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p1185r2.html
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<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title><=> != ==</title>
<style type="text/css">html {
position: relative;
max-width: 1024px;
height: 100%;
}
body {
font-family: Helvetica, arial, sans-serif;
font-size: 14px;
line-height: 1.6;
padding-top: 10px;
padding-bottom: 10px;
background-color: white;
padding: 30px;
}
body>*:first-child {
margin-top: 0 !important;
}
body>*:last-child {
margin-bottom: 0 !important;
}
a {
color: #4183C4;
}
a.absent {
color: #cc0000;
}
a.anchor {
display: block;
padding-left: 30px;
margin-left: -30px;
cursor: pointer;
position: absolute;
top: 0;
left: 0;
bottom: 0;
}
h1, h2, h3, h4, h5, h6 {
margin: 20px 0 10px;
padding: 0;
font-weight: bold;
-webkit-font-smoothing: antialiased;
cursor: text;
position: relative;
}
h1:hover a.anchor, h2:hover a.anchor, h3:hover a.anchor, h4:hover a.anchor, h5:hover a.anchor, h6:hover a.anchor {
background: url(data:image/png;base64,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) no-repeat 10px center;
text-decoration: none;
}
h1 tt, h1 code {
font-size: inherit;
}
h2 tt, h2 code {
font-size: inherit;
}
h3 tt, h3 code {
font-size: inherit;
}
h4 tt, h4 code {
font-size: inherit;
}
h5 tt, h5 code {
font-size: inherit;
}
h6 tt, h6 code {
font-size: inherit;
}
h1 {
font-size: 28px;
color: black;
}
h2 {
font-size: 24px;
border-bottom: 1px solid #cccccc;
color: black;
}
h3 {
font-size: 18px;
}
h4 {
font-size: 16px;
}
h5 {
font-size: 14px;
}
h6 {
color: #777777;
font-size: 14px;
}
p, blockquote, ol, dl, li, table, pre {
margin: 15px 0;
}
hr {
background: transparent url(data:image/png;base64,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) repeat-x 0 0;
border: 0 none;
color: #cccccc;
height: 4px;
padding: 0;
}
body>h2:first-child {
margin-top: 0;
padding-top: 0;
}
body>h1:first-child {
margin-top: 0;
padding-top: 0;
}
body>h1:first-child+h2 {
margin-top: 0;
padding-top: 0;
}
body>h3:first-child, body>h4:first-child, body>h5:first-child, body>h6:first-child {
margin-top: 0;
padding-top: 0;
}
a:first-child h1, a:first-child h2, a:first-child h3, a:first-child h4, a:first-child h5, a:first-child h6 {
margin-top: 0;
padding-top: 0;
}
h1 p, h2 p, h3 p, h4 p, h5 p, h6 p {
margin-top: 0;
}
li p.first {
display: inline-block;
}
li {
margin: 0;
}
ol {
padding-left: 30px;
margin: 5px;
counter-reset: item;
margin-left: -1px;
margin-bottom: -1px;
margin-top: -1px;
}
ol > li {
counter-increment: item;
margin-bottom: -1px;
margin-top: -1px;
}
ol ol > li {
display: block;
margin-bottom: -1px;
margin-top: -1px;
}
ol ol > li:before {
content: counters(item, ".") ". ";
margin-left: -30px;
margin-bottom: -1px;
margin-top: -1px;
}
ul :first-child, ol :first-child {
margin-top: 0;
}
ul ul {
margin-left: -15px;
}
dl {
padding: 0;
}
dl dt {
font-size: 14px;
font-weight: bold;
font-style: italic;
padding: 0;
margin: 15px 0 5px;
}
dl dt:first-child {
padding: 0;
}
dl dt> :first-child {
margin-top: 0;
}
dl dt> :last-child {
margin-bottom: 0;
}
dl dd {
margin: 0 0 15px;
padding: 0 15px;
}
dl dd> :first-child {
margin-top: 0;
}
dl dd> :last-child {
margin-bottom: 0;
}
blockquote {
border-left: 4px solid #dddddd;
padding: 0 15px;
color: #777777;
}
blockquote> :first-child {
margin-top: 0;
}
blockquote> :last-child {
margin-bottom: 0;
}
table {
padding: 0;
border-collapse: collapse;
}
table tr {
border-top: 1px solid #cccccc;
background-color: white;
margin: 0;
padding: 0;
}
table tr:nth-child(2n) {
background-color: #f8f8f8;
}
table tr th {
font-weight: bold;
border: 1px solid #cccccc;
margin: 0;
padding: 6px 13px;
}
table tr td {
border: 1px solid #cccccc;
margin: 0;
padding: 6px 13px;
}
table tr th :first-child, table tr td :first-child {
margin-top: 0;
}
table tr th :last-child, table tr td :last-child {
margin-bottom: 0;
}
td {
vertical-align: top;
}
img {
max-width: 100%;
}
span.frame {
display: block;
overflow: hidden;
}
span.frame>span {
border: 1px solid #dddddd;
display: block;
float: left;
overflow: hidden;
margin: 13px 0 0;
padding: 7px;
width: auto;
}
span.frame span img {
display: block;
float: left;
}
span.frame span span {
clear: both;
color: #333333;
display: block;
padding: 5px 0 0;
}
span.align-center {
display: block;
