<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>P3125R3: constexpr pointer tagging</title>
<style>
@media (prefers-color-scheme: dark) {
	:root {
		--text-color: #BBB;
		--found-highlight: blue;
		--found-text-color: white;
		--main-background: 32,32,32;
		--header-color: white;
		--box-shadow-color: rgba(0,0,0,0.5);
    --thin-box-shadow-color: rgba(0,0,0,0.1);
		--nav-background-color: #101010;
		--code-foreground-color: white;
		--code-info-color: rgba(255,255,255,0.1);
		--code-background-color: var(--nav-background-color);
		--link-color: #8ef3ff;
		--visited-link-color: #f0ff89;
		--hover-link-color: #b3f7ff;
		--hover-visited-link-color: #c8ffb3;
		--line-color: 255,255,255;
		--header-background: 0,0,0;
		--quote-left-color: rgba(255,255,255,0.5);
		--highlight: rgba(255,252,0,0.25);
	}
	::selection {
	  color: black;
	  background: lightyellow;
	}
}

@media (prefers-color-scheme: light) {
	:root {
		--text-color: black;
		--found-highlight: yellow;
		--found-text-color: black;
		--main-background: 255,255,255;
		--header-color: black;
		--box-shadow-color: rgba(0,0,0,0.3);
    --thin-box-shadow-color: rgba(0,0,0,0.1);
		--nav-background-color: #F5F5F5;
		--code-foreground-color: black;
		--code-info-color: rgba(0,0,0,0.1);
		--code-background-color: var(--nav-background-color);
		--link-color: #000082;
		--visited-link-color: #508d0f;
		--hover-link-color: #5757c2;
		--hover-visited-link-color: #94c560;
		--line-color: 12,43,75;
		--header-background: 0,0,0;
		--quote-left-color: rgba(0,0,0,0.5);
		--highlight: rgba(255,254,207,0.5);
	}
	/*
	*::selection {
	  color: black;
	  background: #a4c3f6;
	}*/
}

@media (prefers-color-scheme: dark) {
	svg {
		--hana-text: black;
		--hana-outline: black;
		--hana-contrast-text: rgba(255,255,255,0.75);
		--hana-info: rgba(255,255,255,0.6);
		--hana-lines: white;
		--hana-special-boxes: rgba(0,0,0,0.5);
		--hana-special-boxes-outline: rgba(255,255,255,0.5);
		--hana-boxes: rgba(255,255,255,0.6);
		--hana-boxes-background: rgba(255,255,255,0.1);
		--hana-inside-text: white;
		--hana-outside-text: var(--text-color);
		--hana-shadow: white;
		--hana-structures-outline: white;
		--hana-structures-fill: black;
		--hana-structures-fill-meaningless: #444;
		--hana-pink-fill: #a3567e;
		--hana-purple-fill: #4d539d;
		--hana-green-fill: #1e7451;
		--hana-yellow-fill: #727529;
		--hana-orange-fill: #714530;
	}
}

@media (prefers-color-scheme: light) {
	svg {
		--hana-text: black;
		--hana-outline: black;
		--hana-contrast-text: rgba(255,255,255,1);
		--hana-info: rgba(0,0,0,0.6);
		--hana-lines: black;
		--hana-special-boxes: rgba(0,0,0,0.9);
		--hana-special-boxes-outline: rgba(255,255,255,0.5);
		--hana-boxes: rgba(0,0,0,0.6);
		--hana-boxes-background: rgba(0,0,0,0.1);
		--hana-inside-text: var(--text-color);
		--hana-outside-text: var(--text-color);
		--hana-shadow: black;
		--hana-structures-outline: black;
		--hana-structures-fill: white;
		--hana-structures-fill-meaningless: lightgray;
		--hana-pink-fill: #ffacd6;
		--hana-purple-fill: #acacff;
		--hana-green-fill: #acffd5;
		--hana-yellow-fill: #ffffac;
		--hana-orange-fill: #ffc8ad;
	}
}

svg g#boxes * {
	fill: var(--hana-boxes);
	fill-opacity: 0.1;
	stroke: var(--hana-boxes);
}
svg g#special {
	opacity: 0.25;
}
svg g#black-outline * {
	stroke: var(--hana-outline);
}
svg g#text * {
	fill: var(--hana-text);
}
svg g#info * {
	fill: var(--hana-info);
}
svg g#info text {
	fill: var(--hana-info);
}
svg g#contrast-text * {
	fill: var(--hana-contrast-text);
}
svg g#contrast-black-outline * {
	fill: var(--hana-special-boxes);
	stroke: var(--hana-special-boxes-outline);
}
svg g#black-lines * {
	stroke: var(--hana-lines);
}
svg g#black-lines polygon {
	fill: var(--hana-lines);
}

/* inheritance */
svg g#outside-text * {
	fill: var(--hana-outside-text);
}
svg g#inside-text * {
	fill: var(--hana-inside-text);
}
svg g#shadow path {
	fill: var(--hana-shadow);
	opacity: 0.1;
}
svg g#arrows g path, svg g#arrows g line {
	stroke: var(--hana-structures-outline);
}
svg g#arrows g polygon {
	fill: var(--hana-structures-outline);
}
svg g#structures > * {
	stroke: var(--hana-structures-outline);
	fill: var(--hana-structures-fill);
}
svg g#items g#meaningless > * {
	fill: var(--hana-structures-fill-meaningless);
}
svg g#items g#pink > * {
	fill: var(--hana-pink-fill);
}
svg g#items g#orange > * {
	fill: var(--hana-orange-fill);
}
svg g#items g#purple > * {
	fill: var(--hana-purple-fill);
}
svg g#items g#yellow > * {
	fill: var(--hana-yellow-fill);
}
svg g#items g#green > * {
	fill: var(--hana-green-fill);
}
svg g#items * {
	stroke: var(--hana-structures-outline);
}


span:target, p:target, li:target, div:target {
  background: var(--highlight);
}

.name-of-paper {
	font-size: 28px;
	padding-top: 0.5em;
}

span.found {
	text-shadow: 0 0 10px var(--found-highlight),  0 0 10px var(--found-highlight),  0 0 10px var(--found-highlight),  0 0 10px var(--found-highlight);
	color: var(--found-text-color) !important;
}

body {
	font-family: Helvetica;
	padding: 0;
	margin: 0;
	overflow: hidden;
	color: var(--text-color);
	background-color: rgba(var(--main-background), 1);
}

body > div {
	display: flex;
	padding: 0;
	margin: 0;
}

.hide-on-narrow {
	display: inherit;
}

.hide-on-wide {
	display: none;
}

@media only screen and (max-width: 1100px) {
	body {
		overflow: inherit !important;
	}
	.hide-on-narrow {
		display: none;
	}
	.hide-on-wide {
		display: inherit;
	}
	body > div {
		display: block !important;
	}
	article {
		overflow: inherit !important;
		background-image: linear-gradient(to right, transparent,rgba(var(--main-background),0.6), rgba(var(--main-background),0.8), rgba(var(--main-background),0.6), transparent) !important;
	}
	nav, article {
		flex: initial !important;
	}
	nav {
		min-width: initial !important;
		max-width: initial !important;
		min-height: initial !important;
		max-height: initial !important;
		box-shadow: 0 10px 0 var(--box-shadow-color);
	}
	nav > div {
		overflow: inherit !important;
		position: relative !important;
		max-width: initial !important;
		max-height: initial !important;
	}
	div:has(> input[type=search]) {
		display: none;
	}
	div.quote {
		overflow-x: visible;
    overflow-y: visible;
	}
}

nav {
	padding: 0 0.5em;
	margin: 0;
	flex: 1 1 0;
	min-width: 350px;
	max-width: 350px;
	box-shadow: 0 0 10px var(--box-shadow-color);
	background-color: var(--nav-background-color);
}

nav > div {
	position: fixed;
	max-width: 350px;
	max-height: 100%;
	overflow: scroll;
	top: 0;
	left: 0;
	padding: 0 0.5em;
	margin: 0;
}

nav > div > div {
	padding: 0.5em;
	padding-top: 0;
	padding-bottom: 1em;
}

article {
	flex: 3 1 0;
	overflow: scroll;
	height: 100vh;
	text-align: justify;
	background-image: linear-gradient(to bottom, transparent,rgba(var(--main-background),0.6), rgba(var(--main-background),0.8), rgba(var(--main-background),0.6), transparent);
	padding: 0;
	margin: 0;
}

article > div {
	padding-right: 1.5em;
	padding-left: 1.5em;
	padding-bottom: 1em;
}

code {
	
}

div.quote {
	color: var(--code-foreground-color);
	background: var(--code-background-color);
	padding: 1em;
	border-radius: 0px 15px 15px 0px;
	border-left: 5px solid var(--quote-left-color);
	font-style: italic;
	margin: 1em;
}

code:not(pre > code) {
	color: inherit;
	background: var(--code-background-color);
	border-radius: 5px;
	padding: 0 0.2em;
	margin: 0 2px;
	outline: 2px solid var(--code-background-color);
}

pre > code {
	outline: none;
	line-height: 1.4;
	tab-size: 2;
}

pre:has(code) {
	color: var(--code-foreground-color);
	background: var(--code-background-color);
	padding: 1em;
	border-radius: 15px;
	position: relative;
	z-index: 1;
	overflow-x: visible;
	overflow-y: visible;
}

pre:has(code.language-carbon)::before {
	content: "Carbon";
	text-transform: uppercase;
	position: absolute;
	top: 1em;
	right: 1em;
	color: var(--code-info-color);
	font-weight: bold;
}

p, ul > li {
	text-align: justify;
	overflow-wrap: break-word;
	hyphens: auto;
}

article ul > li {
	padding-bottom: 0.25em;
}

div.description ul {
  padding-top: 0.5em;
	padding-bottom: 0.5em;
}

a {
	color: var(--link-color);
	text-decoration-style: dotted;
}

a:hover {
	color: var(--hover-link-color);
	text-decoration-style: solid;
}

a:visited {
	color: var(--visited-link-color);
}

a:visited:hover {
	color: var(--hover-visited-link-color);
	text-decoration-style: solid;
}

h1, h2, h3, h4, h5 {
	margin: 0;
	margin-bottom: 10px;
	padding: 0.5em;
	padding-top: 20px;
	padding-bottom: 2px;
	z-index: 2;
	color: var(--header-color) !important;
	a {
		color: var(--header-color) !important;
	}
}

article h1, article h2, article h3, article h4, article h5 {
/*	position: sticky;
	position: -webkit-sticky;
	top: 0;*/
	
}

h1 {
	font-weight: 800;
	border-bottom: rgba(var(--line-color), 1) dotted 2px;
}

h2 {
	font-weight: 800;
	border-bottom: rgba(var(--line-color), 0.75) dotted 2px;
}

h3, h4, h5 {
	font-weight: 600;
	border-bottom: rgba(var(--line-color), 0.33) dotted 2px;
}

h1 > a, h2 > a, h3 > a, h4 > a, h5 > a {
	text-decoration: inherit;
}

h1:target::after, h2:target::after, h3:target::after, h4:target::after, h5:target::after {
	text-decoration: inherit;
	content: " ⚓︎";
  font-size: 14px;
}

h1 > a:hover, h2 > a:hover, h3 > a:hover, h4 > a:hover, h5 > a:hover {
	color: var(--hover-link-color);
}

div:has(> input[type=search]) {
	position: fixed;
	top: 0;
	right: 0;
	z-index: 1000;
	padding: 0.5em;
	background-color: var(--nav-background-color);
	box-shadow: 0 0 10px rgba(0,0,0,0.3);
	border-bottom-left-radius: 10px;
}

div > input[type=search] {
	background-color: var(--nav-background-color);
	border: 2px solid var(--text-color);
	color: var(--text-color);
	width: 300px;
}

div.paper-info {
	padding: 0;
	padding-top: 1em;
	
