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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="sidebar"> |
| <div class="titlepage"></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 double 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, 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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| Holin, Bruno Lalande, John Maddock, Johan Råde, Gautam Sewani, Benjamin Sobotta, |
| 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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