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Mateusz Pusz 32808bef78 Reinit docs to shrink git repo
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<h1 id="generic-interfaces">Generic Interfaces<a class="headerlink" href="#generic-interfaces" title="Permanent link">&para;</a></h1>
<p>Using a concrete unit in the interface often makes a lot of sense. It is especially useful if we
store the data internally in the object. In such a case, we have to select a specific unit anyway.</p>
<p>For example, let's consider a simple storage tank:</p>
<div class="language-cpp highlight"><pre><span></span><code><span id="__span-0-1"><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">StorageTank</span><span class="w"> </span><span class="p">{</span>
</span><span id="__span-0-2"><a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w"> </span><span class="n">quantity</span><span class="o">&lt;</span><span class="n">horizontal_area</span><span class="p">[</span><span class="n">m2</span><span class="p">]</span><span class="o">&gt;</span><span class="w"> </span><span class="n">base_</span><span class="p">;</span>
</span><span id="__span-0-3"><a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="w"> </span><span class="n">quantity</span><span class="o">&lt;</span><span class="n">isq</span><span class="o">::</span><span class="n">height</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="o">&gt;</span><span class="w"> </span><span class="n">height_</span><span class="p">;</span>
</span><span id="__span-0-4"><a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="w"> </span><span class="n">quantity</span><span class="o">&lt;</span><span class="n">isq</span><span class="o">::</span><span class="n">mass_density</span><span class="p">[</span><span class="n">kg</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">m3</span><span class="p">]</span><span class="o">&gt;</span><span class="w"> </span><span class="n">density_</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">air_density</span><span class="p">;</span>
</span><span id="__span-0-5"><a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="k">public</span><span class="o">:</span>
</span><span id="__span-0-6"><a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="w"> </span><span class="k">constexpr</span><span class="w"> </span><span class="n">StorageTank</span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="n">quantity</span><span class="o">&lt;</span><span class="n">horizontal_area</span><span class="p">[</span><span class="n">m2</span><span class="p">]</span><span class="o">&gt;&amp;</span><span class="w"> </span><span class="n">base</span><span class="p">,</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n">quantity</span><span class="o">&lt;</span><span class="n">isq</span><span class="o">::</span><span class="n">height</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="o">&gt;&amp;</span><span class="w"> </span><span class="n">height</span><span class="p">)</span><span class="w"> </span><span class="o">:</span>
</span><span id="__span-0-7"><a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="w"> </span><span class="n">base_</span><span class="p">(</span><span class="n">base</span><span class="p">),</span><span class="w"> </span><span class="n">height_</span><span class="p">(</span><span class="n">height</span><span class="p">)</span>
</span><span id="__span-0-8"><a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="w"> </span><span class="p">{</span>
</span><span id="__span-0-9"><a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="w"> </span><span class="p">}</span>
</span><span id="__span-0-10"><a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>
</span><span id="__span-0-11"><a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a><span class="w"> </span><span class="c1">// ...</span>
</span><span id="__span-0-12"><a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="p">};</span>
</span></code></pre></div>
<p>As the quantities provided in the function's interface are then stored in the class, there is probably
no sense in using generic interfaces here.</p>
<h2 id="the-issues-with-unit-specific-interfaces">The issues with unit-specific interfaces<a class="headerlink" href="#the-issues-with-unit-specific-interfaces" title="Permanent link">&para;</a></h2>
<p>However, in many cases, using a specific unit in the interface is counterproductive. Let's consider
the following function:</p>
<div class="language-cpp highlight"><pre><span></span><code><span id="__span-1-1"><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="n">quantity</span><span class="o">&lt;</span><span class="n">km</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">h</span><span class="o">&gt;</span><span class="w"> </span><span class="n">avg_speed</span><span class="p">(</span><span class="n">quantity</span><span class="o">&lt;</span><span class="n">km</span><span class="o">&gt;</span><span class="w"> </span><span class="n">distance</span><span class="p">,</span><span class="w"> </span><span class="n">quantity</span><span class="o">&lt;</span><span class="n">h</span><span class="o">&gt;</span><span class="w"> </span><span class="n">duration</span><span class="p">)</span>
</span><span id="__span-1-2"><a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="p">{</span>
</span><span id="__span-1-3"><a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">distance</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">duration</span><span class="p">;</span>
</span><span id="__span-1-4"><a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="p">}</span>
