feature will still be implementation-defined, even for extended floating-point types.</p>
   <p>The radix of the exponent of each floating-point type is currently implementation-defined.  That is not changing.  This paper will make it easier for the radix of extended floating-point types to be different from the radix of the standard types, allowing implementations to support decimal floating-point while the standard floating-point types remain binary floating-point types.</p>
   <h3 class="heading settled" data-level="5.2" id="extended"><span class="secno">5.2. </span><span class="content">Extended floating-point types</span><a class="self-link" href="#extended"></a></h3>
   <p>In addition to the three standard floating-point types, <code class="highlight"><c- b>float</c-></code>, <code class="highlight"><c- b>double</c-></code>, and <code class="highlight"><c- b>long</c-> <c- b>double</c-></code>, implementations may define any number of <em>extended floating-point types</em>, similar to how implementations may define extended integer types.</p>
   <h4 class="heading settled" data-level="5.2.1" id="extended-reason"><span class="secno">5.2.1. </span><span class="content">Reasoning</span><a class="self-link" href="#extended-reason"></a></h4>
   <p>The set of floating-point types that have hardware support is not possible to accurately predict years into the future.  The standard needs to provide an extensible solution so that implementations can adapt to changing hardware without having to modify the standard.</p>
   <h4 class="heading settled" data-level="5.2.2" id="extended-wording"><span class="secno">5.2.2. </span><span class="content">Wording</span><a class="self-link" href="#extended-wording"></a></h4>
   <p>Modify 6.7.1 "Fundamental types" [<strong>basic.fundamental</strong>] paragraph 12:</p>
   <blockquote>
     There are three <i><ins>standard </ins>floating-point types</i>: <code class="highlight"><c- b>float</c-></code>, <code class="highlight"><c- b>double</c-></code>, and <code class="highlight"><c- b>long</c-> <c- b>double</c-></code>. The type <code class="highlight"><c- b>double</c-></code> provides at least as much precision as <code class="highlight"><c- b>float</c-></code>, and the type <code class="highlight"><c- b>long</c-> <c- b>double</c-></code> provides at least as much precision as <code class="highlight"><c- b>double</c-></code>. The set of values of the type <code class="highlight"><c- b>float</c-></code> is a subset of the set of values of the type <code class="highlight"><c- b>double</c-></code>; the set of values of the type <code class="highlight"><c- b>double</c-></code> is a subset of the set of values of the type <code class="highlight"><c- b>long</c-> <c- b>double</c-></code>. 
    <ins>There may also be implementation-defined <em>extended floating-point types</em>. The standard and extended floating-point types are collectively called <em>floating-point types</em>.</ins>
     The value representation of floating-point types is implementation-defined. [...] 
   </blockquote>
   <h3 class="heading settled" data-level="5.3" id="rank"><span class="secno">5.3. </span><span class="content">Conversion rank</span><a class="self-link" href="#rank"></a></h3>
   <p>Define <em>floating-point conversion rank</em> to mimic in some ways the existing integer conversion rank.  Floating-point conversion rank is defined in terms of the sets of values that the types can represent.  If the set of values of type <code class="highlight"><c- n>T</c-></code> is a strict superset of the set of values of type <code class="highlight"><c- n>U</c-></code>, then <code class="highlight"><c- n>T</c-></code> has a higher conversion rank than <code class="highlight"><c- n>U</c-></code>.  If two types have the exact same sets of values, they still have different conversion ranks; see the wording below for the exact rules.  If the sets of values of two types are neither a subset nor a superset of each other, then the conversion ranks of the two types are unordered.  Floating-point conversion rank forms a partial order, not a total order; this is the biggest difference from integer conversion rank.</p>
   <h4 class="heading settled" data-level="5.3.1" id="rank-reason"><span class="secno">5.3.1. </span><span class="content">Reasoning</span><a class="self-link" href="#rank-reason"></a></h4>
   <p>Earlier versions of this proposal used the range of finite values to define conversion rank, and had the conversion rank be a total ordering.  Discussions in <a href="http://wiki.edg.com/bin/view/Wg21kona2019/SG6MinutesP1468">SG6</a> in Kona 2019 pointed out that that definition resulted in undesirable interactions between IEEE <code class="highlight"><c- n>binary16</c-></code> with 5-bit exponent and 10-bit mantissa, and <code class="highlight"><c- n>bfloat16</c-></code> with 8-bit exponent and 7-bit mantissa. <code class="highlight"><c- n>bfloat16</c-></code> has a much larger finite range, so it would have a higher conversion rank under the old rules.  Mixing <code class="highlight"><c- n>binary16</c-></code> and <code class="highlight"><c- n>bfloat16</c-></code> in an arithmetic operation would result in the <code class="highlight"><c- n>binary16</c-></code> value being converted to <code class="highlight"><c- n>bfloat16</c-></code> despite the loss of three bits of precision.  This implicit loss of precision was worrisome, so the definition of conversion rank was changed so that the usual arithmetic conversions between two floating-point values always preserves the value exactly.</p>
   <p>For the purposes of conversion rank, infinity and NaN are treated just like any other values.  If type <code class="highlight"><c- n>T</c-></code> supports infinity and type <code class="highlight"><c- n>U</c-></code> does not, then <code class="highlight"><c- n>U</c-></code> can never have a greater conversion rank than <code class="highlight"><c- n>T</c-></code>, even if <code class="highlight"><c- n>U</c-></code> has a bigger range and a longer mantissa.</p>
   <p>When an implementation supports both binary and decimal floating-point, the conversion ranks of a binary type and a decimal type will always be unordered, because neither type’s set of values will be a subset of the other due to the different radixes.  As a result, any arithmetic that mixes binary and decimal types will be ill-formed without explicit casts.</p>
   <h4 class="heading settled" data-level="5.3.2" id="rank-wording"><span class="secno">5.3.2. </span><span class="content">Wording</span><a class="self-link" href="#rank-wording"></a></h4>
   <p>
    Change the title of section 6.7.4 [<strong>conv.rank</strong>] from "
    <del>Integer conversion rank</del>
    " to "
    <ins>Conversion ranks</ins>
    ", but leave the stable name unchanged.  Insert a new paragraph at the end of the subclause:
   </p>
   <blockquote class="ins">
     Every floating-point type has a <em>floating-point conversion rank</em> defined as follows: 
    <ul>
     <li data-md>
      <p>The rank of a floating point type <code class="highlight"><c- n>T</c-></code> is greater than the rank of any floating-point type whose set of values is a proper subset of the set of values of <code class="highlight"><c- n>T</c-></code>.</p>
     <li data-md>
      <p>The rank of <code class="highlight"><c- b>long</c-> <c- b>double</c-></code> is greater than the rank of <code class="highlight"><c- b>double</c-></code>, which is greater than the rank of <code class="highlight"><c- b>float</c-></code>.</p>
     <li data-md>
      <p>The rank of any standard floating-point type is greater than the rank of any extended floating-point type with the same set of values.</p>
     <li data-md>
      <p>The rank of any extended floating-point type relative to another extended floating-point type with the same set of values is implementation-defined, but still subject to the other rules for determining the floating-point conversion rank.</p>
     <li data-md>
      <p>For all floating-point types <code class="highlight"><c- n>T1</c-></code>, <code class="highlight"><c- n>T2</c-></code>, and <code class="highlight"><c- n>T3</c-></code>, if <code class="highlight"><c- n>T1</c-></code> has greater rank than <code class="highlight"><c- n>T2</c-></code> and <code class="highlight"><c- n>T2</c-></code> has greater rank than <code class="highlight"><c- n>T3</c-></code>, then <code class="highlight"><c- n>T1</c-></code> has greater rank than <code class="highlight"><c- n>T3</c-></code>.</p>
    </ul>
    <p>[ <em>Note</em>: The conversion ranks of extended floating-point types <code class="highlight"><c- n>T1</c-></code> and <code class="highlight"><c- n>T2</c-></code> will be unordered if the set of values of <code class="highlight"><c- n>T1</c-></code> is neither a subset nor a superset of the set of values of <code class="highlight"><c- n>T2</c-></code>. This can happen when one type has both a larger range and a lower precision than the other. -- <em>end note</em> ] [ <em>Note</em>: The floating-point conversion rank is used in the definition of the usual arithmetic conversions ([expr.arith.conv]). -- <em>end note</em> ]</p>
   </blockquote>
   <h3 class="heading settled" data-level="5.4" id="promotion"><span class="secno">5.4. </span><span class="content">Promotion</span><a class="self-link" href="#promotion"></a></h3>
   <p>Floating-point promotions are unchanged, except when passing an argument to a varargs function.  When a function argument is bound to the ellipsis of a varargs function, any type whose conversion rank is smaller than that of <code class="highlight"><c- b>double</c-></code> is promoted to <code class="highlight"><c- b>double</c-></code>.  In all other situations, only <code class="highlight"><c- b>float</c-></code> is promoted to <code class="highlight"><c- b>double</c-></code>.</p>
   <h4 class="heading settled" data-level="5.4.1" id="promotion-reason"><span class="secno">5.4.1. </span><span class="content">Reasoning</span><a class="self-link" href="#promotion-reason"></a></h4>
   <p>The overload resolution rules work best if there are no floating-point promotions, only standard conversions.  For backward compatibility, <code class="highlight"><c- b>float</c-></code> still promotes to <code class="highlight"><c- b>double</c-></code>.  But no other floating-point conversions are considered promotions.</p>
   <p>But this rule prevents smaller extended floating-point types from being promoted to <code class="highlight"><c- b>double</c-></code> when passed to a varargs function.  Therefore, some wording is added to the ellipsis conversion rules to perform that promotion.</p>
   <p class="note" role="note"><span>Note:</span> The current C floating-point proposal does not promote smaller floating-point types to <code class="highlight"><c- b>double</c-></code> when calling varargs functions.  This is an area where C and C++ should remain compatible, due primarily to <code class="highlight"><c- n>printf</c-></code>.  This issue will be discussed in the C floating-point study group in the near future.  If the C floating-point proposal remains unchanged, then the proposed change to the ellipsis conversion rules will be withdrawn from this proposal, and there won’t be any wording changes related to floating-point promotions.</p>
   <h4 class="heading settled" data-level="5.4.2" id="promotion-wording"><span class="secno">5.4.2. </span><span class="content">Wording</span><a class="self-link" href="#promotion-wording"></a></h4>
   <p>No changes are necessary to 7.3.7 "Floating-point promotion" [conv.fpprom]</p>
   <p>Add a new sentence just before the last sentence in paragraph 12 of 7.6.1.2 "Function call" [<strong>expr.call</strong>]:</p>
   <blockquote>
     [...] If the argument has integral or enumeration type that is subject to the integral promotions (7.3.6), or a floating-point type that is subject to the floating-point promotion (7.3.7), the value of the argument is converted to the promoted type before the call. 
    <ins>If the argument has floating-point type that is not subject to floating-point promotion, and if the argument type has a floating-point conversion rank ([conv.rank]) that is less than the rank of <code class="highlight"><c- b>double</c-></code>, then the value of the argument is converted to <code class="highlight"><c- b>double</c-></code> before the call.</ins>
     These promotions are referred to as the <em>default argument promotions</em>. 
   </blockquote>
   <h3 class="heading settled" data-level="5.5" id="implicit"><span class="secno">5.5. </span><span class="content">Implicit conversions</span><a class="self-link" href="#implicit"></a></h3>
   <p>A conversion between two floating-point types, when at least one of the types is an extended floating-point type, is implicit only if the conversion is non-lossy, if the destination type can represent all values of the source type.  Put another way, a conversion that might change the value is not a standard conversion.</p>
   <h4 class="heading settled" data-level="5.5.1" id="implicit-reason"><span class="secno">5.5.1. </span><span class="content">Reasoning</span><a class="self-link" href="#implicit-reason"></a></h4>
   <p>The standard currently allows implicit conversions between any arithmetic types (except during brace init, when narrowing conversion rules apply), even if the conversion could result in a loss of information.  This rule makes it too easy to write buggy code.  Changing rules for existing types is not feasible because it would be a major breaking change.  But the rules can be changed when types are used in new ways, as was done for brace init and narrowing conversions, or for new types, as is proposed here.</p>
   <p>This was discussed in EWG in Prague, and there was consensus to limit implicit conversions for extended floating-point types.  "Extended floating point types match the current C++ rules for conversions." 2-3-6-19-3  "Implicit conversions are only allowed if non-narrowing." 14-15-8-0-1</p>
   <p>The conversion rules for standard floating-point types can’t be changed without breaking existing code, so conversions from <code class="highlight"><c- b>double</c-></code> to <code class="highlight"><c- b>float</c-></code> and from <code class="highlight"><c- b>long</c-> <c- b>double</c-></code> to <code class="highlight"><c- b>double</c-></code> or <code class="highlight"><c- b>float</c-></code> will still be implicit.</p>
   <h4 class="heading settled" data-level="5.5.2" id="implicit-wording"><span class="secno">5.5.2. </span><span class="content">Wording</span><a class="self-link" href="#implicit-wording"></a></h4>
   <p>Modify section 7.3.9 "Floating-point conversions" [<strong>conv.double</strong>] as follows:</p>
   <blockquote>
    <p>
     A prvalue of floating-point type can be converted to a prvalue of another floating-point type 
     <ins>with a higher conversion rank or with the same set of values, or a prvalue of standard floating-point type can be converted to a prvalue of another standard floating-point type</ins>
     . If the source value can be exactly represented in the destination type, the result of the conversion is that exact representation. If the source value is between two adjacent destination values, the result of the conversion is an implementation-defined choice of either of those values. Otherwise, the behavior is undefined.
