<!doctype html><html lang="en">
 <head>
  <meta content="text/html; charset=utf-8" http-equiv="Content-Type">
  <meta content="width=device-width, initial-scale=1, shrink-to-fit=no" name="viewport">
  <title>P2021R0: Negative zero strikes again</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,
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 <body class="h-entry">
  <div class="head">
   <p data-fill-with="logo"></p>
   <h1 class="p-name no-ref" id="title">P2021R0<br>Negative zero strikes again</h1>
   <h2 class="no-num no-toc no-ref heading settled" id="subtitle"><span class="content">Published Proposal, <time class="dt-updated" datetime="2020-01-05">2020-01-05</time></span></h2>
   <div data-fill-with="spec-metadata">
    <dl>
     <dt>This version:
     <dd><a class="u-url" href="http://fmt.dev/P2021R0.html">http://fmt.dev/P2021R0.html</a>
     <dt>Author:
     <dd>
      <dd class="editor p-author h-card vcard"><a class="p-name fn u-email email" href="mailto:victor.zverovich@gmail.com">Victor Zverovich</a>
     <dt>Audience:
     <dd>LEWG
     <dt>Project:
     <dd>ISO/IEC JTC1/SC22/WG21 14882: Programming Language — C++
    </dl>
   </div>
   <div data-fill-with="warning"></div>
   <hr title="Separator for header">
  </div>
  <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="#imaginary-problem"><span class="secno">1</span> <span class="content">Is negative zero a problem?</span></a>
    <li><a href="#performance"><span class="secno">2</span> <span class="content">Performance</span></a>
    <li><a href="#locale"><span class="secno">3</span> <span class="content">Locale</span></a>
    <li><a href="#example"><span class="secno">4</span> <span class="content">Demotivating example</span></a>
    <li><a href="#fixed"><span class="secno">5</span> <span class="content">Fixed form</span></a>
    <li><a href="#conclusion"><span class="secno">6</span> <span class="content">Conclusion</span></a>
    <li><a href="#ack"><span class="secno">7</span> <span class="content">Acknowledgements</span></a>
    <li>
     <a href="#references"><span class="secno"></span> <span class="content">References</span></a>
     <ol class="toc">
      <li><a href="#informative"><span class="secno"></span> <span class="content">Informative References</span></a>
     </ol>
   </ol>
  </nav>
  <main>
   <p style="text-align: right"> "Your scientists were so preoccupied with whether or not they could, <br> they didn’t stop to think if they should." <br> ― Dr. Ian Malcolm </p>
   <p>National body comment <a data-link-type="biblio" href="#biblio-us227">[US227]</a> proposed adding a new feature to the C++20
formatting library, namely a new format specifier to suppress the output of a
minus sign when formatting a negative zero or a small negative value. This was
an attempt to revisit <a data-link-type="biblio" href="#biblio-p1496">[P1496]</a> that was previously reviewed by LEWG in Kona and
rejected with no consensus for change. R1 of this paper presented in Belfast
after the C++20 feature freeze and didn’t provide any new information, only gave
more examples showing (unfortunately incorrectly) that suppression applies to
small negative values rounding to zero. This was also discussed in Kona as
reflected in the meeting notes.</p>
   <p>Sadly the analysis in <a data-link-type="biblio" href="#biblio-p1496">[P1496]</a> is severely lacking: examples are misleading,
it doesn’t explore performance implications of the change, interactions with
other format specifications, interaction with the locale and there is no
implementation or usage experience, so it’s extremely surprising that the
feature is being seriously considered for C++20. There was also a piece of
incorrect information about performance implications if the suppression was
not a built-in specifier. In this paper we provide a somewhat deeper analysis
of the issue and clarify the following:</p>
   <ul>
    <li data-md>
     <p>there is almost zero evidence that this is a problem worth solving,</p>
    <li data-md>
     <p>sign suppression will add an overhead to calls to <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>format</c-></code> and uses of
built-in formatter specializations even if not used,</p>
    <li data-md>
     <p>the new feature will complicate the grammar and add conceptual overhead,</p>
    <li data-md>
     <p>negative zero doesn’t arise as a result of rounding in all but fixed format
and therefore can be trivially and more efficiently suppressed without a new
specifier,</p>
    <li data-md>
     <p>it can be easily and efficiently implemented via the extension API,</p>
    <li data-md>
     <p>as a user-facing feature it should be locale-specific if implemented.</p>
   </ul>
   <h2 class="heading settled" data-level="1" id="imaginary-problem"><span class="secno">1. </span><span class="content">Is negative zero a problem?</span><a class="self-link" href="#imaginary-problem"></a></h2>
   <p>High school math teaches us that -0 = 0. So does minus in front of zero actually
cause any problems in practice? Unfortunately P1496 only provides anecdotal
evidence from one of the authors of the paper and even original authors of
P1496R0 disagreed whether it’s worth exploring considering problematic
performance and complexity tradeoffs. P1496 casually extrapolates to millions of
affected users but as we know the plural of anecdote is not data.</p>
   <p>In order to find some real evidence we looked at the fmt library (<a data-link-type="biblio" href="#biblio-fmt">[FMT]</a>) and
Folly which includes a similar formatting facility (<a data-link-type="biblio" href="#biblio-folly-format">[FOLLY-FORMAT]</a>). Both of
these are popular open-source formatting libraries that have been around for 7
years each and are widely deployed in software used by billions of people. A
thorough search of the issue trackers of these libraries for issues related to
zero has revealed only a single feature request related to suppression of
negative zero. It has been easily addressed via an extension API without
introducing a new specifier to avoid an overhead when not using the feature.
