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  25 <div class="section">
  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="math_toolkit.pol_tutorial.user_def_err_pol"></a><a class="link" href="user_def_err_pol.html" title="Calling User Defined Error Handlers">Calling User
  28       Defined Error Handlers</a>
  29 </h3></div></div></div>
  30 <p>
  31         Suppose we want our own user-defined error handlers rather than the any of
  32         the default ones supplied by the library to be used. If we set the policy
  33         for a specific type of error to <code class="computeroutput"><span class="identifier">user_error</span></code>
  34         then the library will call a user-supplied error handler. These are forward
  35         declared, but not defined in boost/math/policies/error_handling.hpp like
  36         this:
  37       </p>
  38 <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">policies</span><span class="special">{</span>
  39
  40 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
  41 <span class="identifier">T</span> <span class="identifier">user_domain_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
  42 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
  43 <span class="identifier">T</span> <span class="identifier">user_pole_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
  44 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
  45 <span class="identifier">T</span> <span class="identifier">user_overflow_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
  46 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
  47 <span class="identifier">T</span> <span class="identifier">user_underflow_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
  48 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
  49 <span class="identifier">T</span> <span class="identifier">user_denorm_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
  50 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
  51 <span class="identifier">T</span> <span class="identifier">user_evaluation_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
  52 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">TargetType</span><span class="special">&gt;</span>
  53 <span class="identifier">T</span> <span class="identifier">user_rounding_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">TargetType</span><span class="special">&amp;</span> <span class="identifier">t</span><span class="special">);</span>
  54 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
  55 <span class="identifier">T</span> <span class="identifier">user_indeterminate_result_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
  56
  57 <span class="special">}}}</span> <span class="comment">// namespaces</span>
  58 </pre>
  59 <p>
  60         So out first job is to include the header we want to use, and then provide
  61         definitions for our user-defined error handlers that we want to use. We only
  62         provide our special domain and pole error handlers; other errors like overflow
  63         and underflow use the default.
  64       </p>
  65 <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</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">hpp</span><span class="special">&gt;</span>
  66
  67 <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span>
  68 <span class="special">{</span>
  69   <span class="keyword">namespace</span> <span class="identifier">policies</span>
  70   <span class="special">{</span>
  71     <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
  72     <span class="identifier">T</span> <span class="identifier">user_domain_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">)</span>
  73     <span class="special">{</span> <span class="comment">// Ignoring function, message and val for this example, perhaps unhelpfully.</span>
  74        <span class="identifier">cerr</span> <span class="special">&lt;&lt;</span> <span class="string">"Domain Error!"</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
  75        <span class="keyword">return</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">();</span>
  76     <span class="special">}</span>
  77
  78     <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
  79     <span class="identifier">T</span> <span class="identifier">user_pole_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">)</span>
  80     <span class="special">{</span> <span class="comment">// Ignoring function, message and val for this example, perhaps unhelpfully.</span>
  81        <span class="identifier">cerr</span> <span class="special">&lt;&lt;</span> <span class="string">"Pole Error!"</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
  82        <span class="keyword">return</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">();</span>
  83     <span class="special">}</span>
  84   <span class="special">}</span> <span class="comment">// namespace policies</span>
  85 <span class="special">}}</span> <span class="comment">// namespace boost{ namespace math</span>
  86 </pre>
  87 <p>
  88         Now we'll need to define a suitable policy that will call these handlers,
  89         and define some forwarding functions that make use of the policy:
  90       </p>
  91 <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">mymath</span><span class="special">{</span>
  92
  93 <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">policies</span><span class="special">;</span>
  94
  95 <span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span>
