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<h1 id="quick-start">Quick Start<a class="headerlink" href="#quick-start" title="Permanent link">&para;</a></h1>
<p>This chapter provides a quick introduction to get you started with <strong>mp-units</strong>.
Much more details can be found in our <a href="../../users_guide/terms_and_definitions/">User's Guide</a>.</p>
<h2 id="quantities">Quantities<a class="headerlink" href="#quantities" title="Permanent link">&para;</a></h2>
<p>A <strong>quantity</strong> is a concrete amount of a unit representing a quantity type of a specified dimension with a
specific representation. It is represented in the library with a <code>quantity</code> class template.</p>
<p>The <a href="../../appendix/references/#SIBrochure">SI Brochure</a> says:</p>
<div class="admonition quote">
<p class="admonition-title">SI Brochure</p>
<p>The value of the quantity is the product of the number and the unit. The space between the number
and the unit is regarded as a multiplication sign (just as a space between units implies
multiplication).</p>
</div>
<p>Following the above, the value of a quantity in the <strong>mp-units</strong> library is created by multiplying
a number with a predefined unit:</p>
<div class="tabbed-set tabbed-alternate" data-tabs="1:2"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">C++ modules</label><label for="__tabbed_1_2">Header files</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
<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">import</span><span class="w"> </span><span class="n">mp_units</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><span id="__span-0-3"><a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="k">using</span><span class="w"> </span><span class="k">namespace</span><span class="w"> </span><span class="nn">mp_units</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><span id="__span-0-5"><a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="n">quantity</span><span class="w"> </span><span class="n">q</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">42</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">si</span><span class="o">::</span><span class="n">metre</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">si</span><span class="o">::</span><span class="n">second</span><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-1-1"><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf">&lt;mp-units/systems/si.h&gt;</span>
</span><span id="__span-1-2"><a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a>
</span><span id="__span-1-3"><a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="k">using</span><span class="w"> </span><span class="k">namespace</span><span class="w"> </span><span class="nn">mp_units</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><span id="__span-1-5"><a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="n">quantity</span><span class="w"> </span><span class="n">q</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">42</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">si</span><span class="o">::</span><span class="n">metre</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">si</span><span class="o">::</span><span class="n">second</span><span class="p">;</span>
</span></code></pre></div>
</div>
</div>
</div>
<div class="admonition info">
<p class="admonition-title">Info</p>
<p>In case someone doesn't like the multiply syntax or there is an ambiguity between <code>operator*</code>
provided by this and other libraries, a quantity can also be created with a two-parameter
constructor:</p>
<div class="tabbed-set tabbed-alternate" data-tabs="2:2"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">C++ modules</label><label for="__tabbed_2_2">Header files</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
<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="k">import</span><span class="w"> </span><span class="n">mp_units</span><span class="p">;</span>
</span><span id="__span-2-2"><a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a>
</span><span id="__span-2-3"><a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="k">using</span><span class="w"> </span><span class="k">namespace</span><span class="w"> </span><span class="nn">mp_units</span><span class="p">;</span>
</span><span id="__span-2-4"><a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a>
</span><span id="__span-2-5"><a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="n">quantity</span><span class="w"> </span><span class="n">q</span><span class="p">{</span><span class="mi">42</span><span class="p">,</span><span class="w"> </span><span class="n">si</span><span class="o">::</span><span class="n">metre</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">si</span><span class="o">::</span><span class="n">second</span><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-3-1"><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf">&lt;mp-units/systems/si.h&gt;</span>
</span><span id="__span-3-2"><a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
</span><span id="__span-3-3"><a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="k">using</span><span class="w"> </span><span class="k">namespace</span><span class="w"> </span><span class="nn">mp_units</span><span class="p">;</span>
</span><span id="__span-3-4"><a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a>
</span><span id="__span-3-5"><a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="n">quantity</span><span class="w"> </span><span class="n">q</span><span class="p">{</span><span class="mi">42</span><span class="p">,</span><span class="w"> </span><span class="n">si</span><span class="o">::</span><span class="n">metre</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">si</span><span class="o">::</span><span class="n">second</span><span class="p">};</span>
</span></code></pre></div>
</div>
</div>
</div>
</div>
<p>The above creates an instance of <code>quantity&lt;derived_unit&lt;si::metre, per&lt;si::second&gt;&gt;{}, int&gt;</code>.