    </p>
    <p>The conversions allowed as floating-point promotions are excluded from the set of floating-point conversions.</p>
   </blockquote>
   <p>In section 7.6.1.8 "Static cast" [<strong>expr.static.cast</strong>], add a new paragraph after paragraph 10 ("A value of integral or enumeration type can [...]"):</p>
   <blockquote>
    <div class="ins"> A value of floating-point type can be explicitly converted to any other floating-point type.  If the source value can be exactly represented in the destination type, the result of the conversion is that exact representation. If the source value is between two adjacent destination values, the result of the conversion is an implementation-defined choice of either of those values. Otherwise, the behavior is undefined. </div>
   </blockquote>
   <p class="note" role="note"><span>Note:</span> A <code class="highlight"><c- k>static_cast</c-></code> from a higher floating-point conversion rank to a lower conversion rank is already covered by [expr.static.cast] p7, which talks about inverses of standard conversions.  The new paragraph is necessary to allow explicit conversions between types with unordered conversion ranks.  The wording about what to do with the value is stolen from the floating-point conversions section [conv.double].</p>
   <h3 class="heading settled" data-level="5.6" id="arithmetic"><span class="secno">5.6. </span><span class="content">Usual arithmetic conversions</span><a class="self-link" href="#arithmetic"></a></h3>
   <p>The proposed usual arithmetic conversions for floating-point types are based on the floating-point conversion rank, similar to integer arithmetic conversions.  But because floating-point conversions are a partial ordering, there may be some expressions where neither operand will be converted to the other’s type.  It is proposed that these situations are ill-formed.</p>
   <h4 class="heading settled" data-level="5.6.1" id="arithmetic-example"><span class="secno">5.6.1. </span><span class="content">Example</span><a class="self-link" href="#arithmetic-example"></a></h4>
   <p class="note" role="note"><span>Note:</span> In all the examples in this paper, <code class="highlight"><c- b>float</c-></code> and <code class="highlight"><c- b>double</c-></code> are IEEE 32-bit and 64-bit types, <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>float</c-><i><c- n>N</c-></i><c- n>_t</c-></code> is an extended floating-point type for IEEE <em>N</em>-bit, and <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>bfloat16_t</c-></code> is <code class="highlight"><c- n>bfloat16</c-></code>.</p>
<pre class="highlight"><c- b>float</c-> <c- n>f32</c-> <c- o>=</c-> <c- mf>1.0</c-><c- p>;</c->
<c- n>std</c-><c- o>::</c-><c- n>float16_t</c-> <c- n>f16</c-> <c- o>=</c-> <c- mf>2.0</c-><c- p>;</c->
<c- n>std</c-><c- o>::</c-><c- n>bfloat16_t</c-> <c- n>b16</c-> <c- o>=</c-> <c- mf>3.0</c-><c- p>;</c->
<c- n>f32</c-> <c- o>+</c-> <c- n>f16</c-><c- p>;</c-> <c- c1>// okay, f16 converted to "float", result type is "float"</c->
<c- n>f32</c-> <c- o>+</c-> <c- n>b16</c-><c- p>;</c-> <c- c1>// okay, b16 converted to "float", result type is "float"</c->
<c- n>f16</c-> <c- o>+</c-> <c- n>b16</c-><c- p>;</c-> <c- c1>// error, neither type can convert to the other via arithmetic conversions</c->
</pre>
   <h4 class="heading settled" data-level="5.6.2" id="arithmetic-wording"><span class="secno">5.6.2. </span><span class="content">Wording</span><a class="self-link" href="#arithmetic-wording"></a></h4>
   <p>Modify section 7.4 Usual arithmetic conversions [<strong>expr.arith.conv</strong>] as follows:</p>
   <blockquote>
    <div class="numbered">
      Many binary operators that expect operands of arithmetic or enumeration type cause conversions and yield result types in a similar way. The purpose is to yield a common type, which is also the type of the result. This pattern is called the <em>usual arithmetic conversions</em>, which are defined as follows: 
     <ul>
      <li data-md>
       <p>If either operand is of scoped enumeration type ([dcl.enum]), no conversions are performed; if the other operand does not have the same type, the expression is ill-formed.</p>
      <li data-md>
       <del>If either operand is of type long double, the other shall be converted to long double.</del>
      <li data-md>
       <del>Otherwise, if either operand is double, the other shall be converted to double.</del>
      <li data-md>
       <del>Otherwise, if either operand is float, the other shall be converted to float.</del>
      <li data-md>
       <ins>Otherwise, if either operand has a floating-point type, the following rules shall be applied:</ins>
       <ul>
        <li data-md>
         <ins>If both operands have the same type, no further conversion is needed.</ins>
        <li data-md>
         <ins>Otherwise, if one of the operands has a type that is not a floating-point type, that operand shall be converted to the type of the operand with the floating-point type.</ins>
        <li data-md>
         <ins>Otherwise, if the floating-point conversion ranks ([conv.rank]) of the types of the operands are ordered, then the operand with the type of the lower floating-point conversion rank shall be converted to the type of the other operand.</ins>
        <li data-md>
         <ins>Otherwise, the expression is ill-formed.</ins>
       </ul>
      <li data-md>
       <p>Otherwise, the integral promotions ([conv.prom]) shall be performed on both operands.(59) Then the following rules shall be applied to the promoted operands:</p>
       <ul>
        <li data-md>
         <p>If both operands have the same type, no further conversion is needed.</p>
        <li data-md>
         <p>Otherwise, if both operands have signed integer types or both have unsigned integer types, the operand with the type of lesser integer conversion rank shall be converted to the type of the operand with greater rank.</p>
        <li data-md>
         <p>Otherwise, if the operand that has unsigned integer type has rank greater than or equal to the rank of the type of the other operand, the operand with signed integer type shall be converted to the type of the operand with unsigned integer type.</p>
        <li data-md>
         <p>Otherwise, if the type of the operand with signed integer type can represent all of the values of the type of the operand with unsigned integer type, the operand with unsigned integer type shall be converted to the type of the operand with signed integer type.</p>
        <li data-md>
         <p>Otherwise, both operands shall be converted to the unsigned integer type corresponding to the type of the operand with signed integer type.</p>
       </ul>
     </ul>
    </div>
    <p></p>
    <div class="numbered"> If one operand is of enumeration type and the other operand is of a different enumeration type or a floating-point type, this behavior is deprecated (D.1). </div>
   </blockquote>
   <h3 class="heading settled" data-level="5.7" id="narrow"><span class="secno">5.7. </span><span class="content">Narrowing conversions</span><a class="self-link" href="#narrow"></a></h3>
   <p>A narrowing conversion is a conversion from a type with a higher floating-point conversion rank to a type with a lower conversion rank, or a conversion between two types with unordered conversion rank.</p>
   <h4 class="heading settled" data-level="5.7.1" id="narrow-reason"><span class="secno">5.7.1. </span><span class="content">Same representation</span><a class="self-link" href="#narrow-reason"></a></h4>
   <p>When two different floating-point types have the same representation, one of the types has a higher conversion rank than the other.  Which means that a conversion between the two types will be a narrowing conversion in one of the directions even though the value will be preserved.  For example, on some implementations, <code class="highlight"><c- b>double</c-></code> and <code class="highlight"><c- b>long</c-> <c- b>double</c-></code> have the same representation, but <code class="highlight"><c- b>long</c-> <c- b>double</c-></code> always has a higher conversion rank than <code class="highlight"><c- b>double</c-></code>, so 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 considered a narrowing conversion.</p>
   <p>An earlier version of this paper defined narrowing conversions in terms of sets of representable values, not in terms of conversion rank.  With that definition, conversions between types with the same representation would never be a narrowing conversion. <a href="http://wiki.edg.com/bin/view/Wg21kona2019/SG6MinutesP1468">SG6</a> in Kona preferred using conversion rank over sets of values, so the proposal was changed to the current definition.  One argument against the old definition was that it changed the behavior for standard floating-point types, as in the example of <code class="highlight"><c- b>double</c-></code> and <code class="highlight"><c- b>long</c-> <c- b>double</c-></code> above.</p>
   <p>It would be possible to have different rules for standard floating-point types and extended floating-point types, but the authors feel it is best to maintain consistency between standard and extended types, and to not change the behavior of standard types.</p>
   <h4 class="heading settled" data-level="5.7.2" id="narrow-constant"><span class="secno">5.7.2. </span><span class="content">Constant values</span><a class="self-link" href="#narrow-constant"></a></h4>
   <p>This proposal preserves the existing wording in [dcl.init.list] p7.2, "except where the source is a constant expression and the actual value after conversion is within the range of values that can be represented (even if it cannot be represented exactly)."  A reasonable argument could be made that this constant value exception should not apply to extended floating-point types.  But the authors are not in favor of that change. It would introduce an inconsistency between standard and extended types. It would cause <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>float16_t</c-> <c- n>x</c-><c- p>{</c-><c- mf>2.1</c-><c- p>};</c-></code> to be a narrowing conversion because <code class="highlight"><c- mf>2.1</c-></code> cannot be represented exactly in binary floating-point representations.</p>
   <h4 class="heading settled" data-level="5.7.3" id="narrow-wording"><span class="secno">5.7.3. </span><span class="content">Wording</span><a class="self-link" href="#narrow-wording"></a></h4>
   <p>Modify the definition of narrowing conversions in 9.3.4 "List-initialization" [<strong>dcl.init.list</strong>] paragraph 7 item 2:</p>
   <blockquote>
    <div>
     <ul>
      <li data-md>
       <del>from <code class="highlight"><c- b>long</c-> <c- b>double</c-></code> to <code class="highlight"><c- b>double</c-></code> or <code class="highlight"><c- b>float</c-></code>, or from <code class="highlight"><c- b>double</c-></code> to <code class="highlight"><c- b>float</c-></code></del>
       <ins>from a floating-point type <code class="highlight"><c- n>T</c-></code> to another floating-point type whose floating-point conversion rank is not greater than that of <code class="highlight"><c- n>T</c-></code></ins>
       , except where the source is a constant expression and the actual value after conversion is within the range of values that can be represented (even if it cannot be represented exactly), or
     </ul>
    </div>
   </blockquote>
   <h3 class="heading settled" data-level="5.8" id="overload"><span class="secno">5.8. </span><span class="content">Overload resolution</span><a class="self-link" href="#overload"></a></h3>
   <p>When comparing conversion sequences that involve floating-point conversions, prefer conversions that are value-preserving, and prefer conversions to lower conversion ranks over conversions to higher conversion ranks.</p>
   <h4 class="heading settled" data-level="5.8.1" id="overload-reason"><span class="secno">5.8.1. </span><span class="content">Reasoning</span><a class="self-link" href="#overload-reason"></a></h4>
   <p>With the proposed change to implicit conversions, preferring value-preserving conversions over lossy conversions comes for free, since overloads with lossy conversions won’t be viable candidates (except when both types are standard floating-point types).</p>
   <p>Preferring a conversion to a smaller type over a conversion to a larger type comes from the desire for a function call to be well-formed rather than ambiguous when there are multiple value-preserving conversions available.</p>
<pre class="highlight"><code class="highlight"><c- b><c- b>void</c-></c-> <c- nf><c- nf>f</c-></c-><c- p><c- p>(</c-></c-><c- n><c- n>std</c-></c-><c- o><c- o>::</c-></c-><c- n><c- n>float32_t</c-></c-><c- p><c- p>);</c-></c->
<c- b><c- b>void</c-></c-> <c- nf><c- nf>f</c-></c-><c- p><c- p>(</c-></c-><c- n><c- n>std</c-></c-><c- o><c- o>::</c-></c-><c- n><c- n>float64_t</c-></c-><c- p><c- p>);</c-></c->

<c- n><c- n>f</c-></c-><c- p><c- p>(</c-></c-><c- n><c- n>std</c-></c-><c- o><c- o>::</c-></c-><c- n><c- n>float16_t</c-></c-><c- p><c- p>(</c-></c-><c- mf><c- mf>1.0</c-></c-><c- p><c- p>));</c-></c-> <c- c1><c- c1>// calls std::float32_t, due to smaller conversion rank</c-></c->
<c- n><c- n>f</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>float</c-></c-><c- p><c- p>(</c-></c-><c- mf><c- mf>2.0</c-></c-><c- p><c- p>));</c-></c->          <c- c1><c- c1>// calls std::float32_t, due to smaller conversion rank</c-></c->
<c- n><c- n>f</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>double</c-></c-><c- p><c- p>(</c-></c-><c- mf><c- mf>3.0</c-></c-><c- p><c- p>));</c-></c->         <c- c1><c- c1>// calls std::float64_t, only viable candidate</c-></c->
</code></pre>
   <p>Achieving this behavior is not possible by tweaking the definitions of floating-point promotions and floating-point conversions. It requires a change to the overload resolution rules so that certain floating-point conversions are preferred over others.</p>
   <p>This issue was debated in EWG in Prague, and these overload resolution rules received weak consensus.  "Prefer smaller safe conversions over larger safe conversions in overload resolution." 3-14-10-0-7</p>
   <h4 class="heading settled" data-level="5.8.2" id="overload-wording"><span class="secno">5.8.2. </span><span class="content">Wording</span><a class="self-link" href="#overload-wording"></a></h4>
   <p>In 12.3.3.2 "Ranking implicit conversion sequences" [<strong>over.ics.rank</strong>] paragraph 4, add a new bullet between (4.2) and (4.3):</p>
   <blockquote>
    <ul>
     <li data-md>
      <p>(4.2) A conversion that promotes an enumeration whose underlying type is fixed to its underlying type is better than one that promotes to the promoted underlying type, if the two are different.</p>
     <li data-md>
      <ins>
       (4.3) A conversion from floating-point type <code class="highlight"><c- n>FP1</c-></code> to floating-point type <code class="highlight"><c- n>FP2</c-></code> is better than a conversion from <code class="highlight"><c- n>FP1</c-></code> to floating-point type <code class="highlight"><c- n>FP3</c-></code> if 
       <ul>
        <li data-md>
         <p>(4.3.1) at least one of <code class="highlight"><c- n>FP1</c-></code>, <code class="highlight"><c- n>FP2</c-></code>, or <code class="highlight"><c- n>FP3</c-></code> is an extended floating-point type,</p>
        <li data-md>
         <p>(4.3.2) the set of values of <code class="highlight"><c- n>FP1</c-></code> is a subset of the set of values of <code class="highlight"><c- n>FP2</c-></code>, and</p>
        <li data-md>
         <p>(4.3.3) <code class="highlight"><c- n>FP3</c-></code> has greater floating-point conversion rank ([conv.rank]) than <code class="highlight"><c- n>FP2</c-></code>, or <code class="highlight"><c- n>FP1</c-></code> has greater floating-point conversion rank than <code class="highlight"><c- n>FP3</c-></code>.</p>
       </ul>
      </ins>
     <li data-md>
      <del>(4.3)</del>
      <ins>(4.4)</ins>
       If class <code class="highlight"><c- n>B</c-></code> is derived directly or indirectly from class <code class="highlight"><c- n>A</c-></code>, conversion of <code class="highlight"><c- n>B</c-><c- o>*</c-></code> to <code class="highlight"><c- n>A</c-><c- o>*</c-></code> is better than conversion of <code class="highlight"><c- n>B</c-><c- o>*</c-></code> to <code class="highlight"><c- b>void</c-><c- o>*</c-></code>, and conversion of <code class="highlight"><c- n>A</c-><c- o>*</c-></code> to <code class="highlight"><c- b>void</c-><c- o>*</c-></code> is better than conversion of <code class="highlight"><c- n>B</c-><c- o>*</c-></code> to <code class="highlight"><c- b>void</c-><c- o>*</c-></code>. 
