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1377 lines
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<title>Conceptual Requirements for Real Number Types</title>
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<link rel="up" href="../using_udt.html" title="Chapter 14. Use with User-Defined Floating-Point Types - Boost.Multiprecision and others">
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<link rel="next" href="dist_concept.html" title="Conceptual Requirements for Distribution Types">
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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<table cellpadding="2" width="100%"><tr>
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<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
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<hr>
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<div class="spirit-nav">
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<a accesskey="p" href="high_precision/using_test.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../using_udt.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="dist_concept.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
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<div class="section">
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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
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<a name="math_toolkit.real_concepts"></a><a class="link" href="real_concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for
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Real Number Types</a>
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</h2></div></div></div>
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<p>
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The functions and statistical distributions in this library can be used with
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any type <span class="emphasis"><em>RealType</em></span> that meets the conceptual requirements
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given below. All the built-in floating-point types like <code class="computeroutput"><span class="keyword">double</span></code>
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will meet these requirements. (Built-in types are also called <a href="http://en.cppreference.com/w/cpp/language/types" target="_top">fundamental
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types</a>).
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</p>
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<p>
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User-defined types that meet the conceptual requirements can also be used.
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For example, with <a class="link" href="high_precision/use_ntl.html" title="Using NTL Library">a thin
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wrapper class</a> one of the types provided with <a href="http://shoup.net/ntl/" target="_top">NTL
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(RR)</a> can be used. But now that <a href="../../../../../libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>
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library is available, this has become the preferred real-number type, typically
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<a href="../../../../../libs/multiprecision/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html" target="_top">cpp_dec_float</a>
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or <a href="../../../../../libs/multiprecision/doc/html/boost_multiprecision/tut/floats/cpp_bin_float.html" target="_top">cpp_bin_float</a>.
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</p>
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<p>
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Submissions of binding to other extended precision types would also still be
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welcome.
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</p>
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<p>
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The guiding principal behind these requirements is that a <span class="emphasis"><em>RealType</em></span>
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behaves just like a built-in floating-point type.
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</p>
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<h5>
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<a name="math_toolkit.real_concepts.h0"></a>
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<span class="phrase"><a name="math_toolkit.real_concepts.basic_arithmetic_requirements"></a></span><a class="link" href="real_concepts.html#math_toolkit.real_concepts.basic_arithmetic_requirements">Basic Arithmetic
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Requirements</a>
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</h5>
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<p>
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These requirements are common to all of the functions in this library.
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</p>
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<p>
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In the following table <span class="emphasis"><em>r</em></span> is an object of type <code class="computeroutput"><span class="identifier">RealType</span></code>, <span class="emphasis"><em>cr</em></span> and <span class="emphasis"><em>cr2</em></span>
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are objects of type <code class="computeroutput"><span class="keyword">const</span> <span class="identifier">RealType</span></code>,
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and <span class="emphasis"><em>ca</em></span> is an object of type <code class="computeroutput"><span class="keyword">const</span>
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<span class="identifier">arithmetic</span><span class="special">-</span><span class="identifier">type</span></code> (arithmetic types include all the built
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in integers and floating point types).
