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| <div class="titlepage"><div><div><h3 class="title"> |
| <a name="math_toolkit.main_overview.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> |
| </h3></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="sidebar"> |
| <p class="title"><b></b></p> |
| <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 type="1"> |
| <li> |
| Any arguments that are not template arguments are disregarded from further |
| analysis. |
| </li> |
| <li> |
| For each type in the argument list, if that type is an integer type then |
| it is treated as if it were of type double for the purposes of further |
| analysis. |
| </li> |
| <li> |
| 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> |
| 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> |
| 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> |
| 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, all of the following return an NTL::RR 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, quad_float is convertible to RR, but not vice-versa, so |
| the result will be an NTL::RR. Note that this assumes that you are using |
| a <a class="link" href="../using_udt/use_ntl.html" title="Using With NTL - a High-Precision Floating-Point 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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| <td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, |
| Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and |
| Thijs van den Berg<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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