</span></code></pre></div>
<p>Everything seems fine for now. It also works great if we call it with:</p>
<div class="language-cpp highlight"><pre><span></span><code><span id="__span-2-1"><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="n">quantity</span><span class="o">&lt;</span><span class="n">km</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">h</span><span class="o">&gt;</span><span class="w"> </span><span class="n">s1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">avg_speed</span><span class="p">(</span><span class="mi">220</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">km</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">h</span><span class="p">);</span>
</span></code></pre></div>
<p>However, if the user starts doing the following:</p>
<div class="language-cpp highlight"><pre><span></span><code><span id="__span-3-1"><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="n">quantity</span><span class="o">&lt;</span><span class="n">mi</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">h</span><span class="o">&gt;</span><span class="w"> </span><span class="n">s2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">avg_speed</span><span class="p">(</span><span class="mi">140</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">mi</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">h</span><span class="p">);</span>
</span><span id="__span-3-2"><a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="n">quantity</span><span class="o">&lt;</span><span class="n">m</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">s</span><span class="o">&gt;</span><span class="w"> </span><span class="n">s3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">avg_speed</span><span class="p">(</span><span class="mi">20</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">s</span><span class="p">);</span>
</span></code></pre></div>
<p>some issues start to be clearly visible:</p>
<ol>
<li>The arguments must be converted to units mandated by the function's parameters at each call.
This involves potentially expensive multiplication/division operations at runtime.</li>
<li>After the function returns the <em>speed</em> in a unit of <code>km/h</code>, another potentially expensive
multiplication/division operations must be performed to convert the resulting quantity into
a unit being the derived unit of the initial function's arguments.</li>
<li>Besides the obvious runtime cost, some unit conversions may result in a value truncation, which
means that the result will not be exactly equal to a direct division of the function's arguments.</li>
<li>
<p>We have to use a floating-point representation type (the <code>quantity</code> class template by default uses
<code>double</code> as a representation type) which is considered
<a href="../value_conversions/#value-preserving-conversions">value-preserving</a>.
Trying to use an integral type in this scenario will work only for <code>s1</code>, while <code>s2</code> and <code>s3</code>
will fail to compile. Failing to compile is a good thing here as the library tries to prevent
the user from doing a clearly wrong thing. To make the code compile, the user needs to use
dedicated <a href="../value_conversions/#value-truncating-conversions"><code>value_cast</code> or <code>force_in</code></a> like this:</p>
<div class="language-cpp highlight"><pre><span></span><code><span id="__span-4-1"><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="n">quantity</span><span class="o">&lt;</span><span class="n">isq</span><span class="o">::</span><span class="n">speed</span><span class="p">[</span><span class="n">mi</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">h</span><span class="p">]</span><span class="o">&gt;</span><span class="w"> </span><span class="n">s2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">avg_speed</span><span class="p">(</span><span class="n">value_cast</span><span class="o">&lt;</span><span class="n">km</span><span class="o">&gt;</span><span class="p">(</span><span class="mi">140</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">mi</span><span class="p">),</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">h</span><span class="p">);</span>
</span><span id="__span-4-2"><a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="n">quantity</span><span class="o">&lt;</span><span class="n">isq</span><span class="o">::</span><span class="n">speed</span><span class="p">[</span><span class="n">m</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">s</span><span class="p">]</span><span class="o">&gt;</span><span class="w"> </span><span class="n">s3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">avg_speed</span><span class="p">((</span><span class="mi">20</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">m</span><span class="p">).</span><span class="n">force_in</span><span class="p">(</span><span class="n">km</span><span class="p">),</span><span class="w"> </span><span class="p">(</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">s</span><span class="p">).</span><span class="n">force_in</span><span class="p">(</span><span class="n">h</span><span class="p">));</span>
</span></code></pre></div>
<p>but the above will obviously provide an incorrect behavior (e.g., division by <code>0</code> in the evaluation
of <code>s3</code>).</p>
</li>
</ol>
<h2 id="a-naive-solution">A naive solution<a class="headerlink" href="#a-naive-solution" title="Permanent link">&para;</a></h2>
