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<title>Use With User-Defined Types</title>
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<div class="section">
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<div class="titlepage"><div><div><h3 class="title">
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<a name="math_toolkit.tutorial.user_def"></a><a class="link" href="user_def.html" title="Use With User-Defined Types">Use With User-Defined
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Types</a>
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</h3></div></div></div>
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<p>
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The most common example of a high-precision user-defined type will probably
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be <a href="../../../../../../libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>.
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</p>
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<p>
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The syntax for using the function-call constants with user-defined types
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is the same as it is in the template class, which is to say we use:
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</p>
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<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">/</span><span class="identifier">constants</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
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<span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special"><</span><span class="identifier">UserDefinedType</span><span class="special">>();</span>
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</pre>
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<p>
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For example:
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</p>
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<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_dec_float_50</span><span class="special">>();</span>
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</pre>
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<p>
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giving π with a precision of 50 decimal digits.
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</p>
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<p>
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However, since the precision of the user-defined type may be much greater
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than that of the built-in floating point types, how the value returned is
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created is as follows:
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</p>
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<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
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<li class="listitem">
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If the precision of the type is known at compile time:
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<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; ">
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<li class="listitem">
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If the precision is less than or equal to that of a <code class="computeroutput"><span class="keyword">float</span></code> and the type is constructable
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from a <code class="computeroutput"><span class="keyword">float</span></code> then
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our code returns a <code class="computeroutput"><span class="keyword">float</span></code>
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literal. If the user-defined type is a literal type then the function
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call that returns the constant will be a <code class="computeroutput"><span class="identifier">constexp</span></code>.
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</li>
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<li class="listitem">
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If the precision is less than or equal to that of a <code class="computeroutput"><span class="keyword">double</span></code> and the type is constructable
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from a <code class="computeroutput"><span class="keyword">double</span></code> then
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our code returns a <code class="computeroutput"><span class="keyword">double</span></code>
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literal. If the user-defined type is a literal type then the function
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call that returns the constant will be a <code class="computeroutput"><span class="identifier">constexp</span></code>.
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</li>
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<li class="listitem">
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If the precision is less than or equal to that of a <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>
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and the type is constructable from a <code class="computeroutput"><span class="keyword">long</span>
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<span class="keyword">double</span></code> then our code returns
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a <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>
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literal. If the user-defined type is a literal type then the function
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call that returns the constant will be a <code class="computeroutput"><span class="identifier">constexp</span></code>.
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</li>
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<li class="listitem">
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If the precision is less than or equal to that of a <code class="computeroutput"><span class="identifier">__float128</span></code> (and the compiler
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supports such a type) and the type is constructable from a <code class="computeroutput"><span class="identifier">__float128</span></code> then our code returns
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a <code class="computeroutput"><span class="identifier">__float128</span></code> literal.
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If the user-defined type is a literal type then the function call
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that returns the constant will be a <code class="computeroutput"><span class="identifier">constexp</span></code>.
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</li>
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<li class="listitem">
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If the precision is less than 100 decimal digits, then the constant
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will be constructed (just the once, then cached in a thread-safe
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manner) from a string representation of the constant. In this case
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the value is returned as a const reference to the cached value.
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</li>
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<li class="listitem">
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Otherwise the value is computed (just once, then cached in a thread-safe
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manner). In this case the value is returned as a const reference
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to the cached value.
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</li>
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</ul></div>
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</li>
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<li class="listitem">
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If the precision is unknown at compile time then:
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<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; ">
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<li class="listitem">
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If the runtime precision (obtained from a call to <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">T</span><span class="special">>()</span></code>)
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is less than 100 decimal digits, then the constant is constructed
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"on the fly" from the string representation of the constant.
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</li>
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<li class="listitem">
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Otherwise the value is constructed "on the fly" by calculating
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then value of the constant using the current default precision
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of the type. Note that this can make use of the constants rather
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expensive.
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</li>
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</ul></div>
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</li>
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</ul></div>
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<p>
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In addition, it is possible to pass a <code class="computeroutput"><span class="identifier">Policy</span></code>
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type as a second template argument, and use this to control the precision:
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</p>
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<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">/</span><span class="identifier">constants</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
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<span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">digits2</span><span class="special"><</span><span class="number">80</span><span class="special">></span> <span class="special">></span> <span class="identifier">my_policy_type</span><span class="special">;</span>
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<span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special"><</span><span class="identifier">MyType</span><span class="special">,</span> <span class="identifier">my_policy_type</span><span class="special">>();</span>
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</pre>
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<div class="note"><table border="0" summary="Note">
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<tr>
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<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../doc/src/images/note.png"></td>
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<th align="left">Note</th>
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</tr>
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<tr><td align="left" valign="top"><p>
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Boost.Math doesn't know how to control the internal precision of <code class="computeroutput"><span class="identifier">MyType</span></code>, the policy just controls how
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the selection process above is carried out, and the calculation precision
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if the result is computed.
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</p></td></tr>
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</table></div>
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<p>
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It is also possible to control which method is used to construct the constant
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by specialising the traits class <code class="computeroutput"><span class="identifier">construction_traits</span></code>:
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</p>
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<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">constant</span><span class="special">{</span>
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<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">></span>
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<span class="keyword">struct</span> <span class="identifier">construction_traits</span>
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<span class="special">{</span>
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<span class="keyword">typedef</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special"><</span><span class="identifier">N</span><span class="special">></span> <span class="identifier">type</span><span class="special">;</span>
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<span class="special">};</span>
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<span class="special">}}}</span> <span class="comment">// namespaces</span>
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</pre>
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<p>
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Where <span class="emphasis"><em>N</em></span> takes one of the following values:
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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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</colgroup>
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<thead><tr>
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<th>
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<p>
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<span class="emphasis"><em>N</em></span>
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</p>
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</th>
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<th>
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<p>
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Meaning
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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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0
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</p>
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</td>
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<td>
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<p>
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The precision is unavailable at compile time; either construct
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from a decimal digit string or calculate on the fly depending upon
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the runtime precision.
