<!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>P3505R0: Fix the default floating-point representation in std::format</title>
<style data-fill-with="stylesheet">/******************************************************************************
 *                   Style sheet for the W3C specifications                   *
 *
 * Special classes handled by this style sheet include:
 *
 * Indices
 *   - .toc for the Table of Contents (<ol class="toc">)
 *     + <span class="secno"> for the section numbers
 *   - #toc for the Table of Contents (<nav id="toc">)
 *   - ul.index for Indices (<a href="#ref">term</a><span>, in § N.M</span>)
 *   - table.index for Index Tables (e.g. for properties or elements)
 *
 * Structural Markup
 *   - table.data for general data tables
 *     -> use 'scope' attribute, <colgroup>, <thead>, and <tbody> for best results !
 *     -> use <table class='complex data'> for extra-complex tables
 *     -> use <td class='long'> for paragraph-length cell content
 *     -> use <td class='pre'> when manual line breaks/indentation would help readability
 *   - dl.switch for switch statements
 *   - ol.algorithm for algorithms (helps to visualize nesting)
 *   - .figure and .caption (HTML4) and figure and figcaption (HTML5)
 *     -> .sidefigure for right-floated figures
 *   - ins/del
 *     -> ins/del.c### for candidate and proposed changes (amendments)
 *
 * Code
 *   - pre and code
 *
 * Special Sections
 *   - .note       for informative notes             (div, p, span, aside, details)
 *   - .example    for informative examples          (div, p, pre, span)
 *   - .issue      for issues                        (div, p, span)
 *   - .advisement for loud normative statements     (div, p, strong)
 *   - .annoying-warning for spec obsoletion notices (div, aside, details)
 *   - .correction for "candidate corrections"       (div, aside, details, section)
 *   - .addition   for "candidate additions"         (div, aside, details, section)
 *   - .correction.proposed for "proposed corrections" (div, aside, details, section)
 *   - .addition.proposed   for "proposed additions"   (div, aside, details, section)
 *
 * Definition Boxes
 *   - pre.def   for WebIDL definitions
 *   - table.def for tables that define other entities (e.g. CSS properties)
 *   - dl.def    for definition lists that define other entitles (e.g. HTML elements)
 *
 * Numbering
 *   - .secno for section numbers in .toc and headings (<span class='secno'>3.2</span>)
 *   - .marker for source-inserted example/figure/issue numbers (<span class='marker'>Issue 4</span>)
 *   - ::before styled for CSS-generated issue/example/figure numbers:
 *     -> Documents wishing to use this only need to add
 *        figcaption::before,
 *        .caption::before { content: "Figure "  counter(figure) " ";  }
 *        .example::before { content: "Example " counter(example) " "; }
 *        .issue::before   { content: "Issue "   counter(issue) " ";   }
 *
 * Header Stuff (ignore, just don't conflict with these classes)
 *   - .head for the header
 *   - .copyright for the copyright
 *
 * Outdated warning for old specs
 *
 * Miscellaneous
 *   - .overlarge for things that should be as wide as possible, even if
 *     that overflows the body text area. This can be used on an item or
 *     on its container, depending on the effect desired.
 *     Note that this styling basically doesn't help at all when printing,
 *     since A4 paper isn't much wider than the max-width here.
 *     It's better to design things to fit into a narrower measure if possible.
 *
 *   - js-added ToC jump links (see fixup.js)
 *
 ******************************************************************************/

/* color variables included separately for reliability */

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

	html {
	}

	body {
		counter-reset: example figure issue;

		/* Layout */
		max-width: 50em;			  /* limit line length to 50em for readability   */
		margin: 0 auto;				/* center text within page                    */
		padding: 1.6em 1.5em 2em 50px; /* assume 16px font size for downlevel clients */
		padding: 1.6em 1.5em 2em calc(26px + 1.5em); /* leave space for status flag    */

		/* Typography */
		line-height: 1.5;
		font-family: sans-serif;
		widows: 2;
		orphans: 2;
		word-wrap: break-word;
		overflow-wrap: break-word;
		hyphens: auto;

		color: black;
		color: var(--text);
		background: white top left fixed no-repeat;
		background: var(--bg) top left fixed no-repeat;
		background-size: 25px auto;
	}


/******************************************************************************/
/*                         Front Matter & Navigation                          */
/******************************************************************************/

/** Header ********************************************************************/

	div.head { margin-bottom: 1em; }
	div.head hr { border-style: solid; }

	div.head h1 {
		font-weight: bold;
		margin: 0 0 .1em;
		font-size: 220%;
	}

	div.head h2 { margin-bottom: 1.5em;}

/** W3C Logo ******************************************************************/

	.head .logo {
		float: right;
		margin: 0.4rem 0 0.2rem .4rem;
	}

	.head img[src*="logos/W3C"] {
		display: block;
		border: solid #1a5e9a;
		border: solid var(--logo-bg);
		border-width: .65rem .7rem .6rem;
		border-radius: .4rem;
		background: #1a5e9a;
		background: var(--logo-bg);
		color: white;
		color: var(--logo-text);
		font-weight: bold;
	}

	.head a:hover > img[src*="logos/W3C"],
	.head a:focus > img[src*="logos/W3C"] {
		opacity: .8;
	}

	.head a:active > img[src*="logos/W3C"] {
		background: #c00;
		background: var(--logo-active-bg);
		border-color: #c00;
		border-color: var(--logo-active-bg);
	}

	/* see also additional rules in Link Styling section */

/** Copyright *****************************************************************/

	p.copyright,
	p.copyright small { font-size: small; }

/** Back to Top / ToC Toggle **************************************************/

	@media print {
		#toc-nav {
			display: none;
		}
	}
	@media not print {
		#toc-nav {
			position: fixed;
			z-index: 3;
			bottom: 0; left: 0;
			margin: 0;
			min-width: 1.33em;
			border-top-right-radius: 2rem;
			box-shadow: 0 0 2px;
			font-size: 1.5em;
		}
		#toc-nav > a {
			display: block;
			white-space: nowrap;

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

			box-shadow: 0 0 2px;
			border: none;
			border-top-right-radius: 1.33em;

			color: #707070;
			color: var(--tocnav-normal-text);
			background: white;
			background: var(--tocnav-normal-bg);
		}
		#toc-nav > a:hover,
		#toc-nav > a:focus {
			color: black;
			color: var(--tocnav-hover-text);
			background: #f8f8f8;
			background: var(--tocnav-hover-bg);
		}
		#toc-nav > a:active {
			color: #c00;
			color: var(--tocnav-active-text);
			background: white;
			background: var(--tocnav-active-bg);
		}

		#toc-nav > #toc-jump {
			padding-bottom: 2em;
			margin-bottom: -1.9em;
		}

		/* statusbar gets in the way on keyboard focus; remove once browsers fix */
		#toc-nav > a[href="#toc"]:not(:hover):focus:last-child {
			padding-bottom: 1.5rem;
		}

		#toc-nav:not(:hover) > a:not(:focus) > span + span {
			/* Ideally this uses :focus-within on #toc-nav */
			display: none;
		}
		#toc-nav > a > span + span {
			padding-right: 0.2em;
		}
	}

/** ToC Sidebar ***************************************************************/

	/* Floating sidebar */
	@media screen {
		body.toc-sidebar #toc {
			position: fixed;
			top: 0; bottom: 0;
			left: 0;
			width: 23.5em;
			max-width: 80%;
			max-width: calc(100% - 2em - 26px);
			overflow: auto;
			padding: 0 1em;
			padding-left: 42px;
			padding-left: calc(1em + 26px);
			color: black;
			color: var(--tocsidebar-text);
			background: inherit;
			background-color: #f7f8f9;
			background-color: var(--tocsidebar-bg);
			z-index: 1;
			box-shadow: -.1em 0 .25em rgba(0,0,0,.1) inset;
			box-shadow: -.1em 0 .25em var(--tocsidebar-shadow) inset;
		}
		body.toc-sidebar #toc h2 {
			margin-top: .8rem;
			font-variant: small-caps;
			font-variant: all-small-caps;
			text-transform: lowercase;
			font-weight: bold;
			color: gray;
			color: hsla(203,20%,40%,.7);
			color: var(--tocsidebar-heading-text);
		}
		body.toc-sidebar #toc-jump:not(:focus) {
			width: 0;
			height: 0;
			padding: 0;
			position: absolute;
			overflow: hidden;
		}
	}
	/* Hide main scroller when only the ToC is visible anyway */
	@media screen and (max-width: 28em) {
		body.toc-sidebar {
			overflow: hidden;
		}
	}

