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 <head>
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  <title>P1468R1: Fixed-layout floating-point type aliases</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,
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   <p data-fill-with="logo"></p>
   <h1 class="p-name no-ref" id="title">P1468R1<br>Fixed-layout floating-point type aliases</h1>
   <h2 class="no-num no-toc no-ref heading settled" id="subtitle"><span class="content">Published Proposal, <time class="dt-updated" datetime="2019-06-17">2019-06-17</time></span></h2>
   <div data-fill-with="spec-metadata">
    <dl>
     <dt>This version:
     <dd><a class="u-url" href="https://wg21.link/P1468">https://wg21.link/P1468</a>
     <dt>Authors:
     <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>)
     <dd>
      <dd class="editor p-author h-card vcard"><a class="p-name fn u-email email" href="mailto:boris@stlport.com">Boris Fomitchev</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:me@cvmlib.com">Sergei Nikolaev</a> (<span class="p-org org">NVIDIA</span>)
     <dt>Audience:
     <dd>SG6, 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>
   </div>
   <div data-fill-with="warning"></div>
   <hr title="Separator for header">
  </div>
  <nav data-fill-with="table-of-contents" id="toc">
   <h2 class="no-num no-toc no-ref" id="contents">Table of Contents</h2>
   <ol class="toc" role="directory">
    <li><a href="#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>
     </ol>
    <li><a href="#motivation"><span class="secno">3</span> <span class="content">Motivation</span></a>
    <li>
     <a href="#design"><span class="secno">4</span> <span class="content">Design</span></a>
     <ol class="toc">
      <li><a href="#unique"><span class="secno">4.1</span> <span class="content">Should the types be unique?</span></a>
      <li><a href="#feature-test"><span class="secno">4.2</span> <span class="content">Feature test macros</span></a>
      <li><a href="#hardware"><span class="secno">4.3</span> <span class="content">Encouraging hardware implementation?</span></a>
      <li><a href="#formats"><span class="secno">4.4</span> <span class="content">Supported formats</span></a>
      <li>
       <a href="#naming"><span class="secno">4.5</span> <span class="content">Alias naming</span></a>
       <ol class="toc">
        <li><a href="#naming-simple"><span class="secno">4.5.1</span> <span class="content"><code class="highlight"><c- n>floatXX_t</c-></code></span></a>
        <li><a href="#naming-complicated"><span class="secno">4.5.2</span> <span class="content"><code class="highlight"><c- n>iec559_binaryX_t</c-></code></span></a>
        <li><a href="#naming-confusing"><span class="secno">4.5.3</span> <span class="content"><code class="highlight"><c- n>binaryX_t</c-></code></span></a>
        <li><a href="#naming-nested"><span class="secno">4.5.4</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="#naming-mixed"><span class="secno">4.5.5</span> <span class="content"><code class="highlight"><c- n>fp_binaryX_t</c-></code></span></a>
        <li><a href="#naming-iec-ns"><span class="secno">4.5.6</span> <span class="content"><code class="highlight"><c- n>iec559</c-><c- o>::</c-><c- n>binaryXX_t</c-></code></span></a>
       </ol>
     </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>
   </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>This paper proposes a 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-know floating-point
layouts.</p>
   <p>This is a companion paper to <a data-link-type="biblio" href="#biblio-p1467">[P1467]</a>. While this paper gives convenient names to types, the other paper allows those names to
refer to non-standard, implementation-defined floating-point types.</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>
   <ol>
    <li data-md>
     <p>Add the requirement that the types must not alias any of the standard floating-point types.</p>
    <li data-md>
     <p>Add a design question about feature-test macros.</p>
    <li data-md>
     <p>Add a section on QoI - should we strongly encourage that the aliases to have a hardware implementation?</p>
   </ol>
   <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>The motivation for the general effort of this paper is the same as for <a data-link-type="biblio" href="#biblio-p0192">[P0192]</a>, so we decided to avoid repeating it here, for
brevity.</p>
   <p>Our previous attempt of introducing floating-point types that match shorter-than-<code class="highlight"><c- b>float</c-></code> types already provided by multiple
software and hardware implementations has been rejected on the grounds of not handling cases where multiple different layouts
can be in use by an application at the same time. In our new approach, <a data-link-type="biblio" href="#biblio-p1467">[P1467]</a> gives us a way to talk about floating-point types
other than <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> within the framework of the standard, while this paper provides convenient names
for some of those implementation-defined types.</p>
   <h2 class="heading settled" data-level="4" id="design"><span class="secno">4. </span><span class="content">Design</span><a class="self-link" href="#design"></a></h2>
   <p>This proposal consists of two parts:</p>
   <ol>
    <li data-md>
     <p>Introducing fixed-layout floating-point type aliases.</p>
    <li data-md>
     <p>Introducing fixed-layout literals for those aliases.</p>
   </ol>
   <p>The first part is what we see as the critical part of this paper, and therefore it is what is discussed by the rest of the paper.
