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  <title>P2197R0: Formatting for std::complex</title>
<style data-fill-with="stylesheet">/******************************************************************************
 *                   Style sheet for the W3C specifications                   *
 *
 * Special classes handled by this style sheet include:
 *
 * Indices
 *   - .toc for the Table of Contents (<ol class="toc">)
 *     + <span class="secno"> for the section numbers
 *   - #toc for the Table of Contents (<nav id="toc">)
 *   - ul.index for Indices (<a href="#ref">term</a><span>, in §N.M</span>)
 *   - table.index for Index Tables (e.g. for properties or elements)
 *
 * Structural Markup
 *   - table.data for general data tables
 *     -> use 'scope' attribute, <colgroup>, <thead>, and <tbody> for best results !
 *     -> use <table class='complex data'> for extra-complex tables
 *     -> use <td class='long'> for paragraph-length cell content
 *     -> use <td class='pre'> when manual line breaks/indentation would help readability
 *   - dl.switch for switch statements
 *   - ol.algorithm for algorithms (helps to visualize nesting)
 *   - .figure and .caption (HTML4) and figure and figcaption (HTML5)
 *     -> .sidefigure for right-floated figures
 *   - ins/del
 *
 * Code
 *   - pre and code
 *
 * Special Sections
 *   - .note       for informative notes             (div, p, span, aside, details)
 *   - .example    for informative examples          (div, p, pre, span)
 *   - .issue      for issues                        (div, p, span)
 *   - .assertion  for assertions                    (div, p, span)
 *   - .advisement for loud normative statements     (div, p, strong)
 *   - .annoying-warning for spec obsoletion notices (div, aside, details)
 *
 * Definition Boxes
 *   - pre.def   for WebIDL definitions
 *   - table.def for tables that define other entities (e.g. CSS properties)
 *   - dl.def    for definition lists that define other entitles (e.g. HTML elements)
 *
 * Numbering
 *   - .secno for section numbers in .toc and headings (<span class='secno'>3.2</span>)
 *   - .marker for source-inserted example/figure/issue numbers (<span class='marker'>Issue 4</span>)
 *   - ::before styled for CSS-generated issue/example/figure numbers:
 *     -> Documents wishing to use this only need to add
 *        figcaption::before,
 *        .caption::before { content: "Figure "  counter(figure) " ";  }
 *        .example::before { content: "Example " counter(example) " "; }
 *        .issue::before   { content: "Issue "   counter(issue) " ";   }
 *
 * Header Stuff (ignore, just don't conflict with these classes)
 *   - .head for the header
 *   - .copyright for the copyright
 *
 * Miscellaneous
 *   - .overlarge for things that should be as wide as possible, even if
 *     that overflows the body text area. This can be used on an item or
 *     on its container, depending on the effect desired.
 *     Note that this styling basically doesn't help at all when printing,
 *     since A4 paper isn't much wider than the max-width here.
 *     It's better to design things to fit into a narrower measure if possible.
 *   - js-added ToC jump links (see fixup.js)
 *
 ******************************************************************************/

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

	body {
		counter-reset: example figure issue;

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

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

		/* Colors */
		color: black;
		background: white top left fixed no-repeat;
		background-size: 25px auto;
	}


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

			background: white;
			box-shadow: 0 0 2px;
			border: none;
			border-top-right-radius: 1.33em;
			background: white;
		}
		#toc-nav > #toc-jump {
			padding-bottom: 2em;
			margin-bottom: -1.9em;
		}

		#toc-nav > a:hover,
		#toc-nav > a:focus {
			background: #f8f8f8;
		}
		#toc-nav > a:not(:hover):not(:focus) {
			color: #707070;
		}

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

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

		#toc-toggle-inline {
			vertical-align: 0.05em;
			font-size: 80%;
			color: gray;
			color: hsla(203,20%,40%,.7);
			border-style: none;
			background: transparent;
			position: relative;
		}
		#toc-toggle-inline:hover:not(:active),
		#toc-toggle-inline:focus:not(:active) {
			text-shadow: 1px 1px silver;
			top: -1px;
			left: -1px;
		}

		#toc-nav :active {
			color: #C00;
		}
	}

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

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

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

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

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

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

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

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

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

	h1, h2, h3 {
		color: #005A9C;
		background: transparent;
	}

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

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

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

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

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

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

	p {
		margin: 1em 0;
	}

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

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

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

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

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

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

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

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

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


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

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

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

	del { color: red;  text-decoration: line-through; }
	ins { color: #080; text-decoration: underline;    }

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

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

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

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

	pre, code, samp {
		font-family: Menlo, Consolas, "DejaVu Sans Mono", Monaco, monospace;
		font-size: .9em;
		page-break-inside: avoid;
		hyphens: none;
		text-transform: none;
	}
	pre code,
	code code {
		font-size: 100%;
	}

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

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

  /* Do something nice. */

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

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

	/* We hyperlink a lot, so make it less intrusive */
	a[href] {
		color: #034575;
		text-decoration: none;
		border-bottom: 1px solid #707070;
		/* Need a bit of extending for it to look okay */
		padding: 0 1px 0;
		margin: 0 -1px 0;
	}
	a:visited {
		border-bottom-color: #BBB;
	}