<p>A naive solution here would be to implement the function as an unconstrained function template:</p>
<div class="language-cpp highlight"><pre><span></span><code><span id="__span-5-1"><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="k">auto</span><span class="w"> </span><span class="n">avg_speed</span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="n">distance</span><span class="p">,</span><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="n">duration</span><span class="p">)</span>
</span><span id="__span-5-2"><a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="p">{</span>
</span><span id="__span-5-3"><a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">distance</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">duration</span><span class="p">;</span>
</span><span id="__span-5-4"><a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="p">}</span>
</span></code></pre></div>
<p>Beware, this is not a good solution. The above code is too generic. Such a function template
accepts everything:</p>
<ul>
<li>quantities of other types<ul>
<li>the compiler will not prevent accidental reordering of the function's arguments,</li>
<li>quantities of different types can be passed as well,</li>
</ul>
</li>
<li>plain <code>double</code> arguments,</li>
<li><code>std::vector</code> and <code>std::lock_guard</code> will be accepted as well (of course, this will fail in the
instantiation of a function's body later in the compilation process).</li>
</ul>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>The usage of <code>auto</code> instead of a function parameter type is a C++20 feature. It makes such
a code a function template where the type of such a parameter will be deduced during
the template instantiation process from the argument type passed by the user.</p>
</div>
<h2 id="constraining-function-template-arguments-with-concepts">Constraining function template arguments with concepts<a class="headerlink" href="#constraining-function-template-arguments-with-concepts" title="Permanent link">&para;</a></h2>
<p>Much better generic code can be implemented using <a href="../concepts/">basic concepts</a>
provided with the library:</p>
<div class="tabbed-set tabbed-alternate" data-tabs="1:3"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Original template notation</label><label for="__tabbed_1_2">The shorthand notation</label><label for="__tabbed_1_3">Terse notation</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
<div class="language-cpp highlight"><pre><span></span><code><span id="__span-6-1"><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="k">template</span><span class="o">&lt;</span><span class="k">typename</span><span class="w"> </span><span class="nc">Distance</span><span class="p">,</span><span class="w"> </span><span class="k">typename</span><span class="w"> </span><span class="nc">Duration</span><span class="o">&gt;</span>
</span><span id="__span-6-2"><a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="w"> </span><span class="k">requires</span><span class="w"> </span><span class="n">QuantityOf</span><span class="o">&lt;</span><span class="n">Distance</span><span class="p">,</span><span class="w"> </span><span class="n">isq</span><span class="o">::</span><span class="n">length</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">QuantityOf</span><span class="o">&lt;</span><span class="n">Duration</span><span class="p">,</span><span class="w"> </span><span class="n">isq</span><span class="o">::</span><span class="n">time</span><span class="o">&gt;</span>
</span><span id="__span-6-3"><a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="k">auto</span><span class="w"> </span><span class="n">avg_speed</span><span class="p">(</span><span class="n">Distance</span><span class="w"> </span><span class="n">distance</span><span class="p">,</span><span class="w"> </span><span class="n">Duration</span><span class="w"> </span><span class="n">duration</span><span class="p">)</span>
</span><span id="__span-6-4"><a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="p">{</span>
</span><span id="__span-6-5"><a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">isq</span><span class="o">::</span><span class="n">speed</span><span class="p">(</span><span class="n">distance</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">duration</span><span class="p">);</span>
</span><span id="__span-6-6"><a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="p">}</span>
</span></code></pre></div>
</div>
<div class="tabbed-block">
<div class="language-cpp highlight"><pre><span></span><code><span id="__span-7-1"><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="k">template</span><span class="o">&lt;</span><span class="n">QuantityOf</span><span class="o">&lt;</span><span class="n">isq</span><span class="o">::</span><span class="n">length</span><span class="o">&gt;</span><span class="w"> </span><span class="n">Distance</span><span class="p">,</span><span class="w"> </span><span class="n">QuantityOf</span><span class="o">&lt;</span><span class="n">isq</span><span class="o">::</span><span class="n">time</span><span class="o">&gt;</span><span class="w"> </span><span class="n">Duration</span><span class="o">&gt;</span>
</span><span id="__span-7-2"><a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="k">auto</span><span class="w"> </span><span class="n">avg_speed</span><span class="p">(</span><span class="n">Distance</span><span class="w"> </span><span class="n">distance</span><span class="p">,</span><span class="w"> </span><span class="n">Duration</span><span class="w"> </span><span class="n">duration</span><span class="p">)</span>