overflow: hidden;
clear: both;
}
span.align-center>span {
display: block;
overflow: hidden;
margin: 13px auto 0;
text-align: center;
}
span.align-center span img {
margin: 0 auto;
text-align: center;
}
span.align-right {
display: block;
overflow: hidden;
clear: both;
}
span.align-right>span {
display: block;
overflow: hidden;
margin: 13px 0 0;
text-align: right;
}
span.align-right span img {
margin: 0;
text-align: right;
}
span.float-left {
display: block;
margin-right: 13px;
overflow: hidden;
float: left;
}
span.float-left span {
margin: 13px 0 0;
}
span.float-right {
display: block;
margin-left: 13px;
overflow: hidden;
float: right;
}
span.float-right>span {
display: block;
overflow: hidden;
margin: 13px auto 0;
text-align: right;
}
code, tt {
margin: 0 2px;
padding: 0 5px;
white-space: nowrap;
border: 1px solid #eaeaea;
background-color: #f8f8f8;
border-radius: 3px;
}
pre code {
margin: 0;
padding: 0;
white-space: pre;
border: none;
background: transparent;
}
.highlight pre {
background-color: #f8f8f8;
border: 1px solid #cccccc;
font-size: 13px;
line-height: 19px;
overflow: auto;
padding: 6px 10px;
border-radius: 3px;
}
pre {
background-color: #f8f8f8;
border: 1px solid #cccccc;
font-size: 13px;
line-height: 19px;
overflow: auto;
overflow-x: hidden;
overflow-y: hidden;
padding: 6px 10px;
border-radius: 3px;
}
pre code, pre tt {
background-color: transparent;
border: none;
}
sup {
font-size: 0.83em;
vertical-align: super;
line-height: 0;
}
kbd {
display: inline-block;
padding: 3px 5px;
font-size: 11px;
line-height: 10px;
color: #555;
vertical-align: middle;
background-color: #fcfcfc;
border: solid 1px #ccc;
border-bottom-color: #bbb;
border-radius: 3px;
box-shadow: inset 0 -1px 0 #bbb
}
* {
-webkit-print-color-adjust: exact;
}
ins {
color: #00A000
}
del {
color: #A00000
}
a.self-link {
position: absolute;
top: 0;
left: calc(-1 * (3.5rem - 26px));
width: calc(3.5rem - 26px);
height: 2em;
text-align: center;
border: none;
transition: opacity .2s;
opacity: .5;
font-size: 83%;
}
a.self-link:hover {
opacity: 1;
}
a.self-link::before {
content: "§";
}</style>
<style type="text/css">/* PrismJS 1.15.0
https://prismjs.com/download.html#themes=prism&languages=markup+css+clike+c+cpp&plugins=line-highlight */
/**
* prism.js default theme for JavaScript, CSS and HTML
* Based on dabblet (http://dabblet.com)
* @author Lea Verou
*/
code[class*="language-"],
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font-family: Consolas, Monaco, 'Andale Mono', 'Ubuntu Mono', monospace;
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pre[class*="language-"]::-moz-selection, pre[class*="language-"] ::-moz-selection,
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color: #690;
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.token.operator,
.token.entity,
.token.url,
.language-css .token.string,
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.token.atrule,
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.token.keyword {
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.token.function,
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.token.regex,
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.token.entity {
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right: 0;
padding: inherit 0;
margin-top: 1em; /* Same as .prism’s padding-top */
background: hsla(24, 20%, 50%,.08);
background: linear-gradient(to right, hsla(24, 20%, 50%,.1) 70%, hsla(24, 20%, 50%,0));
pointer-events: none;
line-height: inherit;
white-space: pre;
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padding: 0 .5em;
background-color: hsla(24, 20%, 50%,.4);
color: hsl(24, 20%, 95%);
font: bold 65%/1.5 sans-serif;
text-align: center;
vertical-align: .3em;
border-radius: 999px;
text-shadow: none;
box-shadow: 0 1px white;
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content: attr(data-end);
top: auto;
bottom: .4em;
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.line-numbers .line-highlight:before,
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content: none;
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<address align=right>
Document Number: P1185R2 <br />
Date: 2019-02-22 <br />
Audience: CWG, EWG <br />
Reply-To: Barry Revzin, barry dot revzin at gmail dot com <br />
</address>