    </ul>
   </blockquote>
   <p class="note" role="note"><span>Note:</span> (4.3.2) and the second half of (4.3.3) are necessary to correctly handle lossy conversions between standard floating-point types such as from <code class="highlight"><c- b>double</c-></code> to <code class="highlight"><c- b>float</c-></code>, which are still considered standard conversions and participate in overload resolution.  (4.3.1) is necessary to preserve existing behavior when there are overloads for <code class="highlight"><c- b>float</c-></code> and <code class="highlight"><c- b>long</c-> <c- b>double</c-></code> and the argument type is <code class="highlight"><c- b>double</c-></code>.</p>
   <h4 class="heading settled" data-level="5.8.3" id="overload-alternate"><span class="secno">5.8.3. </span><span class="content">Alternate proposals</span><a class="self-link" href="#overload-alternate"></a></h4>
   <p>The EWG poll about overload resolution did not have strong consensus, due to the significant number of neutral votes and strongly against votes.  In light of that result, we present two alternate options for overload resolution rules.  The authors are in favor of the proposed wording above, not the alternative proposals below.</p>
   <h5 class="heading settled" data-level="5.8.3.1" id="overload-same-rep"><span class="secno">5.8.3.1. </span><span class="content">Prefer same representation</span><a class="self-link" href="#overload-same-rep"></a></h5>
   <p>The first alternative is to prefer conversions to types that have the same representation over safe conversions to bigger types.  With this scheme:</p>
<pre class="highlight"><code class="highlight"><c- b><c- b>void</c-></c-> <c- nf><c- nf>f</c-></c-><c- p><c- p>(</c-></c-><c- n><c- n>std</c-></c-><c- o><c- o>::</c-></c-><c- n><c- n>float32_t</c-></c-><c- p><c- p>);</c-></c->
<c- b><c- b>void</c-></c-> <c- nf><c- nf>f</c-></c-><c- p><c- p>(</c-></c-><c- n><c- n>std</c-></c-><c- o><c- o>::</c-></c-><c- n><c- n>float64_t</c-></c-><c- p><c- p>);</c-></c->

<c- n><c- n>f</c-></c-><c- p><c- p>(</c-></c-><c- n><c- n>std</c-></c-><c- o><c- o>::</c-></c-><c- n><c- n>float16_t</c-></c-><c- p><c- p>(</c-></c-><c- mf><c- mf>1.0</c-></c-><c- p><c- p>));</c-></c-> <c- c1><c- c1>// ambiguous</c-></c->
<c- n><c- n>f</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>float</c-></c-><c- p><c- p>(</c-></c-><c- mf><c- mf>2.0</c-></c-><c- p><c- p>));</c-></c->          <c- c1><c- c1>// calls std::float32_t, because same representation</c-></c->
<c- n><c- n>f</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>double</c-></c-><c- p><c- p>(</c-></c-><c- mf><c- mf>3.0</c-></c-><c- p><c- p>));</c-></c->         <c- c1><c- c1>// calls std::float64_t, only viable candidate</c-></c->
</code></pre>
   <h5 class="heading settled" data-level="5.8.3.2" id="overload-no-change"><span class="secno">5.8.3.2. </span><span class="content">No change</span><a class="self-link" href="#overload-no-change"></a></h5>
   <p>The other alternative is to not change the overload resolution rules at all.  There would be no disambiguation between standard conversions, so any call with multiple viable function overloads with no exact match would be ambiguous.</p>
<pre class="highlight"><code class="highlight"><c- b><c- b>void</c-></c-> <c- nf><c- nf>f</c-></c-><c- p><c- p>(</c-></c-><c- n><c- n>std</c-></c-><c- o><c- o>::</c-></c-><c- n><c- n>float32_t</c-></c-><c- p><c- p>);</c-></c->
<c- b><c- b>void</c-></c-> <c- nf><c- nf>f</c-></c-><c- p><c- p>(</c-></c-><c- n><c- n>std</c-></c-><c- o><c- o>::</c-></c-><c- n><c- n>float64_t</c-></c-><c- p><c- p>);</c-></c->

<c- n><c- n>f</c-></c-><c- p><c- p>(</c-></c-><c- n><c- n>std</c-></c-><c- o><c- o>::</c-></c-><c- n><c- n>float16_t</c-></c-><c- p><c- p>(</c-></c-><c- mf><c- mf>1.0</c-></c-><c- p><c- p>));</c-></c-> <c- c1><c- c1>// ambiguous</c-></c->
<c- n><c- n>f</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>float</c-></c-><c- p><c- p>(</c-></c-><c- mf><c- mf>2.0</c-></c-><c- p><c- p>));</c-></c->          <c- c1><c- c1>// ambiguous</c-></c->
<c- n><c- n>f</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>double</c-></c-><c- p><c- p>(</c-></c-><c- mf><c- mf>3.0</c-></c-><c- p><c- p>));</c-></c->         <c- c1><c- c1>// calls std::float64_t, only viable candidate</c-></c->
</code></pre>
   <h3 class="heading settled" data-level="5.9" id="pointer"><span class="secno">5.9. </span><span class="content">Pointer conversions</span><a class="self-link" href="#pointer"></a></h3>
   <p>The proposal of allowing implicit conversions between pointers to two different floating-point types that have the same representation was voted down by EWG in Prague, so it has been withdrawn from this proposal.  Allowing the implicit pointer conversions would have eased the transition from using the standard floating-point types to the new named floating-point types.  But it complicated the language in a non-obvious way, and the group decided that the benefit was not worth the cost.</p>
   <h3 class="heading settled" data-level="5.10" id="core-test-macro"><span class="secno">5.10. </span><span class="content">Feature test macro</span><a class="self-link" href="#core-test-macro"></a></h3>
   <p class="issue" id="issue-6daed810"><a class="self-link" href="#issue-6daed810"></a> Should there be a feature test macro to indicate that the implementation supports at least one extended floating-point type?</p>
   <p>Implementations could support extended floating-point types without supporting any of the aliases for well-known layouts.  It might be useful to have a feature test macro that indicates support for extended floating-point types listed in 15.11 [<strong>cpp.predefined</strong>].  But it would likely have to be one of the conditionally-defined macros, and not listed in Table 17, since a conforming compiler might choose to not define any extended floating-point types.  If the macro is defined, it would not indicate which extended floating-point types are supported, only that there exists at least one extended floating-point type in the implementation.  The authors believe that such a feature test macro would not be useful, but would like SG10 to confirm that decision.</p>
   <h2 class="heading settled" data-level="6" id="library"><span class="secno">6. </span><span class="content">Library changes</span><a class="self-link" href="#library"></a></h2>
   <p>Making extended floating-point types easy to use does not require introducing any new names to the standard library.  But it does require adding new overloads or new template specializations in several places.  Some of the extended floating-point types will have standard names.  Those new names are covered in <a href="#alias">§ 7 Type aliases</a>.</p>
   <p>To handle I/O of extended floating-point types, changes are proposed to <code class="highlight"><c- o>&lt;</c-><c- n>charconv</c-><c- o>></c-></code> and <code class="highlight"><c- o>&lt;</c-><c- n>format</c-><c- o>></c-></code>, but not to <code class="highlight"><c- o>&lt;</c-><c- n>iostream</c-><c- o>></c-></code> or <code class="highlight"><c- o>&lt;</c-><c- n>cstdio</c-><c- o>></c-></code>.</p>
   <p>Implementations will have to change <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>numeric_limits</c-></code> and <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>is_floating_point</c-></code> to give correct answers for extended floating-point types.  The existing wording in the standard already covers that (by referring to all <em>floating-point types</em> without listing them explicitly), so no wording changes are needed.</p>
   <p>Most of the standard functions that operate on floating-point types need wording changes to add overloads or template specializations for the extended floating-point types.  These classes and functions are in <code class="highlight"><c- o>&lt;</c-><c- n>cmath</c-><c- o>></c-></code>, <code class="highlight"><c- o>&lt;</c-><c- n>complex</c-><c- o>></c-></code>, and <code class="highlight"><c- o>&lt;</c-><c- n>atomic</c-><c- o>></c-></code>.</p>
   <p>No changes are proposed to the following parts of the standard library:</p>
   <ul>
    <li data-md>
     <p><code class="highlight"><c- o>&lt;</c-><c- n>cfloat</c-><c- o>></c-></code>: The header <code class="highlight"><c- o>&lt;</c-><c- n>cfloat</c-><c- o>></c-></code> provides macros describing some of the properties of the standard floating-point types.  The use of macros does not extend very well to extended floating-point types with implementation-specific names.  Users should use <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>numeric_limits</c-></code> rather than macros from <code class="highlight"><c- o>&lt;</c-><c- n>cfloat</c-><c- o>></c-></code> to query the properties of extended floating-point types.</p>
    <li data-md>
     <p>The <code class="highlight"><c- n>printf</c-></code> and <code class="highlight"><c- n>scanf</c-></code> families of functions: There is no practical way to add specifiers for implementation-specific types with implementation-specific names.</p>
    <li data-md>
     <p>The <code class="highlight"><c- n>strtod</c-></code> and <code class="highlight"><c- n>stod</c-></code> families of functions: With different names for each floating-point type (which for <code class="highlight"><c- n>strtod</c-></code> was inherited from C), that scheme doesn’t work well for extended floating-point types.</p>
    <li data-md>
     <p>I/O streams: There is currently no support for extended integer types.  Correctly supporting extended floating-point types larger than <code class="highlight"><c- b>long</c-> <c- b>double</c-></code> would require ABI-breaking changes to <code class="highlight"><c- n>num_get</c-></code> and <code class="highlight"><c- n>num_put</c-></code>.</p>
    <li data-md>
     <p>The <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>to_string</c-></code> family of functions:  They are defined in terms of <code class="highlight"><c- n>snprintf</c-></code>, which will not support extended floating-point types.</p>
    <li data-md>
     <p><code class="highlight"><c- o>&lt;</c-><c- n>random</c-><c- o>></c-></code>:  [rand.req] states that certain template arguments have to be <code class="highlight"><c- b>float</c-></code>, <code class="highlight"><c- b>double</c-></code>, or <code class="highlight"><c- b>long</c-> <c- b>double</c-></code>.  The wording could be changed to allow any floating-point type, but <code class="highlight"><c- o>&lt;</c-><c- n>random</c-><c- o>></c-></code> does not support extended integral types, so we are not proposing that it support extended floating-point types either.</p>
   </ul>
   <p>WG14 is working on adding optional support for additional floating-point types in an annex to C2x.  (See <a href="#c-compat">§ 4 C Compatibility</a>.)  If those changes to the C standard library land in C2x, then C++ users will eventually see support for some of C++'s extended floating-point types through macros defined in <code class="highlight"><c- o>&lt;</c-><c- n>cfloat</c-><c- o>></c-></code> and conversion functions in <code class="highlight"><c- o>&lt;</c-><c- n>cstdlib</c-><c- o>></c-></code>.  This proposal is not suggesting identical changes ahead of C2x in these areas.  The changes will have to come to C++ through C2x.</p>
   <h3 class="heading settled" data-level="6.1" id="new-names"><span class="secno">6.1. </span><span class="content">Possible new names</span><a class="self-link" href="#new-names"></a></h3>
   <p>While no new names need to be added to the standard library for extended floating-point types to be useful, there are some new things that could be useful.  The authors are undecided if these are useful enough to be worth adding, and would appreciate LEWG feedback on the matter.</p>
   <h4 class="heading settled" data-level="6.1.1" id="new-names-standard"><span class="secno">6.1.1. </span><span class="content">Standard/extended floating-point traits</span><a class="self-link" href="#new-names-standard"></a></h4>
   <p><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>is_floating_point_v</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-></code> is true for both standard and extended floating-point types.  Should the standard also provide <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>is_standard_floating_point</c-></code> and/or <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>is_extended_floating_point</c-></code>?  Will users need to distinguish between standard and extended types often enough that <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>is_same_v</c-><c- o>&lt;</c-><c- n>T</c-><c- p>,</c-> <c- b>float</c-><c- o>></c-> <c- o>||</c-> <c- n>std</c-><c- o>::</c-><c- n>is_same_v</c-><c- o>&lt;</c-><c- n>T</c-><c- p>,</c-> <c- b>double</c-><c- o>></c-> <c- o>||</c-> <c- n>std</c-><c- o>::</c-><c- n>is_same_v</c-><c- o>&lt;</c-><c- n>T</c-><c- p>,</c-> <c- b>long</c-> <c- b>double</c-><c- o>></c-></code> becomes too unwieldy?</p>
   <p class="issue" id="issue-5b95c8c1"><a class="self-link" href="#issue-5b95c8c1"></a> Should the new type traits <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>is_standard_floating_point</c-></code> and/or <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>is_extended_floating_point</c-></code> be introduced?</p>
   <h4 class="heading settled" data-level="6.1.2" id="new-names-conv"><span class="secno">6.1.2. </span><span class="content">Conversion rank trait</span><a class="self-link" href="#new-names-conv"></a></h4>
   <p>Should there be a type trait that reports whether or not one floating-point type has a higher conversion rank than another?  This could be useful when writing function templates to figure out which conversions between different floating-point types are safe.  See the <a href="#complex-wording">constructors</a> for <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>complex</c-></code> as an example of where this trait would be useful.</p>
   <p class="issue" id="issue-4dff46e4"><a class="self-link" href="#issue-4dff46e4"></a> Should a new type trait be introduced that can be used to query the floating-point conversion rank relationship?</p>
