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   4 <title>Calculation of the Type of the Result</title>
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  26 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
  27 <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
  28     Result</a>
  29 </h2></div></div></div>
  30 <p>
  31       The functions in this library are all overloaded to accept mixed floating point
  32       (or mixed integer and floating point type) arguments. So for example:
  33     </p>
  34 <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>
  35 <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>
  36 <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>
  37 </pre>
  38 <p>
  39       etc, are all valid calls, as long as "foo" is a function taking two
  40       floating-point arguments. But that leaves the question:
  41     </p>
  42 <div class="blurb">
  43 <div class="titlepage"><div><div><p class="title"><b></b></p></div></div></div>
  44 <p>
  45       <span class="emphasis"><em>"Given a special function with N arguments of types T1, T2,
  46       T3 ... TN, then what type is the result?"</em></span>
  47     </p>
  48 </div>
  49 <p>
  50       <span class="bold"><strong>If all the arguments are of the same (floating point)
  51       type then the result is the same type as the arguments.</strong></span>
  52     </p>
  53 <p>
  54       Otherwise, the type of the result is computed using the following logic:
  55     </p>
  56 <div class="orderedlist"><ol class="orderedlist" type="1">
  57 <li class="listitem">
  58           Any arguments that are not template arguments are disregarded from further
  59           analysis.
  60         </li>
  61 <li class="listitem">
  62           For each type in the argument list, if that type is an integer type then
  63           it is treated as if it were of type <code class="computeroutput"><span class="keyword">double</span></code>
  64           for the purposes of further analysis.
  65         </li>
  66 <li class="listitem">
  67           If any of the arguments is a user-defined class type, then the result type
  68           is the first such class type that is constructible from all of the other
  69           argument types.
  70         </li>
  71 <li class="listitem">
  72           If any of the arguments is of type <code class="computeroutput"><span class="keyword">long</span>
  73           <span class="keyword">double</span></code>, then the result is of type
  74           <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>.
  75         </li>
  76 <li class="listitem">
  77           If any of the arguments is of type <code class="computeroutput"><span class="keyword">double</span></code>,
  78           then the result is of type <code class="computeroutput"><span class="keyword">double</span></code>.
  79         </li>
  80 <li class="listitem">
  81           Otherwise the result is of type <code class="computeroutput"><span class="keyword">float</span></code>.
  82         </li>
  83 </ol></div>
  84 <p>
  85       For example:
  86     </p>
  87 <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>
  88 </pre>
  89 <p>
  90       Returns a <code class="computeroutput"><span class="keyword">double</span></code> result, as does:
  91     </p>
  92 <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>
  93 </pre>
  94 <p>
  95       as in this case the integer first argument is treated as a <code class="computeroutput"><span class="keyword">double</span></code>
  96       and takes precedence over the <code class="computeroutput"><span class="keyword">float</span></code>
  97       second argument. To get a <code class="computeroutput"><span class="keyword">float</span></code>
  98       result we would need all the arguments to be of type float:
  99     </p>
 100 <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>
 101 </pre>
 102 <p>
 103       When one or more of the arguments is not a template argument then it doesn't
 104       effect the return type at all, for example:
 105     </p>
 106 <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>
 107 </pre>
 108 <p>
 109       returns a <code class="computeroutput"><span class="keyword">float</span></code>, since the first
 110       argument is not a template argument and so doesn't effect the result: without
 111       this rule functions that take explicitly integer arguments could never return
 112       <code class="computeroutput"><span class="keyword">float</span></code>.
 113     </p>
 114 <p>
 115       And for user-defined types, typically <a href="../../../../../libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>,
 116     </p>
 117 <p>
 118       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>
 119       result:
 120     </p>
 121 <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>
 122
 123 <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>
 124
 125 <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>
 126 </pre>
 127 <p>
 128       but rely on the parameters provided being exactly representable, avoiding loss
 129       of precision from construction from <code class="computeroutput"><span class="keyword">double</span></code>.
 130     </p>
 131 <div class="tip"><table border="0" summary="Tip">
 132 <tr>
 133 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../doc/src/images/tip.png"></td>
 134 <th align="left">Tip</th>
 135 </tr>
 136 <tr><td align="left" valign="top"><p>
 137         All new projects should use Boost.Multiprecision.
 138       </p></td></tr>
 139 </table></div>
 140 <p>
 141       During development of Boost.Math, <a href="http://www.shoup.net/ntl/" target="_top">NTL
 142       A Library for doing Number Theory</a> was invaluable to create highly precise
 143       tables.
 144     </p>
 145 <p>
 146       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:
 147     </p>
 148 <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>
 149
 150 <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>
 151
 152 <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>
 153 </pre>
 154 <p>
 155       In the last case, <code class="computeroutput"><span class="identifier">quad_float</span></code>
 156       is convertible to <code class="computeroutput"><span class="identifier">RR</span></code>, but not
 157       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
 158       that this assumes that you are using a <a class="link" href="high_precision/use_ntl.html" title="Using NTL Library">patched
 159       NTL library</a>.
 160     </p>
 161 <p>
 162       These rules are chosen to be compatible with the behaviour of <span class="emphasis"><em>ISO/IEC
 163       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
 164       Technical Report on C++ Library Extensions, 2005-06-24, section 5.2.1, paragraph
 165       5</a>.
 166     </p>
 167 </div>
 168 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 169 <td align="left"></td>
 170 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
 171       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
 172       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
 173       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
 174       Daryle Walker and Xiaogang Zhang<p>
 175         Distributed under the Boost Software License, Version 1.0. (See accompanying
 176         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>)
 177       </p>
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