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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="sidebar">
  43 <div class="titlepage"></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 double for the purposes of further
  64           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, 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:
 116     </p>
 117 <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>
 118
 119 <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>
 120
 121 <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>
 122 </pre>
 123 <p>
 124       In the last case, <code class="computeroutput"><span class="identifier">quad_float</span></code>
 125       is convertible to <code class="computeroutput"><span class="identifier">RR</span></code>, but not
 126       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
 127       that this assumes that you are using a <a class="link" href="high_precision/use_ntl.html" title="Using NTL Library">patched
 128       NTL library</a>.
 129     </p>
 130 <p>
 131       These rules are chosen to be compatible with the behaviour of <span class="emphasis"><em>ISO/IEC
 132       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
 133       Technical Report on C++ Library Extensions, 2005-06-24, section 5.2.1, paragraph
 134       5</a>.
 135     </p>
 136 </div>
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 139 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
 140       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
 141       Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
 142       Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
 143         Distributed under the Boost Software License, Version 1.0. (See accompanying
 144         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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