	/* Sidebar with its own space */
	@media screen and (min-width: 78em) {
		body:not(.toc-inline) #toc {
			position: fixed;
			top: 0; bottom: 0;
			left: 0;
			width: 23.5em;
			overflow: auto;
			padding: 0 1em;
			padding-left: 42px;
			padding-left: calc(1em + 26px);
			color: black;
			color: var(--tocsidebar-text);
			background: inherit;
			background-color: #f7f8f9;
			background-color: var(--tocsidebar-bg);
			z-index: 1;
			box-shadow: -.1em 0 .25em rgba(0,0,0,.1) inset;
			box-shadow: -.1em 0 .25em var(--tocsidebar-shadow) inset;
		}
		body:not(.toc-inline) #toc h2 {
			margin-top: .8rem;
			font-variant: small-caps;
			font-variant: all-small-caps;
			text-transform: lowercase;
			font-weight: bold;
			color: gray;
			color: hsla(203,20%,40%,.7);
			color: var(--tocsidebar-heading-text);
		}

		body:not(.toc-inline) {
			padding-left: 29em;
		}
		/* See also Overflow section at the bottom */

		body:not(.toc-inline) #toc-jump:not(:focus) {
			width: 0;
			height: 0;
			padding: 0;
			position: absolute;
			overflow: hidden;
		}
	}
	@media screen and (min-width: 90em) {
		body:not(.toc-inline) {
			margin: 0 4em;
		}
	}

/******************************************************************************/
/*                                Sectioning                                  */
/******************************************************************************/

/** Headings ******************************************************************/

	h1, h2, h3, h4, h5, h6, dt {
		page-break-after: avoid;
		page-break-inside: avoid;
		font: 100% sans-serif;   /* Reset all font styling to clear out UA styles */
		font-family: inherit;	/* Inherit the font family. */
		line-height: 1.2;		/* Keep wrapped headings compact */
		hyphens: manual;		/* Hyphenated headings look weird */
	}

	h2, h3, h4, h5, h6 {
		margin-top: 3rem;
	}

	h1, h2, h3 {
		color: #005A9C;
		color: var(--heading-text);
	}

	h1 { font-size: 170%; }
	h2 { font-size: 140%; }
	h3 { font-size: 120%; }
	h4 { font-weight: bold; }
	h5 { font-style: italic; }
	h6 { font-variant: small-caps; }
	dt { font-weight: bold; }

/** Subheadings ***************************************************************/

	h1 + h2,
	#profile-and-date {
		/* #profile-and-date is a subtitle in an H2 under the H1 */
		margin-top: 0;
	}
	h2 + h3,
	h3 + h4,
	h4 + h5,
	h5 + h6 {
		margin-top: 1.2em; /* = 1 x line-height */
	}

/** Section divider ***********************************************************/

	:not(.head) > :not(.head) + hr {
		font-size: 1.5em;
		text-align: center;
		margin: 1em auto;
		height: auto;
		color: black;
		color: var(--hr-text);
		border: transparent solid 0;
		background: transparent;
	}
	:not(.head) > hr::before {
		content: "\2727\2003\2003\2727\2003\2003\2727";
	}

/******************************************************************************/
/*                            Paragraphs and Lists                            */
/******************************************************************************/

	p {
		margin: 1em 0;
	}

	dd > p:first-child,
	li > p:first-child {
		margin-top: 0;
	}

	ul, ol {
		margin-left: 0;
		padding-left: 2em;
	}

	li {
		margin: 0.25em 0 0.5em;
		padding: 0;
	}

	dl dd {
		margin: 0 0 .5em 2em;
	}

	.head dd + dd { /* compact for header */
		margin-top: -.5em;
	}

	/* Style for algorithms */
	ol.algorithm ol:not(.algorithm),
	.algorithm > ol ol:not(.algorithm) {
	border-left: 0.5em solid #DEF;
	border-left: 0.5em solid var(--algo-border);
	}

	/* Put nice boxes around each algorithm. */
	[data-algorithm]:not(.heading) {
	 padding: .5em;
	 border: thin solid #ddd;
	 border: thin solid var(--algo-border);
	 border-radius: .5em;
	 margin: .5em calc(-0.5em - 1px);
	}
	[data-algorithm]:not(.heading) > :first-child {
	 margin-top: 0;
	}
	[data-algorithm]:not(.heading) > :last-child {
	 margin-bottom: 0;
	}

	/* Style for switch/case <dl>s */
	dl.switch > dd > ol.only,
	dl.switch > dd > .only > ol {
	margin-left: 0;
	}
	dl.switch > dd > ol.algorithm,
	dl.switch > dd > .algorithm > ol {
	margin-left: -2em;
	}
	dl.switch {
	padding-left: 2em;
	}
	dl.switch > dt {
	text-indent: -1.5em;
	margin-top: 1em;
	}
	dl.switch > dt + dt {
	margin-top: 0;
	}
	dl.switch > dt::before {
	content: '\21AA';
	padding: 0 0.5em 0 0;
	display: inline-block;
	width: 1em;
	text-align: right;
	line-height: 0.5em;
	}

/** Terminology Markup ********************************************************/


/******************************************************************************/
/*                                 Inline Markup                              */
/******************************************************************************/

/** Terminology Markup ********************************************************/
	dfn   { /* Defining instance */
		font-weight: bolder;
	}
	a > i { /* Instance of term */
		font-style: normal;
	}
	dt dfn code, code.idl {
		font-size: inherit;
	}
	dfn var {
		font-style: normal;
	}

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

	del {
		color: #aa0000;
		color: var(--del-text);
		background: transparent;
		background: var(--del-bg);
		text-decoration: line-through;
	}
	ins {
		color: #006100;
		color: var(--ins-text);
		background: transparent;
		background: var(--ins-bg);
		text-decoration: underline;
	}

	/* for amendments (candidate/proposed changes) */

	.amendment ins, .correction ins, .addition ins,
	ins[class^=c] {
		text-decoration-style: dotted;
	}
	.amendment del, .correction del, .addition del,
	del[class^=c] {
		text-decoration-style: dotted;
	}
	.amendment.proposed ins, .correction.proposed ins, .addition.proposed ins,
	ins[class^=c].proposed {
		text-decoration-style: double;
	}
	.amendment.proposed del, .correction.proposed del, .addition.proposed del,
	del[class^=c].proposed {
		text-decoration-style: double;
	}

/** Miscellaneous improvements to inline formatting ***************************/

	sup {
		vertical-align: super;
		font-size: 80%
	}

/******************************************************************************/
/*                                    Code                                    */
/******************************************************************************/

/** General monospace/pre rules ***********************************************/

	pre, code, samp {
		font-family: Menlo, Consolas, "DejaVu Sans Mono", Monaco, monospace;
		font-size: .9em;
		hyphens: none;
		text-transform: none;
		text-align: left;
		text-align: start;
		font-variant: normal;
		orphans: 3;
		widows: 3;
		page-break-before: avoid;
	}
	pre code,
	code code {
		font-size: 100%;
	}

	pre {
		margin-top: 1em;
		margin-bottom: 1em;
		overflow: auto;
	}

/** Inline Code fragments *****************************************************/

	/* Do something nice. */

/******************************************************************************/
/*                                    Links                                   */
/******************************************************************************/

/** General Hyperlinks ********************************************************/

	/* We hyperlink a lot, so make it less intrusive */
	a[href] {
		color: #034575;
		color: var(--a-normal-text);
		text-decoration: underline #707070;
		text-decoration: underline var(--a-normal-underline);
		text-decoration-skip-ink: none;
	}
	a:visited {
		color: #034575;
		color: var(--a-visited-text);
		text-decoration-color: #bbb;
		text-decoration-color: var(--a-visited-underline);
	}

	/* Indicate interaction with the link */
	a[href]:focus,
	a[href]:hover {
		text-decoration-thickness: 2px;
	}
	a[href]:active {
		color: #c00;
		color: var(--a-active-text);
		text-decoration-color: #c00;
		text-decoration-color: var(--a-active-underline);
	}

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

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

	img {
		border-style: none;
	}

	img, svg {
		/* Intentionally not color-scheme aware. */
		background: white;
	}

	/* For autogen numbers, add
	  .caption::before, figcaption::before { content: "Figure " counter(figure) ". "; }
	*/

	figure, .figure, .sidefigure {
		page-break-inside: avoid;
		text-align: center;
		margin: 2.5em 0;
	}
	.figure img,	.sidefigure img,	figure img,
	.figure object, .sidefigure object, figure object {
		max-width: 100%;
		margin: auto;
		height: auto;
	}
	.figure pre, .sidefigure pre, figure pre {
		text-align: left;
		display: table;
		margin: 1em auto;
	}
	.figure table, figure table {
		margin: auto;
	}
	@media screen and (min-width: 20em) {
		.sidefigure {
			float: right;
			width: 50%;
			margin: 0 0 0.5em 0.5em;
		}
	}
	.caption, figcaption, caption {
		font-style: italic;
		font-size: 90%;
	}
	.caption::before, figcaption::before, figcaption > .marker {
		font-weight: bold;
	}
	.caption, figcaption {
		counter-increment: figure;
	}

	/* DL list is indented 2em, but figure inside it is not */
	dd > .figure, dd > figure { margin-left: -2em; }

/******************************************************************************/
/*                             Colored Boxes                                  */
/******************************************************************************/

	.issue, .note, .example, .assertion, .advisement, blockquote,
	.amendment, .correction, .addition {
		margin: 1em auto;
		padding: .5em;
		border: .5em;
		border-left-style: solid;
		page-break-inside: avoid;
	}
	span.issue, span.note {
		padding: .1em .5em .15em;
		border-right-style: solid;
	}

	blockquote > :first-child,
	.note  > p:first-child,
	.issue > p:first-child,
	.amendment > p:first-child,
	.correction > p:first-child,
	.addition > p:first-child {
		margin-top: 0;
	}
	blockquote > :last-child,
	.note  > p:last-child,
	.issue > p:last-child,
	.amendment > p:last-child,
	.correction > p:last-child,
	.addition > p:last-child {
		margin-bottom: 0;
	}


