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24 | </div> | |
25 | <div class="section"> | |
26 | <div class="titlepage"><div><div><h3 class="title"> | |
27 | <a name="math_toolkit.special_tut.special_tut_test"></a><a class="link" href="special_tut_test.html" title="Testing">Testing</a> | |
28 | </h3></div></div></div> | |
29 | <p> | |
30 | We work under the assumption that untested code doesn't work, so some tests | |
31 | for your new special function are in order, we'll divide these up in to 3 | |
32 | main categories: | |
33 | </p> | |
34 | <h5> | |
35 | <a name="math_toolkit.special_tut.special_tut_test.h0"></a> | |
36 | <span class="phrase"><a name="math_toolkit.special_tut.special_tut_test.spot_tests"></a></span><a class="link" href="special_tut_test.html#math_toolkit.special_tut.special_tut_test.spot_tests">Spot Tests</a> | |
37 | </h5> | |
38 | <p> | |
39 | Spot tests consist of checking that the expected exception is generated when | |
40 | the inputs are in error (or otherwise generate undefined values), and checking | |
41 | any special values. We can check for expected exceptions with <code class="computeroutput"><span class="identifier">BOOST_CHECK_THROW</span></code>, so for example if it's | |
42 | a domain error for the last parameter to be outside the range <code class="computeroutput"><span class="special">[</span><span class="number">0</span><span class="special">,</span><span class="number">1</span><span class="special">]</span></code> then we | |
43 | might have: | |
44 | </p> | |
45 | <pre class="programlisting"><span class="identifier">BOOST_CHECK_THROW</span><span class="special">(</span><span class="identifier">my_special</span><span class="special">(</span><span class="number">0</span><span class="special">,</span> <span class="special">-</span><span class="number">0.1</span><span class="special">),</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">domain_error</span><span class="special">);</span> | |
46 | <span class="identifier">BOOST_CHECK_THROW</span><span class="special">(</span><span class="identifier">my_special</span><span class="special">(</span><span class="number">0</span><span class="special">,</span> <span class="number">1.1</span><span class="special">),</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">domain_error</span><span class="special">);</span> | |
47 | </pre> | |
48 | <p> | |
49 | When the function has known exact values (typically integer values) we can | |
50 | use <code class="computeroutput"><span class="identifier">BOOST_CHECK_EQUAL</span></code>: | |
51 | </p> | |
52 | <pre class="programlisting"><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="identifier">my_special</span><span class="special">(</span><span class="number">1.0</span><span class="special">,</span> <span class="number">0.0</span><span class="special">),</span> <span class="number">0</span><span class="special">);</span> | |
53 | <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="identifier">my_special</span><span class="special">(</span><span class="number">1.0</span><span class="special">,</span> <span class="number">1.0</span><span class="special">),</span> <span class="number">1</span><span class="special">);</span> | |
54 | </pre> | |
55 | <p> | |
56 | When the function has known values which are not exact (from a floating point | |
57 | perspective) then we can use <code class="computeroutput"><span class="identifier">BOOST_CHECK_CLOSE_FRACTION</span></code>: | |
58 | </p> | |
59 | <pre class="programlisting"><span class="comment">// Assumes 4 epsilon is as close as we can get to a true value of 2Pi:</span> | |
60 | <span class="identifier">BOOST_CHECK_CLOSE_FRACTION</span><span class="special">(</span><span class="identifier">my_special</span><span class="special">(</span><span class="number">0.5</span><span class="special">,</span> <span class="number">0.5</span><span class="special">),</span> <span class="number">2</span> <span class="special">*</span> <span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special"><</span><span class="keyword">double</span><span class="special">>(),</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">double</span><span class="special">>::</span><span class="identifier">epsilon</span><span class="special">()</span> <span class="special">*</span> <span class="number">4</span><span class="special">);</span> | |
61 | </pre> | |
62 | <h5> | |
63 | <a name="math_toolkit.special_tut.special_tut_test.h1"></a> | |
64 | <span class="phrase"><a name="math_toolkit.special_tut.special_tut_test.independent_test_values"></a></span><a class="link" href="special_tut_test.html#math_toolkit.special_tut.special_tut_test.independent_test_values">Independent | |
65 | Test Values</a> | |
66 | </h5> | |
67 | <p> | |
68 | If the function is implemented by some other known good source (for example | |
69 | Mathematica or it's online versions <a href="http://functions.wolfram.com" target="_top">functions.wolfram.com</a> | |
70 | or <a href="http://www.wolframalpha.com" target="_top">www.wolframalpha.com</a> | |
71 | then it's a good idea to sanity check our implementation by having at least | |
72 | one independendly generated value for each code branch our implementation | |
73 | may take. To slot these in nicely with our testing framework it's best to | |
74 | tabulate these like this: | |
75 | </p> | |
76 | <pre class="programlisting"><span class="comment">// function values calculated on http://functions.wolfram.com/</span> | |
77 | <span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="number">3</span><span class="special">>,</span> <span class="number">10</span><span class="special">></span> <span class="identifier">my_special_data</span> <span class="special">=</span> <span class="special">{{</span> | |