<hr /><h1 align=center><p><code class="language-cpp"><=> != ==</code></p></h1>
<h2>Contents</h2>
<div class="toc">
<ol>
<li><a href="#revision-history">Revision History</a></li>
<li><a href="#motivation">Motivation</a><ol>
<li><a href="#why-this-is-really-bad">Why this is really bad</a></li>
<li><a href="#other-languages">Other Languages</a><ol>
<li><a href="#rust">Rust</a></li>
<li><a href="#other-languages_1">Other Languages</a></li>
</ol>
</li>
</ol>
</li>
<li><a href="#proposal">Proposal</a><ol>
<li><a href="#change-the-candidate-set-for-operator-lookup">Change the candidate set for operator lookup</a></li>
<li><a href="#change-the-meaning-of-defaulted-equality-operators">Change the meaning of defaulted equality operators</a></li>
<li><a href="#change-how-we-define-strong-structural-equality">Change how we define strong structural equality</a></li>
<li><a href="#change-defaulted-to-also-generate-a-defaulted">Change defaulted <=> to also generate a defaulted ==</a></li>
</ol>
</li>
<li><a href="#important-implications">Important implications</a><ol>
<li><a href="#implications-for-types-that-have-special-but-not-different-comparisons">Implications for types that have special, but not different, comparisons</a></li>
<li><a href="#implications-for-comparison-categories">Implications for comparison categories</a></li>
</ol>
</li>
<li><a href="#core-design-questions">Core Design Questions</a><ol>
<li><a href="#answers-to-core-questions">Answers to Core Questions</a></li>
</ol>
</li>
<li><a href="#wording">Wording</a></li>
<li><a href="#acknowledgements">Acknowledgements</a></li>
<li><a href="#references">References</a></li>
</ol>
</div>
<h2 id="revision-history">1. Revision History<a class="self-link" href="#revision-history"></a></h2>
<p>R1 of this paper was presented to Evolution in Kona, who preferred that defaulted <code class="language-cpp">operator<=></code> unconditionally declares defaulted <code class="language-cpp">operator==</code>. This has been noted in the questions section. </p>
<p>R0 of this paper was approved in its entirety by Evolution in San Diego. This new revision contains brand new wording after core review. There were two <a href="#core-design-questions">design questions</a> brought up by Core during this review, both based on the meaning of implicitly generated <code class="language-cpp">==</code>, which are discussed in this revision.</p>
<h2 id="motivation">2. Motivation<a class="self-link" href="#motivation"></a></h2>
<p><a href="https://wg21.link/p0515r3" title="Consistent comparison">P0515</a> introduced <code class="language-cpp">operator<=></code> as a way of generating all six comparison operators from a single function, as well as the ability to default this so as to avoid writing any code at all. See David Stone's <a href="https://wg21.link/p1190r0" title="I did not order this! Why is it on my bill?">I did not order this!</a> for a very clear, very thorough description of the problem: it does not seem to be possible to implement <code class="language-cpp"><=></code> optimally for "wrapper" types. What follows is a super brief run-down.</p>
<p>Consider a type like:</p>
<pre class="codehilite"><code class="language-cpp">struct S {
vector<string> names;
auto operator<=>(S const&) const = default;
};</code></pre>
<p>Today, this is ill-formed, because <code class="language-cpp">vector</code> does not implement <code class="language-cpp"><=></code>. In order to make this work, we need to add that implementation. It is <em>not</em> recommended that <code class="language-cpp">vector</code> only provide <code class="language-cpp"><=></code>, but we will start there and it will become clear why that is the recommendation.</p>
<p>The most straightforward implementation of <code class="language-cpp"><=></code> for <code class="language-cpp">vector</code> is (let's just assume <code class="language-cpp">strong_ordering</code> and note that I'm deliberately not using <code class="language-cpp">std::lexicographical_compare_3way()</code> for clarity):</p>
<pre class="codehilite"><code class="language-cpp">template<typename T>
strong_ordering operator<=>(vector<T> const& lhs, vector<T> const& rhs) {
size_t min_size = min(lhs.size(), rhs.size());
for (size_t i = 0; i != min_size; ++i) {