   <h3 class="heading settled" data-level="6.2" id="charconv"><span class="secno">6.2. </span><span class="content"><code class="highlight"><c- o>&lt;</c-><c- n>charconv</c-><c- o>></c-></code></span><a class="self-link" href="#charconv"></a></h3>
   <p>Add overloads for all extended floating-point types for the functions <code class="highlight"><c- n>to_chars</c-></code> and <code class="highlight"><c- n>from_chars</c-></code>.</p>
   <h4 class="heading settled" data-level="6.2.1" id="charconv-wording"><span class="secno">6.2.1. </span><span class="content">Wording</span><a class="self-link" href="#charconv-wording"></a></h4>
   <p>Add a new paragraph to the beginning of 20.19.1 "Header <code class="highlight"><c- o>&lt;</c-><c- n>charconv</c-><c- o>></c-></code> synopsis" [<strong>charconv.syn</strong>], before the start of the synopsis:</p>
   <blockquote class="ins"> When a function has a parameter of type <code class="highlight"><em><c- n>integral</c-></em></code>, the implementation provides overloads for all signed and unsigned integer types and <code class="highlight"><c- b>char</c-></code> as the parameter type.  When a function has a parameter of type <code class="highlight"><em><c- n>floating</c-><c- o>-</c-><c- n>point</c-></em></code>, the implementation provides overloads for all floating-point types as the parameter type. </blockquote>
   <p>Change the header synopsis in [<strong>charconv.syn</strong>] as follows:</p>
   <blockquote>
<pre class="highlight"><code class="highlight">  <c- n><c- n>to_chars_result</c-></c-> <c- nf><c- nf>to_chars</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c-> <del><em><c- n><c- n>see</c-></c-><c- o><c- o>-</c-></c-><c- n><c- n>below</c-></c-></em></del><ins><em><c- n><c- n>integral</c-></c-></em></ins> <c- n><c- n>value</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>int</c-></c-> <c- n><c- n>base</c-></c-> <c- o><c- o>=</c-></c-> <c- mi><c- mi>10</c-></c-><c- p><c- p>);</c-></c->
  <c- n><c- n>to_chars_result</c-></c-> <c- nf><c- nf>to_chars</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c-> <del><c- n><c- n>float</c-></c-></del><ins><em><c- n><c- n>floating</c-></c-><c- o><c- o>-</c-></c-><c- n><c- n>point</c-></c-></em></ins> <c- n><c- n>value</c-></c-><c- p><c- p>);</c-></c->
<del>  <c- n><c- n>to_chars_result</c-></c-> <c- nf><c- nf>to_chars</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>double</c-></c-> <c- n><c- n>value</c-></c-><c- p><c- p>);</c-></c->
  <c- n><c- n>to_chars_result</c-></c-> <c- nf><c- nf>to_chars</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>long</c-></c-> <c- b><c- b>double</c-></c-> <c- n><c- n>value</c-></c-><c- p><c- p>);</c-></c-></del>
  <c- n><c- n>to_chars_result</c-></c-> <c- nf><c- nf>to_chars</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c-> <del><c- n><c- n>float</c-></c-></del><ins><em><c- n><c- n>floating</c-></c-><c- o><c- o>-</c-></c-><c- n><c- n>point</c-></c-></em></ins> <c- n><c- n>value</c-></c-><c- p><c- p>,</c-></c->
                           <c- n><c- n>chars_format</c-></c-> <c- n><c- n>fmt</c-></c-><c- p><c- p>);</c-></c->
<del>  <c- n><c- n>to_chars_result</c-></c-> <c- nf><c- nf>to_chars</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>double</c-></c-> <c- n><c- n>value</c-></c-><c- p><c- p>,</c-></c-> <c- n><c- n>chars_format</c-></c-> <c- n><c- n>fmt</c-></c-><c- p><c- p>);</c-></c->
  <c- n><c- n>to_chars_result</c-></c-> <c- nf><c- nf>to_chars</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>long</c-></c-> <c- b><c- b>double</c-></c-> <c- n><c- n>value</c-></c-><c- p><c- p>,</c-></c-> <c- n><c- n>chars_format</c-></c-> <c- n><c- n>fmt</c-></c-><c- p><c- p>);</c-></c-></del>
  <c- n><c- n>to_chars_result</c-></c-> <c- nf><c- nf>to_chars</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c-> <del><c- n><c- n>float</c-></c-></del><ins><em><c- n><c- n>floating</c-></c-><c- o><c- o>-</c-></c-><c- n><c- n>point</c-></c-></em></ins> <c- n><c- n>value</c-></c-><c- p><c- p>,</c-></c->
                           <c- n><c- n>chars_format</c-></c-> <c- n><c- n>fmt</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>int</c-></c-> <c- n><c- n>precision</c-></c-><c- p><c- p>);</c-></c->
<del>  <c- n><c- n>to_chars_result</c-></c-> <c- nf><c- nf>to_chars</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>double</c-></c-> <c- n><c- n>value</c-></c-><c- p><c- p>,</c-></c->
                           <c- n><c- n>chars_format</c-></c-> <c- n><c- n>fmt</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>int</c-></c-> <c- n><c- n>precision</c-></c-><c- p><c- p>);</c-></c->
  <c- n><c- n>to_chars_result</c-></c-> <c- nf><c- nf>to_chars</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>long</c-></c-> <c- b><c- b>double</c-></c-> <c- n><c- n>value</c-></c-><c- p><c- p>,</c-></c->
                           <c- n><c- n>chars_format</c-></c-> <c- n><c- n>fmt</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>int</c-></c-> <c- n><c- n>precision</c-></c-><c- p><c- p>);</c-></c-></del>

  <c- c1><c- c1>// ...</c-></c->
  
  <c- n><c- n>from_chars_result</c-></c-> <c- nf><c- nf>from_chars</c-></c-><c- p><c- p>(</c-></c-><c- k><c- k>const</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- k><c- k>const</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c->
                               <del><em><c- n><c- n>see</c-></c-> <c- n><c- n>below</c-></c-></em></del><ins><em><c- n><c- n>integral</c-></c-></em></ins><c- o><c- o>&amp;</c-></c-> <c- n><c- n>value</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>int</c-></c-> <c- n><c- n>base</c-></c-> <c- o><c- o>=</c-></c-> <c- mi><c- mi>10</c-></c-><c- p><c- p>);</c-></c->

  <c- n><c- n>from_chars_result</c-></c-> <c- nf><c- nf>from_chars</c-></c-><c- p><c- p>(</c-></c-><c- k><c- k>const</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- k><c- k>const</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c-> <del><c- n><c- n>float</c-></c-></del><ins><em><c- n><c- n>floating</c-></c-><c- o><c- o>-</c-></c-><c- n><c- n>point</c-></c-></em></ins><c- o><c- o>&amp;</c-></c-> <c- n><c- n>value</c-></c-><c- p><c- p>,</c-></c->
                               <c- n><c- n>chars_format</c-></c-> <c- n><c- n>fmt</c-></c-> <c- o><c- o>=</c-></c-> <c- n><c- n>chars_format</c-></c-><c- o><c- o>::</c-></c-><c- n><c- n>general</c-></c-><c- p><c- p>);</c-></c->
<del>  <c- n><c- n>from_chars_result</c-></c-> <c- nf><c- nf>from_chars</c-></c-><c- p><c- p>(</c-></c-><c- k><c- k>const</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- k><c- k>const</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>double</c-></c-> <c- n><c- n>value</c-></c-><c- p><c- p>,</c-></c->
                               <c- n><c- n>chars_format</c-></c-> <c- n><c- n>fmt</c-></c-> <c- o><c- o>=</c-></c-> <c- n><c- n>chars_format</c-></c-><c- o><c- o>::</c-></c-><c- n><c- n>general</c-></c-><c- p><c- p>);</c-></c->
  <c- n><c- n>from_chars_result</c-></c-> <c- nf><c- nf>from_chars</c-></c-><c- p><c- p>(</c-></c-><c- k><c- k>const</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- k><c- k>const</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>long</c-></c-> <c- b><c- b>double</c-></c-> <c- n><c- n>value</c-></c-><c- p><c- p>,</c-></c->
                               <c- n><c- n>chars_format</c-></c-> <c- n><c- n>fmt</c-></c-> <c- o><c- o>=</c-></c-> <c- n><c- n>chars_format</c-></c-><c- o><c- o>::</c-></c-><c- n><c- n>general</c-></c-><c- p><c- p>);</c-></c-></del>
</code></pre>
   </blockquote>
   <p>In 20.19.2 "Primitive numeric output conversion" [<strong>charconv.to.chars</strong>], leave the first three paragraphs unchanged, but modify the rest of the section as follows:</p>
   <blockquote>
<pre class="highlight"><code class="highlight"><c- n><c- n>to_chars_result</c-></c-> <c- nf><c- nf>to_chars</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c-> <del><em><c- n><c- n>see</c-></c-> <c- n><c- n>below</c-></c-></em></del><ins><em><c- n><c- n>integral</c-></c-></em></ins> <c- n><c- n>value</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>int</c-></c-> <c- n><c- n>base</c-></c-> <c- o><c- o>=</c-></c-> <c- mi><c- mi>10</c-></c-><c- p><c- p>);</c-></c-></code></pre>
    <del><em>Requires</em></del>
    <ins><em>Expects</em></ins>
    : <code class="highlight"><c- n>base</c-></code> has a value between 2 and 36 (inclusive). 
    <p><em>Effects</em>: The value of <code class="highlight"><c- n>value</c-></code> is converted to a string of digits in the given base (with no redundant leading zeroes). Digits inthe range 10..35 (inclusive) are represented as lowercase characters <code class="highlight"><c- n>a</c-></code>..<code class="highlight"><c- n>z</c-></code>. If <code class="highlight"><c- n>value</c-></code> isless than zero, the representation starts with <code class="highlight"><c- sc>'-'</c-></code>.</p>
    <p><em>Throws</em>: Nothing.</p>
    <del><em>Remarks</em>:</del>
    <ins>[ <em>Note</em>:</ins>
     The implementation 
    <del>shall provide</del>
    <ins>provides</ins>
     overloads for all signed and unsigned integer types and <code class="highlight"><c- b>char</c-></code> as the type of the parameter <code class="highlight"><c- n>value</c-></code>. 
    <ins>- <em>end note</em> ]</ins>
<pre class="highlight"><code class="highlight"><c- n><c- n>to_chars_result</c-></c-> <c- nf><c- nf>to_chars</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c-> <del><c- n><c- n>float</c-></c-></del><ins><em><c- n><c- n>floating</c-></c-><c- o><c- o>-</c-></c-><c- n><c- n>point</c-></c-></em></ins> <c- n><c- n>value</c-></c-><c- p><c- p>);</c-></c->
<del><c- n><c- n>to_chars_result</c-></c-> <c- nf><c- nf>to_chars</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>double</c-></c-> <c- n><c- n>value</c-></c-><c- p><c- p>);</c-></c->
<c- n><c- n>to_chars_result</c-></c-> <c- nf><c- nf>to_chars</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>long</c-></c-> <c- b><c- b>double</c-></c-> <c- n><c- n>value</c-></c-><c- p><c- p>);</c-></c-></del>
</code></pre>
    <p><em>Effects</em>: <code class="highlight"><c- n>value</c-></code> is converted to a string in the style of <code class="highlight"><c- n>printf</c-></code> in the "C" locale. The conversion specifier is <code class="highlight"><c- n>f</c-></code> or <code class="highlight"><c- n>e</c-></code>, chosen according to the requirement for a shortest representation (see above); a tie is resolved in favor of <code class="highlight"><c- n>f</c-></code>.</p>
    <p><em>Throws</em>: Nothing.</p>
    <ins>[ <em>Note</em>: The implementation provides overloads for all floating-point types as the type of the parameter <code class="highlight"><c- n>value</c-></code>. - <em>end note</em> ]</ins>
<pre class="highlight"><code class="highlight"><c- n><c- n>to_chars_result</c-></c-> <c- nf><c- nf>to_chars</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c-> <del><c- n><c- n>float</c-></c-></del><ins><em><c- n><c- n>floating</c-></c-><c- o><c- o>-</c-></c-><c- n><c- n>point</c-></c-></em></ins> <c- n><c- n>value</c-></c-><c- p><c- p>,</c-></c-> <c- n><c- n>chars_format</c-></c-> <c- n><c- n>fmt</c-></c-><c- p><c- p>);</c-></c->
<del><c- n><c- n>to_chars_result</c-></c-> <c- nf><c- nf>to_chars</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>double</c-></c-> <c- n><c- n>value</c-></c-><c- p><c- p>,</c-></c-> <c- n><c- n>chars_format</c-></c-> <c- n><c- n>fmt</c-></c-><c- p><c- p>);</c-></c->
<c- n><c- n>to_chars_result</c-></c-> <c- nf><c- nf>to_chars</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>long</c-></c-> <c- b><c- b>double</c-></c-> <c- n><c- n>value</c-></c-><c- p><c- p>,</c-></c-> <c- n><c- n>chars_format</c-></c-> <c- n><c- n>fmt</c-></c-><c- p><c- p>);</c-></c-></del>
</code></pre>
    <del><em>Requires</em></del>
    <ins><em>Expects</em></ins>
    : <code class="highlight"><c- n>fmt</c-></code> has the value of one of the enumerators of <code class="highlight"><c- n>chars_format</c-></code>. 
    <p><em>Effects</em>: <code class="highlight"><c- n>value</c-></code> is converted to a string in the style of <code class="highlight"><c- n>printf</c-></code> in the "C" locale.</p>
    <p><em>Throws</em>: Nothing.</p>
    <ins>[ <em>Note</em>: The implementation provides overloads for all floating-point types as the type of the parameter <code class="highlight"><c- n>value</c-></code>. - <em>end note</em> ]</ins>
<pre class="highlight"><code class="highlight"><c- n><c- n>to_chars_result</c-></c-> <c- nf><c- nf>to_chars</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c-> <del><c- n><c- n>float</c-></c-></del><ins><em><c- n><c- n>floating</c-></c-><c- o><c- o>-</c-></c-><c- n><c- n>point</c-></c-></em></ins> <c- n><c- n>value</c-></c-><c- p><c- p>,</c-></c->
                         <c- n><c- n>chars_format</c-></c-> <c- n><c- n>fmt</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>int</c-></c-> <c- n><c- n>precision</c-></c-><c- p><c- p>);</c-></c->
<del><c- n><c- n>to_chars_result</c-></c-> <c- nf><c- nf>to_chars</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>double</c-></c-> <c- n><c- n>value</c-></c-><c- p><c- p>,</c-></c->
                         <c- n><c- n>chars_format</c-></c-> <c- n><c- n>fmt</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>int</c-></c-> <c- n><c- n>precision</c-></c-><c- p><c- p>);</c-></c->
<c- n><c- n>to_chars_result</c-></c-> <c- nf><c- nf>to_chars</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>long</c-></c-> <c- b><c- b>double</c-></c-> <c- n><c- n>value</c-></c-><c- p><c- p>,</c-></c->
                         <c- n><c- n>chars_format</c-></c-> <c- n><c- n>fmt</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>int</c-></c-> <c- n><c- n>precision</c-></c-><c- p><c- p>);</c-></c-></del>
</code></pre>
    <del><em>Requires</em></del>
    <ins><em>Expects</em></ins>
    : <code class="highlight"><c- n>fmt</c-></code> has the value of one of the enumerators of <code class="highlight"><c- n>chars_format</c-></code>. 