The second part is analogous to <a data-link-type="biblio" href="#biblio-p1280">[P1280]</a>, but for the floating-point types defined by the first part. We’d like to hear feedback
on whether the second part is also desired before proposing any specifics.</p>
   <p>The aliases should receive their own standard library header; our strawman proposal for the name of such a header is <code class="highlight"><c- o>&lt;</c-><c- n>fixed_float</c-><c- o>></c-></code>. We welcome any naming suggestions that may help avoid spending precious LEWG time bikeshedding the names at a
meeting.</p>
   <p>Just like the fixed-size integer aliases from <code class="highlight"><c- o>&lt;</c-><c- n>cstdint</c-><c- o>></c-></code> (<code class="highlight"><c- n>std</c-><c- o>::</c-><c- b>int8_t</c-></code> and family), the aliases proposed here are <em>optional</em> if
an implementation does not provide a (possibly extended) floating-point type that matches the layout; they are, however, mandatory
if such a type exist on an implementation.</p>
   <h3 class="heading settled" data-level="4.1" id="unique"><span class="secno">4.1. </span><span class="content">Should the types be unique?</span><a class="self-link" href="#unique"></a></h3>
   <p>During the Kona EWGI discussion, a point was raised about whether these types should be allowed to alias standard floating-point types
or not. An argument has been provided that they should be required to be distinct from them, because it simplifies creating overload
sets (and by extension, template specializations) that want to distinguish between <code class="highlight"><c- b>float</c-></code> and an IEEE-754 <code class="highlight"><c- n>binary32</c-></code>, for instance.
Requiring them to never alias the standard types would be a slight added burden on implementers and on ABIs, because they’d need to
provide a mangling for the extended fixed-layout types even if their standard types match the requirements, but the usability of this
feature will be improved if such aliasing is prohibited. Therefore, we propose that the standard library aliases must not alias standard
floating-point types.</p>
   <h3 class="heading settled" data-level="4.2" id="feature-test"><span class="secno">4.2. </span><span class="content">Feature test macros</span><a class="self-link" href="#feature-test"></a></h3>
   <p>We believe that, since any subset of the proposed (or added in the future) fixed-layout aliases can be supported (or not) independently,
and since there should be _some_ mechanism for detecting them (for instance, for generic libraries to be able to provide additional
overloads or template specializations only on implementations where a type exists), there should be a separate macro for detecting every
one of those types. The name of such macro should be derived from the names of the types that we eventually settle on.</p>
   <p><strong>Design question:</strong> How should feature testing be handled for this feature?</p>
   <h3 class="heading settled" data-level="4.3" id="hardware"><span class="secno">4.3. </span><span class="content">Encouraging hardware implementation?</span><a class="self-link" href="#hardware"></a></h3>
   <p>Another point that was raised during EWGI discussion in Kona was about QoI for this feature. We believe that the fixed-layout aliases
are primarily a portability feature; therefore having a hardware implementation is - obviously - encouraged, but not required, and
implementations should still attempt, to the best of their ability, to provide types that fit the requirements of the aliases.</p>
   <p>There’s another reasonable viewpoint on this feature: that these should primarily be a way to access specific hardware units of the
processor. If this is viewed as the primary function of this feature, then we should (non-normatively) encourage implementations to
only provide the aliases when some form of hardware acceleration for operations is present.</p>
   <p><strong>Design question:</strong> Which of the two viewpoints presented above should we take? Should we consider fixed-layout type aliases to be
primarily a portability feature, or primarily a hardware-access feature?</p>
   <h3 class="heading settled" data-level="4.4" id="formats"><span class="secno">4.4. </span><span class="content">Supported formats</span><a class="self-link" href="#formats"></a></h3>
   <p>We believe the following layouts should be included:</p>