if (auto const cmp = compare_3way(lhs[i], rhs[i]); cmp != 0) {
return cmp;
}
}
return lhs.size() <=> rhs.size();
}</code></pre>
<p>On the one hand, this is great. We wrote one function instead of six, and this function is really easy to understand too. On top of that, this is a really good implementation for <code class="language-cpp"><</code>! As good as you can get. And our code for <code class="language-cpp">S</code> works (assuming we do something similar for <code class="language-cpp">string</code>).</p>
<p>On the other hand, as David goes through in a lot of detail (seriously, read it) this is quite bad for <code class="language-cpp">==</code>. We're failing to short-circuit early on size differences! If two containers have a large common prefix, despite being different sizes, that's an enormous amount of extra work!</p>
<p>In order to do <code class="language-cpp">==</code> efficiently, we have to short-circuit and do <code class="language-cpp">==</code> all the way down. That is:</p>
<pre class="codehilite"><code class="language-cpp">template<typename T>
bool operator==(vector<T> const& lhs, vector<T> const& rhs)
{
// short-circuit on size early
const size_t size = lhs.size();
if (size != rhs.size()) {
return false;
}
for (size_t i = 0; i != size; ++i) {
// use ==, not <=>, in all nested comparisons
if (lhs[i] != rhs[i]) {
return false;
}
}
return true;
}</code></pre>
<h3 id="why-this-is-really-bad">2.1. Why this is really bad<a class="self-link" href="#why-this-is-really-bad"></a></h3>
<p>This is really bad on several levels, significant levels.</p>
<p>First, since <code class="language-cpp">==</code> falls back on <code class="language-cpp"><=></code>, it's easy to fall into the trap that once <code class="language-cpp">v1 == v2</code> compiles and gives the correct answer, we're done. If we didn't implement the efficient <code class="language-cpp">==</code>, outside of very studious code review, we'd have no way of finding out. The problem is that <code class="language-cpp">v1 <=> v2 == 0</code> would always give the <em>correct</em> answer (assuming we correctly implemented <code class="language-cpp"><=></code>). How do you write a test to ensure that we did the short circuiting? The only way you could do it is to time some pathological case - comparing a vector containing a million entries against a vector containing those same million entries plus <code class="language-cpp">1</code> - and checking if it was fast?</p>
<p>Second, the above isn't even complete yet. Because even if we were careful enough to write <code class="language-cpp">==</code>, we'd get an efficient <code class="language-cpp">v1 == v2</code>... but still an inefficient <code class="language-cpp">v1 != v2</code>, because that one would call <code class="language-cpp"><=></code>. We would have to also write this manually:</p>
<pre class="codehilite"><code class="language-cpp">template<typename T>
bool operator!=(vector<T> const& lhs, vector<T> const& rhs)
{
return !(lhs == rhs);
}</code></pre>
<p>Third, this compounds <em>further</em> for any types that have something like this as a member. Getting back to our <code class="language-cpp">S</code> above:</p>
<pre class="codehilite"><code class="language-cpp">struct S {
vector<string> names;
auto operator<=>(S const&) const = default;
};</code></pre>
<p>Even if we correctly implemented <code class="language-cpp">==</code>, <code class="language-cpp">!=</code>, and <code class="language-cpp"><=></code> for <code class="language-cpp">vector</code> and <code class="language-cpp">string</code>, comparing two <code class="language-cpp">S</code>s for equality <em>still</em> calls <code class="language-cpp"><=></code> and is <em>still</em> a completely silent pessimization. Which <em>again</em> we cannot test functionally, only with a timer.</p>
<p>And then, it somehow gets even worse, because it's be easy to fall into yet another trap: you somehow have the diligence to remember that you need to explicitly define <code class="language-cpp">==</code> for this type and you do it this way:</p>
<pre class="codehilite"><code class="language-cpp">struct S {
vector<string> names;
auto operator<=>(S const&) const = default;
bool operator==(S const&) const = default; // problem solved, right?