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</p>
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<div class="informaltable"><table class="table">
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<colgroup>
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<col>
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<col>
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<col>
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</colgroup>
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<thead><tr>
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<th>
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<p>
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Expression
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</p>
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</th>
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<th>
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<p>
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Result Type
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</p>
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</th>
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<th>
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<p>
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Notes
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</p>
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</th>
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</tr></thead>
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<tbody>
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<tr>
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<td>
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<p>
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<code class="computeroutput"><span class="identifier">RealType</span><span class="special">(</span><span class="identifier">cr</span><span class="special">)</span></code>
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</p>
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</td>
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<td>
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<p>
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RealType
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</p>
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</td>
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<td>
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<p>
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RealType is copy constructible.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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<code class="computeroutput"><span class="identifier">RealType</span><span class="special">(</span><span class="identifier">ca</span><span class="special">)</span></code>
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</p>
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</td>
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<td>
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<p>
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RealType
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</p>
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</td>
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<td>
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<p>
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RealType is copy constructible from the arithmetic types.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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<code class="computeroutput"><span class="identifier">r</span> <span class="special">=</span>
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<span class="identifier">cr</span></code>
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</p>
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</td>
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<td>
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<p>
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RealType&
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</p>
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</td>
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<td>
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<p>
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Assignment operator.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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<code class="computeroutput"><span class="identifier">r</span> <span class="special">=</span>
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||
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<span class="identifier">ca</span></code>
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</p>
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</td>
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<td>
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<p>
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RealType&
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</p>
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</td>
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<td>
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<p>
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Assignment operator from the arithmetic types.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
|
||
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<code class="computeroutput"><span class="identifier">r</span> <span class="special">+=</span>
|
||
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<span class="identifier">cr</span></code>
|
||
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</p>
|
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</td>
|
||
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<td>
|
||
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<p>
|
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RealType&
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</p>
|
||
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</td>
|
||
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<td>
|
||
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<p>
|
||
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Adds cr to r.
|
||
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</p>
|
||
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</td>
|
||
|
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</tr>
|
||
|
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<tr>
|
||
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<td>
|
||
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<p>
|
||
|
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<code class="computeroutput"><span class="identifier">r</span> <span class="special">+=</span>
|
||
|
|
<span class="identifier">ca</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
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RealType&
|
||
|
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</p>
|
||
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|
</td>
|
||
|
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<td>
|
||
|
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<p>
|
||
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|
Adds ar to r.
|
||
|
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</p>
|
||
|
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</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
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<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">r</span> <span class="special">-=</span>
|
||
|
|
<span class="identifier">cr</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType&
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
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<p>
|
||
|
|
Subtracts cr from r.
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">r</span> <span class="special">-=</span>
|
||
|
|
<span class="identifier">ca</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType&
|
||
|
|
</p>
|
||
|
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</td>
|
||
|
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<td>
|
||
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<p>
|
||
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Subtracts ca from r.
|
||
|
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</p>
|
||
|
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</td>
|
||
|
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</tr>
|
||
|
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<tr>
|
||
|
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<td>
|
||
|
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<p>
|
||
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<code class="computeroutput"><span class="identifier">r</span> <span class="special">*=</span>
|
||
|
|
<span class="identifier">cr</span></code>
|
||
|
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</p>
|
||
|
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</td>
|
||
|
|
<td>
|
||
|
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<p>
|
||
|
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RealType&
|
||
|
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</p>
|
||
|
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</td>
|
||
|
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<td>
|
||
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<p>
|
||
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Multiplies r by cr.
|
||
|
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</p>
|
||
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</td>
|
||
|
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</tr>
|
||
|
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<tr>
|
||
|
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<td>
|
||
|
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<p>
|
||
|
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<code class="computeroutput"><span class="identifier">r</span> <span class="special">*=</span>
|
||
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<span class="identifier">ca</span></code>
|
||
|
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</p>
|
||
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</td>
|
||
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<td>
|
||
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<p>
|
||
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RealType&
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</p>
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||
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</td>
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||
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<td>
|
||
|
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<p>
|
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Multiplies r by ca.
|
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|
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</p>
|
||
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</td>
|
||
|
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</tr>
|
||
|
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<tr>
|
||
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<td>
|
||
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<p>
|
||
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<code class="computeroutput"><span class="identifier">r</span> <span class="special">/=</span>
|
||
|
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<span class="identifier">cr</span></code>
|
||
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</p>
|
||
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</td>
|
||
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<td>
|
||
|
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<p>
|
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RealType&
|
||
|
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</p>
|
||
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</td>
|
||
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<td>
|
||
|
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<p>
|
||
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Divides r by cr.
|
||
|
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</p>
|
||
|
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</td>
|
||
|
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</tr>
|
||
|
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<tr>
|
||
|
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<td>
|
||
|
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<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">r</span> <span class="special">/=</span>
|
||
|
|
<span class="identifier">ca</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType&
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Divides r by ca.