Another issue that mentioned a negative zero was asking for the output of -0.01
with zero precision to be <code class="highlight"><c- s>"-0"</c-></code> instead of <code class="highlight"><c- s>"-0.0"</c-></code> to be consistent with <code class="highlight"><c- n>printf</c-></code>. Here <code class="highlight"><c- sc>'-'</c-></code> is a desirable part of the output. So the evidence in
support of adding this feature is not zero but close to it and shows that it is
easily solvable by other means.</p>
   <p>Another observation is that negative zero is not the only case that users may
find unusual. Why does <code class="highlight"><c- s>"-0.0"</c-></code> deserve more attention than the following
incomplete list of "interesting" cases:</p>
   <ul>
    <li data-md>
     <p><code class="highlight"><c- s>"1.000000e+42"</c-></code></p>
    <li data-md>
     <p><code class="highlight"><c- s>"+00"</c-></code> in <code class="highlight"><c- s>"1.000000e+00"</c-></code> which is the default "scientific" format of 1.0</p>
    <li data-md>
     <p><code class="highlight"><c- s>"nan"</c-></code></p>
    <li data-md>
     <p><code class="highlight"><c- s>"inf"</c-></code></p>
   </ul>
   <p>If the desire is to make floating-point numbers be presented in a user-friendly
form, just suppressing a sign is obviously not enough. Therefore even if we
assume that it’s an important issue despite very little evidence it only
addresses one of multiple cases. There are more comprehensive solutions to this
problem such as <a data-link-type="biblio" href="#biblio-d3-format">[D3-FORMAT]</a> and they can be implemented using the extension
API without introducing new format specifiers.</p>
   <p>We also looked at standard formatting facilities of popular programming
languages (C, C++, Java, Python) and haven’t found sign suppression available in
any of them.</p>
   <h2 class="heading settled" data-level="2" id="performance"><span class="secno">2. </span><span class="content">Performance</span><a class="self-link" href="#performance"></a></h2>
   <p>P1496 doesn’t discuss performance implications of the change it proposes which
is very unfortunate because adding a built-in formatting option has a nontrivial
cost. The change is deceptively simple: just add a new character to the syntax
and somehow make it suppress the sign. What it means in practice is the
following:</p>
   <ul>
    <li data-md>
     <p>Make the parser for built-in format specifiers recognize the new option</p>
    <li data-md>
     <p>Add a new piece of state to formatter specialization for floating-point types
or all built-in types (depending on the implementation)</p>
    <li data-md>
     <p>Add a new runtime check every time a floating-point number is formatted and
perform additional work to suppress the minus sign</p>
   </ul>
   <p>Note that all of these except the actual suppression add an overhead even if
you don’t use the feature. And as shown later it doesn’t bring any performance
benefits because the minus almost never arises as a result of rounding and in
the few cases when it does it’s trivial to suppress by other mechanisms.</p>
   <p>We implemented a benchmark in <a data-link-type="biblio" href="#biblio-format-benchmark">[FORMAT-BENCHMARK]</a> measuring parsing overhead
of supporting <code class="highlight"><c- sc>'z'</c-></code> in <code class="highlight"><c- n>formatter</c-><c- o>::</c-><c- n>parse</c-></code> and found that it adds approx. 15%
overhead for the common case of parsing a single format specifier (without the <code class="highlight"><c- sc>'z'</c-></code> flag):</p>