78 | <span class="special">{{</span> <span class="identifier">SC_</span><span class="special">(</span><span class="number">0</span><span class="special">),</span> <span class="identifier">SC_</span><span class="special">(</span><span class="number">0</span><span class="special">),</span> <span class="identifier">SC_</span><span class="special">(</span><span class="number">1</span><span class="special">)</span> <span class="special">}},</span> | |
79 | <span class="special">{{</span> <span class="identifier">SC_</span><span class="special">(</span><span class="number">0</span><span class="special">),</span> <span class="identifier">SC_</span><span class="special">(</span><span class="number">1</span><span class="special">),</span> <span class="identifier">SC_</span><span class="special">(</span><span class="number">1.26606587775200833559824462521471753760767031135496220680814</span><span class="special">)</span> <span class="special">}},</span> | |
80 | <span class="comment">/* More values here... */</span> | |
81 | <span class="special">}};</span> | |
82 | </pre> | |
83 | <p> | |
84 | We'll see how to use this table and the meaning of the <code class="computeroutput"><span class="identifier">SC_</span></code> | |
85 | macro later. One important point is to make sure that the input values have | |
86 | exact binary representations: so choose values such as 1.5, 1.25, 1.125 etc. | |
87 | This ensures that if <code class="computeroutput"><span class="identifier">my_special</span></code> | |
88 | is unusually sensitive in one area, that we don't get apparently large errors | |
89 | just because the inputs are 0.5 ulp in error. | |
90 | </p> | |
91 | <h5> | |
92 | <a name="math_toolkit.special_tut.special_tut_test.h2"></a> | |
93 | <span class="phrase"><a name="math_toolkit.special_tut.special_tut_test.random_test_values"></a></span><a class="link" href="special_tut_test.html#math_toolkit.special_tut.special_tut_test.random_test_values">Random | |
94 | Test Values</a> | |
95 | </h5> | |
96 | <p> | |
97 | We can generate a large number of test values to check both for future regressions, | |
98 | and for accumulated rounding or cancellation error in our implementation. | |
99 | Ideally we would use an independent implementation for this (for example | |
100 | my_special may be defined in directly terms of other special functions but | |
101 | not implemented that way for performance or accuracy reasons). Alternatively | |
102 | we may use our own implementation directly, but with any special cases (asymptotic | |
103 | expansions etc) disabled. We have a set of <a class="link" href="../internals/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">tools</a> | |
104 | to generate test data directly, here's a typical example: | |
105 | </p> | |
106 | <pre class="programlisting"><span class="preprocessor">#include</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_dec_float</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> | |
107 | <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">test_data</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> | |
108 | <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">test</span><span class="special">/</span><span class="identifier">included</span><span class="special">/</span><span class="identifier">prg_exec_monitor</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> | |
109 | <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">fstream</span><span class="special">></span> | |
110 | ||
111 | <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">;</span> | |
112 | <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span> | |
113 | <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">std</span><span class="special">;</span> | |
114 | <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> | |
115 | ||
116 | <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> | |
117 | <span class="identifier">T</span> <span class="identifier">my_special</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">b</span><span class="special">)</span> | |
118 | <span class="special">{</span> | |
119 | <span class="comment">// Implementation of my_special here...</span> | |
120 | <span class="keyword">return</span> <span class="identifier">a</span> <span class="special">+</span> <span class="identifier">b</span><span class="special">;</span> | |
121 | <span class="special">}</span> | |
122 | ||
123 | <span class="keyword">int</span> <span class="identifier">cpp_main</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">argc</span><span class="special">,</span> <span class="keyword">char</span><span class="special">*</span><span class="identifier">argv</span> <span class="special">[])</span> | |
124 | <span class="special">{</span> | |
125 | <span class="comment">//</span> | |
126 | <span class="comment">// We'll use so many digits of precision that any</span> | |
127 | <span class="comment">// calculation errors will still leave us with</span> | |
128 | <span class="comment">// 40-50 good digits. We'll only run this program</span> | |
129 | <span class="comment">// once so it doesn't matter too much how long this takes!</span> | |
130 | <span class="comment">//</span> | |
131 | <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_dec_float</span><span class="special"><</span><span class="number">500</span><span class="special">></span> <span class="special">></span> <span class="identifier">bignum</span><span class="special">;</span> | |
132 | ||
133 | <span class="identifier">parameter_info</span><span class="special"><</span><span class="identifier">bignum</span><span class="special">></span> <span class="identifier">arg1</span><span class="special">,</span> <span class="identifier">arg2</span><span class="special">;</span> | |
134 | <span class="identifier">test_data</span><span class="special"><</span><span class="identifier">bignum</span><span class="special">></span> <span class="identifier">data</span><span class="special">;</span> | |