|
||
|
|
</p>
|
||
|
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</td>
|
||
|
|
</tr>
|
||
|
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<tr>
|
||
|
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<td>
|
||
|
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<p>
|
||
|
|
<code class="computeroutput"><span class="special">-</span><span class="identifier">r</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
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</p>
|
||
|
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</td>
|
||
|
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<td>
|
||
|
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<p>
|
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|
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Unary Negation.
|
||
|
|
</p>
|
||
|
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</td>
|
||
|
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</tr>
|
||
|
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<tr>
|
||
|
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<td>
|
||
|
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<p>
|
||
|
|
<code class="computeroutput"><span class="special">+</span><span class="identifier">r</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType&
|
||
|
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</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Identity Operation.
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">+</span>
|
||
|
|
<span class="identifier">cr2</span></code>
|
||
|
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</p>
|
||
|
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</td>
|
||
|
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<td>
|
||
|
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<p>
|
||
|
|
RealType
|
||
|
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</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
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<p>
|
||
|
|
Binary Addition
|
||
|
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</p>
|
||
|
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</td>
|
||
|
|
</tr>
|
||
|
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<tr>
|
||
|
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<td>
|
||
|
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<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">+</span>
|
||
|
|
<span class="identifier">ca</span></code>
|
||
|
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</p>
|
||
|
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</td>
|
||
|
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<td>
|
||
|
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<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Binary Addition
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">ca</span> <span class="special">+</span>
|
||
|
|
<span class="identifier">cr</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Binary Addition
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">-</span>
|
||
|
|
<span class="identifier">cr2</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Binary Subtraction
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">-</span>
|
||
|
|
<span class="identifier">ca</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Binary Subtraction
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">ca</span> <span class="special">-</span>
|
||
|
|
<span class="identifier">cr</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Binary Subtraction
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">*</span>
|
||
|
|
<span class="identifier">cr2</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Binary Multiplication
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">*</span>
|
||
|
|
<span class="identifier">ca</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Binary Multiplication
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">ca</span> <span class="special">*</span>
|
||
|
|
<span class="identifier">cr</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Binary Multiplication
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">/</span>
|
||
|
|
<span class="identifier">cr2</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Binary Subtraction
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">/</span>
|
||
|
|
<span class="identifier">ca</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Binary Subtraction
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">ca</span> <span class="special">/</span>
|
||
|
|
<span class="identifier">cr</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Binary Subtraction
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">==</span>
|
||
|
|
<span class="identifier">cr2</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
bool
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Equality Comparison
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">==</span>
|
||
|
|
<span class="identifier">ca</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
bool
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Equality Comparison
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">ca</span> <span class="special">==</span>
|
||
|
|
<span class="identifier">cr</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
bool
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Equality Comparison
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">!=</span>
|
||
|
|
<span class="identifier">cr2</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
bool
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Inequality Comparison
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">!=</span>
|
||
|
|
<span class="identifier">ca</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
bool
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Inequality Comparison
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">ca</span> <span class="special">!=</span>
|
||
|
|
<span class="identifier">cr</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
bool
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Inequality Comparison
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">cr</span> <span class="special"><=</span>
|
||
|
|
<span class="identifier">cr2</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
bool
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Less than equal to.
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">cr</span> <span class="special"><=</span>
|
||
|
|
<span class="identifier">ca</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
bool
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Less than equal to.
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">ca</span> <span class="special"><=</span>
|
||
|
|
<span class="identifier">cr</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
bool
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Less than equal to.
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">>=</span>
|
||
|
|
<span class="identifier">cr2</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
bool
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Greater than equal to.
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">>=</span>
|
||
|
|
<span class="identifier">ca</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
bool
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Greater than equal to.
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">ca</span> <span class="special">>=</span>
|
||
|
|
<span class="identifier">cr</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
bool
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Greater than equal to.
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">cr</span> <span class="special"><</span>
|
||
|
|
<span class="identifier">cr2</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
bool
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Less than comparison.
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">cr</span> <span class="special"><</span>
|
||
|
|
<span class="identifier">ca</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
bool
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Less than comparison.
