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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>
- </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 © 2006-2019 Nikhar
- Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
- 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>
- 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>)
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