	.issue::before, .issue > .marker,
	.example::before, .example > .marker,
	.note::before, .note > .marker,
	details.note > summary > .marker,
	.amendment::before, .amendment > .marker,
	details.amendment > summary > .marker,
	.addition::before, .addition > .marker,
	addition.amendment > summary > .marker,
	.correction::before, .correction > .marker,
	correction.amendment > summary > .marker
	{
		text-transform: uppercase;
		padding-right: 1em;
	}

	.example::before, .example > .marker {
		display: block;
		padding-right: 0em;
	}

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

	blockquote {
		border-color: silver;
		border-color: var(--blockquote-border);
		background: transparent;
		background: var(--blockquote-bg);
		color: currentcolor;
		color: var(--blockquote-text);
	}

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

	.issue {
		border-color: #e05252;
		border-color: var(--issue-border);
		background: #fbe9e9;
		background: var(--issue-bg);
		color: black;
		color: var(--issue-text);
		counter-increment: issue;
		overflow: auto;
	}
	.issue::before, .issue > .marker {
		color: #831616;
		color: var(--issueheading-text);
	}
	/* Add .issue::before { content: "Issue " counter(issue) " "; } for autogen numbers,
	  or use class="marker" to mark up the issue number in source. */

/** Example *******************************************************************/

	.example {
		border-color: #e0cb52;
		border-color: var(--example-border);
		background: #fcfaee;
		background: var(--example-bg);
		color: black;
		color: var(--example-text);
		counter-increment: example;
		overflow: auto;
		clear: both;
	}
	.example::before, .example > .marker {
		color: #574b0f;
		color: var(--exampleheading-text);
	}
	/* Add .example::before { content: "Example " counter(example) " "; } for autogen numbers,
	  or use class="marker" to mark up the example number in source. */

/** Non-normative Note ********************************************************/

	.note {
		border-color: #52e052;
		border-color: var(--note-border);
		background: #e9fbe9;
		background: var(--note-bg);
		color: black;
		color: var(--note-text);
		overflow: auto;
	}

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

	details.note[open] > summary {
		border-bottom: 1px silver solid;
		border-bottom: 1px var(--notesummary-underline) solid;
	}

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

	.assertion {
		border-color: #AAA;
		border-color: var(--assertion-border);
		background: #EEE;
		background: var(--assertion-bg);
		color: black;
		color: var(--assertion-text);
	}

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

	.advisement {
		border-color: orange;
		border-color: var(--advisement-border);
		border-style: none solid;
		background: #fec;
		background: var(--advisement-bg);
		color: black;
		color: var(--advisement-text);
	}
	strong.advisement {
		display: block;
		text-align: center;
	}
	.advisement::before, .advisement > .marker {
		color: #b35f00;
		color: var(--advisementheading-text);
	}

/** Amendment Box *************************************************************/

	.amendment, .correction, .addition {
		border-color: #330099;
		border-color: var(--amendment-border);
		background: #F5F0FF;
		background: var(--amendment-bg);
		color: black;
		color: var(--amendment-text);
	}
	.amendment.proposed, .correction.proposed, .addition.proposed {
		border-style: solid;
		border-block-width: 0.25em;
	}
	.amendment::before, .amendment > .marker,
	details.amendment > summary::before, details.amendment > summary > .marker,
	.correction::before, .correction > .marker,
	details.correction > summary::before, details.correction > summary > .marker,
	.addition::before, .addition > .marker,
	details.addition > summary::before, details.addition > summary > .marker {
		color: #220066;
		color: var(--amendmentheading-text);
	}
	.amendment.proposed::before, .amendment.proposed > .marker,
	details.amendment.proposed > summary::before, details.amendment.proposed > summary > .marker,
	.correction.proposed::before, .correction.proposed > .marker,
	details.correction.proposed > summary::before, details.correction.proposed > summary > .marker,
	.addition.proposed::before, .addition.proposed > .marker,
	details.addition.proposed > summary::before, details.addition.proposed > summary > .marker {
		font-weight: bold;
	}

/** Spec Obsoletion Notice ****************************************************/
	/* obnoxious obsoletion notice for older/abandoned specs. */

	details {
		display: block;
	}
	summary {
		font-weight: bolder;
	}

	.annoying-warning:not(details),
	details.annoying-warning:not([open]) > summary,
	details.annoying-warning[open] {
		background: hsla(40,100%,50%,0.95);
		background: var(--warning-bg);
		color: black;
		color: var(--warning-text);
		padding: .75em 1em;
		border: red;
		border: var(--warning-border);
		border-style: solid none;
		box-shadow: 0 2px 8px black;
		text-align: center;
	}
	.annoying-warning :last-child {
		margin-bottom: 0;
	}

@media not print {
	details.annoying-warning[open] {
		position: fixed;
		left: 0;
		right: 0;
		bottom: 2em;
		z-index: 1000;
	}
}

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

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

	.def {
		padding: .5em 1em;
		background: #def;
		background: var(--def-bg);
		margin: 1.2em 0;
		border-left: 0.5em solid #8ccbf2;
		border-left: 0.5em solid var(--def-border);
		color: black;
		color: var(--def-text);
	}

/******************************************************************************/
/*                                    Tables                                  */
/******************************************************************************/

	th, td {
		text-align: left;
		text-align: start;
	}

/** Property/Descriptor Definition Tables *************************************/

	table.def {
		/* inherits .def box styling, see above */
		width: 100%;
		border-spacing: 0;
	}

	table.def td,
	table.def th {
		padding: 0.5em;
		vertical-align: baseline;
		border-bottom: 1px solid #bbd7e9;
		border-bottom: 1px solid var(--defrow-border);
	}

	table.def > tbody > tr:last-child th,
	table.def > tbody > tr:last-child td {
		border-bottom: 0;
	}

	table.def th {
		font-style: italic;
		font-weight: normal;
		padding-left: 1em;
		width: 3em;
	}

	/* For when values are extra-complex and need formatting for readability */
	table td.pre {
		white-space: pre-wrap;
	}

	/* A footnote at the bottom of a def table */
	table.def td.footnote {
		padding-top: 0.6em;
	}
	table.def td.footnote::before {
		content: " ";
		display: block;
		height: 0.6em;
		width: 4em;
		border-top: thin solid;
	}

/** Data tables (and properly marked-up index tables) *************************/
	/*
		<table class="data"> highlights structural relationships in a table
		when correct markup is used (e.g. thead/tbody, th vs. td, scope attribute)

		Use class="complex data" for particularly complicated tables --
		(This will draw more lines: busier, but clearer.)

		Use class="long" on table cells with paragraph-like contents
		(This will adjust text alignment accordingly.)
		Alternately use class="longlastcol" on tables, to have the last column assume "long".
	*/

	table {
		word-wrap: normal;
		overflow-wrap: normal;
		hyphens: manual;
	}

	table.data,
	table.index {
		margin: 1em auto;
		border-collapse: collapse;
		border: hidden;
		width: 100%;
	}
	table.data caption,
	table.index caption {
		max-width: 50em;
		margin: 0 auto 1em;
	}

	table.data td,  table.data th,
	table.index td, table.index th {
		padding: 0.5em 1em;
		border-width: 1px;
		border-color: silver;
		border-color: var(--datacell-border);
		border-top-style: solid;
	}

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

	table.data  thead,
	table.index thead,
	table.data  tbody,
	table.index tbody {
		border-bottom: 2px solid;
	}

	table.data colgroup,
	table.index colgroup {
		border-left: 2px solid;
	}

	table.data  tbody th:first-child,
	table.index tbody th:first-child  {
		border-right: 2px solid;
		border-top: 1px solid silver;
		border-top: 1px solid var(--datacell-border);
		padding-right: 1em;
	}

	table.data th[colspan],
	table.data td[colspan] {
		text-align: center;
	}

	table.complex.data th,
	table.complex.data td {
		border: 1px solid silver;
		border: 1px solid var(--datacell-border);
		text-align: center;
	}

	table.data.longlastcol td:last-child,
	table.data td.long {
		vertical-align: baseline;
		text-align: left;
	}

	table.data img {
		vertical-align: middle;
	}


/*
Alternate table alignment rules

	table.data,
	table.index {
		text-align: center;
	}

	table.data  thead th[scope="row"],
	table.index thead th[scope="row"] {
		text-align: right;
	}

	table.data  tbody th:first-child,
	table.index tbody th:first-child  {
		text-align: right;
	}

Possible extra rowspan handling

	table.data  tbody th[rowspan]:not([rowspan='1']),
	table.index tbody th[rowspan]:not([rowspan='1']),
	table.data  tbody td[rowspan]:not([rowspan='1']),
	table.index tbody td[rowspan]:not([rowspan='1']) {
		border-left: 1px solid silver;
	}

	table.data  tbody th[rowspan]:first-child,
	table.index tbody th[rowspan]:first-child,
	table.data  tbody td[rowspan]:first-child,
	table.index tbody td[rowspan]:first-child{
		border-left: 0;
		border-right: 1px solid silver;
	}
*/