135 | ||
136 | <span class="keyword">bool</span> <span class="identifier">cont</span><span class="special">;</span> | |
137 | <span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">line</span><span class="special">;</span> | |
138 | ||
139 | <span class="keyword">if</span><span class="special">(</span><span class="identifier">argc</span> <span class="special"><</span> <span class="number">1</span><span class="special">)</span> | |
140 | <span class="keyword">return</span> <span class="number">1</span><span class="special">;</span> | |
141 | ||
142 | <span class="keyword">do</span><span class="special">{</span> | |
143 | <span class="comment">//</span> | |
144 | <span class="comment">// User interface which prompts for </span> | |
145 | <span class="comment">// range of input parameters:</span> | |
146 | <span class="comment">//</span> | |
147 | <span class="keyword">if</span><span class="special">(</span><span class="number">0</span> <span class="special">==</span> <span class="identifier">get_user_parameter_info</span><span class="special">(</span><span class="identifier">arg1</span><span class="special">,</span> <span class="string">"a"</span><span class="special">))</span> | |
148 | <span class="keyword">return</span> <span class="number">1</span><span class="special">;</span> | |
149 | <span class="keyword">if</span><span class="special">(</span><span class="number">0</span> <span class="special">==</span> <span class="identifier">get_user_parameter_info</span><span class="special">(</span><span class="identifier">arg2</span><span class="special">,</span> <span class="string">"b"</span><span class="special">))</span> | |
150 | <span class="keyword">return</span> <span class="number">1</span><span class="special">;</span> | |
151 | ||
152 | <span class="comment">//</span> | |
153 | <span class="comment">// Get a pointer to the function and call</span> | |
154 | <span class="comment">// test_data::insert to actually generate</span> | |
155 | <span class="comment">// the values.</span> | |
156 | <span class="comment">//</span> | |
157 | <span class="identifier">bignum</span> <span class="special">(*</span><span class="identifier">fp</span><span class="special">)(</span><span class="identifier">bignum</span><span class="special">,</span> <span class="identifier">bignum</span><span class="special">)</span> <span class="special">=</span> <span class="special">&</span><span class="identifier">my_special</span><span class="special">;</span> | |
158 | <span class="identifier">data</span><span class="special">.</span><span class="identifier">insert</span><span class="special">(</span><span class="identifier">fp</span><span class="special">,</span> <span class="identifier">arg2</span><span class="special">,</span> <span class="identifier">arg1</span><span class="special">);</span> | |
159 | ||
160 | <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Any more data [y/n]?"</span><span class="special">;</span> | |
161 | <span class="identifier">std</span><span class="special">::</span><span class="identifier">getline</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">cin</span><span class="special">,</span> <span class="identifier">line</span><span class="special">);</span> | |
162 | <span class="identifier">boost</span><span class="special">::</span><span class="identifier">algorithm</span><span class="special">::</span><span class="identifier">trim</span><span class="special">(</span><span class="identifier">line</span><span class="special">);</span> | |
163 | <span class="identifier">cont</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">line</span> <span class="special">==</span> <span class="string">"y"</span><span class="special">);</span> | |
164 | <span class="special">}</span><span class="keyword">while</span><span class="special">(</span><span class="identifier">cont</span><span class="special">);</span> | |
165 | <span class="comment">//</span> | |
166 | <span class="comment">// Just need to write the results to a file:</span> | |
167 | <span class="comment">//</span> | |
168 | <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Enter name of test data file [default=my_special.ipp]"</span><span class="special">;</span> | |
169 | <span class="identifier">std</span><span class="special">::</span><span class="identifier">getline</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">cin</span><span class="special">,</span> <span class="identifier">line</span><span class="special">);</span> | |
170 | <span class="identifier">boost</span><span class="special">::</span><span class="identifier">algorithm</span><span class="special">::</span><span class="identifier">trim</span><span class="special">(</span><span class="identifier">line</span><span class="special">);</span> | |
171 | <span class="keyword">if</span><span class="special">(</span><span class="identifier">line</span> <span class="special">==</span> <span class="string">""</span><span class="special">)</span> | |
172 | <span class="identifier">line</span> <span class="special">=</span> <span class="string">"my_special.ipp"</span><span class="special">;</span> | |
173 | <span class="identifier">std</span><span class="special">::</span><span class="identifier">ofstream</span> <span class="identifier">ofs</span><span class="special">(</span><span class="identifier">line</span><span class="special">.</span><span class="identifier">c_str</span><span class="special">());</span> | |
174 | <span class="identifier">line</span><span class="special">.</span><span class="identifier">erase</span><span class="special">(</span><span class="identifier">line</span><span class="special">.</span><span class="identifier">find</span><span class="special">(</span><span class="char">'.'</span><span class="special">));</span> | |