};</code></pre>
<p>But what does defaulting <code class="language-cpp">operator==</code> actually do? It <a href="http://eel.is/c++draft/class.rel.eq" title="[class.rel.eq]">invokes <code class="language-cpp"><=></code></a>. So here's explicit code that seems sensible to add to attempt to address this problem, that does absolutely nothing to address this problem. </p>
<p>The only way to get efficiency is to have every type, even <code class="language-cpp">S</code> above, implement both not just <code class="language-cpp"><=></code> but also <code class="language-cpp">==</code> and <code class="language-cpp">!=</code>. By hand. </p>
<pre class="codehilite"><code class="language-cpp">struct S {
vector<string> names;
auto operator<=>(S const&) const = default;
bool operator==(S const& rhs) const { return names == rhs.names; }
bool operator!=(S const& rhs) const { return names != rhs.names; }
};</code></pre>
<p>That is the status quo today and the problem that needs to be solved.</p>
<h3 id="other-languages">2.2. Other Languages<a class="self-link" href="#other-languages"></a></h3>
<p>In order how to best figure out how to solve this problem for C++, it is helpful to look at how other languages have already addressed this issue. While P0515 listed many languages which have a three-way comparison returning a signed integer, there is another set of otherwise mostly-unrelated languages that take a different approach. </p>
<h4 id="rust">2.2.1. Rust<a class="self-link" href="#rust"></a></h4>
<p>Rust, Kotlin, Swift, Haskell, and Scala are rather different languages in many respects. But they all solve this particular problem in basically the same way: they treat <em>equality</em> and <em>comparison</em> as separate operations. I want to focus specifically on Rust here as it's arguably the closest language to C++ of the group, but the other three are largely equivalent for the purposes of this specific discussion.</p>
<p>Rust deals in Traits (which are roughly analogous to C++0x concepts and Swift protocols) and it has four relevant Traits that have to do with comparisons:</p>
<ul>
<li><code class="language-cpp">PartialEq</code> (which is a partial equivalence relation spelled which only requires symmetry and transitivity)</li>
<li><code class="language-cpp">Eq</code> (which extends <code class="language-cpp">PartialEq</code>, adding reflexivity)</li>
<li><code class="language-cpp">PartialOrd</code> (which allows for incomparability by returning <code class="language-cpp">Option<Ordering></code>, where <code class="language-cpp">Ordering</code> is an enum)</li>
<li><code class="language-cpp">Ord</code> (a total order, which extends <code class="language-cpp">Eq</code> and <code class="language-cpp">PartialOrd</code>)</li>
</ul>
<p>The actual operators are <a href="https://doc.rust-lang.org/reference/expressions/operator-expr.html#comparison-operators" title="Comparison Operators - The Rust Reference">implicitly generated</a> from these traits, but not all from the same one. Importantly, <code class="language-cpp">x == y</code> is translated as <code class="language-cpp">PartialEq::eq(x, y)</code> whereas <code class="language-cpp">x < y</code> is translated as <code class="language-cpp">PartialOrd::lt(x, y)</code> (which is effectively checking that <code class="language-cpp">PartialOrd::partial_cmp(x, y)</code> is <code class="language-cpp">Less</code>).</p>
<p>That is, you don't get <em>six</em> functions for the price of one. You need to write <em>two functions</em>. </p>
<p>Even if you don't know Rust (and I really don't know Rust), I think it would be instructive here would be to look at how the equivalent comparisons are implemented for Rust's <code class="language-cpp">vector</code> type. The important parts look like this:</p>
<table style="width:100%">
<tr>
<th style="width:50%">
<p><a href="https://doc.rust-lang.org/src/core/slice/mod.rs.html?search=#4037-4053" title="Implementation of Eq for Slice"><code class="language-cpp">Eq</code></a></p>
</th>
<th>
<p><a href="https://doc.rust-lang.org/src/core/slice/mod.rs.html#4116-4136" title="Implementation of Ord for Slice"><code class="language-cpp">Ord</code></a></p>
</th>
</tr>
<tr>
<td>
<pre style="background:transparent;border:0px" data-line="5,6,7,10"><code class="language-rust">impl<A, B> SlicePartialEq<B> for [A]
where A: PartialEq<B>
{
default fn eq(&self, other: &[B]) -> bool {
if self.len() != other.len() {
return false;
}
for i in 0..self.len() {
if !self[i].eq(&other[i]) {
return false;
}
}
true
}
}</code></pre>
</td>
<td>