</span><span id="__span-7-3"><a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">{</span>
</span><span id="__span-7-4"><a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">isq</span><span class="o">::</span><span class="n">speed</span><span class="p">(</span><span class="n">distance</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">duration</span><span class="p">);</span>
</span><span id="__span-7-5"><a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="p">}</span>
</span></code></pre></div>
</div>
<div class="tabbed-block">
<div class="language-cpp highlight"><pre><span></span><code><span id="__span-8-1"><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="k">auto</span><span class="w"> </span><span class="n">avg_speed</span><span class="p">(</span><span class="n">QuantityOf</span><span class="o">&lt;</span><span class="n">isq</span><span class="o">::</span><span class="n">length</span><span class="o">&gt;</span><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="n">distance</span><span class="p">,</span>
</span><span id="__span-8-2"><a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="w"> </span><span class="n">QuantityOf</span><span class="o">&lt;</span><span class="n">isq</span><span class="o">::</span><span class="n">time</span><span class="o">&gt;</span><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="n">duration</span><span class="p">)</span>
</span><span id="__span-8-3"><a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">{</span>
</span><span id="__span-8-4"><a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">isq</span><span class="o">::</span><span class="n">speed</span><span class="p">(</span><span class="n">distance</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">duration</span><span class="p">);</span>
</span><span id="__span-8-5"><a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="p">}</span>
</span></code></pre></div>
</div>
</div>
</div>
<p>This explicitly states that the arguments passed by the user must not only satisfy
a <a href="../concepts/#Quantity"><code>Quantity</code></a> concept, but also their quantity specification must
be implicitly convertible to <code>isq::length</code> and <code>isq::time</code> accordingly. This no longer leaves
room for error while still allowing the compiler to generate the most efficient code.</p>
<div class="admonition tip">
<p class="admonition-title">Tip</p>
<p>Please note that now it is safe just to use integral types all the way which again
improves the runtime performance as the multiplication/division operations are often
faster on the integral rather than floating-point types.</p>
</div>
<h2 id="constraining-function-template-return-type">Constraining function template return type<a class="headerlink" href="#constraining-function-template-return-type" title="Permanent link">&para;</a></h2>
<p>The above function template resolves all of the <a href="#the-issues-with-unit-specific-interfaces">issues described before</a>.
However, we can do even better here by additionally constraining the return type:</p>
<div class="language-cpp highlight"><pre><span></span><code><span id="__span-9-1"><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="n">QuantityOf</span><span class="o">&lt;</span><span class="n">isq</span><span class="o">::</span><span class="n">speed</span><span class="o">&gt;</span><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="n">avg_speed</span><span class="p">(</span><span class="n">QuantityOf</span><span class="o">&lt;</span><span class="n">isq</span><span class="o">::</span><span class="n">length</span><span class="o">&gt;</span><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="n">distance</span><span class="p">,</span>
</span><span id="__span-9-2"><a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="w"> </span><span class="n">QuantityOf</span><span class="o">&lt;</span><span class="n">isq</span><span class="o">::</span><span class="n">time</span><span class="o">&gt;</span><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="n">duration</span><span class="p">)</span>
</span><span id="__span-9-3"><a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">{</span>
</span><span id="__span-9-4"><a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">isq</span><span class="o">::</span><span class="n">speed</span><span class="p">(</span><span class="n">distance</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">duration</span><span class="p">);</span>
</span><span id="__span-9-5"><a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="p">}</span>
</span></code></pre></div>
<p>Doing so has two important benefits:</p>
<ol>
<li>It informs the users of our interface about what to expect to be the result of a function
invocation. It is superior to just returning <code>auto</code>, which does not provide any hint about
the thing being returned there.</li>
<li>Such a concept constrains the type returned from the function. This means that it works as
a unit test to verify if our function actually performs what it is supposed to do. If there is
an error in <a href="../../../appendix/glossary/#quantity-equation">quantity equations</a>, we will learn
about it right away.</li>
</ol>
<h2 id="constraining-a-variable-on-the-stack">Constraining a variable on the stack<a class="headerlink" href="#constraining-a-variable-on-the-stack" title="Permanent link">&para;</a></h2>
<p>If we know precisely what the function does in its internals and if we know the exact argument types
