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<div class="concept">
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<h1 class="section-header">
<span>
Concept
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<a class="project-name" href="index.html">Subspace</a>
<span class="namespace-dots">::</span>
<a class="namespace-name" href="namespace.sus.html">sus</a>
<span class="namespace-dots">::</span>
<a class="namespace-name" href="sus-namespace.cmp.html">cmp</a>
<span class="namespace-dots">::</span>
<a class="concept-name" href="#">Ord</a>
</h1>
<div class="type-signature"><div class="src rightside"><a href="https://github.com/chromium/subspace/blob/main/sus/cmp/ord.h#L107">source</a></div><pre class="template">template <class Lhs, class Rhs = Lhs></pre><span class="concept">
concept
</span><span class="type-name">
Ord
</span><div>
<div class="requires">
<span class="requires-keyword keyword">
requires
</span>
<div class="requires-constraint"><pre class="requires-constraint-line">StrongOrd<Lhs, Rhs> || requires(const std::remove_reference_t<Lhs>& lhs,</pre><pre class="requires-constraint-line"> const std::remove_reference_t<Rhs>& rhs) {</pre><pre class="requires-constraint-line"> { lhs <=> rhs } -> std::same_as<std::weak_ordering>;</pre><pre class="requires-constraint-line"> }</pre></div>
</div>
</div></div>
<div class="description long">
<p>Concept for types that form a total ordering (aka
<a href="https://en.cppreference.com/w/cpp/utility/compare/weak_ordering"><code>std::weak_ordering</code></a>).</p>
<p>Types that satisfy <a href="sus-cmp-Ord.html"><code>Ord</code></a> can be sorted or compared and
always return a consistent result as all possible values are comparable.
Objects that compare as equivalent for ordering may still be different
internally and compare as different through <code>operator==</code>. If unique identity
is required, use <a href="sus-cmp-StrongOrd.html"><code>StrongOrd</code></a>. Otherwise, typically
use <a href="sus-cmp-Ord.html"><code>Ord</code></a> for constraining types that will be ordered.</p>
<h1><a name="how-can-i-implement-ord?" href="#how-can-i-implement-ord?">How can I implement Ord?</a></h1>
<p><a href="sus-cmp-Ord.html"><code>Ord</code></a> requires that the type has <code>operator<=></code> which
returns
<a href="https://en.cppreference.com/w/cpp/utility/compare/weak_ordering"><code>std::weak_ordering</code></a>
(or
<a href="https://en.cppreference.com/w/cpp/utility/compare/strong_ordering"><code>std::strong_ordering</code></a>).
It will implicitly also be <a href="sus-cmp-Ord.html"><code>Ord</code></a> and
<a href="sus-cmp-PartialOrd.html"><code>PartialOrd</code></a> as a result.</p>
<h1><a name="lexicographical-comparison" href="#lexicographical-comparison">Lexicographical comparison</a></h1>
<p>Lexicographical comparison is an operation with the following properties:</p>
<ul>
<li>Two sequences are compared element by element.</li>
<li>The first mismatching element defines which sequence is lexicographically
less or greater than the other.</li>
<li>If one sequence is a prefix of another, the shorter sequence is
lexicographically less than the other.</li>
<li>If two sequence have equivalent elements and are of the same length, then
the sequences are lexicographically equal.</li>
<li>An empty sequence is lexicographically less than any non-empty sequence.</li>
<li>Two empty sequences are lexicographically equal.</li>
</ul>
<h1><a name="ord-and-eq-interations" href="#ord-and-eq-interations">Ord and Eq interations</a></h1>
<p>While <a href="sus-cmp-Ord.html"><code>Ord</code></a> can report equality, it does not imply that
the type satisfies <a href="sus-cmp-Eq.html"><code>Eq</code></a>, and a separate <code>operator==</code> is
required for that concept. Unlike
<a href="sus-cmp-StrongOrd.html"><code>StrongOrd</code></a>, it is not required that objects which
are ordered as equivalent also compare as equal with <code>operator==</code>.</p>
<p>Generic code that requires a type to be <a href="sus-cmp-Ord.html"><code>Ord</code></a> should
take care to use <code>operator<=></code> and not <code>operator==</code> unless also requiring
<a href="sus-cmp-Eq.html"><code>Eq</code></a>, in which case consider requiring
<a href="sus-cmp-StrongOrd.html"><code>StrongOrd</code></a> in place of both
<a href="sus-cmp-Ord.html"><code>Ord</code></a> and <a href="sus-cmp-Eq.html"><code>Eq</code></a>.</p>
<h1><a name="determining-ord-strictly" href="#determining-ord-strictly">Determining Ord strictly</a></h1>
<p><a href="sus-cmp-Ord.html"><code>Ord</code></a> will be also satisfied if the types satisfy
<a href="sus-cmp-StrongOrd.html"><code>StrongOrd</code></a>. To determine if a
<a href="sus-cmp-Ord.html"><code>Ord</code></a> is the strongest type of ordering between the
types, use <a href="sus-cmp-ExclusiveOrd.html"><code>ExclusiveOrd</code></a>.</p>
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