	.key {
		font-weight: bold;
	}
	
	div {
	}
}

ul {
	padding: 0;
	margin: 0;
	padding-left: 1em;
}

div#toc > ul {
	margin-left: 1em;
}

div#toc ul {
	padding-left: 0.5em;
}

li > ul {
	padding-left: 0.25em;
}

ul > li {
	padding-left: 0.25em;
}

div#toc li {
	text-align: left;
}

code .error, code .before {
	line-height: 1.9;
}

code .error > *, code .before > * {
	background-color: #FF8888 !important;
	color: black !important;
	@media (prefers-color-scheme: dark) {
		color: white;
	}
	border: 3px solid #FF8888;
	font-weight: bold;
}

code .after > * {
	background-color: lightgreen !important;
	color: black !important;
	@media (prefers-color-scheme: dark) {
		color: white;
	}
	border: 3px solid lightgreen;
	font-weight: bold;
}

code .unchanged > * {
	background-color: lightyellow !important;
	color: black !important;
	@media (prefers-color-scheme: dark) {
		color: white;
	}
	border: 3px solid lightyellow;
	font-weight: bold;
}

code .invisible {
	visibility: hidden;
}

.changes {
	display: inline-block;
}

.wording h1, .wording h1 > a, .wording h2, .wording h2 > a {
	font-size: inherit;
	text-decoration: none;
	border: none;
	padding: 0;
	margin: 0;
	@media (prefers-color-scheme: dark) {
		color: white !important;
	}
	@media (prefers-color-scheme: light) {
		color: black !important;
	}
	
	/*color: orange !important;*/
}

.wording p {
	padding: 0;
	padding-top: 0.5em;
	margin: 0;
}

.wording a {
	text-decoration: none;
	color: inherit;
}

.wording a:hover {
	text-decoration: underline;
	color: var(--link-color);
}

.wording a:visited {

}

.wording code {
	background: inherit !important;
	border: none;
	outline: none;
}
	
.wording {
	font-family: "Noto Serif";
	
	padding: 0.5em 1em;
	padding-bottom: 1em;
	color: var(--code-foreground-color);
	background: var(--code-background-color);
	line-height: 1.55;
	
	border-radius: 15px;
	position: relative;
	z-index: 1;
	overflow-x: visible;
	overflow-y: visible;
}
	
.wording .added, pre .added {
	background-color: lightgreen;
	text-decoration: underline;
  text-decoration-color: green;
  text-decoration-thickness: 2px !important;
	z-index: 80;
	padding: 3px;
	@media (prefers-color-scheme: dark) {
		color: black !important;
	}
}

div.added pre.added *, div.added pre.added {
	text-decoration-color: transparent;
}

.wording .added-item {
	background-color: lightgreen;
  text-decoration: underline;
  text-decoration-color: green;
  text-decoration-thickness: 2px !important;
	@media (prefers-color-scheme: dark) {
		color: black;
	}
}
	
.wording .removed {
	background-color: #FF8888;
	z-index: 50;
	padding: 3px;
  text-decoration: line-through;
  text-decoration-color: rgba(255,0,0,0.75);
  text-decoration-thickness: 2px !important;
	@media (prefers-color-scheme: dark) {
		color: black;
	}
}

.wording li.removed-bullet::before {
	background-color: #FF8888;
	z-index: 50;
	padding: 3px;
  text-decoration: line-through;
  text-decoration-color: rgba(255,0,0,0.75);
  text-decoration-thickness: 2px !important;
	@media (prefers-color-scheme: dark) {
		color: black;
	}
}
	
.wording .note {
	font-size: 0.8em;
}
	
.wording	+ .wording {
	margin-top: 0.5em;
}
	
.wording pre:has(code) {
	border: 1px solid var(--code-info-color);
	border-radius: 0;
	padding: 0em;
	z-index: 1;
	overflow-x: scroll;
}
	
.wording	code .addeded span {
	color: black !important;
}

table.poll {
  border-collapse: collapse;
  margin-top: 20px;
}

table.poll th, table.poll td {
  border: 0;
  padding: 5px 10px;
  text-align: center;
  border: 2px solid rgba(128,128,128,0.2);
}

table.poll td:first-child, table.poll th:first-child {
 border-left: none;
}

table.poll td:last-child, table.poll th:last-child {
 border-right: none;
}

table.poll tr:first-child th, table.poll tr:first-child td {
  border-top: none;
}

table.poll tr:last-child th, table.poll tr:last-child td {
  border-bottom: none;
}

.wording .description {
  padding-bottom: 1em;
}

.wording .caps {
  text-transform: uppercase;
}

table th.table-group {
	max-width: 2em;
}

table th.table-group > span {
	max-width: 2em;
	display: block;
	overflow: visible;
	text-align: center;
	transform: translateX(1em);
}

table th.table-group > span > span {
	display: inline-block;
	transform: translateX(-50%) rotate(-90deg);
	width: auto;
}

table.before-after th, table.before-after td  {
  height: 30px;
}



table.before-after .green {
  color: green;
}

table.before-after .orange {
  color: orange;
}

table.before-after .red-normal {
  color: red;
}

table.before-after .in-progress {
	color: blue;
	background-color: rgba(0,231,255,0.5);
}

table.before-after .proposing {
	color: green;
	background-color: rgba(0,255,0,0.5);
}

table.before-after .not-proposing {
	color: red;
	background-color: rgba(255,0,0,0.25);
}

table.before-after .never-proposing {
	color: red;
	background-color: rgba(255,0,0,0.25);
}

table.before-after .proposed-ready-for-future {
	color: green;
	background-color: rgba(203,229,7,0.5);
}

table.before-after .proposed-ready-for-future2 {
	color: green;
	background-color: rgba(255,198,0,0.5);
}

table.before-after .red {
  color: red;
  font-size: 24px;
  line-height: 16px;
}

td a, td a:visited, td a:hover {
	color: inherit;
}

div.wording-note {
  background: rgb(var(--main-background));
  box-shadow: 5px 0 10px var(--thin-box-shadow-color) inset;
  border-radius: 15px;
  color: var(--text-color);
  padding: 10px;
  margin: 10px 20px;
  font-size: 12px;
}

.parnum {
	font-size: 12px;
	margin-right: 0.25em;
	display: inline-block;
}

li:has(> .parnum) {
	list-style-position: inside;
	position: relative;
}

li > .parnum {
	position: absolute;
	left: -30px;
	bottom: 2px;
}

div.svgimg {
	text-align: left;
}

div.svgimg > div {
	
}

div.svgimg > div > svg {

}

@media (prefers-color-scheme: dark) {
	div.svgimg > div > img {
		border-radius: 10px;
		filter: drop-shadow(0px 0px 5px rgb(255 255 255 / 0.4));
	}
}

table.before-after td.disable-bottom, table.before-after th.disable-bottom {
	border-bottom: none;
}
table.before-after th.left, table.before-after td.left {
	text-align: left;
}

td a.note:after {
	vertical-align: super;
	font-size: 75%;
	margin-left: 0.5em;
}

td a.note.n1:after {
	content: "1";
}

td a.note.n2:after {
	content: "2";
}

td a.note.n3:after {
	content: "3";
}

td a.note.n4:after {
	content: "4";
}

td a.note.n5:after {
	content: "5";
}

blockquote {
	background: rgba(0,0,0,0.10);
	font-style: italic;
	padding: 0.05em 1em;
	margin: 0;
	border-left: rgba(0,0,0,0.5) 5px solid;
}

.wording pre code em, .wording pre code em span {
	color: var(--text-color) !important;
}
</style>
<style>
@media (prefers-color-scheme: light) {

pre code.hljs {

}
code.hljs {

}
/*

XCode style (c) Angel Garcia <angelgarcia.mail@gmail.com>

*/
.hljs {
  color: inherit
}
/* Gray DOCTYPE selectors like WebKit */
.xml .hljs-meta {
  color: #c0c0c0
}
.hljs-comment,
.hljs-quote {
  color: #007400
}
.hljs-tag,
.hljs-attribute,
.hljs-keyword,
.hljs-selector-tag,
.hljs-literal,
.hljs-name {
  color: #aa0d91
}
.hljs-variable,
.hljs-template-variable {
  color: #3F6E74
}
.hljs-code,
.hljs-string,
.hljs-meta .hljs-string {
  color: #c41a16
}
.hljs-regexp,
.hljs-link {
  color: #0E0EFF
}
.hljs-title,
.hljs-symbol,
.hljs-bullet,
.hljs-number {
  color: #1c00cf
}
.hljs-section,
.hljs-meta {
  color: #643820
}
.hljs-title.class_,
.hljs-class .hljs-title,
.hljs-type,
.hljs-built_in,
.hljs-params {
  color: #5c2699
}
.hljs-attr {
  color: #836C28
}
.hljs-subst {
  color: #000
}
.hljs-formula {
  font-style: italic
}
.hljs-addition {

}
.hljs-deletion {

}
.hljs-selector-id,
.hljs-selector-class {
  color: #9b703f
}
.hljs-doctag,
.hljs-strong {
  font-weight: bold
}
.hljs-emphasis {
  font-style: italic
}

}

@media (prefers-color-scheme: dark) {

pre code.hljs {

}
code.hljs {

}
/*

XCode style (c) Angel Garcia <angelgarcia.mail@gmail.com>

*/
.hljs {
  color: inherit
}
/* Gray DOCTYPE selectors like WebKit */
.xml .hljs-meta {
  color: #c0c0c0
}
.hljs-comment,
.hljs-quote {
  color: #007400
}
.hljs-tag,
.hljs-attribute,
.hljs-keyword,
.hljs-selector-tag,
.hljs-literal,
.hljs-name {
  color: #aa0d91
}
.hljs-variable,
.hljs-template-variable {
  color: #3F6E74
}
.hljs-code,
.hljs-string,
.hljs-meta .hljs-string {
  color: #c41a16
}
.hljs-regexp,
.hljs-link {
  color: #0E0EFF
}
.hljs-title,
.hljs-symbol,
.hljs-bullet,
.hljs-number {
  color: #9382ff
}
.hljs-section,
.hljs-meta {
  color: #643820
}
.hljs-title.class_,
.hljs-class .hljs-title,
.hljs-type,
.hljs-built_in,
.hljs-params {
  color: #b879ff
}
.hljs-attr {
  color: #836C28
}
.hljs-subst {
  color: #000
}
.hljs-formula {
  font-style: italic
}
.hljs-addition {

}
.hljs-deletion {

}
.hljs-selector-id,
.hljs-selector-class {
  color: #9b703f
}
.hljs-doctag,
.hljs-strong {
  font-weight: bold
}
.hljs-emphasis {
  font-style: italic
}

}



</style>
<style>
.wording  {
    font-family: 'Noto Serif';
    hyphens: auto;
    line-height: 1.5;
    font-size: 10pt;
    padding-left: 3em;
}

.wording div {
    background: inherit;
}

.wording div.wrapper {
    max-width: 20cm;
    margin: auto;
}

.wording div.texpara {
    margin-top: 3pt;
    margin-bottom: 3pt;
}

.wording table div.texpara {
    margin-top: 0;
    margin-bottom: 0;
}

.wording table.enumerate div.texpara {
    margin-top: 3pt;
    margin-bottom: 3pt;
}

.wording ul {
    list-style-type: none;
    padding-left: 9mm;
    margin-top: 0;
    margin-bottom: 0;
}

.wording ol {
    margin-top: 0;
    margin-bottom: 0;
}

.wording a {
    text-decoration: none;
}

.wording a.hidden_link {
    text-decoration: none;
    color: inherit;
}

.wording li {
    margin-top: 3pt;
    margin-bottom: 3pt;
}

.wording h1 {
    line-height: 1;
    margin-top: 10pt;
    margin-bottom: 10pt;
}

.wording h2 {
    line-height: 1;
    font-size: 14pt;
    margin-top: 10pt;
    margin-bottom: 10pt;
}

.wording h2::after {
    content: "";
    clear: both;
    display: table;
}

.wording h3 {
    line-height: 1;
    margin-top: 10pt;
    margin-bottom: 10pt;
}

.wording h3::after {
    content: "";
    clear: both;
    display: table;
}

.wording h4 {
    line-height: 1;
    margin-top: 10pt;
    margin-bottom: 10pt;
}

.wording h4::after {
    content: "";
    clear: both;
    display: table;
}

.wording ul > li:before {
    content: "\2014";
    position: absolute;
    margin-left: -1.5em;
}

.wording .shy:before {
    content: "\00ad";
    /* This is U+00AD SOFT HYPHEN, same as &shy, but we put it in :before
    	to stop it from being included when the text is copied to the clipboard
    	with Firefox, which is especially annoying when copying to a terminal,
    	where the hyphen characters will show up. */
}


.wording .abbr_ref {
    float: right;
}

.wording .folded_abbr_ref {
    float: right;
}

.wording .unfolded_abbr_ref {
    display: none;
}

.wording .secnum {
    display: inline-block;
    min-width: 35pt;
}

.wording .annexnum {
    display: block;
}

.wording div.sourceLinkParent {
    float: right;
}

.wording a.sourceLink {
    position: absolute;
    opacity: 0;
    margin-left: 10pt;
}

.wording a.sourceLink:hover {
    opacity: 1;
}

.wording a.itemDeclLink {
    position: absolute;
    font-size: 75%;
    text-align: right;
    width: 5em;
    opacity: 0;
}