	/* Use distinguishing colors when user is interacting with the link */
	a[href]:focus,
	a[href]:hover {
		background: #f8f8f8;
		background: rgba(75%, 75%, 75%, .25);
		border-bottom-width: 3px;
		margin-bottom: -2px;
	}
	a[href]:active {
		color: #C00;
		border-color: #C00;
	}

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

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

	img {
		border-style: none;
	}

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

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

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

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

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

	.issue,
	.note,
	.example,
	.advisement,
	.assertion,
	blockquote {
		margin: 1em auto;
	}
	.note  > p:first-child,
	.issue > p:first-child,
	blockquote > :first-child {
		margin-top: 0;
	}
	blockquote > :last-child {
		margin-bottom: 0;
	}

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

	blockquote {
		border-color: silver;
	}

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

	.issue {
		border-color: #E05252;
		background: #FBE9E9;
		counter-increment: issue;
		overflow: auto;
	}
	.issue::before, .issue > .marker {
		text-transform: uppercase;
		color: #AE1E1E;
		padding-right: 1em;
		text-transform: uppercase;
	}
	/* Add .issue::before { content: "Issue " counter(issue) " "; } for autogen numbers,
	   or use class="marker" to mark up the issue number in source. */

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

	.example {
		border-color: #E0CB52;
		background: #FCFAEE;
		counter-increment: example;
		overflow: auto;
		clear: both;
	}
	.example::before, .example > .marker {
		text-transform: uppercase;
		color: #827017;
		min-width: 7.5em;
		display: block;
	}
	/* Add .example::before { content: "Example " counter(example) " "; } for autogen numbers,
	   or use class="marker" to mark up the example number in source. */

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

	.note {
		border-color: #52E052;
		background: #E9FBE9;
		overflow: auto;
	}

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

	details.note > summary {
		display: block;
		color: hsl(120, 70%, 30%);
	}
	details.note[open] > summary {
		border-bottom: 1px silver solid;
	}

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

	.assertion {
		border-color: #AAA;
		background: #EEE;
	}

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

	.advisement {
		border-color: orange;
		border-style: none solid;
		background: #FFEECC;
	}
	strong.advisement {
		display: block;
		text-align: center;
	}
	.advisement > .marker {
		color: #B35F00;
	}

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

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

	.annoying-warning:not(details),
	details.annoying-warning:not([open]) > summary,
	details.annoying-warning[open] {
		background: #fdd;
		color: red;
		font-weight: bold;
		padding: .75em 1em;
		border: thick red;
		border-style: solid;
		border-radius: 1em;
	}
	.annoying-warning :last-child {
		margin-bottom: 0;
	}

@media not print {
	details.annoying-warning[open] {
		position: fixed;
		left: 1em;
		right: 1em;
		bottom: 1em;
		z-index: 1000;
	}
}

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

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

	.def {
		padding: .5em 1em;
		background: #DEF;
		margin: 1.2em 0;
		border-left: 0.5em solid #8CCBF2;
	}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

	table.data  thead,
	table.index thead,
	table.data  tbody,
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 <body class="h-entry">
  <div class="head">
   <p data-fill-with="logo"></p>
   <h1 class="p-name no-ref" id="title">P2197R0<br>Formatting for std::complex</h1>
   <h2 class="no-num no-toc no-ref heading settled" id="subtitle"><span class="content">Working Draft, <time class="dt-updated" datetime="2019-12-22">2019-12-22</time></span></h2>
   <div data-fill-with="spec-metadata">
    <dl>
     <dt>This version:
     <dd><a class="u-url" href="http://fmt.dev/papers/p2197r0.html">http://fmt.dev/papers/p2197r0.html</a>
     <dt>Authors:
     <dd>
      <dd class="editor p-author h-card vcard"><a class="p-name fn u-email email" href="mailto:tesch1@gmail.com">Michael Tesch</a>
     <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>
  <div class="p-summary" data-fill-with="abstract">
   <h2 class="no-num no-toc no-ref heading settled" id="abstract"><span class="content">Abstract</span></h2>
   <p>This paper discusses extending coverage of the formatting