175 | <span class="identifier">ofs</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">scientific</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="number">50</span><span class="special">);</span> | |
176 | <span class="identifier">write_code</span><span class="special">(</span><span class="identifier">ofs</span><span class="special">,</span> <span class="identifier">data</span><span class="special">,</span> <span class="identifier">line</span><span class="special">.</span><span class="identifier">c_str</span><span class="special">());</span> | |
177 | ||
178 | <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> | |
179 | <span class="special">}</span> | |
180 | </pre> | |
181 | <p> | |
182 | Typically several sets of data will be generated this way, including random | |
183 | values in some "normal" range, extreme values (very large or very | |
184 | small), and values close to any "interesting" behaviour of the | |
185 | function (singularities etc). | |
186 | </p> | |
187 | <h5> | |
188 | <a name="math_toolkit.special_tut.special_tut_test.h3"></a> | |
189 | <span class="phrase"><a name="math_toolkit.special_tut.special_tut_test.the_test_file_header"></a></span><a class="link" href="special_tut_test.html#math_toolkit.special_tut.special_tut_test.the_test_file_header">The | |
190 | Test File Header</a> | |
191 | </h5> | |
192 | <p> | |
193 | We split the actual test file into 2 distinct parts: a header that contains | |
194 | the testing code as a series of function templates, and the actual .cpp test | |
195 | driver that decides which types are tested, and sets the "expected" | |
196 | error rates for those types. It's done this way because: | |
197 | </p> | |
198 | <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> | |
199 | <li class="listitem"> | |
200 | We want to test with both built in floating point types, and with multiprecision | |
201 | types. However, both compile and runtimes with the latter can be too | |
202 | long for the folks who run the tests to realistically cope with, so it | |
203 | makes sense to split the test into (at least) 2 parts. | |
204 | </li> | |
205 | <li class="listitem"> | |
206 | The definition of the SC_ macro used in our tables of data may differ | |
207 | depending on what type we're testing (see below). Again this is largely | |
208 | a matter of managing compile times as large tables of user-defined-types | |
209 | can take a crazy amount of time to compile with some compilers. | |
210 | </li> | |
211 | </ul></div> | |
212 | <p> | |
213 | The test header contains 2 functions: | |
214 | </p> | |
215 | <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Real</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> | |
216 | <span class="keyword">void</span> <span class="identifier">do_test</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">data</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">type_name</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">test_name</span><span class="special">);</span> | |
217 | ||
218 | <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> | |
219 | <span class="keyword">void</span> <span class="identifier">test</span><span class="special">(</span><span class="identifier">T</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">type_name</span><span class="special">);</span> | |
220 | </pre> | |
221 | <p> | |
222 | Before implementing those, we'll include the headers we'll need, and provide | |
223 | a default definition for the SC_ macro: | |
224 | </p> | |
225 | <pre class="programlisting"><span class="comment">// A couple of Boost.Test headers in case we need any BOOST_CHECK_* macros:</span> | |
226 | <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">test</span><span class="special">/</span><span class="identifier">unit_test</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> | |
227 | <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">test</span><span class="special">/</span><span class="identifier">floating_point_comparison</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> | |
228 | <span class="comment">// Our function to test:</span> | |
229 | <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">my_special</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> | |
230 | <span class="comment">// We need boost::array for our test data, plus a few headers from</span> | |
231 | <span class="comment">// libs/math/test that contain our testing machinary:</span> | |
232 | <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">array</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> | |
233 | <span class="preprocessor">#include</span> <span class="string">"functor.hpp"</span> | |
234 | <span class="preprocessor">#include</span> <span class="string">"handle_test_result.hpp"</span> | |
235 | <span class="preprocessor">#include</span> <span class="string">"table_type.hpp"</span> | |
236 | ||
237 | <span class="preprocessor">#ifndef</span> <span class="identifier">SC_</span> | |
238 | <span class="preprocessor">#define</span> <span class="identifier">SC_</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span> <span class="keyword">static_cast</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">table_type</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">type</span><span class="special">>(</span><span class="identifier">BOOST_JOIN</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span> <span class="identifier">L</span><span class="special">))</span> | |
239 | <span class="preprocessor">#endif</span> | |
240 | </pre> | |
241 | <p> | |
242 | The easiest function to implement is the "test" function which | |
243 | is what we'll be calling from the test-driver program. It simply includes | |
244 | the files containing the tabular test data and calls <code class="computeroutput"><span class="identifier">do_test</span></code> | |
245 | function for each table, along with a description of what's being tested: | |
246 | </p> | |