    <p><em>Effects</em>: <code class="highlight"><c- n>value</c-></code> is converted to a string in the style of <code class="highlight"><c- n>printf</c-></code> in the "C" locale with the given precision.</p>
    <p><em>Throws</em>: Nothing.</p>
    <ins>[ <em>Note</em>: The implementation provides overloads for all floating-point types as the type of the parameter <code class="highlight"><c- n>value</c-></code>. - <em>end note</em> ]</ins>
    <p>See also: ISO C 7.21.6.1</p>
   </blockquote>
   <p>Modify 20.19.3 "Primitive numeric input conversion" [<strong>charconv.from.chars</strong>] as follows:</p>
   <blockquote>
    <div class="numbered"> All functions named <code class="highlight"><c- n>from_chars</c-></code> analyze the string <code class="highlight"><c- p>[</c-><c- n>first</c-><c- p>,</c-> <c- n>last</c-><c- p>)</c-></code> for a pattern, where <code class="highlight"><c- p>[</c-><c- n>first</c-><c- p>,</c-> <c- n>last</c-><c- p>)</c-></code> is required to be a valid range. If no characters match the pattern, <code class="highlight"><c- n>value</c-></code> is unmodified, the member <code class="highlight"><c- n>ptr</c-></code> of the return value is <code class="highlight"><c- n>first</c-></code> and the member <code class="highlight"><c- n>ec</c-></code> is equal to <code class="highlight"><c- n>errc</c->​<c- o>::</c->​<c- n>invalid_argument</c-></code>. [ <em>Note</em>: If the pattern allows for an optional sign, but the string has no digit characters following the sign, no characters match the pattern. — <em>end note</em> ] Otherwise, the characters matching the pattern are interpreted as a representation of a value of the type of <code class="highlight"><c- n>value</c-></code>. The member <code class="highlight"><c- n>ptr</c-></code> of the return value points to the first character not matching the pattern, or has the value <code class="highlight"><c- n>last</c-></code> if all characters match. If the parsed value is not in the range representable by the type of <code class="highlight"><c- n>value</c-></code>, <code class="highlight"><c- n>value</c-></code> is unmodified and the member <code class="highlight"><c- n>ec</c-></code> of the return value is equal to <code class="highlight"><c- n>errc</c->​<c- o>::</c->​<c- n>result_out_of_range</c-></code>. Otherwise, <code class="highlight"><c- n>value</c-></code> is set to the parsed value, after rounding according to <code class="highlight"><c- n>round_to_nearest</c-></code>, and the member <code class="highlight"><c- n>ec</c-></code> is value-initialized. </div>
<pre class="highlight"><code class="highlight"><c- n><c- n>from_chars_result</c-></c-> <c- nf><c- nf>from_chars</c-></c-><c- p><c- p>(</c-></c-><c- k><c- k>const</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- k><c- k>const</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c->
                             <del><em><c- n><c- n>see</c-></c-> <c- n><c- n>below</c-></c-></em></del><ins><em><c- n><c- n>integral</c-></c-></em></ins><c- o><c- o>&amp;</c-></c-> <c- n><c- n>value</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>int</c-></c-> <c- n><c- n>base</c-></c-> <c- o><c- o>=</c-></c-> <c- mi><c- mi>10</c-></c-><c- p><c- p>);</c-></c->
</code></pre>
    <div class="numbered">
     <del><em>Requires</em></del>
     <ins><em>Expects</em></ins>
     : <code class="highlight"><c- n>base</c-></code> has a value between 2 and 36 (inclusive). 
    </div>
    <div class="numbered"> <em>Effects</em>: The pattern is the expected form of the subject sequence in the <code class="highlight"><c- s>"C"</c-></code> locale for the given nonzero base, as described for <code class="highlight"><c- n>strtol</c-></code>, except that no <code class="highlight"><c- s>"0x"</c-></code> or <code class="highlight"><c- s>"0X"</c-></code> prefix shall appear if the value of <code class="highlight"><c- n>base</c-></code> is 16, and except that <code class="highlight"><c- sc>'-'</c-></code> is the only sign that may appear, and only if <code class="highlight"><c- n>value</c-></code> has a signed type. </div>
    <div class="numbered"> <em>Throws</em>: Nothing. </div>
    <div class="numbered">
     <del><em>Remarks</em>:</del>
     <ins>[ <em>Note</em>:</ins>
      The implementation 
     <del>shall provide</del>
     <ins>provides</ins>
      overloads for all signed and unsigned integer types and <code class="highlight"><c- b>char</c-></code> as the referenced type of the parameter <code class="highlight"><c- n>value</c-></code>. 
     <ins>- <em>end note</em> ]</ins>
    </div>
<pre class="highlight"><code class="highlight"><c- n><c- n>from_chars_result</c-></c-> <c- nf><c- nf>from_chars</c-></c-><c- p><c- p>(</c-></c-><c- k><c- k>const</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- k><c- k>const</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c-> <del><c- n><c- n>float</c-></c-></del><ins><em><c- n><c- n>floating</c-></c-><c- o><c- o>-</c-></c-><c- n><c- n>point</c-></c-></em></ins><c- o><c- o>&amp;</c-></c-> <c- n><c- n>value</c-></c-><c- p><c- p>,</c-></c->
                             <c- n><c- n>chars_format</c-></c-> <c- n><c- n>fmt</c-></c-> <c- o><c- o>=</c-></c-> <c- n><c- n>chars_format</c-></c-><c- o><c- o>::</c-></c-><c- n><c- n>general</c-></c-><c- p><c- p>);</c-></c->
<del><c- n><c- n>from_chars_result</c-></c-> <c- nf><c- nf>from_chars</c-></c-><c- p><c- p>(</c-></c-><c- k><c- k>const</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- k><c- k>const</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>double</c-></c-><c- o><c- o>&amp;</c-></c-> <c- n><c- n>value</c-></c-><c- p><c- p>,</c-></c->
                             <c- n><c- n>chars_format</c-></c-> <c- n><c- n>fmt</c-></c-> <c- o><c- o>=</c-></c-> <c- n><c- n>chars_format</c-></c-><c- o><c- o>::</c-></c-><c- n><c- n>general</c-></c-><c- p><c- p>);</c-></c->
<c- n><c- n>from_chars_result</c-></c-> <c- nf><c- nf>from_chars</c-></c-><c- p><c- p>(</c-></c-><c- k><c- k>const</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>first</c-></c-><c- p><c- p>,</c-></c-> <c- k><c- k>const</c-></c-> <c- b><c- b>char</c-></c-><c- o><c- o>*</c-></c-> <c- n><c- n>last</c-></c-><c- p><c- p>,</c-></c-> <c- b><c- b>long</c-></c-> <c- b><c- b>double</c-></c-><c- o><c- o>&amp;</c-></c-> <c- n><c- n>value</c-></c-><c- p><c- p>,</c-></c->
                             <c- n><c- n>chars_format</c-></c-> <c- n><c- n>fmt</c-></c-> <c- o><c- o>=</c-></c-> <c- n><c- n>chars_format</c-></c-><c- o><c- o>::</c-></c-><c- n><c- n>general</c-></c-><c- p><c- p>);</c-></c-></del>
</code></pre>
    <div class="numbered">
     <del><em>Requires</em></del>
     <ins><em>Expects</em></ins>
     : <code class="highlight"><c- n>fmt</c-></code> has the value of one of the enumerators of <code class="highlight"><c- n>chars_format</c-></code>. 
    </div>
    <div class="numbered">
      <em>Effects</em>: The pattern is the expected form of the subject sequence in the <code class="highlight"><c- s>"C"</c-></code> locale, as described for <code class="highlight"><c- n>strtod</c-></code>, except that 
     <ul>
      <li data-md>
       <p>the sign <code class="highlight"><c- sc>'+'</c-></code> may only appear in the exponent part;</p>
      <li data-md>
       <p>if <code class="highlight"><c- n>fmt</c-></code> has <code class="highlight"><c- n>chars_format</c-><c- o>::</c-><c- n>scientific</c-></code> set but not <code class="highlight"><c- n>chars_format</c-><c- o>::</c-><c- n>fixed</c-></code>, the otherwise optional exponent part shall appear;</p>
      <li data-md>
       <p>if <code class="highlight"><c- n>fmt</c-></code> has <code class="highlight"><c- n>chars_format</c-><c- o>::</c-><c- n>fixed</c-></code> set but not <code class="highlight"><c- n>chars_format</c-><c- o>::</c-><c- n>scientific</c-></code>, the optional exponent part shall not appear; and</p>
      <li data-md>
       <p>if <code class="highlight"><c- n>fmt</c-></code> is <code class="highlight"><c- n>chars_format</c-><c- o>::</c-><c- n>hex</c-></code>, the prefix <code class="highlight"><c- s>"0x"</c-></code> or <code class="highlight"><c- s>"0X"</c-></code> is assumed. [ <em>Example</em>: The string <code class="highlight"><c- mh>0x123</c-></code> is parsed to have the value <code class="highlight"><c- mi>0</c-></code> with remaining characters <code class="highlight"><c- n>x123</c-></code>. - <em>end example</em> ]</p>
     </ul>
     <p>In any case, the resulting <code class="highlight"><c- n>value</c-></code> is one of at most two floating-point values closest to the value of the string matching the pattern.</p>
    </div>
    <div class="numbered"> <em>Throws</em>: Nothing. </div>
    <div class="numbered">
     <ins>[ <em>Note</em>: The implementation provides overloads for all floating-point types as the referenced type of the parameter <code class="highlight"><c- n>value</c-></code>. - <em>end note</em> ]</ins>
    </div>
    <p>See also: ISO C 7.22.1.3, 7.22.1.4</p>
   </blockquote>
   <h3 class="heading settled" data-level="6.3" id="format"><span class="secno">6.3. </span><span class="content"><code class="highlight"><c- o>&lt;</c-><c- n>format</c-><c- o>></c-></code></span><a class="self-link" href="#format"></a></h3>
   <p>Change <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>format</c-></code> to support extended floating-point types.</p>
   <h4 class="heading settled" data-level="6.3.1" id="format-wording"><span class="secno">6.3.1. </span><span class="content">Wording</span><a class="self-link" href="#format-wording"></a></h4>
   <p>... to be determined ...</p>
   <h3 class="heading settled" data-level="6.4" id="cmath"><span class="secno">6.4. </span><span class="content"><code class="highlight"><c- o>&lt;</c-><c- n>cmath</c-><c- o>></c-></code></span><a class="self-link" href="#cmath"></a></h3>
   <p>Add overloads for extended floating-point types to the functions in <code class="highlight"><c- o>&lt;</c-><c- n>cmath</c-><c- o>></c-></code>.  It is expected that this will be the most used part of the library changes.</p>
   <h4 class="heading settled" data-level="6.4.1" id="cmath-wording"><span class="secno">6.4.1. </span><span class="content">Wording</span><a class="self-link" href="#cmath-wording"></a></h4>
   <p>Modify 26.8.1 "Header <code class="highlight"><c- o>&lt;</c-><c- n>cmath</c-><c- o>></c-></code> synopsis" [<strong>cmath.syn</strong>] paragraph 2 as follows:</p>
   <blockquote>
     For each set of overloaded functions within <code class="highlight"><c- o>&lt;</c-><c- n>cmath</c-><c- o>></c-></code>, with the exception of <code class="highlight"><c- n>abs</c-></code>, there shall be additional overloads sufficient to ensure: 
    <ul>
     <li data-md>
      <del>1. If any argument of arithmetic type corresponding to a <code class="highlight"><c- b>double</c-></code> parameter has type <code class="highlight"><c- b>long</c-> <c- b>double</c-></code>, then all arguments of arithmetic type (6.7.1) corresponding to <code class="highlight"><c- b>double</c-></code> parameters are effectively cast to <code class="highlight"><c- b>long</c-> <c- b>double</c-></code>.</del>
     <li data-md>
      <del>2. Otherwise, if any argument of arithmetic type corresponding to a <code class="highlight"><c- b>double</c-></code> parameter has type <code class="highlight"><c- b>double</c-></code> or an integer type, then all arguments of arithmetic type corresponding to <code class="highlight"><c- b>double</c-></code> parameters are effectively cast to <code class="highlight"><c- b>double</c-></code>.</del>
     <li data-md>
      <del>3. Otherwise, all arguments of arithmetic type corresponding to <code class="highlight"><c- b>double</c-></code> parameters have type <code class="highlight"><c- b>float</c-></code>.</del>
     <li data-md>
      <ins>1. If any argument corresponding to a <code class="highlight"><c- b>double</c-></code> parameter has floating-point type, then all arguments of arithmetic type ([basic.fundamental]) corresponding to <code class="highlight"><c- b>double</c-></code> parameters are effectively cast to the floating-point type with the highest floating-point conversion rank ([conv.rank]) among the types of such floating-point arguments. If two such floating-point arguments have types whose conversion rank is unordered, the program is ill-formed.</ins>
     <li data-md>
      <ins>2. Otherwise, all arguments of arithmetic type corresponding to <code class="highlight"><c- b>double</c-></code> parameters are effectively cast to <code class="highlight"><c- b>double</c-></code>.</ins>
    </ul>
    <p>[ <em>Note</em>: <code class="highlight"><c- n>abs</c-></code> is exempted from these rules in order to stay compatible with C. -- <em>end note</em> ]</p>
   </blockquote>
   <p>Modify section 26.8.2 "Absolute values" [<strong>c.math.abs</strong>] as follows:</p>
   <blockquote>
    <div class="numbered"> [ <em>Note</em>: The headers <code class="highlight"><c- o>&lt;</c-><c- n>cstdlib</c-><c- o>></c-></code> and <code class="highlight"><c- o>&lt;</c-><c- n>cmath</c-><c- o>></c-></code> declare the functions described in this subclause. — <em>end note</em> ] </div>
<pre class="highlight"><code class="highlight"><c- b><c- b>int</c-></c-> <c- nf><c- nf>abs</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>int</c-></c-> <c- n><c- n>j</c-></c-><c- p><c- p>);</c-></c->
<c- b><c- b>long</c-></c-> <c- b><c- b>int</c-></c-> <c- nf><c- nf>abs</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>long</c-></c-> <c- b><c- b>int</c-></c-> <c- n><c- n>j</c-></c-><c- p><c- p>);</c-></c->
<c- b><c- b>long</c-></c-> <c- b><c- b>long</c-></c-> <c- b><c- b>int</c-></c-> <c- nf><c- nf>abs</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>long</c-></c-> <c- b><c- b>long</c-></c-> <c- b><c- b>int</c-></c-> <c- n><c- n>j</c-></c-><c- p><c- p>);</c-></c->
<del><c- b><c- b>float</c-></c-> <c- nf><c- nf>abs</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>float</c-></c-> <c- n><c- n>j</c-></c-><c- p><c- p>);</c-></c->
<c- b><c- b>double</c-></c-> <c- nf><c- nf>abs</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>double</c-></c-> <c- n><c- n>j</c-></c-><c- p><c- p>);</c-></c->
<c- b><c- b>long</c-></c-> <c- b><c- b>double</c-></c-> <c- nf><c- nf>abs</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>long</c-></c-> <c- b><c- b>double</c-></c-> <c- n><c- n>j</c-></c-><c- p><c- p>);</c-></c-></del>
</code></pre>
    <div class="numbered">
      <em>Effects</em>: The <code class="highlight"><c- n>abs</c-></code> functions 
     <ins>that take integer arguments</ins>
      have the semantics specified in the C standard library for the functions <code class="highlight"><c- n>abs</c-></code>, <code class="highlight"><c- n>labs</c-></code>, 
     <ins>and</ins>
      <code class="highlight"><c- n>llabs</c-></code>
     <del>, <code class="highlight"><c- n>fabsf</c-></code>, <code class="highlight"><c- n>fabs</c-></code>, and <code class="highlight"><c- n>fabsl</c-></code></del>
     . 