.wording a.itemDeclLink:hover {
    opacity: 1;
}

.wording div.marginalizedparent {
    position: relative;
    left: -18mm;
}

.wording a.marginalized {
    width: 15mm;
    position: absolute;
    font-size: 7pt;
    text-align: right;
}

.wording a.enumerated_item_num {
    display: block;
    margin-top: 3pt;
    margin-bottom: 3pt;
    margin-right: 6pt;
}

.wording div.para {
    margin-bottom: 6pt;
    margin-top: 6pt;
    text-align: justify;
    min-height: 1.2em;
}

.wording div.section {
    text-align: justify;
}

.wording div.sentence {
    display: inline;
}

.wording a.index {
    position: relative;
    float: right;
    right: -1em;
    display: none;
}

.wording a.index:before {
    position: absolute;
    content: "⟵";
    background-color: #C9FBC9;
}


.wording .indexitems {
    margin-left: 2em;
    text-indent: -2em;
}

.wording div.itemdescr {
    margin-left: 12mm;
}

.wording .bnf {
    font-family: 'Noto Sans';
    font-size: 10pt;
    font-style: italic;
    margin-left: 25pt;
    margin-top: 0.5em;
    margin-bottom: 0.5em;
    text-indent: -3em;
    padding-left: 3em;
    line-height: 1.5;
}

.wording div.bnf span.texttt {
    font-family: 'Noto Sans Mono';
    font-style: normal;
}

.wording .rebnf {
    font-family: 'Noto Serif';
    font-style: italic;
    margin-top: 0.5em;
    margin-bottom: 0.5em;
    margin-left: 30pt;
    text-indent: -3em;
    padding-left: 3em;
    line-height: 1.5;
}

.wording .simplebnf {
    font-family: 'Noto Serif';
    font-style: italic;
    font-size: 10pt;
    margin-top: 0.5em;
    margin-bottom: 0.5em;
    margin-left: 30pt;
    line-height: 1.5;
}

.wording span.textnormal {
    font-style: normal;
    font-family: 'Noto Serif';
    font-size: 10pt;
    white-space: normal;
}

.wording .bnf span.textnormal {
    font-style: normal;
    font-family: 'Noto Serif';
    font-size: 10pt;
    white-space: normal;
}

.wording p {
    margin-top: 4pt;
    margin-bottom: 4pt;
}

.wording span.rlap {
    display: inline-block;
    width: 0px;
    text-indent: 0;
}

.wording span.terminal {
    font-family: 'Noto Sans Mono';
    font-style: normal;
    font-size: 9pt;
    white-space: pre-wrap;
}

.wording span.noncxxterminal {
    font-family: 'Noto Sans Mono';
    font-style: normal;
    font-size: 9pt;
}

.wording span.term {
    font-style: italic;
}

.wording span.tcode {
    font-family: 'Noto Sans Mono';
    font-style: normal;
}

.wording span.textbf {
    font-weight: bold;
}

.wording span.textsf {
    font-family: 'Noto Sans';
    font-size: 10pt;
}

.wording div.footnote span.textsf {
    font-family: 'Noto Sans';
    font-size: 8pt;
}

.wording .bnf span.textsf {
    font-family: 'Noto Sans';
    font-size: 10pt;
}

.wording .simplebnf span.textsf {
    font-family: 'Noto Sans';
    font-size: 10pt;
}

.wording .example span.textsf {
    font-family: 'Noto Sans';
    font-size: 10pt;
}

.wording span.textsc {
    font-variant: small-caps;
}

.wording span.nontermdef {
    font-style: italic;
    font-family: 'Noto Sans';
    font-size: 10pt;
}

.wording .rebnf a.nontermdef {
    font-style: italic;
    font-family: 'Noto Serif';
}

.wording span.emph {
    font-style: italic;
}

.wording span.techterm {
    font-style: italic;
}

.wording span.mathit {
    font-style: italic;
}

.wording span.mathsf {
    font-family: 'Noto Sans';
}

.wording span.mathrm {
    font-family: 'Noto Serif';
    font-style: normal;
}

.wording span.textrm {
    font-family: 'Noto Serif';
    font-size: 10pt;
}

.wording span.textsl {
    font-style: italic;
}

.wording span.mathtt {
    font-family: 'Noto Sans Mono';
    font-style: normal;
}

.wording span.mbox {
    font-family: 'Noto Serif';
    font-style: normal;
}

.wording span.ungap {
    display: inline-block;
    width: 2pt;
}

.wording span.texttt {
    font-family: 'Noto Sans Mono';
}

.wording span.textit {
    font-style: italic;
}

.wording div.footnote span.texttt {
    font-family: 'Noto Sans Mono';
}

.wording span.tcode_in_codeblock {
    font-family: 'Noto Sans Mono';
    font-style: normal;
    font-size: 9pt;
}

.wording span.phantom {
    color: white;
}
/* Unfortunately, this way the text is still selectable. Another
	option is display:none, but then we lose the nice layout.
	Todo: find proper solution. */

.wording span.math {
    font-style: normal;
    font-family: 'Noto Serif';
    font-size: 10pt;
}

.wording span.mathblock {
    display: block;
    margin-left: auto;
    margin-right: auto;
    margin-top: 1.2em;
    margin-bottom: 1.2em;
    text-align: center;
}

.wording span.mathalpha {
    font-style: italic;
}

.wording span.synopsis {
    font-weight: bold;
    margin-top: 0.5em;
    display: block;
}

.wording span.definition {
    font-weight: bold;
    display: block;
}

.wording .codeblock {
    font-family: 'Noto Sans Mono';
    margin-left: 1.2em;
    line-height: 1.5;
    font-size: 9pt;
    white-space: pre;
    display: block;
    margin-top: 3pt;
    margin-bottom: 3pt;
		overflow-x: visible;
		overflow-y: default;
}

.wording table .codeblock {
    margin-right: 0;
}

.wording .outputblock {
    margin-left: 1.2em;
    line-height: 1.5;
    font-family: 'Noto Sans Mono';
    font-size: 9pt;
}

.wording code {
    font-family: 'Noto Sans Mono';
    font-style: normal;
}

.wording div.itemdecl {
    margin-top: 2ex;
}

.wording code.itemdeclcode {
    white-space: pre;
    font-family: 'Noto Sans Mono';
    font-size: 9pt;
    display: block;
		overflow-x: visible;
		overflow-y: default;
}

.wording .comment {
    color: green;
    font-style: italic;
    font-family: 'Noto Serif';
    font-size: 10pt;
}

.wording .footnote .comment {
    color: green;
    font-style: italic;
    font-family: 'Noto Serif';
    font-size: 8pt;
}

.wording .example .comment {
    color: green;
    font-style: italic;
    font-family: 'Noto Serif';
    font-size: 9pt;
}

.wording .note .comment {
    color: green;
    font-style: italic;
    font-family: 'Noto Serif';
    font-size: 9pt;
}

.wording span.keyword {
    color: #00607c;
    font-style: normal;
}

.wording span.parenthesis {
    color: #af1915;
}

.wording span.curlybracket {
    color: #af1915;
}

.wording span.squarebracket {
    color: #af1915;
}

.wording span.literal {
    color: #9F6807;
}

.wording span.literalterminal {
    color: #9F6807;
    font-family: 'Noto Sans Mono';
    font-style: normal;
}

.wording span.operator {
    color: #570057;
}

.wording span.anglebracket {
    color: #570057;
}

.wording span.preprocessordirective {
    color: #6F4E37;
}

.wording span.textsuperscript {
    vertical-align: super;
    font-size: smaller;
    line-height: 0;
}

.wording .footnoteref {
    vertical-align: super;
    font-size: smaller;
    line-height: 0;
}

.wording .footnote {
    font-size: 8pt;
}

.wording .footnote .math {
    font-size: 8pt;
}

.wording .footnotenum {
    display: inline-block;
    text-align: right;
    margin-right: 1mm;
    width: 4ch;
}

.wording .footnoteBacklink {
    display: none;
}

.wording .footnoteSeparator {
    background: black;
    margin-top: 5mm;
    height: 1px;
    width: 6cm;
}

.wording div.minipage {
    display: inline-block;
    margin-right: 3em;
}

.wording div.numberedTable {
    text-align: center;
    margin-left: 1em;
    margin-right: 1em;
    margin-bottom: 12pt;
    margin-top: 8pt;
}

.wording div.figure {
    text-align: center;
    margin-left: 2em;
    margin-right: 2em;
    margin-bottom: 12pt;
    margin-top: 3pt;
}

.wording table {
    border: 1px solid black;
    border-collapse: collapse;
    margin-left: auto;
    margin-right: auto;
    margin-top: 7pt;
    text-align: left;
}

.wording td, .wording th {
    padding-left: 8pt;
    padding-right: 8pt;
    vertical-align: top;
}

.wording td.empty {
    padding: 0px;
    padding-left: 1px;
}

.wording td.left {
    text-align: left;
}

.wording td.hidden {
    padding: 0;
    width: 0;
}

.wording td.right {
    text-align: right;
}

.wording td.center {
    text-align: center;
}

.wording td.justify {
    text-align: justify;
}

.wording td.border {
    border-left: 1px solid black;
}

.wording tr.rowsep, .wording td.cline {
    border-top: 1px solid black;
}

.wording tr.capsep {
    border-top: 3px solid black;
    border-top-style: double;
}

.wording th {
    border-bottom: 1px solid black;
}

.wording span.centry {
    font-weight: bold;
}

.wording div.table {
    display: block;
    margin-left: auto;
    margin-right: auto;
    text-align: center;
    width: 90%;
}

.wording span.indented {
    background: inherit;
    display: block;
    margin-left: 2em;
    margin-bottom: 1em;
    margin-top: 1em;
}

.wording span.uppercase {
    text-transform: uppercase;
}

.wording span.ucode {
    font-variant: small-caps;
    text-transform: uppercase;
    font-size: 90%;
}

.wording span.uname {
    font-variant: small-caps;
    text-transform: uppercase;
    font-size: 90%;
}

.wording table.enumerate {
    border: 0;
    margin: 0;
}

.wording table.enumerate td {
    padding: 0;
}

.wording table.enumerate td:first-child {
    width: 1cm;
    text-align: right;
}

@media (prefers-color-scheme: dark) {
    .wording {
        background-color: #171717;
        color: #d0d0d0;
    }

    .wording span.mjx-mstyle {
        color: #d0d0d0 !important
    }

    .wording a:link {
        color: #64adff;
    }

    .wording a:visited {
        color: #a36ae6;
    }

    .wording a.hidden_link {
        text-decoration: none;
        color: inherit;
    }

    .wording span.phantom {
        color: #171717;
    }

    .wording a.index:before {
        color: #d0d0d0;
        background-color: #4b6353;
    }

    .wording .comment {
        color: #35da00;
    }

    .wording .footnote .comment {
        color: #35da00;
    }

    .wording .example .comment {
        color: #35da00;
    }

    .wording .note .comment {
        color: #35da00;
    }

    .wording span.keyword {
        color: #12cabe;
    }

    .wording span.parenthesis {
        color: #ff1515;
    }

    .wording span.curlybracket {
        color: #ff1515;
    }

    .wording span.squarebracket {
        color: #ff1515;
    }

    .wording span.literal {
        color: #dfa837;
    }

    .wording span.literalterminal {
        color: #dfa837;
    }

    .wording span.operator {
        color: #baa6b9;
    }

    .wording span.anglebracket {
        color: #baa6b9;
    }

    .wording span.preprocessordirective {
        color: #b27c58;
    }

    .wording table {
        border-color: #d0d0d0;
    }

    .wording td.border {
        border-color: #d0d0d0;
    }

    .wording td.border {
        border-left-color: #d0d0d0;
    }

    .wording tr.rowsep, td.cline {
        border-top-color: #d0d0d0;
    }

    .wording tr.capsep {
        border-top-color: #d0d0d0;
    }

    .wording th {
        border-bottom-color: #d0d0d0;
    }

    .wording .footnoteSeparator {
        background-color: #d0d0d0;
    }

    .wording text {
        fill: #d0d0d0;
    }

    .wording path {
        stroke: #d0d0d0;
    }

    .wording polygon {
        stroke: #d0d0d0;
        fill: #d0d0d0;
    }

    .wording ellipse {
        stroke: #d0d0d0;
    }

}

.wording .mjx-chtml {
    display: inline-block;
    line-height: 0;
    text-indent: 0;
    text-align: left;
    text-transform: none;
    font-style: normal;
    font-weight: normal;
    font-size: 100%;
    font-size-adjust: none;
    letter-spacing: normal;
    word-wrap: normal;
    word-spacing: normal;
    white-space: nowrap;
    float: none;
    direction: ltr;
    max-width: none;
    max-height: none;
    min-width: 0;
    min-height: 0;
    border: 0;
    margin: 0;
    padding: 1px 0
}