<pre class="language-text highlight">---------------------------------------------------—   <wbr>Benchmark         Time           CPU   Iterations
---------------------------------------------------—   <wbr>parse          7.90 ns       7.82 ns   87966221
parse_z        9.12 ns       9.02 ns   78832380
</pre>
   <p>To put these numbers into perspective, formatting a single integer with <code class="highlight"><c- n>format_to</c-></code> on the same system takes ~20ns which includes format string parsing
so the overhead is very significant. This clearly violates "don’t pay for what
you don’t use" philosophy.</p>
   <h2 class="heading settled" data-level="3" id="locale"><span class="secno">3. </span><span class="content">Locale</span><a class="self-link" href="#locale"></a></h2>
   <p>P1496 doesn’t discuss interaction of the proposed option with locales. However,
it mentions that the goal of the proposal is to make the output "unsurprising to
most users". This suggests that the use case for this feature is messages
displayed to end-users. Such formatting should normally be locale-specific as
opposed to locale-independent one that primarily addresses use cases such as
text-based serialization, writing output in JSON, XML or other formats
(<a data-link-type="biblio" href="#biblio-n4412">[N4412]</a>), logging, simple non-localized command-line interfaces. In many of
the latter cases preserving information and performance are important factors
and end-users are not expected to see the output. For this reason we think that
if sign suppression was desirable, it should have been a locale-specific option.
However we do not explore this idea any further because we don’t think there is
enough evidence to justify more work on this feature at all.</p>
   <h2 class="heading settled" data-level="4" id="example"><span class="secno">4. </span><span class="content">Demotivating example</span><a class="self-link" href="#example"></a></h2>
   <p>P1496 proposes adding the <code class="highlight"><c- sc>'z'</c-></code> option to format specifications:</p>
   <blockquote>
    <p>With the <code class="highlight"><c- sc>'z'</c-></code> option a negative zero after rounding is formatted as a
(positive) zero</p>
   </blockquote>
   <p>and provides the following example:</p>
   <blockquote>
<pre class="language-c++ highlight"><c- n>format</c-><c- p>(</c-><c- s>"{0:.0} {0:+.0} {0:-.0} {0: .0}"</c-><c- p>,</c-> <c- mf>0.1</c-><c- p>)</c-> <c- o>-</c-><c- mi>0</c-> <c- o>-</c-><c- mi>0</c-> <c- o>-</c-><c- mi>0</c-> <c- o>-</c-><c- mi>0</c->
</pre>
   </blockquote>
   <p>Unfortunately the example is misleading because the actual output is not <code class="highlight"><c- s>"-0 -0 -0 -0"</c-></code> as the paper claims but <code class="highlight"><c- s>"-0.1 -0.1 -0.1 -0.1"</c-></code> so adding the <code class="highlight"><c- sc>'z'</c-></code> option would have no effect. This issue would be easily caught if the
proposal was actually implemented or at least the current allegedly problematic
behavior tested. The reason why the output is <code class="highlight"><c- s>"-0.1"</c-></code> is that the default
floating-point format is defined as follows in <a href="http://eel.is/c++draft/format#tab:format.type.float">[tab:format.type.float]</a>:</p>
   <blockquote>
    <p>If <code class="highlight"><c- n>precision</c-></code> is specified, equivalent to <code class="highlight"><c- n>to_chars</c-><c- p>(</c-><c- n>first</c-><c- p>,</c-> <c- n>last</c-><c- p>,</c-> <c- n>value</c-><c- p>,</c-> <c- n>chars_format</c-><c- o>::</c-><c- n>general</c-><c- p>,</c-> <c- n>precision</c-><c- p>)</c-></code></p>