/******************************************************************************/
/*                                  Indices                                   */
/******************************************************************************/


/** Table of Contents *********************************************************/

	.toc a {
		/* More spacing; use padding to make it part of the click target. */
		padding: 0.1rem 1px 0;
		/* Larger, more consistently-sized click target */
		display: block;
		/* Switch to using border-bottom for underlines */
		text-decoration: none;
		border-bottom: 1px solid;
		/* Reverse color scheme */
		color: black;
		color: var(--toclink-text);
		border-color: #3980b5;
		border-color: var(--toclink-underline);
	}
	.toc a:visited {
		color: black;
		color: var(--toclink-visited-text);
		border-color: #054572;
		border-color: var(--toclink-visited-underline);
	}
	.toc a:focus,
	.toc a:hover {
		background: rgba(75%, 75%, 75%, .25);
		background: var(--a-hover-bg);
		border-bottom-width: 3px;
		margin-bottom: -2px;
	}
	.toc a:not(:focus):not(:hover) {
		/* Allow colors to cascade through from link styling */
		border-bottom-color: transparent;
	}

	.toc, .toc ol, .toc ul, .toc li {
		list-style: none; /* Numbers must be inlined into source */
		/* because generated content isn't search/selectable and markers can't do multilevel yet */
		margin:  0;
		padding: 0;
	}
	.toc {
		line-height: 1.1em;
	}

	/* ToC not indented until third level, but font style & margins show hierarchy */
	.toc > li			{ font-weight: bold;   }
	.toc > li li		 { font-weight: normal; }
	.toc > li li li	  { font-size:   95%;	}
	.toc > li li li li	{ font-size:   90%;	}
	.toc > li li li li li { font-size:   85%;	}

	/* @supports not (display:grid) { */
		.toc > li			{ margin: 1.5rem 0;	}
		.toc > li li		 { margin: 0.3rem 0;	}
		.toc > li li li	  { margin-left: 2rem;   }

		/* Section numbers in a column of their own */
		.toc .secno {
			float: left;
			width: 4rem;
			white-space: nowrap;
		}
		.toc > li li li li .secno { font-size: 85%; }
		.toc > li li li li li .secno { font-size: 100%; }

		.toc li {
			clear: both;
		}

		:not(li) > .toc			 { margin-left:  5rem; }
		.toc .secno				 { margin-left: -5rem; }
		.toc > li li li .secno	  { margin-left: -7rem; }
		.toc > li li li li .secno	{ margin-left: -9rem; }
		.toc > li li li li li .secno { margin-left: -11rem; }

		/* Tighten up indentation in narrow ToCs */
		@media (max-width: 30em) {
			:not(li) > .toc			 { margin-left:  4rem; }
			.toc .secno				 { margin-left: -4rem; }
			.toc > li li li			 { margin-left:  1rem; }
			.toc > li li li .secno	  { margin-left: -5rem; }
			.toc > li li li li .secno	{ margin-left: -6rem; }
			.toc > li li li li li .secno { margin-left: -7rem; }
		}
		/* Loosen it on wide screens */
		@media screen and (min-width: 78em) {
			body:not(.toc-inline) :not(li) > .toc			 { margin-left:  4rem; }
			body:not(.toc-inline) .toc .secno				 { margin-left: -4rem; }
			body:not(.toc-inline) .toc > li li li			 { margin-left:  1rem; }
			body:not(.toc-inline) .toc > li li li .secno	  { margin-left: -5rem; }
			body:not(.toc-inline) .toc > li li li li .secno	{ margin-left: -6rem; }
			body:not(.toc-inline) .toc > li li li li li .secno { margin-left: -7rem; }
	}
	/* } */

	@supports (display:grid) and (display:contents) {
		/* Use #toc over .toc to override non-@supports rules. */
		#toc {
			display: grid;
			align-content: start;
			grid-template-columns: auto 1fr;
			grid-column-gap: 1rem;
			column-gap: 1rem;
			grid-row-gap: .6rem;
			row-gap: .6rem;
		}
		#toc h2 {
			grid-column: 1 / -1;
			margin-bottom: 0;
		}
		#toc ol,
		#toc li,
		#toc a {
			display: contents;
			/* Switch <a> to subgrid when supported */
		}
		#toc span {
			margin: 0;
		}
		#toc > .toc > li > a > span {
			/* The spans of the top-level list,
			  comprising the first items of each top-level section. */
			margin-top: 1.1rem;
		}
		#toc#toc .secno { /* Ugh, need more specificity to override base.css */
			grid-column: 1;
			width: auto;
			margin-left: 0;
		}
		#toc .content {
			grid-column: 2;
			width: auto;
			margin-right: 1rem;
			border-bottom: 3px solid transparent;
			margin-bottom: -3px;
		}
		#toc .content:hover,
		#toc .content:focus {
			background: rgba(75%, 75%, 75%, .25);
			background: var(--a-hover-bg);
			border-bottom-color: #054572;
			border-bottom-color: var(--toclink-underline);
		}
		#toc li li li .content {
			margin-left: 1rem;
		}
		#toc li li li li .content {
			margin-left: 2rem;
		}
	}


/** Index *********************************************************************/

	/* Index Lists: Layout */
	ul.index	  { margin-left: 0; columns: 15em; text-indent: 1em hanging; }
	ul.index li	{ margin-left: 0; list-style: none; break-inside: avoid; }
	ul.index li li { margin-left: 1em; }
	ul.index dl	{ margin-top: 0; }
	ul.index dt	{ margin: .2em 0 .2em 20px;}
	ul.index dd	{ margin: .2em 0 .2em 40px;}
	/* Index Lists: Typography */
	ul.index ul,
	ul.index dl { font-size: smaller; }
	@media not print {
		ul.index li a + span {
			white-space: nowrap;
			color: transparent; }
		ul.index li a:hover + span,
		ul.index li a:focus + span {
			color: #707070;
			color: var(--indexinfo-text);
		}
	}

/** Index Tables *****************************************************/
	/* See also the data table styling section, which this effectively subclasses */

	table.index {
		font-size: small;
		border-collapse: collapse;
		border-spacing: 0;
		text-align: left;
		margin: 1em 0;
	}

	table.index td,
	table.index th {
		padding: 0.4em;
	}

	table.index tr:hover td:not([rowspan]),
	table.index tr:hover th:not([rowspan]) {
		color: black;
		color: var(--indextable-hover-text);
		background: #f7f8f9;
		background: var(--indextable-hover-bg);
	}

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

/** Outdated warning **********************************************************/

.outdated-spec {
	color: black;
	color: var(--outdatedspec-text);
	background-color: rgba(0,0,0,0.5);
	background-color: var(--outdatedspec-bg);
}

.outdated-warning {
	position: fixed;
	bottom: 50%;
	left: 0;
	right: 0;
	margin: 0 auto;
	width: 50%;
	background: maroon;
	background: var(--outdated-bg);
	color: white;
	color: var(--outdated-text);
	border-radius: 1em;
	box-shadow: 0 0 1em red;
	box-shadow: 0 0 1em var(--outdated-shadow);
	padding: 2em;
	text-align: center;
	z-index: 2;
}

.outdated-warning a {
	color: currentcolor;
	background: transparent;
}

.edited-rec-warning {
	background: darkorange;
	background: var(--editedrec-bg);
	box-shadow: 0 0 1em;
}

.outdated-warning button {
	color: var(--outdated-text);
	border-radius: 1em;
	box-shadow: 0 0 1em red;
	box-shadow: 0 0 1em var(--outdated-shadow);
	padding: 2em;
	text-align: center;
	z-index: 2;
}

.outdated-warning a {
	color: currentcolor;
	background: transparent;
}

.edited-rec-warning {
	background: darkorange;
	background: var(--editedrec-bg);
	box-shadow: 0 0 1em;
}

.outdated-warning button {
	position: absolute;
	top: 0;
	right:0;
	margin: 0;
	border: 0;
	padding: 0.25em 0.5em;
	background: transparent;
	color: white;
	color: var(--outdated-text);
	font:1em sans-serif;
	text-align:center;
}

.outdated-warning span {
	display: block;
}

.outdated-collapsed {
	bottom: 0;
	border-radius: 0;
	width: 100%;
	padding: 0;
}

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

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

		.outdated-warning {
			position: absolute;
			border-style: solid;
			border-color: red;
		}

		.outdated-warning input {
			display: none;
		}
	}
	@page {
		margin: 1.5cm 1.1cm;
	}



/******************************************************************************/
/*                             Overflow Control                               */
/******************************************************************************/

	.figure .caption, .sidefigure .caption, figcaption {
		/* in case figure is overlarge, limit caption to 50em */
		max-width: 50rem;
		margin-left: auto;
		margin-right: auto;
	}
	.overlarge {
		/* Magic to create good item positioning:
		  "content column" is 50ems wide at max; less on smaller screens.
		  Extra space (after ToC + content) is empty on the right.