.wording .MJXc-display {
    display: block;
    background: inherit;
    text-align: center;
    margin: 1em 0;
    padding: 0
}

.wording .mjx-chtml[tabindex]:focus, .wording  :focus .mjx-chtml[tabindex] {
    display: inline-table
}

.wording .mjx-full-width {
    text-align: center;
    display: table-cell !important;
    width: 10000em
}

.wording .mjx-math {
    display: inline-block;
    border-collapse: separate;
    border-spacing: 0
}

.wording .mjx-math * {
    display: inline-block;
    -webkit-box-sizing: content-box !important;
    -moz-box-sizing: content-box !important;
    box-sizing: content-box !important;
    text-align: left
}

.wording .mjx-numerator {
    display: block;
    background: inherit;
    text-align: center
}

.wording .mjx-denominator {
    display: block;
    background: inherit;
    text-align: center
}

.wording .MJXc-stacked {
    height: 0;
    position: relative
}

.wording .MJXc-stacked > * {
    position: absolute
}

.wording .MJXc-bevelled > * {
    display: inline-block
}

.wording .mjx-stack {
    display: inline-block
}

.wording .mjx-op {
    display: block;
    background: inherit
}

.wording .mjx-under {
    display: table-cell
}

.wording .mjx-over {
    display: block;
    background: inherit
}

.wording .mjx-over > * {
    padding-left: 0px !important;
    padding-right: 0px !important
}

.wording .mjx-under > * {
    padding-left: 0px !important;
    padding-right: 0px !important
}

.wording .mjx-stack > .mjx-sup {
    display: block;
    background: inherit
}

.wording .mjx-stack > .mjx-sub {
    display: block;
    background: inherit
}

.wording .mjx-prestack > .mjx-presup {
    display: block;
    background: inherit
}

.wording .mjx-prestack > .mjx-presub {
    display: block;
    background: inherit
}

.wording .mjx-delim-h > .mjx-char {
    display: inline-block
}

.wording .mjx-surd {
    vertical-align: top
}

.wording .mjx-mphantom * {
    visibility: hidden
}

.wording .mjx-merror {
    background-color: #FFFF88;
    color: #CC0000;
    border: 1px solid #CC0000;
    padding: 2px 3px;
    font-style: normal;
    font-size: 90%
}

.wording .mjx-annotation-xml {
    line-height: normal
}

.wording .mjx-menclose > svg {
    fill: none;
    stroke: currentColor
}

.wording .mjx-mtr {
    display: table-row
}

.wording .mjx-mlabeledtr {
    display: table-row
}

.wording .mjx-mtd {
    display: table-cell;
    text-align: center
}

.wording .mjx-label {
    display: table-row
}

.wording .mjx-box {
    display: inline-block
}

.wording .mjx-block {
    display: block;
    background: inherit
}

.wording .mjx-span {
    display: inline
}

.wording .mjx-char {
    display: block;
    background: inherit;
    white-space: pre
}

.wording .mjx-itable {
    display: inline-table;
    width: auto
}

.wording .mjx-row {
    display: table-row
}

.wording .mjx-cell {
    display: table-cell
}

.wording .mjx-table {
    display: table;
    width: 100%
}

.wording .mjx-line {
    display: block;
    background: inherit;
    height: 0
}

.wording .mjx-strut {
    width: 0;
    padding-top: 1em
}

.wording .mjx-vsize {
    width: 0
}

.wording .MJXc-space1 {
    margin-left: .167em
}

.wording .MJXc-space2 {
    margin-left: .222em
}

.wording .MJXc-space3 {
    margin-left: .278em
}

.wording .mjx-ex-box-test {
    position: absolute;
		overflow-x: visible;
		overflow-y: default;
    width: 1px;
    height: 60ex
}

.wording .mjx-line-box-test {
    display: table !important
}

.wording .mjx-line-box-test span {
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}

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}

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}

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}

@font-face {
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}

@font-face {
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}

@font-face {
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}

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<body><div>
<nav><div><div>
<h1 class="hide-on-wide name-of-paper">constexpr pointer tagging</h1>
<div class="paper-info">
	<div><span class="key">Number:</span> P3125R3</div>
	<div><span class="key">Date:</span> <time>2025-01-13</time></div>
	<div><span class="key">Audience:</span> LEWG</div>
	<div><span class="key">Reply-to:</span> <a href="mailto:cpp@hanicka.net">Hana Dusíková</a></div>
</div>

<div id='toc'><h2 id='_toc'><a href='#_toc'>Table of contents</a></h2>
<ul>
<li><a href='#revision-history'>Revision history</a></li><li><a href='#introduction-and-motivation'>Introduction and motivation</a><ul>
<ul>
<li><a href='#use-cases'>Use cases</a></li><li><a href='#safety'>Safety</a><ul>
<ul>
<li><a href='#unsafe-operations'>Unsafe operations</a></li></ul>
</ul>
</li><li><a href='#examples'>Examples</a><ul>
<ul>
<li><a href='#hamt-early-leaves'>HAMT early leaves</a></li><li><a href='#smart-(non-)owning-pointer'>Smart (non-)owning pointer</a></li><li><a href='#llvm's-l-value'>LLVM's L-value</a></li></ul>
</ul>
</li></ul>
</ul>
</li><li><a href='#implementation-experience'>Implementation experience</a><ul>
<ul>
<li><a href='#implementation-in-the-library'>Implementation in the library</a><ul>
<ul>
<li><a href='#accessing-raw-tagged-pointers'>Accessing raw tagged pointers</a></li></ul>
</ul>
</li><li><a href='#implementation-in-the-compiler'>Implementation in the compiler</a><ul>
<ul>
<li><a href='#compiler-builtins'>Compiler builtins</a></li><li><a href='#constant-evaluation'>Constant evaluation</a></li><li><a href='#pointer-provenance-and-optimization'>Pointer provenance and optimization</a></li><li><a href='#alternative-constexpr-compatible-implementation'>Alternative constexpr compatible implementation</a></li></ul>
</ul>
</li></ul>
</ul>
</li><li><a href='#design'>Design</a><ul>
<ul>
<ul>
<ul>
<li><a href='#preconditions-and-eligibility-of-constructors'>Preconditions and eligibility of constructors</a></li><li><a href='#representation-of-tag-value'>Representation of tag value</a></li><li><a href='#converting-to-bit-representation'>Converting to bit representation</a></li></ul>
</ul>
<li><a href='#tuple-protocol'>Tuple protocol</a></li></ul>
</ul>
</li><li><a href='#things-it's-not-doing-and-why'>Things it's not doing and why</a></li><li><a href='#impact-on-existing-code'>Impact on existing code</a></li><li><a href='#proposed-changes-to-wording'>Proposed changes to wording</a><ul>
<ul>
<li><a href='#feature-test-macro'>Feature test macro</a></li></ul>
</ul>
</li></ul>
</div>
</div></div></nav>

<article>
<div><div>
<div><div>
	<h1 class="hide-on-narrow name-of-paper">constexpr pointer tagging</h1>
	<p>This paper proposes a new library non-owning pointer and value pair which has ability to store small amount of information in a <em>tag</em> in alignment low-bits. This functionality is also usable in <code>constexpr</code> environment so. It's meant to be a building tool to build more advanced data-structures and also last requirement for <code>atomic&lt;std::shared_ptr&lt;T&gt;&gt;</code> to be constexpr.</p>
	<h2 id='revision-history'><a href='#revision-history'>Revision history</a></h2>
	<ul>
		<li><a href="https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2024/p3125r2.html">R2</a>&#x2005;→&#x2005;R3: polishing design and <a href="#proposed-changes-to-wording">added wording</a></li>
		<li><a href="https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2024/p3125r1.html">R1</a>&#x2005;→&#x2005;<a href="https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2024/p3125r2.html">R2</a>: simplifying design by removing schemas and the heavy interface, massive simplification as discussed in SG1 (<code>pointer_tag_pair</code>, required <code>sizeof(pointer_tag_pair) == sizeof(T*)</code>)</li>
		<li><a href="https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2024/p3125r0.pdf">R0</a>&#x2005;→&#x2005;<a href="https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2024/p3125r1.html">R1</a>: proposing and explaining design based on existing implementation</li>
	</ul>
	<h2 id='introduction-and-motivation'><a href='#introduction-and-motivation'>Introduction and motivation</a></h2>
	<p>Pointer tagging is widely known and used technique (<a href="https://takenobu-hs.github.io/downloads/haskell_ghc_illustrated.pdf">Glasgow Haskell Compiler</a>, LLVM's <code><a href="https://github.com/llvm/llvm-project/blob/8e5aa538caccef167e8096b2173fdaf2be9cc129/llvm/include/llvm/ADT/PointerIntPair.h#L80">PointerIntPair</a></code>, <code><a href="https://github.com/llvm/llvm-project/blob/8e5aa538caccef167e8096b2173fdaf2be9cc129/llvm/include/llvm/ADT/PointerUnion.h#L112">PointerUnion</a></code>, <a href="https://blog.codingconfessions.com/p/cpython-garbage-collection-internals">CPython's garbage collector</a>, <a href="https://alwaysprocessing.blog/2023/03/19/objc-tagged-ptr">Objective C</a> / Swift, Chrome's <a href="https://v8.dev/blog/pointer-compression">V8 JavaScript engine</a>, <a href="https://www.gap-system.org">GAP</a>, <a href="https://ocaml.org/docs/memory-representation#distinguishing-integers-and-pointers-at-runtime">OCaml</a>, <a href="https://pbr-book.org/4ed/Utilities/Containers_and_Memory_Management#TaggedPointers">PBRT</a>). All major CPU vendors provides mechanism for pointer tagging (Intel's LAM <a href="https://cdrdv2-public.intel.com/835759/325462-sdm-vol-1-2abcd-3abcd-4.pdf">linear address masking</a>, AMD's <a href="https://www.amd.com/content/dam/amd/en/documents/processor-tech-docs/programmer-references/24593.pdf">Upper Address Ignore</a>, ARM's TBI <a href="https://en.wikichip.org/wiki/arm/tbi">top byte ignore</a> and MTE <a href="https://en.wikichip.org/wiki/arm/mte">memory tagging extension</a>). All widely used 64 bit platforms are <a href="https://muxup.com/2023q4/storing-data-in-pointers">not using more than 48 or 49 bits of the pointers</a>.</p>
	<p>This functionality widely supported can't be expressed in a standard conforming way.</p>
	<p><a href="https://doc.rust-lang.org/std/primitive.pointer.html#examples-9">Rust</a>, <a href="https://dlang.org/library/std/bitmanip/tagged_pointer.html">Dlang</a>, or <a href="https://zig.news/orgold/type-safe-tagged-pointers-with-comptime-ghi">Zig</a> has an interface for pointer tagging. This is demonstrating demand for the feature and C++ should have it too and it should also work in <code>constexpr</code>.</p>
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</svg></div></div>	<p>Generally programmer can consider low-bits used for alignment to be safely used for storing an information. Upper bits are available on different platforms under different conditions (runtime processor setting, CPU generation, ...). This proposal only proposes interface to accessing low bits for storing // reading a tag value, not observing bits of a pointer.</p>
	<p>This proposal doesn't propose accessing any other bits other than low-bits which are known to be zero due alignment. <a href="https://github.com/cplusplus/papers/issues/1903#issuecomment-2488661934">SG1 doesn't want</a> to standardize access to high-bits as it's considered dangerous and non-portable. And can limit future development of security features in OS and CPUs for which high-bits are used.</p>
	<h3 id='use-cases'><a href='#use-cases'>Use cases</a></h3>
	<p>There are three basic use-cases of pointer tagging:</p>
	<ul>
		<li>marking pointer with an information (in allocators, used as a tiny refcount, or marking source of the pointer)</li>
		<li>pointee polymorphism (usually in data structures, eg. in trees: next node can be an internal node or a leaf)</li>
		<li>in-place polymorphism (similarly as variant, some bits stores an information about rest of payload, it can be a pointer, a number, a float, a small string, ...)</li>
	</ul>
  <p>This paper aims to solve only first two use-cases.</p>
	<h3 id='safety'><a href='#safety'>Safety</a></h3>
	<p>Pointer tagging can be currently implemented in C++ only with <code>reinterpret_cast</code> and bit manipulating with shifts / bitand / bitor and this approach is prone to be unsafe and hard to debug as it's not expressed clearly in code what is the right intention, so compiler can't even diagnose incompatibility between encode/decode. By giving a name to this tool it allows programmer to express intent clearly and compiler to optimize and diagnose problems properly.</p>
	<p>Preconditions and mandates of proposed <code>std::pointer_tag_pair</code> makes it unlike to use it unsafely as potentially dangerous operations (<code>std::pointer_tag_pair&lt;Pointee, Tag, Bits&gt;::from_tagged(<em>pointer</em>)</code> and <code>std::pointer_tag_pair&lt;Pointee, Tag, Bits&gt;::template from_overaligned&lt;PromisedAlignment&gt;(<em>pointer</em>)</code>) are verbose and visible.</p>
	<h4 id='unsafe-operations'><a href='#unsafe-operations'>Unsafe operations</a></h4>
	<p>Two mentioned functions are provided so user can explicitly provide over-aligned pointer which would otherwise won't be compatible with number of requested bits or interact with existing functionality for pointer tagging (which will allow gradual adoption of the feature and replace old code).</p>
	<h3 id='examples'><a href='#examples'>Examples</a></h3>
	<h4 id='hamt-early-leaves'><a href='#hamt-early-leaves'>HAMT early leaves</a></h4>
	<p>Following example is a recursive search implementation for a <a href="https://en.wikipedia.org/wiki/Hash_array_mapped_trie">HAMT (hash-array-mapped-trie)</a> data structure. Where a tag value indicates leaf node.</p>
	<pre><code class="language-cpp">// requesting only 1 bit of information
using hamt_node_pointer = std::pointer_tag_pair&lt;const void, bool, 1&gt;;
static_assert(sizeof(hamt_node_pointer) == sizeof(void *));