   </blockquote>
   <p>which, in turn, means that the value is formatted in the style of <code class="highlight"><c- n>printf</c-></code> in
the "C" locale with the given precision and the format specifier <code class="highlight"><c- sc>'g'</c-></code>:</p>
   <blockquote>
<pre class="language-c++ highlight"><c- n>printf</c-><c- p>(</c-><c- s>"%.0g"</c-><c- p>,</c-> <c- o>-</c-><c- mf>0.1</c-><c- p>);</c->
</pre>
   </blockquote>
   <p>giving the output of <code class="highlight"><c- s>"-0.1"</c-></code> because printf produces at least one significant
digit in the general format (<a data-link-type="biblio" href="#biblio-c">[C]</a>).</p>
   <p>So the only case when the general or default format can produce -0.0 is when
the input is -0.0 and it can be trivially suppressed:</p>
   <blockquote>
<pre class="language-c++ highlight"><c- b>double</c-> <c- n>x</c-> <c- o>=</c-> <c- o>-</c-><c- mf>0.0</c-><c- p>;</c->
<c- k>auto</c-> <c- n>s</c-> <c- o>=</c-> <c- n>std</c-><c- o>::</c-><c- n>format</c-><c- p>(</c-><c- s>"{}"</c-><c- p>,</c-> <c- o>+</c-><c- n>x</c-><c- p>);</c-> <c- c1>// s == "0.0"</c->
</pre>
   </blockquote>
   <p>Similarly, the <code class="highlight"><c- sc>'z'</c-></code> option would be useless with the <code class="highlight"><c- sc>'e'</c-></code> and <code class="highlight"><c- sc>'a'</c-></code> specifiers
and their uppercase counterparts where the negative zero cannot be produced as a
result of rounding either, for example:</p>
<pre class="language-c++ highlight"><c- k>auto</c-> <c- n>s0</c-> <c- o>=</c-> <c- n>std</c-><c- o>::</c-><c- n>format</c-><c- p>(</c-><c- s>"{:.0e}"</c-><c- p>,</c-> <c- o>-</c-><c- mf>0.1</c-><c- p>);</c-> <c- c1>// s0 == "-1e-01"</c->
<c- k>auto</c-> <c- n>s1</c-> <c- o>=</c-> <c- n>std</c-><c- o>::</c-><c- n>format</c-><c- p>(</c-><c- s>"{:.0a}"</c-><c- p>,</c-> <c- o>-</c-><c- mf>0.5</c-><c- p>);</c-> <c- c1>// s1 == "-0x1p-1"</c->
</pre>
   <p>In addition to that, a user who finds <code class="highlight"><c- o>-</c-></code> confusing won’t be happy about the
output of <code class="highlight"><c- sc>'a'</c-></code> at all, with or without sign.</p>
   <p>The fact that nobody cared enough to check the examples that were clearly broken
since revision 0 of P1496 published February 2019 is another indication that the
motivation to add this feature is very weak.</p>
   <h2 class="heading settled" data-level="5" id="fixed"><span class="secno">5. </span><span class="content">Fixed form</span><a class="self-link" href="#fixed"></a></h2>
   <p>The only case where a negative zero can be produced as a result of rounding is
the fixed form enabled by the <code class="highlight"><c- sc>'f'</c-></code> and <code class="highlight"><c- sc>'F'</c-></code> specifiers:</p>
<pre class="language-c++ highlight"><c- k>auto</c-> <c- n>s</c-> <c- o>=</c-> <c- n>std</c-><c- o>::</c-><c- n>format</c-><c- p>(</c-><c- s>"{:.0f}"</c-><c- p>,</c-> <c- o>-</c-><c- mf>0.1</c-><c- p>);</c-> <c- c1>// s == "-0"</c->
</pre>
   <p>However, this case is also trivially addressed, for example:</p>
<pre class="language-c++ highlight"><c- b>double</c-> <c- nf>no_minus</c-><c- p>(</c-><c- b>double</c-> <c- n>x</c-><c- p>)</c-> <c- p>{</c->
  <c- k>return</c-> <c- n>x</c-> <c- o>>=</c-> <c- o>-</c-><c- mf>0.5</c-> <c- o>&amp;&amp;</c-> <c- n>x</c-> <c- o>&lt;</c-> <c- mi>0</c-> <c- o>?</c-> <c- mi>0</c-> <c- o>:</c-> <c- n>x</c-><c- p>;</c->
<c- p>}</c->
<c- k>auto</c-> <c- n>s</c-> <c- o>=</c-> <c- n>std</c-><c- o>::</c-><c- n>format</c-><c- p>(</c-><c- s>"{:.0f}"</c-><c- p>,</c-> <c- n>no_minus</c-><c- p>(</c-><c- o>-</c-><c- mf>0.1</c-><c- p>));</c-> <c- c1>// s == "0"</c->