		  1. When item < content column, centers item in column.
		  2. When content < item < available, left-aligns.
		  3. When item > available, fills available + scroll bar.
		*/
		display: grid;
		grid-template-columns: minmax(0, 50em);
	}
	.overlarge > table {
		/* limit preferred width of table */
		max-width: 50em;
		margin-left: auto;
		margin-right: auto;
	}

	@media (min-width: 55em) {
		.overlarge {
			margin-right: calc(13px + 26.5rem - 50vw);
			max-width: none;
		}
	}
	@media screen and (min-width: 78em) {
		body:not(.toc-inline) .overlarge {
			/* 30.5em body padding 50em content area */
			margin-right: calc(40em - 50vw) !important;
		}
	}
	@media screen and (min-width: 90em) {
		body:not(.toc-inline) .overlarge {
			/* 4em html margin 30.5em body padding 50em content area */
			margin-right: calc(84.5em - 100vw) !important;
		}
	}

	@media not print {
		.overlarge {
			overflow-x: auto;
			/* See Lea Verou's explanation background-attachment:
			* http://lea.verou.me/2012/04/background-attachment-local/
			*
			background: top left  / 4em 100% linear-gradient(to right,  #ffffff, rgba(255, 255, 255, 0)) local,
						top right / 4em 100% linear-gradient(to left, #ffffff, rgba(255, 255, 255, 0)) local,
						top left  / 1em 100% linear-gradient(to right,  #c3c3c5, rgba(195, 195, 197, 0)) scroll,
						top right / 1em 100% linear-gradient(to left, #c3c3c5, rgba(195, 195, 197, 0)) scroll,
						white;
			background-repeat: no-repeat;
			*/
		}
	}
</style>
<style>
    table, th, td {
      border: 1px solid black;
      border-collapse: collapse;
      vertical-align: top;
    }
    th, td {
      border-left: none;
      border-right: none;
      padding: 0px 10px;
    }
    th {
      text-align: center;
    }