<pre style="background:transparent;border:0px" data-line="11"><code class="language-rust">impl<A> SliceOrd<A> for [A]
where A: Ord
{
default fn cmp(&self, other: &[A]) -> Ordering {
let l = cmp::min(self.len(), other.len());
let lhs = &self[..l];
let rhs = &other[..l];
for i in 0..l {
match lhs[i].cmp(&rhs[i]) {
Ordering::Equal => (),
non_eq => return non_eq,
}
}
self.len().cmp(&other.len())
}
}</code></pre>
</td>
</tr>
</table>
<p>In other words, <code class="language-cpp">eq</code> calls <code class="language-cpp">eq</code> all the way down while doing short-circuiting whereas <code class="language-cpp">cmp</code> calls <code class="language-cpp">cmp</code> all the way down, and these are two separate functions. Both algorithms exactly match our implementation of <code class="language-cpp">==</code> and <code class="language-cpp"><=></code> for <code class="language-cpp">vector</code> above. Even though <code class="language-cpp">cmp</code> performs a 3-way ordering, and you can use the result of <code class="language-cpp">a.cmp(b)</code> to determine that <code class="language-cpp">a == b</code>, it is <em>not</em> the way that Rust (or other languages in this realm like Swift and Kotlin and Haskell) determine equality. </p>
<h4 id="other-languages_1">2.2.2. Other Languages<a class="self-link" href="#other-languages_1"></a></h4>
<p>Swift has <a href="https://developer.apple.com/documentation/swift/equatable" title="Equatable - Swift Standard Library"><code class="language-cpp">Equatable</code></a> and <a href="https://developer.apple.com/documentation/swift/comparable" title="Comparable - Swift Standard Library"><code class="language-cpp">Comparable</code></a> protocols. For types that conform to <code class="language-cpp">Equatable</code>, <code class="language-cpp">!=</code> is implicitly generated from <code class="language-cpp">==</code>. For types that conform to <code class="language-cpp">Comparable</code>, <code class="language-cpp">></code>, <code class="language-cpp">>=</code>, and <code class="language-cpp"><=</code> are implicitly generated from <code class="language-cpp"><</code>. Swift does not have a 3-way comparison function.</p>
<p>There are other languages that make roughly the same decision in this regard that Rust does: <code class="language-cpp">==</code> and <code class="language-cpp">!=</code> are generated from a function that does equality whereas the four relational operators are generated from a three-way comparison. Even though the three-way comparison <em>could</em> be used to determine equality, it is not:</p>
<ul>
<li>Kotlin, like Java, has a <a href="https://kotlinlang.org/api/latest/jvm/stdlib/kotlin/-comparable/index.html" title="Comparable - Kotlin Programming Language"><code class="language-cpp">Comparable</code></a> interface and a separate <code class="language-cpp">equals</code> method inherited from <a href="https://kotlinlang.org/api/latest/jvm/stdlib/kotlin/-any/index.html" title="Any - Kotlin Programming Language"><code class="language-cpp">Any</code></a>. Unlike Java, it has <a href="https://kotlinlang.org/docs/reference/operator-overloading.html#equals" title="Operator overloading - Kotlin Programming Language">operator overloading</a>: <code class="language-cpp">a == b</code> means <code class="language-cpp">a?.equals(b) ?: (b === null)</code> and <code class="language-cpp">a < b</code> means <code class="language-cpp">a.compareTo(b) < 0</code>.</li>
<li>Haskell has the <a href="http://hackage.haskell.org/package/base-4.11.1.0/docs/Data-Eq.html" title="Data.Eq - Haskell documentation"><code class="language-cpp">Data.Eq</code></a> and <a href="http://hackage.haskell.org/package/base-4.11.1.0/docs/Data-Ord.html" title="Data.Ord - Haskell documentation"><code class="language-cpp">Data.Ord</code></a> type classes. <code class="language-cpp">!=</code> is generated from <code class="language-cpp">==</code> (or vice versa, depending on which definition is provided for <code class="language-cpp">Eq</code>). If a <code class="language-cpp">compare</code> method is provided to conform to <code class="language-cpp">Ord</code>, <code class="language-cpp">a < b</code> means <code class="language-cpp">(compare a b) < 0</code>.</li>
<li>Scala's equality operators come from the root <a href="https://www.scala-lang.org/api/current/scala/Any.html#==(x$1:Any):Boolean" title="Scala Standard Library - Any"><code class="language-cpp">Any</code></a> interface, <code class="language-cpp">a == b</code> means <code class="language-cpp">if (a eq null) b eq null else a.equals(b)</code>. Its relational operators come from the <a href="https://www.scala-lang.org/api/current/scala/math/Ordered.html" title="Scala Standard Library - Ordered"><code class="language-cpp">Ordered</code></a> trait, where <code class="language-cpp">a < b</code> means <code class="language-cpp">(a compare b) < 0</code>.</li>