constexpr const T * find_value_in_hamt(hamt_node_pointer tptr, uint32_t hash) {
	if (tptr == nullptr) // checks only pointer part
		return nullptr;
	
	if (tptr.tag()) // we found leaf node, tag is boolean as specified
		return *static_cast&lt;const T *&gt;(tptr.pointer());
	
	const auto * node = static_cast&lt;const internal_node *&gt;(tptr.pointer());
	const auto next_node = node[hash & 0b1111u];
	
	return find_value_in_hamt(next_node, hash >> 4); // recursive descend
}</code></pre>
<h4 id='smart-(non-)owning-pointer'><a href='#smart-(non-)owning-pointer'>Smart (non-)owning pointer</a></h4>
  <p>This example shows <code>maybe_owning_ptr</code> type which can be both a reference or an owner:</p>
  <pre><code class="language-cpp">template &lt;typename T&gt; class maybe_owning_ptr {
  enum class ownership: unsigned {
    reference,
    owning,
  };
  
  std::pointer_tag_pair&lt;T, ownership, 1&gt; _ptr;
public:
  constexpr maybe_owning_ptr(T* && pointer) noexcept: _ptr{pointer, ownership::owning} { }
  constexpr maybe_owning_ptr(T & ref) noexcept: _ptr{&ref, ownership::reference} { }
  
  constexpr decltype(auto) operator*() const noexcept {
    return *_ptr.pointer();
  }
  
  constexpr T * operator->() const noexcept {
    return _ptr.pointer();
  }
  
  constexpr ~maybe_owning_ptr() noexcept {
    if (_ptr.tag() == ownership::owning) {
      delete _ptr.pointer();
    }
  }
};

static_assert(sizeof(maybe_owning_ptr&lt;int&gt;) == sizeof(int *));</code></pre>
<h4 id='llvm's-l-value'><a href='#llvm's-l-value'>LLVM's L-value</a></h4>
<p>Following code is simplification of LLVM's representation of <a href="https://github.com/llvm/llvm-project/blob/171d3edd0507422f64cc11b33dac7b7f2b703f76/clang/include/clang/AST/APValue.h#L146-L149">pointer/reference type</a> which is implemented with LLVM's <code>PointerIntPair</code> and is inside constant evaluator. This type holds subnodes of different kind: pointer to local/static variable, dynamic allocation, type info pointer, result of temporary.</p>
<pre><code class="language-cpp">struct LValueBase {
	using PtrTy = llvm::PointerUnion&lt;const ValueDecl *, 
                                    const Expr *,
                                    TypeInfoLValue,
                                    DynamicAllocLValue&gt;;

	struct PathEntry {
		uint64_t value;
	};
	
	using PathTy = std::vector&lt;PathEntry&gt;;
	
	PtrTy Location;
	PathEntry SubObjectPath;
};

APValue DereferencePointer(EvalInfo &amp; Context, const LValueBase & Base) {
	auto & object = Context.Visit(Base.Location);
	return object.NavigateToSuboject(Base.SubObjectPath);
}</code></pre>
	<h2 id='implementation-experience'><a href='#implementation-experience'>Implementation experience</a></h2>
	<p>Old version of this proposal has been implemented within libc++ &amp; clang and it is accessible on <a href="https://github.com/llvm/llvm-project/pull/111861">github</a> and <a href="https://compiler-explorer.com/z/Y884arzjd">compiler explorer</a>. This functionality can't be implemented as a pure library (<code>reinterpret_cast</code> is not allowed during constant evaluation) and needs compiler support in some form.</p> 
	<h3 id='implementation-in-the-library'><a href='#implementation-in-the-library'>Implementation in the library</a></h3>
	<p>Library is providing a special pair-like type containing pointer and small tag type, and user requested number of bits. The number of bits is by default deduced by default alignment of requested pointee type. Requesting more bits than alignment will disable normal constructor, and force user to use <code>::from_overaligned</code> function as overalignment is not part of C++'s type system.</p>
	<p>In terms of library design there is nothing surprising, and it's pretty straightforward wrapper which encode and decode tagged pointer on its boundaries and provides basic pointer functionality.</p>
	<h4 id='accessing-raw-tagged-pointers'><a href='#accessing-raw-tagged-pointers'>Accessing raw tagged pointers</a></h4>
	<p>The pointer int pair has support to access <em>raw</em> tagged pointer. Which is a pointer which can't be dereferenced or otherwise manipulated with, it's an opaque value usable only with legacy tagging interface or it can be used to construct <code>pointer_tag_pair</code> back from it. Existence of this interface allows ability to store such pointers in existing interfaces (atomic, other smart pointers). Question is if it should be <code>uintptr_t</code> or <code>void*</code>. I prefer <code>void*</code> as roundtriping thru an integer looses information about provenance and can disable some optimization.</p>
	<h3 id='implementation-in-the-compiler'><a href='#implementation-in-the-compiler'>Implementation in the compiler</a></h3>
	<p>The implementation is providing builtins to manipulating raw pointers and isn't meant to be used by end-users, only to allow this library functionality.</p>
	<h4 id='compiler-builtins'><a href='#compiler-builtins'>Compiler builtins</a></h4>
	<p>Implementation needs to manipulate pointers without casting them to integers and back. To do so the provided set of builtins is designed to store/load a value (with size of few bits) into/from unimportant/unused bits of a pointer without observing actual pointer representation.</p>
	<h4 id='constant-evaluation'><a href='#constant-evaluation'>Constant evaluation</a></h4>
	<p>With these builtins it's trivial to implement semantically identical behaviour for the constant evaluation. In case of my implementation, pointers in clang are not represented as addresses but as symbols (original AST variable, allocation, static object + path to subobject, its provenance) and there is no address to manipulate. Actual tag value in such "pointer" is then stored in a metadata of the pointer itself and builtins only provide access to it. Technically such storage can provide more bits than pointer "size", but there are internal checks which make sure it allows only bits which would be accessible in runtime based on alignment of individual pointer.</p>
	<p>Any attempt to deference or otherwise manipulate such pointer, which would be unsafe in runtime, is detected and reported by the interpreter. Only the provided builtins can recover original pointer and tag value.</p>
	<h4 id='pointer-provenance-and-optimization'><a href='#pointer-provenance-and-optimization'>Pointer provenance and optimization</a></h4>
	<p>Easiest way to implement builtins for pointer tagging is to do the same thing <code>reinterpret_cast</code> is doing, which was my first implementation approach. But this approach leads to loosing pointer's provenance and compiler loosing information which otherwise should be accessible for optimizer to use.</p>
	<p>For unmasking there is already <code>ptr.mask</code> LLVM's builtin, but there is no similar intrinsic to do the tagging. Hence the builtins needs to interact with backend and be implemented with a low level backend intrinsic to do the right thing. This shows how actually unimplementable pointer tagging is in existing language.</p>
	<h4 id='alternative-constexpr-compatible-implementation'><a href='#alternative-constexpr-compatible-implementation'>Alternative constexpr compatible implementation</a></h4>
	<p>Alternative way to implement <code>constexpr</code> support (for compiler which don't have heavy pointer representation in their interprets) is inserting a hidden intermediate object holding the metadata and pointer to original object. This allows exactly same semantic as the metadata approach, and can be completely implemented in library using <code>if consteval</code>, but it will need allocation during constant evaluation.</p>
	<h2 id='design'><a href='#design'>Design</a></h2>
	<p>The <code>std::pointer_int_pair</code> is simple pair-like template providing only necessory interface and is not meant to provide heavy interface as it's preferable to not hide pointer tagging / untagging from users. This is mean to be a low-level facility. Main requirement on the type is it must be always same size as stored pointer and not more.</p>
<pre><code class="language-cpp">template &lt;typename PointeeT, typename TagT, unsigned BitsRequested = std::countr_zero(alignof(PointeeT))&gt;
	requires(std::is_object_v&lt;PointeeT&gt; &amp;&amp; std::is_unsigned_v&lt;_underlying_type_or_identity_t&lt;TagT&gt;&gt; &amp;&amp;
					 std::is_same_v&lt;TagT, std::remove_cvref_t&lt;TagT&gt;&gt; &amp;&amp; (BitsRequested &lt; sizeof(PointeeT*) * CHAR_BIT))
struct pointer_tag_pair {
public:
	using element_type				= PointeeT;
	using pointer_type				= element_type*;
	using tagged_pointer_type = void*; // I prefer `void *` to avoid loosing provenance
	using tag_type						= TagT;

private:
	// exposition only
	static constexpr unsigned <em>alignment-needed</em> = (1u &lt;&lt; BitsRequested);
	static constexpr /* unsigned-integer */ <em>tag-mask</em> = (<em>alignment-needed</em> - 1u);
	static constexpr /* unsigned-integer */ <em>pointer-mask</em> = ~<em>tag-mask</em>;
	using <em>numeric-tag</em> = _underlying_type_or_identity_t&lt;tag_type&gt;;

	// conversion to numeric tags
	static constexpr <em>numeric-tag</em> <em>to-numeric-tag</em>(tag_type) noexcept;
	static constexpr tag_type <em>from-numeric-tag</em>(<em>numeric-tag</em>) noexcept;

	// required to have size same as sizeof(Pointee *)
	<em>unspecified-pointer-like-type</em> <em>internal-pointer</em> = nullptr; 

	// internal constructor for `from_overaligned` and `from_tagged` functions
	explicit constexpr pointer_tag_pair(<em>unspecified-pointer-like-type</em> ptr) noexcept : <em>internal-pointer</em>{ptr} {}


public:
	pointer_tag_pair() = default;
	pointer_tag_pair(nullptr_t) = default;
	pointer_tag_pair(const pointer_tag_pair&amp;) = default;
	pointer_tag_pair(pointer_tag_pair&amp;&amp;) = default;
	pointer_tag_pair&amp; operator=(const pointer_tag_pair&amp;) = default;
	pointer_tag_pair&amp; operator=(pointer_tag_pair&amp;&amp;) = default;
	~pointer_tag_pair() = default;

	// Precondition: alignment of `ptr` &gt;= `<em>alignment-needed</em>`
	// Precondition: `tag` value is representable in its underlying type within bit field 
	//   of size `BitsRequested` bits or value of `tag` is equal to zero
	constexpr pointer_tag_pair(pointer_type ptr, tag_type tag)
		requires(alignof(element_type) &gt;= <em>alignment-needed</em>): <em>internal-pointer</em>{
			<em>__builtin_tag_pointer_mask_or</em>(ptr, <em>to-numeric-tag</em>(tag), <em>tag-mask</em>)
		} { }