247 | <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> | |
248 | <span class="keyword">void</span> <span class="identifier">test</span><span class="special">(</span><span class="identifier">T</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">type_name</span><span class="special">)</span> | |
249 | <span class="special">{</span> | |
250 | <span class="comment">//</span> | |
251 | <span class="comment">// The actual test data is rather verbose, so it's in a separate file</span> | |
252 | <span class="comment">//</span> | |
253 | <span class="comment">// The contents are as follows, each row of data contains</span> | |
254 | <span class="comment">// three items, input value a, input value b and my_special(a, b):</span> | |
255 | <span class="comment">//</span> | |
256 | <span class="preprocessor"># include</span> <span class="string">"my_special_1.ipp"</span> | |
257 | ||
258 | <span class="identifier">do_test</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">my_special_1</span><span class="special">,</span> <span class="identifier">name</span><span class="special">,</span> <span class="string">"MySpecial Function: Mathematica Values"</span><span class="special">);</span> | |
259 | ||
260 | <span class="preprocessor"># include</span> <span class="string">"my_special_2.ipp"</span> | |
261 | ||
262 | <span class="identifier">do_test</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">my_special_2</span><span class="special">,</span> <span class="identifier">name</span><span class="special">,</span> <span class="string">"MySpecial Function: Random Values"</span><span class="special">);</span> | |
263 | ||
264 | <span class="preprocessor"># include</span> <span class="string">"my_special_3.ipp"</span> | |
265 | ||
266 | <span class="identifier">do_test</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">my_special_3</span><span class="special">,</span> <span class="identifier">name</span><span class="special">,</span> <span class="string">"MySpecial Function: Very Small Values"</span><span class="special">);</span> | |
267 | <span class="special">}</span> | |
268 | </pre> | |
269 | <p> | |
270 | The function <code class="computeroutput"><span class="identifier">do_test</span></code> takes | |
271 | each table of data and calculates values for each row of data, along with | |
272 | statistics for max and mean error etc, most of this is handled by some boilerplate | |
273 | code: | |
274 | </p> | |
275 | <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Real</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> | |
276 | <span class="keyword">void</span> <span class="identifier">do_test</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">data</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">type_name</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">test_name</span><span class="special">)</span> | |
277 | <span class="special">{</span> | |
278 | <span class="comment">// Get the type of each row and each element in the rows:</span> | |
279 | <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">T</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">row_type</span><span class="special">;</span> | |
280 | <span class="keyword">typedef</span> <span class="identifier">Real</span> <span class="identifier">value_type</span><span class="special">;</span> | |
281 | ||
282 | <span class="comment">// Get a pointer to our function, we have to use a workaround here</span> | |
283 | <span class="comment">// as some compilers require the template types to be explicitly</span> | |
284 | <span class="comment">// specified, while others don't much like it if it is!</span> | |
285 | <span class="keyword">typedef</span> <span class="identifier">value_type</span> <span class="special">(*</span><span class="identifier">pg</span><span class="special">)(</span><span class="identifier">value_type</span><span class="special">,</span> <span class="identifier">value_type</span><span class="special">);</span> | |
286 | <span class="preprocessor">#if</span> <span class="identifier">defined</span><span class="special">(</span><span class="identifier">BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS</span><span class="special">)</span> | |
287 | <span class="identifier">pg</span> <span class="identifier">funcp</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">my_special</span><span class="special"><</span><span class="identifier">value_type</span><span class="special">,</span> <span class="identifier">value_type</span><span class="special">>;</span> | |
288 | <span class="preprocessor">#else</span> | |
289 | <span class="identifier">pg</span> <span class="identifier">funcp</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">my_special</span><span class="special">;</span> | |
290 | <span class="preprocessor">#endif</span> | |
291 | ||
292 | <span class="comment">// Somewhere to hold our results:</span> | |
293 | <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">test_result</span><span class="special"><</span><span class="identifier">value_type</span><span class="special">></span> <span class="identifier">result</span><span class="special">;</span> | |
294 | <span class="comment">// And some pretty printing:</span> | |
295 | <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Testing "</span> <span class="special"><<</span> <span class="identifier">test_name</span> <span class="special"><<</span> <span class="string">" with type "</span> <span class="special"><<</span> <span class="identifier">type_name</span> | |
296 | <span class="special"><<</span> <span class="string">"\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"</span><span class="special">;</span> | |
297 | ||
298 | <span class="comment">//</span> | |
299 | <span class="comment">// Test my_special against data:</span> | |
300 | <span class="comment">//</span> | |