The same can be obtained using optional unit symbols:</p>
<div class="tabbed-set tabbed-alternate" data-tabs="3:2"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">C++ modules</label><label for="__tabbed_3_2">Header files</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
<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="k">import</span><span class="w"> </span><span class="n">mp_units</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><span id="__span-4-3"><a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="k">using</span><span class="w"> </span><span class="k">namespace</span><span class="w"> </span><span class="nn">mp_units</span><span class="p">;</span>
</span><span id="__span-4-4"><a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="k">using</span><span class="w"> </span><span class="k">namespace</span><span class="w"> </span><span class="nn">mp_units</span><span class="o">::</span><span class="nn">si</span><span class="o">::</span><span class="nn">unit_symbols</span><span class="p">;</span>
</span><span id="__span-4-5"><a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a>
</span><span id="__span-4-6"><a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="n">quantity</span><span class="w"> </span><span class="n">q</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">42</span><span class="w"> </span><span class="o">*</span><span class="w"> </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></code></pre></div>
</div>
<div class="tabbed-block">
<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="cp">#include</span><span class="w"> </span><span class="cpf">&lt;mp-units/systems/si.h&gt;</span>
</span><span id="__span-5-2"><a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
</span><span id="__span-5-3"><a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="k">using</span><span class="w"> </span><span class="k">namespace</span><span class="w"> </span><span class="nn">mp_units</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="k">using</span><span class="w"> </span><span class="k">namespace</span><span class="w"> </span><span class="nn">mp_units</span><span class="o">::</span><span class="nn">si</span><span class="o">::</span><span class="nn">unit_symbols</span><span class="p">;</span>
</span><span id="__span-5-5"><a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a>
</span><span id="__span-5-6"><a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="n">quantity</span><span class="w"> </span><span class="n">q</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">42</span><span class="w"> </span><span class="o">*</span><span class="w"> </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></code></pre></div>
</div>
</div>
</div>
<div class="admonition important">
<p class="admonition-title">Important</p>
<p>Unit symbols introduce a lot of short identifiers into the current scope, which may cause
naming collisions with unrelated but already existing identifiers in the code base.
This is why unit symbols are opt-in and typically should be imported only in the context
where they are being used (e.g., function scope).</p>
<p>A user has several options here to choose from depending on the required scenario and possible
naming conflicts:</p>
<div class="tabbed-set tabbed-alternate" data-tabs="4:4"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">using-directive</label><label for="__tabbed_4_2">using-declaration</label><label for="__tabbed_4_3">custom short identifier</label><label for="__tabbed_4_4">unit names</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
<p>Explicitly "import" all of the symbols of a specific system of units from a dedicated
<code>unit_symbols</code> namespace with a
<a href="https://en.cppreference.com/w/cpp/language/namespace#Using-directives">using-directive</a>:</p>
<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">using</span><span class="w"> </span><span class="k">namespace</span><span class="w"> </span><span class="nn">mp_units</span><span class="p">;</span>
</span><span id="__span-6-2"><a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
</span><span id="__span-6-3"><a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="kt">void</span><span class="w"> </span><span class="nf">foo</span><span class="p">(</span><span class="kt">double</span><span class="w"> </span><span class="n">speed_m_s</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="c1">// imports all the SI symbols at once</span>
</span><span id="__span-6-6"><a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w"> </span><span class="k">using</span><span class="w"> </span><span class="k">namespace</span><span class="w"> </span><span class="nn">si</span><span class="o">::</span><span class="nn">unit_symbols</span><span class="p">;</span>
</span><span id="__span-6-7"><a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w"> </span><span class="n">quantity</span><span class="w"> </span><span class="n">speed</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">speed_m_s</span><span class="w"> </span><span class="o">*</span><span class="w"> </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><span id="__span-6-8"><a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w"> </span><span class="c1">// ...</span>
</span><span id="__span-6-9"><a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="p">}</span>
