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25 | <div class="section"> | |
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> | |
137 | <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> | |
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139 | <td align="right"><div class="copyright-footer">Copyright © 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 Råde, 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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