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">ca</span> <span class="special"><</span>
|
||
|
|
<span class="identifier">cr</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
bool
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Less than comparison.
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">></span>
|
||
|
|
<span class="identifier">cr2</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
bool
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Greater than comparison.
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">></span>
|
||
|
|
<span class="identifier">ca</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
bool
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Greater than comparison.
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">ca</span> <span class="special">></span>
|
||
|
|
<span class="identifier">cr</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
bool
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
Greater than comparison.
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">digits</span><span class="special"><</span><span class="identifier">RealType</span><span class="special">>()</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
int
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
The number of digits in the significand of RealType.
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">max_value</span><span class="special"><</span><span class="identifier">RealType</span><span class="special">>()</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
The largest representable number by type RealType.
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">min_value</span><span class="special"><</span><span class="identifier">RealType</span><span class="special">>()</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
The smallest representable number by type RealType.
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">log_max_value</span><span class="special"><</span><span class="identifier">RealType</span><span class="special">>()</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
The natural logarithm of the largest representable number by type
|
||
|
|
RealType.
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">log_min_value</span><span class="special"><</span><span class="identifier">RealType</span><span class="special">>()</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
The natural logarithm of the smallest representable number by type
|
||
|
|
RealType.
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">epsilon</span><span class="special"><</span><span class="identifier">RealType</span><span class="special">>()</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
The machine epsilon of RealType.
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
</tbody>
|
||
|
|
</table></div>
|
||
|
|
<p>
|
||
|
|
Note that:
|
||
|
|
</p>
|
||
|
|
<div class="orderedlist"><ol class="orderedlist" type="1">
|
||
|
|
<li class="listitem">
|
||
|
|
The functions <code class="computeroutput"><span class="identifier">log_max_value</span></code>
|
||
|
|
and <code class="computeroutput"><span class="identifier">log_min_value</span></code> can be
|
||
|
|
synthesised from the others, and so no explicit specialisation is required.
|
||
|
|
</li>
|
||
|
|
<li class="listitem">
|
||
|
|
The function <code class="computeroutput"><span class="identifier">epsilon</span></code> can
|
||
|
|
be synthesised from the others, so no explicit specialisation is required
|
||
|
|
provided the precision of RealType does not vary at runtime (see the header
|
||
|
|
<a href="../../../../../boost/math/bindings/rr.hpp" target="_top">boost/math/bindings/rr.hpp</a>
|
||
|
|
for an example where the precision does vary at runtime).
|
||
|
|
</li>
|
||
|
|
<li class="listitem">
|
||
|
|
The functions <code class="computeroutput"><span class="identifier">digits</span></code>,
|
||
|
|
<code class="computeroutput"><span class="identifier">max_value</span></code> and <code class="computeroutput"><span class="identifier">min_value</span></code>, all get synthesised automatically
|
||
|
|
from <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code>. However, if <code class="computeroutput"><span class="identifier">numeric_limits</span></code> is not specialised for
|
||
|
|
type RealType, then you will get a compiler error when code tries to use
|
||
|
|
these functions, <span class="emphasis"><em>unless</em></span> you explicitly specialise
|
||
|
|
them. For example if the precision of RealType varies at runtime, then
|
||
|
|
<code class="computeroutput"><span class="identifier">numeric_limits</span></code> support
|
||
|
|
may not be appropriate, see <a href="../../../../../boost/math/bindings/rr.hpp" target="_top">boost/math/bindings/rr.hpp</a>
|
||
|
|
for examples.