  96    <span class="identifier">domain_error</span><span class="special">&lt;</span><span class="identifier">user_error</span><span class="special">&gt;,</span>
  97    <span class="identifier">pole_error</span><span class="special">&lt;</span><span class="identifier">user_error</span><span class="special">&gt;</span>
  98 <span class="special">&gt;</span> <span class="identifier">user_error_policy</span><span class="special">;</span>
  99
 100 <span class="identifier">BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS</span><span class="special">(</span><span class="identifier">user_error_policy</span><span class="special">)</span>
 101
 102 <span class="special">}</span> <span class="comment">// close unnamed namespace</span>
 103 </pre>
 104 <p>
 105         We now have a set of forwarding functions defined in namespace mymath that
 106         all look something like this:
 107       </p>
 108 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">&gt;</span>
 109 <span class="keyword">inline</span> <span class="keyword">typename</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">promote_args</span><span class="special">&lt;</span><span class="identifier">RT</span><span class="special">&gt;::</span><span class="identifier">type</span>
 110    <span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">RT</span> <span class="identifier">z</span><span class="special">)</span>
 111 <span class="special">{</span>
 112    <span class="keyword">return</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">user_error_policy</span><span class="special">());</span>
 113 <span class="special">}</span>
 114 </pre>
 115 <p>
 116         So that when we call <code class="computeroutput"><span class="identifier">mymath</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">z</span><span class="special">)</span></code>
 117         we really end up calling <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">z</span><span class="special">,</span>
 118         <span class="identifier">user_error_policy</span><span class="special">())</span></code>,
 119         and any errors will get directed to our own error handlers.
 120       </p>
 121 <pre class="programlisting"><span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
 122 <span class="special">{</span>
 123    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of erf_inv(-10) is: "</span>
 124       <span class="special">&lt;&lt;</span> <span class="identifier">mymath</span><span class="special">::</span><span class="identifier">erf_inv</span><span class="special">(-</span><span class="number">10</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
 125    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of tgamma(-10) is: "</span>
 126       <span class="special">&lt;&lt;</span> <span class="identifier">mymath</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(-</span><span class="number">10</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
 127 <span class="special">}</span>
 128 </pre>
 129 <p>
 130         Which outputs:
 131       </p>
 132 <pre class="programlisting">  Domain Error!
 133   Pole Error!
 134   Result of erf_inv(-10) is: 1.#QNAN
 135   Result of tgamma(-10) is: 1.#QNAN
 136 </pre>
 137 <p>
 138         The previous example was all well and good, but the custom error handlers
 139         didn't really do much of any use. In this example we'll implement all the
 140         custom handlers and show how the information provided to them can be used
 141         to generate nice formatted error messages.
 142       </p>
 143 <p>
 144         Each error handler has the general form:
 145       </p>
 146 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
 147 <span class="identifier">T</span> <span class="identifier">user_</span><span class="emphasis"><em>error_type</em></span><span class="special">(</span>
 148    <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span>
 149    <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span>
 150    <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
 151 </pre>
 152 <p>
 153         and accepts three arguments:
 154       </p>
 155 <div class="variablelist">
 156 <p class="title"><b></b></p>
 157 <dl class="variablelist">
 158 <dt><span class="term">const char* function</span></dt>
 159 <dd><p>
 160               The name of the function that raised the error, this string contains
 161               one or more %1% format specifiers that should be replaced by the name
 162               of real type T, like float or double.
 163             </p></dd>
 164 <dt><span class="term">const char* message</span></dt>
 165 <dd><p>
 166               A message associated with the error, normally this contains a %1% format
 167               specifier that should be replaced with the value of <span class="emphasis"><em>value</em></span>:
 168               however note that overflow and underflow messages do not contain this
 169               %1% specifier (since the value of <span class="emphasis"><em>value</em></span> is immaterial
 170               in these cases).
 171             </p></dd>
 172 <dt><span class="term">const T&amp; value</span></dt>
 173 <dd><p>
 174               The value that caused the error: either an argument to the function
 175               if this is a domain or pole error, the tentative result if this is
 176               a denorm or evaluation error, or zero or infinity for underflow or
 177               overflow errors.