    del { background: #fcc; color: #000; text-decoration: line-through; }
    ins { background: #cfc; color: #000; }
    blockquote .highlight:not(.idl) { background: initial; margin: initial; padding: 0.5em }
    blockquote ul { background: inherit; }
    blockquote code.highlight:not(.idl) { padding: initial; }
    blockquote c-[a] { color: inherit; } /* Keyword.Declaration */
    blockquote c-[b] { color: inherit; } /* Keyword.Type */
    blockquote c-[c] { color: inherit; } /* Comment */
    blockquote c-[d] { color: inherit; } /* Comment.Multiline */
    blockquote c-[e] { color: inherit; } /* Name.Attribute */
    blockquote c-[f] { color: inherit; } /* Name.Tag */
    blockquote c-[g] { color: inherit; } /* Name.Variable */
    blockquote c-[k] { color: inherit; } /* Keyword */
    blockquote c-[l] { color: inherit; } /* Literal */
    blockquote c-[m] { color: inherit; } /* Literal.Number */
    blockquote c-[n] { color: inherit; } /* Name */
    blockquote c-[o] { color: inherit; } /* Operator */
    blockquote c-[p] { color: inherit; } /* Punctuation */
    blockquote c-[s] { color: inherit; } /* Literal.String */
    blockquote c-[t] { color: inherit; } /* Literal.String.Single */
    blockquote c-[u] { color: inherit; } /* Literal.String.Double */
    blockquote c-[cp] { color: inherit; } /* Comment.Preproc */
    blockquote c-[c1] { color: inherit; } /* Comment.Single */
    blockquote c-[cs] { color: inherit; } /* Comment.Special */
    blockquote c-[kc] { color: inherit; } /* Keyword.Constant */
    blockquote c-[kn] { color: inherit; } /* Keyword.Namespace */
    blockquote c-[kp] { color: inherit; } /* Keyword.Pseudo */
    blockquote c-[kr] { color: inherit; } /* Keyword.Reserved */
    blockquote c-[ld] { color: inherit; } /* Literal.Date */
    blockquote c-[nc] { color: inherit; } /* Name.Class */
    blockquote c-[no] { color: inherit; } /* Name.Constant */
    blockquote c-[nd] { color: inherit; } /* Name.Decorator */
    blockquote c-[ni] { color: inherit; } /* Name.Entity */
    blockquote c-[ne] { color: inherit; } /* Name.Exception */
    blockquote c-[nf] { color: inherit; } /* Name.Function */
    blockquote c-[nl] { color: inherit; } /* Name.Label */
    blockquote c-[nn] { color: inherit; } /* Name.Namespace */
    blockquote c-[py] { color: inherit; } /* Name.Property */
    blockquote c-[ow] { color: inherit; } /* Operator.Word */
    blockquote c-[mb] { color: inherit; } /* Literal.Number.Bin */
    blockquote c-[mf] { color: inherit; } /* Literal.Number.Float */
    blockquote c-[mh] { color: inherit; } /* Literal.Number.Hex */
    blockquote c-[mi] { color: inherit; } /* Literal.Number.Integer */
    blockquote c-[mo] { color: inherit; } /* Literal.Number.Oct */
    blockquote c-[sb] { color: inherit; } /* Literal.String.Backtick */
    blockquote c-[sc] { color: inherit; } /* Literal.String.Char */
    blockquote c-[sd] { color: inherit; } /* Literal.String.Doc */
    blockquote c-[se] { color: inherit; } /* Literal.String.Escape */
    blockquote c-[sh] { color: inherit; } /* Literal.String.Heredoc */
    blockquote c-[si] { color: inherit; } /* Literal.String.Interpol */
    blockquote c-[sx] { color: inherit; } /* Literal.String.Other */
    blockquote c-[sr] { color: inherit; } /* Literal.String.Regex */
    blockquote c-[ss] { color: inherit; } /* Literal.String.Symbol */
    blockquote c-[vc] { color: inherit; } /* Name.Variable.Class */
    blockquote c-[vg] { color: inherit; } /* Name.Variable.Global */
    blockquote c-[vi] { color: inherit; } /* Name.Variable.Instance */
    blockquote c-[il] { color: inherit; } /* Literal.Number.Integer.Long */
  </style>
  <meta content="Bikeshed version 4416b18d5, updated Tue Jan 2 15:52:39 2024 -0800" name="generator">
  <link href="https://isocpp.org/favicon.ico" rel="icon">
  <meta content="1576766b3a959373a751c6216b94bad8e0a53049" name="revision">
<style>/* Boilerplate: style-autolinks */
.css.css, .property.property, .descriptor.descriptor {
    color: var(--a-normal-text);
    font-size: inherit;
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   <h1 class="p-name no-ref" id="title">P3505R0<br>Fix the default floating-point representation in std::format</h1>
   <h2 class="no-num no-toc no-ref heading settled" id="profile-and-date"><span class="content">Published Proposal, <time class="dt-updated" datetime="2025-03-16">2025-03-16</time></span></h2>
   <div data-fill-with="spec-metadata">
    <dl>
     <dt class="editor">Authors:
     <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>
     <dd class="editor p-author h-card vcard"><a class="p-name fn u-email email" href="mailto:j6jeon@ucsd.edu">Junekey Jeon</a>
     <dt>Audience:
     <dd>LEWG
     <dt>Project:
     <dd>ISO/IEC 14882 Programming Languages — C++, ISO/IEC JTC1/SC22/WG21
    </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="#intro"><span class="secno">1</span> <span class="content">Introduction</span></a>
    <li><a href="#problem"><span class="secno">2</span> <span class="content">Problem</span></a>
    <li><a href="#proposal"><span class="secno">3</span> <span class="content">Proposal</span></a>
    <li><a href="#wording"><span class="secno">4</span> <span class="content">Wording</span></a>
    <li><a href="#impl"><span class="secno">5</span> <span class="content">Implementation and usage experience</span></a>
    <li><a href="#impact"><span class="secno">6</span> <span class="content">Impact on existing code</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"> "Is floating-point math broken?" - Cato Johnston (<a href="https://stackoverflow.com/q/588004/471164">Stack Overflow</a>) </p>
   <h2 class="heading settled" data-level="1" id="intro"><span class="secno">1. </span><span class="content">Introduction</span><a class="self-link" href="#intro"></a></h2>
   <p>When <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>format</c-></code> was proposed for standardization, floating-point formatting
was defined in terms of <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>to_chars</c-></code> to simplify specification. While being
a positive change overall, this introduced a small but undesirable change
compared to the design and reference implementation in <a data-link-type="biblio" href="#biblio-fmt" title="The {fmt} library">[FMT]</a>, resulting in
surprising behavior to users, performance regression and an inconsistency with
other mainstream programming languages that have similar facilities. This paper
proposes fixing this issue, bringing the floating-point formatting on par with
other languages and in line with the original design intent.</p>
   <h2 class="heading settled" data-level="2" id="problem"><span class="secno">2. </span><span class="content">Problem</span><a class="self-link" href="#problem"></a></h2>
   <p>Since Steele and White’s seminal paper (<a data-link-type="biblio" href="#biblio-steele-white" title="How to Print Floating-Point Numbers Accurately">[STEELE-WHITE]</a>), based on their work
in the 70s, many programming languages converged on similar default
representation of floating point numbers. The properties of an algorithm
that produces such a representation are formulated in the paper as follows:</p>
   <blockquote>
    <ul>
     <li data-md>
      <p>No information is lost; the original fraction can be recovered from the
output by rounding.</p>
     <li data-md>
      <p>No "garbage digits" are produced.</p>
     <li data-md>
      <p>The output is correctly rounded.</p>
     <li data-md>
      <p>It is never necessary to propagate carries on rounding.</p>
    </ul>
   </blockquote>
   <p>The second bullet point means
that the algorithm shouldn’t produce more decimal digits (in the significand)
than necessary to satisfy the other requirements, most importantly the
round-trip guarantee. For example, <code class="highlight"><c- mf>0.1</c-></code> should be formatted as <code class="highlight"><c- mf>0.1</c-></code> and not <code class="highlight"><c- mf>0.10000000000000001</c-></code> even though they produce the same value when read back
into an IEEE 754 <code class="highlight"><c- b>double</c-></code>.</p>
   <p>The last bullet point is more of an optimization for retro computers and is less
relevant on modern systems.</p>
   <p><a data-link-type="biblio" href="#biblio-steele-white" title="How to Print Floating-Point Numbers Accurately">[STEELE-WHITE]</a> and papers that followed referred to the second criteria as
"shortness" even though it only talks about the number of decimal digits in
the significand and ignores other properties such as the exponent and the
decimal point.</p>
   <p>Once such shortest decimal significand and the corresponding exponent are known
the formatting algorithm normally chooses between fixed and exponential
representation based on the value range. For example, in Python
(<a data-link-type="biblio" href="#biblio-python-format" title="The Python Standard Library, Format Specification Mini-Language">[PYTHON-FORMAT]</a>) and Rust (the <code class="highlight"><c- o>?</c-></code> format which gives the "shortest"
representation for FP numbers) if the decimal exponent is greater or equal to 16
for <code class="highlight"><c- b>double</c-></code>, the number is printed in the exponential format:</p>
<pre class="language-python highlight"><c- o>>>></c-> <c- mf>1234567890123456.0</c->
<c- mf>1234567890123456.0</c->
<c- o>>>></c-> <c- mf>12345678901234567.0</c->
<c- mf>1.2345678901234568e+16</c->
</pre>
   <p>16 is a reasonable threshold because IEEE 754 double precision can represent
most 16-digit decimal values with high fidelity, and it balances human
readability with precision retention when switching between fixed and
exponential notation.</p>
   <p><a data-link-type="biblio" href="#biblio-fmt" title="The {fmt} library">[FMT]</a>, which is modeled after Python’s formatting facility, adopted a similar
representation based on the exponent range.</p>
   <p>Swift has similar logic, switching to exponential notation for numbers greater
or equal to 2<sup>53</sup> (9007199254740992). This is also a reasonable choice
although a threshold that is not a power of 10 might be less intuitive to some
users.</p>
   <p>Similarly, languages normally switch from fixed to exponential notation when
the absolute value is smaller than some small decimal power of 10, usually
10<sup>-3</sup> (<a data-link-type="biblio" href="#biblio-java-double" title="Java™ Platform, Standard Edition 8 API Specification, Class Double, toString">[JAVA-DOUBLE]</a>) or 10<sup>-4</sup> (Python, Rust, Swift).</p>
   <p>When <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>format</c-></code> was proposed for standardization, floating-point formatting
was defined in terms of <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>to_chars</c-></code> to simplify specification with the
assumption that the latter follows the industry practice for the default format
described above. It was great for explicit format specifiers such as <code class="highlight"><c- n>e</c-></code> but,
as it turned out recently, it introduced an undesirable change to the default
format. This problem is that <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>to_chars</c-></code> defines "shortness" in terms of the
number of characters in the output which is different from the "shortness" of
decimal significand normally used both in the literature and in the industry.</p>
   <p>The exponent range is much easier to reason about. For example, in this model <code class="highlight"><c- mf>100000.0</c-></code> and <code class="highlight"><c- mf>120000.0</c-></code> are printed in the same format:</p>
<pre class="language-python highlight"><c- o>>>></c-> <c- mf>100000.0</c->
<c- mf>100000.0</c->
<c- o>>>></c-> <c- mf>120000.0</c->
<c- mf>120000.0</c->
</pre>
   <p>However, if we consider the output size the two similar numbers are now printed
completely differently:</p>
<pre class="language-c++ highlight"><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>"{}"</c-><c- p>,</c-> <c- mf>100000.0</c-><c- p>);</c->  <c- c1>// s1 == "1e+05"</c->
<c- k>auto</c-> <c- n>s2</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- mf>120000.0</c-><c- p>);</c->  <c- c1>// s2 == "120000"</c->
</pre>
   <p>It seems surprising and undesirable.</p>
   <p>Note that the output <code class="highlight"><c- mf>1e+05</c-></code> is not really of the shortest possible number of
characters, because + and the leading zero in the exponent are redundant.
In fact, those are required, according to the specification of <code class="highlight"><c- n>to_chars</c-></code> (<a href="https://eel.is/c++draft/charconv.to.chars">[charconv.to.chars</a>]),</p>
   <blockquote>
    <p><code class="highlight"><c- n>value</c-></code> is converted to a string in the style of <code class="highlight"><c- n>printf</c-></code> in the <code class="highlight"><c- s>"C"</c-></code> locale.</p>
   </blockquote>
   <p>and the exponential format is defined as follows by the C standard (<a data-link-type="biblio" href="#biblio-n3220" title="ISO/IEC 9899:2024. Information technology — Programming languages — C. 7.23.6 Formatted input/output functions">[N3220]</a>):</p>
   <blockquote>
    <p>A <code class="highlight"><c- b>double</c-></code> argument representing a floating-point number is converted in the
style <em>[−]d.ddd e±dd</em> ...</p>
   </blockquote>
   <p>Nevertheless, users interpreting the shortness condition too literally may find
this surprising.</p>
   <p>Even more importantly, the current representation violates the original
shortness requirement from <a data-link-type="biblio" href="#biblio-steele-white" title="How to Print Floating-Point Numbers Accurately">[STEELE-WHITE]</a>:</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>"{}"</c-><c- p>,</c-> <c- mf>1234567890123456700000.0</c-><c- p>);</c->
<c- c1>// s == "1234567890123456774144"</c->
</pre>
   <p>The last 5 digits, <code class="highlight"><c- mi>74144</c-></code>, are what Steele and White referred to as "garbage
digits" that almost no modern formatting facilities produce by default.
For example, Python avoids it by switching to the exponential format as one
would expect:</p>
<pre class="language-python highlight"><c- o>>>></c-> <c- mf>12345678901234567800000.0</c->
<c- mf>1.2345678901234568e+22</c->
</pre>
   <p>The current behavior is a consequence of the shortness-in-characters criterion
favoring the fixed format for large numbers while still satisfying the correct
rounding condition
((<a href="https://eel.is/c++draft/charconv.to.chars">[charconv.to.chars</a>])):</p>
   <blockquote>
    <p>If there are several such representations, the representation with the
smallest difference from the floating-point argument value is chosen,
resolving any remaining ties using rounding according to <code class="highlight"><c- n>round_to_nearest</c-></code> (<a href="https://eel.is/c++draft/round.style">[round.style</a>]).</p>
   </blockquote>
   <p>Apart from giving a false sense of accuracy to users it also has negative
performance implications. Many of the optimized float-to-string algorithms
based on Steele and White’s criteria, such as Dragonbox (<a data-link-type="biblio" href="#biblio-dragonbox" title="Dragonbox: A New Floating-Point Binary-to-Decimal Conversion Algorithm">[DRAGONBOX]</a>) and
Ryū (<a data-link-type="biblio" href="#biblio-ryu" title="Ryū: fast float-to-string conversion">[RYU]</a>), only focus on those criteria, especially the shortness of
decimal significand rather than the number of characters. As a result, an
implementation of the default floating-point handling of <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>format</c-></code> (and <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>to_chars</c-></code>) cannot just directly rely on these otherwise perfectly
appropriate algorithms. Instead, it has to introduce non-trivial logic
dedicated for computing these "garbage digits". Furthermore, having to
introduce dedicated logic is likely not just because of the lack of advancement
in the algorithm research, because in this case we do need to compute more
digits than the actual precision implied by the data type, thus it is natural
to expect that we may need more precision than the case without garbage digits.
(In other words, even though a new algorithm that correctly deals with this
garbage digits case according to the current C++ standard is invented, it is
likely that it still includes some special handling of that case, in one form
or another.)</p>
   <p>The performance issue can be illustrated on the following simple benchmark:</p>
<pre class="language-c++ highlight"><c- cp>#include</c-> &lt;format>
<c- cp>#include</c-> &lt;benchmark/benchmark.h>

<c- c1>// Output: "1.2345678901234568e+22"</c->
<c- b>double</c-> <c- n>normal_input</c->  <c- o>=</c-> <c- mf>12345678901234567000000.0</c-><c- p>;</c->

<c- c1>// Output (current): "1234567890123456774144"</c->
<c- c1>// Output (desired): "1.2345678901234568e+21"</c->
<c- b>double</c-> <c- n>garbage_input</c-> <c- o>=</c-> <c- mf>1234567890123456700000.0</c-><c- p>;</c->