passed to such a function, we often know the exact type that will be returned from its invocation.</p>
<p>However, if we care about performance, we should often use the generic interfaces described in this
chapter. A side effect is that we sometimes are unsure about the return type. Even if we know it
today, it might change a week from now due to some code refactoring.</p>
<p>In such cases, we can again use <code>auto</code> to denote the type:</p>
<div class="language-cpp highlight"><pre><span></span><code><span id="__span-10-1"><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="k">auto</span><span class="w"> </span><span class="n">s1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">avg_speed</span><span class="p">(</span><span class="mi">220</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">km</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">h</span><span class="p">);</span>
</span><span id="__span-10-2"><a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="k">auto</span><span class="w"> </span><span class="n">s2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">avg_speed</span><span class="p">(</span><span class="mi">140</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">mi</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">h</span><span class="p">);</span>
</span><span id="__span-10-3"><a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="k">auto</span><span class="w"> </span><span class="n">s3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">avg_speed</span><span class="p">(</span><span class="mi">20</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">s</span><span class="p">);</span>
</span></code></pre></div>
<p>or benefit from <abbr title="Class Template Argument Deduction">CTAD</abbr>:</p>
<div class="language-cpp highlight"><pre><span></span><code><span id="__span-11-1"><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="n">quantity</span><span class="w"> </span><span class="n">s1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">avg_speed</span><span class="p">(</span><span class="mi">220</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">km</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">h</span><span class="p">);</span>
</span><span id="__span-11-2"><a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="n">quantity</span><span class="w"> </span><span class="n">s2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">avg_speed</span><span class="p">(</span><span class="mi">140</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">mi</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">h</span><span class="p">);</span>
</span><span id="__span-11-3"><a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="n">quantity</span><span class="w"> </span><span class="n">s3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">avg_speed</span><span class="p">(</span><span class="mi">20</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">s</span><span class="p">);</span>
</span></code></pre></div>
<p>In both cases, it is probably OK to do so as the <code>avg_speed</code> function name explicitly provides
the information on what to expect as a result.</p>
<p>In other scenarios where the returned quantity type is not so obvious, it is again helpful to
constrain the type with a concept like so:</p>
<div class="language-cpp highlight"><pre><span></span><code><span id="__span-12-1"><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="n">QuantityOf</span><span class="o">&lt;</span><span class="n">isq</span><span class="o">::</span><span class="n">speed</span><span class="o">&gt;</span><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="n">s1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">avg_speed</span><span class="p">(</span><span class="mi">220</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">km</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">h</span><span class="p">);</span>
</span><span id="__span-12-2"><a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="n">QuantityOf</span><span class="o">&lt;</span><span class="n">isq</span><span class="o">::</span><span class="n">speed</span><span class="o">&gt;</span><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="n">s2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">avg_speed</span><span class="p">(</span><span class="mi">140</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">mi</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">h</span><span class="p">);</span>
</span><span id="__span-12-3"><a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="n">QuantityOf</span><span class="o">&lt;</span><span class="n">isq</span><span class="o">::</span><span class="n">speed</span><span class="o">&gt;</span><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="n">s3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">avg_speed</span><span class="p">(</span><span class="mi">20</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">s</span><span class="p">);</span>
</span></code></pre></div>
<p>The above explicitly provides additional information about the quantity we are dealing with in
the code, and it serves as a unit test checking if the "thing" returned from a function is actually
what we expected here.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>The <code>QuantityOf</code> and <code>QuantityPointOf</code> concepts are probably the most useful, but there
are a few more to play with. A list of all the concepts can be found in
the <a href="../concepts/">Basic Concepts</a> chapter.</p>
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