	// Precondition: alignment of `ptr` &gt;= `PromisedAlignment`
	// Precondition: `tag` value is representable in its underlying type within bit field
	//   of size `BitsRequested` bits or value of `tag` is equal to zero
	template &lt;unsigned PromisedAlignment&gt;
	static constexpr pointer_tag_pair from_overaligned(pointer_type ptr, tag_type tag)
		requires(PromisedAlignment &gt;= <em>alignment-needed</em>)
	{
		return pointer_tag_pair{static_cast&lt;<em>unspecified-pointer-like-type</em>&gt;(
			<em>__builtin_tag_pointer_mask_or</em>(ptr, <em>to-numeric-tag</em>(tag), <em>tag-mask</em>)
		)};
	}

	// Precondition: valid pointer if untagged
	static pointer_tag_pair from_tagged(tagged_pointer_type ptr) { // no-constexpr
		return pointer_tag_pair{reinterpret_cast&lt;<em>unspecified-pointer-like-type</em>&gt;(ptr)};
	}

	// access tagged pointer (for interaction with existing tagging mechanisms)
	tagged_pointer_type tagged_pointer() const noexcept { 
		return reinterpret_cast&lt;tagged_pointer_type&gt;(<em>internal-pointer</em>);
	}
	
	// access untagged pointer
	constexpr pointer_type pointer() const noexcept {
		return static_cast&lt;pointer_type&gt;(<em>__builtin_tag_pointer_mask</em>(<em>internal-pointer</em>, <em>pointer-mask</em>));
	}
	
	// access tag value
	constexpr tag_type tag() const noexcept {
		return _from_bitfield_tag(<em>__builtin_tag_pointer_mask_as_int</em>(<em>internal-pointer</em>, <em>tag-mask</em>));
	}

	// swap
	friend constexpr void swap(pointer_tag_pair&amp; lhs, pointer_tag_pair&amp; rhs) noexcept { std::swap(lhs.<em>internal-pointer</em>, rhs.<em>internal-pointer</em>); }

	// comparing {pointer(), tag()} &lt;=&gt; {pointer(), tag()} for consistency
	friend constexpr auto operator&lt;=&gt;(pointer_tag_pair lhs, pointer_tag_pair rhs) noexcept {
		return std::tuple(lhs.pointer(), lhs.tag()) &lt;=&gt; std::tuple(rhs.pointer(), rhs.tag());
	}

	friend bool operator==(pointer_tag_pair, pointer_tag_pair) = default;
};</code></pre><h4 id='preconditions-and-eligibility-of-constructors'><a href='#preconditions-and-eligibility-of-constructors'>Preconditions and eligibility of constructors</a></h4>
  <p>Constructor taking a pointer and tag value is only available if alignment of the pointee type is enough to store requested number of bits.</p>
	<p>Both the constructor and <code>::from_overaligned</code> function have preconditions checking if pointer is aligned enough as expected (in the constructor) or promised overaligned (in the <code>::from_overaligned</code> function). In addition to this there is a precondition to make sure value of tag type is representible with <code>RequestedBits</code>.</p>
<h4 id='representation-of-tag-value'><a href='#representation-of-tag-value'>Representation of tag value</a></h4>
	<p>Tag value can only be unsigned integral type or an enum type with underlying unsigned integral type. The value is converted to the underlying or kepy original unsigned integral type and then it is bit masked with mask based on <em>BitsRequested</em> bits (<code>1u &lt;&lt; BitsRequested - 1u</code>).</p>
	<p>It's precondition failure for the value after this conversion different than original value. An attempt was made to support signed type, but unfortunetely storing unrepresentable value into a bitfield is implementation specific. And this can be added later as extension to current design.</p>
<h4 id='converting-to-bit-representation'><a href='#converting-to-bit-representation'>Converting to bit representation</a></h4>
<pre><code class="language-cpp">template &lt;typename T&gt; struct <em>underlying_type_or_identity</em> {
  using type = T;
};

template &lt;typename T&gt; requires(std::is_enum_v&lt;T&gt;) struct <em>underlying_type_or_identity</em>&lt;T&gt; {
  using type = std::underlying_type_t&lt;T&gt;;
};

static constexpr auto <em>to-bitfield-tag</em>(tag_type _tag) {
  using underlying_type = <em>underlying_type_or_identity</em>&lt;tag_type&gt;::type;
  
  if constexpr (Bits == 0) {
    <em>PRECONDITION-CHECK</em>(0 == (static_cast&lt;underlying_type&gt;(_tag)), "Only zero is representable with Bits == 0");
    return underlying_type{0};
  } else {
    struct {
      underlying_type _value : Bits;
    } _helper{._value = static_cast&lt;underlying_type&gt;(_tag)};
    
    <em>PRECONDITION-CHECK</em>(_helper._value == (static_cast&lt;underlying_type&gt;(_tag)), "Value is not representable in requested amount of Bits.");
    
    return _helper._value;
  }
}

static constexpr auto from-bitfield-tag(std::size_t _tag) -&gt; tag_type {
  using underlying_type = <em>underlying_type_or_identity</em>&lt;tag_type&gt;::type;

  if constexpr (Bits == 0) {
    return tag_type{0};
  } else {
    struct {
      underlying_type _value : Bits;
    } _helper{._value = static_cast&lt;underlying_type&gt;(_tag)};

   return tag_type{_helper._value};
  }
}</code></pre><h3 id='tuple-protocol'><a href='#tuple-protocol'>Tuple protocol</a></h3>
	<p><code>pointer_tag_pair</code> supports being destructured, but it doesn't model <code><em>tuple-like</em></code> (as it would open whole can of worms, as told by STL). But following code should work:</p>
	<pre><code class="language-cpp">auto [ptr, tag] = a_pointer_tag_pair;</code></pre>
<pre><code class="language-cpp">template &lt;typename Pointee, typename Tag, unsigned BitsRequested&gt;
struct tuple_size&lt;pointer_tag_pair&lt;Pointee, Tag, BitsRequested&gt;&gt; : std::integral_constant&lt;std::size_t, 2&gt; {};

template &lt;typename Pointee, typename Tag, unsigned BitsRequested&gt;
struct tuple_element&lt;0, pointer_tag_pair&lt;Pointee, Tag, BitsRequested&gt;&gt; {
  using type = Pointee*;
};

template &lt;typename Pointee, typename Tag, unsigned BitsRequested&gt;
struct tuple_element&lt;1, pointer_tag_pair&lt;Pointee, Tag, BitsRequested&gt;&gt; {
  using type = Tag;
};

template &lt;typename Pointee, typename Tag, unsigned BitsRequested&gt;
struct tuple_element&lt;0, const pointer_tag_pair&lt;Pointee, Tag, BitsRequested&gt;&gt; {
  using type = Pointee*;
};

template &lt;typename Pointee, typename Tag, unsigned BitsRequested&gt;
struct tuple_element&lt;1, const pointer_tag_pair&lt;Pointee, Tag, BitsRequested&gt;&gt; {
  using type = Tag;
};

template &lt;size_t I, typename Pointee, typename Tag, unsigned BitsRequested&gt;
constexpr auto get(pointer_tag_pair&lt;Pointee, Tag, BitsRequested&gt; pair) noexcept
    -&gt; tuple_element&lt;I, pointer_tag_pair&lt;Pointee, Tag, BitsRequested&gt;&gt;::type {
  if constexpr (I == 0) {
    return pair.pointer();
  } else {
    static_assert(I == 1);
    return pair.tag();
  }
}</code></pre><h2 id='things-it's-not-doing-and-why'><a href='#things-it's-not-doing-and-why'>Things it's not doing and why</a></h2>
<ul>
	<li><em>modeling pointer</em> — this is not a pointer type, access to the pointer should be explicitly visible,</li>
	<li><em>convertible to bool</em> — it's not sure if it means <code>.pointer() == nullptr</code> or also <code>.tag() == 0</code>,</li>
	<li><em>manage lifetime</em> — this is not a owning pointer, it's a tool to build one,</li>
	<li><em>using other than non-alignment bits</em> — these are not portable and are subject of being enabled/disabled as an OS setting, this would create at best ABI problems,</li>
	<li><em>changing size based on bits requested</em> — intention of this type to be same size of pointer, not be generic pair of pointer and any value,</li>
	<li><em>supporting function pointers</em> — these doesn't need to be real pointer, but handlers, and can even have bigger size than normal pointer.</li>
	<li><em>supporting signed tag types</em> — it's tricky and using bitfield is implementation specific.</li>
</ul>
<h2 id='impact-on-existing-code'><a href='#impact-on-existing-code'>Impact on existing code</a></h2>
	<p>None, this is purely an API extension. It allows to express semantic clearly for a compiler instead of using an unsafe <code>reinterpret_cast</code> based techniques. Integral part of the proposed design is ability to interact with such existing code and migrate away from it.</p>

<h2 id='proposed-changes-to-wording'><a href='#proposed-changes-to-wording'>Proposed changes to wording</a></h2>
<p>This is probably really incorrect, follow the design, sorry.</p>
	<div class='wording'>
<h1 ><a class='secnum' style='min-width:50pt'>20</a> Memory management library <a class='abbr_ref' href='./#mem'>[mem]</a></h1>

<div id='general' class='section'>
  
<h2 ><a class='secnum' href='#general' style='min-width:65pt'>20.1</a> General <a class='abbr_ref' href='mem.general'>[mem.general]</a></h2>

<div class='para' id='general-1'>
  <div class='marginalizedparent'><a class='marginalized' href='#general-1'>1</a></div>
  <div class='sourceLinkParent'><a class='sourceLink' href='http://github.com/Eelis/draft/tree/eb3b44202e7ac0c1ade1d69df3adba5fe496b94b/source/memory.tex#L6'>#</a></div>

<div class='texpara'><div id='general-1.sentence-1' class='sentence'>This Clause describes components for memory management<a class='hidden_link' href='#general-1.sentence-1'>.</a></div></div>

<div class='para' id='general-2'><div class='marginalizedparent'><a class='marginalized' href='#general-2'>2</a></div><div class='sourceLinkParent'><a class='sourceLink' href='http://github.com/Eelis/draft/tree/eb3b44202e7ac0c1ade1d69df3adba5fe496b94b/source/memory.tex#L9'>#</a></div></div>
<div class='texpara'><div id='general-2.sentence-1' class='sentence'>The following subclauses describe general memory management facilities,
smart pointers, <span class="added">pointer tag pair, </span>memory resources, and scoped allocators,
as summarized in Table <a href='#tab:mem.summary' title='Table 47: Memory management library summary'>47</a><a class='hidden_link' href='#general-2.sentence-1'>.</a></div></div>

<div class='texpara'>
	
<div class='numberedTable' id='tab:mem.summary'>Table <a href='#tab:mem.summary'>47</a> &mdash; Memory management library summary&emsp;<a href='./tab:mem.summary'>[tab:mem.summary]</a><br>
	
<table >
	<tr id='tab:mem.summary-row-1' class='rowsep'><td class='left'><div class='marginalizedparent'><a class='itemDeclLink' href='#tab:mem.summary-row-1'>🔗</a></div></td><td class='left'><div class='texpara'><div id='tab:mem.summary-row-1-column-2-sentence-1' class='sentence'><b>Subclause</b></div></div></td><td class='left'><div class='texpara'><div id='tab:mem.summary-row-1-column-3-sentence-1' class='sentence'><b>Header</b></div></div></td></tr>
	<tr id='tab:mem.summary-row-2' class='capsep'><td class='left'><div class='marginalizedparent'><a class='itemDeclLink' href='#tab:mem.summary-row-2'>🔗</a></div><div class='texpara'><div id='tab:mem.summary-row-2-column-1-sentence-1' class='sentence'><a href='#memory' title='20.2&emsp;Memory'>[memory]</a></div></div></td><td class='left'><div class='texpara'><div id='tab:mem.summary-row-2-column-2-sentence-1' class='sentence'>Memory</div></div></td><td class='left'><div class='texpara'><div id='tab:mem.summary-row-2-column-3-sentence-1' class='sentence'><span class='texttt'><span class='anglebracket'>&lt;</span>cstdlib<span class='anglebracket'>&gt;</span></span>, <span class='texttt'><span class='anglebracket'>&lt;</span>memory<span class='anglebracket'>&gt;</span></span></div></div></td></tr>
	<tr id='tab:mem.summary-row-3' class='rowsep'><td class='left'><div class='marginalizedparent'><a class='itemDeclLink' href='#tab:mem.summary-row-3'>🔗</a></div><div class='texpara'><div id='tab:mem.summary-row-3-column-1-sentence-1' class='sentence'><a href='#smartptr' title='20.3&emsp;Smart pointers'>[smartptr]</a></div></div></td><td class='left'><div class='texpara'><div id='tab:mem.summary-row-3-column-2-sentence-1' class='sentence'>Smart pointers</div></div></td><td class='left'><div class='texpara'><div id='tab:mem.summary-row-3-column-3-sentence-1' class='sentence'><span class='texttt'><span class='anglebracket'>&lt;</span>memory<span class='anglebracket'>&gt;</span></span></div></div></td></tr>
		