301 | <span class="identifier">result</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">test_hetero</span><span class="special"><</span><span class="identifier">Real</span><span class="special">>(</span> | |
302 | <span class="comment">/* First argument is the table */</span> | |
303 | <span class="identifier">data</span><span class="special">,</span> | |
304 | <span class="comment">/* Next comes our function pointer, plus the indexes of it's arguments in the table */</span> | |
305 | <span class="identifier">bind_func</span><span class="special"><</span><span class="identifier">Real</span><span class="special">>(</span><span class="identifier">funcp</span><span class="special">,</span> <span class="number">0</span><span class="special">,</span> <span class="number">1</span><span class="special">),</span> | |
306 | <span class="comment">/* Then the index of the result in the table - potentially we can test several | |
307 | related functions this way, each having the same input arguments, and different | |
308 | output values in different indexes in the table */</span> | |
309 | <span class="identifier">extract_result</span><span class="special"><</span><span class="identifier">Real</span><span class="special">>(</span><span class="number">2</span><span class="special">));</span> | |
310 | <span class="comment">//</span> | |
311 | <span class="comment">// Finish off with some boilerplate to check the results were within the expected errors,</span> | |
312 | <span class="comment">// and pretty print the results:</span> | |
313 | <span class="comment">//</span> | |
314 | <span class="identifier">handle_test_result</span><span class="special">(</span><span class="identifier">result</span><span class="special">,</span> <span class="identifier">data</span><span class="special">[</span><span class="identifier">result</span><span class="special">.</span><span class="identifier">worst</span><span class="special">()],</span> <span class="identifier">result</span><span class="special">.</span><span class="identifier">worst</span><span class="special">(),</span> <span class="identifier">type_name</span><span class="special">,</span> <span class="string">"boost::math::my_special"</span><span class="special">,</span> <span class="identifier">test_name</span><span class="special">);</span> | |
315 | <span class="special">}</span> | |
316 | </pre> | |
317 | <p> | |
318 | Now we just need to write the test driver program, at it's most basic it | |
319 | looks something like this: | |
320 | </p> | |
321 | <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">math_fwd</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> | |
322 | <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">test</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> | |
323 | <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">stats</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> | |
324 | <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">type_traits</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> | |
325 | <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">array</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> | |
326 | <span class="preprocessor">#include</span> <span class="string">"functor.hpp"</span> | |
327 | ||
328 | <span class="preprocessor">#include</span> <span class="string">"handle_test_result.hpp"</span> | |
329 | <span class="preprocessor">#include</span> <span class="string">"test_my_special.hpp"</span> | |
330 | ||
331 | <span class="identifier">BOOST_AUTO_TEST_CASE</span><span class="special">(</span> <span class="identifier">test_main</span> <span class="special">)</span> | |
332 | <span class="special">{</span> | |
333 | <span class="comment">//</span> | |
334 | <span class="comment">// Test each floating point type, plus real_concept.</span> | |
335 | <span class="comment">// We specify the name of each type by hand as typeid(T).name()</span> | |
336 | <span class="comment">// often gives an unreadable mangled name.</span> | |
337 | <span class="comment">//</span> | |
338 | <span class="identifier">test</span><span class="special">(</span><span class="number">0.1F</span><span class="special">,</span> <span class="string">"float"</span><span class="special">);</span> | |
339 | <span class="identifier">test</span><span class="special">(</span><span class="number">0.1</span><span class="special">,</span> <span class="string">"double"</span><span class="special">);</span> | |
340 | <span class="comment">//</span> | |
341 | <span class="comment">// Testing of long double and real_concept is protected</span> | |
342 | <span class="comment">// by some logic to disable these for unsupported</span> | |
343 | <span class="comment">// or problem compilers.</span> | |
344 | <span class="comment">//</span> | |
345 | <span class="preprocessor">#ifndef</span> <span class="identifier">BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS</span> | |
346 | <span class="identifier">test</span><span class="special">(</span><span class="number">0.1L</span><span class="special">,</span> <span class="string">"long double"</span><span class="special">);</span> | |
347 | <span class="preprocessor">#ifndef</span> <span class="identifier">BOOST_MATH_NO_REAL_CONCEPT_TESTS</span> | |
348 | <span class="preprocessor">#if</span> <span class="special">!</span><span class="identifier">BOOST_WORKAROUND</span><span class="special">(</span><span class="identifier">__BORLANDC__</span><span class="special">,</span> <span class="identifier">BOOST_TESTED_AT</span><span class="special">(</span><span class="number">0x582</span><span class="special">))</span> | |
349 | <span class="identifier">test</span><span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">concepts</span><span class="special">::</span><span class="identifier">real_concept</span><span class="special">(</span><span class="number">0.1</span><span class="special">),</span> <span class="string">"real_concept"</span><span class="special">);</span> | |