  functionality of <a data-link-type="biblio" href="#biblio-p0645">[P0645]</a> to <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>complex</c-></code>.</p>
  </div>
  <nav data-fill-with="table-of-contents" id="toc">
   <h2 class="no-num no-toc no-ref" id="contents">Table of Contents</h2>
   <ol class="toc" role="directory">
    <li><a href="#introduction"><span class="secno">1</span> <span class="content">Introduction</span></a>
    <li><a href="#examples"><span class="secno">2</span> <span class="content">Examples</span></a>
    <li><a href="#motivation"><span class="secno">3</span> <span class="content">Motivation</span></a>
    <li>
     <a href="#design-considerations"><span class="secno">4</span> <span class="content">Design Considerations</span></a>
     <ol class="toc">
      <li><a href="#numeric-form"><span class="secno">4.1</span> <span class="content">Numeric form</span></a>
      <li><a href="#imaginary"><span class="secno">4.2</span> <span class="content">Imaginary unit</span></a>
      <li><a href="#omission"><span class="secno">4.3</span> <span class="content">Omission of a part</span></a>
     </ol>
    <li><a href="#parentheses"><span class="secno">5</span> <span class="content">Parentheses</span></a>
    <li><a href="#backwards-compat"><span class="secno">6</span> <span class="content">Backwards Compatibility</span></a>
    <li><a href="#parsing"><span class="secno">7</span> <span class="content">Parsing</span></a>
    <li><a href="#survey"><span class="secno">8</span> <span class="content">Survey of other languages</span></a>
    <li><a href="#wish-list"><span class="secno">9</span> <span class="content">Wish List</span></a>
    <li><a href="#proposed-wording"><span class="secno">10</span> <span class="content">Proposed Wording</span></a>
    <li><a href="#questions"><span class="secno">11</span> <span class="content">Questions</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>
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<script async id="MathJax-script" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
   <h2 class="heading settled" data-level="1" id="introduction"><span class="secno">1. </span><span class="content">Introduction</span><a class="self-link" href="#introduction"></a></h2>
   <p><a data-link-type="biblio" href="#biblio-p0645">[P0645]</a> has proposed a text formatting facility that provides a safe
and extensible alternative to the <code class="highlight"><c- n>printf</c-></code> family of functions. This
paper explores how to format complex numbers represented by <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>complex</c-></code>.</p>
   <h2 class="heading settled" data-level="2" id="examples"><span class="secno">2. </span><span class="content">Examples</span><a class="self-link" href="#examples"></a></h2>
   <p>Default format:</p>
<pre class="highlight"><c- n>std</c-><c- o>::</c-><c- n>string</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>1.0</c-> <c- o>+</c-> <c- mi>2</c-><c- n>i</c-><c- p>);</c-> <c- c1>// s == "(1+2i)"</c->
</pre>
   <p>iostreams-compatible format (optional):</p>
<pre class="highlight"><c- n>std</c-><c- o>::</c-><c- n>string</c-> <c- n>s</c-> <c- o>=</c-> <c- n>std</c-><c- o>::</c-><c- n>format</c-><c- p>(</c-><c- s>"{:p}"</c-><c- p>,</c-> <c- mf>1.0</c-> <c- o>+</c-> <c- mi>2</c-><c- n>i</c-><c- p>);</c-> <c- c1>// s == "(1,2)"</c->
</pre>
   <p>Format specifiers:</p>
<pre class="highlight"><c- n>std</c-><c- o>::</c-><c- n>string</c-> <c- n>s</c-> <c- o>=</c-> <c- n>std</c-><c- o>::</c-><c- n>format</c-><c- p>(</c-><c- s>"{:.2f}"</c-><c- p>,</c-> <c- mf>1.0</c-> <c- o>+</c-> <c- mi>2</c-><c- n>i</c-><c- p>);</c-> <c- c1>// s == "1.00+2.00i"</c->
</pre>
   <h2 class="heading settled" data-level="3" id="motivation"><span class="secno">3. </span><span class="content">Motivation</span><a class="self-link" href="#motivation"></a></h2>
   <p>This is a proposal defining formatting of complex numbers
represented by the library type <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>complex</c-></code>.  The default notation <code class="language-text highlight">(3+4i)</code> is proposed, as it is common in
mathematics, the physical sciences, and many other popular mathematical
software environments. This form is also more consistent with the standard
library literals for <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>complex</c-></code> <a data-link-type="biblio" href="#biblio-n3660">[N3660]</a>.  In addition to defining the
new format and discussing design choices, this proposal attempts to address
questions around introducing a format which differs from the existing
iostreams format, and why the aforementioned advantages outweigh the
disadvantages of introducing a potentially incompatible format.
An option to produce iostreams-compatible output is also provided.</p>
   <p>The formatting of <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>complex</c-></code> should be simple, consistent with
existing conventions of <code class="highlight"><c- o>&lt;</c-><c- n>format</c-><c- o>></c-></code>, and conveniently support the most