</pre>
   <p>which, unlike the specifier, doesn’t add any overhead when you don’t use the
feature. It can be easily generalized to arbitrary precision:</p>
<pre class="language-c++ highlight"><c- k>struct</c-> <c- n>no_minus_zero</c-> <c- p>{</c->
  <c- b>double</c-> <c- n>value</c-><c- p>;</c->
  <c- b>int</c-> <c- n>precision</c-><c- p>;</c->
 
  <c- n>no_minus_zero</c-><c- p>(</c-><c- b>double</c-> <c- n>val</c-><c- p>,</c-> <c- b>int</c-> <c- n>prec</c-><c- p>)</c-> <c- o>:</c-> <c- n>value</c-><c- p>(</c-><c- n>val</c-><c- p>),</c-> <c- n>precision</c-><c- p>(</c-><c- n>prec</c-><c- p>)</c-> <c- p>{</c->
    <c- k>auto</c-> <c- n>bound</c-> <c- o>=</c-> <c- o>-</c-><c- mf>0.5</c-> <c- o>*</c-> <c- n>std</c-><c- o>::</c-><c- n>pow</c-><c- p>(</c-><c- mi>10</c-><c- p>,</c-> <c- o>-</c-><c- n>prec</c-><c- p>);</c->
    <c- k>if</c-> <c- p>(</c-><c- n>val</c-> <c- o>>=</c-> <c- mi>0</c-> <c- o>||</c-> <c- n>val</c-> <c- o>&lt;</c-> <c- n>bound</c-><c- p>)</c-> <c- k>return</c-><c- p>;</c->
    <c- k>if</c-> <c- p>(</c-><c- n>val</c-> <c- o>></c-> <c- n>bound</c-> <c- o>||</c-> <c- n>format</c-><c- p>(</c-><c- s>"{:.{}f}"</c-><c- p>,</c-> <c- n>val</c-><c- p>,</c-> <c- n>prec</c-><c- p>).</c-><c- n>back</c-><c- p>()</c-> <c- o>==</c-> <c- sc>'0'</c-><c- p>)</c->
      <c- n>value</c-> <c- o>=</c-> <c- mi>0</c-><c- p>;</c->
  <c- p>}</c->
<c- p>};</c->
 
<c- n>template</c-> <c- o>&lt;></c->
<c- k>struct</c-> <c- n>formatter</c-><c- o>&lt;</c-><c- n>no_minus_zero</c-><c- o>></c-> <c- p>{</c->
  <c- k>auto</c-> <c- n>parse</c-><c- p>(</c-><c- n>format_parse_context</c-><c- o>&amp;</c-> <c- n>ctx</c-><c- p>)</c-> <c- p>{</c-> <c- k>return</c-> <c- n>ctx</c-><c- p>.</c-><c- n>begin</c-><c- p>();</c-> <c- p>}</c->
 
  <c- k>auto</c-> <c- n>format</c-><c- p>(</c-><c- n>no_minus_zero</c-> <c- n>nmz</c-><c- p>,</c-> <c- n>format_context</c-><c- o>&amp;</c-> <c- n>ctx</c-><c- p>)</c-> <c- p>{</c->
    <c- k>return</c-> <c- n>format_to</c-><c- p>(</c-><c- n>ctx</c-><c- p>.</c-><c- n>out</c-><c- p>(),</c-> <c- s>"{:.{}f}"</c-><c- p>,</c-> <c- n>nmz</c-><c- p>.</c-><c- n>value</c-><c- p>,</c-> <c- n>nmz</c-><c- p>.</c-><c- n>precision</c-><c- p>);</c->
  <c- p>}</c->
<c- p>};</c->
</pre>
   <p>Again, this doesn’t add any overhead if the feature is not used and most cases
require one or two checks when the feature is used. It can be optimized by using
a table of bounds and replacing the <code class="highlight"><c- n>format</c-></code> call with a bound rounding direction
check which can also be precomputed but that’s not essential.</p>
   <p><code class="highlight"><c- n>no_minus_zero</c-></code> can be used as follows:</p>
<pre class="language-c++ highlight"><c- k>auto</c-> <c- n>s</c-> <c- o>=</c-> <c- n>fmt</c-><c- o>::</c-><c- n>format</c-><c- p>(</c-><c- s>"{}"</c-><c- p>,</c-> <c- n>no_minus_zero</c-><c- p>(</c-><c- o>-</c-><c- mf>0.001</c-><c- p>,</c-> <c- mi>2</c-><c- p>))</c-> <c- c1>// s == "0.00"</c->
</pre>
   <p>This will likely be faster than <code class="highlight"><c- n>fmt</c-><c- o>::</c-><c- n>format</c-><c- p>(</c-><c- s>"{:z.2f}"</c-><c- p>)</c-></code> because there is less
parsing of format specifiers and fewer runtime checks.</p>
   <p>So we can clearly see that the analysis in The Problem section of P1496 is
incorrect: negative zero can never appear as a result of rounding with the