	<tr id='tab:mem.summary-row-3' class='rowsep added'><td class='left'><div class='marginalizedparent'><a class='itemDeclLink' href='#tab:mem.summary-row-3'>🔗</a></div><div class='texpara'><div id='tab:mem.summary-row-3-column-1-sentence-1' class='sentence'><a href='#smartptr' title='?.?&emsp;Pointer tag pair'>[ptrtag]</a></div></div></td><td class='left'><div class='texpara'><div id='tab:mem.summary-row-3-column-2-sentence-1' class='sentence'>Pointer tag pair</div></div></td><td class='left'><div class='texpara'><div id='tab:mem.summary-row-3-column-3-sentence-1' class='sentence'><span class='texttt'><span class='anglebracket'>&lt;</span>memory<span class='anglebracket'>&gt;</span></span></div></div></td></tr>
		
	<tr id='tab:mem.summary-row-4' class='rowsep'><td class='left'><div class='marginalizedparent'><a class='itemDeclLink' href='#tab:mem.summary-row-4'>🔗</a></div><div class='texpara'><div id='tab:mem.summary-row-4-column-1-sentence-1' class='sentence'><a href='#res' title='20.4&emsp;Memory resources'>[mem.<span class='shy'></span>res]</a></div></div></td><td class='left'><div class='texpara'><div id='tab:mem.summary-row-4-column-2-sentence-1' class='sentence'>Memory resources</div></div></td><td class='left'><div class='texpara'><div id='tab:mem.summary-row-4-column-3-sentence-1' class='sentence'><span class='texttt'><span class='anglebracket'>&lt;</span>memory_<span class='shy'></span>resource<span class='anglebracket'>&gt;</span></span></div></div></td></tr>
	<tr id='tab:mem.summary-row-5' class='rowsep'><td class='left'><div class='marginalizedparent'><a class='itemDeclLink' href='#tab:mem.summary-row-5'>🔗</a></div><div class='texpara'><div id='tab:mem.summary-row-5-column-1-sentence-1' class='sentence'><a href='#allocator.adaptor' title='20.5&emsp;Class template scoped_&shy;allocator_&shy;adaptor'>[allocator.<span class='shy'></span>adaptor]</a></div></div></td><td class='left'><div class='texpara'><div id='tab:mem.summary-row-5-column-2-sentence-1' class='sentence'>Scoped allocators</div></div></td><td class='left'><div class='texpara'><div id='tab:mem.summary-row-5-column-3-sentence-1' class='sentence'><span class='texttt'><span class='anglebracket'>&lt;</span>scoped_<span class='shy'></span>allocator<span class='anglebracket'>&gt;</span></span></div></div></td></tr>

</table>

</div>
	
</div>

</div>

<div id='memory' class='section'>
<h2 ><a class='secnum' href='#memory' style='min-width:65pt'>20.2</a> Memory <a class='abbr_ref' href='memory'>[memory]</a></h2>

<div id='memory.syn' class='section'><h3 ><a class='secnum' href='#memory.syn' style='min-width:80pt'>20.2.2</a> Header <span class='texttt'>&lt;memory&gt;</span> synopsis <a class='abbr_ref' href='memory.syn'>[memory.syn]</a></h3><div class='para' id='memory.syn-1'><div class='marginalizedparent'><a class='marginalized' href='#memory.syn-1'>1</a></div><div class='sourceLinkParent'><a class='sourceLink' href='http://github.com/Eelis/draft/tree/eb3b44202e7ac0c1ade1d69df3adba5fe496b94b/source/memory.tex#L32'>#</a></div><div class='texpara'><div id='memory.syn-1.sentence-1' class='sentence'>The header <span id='header:<memory>'><span class='texttt'><span class='anglebracket'>&lt;</span>memory<span class='anglebracket'>&gt;</span></span></span> defines several types and function templates that
describe properties of pointers and pointer-like types, manage memory
for containers and other template types, destroy objects, and
construct objects in
uninitialized memory
buffers (<a href='#pointer.traits' title='20.2.3&emsp;Pointer traits'>[pointer.<span class='shy'></span>traits]</a>–<a href='#specialized.addressof' title='20.2.11&emsp;addressof'>[specialized.<span class='shy'></span>addressof]</a> and <a href='specialized.algorithms' title='26.11&emsp;Specialized &lt;memory&gt; algorithms'>[specialized.<span class='shy'></span>algorithms]</a>)<a class='hidden_link' href='#memory.syn-1.sentence-1'>.</a></div> 
  
<div class='sentence added'>The header also defines the template <span class='textt'>pointer_tag_pair</span> for storing additional information into alignment bits of the pointer while keeping size of the object same as raw pointer. </div>
  
  
<div id='memory.syn-1.sentence-2' class='sentence'>The header also defines the templates
<span class='texttt'>unique_<span class='shy'></span>ptr</span>, <span class='texttt'>shared_<span class='shy'></span>ptr</span>, <span class='texttt'>weak_<span class='shy'></span>ptr</span>,
<span class='texttt'>out_<span class='shy'></span>ptr_<span class='shy'></span>t</span>, <span class='texttt'>inout_<span class='shy'></span>ptr_<span class='shy'></span>t</span>, and various function
templates that operate on objects of these types (<a href='#smartptr' title='20.3&emsp;Smart pointers'>[smartptr]</a>)<a class='hidden_link' href='#memory.syn-1.sentence-2'>.</a></div></div></div>
  
  
  <div class='texpara'><span class='codeblock'><span class='preprocessordirective'>
  <span class='keyword'>namespace</span> ranges <span class='curlybracket'>{</span>
    <span class='keyword'>template</span><span class='anglebracket'>&lt;</span><a href='concept.destructible#concept:destructible' title='18.4.10&emsp;Concept destructible&emsp;[concept.destructible]'><span id='conceptref:destructible'><span class='tcode_in_codeblock'>destructible</span></span></a> T<span class='anglebracket'>&gt;</span>
      <span class='keyword'>constexpr</span> <span class='keyword'>void</span> destroy_at<span class='parenthesis'>(</span>T<span class='operator'>*</span> location<span class='parenthesis'>)</span> <span class='keyword'>noexcept</span>;                              <span class='comment'>// freestanding</span>

    <span class='keyword'>template</span><span class='anglebracket'>&lt;</span><a href='special.mem.concepts#concept:nothrow-input-iterator' title='26.11.2&emsp;Special memory concepts&emsp;[special.mem.concepts]'><span id='conceptref:nothrow-input-iterator_'><span class='tcode_in_codeblock'><i >nothrow-input-iterator</i></span></span></a> I, <a href='special.mem.concepts#concept:nothrow-sentinel-for' title='26.11.2&emsp;Special memory concepts&emsp;[special.mem.concepts]'><span id='conceptref:nothrow-sentinel-for________'><span class='tcode_in_codeblock'><i >nothrow-sentinel-for</i></span></span></a><span class='anglebracket'>&lt;</span>I<span class='anglebracket'>&gt;</span> S<span class='anglebracket'>&gt;</span>
      <span class='keyword'>requires</span> <a href='concept.destructible#concept:destructible' title='18.4.10&emsp;Concept destructible&emsp;[concept.destructible]'><span id='conceptref:destructible_'><span class='tcode_in_codeblock'>destructible</span></span></a><span class='anglebracket'>&lt;</span>iter_value_t<span class='anglebracket'>&lt;</span>I<span class='anglebracket'>&gt;</span><span class='anglebracket'>&gt;</span>
        <span class='keyword'>constexpr</span> I destroy<span class='parenthesis'>(</span>I first, S last<span class='parenthesis'>)</span> <span class='keyword'>noexcept</span>;                              <span class='comment'>// freestanding</span>
    <span class='keyword'>template</span><span class='anglebracket'>&lt;</span><a href='special.mem.concepts#concept:nothrow-input-range' title='26.11.2&emsp;Special memory concepts&emsp;[special.mem.concepts]'><span id='conceptref:nothrow-input-range_'><span class='tcode_in_codeblock'><i >nothrow-input-range</i></span></span></a> R<span class='anglebracket'>&gt;</span>
      <span class='keyword'>requires</span> <a href='concept.destructible#concept:destructible' title='18.4.10&emsp;Concept destructible&emsp;[concept.destructible]'><span id='conceptref:destructible__'><span class='tcode_in_codeblock'>destructible</span></span></a><span class='anglebracket'>&lt;</span>range_value_t<span class='anglebracket'>&lt;</span>R<span class='anglebracket'>&gt;</span><span class='anglebracket'>&gt;</span>
        <span class='keyword'>constexpr</span> borrowed_iterator_t<span class='anglebracket'>&lt;</span>R<span class='anglebracket'>&gt;</span> destroy<span class='parenthesis'>(</span>R<span class='operator'>&amp;</span><span class='operator'>&amp;</span> r<span class='parenthesis'>)</span> <span class='keyword'>noexcept</span>;                   <span class='comment'>// freestanding</span>

    <span class='keyword'>template</span><span class='anglebracket'>&lt;</span><a href='special.mem.concepts#concept:nothrow-input-iterator' title='26.11.2&emsp;Special memory concepts&emsp;[special.mem.concepts]'><span id='conceptref:nothrow-input-iterator__'><span class='tcode_in_codeblock'><i >nothrow-input-iterator</i></span></span></a> I<span class='anglebracket'>&gt;</span>
      <span class='keyword'>requires</span> <a href='concept.destructible#concept:destructible' title='18.4.10&emsp;Concept destructible&emsp;[concept.destructible]'><span id='conceptref:destructible___'><span class='tcode_in_codeblock'>destructible</span></span></a><span class='anglebracket'>&lt;</span>iter_value_t<span class='anglebracket'>&lt;</span>I<span class='anglebracket'>&gt;</span><span class='anglebracket'>&gt;</span>
        <span class='keyword'>constexpr</span> I destroy_n<span class='parenthesis'>(</span>I first, iter_difference_t<span class='anglebracket'>&lt;</span>I<span class='anglebracket'>&gt;</span> n<span class='parenthesis'>)</span> <span class='keyword'>noexcept</span>;            <span class='comment'>// freestanding</span>
  <span class='curlybracket'>}</span>
  
<div class="added">  <span class='comment'>// [ptrtag]</a>, class template pointer_tag_pair</span>
  <span class="added"><span class='keyword'>template</span><span class='anglebracket'>&lt;</span><span class='keyword'>class</span> PointeeT, <span class='keyword'>class</span> TagT, <span class='keyword'>unsigned</span> Bits <span class='operator'>=</span> countr_zero(alignof(PointeeT))<span class='anglebracket'>&gt;</span>
    requires (is_object_v&lt;PointeeT&gt; &amp;&amp; is_unsigned_v&lt;underlying-or-identity&lt;TagT&gt;::type 
              &amp;&amp; is_same_v&lt;TagT, std::remove_cvref_t&lt;TagT&gt;&gt;)
  <span class='keyword'>class</span> pointer_tag_pair;                                                          <span class='comment'>// freestanding</span></span></div>

  <span class='comment'>// <a href='#unique.ptr' title='20.3.1&emsp;Unique-ownership pointers'>[unique.<span class='shy'></span>ptr]</a>, class template <span class='tcode_in_codeblock'>unique_<span class='shy'></span>ptr</span></span>
  <span class='keyword'>template</span><span class='anglebracket'>&lt;</span><span class='keyword'>class</span> T<span class='anglebracket'>&gt;</span> <span class='keyword'>struct</span> default_delete;                                          <span class='comment'>// freestanding</span>
  <span class='keyword'>template</span><span class='anglebracket'>&lt;</span><span class='keyword'>class</span> T<span class='anglebracket'>&gt;</span> <span class='keyword'>struct</span> default_delete<span class='anglebracket'>&lt;</span>T<span class='squarebracket'>[</span><span class='squarebracket'>]</span><span class='anglebracket'>&gt;</span>;                                     <span class='comment'>// freestanding</span>
  <span class='keyword'>template</span><span class='anglebracket'>&lt;</span><span class='keyword'>class</span> T, <span class='keyword'>class</span> D <span class='operator'>=</span> default_delete<span class='anglebracket'>&lt;</span>T<span class='anglebracket'>&gt;</span><span class='anglebracket'>&gt;</span> <span class='keyword'>class</span> unique_ptr;                  <span class='comment'>// freestanding</span>
  <span class='keyword'>template</span><span class='anglebracket'>&lt;</span><span class='keyword'>class</span> T, <span class='keyword'>class</span> D<span class='anglebracket'>&gt;</span> <span class='keyword'>class</span> unique_ptr<span class='anglebracket'>&lt;</span>T<span class='squarebracket'>[</span><span class='squarebracket'>]</span>, D<span class='anglebracket'>&gt;</span>;                              <span class='comment'>// freestanding</span>