common use cases of <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>complex</c-></code>.  As the first nested format specified for <code class="highlight"><c- o>&lt;</c-><c- n>format</c-><c- o>></c-></code>, it can also serve as an example for how format nesting can be done.</p>
   <p>Mathematics generally follows the convention that complex numbers
consist of a real part and an orthogonal imaginary part which is
identified by multiplication of the imaginary unit vector \( i \).
Extending the set of unit vectors in this way furthermore implies
straightforward extensions to other useful algebras such as
quaternions \( i, j, k \), dual numbers \( \epsilon \), etc.</p>
   <p>For the types <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>complex</c-><c- o>&lt;</c-><c- p>{</c-><c- b>float</c-><c- p>,</c-><c- b>double</c-><c- p>,</c-><c- b>long</c-> <c- b>double</c-><c- p>}</c-><c- o>></c-></code>, C++14
introduced string literals to the standard library in the namespace <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>complex_literals</c-></code>.  These string literals acknowledge
the common use cases of these types and provide a convenient way to
write complex numbers in code, for example the number \( 1 + 1i \)
can be written in code as as <code class="language-text highlight">1.0f + 1if</code>, <code class="language-text highlight">1.0 + 1i</code>, or <code class="language-text highlight">1.0l + 1il</code>,
depending on the desired underlying type.</p>
   <p>Sometimes it is possible to omit one part in a symbolic representation
yet retain bijectivity in the machine representation to symbolic
mapping.  For example, the complex number \( 0 + 0i \) can be
unambiguously written as either <code class="highlight"><c- mi>0</c-></code> or <code class="highlight"><c- mi>0</c-><c- n>i</c-></code>.  The convention of
mathematics is the former, although the latter has the advantage of
implying the underlying field.</p>
   <p>As specified in <a data-link-type="biblio" href="#biblio-n4849">[N4849]</a>, the existing iostreams formatting of a complex
number <code class="highlight"><c- n>x</c-></code> is essentially</p>
<pre class="highlight"><c- n>s</c-> <c- o>&lt;&lt;</c-> <c- sc>'('</c-> <c- o>&lt;&lt;</c-> <c- n>x</c-><c- p>.</c-><c- n>real</c-><c- p>()</c-> <c- o>&lt;&lt;</c-> <c- s>","</c-> <c- o>&lt;&lt;</c-> <c- n>x</c-><c- p>.</c-><c- n>imag</c-><c- p>()</c-> <c- o>&lt;&lt;</c-> <c- sc>')'</c-><c- p>;</c->
</pre>
   where <code class="highlight"><c- n>s</c-></code> is a stream object. 
   <p>This embedded comma can cause silent unexpected generation of
ambiguous output, which can happen e.g. when the locale’s
decimal separator is set to comma.  This ambiguity does not exist in
the imaginary unit notation, even when an unusual locale is used.</p>
   <h2 class="heading settled" data-level="4" id="design-considerations"><span class="secno">4. </span><span class="content">Design Considerations</span><a class="self-link" href="#design-considerations"></a></h2>
   <p>With an eye to providing a replacement for all the functionality of iostreams,
the following considerations are made.</p>
   <h3 class="heading settled" data-level="4.1" id="numeric-form"><span class="secno">4.1. </span><span class="content">Numeric form</span><a class="self-link" href="#numeric-form"></a></h3>
   <p>The question of how to represent the numeric type <code class="highlight"><c- n>T</c-></code> of <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>complex</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-></code> is simply delegated to the <code class="highlight"><c- n>formatter</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-></code> for that
type.  Special alignment, fill, and sign rules may apply when <code class="highlight"><c- n>T</c-></code> is <code class="highlight"><c- b>float</c-></code>, <code class="highlight"><c- b>double</c-></code> or <code class="highlight"><c- b>long</c-> <c- b>double</c-></code>, but other custom value
types are accomodated.  This is done by optionally forwarding a
designated portion of the <code class="highlight"><c- n>formatter</c-><c- o>&lt;</c-><c- n>std</c-><c- o>::</c-><c- n>complex</c-><c- o>&lt;</c-><c- n>T</c-><c- o>>></c-></code> format spec to <code class="highlight"><c- n>formatter</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-></code>.</p>
   <p>Although the standard does not specify behavior of <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>complex</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-></code> for types other than <code class="highlight"><c- b>float</c-></code>, <code class="highlight"><c- b>double</c-></code>, <code class="highlight"><c- b>long</c-> <c- b>double</c-></code>, it is not
uncommon to use a type for <code class="highlight"><c- n>T</c-></code> which provides functionality such as
extended precision or automatic differentiation.  The formatting
specification should therefore be recursive, so that arbitrary
numerical types for <code class="highlight"><c- n>T</c-></code> are properly formatted.</p>