350 | <span class="preprocessor">#endif</span> | |
351 | <span class="preprocessor">#endif</span> | |
352 | <span class="preprocessor">#else</span> | |
353 | <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"<note>The long double tests have been disabled on this platform "</span> | |
354 | <span class="string">"either because the long double overloads of the usual math functions are "</span> | |
355 | <span class="string">"not available at all, or because they are too inaccurate for these tests "</span> | |
356 | <span class="string">"to pass.</note>"</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">;</span> | |
357 | <span class="preprocessor">#endif</span> | |
358 | <span class="special">}</span> | |
359 | </pre> | |
360 | <p> | |
361 | That's almost all there is too it - except that if the above program is run | |
362 | it's very likely that all the tests will fail as the default maximum allowable | |
363 | error is 1 epsilon. So we'll define a function (don't forget to call it from | |
364 | the start of the <code class="computeroutput"><span class="identifier">test_main</span></code> | |
365 | above) to up the limits to something sensible, based both on the function | |
366 | we're calling and on the particular tests plus the platform and compiler: | |
367 | </p> | |
368 | <pre class="programlisting"><span class="keyword">void</span> <span class="identifier">expected_results</span><span class="special">()</span> | |
369 | <span class="special">{</span> | |
370 | <span class="comment">//</span> | |
371 | <span class="comment">// Define the max and mean errors expected for</span> | |
372 | <span class="comment">// various compilers and platforms.</span> | |
373 | <span class="comment">//</span> | |
374 | <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">largest_type</span><span class="special">;</span> | |
375 | <span class="preprocessor">#ifndef</span> <span class="identifier">BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS</span> | |
376 | <span class="keyword">if</span><span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">digits</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special"><></span> <span class="special">>()</span> <span class="special">==</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">digits</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special"><></span> <span class="special">>())</span> | |
377 | <span class="special">{</span> | |
378 | <span class="identifier">largest_type</span> <span class="special">=</span> <span class="string">"(long\\s+)?double|real_concept"</span><span class="special">;</span> | |
379 | <span class="special">}</span> | |
380 | <span class="keyword">else</span> | |
381 | <span class="special">{</span> | |
382 | <span class="identifier">largest_type</span> <span class="special">=</span> <span class="string">"long double|real_concept"</span><span class="special">;</span> | |
383 | <span class="special">}</span> | |
384 | <span class="preprocessor">#else</span> | |
385 | <span class="identifier">largest_type</span> <span class="special">=</span> <span class="string">"(long\\s+)?double"</span><span class="special">;</span> | |
386 | <span class="preprocessor">#endif</span> | |
387 | <span class="comment">//</span> | |
388 | <span class="comment">// We call add_expected_result for each error rate we wish to adjust, these tell</span> | |
389 | <span class="comment">// handle_test_result what level of error is acceptable. We can have as many calls</span> | |
390 | <span class="comment">// to add_expected_result as we need, each one establishes a rule for acceptable error</span> | |
391 | <span class="comment">// with rules set first given preference.</span> | |
392 | <span class="comment">//</span> | |
393 | <span class="identifier">add_expected_result</span><span class="special">(</span> | |
394 | <span class="comment">/* First argument is a regular expression to match against the name of the compiler | |
395 | set in BOOST_COMPILER */</span> | |
396 | <span class="string">".*"</span><span class="special">,</span> | |
397 | <span class="comment">/* Second argument is a regular expression to match against the name of the | |
398 | C++ standard library as set in BOOST_STDLIB */</span> | |
399 | <span class="string">".*"</span><span class="special">,</span> | |
400 | <span class="comment">/* Third argument is a regular expression to match against the name of the | |
401 | platform as set in BOOST_PLATFORM */</span> | |
402 | <span class="string">".*"</span><span class="special">,</span> | |
403 | <span class="comment">/* Forth argument is the name of the type being tested, normally we will | |
404 | only need to up the acceptable error rate for the widest floating | |
405 | point type being tested */</span> | |
406 | <span class="identifier">largest_real</span><span class="special">,</span> | |
407 | <span class="comment">/* Fifth argument is a regular expression to match against | |
408 | the name of the group of data being tested */</span> | |
409 | <span class="string">"MySpecial Function:.*Small.*"</span><span class="special">,</span> | |
410 | <span class="comment">/* Sixth argument is a regular expression to match against the name | |
411 | of the function being tested */</span> | |
412 | <span class="string">"boost::math::my_special"</span><span class="special">,</span> | |
413 | <span class="comment">/* Seventh argument is the maximum allowable error expressed in units | |
414 | of machine epsilon passed as a long integer value */</span> | |
415 | <span class="number">50</span><span class="special">,</span> | |
416 | <span class="comment">/* Eighth argument is the maximum allowable mean error expressed in units | |
417 | of machine epsilon passed as a long integer value */</span> | |