    </div>
    <div class="numbered"> <em>Remarks</em>: If <code class="highlight"><c- n>abs</c-><c- p>()</c-></code> is called with an argument of type <code class="highlight"><c- n>X</c-></code> for which <code class="highlight"><c- n>is_unsigned_v</c-><c- o>&lt;</c-><c- n>X</c-><c- o>></c-></code> is <code class="highlight">true</code> and if <code class="highlight"><c- n>X</c-></code> cannot be converted to <code class="highlight"><c- b>int</c-></code> by integral promotion, the program is ill-formed.  [ <em>Note</em>: Arguments that can be promoted to <code class="highlight"><c- b>int</c-></code> are permitted for compatibility with C. — <em>end note</em> ] </div>
<pre class="highlight"><code class="highlight"><ins><em><c- n><c- n>floating</c-></c-><c- o><c- o>-</c-></c-><c- n><c- n>point</c-></c-></em> <c- n><c- n>abs</c-></c-><c- p><c- p>(</c-></c-><em><c- n><c- n>floating</c-></c-><c- o><c- o>-</c-></c-><c- n><c- n>point</c-></c-></em> <c- n><c- n>x</c-></c-><c- p><c- p>);</c-></c-></ins>
</code></pre>
    <div class="numbered">
     <ins><em>Returns</em>: The absolute value of <code class="highlight"><c- n>x</c-></code>.</ins>
    </div>
    <div class="numbered">
     <ins><em>Remarks</em>: The implementation provides overloads for all floating-point types as the type of parameter <code class="highlight"><c- n>x</c-></code>, with the same floating-point type as the return type.</ins>
    </div>
    <p>See also: ISO C 7.12.7.2, 7.22.6.1</p>
   </blockquote>
   <h3 class="heading settled" data-level="6.5" id="complex"><span class="secno">6.5. </span><span class="content"><code class="highlight"><c- o>&lt;</c-><c- n>complex</c-><c- o>></c-></code></span><a class="self-link" href="#complex"></a></h3>
   <p>Make <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>complex</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-></code> be well-defined when <code class="highlight"><c- n>T</c-></code> is an extended floating-point type.  The explicit specializations of <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>complex</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-></code> are removed.  The only differences between the explicit specializations was the explicit-ness of the constructors that take a complex number of a different type.  This behavior is incorporated into the main template through <code class="highlight"><c- k>explicit</c-><c- p>(</c-><c- b>bool</c-><c- p>)</c-></code>.</p>
   <h4 class="heading settled" data-level="6.5.1" id="complex-wording"><span class="secno">6.5.1. </span><span class="content">Wording</span><a class="self-link" href="#complex-wording"></a></h4>
   <p>Modify 26.4 "Complex numbers" [<strong>complex.numbers</strong>] paragraph 2 as follows:</p>
   <blockquote>
     The effect of instantiating the template <code class="highlight"><c- n>complex</c-></code> for any type 
    <del>other than <code class="highlight"><c- b>float</c-></code>, <code class="highlight"><c- b>double</c-></code>, or <code class="highlight"><c- b>long</c-> <c- b>double</c-></code></del>
    <ins>that is not a floating-point type</ins>
     is unspecified. The specializations 
    <del><code class="highlight"><c- n>complex</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c-></code>, <code class="highlight"><c- n>complex</c-><c- o>&lt;</c-><c- b>double</c-><c- o>></c-></code>, and <code class="highlight"><c- n>complex</c-><c- o>&lt;</c-><c- b>long</c-> <c- b>double</c-><c- o>></c-></code></del>
    <ins>of <code class="highlight"><c- n>complex</c-></code> for floating-point types</ins>
     are literal types ([basic.types]). 
   </blockquote>
   <p>Delete the explicit specializations from 26.4.1 "Header <code class="highlight"><c- o>&lt;</c-><c- n>complex</c-><c- o>></c-></code> synopsis" [<strong>complex.syn</strong>]:</p>
   <blockquote>
<pre class="highlight"><code class="highlight"><c- k><c- k>namespace</c-></c-> <c- n><c- n>std</c-></c-> <c- p><c- p>{</c-></c->
  <c- c1><c- c1>// </c-></c-><em><c- c1><c- c1>26.4.2, class template</c-></c-></em><c- c1><c- c1> complex</c-></c->
  <c- k><c- k>template</c-></c-><class t> <c- k><c- k>class</c-></c-> <c- nc><c- nc>complex</c-></c-><c- p><c- p>;</c-></c->
  
<del>  <c- c1><c- c1>// </c-></c-><em><c- c1><c- c1>26.4.3, specializations</c-></c-></em>
  <c- k><c- k>template</c-></c-><c- o><c- o>&lt;></c-></c-> <c- k><c- k>class</c-></c-> <c- nc><c- nc>complex</c-></c-><float><c- p><c- p>;</c-></c->
  <c- k><c- k>template</c-></c-><c- o><c- o>&lt;></c-></c-> <c- k><c- k>class</c-></c-> <c- nc><c- nc>complex</c-></c-><double><c- p><c- p>;</c-></c->
  <c- k><c- k>template</c-></c-><c- o><c- o>&lt;></c-></c-> <c- k><c- k>class</c-></c-> <c- nc><c- nc>complex</c-></c-><long double><c- p><c- p>;</c-></c-></long></double></float></del>
  
  <c- c1><c- c1>// ...</c-></c->
</class></code></pre>
   </blockquote>
   <p>In 26.4.2 "Class template <code class="highlight"><c- n>complex</c-></code>" [<strong>complex</strong>], modify the synopsis of the constructors as follows:</p>
   <blockquote>
<pre class="highlight"><code class="highlight"><c- k><c- k>constexpr</c-></c-> <c- nf><c- nf>complex</c-></c-><c- p><c- p>(</c-></c-><c- k><c- k>const</c-></c-> <c- n><c- n>T</c-></c-><c- o><c- o>&amp;</c-></c-> <c- n><c- n>re</c-></c-> <c- o><c- o>=</c-></c-> <c- n><c- n>T</c-></c-><c- p><c- p>(),</c-></c-> <c- k><c- k>const</c-></c-> <c- n><c- n>T</c-></c-><c- o><c- o>&amp;</c-></c-> <c- n><c- n>im</c-></c-> <c- o><c- o>=</c-></c-> <c- n><c- n>T</c-></c-><c- p><c- p>());</c-></c->
<c- k><c- k>constexpr</c-></c-> <c- nf><c- nf>complex</c-></c-><c- p><c- p>(</c-></c-><c- k><c- k>const</c-></c-> <c- n><c- n>complex</c-></c-><c- o><c- o>&amp;</c-></c-><c- p><c- p>)</c-></c-> <ins><c- o><c- o>=</c-></c-> <c- k><c- k>default</c-></c-></ins><c- p><c- p>;</c-></c->
<c- k><c- k>template</c-></c-><c- o><c- o>&lt;</c-></c-><c- k><c- k>class</c-></c-> <c- nc><c- nc>X</c-></c-><c- o><c- o>></c-></c-> <c- k><c- k>constexpr</c-></c-> <ins><c- k><c- k>explicit</c-></c-><c- p><c- p>(</c-></c-><em><c- n><c- n>see</c-></c-> <c- n><c- n>below</c-></c-></em><c- p><c- p>)</c-></c-></ins> <c- n><c- n>complex</c-></c-><c- p><c- p>(</c-></c-><c- k><c- k>const</c-></c-> <c- n><c- n>complex</c-></c-><c- o><c- o>&lt;</c-></c-><c- n><c- n>X</c-></c-><c- o><c- o>>&amp;</c-></c-><c- p><c- p>);</c-></c->
</code></pre>
   </blockquote>
   <p>Remove section 26.4.3 "Specializations" [<strong>complex.special</strong>] in its entirety.</p>
   <p>In 26.4.4 "Member functions" [<strong>complex.members</strong>], add the following after paragraph 2:</p>
   <blockquote class="ins">
<pre class="highlight"><code class="highlight"><c- k><c- k>template</c-></c-><c- o><c- o>&lt;</c-></c-><c- k><c- k>class</c-></c-> <c- nc><c- nc>X</c-></c-><c- o><c- o>></c-></c-> <c- k><c- k>constexpr</c-></c-> <c- k><c- k>explicit</c-></c-><c- p><c- p>(</c-></c-><em><c- n><c- n>see</c-></c-> <c- n><c- n>below</c-></c-></em><c- p><c- p>)</c-></c-> <c- n><c- n>complex</c-></c-><c- p><c- p>(</c-></c-><c- k><c- k>const</c-></c-> <c- n><c- n>complex</c-></c-><c- o><c- o>&lt;</c-></c-><c- n><c- n>X</c-></c-><c- o><c- o>>&amp;</c-></c-> <c- n><c- n>other</c-></c-><c- p><c- p>);</c-></c-></code></pre>
    <p><em>Ensures</em>: <code class="highlight"><c- n>real</c-><c- p>()</c-> <c- o>==</c-> <c- n>other</c-><c- p>.</c-><c- n>real</c-><c- p>()</c-> <c- o>&amp;&amp;</c-> <c- n>imag</c-><c- p>()</c-> <c- o>==</c-> <c- n>other</c-><c- p>.</c-><c- n>imag</c-><c- p>()</c-></code>.</p>
    <p><em>Remarks</em>: The expression inside <code class="highlight"><c- k>explicit</c-></code> evaluates to false if and only if the floating-point conversion rank of <code class="highlight"><c- n>T</c-></code> is greater than the floating-point conversion rank of <code class="highlight"><c- n>X</c-></code>.</p>
   </blockquote>
   <p>In 26.4.6 "Non-member operations" [<strong>complex.ops</strong>], change the streaming operators as follows:</p>
   <blockquote>
<pre class="highlight"><code class="highlight"><c- k><c- k>template</c-></c-><c- o><c- o>&lt;</c-></c-><c- k><c- k>class</c-></c-> <c- nc><c- nc>T</c-></c-><c- p><c- p>,</c-></c-> <c- k><c- k>class</c-></c-> <c- nc><c- nc>CharT</c-></c-><c- p><c- p>,</c-></c-> <c- k><c- k>class</c-></c-> <c- nc><c- nc>traits</c-></c-><c- o><c- o>></c-></c->
  <c- n><c- n>basic_istream</c-></c-><c- o><c- o>&lt;</c-></c-><c- n><c- n>charT</c-></c-><c- p><c- p>,</c-></c-> <c- n><c- n>traits</c-></c-><c- o><c- o>>&amp;</c-></c-> <c- k><c- k>operator</c-></c-><c- o><c- o>>></c-></c-><c- p><c- p>(</c-></c-><c- n><c- n>basic_istream</c-></c-><c- o><c- o>&lt;</c-></c-><c- n><c- n>charT</c-></c-><c- p><c- p>,</c-></c-> <c- n><c- n>traits</c-></c-><c- o><c- o>>&amp;</c-></c-> <c- n><c- n>is</c-></c-><c- p><c- p>,</c-></c-> <c- n><c- n>complex</c-></c-><c- o><c- o>&lt;</c-></c-><c- n><c- n>T</c-></c-><c- o><c- o>>&amp;</c-></c-> <c- n><c- n>x</c-></c-><c- p><c- p>);</c-></c->
</code></pre>
    <ins><em>Constraints</em>: <code class="highlight"><c- n>T</c-></code> is a standard floating-point type.</ins>
    <p>
     <del><em>Requires</em></del>
     <ins><em>Expects</em></ins>
     : The input values 
     <del>shall be</del>
     <ins>are</ins>
      convertible to <code class="highlight"><c- n>T</c-></code>.