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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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1
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</p>
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</td>
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<td>
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<p>
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Return a float precision constant.
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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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2
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</p>
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</td>
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<td>
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<p>
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Return a double precision constant.
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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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3
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</p>
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</td>
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<td>
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<p>
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Return a long double precision constant.
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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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4
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</p>
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</td>
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<td>
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<p>
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Construct the result from the string representation, and cache
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the result.
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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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Any other value <span class="emphasis"><em>N</em></span>
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</p>
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</td>
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<td>
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<p>
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Sets the compile time precision to <span class="emphasis"><em>N</em></span> bits.
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</p>
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</td>
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</tr>
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</tbody>
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</table></div>
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<h6>
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<a name="math_toolkit.tutorial.user_def.h0"></a>
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<span class="phrase"><a name="math_toolkit.tutorial.user_def.custom_specializing_a_constant"></a></span><a class="link" href="user_def.html#math_toolkit.tutorial.user_def.custom_specializing_a_constant">Custom
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Specializing a constant</a>
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</h6>
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<p>
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In addition, for user-defined types that need special handling, it's possible
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to partially-specialize the internal structure used by each constant. For
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example, suppose we're using the C++ wrapper around MPFR <code class="computeroutput"><span class="identifier">mpfr_class</span></code>:
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this has its own representation of Pi which we may well wish to use in place
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of the above mechanism. We can achieve this by specialising the class template
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<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">detail</span><span class="special">::</span><span class="identifier">constant_pi</span></code>:
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</p>
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<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">constants</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">detail</span><span class="special">{</span>
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<span class="keyword">template</span><span class="special"><></span>
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<span class="keyword">struct</span> <span class="identifier">constant_pi</span><span class="special"><</span><span class="identifier">mpfr_class</span><span class="special">></span>
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<span class="special">{</span>
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<span class="keyword">template</span><span class="special"><</span><span class="keyword">int</span> <span class="identifier">N</span><span class="special">></span>
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<span class="keyword">static</span> <span class="identifier">mpfr_class</span> <span class="identifier">get</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special"><</span><span class="identifier">N</span><span class="special">>&)</span>
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<span class="special">{</span>
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<span class="comment">// The template param N is one of the values in the table above,</span>
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<span class="comment">// we can either handle all cases in one as is the case here,</span>
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<span class="comment">// or overload "get" for the different options.</span>
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<span class="identifier">mpfr_class</span> <span class="identifier">result</span><span class="special">;</span>
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<span class="identifier">mpfr_const_pi</span><span class="special">(</span><span class="identifier">result</span><span class="special">.</span><span class="identifier">get_mpfr_t</span><span class="special">(),</span> <span class="identifier">GMP_RNDN</span><span class="special">);</span>
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<span class="keyword">return</span> <span class="identifier">result</span><span class="special">;</span>
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<span class="special">}</span>
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<span class="special">};</span>
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<span class="special">}}}}</span> <span class="comment">// namespaces</span>
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</pre>
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<h6>
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<a name="math_toolkit.tutorial.user_def.h1"></a>
|
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<span class="phrase"><a name="math_toolkit.tutorial.user_def.diagnosing_what_meta_programmed_"></a></span><a class="link" href="user_def.html#math_toolkit.tutorial.user_def.diagnosing_what_meta_programmed_">Diagnosing
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what meta-programmed code is doing</a>
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</h6>
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<p>
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Finally, since it can be tricky to diagnose what meta-programmed code is
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doing, there is a diagnostic routine that prints information about how this
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library will handle a specific type, it can be used like this:
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</p>
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<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">/</span><span class="identifier">info</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
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<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
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<span class="special">{</span>
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<span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">print_info_on_type</span><span class="special"><</span><span class="identifier">MyType</span><span class="special">>();</span>
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<span class="special">}</span>
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</pre>
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<p>
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If you wish, you can also pass an optional std::ostream argument to the
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<code class="computeroutput"><span class="identifier">print_info_on_type</span></code> function.
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Typical output for a user-defined type looks like this:
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</p>
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<pre class="programlisting">Information on the Implementation and Handling of
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Mathematical Constants for Type class boost::math::concepts::real_concept
|
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Checking for std::numeric_limits<class boost::math::concepts::real_concept> specialisation: no
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boost::math::policies::precision<class boost::math::concepts::real_concept, Policy>
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reports that there is no compile type precision available.
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boost::math::tools::digits<class boost::math::concepts::real_concept>()
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reports that the current runtime precision is
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53 binary digits.
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No compile time precision is available, the construction method
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will be decided at runtime and results will not be cached
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- this may lead to poor runtime performance.
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Current runtime precision indicates that
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the constant will be constructed from a string on each call.
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</pre>
|
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</div>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="left"></td>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar
|
|
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
|
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Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
|
|
Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
|
|
Daryle Walker and Xiaogang Zhang<p>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
|
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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>)
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</p>
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</div></td>
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</tr></table>
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<hr>
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