</span></code></pre></div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>This solution is perfect for small and isolated scopes but can cause surprising issues
when used in larger scopes or when used for the entire program namespace.</p>
<p>There are 29 named units in SI, and each of them has many prefixed variations (e.g.,
<code>ng</code>, <code>kcd</code>, ...). It is pretty easy to introduce a name collision with those.</p>
</div>
</div>
<div class="tabbed-block">
<p>Selectively bring only the required and not-conflicting symbols with
<a href="https://en.cppreference.com/w/cpp/language/using_declaration">using-declarations</a>:</p>
<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">using</span><span class="w"> </span><span class="k">namespace</span><span class="w"> </span><span class="nn">mp_units</span><span class="p">;</span>
</span><span id="__span-7-2"><a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
</span><span id="__span-7-3"><a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="kt">void</span><span class="w"> </span><span class="nf">foo</span><span class="p">(</span><span class="kt">double</span><span class="w"> </span><span class="n">N</span><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="p">{</span>
</span><span id="__span-7-5"><a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w"> </span><span class="c1">// &#39;N&#39; function parameter would collide with the SI symbol for Newton, so we only bring what we need</span>
</span><span id="__span-7-6"><a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w"> </span><span class="k">using</span><span class="w"> </span><span class="n">si</span><span class="o">::</span><span class="n">unit_symbols</span><span class="o">::</span><span class="n">m</span><span class="p">;</span>
</span><span id="__span-7-7"><a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w"> </span><span class="k">using</span><span class="w"> </span><span class="n">si</span><span class="o">::</span><span class="n">unit_symbols</span><span class="o">::</span><span class="n">s</span><span class="p">;</span>
</span><span id="__span-7-8"><a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w"> </span><span class="n">quantity</span><span class="w"> </span><span class="n">speed</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">N</span><span class="w"> </span><span class="o">*</span><span class="w"> </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><span id="__span-7-9"><a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w"> </span><span class="c1">// ...</span>
</span><span id="__span-7-10"><a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="p">}</span>
</span></code></pre></div>
</div>
<div class="tabbed-block">
<p>Specify a custom not conflicting unit identifier for a unit:</p>
<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">using</span><span class="w"> </span><span class="k">namespace</span><span class="w"> </span><span class="nn">mp_units</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><span id="__span-8-3"><a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="kt">void</span><span class="w"> </span><span class="nf">foo</span><span class="p">(</span><span class="kt">double</span><span class="w"> </span><span class="n">speed_m_s</span><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="p">{</span>
</span><span id="__span-8-5"><a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w"> </span><span class="c1">// names of some local variables are conflicting with the symbols we want to use</span>
</span><span id="__span-8-6"><a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">...;</span>
</span><span id="__span-8-7"><a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="n">s</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">...;</span>
</span><span id="__span-8-8"><a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a>
</span><span id="__span-8-9"><a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w"> </span><span class="k">constexpr</span><span class="w"> </span><span class="n">Unit</span><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="n">mps</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">si</span><span class="o">::</span><span class="n">metre</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">si</span><span class="o">::</span><span class="n">second</span><span class="p">;</span>
</span><span id="__span-8-10"><a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w"> </span><span class="n">quantity</span><span class="w"> </span><span class="n">speed</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">speed_m_s</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">mps</span><span class="p">;</span>
</span><span id="__span-8-11"><a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="p">}</span>
</span></code></pre></div>
</div>
<div class="tabbed-block">
<p>Full unit names are straightforward to use and often provide the most readable code:</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="k">using</span><span class="w"> </span><span class="k">namespace</span><span class="w"> </span><span class="nn">mp_units</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><span id="__span-9-3"><a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="kt">void</span><span class="w"> </span><span class="nf">foo</span><span class="p">(</span><span class="kt">double</span><span class="w"> </span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">s</span><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="p">{</span>