</ul>
<h2 id="proposal">3. Proposal<a class="self-link" href="#proposal"></a></h2>
<p>Fundamentally, we have two sets of operations: equality and comparison. In order to be efficient and not throw away performance, we need to implement them separately. <code class="language-cpp">operator<=>()</code> as specified in the working draft today generating all six functions just doesn't seem to be a good solution.</p>
<p>This paper proposes to do something similar to the Rust model above and first described in <a href="https://github.com/davidstone/isocpp/blob/master/operator-spaceship/I-did-not-order-this.md#make-operator-create-only-operator-operator-operator-and-operator">this section</a> of the previously linked paper: require two separate functions to implement all the functionality. </p>
<p>The proposal has two core components:</p>
<ul>
<li>change the candidate set for operator lookup</li>
<li>change the meaning of defaulted equality operators</li>
</ul>
<p>And two optional components:</p>
<ul>
<li>change how we define <a href="http://eel.is/c++draft/class.compare#def:equality,strong_structural" title="[class.compare]"><em>strong structural equality</em></a>, which is important for <a href="https://wg21.link/p0732r2" title="Class Types in Non-Type Template Parameters">P0732R2</a></li>
<li>change defaulted <code class="language-cpp"><=></code> to also generate a defaulted <code class="language-cpp">==</code></li>
</ul>
<h3 id="change-the-candidate-set-for-operator-lookup">3.1. Change the candidate set for operator lookup<a class="self-link" href="#change-the-candidate-set-for-operator-lookup"></a></h3>
<p>Today, lookup for any of the relational and equality operators will also consider <a href="http://eel.is/c++draft/over.match.oper#3.4"><code class="language-cpp">operator<=></code></a>, but preferring <a href="http://eel.is/c++draft/over.match.best#1.10">the actual used operator</a>. </p>
<p>The proposed change is for the equality operators to <em>not</em> consider <code class="language-cpp"><=></code> candidates. Instead, inequality will consider equality as a candidate. In other words, here is the proposed set of candidates. There are no changes proposed for the relational operators, only for the equality ones:</p>
<table>
<th>
<p>Source <br />
<code class="language-cpp">a @ b</code></p>
</th>
<th>
<p>Today (P0515/C++2a)</p>
</th>
<th>
<p>Proposed</p>
</th>
</tr>
<tr>
<td>
<pre style="background:transparent;border:0px"><code class="language-cpp">a == b</code></pre>
</td>
<td>
<pre style="background:transparent;border:0px"><code class="language-cpp">a == b
(a <=> b) == 0
0 == (b <=> a)</code></pre>
</td>
<td>
<pre style="background:transparent;border:0px"><code class="language-cpp">a == b
b == a</code></pre>
</td>
</tr>
<tr>
<td>
<pre style="background:transparent;border:0px"><code class="language-cpp">a != b</code></pre>
</td>
<td>
<pre style="background:transparent;border:0px"><code class="language-cpp">a != b
(a <=> b) != 0
0 != (a <=> b)</code></pre>
</td>
<td>
<pre style="background:transparent;border:0px"><code class="language-cpp">a != b
!(a == b)
!(b == a)</code></pre>
</td>
</tr>
<tr>
<td>
<pre style="background:transparent;border:0px"><code class="language-cpp">a < b</code></pre>
</td>
<td colspan="2">
<pre style="background:transparent;border:0px"><code class="language-cpp">a < b
(a <=> b) < 0
0 < (b <=> a)</code></pre>
</td>
</tr>
<tr>
<td>
<pre style="background:transparent;border:0px"><code class="language-cpp">a <= b</code></pre>
</td>
<td colspan="2">
<pre style="background:transparent;border:0px"><code class="language-cpp">a <= b
(a <=> b) <= 0
0 <= (b <=> a)</code></pre>
</td>
</tr>
<tr>
<td>
<pre style="background:transparent;border:0px"><code class="language-cpp">a > b</code></pre>
</td>
<td colspan="2">
<pre style="background:transparent;border:0px"><code class="language-cpp">a > b
(a <=> b) > 0
0 > (b <=> a)</code></pre>
</td>
</tr>
<tr>
<td>
<pre style="background:transparent;border:0px"><code class="language-cpp">a >= b</code></pre>
</td>
<td colspan="2">
<pre style="background:transparent;border:0px"><code class="language-cpp">a >= b
(a <=> b) >= 0
0 >= (b <=> a)</code></pre>
</td>
</tr>
</table>