 178             </p></dd>
 179 </dl>
 180 </div>
 181 <p>
 182         As before we'll include the headers we need first:
 183       </p>
 184 <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</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">hpp</span><span class="special">&gt;</span>
 185 </pre>
 186 <p>
 187         Next we'll implement our own error handlers for each type of error, starting
 188         with domain errors:
 189       </p>
 190 <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
 191 <span class="keyword">namespace</span> <span class="identifier">policies</span>
 192 <span class="special">{</span>
 193
 194 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
 195 <span class="identifier">T</span> <span class="identifier">user_domain_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">)</span>
 196 <span class="special">{</span>
 197 </pre>
 198 <p>
 199         We'll begin with a bit of defensive programming in case function or message
 200         are empty:
 201       </p>
 202 <pre class="programlisting"><span class="keyword">if</span><span class="special">(</span><span class="identifier">function</span> <span class="special">==</span> <span class="number">0</span><span class="special">)</span>
 203     <span class="identifier">function</span> <span class="special">=</span> <span class="string">"Unknown function with arguments of type %1%"</span><span class="special">;</span>
 204 <span class="keyword">if</span><span class="special">(</span><span class="identifier">message</span> <span class="special">==</span> <span class="number">0</span><span class="special">)</span>
 205     <span class="identifier">message</span> <span class="special">=</span> <span class="string">"Cause unknown with bad argument %1%"</span><span class="special">;</span>
 206 </pre>
 207 <p>
 208         Next we'll format the name of the function with the name of type T, perhaps
 209         double:
 210       </p>
 211 <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">msg</span><span class="special">(</span><span class="string">"Error in function "</span><span class="special">);</span>
 212 <span class="identifier">msg</span> <span class="special">+=</span> <span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">format</span><span class="special">(</span><span class="identifier">function</span><span class="special">)</span> <span class="special">%</span> <span class="keyword">typeid</span><span class="special">(</span><span class="identifier">T</span><span class="special">).</span><span class="identifier">name</span><span class="special">()).</span><span class="identifier">str</span><span class="special">();</span>
 213 </pre>
 214 <p>
 215         Then likewise format the error message with the value of parameter <span class="emphasis"><em>val</em></span>,
 216         making sure we output all the potentially significant digits of <span class="emphasis"><em>val</em></span>:
 217       </p>
 218 <pre class="programlisting"><span class="identifier">msg</span> <span class="special">+=</span> <span class="string">": \n"</span><span class="special">;</span>
 219 <span class="keyword">int</span> <span class="identifier">prec</span> <span class="special">=</span> <span class="number">2</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">digits</span> <span class="special">*</span> <span class="number">30103UL</span><span class="special">)</span> <span class="special">/</span> <span class="number">100000UL</span><span class="special">;</span>
 220 <span class="comment">// int prec = std::numeric_limits&lt;T&gt;::max_digits10; //  For C++0X Standard Library</span>
 221 <span class="identifier">msg</span> <span class="special">+=</span> <span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">format</span><span class="special">(</span><span class="identifier">message</span><span class="special">)</span> <span class="special">%</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">io</span><span class="special">::</span><span class="identifier">group</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="identifier">prec</span><span class="special">),</span> <span class="identifier">val</span><span class="special">)).</span><span class="identifier">str</span><span class="special">();</span>
 222 </pre>
 223 <p>
 224         Now we just have to do something with the message, we could throw an exception,
 225         but for the purposes of this example we'll just dump the message to std::cerr:
 226       </p>
 227 <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cerr</span> <span class="special">&lt;&lt;</span> <span class="identifier">msg</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
 228 </pre>
 229 <p>
 230         Finally the only sensible value we can return from a domain error is a NaN:
 231       </p>
 232 <pre class="programlisting">   <span class="keyword">return</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">();</span>
 233 <span class="special">}</span>
 234 </pre>
 235 <p>
 236         Pole errors are essentially a special case of domain errors, so in this example
 237         we'll just return the result of a domain error:
 238       </p>
 239 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
 240 <span class="identifier">T</span> <span class="identifier">user_pole_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">)</span>
 241 <span class="special">{</span>
 242    <span class="keyword">return</span> <span class="identifier">user_domain_error</span><span class="special">(</span><span class="identifier">function</span><span class="special">,</span> <span class="identifier">message</span><span class="special">,</span> <span class="identifier">val</span><span class="special">);</span>
 243 <span class="special">}</span>
 244 </pre>
 245 <p>
 246         Overflow errors are very similar to domain errors, except that there's no
 247         %1% format specifier in the <span class="emphasis"><em>message</em></span> parameter:
 248       </p>
 249 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
 250 <span class="identifier">T</span> <span class="identifier">user_overflow_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">)</span>
 251 <span class="special">{</span>
 252    <span class="keyword">if</span><span class="special">(</span><span class="identifier">function</span> <span class="special">==</span> <span class="number">0</span><span class="special">)</span>
 253        <span class="identifier">function</span> <span class="special">=</span> <span class="string">"Unknown function with arguments of type %1%"</span><span class="special">;</span>
 254    <span class="keyword">if</span><span class="special">(</span><span class="identifier">message</span> <span class="special">==</span> <span class="number">0</span><span class="special">)</span>
 255        <span class="identifier">message</span> <span class="special">=</span> <span class="string">"Result of function is too large to represent"</span><span class="special">;</span>
 256
 257    <span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">msg</span><span class="special">(</span><span class="string">"Error in function "</span><span class="special">);</span>
 258    <span class="identifier">msg</span> <span class="special">+=</span> <span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">format</span><span class="special">(</span><span class="identifier">function</span><span class="special">)</span> <span class="special">%</span> <span class="keyword">typeid</span><span class="special">(</span><span class="identifier">T</span><span class="special">).</span><span class="identifier">name</span><span class="special">()).</span><span class="identifier">str</span><span class="special">();</span>
 259
 260    <span class="identifier">msg</span> <span class="special">+=</span> <span class="string">": \n"</span><span class="special">;</span>
 261    <span class="identifier">msg</span> <span class="special">+=</span> <span class="identifier">message</span><span class="special">;</span>
 262
 263    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cerr</span> <span class="special">&lt;&lt;</span> <span class="identifier">msg</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
 264
 265    <span class="comment">// Value passed to the function is an infinity, just return it:</span>
 266    <span class="keyword">return</span> <span class="identifier">val</span><span class="special">;</span>
 267 <span class="special">}</span>
 268 </pre>
 269 <p>
 270         Underflow errors are much the same as overflow:
 271       </p>
 272 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
 273 <span class="identifier">T</span> <span class="identifier">user_underflow_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">)</span>
 274 <span class="special">{</span>
 275    <span class="keyword">if</span><span class="special">(</span><span class="identifier">function</span> <span class="special">==</span> <span class="number">0</span><span class="special">)</span>
 276        <span class="identifier">function</span> <span class="special">=</span> <span class="string">"Unknown function with arguments of type %1%"</span><span class="special">;</span>
 277    <span class="keyword">if</span><span class="special">(</span><span class="identifier">message</span> <span class="special">==</span> <span class="number">0</span><span class="special">)</span>
 278        <span class="identifier">message</span> <span class="special">=</span> <span class="string">"Result of function is too small to represent"</span><span class="special">;</span>
 279
 280    <span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">msg</span><span class="special">(</span><span class="string">"Error in function "</span><span class="special">);</span>
 281    <span class="identifier">msg</span> <span class="special">+=</span> <span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">format</span><span class="special">(</span><span class="identifier">function</span><span class="special">)</span> <span class="special">%</span> <span class="keyword">typeid</span><span class="special">(</span><span class="identifier">T</span><span class="special">).</span><span class="identifier">name</span><span class="special">()).</span><span class="identifier">str</span><span class="special">();</span>
