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<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.archetypes"></a><a class="link" href="archetypes.html" title="Conceptual Archetypes for Reals and Distributions">Conceptual Archetypes for Reals
    and Distributions</a>
</h2></div></div></div>
<p>
      There are a few concept archetypes available:
    </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Real concept for floating-point types.
        </li>
<li class="listitem">
          Distribution concept for statistical distributions.
        </li>
</ul></div>
<h6>
<a name="math_toolkit.archetypes.h0"></a>
      <span class="phrase"><a name="math_toolkit.archetypes.real_concept"></a></span><a class="link" href="archetypes.html#math_toolkit.archetypes.real_concept">Real
      concept</a>
    </h6>
<p>
      <code class="computeroutput"><span class="identifier">std_real_concept</span></code> is an archetype
      for theReal types, including the built-in float, double, long double.
    </p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">concepts</span><span class="special">/</span><span class="identifier">std_real_concept</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">concepts</span>
<span class="special">{</span>
  <span class="keyword">class</span> <span class="identifier">std_real_concept</span><span class="special">;</span>
<span class="special">}</span>
<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
<p>
      The main purpose in providing this type is to verify that standard library
      functions are found via a using declaration - bringing those functions into
      the current scope - and not just because they happen to be in global scope.
    </p>
<p>
      In order to ensure that a call to say <code class="computeroutput"><span class="identifier">pow</span></code>
      can be found either via argument dependent lookup, or failing that then in
      the std namespace: all calls to standard library functions are unqualified,
      with the std:: versions found via a <code class="computeroutput"><span class="keyword">using</span></code>
      declaration to make them visible in the current scope. Unfortunately it's all
      to easy to forget the <code class="computeroutput"><span class="keyword">using</span></code> declaration,
      and call the double version of the function that happens to be in the global
      scope by mistake.
    </p>
<p>
      For example if the code calls ::pow rather than std::pow, the code will cleanly
      compile, but truncation of long doubles to double will cause a significant
      loss of precision. In contrast a template instantiated with std_real_concept
      will <span class="bold"><strong>only</strong></span> compile if the all the standard
      library functions used have been brought into the current scope with a using
      declaration.
    </p>
<h3>
<a name="math_toolkit.archetypes.h1"></a>
      <span class="phrase"><a name="math_toolkit.archetypes.testing_the_real_concept"></a></span><a class="link" href="archetypes.html#math_toolkit.archetypes.testing_the_real_concept">Testing
      the real concept</a>
    </h3>
<p>
      There is a test program <a href="../../../test/std_real_concept_check.cpp" target="_top">libs/math/test/std_real_concept_check.cpp</a>
      that instantiates every template in this library with type <code class="computeroutput"><span class="identifier">std_real_concept</span></code>
      to verify its usage of standard library functions.
    </p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">concepts</span><span class="special">/</span><span class="identifier">real_concept</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">concepts</span><span class="special">{</span>

<span class="keyword">class</span> <span class="identifier">real_concept</span><span class="special">;</span>

<span class="special">}}}</span> <span class="comment">// namespaces</span>
</pre>
<p>
      <code class="computeroutput"><span class="identifier">real_concept</span></code> is an archetype
      for <a class="link" href="real_concepts.html" title="Conceptual Requirements for Real Number Types">user defined real types</a>,
      it declares its standard library functions in its own namespace: these will
      only be found if they are called unqualified allowing argument dependent lookup
      to locate them. In addition this type is useable at runtime: this allows code
      that would not otherwise be exercised by the built-in floating point types
      to be tested. There is no std::numeric_limits&lt;&gt; support for this type,
      since numeric_limits is not a conceptual requirement for <a class="link" href="real_concepts.html" title="Conceptual Requirements for Real Number Types">RealType</a>s.
    </p>
<p>
      NTL RR is an example of a type meeting the requirements that this type models,
      but note that use of a thin wrapper class is required: refer to <a class="link" href="high_precision/use_ntl.html" title="Using NTL Library">"Using
      With NTL - a High-Precision Floating-Point Library"</a>.
    </p>
<p>
      There is no specific test case for type <code class="computeroutput"><span class="identifier">real_concept</span></code>,
      instead, since this type is usable at runtime, each individual test case as
      well as testing <code class="computeroutput"><span class="keyword">float</span></code>, <code class="computeroutput"><span class="keyword">double</span></code> and <code class="computeroutput"><span class="keyword">long</span>
      <span class="keyword">double</span></code>, also tests <code class="computeroutput"><span class="identifier">real_concept</span></code>.
    </p>
<h3>
<a name="math_toolkit.archetypes.h2"></a>
      <span class="phrase"><a name="math_toolkit.archetypes.distribution_concept"></a></span><a class="link" href="archetypes.html#math_toolkit.archetypes.distribution_concept">Distribution
      Concept</a>
    </h3>
<p>
      Distribution Concept models statistical distributions.
    </p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">concepts</span><span class="special">/</span><span class="identifier">distribution</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">concepts</span>
<span class="special">{</span>
  <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">&gt;</span>
  <span class="keyword">class</span> <span class="identifier">distribution_archetype</span><span class="special">;</span>

  <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Distribution</span><span class="special">&gt;</span>
  <span class="keyword">struct</span> <span class="identifier">DistributionConcept</span><span class="special">;</span>

<span class="special">}}}</span> <span class="comment">// namespaces</span>
</pre>
<p>
      The class template <code class="computeroutput"><span class="identifier">distribution_archetype</span></code>
      is a model of the <a class="link" href="dist_concept.html" title="Conceptual Requirements for Distribution Types">Distribution concept</a>.
    </p>
<p>
      The class template <code class="computeroutput"><span class="identifier">DistributionConcept</span></code>
      is a <a href="../../../../../libs/concept_check/index.html" target="_top">concept checking
      class</a> for distribution types.
    </p>
<h3>
<a name="math_toolkit.archetypes.h3"></a>
      <span class="phrase"><a name="math_toolkit.archetypes.testing_the_distribution_concept"></a></span><a class="link" href="archetypes.html#math_toolkit.archetypes.testing_the_distribution_concept">Testing
      the distribution concept</a>
    </h3>
<p>
      The test program <a href="../../../test/compile_test/distribution_concept_check.cpp" target="_top">distribution_concept_check.cpp</a>
      is responsible for using <code class="computeroutput"><span class="identifier">DistributionConcept</span></code>
      to verify that all the distributions in this library conform to the <a class="link" href="dist_concept.html" title="Conceptual Requirements for Distribution Types">Distribution
      concept</a>.
    </p>
<p>
      The class template <code class="computeroutput"><span class="identifier">DistributionConcept</span></code>
      verifies the existence (but not proper function) of the non-member accessors
      required by the <a class="link" href="dist_concept.html" title="Conceptual Requirements for Distribution Types">Distribution concept</a>.
      These are checked by calls like
    </p>
<pre class="programlisting"><span class="identifier">v</span> <span class="special">=</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">x</span><span class="special">);</span> <span class="comment">// (Result v is ignored).</span>
</pre>
<p>
      And in addition, those that accept two arguments do the right thing when the
      arguments are of different types (the result type is always the same as the
      distribution's value_type). (This is implemented by some additional forwarding-functions
      in derived_accessors.hpp, so that there is no need for any code changes. Likewise
      boilerplate versions of the hazard/chf/coefficient_of_variation functions are
      implemented in there too.)
    </p>
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<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
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      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
      Daryle Walker and Xiaogang Zhang<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
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