</span><span id="__span-9-5"><a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w"> </span><span class="n">quantity</span><span class="w"> </span><span class="n">speed</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">si</span><span class="o">::</span><span class="n">metre</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">si</span><span class="o">::</span><span class="n">second</span><span class="p">);</span>
</span><span id="__span-9-6"><a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w"> </span><span class="c1">// ...</span>
</span><span id="__span-9-7"><a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="p">}</span>
</span></code></pre></div>
</div>
</div>
</div>
</div>
<p>Quantities of the same kind can be added, subtracted, and compared to each other:</p>
<div class="tabbed-set tabbed-alternate" data-tabs="5:2"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">C++ modules</label><label for="__tabbed_5_2">Header files</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
<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">import</span><span class="w"> </span><span class="n">mp_units</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><span id="__span-10-3"><a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="k">using</span><span class="w"> </span><span class="k">namespace</span><span class="w"> </span><span class="nn">mp_units</span><span class="p">;</span>
</span><span id="__span-10-4"><a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="k">using</span><span class="w"> </span><span class="k">namespace</span><span class="w"> </span><span class="nn">mp_units</span><span class="o">::</span><span class="nn">si</span><span class="o">::</span><span class="nn">unit_symbols</span><span class="p">;</span>
</span><span id="__span-10-5"><a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a>
</span><span id="__span-10-6"><a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="k">static_assert</span><span class="p">(</span><span class="mi">1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">km</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">50</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1050</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">m</span><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-11-1"><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf">&lt;mp-units/systems/si.h&gt;</span>
</span><span id="__span-11-2"><a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
</span><span id="__span-11-3"><a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="k">using</span><span class="w"> </span><span class="k">namespace</span><span class="w"> </span><span class="nn">mp_units</span><span class="p">;</span>
</span><span id="__span-11-4"><a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="k">using</span><span class="w"> </span><span class="k">namespace</span><span class="w"> </span><span class="nn">mp_units</span><span class="o">::</span><span class="nn">si</span><span class="o">::</span><span class="nn">unit_symbols</span><span class="p">;</span>
</span><span id="__span-11-5"><a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a>
</span><span id="__span-11-6"><a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="k">static_assert</span><span class="p">(</span><span class="mi">1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">km</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">50</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1050</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">m</span><span class="p">);</span>
</span></code></pre></div>
</div>
</div>
</div>
<p>Various quantities can be multiplied or divided by each other:</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="k">static_assert</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">km</span><span class="w"> </span><span class="o">/</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">h</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">70</span><span class="w"> </span><span class="o">*</span><span class="w"> </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="p">);</span>
</span></code></pre></div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>In case you wonder why this library does not use UDLs to create quantities, please check
our <a href="../faq/#why-dont-we-use-udls-to-create-quantities">FAQ</a>.</p>
</div>
<h2 id="quantity-points">Quantity points<a class="headerlink" href="#quantity-points" title="Permanent link">&para;</a></h2>
<p>The quantity point specifies an absolute quantity with respect to an origin.
If no origin is provided explicitly, an implicit one will be provided by the library.</p>
<p>Together with quantities, they model <a href="../../users_guide/framework_basics/the_affine_space/">The Affine Space</a>.</p>
<p>Quantity points should be used in all places where adding two values is meaningless
(e.g., temperature points, timestamps, altitudes, readouts from the car's odometer, etc.).</p>
<p>The set of operations that can be done on quantity points is limited compared to quantities.