   <h3 class="heading settled" data-level="4.2" id="imaginary"><span class="secno">4.2. </span><span class="content">Imaginary unit</span><a class="self-link" href="#imaginary"></a></h3>
   <p>As previously mentioned, mathematics notation typically uses \( i \) as
the complex unit vector, however it is very common in electrical
engineering to use \( j \) instead.  Mathematica uses the Unicode
character ⅈ for the imaginary unit.  Another common written form of
complex numbers puts the imaginary unit in front of the imaginary part
rather than after it.  Julia uses the dual-character symbol <code class="highlight"><c- n>im</c-></code>, and
it it easy to imagine wanting to explicitly specify the
usually-omitted implied real unit-vector, result in a format like <code class="highlight"><c- mi>3</c-><c- n>re</c-> <c- o>+</c-> <c- mi>4</c-><c- n>im</c-></code>.  Supporting these use cases would be nice, but not with
significant implementation difficulty.</p>
   <h3 class="heading settled" data-level="4.3" id="omission"><span class="secno">4.3. </span><span class="content">Omission of a part</span><a class="self-link" href="#omission"></a></h3>
   <p>Because the complex number is always a pair of real part and imaginary
part, it is not necessary to print both parts if one of the parts is
identical to a known quantity: typically (nonnegative) zero; in this
case omission implies the value uniquely.  Either the real or the
imaginary part can be omitted when this condition is satisfied,
although clearly not both.</p>
   <p>Should a part be dropped?</p>
   <p>The benefits of part dropping include: shorter conversions in the
special but common cases of purely real or imaginary numbers,
adherence to common notation.  There is also a tie-in with the design
consideration discussed below of whether surrounding parenthesis are
necessary: a single numeric value does not need to be surrounded by
parenthesis in order to recognize it as the value for an entire
complex number.</p>
   <p>What are the conditions under which a part can be dropped?</p>
   <p>A simple comparison with zero is usually insufficient to decide
whether a part can be omitted.  While C++ does not specify the
underlying floating-point format, for correct round-trip conversions,
the omitted part must be binary equivalent to <code class="highlight"><c- n>T</c-><c- p>(</c-><c- mi>0</c-><c- p>)</c-></code>.  The function <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>signbit</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-></code> is used to distinguish between <code class="highlight"><c- o>-</c-><c- mi>0</c-></code> and <code class="highlight"><c- mi>0</c-></code>, so the
type <code class="highlight"><c- n>T</c-></code> must have both a defined <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>formatter</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-></code> and <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>signbit</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-></code> to distinguish the two cases.</p>
   <p>This nuance is demonstrated by the result of <code class="highlight"><c- n>sqrt</c-><c- p>(</c-><c- o>-</c-><c- mf>1.</c-> <c- o>+</c-> <c- mi>0</c-><c- n>i</c-><c- p>)</c-></code> vs <code class="highlight"><c- n>sqrt</c-><c- p>(</c-><c- o>-</c-><c- mf>1.</c-> <c- o>-</c-> <c- mi>0</c-><c- n>i</c-><c- p>)</c-></code>.</p>
   <p>Which part should be dropped?</p>
   <p>Either part of an imaginary number could be dropped if it is binary
equal to <code class="highlight"><c- n>T</c-><c- p>(</c-><c- mi>0</c-><c- p>)</c-></code>, but in the special case of \( 0 + 0i \) dropping both
parts would lead to the absurdity of an empty string.  This is an open
question, but it is the opinion of the author that the real part
should be dropped, so that the remaining symbolic representation
retains the imaginary unit vector, indicating use of the complex field
\( \mathbb{C} \).</p>
   <h2 class="heading settled" data-level="5" id="parentheses"><span class="secno">5. </span><span class="content">Parentheses</span><a class="self-link" href="#parentheses"></a></h2>
   <p>Should parentheses be mandatory?</p>
   <p>Are parentheses always neccesary to unambiguously specify a complex
number?</p>
   <p>Do mandatory parentheses significantly improve ease or speed of
complex number parsing?</p>
   <p>If parentheses are not mandatory, when should they be omitted?</p>
   <h2 class="heading settled" data-level="6" id="backwards-compat"><span class="secno">6. </span><span class="content">Backwards Compatibility</span><a class="self-link" href="#backwards-compat"></a></h2>
   <p>To maintain backward compatibility we propose an easy-to-use format
specifier that exactly reproduces the legacy iostreams output format.</p>
   <p>The <code class="highlight"><c- n>ios</c-></code> specifiers that affect complex number output are <code class="highlight"><c- n>precision</c-></code> and <code class="highlight"><c- n>width</c-></code>, these can not be easily guessed, but can be specified
manually in the nested format specifier.  Otherwise the compatibilty
format the output will produce roughly the same output (modulo locale