 282
 283    <span class="identifier">msg</span> <span class="special">+=</span> <span class="string">": \n"</span><span class="special">;</span>
 284    <span class="identifier">msg</span> <span class="special">+=</span> <span class="identifier">message</span><span class="special">;</span>
 285
 286    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cerr</span> <span class="special">&lt;&lt;</span> <span class="identifier">msg</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
 287
 288    <span class="comment">// Value passed to the function is zero, just return it:</span>
 289    <span class="keyword">return</span> <span class="identifier">val</span><span class="special">;</span>
 290 <span class="special">}</span>
 291 </pre>
 292 <p>
 293         Denormalised results are much the same as underflow:
 294       </p>
 295 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
 296 <span class="identifier">T</span> <span class="identifier">user_denorm_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">)</span>
 297 <span class="special">{</span>
 298    <span class="keyword">if</span><span class="special">(</span><span class="identifier">function</span> <span class="special">==</span> <span class="number">0</span><span class="special">)</span>
 299        <span class="identifier">function</span> <span class="special">=</span> <span class="string">"Unknown function with arguments of type %1%"</span><span class="special">;</span>
 300    <span class="keyword">if</span><span class="special">(</span><span class="identifier">message</span> <span class="special">==</span> <span class="number">0</span><span class="special">)</span>
 301        <span class="identifier">message</span> <span class="special">=</span> <span class="string">"Result of function is denormalised"</span><span class="special">;</span>
 302
 303    <span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">msg</span><span class="special">(</span><span class="string">"Error in function "</span><span class="special">);</span>
 304    <span class="identifier">msg</span> <span class="special">+=</span> <span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">format</span><span class="special">(</span><span class="identifier">function</span><span class="special">)</span> <span class="special">%</span> <span class="keyword">typeid</span><span class="special">(</span><span class="identifier">T</span><span class="special">).</span><span class="identifier">name</span><span class="special">()).</span><span class="identifier">str</span><span class="special">();</span>
 305
 306    <span class="identifier">msg</span> <span class="special">+=</span> <span class="string">": \n"</span><span class="special">;</span>
 307    <span class="identifier">msg</span> <span class="special">+=</span> <span class="identifier">message</span><span class="special">;</span>
 308
 309    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cerr</span> <span class="special">&lt;&lt;</span> <span class="identifier">msg</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
 310
 311    <span class="comment">// Value passed to the function is denormalised, just return it:</span>
 312    <span class="keyword">return</span> <span class="identifier">val</span><span class="special">;</span>
 313 <span class="special">}</span>
 314 </pre>
 315 <p>
 316         Which leaves us with evaluation errors: these occur when an internal error
 317         occurs that prevents the function being fully evaluated. The parameter <span class="emphasis"><em>val</em></span>
 318         contains the closest approximation to the result found so far:
 319       </p>
 320 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
 321 <span class="identifier">T</span> <span class="identifier">user_evaluation_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">)</span>
 322 <span class="special">{</span>
 323    <span class="keyword">if</span><span class="special">(</span><span class="identifier">function</span> <span class="special">==</span> <span class="number">0</span><span class="special">)</span>
 324        <span class="identifier">function</span> <span class="special">=</span> <span class="string">"Unknown function with arguments of type %1%"</span><span class="special">;</span>
 325    <span class="keyword">if</span><span class="special">(</span><span class="identifier">message</span> <span class="special">==</span> <span class="number">0</span><span class="special">)</span>
 326        <span class="identifier">message</span> <span class="special">=</span> <span class="string">"An internal evaluation error occurred with "</span>
 327                   <span class="string">"the best value calculated so far of %1%"</span><span class="special">;</span>
 328
 329    <span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">msg</span><span class="special">(</span><span class="string">"Error in function "</span><span class="special">);</span>