<p>In short, <code class="language-cpp">==</code> and <code class="language-cpp">!=</code> never invoke <code class="language-cpp"><=></code> implicitly. </p>
<h3 id="change-the-meaning-of-defaulted-equality-operators">3.2. Change the meaning of defaulted equality operators<a class="self-link" href="#change-the-meaning-of-defaulted-equality-operators"></a></h3>
<p>As mentioned earlier, in the current working draft, defaulting <code class="language-cpp">==</code> or <code class="language-cpp">!=</code> generates a function that invokes <code class="language-cpp"><=></code>. This paper proposes that defaulting <code class="language-cpp">==</code> generates a member-wise equality comparison and that defaulting <code class="language-cpp">!=</code> generate a call to negated <code class="language-cpp">==</code>.</p>
<p>That is:</p>
<table style="width:100%">
<tr>
<th style="width:33%">
<p>Sample Code</p>
</th>
<th style="width:33%">
<p>Meaning Today (P0515/C++2a)</p>
</th>
<th>
<p>Proposed Meaning</p>
</th>
</tr>
<tr>
<td>
<pre style="background:transparent;border:0px"><code class="language-cpp">struct X {
A a;
B b;
C c;
auto operator<=>(X const&) const = default;
bool operator==(X const&) const = default;
bool operator!=(X const&) const = default;
};</code></pre>
</td>
<td>
<pre style="background:transparent;border:0px"><code class="language-cpp">struct X {
A a;
B b;
C c;
??? operator<=>(X const& rhs) const {
if (auto cmp = a <=> rhs.a; cmp != 0)
return cmp;
if (auto cmp = b <=> rhs.b; cmp != 0)
return cmp;
return c <=> rhs.c;
}
bool operator==(X const& rhs) const {
return (*this <=> rhs) == 0;
}
bool operator!=(X const& rhs) const {
return (*this <=> rhs) != 0;
}
};</code></pre>
</td>
<td>
<pre style="background:transparent;border:0px"><code class="language-cpp">struct X {
A a;
B b;
C c;
??? operator<=>(X const& rhs) const {
if (auto cmp = a <=> rhs.a; cmp != 0)
return cmp;
if (auto cmp = b <=> rhs.b; cmp != 0)
return cmp;
return c <=> rhs.c;
}
bool operator==(X const& rhs) const {
return a == rhs.a &&
b == rhs.b &&
c == rhs.c;
}
bool operator!=(X const& rhs) const {
return !(*this == rhs);
}
};</code></pre>
</td>
</tr>
</table>
<p>These two changes ensure that the equality operators and the relational operators remain segregated. </p>
<h3 id="change-how-we-define-strong-structural-equality">3.3. Change how we define strong structural equality<a class="self-link" href="#change-how-we-define-strong-structural-equality"></a></h3>
<p><a href="https://wg21.link/p0732r2" title="Class Types in Non-Type Template Parameters">P0732R2</a> relies on <em>strong structural equality</em> as the criteria to allow a class to be used as a non-type template parameter - which is based on having a defaulted <code class="language-cpp"><=></code> that itself only calls defaulted <code class="language-cpp"><=></code> recursively all the way down and has type either <code class="language-cpp">strong_ordering</code> or <code class="language-cpp">strong_equality</code>.</p>
<p>This criteria clashes somewhat with this proposal, which is fundamentally about not making <code class="language-cpp"><=></code> be about equality. So it would remain odd if, for instance, we rely on a defaulted <code class="language-cpp"><=></code> whose return type is <code class="language-cpp">strong_equality</code> (which itself can never be used to determine actual equality).</p>
<p>We have two options here:</p>
<ol>
<li>
<p>Do nothing. Do not change the rules here at all, still require defaulted <code class="language-cpp"><=></code> for use as a non-type template parameter. This means that there may be types which don't have a natural ordering for which we would have to both default <code class="language-cpp">==</code> and default <code class="language-cpp"><=></code> (with <code class="language-cpp">strong_equality</code>), the latter being a function that <em>only</em> exists to opt-in to this behavior. </p>
</li>
<li>
<p>Change the definition of strong structural equality to use <code class="language-cpp">==</code> instead. The wording here would have to be slightly more complex: define a type <code class="language-cpp">T</code> as having strong structural equality if each subobject recursively has defaulted <code class="language-cpp">==</code> and none of the subobjects are floating point types. </p>
</li>
</ol>
<p>The impact of this change revolves around the code necessary to write a type that is intended to only be equality-comparable (not ordered) but also usable as a non-type template parameter: only <code class="language-cpp">operator==</code> would be necessary.</p>
<table style="width:100%">
<tr>