<c- b>void</c-> <c- nf>normal</c-><c- p>(</c-><c- n>benchmark</c-><c- o>::</c-><c- n>State</c-><c- o>&amp;</c-> <c- n>state</c-><c- p>)</c-> <c- p>{</c->
  <c- k>for</c-> <c- p>(</c-><c- k>auto</c-> <c- n>s</c-> <c- o>:</c-> <c- n>state</c-><c- p>)</c-> <c- p>{</c->
    <c- k>auto</c-> <c- n>result</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- n>normal_input</c-><c- p>);</c->
    <c- n>benchmark</c-><c- o>::</c-><c- n>DoNotOptimize</c-><c- p>(</c-><c- n>result</c-><c- p>);</c->
  <c- p>}</c->
<c- p>}</c->
<c- n>BENCHMARK</c-><c- p>(</c-><c- n>normal</c-><c- p>);</c->

<c- b>void</c-> <c- nf>garbage</c-><c- p>(</c-><c- n>benchmark</c-><c- o>::</c-><c- n>State</c-><c- o>&amp;</c-> <c- n>state</c-><c- p>)</c-> <c- p>{</c->
  <c- k>for</c-> <c- p>(</c-><c- k>auto</c-> <c- n>s</c-> <c- o>:</c-> <c- n>state</c-><c- p>)</c-> <c- p>{</c->
    <c- k>auto</c-> <c- n>result</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- n>garbage_input</c-><c- p>);</c->
    <c- n>benchmark</c-><c- o>::</c-><c- n>DoNotOptimize</c-><c- p>(</c-><c- n>result</c-><c- p>);</c->
  <c- p>}</c->
<c- p>}</c->
<c- n>BENCHMARK</c-><c- p>(</c-><c- n>garbage</c-><c- p>);</c->