and default format for <code class="highlight"><c- n>formatter</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-></code>) that iostreams produces.</p>
   <h2 class="heading settled" data-level="7" id="parsing"><span class="secno">7. </span><span class="content">Parsing</span><a class="self-link" href="#parsing"></a></h2>
   <p>This paper does not address parsing (scan’ing) for the type <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>complex</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-></code> but does aim to produce formatted output that can
unambiguously round trip formatted and parsed.</p>
   <h2 class="heading settled" data-level="8" id="survey"><span class="secno">8. </span><span class="content">Survey of other languages</span><a class="self-link" href="#survey"></a></h2>
   <p>The following programming languages/environments similarly use the
imaginary-unit notation as their default: Python, Julia, R, MATLAB,
Mathematica, Go.  If you know the type of the data, these languages
offer round-trip conversion from complex -> text -> complex, but
because some of them drop the complex part in their textual output
when the complex part is zero (or even negative zero!) some arguably
pertinent information can be lost during formatting.</p>
   <table>
    <tbody>
    <thead>
     <tr>
      <td>Language
      <td>Basic Format
      <td>Result of <code class="highlight"><c- n>sqrt</c-><c- p>(</c-><c- o>-</c-><c- mi>1</c-><c- p>)</c-></code>
      <td>Result of <code class="highlight"><c- n>sqrt</c-><c- p>(</c-><c- o>-</c-><c- mi>1</c-><c- p>)</c-> <c- o>-</c-> <c- n>sqrt</c-><c- p>(</c-><c- o>-</c-><c- mi>1</c-><c- p>)</c-></code> 
    <tbody>
     <tr>
      <td><a href="https://en.cppreference.com/w/cpp/numeric/complex/operator_ltltgtgt">C++ iostreams</a> 
      <td> <code class="highlight"><c- p>(</c-><c- mi>3</c-><c- p>,</c-><c- mi>4</c-><c- p>)</c-></code> 
      <td> <code class="highlight"><c- p>(</c-><c- mi>0</c-><c- p>,</c-><c- mi>1</c-><c- p>)</c-></code> 
      <td> <code class="highlight"><c- p>(</c-><c- mi>0</c-><c- p>,</c-><c- mi>0</c-><c- p>)</c-></code> 
     <tr>
      <td><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.imag.html">NumPy</a> 
      <td> <code class="highlight"><c- p>(</c-><c- mi>3</c-><c- o>+</c-><c- mi>4</c-><c- n>j</c-><c- p>)</c-></code> 
      <td> <code class="highlight"><c- mi>1</c-><c- n>j</c-></code> 
      <td> <code class="highlight"><c- mi>0</c-><c- n>j</c-></code> 
     <tr>
      <td><a href="https://docs.julialang.org/en/v1/manual/complex-and-rational-numbers/">Julia</a> 
      <td> <code class="highlight"><c- mf>3.0</c-> <c- o>+</c-> <c- mf>4.0</c-><c- n>im</c-></code> 
      <td> <code class="highlight"><c- mf>0.0</c-> <c- o>+</c-> <c- mf>1.0</c-><c- n>im</c-></code> 
      <td> <code class="highlight"><c- mf>0.0</c-> <c- o>+</c-> <c- mf>0.0</c-><c- n>im</c-></code> 
     <tr>
      <td><a href="https://octave.org/doc/v4.4.1/Complex-Arithmetic.html">Octave</a> 
      <td> <code class="highlight"><c- mi>3</c-> <c- o>+</c-> <c- mi>4</c-><c- n>i</c-></code> 
      <td> <code class="highlight"><c- mi>0</c-> <c- o>+</c-> <c- mi>1</c-><c- n>i</c-></code> 
      <td> <code class="highlight"><c- mi>0</c-></code> 
     <tr>
      <td><a href="https://reference.wolfram.com/language/ref/I.html">Mathematica*</a> 
      <td> <code class="highlight"><c- mi>1</c-><c- o>+</c->ⅈ</code> 
      <td> <code class="highlight">ⅈ</code> 
      <td> <code class="highlight"><c- mi>0</c-></code> 
     <tr>
      <td><a href="http://www.r-tutor.com/r-introduction/basic-data-types/complex">R</a> 
      <td> <code class="highlight"><c- p>(</c-><c- mi>3</c-><c- o>+</c-><c- mi>4</c-><c- n>i</c-><c- p>)</c-></code> 
      <td> <code class="highlight"><c- p>(</c-><c- mi>0</c-><c- o>+</c-><c- mi>1</c-><c- n>i</c-><c- p>)</c-></code> 
      <td> <code class="highlight"><c- p>(</c-><c- mi>0</c-><c- o>+</c-><c- mi>0</c-><c- n>i</c-><c- p>)</c-></code> 
     <tr>
      <td><a href="https://en.cppreference.com/w/cpp/numeric/complex/operator%22%22i">C++14 literals</a> 
      <td> <code class="highlight"><c- mf>3.0</c-> <c- o>+</c-> <c- mi>4</c-><c- n>i</c-></code> 
      <td> <code class="highlight"><c- mi>1</c-><c- n>i</c-></code> 
      <td> <code class="highlight"><c- mi>0</c-><c- n>i</c-></code> 
     <tr>
      <td><a href="https://golang.org/pkg/fmt/">Go</a> 
      <td> <code class="highlight"><c- p>(</c-><c- mi>3</c-><c- o>+</c-><c- mi>4</c-><c- n>i</c-><c- p>)</c-></code> 
      <td> <code class="highlight"><c- p>(</c-><c- mi>0</c-><c- o>+</c-><c- mi>1</c-><c- n>i</c-><c- p>)</c-></code> 
      <td> <code class="highlight"><c- p>(</c-><c- mi>0</c-><c- o>+</c-><c- mi>0</c-><c- n>i</c-><c- p>)</c-></code> 
   </table>
   <p><code class="highlight"><c- o>*</c-></code> - checked via wolframalpha</p>
   <p>Haskell provides <code class="highlight"><c- nl>a</c-> <c- p>:</c-><c- o>+</c-> <c- n>b</c-></code> notation - this choice does not need much commentary,
this much is offered: it is quite unique.</p>
   <p>C# does not provide this functionality, but the doc page for complex includes an