   <ol>
    <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> - half precision floating-point type. Providing this type was the original motivation of <a data-link-type="biblio" href="#biblio-p0192">[P0192]</a>.</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>.</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>.</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>.</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>
   </ol>
   <p><code class="highlight"><c- n>binary32</c-></code> and <code class="highlight"><c- n>binary64</c-></code> should be self-explanatory. <code class="highlight"><c- n>binary16</c-></code> is a format that exists, among others, in LLVM IR; as an optional
part of the ARM architecture; as a GCC extension implementing that for ARM; in NVIDIA’s CUDA platform. IBM POWER9 has native support
for <code class="highlight"><c- n>binary128</c-></code>. <code class="highlight"><c- n>bfloat16</c-></code> is a format utilized, for instance, in Google’s TPUs, and in TensorFlow.</p>
   <p><strong>Question</strong>: is the above set of formats sufficient? Are there any other formats that we should include in the first version of
this feature?</p>
   <h3 class="heading settled" data-level="4.5" id="naming"><span class="secno">4.5. </span><span class="content">Alias naming</span><a class="self-link" href="#naming"></a></h3>
   <p>We don’t know what the best naming scheme here is. We’d like to propose a few options and leave the decision to the committee.
Each of these options has its own pros and cons.</p>
   <h4 class="heading settled" data-level="4.5.1" id="naming-simple"><span class="secno">4.5.1. </span><span class="content"><code class="highlight"><c- n>floatXX_t</c-></code></span><a class="self-link" href="#naming-simple"></a></h4>
   <ol>
    <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>
   </ol>
   <p>This is the simplest naming scheme of the options presented here; it is also the naming scheme (for <code class="highlight"><c- n>floatXX_t</c-></code>) used Boost.Math’s
fixed-layout floating-point types.</p>
   <p>On the other hand, nothing in the names of the IEEE aliases implies that they are, in fact, IEEE <code class="highlight"><c- n>binaryXX</c-></code>. Additionally, <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>float16_t</c-></code> and <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>bfloat16_t</c-></code> are slightly too similar for us to feel comfortable about using this set of names.</p>
   <h4 class="heading settled" data-level="4.5.2" id="naming-complicated"><span class="secno">4.5.2. </span><span class="content"><code class="highlight"><c- n>iec559_binaryX_t</c-></code></span><a class="self-link" href="#naming-complicated"></a></h4>
   <ol>
    <li data-md>
     <p><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>iec559_binary16_t</c-></code></p>
    <li data-md>
     <p><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>iec559_binary32_t</c-></code></p>
    <li data-md>
     <p><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>iec559_binary64_t</c-></code></p>
    <li data-md>
     <p><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>iec559_binary128_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>
   </ol>
   <p>This naming scheme is as explicit about the layouts that it guarantees as possible. The two downsides, however, are:</p>
   <ol>
    <li data-md>
     <p>these names (short of <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>bfloat16_t</c-></code>) are <em>long</em>, and</p>
    <li data-md>
     <p>most people don’t recognize <code class="highlight"><c- n>iec559</c-></code> as quickly as they’d recognize <code class="highlight"><c- n>ieee754</c-></code>; <code class="highlight"><c- n>iec559</c-></code>, however, is how we refer to <a data-link-type="biblio" href="#biblio-ieee-754-2008">[IEEE-754-2008]</a> in the rest of the library, so if we go this path, we should probably stay consistent with the rest
of the language.</p>
   </ol>
   <h4 class="heading settled" data-level="4.5.3" id="naming-confusing"><span class="secno">4.5.3. </span><span class="content"><code class="highlight"><c- n>binaryX_t</c-></code></span><a class="self-link" href="#naming-confusing"></a></h4>
   <ol>
    <li data-md>
     <p><code class="highlight"><c- n>std</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>binary32_t</c-></code></p>