|
||
|
|
</li>
|
||
|
|
</ol></div>
|
||
|
|
<div class="warning"><table border="0" summary="Warning">
|
||
|
|
<tr>
|
||
|
|
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Warning]" src="../../../../../doc/src/images/warning.png"></td>
|
||
|
|
<th align="left">Warning</th>
|
||
|
|
</tr>
|
||
|
|
<tr><td align="left" valign="top">
|
||
|
|
<p>
|
||
|
|
If <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><></span></code>
|
||
|
|
is <span class="bold"><strong>not specialized</strong></span> for type <span class="emphasis"><em>RealType</em></span>
|
||
|
|
then the default float precision of 6 decimal digits will be used by other
|
||
|
|
Boost programs including:
|
||
|
|
</p>
|
||
|
|
<p>
|
||
|
|
Boost.Test: giving misleading error messages like
|
||
|
|
</p>
|
||
|
|
<p>
|
||
|
|
<span class="emphasis"><em>"difference between {9.79796} and {9.79796} exceeds 5.42101e-19%".</em></span>
|
||
|
|
</p>
|
||
|
|
<p>
|
||
|
|
Boost.LexicalCast and Boost.Serialization when converting the number to a
|
||
|
|
string, causing potentially serious loss of accuracy on output.
|
||
|
|
</p>
|
||
|
|
<p>
|
||
|
|
Although it might seem obvious that RealType should require <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code>
|
||
|
|
to be specialized, this is not sensible for <code class="computeroutput"><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span></code> and
|
||
|
|
similar classes where the <span class="bold"><strong>number of digits is a runtime
|
||
|
|
parameter</strong></span> (whereas for <code class="computeroutput"><span class="identifier">numeric_limits</span></code>
|
||
|
|
everything has to be fixed at compile time).
|
||
|
|
</p>
|
||
|
|
</td></tr>
|
||
|
|
</table></div>
|
||
|
|
<h5>
|
||
|
|
<a name="math_toolkit.real_concepts.h1"></a>
|
||
|
|
<span class="phrase"><a name="math_toolkit.real_concepts.standard_library_support_require"></a></span><a class="link" href="real_concepts.html#math_toolkit.real_concepts.standard_library_support_require">Standard
|
||
|
|
Library Support Requirements</a>
|
||
|
|
</h5>
|
||
|
|
<p>
|
||
|
|
Many (though not all) of the functions in this library make calls to standard
|
||
|
|
library functions, the following table summarises the requirements. Note that
|
||
|
|
most of the functions in this library will only call a small subset of the
|
||
|
|
functions listed here, so if in doubt whether a user-defined type has enough
|
||
|
|
standard library support to be useable the best advise is to try it and see!
|
||
|
|
</p>
|
||
|
|
<p>
|
||
|
|
In the following table <span class="emphasis"><em>r</em></span> is an object of type <code class="computeroutput"><span class="identifier">RealType</span></code>, <span class="emphasis"><em>cr1</em></span> and <span class="emphasis"><em>cr2</em></span>
|
||
|
|
are objects of type <code class="computeroutput"><span class="keyword">const</span> <span class="identifier">RealType</span></code>,
|
||
|
|
and <span class="emphasis"><em>i</em></span> is an object of type <code class="computeroutput"><span class="keyword">int</span></code>.
|
||
|
|
</p>
|
||
|
|
<div class="informaltable"><table class="table">
|
||
|
|
<colgroup>
|
||
|
|
<col>
|
||
|
|
<col>
|
||
|
|
</colgroup>
|
||
|
|
<thead><tr>
|
||
|
|
<th>
|
||
|
|
<p>
|
||
|
|
Expression
|
||
|
|
</p>
|
||
|
|
</th>
|
||
|
|
<th>
|
||
|
|
<p>
|
||
|
|
Result Type
|
||
|
|
</p>
|
||
|
|
</th>
|
||
|
|
</tr></thead>
|
||
|
|
<tbody>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">fabs</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">abs</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">ceil</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">floor</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">exp</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">pow</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">,</span>
|
||
|
|
<span class="identifier">cr2</span><span class="special">)</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">log</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">frexp</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">,</span>
|
||
|
|
<span class="special">&</span><span class="identifier">i</span><span class="special">)</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">ldexp</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">,</span>
|
||
|
|
<span class="identifier">i</span><span class="special">)</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">cos</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">sin</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">asin</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">tan</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">atan</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">fmod</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">round</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">iround</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
int
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">trunc</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
RealType
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
<code class="computeroutput"><span class="identifier">itrunc</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
<p>
|
||
|
|
int
|
||
|
|
</p>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
</tbody>
|
||
|
|
</table></div>
|
||
|
|
<p>
|
||
|
|
Note that the table above lists only those standard library functions known
|
||
|
|
to be used (or likely to be used in the near future) by this library. The following
|
||
|
|
functions: <code class="computeroutput"><span class="identifier">acos</span></code>, <code class="computeroutput"><span class="identifier">atan2</span></code>, <code class="computeroutput"><span class="identifier">fmod</span></code>,
|
||
|
|
<code class="computeroutput"><span class="identifier">cosh</span></code>, <code class="computeroutput"><span class="identifier">sinh</span></code>,
|
||
|
|
<code class="computeroutput"><span class="identifier">tanh</span></code>, <code class="computeroutput"><span class="identifier">log10</span></code>,
|
||
|
|
<code class="computeroutput"><span class="identifier">lround</span></code>, <code class="computeroutput"><span class="identifier">llround</span></code>,
|
||
|
|
<code class="computeroutput"><span class="identifier">ltrunc</span></code>, <code class="computeroutput"><span class="identifier">lltrunc</span></code>
|
||
|
|
and <code class="computeroutput"><span class="identifier">modf</span></code> are not currently
|
||
|
|
used, but may be if further special functions are added.
