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<title>Calculation of the Type of the Result</title>
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<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.result_type"></a><a class="link" href="result_type.html" title="Calculation of the Type of the Result">Calculation of the Type of the
    Result</a>
</h2></div></div></div>
<p>
      The functions in this library are all overloaded to accept mixed floating point
      (or mixed integer and floating point type) arguments. So for example:
    </p>
<pre class="programlisting"><span class="identifier">foo</span><span class="special">(</span><span class="number">1.0</span><span class="special">,</span> <span class="number">2.0</span><span class="special">);</span>
<span class="identifier">foo</span><span class="special">(</span><span class="number">1.0f</span><span class="special">,</span> <span class="number">2</span><span class="special">);</span>
<span class="identifier">foo</span><span class="special">(</span><span class="number">1.0</span><span class="special">,</span> <span class="number">2L</span><span class="special">);</span>
</pre>
<p>
      etc, are all valid calls, as long as "foo" is a function taking two
      floating-point arguments. But that leaves the question:
    </p>
<div class="blurb">
<div class="titlepage"><div><div><p class="title"><b></b></p></div></div></div>
<p>
      <span class="emphasis"><em>"Given a special function with N arguments of types T1, T2,
      T3 ... TN, then what type is the result?"</em></span>
    </p>
</div>
<p>
      <span class="bold"><strong>If all the arguments are of the same (floating point)
      type then the result is the same type as the arguments.</strong></span>
    </p>
<p>
      Otherwise, the type of the result is computed using the following logic:
    </p>
<div class="orderedlist"><ol class="orderedlist" type="1">
<li class="listitem">
          Any arguments that are not template arguments are disregarded from further
          analysis.
        </li>
<li class="listitem">
          For each type in the argument list, if that type is an integer type then
          it is treated as if it were of type <code class="computeroutput"><span class="keyword">double</span></code>
          for the purposes of further analysis.
        </li>
<li class="listitem">
          If any of the arguments is a user-defined class type, then the result type
          is the first such class type that is constructible from all of the other
          argument types.
        </li>
<li class="listitem">
          If any of the arguments is of type <code class="computeroutput"><span class="keyword">long</span>
          <span class="keyword">double</span></code>, then the result is of type
          <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>.
        </li>
<li class="listitem">
          If any of the arguments is of type <code class="computeroutput"><span class="keyword">double</span></code>,
          then the result is of type <code class="computeroutput"><span class="keyword">double</span></code>.
        </li>
<li class="listitem">
          Otherwise the result is of type <code class="computeroutput"><span class="keyword">float</span></code>.
        </li>
</ol></div>
<p>
      For example:
    </p>
<pre class="programlisting"><span class="identifier">cyl_bessel</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="number">3.0</span><span class="special">);</span>
</pre>
<p>
      Returns a <code class="computeroutput"><span class="keyword">double</span></code> result, as does:
    </p>
<pre class="programlisting"><span class="identifier">cyl_bessel</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="number">3.0f</span><span class="special">);</span>
</pre>
<p>
      as in this case the integer first argument is treated as a <code class="computeroutput"><span class="keyword">double</span></code>
      and takes precedence over the <code class="computeroutput"><span class="keyword">float</span></code>
      second argument. To get a <code class="computeroutput"><span class="keyword">float</span></code>
      result we would need all the arguments to be of type float:
    </p>
<pre class="programlisting"><span class="identifier">cyl_bessel_j</span><span class="special">(</span><span class="number">2.0f</span><span class="special">,</span> <span class="number">3.0f</span><span class="special">);</span>
</pre>
<p>
      When one or more of the arguments is not a template argument then it doesn't
      effect the return type at all, for example:
    </p>
<pre class="programlisting"><span class="identifier">sph_bessel</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="number">3.0f</span><span class="special">);</span>
</pre>
<p>
      returns a <code class="computeroutput"><span class="keyword">float</span></code>, since the first
      argument is not a template argument and so doesn't effect the result: without
      this rule functions that take explicitly integer arguments could never return
      <code class="computeroutput"><span class="keyword">float</span></code>.
    </p>
<p>
      And for user-defined types, typically <a href="../../../../../libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>,
    </p>
<p>
      All of the following return a <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_bin_quad_float</span></code>
      result:
    </p>
<pre class="programlisting"><span class="identifier">cyl_bessel_j</span><span class="special">(</span><span class="number">0</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_bin_quad_float</span><span class="special">(</span><span class="number">2</span><span class="special">));</span>

<span class="identifier">cyl_bessel_j</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_bin_quad_float</span><span class="special">(</span><span class="number">2</span><span class="special">),</span> <span class="number">3</span><span class="special">);</span>

<span class="identifier">cyl_bessel_j</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_bin_quad_float</span><span class="special">(</span><span class="number">2</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_bin_quad_float</span><span class="special">(</span><span class="number">3</span><span class="special">));</span>
</pre>
<p>
      but rely on the parameters provided being exactly representable, avoiding loss
      of precision from construction from <code class="computeroutput"><span class="keyword">double</span></code>.
    </p>
<div class="tip"><table border="0" summary="Tip">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../doc/src/images/tip.png"></td>
<th align="left">Tip</th>
</tr>
<tr><td align="left" valign="top"><p>
        All new projects should use Boost.Multiprecision.
      </p></td></tr>
</table></div>
<p>
      During development of Boost.Math, <a href="http://www.shoup.net/ntl/" target="_top">NTL
      A Library for doing Number Theory</a> was invaluable to create highly precise
      tables.
    </p>
<p>
      All of the following return an <code class="computeroutput"><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span></code> result:
    </p>
<pre class="programlisting"><span class="identifier">cyl_bessel_j</span><span class="special">(</span><span class="number">0</span><span class="special">,</span> <span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span><span class="special">(</span><span class="number">2</span><span class="special">));</span>

<span class="identifier">cyl_bessel_j</span><span class="special">(</span><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span><span class="special">(</span><span class="number">2</span><span class="special">),</span> <span class="number">3</span><span class="special">);</span>

<span class="identifier">cyl_bessel_j</span><span class="special">(</span><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">quad_float</span><span class="special">(</span><span class="number">2</span><span class="special">),</span> <span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span><span class="special">(</span><span class="number">3</span><span class="special">));</span>
</pre>
<p>
      In the last case, <code class="computeroutput"><span class="identifier">quad_float</span></code>
      is convertible to <code class="computeroutput"><span class="identifier">RR</span></code>, but not
      vice-versa, so the result will be an <code class="computeroutput"><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span></code>. Note
      that this assumes that you are using a <a class="link" href="high_precision/use_ntl.html" title="Using NTL Library">patched
      NTL library</a>.
    </p>
<p>
      These rules are chosen to be compatible with the behaviour of <span class="emphasis"><em>ISO/IEC
      9899:1999 Programming languages - C</em></span> and with the <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1836.pdf" target="_top">Draft
      Technical Report on C++ Library Extensions, 2005-06-24, section 5.2.1, paragraph
      5</a>.
    </p>
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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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