<c- n>BENCHMARK_MAIN</c-><c- p>();</c->
</pre>
   <p>Results on macOS with Apple clang version 16.0.0 (clang-1600.0.26.6) and libc++:</p>
<pre class="language-text highlight">% ./double-benchmark
Unable to determine clock rate from sysctl: hw.cpufrequency: No such file or directory
This does not affect benchmark measurements, only the metadata output.
***WARNING*** Failed to set thread affinity. Estimated CPU frequency may be incorrect.
2025-02-02T08:06:13-08:00
Running ./double-benchmark
Run on (8 X 24 MHz CPU s)
CPU Caches:
  L1 Data 64 KiB
  L1 Instruction 128 KiB
  L2 Unified 4096 KiB (x8)
Load Average: 7.61, 5.78, 5.16
-----------------------------------------------------
Benchmark           Time             CPU   Iterations
-----------------------------------------------------
normal           77.5 ns         77.5 ns      9040424
garbage          91.4 ns         91.4 ns      7675186
</pre>
   <p>Results on GNU/Linux with gcc (Ubuntu 13.3.0-6ubuntu2~24.04) 13.3.0 and
libstdc++:</p>
<pre class="language-text highlight">$ ./double-benchmark
2025-02-02T17:22:25+00:00
Running ./double-benchmark
Run on (2 X 48 MHz CPU s)
CPU Caches:
  L1 Data 128 KiB (x2)
  L1 Instruction 192 KiB (x2)
  L2 Unified 12288 KiB (x2)
Load Average: 0.25, 0.10, 0.02
-----------------------------------------------------
Benchmark           Time             CPU   Iterations
-----------------------------------------------------
normal           73.1 ns         73.1 ns      9441284
garbage          90.6 ns         90.6 ns      7360351
</pre>
   <p>Results on Windows with Microsoft (R) C/C++ Optimizing Compiler Version
19.40.33811 for ARM64 and Microsoft STL:</p>
<pre class="language-text highlight">>double-benchmark.exe
2025-02-02T08:10:39-08:00
Running double-benchmark.exe
Run on (2 X 2000 MHz CPU s)
CPU Caches:
  L1 Instruction 192 KiB (x2)
  L1 Data 128 KiB (x2)
  L2 Unified 12288 KiB (x2)
-----------------------------------------------------
Benchmark           Time             CPU   Iterations
-----------------------------------------------------
normal            144 ns          143 ns      4480000
garbage           166 ns          165 ns      4072727
</pre>
   <p>Although the output has the same size, producing "garbage digits" makes <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>format</c-></code> 15-24% slower on these inputs. If we exclude string construction
time, the difference will be even more profound. For example, profiling the
benchmark on macOS shows that the <code class="highlight"><c- n>to_chars</c-></code> call itself is more than 50% (!)
slower:</p>
<pre class="highlight"><c- n>garbage</c-><c- p>(</c-><c- n>benchmark</c-><c- o>::</c-><c- n>State</c-><c- o>&amp;</c-><c- p>)</c-><c- o>:</c->
<c- mf>241.00</c-> <c- n>ms</c-> <c- p>...</c-> <c- n>std</c-><c- o>::</c-><c- n>__1</c-><c- o>::</c-><c- n>to_chars_result</c-> <c- n>std</c-><c- o>::</c-><c- n>__1</c-><c- o>::</c-><c- n>_Floating_to_chars</c-><c- p>[</c-><c- n>abi</c-><c- o>:</c-><c- n>ne180100</c-><c- p>]</c-><c- o>&lt;</c-><c- p>...</c-><c- o>></c-><c- p>(</c-><c- b>char</c-><c- o>*</c-><c- p>,</c-> <c- b>char</c-><c- o>*</c-><c- p>,</c-> <c- b>double</c-><c- p>,</c-> <c- n>std</c-><c- o>::</c-><c- n>__1</c-><c- o>::</c-><c- n>chars_format</c-><c- p>,</c-> <c- b>int</c-><c- p>)</c->
<c- n>normal</c-><c- p>(</c-><c- n>benchmark</c-><c- o>::</c-><c- n>State</c-><c- o>&amp;</c-><c- p>)</c-><c- o>:</c->
<c- mf>159.00</c-> <c- n>ms</c-> <c- p>...</c-> <c- n>std</c-><c- o>::</c-><c- n>__1</c-><c- o>::</c-><c- n>to_chars_result</c-> <c- n>std</c-><c- o>::</c-><c- n>__1</c-><c- o>::</c-><c- n>_Floating_to_chars</c-><c- p>[</c-><c- n>abi</c-><c- o>:</c-><c- n>ne180100</c-><c- p>]</c-><c- o>&lt;</c-><c- p>...</c-><c- o>></c-><c- p>(</c-><c- b>char</c-><c- o>*</c-><c- p>,</c-> <c- b>char</c-><c- o>*</c-><c- p>,</c-> <c- b>double</c-><c- p>,</c-> <c- n>std</c-><c- o>::</c-><c- n>__1</c-><c- o>::</c-><c- n>chars_format</c-><c- p>,</c-> <c- b>int</c-><c- p>)</c->
</pre>
   <p>For comparison here are the results of running the same benchmark with <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>format</c-></code> replaced with <code class="highlight"><c- n>fmt</c-><c- o>::</c-><c- n>format</c-></code> which doesn’t produce "garbage
digits":</p>
<pre class="language-text highlight">$ ./double-benchmark
Unable to determine clock rate from sysctl: hw.cpufrequency: No such file or directory
This does not affect benchmark measurements, only the metadata output.
***WARNING*** Failed to set thread affinity. Estimated CPU frequency may be incorrect.
2025-03-15T08:18:56-07:00
Running ./double-benchmark
Run on (8 X 24 MHz CPU s)
CPU Caches:
  L1 Data 64 KiB
  L1 Instruction 128 KiB
  L2 Unified 4096 KiB (x8)
Load Average: 3.00, 3.91, 4.85
------------------------------------------------------
Benchmark            Time             CPU   Iterations
------------------------------------------------------
fmt_normal        53.0 ns         53.0 ns     13428484
fmt_garbage       53.4 ns         53.4 ns     13032712
</pre>
   <p>As expected, the time is nearly identical between the two cases. It demonstrates
that the performance gap can be eliminated if this paper is accepted.</p>
   <p>Locale makes the situation even more confusing to users. Consider the following
example:</p>
<pre class="language-c++ highlight"><c- n>std</c-><c- o>::</c-><c- n>locale</c-><c- o>::</c-><c- n>global</c-><c- p>(</c-><c- n>std</c-><c- o>::</c-><c- n>locale</c-><c- p>(</c-><c- s>"en_US.UTF-8"</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>"{:L}"</c-><c- p>,</c-> <c- mf>1200000.0</c-><c- p>);</c->  <c- c1>// s == "1,200,000"</c->
</pre>
   <p>Here <code class="highlight"><c- n>s</c-></code> is <code class="highlight"><c- s>"1,200,000"</c-></code> even though <code class="highlight"><c- s>"1.2e+06"</c-></code> would be shorter.</p>
   <h2 class="heading settled" data-level="3" id="proposal"><span class="secno">3. </span><span class="content">Proposal</span><a class="self-link" href="#proposal"></a></h2>
   <p>The current paper proposes fixing the default floating-point representation in <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>format</c-></code> to use exponent range, fixing the issues described above.</p>
   <p>Consistent, easy to reason about output format:</p>
   <table>
    <tbody>
     <tr>
      <th>Code 
      <th>Before 
      <th>After 
     <tr>
      <td>
<pre class="highlight"><c- n>std</c-><c- o>::</c-><c- n>format</c-><c- p>(</c-><c- s>"{}"</c-><c- p>,</c-> <c- mf>100000.0</c-><c- p>)</c->
</pre>
      <td>
<pre class="highlight"><c- s>"1e+05"</c->
</pre>
      <td>
<pre class="highlight"><c- s>"100000"</c->
</pre>
     <tr>
      <td>
<pre class="highlight"><c- n>std</c-><c- o>::</c-><c- n>format</c-><c- p>(</c-><c- s>"{}"</c-><c- p>,</c-> <c- mf>120000.0</c-><c- p>)</c->
</pre>
      <td>
<pre class="highlight"><c- s>"120000"</c->
</pre>
      <td>
<pre class="highlight"><c- s>"120000"</c->
</pre>
   </table>
   <p>No "garbage digits":</p>
   <table>
    <tbody>
     <tr>
      <th>Code 
      <th>Before 
      <th>After 
     <tr>
      <td>
<pre class="highlight"><c- n>std</c-><c- o>::</c-><c- n>format</c-><c- p>(</c-><c- s>"{}"</c-><c- p>,</c-> <c- mf>1234567890123456700000.0</c-><c- p>)</c->
</pre>
      <td>
<pre class="highlight"><c- s>"1234567890123456774144"</c->
</pre>
      <td>
<pre class="highlight"><c- s>"1.2345678901234568e+22"</c->
</pre>
   </table>
   <p>Consistent localized output (assuming <code class="highlight">en_US.UTF-8</code> locale):</p>
   <table>
    <tbody>
     <tr>
      <th>Code 
      <th>Before 
      <th>After 
     <tr>
      <td>
<pre class="highlight"><c- n>std</c-><c- o>::</c-><c- n>format</c-><c- p>(</c-><c- s>"{:L}"</c-><c- p>,</c-> <c- mf>1000000.0</c-><c- p>)</c->
</pre>
      <td>
<pre class="highlight"><c- s>"1e+06"</c->
</pre>
      <td>
<pre class="highlight"><c- s>"1,000,000"</c->
</pre>
     <tr>
      <td>
<pre class="highlight"><c- n>std</c-><c- o>::</c-><c- n>format</c-><c- p>(</c-><c- s>"{:L}"</c-><c- p>,</c-> <c- mf>1200000.0</c-><c- p>)</c->
</pre>
      <td>
<pre class="highlight"><c- s>"1,200,000"</c->
</pre>
      <td>
<pre class="highlight"><c- s>"1,200,000"</c->
</pre>
   </table>
   <h2 class="heading settled" data-level="4" id="wording"><span class="secno">4. </span><span class="content">Wording</span><a class="self-link" href="#wording"></a></h2>
   <p>Modify <a href="https://eel.is/c++draft/format.string.std">[format.string.std</a>]:</p>
   <p>Table 105 — Meaning of type options for floating-point types <a href="https://eel.is/c++draft/format.string.std">[tab:format.type.float</a>]</p>
   <table>
    <tbody>
     <tr>
      <td><strong>Type</strong> 
      <td><strong>Meaning</strong> 
     <tr>
      <td><code class="highlight"><c- n>a</c-></code> 
      <td>
        If <em>precision</em> is specified, equivalent to 
<pre 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>hex</c-><c- p>,</c-> <c- n>precision</c-><c- p>)</c->
</pre>
       <p>where <code class="highlight"><c- n>precision</c-></code> is the specified formatting precision; equivalent to</p>
<pre 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>hex</c-><c- p>)</c->
</pre>
       <p>otherwise.</p>
     <tr>
      <td>... 
      <td>... 
     <tr>
      <td><code class="highlight"><c- n>G</c-></code> 
      <td>The same as <code class="highlight"><c- n>g</c-></code>, except that it uses <code class="highlight"><c- n>E</c-></code> to indicate exponent. 
     <tr>
      <td>none 
      <td>
       <ins>Let <code class="highlight"><c- n>fmt</c-></code> be <code class="highlight"><c- n>chars_format</c-><c- o>::</c-><c- n>fixed</c-></code> if <code class="highlight"><c- n>value</c-></code> is in the range [10<sup>-4</sup>, 10<sup><i>n</i></sup>), where
    10<sup><i>n</i></sup> is
    2<sup><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>numeric_limits</c-><c- o>&lt;</c-><c- k>decltype</c-><c- p>(</c-><c- n>value</c-><c- p>)</c-><c- o>>::</c-><c- n>digits</c-></code> + 1</sup> rounded down to the nearest power of 10, <code class="highlight"><c- n>chars_format</c-><c- o>::</c-><c- n>scientific</c-></code> otherwise. </ins>
       <p>If <em>precision</em> is specified, equivalent to</p>
<pre 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->
</pre>
       <p>where <code class="highlight"><c- n>precision</c-></code> is the specified formatting precision; equivalent to</p>
<pre 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-><ins><c- p>,</c-> <c- n>fmt</c-></ins><c- p>)</c->
</pre>
       <p>otherwise.</p>
   </table>
   <h2 class="heading settled" data-level="5" id="impl"><span class="secno">5. </span><span class="content">Implementation and usage experience</span><a class="self-link" href="#impl"></a></h2>
   <p>The current proposal is based on the existing implementation in <a data-link-type="biblio" href="#biblio-fmt" title="The {fmt} library">[FMT]</a> which
has been available and widely used for over 6 years. Similar logic based on the
value range rather than the output size is implemented in Python, Java,
JavaScript, Rust and Swift.</p>
   <h2 class="heading settled" data-level="6" id="impact"><span class="secno">6. </span><span class="content">Impact on existing code</span><a class="self-link" href="#impact"></a></h2>
   <p>This is technically a breaking change for users who rely on the exact
output that is being changed. However, the change doesn’t affect ABI or round
trip guarantees. Also reliance on the exact representation of floating-point
numbers is usually discouraged so the impact of this change is likely moderate.
In the past we had experience with changing the output format in <a data-link-type="biblio" href="#biblio-fmt" title="The {fmt} library">[FMT]</a>, usage
of which is currently at least an order of magnitude higher than that of <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>format</c-></code>.</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-dragonbox">[DRAGONBOX]
   <dd>Junekey Jeon. <a href="https://github.com/jk-jeon/dragonbox/blob/master/other_files/Dragonbox.pdf"><cite>Dragonbox: A New Floating-Point Binary-to-Decimal Conversion Algorithm</cite></a>. URL: <a href="https://github.com/jk-jeon/dragonbox/blob/master/other_files/Dragonbox.pdf">https://github.com/jk-jeon/dragonbox/blob/master/other_files/Dragonbox.pdf</a>
   <dt id="biblio-fmt">[FMT]
   <dd>Victor Zverovich; et al. <a href="https://github.com/fmtlib/fmt"><cite>The {fmt} library</cite></a>. URL: <a href="https://github.com/fmtlib/fmt">https://github.com/fmtlib/fmt</a>
   <dt id="biblio-java-double">[JAVA-DOUBLE]
   <dd><a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Double.html#toString-double-"><cite>Java™ Platform, Standard Edition 8 API Specification, Class Double, toString</cite></a>. URL: <a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Double.html#toString-double-">https://docs.oracle.com/javase/8/docs/api/java/lang/Double.html#toString-double-</a>
   <dt id="biblio-n3220">[N3220]
   <dd>JeanHeyd Meneide; Freek Wiedijk; et al. <a href="https://www.open-std.org/jtc1/sc22/wg14/www/docs/n3220.pdf#page=346"><cite>ISO/IEC 9899:2024. Information technology — Programming languages — C. 7.23.6 Formatted input/output functions</cite></a>. URL: <a href="https://www.open-std.org/jtc1/sc22/wg14/www/docs/n3220.pdf#page=346">https://www.open-std.org/jtc1/sc22/wg14/www/docs/n3220.pdf#page=346</a>
   <dt id="biblio-python-format">[PYTHON-FORMAT]
   <dd><a href="https://docs.python.org/3/library/string.html#format-specification-mini-language"><cite>The Python Standard Library, Format Specification Mini-Language</cite></a>. URL: <a href="https://docs.python.org/3/library/string.html#format-specification-mini-language">https://docs.python.org/3/library/string.html#format-specification-mini-language</a>
   <dt id="biblio-ryu">[RYU]
   <dd>Ulf Adams. <a href="https://dl.acm.org/doi/10.1145/3192366.3192369"><cite>Ryū: fast float-to-string conversion</cite></a>. 2018. URL: <a href="https://dl.acm.org/doi/10.1145/3192366.3192369">https://dl.acm.org/doi/10.1145/3192366.3192369</a>
   <dt id="biblio-steele-white">[STEELE-WHITE]
   <dd>Guy L. Steele Jr.; Jon L White. <cite>How to Print Floating-Point Numbers Accurately</cite>. 1990. 
  </dl>