example code for creating an appropriate formatter.</p>
   <h2 class="heading settled" data-level="9" id="wish-list"><span class="secno">9. </span><span class="content">Wish List</span><a class="self-link" href="#wish-list"></a></h2>
   <p>Feature wish list:</p>
   <ul>
    <li data-md>
     <p>nested specification of real and imaginary parts via <code class="highlight"><c- n>formatter</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-></code></p>
    <li data-md>
     <p>easy substitution of "old style" iostreams format with simply <code class="highlight"><c- p>{</c-><c- o>:</c-><c- n>p</c-><c- p>}</c-></code></p>
    <li data-md>
     <p>defineable symbol for imaginary unit (<code class="highlight"><c- n>j</c-></code>, <code class="highlight"><c- n>im</c-></code>)</p>
    <li data-md>
     <p>option to prefix the imaginary part with the imaginary unit</p>
    <li data-md>
     <p>control over which (real/imag) part omission (<code class="highlight"><c- mi>0</c-></code> or <code class="highlight"><c- mi>0</c-><c- n>j</c-></code>)</p>
    <li data-md>
     <p>default to minimalist unique parseable format: <code class="highlight"><c- mi>1</c-></code>, <code class="highlight"><c- mi>1</c-><c- n>i</c-></code>, <code class="highlight"><c- mi>0</c-><c- n>j</c-></code>, <code class="highlight"><c- p>(</c-><c- mi>1</c-><c- o>+</c-><c- mi>1</c-><c- n>i</c-><c- p>)</c-></code></p>
    <li data-md>
     <p>toggle to turn off surrounding parens: <code class="highlight"><c- mi>1</c-><c- o>+</c-><c- mi>1</c-><c- n>i</c-></code></p>
    <li data-md>
     <p>toggle to turn off outputting <code class="highlight"><c- o>-</c-></code> on negative zero - addressed by P2021</p>
    <li data-md>
     <p>center alignment <code class="highlight"><c- o>^</c-></code> aligns output around the connecting <code class="highlight"><c- o>+/-</c-></code></p>
    <li data-md>
     <p>option for polar formatted output, ie <code class="highlight"><c- p>(</c-><c- mf>1.41421</c-><c- o>*</c-><c- n>exp</c-><c- p>(</c-><c- n>i</c-><c- o>*</c-><c- mf>3.14159</c-><c- p>))</c-></code></p>
   </ul>
   <h2 class="heading settled" data-level="10" id="proposed-wording"><span class="secno">10. </span><span class="content">Proposed Wording</span><a class="self-link" href="#proposed-wording"></a></h2>
   <p>Modify <a href="http://eel.is/c++draft/complex.syn">[complex.syn]</a> as
follows:</p>
<pre class="highlight"><c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>T</c-><c- p>,</c-> <c- k>class</c-> <c- nc>charT</c-><c- p>,</c-> <c- k>class</c-> <c- nc>traits</c-><c- o>></c->
<c- n>basic_ostream</c-><c- o>&lt;</c-><c- n>charT</c-><c- p>,</c-> <c- n>traits</c-><c- o>>&amp;</c-> <c- k>operator</c-><c- o>&lt;&lt;</c-><c- p>(</c-><c- n>basic_ostream</c-><c- o>&lt;</c-><c- n>charT</c-><c- p>,</c-> <c- n>traits</c-><c- o>>&amp;</c-><c- p>,</c-> <c- k>const</c-> <c- n>complex</c-><c- o>&lt;</c-><c- n>T</c-><c- o>>&amp;</c-><c- p>);</c->
<ins>
<c- c1>// 26.4.?, formatting</c->
<c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>charT</c-><c- o>></c-> <c- k>struct</c-> <c- n>formatter</c-><c- o>&lt;</c-><c- n>complex</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c-><c- p>,</c-> <c- n>charT</c-><c- o>></c-><c- p>;</c->
<c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>charT</c-><c- o>></c-> <c- k>struct</c-> <c- n>formatter</c-><c- o>&lt;</c-><c- n>complex</c-><c- o>&lt;</c-><c- b>double</c-><c- o>></c-><c- p>,</c-> <c- n>charT</c-><c- o>></c-><c- p>;</c->
<c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>charT</c-><c- o>></c-> <c- k>struct</c-> <c- n>formatter</c-><c- o>&lt;</c-><c- n>complex</c-><c- o>&lt;</c-><c- b>long</c-> <c- b>double</c-><c- o>></c-><c- p>,</c-> <c- n>charT</c-><c- o>></c-><c- p>;</c->
</ins></pre>
   <p>Add a new section 26.4.? Formatting [complex.format]:</p>
   <ins> Each <code class="highlight"><c- n>formatter</c-><c- o>&lt;</c-><c- n>complex</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-><c- p>,</c-> <c- n>charT</c-><c- o>></c-></code> (<a href="http://eel.is/c++draft/format.formatter">format.formatter</a>) specialization in this section meets
the <em>Formatter</em> requirements (<a href="http://eel.is/c++draft/formatter.requirements">formatter.requirements</a>). The <code class="highlight"><c- n>parse</c-></code> member functions of
these formatters interpret the format specification as <em>std-format-spec</em> (<a href="http://eel.is/c++draft/format.string.std">format.string.std</a>) except that the <code class="highlight"><c- mi>0</c-></code> option is invalid. </ins>
<pre class="highlight"><ins><c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>charT</c-><c- o>></c-> <c- k>struct</c-> <c- n>formatter</c-><c- o>&lt;</c-><c- n>complex</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-><c- p>,</c-> <c- n>charT</c-><c- o>></c-> <c- p>{</c->
  <c- k>typename</c-> <c- n>basic_format_parse_context</c-><c- o>&lt;</c-><c- n>charT</c-><c- o>>::</c-><c- n>iterator</c->
    <c- n>parse</c-><c- p>(</c-><c- n>basic_format_parse_context</c-><c- o>&lt;</c-><c- n>charT</c-><c- o>>&amp;</c-> <c- n>ctx</c-><c- p>);</c->