</span></div></div>

</div>

<div class="added">
<div id='ptrtag' class='section'><h2 ><a class='secnum' href='#ptrrag' style='min-width:65pt'>20.?</a> Class template <code>pointer_tag_pair</code> <a class='abbr_ref' href='ptrtag'>[ptrtag]</a></h2>
</div>

<h3>20.?.1 General</h3>
<div class="section">
  
<div class='para' id='ptrtag-general-1'><div class='marginalizedparent'><a class='marginalized' href='#ptrtag-general-1'>1</a></div><div class="sentence">A <em>pointer tag pair</em> is an object which can hold a pointer to another object which is owned by some other object, and additional <em>tag value</em> of an integral or an enumeration type. </div><div class="sentence">Instance of class template <code>pointer_tag_pair</code> is same size as the stored pointer. </div></div>

<pre class="added"><code>namespace std {
  template &lt;typename T&gt; struct <em>underlying-or-identity</em>; // exposition only
  
  template &lt;typename T&gt; requires (is_enum_v&lt;T&gt;) struct <em>underlying-or-identity</em>&lt;T&gt; {
    using type = underlying_t&lt;T&gt;;
  }
  
  template &lt;typename T&gt; requires (is_integral_v&lt;T&gt;) struct <em>underlying-or-identity</em>&lt;T&gt; {
    using type = T;
  }
  
  template &lt;unsigned Bits, typename T&gt; constexpr auto <em>pass-thru-mask</em>(T value) noexcept { // exposition only
    return static_cast&lt;<em>underlying-or-identity</em>&lt;T&gt;&gt;(value) &amp; ((1u &lt;&lt; Bits) - 1u);
  }
  
  template &lt;typename PointeeT, typename TagT, unsigned BitsRequested = countr_zero(alignof(PointeeT))&gt;
    requires(is_object_v&lt;PointeeT&gt; &amp;&amp; is_unsigned_v&lt;underlying-or-identity&lt;TagT&gt;::type &amp;&amp;
             is_same_v&lt;TagT, remove_cvref_t&lt;TagT&gt;&gt; &amp;&amp; (BitsRequested &lt; sizeof(PointeeT*) * CHAR_BIT))
  struct pointer_tag_pair {   // freestanding
  public:
    using element_type        = PointeeT;
    using pointer_type        = element_type*;
    using tagged_pointer_type = void*;
    using tag_type            = TagT;

  private:
    // exposition only
    static constexpr unsigned <em>alignment-needed</em> = (1u &lt;&lt; BitsRequested);
    
    static constexpr <em>see below</em> <em>tag-mask</em> = (<em>alignment-needed</em> - 1u);
    static constexpr <em>see below</em> <em>pointer-mask</em> = ~<em>tag-mask</em>;
    
    using <em>numeric-tag</em> = <em>underlying-or-identity</em>&lt;tag_type&gt;;
    
    static constexpr <em>numeric-tag</em> <em>to-numeric-tag</em>(tag_type) noexcept;
    static constexpr tag_type <em>from-numeric-tag</em>(<em>numeric-tag</em>) noexcept;

    <em>see below</em> <em>pointer_</em> = nullptr; 
    
  public:
    // Constructors and assignment
    pointer_tag_pair() = default;
    pointer_tag_pair(nullptr_t) = default;
    pointer_tag_pair(const pointer_tag_pair&amp;) = default;
    pointer_tag_pair(pointer_tag_pair&amp;&amp;) = default;
    pointer_tag_pair&amp; operator=(const pointer_tag_pair&amp;) = default;
    pointer_tag_pair&amp; operator=(pointer_tag_pair&amp;&amp;) = default;
    
    constexpr pointer_tag_pair(pointer_type ptr, tag_type tag)
      requires(alignof(element_type) &gt;= <em>alignment-needed</em>);

    // Special construction helpers
    template &lt;unsigned PromisedAlignment&gt;
    static constexpr pointer_tag_pair from_overaligned(pointer_type ptr, tag_type tag)
      requires(PromisedAlignment &gt;= <em>alignment-needed</em>);

    static pointer_tag_pair from_tagged(tagged_pointer_type ptr);
    
    // Destructor
    ~pointer_tag_pair() = default;

    // Accessors
    tagged_pointer_type tagged_pointer() const noexcept;
    constexpr pointer_type pointer() const noexcept;
    constexpr tag_type tag() const noexcept;

    // Swap
    friend constexpr void swap(pointer_tag_pair&amp; lhs, pointer_tag_pair&amp; rhs) noexcept;

    // Comparisons
    friend constexpr <em>see below</em> operator&lt;=&gt;(pointer_tag_pair lhs, pointer_tag_pair rhs) noexcept;
    friend bool operator==(pointer_tag_pair, pointer_tag_pair) = default;
  };
}
</code></pre>

</div>

<h3>20.?.2 Constructors and assignment</h3>
<div class="section">
<pre class="added"><code>constexpr pointer_tag_pair() noexcept = default;</code></pre>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>1</a></div><em>Postconditions</em>: <code>pointer() == nullptr &amp;&amp; tag() == TagType{}</code>.</div>

<pre class="added"><code>constexpr pointer_tag_pair(nullptr_t) noexcept;</code></pre>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>2</a></div><em>Postconditions</em>: <code>pointer() == nullptr &amp;&amp; tag() == TagType{}</code>.</div>

<pre class="added"><code>constexpr pointer_tag_pair(const pointer_tag_pair&amp; other) noexcept = default;</code></pre>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>3</a></div><em>Postconditions</em>: <code>pointer() == other.pointer() &amp;&amp; tag() == other.tag()</code>.</div>

<pre class="added"><code>constexpr pointer_tag_pair(pointer_tag_pair&amp;&amp; other) noexcept = default;</code></pre>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>4</a></div><em>Postconditions</em>: <code>pointer() == other.pointer() &amp;&amp; tag() == other.tag()</code>.</div>

<pre class="added"><code>constexpr pointer_tag_pair(pointer_type p, tag_type t)</code></pre>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>5</a></div><em>Constraints</em>: <code>alignof(pointer_type) >= <em>aligned-needed</em></code>.</div>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>6</a></div><em>Preconditions</em>:
<ul>
  <li><code>p</code> points to an object <em>X</em> of a type similar ([conv.qual]) to element_type, where <em>X</em> has alignment equal or greater than <em>needed-alignment</em>.</li>
  <li><code>bit_width(t) &lt;= BitsRequested</code>.</li>
</ul>
</div>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>7</a></div><em>Postconditions</em>: <code>pointer() == p &amp;&amp; tag() == t</code></div>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>8</a></div><em>Effect</em>: Initializes <em>pointer_</em> with a value representing value <code>p</code> and <code>t</code>.</div>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>9</a></div><em>Throws</em>: Nothing.</div>

<pre class="added"><code>constexpr pointer_tag_pair&amp; operator=(const pointer_tag_pair&amp; other) noexcept = default</code></pre>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>10</a></div><em>Postconditions</em>: <code>pointer() == other.pointer() &amp;&amp; tag() == other.tag()</code>.</div>

<pre class="added"><code>constexpr pointer_tag_pair&amp; operator=(pointer_tag_pair&amp;&amp; other) noexcept = default</code></pre>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>11</a></div><em>Postconditions</em>: <code>pointer() == other.pointer() &amp;&amp; tag() == other.tag()</code>.</div>

</div>


<h3>20.?.2 Special construction helpers</h3>

<div class="section">
<pre class="added"><code>template &lt;unsigned PromisedAlignment&gt; constexpr pointer_tag_pair from_overaligned(pointer_type p, tag_type t);</code></pre>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>1</a></div><em>Constraints</em>: <code>PromisedAlignment >= <em>aligned-needed</em></code>.</div>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>2</a></div><em>Preconditions</em>:
<ul>
  <li><code>p</code> points to an object <em>X</em> of a type similar ([conv.qual]) to element_type, where <em>X</em> has alignment equal or greater than <em>needed-alignment</em>.</li>
  <li><code>bit_width(t) &lt;= BitsRequested</code>.</li>
</ul>
</div>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>3</a></div><em>Returns</em>: <code>pointer_tag_pair</code> as if with constructor <code>pointer_tag_pair(pointer_type, tag_type)</code> was called without checking preconditions.</div>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>4</a></div><em>Throws</em>: Nothing.</div>

<pre class="added"><code>pointer_tag_pair from_tagged(tagged_pointer_type p);</code></pre>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>5</a></div><em>Preconditions</em>: <code>p</code> contains a tagged pointer compatible with internal representation of <em>pointer_</em>.
</div>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>6</a></div><em>Returns</em>: <code>pointer_tag_pair</code> with initialized <em>pointer_</em> with value <code>p</code>.</div>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>7</a></div><em>Throws</em>: Nothing.</div>

</div>

<h3>20.?.3 Destructor</h3>

<div class="section">
<pre class="added"><code>~pointer_tag_pair() = default;</code></pre>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>1</a></div><em>Remarks</em>: This destructor is a trivial destructor.</div>
</div>

<h3>20.?.4 Accessors</h3>
<div class="section">
<pre class="added"><code>constexpr tag_type tag() const noexcept;</code></pre>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>1</a></div><em>Effect</em>: Return value of tag stored in <em>pointer_</em>'s on bits according <em>tag-mask</em>.</div>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>2</a></div><em>Remarks</em>: During constant evaluation the tag value can be stored differently.</div>

<pre class="added"><code>constexpr pointer_type pointer() const noexcept;</code></pre>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>3</a></div><em>Effect</em>: Return value of pointer stored in <em>pointer_</em> on bits according <em>pointer-mask</em>.</div>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>4</a></div><em>Remarks</em>: During constant evaluation the pointer value can be stored differently.</div>

<pre class="added"><code>tagged_pointer_type tagged_pointer() const noexcept;</code></pre>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>3</a></div><em>Effect</em>: Equivalent to: <code>return static_cast&lt;tagged_pointer_type&gt;(pointer_);</code>
<div class="note">[Note 1: This function is meant to be compatible with following pointer tagging approach: <br/><code>reinterpret_cast&lt;pointer_type&gt;(reinterpret_cast&lt;uintptr_t&gt;(<em>pointer_</em>) &amp; static_cast&lt;uintptr_t&gt;(<em>pointer-mask</em>))</code><br/> — end note]</div>
</div>

</div>

<h3>20.?.5 Swap</h3>
<div class="section">
<pre class="added"><code>friend constexpr void swap(pointer_tag_pair lhs, pointer_tag_pair rhs) noexcept;</code></pre>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>1</a></div><em>Effect</em>: Equivalent to: <code>std::swap(lhs.pointer_, rhs.pointer_);</code></div>

</div>

<h3>20.?.6 Comparison</h3>
<div class="section">
<pre class="added"><code>friend constexpr auto operator&lt;=&gt;(pointer_tag_pair lhs, pointer_tag_pair rhs) noexcept;</code></pre>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>1</a></div><em>Returns</em>: <code>tuple(lhs.pointer(), lhs.tag()) &lt;=&gt; tuple(rhs.pointer(), rhs.tag());</code></code></div>

<pre class="added"><code>friend constexpr bool operator==(pointer_tag_pair lhs, pointer_tag_pair rhs) noexcept;</code></pre>
<div class="para"><div class='marginalizedparent'><a class='marginalized' href='#unknown'>1</a></div><em>Returns</em>: <code>tuple(lhs.pointer(), lhs.tag()) == tuple(rhs.pointer(), rhs.tag());</code></div>

</div>

<h3>20.?.7 Tuple protocol</h3>
<div class="section">
  <strong>TODO</strong>
</div>

</div>


</div> <!-- document --->

</div>	
<h3 id='feature-test-macro'><a href='#feature-test-macro'>Feature test macro</a></h3>
<div class="wording"><h2><a href="http://eel.is/c++draft/version.syn">17.3.2 Header &lt;version&gt; synopsis [version.syn]</a></h2><div class="description"><span class="added"><code>#define __cpp_lib_pointer_tag_pair 2025??L // freestanding, also in &lt;memory&gt;</code></span></div></div></div></div></article>
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