 330    <span class="identifier">msg</span> <span class="special">+=</span> <span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">format</span><span class="special">(</span><span class="identifier">function</span><span class="special">)</span> <span class="special">%</span> <span class="keyword">typeid</span><span class="special">(</span><span class="identifier">T</span><span class="special">).</span><span class="identifier">name</span><span class="special">()).</span><span class="identifier">str</span><span class="special">();</span>
 331
 332    <span class="identifier">msg</span> <span class="special">+=</span> <span class="string">": \n"</span><span class="special">;</span>
 333    <span class="keyword">int</span> <span class="identifier">prec</span> <span class="special">=</span> <span class="number">2</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">digits</span> <span class="special">*</span> <span class="number">30103UL</span><span class="special">)</span> <span class="special">/</span> <span class="number">100000UL</span><span class="special">;</span>
 334    <span class="comment">// int prec = std::numeric_limits&lt;T&gt;::max_digits10; // For C++0X Standard Library</span>
 335    <span class="identifier">msg</span> <span class="special">+=</span> <span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">format</span><span class="special">(</span><span class="identifier">message</span><span class="special">)</span> <span class="special">%</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">io</span><span class="special">::</span><span class="identifier">group</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="identifier">prec</span><span class="special">),</span> <span class="identifier">val</span><span class="special">)).</span><span class="identifier">str</span><span class="special">();</span>
 336
 337    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cerr</span> <span class="special">&lt;&lt;</span> <span class="identifier">msg</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
 338
 339    <span class="comment">// What do we return here?  This is generally a fatal error, that should never occur,</span>
 340    <span class="comment">// so we just return a NaN for the purposes of the example:</span>
 341    <span class="keyword">return</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">();</span>
 342 <span class="special">}</span>
 343
 344 <span class="special">}</span> <span class="comment">// policies</span>
 345 <span class="special">}}</span> <span class="comment">// boost::math</span>
 346 </pre>
 347 <p>
 348         Now we'll need to define a suitable policy that will call these handlers,
 349         and define some forwarding functions that make use of the policy:
 350       </p>
 351 <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">mymath</span>
 352 <span class="special">{</span> <span class="comment">// unnamed.</span>
 353
 354 <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">policies</span><span class="special">;</span>
 355
 356 <span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span>
 357    <span class="identifier">domain_error</span><span class="special">&lt;</span><span class="identifier">user_error</span><span class="special">&gt;,</span>
 358    <span class="identifier">pole_error</span><span class="special">&lt;</span><span class="identifier">user_error</span><span class="special">&gt;,</span>
 359    <span class="identifier">overflow_error</span><span class="special">&lt;</span><span class="identifier">user_error</span><span class="special">&gt;,</span>
 360    <span class="identifier">underflow_error</span><span class="special">&lt;</span><span class="identifier">user_error</span><span class="special">&gt;,</span>
 361    <span class="identifier">denorm_error</span><span class="special">&lt;</span><span class="identifier">user_error</span><span class="special">&gt;,</span>
 362    <span class="identifier">evaluation_error</span><span class="special">&lt;</span><span class="identifier">user_error</span><span class="special">&gt;</span>
 363 <span class="special">&gt;</span> <span class="identifier">user_error_policy</span><span class="special">;</span>
 364
 365 <span class="identifier">BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS</span><span class="special">(</span><span class="identifier">user_error_policy</span><span class="special">)</span>
 366
 367 <span class="special">}</span> <span class="comment">// unnamed namespace</span>
 368 </pre>
 369 <p>
 370         We now have a set of forwarding functions, defined in namespace mymath, that
 371         all look something like this:
 372       </p>
 373 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">&gt;</span>
 374 <span class="keyword">inline</span> <span class="keyword">typename</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">promote_args</span><span class="special">&lt;</span><span class="identifier">RT</span><span class="special">&gt;::</span><span class="identifier">type</span>
 375    <span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">RT</span> <span class="identifier">z</span><span class="special">)</span>
 376 <span class="special">{</span>
 377    <span class="keyword">return</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">user_error_policy</span><span class="special">());</span>