    </p>
    <p><em>Effects</em>: Extracts a complex number <code class="highlight"><c- n>x</c-></code> of the form: <code class="highlight"><c- n>u</c-></code>, <code class="highlight"><c- p>(</c-><c- n>u</c-><c- p>)</c-></code>, or <code class="highlight"><c- p>(</c-><c- n>u</c-><c- p>,</c-><c- n>v</c-><c- p>)</c-></code>, where <code class="highlight"><c- n>u</c-></code> is the real part and <code class="highlight"><c- n>v</c-></code> is the imaginary part (29.7.4.2).</p>
    <p>If bad input is encountered, calls <code class="highlight"><c- n>is</c-><c- p>.</c-><c- n>setstate</c-><c- p>(</c-><c- n>ios_base</c-><c- o>::</c-><c- n>failbit</c-><c- p>)</c-></code> (which may throw <code class="highlight"><c- n>ios</c-><c- o>::</c-><c- n>failure</c-></code> (29.5.5.4)).</p>
    <p><em>Returns</em>: <code class="highlight"><c- n>is</c-></code>.</p>
    <p><em>Remarks</em>: This extraction is performed as a series of simpler extractions. Therefore, the skipping of whitespace is specified to be the same for each of the simpler extractions.</p>
<pre class="highlight"><code class="highlight"><c- k><c- k>template</c-></c-><c- o><c- o>&lt;</c-></c-><c- k><c- k>class</c-></c-> <c- nc><c- nc>T</c-></c-><c- p><c- p>,</c-></c-> <c- k><c- k>class</c-></c-> <c- nc><c- nc>charT</c-></c-><c- p><c- p>,</c-></c-> <c- k><c- k>class</c-></c-> <c- nc><c- nc>traits</c-></c-><c- o><c- o>></c-></c->
  <c- n><c- n>basic_ostream</c-></c-><c- o><c- o>&lt;</c-></c-><c- n><c- n>charT</c-></c-><c- p><c- p>,</c-></c-> <c- n><c- n>traits</c-></c-><c- o><c- o>>&amp;</c-></c-> <c- k><c- k>operator</c-></c-><c- o><c- o>&lt;&lt;</c-></c-><c- p><c- p>(</c-></c-><c- n><c- n>basic_ostream</c-></c-><c- o><c- o>&lt;</c-></c-><c- n><c- n>charT</c-></c-><c- p><c- p>,</c-></c-> <c- n><c- n>traits</c-></c-><c- o><c- o>>&amp;</c-></c-> <c- n><c- n>o</c-></c-><c- p><c- p>,</c-></c-> <c- k><c- k>const</c-></c-> <c- n><c- n>complex</c-></c-><c- o><c- o>&lt;</c-></c-><c- n><c- n>T</c-></c-><c- o><c- o>>&amp;</c-></c-> <c- n><c- n>x</c-></c-><c- p><c- p>);</c-></c->
</code></pre>
    <ins><em>Constraints</em>: <code class="highlight"><c- n>T</c-></code> is a standard floating-point type.</ins>
    <p><em>Effects</em>: Inserts the complex number <code class="highlight"><c- n>x</c-></code> ...</p>
   </blockquote>
   <p>Modify 26.4.9 "Additional overloads" [<strong>cmplx.over</strong>] paragraphs 2 and 3 as follows:</p>
   <blockquote>
     The additional overloads shall be sufficient to ensure: 
    <ul>
     <li data-md>
      <del>If the argument has type <code class="highlight"><c- b>long</c-> <c- b>double</c-></code>, then it is effectively cast to <code class="highlight"><c- n>complex</c-><c- o>&lt;</c-><c- b>long</c-> <c- b>double</c-><c- o>></c-></code>.</del>
     <li data-md>
      <del>Otherwise, if the argument has type <code class="highlight"><c- b>double</c-></code> or an integer type, then it is effectively cast to <code class="highlight"><c- n>complex</c-><c- o>&lt;</c-><c- b>double</c-><c- o>></c-></code>.</del>
     <li data-md>
      <del>Otherwise, if the argument has type <code class="highlight"><c- b>float</c-></code>, then it is effectively cast to <code class="highlight"><c- n>complex</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c-></code>.</del>
     <li data-md>
      <ins>If the argument has a floating-point type <code class="highlight"><c- n>T</c-></code>, then it is effectively cast to <code class="highlight"><c- n>complex</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-></code>.</ins>
     <li data-md>
      <ins>Otherwise, if the argument has integer type, then it is effectively cast to <code class="highlight"><c- n>complex</c-><c- o>&lt;</c-><c- b>double</c-><c- o>></c-></code>.</ins>
    </ul>
    <p>Function template <code class="highlight"><c- n>pow</c-></code> shall have additional overloads sufficient to ensure, for a call with at least one argument of type <code class="highlight"><c- n>complex</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-></code>:</p>
    <ul>
     <li data-md>
      <del>If either argument has type <code class="highlight"><c- n>complex</c-><c- o>&lt;</c-><c- b>long</c-> <c- b>double</c-><c- o>></c-></code> or type <code class="highlight"><c- b>long</c-> <c- b>double</c-></code>, then both arguments are effectively cast to <code class="highlight"><c- n>complex</c-><c- o>&lt;</c-><c- b>long</c-> <c- b>double</c-><c- o>></c-></code>.</del>
     <li data-md>
      <del>Otherwise, if either argument has type <code class="highlight"><c- n>complex</c-><c- o>&lt;</c-><c- b>double</c-><c- o>></c-></code>, <code class="highlight"><c- b>double</c-></code>, or an integer type, then both arguments are effectively cast to <code class="highlight"><c- n>complex</c-><c- o>&lt;</c-><c- b>double</c-><c- o>></c-></code>.</del>
     <li data-md>
      <del>Otherwise, if either argument has type <code class="highlight"><c- n>complex</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c-></code> or <code class="highlight"><c- b>float</c-></code>, then both arguments are effectively cast to <code class="highlight"><c- n>complex</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c-></code>.</del>
     <li data-md>
      <ins>If one argument is of type <code class="highlight"><c- n>T1</c-></code> or <code class="highlight"><c- n>complex</c-><c- o>&lt;</c-><c- n>T1</c-><c- o>></c-></code> and the other argument is of type <code class="highlight"><c- n>T2</c-></code> or <code class="highlight"><c- n>complex</c-><c- o>&lt;</c-><c- n>T2</c-><c- o>></c-></code> where <code class="highlight"><c- n>T1</c-></code> and <code class="highlight"><c- n>T2</c-></code> are both floating-point types:</ins>
      <ul>
       <li data-md>
        <ins>If the floating-point conversion ranks ([conv.rank]) of <code class="highlight"><c- n>T1</c-></code> and <code class="highlight"><c- n>T2</c-></code> are different and unordered, the program is ill-formed.</ins>
       <li data-md>
        <ins>Otherwise, if <code class="highlight"><c- n>T1</c-></code> has greater floating-point conversion rank than <code class="highlight"><c- n>T2</c-></code>, then both arguments are effectively cast to <code class="highlight"><c- n>complex</c-><c- o>&lt;</c-><c- n>T1</c-><c- o>></c-></code>.</ins>
       <li data-md>
        <ins>Otherwise, both arguments are effectively cast to <code class="highlight"><c- n>complex</c-><c- o>&lt;</c-><c- n>T2</c-><c- o>></c-></code>.</ins>
      </ul>
     <li data-md>
      <ins>Otherwise, if the other argument has integer type, it is effectively cast to <code class="highlight"><c- n>complex</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-></code>.</ins>
    </ul>
   </blockquote>
   <p class="note" role="note"><span>Note:</span> No literal suffixes are defined for complex numbers of extended floating-point types.  Subclause [complex.literals] is unchanged.</p>
   <p class="issue" id="issue-c91d4ff8"><a class="self-link" href="#issue-c91d4ff8"></a> Should literal suffixes be defined for complex numbers of extended floating-point types with standard names, similar to the non-complex <a href="#literals">suffixes</a>?</p>
   <h3 class="heading settled" data-level="6.6" id="atomic"><span class="secno">6.6. </span><span class="content"><code class="highlight"><c- o>&lt;</c-><c- n>atomic</c-><c- o>></c-></code></span><a class="self-link" href="#atomic"></a></h3>
   <p>Change the wording so that the specializations of <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>atomic</c-></code> for floating-point types apply to all floating-point types, not just the standard floating-point types listed.</p>
   <p>The specializations of <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>atomic</c-></code> for integral types are not required to include specializations for all extended integral types, only for the extended types that are used in <code class="highlight"><c- o>&lt;</c-><c- n>cstdint</c-><c- o>></c-></code>.  It would be reasonable for this proposal to adopt a similar approach.</p>
   <p class="issue" id="issue-604b2730"><a class="self-link" href="#issue-604b2730"></a> Should <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>atomic</c-></code> have specializations for all floating-point types, or only for extended floating-point types with well-known aliases?</p>
   <h4 class="heading settled" data-level="6.6.1" id="atomic-wording"><span class="secno">6.6.1. </span><span class="content">Wording</span><a class="self-link" href="#atomic-wording"></a></h4>
   <p>This wording assumes that <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>atomic</c-></code> supports all extended floating-point types.  The wording would be different if it only needed to support named aliases.</p>
   <p>Modify 31.8.3 "Specializations for floating-point types" [<strong>atomics.types.float</strong>] paragraph 1 as follows:</p>
   <blockquote>
     There are specializations of the <code class="highlight"><c- n>atomic</c-></code> class template for 
    <del>the</del>
    <ins>all</ins>
     floating-point types 
    <del><code class="highlight"><c- b>float</c-></code>, <code class="highlight"><c- b>double</c-></code>, and <code class="highlight"><c- b>long</c-> <c- b>double</c-></code></del>
    . For each such type <code class="highlight"><em><c- n>floating</c-><c- o>-</c-><c- n>point</c-></em></code>, the specialization <code class="highlight"><c- n>atomic</c-><c- o>&lt;</c-><em><c- n>floating</c-><c- o>-</c-><c- n>point</c-></em><c- o>></c-></code> provides additional atomic operations appropriate to floating-point types. 
   </blockquote>
   <h3 class="heading settled" data-level="6.7" id="lib-test-macro"><span class="secno">6.7. </span><span class="content">Feature test macro</span><a class="self-link" href="#lib-test-macro"></a></h3>
   <p>No feature test macro is being proposed for the library changes in this section.  These library changes would be covered by the core language <a href="#core-test-macro">feature test macro</a>, if there is one.</p>
   <h2 class="heading settled" data-level="7" id="alias"><span class="secno">7. </span><span class="content">Type aliases</span><a class="self-link" href="#alias"></a></h2>
   <p>This paper introduces type aliases for several fixed-layout floating-point types.  Each alias will be defined only if a type with that layout is supported by the implementation, similar to the <code class="highlight"><c- n>intN_t</c-></code> and <code class="highlight"><c- n>uintN_t</c-></code> aliases.</p>
   <h3 class="heading settled" data-level="7.1" id="alias-header"><span class="secno">7.1. </span><span class="content">Header name</span><a class="self-link" href="#alias-header"></a></h3>
   <p>The type aliases proposed here do not fit neatly into any existing header.  So we are offering up two possibilities for new header names, neither of which we are thrilled with: <code class="highlight"><c- o>&lt;</c-><c- n>fixed_float</c-><c- o>></c-></code> and <code class="highlight"><c- o>&lt;</c-><c- n>stdfloat</c-><c- o>></c-></code>.  We are open to other names for the header and to arguments that the type aliases should be added to an existing header.</p>
   <p class="issue" id="issue-0ebb1eda"><a class="self-link" href="#issue-0ebb1eda"></a> What new or existing header should the type aliases go into?</p>
   <h3 class="heading settled" data-level="7.2" id="alias-formats"><span class="secno">7.2. </span><span class="content">Supported formats</span><a class="self-link" href="#alias-formats"></a></h3>
   <p>We propose aliases for the following layouts:</p>
   <ul>
    <li data-md>
     <p><a data-link-type="biblio" href="#biblio-ieee-754-2008">[IEEE-754-2008]</a> <code class="highlight"><c- n>binary16</c-></code> - IEEE 16-bit.</p>
    <li data-md>
     <p><a data-link-type="biblio" href="#biblio-ieee-754-2008">[IEEE-754-2008]</a> <code class="highlight"><c- n>binary32</c-></code> - IEEE 32-bit.</p>
    <li data-md>
     <p><a data-link-type="biblio" href="#biblio-ieee-754-2008">[IEEE-754-2008]</a> <code class="highlight"><c- n>binary64</c-></code> - IEEE 64-bit.</p>
    <li data-md>
     <p><a data-link-type="biblio" href="#biblio-ieee-754-2008">[IEEE-754-2008]</a> <code class="highlight"><c- n>binary128</c-></code> - IEEE 128-bit.</p>
    <li data-md>
     <p><code class="highlight"><c- n>bfloat16</c-></code>, which is <code class="highlight"><c- n>binary32</c-></code> with 16 bits of precision truncated; see <a data-link-type="biblio" href="#biblio-bfloat16">[bfloat16]</a>.</p>
   </ul>
   <p><code class="highlight"><c- n>binary32</c-></code> and <code class="highlight"><c- n>binary64</c-></code> are the most widely used floating-point types, and are the formats that <code class="highlight"><c- b>float</c-></code> and <code class="highlight"><c- b>double</c-></code> have in most implementations. <code class="highlight"><c- n>binary16</c-></code> is becoming more widely used; see this paper’s motivation for details. <code class="highlight"><c- n>binary128</c-></code> has hardware support in IBM POWER P9 chips. <code class="highlight"><c- n>bfloat16</c-></code> is used in Google’s TPUs and in TensorFlow and has hardware support in NVIDIA’s latest GPUs.</p>
   <p>The most widely used format that is not in this list is X87 80-bit.  Even though there is hardware support for this format in all current x86 chips, it is used most often because it is the largest type available, not because users specifically want that format.</p>
   <h3 class="heading settled" data-level="7.3" id="alias-alias"><span class="secno">7.3. </span><span class="content">Aliasing standard types</span><a class="self-link" href="#alias-alias"></a></h3>
   <p>This has turned out to be the most contentious issue with the type aliases, with strong opinions on both sides.  In Cologne, SG6 and LEWGI voted in favor of allowing aliasing of standard types, while EWGI was strongly against the idea.  After the Cologne meeting, the authors decided that prohibiting aliases of standard types was the better choice.  EWG discussed the issue in Prague and there was very strong consensus for the authors' position.  "The new floatX_t types aren’t aliases for float / double / long double, they are independent types." 23-13-0-2-0</p>
   <p>The header <code class="highlight"><c- o>&lt;</c-><c- n>cstdint</c-><c- o>></c-></code> defines integer type aliases for certain integer types, such as <code class="highlight"><c- n>std</c-><c- o>::</c-><c- b>int32_t</c-></code> and <code class="highlight"><c- n>std</c-><c- o>::</c-><c- b>int64_t</c-></code>.  These are similar in many ways to the aliases proposed here.  The types in <code class="highlight"><c- o>&lt;</c-><c- n>cstdint</c-><c- o>></c-></code> are allowed to alias standard integer types.  That has resulted in compilation errors when users try to create an overload set with both standard types and fixed-layout aliases, such as:</p>
<pre class="highlight"><code class="highlight"><c- b><c- b>int</c-></c-> <c- nf><c- nf>bit_count</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>int</c-></c-> <c- n><c- n>x</c-></c-><c- p><c- p>)</c-></c-> <c- p><c- p>{</c-></c-> <c- d><c- d>/* ... */</c-></c-> <c- p><c- p>}</c-></c->
<c- b><c- b>int</c-></c-> <c- nf><c- nf>bit_count</c-></c-><c- p><c- p>(</c-></c-><c- n><c- n>std</c-></c-><c- o><c- o>::</c-></c-><c- b><c- b>int32_t</c-></c-> <c- n><c- n>x</c-></c-><c- p><c- p>)</c-></c-> <c- p><c- p>{</c-></c-> <c- d><c- d>/* ... */</c-></c-> <c- p><c- p>}</c-></c->
</code></pre>