    <li data-md>
     <p><code class="highlight"><c- n>std</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>binary128_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>
   </ol>
   <p>These names are shorter than <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>iec559_binaryX_t</c-></code>, but they are less obvious; nothing in their names directly points at them
being floating-point types. On the other hand, when a user of the language knows that these are floating-point types, they should
recognize them as names of <a data-link-type="biblio" href="#biblio-ieee-754-2008">[IEEE-754-2008]</a> formats.</p>
   <p><strong>This is the only one of the presented options that has received strong SG6 discouragement.</strong></p>
   <h4 class="heading settled" data-level="4.5.4" id="naming-nested"><span class="secno">4.5.4. </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="#naming-nested"></a></h4>
   <ol>
    <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>
   </ol>
   <p>The short, nested namespace within <code class="highlight"><c- n>std</c-></code> should make it more obvious that these types are floating-point types; from there,
recognizing <code class="highlight"><c- n>binary16</c-></code> as a name of a specific <a data-link-type="biblio" href="#biblio-ieee-754-2008">[IEEE-754-2008]</a> format is much easier. Users who know what the <code class="highlight"><c- n>binaryX_t</c-></code> types are can just import the contents of the entire namespace, to avoid having to repeat <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>fp</c-></code> everywhere.</p>
   <p>The cons of this approach are:</p>
   <ol>
    <li data-md>
     <p>it introduces a namespace that doesn’t serve a _big_ purpose; and</p>
    <li data-md>
     <p>the alias for <code class="highlight"><c- n>bfloat16</c-></code> already includes <code class="highlight"><c- b>float</c-></code> in its name, which means that <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>fp</c-><c- o>::</c-><c- n>bfloat16_t</c-></code> is somewhat redundant.</p>
   </ol>
   <h4 class="heading settled" data-level="4.5.5" id="naming-mixed"><span class="secno">4.5.5. </span><span class="content"><code class="highlight"><c- n>fp_binaryX_t</c-></code></span><a class="self-link" href="#naming-mixed"></a></h4>
   <ol>
    <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>
   </ol>
   <p>This is a slight modification of the previous scheme, which trades the nested namespace within <code class="highlight"><c- n>std</c-><c- o>::</c-></code> for an <code class="highlight"><c- n>fp_</c-></code> prefix within
the name. This makes it harder to stop repeating the <code class="highlight"><c- n>fp_</c-></code> part, because you can no longer just import a namespace that includes
all of these.</p>
   <h4 class="heading settled" data-level="4.5.6" id="naming-iec-ns"><span class="secno">4.5.6. </span><span class="content"><code class="highlight"><c- n>iec559</c-><c- o>::</c-><c- n>binaryXX_t</c-></code></span><a class="self-link" href="#naming-iec-ns"></a></h4>
   <ol>
    <li data-md>
     <p><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>iec559</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>iec559</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>iec559</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>iec559</c-><c- o>::</c-><c- n>binary128_t</c-></code></p>
    <li data-md>
     <p><code class="highlight"><c- o>???</c-></code> (unsure what the bfloat16 name would be in this scheme)</p>
   </ol>
   <p>This (incomplete) scheme has been proposed during the SG6 discussions by one of the participants.</p>
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  <h2 class="no-num no-ref heading settled" id="references"><span class="content">References</span><a class="self-link" href="#references"></a></h2>
  <h3 class="no-num no-ref heading settled" id="informative"><span class="content">Informative References</span><a class="self-link" href="#informative"></a></h3>
  <dl>
   <dt id="biblio-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-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>
   <dt id="biblio-p1467">[P1467]
   <dd>Michał Dominiak; David Olsen. <a href="https://wg21.link/P1467">Extended floating-point types</a>. URL: <a href="https://wg21.link/P1467">https://wg21.link/P1467</a>
  </dl>