|
||
|
|
</p>
|
||
|
|
<p>
|
||
|
|
Note that the <code class="computeroutput"><span class="identifier">round</span></code>, <code class="computeroutput"><span class="identifier">trunc</span></code> and <code class="computeroutput"><span class="identifier">modf</span></code>
|
||
|
|
functions are not part of the current C++ standard: they are part of the additions
|
||
|
|
added to C99 which will likely be in the next C++ standard. There are Boost
|
||
|
|
versions of these provided as a backup, and the functions are always called
|
||
|
|
unqualified so that argument-dependent-lookup can take place.
|
||
|
|
</p>
|
||
|
|
<p>
|
||
|
|
In addition, for efficient and accurate results, a <a class="link" href="lanczos.html" title="The Lanczos Approximation">Lanczos
|
||
|
|
approximation</a> is highly desirable. You may be able to adapt an existing
|
||
|
|
approximation from <a href="../../../../../boost/math/special_functions/lanczos.hpp" target="_top">boost/math/special_functions/lanczos.hpp</a>
|
||
|
|
or <a href="../../../../../boost/math/bindings/detail/big_lanczos.hpp" target="_top">boost/math/bindings/detail/big_lanczos.hpp</a>:
|
||
|
|
in the former case you will need change <code class="computeroutput"><span class="keyword">static_cast</span></code>'s
|
||
|
|
to <code class="computeroutput"><span class="identifier">lexical_cast</span></code>'s, and the
|
||
|
|
constants to <span class="emphasis"><em>strings</em></span> (in order to ensure the coefficients
|
||
|
|
aren't truncated to <code class="computeroutput"><span class="keyword">long</span> <span class="identifier">doubl</span></code>e)
|
||
|
|
and then specialise <code class="computeroutput"><span class="identifier">lanczos_traits</span></code>
|
||
|
|
for type T. Otherwise you may have to hack <a href="../../../tools/lanczos_generator.cpp" target="_top">libs/math/tools/lanczos_generator.cpp</a>
|
||
|
|
to find a suitable approximation for your RealType. The code will still compile
|
||
|
|
if you don't do this, but both accuracy and efficiency will be greatly compromised
|
||
|
|
in any function that makes use of the gamma/beta/erf family of functions.
|
||
|
|
</p>
|
||
|
|
</div>
|
||
|
|
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||
|
|
<td align="left"></td>
|
||
|
|
<td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal,
|
||
|
|
Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
|
||
|
|
Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani,
|
||
|
|
Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
|
||
|
|
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||
|
|
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
||
|
|
</p>
|
||
|
|
</div></td>
|
||
|
|
</tr></table>
|
||
|
|
<hr>
|
||
|
|
<div class="spirit-nav">
|
||
|
|
<a accesskey="p" href="high_precision/using_test.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../using_udt.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="dist_concept.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
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|
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|
||
|
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</body>
|
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