  <c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>FormatContext</c-><c- o>></c->
    <c- k>typename</c-> <c- n>FormatContext</c-><c- o>::</c-><c- n>iterator</c->
      <c- n>format</c-><c- p>(</c-><c- k>const</c-> <c- n>complex</c-><c- o>&lt;</c-><c- n>T</c-><c- o>>&amp;</c-> <c- n>c</c-><c- p>,</c-> <c- n>FormatContext</c-><c- o>&amp;</c-> <c- n>ctx</c-><c- p>);</c->
<c- p>};</c->

<c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>FormatContext</c-><c- o>></c->
  <c- k>typename</c-> <c- n>FormatContext</c-><c- o>::</c-><c- n>iterator</c->
    <c- n>format</c-><c- p>(</c-><c- k>const</c-> <c- n>complex</c-><c- o>&lt;</c-><c- n>T</c-><c- o>>&amp;</c-> <c- n>c</c-><c- p>,</c-> <c- n>FormatContext</c-><c- o>&amp;</c-> <c- n>ctx</c-><c- p>);</c->
</ins></pre>
   <ins> Let <code class="highlight"><c- n>real</c-> <c- o>=</c-> <c- n>format</c-><c- p>(</c-><c- n>ctx</c-><c- p>.</c-><c- n>locale</c-><c- p>(),</c-> <c- s>"{:&lt;format-specs>}"</c-><c- p>,</c-> <c- n>c</c-><c- p>.</c-><c- n>real</c-><c- p>())</c-></code> and <code class="highlight"><c- n>imag</c-> <c- o>=</c-> <c- n>format</c-><c- p>(</c-><c- n>ctx</c-><c- p>.</c-><c- n>locale</c-><c- p>(),</c-> <c- s>"{:&lt;format-specs>}"</c-><c- p>,</c-> <c- n>c</c-><c- p>.</c-><c- n>imag</c-><c- p>())</c-></code>,
where <code class="highlight"><c- o>&lt;</c-><c- n>format</c-><c- o>-</c-><c- n>specs</c-><c- o>></c-></code> is <em>std-format-spec</em> with <em>fill-and-align</em> and <em>width</em> removed. </ins>
   <p>
    <ins> <em>Effects:</em> Equivalent to: </ins>
   </p>
<pre class="highlight"><ins> <c- n>format_to</c-><c- p>(</c-><c- n>ctx</c-><c- p>.</c-><c- n>out</c-><c- p>(),</c-> <c- s>"{:&lt;fill-align-width>}"</c-><c- p>,</c->
           <c- n>format</c-><c- p>(</c-><c- n>c</c-><c- p>.</c-><c- n>real</c-><c- p>()</c-> <c- o>!=</c-> <c- mi>0</c-> <c- o>?</c-> <c- s>"({0}+{1}i)"</c-> <c- o>:</c-> <c- s>"{1}i"</c-><c- p>,</c-> <c- n>real</c-><c- p>,</c-> <c- n>imag</c-><c- p>))</c->
</ins></pre>
   <ins> where <code class="highlight"><c- o>&lt;</c-><c- n>fill</c-><c- o>-</c-><c- n>align</c-><c- o>-</c-><c- n>width</c-><c- o>></c-></code> is the <em>fill-and-align</em> and <em>width</em> part of <em>std-format-spec</em>. If alignment is not specified <code class="highlight"><c- o>></c-></code> is used. </ins>
   <h2 class="heading settled" data-level="11" id="questions"><span class="secno">11. </span><span class="content">Questions</span><a class="self-link" href="#questions"></a></h2>
   <p><strong>Q1</strong>: Do we want any of this?</p>
   <p><strong>Q2</strong>: The strategy of this paper is to include a laundry list of
        possibilities, which parts do we want?</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-n3660">[N3660]
   <dd>Peter Sommerlad. <a href="https://wg21.link/n3660">User-defined Literals for std::complex, part 2 of UDL for Standard Library Types (version 4)</a>. 19 April 2013. URL: <a href="https://wg21.link/n3660">https://wg21.link/n3660</a>
   <dt id="biblio-n4849">[N4849]
   <dd>Richard Smith. <a href="https://wg21.link/n4849">Working Draft, Standard for Programming Language C++</a>. URL: <a href="https://wg21.link/n4849">https://wg21.link/n4849</a>
   <dt id="biblio-p0645">[P0645]
   <dd>Victor Zverovich. <a href="https://wg21.link/p0645">Text Formatting</a>. URL: <a href="https://wg21.link/p0645">https://wg21.link/p0645</a>
  </dl>