   <p>If aliasing of standard types is allowed for the floating-point type aliases, then similar compilation errors will likely result:</p>
<pre class="highlight"><code class="highlight"><c- b><c- b>int</c-></c-> <c- nf><c- nf>get_exponent</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>double</c-></c-> <c- n><c- n>x</c-></c-><c- p><c- p>)</c-></c-> <c- p><c- p>{</c-></c-> <c- d><c- d>/* ... */</c-></c-> <c- p><c- p>}</c-></c->
<c- b><c- b>int</c-></c-> <c- nf><c- nf>get_exponent</c-></c-><c- p><c- p>(</c-></c-><c- n><c- n>std</c-></c-><c- o><c- o>::</c-></c-><c- n><c- n>float64_t</c-></c-> <c- n><c- n>x</c-></c-><c- p><c- p>)</c-></c-> <c- p><c- p>{</c-></c-> <c- d><c- d>/* ... */</c-></c-> <c- p><c- p>}</c-></c->
</code></pre>
   <p>This is the strongest argument against allowing aliasing of standard types.  People who don’t find this argument persuasive point out that users should not create overload sets with both standard types and fixed-layout type aliases.  An overload set should contain just the standard floating-point types or just the fixed-layout types, but not both.  The example above that fails to compile is considered poor design and should not be encouraged.</p>
   <p>(The arguments about overload sets apply equally to explicit template specializations.)</p>
   <p>Not allowing the aliasing of standard types imposes an implementation burden.  If aliasing were allowed, then implementations that don’t define any extended floating-point types could define some of the aliases with a little bit of library code that boils down to something like:</p>
<pre class="highlight"><code class="highlight"><c- k><c- k>namespace</c-></c-> <c- n><c- n>std</c-></c-> <c- p><c- p>{</c-></c->
  <c- k><c- k>using</c-></c-> <c- n><c- n>float32_t</c-></c-> <c- o><c- o>=</c-></c-> <c- b><c- b>float</c-></c-><c- p><c- p>;</c-></c->
  <c- k><c- k>using</c-></c-> <c- n><c- n>float64_t</c-></c-> <c- o><c- o>=</c-></c-> <c- b><c- b>double</c-></c-><c- p><c- p>;</c-></c->
<c- p><c- p>}</c-></c->
</code></pre>
   <p>But when aliasing is not allowed, implementations have to support extended floating-point types in at least the compiler front end, which is not a trivial task.  There is also a burden on the name mangling ABI, which will have to define how to encode these extended floating-point types.</p>
   <p>The authors feel that the burden on users of allowing aliasing of standard types is greater than the burden on implementers of not allowing such aliasing.</p>
   <p>(This issue of aliasing of standard types is tightly bound to the overload resolution rules (<a href="#overload">§ 5.8 Overload resolution</a>) for extended floating-point types.  If the overload resolution rules are not changed, then having <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>float64_t</c-></code> be an alias of an extended floating-point type rather than an alias of <code class="highlight"><c- b>double</c-></code> will cause the following code to not compile:</p>
<pre class="highlight"><code class="highlight"><c- b><c- b>void</c-></c-> <c- nf><c- nf>f</c-></c-><c- p><c- p>(</c-></c-><c- n><c- n>std</c-></c-><c- o><c- o>::</c-></c-><c- n><c- n>float32_t</c-></c-><c- p><c- p>);</c-></c->
<c- b><c- b>void</c-></c-> <c- nf><c- nf>f</c-></c-><c- p><c- p>(</c-></c-><c- n><c- n>std</c-></c-><c- o><c- o>::</c-></c-><c- n><c- n>float64_t</c-></c-><c- p><c- p>);</c-></c->
<c- b><c- b>void</c-></c-> <c- nf><c- nf>g</c-></c-><c- p><c- p>(</c-></c-><c- b><c- b>double</c-></c-> <c- n><c- n>x</c-></c-><c- p><c- p>)</c-></c-> <c- p><c- p>{</c-></c->
  <c- n><c- n>f</c-></c-><c- p><c- p>(</c-></c-><c- n><c- n>x</c-></c-><c- p><c- p>);</c-></c-> <c- c1><c- c1>// error - ambiguous call without overload resolution changes</c-></c->
<c- p><c- p>}</c-></c->
</code></pre>
   <p>If that code doesn’t compile, that would be a bigger burden on users than not being able to overload on both <code class="highlight"><c- b>double</c-></code> and <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>float64_t</c-></code>.)</p>
   <h3 class="heading settled" data-level="7.4" id="layout-vs-behavior"><span class="secno">7.4. </span><span class="content">Layout vs. behavior</span><a class="self-link" href="#layout-vs-behavior"></a></h3>
   <p>The IEEE-conforming type aliases must have the specified IEEE layout and should have the required behavior.  For the four IEEE-conforming type aliases, <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>numeric_limits</c-><c- o>&lt;</c-><c- n>T</c-><c- o>>::</c-><c- n>is_iec559</c-></code> is true.</p>
   <h3 class="heading settled" data-level="7.5" id="test-macros"><span class="secno">7.5. </span><span class="content">Feature test macros</span><a class="self-link" href="#test-macros"></a></h3>
   <p>Since implementations may choose to support (or not) each of the fixed-layout aliases individually, there should be a separate test macro for detecting each of the type aliases.  The names of the test macros would be derived from whichever type alias names we settle on.  (The authors are not thrilled with introducing so many new test macros, but they have yet to come up with a better idea.)</p>
   <p class="issue" id="issue-50e4e46f"><a class="self-link" href="#issue-50e4e46f"></a> How should feature test macros be handled for this feature?</p>
   <h3 class="heading settled" data-level="7.6" id="names"><span class="secno">7.6. </span><span class="content">Names</span><a class="self-link" href="#names"></a></h3>
   <p>We are proposing several different naming schemes for fixed-layout type alias, and are open to other suggested naming schemes.  In committee discussions so far, no set of names has emerged as the favorites.  The authors have whittled proposed names down to what they feel are the three best choices, and are comfortable leaving it up to the committee to choose between those.</p>
   <h4 class="heading settled" data-level="7.6.1" id="floatX_t"><span class="secno">7.6.1. </span><span class="content"><code class="highlight"><c- n>floatX_t</c-></code></span><a class="self-link" href="#floatX_t"></a></h4>
   <ul>
    <li data-md>
     <p><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>float16_t</c-></code></p>
    <li data-md>
     <p><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>float32_t</c-></code></p>
    <li data-md>
     <p><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>float64_t</c-></code></p>
    <li data-md>
     <p><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>float128_t</c-></code></p>
    <li data-md>
     <p><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>bfloat16_t</c-></code></p>
   </ul>
   <p>This is the simplest of all the options being presented.  It is the naming scheme used by Boost.Math’s fixed-layout floating-point types.</p>
   <p>Nothing in the names of the IEEE aliases implies that they are in fact IEEE binary formats.  Additionally, <code class="highlight"><c- n>float16_t</c-></code> and <code class="highlight"><c- n>bfloat16_t</c-></code> are similar enough that we aren’t fully comfortable using these names.</p>
   <h4 class="heading settled" data-level="7.6.2" id="fp_namespace"><span class="secno">7.6.2. </span><span class="content"><code class="highlight"><c- n>fp</c-><c- o>::</c-><c- n>binaryX_t</c-></code></span><a class="self-link" href="#fp_namespace"></a></h4>
   <ul>
    <li data-md>
     <p><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>fp</c-><c- o>::</c-><c- n>binary16_t</c-></code></p>
    <li data-md>
     <p><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>fp</c-><c- o>::</c-><c- n>binary32_t</c-></code></p>
    <li data-md>
     <p><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>fp</c-><c- o>::</c-><c- n>binary64_t</c-></code></p>
    <li data-md>
     <p><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>fp</c-><c- o>::</c-><c- n>binary128_t</c-></code></p>
    <li data-md>
     <p><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>fp</c-><c- o>::</c-><c- n>bfloat16_t</c-></code></p>
   </ul>
   <p>The namespace <code class="highlight"><c- n>fp</c-></code> makes it more obvious that these types are floating-point types, assisting in the recognition of <code class="highlight"><c- n>binary16</c-></code> as an <a data-link-type="biblio" href="#biblio-ieee-754-2008">[IEEE-754-2008]</a> format.  A using namespace directive can be used to avoid repeating <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>fp</c-><c- o>::</c-></code> everywhere.</p>
   <p>The drawbacks of this approach are that it introduces a new namespace with a very small purpose, and that <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>fp</c-><c- o>::</c-><c- n>bloat16_t</c-></code> is somewhat redundant with two different floating-point indications (<code class="highlight"><c- n>fp</c-></code> and the <code class="highlight"><c- b>float</c-></code> in <code class="highlight"><c- n>bfloat16_t</c-></code>).</p>
   <h4 class="heading settled" data-level="7.6.3" id="fp_binaryX_t"><span class="secno">7.6.3. </span><span class="content"><code class="highlight"><c- n>fp_binaryX_t</c-></code></span><a class="self-link" href="#fp_binaryX_t"></a></h4>
   <ul>
    <li data-md>
     <p><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>fp_binary16_t</c-></code></p>
    <li data-md>
     <p><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>fp_binary32_t</c-></code></p>
    <li data-md>
     <p><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>fp_binary64_t</c-></code></p>
    <li data-md>
     <p><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>fp_binary128_t</c-></code></p>
    <li data-md>
     <p><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>fp_bfloat16_t</c-></code></p>
   </ul>
   <p>This is a slight modification of the previous scheme, which trades the nested namespace for an <code class="highlight"><c- n>fp_</c-></code> prefix.  The advantages and disadvantages are similar.</p>
   <h3 class="heading settled" data-level="7.7" id="literals"><span class="secno">7.7. </span><span class="content">Literal suffixes</span><a class="self-link" href="#literals"></a></h3>
   <p>The types with standard-defined names should also have standard literal suffixes, similar to what is proposed in <a data-link-type="biblio" href="#biblio-p1280">[P1280]</a>.  The suffixes for the IEEE types match what is being proposed for C2x.  An implementation would define literal suffixes only for types supported by that implementation.  The declarations of the literals might look something like this:</p>
   <blockquote>
<pre class="highlight"><code class="highlight"><c- k><c- k>namespace</c-></c-> <c- n><c- n>std</c-></c-> <c- p><c- p>{</c-></c->
  <c- kr><c- kr>inline</c-></c-> <c- k><c- k>namespace</c-></c-> <c- n><c- n>literals</c-></c-> <c- p><c- p>{</c-></c->
  <c- kr><c- kr>inline</c-></c-> <c- k><c- k>namespace</c-></c-> <c- n><c- n>float_literals</c-></c-> <c- p><c- p>{</c-></c->
    <c- k><c- k>constexpr</c-></c-> <c- n><c- n>float16_t</c-></c-> <c- k><c- k>operator</c-></c-><c- s><c- s>""</c-></c-><c- n><c- n>f16</c-></c-><c- p><c- p>(</c-></c-><c- k><c- k>const</c-></c-> <c- b><c- b>char</c-></c-> <c- o><c- o>*</c-></c-><c- p><c- p>);</c-></c->
    <c- k><c- k>constexpr</c-></c-> <c- n><c- n>float32_t</c-></c-> <c- k><c- k>operator</c-></c-><c- s><c- s>""</c-></c-><c- n><c- n>f32</c-></c-><c- p><c- p>(</c-></c-><c- k><c- k>const</c-></c-> <c- b><c- b>char</c-></c-> <c- o><c- o>*</c-></c-><c- p><c- p>);</c-></c->
    <c- k><c- k>constexpr</c-></c-> <c- n><c- n>float64_t</c-></c-> <c- k><c- k>operator</c-></c-><c- s><c- s>""</c-></c-><c- n><c- n>f64</c-></c-><c- p><c- p>(</c-></c-><c- k><c- k>const</c-></c-> <c- b><c- b>char</c-></c-> <c- o><c- o>*</c-></c-><c- p><c- p>);</c-></c->
    <c- k><c- k>constexpr</c-></c-> <c- n><c- n>float128_t</c-></c-> <c- k><c- k>operator</c-></c-><c- s><c- s>""</c-></c-><c- n><c- n>f128</c-></c-><c- p><c- p>(</c-></c-><c- k><c- k>const</c-></c-> <c- b><c- b>char</c-></c-> <c- o><c- o>*</c-></c-><c- p><c- p>);</c-></c->
    <c- k><c- k>constexpr</c-></c-> <c- n><c- n>bfloat16_t</c-></c-> <c- k><c- k>operator</c-></c-><c- s><c- s>""</c-></c-><c- n><c- n>bf16</c-></c-><c- p><c- p>(</c-></c-><c- k><c- k>const</c-></c-> <c- b><c- b>char</c-></c-> <c- o><c- o>*</c-></c-><c- p><c- p>);</c-></c->
  <c- p><c- p>}</c-></c->
  <c- p><c- p>}</c-></c->
<c- p><c- p>}</c-></c->
</code></pre>
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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-bfloat16">[BFLOAT16]
   <dd><a href="https://en.wikipedia.org/wiki/Bfloat16_floating-point_format">bfloat16 floating-point format</a>. URL: <a href="https://en.wikipedia.org/wiki/Bfloat16_floating-point_format">https://en.wikipedia.org/wiki/Bfloat16_floating-point_format</a>
   <dt id="biblio-ieee-754-2008">[IEEE-754-2008]
   <dd><a href="http://ieeexplore.ieee.org/servlet/opac?punumber=4610933">IEEE Standard for Floating-Point Arithmetic</a>. 29 August 2008. URL: <a href="http://ieeexplore.ieee.org/servlet/opac?punumber=4610933">http://ieeexplore.ieee.org/servlet/opac?punumber=4610933</a>
   <dt id="biblio-n1703">[N1703]
   <dd>Paul A. Bristow; Christopher Kormanyos; John Maddock. <a href="http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1703.pdf">Floating-Point Typedefs Having Specified Widths</a>. URL: <a href="http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1703.pdf">http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1703.pdf</a>
   <dt id="biblio-n2405">[N2405]
   <dd><a href="http://www.open-std.org/jtc1/sc22/wg14/www/docs/n2405.pdf">Annex X: IEC 60559 interchange and extended types</a>. URL: <a href="http://www.open-std.org/jtc1/sc22/wg14/www/docs/n2405.pdf">http://www.open-std.org/jtc1/sc22/wg14/www/docs/n2405.pdf</a>
   <dt id="biblio-p0192">[P0192]
   <dd>Michał Dominiak; et al. <a href="https://wg21.link/P0192">`short float` and fixed-size floating point types</a>. URL: <a href="https://wg21.link/P0192">https://wg21.link/P0192</a>
   <dt id="biblio-p1280">[P1280]
   <dd>Isabella Muerte. <a href="https://wg21.link/P1280">Integer Width Literals</a>. URL: <a href="https://wg21.link/P1280">https://wg21.link/P1280</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"> Should there be a feature test macro to indicate that the implementation supports at least one extended floating-point type?<a href="#issue-6daed810"> ↵ </a></div>
   <div class="issue"> Should the new type traits <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>is_standard_floating_point</c-></code> and/or <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>is_extended_floating_point</c-></code> be introduced?<a href="#issue-5b95c8c1"> ↵ </a></div>
   <div class="issue"> Should a new type trait be introduced that can be used to query the floating-point conversion rank relationship?<a href="#issue-4dff46e4"> ↵ </a></div>
   <div class="issue"> Should literal suffixes be defined for complex numbers of extended floating-point types with standard names, similar to the non-complex <a href="#literals">suffixes</a>?<a href="#issue-c91d4ff8"> ↵ </a></div>
   <div class="issue"> Should <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>atomic</c-></code> have specializations for all floating-point types, or only for extended floating-point types with well-known aliases?<a href="#issue-604b2730"> ↵ </a></div>
   <div class="issue"> What new or existing header should the type aliases go into?<a href="#issue-0ebb1eda"> ↵ </a></div>
   <div class="issue"> How should feature test macros be handled for this feature?<a href="#issue-50e4e46f"> ↵ </a></div>
  </div>