This introduces an additional type-safety.</p>
<div class="tabbed-set tabbed-alternate" data-tabs="6:2"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">C++ modules</label><label for="__tabbed_6_2">Header files</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
<div class="language-cpp highlight"><pre><span></span><code><span id="__span-13-1"><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf">&lt;print&gt;</span>
</span><span id="__span-13-2"><a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="k">import</span><span class="w"> </span><span class="n">mp_units</span><span class="p">;</span>
</span><span id="__span-13-3"><a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>
</span><span id="__span-13-4"><a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="kt">int</span><span class="w"> </span><span class="nf">main</span><span class="p">()</span>
</span><span id="__span-13-5"><a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="p">{</span>
</span><span id="__span-13-6"><a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="w"> </span><span class="k">using</span><span class="w"> </span><span class="k">namespace</span><span class="w"> </span><span class="nn">mp_units</span><span class="p">;</span>
</span><span id="__span-13-7"><a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a><span class="w"> </span><span class="k">using</span><span class="w"> </span><span class="k">namespace</span><span class="w"> </span><span class="nn">mp_units</span><span class="o">::</span><span class="nn">si</span><span class="o">::</span><span class="nn">unit_symbols</span><span class="p">;</span>
</span><span id="__span-13-8"><a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="w"> </span><span class="k">using</span><span class="w"> </span><span class="k">namespace</span><span class="w"> </span><span class="nn">mp_units</span><span class="o">::</span><span class="nn">usc</span><span class="o">::</span><span class="nn">unit_symbols</span><span class="p">;</span>
</span><span id="__span-13-9"><a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>
</span><span id="__span-13-10"><a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a><span class="w"> </span><span class="n">quantity_point</span><span class="w"> </span><span class="n">temp</span><span class="p">{</span><span class="mf">20.</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">deg_C</span><span class="p">};</span>
</span><span id="__span-13-11"><a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">println</span><span class="p">(</span><span class="s">&quot;Temperature: {} ({})&quot;</span><span class="p">,</span>
</span><span id="__span-13-12"><a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="n">quantity_from_zero</span><span class="p">(),</span>
</span><span id="__span-13-13"><a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="n">in</span><span class="p">(</span><span class="n">deg_F</span><span class="p">).</span><span class="n">quantity_from_zero</span><span class="p">());</span>
</span><span id="__span-13-14"><a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></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-14-1"><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf">&lt;mp-units/format.h&gt;</span>
</span><span id="__span-14-2"><a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf">&lt;mp-units/systems/si.h&gt;</span>
</span><span id="__span-14-3"><a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf">&lt;mp-units/systems/usc.h&gt;</span>
</span><span id="__span-14-4"><a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf">&lt;print&gt;</span>
</span><span id="__span-14-5"><a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>
</span><span id="__span-14-6"><a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="kt">int</span><span class="w"> </span><span class="nf">main</span><span class="p">()</span>
</span><span id="__span-14-7"><a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="p">{</span>
</span><span id="__span-14-8"><a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w"> </span><span class="k">using</span><span class="w"> </span><span class="k">namespace</span><span class="w"> </span><span class="nn">mp_units</span><span class="p">;</span>
</span><span id="__span-14-9"><a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w"> </span><span class="k">using</span><span class="w"> </span><span class="k">namespace</span><span class="w"> </span><span class="nn">mp_units</span><span class="o">::</span><span class="nn">si</span><span class="o">::</span><span class="nn">unit_symbols</span><span class="p">;</span>
</span><span id="__span-14-10"><a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w"> </span><span class="k">using</span><span class="w"> </span><span class="k">namespace</span><span class="w"> </span><span class="nn">mp_units</span><span class="o">::</span><span class="nn">usc</span><span class="o">::</span><span class="nn">unit_symbols</span><span class="p">;</span>
</span><span id="__span-14-11"><a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a>
</span><span id="__span-14-12"><a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w"> </span><span class="n">quantity_point</span><span class="w"> </span><span class="n">temp</span><span class="p">{</span><span class="mf">20.</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">deg_C</span><span class="p">};</span>
</span><span id="__span-14-13"><a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">println</span><span class="p">(</span><span class="s">&quot;Temperature: {} ({})&quot;</span><span class="p">,</span>
</span><span id="__span-14-14"><a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="n">quantity_from_zero</span><span class="p">(),</span>
</span><span id="__span-14-15"><a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="n">in</span><span class="p">(</span><span class="n">deg_F</span><span class="p">).</span><span class="n">quantity_from_zero</span><span class="p">());</span>
</span><span id="__span-14-16"><a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="p">}</span>
</span></code></pre></div>
</div>
</div>
</div>
<p>The above outputs:</p>
<div class="language-text highlight"><pre><span></span><code><span id="__span-15-1"><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a>Temperature: 20 °C (68 °F)
</span></code></pre></div>
<div class="admonition info">
<p class="admonition-title">Info</p>
<p>Check <a href="../../users_guide/framework_basics/the_affine_space/">The Affine Space</a> chapter to learn
more about quantity points.</p>
</div>
</article>
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