 378 <span class="special">}</span>
 379 </pre>
 380 <p>
 381         So that when we call <code class="computeroutput"><span class="identifier">mymath</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">z</span><span class="special">)</span></code>
 382         we really end up calling <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">z</span><span class="special">,</span>
 383         <span class="identifier">user_error_policy</span><span class="special">())</span></code>,
 384         and any errors will get directed to our own error handlers:
 385       </p>
 386 <pre class="programlisting"><span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
 387 <span class="special">{</span>
 388    <span class="comment">// Raise a domain error:</span>
 389    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of erf_inv(-10) is: "</span>
 390       <span class="special">&lt;&lt;</span> <span class="identifier">mymath</span><span class="special">::</span><span class="identifier">erf_inv</span><span class="special">(-</span><span class="number">10</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
 391    <span class="comment">// Raise a pole error:</span>
 392    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of tgamma(-10) is: "</span>
 393       <span class="special">&lt;&lt;</span> <span class="identifier">mymath</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(-</span><span class="number">10</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
 394    <span class="comment">// Raise an overflow error:</span>
 395    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of tgamma(3000) is: "</span>
 396       <span class="special">&lt;&lt;</span> <span class="identifier">mymath</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="number">3000</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
 397    <span class="comment">// Raise an underflow error:</span>
 398    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of tgamma(-190.5) is: "</span>
 399       <span class="special">&lt;&lt;</span> <span class="identifier">mymath</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(-</span><span class="number">190.5</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
 400    <span class="comment">// Unfortunately we can't predicably raise a denormalised</span>
 401    <span class="comment">// result, nor can we raise an evaluation error in this example</span>
 402    <span class="comment">// since these should never really occur!</span>
 403 <span class="special">}</span> <span class="comment">// int main()</span>
 404 </pre>
 405 <p>
 406         Which outputs:
 407       </p>
 408 <pre class="programlisting">Error in function boost::math::erf_inv&lt;double&gt;(double, double):
 409 Argument outside range [-1, 1] in inverse erf function (got p=-10).
 410 Result of erf_inv(-10) is: 1.#QNAN
 411
 412 Error in function boost::math::tgamma&lt;long double&gt;(long double):
 413 Evaluation of tgamma at a negative integer -10.
 414 Result of tgamma(-10) is: 1.#QNAN
 415
 416 Error in function boost::math::tgamma&lt;long double&gt;(long double):
 417 Result of tgamma is too large to represent.
 418 Error in function boost::math::tgamma&lt;double&gt;(double):
 419 Result of function is too large to represent
 420 Result of tgamma(3000) is: 1.#INF
 421
 422 Error in function boost::math::tgamma&lt;long double&gt;(long double):
 423 Result of tgamma is too large to represent.
 424 Error in function boost::math::tgamma&lt;long double&gt;(long double):
 425 Result of tgamma is too small to represent.
 426 Result of tgamma(-190.5) is: 0
 427 </pre>
 428 <p>
 429         Notice how some of the calls result in an error handler being called more
 430         than once, or for more than one handler to be called: this is an artefact
 431         of the fact that many functions are implemented in terms of one or more sub-routines
 432         each of which may have it's own error handling. For example <code class="computeroutput"><span class="identifier">tgamma</span><span class="special">(-</span><span class="number">190.5</span><span class="special">)</span></code> is implemented
 433         in terms of <code class="computeroutput"><span class="identifier">tgamma</span><span class="special">(</span><span class="number">190.5</span><span class="special">)</span></code> - which
 434         overflows - the reflection formula for <code class="computeroutput"><span class="identifier">tgamma</span></code>
 435         then notices that it is dividing by infinity and so underflows.
 436       </p>
 437 </div>
 438 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 439 <td align="left"></td>
 440 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
 441       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
 442       Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
 443       Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
 444         Distributed under the Boost Software License, Version 1.0. (See accompanying
 445         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>)
 446       </p>
 447 </div></td>
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