418 | <span class="number">20</span><span class="special">);</span> | |
419 | <span class="special">}</span> | |
420 | </pre> | |
421 | <h5> | |
422 | <a name="math_toolkit.special_tut.special_tut_test.h4"></a> | |
423 | <span class="phrase"><a name="math_toolkit.special_tut.special_tut_test.testing_multiprecision_types"></a></span><a class="link" href="special_tut_test.html#math_toolkit.special_tut.special_tut_test.testing_multiprecision_types">Testing | |
424 | Multiprecision Types</a> | |
425 | </h5> | |
426 | <p> | |
427 | Testing of multiprecision types is handled by the test drivers in libs/multiprecision/test/math, | |
428 | please refer to these for examples. Note that these tests are run only occationally | |
429 | as they take a lot of CPU cycles to build and run. | |
430 | </p> | |
431 | <h5> | |
432 | <a name="math_toolkit.special_tut.special_tut_test.h5"></a> | |
433 | <span class="phrase"><a name="math_toolkit.special_tut.special_tut_test.improving_compile_times"></a></span><a class="link" href="special_tut_test.html#math_toolkit.special_tut.special_tut_test.improving_compile_times">Improving | |
434 | Compile Times</a> | |
435 | </h5> | |
436 | <p> | |
437 | As noted above, these test programs can take a while to build as we're instantiating | |
438 | a lot of templates for several different types, and our test runners are | |
439 | already stretched to the limit, and probably using outdated "spare" | |
440 | hardware. There are two things we can do to speed things up: | |
441 | </p> | |
442 | <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> | |
443 | <li class="listitem"> | |
444 | Use a precompiled header. | |
445 | </li> | |
446 | <li class="listitem"> | |
447 | Use separate compilation of our special function templates. | |
448 | </li> | |
449 | </ul></div> | |
450 | <p> | |
451 | We can make these changes by changing the list of includes from: | |
452 | </p> | |
453 | <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">math_fwd</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> | |
454 | <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">test</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> | |
455 | <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">stats</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> | |
456 | <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">type_traits</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> | |
457 | <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">array</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> | |
458 | <span class="preprocessor">#include</span> <span class="string">"functor.hpp"</span> | |
459 | ||
460 | <span class="preprocessor">#include</span> <span class="string">"handle_test_result.hpp"</span> | |
461 | </pre> | |
462 | <p> | |
463 | To just: | |
464 | </p> | |
465 | <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">pch_light</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> | |
466 | </pre> | |
467 | <p> | |
468 | And changing | |
469 | </p> | |
470 | <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">my_special</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> | |
471 | </pre> | |
472 | <p> | |
473 | To: | |
474 | </p> | |
475 | <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">math_fwd</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> | |
476 | </pre> | |
477 | <p> | |
478 | The Jamfile target that builds the test program will need the targets | |
479 | </p> | |
480 | <pre class="programlisting"><span class="identifier">test_instances</span><span class="comment">//test_instances pch_light</span> | |
481 | </pre> | |
482 | <p> | |
483 | adding to it's list of source dependencies (see the Jamfile for examples). | |
484 | </p> | |
485 | <p> | |
486 | Finally the project in libs/math/test/test_instances will need modifying | |
487 | to instantiate function <code class="computeroutput"><span class="identifier">my_special</span></code>. | |
488 | </p> | |
489 | <p> | |
490 | These changes should be made last, when <code class="computeroutput"><span class="identifier">my_special</span></code> | |
491 | is stable and the code is in Trunk. | |
492 | </p> | |
493 | <h5> | |
494 | <a name="math_toolkit.special_tut.special_tut_test.h6"></a> | |
495 | <span class="phrase"><a name="math_toolkit.special_tut.special_tut_test.concept_checks"></a></span><a class="link" href="special_tut_test.html#math_toolkit.special_tut.special_tut_test.concept_checks">Concept | |
496 | Checks</a> | |
497 | </h5> | |
498 | <p> | |
499 | Our concept checks verify that your function's implementation makes no assumptions | |
500 | that aren't required by our <a class="link" href="../real_concepts.html" title="Conceptual Requirements for Real Number Types">Real | |
501 | number conceptual requirements</a>. They also check for various common | |
502 | bugs and programming traps that we've fallen into over time. To add your | |
503 | function to these tests, edit libs/math/test/compile_test/instantiate.hpp | |
504 | to add calls to your function: there are 7 calls to each function, each with | |
505 | a different purpose. Search for something like "ibeta" or "gamm_p" | |
506 | and follow their examples. | |
507 | </p> | |
508 | </div> | |
509 | <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> | |
510 | <td align="left"></td> | |
511 | <td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal, | |
512 | Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert | |
513 | Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani, | |
514 | Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p> | |
515 | Distributed under the Boost Software License, Version 1.0. (See accompanying | |
516 | 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>) | |
517 | </p> | |
518 | </div></td> | |
519 | </tr></table> | |
520 | <hr> | |
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