default, <code class="highlight"><c- sc>'g'</c-></code>, <code class="highlight"><c- sc>'G'</c-></code>, <code class="highlight"><c- sc>'e'</c-></code>, <code class="highlight"><c- sc>'E'</c-></code>, <code class="highlight"><c- sc>'a'</c-></code>, and <code class="highlight"><c- sc>'A'</c-></code> specifiers and can be
trivially handled in the case of <code class="highlight"><c- sc>'f'</c-></code> and <code class="highlight"><c- sc>'F'</c-></code> specifiers due to the nature
of the fixed format (the range that rounds to -0 is easy to compute).</p>
   <h2 class="heading settled" data-level="6" id="conclusion"><span class="secno">6. </span><span class="content">Conclusion</span><a class="self-link" href="#conclusion"></a></h2>
   <p>Considering that there is almost zero evidence that sign suppression is a
problem worth solving, motivating examples in P1496 are incorrect and this new
feature will add significant overhead to calls to <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>format</c-></code> and uses of
built-in <code class="highlight"><c- n>formatter</c-></code> specializations even if not used among other problems and
the fact that it can be easily implemented by other means, we think that it
shouldn’t be standardized. If there is still a strong desire to have this
feature, it can be added via a separate formatter specialization not penalizing
other cases.</p>
   <h2 class="heading settled" data-level="7" id="ack"><span class="secno">7. </span><span class="content">Acknowledgements</span><a class="self-link" href="#ack"></a></h2>
   <p>We would like to thank Peter Brett for bringing to our attention the fact that
negative zero can never appear as a result of rounding in most formats.</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-c">[C]
   <dd>ISO/IEC 9899:2011 Information technology — Programming languages — C. 
   <dt id="biblio-d3-format">[D3-FORMAT]
   <dd><a href="https://github.com/d3/d3-format">d3-format: Format numbers for human consumption</a>. URL: <a href="https://github.com/d3/d3-format">https://github.com/d3/d3-format</a>
   <dt id="biblio-fmt">[FMT]
   <dd><a href="https://github.com/fmtlib/fmt">The fmt library</a>. URL: <a href="https://github.com/fmtlib/fmt">https://github.com/fmtlib/fmt</a>
   <dt id="biblio-folly-format">[FOLLY-FORMAT]
   <dd><a href="https://github.com/facebook/folly/blob/master/folly/docs/Format.md">Folly Format</a>. URL: <a href="https://github.com/facebook/folly/blob/master/folly/docs/Format.md">https://github.com/facebook/folly/blob/master/folly/docs/Format.md</a>
   <dt id="biblio-format-benchmark">[FORMAT-BENCHMARK]
   <dd><a href="https://github.com/fmtlib/format-benchmark">A collection of formatting benchmarks</a>. URL: <a href="https://github.com/fmtlib/format-benchmark">https://github.com/fmtlib/format-benchmark</a>
   <dt id="biblio-n4412">[N4412]
   <dd>Jens Maurer. <a href="http://open-std.org/JTC1/SC22/WG21/docs/papers/2015/n4412.html">Shortcomings of iostreams</a>. URL: <a href="http://open-std.org/JTC1/SC22/WG21/docs/papers/2015/n4412.html">http://open-std.org/JTC1/SC22/WG21/docs/papers/2015/n4412.html</a>
   <dt id="biblio-p1496">[P1496]
   <dd>Alan Talbot; Jorg Brown. <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p1496r1.pdf">Formatting of Negative Zero</a>. URL: <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p1496r1.pdf">http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p1496r1.pdf</a>
   <dt id="biblio-us227">[US227]
   <dd><a href="https://github.com/cplusplus/nbballot/issues/224">Add "z" format modifier to avoid sign for zero-display numbers</a>. URL: <a href="https://github.com/cplusplus/nbballot/issues/224">https://github.com/cplusplus/nbballot/issues/224</a>
  </dl>